Finite Group Databasebeta

← #26218190

Subgroups — #26218190

Order 12032.

1704 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689921C211yesmaximal, characteristic
2#20256589C211yesmaximal, characteristic, complemented
3C2×#15689141C211yesmaximal, characteristic, complemented
4C2×#15689140C211yesmaximal, characteristic, complemented
5#20243886C218yesmaximal, complemented
6C2×#15688893C211yesmaximal, characteristic, complemented
7#20243097C211yesmaximal, characteristic, complemented
8C2×C47×#410C211yesmaximal, characteristic, complemented
9C22×#10625350C2211yescharacteristic
10#15689921—22no—
11#15689921—22no—
12#15689921C414yescomplemented
13#15689921C2214yes—
14C2×#13094055C412yescomplemented
15C2×#13094054—21no—
16C2×#13094050C412yescomplemented
17C2×#13094049—21no—
18C2×#13094044—22no—
19C22×#10625329C2211yescharacteristic
20C22×#10625329C2211yescharacteristic
21#15689604—22no—
22#15689603—22no—
23#15689600—21no—
24#15689597—21no—
25#15689596—22no—
26C4×#10625350—22no—
27#15689591C2214yescomplemented
28C2×#13093983C2211yescharacteristic
29#117×D47—22no—
30#15689141—22no—
31#15689141C2214yescomplemented
32#15689140—22no—
33#15689140—22no—
34C2×#13093952—22no—
35C2×#13093951C2214yescomplemented
36#15688893C2214yescomplemented
37#15688882C2214yescomplemented
38C22×#41×C47C2211yescharacteristic
39C2×#117×C47C2211yescharacteristic
40C2×#117×C47C2211yescharacteristic
41C47×#410—22no—
42C47×#410C2214yescomplemented
43C2×#99×C47—22no—
44C2×#10625350—21no—
45C2×#10625350—21no—
46C2×#10625350—21no—
47C2×#10625350—21no—
48C2×#10625350—21no—
49C2×#10625350—21no—
50C2×#10625350C2×C412yes—
51C2×#10625350C2×C412yes—
52C2×#10625350D412yes—
53C2×#10625350D412yes—
54C2×#10625350D412yes—
55C2×#10625350C2312yes—
56C22×Dic94D411yescharacteristic
57C22×D188D411yescharacteristic
58C22×C22⋊D47—21no—
59C22×C4×D47—21no—
60#13094055—24no—
61#13094055C2×C418yescomplemented
62#13094054—24no—
63#13094054—24no—
64#13094050—24no—
65#13094050C2×C418yescomplemented
66#13094049—24no—
67#13094049—24no—
68#13094044—28no—
69#13094044—28no—
70C2×#10625337—22no—
71C2×#10625335—22no—
72C2×#10625336—22no—
73C2×#10625334—22no—
74C2×#10625329—21no—
75C2×#10625329—21no—
76C2×#10625329—21no—
77C2×#10625329—21no—
78C2×#10625329—21no—
79C2×#10625329—21no—
80C2×#10625329—21no—
81C2×#10625329—21no—
82C2×#10625329C2×C412yescomplemented
83C2×#10625329C2×C412yescomplemented
84C2×#10625329C2312yes—
85C2×#10625329C2312yes—
86C22×C47⋊C8—21no—
87C22×C47⋊C8—21no—
88C4×Dic94—24no—
89#13093989—24no—
90C4×D188—24no—
91#13093986—24no—
92C4×C22⋊D47—28no—
93(C22⋊D47)⋊C4—28no—
94#13093983—21no—
95#13093983—21no—
96#13093983D412yes—
97#13093983D412yes—
98#13093982—24no—
99#13093981—24no—
100#13093980—24no—
101C2×C4⋊Dic47—21no—
102C4⋊C4×D47—24no—
103C2×C22⋊Dic47—21no—
104C22⋊C4×D47—24no—
105C2×C4×Dic47C2312yes—
106C42×D47—24no—
107#13093952—28no—
108#13093951—28no—
109C2×#41×C47—21no—
110C2×#41×C47—21no—
111C2×#41×C47—21no—
112C2×#41×C47—21no—
113C2×#41×C47—21no—
114C2×#41×C47—21no—
115C2×#41×C47—21no—
116C2×#41×C47—21no—
117C2×#41×C47—21no—
118C2×#41×C47—21no—
119C2×#41×C47C2×C412yescomplemented
120C2×#41×C47C2312yes—
121C22×Q8×C47C2×C411yescharacteristic, complemented
122C22×D4×C47—21no—
123C22×D4×C47C2×C411yescharacteristic, complemented
124C23×C4×C47—21no—
125C23×C4×C47C2311yescharacteristic
126#117×C47—21no—
127#117×C47—21no—
128#117×C47—21no—
129#117×C47—21no—
130#117×C47—21no—
131#117×C47D412yes—
132#117×C47C2312yes—
133#117×C47C2312yes—
134C2×C4⋊C4×C47—21no—
135C2×C4⋊C4×C47—21no—
136C2×C22⋊C4×C47—21no—
137C2×C22⋊C4×C47D412yes—
138C2×C42×C47—21no—
139C2×C42×C47—21no—
140#99×C47—28no—
141C24×C47—21no—
142C24×C47C2×D411yescharacteristic
143C23×D47—21no—
144#41×C47—22no—
145#41×C47—22no—
146#41×C47—22no—
147#41×C47—22no—
148#41×C47—22no—
149#41×C47—22no—
150#41×C47—22no—
151#41×C47—22no—
152#41×C47—41no—
153#41×C47—41no—
154#41×C47—41no—
155#41×C47—41no—
156#41×C47—41no—
157#41×C47—41no—
158#41×C47—41no—
159#41×C47—41no—
160C2×Q8×C47—21no—
161C2×Q8×C47—21no—
162C2×Q8×C47—21no—
163C2×Q8×C47—21no—
164C2×Q8×C47—21no—
165C2×Q8×C47C22×C412yes—
166C2×D4×C47—22no—
167C2×D4×C47—22no—
168C2×D4×C47—21no—
169C2×D4×C47—21no—
170C2×D4×C47—21no—
171C2×D4×C47—21no—
172C2×D4×C47—21no—
173C2×D4×C47—41no—
174C2×D4×C47—41no—
175C2×D4×C47—41no—
176C2×D4×C47—41no—
177C2×D4×C47C22×C412yes—
178C22×C4×C47—21no—
179C22×C4×C47—22no—
180C22×C4×C47—22no—
181C22×C4×C47—22no—
182C22×C4×C47—41no—
183C22×C4×C47—41no—
184C22×C4×C47—41no—
185C22×C4×C47—41no—
186C22×C4×C47—41no—
187C22×C4×C47C22×C411yescharacteristic
188C22×C4×C47C22×C411yescharacteristic
189C22×C4×C47C2×D411yescharacteristic
190C22×C4×C47C2×D411yescharacteristic
191C22×C4×C47C2×D411yescharacteristic
192C22×C4×C47C2×D411yescharacteristic
193C22×C4×C47C2×D411yescharacteristic
194C22×C4×C47C2×D411yescharacteristic
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47#4111yescharacteristic
197C22×C4×C47#4111yescharacteristic
198C22×C4×C47#4111yescharacteristic
199C22×C4×C47#4111yescharacteristic
200C22×C4×C47C2411yescharacteristic
201C2×C22⋊D47—22no—
202C2×C22⋊D47—22no—
203C2×C22⋊D47—22no—
204C2×C22⋊D47—22no—
205C2×C22⋊D47—22no—
206C2×C22⋊D47—22no—
207C22×Dic47—21no—
208C22×Dic47—22no—
209#10625350—22no—
210#10625350—22no—
211#10625350—22no—
212#10625350—22no—
213#10625350—22no—
214#10625350—22no—
215#10625350—22no—
216#10625350—22no—
217#10625350—22no—
218#10625350—22no—
219#10625350—22no—
220#10625350—22no—
221#10625350C22⋊C414yes—
222#10625350C22⋊C414yes—
223#10625350C22×C414yes—
224#10625350C2×D414yes—
225C2×D188—21no—
226C2×D188—21no—
227C2×D188—21no—
228C2×D188C22⋊C412yes—
229C2×D188C22⋊C412yes—
230C2×D188C2×D412yes—
231C2×C4×D47—22no—
232C2×C4×D47—22no—
233C2×C4×D47—22no—
234C2×C4×D47—22no—
235C2×C4×D47—22no—
236C2×C4×D47—22no—
237C2×C4×D47—28no—
238C2×Dic94—21no—
239C2×Dic94—21no—
240C2×Dic94—21no—
241C2×Dic94C22⋊C412yes—
242C2×Dic94C22⋊C412yes—
243C2×Dic94C2×D412yes—
244C4⋊C4×C47—22no—
245C4⋊C4×C47—22no—
246C4⋊C4×C47—22no—
247C4⋊C4×C47—41no—
248C22⋊C4×C47—22no—
249C22⋊C4×C47—22no—
250C22⋊C4×C47—41no—
251C22⋊C4×C47C2×D414yes—
252C42×C47—22no—
253C42×C47—22no—
254C42×C47—22no—
255C42×C47—41no—
256C22⋊Dic47—22no—
257C22⋊Dic47—22no—
258#10625337—28no—
259#10625336—28no—
260#10625335—28no—
261#10625334—28no—
262(C2×D47)⋊C4—28no—
263C4⋊Dic47—22no—
264C4⋊Dic47—22no—
265Dic47⋊C4—28no—
266C4×Dic47—28no—
267C4×Dic47—22no—
268C4×Dic47C2×D414yes—
269#10625329—22no—
270#10625329—22no—
271#10625329—22no—
272#10625329—22no—
273#10625329—22no—
274#10625329—41no—
275#10625329—41no—
276#10625329C22×C414yes—
277C2×C47⋊C8—22no—
278C2×C47⋊C8—22no—
279C2×C47⋊C8—22no—
280C2×C47⋊C8—22no—
281C2×C47⋊C8—41no—
282C2×C47⋊C8—41no—
283C23×C47—22no—
284C23×C47—41no—
285C23×C47—41no—
286C23×C47—81no—
287C23×C47—82no—
288C23×C47C4×D411yescharacteristic
289C23×C47C4×D411yescharacteristic
290C23×C47#12011yescharacteristic
291C23×C47#12011yescharacteristic
292C23×C47#12111yescharacteristic
293C23×C47#12111yescharacteristic
294C23×C47C22×D411yescharacteristic
295C22×D47—22no—
296C22×D47—22no—
297C22×D47—22no—
298C22×D47—82no—
299Q8×C47—22no—
300Q8×C47—22no—
301Q8×C47—41no—
302Q8×C47—41no—
303D4×C47—22no—
304D4×C47—22no—
305D4×C47—42no—
306D4×C47—42no—
307D4×C47—42no—
308D4×C47—42no—
309D4×C47—41no—
310D4×C47—41no—
311C2×C4×C47—22no—
312C2×C4×C47—24no—
313C2×C4×C47—41no—
314C2×C4×C47—41no—
315C2×C4×C47—42no—
316C2×C4×C47—42no—
317C2×C4×C47—42no—
318C2×C4×C47—42no—
319C2×C4×C47—42no—
320C2×C4×C47—82no—
321C2×C4×C47—82no—
322C2×C4×C47C2×C22⋊C411yescharacteristic
323C2×C4×C47C2×C22⋊C411yescharacteristic
324C2×C4×C47C2×C22⋊C411yescharacteristic
325C2×C4×C47C2×C22⋊C411yescharacteristic
326C2×C4×C47C4×D411yescharacteristic
327C2×C4×C47C4×D411yescharacteristic
328C2×C4×C47C4×D411yescharacteristic
329C2×C4×C47C4×D411yescharacteristic
330C2×C4×C47C4×D411yescharacteristic
331C2×C4×C47C4×D411yescharacteristic
332C2×C4×C47#12011yescharacteristic
333C2×C4×C47#12011yescharacteristic
334C2×C4×C47#12111yescharacteristic
335C2×C4×C47#12111yescharacteristic
336C2×C4×C47#12111yescharacteristic
337C2×C4×C47#12111yescharacteristic
338C2×C4×C47#12111yescharacteristic
339C2×C4×C47#12111yescharacteristic
340C2×C4×C47#12311yescharacteristic
341C2×C4×C47#12311yescharacteristic
342C2×C4×C47#12311yescharacteristic
343C2×C4×C47#12311yescharacteristic
344C2×C4×C47C23×C411yescharacteristic
345C2×C4×C47C22×D411yescharacteristic
346C2×C4×C47C22×D411yescharacteristic
347C2×C4×C47C22×D411yescharacteristic
348C2×C4×C47C2×#4111yescharacteristic
349C2×C4×C47C2×#4111yescharacteristic
350C22⋊D47—24no—
351C22⋊D47—24no—
352C22⋊D47—24no—
353C22⋊D47—24no—
354C2×Dic47—22no—
355C2×Dic47—22no—
356C2×Dic47—22no—
357C2×Dic47—24no—
358C2×Dic47—82no—
359D188—22no—
360D188—22no—
361D188—22no—
362D188C2×C22⋊C414yes—
363C4×D47—24no—
364C4×D47—24no—
365C4×D47—24no—
366C4×D47—24no—
367C4×D47—88no—
368Dic94—22no—
369Dic94—22no—
370Dic94—22no—
371Dic94C2×C22⋊C414yes—
372C47⋊C8—24no—
373C47⋊C8—42no—
374#21000—471nomaximal, Sylow
375C22×C47—41no—
376C22×C47—41no—
377C22×C47—41no—
378C22×C47—41no—
379C22×C47—41no—
380C22×C47—41no—
381C22×C47—41no—
382C22×C47—42no—
383C22×C47—82no—
384C22×C47—82no—
385C22×C47—82no—
386C22×C47#38611yescharacteristic
387C22×C47#38611yescharacteristic
388C22×C47#38611yescharacteristic
389C22×C47#38611yescharacteristic
390C22×C47C2×C4×D411yescharacteristic
391C22×C47C2×#12011yescharacteristic
392C22×C47C2×#12111yescharacteristic
393C2×D47—24no—
394C2×D47—44no—
395C2×D47—82no—
396C2×D47—82no—
397C4×C47—44no—
398C4×C47—42no—
399C4×C47—82no—
400C4×C47#38611yescharacteristic
401C4×C47#38611yescharacteristic
402C4×C47#38611yescharacteristic
403C4×C47#38611yescharacteristic
404C4×C47C22×C22⋊C411yescharacteristic
405C4×C47C2×C4×D411yescharacteristic
406C4×C47C2×#12111yescharacteristic
407C4×C47C2×#12311yescharacteristic
408Dic47—24no—
409Dic47—44no—
410C2×#575—471no—
411#3428—471no—
412C2×#421—471no—
413C2×#421—471no—
414C2×#410D4711yescharacteristic, complemented
415#1906—478no—
416C2×#344—471no—
417#1733—471no—
418C2×C47—21no—
419C2×C47—21no—
420C2×C47—21no—
421C2×C47—21no—
422C2×C47—21no—
423C2×C47—21no—
424C2×C47—21no—
425C2×C47—82no—
426C2×C47C2×#38611yescharacteristic
427D47—44no—
428C22×#41—471no—
429C22×#41C2×D4711yescharacteristic
430#575—474no—
431#575—474no—
432#575—942no—
433#575—942no—
434C2×#137—472no—
435C2×#137—941no—
436C2×AGL(1,ℤ/8)—472no—
437C2×AGL(1,ℤ/8)—941no—
438C2×#135—942no—
439C22×M16—471no—
440C22×M16—471no—
441#520—942no—
442#520—942no—
443#519—941no—
444#518—941no—
445#518—942no—
446C4×#41—474no—
447C4×#41—942no—
448C2×#117—471no—
449C2×#117—942no—
450C2×#117C2×D4711yescharacteristic
451C2×#117C2×D4711yescharacteristic
452#421—474no—
453#421—942no—
454#421—942no—
455#421—942no—
456C2×#104—474no—
457C2×#104—942no—
458#410—22no—
459#410C2×D4714yescomplemented
460C2×#99—22no—
461#344—474no—
462#339—474no—
463C47#2100011yescharacteristic, complemented, Sylow
464C2×#41—21no—
465C2×#41—21no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41—21no—
469C2×#41—21no—
470C2×#41—21no—
471C2×#41—21no—
472C2×#41—21no—
473C2×#41—21no—
474C2×#41—472no—
475C2×#41—472no—
476C2×#41—472no—
477C2×#41—472no—
478C2×#41—472no—
479C2×#41—472no—
480C2×#41—941no—
481C2×#41—941no—
482C2×#41—941no—
483C2×#41—941no—
484C2×#41—941no—
485C2×#41—941no—
486C2×#41C4×D4712yescomplemented
487C2×#41C22×D4712yes—
488C22×Q8—471no—
489C22×Q8C4×D4711yescharacteristic, complemented
490C22×D4—21no—
491C22×D4—471no—
492C22×D4—941no—
493C22×D4C4×D4711yescharacteristic, complemented
494C23×C4—21no—
495C23×C4—941no—
496C23×C4C22×D4711yescharacteristic
497#137—478no—
498#137—944no—
499#137—944no—
500#137—944no—
501AGL(1,ℤ/8)—478no—
502AGL(1,ℤ/8)—944no—
503AGL(1,ℤ/8)—944no—
504AGL(1,ℤ/8)—944no—
505#135—948no—
506#135—948no—
507C2×Q16—942no—
508C2×SD16—942no—
509C2×SD16—942no—
510C2×D8—942no—
511C2×M16—472no—
512C2×M16—472no—
513C2×M16—472no—
514C2×M16—472no—
515C2×M16—941no—
516C2×M16—941no—
517C2×M16—941no—
518C2×M16—941no—
519C2×M16—941no—
520C2×M16—941no—
521C2×M16—941no—
522C2×M16—941no—
523C22×C8—941no—
524C22×C8—941no—
525C4×Q8—944no—
526C4×Q8—944no—
527C4×D4—944no—
528C4×D4—944no—
529C4×D4—948no—
530C4×D4—948no—
531#117—21no—
532#117—21no—
533#117—21no—
534#117—21no—
535#117—21no—
536#117—472no—
537#117—472no—
538#117—944no—
539#117—944no—
540#117—944no—
541#117—941no—
542#117—941no—
543#117C22⋊D4712yes—
544#117C22×D4712yes—
545#117C22×D4712yes—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—944no—
549C2×C4⋊C4—941no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—944no—
552C2×C22⋊C4—941no—
553C2×C22⋊C4C22⋊D4712yes—
554C2×C42—21no—
555C2×C42—21no—
556C2×C42—472no—
557C2×C42—944no—
558#104—948no—
559#104—948no—
560#99—28no—
561C24—21no—
562C24—941no—
563C24C2×C22⋊D4711yescharacteristic
564#41—22no—
565#41—22no—
566#41—22no—
567#41—22no—
568#41—22no—
569#41—22no—
570#41—22no—
571#41—22no—
572#41—41no—
573#41—41no—
574#41—41no—
575#41—41no—
576#41—41no—
577#41—41no—
578#41—41no—
579#41—41no—
580#41—474no—
581#41—474no—
582#41—474no—
583#41—474no—
584#41—942no—
585#41—942no—
586#41—942no—
587#41—942no—
588#41—942no—
589#41—942no—
590#41—942no—
591#41—942no—
592#41—942no—
593#41—942no—
594#41—942no—
595#41—942no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—472no—
602C2×Q8—472no—
603C2×Q8—472no—
604C2×Q8—941no—
605C2×Q8—941no—
606C2×Q8—941no—
607C2×Q8C2×C4×D4712yes—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—41no—
616C2×D4—41no—
617C2×D4—41no—
618C2×D4—41no—
619C2×D4—472no—
620C2×D4—472no—
621C2×D4—472no—
622C2×D4—942no—
623C2×D4—942no—
624C2×D4—942no—
625C2×D4—942no—
626C2×D4—942no—
627C2×D4—942no—
628C2×D4—941no—
629C2×D4—941no—
630C2×D4—941no—
631C2×D4C2×C4×D4712yes—
632C22×C4—21no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—41no—
637C22×C4—41no—
638C22×C4—41no—
639C22×C4—41no—
640C22×C4—41no—
641C22×C4—948no—
642C22×C4—941no—
643C22×C4—942no—
644C22×C4—942no—
645C22×C4—942no—
646C22×C4—942no—
647C22×C4—942no—
648C22×C4—942no—
649C22×C4—942no—
650C22×C4C2×C4×D4711yescharacteristic
651C22×C4C2×C4×D4711yescharacteristic
652C22×C4#1062535011yescharacteristic
653C22×C4#1062535011yescharacteristic
654C22×C4D4×D4711yescharacteristic
655C22×C4D4×D4711yescharacteristic
656C22×C4D4×D4711yescharacteristic
657C22×C4D4×D4711yescharacteristic
658C22×C4D4×D4711yescharacteristic
659C22×C4D4×D4711yescharacteristic
660C22×C4#1062535211yescharacteristic
661C22×C4#1062535211yescharacteristic
662C22×C4C2×C22⋊D4711yescharacteristic
663C22×C4C23×D4711yescharacteristic
664Q16—948no—
665SD16—948no—
666SD16—948no—
667D8—948no—
668M16—474no—
669M16—942no—
670M16—942no—
671M16—942no—
672M16—942no—
673M16—942no—
674M16—1881no—
675M16—1881no—
676C2×C8—942no—
677C2×C8—942no—
678C2×C8—942no—
679C2×C8—942no—
680C2×C8—1881no—
681C2×C8—1881no—
682C4⋊C4—22no—
683C4⋊C4—22no—
684C4⋊C4—22no—
685C4⋊C4—41no—
686C4⋊C4—948no—
687C4⋊C4—942no—
688C4⋊C4—942no—
689C22⋊C4—22no—
690C22⋊C4—22no—
691C22⋊C4—41no—
692C22⋊C4—948no—
693C22⋊C4—942no—
694C22⋊C4—942no—
695C22⋊C4C2×C22⋊D4714yes—
696C42—22no—
697C42—22no—
698C42—22no—
699C42—41no—
700C42—474no—
701C42—948no—
702C42—942no—
703C23—22no—
704C23—41no—
705C23—41no—
706C23—81no—
707C23—82no—
708C23—942no—
709C23—942no—
710C23—942no—
711C23—3762no—
712C23C4×C22⋊D4711yescharacteristic
713C23C4×C22⋊D4711yescharacteristic
714C23#1309399211yescharacteristic
715C23#1309399211yescharacteristic
716C23#1309399511yescharacteristic
717C23#1309399511yescharacteristic
718C23C22×C22⋊D4711yescharacteristic
719Q8—22no—
720Q8—22no—
721Q8—41no—
722Q8—41no—
723Q8—474no—
724Q8—942no—
725Q8—942no—
726Q8—942no—
727D4—22no—
728D4—22no—
729D4—42no—
730D4—42no—
731D4—42no—
732D4—42no—
733D4—41no—
734D4—41no—
735D4—474no—
736D4—944no—
737D4—944no—
738D4—944no—
739D4—944no—
740D4—942no—
741D4—942no—
742D4—942no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—82no—
753C2×C4—82no—
754C2×C4—942no—
755C2×C4—942no—
756C2×C4—942no—
757C2×C4—944no—
758C2×C4—944no—
759C2×C4—944no—
760C2×C4—944no—
761C2×C4—944no—
762C2×C4—3768no—
763C2×C4—3762no—
764C2×C4C22⋊C4×D4711yescharacteristic
765C2×C4C22⋊C4×D4711yescharacteristic
766C2×C4C22⋊C4×D4711yescharacteristic
767C2×C4C22⋊C4×D4711yescharacteristic
768C2×C4(C22⋊D47)⋊C411yescharacteristic
769C2×C4(C22⋊D47)⋊C411yescharacteristic
770C2×C4(C22⋊D47)⋊C411yescharacteristic
771C2×C4(C22⋊D47)⋊C411yescharacteristic
772C2×C4C4×C22⋊D4711yescharacteristic
773C2×C4C4×C22⋊D4711yescharacteristic
774C2×C4#1309399211yescharacteristic
775C2×C4#1309399211yescharacteristic
776C2×C4#1309399511yescharacteristic
777C2×C4#1309399511yescharacteristic
778C2×C4#1309399711yescharacteristic
779C2×C4#1309399711yescharacteristic
780C2×C4#1309399711yescharacteristic
781C2×C4#1309399711yescharacteristic
782C2×C4#1309400611yescharacteristic
783C2×C4#1309400611yescharacteristic
784C2×C4#1309400611yescharacteristic
785C2×C4#1309400611yescharacteristic
786C2×C4C22×C4×D4711yescharacteristic
787C2×C4C2×D4×D4711yescharacteristic
788C2×C4C2×D4×D4711yescharacteristic
789C2×C4C2×D4×D4711yescharacteristic
790C2×C4C2×#1062535211yescharacteristic
791C2×C4C2×#1062535011yescharacteristic
792C8—944no—
793C8—1882no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—42no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22—944no—
806C22—3762no—
807C22—3762no—
808C22—1884no—
809C22#1568899911yescharacteristic
810C22#1568899911yescharacteristic
811C22#1568899911yescharacteristic
812C22#1568899911yescharacteristic
813C22C2×C4×C22⋊D4711yescharacteristic
814C22C2×#1309399211yescharacteristic
815C22C2×#1309399511yescharacteristic
816C4—44no—
817C4—42no—
818C4—82no—
819C4—944no—
820C4—1884no—
821C4#1568899911yescharacteristic
822C4#1568899911yescharacteristic
823C4#1568899911yescharacteristic
824C4#1568899911yescharacteristic
825C4C2×C22⋊C4×D4711yescharacteristic
826C4C2×(C22⋊D47)⋊C411yescharacteristic
827C4C2×#1309399711yescharacteristic
828C4C2×#1309400611yescharacteristic
829C2—21no—
830C2—21no—
831C2—21no—
832C2—21no—
833C2—21no—
834C2—21no—
835C2—21no—
836C2—82no—
837C2—1884no—
838C2C2×#1568899911yescharacteristic
subgroupG/H
centerC4C2×#13093997
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#410C2
socleC2×C47C2×#386
prime radicalC2×#15689921C2
cosocleC22×C4×C47C24
hypercenterC2×#410D47
hypocenterC47#21000
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
2. #20256589C2semidirect
3. C2×#15689141C2semidirect
4. C2×#15689140C2semidirect
5. #20243886C2semidirect
6. C2×#15688893C2semidirect
7. #20243097C2semidirect
8. C2×C47×#410C2semidirect
12. #15689921C4semidirect
14. C2×#13094055C4semidirect
16. C2×#13094050C4semidirect
27. #15689591C22semidirect
31. #15689141C22semidirect
35. C2×#13093951C22semidirect
36. #15688893C22semidirect
37. #15688882C22semidirect
42. C47×#410C22semidirect
61. #13094055C2×C4semidirect
65. #13094050C2×C4semidirect
82. C2×#10625329C2×C4semidirect
83. C2×#10625329C2×C4semidirect
119. C2×#41×C47C2×C4semidirect
121. C22×Q8×C47C2×C4semidirect
123. C22×D4×C47C2×C4semidirect
414. C2×#410D47semidirect
459. #410C2×D47semidirect
463. C47#21000semidirect
486. C2×#41C4×D47semidirect
489. C22×Q8C4×D47semidirect
493. C22×D4C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156899212
#202565892
C2×#156891412
C2×#156891402
#202438862
C2×#156888932
#202430972
C2×C47×#4102
#2100047