Subgroups — C₂×#6386 #89869

Order 448.

90 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	#6386	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₇⋊C₁₆	C₂	1	2	yes	maximal, complemented
4	C₂²×C₄×C₇	C₄	1	1	yes	characteristic
5	C₂×C₇×C₈	C₄	1	1	yes	characteristic
6	C₂×C₇×C₈	C₄	1	2	yes	—
7	C₂×C₇×C₈	C₂²	1	2	yes	—
8	C₂×C₇×C₈	C₂²	1	1	yes	characteristic
9	C₇⋊C₁₆	C₂²	1	4	yes	complemented
10	C₂×M₃₂	—	7	1	no	maximal, Sylow
11	C₂³×C₇	C₈	1	1	yes	characteristic
12	C₂×C₄×C₇	C₈	1	2	yes	—
13	C₂×C₄×C₇	C₈	1	1	yes	characteristic
14	C₂×C₄×C₇	C₂×C₄	1	2	yes	—
15	C₂×C₄×C₇	C₂×C₄	1	1	yes	characteristic
16	C₇×C₈	C₂×C₄	1	2	yes	—
17	C₇×C₈	C₂×C₄	1	1	yes	characteristic
18	C₇×C₈	C₂³	1	1	yes	characteristic
19	C₂²×C₈	D₇	1	1	yes	characteristic
20	M₃₂	—	7	4	no	—
21	C₂×C₁₆	—	7	2	no	—
22	C₂²×C₇	—	2	2	no	—
23	C₂²×C₇	C₂×C₈	1	2	yes	—
24	C₂²×C₇	C₂×C₈	1	1	yes	characteristic
25	C₄×C₇	C₂×C₈	1	2	yes	—
26	C₄×C₇	C₂×C₈	1	1	yes	characteristic
27	C₄×C₇	C₂²×C₄	1	1	yes	characteristic
28	C₂²×C₄	Dic₇	1	1	yes	characteristic
29	C₂×C₈	Dic₇	1	1	yes	characteristic
30	C₂×C₈	Dic₇	1	2	yes	—
31	C₂×C₈	C₂×D₇	1	2	yes	—
32	C₂×C₈	C₂×D₇	1	1	yes	characteristic
33	C₁₆	—	7	4	no	—
34	C₂×C₇	—	2	2	no	—
35	C₂×C₇	M₃₂	1	2	yes	complemented
36	C₂×C₇	C₂²×C₈	1	1	yes	characteristic
37	C₂³	C₇⋊C₈	1	1	yes	characteristic
38	C₂×C₄	C₇⋊C₈	1	2	yes	—
39	C₂×C₄	C₇⋊C₈	1	1	yes	characteristic
40	C₂×C₄	C₂×Dic₇	1	2	yes	—
41	C₂×C₄	C₂×Dic₇	1	1	yes	characteristic
42	C₈	C₂×Dic₇	1	2	yes	—
43	C₈	C₂×Dic₇	1	1	yes	characteristic
44	C₈	C₂²×D₇	1	1	yes	characteristic
45	C₇	C₂×M₃₂	1	1	yes	characteristic, complemented, Sylow
46	C₂²	—	2	2	no	—
47	C₂²	C₂×C₇⋊C₈	1	2	yes	—
48	C₂²	C₂×C₇⋊C₈	1	1	yes	characteristic
49	C₄	C₂×C₇⋊C₈	1	2	yes	—
50	C₄	C₂×C₇⋊C₈	1	1	yes	characteristic
51	C₄	C₂²×Dic₇	1	1	yes	characteristic
52	C₂	—	2	2	no	—
53	C₂	#6386	1	2	yes	direct product factor
54	C₂	C₂²×C₇⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₇
commutator	C₂×C₇	C₂²×C₈
Frattini	C₈	C₂²×D₇
Fitting	C₂²×C₇×C₈	C₂
socle	C₂²×C₇	C₂×C₈
prime radical	C₂³×C₇	C₈
cosocle	C₇×C₈	C₂³
hypercenter	C₂²×C₈	D₇
hypocenter	C₇	C₂×M₃₂
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. #6386	C₂	direct (N × H)
3. C₂×C₇⋊C₁₆	C₂	semidirect
9. C₇⋊C₁₆	C₂²	semidirect
35. C₂×C₇	M₃₂	semidirect
45. C₇	C₂×M₃₂	semidirect
53. C₂	#6386	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
#6386	2
C₂×C₇⋊C₁₆	2
C₂×M₃₂	7

Subgroups — C2×#6386 #89869

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#6386 #89869