Finite Group Databasebeta

← #3301×D71 #32873867

Subgroups — #3301×D71 #32873867

Order 18176.

2210 conjugacy classes of subgroups.

The subgroup lattice has 1854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#553×D71C211yesmaximal, characteristic, complemented
2#548×D71C211yesmaximal, characteristic, complemented
3#22600249C211yesmaximal, characteristic, complemented
4#22600248C211yesmaximal, characteristic, complemented
5#22600247C211yesmaximal, characteristic, complemented
6#22600246C211yesmaximal, characteristic, complemented
7#22600245C211yesmaximal, characteristic, complemented
8#22600244C211yesmaximal, characteristic, complemented
9#22600243C211yesmaximal, characteristic, complemented
10#22600242C211yesmaximal, characteristic, complemented
11#22600241C211yesmaximal, characteristic, complemented
12#22600240C211yesmaximal, characteristic, complemented
13#22600239C211yesmaximal, characteristic, complemented
14#22600238C211yesmaximal, characteristic, complemented
15#22600237C211yesmaximal, characteristic, complemented
16#22600236C211yesmaximal, characteristic, complemented
17#22600235C211yesmaximal, characteristic, complemented
18#488×D71C211yesmaximal, characteristic, complemented
19#481×D71C211yesmaximal, characteristic, complemented
20#485×D71C211yesmaximal, characteristic, complemented
21#479×D71C211yesmaximal, characteristic, complemented
22#466×D71C211yesmaximal, characteristic, complemented
23#465×D71C211yesmaximal, characteristic, complemented
24#463×D71C211yesmaximal, characteristic, complemented
25#449×D71C211yesmaximal, characteristic, complemented
26#448×D71C211yesmaximal, characteristic, complemented
27C4×SD16×D71C211yesmaximal, characteristic, complemented
28C8×D4×D71C211yesmaximal, characteristic, complemented
29#416×D71C211yesmaximal, characteristic, complemented
30C2×#103×D71C211yesmaximal, characteristic, complemented
31C71×#3301C211yesmaximal, characteristic, complemented
32C2×#41×D71C2211yescharacteristic
33C22×Q8×D71C2211yescharacteristic
34C2×SD16×D71C2211yescharacteristic
35C2×SD16×D71C2211yescharacteristic
36C2×D8×D71C2211yescharacteristic
37C22×C8×D71C2211yescharacteristic
38C22×C8×D71C2211yescharacteristic
39#17986702C2211yescharacteristic, complemented
40#17986701C2211yescharacteristic, complemented
41#17986700—21no—
42#17986699C2211yescharacteristic, complemented
43#17986698—21no—
44#17986697C2211yescharacteristic, complemented
45#17986696C2211yescharacteristic, complemented
46#17986695C2211yescharacteristic, complemented
47#17986694—21no—
48#17986693C2211yescharacteristic, complemented
49#17986692—21no—
50#17986661C2211yescharacteristic, complemented
51#17986660C2211yescharacteristic, complemented
52#17986659—21no—
53#17986659C2211yescharacteristic, complemented
54#17986658—21no—
55#17986658C2211yescharacteristic, complemented
56#17986657—21no—
57#17986657C2211yescharacteristic, complemented
58#17986656C2211yescharacteristic, complemented
59#17986655—21no—
60#17986655C2211yescharacteristic, complemented
61#126×D71—21no—
62#125×D71C2211yescharacteristic
63#124×D71—21no—
64#124×D71C2211yescharacteristic
65#123×D71—21no—
66C22⋊Q8×D71—21no—
67C22⋊Q8×D71C2211yescharacteristic
68#121×D71—21no—
69#121×D71—21no—
70#121×D71C2211yescharacteristic
71#121×D71C2211yescharacteristic
72#121×D71C2211yescharacteristic
73C4×Q8×D71C2211yescharacteristic
74C4×D4×D71—21no—
75C4×D4×D71—21no—
76C4×D4×D71C2211yescharacteristic
77C4×D4×D71C2211yescharacteristic
78#117×D71C2211yescharacteristic
79C2×C4⋊C4×D71C2211yescharacteristic
80#17986356C2211yescharacteristic, complemented
81#17986355C2211yescharacteristic, complemented
82#17986355C2211yescharacteristic, complemented
83#17986354C2211yescharacteristic, complemented
84#17986353C2211yescharacteristic, complemented
85#17986352C2211yescharacteristic, complemented
86#17986352C2211yescharacteristic, complemented
87#17986343C2211yescharacteristic, complemented
88#17986342C2211yescharacteristic, complemented
89#17986341C2211yescharacteristic, complemented
90#17986340C2211yescharacteristic, complemented
91#17986339C2211yescharacteristic, complemented
92#17986338C2211yescharacteristic, complemented
93#17986337C2211yescharacteristic, complemented
94#17986319C2211yescharacteristic, complemented
95#17986319C2211yescharacteristic, complemented
96#17986318C2211yescharacteristic, complemented
97#17986317C2211yescharacteristic, complemented
98#17986316C2211yescharacteristic, complemented
99#17986316C2211yescharacteristic, complemented
100#17986315C2211yescharacteristic, complemented
101#17986309C2211yescharacteristic, complemented
102#17986308C2211yescharacteristic, complemented
103#17986307C2211yescharacteristic, complemented
104#17986306C2211yescharacteristic, complemented
105#17986305C2211yescharacteristic, complemented
106#17986304C2211yescharacteristic, complemented
107#17986303C2211yescharacteristic, complemented
108#17986236C2211yescharacteristic, complemented
109#17986235C2211yescharacteristic, complemented
110#17986234C2211yescharacteristic, complemented
111#17986234C2211yescharacteristic, complemented
112#17986233C2211yescharacteristic, complemented
113#17986233C2211yescharacteristic, complemented
114#17986232C2211yescharacteristic, complemented
115#17986231C2211yescharacteristic, complemented
116#17986230C2211yescharacteristic, complemented
117#17986229C2211yescharacteristic, complemented
118#17986228C2211yescharacteristic, complemented
119#17986227C2211yescharacteristic, complemented
120#17986226C2211yescharacteristic, complemented
121#17986225C2211yescharacteristic, complemented
122#17986217C2211yescharacteristic, complemented
123#17986216C2211yescharacteristic, complemented
124#17986215C2211yescharacteristic, complemented
125#17986214C2211yescharacteristic, complemented
126#17986213C2211yescharacteristic, complemented
127#17986212C2211yescharacteristic, complemented
128#17986211C2211yescharacteristic, complemented
129#17986147C2211yescharacteristic, complemented
130#17986146C2211yescharacteristic, complemented
131#17986145C2211yescharacteristic, complemented
132#17986144C2211yescharacteristic, complemented
133#17986143C2211yescharacteristic, complemented
134#17986142C2211yescharacteristic, complemented
135#17986141C2211yescharacteristic, complemented
136#17986140C2211yescharacteristic, complemented
137#17986139C2211yescharacteristic, complemented
138#17986139C2211yescharacteristic, complemented
139#17986138C2211yescharacteristic, complemented
140#17986137C2211yescharacteristic, complemented
141#17986136C2211yescharacteristic, complemented
142#17986136C2211yescharacteristic, complemented
143#17986090C2211yescharacteristic, complemented
144C4×#11765854C2211yescharacteristic, complemented
145SD16×Dic71C2211yescharacteristic, complemented
146C4×#11765852C2211yescharacteristic, complemented
147#17986086C2211yescharacteristic, complemented
148C4×#11765853C2211yescharacteristic, complemented
149#17986084C2211yescharacteristic, complemented
150C8×D284C2211yescharacteristic, complemented
151D4×C71⋊C8C2211yescharacteristic, complemented
152#17986064C2211yescharacteristic, complemented
153C8×C22⋊D71C2211yescharacteristic, complemented
154C8×C22⋊D71C2211yescharacteristic, complemented
155(C22⋊D71)⋊C8C2211yescharacteristic, complemented
156(C22⋊D71)⋊C8C2211yescharacteristic, complemented
157#107×D71C2211yescharacteristic
158#106×D71C2211yescharacteristic
159#106×D71C2211yescharacteristic
160C4⋊C8×D71C2211yescharacteristic
161#17985996C2211yescharacteristic, complemented
162#17985995C2211yescharacteristic, complemented
163#17985994C2211yescharacteristic, complemented
164#17985994C2211yescharacteristic, complemented
165#17985993C2211yescharacteristic, complemented
166#17985992C2211yescharacteristic, complemented
167#17985992C2211yescharacteristic, complemented
168C2×#14556053C2211yescharacteristic, complemented
169C2×#14556052C2211yescharacteristic, complemented
170C2×#14556051C2211yescharacteristic, complemented
171#103×D71C2211yescharacteristic
172#103×D71C2211yescharacteristic
173#103×D71C2211yescharacteristic
174#103×D71C2211yescharacteristic
175#103×D71C2211yescharacteristic
176#103×D71C2211yescharacteristic
177#103×D71C2211yescharacteristic, complemented
178#103×D71C2211yescharacteristic, complemented
179#103×D71C2211yescharacteristic, complemented
180#103×D71C2211yescharacteristic, complemented
181#102×D71C2211yescharacteristic
182#102×D71C2211yescharacteristic
183#102×D71C2211yescharacteristic
184#102×D71C2211yescharacteristic
185C22⋊C8×D71C2211yescharacteristic
186C22⋊C8×D71C2211yescharacteristic
187C4×C8×D71C2211yescharacteristic
188#553×C71C2211yescharacteristic, complemented
189#548×C71C2211yescharacteristic, complemented
190#488×C71C2211yescharacteristic, complemented
191#485×C71C2211yescharacteristic, complemented
192#481×C71C2211yescharacteristic, complemented
193#479×C71C2211yescharacteristic, complemented
194#466×C71C2211yescharacteristic, complemented
195#465×C71C2211yescharacteristic, complemented
196#463×C71C2211yescharacteristic, complemented
197#449×C71C2211yescharacteristic, complemented
198#448×C71C2211yescharacteristic, complemented
199C4×SD16×C71C2211yescharacteristic, complemented
200C8×D4×C71C2211yescharacteristic, complemented
201#416×C71C2211yescharacteristic, complemented
202C2×#103×C71C2211yescharacteristic, complemented
203C2×#11765866C2311yescharacteristic
204C2×#11765865—21no—
205C2×#11765865C2311yescharacteristic
206C2×#11765864—21no—
207C2×#11765864C2311yescharacteristic
208#41×D71—24no—
209#41×D71—42no—
210C22×Dic142—21no—
211C22×Dic142C2311yescharacteristic
212C2×Q8×D71—21no—
213C2×Q8×D71—21no—
214C2×Q8×D71—24no—
215C2×Q8×D71—42no—
216C2×Q8×D71C2311yescharacteristic
217C2×Q8×D71C2311yescharacteristic
218C2×Q8×D71C2311yescharacteristic
219C2×Q8×D71C2311yescharacteristic
220C2×D4×D71—21no—
221C2×D4×D71—21no—
222C2×D4×D71—21no—
223C2×D4×D71—21no—
224C2×D4×D71D411yescharacteristic
225C2×D4×D71C2311yescharacteristic
226C2×D4×D71C2311yescharacteristic
227C22×C4×D71—21no—
228C22×C4×D71—21no—
229C22×C4×D71—21no—
230C22×C4×D71—21no—
231C22×C4×D71C2311yescharacteristic
232C22×C4×D71C2311yescharacteristic
233C2×#11765854C2311yescharacteristic
234C2×#11765854C2311yescharacteristic
235C2×#11765853C2311yescharacteristic
236C2×#11765853C2311yescharacteristic
237C2×#11765852C2311yescharacteristic
238C2×#11765852C2311yescharacteristic
239SD16×D71—24no—
240SD16×D71—42no—
241C2×D568C2311yescharacteristic
242C2×#11765850C2311yescharacteristic
243C2×#11765850C2311yescharacteristic
244D8×D71—42no—
245C22×C71⋊C8C2311yescharacteristic
246C22×C71⋊C8C2311yescharacteristic
247C2×C8×D71—42no—
248C2×C8×D71—42no—
249C2×C8×D71C2311yescharacteristic
250C2×C8×D71C2311yescharacteristic
251C2×C8×D71C2311yescharacteristic
252C2×C8×D71C2311yescharacteristic
253C2×C8×D71C2311yescharacteristic
254C2×C8×D71C2311yescharacteristic
255C2×C8×D71C2311yescharacteristic
256C2×C8×D71C2311yescharacteristic
257#14556123—21no—
258#14556123—21no—
259#14556123—21no—
260#14556122—21no—
261#14556121—21no—
262#14556121—21no—
263#14556121—21no—
264#14556120C2311yescharacteristic
265#14556119C2311yescharacteristic
266#14556119C2311yescharacteristic
267#14556118—21no—
268#14556118—21no—
269#14556117—21no—
270#14556117C2311yescharacteristic
271#14556116—21no—
272#14556116C2311yescharacteristic
273#14556115—21no—
274#14556115C2311yescharacteristic
275#14556114—21no—
276#14556114—21no—
277#14556114—21no—
278#14556114—21no—
279#14556114—21no—
280#14556114—21no—
281#14556113—21no—
282#14556113—21no—
283#14556112—21no—
284#14556111—21no—
285#14556110—21no—
286#14556110—21no—
287#14556109—21no—
288#14556108—21no—
289#14556108C2311yescharacteristic
290#14556107—21no—
291#14556107C2311yescharacteristic
292#14556106—21no—
293#14556106—21no—
294#14556106—21no—
295#14556105—21no—
296#14556105—21no—
297#14556105—21no—
298#14556104—21no—
299#14556104C2311yescharacteristic
300#14556103—21no—
301#14556103—21no—
302#14556103C2311yescharacteristic
303#14556103C2311yescharacteristic
304#14556103C2311yescharacteristic
305#14556102—21no—
306#14556102—21no—
307#14556102C2311yescharacteristic
308#14556102C2311yescharacteristic
309#14556102C2311yescharacteristic
310#14556101—21no—
311#14556101—21no—
312#14556101—21no—
313#14556101—21no—
314#14556101—21no—
315#14556101—21no—
316#14556101—21no—
317#14556100—21no—
318#14556100—21no—
319#14556100—21no—
320#14556100—21no—
321#14556100—21no—
322#14556100—21no—
323#14556100—21no—
324#14556099—21no—
325#14556099—21no—
326#14556099C2311yescharacteristic
327#14556099C2311yescharacteristic
328#14556099C2311yescharacteristic
329Q8×Dic71C2311yescharacteristic
330C4×Dic142—21no—
331C4×Dic142C2311yescharacteristic
332#14556093—21no—
333#14556093C2311yescharacteristic
334C4×D284—21no—
335C4×D284—21no—
336C4×D284C2311yescharacteristic
337C4×D284C2311yescharacteristic
338D4×Dic71—21no—
339D4×Dic71—21no—
340D4×Dic71D411yescharacteristic
341D4×Dic71C2311yescharacteristic
342#14556090—21no—
343#14556090—21no—
344#14556090D411yescharacteristic
345#14556090C2311yescharacteristic
346C4×C22⋊D71—21no—
347C4×C22⋊D71—21no—
348C4×C22⋊D71—21no—
349C4×C22⋊D71—21no—
350C4×C22⋊D71—21no—
351C4×C22⋊D71C2311yescharacteristic
352C4×C22⋊D71C2311yescharacteristic
353(C22⋊D71)⋊C4—21no—
354(C22⋊D71)⋊C4—21no—
355(C22⋊D71)⋊C4—21no—
356(C22⋊D71)⋊C4—21no—
357(C22⋊D71)⋊C4—21no—
358(C22⋊D71)⋊C4D411yescharacteristic
359(C22⋊D71)⋊C4D411yescharacteristic
360#14556087C2311yescharacteristic
361#14556086C2311yescharacteristic
362#14556086C2311yescharacteristic
363#14556085—21no—
364#14556084—21no—
365C2×C4⋊Dic71C2311yescharacteristic
366C2×Dic71⋊C4—21no—
367C4⋊C4×D71—21no—
368C4⋊C4×D71—21no—
369C4⋊C4×D71—21no—
370C4⋊C4×D71—21no—
371C4⋊C4×D71—21no—
372C4⋊C4×D71—21no—
373C4⋊C4×D71D411yescharacteristic
374C4⋊C4×D71C2311yescharacteristic
375C4⋊C4×D71C2311yescharacteristic
376C4⋊C4×D71C2311yescharacteristic
377C4⋊C4×D71C2311yescharacteristic
378C4⋊C4×D71C2311yescharacteristic
379C4⋊C4×D71C2311yescharacteristic
380C22⋊C4×D71—21no—
381C22⋊C4×D71—21no—
382C22⋊C4×D71—21no—
383C22⋊C4×D71—21no—
384C22⋊C4×D71—21no—
385C22⋊C4×D71—21no—
386C22⋊C4×D71—21no—
387C22⋊C4×D71—21no—
388C22⋊C4×D71D411yescharacteristic
389C22⋊C4×D71D411yescharacteristic
390C42×D71—21no—
391C42×D71—21no—
392C42×D71C2311yescharacteristic
393#14556062C2311yescharacteristic
394#14556061C2311yescharacteristic
395#14556061C2311yescharacteristic
396#14556060C2311yescharacteristic
397#14556060C2311yescharacteristic
398#14556059C2311yescharacteristic
399#14556059C2311yescharacteristic
400#14556059C2311yescharacteristic
401#14556059C2311yescharacteristic
402C4⋊(C71⋊C8)C2311yescharacteristic
403Dic71⋊C8C2311yescharacteristic
404Dic71⋊C8C2311yescharacteristic
405#14556053C2311yescharacteristic
406#14556053C2311yescharacteristic
407#14556053C2311yescharacteristic
408#14556053C2311yescharacteristic
409#14556053C2311yescharacteristic
410#14556053C2311yescharacteristic
411#14556052C2311yescharacteristic
412#14556052C2311yescharacteristic
413#14556052C2311yescharacteristic
414#14556052C2311yescharacteristic
415#14556052C2311yescharacteristic
416#14556052C2311yescharacteristic
417#14556051C2311yescharacteristic
418#14556051C2311yescharacteristic
419#14556051C2311yescharacteristic
420#14556051C2311yescharacteristic
421#14556051C2311yescharacteristic
422#14556051C2311yescharacteristic
423#14556050C2311yescharacteristic
424#14556050C2311yescharacteristic
425#14556050C2311yescharacteristic
426#14556050C2311yescharacteristic
427#14556049C2311yescharacteristic
428#14556049C2311yescharacteristic
429#14556049C2311yescharacteristic
430#14556049C2311yescharacteristic
431#14556048C2311yescharacteristic
432#14556048C2311yescharacteristic
433#14556048C2311yescharacteristic
434#14556048C2311yescharacteristic
435C22⋊(C71⋊C8)C2311yescharacteristic
436C22⋊(C71⋊C8)C2311yescharacteristic
437(C2×D71)⋊C8C2311yescharacteristic
438(C2×D71)⋊C8C2311yescharacteristic
439(C2×D71)⋊C8C2311yescharacteristic
440(C2×D71)⋊C8C2311yescharacteristic
441C4×C71⋊C8C2311yescharacteristic
442C8×Dic71C2311yescharacteristic
443C8×Dic71C2311yescharacteristic
444C2×#41×C71C2311yescharacteristic
445C22×Q8×C71C2311yescharacteristic
446C2×SD16×C71C2311yescharacteristic
447C2×SD16×C71C2311yescharacteristic
448C2×D8×C71C2311yescharacteristic
449C22×C8×C71C2311yescharacteristic
450C22×C8×C71C2311yescharacteristic
451#126×C71—21no—
452#125×C71C2311yescharacteristic
453#124×C71—21no—
454#124×C71C2311yescharacteristic
455#123×C71—21no—
456C22⋊Q8×C71—21no—
457C22⋊Q8×C71C2311yescharacteristic
458#121×C71—21no—
459#121×C71—21no—
460#121×C71C2311yescharacteristic
461#121×C71C2311yescharacteristic
462#121×C71C2311yescharacteristic
463C4×Q8×C71C2311yescharacteristic
464C4×D4×C71—21no—
465C4×D4×C71—21no—
466C4×D4×C71C2311yescharacteristic
467C4×D4×C71C2311yescharacteristic
468#117×C71C2311yescharacteristic
469C2×C4⋊C4×C71C2311yescharacteristic
470#107×C71C2311yescharacteristic
471#106×C71C2311yescharacteristic
472#106×C71C2311yescharacteristic
473C4⋊C8×C71C2311yescharacteristic
474#103×C71C2311yescharacteristic
475#103×C71C2311yescharacteristic
476#103×C71C2311yescharacteristic
477#103×C71C2311yescharacteristic
478#103×C71C2311yescharacteristic
479#103×C71C2311yescharacteristic
480#102×C71C2311yescharacteristic
481#102×C71C2311yescharacteristic
482#102×C71C2311yescharacteristic
483#102×C71C2311yescharacteristic
484C22⋊C8×C71C2311yescharacteristic
485C22⋊C8×C71C2311yescharacteristic
486C4×C8×C71C2311yescharacteristic
487C23×D71—21no—
488C23×D71—21no—
489C23×D71C2×D411yescharacteristic
490C23×D71C2×D411yescharacteristic
491#11765866—22no—
492#11765866—41no—
493#11765865—22no—
494#11765865—44no—
495#11765865—41no—
496#11765864—22no—
497#11765864—41no—
498#11765864—44no—
499C2×Dic142—21no—
500C2×Dic142—22no—
501C2×Dic142—21no—
502C2×Dic142—21no—
503C2×Dic142—21no—
504C2×Dic142—21no—
505C2×Dic142—41no—
506C2×Dic142—44no—
507C2×Dic142C2411yescharacteristic
508C2×Dic142C2411yescharacteristic
509Q8×D71—22no—
510Q8×D71—22no—
511Q8×D71—22no—
512Q8×D71—22no—
513Q8×D71—22no—
514Q8×D71—41no—
515Q8×D71—41no—
516Q8×D71—44no—
517Q8×D71—44no—
518Q8×D71#4114yes—
519C2×D284—21no—
520C2×D284—21no—
521C2×D284—21no—
522C2×D284—21no—
523C2×D284C2×D411yescharacteristic
524C2×D284C2411yescharacteristic
525C2×D284C2411yescharacteristic
526C2×C22⋊D71—21no—
527C2×C22⋊D71—21no—
528C2×C22⋊D71—21no—
529C2×C22⋊D71—21no—
530C2×C22⋊D71—21no—
531C2×C22⋊D71—21no—
532C2×C22⋊D71—21no—
533C2×C22⋊D71—21no—
534C2×C22⋊D71—21no—
535C2×C22⋊D71—21no—
536C2×C22⋊D71C2×D411yescharacteristic
537C2×C22⋊D71C2×D411yescharacteristic
538D4×D71—24no—
539D4×D71—22no—
540D4×D71—22no—
541D4×D71—22no—
542D4×D71—22no—
543D4×D71—44no—
544D4×D71—44no—
545D4×D71—44no—
546D4×D71—82no—
547C22×Dic71—21no—
548C22×Dic71—21no—
549C22×Dic71—21no—
550C22×Dic71—21no—
551C22×Dic71C2×D411yescharacteristic
552C22×Dic71C2×D411yescharacteristic
553C2×C4×D71—21no—
554C2×C4×D71—22no—
555C2×C4×D71—22no—
556C2×C4×D71—22no—
557C2×C4×D71—22no—
558C2×C4×D71—21no—
559C2×C4×D71—21no—
560C2×C4×D71—21no—
561C2×C4×D71—21no—
562C2×C4×D71—21no—
563C2×C4×D71—21no—
564C2×C4×D71—21no—
565C2×C4×D71—21no—
566C2×C4×D71—21no—
567C2×C4×D71—21no—
568C2×C4×D71—21no—
569C2×C4×D71—21no—
570C2×C4×D71—21no—
571C2×C4×D71—44no—
572C2×C4×D71—44no—
573C2×C4×D71—82no—
574C2×C4×D71—82no—
575C2×C4×D71C2×D411yescharacteristic
576C2×C4×D71C2×D411yescharacteristic
577C2×C4×D71C2×D411yescharacteristic
578C2×C4×D71C2×D411yescharacteristic
579C2×C4×D71C2×D411yescharacteristic
580C2×C4×D71C2×D411yescharacteristic
581C2×C4×D71C2411yescharacteristic
582C2×C4×D71C2411yescharacteristic
583C2×C4×D71C2411yescharacteristic
584#11765854—22no—
585#11765854—41no—
586#11765853—22no—
587#11765853—41no—
588#11765852—22no—
589#11765852—41no—
590D568—41no—
591#11765850—41no—
592#11765850—41no—
593C2×C71⋊C8—41no—
594C2×C71⋊C8—41no—
595C2×C71⋊C8C2411yescharacteristic
596C2×C71⋊C8C2411yescharacteristic
597C2×C71⋊C8C2411yescharacteristic
598C2×C71⋊C8C2411yescharacteristic
599C8×D71—22no—
600C8×D71—22no—
601C8×D71—22no—
602C8×D71—22no—
603C8×D71—41no—
604C8×D71—41no—
605C8×D71—41no—
606C8×D71—41no—
607C4⋊Dic71—21no—
608C4⋊Dic71—21no—
609C4⋊Dic71—21no—
610C4⋊Dic71—21no—
611C4⋊Dic71—21no—
612C4⋊Dic71C2×D411yescharacteristic
613C4⋊Dic71C2411yescharacteristic
614C4⋊Dic71C2411yescharacteristic
615C4⋊Dic71C2411yescharacteristic
616C4⋊Dic71C2411yescharacteristic
617Dic71⋊C4—21no—
618Dic71⋊C4—21no—
619Dic71⋊C4—21no—
620Dic71⋊C4—21no—
621Dic71⋊C4—21no—
622Dic71⋊C4—21no—
623Dic71⋊C4—21no—
624Dic71⋊C4—21no—
625Dic71⋊C4—21no—
626Dic71⋊C4—21no—
627Dic71⋊C4—21no—
628Dic71⋊C4—21no—
629Dic71⋊C4—21no—
630Dic71⋊C4—21no—
631Dic71⋊C4C2×D411yescharacteristic
632Dic71⋊C4C2×D411yescharacteristic
633C22⋊Dic71—21no—
634C22⋊Dic71—21no—
635C22⋊Dic71—21no—
636C22⋊Dic71—21no—
637C22⋊Dic71—21no—
638C22⋊Dic71—21no—
639C22⋊Dic71—21no—
640C22⋊Dic71—21no—
641C22⋊Dic71C2×D411yescharacteristic
642C22⋊Dic71C2×D411yescharacteristic
643(C2×D71)⋊C4—21no—
644(C2×D71)⋊C4—21no—
645(C2×D71)⋊C4—21no—
646(C2×D71)⋊C4—21no—
647(C2×D71)⋊C4—21no—
648(C2×D71)⋊C4—21no—
649(C2×D71)⋊C4—21no—
650(C2×D71)⋊C4—21no—
651(C2×D71)⋊C4—21no—
652(C2×D71)⋊C4—21no—
653(C2×D71)⋊C4—21no—
654(C2×D71)⋊C4—21no—
655(C2×D71)⋊C4—21no—
656(C2×D71)⋊C4—21no—
657(C2×D71)⋊C4—21no—
658(C2×D71)⋊C4—21no—
659(C2×D71)⋊C4C2×D411yescharacteristic
660(C2×D71)⋊C4C2×D411yescharacteristic
661(C2×D71)⋊C4C2×D411yescharacteristic
662(C2×D71)⋊C4C2×D411yescharacteristic
663C4×Dic71—21no—
664C4×Dic71—21no—
665C4×Dic71—21no—
666C4×Dic71—21no—
667C4×Dic71—21no—
668C4×Dic71—21no—
669C4×Dic71C2×D411yescharacteristic
670C4×Dic71C2×D411yescharacteristic
671C4×Dic71C2411yescharacteristic
672#41×C71—22no—
673#41×C71—41no—
674C2×Q8×C71—21no—
675C2×Q8×C71—22no—
676C2×Q8×C71—41no—
677C2×Q8×C71C2411yescharacteristic
678C2×Q8×C71C2411yescharacteristic
679C2×D4×C71—21no—
680C2×D4×C71—21no—
681C2×D4×C71—21no—
682C2×D4×C71—21no—
683C2×D4×C71C2×D411yescharacteristic
684C2×D4×C71C2411yescharacteristic
685C2×D4×C71C2411yescharacteristic
686C22×C4×C71—21no—
687C22×C4×C71—21no—
688C22×C4×C71—21no—
689C22×C4×C71—21no—
690C22×C4×C71C2411yescharacteristic
691C22×C4×C71C2411yescharacteristic
692SD16×C71—22no—
693SD16×C71—41no—
694D8×C71—41no—
695C2×C8×C71—41no—
696C2×C8×C71—41no—
697C2×C8×C71C2411yescharacteristic
698C2×C8×C71C2411yescharacteristic
699C2×C8×C71C2411yescharacteristic
700C2×C8×C71C2411yescharacteristic
701C4⋊C4×C71—21no—
702C4⋊C4×C71—21no—
703C4⋊C4×C71—21no—
704C4⋊C4×C71—21no—
705C4⋊C4×C71—21no—
706C4⋊C4×C71C2×D411yescharacteristic
707C4⋊C4×C71C2411yescharacteristic
708C4⋊C4×C71C2411yescharacteristic
709C4⋊C4×C71C2411yescharacteristic
710C4⋊C4×C71C2411yescharacteristic
711C22⋊C4×C71—21no—
712C22⋊C4×C71—21no—
713C22⋊C4×C71—21no—
714C22⋊C4×C71—21no—
715C22⋊C4×C71—21no—
716C22⋊C4×C71—21no—
717C22⋊C4×C71—21no—
718C22⋊C4×C71—21no—
719C22⋊C4×C71C2×D411yescharacteristic
720C22⋊C4×C71C2×D411yescharacteristic
721C42×C71—21no—
722C42×C71—21no—
723C42×C71C2411yescharacteristic
724C23×C71—21no—
725C23×C71—21no—
726C23×C71C22×D411yescharacteristic
727C23×C71C22×D411yescharacteristic
728C22×D71—22no—
729C22×D71—22no—
730C22×D71—22no—
731C22×D71—22no—
732C22×D71—22no—
733C22×D71—21no—
734C22×D71—21no—
735C22×D71—42no—
736C22×D71—42no—
737C22×D71—42no—
738C22×D71—42no—
739C22×D71—42no—
740C22×D71—42no—
741C22×D71#13514yes—
742C22×D71C22×D411yescharacteristic
743C22×D71C22×D411yescharacteristic
744C22×D71C22×D411yescharacteristic
745Q8×C71—21no—
746Q8×C71—21no—
747Q8×C71—21no—
748Q8×C71—42no—
749Q8×C71C2×#4112yes—
750D4×C71—22no—
751D4×C71—21no—
752D4×C71—21no—
753D4×C71—21no—
754D4×C71—21no—
755D4×C71—42no—
756D4×C71—42no—
757D4×C71—42no—
758D4×C71—81no—
759C2×C4×C71—21no—
760C2×C4×C71—21no—
761C2×C4×C71—21no—
762C2×C4×C71—21no—
763C2×C4×C71—21no—
764C2×C4×C71—21no—
765C2×C4×C71—21no—
766C2×C4×C71—21no—
767C2×C4×C71—21no—
768C2×C4×C71—21no—
769C2×C4×C71—42no—
770C2×C4×C71—42no—
771C2×C4×C71—81no—
772C2×C4×C71—81no—
773C2×C4×C71C22×D411yescharacteristic
774C2×C4×C71C22×D411yescharacteristic
775C2×C4×C71C22×D411yescharacteristic
776C2×C4×C71C22×D411yescharacteristic
777C2×C4×C71C2511yescharacteristic
778C22⋊D71—22no—
779C22⋊D71—22no—
780C22⋊D71—42no—
781C22⋊D71—42no—
782C22⋊D71—42no—
783C22⋊D71—42no—
784C22⋊D71—42no—
785C22⋊D71—42no—
786C22⋊D71—42no—
787C22⋊D71—42no—
788C22⋊D71—81no—
789C22⋊D71—81no—
790C2×Dic71—21no—
791C2×Dic71—22no—
792C2×Dic71—22no—
793C2×Dic71—21no—
794C2×Dic71—21no—
795C2×Dic71—21no—
796C2×Dic71—21no—
797C2×Dic71—21no—
798C2×Dic71—42no—
799C2×Dic71—42no—
800C2×Dic71—81no—
801C2×Dic71—81no—
802C2×Dic71C22×D411yescharacteristic
803C2×Dic71C22×D411yescharacteristic
804C2×Dic71C22×D411yescharacteristic
805C2×Dic71C22×D411yescharacteristic
806C2×Dic71C22×D411yescharacteristic
807D284—22no—
808D284—21no—
809D284—21no—
810D284—21no—
811D284—21no—
812D284—42no—
813D284—42no—
814D284—42no—
815D284—81no—
816C4×D71—22no—
817C4×D71—22no—
818C4×D71—24no—
819C4×D71—22no—
820C4×D71—22no—
821C4×D71—21no—
822C4×D71—21no—
823C4×D71—21no—
824C4×D71—21no—
825C4×D71—22no—
826C4×D71—22no—
827C4×D71—42no—
828C4×D71—42no—
829C4×D71—42no—
830C4×D71—42no—
831C4×D71—42no—
832C4×D71—42no—
833C4×D71—42no—
834C4×D71—42no—
835C4×D71—42no—
836C4×D71—81no—
837C4×D71—81no—
838C4×D71—81no—
839C4×D71—81no—
840C4×D71C2×#4112yes—
841C4×D71H(5,𝔽2)12yes—
842Dic142—21no—
843Dic142—24no—
844Dic142—21no—
845Dic142—21no—
846Dic142—42no—
847Dic142—42no—
848Dic142—42no—
849Dic142—42no—
850Dic142C2×#4112yes—
851C8×C71—21no—
852C8×C71—21no—
853C8×C71—21no—
854C8×C71—21no—
855C71⋊C8—21no—
856C71⋊C8—21no—
857C71⋊C8—21no—
858C71⋊C8—21no—
859C22×C71—21no—
860C22×C71—21no—
861C22×C71—21no—
862C22×C71—21no—
863C22×C71—21no—
864C22×C71—41no—
865C22×C71—41no—
866C22×C71—41no—
867C22×C71—41no—
868C22×C71—41no—
869C22×C71—41no—
870C22×C71C2×#13512yes—
871C22×C71C23×D411yescharacteristic
872C2×D71—21no—
873C2×D71—21no—
874C2×D71—28no—
875C2×D71—21no—
876C2×D71—21no—
877C2×D71—21no—
878C2×D71—44no—
879C2×D71—41no—
880C2×D71—41no—
881C2×D71—41no—
882C2×D71—41no—
883C2×D71—41no—
884C2×D71—41no—
885C2×D71—84no—
886C2×D71—84no—
887C2×D71#54612yes—
888C2×D71C2×#13512yes—
889C2×D71C2×#13512yes—
890C2×D71#57712yes—
891C4×C71—22no—
892C4×C71—21no—
893C4×C71—21no—
894C4×C71—21no—
895C4×C71—21no—
896C4×C71—41no—
897C4×C71—41no—
898C4×C71—41no—
899C4×C71—41no—
900C4×C71—41no—
901C4×C71C22×#4111yescharacteristic
902C4×C71C2×H(5,𝔽2)11yescharacteristic
903Dic71—22no—
904Dic71—21no—
905Dic71—21no—
906Dic71—21no—
907Dic71—21no—
908Dic71—41no—
909Dic71—41no—
910Dic71—41no—
911Dic71—41no—
912Dic71—41no—
913Dic71#54612yes—
914C2×#3301—711nomaximal, Sylow
915C2×C71—22no—
916C2×C71—41no—
917C2×C71—81no—
918C2×C71—81no—
919C2×C71C2×#54611yescharacteristic
920C2×C71C22×#13511yescharacteristic
921C2×C71C2×#57711yescharacteristic
922D71—22no—
923D71—41no—
924D71—81no—
925D71—81no—
926D71#330114yesdirect product factor
927C2×#553—711no—
928C2×#548—711no—
929#3301—711no—
930#3301—711no—
931#3301—711no—
932#3301—711no—
933#3301—711no—
934#3301—711no—
935#3301—711no—
936#3301—711no—
937#3301—711no—
938#3301—711no—
939#3301—711no—
940#3301—711no—
941#3301—711no—
942#3301—711no—
943#3301—711no—
944#3301D7111yescharacteristic, direct product factor
945C2×#488—711no—
946C2×#481—711no—
947C2×#485—711no—
948C2×#479—711no—
949C2×#466—711no—
950C2×#465—711no—
951C2×#463—711no—
952C2×#449—711no—
953C2×#448—711no—
954C2×C4×SD16—711no—
955C2×C8×D4—711no—
956C2×#416—711no—
957C22×#103—711no—
958C71C2×#330111yescharacteristic, complemented, Sylow
959C22×#41—711no—
960C23×Q8—711no—
961C22×SD16—711no—
962C22×SD16—711no—
963C22×D8—711no—
964C23×C8—711no—
965C23×C8—711no—
966#553—711no—
967#553—711no—
968#553—711no—
969#553—711no—
970#553—711no—
971#553—711no—
972#553—711no—
973#553—1421no—
974#553—1421no—
975#553—1421no—
976#553—1421no—
977#553C2×D7111yescharacteristic, complemented
978#548—711no—
979#548—711no—
980#548—711no—
981#548—711no—
982#548—711no—
983#548—711no—
984#548—711no—
985#548—1421no—
986#548—1421no—
987#548—1421no—
988#548—1421no—
989#548C2×D7111yescharacteristic, complemented
990C2×#126—1421no—
991C2×#125—711no—
992C2×#124—711no—
993C2×#124—1421no—
994C2×#123—1421no—
995C2×C22⋊Q8—711no—
996C2×C22⋊Q8—1421no—
997C2×#121—711no—
998C2×#121—711no—
999C2×#121—711no—
1000C2×#121—1421no—
1001C2×#121—1421no—
1002C2×C4×Q8—711no—
1003C2×C4×D4—711no—
1004C2×C4×D4—711no—
1005C2×C4×D4—1421no—
1006C2×C4×D4—1421no—
1007C2×#117—711no—
1008C22×C4⋊C4—711no—
1009#488—711no—
1010#488—711no—
1011#488—711no—
1012#488—711no—
1013#488—711no—
1014#488—711no—
1015#488—711no—
1016#488C2×D7111yescharacteristic, complemented
1017#485—711no—
1018#485—711no—
1019#485—711no—
1020#485—711no—
1021#485—711no—
1022#485—711no—
1023#485—711no—
1024#485C2×D7111yescharacteristic, complemented
1025#481—711no—
1026#481—711no—
1027#481—711no—
1028#481—711no—
1029#481—711no—
1030#481—711no—
1031#481—711no—
1032#481C2×D7111yescharacteristic, complemented
1033#479—711no—
1034#479—711no—
1035#479—711no—
1036#479—711no—
1037#479—711no—
1038#479—711no—
1039#479—711no—
1040#479C2×D7111yescharacteristic, complemented
1041#466—711no—
1042#466—711no—
1043#466—711no—
1044#466—711no—
1045#466—711no—
1046#466—711no—
1047#466—711no—
1048#466C2×D7111yescharacteristic, complemented
1049#465—711no—
1050#465—711no—
1051#465—711no—
1052#465—711no—
1053#465—711no—
1054#465—711no—
1055#465—711no—
1056#465C2×D7111yescharacteristic, complemented
1057#463—711no—
1058#463—711no—
1059#463—711no—
1060#463—711no—
1061#463—711no—
1062#463—711no—
1063#463—711no—
1064#463C2×D7111yescharacteristic, complemented
1065#449—711no—
1066#449—711no—
1067#449—711no—
1068#449—711no—
1069#449—711no—
1070#449—711no—
1071#449—711no—
1072#449C2×D7111yescharacteristic, complemented
1073#448—711no—
1074#448—711no—
1075#448—711no—
1076#448—711no—
1077#448—711no—
1078#448—711no—
1079#448—711no—
1080#448C2×D7111yescharacteristic, complemented
1081C4×SD16—711no—
1082C4×SD16—711no—
1083C4×SD16—711no—
1084C4×SD16—711no—
1085C4×SD16—711no—
1086C4×SD16—711no—
1087C4×SD16—711no—
1088C4×SD16C2×D7111yescharacteristic, complemented
1089C8×D4—711no—
1090C8×D4—711no—
1091C8×D4—711no—
1092C8×D4—711no—
1093C8×D4—711no—
1094C8×D4—711no—
1095C8×D4—711no—
1096C8×D4C2×D7111yescharacteristic, complemented
1097C2×#107—711no—
1098C2×#106—711no—
1099C2×#106—711no—
1100C2×C4⋊C8—711no—
1101#416—711no—
1102#416—711no—
1103#416—711no—
1104#416—711no—
1105#416—711no—
1106#416—711no—
1107#416—711no—
1108#416C2×D7111yescharacteristic, complemented
1109C2×#103—711no—
1110C2×#103—711no—
1111C2×#103—711no—
1112C2×#103—711no—
1113C2×#103—711no—
1114C2×#103—711no—
1115C2×#103—711no—
1116C2×#103—711no—
1117C2×#103—711no—
1118C2×#103—711no—
1119C2×#103—711no—
1120C2×#103—711no—
1121C2×#103—711no—
1122C2×#103C2×D7111yescharacteristic, complemented
1123C2×#102—711no—
1124C2×#102—711no—
1125C2×#102—711no—
1126C2×#102—711no—
1127C2×C22⋊C8—711no—
1128C2×C22⋊C8—711no—
1129C2×C4×C8—711no—
1130C2×#41—2842no—
1131C2×#41—711no—
1132C2×#41—711no—
1133C2×#41—711no—
1134C2×#41—1421no—
1135C2×#41—1424no—
1136C2×#41—1421no—
1137C2×#41C22×D7111yescharacteristic
1138C22×Q8—2842no—
1139C22×Q8—711no—
1140C22×Q8—711no—
1141C22×Q8—711no—
1142C22×Q8—711no—
1143C22×Q8—711no—
1144C22×Q8—1421no—
1145C22×Q8—1424no—
1146C22×Q8—1421no—
1147C22×Q8—1421no—
1148C22×Q8C22×D7111yescharacteristic
1149C22×D4—711no—
1150C22×D4—711no—
1151C22×D4—711no—
1152C22×D4—1421no—
1153C22×D4—1421no—
1154C22×D4—1421no—
1155C22×D4—1421no—
1156C23×C4—711no—
1157C23×C4—711no—
1158C23×C4—1421no—
1159C23×C4—1421no—
1160C23×C4—1421no—
1161C23×C4—1421no—
1162C2×SD16—2842no—
1163C2×SD16—711no—
1164C2×SD16—711no—
1165C2×SD16—711no—
1166C2×SD16—711no—
1167C2×SD16—711no—
1168C2×SD16—711no—
1169C2×SD16—1424no—
1170C2×SD16C22×D7111yescharacteristic
1171C2×SD16C22×D7111yescharacteristic
1172C2×D8—2842no—
1173C2×D8—711no—
1174C2×D8—711no—
1175C2×D8—711no—
1176C2×D8C22×D7111yescharacteristic
1177C22×C8—2842no—
1178C22×C8—2842no—
1179C22×C8—711no—
1180C22×C8—711no—
1181C22×C8—711no—
1182C22×C8—711no—
1183C22×C8—711no—
1184C22×C8—711no—
1185C22×C8—711no—
1186C22×C8—711no—
1187C22×C8—711no—
1188C22×C8—711no—
1189C22×C8C22×D7111yescharacteristic
1190C22×C8C22×D7111yescharacteristic
1191#126—21no—
1192#126—1421no—
1193#126—1421no—
1194#126—1421no—
1195#126—1421no—
1196#126—1421no—
1197#126—1421no—
1198#126—1421no—
1199#125—711no—
1200#125—711no—
1201#125—711no—
1202#125—1421no—
1203#125—1421no—
1204#125C22×D7111yescharacteristic
1205#124—21no—
1206#124—711no—
1207#124—711no—
1208#124—711no—
1209#124—1421no—
1210#124—1421no—
1211#124—1421no—
1212#124—1421no—
1213#124—1421no—
1214#124—1421no—
1215#124—1421no—
1216#124—1421no—
1217#124—1421no—
1218#124C22×D7111yescharacteristic
1219#123—21no—
1220#123—1421no—
1221#123—1421no—
1222#123—1421no—
1223#123—1421no—
1224#123—1421no—
1225#123—1421no—
1226#123—1421no—
1227C22⋊Q8—21no—
1228C22⋊Q8—711no—
1229C22⋊Q8—711no—
1230C22⋊Q8—711no—
1231C22⋊Q8—1421no—
1232C22⋊Q8—1421no—
1233C22⋊Q8—1421no—
1234C22⋊Q8—1421no—
1235C22⋊Q8—1421no—
1236C22⋊Q8—1421no—
1237C22⋊Q8—1421no—
1238C22⋊Q8—1421no—
1239C22⋊Q8—1421no—
1240C22⋊Q8C22×D7111yescharacteristic
1241#121—21no—
1242#121—21no—
1243#121—711no—
1244#121—711no—
1245#121—711no—
1246#121—711no—
1247#121—711no—
1248#121—711no—
1249#121—711no—
1250#121—711no—
1251#121—711no—
1252#121—1421no—
1253#121—1421no—
1254#121—1421no—
1255#121—1421no—
1256#121—1421no—
1257#121—1421no—
1258#121—1421no—
1259#121—1421no—
1260#121—1421no—
1261#121—1421no—
1262#121—1421no—
1263#121—1421no—
1264#121—1421no—
1265#121—1421no—
1266#121—1421no—
1267#121—1421no—
1268#121—1421no—
1269#121—1421no—
1270#121—1421no—
1271#121—1421no—
1272#121C22×D7111yescharacteristic
1273#121C22×D7111yescharacteristic
1274#121C22×D7111yescharacteristic
1275C4×Q8—711no—
1276C4×Q8—711no—
1277C4×Q8—711no—
1278C4×Q8—1421no—
1279C4×Q8—1421no—
1280C4×Q8C22×D7111yescharacteristic
1281C4×D4—21no—
1282C4×D4—21no—
1283C4×D4—711no—
1284C4×D4—711no—
1285C4×D4—711no—
1286C4×D4—711no—
1287C4×D4—711no—
1288C4×D4—711no—
1289C4×D4—711no—
1290C4×D4—711no—
1291C4×D4—711no—
1292C4×D4—711no—
1293C4×D4—1421no—
1294C4×D4—1421no—
1295C4×D4—1421no—
1296C4×D4—1421no—
1297C4×D4—1421no—
1298C4×D4—1421no—
1299C4×D4—1421no—
1300C4×D4—1421no—
1301C4×D4—1421no—
1302C4×D4—1421no—
1303C4×D4—1421no—
1304C4×D4—1421no—
1305C4×D4—1421no—
1306C4×D4—1421no—
1307C4×D4—1421no—
1308C4×D4—1421no—
1309C4×D4C22×D7111yescharacteristic
1310C4×D4C22×D7111yescharacteristic
1311#117—711no—
1312#117—711no—
1313#117—711no—
1314#117—1421no—
1315#117—1421no—
1316#117C22×D7111yescharacteristic
1317C2×C4⋊C4—711no—
1318C2×C4⋊C4—711no—
1319C2×C4⋊C4—711no—
1320C2×C4⋊C4—711no—
1321C2×C4⋊C4—711no—
1322C2×C4⋊C4—711no—
1323C2×C4⋊C4—711no—
1324C2×C4⋊C4—711no—
1325C2×C4⋊C4—1421no—
1326C2×C4⋊C4—1421no—
1327C2×C4⋊C4—1421no—
1328C2×C4⋊C4—1421no—
1329C2×C4⋊C4—1421no—
1330C2×C4⋊C4—1421no—
1331C2×C4⋊C4—1421no—
1332C2×C4⋊C4C22×D7111yescharacteristic
1333C2×C22⋊C4—711no—
1334C2×C22⋊C4—711no—
1335C2×C22⋊C4—1421no—
1336C2×C22⋊C4—1421no—
1337C2×C22⋊C4—1421no—
1338C2×C22⋊C4—1421no—
1339C2×C22⋊C4—1421no—
1340C2×C22⋊C4—1421no—
1341C2×C22⋊C4—1421no—
1342C2×C22⋊C4—1421no—
1343C2×C42—711no—
1344C2×C42—1421no—
1345C2×C42—1421no—
1346#107—711no—
1347#107—711no—
1348#107—711no—
1349#107C22×D7111yescharacteristic
1350#106—711no—
1351#106—711no—
1352#106—711no—
1353#106—711no—
1354#106—711no—
1355#106—711no—
1356#106C22×D7111yescharacteristic
1357#106C22×D7111yescharacteristic
1358C4⋊C8—711no—
1359C4⋊C8—711no—
1360C4⋊C8—711no—
1361C4⋊C8C22×D7111yescharacteristic
1362#103—711no—
1363#103—711no—
1364#103—711no—
1365#103—711no—
1366#103—711no—
1367#103—711no—
1368#103—711no—
1369#103—711no—
1370#103—711no—
1371#103—711no—
1372#103—711no—
1373#103—711no—
1374#103—711no—
1375#103—711no—
1376#103—711no—
1377#103—711no—
1378#103—711no—
1379#103—711no—
1380#103C22×D7111yescharacteristic
1381#103C22×D7111yescharacteristic
1382#103C22×D7111yescharacteristic
1383#103C22×D7111yescharacteristic
1384#103C22×D7111yescharacteristic
1385#103C22×D7111yescharacteristic
1386#102—711no—
1387#102—711no—
1388#102—711no—
1389#102—711no—
1390#102—711no—
1391#102—711no—
1392#102—711no—
1393#102—711no—
1394#102—711no—
1395#102—711no—
1396#102—711no—
1397#102—711no—
1398#102C22×D7111yescharacteristic
1399#102C22×D7111yescharacteristic
1400#102C22×D7111yescharacteristic
1401#102C22×D7111yescharacteristic
1402C22⋊C8—711no—
1403C22⋊C8—711no—
1404C22⋊C8—711no—
1405C22⋊C8—711no—
1406C22⋊C8—711no—
1407C22⋊C8—711no—
1408C22⋊C8C22×D7111yescharacteristic
1409C22⋊C8C22×D7111yescharacteristic
1410C4×C8—711no—
1411C4×C8—711no—
1412C4×C8—711no—
1413C4×C8C22×D7111yescharacteristic
1414C24—711no—
1415C24—711no—
1416C24—1421no—
1417C24—1421no—
1418#41—22no—
1419#41—41no—
1420#41—2841no—
1421#41—2844no—
1422#41—2841no—
1423#41—2844no—
1424#41—2841no—
1425#41—1422no—
1426#41—1422no—
1427#41—1422no—
1428C2×Q8—21no—
1429C2×Q8—22no—
1430C2×Q8—41no—
1431C2×Q8—2841no—
1432C2×Q8—2844no—
1433C2×Q8—2841no—
1434C2×Q8—2841no—
1435C2×Q8—2844no—
1436C2×Q8—2844no—
1437C2×Q8—714no—
1438C2×Q8—711no—
1439C2×Q8—711no—
1440C2×Q8—1422no—
1441C2×Q8—1421no—
1442C2×Q8—1421no—
1443C2×Q8—1421no—
1444C2×Q8—1421no—
1445C2×Q8—1422no—
1446C2×Q8—1422no—
1447C2×Q8—1422no—
1448C2×Q8—1422no—
1449C2×Q8—1422no—
1450C2×Q8—1421no—
1451C2×Q8C23×D7111yescharacteristic
1452C2×Q8C23×D7111yescharacteristic
1453C2×D4—21no—
1454C2×D4—21no—
1455C2×D4—21no—
1456C2×D4—21no—
1457C2×D4—2844no—
1458C2×D4—2844no—
1459C2×D4—2844no—
1460C2×D4—5682no—
1461C2×D4—711no—
1462C2×D4—711no—
1463C2×D4—711no—
1464C2×D4—711no—
1465C2×D4—711no—
1466C2×D4—1421no—
1467C2×D4—1421no—
1468C2×D4—1421no—
1469C2×D4—1421no—
1470C2×D4—1422no—
1471C2×D4—1422no—
1472C2×D4—1422no—
1473C2×D4—1422no—
1474C2×D4—1421no—
1475C2×D4—1421no—
1476C2×D4—1424no—
1477C2×D4—1421no—
1478C2×D4—1421no—
1479C2×D4—1421no—
1480C2×D4—1421no—
1481C2×D4—1421no—
1482C2×D4—1421no—
1483C2×D4—1421no—
1484C2×D4—1421no—
1485C2×D4D4×D7111yescharacteristic
1486C2×D4C23×D7111yescharacteristic
1487C2×D4C23×D7111yescharacteristic
1488C22×C4—21no—
1489C22×C4—21no—
1490C22×C4—21no—
1491C22×C4—21no—
1492C22×C4—2844no—
1493C22×C4—2844no—
1494C22×C4—5682no—
1495C22×C4—5682no—
1496C22×C4—711no—
1497C22×C4—711no—
1498C22×C4—711no—
1499C22×C4—711no—
1500C22×C4—711no—
1501C22×C4—711no—
1502C22×C4—711no—
1503C22×C4—711no—
1504C22×C4—711no—
1505C22×C4—711no—
1506C22×C4—711no—
1507C22×C4—1421no—
1508C22×C4—1421no—
1509C22×C4—1421no—
1510C22×C4—1421no—
1511C22×C4—1421no—
1512C22×C4—1421no—
1513C22×C4—1421no—
1514C22×C4—1421no—
1515C22×C4—1421no—
1516C22×C4—1421no—
1517C22×C4—1421no—
1518C22×C4—1422no—
1519C22×C4—1422no—
1520C22×C4—1422no—
1521C22×C4—1422no—
1522C22×C4—1421no—
1523C22×C4—1421no—
1524C22×C4—1421no—
1525C22×C4—1421no—
1526C22×C4—1421no—
1527C22×C4—1421no—
1528C22×C4—1421no—
1529C22×C4C23×D7111yescharacteristic
1530C22×C4C23×D7111yescharacteristic
1531SD16—22no—
1532SD16—41no—
1533SD16—2841no—
1534SD16—2841no—
1535SD16—2841no—
1536SD16—1422no—
1537SD16—1422no—
1538SD16—1422no—
1539D8—41no—
1540D8—2841no—
1541D8—2841no—
1542D8—2841no—
1543C2×C8—41no—
1544C2×C8—41no—
1545C2×C8—2841no—
1546C2×C8—2841no—
1547C2×C8—2841no—
1548C2×C8—2841no—
1549C2×C8—2841no—
1550C2×C8—2841no—
1551C2×C8—711no—
1552C2×C8—711no—
1553C2×C8—711no—
1554C2×C8—711no—
1555C2×C8—1422no—
1556C2×C8—1422no—
1557C2×C8—1422no—
1558C2×C8—1422no—
1559C2×C8C23×D7111yescharacteristic
1560C2×C8C23×D7111yescharacteristic
1561C2×C8C23×D7111yescharacteristic
1562C2×C8C23×D7111yescharacteristic
1563C4⋊C4—21no—
1564C4⋊C4—21no—
1565C4⋊C4—21no—
1566C4⋊C4—21no—
1567C4⋊C4—21no—
1568C4⋊C4—711no—
1569C4⋊C4—711no—
1570C4⋊C4—711no—
1571C4⋊C4—711no—
1572C4⋊C4—711no—
1573C4⋊C4—711no—
1574C4⋊C4—711no—
1575C4⋊C4—1421no—
1576C4⋊C4—1421no—
1577C4⋊C4—1421no—
1578C4⋊C4—1421no—
1579C4⋊C4—1421no—
1580C4⋊C4—1421no—
1581C4⋊C4—1421no—
1582C4⋊C4—1421no—
1583C4⋊C4—1421no—
1584C4⋊C4—1421no—
1585C4⋊C4—1421no—
1586C4⋊C4—1421no—
1587C4⋊C4—1421no—
1588C4⋊C4—1421no—
1589C4⋊C4—1421no—
1590C4⋊C4—1421no—
1591C4⋊C4—1421no—
1592C4⋊C4—1421no—
1593C4⋊C4—1421no—
1594C4⋊C4D4×D7111yescharacteristic
1595C4⋊C4C23×D7111yescharacteristic
1596C4⋊C4C23×D7111yescharacteristic
1597C4⋊C4C23×D7111yescharacteristic
1598C4⋊C4C23×D7111yescharacteristic
1599C22⋊C4—21no—
1600C22⋊C4—21no—
1601C22⋊C4—21no—
1602C22⋊C4—21no—
1603C22⋊C4—21no—
1604C22⋊C4—21no—
1605C22⋊C4—21no—
1606C22⋊C4—21no—
1607C22⋊C4—711no—
1608C22⋊C4—711no—
1609C22⋊C4—711no—
1610C22⋊C4—711no—
1611C22⋊C4—711no—
1612C22⋊C4—711no—
1613C22⋊C4—1421no—
1614C22⋊C4—1421no—
1615C22⋊C4—1421no—
1616C22⋊C4—1421no—
1617C22⋊C4—1421no—
1618C22⋊C4—1421no—
1619C22⋊C4—1421no—
1620C22⋊C4—1421no—
1621C22⋊C4—1421no—
1622C22⋊C4—1421no—
1623C22⋊C4—1421no—
1624C22⋊C4—1421no—
1625C22⋊C4—1421no—
1626C22⋊C4—1421no—
1627C22⋊C4—1421no—
1628C22⋊C4—1421no—
1629C22⋊C4—1421no—
1630C22⋊C4—1421no—
1631C22⋊C4—1421no—
1632C22⋊C4—1421no—
1633C22⋊C4—1421no—
1634C22⋊C4—1421no—
1635C22⋊C4—1421no—
1636C22⋊C4—1421no—
1637C22⋊C4D4×D7111yescharacteristic
1638C22⋊C4D4×D7111yescharacteristic
1639C42—21no—
1640C42—21no—
1641C42—711no—
1642C42—711no—
1643C42—711no—
1644C42—1421no—
1645C42—1421no—
1646C42—1421no—
1647C42—1421no—
1648C42—1421no—
1649C42—1421no—
1650C42C23×D7111yescharacteristic
1651C23—21no—
1652C23—21no—
1653C23—2842no—
1654C23—2842no—
1655C23—2842no—
1656C23—2842no—
1657C23—2842no—
1658C23—2842no—
1659C23—711no—
1660C23—711no—
1661C23—714no—
1662C23—711no—
1663C23—1422no—
1664C23—1422no—
1665C23—1422no—
1666C23—1422no—
1667C23—1422no—
1668C23—1421no—
1669C23—1421no—
1670C23C2×D4×D7111yescharacteristic
1671C23C2×D4×D7111yescharacteristic
1672Q8—21no—
1673Q8—21no—
1674Q8—21no—
1675Q8—42no—
1676Q8—2842no—
1677Q8—2842no—
1678Q8—2842no—
1679Q8—2842no—
1680Q8—712no—
1681Q8—1424no—
1682Q8—1421no—
1683Q8—1421no—
1684Q8—1421no—
1685Q8#41×D7112yes—
1686D4—22no—
1687D4—21no—
1688D4—21no—
1689D4—21no—
1690D4—21no—
1691D4—42no—
1692D4—42no—
1693D4—42no—
1694D4—81no—
1695D4—2842no—
1696D4—2842no—
1697D4—2842no—
1698D4—2842no—
1699D4—2842no—
1700D4—2842no—
1701D4—2842no—
1702D4—2842no—
1703D4—2842no—
1704D4—2842no—
1705D4—2842no—
1706D4—5681no—
1707D4—5681no—
1708D4—5681no—
1709D4—1422no—
1710D4—1422no—
1711D4—1422no—
1712D4—1421no—
1713D4—1421no—
1714D4—1421no—
1715D4—1421no—
1716C2×C4—21no—
1717C2×C4—21no—
1718C2×C4—21no—
1719C2×C4—21no—
1720C2×C4—21no—
1721C2×C4—21no—
1722C2×C4—21no—
1723C2×C4—21no—
1724C2×C4—21no—
1725C2×C4—21no—
1726C2×C4—42no—
1727C2×C4—42no—
1728C2×C4—81no—
1729C2×C4—81no—
1730C2×C4—2842no—
1731C2×C4—2842no—
1732C2×C4—2842no—
1733C2×C4—2842no—
1734C2×C4—2842no—
1735C2×C4—2842no—
1736C2×C4—2842no—
1737C2×C4—2842no—
1738C2×C4—2842no—
1739C2×C4—2842no—
1740C2×C4—2842no—
1741C2×C4—5681no—
1742C2×C4—5681no—
1743C2×C4—5681no—
1744C2×C4—5681no—
1745C2×C4—5681no—
1746C2×C4—5681no—
1747C2×C4—711no—
1748C2×C4—712no—
1749C2×C4—712no—
1750C2×C4—711no—
1751C2×C4—711no—
1752C2×C4—711no—
1753C2×C4—711no—
1754C2×C4—1422no—
1755C2×C4—1422no—
1756C2×C4—1422no—
1757C2×C4—1424no—
1758C2×C4—1422no—
1759C2×C4—1422no—
1760C2×C4—1422no—
1761C2×C4—1421no—
1762C2×C4—1421no—
1763C2×C4—1421no—
1764C2×C4—1421no—
1765C2×C4—1421no—
1766C2×C4—1422no—
1767C2×C4—1422no—
1768C2×C4—1421no—
1769C2×C4—1421no—
1770C2×C4—1421no—
1771C2×C4—1421no—
1772C2×C4—1421no—
1773C2×C4C2×D4×D7111yescharacteristic
1774C2×C4C2×D4×D7111yescharacteristic
1775C2×C4C2×D4×D7111yescharacteristic
1776C2×C4C2×D4×D7111yescharacteristic
1777C2×C4C24×D7111yescharacteristic
1778C8—21no—
1779C8—21no—
1780C8—21no—
1781C8—21no—
1782C8—1421no—
1783C8—1421no—
1784C8—1421no—
1785C8—1421no—
1786C22—21no—
1787C22—21no—
1788C22—21no—
1789C22—21no—
1790C22—21no—
1791C22—41no—
1792C22—41no—
1793C22—41no—
1794C22—41no—
1795C22—41no—
1796C22—41no—
1797C22—2844no—
1798C22—2841no—
1799C22—2841no—
1800C22—2841no—
1801C22—2841no—
1802C22—2841no—
1803C22—2841no—
1804C22—5684no—
1805C22—5684no—
1806C22—712no—
1807C22—712no—
1808C22—712no—
1809C22—712no—
1810C22—1428no—
1811C22—1421no—
1812C22—1421no—
1813C22—1421no—
1814C22—1421no—
1815C22—1421no—
1816C22#135×D7112yes—
1817C22C22×D4×D7111yescharacteristic
1818C4—21no—
1819C4—21no—
1820C4—22no—
1821C4—21no—
1822C4—21no—
1823C4—41no—
1824C4—41no—
1825C4—41no—
1826C4—41no—
1827C4—41no—
1828C4—2841no—
1829C4—2841no—
1830C4—2841no—
1831C4—2841no—
1832C4—2841no—
1833C4—712no—
1834C4—1421no—
1835C4—1422no—
1836C4—1421no—
1837C4—1421no—
1838C4—1421no—
1839C4C2×#41×D7111yescharacteristic
1840C4H(5,𝔽2)×D7111yescharacteristic
1841C2—22no—
1842C2—41no—
1843C2—81no—
1844C2—81no—
1845C2—2841no—
1846C2—5681no—
1847C2—5681no—
1848C2—714no—
1849C2—1422no—
1850C2#546×D7111yescharacteristic
1851C2C2×#135×D7111yescharacteristic
1852C2#577×D7111yescharacteristic
subgroupG/H
centerC22C22×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC71×#3301C2
socleC22×C71C23×D4
hypercenter#3301D71
hypocenterC71C2×#3301
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3301

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #553×D71C2semidirect
2. #548×D71C2semidirect
3. #22600249C2semidirect
4. #22600248C2semidirect
5. #22600247C2semidirect
6. #22600246C2semidirect
7. #22600245C2semidirect
8. #22600244C2semidirect
9. #22600243C2semidirect
10. #22600242C2semidirect
11. #22600241C2semidirect
12. #22600240C2semidirect
13. #22600239C2semidirect
14. #22600238C2semidirect
15. #22600237C2semidirect
16. #22600236C2semidirect
17. #22600235C2semidirect
18. #488×D71C2semidirect
19. #481×D71C2semidirect
20. #485×D71C2semidirect
21. #479×D71C2semidirect
22. #466×D71C2semidirect
23. #465×D71C2semidirect
24. #463×D71C2semidirect
25. #449×D71C2semidirect
26. #448×D71C2semidirect
27. C4×SD16×D71C2semidirect
28. C8×D4×D71C2semidirect
29. #416×D71C2semidirect
30. C2×#103×D71C2semidirect
31. C71×#3301C2semidirect
39. #17986702C22semidirect
40. #17986701C22semidirect
42. #17986699C22semidirect
44. #17986697C22semidirect
45. #17986696C22semidirect
46. #17986695C22semidirect
48. #17986693C22semidirect
50. #17986661C22semidirect
51. #17986660C22semidirect
53. #17986659C22semidirect
55. #17986658C22semidirect
57. #17986657C22semidirect
58. #17986656C22semidirect
60. #17986655C22semidirect
80. #17986356C22semidirect
81. #17986355C22semidirect
82. #17986355C22semidirect
83. #17986354C22semidirect
84. #17986353C22semidirect
85. #17986352C22semidirect
86. #17986352C22semidirect
87. #17986343C22semidirect
88. #17986342C22semidirect
89. #17986341C22semidirect
90. #17986340C22semidirect
91. #17986339C22semidirect
92. #17986338C22semidirect
93. #17986337C22semidirect
94. #17986319C22semidirect
95. #17986319C22semidirect
96. #17986318C22semidirect
97. #17986317C22semidirect
98. #17986316C22semidirect
99. #17986316C22semidirect
100. #17986315C22semidirect
101. #17986309C22semidirect
102. #17986308C22semidirect
103. #17986307C22semidirect
104. #17986306C22semidirect
105. #17986305C22semidirect
106. #17986304C22semidirect
107. #17986303C22semidirect
108. #17986236C22semidirect
109. #17986235C22semidirect
110. #17986234C22semidirect
111. #17986234C22semidirect
112. #17986233C22semidirect
113. #17986233C22semidirect
114. #17986232C22semidirect
115. #17986231C22semidirect
116. #17986230C22semidirect
117. #17986229C22semidirect
118. #17986228C22semidirect
119. #17986227C22semidirect
120. #17986226C22semidirect
121. #17986225C22semidirect
122. #17986217C22semidirect
123. #17986216C22semidirect
124. #17986215C22semidirect
125. #17986214C22semidirect
126. #17986213C22semidirect
127. #17986212C22semidirect
128. #17986211C22semidirect
129. #17986147C22semidirect
130. #17986146C22semidirect
131. #17986145C22semidirect
132. #17986144C22semidirect
133. #17986143C22semidirect
134. #17986142C22semidirect
135. #17986141C22semidirect
136. #17986140C22semidirect
137. #17986139C22semidirect
138. #17986139C22semidirect
139. #17986138C22semidirect
140. #17986137C22semidirect
141. #17986136C22semidirect
142. #17986136C22semidirect
143. #17986090C22semidirect
144. C4×#11765854C22semidirect
145. SD16×Dic71C22semidirect
146. C4×#11765852C22semidirect
147. #17986086C22semidirect
148. C4×#11765853C22semidirect
149. #17986084C22semidirect
150. C8×D284C22semidirect
151. D4×C71⋊C8C22semidirect
152. #17986064C22semidirect
153. C8×C22⋊D71C22semidirect
154. C8×C22⋊D71C22semidirect
155. (C22⋊D71)⋊C8C22semidirect
156. (C22⋊D71)⋊C8C22semidirect
161. #17985996C22semidirect
162. #17985995C22semidirect
163. #17985994C22semidirect
164. #17985994C22semidirect
165. #17985993C22semidirect
166. #17985992C22semidirect
167. #17985992C22semidirect
168. C2×#14556053C22semidirect
169. C2×#14556052C22semidirect
170. C2×#14556051C22semidirect
177. #103×D71C22semidirect
178. #103×D71C22semidirect
179. #103×D71C22semidirect
180. #103×D71C22semidirect
188. #553×C71C22semidirect
189. #548×C71C22semidirect
190. #488×C71C22semidirect
191. #485×C71C22semidirect
192. #481×C71C22semidirect
193. #479×C71C22semidirect
194. #466×C71C22semidirect
195. #465×C71C22semidirect
196. #463×C71C22semidirect
197. #449×C71C22semidirect
198. #448×C71C22semidirect
199. C4×SD16×C71C22semidirect
200. C8×D4×C71C22semidirect
201. #416×C71C22semidirect
202. C2×#103×C71C22semidirect
926. D71#3301direct (N × H)
944. #3301D71direct (N × H)
958. C71C2×#3301semidirect
977. #553C2×D71semidirect
989. #548C2×D71semidirect
1016. #488C2×D71semidirect
1024. #485C2×D71semidirect
1032. #481C2×D71semidirect
1040. #479C2×D71semidirect
1048. #466C2×D71semidirect
1056. #465C2×D71semidirect
1064. #463C2×D71semidirect
1072. #449C2×D71semidirect
1080. #448C2×D71semidirect
1088. C4×SD16C2×D71semidirect
1096. C8×D4C2×D71semidirect
1108. #416C2×D71semidirect
1122. C2×#103C2×D71semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#553×D712
#548×D712
#226002492
#226002482
#226002472
#226002462
#226002452
#226002442
#226002432
#226002422
#226002412
#226002402
#226002392
#226002382
#226002372
#226002362
#226002352
#488×D712
#481×D712
#485×D712
#479×D712
#466×D712
#465×D712
#463×D712
#449×D712
#448×D712
C4×SD16×D712
C8×D4×D712
#416×D712
C2×#103×D712
C71×#33012
C2×#330171