Finite Group Databasebeta

← #26216390

Subgroups — #26216390

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×#15689603C211yesmaximal, characteristic
2#20245997C211yesmaximal, characteristic, complemented
3#20243479C211yesmaximal, characteristic, complemented
4#20243475C211yesmaximal, characteristic, complemented
5#20243404C211yesmaximal, characteristic, complemented
6#20243399C211yesmaximal, characteristic, complemented
7#20243394C211yesmaximal, characteristic, complemented
8#20243389C211yesmaximal, characteristic, complemented
9#20243329C211yesmaximal, characteristic
10#20243329C211yesmaximal, characteristic
11#20243219C211yesmaximal, characteristic, complemented
12#20243214C211yesmaximal, characteristic, complemented
13C4×#13093949C211yesmaximal, characteristic, complemented
14C4×#13093946C211yesmaximal, characteristic, complemented
15C2×C47×#433C211yesmaximal, characteristic, complemented
16C22×#10625350C2211yescharacteristic
17#15689603—24no—
18#15689603C418yescomplemented
19C2×C4×Dic94C2211yescharacteristic
20C2×C4×Dic94C2211yescharacteristic
21C2×C4×D188C2211yescharacteristic
22C2×C4×D188C2211yescharacteristic
23C2×(C22⋊D47)⋊C4—21no—
24C2×(C22⋊D47)⋊C4—21no—
25C2×#13093982—21no—
26C22×C4⋊Dic47C2211yescharacteristic
27C2×C4⋊C4×D47—21no—
28C2×#13093949C2211yescharacteristic
29C2×#13093949C2211yescharacteristic
30C2×#13093949C2211yescharacteristic
31C2×#13093949C2211yescharacteristic
32C2×#13093946C2211yescharacteristic
33C2×#13093946C2211yescharacteristic
34C2×#13093946C2211yescharacteristic
35C2×#13093946C2211yescharacteristic
36#15689016—21no—
37#15689016—21no—
38#15689009—21no—
39#15689009—21no—
40#15688993C2211yescharacteristic
41#15688989C2211yescharacteristic
42#15688983C2211yescharacteristic
43#15688983C2211yescharacteristic
44C4×C4⋊Dic47C2211yescharacteristic
45C4×C4⋊Dic47C2211yescharacteristic
46#15688886C2211yescharacteristic
47#15688886C2211yescharacteristic
48#15688886C2211yescharacteristic
49#15688886C2211yescharacteristic
50#15688886C2211yescharacteristic
51#15688886C2211yescharacteristic
52#15688886C2211yescharacteristic
53#15688886C2211yescharacteristic
54C2×#117×C47C2211yescharacteristic
55C47×#433—24no—
56C2×C4⋊C8×C47C2211yescharacteristic
57C2×C4⋊C8×C47C2211yescharacteristic
58C2×C22⋊C8×C47C2211yescharacteristic
59C2×C22⋊C8×C47C2211yescharacteristic
60C2×#97×C47C2211yescharacteristic
61C2×C4×C8×C47C2211yescharacteristic
62C2×#10625350—22no—
63C2×#10625350—22no—
64C2×#10625350—22no—
65C2×#10625350—22no—
66C2×#10625350—22no—
67C2×#10625350C2×C414yes—
68C22×Dic94C2311yescharacteristic
69C22×D188C2311yescharacteristic
70C22×C22⋊D47—21no—
71C23×Dic47—21no—
72C22×C4×D47—21no—
73C22×C4×D47—21no—
74C22×C4×D47—21no—
75C4×Dic94—22no—
76C4×Dic94—22no—
77C4×Dic94C2×C414yes—
78C4×Dic94C2×C414yes—
79C4×D188—22no—
80C4×D188—22no—
81C4×D188C2×C414yes—
82C4×D188C2×C414yes—
83(C22⋊D47)⋊C4—28no—
84(C22⋊D47)⋊C4—28no—
85#13093982—28no—
86C2×C4⋊Dic47—21no—
87C2×C4⋊Dic47—22no—
88C2×C4⋊Dic47—21no—
89C2×C4⋊Dic47—21no—
90C2×C4⋊Dic47C2×C414yes—
91C2×C4⋊Dic47C2311yescharacteristic
92C2×C4⋊Dic47C2311yescharacteristic
93C2×C4⋊Dic47C2311yescharacteristic
94C2×C4⋊Dic47C2311yescharacteristic
95C2×C4⋊Dic47C2311yescharacteristic
96C2×C4⋊Dic47C2311yescharacteristic
97C2×Dic47⋊C4—21no—
98C2×Dic47⋊C4—21no—
99C4⋊C4×D47—28no—
100C2×C22⋊Dic47—21no—
101C2×C22⋊Dic47—21no—
102C2×(C2×D47)⋊C4—21no—
103C2×(C2×D47)⋊C4—21no—
104C2×C4×Dic47—21no—
105C2×C4×Dic47—21no—
106C2×C4×Dic47—21no—
107C2×C4×Dic47—21no—
108#13093949—22no—
109#13093949—22no—
110#13093949—22no—
111#13093949—22no—
112#13093946—22no—
113#13093946—22no—
114#13093946—22no—
115#13093946—22no—
116C47⋊#95—21no—
117C47⋊#95—21no—
118C47⋊#95—21no—
119C47⋊#95—21no—
120C47⋊#95—21no—
121C47⋊#95—21no—
122C23×C4×C47C2311yescharacteristic
123C22×C8×C47C2311yescharacteristic
124C22×C8×C47C2311yescharacteristic
125C22×C8×C47C2311yescharacteristic
126C22×C8×C47C2311yescharacteristic
127#117×C47C2×C414yes—
128#117×C47D414yes—
129C2×C4⋊C4×C47D411yescharacteristic
130C2×C4⋊C4×C47D411yescharacteristic
131C2×C22⋊C4×C47D411yescharacteristic
132C2×C22⋊C4×C47D411yescharacteristic
133C2×C42×C47C2311yescharacteristic
134C2×C42×C47C2311yescharacteristic
135C4⋊C8×C47—22no—
136C4⋊C8×C47—22no—
137C22⋊C8×C47—22no—
138C22⋊C8×C47—22no—
139#97×C47—22no—
140C4×C8×C47—22no—
141C24×C47C2×D411yescharacteristic
142C23×D47—21no—
143C22×C4×C47—21no—
144C22×C4×C47—21no—
145C22×C4×C47—21no—
146C22×C4×C47—21no—
147C22×C4×C47C22×C412yes—
148C22×C4×C47C2×D411yescharacteristic
149C22×C4×C47C2×D411yescharacteristic
150C22×C4×C47C2×D411yescharacteristic
151C22×C4×C47C2×D411yescharacteristic
152C22×C4×C47C2×D411yescharacteristic
153C22×C4×C47C2×D412yes—
154C22×C4×C47C2411yescharacteristic
155C2×C22⋊D47—24no—
156C2×C22⋊D47—24no—
157C2×C22⋊D47—24no—
158C22×Dic47—21no—
159C22×Dic47—21no—
160C22×Dic47—21no—
161C22×Dic47—24no—
162C22×Dic47—21no—
163C22×Dic47—21no—
164C22×Dic47—21no—
165C22×Dic47—21no—
166C22×Dic47—81no—
167C22×Dic47—81no—
168#10625350—28no—
169#10625350—28no—
170#10625350—28no—
171#10625350—28no—
172C2×D188—21no—
173C2×D188—21no—
174C2×D188—21no—
175C2×D188C22×C412yes—
176C2×D188#4112yes—
177C2×D188#4112yes—
178C2×C4×D47—24no—
179C2×C4×D47—24no—
180C2×C4×D47—24no—
181C2×C4×D47—24no—
182C2×C4×D47—24no—
183C2×C4×D47—81no—
184C2×C4×D47—81no—
185C2×C4×D47—81no—
186C2×C4×D47—81no—
187C2×Dic94—21no—
188C2×Dic94—21no—
189C2×Dic94—21no—
190C2×Dic94C22×C412yes—
191C2×Dic94#4112yes—
192C2×Dic94#4112yes—
193C2×C8×C47—21no—
194C2×C8×C47—21no—
195C2×C8×C47—21no—
196C2×C8×C47—21no—
197C2×C8×C47—21no—
198C2×C8×C47—21no—
199C2×C8×C47—21no—
200C2×C8×C47—21no—
201C2×C8×C47—21no—
202C2×C8×C47—21no—
203C2×C8×C47—21no—
204C2×C8×C47—21no—
205C4⋊C4×C47C22⋊C414yes—
206C4⋊C4×C47C22⋊C414yes—
207C22⋊C4×C47C22⋊C414yes—
208C22⋊C4×C47C22⋊C414yes—
209C42×C47C22×C412yes—
210C42×C47C22×C412yes—
211C42×C47C2×D412yes—
212C42×C47C2×D412yes—
213C22⋊Dic47—81no—
214C22⋊Dic47—81no—
215(C2×D47)⋊C4—24no—
216(C2×D47)⋊C4—24no—
217C4⋊Dic47—24no—
218C4⋊Dic47—21no—
219C4⋊Dic47—21no—
220C4⋊Dic47—21no—
221C4⋊Dic47—21no—
222C4⋊Dic47—21no—
223C4⋊Dic47—21no—
224C4⋊Dic47—21no—
225C4⋊Dic47—21no—
226C4⋊Dic47—21no—
227C4⋊Dic47—21no—
228C4⋊Dic47—81no—
229C4⋊Dic47—81no—
230C4⋊Dic47C22×C412yes—
231C4⋊Dic47C22×C412yes—
232Dic47⋊C4—24no—
233Dic47⋊C4—24no—
234C4×Dic47—24no—
235C4×Dic47—24no—
236C4×Dic47—81no—
237C4×Dic47—81no—
238C23×C47—21no—
239C23×C47—21no—
240C23×C47—21no—
241C23×C47—21no—
242C23×C47—21no—
243C23×C47—21no—
244C23×C47C2×C22⋊C412yes—
245C23×C47C22×D411yescharacteristic
246C22×D47—22no—
247C22×D47—22no—
248C22×D47—22no—
249C22×D47—41no—
250C22×D47—41no—
251C22×D47—41no—
252C22×D47—41no—
253C2×C4×C47—21no—
254C2×C4×C47—21no—
255C2×C4×C47—21no—
256C2×C4×C47—21no—
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—22no—
264C2×C4×C47—22no—
265C2×C4×C47—22no—
266C2×C4×C47—22no—
267C2×C4×C47C2×C22⋊C412yes—
268C2×C4×C47C2×C22⋊C412yes—
269C2×C4×C47C2×C22⋊C412yes—
270C2×C4×C47C2×C22⋊C412yes—
271C2×C4×C47C2×C22⋊C412yes—
272C2×C4×C47C23×C411yescharacteristic
273C2×C4×C47C22×D411yescharacteristic
274C2×C4×C47C2×#4111yescharacteristic
275C2×C4×C47C2×#4111yescharacteristic
276C2×C4×C47C2×#4111yescharacteristic
277C2×C4×C47C2×#4111yescharacteristic
278C22⋊D47—216no—
279C2×Dic47—22no—
280C2×Dic47—22no—
281C2×Dic47—22no—
282C2×Dic47—22no—
283C2×Dic47—22no—
284C2×Dic47—41no—
285C2×Dic47—41no—
286C2×Dic47—41no—
287C2×Dic47—41no—
288C2×Dic47—41no—
289C2×Dic47—41no—
290C2×Dic47—41no—
291C2×Dic47—41no—
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—84no—
301D188—22no—
302D188—22no—
303D188—22no—
304D188#11714yes—
305C4×D47—216no—
306C4×D47—84no—
307C4×D47—84no—
308Dic94—22no—
309Dic94—22no—
310Dic94—22no—
311Dic94#11714yes—
312C8×C47—41no—
313C8×C47—41no—
314C8×C47—41no—
315C8×C47—41no—
316#20746—471nomaximal, Sylow
317C22×C47—22no—
318C22×C47—22no—
319C22×C47—22no—
320C22×C47—41no—
321C22×C47—41no—
322C22×C47—41no—
323C22×C47—41no—
324C22×C47C22×C22⋊C411yescharacteristic
325C22×C47#52511yescharacteristic
326C22×C47#52511yescharacteristic
327C22×C47#57611yescharacteristic
328C22×C47#57711yescharacteristic
329C22×C47#57711yescharacteristic
330C22×C47#57811yescharacteristic
331C2×D47—24no—
332C2×D47—42no—
333C2×D47—42no—
334C2×D47—42no—
335C2×D47—42no—
336C2×D47—42no—
337C2×D47—42no—
338C4×C47—22no—
339C4×C47—22no—
340C4×C47—22no—
341C4×C47—22no—
342C4×C47—22no—
343C4×C47C2×#11711yescharacteristic
344C4×C47C2×#11711yescharacteristic
345C4×C47#52511yescharacteristic
346C4×C47#52511yescharacteristic
347Dic47—24no—
348Dic47—42no—
349Dic47—42no—
350Dic47—81no—
351Dic47—81no—
352Dic47—81no—
353Dic47—81no—
354C2×#520—471no—
355C2×#433D4711yescharacteristic, complemented
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#228011yescharacteristic
371C2×C47#289711yescharacteristic
372C2×C47#289811yescharacteristic
373C2×C47#311911yescharacteristic
374C2×C47#312011yescharacteristic
375C2×C47#312411yescharacteristic
376C2×C47#312511yescharacteristic
377D47—44no—
378C22×#41—471no—
379#520—478no—
380#520—944no—
381C2×C4×Q8—471no—
382C2×C4×Q8—471no—
383C2×C4×D4—471no—
384C2×C4×D4—471no—
385C2×C4×D4—941no—
386C2×C4×D4—941no—
387C2×#117—941no—
388C2×#117C2×D4711yescharacteristic
389C22×C4⋊C4—471no—
390C22×C4⋊C4—941no—
391#433—24no—
392C2×C4⋊C8C2×D4711yescharacteristic
393C2×C4⋊C8C2×D4711yescharacteristic
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⋊C8C2×D4711yescharacteristic
403C2×C22⋊C8C2×D4711yescharacteristic
404C2×#97C2×D4711yescharacteristic
405C2×C4×C8C2×D4711yescharacteristic
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—474no—
426C2×#41—942no—
427C2×#41—942no—
428C2×#41—942no—
429C2×#41—942no—
430C2×#41—942no—
431C22×Q8—471no—
432C22×D4—471no—
433C22×D4—941no—
434C23×C4—941no—
435C23×C4—941no—
436C23×C4—941no—
437C23×C4—941no—
438C23×C4C22×D4711yescharacteristic
439C22×C8C22×D4711yescharacteristic
440C22×C8C22×D4711yescharacteristic
441C22×C8C22×D4711yescharacteristic
442C22×C8C22×D4711yescharacteristic
443C4×Q8—474no—
444C4×Q8—474no—
445C4×Q8—942no—
446C4×Q8—942no—
447C4×D4—474no—
448C4×D4—474no—
449C4×D4—948no—
450C4×D4—948no—
451C4×D4—942no—
452C4×D4—942no—
453#117—948no—
454#117C4×D4714yes—
455#117C22⋊D4714yes—
456C2×C4⋊C4—474no—
457C2×C4⋊C4—471no—
458C2×C4⋊C4—471no—
459C2×C4⋊C4—471no—
460C2×C4⋊C4—471no—
461C2×C4⋊C4—471no—
462C2×C4⋊C4—471no—
463C2×C4⋊C4—941no—
464C2×C4⋊C4—941no—
465C2×C4⋊C4—941no—
466C2×C4⋊C4—942no—
467C2×C4⋊C4—948no—
468C2×C4⋊C4—941no—
469C2×C4⋊C4—941no—
470C2×C4⋊C4D18811yescharacteristic
471C2×C4⋊C4D18811yescharacteristic
472C2×C22⋊C4—941no—
473C2×C22⋊C4—941no—
474C2×C22⋊C4—941no—
475C2×C22⋊C4—941no—
476C2×C22⋊C4D18811yescharacteristic
477C2×C22⋊C4D18811yescharacteristic
478C2×C42—941no—
479C2×C42—941no—
480C2×C42—941no—
481C2×C42—941no—
482C2×C42C22×D4711yescharacteristic
483C2×C42C22×D4711yescharacteristic
484C4⋊C8—22no—
485C4⋊C8—22no—
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—22no—
495C22⋊C8—22no—
496#97—22no—
497C4×C8—22no—
498#95—941no—
499#95—941no—
500#95—941no—
501#95—941no—
502#95—941no—
503#95—941no—
504C24—941no—
505C24C2×D18811yescharacteristic
506#41—948no—
507#41—948no—
508#41—948no—
509#41—948no—
510C2×Q8—472no—
511C2×Q8—472no—
512C2×Q8—472no—
513C2×Q8—941no—
514C2×Q8—941no—
515C2×Q8—941no—
516C2×D4—472no—
517C2×D4—472no—
518C2×D4—472no—
519C2×D4—944no—
520C2×D4—944no—
521C2×D4—944no—
522C2×D4—941no—
523C2×D4—941no—
524C2×D4—941no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—944no—
530C22×C4—944no—
531C22×C4—941no—
532C22×C4—944no—
533C22×C4—944no—
534C22×C4—941no—
535C22×C4—941no—
536C22×C4—944no—
537C22×C4—944no—
538C22×C4—941no—
539C22×C4—941no—
540C22×C4—941no—
541C22×C4—941no—
542C22×C4—3761no—
543C22×C4—3761no—
544C22×C4—3761no—
545C22×C4—3761no—
546C22×C4—3761no—
547C22×C4—3761no—
548C22×C4C2×C4×D4712yes—
549C22×C4C2×D18811yescharacteristic
550C22×C4C2×D18811yescharacteristic
551C22×C4C2×D18811yescharacteristic
552C22×C4C2×D18811yescharacteristic
553C22×C4C2×D18811yescharacteristic
554C22×C4C2×C22⋊D4712yes—
555C22×C4C23×D4711yescharacteristic
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C4⋊C4—472no—
569C4⋊C4—472no—
570C4⋊C4—944no—
571C4⋊C4—944no—
572C4⋊C4—944no—
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—941no—
582C4⋊C4—941no—
583C4⋊C4—3761no—
584C4⋊C4—3761no—
585C4⋊C4(C2×D47)⋊C414yes—
586C4⋊C4(C2×D47)⋊C414yes—
587C22⋊C4—944no—
588C22⋊C4—944no—
589C22⋊C4—3761no—
590C22⋊C4—3761no—
591C22⋊C4(C2×D47)⋊C414yes—
592C22⋊C4(C2×D47)⋊C414yes—
593C42—944no—
594C42—944no—
595C42—3761no—
596C42—3761no—
597C42C2×C4×D4712yes—
598C42C2×C4×D4712yes—
599C42C2×C22⋊D4712yes—
600C42C2×C22⋊D4712yes—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—942no—
608C23—942no—
609C23—942no—
610C23—1881no—
611C23—1881no—
612C23—1881no—
613C23—1881no—
614C23C2×(C2×D47)⋊C412yes—
615C23C22×D18811yescharacteristic
616Q8—474no—
617Q8—942no—
618Q8—942no—
619Q8—942no—
620D4—474no—
621D4—9416no—
622D4—942no—
623D4—942no—
624D4—942no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—9416no—
640C2×C4—942no—
641C2×C4—942no—
642C2×C4—942no—
643C2×C4—942no—
644C2×C4—942no—
645C2×C4—3764no—
646C2×C4—3764no—
647C2×C4—3764no—
648C2×C4—1881no—
649C2×C4—1881no—
650C2×C4—1881no—
651C2×C4—1881no—
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×(C2×D47)⋊C412yes—
665C2×C4C2×(C2×D47)⋊C412yes—
666C2×C4C2×(C2×D47)⋊C412yes—
667C2×C4C2×(C2×D47)⋊C412yes—
668C2×C4C2×(C2×D47)⋊C412yes—
669C2×C4C22×C4×D4711yescharacteristic
670C2×C4C22×C22⋊D4711yescharacteristic
671C2×C4#41×D4711yescharacteristic
672C2×C4#41×D4711yescharacteristic
673C2×C4#41×D4711yescharacteristic
674C2×C4#41×D4711yescharacteristic
675C8—41no—
676C8—41no—
677C8—41no—
678C8—41no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—944no—
687C22—1882no—
688C22—1882no—
689C22—1882no—
690C22—1882no—
691C22—1882no—
692C22—1882no—
693C22C22×(C2×D47)⋊C411yescharacteristic
694C22#1568963511yescharacteristic
695C22#1568963511yescharacteristic
696C22#1568992811yescharacteristic
697C22#1568993511yescharacteristic
698C22#1568993511yescharacteristic
699C22#1568994011yescharacteristic
700C4—22no—
701C4—22no—
702C4—22no—
703C4—22no—
704C4—22no—
705C4—944no—
706C4—3761no—
707C4—3761no—
708C4—3761no—
709C4—3761no—
710C4—1882no—
711C4—1882no—
712C4#117×D4711yescharacteristic
713C4#117×D4711yescharacteristic
714C4#1568963011yescharacteristic
715C4#1568963011yescharacteristic
716C2—42no—
717C2—1884no—
718C2#2024576711yescharacteristic
719C2#2025191511yescharacteristic
720C2#2025192211yescharacteristic
721C2#2025358911yescharacteristic
722C2#2025360411yescharacteristic
723C2#2025365211yescharacteristic
724C2#2025366711yescharacteristic
subgroupG/H
centerC23C22×D188
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#433C2
socleC23×C47C22×D4
prime radicalC22×#10625350C22
cosocleC22×C4×C47C24
hypercenterC2×#433D47
hypocenterC47#20746
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. #20245997C2semidirect
3. #20243479C2semidirect
4. #20243475C2semidirect
5. #20243404C2semidirect
6. #20243399C2semidirect
7. #20243394C2semidirect
8. #20243389C2semidirect
11. #20243219C2semidirect
12. #20243214C2semidirect
13. C4×#13093949C2semidirect
14. C4×#13093946C2semidirect
15. C2×C47×#433C2semidirect
18. #15689603C4semidirect
355. C2×#433D47semidirect
424. C47#20746semidirect

Maximal subgroups

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

subgroupindex
C2×#156896032
#202459972
#202434792
#202434752
#202434042
#202433992
#202433942
#202433892
#202433292
#202432192
#202432142
C4×#130939492
C4×#130939462
C2×C47×#4332
#2074647