Finite Group Databasebeta

← #11664111

Subgroups — #11664111

Order 768.

2134 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86027C211yesmaximal, characteristic, complemented
2C2×#5504C211yesmaximal, characteristic, complemented
3C3×#3092C211yesmaximal, characteristic, complemented
4#82926C211yesmaximal, characteristic, complemented
5C2×#4968C211yesmaximal, characteristic, complemented
6#81455C212yesmaximal, complemented
7#81453C212yesmaximal, complemented
8#81417C214yesmaximal, complemented
9#81310C212yesmaximal, complemented
10#81308C212yesmaximal, complemented
11#81272C214yesmaximal, complemented
12#79244C212yesmaximal, complemented
13#79201C212yesmaximal, complemented
14#78911C212yesmaximal, complemented
15#78869C212yesmaximal, complemented
16#78639C211yesmaximal, characteristic, complemented
17#78621C211yesmaximal, characteristic, complemented
18#60588—31nomaximal, Sylow
19C22×#235C2211yescharacteristic
20C3×#525C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22#5830C2211yescharacteristic, complemented
23#5827C2211yescharacteristic, complemented
24C2×#950C2212yes—
25C2×#930C2211yescharacteristic
26C2×C4×#67—22no—
27C2×#926C2211yescharacteristic
28C2×#908C2212yes—
29#5658—22no—
30#5643C2212yescomplemented
31#5624C2212yes—
32#5619C2212yescomplemented
33#5596C2212yes—
34#5591—22no—
35#5565—21no—
36#5565—21no—
37#5563—21no—
38#5555—21no—
39#5521C2211yescharacteristic, complemented
40#5519C2211yescharacteristic, complemented
41#5504—21no—
42#5504—21no—
43#5504—22no—
44#5504C2212yes—
45#5504C2212yes—
46#5504C2214yescomplemented
47C2×#893C2212yescomplemented
48C2×#892—21no—
49C2×D3×C4⋊C4—21no—
50C2×#887C2212yescomplemented
51C3×#484C2212yescomplemented
52C3×#483C2212yescomplemented
53C3×#481C2212yescomplemented
54C3×#480C2212yescomplemented
55C3×#428C2212yescomplemented
56C3×#417C2212yescomplemented
57C3×#407C2211yescharacteristic
58C2×#830C2211yescharacteristic
59#5133C2212yes—
60#5122C2212yescomplemented
61#5119C2212yescomplemented
62#5050C2211yescharacteristic, complemented
63#5047C2212yescomplemented
64#5046C2211yescharacteristic, complemented
65#5040C2211yescharacteristic, complemented
66#5037C2212yescomplemented
67#5036C2211yescharacteristic, complemented
68#5002C2212yes—
69#4968C2212yes—
70#4968C2212yes—
71#4968C2214yescomplemented
72C2×#809C2212yescomplemented
73C2×#808C2212yescomplemented
74#4891C2214yescomplemented
75#4889C2214yescomplemented
76#4877C2214yescomplemented
77#4872C2214yescomplemented
78#4870C2214yescomplemented
79#4869C2214yescomplemented
80#4854C2214yescomplemented
81#4852C2214yescomplemented
82#4819C2214yescomplemented
83#4798C2214yescomplemented
84#4789C2214yescomplemented
85#4788C2214yescomplemented
86#4786C2214yescomplemented
87#4785C2214yescomplemented
88#4762C2214yescomplemented
89#4758C2214yescomplemented
90#4738C2212yes—
91#4734C2214yes—
92#4732C2212yes—
93#4720C2214yescomplemented
94#4719C2212yescomplemented
95#4718C2212yescomplemented
96#3494—31no—
97C2×#520—31no—
98#3125—34no—
99#3119—34no—
100#3117—32no—
101#3109—32no—
102#3105—32no—
103#3103—32no—
104#3092D311yescharacteristic, complemented
105C2×#481—31no—
106#3084—32no—
107#3045—32no—
108#3006—31no—
109#3002—31no—
110#2952—32no—
111#2946—32no—
112#2924—31no—
113C2×C3×#41C2311yescharacteristic
114C23×C3×C4—21no—
115C23×C3×C4C2311yescharacteristic
116C22×#67—21no—
117C22×#67—21no—
118C2×#237—22no—
119C2×#235—21no—
120C2×#235—21no—
121C2×#235—28no—
122C2×#235C2312yes—
123C2×#235C2312yes—
124C22×D12C2311yescharacteristic
125C22×D12C2311yescharacteristic
126C22×C4×D3—21no—
127C22×C4×D3—22no—
128C22×Dic6C2311yescharacteristic
129C2×C3×M16C2312yes—
130C3×#123—21no—
131C3×C22⋊Q8C2311yescharacteristic
132C3×C22⋊Q8C2311yescharacteristic
133C3×#121C2311yescharacteristic
134C3×#121C2311yescharacteristic
135C3×#120—21no—
136C3×C4×D4—21no—
137C3×C4×D4—21no—
138C3×#117C2311yescharacteristic
139C2×C3×C4⋊C4—21no—
140C2×C3×C4⋊C4—21no—
141C2×C3×C4⋊C4—21no—
142C2×C3×C4⋊C4C2312yes—
143C2×C3×C4⋊C4C2312yes—
144C2×C3×C4⋊C4C2312yes—
145C2×#217D412yes—
146#950—28no—
147#947C2312yes—
148Q8×Dic3C2312yes—
149C2×#216C2312yes—
150C2×#215C2312yes—
151#940C2312yes—
152#939—22no—
153#939—22no—
154#938—22no—
155#937—22no—
156D4×Dic3—22no—
157D4×Dic3C2312yes—
158C2×#214C2312yes—
159C2×#213C2312yes—
160#930—21no—
161#930—21no—
162#930—21no—
163#930—21no—
164#930C2312yes—
165#930C2312yes—
166C4×#67—24no—
167C4×#67—24no—
168C4×#67—24no—
169C4×#67—24no—
170C2×(C2×D3)⋊C4—21no—
171C2×(C2×D3)⋊C4—22no—
172#926—21no—
173#926D412yes—
174#926D411yescharacteristic
175#926D411yescharacteristic
176#926C2311yescharacteristic
177#926C2312yes—
178#926C2311yescharacteristic
179C2×C4⋊Dic3—21no—
180C2×C4⋊Dic3D411yescharacteristic
181C2×C4⋊Dic3D411yescharacteristic
182C2×C4⋊Dic3C2311yescharacteristic
183C2×Dic3⋊C4—22no—
184C2×C4×Dic3—22no—
185C2×C4×Dic3C2312yes—
186C22×C3⋊C8C2312yes—
187#908—28no—
188C2×D24C2314yes—
189C2×#204C2314yes—
190#898—22no—
191#898—22no—
192#897—22no—
193#893—22no—
194#893—22no—
195#893C2312yes—
196#893C2314yes—
197#893C2314yes—
198#893C2312yes—
199#892—22no—
200#892—22no—
201#892—24no—
202#892—22no—
203D3×C4⋊C4—22no—
204D3×C4⋊C4—22no—
205D3×C4⋊C4—24no—
206#890C2312yes—
207#888C2312yes—
208#887—22no—
209#887—22no—
210#887C2314yes—
211#887C2314yes—
212#886—22no—
213#886—22no—
214#885—22no—
215#885—22no—
216#883—22no—
217#883—22no—
218#67⋊C4—22no—
219#67⋊C4—22no—
220D3×C22⋊C4—22no—
221#878—22no—
222C4×D12—21no—
223C4×D12—21no—
224#870—21no—
225#869—21no—
226C3×#107C2314yes—
227C3×#106C2314yes—
228C3×#103C2314yes—
229C3×#102C2314yes—
230C3×C22⋊C8C2312yes—
231C3×C22⋊C8C2312yes—
232#830C2311yescharacteristic
233#830C2311yescharacteristic
234#830C2312yes—
235#821C2314yes—
236#816C2314yes—
237#815C2314yes—
238Dic3⋊C8C2314yes—
239Dic3⋊C8C2314yes—
240C8×Dic3C2314yes—
241#810C2312yes—
242#810C2312yes—
243#809C2312yes—
244#809C2314yes—
245#809C2312yes—
246#809C2314yes—
247#808C2314yes—
248#808C2314yes—
249C22×#41—31no—
250C2×AGL(1,ℤ/8)—32no—
251C2×#135—32no—
252#555—61no—
253#553—61no—
254#553—61no—
255#551—62no—
256#547—61no—
257#546—62no—
258#544—31no—
259#542—32no—
260#540—32no—
261#535—31no—
262#532—32no—
263#529—32no—
264#525C2×D311yescharacteristic
265C2×#121—31no—
266#520—31no—
267#520—32no—
268#520—34no—
269#520—32no—
270#520—62no—
271#520—61no—
272#520—61no—
273#518—31no—
274C2×C4×Q8—32no—
275C2×C4×D4—32no—
276C2×C4×D4—62no—
277C2×#117—31no—
278C2×#117—61no—
279C22×C4⋊C4—61no—
280C22×C4⋊C4C2×D311yescharacteristic
281#484C2×D312yescomplemented
282#483C2×D312yescomplemented
283#481—32no—
284#481—32no—
285#481—34no—
286#481C2×D312yescomplemented
287#480C2×D312yescomplemented
288#479—34no—
289#478—34no—
290#476—34no—
291#475—34no—
292#464—34no—
293#463—34no—
294#460—34no—
295#459—34no—
296#452—32no—
297#451—31no—
298#450—31no—
299#449—32no—
300#449—34no—
301#448—31no—
302#448—32no—
303#447—31no—
304#447—32no—
305#442—34no—
306#442—34no—
307#441—34no—
308#440—34no—
309C4×SD16—34no—
310C4×SD16—34no—
311C4×SD16—34no—
312C4×D8—34no—
313#433—34no—
314#432—32no—
315#431—32no—
316#428C2×D312yescomplemented
317C2×#106—32no—
318#424—32no—
319#417—32no—
320#417C2×D312yescomplemented
321#416—32no—
322C2×#102—32no—
323#407C2×D311yescharacteristic
324C2×C22⋊C8—31no—
325#405—32no—
326C24×C3C2×D411yescharacteristic
327C23×D3—21no—
328C23×D3—21no—
329C3×#41—24no—
330C2×C3×Q8C2411yescharacteristic
331C2×C3×D4—21no—
332C2×C3×D4—21no—
333C2×C3×D4—21no—
334C2×C3×D4C2411yescharacteristic
335C22×C3×C4—24no—
336C22×C3×C4—22no—
337C22×C3×C4—22no—
338C22×C3×C4—22no—
339C22×C3×C4—21no—
340C22×C3×C4—82no—
341C22×C3×C4C2×D411yescharacteristic
342C22×C3×C4C2×D411yescharacteristic
343C22×C3×C4C2×D411yescharacteristic
344C22×C3×C4C2411yescharacteristic
345C22×C3×C4C2411yescharacteristic
346C22×C3×C4C2411yescharacteristic
347C2×#67—28no—
348C2×#67—22no—
349C2×#67—22no—
350C2×#67—22no—
351C2×#67—22no—
352C2×#67—22no—
353C2×#67—22no—
354C2×#67—82no—
355C22×Dic3—21no—
356C22×Dic3—21no—
357C22×Dic3—22no—
358C22×Dic3C2×D412yes—
359C22×Dic3C2×D412yes—
360#237—84no—
361#235—28no—
362#235—28no—
363#235—24no—
364#235—24no—
365#235—24no—
366#235#4118yescomplemented
367C2×D12—21no—
368C2×D12—24no—
369C2×D12—24no—
370C2×D12—21no—
371C2×D12C2412yes—
372C2×D12C2412yes—
373C2×C4×D3—28no—
374C2×C4×D3—22no—
375C2×C4×D3—22no—
376C2×C4×D3—22no—
377C2×C4×D3—22no—
378C2×C4×D3—24no—
379C2×C4×D3—24no—
380C2×C4×D3—84no—
381C2×Dic6—21no—
382C2×Dic6—24no—
383C2×Dic6—22no—
384C2×Dic6C2412yes—
385C3×M16—24no—
386C2×C3×C8C2414yes—
387C3×C4⋊C4—22no—
388C3×C4⋊C4—22no—
389C3×C4⋊C4—22no—
390C3×C4⋊C4—21no—
391C3×C4⋊C4—21no—
392C3×C4⋊C4C2414yes—
393C3×C4⋊C4C2411yescharacteristic
394C3×C4⋊C4C2411yescharacteristic
395C3×C22⋊C4—21no—
396C3×C22⋊C4—21no—
397C3×C22⋊C4—21no—
398C3×C22⋊C4—21no—
399C3×C22⋊C4—21no—
400C3×C42—21no—
401#217—22no—
402#217C2×D412yes—
403#217C2×D412yes—
404#217C2×D412yes—
405#217C2×D412yes—
406#216—24no—
407#215—24no—
408#214—24no—
409#213—24no—
410(C2×D3)⋊C4—22no—
411(C2×D3)⋊C4—22no—
412(C2×D3)⋊C4—22no—
413(C2×D3)⋊C4—22no—
414(C2×D3)⋊C4—22no—
415(C2×D3)⋊C4—22no—
416(C2×D3)⋊C4—24no—
417(C2×D3)⋊C4—24no—
418C4⋊Dic3—21no—
419C4⋊Dic3—22no—
420C4⋊Dic3—22no—
421C4⋊Dic3C2×D411yescharacteristic
422C4⋊Dic3C2×D411yescharacteristic
423C4⋊Dic3C2×D411yescharacteristic
424C4⋊Dic3C2×D411yescharacteristic
425C4⋊Dic3C2×D412yes—
426C4⋊Dic3C2×D412yes—
427C4⋊Dic3C2412yes—
428Dic3⋊C4—22no—
429Dic3⋊C4—22no—
430Dic3⋊C4—24no—
431Dic3⋊C4—24no—
432C4×Dic3—22no—
433C4×Dic3—24no—
434C4×Dic3—24no—
435C4×Dic3C2×D412yes—
436C4×Dic3C2×D412yes—
437C4×Dic3C2412yes—
438C4×Dic3C2412yes—
439C2×C3⋊C8—24no—
440C2×C3⋊C8C2412yes—
441C2×C3⋊C8C2412yes—
442D24—28no—
443#204—28no—
444C2×#41—32no—
445C2×#41—32no—
446C2×#41—68no—
447C2×#41—62no—
448C2×#41—61no—
449C2×#41—61no—
450C2×#41C22×D311yescharacteristic
451C22×Q8—31no—
452C22×D4—31no—
453C22×D4—31no—
454C22×D4—61no—
455C22×D4—61no—
456C23×C4—21no—
457C23×C4—62no—
458C23×C4—61no—
459C23×C4C22×D311yescharacteristic
460AGL(1,ℤ/8)—68no—
461#135—68no—
462C2×Q16—32no—
463C2×SD16—32no—
464C2×SD16—32no—
465C2×SD16—34no—
466C2×D8—32no—
467C2×D8—34no—
468C2×M16C22×D312yes—
469C22×C8—32no—
470C4⋊Q8—32no—
471C4⋊Q8—61no—
472#127—32no—
473#126—62no—
474#126—62no—
475#125—32no—
476#125—61no—
477#124—32no—
478#124—62no—
479#124—62no—
480#123—21no—
481#123—62no—
482#123—62no—
483#123—62no—
484#123—62no—
485C22⋊Q8—62no—
486C22⋊Q8—62no—
487C22⋊Q8C22×D311yescharacteristic
488C22⋊Q8C22×D311yescharacteristic
489#121—32no—
490#121—32no—
491#121—62no—
492#121—62no—
493#121—61no—
494#121—61no—
495#121—62no—
496#121—61no—
497#121—61no—
498#121C22×D311yescharacteristic
499#121C22×D311yescharacteristic
500#120—21no—
501#120—62no—
502C4×Q8—32no—
503C4×Q8—34no—
504C4×Q8—34no—
505C4×Q8—62no—
506C4×Q8—62no—
507C4×D4—21no—
508C4×D4—21no—
509C4×D4—32no—
510C4×D4—34no—
511C4×D4—34no—
512C4×D4—32no—
513C4×D4—32no—
514C4×D4—61no—
515C4×D4—61no—
516C4×D4—62no—
517C4×D4—62no—
518C4×D4—62no—
519C4×D4—62no—
520C4×D4—64no—
521C4×D4—64no—
522C4×D4—64no—
523C4×D4—64no—
524C4×D4—62no—
525#117—32no—
526#117—31no—
527#117—31no—
528#117—31no—
529#117—31no—
530#117—32no—
531#117—62no—
532#117—62no—
533#117—62no—
534#117—64no—
535#117—61no—
536#117C22×D311yescharacteristic
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—31no—
541C2×C4⋊C4—31no—
542C2×C4⋊C4—31no—
543C2×C4⋊C4—62no—
544C2×C4⋊C4—62no—
545C2×C4⋊C4—64no—
546C2×C4⋊C4—61no—
547C2×C4⋊C4—62no—
548C2×C4⋊C4C22×D312yes—
549C2×C4⋊C4C22×D312yes—
550C2×C4⋊C4C22×D312yes—
551C2×C22⋊C4—32no—
552C2×C22⋊C4—62no—
553C2×C22⋊C4—62no—
554C2×C22⋊C4—61no—
555C2×C42—32no—
556C2×C42—62no—
557#107C22×D314yes—
558#106—34no—
559#106—34no—
560#106C22×D314yes—
561C4⋊C8—34no—
562C4⋊C8—34no—
563#103—34no—
564#103—32no—
565#103—32no—
566#103C22×D314yes—
567#102—34no—
568#102—34no—
569#102—34no—
570#102—32no—
571#102—32no—
572#102C22×D314yes—
573C22⋊C8—31no—
574C22⋊C8—31no—
575C22⋊C8—32no—
576C22⋊C8C22×D312yes—
577C22⋊C8C22×D312yes—
578#97—34no—
579C4×C8—34no—
580C23×C3—22no—
581C23×C3—22no—
582C23×C3—21no—
583C23×C3—41no—
584C23×C3C22×D411yescharacteristic
585C23×C3C22×D411yescharacteristic
586C23×C3C22×D411yescharacteristic
587C22×D3—24no—
588C22×D3—22no—
589C22×D3—22no—
590C22×D3—42no—
591C22×D3—42no—
592C22×D3—42no—
593C22×D3—81no—
594C22×D3—81no—
595C3×Q8—22no—
596C3×D4—22no—
597C3×D4—42no—
598C3×D4—42no—
599C3×D4—81no—
600C2×C3×C4—22no—
601C2×C3×C4—22no—
602C2×C3×C4—22no—
603C2×C3×C4—22no—
604C2×C3×C4—22no—
605C2×C3×C4—24no—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—21no—
609C2×C3×C4—44no—
610C2×C3×C4—42no—
611C2×C3×C4—82no—
612C2×C3×C4—82no—
613C2×C3×C4C22×D411yescharacteristic
614C2×C3×C4C22×D411yescharacteristic
615C2×C3×C4C22×D411yescharacteristic
616C2×C3×C4C2×#4114yes—
617C2×C3×C4C2511yescharacteristic
618#67—28no—
619#67—28no—
620#67—44no—
621#67—82no—
622#67—82no—
623#67—82no—
624C2×Dic3—24no—
625C2×Dic3—24no—
626C2×Dic3—22no—
627C2×Dic3—22no—
628C2×Dic3—42no—
629C2×Dic3—82no—
630C2×Dic3—81no—
631C2×Dic3C22×D412yes—
632C2×Dic3C22×D412yes—
633C2×Dic3C22×D412yes—
634C2×Dic3C22×D412yes—
635D12—24no—
636D12—22no—
637D12—24no—
638D12—42no—
639D12C2×#4114yes—
640C4×D3—28no—
641C4×D3—28no—
642C4×D3—82no—
643C4×D3—84no—
644C4×D3—84no—
645C4×D3—82no—
646Dic6—24no—
647Dic6—22no—
648Dic6—82no—
649Dic6C2×#4114yes—
650C3×C8—24no—
651C3⋊C8—22no—
652C3⋊C8—22no—
653C24—61no—
654C24—61no—
655C24D3×D411yescharacteristic
656#41—24no—
657#41—38no—
658#41—64no—
659#41—64no—
660#41—68no—
661#41—68no—
662#41—64no—
663#41—244no—
664C2×Q8—32no—
665C2×Q8—62no—
666C2×Q8—64no—
667C2×Q8—61no—
668C2×Q8C23×D311yescharacteristic
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—32no—
673C2×D4—32no—
674C2×D4—64no—
675C2×D4—62no—
676C2×D4—62no—
677C2×D4—68no—
678C2×D4—62no—
679C2×D4—62no—
680C2×D4—62no—
681C2×D4—62no—
682C2×D4—61no—
683C2×D4—61no—
684C2×D4—64no—
685C2×D4—242no—
686C2×D4C23×D311yescharacteristic
687C22×C4—24no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—21no—
692C22×C4—32no—
693C22×C4—32no—
694C22×C4—62no—
695C22×C4—62no—
696C22×C4—64no—
697C22×C4—64no—
698C22×C4—68no—
699C22×C4—62no—
700C22×C4—61no—
701C22×C4—62no—
702C22×C4—62no—
703C22×C4—61no—
704C22×C4—82no—
705C22×C4—244no—
706C22×C4D3×D411yescharacteristic
707C22×C4D3×D411yescharacteristic
708C22×C4D3×D411yescharacteristic
709C22×C4C23×D311yescharacteristic
710C22×C4C23×D311yescharacteristic
711C22×C4C23×D311yescharacteristic
712Q16—64no—
713SD16—68no—
714SD16—64no—
715SD16—64no—
716D8—68no—
717D8—64no—
718M16—24no—
719C2×C8—32no—
720C2×C8—32no—
721C2×C8—64no—
722C2×C8C23×D314yes—
723C4⋊C4—22no—
724C4⋊C4—22no—
725C4⋊C4—22no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—31no—
729C4⋊C4—31no—
730C4⋊C4—32no—
731C4⋊C4—31no—
732C4⋊C4—31no—
733C4⋊C4—32no—
734C4⋊C4—32no—
735C4⋊C4—64no—
736C4⋊C4—64no—
737C4⋊C4—62no—
738C4⋊C4—62no—
739C4⋊C4—62no—
740C4⋊C4—62no—
741C4⋊C4—61no—
742C4⋊C4C23×D314yes—
743C4⋊C4C23×D311yescharacteristic
744C4⋊C4C23×D311yescharacteristic
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—32no—
751C22⋊C4—32no—
752C22⋊C4—32no—
753C22⋊C4—32no—
754C22⋊C4—64no—
755C22⋊C4—64no—
756C22⋊C4—62no—
757C22⋊C4—62no—
758C22⋊C4—62no—
759C22⋊C4—62no—
760C22⋊C4—62no—
761C22⋊C4—62no—
762C22⋊C4—62no—
763C42—21no—
764C42—32no—
765C42—32no—
766C42—32no—
767C42—32no—
768C42—64no—
769C42—64no—
770C42—62no—
771C22×C3—21no—
772C22×C3—21no—
773C22×C3—21no—
774C22×C3—21no—
775C22×C3—21no—
776C22×C3—21no—
777C22×C3—21no—
778C22×C3—44no—
779C22×C3—41no—
780C22×C3—41no—
781C22×C3—41no—
782C22×C3#52512yes—
783C22×C3#57712yes—
784C22×C3C23×D411yescharacteristic
785C2×D3—24no—
786C2×D3—48no—
787C2×D3—42no—
788C2×D3—42no—
789C2×D3—42no—
790C2×D3—42no—
791C2×D3—42no—
792C2×D3—162no—
793C3×C4—21no—
794C3×C4—21no—
795C3×C4—44no—
796C3×C4—41no—
797C3×C4—41no—
798C3×C4—41no—
799C3×C4#52512yes—
800C3×C4C22×#4112yes—
801Dic3—22no—
802Dic3—22no—
803Dic3—24no—
804Dic3—22no—
805Dic3—22no—
806Dic3—42no—
807C23—22no—
808C23—22no—
809C23—21no—
810C23—41no—
811C23—64no—
812C23—62no—
813C23—62no—
814C23—122no—
815C23—122no—
816C23—122no—
817C23—241no—
818C23—241no—
819C23C2×D3×D411yescharacteristic
820C23C2×D3×D411yescharacteristic
821C23C2×D3×D411yescharacteristic
822Q8—22no—
823Q8—34no—
824Q8—64no—
825Q8—62no—
826Q8—242no—
827D4—22no—
828D4—34no—
829D4—42no—
830D4—42no—
831D4—64no—
832D4—68no—
833D4—68no—
834D4—62no—
835D4—64no—
836D4—81no—
837D4—124no—
838D4—122no—
839D4—242no—
840D4—242no—
841D4—242no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—24no—
851C2×C4—32no—
852C2×C4—32no—
853C2×C4—32no—
854C2×C4—32no—
855C2×C4—44no—
856C2×C4—42no—
857C2×C4—68no—
858C2×C4—64no—
859C2×C4—62no—
860C2×C4—64no—
861C2×C4—68no—
862C2×C4—62no—
863C2×C4—82no—
864C2×C4—82no—
865C2×C4—122no—
866C2×C4—244no—
867C2×C4—244no—
868C2×C4—242no—
869C2×C4—242no—
870C2×C4—242no—
871C2×C4—241no—
872C2×C4C2×D3×D411yescharacteristic
873C2×C4C2×D3×D411yescharacteristic
874C2×C4C2×D3×D411yescharacteristic
875C2×C4D3×#4114yes—
876C2×C4C24×D311yescharacteristic
877C8—24no—
878C8—62no—
879C8—62no—
880C2×C3—22no—
881C2×C3—22no—
882C2×C3—41no—
883C2×C3—81no—
884C2×C3C2×#52511yescharacteristic
885C2×C3C2×#57711yescharacteristic
886C2×C3#358511yescharacteristic
887D3—44no—
888D3—82no—
889C22—21no—
890C22—21no—
891C22—21no—
892C22—21no—
893C22—21no—
894C22—21no—
895C22—21no—
896C22—44no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—64no—
901C22—128no—
902C22—122no—
903C22—122no—
904C22—122no—
905C22—122no—
906C22—122no—
907C22—482no—
908C22#565612yes—
909C22#577812yes—
910C22C22×D3×D411yescharacteristic
911C4—21no—
912C4—21no—
913C4—44no—
914C4—41no—
915C4—41no—
916C4—41no—
917C4—62no—
918C4—62no—
919C4—62no—
920C4—62no—
921C4—64no—
922C4—122no—
923C4#565612yes—
924C4C2×D3×#4112yes—
925C3#6058811yescharacteristic, complemented, Sylow
926C2—22no—
927C2—22no—
928C2—41no—
929C2—81no—
930C2—124no—
931C2—242no—
932C2C2×#565611yescharacteristic
933C2#8719211yescharacteristic
934C2C2×#577811yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3092C2
socleC22×C3C23×D4
hypercenter#3092D3
hypocenterC3#60588
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3092

Complements

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

NH ≅ G/Ntype
1. #86027C2semidirect
2. C2×#5504C2semidirect
3. C3×#3092C2semidirect
4. #82926C2semidirect
5. C2×#4968C2semidirect
6. #81455C2semidirect
7. #81453C2semidirect
8. #81417C2semidirect
9. #81310C2semidirect
10. #81308C2semidirect
11. #81272C2semidirect
12. #79244C2semidirect
13. #79201C2semidirect
14. #78911C2semidirect
15. #78869C2semidirect
16. #78639C2semidirect
17. #78621C2semidirect
22. #5830C22semidirect
23. #5827C22semidirect
30. #5643C22semidirect
32. #5619C22semidirect
39. #5521C22semidirect
40. #5519C22semidirect
46. #5504C22semidirect
47. C2×#893C22semidirect
50. C2×#887C22semidirect
51. C3×#484C22semidirect
52. C3×#483C22semidirect
53. C3×#481C22semidirect
54. C3×#480C22semidirect
55. C3×#428C22semidirect
56. C3×#417C22semidirect
60. #5122C22semidirect
61. #5119C22semidirect
62. #5050C22semidirect
63. #5047C22semidirect
64. #5046C22semidirect
65. #5040C22semidirect
66. #5037C22semidirect
67. #5036C22semidirect
71. #4968C22semidirect
72. C2×#809C22semidirect
73. C2×#808C22semidirect
74. #4891C22semidirect
75. #4889C22semidirect
76. #4877C22semidirect
77. #4872C22semidirect
78. #4870C22semidirect
79. #4869C22semidirect
80. #4854C22semidirect
81. #4852C22semidirect
82. #4819C22semidirect
83. #4798C22semidirect
84. #4789C22semidirect
85. #4788C22semidirect
86. #4786C22semidirect
87. #4785C22semidirect
88. #4762C22semidirect
89. #4758C22semidirect
93. #4720C22semidirect
94. #4719C22semidirect
95. #4718C22semidirect
104. #3092D3semidirect
281. #484C2×D3semidirect
282. #483C2×D3semidirect
286. #481C2×D3semidirect
287. #480C2×D3semidirect
316. #428C2×D3semidirect
320. #417C2×D3semidirect
366. #235#41semidirect
925. C3#60588semidirect

Maximal subgroups

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

subgroupindex
#860272
C2×#55042
C3×#30922
#829262
C2×#49682
#814552
#814532
#814172
#813102
#813082
#812722
#792442
#792012
#789112
#788692
#786392
#786212
#605883