Subgroups — C₂×#6451 #90188

Order 448.

290 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₁₄	C₂	1	2	yes	maximal
2	C₂×C₇×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊Dic₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₇⋊C₄	C₂	1	2	yes	maximal
5	C₂×C₄×Dic₇	C₂	1	1	yes	maximal, characteristic
6	#6451	C₂	1	8	yes	maximal, direct product factor
7	C₂²×C₄×C₇	C₂²	1	2	yes	—
8	C₂²×C₄×C₇	C₂²	1	1	yes	characteristic
9	C₂²×Dic₇	C₂²	1	2	yes	—
10	C₂²×Dic₇	C₂²	1	1	yes	characteristic
11	C₂²×Dic₇	C₂²	1	1	yes	characteristic
12	C₂×Dic₁₄	—	2	8	no	—
13	C₂×Dic₁₄	C₂²	1	8	yes	—
14	C₇×C₄⋊C₄	C₂²	1	4	yes	—
15	C₄⋊Dic₇	C₂²	1	4	yes	—
16	Dic₇⋊C₄	C₂²	1	8	yes	—
17	C₄×Dic₇	C₂²	1	4	yes	—
18	C₂×C₄⋊Q₈	—	7	1	no	maximal, Sylow
19	C₂³×C₇	C₂³	1	1	yes	characteristic
20	C₂×C₄×C₇	—	2	4	no	—
21	C₂×C₄×C₇	Q₈	1	4	yes	complemented
22	C₂×C₄×C₇	C₂³	1	4	yes	—
23	C₂×C₄×C₇	C₂³	1	2	yes	—
24	C₂×Dic₇	—	2	4	no	—
25	C₂×Dic₇	D₄	1	4	yes	—
26	C₂×Dic₇	Q₈	1	4	yes	complemented
27	C₂×Dic₇	C₂³	1	4	yes	—
28	C₂×Dic₇	C₂³	1	2	yes	—
29	C₂×Dic₇	C₂³	1	2	yes	—
30	Dic₁₄	—	2	16	no	—
31	C₂²×Q₈	—	7	2	no	—
32	C₄⋊Q₈	—	7	8	no	—
33	C₂×C₄⋊C₄	—	7	2	no	—
34	C₂×C₄⋊C₄	—	7	1	no	—
35	C₂×C₄⋊C₄	D₇	1	1	yes	characteristic
36	C₂×C₄²	—	7	1	no	—
37	C₂²×C₇	C₂×D₄	1	2	yes	—
38	C₂²×C₇	C₂×Q₈	1	2	yes	—
39	C₂²×C₇	C₂×Q₈	1	2	yes	—
40	C₂²×C₇	C₂⁴	1	1	yes	characteristic
41	C₄×C₇	—	2	4	no	—
42	C₄×C₇	C₂×Q₈	1	4	yes	complemented
43	Dic₇	—	2	4	no	—
44	Dic₇	C₂×D₄	1	4	yes	—
45	Dic₇	C₂×Q₈	1	4	yes	complemented
46	C₂×Q₈	—	7	8	no	—
47	C₂×Q₈	—	14	8	no	—
48	C₂²×C₄	—	7	1	no	—
49	C₂²×C₄	—	7	1	no	—
50	C₂²×C₄	—	7	2	no	—
51	C₂²×C₄	C₂×D₇	1	2	yes	—
52	C₂²×C₄	C₂×D₇	1	1	yes	characteristic
53	C₄⋊C₄	—	7	8	no	—
54	C₄⋊C₄	—	7	4	no	—
55	C₄⋊C₄	C₂×D₇	1	4	yes	—
56	C₄²	—	7	4	no	—
57	C₂×C₇	C₄⋊Q₈	1	4	yes	complemented
58	C₂×C₇	C₂²×D₄	1	1	yes	characteristic
59	C₂×C₇	C₂²×Q₈	1	1	yes	characteristic
60	C₂×C₇	C₂²×Q₈	1	1	yes	characteristic
61	C₂³	C₂²×D₇	1	1	yes	characteristic
62	Q₈	—	14	16	no	—
63	C₂×C₄	—	2	4	no	—
64	C₂×C₄	—	7	4	no	—
65	C₂×C₄	—	7	4	no	—
66	C₂×C₄	—	7	2	no	—
67	C₂×C₄	—	7	2	no	—
68	C₂×C₄	—	7	4	no	—
69	C₂×C₄	—	14	4	no	—
70	C₂×C₄	Dic₁₄	1	4	yes	complemented
71	C₂×C₄	C₂²×D₇	1	4	yes	—
72	C₂×C₄	C₂²×D₇	1	2	yes	—
73	C₇	C₂×C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
74	C₂²	C₂×Dic₁₄	1	2	yes	—
75	C₂²	D₄×D₇	1	2	yes	—
76	C₂²	Q₈×D₇	1	2	yes	—
77	C₂²	C₂³×D₇	1	1	yes	characteristic
78	C₄	—	2	4	no	—
79	C₄	—	7	4	no	—
80	C₄	—	7	4	no	—
81	C₄	—	14	4	no	—
82	C₄	C₂×Dic₁₄	1	4	yes	complemented
83	C₂	#6451	1	4	yes	direct product factor
84	C₂	C₂²×Dic₁₄	1	1	yes	characteristic
85	C₂	C₂×D₄×D₇	1	1	yes	characteristic
86	C₂	C₂×Q₈×D₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₇
commutator, cosocle	C₂²×C₇	C₂⁴
Frattini	C₂²	C₂³×D₇
Fitting	C₂×C₇×C₄⋊C₄	C₂
socle, prime radical	C₂³×C₇	C₂³
hypercenter	C₂×C₄⋊C₄	D₇
hypocenter	C₇	C₂×C₄⋊Q₈
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
6. #6451	C₂	direct (N × H)
21. C₂×C₄×C₇	Q₈	semidirect
26. C₂×Dic₇	Q₈	semidirect
42. C₄×C₇	C₂×Q₈	semidirect
45. Dic₇	C₂×Q₈	semidirect
57. C₂×C₇	C₄⋊Q₈	semidirect
70. C₂×C₄	Dic₁₄	semidirect
73. C₇	C₂×C₄⋊Q₈	semidirect
82. C₄	C₂×Dic₁₄	semidirect
83. C₂	#6451	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×Dic₁₄	2
C₂×C₇×C₄⋊C₄	2
C₂×C₄⋊Dic₇	2
C₂×Dic₇⋊C₄	2
C₂×C₄×Dic₇	2
#6451	2
C₂×C₄⋊Q₈	7

Subgroups — C2×#6451 #90188

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#6451 #90188