Subgroups — C₇×#5932 #13062129

Order 1344.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#997	C₂	1	1	yes	maximal, characteristic
2	C₇×#458	—	3	1	no	maximal, Hall
3	C₇×SL(2,ℤ/4)	—	4	3	no	maximal
4	C₇×H(5,𝔽₂)	D₃	1	1	yes	characteristic
5	C₇×#123	—	3	3	no	—
6	C₇×#99	—	3	3	no	—
7	#5932	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₇×A₄	—	4	3	no	—
9	C₇×SL(2,𝔽₃)	—	8	1	no	—
10	C₇×#41	—	6	1	no	—
11	C₂×C₇×D₄	—	3	3	no	—
12	C₂²×C₄×C₇	—	3	1	no	—
13	C₇×C₄⋊C₄	—	6	3	no	—
14	C₇×C₂²⋊C₄	—	3	3	no	—
15	C₇×C₂²⋊C₄	—	6	3	no	—
16	#997	C₂×C₇	1	1	yes	characteristic
17	C₇×A₄	—	4	3	no	—
18	C₇×Dic₃	—	16	1	no	—
19	#458	—	3	1	no	Sylow
20	C₂³×C₇	—	3	1	no	—
21	C₂³×C₇	S₄	1	3	yes	—
22	C₇×Q₈	—	2	1	no	—
23	C₇×D₄	—	6	3	no	—
24	C₂×C₄×C₇	—	3	3	no	—
25	C₂×C₄×C₇	—	6	3	no	—
26	C₂×C₄×C₇	—	6	3	no	—
27	SL(2,ℤ/4)	—	4	3	no	—
28	C₂×C₃×C₇	—	16	1	no	—
29	H(5,𝔽₂)	D₃×C₇	1	1	yes	characteristic
30	#123	—	3	3	no	—
31	#99	—	3	3	no	—
32	C₂²×C₇	—	3	3	no	—
33	C₂²×C₇	—	4	3	no	—
34	C₂²×C₇	—	12	1	no	—
35	C₄×C₇	—	6	1	no	—
36	C₄×C₇	—	12	3	no	—
37	C₄×C₇	—	12	1	no	—
38	C₂×A₄	—	4	3	no	—
39	SL(2,𝔽₃)	—	8	1	no	—
40	C₃×C₇	—	16	1	no	Hall
41	#41	—	6	1	no	—
42	C₂×D₄	—	3	3	no	—
43	C₂²×C₄	—	3	1	no	—
44	C₄⋊C₄	—	6	3	no	—
45	C₂²⋊C₄	—	3	3	no	—
46	C₂²⋊C₄	—	6	3	no	—
47	C₂×C₇	—	6	3	no	—
48	C₂×C₇	#1020	1	1	yes	characteristic
49	A₄	—	4	3	no	—
50	Dic₃	—	16	1	no	—
51	C₂³	—	3	1	no	—
52	C₂³	C₇×S₄	1	3	yes	—
53	Q₈	—	2	1	no	—
54	D₄	—	6	3	no	—
55	C₂×C₄	—	3	3	no	—
56	C₂×C₄	—	6	3	no	—
57	C₂×C₄	—	6	3	no	—
58	C₇	#5932	1	1	yes	characteristic, direct product factor, Sylow
59	C₂×C₃	—	16	1	no	—
60	C₂²	—	3	3	no	—
61	C₂²	—	4	3	no	—
62	C₂²	—	12	1	no	—
63	C₄	—	6	1	no	—
64	C₄	—	12	3	no	—
65	C₄	—	12	1	no	—
66	C₃	—	16	1	no	Sylow
67	C₂	—	6	3	no	—
68	C₂	C₇×#1020	1	1	yes	characteristic

	subgroup	G/H
center, socle, hypercenter	C₂×C₇	#1020
commutator, cosocle, hypocenter	#997	C₂×C₇
Frattini	C₂	C₇×#1020
Fitting	C₇×H(5,𝔽₂)	D₃
prime radical	C₇×#997	C₂
LCS	G ▷ #997
UCS	C₁ ◁ C₂×C₇

Complements

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

N	H ≅ G/N	type
7. #5932	C₇	direct (N × H)
58. C₇	#5932	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×#997	2
C₇×#458	3
C₇×SL(2,ℤ/4)	4
#5932	7

Subgroups — C7×#5932 #13062129

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#5932 #13062129