Subgroups — #11924239

Order 1176.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊(C₇⋊D₇)	C₂	1	1	yes	maximal, characteristic
2	C₇²×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇⋊Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₇⋊D₇	—	3	1	no	maximal, Hall
5	C₂×C₃×C₇²	C₂²	1	1	yes	characteristic
6	C₃⋊(C₇⋊D₇)	C₄	1	2	yes	complemented
7	C₂×C₇⋊D₇	—	3	1	no	—
8	C₄×C₇²	—	3	1	no	—
9	C₇⋊Dic₇	D₃	1	1	yes	characteristic, complemented
10	D₂₁⋊C₄	—	7	8	no	maximal
11	C₃×C₇²	C₂×C₄	1	1	yes	characteristic, complemented, Hall
12	C₂×C₇²	C₂×D₃	1	1	yes	characteristic
13	C₇⋊D₇	—	3	2	no	—
14	C₂×D₂₁	—	7	8	no	—
15	C₃×Dic₇	—	7	8	no	—
16	C₇×Dic₃	D₇	1	8	yes	complemented
17	C₄×D₇	—	21	8	no	—
18	C₇²	C₄×D₃	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃×C₇	C₂×D₇	1	8	yes	—
20	D₂₁	—	7	16	no	—
21	C₂×D₇	—	21	8	no	—
22	C₄×C₇	—	3	8	no	—
23	Dic₇	—	7	8	no	—
24	C₄×D₃	—	49	1	no	Hall
25	C₃×C₇	C₄×D₇	1	8	yes	complemented
26	C₂×C₇	D₃×D₇	1	8	yes	—
27	D₇	—	21	16	no	—
28	C₂×D₃	—	49	1	no	—
29	C₃×C₄	—	49	1	no	—
30	Dic₃	C₇⋊D₇	1	1	yes	characteristic, complemented
31	C₂×C₄	—	147	1	no	Sylow
32	C₇	D₂₁⋊C₄	1	8	yes	complemented
33	C₂×C₃	C₂×C₇⋊D₇	1	1	yes	characteristic
34	D₃	—	49	2	no	—
35	C₂²	—	147	1	no	—
36	C₄	—	3	1	no	—
37	C₄	—	49	1	no	—
38	C₃	C₄×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
39	C₂	—	147	2	no	—
40	C₂	D₃×C₇⋊D₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×C₇⋊D₇
commutator, hypocenter	C₃×C₇²	C₂×C₄
Fitting, socle, cosocle	C₂×C₃×C₇²	C₂²
prime radical	C₂×C₃⋊(C₇⋊D₇)	C₂
LCS	G ▷ C₃×C₇²
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.