Subgroups — C₂×#6432 #90159

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×C₄²×C₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊Dic₇	C₂	1	4	yes	maximal
4	#6432	C₂	1	8	yes	maximal, direct product factor
5	C₂²×C₄×C₇	C₂²	1	1	yes	characteristic
6	C₂²×C₄×C₇	C₂²	1	2	yes	—
7	C₂²×Dic₇	C₂²	1	4	yes	—
8	C₂×Dic₁₄	—	2	8	no	—
9	C₂×Dic₁₄	C₂²	1	8	yes	—
10	C₄²×C₇	C₂²	1	4	yes	—
11	C₄⋊Dic₇	C₂²	1	16	yes	—
12	C₂×C₄⋊Q₈	—	7	1	no	maximal, Sylow
13	C₂³×C₇	C₂³	1	1	yes	characteristic
14	C₂×C₄×C₇	D₄	1	4	yes	—
15	C₂×C₄×C₇	Q₈	1	8	yes	complemented
16	C₂×C₄×C₇	C₂³	1	2	yes	—
17	C₂×C₄×C₇	C₂³	1	4	yes	—
18	C₂×Dic₇	—	2	8	no	—
19	C₂×Dic₇	C₂³	1	8	yes	—
20	Dic₁₄	—	2	16	no	—
21	C₂²×Q₈	—	7	2	no	—
22	C₄⋊Q₈	—	7	8	no	—
23	C₂×C₄⋊C₄	—	7	4	no	—
24	C₂×C₄²	D₇	1	1	yes	characteristic
25	C₂²×C₇	C₂×D₄	1	2	yes	—
26	C₂²×C₇	C₂×Q₈	1	4	yes	—
27	C₂²×C₇	C₂⁴	1	1	yes	characteristic
28	C₄×C₇	C₂×D₄	1	4	yes	—
29	C₄×C₇	C₂×Q₈	1	8	yes	complemented
30	Dic₇	—	2	8	no	—
31	C₂×Q₈	—	7	8	no	—
32	C₂×Q₈	—	14	8	no	—
33	C₂²×C₄	—	7	4	no	—
34	C₂²×C₄	C₂×D₇	1	2	yes	—
35	C₂²×C₄	C₂×D₇	1	1	yes	characteristic
36	C₄⋊C₄	—	7	16	no	—
37	C₄²	C₂×D₇	1	4	yes	—
38	C₂×C₇	C₄⋊Q₈	1	4	yes	complemented
39	C₂×C₇	C₂²×D₄	1	1	yes	characteristic
40	C₂×C₇	C₂²×Q₈	1	2	yes	—
41	C₂³	C₂²×D₇	1	1	yes	characteristic
42	Q₈	—	14	16	no	—
43	C₂×C₄	—	7	8	no	—
44	C₂×C₄	—	14	8	no	—
45	C₂×C₄	Dic₁₄	1	8	yes	complemented
46	C₂×C₄	D₂₈	1	4	yes	—
47	C₂×C₄	C₂²×D₇	1	4	yes	—
48	C₂×C₄	C₂²×D₇	1	2	yes	—
49	C₇	C₂×C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
50	C₂²	C₂×Dic₁₄	1	4	yes	—
51	C₂²	C₂×D₂₈	1	2	yes	—
52	C₂²	C₂³×D₇	1	1	yes	characteristic
53	C₄	—	14	8	no	—
54	C₄	C₂×Dic₁₄	1	8	yes	complemented
55	C₄	C₂×D₂₈	1	4	yes	—
56	C₂	#6432	1	4	yes	direct product factor
57	C₂	C₂²×Dic₁₄	1	2	yes	—
58	C₂	C₂²×D₂₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₇
commutator, cosocle	C₂²×C₇	C₂⁴
Frattini	C₂²	C₂³×D₇
Fitting	C₂×C₄²×C₇	C₂
socle, prime radical	C₂³×C₇	C₂³
hypercenter	C₂×C₄²	D₇
hypocenter	C₇	C₂×C₄⋊Q₈
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
4. #6432	C₂	direct (N × H)
15. C₂×C₄×C₇	Q₈	semidirect
29. C₄×C₇	C₂×Q₈	semidirect
38. C₂×C₇	C₄⋊Q₈	semidirect
45. C₂×C₄	Dic₁₄	semidirect
49. C₇	C₂×C₄⋊Q₈	semidirect
54. C₄	C₂×Dic₁₄	semidirect
56. C₂	#6432	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×C₄²×C₇	2
C₂×C₄⋊Dic₇	2
#6432	2
C₂×C₄⋊Q₈	7

Subgroups — C2×#6432 #90159

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#6432 #90159