Subgroups — C₂²×Dic₇⋊C₄ #90474

Order 448.

418 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×C₇	C₂	1	1	yes	maximal, characteristic
2	C₂³×Dic₇	C₂	1	1	yes	maximal, characteristic
3	C₂³×Dic₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₇⋊C₄	C₂	1	12	yes	maximal, direct product factor
5	C₂⁴×C₇	C₂²	1	1	yes	characteristic
6	C₂²×C₄×C₇	—	2	4	no	—
7	C₂²×C₄×C₇	C₂²	1	6	yes	—
8	C₂²×Dic₇	—	2	4	no	—
9	C₂²×Dic₇	C₄	1	8	yes	complemented
10	C₂²×Dic₇	C₂²	1	6	yes	—
11	C₂²×Dic₇	C₂²	1	6	yes	—
12	Dic₇⋊C₄	C₂²	1	16	yes	direct product factor
13	C₂²×C₄⋊C₄	—	7	1	no	maximal, Sylow
14	C₂³×C₇	C₂×C₄	1	4	yes	—
15	C₂³×C₇	D₄	1	4	yes	—
16	C₂³×C₇	Q₈	1	4	yes	—
17	C₂³×C₇	C₂³	1	3	yes	—
18	C₂×C₄×C₇	—	2	12	no	—
19	C₂×C₄×C₇	C₂³	1	4	yes	—
20	C₂×Dic₇	—	2	12	no	—
21	C₂×Dic₇	C₂×C₄	1	24	yes	complemented
22	C₂×Dic₇	C₂³	1	4	yes	—
23	C₂×Dic₇	C₂³	1	4	yes	—
24	C₂³×C₄	—	7	1	no	—
25	C₂³×C₄	—	7	1	no	—
26	C₂³×C₄	D₇	1	1	yes	characteristic
27	C₂×C₄⋊C₄	—	7	12	no	—
28	C₂²×C₇	C₄⋊C₄	1	16	yes	complemented
29	C₂²×C₇	C₂²×C₄	1	6	yes	—
30	C₂²×C₇	C₂×D₄	1	6	yes	—
31	C₂²×C₇	C₂×Q₈	1	6	yes	—
32	C₂²×C₇	C₂⁴	1	1	yes	characteristic
33	C₄×C₇	—	2	4	no	—
34	Dic₇	—	2	4	no	—
35	Dic₇	C₂²×C₄	1	8	yes	complemented
36	C₂⁴	C₂×D₇	1	1	yes	characteristic
37	C₂²×C₄	—	2	4	no	—
38	C₂²×C₄	—	7	8	no	—
39	C₂²×C₄	—	7	6	no	—
40	C₂²×C₄	—	7	6	no	—
41	C₂²×C₄	—	14	4	no	—
42	C₂²×C₄	C₂×D₇	1	6	yes	—
43	C₄⋊C₄	—	7	16	no	—
44	C₂×C₇	C₂×C₄⋊C₄	1	12	yes	complemented
45	C₂×C₇	C₂³×C₄	1	1	yes	characteristic
46	C₂×C₇	C₂²×D₄	1	1	yes	characteristic
47	C₂×C₇	C₂²×Q₈	1	1	yes	characteristic
48	C₂³	Dic₁₄	1	4	yes	—
49	C₂³	C₄×D₇	1	4	yes	—
50	C₂³	C₂²⋊D₇	1	4	yes	—
51	C₂³	C₂²×D₇	1	3	yes	—
52	C₂×C₄	—	2	12	no	—
53	C₂×C₄	—	7	24	no	—
54	C₂×C₄	—	7	4	no	—
55	C₂×C₄	—	7	4	no	—
56	C₂×C₄	—	14	12	no	—
57	C₂×C₄	C₂²×D₇	1	4	yes	—
58	C₇	C₂²×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
59	C₂²	Dic₇⋊C₄	1	16	yes	direct product factor
60	C₂²	C₂×Dic₁₄	1	6	yes	—
61	C₂²	C₂×C₄×D₇	1	6	yes	—
62	C₂²	C₂×C₂²⋊D₇	1	6	yes	—
63	C₂²	C₂³×D₇	1	1	yes	characteristic
64	C₄	—	2	4	no	—
65	C₄	—	7	8	no	—
66	C₄	—	14	4	no	—
67	C₂	C₂×Dic₇⋊C₄	1	12	yes	direct product factor
68	C₂	C₂²×Dic₁₄	1	1	yes	characteristic
69	C₂	C₂²×C₄×D₇	1	1	yes	characteristic
70	C₂	C₂²×C₂²⋊D₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×D₇
commutator	C₂×C₇	C₂³×C₄
Frattini	C₂²	C₂³×D₇
Fitting	C₂³×C₄×C₇	C₂
socle, prime radical	C₂⁴×C₇	C₂²
cosocle	C₂²×C₇	C₂⁴
hypercenter	C₂³×C₄	D₇
hypocenter	C₇	C₂²×C₄⋊C₄
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
4. C₂×Dic₇⋊C₄	C₂	direct (N × H)
9. C₂²×Dic₇	C₄	semidirect
12. Dic₇⋊C₄	C₂²	direct (N × H)
21. C₂×Dic₇	C₂×C₄	semidirect
28. C₂²×C₇	C₄⋊C₄	semidirect
35. Dic₇	C₂²×C₄	semidirect
44. C₂×C₇	C₂×C₄⋊C₄	semidirect
58. C₇	C₂²×C₄⋊C₄	semidirect
59. C₂²	Dic₇⋊C₄	direct (N × H)
67. C₂	C₂×Dic₇⋊C₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄×C₇	2
C₂³×Dic₇	2
C₂×Dic₇⋊C₄	2
C₂²×C₄⋊C₄	7

Subgroups — C22×Dic7⋊C4 #90474

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×Dic₇⋊C₄ #90474