Finite Group Databasebeta

← #11661734

Subgroups — #11661734

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×#5762C212yesmaximal, complemented
3#85949C211yesmaximal, characteristic, complemented
4C2×C3×#448C211yesmaximal, characteristic, complemented
5#84059C211yesmaximal, characteristic, complemented
6#83860C212yesmaximal, complemented
7#82624C211yesmaximal, characteristic, complemented
8#80042C214yesmaximal, complemented
9#80041C214yesmaximal, complemented
10#80040C212yesmaximal, complemented
11#80039C212yesmaximal, complemented
12#80038C212yesmaximal, complemented
13D3×#448C212yesmaximal, complemented
14#78795C212yesmaximal, complemented
15#78790C212yesmaximal, complemented
16#78610C211yesmaximal, characteristic, complemented
17#78600C211yesmaximal, characteristic, complemented
18#60374—31nomaximal, Sylow
19C23×C3×Q8C2211yescharacteristic, complemented
20C2×#1007—216no—
21C2×#1007—22no—
22C2×#1007—21no—
23C2×#1007—21no—
24C2×#1007C2212yes—
25C2×#1007C2212yescomplemented
26C2×#1007C2214yescomplemented
27C22×#239—21no—
28C22×#239C2212yescomplemented
29C22×D3×Q8—21no—
30C22×D3×Q8C2212yescomplemented
31C2×#1004C2211yescharacteristic, complemented
32C22×#235—22no—
33C22×#235C2211yescharacteristic
34C22×#235C2211yescharacteristic, complemented
35C22×C3×SD16C2212yescomplemented
36C2×C3×#121C2211yescharacteristic
37C2×#942C2212yescomplemented
38#5805C2211yescharacteristic, complemented
39D4×#67—22no—
40C2×#932C2212yescomplemented
41#5791C2211yescharacteristic
42#5762—216no—
43C2×#916C2214yescomplemented
44C2×#915C2214yescomplemented
45C2×#914C2214yescomplemented
46C2×D3×SD16C2214yescomplemented
47C2×#904C2212yescomplemented
48C2×#901C2212yescomplemented
49#5612—21no—
50#5609—21no—
51#5608C2212yescomplemented
52#5607C2212yescomplemented
53#5606C2212yes—
54D3×#121C2212yes—
55#5599—21no—
56#5598—21no—
57#5510C2211yescharacteristic, complemented
58#5504C2211yescharacteristic, complemented
59#5490—22no—
60C3×#448C2212yescomplemented
61C3×#448C2212yescomplemented
62C3×#448C2214yescomplemented
63C2×C3×#103C2212yescomplemented
64C2×C3×C22⋊C8C2211yescharacteristic, complemented
65#5228C2212yescomplemented
66#5228C2212yescomplemented
67#5227C2212yescomplemented
68#5227C2212yescomplemented
69#5225C2212yescomplemented
70#5207C2211yescharacteristic, complemented
71#5172C2214yescomplemented
72#5172C2214yescomplemented
73#5170C2214yescomplemented
74#5170C2214yescomplemented
75#5113C2212yescomplemented
76#5110C2212yescomplemented
77#5040C2212yescomplemented
78#5037C2214yescomplemented
79#5036C2212yescomplemented
80#4966C2212yescomplemented
81#4810C2214yescomplemented
82#4809C2214yescomplemented
83#4808C2214yescomplemented
84#4806C2214yescomplemented
85#4804C2214yescomplemented
86#4803C2214yescomplemented
87#4802C2214yescomplemented
88D3×#103C2214yescomplemented
89#4739C2211yescharacteristic, complemented
90#4738C2211yescharacteristic, complemented
91#4734C2212yescomplemented
92#4733C2212yescomplemented
93#4732C2211yescharacteristic, complemented
94#4731C2211yescharacteristic, complemented
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#3004—31no—
109#3002—32no—
110#3002—31no—
111C2×#448—32no—
112C2×#448D311yescharacteristic, complemented
113#2898—32no—
114#2880—31no—
115C22×C3×Q8—28no—
116C22×C3×Q8—21no—
117C22×C3×Q8—21no—
118C22×C3×Q8—21no—
119C22×C3×Q8C2312yes—
120C22×C3×Q8C2312yes—
121C22×C3×Q8C2312yes—
122C22×C3×D4—21no—
123C22×C3×D4C2311yescharacteristic
124C23×C3×C4—21no—
125C23×C3×C4C2311yescharacteristic
126C22×#67—21no—
127C22×#67—22no—
128C22×#67D412yes—
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—24no—
142C2×#239—22no—
143C2×#239—22no—
144C2×#239—22no—
145C2×#239C2314yes—
146C2×#239C2314yes—
147C2×D3×Q8—216no—
148C2×D3×Q8—216no—
149C2×D3×Q8—22no—
150C2×D3×Q8—22no—
151C2×D3×Q8—22no—
152C2×D3×Q8—24no—
153C2×D3×Q8—22no—
154C2×D3×Q8C2314yes—
155C2×D3×Q8C2314yes—
156#1004—28no—
157C2×#237—21no—
158C2×#237C2312yes—
159C2×D3×D4—22no—
160C2×D3×D4—21no—
161C2×D3×D4C2312yes—
162C2×#235—232no—
163C2×#235—21no—
164C2×#235—21no—
165C2×#235—24no—
166C2×#235—24no—
167C2×#235—24no—
168C2×#235—24no—
169C2×#235—28no—
170C2×#235—28no—
171C2×#235D412yes—
172C2×#235D411yescharacteristic
173C2×#235D411yescharacteristic
174C2×#235C2312yes—
175C2×#235C2311yescharacteristic
176C2×#235C2311yescharacteristic
177C2×#235C2312yes—
178C2×#235C2311yescharacteristic
179C2×#235C2312yes—
180C22×D12—22no—
181C22×D12D411yescharacteristic
182C22×D12C2311yescharacteristic
183C22×C4×D3—22no—
184C22×C4×D3—21no—
185C22×C4×D3—22no—
186C22×C4×D3C2312yes—
187C22×Dic6—22no—
188C22×Dic6D411yescharacteristic
189C22×Dic6C2311yescharacteristic
190C2×C3×SD16—28no—
191C2×C3×SD16C2314yes—
192C2×C3×SD16C2314yes—
193C22×C3×C8C2312yes—
194C3×#121—21no—
195C3×#121—21no—
196C3×#121C2312yes—
197C3×#121C2312yes—
198C2×C3×C4⋊C4C2311yescharacteristic
199C2×C3×C22⋊C4—21no—
200#953—21no—
201#953—22no—
202C2×#216C2314yes—
203#942—28no—
204C2×#215C2314yes—
205#940—22no—
206#940—21no—
207#939—22no—
208#939—22no—
209#938—22no—
210#938C2312yes—
211#938C2312yes—
212#937—22no—
213#937—22no—
214#936—21no—
215D4×Dic3—22no—
216C2×#214C2314yes—
217#932—28no—
218C2×#213C2314yes—
219#930—22no—
220#930C2311yescharacteristic
221#930C2311yescharacteristic
222#929—21no—
223C4×#67—21no—
224C4×#67—21no—
225C4×#67—22no—
226#926C2311yescharacteristic
227#924C2311yescharacteristic
228#924C2311yescharacteristic
229C2×#208C2312yes—
230#916—216no—
231#915—216no—
232#914—216no—
233D3×SD16—216no—
234C2×Dic12C2312yes—
235#904—28no—
236C2×D24C2312yes—
237C2×#204C2312yes—
238C2×#204C2312yes—
239#901—28no—
240C2×ΓL(1,𝔽25)C2314yes—
241C2×D3×C8C2314yes—
242#897—21no—
243#897C2312yes—
244#895—21no—
245#895C2312yes—
246#893—21no—
247#892C2312yes—
248D3×C4⋊C4C2312yes—
249#887—21no—
250#885—22no—
251#884—22no—
252#884—22no—
253#883—22no—
254#882—22no—
255#67⋊C4—22no—
256D3×C22⋊C4—22no—
257#878—22no—
258C3×#103C2314yes—
259C3×#103C2314yes—
260C3×C22⋊C8C2311yescharacteristic
261C3×C22⋊C8C2311yescharacteristic
262C3×C22⋊C8C2312yes—
263#835C2314yes—
264#835C2314yes—
265#830C2312yes—
266#830C2312yes—
267#821C2312yes—
268#821C2312yes—
269(C2×D3)⋊C8C2314yes—
270(C2×D3)⋊C8C2314yes—
271#816C2312yes—
272#816C2312yes—
273#810C2314yes—
274#809C2314yes—
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—32no—
293C2×#137—34no—
294C2×AGL(1,ℤ/8)—32no—
295C2×AGL(1,ℤ/8)—34no—
296C2×#135—34no—
297C2×#135—32no—
298C22×SD16—34no—
299C22×SD16C2×D312yescomplemented
300C2×#131—32no—
301#550—61no—
302#548—61no—
303#546—62no—
304#546—61no—
305D42—61no—
306D42—62no—
307#537—32no—
308#537—31no—
309#535—31no—
310#535—32no—
311#525—31no—
312#525—32no—
313C2×#121—32no—
314C2×#121C2×D311yescharacteristic
315#520—31no—
316#452—34no—
317#452—32no—
318#451—32no—
319#451—32no—
320#451—34no—
321#451—31no—
322#450—31no—
323#449—34no—
324#449—34no—
325#449—34no—
326#449—34no—
327#449—32no—
328#448—32no—
329#448—32no—
330#448—34no—
331#448—34no—
332#448—32no—
333#448—34no—
334#448—31no—
335#448C2×D312yescomplemented
336#448C2×D312yescomplemented
337#448C2×D314yescomplemented
338#447—32no—
339#447—31no—
340#419—32no—
341#419—34no—
342#417—32no—
343#417—34no—
344#416—32no—
345#416—34no—
346C2×#103—34no—
347C2×#103C2×D312yescomplemented
348#408—32no—
349#408—34no—
350#407—31no—
351#407—32no—
352C2×C22⋊C8—32no—
353C2×C22⋊C8C2×D311yescharacteristic, complemented
354C24×C3—21no—
355C24×C3C2×D411yescharacteristic
356C23×D3—21no—
357C23×D3—22no—
358C23×D3C2×D412yes—
359C2×C3×Q8—28no—
360C2×C3×Q8—28no—
361C2×C3×Q8—28no—
362C2×C3×Q8—28no—
363C2×C3×Q8—28no—
364C2×C3×Q8—22no—
365C2×C3×Q8—22no—
366C2×C3×Q8—22no—
367C2×C3×Q8—24no—
368C2×C3×Q8C2×D418yescomplemented
369C2×C3×Q8C2414yes—
370C2×C3×D4—22no—
371C2×C3×D4—22no—
372C2×C3×D4—24no—
373C2×C3×D4—21no—
374C2×C3×D4—82no—
375C2×C3×D4C2412yes—
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—21no—
393C2×#67—21no—
394C2×#67—22no—
395C2×#67—21no—
396C2×#67—22no—
397C2×#67—22no—
398C2×#67—22no—
399C2×#67—48no—
400C2×#67C2×D412yes—
401C2×#67C2×D412yes—
402C2×#67C2×D412yes—
403C2×#67C2×D412yes—
404C22×Dic3—21no—
405C22×Dic3—22no—
406C22×Dic3C2×D412yes—
407#239—232no—
408#239—216no—
409#239—216no—
410#239—216no—
411#239—28no—
412#239—216no—
413#239—28no—
414#239—28no—
415#239C2×D4116yescomplemented
416D3×Q8—216no—
417D3×Q8—216no—
418D3×Q8—216no—
419D3×Q8—232no—
420D3×Q8—28no—
421D3×Q8—28no—
422D3×Q8—216no—
423D3×Q8—28no—
424D3×Q8C2×D4116yescomplemented
425#237—28no—
426#237—44no—
427D3×D4—28no—
428D3×D4—44no—
429D3×D4—84no—
430#235—232no—
431#235—28no—
432#235—232no—
433#235—28no—
434#235—232no—
435#235—24no—
436#235—24no—
437#235—232no—
438#235—28no—
439#235—24no—
440#235—24no—
441#235—28no—
442#235—24no—
443#235—24no—
444#235—24no—
445#235C2×D418yes—
446#235C2×D418yescomplemented
447C2×D12—216no—
448C2×D12—24no—
449C2×D12—24no—
450C2×D12—21no—
451C2×D12—24no—
452C2×D12—24no—
453C2×D12—22no—
454C2×D12C2×D412yes—
455C2×D12C2×D411yescharacteristic
456C2×D12C2×D411yescharacteristic
457C2×D12C2411yescharacteristic
458C2×D12C2412yes—
459C2×C4×D3—216no—
460C2×C4×D3—28no—
461C2×C4×D3—216no—
462C2×C4×D3—24no—
463C2×C4×D3—24no—
464C2×C4×D3—22no—
465C2×C4×D3—22no—
466C2×C4×D3—24no—
467C2×C4×D3—24no—
468C2×C4×D3—28no—
469C2×C4×D3—21no—
470C2×C4×D3—22no—
471C2×C4×D3C2×D412yes—
472C2×C4×D3C2×D412yes—
473C2×C4×D3C2412yes—
474C2×C4×D3C2412yes—
475C2×Dic6—216no—
476C2×Dic6—21no—
477C2×Dic6—24no—
478C2×Dic6—24no—
479C2×Dic6—24no—
480C2×Dic6—24no—
481C2×Dic6C2×D412yes—
482C2×Dic6C2×D411yescharacteristic
483C2×Dic6C2×D411yescharacteristic
484C2×Dic6C2411yescharacteristic
485C2×Dic6C2412yes—
486C3×SD16—28no—
487C3×SD16—28no—
488C2×C3×C8—24no—
489C2×C3×C8C2412yes—
490C2×C3×C8C2412yes—
491C3×C4⋊C4—21no—
492C3×C4⋊C4C2412yes—
493C3×C22⋊C4—22no—
494C3×C22⋊C4—22no—
495#217—21no—
496#217—21no—
497#217—21no—
498#217—22no—
499#217—22no—
500#216—28no—
501#215—28no—
502#214—28no—
503#213—28no—
504(C2×D3)⋊C4—22no—
505(C2×D3)⋊C4—22no—
506(C2×D3)⋊C4—21no—
507(C2×D3)⋊C4—21no—
508(C2×D3)⋊C4—22no—
509C4⋊Dic3—22no—
510C4⋊Dic3C2411yescharacteristic
511C4⋊Dic3C2411yescharacteristic
512Dic3⋊C4—21no—
513Dic3⋊C4—21no—
514Dic3⋊C4—22no—
515C4×Dic3—21no—
516C4×Dic3—22no—
517#208—24no—
518C2×C3⋊C8C2414yes—
519Dic12—24no—
520D24—24no—
521#204—24no—
522#204—24no—
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—34no—
543C2×#41—32no—
544C2×#41—32no—
545C2×#41—31no—
546C2×#41—32no—
547C2×#41—64no—
548C2×#41—64no—
549C2×#41—64no—
550C2×#41—64no—
551C2×#41—68no—
552C2×#41—68no—
553C2×#41—632no—
554C2×#41—62no—
555C2×#41—62no—
556C2×#41—61no—
557C2×#41—62no—
558C2×#41—64no—
559C2×#41—62no—
560C2×#41—616no—
561C2×#41—616no—
562C2×#41—61no—
563C2×#41—61no—
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—21no—
584C22×D4—32no—
585C22×D4—32no—
586C22×D4—31no—
587C22×D4—31no—
588C22×D4—62no—
589C22×D4—61no—
590C22×D4—62no—
591C22×D4—62no—
592C22×D4—61no—
593C22×D4C22×D311yescharacteristic
594C23×C4—21no—
595C23×C4—32no—
596C23×C4—62no—
597C23×C4—62no—
598C23×C4—61no—
599C23×C4C22×D311yescharacteristic
600#137—616no—
601#137—68no—
602AGL(1,ℤ/8)—616no—
603AGL(1,ℤ/8)—68no—
604#135—68no—
605#135—616no—
606C2×Q16—34no—
607C2×Q16—32no—
608C2×SD16—28no—
609C2×SD16—34no—
610C2×SD16—34no—
611C2×SD16—32no—
612C2×SD16—32no—
613C2×SD16—616no—
614C2×SD16C22×D314yes—
615C2×SD16C22×D314yes—
616C2×D8—34no—
617C2×D8—32no—
618#131—68no—
619C2×M16—32no—
620C2×M16—34no—
621C22×C8—34no—
622C22×C8C22×D312yes—
623#127—62no—
624#127—61no—
625#124—62no—
626#124—61no—
627#123—62no—
628#123—61no—
629C22⋊Q8—31no—
630C22⋊Q8—31no—
631C22⋊Q8—32no—
632C22⋊Q8—62no—
633C22⋊Q8—61no—
634#121—21no—
635#121—21no—
636#121—32no—
637#121—32no—
638#121—31no—
639#121—31no—
640#121—32no—
641#121—62no—
642#121—62no—
643#121—61no—
644#121—62no—
645#121—62no—
646#121—62no—
647#121—62no—
648#121C22×D312yes—
649#121C22×D312yes—
650#120—62no—
651#120—62no—
652#120—62no—
653#120—62no—
654#120—61no—
655C4×Q8—61no—
656C4×D4—62no—
657C4×D4—61no—
658C4×D4—62no—
659C4×D4—62no—
660C4×D4—61no—
661C4×D4—61no—
662#117—31no—
663#117—32no—
664C2×C4⋊C4—32no—
665C2×C4⋊C4C22×D311yescharacteristic
666C2×C22⋊C4—21no—
667C2×C22⋊C4—62no—
668#103—34no—
669#103—34no—
670#103—32no—
671#103—32no—
672#103—34no—
673#103C22×D314yes—
674#103C22×D314yes—
675#102—32no—
676#102—32no—
677#102—34no—
678C22⋊C8—32no—
679C22⋊C8—32no—
680C22⋊C8—34no—
681C22⋊C8—34no—
682C22⋊C8C22×D311yescharacteristic
683C22⋊C8C22×D311yescharacteristic
684C22⋊C8C22×D312yes—
685C23×C3—22no—
686C23×C3—22no—
687C23×C3—22no—
688C23×C3—41no—
689C23×C3—42no—
690C23×C3—81no—
691C23×C3—81no—
692C23×C3C22×D411yescharacteristic
693C23×C3C22×D411yescharacteristic
694C23×C3C22×D411yescharacteristic
695C22×D3—24no—
696C22×D3—24no—
697C22×D3—22no—
698C22×D3—24no—
699C22×D3—21no—
700C22×D3—42no—
701C22×D3—42no—
702C22×D3—42no—
703C22×D3—44no—
704C22×D3—82no—
705C22×D3—82no—
706C22×D3C22×D412yes—
707C22×D3C22×D412yes—
708C3×Q8—28no—
709C3×Q8—28no—
710C3×Q8—28no—
711C3×Q8—24no—
712C3×Q8C22×D418yes—
713C3×D4—24no—
714C3×D4—44no—
715C3×D4—42no—
716C3×D4—82no—
717C2×C3×C4—28no—
718C2×C3×C4—28no—
719C2×C3×C4—28no—
720C2×C3×C4—22no—
721C2×C3×C4—24no—
722C2×C3×C4—22no—
723C2×C3×C4—22no—
724C2×C3×C4—22no—
725C2×C3×C4—22no—
726C2×C3×C4—22no—
727C2×C3×C4—81no—
728C2×C3×C4C22×D411yescharacteristic
729C2×C3×C4C22×D411yescharacteristic
730C2×C3×C4C22×D411yescharacteristic
731C2×C3×C4C22×D414yes—
732C2×C3×C4C2511yescharacteristic
733#67—28no—
734#67—24no—
735#67—28no—
736#67—24no—
737#67—24no—
738#67—42no—
739#67—42no—
740#67—44no—
741#67—44no—
742#67—82no—
743#67—82no—
744#67—81no—
745#67#12018yes—
746C2×Dic3—24no—
747C2×Dic3—22no—
748C2×Dic3—24no—
749C2×Dic3—21no—
750C2×Dic3—21no—
751C2×Dic3—21no—
752C2×Dic3—44no—
753C2×Dic3C22×D412yes—
754C2×Dic3C22×D412yes—
755D12—216no—
756D12—24no—
757D12—216no—
758D12—24no—
759D12—22no—
760D12—22no—
761D12—22no—
762D12—82no—
763D12#12014yes—
764D12C22×D414yes—
765C4×D3—216no—
766C4×D3—216no—
767C4×D3—28no—
768C4×D3—216no—
769C4×D3—24no—
770C4×D3—28no—
771C4×D3—24no—
772C4×D3—216no—
773C4×D3—24no—
774C4×D3—42no—
775C4×D3—82no—
776C4×D3C22×D418yes—
777Dic6—216no—
778Dic6—24no—
779Dic6—22no—
780Dic6—22no—
781Dic6—216no—
782Dic6—24no—
783Dic6—22no—
784Dic6#12014yes—
785Dic6C22×D414yes—
786C3×C8—22no—
787C3×C8—22no—
788C3⋊C8—24no—
789C24—21no—
790C24—32no—
791C24—62no—
792C24—61no—
793C24D3×D411yescharacteristic
794#41—38no—
795#41—316no—
796#41—38no—
797#41—68no—
798#41—68no—
799#41—64no—
800#41—64no—
801#41—632no—
802#41—64no—
803#41—64no—
804#41—632no—
805#41—632no—
806#41—632no—
807#41—68no—
808#41—68no—
809#41—68no—
810#41—68no—
811#41—68no—
812#41—616no—
813#41—616no—
814#41—616no—
815#41—632no—
816#41—616no—
817#41—68no—
818#41—64no—
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—31no—
837C2×Q8—64no—
838C2×Q8—64no—
839C2×Q8—64no—
840C2×Q8—64no—
841C2×Q8—616no—
842C2×Q8—68no—
843C2×Q8—68no—
844C2×Q8—616no—
845C2×Q8—616no—
846C2×Q8—632no—
847C2×Q8—616no—
848C2×Q8—616no—
849C2×Q8—68no—
850C2×Q8—61no—
851C2×Q8D3×D418yescomplemented
852C2×Q8C23×D314yes—
853C2×D4—22no—
854C2×D4—22no—
855C2×D4—24no—
856C2×D4—21no—
857C2×D4—32no—
858C2×D4—32no—
859C2×D4—32no—
860C2×D4—32no—
861C2×D4—31no—
862C2×D4—32no—
863C2×D4—31no—
864C2×D4—32no—
865C2×D4—31no—
866C2×D4—64no—
867C2×D4—64no—
868C2×D4—64no—
869C2×D4—64no—
870C2×D4—616no—
871C2×D4—62no—
872C2×D4—68no—
873C2×D4—62no—
874C2×D4—68no—
875C2×D4—68no—
876C2×D4—62no—
877C2×D4—62no—
878C2×D4—62no—
879C2×D4—61no—
880C2×D4—61no—
881C2×D4—62no—
882C2×D4—62no—
883C2×D4—61no—
884C2×D4—61no—
885C2×D4—82no—
886C2×D4—124no—
887C2×D4—128no—
888C2×D4—244no—
889C2×D4C23×D312yes—
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—64no—
905C22×C4—64no—
906C22×C4—616no—
907C22×C4—616no—
908C22×C4—68no—
909C22×C4—62no—
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—64no—
922Q16—68no—
923SD16—28no—
924SD16—28no—
925SD16—64no—
926SD16—64no—
927SD16—68no—
928SD16—68no—
929D8—64no—
930D8—68no—
931M16—68no—
932M16—64no—
933C2×C8—24no—
934C2×C8—34no—
935C2×C8—68no—
936C2×C8C23×D312yes—
937C2×C8C23×D312yes—
938C4⋊C4—21no—
939C4⋊C4—31no—
940C4⋊C4—31no—
941C4⋊C4—62no—
942C4⋊C4—62no—
943C4⋊C4—61no—
944C4⋊C4—61no—
945C4⋊C4C23×D312yes—
946C22⋊C4—22no—
947C22⋊C4—22no—
948C22⋊C4—62no—
949C22⋊C4—62no—
950C22⋊C4—62no—
951C22⋊C4—62no—
952C22⋊C4—62no—
953C22⋊C4—61no—
954C22⋊C4—61no—
955C22⋊C4—61no—
956C22⋊C4—61no—
957C22⋊C4—61no—
958C42—62no—
959C42—61no—
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—42no—
969C22×C3—42no—
970C22×C3—42no—
971C22×C3—162no—
972C22×C3C2×#12012yes—
973C22×C3#57712yescomplemented
974C22×C3C23×D411yescharacteristic
975C2×D3—22no—
976C2×D3—22no—
977C2×D3—22no—
978C2×D3—22no—
979C2×D3—24no—
980C2×D3—22no—
981C2×D3—48no—
982C2×D3—48no—
983C2×D3—42no—
984C2×D3—42no—
985C2×D3—41no—
986C2×D3—41no—
987C2×D3—41no—
988C2×D3—164no—
989C2×D3C2×#12014yes—
990C3×C4—28no—
991C3×C4—21no—
992C3×C4—21no—
993C3×C4—42no—
994C3×C4C2×#12012yes—
995C3×C4C23×D412yes—
996Dic3—22no—
997Dic3—24no—
998Dic3—41no—
999Dic3—41no—
1000Dic3—41no—
1001Dic3C2×#12014yes—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—32no—
1006C23—32no—
1007C23—41no—
1008C23—42no—
1009C23—64no—
1010C23—64no—
1011C23—62no—
1012C23—64no—
1013C23—61no—
1014C23—81no—
1015C23—81no—
1016C23—122no—
1017C23—122no—
1018C23—124no—
1019C23—122no—
1020C23—242no—
1021C23—242no—
1022C23C2×D3×D411yescharacteristic
1023C23C2×D3×D411yescharacteristic
1024C23C2×D3×D411yescharacteristic
1025Q8—28no—
1026Q8—28no—
1027Q8—24no—
1028Q8—28no—
1029Q8—34no—
1030Q8—34no—
1031Q8—616no—
1032Q8—64no—
1033Q8—616no—
1034Q8—64no—
1035Q8—62no—
1036Q8—62no—
1037Q8—62no—
1038Q8C2×D3×D418yes—
1039D4—24no—
1040D4—38no—
1041D4—34no—
1042D4—34no—
1043D4—44no—
1044D4—42no—
1045D4—64no—
1046D4—616no—
1047D4—616no—
1048D4—64no—
1049D4—64no—
1050D4—64no—
1051D4—68no—
1052D4—64no—
1053D4—68no—
1054D4—62no—
1055D4—62no—
1056D4—62no—
1057D4—82no—
1058D4—124no—
1059D4—124no—
1060D4—122no—
1061D4—122no—
1062D4—242no—
1063D4—241no—
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—22no—
1076C2×C4—32no—
1077C2×C4—38no—
1078C2×C4—32no—
1079C2×C4—64no—
1080C2×C4—616no—
1081C2×C4—64no—
1082C2×C4—616no—
1083C2×C4—616no—
1084C2×C4—616no—
1085C2×C4—68no—
1086C2×C4—64no—
1087C2×C4—64no—
1088C2×C4—62no—
1089C2×C4—64no—
1090C2×C4—68no—
1091C2×C4—61no—
1092C2×C4—61no—
1093C2×C4—61no—
1094C2×C4—81no—
1095C2×C4—124no—
1096C2×C4—122no—
1097C2×C4—242no—
1098C2×C4C2×D3×D411yescharacteristic
1099C2×C4C2×D3×D411yescharacteristic
1100C2×C4C2×D3×D414yes—
1101C2×C4C2×D3×D411yescharacteristic
1102C2×C4C24×D311yescharacteristic
1103C8—22no—
1104C8—22no—
1105C8—64no—
1106C2×C3—22no—
1107C2×C3—22no—
1108C2×C3—41no—
1109C2×C3—82no—
1110C2×C3C22×#12011yescharacteristic
1111C2×C3C2×#57711yescharacteristic
1112C2×C3#358611yescharacteristic
1113D3—24no—
1114D3—42no—
1115D3—44no—
1116D3—81no—
1117C22—21no—
1118C22—21no—
1119C22—21no—
1120C22—21no—
1121C22—21no—
1122C22—21no—
1123C22—21no—
1124C22—34no—
1125C22—44no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—62no—
1130C22—62no—
1131C22—62no—
1132C22—64no—
1133C22—62no—
1134C22—62no—
1135C22—128no—
1136C22—128no—
1137C22—122no—
1138C22—122no—
1139C22—121no—
1140C22—121no—
1141C22—121no—
1142C22—162no—
1143C22—484no—
1144C22D3×#12012yes—
1145C22#576212yescomplemented
1146C22C22×D3×D411yescharacteristic
1147C4—28no—
1148C4—21no—
1149C4—21no—
1150C4—34no—
1151C4—42no—
1152C4—62no—
1153C4—64no—
1154C4—121no—
1155C4—121no—
1156C4—121no—
1157C4D3×#12012yes—
1158C4C22×D3×D412yes—
1159C3#6037411yescharacteristic, complemented, Sylow
1160C2—22no—
1161C2—22no—
1162C2—41no—
1163C2—64no—
1164C2—82no—
1165C2—122no—
1166C2—124no—
1167C2—241no—
1168C2C2×D3×#12011yescharacteristic
1169C2C2×#576211yescharacteristic
1170C2#8719711yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#448C2
socleC22×C3C23×D4
hypercenterC2×#448D3
hypocenterC3#60374
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
1. C22×#1007C2semidirect
2. C2×#5762C2semidirect
3. #85949C2semidirect
4. C2×C3×#448C2semidirect
5. #84059C2semidirect
6. #83860C2semidirect
7. #82624C2semidirect
8. #80042C2semidirect
9. #80041C2semidirect
10. #80040C2semidirect
11. #80039C2semidirect
12. #80038C2semidirect
13. D3×#448C2semidirect
14. #78795C2semidirect
15. #78790C2semidirect
16. #78610C2semidirect
17. #78600C2semidirect
19. C23×C3×Q8C22semidirect
25. C2×#1007C22semidirect
26. C2×#1007C22semidirect
28. C22×#239C22semidirect
30. C22×D3×Q8C22semidirect
31. C2×#1004C22semidirect
34. C22×#235C22semidirect
35. C22×C3×SD16C22semidirect
37. C2×#942C22semidirect
38. #5805C22semidirect
40. C2×#932C22semidirect
43. C2×#916C22semidirect
44. C2×#915C22semidirect
45. C2×#914C22semidirect
46. C2×D3×SD16C22semidirect
47. C2×#904C22semidirect
48. C2×#901C22semidirect
51. #5608C22semidirect
52. #5607C22semidirect
57. #5510C22semidirect
58. #5504C22semidirect
60. C3×#448C22semidirect
61. C3×#448C22semidirect
62. C3×#448C22semidirect
63. C2×C3×#103C22semidirect
64. C2×C3×C22⋊C8C22semidirect
65. #5228C22semidirect
66. #5228C22semidirect
67. #5227C22semidirect
68. #5227C22semidirect
69. #5225C22semidirect
70. #5207C22semidirect
71. #5172C22semidirect
72. #5172C22semidirect
73. #5170C22semidirect
74. #5170C22semidirect
75. #5113C22semidirect
76. #5110C22semidirect
77. #5040C22semidirect
78. #5037C22semidirect
79. #5036C22semidirect
80. #4966C22semidirect
81. #4810C22semidirect
82. #4809C22semidirect
83. #4808C22semidirect
84. #4806C22semidirect
85. #4804C22semidirect
86. #4803C22semidirect
87. #4802C22semidirect
88. D3×#103C22semidirect
89. #4739C22semidirect
90. #4738C22semidirect
91. #4734C22semidirect
92. #4733C22semidirect
93. #4732C22semidirect
94. #4731C22semidirect
95. #4727C22semidirect
96. #4726C22semidirect
97. D3×C22⋊C8C22semidirect
112. C2×#448D3semidirect
137. #1007D4semidirect
290. C23×Q8C2×D3semidirect
299. C22×SD16C2×D3semidirect
335. #448C2×D3semidirect
336. #448C2×D3semidirect
337. #448C2×D3semidirect
347. C2×#103C2×D3semidirect
353. C2×C22⋊C8C2×D3semidirect
368. C2×C3×Q8C2×D4semidirect
415. #239C2×D4semidirect
424. D3×Q8C2×D4semidirect
446. #235C2×D4semidirect
851. C2×Q8D3×D4semidirect
973. C22×C3#577semidirect
1145. C22#5762semidirect
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×#57622
#859492
C2×C3×#4482
#840592
#838602
#826242
#800422
#800412
#800402
#800392
#800382
D3×#4482
#787952
#787902
#786102
#786002
#603743