Subgroups — C₂×C₇⋊#95 #89980

Order 448.

330 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×C₇	C₂	1	1	yes	maximal, characteristic
2	C₂³×Dic₇	C₂	1	2	yes	maximal
3	C₇⋊#95	C₂	1	4	yes	maximal, direct product factor
4	C₂⁴×C₇	C₂²	1	1	yes	characteristic
5	C₂²×C₄×C₇	—	2	4	no	—
6	C₂²×C₄×C₇	C₄	1	4	yes	complemented
7	C₂²×C₄×C₇	C₂²	1	2	yes	—
8	C₂²×Dic₇	—	2	4	no	—
9	C₂²×Dic₇	—	2	4	no	—
10	C₂²×Dic₇	C₄	1	8	yes	complemented
11	C₂²×Dic₇	C₂²	1	4	yes	—
12	C₂×#95	—	7	1	no	maximal, Sylow
13	C₂³×C₇	C₂×C₄	1	4	yes	—
14	C₂³×C₇	C₂×C₄	1	2	yes	—
15	C₂³×C₇	D₄	1	2	yes	—
16	C₂³×C₇	D₄	1	4	yes	—
17	C₂³×C₇	Q₈	1	2	yes	—
18	C₂³×C₇	C₂³	1	1	yes	characteristic
19	C₂×C₄×C₇	—	2	8	no	—
20	C₂×C₄×C₇	—	2	4	no	—
21	C₂×C₄×C₇	C₂×C₄	1	4	yes	complemented
22	C₂×Dic₇	—	2	16	no	—
23	C₂×Dic₇	—	2	4	no	—
24	C₂×Dic₇	—	2	4	no	—
25	C₂×Dic₇	C₂×C₄	1	8	yes	complemented
26	C₂³×C₄	—	7	2	no	—
27	C₂³×C₄	D₇	1	1	yes	characteristic
28	#95	—	7	4	no	—
29	C₂²×C₇	C₄²	1	4	yes	—
30	C₂²×C₇	C₂²⋊C₄	1	8	yes	—
31	C₂²×C₇	C₂²⋊C₄	1	4	yes	—
32	C₂²×C₇	C₄⋊C₄	1	8	yes	—
33	C₂²×C₇	C₄⋊C₄	1	4	yes	—
34	C₂²×C₇	C₂²×C₄	1	2	yes	—
35	C₂²×C₇	C₂²×C₄	1	1	yes	characteristic
36	C₂²×C₇	C₂×D₄	1	1	yes	characteristic
37	C₂²×C₇	C₂×D₄	1	2	yes	—
38	C₂²×C₇	C₂×Q₈	1	1	yes	characteristic
39	C₄×C₇	—	2	4	no	—
40	Dic₇	—	2	8	no	—
41	C₂⁴	C₂×D₇	1	1	yes	characteristic
42	C₂²×C₄	—	2	4	no	—
43	C₂²×C₄	—	7	8	no	—
44	C₂²×C₄	—	7	4	no	—
45	C₂²×C₄	—	14	4	no	—
46	C₂²×C₄	—	14	4	no	—
47	C₂²×C₄	Dic₇	1	4	yes	complemented
48	C₂²×C₄	C₂×D₇	1	2	yes	—
49	C₂×C₇	#95	1	8	yes	complemented
50	C₂×C₇	C₂×C₄²	1	1	yes	characteristic
51	C₂×C₇	C₂×C₂²⋊C₄	1	2	yes	—
52	C₂×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
53	C₂×C₇	C₂×C₄⋊C₄	1	2	yes	—
54	C₂×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
55	C₂³	Dic₁₄	1	2	yes	—
56	C₂³	C₄×D₇	1	4	yes	—
57	C₂³	D₂₈	1	2	yes	—
58	C₂³	C₂×Dic₇	1	2	yes	—
59	C₂³	C₂²⋊D₇	1	4	yes	—
60	C₂³	C₂²×D₇	1	1	yes	characteristic
61	C₂×C₄	—	2	8	no	—
62	C₂×C₄	—	2	4	no	—
63	C₂×C₄	—	7	8	no	—
64	C₂×C₄	—	14	16	no	—
65	C₂×C₄	—	14	4	no	—
66	C₂×C₄	—	14	4	no	—
67	C₂×C₄	C₂×Dic₇	1	4	yes	complemented
68	C₇	C₂×#95	1	1	yes	characteristic, complemented, Sylow
69	C₂²	C₄×Dic₇	1	4	yes	—
70	C₂²	Dic₇⋊C₄	1	8	yes	—
71	C₂²	C₄⋊Dic₇	1	4	yes	—
72	C₂²	(C₂×D₇)⋊C₄	1	8	yes	—
73	C₂²	C₂²⋊Dic₇	1	4	yes	—
74	C₂²	C₂×Dic₁₄	1	1	yes	characteristic
75	C₂²	C₂×C₄×D₇	1	2	yes	—
76	C₂²	C₂×D₂₈	1	1	yes	characteristic
77	C₂²	C₂²×Dic₇	1	1	yes	characteristic
78	C₂²	C₂×C₂²⋊D₇	1	2	yes	—
79	C₄	—	2	4	no	—
80	C₄	—	14	8	no	—
81	C₂	C₇⋊#95	1	8	yes	direct product factor
82	C₂	C₂×C₄×Dic₇	1	1	yes	characteristic
83	C₂	C₂×Dic₇⋊C₄	1	2	yes	—
84	C₂	C₂×C₄⋊Dic₇	1	1	yes	characteristic
85	C₂	C₂×(C₂×D₇)⋊C₄	1	2	yes	—
86	C₂	C₂×C₂²⋊Dic₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×D₇
commutator	C₂×C₇	C₂×C₄²
Frattini	C₂³	C₂²×D₇
Fitting	C₂³×C₄×C₇	C₂
socle, prime radical	C₂⁴×C₇	C₂²
cosocle	C₂³×C₇	C₂³
hypercenter	C₂³×C₄	D₇
hypocenter	C₇	C₂×#95
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
3. C₇⋊#95	C₂	direct (N × H)
6. C₂²×C₄×C₇	C₄	semidirect
10. C₂²×Dic₇	C₄	semidirect
21. C₂×C₄×C₇	C₂×C₄	semidirect
25. C₂×Dic₇	C₂×C₄	semidirect
47. C₂²×C₄	Dic₇	semidirect
49. C₂×C₇	#95	semidirect
67. C₂×C₄	C₂×Dic₇	semidirect
68. C₇	C₂×#95	semidirect
81. C₂	C₇⋊#95	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄×C₇	2
C₂³×Dic₇	2
C₇⋊#95	2
C₂×#95	7

Subgroups — C2×C7⋊#95 #89980

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇⋊#95 #89980