Finite Group Databasebeta

← #11675079

Subgroups — #11675079

Order 768.

2126 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86277C211yesmaximal, characteristic, complemented
2C2×#5553C211yesmaximal, characteristic, complemented
3C3×#3077C211yesmaximal, characteristic, complemented
4#83336C211yesmaximal, characteristic, complemented
5C4×#932C211yesmaximal, characteristic, complemented
6#81153C214yesmaximal, complemented
7#81152C214yesmaximal, complemented
8#81090C212yesmaximal, complemented
9#81088C212yesmaximal, complemented
10#80995C212yesmaximal, complemented
11#80992C212yesmaximal, complemented
12#79239C212yesmaximal, complemented
13#79199C212yesmaximal, complemented
14#79056C211yesmaximal, characteristic, complemented
15#79046C211yesmaximal, characteristic, complemented
16#78942C212yesmaximal, complemented
17#78921C212yesmaximal, complemented
18#61321—31nomaximal, Sylow
19C22×#235—21no—
20C3×#533C2211yescharacteristic
21C2×C3×C4×D4C2211yescharacteristic
22C2×#940C2212yes—
23C2×#932C2211yescharacteristic
24C2×#930—21no—
25C2×#908C2212yes—
26#5730C2211yescharacteristic, complemented
27#5727C2211yescharacteristic, complemented
28#5722C2211yescharacteristic, complemented
29#5721C2211yescharacteristic, complemented
30#5690C2212yescomplemented
31#5685C2212yescomplemented
32#5636—22no—
33#5635—21no—
34#5632—21no—
35#5578—22no—
36#5578—21no—
37C4×D3×Q8—21no—
38#5553—21no—
39#5553—22no—
40#5553—21no—
41#5553C2214yes—
42#5553C2212yes—
43#5553C2212yes—
44#5522C2212yes—
45#5517C2212yes—
46C2×#893C2212yes—
47C2×#884—22no—
48C2×#874C2211yescharacteristic
49C4×#235C2211yescharacteristic
50C2×C4×Dic6C2211yescharacteristic
51C3×#478C2214yescomplemented
52C3×#476C2212yescomplemented
53C3×#474C2212yescomplemented
54C3×#428C2212yes—
55C3×#423C2211yescharacteristic
56C3×#418C2212yes—
57#5215C2211yescharacteristic
58#5131C2212yes—
59#5118C2212yes—
60Dic3×M16C2212yes—
61#5088C2212yescomplemented
62#5088C2212yescomplemented
63#5067C2214yescomplemented
64#5018C2212yescomplemented
65C4×#214C2212yescomplemented
66#5014C2212yescomplemented
67C4×#213C2212yescomplemented
68#5001C2212yes—
69#5001C2212yes—
70#4966C2211yescharacteristic
71#4964C2211yescharacteristic
72C4×#208C2211yescharacteristic
73#4891C2214yescomplemented
74#4890C2214yescomplemented
75#4889C2214yescomplemented
76#4872C2214yescomplemented
77#4871C2214yescomplemented
78#4870C2214yescomplemented
79#4869C2214yescomplemented
80#4852C2214yescomplemented
81#4848C2212yescomplemented
82#4848C2212yescomplemented
83#4843C2212yescomplemented
84#4843C2212yescomplemented
85#4831C2212yescomplemented
86#4830C2212yescomplemented
87#4828C2214yescomplemented
88#4786C2214yescomplemented
89#4786C2214yescomplemented
90#4764C2214yescomplemented
91#4764C2214yescomplemented
92#4762C2214yescomplemented
93#4762C2214yescomplemented
94#4760C2214yescomplemented
95#4760C2214yescomplemented
96Q8×#41—31no—
97C2×#550—31no—
98#3368—34no—
99#3368—32no—
100#3366—34no—
101#3366—32no—
102#3362—32no—
103#3358—32no—
104#3138—32no—
105#3138—31no—
106#3077—32no—
107#3077D311yescharacteristic, complemented
108#3038—31no—
109#3038—32no—
110Q8×M16—31no—
111C4×AGL(1,ℤ/8)—32no—
112C4×AGL(1,ℤ/8)—31no—
113C22×C3×D4C2311yescharacteristic
114C23×C3×C4—21no—
115C22×#67—22no—
116C22×#67—22no—
117C2×D3×Q8—21no—
118C2×#235—24no—
119C2×#235—22no—
120C2×#235—22no—
121C2×#235—48no—
122C2×#235C2311yescharacteristic
123C22×D12—21no—
124C22×D12—21no—
125C22×D12C2312yes—
126C22×C4×D3—22no—
127C22×Dic6D411yescharacteristic
128C2×C3×M16C2312yes—
129C3×C4⋊Q8C2311yescharacteristic
130C3×C4⋊Q8C2311yescharacteristic
131C3×#125C2312yes—
132C3×C22⋊Q8—21no—
133C3×C22⋊Q8—21no—
134C3×C4×Q8—21no—
135C3×C4×Q8—21no—
136C3×C4×D4—21no—
137C3×C4×D4—21no—
138C3×C4×D4C2312yes—
139C3×C4×D4C2312yes—
140C3×#117C2312yes—
141C2×C3×C4⋊C4C2311yescharacteristic
142C2×C3×C22⋊C4—21no—
143C2×C3×C42C2311yescharacteristic
144#946—21no—
145#946—22no—
146Q8×Dic3—21no—
147#944—21no—
148#944—22no—
149#940—22no—
150#940—22no—
151#940C2314yes—
152#940C2314yes—
153C2×#214C2312yes—
154#932—24no—
155C2×#213C2312yes—
156#930—22no—
157#930—24no—
158#930—22no—
159C4×#67—21no—
160C4×#67—21no—
161C2×(C2×D3)⋊C4—22no—
162#926C2311yescharacteristic
163C2×C4⋊Dic3D411yescharacteristic
164C2×Dic3⋊C4D412yes—
165C2×C4×Dic3C2312yes—
166C2×#208C2311yescharacteristic
167C2×#208C2311yescharacteristic
168#908—28no—
169C2×D24C2314yes—
170C2×#204C2314yes—
171#897—21no—
172#897—22no—
173#896—22no—
174#896—22no—
175#896—22no—
176#893—22no—
177#893—22no—
178#893C2312yes—
179#893C2314yes—
180#893C2314yes—
181#893C2312yes—
182D3×C4⋊C4—21no—
183D3×C4⋊C4—22no—
184#890C2312yes—
185#890C2312yes—
186#889—22no—
187#889—22no—
188#889—22no—
189#888—22no—
190#888—21no—
191#888C2312yes—
192#888C2312yes—
193#887—21no—
194#887—22no—
195#887C2312yes—
196#887C2312yes—
197#884—24no—
198#884—24no—
199#884—24no—
200#884—24no—
201#67⋊C4—22no—
202#67⋊C4—22no—
203#878—22no—
204#878—22no—
205#874—21no—
206#874—21no—
207#874C2312yes—
208#874C2312yes—
209C4×D12C2311yescharacteristic
210C4×D12C2311yescharacteristic
211#872—21no—
212#872—22no—
213C42×D3—21no—
214C42×D3—22no—
215C4×Dic6—22no—
216C4×Dic6—22no—
217C4×Dic6D411yescharacteristic
218C4×Dic6D412yes—
219C4×Dic6D411yescharacteristic
220C4×Dic6C2311yescharacteristic
221C4×Dic6C2311yescharacteristic
222C4×Dic6C2312yes—
223C4×Dic6C2311yescharacteristic
224C4×Dic6C2311yescharacteristic
225C3×#107C2314yes—
226C3×#106C2314yes—
227C3×C4⋊C8C2312yes—
228C3×C4⋊C8C2312yes—
229C3×#102C2314yes—
230C3×#102C2314yes—
231#832C2312yes—
232#832C2312yes—
233#821C2314yes—
234#821C2314yes—
235#815C2314yes—
236Dic3⋊C8C2314yes—
237Dic3⋊C8C2314yes—
238C8×Dic3C2314yes—
239#810C2312yes—
240#809C2312yes—
241#809C2314yes—
242#809C2314yes—
243#809C2314yes—
244#809C2314yes—
245#808C2312yes—
246#807C2312yes—
247#803C2312yes—
248C4×C3⋊C8C2312yes—
249C22×#41—61no—
250C2×AGL(1,ℤ/8)—31no—
251C2×AGL(1,ℤ/8)—32no—
252Q82—31no—
253#557—31no—
254#557—32no—
255#554—31no—
256#554—32no—
257#554—61no—
258#554—62no—
259#550—32no—
260#550—34no—
261#550—32no—
262#550—61no—
263#550—61no—
264#550—62no—
265D4×Q8—31no—
266D4×Q8—61no—
267#533—32no—
268#533—62no—
269#533—61no—
270#533C2×D311yescharacteristic
271C2×#127—32no—
272C2×#127—31no—
273C2×#121—62no—
274C2×#121—61no—
275C4×#41—32no—
276C4×#41—31no—
277C2×C4×Q8—31no—
278C2×C4×Q8—61no—
279C2×C4×D4—32no—
280C2×C4×D4C2×D311yescharacteristic
281#490—34no—
282#490—34no—
283#490—34no—
284#486—32no—
285#486—32no—
286#486—34no—
287#486—34no—
288#478—34no—
289#478—34no—
290#478C2×D314yescomplemented
291#476—34no—
292#476C2×D312yescomplemented
293#474—34no—
294#474C2×D312yescomplemented
295#460—32no—
296#460—32no—
297#460—34no—
298#460—34no—
299#459—32no—
300#459—32no—
301#459—34no—
302#459—34no—
303#446—34no—
304#446—32no—
305C8×Q8—32no—
306#442—32no—
307#442—34no—
308#440—32no—
309#440—34no—
310C4×SD16—32no—
311C4×SD16—34no—
312C4×D8—32no—
313C4×D8—34no—
314#428—31no—
315#428C2×D312yes—
316#423—32no—
317#423C2×D311yescharacteristic
318#418—31no—
319#418—32no—
320#418—32no—
321#418—32no—
322#418C2×D312yes—
323#417—31no—
324C4×M16—32no—
325C4×M16—31no—
326C24×C3—21no—
327C23×D3—22no—
328C2×C3×Q8—21no—
329C2×C3×Q8—21no—
330C2×C3×D4—21no—
331C2×C3×D4—22no—
332C2×C3×D4—22no—
333C2×C3×D4C2412yes—
334C22×C3×C4—21no—
335C22×C3×C4—22no—
336C22×C3×C4—22no—
337C22×C3×C4—44no—
338C22×C3×C4C2×D411yescharacteristic
339C22×C3×C4C2×D411yescharacteristic
340C22×C3×C4C2411yescharacteristic
341C2×#67—21no—
342C2×#67—24no—
343C2×#67—24no—
344C2×#67—24no—
345C2×#67—24no—
346C2×#67—48no—
347C2×#67—84no—
348C22×Dic3C2×D412yes—
349C22×Dic3C2×D412yes—
350D3×Q8—44no—
351#235—22no—
352#235—48no—
353#235—416no—
354#235—48no—
355#235#4114yescomplemented
356C2×D12—24no—
357C2×D12—24no—
358C2×D12—22no—
359C2×D12—22no—
360C2×D12—22no—
361C2×D12—22no—
362C2×D12—22no—
363C2×D12—44no—
364C2×D12—82no—
365C2×D12C2414yes—
366C2×D12C2411yescharacteristic
367C2×C4×D3—21no—
368C2×C4×D3—21no—
369C2×C4×D3—22no—
370C2×C4×D3—24no—
371C2×C4×D3—24no—
372C2×C4×D3—21no—
373C2×C4×D3—22no—
374C2×C4×D3—48no—
375C2×Dic6—24no—
376C2×Dic6—22no—
377C2×Dic6—22no—
378C2×Dic6C2×D412yes—
379C2×Dic6C2×D411yescharacteristic
380C2×Dic6C2×D411yescharacteristic
381C2×Dic6C2411yescharacteristic
382C3×M16—24no—
383C2×C3×C8C2414yes—
384C3×C4⋊C4—21no—
385C3×C4⋊C4—22no—
386C3×C4⋊C4—22no—
387C3×C4⋊C4—21no—
388C3×C4⋊C4—21no—
389C3×C4⋊C4C2412yes—
390C3×C4⋊C4C2412yes—
391C3×C4⋊C4C2412yes—
392C3×C22⋊C4—22no—
393C3×C22⋊C4—22no—
394C3×C22⋊C4—22no—
395C3×C42—22no—
396C3×C42C2×D411yescharacteristic
397C3×C42C2×D411yescharacteristic
398C3×C42C2411yescharacteristic
399C3×C42C2411yescharacteristic
400#217—21no—
401#214—24no—
402#213—24no—
403(C2×D3)⋊C4—21no—
404(C2×D3)⋊C4—21no—
405(C2×D3)⋊C4—22no—
406(C2×D3)⋊C4—22no—
407(C2×D3)⋊C4—24no—
408(C2×D3)⋊C4—24no—
409C4⋊Dic3—22no—
410C4⋊Dic3—22no—
411C4⋊Dic3C2×D411yescharacteristic
412C4⋊Dic3C2×D412yes—
413C4⋊Dic3C2×D411yescharacteristic
414C4⋊Dic3C2411yescharacteristic
415C4⋊Dic3C2411yescharacteristic
416Dic3⋊C4—21no—
417Dic3⋊C4—21no—
418Dic3⋊C4—22no—
419Dic3⋊C4—22no—
420Dic3⋊C4—22no—
421Dic3⋊C4—22no—
422Dic3⋊C4—22no—
423Dic3⋊C4—22no—
424Dic3⋊C4C2×D412yes—
425Dic3⋊C4C2×D412yes—
426Dic3⋊C4C2×D412yes—
427Dic3⋊C4C2×D412yes—
428C4×Dic3—21no—
429C4×Dic3—21no—
430C4×Dic3—21no—
431C4×Dic3—22no—
432C4×Dic3—22no—
433C4×Dic3C2×D412yes—
434C4×Dic3C2×D412yes—
435C4×Dic3C2412yes—
436C4×Dic3C2412yes—
437#208—22no—
438#208—22no—
439C2×C3⋊C8C2412yes—
440C2×C3⋊C8C2412yes—
441D24—28no—
442#204—28no—
443C2×#41—31no—
444C2×#41—62no—
445C2×#41—64no—
446C2×#41—62no—
447C2×#41—128no—
448C22×Q8—31no—
449C22×Q8—61no—
450C22×D4—32no—
451C22×D4—62no—
452C22×D4—62no—
453C22×D4—61no—
454C22×D4—61no—
455C22×D4C22×D311yescharacteristic
456C23×C4—21no—
457C23×C4—62no—
458AGL(1,ℤ/8)—68no—
459AGL(1,ℤ/8)—64no—
460C2×SD16—32no—
461C2×SD16—34no—
462C2×D8—32no—
463C2×D8—34no—
464C2×M16—31no—
465C2×M16—31no—
466C2×M16C22×D312yes—
467C4⋊Q8—32no—
468C4⋊Q8—32no—
469C4⋊Q8—61no—
470C4⋊Q8—62no—
471C4⋊Q8—62no—
472C4⋊Q8—61no—
473C4⋊Q8C22×D311yescharacteristic
474C4⋊Q8C22×D311yescharacteristic
475#127—34no—
476#127—34no—
477#127—32no—
478#127—32no—
479#127—62no—
480#127—62no—
481#127—61no—
482#127—61no—
483#125—32no—
484#125—32no—
485#125—62no—
486#125—62no—
487#125—62no—
488#125C22×D312yes—
489C22⋊Q8—21no—
490C22⋊Q8—21no—
491C22⋊Q8—62no—
492C22⋊Q8—62no—
493C22⋊Q8—62no—
494C22⋊Q8—62no—
495C22⋊Q8—62no—
496C22⋊Q8—62no—
497C22⋊Q8—61no—
498C22⋊Q8—61no—
499C22⋊Q8—62no—
500#121—64no—
501#121—64no—
502#121—64no—
503#121—64no—
504#121—62no—
505#121—64no—
506#121—62no—
507C4×Q8—21no—
508C4×Q8—21no—
509C4×Q8—31no—
510C4×Q8—32no—
511C4×Q8—31no—
512C4×Q8—31no—
513C4×Q8—32no—
514C4×Q8—31no—
515C4×Q8—32no—
516C4×Q8—32no—
517C4×Q8—31no—
518C4×Q8—31no—
519C4×Q8—62no—
520C4×Q8—62no—
521C4×Q8—62no—
522C4×Q8—61no—
523C4×Q8—61no—
524C4×D4—21no—
525C4×D4—21no—
526C4×D4—34no—
527C4×D4—34no—
528C4×D4—32no—
529C4×D4—32no—
530C4×D4—31no—
531C4×D4—31no—
532C4×D4—62no—
533C4×D4—62no—
534C4×D4—62no—
535C4×D4—62no—
536C4×D4—61no—
537C4×D4—61no—
538C4×D4C22×D312yes—
539C4×D4C22×D312yes—
540#117—31no—
541#117—62no—
542#117—61no—
543#117C22×D312yes—
544C2×C4⋊C4—32no—
545C2×C4⋊C4—31no—
546C2×C4⋊C4—62no—
547C2×C4⋊C4—61no—
548C2×C4⋊C4C22×D311yescharacteristic
549C2×C22⋊C4—21no—
550C2×C22⋊C4—62no—
551C2×C42—32no—
552C2×C42—62no—
553C2×C42—61no—
554C2×C42C22×D311yescharacteristic
555#107—32no—
556#107C22×D314yes—
557#106—32no—
558#106C22×D314yes—
559C4⋊C8—34no—
560C4⋊C8—34no—
561C4⋊C8C22×D312yes—
562C4⋊C8C22×D312yes—
563#103—32no—
564#102—32no—
565#102—32no—
566#102—34no—
567#102—34no—
568#102—32no—
569#102—34no—
570#102—34no—
571#102—34no—
572#102—34no—
573#102C22×D314yes—
574#102C22×D314yes—
575#97—34no—
576#97—32no—
577C4×C8—34no—
578C4×C8—32no—
579C23×C3—22no—
580C23×C3—42no—
581C23×C3—42no—
582C23×C3—42no—
583C23×C3C22×D411yescharacteristic
584C22×D3—21no—
585C22×D3—24no—
586C22×D3—44no—
587C22×D3—44no—
588C22×D3—44no—
589C3×Q8—42no—
590C3×Q8—81no—
591C3×D4—22no—
592C3×D4—22no—
593C3×D4—42no—
594C2×C3×C4—22no—
595C2×C3×C4—22no—
596C2×C3×C4—22no—
597C2×C3×C4—22no—
598C2×C3×C4—41no—
599C2×C3×C4—44no—
600C2×C3×C4—42no—
601C2×C3×C4—44no—
602C2×C3×C4C22×D411yescharacteristic
603C2×C3×C4C22×D411yescharacteristic
604C2×C3×C4C22×D411yescharacteristic
605C2×C3×C4C22×D411yescharacteristic
606C2×C3×C4C22×D411yescharacteristic
607C2×C3×C4C2×#4112yes—
608C2×C3×C42−1+412yes—
609C2×C3×C4C2511yescharacteristic
610#67—24no—
611#67—48no—
612#67—48no—
613#67—84no—
614#67—84no—
615C2×Dic3—21no—
616C2×Dic3—24no—
617C2×Dic3—21no—
618C2×Dic3—21no—
619C2×Dic3—42no—
620C2×Dic3C22×D412yes—
621C2×Dic3C22×D412yes—
622C2×Dic3C22×D412yes—
623C2×Dic3C22×D412yes—
624D12—24no—
625D12—21no—
626D12—24no—
627D12—44no—
628D12—44no—
629D12—44no—
630D12—82no—
631D12—82no—
632D12C2×#4112yescomplemented
633C4×D3—24no—
634C4×D3—48no—
635C4×D3—42no—
636C4×D3—48no—
637C4×D3—44no—
638C4×D3—82no—
639C4×D3—81no—
640Dic6—22no—
641Dic6—21no—
642Dic6—24no—
643Dic6—44no—
644Dic6—82no—
645Dic6AGL(1,ℤ/8)14yescomplemented
646Dic6C2×#4112yescomplemented
647C3×C8—24no—
648C3⋊C8—22no—
649C3⋊C8—22no—
650C24—21no—
651C24—62no—
652#41—34no—
653#41—62no—
654#41—128no—
655#41—1216no—
656#41—128no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—31no—
660C2×Q8—32no—
661C2×Q8—31no—
662C2×Q8—31no—
663C2×Q8—62no—
664C2×Q8—62no—
665C2×Q8—64no—
666C2×Q8—124no—
667C2×D4—21no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—31no—
671C2×D4—34no—
672C2×D4—64no—
673C2×D4—64no—
674C2×D4—64no—
675C2×D4—64no—
676C2×D4—61no—
677C2×D4—62no—
678C2×D4—62no—
679C2×D4—62no—
680C2×D4—62no—
681C2×D4—62no—
682C2×D4—64no—
683C2×D4—64no—
684C2×D4—124no—
685C2×D4—128no—
686C2×D4—242no—
687C2×D4—244no—
688C2×D4C23×D312yes—
689C22×C4—21no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—32no—
693C22×C4—32no—
694C22×C4—44no—
695C22×C4—62no—
696C22×C4—64no—
697C22×C4—64no—
698C22×C4—62no—
699C22×C4—61no—
700C22×C4—61no—
701C22×C4—61no—
702C22×C4—128no—
703C22×C4D3×D411yescharacteristic
704C22×C4D3×D411yescharacteristic
705C22×C4C23×D311yescharacteristic
706SD16—68no—
707SD16—64no—
708D8—68no—
709D8—64no—
710M16—24no—
711M16—62no—
712M16—62no—
713C2×C8—32no—
714C2×C8—32no—
715C2×C8C23×D314yes—
716C4⋊C4—22no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—22no—
721C4⋊C4—32no—
722C4⋊C4—31no—
723C4⋊C4—32no—
724C4⋊C4—32no—
725C4⋊C4—32no—
726C4⋊C4—32no—
727C4⋊C4—31no—
728C4⋊C4—31no—
729C4⋊C4—31no—
730C4⋊C4—62no—
731C4⋊C4—62no—
732C4⋊C4—62no—
733C4⋊C4—62no—
734C4⋊C4—62no—
735C4⋊C4—62no—
736C4⋊C4—62no—
737C4⋊C4—62no—
738C4⋊C4—61no—
739C4⋊C4—61no—
740C4⋊C4C23×D312yes—
741C4⋊C4C23×D312yes—
742C4⋊C4C23×D312yes—
743C22⋊C4—22no—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—64no—
747C22⋊C4—64no—
748C22⋊C4—62no—
749C22⋊C4—62no—
750C22⋊C4—61no—
751C22⋊C4—61no—
752C22⋊C4—61no—
753C42—22no—
754C42—32no—
755C42—32no—
756C42—32no—
757C42—32no—
758C42—62no—
759C42—62no—
760C42—61no—
761C42—61no—
762C42—61no—
763C42D3×D411yescharacteristic
764C42D3×D411yescharacteristic
765C42C23×D311yescharacteristic
766C42C23×D311yescharacteristic
767C22×C3—21no—
768C22×C3—21no—
769C22×C3—42no—
770C22×C3—42no—
771C22×C3—42no—
772C22×C3—84no—
773C22×C3#54812yes—
774C22×C3C23×D411yescharacteristic
775C2×D3—22no—
776C2×D3—41no—
777C2×D3—41no—
778C2×D3—44no—
779C2×D3—44no—
780C2×D3—44no—
781C2×D3—88no—
782C3×C4—21no—
783C3×C4—21no—
784C3×C4—21no—
785C3×C4—42no—
786C3×C4—42no—
787C3×C4—42no—
788C3×C4#54812yes—
789C3×C4C2×AGL(1,ℤ/8)12yes—
790C3×C4C22×#4111yescharacteristic
791C3×C4C2×2−1+411yescharacteristic
792Dic3—22no—
793Dic3—22no—
794Dic3—22no—
795Dic3—22no—
796Dic3—41no—
797Dic3—41no—
798Dic3C2×AGL(1,ℤ/8)14yes—
799C23—22no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—61no—
804C23—64no—
805C23—124no—
806C23—124no—
807C23—124no—
808C23C2×D3×D411yescharacteristic
809Q8—34no—
810Q8—32no—
811Q8—42no—
812Q8—64no—
813Q8—61no—
814Q8—62no—
815Q8—81no—
816Q8—124no—
817Q8—242no—
818D4—22no—
819D4—22no—
820D4—32no—
821D4—42no—
822D4—64no—
823D4—61no—
824D4—64no—
825D4—64no—
826D4—124no—
827D4—128no—
828D4—128no—
829D4—124no—
830D4—124no—
831D4—242no—
832D4—242no—
833D4—244no—
834D4—244no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—32no—
840C2×C4—32no—
841C2×C4—32no—
842C2×C4—32no—
843C2×C4—41no—
844C2×C4—44no—
845C2×C4—42no—
846C2×C4—44no—
847C2×C4—64no—
848C2×C4—61no—
849C2×C4—64no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—128no—
853C2×C4—124no—
854C2×C4—128no—
855C2×C4—122no—
856C2×C4—122no—
857C2×C4—241no—
858C2×C4—242no—
859C2×C4C2×D3×D411yescharacteristic
860C2×C4C2×D3×D411yescharacteristic
861C2×C4C2×D3×D411yescharacteristic
862C2×C4C2×D3×D411yescharacteristic
863C2×C4C2×D3×D411yescharacteristic
864C2×C4#100712yes—
865C2×C4D3×#4112yes—
866C2×C4C24×D311yescharacteristic
867C8—24no—
868C8—62no—
869C8—62no—
870C2×C3—22no—
871C2×C3—82no—
872C2×C3C2×#54811yescharacteristic
873C2×C3C22×AGL(1,ℤ/8)11yescharacteristic
874C2×C3#358511yescharacteristic
875D3—42no—
876D3—84no—
877C22—21no—
878C22—21no—
879C22—42no—
880C22—42no—
881C22—42no—
882C22—62no—
883C22—84no—
884C22—121no—
885C22—121no—
886C22—124no—
887C22—124no—
888C22—124no—
889C22—248no—
890C22#563312yes—
891C22C22×D3×D411yescharacteristic
892C4—21no—
893C4—21no—
894C4—21no—
895C4—34no—
896C4—42no—
897C4—42no—
898C4—42no—
899C4—62no—
900C4—62no—
901C4—62no—
902C4—62no—
903C4—121no—
904C4—121no—
905C4#563312yes—
906C4D3×AGL(1,ℤ/8)12yes—
907C4C2×#100711yescharacteristic
908C4C2×D3×#4111yescharacteristic
909C3#6132111yescharacteristic, complemented, Sylow
910C2—22no—
911C2—82no—
912C2—122no—
913C2—244no—
914C2C2×#563311yescharacteristic
915C2C2×D3×AGL(1,ℤ/8)11yescharacteristic
916C2#8720011yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3077C2
socleC22×C3C23×D4
hypercenter#3077D3
hypocenterC3#61321
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3077

Complements

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

NH ≅ G/Ntype
1. #86277C2semidirect
2. C2×#5553C2semidirect
3. C3×#3077C2semidirect
4. #83336C2semidirect
5. C4×#932C2semidirect
6. #81153C2semidirect
7. #81152C2semidirect
8. #81090C2semidirect
9. #81088C2semidirect
10. #80995C2semidirect
11. #80992C2semidirect
12. #79239C2semidirect
13. #79199C2semidirect
14. #79056C2semidirect
15. #79046C2semidirect
16. #78942C2semidirect
17. #78921C2semidirect
26. #5730C22semidirect
27. #5727C22semidirect
28. #5722C22semidirect
29. #5721C22semidirect
30. #5690C22semidirect
31. #5685C22semidirect
51. C3×#478C22semidirect
52. C3×#476C22semidirect
53. C3×#474C22semidirect
61. #5088C22semidirect
62. #5088C22semidirect
63. #5067C22semidirect
64. #5018C22semidirect
65. C4×#214C22semidirect
66. #5014C22semidirect
67. C4×#213C22semidirect
73. #4891C22semidirect
74. #4890C22semidirect
75. #4889C22semidirect
76. #4872C22semidirect
77. #4871C22semidirect
78. #4870C22semidirect
79. #4869C22semidirect
80. #4852C22semidirect
81. #4848C22semidirect
82. #4848C22semidirect
83. #4843C22semidirect
84. #4843C22semidirect
85. #4831C22semidirect
86. #4830C22semidirect
87. #4828C22semidirect
88. #4786C22semidirect
89. #4786C22semidirect
90. #4764C22semidirect
91. #4764C22semidirect
92. #4762C22semidirect
93. #4762C22semidirect
94. #4760C22semidirect
95. #4760C22semidirect
107. #3077D3semidirect
290. #478C2×D3semidirect
292. #476C2×D3semidirect
294. #474C2×D3semidirect
355. #235#41semidirect
632. D12C2×#41semidirect
645. Dic6AGL(1,ℤ/8)semidirect
646. Dic6C2×#41semidirect
909. C3#61321semidirect

Maximal subgroups

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

subgroupindex
#862772
C2×#55532
C3×#30772
#833362
C4×#9322
#811532
#811522
#810902
#810882
#809952
#809922
#792392
#791992
#790562
#790462
#789422
#789212
#613213