Subgroups — C₂×Dic₇⋊C₈ #89871

Order 448.

138 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	1	yes	maximal, characteristic
3	C₂²×C₇⋊C₈	C₂	1	1	yes	maximal, characteristic
4	Dic₇⋊C₈	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₄×C₇	C₂²	1	1	yes	characteristic
6	C₂²×Dic₇	C₄	1	1	yes	characteristic
7	C₂²×Dic₇	C₄	1	1	yes	characteristic
8	C₂×C₇×C₈	—	2	2	no	—
9	C₂×C₇×C₈	C₂²	1	2	yes	—
10	C₄×Dic₇	C₄	1	2	yes	—
11	C₄×Dic₇	C₂²	1	2	yes	—
12	C₂×C₇⋊C₈	—	2	2	no	—
13	C₂×C₇⋊C₈	C₂²	1	2	yes	—
14	C₂×C₄⋊C₈	—	7	1	no	maximal, Sylow
15	C₂³×C₇	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₇	D₄	1	2	yes	—
18	C₂×C₄×C₇	Q₈	1	2	yes	—
19	C₂×C₄×C₇	C₂³	1	1	yes	characteristic
20	C₂×Dic₇	—	2	2	no	—
21	C₂×Dic₇	C₈	1	4	yes	complemented
22	C₂×Dic₇	C₂×C₄	1	2	yes	—
23	C₂×Dic₇	C₂×C₄	1	2	yes	—
24	C₇×C₈	—	2	2	no	—
25	C₇⋊C₈	—	2	2	no	—
26	C₂²×C₈	—	7	1	no	—
27	C₂²×C₈	D₇	1	1	yes	characteristic
28	C₂×C₄²	—	7	1	no	—
29	C₄⋊C₈	—	7	4	no	—
30	C₂²×C₇	C₄⋊C₄	1	2	yes	—
31	C₂²×C₇	C₂×C₈	1	2	yes	—
32	C₂²×C₇	M₁₆	1	2	yes	—
33	C₂²×C₇	C₂²×C₄	1	1	yes	characteristic
34	C₄×C₇	C₄⋊C₄	1	2	yes	—
35	C₄×C₇	C₂×D₄	1	1	yes	characteristic
36	C₄×C₇	C₂×Q₈	1	1	yes	characteristic
37	Dic₇	—	2	2	no	—
38	Dic₇	C₂×C₈	1	4	yes	complemented
39	C₂²×C₄	—	7	1	no	—
40	C₂²×C₄	—	7	1	no	—
41	C₂²×C₄	C₂×D₇	1	1	yes	characteristic
42	C₂×C₈	—	2	2	no	—
43	C₂×C₈	—	7	2	no	—
44	C₂×C₈	—	14	2	no	—
45	C₂×C₈	C₂×D₇	1	2	yes	—
46	C₄²	—	7	2	no	—
47	C₄²	—	7	2	no	—
48	C₂×C₇	C₄⋊C₈	1	4	yes	complemented
49	C₂×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
50	C₂×C₇	C₂²×C₈	1	1	yes	characteristic
51	C₂×C₇	C₂×M₁₆	1	1	yes	characteristic
52	C₂³	C₄×D₇	1	1	yes	characteristic
53	C₂×C₄	—	7	4	no	—
54	C₂×C₄	—	7	2	no	—
55	C₂×C₄	—	7	2	no	—
56	C₂×C₄	—	14	2	no	—
57	C₂×C₄	Dic₁₄	1	2	yes	—
58	C₂×C₄	C₄×D₇	1	1	yes	characteristic
59	C₂×C₄	C₂²⋊D₇	1	2	yes	—
60	C₂×C₄	C₂²×D₇	1	1	yes	characteristic
61	C₈	—	2	2	no	—
62	C₈	—	14	2	no	—
63	C₇	C₂×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
64	C₂²	C₈×D₇	1	2	yes	—
65	C₂²	#1131	1	2	yes	—
66	C₂²	Dic₇⋊C₄	1	2	yes	—
67	C₂²	C₂×C₄×D₇	1	1	yes	characteristic
68	C₄	—	7	4	no	—
69	C₄	—	14	2	no	—
70	C₄	Dic₇⋊C₄	1	2	yes	—
71	C₄	C₂×Dic₁₄	1	1	yes	characteristic
72	C₄	C₂×C₂²⋊D₇	1	1	yes	characteristic
73	C₂	Dic₇⋊C₈	1	4	yes	direct product factor
74	C₂	C₂×C₈×D₇	1	1	yes	characteristic
75	C₂	C₂×#1131	1	1	yes	characteristic
76	C₂	C₂×Dic₇⋊C₄	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. Dic₇⋊C₈	C₂	direct (N × H)
21. C₂×Dic₇	C₈	semidirect
38. Dic₇	C₂×C₈	semidirect
48. C₂×C₇	C₄⋊C₈	semidirect
63. C₇	C₂×C₄⋊C₈	semidirect
73. C₂	Dic₇⋊C₈	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
C₂²×C₇⋊C₈	2
Dic₇⋊C₈	2
C₂×C₄⋊C₈	7

Subgroups — C2×Dic7⋊C8 #89871

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Dic₇⋊C₈ #89871