Subgroups — C₇×D₃₁² #41002062

Order 26908.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₃₁×D₃₁	C₂	1	2	yes	maximal, complemented
2	C₇×C₃₁⋊D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₃₁²	C₂²	1	1	yes	characteristic, complemented, Hall
4	D₃₁²	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃₁⋊D₃₁	C₂×C₇	1	1	yes	characteristic, complemented
6	C₃₁×D₃₁	C₂×C₇	1	2	yes	complemented
7	C₃₁²	C₂²×C₇	1	1	yes	characteristic, complemented, Sylow
8	C₂×C₇×D₃₁	—	31	2	no	maximal
9	C₂×C₇×C₃₁	—	31	2	no	—
10	C₇×D₃₁	—	31	2	no	—
11	C₇×D₃₁	—	62	15	no	—
12	C₇×D₃₁	D₃₁	1	2	yes	direct product factor
13	C₇×C₃₁	—	2	15	no	—
14	C₇×C₃₁	C₂×D₃₁	1	2	yes	complemented
15	C₂×D₃₁	—	31	2	no	—
16	C₂×C₃₁	—	31	2	no	—
17	D₃₁	—	31	2	no	—
18	D₃₁	—	62	15	no	—
19	D₃₁	C₇×D₃₁	1	2	yes	direct product factor
20	C₃₁	—	2	15	no	—
21	C₃₁	C₂×C₇×D₃₁	1	2	yes	complemented
22	C₂²×C₇	—	961	1	no	Hall
23	C₂×C₇	—	31	2	no	—
24	C₂×C₇	—	961	1	no	—
25	C₇	D₃₁²	1	1	yes	characteristic, direct product factor, Sylow
26	C₂²	—	961	1	no	Sylow
27	C₂	—	31	2	no	—
28	C₂	—	961	1	no	—

	subgroup	G/H
center, hypercenter	C₇	D₃₁²
commutator, cosocle, hypocenter	C₃₁²	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₇×C₃₁²	C₂²
LCS	G ▷ C₃₁²
UCS	C₁ ◁ C₇

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.