Subgroups — (C₂×D₇)⋊C₁₆ #89302

Order 448.

66 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	C₂×C₄×D₇	C₄	1	1	yes	characteristic
5	C₂×C₇×C₈	C₂²	1	1	yes	characteristic
6	C₂×C₇⋊C₈	C₄	1	1	yes	characteristic
7	C₈×D₇	—	2	1	no	—
8	C₈×D₇	—	2	1	no	—
9	C₇×C₁₆	—	2	1	no	—
10	C₇⋊C₁₆	—	2	1	no	—
11	C₂²⋊C₁₆	—	7	1	no	maximal, Sylow
12	C₂²×D₇	C₈	1	1	yes	characteristic
13	C₂×C₄×C₇	C₂×C₄	1	1	yes	characteristic
14	C₂×Dic₇	C₈	1	1	yes	characteristic
15	C₄×D₇	—	2	1	no	—
16	C₄×D₇	—	2	1	no	—
17	C₇×C₈	D₄	1	1	yes	characteristic
18	C₇×C₈	D₄	1	1	yes	characteristic
19	C₇⋊C₈	—	2	1	no	—
20	C₂²×C₈	—	7	1	no	—
21	C₂×C₁₆	—	7	1	no	—
22	C₂×C₁₆	D₇	1	1	yes	characteristic, complemented
23	C₂²×C₇	C₂×C₈	1	1	yes	characteristic
24	C₂×D₇	—	2	1	no	—
25	C₂×D₇	—	2	1	no	—
26	C₂×D₇	C₁₆	1	2	yes	complemented
27	C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
28	C₄×C₇	M₁₆	1	1	yes	characteristic
29	Dic₇	—	2	1	no	—
30	C₂²×C₄	—	7	1	no	—
31	C₂×C₈	—	7	1	no	—
32	C₂×C₈	—	14	1	no	—
33	C₂×C₈	—	14	1	no	—
34	C₂×C₈	C₂×D₇	1	1	yes	characteristic
35	C₁₆	—	2	1	no	—
36	C₁₆	—	14	1	no	—
37	C₂×C₇	C₂²⋊C₈	1	1	yes	characteristic
38	C₂×C₇	C₂×C₁₆	1	1	yes	characteristic
39	C₂×C₇	M₃₂	1	1	yes	characteristic
40	D₇	—	2	2	no	—
41	C₂³	—	7	1	no	—
42	C₂×C₄	—	7	1	no	—
43	C₂×C₄	—	14	1	no	—
44	C₂×C₄	—	14	1	no	—
45	C₂×C₄	C₄×D₇	1	1	yes	characteristic
46	C₈	—	14	1	no	—
47	C₈	D₂₈	1	1	yes	characteristic
48	C₈	C₂²⋊D₇	1	1	yes	characteristic
49	C₇	C₂²⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
50	C₂²	—	7	2	no	—
51	C₂²	—	14	1	no	—
52	C₂²	—	14	1	no	—
53	C₂²	C₈×D₇	1	1	yes	characteristic
54	C₄	—	14	1	no	—
55	C₄	#1131	1	1	yes	characteristic
56	C₄	(C₂×D₇)⋊C₄	1	1	yes	characteristic
57	C₂	—	14	2	no	—
58	C₂	D₇×C₁₆	1	1	yes	characteristic
59	C₂	#6372	1	1	yes	characteristic
60	C₂	(C₂×D₇)⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×D₇
commutator	C₂×C₇	C₂×C₁₆
Fitting	C₂×C₇×C₁₆	C₂
socle	C₂²×C₇	C₂×C₈
prime radical	C₂²×D₇	C₈
cosocle	C₂×C₇×C₈	C₂²
hypercenter	C₂×C₁₆	D₇
hypocenter	C₇	C₂²⋊C₁₆
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
22. C₂×C₁₆	D₇	semidirect
26. C₂×D₇	C₁₆	semidirect
49. C₇	C₂²⋊C₁₆	semidirect

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
C₂²⋊C₁₆	7

Subgroups — (C2×D7)⋊C16 #89302

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₂×D₇)⋊C₁₆ #89302