Subgroups — #20267539

Order 6592.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15693021	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₁₀₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₈×C₁₀₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₀₆	C₄	1	2	yes	—
5	C₂×C₁₀₃⋊C₈	—	2	1	no	—
6	C₄⋊Dic₁₀₃	—	2	1	no	—
7	C₄⋊Dic₁₀₃	—	2	1	no	—
8	C₂×C₈×C₁₀₃	—	2	1	no	—
9	C₄²×C₁₀₃	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₁₀₃	C₂×C₄	1	1	yes	characteristic
11	C₂×C₄×C₁₀₃	D₄	1	1	yes	characteristic
12	C₂×C₄×C₁₀₃	D₄	1	1	yes	characteristic
13	C₂×Dic₁₀₃	—	2	2	no	—
14	Dic₂₀₆	—	4	2	no	—
15	C₈×C₁₀₃	—	4	1	no	—
16	C₁₀₃⋊C₈	—	4	1	no	—
17	C₂²×C₁₀₃	C₂²⋊C₄	1	1	yes	characteristic
18	C₄×C₁₀₃	—	2	1	no	—
19	C₄×C₁₀₃	SD₁₆	1	1	yes	characteristic
20	C₄×C₁₀₃	SD₁₆	1	1	yes	characteristic
21	C₄×C₁₀₃	Q₁₆	1	1	yes	characteristic
22	C₄×C₁₀₃	Q₁₆	1	1	yes	characteristic
23	Dic₁₀₃	—	4	2	no	—
24	C₂×C₁₀₃	#100	1	1	yes	characteristic
25	C₂×C₁₀₃	#103	1	1	yes	characteristic
26	C₂×C₁₀₃	#103	1	1	yes	characteristic
27	C₁₀₃	#333	1	1	yes	characteristic, complemented, Sylow
28	#333	—	103	1	no	maximal, Sylow
29	C₄⋊Q₈	—	103	1	no	—
30	C₄⋊C₈	—	103	1	no	—
31	C₄⋊C₈	D₁₀₃	1	1	yes	characteristic
32	C₂×Q₈	—	103	2	no	—
33	C₂×C₈	—	2	1	no	—
34	C₂×C₈	—	206	1	no	—
35	C₄⋊C₄	—	206	1	no	—
36	C₄⋊C₄	—	206	1	no	—
37	C₄²	C₂×D₁₀₃	1	1	yes	characteristic
38	Q₈	—	412	2	no	—
39	C₂×C₄	—	206	2	no	—
40	C₂×C₄	C₄×D₁₀₃	1	1	yes	characteristic
41	C₂×C₄	D₄₁₂	1	1	yes	characteristic
42	C₂×C₄	C₂²⋊D₁₀₃	1	1	yes	characteristic
43	C₈	—	4	1	no	—
44	C₈	—	412	1	no	—
45	C₂²	(C₂×D₁₀₃)⋊C₄	1	1	yes	characteristic
46	C₄	—	2	1	no	—
47	C₄	—	412	2	no	—
48	C₄	#13110093	1	1	yes	characteristic
49	C₄	#13110094	1	1	yes	characteristic
50	C₄	#13110095	1	1	yes	characteristic
51	C₄	Dic₄₁₂	1	1	yes	characteristic
52	C₂	#15692937	1	1	yes	characteristic
53	C₂	#15692944	1	1	yes	characteristic
54	C₂	#15692946	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	#333
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
27. C₁₀₃	#333	semidirect