Subgroups — C₇×#487 #90133

Order 448.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₇×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₇×#103	C₂	1	4	yes	maximal
4	C₄×C₇×C₈	C₂	1	1	yes	maximal, characteristic
5	C₂×C₇×Q₈	—	2	1	no	—
6	C₂×C₇×Q₈	C₂²	1	2	yes	—
7	C₂×C₇×C₈	C₂²	1	2	yes	—
8	C₇×C₄⋊C₄	—	2	1	no	—
9	C₇×C₄⋊C₄	—	2	1	no	—
10	C₇×C₄⋊C₄	—	2	1	no	—
11	C₇×C₄⋊C₄	C₂²	1	2	yes	—
12	C₄²×C₇	C₂²	1	1	yes	characteristic
13	#487	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₇×Q₈	—	2	4	no	—
15	C₇×Q₈	—	4	2	no	—
16	C₂×C₄×C₇	—	2	2	no	—
17	C₂×C₄×C₇	—	2	2	no	—
18	C₂×C₄×C₇	D₄	1	1	yes	characteristic
19	C₂×C₄×C₇	D₄	1	1	yes	characteristic
20	C₂×C₄×C₇	C₂³	1	1	yes	characteristic
21	C₇×C₈	—	2	2	no	—
22	C₄⋊Q₈	C₂×C₇	1	1	yes	characteristic
23	C₄⋊Q₈	C₂×C₇	1	1	yes	characteristic
24	#103	C₂×C₇	1	4	yes	—
25	C₄×C₈	C₂×C₇	1	1	yes	characteristic
26	C₂²×C₇	C₂×D₄	1	1	yes	characteristic
27	C₄×C₇	—	4	2	no	—
28	C₄×C₇	—	4	2	no	—
29	C₄×C₇	SD₁₆	1	2	yes	—
30	C₄×C₇	Q₁₆	1	2	yes	—
31	C₄×C₇	#41	1	2	yes	—
32	C₂×Q₈	—	2	1	no	—
33	C₂×Q₈	C₂²×C₇	1	2	yes	—
34	C₂×C₈	C₂²×C₇	1	2	yes	—
35	C₄⋊C₄	—	2	1	no	—
36	C₄⋊C₄	—	2	1	no	—
37	C₄⋊C₄	—	2	1	no	—
38	C₄⋊C₄	C₂²×C₇	1	2	yes	—
39	C₄²	C₂²×C₇	1	1	yes	characteristic
40	C₂×C₇	#124	1	1	yes	characteristic
41	C₂×C₇	C₂×SD₁₆	1	1	yes	characteristic
42	C₂×C₇	C₂×Q₁₆	1	1	yes	characteristic
43	Q₈	—	2	4	no	—
44	Q₈	—	4	2	no	—
45	C₂×C₄	—	2	2	no	—
46	C₂×C₄	—	2	2	no	—
47	C₂×C₄	C₇×D₄	1	1	yes	characteristic
48	C₂×C₄	C₇×D₄	1	1	yes	characteristic
49	C₂×C₄	C₂³×C₇	1	1	yes	characteristic
50	C₈	—	2	2	no	—
51	C₇	#487	1	1	yes	characteristic, direct product factor, Sylow
52	C₂²	C₂×C₇×D₄	1	1	yes	characteristic
53	C₄	—	4	2	no	—
54	C₄	—	4	2	no	—
55	C₄	C₇×SD₁₆	1	2	yes	—
56	C₄	C₇×Q₁₆	1	2	yes	—
57	C₄	C₇×#41	1	2	yes	—
58	C₂	C₇×#124	1	1	yes	characteristic
59	C₂	C₂×C₇×SD₁₆	1	1	yes	characteristic
60	C₂	C₂×C₇×Q₁₆	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
13. #487	C₇	direct (N × H)
51. C₇	#487	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×C₄⋊Q₈	2
C₇×#103	2
C₄×C₇×C₈	2
#487	7

Subgroups — C7×#487 #90133

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#487 #90133