Subgroups — C₇×#446 #90092

Order 448.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₇×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₇×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₇×C₄⋊C₈	C₂	1	2	yes	maximal
4	C₇×#97	C₂	1	2	yes	maximal
5	C₄×C₇×C₈	C₂	1	1	yes	maximal, characteristic
6	C₂×C₇×Q₈	C₄	1	1	yes	characteristic
7	C₂×C₇×C₈	C₂²	1	1	yes	characteristic
8	C₂×C₇×C₈	C₂²	1	2	yes	—
9	C₂×C₇×C₈	C₂²	1	1	yes	characteristic
10	C₇×C₄⋊C₄	C₄	1	2	yes	—
11	C₇×C₄⋊C₄	C₄	1	1	yes	characteristic
12	C₄²×C₇	C₂²	1	1	yes	characteristic
13	C₄²×C₇	C₂²	1	2	yes	—
14	#446	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₇×Q₈	—	2	2	no	—
16	C₂×C₄×C₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₇	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₇	C₂×C₄	1	2	yes	—
19	C₂×C₄×C₇	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×C₇	C₂³	1	1	yes	characteristic
21	C₇×C₈	—	2	1	no	—
22	C₇×C₈	—	2	2	no	—
23	C₇×C₈	Q₈	1	2	yes	complemented
24	C₄×Q₈	C₂×C₇	1	1	yes	characteristic
25	C₄⋊C₈	C₂×C₇	1	1	yes	characteristic
26	C₄⋊C₈	C₂×C₇	1	2	yes	—
27	#97	C₂×C₇	1	2	yes	—
28	C₄×C₈	C₂×C₇	1	1	yes	characteristic
29	C₂²×C₇	C₂²×C₄	1	1	yes	characteristic
30	C₄×C₇	—	2	2	no	—
31	C₄×C₇	—	2	1	no	—
32	C₄×C₇	—	2	2	no	—
33	C₄×C₇	M₁₆	1	2	yes	—
34	C₄×C₇	C₂×Q₈	1	1	yes	characteristic
35	C₄×C₇	#41	1	1	yes	characteristic
36	C₂×Q₈	C₄×C₇	1	1	yes	characteristic
37	C₂×C₈	C₂²×C₇	1	1	yes	characteristic
38	C₂×C₈	C₂²×C₇	1	2	yes	—
39	C₂×C₈	C₂²×C₇	1	1	yes	characteristic
40	C₄⋊C₄	C₄×C₇	1	2	yes	—
41	C₄⋊C₄	C₄×C₇	1	1	yes	characteristic
42	C₄²	C₂²×C₇	1	1	yes	characteristic
43	C₄²	C₂²×C₇	1	2	yes	—
44	C₂×C₇	C₄×Q₈	1	1	yes	characteristic
45	C₂×C₇	C₂×M₁₆	1	1	yes	characteristic
46	C₂×C₇	#131	1	1	yes	characteristic
47	Q₈	—	2	2	no	—
48	C₂×C₄	C₂×C₄×C₇	1	1	yes	characteristic
49	C₂×C₄	C₂×C₄×C₇	1	2	yes	—
50	C₂×C₄	C₂×C₄×C₇	1	2	yes	—
51	C₂×C₄	C₂×C₄×C₇	1	1	yes	characteristic
52	C₂×C₄	C₂³×C₇	1	1	yes	characteristic
53	C₈	—	2	1	no	—
54	C₈	—	2	2	no	—
55	C₈	C₇×Q₈	1	2	yes	complemented
56	C₇	#446	1	1	yes	characteristic, direct product factor, Sylow
57	C₂²	C₂²×C₄×C₇	1	1	yes	characteristic
58	C₄	—	2	2	no	—
59	C₄	—	2	1	no	—
60	C₄	—	2	2	no	—
61	C₄	C₇×M₁₆	1	2	yes	—
62	C₄	C₂×C₇×Q₈	1	1	yes	characteristic
63	C₄	C₇×#41	1	1	yes	characteristic
64	C₂	C₄×C₇×Q₈	1	1	yes	characteristic
65	C₂	C₂×C₇×M₁₆	1	1	yes	characteristic
66	C₂	C₇×#131	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
14. #446	C₇	direct (N × H)
23. C₇×C₈	Q₈	semidirect
55. C₈	C₇×Q₈	semidirect
56. C₇	#446	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₇×Q₈	2
C₇×C₄⋊C₈	2
C₇×#97	2
C₄×C₇×C₈	2
#446	7

Subgroups — C7×#446 #90092

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#446 #90092