Subgroups — D₇₇×C₆₇⋊C₃ #44526272

Order 30954.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₁×C₆₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₆₇×D₇₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₁₁×C₆₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	D₁₁×C₆₇⋊C₃	—	7	1	no	maximal, Hall
5	D₇×C₆₇⋊C₃	—	11	1	no	maximal, Hall
6	C₁₁×C₆₇⋊C₃	D₇	1	1	yes	characteristic, complemented, Hall
7	D₁₁×C₆₇	—	7	1	no	Hall
8	C₇×C₆₇⋊C₃	D₁₁	1	1	yes	characteristic, complemented, Hall
9	D₇×C₆₇	—	11	1	no	Hall
10	C₁₁×C₆₇	C₃×D₇	1	1	yes	characteristic, complemented, Hall
11	C₇×C₆₇	C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
12	C₃×D₇₇	—	67	1	no	maximal, Hall
13	C₂×C₆₇⋊C₃	—	77	1	no	Hall
14	C₃×C₇×C₁₁	—	67	1	no	Hall
15	C₆₇⋊C₃	D₇₇	1	1	yes	characteristic, direct product factor, Hall
16	D₇₇	C₆₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₆₇	—	77	1	no	Hall
18	C₇×C₁₁	C₂×C₆₇⋊C₃	1	1	yes	characteristic, complemented, Hall
19	C₆₇	C₃×D₇₇	1	1	yes	characteristic, complemented, Sylow
20	C₃×D₁₁	—	469	1	no	Hall
21	C₃×D₇	—	737	1	no	Hall
22	C₃×C₁₁	—	67	1	no	Hall
23	D₁₁	—	7	1	no	Hall
24	C₃×C₇	—	67	1	no	Hall
25	D₇	—	11	1	no	Hall
26	C₁₁	D₇×C₆₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
27	C₇	D₁₁×C₆₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	5159	1	no	Hall
29	C₃	—	67	1	no	Sylow
30	C₂	—	77	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₁×C₆₇	C₂×C₃
LCS	G ▷ C₇×C₁₁×C₆₇
UCS	C₁

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

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