Subgroups — C₂²×#1141 #90483

Order 448.

338 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₂₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#1141	C₂	1	12	yes	maximal, direct product factor
4	C₂²×C₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂⁴×C₇	—	2	1	no	—
6	C₂³×D₇	—	2	1	no	—
7	C₂×C₇×D₄	—	2	3	no	—
8	C₂×C₇×D₄	C₂²	1	6	yes	complemented
9	C₂²×C₄×C₇	C₂²	1	1	yes	characteristic
10	C₂×D₂₈	—	2	3	no	—
11	C₂×D₂₈	C₂²	1	6	yes	complemented
12	#1141	C₂²	1	16	yes	direct product factor
13	C₂×C₇⋊C₈	C₂²	1	6	yes	complemented
14	C₂²×D₈	—	7	1	no	maximal, Sylow
15	C₂³×C₇	—	2	6	no	—
16	C₂³×C₇	—	4	4	no	—
17	C₂³×C₇	D₄	1	1	yes	characteristic
18	C₂²×D₇	—	2	6	no	—
19	C₂²×D₇	—	4	4	no	—
20	C₇×D₄	—	2	6	no	—
21	C₇×D₄	C₂³	1	4	yes	complemented
22	C₂×C₄×C₇	D₄	1	3	yes	—
23	C₂×C₄×C₇	C₂³	1	3	yes	—
24	D₂₈	—	2	6	no	—
25	D₂₈	C₂³	1	4	yes	complemented
26	C₇⋊C₈	C₂³	1	4	yes	complemented
27	C₂²×D₄	—	7	1	no	—
28	C₂²×D₄	D₇	1	1	yes	characteristic, complemented
29	C₂×D₈	—	7	12	no	—
30	C₂²×C₈	—	7	1	no	—
31	C₂²×C₇	—	2	4	no	—
32	C₂²×C₇	—	4	12	no	—
33	C₂²×C₇	D₈	1	4	yes	complemented
34	C₂²×C₇	C₂×D₄	1	3	yes	—
35	C₂×D₇	—	2	4	no	—
36	C₂×D₇	—	4	12	no	—
37	C₄×C₇	C₂×D₄	1	3	yes	—
38	C₄×C₇	C₂⁴	1	1	yes	characteristic
39	C₂⁴	—	2	1	no	—
40	C₂⁴	—	14	1	no	—
41	C₂×D₄	—	2	3	no	—
42	C₂×D₄	—	7	6	no	—
43	C₂×D₄	—	14	3	no	—
44	C₂×D₄	C₂×D₇	1	6	yes	complemented
45	C₂²×C₄	C₂×D₇	1	1	yes	characteristic
46	D₈	—	7	16	no	—
47	C₂×C₈	—	7	6	no	—
48	C₂×C₇	—	4	4	no	—
49	C₂×C₇	C₂×D₈	1	6	yes	complemented
50	C₂×C₇	C₂²×D₄	1	1	yes	characteristic
51	D₇	—	4	4	no	—
52	C₂³	—	2	6	no	—
53	C₂³	—	4	4	no	—
54	C₂³	—	14	6	no	—
55	C₂³	—	28	4	no	—
56	C₂³	C₂²⋊D₇	1	1	yes	characteristic
57	D₄	—	2	6	no	—
58	D₄	—	7	4	no	—
59	D₄	—	14	6	no	—
60	D₄	C₂²×D₇	1	4	yes	complemented
61	C₂×C₄	C₂²⋊D₇	1	3	yes	—
62	C₂×C₄	C₂²×D₇	1	3	yes	—
63	C₈	—	7	4	no	—
64	C₇	C₂²×D₈	1	1	yes	characteristic, complemented, Sylow
65	C₂²	—	2	4	no	—
66	C₂²	—	4	12	no	—
67	C₂²	—	14	4	no	—
68	C₂²	—	28	12	no	—
69	C₂²	#1141	1	4	yes	direct product factor
70	C₂²	C₂×C₂²⋊D₇	1	3	yes	—
71	C₄	C₂×C₂²⋊D₇	1	3	yes	—
72	C₄	C₂³×D₇	1	1	yes	characteristic
73	C₂	—	4	4	no	—
74	C₂	—	28	4	no	—
75	C₂	C₂×#1141	1	6	yes	direct product factor
76	C₂	C₂²×C₂²⋊D₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊D₇
commutator, cosocle	C₄×C₇	C₂⁴
Frattini	C₄	C₂³×D₇
Fitting	C₂²×C₇×D₄	C₂
socle	C₂³×C₇	D₄
hypercenter	C₂²×D₄	D₇
hypocenter	C₇	C₂²×D₈
LCS	G ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₇×D₄	C₂	semidirect
2. C₂²×D₂₈	C₂	semidirect
3. C₂×#1141	C₂	direct (N × H)
4. C₂²×C₇⋊C₈	C₂	semidirect
8. C₂×C₇×D₄	C₂²	semidirect
11. C₂×D₂₈	C₂²	semidirect
12. #1141	C₂²	direct (N × H)
13. C₂×C₇⋊C₈	C₂²	semidirect
21. C₇×D₄	C₂³	semidirect
25. D₂₈	C₂³	semidirect
26. C₇⋊C₈	C₂³	semidirect
28. C₂²×D₄	D₇	semidirect
33. C₂²×C₇	D₈	semidirect
44. C₂×D₄	C₂×D₇	semidirect
49. C₂×C₇	C₂×D₈	semidirect
60. D₄	C₂²×D₇	semidirect
64. C₇	C₂²×D₈	semidirect
69. C₂²	#1141	direct (N × H)
75. C₂	C₂×#1141	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₇×D₄	2
C₂²×D₂₈	2
C₂×#1141	2
C₂²×C₇⋊C₈	2
C₂²×D₈	7

Subgroups — C22×#1141 #90483

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#1141 #90483