Subgroups — #11924243

Order 1176.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₇⋊Dic₇)	C₂	1	1	yes	maximal, characteristic
2	C₇²×Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₃×C₇⋊Dic₇	C₂	1	1	yes	maximal, characteristic
4	#87648	—	3	1	no	maximal, Hall
5	C₂×C₃×C₇²	C₂²	1	1	yes	characteristic
6	C₄×C₇²	—	3	1	no	—
7	C₇⋊Dic₇	—	3	1	no	—
8	C₇⋊Dic₇	D₃	1	1	yes	characteristic
9	#4248	—	7	8	no	maximal
10	C₃×C₇²	Q₈	1	1	yes	characteristic, complemented, Hall
11	C₂×C₇²	C₂×D₃	1	1	yes	characteristic
12	Dic₂₁	—	7	8	no	—
13	C₃×Dic₇	—	7	8	no	—
14	C₇×Dic₃	D₇	1	8	yes	—
15	Dic₁₄	—	21	8	no	—
16	C₇²	Dic₆	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₃×C₇	C₂×D₇	1	8	yes	—
18	C₄×C₇	—	3	8	no	—
19	Dic₇	—	7	8	no	—
20	Dic₇	—	21	8	no	—
21	Dic₆	—	49	1	no	Hall
22	C₃×C₇	Dic₁₄	1	8	yes	complemented
23	C₂×C₇	D₃×D₇	1	8	yes	—
24	C₃×C₄	—	49	1	no	—
25	Dic₃	—	49	1	no	—
26	Dic₃	C₇⋊D₇	1	1	yes	characteristic
27	Q₈	—	147	1	no	Sylow
28	C₇	#4248	1	8	yes	complemented
29	C₂×C₃	C₂×C₇⋊D₇	1	1	yes	characteristic
30	C₄	—	3	1	no	—
31	C₄	—	49	1	no	—
32	C₄	—	147	1	no	—
33	C₃	#87648	1	1	yes	characteristic, complemented, Sylow
34	C₂	D₃×C₇⋊D₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×C₇⋊D₇
commutator, Fitting, socle, prime radical, cosocle	C₂×C₃×C₇²	C₂²
hypocenter	C₃×C₇²	Q₈
LCS	G ▷ C₂×C₃×C₇² ▷ 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.