Finite Group Databasebeta

← #26184434

Subgroups — #26184434

Order 12032.

878 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257366C211yesmaximal, characteristic
2#20252402C211yesmaximal, characteristic, complemented
3#20242025C211yesmaximal, characteristic, complemented
4#20242020C211yesmaximal, characteristic, complemented
5#20242017C211yesmaximal, characteristic, complemented
6#20242014C211yesmaximal, characteristic, complemented
7#20242009C211yesmaximal, characteristic, complemented
8#20242006C211yesmaximal, characteristic, complemented
9#20242004C211yesmaximal, characteristic, complemented
10#20241996C211yesmaximal, characteristic, complemented
11#20241991C211yesmaximal, characteristic, complemented
12#20241989C211yesmaximal, characteristic, complemented
13#20241977C211yesmaximal, characteristic, complemented
14C2×#15688864C211yesmaximal, characteristic, complemented
15C47×#2923C211yesmaximal, characteristic, complemented
16#15689851C411yescharacteristic
17#15689833C411yescharacteristic
18#15689830C411yescharacteristic
19#15689819C411yescharacteristic
20#15689819C411yescharacteristic
21#15689813C411yescharacteristic
22#15689813C411yescharacteristic
23#15689812—21no—
24#15689806—21no—
25#15689806—21no—
26#15689777C411yescharacteristic
27#15689772—21no—
28#15689731—21no—
29#15689715—21no—
30#15689715—21no—
31#15689680C2211yescharacteristic
32#15689657C2211yescharacteristic
33#15689657C2211yescharacteristic
34#15689657C2211yescharacteristic
35C2×#13094016C2211yescharacteristic
36C2×#13094016C2211yescharacteristic
37#15689602—21no—
38#15689254—21no—
39#15689195—21no—
40#15689195—21no—
41D4×C47⋊C8—21no—
42#15689180C2211yescharacteristic
43#15689180C2211yescharacteristic
44#15689180C2211yescharacteristic
45C4×#10625329C2211yescharacteristic
46C2×#13093935C2211yescharacteristic
47C2×#13093935C2211yescharacteristic
48#15688864C2211yescharacteristic
49#15688864C2211yescharacteristic
50#15688864C2211yescharacteristic
51#15688864C2211yescharacteristic
52#15688864C2211yescharacteristic
53#15688864C2211yescharacteristic
54#15688864C2211yescharacteristic
55#15688864C2211yescharacteristic
56#15688864C2211yescharacteristic
57#15688864C2211yescharacteristic
58#15688864C2211yescharacteristic
59#15688864C2211yescharacteristic
60#15688862C2211yescharacteristic
61#15688862C2211yescharacteristic
62#15688862C2211yescharacteristic
63#15688862C2211yescharacteristic
64C4×#41×C47C2211yescharacteristic
65C47×#433—21no—
66C47×#433—21no—
67C47×#432C2211yescharacteristic
68C47×#432C2211yescharacteristic
69C47×#432C2211yescharacteristic
70C47×#432C2211yescharacteristic
71C47×#424—21no—
72C47×#408—21no—
73C4×M16×C47C2211yescharacteristic
74C2×#97×C47C2211yescharacteristic
75C2×#10625352—21no—
76C2×#10625329—21no—
77C22×C47⋊C8—21no—
78C22×C47⋊C8—21no—
79#13094024C2×C411yescharacteristic
80#13094024C2×C411yescharacteristic
81#13094022—21no—
82#13094019—21no—
83#13094019—21no—
84#13094018—21no—
85#13094018—21no—
86#13094018—21no—
87#13094017—21no—
88#13094017—21no—
89#13094016—21no—
90#13094016—21no—
91#13094016—21no—
92#13094016—21no—
93#13094016C2×C411yescharacteristic
94#13094016C2×C411yescharacteristic
95#13094016C2×C411yescharacteristic
96#13094016C2×C411yescharacteristic
97#13094016C2311yescharacteristic
98#13094016C2311yescharacteristic
99#13094016C2311yescharacteristic
100#13094015—21no—
101#13094014—21no—
102#13094014—21no—
103#13094014—21no—
104#13094014—21no—
105#13094012C2311yescharacteristic
106#13094008—21no—
107#13094008—21no—
108#13094007—21no—
109#13094007—21no—
110#13094007—21no—
111#13094006—21no—
112#13094006—21no—
113#13094005—21no—
114#13094005—21no—
115#13094004—21no—
116#13094003—21no—
117#13094003—21no—
118#13094003C2×C411yescharacteristic
119#13094003C2×C411yescharacteristic
120#13094003C2×C411yescharacteristic
121#13094002—21no—
122#13094002—21no—
123#13094001—21no—
124#13094001—21no—
125#13094000—21no—
126#13093998C2×C411yescharacteristic
127#13093998C2×C411yescharacteristic
128#13093998C2×C411yescharacteristic
129#13093996—21no—
130#13093996—21no—
131C4×Dic94—21no—
132C4×Dic94—21no—
133C4×Dic94C2×C411yescharacteristic
134C4×Dic94C2×C411yescharacteristic
135C4×Dic94C2×C411yescharacteristic
136#13093989—21no—
137C4×D188C2×C411yescharacteristic
138C4×D188C2×C411yescharacteristic
139C4×D188C2×C411yescharacteristic
140D4×Dic47—21no—
141C4×C22⋊D47—21no—
142C4×C22⋊D47—21no—
143C4×C22⋊D47—21no—
144(C22⋊D47)⋊C4—21no—
145(C22⋊D47)⋊C4—21no—
146#13093983C2×C411yescharacteristic
147#13093983C2×C411yescharacteristic
148#13093981—21no—
149#13093981—21no—
150#13093981—21no—
151#13093980—21no—
152#13093980—21no—
153C2×C4⋊Dic47C2×C411yescharacteristic
154C2×C4⋊Dic47C2×C411yescharacteristic
155C2×C4⋊Dic47C2×C411yescharacteristic
156C2×C4⋊Dic47C2×C411yescharacteristic
157C2×Dic47⋊C4—21no—
158C2×Dic47⋊C4—21no—
159C2×Dic47⋊C4—21no—
160C2×Dic47⋊C4—21no—
161C4⋊C4×D47—21no—
162C4⋊(C47⋊C8)—21no—
163C4⋊(C47⋊C8)—21no—
164C4⋊(C47⋊C8)—21no—
165C22⋊(C47⋊C8)—21no—
166C22⋊(C47⋊C8)—21no—
167C22⋊(C47⋊C8)—21no—
168#13093935—21no—
169#13093935—21no—
170#13093935C2311yescharacteristic
171#13093935C2311yescharacteristic
172#13093935C2311yescharacteristic
173#13093935C2311yescharacteristic
174C4×C47⋊C8—21no—
175C2×#41×C47D411yescharacteristic
176C2×M16×C47—21no—
177C22×C8×C47—21no—
178C4×Q8×C47C2×C411yescharacteristic
179C4×Q8×C47D411yescharacteristic
180C4×D4×C47C2×C411yescharacteristic
181C4×D4×C47C2×C411yescharacteristic
182C4×D4×C47C2×C411yescharacteristic
183C4×D4×C47D411yescharacteristic
184C4×D4×C47D411yescharacteristic
185C4×D4×C47D411yescharacteristic
186#117×C47D411yescharacteristic
187#117×C47D411yescharacteristic
188#117×C47D411yescharacteristic
189C2×C42×C47C2311yescharacteristic
190C2×C42×C47C2311yescharacteristic
191C2×C42×C47C2311yescharacteristic
192C4⋊C8×C47—21no—
193C4⋊C8×C47—21no—
194C4⋊C8×C47—21no—
195C4⋊C8×C47—21no—
196C22⋊C8×C47—21no—
197C22⋊C8×C47—21no—
198C22⋊C8×C47—21no—
199C22⋊C8×C47—21no—
200#97×C47—21no—
201#97×C47C2311yescharacteristic
202#97×C47C2311yescharacteristic
203#97×C47C2311yescharacteristic
204#97×C47C2311yescharacteristic
205C4×C8×C47—21no—
206#41×C47—42no—
207C2×Q8×C47C22⋊C411yescharacteristic
208C2×D4×C47C22⋊C411yescharacteristic
209C2×D4×C47C22⋊C411yescharacteristic
210C2×D4×C47C22⋊C411yescharacteristic
211C22×C4×C47C22×C411yescharacteristic
212C22×C4×C47C22×C411yescharacteristic
213C22×C4×C47C22×C411yescharacteristic
214C22×C4×C47C2×D411yescharacteristic
215C22×C4×C47C2×D411yescharacteristic
216C22×C4×C47C2×D411yescharacteristic
217C22×C4×C47C2×D411yescharacteristic
218C22×C4×C47C2×D411yescharacteristic
219C22×C4×C47C2×D411yescharacteristic
220C2×C22⋊D47—21no—
221C2×C22⋊D47—21no—
222C2×C22⋊D47—21no—
223C22×Dic47—21no—
224C22×Dic47—21no—
225C22×Dic47—21no—
226C22×Dic47—21no—
227#10625352—44no—
228C2×D188C22×C411yescharacteristic
229C2×C4×D47—21no—
230C2×C4×D47—21no—
231C2×C4×D47—21no—
232C2×Dic94—21no—
233C2×Dic94—21no—
234C2×Dic94C22×C411yescharacteristic
235M16×C47—42no—
236C2×C8×C47—21no—
237C2×C8×C47—21no—
238C2×C8×C47—21no—
239C2×C8×C47—21no—
240C2×C8×C47—42no—
241C4⋊C4×C47C22⋊C411yescharacteristic
242C4⋊C4×C47C22⋊C411yescharacteristic
243C4⋊C4×C47C22⋊C411yescharacteristic
244C4⋊C4×C47C22⋊C411yescharacteristic
245C4⋊C4×C47C22⋊C411yescharacteristic
246C4⋊C4×C47C22⋊C411yescharacteristic
247C22⋊C4×C47C22⋊C411yescharacteristic
248C22⋊C4×C47C22⋊C411yescharacteristic
249C22⋊C4×C47C22⋊C411yescharacteristic
250C22⋊C4×C47C22⋊C411yescharacteristic
251C22⋊C4×C47C22⋊C411yescharacteristic
252C22⋊C4×C47C22⋊C411yescharacteristic
253C42×C47C22×C411yescharacteristic
254C42×C47C22×C411yescharacteristic
255C42×C47C22×C411yescharacteristic
256C42×C47C2×D411yescharacteristic
257C42×C47C2×D411yescharacteristic
258C42×C47C2×D411yescharacteristic
259C42×C47C2×D411yescharacteristic
260C42×C47C2×D411yescharacteristic
261C42×C47C2×D411yescharacteristic
262C42×C47C2411yescharacteristic
263C22⋊Dic47—21no—
264C22⋊Dic47—21no—
265C22⋊Dic47—21no—
266C22⋊Dic47—21no—
267C22⋊Dic47—21no—
268(C2×D47)⋊C4—21no—
269(C2×D47)⋊C4—21no—
270(C2×D47)⋊C4—21no—
271(C2×D47)⋊C4—21no—
272(C2×D47)⋊C4—21no—
273(C2×D47)⋊C4—21no—
274(C2×D47)⋊C4—21no—
275(C2×D47)⋊C4—21no—
276C4⋊Dic47—21no—
277C4⋊Dic47—21no—
278C4⋊Dic47—21no—
279C4⋊Dic47—21no—
280C4⋊Dic47—21no—
281C4⋊Dic47—21no—
282C4⋊Dic47C22×C411yescharacteristic
283C4⋊Dic47C22×C411yescharacteristic
284C4⋊Dic47C22×C411yescharacteristic
285C4⋊Dic47C22×C411yescharacteristic
286C4⋊Dic47C22×C411yescharacteristic
287C4⋊Dic47C22×C411yescharacteristic
288Dic47⋊C4—21no—
289Dic47⋊C4—21no—
290Dic47⋊C4—21no—
291Dic47⋊C4—21no—
292Dic47⋊C4—21no—
293Dic47⋊C4—21no—
294Dic47⋊C4—21no—
295Dic47⋊C4—21no—
296Dic47⋊C4—21no—
297Dic47⋊C4—21no—
298Dic47⋊C4—21no—
299Dic47⋊C4—21no—
300Dic47⋊C4—21no—
301Dic47⋊C4—21no—
302Dic47⋊C4—21no—
303Dic47⋊C4—21no—
304Dic47⋊C4—21no—
305Dic47⋊C4—21no—
306Dic47⋊C4—21no—
307Dic47⋊C4—21no—
308C4×Dic47—21no—
309C4×Dic47—21no—
310C4×Dic47—21no—
311C4×Dic47—21no—
312C4×Dic47—21no—
313#10625329—42no—
314C2×C47⋊C8—21no—
315C2×C47⋊C8—21no—
316C2×C47⋊C8—21no—
317C2×C47⋊C8—21no—
318C2×C47⋊C8—42no—
319C2×C47⋊C8—42no—
320C23×C47C2×C22⋊C411yescharacteristic
321C23×C47C2×C22⋊C411yescharacteristic
322C23×C47C2×C22⋊C411yescharacteristic
323C22×D47—21no—
324Q8×C47—41no—
325D4×C47—22no—
326D4×C47—22no—
327D4×C47—41no—
328C2×C4×C47—22no—
329C2×C4×C47—41no—
330C2×C4×C47—41no—
331C2×C4×C47—41no—
332C2×C4×C47—41no—
333C2×C4×C47—41no—
334C2×C4×C47—41no—
335C2×C4×C47—41no—
336C2×C4×C47—41no—
337C2×C4×C47C2×C22⋊C411yescharacteristic
338C2×C4×C47C2×C22⋊C411yescharacteristic
339C2×C4×C47C2×C22⋊C411yescharacteristic
340C2×C4×C47C2×C22⋊C411yescharacteristic
341C2×C4×C47C2×C22⋊C411yescharacteristic
342C2×C4×C47C2×C22⋊C411yescharacteristic
343C2×C4×C47C2×C22⋊C411yescharacteristic
344C2×C4×C47C2×C22⋊C411yescharacteristic
345C2×C4×C47C2×C22⋊C411yescharacteristic
346C2×C4×C47C23×C411yescharacteristic
347C2×C4×C47C22×D411yescharacteristic
348C2×C4×C47C22×D411yescharacteristic
349C22⋊D47—42no—
350C22⋊D47—42no—
351C22⋊D47—81no—
352C2×Dic47—21no—
353C2×Dic47—21no—
354C2×Dic47—21no—
355C2×Dic47—21no—
356C2×Dic47—21no—
357C2×Dic47—21no—
358C2×Dic47—21no—
359C2×Dic47—42no—
360C2×Dic47—42no—
361C2×Dic47—81no—
362C2×Dic47—81no—
363D188—41no—
364C4×D47—42no—
365C4×D47—81no—
366C4×D47—81no—
367Dic94—42no—
368Dic94—41no—
369Dic94—81no—
370C8×C47—41no—
371C8×C47—41no—
372C8×C47—41no—
373C8×C47—41no—
374C47⋊C8—22no—
375C47⋊C8—41no—
376C47⋊C8—41no—
377C47⋊C8—41no—
378#17680—471nomaximal, Sylow
379C22×C47—21no—
380C22×C47—21no—
381C22×C47—21no—
382C22×C47—21no—
383C22×C47—21no—
384C22×C47—21no—
385C22×C47—21no—
386C22×C47—21no—
387C22×C47#42112yes—
388C22×C47C22×C22⋊C411yescharacteristic
389C2×D47—41no—
390C2×D47—41no—
391C2×D47—41no—
392C4×C47—21no—
393C4×C47—21no—
394C4×C47—21no—
395C4×C47—21no—
396C4×C47—21no—
397C4×C47—21no—
398C4×C47—21no—
399C4×C47—21no—
400C4×C47—21no—
401C4×C47—21no—
402C4×C47—21no—
403C4×C47—21no—
404Dic47—41no—
405Dic47—41no—
406Dic47—41no—
407Dic47—41no—
408Dic47—41no—
409Dic47—41no—
410Dic47—41no—
411#3515—471no—
412#2970—471no—
413#2923D4711yescharacteristic, complemented
414#1537—471no—
415#1535—471no—
416#1535—471no—
417#1534—471no—
418#1532—471no—
419#1532—471no—
420#1531—471no—
421#1529—471no—
422#1528—471no—
423#1528—471no—
424#1524—471no—
425C2×#330—471no—
426C2×C47—22no—
427C2×C47—41no—
428C2×C47—41no—
429C2×C47#288911yescharacteristic
430C2×C47C2×#42111yescharacteristic
431C2×C47#290111yescharacteristic
432D47—81no—
433#557—471no—
434#554—471no—
435#554—471no—
436#553—471no—
437#553—471no—
438#552—471no—
439#552—471no—
440#552—941no—
441#552—941no—
442#552—941no—
443#547—471no—
444#547—941no—
445#541—941no—
446#539—941no—
447#539—941no—
448#533—471no—
449#529—471no—
450#529—471no—
451#529—471no—
452C2×#125—471no—
453C2×#125—471no—
454#520—941no—
455C4×#41C2×D4711yescharacteristic
456#446—941no—
457#435—941no—
458#435—941no—
459C8×D4—941no—
460#433—21no—
461#433—21no—
462#432—471no—
463#432—471no—
464#432—471no—
465#432C2×D4711yescharacteristic
466#432C2×D4711yescharacteristic
467#432C2×D4711yescharacteristic
468#432C2×D4711yescharacteristic
469#424—21no—
470#408—21no—
471C4×M16—471no—
472C4×M16C2×D4711yescharacteristic
473C2×#97—471no—
474C2×#97—471no—
475C2×#97C2×D4711yescharacteristic
476#330—471no—
477#330—471no—
478#330—471no—
479#330—471no—
480#330—471no—
481#330—471no—
482#330—471no—
483#330—471no—
484#330—471no—
485#330—471no—
486#330—471no—
487#330—471no—
488#329—471no—
489#329—471no—
490#329—471no—
491#329—471no—
492C47#1768011yescharacteristic, complemented, Sylow
493C2×#41—941no—
494C2×#41C22⋊D4711yescharacteristic
495C2×M16—21no—
496C2×M16—941no—
497C22×C8—21no—
498C22×C8—941no—
499C22×C8—941no—
500C4⋊Q8—471no—
501C4⋊Q8—471no—
502C4⋊Q8—941no—
503#126—941no—
504#126—941no—
505#126—941no—
506#126—941no—
507#126—941no—
508#126—941no—
509#126—941no—
510#125—471no—
511#125—471no—
512#125—471no—
513#125—471no—
514#125—471no—
515#125—471no—
516#125—471no—
517#125—941no—
518#125—941no—
519#125—941no—
520#125—941no—
521#125—941no—
522#125—941no—
523#125—941no—
524#125—941no—
525#125—941no—
526#124—471no—
527#123—941no—
528#123—941no—
529#123—941no—
530#123—941no—
531#123—941no—
532#123—941no—
533#123—941no—
534#123—941no—
535#123—941no—
536C22⋊Q8—471no—
537C22⋊Q8—471no—
538C22⋊Q8—471no—
539C22⋊Q8—941no—
540C22⋊Q8—941no—
541C22⋊Q8—941no—
542C22⋊Q8—941no—
543C22⋊Q8—941no—
544C22⋊Q8—941no—
545C22⋊Q8—941no—
546C22⋊Q8—941no—
547#121—471no—
548#121—471no—
549#121—471no—
550#121—941no—
551#121—941no—
552C4×Q8—471no—
553C4×Q8—471no—
554C4×Q8—471no—
555C4×Q8—941no—
556C4×Q8—941no—
557C4×Q8—941no—
558C4×Q8C4×D4711yescharacteristic
559C4×Q8D18811yescharacteristic
560C4×D4—471no—
561C4×D4—471no—
562C4×D4—471no—
563C4×D4—941no—
564C4×D4—941no—
565C4×D4—941no—
566C4×D4—941no—
567C4×D4—941no—
568C4×D4—941no—
569C4×D4C4×D4711yescharacteristic
570C4×D4C4×D4711yescharacteristic
571C4×D4C4×D4711yescharacteristic
572C4×D4D18811yescharacteristic
573C4×D4D18811yescharacteristic
574C4×D4D18811yescharacteristic
575#117—471no—
576#117—471no—
577#117—941no—
578#117—941no—
579#117—941no—
580#117—941no—
581#117—941no—
582#117C22⋊D4711yescharacteristic
583#117C22⋊D4711yescharacteristic
584#117C22⋊D4711yescharacteristic
585C2×C4⋊C4—471no—
586C2×C4⋊C4—471no—
587C2×C4⋊C4—471no—
588C2×C4⋊C4—471no—
589C2×C4⋊C4—941no—
590C2×C4⋊C4—941no—
591C2×C4⋊C4—941no—
592C2×C4⋊C4—941no—
593C2×C4⋊C4—941no—
594C2×C42C22×D4711yescharacteristic
595C2×C42C22×D4711yescharacteristic
596C2×C42C22×D4711yescharacteristic
597C4⋊C8—21no—
598C4⋊C8—21no—
599C4⋊C8—21no—
600C4⋊C8—21no—
601C4⋊C8—941no—
602C4⋊C8—941no—
603C4⋊C8—941no—
604C22⋊C8—21no—
605C22⋊C8—21no—
606C22⋊C8—21no—
607C22⋊C8—21no—
608C22⋊C8—941no—
609C22⋊C8—941no—
610C22⋊C8—941no—
611#97—21no—
612#97—471no—
613#97—471no—
614#97—471no—
615#97—471no—
616#97—941no—
617#97—941no—
618#97C22×D4711yescharacteristic
619#97C22×D4711yescharacteristic
620#97C22×D4711yescharacteristic
621#97C22×D4711yescharacteristic
622C4×C8—21no—
623C4×C8—941no—
624#41—42no—
625#41—1884no—
626C2×Q8—471no—
627C2×Q8—941no—
628C2×Q8—941no—
629C2×Q8(C2×D47)⋊C411yescharacteristic
630C2×D4—471no—
631C2×D4—941no—
632C2×D4—941no—
633C2×D4—941no—
634C2×D4(C2×D47)⋊C411yescharacteristic
635C2×D4(C2×D47)⋊C411yescharacteristic
636C2×D4(C2×D47)⋊C411yescharacteristic
637C22×C4—941no—
638C22×C4—941no—
639C22×C4—941no—
640C22×C4—941no—
641C22×C4—941no—
642C22×C4—941no—
643C22×C4—941no—
644C22×C4C2×C4×D4711yescharacteristic
645C22×C4C2×C4×D4711yescharacteristic
646C22×C4C2×C4×D4711yescharacteristic
647C22×C4C2×D18811yescharacteristic
648C22×C4C2×D18811yescharacteristic
649C22×C4C2×D18811yescharacteristic
650C22×C4C2×C22⋊D4711yescharacteristic
651C22×C4C2×C22⋊D4711yescharacteristic
652C22×C4C2×C22⋊D4711yescharacteristic
653M16—42no—
654M16—1882no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—42no—
660C2×C8—941no—
661C2×C8—941no—
662C2×C8—941no—
663C2×C8—941no—
664C2×C8—1882no—
665C2×C8—1882no—
666C4⋊C4—471no—
667C4⋊C4—471no—
668C4⋊C4—471no—
669C4⋊C4—471no—
670C4⋊C4—471no—
671C4⋊C4—471no—
672C4⋊C4—941no—
673C4⋊C4—941no—
674C4⋊C4—941no—
675C4⋊C4—941no—
676C4⋊C4—941no—
677C4⋊C4—941no—
678C4⋊C4—941no—
679C4⋊C4—941no—
680C4⋊C4—941no—
681C4⋊C4—941no—
682C4⋊C4—941no—
683C4⋊C4—941no—
684C4⋊C4—941no—
685C4⋊C4—941no—
686C4⋊C4—941no—
687C4⋊C4—941no—
688C4⋊C4—941no—
689C4⋊C4—941no—
690C4⋊C4—941no—
691C4⋊C4—941no—
692C4⋊C4—941no—
693C4⋊C4—941no—
694C4⋊C4—941no—
695C4⋊C4—941no—
696C4⋊C4—941no—
697C4⋊C4—941no—
698C4⋊C4(C2×D47)⋊C411yescharacteristic
699C4⋊C4(C2×D47)⋊C411yescharacteristic
700C4⋊C4(C2×D47)⋊C411yescharacteristic
701C4⋊C4(C2×D47)⋊C411yescharacteristic
702C4⋊C4(C2×D47)⋊C411yescharacteristic
703C4⋊C4(C2×D47)⋊C411yescharacteristic
704C22⋊C4—941no—
705C22⋊C4—941no—
706C22⋊C4—941no—
707C22⋊C4—941no—
708C22⋊C4—941no—
709C22⋊C4—941no—
710C22⋊C4—941no—
711C22⋊C4—941no—
712C22⋊C4—941no—
713C22⋊C4—941no—
714C22⋊C4—941no—
715C22⋊C4—941no—
716C22⋊C4—941no—
717C22⋊C4(C2×D47)⋊C411yescharacteristic
718C22⋊C4(C2×D47)⋊C411yescharacteristic
719C22⋊C4(C2×D47)⋊C411yescharacteristic
720C22⋊C4(C2×D47)⋊C411yescharacteristic
721C22⋊C4(C2×D47)⋊C411yescharacteristic
722C22⋊C4(C2×D47)⋊C411yescharacteristic
723C42—941no—
724C42—941no—
725C42—941no—
726C42—941no—
727C42—941no—
728C42C2×C4×D4711yescharacteristic
729C42C2×C4×D4711yescharacteristic
730C42C2×C4×D4711yescharacteristic
731C42C2×D18811yescharacteristic
732C42C2×D18811yescharacteristic
733C42C2×D18811yescharacteristic
734C42C2×C22⋊D4711yescharacteristic
735C42C2×C22⋊D4711yescharacteristic
736C42C2×C22⋊D4711yescharacteristic
737C42C23×D4711yescharacteristic
738C23—941no—
739C23C2×(C2×D47)⋊C411yescharacteristic
740C23C2×(C2×D47)⋊C411yescharacteristic
741C23C2×(C2×D47)⋊C411yescharacteristic
742Q8—41no—
743Q8—3761no—
744Q8—1881no—
745Q8—1882no—
746D4—22no—
747D4—22no—
748D4—41no—
749D4—3761no—
750D4—1881no—
751D4—1882no—
752D4—1882no—
753C2×C4—22no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—941no—
763C2×C4—941no—
764C2×C4—941no—
765C2×C4—941no—
766C2×C4—941no—
767C2×C4—941no—
768C2×C4—941no—
769C2×C4—3761no—
770C2×C4—3761no—
771C2×C4—3761no—
772C2×C4—3761no—
773C2×C4—1882no—
774C2×C4—1882no—
775C2×C4—1882no—
776C2×C4C2×(C2×D47)⋊C411yescharacteristic
777C2×C4C2×(C2×D47)⋊C411yescharacteristic
778C2×C4C2×(C2×D47)⋊C411yescharacteristic
779C2×C4C2×(C2×D47)⋊C411yescharacteristic
780C2×C4C2×(C2×D47)⋊C411yescharacteristic
781C2×C4C2×(C2×D47)⋊C411yescharacteristic
782C2×C4C2×(C2×D47)⋊C411yescharacteristic
783C2×C4C2×(C2×D47)⋊C411yescharacteristic
784C2×C4C2×(C2×D47)⋊C411yescharacteristic
785C2×C4C22×C4×D4711yescharacteristic
786C2×C4C22×C22⋊D4711yescharacteristic
787C2×C4C22×D18811yescharacteristic
788C8—41no—
789C8—41no—
790C8—41no—
791C8—41no—
792C8—942no—
793C8—1881no—
794C8—1881no—
795C8—1881no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—1881no—
805C22—1881no—
806C22—1881no—
807C22#1568914112yes—
808C22C22×(C2×D47)⋊C411yescharacteristic
809C4—21no—
810C4—21no—
811C4—21no—
812C4—21no—
813C4—21no—
814C4—21no—
815C4—21no—
816C4—21no—
817C4—21no—
818C4—21no—
819C4—21no—
820C4—21no—
821C4—1881no—
822C4—1881no—
823C4—1881no—
824C4—1881no—
825C4—1881no—
826C4—1881no—
827C4—1881no—
828C2—22no—
829C2—41no—
830C2—41no—
831C2—3761no—
832C2#2025187011yescharacteristic
833C2C2×#1568914111yescharacteristic
834C2#2025193311yescharacteristic
subgroupG/H
centerC22C22×(C2×D47)⋊C4
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#2923C2
socleC22×C47C22×C22⋊C4
prime radical#20257366C2
cosocleC42×C47C24
hypercenter#2923D47
hypocenterC47#17680
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2923

Complements

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

NH ≅ G/Ntype
2. #20252402C2semidirect
3. #20242025C2semidirect
4. #20242020C2semidirect
5. #20242017C2semidirect
6. #20242014C2semidirect
7. #20242009C2semidirect
8. #20242006C2semidirect
9. #20242004C2semidirect
10. #20241996C2semidirect
11. #20241991C2semidirect
12. #20241989C2semidirect
13. #20241977C2semidirect
14. C2×#15688864C2semidirect
15. C47×#2923C2semidirect
413. #2923D47semidirect
492. C47#17680semidirect

Maximal subgroups

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

subgroupindex
#202573662
#202524022
#202420252
#202420202
#202420172
#202420142
#202420092
#202420062
#202420042
#202419962
#202419912
#202419892
#202419772
C2×#156888642
C47×#29232
#1768047