Subgroups — C₂×#6410 #89998

Order 448.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#1136	C₂	1	2	yes	maximal
3	#6410	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₇×Q₈	—	2	2	no	—
5	C₂×C₇×Q₈	—	2	2	no	—
6	C₂×C₇×Q₈	C₄	1	2	yes	—
7	C₂×C₇×Q₈	C₂²	1	2	yes	—
8	C₂²×C₄×C₇	C₄	1	2	yes	—
9	C₂²×C₄×C₇	C₂²	1	1	yes	characteristic
10	#1136	—	2	2	no	—
11	#1136	C₂²	1	4	yes	—
12	C₂×C₇⋊C₈	—	2	2	no	—
13	C₂×#101	—	7	1	no	maximal, Sylow
14	C₂³×C₇	C₂×C₄	1	1	yes	characteristic
15	C₇×Q₈	—	2	4	no	—
16	C₇×Q₈	—	2	4	no	—
17	C₂×C₄×C₇	—	2	2	no	—
18	C₂×C₄×C₇	—	2	2	no	—
19	C₂×C₄×C₇	C₂×C₄	1	4	yes	—
20	C₂×C₄×C₇	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×C₇	D₄	1	2	yes	—
22	C₂×C₄×C₇	D₄	1	2	yes	—
23	C₂×C₄×C₇	C₂³	1	1	yes	characteristic
24	C₇⋊C₈	—	2	4	no	—
25	C₂²×Q₈	D₇	1	1	yes	characteristic
26	C₂×M₁₆	—	7	2	no	—
27	#101	—	7	4	no	—
28	C₂²×C₇	—	2	2	no	—
29	C₂²×C₇	C₂²⋊C₄	1	1	yes	characteristic
30	C₂²×C₇	C₂²⋊C₄	1	1	yes	characteristic
31	C₂²×C₇	C₂²×C₄	1	1	yes	characteristic
32	C₄×C₇	—	2	4	no	—
33	C₄×C₇	C₂²⋊C₄	1	2	yes	—
34	C₄×C₇	C₂×D₄	1	2	yes	—
35	C₂×Q₈	—	2	2	no	—
36	C₂×Q₈	—	2	2	no	—
37	C₂×Q₈	Dic₇	1	2	yes	—
38	C₂×Q₈	C₂×D₇	1	2	yes	—
39	C₂²×C₄	Dic₇	1	2	yes	—
40	C₂²×C₄	C₂×D₇	1	1	yes	characteristic
41	M₁₆	—	7	4	no	—
42	M₁₆	—	14	2	no	—
43	C₂×C₈	—	14	2	no	—
44	C₂×C₇	—	2	1	no	—
45	C₂×C₇	—	2	1	no	—
46	C₂×C₇	#101	1	2	yes	complemented
47	C₂×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
48	C₂³	C₂×Dic₇	1	1	yes	characteristic
49	Q₈	—	2	4	no	—
50	Q₈	—	2	4	no	—
51	C₂×C₄	—	2	2	no	—
52	C₂×C₄	—	2	2	no	—
53	C₂×C₄	C₂×Dic₇	1	4	yes	—
54	C₂×C₄	C₂×Dic₇	1	1	yes	characteristic
55	C₂×C₄	C₂²⋊D₇	1	2	yes	—
56	C₂×C₄	C₂²⋊D₇	1	2	yes	—
57	C₂×C₄	C₂²×D₇	1	1	yes	characteristic
58	C₈	—	14	4	no	—
59	C₇	C₂×#101	1	1	yes	characteristic, complemented, Sylow
60	C₂²	—	2	2	no	—
61	C₂²	C₂²⋊Dic₇	1	1	yes	characteristic
62	C₂²	C₂²⋊Dic₇	1	1	yes	characteristic
63	C₂²	C₂²×Dic₇	1	1	yes	characteristic
64	C₄	—	2	4	no	—
65	C₄	C₂²⋊Dic₇	1	2	yes	—
66	C₄	C₂×C₂²⋊D₇	1	2	yes	—
67	C₂	—	2	1	no	—
68	C₂	—	2	1	no	—
69	C₂	#6410	1	2	yes	direct product factor
70	C₂	C₂×C₂²⋊Dic₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊Dic₇
commutator	C₂²×C₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₇
Fitting	C₂²×C₇×Q₈	C₂
socle	C₂²×C₇	C₂²⋊C₄
prime radical	C₂³×C₇	C₂×C₄
cosocle	C₂×C₄×C₇	C₂³
hypercenter	C₂²×Q₈	D₇
hypocenter	C₇	C₂×#101
LCS	G ▷ C₂²×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×Q₈

Complements

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

N	H ≅ G/N	type
3. #6410	C₂	direct (N × H)
46. C₂×C₇	#101	semidirect
59. C₇	C₂×#101	semidirect
69. C₂	#6410	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×C₇×Q₈	2
C₂×#1136	2
#6410	2
C₂×#101	7

Subgroups — C2×#6410 #89998

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#6410 #89998