Subgroups — C₁₁⋊(Dic₆₇⋊C₁₁) #44569827

Order 32428.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×C₆₇⋊C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₆₇⋊C₁₁	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₇₃₇	C₁₁	1	1	yes	maximal, characteristic, complemented
4	Dic₆₇⋊C₁₁	—	11	1	no	maximal
5	C₂×C₁₁×C₆₇	C₂×C₁₁	1	1	yes	characteristic
6	C₂×C₆₇⋊C₁₁	—	2	5	no	—
7	C₂×C₆₇⋊C₁₁	D₁₁	1	1	yes	characteristic
8	C₁₁×C₆₇	C₄×C₁₁	1	1	yes	characteristic, complemented
9	C₆₇⋊C₁₁	—	2	5	no	—
10	C₆₇⋊C₁₁	Dic₁₁	1	1	yes	characteristic, complemented
11	C₁₁×Dic₁₁	—	67	1	no	maximal, Hall
12	Dic₆₇	—	11	1	no	Hall
13	C₂×C₁₁²	—	67	1	no	—
14	C₂×C₆₇	C₁₁×D₁₁	1	1	yes	characteristic
15	C₁₁²	—	67	1	no	Sylow
16	C₆₇	C₁₁×Dic₁₁	1	1	yes	characteristic, complemented, Sylow
17	C₄×C₁₁	—	737	1	no	—
18	Dic₁₁	—	67	1	no	—
19	C₂×C₁₁	—	67	1	no	—
20	C₂×C₁₁	—	134	5	no	—
21	C₂×C₁₁	D₆₇⋊C₁₁	1	1	yes	characteristic
22	C₁₁	—	67	1	no	—
23	C₁₁	—	134	5	no	—
24	C₁₁	Dic₆₇⋊C₁₁	1	1	yes	characteristic, complemented
25	C₄	—	737	1	no	Sylow
26	C₂	C₁₁⋊(D₆₇⋊C₁₁)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₁₁⋊(D₆₇⋊C₁₁)
commutator, hypocenter	C₁₁×C₆₇	C₄×C₁₁
Fitting, socle, cosocle	C₂×C₁₁×C₆₇	C₂×C₁₁
prime radical	C₂×C₁₁×C₆₇⋊C₁₁	C₂
LCS	G ▷ C₁₁×C₆₇
UCS	C₁ ◁ C₂

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.