Finite Group Databasebeta

← #26221551

Subgroups — #26221551

Order 12032.

1134 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689079C211yesmaximal, characteristic, complemented
2#20245997C211yesmaximal, characteristic, complemented
3#20244362C211yesmaximal, characteristic, complemented
4#20244350C211yesmaximal, characteristic, complemented
5#20244205C211yesmaximal, characteristic, complemented
6#20244200C211yesmaximal, characteristic, complemented
7#20243827C211yesmaximal, characteristic
8#20243822C211yesmaximal, characteristic, complemented
9#20243817C211yesmaximal, characteristic
10#20243812C211yesmaximal, characteristic, complemented
11#20243218C211yesmaximal, characteristic, complemented
12#20243213C211yesmaximal, characteristic, complemented
13C4×#13093948C211yesmaximal, characteristic, complemented
14C4×#13093945C211yesmaximal, characteristic, complemented
15C2×C47×#542C211yesmaximal, characteristic
16C22×#10625329C2211yescharacteristic
17C23×C47⋊C8C2211yescharacteristic
18C2×#13093948C2211yescharacteristic
19C2×#13093948C2211yescharacteristic
20C2×#13093948C2211yescharacteristic
21C2×#13093948C2211yescharacteristic
22C2×#13093945C2211yescharacteristic
23C2×#13093945C2211yescharacteristic
24C2×#13093945C2211yescharacteristic
25C2×#13093945C2211yescharacteristic
26#15689079—24no—
27C2×#13093935C2211yescharacteristic
28C2×#13093935C2211yescharacteristic
29C2×C4×C47⋊C8C2211yescharacteristic
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
49C47×#542—24no—
50C47×#542C418yescomplemented
51C2×C4⋊Q8×C47C2211yescharacteristic
52C2×#126×C47—21no—
53C2×#124×C47—21no—
54C2×#124×C47C2211yescharacteristic
55C2×#123×C47—21no—
56C2×C22⋊Q8×C47—21no—
57C2×C22⋊Q8×C47C2211yescharacteristic
58C2×#121×C47C2211yescharacteristic
59C2×C4×Q8×C47C2211yescharacteristic
60C2×C4×D4×C47C2211yescharacteristic
61C2×#117×C47C2211yescharacteristic
62C2×#10625329—22no—
63C2×#10625329—22no—
64C2×#10625329—22no—
65C22×C47⋊C8—22no—
66C22×C47⋊C8—22no—
67C22×C47⋊C8—22no—
68C22×C47⋊C8C2311yescharacteristic
69C22×C47⋊C8C2311yescharacteristic
70C22×C47⋊C8C2311yescharacteristic
71C22×C47⋊C8C2311yescharacteristic
72C2×C4⋊Dic47—21no—
73C2×C4⋊Dic47—21no—
74C2×C4⋊Dic47C2311yescharacteristic
75C2×C4⋊Dic47C2311yescharacteristic
76C2×C4⋊Dic47C2311yescharacteristic
77C2×C4⋊Dic47C2311yescharacteristic
78C2×C22⋊Dic47—21no—
79C2×C22⋊Dic47—21no—
80C2×C4×Dic47—21no—
81C2×C4×Dic47—21no—
82#13093948—22no—
83#13093948—22no—
84#13093948—22no—
85#13093948—22no—
86#13093945—22no—
87#13093945—22no—
88#13093945—22no—
89#13093945—22no—
90#13093935—22no—
91#13093935—22no—
92C4×C47⋊C8—22no—
93C4×C47⋊C8—22no—
94C47⋊#95—21no—
95C47⋊#95—21no—
96C47⋊#95—21no—
97C47⋊#95—21no—
98C47⋊#95—21no—
99C47⋊#95—21no—
100C22×Q8×C47—21no—
101C22×Q8×C47C2311yescharacteristic
102C22×D4×C47—21no—
103C22×D4×C47C2311yescharacteristic
104C23×C4×C47—21no—
105C23×C4×C47C2311yescharacteristic
106C4⋊Q8×C47—22no—
107C4⋊Q8×C47C2×C414yes—
108#126×C47—28no—
109#124×C47—28no—
110#124×C47—22no—
111#124×C47C2×C414yes—
112#123×C47—28no—
113C22⋊Q8×C47—22no—
114C22⋊Q8×C47—28no—
115C22⋊Q8×C47C2×C414yes—
116#121×C47—22no—
117#121×C47C2×C414yes—
118C4×Q8×C47—22no—
119C4×Q8×C47C2×C414yes—
120C4×D4×C47—22no—
121C4×D4×C47C2×C414yes—
122#117×C47C2×C414yes—
123#117×C47D414yes—
124C2×C4⋊C4×C47—21no—
125C2×C4⋊C4×C47—21no—
126C2×C4⋊C4×C47—21no—
127C2×C4⋊C4×C47D411yescharacteristic
128C2×C4⋊C4×C47D411yescharacteristic
129C2×C4⋊C4×C47C2311yescharacteristic
130C2×C4⋊C4×C47C2311yescharacteristic
131C2×C22⋊C4×C47—21no—
132C2×C22⋊C4×C47—21no—
133C2×C22⋊C4×C47—21no—
134C2×C22⋊C4×C47—21no—
135C2×C22⋊C4×C47—21no—
136C2×C22⋊C4×C47D411yescharacteristic
137C2×C22⋊C4×C47D411yescharacteristic
138C2×C42×C47—21no—
139C2×C42×C47C2311yescharacteristic
140C2×C42×C47C2311yescharacteristic
141C24×C47—21no—
142C24×C47C2×D411yescharacteristic
143C2×Q8×C47—24no—
144C2×Q8×C47—21no—
145C2×Q8×C47—21no—
146C2×Q8×C47—21no—
147C2×Q8×C47—21no—
148C2×Q8×C47—21no—
149C2×Q8×C47—81no—
150C2×Q8×C47—81no—
151C2×Q8×C47C22×C412yes—
152C2×D4×C47—24no—
153C2×D4×C47—21no—
154C2×D4×C47—21no—
155C2×D4×C47—21no—
156C2×D4×C47—21no—
157C2×D4×C47—21no—
158C2×D4×C47—81no—
159C2×D4×C47—81no—
160C2×D4×C47C22×C412yes—
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—24no—
169C22×C4×C47—81no—
170C22×C4×C47—81no—
171C22×C4×C47C22×C412yes—
172C22×C4×C47C2×D411yescharacteristic
173C22×C4×C47C2×D411yescharacteristic
174C22×C4×C47C2×D411yescharacteristic
175C22×C4×C47C2×D411yescharacteristic
176C22×C4×C47C2×D411yescharacteristic
177C22×C4×C47C2×D412yes—
178C22×C4×C47C2411yescharacteristic
179C22×Dic47—21no—
180C22×Dic47—21no—
181C22×Dic47—21no—
182C22×Dic47—21no—
183C4⋊C4×C47—24no—
184C4⋊C4×C47—24no—
185C4⋊C4×C47—24no—
186C4⋊C4×C47—21no—
187C4⋊C4×C47—21no—
188C4⋊C4×C47C22⋊C414yes—
189C4⋊C4×C47C22⋊C414yes—
190C4⋊C4×C47C22×C412yes—
191C4⋊C4×C47C22×C412yes—
192C22⋊C4×C47—24no—
193C22⋊C4×C47—24no—
194C22⋊C4×C47—24no—
195C22⋊C4×C47—24no—
196C22⋊C4×C47—24no—
197C22⋊C4×C47C22⋊C414yes—
198C22⋊C4×C47C22⋊C414yes—
199C42×C47—24no—
200C42×C47C22×C412yes—
201C42×C47C22×C412yes—
202C42×C47C2×D412yes—
203C42×C47C2×D412yes—
204C22⋊Dic47—81no—
205C22⋊Dic47—81no—
206C4⋊Dic47—21no—
207C4⋊Dic47—21no—
208C4⋊Dic47—21no—
209C4⋊Dic47—21no—
210C4⋊Dic47—21no—
211C4⋊Dic47—21no—
212C4⋊Dic47—21no—
213C4⋊Dic47—21no—
214C4⋊Dic47—81no—
215C4⋊Dic47—81no—
216C4×Dic47—81no—
217C4×Dic47—81no—
218#10625329—28no—
219C2×C47⋊C8—28no—
220C2×C47⋊C8—21no—
221C2×C47⋊C8—21no—
222C2×C47⋊C8—21no—
223C2×C47⋊C8—21no—
224C2×C47⋊C8—21no—
225C2×C47⋊C8—21no—
226C2×C47⋊C8—21no—
227C2×C47⋊C8—21no—
228C2×C47⋊C8#4112yes—
229C2×C47⋊C8#4112yes—
230C2×C47⋊C8#4112yes—
231C2×C47⋊C8#4112yes—
232C23×C47—21no—
233C23×C47—21no—
234C23×C47—21no—
235C23×C47—21no—
236C23×C47—21no—
237C23×C47—21no—
238C23×C47—22no—
239C23×C47—41no—
240C23×C47—41no—
241C23×C47—41no—
242C23×C47—41no—
243C23×C47—41no—
244C23×C47—41no—
245C23×C47C2×C22⋊C412yes—
246C23×C47C22×D411yescharacteristic
247Q8×C47—22no—
248Q8×C47—22no—
249Q8×C47—41no—
250Q8×C47—41no—
251Q8×C47—84no—
252D4×C47—22no—
253D4×C47—22no—
254D4×C47—41no—
255D4×C47—41no—
256D4×C47—84no—
257C2×C4×C47—21no—
258C2×C4×C47—21no—
259C2×C4×C47—21no—
260C2×C4×C47—21no—
261C2×C4×C47—21no—
262C2×C4×C47—21no—
263C2×C4×C47—21no—
264C2×C4×C47—21no—
265C2×C4×C47—21no—
266C2×C4×C47—21no—
267C2×C4×C47—22no—
268C2×C4×C47—22no—
269C2×C4×C47—22no—
270C2×C4×C47—22no—
271C2×C4×C47—22no—
272C2×C4×C47—22no—
273C2×C4×C47—22no—
274C2×C4×C47—41no—
275C2×C4×C47—41no—
276C2×C4×C47—41no—
277C2×C4×C47—41no—
278C2×C4×C47—41no—
279C2×C4×C47—41no—
280C2×C4×C47—84no—
281C2×C4×C47C2×C22⋊C412yes—
282C2×C4×C47C2×C22⋊C412yes—
283C2×C4×C47C2×C22⋊C412yes—
284C2×C4×C47C2×C22⋊C412yes—
285C2×C4×C47C2×C22⋊C412yes—
286C2×C4×C47C23×C411yescharacteristic
287C2×C4×C47C22×D411yescharacteristic
288C2×C4×C47C2×#4111yescharacteristic
289C2×C4×C47C2×#4111yescharacteristic
290C2×C4×C47C2×#4111yescharacteristic
291C2×C4×C47C2×#4111yescharacteristic
292C2×Dic47—41no—
293C2×Dic47—41no—
294C2×Dic47—41no—
295C2×Dic47—41no—
296C2×Dic47—41no—
297C2×Dic47—41no—
298C2×Dic47—41no—
299C2×Dic47—41no—
300C2×Dic47—41no—
301C2×Dic47—41no—
302C2×Dic47—41no—
303C2×Dic47—41no—
304C47⋊C8—22no—
305C47⋊C8—22no—
306C47⋊C8—22no—
307C47⋊C8—22no—
308#21412—471nomaximal, Sylow
309C22×C47—22no—
310C22×C47—22no—
311C22×C47—22no—
312C22×C47—41no—
313C22×C47—41no—
314C22×C47—41no—
315C22×C47—41no—
316C22×C47—42no—
317C22×C47—42no—
318C22×C47—42no—
319C22×C47—81no—
320C22×C47—81no—
321C22×C47—81no—
322C22×C47—81no—
323C22×C47C22×C22⋊C411yescharacteristic
324C22×C47#53211yescharacteristic
325C22×C47#53211yescharacteristic
326C22×C47#57611yescharacteristic
327C22×C47#57711yescharacteristic
328C22×C47#57711yescharacteristic
329C22×C47#57811yescharacteristic
330C4×C47—22no—
331C4×C47—22no—
332C4×C47—22no—
333C4×C47—22no—
334C4×C47—22no—
335C4×C47—42no—
336C4×C47—42no—
337C4×C47—42no—
338C4×C47C4×#4111yescharacteristic
339C4×C47C4×#4111yescharacteristic
340C4×C47#52511yescharacteristic
341C4×C47#52511yescharacteristic
342Dic47—81no—
343Dic47—81no—
344Dic47—81no—
345Dic47—81no—
346C2×#542D4711yescharacteristic
347C2×#405—471no—
348#2314—471no—
349#1993—471no—
350#1990—471no—
351#1959—471no—
352#1958—471no—
353#1895—471no—
354#1894—471no—
355#1893—471no—
356#1892—471no—
357#1763—471no—
358#1762—471no—
359C4×#103—471no—
360C4×#102—471no—
361C2×C47—42no—
362C2×C47—82no—
363C2×C47#229711yescharacteristic
364C2×C47#289711yescharacteristic
365C2×C47#289811yescharacteristic
366C2×C47#317311yescharacteristic
367C2×C47#317511yescharacteristic
368C2×C47#317811yescharacteristic
369C2×C47#317911yescharacteristic
370C22×M16—471no—
371C23×C8—471no—
372#542—24no—
373#542Dic4718yescomplemented
374C2×C4⋊Q8C2×D4711yescharacteristic
375C2×#126—21no—
376C2×#124—21no—
377C2×#124C2×D4711yescharacteristic
378C2×#123—21no—
379C2×C22⋊Q8—21no—
380C2×C22⋊Q8C2×D4711yescharacteristic
381C2×#121C2×D4711yescharacteristic
382C2×C4×Q8C2×D4711yescharacteristic
383C2×C4×D4C2×D4711yescharacteristic
384C2×#117C2×D4711yescharacteristic
385C2×#103—471no—
386C2×#103—471no—
387C2×#103—471no—
388C2×#103—471no—
389C2×#102—471no—
390C2×#102—471no—
391C2×#102—471no—
392C2×#102—471no—
393#405—944no—
394C2×#97—471no—
395C2×#97—471no—
396C2×C4×C8—471no—
397C2×C4×C8—471no—
398#388—941no—
399#388—941no—
400#387—941no—
401#387—941no—
402#384—471no—
403#382—471no—
404#380—471no—
405#380—471no—
406C4×C4⋊C4—471no—
407C4×C4⋊C4—471no—
408#340—471no—
409#340—471no—
410#340—471no—
411#340—471no—
412#340—471no—
413#340—471no—
414#340—471no—
415#340—471no—
416C47#2141211yescharacteristic, complemented, Sylow
417C22×Q8—21no—
418C22×Q8C22×D4711yescharacteristic
419C22×D4—21no—
420C22×D4C22×D4711yescharacteristic
421C23×C4—21no—
422C23×C4C22×D4711yescharacteristic
423C2×M16—942no—
424C2×M16—942no—
425C2×M16—942no—
426C22×C8—471no—
427C22×C8—471no—
428C22×C8—471no—
429C22×C8—471no—
430C22×C8—942no—
431C22×C8—942no—
432C22×C8—942no—
433C4⋊Q8—22no—
434C4⋊Q8C2×Dic4714yes—
435#126—28no—
436#124—28no—
437#124—22no—
438#124C2×Dic4714yes—
439#123—28no—
440C22⋊Q8—22no—
441C22⋊Q8—28no—
442C22⋊Q8C2×Dic4714yes—
443#121—22no—
444#121C2×Dic4714yes—
445C4×Q8—22no—
446C4×Q8C2×Dic4714yes—
447C4×D4—22no—
448C4×D4C2×Dic4714yes—
449#117C2×Dic4714yes—
450#117C22⋊D4714yes—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—471no—
455C2×C4⋊C4—471no—
456C2×C4⋊C4—471no—
457C2×C4⋊C4—471no—
458C2×C4⋊C4—941no—
459C2×C4⋊C4—941no—
460C2×C4⋊C4C22⋊D4711yescharacteristic
461C2×C4⋊C4C22⋊D4711yescharacteristic
462C2×C4⋊C4C22×D4711yescharacteristic
463C2×C4⋊C4C22×D4711yescharacteristic
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—941no—
470C2×C22⋊C4—941no—
471C2×C22⋊C4C22⋊D4711yescharacteristic
472C2×C22⋊C4C22⋊D4711yescharacteristic
473C2×C42—21no—
474C2×C42—941no—
475C2×C42—941no—
476C2×C42C22×D4711yescharacteristic
477C2×C42C22×D4711yescharacteristic
478#103—942no—
479#103—942no—
480#103—942no—
481#103—942no—
482#102—942no—
483#102—942no—
484#102—942no—
485#102—942no—
486#97—942no—
487#97—942no—
488C4×C8—942no—
489C4×C8—942no—
490#95—941no—
491#95—941no—
492#95—941no—
493#95—941no—
494#95—941no—
495#95—941no—
496C24—21no—
497C24C2×C22⋊D4711yescharacteristic
498C2×Q8—24no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—81no—
505C2×Q8—81no—
506C2×Q8C22×Dic4712yes—
507C2×D4—24no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—81no—
514C2×D4—81no—
515C2×D4C22×Dic4712yes—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—24no—
524C22×C4—81no—
525C22×C4—81no—
526C22×C4—941no—
527C22×C4—941no—
528C22×C4—941no—
529C22×C4—941no—
530C22×C4C22×Dic4712yes—
531C22×C4C2×C22⋊D4711yescharacteristic
532C22×C4C2×C22⋊D4711yescharacteristic
533C22×C4C2×C22⋊D4711yescharacteristic
534C22×C4C2×C22⋊D4711yescharacteristic
535C22×C4C2×C22⋊D4711yescharacteristic
536C22×C4C2×C22⋊D4712yes—
537C22×C4C23×D4711yescharacteristic
538M16—948no—
539C2×C8—472no—
540C2×C8—472no—
541C2×C8—472no—
542C2×C8—472no—
543C2×C8—948no—
544C2×C8—941no—
545C2×C8—941no—
546C2×C8—941no—
547C2×C8—941no—
548C2×C8—941no—
549C2×C8—941no—
550C2×C8—941no—
551C2×C8—941no—
552C4⋊C4—24no—
553C4⋊C4—24no—
554C4⋊C4—24no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—941no—
558C4⋊C4—941no—
559C4⋊C4—941no—
560C4⋊C4—941no—
561C4⋊C4—941no—
562C4⋊C4—941no—
563C4⋊C4—941no—
564C4⋊C4—941no—
565C4⋊C4—3761no—
566C4⋊C4—3761no—
567C4⋊C4C22⋊Dic4714yes—
568C4⋊C4C22⋊Dic4714yes—
569C4⋊C4C22×Dic4712yes—
570C4⋊C4C22×Dic4712yes—
571C22⋊C4—24no—
572C22⋊C4—24no—
573C22⋊C4—24no—
574C22⋊C4—24no—
575C22⋊C4—24no—
576C22⋊C4—3761no—
577C22⋊C4—3761no—
578C22⋊C4C22⋊Dic4714yes—
579C22⋊C4C22⋊Dic4714yes—
580C42—24no—
581C42—3761no—
582C42—3761no—
583C42C22×Dic4712yes—
584C42C22×Dic4712yes—
585C42C2×C22⋊D4712yes—
586C42C2×C22⋊D4712yes—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—22no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23C2×C22⋊Dic4712yes—
601C23C22×C22⋊D4711yescharacteristic
602Q8—22no—
603Q8—22no—
604Q8—41no—
605Q8—41no—
606Q8—84no—
607D4—22no—
608D4—22no—
609D4—41no—
610D4—41no—
611D4—84no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—84no—
636C2×C4—1881no—
637C2×C4—1881no—
638C2×C4—1881no—
639C2×C4—1881no—
640C2×C4—1881no—
641C2×C4—1881no—
642C2×C4—1881no—
643C2×C4—1881no—
644C2×C4—1881no—
645C2×C4—1881no—
646C2×C4—1881no—
647C2×C4—1881no—
648C2×C4C2×C22⋊Dic4712yes—
649C2×C4C2×C22⋊Dic4712yes—
650C2×C4C2×C22⋊Dic4712yes—
651C2×C4C2×C22⋊Dic4712yes—
652C2×C4C2×C22⋊Dic4712yes—
653C2×C4C23×Dic4711yescharacteristic
654C2×C4C22×C22⋊D4711yescharacteristic
655C2×C4#41×D4711yescharacteristic
656C2×C4#41×D4711yescharacteristic
657C2×C4#41×D4711yescharacteristic
658C2×C4#41×D4711yescharacteristic
659C8—942no—
660C8—942no—
661C8—942no—
662C8—942no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—42no—
671C22—42no—
672C22—42no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22C22×C22⋊Dic4711yescharacteristic
678C22#1568966911yescharacteristic
679C22#1568966911yescharacteristic
680C22#1568992611yescharacteristic
681C22#1568993111yescharacteristic
682C22#1568993411yescharacteristic
683C22#1568993811yescharacteristic
684C4—22no—
685C4—22no—
686C4—22no—
687C4—22no—
688C4—22no—
689C4—42no—
690C4—42no—
691C4—42no—
692C4—3761no—
693C4—3761no—
694C4—3761no—
695C4—3761no—
696C4#41×Dic4711yescharacteristic
697C4#41×Dic4711yescharacteristic
698C4#1568963011yescharacteristic
699C4#1568963011yescharacteristic
700C2—42no—
701C2—82no—
702C2#2024587911yescharacteristic
703C2#2025191411yescharacteristic
704C2#2025192111yescharacteristic
705C2#2025399911yescharacteristic
706C2#2025402111yescharacteristic
707C2#2025405011yescharacteristic
708C2#2025406511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#542C2
socleC23×C47C22×D4
prime radicalC2×#121×C47C22
cosocleC22×C4×C47C24
hypercenterC2×#542D47
hypocenterC47#21412
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#15689079C2semidirect
2. #20245997C2semidirect
3. #20244362C2semidirect
4. #20244350C2semidirect
5. #20244205C2semidirect
6. #20244200C2semidirect
8. #20243822C2semidirect
10. #20243812C2semidirect
11. #20243218C2semidirect
12. #20243213C2semidirect
13. C4×#13093948C2semidirect
14. C4×#13093945C2semidirect
50. C47×#542C4semidirect
373. #542Dic47semidirect
416. C47#21412semidirect

Maximal subgroups

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

subgroupindex
C2×#156890792
#202459972
#202443622
#202443502
#202442052
#202442002
#202438272
#202438222
#202438172
#202438122
#202432182
#202432132
C4×#130939482
C4×#130939452
C2×C47×#5422
#2141247