Finite Group Databasebeta

← #26185176

Subgroups — #26185176

Order 12032.

926 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257299C211yesmaximal, characteristic
2#20252513C211yesmaximal, characteristic, complemented
3#20242116C211yesmaximal, characteristic, complemented
4#20242111C211yesmaximal, characteristic, complemented
5#20242106C211yesmaximal, characteristic, complemented
6#20242099C211yesmaximal, characteristic, complemented
7#20242091C211yesmaximal, characteristic, complemented
8#20242084C211yesmaximal, characteristic, complemented
9#20242081C211yesmaximal, characteristic, complemented
10#20242076C211yesmaximal, characteristic, complemented
11#20242066C211yesmaximal, characteristic, complemented
12#20242043C211yesmaximal, characteristic, complemented
13#20242038C211yesmaximal, characteristic, complemented
14C2×#15688870C211yesmaximal, characteristic, complemented
15C47×#2990C211yesmaximal, characteristic, complemented
16#15689846—21no—
17#15689838—21no—
18#15689833—21no—
19#15689819—21no—
20#15689819—21no—
21#15689782—21no—
22#15689782—21no—
23#15689778—21no—
24#15689744C412yes—
25#15689744C412yes—
26#15689701C412yes—
27#15689680C2211yescharacteristic
28#15689680C2211yescharacteristic
29#15689673C2211yescharacteristic
30#15689673C2211yescharacteristic
31#15689673C2211yescharacteristic
32C2×#13094024C2211yescharacteristic
33#15689603C412yes—
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#15688870C2211yescharacteristic
49#15688870C2211yescharacteristic
50#15688870C2211yescharacteristic
51#15688870C2211yescharacteristic
52#15688870C2211yescharacteristic
53#15688870C2211yescharacteristic
54#15688870C2211yescharacteristic
55#15688870C2211yescharacteristic
56#15688866C2211yescharacteristic
57#15688866C2211yescharacteristic
58#15688866C2211yescharacteristic
59#15688866C2211yescharacteristic
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
71C2×#10625350—21no—
72C2×#10625350—21no—
73C2×#10625350C2×C412yes—
74C22×Dic94—21no—
75C2×#10625329—21no—
76C22×C47⋊C8—21no—
77C22×C47⋊C8—21no—
78#13094024—21no—
79#13094024—21no—
80#13094024C2×C412yes—
81#13094024C2311yescharacteristic
82#13094024C2311yescharacteristic
83#13094024C2311yescharacteristic
84#13094021C2311yescharacteristic
85#13094019—22no—
86#13094019—22no—
87#13094016—21no—
88#13094016—21no—
89#13094012—21no—
90#13094012—21no—
91#13094012C2×C412yes—
92#13094010—22no—
93#13094010—22no—
94#13094006—22no—
95#13094006—22no—
96#13094003—21no—
97#13094003—21no—
98#13094003C2×C412yes—
99#13094003C2×C412yes—
100#13094002—22no—
101#13094002—22no—
102#13094000—22no—
103#13093998—21no—
104#13093998—21no—
105#13093998—21no—
106#13093998—21no—
107#13093998C2×C412yes—
108#13093998C2×C412yes—
109#13093996—22no—
110#13093996—22no—
111#13093995—22no—
112C4×Dic94—21no—
113C4×Dic94—21no—
114C4×Dic94C2×C412yes—
115C4×Dic94C2×C412yes—
116C4×D188—21no—
117C4×D188—21no—
118C4×D188—21no—
119C4×D188—21no—
120C4×D188C2×C412yes—
121C4×D188C2×C412yes—
122(C22⋊D47)⋊C4—22no—
123(C22⋊D47)⋊C4—22no—
124#13093983—21no—
125#13093983—21no—
126#13093982—22no—
127C2×C4⋊Dic47—21no—
128C2×C4⋊Dic47C2×C412yes—
129C4⋊C4×D47—22no—
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
188C2×C22⋊D47—22no—
189C2×C22⋊D47—22no—
190C2×C22⋊D47—22no—
191C22×Dic47—22no—
192#10625350—44no—
193#10625350—81no—
194#10625350—81no—
195#10625350—81no—
196#10625350—81no—
197C2×D188—21no—
198C2×D188—21no—
199C2×D188C22×C412yes—
200C2×C4×D47—22no—
201C2×C4×D47—22no—
202C2×C4×D47—22no—
203C2×Dic94—21no—
204C2×Dic94—21no—
205C2×Dic94—22no—
206C2×Dic94—81no—
207C2×Dic94—81no—
208C2×Dic94C22×C412yes—
209M16×C47—81no—
210C2×C8×C47—21no—
211C2×C8×C47—21no—
212C2×C8×C47—21no—
213C2×C8×C47—21no—
214C2×C8×C47—81no—
215C2×C8×C47—81no—
216C4⋊C4×C47C22⋊C411yescharacteristic
217C4⋊C4×C47C22⋊C411yescharacteristic
218C4⋊C4×C47C22⋊C411yescharacteristic
219C4⋊C4×C47C22⋊C411yescharacteristic
220C4⋊C4×C47C22⋊C411yescharacteristic
221C4⋊C4×C47C22⋊C411yescharacteristic
222C22⋊C4×C47C22⋊C411yescharacteristic
223C22⋊C4×C47C22⋊C411yescharacteristic
224C22⋊C4×C47C22⋊C411yescharacteristic
225C22⋊C4×C47C22⋊C411yescharacteristic
226C22⋊C4×C47C22⋊C411yescharacteristic
227C22⋊C4×C47C22⋊C411yescharacteristic
228C42×C47C22×C411yescharacteristic
229C42×C47C22×C411yescharacteristic
230C42×C47C22×C411yescharacteristic
231C42×C47C2×D411yescharacteristic
232C42×C47C2×D411yescharacteristic
233C42×C47C2×D411yescharacteristic
234C42×C47C2×D411yescharacteristic
235C42×C47C2×D411yescharacteristic
236C42×C47C2×D411yescharacteristic
237C42×C47C2411yescharacteristic
238C22⋊Dic47—22no—
239C22⋊Dic47—22no—
240(C2×D47)⋊C4—22no—
241(C2×D47)⋊C4—22no—
242(C2×D47)⋊C4—22no—
243(C2×D47)⋊C4—22no—
244(C2×D47)⋊C4—22no—
245(C2×D47)⋊C4—22no—
246C4⋊Dic47—22no—
247C4⋊Dic47—22no—
248C4⋊Dic47—21no—
249C4⋊Dic47—21no—
250C4⋊Dic47—21no—
251C4⋊Dic47—21no—
252C4⋊Dic47C22×C412yes—
253C4⋊Dic47C22×C412yes—
254Dic47⋊C4—22no—
255Dic47⋊C4—22no—
256Dic47⋊C4—22no—
257Dic47⋊C4—22no—
258C4×Dic47—22no—
259C4×Dic47—22no—
260#10625329—81no—
261C2×C47⋊C8—21no—
262C2×C47⋊C8—21no—
263C2×C47⋊C8—21no—
264C2×C47⋊C8—21no—
265C2×C47⋊C8—81no—
266C2×C47⋊C8—81no—
267C23×C47C2×C22⋊C411yescharacteristic
268C23×C47C2×C22⋊C411yescharacteristic
269C23×C47C2×C22⋊C411yescharacteristic
270C22×D47—22no—
271Q8×C47—41no—
272D4×C47—22no—
273D4×C47—22no—
274D4×C47—41no—
275C2×C4×C47—22no—
276C2×C4×C47—21no—
277C2×C4×C47—21no—
278C2×C4×C47—21no—
279C2×C4×C47—21no—
280C2×C4×C47—21no—
281C2×C4×C47—21no—
282C2×C4×C47—21no—
283C2×C4×C47—21no—
284C2×C4×C47—21no—
285C2×C4×C47—21no—
286C2×C4×C47—21no—
287C2×C4×C47—21no—
288C2×C4×C47—41no—
289C2×C4×C47—41no—
290C2×C4×C47C2×C22⋊C411yescharacteristic
291C2×C4×C47C2×C22⋊C411yescharacteristic
292C2×C4×C47C2×C22⋊C411yescharacteristic
293C2×C4×C47C2×C22⋊C411yescharacteristic
294C2×C4×C47C2×C22⋊C411yescharacteristic
295C2×C4×C47C2×C22⋊C411yescharacteristic
296C2×C4×C47C2×C22⋊C411yescharacteristic
297C2×C4×C47C2×C22⋊C411yescharacteristic
298C2×C4×C47C2×C22⋊C411yescharacteristic
299C2×C4×C47C23×C411yescharacteristic
300C2×C4×C47C22×D411yescharacteristic
301C2×C4×C47C22×D411yescharacteristic
302C22⋊D47—44no—
303C22⋊D47—82no—
304C22⋊D47—82no—
305C2×Dic47—22no—
306C2×Dic47—22no—
307C2×Dic47—22no—
308C2×Dic47—82no—
309D188—42no—
310D188—41no—
311D188—41no—
312D188—41no—
313D188—41no—
314C4×D47—44no—
315C4×D47—82no—
316C4×D47—82no—
317Dic94—41no—
318Dic94—41no—
319Dic94—41no—
320Dic94—41no—
321Dic94—42no—
322Dic94—82no—
323C8×C47—41no—
324C8×C47—41no—
325C8×C47—41no—
326C8×C47—41no—
327C47⋊C8—41no—
328C47⋊C8—41no—
329C47⋊C8—41no—
330C47⋊C8—41no—
331#17775—471nomaximal, Sylow
332C22×C47—21no—
333C22×C47—21no—
334C22×C47—21no—
335C22×C47—21no—
336C22×C47—21no—
337C22×C47—21no—
338C22×C47—21no—
339C22×C47—21no—
340C22×C47#41312yes—
341C22×C47C22×C22⋊C411yescharacteristic
342C2×D47—42no—
343C2×D47—42no—
344C2×D47—42no—
345C4×C47—21no—
346C4×C47—21no—
347C4×C47—21no—
348C4×C47—21no—
349C4×C47—21no—
350C4×C47—21no—
351C4×C47—21no—
352C4×C47—21no—
353C4×C47—21no—
354C4×C47—21no—
355C4×C47#57611yescharacteristic
356C4×C47#57711yescharacteristic
357C4×C47#57711yescharacteristic
358C4×C47#57811yescharacteristic
359Dic47—42no—
360Dic47—42no—
361Dic47—42no—
362#3511—471no—
363#2990—471no—
364#2990D4711yescharacteristic, complemented
365#1559—471no—
366#1557—471no—
367#1556—471no—
368#1554—471no—
369#1553—471no—
370#1551—471no—
371#1551—471no—
372#1550—471no—
373#1547—471no—
374#1542—471no—
375#1540—471no—
376C2×#332—471no—
377C2×C47—22no—
378C2×C47—41no—
379C2×C47—41no—
380C2×C47C2×#41311yescharacteristic
381C2×C47#289711yescharacteristic
382C2×C47#289811yescharacteristic
383D47—82no—
384#556—941no—
385#555—941no—
386#554—941no—
387#553—941no—
388#553—941no—
389#548—941no—
390#548—941no—
391#547—941no—
392#542—472no—
393#542—472no—
394#537—472no—
395#533—471no—
396#533—471no—
397#532—471no—
398#532—471no—
399#532—471no—
400C2×C4⋊Q8—471no—
401#520—472no—
402C4×#41C2×D4711yescharacteristic
403#446—21no—
404#446—941no—
405#435—21no—
406#435—21no—
407#435—941no—
408#435—941no—
409C8×D4—21no—
410C8×D4—941no—
411#432—471no—
412#432—471no—
413#432C2×D4711yescharacteristic
414#432C2×D4711yescharacteristic
415#431—471no—
416#431C2×D4711yescharacteristic
417#423—471no—
418#423C2×D4711yescharacteristic
419C2×C4⋊C8—471no—
420C2×C4⋊C8—471no—
421C2×C4⋊C8C2×D4711yescharacteristic
422C2×C4⋊C8C2×D4711yescharacteristic
423#333—471no—
424#333—471no—
425#333—471no—
426#333—471no—
427#332—471no—
428#332—471no—
429#332—471no—
430#332—471no—
431#332—471no—
432#332—471no—
433#332—471no—
434#332—471no—
435#331—471no—
436#331—471no—
437#331—471no—
438#331—471no—
439C47#1777511yescharacteristic, complemented, Sylow
440C2×#41—472no—
441C2×#41—941no—
442C2×#41—941no—
443C2×#41C4×D4711yescharacteristic
444C22×Q8—941no—
445C2×M16—21no—
446C2×M16—941no—
447C22×C8—21no—
448C22×C8—21no—
449C22×C8—941no—
450C22×C8—941no—
451C4⋊Q8—472no—
452C4⋊Q8—471no—
453C4⋊Q8—471no—
454C4⋊Q8—471no—
455C4⋊Q8—941no—
456C4⋊Q8—941no—
457#127—471no—
458#126—942no—
459#126—942no—
460#125—941no—
461#125—941no—
462#124—472no—
463#124—942no—
464#124—942no—
465#124—941no—
466#124—941no—
467#123—942no—
468#123—942no—
469C22⋊Q8—472no—
470C22⋊Q8—472no—
471C22⋊Q8—942no—
472C22⋊Q8—941no—
473C22⋊Q8—941no—
474C22⋊Q8—942no—
475C22⋊Q8—942no—
476#121—472no—
477#121—472no—
478#121—942no—
479#121—942no—
480#121—942no—
481#121—941no—
482#121—941no—
483#121—941no—
484#121—941no—
485C4×Q8—472no—
486C4×Q8—472no—
487C4×Q8—941no—
488C4×Q8—941no—
489C4×Q8D18811yescharacteristic
490C4×Q8C22⋊D4711yescharacteristic
491C4×D4—472no—
492C4×D4—472no—
493C4×D4—942no—
494C4×D4—942no—
495C4×D4—941no—
496C4×D4—941no—
497C4×D4—941no—
498C4×D4—941no—
499C4×D4D18811yescharacteristic
500C4×D4D18811yescharacteristic
501C4×D4D18811yescharacteristic
502C4×D4C22⋊D4711yescharacteristic
503C4×D4C22⋊D4711yescharacteristic
504C4×D4C22⋊D4711yescharacteristic
505#117—941no—
506#117—941no—
507#117—942no—
508#117C4×D4711yescharacteristic
509#117C4×D4711yescharacteristic
510#117C4×D4711yescharacteristic
511C2×C4⋊C4—472no—
512C2×C4⋊C4—941no—
513C2×C4⋊C4—942no—
514C2×C42C22×D4711yescharacteristic
515C2×C42C22×D4711yescharacteristic
516C2×C42C22×D4711yescharacteristic
517C4⋊C8—21no—
518C4⋊C8—21no—
519C4⋊C8—21no—
520C4⋊C8—471no—
521C4⋊C8—471no—
522C4⋊C8—471no—
523C4⋊C8—471no—
524C4⋊C8—941no—
525C4⋊C8—941no—
526C4⋊C8—941no—
527C4⋊C8C22×D4711yescharacteristic
528C4⋊C8C22×D4711yescharacteristic
529C4⋊C8C22×D4711yescharacteristic
530C4⋊C8C22×D4711yescharacteristic
531C22⋊C8—21no—
532C22⋊C8—21no—
533C22⋊C8—21no—
534C22⋊C8—941no—
535C22⋊C8—941no—
536C22⋊C8—941no—
537#97—21no—
538#97—21no—
539#97—941no—
540#97—941no—
541C4×C8—21no—
542C4×C8—941no—
543#41—42no—
544#41—3761no—
545#41—3761no—
546#41—3761no—
547#41—3761no—
548#41—1884no—
549C2×Q8—472no—
550C2×Q8—942no—
551C2×Q8—941no—
552C2×Q8—941no—
553C2×Q8—3761no—
554C2×Q8—3761no—
555C2×Q8(C2×D47)⋊C411yescharacteristic
556C2×D4—472no—
557C2×D4—942no—
558C2×D4—942no—
559C2×D4—942no—
560C2×D4—941no—
561C2×D4—941no—
562C2×D4(C2×D47)⋊C411yescharacteristic
563C2×D4(C2×D47)⋊C411yescharacteristic
564C2×D4(C2×D47)⋊C411yescharacteristic
565C22×C4—942no—
566C22×C4—942no—
567C22×C4—942no—
568C22×C4—942no—
569C22×C4C2×C4×D4711yescharacteristic
570C22×C4C2×C4×D4711yescharacteristic
571C22×C4C2×C4×D4711yescharacteristic
572C22×C4C2×D18811yescharacteristic
573C22×C4C2×D18811yescharacteristic
574C22×C4C2×D18811yescharacteristic
575C22×C4C2×C22⋊D4711yescharacteristic
576C22×C4C2×C22⋊D4711yescharacteristic
577C22×C4C2×C22⋊D4711yescharacteristic
578M16—81no—
579M16—3761no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—81no—
585C2×C8—81no—
586C2×C8—941no—
587C2×C8—941no—
588C2×C8—941no—
589C2×C8—941no—
590C2×C8—3761no—
591C2×C8—3761no—
592C4⋊C4—472no—
593C4⋊C4—472no—
594C4⋊C4—942no—
595C4⋊C4—942no—
596C4⋊C4—942no—
597C4⋊C4—942no—
598C4⋊C4—942no—
599C4⋊C4—942no—
600C4⋊C4—941no—
601C4⋊C4—941no—
602C4⋊C4—941no—
603C4⋊C4—941no—
604C4⋊C4(C2×D47)⋊C411yescharacteristic
605C4⋊C4(C2×D47)⋊C411yescharacteristic
606C4⋊C4(C2×D47)⋊C411yescharacteristic
607C4⋊C4(C2×D47)⋊C411yescharacteristic
608C4⋊C4(C2×D47)⋊C411yescharacteristic
609C4⋊C4(C2×D47)⋊C411yescharacteristic
610C22⋊C4—942no—
611C22⋊C4—942no—
612C22⋊C4—942no—
613C22⋊C4—942no—
614C22⋊C4—942no—
615C22⋊C4—942no—
616C22⋊C4—942no—
617C22⋊C4—942no—
618C22⋊C4(C2×D47)⋊C411yescharacteristic
619C22⋊C4(C2×D47)⋊C411yescharacteristic
620C22⋊C4(C2×D47)⋊C411yescharacteristic
621C22⋊C4(C2×D47)⋊C411yescharacteristic
622C22⋊C4(C2×D47)⋊C411yescharacteristic
623C22⋊C4(C2×D47)⋊C411yescharacteristic
624C42—942no—
625C42—942no—
626C42C2×C4×D4711yescharacteristic
627C42C2×C4×D4711yescharacteristic
628C42C2×C4×D4711yescharacteristic
629C42C2×D18811yescharacteristic
630C42C2×D18811yescharacteristic
631C42C2×D18811yescharacteristic
632C42C2×C22⋊D4711yescharacteristic
633C42C2×C22⋊D4711yescharacteristic
634C42C2×C22⋊D4711yescharacteristic
635C42C23×D4711yescharacteristic
636C23—942no—
637C23C2×(C2×D47)⋊C411yescharacteristic
638C23C2×(C2×D47)⋊C411yescharacteristic
639C23C2×(C2×D47)⋊C411yescharacteristic
640Q8—41no—
641Q8—3762no—
642Q8—1882no—
643Q8—1881no—
644Q8—1881no—
645Q8—1881no—
646Q8—1881no—
647D4—22no—
648D4—22no—
649D4—41no—
650D4—3762no—
651D4—3762no—
652D4—1882no—
653D4—1884no—
654D4—1881no—
655D4—1881no—
656D4—1881no—
657D4—1881no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—942no—
674C2×C4—942no—
675C2×C4—942no—
676C2×C4—3762no—
677C2×C4—3762no—
678C2×C4—3762no—
679C2×C4—1884no—
680C2×C4C2×(C2×D47)⋊C411yescharacteristic
681C2×C4C2×(C2×D47)⋊C411yescharacteristic
682C2×C4C2×(C2×D47)⋊C411yescharacteristic
683C2×C4C2×(C2×D47)⋊C411yescharacteristic
684C2×C4C2×(C2×D47)⋊C411yescharacteristic
685C2×C4C2×(C2×D47)⋊C411yescharacteristic
686C2×C4C2×(C2×D47)⋊C411yescharacteristic
687C2×C4C2×(C2×D47)⋊C411yescharacteristic
688C2×C4C2×(C2×D47)⋊C411yescharacteristic
689C2×C4C22×C4×D4711yescharacteristic
690C2×C4C22×C22⋊D4711yescharacteristic
691C2×C4C22×D18811yescharacteristic
692C8—41no—
693C8—41no—
694C8—41no—
695C8—41no—
696C8—1881no—
697C8—1881no—
698C8—1881no—
699C8—1881no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—21no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—21no—
708C22—1882no—
709C22—1882no—
710C22—1882no—
711C22#1568910512yes—
712C22C22×(C2×D47)⋊C411yescharacteristic
713C4—21no—
714C4—21no—
715C4—21no—
716C4—21no—
717C4—21no—
718C4—21no—
719C4—21no—
720C4—21no—
721C4—21no—
722C4—21no—
723C4—1882no—
724C4—1882no—
725C4—1882no—
726C4#1568992611yescharacteristic
727C4#1568993111yescharacteristic
728C4#1568993511yescharacteristic
729C4#1568994011yescharacteristic
730C2—22no—
731C2—41no—
732C2—41no—
733C2—3762no—
734C2C2×#1568910511yescharacteristic
735C2#2025191111yescharacteristic
736C2#2025192211yescharacteristic
subgroupG/H
centerC22C22×(C2×D47)⋊C4
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#2990C2
socleC22×C47C22×C22⋊C4
prime radical#20257299C2
cosocleC42×C47C24
hypercenter#2990D47
hypocenterC47#17775
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
2. #20252513C2semidirect
3. #20242116C2semidirect
4. #20242111C2semidirect
5. #20242106C2semidirect
6. #20242099C2semidirect
7. #20242091C2semidirect
8. #20242084C2semidirect
9. #20242081C2semidirect
10. #20242076C2semidirect
11. #20242066C2semidirect
12. #20242043C2semidirect
13. #20242038C2semidirect
14. C2×#15688870C2semidirect
15. C47×#2990C2semidirect
364. #2990D47semidirect
439. C47#17775semidirect

Maximal subgroups

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

subgroupindex
#202572992
#202525132
#202421162
#202421112
#202421062
#202420992
#202420912
#202420842
#202420812
#202420762
#202420662
#202420432
#202420382
C2×#156888702
C47×#29902
#1777547