Finite Group Databasebeta

← #31965612

Subgroups — #31965612

Order 18176.

878 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22597354C211yesmaximal, characteristic, complemented
2#22596991C211yesmaximal, characteristic, complemented
3#22586978C211yesmaximal, characteristic, complemented
4#22586971C211yesmaximal, characteristic, complemented
5#22586971C211yesmaximal, characteristic, complemented
6#22586967C211yesmaximal, characteristic, complemented
7#22586960C211yesmaximal, characteristic, complemented
8#22586960C211yesmaximal, characteristic, complemented
9#22586955C211yesmaximal, characteristic, complemented
10#22586947C211yesmaximal, characteristic, complemented
11#22586942C211yesmaximal, characteristic, complemented
12#22586942C211yesmaximal, characteristic, complemented
13#22586928C211yesmaximal, characteristic, complemented
14C2×#17985741C211yesmaximal, characteristic, complemented
15C71×#3515C211yesmaximal, characteristic
16#17986130—21no—
17#17986071—21no—
18#17986071—21no—
19D4×C71⋊C8—21no—
20#17986060—21no—
21#17986060—21no—
22#17986056C2211yescharacteristic
23#17986056C2211yescharacteristic
24#17986056C2211yescharacteristic
25#17986056C2211yescharacteristic
26#17986056C2211yescharacteristic
27#17986056C2211yescharacteristic
28#17986056C2211yescharacteristic
29#17986026—21no—
30#17985966—21no—
31C4×#11765849C2211yescharacteristic
32C4×#11765849C2211yescharacteristic
33C2×#14556039C2211yescharacteristic
34C2×#14556039C2211yescharacteristic
35C2×#14556039C2211yescharacteristic
36#17985741C2211yescharacteristic
37#17985741C2211yescharacteristic
38#17985741C2211yescharacteristic
39#17985741C2211yescharacteristic
40#17985741C2211yescharacteristic
41#17985741C2211yescharacteristic
42#17985741C2211yescharacteristic
43#17985741C2211yescharacteristic
44#17985741C2211yescharacteristic
45#17985741C2211yescharacteristic
46#17985741C2211yescharacteristic
47#17985741C2211yescharacteristic
48#17985739C2211yescharacteristic
49#17985739C2211yescharacteristic
50#17985739C2211yescharacteristic
51#17985739C2211yescharacteristic
52#557×C71C411yescharacteristic
53#554×C71C411yescharacteristic
54#554×C71C411yescharacteristic
55#553×C71C411yescharacteristic
56#553×C71C411yescharacteristic
57#552×C71—21no—
58#552×C71—21no—
59#552×C71—21no—
60#552×C71C411yescharacteristic
61#552×C71C411yescharacteristic
62#547×C71—21no—
63#547×C71C411yescharacteristic
64#541×C71—21no—
65#539×C71—21no—
66#539×C71—21no—
67#533×C71C2211yescharacteristic
68#529×C71C2211yescharacteristic
69#529×C71C2211yescharacteristic
70#529×C71C2211yescharacteristic
71C2×#125×C71C2211yescharacteristic
72C2×#125×C71C2211yescharacteristic
73#520×C71—21no—
74C4×#41×C71C2211yescharacteristic
75C2×#11765849—21no—
76C2×#11765849—21no—
77C22×C71⋊C8—21no—
78C22×C71⋊C8—21no—
79C22×C71⋊C8—21no—
80C4⋊(C71⋊C8)—21no—
81C4⋊(C71⋊C8)—21no—
82C4⋊(C71⋊C8)—21no—
83C4⋊(C71⋊C8)—21no—
84C4⋊(C71⋊C8)—21no—
85C4⋊(C71⋊C8)—21no—
86C4⋊(C71⋊C8)—21no—
87C22⋊(C71⋊C8)—21no—
88C22⋊(C71⋊C8)—21no—
89C22⋊(C71⋊C8)—21no—
90C22⋊(C71⋊C8)—21no—
91C22⋊(C71⋊C8)—21no—
92C22⋊(C71⋊C8)—21no—
93C22⋊(C71⋊C8)—21no—
94#14556039—21no—
95#14556039—21no—
96#14556039—21no—
97#14556039C2311yescharacteristic
98#14556039C2311yescharacteristic
99#14556039C2311yescharacteristic
100#14556039C2311yescharacteristic
101#14556039C2311yescharacteristic
102#14556039C2311yescharacteristic
103#14556039C2311yescharacteristic
104#14556039C2311yescharacteristic
105C4×C71⋊C8—21no—
106C4×C71⋊C8—21no—
107C2×#41×C71—21no—
108C2×#41×C71D411yescharacteristic
109C4⋊Q8×C71—21no—
110C4⋊Q8×C71C2×C411yescharacteristic
111C4⋊Q8×C71C2×C411yescharacteristic
112#126×C71—21no—
113#126×C71—21no—
114#126×C71—21no—
115#126×C71—21no—
116#126×C71—21no—
117#126×C71—21no—
118#126×C71—21no—
119#125×C71—21no—
120#125×C71—21no—
121#125×C71—21no—
122#125×C71—21no—
123#125×C71—21no—
124#125×C71—21no—
125#125×C71—21no—
126#125×C71—21no—
127#125×C71—21no—
128#125×C71C2×C411yescharacteristic
129#125×C71C2×C411yescharacteristic
130#125×C71C2×C411yescharacteristic
131#125×C71C2×C411yescharacteristic
132#125×C71C2311yescharacteristic
133#125×C71C2311yescharacteristic
134#125×C71C2311yescharacteristic
135#124×C71C2311yescharacteristic
136#123×C71—21no—
137#123×C71—21no—
138#123×C71—21no—
139#123×C71—21no—
140#123×C71—21no—
141#123×C71—21no—
142#123×C71—21no—
143#123×C71—21no—
144#123×C71—21no—
145C22⋊Q8×C71—21no—
146C22⋊Q8×C71—21no—
147C22⋊Q8×C71—21no—
148C22⋊Q8×C71—21no—
149C22⋊Q8×C71—21no—
150C22⋊Q8×C71—21no—
151C22⋊Q8×C71—21no—
152C22⋊Q8×C71—21no—
153C22⋊Q8×C71C2×C411yescharacteristic
154C22⋊Q8×C71C2×C411yescharacteristic
155C22⋊Q8×C71C2×C411yescharacteristic
156#121×C71—21no—
157#121×C71—21no—
158#121×C71C2×C411yescharacteristic
159#121×C71C2×C411yescharacteristic
160#121×C71C2×C411yescharacteristic
161C4×Q8×C71—21no—
162C4×Q8×C71—21no—
163C4×Q8×C71—21no—
164C4×Q8×C71C2×C411yescharacteristic
165C4×Q8×C71C2×C411yescharacteristic
166C4×Q8×C71C2×C411yescharacteristic
167C4×Q8×C71C2×C411yescharacteristic
168C4×Q8×C71D411yescharacteristic
169C4×D4×C71—21no—
170C4×D4×C71—21no—
171C4×D4×C71—21no—
172C4×D4×C71—21no—
173C4×D4×C71—21no—
174C4×D4×C71—21no—
175C4×D4×C71C2×C411yescharacteristic
176C4×D4×C71C2×C411yescharacteristic
177C4×D4×C71C2×C411yescharacteristic
178C4×D4×C71C2×C411yescharacteristic
179C4×D4×C71C2×C411yescharacteristic
180C4×D4×C71C2×C411yescharacteristic
181C4×D4×C71D411yescharacteristic
182C4×D4×C71D411yescharacteristic
183C4×D4×C71D411yescharacteristic
184#117×C71—21no—
185#117×C71—21no—
186#117×C71—21no—
187#117×C71—21no—
188#117×C71—21no—
189#117×C71C2×C411yescharacteristic
190#117×C71C2×C411yescharacteristic
191#117×C71D411yescharacteristic
192#117×C71D411yescharacteristic
193#117×C71D411yescharacteristic
194C2×C4⋊C4×C71—21no—
195C2×C4⋊C4×C71—21no—
196C2×C4⋊C4×C71—21no—
197C2×C4⋊C4×C71—21no—
198C2×C4⋊C4×C71—21no—
199C2×C4⋊C4×C71C2×C411yescharacteristic
200C2×C4⋊C4×C71C2×C411yescharacteristic
201C2×C4⋊C4×C71C2×C411yescharacteristic
202C2×C4⋊C4×C71C2×C411yescharacteristic
203C2×C42×C71C2311yescharacteristic
204C2×C42×C71C2311yescharacteristic
205C2×C42×C71C2311yescharacteristic
206#11765849—42no—
207#11765849—42no—
208C2×C71⋊C8—21no—
209C2×C71⋊C8—21no—
210C2×C71⋊C8—21no—
211C2×C71⋊C8—21no—
212C2×C71⋊C8—21no—
213C2×C71⋊C8—21no—
214C2×C71⋊C8—21no—
215C2×C71⋊C8—21no—
216C2×C71⋊C8—42no—
217C2×C71⋊C8—42no—
218C2×C71⋊C8—42no—
219#41×C71—42no—
220#41×C71—44no—
221C2×Q8×C71—21no—
222C2×Q8×C71—21no—
223C2×Q8×C71C22⋊C411yescharacteristic
224C2×Q8×C71C22×C411yescharacteristic
225C2×D4×C71—21no—
226C2×D4×C71—21no—
227C2×D4×C71—21no—
228C2×D4×C71C22⋊C411yescharacteristic
229C2×D4×C71C22⋊C411yescharacteristic
230C2×D4×C71C22⋊C411yescharacteristic
231C2×D4×C71C22×C411yescharacteristic
232C22×C4×C71—21no—
233C22×C4×C71—21no—
234C22×C4×C71—21no—
235C22×C4×C71—21no—
236C22×C4×C71—21no—
237C22×C4×C71—21no—
238C22×C4×C71—21no—
239C22×C4×C71C22×C411yescharacteristic
240C22×C4×C71C22×C411yescharacteristic
241C22×C4×C71C22×C411yescharacteristic
242C22×C4×C71C2×D411yescharacteristic
243C22×C4×C71C2×D411yescharacteristic
244C22×C4×C71C2×D411yescharacteristic
245C22×C4×C71C2×D411yescharacteristic
246C22×C4×C71C2×D411yescharacteristic
247C22×C4×C71C2×D411yescharacteristic
248C4⋊C4×C71—21no—
249C4⋊C4×C71—21no—
250C4⋊C4×C71—21no—
251C4⋊C4×C71—21no—
252C4⋊C4×C71—21no—
253C4⋊C4×C71—21no—
254C4⋊C4×C71—21no—
255C4⋊C4×C71—21no—
256C4⋊C4×C71—21no—
257C4⋊C4×C71—21no—
258C4⋊C4×C71—21no—
259C4⋊C4×C71—21no—
260C4⋊C4×C71—21no—
261C4⋊C4×C71—21no—
262C4⋊C4×C71—21no—
263C4⋊C4×C71—21no—
264C4⋊C4×C71—21no—
265C4⋊C4×C71—21no—
266C4⋊C4×C71—21no—
267C4⋊C4×C71—21no—
268C4⋊C4×C71—21no—
269C4⋊C4×C71—21no—
270C4⋊C4×C71—21no—
271C4⋊C4×C71—21no—
272C4⋊C4×C71—21no—
273C4⋊C4×C71—21no—
274C4⋊C4×C71C22⋊C411yescharacteristic
275C4⋊C4×C71C22⋊C411yescharacteristic
276C4⋊C4×C71C22⋊C411yescharacteristic
277C4⋊C4×C71C22⋊C411yescharacteristic
278C4⋊C4×C71C22⋊C411yescharacteristic
279C4⋊C4×C71C22⋊C411yescharacteristic
280C4⋊C4×C71C22×C411yescharacteristic
281C4⋊C4×C71C22×C411yescharacteristic
282C4⋊C4×C71C22×C411yescharacteristic
283C4⋊C4×C71C22×C411yescharacteristic
284C4⋊C4×C71C22×C411yescharacteristic
285C4⋊C4×C71C22×C411yescharacteristic
286C22⋊C4×C71—21no—
287C22⋊C4×C71—21no—
288C22⋊C4×C71—21no—
289C22⋊C4×C71—21no—
290C22⋊C4×C71—21no—
291C22⋊C4×C71—21no—
292C22⋊C4×C71—21no—
293C22⋊C4×C71—21no—
294C22⋊C4×C71—21no—
295C22⋊C4×C71—21no—
296C22⋊C4×C71—21no—
297C22⋊C4×C71—21no—
298C22⋊C4×C71—21no—
299C22⋊C4×C71C22⋊C411yescharacteristic
300C22⋊C4×C71C22⋊C411yescharacteristic
301C22⋊C4×C71C22⋊C411yescharacteristic
302C22⋊C4×C71C22⋊C411yescharacteristic
303C22⋊C4×C71C22⋊C411yescharacteristic
304C22⋊C4×C71C22⋊C411yescharacteristic
305C42×C71—21no—
306C42×C71—21no—
307C42×C71—21no—
308C42×C71—21no—
309C42×C71—21no—
310C42×C71C22×C411yescharacteristic
311C42×C71C22×C411yescharacteristic
312C42×C71C22×C411yescharacteristic
313C42×C71C2×D411yescharacteristic
314C42×C71C2×D411yescharacteristic
315C42×C71C2×D411yescharacteristic
316C42×C71C2×D411yescharacteristic
317C42×C71C2×D411yescharacteristic
318C42×C71C2×D411yescharacteristic
319C42×C71C2411yescharacteristic
320C23×C71—21no—
321C23×C71C2×C22⋊C411yescharacteristic
322C23×C71C2×C22⋊C411yescharacteristic
323C23×C71C2×C22⋊C411yescharacteristic
324Q8×C71—41no—
325Q8×C71—41no—
326Q8×C71—42no—
327Q8×C71—81no—
328D4×C71—22no—
329D4×C71—22no—
330D4×C71—41no—
331D4×C71—41no—
332D4×C71—42no—
333D4×C71—42no—
334D4×C71—81no—
335C2×C4×C71—22no—
336C2×C4×C71—21no—
337C2×C4×C71—21no—
338C2×C4×C71—21no—
339C2×C4×C71—21no—
340C2×C4×C71—21no—
341C2×C4×C71—21no—
342C2×C4×C71—21no—
343C2×C4×C71—41no—
344C2×C4×C71—41no—
345C2×C4×C71—41no—
346C2×C4×C71—41no—
347C2×C4×C71—41no—
348C2×C4×C71—41no—
349C2×C4×C71—41no—
350C2×C4×C71—41no—
351C2×C4×C71—42no—
352C2×C4×C71—42no—
353C2×C4×C71—42no—
354C2×C4×C71—81no—
355C2×C4×C71—81no—
356C2×C4×C71—81no—
357C2×C4×C71—81no—
358C2×C4×C71C2×C22⋊C411yescharacteristic
359C2×C4×C71C2×C22⋊C411yescharacteristic
360C2×C4×C71C2×C22⋊C411yescharacteristic
361C2×C4×C71C2×C22⋊C411yescharacteristic
362C2×C4×C71C2×C22⋊C411yescharacteristic
363C2×C4×C71C2×C22⋊C411yescharacteristic
364C2×C4×C71C2×C22⋊C411yescharacteristic
365C2×C4×C71C2×C22⋊C411yescharacteristic
366C2×C4×C71C2×C22⋊C411yescharacteristic
367C2×C4×C71C23×C411yescharacteristic
368C2×C4×C71C22×D411yescharacteristic
369C2×C4×C71C22×D411yescharacteristic
370C71⋊C8—22no—
371C71⋊C8—41no—
372C71⋊C8—41no—
373C71⋊C8—41no—
374C71⋊C8—41no—
375C71⋊C8—41no—
376C71⋊C8—41no—
377C71⋊C8—41no—
378C22×C71—21no—
379C22×C71—21no—
380C22×C71—21no—
381C22×C71—21no—
382C22×C71—21no—
383C22×C71—21no—
384C22×C71—21no—
385C22×C71—21no—
386C22×C71—41no—
387C22×C71—41no—
388C22×C71—41no—
389C22×C71#42112yes—
390C22×C71C22×C22⋊C411yescharacteristic
391C4×C71—21no—
392C4×C71—21no—
393C4×C71—21no—
394C4×C71—21no—
395C4×C71—21no—
396C4×C71—21no—
397C4×C71—21no—
398C4×C71—21no—
399C4×C71—21no—
400C4×C71—21no—
401C4×C71—21no—
402C4×C71—21no—
403C4×C71—41no—
404C4×C71—41no—
405C4×C71—41no—
406C4×C71—41no—
407C4×C71—41no—
408C4×C71—41no—
409C4×C71—41no—
410#17680—711nomaximal, Sylow
411C2×C71—22no—
412C2×C71—41no—
413C2×C71—41no—
414C2×C71—81no—
415C2×C71#288911yescharacteristic
416C2×C71C2×#42111yescharacteristic
417C2×C71#290111yescharacteristic
418#3515D7111yescharacteristic
419#2970—711no—
420#2923—711no—
421#1537—711no—
422#1535—711no—
423#1535—711no—
424#1534—711no—
425#1532—711no—
426#1532—711no—
427#1531—711no—
428#1529—711no—
429#1528—711no—
430#1528—711no—
431#1524—711no—
432C2×#330—711no—
433C71#1768011yescharacteristic, complemented, Sylow
434#557Dic7111yescharacteristic
435#554Dic7111yescharacteristic
436#554Dic7111yescharacteristic
437#553Dic7111yescharacteristic
438#553Dic7111yescharacteristic
439#552—21no—
440#552—21no—
441#552—21no—
442#552Dic7111yescharacteristic
443#552Dic7111yescharacteristic
444#547—21no—
445#547Dic7111yescharacteristic
446#541—21no—
447#539—21no—
448#539—21no—
449#533C2×D7111yescharacteristic
450#529C2×D7111yescharacteristic
451#529C2×D7111yescharacteristic
452#529C2×D7111yescharacteristic
453C2×#125C2×D7111yescharacteristic
454C2×#125C2×D7111yescharacteristic
455#520—21no—
456C4×#41C2×D7111yescharacteristic
457#446—1421no—
458#435—1421no—
459#435—1421no—
460C8×D4—1421no—
461#433—1421no—
462#433—1421no—
463#432—711no—
464#432—711no—
465#432—711no—
466#432—711no—
467#432—711no—
468#432—711no—
469#432—711no—
470#424—1421no—
471#408—1421no—
472C4×M16—711no—
473C4×M16—711no—
474C2×#97—711no—
475C2×#97—711no—
476C2×#97—711no—
477#330—711no—
478#330—711no—
479#330—711no—
480#330—711no—
481#330—711no—
482#330—711no—
483#330—711no—
484#330—711no—
485#330—711no—
486#330—711no—
487#330—711no—
488#330—711no—
489#329—711no—
490#329—711no—
491#329—711no—
492#329—711no—
493C2×#41—21no—
494C2×#41C22⋊D7111yescharacteristic
495C2×M16—1421no—
496C2×M16—1421no—
497C22×C8—1421no—
498C22×C8—1421no—
499C22×C8—1421no—
500C4⋊Q8—21no—
501C4⋊Q8C2×Dic7111yescharacteristic
502C4⋊Q8C2×Dic7111yescharacteristic
503#126—21no—
504#126—21no—
505#126—21no—
506#126—21no—
507#126—21no—
508#126—21no—
509#126—21no—
510#125—21no—
511#125—21no—
512#125—21no—
513#125—21no—
514#125—21no—
515#125—21no—
516#125—21no—
517#125—21no—
518#125—21no—
519#125C2×Dic7111yescharacteristic
520#125C2×Dic7111yescharacteristic
521#125C2×Dic7111yescharacteristic
522#125C2×Dic7111yescharacteristic
523#125C22×D7111yescharacteristic
524#125C22×D7111yescharacteristic
525#125C22×D7111yescharacteristic
526#124C22×D7111yescharacteristic
527#123—21no—
528#123—21no—
529#123—21no—
530#123—21no—
531#123—21no—
532#123—21no—
533#123—21no—
534#123—21no—
535#123—21no—
536C22⋊Q8—21no—
537C22⋊Q8—21no—
538C22⋊Q8—21no—
539C22⋊Q8—21no—
540C22⋊Q8—21no—
541C22⋊Q8—21no—
542C22⋊Q8—21no—
543C22⋊Q8—21no—
544C22⋊Q8C2×Dic7111yescharacteristic
545C22⋊Q8C2×Dic7111yescharacteristic
546C22⋊Q8C2×Dic7111yescharacteristic
547#121—21no—
548#121—21no—
549#121C2×Dic7111yescharacteristic
550#121C2×Dic7111yescharacteristic
551#121C2×Dic7111yescharacteristic
552C4×Q8—21no—
553C4×Q8—21no—
554C4×Q8—21no—
555C4×Q8C2×Dic7111yescharacteristic
556C4×Q8C2×Dic7111yescharacteristic
557C4×Q8C2×Dic7111yescharacteristic
558C4×Q8C2×Dic7111yescharacteristic
559C4×Q8C22⋊D7111yescharacteristic
560C4×D4—21no—
561C4×D4—21no—
562C4×D4—21no—
563C4×D4—21no—
564C4×D4—21no—
565C4×D4—21no—
566C4×D4C2×Dic7111yescharacteristic
567C4×D4C2×Dic7111yescharacteristic
568C4×D4C2×Dic7111yescharacteristic
569C4×D4C2×Dic7111yescharacteristic
570C4×D4C2×Dic7111yescharacteristic
571C4×D4C2×Dic7111yescharacteristic
572C4×D4C22⋊D7111yescharacteristic
573C4×D4C22⋊D7111yescharacteristic
574C4×D4C22⋊D7111yescharacteristic
575#117—21no—
576#117—21no—
577#117—21no—
578#117—21no—
579#117—21no—
580#117C2×Dic7111yescharacteristic
581#117C2×Dic7111yescharacteristic
582#117C22⋊D7111yescharacteristic
583#117C22⋊D7111yescharacteristic
584#117C22⋊D7111yescharacteristic
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4C2×Dic7111yescharacteristic
591C2×C4⋊C4C2×Dic7111yescharacteristic
592C2×C4⋊C4C2×Dic7111yescharacteristic
593C2×C4⋊C4C2×Dic7111yescharacteristic
594C2×C42C22×D7111yescharacteristic
595C2×C42C22×D7111yescharacteristic
596C2×C42C22×D7111yescharacteristic
597C4⋊C8—1421no—
598C4⋊C8—1421no—
599C4⋊C8—1421no—
600C4⋊C8—1421no—
601C4⋊C8—1421no—
602C4⋊C8—1421no—
603C4⋊C8—1421no—
604C22⋊C8—1421no—
605C22⋊C8—1421no—
606C22⋊C8—1421no—
607C22⋊C8—1421no—
608C22⋊C8—1421no—
609C22⋊C8—1421no—
610C22⋊C8—1421no—
611#97—711no—
612#97—711no—
613#97—711no—
614#97—711no—
615#97—711no—
616#97—711no—
617#97—711no—
618#97—711no—
619#97—1421no—
620#97—1421no—
621#97—1421no—
622C4×C8—1421no—
623C4×C8—1421no—
624#41—42no—
625#41—44no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8C22⋊Dic7111yescharacteristic
629C2×Q8C22×Dic7111yescharacteristic
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4C22⋊Dic7111yescharacteristic
634C2×D4C22⋊Dic7111yescharacteristic
635C2×D4C22⋊Dic7111yescharacteristic
636C2×D4C22×Dic7111yescharacteristic
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4C22×Dic7111yescharacteristic
645C22×C4C22×Dic7111yescharacteristic
646C22×C4C22×Dic7111yescharacteristic
647C22×C4C2×C22⋊D7111yescharacteristic
648C22×C4C2×C22⋊D7111yescharacteristic
649C22×C4C2×C22⋊D7111yescharacteristic
650C22×C4C2×C22⋊D7111yescharacteristic
651C22×C4C2×C22⋊D7111yescharacteristic
652C22×C4C2×C22⋊D7111yescharacteristic
653M16—2842no—
654M16—2842no—
655C2×C8—2842no—
656C2×C8—2842no—
657C2×C8—2842no—
658C2×C8—1421no—
659C2×C8—1421no—
660C2×C8—1421no—
661C2×C8—1421no—
662C2×C8—1421no—
663C2×C8—1421no—
664C2×C8—1421no—
665C2×C8—1421no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4C22⋊Dic7111yescharacteristic
693C4⋊C4C22⋊Dic7111yescharacteristic
694C4⋊C4C22⋊Dic7111yescharacteristic
695C4⋊C4C22⋊Dic7111yescharacteristic
696C4⋊C4C22⋊Dic7111yescharacteristic
697C4⋊C4C22⋊Dic7111yescharacteristic
698C4⋊C4C22×Dic7111yescharacteristic
699C4⋊C4C22×Dic7111yescharacteristic
700C4⋊C4C22×Dic7111yescharacteristic
701C4⋊C4C22×Dic7111yescharacteristic
702C4⋊C4C22×Dic7111yescharacteristic
703C4⋊C4C22×Dic7111yescharacteristic
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—21no—
709C22⋊C4—21no—
710C22⋊C4—21no—
711C22⋊C4—21no—
712C22⋊C4—21no—
713C22⋊C4—21no—
714C22⋊C4—21no—
715C22⋊C4—21no—
716C22⋊C4—21no—
717C22⋊C4C22⋊Dic7111yescharacteristic
718C22⋊C4C22⋊Dic7111yescharacteristic
719C22⋊C4C22⋊Dic7111yescharacteristic
720C22⋊C4C22⋊Dic7111yescharacteristic
721C22⋊C4C22⋊Dic7111yescharacteristic
722C22⋊C4C22⋊Dic7111yescharacteristic
723C42—21no—
724C42—21no—
725C42—21no—
726C42—21no—
727C42—21no—
728C42C22×Dic7111yescharacteristic
729C42C22×Dic7111yescharacteristic
730C42C22×Dic7111yescharacteristic
731C42C2×C22⋊D7111yescharacteristic
732C42C2×C22⋊D7111yescharacteristic
733C42C2×C22⋊D7111yescharacteristic
734C42C2×C22⋊D7111yescharacteristic
735C42C2×C22⋊D7111yescharacteristic
736C42C2×C22⋊D7111yescharacteristic
737C42C23×D7111yescharacteristic
738C23—21no—
739C23C2×C22⋊Dic7111yescharacteristic
740C23C2×C22⋊Dic7111yescharacteristic
741C23C2×C22⋊Dic7111yescharacteristic
742Q8—41no—
743Q8—41no—
744Q8—42no—
745Q8—81no—
746D4—22no—
747D4—22no—
748D4—41no—
749D4—41no—
750D4—42no—
751D4—42no—
752D4—81no—
753C2×C4—22no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—81no—
773C2×C4—81no—
774C2×C4—81no—
775C2×C4—81no—
776C2×C4C2×C22⋊Dic7111yescharacteristic
777C2×C4C2×C22⋊Dic7111yescharacteristic
778C2×C4C2×C22⋊Dic7111yescharacteristic
779C2×C4C2×C22⋊Dic7111yescharacteristic
780C2×C4C2×C22⋊Dic7111yescharacteristic
781C2×C4C2×C22⋊Dic7111yescharacteristic
782C2×C4C2×C22⋊Dic7111yescharacteristic
783C2×C4C2×C22⋊Dic7111yescharacteristic
784C2×C4C2×C22⋊Dic7111yescharacteristic
785C2×C4C23×Dic7111yescharacteristic
786C2×C4C22×C22⋊D7111yescharacteristic
787C2×C4C22×C22⋊D7111yescharacteristic
788C8—2841no—
789C8—2841no—
790C8—2841no—
791C8—2841no—
792C8—2841no—
793C8—2841no—
794C8—2841no—
795C8—1422no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22#1798601612yes—
808C22C22×C22⋊Dic7111yescharacteristic
809C4—21no—
810C4—21no—
811C4—21no—
812C4—21no—
813C4—21no—
814C4—21no—
815C4—21no—
816C4—21no—
817C4—21no—
818C4—21no—
819C4—21no—
820C4—21no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—41no—
828C2—22no—
829C2—41no—
830C2—41no—
831C2—81no—
832C2#2259682311yescharacteristic
833C2C2×#1798601611yescharacteristic
834C2#2259688711yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic71
commutatorC2×C4×C71C23×C4
FrattiniC42C23×D71
Fitting, prime radicalC71×#3515C2
socleC22×C71C22×C22⋊C4
cosocleC42×C71C24
hypercenter#3515D71
hypocenterC71#17680
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3515

Complements

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

NH ≅ G/Ntype
1. #22597354C2semidirect
2. #22596991C2semidirect
3. #22586978C2semidirect
4. #22586971C2semidirect
5. #22586971C2semidirect
6. #22586967C2semidirect
7. #22586960C2semidirect
8. #22586960C2semidirect
9. #22586955C2semidirect
10. #22586947C2semidirect
11. #22586942C2semidirect
12. #22586942C2semidirect
13. #22586928C2semidirect
14. C2×#17985741C2semidirect
433. C71#17680semidirect

Maximal subgroups

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

subgroupindex
#225973542
#225969912
#225869782
#225869712
#225869672
#225869602
#225869552
#225869472
#225869422
#225869282
C2×#179857412
C71×#35152
#1768071