Finite Group Databasebeta

← #31965597

Subgroups — #31965597

Order 18176.

942 conjugacy classes of subgroups.

The subgroup lattice has 896 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#22586975C211yesmaximal, characteristic, complemented
4#22586971C211yesmaximal, characteristic, complemented
5#22586971C211yesmaximal, characteristic, complemented
6#22586964C211yesmaximal, characteristic, complemented
7#22586960C211yesmaximal, characteristic, complemented
8#22586960C211yesmaximal, characteristic, complemented
9#22586951C211yesmaximal, characteristic, complemented
10#22586947C211yesmaximal, characteristic, complemented
11#22586938C211yesmaximal, characteristic, complemented
12#22586938C211yesmaximal, characteristic, complemented
13#22586928C211yesmaximal, characteristic, complemented
14C2×#17985739C211yesmaximal, characteristic, complemented
15C71×#3514C211yesmaximal, characteristic
16#17986130—21no—
17#17986071—21no—
18#17986071—21no—
19D4×C71⋊C8—21no—
20#17986060—21no—
21#17986060—21no—
22#17986056C2211yescharacteristic, complemented
23#17986056C2211yescharacteristic, complemented
24#17986056C2211yescharacteristic, complemented
25#17986056C2211yescharacteristic, complemented
26#17986056C2211yescharacteristic, complemented
27#17986056C2211yescharacteristic, complemented
28#17986056C2211yescharacteristic, complemented
29#17986026—21no—
30#17985966—21no—
31C4×#11765849C2211yescharacteristic, complemented
32C4×#11765849C2211yescharacteristic, complemented
33C2×#14556039C2211yescharacteristic, complemented
34C2×#14556039C2211yescharacteristic, complemented
35C2×#14556039C2211yescharacteristic, complemented
36#17985741C2211yescharacteristic, complemented
37#17985741C2211yescharacteristic, complemented
38#17985741C2211yescharacteristic, complemented
39#17985741C2211yescharacteristic, complemented
40#17985739C2211yescharacteristic
41#17985739C2211yescharacteristic
42#17985739C2211yescharacteristic
43#17985739C2211yescharacteristic
44#17985739C2211yescharacteristic, complemented
45#17985739C2211yescharacteristic, complemented
46#17985739C2211yescharacteristic, complemented
47#17985739C2211yescharacteristic, complemented
48#17985739C2211yescharacteristic, complemented
49#17985739C2211yescharacteristic, complemented
50#17985739C2211yescharacteristic, complemented
51#17985739C2211yescharacteristic, complemented
52#559×C71C411yescharacteristic
53#556×C71C411yescharacteristic
54#555×C71—21no—
55#551×C71—21no—
56#551×C71—21no—
57D4×Q8×C71C411yescharacteristic
58#548×C71C411yescharacteristic
59#548×C71C411yescharacteristic
60#546×C71—21no—
61#546×C71C411yescharacteristic
62#546×C71C411yescharacteristic
63D42×C71C411yescharacteristic
64#542×C71—21no—
65#538×C71—21no—
66#538×C71—21no—
67#532×C71C2211yescharacteristic
68#529×C71C2211yescharacteristic
69#529×C71C2211yescharacteristic
70#529×C71C2211yescharacteristic
71C2×#124×C71C2211yescharacteristic
72C2×#124×C71C2211yescharacteristic
73#518×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×C71C2×C411yescharacteristic
108C2×#41×C71C2×C411yescharacteristic
109C2×#41×C71D411yescharacteristic
110C22×Q8×C71C2×C411yescharacteristic
111C22×Q8×C71C2×C411yescharacteristic
112C22×D4×C71—21no—
113C22×D4×C71C2×C411yescharacteristic
114C22×D4×C71C2×C411yescharacteristic
115C4⋊Q8×C71—21no—
116C4⋊Q8×C71C2×C411yescharacteristic
117#127×C71C2×C411yescharacteristic
118#126×C71—21no—
119#126×C71—21no—
120#126×C71—21no—
121#126×C71—21no—
122#126×C71—21no—
123#125×C71C2311yescharacteristic
124#124×C71—21no—
125#124×C71—21no—
126#124×C71—21no—
127#124×C71—21no—
128#124×C71—21no—
129#124×C71—21no—
130#124×C71—21no—
131#124×C71C2×C411yescharacteristic
132#124×C71C2×C411yescharacteristic
133#124×C71C2×C411yescharacteristic
134#124×C71C2×C411yescharacteristic
135#124×C71C2311yescharacteristic
136#124×C71C2311yescharacteristic
137#124×C71C2311yescharacteristic
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×C71C2×C411yescharacteristic
151C22⋊Q8×C71C2×C411yescharacteristic
152C22⋊Q8×C71C2×C411yescharacteristic
153#121×C71—21no—
154#121×C71—21no—
155#121×C71—21no—
156#121×C71—21no—
157#121×C71—21no—
158#121×C71—21no—
159#121×C71—21no—
160#121×C71C2×C411yescharacteristic
161#121×C71C2×C411yescharacteristic
162#121×C71C2×C411yescharacteristic
163#120×C71—21no—
164#120×C71—21no—
165#120×C71—21no—
166#120×C71—21no—
167C4×Q8×C71C2×C411yescharacteristic
168C4×Q8×C71C2×C411yescharacteristic
169C4×Q8×C71C2×C411yescharacteristic
170C4×Q8×C71C2×C411yescharacteristic
171C4×Q8×C71D411yescharacteristic
172C4×D4×C71—21no—
173C4×D4×C71—21no—
174C4×D4×C71—21no—
175C4×D4×C71—21no—
176C4×D4×C71—21no—
177C4×D4×C71—21no—
178C4×D4×C71—21no—
179C4×D4×C71—21no—
180C4×D4×C71—21no—
181C4×D4×C71C2×C411yescharacteristic
182C4×D4×C71C2×C411yescharacteristic
183C4×D4×C71C2×C411yescharacteristic
184C4×D4×C71C2×C411yescharacteristic
185C4×D4×C71C2×C411yescharacteristic
186C4×D4×C71C2×C411yescharacteristic
187C4×D4×C71D411yescharacteristic
188C4×D4×C71D411yescharacteristic
189C4×D4×C71D411yescharacteristic
190#117×C71—21no—
191#117×C71—21no—
192#117×C71—21no—
193#117×C71—21no—
194#117×C71D411yescharacteristic
195#117×C71D411yescharacteristic
196#117×C71D411yescharacteristic
197C2×C22⋊C4×C71—21no—
198C2×C22⋊C4×C71—21no—
199C2×C22⋊C4×C71—21no—
200C2×C22⋊C4×C71—21no—
201C2×C22⋊C4×C71—21no—
202C2×C22⋊C4×C71—21no—
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—
219C24×C71—21no—
220C24×C71—21no—
221#41×C71—42no—
222#41×C71—81no—
223#41×C71—81no—
224C2×Q8×C71—21no—
225C2×Q8×C71—21no—
226C2×Q8×C71—81no—
227C2×Q8×C71—81no—
228C2×Q8×C71C22⋊C411yescharacteristic
229C2×Q8×C71C22×C411yescharacteristic
230C2×Q8×C71C22×C411yescharacteristic
231C2×Q8×C71C22×C411yescharacteristic
232C2×D4×C71—21no—
233C2×D4×C71—21no—
234C2×D4×C71—21no—
235C2×D4×C71—21no—
236C2×D4×C71—21no—
237C2×D4×C71—21no—
238C2×D4×C71—21no—
239C2×D4×C71—21no—
240C2×D4×C71—21no—
241C2×D4×C71—44no—
242C2×D4×C71—81no—
243C2×D4×C71—81no—
244C2×D4×C71C22⋊C411yescharacteristic
245C2×D4×C71C22⋊C411yescharacteristic
246C2×D4×C71C22⋊C411yescharacteristic
247C2×D4×C71C22×C411yescharacteristic
248C2×D4×C71C22×C411yescharacteristic
249C2×D4×C71C22×C411yescharacteristic
250C22×C4×C71—21no—
251C22×C4×C71—21no—
252C22×C4×C71—21no—
253C22×C4×C71—21no—
254C22×C4×C71—21no—
255C22×C4×C71—21no—
256C22×C4×C71—21no—
257C22×C4×C71C22×C411yescharacteristic
258C22×C4×C71C22×C411yescharacteristic
259C22×C4×C71C22×C411yescharacteristic
260C22×C4×C71C2×D411yescharacteristic
261C22×C4×C71C2×D411yescharacteristic
262C22×C4×C71C2×D411yescharacteristic
263C22×C4×C71C2×D411yescharacteristic
264C22×C4×C71C2×D411yescharacteristic
265C22×C4×C71C2×D411yescharacteristic
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×C71—21no—
275C4⋊C4×C71—21no—
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
284C22⋊C4×C71—21no—
285C22⋊C4×C71—21no—
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×C71—21no—
300C22⋊C4×C71—21no—
301C22⋊C4×C71—21no—
302C22⋊C4×C71—21no—
303C22⋊C4×C71—21no—
304C22⋊C4×C71—21no—
305C22⋊C4×C71—21no—
306C22⋊C4×C71—21no—
307C22⋊C4×C71C22⋊C411yescharacteristic
308C22⋊C4×C71C22⋊C411yescharacteristic
309C22⋊C4×C71C22⋊C411yescharacteristic
310C22⋊C4×C71C22⋊C411yescharacteristic
311C22⋊C4×C71C22⋊C411yescharacteristic
312C22⋊C4×C71C22⋊C411yescharacteristic
313C42×C71—21no—
314C42×C71—21no—
315C42×C71—21no—
316C42×C71C22×C411yescharacteristic
317C42×C71C22×C411yescharacteristic
318C42×C71C22×C411yescharacteristic
319C42×C71C2×D411yescharacteristic
320C42×C71C2×D411yescharacteristic
321C42×C71C2×D411yescharacteristic
322C42×C71C2×D411yescharacteristic
323C42×C71C2×D411yescharacteristic
324C42×C71C2×D411yescharacteristic
325C42×C71C2411yescharacteristic
326C23×C71—21no—
327C23×C71—21no—
328C23×C71—21no—
329C23×C71—42no—
330C23×C71—42no—
331C23×C71—81no—
332C23×C71—81no—
333C23×C71—81no—
334C23×C71—81no—
335C23×C71C2×C22⋊C411yescharacteristic
336C23×C71C2×C22⋊C411yescharacteristic
337C23×C71C2×C22⋊C411yescharacteristic
338Q8×C71—41no—
339Q8×C71—41no—
340Q8×C71—41no—
341Q8×C71—41no—
342Q8×C71—81no—
343Q8×C71—81no—
344D4×C71—22no—
345D4×C71—22no—
346D4×C71—41no—
347D4×C71—41no—
348D4×C71—41no—
349D4×C71—41no—
350D4×C71—42no—
351D4×C71—42no—
352D4×C71—42no—
353D4×C71—81no—
354D4×C71—81no—
355D4×C71—81no—
356D4×C71—81no—
357D4×C71—81no—
358D4×C71—81no—
359C2×C4×C71—22no—
360C2×C4×C71—21no—
361C2×C4×C71—21no—
362C2×C4×C71—21no—
363C2×C4×C71—21no—
364C2×C4×C71—21no—
365C2×C4×C71—41no—
366C2×C4×C71—41no—
367C2×C4×C71—41no—
368C2×C4×C71—41no—
369C2×C4×C71—41no—
370C2×C4×C71—41no—
371C2×C4×C71—41no—
372C2×C4×C71—41no—
373C2×C4×C71—42no—
374C2×C4×C71—81no—
375C2×C4×C71—81no—
376C2×C4×C71—81no—
377C2×C4×C71—81no—
378C2×C4×C71—81no—
379C2×C4×C71—81no—
380C2×C4×C71C2×C22⋊C411yescharacteristic
381C2×C4×C71C2×C22⋊C411yescharacteristic
382C2×C4×C71C2×C22⋊C411yescharacteristic
383C2×C4×C71C2×C22⋊C411yescharacteristic
384C2×C4×C71C2×C22⋊C411yescharacteristic
385C2×C4×C71C2×C22⋊C411yescharacteristic
386C2×C4×C71C2×C22⋊C411yescharacteristic
387C2×C4×C71C2×C22⋊C411yescharacteristic
388C2×C4×C71C2×C22⋊C411yescharacteristic
389C2×C4×C71C23×C411yescharacteristic
390C2×C4×C71C22×D411yescharacteristic
391C2×C4×C71C22×D411yescharacteristic
392C71⋊C8—22no—
393C71⋊C8—41no—
394C71⋊C8—41no—
395C71⋊C8—41no—
396C71⋊C8—41no—
397C71⋊C8—41no—
398C71⋊C8—41no—
399C71⋊C8—41no—
400C22×C71—21no—
401C22×C71—21no—
402C22×C71—21no—
403C22×C71—21no—
404C22×C71—21no—
405C22×C71—21no—
406C22×C71—21no—
407C22×C71—21no—
408C22×C71—41no—
409C22×C71—41no—
410C22×C71—41no—
411C22×C71—41no—
412C22×C71—41no—
413C22×C71—41no—
414C22×C71—41no—
415C22×C71—41no—
416C22×C71—41no—
417C22×C71—162no—
418C22×C71—162no—
419C22×C71#42112yes—
420C22×C71C22×C22⋊C411yescharacteristic
421C4×C71—21no—
422C4×C71—21no—
423C4×C71—21no—
424C4×C71—21no—
425C4×C71—21no—
426C4×C71—21no—
427C4×C71—21no—
428C4×C71—21no—
429C4×C71—21no—
430C4×C71—21no—
431C4×C71—21no—
432C4×C71—21no—
433C4×C71—41no—
434C4×C71—41no—
435C4×C71—41no—
436C4×C71—41no—
437C4×C71—41no—
438#17679—711nomaximal, Sylow
439C2×C71—22no—
440C2×C71—41no—
441C2×C71—41no—
442C2×C71—81no—
443C2×C71—81no—
444C2×C71—81no—
445C2×C71#288811yescharacteristic
446C2×C71C2×#42111yescharacteristic
447C2×C71#290111yescharacteristic
448#3514D7111yescharacteristic
449#2970—711no—
450#2923—711no—
451#1536—711no—
452#1535—711no—
453#1535—711no—
454#1533—711no—
455#1532—711no—
456#1532—711no—
457#1530—711no—
458#1529—711no—
459#1527—711no—
460#1527—711no—
461#1524—711no—
462C2×#329—711no—
463C71#1767911yescharacteristic, complemented, Sylow
464#559Dic7111yescharacteristic
465#556Dic7111yescharacteristic
466#555—21no—
467#551—21no—
468#551—21no—
469D4×Q8Dic7111yescharacteristic
470#548Dic7111yescharacteristic
471#548Dic7111yescharacteristic
472#546—21no—
473#546Dic7111yescharacteristic
474#546Dic7111yescharacteristic
475D42Dic7111yescharacteristic
476#542—21no—
477#538—21no—
478#538—21no—
479#532C2×D7111yescharacteristic
480#529C2×D7111yescharacteristic
481#529C2×D7111yescharacteristic
482#529C2×D7111yescharacteristic
483C2×#124C2×D7111yescharacteristic
484C2×#124C2×D7111yescharacteristic
485#518—21no—
486C4×#41C2×D7111yescharacteristic
487#446—1421no—
488#435—1421no—
489#435—1421no—
490C8×D4—1421no—
491#433—1421no—
492#433—1421no—
493#432—711no—
494#432—711no—
495#432—711no—
496#432—711no—
497#432—711no—
498#432—711no—
499#432—711no—
500#424—1421no—
501#408—1421no—
502C4×M16—711no—
503C4×M16—711no—
504C2×#97—711no—
505C2×#97—711no—
506C2×#97—711no—
507#330—711no—
508#330—711no—
509#330—711no—
510#330—711no—
511#329—711no—
512#329—711no—
513#329—711no—
514#329—711no—
515#329—711no—
516#329—711no—
517#329—711no—
518#329—711no—
519#329—711no—
520#329—711no—
521#329—711no—
522#329—711no—
523C2×#41C2×Dic7111yescharacteristic
524C2×#41C2×Dic7111yescharacteristic
525C2×#41C22⋊D7111yescharacteristic
526C22×Q8C2×Dic7111yescharacteristic
527C22×Q8C2×Dic7111yescharacteristic
528C22×D4—21no—
529C22×D4C2×Dic7111yescharacteristic
530C22×D4C2×Dic7111yescharacteristic
531C2×M16—1421no—
532C2×M16—1421no—
533C22×C8—1421no—
534C22×C8—1421no—
535C22×C8—1421no—
536C4⋊Q8—21no—
537C4⋊Q8C2×Dic7111yescharacteristic
538#127C2×Dic7111yescharacteristic
539#126—21no—
540#126—21no—
541#126—21no—
542#126—21no—
543#126—21no—
544#125C22×D7111yescharacteristic
545#124—21no—
546#124—21no—
547#124—21no—
548#124—21no—
549#124—21no—
550#124—21no—
551#124—21no—
552#124C2×Dic7111yescharacteristic
553#124C2×Dic7111yescharacteristic
554#124C2×Dic7111yescharacteristic
555#124C2×Dic7111yescharacteristic
556#124C22×D7111yescharacteristic
557#124C22×D7111yescharacteristic
558#124C22×D7111yescharacteristic
559#123—21no—
560#123—21no—
561#123—21no—
562#123—21no—
563#123—21no—
564#123—21no—
565#123—21no—
566C22⋊Q8—21no—
567C22⋊Q8—21no—
568C22⋊Q8—21no—
569C22⋊Q8—21no—
570C22⋊Q8—21no—
571C22⋊Q8C2×Dic7111yescharacteristic
572C22⋊Q8C2×Dic7111yescharacteristic
573C22⋊Q8C2×Dic7111yescharacteristic
574#121—21no—
575#121—21no—
576#121—21no—
577#121—21no—
578#121—21no—
579#121—21no—
580#121—21no—
581#121C2×Dic7111yescharacteristic
582#121C2×Dic7111yescharacteristic
583#121C2×Dic7111yescharacteristic
584#120—21no—
585#120—21no—
586#120—21no—
587#120—21no—
588C4×Q8C2×Dic7111yescharacteristic
589C4×Q8C2×Dic7111yescharacteristic
590C4×Q8C2×Dic7111yescharacteristic
591C4×Q8C2×Dic7111yescharacteristic
592C4×Q8C22⋊D7111yescharacteristic
593C4×D4—21no—
594C4×D4—21no—
595C4×D4—21no—
596C4×D4—21no—
597C4×D4—21no—
598C4×D4—21no—
599C4×D4—21no—
600C4×D4—21no—
601C4×D4—21no—
602C4×D4C2×Dic7111yescharacteristic
603C4×D4C2×Dic7111yescharacteristic
604C4×D4C2×Dic7111yescharacteristic
605C4×D4C2×Dic7111yescharacteristic
606C4×D4C2×Dic7111yescharacteristic
607C4×D4C2×Dic7111yescharacteristic
608C4×D4C22⋊D7111yescharacteristic
609C4×D4C22⋊D7111yescharacteristic
610C4×D4C22⋊D7111yescharacteristic
611#117—21no—
612#117—21no—
613#117—21no—
614#117—21no—
615#117C22⋊D7111yescharacteristic
616#117C22⋊D7111yescharacteristic
617#117C22⋊D7111yescharacteristic
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C42C22×D7111yescharacteristic
625C2×C42C22×D7111yescharacteristic
626C2×C42C22×D7111yescharacteristic
627C4⋊C8—1421no—
628C4⋊C8—1421no—
629C4⋊C8—1421no—
630C4⋊C8—1421no—
631C4⋊C8—1421no—
632C4⋊C8—1421no—
633C4⋊C8—1421no—
634C22⋊C8—1421no—
635C22⋊C8—1421no—
636C22⋊C8—1421no—
637C22⋊C8—1421no—
638C22⋊C8—1421no—
639C22⋊C8—1421no—
640C22⋊C8—1421no—
641#97—711no—
642#97—711no—
643#97—711no—
644#97—711no—
645#97—711no—
646#97—711no—
647#97—711no—
648#97—711no—
649#97—1421no—
650#97—1421no—
651#97—1421no—
652C4×C8—1421no—
653C4×C8—1421no—
654C24—21no—
655C24—21no—
656#41—42no—
657#41—81no—
658#41—81no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—81no—
662C2×Q8—81no—
663C2×Q8C22⋊Dic7111yescharacteristic
664C2×Q8C22×Dic7111yescharacteristic
665C2×Q8C22×Dic7111yescharacteristic
666C2×Q8C22×Dic7111yescharacteristic
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—44no—
677C2×D4—81no—
678C2×D4—81no—
679C2×D4C22⋊Dic7111yescharacteristic
680C2×D4C22⋊Dic7111yescharacteristic
681C2×D4C22⋊Dic7111yescharacteristic
682C2×D4C22×Dic7111yescharacteristic
683C2×D4C22×Dic7111yescharacteristic
684C2×D4C22×Dic7111yescharacteristic
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4C22×Dic7111yescharacteristic
693C22×C4C22×Dic7111yescharacteristic
694C22×C4C22×Dic7111yescharacteristic
695C22×C4C2×C22⋊D7111yescharacteristic
696C22×C4C2×C22⋊D7111yescharacteristic
697C22×C4C2×C22⋊D7111yescharacteristic
698C22×C4C2×C22⋊D7111yescharacteristic
699C22×C4C2×C22⋊D7111yescharacteristic
700C22×C4C2×C22⋊D7111yescharacteristic
701M16—2842no—
702M16—2842no—
703C2×C8—2842no—
704C2×C8—2842no—
705C2×C8—2842no—
706C2×C8—1421no—
707C2×C8—1421no—
708C2×C8—1421no—
709C2×C8—1421no—
710C2×C8—1421no—
711C2×C8—1421no—
712C2×C8—1421no—
713C2×C8—1421no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4C22⋊Dic7111yescharacteristic
725C4⋊C4C22⋊Dic7111yescharacteristic
726C4⋊C4C22⋊Dic7111yescharacteristic
727C4⋊C4C22⋊Dic7111yescharacteristic
728C4⋊C4C22⋊Dic7111yescharacteristic
729C4⋊C4C22⋊Dic7111yescharacteristic
730C4⋊C4C22×Dic7111yescharacteristic
731C4⋊C4C22×Dic7111yescharacteristic
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4C22⋊Dic7111yescharacteristic
756C22⋊C4C22⋊Dic7111yescharacteristic
757C22⋊C4C22⋊Dic7111yescharacteristic
758C22⋊C4C22⋊Dic7111yescharacteristic
759C22⋊C4C22⋊Dic7111yescharacteristic
760C22⋊C4C22⋊Dic7111yescharacteristic
761C42—21no—
762C42—21no—
763C42—21no—
764C42C22×Dic7111yescharacteristic
765C42C22×Dic7111yescharacteristic
766C42C22×Dic7111yescharacteristic
767C42C2×C22⋊D7111yescharacteristic
768C42C2×C22⋊D7111yescharacteristic
769C42C2×C22⋊D7111yescharacteristic
770C42C2×C22⋊D7111yescharacteristic
771C42C2×C22⋊D7111yescharacteristic
772C42C2×C22⋊D7111yescharacteristic
773C42C23×D7111yescharacteristic
774C23—21no—
775C23—21no—
776C23—21no—
777C23—42no—
778C23—42no—
779C23—81no—
780C23—81no—
781C23—81no—
782C23—81no—
783C23C2×C22⋊Dic7111yescharacteristic
784C23C2×C22⋊Dic7111yescharacteristic
785C23C2×C22⋊Dic7111yescharacteristic
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8—41no—
790Q8—81no—
791Q8—81no—
792D4—22no—
793D4—22no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—41no—
798D4—42no—
799D4—42no—
800D4—42no—
801D4—81no—
802D4—81no—
803D4—81no—
804D4—81no—
805D4—81no—
806D4—81no—
807C2×C4—22no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—42no—
822C2×C4—81no—
823C2×C4—81no—
824C2×C4—81no—
825C2×C4—81no—
826C2×C4—81no—
827C2×C4—81no—
828C2×C4C2×C22⋊Dic7111yescharacteristic
829C2×C4C2×C22⋊Dic7111yescharacteristic
830C2×C4C2×C22⋊Dic7111yescharacteristic
831C2×C4C2×C22⋊Dic7111yescharacteristic
832C2×C4C2×C22⋊Dic7111yescharacteristic
833C2×C4C2×C22⋊Dic7111yescharacteristic
834C2×C4C2×C22⋊Dic7111yescharacteristic
835C2×C4C2×C22⋊Dic7111yescharacteristic
836C2×C4C2×C22⋊Dic7111yescharacteristic
837C2×C4C23×Dic7111yescharacteristic
838C2×C4C22×C22⋊D7111yescharacteristic
839C2×C4C22×C22⋊D7111yescharacteristic
840C8—2841no—
841C8—2841no—
842C8—2841no—
843C8—2841no—
844C8—2841no—
845C8—2841no—
846C8—2841no—
847C8—1422no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—162no—
866C22—162no—
867C22#1798601612yes—
868C22C22×C22⋊Dic7111yescharacteristic
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—21no—
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—21no—
880C4—21no—
881C4—41no—
882C4—41no—
883C4—41no—
884C4—41no—
885C4—41no—
886C2—22no—
887C2—41no—
888C2—41no—
889C2—81no—
890C2—81no—
891C2—81no—
892C2#2259681911yescharacteristic
893C2C2×#1798601611yescharacteristic
894C2#2259688711yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic71
commutatorC2×C4×C71C23×C4
FrattiniC42C23×D71
Fitting, prime radicalC71×#3514C2
socleC22×C71C22×C22⋊C4
cosocleC42×C71C24
hypercenter#3514D71
hypocenterC71#17679
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3514

Complements

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

NH ≅ G/Ntype
1. #22597354C2semidirect
2. #22596991C2semidirect
3. #22586975C2semidirect
4. #22586971C2semidirect
5. #22586971C2semidirect
6. #22586964C2semidirect
7. #22586960C2semidirect
8. #22586960C2semidirect
9. #22586951C2semidirect
10. #22586947C2semidirect
11. #22586938C2semidirect
12. #22586938C2semidirect
13. #22586928C2semidirect
14. C2×#17985739C2semidirect
22. #17986056C22semidirect
23. #17986056C22semidirect
24. #17986056C22semidirect
25. #17986056C22semidirect
26. #17986056C22semidirect
27. #17986056C22semidirect
28. #17986056C22semidirect
31. C4×#11765849C22semidirect
32. C4×#11765849C22semidirect
33. C2×#14556039C22semidirect
34. C2×#14556039C22semidirect
35. C2×#14556039C22semidirect
36. #17985741C22semidirect
37. #17985741C22semidirect
38. #17985741C22semidirect
39. #17985741C22semidirect
44. #17985739C22semidirect
45. #17985739C22semidirect
46. #17985739C22semidirect
47. #17985739C22semidirect
48. #17985739C22semidirect
49. #17985739C22semidirect
50. #17985739C22semidirect
51. #17985739C22semidirect
463. C71#17679semidirect

Maximal subgroups

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

subgroupindex
#225973542
#225969912
#225869752
#225869712
#225869642
#225869602
#225869512
#225869472
#225869382
#225869282
C2×#179857392
C71×#35142
#1767971