Subgroups — C₇×#2867 #11742176

Order 896.

1272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#127	C₂	1	14	yes	maximal, complemented
2	C₄³×C₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₇×D₄	C₂²	1	28	yes	—
4	C₇×#127	—	2	56	no	—
5	C₂×C₄²×C₇	C₂²	1	7	yes	—
6	#2867	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂⁴×C₇	C₂³	1	8	yes	—
8	C₂×C₇×D₄	—	2	168	no	—
9	C₂²×C₄×C₇	C₂³	1	7	yes	—
10	C₄²×C₇	D₄	1	28	yes	complemented
11	C₂×#127	C₂×C₇	1	14	yes	complemented
12	C₄³	C₂×C₇	1	1	yes	characteristic, complemented
13	C₂³×C₇	—	2	56	no	—
14	C₂³×C₇	C₂⁴	1	1	yes	characteristic
15	C₇×D₄	—	4	112	no	—
16	C₂×C₄×C₇	C₂×D₄	1	42	yes	—
17	C₂²×D₄	C₂²×C₇	1	28	yes	—
18	#127	—	2	56	no	—
19	C₂×C₄²	C₂²×C₇	1	7	yes	—
20	C₂²×C₇	—	4	56	no	—
21	C₂²×C₇	C₂²×D₄	1	7	yes	—
22	C₄×C₇	#127	1	28	yes	complemented
23	C₂⁴	C₂³×C₇	1	8	yes	—
24	C₂×D₄	—	2	168	no	—
25	C₂²×C₄	C₂³×C₇	1	7	yes	—
26	C₄²	C₇×D₄	1	28	yes	complemented
27	C₂×C₇	—	8	8	no	—
28	C₂×C₇	C₂×#127	1	7	yes	—
29	C₂³	—	2	56	no	—
30	C₂³	C₂⁴×C₇	1	1	yes	characteristic
31	D₄	—	4	112	no	—
32	C₂×C₄	C₂×C₇×D₄	1	42	yes	—
33	C₇	#2867	1	1	yes	characteristic, direct product factor, Sylow
34	C₂²	—	4	56	no	—
35	C₂²	C₂²×C₇×D₄	1	7	yes	—
36	C₄	C₇×#127	1	28	yes	complemented
37	C₂	—	8	8	no	—
38	C₂	C₂×C₇×#127	1	7	yes	—

	subgroup	G/H
center, socle	C₂³×C₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₇
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ G

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.