Finite Group Databasebeta

← #11664120

Subgroups — #11664120

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#85936C211yesmaximal, characteristic, complemented
2C2×#5504C211yesmaximal, characteristic, complemented
3C2×C3×#481C211yesmaximal, characteristic, complemented
4#82624C211yesmaximal, characteristic, complemented
5#82139C211yesmaximal, characteristic, complemented
6#81313C214yesmaximal, complemented
7#81312C214yesmaximal, complemented
8#81311C212yesmaximal, complemented
9#81310C212yesmaximal, complemented
10#81309C212yesmaximal, complemented
11#81308C212yesmaximal, complemented
12#79130C212yesmaximal, complemented
13#79106C212yesmaximal, complemented
14#78767C212yesmaximal, complemented
15#78726C212yesmaximal, complemented
16#78610C211yesmaximal, characteristic, complemented
17#78584C211yesmaximal, characteristic, complemented
18#60588—31nomaximal, Sylow
19C22×#235C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22#5806—22no—
23#5805C2211yescharacteristic, complemented
24#5798C2211yescharacteristic, complemented
25C2×#932C2212yes—
26#5791C2211yescharacteristic
27C2×C4×#67—22no—
28C2×#926C2211yescharacteristic
29C2×#904C2212yes—
30#5619C2212yescomplemented
31#5618—21no—
32#5616—21no—
33#5614—21no—
34#5611—21no—
35#5603C2212yescomplemented
36#5600C2212yes—
37#5596C2212yes—
38#5504—21no—
39#5504—21no—
40#5504—22no—
41#5504C2212yes—
42#5504C2212yes—
43#5504C2211yescharacteristic, complemented
44#5504C2214yescomplemented
45C2×#893C2212yescomplemented
46C2×#892—21no—
47C2×D3×C4⋊C4—21no—
48#5500C2211yescharacteristic, complemented
49C2×#887C2212yescomplemented
50#5495—22no—
51C3×#481C2212yes—
52C3×#481C2212yes—
53C3×#481C2214yescomplemented
54C2×C3×#106C2212yescomplemented
55C2×C3×#102C2212yescomplemented
56C2×C3×C22⋊C8C2211yescharacteristic
57#5207C2211yescharacteristic
58#5113C2212yes—
59#5102C2212yescomplemented
60#5101C2212yescomplemented
61#5040C2212yes—
62#5037C2214yes—
63#5036C2212yes—
64#4971C2212yescomplemented
65#4970C2212yescomplemented
66#4968C2212yescomplemented
67#4967C2212yescomplemented
68#4966C2212yes—
69#4966C2212yescomplemented
70#4964C2212yescomplemented
71#4871C2214yescomplemented
72#4870C2214yescomplemented
73#4869C2214yescomplemented
74#4857C2214yescomplemented
75#4854C2214yescomplemented
76#4853C2214yescomplemented
77#4852C2214yescomplemented
78#4852C2214yescomplemented
79#4787C2214yescomplemented
80#4786C2214yescomplemented
81#4785C2214yescomplemented
82#4767C2214yescomplemented
83#4762C2214yescomplemented
84#4758C2214yescomplemented
85#4757C2214yescomplemented
86#4756C2214yescomplemented
87#4739C2211yescharacteristic, complemented
88#4738C2211yescharacteristic, complemented
89#4734C2212yescomplemented
90#4733C2212yescomplemented
91#4732C2211yescharacteristic, complemented
92#4731C2211yescharacteristic, complemented
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#3092—31no—
105C2×#481D311yescharacteristic, complemented
106#3084—32no—
107#3045—32no—
108#3006—31no—
109#3002—31no—
110#2952—32no—
111#2946—32no—
112#2924—31no—
113C22×C3×D4—21no—
114C22×C3×D4C2311yescharacteristic
115C23×C3×C4—21no—
116C23×C3×C4C2311yescharacteristic
117C22×#67—21no—
118C2×#237—22no—
119C2×#235—21no—
120C2×#235—21no—
121C2×#235—28no—
122C2×#235C2312yes—
123C2×#235C2311yescharacteristic
124C2×#235C2312yes—
125C22×D12C2311yescharacteristic
126C22×C4×D3—21no—
127C22×C4×D3—22no—
128C22×Dic6C2311yescharacteristic
129C22×C3×C8C2312yes—
130C3×#121—21no—
131C3×#121—21no—
132C3×#121C2312yes—
133C3×#121C2312yes—
134C2×C3×C4⋊C4—21no—
135C2×C3×C4⋊C4—21no—
136C2×C3×C4⋊C4—21no—
137C2×C3×C4⋊C4C2312yes—
138C2×C3×C4⋊C4C2311yescharacteristic
139C2×C3×C4⋊C4C2312yes—
140C2×C3×C4⋊C4C2312yes—
141C2×C3×C22⋊C4—21no—
142#953—21no—
143#953—22no—
144C2×#217—22no—
145C2×#217D412yes—
146#940C2312yes—
147#939—22no—
148#939—22no—
149#938—22no—
150#938—21no—
151#938—21no—
152#936—22no—
153#936C2312yes—
154#935—22no—
155#935—22no—
156D4×Dic3—22no—
157D4×Dic3—21no—
158D4×Dic3—21no—
159D4×Dic3C2312yes—
160D4×Dic3C2312yes—
161C2×#214C2314yes—
162#932—28no—
163C2×#213C2314yes—
164#930C2311yescharacteristic
165#930C2311yescharacteristic
166#929—21no—
167C4×#67—21no—
168C4×#67—21no—
169C4×#67—22no—
170C4×#67—24no—
171C4×#67—24no—
172C4×#67—24no—
173C4×#67—24no—
174C2×(C2×D3)⋊C4—22no—
175#926D412yes—
176#926D411yescharacteristic
177#926D411yescharacteristic
178#926C2311yescharacteristic
179#926C2312yes—
180#926C2311yescharacteristic
181#926C2311yescharacteristic
182C2×C4⋊Dic3D411yescharacteristic
183C2×C4⋊Dic3D411yescharacteristic
184#924—22no—
185#924C2311yescharacteristic
186#924C2311yescharacteristic
187C2×Dic3⋊C4—22no—
188C2×C4×Dic3—22no—
189C2×C4×Dic3C2312yes—
190C2×#208C2312yes—
191C2×Dic12C2312yes—
192#904—28no—
193C2×D24C2312yes—
194C2×#204C2312yes—
195C2×#204C2312yes—
196#893—22no—
197#893—22no—
198#893C2312yes—
199#893C2314yes—
200#893C2314yes—
201#892—22no—
202#892—22no—
203#892—24no—
204#892—21no—
205D3×C4⋊C4—22no—
206D3×C4⋊C4—22no—
207D3×C4⋊C4—24no—
208D3×C4⋊C4—21no—
209#890—21no—
210#890C2312yes—
211#888—21no—
212#888C2312yes—
213#887—22no—
214#887—22no—
215#887C2314yes—
216#887C2314yes—
217#887C2312yes—
218#886—22no—
219#885—22no—
220#883—22no—
221#67⋊C4—22no—
222#879—22no—
223#879—22no—
224#878—22no—
225#877—22no—
226C3×#106C2314yes—
227C3×#106C2314yes—
228C3×#102C2314yes—
229C3×#102C2314yes—
230C3×C22⋊C8C2311yescharacteristic
231C3×C22⋊C8C2311yescharacteristic
232C3×C22⋊C8C2312yes—
233#830C2312yes—
234#830C2312yes—
235#821C2312yes—
236#821C2312yes—
237#816C2312yes—
238#816C2312yes—
239#815C2314yes—
240Dic3⋊C8C2314yes—
241Dic3⋊C8C2314yes—
242C8×Dic3C2314yes—
243#810C2314yes—
244#810C2314yes—
245#809C2314yes—
246#809C2314yes—
247#808C2314yes—
248#807C2314yes—
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#525—31no—
265C2×#121C2×D311yescharacteristic
266#520—32no—
267#520—34no—
268#520—32no—
269#520—31no—
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#484—32no—
282#483—32no—
283#481—32no—
284#481C2×D312yes—
285#481C2×D312yes—
286#481C2×D314yescomplemented
287#480—32no—
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—34no—
300#449—32no—
301#448—32no—
302#448—31no—
303#447—32no—
304#447—31no—
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#428—32no—
317C2×#106C2×D312yescomplemented
318#424—32no—
319#417—32no—
320#417—32no—
321#416—32no—
322C2×#102C2×D312yescomplemented
323#407—31no—
324C2×C22⋊C8C2×D311yescharacteristic
325#405—32no—
326C24×C3—21no—
327C24×C3C2×D411yescharacteristic
328C23×D3—21no—
329C2×C3×D4—22no—
330C2×C3×D4—22no—
331C2×C3×D4—21no—
332C2×C3×D4—24no—
333C2×C3×D4—82no—
334C2×C3×D4C2412yes—
335C22×C3×C4—24no—
336C22×C3×C4—22no—
337C22×C3×C4—21no—
338C22×C3×C4—22no—
339C22×C3×C4—22no—
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—21no—
351C2×#67—21no—
352C2×#67—21no—
353C2×#67—22no—
354C2×#67—22no—
355C22×Dic3—21no—
356C22×Dic3—22no—
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—24no—
367#235#4118yescomplemented
368C2×D12—21no—
369C2×D12—24no—
370C2×D12C2411yescharacteristic
371C2×D12C2412yes—
372C2×C4×D3—28no—
373C2×C4×D3—22no—
374C2×C4×D3—22no—
375C2×C4×D3—21no—
376C2×C4×D3—22no—
377C2×C4×D3—24no—
378C2×C4×D3—24no—
379C2×C4×D3—84no—
380C2×Dic6—21no—
381C2×Dic6—24no—
382C2×Dic6—22no—
383C2×Dic6C2411yescharacteristic
384C2×Dic6C2412yes—
385C2×C3×C8—24no—
386C2×C3×C8C2412yes—
387C2×C3×C8C2412yes—
388C3×C4⋊C4—22no—
389C3×C4⋊C4—21no—
390C3×C4⋊C4—22no—
391C3×C4⋊C4—22no—
392C3×C4⋊C4C2414yes—
393C3×C4⋊C4C2412yes—
394C3×C22⋊C4—22no—
395C3×C22⋊C4—22no—
396#217—21no—
397#217—21no—
398#217—21no—
399#217—22no—
400#217—22no—
401#217—22no—
402#217—22no—
403#217C2×D412yes—
404#217C2×D412yes—
405#217C2×D412yes—
406#217C2×D412yes—
407#214—28no—
408#213—28no—
409(C2×D3)⋊C4—21no—
410(C2×D3)⋊C4—21no—
411(C2×D3)⋊C4—22no—
412(C2×D3)⋊C4—24no—
413(C2×D3)⋊C4—24no—
414C4⋊Dic3—22no—
415C4⋊Dic3C2×D412yes—
416C4⋊Dic3C2×D412yes—
417C4⋊Dic3C2×D411yescharacteristic
418C4⋊Dic3C2×D411yescharacteristic
419C4⋊Dic3C2×D411yescharacteristic
420C4⋊Dic3C2×D411yescharacteristic
421C4⋊Dic3C2411yescharacteristic
422C4⋊Dic3C2411yescharacteristic
423Dic3⋊C4—21no—
424Dic3⋊C4—21no—
425Dic3⋊C4—22no—
426Dic3⋊C4—22no—
427Dic3⋊C4—22no—
428Dic3⋊C4—24no—
429Dic3⋊C4—24no—
430C4×Dic3—21no—
431C4×Dic3—22no—
432C4×Dic3—24no—
433C4×Dic3—24no—
434C4×Dic3C2×D412yes—
435C4×Dic3C2×D412yes—
436C4×Dic3C2412yes—
437C4×Dic3C2412yes—
438#208—24no—
439C2×C3⋊C8C2414yes—
440Dic12—24no—
441D24—24no—
442#204—24no—
443#204—24no—
444C2×#41—32no—
445C2×#41—32no—
446C2×#41—31no—
447C2×#41—68no—
448C2×#41—62no—
449C2×#41—61no—
450C2×#41—61no—
451C22×Q8—31no—
452C22×D4—21no—
453C22×D4—31no—
454C22×D4—61no—
455C22×D4C22×D311yescharacteristic
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—34no—
464C2×SD16—32no—
465C2×SD16—32no—
466C2×D8—34no—
467C2×D8—32no—
468C2×M16—32no—
469C22×C8C22×D312yes—
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—62no—
481#123—62no—
482#123—62no—
483#123—62no—
484#123—61no—
485C22⋊Q8—31no—
486C22⋊Q8—31no—
487C22⋊Q8—62no—
488C22⋊Q8—62no—
489#121—21no—
490#121—21no—
491#121—31no—
492#121—31no—
493#121—62no—
494#121—62no—
495#121—61no—
496#121—61no—
497#121—62no—
498#121C22×D312yes—
499#121C22×D312yes—
500#120—62no—
501#120—61no—
502C4×Q8—34no—
503C4×Q8—34no—
504C4×Q8—32no—
505C4×Q8—62no—
506C4×Q8—62no—
507C4×D4—32no—
508C4×D4—32no—
509C4×D4—34no—
510C4×D4—34no—
511C4×D4—32no—
512C4×D4—62no—
513C4×D4—62no—
514C4×D4—62no—
515C4×D4—64no—
516C4×D4—64no—
517C4×D4—64no—
518C4×D4—64no—
519C4×D4—62no—
520C4×D4—61no—
521C4×D4—61no—
522C4×D4—62no—
523C4×D4—61no—
524C4×D4—61no—
525#117—32no—
526#117—31no—
527#117—31no—
528#117—31no—
529#117—31no—
530#117—32no—
531#117—31no—
532#117—62no—
533#117—62no—
534#117—62no—
535#117—64no—
536#117—61no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—31no—
541C2×C4⋊C4—31no—
542C2×C4⋊C4—62no—
543C2×C4⋊C4—62no—
544C2×C4⋊C4—64no—
545C2×C4⋊C4—61no—
546C2×C4⋊C4—62no—
547C2×C4⋊C4C22×D312yes—
548C2×C4⋊C4C22×D312yes—
549C2×C4⋊C4C22×D312yes—
550C2×C4⋊C4C22×D311yescharacteristic
551C2×C22⋊C4—21no—
552C2×C22⋊C4—32no—
553C2×C22⋊C4—62no—
554C2×C22⋊C4—62no—
555C2×C42—32no—
556C2×C42—62no—
557#107—34no—
558#106—34no—
559#106C22×D314yes—
560#106C22×D314yes—
561C4⋊C8—34no—
562C4⋊C8—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—
571#102C22×D314yes—
572#102C22×D314yes—
573C22⋊C8—32no—
574C22⋊C8—32no—
575C22⋊C8C22×D311yescharacteristic
576C22⋊C8C22×D311yescharacteristic
577C22⋊C8C22×D312yes—
578#97—34no—
579C4×C8—34no—
580C23×C3—22no—
581C23×C3—22no—
582C23×C3—22no—
583C23×C3—41no—
584C23×C3—42no—
585C23×C3—81no—
586C23×C3—81no—
587C23×C3C22×D411yescharacteristic
588C23×C3C22×D411yescharacteristic
589C23×C3C22×D411yescharacteristic
590C22×D3—24no—
591C22×D3—22no—
592C22×D3—21no—
593C22×D3—42no—
594C22×D3—42no—
595C3×D4—24no—
596C3×D4—44no—
597C3×D4—42no—
598C3×D4—82no—
599C2×C3×C4—22no—
600C2×C3×C4—22no—
601C2×C3×C4—22no—
602C2×C3×C4—22no—
603C2×C3×C4—22no—
604C2×C3×C4—24no—
605C2×C3×C4—22no—
606C2×C3×C4—44no—
607C2×C3×C4—82no—
608C2×C3×C4—82no—
609C2×C3×C4—81no—
610C2×C3×C4C22×D411yescharacteristic
611C2×C3×C4C22×D411yescharacteristic
612C2×C3×C4C22×D411yescharacteristic
613C2×C3×C4C2×#4114yes—
614C2×C3×C4C2511yescharacteristic
615#67—28no—
616#67—28no—
617#67—42no—
618#67—42no—
619#67—82no—
620#67—82no—
621#67—81no—
622C2×Dic3—24no—
623C2×Dic3—24no—
624C2×Dic3—22no—
625C2×Dic3—21no—
626C2×Dic3—21no—
627C2×Dic3—21no—
628C2×Dic3—42no—
629C2×Dic3—82no—
630C2×Dic3—82no—
631C2×Dic3C22×D412yes—
632C2×Dic3C22×D412yes—
633C2×Dic3C22×D412yes—
634C2×Dic3C22×D412yes—
635D12—24no—
636D12—22no—
637D12—22no—
638D12C2×#4114yes—
639C4×D3—28no—
640C4×D3—28no—
641C4×D3—42no—
642C4×D3—84no—
643C4×D3—84no—
644C4×D3—82no—
645Dic6—24no—
646Dic6—22no—
647Dic6—22no—
648Dic6—82no—
649Dic6C2×#4114yes—
650C3×C8—22no—
651C3×C8—22no—
652C3⋊C8—24no—
653C24—21no—
654C24—61no—
655C24D3×D411yescharacteristic
656#41—38no—
657#41—64no—
658#41—64no—
659#41—68no—
660#41—68no—
661#41—64no—
662#41—64no—
663#41—244no—
664C2×Q8—32no—
665C2×Q8—31no—
666C2×Q8—62no—
667C2×Q8—64no—
668C2×Q8—61no—
669C2×D4—22no—
670C2×D4—22no—
671C2×D4—21no—
672C2×D4—24no—
673C2×D4—32no—
674C2×D4—31no—
675C2×D4—64no—
676C2×D4—62no—
677C2×D4—62no—
678C2×D4—68no—
679C2×D4—62no—
680C2×D4—62no—
681C2×D4—61no—
682C2×D4—61no—
683C2×D4—61no—
684C2×D4—61no—
685C2×D4—82no—
686C2×D4C23×D312yes—
687C22×C4—24no—
688C22×C4—22no—
689C22×C4—21no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—32no—
693C22×C4—32no—
694C22×C4—64no—
695C22×C4—64no—
696C22×C4—62no—
697C22×C4—68no—
698C22×C4—62no—
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—64no—
714SD16—64no—
715SD16—68no—
716D8—64no—
717D8—68no—
718M16—64no—
719C2×C8—24no—
720C2×C8—34no—
721C2×C8C23×D312yes—
722C2×C8C23×D312yes—
723C4⋊C4—22no—
724C4⋊C4—22no—
725C4⋊C4—22no—
726C4⋊C4—21no—
727C4⋊C4—31no—
728C4⋊C4—31no—
729C4⋊C4—32no—
730C4⋊C4—31no—
731C4⋊C4—31no—
732C4⋊C4—32no—
733C4⋊C4—31no—
734C4⋊C4—31no—
735C4⋊C4—64no—
736C4⋊C4—64no—
737C4⋊C4—62no—
738C4⋊C4—62no—
739C4⋊C4—62no—
740C4⋊C4—62no—
741C4⋊C4—61no—
742C4⋊C4—61no—
743C4⋊C4C23×D312yes—
744C4⋊C4C23×D314yes—
745C22⋊C4—22no—
746C22⋊C4—22no—
747C22⋊C4—32no—
748C22⋊C4—32no—
749C22⋊C4—32no—
750C22⋊C4—32no—
751C22⋊C4—64no—
752C22⋊C4—64no—
753C22⋊C4—62no—
754C22⋊C4—62no—
755C22⋊C4—62no—
756C22⋊C4—62no—
757C22⋊C4—62no—
758C22⋊C4—61no—
759C22⋊C4—61no—
760C22⋊C4—61no—
761C22⋊C4—61no—
762C22⋊C4—61no—
763C42—32no—
764C42—32no—
765C42—32no—
766C42—32no—
767C42—64no—
768C42—64no—
769C42—62no—
770C42—61no—
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—42no—
780C22×C3—42no—
781C22×C3—42no—
782C22×C3—162no—
783C22×C3#52512yes—
784C22×C3#57712yes—
785C22×C3C23×D411yescharacteristic
786C2×D3—24no—
787C2×D3—48no—
788C2×D3—42no—
789C2×D3—42no—
790C2×D3—41no—
791C2×D3—41no—
792C2×D3—41no—
793C3×C4—21no—
794C3×C4—21no—
795C3×C4—44no—
796C3×C4—42no—
797C3×C4#52512yes—
798C3×C4C22×#4112yes—
799Dic3—22no—
800Dic3—22no—
801Dic3—24no—
802Dic3—22no—
803Dic3—22no—
804Dic3—41no—
805Dic3—41no—
806Dic3—41no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—42no—
812C23—64no—
813C23—62no—
814C23—61no—
815C23—81no—
816C23—81no—
817C23—122no—
818C23—122no—
819C23C2×D3×D411yescharacteristic
820C23C2×D3×D411yescharacteristic
821C23C2×D3×D411yescharacteristic
822Q8—34no—
823Q8—64no—
824Q8—62no—
825Q8—62no—
826Q8—242no—
827D4—24no—
828D4—34no—
829D4—44no—
830D4—42no—
831D4—64no—
832D4—68no—
833D4—68no—
834D4—62no—
835D4—62no—
836D4—82no—
837D4—122no—
838D4—122no—
839D4—242no—
840D4—242no—
841D4—241no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—24no—
848C2×C4—22no—
849C2×C4—32no—
850C2×C4—32no—
851C2×C4—32no—
852C2×C4—32no—
853C2×C4—44no—
854C2×C4—68no—
855C2×C4—64no—
856C2×C4—62no—
857C2×C4—64no—
858C2×C4—68no—
859C2×C4—61no—
860C2×C4—61no—
861C2×C4—61no—
862C2×C4—82no—
863C2×C4—82no—
864C2×C4—81no—
865C2×C4—122no—
866C2×C4—122no—
867C2×C4—244no—
868C2×C4—244no—
869C2×C4—242no—
870C2×C4—242no—
871C2×C4—242no—
872C2×C4C2×D3×D411yescharacteristic
873C2×C4C2×D3×D411yescharacteristic
874C2×C4C2×D3×D411yescharacteristic
875C2×C4D3×#4114yes—
876C2×C4C24×D311yescharacteristic
877C8—22no—
878C8—22no—
879C8—64no—
880C2×C3—22no—
881C2×C3—22no—
882C2×C3—41no—
883C2×C3—82no—
884C2×C3C2×#52511yescharacteristic
885C2×C3C2×#57711yescharacteristic
886C2×C3#358511yescharacteristic
887D3—44no—
888D3—81no—
889C22—21no—
890C22—21no—
891C22—21no—
892C22—21no—
893C22—21no—
894C22—21no—
895C22—21no—
896C22—44no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—64no—
901C22—128no—
902C22—122no—
903C22—122no—
904C22—121no—
905C22—121no—
906C22—121no—
907C22—162no—
908C22#565612yes—
909C22#576212yes—
910C22C22×D3×D411yescharacteristic
911C4—21no—
912C4—21no—
913C4—42no—
914C4—44no—
915C4—62no—
916C4—62no—
917C4—62no—
918C4—62no—
919C4—64no—
920C4—121no—
921C4—121no—
922C4—121no—
923C4#565612yes—
924C4C2×D3×#4112yes—
925C3#6058811yescharacteristic, complemented, Sylow
926C2—22no—
927C2—22no—
928C2—41no—
929C2—82no—
930C2—124no—
931C2—241no—
932C2C2×#565611yescharacteristic
933C2C2×#576211yescharacteristic
934C2#8719211yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#481C2
socleC22×C3C23×D4
hypercenterC2×#481D3
hypocenterC3#60588
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
1. #85936C2semidirect
2. C2×#5504C2semidirect
3. C2×C3×#481C2semidirect
4. #82624C2semidirect
5. #82139C2semidirect
6. #81313C2semidirect
7. #81312C2semidirect
8. #81311C2semidirect
9. #81310C2semidirect
10. #81309C2semidirect
11. #81308C2semidirect
12. #79130C2semidirect
13. #79106C2semidirect
14. #78767C2semidirect
15. #78726C2semidirect
16. #78610C2semidirect
17. #78584C2semidirect
23. #5805C22semidirect
24. #5798C22semidirect
30. #5619C22semidirect
35. #5603C22semidirect
43. #5504C22semidirect
44. #5504C22semidirect
45. C2×#893C22semidirect
48. #5500C22semidirect
49. C2×#887C22semidirect
53. C3×#481C22semidirect
54. C2×C3×#106C22semidirect
55. C2×C3×#102C22semidirect
59. #5102C22semidirect
60. #5101C22semidirect
64. #4971C22semidirect
65. #4970C22semidirect
66. #4968C22semidirect
67. #4967C22semidirect
69. #4966C22semidirect
70. #4964C22semidirect
71. #4871C22semidirect
72. #4870C22semidirect
73. #4869C22semidirect
74. #4857C22semidirect
75. #4854C22semidirect
76. #4853C22semidirect
77. #4852C22semidirect
78. #4852C22semidirect
79. #4787C22semidirect
80. #4786C22semidirect
81. #4785C22semidirect
82. #4767C22semidirect
83. #4762C22semidirect
84. #4758C22semidirect
85. #4757C22semidirect
86. #4756C22semidirect
87. #4739C22semidirect
88. #4738C22semidirect
89. #4734C22semidirect
90. #4733C22semidirect
91. #4732C22semidirect
92. #4731C22semidirect
93. #4720C22semidirect
94. #4719C22semidirect
95. #4718C22semidirect
105. C2×#481D3semidirect
286. #481C2×D3semidirect
317. C2×#106C2×D3semidirect
322. C2×#102C2×D3semidirect
367. #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
#859362
C2×#55042
C2×C3×#4812
#826242
#821392
#813132
#813122
#813112
#813102
#813092
#813082
#791302
#791062
#787672
#787262
#786102
#785842
#605883