Subgroups — #20267534

Order 6592.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15693018	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₁₀₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊C₈×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄₁₂	—	2	1	no	—
5	C₂×D₄₁₂	—	2	1	no	—
6	C₂×D₄₁₂	C₄	1	2	yes	—
7	C₂×C₁₀₃⋊C₈	—	2	1	no	—
8	C₂×C₈×C₁₀₃	—	2	1	no	—
9	C₄²×C₁₀₃	C₂²	1	1	yes	characteristic
10	C₂²×D₁₀₃	—	2	2	no	—
11	C₂×C₄×C₁₀₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₁₀₃	D₄	1	1	yes	characteristic
13	C₂×C₄×C₁₀₃	D₄	1	1	yes	characteristic
14	D₄₁₂	—	4	2	no	—
15	D₄₁₂	—	4	1	no	—
16	D₄₁₂	—	4	1	no	—
17	D₄₁₂	—	4	1	no	—
18	D₄₁₂	—	4	1	no	—
19	C₈×C₁₀₃	—	4	1	no	—
20	C₁₀₃⋊C₈	—	4	1	no	—
21	C₂²×C₁₀₃	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×D₁₀₃	—	4	2	no	—
23	C₂×D₁₀₃	—	4	2	no	—
24	C₂×D₁₀₃	—	4	2	no	—
25	C₄×C₁₀₃	—	2	1	no	—
26	C₄×C₁₀₃	D₈	1	1	yes	characteristic
27	C₄×C₁₀₃	D₈	1	1	yes	characteristic
28	C₄×C₁₀₃	SD₁₆	1	1	yes	characteristic
29	C₄×C₁₀₃	SD₁₆	1	1	yes	characteristic
30	C₂×C₁₀₃	#100	1	1	yes	characteristic
31	C₂×C₁₀₃	#102	1	1	yes	characteristic
32	C₂×C₁₀₃	#102	1	1	yes	characteristic
33	D₁₀₃	—	8	2	no	—
34	C₁₀₃	#331	1	1	yes	characteristic, complemented, Sylow
35	#331	—	103	1	no	maximal, Sylow
36	#127	—	103	1	no	—
37	C₄⋊C₈	—	103	1	no	—
38	C₄⋊C₈	D₁₀₃	1	1	yes	characteristic, complemented
39	C₂×D₄	—	103	2	no	—
40	C₂×D₄	—	206	1	no	—
41	C₂×D₄	—	206	1	no	—
42	C₂×C₈	—	2	1	no	—
43	C₂×C₈	—	206	1	no	—
44	C₄²	C₂×D₁₀₃	1	1	yes	characteristic
45	C₂³	—	206	2	no	—
46	D₄	—	412	2	no	—
47	D₄	—	412	1	no	—
48	D₄	—	412	1	no	—
49	D₄	—	412	1	no	—
50	D₄	—	412	1	no	—
51	C₂×C₄	C₄×D₁₀₃	1	1	yes	characteristic
52	C₂×C₄	D₄₁₂	1	1	yes	characteristic
53	C₂×C₄	C₂²⋊D₁₀₃	1	1	yes	characteristic
54	C₈	—	4	1	no	—
55	C₈	—	412	1	no	—
56	C₂²	—	412	2	no	—
57	C₂²	—	412	2	no	—
58	C₂²	—	412	2	no	—
59	C₂²	(C₂×D₁₀₃)⋊C₄	1	1	yes	characteristic
60	C₄	—	2	1	no	—
61	C₄	#13110090	1	1	yes	characteristic
62	C₄	D₈₂₄	1	1	yes	characteristic
63	C₄	#13110092	1	1	yes	characteristic
64	C₄	#13110094	1	1	yes	characteristic
65	C₂	—	824	2	no	—
66	C₂	#15692937	1	1	yes	characteristic
67	C₂	#15692941	1	1	yes	characteristic
68	C₂	#15692943	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	(C₂×D₁₀₃)⋊C₄
commutator	C₂×C₄×C₁₀₃	C₂×C₄
Frattini	C₄²	C₂×D₁₀₃
Fitting	C₄⋊C₈×C₁₀₃	C₂
socle	C₂²×C₁₀₃	C₂²⋊C₄
hypercenter	C₄⋊C₈	D₁₀₃
hypocenter	C₁₀₃	#331
LCS	G ▷ C₂×C₄×C₁₀₃ ▷ C₂²×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₄⋊(C₁₀₃⋊C₈)	C₂	semidirect
3. C₄⋊C₈×C₁₀₃	C₂	semidirect
34. C₁₀₃	#331	semidirect
38. C₄⋊C₈	D₁₀₃	semidirect