Subgroups — C₂×#1141 #6494

Order 224.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₂₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#1141	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×C₇	—	2	1	no	—
6	C₂²×D₇	—	2	1	no	—
7	C₇×D₄	—	2	1	no	—
8	C₇×D₄	C₂²	1	2	yes	complemented
9	C₂×C₄×C₇	C₂²	1	1	yes	characteristic
10	D₂₈	—	2	1	no	—
11	D₂₈	C₂²	1	2	yes	complemented
12	C₇⋊C₈	C₂²	1	2	yes	complemented
13	C₂×D₈	—	7	1	no	maximal, Sylow
14	C₂²×C₇	—	2	2	no	—
15	C₂²×C₇	—	4	2	no	—
16	C₂²×C₇	D₄	1	1	yes	characteristic
17	C₂×D₇	—	2	2	no	—
18	C₂×D₇	—	4	2	no	—
19	C₄×C₇	D₄	1	1	yes	characteristic
20	C₄×C₇	C₂³	1	1	yes	characteristic
21	C₂×D₄	—	7	1	no	—
22	C₂×D₄	D₇	1	1	yes	characteristic, complemented
23	D₈	—	7	4	no	—
24	C₂×C₈	—	7	1	no	—
25	C₂×C₇	—	4	2	no	—
26	C₂×C₇	D₈	1	2	yes	complemented
27	C₂×C₇	C₂×D₄	1	1	yes	characteristic
28	D₇	—	4	2	no	—
29	C₂³	—	2	1	no	—
30	C₂³	—	14	1	no	—
31	D₄	—	2	1	no	—
32	D₄	—	7	2	no	—
33	D₄	—	14	1	no	—
34	D₄	C₂×D₇	1	2	yes	complemented
35	C₂×C₄	C₂×D₇	1	1	yes	characteristic
36	C₈	—	7	2	no	—
37	C₇	C₂×D₈	1	1	yes	characteristic, complemented, Sylow
38	C₂²	—	2	2	no	—
39	C₂²	—	4	2	no	—
40	C₂²	—	14	2	no	—
41	C₂²	—	28	2	no	—
42	C₂²	C₂²⋊D₇	1	1	yes	characteristic
43	C₄	C₂²⋊D₇	1	1	yes	characteristic
44	C₄	C₂²×D₇	1	1	yes	characteristic
45	C₂	—	4	2	no	—
46	C₂	—	28	2	no	—
47	C₂	#1141	1	2	yes	direct product factor
48	C₂	C₂×C₂²⋊D₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊D₇
commutator, cosocle	C₄×C₇	C₂³
Frattini	C₄	C₂²×D₇
Fitting	C₂×C₇×D₄	C₂
socle	C₂²×C₇	D₄
hypercenter	C₂×D₄	D₇
hypocenter	C₇	C₂×D₈
LCS	G ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×D₄	C₂	semidirect
2. C₂×D₂₈	C₂	semidirect
3. #1141	C₂	direct (N × H)
4. C₂×C₇⋊C₈	C₂	semidirect
8. C₇×D₄	C₂²	semidirect
11. D₂₈	C₂²	semidirect
12. C₇⋊C₈	C₂²	semidirect
22. C₂×D₄	D₇	semidirect
26. C₂×C₇	D₈	semidirect
34. D₄	C₂×D₇	semidirect
37. C₇	C₂×D₈	semidirect
47. C₂	#1141	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₇×D₄	2
C₂×D₂₈	2
#1141	2
C₂×C₇⋊C₈	2
C₂×D₈	7

Subgroups — C2×#1141 #6494

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1141 #6494