Subgroups — C₂²×#1142 #90485

Order 448.

298 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
2	C₂²×Dic₁₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#1142	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	C₂×C₇×D₄	—	2	3	no	—
7	C₂×C₇×D₄	C₂²	1	6	yes	—
8	C₂²×C₄×C₇	C₂²	1	1	yes	characteristic
9	C₂²×Dic₇	—	2	1	no	—
10	C₂×Dic₁₄	—	2	3	no	—
11	C₂×Dic₁₄	C₂²	1	6	yes	complemented
12	#1142	C₂²	1	16	yes	direct product factor
13	C₂×C₇⋊C₈	C₂²	1	6	yes	complemented
14	C₂²×SD₁₆	—	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	C₇×D₄	—	2	6	no	—
19	C₇×D₄	C₂³	1	4	yes	—
20	C₂×C₄×C₇	D₄	1	3	yes	—
21	C₂×C₄×C₇	C₂³	1	3	yes	—
22	C₂×Dic₇	—	2	6	no	—
23	Dic₁₄	—	2	6	no	—
24	Dic₁₄	C₂³	1	4	yes	complemented
25	C₇⋊C₈	C₂³	1	4	yes	complemented
26	C₂²×Q₈	—	7	1	no	—
27	C₂²×D₄	D₇	1	1	yes	characteristic
28	C₂×SD₁₆	—	7	12	no	—
29	C₂²×C₈	—	7	1	no	—
30	C₂²×C₇	—	2	4	no	—
31	C₂²×C₇	—	4	12	no	—
32	C₂²×C₇	SD₁₆	1	4	yes	complemented
33	C₂²×C₇	C₂×D₄	1	3	yes	—
34	C₄×C₇	C₂×D₄	1	3	yes	—
35	C₄×C₇	C₂⁴	1	1	yes	characteristic
36	Dic₇	—	2	4	no	—
37	C₂⁴	—	2	1	no	—
38	C₂×Q₈	—	7	6	no	—
39	C₂×Q₈	—	14	3	no	—
40	C₂×D₄	—	2	3	no	—
41	C₂×D₄	C₂×D₇	1	6	yes	—
42	C₂²×C₄	—	14	1	no	—
43	C₂²×C₄	C₂×D₇	1	1	yes	characteristic
44	SD₁₆	—	7	16	no	—
45	C₂×C₈	—	7	6	no	—
46	C₂×C₇	—	4	4	no	—
47	C₂×C₇	C₂×SD₁₆	1	6	yes	complemented
48	C₂×C₇	C₂²×D₄	1	1	yes	characteristic
49	C₂³	—	2	6	no	—
50	C₂³	—	4	4	no	—
51	C₂³	C₂²⋊D₇	1	1	yes	characteristic
52	Q₈	—	7	4	no	—
53	Q₈	—	14	6	no	—
54	D₄	—	2	6	no	—
55	D₄	C₂²×D₇	1	4	yes	—
56	C₂×C₄	—	14	6	no	—
57	C₂×C₄	C₂²⋊D₇	1	3	yes	—
58	C₂×C₄	C₂²×D₇	1	3	yes	—
59	C₈	—	7	4	no	—
60	C₇	C₂²×SD₁₆	1	1	yes	characteristic, complemented, Sylow
61	C₂²	—	2	4	no	—
62	C₂²	—	4	12	no	—
63	C₂²	#1142	1	4	yes	direct product factor
64	C₂²	C₂×C₂²⋊D₇	1	3	yes	—
65	C₄	—	14	4	no	—
66	C₄	C₂×C₂²⋊D₇	1	3	yes	—
67	C₄	C₂³×D₇	1	1	yes	characteristic
68	C₂	—	4	4	no	—
69	C₂	C₂×#1142	1	6	yes	direct product factor
70	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, prime radical	C₂²×C₇×D₄	C₂
socle	C₂³×C₇	D₄
hypercenter	C₂²×D₄	D₇
hypocenter	C₇	C₂²×SD₁₆
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
2. C₂²×Dic₁₄	C₂	semidirect
3. C₂×#1142	C₂	direct (N × H)
4. C₂²×C₇⋊C₈	C₂	semidirect
11. C₂×Dic₁₄	C₂²	semidirect
12. #1142	C₂²	direct (N × H)
13. C₂×C₇⋊C₈	C₂²	semidirect
24. Dic₁₄	C₂³	semidirect
25. C₇⋊C₈	C₂³	semidirect
32. C₂²×C₇	SD₁₆	semidirect
47. C₂×C₇	C₂×SD₁₆	semidirect
60. C₇	C₂²×SD₁₆	semidirect
63. C₂²	#1142	direct (N × H)
69. C₂	C₂×#1142	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×Dic₁₄	2
C₂×#1142	2
C₂²×C₇⋊C₈	2
C₂²×SD₁₆	7

Subgroups — C22×#1142 #90485

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#1142 #90485