Finite Group Databasebeta

← C71×#62025 #31882897

Subgroups — C71×#62025 #31882897

Order 18176.

1786 conjugacy classes of subgroups.

The subgroup lattice has 1738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C71×#3554C211yesmaximal, characteristic, complemented
2C71×#3524C211yesmaximal, characteristic, complemented
3C71×#3403C211yesmaximal, characteristic, complemented
4C71×#3400C211yesmaximal, characteristic, complemented
5C71×#3374C211yesmaximal, characteristic, complemented
6C71×#3371C211yesmaximal, characteristic, complemented
7C71×#3321C211yesmaximal, characteristic, complemented
8C71×#3320C211yesmaximal, characteristic, complemented
9C71×#3315C211yesmaximal, characteristic, complemented
10C71×#3309C211yesmaximal, characteristic, complemented
11C71×#3303C211yesmaximal, characteristic, complemented
12C71×#3300C211yesmaximal, characteristic, complemented
13C71×#3285C211yesmaximal, characteristic, complemented
14C71×#3284C211yesmaximal, characteristic, complemented
15C71×#3271C211yesmaximal, characteristic, complemented
16C71×#3271C211yesmaximal, characteristic, complemented
17C71×#3270C211yesmaximal, characteristic, complemented
18C71×#3269C211yesmaximal, characteristic, complemented
19C71×#3263C211yesmaximal, characteristic, complemented
20C71×#3257C211yesmaximal, characteristic, complemented
21C71×#3248C211yesmaximal, characteristic, complemented
22C71×#3225C211yesmaximal, characteristic, complemented
23C71×#3221C211yesmaximal, characteristic, complemented
24C71×#3219C211yesmaximal, characteristic, complemented
25C71×#3124C211yesmaximal, characteristic, complemented
26C71×#3121C211yesmaximal, characteristic, complemented
27C71×#3116C211yesmaximal, characteristic, complemented
28C71×#3046C211yesmaximal, characteristic, complemented
29C71×#3044C211yesmaximal, characteristic, complemented
30C71×#3035C211yesmaximal, characteristic, complemented
31C71×#2992C211yesmaximal, characteristic, complemented
32C2×#137×C71C2211yescharacteristic
33C2×#137×C71C2211yescharacteristic
34C2×#135×C71C2211yescharacteristic
35C2×#135×C71C2211yescharacteristic
36C2×#135×C71C2211yescharacteristic
37C22×Q16×C71C2211yescharacteristic
38#562×C71—21no—
39#562×C71—21no—
40#559×C71—21no—
41#559×C71—21no—
42#559×C71C2211yescharacteristic
43#559×C71C2211yescharacteristic
44#557×C71C2211yescharacteristic
45#557×C71C2211yescharacteristic
46#555×C71—21no—
47#555×C71C2211yescharacteristic
48#554×C71—21no—
49#553×C71—21no—
50#553×C71C2211yescharacteristic
51#552×C71—21no—
52#552×C71C2211yescharacteristic
53#550×C71C2211yescharacteristic
54#550×C71C2211yescharacteristic
55D4×Q8×C71C2211yescharacteristic
56#548×C71C2211yescharacteristic
57#548×C71C2211yescharacteristic
58#548×C71C2211yescharacteristic
59#548×C71C2211yescharacteristic
60#547×C71C2211yescharacteristic
61#547×C71C2211yescharacteristic
62#542×C71—21no—
63#542×C71—21no—
64#542×C71C2211yescharacteristic
65#542×C71C2211yescharacteristic
66#542×C71C2211yescharacteristic
67#540×C71—21no—
68#540×C71—21no—
69#540×C71C2211yescharacteristic
70#539×C71—21no—
71#539×C71—21no—
72#536×C71C2211yescharacteristic
73#536×C71C2211yescharacteristic
74#533×C71C2211yescharacteristic
75#532×C71C2211yescharacteristic
76#529×C71—21no—
77#529×C71—21no—
78#529×C71C2211yescharacteristic
79#529×C71C2211yescharacteristic
80#520×C71C2211yescharacteristic
81#519×C71C2211yescharacteristic
82C4×#41×C71C2211yescharacteristic
83#497×C71C2211yescharacteristic
84#497×C71C2211yescharacteristic
85#496×C71C2211yescharacteristic
86#496×C71C2211yescharacteristic
87#495×C71C2211yescharacteristic
88#492×C71C2211yescharacteristic
89#491×C71C2211yescharacteristic
90#491×C71C2211yescharacteristic
91#490×C71C2211yescharacteristic
92#489×C71C2211yescharacteristic
93#488×C71C2211yescharacteristic
94#487×C71C2211yescharacteristic
95#485×C71C2211yescharacteristic
96#485×C71C2211yescharacteristic
97#485×C71C2211yescharacteristic
98#484×C71C2211yescharacteristic
99#482×C71C2211yescharacteristic
100#480×C71C2211yescharacteristic
101#479×C71C2211yescharacteristic
102#479×C71C2211yescharacteristic
103#479×C71C2211yescharacteristic
104#478×C71C2211yescharacteristic
105#477×C71C2211yescharacteristic
106#476×C71C2211yescharacteristic
107#476×C71C2211yescharacteristic
108#475×C71C2211yescharacteristic
109#475×C71C2211yescharacteristic
110#474×C71C2211yescharacteristic
111#470×C71C2211yescharacteristic
112#469×C71C2211yescharacteristic
113#469×C71C2211yescharacteristic
114#468×C71C2211yescharacteristic
115#467×C71C2211yescharacteristic
116#467×C71C2211yescharacteristic
117#466×C71C2211yescharacteristic
118#465×C71C2211yescharacteristic
119#465×C71C2211yescharacteristic
120#465×C71C2211yescharacteristic
121#465×C71C2211yescharacteristic
122#465×C71C2211yescharacteristic
123#464×C71C2211yescharacteristic
124#464×C71C2211yescharacteristic
125#464×C71C2211yescharacteristic
126#464×C71C2211yescharacteristic
127#464×C71C2211yescharacteristic
128#464×C71C2211yescharacteristic
129#464×C71C2211yescharacteristic
130#464×C71C2211yescharacteristic
131#464×C71C2211yescharacteristic
132#464×C71C2211yescharacteristic
133#463×C71C2211yescharacteristic
134#463×C71C2211yescharacteristic
135#463×C71C2211yescharacteristic
136#463×C71C2211yescharacteristic
137#463×C71C2211yescharacteristic
138#463×C71C2211yescharacteristic
139#462×C71C2211yescharacteristic
140#462×C71C2211yescharacteristic
141#462×C71C2211yescharacteristic
142#462×C71C2211yescharacteristic
143#462×C71C2211yescharacteristic
144#462×C71C2211yescharacteristic
145#461×C71C2211yescharacteristic
146#461×C71C2211yescharacteristic
147#461×C71C2211yescharacteristic
148#461×C71C2211yescharacteristic
149#460×C71C2211yescharacteristic
150#460×C71C2211yescharacteristic
151#459×C71C2211yescharacteristic
152#459×C71C2211yescharacteristic
153#452×C71C2211yescharacteristic
154#452×C71C2211yescharacteristic
155#452×C71C2211yescharacteristic
156#452×C71C2211yescharacteristic
157#452×C71C2211yescharacteristic
158#452×C71C2211yescharacteristic
159#451×C71C2211yescharacteristic
160#451×C71C2211yescharacteristic
161#449×C71C2211yescharacteristic
162#449×C71C2211yescharacteristic
163#449×C71C2211yescharacteristic
164#449×C71C2211yescharacteristic
165#449×C71C2211yescharacteristic
166#449×C71C2211yescharacteristic
167#448×C71C2211yescharacteristic
168#448×C71C2211yescharacteristic
169#448×C71C2211yescharacteristic
170#448×C71C2211yescharacteristic
171#446×C71C2211yescharacteristic
172#446×C71C2211yescharacteristic
173#441×C71C2211yescharacteristic
174#441×C71C2211yescharacteristic
175#441×C71C2211yescharacteristic
176#440×C71C2211yescharacteristic
177#440×C71C2211yescharacteristic
178#440×C71C2211yescharacteristic
179#440×C71C2211yescharacteristic
180#440×C71C2211yescharacteristic
181C4×Q16×C71C2211yescharacteristic
182C4×Q16×C71C2211yescharacteristic
183C4×SD16×C71C2211yescharacteristic
184C4×D8×C71C2211yescharacteristic
185#435×C71C2211yescharacteristic
186#435×C71C2211yescharacteristic
187#435×C71C2211yescharacteristic
188#435×C71C2211yescharacteristic
189C8×D4×C71C2211yescharacteristic
190C8×D4×C71C2211yescharacteristic
191#433×C71C2211yescharacteristic
192#433×C71C2211yescharacteristic
193#432×C71C2211yescharacteristic
194#424×C71C2211yescharacteristic
195#424×C71C2211yescharacteristic
196C2×C4⋊C8×C71C2211yescharacteristic
197#419×C71C2211yescharacteristic
198#417×C71C2211yescharacteristic
199#416×C71C2211yescharacteristic
200#416×C71C2211yescharacteristic
201#416×C71C2211yescharacteristic
202C2×#103×C71C2211yescharacteristic
203C2×#41×C71C2311yescharacteristic
204C2×#41×C71C2311yescharacteristic
205C2×#41×C71C2311yescharacteristic
206C2×#41×C71C2311yescharacteristic
207C2×#41×C71C2311yescharacteristic
208C2×#41×C71C2311yescharacteristic
209C22×Q8×C71C2311yescharacteristic
210C22×Q8×C71C2311yescharacteristic
211C22×Q8×C71C2311yescharacteristic
212#137×C71—42no—
213#137×C71—42no—
214#135×C71—42no—
215#135×C71—42no—
216#135×C71—42no—
217C2×Q16×C71—42no—
218C2×Q16×C71C2311yescharacteristic
219C2×Q16×C71C2311yescharacteristic
220C2×Q16×C71C2311yescharacteristic
221C2×Q16×C71C2311yescharacteristic
222C2×Q16×C71C2311yescharacteristic
223C2×Q16×C71C2311yescharacteristic
224C2×Q16×C71C2311yescharacteristic
225C2×Q16×C71C2311yescharacteristic
226C2×SD16×C71C2311yescharacteristic
227C2×SD16×C71C2311yescharacteristic
228C2×SD16×C71C2311yescharacteristic
229C2×SD16×C71C2311yescharacteristic
230C2×SD16×C71C2311yescharacteristic
231C2×SD16×C71C2311yescharacteristic
232C2×SD16×C71C2311yescharacteristic
233C2×SD16×C71C2311yescharacteristic
234C2×SD16×C71C2311yescharacteristic
235C2×SD16×C71C2311yescharacteristic
236C2×SD16×C71C2311yescharacteristic
237C2×SD16×C71C2311yescharacteristic
238C2×D8×C71C2311yescharacteristic
239C2×D8×C71C2311yescharacteristic
240C2×D8×C71C2311yescharacteristic
241C2×D8×C71C2311yescharacteristic
242C2×M16×C71C2311yescharacteristic
243C2×M16×C71C2311yescharacteristic
244C22×C8×C71C2311yescharacteristic
245C22×C8×C71C2311yescharacteristic
246C22×C8×C71C2311yescharacteristic
247C22×C8×C71C2311yescharacteristic
248C4⋊Q8×C71—21no—
249C4⋊Q8×C71—21no—
250C4⋊Q8×C71C2311yescharacteristic
251C4⋊Q8×C71C2311yescharacteristic
252C4⋊Q8×C71C2311yescharacteristic
253C4⋊Q8×C71C2311yescharacteristic
254C4⋊Q8×C71C2311yescharacteristic
255C4⋊Q8×C71C2311yescharacteristic
256#127×C71—21no—
257#127×C71—21no—
258#127×C71C2311yescharacteristic
259#127×C71C2311yescharacteristic
260#126×C71—21no—
261#126×C71—21no—
262#126×C71—21no—
263#126×C71—21no—
264#126×C71—21no—
265#126×C71—21no—
266#126×C71D411yescharacteristic
267#126×C71D411yescharacteristic
268#125×C71—21no—
269#125×C71—21no—
270#125×C71—21no—
271#125×C71—21no—
272#125×C71—21no—
273#125×C71—21no—
274#125×C71—21no—
275#125×C71D411yescharacteristic
276#125×C71C2311yescharacteristic
277#125×C71C2311yescharacteristic
278#124×C71—21no—
279#124×C71—21no—
280#124×C71—21no—
281#124×C71—21no—
282#124×C71—21no—
283#124×C71—21no—
284#124×C71—21no—
285#124×C71—21no—
286#124×C71—21no—
287#124×C71—21no—
288#124×C71—21no—
289#124×C71D411yescharacteristic
290#124×C71C2311yescharacteristic
291#124×C71C2311yescharacteristic
292#124×C71C2311yescharacteristic
293#124×C71C2311yescharacteristic
294#124×C71C2311yescharacteristic
295#124×C71C2311yescharacteristic
296#123×C71—21no—
297#123×C71—21no—
298#123×C71—21no—
299#123×C71—21no—
300#123×C71—21no—
301#123×C71—21no—
302#123×C71—21no—
303#123×C71—21no—
304#123×C71—21no—
305#123×C71—21no—
306#123×C71—21no—
307#123×C71—21no—
308#123×C71—21no—
309#123×C71—21no—
310#123×C71—21no—
311#123×C71—21no—
312#123×C71—21no—
313#123×C71—21no—
314#123×C71—21no—
315#123×C71—21no—
316#123×C71D411yescharacteristic
317#123×C71D411yescharacteristic
318C22⋊Q8×C71—21no—
319C22⋊Q8×C71—21no—
320C22⋊Q8×C71—21no—
321C22⋊Q8×C71—21no—
322C22⋊Q8×C71—21no—
323C22⋊Q8×C71—21no—
324C22⋊Q8×C71—21no—
325C22⋊Q8×C71—21no—
326C22⋊Q8×C71—21no—
327C22⋊Q8×C71—21no—
328C22⋊Q8×C71—21no—
329C22⋊Q8×C71—21no—
330C22⋊Q8×C71—21no—
331C22⋊Q8×C71—21no—
332C22⋊Q8×C71D411yescharacteristic
333C22⋊Q8×C71C2311yescharacteristic
334C22⋊Q8×C71C2311yescharacteristic
335C22⋊Q8×C71C2311yescharacteristic
336C22⋊Q8×C71C2311yescharacteristic
337C22⋊Q8×C71C2311yescharacteristic
338C22⋊Q8×C71C2311yescharacteristic
339#121×C71—21no—
340#121×C71—21no—
341#121×C71—21no—
342#121×C71—21no—
343#121×C71—21no—
344#121×C71—21no—
345#121×C71—21no—
346#121×C71—21no—
347#121×C71—21no—
348#121×C71—21no—
349#121×C71—21no—
350#121×C71—21no—
351#121×C71—21no—
352#121×C71—21no—
353#121×C71—21no—
354#121×C71—21no—
355#121×C71D411yescharacteristic
356#121×C71C2311yescharacteristic
357#121×C71C2311yescharacteristic
358#121×C71C2311yescharacteristic
359#121×C71C2311yescharacteristic
360#121×C71C2311yescharacteristic
361#121×C71C2311yescharacteristic
362C4×Q8×C71—21no—
363C4×Q8×C71—21no—
364C4×Q8×C71—21no—
365C4×Q8×C71—21no—
366C4×Q8×C71—21no—
367C4×Q8×C71C2311yescharacteristic
368C4×Q8×C71C2311yescharacteristic
369C4×Q8×C71C2311yescharacteristic
370C4×Q8×C71C2311yescharacteristic
371C4×Q8×C71C2311yescharacteristic
372C4×Q8×C71C2311yescharacteristic
373C4×Q8×C71C2311yescharacteristic
374C4×Q8×C71C2311yescharacteristic
375C4×Q8×C71C2311yescharacteristic
376C4×Q8×C71C2311yescharacteristic
377C4×Q8×C71C2311yescharacteristic
378C4×D4×C71—21no—
379C4×D4×C71—21no—
380C4×D4×C71—21no—
381C4×D4×C71—21no—
382C4×D4×C71—21no—
383C4×D4×C71—21no—
384C4×D4×C71—21no—
385C4×D4×C71—21no—
386C4×D4×C71—21no—
387C4×D4×C71—21no—
388C4×D4×C71—21no—
389C4×D4×C71—21no—
390C4×D4×C71—21no—
391C4×D4×C71—21no—
392C4×D4×C71—21no—
393C4×D4×C71—21no—
394C4×D4×C71—21no—
395C4×D4×C71C2311yescharacteristic
396C4×D4×C71C2311yescharacteristic
397C4×D4×C71C2311yescharacteristic
398C4×D4×C71C2311yescharacteristic
399C4×D4×C71C2311yescharacteristic
400C4×D4×C71C2311yescharacteristic
401C4×D4×C71C2311yescharacteristic
402C4×D4×C71C2311yescharacteristic
403C4×D4×C71C2311yescharacteristic
404#117×C71—21no—
405#117×C71—21no—
406#117×C71—21no—
407#117×C71—21no—
408#117×C71—21no—
409#117×C71—21no—
410#117×C71—21no—
411#117×C71—21no—
412#117×C71C2311yescharacteristic
413#117×C71C2311yescharacteristic
414#117×C71C2311yescharacteristic
415#117×C71C2311yescharacteristic
416C2×C4⋊C4×C71—21no—
417C2×C4⋊C4×C71—21no—
418C2×C4⋊C4×C71—21no—
419C2×C4⋊C4×C71C2311yescharacteristic
420C2×C42×C71—21no—
421C2×C42×C71C2311yescharacteristic
422#107×C71C2311yescharacteristic
423#107×C71C2311yescharacteristic
424#107×C71C2311yescharacteristic
425#107×C71C2311yescharacteristic
426#106×C71C2311yescharacteristic
427#106×C71C2311yescharacteristic
428#106×C71C2311yescharacteristic
429#106×C71C2311yescharacteristic
430C4⋊C8×C71C2311yescharacteristic
431C4⋊C8×C71C2311yescharacteristic
432C4⋊C8×C71C2311yescharacteristic
433C4⋊C8×C71C2311yescharacteristic
434C4⋊C8×C71C2311yescharacteristic
435C4⋊C8×C71C2311yescharacteristic
436C4⋊C8×C71C2311yescharacteristic
437C4⋊C8×C71C2311yescharacteristic
438C4⋊C8×C71C2311yescharacteristic
439C4⋊C8×C71C2311yescharacteristic
440#103×C71C2311yescharacteristic
441#103×C71C2311yescharacteristic
442#103×C71C2311yescharacteristic
443#103×C71C2311yescharacteristic
444#103×C71C2311yescharacteristic
445#103×C71C2311yescharacteristic
446#103×C71C2311yescharacteristic
447#103×C71C2311yescharacteristic
448#103×C71C2311yescharacteristic
449#103×C71C2311yescharacteristic
450#103×C71C2311yescharacteristic
451#103×C71C2311yescharacteristic
452#103×C71C2311yescharacteristic
453#103×C71C2311yescharacteristic
454#103×C71C2311yescharacteristic
455#103×C71C2311yescharacteristic
456#103×C71C2311yescharacteristic
457#103×C71C2311yescharacteristic
458#103×C71C2311yescharacteristic
459#103×C71C2311yescharacteristic
460#102×C71C2311yescharacteristic
461#102×C71C2311yescharacteristic
462#102×C71C2311yescharacteristic
463#102×C71C2311yescharacteristic
464#102×C71C2311yescharacteristic
465#102×C71C2311yescharacteristic
466#102×C71C2311yescharacteristic
467#102×C71C2311yescharacteristic
468#102×C71C2311yescharacteristic
469#102×C71C2311yescharacteristic
470#102×C71C2311yescharacteristic
471#102×C71C2311yescharacteristic
472C22⋊C8×C71C2311yescharacteristic
473C22⋊C8×C71C2311yescharacteristic
474C22⋊C8×C71C2311yescharacteristic
475C22⋊C8×C71C2311yescharacteristic
476C22⋊C8×C71C2311yescharacteristic
477C22⋊C8×C71C2311yescharacteristic
478#97×C71C2311yescharacteristic
479#97×C71C2311yescharacteristic
480#97×C71C2311yescharacteristic
481#97×C71C2311yescharacteristic
482C4×C8×C71C2311yescharacteristic
483C4×C8×C71C2311yescharacteristic
484#41×C71—22no—
485#41×C71—22no—
486#41×C71—41no—
487#41×C71—41no—
488#41×C71—41no—
489#41×C71—41no—
490#41×C71—41no—
491#41×C71—41no—
492#41×C71—41no—
493#41×C71—41no—
494#41×C71—41no—
495#41×C71—41no—
496C2×Q8×C71—21no—
497C2×Q8×C71—21no—
498C2×Q8×C71—21no—
499C2×Q8×C71—21no—
500C2×Q8×C71—21no—
501C2×Q8×C71—22no—
502C2×Q8×C71—41no—
503C2×Q8×C71—41no—
504C2×Q8×C71—41no—
505C2×Q8×C71—41no—
506C2×Q8×C71—41no—
507C2×Q8×C71C2×D411yescharacteristic
508C2×Q8×C71C2411yescharacteristic
509C2×Q8×C71C2411yescharacteristic
510C2×Q8×C71C2411yescharacteristic
511C2×Q8×C71C2411yescharacteristic
512C2×Q8×C71C2411yescharacteristic
513C2×Q8×C71C2411yescharacteristic
514C2×D4×C71—21no—
515C2×D4×C71—21no—
516C2×D4×C71—21no—
517C2×D4×C71—21no—
518C2×D4×C71—21no—
519C2×D4×C71—21no—
520C2×D4×C71—21no—
521C2×D4×C71—21no—
522C2×D4×C71—21no—
523C2×D4×C71—21no—
524C2×D4×C71—21no—
525C2×D4×C71—21no—
526C2×D4×C71—21no—
527C2×D4×C71—21no—
528C2×D4×C71—21no—
529C2×D4×C71—21no—
530C2×D4×C71C2×D411yescharacteristic
531C2×D4×C71C2×D411yescharacteristic
532C2×D4×C71C2×D411yescharacteristic
533C2×D4×C71C2411yescharacteristic
534C2×D4×C71C2411yescharacteristic
535C2×D4×C71C2411yescharacteristic
536C2×D4×C71C2411yescharacteristic
537C22×C4×C71—21no—
538C22×C4×C71—21no—
539C22×C4×C71—21no—
540C22×C4×C71—21no—
541C22×C4×C71—21no—
542C22×C4×C71—21no—
543C22×C4×C71—21no—
544C22×C4×C71—21no—
545C22×C4×C71—21no—
546C22×C4×C71—21no—
547C22×C4×C71—21no—
548C22×C4×C71—21no—
549C22×C4×C71—21no—
550C22×C4×C71—21no—
551C22×C4×C71—21no—
552C22×C4×C71—21no—
553C22×C4×C71C2×D411yescharacteristic
554C22×C4×C71C2×D411yescharacteristic
555C22×C4×C71C2411yescharacteristic
556C22×C4×C71C2411yescharacteristic
557C22×C4×C71C2411yescharacteristic
558Q16×C71—22no—
559Q16×C71—22no—
560Q16×C71—22no—
561Q16×C71—22no—
562Q16×C71—41no—
563Q16×C71—41no—
564Q16×C71—41no—
565Q16×C71—41no—
566SD16×C71—22no—
567SD16×C71—22no—
568SD16×C71—41no—
569SD16×C71—41no—
570SD16×C71—41no—
571SD16×C71—41no—
572SD16×C71—41no—
573SD16×C71—41no—
574SD16×C71—41no—
575SD16×C71—41no—
576SD16×C71—41no—
577SD16×C71—41no—
578D8×C71—41no—
579D8×C71—41no—
580D8×C71—41no—
581D8×C71—41no—
582M16×C71—41no—
583M16×C71—41no—
584C2×C8×C71—41no—
585C2×C8×C71—41no—
586C2×C8×C71—41no—
587C2×C8×C71—41no—
588C2×C8×C71C2411yescharacteristic
589C2×C8×C71C2411yescharacteristic
590C2×C8×C71C2411yescharacteristic
591C2×C8×C71C2411yescharacteristic
592C2×C8×C71C2411yescharacteristic
593C2×C8×C71C2411yescharacteristic
594C2×C8×C71C2411yescharacteristic
595C2×C8×C71C2411yescharacteristic
596C4⋊C4×C71—21no—
597C4⋊C4×C71—21no—
598C4⋊C4×C71—21no—
599C4⋊C4×C71—21no—
600C4⋊C4×C71—21no—
601C4⋊C4×C71—21no—
602C4⋊C4×C71—21no—
603C4⋊C4×C71—21no—
604C4⋊C4×C71—21no—
605C4⋊C4×C71—21no—
606C4⋊C4×C71—21no—
607C4⋊C4×C71—21no—
608C4⋊C4×C71—21no—
609C4⋊C4×C71—21no—
610C4⋊C4×C71—21no—
611C4⋊C4×C71—21no—
612C4⋊C4×C71—21no—
613C4⋊C4×C71—21no—
614C4⋊C4×C71—21no—
615C4⋊C4×C71—21no—
616C4⋊C4×C71—21no—
617C4⋊C4×C71—21no—
618C4⋊C4×C71—21no—
619C4⋊C4×C71—21no—
620C4⋊C4×C71—21no—
621C4⋊C4×C71—21no—
622C4⋊C4×C71—21no—
623C4⋊C4×C71—21no—
624C4⋊C4×C71—21no—
625C4⋊C4×C71—21no—
626C4⋊C4×C71—21no—
627C4⋊C4×C71C2×D411yescharacteristic
628C4⋊C4×C71C2×D411yescharacteristic
629C4⋊C4×C71C2×D411yescharacteristic
630C4⋊C4×C71C2×D411yescharacteristic
631C4⋊C4×C71C2×D411yescharacteristic
632C4⋊C4×C71C2×D411yescharacteristic
633C4⋊C4×C71C2×D411yescharacteristic
634C4⋊C4×C71C2×D411yescharacteristic
635C4⋊C4×C71C2×D411yescharacteristic
636C4⋊C4×C71C2×D411yescharacteristic
637C4⋊C4×C71C2411yescharacteristic
638C4⋊C4×C71C2411yescharacteristic
639C4⋊C4×C71C2411yescharacteristic
640C4⋊C4×C71C2411yescharacteristic
641C4⋊C4×C71C2411yescharacteristic
642C4⋊C4×C71C2411yescharacteristic
643C22⋊C4×C71—21no—
644C22⋊C4×C71—21no—
645C22⋊C4×C71—21no—
646C22⋊C4×C71—21no—
647C22⋊C4×C71—21no—
648C22⋊C4×C71—21no—
649C22⋊C4×C71—21no—
650C22⋊C4×C71—21no—
651C22⋊C4×C71—21no—
652C22⋊C4×C71—21no—
653C22⋊C4×C71—21no—
654C22⋊C4×C71—21no—
655C22⋊C4×C71—21no—
656C22⋊C4×C71—21no—
657C22⋊C4×C71—21no—
658C22⋊C4×C71—21no—
659C22⋊C4×C71—21no—
660C22⋊C4×C71—21no—
661C22⋊C4×C71—21no—
662C22⋊C4×C71—21no—
663C22⋊C4×C71—21no—
664C22⋊C4×C71—21no—
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×C71—21no—
672C22⋊C4×C71—21no—
673C22⋊C4×C71—21no—
674C22⋊C4×C71—21no—
675C22⋊C4×C71C2×D411yescharacteristic
676C22⋊C4×C71C2×D411yescharacteristic
677C22⋊C4×C71C2×D411yescharacteristic
678C22⋊C4×C71C2×D411yescharacteristic
679C22⋊C4×C71C2×D411yescharacteristic
680C22⋊C4×C71C2×D411yescharacteristic
681C22⋊C4×C71C2×D411yescharacteristic
682C22⋊C4×C71C2×D411yescharacteristic
683C22⋊C4×C71C2×D411yescharacteristic
684C22⋊C4×C71C2×D411yescharacteristic
685C42×C71—21no—
686C42×C71—21no—
687C42×C71—21no—
688C42×C71—21no—
689C42×C71—21no—
690C42×C71—21no—
691C42×C71—21no—
692C42×C71—21no—
693C42×C71—21no—
694C42×C71—21no—
695C42×C71—21no—
696C42×C71—21no—
697C42×C71C2×D411yescharacteristic
698C42×C71C2×D411yescharacteristic
699C42×C71C2411yescharacteristic
700C42×C71C2411yescharacteristic
701C42×C71C2411yescharacteristic
702C42×C71C2411yescharacteristic
703C23×C71—21no—
704C23×C71—21no—
705C23×C71—21no—
706C23×C71—21no—
707C23×C71C22×D411yescharacteristic
708C23×C71C22×D411yescharacteristic
709C23×C71C22×D411yescharacteristic
710Q8×C71—21no—
711Q8×C71—21no—
712Q8×C71—21no—
713Q8×C71—21no—
714Q8×C71—21no—
715Q8×C71—21no—
716Q8×C71—21no—
717Q8×C71—21no—
718Q8×C71—21no—
719Q8×C71—21no—
720Q8×C71—21no—
721Q8×C71—41no—
722Q8×C71—42no—
723Q8×C71—81no—
724Q8×C71—81no—
725Q8×C71—81no—
726Q8×C71—81no—
727Q8×C71H(5,𝔽2)12yes—
728D4×C71—21no—
729D4×C71—21no—
730D4×C71—21no—
731D4×C71—21no—
732D4×C71—21no—
733D4×C71—21no—
734D4×C71—21no—
735D4×C71—21no—
736D4×C71—41no—
737D4×C71—41no—
738D4×C71—41no—
739D4×C71—42no—
740D4×C71—42no—
741D4×C71—42no—
742D4×C71—81no—
743D4×C71—81no—
744D4×C71—81no—
745D4×C71—81no—
746D4×C71—81no—
747D4×C71—81no—
748D4×C71—81no—
749D4×C71—81no—
750D4×C71—81no—
751D4×C71—81no—
752D4×C71—81no—
753D4×C71—81no—
754D4×C71—81no—
755C2×C4×C71—21no—
756C2×C4×C71—21no—
757C2×C4×C71—21no—
758C2×C4×C71—21no—
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—21no—
770C2×C4×C71—21no—
771C2×C4×C71—21no—
772C2×C4×C71—21no—
773C2×C4×C71—41no—
774C2×C4×C71—41no—
775C2×C4×C71—42no—
776C2×C4×C71—42no—
777C2×C4×C71—42no—
778C2×C4×C71—81no—
779C2×C4×C71—81no—
780C2×C4×C71—81no—
781C2×C4×C71—81no—
782C2×C4×C71—81no—
783C2×C4×C71—81no—
784C2×C4×C71—81no—
785C2×C4×C71—81no—
786C2×C4×C71—81no—
787C2×C4×C71—81no—
788C2×C4×C71—81no—
789C2×C4×C71—81no—
790C2×C4×C71—81no—
791C2×C4×C71C22×D411yescharacteristic
792C2×C4×C71C22×D411yescharacteristic
793C2×C4×C71C22×D411yescharacteristic
794C2×C4×C71C22×D411yescharacteristic
795C2×C4×C71C22×D411yescharacteristic
796C2×C4×C71C22×D411yescharacteristic
797C2×C4×C71C22×D411yescharacteristic
798C2×C4×C71C22×D411yescharacteristic
799C2×C4×C71C22×D411yescharacteristic
800C2×C4×C71C22×D411yescharacteristic
801C2×C4×C71C22×D411yescharacteristic
802C2×C4×C71C2511yescharacteristic
803C8×C71—21no—
804C8×C71—21no—
805C8×C71—21no—
806C8×C71—21no—
807C8×C71—21no—
808C8×C71—21no—
809C8×C71—21no—
810C8×C71—21no—
811C22×C71—21no—
812C22×C71—21no—
813C22×C71—21no—
814C22×C71—21no—
815C22×C71—21no—
816C22×C71—21no—
817C22×C71—21no—
818C22×C71—21no—
819C22×C71—21no—
820C22×C71—41no—
821C22×C71—41no—
822C22×C71—41no—
823C22×C71—41no—
824C22×C71—41no—
825C22×C71—41no—
826C22×C71—41no—
827C22×C71—41no—
828C22×C71—41no—
829C22×C71—41no—
830C22×C71—41no—
831C22×C71—41no—
832C22×C71C23×D411yescharacteristic
833C4×C71—21no—
834C4×C71—21no—
835C4×C71—21no—
836C4×C71—21no—
837C4×C71—21no—
838C4×C71—21no—
839C4×C71—21no—
840C4×C71—21no—
841C4×C71—21no—
842C4×C71—21no—
843C4×C71—21no—
844C4×C71—22no—
845C4×C71—41no—
846C4×C71—41no—
847C4×C71—41no—
848C4×C71—41no—
849C4×C71—41no—
850C4×C71—41no—
851C4×C71—41no—
852C4×C71—41no—
853C4×C71—41no—
854C4×C71—41no—
855C4×C71—41no—
856C4×C71C2×H(5,𝔽2)11yescharacteristic
857C4×C71#58511yescharacteristic
858#62025C7111yesmaximal, characteristic, direct product factor, Sylow
859C2×C71—41no—
860C2×C71—41no—
861C2×C71—41no—
862C2×C71—81no—
863C2×C71—81no—
864C2×C71—81no—
865C2×C71—81no—
866C2×C71#348811yescharacteristic
867C2×C71#358411yescharacteristic
868C2×C71#358611yescharacteristic
869#3554C2×C7111yescharacteristic, complemented
870#3524C2×C7111yescharacteristic, complemented
871#3403C2×C7111yescharacteristic, complemented
872#3400C2×C7111yescharacteristic, complemented
873#3374C2×C7111yescharacteristic, complemented
874#3371C2×C7111yescharacteristic, complemented
875#3321C2×C7111yescharacteristic, complemented
876#3320C2×C7111yescharacteristic, complemented
877#3315C2×C7111yescharacteristic, complemented
878#3309C2×C7111yescharacteristic, complemented
879#3303C2×C7111yescharacteristic, complemented
880#3300C2×C7111yescharacteristic, complemented
881#3285C2×C7111yescharacteristic, complemented
882#3284C2×C7111yescharacteristic, complemented
883#3271C2×C7111yescharacteristic, complemented
884#3271C2×C7111yescharacteristic, complemented
885#3270C2×C7111yescharacteristic, complemented
886#3269C2×C7111yescharacteristic, complemented
887#3263C2×C7111yescharacteristic, complemented
888#3257C2×C7111yescharacteristic, complemented
889#3248C2×C7111yescharacteristic, complemented
890#3225C2×C7111yescharacteristic, complemented
891#3221C2×C7111yescharacteristic, complemented
892#3219C2×C7111yescharacteristic, complemented
893#3124C2×C7111yescharacteristic, complemented
894#3121C2×C7111yescharacteristic, complemented
895#3116C2×C7111yescharacteristic, complemented
896#3046C2×C7111yescharacteristic, complemented
897#3044C2×C7111yescharacteristic, complemented
898#3035C2×C7111yescharacteristic, complemented
899#2992C2×C7111yescharacteristic, complemented
900C71#6202511yescharacteristic, direct product factor, Sylow
901C2×#137C22×C7111yescharacteristic
902C2×#137C22×C7111yescharacteristic
903C2×#135C22×C7111yescharacteristic
904C2×#135C22×C7111yescharacteristic
905C2×#135C22×C7111yescharacteristic
906C22×Q16C22×C7111yescharacteristic
907#562—21no—
908#562—21no—
909#559—21no—
910#559—21no—
911#559C22×C7111yescharacteristic
912#559C22×C7111yescharacteristic
913#557C22×C7111yescharacteristic
914#557C22×C7111yescharacteristic
915#555—21no—
916#555C22×C7111yescharacteristic
917#554—21no—
918#553—21no—
919#553C22×C7111yescharacteristic
920#552—21no—
921#552C22×C7111yescharacteristic
922#550C22×C7111yescharacteristic
923#550C22×C7111yescharacteristic
924D4×Q8C22×C7111yescharacteristic
925#548C22×C7111yescharacteristic
926#548C22×C7111yescharacteristic
927#548C22×C7111yescharacteristic
928#548C22×C7111yescharacteristic
929#547C22×C7111yescharacteristic
930#547C22×C7111yescharacteristic
931#542—21no—
932#542—21no—
933#542C22×C7111yescharacteristic
934#542C22×C7111yescharacteristic
935#542C22×C7111yescharacteristic
936#540—21no—
937#540—21no—
938#540C22×C7111yescharacteristic
939#539—21no—
940#539—21no—
941#536C22×C7111yescharacteristic
942#536C22×C7111yescharacteristic
943#533C22×C7111yescharacteristic
944#532C22×C7111yescharacteristic
945#529—21no—
946#529—21no—
947#529C22×C7111yescharacteristic
948#529C22×C7111yescharacteristic
949#520C22×C7111yescharacteristic
950#519C22×C7111yescharacteristic
951C4×#41C22×C7111yescharacteristic
952#497C22×C7111yescharacteristic
953#497C22×C7111yescharacteristic
954#496C22×C7111yescharacteristic
955#496C22×C7111yescharacteristic
956#495C22×C7111yescharacteristic
957#492C22×C7111yescharacteristic
958#491C22×C7111yescharacteristic
959#491C22×C7111yescharacteristic
960#490C22×C7111yescharacteristic
961#489C22×C7111yescharacteristic
962#488C22×C7111yescharacteristic
963#487C22×C7111yescharacteristic
964#485C22×C7111yescharacteristic
965#485C22×C7111yescharacteristic
966#485C22×C7111yescharacteristic
967#484C22×C7111yescharacteristic
968#482C22×C7111yescharacteristic
969#480C22×C7111yescharacteristic
970#479C22×C7111yescharacteristic
971#479C22×C7111yescharacteristic
972#479C22×C7111yescharacteristic
973#478C22×C7111yescharacteristic
974#477C22×C7111yescharacteristic
975#476C22×C7111yescharacteristic
976#476C22×C7111yescharacteristic
977#475C22×C7111yescharacteristic
978#475C22×C7111yescharacteristic
979#474C22×C7111yescharacteristic
980#470C22×C7111yescharacteristic
981#469C22×C7111yescharacteristic
982#469C22×C7111yescharacteristic
983#468C22×C7111yescharacteristic
984#467C22×C7111yescharacteristic
985#467C22×C7111yescharacteristic
986#466C22×C7111yescharacteristic
987#465C22×C7111yescharacteristic
988#465C22×C7111yescharacteristic
989#465C22×C7111yescharacteristic
990#465C22×C7111yescharacteristic
991#465C22×C7111yescharacteristic
992#464C22×C7111yescharacteristic
993#464C22×C7111yescharacteristic
994#464C22×C7111yescharacteristic
995#464C22×C7111yescharacteristic
996#464C22×C7111yescharacteristic
997#464C22×C7111yescharacteristic
998#464C22×C7111yescharacteristic
999#464C22×C7111yescharacteristic
1000#464C22×C7111yescharacteristic
1001#464C22×C7111yescharacteristic
1002#463C22×C7111yescharacteristic
1003#463C22×C7111yescharacteristic
1004#463C22×C7111yescharacteristic
1005#463C22×C7111yescharacteristic
1006#463C22×C7111yescharacteristic
1007#463C22×C7111yescharacteristic
1008#462C22×C7111yescharacteristic
1009#462C22×C7111yescharacteristic
1010#462C22×C7111yescharacteristic
1011#462C22×C7111yescharacteristic
1012#462C22×C7111yescharacteristic
1013#462C22×C7111yescharacteristic
1014#461C22×C7111yescharacteristic
1015#461C22×C7111yescharacteristic
1016#461C22×C7111yescharacteristic
1017#461C22×C7111yescharacteristic
1018#460C22×C7111yescharacteristic
1019#460C22×C7111yescharacteristic
1020#459C22×C7111yescharacteristic
1021#459C22×C7111yescharacteristic
1022#452C22×C7111yescharacteristic
1023#452C22×C7111yescharacteristic
1024#452C22×C7111yescharacteristic
1025#452C22×C7111yescharacteristic
1026#452C22×C7111yescharacteristic
1027#452C22×C7111yescharacteristic
1028#451C22×C7111yescharacteristic
1029#451C22×C7111yescharacteristic
1030#449C22×C7111yescharacteristic
1031#449C22×C7111yescharacteristic
1032#449C22×C7111yescharacteristic
1033#449C22×C7111yescharacteristic
1034#449C22×C7111yescharacteristic
1035#449C22×C7111yescharacteristic
1036#448C22×C7111yescharacteristic
1037#448C22×C7111yescharacteristic
1038#448C22×C7111yescharacteristic
1039#448C22×C7111yescharacteristic
1040#446C22×C7111yescharacteristic
1041#446C22×C7111yescharacteristic
1042#441C22×C7111yescharacteristic
1043#441C22×C7111yescharacteristic
1044#441C22×C7111yescharacteristic
1045#440C22×C7111yescharacteristic
1046#440C22×C7111yescharacteristic
1047#440C22×C7111yescharacteristic
1048#440C22×C7111yescharacteristic
1049#440C22×C7111yescharacteristic
1050C4×Q16C22×C7111yescharacteristic
1051C4×Q16C22×C7111yescharacteristic
1052C4×SD16C22×C7111yescharacteristic
1053C4×D8C22×C7111yescharacteristic
1054#435C22×C7111yescharacteristic
1055#435C22×C7111yescharacteristic
1056#435C22×C7111yescharacteristic
1057#435C22×C7111yescharacteristic
1058C8×D4C22×C7111yescharacteristic
1059C8×D4C22×C7111yescharacteristic
1060#433C22×C7111yescharacteristic
1061#433C22×C7111yescharacteristic
1062#432C22×C7111yescharacteristic
1063#424C22×C7111yescharacteristic
1064#424C22×C7111yescharacteristic
1065C2×C4⋊C8C22×C7111yescharacteristic
1066#419C22×C7111yescharacteristic
1067#417C22×C7111yescharacteristic
1068#416C22×C7111yescharacteristic
1069#416C22×C7111yescharacteristic
1070#416C22×C7111yescharacteristic
1071C2×#103C22×C7111yescharacteristic
1072C2×#41C23×C7111yescharacteristic
1073C2×#41C23×C7111yescharacteristic
1074C2×#41C23×C7111yescharacteristic
1075C2×#41C23×C7111yescharacteristic
1076C2×#41C23×C7111yescharacteristic
1077C2×#41C23×C7111yescharacteristic
1078C22×Q8C23×C7111yescharacteristic
1079C22×Q8C23×C7111yescharacteristic
1080C22×Q8C23×C7111yescharacteristic
1081#137—42no—
1082#137—42no—
1083#135—42no—
1084#135—42no—
1085#135—42no—
1086C2×Q16—42no—
1087C2×Q16C23×C7111yescharacteristic
1088C2×Q16C23×C7111yescharacteristic
1089C2×Q16C23×C7111yescharacteristic
1090C2×Q16C23×C7111yescharacteristic
1091C2×Q16C23×C7111yescharacteristic
1092C2×Q16C23×C7111yescharacteristic
1093C2×Q16C23×C7111yescharacteristic
1094C2×Q16C23×C7111yescharacteristic
1095C2×SD16C23×C7111yescharacteristic
1096C2×SD16C23×C7111yescharacteristic
1097C2×SD16C23×C7111yescharacteristic
1098C2×SD16C23×C7111yescharacteristic
1099C2×SD16C23×C7111yescharacteristic
1100C2×SD16C23×C7111yescharacteristic
1101C2×SD16C23×C7111yescharacteristic
1102C2×SD16C23×C7111yescharacteristic
1103C2×SD16C23×C7111yescharacteristic
1104C2×SD16C23×C7111yescharacteristic
1105C2×SD16C23×C7111yescharacteristic
1106C2×SD16C23×C7111yescharacteristic
1107C2×D8C23×C7111yescharacteristic
1108C2×D8C23×C7111yescharacteristic
1109C2×D8C23×C7111yescharacteristic
1110C2×D8C23×C7111yescharacteristic
1111C2×M16C23×C7111yescharacteristic
1112C2×M16C23×C7111yescharacteristic
1113C22×C8C23×C7111yescharacteristic
1114C22×C8C23×C7111yescharacteristic
1115C22×C8C23×C7111yescharacteristic
1116C22×C8C23×C7111yescharacteristic
1117C4⋊Q8—21no—
1118C4⋊Q8—21no—
1119C4⋊Q8C23×C7111yescharacteristic
1120C4⋊Q8C23×C7111yescharacteristic
1121C4⋊Q8C23×C7111yescharacteristic
1122C4⋊Q8C23×C7111yescharacteristic
1123C4⋊Q8C23×C7111yescharacteristic
1124C4⋊Q8C23×C7111yescharacteristic
1125#127—21no—
1126#127—21no—
1127#127C23×C7111yescharacteristic
1128#127C23×C7111yescharacteristic
1129#126—21no—
1130#126—21no—
1131#126—21no—
1132#126—21no—
1133#126—21no—
1134#126—21no—
1135#126D4×C7111yescharacteristic
1136#126D4×C7111yescharacteristic
1137#125—21no—
1138#125—21no—
1139#125—21no—
1140#125—21no—
1141#125—21no—
1142#125—21no—
1143#125—21no—
1144#125D4×C7111yescharacteristic
1145#125C23×C7111yescharacteristic
1146#125C23×C7111yescharacteristic
1147#124—21no—
1148#124—21no—
1149#124—21no—
1150#124—21no—
1151#124—21no—
1152#124—21no—
1153#124—21no—
1154#124—21no—
1155#124—21no—
1156#124—21no—
1157#124—21no—
1158#124D4×C7111yescharacteristic
1159#124C23×C7111yescharacteristic
1160#124C23×C7111yescharacteristic
1161#124C23×C7111yescharacteristic
1162#124C23×C7111yescharacteristic
1163#124C23×C7111yescharacteristic
1164#124C23×C7111yescharacteristic
1165#123—21no—
1166#123—21no—
1167#123—21no—
1168#123—21no—
1169#123—21no—
1170#123—21no—
1171#123—21no—
1172#123—21no—
1173#123—21no—
1174#123—21no—
1175#123—21no—
1176#123—21no—
1177#123—21no—
1178#123—21no—
1179#123—21no—
1180#123—21no—
1181#123—21no—
1182#123—21no—
1183#123—21no—
1184#123—21no—
1185#123D4×C7111yescharacteristic
1186#123D4×C7111yescharacteristic
1187C22⋊Q8—21no—
1188C22⋊Q8—21no—
1189C22⋊Q8—21no—
1190C22⋊Q8—21no—
1191C22⋊Q8—21no—
1192C22⋊Q8—21no—
1193C22⋊Q8—21no—
1194C22⋊Q8—21no—
1195C22⋊Q8—21no—
1196C22⋊Q8—21no—
1197C22⋊Q8—21no—
1198C22⋊Q8—21no—
1199C22⋊Q8—21no—
1200C22⋊Q8—21no—
1201C22⋊Q8D4×C7111yescharacteristic
1202C22⋊Q8C23×C7111yescharacteristic
1203C22⋊Q8C23×C7111yescharacteristic
1204C22⋊Q8C23×C7111yescharacteristic
1205C22⋊Q8C23×C7111yescharacteristic
1206C22⋊Q8C23×C7111yescharacteristic
1207C22⋊Q8C23×C7111yescharacteristic
1208#121—21no—
1209#121—21no—
1210#121—21no—
1211#121—21no—
1212#121—21no—
1213#121—21no—
1214#121—21no—
1215#121—21no—
1216#121—21no—
1217#121—21no—
1218#121—21no—
1219#121—21no—
1220#121—21no—
1221#121—21no—
1222#121—21no—
1223#121—21no—
1224#121D4×C7111yescharacteristic
1225#121C23×C7111yescharacteristic
1226#121C23×C7111yescharacteristic
1227#121C23×C7111yescharacteristic
1228#121C23×C7111yescharacteristic
1229#121C23×C7111yescharacteristic
1230#121C23×C7111yescharacteristic
1231C4×Q8—21no—
1232C4×Q8—21no—
1233C4×Q8—21no—
1234C4×Q8—21no—
1235C4×Q8—21no—
1236C4×Q8C23×C7111yescharacteristic
1237C4×Q8C23×C7111yescharacteristic
1238C4×Q8C23×C7111yescharacteristic
1239C4×Q8C23×C7111yescharacteristic
1240C4×Q8C23×C7111yescharacteristic
1241C4×Q8C23×C7111yescharacteristic
1242C4×Q8C23×C7111yescharacteristic
1243C4×Q8C23×C7111yescharacteristic
1244C4×Q8C23×C7111yescharacteristic
1245C4×Q8C23×C7111yescharacteristic
1246C4×Q8C23×C7111yescharacteristic
1247C4×D4—21no—
1248C4×D4—21no—
1249C4×D4—21no—
1250C4×D4—21no—
1251C4×D4—21no—
1252C4×D4—21no—
1253C4×D4—21no—
1254C4×D4—21no—
1255C4×D4—21no—
1256C4×D4—21no—
1257C4×D4—21no—
1258C4×D4—21no—
1259C4×D4—21no—
1260C4×D4—21no—
1261C4×D4—21no—
1262C4×D4—21no—
1263C4×D4—21no—
1264C4×D4C23×C7111yescharacteristic
1265C4×D4C23×C7111yescharacteristic
1266C4×D4C23×C7111yescharacteristic
1267C4×D4C23×C7111yescharacteristic
1268C4×D4C23×C7111yescharacteristic
1269C4×D4C23×C7111yescharacteristic
1270C4×D4C23×C7111yescharacteristic
1271C4×D4C23×C7111yescharacteristic
1272C4×D4C23×C7111yescharacteristic
1273#117—21no—
1274#117—21no—
1275#117—21no—
1276#117—21no—
1277#117—21no—
1278#117—21no—
1279#117—21no—
1280#117—21no—
1281#117C23×C7111yescharacteristic
1282#117C23×C7111yescharacteristic
1283#117C23×C7111yescharacteristic
1284#117C23×C7111yescharacteristic
1285C2×C4⋊C4—21no—
1286C2×C4⋊C4—21no—
1287C2×C4⋊C4—21no—
1288C2×C4⋊C4C23×C7111yescharacteristic
1289C2×C42—21no—
1290C2×C42C23×C7111yescharacteristic
1291#107C23×C7111yescharacteristic
1292#107C23×C7111yescharacteristic
1293#107C23×C7111yescharacteristic
1294#107C23×C7111yescharacteristic
1295#106C23×C7111yescharacteristic
1296#106C23×C7111yescharacteristic
1297#106C23×C7111yescharacteristic
1298#106C23×C7111yescharacteristic
1299C4⋊C8C23×C7111yescharacteristic
1300C4⋊C8C23×C7111yescharacteristic
1301C4⋊C8C23×C7111yescharacteristic
1302C4⋊C8C23×C7111yescharacteristic
1303C4⋊C8C23×C7111yescharacteristic
1304C4⋊C8C23×C7111yescharacteristic
1305C4⋊C8C23×C7111yescharacteristic
1306C4⋊C8C23×C7111yescharacteristic
1307C4⋊C8C23×C7111yescharacteristic
1308C4⋊C8C23×C7111yescharacteristic
1309#103C23×C7111yescharacteristic
1310#103C23×C7111yescharacteristic
1311#103C23×C7111yescharacteristic
1312#103C23×C7111yescharacteristic
1313#103C23×C7111yescharacteristic
1314#103C23×C7111yescharacteristic
1315#103C23×C7111yescharacteristic
1316#103C23×C7111yescharacteristic
1317#103C23×C7111yescharacteristic
1318#103C23×C7111yescharacteristic
1319#103C23×C7111yescharacteristic
1320#103C23×C7111yescharacteristic
1321#103C23×C7111yescharacteristic
1322#103C23×C7111yescharacteristic
1323#103C23×C7111yescharacteristic
1324#103C23×C7111yescharacteristic
1325#103C23×C7111yescharacteristic
1326#103C23×C7111yescharacteristic
1327#103C23×C7111yescharacteristic
1328#103C23×C7111yescharacteristic
1329#102C23×C7111yescharacteristic
1330#102C23×C7111yescharacteristic
1331#102C23×C7111yescharacteristic
1332#102C23×C7111yescharacteristic
1333#102C23×C7111yescharacteristic
1334#102C23×C7111yescharacteristic
1335#102C23×C7111yescharacteristic
1336#102C23×C7111yescharacteristic
1337#102C23×C7111yescharacteristic
1338#102C23×C7111yescharacteristic
1339#102C23×C7111yescharacteristic
1340#102C23×C7111yescharacteristic
1341C22⋊C8C23×C7111yescharacteristic
1342C22⋊C8C23×C7111yescharacteristic
1343C22⋊C8C23×C7111yescharacteristic
1344C22⋊C8C23×C7111yescharacteristic
1345C22⋊C8C23×C7111yescharacteristic
1346C22⋊C8C23×C7111yescharacteristic
1347#97C23×C7111yescharacteristic
1348#97C23×C7111yescharacteristic
1349#97C23×C7111yescharacteristic
1350#97C23×C7111yescharacteristic
1351C4×C8C23×C7111yescharacteristic
1352C4×C8C23×C7111yescharacteristic
1353#41—22no—
1354#41—22no—
1355#41—41no—
1356#41—41no—
1357#41—41no—
1358#41—41no—
1359#41—41no—
1360#41—41no—
1361#41—41no—
1362#41—41no—
1363#41—41no—
1364#41—41no—
1365C2×Q8—21no—
1366C2×Q8—21no—
1367C2×Q8—21no—
1368C2×Q8—21no—
1369C2×Q8—21no—
1370C2×Q8—22no—
1371C2×Q8—41no—
1372C2×Q8—41no—
1373C2×Q8—41no—
1374C2×Q8—41no—
1375C2×Q8—41no—
1376C2×Q8C2×D4×C7111yescharacteristic
1377C2×Q8C24×C7111yescharacteristic
1378C2×Q8C24×C7111yescharacteristic
1379C2×Q8C24×C7111yescharacteristic
1380C2×Q8C24×C7111yescharacteristic
1381C2×Q8C24×C7111yescharacteristic
1382C2×Q8C24×C7111yescharacteristic
1383C2×D4—21no—
1384C2×D4—21no—
1385C2×D4—21no—
1386C2×D4—21no—
1387C2×D4—21no—
1388C2×D4—21no—
1389C2×D4—21no—
1390C2×D4—21no—
1391C2×D4—21no—
1392C2×D4—21no—
1393C2×D4—21no—
1394C2×D4—21no—
1395C2×D4—21no—
1396C2×D4—21no—
1397C2×D4—21no—
1398C2×D4—21no—
1399C2×D4C2×D4×C7111yescharacteristic
1400C2×D4C2×D4×C7111yescharacteristic
1401C2×D4C2×D4×C7111yescharacteristic
1402C2×D4C24×C7111yescharacteristic
1403C2×D4C24×C7111yescharacteristic
1404C2×D4C24×C7111yescharacteristic
1405C2×D4C24×C7111yescharacteristic
1406C22×C4—21no—
1407C22×C4—21no—
1408C22×C4—21no—
1409C22×C4—21no—
1410C22×C4—21no—
1411C22×C4—21no—
1412C22×C4—21no—
1413C22×C4—21no—
1414C22×C4—21no—
1415C22×C4—21no—
1416C22×C4—21no—
1417C22×C4—21no—
1418C22×C4—21no—
1419C22×C4—21no—
1420C22×C4—21no—
1421C22×C4—21no—
1422C22×C4C2×D4×C7111yescharacteristic
1423C22×C4C2×D4×C7111yescharacteristic
1424C22×C4C24×C7111yescharacteristic
1425C22×C4C24×C7111yescharacteristic
1426C22×C4C24×C7111yescharacteristic
1427Q16—22no—
1428Q16—22no—
1429Q16—22no—
1430Q16—22no—
1431Q16—41no—
1432Q16—41no—
1433Q16—41no—
1434Q16—41no—
1435SD16—22no—
1436SD16—22no—
1437SD16—41no—
1438SD16—41no—
1439SD16—41no—
1440SD16—41no—
1441SD16—41no—
1442SD16—41no—
1443SD16—41no—
1444SD16—41no—
1445SD16—41no—
1446SD16—41no—
1447D8—41no—
1448D8—41no—
1449D8—41no—
1450D8—41no—
1451M16—41no—
1452M16—41no—
1453C2×C8—41no—
1454C2×C8—41no—
1455C2×C8—41no—
1456C2×C8—41no—
1457C2×C8C24×C7111yescharacteristic
1458C2×C8C24×C7111yescharacteristic
1459C2×C8C24×C7111yescharacteristic
1460C2×C8C24×C7111yescharacteristic
1461C2×C8C24×C7111yescharacteristic
1462C2×C8C24×C7111yescharacteristic
1463C2×C8C24×C7111yescharacteristic
1464C2×C8C24×C7111yescharacteristic
1465C4⋊C4—21no—
1466C4⋊C4—21no—
1467C4⋊C4—21no—
1468C4⋊C4—21no—
1469C4⋊C4—21no—
1470C4⋊C4—21no—
1471C4⋊C4—21no—
1472C4⋊C4—21no—
1473C4⋊C4—21no—
1474C4⋊C4—21no—
1475C4⋊C4—21no—
1476C4⋊C4—21no—
1477C4⋊C4—21no—
1478C4⋊C4—21no—
1479C4⋊C4—21no—
1480C4⋊C4—21no—
1481C4⋊C4—21no—
1482C4⋊C4—21no—
1483C4⋊C4—21no—
1484C4⋊C4—21no—
1485C4⋊C4—21no—
1486C4⋊C4—21no—
1487C4⋊C4—21no—
1488C4⋊C4—21no—
1489C4⋊C4—21no—
1490C4⋊C4—21no—
1491C4⋊C4—21no—
1492C4⋊C4—21no—
1493C4⋊C4—21no—
1494C4⋊C4—21no—
1495C4⋊C4—21no—
1496C4⋊C4C2×D4×C7111yescharacteristic
1497C4⋊C4C2×D4×C7111yescharacteristic
1498C4⋊C4C2×D4×C7111yescharacteristic
1499C4⋊C4C2×D4×C7111yescharacteristic
1500C4⋊C4C2×D4×C7111yescharacteristic
1501C4⋊C4C2×D4×C7111yescharacteristic
1502C4⋊C4C2×D4×C7111yescharacteristic
1503C4⋊C4C2×D4×C7111yescharacteristic
1504C4⋊C4C2×D4×C7111yescharacteristic
1505C4⋊C4C2×D4×C7111yescharacteristic
1506C4⋊C4C24×C7111yescharacteristic
1507C4⋊C4C24×C7111yescharacteristic
1508C4⋊C4C24×C7111yescharacteristic
1509C4⋊C4C24×C7111yescharacteristic
1510C4⋊C4C24×C7111yescharacteristic
1511C4⋊C4C24×C7111yescharacteristic
1512C22⋊C4—21no—
1513C22⋊C4—21no—
1514C22⋊C4—21no—
1515C22⋊C4—21no—
1516C22⋊C4—21no—
1517C22⋊C4—21no—
1518C22⋊C4—21no—
1519C22⋊C4—21no—
1520C22⋊C4—21no—
1521C22⋊C4—21no—
1522C22⋊C4—21no—
1523C22⋊C4—21no—
1524C22⋊C4—21no—
1525C22⋊C4—21no—
1526C22⋊C4—21no—
1527C22⋊C4—21no—
1528C22⋊C4—21no—
1529C22⋊C4—21no—
1530C22⋊C4—21no—
1531C22⋊C4—21no—
1532C22⋊C4—21no—
1533C22⋊C4—21no—
1534C22⋊C4—21no—
1535C22⋊C4—21no—
1536C22⋊C4—21no—
1537C22⋊C4—21no—
1538C22⋊C4—21no—
1539C22⋊C4—21no—
1540C22⋊C4—21no—
1541C22⋊C4—21no—
1542C22⋊C4—21no—
1543C22⋊C4—21no—
1544C22⋊C4C2×D4×C7111yescharacteristic
1545C22⋊C4C2×D4×C7111yescharacteristic
1546C22⋊C4C2×D4×C7111yescharacteristic
1547C22⋊C4C2×D4×C7111yescharacteristic
1548C22⋊C4C2×D4×C7111yescharacteristic
1549C22⋊C4C2×D4×C7111yescharacteristic
1550C22⋊C4C2×D4×C7111yescharacteristic
1551C22⋊C4C2×D4×C7111yescharacteristic
1552C22⋊C4C2×D4×C7111yescharacteristic
1553C22⋊C4C2×D4×C7111yescharacteristic
1554C42—21no—
1555C42—21no—
1556C42—21no—
1557C42—21no—
1558C42—21no—
1559C42—21no—
1560C42—21no—
1561C42—21no—
1562C42—21no—
1563C42—21no—
1564C42—21no—
1565C42—21no—
1566C42C2×D4×C7111yescharacteristic
1567C42C2×D4×C7111yescharacteristic
1568C42C24×C7111yescharacteristic
1569C42C24×C7111yescharacteristic
1570C42C24×C7111yescharacteristic
1571C42C24×C7111yescharacteristic
1572C23—21no—
1573C23—21no—
1574C23—21no—
1575C23—21no—
1576C23C22×D4×C7111yescharacteristic
1577C23C22×D4×C7111yescharacteristic
1578C23C22×D4×C7111yescharacteristic
1579Q8—21no—
1580Q8—21no—
1581Q8—21no—
1582Q8—21no—
1583Q8—21no—
1584Q8—21no—
1585Q8—21no—
1586Q8—21no—
1587Q8—21no—
1588Q8—21no—
1589Q8—21no—
1590Q8—41no—
1591Q8—42no—
1592Q8—81no—
1593Q8—81no—
1594Q8—81no—
1595Q8—81no—
1596Q8H(5,𝔽2)×C7112yes—
1597D4—21no—
1598D4—21no—
1599D4—21no—
1600D4—21no—
1601D4—21no—
1602D4—21no—
1603D4—21no—
1604D4—21no—
1605D4—41no—
1606D4—41no—
1607D4—41no—
1608D4—42no—
1609D4—42no—
1610D4—42no—
1611D4—81no—
1612D4—81no—
1613D4—81no—
1614D4—81no—
1615D4—81no—
1616D4—81no—
1617D4—81no—
1618D4—81no—
1619D4—81no—
1620D4—81no—
1621D4—81no—
1622D4—81no—
1623D4—81no—
1624C2×C4—21no—
1625C2×C4—21no—
1626C2×C4—21no—
1627C2×C4—21no—
1628C2×C4—21no—
1629C2×C4—21no—
1630C2×C4—21no—
1631C2×C4—21no—
1632C2×C4—21no—
1633C2×C4—21no—
1634C2×C4—21no—
1635C2×C4—21no—
1636C2×C4—21no—
1637C2×C4—21no—
1638C2×C4—21no—
1639C2×C4—21no—
1640C2×C4—21no—
1641C2×C4—21no—
1642C2×C4—41no—
1643C2×C4—41no—
1644C2×C4—42no—
1645C2×C4—42no—
1646C2×C4—42no—
1647C2×C4—81no—
1648C2×C4—81no—
1649C2×C4—81no—
1650C2×C4—81no—
1651C2×C4—81no—
1652C2×C4—81no—
1653C2×C4—81no—
1654C2×C4—81no—
1655C2×C4—81no—
1656C2×C4—81no—
1657C2×C4—81no—
1658C2×C4—81no—
1659C2×C4—81no—
1660C2×C4C22×D4×C7111yescharacteristic
1661C2×C4C22×D4×C7111yescharacteristic
1662C2×C4C22×D4×C7111yescharacteristic
1663C2×C4C22×D4×C7111yescharacteristic
1664C2×C4C22×D4×C7111yescharacteristic
1665C2×C4C22×D4×C7111yescharacteristic
1666C2×C4C22×D4×C7111yescharacteristic
1667C2×C4C22×D4×C7111yescharacteristic
1668C2×C4C22×D4×C7111yescharacteristic
1669C2×C4C22×D4×C7111yescharacteristic
1670C2×C4C22×D4×C7111yescharacteristic
1671C2×C4C25×C7111yescharacteristic
1672C8—21no—
1673C8—21no—
1674C8—21no—
1675C8—21no—
1676C8—21no—
1677C8—21no—
1678C8—21no—
1679C8—21no—
1680C22—21no—
1681C22—21no—
1682C22—21no—
1683C22—21no—
1684C22—21no—
1685C22—21no—
1686C22—21no—
1687C22—21no—
1688C22—21no—
1689C22—41no—
1690C22—41no—
1691C22—41no—
1692C22—41no—
1693C22—41no—
1694C22—41no—
1695C22—41no—
1696C22—41no—
1697C22—41no—
1698C22—41no—
1699C22—41no—
1700C22—41no—
1701C22C23×D4×C7111yescharacteristic
1702C4—21no—
1703C4—21no—
1704C4—21no—
1705C4—21no—
1706C4—21no—
1707C4—21no—
1708C4—21no—
1709C4—21no—
1710C4—21no—
1711C4—21no—
1712C4—21no—
1713C4—22no—
1714C4—41no—
1715C4—41no—
1716C4—41no—
1717C4—41no—
1718C4—41no—
1719C4—41no—
1720C4—41no—
1721C4—41no—
1722C4—41no—
1723C4—41no—
1724C4—41no—
1725C4C2×H(5,𝔽2)×C7111yescharacteristic
1726C4#585×C7111yescharacteristic
1727C2—41no—
1728C2—41no—
1729C2—41no—
1730C2—81no—
1731C2—81no—
1732C2—81no—
1733C2—81no—
1734C2C71×#348811yescharacteristic
1735C2C71×#358411yescharacteristic
1736C2C71×#358611yescharacteristic
subgroupG/H
center, socleC22×C71C23×D4
commutator, Frattini, cosocleC2×C4C25×C71
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C71 ◁ #529×C71 ◁ G

Complements

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

NH ≅ G/Ntype
1. C71×#3554C2semidirect
2. C71×#3524C2semidirect
3. C71×#3403C2semidirect
4. C71×#3400C2semidirect
5. C71×#3374C2semidirect
6. C71×#3371C2semidirect
7. C71×#3321C2semidirect
8. C71×#3320C2semidirect
9. C71×#3315C2semidirect
10. C71×#3309C2semidirect
11. C71×#3303C2semidirect
12. C71×#3300C2semidirect
13. C71×#3285C2semidirect
14. C71×#3284C2semidirect
15. C71×#3271C2semidirect
16. C71×#3271C2semidirect
17. C71×#3270C2semidirect
18. C71×#3269C2semidirect
19. C71×#3263C2semidirect
20. C71×#3257C2semidirect
21. C71×#3248C2semidirect
22. C71×#3225C2semidirect
23. C71×#3221C2semidirect
24. C71×#3219C2semidirect
25. C71×#3124C2semidirect
26. C71×#3121C2semidirect
27. C71×#3116C2semidirect
28. C71×#3046C2semidirect
29. C71×#3044C2semidirect
30. C71×#3035C2semidirect
31. C71×#2992C2semidirect
858. #62025C71direct (N × H)
869. #3554C2×C71semidirect
870. #3524C2×C71semidirect
871. #3403C2×C71semidirect
872. #3400C2×C71semidirect
873. #3374C2×C71semidirect
874. #3371C2×C71semidirect
875. #3321C2×C71semidirect
876. #3320C2×C71semidirect
877. #3315C2×C71semidirect
878. #3309C2×C71semidirect
879. #3303C2×C71semidirect
880. #3300C2×C71semidirect
881. #3285C2×C71semidirect
882. #3284C2×C71semidirect
883. #3271C2×C71semidirect
884. #3271C2×C71semidirect
885. #3270C2×C71semidirect
886. #3269C2×C71semidirect
887. #3263C2×C71semidirect
888. #3257C2×C71semidirect
889. #3248C2×C71semidirect
890. #3225C2×C71semidirect
891. #3221C2×C71semidirect
892. #3219C2×C71semidirect
893. #3124C2×C71semidirect
894. #3121C2×C71semidirect
895. #3116C2×C71semidirect
896. #3046C2×C71semidirect
897. #3044C2×C71semidirect
898. #3035C2×C71semidirect
899. #2992C2×C71semidirect
900. C71#62025direct (N × H)

Maximal subgroups

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

subgroupindex
C71×#35542
C71×#35242
C71×#34032
C71×#34002
C71×#33742
C71×#33712
C71×#33212
C71×#33202
C71×#33152
C71×#33092
C71×#33032
C71×#33002
C71×#32852
C71×#32842
C71×#32712
C71×#32702
C71×#32692
C71×#32632
C71×#32572
C71×#32482
C71×#32252
C71×#32212
C71×#32192
C71×#31242
C71×#31212
C71×#31162
C71×#30462
C71×#30442
C71×#30352
C71×#29922
#6202571