Subgroups — C₂×#6392 #89877

Order 448.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₇	C₂	1	2	yes	maximal
3	#6392	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₄×C₇	C₂²	1	1	yes	characteristic
5	C₂²×Dic₇	—	2	2	no	—
6	C₂×C₇×C₈	C₄	1	4	yes	complemented
7	C₂×C₇×C₈	C₂²	1	2	yes	—
8	C₄⋊Dic₇	—	2	2	no	—
9	C₄⋊Dic₇	C₂²	1	4	yes	—
10	C₂×#107	—	7	1	no	maximal, Sylow
11	C₂³×C₇	D₄	1	1	yes	characteristic
12	C₂×C₄×C₇	C₂×C₄	1	2	yes	—
13	C₂×C₄×C₇	D₄	1	1	yes	characteristic
14	C₂×C₄×C₇	Q₈	1	2	yes	—
15	C₂×C₄×C₇	C₂³	1	1	yes	characteristic
16	C₂×Dic₇	—	2	4	no	—
17	C₂×Dic₇	—	4	4	no	—
18	C₇×C₈	C₂×C₄	1	4	yes	complemented
19	C₂²×C₈	D₇	1	1	yes	characteristic
20	C₂×C₄⋊C₄	—	7	2	no	—
21	#107	—	7	4	no	—
22	C₂²×C₇	C₄⋊C₄	1	2	yes	—
23	C₂²×C₇	D₈	1	2	yes	—
24	C₂²×C₇	Q₁₆	1	2	yes	—
25	C₂²×C₇	C₂×D₄	1	1	yes	characteristic
26	C₄×C₇	C₄⋊C₄	1	2	yes	—
27	C₄×C₇	C₂²×C₄	1	1	yes	characteristic
28	C₄×C₇	C₂×Q₈	1	1	yes	characteristic
29	Dic₇	—	4	4	no	—
30	C₂²×C₄	—	14	2	no	—
31	C₂²×C₄	C₂×D₇	1	1	yes	characteristic
32	C₂×C₈	Dic₇	1	4	yes	complemented
33	C₂×C₈	C₂×D₇	1	2	yes	—
34	C₄⋊C₄	—	7	4	no	—
35	C₄⋊C₄	—	14	2	no	—
36	C₂×C₇	#107	1	4	yes	complemented
37	C₂×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₇	C₂×D₈	1	1	yes	characteristic
39	C₂×C₇	C₂×Q₁₆	1	1	yes	characteristic
40	C₂³	D₂₈	1	1	yes	characteristic
41	C₂×C₄	—	14	4	no	—
42	C₂×C₄	—	28	4	no	—
43	C₂×C₄	Dic₁₄	1	2	yes	—
44	C₂×C₄	D₂₈	1	1	yes	characteristic
45	C₂×C₄	C₂×Dic₇	1	2	yes	—
46	C₂×C₄	C₂²×D₇	1	1	yes	characteristic
47	C₈	C₂×Dic₇	1	4	yes	complemented
48	C₇	C₂×#107	1	1	yes	characteristic, complemented, Sylow
49	C₂²	D₅₆	1	2	yes	—
50	C₂²	Dic₂₈	1	2	yes	—
51	C₂²	C₄⋊Dic₇	1	2	yes	—
52	C₂²	C₂×D₂₈	1	1	yes	characteristic
53	C₄	—	28	4	no	—
54	C₄	C₄⋊Dic₇	1	2	yes	—
55	C₄	C₂×Dic₁₄	1	1	yes	characteristic
56	C₄	C₂²×Dic₇	1	1	yes	characteristic
57	C₂	#6392	1	4	yes	direct product factor
58	C₂	C₂×D₅₆	1	1	yes	characteristic
59	C₂	C₂×Dic₂₈	1	1	yes	characteristic
60	C₂	C₂×C₄⋊Dic₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₂₈
commutator	C₄×C₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₇
Fitting	C₂²×C₇×C₈	C₂
socle, prime radical	C₂³×C₇	D₄
cosocle	C₂×C₄×C₇	C₂³
hypercenter	C₂²×C₈	D₇
hypocenter	C₇	C₂×#107
LCS	G ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
3. #6392	C₂	direct (N × H)
6. C₂×C₇×C₈	C₄	semidirect
18. C₇×C₈	C₂×C₄	semidirect
32. C₂×C₈	Dic₇	semidirect
36. C₂×C₇	#107	semidirect
47. C₈	C₂×Dic₇	semidirect
48. C₇	C₂×#107	semidirect
57. C₂	#6392	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×C₈	2
C₂×C₄⋊Dic₇	2
#6392	2
C₂×#107	7

Subgroups — C2×#6392 #89877

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#6392 #89877