Finite Group Databasebeta

← #11664128

Subgroups — #11664128

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
1#86028C211yesmaximal, characteristic, complemented
2C2×#5504C211yesmaximal, characteristic, complemented
3C3×#3092C211yesmaximal, characteristic, complemented
4#82926C211yesmaximal, characteristic
5C2×#4970C211yesmaximal, characteristic, complemented
6#81454C212yesmaximal, complemented
7#81452C212yesmaximal, complemented
8#81416C214yesmaximal, complemented
9#81311C212yesmaximal, complemented
10#81309C212yesmaximal, complemented
11#81273C214yesmaximal, complemented
12#79243C212yesmaximal, complemented
13#79202C212yesmaximal, complemented
14#78912C212yesmaximal, complemented
15#78868C212yesmaximal, complemented
16#78640C211yesmaximal, characteristic, complemented
17#78621C211yesmaximal, characteristic, complemented
18#60589—31nomaximal, Sylow
19C22×#235C2211yescharacteristic
20C3×#525C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22#5827C2211yescharacteristic, complemented
23#5825C2211yescharacteristic, complemented
24C2×#950C2212yes—
25C2×C4×#67—22no—
26C2×#926C2211yescharacteristic
27C2×#924C2211yescharacteristic
28C2×#909C2212yes—
29#5650—22no—
30#5625C2212yescomplemented
31#5622C2212yes—
32#5603C2212yescomplemented
33#5600C2212yes—
34#5587—22no—
35#5543—21no—
36#5542—21no—
37#5541—21no—
38#5541—21no—
39#5519C2211yescharacteristic, complemented
40#5516C2211yescharacteristic, complemented
41#5504—22no—
42#5504—21no—
43#5504—21no—
44#5504C2214yes—
45#5504C2212yes—
46#5504C2212yes—
47C2×#893C2212yes—
48C2×#892—21no—
49C2×D3×C4⋊C4—21no—
50C2×#887C2212yes—
51C3×#484C2212yes—
52C3×#483C2212yescomplemented
53C3×#481C2212yes—
54C3×#480C2212yescomplemented
55C3×#428C2212yescomplemented
56C3×#417C2212yescomplemented
57C3×#407C2211yescharacteristic
58C2×#830C2211yescharacteristic
59#5133C2212yes—
60#5122C2212yescomplemented
61#5119C2212yescomplemented
62#5050C2211yescharacteristic
63#5047C2212yes—
64#5046C2211yescharacteristic
65#5040C2211yescharacteristic
66#5037C2212yes—
67#5036C2211yescharacteristic
68#5002C2212yes—
69#4970C2212yes—
70#4970C2212yes—
71#4970C2214yescomplemented
72C2×#810C2212yescomplemented
73C2×#807C2212yescomplemented
74#4890C2214yescomplemented
75#4889C2214yescomplemented
76#4875C2214yescomplemented
77#4873C2214yescomplemented
78#4871C2214yescomplemented
79#4857C2214yescomplemented
80#4853C2214yescomplemented
81#4852C2214yescomplemented
82#4818C2214yescomplemented
83#4817C2214yescomplemented
84#4795C2214yescomplemented
85#4790C2214yescomplemented
86#4787C2214yescomplemented
87#4767C2214yescomplemented
88#4757C2214yescomplemented
89#4756C2214yescomplemented
90#4739C2212yes—
91#4733C2214yes—
92#4731C2212yes—
93#4720C2214yescomplemented
94#4719C2212yes—
95#4718C2212yes—
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#3092D311yescharacteristic, complemented
105C2×#484—31no—
106#3083—32no—
107#3046—32no—
108#3007—31no—
109#3002—31no—
110#2951—32no—
111#2947—32no—
112#2924—31no—
113C2×C3×#41C2311yescharacteristic
114C23×C3×C4—21no—
115C23×C3×C4C2311yescharacteristic
116C22×#67—21no—
117C2×#235—21no—
118C2×#235—21no—
119C2×#235—28no—
120C2×#235C2312yes—
121C2×#235C2312yes—
122C22×D12C2311yescharacteristic
123C22×C4×D3—21no—
124C22×C4×D3—22no—
125C22×Dic6C2311yescharacteristic
126C22×Dic6C2311yescharacteristic
127C2×C3×M16C2312yes—
128C3×#123—21no—
129C3×C22⋊Q8C2311yescharacteristic
130C3×C22⋊Q8C2311yescharacteristic
131C3×#121C2311yescharacteristic
132C3×#121C2311yescharacteristic
133C3×#120—21no—
134C3×C4×D4—21no—
135C3×C4×D4—21no—
136C3×#117C2311yescharacteristic
137C2×C3×C4⋊C4—21no—
138C2×C3×C4⋊C4—21no—
139C2×C3×C4⋊C4—21no—
140C2×C3×C4⋊C4C2312yes—
141C2×C3×C4⋊C4C2312yes—
142C2×C3×C4⋊C4C2312yes—
143C2×#217—21no—
144C2×#217D412yes—
145#950—28no—
146Q8×Dic3C2312yes—
147#944C2312yes—
148C2×#216C2312yes—
149C2×#215C2312yes—
150#936—22no—
151#936C2312yes—
152#935—22no—
153#935—22no—
154#935—22no—
155D4×Dic3—22no—
156D4×Dic3—22no—
157D4×Dic3C2312yes—
158C2×#214C2312yes—
159C2×#213C2312yes—
160C4×#67—24no—
161C4×#67—24no—
162C4×#67—24no—
163C4×#67—24no—
164C2×(C2×D3)⋊C4—22no—
165#926—21no—
166#926D412yes—
167#926D411yescharacteristic
168#926D411yescharacteristic
169#926C2311yescharacteristic
170#926C2312yes—
171#926C2311yescharacteristic
172C2×C4⋊Dic3—21no—
173C2×C4⋊Dic3D411yescharacteristic
174C2×C4⋊Dic3D411yescharacteristic
175C2×C4⋊Dic3C2311yescharacteristic
176#924—21no—
177#924—21no—
178#924—21no—
179#924—21no—
180#924C2312yes—
181#924C2312yes—
182C2×Dic3⋊C4—21no—
183C2×Dic3⋊C4—22no—
184C2×C4×Dic3—22no—
185C2×C4×Dic3C2312yes—
186C22×C3⋊C8C2312yes—
187#909—28no—
188C2×Dic12C2314yes—
189C2×#204C2314yes—
190#893—22no—
191#893—22no—
192#893C2314yes—
193#893C2314yes—
194#892—22no—
195#892—22no—
196#892—24no—
197D3×C4⋊C4—22no—
198D3×C4⋊C4—22no—
199D3×C4⋊C4—24no—
200#890—22no—
201#890C2312yes—
202#889—22no—
203#889—22no—
204#888C2312yes—
205#887—22no—
206#887—22no—
207#887—22no—
208#887C2312yes—
209#887C2314yes—
210#887C2314yes—
211#887C2312yes—
212#879—22no—
213#879—22no—
214#879—22no—
215#879—22no—
216#878—22no—
217#878—22no—
218#878—22no—
219#877—22no—
220#877—22no—
221#877—22no—
222#870—21no—
223#869—21no—
224C4×Dic6—21no—
225C4×Dic6—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#810C2314yes—
243#810C2314yes—
244#810C2312yes—
245#809C2312yes—
246#809C2312yes—
247#807C2314yes—
248#807C2314yes—
249C22×#41—31no—
250C2×#137—32no—
251C2×#135—32no—
252#556—61no—
253#554—61no—
254#552—61no—
255#552—61no—
256#552—62no—
257#551—62no—
258#544—31no—
259#542—32no—
260#541—32no—
261#536—31no—
262#533—32no—
263#529—32no—
264#525C2×D311yescharacteristic
265C2×C22⋊Q8—31no—
266#520—31no—
267#520—32no—
268#520—34no—
269#520—32no—
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—31no—
278C2×#117—61no—
279C22×C4⋊C4—61no—
280C22×C4⋊C4C2×D311yescharacteristic
281#484—32no—
282#484—32no—
283#484—34no—
284#484C2×D312yes—
285#483C2×D312yescomplemented
286#481C2×D312yes—
287#480C2×D312yescomplemented
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—31no—
301#450—32no—
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#433—34no—
314#432—32no—
315#431—32no—
316#428C2×D312yescomplemented
317C2×#107—32no—
318#424—32no—
319#417—32no—
320#417C2×D312yescomplemented
321#416—32no—
322C2×#103—32no—
323#407C2×D311yescharacteristic
324C2×C22⋊C8—31no—
325#405—32no—
326C24×C3C2×D411yescharacteristic
327C23×D3—21no—
328C3×#41—24no—
329C2×C3×Q8C2411yescharacteristic
330C2×C3×D4—21no—
331C2×C3×D4—21no—
332C2×C3×D4—21no—
333C2×C3×D4C2411yescharacteristic
334C22×C3×C4—24no—
335C22×C3×C4—22no—
336C22×C3×C4—22no—
337C22×C3×C4—22no—
338C22×C3×C4—21no—
339C22×C3×C4—82no—
340C22×C3×C4C2×D411yescharacteristic
341C22×C3×C4C2×D411yescharacteristic
342C22×C3×C4C2×D411yescharacteristic
343C22×C3×C4C2411yescharacteristic
344C22×C3×C4C2411yescharacteristic
345C22×C3×C4C2411yescharacteristic
346C2×#67—28no—
347C2×#67—22no—
348C2×#67—22no—
349C22×Dic3—21no—
350C22×Dic3—21no—
351C22×Dic3—21no—
352C22×Dic3—22no—
353C22×Dic3C2×D412yes—
354C22×Dic3C2×D412yes—
355#235—28no—
356#235—28no—
357#235—24no—
358#235—24no—
359#235—24no—
360#235#4118yes—
361C2×D12—21no—
362C2×D12—24no—
363C2×D12C2412yes—
364C2×C4×D3—28no—
365C2×C4×D3—22no—
366C2×C4×D3—22no—
367C2×C4×D3—24no—
368C2×C4×D3—24no—
369C2×C4×D3—84no—
370C2×Dic6—21no—
371C2×Dic6—24no—
372C2×Dic6—24no—
373C2×Dic6—21no—
374C2×Dic6—22no—
375C2×Dic6C2412yes—
376C2×Dic6C2412yes—
377C3×M16—24no—
378C2×C3×C8C2414yes—
379C3×C4⋊C4—21no—
380C3×C4⋊C4—22no—
381C3×C4⋊C4—21no—
382C3×C4⋊C4—22no—
383C3×C4⋊C4—22no—
384C3×C4⋊C4C2414yes—
385C3×C4⋊C4C2411yescharacteristic
386C3×C4⋊C4C2411yescharacteristic
387C3×C22⋊C4—21no—
388C3×C22⋊C4—21no—
389C3×C22⋊C4—21no—
390C3×C22⋊C4—21no—
391C3×C22⋊C4—21no—
392C3×C42—21no—
393#217—22no—
394#217—22no—
395#217—22no—
396#217—22no—
397#217—22no—
398#217C2×D412yes—
399#217C2×D412yes—
400#217C2×D412yes—
401#217C2×D412yes—
402#216—24no—
403#215—24no—
404#214—24no—
405#213—24no—
406(C2×D3)⋊C4—24no—
407(C2×D3)⋊C4—24no—
408C4⋊Dic3—21no—
409C4⋊Dic3—22no—
410C4⋊Dic3—22no—
411C4⋊Dic3C2×D411yescharacteristic
412C4⋊Dic3C2×D411yescharacteristic
413C4⋊Dic3C2×D411yescharacteristic
414C4⋊Dic3C2×D411yescharacteristic
415C4⋊Dic3C2×D412yes—
416C4⋊Dic3C2×D412yes—
417C4⋊Dic3C2412yes—
418Dic3⋊C4—22no—
419Dic3⋊C4—22no—
420Dic3⋊C4—22no—
421Dic3⋊C4—22no—
422Dic3⋊C4—22no—
423Dic3⋊C4—22no—
424Dic3⋊C4—22no—
425Dic3⋊C4—22no—
426Dic3⋊C4—24no—
427Dic3⋊C4—24no—
428C4×Dic3—22no—
429C4×Dic3—22no—
430C4×Dic3—22no—
431C4×Dic3—24no—
432C4×Dic3—24no—
433C4×Dic3C2×D412yes—
434C4×Dic3C2×D412yes—
435C4×Dic3C2412yes—
436C4×Dic3C2412yes—
437C2×C3⋊C8—24no—
438C2×C3⋊C8C2412yes—
439C2×C3⋊C8C2412yes—
440Dic12—28no—
441#204—28no—
442C2×#41—32no—
443C2×#41—32no—
444C2×#41—68no—
445C2×#41—61no—
446C2×#41—61no—
447C2×#41C22×D311yescharacteristic
448C22×Q8—31no—
449C22×Q8—31no—
450C22×D4—31no—
451C22×D4—61no—
452C23×C4—21no—
453C23×C4—62no—
454C23×C4—61no—
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×C8—32no—
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—61no—
475#125—62no—
476#125—62no—
477#125—62no—
478#124—32no—
479#124—62no—
480#123—21no—
481#123—62no—
482#123—62no—
483#123—62no—
484C22⋊Q8—32no—
485C22⋊Q8—32no—
486C22⋊Q8—62no—
487C22⋊Q8—62no—
488C22⋊Q8—62no—
489C22⋊Q8—61no—
490C22⋊Q8—61no—
491C22⋊Q8—61no—
492C22⋊Q8—61no—
493C22⋊Q8C22×D311yescharacteristic
494C22⋊Q8C22×D311yescharacteristic
495#121C22×D311yescharacteristic
496#121C22×D311yescharacteristic
497#120—21no—
498C4×Q8—32no—
499C4×Q8—34no—
500C4×Q8—34no—
501C4×Q8—32no—
502C4×Q8—32no—
503C4×Q8—61no—
504C4×Q8—61no—
505C4×Q8—62no—
506C4×Q8—62no—
507C4×Q8—62no—
508C4×D4—21no—
509C4×D4—21no—
510C4×D4—32no—
511C4×D4—34no—
512C4×D4—34no—
513C4×D4—62no—
514C4×D4—62no—
515C4×D4—64no—
516C4×D4—64no—
517C4×D4—64no—
518C4×D4—64no—
519C4×D4—62no—
520C4×D4—62no—
521#117—31no—
522#117—32no—
523#117—31no—
524#117—31no—
525#117—31no—
526#117—32no—
527#117—62no—
528#117—62no—
529#117—62no—
530#117—62no—
531#117—62no—
532#117—64no—
533#117—61no—
534#117C22×D311yescharacteristic
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—31no—
539C2×C4⋊C4—31no—
540C2×C4⋊C4—31no—
541C2×C4⋊C4—62no—
542C2×C4⋊C4—64no—
543C2×C4⋊C4—62no—
544C2×C4⋊C4—61no—
545C2×C4⋊C4—62no—
546C2×C4⋊C4—61no—
547C2×C4⋊C4C22×D312yes—
548C2×C4⋊C4C22×D312yes—
549C2×C4⋊C4C22×D312yes—
550C2×C22⋊C4—32no—
551C2×C22⋊C4—62no—
552C2×C22⋊C4—61no—
553C2×C42—32no—
554C2×C42—62no—
555#107—34no—
556#107—34no—
557#107C22×D314yes—
558#106C22×D314yes—
559C4⋊C8—34no—
560C4⋊C8—34no—
561#103—34no—
562#103—34no—
563#103—34no—
564#103—32no—
565#103—32no—
566#103C22×D314yes—
567#102—34no—
568#102—32no—
569#102—32no—
570#102C22×D314yes—
571C22⋊C8—31no—
572C22⋊C8—31no—
573C22⋊C8—32no—
574C22⋊C8C22×D312yes—
575C22⋊C8C22×D312yes—
576#97—34no—
577C4×C8—34no—
578C23×C3—22no—
579C23×C3—22no—
580C23×C3—21no—
581C23×C3—41no—
582C23×C3C22×D411yescharacteristic
583C23×C3C22×D411yescharacteristic
584C23×C3C22×D411yescharacteristic
585C22×D3—24no—
586C22×D3—22no—
587C22×D3—42no—
588C22×D3—42no—
589C3×Q8—22no—
590C3×D4—22no—
591C3×D4—42no—
592C3×D4—42no—
593C3×D4—81no—
594C2×C3×C4—22no—
595C2×C3×C4—22no—
596C2×C3×C4—22no—
597C2×C3×C4—22no—
598C2×C3×C4—22no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—21no—
602C2×C3×C4—24no—
603C2×C3×C4—44no—
604C2×C3×C4—42no—
605C2×C3×C4—82no—
606C2×C3×C4—82no—
607C2×C3×C4C22×D411yescharacteristic
608C2×C3×C4C22×D411yescharacteristic
609C2×C3×C4C22×D411yescharacteristic
610C2×C3×C4C2×#4114yes—
611C2×C3×C4C2511yescharacteristic
612#67—28no—
613#67—28no—
614C2×Dic3—24no—
615C2×Dic3—24no—
616C2×Dic3—22no—
617C2×Dic3—22no—
618C2×Dic3—22no—
619C2×Dic3—42no—
620C2×Dic3—42no—
621C2×Dic3—82no—
622C2×Dic3—81no—
623C2×Dic3C22×D412yes—
624C2×Dic3C22×D412yes—
625C2×Dic3C22×D412yes—
626C2×Dic3C22×D412yes—
627D12—24no—
628D12—22no—
629D12C2×#4114yes—
630C4×D3—28no—
631C4×D3—28no—
632C4×D3—84no—
633C4×D3—84no—
634Dic6—24no—
635Dic6—22no—
636Dic6—24no—
637Dic6—42no—
638Dic6—82no—
639Dic6C2×#4114yes—
640C3×C8—24no—
641C3⋊C8—22no—
642C3⋊C8—22no—
643C24—61no—
644C24D3×D411yescharacteristic
645#41—24no—
646#41—38no—
647#41—64no—
648#41—64no—
649#41—68no—
650#41—68no—
651#41—64no—
652C2×Q8—32no—
653C2×Q8—32no—
654C2×Q8—62no—
655C2×Q8—64no—
656C2×Q8—61no—
657C2×Q8—61no—
658C2×Q8—64no—
659C2×Q8C23×D311yescharacteristic
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—32no—
664C2×D4—64no—
665C2×D4—68no—
666C2×D4—62no—
667C2×D4—62no—
668C2×D4—61no—
669C2×D4C23×D311yescharacteristic
670C22×C4—24no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—21no—
675C22×C4—32no—
676C22×C4—32no—
677C22×C4—64no—
678C22×C4—64no—
679C22×C4—68no—
680C22×C4—62no—
681C22×C4—61no—
682C22×C4—62no—
683C22×C4—62no—
684C22×C4—61no—
685C22×C4—61no—
686C22×C4—82no—
687C22×C4—244no—
688C22×C4D3×D411yescharacteristic
689C22×C4D3×D411yescharacteristic
690C22×C4D3×D411yescharacteristic
691C22×C4C23×D311yescharacteristic
692C22×C4C23×D311yescharacteristic
693C22×C4C23×D311yescharacteristic
694Q16—68no—
695Q16—64no—
696SD16—68no—
697SD16—64no—
698SD16—64no—
699D8—64no—
700M16—24no—
701C2×C8—32no—
702C2×C8—32no—
703C2×C8—64no—
704C2×C8C23×D314yes—
705C4⋊C4—22no—
706C4⋊C4—22no—
707C4⋊C4—22no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—31no—
711C4⋊C4—32no—
712C4⋊C4—31no—
713C4⋊C4—31no—
714C4⋊C4—31no—
715C4⋊C4—32no—
716C4⋊C4—32no—
717C4⋊C4—64no—
718C4⋊C4—64no—
719C4⋊C4—62no—
720C4⋊C4—62no—
721C4⋊C4—62no—
722C4⋊C4—62no—
723C4⋊C4—62no—
724C4⋊C4—62no—
725C4⋊C4—62no—
726C4⋊C4—62no—
727C4⋊C4—61no—
728C4⋊C4—62no—
729C4⋊C4—62no—
730C4⋊C4C23×D311yescharacteristic
731C4⋊C4C23×D311yescharacteristic
732C4⋊C4C23×D314yes—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—32no—
739C22⋊C4—32no—
740C22⋊C4—32no—
741C22⋊C4—32no—
742C22⋊C4—64no—
743C22⋊C4—64no—
744C22⋊C4—62no—
745C22⋊C4—62no—
746C22⋊C4—62no—
747C22⋊C4—62no—
748C22⋊C4—62no—
749C42—21no—
750C42—32no—
751C42—32no—
752C42—32no—
753C42—32no—
754C42—64no—
755C42—64no—
756C42—62no—
757C42—62no—
758C42—62no—
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—41no—
768C22×C3—41no—
769C22×C3—41no—
770C22×C3#52512yes—
771C22×C3#57812yes—
772C22×C3C23×D411yescharacteristic
773C2×D3—24no—
774C2×D3—48no—
775C2×D3—42no—
776C2×D3—42no—
777C3×C4—21no—
778C3×C4—21no—
779C3×C4—41no—
780C3×C4—44no—
781C3×C4—41no—
782C3×C4—41no—
783C3×C4#52512yes—
784C3×C4C22×#4112yes—
785Dic3—22no—
786Dic3—22no—
787Dic3—24no—
788Dic3—22no—
789Dic3—22no—
790Dic3—42no—
791Dic3—42no—
792C23—22no—
793C23—22no—
794C23—21no—
795C23—41no—
796C23—64no—
797C23—62no—
798C23—122no—
799C23—122no—
800C23C2×D3×D411yescharacteristic
801C23C2×D3×D411yescharacteristic
802C23C2×D3×D411yescharacteristic
803Q8—22no—
804Q8—34no—
805Q8—64no—
806Q8—62no—
807Q8—64no—
808Q8—122no—
809Q8—242no—
810D4—22no—
811D4—34no—
812D4—42no—
813D4—42no—
814D4—64no—
815D4—68no—
816D4—68no—
817D4—62no—
818D4—81no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—24no—
828C2×C4—32no—
829C2×C4—32no—
830C2×C4—32no—
831C2×C4—32no—
832C2×C4—44no—
833C2×C4—42no—
834C2×C4—68no—
835C2×C4—64no—
836C2×C4—62no—
837C2×C4—64no—
838C2×C4—68no—
839C2×C4—62no—
840C2×C4—62no—
841C2×C4—82no—
842C2×C4—82no—
843C2×C4—122no—
844C2×C4—122no—
845C2×C4—244no—
846C2×C4—244no—
847C2×C4—242no—
848C2×C4—241no—
849C2×C4C2×D3×D411yescharacteristic
850C2×C4C2×D3×D411yescharacteristic
851C2×C4C2×D3×D411yescharacteristic
852C2×C4D3×#4114yes—
853C2×C4C24×D311yescharacteristic
854C8—24no—
855C8—62no—
856C8—62no—
857C2×C3—22no—
858C2×C3—22no—
859C2×C3—41no—
860C2×C3—81no—
861C2×C3C2×#52511yescharacteristic
862C2×C3C2×#57811yescharacteristic
863C2×C3#358511yescharacteristic
864D3—44no—
865C22—21no—
866C22—21no—
867C22—21no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—21no—
872C22—44no—
873C22—41no—
874C22—41no—
875C22—41no—
876C22—64no—
877C22—128no—
878C22—122no—
879C22—122no—
880C22#565612yes—
881C22#577912yes—
882C22C22×D3×D411yescharacteristic
883C4—21no—
884C4—21no—
885C4—44no—
886C4—41no—
887C4—41no—
888C4—41no—
889C4—62no—
890C4—62no—
891C4—62no—
892C4—62no—
893C4—64no—
894C4—122no—
895C4—122no—
896C4#565612yes—
897C4C2×D3×#4112yes—
898C3#6058911yescharacteristic, complemented, Sylow
899C2—22no—
900C2—22no—
901C2—41no—
902C2—81no—
903C2—124no—
904C2C2×#565611yescharacteristic
905C2#8719211yescharacteristic
906C2C2×#577911yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3092C2
socleC22×C3C23×D4
prime radical#82926C2
hypercenter#3092D3
hypocenterC3#60589
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. #86028C2semidirect
2. C2×#5504C2semidirect
3. C3×#3092C2semidirect
5. C2×#4970C2semidirect
6. #81454C2semidirect
7. #81452C2semidirect
8. #81416C2semidirect
9. #81311C2semidirect
10. #81309C2semidirect
11. #81273C2semidirect
12. #79243C2semidirect
13. #79202C2semidirect
14. #78912C2semidirect
15. #78868C2semidirect
16. #78640C2semidirect
17. #78621C2semidirect
22. #5827C22semidirect
23. #5825C22semidirect
30. #5625C22semidirect
32. #5603C22semidirect
39. #5519C22semidirect
40. #5516C22semidirect
52. C3×#483C22semidirect
54. C3×#480C22semidirect
55. C3×#428C22semidirect
56. C3×#417C22semidirect
60. #5122C22semidirect
61. #5119C22semidirect
71. #4970C22semidirect
72. C2×#810C22semidirect
73. C2×#807C22semidirect
74. #4890C22semidirect
75. #4889C22semidirect
76. #4875C22semidirect
77. #4873C22semidirect
78. #4871C22semidirect
79. #4857C22semidirect
80. #4853C22semidirect
81. #4852C22semidirect
82. #4818C22semidirect
83. #4817C22semidirect
84. #4795C22semidirect
85. #4790C22semidirect
86. #4787C22semidirect
87. #4767C22semidirect
88. #4757C22semidirect
89. #4756C22semidirect
93. #4720C22semidirect
104. #3092D3semidirect
285. #483C2×D3semidirect
287. #480C2×D3semidirect
316. #428C2×D3semidirect
320. #417C2×D3semidirect
898. C3#60589semidirect

Maximal subgroups

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

subgroupindex
#860282
C2×#55042
C3×#30922
#829262
C2×#49702
#814542
#814522
#814162
#813112
#813092
#812732
#792432
#792022
#789122
#788682
#786402
#786212
#605893