Subgroups — C₄×C₄⋊(C₇⋊D₇) #13096513

Order 1568.

470 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊(C₇⋊D₇)	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₇⋊D₇	C₂	1	2	yes	maximal, complemented
3	C₄²×C₇²	C₂	1	1	yes	maximal, characteristic, complemented
4	#11716070	C₂	1	2	yes	maximal, complemented
5	C₄⋊(C₇⋊Dic₇)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₇⋊D₇	C₂²	1	2	yes	—
7	C₂×C₄×C₇²	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₇²	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₇²	C₂²	1	1	yes	characteristic
10	C₂×C₇⋊Dic₇	C₂²	1	2	yes	—
11	C₄⋊(C₇⋊D₇)	C₄	1	4	yes	direct product factor
12	C₄×C₇⋊D₇	—	2	4	no	—
13	C₄×D₂₈	—	7	8	no	maximal
14	C₂²×C₇²	C₂³	1	1	yes	characteristic
15	C₂×C₇⋊D₇	—	2	2	no	—
16	C₂×C₇⋊D₇	—	2	2	no	—
17	C₂×C₇⋊D₇	C₂×C₄	1	4	yes	complemented
18	C₄×C₇²	—	2	1	no	—
19	C₄×C₇²	C₂×C₄	1	2	yes	complemented
20	C₄×C₇²	D₄	1	2	yes	complemented
21	C₇⋊Dic₇	—	2	2	no	—
22	C₂×D₂₈	—	7	8	no	—
23	C₂×C₄×D₇	—	7	16	no	—
24	C₄²×C₇	D₇	1	8	yes	complemented
25	(C₂×D₇)⋊C₄	—	7	16	no	—
26	C₄⋊Dic₇	—	7	8	no	—
27	C₂×C₇²	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₇²	C₂×D₄	1	1	yes	characteristic
29	C₂×C₇²	#41	1	1	yes	characteristic
30	C₇⋊D₇	—	2	4	no	—
31	C₂²×D₇	—	7	16	no	—
32	C₂×C₄×C₇	C₂×D₇	1	8	yes	—
33	C₂×C₄×C₇	C₂×D₇	1	8	yes	—
34	C₂×C₄×C₇	C₂×D₇	1	8	yes	—
35	C₂×Dic₇	—	7	16	no	—
36	D₂₈	—	7	32	no	—
37	C₄×D₇	—	14	32	no	—
38	C₇²	C₄×D₄	1	1	yes	characteristic, complemented, Sylow
39	C₄×D₄	—	49	1	no	Sylow
40	C₂²×C₇	C₂²×D₇	1	8	yes	—
41	C₂×D₇	—	7	32	no	—
42	C₂×D₇	—	14	16	no	—
43	C₂×D₇	—	14	16	no	—
44	C₄×C₇	—	2	8	no	—
45	C₄×C₇	C₄×D₇	1	16	yes	complemented
46	C₄×C₇	D₂₈	1	16	yes	complemented
47	Dic₇	—	14	16	no	—
48	C₂×D₄	—	49	1	no	—
49	C₂²×C₄	—	49	2	no	—
50	C₄⋊C₄	—	49	1	no	—
51	C₂²⋊C₄	—	49	2	no	—
52	C₄²	C₇⋊D₇	1	1	yes	characteristic, complemented
53	C₂×C₇	C₂×C₄×D₇	1	8	yes	—
54	C₂×C₇	C₂×D₂₈	1	8	yes	—
55	C₂×C₇	#1157	1	8	yes	—
56	D₇	—	14	32	no	—
57	C₂³	—	49	2	no	—
58	D₄	—	49	4	no	—
59	C₂×C₄	—	49	2	no	—
60	C₂×C₄	—	98	4	no	—
61	C₂×C₄	C₂×C₇⋊D₇	1	1	yes	characteristic
62	C₂×C₄	C₂×C₇⋊D₇	1	1	yes	characteristic
63	C₂×C₄	C₂×C₇⋊D₇	1	1	yes	characteristic
64	C₇	C₄×D₂₈	1	8	yes	complemented
65	C₂²	—	49	4	no	—
66	C₂²	—	98	2	no	—
67	C₂²	—	98	2	no	—
68	C₂²	C₂²×C₇⋊D₇	1	1	yes	characteristic
69	C₄	—	2	1	no	—
70	C₄	—	98	2	no	—
71	C₄	C₄×C₇⋊D₇	1	2	yes	complemented
72	C₄	C₄⋊(C₇⋊D₇)	1	2	yes	direct product factor
73	C₂	—	98	4	no	—
74	C₂	C₂×C₄×C₇⋊D₇	1	1	yes	characteristic
75	C₂	C₂×C₄⋊(C₇⋊D₇)	1	1	yes	characteristic
76	C₂	#11716129	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₇⋊D₇
commutator	C₂×C₇²	C₂²×C₄
Frattini	C₂²	C₂²×C₇⋊D₇
Fitting	C₄²×C₇²	C₂
socle, cosocle	C₂²×C₇²	C₂³
prime radical	C₂×C₄⋊(C₇⋊D₇)	C₂
hypercenter	C₄²	C₇⋊D₇
hypocenter	C₇²	C₄×D₄
LCS	G ▷ C₂×C₇² ▷ C₇²
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₇⋊D₇	C₂	semidirect
3. C₄²×C₇²	C₂	semidirect
4. #11716070	C₂	semidirect
5. C₄⋊(C₇⋊Dic₇)	C₂	semidirect
11. C₄⋊(C₇⋊D₇)	C₄	direct (N × H)
17. C₂×C₇⋊D₇	C₂×C₄	semidirect
19. C₄×C₇²	C₂×C₄	semidirect
20. C₄×C₇²	D₄	semidirect
24. C₄²×C₇	D₇	semidirect
38. C₇²	C₄×D₄	semidirect
45. C₄×C₇	C₄×D₇	semidirect
46. C₄×C₇	D₂₈	semidirect
52. C₄²	C₇⋊D₇	semidirect
64. C₇	C₄×D₂₈	semidirect
71. C₄	C₄×C₇⋊D₇	semidirect
72. C₄	C₄⋊(C₇⋊D₇)	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×C₄⋊(C₇⋊D₇)	2
C₂×C₄×C₇⋊D₇	2
C₄²×C₇²	2
#11716070	2
C₄⋊(C₇⋊Dic₇)	2
C₄×D₂₈	7

Subgroups — C4×C4⋊(C7⋊D7) #13096513

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₄⋊(C₇⋊D₇) #13096513