Finite Group Databasebeta

← #11675222

Subgroups — #11675222

Order 768.

1776 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86215C211yesmaximal, characteristic, complemented
2#85830C211yesmaximal, characteristic, complemented
3C3×#3079C211yesmaximal, characteristic, complemented
4C2×#5093C211yesmaximal, characteristic, complemented
5C4×#950C211yesmaximal, characteristic
6#81138C212yesmaximal, complemented
7#81135C212yesmaximal, complemented
8#81091C212yesmaximal, complemented
9#81087C212yesmaximal, complemented
10#81042C212yesmaximal, complemented
11#81037C212yesmaximal, complemented
12#80994C212yesmaximal, complemented
13#80993C212yesmaximal, complemented
14#79246C212yesmaximal, complemented
15#79202C212yesmaximal, complemented
16#79057C211yesmaximal, characteristic, complemented
17#79044C211yesmaximal, characteristic, complemented
18#78912C212yesmaximal
19#78877C212yesmaximal, complemented
20#61330—31nomaximal, Sylow
21C2×C3×C4⋊Q8C2211yescharacteristic
22C3×C4×#41C2211yescharacteristic
23#5825C2212yes—
24C2×#950C2211yescharacteristic
25Q8×#67—22no—
26C2×#909C2212yes—
27#5730C2212yes—
28#5729—22no—
29#5728—21no—
30#5727C2212yes—
31D3×C4⋊Q8—21no—
32#5722C2212yes—
33#5721C2212yes—
34#5567C2212yes—
35#5567C2212yes—
36#5542C2212yes—
37#5542C2212yes—
38#5541—22no—
39#5541—22no—
40#5518—22no—
41#5516C2212yes—
42#5511—22no—
43#5504C2212yes—
44#5500C2212yes—
45C4×#235C2211yescharacteristic
46#5470—21no—
47#5470—21no—
48#5470C2211yescharacteristic
49C2×#869C2211yescharacteristic
50C3×#477C2212yes—
51C3×#476C2212yes—
52C3×#475C2212yes—
53C3×#474C2212yes—
54C3×#428C2212yes—
55C3×#423C2211yescharacteristic
56C3×#417C2212yes—
57#5233C2211yescharacteristic
58#5122C2212yes—
59#5120C2212yes—
60#5119C2212yes—
61#5093C2212yes—
62#5093C2212yes—
63#5093C2212yes—
64#5093C2212yes—
65C4×#216C2211yescharacteristic
66C4×#216C2211yescharacteristic
67C4×#215C2211yescharacteristic
68C4×#215C2211yescharacteristic
69C4×#214C2211yescharacteristic
70C4×#214C2211yescharacteristic
71C4×#213C2211yescharacteristic
72C4×#213C2211yescharacteristic
73#5002C2211yescharacteristic
74#4998C2211yescharacteristic
75C2×#810C2212yes—
76C2×#810C2212yes—
77C2×C4×C3⋊C8C2211yescharacteristic
78#4889C2214yes—
79#4877C2214yes—
80#4875C2214yes—
81#4873C2214yes—
82#4857C2214yes—
83#4854C2214yes—
84#4853C2214yes—
85#4852C2214yes—
86#4849C2212yes—
87#4849C2212yes—
88#4841C2212yes—
89#4841C2212yes—
90#4831C2212yes—
91#4831C2212yes—
92#4830C2212yes—
93#4830C2212yes—
94#4818C2214yes—
95#4797C2214yes—
96#4795C2214yes—
97#4792C2214yes—
98#4787C2214yes—
99#4768C2214yes—
100#4767C2214yes—
101#4765C2214yes—
102#3509—31no—
103#3503—31no—
104#3374—32no—
105#3372—32no—
106#3369—32no—
107#3367—32no—
108#3364—32no—
109#3363—32no—
110#3360—32no—
111#3359—32no—
112#3137—32no—
113C2×#487—31no—
114#3082—32no—
115#3079D311yescharacteristic, complemented
116#3046—32no—
117#3039—31no—
118#2960—31no—
119#2947—32no—
120C4×#135—31no—
121C2×C3×#41C2311yescharacteristic
122C22×C3×Q8—21no—
123C2×D3×Q8—22no—
124C2×#235C2311yescharacteristic
125C22×Dic6C2312yes—
126C2×C3×M16C2312yes—
127C3×C4⋊Q8—21no—
128C3×C4⋊Q8—21no—
129C3×C4⋊Q8C2312yes—
130C3×C4⋊Q8C2312yes—
131C3×C4×Q8C2311yescharacteristic
132C3×C4×Q8C2311yescharacteristic
133C3×C4×D4—21no—
134C3×C4×D4—21no—
135C3×C4×D4C2311yescharacteristic
136C3×C4×D4C2311yescharacteristic
137C3×#117—21no—
138C3×#117C2311yescharacteristic
139C2×C3×C4⋊C4—21no—
140C2×C3×C4⋊C4C2312yes—
141C2×C3×C42—21no—
142C2×C3×C42C2311yescharacteristic
143#950—24no—
144#946—22no—
145#946—24no—
146Q8×Dic3—22no—
147#944—22no—
148#944—24no—
149#944C2314yes—
150C2×#216C2311yescharacteristic
151C2×#215C2311yescharacteristic
152#936C2314yes—
153#935—24no—
154C2×#214C2311yescharacteristic
155C2×#213C2311yescharacteristic
156C4×#67—21no—
157C4×#67—21no—
158C4×#67—24no—
159#926—22no—
160#926—22no—
161#926C2311yescharacteristic
162#926C2312yes—
163C2×C4⋊Dic3—21no—
164C2×C4⋊Dic3—21no—
165#924—22no—
166#924—22no—
167#924—24no—
168#924—22no—
169#924—22no—
170#924D412yes—
171#924D412yes—
172C22×C3⋊C8C2311yescharacteristic
173C22×C3⋊C8C2311yescharacteristic
174#909—28no—
175C2×Dic12C2314yes—
176C2×#204C2314yes—
177#897—22no—
178#896—24no—
179#893C2314yes—
180#892—22no—
181D3×C4⋊C4—22no—
182D3×C4⋊C4—22no—
183#890—22no—
184#890C2314yes—
185#889—24no—
186#889—24no—
187#889—24no—
188#888—22no—
189#888—22no—
190#888C2314yes—
191#887—22no—
192#887C2314yes—
193#887C2314yes—
194#887C2314yes—
195#879—24no—
196#879—24no—
197#877—24no—
198C4×D12C2311yescharacteristic
199C4×D12C2311yescharacteristic
200#872—21no—
201C42×D3—21no—
202#870—22no—
203#870—22no—
204#870D412yes—
205#869—21no—
206#869—21no—
207#869D411yescharacteristic
208#869D411yescharacteristic
209#869C2312yes—
210#869C2312yes—
211C4×Dic6—22no—
212C4×Dic6—22no—
213C4×Dic6—22no—
214C4×Dic6—22no—
215C4×Dic6C2311yescharacteristic
216C4×Dic6C2311yescharacteristic
217C4×Dic6C2312yes—
218C4×Dic6C2312yes—
219C3×#107C2314yes—
220C3×#106C2314yes—
221C3×C4⋊C8C2312yes—
222C3×C4⋊C8C2312yes—
223C3×#103C2314yes—
224C3×#102C2314yes—
225#835C2311yescharacteristic
226#835C2311yescharacteristic
227#832C2311yescharacteristic
228#832C2311yescharacteristic
229#816C2314yes—
230#816C2314yes—
231#815C2314yes—
232Dic3⋊C8C2314yes—
233Dic3⋊C8C2314yes—
234C8×Dic3C2314yes—
235#810C2311yescharacteristic
236#810C2314yes—
237#810C2314yes—
238#810C2314yes—
239#810C2314yes—
240#810C2311yescharacteristic
241#809C2311yescharacteristic
242#809C2311yescharacteristic
243#808C2311yescharacteristic
244#808C2311yescharacteristic
245#807C2311yescharacteristic
246#807C2311yescharacteristic
247C4×C3⋊C8C2311yescharacteristic
248C4×C3⋊C8C2311yescharacteristic
249C4×C3⋊C8C2311yescharacteristic
250C4×C3⋊C8C2311yescharacteristic
251C2×#137—32no—
252C2×#135—31no—
253Q82—32no—
254#557—32no—
255#557—32no—
256#557—32no—
257#556—32no—
258#556—32no—
259#554—32no—
260#554—62no—
261#552—62no—
262#552—62no—
263D4×Q8—32no—
264D4×Q8—62no—
265#544—32no—
266#544—62no—
267#541—62no—
268#536—32no—
269#533—31no—
270#533—61no—
271#533—61no—
272#533—61no—
273C2×C4⋊Q8—31no—
274C2×C4⋊Q8—61no—
275C2×C4⋊Q8C2×D311yescharacteristic
276#520—32no—
277#519—32no—
278C4×#41—31no—
279C4×#41C2×D311yescharacteristic
280#491—34no—
281#489—34no—
282#488—34no—
283#487—32no—
284#487—32no—
285#487—32no—
286#487—32no—
287#487—34no—
288#479—34no—
289#479—34no—
290#477—34no—
291#477C2×D312yes—
292#476C2×D312yes—
293#475—34no—
294#475C2×D312yes—
295#474C2×D312yes—
296#464—34no—
297#463—34no—
298#462—32no—
299#462—32no—
300#462—34no—
301#461—32no—
302#461—32no—
303#461—34no—
304#446—32no—
305#446—32no—
306C8×Q8—32no—
307C8×Q8—32no—
308#441—34no—
309#440—34no—
310C4×Q16—31no—
311C4×Q16—31no—
312C4×Q16—34no—
313C4×SD16—31no—
314C4×SD16—31no—
315C4×SD16—31no—
316C4×SD16—31no—
317C4×SD16—34no—
318C4×D8—31no—
319C4×D8—31no—
320#428C2×D312yes—
321#427—31no—
322#424—32no—
323#423C2×D311yescharacteristic
324#419—32no—
325#417C2×D312yes—
326#416—31no—
327#416—31no—
328C2×#103—32no—
329C2×#103—32no—
330#405—32no—
331C2×C4×C8—31no—
332C3×#41—22no—
333C3×#41—22no—
334C2×C3×Q8—22no—
335C2×C3×Q8—22no—
336C2×C3×Q8—82no—
337C2×C3×Q8C2411yescharacteristic
338C2×C3×D4—21no—
339C2×C3×D4C2411yescharacteristic
340C22×C3×C4—22no—
341C22×C3×C4—21no—
342C22×C3×C4—21no—
343C22×C3×C4—21no—
344C22×C3×C4C2×D411yescharacteristic
345C22×C3×C4C2×D411yescharacteristic
346C22×C3×C4C2411yescharacteristic
347C2×#67—21no—
348C22×Dic3—22no—
349D3×Q8—84no—
350#235—22no—
351#235#4114yes—
352C2×D12C2411yescharacteristic
353C2×C4×D3—21no—
354C2×C4×D3—21no—
355C2×C4×D3—21no—
356C2×C4×D3—24no—
357C2×Dic6—24no—
358C2×Dic6—24no—
359C2×Dic6—22no—
360C2×Dic6—24no—
361C2×Dic6C2×D412yes—
362C2×Dic6C2×D412yes—
363C2×Dic6C2414yes—
364C2×Dic6C2411yescharacteristic
365C3×M16—24no—
366C2×C3×C8C2414yes—
367C3×C4⋊C4—22no—
368C3×C4⋊C4—22no—
369C3×C4⋊C4—21no—
370C3×C4⋊C4—21no—
371C3×C4⋊C4—22no—
372C3×C4⋊C4C2411yescharacteristic
373C3×C4⋊C4C2411yescharacteristic
374C3×C4⋊C4C2414yes—
375C3×C22⋊C4—21no—
376C3×C22⋊C4—21no—
377C3×C22⋊C4—21no—
378C3×C42—21no—
379C3×C42—21no—
380C3×C42—21no—
381C3×C42C2×D411yescharacteristic
382C3×C42C2×D411yescharacteristic
383C3×C42C2411yescharacteristic
384C3×C42C2411yescharacteristic
385#217—21no—
386#217—24no—
387#217—24no—
388#217C2×D414yes—
389#216—22no—
390#215—22no—
391#214—22no—
392#213—22no—
393(C2×D3)⋊C4—21no—
394(C2×D3)⋊C4—21no—
395(C2×D3)⋊C4—24no—
396C4⋊Dic3—22no—
397C4⋊Dic3—22no—
398C4⋊Dic3—22no—
399C4⋊Dic3—22no—
400C4⋊Dic3—24no—
401C4⋊Dic3C2×D412yes—
402C4⋊Dic3C2×D412yes—
403C4⋊Dic3C2×D412yes—
404C4⋊Dic3C2×D412yes—
405C4⋊Dic3C2411yescharacteristic
406C4⋊Dic3C2411yescharacteristic
407Dic3⋊C4—21no—
408Dic3⋊C4—21no—
409Dic3⋊C4—24no—
410Dic3⋊C4—24no—
411Dic3⋊C4—24no—
412Dic3⋊C4—24no—
413Dic3⋊C4—24no—
414Dic3⋊C4—24no—
415Dic3⋊C4—24no—
416Dic3⋊C4C2×D414yes—
417Dic3⋊C4C2×D414yes—
418C4×Dic3—21no—
419C4×Dic3—21no—
420C4×Dic3—21no—
421C4×Dic3—24no—
422C4×Dic3—24no—
423C4×Dic3—24no—
424C4×Dic3C2414yes—
425C2×C3⋊C8—22no—
426C2×C3⋊C8—22no—
427C2×C3⋊C8C2411yescharacteristic
428C2×C3⋊C8C2411yescharacteristic
429C2×C3⋊C8C2411yescharacteristic
430C2×C3⋊C8C2411yescharacteristic
431Dic12—28no—
432#204—28no—
433C2×#41—31no—
434C2×#41C22×D311yescharacteristic
435C22×Q8—21no—
436C22×Q8—32no—
437C22×Q8—62no—
438#137—68no—
439#135—64no—
440C2×Q16—31no—
441C2×Q16—34no—
442C2×SD16—31no—
443C2×SD16—31no—
444C2×SD16—34no—
445C2×D8—31no—
446C2×M16C22×D312yes—
447C22×C8—31no—
448C22×C8—31no—
449C4⋊Q8—21no—
450C4⋊Q8—21no—
451C4⋊Q8—34no—
452C4⋊Q8—34no—
453C4⋊Q8—31no—
454C4⋊Q8—31no—
455C4⋊Q8—32no—
456C4⋊Q8—32no—
457C4⋊Q8—62no—
458C4⋊Q8—62no—
459C4⋊Q8—64no—
460C4⋊Q8—62no—
461C4⋊Q8—61no—
462C4⋊Q8—61no—
463C4⋊Q8C22×D312yes—
464C4⋊Q8C22×D312yes—
465#126—64no—
466#126—64no—
467#125—34no—
468#125—32no—
469#125—62no—
470#125—62no—
471#125—62no—
472#125—64no—
473#125—64no—
474#125—64no—
475#124—34no—
476#123—64no—
477C22⋊Q8—32no—
478C22⋊Q8—32no—
479C22⋊Q8—64no—
480C22⋊Q8—64no—
481C22⋊Q8—62no—
482C22⋊Q8—62no—
483C22⋊Q8—62no—
484C22⋊Q8—62no—
485C22⋊Q8—64no—
486C22⋊Q8—62no—
487C22⋊Q8—62no—
488C4×Q8—32no—
489C4×Q8—32no—
490C4×Q8—34no—
491C4×Q8—34no—
492C4×Q8—34no—
493C4×Q8—31no—
494C4×Q8—31no—
495C4×Q8—62no—
496C4×Q8—62no—
497C4×Q8—62no—
498C4×Q8—62no—
499C4×Q8—62no—
500C4×Q8—62no—
501C4×Q8C22×D311yescharacteristic
502C4×Q8C22×D311yescharacteristic
503C4×D4—21no—
504C4×D4—21no—
505C4×D4—34no—
506C4×D4—31no—
507C4×D4—31no—
508C4×D4—64no—
509C4×D4—61no—
510C4×D4—61no—
511C4×D4C22×D311yescharacteristic
512C4×D4C22×D311yescharacteristic
513#117—21no—
514#117—32no—
515#117—31no—
516#117—64no—
517#117—62no—
518#117—62no—
519#117—62no—
520#117—61no—
521#117C22×D311yescharacteristic
522C2×C4⋊C4—21no—
523C2×C4⋊C4—62no—
524C2×C4⋊C4—62no—
525C2×C4⋊C4—61no—
526C2×C4⋊C4—61no—
527C2×C4⋊C4C22×D312yes—
528C2×C42—21no—
529C2×C42—61no—
530C2×C42C22×D311yescharacteristic
531#107—31no—
532#107—31no—
533#107C22×D314yes—
534#106—31no—
535#106—31no—
536#106C22×D314yes—
537C4⋊C8—34no—
538C4⋊C8—34no—
539C4⋊C8C22×D312yes—
540C4⋊C8C22×D312yes—
541#103—31no—
542#103—31no—
543#103—34no—
544#103—34no—
545#103—34no—
546#103—34no—
547#103—34no—
548#103—34no—
549#103—31no—
550#103—31no—
551#103C22×D314yes—
552#102—31no—
553#102—31no—
554#102—31no—
555#102—31no—
556#102C22×D314yes—
557#97—34no—
558C4×C8—34no—
559C4×C8—31no—
560C4×C8—31no—
561C4×C8—31no—
562C4×C8—31no—
563C23×C3—21no—
564C23×C3C22×D411yescharacteristic
565C22×D3—21no—
566C3×Q8—21no—
567C3×Q8—21no—
568C3×Q8—44no—
569C3×Q8—82no—
570C3×D4—21no—
571C3×D4—21no—
572C3×D4—42no—
573C2×C3×C4—22no—
574C2×C3×C4—22no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—24no—
578C2×C3×C4—21no—
579C2×C3×C4—42no—
580C2×C3×C4—42no—
581C2×C3×C4—42no—
582C2×C3×C4—82no—
583C2×C3×C4C22×D411yescharacteristic
584C2×C3×C4C22×D411yescharacteristic
585C2×C3×C4C22×D411yescharacteristic
586C2×C3×C4C22×D411yescharacteristic
587C2×C3×C4C22×D411yescharacteristic
588C2×C3×C4C2×#4112yes—
589C2×C3×C42−1+412yes—
590C2×C3×C4C2511yescharacteristic
591#67—24no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—21no—
595C2×Dic3—24no—
596C2×Dic3—44no—
597C2×Dic3C22×D414yes—
598C2×Dic3C22×D414yes—
599D12—21no—
600D12C2×#4112yes—
601C4×D3—24no—
602C4×D3—42no—
603C4×D3—42no—
604C4×D3—84no—
605Dic6—24no—
606Dic6—24no—
607Dic6—21no—
608Dic6—24no—
609Dic6—24no—
610Dic6—44no—
611Dic6—84no—
612Dic6C2×#4112yes—
613C3×C8—24no—
614C3⋊C8—21no—
615C3⋊C8—21no—
616C3⋊C8—21no—
617C3⋊C8—21no—
618#41—22no—
619#41—22no—
620#41—34no—
621#41—62no—
622C2×Q8—22no—
623C2×Q8—22no—
624C2×Q8—32no—
625C2×Q8—32no—
626C2×Q8—31no—
627C2×Q8—34no—
628C2×Q8—64no—
629C2×Q8—62no—
630C2×Q8—64no—
631C2×Q8—64no—
632C2×Q8—82no—
633C2×Q8—244no—
634C2×Q8C23×D311yescharacteristic
635C2×D4—21no—
636C2×D4—31no—
637C2×D4—61no—
638C2×D4C23×D311yescharacteristic
639C22×C4—22no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—64no—
644C22×C4—61no—
645C22×C4—62no—
646C22×C4—61no—
647C22×C4—61no—
648C22×C4D3×D411yescharacteristic
649C22×C4D3×D411yescharacteristic
650C22×C4C23×D311yescharacteristic
651Q16—68no—
652Q16—62no—
653SD16—68no—
654SD16—62no—
655SD16—62no—
656D8—62no—
657M16—24no—
658C2×C8—31no—
659C2×C8—31no—
660C2×C8—31no—
661C2×C8—31no—
662C2×C8—62no—
663C2×C8—62no—
664C2×C8C23×D314yes—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—32no—
671C4⋊C4—32no—
672C4⋊C4—32no—
673C4⋊C4—32no—
674C4⋊C4—34no—
675C4⋊C4—34no—
676C4⋊C4—31no—
677C4⋊C4—31no—
678C4⋊C4—64no—
679C4⋊C4—64no—
680C4⋊C4—64no—
681C4⋊C4—64no—
682C4⋊C4—64no—
683C4⋊C4—64no—
684C4⋊C4—64no—
685C4⋊C4—64no—
686C4⋊C4—62no—
687C4⋊C4—62no—
688C4⋊C4—62no—
689C4⋊C4—62no—
690C4⋊C4—61no—
691C4⋊C4—61no—
692C4⋊C4C23×D311yescharacteristic
693C4⋊C4C23×D311yescharacteristic
694C4⋊C4C23×D314yes—
695C22⋊C4—21no—
696C22⋊C4—21no—
697C22⋊C4—21no—
698C22⋊C4—34no—
699C22⋊C4—64no—
700C22⋊C4—64no—
701C22⋊C4—64no—
702C22⋊C4—61no—
703C22⋊C4—61no—
704C22⋊C4—61no—
705C42—21no—
706C42—21no—
707C42—21no—
708C42—34no—
709C42—64no—
710C42—64no—
711C42—64no—
712C42—61no—
713C42—61no—
714C42—61no—
715C42D3×D411yescharacteristic
716C42D3×D411yescharacteristic
717C42C23×D311yescharacteristic
718C42C23×D311yescharacteristic
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—41no—
724C22×C3#54812yes—
725C22×C3C23×D411yescharacteristic
726C2×D3—22no—
727C2×D3—41no—
728C2×D3—41no—
729C3×C4—21no—
730C3×C4—21no—
731C3×C4—41no—
732C3×C4—44no—
733C3×C4—41no—
734C3×C4—41no—
735C3×C4#54812yes—
736C3×C4#57712yes—
737C3×C4#57812yes—
738C3×C4C22×#4111yescharacteristic
739C3×C4C2×2−1+411yescharacteristic
740Dic3—22no—
741Dic3—24no—
742Dic3—24no—
743Dic3—44no—
744Dic3—41no—
745Dic3—41no—
746C23—21no—
747C23—61no—
748C23C2×D3×D411yescharacteristic
749Q8—21no—
750Q8—21no—
751Q8—32no—
752Q8—44no—
753Q8—61no—
754Q8—64no—
755Q8—64no—
756Q8—64no—
757Q8—64no—
758Q8—82no—
759Q8—124no—
760Q8—244no—
761D4—21no—
762D4—21no—
763D4—32no—
764D4—42no—
765D4—64no—
766D4—61no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—24no—
773C2×C4—34no—
774C2×C4—34no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—61no—
779C2×C4—64no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—64no—
783C2×C4—82no—
784C2×C4—124no—
785C2×C4—122no—
786C2×C4—122no—
787C2×C4—244no—
788C2×C4C2×D3×D411yescharacteristic
789C2×C4C2×D3×D411yescharacteristic
790C2×C4C2×D3×D411yescharacteristic
791C2×C4C2×D3×D411yescharacteristic
792C2×C4C2×D3×D411yescharacteristic
793C2×C4#100712yes—
794C2×C4D3×#4112yes—
795C2×C4C24×D311yescharacteristic
796C8—24no—
797C8—61no—
798C8—61no—
799C8—61no—
800C8—61no—
801C2×C3—22no—
802C2×C3—81no—
803C2×C3C2×#54811yescharacteristic
804C2×C3C2×#57711yescharacteristic
805C2×C3C2×#57811yescharacteristic
806D3—42no—
807C22—21no—
808C22—21no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—62no—
813C22—121no—
814C22—121no—
815C22#563312yes—
816C22C22×D3×D411yescharacteristic
817C4—21no—
818C4—21no—
819C4—41no—
820C4—44no—
821C4—41no—
822C4—41no—
823C4—64no—
824C4—64no—
825C4—62no—
826C4—121no—
827C4—121no—
828C4—124no—
829C4#563312yes—
830C4#577512yes—
831C4#577912yes—
832C4C2×#100711yescharacteristic
833C4C2×D3×#4111yescharacteristic
834C3#6133011yescharacteristic, complemented, Sylow
835C2—22no—
836C2—81no—
837C2—122no—
838C2C2×#563311yescharacteristic
839C2C2×#577511yescharacteristic
840C2C2×#577911yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3079C2
socleC22×C3C23×D4
prime radicalC2×#950C22
hypercenter#3079D3
hypocenterC3#61330
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3079

Complements

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

NH ≅ G/Ntype
1. #86215C2semidirect
2. #85830C2semidirect
3. C3×#3079C2semidirect
4. C2×#5093C2semidirect
6. #81138C2semidirect
7. #81135C2semidirect
8. #81091C2semidirect
9. #81087C2semidirect
10. #81042C2semidirect
11. #81037C2semidirect
12. #80994C2semidirect
13. #80993C2semidirect
14. #79246C2semidirect
15. #79202C2semidirect
16. #79057C2semidirect
17. #79044C2semidirect
19. #78877C2semidirect
115. #3079D3semidirect
834. C3#61330semidirect

Maximal subgroups

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

subgroupindex
#862152
#858302
C3×#30792
C2×#50932
C4×#9502
#811382
#811352
#810912
#810872
#810422
#810372
#809942
#809932
#792462
#792022
#790572
#790442
#789122
#788772
#613303