Finite Group Databasebeta

← #27085104

Subgroups — #27085104

Order 12032.

1998 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689600C211yesmaximal, characteristic, complemented
2#20253683C214yesmaximal, complemented
3#20253611C214yesmaximal, complemented
4#20253555C212yesmaximal, complemented
5#20253514C212yesmaximal, complemented
6#20253464C212yesmaximal, complemented
7#20253423C212yesmaximal, complemented
8#20253332C211yesmaximal, characteristic, complemented
9#20253297C211yesmaximal, characteristic
10#20253224C212yesmaximal, complemented
11#20252914C212yesmaximal, complemented
12#20252621C211yesmaximal, characteristic
13C2×#15689278C211yesmaximal, characteristic, complemented
14#20252254C212yesmaximal, complemented
15#20252227C212yesmaximal, complemented
16#20252046C211yesmaximal, characteristic, complemented
17C47×#3495C211yesmaximal, characteristic
18C23×Dic94C2211yescharacteristic
19C2×#13094054C2212yes—
20C22×#10625337C2212yes—
21#15689600—21no—
22#15689600—22no—
23#15689600—21no—
24#15689600C2212yes—
25#15689600C2212yes—
26#15689600C2214yes—
27C2×C4×Dic94C2212yes—
28C2×C4×Dic94C2212yes—
29C2×#13093989—21no—
30C2×#13093989—21no—
31C2×#13093983C2211yescharacteristic
32C2×#13093980—22no—
33#15689461C2212yes—
34#15689461C2214yes—
35#15689456C2211yescharacteristic
36#15689456C2212yes—
37#15689451C2212yes—
38#15689451C2211yescharacteristic
39#15689444C2212yes—
40#15689439C2211yescharacteristic
41#15689434C2211yescharacteristic
42#15689427C2214yescomplemented
43#15689427C2214yescomplemented
44#15689415C2214yescomplemented
45#15689405C2214yescomplemented
46#15689342C2214yescomplemented
47#15689342C2214yescomplemented
48#15689330C2214yescomplemented
49#15689330C2214yescomplemented
50#15689278C2212yes—
51#15689278C2212yes—
52#15689278C2212yes—
53#15689278C2214yes—
54#15689278C2212yes—
55#15689261C2212yes—
56#15689261C2212yes—
57#15689228C2214yescomplemented
58#15689228C2214yescomplemented
59#15689228C2214yescomplemented
60#15689223C2214yescomplemented
61C4×#10625337C2214yescomplemented
62C4×#10625337C2214yescomplemented
63C4×#10625337C2214yescomplemented
64C4×#10625335C2214yescomplemented
65#15689184C2214yes—
66#15689180C2212yes—
67#15689176C2212yes—
68#15689163C2212yes—
69#15689159C2212yes—
70#15689150C2212yes—
71#15689132C2212yes—
72#15689131C2212yes—
73#15689119C2212yes—
74C2×#13093947C2212yes—
75#15689087C2211yescharacteristic
76C2×C22⋊(C47⋊C8)C2211yescharacteristic
77#15689079C2212yes—
78C47×#556—21no—
79C47×#554—21no—
80C47×#552—22no—
81C47×#552—21no—
82C47×#552—21no—
83C47×#551—22no—
84C47×#544C2211yescharacteristic
85C47×#542C2212yes—
86C47×#541C2212yes—
87C47×#536C2211yescharacteristic
88C47×#533C2212yes—
89C47×#529C2212yes—
90C47×#525C2211yescharacteristic
91C2×C22⋊Q8×C47C2211yescharacteristic
92C47×#520C2211yescharacteristic
93C47×#519C2211yescharacteristic
94C2×#117×C47C2211yescharacteristic
95C22×Dic94—21no—
96C22×Dic94—21no—
97C22×Dic94—21no—
98C22×Dic94—28no—
99C22×Dic94C2312yes—
100C22×Dic94C2312yes—
101C22×Dic94C2312yes—
102C23×Dic47—21no—
103#13094054—28no—
104C2×#10625337—28no—
105C2×#10625337C2314yes—
106C2×#10625337C2314yes—
107C2×#10625337C2314yes—
108C2×#10625335C2314yes—
109C2×#10625329C2312yes—
110C22×C47⋊C8C2312yes—
111C4×Dic94—22no—
112C4×Dic94—22no—
113C4×Dic94—22no—
114C4×Dic94—22no—
115C4×Dic94C2314yes—
116C4×Dic94C2314yes—
117C4×Dic94C2314yes—
118C4×Dic94C2314yes—
119#13093989—22no—
120#13093989—22no—
121#13093989—22no—
122#13093989—24no—
123#13093989—22no—
124#13093989—24no—
125#13093983—21no—
126#13093983—21no—
127#13093983C2312yes—
128#13093983C2312yes—
129#13093980—24no—
130#13093980—24no—
131#13093980—24no—
132#13093980—24no—
133C2×C4⋊Dic47C2311yescharacteristic
134C2×C4⋊Dic47C2311yescharacteristic
135C2×Dic47⋊C4—22no—
136C2×Dic47⋊C4—22no—
137C2×C22⋊Dic47—21no—
138C2×C4×Dic47—22no—
139C2×C4×Dic47—22no—
140C2×C4×Dic47—21no—
141#13093957C2312yes—
142#13093957C2312yes—
143#13093957C2314yes—
144#13093955C2312yes—
145#13093955C2312yes—
146#13093955C2314yes—
147C4⋊(C47⋊C8)C2314yes—
148C4⋊(C47⋊C8)C2314yes—
149#13093948C2312yes—
150#13093948C2314yes—
151#13093948C2314yes—
152#13093948C2312yes—
153#13093947C2314yes—
154#13093947C2314yes—
155#13093947C2314yes—
156#13093947C2314yes—
157#13093945C2312yes—
158#13093945C2312yes—
159C22⋊(C47⋊C8)C2312yes—
160C22⋊(C47⋊C8)C2312yes—
161C22⋊(C47⋊C8)C2311yescharacteristic
162C22⋊(C47⋊C8)C2311yescharacteristic
163C22⋊(C47⋊C8)C2312yes—
164#13093935C2314yes—
165C4×C47⋊C8C2314yes—
166C2×#41×C47C2311yescharacteristic
167C22×Q8×C47C2311yescharacteristic
168C23×C4×C47C2311yescharacteristic
169C4⋊Q8×C47—21no—
170C4⋊Q8×C47C2312yes—
171C4⋊Q8×C47C2312yes—
172#126×C47—22no—
173#126×C47—22no—
174#126×C47—22no—
175#126×C47—22no—
176#125×C47—22no—
177#125×C47—22no—
178#125×C47—21no—
179#125×C47—22no—
180#125×C47C2312yes—
181#124×C47—22no—
182#124×C47C2312yes—
183#123×C47—21no—
184#123×C47—22no—
185#123×C47—22no—
186#123×C47—22no—
187C22⋊Q8×C47—21no—
188C22⋊Q8×C47—21no—
189C22⋊Q8×C47—22no—
190C22⋊Q8×C47—21no—
191C22⋊Q8×C47—21no—
192C22⋊Q8×C47—22no—
193C22⋊Q8×C47—22no—
194C22⋊Q8×C47C2312yes—
195C22⋊Q8×C47C2312yes—
196C22⋊Q8×C47C2311yescharacteristic
197C22⋊Q8×C47C2311yescharacteristic
198#121×C47C2311yescharacteristic
199#121×C47C2311yescharacteristic
200#120×C47—21no—
201C4×Q8×C47—21no—
202C4×Q8×C47—21no—
203C4×Q8×C47—22no—
204C4×Q8×C47C2312yes—
205C4×Q8×C47C2312yes—
206C4×Q8×C47C2312yes—
207C4×D4×C47—21no—
208C4×D4×C47—21no—
209C4×D4×C47—22no—
210C4×D4×C47—22no—
211C4×D4×C47C2312yes—
212#117×C47—22no—
213#117×C47—21no—
214#117×C47—22no—
215#117×C47—22no—
216#117×C47D411yescharacteristic
217#117×C47D412yes—
218#117×C47D411yescharacteristic
219#117×C47C2311yescharacteristic
220#117×C47C2311yescharacteristic
221#117×C47C2311yescharacteristic
222#117×C47C2312yes—
223C2×C4⋊C4×C47—21no—
224C2×C4⋊C4×C47—21no—
225C2×C4⋊C4×C47D411yescharacteristic
226C2×C4⋊C4×C47D411yescharacteristic
227C2×C4⋊C4×C47C2311yescharacteristic
228C2×C22⋊C4×C47—21no—
229C2×C22⋊C4×C47D412yes—
230C2×C42×C47C2312yes—
231C24×C47C2×D411yescharacteristic
232#41×C47—24no—
233C2×Q8×C47—21no—
234C2×Q8×C47—22no—
235C2×Q8×C47—24no—
236C2×Q8×C47C2412yes—
237C2×Q8×C47C2411yescharacteristic
238C2×D4×C47—21no—
239C2×D4×C47—21no—
240C2×D4×C47—21no—
241C2×D4×C47C2411yescharacteristic
242C22×C4×C47—24no—
243C22×C4×C47—21no—
244C22×C4×C47—21no—
245C22×C4×C47—21no—
246C22×C4×C47—22no—
247C22×C4×C47C2×D412yes—
248C22×C4×C47C2×D411yescharacteristic
249C22×C4×C47C2×D411yescharacteristic
250C22×C4×C47C2×D411yescharacteristic
251C22×C4×C47C2×D412yes—
252C22×C4×C47C2411yescharacteristic
253C22×C4×C47C2411yescharacteristic
254C22×C4×C47C2411yescharacteristic
255C22×Dic47—28no—
256C22×Dic47—22no—
257C22×Dic47—22no—
258C22×Dic47—22no—
259C22×Dic47—21no—
260C22×Dic47—21no—
261C2×Dic94—28no—
262C2×Dic94—28no—
263C2×Dic94—28no—
264C2×Dic94—22no—
265C2×Dic94—22no—
266C2×Dic94—22no—
267C2×Dic94—24no—
268C2×Dic94—28no—
269C2×Dic94—28no—
270C2×Dic94#4118yes—
271C2×Dic94C2414yes—
272C4⋊C4×C47—21no—
273C4⋊C4×C47—22no—
274C4⋊C4×C47—22no—
275C4⋊C4×C47—22no—
276C4⋊C4×C47—22no—
277C4⋊C4×C47—22no—
278C4⋊C4×C47—22no—
279C4⋊C4×C47—22no—
280C4⋊C4×C47—22no—
281C4⋊C4×C47—21no—
282C4⋊C4×C47—22no—
283C4⋊C4×C47—21no—
284C4⋊C4×C47—22no—
285C4⋊C4×C47C2×D411yescharacteristic
286C4⋊C4×C47C2×D411yescharacteristic
287C4⋊C4×C47C2×D412yes—
288C4⋊C4×C47C2×D411yescharacteristic
289C4⋊C4×C47C2×D411yescharacteristic
290C4⋊C4×C47C2×D412yes—
291C4⋊C4×C47C2412yes—
292C4⋊C4×C47C2411yescharacteristic
293C4⋊C4×C47C2411yescharacteristic
294C22⋊C4×C47—22no—
295C22⋊C4×C47—22no—
296C22⋊C4×C47—21no—
297C22⋊C4×C47—21no—
298C22⋊C4×C47—21no—
299C22⋊C4×C47—21no—
300C22⋊C4×C47—22no—
301C22⋊C4×C47—22no—
302C22⋊C4×C47—21no—
303C22⋊C4×C47—22no—
304C22⋊C4×C47C2×D412yes—
305C22⋊C4×C47C2×D412yes—
306C22⋊C4×C47C2×D412yes—
307C22⋊C4×C47C2×D412yes—
308C42×C47—22no—
309C42×C47—22no—
310C42×C47—22no—
311C42×C47—21no—
312C42×C47C2×D412yes—
313C42×C47C2×D412yes—
314C42×C47C2412yes—
315C42×C47C2412yes—
316C22⋊Dic47—22no—
317C22⋊Dic47—22no—
318#10625337—28no—
319#10625337—28no—
320#10625337—28no—
321#10625335—28no—
322C4⋊Dic47—21no—
323C4⋊Dic47—21no—
324C4⋊Dic47C2412yes—
325C4⋊Dic47C2412yes—
326Dic47⋊C4—24no—
327Dic47⋊C4—24no—
328Dic47⋊C4—24no—
329Dic47⋊C4—24no—
330C4×Dic47—24no—
331C4×Dic47—24no—
332C4×Dic47—24no—
333C4×Dic47—24no—
334C4×Dic47—22no—
335C4×Dic47—22no—
336#10625329—24no—
337C2×C47⋊C8—24no—
338C2×C47⋊C8C2412yes—
339C2×C47⋊C8C2414yes—
340C2×C47⋊C8C2412yes—
341C23×C47—22no—
342C23×C47—22no—
343C23×C47—21no—
344C23×C47—41no—
345C23×C47C22×D411yescharacteristic
346C23×C47C22×D411yescharacteristic
347C23×C47C22×D411yescharacteristic
348Q8×C47—24no—
349Q8×C47—22no—
350Q8×C47—42no—
351Q8×C47—82no—
352D4×C47—22no—
353D4×C47—42no—
354D4×C47—42no—
355D4×C47—81no—
356C2×C4×C47—22no—
357C2×C4×C47—24no—
358C2×C4×C47—22no—
359C2×C4×C47—22no—
360C2×C4×C47—22no—
361C2×C4×C47—22no—
362C2×C4×C47—21no—
363C2×C4×C47—21no—
364C2×C4×C47—22no—
365C2×C4×C47—21no—
366C2×C4×C47—22no—
367C2×C4×C47—42no—
368C2×C4×C47—42no—
369C2×C4×C47—42no—
370C2×C4×C47—82no—
371C2×C4×C47—81no—
372C2×C4×C47C22×D412yes—
373C2×C4×C47C22×D412yes—
374C2×C4×C47C22×D412yes—
375C2×C4×C47C22×D412yes—
376C2×C4×C47C22×D411yescharacteristic
377C2×C4×C47C22×D411yescharacteristic
378C2×C4×C47C22×D411yescharacteristic
379C2×C4×C47C2×#4114yes—
380C2×C4×C47C2511yescharacteristic
381C2×Dic47—28no—
382C2×Dic47—28no—
383C2×Dic47—28no—
384C2×Dic47—24no—
385C2×Dic47—22no—
386C2×Dic47—22no—
387C2×Dic47—42no—
388C2×Dic47—42no—
389Dic94—28no—
390Dic94—28no—
391Dic94—28no—
392Dic94—24no—
393Dic94C2×#4118yes—
394C47⋊C8—22no—
395C47⋊C8—22no—
396C47⋊C8—24no—
397#60583—471nomaximal, Sylow
398C22×C47—21no—
399C22×C47—21no—
400C22×C47—21no—
401C22×C47—21no—
402C22×C47—21no—
403C22×C47—21no—
404C22×C47—21no—
405C22×C47—44no—
406C22×C47—41no—
407C22×C47—41no—
408C22×C47—41no—
409C22×C47#52512yes—
410C22×C47#57812yes—
411C22×C47C23×D411yescharacteristic
412C4×C47—22no—
413C4×C47—22no—
414C4×C47—21no—
415C4×C47—21no—
416C4×C47—22no—
417C4×C47—22no—
418C4×C47—42no—
419C4×C47—41no—
420C4×C47—41no—
421C4×C47—42no—
422C4×C47—41no—
423C4×C47#52512yes—
424C4×C47C22×#4112yes—
425Dic47—28no—
426Dic47—42no—
427Dic47—42no—
428#3495D4711yescharacteristic
429C2×#519—471no—
430#3127—474no—
431#3121—474no—
432#3117—472no—
433#3113—472no—
434#3108—472no—
435#3104—472no—
436#3095—471no—
437#3091—471no—
438#3082—472no—
439#3044—472no—
440#3004—471no—
441C2×#451—471no—
442#2950—472no—
443#2947—472no—
444#2924—471no—
445C2×C47—22no—
446C2×C47—22no—
447C2×C47—41no—
448C2×C47—81no—
449C2×C47C2×#52511yescharacteristic
450C2×C47C2×#57811yescharacteristic
451C2×C47#358611yescharacteristic
452C23×Q8—471no—
453C2×#137—472no—
454C22×Q16—472no—
455#556—21no—
456#554—21no—
457#552—22no—
458#552—21no—
459#552—21no—
460#551—22no—
461#544C2×D4711yescharacteristic
462#542C2×D4712yes—
463#541C2×D4712yes—
464#536C2×D4711yescharacteristic
465#533C2×D4712yes—
466#529C2×D4712yes—
467#525C2×D4711yescharacteristic
468C2×C22⋊Q8C2×D4711yescharacteristic
469#520C2×D4711yescharacteristic
470#519—472no—
471#519—474no—
472#519—472no—
473#519—942no—
474#519—941no—
475#519—941no—
476#519C2×D4711yescharacteristic
477C2×C4×Q8—472no—
478C2×C4×Q8—472no—
479C2×C4×Q8—941no—
480C2×C4×Q8—941no—
481C2×#117—471no—
482C2×#117—942no—
483C2×#117C2×D4711yescharacteristic
484#485—472no—
485#485—474no—
486#484—471no—
487#484—472no—
488#483—471no—
489#483—472no—
490#482—472no—
491#481—471no—
492#480—471no—
493#479—474no—
494#479—474no—
495#477—474no—
496#475—474no—
497#464—474no—
498#464—474no—
499#462—474no—
500#462—474no—
501#451—472no—
502#451—472no—
503#451—472no—
504#451—474no—
505#451—472no—
506#448—472no—
507#448—472no—
508#441—474no—
509#441—474no—
510#441—474no—
511#440—474no—
512C4×Q16—474no—
513C4×Q16—474no—
514C4×Q16—474no—
515C4×SD16—474no—
516#433—474no—
517#432—472no—
518#431—472no—
519#428—472no—
520#427—472no—
521#424—472no—
522#419—472no—
523#419—472no—
524#416—472no—
525C2×#103—472no—
526#407—471no—
527C2×C22⋊C8—471no—
528#405—472no—
529C47#6058311yescharacteristic, complemented, Sylow
530C2×#41C22×D4711yescharacteristic
531C22×Q8—472no—
532C22×Q8—472no—
533C22×Q8—472no—
534C22×Q8—948no—
535C22×Q8—941no—
536C22×Q8—941no—
537C22×Q8—941no—
538C22×Q8C22×D4711yescharacteristic
539C23×C4—941no—
540C23×C4C22×D4711yescharacteristic
541#137—948no—
542C2×Q16—474no—
543C2×Q16—474no—
544C2×Q16—474no—
545C2×Q16—948no—
546C2×SD16—474no—
547C2×M16—472no—
548C22×C8—472no—
549C4⋊Q8—21no—
550C4⋊Q8C22×D4712yes—
551C4⋊Q8C22×D4712yes—
552#126—22no—
553#126—22no—
554#126—22no—
555#126—22no—
556#125—22no—
557#125—22no—
558#125—21no—
559#125—22no—
560#125C22×D4712yes—
561#124—22no—
562#124C22×D4712yes—
563#123—21no—
564#123—22no—
565#123—22no—
566#123—22no—
567C22⋊Q8—21no—
568C22⋊Q8—21no—
569C22⋊Q8—22no—
570C22⋊Q8—21no—
571C22⋊Q8—21no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8C22×D4712yes—
575C22⋊Q8C22×D4712yes—
576C22⋊Q8C22×D4711yescharacteristic
577C22⋊Q8C22×D4711yescharacteristic
578#121C22×D4711yescharacteristic
579#121C22×D4711yescharacteristic
580#120—21no—
581C4×Q8—21no—
582C4×Q8—21no—
583C4×Q8—22no—
584C4×Q8—474no—
585C4×Q8—474no—
586C4×Q8—474no—
587C4×Q8—474no—
588C4×Q8—942no—
589C4×Q8—942no—
590C4×Q8—942no—
591C4×Q8—944no—
592C4×Q8—942no—
593C4×Q8—944no—
594C4×Q8—942no—
595C4×Q8—942no—
596C4×Q8—942no—
597C4×Q8—942no—
598C4×Q8C22×D4712yes—
599C4×Q8C22×D4712yes—
600C4×Q8C22×D4712yes—
601C4×D4—21no—
602C4×D4—21no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4C22×D4712yes—
606#117—22no—
607#117—21no—
608#117—22no—
609#117—22no—
610#117—472no—
611#117—472no—
612#117—941no—
613#117—941no—
614#117—944no—
615#117—944no—
616#117—944no—
617#117—944no—
618#117C22⋊D4711yescharacteristic
619#117C22⋊D4712yes—
620#117C22⋊D4711yescharacteristic
621#117C22×D4711yescharacteristic
622#117C22×D4711yescharacteristic
623#117C22×D4711yescharacteristic
624#117C22×D4712yes—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—471no—
628C2×C4⋊C4—471no—
629C2×C4⋊C4—942no—
630C2×C4⋊C4—942no—
631C2×C4⋊C4C22⋊D4711yescharacteristic
632C2×C4⋊C4C22⋊D4711yescharacteristic
633C2×C4⋊C4C22×D4711yescharacteristic
634C2×C22⋊C4—21no—
635C2×C22⋊C4—941no—
636C2×C22⋊C4C22⋊D4712yes—
637C2×C42—941no—
638C2×C42—942no—
639C2×C42—942no—
640C2×C42C22×D4712yes—
641#107—472no—
642#107—472no—
643#107—474no—
644#106—472no—
645#106—472no—
646#106—474no—
647C4⋊C8—474no—
648C4⋊C8—474no—
649#103—472no—
650#103—472no—
651#103—474no—
652#103—474no—
653#103—474no—
654#103—474no—
655#103—474no—
656#103—474no—
657#102—472no—
658#102—472no—
659C22⋊C8—471no—
660C22⋊C8—471no—
661C22⋊C8—472no—
662C22⋊C8—472no—
663C22⋊C8—472no—
664#97—474no—
665C4×C8—474no—
666C24C2×C22⋊D4711yescharacteristic
667#41—24no—
668C2×Q8—21no—
669C2×Q8—22no—
670C2×Q8—24no—
671C2×Q8—478no—
672C2×Q8—474no—
673C2×Q8—948no—
674C2×Q8—948no—
675C2×Q8—948no—
676C2×Q8—948no—
677C2×Q8—948no—
678C2×Q8—942no—
679C2×Q8—942no—
680C2×Q8—942no—
681C2×Q8—944no—
682C2×Q8C23×D4712yes—
683C2×Q8C23×D4711yescharacteristic
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4C23×D4711yescharacteristic
688C22×C4—24no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—22no—
693C22×C4—948no—
694C22×C4—942no—
695C22×C4—942no—
696C22×C4—942no—
697C22×C4—941no—
698C22×C4—941no—
699C22×C4C2×C22⋊D4712yes—
700C22×C4C2×C22⋊D4711yescharacteristic
701C22×C4C2×C22⋊D4711yescharacteristic
702C22×C4C2×C22⋊D4711yescharacteristic
703C22×C4C2×C22⋊D4712yes—
704C22×C4C23×D4711yescharacteristic
705C22×C4C23×D4711yescharacteristic
706C22×C4C23×D4711yescharacteristic
707Q16—948no—
708Q16—948no—
709Q16—948no—
710SD16—948no—
711M16—944no—
712C2×C8—472no—
713C2×C8—474no—
714C2×C8—472no—
715C2×C8—944no—
716C4⋊C4—21no—
717C4⋊C4—22no—
718C4⋊C4—22no—
719C4⋊C4—22no—
720C4⋊C4—22no—
721C4⋊C4—22no—
722C4⋊C4—22no—
723C4⋊C4—22no—
724C4⋊C4—22no—
725C4⋊C4—21no—
726C4⋊C4—22no—
727C4⋊C4—21no—
728C4⋊C4—22no—
729C4⋊C4—472no—
730C4⋊C4—472no—
731C4⋊C4—944no—
732C4⋊C4—944no—
733C4⋊C4—944no—
734C4⋊C4—944no—
735C4⋊C4—941no—
736C4⋊C4—941no—
737C4⋊C4C2×C22⋊D4711yescharacteristic
738C4⋊C4C2×C22⋊D4711yescharacteristic
739C4⋊C4C2×C22⋊D4712yes—
740C4⋊C4C2×C22⋊D4711yescharacteristic
741C4⋊C4C2×C22⋊D4711yescharacteristic
742C4⋊C4C2×C22⋊D4712yes—
743C4⋊C4C23×D4712yes—
744C4⋊C4C23×D4711yescharacteristic
745C4⋊C4C23×D4711yescharacteristic
746C22⋊C4—22no—
747C22⋊C4—22no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—22no—
753C22⋊C4—22no—
754C22⋊C4—21no—
755C22⋊C4—22no—
756C22⋊C4—942no—
757C22⋊C4—942no—
758C22⋊C4C2×C22⋊D4712yes—
759C22⋊C4C2×C22⋊D4712yes—
760C22⋊C4C2×C22⋊D4712yes—
761C22⋊C4C2×C22⋊D4712yes—
762C42—22no—
763C42—22no—
764C42—22no—
765C42—21no—
766C42—942no—
767C42—942no—
768C42—944no—
769C42—944no—
770C42—944no—
771C42—944no—
772C42C2×C22⋊D4712yes—
773C42C2×C22⋊D4712yes—
774C42C23×D4712yes—
775C42C23×D4712yes—
776C23—22no—
777C23—22no—
778C23—21no—
779C23—41no—
780C23C22×C22⋊D4711yescharacteristic
781C23C22×C22⋊D4711yescharacteristic
782C23C22×C22⋊D4711yescharacteristic
783Q8—24no—
784Q8—22no—
785Q8—42no—
786Q8—82no—
787Q8—478no—
788Q8—948no—
789Q8—948no—
790Q8—948no—
791Q8—944no—
792D4—22no—
793D4—42no—
794D4—42no—
795D4—81no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—22no—
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—82no—
811C2×C4—81no—
812C2×C4—948no—
813C2×C4—948no—
814C2×C4—948no—
815C2×C4—944no—
816C2×C4—942no—
817C2×C4—942no—
818C2×C4—1882no—
819C2×C4—1882no—
820C2×C4C22×C22⋊D4712yes—
821C2×C4C22×C22⋊D4712yes—
822C2×C4C22×C22⋊D4712yes—
823C2×C4C22×C22⋊D4712yes—
824C2×C4C22×C22⋊D4711yescharacteristic
825C2×C4C22×C22⋊D4711yescharacteristic
826C2×C4C22×C22⋊D4711yescharacteristic
827C2×C4#41×D4714yes—
828C2×C4C24×D4711yescharacteristic
829C8—942no—
830C8—942no—
831C8—944no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—44no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22#1568963012yes—
844C22#1568993812yes—
845C22C23×C22⋊D4711yescharacteristic
846C4—22no—
847C4—22no—
848C4—21no—
849C4—21no—
850C4—22no—
851C4—22no—
852C4—41no—
853C4—41no—
854C4—42no—
855C4—42no—
856C4—41no—
857C4—948no—
858C4—1882no—
859C4—1882no—
860C4#1568963012yes—
861C4C2×#41×D4712yes—
862C2—22no—
863C2—22no—
864C2—41no—
865C2—81no—
866C2C2×#1568963011yescharacteristic
867C2C2×#1568993811yescharacteristic
868C2#2025817411yescharacteristic
subgroupG/H
centerC22C23×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC47×#3495C2
socleC22×C47C23×D4
prime radicalC47×#525C22
hypercenter#3495D47
hypocenterC47#60583
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×#117 ◁ #3495

Complements

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

NH ≅ G/Ntype
1. C2×#15689600C2semidirect
2. #20253683C2semidirect
3. #20253611C2semidirect
4. #20253555C2semidirect
5. #20253514C2semidirect
6. #20253464C2semidirect
7. #20253423C2semidirect
8. #20253332C2semidirect
10. #20253224C2semidirect
11. #20252914C2semidirect
13. C2×#15689278C2semidirect
14. #20252254C2semidirect
15. #20252227C2semidirect
16. #20252046C2semidirect
42. #15689427C22semidirect
43. #15689427C22semidirect
44. #15689415C22semidirect
45. #15689405C22semidirect
46. #15689342C22semidirect
47. #15689342C22semidirect
48. #15689330C22semidirect
49. #15689330C22semidirect
57. #15689228C22semidirect
58. #15689228C22semidirect
59. #15689228C22semidirect
60. #15689223C22semidirect
61. C4×#10625337C22semidirect
62. C4×#10625337C22semidirect
63. C4×#10625337C22semidirect
64. C4×#10625335C22semidirect
529. C47#60583semidirect

Maximal subgroups

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

subgroupindex
C2×#156896002
#202536832
#202536112
#202535552
#202535142
#202534642
#202534232
#202533322
#202532972
#202532242
#202529142
#202526212
C2×#156892782
#202522542
#202522272
#202520462
C47×#34952
#6058347