Subgroups — C₂×C₇×#125 #90548

Order 448.

226 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#125	C₂	1	8	yes	maximal, direct product factor
2	C₂×C₇×C₄⋊C₄	C₂	1	4	yes	maximal
3	C₂×C₇×C₄⋊C₄	C₂	1	2	yes	maximal
4	C₂×C₄²×C₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄×C₇	C₂²	1	2	yes	—
6	C₂²×C₄×C₇	C₂²	1	4	yes	—
7	C₂²×C₄×C₇	C₂²	1	1	yes	characteristic
8	C₇×C₄⋊C₄	C₂²	1	16	yes	—
9	C₇×C₄⋊C₄	C₂²	1	8	yes	—
10	C₄²×C₇	C₂²	1	4	yes	—
11	C₂×#125	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₂³×C₇	C₂³	1	1	yes	characteristic
13	C₂×C₄×C₇	—	2	4	no	—
14	C₂×C₄×C₇	—	2	8	no	—
15	C₂×C₄×C₇	Q₈	1	4	yes	—
16	C₂×C₄×C₇	C₂³	1	4	yes	—
17	C₂×C₄×C₇	C₂³	1	8	yes	—
18	C₂×C₄×C₇	C₂³	1	2	yes	—
19	#125	C₂×C₇	1	8	yes	direct product factor
20	C₂×C₄⋊C₄	C₂×C₇	1	4	yes	—
21	C₂×C₄⋊C₄	C₂×C₇	1	2	yes	—
22	C₂×C₄²	C₂×C₇	1	1	yes	characteristic
23	C₂²×C₇	C₂×Q₈	1	2	yes	—
24	C₂²×C₇	#41	1	4	yes	—
25	C₂²×C₇	C₂⁴	1	1	yes	characteristic
26	C₄×C₇	—	2	4	no	—
27	C₄×C₇	—	2	8	no	—
28	C₄×C₇	C₂×Q₈	1	4	yes	—
29	C₂²×C₄	C₂²×C₇	1	2	yes	—
30	C₂²×C₄	C₂²×C₇	1	4	yes	—
31	C₂²×C₄	C₂²×C₇	1	1	yes	characteristic
32	C₄⋊C₄	C₂²×C₇	1	16	yes	—
33	C₄⋊C₄	C₂²×C₇	1	8	yes	—
34	C₄²	C₂²×C₇	1	4	yes	—
35	C₂×C₇	#125	1	4	yes	direct product factor
36	C₂×C₇	C₂²×Q₈	1	1	yes	characteristic
37	C₂×C₇	C₂×#41	1	2	yes	—
38	C₂³	C₂³×C₇	1	1	yes	characteristic
39	C₂×C₄	—	2	4	no	—
40	C₂×C₄	—	2	8	no	—
41	C₂×C₄	C₇×Q₈	1	4	yes	—
42	C₂×C₄	C₂³×C₇	1	4	yes	—
43	C₂×C₄	C₂³×C₇	1	8	yes	—
44	C₂×C₄	C₂³×C₇	1	2	yes	—
45	C₇	C₂×#125	1	1	yes	characteristic, direct product factor, Sylow
46	C₂²	C₂×C₇×Q₈	1	2	yes	—
47	C₂²	C₇×#41	1	4	yes	—
48	C₂²	C₂⁴×C₇	1	1	yes	characteristic
49	C₄	—	2	4	no	—
50	C₄	—	2	8	no	—
51	C₄	C₂×C₇×Q₈	1	4	yes	—
52	C₂	C₇×#125	1	4	yes	direct product factor
53	C₂	C₂²×C₇×Q₈	1	1	yes	characteristic
54	C₂	C₂×C₇×#41	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₇	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁴×C₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₇×#125	C₂	direct (N × H)
11. C₂×#125	C₇	direct (N × H)
19. #125	C₂×C₇	direct (N × H)
35. C₂×C₇	#125	direct (N × H)
45. C₇	C₂×#125	direct (N × H)
52. C₂	C₇×#125	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₇×#125	2
C₂×C₇×C₄⋊C₄	2
C₂×C₄²×C₇	2
C₂×#125	7

Subgroups — C2×C7×#125 #90548

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#125 #90548