Subgroups — C₂×#6372 #89672

Order 448.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#6372	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₄×D₇	C₄	1	1	yes	characteristic
6	C₂×C₇×C₈	C₂²	1	1	yes	characteristic
7	C₂×C₇⋊C₈	C₄	1	1	yes	characteristic
8	C₈×D₇	C₄	1	2	yes	—
9	C₈×D₇	C₂²	1	2	yes	—
10	C₇×C₁₆	C₂²	1	2	yes	complemented
11	C₇⋊C₁₆	C₂²	1	2	yes	complemented
12	C₂×M₃₂	—	7	1	no	maximal, Sylow
13	C₂²×D₇	C₈	1	1	yes	characteristic
14	C₂×C₄×C₇	C₂×C₄	1	1	yes	characteristic
15	C₂×Dic₇	C₈	1	1	yes	characteristic
16	C₄×D₇	C₈	1	2	yes	—
17	C₄×D₇	C₂×C₄	1	2	yes	—
18	C₇×C₈	C₂×C₄	1	1	yes	characteristic
19	C₇×C₈	C₂³	1	1	yes	characteristic
20	C₇⋊C₈	C₂×C₄	1	2	yes	—
21	C₂²×C₈	—	7	1	no	—
22	M₃₂	—	7	4	no	—
23	C₂×C₁₆	—	7	1	no	—
24	C₂×C₁₆	D₇	1	1	yes	characteristic, complemented
25	C₂²×C₇	C₂×C₈	1	1	yes	characteristic
26	C₂×D₇	—	2	2	no	—
27	C₂×D₇	C₂×C₈	1	2	yes	—
28	C₄×C₇	C₂×C₈	1	1	yes	characteristic
29	C₄×C₇	C₂²×C₄	1	1	yes	characteristic
30	Dic₇	C₂×C₈	1	2	yes	—
31	C₂²×C₄	—	7	1	no	—
32	C₂×C₈	—	7	1	no	—
33	C₂×C₈	—	7	2	no	—
34	C₂×C₈	—	7	2	no	—
35	C₂×C₈	C₂×D₇	1	1	yes	characteristic
36	C₁₆	—	7	2	no	—
37	C₁₆	C₂×D₇	1	2	yes	complemented
38	C₂×C₇	M₃₂	1	2	yes	complemented
39	C₂×C₇	C₂²×C₈	1	1	yes	characteristic
40	D₇	—	2	2	no	—
41	C₂³	—	7	1	no	—
42	C₂×C₄	—	7	1	no	—
43	C₂×C₄	—	7	2	no	—
44	C₂×C₄	—	7	2	no	—
45	C₂×C₄	C₄×D₇	1	1	yes	characteristic
46	C₈	—	7	2	no	—
47	C₈	C₄×D₇	1	1	yes	characteristic
48	C₈	C₂²×D₇	1	1	yes	characteristic
49	C₇	C₂×M₃₂	1	1	yes	characteristic, complemented, Sylow
50	C₂²	—	7	2	no	—
51	C₂²	—	14	2	no	—
52	C₂²	C₈×D₇	1	1	yes	characteristic
53	C₄	—	7	2	no	—
54	C₄	C₈×D₇	1	1	yes	characteristic
55	C₄	C₂×C₄×D₇	1	1	yes	characteristic
56	C₂	—	14	2	no	—
57	C₂	#6372	1	2	yes	direct product factor
58	C₂	C₂×C₈×D₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₇
commutator	C₂×C₇	C₂²×C₈
Frattini	C₈	C₂²×D₇
Fitting	C₂×C₇×C₁₆	C₂
socle	C₂²×C₇	C₂×C₈
prime radical	C₂²×D₇	C₈
cosocle	C₇×C₈	C₂³
hypercenter	C₂×C₁₆	D₇
hypocenter	C₇	C₂×M₃₂
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×C₇×C₁₆	C₂	semidirect
3. C₂×C₇⋊C₁₆	C₂	semidirect
4. #6372	C₂	direct (N × H)
10. C₇×C₁₆	C₂²	semidirect
11. C₇⋊C₁₆	C₂²	semidirect
24. C₂×C₁₆	D₇	semidirect
37. C₁₆	C₂×D₇	semidirect
38. C₂×C₇	M₃₂	semidirect
49. C₇	C₂×M₃₂	semidirect
57. C₂	#6372	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×C₈×D₇	2
C₂×C₇×C₁₆	2
C₂×C₇⋊C₁₆	2
#6372	2
C₂×M₃₂	7

Subgroups — C2×#6372 #89672

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#6372 #89672