Subgroups — C₇⋊D₇×D₁₃₇ #41001663

Order 26852.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×D₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇⋊D₇×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇⋊D₉₅₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇²×C₁₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₇×D₁₃₇	—	7	8	no	maximal
6	D₉₅₉	—	7	8	no	—
7	C₇×D₁₃₇	D₇	1	8	yes	complemented
8	D₇×C₁₃₇	—	7	8	no	—
9	C₇×C₁₃₇	C₂×D₇	1	8	yes	complemented
10	C₂×D₁₃₇	—	49	1	no	Hall
11	C₂×C₁₃₇	—	49	1	no	—
12	D₁₃₇	—	49	1	no	—
13	D₁₃₇	C₇⋊D₇	1	1	yes	characteristic, direct product factor
14	C₂×C₇⋊D₇	—	137	1	no	maximal, Hall
15	C₁₃₇	C₂×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₇²	—	137	1	no	—
17	C₇⋊D₇	—	137	1	no	—
18	C₇⋊D₇	D₁₃₇	1	1	yes	characteristic, direct product factor
19	C₇²	C₂×D₁₃₇	1	1	yes	characteristic, complemented, Sylow
20	C₂×D₇	—	959	8	no	—
21	C₂×C₇	—	137	8	no	—
22	D₇	—	7	8	no	—
23	D₇	—	959	8	no	—
24	C₇	D₇×D₁₃₇	1	8	yes	complemented
25	C₂²	—	6713	1	no	Sylow
26	C₂	—	49	1	no	—
27	C₂	—	6713	1	no	—
28	C₂	—	137	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇²×C₁₃₇	C₂²
LCS	G ▷ C₇²×C₁₃₇
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.