Finite Group Databasebeta

← #26184438

Subgroups — #26184438

Order 12032.

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#20252402C211yesmaximal, characteristic, complemented
2#20252039C211yesmaximal, characteristic, complemented
3#20242026C211yesmaximal, characteristic, complemented
4#20242019C211yesmaximal, characteristic, complemented
5#20242019C211yesmaximal, characteristic, complemented
6#20242015C211yesmaximal, characteristic, complemented
7#20242008C211yesmaximal, characteristic, complemented
8#20242008C211yesmaximal, characteristic, complemented
9#20242003C211yesmaximal, characteristic, complemented
10#20241995C211yesmaximal, characteristic, complemented
11#20241990C211yesmaximal, characteristic, complemented
12#20241990C211yesmaximal, characteristic, complemented
13#20241976C211yesmaximal, characteristic, complemented
14C2×#15688865C211yesmaximal, characteristic, complemented
15C47×#3515C211yesmaximal, characteristic
16#15689254—21no—
17#15689195—21no—
18#15689195—21no—
19D4×C47⋊C8—21no—
20#15689184—21no—
21#15689184—21no—
22#15689180C2211yescharacteristic
23#15689180C2211yescharacteristic
24#15689180C2211yescharacteristic
25#15689180C2211yescharacteristic
26#15689180C2211yescharacteristic
27#15689180C2211yescharacteristic
28#15689180C2211yescharacteristic
29#15689150—21no—
30#15689090—21no—
31C4×#10625329C2211yescharacteristic
32C4×#10625329C2211yescharacteristic
33C2×#13093935C2211yescharacteristic
34C2×#13093935C2211yescharacteristic
35C2×#13093935C2211yescharacteristic
36#15688865C2211yescharacteristic
37#15688865C2211yescharacteristic
38#15688865C2211yescharacteristic
39#15688865C2211yescharacteristic
40#15688865C2211yescharacteristic
41#15688865C2211yescharacteristic
42#15688865C2211yescharacteristic
43#15688865C2211yescharacteristic
44#15688865C2211yescharacteristic
45#15688865C2211yescharacteristic
46#15688865C2211yescharacteristic
47#15688865C2211yescharacteristic
48#15688863C2211yescharacteristic
49#15688863C2211yescharacteristic
50#15688863C2211yescharacteristic
51#15688863C2211yescharacteristic
52C47×#557C411yescharacteristic
53C47×#554C411yescharacteristic
54C47×#554C411yescharacteristic
55C47×#553C411yescharacteristic
56C47×#553C411yescharacteristic
57C47×#552—21no—
58C47×#552—21no—
59C47×#552—21no—
60C47×#552C411yescharacteristic
61C47×#552C411yescharacteristic
62C47×#547—21no—
63C47×#547C411yescharacteristic
64C47×#541—21no—
65C47×#539—21no—
66C47×#539—21no—
67C47×#533C2211yescharacteristic
68C47×#529C2211yescharacteristic
69C47×#529C2211yescharacteristic
70C47×#529C2211yescharacteristic
71C2×#125×C47C2211yescharacteristic
72C2×#125×C47C2211yescharacteristic
73C47×#520—21no—
74C4×#41×C47C2211yescharacteristic
75C2×#10625329—21no—
76C2×#10625329—21no—
77C22×C47⋊C8—21no—
78C22×C47⋊C8—21no—
79C22×C47⋊C8—21no—
80C4⋊(C47⋊C8)—21no—
81C4⋊(C47⋊C8)—21no—
82C4⋊(C47⋊C8)—21no—
83C4⋊(C47⋊C8)—21no—
84C4⋊(C47⋊C8)—21no—
85C4⋊(C47⋊C8)—21no—
86C4⋊(C47⋊C8)—21no—
87C22⋊(C47⋊C8)—21no—
88C22⋊(C47⋊C8)—21no—
89C22⋊(C47⋊C8)—21no—
90C22⋊(C47⋊C8)—21no—
91C22⋊(C47⋊C8)—21no—
92C22⋊(C47⋊C8)—21no—
93C22⋊(C47⋊C8)—21no—
94#13093935—21no—
95#13093935—21no—
96#13093935—21no—
97#13093935C2311yescharacteristic
98#13093935C2311yescharacteristic
99#13093935C2311yescharacteristic
100#13093935C2311yescharacteristic
101#13093935C2311yescharacteristic
102#13093935C2311yescharacteristic
103#13093935C2311yescharacteristic
104#13093935C2311yescharacteristic
105C4×C47⋊C8—21no—
106C4×C47⋊C8—21no—
107C2×#41×C47—21no—
108C2×#41×C47D411yescharacteristic
109C4⋊Q8×C47—21no—
110C4⋊Q8×C47C2×C411yescharacteristic
111C4⋊Q8×C47C2×C411yescharacteristic
112#126×C47—21no—
113#126×C47—21no—
114#126×C47—21no—
115#126×C47—21no—
116#126×C47—21no—
117#126×C47—21no—
118#126×C47—21no—
119#125×C47—21no—
120#125×C47—21no—
121#125×C47—21no—
122#125×C47—21no—
123#125×C47—21no—
124#125×C47—21no—
125#125×C47—21no—
126#125×C47—21no—
127#125×C47—21no—
128#125×C47C2×C411yescharacteristic
129#125×C47C2×C411yescharacteristic
130#125×C47C2×C411yescharacteristic
131#125×C47C2×C411yescharacteristic
132#125×C47C2311yescharacteristic
133#125×C47C2311yescharacteristic
134#125×C47C2311yescharacteristic
135#124×C47C2311yescharacteristic
136#123×C47—21no—
137#123×C47—21no—
138#123×C47—21no—
139#123×C47—21no—
140#123×C47—21no—
141#123×C47—21no—
142#123×C47—21no—
143#123×C47—21no—
144#123×C47—21no—
145C22⋊Q8×C47—21no—
146C22⋊Q8×C47—21no—
147C22⋊Q8×C47—21no—
148C22⋊Q8×C47—21no—
149C22⋊Q8×C47—21no—
150C22⋊Q8×C47—21no—
151C22⋊Q8×C47—21no—
152C22⋊Q8×C47—21no—
153C22⋊Q8×C47C2×C411yescharacteristic
154C22⋊Q8×C47C2×C411yescharacteristic
155C22⋊Q8×C47C2×C411yescharacteristic
156#121×C47—21no—
157#121×C47—21no—
158#121×C47C2×C411yescharacteristic
159#121×C47C2×C411yescharacteristic
160#121×C47C2×C411yescharacteristic
161C4×Q8×C47—21no—
162C4×Q8×C47—21no—
163C4×Q8×C47—21no—
164C4×Q8×C47C2×C411yescharacteristic
165C4×Q8×C47C2×C411yescharacteristic
166C4×Q8×C47C2×C411yescharacteristic
167C4×Q8×C47C2×C411yescharacteristic
168C4×Q8×C47D411yescharacteristic
169C4×D4×C47—21no—
170C4×D4×C47—21no—
171C4×D4×C47—21no—
172C4×D4×C47—21no—
173C4×D4×C47—21no—
174C4×D4×C47—21no—
175C4×D4×C47C2×C411yescharacteristic
176C4×D4×C47C2×C411yescharacteristic
177C4×D4×C47C2×C411yescharacteristic
178C4×D4×C47C2×C411yescharacteristic
179C4×D4×C47C2×C411yescharacteristic
180C4×D4×C47C2×C411yescharacteristic
181C4×D4×C47D411yescharacteristic
182C4×D4×C47D411yescharacteristic
183C4×D4×C47D411yescharacteristic
184#117×C47—21no—
185#117×C47—21no—
186#117×C47—21no—
187#117×C47—21no—
188#117×C47—21no—
189#117×C47C2×C411yescharacteristic
190#117×C47C2×C411yescharacteristic
191#117×C47D411yescharacteristic
192#117×C47D411yescharacteristic
193#117×C47D411yescharacteristic
194C2×C4⋊C4×C47—21no—
195C2×C4⋊C4×C47—21no—
196C2×C4⋊C4×C47—21no—
197C2×C4⋊C4×C47—21no—
198C2×C4⋊C4×C47—21no—
199C2×C4⋊C4×C47C2×C411yescharacteristic
200C2×C4⋊C4×C47C2×C411yescharacteristic
201C2×C4⋊C4×C47C2×C411yescharacteristic
202C2×C4⋊C4×C47C2×C411yescharacteristic
203C2×C42×C47C2311yescharacteristic
204C2×C42×C47C2311yescharacteristic
205C2×C42×C47C2311yescharacteristic
206#41×C47—42no—
207#41×C47—44no—
208C2×Q8×C47—21no—
209C2×Q8×C47—21no—
210C2×Q8×C47C22⋊C411yescharacteristic
211C2×Q8×C47C22×C411yescharacteristic
212C2×D4×C47—21no—
213C2×D4×C47—21no—
214C2×D4×C47—21no—
215C2×D4×C47C22⋊C411yescharacteristic
216C2×D4×C47C22⋊C411yescharacteristic
217C2×D4×C47C22⋊C411yescharacteristic
218C2×D4×C47C22×C411yescharacteristic
219C22×C4×C47—21no—
220C22×C4×C47—21no—
221C22×C4×C47—21no—
222C22×C4×C47—21no—
223C22×C4×C47—21no—
224C22×C4×C47—21no—
225C22×C4×C47—21no—
226C22×C4×C47C22×C411yescharacteristic
227C22×C4×C47C22×C411yescharacteristic
228C22×C4×C47C22×C411yescharacteristic
229C22×C4×C47C2×D411yescharacteristic
230C22×C4×C47C2×D411yescharacteristic
231C22×C4×C47C2×D411yescharacteristic
232C22×C4×C47C2×D411yescharacteristic
233C22×C4×C47C2×D411yescharacteristic
234C22×C4×C47C2×D411yescharacteristic
235C4⋊C4×C47—21no—
236C4⋊C4×C47—21no—
237C4⋊C4×C47—21no—
238C4⋊C4×C47—21no—
239C4⋊C4×C47—21no—
240C4⋊C4×C47—21no—
241C4⋊C4×C47—21no—
242C4⋊C4×C47—21no—
243C4⋊C4×C47—21no—
244C4⋊C4×C47—21no—
245C4⋊C4×C47—21no—
246C4⋊C4×C47—21no—
247C4⋊C4×C47—21no—
248C4⋊C4×C47—21no—
249C4⋊C4×C47—21no—
250C4⋊C4×C47—21no—
251C4⋊C4×C47—21no—
252C4⋊C4×C47—21no—
253C4⋊C4×C47—21no—
254C4⋊C4×C47—21no—
255C4⋊C4×C47—21no—
256C4⋊C4×C47—21no—
257C4⋊C4×C47—21no—
258C4⋊C4×C47—21no—
259C4⋊C4×C47—21no—
260C4⋊C4×C47—21no—
261C4⋊C4×C47C22⋊C411yescharacteristic
262C4⋊C4×C47C22⋊C411yescharacteristic
263C4⋊C4×C47C22⋊C411yescharacteristic
264C4⋊C4×C47C22⋊C411yescharacteristic
265C4⋊C4×C47C22⋊C411yescharacteristic
266C4⋊C4×C47C22⋊C411yescharacteristic
267C4⋊C4×C47C22×C411yescharacteristic
268C4⋊C4×C47C22×C411yescharacteristic
269C4⋊C4×C47C22×C411yescharacteristic
270C4⋊C4×C47C22×C411yescharacteristic
271C4⋊C4×C47C22×C411yescharacteristic
272C4⋊C4×C47C22×C411yescharacteristic
273C22⋊C4×C47—21no—
274C22⋊C4×C47—21no—
275C22⋊C4×C47—21no—
276C22⋊C4×C47—21no—
277C22⋊C4×C47—21no—
278C22⋊C4×C47—21no—
279C22⋊C4×C47—21no—
280C22⋊C4×C47—21no—
281C22⋊C4×C47—21no—
282C22⋊C4×C47—21no—
283C22⋊C4×C47—21no—
284C22⋊C4×C47—21no—
285C22⋊C4×C47—21no—
286C22⋊C4×C47C22⋊C411yescharacteristic
287C22⋊C4×C47C22⋊C411yescharacteristic
288C22⋊C4×C47C22⋊C411yescharacteristic
289C22⋊C4×C47C22⋊C411yescharacteristic
290C22⋊C4×C47C22⋊C411yescharacteristic
291C22⋊C4×C47C22⋊C411yescharacteristic
292C42×C47—21no—
293C42×C47—21no—
294C42×C47—21no—
295C42×C47—21no—
296C42×C47—21no—
297C42×C47C22×C411yescharacteristic
298C42×C47C22×C411yescharacteristic
299C42×C47C22×C411yescharacteristic
300C42×C47C2×D411yescharacteristic
301C42×C47C2×D411yescharacteristic
302C42×C47C2×D411yescharacteristic
303C42×C47C2×D411yescharacteristic
304C42×C47C2×D411yescharacteristic
305C42×C47C2×D411yescharacteristic
306C42×C47C2411yescharacteristic
307#10625329—42no—
308#10625329—42no—
309C2×C47⋊C8—21no—
310C2×C47⋊C8—21no—
311C2×C47⋊C8—21no—
312C2×C47⋊C8—21no—
313C2×C47⋊C8—21no—
314C2×C47⋊C8—21no—
315C2×C47⋊C8—21no—
316C2×C47⋊C8—21no—
317C2×C47⋊C8—42no—
318C2×C47⋊C8—42no—
319C2×C47⋊C8—42no—
320C23×C47—21no—
321C23×C47C2×C22⋊C411yescharacteristic
322C23×C47C2×C22⋊C411yescharacteristic
323C23×C47C2×C22⋊C411yescharacteristic
324Q8×C47—41no—
325Q8×C47—41no—
326Q8×C47—42no—
327Q8×C47—81no—
328D4×C47—22no—
329D4×C47—22no—
330D4×C47—41no—
331D4×C47—41no—
332D4×C47—42no—
333D4×C47—42no—
334D4×C47—81no—
335C2×C4×C47—22no—
336C2×C4×C47—21no—
337C2×C4×C47—21no—
338C2×C4×C47—21no—
339C2×C4×C47—21no—
340C2×C4×C47—21no—
341C2×C4×C47—21no—
342C2×C4×C47—21no—
343C2×C4×C47—41no—
344C2×C4×C47—41no—
345C2×C4×C47—41no—
346C2×C4×C47—41no—
347C2×C4×C47—41no—
348C2×C4×C47—41no—
349C2×C4×C47—41no—
350C2×C4×C47—41no—
351C2×C4×C47—42no—
352C2×C4×C47—42no—
353C2×C4×C47—42no—
354C2×C4×C47—81no—
355C2×C4×C47—81no—
356C2×C4×C47—81no—
357C2×C4×C47—81no—
358C2×C4×C47C2×C22⋊C411yescharacteristic
359C2×C4×C47C2×C22⋊C411yescharacteristic
360C2×C4×C47C2×C22⋊C411yescharacteristic
361C2×C4×C47C2×C22⋊C411yescharacteristic
362C2×C4×C47C2×C22⋊C411yescharacteristic
363C2×C4×C47C2×C22⋊C411yescharacteristic
364C2×C4×C47C2×C22⋊C411yescharacteristic
365C2×C4×C47C2×C22⋊C411yescharacteristic
366C2×C4×C47C2×C22⋊C411yescharacteristic
367C2×C4×C47C23×C411yescharacteristic
368C2×C4×C47C22×D411yescharacteristic
369C2×C4×C47C22×D411yescharacteristic
370C47⋊C8—22no—
371C47⋊C8—41no—
372C47⋊C8—41no—
373C47⋊C8—41no—
374C47⋊C8—41no—
375C47⋊C8—41no—
376C47⋊C8—41no—
377C47⋊C8—41no—
378#17680—471nomaximal, Sylow
379C22×C47—21no—
380C22×C47—21no—
381C22×C47—21no—
382C22×C47—21no—
383C22×C47—21no—
384C22×C47—21no—
385C22×C47—21no—
386C22×C47—21no—
387C22×C47—41no—
388C22×C47—41no—
389C22×C47—41no—
390C22×C47#42112yes—
391C22×C47C22×C22⋊C411yescharacteristic
392C4×C47—21no—
393C4×C47—21no—
394C4×C47—21no—
395C4×C47—21no—
396C4×C47—21no—
397C4×C47—21no—
398C4×C47—21no—
399C4×C47—21no—
400C4×C47—21no—
401C4×C47—21no—
402C4×C47—21no—
403C4×C47—21no—
404C4×C47—41no—
405C4×C47—41no—
406C4×C47—41no—
407C4×C47—41no—
408C4×C47—41no—
409C4×C47—41no—
410C4×C47—41no—
411#3515D4711yescharacteristic
412#2970—471no—
413#2923—471no—
414#1537—471no—
415#1535—471no—
416#1535—471no—
417#1534—471no—
418#1532—471no—
419#1532—471no—
420#1531—471no—
421#1529—471no—
422#1528—471no—
423#1528—471no—
424#1524—471no—
425C2×#330—471no—
426C2×C47—22no—
427C2×C47—41no—
428C2×C47—41no—
429C2×C47—81no—
430C2×C47#288911yescharacteristic
431C2×C47C2×#42111yescharacteristic
432C2×C47#290111yescharacteristic
433#557Dic4711yescharacteristic
434#554Dic4711yescharacteristic
435#554Dic4711yescharacteristic
436#553Dic4711yescharacteristic
437#553Dic4711yescharacteristic
438#552—21no—
439#552—21no—
440#552—21no—
441#552Dic4711yescharacteristic
442#552Dic4711yescharacteristic
443#547—21no—
444#547Dic4711yescharacteristic
445#541—21no—
446#539—21no—
447#539—21no—
448#533C2×D4711yescharacteristic
449#529C2×D4711yescharacteristic
450#529C2×D4711yescharacteristic
451#529C2×D4711yescharacteristic
452C2×#125C2×D4711yescharacteristic
453C2×#125C2×D4711yescharacteristic
454#520—21no—
455C4×#41C2×D4711yescharacteristic
456#446—941no—
457#435—941no—
458#435—941no—
459C8×D4—941no—
460#433—941no—
461#433—941no—
462#432—471no—
463#432—471no—
464#432—471no—
465#432—471no—
466#432—471no—
467#432—471no—
468#432—471no—
469#424—941no—
470#408—941no—
471C4×M16—471no—
472C4×M16—471no—
473C2×#97—471no—
474C2×#97—471no—
475C2×#97—471no—
476#330—471no—
477#330—471no—
478#330—471no—
479#330—471no—
480#330—471no—
481#330—471no—
482#330—471no—
483#330—471no—
484#330—471no—
485#330—471no—
486#330—471no—
487#330—471no—
488#329—471no—
489#329—471no—
490#329—471no—
491#329—471no—
492C47#1768011yescharacteristic, complemented, Sylow
493C2×#41—21no—
494C2×#41C22⋊D4711yescharacteristic
495C2×M16—941no—
496C2×M16—941no—
497C22×C8—941no—
498C22×C8—941no—
499C22×C8—941no—
500C4⋊Q8—21no—
501C4⋊Q8C2×Dic4711yescharacteristic
502C4⋊Q8C2×Dic4711yescharacteristic
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×Dic4711yescharacteristic
520#125C2×Dic4711yescharacteristic
521#125C2×Dic4711yescharacteristic
522#125C2×Dic4711yescharacteristic
523#125C22×D4711yescharacteristic
524#125C22×D4711yescharacteristic
525#125C22×D4711yescharacteristic
526#124C22×D4711yescharacteristic
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×Dic4711yescharacteristic
545C22⋊Q8C2×Dic4711yescharacteristic
546C22⋊Q8C2×Dic4711yescharacteristic
547#121—21no—
548#121—21no—
549#121C2×Dic4711yescharacteristic
550#121C2×Dic4711yescharacteristic
551#121C2×Dic4711yescharacteristic
552C4×Q8—21no—
553C4×Q8—21no—
554C4×Q8—21no—
555C4×Q8C2×Dic4711yescharacteristic
556C4×Q8C2×Dic4711yescharacteristic
557C4×Q8C2×Dic4711yescharacteristic
558C4×Q8C2×Dic4711yescharacteristic
559C4×Q8C22⋊D4711yescharacteristic
560C4×D4—21no—
561C4×D4—21no—
562C4×D4—21no—
563C4×D4—21no—
564C4×D4—21no—
565C4×D4—21no—
566C4×D4C2×Dic4711yescharacteristic
567C4×D4C2×Dic4711yescharacteristic
568C4×D4C2×Dic4711yescharacteristic
569C4×D4C2×Dic4711yescharacteristic
570C4×D4C2×Dic4711yescharacteristic
571C4×D4C2×Dic4711yescharacteristic
572C4×D4C22⋊D4711yescharacteristic
573C4×D4C22⋊D4711yescharacteristic
574C4×D4C22⋊D4711yescharacteristic
575#117—21no—
576#117—21no—
577#117—21no—
578#117—21no—
579#117—21no—
580#117C2×Dic4711yescharacteristic
581#117C2×Dic4711yescharacteristic
582#117C22⋊D4711yescharacteristic
583#117C22⋊D4711yescharacteristic
584#117C22⋊D4711yescharacteristic
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4C2×Dic4711yescharacteristic
591C2×C4⋊C4C2×Dic4711yescharacteristic
592C2×C4⋊C4C2×Dic4711yescharacteristic
593C2×C4⋊C4C2×Dic4711yescharacteristic
594C2×C42C22×D4711yescharacteristic
595C2×C42C22×D4711yescharacteristic
596C2×C42C22×D4711yescharacteristic
597C4⋊C8—941no—
598C4⋊C8—941no—
599C4⋊C8—941no—
600C4⋊C8—941no—
601C4⋊C8—941no—
602C4⋊C8—941no—
603C4⋊C8—941no—
604C22⋊C8—941no—
605C22⋊C8—941no—
606C22⋊C8—941no—
607C22⋊C8—941no—
608C22⋊C8—941no—
609C22⋊C8—941no—
610C22⋊C8—941no—
611#97—471no—
612#97—471no—
613#97—471no—
614#97—471no—
615#97—471no—
616#97—471no—
617#97—471no—
618#97—471no—
619#97—941no—
620#97—941no—
621#97—941no—
622C4×C8—941no—
623C4×C8—941no—
624#41—42no—
625#41—44no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8C22⋊Dic4711yescharacteristic
629C2×Q8C22×Dic4711yescharacteristic
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4C22⋊Dic4711yescharacteristic
634C2×D4C22⋊Dic4711yescharacteristic
635C2×D4C22⋊Dic4711yescharacteristic
636C2×D4C22×Dic4711yescharacteristic
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4C22×Dic4711yescharacteristic
645C22×C4C22×Dic4711yescharacteristic
646C22×C4C22×Dic4711yescharacteristic
647C22×C4C2×C22⋊D4711yescharacteristic
648C22×C4C2×C22⋊D4711yescharacteristic
649C22×C4C2×C22⋊D4711yescharacteristic
650C22×C4C2×C22⋊D4711yescharacteristic
651C22×C4C2×C22⋊D4711yescharacteristic
652C22×C4C2×C22⋊D4711yescharacteristic
653M16—1882no—
654M16—1882no—
655C2×C8—941no—
656C2×C8—941no—
657C2×C8—941no—
658C2×C8—941no—
659C2×C8—941no—
660C2×C8—941no—
661C2×C8—941no—
662C2×C8—941no—
663C2×C8—1882no—
664C2×C8—1882no—
665C2×C8—1882no—
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⋊Dic4711yescharacteristic
693C4⋊C4C22⋊Dic4711yescharacteristic
694C4⋊C4C22⋊Dic4711yescharacteristic
695C4⋊C4C22⋊Dic4711yescharacteristic
696C4⋊C4C22⋊Dic4711yescharacteristic
697C4⋊C4C22⋊Dic4711yescharacteristic
698C4⋊C4C22×Dic4711yescharacteristic
699C4⋊C4C22×Dic4711yescharacteristic
700C4⋊C4C22×Dic4711yescharacteristic
701C4⋊C4C22×Dic4711yescharacteristic
702C4⋊C4C22×Dic4711yescharacteristic
703C4⋊C4C22×Dic4711yescharacteristic
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⋊Dic4711yescharacteristic
718C22⋊C4C22⋊Dic4711yescharacteristic
719C22⋊C4C22⋊Dic4711yescharacteristic
720C22⋊C4C22⋊Dic4711yescharacteristic
721C22⋊C4C22⋊Dic4711yescharacteristic
722C22⋊C4C22⋊Dic4711yescharacteristic
723C42—21no—
724C42—21no—
725C42—21no—
726C42—21no—
727C42—21no—
728C42C22×Dic4711yescharacteristic
729C42C22×Dic4711yescharacteristic
730C42C22×Dic4711yescharacteristic
731C42C2×C22⋊D4711yescharacteristic
732C42C2×C22⋊D4711yescharacteristic
733C42C2×C22⋊D4711yescharacteristic
734C42C2×C22⋊D4711yescharacteristic
735C42C2×C22⋊D4711yescharacteristic
736C42C2×C22⋊D4711yescharacteristic
737C42C23×D4711yescharacteristic
738C23—21no—
739C23C2×C22⋊Dic4711yescharacteristic
740C23C2×C22⋊Dic4711yescharacteristic
741C23C2×C22⋊Dic4711yescharacteristic
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⋊Dic4711yescharacteristic
777C2×C4C2×C22⋊Dic4711yescharacteristic
778C2×C4C2×C22⋊Dic4711yescharacteristic
779C2×C4C2×C22⋊Dic4711yescharacteristic
780C2×C4C2×C22⋊Dic4711yescharacteristic
781C2×C4C2×C22⋊Dic4711yescharacteristic
782C2×C4C2×C22⋊Dic4711yescharacteristic
783C2×C4C2×C22⋊Dic4711yescharacteristic
784C2×C4C2×C22⋊Dic4711yescharacteristic
785C2×C4C23×Dic4711yescharacteristic
786C2×C4C22×C22⋊D4711yescharacteristic
787C2×C4C22×C22⋊D4711yescharacteristic
788C8—942no—
789C8—1881no—
790C8—1881no—
791C8—1881no—
792C8—1881no—
793C8—1881no—
794C8—1881no—
795C8—1881no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22#1568914012yes—
808C22C22×C22⋊Dic4711yescharacteristic
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#2025187111yescharacteristic
833C2C2×#1568914011yescharacteristic
834C2#2025193511yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
Fitting, prime radicalC47×#3515C2
socleC22×C47C22×C22⋊C4
cosocleC42×C47C24
hypercenter#3515D47
hypocenterC47#17680
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3515

Complements

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

NH ≅ G/Ntype
1. #20252402C2semidirect
2. #20252039C2semidirect
3. #20242026C2semidirect
4. #20242019C2semidirect
5. #20242019C2semidirect
6. #20242015C2semidirect
7. #20242008C2semidirect
8. #20242008C2semidirect
9. #20242003C2semidirect
10. #20241995C2semidirect
11. #20241990C2semidirect
12. #20241990C2semidirect
13. #20241976C2semidirect
14. C2×#15688865C2semidirect
492. C47#17680semidirect

Maximal subgroups

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

subgroupindex
#202524022
#202520392
#202420262
#202420192
#202420152
#202420082
#202420032
#202419952
#202419902
#202419762
C2×#156888652
C47×#35152
#1768047