Subgroups — #20267530

Order 6592.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15693009	C₂	1	1	yes	maximal, characteristic
2	#15692932	C₂	1	1	yes	maximal, characteristic, complemented
3	#97×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×Dic₂₀₆	C₄	1	1	yes	characteristic
5	C₂×D₄₁₂	C₄	1	1	yes	characteristic
6	C₂×C₁₀₃⋊C₈	—	2	1	no	—
7	(C₂×D₁₀₃)⋊C₄	—	2	1	no	—
8	(C₂×D₁₀₃)⋊C₄	—	2	1	no	—
9	C₂×C₈×C₁₀₃	—	2	1	no	—
10	C₄²×C₁₀₃	C₂²	1	1	yes	characteristic
11	C₂²×D₁₀₃	—	2	1	no	—
12	C₂×C₄×C₁₀₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄×C₁₀₃	D₄	1	1	yes	characteristic
14	C₂×C₄×C₁₀₃	D₄	1	1	yes	characteristic
15	C₂×Dic₁₀₃	—	2	1	no	—
16	D₄₁₂	—	4	1	no	—
17	Dic₂₀₆	—	4	1	no	—
18	C₈×C₁₀₃	—	2	2	no	—
19	C₁₀₃⋊C₈	—	2	2	no	—
20	C₂²×C₁₀₃	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×D₁₀₃	—	4	1	no	—
22	C₂×D₁₀₃	—	4	1	no	—
23	C₂×D₁₀₃	—	4	1	no	—
24	C₄×C₁₀₃	—	2	1	no	—
25	C₄×C₁₀₃	—	2	1	no	—
26	C₄×C₁₀₃	—	2	1	no	—
27	Dic₁₀₃	—	4	1	no	—
28	C₂×C₁₀₃	#100	1	1	yes	characteristic
29	C₂×C₁₀₃	#104	1	1	yes	characteristic
30	C₂×C₁₀₃	#104	1	1	yes	characteristic
31	D₁₀₃	—	8	1	no	—
32	C₁₀₃	#329	1	1	yes	characteristic, complemented, Sylow
33	#329	—	103	1	no	maximal, Sylow
34	#124	—	103	1	no	—
35	#97	—	103	1	no	—
36	#97	D₁₀₃	1	1	yes	characteristic, complemented
37	C₂×Q₈	—	103	1	no	—
38	C₂×D₄	—	103	1	no	—
39	C₂×C₈	—	2	1	no	—
40	C₂×C₈	—	206	1	no	—
41	C₂²⋊C₄	—	206	1	no	—
42	C₂²⋊C₄	—	206	1	no	—
43	C₄²	C₂×D₁₀₃	1	1	yes	characteristic
44	C₂³	—	206	1	no	—
45	Q₈	—	412	1	no	—
46	D₄	—	412	1	no	—
47	C₂×C₄	—	206	1	no	—
48	C₂×C₄	C₄×D₁₀₃	1	1	yes	characteristic
49	C₂×C₄	D₄₁₂	1	1	yes	characteristic
50	C₂×C₄	C₂²⋊D₁₀₃	1	1	yes	characteristic
51	C₈	—	2	2	no	—
52	C₈	—	206	2	no	—
53	C₂²	—	412	1	no	—
54	C₂²	—	412	1	no	—
55	C₂²	—	412	1	no	—
56	C₂²	(C₂×D₁₀₃)⋊C₄	1	1	yes	characteristic
57	C₄	—	2	1	no	—
58	C₄	—	2	1	no	—
59	C₄	—	2	1	no	—
60	C₄	—	412	1	no	—
61	C₂	—	824	1	no	—
62	C₂	#15692937	1	1	yes	characteristic
63	C₂	#15692947	1	1	yes	characteristic
64	C₂	#15692949	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	(C₂×D₁₀₃)⋊C₄
commutator	C₂×C₄×C₁₀₃	C₂×C₄
Frattini	C₄²	C₂×D₁₀₃
Fitting	#97×C₁₀₃	C₂
socle	C₂²×C₁₀₃	C₂²⋊C₄
hypercenter	#97	D₁₀₃
hypocenter	C₁₀₃	#329
LCS	G ▷ C₂×C₄×C₁₀₃ ▷ C₂²×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
2. #15692932	C₂	semidirect
3. #97×C₁₀₃	C₂	semidirect
32. C₁₀₃	#329	semidirect
36. #97	D₁₀₃	semidirect