Subgroups — C₄×C₄⋊Dic₇ #89706

Order 448.

194 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×C₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₇	C₂	1	2	yes	maximal
3	C₂×C₄×Dic₇	C₂	1	2	yes	maximal
4	C₇⋊#95	C₂	1	2	yes	maximal
5	C₂²×C₄×C₇	C₂²	1	1	yes	characteristic
6	C₂²×C₄×C₇	C₂²	1	1	yes	characteristic
7	C₂²×C₄×C₇	C₂²	1	1	yes	characteristic
8	C₂²×Dic₇	C₂²	1	4	yes	—
9	C₄²×C₇	C₄	1	4	yes	complemented
10	C₄⋊Dic₇	C₄	1	8	yes	direct product factor
11	C₄×Dic₇	—	2	4	no	—
12	C₄×C₄⋊C₄	—	7	1	no	maximal, Sylow
13	C₂³×C₇	C₂³	1	1	yes	characteristic
14	C₂×C₄×C₇	—	2	2	no	—
15	C₂×C₄×C₇	C₂×C₄	1	4	yes	—
16	C₂×C₄×C₇	C₂×C₄	1	2	yes	—
17	C₂×C₄×C₇	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₇	C₂×C₄	1	2	yes	—
19	C₂×C₄×C₇	D₄	1	2	yes	—
20	C₂×C₄×C₇	Q₈	1	2	yes	—
21	C₂×Dic₇	—	2	4	no	—
22	C₂×Dic₇	—	2	4	no	—
23	C₂×Dic₇	C₂×C₄	1	8	yes	—
24	C₂×C₄⋊C₄	—	7	2	no	—
25	C₂×C₄²	—	7	2	no	—
26	C₂×C₄²	D₇	1	1	yes	characteristic
27	#95	—	7	2	no	—
28	C₂²×C₇	C₂²×C₄	1	2	yes	—
29	C₂²×C₇	C₂²×C₄	1	1	yes	characteristic
30	C₂²×C₇	C₂×D₄	1	1	yes	characteristic
31	C₂²×C₇	C₂×Q₈	1	1	yes	characteristic
32	C₂²×C₇	#41	1	2	yes	—
33	C₄×C₇	—	2	2	no	—
34	C₄×C₇	C₄²	1	4	yes	complemented
35	C₄×C₇	C₄⋊C₄	1	4	yes	complemented
36	Dic₇	—	2	8	no	—
37	C₂²×C₄	—	7	4	no	—
38	C₂²×C₄	C₂×D₇	1	1	yes	characteristic
39	C₂²×C₄	C₂×D₇	1	1	yes	characteristic
40	C₂²×C₄	C₂×D₇	1	1	yes	characteristic
41	C₄⋊C₄	—	7	8	no	—
42	C₄²	—	14	4	no	—
43	C₄²	Dic₇	1	4	yes	complemented
44	C₂×C₇	C₂×C₄²	1	1	yes	characteristic
45	C₂×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
46	C₂×C₇	#117	1	1	yes	characteristic
47	C₂×C₇	C₄×D₄	1	2	yes	—
48	C₂×C₇	C₄×Q₈	1	2	yes	—
49	C₂³	C₂²×D₇	1	1	yes	characteristic
50	C₂×C₄	—	2	2	no	—
51	C₂×C₄	—	7	8	no	—
52	C₂×C₄	—	14	4	no	—
53	C₂×C₄	—	14	4	no	—
54	C₂×C₄	Dic₁₄	1	2	yes	—
55	C₂×C₄	C₄×D₇	1	4	yes	—
56	C₂×C₄	D₂₈	1	2	yes	—
57	C₂×C₄	C₂×Dic₇	1	2	yes	—
58	C₂×C₄	C₂×Dic₇	1	2	yes	—
59	C₂×C₄	C₂×Dic₇	1	2	yes	—
60	C₇	C₄×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
61	C₂²	C₂×Dic₁₄	1	1	yes	characteristic
62	C₂²	C₂×C₄×D₇	1	2	yes	—
63	C₂²	C₂×D₂₈	1	1	yes	characteristic
64	C₂²	#1157	1	2	yes	—
65	C₂²	C₂²×Dic₇	1	1	yes	characteristic
66	C₄	—	2	2	no	—
67	C₄	—	14	8	no	—
68	C₄	C₄×Dic₇	1	4	yes	complemented
69	C₄	C₄⋊Dic₇	1	4	yes	direct product factor
70	C₂	C₄×Dic₁₄	1	2	yes	—
71	C₂	C₄×D₂₈	1	2	yes	—
72	C₂	C₂×C₄×Dic₇	1	1	yes	characteristic
73	C₂	C₂×C₄⋊Dic₇	1	1	yes	characteristic
74	C₂	#6489	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₇
commutator	C₂×C₇	C₂×C₄²
Frattini	C₂³	C₂²×D₇
Fitting	C₂×C₄²×C₇	C₂
socle, prime radical, cosocle	C₂³×C₇	C₂³
hypercenter	C₂×C₄²	D₇
hypocenter	C₇	C₄×C₄⋊C₄
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
9. C₄²×C₇	C₄	semidirect
10. C₄⋊Dic₇	C₄	direct (N × H)
34. C₄×C₇	C₄²	semidirect
35. C₄×C₇	C₄⋊C₄	semidirect
43. C₄²	Dic₇	semidirect
60. C₇	C₄×C₄⋊C₄	semidirect
68. C₄	C₄×Dic₇	semidirect
69. C₄	C₄⋊Dic₇	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×C₄²×C₇	2
C₂×C₄⋊Dic₇	2
C₂×C₄×Dic₇	2
C₇⋊#95	2
C₄×C₄⋊C₄	7

Subgroups — C4×C4⋊Dic7 #89706

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₄⋊Dic₇ #89706