Finite Group Databasebeta

← #25979169

Subgroups — #25979169

Order 11008.

2010 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148629C212yesmaximal, complemented
2#19147570C211yesmaximal, characteristic, complemented
3#19147463C211yesmaximal, characteristic, complemented
4#19147304C212yesmaximal, complemented
5#19147018C211yesmaximal, characteristic, complemented
6#19146998C212yesmaximal, complemented
7#19146838C212yesmaximal, complemented
8#19146738C214yesmaximal, complemented
9D4×D344C212yesmaximal, complemented
10D4×D344C211yesmaximal, characteristic, complemented
11#19145245C212yesmaximal, complemented
12#19145174C211yesmaximal, characteristic, complemented
13#19144839C214yesmaximal, complemented
14#19144687C212yesmaximal, complemented
15#19143448C212yesmaximal, complemented
16C2×C4×D344C211yesmaximal, characteristic, complemented
17C43×#2966C211yesmaximal, characteristic, complemented
18C22×D344C2212yes—
19C22×D344C2211yescharacteristic
20#14583614C2212yescomplemented
21#14583609C2212yescomplemented
22#14583602—22no—
23#14583595C2214yescomplemented
24#14583571C2212yescomplemented
25#14583542—22no—
26#14583541—24no—
27D4×D172C2212yescomplemented
28D4×D172C2214yescomplemented
29#14583504C2214yescomplemented
30#14583488—24no—
31#14583449C2212yescomplemented
32#14583412—22no—
33#121×D43—22no—
34#14583373C2214yescomplemented
35C2×C4×D172C2212yescomplemented
36#14583304C2211yescharacteristic, complemented
37#14583301C2212yescomplemented
38#14583276C2212yescomplemented
39#14583276C2211yescharacteristic, complemented
40#14583264C2214yescomplemented
41#14583246C2212yescomplemented
42#14583224C2214yescomplemented
43#14583224C2214yescomplemented
44#14583218C2214yescomplemented
45#14583200C2214yescomplemented
46#14583200C2214yescomplemented
47#14583190C2212yescomplemented
48#14583190C2212yescomplemented
49#14583152C2214yescomplemented
50#14583135C2212yescomplemented
51#14583135C2212yescomplemented
52#14583135C2212yescomplemented
53#14583135C2212yescomplemented
54#14583095C2214yescomplemented
55#14583095C2212yescomplemented
56#14583095C2212yescomplemented
57#14583095C2214yescomplemented
58#14583035C2214yescomplemented
59#14583035C2214yescomplemented
60#14583035C2214yescomplemented
61#14583012C2214yescomplemented
62#14583012C2214yescomplemented
63#14583012C2214yescomplemented
64C4×D344C2211yescharacteristic
65C4×D344C2212yes—
66C4×D344C2211yescharacteristic
67C4×D344C2211yescharacteristic, complemented
68C4×D344C2212yescomplemented
69C4×D344C2212yescomplemented
70C4×D344C2211yescharacteristic, complemented
71C4×D344C2212yescomplemented
72C4×D344C2212yescomplemented
73C4×D344C2212yescomplemented
74#14582937C2212yescomplemented
75C2×#13063259C2211yescharacteristic, complemented
76#14582905C2214yescomplemented
77C2×#13063247C2212yescomplemented
78C43×#529C2211yescharacteristic
79C43×#446C2211yescharacteristic, complemented
80C8×Q8×C43C2211yescharacteristic, complemented
81C43×#436C2211yescharacteristic, complemented
82C43×#435C2212yescomplemented
83C8×D4×C43C2211yescharacteristic, complemented
84C8×D4×C43C2212yescomplemented
85C43×#433C2212yescomplemented
86C43×#432C2211yescharacteristic, complemented
87C43×#405C2212yescomplemented
88C2×C4×C8×C43C2211yescharacteristic, complemented
89C2×#10621902—22no—
90C2×#10621898—22no—
91C22×D172C2312yes—
92C22×D172C2314yes—
93C2×D4×D43—24no—
94C2×D4×D43—22no—
95C22×C4×D43—22no—
96C2×D344—28no—
97C2×D344—24no—
98C2×D344C2312yes—
99C2×D344C2314yes—
100C2×D344C2311yescharacteristic
101C2×D344C2312yes—
102C2×D344C2312yes—
103C2×D344C2314yes—
104C2×D344C2311yescharacteristic
105#13063325C2312yes—
106#13063322C2312yes—
107#13063322C2314yes—
108#13063320—24no—
109#13063317C2314yes—
110#13063313—22no—
111#13063311—24no—
112#13063310—24no—
113#13063310—24no—
114#13063307—24no—
115#13063303—24no—
116#13063301—22no—
117#13063300—22no—
118#13063300—24no—
119#13063300—22no—
120#13063300—24no—
121#13063299—22no—
122#13063299C2314yes—
123#13063299C2314yes—
124#13063299C2314yes—
125#13063298—24no—
126#13063298—24no—
127#13063297—24no—
128#13063296—22no—
129#13063295—24no—
130#13063295—24no—
131#13063295—24no—
132C4×D172—22no—
133C4×D172—22no—
134C4×D172—22no—
135C4×D172C2314yes—
136C4×D172C2312yes—
137C4×D172C2312yes—
138C4×D172C2314yes—
139C4×D172C2312yes—
140C4×D172C2312yes—
141C4×D172C2314yes—
142#13063287—24no—
143#13063287—24no—
144(C22⋊D43)⋊C4—24no—
145#13063284C2314yes—
146#13063283—22no—
147C2×C4⋊Dic43C2312yes—
148C4⋊C4×D43—22no—
149C2×(C2×D43)⋊C4—22no—
150C22⋊C4×D43—24no—
151C22⋊C4×D43—24no—
152#13063259C2311yescharacteristic
153#13063259C2312yes—
154#13063259C2312yes—
155#13063259C2311yescharacteristic
156#13063259C2312yes—
157#13063257C2314yes—
158#13063257C2314yes—
159#13063247C2312yes—
160#13063247C2314yes—
161#13063247C2314yes—
162#13063247C2314yes—
163#13063247C2314yes—
164#13063247C2314yes—
165#13063247C2312yes—
166#13063247C2312yes—
167#13063247C2312yes—
168#13063247C2314yes—
169C2×M16×C43C2312yes—
170C22×C8×C43C2311yescharacteristic
171C22×C8×C43C2312yes—
172C22×C8×C43C2311yescharacteristic
173#126×C43D412yes—
174#125×C43D411yescharacteristic
175#124×C43D411yescharacteristic
176#123×C43D412yes—
177C22⋊Q8×C43D411yescharacteristic
178#121×C43D411yescharacteristic
179C4×Q8×C43C2311yescharacteristic
180C4×D4×C43C2312yes—
181C4×D4×C43C2311yescharacteristic
182#117×C43C2312yes—
183C2×C42×C43C2311yescharacteristic
184C4⋊C8×C43C2311yescharacteristic
185C4⋊C8×C43C2311yescharacteristic
186C4⋊C8×C43C2312yes—
187C4⋊C8×C43C2312yes—
188C22⋊C8×C43C2312yes—
189C22⋊C8×C43C2312yes—
190C22⋊C8×C43C2312yes—
191#97×C43C2312yes—
192#97×C43C2312yes—
193C4×C8×C43C2312yes—
194C4×C8×C43C2311yescharacteristic
195C4×C8×C43C2311yescharacteristic
196C4×C8×C43C2311yescharacteristic
197C4×C8×C43C2311yescharacteristic
198C23×D43—22no—
199C23×D43—24no—
200C2×Q8×C43C2×D411yescharacteristic
201C2×D4×C43C2×D412yes—
202C2×D4×C43C2×D411yescharacteristic
203C22×C4×C43C2×D411yescharacteristic
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43C2411yescharacteristic
206C22×C4×C43C2412yes—
207C2×C22⋊D43—24no—
208C2×C22⋊D43—24no—
209C2×C22⋊D43—24no—
210C22×Dic43—22no—
211#10621902—84no—
212D4×D43—88no—
213D4×D43—84no—
214#10621898—84no—
215C2×D172—24no—
216C2×D172—22no—
217C2×D172—22no—
218C2×D172—24no—
219C2×D172—22no—
220C2×D172—24no—
221C2×D172—24no—
222C2×D172—28no—
223C2×D172—42no—
224C2×D172—44no—
225C2×D172C2412yes—
226C2×D172C2414yes—
227C2×D172C2412yes—
228C2×C4×D43—22no—
229C2×C4×D43—22no—
230C2×C4×D43—22no—
231C2×C4×D43—24no—
232C2×C4×D43—24no—
233C2×C4×D43—24no—
234C2×C4×D43—22no—
235C2×C4×D43—84no—
236C2×Dic86—22no—
237M16×C43—42no—
238C2×C8×C43—22no—
239C2×C8×C43—24no—
240C2×C8×C43—41no—
241C2×C8×C43C2411yescharacteristic
242C2×C8×C43C2411yescharacteristic
243C2×C8×C43C2411yescharacteristic
244C2×C8×C43C2412yes—
245C2×C8×C43C2412yes—
246C2×C8×C43C2411yescharacteristic
247C4⋊C4×C43C2×D412yes—
248C4⋊C4×C43C2×D412yes—
249C4⋊C4×C43C2×D411yescharacteristic
250C4⋊C4×C43C2×D412yes—
251C4⋊C4×C43C2×D411yescharacteristic
252C4⋊C4×C43C2×D412yes—
253C22⋊C4×C43C2×D412yes—
254C22⋊C4×C43C2×D412yes—
255C22⋊C4×C43C2×D412yes—
256C22⋊C4×C43C2×D412yes—
257C22⋊C4×C43C2×D412yes—
258C42×C43C2×D411yescharacteristic
259C42×C43C2×D411yescharacteristic
260C42×C43C2411yescharacteristic
261C42×C43C2411yescharacteristic
262C42×C43C2412yes—
263C22⋊Dic43—24no—
264(C2×D43)⋊C4—22no—
265(C2×D43)⋊C4—24no—
266(C2×D43)⋊C4—24no—
267(C2×D43)⋊C4—24no—
268(C2×D43)⋊C4—22no—
269(C2×D43)⋊C4—22no—
270(C2×D43)⋊C4—22no—
271(C2×D43)⋊C4—24no—
272(C2×D43)⋊C4—24no—
273(C2×D43)⋊C4—24no—
274C4⋊Dic43—22no—
275C4⋊Dic43—22no—
276C4⋊Dic43C2412yes—
277C4⋊Dic43C2412yes—
278C4⋊Dic43C2414yes—
279Dic43⋊C4—24no—
280Dic43⋊C4—24no—
281C4×Dic43—24no—
282D344—24no—
283D344—28no—
284D344—24no—
285D344—22no—
286D344—42no—
287D344—44no—
288D344#4114yescomplemented
289C23×C43C22×D412yes—
290C23×C43C22×D411yescharacteristic
291C22×D43—22no—
292C22×D43—22no—
293C22×D43—24no—
294C22×D43—44no—
295C22×D43—48no—
296C22×D43—44no—
297C22×D43—82no—
298C22×D43—84no—
299C22×D43—84no—
300Q8×C43—22no—
301D4×C43—24no—
302D4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—22no—
305C2×C4×C43—21no—
306C2×C4×C43—22no—
307C2×C4×C43—21no—
308C2×C4×C43—22no—
309C2×C4×C43C22×D412yes—
310C2×C4×C43C22×D412yes—
311C2×C4×C43C22×D412yes—
312C2×C4×C43C22×D411yescharacteristic
313C2×C4×C43C22×D411yescharacteristic
314C2×C4×C43C22×D411yescharacteristic
315C2×C4×C43C22×D411yescharacteristic
316C2×C4×C43C22×D411yescharacteristic
317C2×C4×C43C2511yescharacteristic
318C22⋊D43—48no—
319C22⋊D43—84no—
320C22⋊D43—84no—
321C2×Dic43—22no—
322C2×Dic43—24no—
323C2×Dic43—22no—
324C2×Dic43—82no—
325D172—22no—
326D172—24no—
327D172—22no—
328D172—22no—
329D172—24no—
330D172—48no—
331D172—44no—
332D172—44no—
333D172—82no—
334D172—84no—
335D172—84no—
336D172C2×#4114yes—
337C4×D43—44no—
338C4×D43—44no—
339C4×D43—82no—
340C4×D43—82no—
341C4×D43—84no—
342C4×D43—84no—
343C4×D43—84no—
344Dic86—82no—
345C8×C43—21no—
346C8×C43—22no—
347C8×C43—21no—
348C8×C43—22no—
349C8×C43—21no—
350C8×C43C2×#4112yes—
351#61480—431nomaximal, Sylow
352C22×C43—21no—
353C22×C43—21no—
354C22×C43—22no—
355C22×C43—22no—
356C22×C43—22no—
357C22×C43#57612yes—
358C22×C43C23×D411yescharacteristic
359C2×D43—24no—
360C2×D43—42no—
361C2×D43—42no—
362C2×D43—42no—
363C2×D43—44no—
364C2×D43—42no—
365C2×D43—42no—
366C2×D43—44no—
367C2×D43—44no—
368C2×D43—88no—
369C2×D43—168no—
370C4×C43—21no—
371C4×C43—22no—
372C4×C43—21no—
373C4×C43—21no—
374C4×C43—21no—
375C4×C43—22no—
376C4×C43—22no—
377C4×C43#57612yes—
378C4×C43C22×#4111yescharacteristic
379C4×C43#58511yescharacteristic
380Dic43—44no—
381Dic43—42no—
382Dic43—42no—
383#3519—432no—
384#3391—431no—
385#3380—431no—
386#3366—432no—
387#3341—431no—
388#3339—432no—
389#3325—432no—
390#3318—434no—
391D4×D8—432no—
392D4×D8—431no—
393#3176—432no—
394#3169—431no—
395#3122—434no—
396#3109—432no—
397#2966D4311yescharacteristic, complemented
398#2948—432no—
399C2×C4×D8—431no—
400C2×C43—22no—
401C2×C43—42no—
402C2×C43D4×#4111yescharacteristic
403C2×C43C2×#57611yescharacteristic
404C2×C43C2×#57611yescharacteristic
405D43—44no—
406D43—82no—
407D43—84no—
408C22×D8—431no—
409C22×D8—432no—
410#555—432no—
411#554—432no—
412#553—434no—
413#553—862no—
414#550—432no—
415#546—862no—
416#546—864no—
417D42—434no—
418D42—432no—
419#540—434no—
420#538—864no—
421#532—432no—
422#529C2×D4311yescharacteristic
423#525—862no—
424C2×#121—862no—
425#518—434no—
426C2×C4×D4—432no—
427#500—431no—
428#499—432no—
429#493—431no—
430#493—432no—
431#490—434no—
432#486—432no—
433#482—434no—
434#482—434no—
435#481—434no—
436#478—434no—
437#478—434no—
438#476—432no—
439#476—432no—
440#469—434no—
441#466—432no—
442#466—432no—
443#466—432no—
444#466—432no—
445#459—432no—
446#459—432no—
447#459—434no—
448#459—434no—
449#447—434no—
450#447—434no—
451#447—434no—
452#446C2×D4311yescharacteristic, complemented
453C8×Q8C2×D4311yescharacteristic, complemented
454#442—434no—
455#442—434no—
456#442—434no—
457C4×D8—432no—
458C4×D8—431no—
459C4×D8—432no—
460C4×D8—432no—
461C4×D8—432no—
462C4×D8—431no—
463C4×D8—432no—
464C4×D8—432no—
465C4×D8—431no—
466C4×D8—431no—
467#436C2×D4311yescharacteristic, complemented
468#435C2×D4312yescomplemented
469C8×D4C2×D4312yescomplemented
470C8×D4C2×D4311yescharacteristic, complemented
471#433C2×D4312yescomplemented
472#432C2×D4311yescharacteristic, complemented
473#427—432no—
474C2×#107—431no—
475#418—434no—
476C2×#102—432no—
477#405C2×D4312yescomplemented
478C2×C4×C8C2×D4311yescharacteristic, complemented
479C43#6148011yescharacteristic, complemented, Sylow
480C2×#41—862no—
481C2×#41—862no—
482C22×D4—432no—
483C22×D4—434no—
484C22×D4—864no—
485C22×D4—862no—
486C23×C4—862no—
487C2×D8—431no—
488C2×D8—432no—
489C2×D8—431no—
490C2×D8—432no—
491C2×D8—434no—
492C2×D8—432no—
493C2×D8—434no—
494C2×D8—864no—
495C2×D8—868no—
496C2×M16C22×D4312yes—
497C22×C8C22×D4311yescharacteristic
498C22×C8C22×D4312yes—
499C22×C8C22×D4311yescharacteristic
500C4⋊Q8—432no—
501#127—432no—
502#127—434no—
503#126—864no—
504#126D17212yes—
505#125—434no—
506#125D17211yescharacteristic
507#124—864no—
508#124—862no—
509#124D17211yescharacteristic
510#123—864no—
511#123—864no—
512#123—864no—
513#123D17212yes—
514C22⋊Q8—862no—
515C22⋊Q8—864no—
516C22⋊Q8D17211yescharacteristic
517#121—434no—
518#121—434no—
519#121—434no—
520#121—864no—
521#121—862no—
522#121—862no—
523#121—862no—
524#121—862no—
525#121—864no—
526#121—864no—
527#121—864no—
528#121—864no—
529#121D17211yescharacteristic
530#120—864no—
531#120—864no—
532#120—864no—
533C4×Q8C22×D4311yescharacteristic
534C4×D4—432no—
535C4×D4—432no—
536C4×D4—432no—
537C4×D4—432no—
538C4×D4—434no—
539C4×D4—434no—
540C4×D4—434no—
541C4×D4—864no—
542C4×D4—864no—
543C4×D4—864no—
544C4×D4—862no—
545C4×D4—862no—
546C4×D4—862no—
547C4×D4C22×D4312yes—
548C4×D4C22×D4311yescharacteristic
549#117—434no—
550#117—862no—
551#117C22×D4312yes—
552C2×C4⋊C4—432no—
553C2×C4⋊C4—862no—
554C2×C22⋊C4—862no—
555C2×C22⋊C4—864no—
556C2×C22⋊C4—864no—
557C2×C42C22×D4311yescharacteristic
558#107—431no—
559#107—431no—
560#107—432no—
561#107—432no—
562#107—432no—
563#106—434no—
564#106—434no—
565C4⋊C8C22×D4311yescharacteristic
566C4⋊C8C22×D4311yescharacteristic
567C4⋊C8C22×D4312yes—
568C4⋊C8C22×D4312yes—
569#102—432no—
570#102—432no—
571#102—432no—
572#102—432no—
573#102—434no—
574#102—434no—
575#102—434no—
576#102—434no—
577#102—434no—
578#102—434no—
579C22⋊C8C22×D4312yes—
580C22⋊C8C22×D4312yes—
581C22⋊C8C22×D4312yes—
582#97C22×D4312yes—
583#97C22×D4312yes—
584C4×C8C22×D4311yescharacteristic
585C4×C8C22×D4311yescharacteristic
586C4×C8C22×D4311yescharacteristic
587C4×C8C22×D4311yescharacteristic
588C4×C8C22×D4312yes—
589C24—864no—
590C24—862no—
591#41—3444no—
592#41—3444no—
593C2×Q8—862no—
594C2×Q8C2×D17211yescharacteristic
595C2×D4—432no—
596C2×D4—432no—
597C2×D4—434no—
598C2×D4—864no—
599C2×D4—868no—
600C2×D4—864no—
601C2×D4—864no—
602C2×D4—864no—
603C2×D4—864no—
604C2×D4—862no—
605C2×D4—864no—
606C2×D4—864no—
607C2×D4—862no—
608C2×D4—862no—
609C2×D4—3448no—
610C2×D4—3444no—
611C2×D4—1722no—
612C2×D4—1724no—
613C2×D4C2×D17212yes—
614C2×D4C2×D17211yescharacteristic
615C22×C4—862no—
616C22×C4—862no—
617C22×C4—864no—
618C22×C4—864no—
619C22×C4—864no—
620C22×C4—862no—
621C22×C4—862no—
622C22×C4—862no—
623C22×C4—3444no—
624C22×C4C2×D17211yescharacteristic
625C22×C4C2×D17211yescharacteristic
626C22×C4C23×D4311yescharacteristic
627C22×C4C23×D4312yes—
628D8—434no—
629D8—864no—
630D8—868no—
631D8—862no—
632D8—864no—
633D8—1722no—
634D8—1724no—
635M16—42no—
636C2×C8—22no—
637C2×C8—24no—
638C2×C8—41no—
639C2×C8C23×D4311yescharacteristic
640C2×C8C23×D4311yescharacteristic
641C2×C8C23×D4311yescharacteristic
642C2×C8C23×D4312yes—
643C2×C8C23×D4312yes—
644C2×C8C23×D4311yescharacteristic
645C4⋊C4—432no—
646C4⋊C4—432no—
647C4⋊C4—434no—
648C4⋊C4—862no—
649C4⋊C4—862no—
650C4⋊C4—864no—
651C4⋊C4—864no—
652C4⋊C4C2×D17211yescharacteristic
653C4⋊C4C2×D17211yescharacteristic
654C4⋊C4C2×D17212yes—
655C4⋊C4C2×D17212yes—
656C4⋊C4C2×D17212yes—
657C4⋊C4C2×D17212yes—
658C22⋊C4—864no—
659C22⋊C4—862no—
660C22⋊C4—864no—
661C22⋊C4—862no—
662C22⋊C4—864no—
663C22⋊C4—862no—
664C22⋊C4—864no—
665C22⋊C4—862no—
666C22⋊C4—864no—
667C22⋊C4—864no—
668C22⋊C4—864no—
669C22⋊C4C2×D17212yes—
670C22⋊C4C2×D17212yes—
671C22⋊C4C2×D17212yes—
672C22⋊C4C2×D17212yes—
673C22⋊C4C2×D17212yes—
674C42—864no—
675C42C2×D17211yescharacteristic
676C42C2×D17211yescharacteristic
677C42C23×D4311yescharacteristic
678C42C23×D4311yescharacteristic
679C42C23×D4312yes—
680C23—862no—
681C23—862no—
682C23—864no—
683C23—3442no—
684C23—3444no—
685C23—3444no—
686C23—1724no—
687C23—1728no—
688C23—1724no—
689C23C22×D17212yes—
690C23C22×D17211yescharacteristic
691Q8—22no—
692Q8—3442no—
693D4—24no—
694D4—22no—
695D4—434no—
696D4—862no—
697D4—864no—
698D4—862no—
699D4—862no—
700D4—864no—
701D4—3444no—
702D4—3442no—
703D4—3444no—
704D4—3444no—
705D4—3444no—
706D4—1724no—
707D4—1728no—
708D4—1728no—
709D4—1724no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—862no—
717C2×C4—864no—
718C2×C4—862no—
719C2×C4—3442no—
720C2×C4—3442no—
721C2×C4—3444no—
722C2×C4—3444no—
723C2×C4—3444no—
724C2×C4—3442no—
725C2×C4—1724no—
726C2×C4—1724no—
727C2×C4C22×D17212yes—
728C2×C4C22×D17211yescharacteristic
729C2×C4C22×D17211yescharacteristic
730C2×C4C22×D17211yescharacteristic
731C2×C4C22×D17211yescharacteristic
732C2×C4C22×D17212yes—
733C2×C4C22×D17212yes—
734C2×C4C22×D17211yescharacteristic
735C2×C4C24×D4311yescharacteristic
736C8—21no—
737C8—22no—
738C8—21no—
739C8—21no—
740C8—22no—
741C8#41×D4312yes—
742C22—21no—
743C22—21no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—864no—
748C22—3448no—
749C22—1722no—
750C22—1724no—
751C22—1724no—
752C22—1722no—
753C22—1722no—
754C22—1724no—
755C22—1722no—
756C22—1722no—
757C22—6888no—
758C22#1458370412yes—
759C22C23×D17211yescharacteristic
760C4—21no—
761C4—21no—
762C4—21no—
763C4—22no—
764C4—22no—
765C4—21no—
766C4—22no—
767C4—1722no—
768C4—1722no—
769C4—1724no—
770C4#1458370412yes—
771C4C2×#41×D4311yescharacteristic
772C4#1458373511yescharacteristic
773C2—22no—
774C2—42no—
775C2—3442no—
776C2—3444no—
777C2—1724no—
778C2#41×D17211yescharacteristic
779C2C2×#1458370411yescharacteristic
780C2C2×#1458370411yescharacteristic
subgroupG/H
centerC22C23×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#2966C2
socleC22×C43C23×D4
hypercenter#2966D43
hypocenterC43#61480
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #529 ◁ #2966

Complements

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

NH ≅ G/Ntype
1. #19148629C2semidirect
2. #19147570C2semidirect
3. #19147463C2semidirect
4. #19147304C2semidirect
5. #19147018C2semidirect
6. #19146998C2semidirect
7. #19146838C2semidirect
8. #19146738C2semidirect
9. D4×D344C2semidirect
10. D4×D344C2semidirect
11. #19145245C2semidirect
12. #19145174C2semidirect
13. #19144839C2semidirect
14. #19144687C2semidirect
15. #19143448C2semidirect
16. C2×C4×D344C2semidirect
17. C43×#2966C2semidirect
20. #14583614C22semidirect
21. #14583609C22semidirect
23. #14583595C22semidirect
24. #14583571C22semidirect
27. D4×D172C22semidirect
28. D4×D172C22semidirect
29. #14583504C22semidirect
31. #14583449C22semidirect
34. #14583373C22semidirect
35. C2×C4×D172C22semidirect
36. #14583304C22semidirect
37. #14583301C22semidirect
38. #14583276C22semidirect
39. #14583276C22semidirect
40. #14583264C22semidirect
41. #14583246C22semidirect
42. #14583224C22semidirect
43. #14583224C22semidirect
44. #14583218C22semidirect
45. #14583200C22semidirect
46. #14583200C22semidirect
47. #14583190C22semidirect
48. #14583190C22semidirect
49. #14583152C22semidirect
50. #14583135C22semidirect
51. #14583135C22semidirect
52. #14583135C22semidirect
53. #14583135C22semidirect
54. #14583095C22semidirect
55. #14583095C22semidirect
56. #14583095C22semidirect
57. #14583095C22semidirect
58. #14583035C22semidirect
59. #14583035C22semidirect
60. #14583035C22semidirect
61. #14583012C22semidirect
62. #14583012C22semidirect
63. #14583012C22semidirect
67. C4×D344C22semidirect
68. C4×D344C22semidirect
69. C4×D344C22semidirect
70. C4×D344C22semidirect
71. C4×D344C22semidirect
72. C4×D344C22semidirect
73. C4×D344C22semidirect
74. #14582937C22semidirect
75. C2×#13063259C22semidirect
76. #14582905C22semidirect
77. C2×#13063247C22semidirect
79. C43×#446C22semidirect
80. C8×Q8×C43C22semidirect
81. C43×#436C22semidirect
82. C43×#435C22semidirect
83. C8×D4×C43C22semidirect
84. C8×D4×C43C22semidirect
85. C43×#433C22semidirect
86. C43×#432C22semidirect
87. C43×#405C22semidirect
88. C2×C4×C8×C43C22semidirect
288. D344#41semidirect
397. #2966D43semidirect
452. #446C2×D43semidirect
453. C8×Q8C2×D43semidirect
467. #436C2×D43semidirect
468. #435C2×D43semidirect
469. C8×D4C2×D43semidirect
470. C8×D4C2×D43semidirect
471. #433C2×D43semidirect
472. #432C2×D43semidirect
477. #405C2×D43semidirect
478. C2×C4×C8C2×D43semidirect
479. C43#61480semidirect

Maximal subgroups

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

subgroupindex
#191486292
#191475702
#191474632
#191473042
#191470182
#191469982
#191468382
#191467382
D4×D3442
#191452452
#191451742
#191448392
#191446872
#191434482
C2×C4×D3442
C43×#29662
#6148043