Subgroups — C₄×C₂²⋊Dic₇ #89981

Order 448.

258 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	C₂×C₂²⋊Dic₇	C₂	1	2	yes	maximal
3	C₂×C₄×Dic₇	C₂	1	2	yes	maximal, complemented
4	C₇⋊#95	C₂	1	2	yes	maximal, complemented
5	C₂⁴×C₇	C₂²	1	1	yes	characteristic
6	C₂²×C₄×C₇	—	2	4	no	—
7	C₂²×C₄×C₇	C₄	1	4	yes	complemented
8	C₂²×C₄×C₇	C₂²	1	1	yes	characteristic
9	C₂²×C₄×C₇	C₂²	1	1	yes	characteristic
10	C₂²×Dic₇	C₂²	1	4	yes	—
11	C₂²⋊Dic₇	C₄	1	8	yes	direct product factor
12	C₄×Dic₇	—	2	4	no	—
13	C₄×C₂²⋊C₄	—	7	1	no	maximal, Sylow
14	C₂³×C₇	—	2	2	no	—
15	C₂³×C₇	—	2	2	no	—
16	C₂³×C₇	C₂×C₄	1	4	yes	—
17	C₂³×C₇	C₂×C₄	1	2	yes	—
18	C₂³×C₇	C₂³	1	1	yes	characteristic
19	C₂×C₄×C₇	—	2	2	no	—
20	C₂×C₄×C₇	—	2	8	no	—
21	C₂×C₄×C₇	C₂×C₄	1	2	yes	—
22	C₂×C₄×C₇	C₂×C₄	1	2	yes	—
23	C₂×C₄×C₇	D₄	1	4	yes	—
24	C₂×Dic₇	—	2	4	no	—
25	C₂×Dic₇	—	2	4	no	—
26	C₂×Dic₇	C₂×C₄	1	8	yes	complemented
27	C₂³×C₄	D₇	1	1	yes	characteristic
28	C₂×C₂²⋊C₄	—	7	2	no	—
29	C₂×C₄²	—	7	2	no	—
30	#95	—	7	2	no	—
31	C₂²×C₇	—	2	2	no	—
32	C₂²×C₇	—	2	2	no	—
33	C₂²×C₇	—	2	8	no	—
34	C₂²×C₇	C₄²	1	4	yes	complemented
35	C₂²×C₇	C₂²×C₄	1	2	yes	—
36	C₂²×C₇	C₂²×C₄	1	1	yes	characteristic
37	C₂²×C₇	C₂×D₄	1	2	yes	—
38	C₂²×C₇	#41	1	2	yes	—
39	C₄×C₇	—	2	2	no	—
40	C₄×C₇	C₂²⋊C₄	1	4	yes	complemented
41	Dic₇	—	2	8	no	—
42	C₂⁴	C₂×D₇	1	1	yes	characteristic
43	C₂²×C₄	—	2	4	no	—
44	C₂²×C₄	—	7	4	no	—
45	C₂²×C₄	Dic₇	1	4	yes	complemented
46	C₂²×C₄	C₂×D₇	1	1	yes	characteristic
47	C₂²×C₄	C₂×D₇	1	1	yes	characteristic
48	C₂²⋊C₄	—	7	8	no	—
49	C₄²	—	14	4	no	—
50	C₂×C₇	—	2	4	no	—
51	C₂×C₇	C₂×C₄²	1	1	yes	characteristic
52	C₂×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
53	C₂×C₇	#117	1	1	yes	characteristic
54	C₂×C₇	C₄×D₄	1	4	yes	—
55	C₂³	—	2	2	no	—
56	C₂³	—	2	2	no	—
57	C₂³	C₄×D₇	1	4	yes	—
58	C₂³	C₂×Dic₇	1	2	yes	—
59	C₂³	C₂²×D₇	1	1	yes	characteristic
60	C₂×C₄	—	2	2	no	—
61	C₂×C₄	—	2	8	no	—
62	C₂×C₄	—	7	8	no	—
63	C₂×C₄	—	14	4	no	—
64	C₂×C₄	—	14	4	no	—
65	C₂×C₄	C₂×Dic₇	1	2	yes	—
66	C₂×C₄	C₂×Dic₇	1	2	yes	—
67	C₂×C₄	C₂²⋊D₇	1	4	yes	—
68	C₇	C₄×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
69	C₂²	—	2	2	no	—
70	C₂²	—	2	8	no	—
71	C₂²	—	2	2	no	—
72	C₂²	C₄×Dic₇	1	4	yes	complemented
73	C₂²	C₂×C₄×D₇	1	2	yes	—
74	C₂²	#1157	1	2	yes	—
75	C₂²	C₂²×Dic₇	1	1	yes	characteristic
76	C₂²	C₂×C₂²⋊D₇	1	2	yes	—
77	C₄	—	2	2	no	—
78	C₄	—	14	8	no	—
79	C₄	C₂²⋊Dic₇	1	4	yes	direct product factor
80	C₂	—	2	4	no	—
81	C₂	C₂×C₄×Dic₇	1	1	yes	characteristic
82	C₂	#6489	1	1	yes	characteristic
83	C₂	C₄×C₂²⋊D₇	1	4	yes	—
84	C₂	C₂×C₂²⋊Dic₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₇
commutator	C₂×C₇	C₂×C₄²
Frattini	C₂³	C₂²×D₇
Fitting	C₂³×C₄×C₇	C₂
socle, cosocle	C₂³×C₇	C₂³
prime radical	C₂⁴×C₇	C₂²
hypercenter	C₂³×C₄	D₇
hypocenter	C₇	C₄×C₂²⋊C₄
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×Dic₇	C₂	semidirect
4. C₇⋊#95	C₂	semidirect
7. C₂²×C₄×C₇	C₄	semidirect
11. C₂²⋊Dic₇	C₄	direct (N × H)
26. C₂×Dic₇	C₂×C₄	semidirect
34. C₂²×C₇	C₄²	semidirect
40. C₄×C₇	C₂²⋊C₄	semidirect
45. C₂²×C₄	Dic₇	semidirect
68. C₇	C₄×C₂²⋊C₄	semidirect
72. C₂²	C₄×Dic₇	semidirect
79. C₄	C₂²⋊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
C₂³×C₄×C₇	2
C₂×C₂²⋊Dic₇	2
C₂×C₄×Dic₇	2
C₇⋊#95	2
C₄×C₂²⋊C₄	7

Subgroups — C4×C22⋊Dic7 #89981

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₂²⋊Dic₇ #89981