Finite Group Databasebeta

← #26184500

Subgroups — #26184500

Order 12032.

902 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257284C211yesmaximal, characteristic
2#20252402C211yesmaximal, characteristic, complemented
3#20242020C211yesmaximal, characteristic, complemented
4#20242017C211yesmaximal, characteristic, complemented
5#20242011C211yesmaximal, characteristic, complemented
6#20242009C211yesmaximal, characteristic, complemented
7#20242006C211yesmaximal, characteristic, complemented
8#20242004C211yesmaximal, characteristic, complemented
9#20242002C211yesmaximal, characteristic, complemented
10#20241996C211yesmaximal, characteristic, complemented
11#20241993C211yesmaximal, characteristic, complemented
12#20241977C211yesmaximal, characteristic, complemented
13#20241974C211yesmaximal, characteristic, complemented
14C2×#15688862C211yesmaximal, characteristic, complemented
15C47×#2970C211yesmaximal, characteristic, complemented
16#15689856—21no—
17#15689856—21no—
18#15689845—21no—
19#15689845—21no—
20#15689802—21no—
21#15689802—21no—
22#15689802—21no—
23#15689802—21no—
24#15689744C411yescharacteristic
25#15689744C411yescharacteristic
26#15689744C411yescharacteristic
27#15689744C411yescharacteristic
28#15689694C411yescharacteristic
29#15689687C411yescharacteristic
30#15689680C2211yescharacteristic
31#15689657C2211yescharacteristic
32#15689657C2211yescharacteristic
33#15689657C2211yescharacteristic
34#15689657C2211yescharacteristic
35C2×#13094012C2211yescharacteristic
36#15689600C411yescharacteristic
37#15689597C411yescharacteristic
38#15689254—21no—
39#15689195—21no—
40#15689195—21no—
41D4×C47⋊C8—21no—
42#15689180C2211yescharacteristic
43#15689180C2211yescharacteristic, complemented
44#15689180C2211yescharacteristic, complemented
45C4×#10625329C2211yescharacteristic, complemented
46C2×#13093935C2211yescharacteristic
47C2×#13093935C2211yescharacteristic, complemented
48#15688864C2211yescharacteristic, complemented
49#15688864C2211yescharacteristic, complemented
50#15688864C2211yescharacteristic, complemented
51#15688864C2211yescharacteristic, complemented
52#15688864C2211yescharacteristic, complemented
53#15688864C2211yescharacteristic, complemented
54#15688864C2211yescharacteristic, complemented
55#15688864C2211yescharacteristic, complemented
56#15688862C2211yescharacteristic
57#15688862C2211yescharacteristic
58#15688862C2211yescharacteristic
59#15688862C2211yescharacteristic
60#15688862C2211yescharacteristic
61#15688862C2211yescharacteristic
62#15688862C2211yescharacteristic
63#15688862C2211yescharacteristic
64C4×#41×C47C2211yescharacteristic
65C47×#446—21no—
66C47×#435—21no—
67C47×#435—21no—
68C8×D4×C47—21no—
69C47×#432C2211yescharacteristic
70C47×#432C2211yescharacteristic, complemented
71C47×#432C2211yescharacteristic, complemented
72C4×M16×C47C2211yescharacteristic, complemented
73C2×#97×C47C2211yescharacteristic
74C2×#97×C47C2211yescharacteristic, complemented
75C22×Dic94C2×C411yescharacteristic
76C22×D188C2×C411yescharacteristic
77C2×#10625329—21no—
78C22×C47⋊C8—21no—
79C22×C47⋊C8—21no—
80#13094024C2×C411yescharacteristic
81#13094024C2×C411yescharacteristic
82#13094022—21no—
83#13094020—21no—
84#13094019—21no—
85#13094019—21no—
86#13094019—21no—
87#13094019—21no—
88#13094018—21no—
89#13094018—21no—
90#13094018—21no—
91#13094018—21no—
92#13094016C2311yescharacteristic
93#13094016C2311yescharacteristic
94#13094013—21no—
95#13094012—21no—
96#13094012—21no—
97#13094012C2×C411yescharacteristic
98#13094012C2×C411yescharacteristic
99#13094012C2311yescharacteristic
100#13094012C2311yescharacteristic
101#13094011—21no—
102#13094010—21no—
103#13094010—21no—
104#13094010—21no—
105#13094010—21no—
106#13094007—21no—
107#13094007—21no—
108#13094007—21no—
109#13094007—21no—
110#13094006—21no—
111#13094006—21no—
112#13094006—21no—
113#13094006—21no—
114#13094005—21no—
115#13094005—21no—
116#13094003—21no—
117#13094003—21no—
118#13094003C2×C411yescharacteristic
119#13094003C2×C411yescharacteristic
120#13094003C2×C411yescharacteristic
121#13094003C2×C411yescharacteristic
122#13094002—21no—
123#13094002—21no—
124#13094002—21no—
125#13094002—21no—
126#13093998C2×C411yescharacteristic
127#13093998C2×C411yescharacteristic
128#13093998C2×C411yescharacteristic
129#13093998C2×C411yescharacteristic
130#13093992—21no—
131#13093992—21no—
132C4×Dic94—21no—
133C4×Dic94—21no—
134C4×Dic94C2×C411yescharacteristic
135C4×Dic94C2×C411yescharacteristic
136C4×Dic94C2×C411yescharacteristic
137C4×Dic94C2×C411yescharacteristic
138#13093989—21no—
139#13093989—21no—
140C4×D188C2×C411yescharacteristic
141C4×D188C2×C411yescharacteristic
142C4×D188C2×C411yescharacteristic
143C4×D188C2×C411yescharacteristic
144#13093986—21no—
145#13093986—21no—
146C4×C22⋊D47—21no—
147C4×C22⋊D47—21no—
148C4×C22⋊D47—21no—
149C4×C22⋊D47—21no—
150#13093983C2×C411yescharacteristic
151#13093983C2×C411yescharacteristic
152#13093981—21no—
153#13093981—21no—
154#13093981—21no—
155#13093981—21no—
156#13093980—21no—
157#13093980—21no—
158C2×(C2×D47)⋊C4—21no—
159C2×(C2×D47)⋊C4—21no—
160C22⋊C4×D47—21no—
161C22⋊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×C47C2×C411yescharacteristic
176C2×M16×C47—21no—
177C22×C8×C47—21no—
178C22×C8×C47—21no—
179C4×Q8×C47D411yescharacteristic
180C4×Q8×C47D411yescharacteristic
181C4×D4×C47D411yescharacteristic
182C4×D4×C47D411yescharacteristic
183C4×D4×C47D411yescharacteristic
184C4×D4×C47D411yescharacteristic
185C4×D4×C47D411yescharacteristic
186C4×D4×C47D411yescharacteristic
187#117×C47C2×C411yescharacteristic
188#117×C47C2×C411yescharacteristic
189#117×C47C2×C411yescharacteristic
190C2×C42×C47C2311yescharacteristic
191C2×C42×C47C2311yescharacteristic
192C2×C42×C47C2311yescharacteristic
193C4⋊C8×C47—21no—
194C4⋊C8×C47—21no—
195C4⋊C8×C47—21no—
196C22⋊C8×C47—21no—
197C22⋊C8×C47—21no—
198C22⋊C8×C47—21no—
199#97×C47—21no—
200#97×C47—21no—
201#97×C47C2311yescharacteristic
202#97×C47C2311yescharacteristic
203#97×C47C2311yescharacteristic
204#97×C47C2311yescharacteristic
205C4×C8×C47—21no—
206C23×D47—21no—
207#41×C47—42no—
208C2×Q8×C47C22⋊C411yescharacteristic
209C2×D4×C47C22⋊C411yescharacteristic
210C2×D4×C47C22⋊C411yescharacteristic
211C2×D4×C47C22⋊C411yescharacteristic
212C22×C4×C47C22×C411yescharacteristic
213C22×C4×C47C22×C411yescharacteristic
214C22×C4×C47C22×C411yescharacteristic
215C22×C4×C47C2×D411yescharacteristic
216C22×C4×C47C2×D411yescharacteristic
217C22×C4×C47C2×D411yescharacteristic
218C22×C4×C47C2×D411yescharacteristic
219C22×C4×C47C2×D411yescharacteristic
220C22×C4×C47C2×D411yescharacteristic
221C2×C22⋊D47—21no—
222C2×C22⋊D47—21no—
223C2×C22⋊D47—21no—
224C2×C22⋊D47—21no—
225C22×Dic47—21no—
226C2×D188—21no—
227C2×D188—42no—
228C2×D188C22×C411yescharacteristic
229C2×D188C22×C411yescharacteristic
230C2×C4×D47—21no—
231C2×C4×D47—21no—
232C2×C4×D47—21no—
233C2×C4×D47—21no—
234C2×Dic94—21no—
235C2×Dic94—21no—
236C2×Dic94—21no—
237C2×Dic94—42no—
238C2×Dic94C22×C411yescharacteristic
239C2×Dic94C22×C411yescharacteristic
240M16×C47—42no—
241C2×C8×C47—21no—
242C2×C8×C47—21no—
243C2×C8×C47—21no—
244C2×C8×C47—21no—
245C2×C8×C47—42no—
246C2×C8×C47—42no—
247C4⋊C4×C47C22⋊C411yescharacteristic
248C4⋊C4×C47C22⋊C411yescharacteristic
249C4⋊C4×C47C22⋊C411yescharacteristic
250C4⋊C4×C47C22⋊C411yescharacteristic
251C4⋊C4×C47C22⋊C411yescharacteristic
252C4⋊C4×C47C22⋊C411yescharacteristic
253C22⋊C4×C47C22⋊C411yescharacteristic
254C22⋊C4×C47C22⋊C411yescharacteristic
255C22⋊C4×C47C22⋊C411yescharacteristic
256C22⋊C4×C47C22⋊C411yescharacteristic
257C22⋊C4×C47C22⋊C411yescharacteristic
258C22⋊C4×C47C22⋊C411yescharacteristic
259C42×C47C22×C411yescharacteristic
260C42×C47C22×C411yescharacteristic
261C42×C47C22×C411yescharacteristic
262C42×C47C2×D411yescharacteristic
263C42×C47C2×D411yescharacteristic
264C42×C47C2×D411yescharacteristic
265C42×C47C2×D411yescharacteristic
266C42×C47C2×D411yescharacteristic
267C42×C47C2×D411yescharacteristic
268C42×C47C2411yescharacteristic
269C22⋊Dic47—21no—
270C22⋊Dic47—21no—
271C22⋊Dic47—21no—
272C22⋊Dic47—21no—
273C22⋊Dic47—21no—
274C22⋊Dic47—21no—
275(C2×D47)⋊C4—21no—
276(C2×D47)⋊C4—21no—
277(C2×D47)⋊C4—21no—
278(C2×D47)⋊C4—21no—
279(C2×D47)⋊C4—21no—
280(C2×D47)⋊C4—21no—
281(C2×D47)⋊C4—21no—
282(C2×D47)⋊C4—21no—
283(C2×D47)⋊C4—21no—
284(C2×D47)⋊C4—21no—
285(C2×D47)⋊C4—21no—
286(C2×D47)⋊C4—21no—
287(C2×D47)⋊C4—21no—
288(C2×D47)⋊C4—21no—
289(C2×D47)⋊C4—21no—
290(C2×D47)⋊C4—21no—
291C4⋊Dic47—21no—
292C4⋊Dic47—21no—
293C4⋊Dic47C22×C411yescharacteristic
294C4⋊Dic47C22×C411yescharacteristic
295C4⋊Dic47C22×C411yescharacteristic
296C4⋊Dic47C22×C411yescharacteristic
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—
308Dic47⋊C4—21no—
309C4×Dic47—21no—
310C4×Dic47—21no—
311C4×Dic47—21no—
312C4×Dic47—21no—
313C4×Dic47—21no—
314C4×Dic47—21no—
315#10625329—42no—
316C2×C47⋊C8—21no—
317C2×C47⋊C8—21no—
318C2×C47⋊C8—21no—
319C2×C47⋊C8—21no—
320C2×C47⋊C8—42no—
321C2×C47⋊C8—42no—
322C23×C47C2×C22⋊C411yescharacteristic
323C23×C47C2×C22⋊C411yescharacteristic
324C23×C47C2×C22⋊C411yescharacteristic
325C22×D47—21no—
326C22×D47—21no—
327C22×D47—42no—
328C22×D47—81no—
329C22×D47—81no—
330Q8×C47—41no—
331D4×C47—22no—
332D4×C47—22no—
333D4×C47—41no—
334C2×C4×C47—22no—
335C2×C4×C47—41no—
336C2×C4×C47—41no—
337C2×C4×C47—41no—
338C2×C4×C47—41no—
339C2×C4×C47—41no—
340C2×C4×C47—41no—
341C2×C4×C47—41no—
342C2×C4×C47—41no—
343C2×C4×C47C2×C22⋊C411yescharacteristic
344C2×C4×C47C2×C22⋊C411yescharacteristic
345C2×C4×C47C2×C22⋊C411yescharacteristic
346C2×C4×C47C2×C22⋊C411yescharacteristic
347C2×C4×C47C2×C22⋊C411yescharacteristic
348C2×C4×C47C2×C22⋊C411yescharacteristic
349C2×C4×C47C2×C22⋊C411yescharacteristic
350C2×C4×C47C2×C22⋊C411yescharacteristic
351C2×C4×C47C2×C22⋊C411yescharacteristic
352C2×C4×C47C23×C411yescharacteristic
353C2×C4×C47C22×D411yescharacteristic
354C2×C4×C47C22×D411yescharacteristic
355C22⋊D47—81no—
356C22⋊D47—81no—
357C22⋊D47—81no—
358C22⋊D47—81no—
359C2×Dic47—21no—
360C2×Dic47—21no—
361C2×Dic47—21no—
362C2×Dic47—21no—
363C2×Dic47—21no—
364C2×Dic47—21no—
365C2×Dic47—42no—
366D188—41no—
367D188—41no—
368D188—42no—
369C4×D47—81no—
370C4×D47—81no—
371C4×D47—81no—
372C4×D47—81no—
373Dic94—42no—
374Dic94—41no—
375Dic94—41no—
376Dic94—81no—
377Dic94—81no—
378C8×C47—22no—
379C8×C47—41no—
380C8×C47—41no—
381C8×C47—41no—
382C47⋊C8—22no—
383C47⋊C8—41no—
384C47⋊C8—41no—
385C47⋊C8—41no—
386#17686—471nomaximal, Sylow
387C22×C47—21no—
388C22×C47—21no—
389C22×C47—21no—
390C22×C47—21no—
391C22×C47—21no—
392C22×C47—21no—
393C22×C47—21no—
394C22×C47—21no—
395C22×C47#41312yes—
396C22×C47C22×C22⋊C411yescharacteristic
397C2×D47—41no—
398C2×D47—41no—
399C2×D47—41no—
400C2×D47—41no—
401C2×D47—41no—
402C2×D47—41no—
403C2×D47—162no—
404C4×C47—21no—
405C4×C47—21no—
406C4×C47—21no—
407C4×C47—21no—
408C4×C47—21no—
409C4×C47—21no—
410C4×C47—21no—
411C4×C47—21no—
412C4×C47—21no—
413C4×C47—21no—
414C4×C47—21no—
415C4×C47—21no—
416Dic47—41no—
417Dic47—41no—
418Dic47—41no—
419Dic47—41no—
420Dic47—41no—
421Dic47—41no—
422#3510—471no—
423#2970—471no—
424#2970D4711yescharacteristic, complemented
425#1535—471no—
426#1535—471no—
427#1533—471no—
428#1532—471no—
429#1532—471no—
430#1531—471no—
431#1531—471no—
432#1529—471no—
433#1529—471no—
434#1524—471no—
435#1524—471no—
436C2×#329—471no—
437C2×C47—22no—
438C2×C47—41no—
439C2×C47—41no—
440C2×C47C2×#41311yescharacteristic
441C2×C47#290111yescharacteristic
442C2×C47#290111yescharacteristic
443D47—81no—
444D47—81no—
445#559—941no—
446#559—941no—
447#556—941no—
448#556—941no—
449#551—941no—
450#551—941no—
451#551—941no—
452#551—941no—
453#542—471no—
454#542—471no—
455#542—471no—
456#542—471no—
457#536—471no—
458#535—471no—
459#533—471no—
460#529—471no—
461#529—471no—
462#529—471no—
463#529—471no—
464C2×#124—471no—
465#519—471no—
466#518—471no—
467C4×#41C2×D4711yescharacteristic
468#446—21no—
469#446—941no—
470#435—21no—
471#435—21no—
472#435—941no—
473#435—941no—
474C8×D4—21no—
475C8×D4—941no—
476#432—471no—
477#432—471no—
478#432—471no—
479#432C2×D4711yescharacteristic
480#432C2×D4711yescharacteristic, complemented
481#432C2×D4711yescharacteristic, complemented
482C4×M16—471no—
483C4×M16C2×D4711yescharacteristic, complemented
484C2×#97—471no—
485C2×#97—471no—
486C2×#97C2×D4711yescharacteristic
487C2×#97C2×D4711yescharacteristic, complemented
488#330—471no—
489#330—471no—
490#330—471no—
491#330—471no—
492#330—471no—
493#330—471no—
494#330—471no—
495#330—471no—
496#329—471no—
497#329—471no—
498#329—471no—
499#329—471no—
500#329—471no—
501#329—471no—
502#329—471no—
503#329—471no—
504C47#1768611yescharacteristic, complemented, Sylow
505C2×#41C4×D4711yescharacteristic
506C22×Q8—471no—
507C22×D4—471no—
508C2×M16—21no—
509C2×M16—941no—
510C22×C8—21no—
511C22×C8—21no—
512C22×C8—941no—
513C22×C8—941no—
514C4⋊Q8—471no—
515C4⋊Q8—471no—
516C4⋊Q8—941no—
517#127—941no—
518#126—941no—
519#126—941no—
520#126—941no—
521#126—941no—
522#126—941no—
523#126—941no—
524#126—941no—
525#126—941no—
526#125—471no—
527#125—471no—
528#124—471no—
529#124—471no—
530#124—471no—
531#124—471no—
532#124—941no—
533#124—941no—
534#124—941no—
535#124—941no—
536#124—941no—
537#124—941no—
538#124—941no—
539#124—941no—
540#123—941no—
541#123—941no—
542#123—941no—
543#123—941no—
544#123—941no—
545#123—941no—
546#123—941no—
547#123—941no—
548#123—941no—
549#123—941no—
550C22⋊Q8—471no—
551C22⋊Q8—471no—
552C22⋊Q8—471no—
553C22⋊Q8—471no—
554C22⋊Q8—941no—
555C22⋊Q8—941no—
556C22⋊Q8—941no—
557C22⋊Q8—941no—
558C22⋊Q8—941no—
559C22⋊Q8—941no—
560#121—471no—
561#121—471no—
562#121—471no—
563#121—471no—
564#120—941no—
565#120—941no—
566C4×Q8—471no—
567C4×Q8—471no—
568C4×Q8—471no—
569C4×Q8—471no—
570C4×Q8—941no—
571C4×Q8—941no—
572C4×Q8—941no—
573C4×Q8—941no—
574C4×Q8D18811yescharacteristic
575C4×Q8C22⋊D4711yescharacteristic
576C4×D4—471no—
577C4×D4—471no—
578C4×D4—471no—
579C4×D4—471no—
580C4×D4—941no—
581C4×D4—941no—
582C4×D4—941no—
583C4×D4—941no—
584C4×D4—941no—
585C4×D4—941no—
586C4×D4D18811yescharacteristic
587C4×D4D18811yescharacteristic
588C4×D4D18811yescharacteristic
589C4×D4C22⋊D4711yescharacteristic
590C4×D4C22⋊D4711yescharacteristic
591C4×D4C22⋊D4711yescharacteristic
592#117—471no—
593#117—471no—
594#117—941no—
595#117—941no—
596#117—941no—
597#117—941no—
598#117—941no—
599#117—941no—
600#117C4×D4711yescharacteristic
601#117C4×D4711yescharacteristic
602#117C4×D4711yescharacteristic
603C2×C22⋊C4—941no—
604C2×C22⋊C4—941no—
605C2×C22⋊C4—941no—
606C2×C22⋊C4—941no—
607C2×C42C22×D4711yescharacteristic
608C2×C42C22×D4711yescharacteristic
609C2×C42C22×D4711yescharacteristic
610C4⋊C8—21no—
611C4⋊C8—21no—
612C4⋊C8—21no—
613C4⋊C8—941no—
614C4⋊C8—941no—
615C4⋊C8—941no—
616C22⋊C8—21no—
617C22⋊C8—21no—
618C22⋊C8—21no—
619C22⋊C8—941no—
620C22⋊C8—941no—
621C22⋊C8—941no—
622#97—21no—
623#97—21no—
624#97—471no—
625#97—471no—
626#97—471no—
627#97—471no—
628#97—941no—
629#97—941no—
630#97C22×D4711yescharacteristic
631#97C22×D4711yescharacteristic
632#97C22×D4711yescharacteristic
633#97C22×D4711yescharacteristic
634C4×C8—21no—
635C4×C8—941no—
636C24—941no—
637#41—42no—
638C2×Q8—471no—
639C2×Q8—471no—
640C2×Q8—941no—
641C2×Q8—941no—
642C2×Q8—941no—
643C2×Q8—1882no—
644C2×Q8(C2×D47)⋊C411yescharacteristic
645C2×D4—471no—
646C2×D4—471no—
647C2×D4—941no—
648C2×D4—941no—
649C2×D4—941no—
650C2×D4—941no—
651C2×D4—941no—
652C2×D4—1882no—
653C2×D4(C2×D47)⋊C411yescharacteristic
654C2×D4(C2×D47)⋊C411yescharacteristic
655C2×D4(C2×D47)⋊C411yescharacteristic
656C22×C4—941no—
657C22×C4—941no—
658C22×C4—941no—
659C22×C4—941no—
660C22×C4—941no—
661C22×C4C2×C4×D4711yescharacteristic
662C22×C4C2×C4×D4711yescharacteristic
663C22×C4C2×C4×D4711yescharacteristic
664C22×C4C2×D18811yescharacteristic
665C22×C4C2×D18811yescharacteristic
666C22×C4C2×D18811yescharacteristic
667C22×C4C2×C22⋊D4711yescharacteristic
668C22×C4C2×C22⋊D4711yescharacteristic
669C22×C4C2×C22⋊D4711yescharacteristic
670M16—42no—
671M16—1882no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—42no—
677C2×C8—42no—
678C2×C8—941no—
679C2×C8—941no—
680C2×C8—941no—
681C2×C8—941no—
682C2×C8—1882no—
683C2×C8—1882no—
684C4⋊C4—471no—
685C4⋊C4—471no—
686C4⋊C4—471no—
687C4⋊C4—471no—
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—941no—
699C4⋊C4—941no—
700C4⋊C4—941no—
701C4⋊C4—941no—
702C4⋊C4(C2×D47)⋊C411yescharacteristic
703C4⋊C4(C2×D47)⋊C411yescharacteristic
704C4⋊C4(C2×D47)⋊C411yescharacteristic
705C4⋊C4(C2×D47)⋊C411yescharacteristic
706C4⋊C4(C2×D47)⋊C411yescharacteristic
707C4⋊C4(C2×D47)⋊C411yescharacteristic
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—941no—
718C22⋊C4—941no—
719C22⋊C4—941no—
720C22⋊C4—941no—
721C22⋊C4—941no—
722C22⋊C4—941no—
723C22⋊C4—941no—
724C22⋊C4—941no—
725C22⋊C4—941no—
726C22⋊C4—941no—
727C22⋊C4—941no—
728C22⋊C4—941no—
729C22⋊C4—941no—
730C22⋊C4(C2×D47)⋊C411yescharacteristic
731C22⋊C4(C2×D47)⋊C411yescharacteristic
732C22⋊C4(C2×D47)⋊C411yescharacteristic
733C22⋊C4(C2×D47)⋊C411yescharacteristic
734C22⋊C4(C2×D47)⋊C411yescharacteristic
735C22⋊C4(C2×D47)⋊C411yescharacteristic
736C42—941no—
737C42—941no—
738C42—941no—
739C42—941no—
740C42—941no—
741C42—941no—
742C42C2×C4×D4711yescharacteristic
743C42C2×C4×D4711yescharacteristic
744C42C2×C4×D4711yescharacteristic
745C42C2×D18811yescharacteristic
746C42C2×D18811yescharacteristic
747C42C2×D18811yescharacteristic
748C42C2×C22⋊D4711yescharacteristic
749C42C2×C22⋊D4711yescharacteristic
750C42C2×C22⋊D4711yescharacteristic
751C42C23×D4711yescharacteristic
752C23—941no—
753C23—941no—
754C23—3761no—
755C23—3761no—
756C23—1882no—
757C23C2×(C2×D47)⋊C411yescharacteristic
758C23C2×(C2×D47)⋊C411yescharacteristic
759C23C2×(C2×D47)⋊C411yescharacteristic
760Q8—41no—
761Q8—3761no—
762Q8—3761no—
763Q8—1881no—
764Q8—1881no—
765Q8—1882no—
766D4—22no—
767D4—22no—
768D4—41no—
769D4—3761no—
770D4—3761no—
771D4—3761no—
772D4—3761no—
773D4—1881no—
774D4—1881no—
775D4—1882no—
776C2×C4—22no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—941no—
786C2×C4—941no—
787C2×C4—941no—
788C2×C4—941no—
789C2×C4—941no—
790C2×C4—941no—
791C2×C4—3761no—
792C2×C4—3761no—
793C2×C4—3761no—
794C2×C4—3761no—
795C2×C4—1882no—
796C2×C4C2×(C2×D47)⋊C411yescharacteristic
797C2×C4C2×(C2×D47)⋊C411yescharacteristic
798C2×C4C2×(C2×D47)⋊C411yescharacteristic
799C2×C4C2×(C2×D47)⋊C411yescharacteristic
800C2×C4C2×(C2×D47)⋊C411yescharacteristic
801C2×C4C2×(C2×D47)⋊C411yescharacteristic
802C2×C4C2×(C2×D47)⋊C411yescharacteristic
803C2×C4C2×(C2×D47)⋊C411yescharacteristic
804C2×C4C2×(C2×D47)⋊C411yescharacteristic
805C2×C4C22×C4×D4711yescharacteristic
806C2×C4C22×C22⋊D4711yescharacteristic
807C2×C4C22×D18811yescharacteristic
808C8—22no—
809C8—41no—
810C8—41no—
811C8—41no—
812C8—942no—
813C8—1881no—
814C8—1881no—
815C8—1881no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—1881no—
825C22—1881no—
826C22—1881no—
827C22—1881no—
828C22—1881no—
829C22—1881no—
830C22—7522no—
831C22#1568910512yes—
832C22C22×(C2×D47)⋊C411yescharacteristic
833C4—21no—
834C4—21no—
835C4—21no—
836C4—21no—
837C4—21no—
838C4—21no—
839C4—21no—
840C4—21no—
841C4—21no—
842C4—21no—
843C4—21no—
844C4—21no—
845C4—1881no—
846C4—1881no—
847C4—1881no—
848C4—1881no—
849C4—1881no—
850C4—1881no—
851C2—22no—
852C2—41no—
853C2—41no—
854C2—3761no—
855C2—3761no—
856C2C2×#1568910511yescharacteristic
857C2#2025193311yescharacteristic
858C2#2025193611yescharacteristic
subgroupG/H
centerC22C22×(C2×D47)⋊C4
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#2970C2
socleC22×C47C22×C22⋊C4
prime radical#15689687C4
cosocleC42×C47C24
hypercenter#2970D47
hypocenterC47#17686
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2970

Complements

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

NH ≅ G/Ntype
2. #20252402C2semidirect
3. #20242020C2semidirect
4. #20242017C2semidirect
5. #20242011C2semidirect
6. #20242009C2semidirect
7. #20242006C2semidirect
8. #20242004C2semidirect
9. #20242002C2semidirect
10. #20241996C2semidirect
11. #20241993C2semidirect
12. #20241977C2semidirect
13. #20241974C2semidirect
14. C2×#15688862C2semidirect
15. C47×#2970C2semidirect
43. #15689180C22semidirect
44. #15689180C22semidirect
45. C4×#10625329C22semidirect
47. C2×#13093935C22semidirect
48. #15688864C22semidirect
49. #15688864C22semidirect
50. #15688864C22semidirect
51. #15688864C22semidirect
52. #15688864C22semidirect
53. #15688864C22semidirect
54. #15688864C22semidirect
55. #15688864C22semidirect
70. C47×#432C22semidirect
71. C47×#432C22semidirect
72. C4×M16×C47C22semidirect
74. C2×#97×C47C22semidirect
424. #2970D47semidirect
480. #432C2×D47semidirect
481. #432C2×D47semidirect
483. C4×M16C2×D47semidirect
487. C2×#97C2×D47semidirect
504. C47#17686semidirect

Maximal subgroups

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

subgroupindex
#202572842
#202524022
#202420202
#202420172
#202420112
#202420092
#202420062
#202420042
#202420022
#202419962
#202419932
#202419772
#202419742
C2×#156888622
C47×#29702
#1768647