Subgroups — C₇×#490 #90136

Order 448.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#127	C₂	1	1	yes	maximal, characteristic
2	C₇×#125	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#102	C₂	1	4	yes	maximal, complemented
4	C₇×#97	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×D₄	—	2	2	no	—
6	C₂×C₇×D₄	C₂²	1	2	yes	—
7	C₂×C₇×C₈	C₂²	1	2	yes	—
8	C₇×C₄⋊C₄	—	2	2	no	—
9	C₇×C₄⋊C₄	C₂²	1	2	yes	—
10	C₄²×C₇	C₂²	1	1	yes	characteristic
11	#490	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₂³×C₇	—	2	2	no	—
13	C₇×D₄	—	2	4	no	—
14	C₇×D₄	—	4	4	no	—
15	C₂×C₄×C₇	—	2	2	no	—
16	C₂×C₄×C₇	D₄	1	2	yes	—
17	C₂×C₄×C₇	C₂³	1	1	yes	characteristic
18	C₇×C₈	—	2	2	no	—
19	#127	C₂×C₇	1	1	yes	characteristic
20	#125	C₂×C₇	1	1	yes	characteristic, complemented
21	#102	C₂×C₇	1	4	yes	complemented
22	#97	C₂×C₇	1	1	yes	characteristic, complemented
23	C₂²×C₇	—	4	2	no	—
24	C₂²×C₇	—	4	4	no	—
25	C₂²×C₇	C₂×D₄	1	1	yes	characteristic
26	C₄×C₇	—	2	2	no	—
27	C₄×C₇	—	4	2	no	—
28	C₄×C₇	#41	1	2	yes	—
29	C₂×D₄	—	2	2	no	—
30	C₂×D₄	C₂²×C₇	1	2	yes	—
31	C₂×C₈	C₂²×C₇	1	2	yes	—
32	C₄⋊C₄	—	2	2	no	—
33	C₄⋊C₄	C₂²×C₇	1	2	yes	—
34	C₄²	C₂²×C₇	1	1	yes	characteristic
35	C₂×C₇	—	8	2	no	—
36	C₂×C₇	#124	1	1	yes	characteristic
37	C₂×C₇	AGL(1,ℤ/8)	1	2	yes	—
38	C₂³	—	2	2	no	—
39	D₄	—	2	4	no	—
40	D₄	—	4	4	no	—
41	C₂×C₄	—	2	2	no	—
42	C₂×C₄	C₇×D₄	1	2	yes	—
43	C₂×C₄	C₂³×C₇	1	1	yes	characteristic
44	C₈	—	2	2	no	—
45	C₇	#490	1	1	yes	characteristic, direct product factor, Sylow
46	C₂²	—	4	2	no	—
47	C₂²	—	4	4	no	—
48	C₂²	C₂×C₇×D₄	1	1	yes	characteristic
49	C₄	—	2	2	no	—
50	C₄	—	4	2	no	—
51	C₄	C₇×#41	1	2	yes	—
52	C₂	—	8	2	no	—
53	C₂	C₇×#124	1	1	yes	characteristic
54	C₂	C₇×AGL(1,ℤ/8)	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₇
prime radical	C₇×#127	C₂
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
2. C₇×#125	C₂	semidirect
3. C₇×#102	C₂	semidirect
4. C₇×#97	C₂	semidirect
11. #490	C₇	direct (N × H)
20. #125	C₂×C₇	semidirect
21. #102	C₂×C₇	semidirect
22. #97	C₂×C₇	semidirect
45. C₇	#490	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×#127	2
C₇×#125	2
C₇×#102	2
C₇×#97	2
#490	7

Subgroups — C7×#490 #90136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#490 #90136