Subgroups — #20267799

Order 6592.

150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₂₀₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#13110089	C₂	1	1	yes	maximal, characteristic
3	#15692944	C₂	1	4	yes	maximal, complemented
4	#117×C₁₀₃	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₂₀₆	—	2	2	no	—
6	C₂×Dic₂₀₆	—	2	1	no	—
7	C₂×Dic₂₀₆	C₄	1	4	yes	complemented
8	C₂×Dic₂₀₆	C₂²	1	2	yes	—
9	C₂²×Dic₁₀₃	—	2	1	no	—
10	#13110089	—	2	2	no	—
11	C₂×C₁₀₃⋊C₈	C₂²	1	2	yes	—
12	C₂²×C₄×C₁₀₃	C₂²	1	1	yes	characteristic
13	C₄⋊C₄×C₁₀₃	C₂²	1	2	yes	—
14	C₂²⋊C₄×C₁₀₃	—	2	1	no	—
15	C₄²×C₁₀₃	—	2	1	no	—
16	C₂³×C₁₀₃	D₄	1	1	yes	characteristic
17	C₂×C₄×C₁₀₃	—	2	2	no	—
18	C₂×C₄×C₁₀₃	C₂×C₄	1	2	yes	—
19	C₂×C₄×C₁₀₃	D₄	1	2	yes	—
20	C₂×C₄×C₁₀₃	D₄	1	1	yes	characteristic
21	C₂×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
22	C₂×Dic₁₀₃	—	2	4	no	—
23	C₂×Dic₁₀₃	—	2	2	no	—
24	Dic₂₀₆	—	2	4	no	—
25	Dic₂₀₆	—	2	2	no	—
26	Dic₂₀₆	C₂×C₄	1	4	yes	—
27	C₁₀₃⋊C₈	—	2	2	no	—
28	C₂²×C₁₀₃	—	2	2	no	—
29	C₂²×C₁₀₃	C₂²⋊C₄	1	2	yes	—
30	C₂²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
31	C₄×C₁₀₃	—	4	2	no	—
32	C₄×C₁₀₃	C₂²⋊C₄	1	2	yes	—
33	C₄×C₁₀₃	C₂²×C₄	1	1	yes	characteristic
34	C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
35	Dic₁₀₃	—	2	4	no	—
36	C₂×C₁₀₃	—	2	2	no	—
37	C₂×C₁₀₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
38	C₂×C₁₀₃	#137	1	2	yes	—
39	C₁₀₃	#419	1	1	yes	characteristic, complemented, Sylow
40	#419	—	103	1	no	maximal, Sylow
41	C₂²×Q₈	—	103	1	no	—
42	C₂×M₁₆	—	103	1	no	—
43	#117	D₁₀₃	1	1	yes	characteristic
44	#103	—	103	4	no	—
45	C₂×Q₈	—	103	4	no	—
46	C₂×Q₈	—	103	2	no	—
47	C₂×Q₈	—	206	2	no	—
48	C₂×Q₈	—	206	1	no	—
49	C₂²×C₄	—	206	1	no	—
50	C₂²×C₄	C₂×D₁₀₃	1	1	yes	characteristic
51	M₁₆	—	206	2	no	—
52	C₂×C₈	—	103	2	no	—
53	C₄⋊C₄	C₂×D₁₀₃	1	2	yes	—
54	C₂²⋊C₄	—	2	1	no	—
55	C₄²	—	2	1	no	—
56	C₂³	C₂²⋊D₁₀₃	1	1	yes	characteristic
57	Q₈	—	103	4	no	—
58	Q₈	—	206	4	no	—
59	Q₈	—	206	2	no	—
60	C₂×C₄	—	2	2	no	—
61	C₂×C₄	—	206	4	no	—
62	C₂×C₄	—	206	2	no	—
63	C₂×C₄	C₄×D₁₀₃	1	2	yes	—
64	C₂×C₄	D₄₁₂	1	2	yes	—
65	C₂×C₄	C₂²⋊D₁₀₃	1	1	yes	characteristic
66	C₂×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
67	C₈	—	206	2	no	—
68	C₂²	—	2	2	no	—
69	C₂²	(C₂×D₁₀₃)⋊C₄	1	2	yes	—
70	C₂²	C₂×C₂²⋊D₁₀₃	1	1	yes	characteristic
71	C₄	—	4	2	no	—
72	C₄	—	206	4	no	—
73	C₄	(C₂×D₁₀₃)⋊C₄	1	2	yes	—
74	C₄	C₂×C₄×D₁₀₃	1	1	yes	characteristic
75	C₄	C₂×D₄₁₂	1	1	yes	characteristic
76	C₂	—	2	2	no	—
77	C₂	C₂×(C₂×D₁₀₃)⋊C₄	1	1	yes	characteristic
78	C₂	#15693051	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₁₀₃
commutator	C₄×C₁₀₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₀₃
Fitting	#117×C₁₀₃	C₂
socle	C₂²×C₁₀₃	C₂×D₄
hypercenter	#117	D₁₀₃
hypocenter	C₁₀₃	#419
LCS	G ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
3. #15692944	C₂	semidirect
7. C₂×Dic₂₀₆	C₄	semidirect
39. C₁₀₃	#419	semidirect