Subgroups — C₂×C₇⋊(#95⋊C₃) #13055060

Order 1344.

150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇⋊(#95⋊C₃)	C₂	1	1	yes	maximal, characteristic, direct product factor
2	C₂×C₇×#95	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂²×C₂²⋊ΓL(1,𝔽₈)	—	4	1	no	maximal
4	C₂³×C₄×C₇	—	3	1	no	—
5	C₇×#95	—	3	1	no	—
6	C₇×#95	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×#95⋊C₃	—	7	1	no	maximal, Hall
8	C₂×C₂²⋊ΓL(1,𝔽₈)	—	4	2	no	—
9	C₂×C₂²⋊ΓL(1,𝔽₈)	—	4	1	no	—
10	C₂⁴×C₇	A₄	1	1	yes	characteristic
11	C₂²×C₄×C₇	—	3	2	no	—
12	C₂²×C₄×C₇	—	3	2	no	—
13	C₂²×C₄×C₇	—	3	1	no	—
14	C₂²×C₄×C₇	—	3	1	no	—
15	C₂²×C₄×C₇	—	6	4	no	—
16	#95⋊C₃	—	7	1	no	—
17	C₂²⋊ΓL(1,𝔽₈)	—	4	1	no	—
18	C₂²×ΓL(1,𝔽₈)	—	16	1	no	—
19	C₂×#95	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
20	C₂³×C₇	—	3	1	no	—
21	C₂³×C₇	—	3	2	no	—
22	C₂³×C₇	—	3	1	no	—
23	C₂³×C₇	SL(2,𝔽₃)	1	2	yes	—
24	C₂³×C₇	C₂×A₄	1	1	yes	characteristic
25	C₂×C₄×C₇	—	3	2	no	—
26	C₂×C₄×C₇	—	3	2	no	—
27	C₂×C₄×C₇	—	6	2	no	—
28	C₂×C₄×C₇	—	6	2	no	—
29	C₂×C₄×C₇	—	6	4	no	—
30	C₂×C₄×C₇	—	6	4	no	—
31	C₂²×A₄	—	28	1	no	—
32	C₂×ΓL(1,𝔽₈)	—	16	2	no	—
33	C₂×ΓL(1,𝔽₈)	—	16	1	no	—
34	C₂³×C₄	—	3	1	no	—
35	#95	—	3	1	no	—
36	#95	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
37	C₂²×C₇	—	3	1	no	—
38	C₂²×C₇	—	3	2	no	—
39	C₂²×C₇	—	3	2	no	—
40	C₂²×C₇	—	3	2	no	—
41	C₂²×C₇	—	3	2	no	—
42	C₂²×C₇	—	3	1	no	—
43	C₂²×C₇	—	3	1	no	—
44	C₂²×C₇	C₄²⋊C₃	1	1	yes	characteristic
45	C₂²×C₇	C₂×SL(2,𝔽₃)	1	1	yes	characteristic
46	C₄×C₇	—	6	2	no	—
47	C₄×C₇	—	6	2	no	—
48	C₂×A₄	—	28	2	no	—
49	C₂×A₄	—	28	1	no	—
50	ΓL(1,𝔽₈)	—	16	1	no	Hall
51	C₂⁴	C₂²⋊ΓL(1,𝔽₈)	1	1	yes	characteristic
52	C₂²×C₄	—	3	2	no	—
53	C₂²×C₄	—	3	2	no	—
54	C₂²×C₄	—	3	1	no	—
55	C₂²×C₄	—	3	1	no	—
56	C₂²×C₄	—	6	4	no	—
57	C₂×C₇	—	3	1	no	—
58	C₂×C₇	—	3	2	no	—
59	C₂×C₇	—	3	1	no	—
60	C₂×C₇	#95⋊C₃	1	2	yes	complemented
61	C₂×C₇	C₂×C₄²⋊C₃	1	1	yes	characteristic
62	C₂²×C₃	—	112	1	no	—
63	A₄	—	28	1	no	—
64	C₂³	—	3	1	no	—
65	C₂³	—	3	2	no	—
66	C₂³	—	3	1	no	—
67	C₂³	C₇⋊SL(2,𝔽₃)	1	2	yes	—
68	C₂³	C₂×C₂²⋊ΓL(1,𝔽₈)	1	1	yes	characteristic
69	C₂×C₄	—	3	2	no	—
70	C₂×C₄	—	3	2	no	—
71	C₂×C₄	—	6	2	no	—
72	C₂×C₄	—	6	2	no	—
73	C₂×C₄	—	6	4	no	—
74	C₂×C₄	—	6	4	no	—
75	C₇	C₂×#95⋊C₃	1	1	yes	characteristic, complemented, Sylow
76	C₂×C₃	—	112	2	no	—
77	C₂×C₃	—	112	1	no	—
78	C₂²	—	3	1	no	—
79	C₂²	—	3	2	no	—
80	C₂²	—	3	2	no	—
81	C₂²	—	3	2	no	—
82	C₂²	—	3	2	no	—
83	C₂²	—	3	1	no	—
84	C₂²	—	3	1	no	—
85	C₂²	C₇⋊(C₄²⋊C₃)	1	1	yes	characteristic
86	C₂²	C₂×C₇⋊SL(2,𝔽₃)	1	1	yes	characteristic
87	C₄	—	6	2	no	—
88	C₄	—	6	2	no	—
89	C₃	—	112	1	no	Sylow
90	C₂	—	3	1	no	—
91	C₂	—	3	1	no	—
92	C₂	—	3	2	no	—
93	C₂	C₇⋊(#95⋊C₃)	1	2	yes	direct product factor
94	C₂	C₂×C₇⋊(C₄²⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²	C₇⋊(C₄²⋊C₃)
commutator, cosocle, hypocenter	C₇×#95	C₂×C₃
Frattini	C₂³	C₂×C₂²⋊ΓL(1,𝔽₈)
Fitting	C₂×C₇×#95	C₃
socle	C₂⁴×C₇	A₄
LCS	G ▷ C₇×#95
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. C₇⋊(#95⋊C₃)	C₂	direct (N × H)
2. C₂×C₇×#95	C₃	semidirect
6. C₇×#95	C₂×C₃	semidirect
19. C₂×#95	ΓL(1,𝔽₈)	semidirect
36. #95	C₂×ΓL(1,𝔽₈)	semidirect
60. C₂×C₇	#95⋊C₃	semidirect
75. C₇	C₂×#95⋊C₃	semidirect
93. C₂	C₇⋊(#95⋊C₃)	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⋊(#95⋊C₃)	2
C₂×C₇×#95	3
C₂²×C₂²⋊ΓL(1,𝔽₈)	4
C₂×#95⋊C₃	7

Subgroups — C2×C7⋊(#95⋊C3) #13055060

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇⋊(#95⋊C₃) #13055060