Finite Group Databasebeta

← #26216388

Subgroups — #26216388

Order 12032.

1298 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689184C211yesmaximal, characteristic, complemented
2#20245997C211yesmaximal, characteristic, complemented
3#20243478C211yesmaximal, characteristic, complemented
4#20243474C211yesmaximal, characteristic, complemented
5#20243403C211yesmaximal, characteristic, complemented
6#20243398C211yesmaximal, characteristic, complemented
7#20243393C211yesmaximal, characteristic, complemented
8#20243388C211yesmaximal, characteristic, complemented
9#20243328C211yesmaximal, characteristic
10#20243328C211yesmaximal, characteristic
11#20243218C211yesmaximal, characteristic, complemented
12#20243213C211yesmaximal, characteristic, complemented
13C4×#13093948C211yesmaximal, characteristic, complemented
14C4×#13093945C211yesmaximal, characteristic, complemented
15C2×C47×#520C211yesmaximal, characteristic
16#15689184—24no—
17C2×C4⋊(C47⋊C8)C2211yescharacteristic
18C2×C4⋊(C47⋊C8)C2211yescharacteristic
19C2×#13093948C2211yescharacteristic
20C2×#13093948C2211yescharacteristic
21C2×#13093948C2211yescharacteristic
22C2×#13093948C2211yescharacteristic
23C2×#13093945C2211yescharacteristic
24C2×#13093945C2211yescharacteristic
25C2×#13093945C2211yescharacteristic
26C2×#13093945C2211yescharacteristic
27C2×C22⋊(C47⋊C8)C2211yescharacteristic
28C2×C22⋊(C47⋊C8)C2211yescharacteristic
29C2×#13093935C2211yescharacteristic
30C2×C4×C47⋊C8C2211yescharacteristic
31#15689016—21no—
32#15689016—21no—
33#15689009—21no—
34#15689009—21no—
35#15688993C2211yescharacteristic
36#15688989C2211yescharacteristic
37#15688983C2211yescharacteristic
38#15688983C2211yescharacteristic
39C4×C4⋊Dic47C2211yescharacteristic
40C4×C4⋊Dic47C2211yescharacteristic
41#15688885C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49C22×#41×C47C2211yescharacteristic
50C47×#520—24no—
51C47×#520C418yescomplemented
52C2×C4×Q8×C47C2211yescharacteristic
53C2×C4×Q8×C47C2211yescharacteristic
54C2×C4×D4×C47—21no—
55C2×C4×D4×C47—21no—
56C2×C4×D4×C47C2211yescharacteristic
57C2×C4×D4×C47C2211yescharacteristic
58C2×#117×C47—21no—
59C2×#117×C47C2211yescharacteristic
60C22×C4⋊C4×C47—21no—
61C22×C4⋊C4×C47C2211yescharacteristic
62C22×C47⋊C8C2311yescharacteristic
63C22×C47⋊C8C2311yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66C2×C4⋊Dic47—21no—
67C2×C4⋊Dic47—21no—
68C2×C4⋊Dic47C2311yescharacteristic
69C2×C4⋊Dic47C2311yescharacteristic
70C2×C4⋊Dic47C2311yescharacteristic
71C2×C4⋊Dic47C2311yescharacteristic
72C2×C22⋊Dic47—21no—
73C2×C22⋊Dic47—21no—
74C2×C4×Dic47—21no—
75C2×C4×Dic47—21no—
76C4⋊(C47⋊C8)—22no—
77C4⋊(C47⋊C8)—22no—
78#13093948—22no—
79#13093948—22no—
80#13093948—22no—
81#13093948—22no—
82#13093945—22no—
83#13093945—22no—
84#13093945—22no—
85#13093945—22no—
86C22⋊(C47⋊C8)—22no—
87C22⋊(C47⋊C8)—22no—
88#13093935—22no—
89C4×C47⋊C8—22no—
90C47⋊#95—21no—
91C47⋊#95—21no—
92C47⋊#95—21no—
93C47⋊#95—21no—
94C47⋊#95—21no—
95C47⋊#95—21no—
96C2×#41×C47—22no—
97C2×#41×C47—22no—
98C2×#41×C47—22no—
99C2×#41×C47—22no—
100C2×#41×C47—22no—
101C2×#41×C47C2×C414yes—
102C22×Q8×C47C2311yescharacteristic
103C22×D4×C47—21no—
104C22×D4×C47C2311yescharacteristic
105C23×C4×C47—21no—
106C23×C4×C47—21no—
107C23×C4×C47—21no—
108C23×C4×C47—21no—
109C23×C4×C47C2311yescharacteristic
110C4×Q8×C47—22no—
111C4×Q8×C47—22no—
112C4×Q8×C47C2×C414yes—
113C4×Q8×C47C2×C414yes—
114C4×D4×C47—28no—
115C4×D4×C47—28no—
116C4×D4×C47—22no—
117C4×D4×C47—22no—
118C4×D4×C47C2×C414yes—
119C4×D4×C47C2×C414yes—
120#117×C47—28no—
121#117×C47C2×C414yes—
122#117×C47D414yes—
123C2×C4⋊C4×C47—21no—
124C2×C4⋊C4×C47—21no—
125C2×C4⋊C4×C47—21no—
126C2×C4⋊C4×C47—22no—
127C2×C4⋊C4×C47—28no—
128C2×C4⋊C4×C47C2×C414yes—
129C2×C4⋊C4×C47D411yescharacteristic
130C2×C4⋊C4×C47D411yescharacteristic
131C2×C4⋊C4×C47C2311yescharacteristic
132C2×C4⋊C4×C47C2311yescharacteristic
133C2×C22⋊C4×C47—21no—
134C2×C22⋊C4×C47—21no—
135C2×C22⋊C4×C47D411yescharacteristic
136C2×C22⋊C4×C47D411yescharacteristic
137C2×C42×C47—21no—
138C2×C42×C47—21no—
139C2×C42×C47C2311yescharacteristic
140C2×C42×C47C2311yescharacteristic
141C24×C47—21no—
142C24×C47C2×D411yescharacteristic
143#41×C47—28no—
144#41×C47—28no—
145#41×C47—28no—
146#41×C47—28no—
147C2×Q8×C47—21no—
148C2×Q8×C47—21no—
149C2×Q8×C47—21no—
150C2×Q8×C47C22×C412yes—
151C2×Q8×C47#4112yes—
152C2×Q8×C47#4112yes—
153C2×D4×C47—24no—
154C2×D4×C47—24no—
155C2×D4×C47—24no—
156C2×D4×C47—21no—
157C2×D4×C47—21no—
158C2×D4×C47—21no—
159C2×D4×C47C22×C412yes—
160C2×D4×C47#4112yes—
161C2×D4×C47#4112yes—
162C22×C4×C47—24no—
163C22×C4×C47—24no—
164C22×C4×C47—21no—
165C22×C4×C47—24no—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—21no—
169C22×C4×C47—21no—
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—24no—
173C22×C4×C47—24no—
174C22×C4×C47—24no—
175C22×C4×C47—81no—
176C22×C4×C47—81no—
177C22×C4×C47—81no—
178C22×C4×C47—81no—
179C22×C4×C47—81no—
180C22×C4×C47—81no—
181C22×C4×C47C22×C412yes—
182C22×C4×C47C2×D411yescharacteristic
183C22×C4×C47C2×D411yescharacteristic
184C22×C4×C47C2×D411yescharacteristic
185C22×C4×C47C2×D411yescharacteristic
186C22×C4×C47C2×D411yescharacteristic
187C22×C4×C47C2×D412yes—
188C22×C4×C47C2411yescharacteristic
189C22×Dic47—21no—
190C22×Dic47—21no—
191C22×Dic47—21no—
192C22×Dic47—21no—
193C4⋊C4×C47—24no—
194C4⋊C4×C47—24no—
195C4⋊C4×C47—24no—
196C4⋊C4×C47—21no—
197C4⋊C4×C47—21no—
198C4⋊C4×C47C22⋊C414yes—
199C4⋊C4×C47C22⋊C414yes—
200C4⋊C4×C47C22×C412yes—
201C4⋊C4×C47C22×C412yes—
202C22⋊C4×C47—24no—
203C22⋊C4×C47—24no—
204C22⋊C4×C47C22⋊C414yes—
205C22⋊C4×C47C22⋊C414yes—
206C42×C47—24no—
207C42×C47—24no—
208C42×C47C22×C412yes—
209C42×C47C22×C412yes—
210C42×C47C2×D412yes—
211C42×C47C2×D412yes—
212C22⋊Dic47—81no—
213C22⋊Dic47—81no—
214C4⋊Dic47—21no—
215C4⋊Dic47—21no—
216C4⋊Dic47—21no—
217C4⋊Dic47—21no—
218C4⋊Dic47—21no—
219C4⋊Dic47—21no—
220C4⋊Dic47—21no—
221C4⋊Dic47—21no—
222C4⋊Dic47—81no—
223C4⋊Dic47—81no—
224C4×Dic47—81no—
225C4×Dic47—81no—
226C2×C47⋊C8—21no—
227C2×C47⋊C8—21no—
228C2×C47⋊C8—21no—
229C2×C47⋊C8—21no—
230C2×C47⋊C8—21no—
231C2×C47⋊C8—21no—
232C2×C47⋊C8—21no—
233C2×C47⋊C8—21no—
234C2×C47⋊C8—21no—
235C2×C47⋊C8—21no—
236C2×C47⋊C8—21no—
237C2×C47⋊C8—21no—
238C23×C47—22no—
239C23×C47—21no—
240C23×C47—21no—
241C23×C47—22no—
242C23×C47—22no—
243C23×C47—21no—
244C23×C47—21no—
245C23×C47—21no—
246C23×C47—21no—
247C23×C47—41no—
248C23×C47—41no—
249C23×C47—41no—
250C23×C47—41no—
251C23×C47C2×C22⋊C412yes—
252C23×C47C22×D411yescharacteristic
253Q8×C47—22no—
254Q8×C47—22no—
255Q8×C47—22no—
256Q8×C47#11714yes—
257D4×C47—216no—
258D4×C47—22no—
259D4×C47—22no—
260D4×C47—22no—
261D4×C47#11714yes—
262C2×C4×C47—216no—
263C2×C4×C47—22no—
264C2×C4×C47—21no—
265C2×C4×C47—21no—
266C2×C4×C47—22no—
267C2×C4×C47—22no—
268C2×C4×C47—21no—
269C2×C4×C47—21no—
270C2×C4×C47—21no—
271C2×C4×C47—21no—
272C2×C4×C47—21no—
273C2×C4×C47—21no—
274C2×C4×C47—21no—
275C2×C4×C47—21no—
276C2×C4×C47—22no—
277C2×C4×C47—22no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—22no—
282C2×C4×C47—41no—
283C2×C4×C47—41no—
284C2×C4×C47—41no—
285C2×C4×C47—41no—
286C2×C4×C47—84no—
287C2×C4×C47—84no—
288C2×C4×C47—84no—
289C2×C4×C47C2×C22⋊C412yes—
290C2×C4×C47C2×C22⋊C412yes—
291C2×C4×C47C2×C22⋊C412yes—
292C2×C4×C47C2×C22⋊C412yes—
293C2×C4×C47C2×C22⋊C412yes—
294C2×C4×C47C23×C411yescharacteristic
295C2×C4×C47C22×D411yescharacteristic
296C2×C4×C47C2×#4111yescharacteristic
297C2×C4×C47C2×#4111yescharacteristic
298C2×C4×C47C2×#4111yescharacteristic
299C2×C4×C47C2×#4111yescharacteristic
300C2×Dic47—41no—
301C2×Dic47—41no—
302C2×Dic47—41no—
303C2×Dic47—41no—
304C2×Dic47—41no—
305C2×Dic47—41no—
306C2×Dic47—41no—
307C2×Dic47—41no—
308C2×Dic47—41no—
309C2×Dic47—41no—
310C2×Dic47—41no—
311C2×Dic47—41no—
312C47⋊C8—41no—
313C47⋊C8—41no—
314C47⋊C8—41no—
315C47⋊C8—41no—
316#20746—471nomaximal, Sylow
317C22×C47—22no—
318C22×C47—22no—
319C22×C47—22no—
320C22×C47—24no—
321C22×C47—41no—
322C22×C47—42no—
323C22×C47—41no—
324C22×C47—42no—
325C22×C47—41no—
326C22×C47—42no—
327C22×C47—41no—
328C22×C47—42no—
329C22×C47—42no—
330C22×C47—42no—
331C22×C47C22×C22⋊C411yescharacteristic
332C22×C47#52511yescharacteristic
333C22×C47#52511yescharacteristic
334C22×C47#57611yescharacteristic
335C22×C47#57711yescharacteristic
336C22×C47#57711yescharacteristic
337C22×C47#57811yescharacteristic
338C4×C47—22no—
339C4×C47—22no—
340C4×C47—22no—
341C4×C47—22no—
342C4×C47—22no—
343C4×C47—24no—
344C4×C47—42no—
345C4×C47—42no—
346C4×C47C2×#11711yescharacteristic
347C4×C47C2×#11711yescharacteristic
348C4×C47#52511yescharacteristic
349C4×C47#52511yescharacteristic
350Dic47—81no—
351Dic47—81no—
352Dic47—81no—
353Dic47—81no—
354C2×#520D4711yescharacteristic
355C2×#433—471no—
356#2314—471no—
357#1824—471no—
358#1823—471no—
359#1805—471no—
360#1804—471no—
361#1803—471no—
362#1802—471no—
363#1788—471no—
364#1788—471no—
365#1763—471no—
366#1762—471no—
367C4×#103—471no—
368C4×#102—471no—
369C2×C47—42no—
370C2×C47—44no—
371C2×C47#228011yescharacteristic
372C2×C47#289711yescharacteristic
373C2×C47#289811yescharacteristic
374C2×C47#311911yescharacteristic
375C2×C47#312011yescharacteristic
376C2×C47#312411yescharacteristic
377C2×C47#312511yescharacteristic
378C22×#41C2×D4711yescharacteristic
379#520—24no—
380#520Dic4718yescomplemented
381C2×C4×Q8C2×D4711yescharacteristic
382C2×C4×Q8C2×D4711yescharacteristic
383C2×C4×D4—21no—
384C2×C4×D4—21no—
385C2×C4×D4C2×D4711yescharacteristic
386C2×C4×D4C2×D4711yescharacteristic
387C2×#117—21no—
388C2×#117C2×D4711yescharacteristic
389C22×C4⋊C4—21no—
390C22×C4⋊C4C2×D4711yescharacteristic
391#433—944no—
392C2×C4⋊C8—471no—
393C2×C4⋊C8—471no—
394C2×#103—471no—
395C2×#103—471no—
396C2×#103—471no—
397C2×#103—471no—
398C2×#102—471no—
399C2×#102—471no—
400C2×#102—471no—
401C2×#102—471no—
402C2×C22⋊C8—471no—
403C2×C22⋊C8—471no—
404C2×#97—471no—
405C2×C4×C8—471no—
406#388—941no—
407#388—941no—
408#387—941no—
409#387—941no—
410#384—471no—
411#382—471no—
412#380—471no—
413#380—471no—
414C4×C4⋊C4—471no—
415C4×C4⋊C4—471no—
416#340—471no—
417#340—471no—
418#340—471no—
419#340—471no—
420#340—471no—
421#340—471no—
422#340—471no—
423#340—471no—
424C47#2074611yescharacteristic, complemented, Sylow
425C2×#41—22no—
426C2×#41—22no—
427C2×#41—22no—
428C2×#41—22no—
429C2×#41—22no—
430C2×#41C2×Dic4714yes—
431C22×Q8C22×D4711yescharacteristic
432C22×D4—21no—
433C22×D4C22×D4711yescharacteristic
434C23×C4—21no—
435C23×C4—21no—
436C23×C4—21no—
437C23×C4—21no—
438C23×C4C22×D4711yescharacteristic
439C22×C8—471no—
440C22×C8—471no—
441C22×C8—471no—
442C22×C8—471no—
443C4×Q8—22no—
444C4×Q8—22no—
445C4×Q8C2×Dic4714yes—
446C4×Q8C2×Dic4714yes—
447C4×D4—28no—
448C4×D4—28no—
449C4×D4—22no—
450C4×D4—22no—
451C4×D4C2×Dic4714yes—
452C4×D4C2×Dic4714yes—
453#117—28no—
454#117C2×Dic4714yes—
455#117C22⋊D4714yes—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—28no—
461C2×C4⋊C4—471no—
462C2×C4⋊C4—471no—
463C2×C4⋊C4—471no—
464C2×C4⋊C4—471no—
465C2×C4⋊C4—941no—
466C2×C4⋊C4—941no—
467C2×C4⋊C4C2×Dic4714yes—
468C2×C4⋊C4C22⋊D4711yescharacteristic
469C2×C4⋊C4C22⋊D4711yescharacteristic
470C2×C4⋊C4C22×D4711yescharacteristic
471C2×C4⋊C4C22×D4711yescharacteristic
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—941no—
475C2×C22⋊C4—941no—
476C2×C22⋊C4C22⋊D4711yescharacteristic
477C2×C22⋊C4C22⋊D4711yescharacteristic
478C2×C42—21no—
479C2×C42—21no—
480C2×C42—941no—
481C2×C42—941no—
482C2×C42C22×D4711yescharacteristic
483C2×C42C22×D4711yescharacteristic
484C4⋊C8—942no—
485C4⋊C8—942no—
486#103—942no—
487#103—942no—
488#103—942no—
489#103—942no—
490#102—942no—
491#102—942no—
492#102—942no—
493#102—942no—
494C22⋊C8—942no—
495C22⋊C8—942no—
496#97—942no—
497C4×C8—942no—
498#95—941no—
499#95—941no—
500#95—941no—
501#95—941no—
502#95—941no—
503#95—941no—
504C24—21no—
505C24C2×C22⋊D4711yescharacteristic
506#41—28no—
507#41—28no—
508#41—28no—
509#41—28no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8#1062535012yes—
514C2×Q8#1062535012yes—
515C2×Q8C22×Dic4712yes—
516C2×D4—24no—
517C2×D4—24no—
518C2×D4—24no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4#1062535012yes—
523C2×D4#1062535012yes—
524C2×D4C22×Dic4712yes—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—21no—
528C22×C4—24no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—81no—
539C22×C4—81no—
540C22×C4—81no—
541C22×C4—81no—
542C22×C4—81no—
543C22×C4—81no—
544C22×C4—941no—
545C22×C4—941no—
546C22×C4—941no—
547C22×C4—941no—
548C22×C4C22×Dic4712yes—
549C22×C4C2×C22⋊D4711yescharacteristic
550C22×C4C2×C22⋊D4711yescharacteristic
551C22×C4C2×C22⋊D4711yescharacteristic
552C22×C4C2×C22⋊D4711yescharacteristic
553C22×C4C2×C22⋊D4711yescharacteristic
554C22×C4C2×C22⋊D4712yes—
555C22×C4C23×D4711yescharacteristic
556C2×C8—941no—
557C2×C8—941no—
558C2×C8—941no—
559C2×C8—941no—
560C2×C8—941no—
561C2×C8—941no—
562C2×C8—941no—
563C2×C8—941no—
564C2×C8—941no—
565C2×C8—941no—
566C2×C8—941no—
567C2×C8—941no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—941no—
574C4⋊C4—941no—
575C4⋊C4—941no—
576C4⋊C4—941no—
577C4⋊C4—941no—
578C4⋊C4—941no—
579C4⋊C4—941no—
580C4⋊C4—941no—
581C4⋊C4—3761no—
582C4⋊C4—3761no—
583C4⋊C4C22⋊Dic4714yes—
584C4⋊C4C22⋊Dic4714yes—
585C4⋊C4C22×Dic4712yes—
586C4⋊C4C22×Dic4712yes—
587C22⋊C4—24no—
588C22⋊C4—24no—
589C22⋊C4—3761no—
590C22⋊C4—3761no—
591C22⋊C4C22⋊Dic4714yes—
592C22⋊C4C22⋊Dic4714yes—
593C42—24no—
594C42—24no—
595C42—3761no—
596C42—3761no—
597C42C22×Dic4712yes—
598C42C22×Dic4712yes—
599C42C2×C22⋊D4712yes—
600C42C2×C22⋊D4712yes—
601C23—22no—
602C23—21no—
603C23—21no—
604C23—22no—
605C23—22no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23C2×C22⋊Dic4712yes—
615C23C22×C22⋊D4711yescharacteristic
616Q8—22no—
617Q8—22no—
618Q8—22no—
619Q8#1309398314yes—
620D4—216no—
621D4—22no—
622D4—22no—
623D4—22no—
624D4#1309398314yes—
625C2×C4—216no—
626C2×C4—22no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—84no—
650C2×C4—84no—
651C2×C4—84no—
652C2×C4—1881no—
653C2×C4—1881no—
654C2×C4—1881no—
655C2×C4—1881no—
656C2×C4—1881no—
657C2×C4—1881no—
658C2×C4—1881no—
659C2×C4—1881no—
660C2×C4—1881no—
661C2×C4—1881no—
662C2×C4—1881no—
663C2×C4—1881no—
664C2×C4C2×C22⋊Dic4712yes—
665C2×C4C2×C22⋊Dic4712yes—
666C2×C4C2×C22⋊Dic4712yes—
667C2×C4C2×C22⋊Dic4712yes—
668C2×C4C2×C22⋊Dic4712yes—
669C2×C4C23×Dic4711yescharacteristic
670C2×C4C22×C22⋊D4711yescharacteristic
671C2×C4C2×#1062535011yescharacteristic
672C2×C4C2×#1062535011yescharacteristic
673C2×C4C2×#1062535011yescharacteristic
674C2×C4C2×#1062535011yescharacteristic
675C8—1881no—
676C8—1881no—
677C8—1881no—
678C8—1881no—
679C22—22no—
680C22—22no—
681C22—24no—
682C22—22no—
683C22—42no—
684C22—42no—
685C22—41no—
686C22—42no—
687C22—41no—
688C22—42no—
689C22—41no—
690C22—42no—
691C22—41no—
692C22—42no—
693C22C22×C22⋊Dic4711yescharacteristic
694C22#1568963411yescharacteristic
695C22#1568963411yescharacteristic
696C22#1568992611yescharacteristic
697C22#1568993111yescharacteristic
698C22#1568993411yescharacteristic
699C22#1568993811yescharacteristic
700C4—22no—
701C4—22no—
702C4—22no—
703C4—24no—
704C4—22no—
705C4—22no—
706C4—42no—
707C4—42no—
708C4—3761no—
709C4—3761no—
710C4—3761no—
711C4—3761no—
712C4C2×#1309398311yescharacteristic
713C4C2×#1309398311yescharacteristic
714C4#1568963411yescharacteristic
715C4#1568963411yescharacteristic
716C2—42no—
717C2—44no—
718C2#2024577111yescharacteristic
719C2#2025191411yescharacteristic
720C2#2025192111yescharacteristic
721C2#2025358711yescharacteristic
722C2#2025360211yescharacteristic
723C2#2025365011yescharacteristic
724C2#2025366511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#520C2
socleC23×C47C22×D4
prime radicalC22×#41×C47C22
cosocleC22×C4×C47C24
hypercenterC2×#520D47
hypocenterC47#20746
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. C2×#15689184C2semidirect
2. #20245997C2semidirect
3. #20243478C2semidirect
4. #20243474C2semidirect
5. #20243403C2semidirect
6. #20243398C2semidirect
7. #20243393C2semidirect
8. #20243388C2semidirect
11. #20243218C2semidirect
12. #20243213C2semidirect
13. C4×#13093948C2semidirect
14. C4×#13093945C2semidirect
51. C47×#520C4semidirect
380. #520Dic47semidirect
424. C47#20746semidirect

Maximal subgroups

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

subgroupindex
C2×#156891842
#202459972
#202434782
#202434742
#202434032
#202433982
#202433932
#202433882
#202433282
#202432182
#202432132
C4×#130939482
C4×#130939452
C2×C47×#5202
#2074647