Finite Group Databasebeta

← #32865972

Subgroups — #32865972

Order 18176.

2138 conjugacy classes of subgroups.

The subgroup lattice has 1800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#540×D71C211yesmaximal, characteristic, complemented
2#22601540C211yesmaximal, characteristic, complemented
3#22598633C211yesmaximal, characteristic, complemented
4#22598630C211yesmaximal, characteristic, complemented
5#22598629C211yesmaximal, characteristic, complemented
6#22598628C211yesmaximal, characteristic, complemented
7#22598585C211yesmaximal, characteristic, complemented
8#22598582C211yesmaximal, characteristic, complemented
9#22598581C211yesmaximal, characteristic, complemented
10#22598580C211yesmaximal, characteristic, complemented
11#22598542C211yesmaximal, characteristic, complemented
12#22598541C211yesmaximal, characteristic, complemented
13#22598540C211yesmaximal, characteristic, complemented
14#22598539C211yesmaximal, characteristic, complemented
15#22598534C211yesmaximal, characteristic, complemented
16#22598533C211yesmaximal, characteristic, complemented
17#22598532C211yesmaximal, characteristic, complemented
18#22598277C211yesmaximal, characteristic, complemented
19#22598275C211yesmaximal, characteristic, complemented
20#22598159C211yesmaximal, characteristic, complemented
21#22598157C211yesmaximal, characteristic, complemented
22#22597817C211yesmaximal, characteristic, complemented
23#22597815C211yesmaximal, characteristic, complemented
24#22597589C211yesmaximal, characteristic, complemented
25#22597589C211yesmaximal, characteristic, complemented
26#22597151C211yesmaximal, characteristic, complemented
27C4×#14556155C211yesmaximal, characteristic, complemented
28#22597145C211yesmaximal, characteristic, complemented
29C4×#14556152C211yesmaximal, characteristic, complemented
30#22596974C211yesmaximal, characteristic, complemented
31C71×#3119C211yesmaximal, characteristic, complemented
32C2×#41×D71C2211yescharacteristic
33C2×#14556155C2211yescharacteristic
34C2×#14556155C2211yescharacteristic
35C2×#14556152C2211yescharacteristic
36C2×#14556152C2211yescharacteristic
37#17986605C2211yescharacteristic
38#17986604C2211yescharacteristic, complemented
39#17986603C2211yescharacteristic
40#17986602C2211yescharacteristic, complemented
41#17986602C2211yescharacteristic, complemented
42#17986601—21no—
43#17986601—21no—
44#17986600C2211yescharacteristic
45#17986600C2211yescharacteristic
46#17986599—21no—
47#17986599—21no—
48#127×D71C2211yescharacteristic, complemented
49#125×D71C2211yescharacteristic, complemented
50#123×D71—21no—
51#123×D71—21no—
52#121×D71—21no—
53#121×D71—21no—
54#121×D71C2211yescharacteristic
55#121×D71C2211yescharacteristic
56#17986482C2211yescharacteristic, complemented
57#17986480—21no—
58#17986480C2211yescharacteristic, complemented
59#17986479—21no—
60#17986479C2211yescharacteristic, complemented
61#17986475C2211yescharacteristic, complemented
62#17986475C2211yescharacteristic, complemented
63#17986471—21no—
64#17986471—21no—
65#17986471C2211yescharacteristic, complemented
66#17986471C2211yescharacteristic, complemented
67C4×#11765866C2211yescharacteristic
68C4×#11765866C2211yescharacteristic
69C4×#11765864—21no—
70C4×#11765864—21no—
71C4×#11765864C2211yescharacteristic
72C4×#11765864C2211yescharacteristic
73C4×D4×D71C2211yescharacteristic, complemented
74C4×D4×D71C2211yescharacteristic, complemented
75C2×#14556086—21no—
76C2×#14556086C2211yescharacteristic
77#117×D71—21no—
78#117×D71C2211yescharacteristic
79#17986326C2211yescharacteristic, complemented
80#17986326C2211yescharacteristic, complemented
81#17986325C2211yescharacteristic, complemented
82#17986325C2211yescharacteristic, complemented
83#17986322C2211yescharacteristic, complemented
84#17986322C2211yescharacteristic, complemented
85#17986321C2211yescharacteristic, complemented
86#17986321C2211yescharacteristic, complemented
87#17986318C2211yescharacteristic, complemented
88#17986317C2211yescharacteristic, complemented
89#17986315C2211yescharacteristic, complemented
90#17986313C2211yescharacteristic, complemented
91#17986312C2211yescharacteristic, complemented
92#17986310C2211yescharacteristic, complemented
93#17986309C2211yescharacteristic, complemented
94#17986308C2211yescharacteristic, complemented
95#17986307C2211yescharacteristic, complemented
96#17986306C2211yescharacteristic, complemented
97#17986305C2211yescharacteristic, complemented
98#17986304C2211yescharacteristic, complemented
99#17986303C2211yescharacteristic, complemented
100#17986302C2211yescharacteristic, complemented
101#17986301C2211yescharacteristic, complemented
102#17986300C2211yescharacteristic, complemented
103#17986299C2211yescharacteristic, complemented
104#17986298C2211yescharacteristic, complemented
105#17986297C2211yescharacteristic, complemented
106#17986296C2211yescharacteristic, complemented
107#17986200C2211yescharacteristic, complemented
108#17986199C2211yescharacteristic, complemented
109#17986198C2211yescharacteristic, complemented
110#17986198C2211yescharacteristic, complemented
111#17986197C2211yescharacteristic, complemented
112#17986197C2211yescharacteristic, complemented
113#17986196C2211yescharacteristic, complemented
114#17986195C2211yescharacteristic, complemented
115#17986194C2211yescharacteristic, complemented
116#17986193C2211yescharacteristic, complemented
117#17986193C2211yescharacteristic, complemented
118#17986192C2211yescharacteristic, complemented
119#17986192C2211yescharacteristic, complemented
120#17986191C2211yescharacteristic, complemented
121#17986146C2211yescharacteristic, complemented
122#17986146C2211yescharacteristic, complemented
123#17986144C2211yescharacteristic, complemented
124#17986144C2211yescharacteristic, complemented
125#17986142C2211yescharacteristic, complemented
126#17986142C2211yescharacteristic, complemented
127#17986139C2211yescharacteristic, complemented
128#17986139C2211yescharacteristic, complemented
129#17986136C2211yescharacteristic, complemented
130#17986136C2211yescharacteristic, complemented
131#17986134C2211yescharacteristic, complemented
132#17986134C2211yescharacteristic, complemented
133#17986131C2211yescharacteristic, complemented
134#17986131C2211yescharacteristic, complemented
135#17986112C2211yescharacteristic, complemented
136#17986111C2211yescharacteristic, complemented
137#17986110C2211yescharacteristic, complemented
138#17986109C2211yescharacteristic, complemented
139#17986109C2211yescharacteristic, complemented
140#17986108C2211yescharacteristic, complemented
141#17986108C2211yescharacteristic, complemented
142#17986102C2211yescharacteristic, complemented
143#17986101C2211yescharacteristic, complemented
144#17986100C2211yescharacteristic, complemented
145#17986099C2211yescharacteristic, complemented
146#17986098C2211yescharacteristic, complemented
147#17986097C2211yescharacteristic, complemented
148#17986096C2211yescharacteristic, complemented
149#17986090C2211yescharacteristic, complemented
150C4×#11765854C2211yescharacteristic, complemented
151SD16×Dic71C2211yescharacteristic, complemented
152C4×#11765852C2211yescharacteristic, complemented
153#17986086C2211yescharacteristic, complemented
154C4×#11765853C2211yescharacteristic, complemented
155#17986084C2211yescharacteristic, complemented
156C4×D568C2211yescharacteristic, complemented
157D8×Dic71C2211yescharacteristic, complemented
158#17986081C2211yescharacteristic, complemented
159C4×#11765850C2211yescharacteristic, complemented
160C4×#11765850C2211yescharacteristic, complemented
161#17986079C2211yescharacteristic, complemented
162#17986079C2211yescharacteristic, complemented
163#17986061C2211yescharacteristic, complemented
164#17986060C2211yescharacteristic, complemented
165#17986059C2211yescharacteristic, complemented
166#17986059C2211yescharacteristic, complemented
167#17986058C2211yescharacteristic, complemented
168#17986057C2211yescharacteristic, complemented
169#17986057C2211yescharacteristic, complemented
170#17986040C2211yescharacteristic, complemented
171#17986040C2211yescharacteristic, complemented
172#17986038C2211yescharacteristic, complemented
173#17986038C2211yescharacteristic, complemented
174#17986021C2211yescharacteristic, complemented
175#17986021C2211yescharacteristic, complemented
176#17986002C2211yescharacteristic, complemented
177#17986002C2211yescharacteristic, complemented
178#17986002C2211yescharacteristic, complemented
179#17986002C2211yescharacteristic, complemented
180#17985999C2211yescharacteristic
181#17985999C2211yescharacteristic
182#17985997C2211yescharacteristic
183#17985997C2211yescharacteristic
184#17985961C2211yescharacteristic
185#17985961C2211yescharacteristic
186#17985951C2211yescharacteristic, complemented
187C4×#11765848C2211yescharacteristic, complemented
188#540×C71C2211yescharacteristic, complemented
189#520×C71C2211yescharacteristic, complemented
190#481×C71C2211yescharacteristic, complemented
191#480×C71C2211yescharacteristic, complemented
192#479×C71C2211yescharacteristic, complemented
193#478×C71C2211yescharacteristic, complemented
194#460×C71C2211yescharacteristic, complemented
195#459×C71C2211yescharacteristic, complemented
196#449×C71C2211yescharacteristic, complemented
197#449×C71C2211yescharacteristic, complemented
198#442×C71C2211yescharacteristic, complemented
199#440×C71C2211yescharacteristic, complemented
200C4×SD16×C71C2211yescharacteristic, complemented
201C4×D8×C71C2211yescharacteristic, complemented
202#433×C71C2211yescharacteristic, complemented
203C2×#11765866C2311yescharacteristic
204C2×#11765865—21no—
205C2×#11765865C2311yescharacteristic
206C2×#11765864—21no—
207C2×#11765864C2311yescharacteristic
208#41×D71—24no—
209#41×D71—24no—
210C2×Q8×D71C2311yescharacteristic
211C2×D4×D71—21no—
212C2×D4×D71—21no—
213C2×D4×D71—21no—
214C2×D4×D71—21no—
215C2×D4×D71—21no—
216C2×D4×D71C2311yescharacteristic
217C2×D4×D71C2311yescharacteristic
218C2×D4×D71C2311yescharacteristic
219C22×C4×D71—21no—
220C22×C4×D71—21no—
221C22×C4×D71—21no—
222C22×C4×D71C2311yescharacteristic
223#14556155—24no—
224#14556155—24no—
225#14556152—24no—
226#14556152—24no—
227C2×#11765854C2311yescharacteristic
228C2×#11765854C2311yescharacteristic
229C2×#11765853C2311yescharacteristic
230C2×#11765853C2311yescharacteristic
231C2×#11765852C2311yescharacteristic
232C2×#11765852C2311yescharacteristic
233C2×D568C2311yescharacteristic
234C2×D568C2311yescharacteristic
235C2×#11765850C2311yescharacteristic
236C2×#11765850C2311yescharacteristic
237C2×#11765850C2311yescharacteristic
238C2×#11765850C2311yescharacteristic
239C2×#11765848C2311yescharacteristic
240C2×#11765848C2311yescharacteristic
241C2×#11765848C2311yescharacteristic
242C2×#11765848C2311yescharacteristic
243#14556125C2311yescharacteristic
244#14556124—21no—
245#14556124—21no—
246#14556124C2311yescharacteristic
247#14556124C2311yescharacteristic
248#14556120C2311yescharacteristic
249#14556119C2311yescharacteristic
250#14556119C2311yescharacteristic
251#14556118—21no—
252#14556118—21no—
253#14556113—21no—
254#14556113—21no—
255#14556113—21no—
256#14556113—21no—
257#14556112—21no—
258#14556112—21no—
259#14556111—21no—
260#14556111—21no—
261#14556110—21no—
262#14556110—21no—
263#14556110—21no—
264#14556110—21no—
265#14556109—21no—
266#14556109—21no—
267#14556103—21no—
268#14556103—21no—
269#14556103C2311yescharacteristic
270#14556103C2311yescharacteristic
271#14556102—21no—
272#14556102—21no—
273#14556102C2311yescharacteristic
274#14556102C2311yescharacteristic
275#14556101—21no—
276#14556101—21no—
277#14556101—21no—
278#14556101—21no—
279#14556101—21no—
280#14556101—21no—
281#14556100—21no—
282#14556100—21no—
283#14556100—21no—
284#14556100—21no—
285#14556100—21no—
286#14556100—21no—
287#14556099—21no—
288#14556099—21no—
289#14556099C2311yescharacteristic
290#14556099C2311yescharacteristic
291Q8×Dic71C2311yescharacteristic
292Q8×Dic71C2311yescharacteristic
293C4×Dic142—21no—
294C4×Dic142—21no—
295C4×Dic142C2311yescharacteristic
296C4×Dic142C2311yescharacteristic
297#14556093—21no—
298#14556093—21no—
299#14556093C2311yescharacteristic
300#14556093C2311yescharacteristic
301C4×D284—21no—
302C4×D284—21no—
303C4×D284C2311yescharacteristic
304C4×D284C2311yescharacteristic
305C4×D284C2311yescharacteristic
306C4×D284C2311yescharacteristic
307D4×Dic71—21no—
308D4×Dic71—21no—
309D4×Dic71C2311yescharacteristic
310D4×Dic71C2311yescharacteristic
311D4×Dic71C2311yescharacteristic
312D4×Dic71C2311yescharacteristic
313#14556090—21no—
314#14556090—21no—
315#14556090C2311yescharacteristic
316#14556090C2311yescharacteristic
317#14556090C2311yescharacteristic
318#14556090C2311yescharacteristic
319C4×C22⋊D71—21no—
320C4×C22⋊D71—21no—
321C4×C22⋊D71—21no—
322C4×C22⋊D71—21no—
323C4×C22⋊D71—21no—
324C4×C22⋊D71—21no—
325C4×C22⋊D71—21no—
326C4×C22⋊D71—21no—
327(C22⋊D71)⋊C4—21no—
328(C22⋊D71)⋊C4—21no—
329(C22⋊D71)⋊C4—21no—
330(C22⋊D71)⋊C4—21no—
331(C22⋊D71)⋊C4—21no—
332(C22⋊D71)⋊C4—21no—
333(C22⋊D71)⋊C4—21no—
334(C22⋊D71)⋊C4—21no—
335#14556087—21no—
336#14556087C2311yescharacteristic
337#14556086—21no—
338#14556086—21no—
339#14556086—21no—
340#14556086—21no—
341#14556086—21no—
342#14556086—21no—
343#14556086—21no—
344#14556086—21no—
345#14556086D411yescharacteristic
346#14556086D411yescharacteristic
347#14556086C2311yescharacteristic
348#14556086C2311yescharacteristic
349#14556086C2311yescharacteristic
350#14556086C2311yescharacteristic
351#14556085—21no—
352#14556085—21no—
353#14556085C2311yescharacteristic
354#14556085C2311yescharacteristic
355#14556084—21no—
356#14556084—21no—
357#14556084D411yescharacteristic
358#14556084D411yescharacteristic
359C2×C4⋊Dic71—21no—
360C2×C4⋊Dic71C2311yescharacteristic
361C4⋊C4×D71—21no—
362C4⋊C4×D71—21no—
363C4⋊C4×D71—21no—
364C4⋊C4×D71—21no—
365C4⋊C4×D71D411yescharacteristic
366C4⋊C4×D71D411yescharacteristic
367C4⋊C4×D71C2311yescharacteristic
368C4⋊C4×D71C2311yescharacteristic
369C2×(C2×D71)⋊C4—21no—
370C2×(C2×D71)⋊C4—21no—
371C2×(C2×D71)⋊C4—21no—
372C22⋊C4×D71—21no—
373C22⋊C4×D71—21no—
374C22⋊C4×D71—21no—
375C22⋊C4×D71—21no—
376C22⋊C4×D71—21no—
377C22⋊C4×D71—21no—
378C22⋊C4×D71D411yescharacteristic
379C22⋊C4×D71D411yescharacteristic
380C2×C4×Dic71—21no—
381C2×C4×Dic71—21no—
382C2×C4×Dic71—21no—
383C42×D71—21no—
384C42×D71—21no—
385C42×D71C2311yescharacteristic
386C42×D71C2311yescharacteristic
387#14556062C2311yescharacteristic
388#14556062C2311yescharacteristic
389#14556061C2311yescharacteristic
390#14556061C2311yescharacteristic
391#14556061C2311yescharacteristic
392#14556061C2311yescharacteristic
393#14556060C2311yescharacteristic
394#14556060C2311yescharacteristic
395#14556059C2311yescharacteristic
396#14556059C2311yescharacteristic
397#14556059C2311yescharacteristic
398#14556059C2311yescharacteristic
399C4⋊(C71⋊C8)C2311yescharacteristic
400C4⋊(C71⋊C8)C2311yescharacteristic
401Dic71⋊C8C2311yescharacteristic
402Dic71⋊C8C2311yescharacteristic
403Dic71⋊C8C2311yescharacteristic
404Dic71⋊C8C2311yescharacteristic
405#14556053C2311yescharacteristic
406#14556053C2311yescharacteristic
407#14556052C2311yescharacteristic
408#14556052C2311yescharacteristic
409#14556051C2311yescharacteristic
410#14556051C2311yescharacteristic
411#14556050C2311yescharacteristic
412#14556050C2311yescharacteristic
413#14556050C2311yescharacteristic
414#14556050C2311yescharacteristic
415#14556050C2311yescharacteristic
416#14556050C2311yescharacteristic
417#14556049C2311yescharacteristic
418#14556049C2311yescharacteristic
419#14556049C2311yescharacteristic
420#14556049C2311yescharacteristic
421#14556049C2311yescharacteristic
422#14556049C2311yescharacteristic
423#14556048C2311yescharacteristic
424#14556048C2311yescharacteristic
425#14556048C2311yescharacteristic
426#14556048C2311yescharacteristic
427#14556048C2311yescharacteristic
428#14556048C2311yescharacteristic
429C22⋊(C71⋊C8)C2311yescharacteristic
430C22⋊(C71⋊C8)C2311yescharacteristic
431(C2×D71)⋊C8C2311yescharacteristic
432(C2×D71)⋊C8C2311yescharacteristic
433(C2×D71)⋊C8C2311yescharacteristic
434(C2×D71)⋊C8C2311yescharacteristic
435#14556039C2311yescharacteristic
436#14556038C2311yescharacteristic
437#14556038C2311yescharacteristic
438C4×C71⋊C8C2311yescharacteristic
439C8×Dic71C2311yescharacteristic
440C8×Dic71C2311yescharacteristic
441C2×#41×C71C2311yescharacteristic
442C2×SD16×C71C2311yescharacteristic
443C2×SD16×C71C2311yescharacteristic
444C2×D8×C71C2311yescharacteristic
445C2×D8×C71C2311yescharacteristic
446#127×C71C2311yescharacteristic
447#125×C71C2311yescharacteristic
448#123×C71—21no—
449#123×C71—21no—
450#121×C71—21no—
451#121×C71—21no—
452#121×C71C2311yescharacteristic
453#121×C71C2311yescharacteristic
454C4×Q8×C71C2311yescharacteristic
455C4×Q8×C71C2311yescharacteristic
456C4×D4×C71—21no—
457C4×D4×C71—21no—
458C4×D4×C71C2311yescharacteristic
459C4×D4×C71C2311yescharacteristic
460C4×D4×C71C2311yescharacteristic
461C4×D4×C71C2311yescharacteristic
462#117×C71—21no—
463#117×C71C2311yescharacteristic
464C2×C4⋊C4×C71—21no—
465C2×C4⋊C4×C71C2311yescharacteristic
466#107×C71C2311yescharacteristic
467#107×C71C2311yescharacteristic
468#106×C71C2311yescharacteristic
469#106×C71C2311yescharacteristic
470C4⋊C8×C71C2311yescharacteristic
471C4⋊C8×C71C2311yescharacteristic
472#103×C71C2311yescharacteristic
473#103×C71C2311yescharacteristic
474#102×C71C2311yescharacteristic
475#102×C71C2311yescharacteristic
476#102×C71C2311yescharacteristic
477#102×C71C2311yescharacteristic
478#102×C71C2311yescharacteristic
479#102×C71C2311yescharacteristic
480C22⋊C8×C71C2311yescharacteristic
481C22⋊C8×C71C2311yescharacteristic
482#97×C71C2311yescharacteristic
483C4×C8×C71C2311yescharacteristic
484C23×D71—21no—
485C23×D71—21no—
486C23×D71—21no—
487C23×D71C2×D411yescharacteristic
488#11765866—22no—
489#11765866#4114yes—
490#11765865—28no—
491#11765865—22no—
492#11765865—22no—
493#11765864—28no—
494#11765864—22no—
495#11765864#4114yes—
496C2×Dic142—21no—
497C2×Dic142C2411yescharacteristic
498Q8×D71—22no—
499Q8×D71—22no—
500C2×D284—21no—
501C2×D284—21no—
502C2×D284—21no—
503C2×D284—21no—
504C2×D284—21no—
505C2×D284C2411yescharacteristic
506C2×D284C2411yescharacteristic
507C2×D284C2411yescharacteristic
508C2×C22⋊D71—21no—
509C2×C22⋊D71—21no—
510C2×C22⋊D71—21no—
511C2×C22⋊D71—21no—
512C2×C22⋊D71—21no—
513C2×C22⋊D71—21no—
514C2×C22⋊D71—21no—
515C2×C22⋊D71—21no—
516C2×C22⋊D71—21no—
517C2×C22⋊D71—21no—
518C2×C22⋊D71—21no—
519C2×C22⋊D71—21no—
520C2×C22⋊D71—21no—
521D4×D71—28no—
522D4×D71—22no—
523D4×D71—22no—
524D4×D71—22no—
525D4×D71—22no—
526D4×D71—22no—
527D4×D71—22no—
528D4×D71—82no—
529D4×D71—82no—
530D4×D71—82no—
531D4×D71—82no—
532C22×Dic71—21no—
533C22×Dic71—21no—
534C22×Dic71—21no—
535C22×Dic71—21no—
536C22×Dic71—21no—
537C22×Dic71—21no—
538C22×Dic71C2×D411yescharacteristic
539C2×C4×D71—28no—
540C2×C4×D71—21no—
541C2×C4×D71—21no—
542C2×C4×D71—21no—
543C2×C4×D71—22no—
544C2×C4×D71—22no—
545C2×C4×D71—21no—
546C2×C4×D71—21no—
547C2×C4×D71—21no—
548C2×C4×D71—21no—
549C2×C4×D71—21no—
550C2×C4×D71—21no—
551C2×C4×D71—21no—
552C2×C4×D71—21no—
553C2×C4×D71—21no—
554C2×C4×D71—21no—
555C2×C4×D71—82no—
556C2×C4×D71—82no—
557C2×C4×D71C2×D411yescharacteristic
558C2×C4×D71C2×D411yescharacteristic
559C2×C4×D71C2×D411yescharacteristic
560C2×C4×D71C2×D411yescharacteristic
561C2×C4×D71C2×D411yescharacteristic
562C2×C4×D71C2×D411yescharacteristic
563C2×C4×D71C2411yescharacteristic
564C2×C4×D71C2411yescharacteristic
565#11765854—22no—
566#11765854—22no—
567#11765853—22no—
568#11765853—22no—
569#11765852—22no—
570#11765852—22no—
571D568—22no—
572D568—22no—
573#11765850—22no—
574#11765850—22no—
575#11765850—22no—
576#11765850—22no—
577#11765848—22no—
578#11765848—22no—
579#11765848—22no—
580#11765848—22no—
581C2×C71⋊C8C2411yescharacteristic
582C2×C71⋊C8C2411yescharacteristic
583C2×C71⋊C8C2411yescharacteristic
584C2×C71⋊C8C2411yescharacteristic
585C4⋊Dic71—21no—
586C4⋊Dic71—21no—
587C4⋊Dic71—21no—
588C4⋊Dic71—21no—
589C4⋊Dic71—21no—
590C4⋊Dic71C2×D411yescharacteristic
591C4⋊Dic71C2×D411yescharacteristic
592C4⋊Dic71C2411yescharacteristic
593C4⋊Dic71C2411yescharacteristic
594C4⋊Dic71C2411yescharacteristic
595C4⋊Dic71C2411yescharacteristic
596Dic71⋊C4—21no—
597Dic71⋊C4—21no—
598Dic71⋊C4—21no—
599Dic71⋊C4—21no—
600Dic71⋊C4—21no—
601Dic71⋊C4—21no—
602Dic71⋊C4—21no—
603Dic71⋊C4—21no—
604Dic71⋊C4—21no—
605Dic71⋊C4—21no—
606Dic71⋊C4C2×D411yescharacteristic
607Dic71⋊C4C2×D411yescharacteristic
608Dic71⋊C4C2×D411yescharacteristic
609Dic71⋊C4C2×D411yescharacteristic
610C22⋊Dic71—21no—
611C22⋊Dic71—21no—
612C22⋊Dic71—21no—
613C22⋊Dic71—21no—
614C22⋊Dic71—21no—
615C22⋊Dic71—21no—
616C22⋊Dic71C2×D411yescharacteristic
617C22⋊Dic71C2×D411yescharacteristic
618(C2×D71)⋊C4—21no—
619(C2×D71)⋊C4—21no—
620(C2×D71)⋊C4—21no—
621(C2×D71)⋊C4—21no—
622(C2×D71)⋊C4—21no—
623(C2×D71)⋊C4—21no—
624(C2×D71)⋊C4—21no—
625(C2×D71)⋊C4—21no—
626(C2×D71)⋊C4—21no—
627(C2×D71)⋊C4—21no—
628(C2×D71)⋊C4—21no—
629(C2×D71)⋊C4—21no—
630(C2×D71)⋊C4—21no—
631(C2×D71)⋊C4—21no—
632(C2×D71)⋊C4—21no—
633(C2×D71)⋊C4—21no—
634(C2×D71)⋊C4C2×D411yescharacteristic
635(C2×D71)⋊C4C2×D411yescharacteristic
636(C2×D71)⋊C4C2×D411yescharacteristic
637(C2×D71)⋊C4C2×D411yescharacteristic
638C4×Dic71—21no—
639C4×Dic71—21no—
640C4×Dic71—21no—
641C4×Dic71—21no—
642C4×Dic71—21no—
643C4×Dic71—21no—
644C4×Dic71—21no—
645C4×Dic71—21no—
646C4×Dic71—21no—
647C4×Dic71—21no—
648C4×Dic71C2×D411yescharacteristic
649C4×Dic71C2×D411yescharacteristic
650C4×Dic71C2×D411yescharacteristic
651C4×Dic71C2×D411yescharacteristic
652C4×Dic71C2411yescharacteristic
653C4×Dic71C2411yescharacteristic
654#41×C71—22no—
655#41×C71—22no—
656C2×Q8×C71C2411yescharacteristic
657C2×D4×C71—21no—
658C2×D4×C71—21no—
659C2×D4×C71—21no—
660C2×D4×C71—21no—
661C2×D4×C71—21no—
662C2×D4×C71C2411yescharacteristic
663C2×D4×C71C2411yescharacteristic
664C2×D4×C71C2411yescharacteristic
665C22×C4×C71—21no—
666C22×C4×C71—21no—
667C22×C4×C71—21no—
668C22×C4×C71—21no—
669C22×C4×C71—21no—
670C22×C4×C71—21no—
671C22×C4×C71C2411yescharacteristic
672SD16×C71—22no—
673SD16×C71—22no—
674D8×C71—22no—
675D8×C71—22no—
676C2×C8×C71C2411yescharacteristic
677C2×C8×C71C2411yescharacteristic
678C2×C8×C71C2411yescharacteristic
679C2×C8×C71C2411yescharacteristic
680C4⋊C4×C71—21no—
681C4⋊C4×C71—21no—
682C4⋊C4×C71—21no—
683C4⋊C4×C71—21no—
684C4⋊C4×C71—21no—
685C4⋊C4×C71C2×D411yescharacteristic
686C4⋊C4×C71C2×D411yescharacteristic
687C4⋊C4×C71C2411yescharacteristic
688C4⋊C4×C71C2411yescharacteristic
689C4⋊C4×C71C2411yescharacteristic
690C4⋊C4×C71C2411yescharacteristic
691C22⋊C4×C71—21no—
692C22⋊C4×C71—21no—
693C22⋊C4×C71—21no—
694C22⋊C4×C71—21no—
695C22⋊C4×C71—21no—
696C22⋊C4×C71—21no—
697C22⋊C4×C71C2×D411yescharacteristic
698C22⋊C4×C71C2×D411yescharacteristic
699C42×C71—21no—
700C42×C71—21no—
701C42×C71C2411yescharacteristic
702C42×C71C2411yescharacteristic
703C23×C71—21no—
704C23×C71—21no—
705C23×C71—21no—
706C23×C71C22×D411yescharacteristic
707C22×D71—21no—
708C22×D71—24no—
709C22×D71—22no—
710C22×D71—21no—
711C22×D71—21no—
712C22×D71—41no—
713C22×D71—41no—
714C22×D71—42no—
715C22×D71—42no—
716C22×D71—42no—
717C22×D71—42no—
718C22×D71—42no—
719C22×D71—42no—
720C22×D71—81no—
721C22×D71—81no—
722C22×D71C22×D411yescharacteristic
723C22×D71C22×D411yescharacteristic
724Q8×C71—21no—
725Q8×C71C2×#4112yes—
726D4×C71—24no—
727D4×C71—21no—
728D4×C71—21no—
729D4×C71—21no—
730D4×C71—21no—
731D4×C71—21no—
732D4×C71—81no—
733D4×C71—81no—
734D4×C71—81no—
735D4×C71—81no—
736D4×C71C2×#4112yes—
737C2×C4×C71—24no—
738C2×C4×C71—21no—
739C2×C4×C71—21no—
740C2×C4×C71—21no—
741C2×C4×C71—21no—
742C2×C4×C71—21no—
743C2×C4×C71—21no—
744C2×C4×C71—21no—
745C2×C4×C71—81no—
746C2×C4×C71—81no—
747C2×C4×C71—81no—
748C2×C4×C71—81no—
749C2×C4×C71—81no—
750C2×C4×C71C22×D411yescharacteristic
751C2×C4×C71C22×D411yescharacteristic
752C2×C4×C71C22×D411yescharacteristic
753C2×C4×C71C22×D411yescharacteristic
754C2×C4×C71C22×D411yescharacteristic
755C2×C4×C71C2511yescharacteristic
756C22⋊D71—24no—
757C22⋊D71—24no—
758C22⋊D71—24no—
759C22⋊D71—42no—
760C22⋊D71—42no—
761C22⋊D71—81no—
762C22⋊D71—81no—
763C22⋊D71—81no—
764C22⋊D71—81no—
765C22⋊D71—81no—
766C22⋊D71—81no—
767C22⋊D71—81no—
768C22⋊D71—81no—
769C2×Dic71—21no—
770C2×Dic71—24no—
771C2×Dic71—22no—
772C2×Dic71—21no—
773C2×Dic71—21no—
774C2×Dic71—21no—
775C2×Dic71—21no—
776C2×Dic71—81no—
777C2×Dic71—81no—
778C2×Dic71—81no—
779C2×Dic71—81no—
780C2×Dic71—81no—
781C2×Dic71C22×D411yescharacteristic
782C2×Dic71C22×D411yescharacteristic
783C2×Dic71C22×D411yescharacteristic
784C2×Dic71C22×D411yescharacteristic
785C2×Dic71C22×D411yescharacteristic
786C2×Dic71C22×D411yescharacteristic
787D284—24no—
788D284—21no—
789D284—21no—
790D284—21no—
791D284—21no—
792D284—21no—
793D284—81no—
794D284—81no—
795D284—81no—
796D284—81no—
797D284C2×#4112yes—
798C4×D71—24no—
799C4×D71—24no—
800C4×D71—22no—
801C4×D71—21no—
802C4×D71—21no—
803C4×D71—22no—
804C4×D71—24no—
805C4×D71—41no—
806C4×D71—41no—
807C4×D71—41no—
808C4×D71—41no—
809C4×D71—42no—
810C4×D71—42no—
811C4×D71—81no—
812C4×D71—81no—
813C4×D71—81no—
814C4×D71—81no—
815C4×D71—81no—
816C4×D71—81no—
817C4×D71—81no—
818C4×D71—81no—
819C4×D71C2×#4112yes—
820C4×D71C2×#4112yes—
821Dic142—24no—
822Dic142—21no—
823Dic142C2×#4112yes—
824C8×C71—21no—
825C8×C71—21no—
826C8×C71—21no—
827C8×C71—21no—
828C71⋊C8—21no—
829C71⋊C8—21no—
830C71⋊C8—21no—
831C71⋊C8—21no—
832C22×C71—21no—
833C22×C71—21no—
834C22×C71—21no—
835C22×C71—22no—
836C22×C71—41no—
837C22×C71—41no—
838C22×C71—41no—
839C22×C71—41no—
840C22×C71—41no—
841C22×C71—41no—
842C22×C71—41no—
843C22×C71—41no—
844C22×C71C23×D411yescharacteristic
845C2×D71—21no—
846C2×D71—21no—
847C2×D71—21no—
848C2×D71—21no—
849C2×D71—21no—
850C2×D71—22no—
851C2×D71—41no—
852C2×D71—41no—
853C2×D71—41no—
854C2×D71—41no—
855C2×D71—41no—
856C2×D71—41no—
857C2×D71—41no—
858C2×D71—41no—
859C2×D71—82no—
860C2×D71—84no—
861C2×D71—84no—
862C2×D71—84no—
863C2×D71#52512yes—
864C4×C71—21no—
865C4×C71—21no—
866C4×C71—21no—
867C4×C71—21no—
868C4×C71—22no—
869C4×C71—21no—
870C4×C71—41no—
871C4×C71—41no—
872C4×C71—41no—
873C4×C71—41no—
874C4×C71C22×#4111yescharacteristic
875C4×C71C22×#4111yescharacteristic
876Dic71—21no—
877Dic71—21no—
878Dic71—21no—
879Dic71—21no—
880Dic71—21no—
881Dic71—22no—
882Dic71—41no—
883Dic71—41no—
884Dic71—41no—
885Dic71—41no—
886Dic71#52512yes—
887#60568—711nomaximal, Sylow
888C2×C71—41no—
889C2×C71—42no—
890C2×C71—81no—
891C2×C71—81no—
892C2×C71C2×#52511yescharacteristic
893C2×C71#358511yescharacteristic
894C2×C71#358511yescharacteristic
895D71—22no—
896D71—41no—
897D71—42no—
898D71—81no—
899D71—81no—
900C2×#540—711no—
901#3428—711no—
902#3126—711no—
903#3126—711no—
904#3126—711no—
905#3126—711no—
906#3122—711no—
907#3122—711no—
908#3122—711no—
909#3122—711no—
910#3119—711no—
911#3119—711no—
912#3119—711no—
913#3119—711no—
914#3119—711no—
915#3119—711no—
916#3119—711no—
917#3119D7111yescharacteristic, complemented
918#3094—711no—
919#3094—711no—
920#3080—711no—
921#3080—711no—
922#3038—711no—
923#3038—711no—
924#3006—711no—
925#3006—711no—
926C4×AGL(1,ℤ/8)—711no—
927C4×AGL(1,ℤ/8)—711no—
928C4×AGL(1,ℤ/8)—711no—
929C4×AGL(1,ℤ/8)—711no—
930#2921—711no—
931C71#6056811yescharacteristic, complemented, Sylow
932C22×#41—711no—
933C2×AGL(1,ℤ/8)—711no—
934C2×AGL(1,ℤ/8)—711no—
935C2×AGL(1,ℤ/8)—711no—
936C2×AGL(1,ℤ/8)—711no—
937#540—711no—
938#540—711no—
939#540—711no—
940#540—711no—
941#540—711no—
942#540—711no—
943#540—711no—
944#540—1421no—
945#540—1421no—
946#540—1421no—
947#540—1421no—
948#540C2×D7111yescharacteristic, complemented
949C2×#127—711no—
950C2×#125—711no—
951C2×#123—1421no—
952C2×#123—1421no—
953C2×#121—711no—
954C2×#121—711no—
955C2×#121—1421no—
956C2×#121—1421no—
957#520—711no—
958#520—711no—
959#520—711no—
960#520—1421no—
961#520—1421no—
962#520C2×D7111yescharacteristic, complemented
963#519—711no—
964#519—711no—
965#518—711no—
966#518—711no—
967#518—1421no—
968#518—1421no—
969C4×#41—711no—
970C4×#41—711no—
971C4×#41—711no—
972C4×#41—711no—
973C4×#41—1421no—
974C4×#41—1421no—
975C2×C4×D4—711no—
976C2×C4×D4—711no—
977C2×#117—711no—
978C2×#117—711no—
979C2×#117—1421no—
980C2×#117—1421no—
981#482—711no—
982#482—711no—
983#482—711no—
984#482—711no—
985#482—711no—
986#482—711no—
987#482—711no—
988#482—711no—
989#481—711no—
990#481—711no—
991#481—711no—
992#481C2×D7111yescharacteristic, complemented
993#480—711no—
994#480—711no—
995#480—711no—
996#480C2×D7111yescharacteristic, complemented
997#479—711no—
998#479—711no—
999#479—711no—
1000#479—711no—
1001#479—711no—
1002#479—711no—
1003#479—711no—
1004#479C2×D7111yescharacteristic, complemented
1005#478—711no—
1006#478—711no—
1007#478—711no—
1008#478—711no—
1009#478—711no—
1010#478—711no—
1011#478—711no—
1012#478C2×D7111yescharacteristic, complemented
1013#460—711no—
1014#460—711no—
1015#460—711no—
1016#460—711no—
1017#460—711no—
1018#460—711no—
1019#460—711no—
1020#460C2×D7111yescharacteristic, complemented
1021#459—711no—
1022#459—711no—
1023#459—711no—
1024#459—711no—
1025#459—711no—
1026#459—711no—
1027#459—711no—
1028#459C2×D7111yescharacteristic, complemented
1029#449—711no—
1030#449—711no—
1031#449—711no—
1032#449—711no—
1033#449—711no—
1034#449—711no—
1035#449C2×D7111yescharacteristic, complemented
1036#449C2×D7111yescharacteristic, complemented
1037#448—711no—
1038#448—711no—
1039#448—711no—
1040#448—711no—
1041#447—711no—
1042#447—711no—
1043#447—711no—
1044#447—711no—
1045#442—711no—
1046#442—711no—
1047#442—711no—
1048#442—711no—
1049#442—711no—
1050#442—711no—
1051#442—711no—
1052#442C2×D7111yescharacteristic, complemented
1053#440—711no—
1054#440—711no—
1055#440—711no—
1056#440—711no—
1057#440—711no—
1058#440—711no—
1059#440—711no—
1060#440C2×D7111yescharacteristic, complemented
1061C4×SD16—711no—
1062C4×SD16—711no—
1063C4×SD16—711no—
1064C4×SD16—711no—
1065C4×SD16—711no—
1066C4×SD16—711no—
1067C4×SD16—711no—
1068C4×SD16C2×D7111yescharacteristic, complemented
1069C4×D8—711no—
1070C4×D8—711no—
1071C4×D8—711no—
1072C4×D8—711no—
1073C4×D8—711no—
1074C4×D8—711no—
1075C4×D8—711no—
1076C4×D8C2×D7111yescharacteristic, complemented
1077#433—711no—
1078#433—711no—
1079#433—711no—
1080#433—711no—
1081#433—711no—
1082#433—711no—
1083#433—711no—
1084#433C2×D7111yescharacteristic, complemented
1085#428—711no—
1086#428—711no—
1087#428—711no—
1088#428—711no—
1089#423—711no—
1090#423—711no—
1091#418—711no—
1092#418—711no—
1093#418—711no—
1094#418—711no—
1095#417—711no—
1096#417—711no—
1097#417—711no—
1098#417—711no—
1099#407—711no—
1100#407—711no—
1101C4×M16—711no—
1102C4×M16—711no—
1103C2×#41—711no—
1104C2×#41—711no—
1105C2×#41—711no—
1106C2×#41—1421no—
1107C2×#41—1421no—
1108C2×#41—1424no—
1109C2×#41—1424no—
1110C2×#41C22×D7111yescharacteristic
1111C22×Q8—711no—
1112C22×D4—711no—
1113C22×D4—711no—
1114C22×D4—711no—
1115C22×D4—1421no—
1116C22×D4—1421no—
1117C22×D4—1421no—
1118C22×D4—1421no—
1119C22×D4—1421no—
1120C23×C4—711no—
1121C23×C4—1421no—
1122C23×C4—1421no—
1123C23×C4—1421no—
1124AGL(1,ℤ/8)—1424no—
1125AGL(1,ℤ/8)—1424no—
1126AGL(1,ℤ/8)—1424no—
1127AGL(1,ℤ/8)—1424no—
1128C2×SD16—711no—
1129C2×SD16—711no—
1130C2×SD16—711no—
1131C2×SD16—711no—
1132C2×SD16—711no—
1133C2×SD16—711no—
1134C2×SD16C22×D7111yescharacteristic
1135C2×SD16C22×D7111yescharacteristic
1136C2×D8—711no—
1137C2×D8—711no—
1138C2×D8—711no—
1139C2×D8—711no—
1140C2×D8—711no—
1141C2×D8—711no—
1142C2×D8C22×D7111yescharacteristic
1143C2×D8C22×D7111yescharacteristic
1144C2×M16—711no—
1145C2×M16—711no—
1146C2×M16—711no—
1147C2×M16—711no—
1148#127—711no—
1149#127—711no—
1150#127—711no—
1151#127—1421no—
1152#127—1421no—
1153#127C22×D7111yescharacteristic
1154#125—711no—
1155#125—711no—
1156#125—711no—
1157#125—1421no—
1158#125—1421no—
1159#125C22×D7111yescharacteristic
1160#123—21no—
1161#123—21no—
1162#123—1421no—
1163#123—1421no—
1164#123—1421no—
1165#123—1421no—
1166#123—1421no—
1167#123—1421no—
1168#123—1421no—
1169#123—1421no—
1170#123—1421no—
1171#123—1421no—
1172#123—1421no—
1173#123—1421no—
1174#123—1421no—
1175#123—1421no—
1176#121—21no—
1177#121—21no—
1178#121—711no—
1179#121—711no—
1180#121—711no—
1181#121—711no—
1182#121—711no—
1183#121—711no—
1184#121—1421no—
1185#121—1421no—
1186#121—1421no—
1187#121—1421no—
1188#121—1421no—
1189#121—1421no—
1190#121—1421no—
1191#121—1421no—
1192#121—1421no—
1193#121—1421no—
1194#121—1421no—
1195#121—1421no—
1196#121—1421no—
1197#121—1421no—
1198#121—1421no—
1199#121—1421no—
1200#121—1421no—
1201#121—1421no—
1202#121C22×D7111yescharacteristic
1203#121C22×D7111yescharacteristic
1204C4×Q8—711no—
1205C4×Q8—711no—
1206C4×Q8—711no—
1207C4×Q8—711no—
1208C4×Q8—711no—
1209C4×Q8—711no—
1210C4×Q8—1421no—
1211C4×Q8—1421no—
1212C4×Q8—1421no—
1213C4×Q8—1421no—
1214C4×Q8C22×D7111yescharacteristic
1215C4×Q8C22×D7111yescharacteristic
1216C4×D4—21no—
1217C4×D4—21no—
1218C4×D4—711no—
1219C4×D4—711no—
1220C4×D4—711no—
1221C4×D4—711no—
1222C4×D4—711no—
1223C4×D4—711no—
1224C4×D4—711no—
1225C4×D4—711no—
1226C4×D4—711no—
1227C4×D4—711no—
1228C4×D4—711no—
1229C4×D4—711no—
1230C4×D4—1421no—
1231C4×D4—1421no—
1232C4×D4—1421no—
1233C4×D4—1421no—
1234C4×D4—1421no—
1235C4×D4—1421no—
1236C4×D4—1421no—
1237C4×D4—1421no—
1238C4×D4—1421no—
1239C4×D4—1421no—
1240C4×D4—1421no—
1241C4×D4—1421no—
1242C4×D4—1421no—
1243C4×D4—1421no—
1244C4×D4—1421no—
1245C4×D4—1421no—
1246C4×D4—1421no—
1247C4×D4—1421no—
1248C4×D4—1421no—
1249C4×D4—1421no—
1250C4×D4—1421no—
1251C4×D4—1421no—
1252C4×D4C22×D7111yescharacteristic
1253C4×D4C22×D7111yescharacteristic
1254C4×D4C22×D7111yescharacteristic
1255C4×D4C22×D7111yescharacteristic
1256#117—21no—
1257#117—711no—
1258#117—711no—
1259#117—711no—
1260#117—711no—
1261#117—711no—
1262#117—711no—
1263#117—711no—
1264#117—711no—
1265#117—711no—
1266#117—711no—
1267#117—711no—
1268#117—1421no—
1269#117—1421no—
1270#117—1421no—
1271#117—1421no—
1272#117—1421no—
1273#117—1421no—
1274#117—1421no—
1275#117—1421no—
1276#117—1421no—
1277#117—1421no—
1278#117—1421no—
1279#117—1421no—
1280#117—1421no—
1281#117C22×D7111yescharacteristic
1282C2×C4⋊C4—21no—
1283C2×C4⋊C4—711no—
1284C2×C4⋊C4—711no—
1285C2×C4⋊C4—711no—
1286C2×C4⋊C4—711no—
1287C2×C4⋊C4—711no—
1288C2×C4⋊C4—1421no—
1289C2×C4⋊C4—1421no—
1290C2×C4⋊C4—1421no—
1291C2×C4⋊C4—1421no—
1292C2×C4⋊C4—1421no—
1293C2×C4⋊C4C22×D7111yescharacteristic
1294C2×C22⋊C4—711no—
1295C2×C22⋊C4—711no—
1296C2×C22⋊C4—1421no—
1297C2×C22⋊C4—1421no—
1298C2×C22⋊C4—1421no—
1299C2×C22⋊C4—1421no—
1300C2×C22⋊C4—1421no—
1301C2×C22⋊C4—1421no—
1302C2×C22⋊C4—1421no—
1303C2×C22⋊C4—1421no—
1304C2×C22⋊C4—1421no—
1305C2×C42—711no—
1306C2×C42—711no—
1307C2×C42—1421no—
1308C2×C42—1421no—
1309C2×C42—1421no—
1310C2×C42—1421no—
1311C2×C42—1421no—
1312#107—711no—
1313#107—711no—
1314#107—711no—
1315#107—711no—
1316#107—711no—
1317#107—711no—
1318#107C22×D7111yescharacteristic
1319#107C22×D7111yescharacteristic
1320#106—711no—
1321#106—711no—
1322#106—711no—
1323#106—711no—
1324#106—711no—
1325#106—711no—
1326#106C22×D7111yescharacteristic
1327#106C22×D7111yescharacteristic
1328C4⋊C8—711no—
1329C4⋊C8—711no—
1330C4⋊C8—711no—
1331C4⋊C8—711no—
1332C4⋊C8—711no—
1333C4⋊C8—711no—
1334C4⋊C8C22×D7111yescharacteristic
1335C4⋊C8C22×D7111yescharacteristic
1336#103—711no—
1337#103—711no—
1338#103—711no—
1339#103—711no—
1340#103—711no—
1341#103—711no—
1342#103C22×D7111yescharacteristic
1343#103C22×D7111yescharacteristic
1344#102—711no—
1345#102—711no—
1346#102—711no—
1347#102—711no—
1348#102—711no—
1349#102—711no—
1350#102—711no—
1351#102—711no—
1352#102—711no—
1353#102—711no—
1354#102—711no—
1355#102—711no—
1356#102—711no—
1357#102—711no—
1358#102—711no—
1359#102—711no—
1360#102—711no—
1361#102—711no—
1362#102C22×D7111yescharacteristic
1363#102C22×D7111yescharacteristic
1364#102C22×D7111yescharacteristic
1365#102C22×D7111yescharacteristic
1366#102C22×D7111yescharacteristic
1367#102C22×D7111yescharacteristic
1368C22⋊C8—711no—
1369C22⋊C8—711no—
1370C22⋊C8—711no—
1371C22⋊C8—711no—
1372C22⋊C8—711no—
1373C22⋊C8—711no—
1374C22⋊C8C22×D7111yescharacteristic
1375C22⋊C8C22×D7111yescharacteristic
1376#97—711no—
1377#97—711no—
1378#97—711no—
1379#97C22×D7111yescharacteristic
1380C4×C8—711no—
1381C4×C8—711no—
1382C4×C8—711no—
1383C4×C8C22×D7111yescharacteristic
1384C24—711no—
1385C24—1421no—
1386C24—1421no—
1387C24—1421no—
1388#41—22no—
1389#41—22no—
1390#41—714no—
1391#41—714no—
1392#41—1422no—
1393#41—1422no—
1394#41—1428no—
1395#41—1422no—
1396#41—1422no—
1397#41—1428no—
1398C2×Q8—711no—
1399C2×Q8—1421no—
1400C2×Q8—1422no—
1401C2×Q8—1422no—
1402C2×Q8C23×D7111yescharacteristic
1403C2×D4—21no—
1404C2×D4—21no—
1405C2×D4—21no—
1406C2×D4—21no—
1407C2×D4—21no—
1408C2×D4—5682no—
1409C2×D4—5682no—
1410C2×D4—5682no—
1411C2×D4—5682no—
1412C2×D4—711no—
1413C2×D4—711no—
1414C2×D4—711no—
1415C2×D4—1421no—
1416C2×D4—1421no—
1417C2×D4—1421no—
1418C2×D4—1422no—
1419C2×D4—1422no—
1420C2×D4—1422no—
1421C2×D4—1422no—
1422C2×D4—1421no—
1423C2×D4—1421no—
1424C2×D4—1421no—
1425C2×D4—1421no—
1426C2×D4—1421no—
1427C2×D4—1421no—
1428C2×D4—1421no—
1429C2×D4—1422no—
1430C2×D4—1428no—
1431C2×D4—1421no—
1432C2×D4—1421no—
1433C2×D4—1421no—
1434C2×D4—1421no—
1435C2×D4—1421no—
1436C2×D4—1421no—
1437C2×D4—1422no—
1438C2×D4—1421no—
1439C2×D4—1421no—
1440C2×D4C23×D7111yescharacteristic
1441C2×D4C23×D7111yescharacteristic
1442C2×D4C23×D7111yescharacteristic
1443C22×C4—21no—
1444C22×C4—21no—
1445C22×C4—21no—
1446C22×C4—21no—
1447C22×C4—21no—
1448C22×C4—21no—
1449C22×C4—5682no—
1450C22×C4—5682no—
1451C22×C4—711no—
1452C22×C4—711no—
1453C22×C4—711no—
1454C22×C4—711no—
1455C22×C4—711no—
1456C22×C4—711no—
1457C22×C4—711no—
1458C22×C4—711no—
1459C22×C4—711no—
1460C22×C4—1421no—
1461C22×C4—1421no—
1462C22×C4—1421no—
1463C22×C4—1421no—
1464C22×C4—1421no—
1465C22×C4—1421no—
1466C22×C4—1421no—
1467C22×C4—1422no—
1468C22×C4—1422no—
1469C22×C4—1421no—
1470C22×C4—1428no—
1471C22×C4—1421no—
1472C22×C4—1421no—
1473C22×C4—1421no—
1474C22×C4—1421no—
1475C22×C4—1421no—
1476C22×C4—1421no—
1477C22×C4—1421no—
1478C22×C4—1421no—
1479C22×C4—1421no—
1480C22×C4—1421no—
1481C22×C4—1421no—
1482C22×C4C23×D7111yescharacteristic
1483SD16—22no—
1484SD16—22no—
1485SD16—1422no—
1486SD16—1422no—
1487SD16—1422no—
1488SD16—1422no—
1489SD16—1422no—
1490SD16—1422no—
1491D8—22no—
1492D8—22no—
1493D8—1422no—
1494D8—1422no—
1495D8—1422no—
1496D8—1422no—
1497D8—1422no—
1498D8—1422no—
1499M16—1422no—
1500M16—1422no—
1501M16—1422no—
1502M16—1422no—
1503C2×C8—711no—
1504C2×C8—711no—
1505C2×C8—711no—
1506C2×C8—711no—
1507C2×C8C23×D7111yescharacteristic
1508C2×C8C23×D7111yescharacteristic
1509C2×C8C23×D7111yescharacteristic
1510C2×C8C23×D7111yescharacteristic
1511C4⋊C4—21no—
1512C4⋊C4—21no—
1513C4⋊C4—21no—
1514C4⋊C4—21no—
1515C4⋊C4—21no—
1516C4⋊C4—711no—
1517C4⋊C4—711no—
1518C4⋊C4—711no—
1519C4⋊C4—711no—
1520C4⋊C4—711no—
1521C4⋊C4—711no—
1522C4⋊C4—711no—
1523C4⋊C4—711no—
1524C4⋊C4—711no—
1525C4⋊C4—711no—
1526C4⋊C4—1421no—
1527C4⋊C4—1421no—
1528C4⋊C4—1421no—
1529C4⋊C4—1421no—
1530C4⋊C4—1421no—
1531C4⋊C4—1421no—
1532C4⋊C4—1421no—
1533C4⋊C4—1421no—
1534C4⋊C4—1421no—
1535C4⋊C4—1421no—
1536C4⋊C4—1421no—
1537C4⋊C4—1421no—
1538C4⋊C4—1421no—
1539C4⋊C4—1421no—
1540C4⋊C4—1421no—
1541C4⋊C4D4×D7111yescharacteristic
1542C4⋊C4D4×D7111yescharacteristic
1543C4⋊C4C23×D7111yescharacteristic
1544C4⋊C4C23×D7111yescharacteristic
1545C4⋊C4C23×D7111yescharacteristic
1546C4⋊C4C23×D7111yescharacteristic
1547C22⋊C4—21no—
1548C22⋊C4—21no—
1549C22⋊C4—21no—
1550C22⋊C4—21no—
1551C22⋊C4—21no—
1552C22⋊C4—21no—
1553C22⋊C4—711no—
1554C22⋊C4—711no—
1555C22⋊C4—711no—
1556C22⋊C4—711no—
1557C22⋊C4—711no—
1558C22⋊C4—711no—
1559C22⋊C4—1421no—
1560C22⋊C4—1421no—
1561C22⋊C4—1421no—
1562C22⋊C4—1421no—
1563C22⋊C4—1421no—
1564C22⋊C4—1421no—
1565C22⋊C4—1421no—
1566C22⋊C4—1421no—
1567C22⋊C4—1421no—
1568C22⋊C4—1421no—
1569C22⋊C4—1421no—
1570C22⋊C4—1421no—
1571C22⋊C4—1421no—
1572C22⋊C4—1421no—
1573C22⋊C4—1421no—
1574C22⋊C4—1421no—
1575C22⋊C4—1421no—
1576C22⋊C4—1421no—
1577C22⋊C4—1421no—
1578C22⋊C4—1421no—
1579C22⋊C4—1421no—
1580C22⋊C4—1421no—
1581C22⋊C4D4×D7111yescharacteristic
1582C22⋊C4D4×D7111yescharacteristic
1583C42—21no—
1584C42—21no—
1585C42—711no—
1586C42—711no—
1587C42—711no—
1588C42—711no—
1589C42—711no—
1590C42—711no—
1591C42—1421no—
1592C42—1421no—
1593C42—1421no—
1594C42—1421no—
1595C42—1421no—
1596C42—1421no—
1597C42—1421no—
1598C42—1421no—
1599C42—1421no—
1600C42—1421no—
1601C42C23×D7111yescharacteristic
1602C42C23×D7111yescharacteristic
1603C23—21no—
1604C23—21no—
1605C23—21no—
1606C23—2841no—
1607C23—2841no—
1608C23—2842no—
1609C23—2842no—
1610C23—2842no—
1611C23—2842no—
1612C23—2842no—
1613C23—2842no—
1614C23—5681no—
1615C23—5681no—
1616C23—711no—
1617C23—711no—
1618C23—1422no—
1619C23—1424no—
1620C23—1421no—
1621C23—1421no—
1622C23—1421no—
1623C23C2×D4×D7111yescharacteristic
1624Q8—21no—
1625Q8—712no—
1626Q8—1424no—
1627Q8—1421no—
1628Q8#41×D7112yes—
1629D4—24no—
1630D4—21no—
1631D4—21no—
1632D4—21no—
1633D4—21no—
1634D4—21no—
1635D4—81no—
1636D4—81no—
1637D4—81no—
1638D4—81no—
1639D4—2842no—
1640D4—2842no—
1641D4—5681no—
1642D4—5681no—
1643D4—5681no—
1644D4—5681no—
1645D4—5681no—
1646D4—5681no—
1647D4—5681no—
1648D4—5681no—
1649D4—5681no—
1650D4—5681no—
1651D4—5681no—
1652D4—5681no—
1653D4—712no—
1654D4—1424no—
1655D4—1424no—
1656D4—1424no—
1657D4—1424no—
1658D4—1421no—
1659D4—1421no—
1660D4—1421no—
1661D4—1421no—
1662D4—1421no—
1663D4#41×D7112yes—
1664C2×C4—24no—
1665C2×C4—21no—
1666C2×C4—21no—
1667C2×C4—21no—
1668C2×C4—21no—
1669C2×C4—21no—
1670C2×C4—21no—
1671C2×C4—21no—
1672C2×C4—81no—
1673C2×C4—81no—
1674C2×C4—81no—
1675C2×C4—81no—
1676C2×C4—81no—
1677C2×C4—2841no—
1678C2×C4—2841no—
1679C2×C4—2841no—
1680C2×C4—2841no—
1681C2×C4—2842no—
1682C2×C4—2842no—
1683C2×C4—5681no—
1684C2×C4—5681no—
1685C2×C4—5681no—
1686C2×C4—5681no—
1687C2×C4—5681no—
1688C2×C4—5681no—
1689C2×C4—5681no—
1690C2×C4—5681no—
1691C2×C4—5681no—
1692C2×C4—5681no—
1693C2×C4—5681no—
1694C2×C4—5681no—
1695C2×C4—5681no—
1696C2×C4—711no—
1697C2×C4—712no—
1698C2×C4—712no—
1699C2×C4—711no—
1700C2×C4—711no—
1701C2×C4—711no—
1702C2×C4—711no—
1703C2×C4—711no—
1704C2×C4—1422no—
1705C2×C4—1424no—
1706C2×C4—1422no—
1707C2×C4—1424no—
1708C2×C4—1424no—
1709C2×C4—1421no—
1710C2×C4—1421no—
1711C2×C4—1421no—
1712C2×C4—1421no—
1713C2×C4—1422no—
1714C2×C4—1424no—
1715C2×C4—1421no—
1716C2×C4—1421no—
1717C2×C4—1421no—
1718C2×C4C2×D4×D7111yescharacteristic
1719C2×C4C2×D4×D7111yescharacteristic
1720C2×C4C2×D4×D7111yescharacteristic
1721C2×C4C2×D4×D7111yescharacteristic
1722C2×C4C2×D4×D7111yescharacteristic
1723C2×C4C24×D7111yescharacteristic
1724C8—21no—
1725C8—21no—
1726C8—21no—
1727C8—21no—
1728C8—1421no—
1729C8—1421no—
1730C8—1421no—
1731C8—1421no—
1732C22—21no—
1733C22—22no—
1734C22—21no—
1735C22—21no—
1736C22—41no—
1737C22—41no—
1738C22—41no—
1739C22—41no—
1740C22—41no—
1741C22—41no—
1742C22—41no—
1743C22—41no—
1744C22—2841no—
1745C22—2841no—
1746C22—2841no—
1747C22—2841no—
1748C22—2841no—
1749C22—2841no—
1750C22—2841no—
1751C22—2841no—
1752C22—5684no—
1753C22—5682no—
1754C22—5684no—
1755C22—5684no—
1756C22—712no—
1757C22—1421no—
1758C22—1422no—
1759C22—1421no—
1760C22—1421no—
1761C22—1421no—
1762C22—1421no—
1763C22C22×D4×D7111yescharacteristic
1764C4—21no—
1765C4—22no—
1766C4—21no—
1767C4—21no—
1768C4—21no—
1769C4—21no—
1770C4—41no—
1771C4—41no—
1772C4—41no—
1773C4—41no—
1774C4—2841no—
1775C4—2841no—
1776C4—2841no—
1777C4—2841no—
1778C4—712no—
1779C4—1421no—
1780C4—1422no—
1781C4—1421no—
1782C4—1421no—
1783C4—1421no—
1784C4—1421no—
1785C4C2×#41×D7111yescharacteristic
1786C4C2×#41×D7111yescharacteristic
1787C2—41no—
1788C2—42no—
1789C2—81no—
1790C2—81no—
1791C2—2842no—
1792C2—2841no—
1793C2—5681no—
1794C2—5681no—
1795C2—1422no—
1796C2#525×D7111yescharacteristic
1797C2#2260311511yescharacteristic
1798C2#2260311811yescharacteristic
subgroupG/H
centerC22C22×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC71×#3119C2
socleC22×C71C23×D4
hypercenter#3119D71
hypocenterC71#60568
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ #117 ◁ #3119

Complements

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

NH ≅ G/Ntype
1. #540×D71C2semidirect
2. #22601540C2semidirect
3. #22598633C2semidirect
4. #22598630C2semidirect
5. #22598629C2semidirect
6. #22598628C2semidirect
7. #22598585C2semidirect
8. #22598582C2semidirect
9. #22598581C2semidirect
10. #22598580C2semidirect
11. #22598542C2semidirect
12. #22598541C2semidirect
13. #22598540C2semidirect
14. #22598539C2semidirect
15. #22598534C2semidirect
16. #22598533C2semidirect
17. #22598532C2semidirect
18. #22598277C2semidirect
19. #22598275C2semidirect
20. #22598159C2semidirect
21. #22598157C2semidirect
22. #22597817C2semidirect
23. #22597815C2semidirect
24. #22597589C2semidirect
25. #22597589C2semidirect
26. #22597151C2semidirect
27. C4×#14556155C2semidirect
28. #22597145C2semidirect
29. C4×#14556152C2semidirect
30. #22596974C2semidirect
31. C71×#3119C2semidirect
38. #17986604C22semidirect
40. #17986602C22semidirect
41. #17986602C22semidirect
48. #127×D71C22semidirect
49. #125×D71C22semidirect
56. #17986482C22semidirect
58. #17986480C22semidirect
60. #17986479C22semidirect
61. #17986475C22semidirect
62. #17986475C22semidirect
65. #17986471C22semidirect
66. #17986471C22semidirect
73. C4×D4×D71C22semidirect
74. C4×D4×D71C22semidirect
79. #17986326C22semidirect
80. #17986326C22semidirect
81. #17986325C22semidirect
82. #17986325C22semidirect
83. #17986322C22semidirect
84. #17986322C22semidirect
85. #17986321C22semidirect
86. #17986321C22semidirect
87. #17986318C22semidirect
88. #17986317C22semidirect
89. #17986315C22semidirect
90. #17986313C22semidirect
91. #17986312C22semidirect
92. #17986310C22semidirect
93. #17986309C22semidirect
94. #17986308C22semidirect
95. #17986307C22semidirect
96. #17986306C22semidirect
97. #17986305C22semidirect
98. #17986304C22semidirect
99. #17986303C22semidirect
100. #17986302C22semidirect
101. #17986301C22semidirect
102. #17986300C22semidirect
103. #17986299C22semidirect
104. #17986298C22semidirect
105. #17986297C22semidirect
106. #17986296C22semidirect
107. #17986200C22semidirect
108. #17986199C22semidirect
109. #17986198C22semidirect
110. #17986198C22semidirect
111. #17986197C22semidirect
112. #17986197C22semidirect
113. #17986196C22semidirect
114. #17986195C22semidirect
115. #17986194C22semidirect
116. #17986193C22semidirect
117. #17986193C22semidirect
118. #17986192C22semidirect
119. #17986192C22semidirect
120. #17986191C22semidirect
121. #17986146C22semidirect
122. #17986146C22semidirect
123. #17986144C22semidirect
124. #17986144C22semidirect
125. #17986142C22semidirect
126. #17986142C22semidirect
127. #17986139C22semidirect
128. #17986139C22semidirect
129. #17986136C22semidirect
130. #17986136C22semidirect
131. #17986134C22semidirect
132. #17986134C22semidirect
133. #17986131C22semidirect
134. #17986131C22semidirect
135. #17986112C22semidirect
136. #17986111C22semidirect
137. #17986110C22semidirect
138. #17986109C22semidirect
139. #17986109C22semidirect
140. #17986108C22semidirect
141. #17986108C22semidirect
142. #17986102C22semidirect
143. #17986101C22semidirect
144. #17986100C22semidirect
145. #17986099C22semidirect
146. #17986098C22semidirect
147. #17986097C22semidirect
148. #17986096C22semidirect
149. #17986090C22semidirect
150. C4×#11765854C22semidirect
151. SD16×Dic71C22semidirect
152. C4×#11765852C22semidirect
153. #17986086C22semidirect
154. C4×#11765853C22semidirect
155. #17986084C22semidirect
156. C4×D568C22semidirect
157. D8×Dic71C22semidirect
158. #17986081C22semidirect
159. C4×#11765850C22semidirect
160. C4×#11765850C22semidirect
161. #17986079C22semidirect
162. #17986079C22semidirect
163. #17986061C22semidirect
164. #17986060C22semidirect
165. #17986059C22semidirect
166. #17986059C22semidirect
167. #17986058C22semidirect
168. #17986057C22semidirect
169. #17986057C22semidirect
170. #17986040C22semidirect
171. #17986040C22semidirect
172. #17986038C22semidirect
173. #17986038C22semidirect
174. #17986021C22semidirect
175. #17986021C22semidirect
176. #17986002C22semidirect
177. #17986002C22semidirect
178. #17986002C22semidirect
179. #17986002C22semidirect
186. #17985951C22semidirect
187. C4×#11765848C22semidirect
188. #540×C71C22semidirect
189. #520×C71C22semidirect
190. #481×C71C22semidirect
191. #480×C71C22semidirect
192. #479×C71C22semidirect
193. #478×C71C22semidirect
194. #460×C71C22semidirect
195. #459×C71C22semidirect
196. #449×C71C22semidirect
197. #449×C71C22semidirect
198. #442×C71C22semidirect
199. #440×C71C22semidirect
200. C4×SD16×C71C22semidirect
201. C4×D8×C71C22semidirect
202. #433×C71C22semidirect
917. #3119D71semidirect
931. C71#60568semidirect
948. #540C2×D71semidirect
962. #520C2×D71semidirect
992. #481C2×D71semidirect
996. #480C2×D71semidirect
1004. #479C2×D71semidirect
1012. #478C2×D71semidirect
1020. #460C2×D71semidirect
1028. #459C2×D71semidirect
1035. #449C2×D71semidirect
1036. #449C2×D71semidirect
1052. #442C2×D71semidirect
1060. #440C2×D71semidirect
1068. C4×SD16C2×D71semidirect
1076. C4×D8C2×D71semidirect
1084. #433C2×D71semidirect

Maximal subgroups

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

subgroupindex
#540×D712
#226015402
#225986332
#225986302
#225986292
#225986282
#225985852
#225985822
#225985812
#225985802
#225985422
#225985412
#225985402
#225985392
#225985342
#225985332
#225985322
#225982772
#225982752
#225981592
#225981572
#225978172
#225978152
#225975892
#225971512
C4×#145561552
#225971452
C4×#145561522
#225969742
C71×#31192
#6056871