Subgroups — C₂²×#14268632 #20299367

Order 7232.

338 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₄₅₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14268632	C₂	1	12	yes	maximal, direct product factor
3	C₂²×#11744751	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₄×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×D₁₁₃	—	2	1	no	—
6	C₂×D₄₅₂	—	2	3	no	—
7	C₂×D₄₅₂	C₂²	1	6	yes	complemented
8	#14268632	C₂²	1	16	yes	direct product factor
9	C₂×#11744751	C₂²	1	6	yes	complemented
10	C₂⁴×C₁₁₃	—	2	1	no	—
11	C₂×D₄×C₁₁₃	—	2	3	no	—
12	C₂×D₄×C₁₁₃	C₂²	1	6	yes	complemented
13	C₂²×C₄×C₁₁₃	C₂²	1	1	yes	characteristic
14	C₂³×C₁₁₃	—	2	6	no	—
15	C₂³×C₁₁₃	—	4	4	no	—
16	C₂³×C₁₁₃	D₄	1	1	yes	characteristic
17	C₂²×D₁₁₃	—	2	6	no	—
18	C₂²×D₁₁₃	—	4	4	no	—
19	D₄×C₁₁₃	—	2	6	no	—
20	D₄×C₁₁₃	C₂³	1	4	yes	complemented
21	C₂×C₄×C₁₁₃	D₄	1	3	yes	—
22	C₂×C₄×C₁₁₃	C₂³	1	3	yes	—
23	D₄₅₂	—	2	6	no	—
24	D₄₅₂	C₂³	1	4	yes	complemented
25	#11744751	C₂³	1	4	yes	complemented
26	C₂²×C₁₁₃	—	2	4	no	—
27	C₂²×C₁₁₃	—	4	12	no	—
28	C₂²×C₁₁₃	D₈	1	4	yes	complemented
29	C₂²×C₁₁₃	C₂×D₄	1	3	yes	—
30	C₂×D₁₁₃	—	2	4	no	—
31	C₂×D₁₁₃	—	4	12	no	—
32	C₄×C₁₁₃	C₂×D₄	1	3	yes	—
33	C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
34	C₂×C₁₁₃	—	4	4	no	—
35	C₂×C₁₁₃	C₂×D₈	1	6	yes	complemented
36	C₂×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
37	D₁₁₃	—	4	4	no	—
38	C₁₁₃	C₂²×D₈	1	1	yes	characteristic, complemented, Sylow
39	C₂²×D₈	—	113	1	no	maximal, Sylow
40	C₂²×D₄	—	113	1	no	—
41	C₂²×D₄	D₁₁₃	1	1	yes	characteristic, complemented
42	C₂×D₈	—	113	12	no	—
43	C₂²×C₈	—	113	1	no	—
44	C₂⁴	—	2	1	no	—
45	C₂⁴	—	226	1	no	—
46	C₂×D₄	—	2	3	no	—
47	C₂×D₄	—	113	6	no	—
48	C₂×D₄	—	226	3	no	—
49	C₂×D₄	C₂×D₁₁₃	1	6	yes	complemented
50	C₂²×C₄	C₂×D₁₁₃	1	1	yes	characteristic
51	D₈	—	113	16	no	—
52	C₂×C₈	—	113	6	no	—
53	C₂³	—	2	6	no	—
54	C₂³	—	4	4	no	—
55	C₂³	—	452	4	no	—
56	C₂³	—	226	6	no	—
57	C₂³	C₂²⋊D₁₁₃	1	1	yes	characteristic
58	D₄	—	2	6	no	—
59	D₄	—	113	4	no	—
60	D₄	—	226	6	no	—
61	D₄	C₂²×D₁₁₃	1	4	yes	complemented
62	C₂×C₄	C₂²⋊D₁₁₃	1	3	yes	—
63	C₂×C₄	C₂²×D₁₁₃	1	3	yes	—
64	C₈	—	113	4	no	—
65	C₂²	—	2	4	no	—
66	C₂²	—	4	12	no	—
67	C₂²	—	452	12	no	—
68	C₂²	—	226	4	no	—
69	C₂²	#14268632	1	4	yes	direct product factor
70	C₂²	C₂×C₂²⋊D₁₁₃	1	3	yes	—
71	C₄	C₂×C₂²⋊D₁₁₃	1	3	yes	—
72	C₄	C₂³×D₁₁₃	1	1	yes	characteristic
73	C₂	—	4	4	no	—
74	C₂	—	452	4	no	—
75	C₂	C₂×#14268632	1	6	yes	direct product factor
76	C₂	C₂²×C₂²⋊D₁₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊D₁₁₃
commutator	C₄×C₁₁₃	C₂⁴
Frattini	C₄	C₂³×D₁₁₃
Fitting	C₂²×D₄×C₁₁₃	C₂
socle	C₂³×C₁₁₃	D₄
hypercenter	C₂²×D₄	D₁₁₃
hypocenter	C₁₁₃	C₂²×D₈
LCS	G ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
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×D₄₅₂	C₂	semidirect
2. C₂×#14268632	C₂	direct (N × H)
3. C₂²×#11744751	C₂	semidirect
4. C₂²×D₄×C₁₁₃	C₂	semidirect
7. C₂×D₄₅₂	C₂²	semidirect
8. #14268632	C₂²	direct (N × H)
9. C₂×#11744751	C₂²	semidirect
12. C₂×D₄×C₁₁₃	C₂²	semidirect
20. D₄×C₁₁₃	C₂³	semidirect
24. D₄₅₂	C₂³	semidirect
25. #11744751	C₂³	semidirect
28. C₂²×C₁₁₃	D₈	semidirect
35. C₂×C₁₁₃	C₂×D₈	semidirect
38. C₁₁₃	C₂²×D₈	semidirect
41. C₂²×D₄	D₁₁₃	semidirect
49. C₂×D₄	C₂×D₁₁₃	semidirect
61. D₄	C₂²×D₁₁₃	semidirect
69. C₂²	#14268632	direct (N × H)
75. C₂	C₂×#14268632	direct (N × H)

Subgroups — C22×#14268632 #20299367

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×#14268632 #20299367