Subgroups — C₂²×#13110090 #20268560

Order 6592.

338 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₄₁₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13110090	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₁₀₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₄×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×D₁₀₃	—	2	1	no	—
6	C₂×D₄₁₂	—	2	3	no	—
7	C₂×D₄₁₂	C₂²	1	6	yes	complemented
8	#13110090	C₂²	1	16	yes	direct product factor
9	C₂×C₁₀₃⋊C₈	C₂²	1	6	yes	complemented
10	C₂⁴×C₁₀₃	—	2	1	no	—
11	C₂×D₄×C₁₀₃	—	2	3	no	—
12	C₂×D₄×C₁₀₃	C₂²	1	6	yes	complemented
13	C₂²×C₄×C₁₀₃	C₂²	1	1	yes	characteristic
14	C₂³×C₁₀₃	—	2	6	no	—
15	C₂³×C₁₀₃	—	4	4	no	—
16	C₂³×C₁₀₃	D₄	1	1	yes	characteristic
17	C₂²×D₁₀₃	—	2	6	no	—
18	C₂²×D₁₀₃	—	4	4	no	—
19	D₄×C₁₀₃	—	2	6	no	—
20	D₄×C₁₀₃	C₂³	1	4	yes	complemented
21	C₂×C₄×C₁₀₃	D₄	1	3	yes	—
22	C₂×C₄×C₁₀₃	C₂³	1	3	yes	—
23	D₄₁₂	—	2	6	no	—
24	D₄₁₂	C₂³	1	4	yes	complemented
25	C₁₀₃⋊C₈	C₂³	1	4	yes	complemented
26	C₂²×C₁₀₃	—	2	4	no	—
27	C₂²×C₁₀₃	—	4	12	no	—
28	C₂²×C₁₀₃	D₈	1	4	yes	complemented
29	C₂²×C₁₀₃	C₂×D₄	1	3	yes	—
30	C₂×D₁₀₃	—	2	4	no	—
31	C₂×D₁₀₃	—	4	12	no	—
32	C₄×C₁₀₃	C₂×D₄	1	3	yes	—
33	C₄×C₁₀₃	C₂⁴	1	1	yes	characteristic
34	C₂×C₁₀₃	—	4	4	no	—
35	C₂×C₁₀₃	C₂×D₈	1	6	yes	complemented
36	C₂×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
37	D₁₀₃	—	4	4	no	—
38	C₁₀₃	C₂²×D₈	1	1	yes	characteristic, complemented, Sylow
39	C₂²×D₈	—	103	1	no	maximal, Sylow
40	C₂²×D₄	—	103	1	no	—
41	C₂²×D₄	D₁₀₃	1	1	yes	characteristic, complemented
42	C₂×D₈	—	103	12	no	—
43	C₂²×C₈	—	103	1	no	—
44	C₂⁴	—	2	1	no	—
45	C₂⁴	—	206	1	no	—
46	C₂×D₄	—	2	3	no	—
47	C₂×D₄	—	103	6	no	—
48	C₂×D₄	—	206	3	no	—
49	C₂×D₄	C₂×D₁₀₃	1	6	yes	complemented
50	C₂²×C₄	C₂×D₁₀₃	1	1	yes	characteristic
51	D₈	—	103	16	no	—
52	C₂×C₈	—	103	6	no	—
53	C₂³	—	2	6	no	—
54	C₂³	—	4	4	no	—
55	C₂³	—	412	4	no	—
56	C₂³	—	206	6	no	—
57	C₂³	C₂²⋊D₁₀₃	1	1	yes	characteristic
58	D₄	—	2	6	no	—
59	D₄	—	103	4	no	—
60	D₄	—	206	6	no	—
61	D₄	C₂²×D₁₀₃	1	4	yes	complemented
62	C₂×C₄	C₂²⋊D₁₀₃	1	3	yes	—
63	C₂×C₄	C₂²×D₁₀₃	1	3	yes	—
64	C₈	—	103	4	no	—
65	C₂²	—	2	4	no	—
66	C₂²	—	4	12	no	—
67	C₂²	—	412	12	no	—
68	C₂²	—	206	4	no	—
69	C₂²	#13110090	1	4	yes	direct product factor
70	C₂²	C₂×C₂²⋊D₁₀₃	1	3	yes	—
71	C₄	C₂×C₂²⋊D₁₀₃	1	3	yes	—
72	C₄	C₂³×D₁₀₃	1	1	yes	characteristic
73	C₂	—	4	4	no	—
74	C₂	—	412	4	no	—
75	C₂	C₂×#13110090	1	6	yes	direct product factor
76	C₂	C₂²×C₂²⋊D₁₀₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊D₁₀₃
commutator	C₄×C₁₀₃	C₂⁴
Frattini	C₄	C₂³×D₁₀₃
Fitting	C₂²×D₄×C₁₀₃	C₂
socle	C₂³×C₁₀₃	D₄
hypercenter	C₂²×D₄	D₁₀₃
hypocenter	C₁₀₃	C₂²×D₈
LCS	G ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
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×D₄₁₂	C₂	semidirect
2. C₂×#13110090	C₂	direct (N × H)
3. C₂²×C₁₀₃⋊C₈	C₂	semidirect
4. C₂²×D₄×C₁₀₃	C₂	semidirect
7. C₂×D₄₁₂	C₂²	semidirect
8. #13110090	C₂²	direct (N × H)
9. C₂×C₁₀₃⋊C₈	C₂²	semidirect
12. C₂×D₄×C₁₀₃	C₂²	semidirect
20. D₄×C₁₀₃	C₂³	semidirect
24. D₄₁₂	C₂³	semidirect
25. C₁₀₃⋊C₈	C₂³	semidirect
28. C₂²×C₁₀₃	D₈	semidirect
35. C₂×C₁₀₃	C₂×D₈	semidirect
38. C₁₀₃	C₂²×D₈	semidirect
41. C₂²×D₄	D₁₀₃	semidirect
49. C₂×D₄	C₂×D₁₀₃	semidirect
61. D₄	C₂²×D₁₀₃	semidirect
69. C₂²	#13110090	direct (N × H)
75. C₂	C₂×#13110090	direct (N × H)

Subgroups — C22×#13110090 #20268560

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×#13110090 #20268560