Subgroups — C₇×#479 #90125

Order 448.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#125	C₂	1	1	yes	maximal, characteristic
2	C₄×C₇×Q₈	C₂	1	1	yes	maximal, characteristic
3	C₇×#107	C₂	1	1	yes	maximal, characteristic
4	C₇×#106	C₂	1	1	yes	maximal, characteristic
5	C₇×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
6	C₇×#103	C₂	1	1	yes	maximal, characteristic
7	C₇×#103	C₂	1	1	yes	maximal, characteristic
8	C₂×C₇×Q₈	C₂²	1	1	yes	characteristic
9	C₂×C₇×C₈	C₂²	1	1	yes	characteristic
10	C₂×C₇×C₈	C₂²	1	1	yes	characteristic
11	C₇×C₄⋊C₄	—	2	1	no	—
12	C₇×C₄⋊C₄	—	2	1	no	—
13	C₇×C₄⋊C₄	—	2	1	no	—
14	C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₄²×C₇	—	2	1	no	—
18	C₄²×C₇	C₂²	1	1	yes	characteristic
19	#479	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
20	C₇×Q₈	—	2	1	no	—
21	C₇×Q₈	Q₈	1	2	yes	—
22	C₂×C₄×C₇	—	2	1	no	—
23	C₂×C₄×C₇	—	2	1	no	—
24	C₂×C₄×C₇	—	2	1	no	—
25	C₂×C₄×C₇	—	2	1	no	—
26	C₂×C₄×C₇	D₄	1	1	yes	characteristic
27	C₂×C₄×C₇	D₄	1	1	yes	characteristic
28	C₂×C₄×C₇	C₂³	1	1	yes	characteristic
29	C₇×C₈	—	2	1	no	—
30	C₇×C₈	—	2	1	no	—
31	#125	C₂×C₇	1	1	yes	characteristic
32	C₄×Q₈	C₂×C₇	1	1	yes	characteristic
33	#107	C₂×C₇	1	1	yes	characteristic
34	#106	C₂×C₇	1	1	yes	characteristic
35	C₄⋊C₈	C₂×C₇	1	1	yes	characteristic
36	#103	C₂×C₇	1	1	yes	characteristic
37	#103	C₂×C₇	1	1	yes	characteristic
38	C₂²×C₇	C₂×D₄	1	1	yes	characteristic
39	C₄×C₇	—	2	2	no	—
40	C₄×C₇	—	2	1	no	—
41	C₄×C₇	—	2	1	no	—
42	C₄×C₇	—	4	1	no	—
43	C₄×C₇	—	4	1	no	—
44	C₄×C₇	—	4	1	no	—
45	C₄×C₇	C₂×Q₈	1	1	yes	characteristic
46	C₄×C₇	#41	1	1	yes	characteristic
47	C₂×Q₈	C₂²×C₇	1	1	yes	characteristic
48	C₂×C₈	C₂²×C₇	1	1	yes	characteristic
49	C₂×C₈	C₂²×C₇	1	1	yes	characteristic
50	C₄⋊C₄	—	2	1	no	—
51	C₄⋊C₄	—	2	1	no	—
52	C₄⋊C₄	—	2	1	no	—
53	C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
54	C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
55	C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
56	C₄²	—	2	1	no	—
57	C₄²	C₂²×C₇	1	1	yes	characteristic
58	C₂×C₇	C₂²⋊Q₈	1	1	yes	characteristic
59	C₂×C₇	#135	1	1	yes	characteristic
60	C₂×C₇	#137	1	1	yes	characteristic
61	Q₈	—	2	1	no	—
62	Q₈	C₇×Q₈	1	2	yes	—
63	C₂×C₄	—	2	1	no	—
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	C₇×D₄	1	1	yes	characteristic
68	C₂×C₄	C₇×D₄	1	1	yes	characteristic
69	C₂×C₄	C₂³×C₇	1	1	yes	characteristic
70	C₈	—	2	1	no	—
71	C₈	—	2	1	no	—
72	C₇	#479	1	1	yes	characteristic, direct product factor, Sylow
73	C₂²	C₂×C₇×D₄	1	1	yes	characteristic
74	C₄	—	2	2	no	—
75	C₄	—	2	1	no	—
76	C₄	—	2	1	no	—
77	C₄	—	4	1	no	—
78	C₄	—	4	1	no	—
79	C₄	—	4	1	no	—
80	C₄	C₂×C₇×Q₈	1	1	yes	characteristic
81	C₄	C₇×#41	1	1	yes	characteristic
82	C₂	C₇×C₂²⋊Q₈	1	1	yes	characteristic
83	C₂	C₇×#135	1	1	yes	characteristic
84	C₂	C₇×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
19. #479	C₇	direct (N × H)
72. C₇	#479	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
C₄×C₇×Q₈	2
C₇×#107	2
C₇×#106	2
C₇×C₄⋊C₈	2
C₇×#103	2
#479	7

Subgroups — C7×#479 #90125

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#479 #90125