Subgroups — #20268128

Order 6592.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15693001	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₄×D₁₀₃	C₂	1	1	yes	maximal, characteristic
3	#15692954	C₂	1	1	yes	maximal, characteristic, complemented
4	#15692946	C₂	1	1	yes	maximal, characteristic, complemented
5	#15692944	C₂	1	1	yes	maximal, characteristic, complemented
6	(C₂×D₁₀₃)⋊C₈	C₂	1	1	yes	maximal, characteristic
7	#107×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₂₀₆	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₁₀₃	—	2	1	no	—
10	C₂×C₄×D₁₀₃	C₂²	1	1	yes	characteristic
11	C₂×C₁₀₃⋊C₈	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₁₀₃	—	2	1	no	—
13	C₄⋊Dic₁₀₃	C₂²	1	1	yes	characteristic
14	Dic₁₀₃⋊C₄	—	2	1	no	—
15	(C₂×D₁₀₃)⋊C₄	—	2	1	no	—
16	C₂×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
17	C₄⋊C₄×C₁₀₃	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₁₀₃	C₂²	1	1	yes	characteristic
19	C₂²×D₁₀₃	D₄	1	1	yes	characteristic
20	C₂×C₄×C₁₀₃	—	2	1	no	—
21	C₂×C₄×C₁₀₃	—	2	1	no	—
22	C₂×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
23	C₂×Dic₁₀₃	—	2	1	no	—
24	C₂×Dic₁₀₃	—	2	1	no	—
25	C₂×Dic₁₀₃	D₄	1	1	yes	characteristic
26	C₄×D₁₀₃	—	2	1	no	—
27	C₄×D₁₀₃	—	2	1	no	—
28	C₄×D₁₀₃	—	4	2	no	—
29	Dic₂₀₆	—	2	1	no	—
30	Dic₂₀₆	—	2	1	no	—
31	C₈×C₁₀₃	—	2	1	no	—
32	C₁₀₃⋊C₈	—	2	1	no	—
33	C₂²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
34	C₂×D₁₀₃	—	2	1	no	—
35	C₂×D₁₀₃	—	2	1	no	—
36	C₂×D₁₀₃	Q₁₆	1	2	yes	—
37	C₄×C₁₀₃	—	4	1	no	—
38	C₄×C₁₀₃	—	4	1	no	—
39	C₄×C₁₀₃	#41	1	1	yes	characteristic
40	C₄×C₁₀₃	#41	1	1	yes	characteristic
41	Dic₁₀₃	—	2	1	no	—
42	Dic₁₀₃	—	4	1	no	—
43	Dic₁₀₃	—	4	1	no	—
44	C₂×C₁₀₃	#123	1	1	yes	characteristic
45	C₂×C₁₀₃	C₂×Q₁₆	1	1	yes	characteristic
46	C₂×C₁₀₃	AGL(1,ℤ/8)	1	1	yes	characteristic
47	D₁₀₃	—	2	2	no	—
48	C₁₀₃	#484	1	1	yes	characteristic, complemented, Sylow
49	#484	—	103	1	no	maximal, Sylow
50	C₂²⋊Q₈	—	103	1	no	—
51	C₂×C₄⋊C₄	—	103	1	no	—
52	#107	—	103	1	no	—
53	#107	D₁₀₃	1	1	yes	characteristic, complemented
54	#103	—	103	1	no	—
55	#103	—	103	1	no	—
56	C₂²⋊C₈	—	103	1	no	—
57	C₂×Q₈	—	103	1	no	—
58	C₂²×C₄	—	103	1	no	—
59	C₂²×C₄	—	206	1	no	—
60	C₂×C₈	—	103	1	no	—
61	C₂×C₈	C₂×D₁₀₃	1	1	yes	characteristic
62	C₄⋊C₄	—	103	1	no	—
63	C₄⋊C₄	—	206	1	no	—
64	C₄⋊C₄	—	206	1	no	—
65	C₄⋊C₄	C₂×D₁₀₃	1	1	yes	characteristic
66	C₄⋊C₄	C₂×D₁₀₃	1	1	yes	characteristic
67	C₂²⋊C₄	—	206	1	no	—
68	C₂³	—	103	1	no	—
69	Q₈	—	206	1	no	—
70	Q₈	—	206	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	2	1	no	—
73	C₂×C₄	—	103	1	no	—
74	C₂×C₄	—	412	2	no	—
75	C₂×C₄	—	206	1	no	—
76	C₂×C₄	—	206	1	no	—
77	C₂×C₄	—	206	1	no	—
78	C₂×C₄	—	206	1	no	—
79	C₂×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
80	C₈	—	2	1	no	—
81	C₈	—	206	1	no	—
82	C₂²	—	103	2	no	—
83	C₂²	—	206	1	no	—
84	C₂²	—	206	1	no	—
85	C₂²	D₄×D₁₀₃	1	1	yes	characteristic
86	C₄	—	4	1	no	—
87	C₄	—	4	1	no	—
88	C₄	—	412	1	no	—
89	C₄	—	412	1	no	—
90	C₄	—	206	1	no	—
91	C₄	#13110105	1	1	yes	characteristic
92	C₄	#13110106	1	1	yes	characteristic
93	C₂	—	206	2	no	—
94	C₂	#15693006	1	1	yes	characteristic
95	C₂	Q₁₆×D₁₀₃	1	1	yes	characteristic
96	C₂	#15693045	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₀₃
commutator	C₂×C₄×C₁₀₃	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₃
Fitting	#107×C₁₀₃	C₂
socle	C₂²×C₁₀₃	C₂×D₄
hypercenter	#107	D₁₀₃
hypocenter	C₁₀₃	#484
LCS	G ▷ C₂×C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
3. #15692954	C₂	semidirect
4. #15692946	C₂	semidirect
5. #15692944	C₂	semidirect
7. #107×C₁₀₃	C₂	semidirect
48. C₁₀₃	#484	semidirect
53. #107	D₁₀₃	semidirect