Finite Group Databasebeta

← #11661741

Subgroups — #11661741

Order 768.

4782 conjugacy classes of subgroups.

The subgroup lattice has 1172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#1007C211yesmaximal, characteristic, complemented
2C2×#5778C212yesmaximal, complemented
3#86041C211yesmaximal, characteristic, complemented
4C3×#3004C211yesmaximal, characteristic, complemented
5C2×#5227C211yesmaximal, characteristic, complemented
6#83984C212yesmaximal, complemented
7#82926C211yesmaximal, characteristic, complemented
8#80186C214yesmaximal, complemented
9#80183C212yesmaximal, complemented
10#80182C212yesmaximal, complemented
11#80041C214yesmaximal, complemented
12#80040C212yesmaximal, complemented
13D3×#448C212yesmaximal, complemented
14#78960C212yesmaximal, complemented
15#78957C212yesmaximal, complemented
16#78639C211yesmaximal, characteristic, complemented
17#78631C211yesmaximal, characteristic, complemented
18#60374—31nomaximal, Sylow
19C23×C3×Q8C2211yescharacteristic, complemented
20C2×#1009C2211yescharacteristic, complemented
21C2×#1007—216no—
22C2×#1007—22no—
23C2×#1007—21no—
24C2×#1007—21no—
25C2×#1007C2212yes—
26C2×#1007C2212yescomplemented
27C2×#1007C2214yescomplemented
28C22×#239—21no—
29C22×#239C2212yescomplemented
30C22×D3×Q8—21no—
31C22×D3×Q8C2212yescomplemented
32C22×#235—22no—
33C22×#235C2211yescharacteristic
34C22×#235C2211yescharacteristic, complemented
35C2×C3×#137C2212yescomplemented
36C3×#525C2211yescharacteristic
37#5833C2211yescharacteristic, complemented
38C2×#950C2212yescomplemented
39C22×#215C2212yescomplemented
40C2×#930C2211yescharacteristic
41#5778—216no—
42C2×#919C2214yescomplemented
43C2×#918C2214yescomplemented
44C2×#914C2214yescomplemented
45C2×D3×SD16C2214yescomplemented
46C2×#908C2212yescomplemented
47C2×#907C2212yescomplemented
48#5654—22no—
49#5629C2212yescomplemented
50#5627C2212yes—
51#5607C2212yescomplemented
52D3×#121C2212yes—
53#5590—22no—
54#5553—21no—
55#5552—21no—
56#5550—21no—
57D4×D12—21no—
58#5525C2211yescharacteristic, complemented
59#5523C2211yescharacteristic, complemented
60C3×#451C2212yescomplemented
61C3×#451C2212yescomplemented
62C3×#448C2212yescomplemented
63C3×#448C2212yescomplemented
64C3×#419C2212yescomplemented
65C3×#407C2211yescharacteristic, complemented
66#5227C2212yescomplemented
67#5227C2212yescomplemented
68#5227C2214yescomplemented
69C2×#835C2212yescomplemented
70C2×#830C2211yescharacteristic, complemented
71#5187C2214yescomplemented
72#5186C2214yescomplemented
73#5172C2214yescomplemented
74#5170C2214yescomplemented
75#5133C2212yescomplemented
76#5129C2212yescomplemented
77#5050C2211yescharacteristic, complemented
78#5047C2212yescomplemented
79#5046C2211yescharacteristic, complemented
80#5040C2211yescharacteristic, complemented
81#5037C2212yescomplemented
82#5036C2211yescharacteristic, complemented
83#5002C2212yescomplemented
84#4810C2214yescomplemented
85#4810C2214yescomplemented
86#4806C2214yescomplemented
87#4806C2214yescomplemented
88#4804C2214yescomplemented
89#4803C2214yescomplemented
90#4802C2214yescomplemented
91D3×#103C2214yescomplemented
92#4738C2212yescomplemented
93#4734C2214yescomplemented
94#4732C2212yescomplemented
95#4727C2214yescomplemented
96#4726C2212yescomplemented
97D3×C22⋊C8C2212yescomplemented
98C22×2−1+4—31no—
99C2×#577—32no—
100#3488—31no—
101#3013—34no—
102#3013—32no—
103#3010—34no—
104#3010—32no—
105#3006—32no—
106#3006—31no—
107#3004—32no—
108#3004D311yescharacteristic, complemented
109#3002—32no—
110#3002—31no—
111C2×#448—32no—
112C2×#448—31no—
113#2898—32no—
114#2880—31no—
115C2×C3×#41C2311yescharacteristic
116C22×C3×Q8—28no—
117C22×C3×Q8—21no—
118C22×C3×Q8—21no—
119C22×C3×Q8—21no—
120C22×C3×Q8C2312yes—
121C22×C3×Q8C2312yes—
122C22×C3×Q8C2312yes—
123C23×C3×C4—21no—
124C23×C3×C4C2311yescharacteristic
125C22×#67—21no—
126C22×#67—21no—
127C22×#67D412yes—
128#1009—28no—
129#1007—216no—
130#1007—216no—
131#1007—232no—
132#1007—28no—
133#1007—216no—
134#1007—216no—
135#1007—28no—
136#1007—28no—
137#1007D4116yescomplemented
138C2×#239—216no—
139C2×#239—216no—
140C2×#239—22no—
141C2×#239—22no—
142C2×#239—24no—
143C2×#239—22no—
144C2×#239—22no—
145C2×#239C2314yes—
146C2×#239C2312yes—
147C2×#239C2314yes—
148C2×D3×Q8—216no—
149C2×D3×Q8—216no—
150C2×D3×Q8—22no—
151C2×D3×Q8—22no—
152C2×D3×Q8—22no—
153C2×D3×Q8—22no—
154C2×D3×Q8—24no—
155C2×D3×Q8C2314yes—
156C2×D3×Q8C2314yes—
157C2×D3×D4—22no—
158C2×D3×D4—22no—
159C2×D3×D4C2312yes—
160C2×#235—232no—
161C2×#235—21no—
162C2×#235—21no—
163C2×#235—24no—
164C2×#235—24no—
165C2×#235—24no—
166C2×#235—24no—
167C2×#235—28no—
168C2×#235—28no—
169C2×#235—21no—
170C2×#235D412yes—
171C2×#235D411yescharacteristic
172C2×#235D411yescharacteristic
173C2×#235C2311yescharacteristic
174C2×#235C2312yes—
175C2×#235C2311yescharacteristic
176C2×#235C2312yes—
177C2×#235C2312yes—
178C22×D12—22no—
179C22×D12—21no—
180C22×D12D411yescharacteristic
181C22×D12C2311yescharacteristic
182C22×D12C2311yescharacteristic
183C22×C4×D3—22no—
184C22×C4×D3—21no—
185C22×C4×D3—22no—
186C22×C4×D3C2312yes—
187C22×Dic6—22no—
188C22×Dic6D411yescharacteristic
189C22×Dic6C2311yescharacteristic
190C3×#137—28no—
191C2×C3×Q16C2314yes—
192C2×C3×SD16C2314yes—
193C2×C3×M16C2312yes—
194C3×#123—21no—
195C3×C22⋊Q8C2311yescharacteristic
196C3×C22⋊Q8C2311yescharacteristic
197C3×#121C2311yescharacteristic
198C3×#121C2311yescharacteristic
199C3×#120—21no—
200C3×C4×D4—21no—
201C3×C4×D4—21no—
202C3×#117C2311yescharacteristic
203#950—28no—
204#946C2312yes—
205C2×#216C2312yes—
206C2×#215—28no—
207C2×#215C2312yes—
208C2×#215C2314yes—
209C2×#215C2314yes—
210#940—22no—
211#939—22no—
212#939—22no—
213#938C2312yes—
214#937—22no—
215C2×#214C2312yes—
216C2×#213C2312yes—
217#930—21no—
218#930—21no—
219#930—21no—
220#930C2312yes—
221#930C2312yes—
222C2×(C2×D3)⋊C4—21no—
223C2×C4⋊Dic3C2311yescharacteristic
224#924—21no—
225C22×C3⋊C8C2312yes—
226#919—216no—
227#918—216no—
228#914—216no—
229D3×SD16—216no—
230#908—28no—
231#907—28no—
232C2×D24C2314yes—
233C2×#204C2314yes—
234C2×ΓL(1,𝔽25)C2314yes—
235C2×D3×C8C2314yes—
236#896—22no—
237#895—22no—
238#895C2312yes—
239#895C2312yes—
240#894—22no—
241#893—22no—
242#892C2312yes—
243D3×C4⋊C4C2312yes—
244#885—22no—
245#884—22no—
246#884—22no—
247#884—22no—
248#882—22no—
249#882—22no—
250#882—22no—
251#67⋊C4—22no—
252#67⋊C4—22no—
253D3×C22⋊C4—22no—
254#875—21no—
255#874—21no—
256C4×D12—21no—
257C4×Dic6—21no—
258C3×#103C2314yes—
259C3×#103C2314yes—
260C3×C22⋊C8C2312yes—
261C3×C22⋊C8C2312yes—
262#835C2314yes—
263#835C2314yes—
264#830C2311yescharacteristic
265#830C2311yescharacteristic
266#830C2312yes—
267#821C2314yes—
268(C2×D3)⋊C8C2314yes—
269(C2×D3)⋊C8C2314yes—
270#816C2314yes—
271#810C2312yes—
272#810C2312yes—
273#809C2312yes—
274#809C2312yes—
275C2×2−1+4—32no—
276C2×2−1+4—34no—
277C2×2−1+4—32no—
278C2×2−1+4—62no—
279C2×2−1+4—61no—
280C2×2−1+4—61no—
281C2×2−1+4—616no—
282C2×H(5,𝔽2)—31no—
283C22×#41—31no—
284C22×#41—32no—
285C22×#41—31no—
286C22×#41—62no—
287C22×#41—61no—
288C23×Q8—32no—
289C23×Q8—61no—
290C23×Q8C2×D311yescharacteristic, complemented
291#577—616no—
292C2×#137—34no—
293C2×#137C2×D312yescomplemented
294C2×AGL(1,ℤ/8)—34no—
295C2×AGL(1,ℤ/8)—32no—
296C2×#135—32no—
297C2×#135—34no—
298C22×SD16—32no—
299C22×SD16—34no—
300C2×#131—32no—
301#550—61no—
302#548—61no—
303#546—61no—
304#546—62no—
305D42—61no—
306D42—62no—
307#537—31no—
308#537—32no—
309#535—32no—
310#535—31no—
311#525—32no—
312#525C2×D311yescharacteristic
313C2×#121—31no—
314C2×#121—32no—
315#520—31no—
316#452—34no—
317#452—32no—
318#451—34no—
319#451—31no—
320#451C2×D312yescomplemented
321#451C2×D312yescomplemented
322#450—31no—
323#449—34no—
324#449—32no—
325#449—34no—
326#449—34no—
327#449—34no—
328#448—32no—
329#448—32no—
330#448—34no—
331#448—34no—
332#448—31no—
333#448—34no—
334#448—34no—
335#448—32no—
336#448C2×D312yescomplemented
337#448C2×D312yescomplemented
338#447—31no—
339#447—32no—
340#419—34no—
341#419C2×D312yescomplemented
342#417—32no—
343#417—34no—
344#416—32no—
345#416—34no—
346C2×#103—32no—
347C2×#103—34no—
348#408—32no—
349#408—34no—
350#407—32no—
351#407C2×D311yescharacteristic, complemented
352C2×C22⋊C8—31no—
353C2×C22⋊C8—32no—
354C24×C3C2×D411yescharacteristic
355C23×D3—21no—
356C23×D3—21no—
357C23×D3—22no—
358C23×D3C2×D412yes—
359C3×#41—24no—
360C2×C3×Q8—28no—
361C2×C3×Q8—28no—
362C2×C3×Q8—28no—
363C2×C3×Q8—28no—
364C2×C3×Q8—28no—
365C2×C3×Q8—22no—
366C2×C3×Q8—22no—
367C2×C3×Q8—22no—
368C2×C3×Q8—24no—
369C2×C3×Q8C2×D418yescomplemented
370C2×C3×Q8C2411yescharacteristic
371C2×C3×Q8C2414yes—
372C2×C3×D4—21no—
373C2×C3×D4—21no—
374C2×C3×D4—21no—
375C2×C3×D4C2411yescharacteristic
376C22×C3×C4—28no—
377C22×C3×C4—22no—
378C22×C3×C4—22no—
379C22×C3×C4—22no—
380C22×C3×C4—24no—
381C22×C3×C4—21no—
382C22×C3×C4C2×D411yescharacteristic
383C22×C3×C4C2×D411yescharacteristic
384C22×C3×C4C2×D411yescharacteristic
385C22×C3×C4C2411yescharacteristic
386C22×C3×C4C2411yescharacteristic
387C22×C3×C4C2411yescharacteristic
388C2×#67—28no—
389C2×#67—22no—
390C2×#67—22no—
391C2×#67—28no—
392C2×#67—22no—
393C2×#67—22no—
394C2×#67—22no—
395C2×#67—22no—
396C2×#67—82no—
397C2×#67C2×D412yes—
398C2×#67C2×D412yes—
399C2×#67C2×D412yes—
400C2×#67C2×D412yes—
401C22×Dic3—21no—
402C22×Dic3—21no—
403C22×Dic3C2×D412yes—
404#239—232no—
405#239—216no—
406#239—216no—
407#239—216no—
408#239—28no—
409#239—216no—
410#239—28no—
411#239—28no—
412#239—28no—
413#239C2×D4116yescomplemented
414D3×Q8—216no—
415D3×Q8—216no—
416D3×Q8—216no—
417D3×Q8—232no—
418D3×Q8—28no—
419D3×Q8—28no—
420D3×Q8—216no—
421D3×Q8—28no—
422D3×Q8C2×D4116yescomplemented
423D3×D4—28no—
424D3×D4—48no—
425D3×D4—84no—
426#235—232no—
427#235—28no—
428#235—232no—
429#235—28no—
430#235—232no—
431#235—24no—
432#235—24no—
433#235—232no—
434#235—28no—
435#235—24no—
436#235—24no—
437#235—28no—
438#235—24no—
439#235—24no—
440#235—44no—
441#235C2×D418yes—
442#235C2×D418yescomplemented
443C2×D12—216no—
444C2×D12—24no—
445C2×D12—24no—
446C2×D12—21no—
447C2×D12—24no—
448C2×D12—24no—
449C2×D12—24no—
450C2×D12—22no—
451C2×D12—21no—
452C2×D12—22no—
453C2×D12—22no—
454C2×D12—44no—
455C2×D12C2×D411yescharacteristic
456C2×D12C2×D412yes—
457C2×D12C2×D411yescharacteristic
458C2×D12C2412yes—
459C2×D12C2412yes—
460C2×C4×D3—216no—
461C2×C4×D3—28no—
462C2×C4×D3—216no—
463C2×C4×D3—24no—
464C2×C4×D3—24no—
465C2×C4×D3—22no—
466C2×C4×D3—22no—
467C2×C4×D3—24no—
468C2×C4×D3—24no—
469C2×C4×D3—28no—
470C2×C4×D3—22no—
471C2×C4×D3—22no—
472C2×C4×D3C2×D412yes—
473C2×C4×D3C2×D412yes—
474C2×C4×D3C2412yes—
475C2×C4×D3C2412yes—
476C2×Dic6—216no—
477C2×Dic6—21no—
478C2×Dic6—24no—
479C2×Dic6—24no—
480C2×Dic6—24no—
481C2×Dic6—24no—
482C2×Dic6C2×D411yescharacteristic
483C2×Dic6C2×D412yes—
484C2×Dic6C2×D411yescharacteristic
485C2×Dic6C2412yes—
486C3×Q16—28no—
487C3×SD16—28no—
488C3×M16—24no—
489C2×C3×C8C2414yes—
490C3×C4⋊C4—21no—
491C3×C4⋊C4—21no—
492C3×C4⋊C4C2411yescharacteristic
493C3×C4⋊C4C2411yescharacteristic
494C3×C22⋊C4—21no—
495C3×C22⋊C4—21no—
496C3×C22⋊C4—21no—
497C3×C22⋊C4—21no—
498C3×C22⋊C4—21no—
499C3×C42—21no—
500#217—22no—
501#216—24no—
502#215—28no—
503#215—28no—
504#215—24no—
505#214—24no—
506#213—24no—
507(C2×D3)⋊C4—22no—
508(C2×D3)⋊C4—22no—
509(C2×D3)⋊C4—22no—
510(C2×D3)⋊C4—22no—
511(C2×D3)⋊C4—22no—
512(C2×D3)⋊C4—22no—
513C4⋊Dic3—21no—
514C4⋊Dic3C2412yes—
515Dic3⋊C4—22no—
516Dic3⋊C4—22no—
517C4×Dic3—22no—
518C2×C3⋊C8—24no—
519C2×C3⋊C8C2412yes—
520C2×C3⋊C8C2412yes—
521D24—28no—
522#204—28no—
523ΓL(1,𝔽25)—28no—
524D3×C8—28no—
5252−1+4—316no—
5262−1+4—616no—
5272−1+4—616no—
5282−1+4—68no—
5292−1+4—68no—
5302−1+4—616no—
5312−1+4—632no—
5322−1+4—616no—
5332−1+4—68no—
534H(5,𝔽2)—68no—
535C2×#41—31no—
536C2×#41—32no—
537C2×#41—31no—
538C2×#41—31no—
539C2×#41—32no—
540C2×#41—31no—
541C2×#41—34no—
542C2×#41—32no—
543C2×#41—34no—
544C2×#41—32no—
545C2×#41—32no—
546C2×#41—64no—
547C2×#41—64no—
548C2×#41—64no—
549C2×#41—64no—
550C2×#41—61no—
551C2×#41—68no—
552C2×#41—68no—
553C2×#41—632no—
554C2×#41—62no—
555C2×#41—62no—
556C2×#41—62no—
557C2×#41—64no—
558C2×#41—62no—
559C2×#41—616no—
560C2×#41—616no—
561C2×#41—61no—
562C2×#41—61no—
563C2×#41C22×D311yescharacteristic
564C22×Q8—28no—
565C22×Q8—21no—
566C22×Q8—21no—
567C22×Q8—21no—
568C22×Q8—31no—
569C22×Q8—34no—
570C22×Q8—34no—
571C22×Q8—31no—
572C22×Q8—62no—
573C22×Q8—62no—
574C22×Q8—62no—
575C22×Q8—616no—
576C22×Q8—62no—
577C22×Q8—64no—
578C22×Q8—62no—
579C22×Q8—616no—
580C22×Q8C22×D312yes—
581C22×Q8C22×D312yes—
582C22×Q8C22×D312yes—
583C22×D4—32no—
584C22×D4—32no—
585C22×D4—31no—
586C22×D4—31no—
587C22×D4—31no—
588C22×D4—61no—
589C22×D4—62no—
590C22×D4—62no—
591C22×D4—62no—
592C22×D4—61no—
593C22×D4—61no—
594C23×C4—21no—
595C23×C4—32no—
596C23×C4—62no—
597C23×C4—62no—
598C23×C4—61no—
599C23×C4C22×D311yescharacteristic
600#137—28no—
601#137—616no—
602AGL(1,ℤ/8)—68no—
603AGL(1,ℤ/8)—616no—
604#135—616no—
605#135—68no—
606C2×Q16—32no—
607C2×Q16C22×D314yes—
608C2×SD16—34no—
609C2×SD16—34no—
610C2×SD16—32no—
611C2×SD16—32no—
612C2×SD16—34no—
613C2×SD16—616no—
614C2×SD16—68no—
615C2×SD16C22×D314yes—
616C2×D8—32no—
617C2×D8—34no—
618#131—68no—
619C2×M16—34no—
620C2×M16C22×D312yes—
621C22×C8—32no—
622C22×C8—34no—
623#127—61no—
624#127—62no—
625#124—61no—
626#124—62no—
627#123—21no—
628#123—62no—
629C22⋊Q8—32no—
630C22⋊Q8—62no—
631C22⋊Q8—61no—
632C22⋊Q8C22×D311yescharacteristic
633C22⋊Q8C22×D311yescharacteristic
634#121—32no—
635#121—32no—
636#121—32no—
637#121—32no—
638#121—32no—
639#121—62no—
640#121—62no—
641#121—62no—
642#121—62no—
643#121—61no—
644#121—62no—
645#121—62no—
646#121—61no—
647#121—61no—
648#121C22×D311yescharacteristic
649#121C22×D311yescharacteristic
650#120—21no—
651#120—62no—
652#120—62no—
653#120—62no—
654#120—62no—
655C4×Q8—61no—
656C4×D4—21no—
657C4×D4—21no—
658C4×D4—61no—
659C4×D4—62no—
660C4×D4—62no—
661C4×D4—62no—
662#117—32no—
663#117C22×D311yescharacteristic
664C2×C4⋊C4—31no—
665C2×C4⋊C4—32no—
666C2×C22⋊C4—62no—
667C2×C22⋊C4—61no—
668#103—34no—
669#103—34no—
670#103—34no—
671#103—32no—
672#103—32no—
673#103C22×D314yes—
674#103C22×D314yes—
675#102—34no—
676#102—32no—
677#102—32no—
678C22⋊C8—31no—
679C22⋊C8—31no—
680C22⋊C8—32no—
681C22⋊C8—34no—
682C22⋊C8—34no—
683C22⋊C8C22×D312yes—
684C22⋊C8C22×D312yes—
685C23×C3—22no—
686C23×C3—22no—
687C23×C3—21no—
688C23×C3—41no—
689C23×C3C22×D411yescharacteristic
690C23×C3C22×D411yescharacteristic
691C23×C3C22×D411yescharacteristic
692C22×D3—24no—
693C22×D3—24no—
694C22×D3—22no—
695C22×D3—24no—
696C22×D3—22no—
697C22×D3—42no—
698C22×D3—42no—
699C22×D3—42no—
700C22×D3—42no—
701C22×D3—44no—
702C22×D3—82no—
703C22×D3—82no—
704C22×D3—81no—
705C22×D3—81no—
706C22×D3C22×D412yes—
707C22×D3C22×D412yes—
708C3×Q8—28no—
709C3×Q8—28no—
710C3×Q8—28no—
711C3×Q8—24no—
712C3×Q8—22no—
713C3×Q8C22×D418yes—
714C3×D4—22no—
715C3×D4—42no—
716C3×D4—42no—
717C3×D4—81no—
718C2×C3×C4—28no—
719C2×C3×C4—28no—
720C2×C3×C4—28no—
721C2×C3×C4—22no—
722C2×C3×C4—24no—
723C2×C3×C4—22no—
724C2×C3×C4—22no—
725C2×C3×C4—22no—
726C2×C3×C4—22no—
727C2×C3×C4—21no—
728C2×C3×C4—21no—
729C2×C3×C4—21no—
730C2×C3×C4—42no—
731C2×C3×C4C22×D411yescharacteristic
732C2×C3×C4C22×D411yescharacteristic
733C2×C3×C4C22×D411yescharacteristic
734C2×C3×C4C22×D414yes—
735C2×C3×C4C2511yescharacteristic
736#67—28no—
737#67—24no—
738#67—28no—
739#67—24no—
740#67—24no—
741#67—44no—
742#67—44no—
743#67—82no—
744#67—82no—
745#67#12018yes—
746C2×Dic3—24no—
747C2×Dic3—22no—
748C2×Dic3—24no—
749C2×Dic3—22no—
750C2×Dic3—81no—
751C2×Dic3C22×D412yes—
752C2×Dic3C22×D412yes—
753D12—216no—
754D12—24no—
755D12—216no—
756D12—24no—
757D12—22no—
758D12—22no—
759D12—24no—
760D12—44no—
761D12—42no—
762D12—82no—
763D12—82no—
764D12#12014yes—
765D12C22×D414yes—
766C4×D3—216no—
767C4×D3—216no—
768C4×D3—28no—
769C4×D3—216no—
770C4×D3—24no—
771C4×D3—28no—
772C4×D3—24no—
773C4×D3—216no—
774C4×D3—24no—
775C4×D3—44no—
776C4×D3—82no—
777C4×D3C22×D418yes—
778Dic6—216no—
779Dic6—24no—
780Dic6—22no—
781Dic6—22no—
782Dic6—216no—
783Dic6—24no—
784Dic6#12014yes—
785Dic6C22×D414yes—
786C3×C8—24no—
787C3⋊C8—22no—
788C3⋊C8—22no—
789C24—32no—
790C24—62no—
791C24—61no—
792C24—61no—
793C24D3×D411yescharacteristic
794#41—24no—
795#41—38no—
796#41—316no—
797#41—38no—
798#41—68no—
799#41—68no—
800#41—64no—
801#41—64no—
802#41—632no—
803#41—64no—
804#41—64no—
805#41—632no—
806#41—632no—
807#41—632no—
808#41—68no—
809#41—68no—
810#41—68no—
811#41—68no—
812#41—68no—
813#41—616no—
814#41—616no—
815#41—616no—
816#41—632no—
817#41—616no—
818#41—68no—
819#41—64no—
820#41—64no—
821#41—124no—
822C2×Q8—28no—
823C2×Q8—28no—
824C2×Q8—28no—
825C2×Q8—28no—
826C2×Q8—28no—
827C2×Q8—22no—
828C2×Q8—22no—
829C2×Q8—22no—
830C2×Q8—24no—
831C2×Q8—31no—
832C2×Q8—32no—
833C2×Q8—31no—
834C2×Q8—316no—
835C2×Q8—32no—
836C2×Q8—64no—
837C2×Q8—64no—
838C2×Q8—64no—
839C2×Q8—64no—
840C2×Q8—616no—
841C2×Q8—68no—
842C2×Q8—68no—
843C2×Q8—616no—
844C2×Q8—616no—
845C2×Q8—632no—
846C2×Q8—616no—
847C2×Q8—616no—
848C2×Q8—68no—
849C2×Q8—61no—
850C2×Q8D3×D418yescomplemented
851C2×Q8C23×D311yescharacteristic
852C2×Q8C23×D314yes—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—32no—
857C2×D4—32no—
858C2×D4—32no—
859C2×D4—32no—
860C2×D4—31no—
861C2×D4—32no—
862C2×D4—31no—
863C2×D4—32no—
864C2×D4—32no—
865C2×D4—64no—
866C2×D4—64no—
867C2×D4—64no—
868C2×D4—64no—
869C2×D4—616no—
870C2×D4—62no—
871C2×D4—62no—
872C2×D4—62no—
873C2×D4—68no—
874C2×D4—62no—
875C2×D4—68no—
876C2×D4—68no—
877C2×D4—62no—
878C2×D4—62no—
879C2×D4—62no—
880C2×D4—62no—
881C2×D4—62no—
882C2×D4—61no—
883C2×D4—64no—
884C2×D4—61no—
885C2×D4—124no—
886C2×D4—128no—
887C2×D4—244no—
888C2×D4—242no—
889C2×D4C23×D311yescharacteristic
890C22×C4—28no—
891C22×C4—22no—
892C22×C4—22no—
893C22×C4—22no—
894C22×C4—24no—
895C22×C4—21no—
896C22×C4—32no—
897C22×C4—32no—
898C22×C4—32no—
899C22×C4—32no—
900C22×C4—32no—
901C22×C4—68no—
902C22×C4—64no—
903C22×C4—64no—
904C22×C4—62no—
905C22×C4—64no—
906C22×C4—64no—
907C22×C4—616no—
908C22×C4—616no—
909C22×C4—68no—
910C22×C4—62no—
911C22×C4—61no—
912C22×C4—62no—
913C22×C4—62no—
914C22×C4—61no—
915C22×C4D3×D411yescharacteristic
916C22×C4D3×D411yescharacteristic
917C22×C4D3×D411yescharacteristic
918C22×C4C23×D311yescharacteristic
919C22×C4C23×D311yescharacteristic
920C22×C4C23×D311yescharacteristic
921Q16—28no—
922Q16—64no—
923SD16—28no—
924SD16—68no—
925SD16—64no—
926SD16—64no—
927SD16—68no—
928SD16—68no—
929D8—68no—
930D8—64no—
931M16—24no—
932M16—68no—
933C2×C8—32no—
934C2×C8—32no—
935C2×C8—68no—
936C2×C8—64no—
937C2×C8C23×D314yes—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—32no—
941C4⋊C4—62no—
942C4⋊C4—62no—
943C4⋊C4—61no—
944C4⋊C4C23×D311yescharacteristic
945C4⋊C4C23×D311yescharacteristic
946C22⋊C4—21no—
947C22⋊C4—21no—
948C22⋊C4—21no—
949C22⋊C4—21no—
950C22⋊C4—21no—
951C22⋊C4—62no—
952C22⋊C4—62no—
953C22⋊C4—62no—
954C22⋊C4—62no—
955C22⋊C4—62no—
956C22⋊C4—62no—
957C22⋊C4—62no—
958C42—21no—
959C42—62no—
960C22×C3—21no—
961C22×C3—21no—
962C22×C3—21no—
963C22×C3—21no—
964C22×C3—21no—
965C22×C3—21no—
966C22×C3—21no—
967C22×C3—44no—
968C22×C3—41no—
969C22×C3—41no—
970C22×C3—41no—
971C22×C3C2×#12012yes—
972C22×C3#57712yescomplemented
973C22×C3C23×D411yescharacteristic
974C2×D3—22no—
975C2×D3—22no—
976C2×D3—22no—
977C2×D3—22no—
978C2×D3—24no—
979C2×D3—22no—
980C2×D3—48no—
981C2×D3—48no—
982C2×D3—42no—
983C2×D3—42no—
984C2×D3—42no—
985C2×D3—42no—
986C2×D3—42no—
987C2×D3—164no—
988C2×D3—162no—
989C2×D3C2×#12014yes—
990C3×C4—28no—
991C3×C4—21no—
992C3×C4—21no—
993C3×C4—41no—
994C3×C4—41no—
995C3×C4—41no—
996C3×C4C2×#12012yes—
997C3×C4C23×D412yes—
998Dic3—22no—
999Dic3—24no—
1000Dic3—42no—
1001Dic3C2×#12014yes—
1002C23—22no—
1003C23—22no—
1004C23—21no—
1005C23—32no—
1006C23—32no—
1007C23—41no—
1008C23—64no—
1009C23—64no—
1010C23—62no—
1011C23—64no—
1012C23—62no—
1013C23—122no—
1014C23—122no—
1015C23—124no—
1016C23—122no—
1017C23—122no—
1018C23—241no—
1019C23—241no—
1020C23—242no—
1021C23—242no—
1022C23C2×D3×D411yescharacteristic
1023C23C2×D3×D411yescharacteristic
1024C23C2×D3×D411yescharacteristic
1025Q8—28no—
1026Q8—28no—
1027Q8—24no—
1028Q8—28no—
1029Q8—22no—
1030Q8—34no—
1031Q8—34no—
1032Q8—616no—
1033Q8—64no—
1034Q8—616no—
1035Q8—64no—
1036Q8—62no—
1037Q8—62no—
1038Q8C2×D3×D418yes—
1039D4—22no—
1040D4—38no—
1041D4—34no—
1042D4—34no—
1043D4—42no—
1044D4—42no—
1045D4—64no—
1046D4—616no—
1047D4—616no—
1048D4—64no—
1049D4—64no—
1050D4—64no—
1051D4—68no—
1052D4—64no—
1053D4—68no—
1054D4—62no—
1055D4—64no—
1056D4—62no—
1057D4—81no—
1058D4—124no—
1059D4—124no—
1060D4—124no—
1061D4—122no—
1062D4—242no—
1063D4—242no—
1064D4—242no—
1065D4—242no—
1066C2×C4—28no—
1067C2×C4—28no—
1068C2×C4—24no—
1069C2×C4—28no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—32no—
1079C2×C4—38no—
1080C2×C4—32no—
1081C2×C4—42no—
1082C2×C4—64no—
1083C2×C4—616no—
1084C2×C4—64no—
1085C2×C4—616no—
1086C2×C4—616no—
1087C2×C4—616no—
1088C2×C4—68no—
1089C2×C4—64no—
1090C2×C4—64no—
1091C2×C4—62no—
1092C2×C4—64no—
1093C2×C4—68no—
1094C2×C4—62no—
1095C2×C4—124no—
1096C2×C4—242no—
1097C2×C4—241no—
1098C2×C4C2×D3×D411yescharacteristic
1099C2×C4C2×D3×D411yescharacteristic
1100C2×C4C2×D3×D414yes—
1101C2×C4C2×D3×D411yescharacteristic
1102C2×C4C24×D311yescharacteristic
1103C8—24no—
1104C8—62no—
1105C8—62no—
1106C2×C3—22no—
1107C2×C3—22no—
1108C2×C3—41no—
1109C2×C3—81no—
1110C2×C3C22×#12011yescharacteristic
1111C2×C3C2×#57711yescharacteristic
1112C2×C3#358611yescharacteristic
1113D3—24no—
1114D3—42no—
1115D3—44no—
1116D3—82no—
1117C22—21no—
1118C22—21no—
1119C22—21no—
1120C22—21no—
1121C22—21no—
1122C22—21no—
1123C22—21no—
1124C22—34no—
1125C22—44no—
1126C22—41no—
1127C22—41no—
1128C22—41no—
1129C22—62no—
1130C22—62no—
1131C22—64no—
1132C22—62no—
1133C22—62no—
1134C22—62no—
1135C22—128no—
1136C22—128no—
1137C22—122no—
1138C22—122no—
1139C22—122no—
1140C22—122no—
1141C22—122no—
1142C22—482no—
1143C22—484no—
1144C22D3×#12012yes—
1145C22#577812yescomplemented
1146C22C22×D3×D411yescharacteristic
1147C4—28no—
1148C4—21no—
1149C4—21no—
1150C4—34no—
1151C4—41no—
1152C4—41no—
1153C4—41no—
1154C4—62no—
1155C4—64no—
1156C4—122no—
1157C4D3×#12012yes—
1158C4C22×D3×D412yes—
1159C3#6037411yescharacteristic, complemented, Sylow
1160C2—22no—
1161C2—22no—
1162C2—41no—
1163C2—64no—
1164C2—81no—
1165C2—122no—
1166C2—124no—
1167C2—242no—
1168C2C2×D3×#12011yescharacteristic
1169C2C2×#577811yescharacteristic
1170C2#8719711yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3004C2
socleC22×C3C23×D4
hypercenter#3004D3
hypocenterC3#60374
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3004

Complements

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

NH ≅ G/Ntype
1. C22×#1007C2semidirect
2. C2×#5778C2semidirect
3. #86041C2semidirect
4. C3×#3004C2semidirect
5. C2×#5227C2semidirect
6. #83984C2semidirect
7. #82926C2semidirect
8. #80186C2semidirect
9. #80183C2semidirect
10. #80182C2semidirect
11. #80041C2semidirect
12. #80040C2semidirect
13. D3×#448C2semidirect
14. #78960C2semidirect
15. #78957C2semidirect
16. #78639C2semidirect
17. #78631C2semidirect
19. C23×C3×Q8C22semidirect
20. C2×#1009C22semidirect
26. C2×#1007C22semidirect
27. C2×#1007C22semidirect
29. C22×#239C22semidirect
31. C22×D3×Q8C22semidirect
34. C22×#235C22semidirect
35. C2×C3×#137C22semidirect
37. #5833C22semidirect
38. C2×#950C22semidirect
39. C22×#215C22semidirect
42. C2×#919C22semidirect
43. C2×#918C22semidirect
44. C2×#914C22semidirect
45. C2×D3×SD16C22semidirect
46. C2×#908C22semidirect
47. C2×#907C22semidirect
49. #5629C22semidirect
51. #5607C22semidirect
58. #5525C22semidirect
59. #5523C22semidirect
60. C3×#451C22semidirect
61. C3×#451C22semidirect
62. C3×#448C22semidirect
63. C3×#448C22semidirect
64. C3×#419C22semidirect
65. C3×#407C22semidirect
66. #5227C22semidirect
67. #5227C22semidirect
68. #5227C22semidirect
69. C2×#835C22semidirect
70. C2×#830C22semidirect
71. #5187C22semidirect
72. #5186C22semidirect
73. #5172C22semidirect
74. #5170C22semidirect
75. #5133C22semidirect
76. #5129C22semidirect
77. #5050C22semidirect
78. #5047C22semidirect
79. #5046C22semidirect
80. #5040C22semidirect
81. #5037C22semidirect
82. #5036C22semidirect
83. #5002C22semidirect
84. #4810C22semidirect
85. #4810C22semidirect
86. #4806C22semidirect
87. #4806C22semidirect
88. #4804C22semidirect
89. #4803C22semidirect
90. #4802C22semidirect
91. D3×#103C22semidirect
92. #4738C22semidirect
93. #4734C22semidirect
94. #4732C22semidirect
95. #4727C22semidirect
96. #4726C22semidirect
97. D3×C22⋊C8C22semidirect
108. #3004D3semidirect
137. #1007D4semidirect
290. C23×Q8C2×D3semidirect
293. C2×#137C2×D3semidirect
320. #451C2×D3semidirect
321. #451C2×D3semidirect
336. #448C2×D3semidirect
337. #448C2×D3semidirect
341. #419C2×D3semidirect
351. #407C2×D3semidirect
369. C2×C3×Q8C2×D4semidirect
413. #239C2×D4semidirect
422. D3×Q8C2×D4semidirect
442. #235C2×D4semidirect
850. C2×Q8D3×D4semidirect
972. C22×C3#577semidirect
1145. C22#5778semidirect
1159. C3#60374semidirect

Maximal subgroups

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

subgroupindex
C22×#10072
C2×#57782
#860412
C3×#30042
C2×#52272
#839842
#829262
#801862
#801832
#801822
#800412
#800402
D3×#4482
#789602
#789572
#786392
#786312
#603743