Finite Group Databasebeta

← #11670545

Subgroups — #11670545

Order 768.

2722 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#87280C211yesmaximal, characteristic, complemented
2C2×#5836C211yesmaximal, characteristic, complemented
3C22×#912C211yesmaximal, characteristic, complemented
4#86315C211yesmaximal, characteristic, complemented
5C3×#3008C211yesmaximal, characteristic, complemented
6#83945C211yesmaximal, characteristic, complemented
7#83939C211yesmaximal, characteristic, complemented
8#83826C211yesmaximal, characteristic, complemented
9#83377C211yesmaximal, characteristic, complemented
10#80130C214yesmaximal, complemented
11#80097C214yesmaximal, complemented
12#80027C214yesmaximal, complemented
13#80013C214yesmaximal, complemented
14#78927C211yesmaximal, characteristic, complemented
15#78916C211yesmaximal, characteristic, complemented
16#78865C211yesmaximal, characteristic, complemented
17#78838C211yesmaximal, characteristic, complemented
18#78679C211yesmaximal, characteristic, complemented
19#78655C211yesmaximal, characteristic, complemented
20#61052—31nomaximal, Sylow
21C2×C3×H(5,𝔽2)C2211yescharacteristic
22C2×#1010C2211yescharacteristic
23C22×#237C2211yescharacteristic
24C22×#237C2211yescharacteristic, complemented
25C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
26C22×C3×D8C2211yescharacteristic
27C3×#535C2211yescharacteristic
28#5836—28no—
29#5828C2211yescharacteristic
30#5828C2211yescharacteristic
31#5825C2211yescharacteristic
32#5825C2211yescharacteristic
33#5824—22no—
34#5824C2214yescomplemented
35C2×#951C2211yescharacteristic
36C2×#951C2212yescomplemented
37C2×#950C2211yescharacteristic
38C2×#950C2212yescomplemented
39C2×#948C2211yescharacteristic
40#5806—22no—
41#5806C2214yescomplemented
42#5805C2211yescharacteristic, complemented
43#5804—22no—
44#5798C2211yescharacteristic
45C2×#935—22no—
46C22×#214C2211yescharacteristic
47C22×#214C2211yescharacteristic, complemented
48C22×#214C2212yescomplemented
49C2×#932C2211yescharacteristic
50C2×#932C2212yescomplemented
51C2×#912—28no—
52C2×#912C2214yescomplemented
53C2×#912C2214yescomplemented
54C2×#909C2211yescharacteristic, complemented
55C22×Dic12C2211yescharacteristic, complemented
56C22×D3×C8C2211yescharacteristic, complemented
57#5718—22no—
58#5677—22no—
59#5599C2214yescomplemented
60#5598C2214yescomplemented
61#5592—22no—
62#5586—22no—
63#5524C2211yescharacteristic, complemented
64#5516C2211yescharacteristic, complemented
65C3×#449C2214yescomplemented
66C3×#447C2214yescomplemented
67C3×#418C2211yescharacteristic
68C3×#416C2211yescharacteristic
69C3×#408C2211yescharacteristic
70#5215C2211yescharacteristic, complemented
71#5175C2212yescomplemented
72#5173C2214yescomplemented
73#5167C2212yescomplemented
74#5158C2214yescomplemented
75#5155C2212yescomplemented
76#5154C2212yescomplemented
77#5153C2214yescomplemented
78#5150C2214yescomplemented
79#5126C2211yescharacteristic, complemented
80#5122C2211yescharacteristic, complemented
81#5120C2211yescharacteristic, complemented
82#5113C2211yescharacteristic, complemented
83#5102C2211yescharacteristic, complemented
84#5042C2214yescomplemented
85#5041C2214yescomplemented
86#5004C2211yescharacteristic, complemented
87#4998C2211yescharacteristic, complemented
88#4813C2212yescomplemented
89#4807C2212yescomplemented
90#4795C2214yescomplemented
91#4783C2214yescomplemented
92#4781C2214yescomplemented
93#4778C2212yescomplemented
94#4775C2212yescomplemented
95#4767C2214yescomplemented
96#4758C2214yescomplemented
97#4757C2214yescomplemented
98#4739C2214yescomplemented
99#4733C2214yescomplemented
100#4728C2214yescomplemented
101#67⋊C8C2214yescomplemented
102C2×#577—31no—
103C22×#135—31no—
104#3487—31no—
105#3485—31no—
106#3284—34no—
107#3282—34no—
108#3269—34no—
109#3268—34no—
110#3154—31no—
111#3057—31no—
112#3050—31no—
113#3044—31no—
114#3041—31no—
115#3011—31no—
116#3008D311yescharacteristic, complemented
117#3005—31no—
118#3005—31no—
119#2949—31no—
120#2929—31no—
121C3×H(5,𝔽2)—24no—
122C3×H(5,𝔽2)—42no—
123C2×C3×#41—21no—
124C2×C3×#41C2311yescharacteristic
125C2×C3×#41C2312yes—
126C2×C3×#41C2311yescharacteristic
127C22×C3×D4—22no—
128C22×C3×D4—21no—
129C22×C3×D4C2311yescharacteristic
130C22×C3×D4C2312yes—
131C22×C3×D4C2311yescharacteristic
132C22×#67—21no—
133C22×#67—21no—
134C23×Dic3—21no—
135C23×Dic3—21no—
136#1010—24no—
137#1010—42no—
138C2×D3×Q8—21no—
139C2×#237—24no—
140C2×#237—21no—
141C2×#237—22no—
142C2×#237—22no—
143C2×#237—22no—
144C2×#237—24no—
145C2×#237—42no—
146C2×#237—42no—
147C2×#237C2314yes—
148C2×#237C2314yes—
149C2×#235C2311yescharacteristic
150C2×#235C2312yes—
151C22×C4×D3C2311yescharacteristic
152C22×Dic6C2311yescharacteristic
153C22×Dic6C2312yes—
154C22×Dic6C2311yescharacteristic
155C3×AGL(1,ℤ/8)—42no—
156C2×C3×SD16C2312yes—
157C2×C3×D8—24no—
158C2×C3×D8C2314yes—
159C2×C3×D8C2312yes—
160C2×C3×M16C2311yescharacteristic
161C22×C3×C8C2311yescharacteristic
162C3×#127—21no—
163C3×#124—21no—
164C3×#121C2314yes—
165C3×#120—22no—
166C3×#117C2311yescharacteristic
167#953—24no—
168#953—22no—
169C2×#217—22no—
170C2×#217—24no—
171#951—24no—
172#951—28no—
173#950—28no—
174#950—24no—
175#948—24no—
176#946D412yes—
177#946C2312yes—
178#944—21no—
179#944C2312yes—
180C2×#216C2311yescharacteristic
181C2×#216C2312yes—
182C2×#215C2311yescharacteristic
183#940—24no—
184#940C2312yes—
185#939—24no—
186#939—24no—
187#939—24no—
188#939—24no—
189#938—22no—
190#938D412yes—
191#938C2312yes—
192#937—21no—
193#937D412yes—
194#936—21no—
195#936C2312yes—
196#936C2312yes—
197#935—22no—
198#935—21no—
199#935—22no—
200#935—24no—
201#935—24no—
202#935D412yes—
203D4×Dic3—24no—
204D4×Dic3—22no—
205D4×Dic3C2314yes—
206C2×#214—28no—
207C2×#214—24no—
208C2×#214D418yescomplemented
209C2×#214C2312yes—
210C2×#214C2312yes—
211C2×#214C2311yescharacteristic
212C2×#214C2312yes—
213C2×#214C2312yes—
214C2×#214C2312yes—
215C2×#214C2312yes—
216#932—24no—
217#932—28no—
218C2×#213C2312yes—
219C2×#213C2311yescharacteristic
220#929—24no—
221C4×#67—22no—
222C4×#67C2314yes—
223#926C2311yescharacteristic
224#926C2311yescharacteristic
225#924—22no—
226#924C2314yes—
227C2×Dic3⋊C4—24no—
228C2×#208C2311yescharacteristic
229C2×#208C2312yes—
230C22×C3⋊C8C2312yes—
231C22×C3⋊C8C2311yescharacteristic
232#912—216no—
233#912—216no—
234#909—42no—
235C2×Dic12—24no—
236C2×Dic12C2314yes—
237C2×Dic12C2312yes—
238C2×#204C2312yes—
239C2×D3×C8—24no—
240C2×D3×C8C2312yes—
241C2×D3×C8C2312yes—
242#897C2312yes—
243#895C2312yes—
244#887C2314yes—
245#886—21no—
246#885—24no—
247#884—24no—
248#882—21no—
249#67⋊C4—24no—
250#878—24no—
251#877—22no—
252C4×D12—22no—
253C4×Dic6—22no—
254C3×#103C2312yes—
255C3×#102C2314yes—
256C3×#102C2312yes—
257C3×C22⋊C8C2314yes—
258#832C2314yes—
259#821C2312yes—
260(C2×D3)⋊C8C2314yes—
261#816C2314yes—
262#816C2312yes—
263#815C2312yes—
264Dic3⋊C8C2314yes—
265C8×Dic3C2312yes—
266#810C2314yes—
267#808C2312yes—
268#807C2312yes—
269C2×2−1+4—31no—
270C2×H(5,𝔽2)C2×D311yescharacteristic
271C22×#41—31no—
272C22×#41—31no—
273#577—68no—
274C2×#137—31no—
275C2×#137—32no—
276C2×#137—31no—
277C2×AGL(1,ℤ/8)—31no—
278C2×AGL(1,ℤ/8)—32no—
279C2×AGL(1,ℤ/8)C2×D311yescharacteristic
280C2×#135—31no—
281C2×#135—32no—
282C2×#135—34no—
283C2×#135—34no—
284C2×#135—68no—
285C22×Q16—31no—
286C22×SD16—31no—
287C22×SD16—31no—
288C22×SD16—32no—
289C22×D8C2×D311yescharacteristic
290C2×#131—31no—
291C23×C8—31no—
292#550—34no—
293#550—62no—
294#548—34no—
295#548—62no—
296#547—34no—
297#547—62no—
298#546—34no—
299#546—62no—
300#536—31no—
301#536—31no—
302#535—31no—
303#535—62no—
304#535C2×D311yescharacteristic
305#534—62no—
306#525—31no—
307#525—31no—
308#525—31no—
309#525—62no—
310C2×#123—62no—
311#519—31no—
312#518—31no—
313#497—32no—
314#496—32no—
315#495—32no—
316#492—32no—
317#468—34no—
318#467—32no—
319#466—32no—
320#465—34no—
321#465—32no—
322#465—32no—
323#464—34no—
324#463—34no—
325#462—34no—
326#459—34no—
327#452—34no—
328#452—34no—
329#452—34no—
330#451—34no—
331#449—34no—
332#449—34no—
333#449C2×D314yescomplemented
334#447C2×D314yescomplemented
335#440—34no—
336C4×SD16—34no—
337#435—34no—
338C8×D4—34no—
339#427—31no—
340#424—31no—
341#419—31no—
342#419—31no—
343#418—31no—
344#418C2×D311yescharacteristic
345#416—31no—
346#416C2×D311yescharacteristic
347#408C2×D311yescharacteristic
348#407—31no—
349#405—31no—
350C24×C3—21no—
351C24×C3—22no—
352C24×C3—21no—
353C23×D3C2×D411yescharacteristic
354C3×#41—22no—
355C3×#41—22no—
356C3×#41—24no—
357C3×#41—22no—
358C3×#41—22no—
359C3×#41—42no—
360C3×#41—44no—
361C2×C3×Q8C2×D411yescharacteristic
362C2×C3×Q8C2411yescharacteristic
363C2×C3×D4—24no—
364C2×C3×D4—21no—
365C2×C3×D4—22no—
366C2×C3×D4—24no—
367C2×C3×D4—21no—
368C2×C3×D4—22no—
369C2×C3×D4—22no—
370C2×C3×D4—21no—
371C2×C3×D4—22no—
372C2×C3×D4—22no—
373C2×C3×D4—42no—
374C2×C3×D4—44no—
375C2×C3×D4—48no—
376C2×C3×D4C2×D412yes—
377C2×C3×D4C2×D411yescharacteristic
378C2×C3×D4C2×D414yes—
379C2×C3×D4C2412yes—
380C2×C3×D4C2411yescharacteristic
381C2×C3×D4C2412yes—
382C22×C3×C4—22no—
383C22×C3×C4—21no—
384C22×C3×C4C2412yes—
385C22×C3×C4C2411yescharacteristic
386C2×#67—21no—
387C2×#67—22no—
388C2×#67—24no—
389C2×#67—24no—
390C2×#67—22no—
391C2×#67—24no—
392C2×#67—44no—
393C2×#67—44no—
394C2×#67C2×D414yes—
395C22×Dic3—21no—
396C22×Dic3—22no—
397C22×Dic3—21no—
398C22×Dic3—24no—
399C22×Dic3—24no—
400C22×Dic3—24no—
401C22×Dic3—44no—
402C22×Dic3—44no—
403C22×Dic3C2×D411yescharacteristic
404D3×Q8—44no—
405#237—28no—
406#237—28no—
407#237—44no—
408#237—44no—
409#237—48no—
410#237—44no—
411#237—48no—
412#237—48no—
413#235—22no—
414#235—22no—
415#235—24no—
416#235—42no—
417C2×D12—22no—
418C2×D12C2411yescharacteristic
419C2×C4×D3—22no—
420C2×C4×D3—22no—
421C2×C4×D3—21no—
422C2×C4×D3—22no—
423C2×C4×D3C2×D412yes—
424C2×C4×D3C2412yes—
425C2×Dic6—21no—
426C2×Dic6—22no—
427C2×Dic6—22no—
428C2×Dic6—22no—
429C2×Dic6—24no—
430C2×Dic6—22no—
431C2×Dic6—21no—
432C2×Dic6—42no—
433C2×Dic6C2×D414yes—
434C2×Dic6C2412yes—
435C2×Dic6C2411yescharacteristic
436C2×Dic6C2412yes—
437C3×SD16—42no—
438C3×D8—28no—
439C3×D8—42no—
440C3×M16—22no—
441C2×C3×C8—22no—
442C2×C3×C8C2412yes—
443C2×C3×C8C2412yes—
444C3×C4⋊C4C2412yes—
445C3×C22⋊C4—21no—
446C3×C22⋊C4—24no—
447C3×C42—21no—
448#217—24no—
449#217—21no—
450#217—24no—
451#217—24no—
452#217—22no—
453#217—24no—
454#217C2×D412yes—
455#217C2×D414yes—
456#216—24no—
457#216—22no—
458#215—22no—
459#214—24no—
460#214—24no—
461#214—24no—
462#214—24no—
463#214—22no—
464#214C2×D418yes—
465#214C2×D418yes—
466#213—24no—
467#213—22no—
468(C2×D3)⋊C4—22no—
469(C2×D3)⋊C4—22no—
470(C2×D3)⋊C4—22no—
471(C2×D3)⋊C4C2×D414yes—
472C4⋊Dic3—22no—
473C4⋊Dic3C2×D412yes—
474C4⋊Dic3C2412yes—
475Dic3⋊C4—24no—
476Dic3⋊C4—24no—
477Dic3⋊C4—22no—
478Dic3⋊C4—24no—
479Dic3⋊C4C2×D414yes—
480C4×Dic3—21no—
481C4×Dic3—24no—
482C4×Dic3C2412yes—
483#208—22no—
484#208—24no—
485C2×C3⋊C8—24no—
486C2×C3⋊C8C2×D414yes—
487C2×C3⋊C8C2412yes—
488C2×C3⋊C8C2411yescharacteristic
489C2×C3⋊C8C2411yescharacteristic
490Dic12—28no—
491Dic12—42no—
492#204—42no—
493D3×C8—24no—
494D3×C8—24no—
4952−1+4—64no—
4962−1+4—122no—
497H(5,𝔽2)—24no—
498H(5,𝔽2)—42no—
499C2×#41—21no—
500C2×#41—34no—
501C2×#41—34no—
502C2×#41—31no—
503C2×#41—32no—
504C2×#41—62no—
505C2×#41—62no—
506C2×#41—62no—
507C2×#41—61no—
508C2×#41—64no—
509C2×#41—64no—
510C2×#41—122no—
511C2×#41—122no—
512C2×#41C22×D311yescharacteristic
513C2×#41C22×D312yes—
514C2×#41C22×D311yescharacteristic
515C22×Q8—31no—
516C22×Q8—31no—
517C22×Q8—32no—
518C22×Q8—61no—
519C22×D4—22no—
520C22×D4—21no—
521C22×D4—61no—
522C22×D4—61no—
523C22×D4C22×D311yescharacteristic
524C22×D4C22×D312yes—
525C22×D4C22×D311yescharacteristic
526C23×C4—31no—
527C23×C4—61no—
528C23×C4—61no—
529#137—68no—
530#137—64no—
531#137—122no—
532AGL(1,ℤ/8)—42no—
533AGL(1,ℤ/8)—68no—
534AGL(1,ℤ/8)—64no—
535#135—64no—
536#135—616no—
537#135—616no—
538#135—68no—
539C2×Q16—32no—
540C2×Q16—31no—
541C2×Q16—34no—
542C2×Q16—32no—
543C2×Q16—64no—
544C2×SD16—38no—
545C2×SD16—32no—
546C2×SD16—32no—
547C2×SD16—31no—
548C2×SD16—31no—
549C2×SD16—32no—
550C2×SD16—32no—
551C2×SD16—32no—
552C2×SD16—32no—
553C2×SD16—32no—
554C2×SD16—64no—
555C2×SD16—68no—
556C2×SD16C22×D312yes—
557C2×D8—24no—
558C2×D8—32no—
559C2×D8—31no—
560C2×D8C22×D314yes—
561C2×D8C22×D312yes—
562#131—64no—
563C2×M16—31no—
564C2×M16—32no—
565C2×M16C22×D311yescharacteristic
566C22×C8—31no—
567C22×C8—32no—
568C22×C8—32no—
569C22×C8—32no—
570C22×C8—64no—
571C22×C8C22×D311yescharacteristic
572C4⋊Q8—32no—
573C4⋊Q8—61no—
574#127—21no—
575#127—32no—
576#127—64no—
577#124—21no—
578#124—32no—
579#124—32no—
580#124—64no—
581#124—61no—
582#123—32no—
583#123—61no—
584#123—64no—
585#123—62no—
586#123—64no—
587#123—64no—
588#123—61no—
589#123—62no—
590C22⋊Q8—32no—
591C22⋊Q8—32no—
592C22⋊Q8—34no—
593C22⋊Q8—32no—
594C22⋊Q8—64no—
595C22⋊Q8—62no—
596#121—32no—
597#121—32no—
598#121—32no—
599#121—64no—
600#121—64no—
601#121—64no—
602#121—62no—
603#121—64no—
604#121—64no—
605#121C22×D314yes—
606#120—22no—
607#120—32no—
608#120—61no—
609#120—62no—
610#120—61no—
611#120—64no—
612C4×Q8—34no—
613C4×Q8—62no—
614C4×D4—34no—
615C4×D4—34no—
616C4×D4—62no—
617C4×D4—64no—
618C4×D4—64no—
619C4×D4—62no—
620C4×D4—62no—
621#117—31no—
622#117—31no—
623#117—62no—
624#117C22×D311yescharacteristic
625C2×C4⋊C4—64no—
626C2×C22⋊C4—62no—
627C2×C22⋊C4—64no—
628#107—32no—
629#106—32no—
630C4⋊C8—34no—
631#103—32no—
632#103—34no—
633#103—34no—
634#103C22×D312yes—
635#102—34no—
636#102—32no—
637#102C22×D312yes—
638#102C22×D314yes—
639C22⋊C8—34no—
640C22⋊C8C22×D314yes—
641#97—32no—
642C4×C8—32no—
643C23×C3—22no—
644C23×C3—24no—
645C23×C3—21no—
646C23×C3—22no—
647C23×C3—44no—
648C23×C3—42no—
649C23×C3—82no—
650C23×C3—82no—
651C23×C3—84no—
652C23×C3C22×D412yes—
653C23×C3C22×D411yescharacteristic
654C22×D3—22no—
655C22×D3—21no—
656C22×D3—42no—
657C22×D3C22×D412yes—
658C3×Q8—22no—
659C3×Q8—21no—
660C3×Q8—21no—
661C3×D4—24no—
662C3×D4—24no—
663C3×D4—22no—
664C3×D4—21no—
665C3×D4—22no—
666C3×D4—22no—
667C3×D4—21no—
668C3×D4—22no—
669C3×D4—44no—
670C3×D4—44no—
671C3×D4—42no—
672C3×D4—42no—
673C3×D4—84no—
674C3×D4C22×D414yes—
675C2×C3×C4—22no—
676C2×C3×C4—22no—
677C2×C3×C4—22no—
678C2×C3×C4—21no—
679C2×C3×C4—44no—
680C2×C3×C4—42no—
681C2×C3×C4C22×D412yes—
682C2×C3×C4C22×D411yescharacteristic
683C2×C3×C4C22×D412yes—
684C2×C3×C4H(5,𝔽2)12yes—
685C2×C3×C4C2511yescharacteristic
686#67—44no—
687#67—48no—
688#67—44no—
689#67—48no—
690#67—42no—
691#67—84no—
692#67—82no—
693C2×Dic3—24no—
694C2×Dic3—22no—
695C2×Dic3—22no—
696C2×Dic3—22no—
697C2×Dic3—22no—
698C2×Dic3—21no—
699C2×Dic3—48no—
700C2×Dic3—44no—
701C2×Dic3—48no—
702C2×Dic3—42no—
703C2×Dic3—84no—
704C2×Dic3C22×D414yes—
705C2×Dic3C22×D412yes—
706D12—21no—
707D12—21no—
708D12—82no—
709C4×D3—24no—
710C4×D3—22no—
711C4×D3—22no—
712C4×D3—44no—
713C4×D3—42no—
714Dic6—24no—
715Dic6—22no—
716Dic6—22no—
717Dic6—21no—
718Dic6—22no—
719Dic6—21no—
720Dic6—44no—
721Dic6—42no—
722Dic6C22×D414yes—
723C3×C8—22no—
724C3×C8—22no—
725C3⋊C8—22no—
726C3⋊C8C22×D412yes—
727C3⋊C8C22×D412yes—
728C24—21no—
729C24—22no—
730C24—21no—
731C24—31no—
732#41—22no—
733#41—22no—
734#41—24no—
735#41—22no—
736#41—22no—
737#41—42no—
738#41—44no—
739#41—64no—
740#41—68no—
741#41—68no—
742#41—62no—
743#41—62no—
744#41—122no—
745#41—124no—
746#41—124no—
747#41—128no—
748#41—128no—
749#41—128no—
750#41—124no—
751C2×Q8—34no—
752C2×Q8—32no—
753C2×Q8—31no—
754C2×Q8—32no—
755C2×Q8—64no—
756C2×Q8—61no—
757C2×Q8—62no—
758C2×Q8—61no—
759C2×Q8—62no—
760C2×Q8—62no—
761C2×Q8—62no—
762C2×Q8—122no—
763C2×Q8—124no—
764C2×Q8D3×D411yescharacteristic
765C2×Q8C23×D311yescharacteristic
766C2×D4—24no—
767C2×D4—21no—
768C2×D4—22no—
769C2×D4—24no—
770C2×D4—21no—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—21no—
774C2×D4—22no—
775C2×D4—22no—
776C2×D4—34no—
777C2×D4—31no—
778C2×D4—42no—
779C2×D4—44no—
780C2×D4—48no—
781C2×D4—62no—
782C2×D4—64no—
783C2×D4—64no—
784C2×D4—64no—
785C2×D4—61no—
786C2×D4—62no—
787C2×D4—62no—
788C2×D4—124no—
789C2×D4—124no—
790C2×D4D3×D412yes—
791C2×D4D3×D411yescharacteristic
792C2×D4D3×D414yes—
793C2×D4C23×D312yes—
794C2×D4C23×D311yescharacteristic
795C2×D4C23×D312yes—
796C22×C4—22no—
797C22×C4—21no—
798C22×C4—31no—
799C22×C4—32no—
800C22×C4—32no—
801C22×C4—64no—
802C22×C4—64no—
803C22×C4—64no—
804C22×C4—61no—
805C22×C4—62no—
806C22×C4—62no—
807C22×C4—62no—
808C22×C4—61no—
809C22×C4—62no—
810C22×C4—61no—
811C22×C4—124no—
812C22×C4—124no—
813C22×C4C23×D312yes—
814C22×C4C23×D311yescharacteristic
815Q16—68no—
816Q16—62no—
817Q16—64no—
818Q16—122no—
819SD16—38no—
820SD16—38no—
821SD16—42no—
822SD16—62no—
823SD16—64no—
824SD16—64no—
825SD16—62no—
826SD16—64no—
827SD16—64no—
828SD16—122no—
829D8—28no—
830D8—42no—
831D8—62no—
832D8—64no—
833M16—22no—
834M16—64no—
835M16—62no—
836C2×C8—22no—
837C2×C8—34no—
838C2×C8—31no—
839C2×C8—31no—
840C2×C8—32no—
841C2×C8—64no—
842C2×C8—64no—
843C2×C8—64no—
844C2×C8C23×D312yes—
845C2×C8C23×D312yes—
846C4⋊C4—34no—
847C4⋊C4—32no—
848C4⋊C4—32no—
849C4⋊C4—62no—
850C4⋊C4—64no—
851C4⋊C4—64no—
852C4⋊C4—62no—
853C4⋊C4—64no—
854C4⋊C4C23×D312yes—
855C22⋊C4—21no—
856C22⋊C4—24no—
857C22⋊C4—32no—
858C22⋊C4—34no—
859C22⋊C4—34no—
860C22⋊C4—62no—
861C22⋊C4—62no—
862C22⋊C4—62no—
863C22⋊C4—62no—
864C22⋊C4—64no—
865C22⋊C4—64no—
866C22⋊C4—64no—
867C22⋊C4—61no—
868C22⋊C4—64no—
869C42—21no—
870C42—32no—
871C42—64no—
872C42—61no—
873C22×C3—22no—
874C22×C3—24no—
875C22×C3—22no—
876C22×C3—24no—
877C22×C3—44no—
878C22×C3—44no—
879C22×C3—42no—
880C22×C3—42no—
881C22×C3—41no—
882C22×C3—84no—
883C22×C3—84no—
884C22×C3—164no—
885C22×C3D4212yes—
886C22×C3C23×D411yescharacteristic
887C2×D3—22no—
888C2×D3—22no—
889C2×D3—22no—
890C2×D3—44no—
891C2×D3—42no—
892C2×D3—41no—
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—
904Dic3—42no—
905C23—22no—
906C23—24no—
907C23—22no—
908C23—21no—
909C23—32no—
910C23—44no—
911C23—42no—
912C23—62no—
913C23—61no—
914C23—82no—
915C23—82no—
916C23—84no—
917C23—122no—
918C23C2×D3×D412yes—
919C23C2×D3×D411yescharacteristic
920Q8—22no—
921Q8—21no—
922Q8—21no—
923Q8—34no—
924Q8—62no—
925Q8—64no—
926Q8—61no—
927Q8—62no—
928Q8—62no—
929Q8—61no—
930Q8—124no—
931Q8—122no—
932D4—24no—
933D4—22no—
934D4—21no—
935D4—22no—
936D4—21no—
937D4—22no—
938D4—24no—
939D4—22no—
940D4—44no—
941D4—44no—
942D4—42no—
943D4—42no—
944D4—61no—
945D4—61no—
946D4—84no—
947D4—124no—
948D4—124no—
949D4—128no—
950D4—128no—
951D4—122no—
952D4—242no—
953D4—244no—
954D4—242no—
955D4C2×D3×D414yes—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—21no—
960C2×C4—34no—
961C2×C4—32no—
962C2×C4—44no—
963C2×C4—42no—
964C2×C4—62no—
965C2×C4—62no—
966C2×C4—64no—
967C2×C4—62no—
968C2×C4—62no—
969C2×C4—64no—
970C2×C4—62no—
971C2×C4—61no—
972C2×C4—62no—
973C2×C4—124no—
974C2×C4—128no—
975C2×C4—128no—
976C2×C4—124no—
977C2×C4—122no—
978C2×C4—122no—
979C2×C4—244no—
980C2×C4C2×D3×D412yes—
981C2×C4C2×D3×D412yes—
982C2×C4C2×D3×D411yescharacteristic
983C2×C4#100412yes—
984C2×C4C24×D311yescharacteristic
985C8—22no—
986C8—22no—
987C8—32no—
988C8—32no—
989C8—62no—
990C2×C3—22no—
991C2×C3—42no—
992C2×C3—44no—
993C2×C3—82no—
994C2×C3—81no—
995C2×C3C2×D4211yescharacteristic
996C2×C3#358412yes—
997D3—42no—
998D3—81no—
999C22—22no—
1000C22—22no—
1001C22—24no—
1002C22—24no—
1003C22—44no—
1004C22—41no—
1005C22—42no—
1006C22—44no—
1007C22—42no—
1008C22—62no—
1009C22—62no—
1010C22—62no—
1011C22—84no—
1012C22—84no—
1013C22—124no—
1014C22—121no—
1015C22—122no—
1016C22—164no—
1017C22#559012yes—
1018C22C22×D3×D411yescharacteristic
1019C4—22no—
1020C4—41no—
1021C4—42no—
1022C4—62no—
1023C4—64no—
1024C4—64no—
1025C4—122no—
1026C4—121no—
1027C4—122no—
1028C4#559012yes—
1029C4C22×D3×D411yescharacteristic
1030C4C2×#100411yescharacteristic
1031C3#6105211yescharacteristic, complemented, Sylow
1032C2—22no—
1033C2—42no—
1034C2—44no—
1035C2—82no—
1036C2—81no—
1037C2—122no—
1038C2—241no—
1039C2C2×#559011yescharacteristic
1040C2#8720312yes—
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3008C2
socleC22×C3C23×D4
hypercenter#3008D3
hypocenterC3#61052
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×#41 ◁ #3008

Complements

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

NH ≅ G/Ntype
1. #87280C2semidirect
2. C2×#5836C2semidirect
3. C22×#912C2semidirect
4. #86315C2semidirect
5. C3×#3008C2semidirect
6. #83945C2semidirect
7. #83939C2semidirect
8. #83826C2semidirect
9. #83377C2semidirect
10. #80130C2semidirect
11. #80097C2semidirect
12. #80027C2semidirect
13. #80013C2semidirect
14. #78927C2semidirect
15. #78916C2semidirect
16. #78865C2semidirect
17. #78838C2semidirect
18. #78679C2semidirect
19. #78655C2semidirect
24. C22×#237C22semidirect
34. #5824C22semidirect
36. C2×#951C22semidirect
38. C2×#950C22semidirect
41. #5806C22semidirect
42. #5805C22semidirect
47. C22×#214C22semidirect
48. C22×#214C22semidirect
50. C2×#932C22semidirect
52. C2×#912C22semidirect
53. C2×#912C22semidirect
54. C2×#909C22semidirect
55. C22×Dic12C22semidirect
56. C22×D3×C8C22semidirect
59. #5599C22semidirect
60. #5598C22semidirect
63. #5524C22semidirect
64. #5516C22semidirect
65. C3×#449C22semidirect
66. C3×#447C22semidirect
70. #5215C22semidirect
71. #5175C22semidirect
72. #5173C22semidirect
73. #5167C22semidirect
74. #5158C22semidirect
75. #5155C22semidirect
76. #5154C22semidirect
77. #5153C22semidirect
78. #5150C22semidirect
79. #5126C22semidirect
80. #5122C22semidirect
81. #5120C22semidirect
82. #5113C22semidirect
83. #5102C22semidirect
84. #5042C22semidirect
85. #5041C22semidirect
86. #5004C22semidirect
87. #4998C22semidirect
88. #4813C22semidirect
89. #4807C22semidirect
90. #4795C22semidirect
91. #4783C22semidirect
92. #4781C22semidirect
93. #4778C22semidirect
94. #4775C22semidirect
95. #4767C22semidirect
96. #4758C22semidirect
97. #4757C22semidirect
98. #4739C22semidirect
99. #4733C22semidirect
100. #4728C22semidirect
101. #67⋊C8C22semidirect
116. #3008D3semidirect
208. C2×#214D4semidirect
333. #449C2×D3semidirect
334. #447C2×D3semidirect
1031. C3#61052semidirect

Maximal subgroups

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

subgroupindex
#872802
C2×#58362
C22×#9122
#863152
C3×#30082
#839452
#839392
#838262
#833772
#801302
#800972
#800272
#800132
#789272
#789162
#788652
#788382
#786792
#786552
#610523