Finite Group Databasebeta

← #11664135

Subgroups — #11664135

Order 768.

2074 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5523C211yesmaximal, characteristic, complemented
2#85727C211yesmaximal, characteristic, complemented
3C3×#2924C211yesmaximal, characteristic, complemented
4#79388C214yesmaximal, complemented
5#79385C214yesmaximal, complemented
6#79357C212yesmaximal, complemented
7#79344C212yesmaximal, complemented
8#79310C212yesmaximal, complemented
9#79300C212yesmaximal, complemented
10#79091C212yesmaximal, complemented
11#79089C212yesmaximal, complemented
12#78640C211yesmaximal, characteristic, complemented
13#78622C211yesmaximal, characteristic, complemented
14#78610C211yesmaximal, characteristic
15C2×#4722C211yesmaximal, characteristic, complemented
16#78571C212yesmaximal, complemented
17#78562C212yesmaximal, complemented
18#60589—31nomaximal, Sylow
19C22×#235C2211yescharacteristic
20C2×C3×#117C2211yescharacteristic
21#5791C2211yescharacteristic
22C22×C4⋊Dic3C2211yescharacteristic
23C2×#924C2211yescharacteristic
24C2×#909C2212yes—
25C2×#904C2212yes—
26#5534C2212yescomplemented
27#5533—21no—
28#5531—22no—
29#5529—21no—
30#5526C2211yescharacteristic, complemented
31#5523—21no—
32#5523—22no—
33#5523—21no—
34#5523C2214yes—
35#5523C2212yes—
36#5523C2212yes—
37#5523C2211yescharacteristic, complemented
38#5519C2211yescharacteristic, complemented
39#5518C2212yescomplemented
40#5516C2211yescharacteristic, complemented
41#5513—21no—
42#5511—21no—
43C2×#892—21no—
44C2×D3×C4⋊C4—21no—
45#5495—22no—
46C2×#67⋊C4—22no—
47#5479C2212yes—
48C2×C4×D12C2212yes—
49#5470C2212yes—
50C2×C4×Dic6C2212yes—
51C3×#433C2214yescomplemented
52C3×#432C2212yes—
53C3×#431C2212yes—
54C3×#424C2212yescomplemented
55C3×#407C2211yescharacteristic
56C2×C3×C22⋊C8C2211yescharacteristic
57C3×#405C2212yescomplemented
58#5133C2212yes—
59#5133C2212yescomplemented
60#5121C2212yescomplemented
61#5113C2212yes—
62C2×#818C2212yescomplemented
63C2×#816C2212yescomplemented
64#4850C2214yescomplemented
65#4849C2214yescomplemented
66#4847C2214yescomplemented
67#4846C2214yescomplemented
68#4845C2214yescomplemented
69#4844C2214yescomplemented
70#4841C2214yescomplemented
71#4829C2214yescomplemented
72#4739C2211yescharacteristic
73#4739C2212yes—
74#4738C2211yescharacteristic
75#4736C2212yescomplemented
76#4735C2212yes—
77#4734C2212yes—
78#4733C2212yes—
79#4733C2214yes—
80#4732C2211yescharacteristic
81#4731C2211yescharacteristic
82#4731C2212yes—
83#4722C2212yes—
84#4722C2212yes—
85#4722C2212yes—
86#4722C2214yescomplemented
87#4721C2212yescomplemented
88#4716C2214yescomplemented
89#4710C2214yescomplemented
90#4710C2214yescomplemented
91#4710C2214yescomplemented
92C4×Dic12C2214yescomplemented
93C4×Dic12C2214yescomplemented
94C4×D24C2214yescomplemented
95C4×#204C2214yescomplemented
96#3495—31no—
97C2×#520—31no—
98#3124—34no—
99#3120—34no—
100#3117—32no—
101#3110—32no—
102#3105—32no—
103#3104—32no—
104#3092—31no—
105C2×#484—31no—
106#3083—32no—
107#3046—32no—
108#3007—31no—
109#3002—31no—
110#2951—32no—
111#2947—32no—
112#2924D311yescharacteristic, complemented
113C23×C3×C4C2311yescharacteristic
114C22×#67—21no—
115C23×Dic3—21no—
116C2×#235—21no—
117C2×#235—21no—
118C2×#235—28no—
119C2×#235C2311yescharacteristic
120C2×#235C2312yes—
121C2×#235C2312yes—
122C22×D12C2311yescharacteristic
123C22×C4×D3—21no—
124C22×C4×D3—22no—
125C22×Dic6C2311yescharacteristic
126C22×Dic6C2311yescharacteristic
127C2×C3×M16C2312yes—
128C22×C3×C8C2312yes—
129C3×#117D411yescharacteristic
130C3×#117D412yes—
131C3×#117D411yescharacteristic
132C3×#117C2311yescharacteristic
133C3×#117C2312yes—
134C3×#117C2311yescharacteristic
135C2×C3×C4⋊C4D411yescharacteristic
136C2×C3×C4⋊C4D411yescharacteristic
137C2×C3×C22⋊C4D412yes—
138C2×C3×C42C2312yes—
139#953—21no—
140C2×#217—21no—
141#930C2311yescharacteristic
142#930C2311yescharacteristic
143#929—22no—
144#929—21no—
145C4×#67—22no—
146C4×#67—21no—
147C4×#67—21no—
148C2×(C2×D3)⋊C4—22no—
149#926—22no—
150#926C2311yescharacteristic
151C2×C4⋊Dic3—21no—
152C2×C4⋊Dic3—21no—
153C2×C4⋊Dic3—21no—
154C2×C4⋊Dic3C2312yes—
155C2×C4⋊Dic3C2311yescharacteristic
156C2×C4⋊Dic3C2312yes—
157C2×C4⋊Dic3C2312yes—
158#924—22no—
159#924—21no—
160#924—21no—
161#924C2311yescharacteristic
162#924C2312yes—
163#924C2311yescharacteristic
164#924C2312yes—
165C2×Dic3⋊C4—22no—
166C2×Dic3⋊C4—21no—
167C2×C4×Dic3—22no—
168#909—28no—
169C2×Dic12C2312yes—
170C2×Dic12C2314yes—
171#904—28no—
172C2×D24C2312yes—
173C2×#204C2314yes—
174C2×#204C2312yes—
175C2×#204C2312yes—
176#898—22no—
177#897—21no—
178#897—21no—
179#896—22no—
180#892—22no—
181#892—24no—
182#892—22no—
183#892—21no—
184D3×C4⋊C4—22no—
185D3×C4⋊C4—22no—
186D3×C4⋊C4—24no—
187D3×C4⋊C4—21no—
188#890—21no—
189#889—22no—
190#889—22no—
191#888—21no—
192#887—21no—
193#887—21no—
194#886—22no—
195#885—22no—
196#883—22no—
197#67⋊C4—24no—
198#67⋊C4—24no—
199#67⋊C4—24no—
200#67⋊C4—24no—
201#67⋊C4—22no—
202#879—22no—
203#879—22no—
204#878—22no—
205#877—22no—
206#876—22no—
207#875C2312yes—
208C4×D12—22no—
209C4×D12—22no—
210C4×D12C2314yes—
211C4×D12C2312yes—
212C4×D12C2314yes—
213#872—22no—
214#870—22no—
215#870C2312yes—
216#869C2312yes—
217#869C2312yes—
218C4×Dic6—22no—
219C4×Dic6—22no—
220C4×Dic6—22no—
221C4×Dic6C2312yes—
222C4×Dic6C2314yes—
223C4×Dic6C2312yes—
224C4×Dic6C2312yes—
225C4×Dic6C2314yes—
226C3×C4⋊C8C2314yes—
227C3×C4⋊C8C2314yes—
228C3×C22⋊C8C2312yes—
229C3×C22⋊C8C2311yescharacteristic
230C3×C22⋊C8C2311yescharacteristic
231C3×C22⋊C8C2312yes—
232C3×C22⋊C8C2312yes—
233C3×#97C2314yes—
234C3×C4×C8C2314yes—
235#821C2314yes—
236#821C2314yes—
237#821C2312yes—
238#821C2312yes—
239#818C2314yes—
240#818C2314yes—
241#818C2314yes—
242#817C2314yes—
243#816C2314yes—
244#816C2314yes—
245#816C2314yes—
246#816C2312yes—
247#816C2314yes—
248#816C2312yes—
249C22×#41—31no—
250C2×#137—32no—
251C2×#135—32no—
252#556—61no—
253#554—61no—
254#552—61no—
255#552—62no—
256#552—61no—
257#551—62no—
258#544—31no—
259#542—32no—
260#541—32no—
261#536—31no—
262#533—32no—
263#529—32no—
264#525—31no—
265C2×C22⋊Q8—31no—
266#520—32no—
267#520—34no—
268#520—32no—
269#520—31no—
270#520—62no—
271#520—61no—
272#520—61no—
273#519—31no—
274C2×C4×Q8—32no—
275C2×C4×D4—32no—
276C2×C4×D4—62no—
277C2×#117—61no—
278C2×#117C2×D311yescharacteristic
279C22×C4⋊C4—31no—
280C22×C4⋊C4—61no—
281#484—32no—
282#484—32no—
283#484—34no—
284#484—32no—
285#483—32no—
286#481—32no—
287#480—32no—
288#479—34no—
289#478—34no—
290#477—34no—
291#474—34no—
292#464—34no—
293#463—34no—
294#462—34no—
295#461—34no—
296#452—32no—
297#452—34no—
298#451—31no—
299#451—32no—
300#450—32no—
301#450—31no—
302#449—32no—
303#448—31no—
304#447—31no—
305#441—34no—
306#440—34no—
307#440—34no—
308#440—34no—
309C4×Q16—34no—
310C4×Q16—34no—
311C4×SD16—34no—
312C4×D8—34no—
313#433C2×D314yescomplemented
314#432C2×D312yes—
315#431C2×D312yes—
316#428—32no—
317C2×#107—32no—
318#424C2×D312yescomplemented
319#417—32no—
320#417—32no—
321#416—32no—
322C2×#103—32no—
323#407C2×D311yescharacteristic
324C2×C22⋊C8C2×D311yescharacteristic
325#405C2×D312yescomplemented
326C24×C3C2×D411yescharacteristic
327C23×D3—21no—
328C22×C3×C4—24no—
329C22×C3×C4C2×D412yes—
330C22×C3×C4C2×D411yescharacteristic
331C22×C3×C4C2×D411yescharacteristic
332C22×C3×C4C2×D411yescharacteristic
333C22×C3×C4C2×D412yes—
334C22×C3×C4C2411yescharacteristic
335C22×C3×C4C2411yescharacteristic
336C22×C3×C4C2411yescharacteristic
337C2×#67—28no—
338C2×#67—22no—
339C2×#67—22no—
340C2×#67—21no—
341C2×#67—21no—
342C2×#67—21no—
343C22×Dic3—21no—
344C22×Dic3—21no—
345C22×Dic3—22no—
346C22×Dic3—21no—
347C22×Dic3—22no—
348C22×Dic3—22no—
349C22×Dic3—82no—
350#235—28no—
351#235—28no—
352#235—24no—
353#235—24no—
354#235—24no—
355#235—24no—
356#235#4118yes—
357C2×D12—21no—
358C2×D12—24no—
359C2×D12C2411yescharacteristic
360C2×D12C2412yes—
361C2×C4×D3—28no—
362C2×C4×D3—22no—
363C2×C4×D3—22no—
364C2×C4×D3—21no—
365C2×C4×D3—22no—
366C2×C4×D3—24no—
367C2×C4×D3—24no—
368C2×C4×D3—84no—
369C2×Dic6—21no—
370C2×Dic6—24no—
371C2×Dic6—24no—
372C2×Dic6—21no—
373C2×Dic6—22no—
374C2×Dic6C2411yescharacteristic
375C2×Dic6C2412yes—
376C2×Dic6C2412yes—
377C3×M16—24no—
378C2×C3×C8—24no—
379C2×C3×C8C2412yes—
380C2×C3×C8C2412yes—
381C2×C3×C8C2414yes—
382C3×C4⋊C4C2×D411yescharacteristic
383C3×C4⋊C4C2×D411yescharacteristic
384C3×C4⋊C4C2×D411yescharacteristic
385C3×C4⋊C4C2×D412yes—
386C3×C4⋊C4C2×D412yes—
387C3×C4⋊C4C2×D411yescharacteristic
388C3×C22⋊C4C2×D412yes—
389C3×C22⋊C4C2×D412yes—
390C3×C22⋊C4C2×D412yes—
391C3×C22⋊C4C2×D412yes—
392C3×C42C2×D412yes—
393C3×C42C2×D412yes—
394C3×C42C2412yes—
395C3×C42C2412yes—
396#217—21no—
397#217—21no—
398#217—22no—
399#217—21no—
400#217—22no—
401(C2×D3)⋊C4—21no—
402(C2×D3)⋊C4—22no—
403(C2×D3)⋊C4—24no—
404(C2×D3)⋊C4—24no—
405(C2×D3)⋊C4—22no—
406(C2×D3)⋊C4—22no—
407(C2×D3)⋊C4—21no—
408C4⋊Dic3—22no—
409C4⋊Dic3—22no—
410C4⋊Dic3—22no—
411C4⋊Dic3—22no—
412C4⋊Dic3—21no—
413C4⋊Dic3—22no—
414C4⋊Dic3—22no—
415C4⋊Dic3C2414yes—
416C4⋊Dic3C2411yescharacteristic
417C4⋊Dic3C2411yescharacteristic
418C4⋊Dic3C2412yes—
419Dic3⋊C4—21no—
420Dic3⋊C4—24no—
421Dic3⋊C4—24no—
422Dic3⋊C4—22no—
423Dic3⋊C4—22no—
424Dic3⋊C4—22no—
425Dic3⋊C4—22no—
426Dic3⋊C4—22no—
427Dic3⋊C4—22no—
428Dic3⋊C4—21no—
429Dic3⋊C4—22no—
430C4×Dic3—22no—
431C4×Dic3—22no—
432C4×Dic3—24no—
433C4×Dic3—24no—
434C4×Dic3—22no—
435C4×Dic3—21no—
436Dic12—24no—
437Dic12—28no—
438D24—24no—
439#204—24no—
440#204—28no—
441#204—24no—
442C2×#41—32no—
443C2×#41—32no—
444C2×#41—31no—
445C2×#41—68no—
446C2×#41—61no—
447C2×#41—61no—
448C22×Q8—31no—
449C22×Q8—31no—
450C22×D4—31no—
451C22×D4—61no—
452C23×C4—61no—
453C23×C4—61no—
454C23×C4—62no—
455C23×C4C22×D311yescharacteristic
456#137—68no—
457#135—68no—
458C2×Q16—32no—
459C2×Q16—34no—
460C2×SD16—32no—
461C2×SD16—32no—
462C2×SD16—34no—
463C2×D8—32no—
464C2×M16C22×D312yes—
465C22×C8C22×D312yes—
466C4⋊Q8—32no—
467C4⋊Q8—32no—
468C4⋊Q8—61no—
469#126—62no—
470#126—62no—
471#126—62no—
472#126—62no—
473#125—32no—
474#125—62no—
475#125—62no—
476#125—61no—
477#125—62no—
478#124—32no—
479#124—62no—
480#123—61no—
481#123—62no—
482#123—62no—
483#123—62no—
484C22⋊Q8—32no—
485C22⋊Q8—32no—
486C22⋊Q8—31no—
487C22⋊Q8—31no—
488C22⋊Q8—61no—
489C22⋊Q8—61no—
490C22⋊Q8—62no—
491C22⋊Q8—61no—
492C22⋊Q8—61no—
493C22⋊Q8—62no—
494C22⋊Q8—62no—
495#121—31no—
496#121—31no—
497#120—61no—
498C4×Q8—34no—
499C4×Q8—34no—
500C4×Q8—32no—
501C4×Q8—32no—
502C4×Q8—32no—
503C4×Q8—61no—
504C4×Q8—61no—
505C4×Q8—62no—
506C4×Q8—62no—
507C4×Q8—62no—
508C4×D4—34no—
509C4×D4—34no—
510C4×D4—32no—
511C4×D4—61no—
512C4×D4—61no—
513C4×D4—62no—
514C4×D4—64no—
515C4×D4—64no—
516C4×D4—64no—
517C4×D4—64no—
518C4×D4—62no—
519C4×D4—62no—
520C4×D4—62no—
521#117—31no—
522#117—62no—
523#117—62no—
524#117—62no—
525#117—64no—
526#117—61no—
527#117—62no—
528#117—62no—
529#117D1211yescharacteristic
530#117D1212yes—
531#117D1211yescharacteristic
532#117C22×D311yescharacteristic
533#117C22×D311yescharacteristic
534#117C22×D312yes—
535C2×C4⋊C4—32no—
536C2×C4⋊C4—32no—
537C2×C4⋊C4—32no—
538C2×C4⋊C4—31no—
539C2×C4⋊C4—61no—
540C2×C4⋊C4—61no—
541C2×C4⋊C4—61no—
542C2×C4⋊C4—62no—
543C2×C4⋊C4—61no—
544C2×C4⋊C4—62no—
545C2×C4⋊C4—64no—
546C2×C4⋊C4—62no—
547C2×C4⋊C4—61no—
548C2×C4⋊C4D1211yescharacteristic
549C2×C4⋊C4D1211yescharacteristic
550C2×C22⋊C4—61no—
551C2×C22⋊C4—62no—
552C2×C22⋊C4D1212yes—
553C2×C42—62no—
554C2×C42C22×D312yes—
555#107—34no—
556#107—34no—
557#107—34no—
558#106—34no—
559C4⋊C8C22×D314yes—
560C4⋊C8C22×D314yes—
561#103—34no—
562#103—34no—
563#103—32no—
564#103—32no—
565#103—34no—
566#103—34no—
567#102—32no—
568#102—32no—
569#102—34no—
570#102—34no—
571C22⋊C8C22×D311yescharacteristic
572C22⋊C8C22×D311yescharacteristic
573C22⋊C8C22×D312yes—
574C22⋊C8C22×D312yes—
575C22⋊C8C22×D312yes—
576#97C22×D314yes—
577C4×C8C22×D314yes—
578C23×C3—22no—
579C23×C3—22no—
580C23×C3—41no—
581C23×C3C22×D411yescharacteristic
582C23×C3C22×D411yescharacteristic
583C23×C3C22×D411yescharacteristic
584C22×D3—24no—
585C22×D3—22no—
586C22×D3—21no—
587C22×D3—42no—
588C22×D3—42no—
589C2×C3×C4—22no—
590C2×C3×C4—24no—
591C2×C3×C4—22no—
592C2×C3×C4—22no—
593C2×C3×C4—22no—
594C2×C3×C4—22no—
595C2×C3×C4—42no—
596C2×C3×C4C22×D412yes—
597C2×C3×C4C22×D412yes—
598C2×C3×C4C22×D412yes—
599C2×C3×C4C22×D411yescharacteristic
600C2×C3×C4C22×D411yescharacteristic
601C2×C3×C4C22×D412yes—
602C2×C3×C4C22×D411yescharacteristic
603C2×C3×C4C2×#4114yes—
604C2×C3×C4C2511yescharacteristic
605#67—28no—
606#67—28no—
607#67—42no—
608#67—42no—
609#67—81no—
610C2×Dic3—24no—
611C2×Dic3—22no—
612C2×Dic3—21no—
613C2×Dic3—21no—
614C2×Dic3—21no—
615C2×Dic3—22no—
616C2×Dic3—24no—
617C2×Dic3—22no—
618C2×Dic3—44no—
619C2×Dic3—42no—
620C2×Dic3—81no—
621C2×Dic3—82no—
622C2×Dic3—82no—
623D12—24no—
624D12—22no—
625D12—22no—
626D12C2×#4114yes—
627C4×D3—28no—
628C4×D3—28no—
629C4×D3—42no—
630C4×D3—82no—
631C4×D3—84no—
632C4×D3—84no—
633Dic6—24no—
634Dic6—22no—
635Dic6—24no—
636Dic6—22no—
637Dic6—42no—
638Dic6—82no—
639Dic6C2×#4114yes—
640C3×C8—22no—
641C3×C8—24no—
642C3×C8—22no—
643C24—61no—
644C24C2×D1211yescharacteristic
645#41—38no—
646#41—64no—
647#41—64no—
648#41—68no—
649#41—68no—
650#41—64no—
651#41—64no—
652C2×Q8—32no—
653C2×Q8—32no—
654C2×Q8—31no—
655C2×Q8—64no—
656C2×Q8—61no—
657C2×Q8—61no—
658C2×Q8—62no—
659C2×Q8—64no—
660C2×D4—32no—
661C2×D4—31no—
662C2×D4—64no—
663C2×D4—68no—
664C2×D4—62no—
665C2×D4—62no—
666C2×D4—61no—
667C2×D4—61no—
668C2×D4—61no—
669C2×D4—61no—
670C22×C4—24no—
671C22×C4—68no—
672C22×C4—61no—
673C22×C4—62no—
674C22×C4—62no—
675C22×C4—62no—
676C22×C4—61no—
677C22×C4—61no—
678C22×C4—62no—
679C22×C4—62no—
680C22×C4—61no—
681C22×C4—64no—
682C22×C4—64no—
683C22×C4—62no—
684C22×C4—244no—
685C22×C4—242no—
686C22×C4C2×D1212yes—
687C22×C4C2×D1211yescharacteristic
688C22×C4C2×D1211yescharacteristic
689C22×C4C2×D1211yescharacteristic
690C22×C4C2×D1212yes—
691C22×C4C23×D311yescharacteristic
692C22×C4C23×D311yescharacteristic
693C22×C4C23×D311yescharacteristic
694Q16—64no—
695Q16—68no—
696SD16—64no—
697SD16—68no—
698SD16—64no—
699D8—64no—
700M16—24no—
701C2×C8—24no—
702C2×C8C23×D312yes—
703C2×C8C23×D314yes—
704C2×C8C23×D312yes—
705C4⋊C4—31no—
706C4⋊C4—32no—
707C4⋊C4—31no—
708C4⋊C4—34no—
709C4⋊C4—62no—
710C4⋊C4—62no—
711C4⋊C4—62no—
712C4⋊C4—61no—
713C4⋊C4—64no—
714C4⋊C4—64no—
715C4⋊C4—62no—
716C4⋊C4—62no—
717C4⋊C4—62no—
718C4⋊C4—62no—
719C4⋊C4—62no—
720C4⋊C4—62no—
721C4⋊C4—62no—
722C4⋊C4—62no—
723C4⋊C4—61no—
724C4⋊C4—61no—
725C4⋊C4—62no—
726C4⋊C4—62no—
727C4⋊C4C2×D1211yescharacteristic
728C4⋊C4C2×D1212yes—
729C4⋊C4C2×D1211yescharacteristic
730C4⋊C4C2×D1211yescharacteristic
731C4⋊C4C2×D1211yescharacteristic
732C4⋊C4C2×D1212yes—
733C22⋊C4—62no—
734C22⋊C4—62no—
735C22⋊C4—61no—
736C22⋊C4—61no—
737C22⋊C4—61no—
738C22⋊C4—64no—
739C22⋊C4—64no—
740C22⋊C4—61no—
741C22⋊C4—62no—
742C22⋊C4—62no—
743C22⋊C4—61no—
744C22⋊C4—62no—
745C22⋊C4C2×D1212yes—
746C22⋊C4C2×D1212yes—
747C22⋊C4C2×D1212yes—
748C22⋊C4C2×D1212yes—
749C42—64no—
750C42—64no—
751C42—61no—
752C42—62no—
753C42—62no—
754C42—62no—
755C42C2×D1212yes—
756C42C2×D1212yes—
757C42C23×D312yes—
758C42C23×D312yes—
759C22×C3—21no—
760C22×C3—21no—
761C22×C3—21no—
762C22×C3—21no—
763C22×C3—21no—
764C22×C3—21no—
765C22×C3—21no—
766C22×C3—44no—
767C22×C3#52512yes—
768C22×C3#57812yes—
769C22×C3C23×D411yescharacteristic
770C2×D3—24no—
771C2×D3—48no—
772C2×D3—42no—
773C2×D3—42no—
774C2×D3—41no—
775C2×D3—41no—
776C2×D3—41no—
777C3×C4—22no—
778C3×C4—22no—
779C3×C4—21no—
780C3×C4—21no—
781C3×C4—22no—
782C3×C4—22no—
783C3×C4#52512yes—
784C3×C4C22×#4112yes—
785Dic3—24no—
786Dic3—41no—
787Dic3—42no—
788Dic3—44no—
789Dic3—42no—
790Dic3—41no—
791Dic3—41no—
792C23—22no—
793C23—22no—
794C23—41no—
795C23—64no—
796C23—62no—
797C23—61no—
798C23—122no—
799C23—122no—
800C23C22×D1211yescharacteristic
801C23C22×D1211yescharacteristic
802C23C22×D1211yescharacteristic
803Q8—34no—
804Q8—64no—
805Q8—62no—
806Q8—64no—
807Q8—62no—
808Q8—122no—
809Q8—242no—
810D4—34no—
811D4—64no—
812D4—68no—
813D4—68no—
814D4—62no—
815D4—62no—
816D4—122no—
817D4—122no—
818D4—241no—
819C2×C4—24no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—42no—
826C2×C4—68no—
827C2×C4—64no—
828C2×C4—62no—
829C2×C4—68no—
830C2×C4—61no—
831C2×C4—61no—
832C2×C4—62no—
833C2×C4—64no—
834C2×C4—61no—
835C2×C4—62no—
836C2×C4—124no—
837C2×C4—122no—
838C2×C4—122no—
839C2×C4—244no—
840C2×C4—244no—
841C2×C4—242no—
842C2×C4—242no—
843C2×C4—242no—
844C2×C4—241no—
845C2×C4C22×D1212yes—
846C2×C4C22×D1212yes—
847C2×C4C22×D1212yes—
848C2×C4C22×D1211yescharacteristic
849C2×C4C22×D1212yes—
850C2×C4C22×D1211yescharacteristic
851C2×C4C22×D1211yescharacteristic
852C2×C4D3×#4114yes—
853C2×C4C24×D311yescharacteristic
854C8—22no—
855C8—22no—
856C8—24no—
857C2×C3—22no—
858C2×C3—22no—
859C2×C3—41no—
860C2×C3C2×#52511yescharacteristic
861C2×C3C2×#57811yescharacteristic
862C2×C3#358511yescharacteristic
863D3—44no—
864D3—81no—
865C22—21no—
866C22—21no—
867C22—21no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—21no—
872C22—44no—
873C22—64no—
874C22—128no—
875C22—122no—
876C22—122no—
877C22—121no—
878C22—121no—
879C22—121no—
880C22#552412yes—
881C22#575312yes—
882C22C23×D1211yescharacteristic
883C4—22no—
884C4—22no—
885C4—22no—
886C4—22no—
887C4—21no—
888C4—21no—
889C4—64no—
890C4—121no—
891C4—124no—
892C4—122no—
893C4—121no—
894C4—121no—
895C4—122no—
896C4#552412yes—
897C4C2×D3×#4112yes—
898C3#6058911yescharacteristic, complemented, Sylow
899C2—22no—
900C2—22no—
901C2—41no—
902C2—124no—
903C2—241no—
904C2C2×#552411yescharacteristic
905C2C2×#575311yescharacteristic
906C2#8716711yescharacteristic
subgroupG/H
centerC22C23×D12
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#2924C2
socleC22×C3C23×D4
prime radical#78610C2
hypercenter#2924D3
hypocenterC3#60589
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2924

Complements

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

NH ≅ G/Ntype
1. C2×#5523C2semidirect
2. #85727C2semidirect
3. C3×#2924C2semidirect
4. #79388C2semidirect
5. #79385C2semidirect
6. #79357C2semidirect
7. #79344C2semidirect
8. #79310C2semidirect
9. #79300C2semidirect
10. #79091C2semidirect
11. #79089C2semidirect
12. #78640C2semidirect
13. #78622C2semidirect
15. C2×#4722C2semidirect
16. #78571C2semidirect
17. #78562C2semidirect
26. #5534C22semidirect
30. #5526C22semidirect
37. #5523C22semidirect
38. #5519C22semidirect
39. #5518C22semidirect
40. #5516C22semidirect
51. C3×#433C22semidirect
54. C3×#424C22semidirect
57. C3×#405C22semidirect
59. #5133C22semidirect
60. #5121C22semidirect
62. C2×#818C22semidirect
63. C2×#816C22semidirect
64. #4850C22semidirect
65. #4849C22semidirect
66. #4847C22semidirect
67. #4846C22semidirect
68. #4845C22semidirect
69. #4844C22semidirect
70. #4841C22semidirect
71. #4829C22semidirect
75. #4736C22semidirect
86. #4722C22semidirect
87. #4721C22semidirect
88. #4716C22semidirect
89. #4710C22semidirect
90. #4710C22semidirect
91. #4710C22semidirect
92. C4×Dic12C22semidirect
93. C4×Dic12C22semidirect
94. C4×D24C22semidirect
95. C4×#204C22semidirect
112. #2924D3semidirect
313. #433C2×D3semidirect
318. #424C2×D3semidirect
325. #405C2×D3semidirect
898. C3#60589semidirect

Maximal subgroups

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

subgroupindex
C2×#55232
#857272
C3×#29242
#793882
#793852
#793572
#793442
#793102
#793002
#790912
#790892
#786402
#786222
#786102
C2×#47222
#785712
#785622
#605893