Finite Group Databasebeta

← #27087600

Subgroups — #27087600

Order 12032.

2188 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256684C211yesmaximal, characteristic, complemented
2C2×#15689673C211yesmaximal, characteristic, complemented
3#20254427C214yesmaximal, complemented
4#20254417C212yesmaximal, complemented
5#20254408C212yesmaximal, complemented
6#20254401C212yesmaximal, complemented
7#20254393C212yesmaximal, complemented
8#20254385C212yesmaximal, complemented
9#20254377C212yesmaximal, complemented
10#20253834C212yesmaximal, complemented
11#20253734C212yesmaximal, complemented
12#20252845C214yesmaximal, complemented
13#20252610C214yesmaximal, complemented
14C2×C47×#432C211yesmaximal, characteristic, complemented
15C22×#10625350C2212yes—
16C2×#13094046C2218yescomplemented
17#15689680C2211yescharacteristic
18#15689680C2211yescharacteristic, complemented
19#15689680C2211yescharacteristic, complemented
20#15689673—21no—
21#15689673—21no—
22#15689673—21no—
23#15689673—21no—
24#15689673C2212yes—
25#15689673C2212yes—
26#15689673C2212yes—
27#15689673C2212yes—
28#15689673C2211yescharacteristic
29#15689673C2211yescharacteristic, complemented
30#15689673C2211yescharacteristic, complemented
31C2×#13094024C2211yescharacteristic
32C2×#13094021C2211yescharacteristic
33#15689657—21no—
34#15689657—21no—
35#15689657—21no—
36#15689657—21no—
37#15689657C2212yes—
38#15689657C2212yescomplemented
39C2×#13094012C2212yes—
40#15689634—21no—
41#15689634—21no—
42#15689634C2212yes—
43C2×#13093998—21no—
44C2×#13093998—21no—
45C4×#10625350—21no—
46C4×#10625350—21no—
47C4×#10625350C2212yescomplemented
48C2×C4×D188—21no—
49C2×C4×D188—21no—
50#15689517C2214yescomplemented
51#15689517C2214yescomplemented
52#15689512C2214yescomplemented
53#15689512C2214yescomplemented
54#15689492C2214yescomplemented
55#15689488C2214yescomplemented
56#15689483C2214yescomplemented
57#15689483C2214yescomplemented
58#15689346C2218yescomplemented
59#15689339C2218yescomplemented
60#15689334C2214yescomplemented
61#15689329C2214yescomplemented
62#15689324C2214yescomplemented
63#15689319C2214yescomplemented
64#15689287C2218yescomplemented
65#15689281C2214yes—
66#15689276C2214yes—
67#15689270C2218yescomplemented
68#15689264C2214yes—
69#15689259C2214yes—
70#15689120C2218yescomplemented
71C22×C42×C47C2211yescharacteristic
72C47×#432C2212yes—
73C47×#432C2212yes—
74C47×#432C2212yescomplemented
75C47×#432C2212yescomplemented
76C2×C4⋊C8×C47C2212yescomplemented
77C2×C22⋊C8×C47C2212yes—
78C2×#97×C47C2212yescomplemented
79C2×#10625350—21no—
80C2×#10625350—21no—
81C2×#10625350—22no—
82C2×#10625350—22no—
83C2×#10625350—48no—
84C2×#10625350C2312yes—
85C2×#10625350C2314yes—
86C2×#10625350C2314yes—
87C22×Dic94C2312yes—
88C22×D188—21no—
89C22×D188—21no—
90C22×D188C2312yes—
91C22×C22⋊D47—22no—
92C22×C4×D47—22no—
93#13094046—416no—
94C2×Dic188C2318yes—
95C2×#10625325C2318yes—
96C2×#10625325C2318yes—
97C2×D376C2318yes—
98#13094024—21no—
99#13094024—21no—
100#13094024C2312yes—
101#13094024C2311yescharacteristic
102#13094024C2312yes—
103#13094024C2311yescharacteristic
104#13094024C2311yescharacteristic
105#13094021—21no—
106#13094021—21no—
107#13094021C2312yes—
108#13094021C2311yescharacteristic
109#13094021C2312yes—
110#13094018—22no—
111#13094018—22no—
112#13094016—21no—
113#13094016—21no—
114#13094016C2312yes—
115#13094012—22no—
116#13094012—22no—
117#13094012—21no—
118#13094012—21no—
119#13094012C2314yes—
120#13094012C2312yes—
121#13094012C2314yes—
122#13094007—22no—
123#13094007—22no—
124#13094007—22no—
125#13094003—21no—
126#13094003—21no—
127#13094003—21no—
128#13094003—21no—
129#13094003C2312yes—
130#13094003C2312yes—
131#13093998—22no—
132#13093998—22no—
133#13093998—22no—
134#13093998—22no—
135#13093998—22no—
136#13093998—22no—
137#13093998—22no—
138#13093998—22no—
139#13093998—21no—
140#13093998—21no—
141#13093998—21no—
142#13093998—21no—
143#13093998C2312yes—
144#13093998C2312yes—
145#13093993—22no—
146C4×Dic94—21no—
147C4×Dic94—21no—
148C4×Dic94—21no—
149C4×Dic94—21no—
150C4×Dic94C2312yes—
151C4×Dic94C2312yes—
152C4×D188—22no—
153C4×D188—22no—
154C4×D188—22no—
155C4×D188—22no—
156C4×D188—22no—
157C4×D188—22no—
158C4×D188—22no—
159C4×D188—22no—
160C4×D188—21no—
161C4×D188—21no—
162C4×D188—21no—
163C4×D188—21no—
164C4×D188C2312yes—
165C4×D188C2312yes—
166C4×C22⋊D47—22no—
167C4×C22⋊D47—22no—
168C4×C22⋊D47—22no—
169C4×C22⋊D47—22no—
170C4×C22⋊D47—22no—
171C4×C22⋊D47—22no—
172#13093983—21no—
173#13093983—21no—
174#13093983C2312yes—
175#13093981—22no—
176#13093981—22no—
177#13093981—22no—
178C2×C4⋊Dic47—21no—
179C2×C4⋊Dic47—21no—
180C2×(C2×D47)⋊C4—22no—
181C2×(C2×D47)⋊C4—22no—
182C42×D47—22no—
183#13093949C2318yes—
184#13093949C2318yes—
185#13093946C2318yes—
186#13093946C2318yes—
187C23×C4×C47D411yescharacteristic
188C23×C4×C47D411yescharacteristic
189C23×C4×C47C2311yescharacteristic
190C22×C8×C47C2314yes—
191C2×C42×C47D411yescharacteristic
192C2×C42×C47D411yescharacteristic
193C2×C42×C47D411yescharacteristic
194C2×C42×C47D411yescharacteristic
195C2×C42×C47D411yescharacteristic
196C2×C42×C47D411yescharacteristic
197C2×C42×C47C2311yescharacteristic
198C2×C42×C47C2311yescharacteristic
199C2×C42×C47C2311yescharacteristic
200C2×C42×C47C2311yescharacteristic
201C2×C42×C47C2311yescharacteristic
202C2×C42×C47C2311yescharacteristic
203C4⋊C8×C47C2314yes—
204C4⋊C8×C47C2314yes—
205C22⋊C8×C47C2314yes—
206C22⋊C8×C47C2314yes—
207#97×C47C2314yes—
208#97×C47C2314yes—
209C24×C47C2×D411yescharacteristic
210C23×D47—22no—
211C22×C4×C47—24no—
212C22×C4×C47—42no—
213C22×C4×C47—42no—
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×C47C2×D411yescharacteristic
227C22×C4×C47C2×D411yescharacteristic
228C22×C4×C47C2×D411yescharacteristic
229C22×C4×C47C2411yescharacteristic
230C22×C4×C47C2411yescharacteristic
231C22×C4×C47C2411yescharacteristic
232C2×C22⋊D47—22no—
233C2×C22⋊D47—22no—
234C2×C22⋊D47—22no—
235C2×C22⋊D47—24no—
236C2×C22⋊D47—24no—
237C2×C22⋊D47—48no—
238C22×Dic47—22no—
239#10625350—28no—
240#10625350—216no—
241#10625350—48no—
242#10625350—44no—
243#10625350—44no—
244#10625350—48no—
245#10625350—48no—
246C2×D188—21no—
247C2×D188—21no—
248C2×D188—22no—
249C2×D188—22no—
250C2×D188—22no—
251C2×D188—22no—
252C2×D188—22no—
253C2×D188—44no—
254C2×D188—44no—
255C2×D188—44no—
256C2×D188C2414yes—
257C2×D188C2412yes—
258C2×C4×D47—22no—
259C2×C4×D47—22no—
260C2×C4×D47—22no—
261C2×C4×D47—24no—
262C2×C4×D47—24no—
263C2×C4×D47—48no—
264C2×Dic94—21no—
265C2×Dic94—21no—
266C2×Dic94—22no—
267C2×Dic94—44no—
268C2×Dic94C2414yes—
269C2×Dic94C2412yes—
270C2×C8×C47—28no—
271C2×C8×C47C2418yes—
272C42×C47C2×D411yescharacteristic
273C42×C47C2×D411yescharacteristic
274C42×C47C2×D411yescharacteristic
275C42×C47C2×D411yescharacteristic
276C42×C47C2×D411yescharacteristic
277C42×C47C2×D411yescharacteristic
278C42×C47C2×D411yescharacteristic
279C42×C47C2×D411yescharacteristic
280C42×C47C2×D411yescharacteristic
281C42×C47C2×D411yescharacteristic
282C42×C47C2×D411yescharacteristic
283C42×C47C2×D411yescharacteristic
284C42×C47C2411yescharacteristic
285C42×C47C2411yescharacteristic
286C42×C47C2411yescharacteristic
287C42×C47C2411yescharacteristic
288C22⋊Dic47—22no—
289C22⋊Dic47—22no—
290C22⋊Dic47—22no—
291(C2×D47)⋊C4—24no—
292(C2×D47)⋊C4—24no—
293(C2×D47)⋊C4—24no—
294(C2×D47)⋊C4—24no—
295(C2×D47)⋊C4—22no—
296(C2×D47)⋊C4—22no—
297(C2×D47)⋊C4—22no—
298(C2×D47)⋊C4—22no—
299(C2×D47)⋊C4—22no—
300(C2×D47)⋊C4—22no—
301C4⋊Dic47—22no—
302C4⋊Dic47—22no—
303C4⋊Dic47—22no—
304C4⋊Dic47—22no—
305C4⋊Dic47—21no—
306C4⋊Dic47—21no—
307C4⋊Dic47—21no—
308C4⋊Dic47—21no—
309C4⋊Dic47C2412yes—
310C4⋊Dic47C2412yes—
311Dic47⋊C4—22no—
312Dic47⋊C4—22no—
313Dic47⋊C4—22no—
314Dic47⋊C4—22no—
315Dic47⋊C4—22no—
316Dic47⋊C4—22no—
317C4×Dic47—22no—
318C4×Dic47—22no—
319C4×Dic47—22no—
320Dic188—48no—
321D376—48no—
322#10625325—48no—
323#10625325—48no—
324C23×C47—22no—
325C23×C47—22no—
326C23×C47—41no—
327C23×C47C22×D411yescharacteristic
328C23×C47C22×D411yescharacteristic
329C23×C47C22×D411yescharacteristic
330C22×D47—22no—
331C22×D47—24no—
332C22×D47—44no—
333C22×D47—44no—
334C22×D47—44no—
335C2×C4×C47—22no—
336C2×C4×C47—22no—
337C2×C4×C47—22no—
338C2×C4×C47—22no—
339C2×C4×C47—22no—
340C2×C4×C47—22no—
341C2×C4×C47—22no—
342C2×C4×C47—22no—
343C2×C4×C47—22no—
344C2×C4×C47—22no—
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×C47—41no—
352C2×C4×C47C22×D411yescharacteristic
353C2×C4×C47C22×D411yescharacteristic
354C2×C4×C47C22×D411yescharacteristic
355C2×C4×C47C22×D411yescharacteristic
356C2×C4×C47C22×D411yescharacteristic
357C2×C4×C47C22×D411yescharacteristic
358C2×C4×C47C22×D411yescharacteristic
359C2×C4×C47C22×D411yescharacteristic
360C2×C4×C47C22×D411yescharacteristic
361C2×C4×C47C22×D411yescharacteristic
362C2×C4×C47C22×D411yescharacteristic
363C2×C4×C47H(5,𝔽2)14yes—
364C2×C4×C47C2511yescharacteristic
365C22⋊D47—48no—
366C22⋊D47—44no—
367C22⋊D47—48no—
368C22⋊D47—44no—
369C22⋊D47—44no—
370C2×Dic47—22no—
371C2×Dic47—22no—
372C2×Dic47—22no—
373C2×Dic47—24no—
374C2×Dic47—44no—
375D188—24no—
376D188—28no—
377D188—44no—
378D188—44no—
379D188—44no—
380D188—44no—
381D188—42no—
382D188—42no—
383D188—44no—
384C4×D47—48no—
385C4×D47—44no—
386C4×D47—48no—
387C4×D47—44no—
388C4×D47—44no—
389Dic94—24no—
390Dic94—28no—
391Dic94—44no—
392Dic94—42no—
393Dic94—42no—
394C8×C47—28no—
395#60790—471nomaximal, Sylow
396C22×C47—21no—
397C22×C47—21no—
398C22×C47—21no—
399C22×C47—21no—
400C22×C47—21no—
401C22×C47—21no—
402C22×C47—21no—
403C22×C47—44no—
404C22×C47#53512yes—
405C22×C47#57512yes—
406C22×C47C23×D411yescharacteristic
407C2×D47—44no—
408C2×D47—42no—
409C2×D47—42no—
410C2×D47—42no—
411C2×D47—44no—
412C2×D47—44no—
413C2×D47—88no—
414C4×C47—21no—
415C4×C47—21no—
416C4×C47—21no—
417C4×C47—21no—
418C4×C47—21no—
419C4×C47—21no—
420C4×C47—21no—
421C4×C47—21no—
422C4×C47—21no—
423C4×C47#53512yes—
424C4×C47#57512yes—
425C4×C47C2×H(5,𝔽2)12yes—
426Dic47—44no—
427Dic47—42no—
428Dic47—42no—
429Dic47—42no—
430#3444—471no—
431C2×#532—471no—
432#3219—474no—
433#3218—472no—
434#3217—472no—
435#3216—472no—
436#3215—472no—
437#3214—472no—
438#3213—472no—
439#3150—472no—
440#3135—472no—
441#3035—474no—
442#3002—474no—
443C2×#432D4711yescharacteristic, complemented
444C2×C47—22no—
445C2×C47—22no—
446C2×C47—41no—
447C2×C47C2×#53511yescharacteristic
448C2×C47C2×#57511yescharacteristic
449C2×C47C2×#57511yescharacteristic
450D47—82no—
451D47—84no—
452C22×#41—472no—
453C2×#135—478no—
454#533—471no—
455#533—471no—
456#533—471no—
457#532—471no—
458#532—471no—
459#532—472no—
460#532—471no—
461#532—472no—
462#532—472no—
463#532—472no—
464#532—941no—
465#532—941no—
466#532—941no—
467#532—941no—
468C2×C4⋊Q8—471no—
469C2×#127—471no—
470#529—472no—
471#529—472no—
472#529—941no—
473#529—941no—
474#529—941no—
475#529—941no—
476C2×#124—472no—
477#525—472no—
478#525—941no—
479#525—941no—
480C2×#121—941no—
481C2×#121—941no—
482C4×#41—472no—
483C4×#41—941no—
484C4×#41—941no—
485C2×C4×D4—941no—
486C2×C4×D4—941no—
487C22×C42C2×D4711yescharacteristic
488#497—474no—
489#497—474no—
490#496—474no—
491#496—474no—
492#491—474no—
493#490—474no—
494#489—474no—
495#489—474no—
496#464—478no—
497#463—478no—
498#462—474no—
499#461—474no—
500#460—474no—
501#459—474no—
502#452—478no—
503#451—474no—
504#450—474no—
505#449—478no—
506#448—474no—
507#447—474no—
508#432C2×D4712yes—
509#432C2×D4712yes—
510#432C2×D4712yescomplemented
511#432C2×D4712yescomplemented
512C2×C4⋊C8C2×D4712yescomplemented
513#416—478no—
514C2×C22⋊C8C2×D4712yes—
515C2×#97C2×D4712yescomplemented
516C47#6079011yescharacteristic, complemented, Sylow
517C2×#41—472no—
518C2×#41—474no—
519C2×#41—474no—
520C2×#41—941no—
521C2×#41—941no—
522C2×#41—942no—
523C2×#41—942no—
524C2×#41—1888no—
525C22×Q8—472no—
526C22×D4—472no—
527C22×D4—942no—
528C22×D4—941no—
529C22×D4—941no—
530C23×C4—942no—
531C23×C4D18811yescharacteristic
532C23×C4D18811yescharacteristic
533C23×C4C22×D4711yescharacteristic
534#135—18816no—
535C2×Q16—478no—
536C2×SD16—478no—
537C2×SD16—478no—
538C2×D8—478no—
539C22×C8C22×D4714yes—
540C4⋊Q8—471no—
541C4⋊Q8—471no—
542C4⋊Q8—472no—
543C4⋊Q8—472no—
544C4⋊Q8—471no—
545C4⋊Q8—941no—
546C4⋊Q8—941no—
547#127—472no—
548#127—472no—
549#127—471no—
550#127—941no—
551#127—941no—
552#126—942no—
553#126—942no—
554#125—472no—
555#125—941no—
556#125—941no—
557#124—474no—
558#124—474no—
559#124—472no—
560#124—942no—
561#124—942no—
562#124—941no—
563#124—941no—
564#123—942no—
565#123—942no—
566#123—942no—
567C22⋊Q8—472no—
568C22⋊Q8—472no—
569C22⋊Q8—941no—
570C22⋊Q8—941no—
571C22⋊Q8—941no—
572C22⋊Q8—941no—
573#121—472no—
574#121—472no—
575#121—942no—
576#121—942no—
577#121—942no—
578#121—942no—
579#121—942no—
580#121—942no—
581#121—942no—
582#121—942no—
583#121—941no—
584#121—941no—
585#121—941no—
586#121—941no—
587#120—942no—
588C4×Q8—472no—
589C4×Q8—472no—
590C4×Q8—941no—
591C4×Q8—941no—
592C4×Q8—941no—
593C4×Q8—941no—
594C4×D4—472no—
595C4×D4—472no—
596C4×D4—942no—
597C4×D4—942no—
598C4×D4—942no—
599C4×D4—942no—
600C4×D4—942no—
601C4×D4—942no—
602C4×D4—942no—
603C4×D4—942no—
604C4×D4—942no—
605C4×D4—942no—
606C4×D4—942no—
607C4×D4—942no—
608C4×D4—942no—
609C4×D4—942no—
610C4×D4—941no—
611C4×D4—941no—
612C4×D4—941no—
613C4×D4—941no—
614#117—472no—
615#117—941no—
616#117—941no—
617#117—942no—
618#117—942no—
619#117—942no—
620C2×C4⋊C4—941no—
621C2×C4⋊C4—941no—
622C2×C22⋊C4—942no—
623C2×C22⋊C4—942no—
624C2×C42—942no—
625C2×C42D18811yescharacteristic
626C2×C42D18811yescharacteristic
627C2×C42D18811yescharacteristic
628C2×C42D18811yescharacteristic
629C2×C42D18811yescharacteristic
630C2×C42D18811yescharacteristic
631C2×C42C22×D4711yescharacteristic
632C2×C42C22×D4711yescharacteristic
633C2×C42C22×D4711yescharacteristic
634C2×C42C22×D4711yescharacteristic
635C2×C42C22×D4711yescharacteristic
636C2×C42C22×D4711yescharacteristic
637C4⋊C8C22×D4714yes—
638C4⋊C8C22×D4714yes—
639#103—478no—
640#103—478no—
641#102—478no—
642#102—478no—
643C22⋊C8C22×D4714yes—
644C22⋊C8C22×D4714yes—
645#97C22×D4714yes—
646#97C22×D4714yes—
647C24—942no—
648C24C2×D18811yescharacteristic
649#41—948no—
650#41—9416no—
651#41—1888no—
652#41—1884no—
653#41—1884no—
654#41—1888no—
655#41—1888no—
656C2×Q8—474no—
657C2×Q8—472no—
658C2×Q8—941no—
659C2×Q8—941no—
660C2×Q8—942no—
661C2×Q8—1884no—
662C2×D4—474no—
663C2×D4—472no—
664C2×D4—942no—
665C2×D4—942no—
666C2×D4—942no—
667C2×D4—944no—
668C2×D4—944no—
669C2×D4—941no—
670C2×D4—941no—
671C2×D4—942no—
672C2×D4—942no—
673C2×D4—942no—
674C2×D4—942no—
675C2×D4—942no—
676C2×D4—1884no—
677C2×D4—1884no—
678C2×D4—1884no—
679C2×D4—1888no—
680C22×C4—24no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—942no—
684C22×C4—942no—
685C22×C4—942no—
686C22×C4—944no—
687C22×C4—942no—
688C22×C4—944no—
689C22×C4—1888no—
690C22×C4C2×D18811yescharacteristic
691C22×C4C2×D18811yescharacteristic
692C22×C4C2×D18811yescharacteristic
693C22×C4C2×D18811yescharacteristic
694C22×C4C2×D18811yescharacteristic
695C22×C4C2×D18811yescharacteristic
696C22×C4C2×D18811yescharacteristic
697C22×C4C2×D18811yescharacteristic
698C22×C4C2×D18811yescharacteristic
699C22×C4C2×D18811yescharacteristic
700C22×C4C2×D18811yescharacteristic
701C22×C4C2×D18811yescharacteristic
702C22×C4C2×D18811yescharacteristic
703C22×C4C2×D18811yescharacteristic
704C22×C4C2×D18811yescharacteristic
705C22×C4C23×D4711yescharacteristic
706C22×C4C23×D4711yescharacteristic
707C22×C4C23×D4711yescharacteristic
708Q16—1888no—
709SD16—1888no—
710SD16—1888no—
711D8—1888no—
712C2×C8—28no—
713C2×C8C23×D4718yes—
714C4⋊C4—472no—
715C4⋊C4—472no—
716C4⋊C4—942no—
717C4⋊C4—942no—
718C4⋊C4—942no—
719C4⋊C4—942no—
720C4⋊C4—942no—
721C4⋊C4—942no—
722C4⋊C4—942no—
723C4⋊C4—942no—
724C4⋊C4—942no—
725C4⋊C4—942no—
726C4⋊C4—941no—
727C4⋊C4—941no—
728C4⋊C4—941no—
729C4⋊C4—941no—
730C22⋊C4—942no—
731C22⋊C4—942no—
732C22⋊C4—942no—
733C22⋊C4—944no—
734C22⋊C4—944no—
735C22⋊C4—944no—
736C22⋊C4—944no—
737C22⋊C4—942no—
738C22⋊C4—942no—
739C22⋊C4—942no—
740C22⋊C4—942no—
741C22⋊C4—942no—
742C22⋊C4—942no—
743C42—942no—
744C42—942no—
745C42—942no—
746C42C2×D18811yescharacteristic
747C42C2×D18811yescharacteristic
748C42C2×D18811yescharacteristic
749C42C2×D18811yescharacteristic
750C42C2×D18811yescharacteristic
751C42C2×D18811yescharacteristic
752C42C2×D18811yescharacteristic
753C42C2×D18811yescharacteristic
754C42C2×D18811yescharacteristic
755C42C2×D18811yescharacteristic
756C42C2×D18811yescharacteristic
757C42C2×D18811yescharacteristic
758C42C23×D4711yescharacteristic
759C42C23×D4711yescharacteristic
760C42C23×D4711yescharacteristic
761C42C23×D4711yescharacteristic
762C23—22no—
763C23—22no—
764C23—41no—
765C23—942no—
766C23—944no—
767C23—1884no—
768C23—1884no—
769C23—1884no—
770C23C22×D18811yescharacteristic
771C23C22×D18811yescharacteristic
772C23C22×D18811yescharacteristic
773Q8—944no—
774Q8—948no—
775Q8—1884no—
776Q8—1882no—
777Q8—1882no—
778D4—944no—
779D4—948no—
780D4—1884no—
781D4—1884no—
782D4—1884no—
783D4—1884no—
784D4—1882no—
785D4—1882no—
786D4—1888no—
787D4—1884no—
788D4—1884no—
789D4—1888no—
790D4—1884no—
791D4—1884no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—942no—
810C2×C4—942no—
811C2×C4—942no—
812C2×C4—944no—
813C2×C4—1888no—
814C2×C4—1884no—
815C2×C4—1884no—
816C2×C4—1884no—
817C2×C4—1888no—
818C2×C4—1884no—
819C2×C4C22×D18811yescharacteristic
820C2×C4C22×D18811yescharacteristic
821C2×C4C22×D18811yescharacteristic
822C2×C4C22×D18811yescharacteristic
823C2×C4C22×D18811yescharacteristic
824C2×C4C22×D18811yescharacteristic
825C2×C4C22×D18811yescharacteristic
826C2×C4C22×D18811yescharacteristic
827C2×C4C22×D18811yescharacteristic
828C2×C4C22×D18811yescharacteristic
829C2×C4C22×D18811yescharacteristic
830C2×C4#1309407014yes—
831C2×C4C24×D4711yescharacteristic
832C8—28no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—21no—
840C22—44no—
841C22—3768no—
842C22—1882no—
843C22—1882no—
844C22—1884no—
845C22—1884no—
846C22—1884no—
847C22—1882no—
848C22#1568969212yes—
849C22#1568992312yes—
850C22C23×D18811yescharacteristic
851C4—21no—
852C4—21no—
853C4—21no—
854C4—21no—
855C4—21no—
856C4—21no—
857C4—21no—
858C4—21no—
859C4—21no—
860C4—1882no—
861C4—1882no—
862C4—1884no—
863C4—1882no—
864C4#1568969212yes—
865C4#1568992312yes—
866C4C2×#1309407012yes—
867C2—22no—
868C2—22no—
869C2—41no—
870C2—3764no—
871C2—3762no—
872C2C2×#1568969211yescharacteristic
873C2C2×#1568992311yescharacteristic
874C2C2×#1568992311yescharacteristic
subgroupG/H
centerC2×C4C22×D188
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#432C2
socleC22×C47C23×D4
hypercenterC2×#432D47
hypocenterC47#60790
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
1. #20256684C2semidirect
2. C2×#15689673C2semidirect
3. #20254427C2semidirect
4. #20254417C2semidirect
5. #20254408C2semidirect
6. #20254401C2semidirect
7. #20254393C2semidirect
8. #20254385C2semidirect
9. #20254377C2semidirect
10. #20253834C2semidirect
11. #20253734C2semidirect
12. #20252845C2semidirect
13. #20252610C2semidirect
14. C2×C47×#432C2semidirect
16. C2×#13094046C22semidirect
18. #15689680C22semidirect
19. #15689680C22semidirect
29. #15689673C22semidirect
30. #15689673C22semidirect
38. #15689657C22semidirect
47. C4×#10625350C22semidirect
50. #15689517C22semidirect
51. #15689517C22semidirect
52. #15689512C22semidirect
53. #15689512C22semidirect
54. #15689492C22semidirect
55. #15689488C22semidirect
56. #15689483C22semidirect
57. #15689483C22semidirect
58. #15689346C22semidirect
59. #15689339C22semidirect
60. #15689334C22semidirect
61. #15689329C22semidirect
62. #15689324C22semidirect
63. #15689319C22semidirect
64. #15689287C22semidirect
67. #15689270C22semidirect
70. #15689120C22semidirect
74. C47×#432C22semidirect
75. C47×#432C22semidirect
76. C2×C4⋊C8×C47C22semidirect
78. C2×#97×C47C22semidirect
443. C2×#432D47semidirect
510. #432C2×D47semidirect
511. #432C2×D47semidirect
512. C2×C4⋊C8C2×D47semidirect
515. C2×#97C2×D47semidirect
516. C47#60790semidirect

Maximal subgroups

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

subgroupindex
#202566842
C2×#156896732
#202544272
#202544172
#202544082
#202544012
#202543932
#202543852
#202543772
#202538342
#202537342
#202528452
#202526102
C2×C47×#4322
#6079047