Finite Group Databasebeta

← #26183818

Subgroups — #26183818

Order 12032.

996 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252423C211yesmaximal, characteristic, complemented
2#20246021C211yesmaximal, characteristic, complemented
3#20241965C211yesmaximal, characteristic, complemented
4#20241960C211yesmaximal, characteristic, complemented
5#20241952C211yesmaximal, characteristic, complemented
6#20241944C211yesmaximal, characteristic, complemented
7#20241939C211yesmaximal, characteristic, complemented
8#20241931C211yesmaximal, characteristic, complemented
9#20241926C211yesmaximal, characteristic, complemented
10#20241921C211yesmaximal, characteristic, complemented
11#20241908C211yesmaximal, characteristic, complemented
12#20241892C211yesmaximal, characteristic, complemented
13#20241879C211yesmaximal, characteristic, complemented
14C2×#15688860C211yesmaximal, characteristic, complemented
15C47×#3520C211yesmaximal, characteristic
16#15689201—21no—
17#15689195—21no—
18#15689195—21no—
19D4×C47⋊C8—21no—
20#15689180C2211yescharacteristic
21#15689176C2211yescharacteristic
22#15689087C2211yescharacteristic
23#15689087C2211yescharacteristic
24C2×C22⋊(C47⋊C8)C2211yescharacteristic
25C2×C22⋊(C47⋊C8)C2211yescharacteristic
26#15689016—21no—
27#15689009—21no—
28#15689003—21no—
29#15688998—21no—
30#15688991C2211yescharacteristic
31#15688989C2211yescharacteristic
32#15688986C2211yescharacteristic
33#15688983C2211yescharacteristic
34C4×C22⋊Dic47C2211yescharacteristic
35C2×C47⋊#95C2211yescharacteristic
36#15688860C2211yescharacteristic
37#15688860C2211yescharacteristic
38#15688860C2211yescharacteristic
39#15688860C2211yescharacteristic
40#15688860C2211yescharacteristic
41#15688860C2211yescharacteristic
42#15688860C2211yescharacteristic
43#15688860C2211yescharacteristic
44#15688860C2211yescharacteristic
45#15688860C2211yescharacteristic
46#15688860C2211yescharacteristic
47#15688860C2211yescharacteristic
48#15688857C2211yescharacteristic
49#15688857C2211yescharacteristic
50#15688857C2211yescharacteristic
51#15688857C2211yescharacteristic
52C47×#556C411yescharacteristic, complemented
53C47×#554—21no—
54C47×#552C411yescharacteristic, complemented
55C47×#552C411yescharacteristic, complemented
56C47×#551—21no—
57C47×#551—21no—
58D4×Q8×C47C411yescharacteristic, complemented
59C47×#548C411yescharacteristic, complemented
60C47×#548C411yescharacteristic, complemented
61C47×#547C411yescharacteristic, complemented
62C47×#547C411yescharacteristic, complemented
63C47×#546—21no—
64C47×#542—21no—
65C47×#539—21no—
66C47×#539—21no—
67C47×#533C2211yescharacteristic
68C47×#529C2211yescharacteristic
69C47×#525C2211yescharacteristic
70C47×#525C2211yescharacteristic
71C2×C22⋊Q8×C47C2211yescharacteristic
72C2×C22⋊Q8×C47C2211yescharacteristic
73C47×#520—21no—
74C2×C4×D4×C47C2211yescharacteristic
75C23×Dic47—21no—
76C2×#10625329—21no—
77C2×#10625329—21no—
78C22×C47⋊C8—21no—
79C22×C47⋊C8—21no—
80C2×C4⋊Dic47—21no—
81C2×C4⋊Dic47—21no—
82C2×C22⋊Dic47—21no—
83C2×C22⋊Dic47—21no—
84C2×C22⋊Dic47—21no—
85C2×C4×Dic47—21no—
86C4⋊(C47⋊C8)—21no—
87C4⋊(C47⋊C8)—21no—
88C22⋊(C47⋊C8)—21no—
89C22⋊(C47⋊C8)—21no—
90C22⋊(C47⋊C8)—21no—
91C22⋊(C47⋊C8)—21no—
92C22⋊(C47⋊C8)C2311yescharacteristic
93C22⋊(C47⋊C8)C2311yescharacteristic
94C22⋊(C47⋊C8)C2311yescharacteristic
95C22⋊(C47⋊C8)C2311yescharacteristic
96#13093935—21no—
97C4×C47⋊C8—21no—
98C47⋊#95—21no—
99C47⋊#95—21no—
100C47⋊#95—21no—
101C47⋊#95—21no—
102C47⋊#95—21no—
103C47⋊#95C2311yescharacteristic
104C47⋊#95C2311yescharacteristic
105C47⋊#95C2311yescharacteristic
106C47⋊#95C2311yescharacteristic
107C2×#41×C47—21no—
108C2×#41×C47C2×C411yescharacteristic
109C2×#41×C47C2×C411yescharacteristic, complemented
110C22×Q8×C47C2×C411yescharacteristic
111C22×Q8×C47C2×C411yescharacteristic, complemented
112C22×D4×C47D411yescharacteristic
113C23×C4×C47C2311yescharacteristic
114C23×C4×C47C2311yescharacteristic
115C4⋊Q8×C47—21no—
116C4⋊Q8×C47C2×C411yescharacteristic, complemented
117C4⋊Q8×C47C2×C411yescharacteristic, complemented
118#126×C47—21no—
119#126×C47—21no—
120#126×C47—21no—
121#126×C47—21no—
122#126×C47—21no—
123#125×C47—21no—
124#125×C47—21no—
125#125×C47—21no—
126#125×C47C2×C411yescharacteristic, complemented
127#124×C47—21no—
128#124×C47—21no—
129#124×C47—21no—
130#124×C47C2×C411yescharacteristic, complemented
131#123×C47—21no—
132#123×C47—21no—
133#123×C47—21no—
134#123×C47—21no—
135#123×C47—21no—
136#123×C47—21no—
137#123×C47—21no—
138#123×C47—21no—
139#123×C47—21no—
140C22⋊Q8×C47—21no—
141C22⋊Q8×C47—21no—
142C22⋊Q8×C47—21no—
143C22⋊Q8×C47—21no—
144C22⋊Q8×C47—21no—
145C22⋊Q8×C47—21no—
146C22⋊Q8×C47—21no—
147C22⋊Q8×C47—21no—
148C22⋊Q8×C47—21no—
149C22⋊Q8×C47—21no—
150C22⋊Q8×C47C2×C411yescharacteristic
151C22⋊Q8×C47C2×C411yescharacteristic
152C22⋊Q8×C47C2×C411yescharacteristic
153C22⋊Q8×C47C2×C411yescharacteristic, complemented
154C22⋊Q8×C47C2×C411yescharacteristic, complemented
155C22⋊Q8×C47C2×C411yescharacteristic, complemented
156C22⋊Q8×C47C2311yescharacteristic
157C22⋊Q8×C47C2311yescharacteristic
158C22⋊Q8×C47C2311yescharacteristic
159#121×C47—21no—
160#121×C47—21no—
161#121×C47—21no—
162#121×C47C2×C411yescharacteristic
163#121×C47C2×C411yescharacteristic, complemented
164#121×C47C2311yescharacteristic
165#120×C47—21no—
166#120×C47—21no—
167C4×Q8×C47—21no—
168C4×Q8×C47—21no—
169C4×Q8×C47C2×C411yescharacteristic, complemented
170C4×Q8×C47C2×C411yescharacteristic, complemented
171C4×Q8×C47C2×C411yescharacteristic, complemented
172C4×D4×C47—21no—
173C4×D4×C47—21no—
174C4×D4×C47—21no—
175C4×D4×C47—21no—
176C4×D4×C47—21no—
177C4×D4×C47—21no—
178C4×D4×C47—21no—
179C4×D4×C47—21no—
180C4×D4×C47C2×C411yescharacteristic
181C4×D4×C47C2×C411yescharacteristic
182C4×D4×C47C2×C411yescharacteristic
183C4×D4×C47C2×C411yescharacteristic
184C4×D4×C47C2×C411yescharacteristic, complemented
185C4×D4×C47D411yescharacteristic
186C4×D4×C47D411yescharacteristic
187C4×D4×C47D411yescharacteristic
188C4×D4×C47D411yescharacteristic
189#117×C47—21no—
190#117×C47—21no—
191#117×C47—21no—
192#117×C47—21no—
193#117×C47C2×C411yescharacteristic
194#117×C47C2×C411yescharacteristic, complemented
195C2×C4⋊C4×C47—21no—
196C2×C4⋊C4×C47—21no—
197C2×C4⋊C4×C47—21no—
198C2×C4⋊C4×C47C2×C411yescharacteristic
199C2×C4⋊C4×C47C2×C411yescharacteristic, complemented
200C2×C4⋊C4×C47D411yescharacteristic
201C2×C22⋊C4×C47—21no—
202C2×C22⋊C4×C47—21no—
203C2×C22⋊C4×C47D411yescharacteristic
204C2×C22⋊C4×C47D411yescharacteristic
205C2×C42×C47C2311yescharacteristic
206C24×C47C2×D411yescharacteristic
207C24×C47C2×D411yescharacteristic
208#41×C47—44no—
209#41×C47—81no—
210#41×C47—81no—
211C2×Q8×C47—21no—
212C2×Q8×C47—21no—
213C2×Q8×C47—21no—
214C2×Q8×C47—81no—
215C2×Q8×C47—81no—
216C2×Q8×C47C22×C411yescharacteristic
217C2×Q8×C47C22×C411yescharacteristic
218C2×Q8×C47C22×C411yescharacteristic
219C2×D4×C47—21no—
220C2×D4×C47—21no—
221C2×D4×C47—21no—
222C2×D4×C47—21no—
223C2×D4×C47—21no—
224C2×D4×C47—42no—
225C2×D4×C47C22⋊C411yescharacteristic
226C2×D4×C47C22⋊C411yescharacteristic
227C2×D4×C47C22⋊C411yescharacteristic
228C2×D4×C47C22⋊C411yescharacteristic
229C2×D4×C47C22×C411yescharacteristic
230C22×C4×C47—21no—
231C22×C4×C47—21no—
232C22×C4×C47—21no—
233C22×C4×C47—21no—
234C22×C4×C47—21no—
235C22×C4×C47—21no—
236C22×C4×C47—21no—
237C22×C4×C47—81no—
238C22×C4×C47—81no—
239C22×C4×C47C22×C411yescharacteristic
240C22×C4×C47C22×C411yescharacteristic
241C22×C4×C47C22×C411yescharacteristic
242C22×C4×C47C22×C411yescharacteristic
243C22×C4×C47C2×D411yescharacteristic
244C22×C4×C47C2×D411yescharacteristic
245C22×C4×C47C2×D411yescharacteristic
246C22×C4×C47C2×D411yescharacteristic
247C22×C4×C47C2×D411yescharacteristic
248C22×C4×C47C2×D411yescharacteristic
249C22×C4×C47C2×D411yescharacteristic
250C22×C4×C47C2×D411yescharacteristic
251C22×C4×C47C2411yescharacteristic
252C22×Dic47—21no—
253C22×Dic47—21no—
254C22×Dic47—21no—
255C22×Dic47—21no—
256C22×Dic47—42no—
257C22×Dic47—81no—
258C22×Dic47—81no—
259C4⋊C4×C47—21no—
260C4⋊C4×C47—21no—
261C4⋊C4×C47—21no—
262C4⋊C4×C47—21no—
263C4⋊C4×C47—21no—
264C4⋊C4×C47—21no—
265C4⋊C4×C47—21no—
266C4⋊C4×C47—21no—
267C4⋊C4×C47—21no—
268C4⋊C4×C47—21no—
269C4⋊C4×C47—21no—
270C4⋊C4×C47—21no—
271C4⋊C4×C47—21no—
272C4⋊C4×C47—21no—
273C4⋊C4×C47—21no—
274C4⋊C4×C47—21no—
275C4⋊C4×C47—21no—
276C4⋊C4×C47—21no—
277C4⋊C4×C47—21no—
278C4⋊C4×C47C22⋊C411yescharacteristic
279C4⋊C4×C47C22⋊C411yescharacteristic
280C4⋊C4×C47C22⋊C411yescharacteristic
281C4⋊C4×C47C22⋊C411yescharacteristic
282C4⋊C4×C47C22×C411yescharacteristic
283C4⋊C4×C47C22×C411yescharacteristic
284C4⋊C4×C47C22×C411yescharacteristic
285C4⋊C4×C47C22×C411yescharacteristic
286C22⋊C4×C47—21no—
287C22⋊C4×C47—21no—
288C22⋊C4×C47—21no—
289C22⋊C4×C47—21no—
290C22⋊C4×C47—21no—
291C22⋊C4×C47—21no—
292C22⋊C4×C47—21no—
293C22⋊C4×C47—21no—
294C22⋊C4×C47—21no—
295C22⋊C4×C47—21no—
296C22⋊C4×C47—21no—
297C22⋊C4×C47—21no—
298C22⋊C4×C47—21no—
299C22⋊C4×C47—21no—
300C22⋊C4×C47—21no—
301C22⋊C4×C47—21no—
302C22⋊C4×C47—21no—
303C22⋊C4×C47C22⋊C411yescharacteristic
304C22⋊C4×C47C22⋊C411yescharacteristic
305C22⋊C4×C47C22⋊C411yescharacteristic
306C22⋊C4×C47C22⋊C411yescharacteristic
307C22⋊C4×C47C22⋊C411yescharacteristic
308C22⋊C4×C47C22⋊C411yescharacteristic
309C22⋊C4×C47C22⋊C411yescharacteristic
310C22⋊C4×C47C22⋊C411yescharacteristic
311C42×C47—21no—
312C42×C47—21no—
313C42×C47—21no—
314C42×C47—21no—
315C42×C47—21no—
316C42×C47C22×C411yescharacteristic
317C42×C47C22×C411yescharacteristic
318C42×C47C2×D411yescharacteristic
319C42×C47C2×D411yescharacteristic
320C22⋊Dic47—42no—
321C22⋊Dic47—81no—
322C22⋊Dic47—81no—
323C4⋊Dic47—81no—
324C4⋊Dic47—81no—
325C4×Dic47—81no—
326#10625329—81no—
327#10625329—81no—
328C2×C47⋊C8—21no—
329C2×C47⋊C8—21no—
330C2×C47⋊C8—21no—
331C2×C47⋊C8—21no—
332C2×C47⋊C8—81no—
333C2×C47⋊C8—81no—
334C23×C47—21no—
335C23×C47—21no—
336C23×C47—22no—
337C23×C47—21no—
338C23×C47—21no—
339C23×C47—21no—
340C23×C47—41no—
341C23×C47—41no—
342C23×C47—41no—
343C23×C47C2×C22⋊C411yescharacteristic
344C23×C47C2×C22⋊C411yescharacteristic
345C23×C47C2×C22⋊C411yescharacteristic
346C23×C47C2×C22⋊C411yescharacteristic
347C23×C47C22×D411yescharacteristic
348Q8×C47—41no—
349Q8×C47—41no—
350Q8×C47—41no—
351Q8×C47—42no—
352Q8×C47—81no—
353Q8×C47—81no—
354D4×C47—22no—
355D4×C47—22no—
356D4×C47—41no—
357D4×C47—41no—
358D4×C47—41no—
359D4×C47—42no—
360D4×C47—41no—
361D4×C47—41no—
362D4×C47—42no—
363D4×C47—81no—
364D4×C47—81no—
365C2×C4×C47—21no—
366C2×C4×C47—21no—
367C2×C4×C47—21no—
368C2×C4×C47—21no—
369C2×C4×C47—21no—
370C2×C4×C47—21no—
371C2×C4×C47—21no—
372C2×C4×C47—21no—
373C2×C4×C47—21no—
374C2×C4×C47—41no—
375C2×C4×C47—41no—
376C2×C4×C47—41no—
377C2×C4×C47—41no—
378C2×C4×C47—41no—
379C2×C4×C47—41no—
380C2×C4×C47—41no—
381C2×C4×C47—41no—
382C2×C4×C47—41no—
383C2×C4×C47—41no—
384C2×C4×C47—41no—
385C2×C4×C47—41no—
386C2×C4×C47—42no—
387C2×C4×C47—42no—
388C2×C4×C47—42no—
389C2×C4×C47—81no—
390C2×C4×C47—81no—
391C2×C4×C47—81no—
392C2×C4×C47—81no—
393C2×C4×C47C2×C22⋊C411yescharacteristic
394C2×C4×C47C2×C22⋊C411yescharacteristic
395C2×C4×C47C2×C22⋊C411yescharacteristic
396C2×C4×C47C2×C22⋊C411yescharacteristic
397C2×C4×C47C2×C22⋊C411yescharacteristic
398C2×C4×C47C2×C22⋊C411yescharacteristic
399C2×C4×C47C2×C22⋊C411yescharacteristic
400C2×C4×C47C2×C22⋊C411yescharacteristic
401C2×C4×C47C23×C411yescharacteristic
402C2×C4×C47C22×D411yescharacteristic
403C2×Dic47—41no—
404C2×Dic47—41no—
405C2×Dic47—41no—
406C2×Dic47—41no—
407C2×Dic47—41no—
408C2×Dic47—41no—
409C2×Dic47—41no—
410C2×Dic47—41no—
411C2×Dic47—41no—
412C2×Dic47—41no—
413C2×Dic47—41no—
414C2×Dic47—41no—
415C2×Dic47—84no—
416C47⋊C8—41no—
417C47⋊C8—41no—
418C47⋊C8—41no—
419C47⋊C8—41no—
420#17598—471nomaximal, Sylow
421C22×C47—21no—
422C22×C47—21no—
423C22×C47—21no—
424C22×C47—21no—
425C22×C47—21no—
426C22×C47—21no—
427C22×C47—21no—
428C22×C47—21no—
429C22×C47—21no—
430C22×C47—21no—
431C22×C47—21no—
432C22×C47—21no—
433C22×C47—21no—
434C22×C47—42no—
435C22×C47—42no—
436C22×C47—41no—
437C22×C47—41no—
438C22×C47—41no—
439C22×C47—81no—
440C22×C47—81no—
441C22×C47#42112yes—
442C22×C47C22×C22⋊C411yescharacteristic
443C22×C47#57711yescharacteristic
444C22×C47#57811yescharacteristic
445C4×C47—21no—
446C4×C47—21no—
447C4×C47—21no—
448C4×C47—21no—
449C4×C47—21no—
450C4×C47—21no—
451C4×C47—21no—
452C4×C47—21no—
453C4×C47—21no—
454C4×C47—21no—
455C4×C47—41no—
456C4×C47—41no—
457C4×C47—41no—
458C4×C47—41no—
459C4×C47—41no—
460C4×C47—41no—
461C4×C47—41no—
462Dic47—81no—
463Dic47—81no—
464Dic47—81no—
465Dic47—81no—
466#3520D4711yescharacteristic
467#2974—471no—
468#2318—471no—
469#1521—471no—
470#1520—471no—
471#1518—471no—
472#1516—471no—
473#1515—471no—
474#1513—471no—
475#1512—471no—
476#1511—471no—
477#1508—471no—
478#1504—471no—
479#1501—471no—
480C2×#328—471no—
481C2×C47—21no—
482C2×C47—21no—
483C2×C47—22no—
484C2×C47—41no—
485C2×C47—41no—
486C2×C47—41no—
487C2×C47—81no—
488C2×C47#288311yescharacteristic
489C2×C47#289811yescharacteristic
490C2×C47C2×#42111yescharacteristic
491#556Dic4711yescharacteristic, complemented
492#554—21no—
493#552Dic4711yescharacteristic, complemented
494#552Dic4711yescharacteristic, complemented
495#551—21no—
496#551—21no—
497D4×Q8Dic4711yescharacteristic, complemented
498#548Dic4711yescharacteristic, complemented
499#548Dic4711yescharacteristic, complemented
500#547Dic4711yescharacteristic, complemented
501#547Dic4711yescharacteristic, complemented
502#546—21no—
503#542—21no—
504#539—21no—
505#539—21no—
506#533C2×D4711yescharacteristic
507#529C2×D4711yescharacteristic
508#525C2×D4711yescharacteristic
509#525C2×D4711yescharacteristic
510C2×C22⋊Q8C2×D4711yescharacteristic
511C2×C22⋊Q8C2×D4711yescharacteristic
512#520—21no—
513C2×C4×D4C2×D4711yescharacteristic
514#436—941no—
515#435—941no—
516#435—941no—
517C8×D4—941no—
518#432—471no—
519#431—471no—
520#407—471no—
521#407—471no—
522C2×C22⋊C8—471no—
523C2×C22⋊C8—471no—
524#388—941no—
525#387—941no—
526#386—941no—
527#385—941no—
528#383—471no—
529#382—471no—
530#381—471no—
531#380—471no—
532C4×C22⋊C4—471no—
533C2×#95—471no—
534#328—471no—
535#328—471no—
536#328—471no—
537#328—471no—
538#328—471no—
539#328—471no—
540#328—471no—
541#328—471no—
542#328—471no—
543#328—471no—
544#328—471no—
545#328—471no—
546#327—471no—
547#327—471no—
548#327—471no—
549#327—471no—
550C47#1759811yescharacteristic, complemented, Sylow
551C2×#41—21no—
552C2×#41C2×Dic4711yescharacteristic
553C2×#41C2×Dic4711yescharacteristic, complemented
554C22×Q8C2×Dic4711yescharacteristic
555C22×Q8C2×Dic4711yescharacteristic, complemented
556C22×D4C22⋊D4711yescharacteristic
557C23×C4—941no—
558C23×C4C22×D4711yescharacteristic
559C23×C4C22×D4711yescharacteristic
560C2×M16—941no—
561C2×M16—941no—
562C22×C8—941no—
563C22×C8—941no—
564C4⋊Q8—21no—
565C4⋊Q8C2×Dic4711yescharacteristic, complemented
566C4⋊Q8C2×Dic4711yescharacteristic, complemented
567#126—21no—
568#126—21no—
569#126—21no—
570#126—21no—
571#126—21no—
572#125—21no—
573#125—21no—
574#125—21no—
575#125C2×Dic4711yescharacteristic, complemented
576#124—21no—
577#124—21no—
578#124—21no—
579#124C2×Dic4711yescharacteristic, complemented
580#123—21no—
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589C22⋊Q8—21no—
590C22⋊Q8—21no—
591C22⋊Q8—21no—
592C22⋊Q8—21no—
593C22⋊Q8—21no—
594C22⋊Q8—21no—
595C22⋊Q8—21no—
596C22⋊Q8—21no—
597C22⋊Q8—21no—
598C22⋊Q8—21no—
599C22⋊Q8C2×Dic4711yescharacteristic
600C22⋊Q8C2×Dic4711yescharacteristic
601C22⋊Q8C2×Dic4711yescharacteristic
602C22⋊Q8C2×Dic4711yescharacteristic, complemented
603C22⋊Q8C2×Dic4711yescharacteristic, complemented
604C22⋊Q8C2×Dic4711yescharacteristic, complemented
605C22⋊Q8C22×D4711yescharacteristic
606C22⋊Q8C22×D4711yescharacteristic
607C22⋊Q8C22×D4711yescharacteristic
608#121—21no—
609#121—21no—
610#121—21no—
611#121C2×Dic4711yescharacteristic
612#121C2×Dic4711yescharacteristic, complemented
613#121C22×D4711yescharacteristic
614#120—21no—
615#120—21no—
616C4×Q8—21no—
617C4×Q8—21no—
618C4×Q8C2×Dic4711yescharacteristic, complemented
619C4×Q8C2×Dic4711yescharacteristic, complemented
620C4×Q8C2×Dic4711yescharacteristic, complemented
621C4×D4—21no—
622C4×D4—21no—
623C4×D4—21no—
624C4×D4—21no—
625C4×D4—21no—
626C4×D4—21no—
627C4×D4—21no—
628C4×D4—21no—
629C4×D4C2×Dic4711yescharacteristic
630C4×D4C2×Dic4711yescharacteristic
631C4×D4C2×Dic4711yescharacteristic
632C4×D4C2×Dic4711yescharacteristic
633C4×D4C2×Dic4711yescharacteristic, complemented
634C4×D4C22⋊D4711yescharacteristic
635C4×D4C22⋊D4711yescharacteristic
636C4×D4C22⋊D4711yescharacteristic
637C4×D4C22⋊D4711yescharacteristic
638#117—21no—
639#117—21no—
640#117—21no—
641#117—21no—
642#117C2×Dic4711yescharacteristic
643#117C2×Dic4711yescharacteristic, complemented
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—941no—
648C2×C4⋊C4—941no—
649C2×C4⋊C4C2×Dic4711yescharacteristic
650C2×C4⋊C4C2×Dic4711yescharacteristic, complemented
651C2×C4⋊C4C22⋊D4711yescharacteristic
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—941no—
655C2×C22⋊C4—941no—
656C2×C22⋊C4—941no—
657C2×C22⋊C4C22⋊D4711yescharacteristic
658C2×C22⋊C4C22⋊D4711yescharacteristic
659C2×C42—941no—
660C2×C42C22×D4711yescharacteristic
661C4⋊C8—941no—
662C4⋊C8—941no—
663C22⋊C8—471no—
664C22⋊C8—471no—
665C22⋊C8—471no—
666C22⋊C8—471no—
667C22⋊C8—941no—
668C22⋊C8—941no—
669C22⋊C8—941no—
670C22⋊C8—941no—
671#97—941no—
672C4×C8—941no—
673#95—471no—
674#95—471no—
675#95—471no—
676#95—471no—
677#95—941no—
678#95—941no—
679#95—941no—
680#95—941no—
681#95—941no—
682C24C2×C22⋊D4711yescharacteristic
683C24C2×C22⋊D4711yescharacteristic
684#41—44no—
685#41—81no—
686#41—81no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—81no—
691C2×Q8—81no—
692C2×Q8C22×Dic4711yescharacteristic
693C2×Q8C22×Dic4711yescharacteristic
694C2×Q8C22×Dic4711yescharacteristic
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—42no—
701C2×D4C22⋊Dic4711yescharacteristic
702C2×D4C22⋊Dic4711yescharacteristic
703C2×D4C22⋊Dic4711yescharacteristic
704C2×D4C22⋊Dic4711yescharacteristic
705C2×D4C22×Dic4711yescharacteristic
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—81no—
714C22×C4—81no—
715C22×C4—941no—
716C22×C4—941no—
717C22×C4—941no—
718C22×C4—941no—
719C22×C4—3761no—
720C22×C4—3761no—
721C22×C4—1882no—
722C22×C4C22×Dic4711yescharacteristic
723C22×C4C22×Dic4711yescharacteristic
724C22×C4C22×Dic4711yescharacteristic
725C22×C4C22×Dic4711yescharacteristic
726C22×C4C2×C22⋊D4711yescharacteristic
727C22×C4C2×C22⋊D4711yescharacteristic
728C22×C4C2×C22⋊D4711yescharacteristic
729C22×C4C2×C22⋊D4711yescharacteristic
730C22×C4C2×C22⋊D4711yescharacteristic
731C22×C4C2×C22⋊D4711yescharacteristic
732C22×C4C2×C22⋊D4711yescharacteristic
733C22×C4C2×C22⋊D4711yescharacteristic
734C22×C4C23×D4711yescharacteristic
735M16—3761no—
736M16—3761no—
737C2×C8—941no—
738C2×C8—941no—
739C2×C8—941no—
740C2×C8—941no—
741C2×C8—3761no—
742C2×C8—3761no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—3761no—
763C4⋊C4—3761no—
764C4⋊C4C22⋊Dic4711yescharacteristic
765C4⋊C4C22⋊Dic4711yescharacteristic
766C4⋊C4C22⋊Dic4711yescharacteristic
767C4⋊C4C22⋊Dic4711yescharacteristic
768C4⋊C4C22×Dic4711yescharacteristic
769C4⋊C4C22×Dic4711yescharacteristic
770C4⋊C4C22×Dic4711yescharacteristic
771C4⋊C4C22×Dic4711yescharacteristic
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—3761no—
790C22⋊C4—3761no—
791C22⋊C4—1882no—
792C22⋊C4C22⋊Dic4711yescharacteristic
793C22⋊C4C22⋊Dic4711yescharacteristic
794C22⋊C4C22⋊Dic4711yescharacteristic
795C22⋊C4C22⋊Dic4711yescharacteristic
796C22⋊C4C22⋊Dic4711yescharacteristic
797C22⋊C4C22⋊Dic4711yescharacteristic
798C22⋊C4C22⋊Dic4711yescharacteristic
799C22⋊C4C22⋊Dic4711yescharacteristic
800C42—21no—
801C42—21no—
802C42—21no—
803C42—21no—
804C42—21no—
805C42—3761no—
806C42C22×Dic4711yescharacteristic
807C42C22×Dic4711yescharacteristic
808C42C2×C22⋊D4711yescharacteristic
809C42C2×C22⋊D4711yescharacteristic
810C23—22no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23C2×C22⋊Dic4711yescharacteristic
820C23C2×C22⋊Dic4711yescharacteristic
821C23C2×C22⋊Dic4711yescharacteristic
822C23C2×C22⋊Dic4711yescharacteristic
823C23C22×C22⋊D4711yescharacteristic
824Q8—41no—
825Q8—41no—
826Q8—41no—
827Q8—42no—
828Q8—81no—
829Q8—81no—
830D4—22no—
831D4—22no—
832D4—41no—
833D4—41no—
834D4—41no—
835D4—42no—
836D4—42no—
837D4—41no—
838D4—41no—
839D4—81no—
840D4—81no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—81no—
866C2×C4—81no—
867C2×C4—81no—
868C2×C4—81no—
869C2×C4—3764no—
870C2×C4—1881no—
871C2×C4—1881no—
872C2×C4—1881no—
873C2×C4—1881no—
874C2×C4—1881no—
875C2×C4—1881no—
876C2×C4—1881no—
877C2×C4—1881no—
878C2×C4—1881no—
879C2×C4—1881no—
880C2×C4—1881no—
881C2×C4—1881no—
882C2×C4C2×C22⋊Dic4711yescharacteristic
883C2×C4C2×C22⋊Dic4711yescharacteristic
884C2×C4C2×C22⋊Dic4711yescharacteristic
885C2×C4C2×C22⋊Dic4711yescharacteristic
886C2×C4C2×C22⋊Dic4711yescharacteristic
887C2×C4C2×C22⋊Dic4711yescharacteristic
888C2×C4C2×C22⋊Dic4711yescharacteristic
889C2×C4C2×C22⋊Dic4711yescharacteristic
890C2×C4C23×Dic4711yescharacteristic
891C2×C4C22×C22⋊D4711yescharacteristic
892C8—1881no—
893C8—1881no—
894C8—1881no—
895C8—1881no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—21no—
907C22—21no—
908C22—21no—
909C22—42no—
910C22—42no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—81no—
915C22—81no—
916C22#1568914012yes—
917C22C22×C22⋊Dic4711yescharacteristic
918C22#1568993111yescharacteristic
919C22#1568993811yescharacteristic
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—21no—
929C4—21no—
930C4—41no—
931C4—41no—
932C4—41no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—3761no—
938C4—3761no—
939C4—3761no—
940C4—3761no—
941C2—21no—
942C2—21no—
943C2—22no—
944C2—41no—
945C2—41no—
946C2—41no—
947C2—81no—
948C2#2025184911yescharacteristic
949C2#2025192111yescharacteristic
950C2C2×#1568914011yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
Fitting, prime radicalC47×#3520C2
socleC22×C47C22×C22⋊C4
cosocleC22×C4×C47C24
hypercenter#3520D47
hypocenterC47#17598
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #3520

Complements

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

NH ≅ G/Ntype
1. #20252423C2semidirect
2. #20246021C2semidirect
3. #20241965C2semidirect
4. #20241960C2semidirect
5. #20241952C2semidirect
6. #20241944C2semidirect
7. #20241939C2semidirect
8. #20241931C2semidirect
9. #20241926C2semidirect
10. #20241921C2semidirect
11. #20241908C2semidirect
12. #20241892C2semidirect
13. #20241879C2semidirect
14. C2×#15688860C2semidirect
52. C47×#556C4semidirect
54. C47×#552C4semidirect
55. C47×#552C4semidirect
58. D4×Q8×C47C4semidirect
59. C47×#548C4semidirect
60. C47×#548C4semidirect
61. C47×#547C4semidirect
62. C47×#547C4semidirect
109. C2×#41×C47C2×C4semidirect
111. C22×Q8×C47C2×C4semidirect
116. C4⋊Q8×C47C2×C4semidirect
117. C4⋊Q8×C47C2×C4semidirect
126. #125×C47C2×C4semidirect
130. #124×C47C2×C4semidirect
153. C22⋊Q8×C47C2×C4semidirect
154. C22⋊Q8×C47C2×C4semidirect
155. C22⋊Q8×C47C2×C4semidirect
163. #121×C47C2×C4semidirect
169. C4×Q8×C47C2×C4semidirect
170. C4×Q8×C47C2×C4semidirect
171. C4×Q8×C47C2×C4semidirect
184. C4×D4×C47C2×C4semidirect
194. #117×C47C2×C4semidirect
199. C2×C4⋊C4×C47C2×C4semidirect
491. #556Dic47semidirect
493. #552Dic47semidirect
494. #552Dic47semidirect
497. D4×Q8Dic47semidirect
498. #548Dic47semidirect
499. #548Dic47semidirect
500. #547Dic47semidirect
501. #547Dic47semidirect
550. C47#17598semidirect
553. C2×#41C2×Dic47semidirect
555. C22×Q8C2×Dic47semidirect
565. C4⋊Q8C2×Dic47semidirect
566. C4⋊Q8C2×Dic47semidirect
575. #125C2×Dic47semidirect
579. #124C2×Dic47semidirect
602. C22⋊Q8C2×Dic47semidirect
603. C22⋊Q8C2×Dic47semidirect
604. C22⋊Q8C2×Dic47semidirect
612. #121C2×Dic47semidirect
618. C4×Q8C2×Dic47semidirect
619. C4×Q8C2×Dic47semidirect
620. C4×Q8C2×Dic47semidirect
633. C4×D4C2×Dic47semidirect
643. #117C2×Dic47semidirect
650. C2×C4⋊C4C2×Dic47semidirect

Maximal subgroups

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

subgroupindex
#202524232
#202460212
#202419652
#202419602
#202419522
#202419442
#202419392
#202419312
#202419262
#202419212
#202419082
#202418922
#202418792
C2×#156888602
C47×#35202
#1759847