Finite Group Databasebeta

← #26252894

Subgroups — #26252894

Order 12032.

1140 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689420C211yesmaximal, characteristic, complemented
2C2×#15689233C211yesmaximal, characteristic
3#20248306C211yesmaximal, characteristic, complemented
4#20244723C211yesmaximal, characteristic, complemented
5#20244718C211yesmaximal, characteristic, complemented
6#20244531C211yesmaximal, characteristic, complemented
7#20244521C211yesmaximal, characteristic, complemented
8#20244358C211yesmaximal, characteristic, complemented
9#20244329C211yesmaximal, characteristic, complemented
10#20243736C211yesmaximal, characteristic
11#20243736C211yesmaximal, characteristic
12#20243649C211yesmaximal, characteristic, complemented
13#20243635C211yesmaximal, characteristic, complemented
14#20243388C211yesmaximal, characteristic, complemented
15C2×C47×#554C211yesmaximal, characteristic, complemented
16C22×#10625334C2211yescharacteristic
17C2×#13094000—21no—
18C2×C4×D188C2211yescharacteristic
19#15689420—24no—
20#15689233—24no—
21C2×#13093957C2211yescharacteristic
22C2×#13093955C2211yescharacteristic
23C2×#13093955C2211yescharacteristic
24C2×C4⋊(C47⋊C8)C2211yescharacteristic
25C2×#13093945C2211yescharacteristic
26C2×#13093945C2211yescharacteristic
27C2×#13093945C2211yescharacteristic
28C2×#13093944C2211yescharacteristic
29C2×#13093944C2211yescharacteristic
30C2×#13093944C2211yescharacteristic
31C2×#13093935C2211yescharacteristic
32#15689045—21no—
33#15689045—21no—
34#15689025C2211yescharacteristic
35#15689025C2211yescharacteristic
36#15689021C2211yescharacteristic
37#15689021C2211yescharacteristic
38#15688993C2211yescharacteristic
39#15688980—21no—
40#15688885C2211yescharacteristic
41#15688885C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688878C2211yescharacteristic
47#15688878C2211yescharacteristic
48#15688878C2211yescharacteristic
49#15688878C2211yescharacteristic
50C47×#554—24no—
51C47×#554—24no—
52C2×C4⋊Q8×C47C2211yescharacteristic
53C2×#125×C47C2211yescharacteristic
54C2×#125×C47C2211yescharacteristic
55C2×C22⋊Q8×C47—21no—
56C2×C22⋊Q8×C47—21no—
57C2×C22⋊Q8×C47—21no—
58C2×C4×Q8×C47C2211yescharacteristic
59C2×C4×D4×C47C2211yescharacteristic
60C2×C4×D4×C47C2211yescharacteristic
61C2×C4×D4×C47C2211yescharacteristic
62C22×C4⋊C4×C47—21no—
63C22×D188C2311yescharacteristic
64C22×C4×D47—21no—
65C2×#10625334—22no—
66C2×#10625334—22no—
67C2×#10625334Q814yescomplemented
68C22×C47⋊C8C2311yescharacteristic
69C22×C47⋊C8C2311yescharacteristic
70C22×C47⋊C8C2311yescharacteristic
71C22×C47⋊C8C2311yescharacteristic
72#13094000—44no—
73C4×D188—22no—
74C4×D188—22no—
75C2×C4⋊Dic47—21no—
76C2×C4⋊Dic47—21no—
77C2×C4⋊Dic47C2311yescharacteristic
78C2×C4⋊Dic47C2311yescharacteristic
79C2×C4⋊Dic47C2311yescharacteristic
80C2×Dic47⋊C4—21no—
81C2×Dic47⋊C4—21no—
82C2×(C2×D47)⋊C4—21no—
83C2×(C2×D47)⋊C4—21no—
84C2×(C2×D47)⋊C4—21no—
85C2×(C2×D47)⋊C4—21no—
86C2×(C2×D47)⋊C4—21no—
87#13093957—22no—
88#13093955—22no—
89#13093955—22no—
90C4⋊(C47⋊C8)—22no—
91#13093945—22no—
92#13093945—22no—
93#13093945—22no—
94#13093944—22no—
95#13093944—22no—
96#13093944—22no—
97#13093935—22no—
98C47⋊#95—21no—
99C47⋊#95—21no—
100C22×Q8×C47—21no—
101C22×Q8×C47D411yescharacteristic
102C22×D4×C47C2311yescharacteristic
103C23×C4×C47—21no—
104C23×C4×C47—21no—
105C23×C4×C47—21no—
106C4⋊Q8×C47—22no—
107C4⋊Q8×C47—22no—
108#125×C47—22no—
109#125×C47—22no—
110#125×C47—22no—
111#125×C47D414yes—
112C22⋊Q8×C47—28no—
113C22⋊Q8×C47—28no—
114C22⋊Q8×C47—28no—
115C4×Q8×C47—22no—
116C4×Q8×C47—22no—
117C4×D4×C47—22no—
118C4×D4×C47—22no—
119C4×D4×C47—22no—
120C4×D4×C47—22no—
121C4×D4×C47—22no—
122C4×D4×C47D414yes—
123C2×C4⋊C4×C47—28no—
124C2×C4⋊C4×C47—21no—
125C2×C4⋊C4×C47—21no—
126C2×C4⋊C4×C47—21no—
127C2×C4⋊C4×C47—21no—
128C2×C4⋊C4×C47—21no—
129C2×C4⋊C4×C47D411yescharacteristic
130C2×C4⋊C4×C47D411yescharacteristic
131C2×C4⋊C4×C47D411yescharacteristic
132C2×C4⋊C4×C47C2311yescharacteristic
133C2×C4⋊C4×C47C2311yescharacteristic
134C2×C4⋊C4×C47C2311yescharacteristic
135C2×C22⋊C4×C47—21no—
136C2×C22⋊C4×C47—21no—
137C2×C22⋊C4×C47—21no—
138C2×C42×C47C2311yescharacteristic
139C2×C42×C47C2311yescharacteristic
140C2×C42×C47C2311yescharacteristic
141C24×C47—21no—
142C23×D47—21no—
143C2×Q8×C47—24no—
144C2×Q8×C47—22no—
145C2×Q8×C47—22no—
146C2×Q8×C47—41no—
147C2×Q8×C47—81no—
148C2×Q8×C47—81no—
149C2×D4×C47—21no—
150C2×D4×C47—21no—
151C2×D4×C47—21no—
152C2×D4×C47C2×D412yes—
153C2×D4×C47C2×Q812yes—
154C2×D4×C47#4112yes—
155C22×C4×C47—24no—
156C22×C4×C47—21no—
157C22×C4×C47—21no—
158C22×C4×C47—21no—
159C22×C4×C47—24no—
160C22×C4×C47—24no—
161C22×C4×C47—42no—
162C22×C4×C47—42no—
163C22×C4×C47—81no—
164C22×C4×C47—81no—
165C22×C4×C47—81no—
166C22×C4×C47—81no—
167C22×C4×C47C2×D411yescharacteristic
168C22×C4×C47C2×D411yescharacteristic
169C22×C4×C47C2×D411yescharacteristic
170C22×C4×C47C2×D411yescharacteristic
171C22×C4×C47C2×D411yescharacteristic
172C22×C4×C47C2×D411yescharacteristic
173C22×C4×C47C2411yescharacteristic
174C22×Dic47—21no—
175C22×Dic47—21no—
176C22×Dic47—21no—
177C2×D188—21no—
178C2×D188—21no—
179C2×D188—21no—
180C2×D188—21no—
181C2×D188—21no—
182C2×D188C2×Q812yes—
183C2×C4×D47—42no—
184C2×C4×D47—42no—
185C2×C4×D47—42no—
186C4⋊C4×C47—24no—
187C4⋊C4×C47—24no—
188C4⋊C4×C47—24no—
189C4⋊C4×C47—22no—
190C4⋊C4×C47—24no—
191C4⋊C4×C47—24no—
192C4⋊C4×C47—22no—
193C4⋊C4×C47—22no—
194C4⋊C4×C47—21no—
195C4⋊C4×C47—21no—
196C4⋊C4×C47—21no—
197C4⋊C4×C47C2×D412yes—
198C4⋊C4×C47C2×D412yes—
199C4⋊C4×C47C2×D412yes—
200C22⋊C4×C47—24no—
201C22⋊C4×C47—24no—
202C22⋊C4×C47—24no—
203C42×C47—21no—
204C42×C47—21no—
205C42×C47—21no—
206C42×C47—21no—
207C42×C47C2×D412yes—
208C42×C47C2×D412yes—
209#10625334—28no—
210(C2×D47)⋊C4—42no—
211(C2×D47)⋊C4—42no—
212(C2×D47)⋊C4—42no—
213(C2×D47)⋊C4—81no—
214(C2×D47)⋊C4—81no—
215C4⋊Dic47—21no—
216C4⋊Dic47—21no—
217C4⋊Dic47—21no—
218C4⋊Dic47—21no—
219C4⋊Dic47—21no—
220C4⋊Dic47—21no—
221C4⋊Dic47—42no—
222C4⋊Dic47—81no—
223Dic47⋊C4—42no—
224Dic47⋊C4—42no—
225C2×C47⋊C8—21no—
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⋊C8C2×Q812yes—
237C23×C47—22no—
238C23×C47—22no—
239C23×C47—22no—
240C23×C47—41no—
241C23×C47—41no—
242C23×C47—41no—
243C23×C47—41no—
244C23×C47C22×D411yescharacteristic
245C22×D47—22no—
246C22×D47—41no—
247C22×D47—41no—
248C22×D47—41no—
249C22×D47—41no—
250C22×D47—41no—
251C22×D47—41no—
252Q8×C47—44no—
253Q8×C47—84no—
254D4×C47—22no—
255D4×C47—22no—
256D4×C47—22no—
257D4×C47C22⋊Q814yescomplemented
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—21no—
271C2×C4×C47—21no—
272C2×C4×C47—21no—
273C2×C4×C47—21no—
274C2×C4×C47—21no—
275C2×C4×C47—21no—
276C2×C4×C47—48no—
277C2×C4×C47—41no—
278C2×C4×C47—41no—
279C2×C4×C47—41no—
280C2×C4×C47—41no—
281C2×C4×C47—41no—
282C2×C4×C47—41no—
283C2×C4×C47—84no—
284C2×C4×C47—84no—
285C2×C4×C47#12012yes—
286C2×C4×C47#12012yes—
287C2×C4×C47AGL(1,ℤ/8)12yes—
288C2×C4×C47C22×D411yescharacteristic
289C2×C4×C47C22×D411yescharacteristic
290C2×C4×C47C22×Q811yescharacteristic
291C2×C4×C47C2×#4111yescharacteristic
292C2×C4×C472−1+411yescharacteristic
293C2×C4×C472−1+411yescharacteristic
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—
303D188—22no—
304D188—22no—
305D188—41no—
306D188—41no—
307C4×D47—84no—
308C47⋊C8—22no—
309C47⋊C8—41no—
310C47⋊C8—41no—
311C47⋊C8—41no—
312#24347—471nomaximal, Sylow
313C22×C47—24no—
314C22×C47—42no—
315C22×C47—42no—
316C22×C47—42no—
317C22×C47—42no—
318C22×C47—42no—
319C22×C47—42no—
320C22×C47C2×#12011yescharacteristic
321C22×C47#54811yescharacteristic
322C22×C47D4×Q811yescharacteristic
323C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
324C22×C47#57511yescharacteristic
325C22×C47#57611yescharacteristic
326C22×C47#57711yescharacteristic
327C2×D47—42no—
328C2×D47—42no—
329C2×D47—42no—
330C2×D47—81no—
331C2×D47—81no—
332C2×D47—81no—
333C2×D47—81no—
334C4×C47—22no—
335C4×C47—22no—
336C4×C47—22no—
337C4×C47—41no—
338C4×C47—42no—
339C4×C47—41no—
340C4×C47—41no—
341C4×C47—42no—
342C4×C47—42no—
343C4×C47C2×C22⋊Q811yescharacteristic
344C4×C47#53611yescharacteristic
345C4×C47#54811yescharacteristic
346C4×C47D4×Q811yescharacteristic
347Dic47—81no—
348Dic47—81no—
349Dic47—81no—
350C2×#554D4711yescharacteristic, complemented
351C2×#478—471no—
352C2×#442—471no—
353#2538—471no—
354#2059—471no—
355#2058—471no—
356#2025—471no—
357#2023—471no—
358#1992—471no—
359#1985—471no—
360#1879—471no—
361#1879—471no—
362#1864—471no—
363#1862—471no—
364#1802—471no—
365C2×C47—44no—
366C2×C47#240911yescharacteristic
367C2×C47#300611yescharacteristic
368C2×C47#301211yescharacteristic
369C2×C47#336611yescharacteristic
370C2×C47#337611yescharacteristic
371C2×C47#338411yescharacteristic
372C2×C47#338911yescharacteristic
373D47—82no—
374C22×D8—471no—
375#554—24no—
376#554—24no—
377C2×C4⋊Q8C2×D4711yescharacteristic
378C2×#125C2×D4711yescharacteristic
379C2×#125C2×D4711yescharacteristic
380C2×C22⋊Q8—21no—
381C2×C22⋊Q8—21no—
382C2×C22⋊Q8—21no—
383C2×C22⋊Q8—941no—
384C2×C4×Q8C2×D4711yescharacteristic
385C2×C4×D4—471no—
386C2×C4×D4C2×D4711yescharacteristic
387C2×C4×D4C2×D4711yescharacteristic
388C2×C4×D4C2×D4711yescharacteristic
389C22×C4⋊C4—21no—
390#478—944no—
391#442—944no—
392C2×#107—471no—
393C2×#106—471no—
394C2×#106—471no—
395C2×C4⋊C8—471no—
396C2×#102—471no—
397C2×#102—471no—
398C2×#102—471no—
399C2×#102—471no—
400C2×#102—471no—
401C2×#102—471no—
402C2×#97—471no—
403#396—941no—
404#396—941no—
405#390—471no—
406#390—471no—
407#389—471no—
408#389—471no—
409#384—471no—
410#380—941no—
411#340—471no—
412#340—471no—
413#340—471no—
414#340—471no—
415#340—471no—
416#340—471no—
417#336—471no—
418#336—471no—
419#336—471no—
420#336—471no—
421C47#2434711yescharacteristic, complemented, Sylow
422C22×Q8—21no—
423C22×Q8C22⋊D4711yescharacteristic
424C22×D4—471no—
425C22×D4C22×D4711yescharacteristic
426C23×C4—21no—
427C23×C4—21no—
428C23×C4—21no—
429C23×C4—941no—
430C2×D8—474no—
431C2×D8—942no—
432C2×D8—942no—
433C22×C8—471no—
434C22×C8—471no—
435C22×C8—471no—
436C22×C8—471no—
437C4⋊Q8—22no—
438C4⋊Q8—22no—
439#125—22no—
440#125—22no—
441#125—22no—
442#125C22⋊D4714yes—
443C22⋊Q8—28no—
444C22⋊Q8—28no—
445C22⋊Q8—28no—
446C22⋊Q8—1884no—
447C4×Q8—22no—
448C4×Q8—22no—
449C4×D4—22no—
450C4×D4—22no—
451C4×D4—22no—
452C4×D4—22no—
453C4×D4—22no—
454C4×D4—942no—
455C4×D4—942no—
456C4×D4C22⋊D4714yes—
457C2×C4⋊C4—28no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—471no—
464C2×C4⋊C4—471no—
465C2×C4⋊C4—471no—
466C2×C4⋊C4—941no—
467C2×C4⋊C4—941no—
468C2×C4⋊C4—941no—
469C2×C4⋊C4—941no—
470C2×C4⋊C4C22⋊D4711yescharacteristic
471C2×C4⋊C4C22⋊D4711yescharacteristic
472C2×C4⋊C4C22⋊D4711yescharacteristic
473C2×C4⋊C4C22×D4711yescharacteristic
474C2×C4⋊C4C22×D4711yescharacteristic
475C2×C4⋊C4C22×D4711yescharacteristic
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—941no—
480C2×C22⋊C4—941no—
481C2×C22⋊C4—941no—
482C2×C22⋊C4—941no—
483C2×C22⋊C4—941no—
484C2×C42C22×D4711yescharacteristic
485C2×C42C22×D4711yescharacteristic
486C2×C42C22×D4711yescharacteristic
487#107—942no—
488#106—942no—
489#106—942no—
490C4⋊C8—942no—
491#102—942no—
492#102—942no—
493#102—942no—
494#102—942no—
495#102—942no—
496#102—942no—
497#97—942no—
498#95—941no—
499#95—941no—
500C24—21no—
501C24—941no—
502C2×Q8—24no—
503C2×Q8—22no—
504C2×Q8—22no—
505C2×Q8—41no—
506C2×Q8—81no—
507C2×Q8—81no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—472no—
512C2×D4—941no—
513C2×D4—941no—
514C2×D4—941no—
515C2×D4—941no—
516C2×D4—941no—
517C2×D4Q8×D4712yes—
518C2×D4#1062535412yes—
519C2×D4C2×C22⋊D4712yes—
520C22×C4—24no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—81no—
529C22×C4—81no—
530C22×C4—81no—
531C22×C4—81no—
532C22×C4—941no—
533C22×C4—941no—
534C22×C4—941no—
535C22×C4—1882no—
536C22×C4—1882no—
537C22×C4—1882no—
538C22×C4C2×C22⋊D4711yescharacteristic
539C22×C4C2×C22⋊D4711yescharacteristic
540C22×C4C2×C22⋊D4711yescharacteristic
541C22×C4C2×C22⋊D4711yescharacteristic
542C22×C4C2×C22⋊D4711yescharacteristic
543C22×C4C2×C22⋊D4711yescharacteristic
544C22×C4C23×D4711yescharacteristic
545D8—948no—
546C2×C8—472no—
547C2×C8—941no—
548C2×C8—941no—
549C2×C8—941no—
550C2×C8—941no—
551C2×C8—941no—
552C2×C8—941no—
553C2×C8—941no—
554C2×C8—941no—
555C2×C8—941no—
556C2×C8—941no—
557C2×C8—941no—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—24no—
561C4⋊C4—22no—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—941no—
570C4⋊C4—941no—
571C4⋊C4—941no—
572C4⋊C4—941no—
573C4⋊C4—941no—
574C4⋊C4—941no—
575C4⋊C4—3761no—
576C4⋊C4—1882no—
577C4⋊C4—1882no—
578C4⋊C4—1882no—
579C4⋊C4C2×C22⋊D4712yes—
580C4⋊C4C2×C22⋊D4712yes—
581C4⋊C4C2×C22⋊D4712yes—
582C22⋊C4—24no—
583C22⋊C4—24no—
584C22⋊C4—24no—
585C22⋊C4—3761no—
586C22⋊C4—3761no—
587C22⋊C4—1882no—
588C22⋊C4—1882no—
589C22⋊C4—1882no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42—21no—
594C42C2×C22⋊D4712yes—
595C42C2×C22⋊D4712yes—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—942no—
604C23—1881no—
605C23—1881no—
606C23—1881no—
607C23—1881no—
608C23—1881no—
609C23—1881no—
610C23C22×C22⋊D4711yescharacteristic
611Q8—44no—
612Q8—84no—
613D4—22no—
614D4—22no—
615D4—22no—
616D4—942no—
617D4—942no—
618D4—1881no—
619D4—1881no—
620D4#1309400014yescomplemented
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—48no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—84no—
647C2×C4—84no—
648C2×C4—3764no—
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#1309399312yes—
659C2×C4#1309399312yes—
660C2×C4#1309404912yes—
661C2×C4C22×C22⋊D4711yescharacteristic
662C2×C4C22×C22⋊D4711yescharacteristic
663C2×C4C2×Q8×D4711yescharacteristic
664C2×C4C2×#1062535411yescharacteristic
665C2×C4#1309407211yescharacteristic
666C2×C4#1309407211yescharacteristic
667C8—942no—
668C8—1881no—
669C8—1881no—
670C8—1881no—
671C22—24no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—42no—
678C22—3761no—
679C22—3761no—
680C22—3761no—
681C22—3761no—
682C22—1882no—
683C22—1882no—
684C22—1882no—
685C22C2×#1309399311yescharacteristic
686C22#1568978411yescharacteristic
687C22Q8×C22⋊D4711yescharacteristic
688C22C2×#1309404911yescharacteristic
689C22#1568992111yescharacteristic
690C22#1568992611yescharacteristic
691C22#1568993411yescharacteristic
692C4—22no—
693C4—22no—
694C4—22no—
695C4—41no—
696C4—41no—
697C4—42no—
698C4—42no—
699C4—41no—
700C4—42no—
701C4—3761no—
702C4—3761no—
703C4—3761no—
704C4C2×#1309400011yescharacteristic
705C4#1568969711yescharacteristic
706C4#1568978411yescharacteristic
707C4Q8×C22⋊D4711yescharacteristic
708C2—44no—
709C2—3762no—
710C2#2024674711yescharacteristic
711C2#2025264011yescharacteristic
712C2#2025269211yescharacteristic
713C2#2025609511yescharacteristic
714C2#2025621511yescharacteristic
715C2#2025628711yescharacteristic
716C2#2025634211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC2×C47×#554C2
socleC23×C47C22×D4
prime radicalC22×#10625334C22
hypercenterC2×#554D47
hypocenterC47#24347
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#15689420C2semidirect
3. #20248306C2semidirect
4. #20244723C2semidirect
5. #20244718C2semidirect
6. #20244531C2semidirect
7. #20244521C2semidirect
8. #20244358C2semidirect
9. #20244329C2semidirect
12. #20243649C2semidirect
13. #20243635C2semidirect
14. #20243388C2semidirect
15. C2×C47×#554C2semidirect
67. C2×#10625334Q8semidirect
257. D4×C47C22⋊Q8semidirect
350. C2×#554D47semidirect
421. C47#24347semidirect
620. D4#13094000semidirect

Maximal subgroups

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

subgroupindex
C2×#156894202
C2×#156892332
#202483062
#202447232
#202447182
#202445312
#202445212
#202443582
#202443292
#202437362
#202436492
#202436352
#202433882
C2×C47×#5542
#2434747