Finite Group Databasebeta

← #27088458

Subgroups — #27088458

Order 12032.

1780 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256684C211yesmaximal, characteristic
2C2×#15689680C211yesmaximal, characteristic, complemented
3#20254630C214yesmaximal, complemented
4#20254620C212yesmaximal, complemented
5#20254611C212yesmaximal, complemented
6#20254604C212yesmaximal, complemented
7#20254596C212yesmaximal, complemented
8#20254588C212yesmaximal, complemented
9#20254580C212yesmaximal, complemented
10#20253912C212yesmaximal, complemented
11#20253734C212yesmaximal, complemented
12#20253303C214yesmaximal, complemented
13#20253178C214yesmaximal, complemented
14C2×C47×#432C211yesmaximal, characteristic, complemented
15#15689680—21no—
16#15689680—21no—
17#15689680—21no—
18#15689680—21no—
19#15689680C2211yescharacteristic
20#15689680C2211yescharacteristic
21#15689680C2212yes—
22#15689680C2212yes—
23#15689680C2212yes—
24#15689680C2212yes—
25#15689680C2211yescharacteristic
26#15689673C2211yescharacteristic
27#15689673C2211yescharacteristic
28#15689673C2211yescharacteristic
29C2×#13094024C2211yescharacteristic
30C2×#13094024C2211yescharacteristic
31#15689657—21no—
32#15689657—21no—
33#15689657—21no—
34#15689657—21no—
35#15689657C2212yes—
36#15689657C2212yes—
37C2×#13094016C2212yes—
38#15689634—21no—
39#15689634—21no—
40#15689634C2212yes—
41C2×#13094003—21no—
42C2×#13094003—21no—
43C4×#10625350—21no—
44C4×#10625350—21no—
45C4×#10625350C2212yes—
46C2×C4×Dic94—21no—
47C2×C4×Dic94—21no—
48C2×#13093983C2212yes—
49#15689532C2214yescomplemented
50#15689532C2214yescomplemented
51#15689532C2214yescomplemented
52#15689532C2214yescomplemented
53#15689492C2214yescomplemented
54#15689488C2214yescomplemented
55#15689483C2214yescomplemented
56#15689483C2214yescomplemented
57#15689465C2218yes—
58#15689459C2214yes—
59#15689454C2214yes—
60#15689448C2218yes—
61#15689442C2214yes—
62#15689437C2214yes—
63#15689431C2218yescomplemented
64#15689424C2218yescomplemented
65#15689419C2214yescomplemented
66#15689414C2214yescomplemented
67#15689409C2214yescomplemented
68#15689404C2214yescomplemented
69#15689161C2218yes—
70#15689120C2218yes—
71C22×C42×C47C2211yescharacteristic
72C47×#432C2212yes—
73C47×#432C2212yes—
74C47×#432C2212yes—
75C47×#432C2212yes—
76C2×C4⋊C8×C47C2212yes—
77C2×C22⋊C8×C47C2212yes—
78C2×#97×C47C2212yes—
79C2×#10625350—21no—
80C2×#10625350—21no—
81C2×#10625350C2312yes—
82C22×Dic94—21no—
83C22×Dic94—21no—
84#13094024—21no—
85#13094024—21no—
86#13094024—21no—
87#13094024—21no—
88#13094024C2311yescharacteristic
89#13094024C2312yes—
90#13094024C2312yes—
91#13094024C2311yescharacteristic
92#13094024C2311yescharacteristic
93#13094024C2312yes—
94#13094024C2312yes—
95#13094021C2311yescharacteristic
96#13094018—22no—
97#13094018—22no—
98#13094016—22no—
99#13094016—22no—
100#13094016—21no—
101#13094016—21no—
102#13094016C2314yes—
103#13094016C2312yes—
104#13094016C2314yes—
105#13094012—21no—
106#13094012—21no—
107#13094012C2312yes—
108#13094007—22no—
109#13094007—22no—
110#13094007—22no—
111#13094003—22no—
112#13094003—22no—
113#13094003—22no—
114#13094003—22no—
115#13094003—22no—
116#13094003—22no—
117#13094003—22no—
118#13094003—22no—
119#13094003—21no—
120#13094003—21no—
121#13094003—21no—
122#13094003—21no—
123#13094003C2312yes—
124#13094003C2312yes—
125#13093998—21no—
126#13093998—21no—
127#13093998—21no—
128#13093998—21no—
129#13093998C2312yes—
130#13093998C2312yes—
131#13093993—22no—
132C4×Dic94—22no—
133C4×Dic94—22no—
134C4×Dic94—22no—
135C4×Dic94—22no—
136C4×Dic94—22no—
137C4×Dic94—22no—
138C4×Dic94—22no—
139C4×Dic94—22no—
140C4×Dic94—21no—
141C4×Dic94—21no—
142C4×Dic94—21no—
143C4×Dic94—21no—
144C4×Dic94C2312yes—
145C4×Dic94C2312yes—
146C4×D188—21no—
147C4×D188—21no—
148C4×D188—21no—
149C4×D188—21no—
150C4×D188C2312yes—
151C4×D188C2312yes—
152C4×C22⋊D47—22no—
153C4×C22⋊D47—22no—
154C4×C22⋊D47—22no—
155C4×C22⋊D47—22no—
156C4×C22⋊D47—22no—
157C4×C22⋊D47—22no—
158#13093983—22no—
159#13093983—22no—
160#13093983—21no—
161#13093983—21no—
162#13093983C2314yes—
163#13093983C2314yes—
164#13093983C2312yes—
165#13093981—22no—
166#13093981—22no—
167#13093981—22no—
168C2×C4⋊Dic47—21no—
169C2×C4⋊Dic47—21no—
170C2×C4⋊Dic47C2312yes—
171C2×C4⋊Dic47C2312yes—
172C2×Dic47⋊C4—22no—
173C2×Dic47⋊C4—22no—
174C2×C22⋊Dic47—22no—
175C2×C4×Dic47—22no—
176C42×D47—22no—
177#13093958C2318yes—
178#13093958C2318yes—
179#13093956C2318yes—
180#13093956C2318yes—
181#13093949C2318yes—
182#13093949C2318yes—
183#13093946C2318yes—
184#13093946C2318yes—
185C23×C4×C47D411yescharacteristic
186C23×C4×C47D411yescharacteristic
187C23×C4×C47C2311yescharacteristic
188C22×C8×C47C2314yes—
189C2×C42×C47D411yescharacteristic
190C2×C42×C47D411yescharacteristic
191C2×C42×C47D411yescharacteristic
192C2×C42×C47D411yescharacteristic
193C2×C42×C47D411yescharacteristic
194C2×C42×C47D411yescharacteristic
195C2×C42×C47C2311yescharacteristic
196C2×C42×C47C2311yescharacteristic
197C2×C42×C47C2311yescharacteristic
198C2×C42×C47C2311yescharacteristic
199C2×C42×C47C2311yescharacteristic
200C2×C42×C47C2311yescharacteristic
201C4⋊C8×C47C2314yes—
202C4⋊C8×C47C2314yes—
203C22⋊C8×C47C2314yes—
204C22⋊C8×C47C2314yes—
205#97×C47C2314yes—
206#97×C47C2314yes—
207C24×C47C2×D411yescharacteristic
208C22×C4×C47—24no—
209C22×C4×C47—42no—
210C22×C4×C47—42no—
211C22×C4×C47C2×D411yescharacteristic
212C22×C4×C47C2×D411yescharacteristic
213C22×C4×C47C2×D411yescharacteristic
214C22×C4×C47C2×D411yescharacteristic
215C22×C4×C47C2×D411yescharacteristic
216C22×C4×C47C2×D411yescharacteristic
217C22×C4×C47C2×D411yescharacteristic
218C22×C4×C47C2×D411yescharacteristic
219C22×C4×C47C2×D411yescharacteristic
220C22×C4×C47C2×D411yescharacteristic
221C22×C4×C47C2×D411yescharacteristic
222C22×C4×C47C2×D411yescharacteristic
223C22×C4×C47C2×D411yescharacteristic
224C22×C4×C47C2×D411yescharacteristic
225C22×C4×C47C2×D411yescharacteristic
226C22×C4×C47C2411yescharacteristic
227C22×C4×C47C2411yescharacteristic
228C22×C4×C47C2411yescharacteristic
229C2×C22⋊D47—22no—
230C2×C22⋊D47—22no—
231C2×C22⋊D47—22no—
232C22×Dic47—22no—
233C22×Dic47—22no—
234#10625350—28no—
235#10625350—44no—
236#10625350—44no—
237C2×D188—21no—
238C2×D188—21no—
239C2×D188C2412yes—
240C2×C4×D47—22no—
241C2×C4×D47—22no—
242C2×C4×D47—22no—
243C2×Dic94—21no—
244C2×Dic94—21no—
245C2×Dic94—22no—
246C2×Dic94—22no—
247C2×Dic94—22no—
248C2×Dic94—22no—
249C2×Dic94—44no—
250C2×Dic94—44no—
251C2×Dic94C2412yes—
252C2×C8×C47—28no—
253C2×C8×C47C2418yes—
254C42×C47C2×D411yescharacteristic
255C42×C47C2×D411yescharacteristic
256C42×C47C2×D411yescharacteristic
257C42×C47C2×D411yescharacteristic
258C42×C47C2×D411yescharacteristic
259C42×C47C2×D411yescharacteristic
260C42×C47C2×D411yescharacteristic
261C42×C47C2×D411yescharacteristic
262C42×C47C2×D411yescharacteristic
263C42×C47C2×D411yescharacteristic
264C42×C47C2×D411yescharacteristic
265C42×C47C2×D411yescharacteristic
266C42×C47C2411yescharacteristic
267C42×C47C2411yescharacteristic
268C42×C47C2411yescharacteristic
269C42×C47C2411yescharacteristic
270C22⋊Dic47—24no—
271C22⋊Dic47—24no—
272C22⋊Dic47—22no—
273C22⋊Dic47—22no—
274C22⋊Dic47—22no—
275(C2×D47)⋊C4—22no—
276(C2×D47)⋊C4—22no—
277(C2×D47)⋊C4—22no—
278(C2×D47)⋊C4—22no—
279(C2×D47)⋊C4—22no—
280(C2×D47)⋊C4—22no—
281C4⋊Dic47—22no—
282C4⋊Dic47—22no—
283C4⋊Dic47—22no—
284C4⋊Dic47—22no—
285C4⋊Dic47—22no—
286C4⋊Dic47—22no—
287C4⋊Dic47—21no—
288C4⋊Dic47—21no—
289C4⋊Dic47—21no—
290C4⋊Dic47—21no—
291C4⋊Dic47C2414yes—
292C4⋊Dic47C2414yes—
293C4⋊Dic47C2412yes—
294C4⋊Dic47C2412yes—
295Dic47⋊C4—24no—
296Dic47⋊C4—24no—
297Dic47⋊C4—24no—
298Dic47⋊C4—24no—
299Dic47⋊C4—22no—
300Dic47⋊C4—22no—
301Dic47⋊C4—22no—
302Dic47⋊C4—22no—
303Dic47⋊C4—22no—
304Dic47⋊C4—22no—
305C4×Dic47—22no—
306C4×Dic47—22no—
307C4×Dic47—22no—
308C4×Dic47—24no—
309C4×Dic47—24no—
310C23×C47—22no—
311C23×C47—22no—
312C23×C47—41no—
313C23×C47C22×D411yescharacteristic
314C23×C47C22×D411yescharacteristic
315C23×C47C22×D411yescharacteristic
316C22×D47—22no—
317C2×C4×C47—22no—
318C2×C4×C47—22no—
319C2×C4×C47—22no—
320C2×C4×C47—22no—
321C2×C4×C47—22no—
322C2×C4×C47—22no—
323C2×C4×C47—22no—
324C2×C4×C47—22no—
325C2×C4×C47—22no—
326C2×C4×C47—22no—
327C2×C4×C47—41no—
328C2×C4×C47—41no—
329C2×C4×C47—41no—
330C2×C4×C47—41no—
331C2×C4×C47—41no—
332C2×C4×C47—41no—
333C2×C4×C47—41no—
334C2×C4×C47C22×D411yescharacteristic
335C2×C4×C47C22×D411yescharacteristic
336C2×C4×C47C22×D411yescharacteristic
337C2×C4×C47C22×D411yescharacteristic
338C2×C4×C47C22×D411yescharacteristic
339C2×C4×C47C22×D411yescharacteristic
340C2×C4×C47C22×D411yescharacteristic
341C2×C4×C47C22×D411yescharacteristic
342C2×C4×C47C22×D411yescharacteristic
343C2×C4×C47C22×D411yescharacteristic
344C2×C4×C47C22×D411yescharacteristic
345C2×C4×C472−1+414yes—
346C2×C4×C47C2511yescharacteristic
347C22⋊D47—44no—
348C22⋊D47—44no—
349C22⋊D47—44no—
350C2×Dic47—24no—
351C2×Dic47—24no—
352C2×Dic47—22no—
353C2×Dic47—22no—
354C2×Dic47—22no—
355C2×Dic47—44no—
356C2×Dic47—44no—
357D188—24no—
358D188—42no—
359D188—42no—
360C4×D47—44no—
361C4×D47—44no—
362C4×D47—44no—
363Dic94—24no—
364Dic94—44no—
365Dic94—44no—
366Dic94—44no—
367Dic94—42no—
368Dic94—42no—
369Dic94—44no—
370C8×C47—28no—
371#60854—471nomaximal, Sylow
372C22×C47—21no—
373C22×C47—21no—
374C22×C47—21no—
375C22×C47—21no—
376C22×C47—21no—
377C22×C47—21no—
378C22×C47—21no—
379C22×C47—44no—
380C22×C47#53612yes—
381C22×C47#57512yes—
382C22×C47C23×D411yescharacteristic
383C2×D47—42no—
384C2×D47—42no—
385C2×D47—42no—
386C4×C47—21no—
387C4×C47—21no—
388C4×C47—21no—
389C4×C47—21no—
390C4×C47—21no—
391C4×C47—21no—
392C4×C47—21no—
393C4×C47—21no—
394C4×C47—21no—
395C4×C47#53612yes—
396C4×C47#57512yes—
397C4×C47C2×2−1+412yes—
398Dic47—42no—
399Dic47—44no—
400Dic47—44no—
401Dic47—42no—
402Dic47—42no—
403#3444—471no—
404C2×#533—471no—
405#3240—474no—
406#3239—472no—
407#3238—472no—
408#3237—472no—
409#3236—472no—
410#3235—472no—
411#3234—472no—
412#3162—472no—
413#3135—472no—
414#3091—474no—
415#3076—474no—
416C2×#432D4711yescharacteristic, complemented
417C2×C47—22no—
418C2×C47—22no—
419C2×C47—41no—
420C2×C47C2×#53611yescharacteristic
421C2×C47C2×#57511yescharacteristic
422C2×C47C2×#57511yescharacteristic
423D47—82no—
424#533—472no—
425#533—472no—
426#533—471no—
427#533—472no—
428#533—472no—
429#533—471no—
430#533—471no—
431#533—941no—
432#533—941no—
433#533—941no—
434#533—941no—
435#532—471no—
436#532—471no—
437#532—471no—
438C2×C4⋊Q8—471no—
439C2×C4⋊Q8—471no—
440#529—472no—
441#529—472no—
442#529—941no—
443#529—941no—
444#529—941no—
445#529—941no—
446C2×#125—472no—
447#525—472no—
448#525—941no—
449#525—941no—
450C2×C22⋊Q8—941no—
451C2×C22⋊Q8—941no—
452C4×#41—472no—
453C4×#41—941no—
454C4×#41—941no—
455C2×C4×Q8—941no—
456C2×C4×Q8—941no—
457C2×#117—472no—
458C22×C42C2×D4711yescharacteristic
459#501—474no—
460#501—474no—
461#501—474no—
462#501—474no—
463#491—474no—
464#490—474no—
465#489—474no—
466#489—474no—
467#485—478no—
468#484—474no—
469#483—474no—
470#482—478no—
471#481—474no—
472#480—474no—
473#479—478no—
474#478—478no—
475#477—474no—
476#476—474no—
477#475—474no—
478#474—474no—
479#432C2×D4712yes—
480#432C2×D4712yes—
481#432C2×D4712yes—
482#432C2×D4712yes—
483#427—478no—
484C2×C4⋊C8C2×D4712yes—
485#416—478no—
486C2×C22⋊C8C2×D4712yes—
487C2×#97C2×D4712yes—
488C47#6085411yescharacteristic, complemented, Sylow
489C2×#41—472no—
490C2×#41—941no—
491C2×#41—941no—
492C22×Q8—941no—
493C22×Q8—941no—
494C23×C4D18811yescharacteristic
495C23×C4D18811yescharacteristic
496C23×C4C22×D4711yescharacteristic
497C22×C8C22×D4714yes—
498C4⋊Q8—472no—
499C4⋊Q8—472no—
500C4⋊Q8—472no—
501C4⋊Q8—472no—
502C4⋊Q8—471no—
503C4⋊Q8—471no—
504C4⋊Q8—471no—
505C4⋊Q8—941no—
506C4⋊Q8—941no—
507C4⋊Q8—941no—
508C4⋊Q8—941no—
509#127—471no—
510#126—942no—
511#126—942no—
512#125—474no—
513#125—474no—
514#125—472no—
515#125—942no—
516#125—942no—
517#125—941no—
518#125—941no—
519#124—472no—
520#124—941no—
521#124—941no—
522#123—942no—
523#123—942no—
524#123—942no—
525C22⋊Q8—472no—
526C22⋊Q8—472no—
527C22⋊Q8—942no—
528C22⋊Q8—942no—
529C22⋊Q8—942no—
530C22⋊Q8—942no—
531C22⋊Q8—942no—
532C22⋊Q8—942no—
533C22⋊Q8—942no—
534C22⋊Q8—942no—
535C22⋊Q8—941no—
536C22⋊Q8—941no—
537C22⋊Q8—941no—
538C22⋊Q8—941no—
539#121—472no—
540#121—472no—
541#121—941no—
542#121—941no—
543#121—941no—
544#121—941no—
545#120—942no—
546C4×Q8—472no—
547C4×Q8—472no—
548C4×Q8—942no—
549C4×Q8—942no—
550C4×Q8—942no—
551C4×Q8—942no—
552C4×Q8—942no—
553C4×Q8—942no—
554C4×Q8—942no—
555C4×Q8—942no—
556C4×Q8—941no—
557C4×Q8—941no—
558C4×Q8—941no—
559C4×Q8—941no—
560C4×D4—472no—
561C4×D4—472no—
562C4×D4—942no—
563C4×D4—942no—
564C4×D4—942no—
565C4×D4—942no—
566C4×D4—942no—
567C4×D4—942no—
568C4×D4—941no—
569C4×D4—941no—
570C4×D4—941no—
571C4×D4—941no—
572#117—474no—
573#117—474no—
574#117—472no—
575#117—942no—
576#117—942no—
577#117—941no—
578#117—941no—
579#117—942no—
580#117—942no—
581#117—942no—
582C2×C4⋊C4—472no—
583C2×C4⋊C4—472no—
584C2×C4⋊C4—942no—
585C2×C4⋊C4—942no—
586C2×C4⋊C4—941no—
587C2×C4⋊C4—941no—
588C2×C22⋊C4—942no—
589C2×C42—942no—
590C2×C42—942no—
591C2×C42D18811yescharacteristic
592C2×C42D18811yescharacteristic
593C2×C42D18811yescharacteristic
594C2×C42D18811yescharacteristic
595C2×C42D18811yescharacteristic
596C2×C42D18811yescharacteristic
597C2×C42C22×D4711yescharacteristic
598C2×C42C22×D4711yescharacteristic
599C2×C42C22×D4711yescharacteristic
600C2×C42C22×D4711yescharacteristic
601C2×C42C22×D4711yescharacteristic
602C2×C42C22×D4711yescharacteristic
603#107—478no—
604#107—478no—
605#106—478no—
606#106—478no—
607C4⋊C8C22×D4714yes—
608C4⋊C8C22×D4714yes—
609#103—478no—
610#103—478no—
611#102—478no—
612#102—478no—
613C22⋊C8C22×D4714yes—
614C22⋊C8C22×D4714yes—
615#97C22×D4714yes—
616#97C22×D4714yes—
617C24C2×D18811yescharacteristic
618#41—948no—
619#41—1884no—
620#41—1884no—
621C2×Q8—472no—
622C2×Q8—941no—
623C2×Q8—941no—
624C2×Q8—942no—
625C2×Q8—942no—
626C2×Q8—942no—
627C2×Q8—942no—
628C2×Q8—1884no—
629C2×Q8—1884no—
630C2×D4—472no—
631C2×D4—942no—
632C2×D4—942no—
633C2×D4—942no—
634C2×D4—941no—
635C2×D4—941no—
636C22×C4—24no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—942no—
640C22×C4—942no—
641C22×C4—942no—
642C22×C4—942no—
643C22×C4—942no—
644C22×C4C2×D18811yescharacteristic
645C22×C4C2×D18811yescharacteristic
646C22×C4C2×D18811yescharacteristic
647C22×C4C2×D18811yescharacteristic
648C22×C4C2×D18811yescharacteristic
649C22×C4C2×D18811yescharacteristic
650C22×C4C2×D18811yescharacteristic
651C22×C4C2×D18811yescharacteristic
652C22×C4C2×D18811yescharacteristic
653C22×C4C2×D18811yescharacteristic
654C22×C4C2×D18811yescharacteristic
655C22×C4C2×D18811yescharacteristic
656C22×C4C2×D18811yescharacteristic
657C22×C4C2×D18811yescharacteristic
658C22×C4C2×D18811yescharacteristic
659C22×C4C23×D4711yescharacteristic
660C22×C4C23×D4711yescharacteristic
661C22×C4C23×D4711yescharacteristic
662C2×C8—28no—
663C2×C8C23×D4718yes—
664C4⋊C4—474no—
665C4⋊C4—474no—
666C4⋊C4—472no—
667C4⋊C4—472no—
668C4⋊C4—944no—
669C4⋊C4—944no—
670C4⋊C4—944no—
671C4⋊C4—944no—
672C4⋊C4—942no—
673C4⋊C4—942no—
674C4⋊C4—942no—
675C4⋊C4—942no—
676C4⋊C4—942no—
677C4⋊C4—942no—
678C4⋊C4—942no—
679C4⋊C4—942no—
680C4⋊C4—942no—
681C4⋊C4—942no—
682C4⋊C4—942no—
683C4⋊C4—942no—
684C4⋊C4—941no—
685C4⋊C4—941no—
686C4⋊C4—941no—
687C4⋊C4—941no—
688C22⋊C4—944no—
689C22⋊C4—944no—
690C22⋊C4—942no—
691C22⋊C4—942no—
692C22⋊C4—942no—
693C22⋊C4—942no—
694C22⋊C4—942no—
695C22⋊C4—942no—
696C22⋊C4—942no—
697C22⋊C4—942no—
698C22⋊C4—942no—
699C42—944no—
700C42—942no—
701C42—942no—
702C42—942no—
703C42—944no—
704C42C2×D18811yescharacteristic
705C42C2×D18811yescharacteristic
706C42C2×D18811yescharacteristic
707C42C2×D18811yescharacteristic
708C42C2×D18811yescharacteristic
709C42C2×D18811yescharacteristic
710C42C2×D18811yescharacteristic
711C42C2×D18811yescharacteristic
712C42C2×D18811yescharacteristic
713C42C2×D18811yescharacteristic
714C42C2×D18811yescharacteristic
715C42C2×D18811yescharacteristic
716C42C23×D4711yescharacteristic
717C42C23×D4711yescharacteristic
718C42C23×D4711yescharacteristic
719C42C23×D4711yescharacteristic
720C23—22no—
721C23—22no—
722C23—41no—
723C23—942no—
724C23C22×D18811yescharacteristic
725C23C22×D18811yescharacteristic
726C23C22×D18811yescharacteristic
727Q8—944no—
728Q8—1884no—
729Q8—1884no—
730Q8—1884no—
731Q8—1882no—
732Q8—1882no—
733Q8—1884no—
734D4—944no—
735D4—1882no—
736D4—1882no—
737D4—1884no—
738D4—1884no—
739D4—1884no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—942no—
758C2×C4—942no—
759C2×C4—942no—
760C2×C4—944no—
761C2×C4—944no—
762C2×C4—1884no—
763C2×C4—1884no—
764C2×C4—1884no—
765C2×C4—1884no—
766C2×C4—1884no—
767C2×C4C22×D18811yescharacteristic
768C2×C4C22×D18811yescharacteristic
769C2×C4C22×D18811yescharacteristic
770C2×C4C22×D18811yescharacteristic
771C2×C4C22×D18811yescharacteristic
772C2×C4C22×D18811yescharacteristic
773C2×C4C22×D18811yescharacteristic
774C2×C4C22×D18811yescharacteristic
775C2×C4C22×D18811yescharacteristic
776C2×C4C22×D18811yescharacteristic
777C2×C4C22×D18811yescharacteristic
778C2×C4#1309407114yes—
779C2×C4C24×D4711yescharacteristic
780C8—28no—
781C22—21no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—21no—
787C22—21no—
788C22—44no—
789C22—1882no—
790C22—1882no—
791C22—1882no—
792C22#1568969912yes—
793C22#1568992312yes—
794C22C23×D18811yescharacteristic
795C4—21no—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—21no—
800C4—21no—
801C4—21no—
802C4—21no—
803C4—21no—
804C4—1882no—
805C4—1882no—
806C4—1884no—
807C4—1884no—
808C4—1882no—
809C4#1568969912yes—
810C4#1568992312yes—
811C4C2×#1309407112yes—
812C2—22no—
813C2—22no—
814C2—41no—
815C2—3762no—
816C2C2×#1568969911yescharacteristic
817C2C2×#1568992311yescharacteristic
818C2C2×#1568992311yescharacteristic
subgroupG/H
centerC2×C4C22×D188
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#432C2
socleC22×C47C23×D4
prime radical#20256684C2
hypercenterC2×#432D47
hypocenterC47#60854
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C2×#432

Complements

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

NH ≅ G/Ntype
2. C2×#15689680C2semidirect
3. #20254630C2semidirect
4. #20254620C2semidirect
5. #20254611C2semidirect
6. #20254604C2semidirect
7. #20254596C2semidirect
8. #20254588C2semidirect
9. #20254580C2semidirect
10. #20253912C2semidirect
11. #20253734C2semidirect
12. #20253303C2semidirect
13. #20253178C2semidirect
14. C2×C47×#432C2semidirect
49. #15689532C22semidirect
50. #15689532C22semidirect
51. #15689532C22semidirect
52. #15689532C22semidirect
53. #15689492C22semidirect
54. #15689488C22semidirect
55. #15689483C22semidirect
56. #15689483C22semidirect
63. #15689431C22semidirect
64. #15689424C22semidirect
65. #15689419C22semidirect
66. #15689414C22semidirect
67. #15689409C22semidirect
68. #15689404C22semidirect
416. C2×#432D47semidirect
488. C47#60854semidirect

Maximal subgroups

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

subgroupindex
#202566842
C2×#156896802
#202546302
#202546202
#202546112
#202546042
#202545962
#202545882
#202545802
#202539122
#202537342
#202533032
#202531782
C2×C47×#4322
#6085447