Subgroups — C₇⋊#564 #90377

Order 448.

172 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	#6453	C₂	1	4	yes	maximal
3	#6452	C₂	1	4	yes	maximal
4	#6452	C₂	1	4	yes	maximal
5	#6433	C₂	1	2	yes	maximal
6	C₇×C₄⋊C₄	C₂²	1	2	yes	—
7	C₇×C₄⋊C₄	C₂²	1	4	yes	—
8	C₄²×C₇	C₂²	1	1	yes	characteristic
9	C₄⋊Dic₇	C₂²	1	2	yes	—
10	C₄⋊Dic₇	C₂²	1	2	yes	—
11	C₄⋊Dic₇	C₂²	1	4	yes	—
12	Dic₇⋊C₄	C₂²	1	4	yes	—
13	Dic₇⋊C₄	C₂²	1	4	yes	—
14	Dic₇⋊C₄	C₂²	1	4	yes	—
15	Dic₇⋊C₄	C₂²	1	4	yes	—
16	C₄×Dic₇	C₂²	1	4	yes	—
17	#564	—	7	1	no	maximal, Sylow
18	C₂×C₄×C₇	C₂³	1	4	yes	—
19	C₂×C₄×C₇	C₂³	1	1	yes	characteristic
20	C₂×C₄×C₇	C₂³	1	2	yes	—
21	C₂×Dic₇	C₂³	1	4	yes	—
22	C₂×Dic₇	C₂³	1	4	yes	—
23	#125	—	7	4	no	—
24	#125	—	7	4	no	—
25	#125	—	7	4	no	—
26	#125	—	7	2	no	—
27	#125	D₇	1	1	yes	characteristic
28	C₂²×C₇	C₂⁴	1	1	yes	characteristic
29	C₄×C₇	—	2	1	no	—
30	C₄×C₇	—	2	4	no	—
31	C₄×C₇	—	2	2	no	—
32	Dic₇	—	2	4	no	—
33	Dic₇	—	2	4	no	—
34	C₄⋊C₄	—	7	4	no	—
35	C₄⋊C₄	—	7	4	no	—
36	C₄⋊C₄	—	7	4	no	—
37	C₄⋊C₄	—	7	4	no	—
38	C₄⋊C₄	—	7	4	no	—
39	C₄⋊C₄	—	7	2	no	—
40	C₄⋊C₄	—	7	2	no	—
41	C₄⋊C₄	C₂×D₇	1	2	yes	—
42	C₄⋊C₄	C₂×D₇	1	4	yes	—
43	C₄²	—	7	4	no	—
44	C₄²	C₂×D₇	1	1	yes	characteristic
45	C₂×C₇	2₋¹⁺⁴	1	1	yes	characteristic
46	C₂×C₇	2₋¹⁺⁴	1	2	yes	—
47	C₂×C₄	—	7	4	no	—
48	C₂×C₄	—	7	4	no	—
49	C₂×C₄	C₂²×D₇	1	4	yes	—
50	C₂×C₄	C₂²×D₇	1	1	yes	characteristic
51	C₂×C₄	C₂²×D₇	1	2	yes	—
52	C₇	#564	1	1	yes	characteristic, complemented, Sylow
53	C₂²	C₂³×D₇	1	1	yes	characteristic
54	C₄	—	2	1	no	—
55	C₄	—	2	4	no	—
56	C₄	—	2	2	no	—
57	C₄	—	14	4	no	—
58	C₄	—	14	4	no	—
59	C₂	#6551	1	1	yes	characteristic
60	C₂	#6554	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₇
commutator, socle, prime radical, cosocle	C₂²×C₇	C₂⁴
Fitting	C₇×#125	C₂
hypercenter	#125	D₇
hypocenter	C₇	#564
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ #125

Complements

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

N	H ≅ G/N	type
52. C₇	#564	semidirect

Maximal subgroups

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

subgroup	index
C₇×#125	2
#6453	2
#6452	2
#6433	2
#564	7

Subgroups — C7⋊#564 #90377

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇⋊#564 #90377