Subgroups — C₇×#382 #90028

Order 448.

154 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₄⋊C₄	C₂	1	2	yes	maximal
2	C₂×C₄²×C₇	C₂	1	1	yes	maximal, characteristic
3	C₇×#95	C₂	1	4	yes	maximal
4	C₂²×C₄×C₇	C₂²	1	4	yes	—
5	C₂²×C₄×C₇	C₂²	1	2	yes	—
6	C₂²×C₄×C₇	C₂²	1	1	yes	characteristic
7	C₇×C₄⋊C₄	—	2	4	no	—
8	C₄²×C₇	C₄	1	4	yes	complemented
9	#382	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂³×C₇	C₂³	1	1	yes	characteristic
11	C₂×C₄×C₇	—	2	4	no	—
12	C₂×C₄×C₇	—	2	4	no	—
13	C₂×C₄×C₇	—	2	8	no	—
14	C₂×C₄×C₇	C₂×C₄	1	4	yes	—
15	C₂×C₄×C₇	C₂×C₄	1	2	yes	—
16	C₂×C₄×C₇	D₄	1	2	yes	—
17	C₂×C₄×C₇	Q₈	1	2	yes	—
18	C₂×C₄⋊C₄	C₂×C₇	1	2	yes	—
19	C₂×C₄²	C₂×C₇	1	1	yes	characteristic
20	#95	C₂×C₇	1	4	yes	—
21	C₂²×C₇	C₂²×C₄	1	1	yes	characteristic
22	C₂²×C₇	C₂×D₄	1	1	yes	characteristic
23	C₂²×C₇	C₂×Q₈	1	1	yes	characteristic
24	C₂²×C₇	#41	1	4	yes	—
25	C₄×C₇	—	2	4	no	—
26	C₄×C₇	—	4	4	no	—
27	C₄×C₇	C₄⋊C₄	1	4	yes	—
28	C₂²×C₄	C₂²×C₇	1	4	yes	—
29	C₂²×C₄	C₂²×C₇	1	2	yes	—
30	C₂²×C₄	C₂²×C₇	1	1	yes	characteristic
31	C₄⋊C₄	—	2	4	no	—
32	C₄²	C₄×C₇	1	4	yes	complemented
33	C₂×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₇	#117	1	2	yes	—
35	C₂×C₇	#124	1	2	yes	—
36	C₂×C₇	#125	1	2	yes	—
37	C₂³	C₂³×C₇	1	1	yes	characteristic
38	C₂×C₄	—	2	4	no	—
39	C₂×C₄	—	2	4	no	—
40	C₂×C₄	—	2	8	no	—
41	C₂×C₄	C₂×C₄×C₇	1	4	yes	—
42	C₂×C₄	C₂×C₄×C₇	1	2	yes	—
43	C₂×C₄	C₇×D₄	1	2	yes	—
44	C₂×C₄	C₇×Q₈	1	2	yes	—
45	C₇	#382	1	1	yes	characteristic, direct product factor, Sylow
46	C₂²	C₂²×C₄×C₇	1	1	yes	characteristic
47	C₂²	C₂×C₇×D₄	1	1	yes	characteristic
48	C₂²	C₂×C₇×Q₈	1	1	yes	characteristic
49	C₂²	C₇×#41	1	4	yes	—
50	C₄	—	2	4	no	—
51	C₄	—	4	4	no	—
52	C₄	C₇×C₄⋊C₄	1	4	yes	—
53	C₂	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
54	C₂	C₇×#117	1	2	yes	—
55	C₂	C₇×#124	1	2	yes	—
56	C₂	C₇×#125	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₇	C₂³
commutator	C₂²	C₂²×C₄×C₇
Frattini, cosocle	C₂³	C₂³×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
8. C₄²×C₇	C₄	semidirect
9. #382	C₇	direct (N × H)
32. C₄²	C₄×C₇	semidirect
45. C₇	#382	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₇×C₄⋊C₄	2
C₂×C₄²×C₇	2
C₇×#95	2
#382	7

Subgroups — C7×#382 #90028

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#382 #90028