Finite Group Databasebeta

← #25098515

Subgroups — #25098515

Order 11008.

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×#14583697C211yesmaximal, characteristic
2#19147796C211yesmaximal, characteristic, complemented
3C2×#14582915C211yesmaximal, characteristic, complemented
4C2×#14582873C211yesmaximal, characteristic, complemented
5#19135099C218yesmaximal, complemented
6C2×#14582670C211yesmaximal, characteristic, complemented
7#19134305C211yesmaximal, characteristic, complemented
8C2×C43×#421C211yesmaximal, characteristic, complemented
9C22×#10621898C2211yescharacteristic
10#14583697—22no—
11#14583697—22no—
12#14583697C414yescomplemented
13#14583697C2214yes—
14C2×#13063356C412yescomplemented
15C2×#13063355—21no—
16C2×#13063351C412yescomplemented
17C2×#13063350—21no—
18C2×#13063345—22no—
19C22×#10621877C2211yescharacteristic
20#14583380—22no—
21#14583379—22no—
22#14583376—21no—
23#14583373—21no—
24#14583372—22no—
25C4×#10621898C2214yescomplemented
26#14583367—22no—
27C2×#13063284C2211yescharacteristic
28C2×#13063284C2211yescharacteristic
29#117×D43—22no—
30#14582915—22no—
31#14582915C2214yescomplemented
32C2×#13063251—22no—
33#14582873—22no—
34#14582873C2214yescomplemented
35C2×#13063240—22no—
36#14582670C2214yescomplemented
37#14582659C2214yescomplemented
38C22×#41×C43C2211yescharacteristic
39C22×M16×C43C2211yescharacteristic
40C2×#117×C43C2211yescharacteristic
41C43×#421—22no—
42C43×#421—22no—
43C2×#104×C43C2214yescomplemented
44C2×#10621898—21no—
45C2×#10621898—21no—
46C2×#10621898—21no—
47C2×#10621898—21no—
48C2×#10621898—21no—
49C2×#10621898—21no—
50C2×#10621898C2×C412yes—
51C2×#10621898C2×C412yes—
52C2×#10621898D412yes—
53C2×#10621898D412yes—
54C2×#10621898D412yes—
55C2×#10621898C2312yes—
56C22×Dic86D411yescharacteristic
57C22×D172D411yescharacteristic
58C22×C22⋊D43—21no—
59C22×C4×D43—21no—
60#13063356—24no—
61#13063356C2×C418yescomplemented
62#13063355—24no—
63#13063355—24no—
64#13063351—24no—
65#13063351C2×C418yescomplemented
66#13063350—24no—
67#13063350—24no—
68#13063345—28no—
69#13063345—28no—
70C2×#10621885—22no—
71C2×#10621883—22no—
72C2×#10621884—22no—
73C2×#10621882—22no—
74C2×#10621877—21no—
75C2×#10621877—21no—
76C2×#10621877—21no—
77C2×#10621877C2×C412yescomplemented
78C2×#10621877C2×C412yescomplemented
79C2×#10621877C2312yes—
80C22×C43⋊C8—21no—
81C4×Dic86—24no—
82#13063290—24no—
83C4×D172—24no—
84#13063287—24no—
85C4×C22⋊D43—28no—
86(C22⋊D43)⋊C4—28no—
87#13063284—21no—
88#13063284—21no—
89#13063284—21no—
90#13063284—21no—
91#13063284—21no—
92#13063284D412yes—
93#13063284C2312yes—
94#13063284C2312yes—
95#13063283—24no—
96#13063282—24no—
97#13063281—24no—
98C2×C4⋊Dic43—21no—
99C2×C4⋊Dic43—21no—
100C4⋊C4×D43—24no—
101C2×C22⋊Dic43—21no—
102C2×C22⋊Dic43D412yes—
103C22⋊C4×D43—24no—
104C2×C4×Dic43—21no—
105C2×C4×Dic43—21no—
106C42×D43—24no—
107#13063251—28no—
108#13063240—28no—
109C2×#41×C43—21no—
110C2×#41×C43—21no—
111C2×#41×C43—21no—
112C2×#41×C43—21no—
113C2×#41×C43—21no—
114C2×#41×C43—21no—
115C2×#41×C43—21no—
116C2×#41×C43—21no—
117C2×#41×C43—21no—
118C2×#41×C43—21no—
119C2×#41×C43C2×C412yescomplemented
120C2×#41×C43C2312yes—
121C22×Q8×C43C2×C411yescharacteristic, complemented
122C22×D4×C43—21no—
123C22×D4×C43C2×C411yescharacteristic, complemented
124C23×C4×C43—21no—
125C23×C4×C43C2311yescharacteristic
126C2×M16×C43—21no—
127C2×M16×C43—21no—
128C2×M16×C43—21no—
129C2×M16×C43—21no—
130C2×M16×C43—21no—
131C2×M16×C43C2312yes—
132C22×C8×C43—21no—
133#117×C43—21no—
134#117×C43—21no—
135#117×C43D412yes—
136#117×C43D412yes—
137C2×C4⋊C4×C43—21no—
138C2×C22⋊C4×C43—21no—
139C2×C42×C43C2312yes—
140#104×C43—28no—
141C24×C43—21no—
142C24×C43C2×D411yescharacteristic
143C23×D43—21no—
144#41×C43—22no—
145#41×C43—22no—
146#41×C43—22no—
147#41×C43—22no—
148#41×C43—22no—
149#41×C43—22no—
150#41×C43—22no—
151#41×C43—22no—
152#41×C43—41no—
153#41×C43—41no—
154#41×C43—41no—
155#41×C43—41no—
156#41×C43—41no—
157#41×C43—41no—
158#41×C43—41no—
159#41×C43—41no—
160C2×Q8×C43—21no—
161C2×Q8×C43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×Q8×C43C22×C412yes—
166C2×D4×C43—21no—
167C2×D4×C43—22no—
168C2×D4×C43—22no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43—41no—
174C2×D4×C43—41no—
175C2×D4×C43—41no—
176C2×D4×C43—41no—
177C2×D4×C43C22×C412yes—
178C22×C4×C43—22no—
179C22×C4×C43—22no—
180C22×C4×C43—21no—
181C22×C4×C43—22no—
182C22×C4×C43—41no—
183C22×C4×C43—41no—
184C22×C4×C43—41no—
185C22×C4×C43—41no—
186C22×C4×C43C22×C411yescharacteristic
187C22×C4×C43C22×C411yescharacteristic
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43#4111yescharacteristic
196C22×C4×C43#4111yescharacteristic
197C22×C4×C43#4111yescharacteristic
198C22×C4×C43#4111yescharacteristic
199C22×C4×C43C2411yescharacteristic
200C2×C22⋊D43—22no—
201C2×C22⋊D43—22no—
202C2×C22⋊D43—22no—
203C2×C22⋊D43—22no—
204C2×C22⋊D43—22no—
205C2×C22⋊D43—22no—
206C22×Dic43—21no—
207C22×Dic43—22no—
208C22×Dic43—41no—
209#10621898—22no—
210#10621898—22no—
211#10621898—22no—
212#10621898—22no—
213#10621898—22no—
214#10621898—22no—
215#10621898—22no—
216#10621898—22no—
217#10621898—22no—
218#10621898—22no—
219#10621898—22no—
220#10621898—22no—
221#10621898C22⋊C414yes—
222#10621898C22⋊C414yes—
223#10621898C22×C414yes—
224#10621898C2×D414yes—
225C2×D172—21no—
226C2×D172—21no—
227C2×D172—21no—
228C2×D172C22⋊C412yes—
229C2×D172C22⋊C412yes—
230C2×D172C2×D412yes—
231C2×C4×D43—22no—
232C2×C4×D43—22no—
233C2×C4×D43—22no—
234C2×C4×D43—22no—
235C2×C4×D43—22no—
236C2×C4×D43—22no—
237C2×C4×D43—28no—
238C2×Dic86—21no—
239C2×Dic86—21no—
240C2×Dic86—21no—
241C2×Dic86C22⋊C412yes—
242C2×Dic86C22⋊C412yes—
243C2×Dic86C2×D412yes—
244M16×C43—22no—
245M16×C43—22no—
246M16×C43—41no—
247M16×C43—41no—
248C2×C8×C43—22no—
249C2×C8×C43—41no—
250C2×C8×C43—41no—
251C4⋊C4×C43—22no—
252C4⋊C4×C43—22no—
253C22⋊C4×C43—22no—
254C22⋊C4×C43—22no—
255C42×C43—22no—
256C42×C43C2×D414yes—
257C22⋊Dic43—22no—
258C22⋊Dic43—22no—
259C22⋊Dic43—41no—
260C22⋊Dic43C2×D414yes—
261#10621885—28no—
262#10621884—28no—
263#10621883—28no—
264#10621882—28no—
265(C2×D43)⋊C4—28no—
266C4⋊Dic43—22no—
267C4⋊Dic43—22no—
268C4⋊Dic43—22no—
269C4⋊Dic43—41no—
270Dic43⋊C4—28no—
271C4×Dic43—28no—
272C4×Dic43—22no—
273C4×Dic43—22no—
274C4×Dic43—22no—
275C4×Dic43—41no—
276#10621877—22no—
277#10621877—22no—
278#10621877—22no—
279#10621877C22×C414yes—
280C2×C43⋊C8—22no—
281C2×C43⋊C8—22no—
282C2×C43⋊C8—22no—
283C23×C43—22no—
284C23×C43—41no—
285C23×C43—41no—
286C23×C43—81no—
287C23×C43—82no—
288C23×C43C4×D411yescharacteristic
289C23×C43C4×D411yescharacteristic
290C23×C43#12011yescharacteristic
291C23×C43#12011yescharacteristic
292C23×C43#12111yescharacteristic
293C23×C43#12111yescharacteristic
294C23×C43C22×D411yescharacteristic
295C22×D43—22no—
296C22×D43—22no—
297C22×D43—22no—
298C22×D43—82no—
299Q8×C43—22no—
300Q8×C43—22no—
301Q8×C43—41no—
302Q8×C43—41no—
303D4×C43—22no—
304D4×C43—22no—
305D4×C43—42no—
306D4×C43—42no—
307D4×C43—42no—
308D4×C43—42no—
309D4×C43—41no—
310D4×C43—41no—
311C2×C4×C43—22no—
312C2×C4×C43—24no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43—42no—
316C2×C4×C43—42no—
317C2×C4×C43—42no—
318C2×C4×C43—42no—
319C2×C4×C43—82no—
320C2×C4×C43C2×C22⋊C411yescharacteristic
321C2×C4×C43C2×C22⋊C411yescharacteristic
322C2×C4×C43C2×C22⋊C411yescharacteristic
323C2×C4×C43C2×C22⋊C411yescharacteristic
324C2×C4×C43C4×D411yescharacteristic
325C2×C4×C43C4×D411yescharacteristic
326C2×C4×C43C4×D411yescharacteristic
327C2×C4×C43C4×D411yescharacteristic
328C2×C4×C43C4×D411yescharacteristic
329C2×C4×C43C4×D411yescharacteristic
330C2×C4×C43#12011yescharacteristic
331C2×C4×C43#12011yescharacteristic
332C2×C4×C43#12111yescharacteristic
333C2×C4×C43#12111yescharacteristic
334C2×C4×C43#12111yescharacteristic
335C2×C4×C43#12111yescharacteristic
336C2×C4×C43#12111yescharacteristic
337C2×C4×C43#12111yescharacteristic
338C2×C4×C43#12311yescharacteristic
339C2×C4×C43#12311yescharacteristic
340C2×C4×C43#12311yescharacteristic
341C2×C4×C43#12311yescharacteristic
342C2×C4×C43C23×C411yescharacteristic
343C2×C4×C43C22×D411yescharacteristic
344C2×C4×C43C22×D411yescharacteristic
345C2×C4×C43C22×D411yescharacteristic
346C2×C4×C43C2×#4111yescharacteristic
347C2×C4×C43C2×#4111yescharacteristic
348C22⋊D43—24no—
349C22⋊D43—24no—
350C22⋊D43—24no—
351C22⋊D43—24no—
352C2×Dic43—22no—
353C2×Dic43—22no—
354C2×Dic43—22no—
355C2×Dic43—24no—
356C2×Dic43—42no—
357C2×Dic43—82no—
358C2×Dic43—82no—
359D172—22no—
360D172—22no—
361D172—22no—
362D172C2×C22⋊C414yes—
363C4×D43—24no—
364C4×D43—24no—
365C4×D43—24no—
366C4×D43—24no—
367C4×D43—88no—
368Dic86—22no—
369Dic86—22no—
370Dic86—22no—
371Dic86C2×C22⋊C414yes—
372C8×C43—42no—
373C43⋊C8—24no—
374#21000—431nomaximal, Sylow
375C22×C43—41no—
376C22×C43—41no—
377C22×C43—41no—
378C22×C43—41no—
379C22×C43—41no—
380C22×C43—41no—
381C22×C43—41no—
382C22×C43—42no—
383C22×C43—82no—
384C22×C43—82no—
385C22×C43—82no—
386C22×C43#38611yescharacteristic
387C22×C43#38611yescharacteristic
388C22×C43#38611yescharacteristic
389C22×C43#38611yescharacteristic
390C22×C43C2×C4×D411yescharacteristic
391C22×C43C2×#12011yescharacteristic
392C22×C43C2×#12111yescharacteristic
393C2×D43—24no—
394C2×D43—44no—
395C2×D43—82no—
396C2×D43—82no—
397C4×C43—44no—
398C4×C43—42no—
399C4×C43#38611yescharacteristic
400C4×C43#38611yescharacteristic
401C4×C43#38611yescharacteristic
402C4×C43#38611yescharacteristic
403C4×C43C22×C22⋊C411yescharacteristic
404C4×C43C2×C4×D411yescharacteristic
405C4×C43C2×#12111yescharacteristic
406C4×C43C2×#12311yescharacteristic
407Dic43—24no—
408Dic43—44no—
409Dic43—82no—
410C2×#575—431no—
411#3428—431no—
412C2×#421—431no—
413C2×#421D4311yescharacteristic, complemented
414C2×#410—431no—
415#1906—438no—
416C2×#344—431no—
417#1733—431no—
418C2×C43—21no—
419C2×C43—21no—
420C2×C43—21no—
421C2×C43—21no—
422C2×C43—21no—
423C2×C43—21no—
424C2×C43—21no—
425C2×C43—82no—
426C2×C43C2×#38611yescharacteristic
427D43—44no—
428C22×#41—431no—
429C22×#41C2×D4311yescharacteristic
430#575—434no—
431#575—434no—
432#575—862no—
433#575—862no—
434C2×#137—432no—
435C2×#137—861no—
436C2×AGL(1,ℤ/8)—432no—
437C2×AGL(1,ℤ/8)—861no—
438C2×#135—862no—
439C22×M16—431no—
440C22×M16C2×D4311yescharacteristic
441#520—862no—
442#520—862no—
443#519—861no—
444#518—862no—
445#518—861no—
446C4×#41—434no—
447C4×#41—862no—
448C2×#117—431no—
449C2×#117—431no—
450C2×#117—862no—
451C2×#117C2×D4311yescharacteristic
452#421—22no—
453#421—22no—
454#421—434no—
455#421—862no—
456C2×#104—862no—
457C2×#104C2×D4314yescomplemented
458#410—434no—
459#410—862no—
460C2×#99—862no—
461#344—434no—
462#339—434no—
463C43#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—432no—
475C2×#41—432no—
476C2×#41—432no—
477C2×#41—432no—
478C2×#41—432no—
479C2×#41—432no—
480C2×#41—861no—
481C2×#41—861no—
482C2×#41—861no—
483C2×#41—861no—
484C2×#41—861no—
485C2×#41—861no—
486C2×#41C4×D4312yescomplemented
487C2×#41C22×D4312yes—
488C22×Q8—431no—
489C22×Q8C4×D4311yescharacteristic, complemented
490C22×D4—21no—
491C22×D4—431no—
492C22×D4—861no—
493C22×D4C4×D4311yescharacteristic, complemented
494C23×C4—21no—
495C23×C4—861no—
496C23×C4C22×D4311yescharacteristic
497#137—438no—
498#137—864no—
499#137—864no—
500#137—864no—
501AGL(1,ℤ/8)—438no—
502AGL(1,ℤ/8)—864no—
503AGL(1,ℤ/8)—864no—
504AGL(1,ℤ/8)—864no—
505#135—868no—
506#135—868no—
507C2×Q16—862no—
508C2×SD16—862no—
509C2×SD16—862no—
510C2×D8—862no—
511C2×M16—21no—
512C2×M16—21no—
513C2×M16—21no—
514C2×M16—21no—
515C2×M16—21no—
516C2×M16—432no—
517C2×M16—432no—
518C2×M16—432no—
519C2×M16—861no—
520C2×M16—861no—
521C2×M16—861no—
522C2×M16C22×D4312yes—
523C22×C8—21no—
524C22×C8—861no—
525C4×Q8—864no—
526C4×Q8—864no—
527C4×D4—864no—
528C4×D4—868no—
529C4×D4—868no—
530C4×D4—864no—
531#117—21no—
532#117—21no—
533#117—432no—
534#117—432no—
535#117—432no—
536#117—864no—
537#117—864no—
538#117—861no—
539#117—861no—
540#117—861no—
541#117—864no—
542#117—861no—
543#117—861no—
544#117C22⋊D4312yes—
545#117C22⋊D4312yes—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—864no—
548C2×C4⋊C4—861no—
549C2×C4⋊C4—861no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—432no—
552C2×C22⋊C4—864no—
553C2×C22⋊C4—861no—
554C2×C42—861no—
555C2×C42—864no—
556C2×C42—861no—
557C2×C42C22×D4312yes—
558#104—28no—
559#104—868no—
560#99—868no—
561C24—21no—
562C24—861no—
563C24D4×D4311yescharacteristic
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—434no—
581#41—434no—
582#41—434no—
583#41—434no—
584#41—862no—
585#41—862no—
586#41—862no—
587#41—862no—
588#41—862no—
589#41—862no—
590#41—862no—
591#41—862no—
592#41—862no—
593#41—862no—
594#41—862no—
595#41—862no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—432no—
602C2×Q8—432no—
603C2×Q8—432no—
604C2×Q8—861no—
605C2×Q8—861no—
606C2×Q8—861no—
607C2×Q8C2×C4×D4312yes—
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—432no—
620C2×D4—432no—
621C2×D4—432no—
622C2×D4—862no—
623C2×D4—862no—
624C2×D4—862no—
625C2×D4—862no—
626C2×D4—862no—
627C2×D4—862no—
628C2×D4—861no—
629C2×D4—861no—
630C2×D4—861no—
631C2×D4C2×C4×D4312yes—
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—868no—
641C22×C4—861no—
642C22×C4—862no—
643C22×C4—862no—
644C22×C4—862no—
645C22×C4—862no—
646C22×C4—862no—
647C22×C4—862no—
648C22×C4—862no—
649C22×C4—1721no—
650C22×C4C2×C4×D4311yescharacteristic
651C22×C4C2×C4×D4311yescharacteristic
652C22×C4#1062189811yescharacteristic
653C22×C4#1062189811yescharacteristic
654C22×C4D4×D4311yescharacteristic
655C22×C4D4×D4311yescharacteristic
656C22×C4D4×D4311yescharacteristic
657C22×C4D4×D4311yescharacteristic
658C22×C4D4×D4311yescharacteristic
659C22×C4#1062190011yescharacteristic
660C22×C4#1062190011yescharacteristic
661C22×C4C2×C22⋊D4311yescharacteristic
662C22×C4C2×C22⋊D4311yescharacteristic
663C22×C4C23×D4311yescharacteristic
664Q16—868no—
665SD16—868no—
666SD16—868no—
667D8—868no—
668M16—22no—
669M16—22no—
670M16—41no—
671M16—41no—
672M16—434no—
673M16—862no—
674M16—862no—
675M16—862no—
676C2×C8—22no—
677C2×C8—41no—
678C2×C8—41no—
679C2×C8—862no—
680C2×C8—862no—
681C2×C8—862no—
682C4⋊C4—22no—
683C4⋊C4—22no—
684C4⋊C4—868no—
685C4⋊C4—862no—
686C4⋊C4—862no—
687C4⋊C4—862no—
688C4⋊C4—1721no—
689C22⋊C4—22no—
690C22⋊C4—22no—
691C22⋊C4—434no—
692C22⋊C4—868no—
693C22⋊C4—862no—
694C22⋊C4—862no—
695C22⋊C4—1721no—
696C42—22no—
697C42—868no—
698C42—862no—
699C42—862no—
700C42—862no—
701C42—1721no—
702C42C2×C22⋊D4314yes—
703C23—22no—
704C23—41no—
705C23—41no—
706C23—81no—
707C23—82no—
708C23—862no—
709C23—862no—
710C23—862no—
711C23—3442no—
712C23(C22⋊D43)⋊C411yescharacteristic
713C23(C22⋊D43)⋊C411yescharacteristic
714C23#1306329311yescharacteristic
715C23#1306329311yescharacteristic
716C23#1306329811yescharacteristic
717C23#1306329811yescharacteristic
718C23C2×D4×D4311yescharacteristic
719Q8—22no—
720Q8—22no—
721Q8—41no—
722Q8—41no—
723Q8—434no—
724Q8—862no—
725Q8—862no—
726Q8—862no—
727D4—22no—
728D4—22no—
729D4—42no—
730D4—42no—
731D4—42no—
732D4—42no—
733D4—41no—
734D4—41no—
735D4—434no—
736D4—864no—
737D4—864no—
738D4—864no—
739D4—864no—
740D4—862no—
741D4—862no—
742D4—862no—
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—82no—
752C2×C4—862no—
753C2×C4—862no—
754C2×C4—862no—
755C2×C4—864no—
756C2×C4—864no—
757C2×C4—864no—
758C2×C4—864no—
759C2×C4—864no—
760C2×C4—3448no—
761C2×C4—3442no—
762C2×C4—3442no—
763C2×C4—1722no—
764C2×C4C22⋊C4×D4311yescharacteristic
765C2×C4C22⋊C4×D4311yescharacteristic
766C2×C4C22⋊C4×D4311yescharacteristic
767C2×C4C22⋊C4×D4311yescharacteristic
768C2×C4(C22⋊D43)⋊C411yescharacteristic
769C2×C4(C22⋊D43)⋊C411yescharacteristic
770C2×C4C4×C22⋊D4311yescharacteristic
771C2×C4C4×C22⋊D4311yescharacteristic
772C2×C4C4×C22⋊D4311yescharacteristic
773C2×C4C4×C22⋊D4311yescharacteristic
774C2×C4#1306329311yescharacteristic
775C2×C4#1306329311yescharacteristic
776C2×C4#1306329611yescharacteristic
777C2×C4#1306329611yescharacteristic
778C2×C4#1306329611yescharacteristic
779C2×C4#1306329611yescharacteristic
780C2×C4#1306329811yescharacteristic
781C2×C4#1306329811yescharacteristic
782C2×C4#1306330711yescharacteristic
783C2×C4#1306330711yescharacteristic
784C2×C4#1306330711yescharacteristic
785C2×C4#1306330711yescharacteristic
786C2×C4C22×C4×D4311yescharacteristic
787C2×C4C2×D4×D4311yescharacteristic
788C2×C4C2×D4×D4311yescharacteristic
789C2×C4C22×C22⋊D4311yescharacteristic
790C2×C4C2×#1062190011yescharacteristic
791C2×C4C2×#1062189811yescharacteristic
792C8—42no—
793C8—864no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—42no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22—864no—
806C22—3442no—
807C22—3442no—
808C22—1724no—
809C22#1458277511yescharacteristic
810C22#1458277511yescharacteristic
811C22#1458277511yescharacteristic
812C22#1458277511yescharacteristic
813C22C2×(C22⋊D43)⋊C411yescharacteristic
814C22C2×#1306329311yescharacteristic
815C22C2×#1306329811yescharacteristic
816C4—44no—
817C4—42no—
818C4—864no—
819C4—3442no—
820C4—1724no—
821C4#1458277511yescharacteristic
822C4#1458277511yescharacteristic
823C4#1458277511yescharacteristic
824C4#1458277511yescharacteristic
825C4C2×C22⋊C4×D4311yescharacteristic
826C4C2×C4×C22⋊D4311yescharacteristic
827C4C2×#1306329611yescharacteristic
828C4C2×#1306330711yescharacteristic
829C2—21no—
830C2—21no—
831C2—21no—
832C2—21no—
833C2—21no—
834C2—21no—
835C2—21no—
836C2—82no—
837C2—1724no—
838C2C2×#1458277511yescharacteristic
subgroupG/H
centerC4C2×#13063296
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#421C2
socleC2×C43C2×#386
prime radicalC2×#14583697C2
cosocleC22×C4×C43C24
hypercenterC2×#421D43
hypocenterC43#21000
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. #19147796C2semidirect
3. C2×#14582915C2semidirect
4. C2×#14582873C2semidirect
5. #19135099C2semidirect
6. C2×#14582670C2semidirect
7. #19134305C2semidirect
8. C2×C43×#421C2semidirect
12. #14583697C4semidirect
14. C2×#13063356C4semidirect
16. C2×#13063351C4semidirect
25. C4×#10621898C22semidirect
31. #14582915C22semidirect
34. #14582873C22semidirect
36. #14582670C22semidirect
37. #14582659C22semidirect
43. C2×#104×C43C22semidirect
61. #13063356C2×C4semidirect
65. #13063351C2×C4semidirect
77. C2×#10621877C2×C4semidirect
78. C2×#10621877C2×C4semidirect
119. C2×#41×C43C2×C4semidirect
121. C22×Q8×C43C2×C4semidirect
123. C22×D4×C43C2×C4semidirect
413. C2×#421D43semidirect
457. C2×#104C2×D43semidirect
463. C43#21000semidirect
486. C2×#41C4×D43semidirect
489. C22×Q8C4×D43semidirect
493. C22×D4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145836972
#191477962
C2×#145829152
C2×#145828732
#191350992
C2×#145826702
#191343052
C2×C43×#4212
#2100043