Finite Group Databasebeta

← #26184427

Subgroups — #26184427

Order 12032.

942 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257349C211yesmaximal, characteristic
2#20252039C211yesmaximal, characteristic, complemented
3#20242022C211yesmaximal, characteristic, complemented
4#20242020C211yesmaximal, characteristic, complemented
5#20242017C211yesmaximal, characteristic, complemented
6#20242011C211yesmaximal, characteristic, complemented
7#20242009C211yesmaximal, characteristic, complemented
8#20242006C211yesmaximal, characteristic, complemented
9#20241998C211yesmaximal, characteristic, complemented
10#20241993C211yesmaximal, characteristic, complemented
11#20241987C211yesmaximal, characteristic, complemented
12#20241985C211yesmaximal, characteristic, complemented
13#20241974C211yesmaximal, characteristic, complemented
14C2×#15688862C211yesmaximal, characteristic, complemented
15C47×#2970C211yesmaximal, characteristic, complemented
16#15689858C411yescharacteristic
17#15689846C411yescharacteristic
18#15689836—21no—
19#15689797—21no—
20#15689797—21no—
21D4×Dic94C411yescharacteristic
22#15689782C411yescharacteristic
23#15689782C411yescharacteristic
24#15689769C411yescharacteristic
25#15689769C411yescharacteristic
26#15689761—21no—
27D4×D188C411yescharacteristic
28#15689745—21no—
29#15689706—21no—
30#15689706—21no—
31#15689673C2211yescharacteristic
32#15689657C2211yescharacteristic
33#15689657C2211yescharacteristic
34#15689657C2211yescharacteristic
35C2×#13094012C2211yescharacteristic
36C2×#13094012C2211yescharacteristic
37#15689595—21no—
38#15689184—21no—
39#15689184—21no—
40#15689180C2211yescharacteristic, complemented
41#15689180C2211yescharacteristic, complemented
42#15689180C2211yescharacteristic, complemented
43#15689180C2211yescharacteristic, complemented
44#15689150—21no—
45#15689090—21no—
46C4×#10625329C2211yescharacteristic, complemented
47C2×#13093935C2211yescharacteristic, complemented
48#15688864C2211yescharacteristic, complemented
49#15688864C2211yescharacteristic, complemented
50#15688864C2211yescharacteristic, complemented
51#15688864C2211yescharacteristic, complemented
52#15688862C2211yescharacteristic
53#15688862C2211yescharacteristic
54#15688862C2211yescharacteristic
55#15688862C2211yescharacteristic
56#15688862C2211yescharacteristic, complemented
57#15688862C2211yescharacteristic, complemented
58#15688862C2211yescharacteristic, complemented
59#15688862C2211yescharacteristic, complemented
60#15688862C2211yescharacteristic, complemented
61#15688862C2211yescharacteristic, complemented
62#15688862C2211yescharacteristic, complemented
63#15688862C2211yescharacteristic, complemented
64C4×#41×C47C2211yescharacteristic
65C47×#446—21no—
66C47×#435—21no—
67C47×#435—21no—
68C8×D4×C47—21no—
69C47×#432C2211yescharacteristic, complemented
70C47×#432C2211yescharacteristic, complemented
71C47×#432C2211yescharacteristic, complemented
72C4×M16×C47C2211yescharacteristic, complemented
73C2×#97×C47C2211yescharacteristic, complemented
74C2×#97×C47C2211yescharacteristic, complemented
75C2×#10625350C2×C411yescharacteristic
76C2×#10625350C2×C411yescharacteristic
77C22×Dic94C2×C411yescharacteristic
78C22×Dic94C2×C411yescharacteristic
79C22×D188C2×C411yescharacteristic
80C22×D188C2×C411yescharacteristic
81C2×D4×D47—21no—
82C2×#10625329—21no—
83C22×C47⋊C8—21no—
84#13094024C2×C411yescharacteristic
85#13094023—21no—
86#13094021C2×C411yescharacteristic
87#13094019—21no—
88#13094019—21no—
89#13094018—21no—
90#13094018—21no—
91#13094018—21no—
92#13094016C2311yescharacteristic
93#13094013—21no—
94#13094012—21no—
95#13094012—21no—
96#13094012—21no—
97#13094012—21no—
98#13094012C2×C411yescharacteristic
99#13094012C2×C411yescharacteristic
100#13094012C2×C411yescharacteristic
101#13094012C2×C411yescharacteristic
102#13094012C2311yescharacteristic
103#13094012C2311yescharacteristic
104#13094012C2311yescharacteristic
105#13094010—21no—
106#13094010—21no—
107#13094009—21no—
108#13094009—21no—
109#13094009—21no—
110#13094009—21no—
111#13094007—21no—
112#13094007—21no—
113#13094007—21no—
114#13094003C2×C411yescharacteristic
115#13094003C2×C411yescharacteristic
116#13094003C2×C411yescharacteristic
117#13094002—21no—
118#13094002—21no—
119#13094001—21no—
120#13094001—21no—
121#13094000—21no—
122#13093999—21no—
123#13093998—21no—
124#13093998—21no—
125#13093998C2×C411yescharacteristic
126#13093998C2×C411yescharacteristic
127#13093998C2×C411yescharacteristic
128#13093997—21no—
129#13093997—21no—
130#13093996—21no—
131#13093996—21no—
132#13093994—21no—
133#13093994—21no—
134#13093992—21no—
135#13093992—21no—
136C4×Dic94C2×C411yescharacteristic
137C4×Dic94C2×C411yescharacteristic
138C4×Dic94C2×C411yescharacteristic
139C4×D188—21no—
140C4×D188—21no—
141C4×D188C2×C411yescharacteristic
142C4×D188C2×C411yescharacteristic
143C4×D188C2×C411yescharacteristic
144D4×Dic47—21no—
145#13093986—21no—
146C4×C22⋊D47—21no—
147C4×C22⋊D47—21no—
148C4×C22⋊D47—21no—
149(C22⋊D47)⋊C4—21no—
150(C22⋊D47)⋊C4—21no—
151#13093982—21no—
152#13093981—21no—
153#13093981—21no—
154#13093981—21no—
155C2×(C2×D47)⋊C4—21no—
156C2×(C2×D47)⋊C4—21no—
157C2×(C2×D47)⋊C4—21no—
158C2×(C2×D47)⋊C4—21no—
159C22⋊C4×D47—21no—
160C22⋊C4×D47—21no—
161C4⋊(C47⋊C8)—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—
168C22⋊(C47⋊C8)—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—
178C22×C8×C47—21no—
179C4×Q8×C47C2×C411yescharacteristic
180C4×Q8×C47D411yescharacteristic
181C4×D4×C47C2×C411yescharacteristic
182C4×D4×C47C2×C411yescharacteristic
183C4×D4×C47C2×C411yescharacteristic
184C4×D4×C47D411yescharacteristic
185C4×D4×C47D411yescharacteristic
186C4×D4×C47D411yescharacteristic
187#117×C47D411yescharacteristic
188#117×C47D411yescharacteristic
189#117×C47D411yescharacteristic
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—
207C23×D47—21no—
208#41×C47—42no—
209C2×Q8×C47C22⋊C411yescharacteristic
210C2×D4×C47C22⋊C411yescharacteristic
211C2×D4×C47C22⋊C411yescharacteristic
212C2×D4×C47C22⋊C411yescharacteristic
213C22×C4×C47C22×C411yescharacteristic
214C22×C4×C47C22×C411yescharacteristic
215C22×C4×C47C22×C411yescharacteristic
216C22×C4×C47C2×D411yescharacteristic
217C22×C4×C47C2×D411yescharacteristic
218C22×C4×C47C2×D411yescharacteristic
219C22×C4×C47C2×D411yescharacteristic
220C22×C4×C47C2×D411yescharacteristic
221C22×C4×C47C2×D411yescharacteristic
222C2×C22⋊D47—21no—
223C2×C22⋊D47—21no—
224C2×C22⋊D47—21no—
225C2×C22⋊D47—21no—
226C2×C22⋊D47—21no—
227C22×Dic47—21no—
228C22×Dic47—21no—
229D4×D47—44no—
230#10625350—81no—
231#10625350—81no—
232C2×D188—21no—
233C2×D188—21no—
234C2×D188—21no—
235C2×D188—21no—
236C2×D188—81no—
237C2×D188—81no—
238C2×D188C22×C411yescharacteristic
239C2×D188C22×C411yescharacteristic
240C2×D188C22×C411yescharacteristic
241C2×C4×D47—21no—
242C2×C4×D47—21no—
243C2×C4×D47—21no—
244C2×C4×D47—21no—
245C2×C4×D47—21no—
246C2×Dic94—21no—
247C2×Dic94—21no—
248C2×Dic94—81no—
249C2×Dic94—81no—
250C2×Dic94C22×C411yescharacteristic
251C2×Dic94C22×C411yescharacteristic
252C2×Dic94C22×C411yescharacteristic
253M16×C47—42no—
254C2×C8×C47—21no—
255C2×C8×C47—21no—
256C2×C8×C47—21no—
257C2×C8×C47—21no—
258C2×C8×C47—42no—
259C2×C8×C47—42no—
260C4⋊C4×C47C22⋊C411yescharacteristic
261C4⋊C4×C47C22⋊C411yescharacteristic
262C4⋊C4×C47C22⋊C411yescharacteristic
263C4⋊C4×C47C22⋊C411yescharacteristic
264C4⋊C4×C47C22⋊C411yescharacteristic
265C4⋊C4×C47C22⋊C411yescharacteristic
266C22⋊C4×C47C22⋊C411yescharacteristic
267C22⋊C4×C47C22⋊C411yescharacteristic
268C22⋊C4×C47C22⋊C411yescharacteristic
269C22⋊C4×C47C22⋊C411yescharacteristic
270C22⋊C4×C47C22⋊C411yescharacteristic
271C22⋊C4×C47C22⋊C411yescharacteristic
272C42×C47C22×C411yescharacteristic
273C42×C47C22×C411yescharacteristic
274C42×C47C22×C411yescharacteristic
275C42×C47C2×D411yescharacteristic
276C42×C47C2×D411yescharacteristic
277C42×C47C2×D411yescharacteristic
278C42×C47C2×D411yescharacteristic
279C42×C47C2×D411yescharacteristic
280C42×C47C2×D411yescharacteristic
281C42×C47C2411yescharacteristic
282C22⋊Dic47—21no—
283C22⋊Dic47—21no—
284C22⋊Dic47—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—
291(C2×D47)⋊C4—21no—
292(C2×D47)⋊C4—21no—
293(C2×D47)⋊C4—21no—
294(C2×D47)⋊C4—21no—
295(C2×D47)⋊C4—21no—
296(C2×D47)⋊C4—21no—
297(C2×D47)⋊C4—21no—
298(C2×D47)⋊C4—21no—
299(C2×D47)⋊C4—21no—
300(C2×D47)⋊C4—21no—
301(C2×D47)⋊C4—21no—
302(C2×D47)⋊C4—21no—
303(C2×D47)⋊C4—21no—
304(C2×D47)⋊C4—21no—
305C4⋊Dic47—21no—
306C4⋊Dic47—21no—
307C4⋊Dic47C22×C411yescharacteristic
308C4⋊Dic47C22×C411yescharacteristic
309Dic47⋊C4—21no—
310Dic47⋊C4—21no—
311Dic47⋊C4—21no—
312Dic47⋊C4—21no—
313Dic47⋊C4—21no—
314Dic47⋊C4—21no—
315Dic47⋊C4—21no—
316Dic47⋊C4—21no—
317C4×Dic47—21no—
318C4×Dic47—21no—
319C4×Dic47—21no—
320#10625329—42no—
321C2×C47⋊C8—21no—
322C2×C47⋊C8—21no—
323C2×C47⋊C8—21no—
324C2×C47⋊C8—21no—
325C2×C47⋊C8—42no—
326C23×C47C2×C22⋊C411yescharacteristic
327C23×C47C2×C22⋊C411yescharacteristic
328C23×C47C2×C22⋊C411yescharacteristic
329C22×D47—21no—
330C22×D47—21no—
331C22×D47—21no—
332C22×D47—42no—
333C22×D47—42no—
334C22×D47—81no—
335C22×D47—81no—
336C22×D47—81no—
337C22×D47—81no—
338Q8×C47—41no—
339D4×C47—22no—
340D4×C47—22no—
341D4×C47—41no—
342C2×C4×C47—22no—
343C2×C4×C47—41no—
344C2×C4×C47—41no—
345C2×C4×C47—41no—
346C2×C4×C47—41no—
347C2×C4×C47—41no—
348C2×C4×C47—41no—
349C2×C4×C47—41no—
350C2×C4×C47—41no—
351C2×C4×C47C2×C22⋊C411yescharacteristic
352C2×C4×C47C2×C22⋊C411yescharacteristic
353C2×C4×C47C2×C22⋊C411yescharacteristic
354C2×C4×C47C2×C22⋊C411yescharacteristic
355C2×C4×C47C2×C22⋊C411yescharacteristic
356C2×C4×C47C2×C22⋊C411yescharacteristic
357C2×C4×C47C2×C22⋊C411yescharacteristic
358C2×C4×C47C2×C22⋊C411yescharacteristic
359C2×C4×C47C2×C22⋊C411yescharacteristic
360C2×C4×C47C23×C411yescharacteristic
361C2×C4×C47C22×D411yescharacteristic
362C2×C4×C47C22×D411yescharacteristic
363C22⋊D47—42no—
364C22⋊D47—42no—
365C22⋊D47—81no—
366C22⋊D47—81no—
367C22⋊D47—81no—
368C2×Dic47—21no—
369C2×Dic47—21no—
370C2×Dic47—21no—
371C2×Dic47—21no—
372C2×Dic47—21no—
373C2×Dic47—81no—
374C2×Dic47—81no—
375D188—41no—
376D188—41no—
377D188—41no—
378D188—42no—
379D188—81no—
380D188—81no—
381D188—81no—
382C4×D47—42no—
383C4×D47—81no—
384C4×D47—81no—
385C4×D47—81no—
386C4×D47—81no—
387Dic94—41no—
388Dic94—41no—
389Dic94—41no—
390Dic94—81no—
391Dic94—81no—
392C8×C47—22no—
393C8×C47—41no—
394C8×C47—41no—
395C8×C47—41no—
396C47⋊C8—41no—
397C47⋊C8—41no—
398C47⋊C8—41no—
399C47⋊C8—41no—
400#17679—471nomaximal, Sylow
401C22×C47—21no—
402C22×C47—21no—
403C22×C47—21no—
404C22×C47—21no—
405C22×C47—21no—
406C22×C47—21no—
407C22×C47—21no—
408C22×C47—21no—
409C22×C47#42112yes—
410C22×C47C22×C22⋊C411yescharacteristic
411C2×D47—41no—
412C2×D47—41no—
413C2×D47—41no—
414C2×D47—41no—
415C2×D47—41no—
416C2×D47—41no—
417C2×D47—41no—
418C2×D47—41no—
419C2×D47—41no—
420C2×D47—162no—
421C2×D47—162no—
422C4×C47—21no—
423C4×C47—21no—
424C4×C47—21no—
425C4×C47—21no—
426C4×C47—21no—
427C4×C47—21no—
428C4×C47—21no—
429C4×C47—21no—
430C4×C47—21no—
431C4×C47—21no—
432C4×C47—21no—
433C4×C47—21no—
434Dic47—41no—
435Dic47—41no—
436Dic47—41no—
437Dic47—41no—
438Dic47—41no—
439#3514—471no—
440#2970D4711yescharacteristic, complemented
441#2923—471no—
442#1536—471no—
443#1535—471no—
444#1535—471no—
445#1533—471no—
446#1532—471no—
447#1532—471no—
448#1530—471no—
449#1529—471no—
450#1527—471no—
451#1527—471no—
452#1524—471no—
453C2×#329—471no—
454C2×C47—22no—
455C2×C47—41no—
456C2×C47—41no—
457C2×C47#288811yescharacteristic
458C2×C47C2×#42111yescharacteristic
459C2×C47#290111yescharacteristic
460D47—81no—
461D47—81no—
462D47—81no—
463#559—471no—
464#556—471no—
465#555—941no—
466#551—941no—
467#551—941no—
468D4×Q8—471no—
469#548—471no—
470#548—471no—
471#546—471no—
472#546—471no—
473#546—941no—
474D42—471no—
475#542—941no—
476#538—941no—
477#538—941no—
478#532—471no—
479#529—471no—
480#529—471no—
481#529—471no—
482C2×#124—471no—
483C2×#124—471no—
484#518—941no—
485C4×#41C2×D4711yescharacteristic
486#446—21no—
487#435—21no—
488#435—21no—
489C8×D4—21no—
490#433—941no—
491#433—941no—
492#432—471no—
493#432—471no—
494#432—471no—
495#432—471no—
496#432C2×D4711yescharacteristic, complemented
497#432C2×D4711yescharacteristic, complemented
498#432C2×D4711yescharacteristic, complemented
499#424—941no—
500#408—941no—
501C4×M16—471no—
502C4×M16C2×D4711yescharacteristic, complemented
503C2×#97—471no—
504C2×#97C2×D4711yescharacteristic, complemented
505C2×#97C2×D4711yescharacteristic, complemented
506#330—471no—
507#330—471no—
508#330—471no—
509#330—471no—
510#329—471no—
511#329—471no—
512#329—471no—
513#329—471no—
514#329—471no—
515#329—471no—
516#329—471no—
517#329—471no—
518#329—471no—
519#329—471no—
520#329—471no—
521#329—471no—
522C47#1767911yescharacteristic, complemented, Sylow
523C2×#41—471no—
524C2×#41—471no—
525C2×#41D18811yescharacteristic
526C22×Q8—471no—
527C22×Q8—471no—
528C22×D4—471no—
529C22×D4—471no—
530C22×D4—941no—
531C2×M16—21no—
532C2×M16—941no—
533C22×C8—21no—
534C22×C8—21no—
535C22×C8—941no—
536C4⋊Q8—471no—
537C4⋊Q8—941no—
538#127—471no—
539#126—941no—
540#126—941no—
541#126—941no—
542#126—941no—
543#126—941no—
544#125—471no—
545#124—471no—
546#124—471no—
547#124—471no—
548#124—471no—
549#124—471no—
550#124—471no—
551#124—471no—
552#124—941no—
553#124—941no—
554#124—941no—
555#124—941no—
556#124—941no—
557#124—941no—
558#124—941no—
559#123—941no—
560#123—941no—
561#123—941no—
562#123—941no—
563#123—941no—
564#123—941no—
565#123—941no—
566C22⋊Q8—471no—
567C22⋊Q8—471no—
568C22⋊Q8—471no—
569C22⋊Q8—941no—
570C22⋊Q8—941no—
571C22⋊Q8—941no—
572C22⋊Q8—941no—
573C22⋊Q8—941no—
574#121—471no—
575#121—471no—
576#121—471no—
577#121—941no—
578#121—941no—
579#121—941no—
580#121—941no—
581#121—941no—
582#121—941no—
583#121—941no—
584#120—941no—
585#120—941no—
586#120—941no—
587#120—941no—
588C4×Q8—471no—
589C4×Q8—471no—
590C4×Q8—471no—
591C4×Q8C4×D4711yescharacteristic
592C4×Q8C22⋊D4711yescharacteristic
593C4×D4—471no—
594C4×D4—471no—
595C4×D4—471no—
596C4×D4—941no—
597C4×D4—941no—
598C4×D4—941no—
599C4×D4—941no—
600C4×D4—941no—
601C4×D4—941no—
602C4×D4—941no—
603C4×D4—941no—
604C4×D4—941no—
605C4×D4C4×D4711yescharacteristic
606C4×D4C4×D4711yescharacteristic
607C4×D4C4×D4711yescharacteristic
608C4×D4C22⋊D4711yescharacteristic
609C4×D4C22⋊D4711yescharacteristic
610C4×D4C22⋊D4711yescharacteristic
611#117—941no—
612#117—941no—
613#117—941no—
614#117—941no—
615#117D18811yescharacteristic
616#117D18811yescharacteristic
617#117D18811yescharacteristic
618C2×C22⋊C4—941no—
619C2×C22⋊C4—941no—
620C2×C22⋊C4—941no—
621C2×C22⋊C4—941no—
622C2×C22⋊C4—941no—
623C2×C22⋊C4—941no—
624C2×C42C22×D4711yescharacteristic
625C2×C42C22×D4711yescharacteristic
626C2×C42C22×D4711yescharacteristic
627C4⋊C8—21no—
628C4⋊C8—21no—
629C4⋊C8—21no—
630C4⋊C8—941no—
631C4⋊C8—941no—
632C4⋊C8—941no—
633C4⋊C8—941no—
634C22⋊C8—21no—
635C22⋊C8—21no—
636C22⋊C8—21no—
637C22⋊C8—941no—
638C22⋊C8—941no—
639C22⋊C8—941no—
640C22⋊C8—941no—
641#97—21no—
642#97—21no—
643#97—471no—
644#97—471no—
645#97—471no—
646#97—471no—
647#97—941no—
648#97C22×D4711yescharacteristic
649#97C22×D4711yescharacteristic
650#97C22×D4711yescharacteristic
651#97C22×D4711yescharacteristic
652C4×C8—21no—
653C4×C8—941no—
654C24—941no—
655C24—941no—
656#41—42no—
657#41—3761no—
658#41—3761no—
659C2×Q8—471no—
660C2×Q8—471no—
661C2×Q8—471no—
662C2×Q8—941no—
663C2×Q8—941no—
664C2×Q8—3761no—
665C2×Q8—3761no—
666C2×Q8(C2×D47)⋊C411yescharacteristic
667C2×D4—471no—
668C2×D4—471no—
669C2×D4—471no—
670C2×D4—941no—
671C2×D4—941no—
672C2×D4—941no—
673C2×D4—941no—
674C2×D4—941no—
675C2×D4—941no—
676C2×D4—941no—
677C2×D4—941no—
678C2×D4—941no—
679C2×D4—3761no—
680C2×D4—3761no—
681C2×D4—1884no—
682C2×D4(C2×D47)⋊C411yescharacteristic
683C2×D4(C2×D47)⋊C411yescharacteristic
684C2×D4(C2×D47)⋊C411yescharacteristic
685C22×C4—941no—
686C22×C4—941no—
687C22×C4—941no—
688C22×C4—941no—
689C22×C4—941no—
690C22×C4—941no—
691C22×C4—941no—
692C22×C4C2×C4×D4711yescharacteristic
693C22×C4C2×C4×D4711yescharacteristic
694C22×C4C2×C4×D4711yescharacteristic
695C22×C4C2×D18811yescharacteristic
696C22×C4C2×D18811yescharacteristic
697C22×C4C2×D18811yescharacteristic
698C22×C4C2×C22⋊D4711yescharacteristic
699C22×C4C2×C22⋊D4711yescharacteristic
700C22×C4C2×C22⋊D4711yescharacteristic
701M16—42no—
702M16—1882no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—42no—
708C2×C8—42no—
709C2×C8—941no—
710C2×C8—941no—
711C2×C8—941no—
712C2×C8—941no—
713C2×C8—1882no—
714C4⋊C4—471no—
715C4⋊C4—471no—
716C4⋊C4—941no—
717C4⋊C4—941no—
718C4⋊C4—941no—
719C4⋊C4—941no—
720C4⋊C4—941no—
721C4⋊C4—941no—
722C4⋊C4—941no—
723C4⋊C4—941no—
724C4⋊C4—941no—
725C4⋊C4—941no—
726C4⋊C4(C2×D47)⋊C411yescharacteristic
727C4⋊C4(C2×D47)⋊C411yescharacteristic
728C4⋊C4(C2×D47)⋊C411yescharacteristic
729C4⋊C4(C2×D47)⋊C411yescharacteristic
730C4⋊C4(C2×D47)⋊C411yescharacteristic
731C4⋊C4(C2×D47)⋊C411yescharacteristic
732C22⋊C4—941no—
733C22⋊C4—941no—
734C22⋊C4—941no—
735C22⋊C4—941no—
736C22⋊C4—941no—
737C22⋊C4—941no—
738C22⋊C4—941no—
739C22⋊C4—941no—
740C22⋊C4—941no—
741C22⋊C4—941no—
742C22⋊C4—941no—
743C22⋊C4—941no—
744C22⋊C4—941no—
745C22⋊C4—941no—
746C22⋊C4—941no—
747C22⋊C4—941no—
748C22⋊C4—941no—
749C22⋊C4—941no—
750C22⋊C4—941no—
751C22⋊C4—941no—
752C22⋊C4—941no—
753C22⋊C4—941no—
754C22⋊C4—941no—
755C22⋊C4(C2×D47)⋊C411yescharacteristic
756C22⋊C4(C2×D47)⋊C411yescharacteristic
757C22⋊C4(C2×D47)⋊C411yescharacteristic
758C22⋊C4(C2×D47)⋊C411yescharacteristic
759C22⋊C4(C2×D47)⋊C411yescharacteristic
760C22⋊C4(C2×D47)⋊C411yescharacteristic
761C42—941no—
762C42—941no—
763C42—941no—
764C42C2×C4×D4711yescharacteristic
765C42C2×C4×D4711yescharacteristic
766C42C2×C4×D4711yescharacteristic
767C42C2×D18811yescharacteristic
768C42C2×D18811yescharacteristic
769C42C2×D18811yescharacteristic
770C42C2×C22⋊D4711yescharacteristic
771C42C2×C22⋊D4711yescharacteristic
772C42C2×C22⋊D4711yescharacteristic
773C42C23×D4711yescharacteristic
774C23—941no—
775C23—941no—
776C23—941no—
777C23—3761no—
778C23—3761no—
779C23—3761no—
780C23—3761no—
781C23—1882no—
782C23—1882no—
783C23C2×(C2×D47)⋊C411yescharacteristic
784C23C2×(C2×D47)⋊C411yescharacteristic
785C23C2×(C2×D47)⋊C411yescharacteristic
786Q8—41no—
787Q8—3761no—
788Q8—3761no—
789Q8—1881no—
790Q8—1881no—
791Q8—1881no—
792D4—22no—
793D4—22no—
794D4—41no—
795D4—3761no—
796D4—3761no—
797D4—3761no—
798D4—3761no—
799D4—3761no—
800D4—3761no—
801D4—1881no—
802D4—1881no—
803D4—1881no—
804D4—1882no—
805D4—1882no—
806D4—1882no—
807C2×C4—22no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—941no—
817C2×C4—941no—
818C2×C4—941no—
819C2×C4—941no—
820C2×C4—941no—
821C2×C4—3761no—
822C2×C4—3761no—
823C2×C4—3761no—
824C2×C4—3761no—
825C2×C4—3761no—
826C2×C4—3761no—
827C2×C4—1882no—
828C2×C4C2×(C2×D47)⋊C411yescharacteristic
829C2×C4C2×(C2×D47)⋊C411yescharacteristic
830C2×C4C2×(C2×D47)⋊C411yescharacteristic
831C2×C4C2×(C2×D47)⋊C411yescharacteristic
832C2×C4C2×(C2×D47)⋊C411yescharacteristic
833C2×C4C2×(C2×D47)⋊C411yescharacteristic
834C2×C4C2×(C2×D47)⋊C411yescharacteristic
835C2×C4C2×(C2×D47)⋊C411yescharacteristic
836C2×C4C2×(C2×D47)⋊C411yescharacteristic
837C2×C4C22×C4×D4711yescharacteristic
838C2×C4C22×C22⋊D4711yescharacteristic
839C2×C4C22×D18811yescharacteristic
840C8—22no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—1881no—
845C8—1881no—
846C8—1881no—
847C8—1881no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—1881no—
857C22—1881no—
858C22—1881no—
859C22—1881no—
860C22—1881no—
861C22—1881no—
862C22—1881no—
863C22—1881no—
864C22—1881no—
865C22—7522no—
866C22—7522no—
867C22#1568913912yes—
868C22C22×(C2×D47)⋊C411yescharacteristic
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—21no—
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—21no—
880C4—21no—
881C4—1881no—
882C4—1881no—
883C4—1881no—
884C4—1881no—
885C4—1881no—
886C2—22no—
887C2—41no—
888C2—41no—
889C2—3761no—
890C2—3761no—
891C2—3761no—
892C2#2025186611yescharacteristic
893C2C2×#1568913911yescharacteristic
894C2#2025193611yescharacteristic
subgroupG/H
centerC22C22×(C2×D47)⋊C4
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#2970C2
socleC22×C47C22×C22⋊C4
prime radical#20257349C2
cosocleC42×C47C24
hypercenter#2970D47
hypocenterC47#17679
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. #20252039C2semidirect
3. #20242022C2semidirect
4. #20242020C2semidirect
5. #20242017C2semidirect
6. #20242011C2semidirect
7. #20242009C2semidirect
8. #20242006C2semidirect
9. #20241998C2semidirect
10. #20241993C2semidirect
11. #20241987C2semidirect
12. #20241985C2semidirect
13. #20241974C2semidirect
14. C2×#15688862C2semidirect
15. C47×#2970C2semidirect
40. #15689180C22semidirect
41. #15689180C22semidirect
42. #15689180C22semidirect
43. #15689180C22semidirect
46. C4×#10625329C22semidirect
47. C2×#13093935C22semidirect
48. #15688864C22semidirect
49. #15688864C22semidirect
50. #15688864C22semidirect
51. #15688864C22semidirect
56. #15688862C22semidirect
57. #15688862C22semidirect
58. #15688862C22semidirect
59. #15688862C22semidirect
60. #15688862C22semidirect
61. #15688862C22semidirect
62. #15688862C22semidirect
63. #15688862C22semidirect
69. C47×#432C22semidirect
70. C47×#432C22semidirect
71. C47×#432C22semidirect
72. C4×M16×C47C22semidirect
73. C2×#97×C47C22semidirect
74. C2×#97×C47C22semidirect
440. #2970D47semidirect
496. #432C2×D47semidirect
497. #432C2×D47semidirect
498. #432C2×D47semidirect
502. C4×M16C2×D47semidirect
504. C2×#97C2×D47semidirect
505. C2×#97C2×D47semidirect
522. C47#17679semidirect

Maximal subgroups

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

subgroupindex
#202573492
#202520392
#202420222
#202420202
#202420172
#202420112
#202420092
#202420062
#202419982
#202419932
#202419872
#202419852
#202419742
C2×#156888622
C47×#29702
#1767947