Finite Group Databasebeta

← #11670572

Subgroups — #11670572

Order 768.

2710 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#87274C211yesmaximal, characteristic, complemented
2C22×#950C211yesmaximal, characteristic, complemented
3C2×#5779C211yesmaximal, characteristic, complemented
4#86023C211yesmaximal, characteristic, complemented
5C3×#3005C211yesmaximal, characteristic, complemented
6#83969C211yesmaximal, characteristic, complemented
7#83948C211yesmaximal, characteristic, complemented
8#83940C211yesmaximal, characteristic, complemented
9#82922C211yesmaximal, characteristic, complemented
10#80273C214yesmaximal, complemented
11#80245C214yesmaximal, complemented
12#80131C214yesmaximal, complemented
13#80129C214yesmaximal, complemented
14#78960C211yesmaximal, characteristic, complemented
15#78948C211yesmaximal, characteristic, complemented
16#78945C211yesmaximal, characteristic, complemented
17#78932C211yesmaximal, characteristic, complemented
18#78638C211yesmaximal, characteristic, complemented
19#78626C211yesmaximal, characteristic, complemented
20#61054—31nomaximal, Sylow
21C22×C3×#41C2211yescharacteristic
22C2×#1010C2211yescharacteristic
23C2×#1007C2211yescharacteristic
24C22×#235C2211yescharacteristic
25C2×C3×#137C2211yescharacteristic
26C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
27C3×#525C2211yescharacteristic
28#5834—22no—
29#5834C2214yescomplemented
30#5831—22no—
31#5831C2214yescomplemented
32#5830C2211yescharacteristic
33C2×#950—28no—
34C2×#950C2214yes—
35C2×#950C2214yes—
36C2×#950C2211yescharacteristic
37#5812C2211yescharacteristic
38C22×#216C2211yescharacteristic
39C22×#215C2211yescharacteristic
40#5805—22no—
41#5805C2211yescharacteristic
42#5805C2211yescharacteristic
43C22×#214C2211yescharacteristic
44C22×#213C2211yescharacteristic
45#5791—22no—
46#5791C2211yescharacteristic
47#5791C2211yescharacteristic
48C23×C3⋊C8C2211yescharacteristic
49#5779—28no—
50C2×#918C2212yescomplemented
51C2×D3×Q16C2212yescomplemented
52C2×#916C2212yescomplemented
53C2×#915C2212yescomplemented
54C2×#909C2211yescharacteristic
55C2×#908C2211yescharacteristic
56C2×#907C2211yescharacteristic
57#5656—22no—
58#5633C2214yescomplemented
59#5599C2214yescomplemented
60#5592—22no—
61#5553—22no—
62#5552—22no—
63#5525C2211yescharacteristic
64#5516C2211yescharacteristic
65C3×#452C2214yescomplemented
66C3×#449C2214yescomplemented
67C3×#419C2211yescharacteristic
68C3×#418C2211yescharacteristic
69C3×#407C2211yescharacteristic
70#5233C2211yescharacteristic
71#5185C2214yescomplemented
72#5176C2212yescomplemented
73#5170C2214yescomplemented
74#5168C2212yescomplemented
75#5163C2214yescomplemented
76#5158C2214yescomplemented
77#5154C2212yescomplemented
78#5151C2212yescomplemented
79#5131C2211yescharacteristic
80#5129C2211yescharacteristic
81#5122C2211yescharacteristic
82#5120C2211yescharacteristic
83#5119C2211yescharacteristic
84#5051C2212yescomplemented
85#5048C2212yescomplemented
86#5041C2212yescomplemented
87#5038C2212yescomplemented
88#5002C2211yescharacteristic
89#4998C2211yescharacteristic
90#4810C2214yescomplemented
91#4806C2214yescomplemented
92#4790C2214yescomplemented
93#4789C2214yescomplemented
94#4782C2214yescomplemented
95#4775C2214yescomplemented
96#4767C2214yescomplemented
97#4762C2214yescomplemented
98#4734C2214yescomplemented
99#4733C2214yescomplemented
100#4730C2214yescomplemented
101#67⋊C8C2214yescomplemented
102C2×#578—31no—
103C22×#135—31no—
104#3487—31no—
105#3487—31no—
106#3287—34no—
107#3285—34no—
108#3271—34no—
109#3271—34no—
110#3155—31no—
111#3058—31no—
112#3050—31no—
113#3043—31no—
114#3043—31no—
115#3010—31no—
116#3010—31no—
117#3005—31no—
118#3005D311yescharacteristic, complemented
119#2950—31no—
120#2929—31no—
121C2×C3×#41—22no—
122C2×C3×#41—24no—
123C2×C3×#41—42no—
124C2×C3×#41C2311yescharacteristic
125C2×C3×#41C2314yes—
126C22×C3×Q8C2311yescharacteristic
127C22×C3×D4—21no—
128C22×C3×D4C2311yescharacteristic
129C23×C3×C4—21no—
130C23×C3×C4C2311yescharacteristic
131C22×#67—21no—
132#1010—24no—
133#1010—42no—
134#1007—24no—
135#1007—42no—
136C2×#239—21no—
137C2×#239C2312yes—
138C2×D3×Q8—21no—
139C2×D3×Q8C2312yes—
140C2×D3×Q8C2312yes—
141C2×#237—22no—
142C2×#237C2312yes—
143C2×#235—22no—
144C2×#235—22no—
145C2×#235—21no—
146C2×#235—24no—
147C2×#235—42no—
148C2×#235C2311yescharacteristic
149C2×#235C2311yescharacteristic
150C2×#235C2314yes—
151C22×D12C2311yescharacteristic
152C22×C4×D3—21no—
153C22×Dic6—21no—
154C22×Dic6C2311yescharacteristic
155C3×#137—24no—
156C3×AGL(1,ℤ/8)—42no—
157C2×C3×Q16C2312yes—
158C2×C3×SD16C2312yes—
159C2×C3×SD16C2312yes—
160C2×C3×D8C2312yes—
161C2×C3×M16C2311yescharacteristic
162C2×C3×M16C2311yescharacteristic
163C3×#123—21no—
164C3×C22⋊Q8C2312yes—
165C3×#121C2312yes—
166C3×#120—21no—
167C3×C4×D4—22no—
168C3×#117C2311yescharacteristic
169#953—21no—
170#953—22no—
171#953—22no—
172#953D412yes—
173#950—216no—
174#950—216no—
175#950—24no—
176#947C2312yes—
177Q8×Dic3—22no—
178Q8×Dic3C2314yes—
179C2×#216D418yescomplemented
180C2×#216C2311yescharacteristic
181C2×#216C2312yes—
182C2×#216C2312yes—
183C2×#215—24no—
184C2×#215C2314yes—
185C2×#215C2311yescharacteristic
186#940—24no—
187#940—24no—
188#940—21no—
189#940C2312yes—
190#940C2312yes—
191#939—24no—
192#938—24no—
193#938—24no—
194#938—22no—
195#938C2314yes—
196#937—22no—
197#936—21no—
198#936—24no—
199#936C2312yes—
200C2×#214—24no—
201C2×#214C2311yescharacteristic
202C2×#214C2314yes—
203C2×#213—24no—
204C2×#213C2311yescharacteristic
205C2×#213C2312yes—
206C2×#213C2312yes—
207#930—24no—
208#930—22no—
209#930D412yes—
210#930C2312yes—
211#929—21no—
212#929D412yes—
213C4×#67—22no—
214C4×#67—24no—
215C4×#67—24no—
216C4×#67C2314yes—
217#926—22no—
218#926C2311yescharacteristic
219#926C2311yescharacteristic
220#924—24no—
221#924D412yes—
222#924C2312yes—
223C22×C3⋊C8—24no—
224C22×C3⋊C8C2311yescharacteristic
225C22×C3⋊C8C2312yes—
226C22×C3⋊C8C2312yes—
227C22×C3⋊C8C2311yescharacteristic
228#918—28no—
229D3×Q16—28no—
230#916—28no—
231#915—28no—
232#909—24no—
233#908—42no—
234#907—24no—
235C2×Dic12C2312yes—
236C2×D24C2312yes—
237C2×#204C2312yes—
238C2×#204C2312yes—
239C2×ΓL(1,𝔽25)C2312yes—
240C2×D3×C8C2312yes—
241#896—24no—
242#895C2314yes—
243#893—24no—
244#887C2314yes—
245#885—24no—
246#884—24no—
247#884—24no—
248#882—22no—
249#67⋊C4—24no—
250#877—22no—
251#875—21no—
252#874—21no—
253C4×Dic6—22no—
254C3×#103C2314yes—
255C3×#102C2314yes—
256C3×C22⋊C8C2314yes—
257#835C2312yes—
258#832C2312yes—
259#821C2314yes—
260(C2×D3)⋊C8C2314yes—
261#816C2314yes—
262#815C2312yes—
263Dic3⋊C8C2314yes—
264C8×Dic3C2312yes—
265#810C2312yes—
266#809C2312yes—
267#808C2312yes—
268#807C2312yes—
269C2×2−1+4—31no—
270C2×2−1+4—31no—
271C22×#41—31no—
272C22×#41C2×D311yescharacteristic
273#578—68no—
274C2×#137—32no—
275C2×#137—32no—
276C2×#137—31no—
277C2×#137C2×D311yescharacteristic
278C2×AGL(1,ℤ/8)—31no—
279C2×AGL(1,ℤ/8)C2×D311yescharacteristic
280C2×#135—31no—
281C2×#135—34no—
282C2×#135—34no—
283C2×#135—32no—
284C2×#135—68no—
285C22×Q16—31no—
286C22×Q16—32no—
287C22×SD16—31no—
288C22×SD16—31no—
289C22×D8—31no—
290C2×#131—31no—
291C23×C8—31no—
292#550—34no—
293#550—34no—
294#550—62no—
295#550—62no—
296#548—34no—
297#548—34no—
298#548—62no—
299#548—62no—
300#535—31no—
301#535—31no—
302#535—31no—
303#535—31no—
304#535—62no—
305#535—62no—
306#525—31no—
307#525—31no—
308#525—62no—
309#525—62no—
310#525C2×D311yescharacteristic
311#519—31no—
312#519—31no—
313#496—32no—
314#496—32no—
315#495—32no—
316#493—32no—
317#469—34no—
318#467—32no—
319#466—32no—
320#466—34no—
321#465—32no—
322#465—32no—
323#464—34no—
324#464—34no—
325#460—34no—
326#460—34no—
327#452—34no—
328#452C2×D314yescomplemented
329#449—34no—
330#449—34no—
331#449—34no—
332#449C2×D314yescomplemented
333#448—34no—
334#448—34no—
335#441—34no—
336C4×Q16—34no—
337#435—34no—
338C8×D4—34no—
339#427—31no—
340#424—31no—
341#419—31no—
342#419C2×D311yescharacteristic
343#418—31no—
344#418C2×D311yescharacteristic
345#416—31no—
346#416—31no—
347#408—31no—
348#407C2×D311yescharacteristic
349#405—31no—
350C24×C3—21no—
351C24×C3C2×D411yescharacteristic
352C23×D3—21no—
353C3×#41—28no—
354C3×#41—22no—
355C3×#41—22no—
356C3×#41—44no—
357C3×#41—48no—
358C2×C3×Q8—21no—
359C2×C3×Q8—22no—
360C2×C3×Q8C2×D414yes—
361C2×C3×Q8C2411yescharacteristic
362C2×C3×Q8C2412yes—
363C2×C3×D4—24no—
364C2×C3×D4—21no—
365C2×C3×D4—22no—
366C2×C3×D4—22no—
367C2×C3×D4—21no—
368C2×C3×D4—22no—
369C2×C3×D4—44no—
370C2×C3×D4C2411yescharacteristic
371C2×C3×D4C2412yes—
372C22×C3×C4—21no—
373C22×C3×C4—22no—
374C22×C3×C4—22no—
375C22×C3×C4—24no—
376C22×C3×C4—21no—
377C22×C3×C4—44no—
378C22×C3×C4C2×D412yes—
379C22×C3×C4C2×D411yescharacteristic
380C22×C3×C4C2412yes—
381C22×C3×C4C2411yescharacteristic
382C2×#67—24no—
383C2×#67—21no—
384C2×#67—22no—
385C2×#67—22no—
386C2×#67—24no—
387C2×#67—24no—
388C2×#67—24no—
389C2×#67—44no—
390C2×#67C2×D412yes—
391C2×#67C2×D414yes—
392C22×Dic3—21no—
393C22×Dic3—22no—
394#239—24no—
395#239—42no—
396#239—44no—
397D3×Q8—24no—
398D3×Q8—24no—
399D3×Q8—42no—
400D3×Q8—42no—
401D3×Q8—44no—
402#237—24no—
403#237—42no—
404#237—48no—
405#235—22no—
406#235—22no—
407#235—22no—
408#235—22no—
409#235—28no—
410#235—44no—
411#235—44no—
412#235—48no—
413#235—48no—
414C2×D12—22no—
415C2×D12—22no—
416C2×D12—22no—
417C2×D12—21no—
418C2×D12—24no—
419C2×D12C2×D411yescharacteristic
420C2×D12C2411yescharacteristic
421C2×D12C2412yes—
422C2×C4×D3—22no—
423C2×C4×D3—22no—
424C2×C4×D3—24no—
425C2×C4×D3—21no—
426C2×C4×D3—22no—
427C2×C4×D3—44no—
428C2×C4×D3C2412yes—
429C2×Dic6—21no—
430C2×Dic6—22no—
431C2×Dic6—22no—
432C2×Dic6—22no—
433C2×Dic6—44no—
434C2×Dic6C2×D411yescharacteristic
435C2×Dic6C2×D414yes—
436C2×Dic6C2411yescharacteristic
437C2×Dic6C2412yes—
438C3×Q16—24no—
439C3×SD16—24no—
440C3×SD16—42no—
441C3×D8—42no—
442C3×M16—22no—
443C3×M16—22no—
444C2×C3×C8C2412yes—
445C2×C3×C8C2412yes—
446C3×C4⋊C4—22no—
447C3×C4⋊C4C2412yes—
448C3×C22⋊C4—21no—
449C3×C22⋊C4—22no—
450C3×C22⋊C4—22no—
451C3×C42—21no—
452#217—22no—
453#217—21no—
454#217—24no—
455#217—24no—
456#217C2×D412yes—
457#217C2×D414yes—
458#216—22no—
459#216C2×D418yes—
460#216C2×D418yes—
461#215—28no—
462#215—22no—
463#214—28no—
464#214—22no—
465#213—22no—
466#213—24no—
467#213—24no—
468(C2×D3)⋊C4—22no—
469(C2×D3)⋊C4—24no—
470(C2×D3)⋊C4—24no—
471(C2×D3)⋊C4C2×D414yes—
472C4⋊Dic3—24no—
473C4⋊Dic3C2×D412yes—
474C4⋊Dic3C2412yes—
475Dic3⋊C4—22no—
476Dic3⋊C4—24no—
477Dic3⋊C4C2×D414yes—
478C4×Dic3—21no—
479C4×Dic3—24no—
480C4×Dic3—24no—
481C4×Dic3C2412yes—
482C2×C3⋊C8—22no—
483C2×C3⋊C8—24no—
484C2×C3⋊C8—24no—
485C2×C3⋊C8C2×D414yes—
486C2×C3⋊C8C2412yes—
487C2×C3⋊C8C2411yescharacteristic
488C2×C3⋊C8C2411yescharacteristic
489Dic12—24no—
490D24—42no—
491#204—24no—
492#204—42no—
493ΓL(1,𝔽25)—24no—
494D3×C8—24no—
4952−1+4—64no—
4962−1+4—64no—
4972−1+4—122no—
4982−1+4—122no—
499C2×#41—22no—
500C2×#41—24no—
501C2×#41—31no—
502C2×#41—32no—
503C2×#41—32no—
504C2×#41—31no—
505C2×#41—34no—
506C2×#41—42no—
507C2×#41—62no—
508C2×#41—61no—
509C2×#41—64no—
510C2×#41—62no—
511C2×#41—61no—
512C2×#41—62no—
513C2×#41—122no—
514C2×#41C22×D311yescharacteristic
515C2×#41C22×D314yes—
516C22×Q8—32no—
517C22×Q8—32no—
518C22×Q8—31no—
519C22×Q8—61no—
520C22×Q8—61no—
521C22×Q8C22×D311yescharacteristic
522C22×D4—21no—
523C22×D4—31no—
524C22×D4—61no—
525C22×D4C22×D311yescharacteristic
526C23×C4—21no—
527C23×C4—61no—
528C23×C4C22×D311yescharacteristic
529#137—24no—
530#137—64no—
531#137—68no—
532#137—68no—
533AGL(1,ℤ/8)—42no—
534AGL(1,ℤ/8)—122no—
535#135—64no—
536#135—68no—
537#135—616no—
538#135—616no—
539C2×Q16—38no—
540C2×Q16—32no—
541C2×Q16—32no—
542C2×Q16—31no—
543C2×Q16—32no—
544C2×Q16—68no—
545C2×Q16C22×D312yes—
546C2×SD16—34no—
547C2×SD16—31no—
548C2×SD16—34no—
549C2×SD16—31no—
550C2×SD16—32no—
551C2×SD16—32no—
552C2×SD16—64no—
553C2×SD16—64no—
554C2×SD16C22×D312yes—
555C2×SD16C22×D312yes—
556C2×D8—32no—
557C2×D8—32no—
558C2×D8—31no—
559C2×D8—32no—
560C2×D8—64no—
561C2×D8C22×D312yes—
562#131—64no—
563C2×M16—32no—
564C2×M16C22×D311yescharacteristic
565C2×M16C22×D311yescharacteristic
566C22×C8—31no—
567C22×C8—31no—
568C22×C8—32no—
569C22×C8—32no—
570C22×C8—32no—
571C22×C8—64no—
572#127—32no—
573#127—32no—
574#127—61no—
575#127—61no—
576#127—64no—
577#127—64no—
578#124—32no—
579#124—32no—
580#124—61no—
581#124—64no—
582#124—64no—
583#124—61no—
584#123—21no—
585#123—32no—
586#123—61no—
587C22⋊Q8—32no—
588C22⋊Q8—32no—
589C22⋊Q8—64no—
590C22⋊Q8—64no—
591C22⋊Q8C22×D312yes—
592#121—32no—
593#121—34no—
594#121—32no—
595#121—34no—
596#121—64no—
597#121—64no—
598#121—64no—
599#121—64no—
600#121—64no—
601#121—62no—
602#121—62no—
603#121—64no—
604#121C22×D312yes—
605#120—21no—
606#120—32no—
607#120—62no—
608#120—62no—
609#120—62no—
610#120—62no—
611#120—61no—
612C4×Q8—34no—
613C4×Q8—34no—
614C4×Q8—62no—
615C4×Q8—62no—
616C4×D4—22no—
617C4×D4—34no—
618C4×D4—64no—
619C4×D4—64no—
620C4×D4—64no—
621C4×D4—64no—
622C4×D4—62no—
623#117—31no—
624#117—31no—
625#117—62no—
626#117—62no—
627#117C22×D311yescharacteristic
628#107—32no—
629#106—32no—
630C4⋊C8—34no—
631#103—32no—
632#103—34no—
633#103—32no—
634#103C22×D314yes—
635#102—32no—
636#102—34no—
637#102—32no—
638#102C22×D314yes—
639C22⋊C8—34no—
640C22⋊C8C22×D314yes—
641#97—32no—
642C4×C8—32no—
643C23×C3—22no—
644C23×C3—22no—
645C23×C3—21no—
646C23×C3—42no—
647C23×C3—42no—
648C23×C3—82no—
649C23×C3C22×D412yes—
650C23×C3C22×D411yescharacteristic
651C22×D3—22no—
652C22×D3—21no—
653C22×D3—42no—
654C22×D3—82no—
655C22×D3C22×D412yes—
656C3×Q8—24no—
657C3×Q8—22no—
658C3×Q8—21no—
659C3×Q8—21no—
660C3×Q8C22×D414yes—
661C3×D4—22no—
662C3×D4—21no—
663C3×D4—21no—
664C3×D4—22no—
665C3×D4—48no—
666C3×D4—42no—
667C3×D4—42no—
668C3×D4—82no—
669C2×C3×C4—22no—
670C2×C3×C4—24no—
671C2×C3×C4—22no—
672C2×C3×C4—24no—
673C2×C3×C4—22no—
674C2×C3×C4—22no—
675C2×C3×C4—22no—
676C2×C3×C4—21no—
677C2×C3×C4—48no—
678C2×C3×C4—42no—
679C2×C3×C4C22×D412yes—
680C2×C3×C4C22×D411yescharacteristic
681C2×C3×C4C22×D412yes—
682C2×C3×C4H(5,𝔽2)12yes—
683C2×C3×C4C2511yescharacteristic
684#67—24no—
685#67—44no—
686#67—44no—
687#67—48no—
688#67—42no—
689#67—84no—
690#67—84no—
691#67—84no—
692#67—82no—
693C2×Dic3—24no—
694C2×Dic3—22no—
695C2×Dic3—22no—
696C2×Dic3—21no—
697C2×Dic3—44no—
698C2×Dic3C22×D414yes—
699C2×Dic3C22×D412yes—
700D12—22no—
701D12—21no—
702D12—22no—
703D12—22no—
704D12—21no—
705D12—44no—
706D12—42no—
707D12—84no—
708C4×D3—22no—
709C4×D3—22no—
710C4×D3—48no—
711C4×D3—44no—
712C4×D3—44no—
713C4×D3—44no—
714C4×D3—42no—
715Dic6—24no—
716Dic6—22no—
717Dic6—22no—
718Dic6—21no—
719Dic6—21no—
720Dic6—44no—
721Dic6—44no—
722Dic6C22×D414yes—
723C3×C8—22no—
724C3×C8—22no—
725C3⋊C8—22no—
726C3⋊C8C22×D412yes—
727C3⋊C8C22×D412yes—
728C24—21no—
729C24—61no—
730C24D3×D411yescharacteristic
731#41—28no—
732#41—22no—
733#41—22no—
734#41—44no—
735#41—48no—
736#41—68no—
737#41—62no—
738#41—62no—
739#41—64no—
740#41—64no—
741#41—62no—
742#41—62no—
743#41—124no—
744#41—128no—
745#41—128no—
746#41—124no—
747#41—122no—
748#41—128no—
749#41—122no—
750#41—124no—
751C2×Q8—21no—
752C2×Q8—22no—
753C2×Q8—31no—
754C2×Q8—34no—
755C2×Q8—32no—
756C2×Q8—31no—
757C2×Q8—62no—
758C2×Q8—62no—
759C2×Q8—61no—
760C2×Q8—62no—
761C2×Q8—64no—
762C2×Q8—64no—
763C2×Q8—124no—
764C2×Q8—122no—
765C2×Q8—122no—
766C2×Q8—124no—
767C2×Q8D3×D414yes—
768C2×Q8C23×D311yescharacteristic
769C2×Q8C23×D312yes—
770C2×D4—21no—
771C2×D4—24no—
772C2×D4—22no—
773C2×D4—22no—
774C2×D4—21no—
775C2×D4—22no—
776C2×D4—32no—
777C2×D4—34no—
778C2×D4—31no—
779C2×D4—32no—
780C2×D4—31no—
781C2×D4—44no—
782C2×D4—62no—
783C2×D4—64no—
784C2×D4—64no—
785C2×D4—64no—
786C2×D4—62no—
787C2×D4—61no—
788C2×D4—64no—
789C2×D4—64no—
790C2×D4—62no—
791C2×D4—62no—
792C2×D4—61no—
793C2×D4—62no—
794C2×D4—124no—
795C2×D4C23×D311yescharacteristic
796C2×D4C23×D312yes—
797C22×C4—21no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—21no—
801C22×C4—24no—
802C22×C4—32no—
803C22×C4—44no—
804C22×C4—62no—
805C22×C4—62no—
806C22×C4—62no—
807C22×C4—62no—
808C22×C4—61no—
809C22×C4—61no—
810C22×C4—64no—
811C22×C4—124no—
812C22×C4D3×D412yes—
813C22×C4D3×D411yescharacteristic
814C22×C4C23×D312yes—
815C22×C4C23×D311yescharacteristic
816Q16—24no—
817Q16—38no—
818Q16—38no—
819Q16—64no—
820Q16—62no—
821SD16—24no—
822SD16—42no—
823SD16—64no—
824SD16—62no—
825SD16—62no—
826SD16—68no—
827SD16—68no—
828SD16—122no—
829D8—42no—
830D8—64no—
831D8—64no—
832D8—62no—
833D8—122no—
834M16—22no—
835M16—22no—
836M16—64no—
837C2×C8—34no—
838C2×C8—31no—
839C2×C8—31no—
840C2×C8—32no—
841C2×C8—64no—
842C2×C8—64no—
843C2×C8—64no—
844C2×C8—62no—
845C2×C8C23×D312yes—
846C2×C8C23×D312yes—
847C4⋊C4—22no—
848C4⋊C4—32no—
849C4⋊C4—34no—
850C4⋊C4—32no—
851C4⋊C4—64no—
852C4⋊C4—64no—
853C4⋊C4—62no—
854C4⋊C4C23×D312yes—
855C22⋊C4—21no—
856C22⋊C4—22no—
857C22⋊C4—22no—
858C22⋊C4—32no—
859C22⋊C4—34no—
860C22⋊C4—34no—
861C22⋊C4—64no—
862C22⋊C4—64no—
863C22⋊C4—64no—
864C22⋊C4—64no—
865C22⋊C4—61no—
866C22⋊C4—62no—
867C22⋊C4—62no—
868C42—21no—
869C42—32no—
870C42—64no—
871C42—64no—
872C42—61no—
873C22×C3—22no—
874C22×C3—22no—
875C22×C3—22no—
876C22×C3—22no—
877C22×C3—44no—
878C22×C3—42no—
879C22×C3—44no—
880C22×C3—41no—
881C22×C3—42no—
882C22×C3—84no—
883C22×C3D4212yes—
884C22×C3C23×D411yescharacteristic
885C2×D3—24no—
886C2×D3—22no—
887C2×D3—44no—
888C2×D3—42no—
889C2×D3—41no—
890C2×D3—42no—
891C2×D3—84no—
892C3×C4—24no—
893C3×C4—22no—
894C3×C4—42no—
895C3×C4—41no—
896C3×C4D4212yes—
897C3×C4C23×D411yescharacteristic
898C3×C4C2×H(5,𝔽2)11yescharacteristic
899Dic3—24no—
900Dic3—24no—
901Dic3—22no—
902Dic3—42no—
903Dic3—41no—
904C23—22no—
905C23—21no—
906C23—22no—
907C23—32no—
908C23—42no—
909C23—42no—
910C23—62no—
911C23—61no—
912C23—82no—
913C23—122no—
914C23—242no—
915C23C2×D3×D412yes—
916C23C2×D3×D411yescharacteristic
917Q8—22no—
918Q8—24no—
919Q8—21no—
920Q8—21no—
921Q8—34no—
922Q8—62no—
923Q8—64no—
924Q8—62no—
925Q8—61no—
926Q8—61no—
927Q8—124no—
928Q8—124no—
929Q8C2×D3×D414yes—
930D4—22no—
931D4—21no—
932D4—21no—
933D4—22no—
934D4—48no—
935D4—42no—
936D4—42no—
937D4—64no—
938D4—62no—
939D4—61no—
940D4—61no—
941D4—62no—
942D4—62no—
943D4—82no—
944D4—124no—
945D4—124no—
946D4—128no—
947D4—124no—
948D4—122no—
949D4—122no—
950D4—244no—
951D4—244no—
952D4—244no—
953D4—242no—
954D4—244no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—24no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—24no—
961C2×C4—22no—
962C2×C4—21no—
963C2×C4—34no—
964C2×C4—32no—
965C2×C4—48no—
966C2×C4—42no—
967C2×C4—62no—
968C2×C4—64no—
969C2×C4—62no—
970C2×C4—62no—
971C2×C4—62no—
972C2×C4—61no—
973C2×C4—128no—
974C2×C4—124no—
975C2×C4—124no—
976C2×C4—124no—
977C2×C4—124no—
978C2×C4—122no—
979C2×C4C2×D3×D412yes—
980C2×C4C2×D3×D412yes—
981C2×C4C2×D3×D411yescharacteristic
982C2×C4#100412yes—
983C2×C4C24×D311yescharacteristic
984C8—22no—
985C8—22no—
986C8—32no—
987C8—32no—
988C8—62no—
989C2×C3—22no—
990C2×C3—42no—
991C2×C3—81no—
992C2×C3—82no—
993C2×C3C2×D4211yescharacteristic
994C2×C3#358412yes—
995D3—42no—
996D3—81no—
997D3—82no—
998C22—22no—
999C22—22no—
1000C22—22no—
1001C22—22no—
1002C22—44no—
1003C22—42no—
1004C22—41no—
1005C22—42no—
1006C22—44no—
1007C22—62no—
1008C22—64no—
1009C22—84no—
1010C22—121no—
1011C22—122no—
1012C22—122no—
1013C22—124no—
1014C22—244no—
1015C22#559012yes—
1016C22C22×D3×D411yescharacteristic
1017C4—22no—
1018C4—24no—
1019C4—41no—
1020C4—42no—
1021C4—62no—
1022C4—64no—
1023C4—64no—
1024C4—121no—
1025C4—122no—
1026C4#559012yes—
1027C4C22×D3×D411yescharacteristic
1028C4C2×#100411yescharacteristic
1029C3#6105411yescharacteristic, complemented, Sylow
1030C2—22no—
1031C2—42no—
1032C2—82no—
1033C2—81no—
1034C2—122no—
1035C2—242no—
1036C2—241no—
1037C2C2×#559011yescharacteristic
1038C2#8719912yes—
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3005C2
socleC22×C3C23×D4
hypercenter#3005D3
hypocenterC3#61054
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3005

Complements

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

NH ≅ G/Ntype
1. #87274C2semidirect
2. C22×#950C2semidirect
3. C2×#5779C2semidirect
4. #86023C2semidirect
5. C3×#3005C2semidirect
6. #83969C2semidirect
7. #83948C2semidirect
8. #83940C2semidirect
9. #82922C2semidirect
10. #80273C2semidirect
11. #80245C2semidirect
12. #80131C2semidirect
13. #80129C2semidirect
14. #78960C2semidirect
15. #78948C2semidirect
16. #78945C2semidirect
17. #78932C2semidirect
18. #78638C2semidirect
19. #78626C2semidirect
29. #5834C22semidirect
31. #5831C22semidirect
50. C2×#918C22semidirect
51. C2×D3×Q16C22semidirect
52. C2×#916C22semidirect
53. C2×#915C22semidirect
58. #5633C22semidirect
59. #5599C22semidirect
65. C3×#452C22semidirect
66. C3×#449C22semidirect
71. #5185C22semidirect
72. #5176C22semidirect
73. #5170C22semidirect
74. #5168C22semidirect
75. #5163C22semidirect
76. #5158C22semidirect
77. #5154C22semidirect
78. #5151C22semidirect
84. #5051C22semidirect
85. #5048C22semidirect
86. #5041C22semidirect
87. #5038C22semidirect
90. #4810C22semidirect
91. #4806C22semidirect
92. #4790C22semidirect
93. #4789C22semidirect
94. #4782C22semidirect
95. #4775C22semidirect
96. #4767C22semidirect
97. #4762C22semidirect
98. #4734C22semidirect
99. #4733C22semidirect
100. #4730C22semidirect
101. #67⋊C8C22semidirect
118. #3005D3semidirect
179. C2×#216D4semidirect
328. #452C2×D3semidirect
332. #449C2×D3semidirect
1029. C3#61054semidirect

Maximal subgroups

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

subgroupindex
#872742
C22×#9502
C2×#57792
#860232
C3×#30052
#839692
#839482
#839402
#829222
#802732
#802452
#801312
#801292
#789602
#789482
#789452
#789322
#786382
#786262
#610543