Finite Group Databasebeta

← #26185219

Subgroups — #26185219

Order 12032.

870 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257274C211yesmaximal, characteristic
2#20252513C211yesmaximal, characteristic
3#20242119C211yesmaximal, characteristic, complemented
4#20242116C211yesmaximal, characteristic, complemented
5#20242113C211yesmaximal, characteristic, complemented
6#20242099C211yesmaximal, characteristic, complemented
7#20242096C211yesmaximal, characteristic, complemented
8#20242089C211yesmaximal, characteristic, complemented
9#20242086C211yesmaximal, characteristic, complemented
10#20242079C211yesmaximal, characteristic, complemented
11#20242076C211yesmaximal, characteristic, complemented
12#20242046C211yesmaximal, characteristic, complemented
13#20242043C211yesmaximal, characteristic, complemented
14C2×#15688871C211yesmaximal, characteristic, complemented
15C47×#2990C211yesmaximal, characteristic
16#15689851—21no—
17#15689851—21no—
18#15689843—21no—
19#15689843—21no—
20#15689813—21no—
21#15689813—21no—
22#15689813—21no—
23#15689813—21no—
24#15689735C412yes—
25#15689735C412yes—
26#15689694C412yes—
27#15689680C2211yescharacteristic
28#15689680C2211yescharacteristic
29#15689680C2211yescharacteristic
30#15689680C2211yescharacteristic
31#15689680C2211yescharacteristic
32C2×#13094024C2211yescharacteristic
33#15689600C412yes—
34#15689254—21no—
35#15689195—21no—
36#15689195—21no—
37D4×C47⋊C8—21no—
38#15689180C2211yescharacteristic
39#15689180C2211yescharacteristic
40#15689176C2211yescharacteristic
41#15689147C2211yescharacteristic
42C2×C4⋊(C47⋊C8)C2211yescharacteristic
43C2×C4⋊(C47⋊C8)C2211yescharacteristic
44#15688871C2211yescharacteristic
45#15688871C2211yescharacteristic
46#15688871C2211yescharacteristic
47#15688871C2211yescharacteristic
48#15688871C2211yescharacteristic
49#15688871C2211yescharacteristic
50#15688871C2211yescharacteristic
51#15688871C2211yescharacteristic
52#15688870C2211yescharacteristic
53#15688870C2211yescharacteristic
54#15688870C2211yescharacteristic
55#15688870C2211yescharacteristic
56#15688868C2211yescharacteristic
57#15688868C2211yescharacteristic
58#15688868C2211yescharacteristic
59#15688868C2211yescharacteristic
60C4×#41×C47C2211yescharacteristic
61C47×#446—21no—
62C47×#435—21no—
63C47×#435—21no—
64C8×D4×C47—21no—
65C47×#432C2211yescharacteristic
66C47×#432C2211yescharacteristic
67C47×#431C2211yescharacteristic
68C47×#423C2211yescharacteristic
69C2×C4⋊C8×C47C2211yescharacteristic
70C2×C4⋊C8×C47C2211yescharacteristic
71C22×Dic94C2×C412yes—
72C2×#10625329—21no—
73C22×C47⋊C8—21no—
74C22×C47⋊C8—21no—
75#13094024—21no—
76#13094024—21no—
77#13094024C2×C412yes—
78#13094024C2311yescharacteristic
79#13094024C2311yescharacteristic
80#13094024C2311yescharacteristic
81#13094024C2311yescharacteristic
82#13094022—22no—
83#13094017—22no—
84#13094017—22no—
85#13094017—22no—
86#13094017—22no—
87#13094016—21no—
88#13094016—21no—
89#13094016—21no—
90#13094016—21no—
91#13094016C2×C412yes—
92#13094014—22no—
93#13094014—22no—
94#13094014—22no—
95#13094014—22no—
96#13094011—22no—
97#13094005—22no—
98#13094005—22no—
99#13094003—21no—
100#13094003—21no—
101#13094003—21no—
102#13094003—21no—
103#13094003—21no—
104#13094003—21no—
105#13094003C2×C412yes—
106#13094003C2×C412yes—
107#13094003C2×C412yes—
108#13094003C2×C412yes—
109C4×Dic94—21no—
110C4×Dic94—21no—
111C4×Dic94—21no—
112C4×Dic94—21no—
113C4×Dic94—21no—
114C4×Dic94—21no—
115C4×Dic94C2×C412yes—
116C4×Dic94C2×C412yes—
117C4×Dic94C2×C412yes—
118C4×Dic94C2×C412yes—
119#13093989—22no—
120#13093989—22no—
121#13093983—21no—
122#13093983—21no—
123#13093983—21no—
124#13093983—21no—
125#13093983C2×C412yes—
126#13093980—22no—
127#13093980—22no—
128C2×C4⋊Dic47—21no—
129C2×C4⋊Dic47—21no—
130C4⋊(C47⋊C8)—21no—
131C4⋊(C47⋊C8)—21no—
132C4⋊(C47⋊C8)—21no—
133C4⋊(C47⋊C8)C2311yescharacteristic
134C4⋊(C47⋊C8)C2311yescharacteristic
135C4⋊(C47⋊C8)C2311yescharacteristic
136C4⋊(C47⋊C8)C2311yescharacteristic
137C22⋊(C47⋊C8)—21no—
138C22⋊(C47⋊C8)—21no—
139C22⋊(C47⋊C8)—21no—
140#13093935—21no—
141#13093935—21no—
142C4×C47⋊C8—21no—
143C2×#41×C47C2×C411yescharacteristic
144C2×M16×C47—21no—
145C22×C8×C47—21no—
146C22×C8×C47—21no—
147C4×Q8×C47D411yescharacteristic
148C4×Q8×C47D411yescharacteristic
149C4×D4×C47D411yescharacteristic
150C4×D4×C47D411yescharacteristic
151C4×D4×C47D411yescharacteristic
152C4×D4×C47D411yescharacteristic
153C4×D4×C47D411yescharacteristic
154C4×D4×C47D411yescharacteristic
155#117×C47C2×C411yescharacteristic
156#117×C47C2×C411yescharacteristic
157#117×C47C2×C411yescharacteristic
158C2×C42×C47C2311yescharacteristic
159C2×C42×C47C2311yescharacteristic
160C2×C42×C47C2311yescharacteristic
161C4⋊C8×C47—21no—
162C4⋊C8×C47—21no—
163C4⋊C8×C47—21no—
164C4⋊C8×C47C2311yescharacteristic
165C4⋊C8×C47C2311yescharacteristic
166C4⋊C8×C47C2311yescharacteristic
167C4⋊C8×C47C2311yescharacteristic
168C22⋊C8×C47—21no—
169C22⋊C8×C47—21no—
170C22⋊C8×C47—21no—
171#97×C47—21no—
172#97×C47—21no—
173C4×C8×C47—21no—
174#41×C47—42no—
175C2×Q8×C47C22⋊C411yescharacteristic
176C2×D4×C47C22⋊C411yescharacteristic
177C2×D4×C47C22⋊C411yescharacteristic
178C2×D4×C47C22⋊C411yescharacteristic
179C22×C4×C47C22×C411yescharacteristic
180C22×C4×C47C22×C411yescharacteristic
181C22×C4×C47C22×C411yescharacteristic
182C22×C4×C47C2×D411yescharacteristic
183C22×C4×C47C2×D411yescharacteristic
184C22×C4×C47C2×D411yescharacteristic
185C22×C4×C47C2×D411yescharacteristic
186C22×C4×C47C2×D411yescharacteristic
187C22×C4×C47C2×D411yescharacteristic
188C22×Dic47—22no—
189C2×Dic94—22no—
190C2×Dic94—21no—
191C2×Dic94—21no—
192C2×Dic94—44no—
193C2×Dic94C22×C412yes—
194C2×Dic94C22×C412yes—
195M16×C47—81no—
196C2×C8×C47—21no—
197C2×C8×C47—21no—
198C2×C8×C47—21no—
199C2×C8×C47—21no—
200C2×C8×C47—81no—
201C2×C8×C47—81no—
202C4⋊C4×C47C22⋊C411yescharacteristic
203C4⋊C4×C47C22⋊C411yescharacteristic
204C4⋊C4×C47C22⋊C411yescharacteristic
205C4⋊C4×C47C22⋊C411yescharacteristic
206C4⋊C4×C47C22⋊C411yescharacteristic
207C4⋊C4×C47C22⋊C411yescharacteristic
208C22⋊C4×C47C22⋊C411yescharacteristic
209C22⋊C4×C47C22⋊C411yescharacteristic
210C22⋊C4×C47C22⋊C411yescharacteristic
211C22⋊C4×C47C22⋊C411yescharacteristic
212C22⋊C4×C47C22⋊C411yescharacteristic
213C22⋊C4×C47C22⋊C411yescharacteristic
214C42×C47C22×C411yescharacteristic
215C42×C47C22×C411yescharacteristic
216C42×C47C22×C411yescharacteristic
217C42×C47C2×D411yescharacteristic
218C42×C47C2×D411yescharacteristic
219C42×C47C2×D411yescharacteristic
220C42×C47C2×D411yescharacteristic
221C42×C47C2×D411yescharacteristic
222C42×C47C2×D411yescharacteristic
223C42×C47C2411yescharacteristic
224C22⋊Dic47—22no—
225C22⋊Dic47—22no—
226C22⋊Dic47—22no—
227C22⋊Dic47—22no—
228C22⋊Dic47—22no—
229C4⋊Dic47—22no—
230C4⋊Dic47—22no—
231C4⋊Dic47—21no—
232C4⋊Dic47—21no—
233C4⋊Dic47—21no—
234C4⋊Dic47—21no—
235C4⋊Dic47—21no—
236C4⋊Dic47—21no—
237C4⋊Dic47C22×C412yes—
238C4⋊Dic47C22×C412yes—
239Dic47⋊C4—22no—
240Dic47⋊C4—22no—
241Dic47⋊C4—22no—
242Dic47⋊C4—22no—
243Dic47⋊C4—22no—
244Dic47⋊C4—22no—
245Dic47⋊C4—22no—
246Dic47⋊C4—22no—
247Dic47⋊C4—22no—
248Dic47⋊C4—22no—
249C4×Dic47—22no—
250C4×Dic47—22no—
251C4×Dic47—22no—
252C4×Dic47—22no—
253C4×Dic47—22no—
254#10625329—81no—
255C2×C47⋊C8—21no—
256C2×C47⋊C8—21no—
257C2×C47⋊C8—21no—
258C2×C47⋊C8—21no—
259C2×C47⋊C8—81no—
260C2×C47⋊C8—81no—
261C23×C47C2×C22⋊C411yescharacteristic
262C23×C47C2×C22⋊C411yescharacteristic
263C23×C47C2×C22⋊C411yescharacteristic
264Q8×C47—41no—
265D4×C47—22no—
266D4×C47—22no—
267D4×C47—41no—
268C2×C4×C47—22no—
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—21no—
277C2×C4×C47—21no—
278C2×C4×C47—21no—
279C2×C4×C47—21no—
280C2×C4×C47—21no—
281C2×C4×C47—41no—
282C2×C4×C47—41no—
283C2×C4×C47C2×C22⋊C411yescharacteristic
284C2×C4×C47C2×C22⋊C411yescharacteristic
285C2×C4×C47C2×C22⋊C411yescharacteristic
286C2×C4×C47C2×C22⋊C411yescharacteristic
287C2×C4×C47C2×C22⋊C411yescharacteristic
288C2×C4×C47C2×C22⋊C411yescharacteristic
289C2×C4×C47C2×C22⋊C411yescharacteristic
290C2×C4×C47C2×C22⋊C411yescharacteristic
291C2×C4×C47C2×C22⋊C411yescharacteristic
292C2×C4×C47C23×C411yescharacteristic
293C2×C4×C47C22×D411yescharacteristic
294C2×C4×C47C22×D411yescharacteristic
295C2×Dic47—22no—
296C2×Dic47—22no—
297C2×Dic47—22no—
298C2×Dic47—22no—
299C2×Dic47—44no—
300Dic94—44no—
301Dic94—41no—
302Dic94—41no—
303Dic94—41no—
304Dic94—41no—
305Dic94—42no—
306Dic94—42no—
307C8×C47—41no—
308C8×C47—41no—
309C8×C47—41no—
310C8×C47—41no—
311C47⋊C8—41no—
312C47⋊C8—41no—
313C47⋊C8—41no—
314C47⋊C8—41no—
315#17780—471nomaximal, Sylow
316C22×C47—21no—
317C22×C47—21no—
318C22×C47—21no—
319C22×C47—21no—
320C22×C47—21no—
321C22×C47—21no—
322C22×C47—21no—
323C22×C47—21no—
324C22×C47#41312yes—
325C22×C47C22×C22⋊C411yescharacteristic
326C4×C47—21no—
327C4×C47—21no—
328C4×C47—21no—
329C4×C47—21no—
330C4×C47—21no—
331C4×C47—21no—
332C4×C47—21no—
333C4×C47—21no—
334C4×C47—21no—
335C4×C47—21no—
336C4×C47#57711yescharacteristic
337C4×C47#57711yescharacteristic
338C4×C47#57811yescharacteristic
339C4×C47#57811yescharacteristic
340Dic47—42no—
341Dic47—42no—
342Dic47—42no—
343Dic47—42no—
344#3509—471no—
345#2990—471no—
346#2990D4711yescharacteristic
347#1559—471no—
348#1559—471no—
349#1558—471no—
350#1554—471no—
351#1554—471no—
352#1552—471no—
353#1552—471no—
354#1550—471no—
355#1550—471no—
356#1542—471no—
357#1542—471no—
358C2×#333—471no—
359C2×C47—22no—
360C2×C47—41no—
361C2×C47—41no—
362C2×C47C2×#41311yescharacteristic
363C2×C47#289811yescharacteristic
364C2×C47#289811yescharacteristic
365#557—941no—
366#557—941no—
367#556—941no—
368#556—941no—
369#552—941no—
370#552—941no—
371#552—941no—
372#552—941no—
373#541—472no—
374#541—472no—
375#536—472no—
376#533—471no—
377#533—471no—
378#533—471no—
379#533—471no—
380#533—471no—
381C2×C4⋊Q8—471no—
382#519—472no—
383C4×#41C2×D4711yescharacteristic
384#446—21no—
385#446—941no—
386#435—21no—
387#435—21no—
388#435—941no—
389#435—941no—
390C8×D4—21no—
391C8×D4—941no—
392#432—471no—
393#432—471no—
394#432C2×D4711yescharacteristic
395#432C2×D4711yescharacteristic
396#431—471no—
397#431C2×D4711yescharacteristic
398#423—471no—
399#423C2×D4711yescharacteristic
400C2×C4⋊C8—471no—
401C2×C4⋊C8—471no—
402C2×C4⋊C8C2×D4711yescharacteristic
403C2×C4⋊C8C2×D4711yescharacteristic
404#333—471no—
405#333—471no—
406#333—471no—
407#333—471no—
408#333—471no—
409#333—471no—
410#333—471no—
411#333—471no—
412#332—471no—
413#332—471no—
414#332—471no—
415#332—471no—
416#332—471no—
417#332—471no—
418#332—471no—
419#332—471no—
420C47#1778011yescharacteristic, complemented, Sylow
421C2×#41C4×D4711yescharacteristic
422C22×Q8—472no—
423C2×M16—21no—
424C2×M16—941no—
425C22×C8—21no—
426C22×C8—21no—
427C22×C8—941no—
428C22×C8—941no—
429C4⋊Q8—472no—
430C4⋊Q8—471no—
431C4⋊Q8—471no—
432C4⋊Q8—471no—
433C4⋊Q8—471no—
434C4⋊Q8—942no—
435C4⋊Q8—941no—
436C4⋊Q8—941no—
437#126—942no—
438#126—942no—
439#126—942no—
440#126—942no—
441#125—472no—
442#125—942no—
443#125—942no—
444#125—942no—
445#125—942no—
446#125—941no—
447#125—941no—
448#125—941no—
449#125—941no—
450#124—942no—
451#123—942no—
452#123—942no—
453C22⋊Q8—472no—
454C22⋊Q8—472no—
455C22⋊Q8—472no—
456C22⋊Q8—472no—
457C22⋊Q8—941no—
458C22⋊Q8—941no—
459C22⋊Q8—941no—
460C22⋊Q8—941no—
461C22⋊Q8—941no—
462C22⋊Q8—941no—
463C4×Q8—472no—
464C4×Q8—472no—
465C4×Q8—472no—
466C4×Q8—472no—
467C4×Q8—942no—
468C4×Q8—942no—
469C4×Q8—941no—
470C4×Q8—941no—
471C4×Q8—941no—
472C4×Q8—941no—
473C4×Q8—941no—
474C4×Q8—941no—
475C4×Q8D18811yescharacteristic
476C4×Q8C22⋊D4711yescharacteristic
477C4×D4D18811yescharacteristic
478C4×D4D18811yescharacteristic
479C4×D4D18811yescharacteristic
480C4×D4C22⋊D4711yescharacteristic
481C4×D4C22⋊D4711yescharacteristic
482C4×D4C22⋊D4711yescharacteristic
483#117—472no—
484#117—941no—
485#117—941no—
486#117—941no—
487#117—941no—
488#117—942no—
489#117—942no—
490#117C4×D4711yescharacteristic
491#117C4×D4711yescharacteristic
492#117C4×D4711yescharacteristic
493C2×C4⋊C4—941no—
494C2×C4⋊C4—941no—
495C2×C42C22×D4711yescharacteristic
496C2×C42C22×D4711yescharacteristic
497C2×C42C22×D4711yescharacteristic
498C4⋊C8—21no—
499C4⋊C8—21no—
500C4⋊C8—21no—
501C4⋊C8—471no—
502C4⋊C8—471no—
503C4⋊C8—471no—
504C4⋊C8—471no—
505C4⋊C8—941no—
506C4⋊C8—941no—
507C4⋊C8—941no—
508C4⋊C8C22×D4711yescharacteristic
509C4⋊C8C22×D4711yescharacteristic
510C4⋊C8C22×D4711yescharacteristic
511C4⋊C8C22×D4711yescharacteristic
512C22⋊C8—21no—
513C22⋊C8—21no—
514C22⋊C8—21no—
515C22⋊C8—941no—
516C22⋊C8—941no—
517C22⋊C8—941no—
518#97—21no—
519#97—21no—
520#97—941no—
521#97—941no—
522C4×C8—21no—
523C4×C8—941no—
524#41—42no—
525C2×Q8—472no—
526C2×Q8—472no—
527C2×Q8—942no—
528C2×Q8—941no—
529C2×Q8—941no—
530C2×Q8—1884no—
531C2×Q8(C2×D47)⋊C411yescharacteristic
532C2×D4(C2×D47)⋊C411yescharacteristic
533C2×D4(C2×D47)⋊C411yescharacteristic
534C2×D4(C2×D47)⋊C411yescharacteristic
535C22×C4—942no—
536C22×C4C2×C4×D4711yescharacteristic
537C22×C4C2×C4×D4711yescharacteristic
538C22×C4C2×C4×D4711yescharacteristic
539C22×C4C2×D18811yescharacteristic
540C22×C4C2×D18811yescharacteristic
541C22×C4C2×D18811yescharacteristic
542C22×C4C2×C22⋊D4711yescharacteristic
543C22×C4C2×C22⋊D4711yescharacteristic
544C22×C4C2×C22⋊D4711yescharacteristic
545M16—81no—
546M16—3761no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—81no—
552C2×C8—81no—
553C2×C8—941no—
554C2×C8—941no—
555C2×C8—941no—
556C2×C8—941no—
557C2×C8—3761no—
558C2×C8—3761no—
559C4⋊C4—472no—
560C4⋊C4—472no—
561C4⋊C4—942no—
562C4⋊C4—942no—
563C4⋊C4—942no—
564C4⋊C4—942no—
565C4⋊C4—942no—
566C4⋊C4—942no—
567C4⋊C4—942no—
568C4⋊C4—942no—
569C4⋊C4—942no—
570C4⋊C4—942no—
571C4⋊C4—942no—
572C4⋊C4—942no—
573C4⋊C4—941no—
574C4⋊C4—941no—
575C4⋊C4—941no—
576C4⋊C4—941no—
577C4⋊C4—941no—
578C4⋊C4—941no—
579C4⋊C4(C2×D47)⋊C411yescharacteristic
580C4⋊C4(C2×D47)⋊C411yescharacteristic
581C4⋊C4(C2×D47)⋊C411yescharacteristic
582C4⋊C4(C2×D47)⋊C411yescharacteristic
583C4⋊C4(C2×D47)⋊C411yescharacteristic
584C4⋊C4(C2×D47)⋊C411yescharacteristic
585C22⋊C4—942no—
586C22⋊C4—942no—
587C22⋊C4—942no—
588C22⋊C4—942no—
589C22⋊C4—942no—
590C22⋊C4(C2×D47)⋊C411yescharacteristic
591C22⋊C4(C2×D47)⋊C411yescharacteristic
592C22⋊C4(C2×D47)⋊C411yescharacteristic
593C22⋊C4(C2×D47)⋊C411yescharacteristic
594C22⋊C4(C2×D47)⋊C411yescharacteristic
595C22⋊C4(C2×D47)⋊C411yescharacteristic
596C42—942no—
597C42—942no—
598C42—942no—
599C42—942no—
600C42—942no—
601C42C2×C4×D4711yescharacteristic
602C42C2×C4×D4711yescharacteristic
603C42C2×C4×D4711yescharacteristic
604C42C2×D18811yescharacteristic
605C42C2×D18811yescharacteristic
606C42C2×D18811yescharacteristic
607C42C2×C22⋊D4711yescharacteristic
608C42C2×C22⋊D4711yescharacteristic
609C42C2×C22⋊D4711yescharacteristic
610C42C23×D4711yescharacteristic
611C23C2×(C2×D47)⋊C411yescharacteristic
612C23C2×(C2×D47)⋊C411yescharacteristic
613C23C2×(C2×D47)⋊C411yescharacteristic
614Q8—41no—
615Q8—1882no—
616Q8—1882no—
617Q8—1884no—
618Q8—1881no—
619Q8—1881no—
620Q8—1881no—
621Q8—1881no—
622D4—22no—
623D4—22no—
624D4—41no—
625C2×C4—22no—
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—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—942no—
641C2×C4—942no—
642C2×C4—942no—
643C2×C4—942no—
644C2×C4—1884no—
645C2×C4C2×(C2×D47)⋊C411yescharacteristic
646C2×C4C2×(C2×D47)⋊C411yescharacteristic
647C2×C4C2×(C2×D47)⋊C411yescharacteristic
648C2×C4C2×(C2×D47)⋊C411yescharacteristic
649C2×C4C2×(C2×D47)⋊C411yescharacteristic
650C2×C4C2×(C2×D47)⋊C411yescharacteristic
651C2×C4C2×(C2×D47)⋊C411yescharacteristic
652C2×C4C2×(C2×D47)⋊C411yescharacteristic
653C2×C4C2×(C2×D47)⋊C411yescharacteristic
654C2×C4C22×C4×D4711yescharacteristic
655C2×C4C22×C22⋊D4711yescharacteristic
656C2×C4C22×D18811yescharacteristic
657C8—41no—
658C8—41no—
659C8—41no—
660C8—41no—
661C8—1881no—
662C8—1881no—
663C8—1881no—
664C8—1881no—
665C22—21no—
666C22—21no—
667C22—21no—
668C22—21no—
669C22—21no—
670C22—21no—
671C22—21no—
672C22—21no—
673C22#1568910512yes—
674C22C22×(C2×D47)⋊C411yescharacteristic
675C4—21no—
676C4—21no—
677C4—21no—
678C4—21no—
679C4—21no—
680C4—21no—
681C4—21no—
682C4—21no—
683C4—21no—
684C4—21no—
685C4—1882no—
686C4—1882no—
687C4—1882no—
688C4—1882no—
689C4#1568993411yescharacteristic
690C4#1568993511yescharacteristic
691C4#1568993811yescharacteristic
692C4#1568994011yescharacteristic
693C2—22no—
694C2—41no—
695C2—41no—
696C2C2×#1568910511yescharacteristic
697C2#2025191811yescharacteristic
698C2#2025192211yescharacteristic
subgroupG/H
centerC22C22×(C2×D47)⋊C4
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#2990C2
socleC22×C47C22×C22⋊C4
prime radicalC2×#41×C47C2×C4
cosocleC42×C47C24
hypercenter#2990D47
hypocenterC47#17780
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2990

Complements

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

NH ≅ G/Ntype
3. #20242119C2semidirect
4. #20242116C2semidirect
5. #20242113C2semidirect
6. #20242099C2semidirect
7. #20242096C2semidirect
8. #20242089C2semidirect
9. #20242086C2semidirect
10. #20242079C2semidirect
11. #20242076C2semidirect
12. #20242046C2semidirect
13. #20242043C2semidirect
14. C2×#15688871C2semidirect
420. C47#17780semidirect

Maximal subgroups

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

subgroupindex
#202572742
#202525132
#202421192
#202421162
#202421132
#202420992
#202420962
#202420892
#202420862
#202420792
#202420762
#202420462
#202420432
C2×#156888712
C47×#29902
#1778047