Subgroups — C₄×C₇×C₂²⋊C₄ #90023

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×C₇×C₂²⋊C₄	C₂	1	2	yes	maximal
3	C₂×C₄²×C₇	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	4	yes	—
10	C₂²×C₄×C₇	C₂²	1	1	yes	characteristic
11	C₇×C₂²⋊C₄	C₄	1	8	yes	direct product factor
12	C₄²×C₇	—	2	4	no	—
13	C₄×C₂²⋊C₄	C₇	1	1	yes	maximal, characteristic, direct product factor, 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	4	no	—
20	C₂×C₄×C₇	—	2	2	no	—
21	C₂×C₄×C₇	—	2	4	no	—
22	C₂×C₄×C₇	—	2	8	no	—
23	C₂×C₄×C₇	C₂×C₄	1	2	yes	—
24	C₂×C₄×C₇	C₂×C₄	1	2	yes	—
25	C₂×C₄×C₇	C₂×C₄	1	8	yes	complemented
26	C₂×C₄×C₇	D₄	1	4	yes	—
27	C₂³×C₄	C₂×C₇	1	1	yes	characteristic
28	C₂×C₂²⋊C₄	C₂×C₇	1	2	yes	—
29	C₂×C₄²	C₂×C₇	1	2	yes	complemented
30	#95	C₂×C₇	1	2	yes	complemented
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	1	yes	characteristic
36	C₂²×C₇	C₂²×C₄	1	2	yes	—
37	C₂²×C₇	C₂×D₄	1	2	yes	—
38	C₂²×C₇	#41	1	2	yes	—
39	C₄×C₇	—	2	2	no	—
40	C₄×C₇	—	2	8	no	—
41	C₄×C₇	C₂²⋊C₄	1	4	yes	direct product factor
42	C₂⁴	C₂²×C₇	1	1	yes	characteristic
43	C₂²×C₄	—	2	4	no	—
44	C₂²×C₄	C₄×C₇	1	4	yes	complemented
45	C₂²×C₄	C₂²×C₇	1	1	yes	characteristic
46	C₂²×C₄	C₂²×C₇	1	4	yes	—
47	C₂²×C₄	C₂²×C₇	1	1	yes	characteristic
48	C₂²⋊C₄	C₄×C₇	1	8	yes	direct product factor
49	C₄²	—	2	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	C₂×C₄×C₇	1	4	yes	—
58	C₂³	C₂×C₄×C₇	1	2	yes	—
59	C₂³	C₂³×C₇	1	1	yes	characteristic
60	C₂×C₄	—	2	4	no	—
61	C₂×C₄	—	2	2	no	—
62	C₂×C₄	—	2	4	no	—
63	C₂×C₄	—	2	8	no	—
64	C₂×C₄	C₂×C₄×C₇	1	2	yes	—
65	C₂×C₄	C₂×C₄×C₇	1	2	yes	—
66	C₂×C₄	C₂×C₄×C₇	1	8	yes	complemented
67	C₂×C₄	C₇×D₄	1	4	yes	—
68	C₇	C₄×C₂²⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
69	C₂²	—	2	2	no	—
70	C₂²	—	2	2	no	—
71	C₂²	—	2	8	no	—
72	C₂²	C₄²×C₇	1	4	yes	complemented
73	C₂²	C₂²×C₄×C₇	1	1	yes	characteristic
74	C₂²	C₂²×C₄×C₇	1	2	yes	—
75	C₂²	C₂×C₇×D₄	1	2	yes	—
76	C₂²	C₇×#41	1	2	yes	—
77	C₄	—	2	2	no	—
78	C₄	—	2	8	no	—
79	C₄	C₇×C₂²⋊C₄	1	4	yes	direct product factor
80	C₂	—	2	4	no	—
81	C₂	C₂×C₄²×C₇	1	1	yes	characteristic
82	C₂	C₂×C₇×C₂²⋊C₄	1	1	yes	characteristic
83	C₂	C₇×#117	1	1	yes	characteristic
84	C₂	C₄×C₇×D₄	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₂×C₄²×C₇	C₂	semidirect
4. C₇×#95	C₂	semidirect
7. C₂²×C₄×C₇	C₄	semidirect
11. C₇×C₂²⋊C₄	C₄	direct (N × H)
13. C₄×C₂²⋊C₄	C₇	direct (N × H)
25. C₂×C₄×C₇	C₂×C₄	semidirect
29. C₂×C₄²	C₂×C₇	semidirect
30. #95	C₂×C₇	semidirect
34. C₂²×C₇	C₄²	semidirect
41. C₄×C₇	C₂²⋊C₄	direct (N × H)
44. C₂²×C₄	C₄×C₇	semidirect
48. C₂²⋊C₄	C₄×C₇	direct (N × H)
66. C₂×C₄	C₂×C₄×C₇	semidirect
68. C₇	C₄×C₂²⋊C₄	direct (N × H)
72. C₂²	C₄²×C₇	semidirect
79. C₄	C₇×C₂²⋊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
C₂×C₇×C₂²⋊C₄	2
C₂×C₄²×C₇	2
C₇×#95	2
C₄×C₂²⋊C₄	7

Subgroups — C4×C7×C22⋊C4 #90023

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₇×C₂²⋊C₄ #90023