Subgroups — #20268088

Order 6592.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₄₁₂	C₂	1	1	yes	maximal, characteristic
2	#15692954	C₂	1	1	yes	maximal, characteristic, complemented
3	#15692952	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄⋊(C₁₀₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
5	#15692941	C₂	1	1	yes	maximal, characteristic
6	#15692941	C₂	1	1	yes	maximal, characteristic
7	#125×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₄₁₂	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₁₀₃	—	2	1	no	—
10	C₂×C₁₀₃⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×C₁₀₃⋊C₈	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₁₀₃	C₂²	1	1	yes	characteristic
13	(C₂×D₁₀₃)⋊C₄	—	2	1	no	—
14	C₄⋊C₄×C₁₀₃	—	2	1	no	—
15	C₄⋊C₄×C₁₀₃	—	2	1	no	—
16	C₄⋊C₄×C₁₀₃	C₂²	1	1	yes	characteristic
17	C₄⋊C₄×C₁₀₃	C₂²	1	1	yes	characteristic
18	C₄²×C₁₀₃	C₂²	1	1	yes	characteristic
19	C₂²×D₁₀₃	—	2	1	no	—
20	C₂×C₄×C₁₀₃	—	2	1	no	—
21	C₂×C₄×C₁₀₃	—	2	1	no	—
22	C₂×C₄×C₁₀₃	D₄	1	1	yes	characteristic
23	C₂×C₄×C₁₀₃	D₄	1	1	yes	characteristic
24	C₂×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
25	C₂×Dic₁₀₃	—	2	1	no	—
26	D₄₁₂	—	2	1	no	—
27	D₄₁₂	Q₈	1	2	yes	—
28	C₄×D₁₀₃	—	4	2	no	—
29	C₁₀₃⋊C₈	—	2	1	no	—
30	C₁₀₃⋊C₈	—	2	1	no	—
31	C₂²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
32	C₂×D₁₀₃	—	2	2	no	—
33	C₂×D₁₀₃	—	4	1	no	—
34	C₂×D₁₀₃	—	4	1	no	—
35	C₄×C₁₀₃	—	2	1	no	—
36	C₄×C₁₀₃	—	2	1	no	—
37	C₄×C₁₀₃	—	4	1	no	—
38	C₄×C₁₀₃	—	4	1	no	—
39	C₄×C₁₀₃	C₂×Q₈	1	1	yes	characteristic
40	C₄×C₁₀₃	#41	1	1	yes	characteristic
41	Dic₁₀₃	—	4	1	no	—
42	C₂×C₁₀₃	C₂²⋊Q₈	1	1	yes	characteristic
43	C₂×C₁₀₃	#135	1	1	yes	characteristic
44	C₂×C₁₀₃	AGL(1,ℤ/8)	1	1	yes	characteristic
45	D₁₀₃	—	4	2	no	—
46	C₁₀₃	#478	1	1	yes	characteristic, complemented, Sylow
47	#478	—	103	1	no	maximal, Sylow
48	#125	D₁₀₃	1	1	yes	characteristic, complemented
49	C₄×D₄	—	103	1	no	—
50	#107	—	103	1	no	—
51	#106	—	103	1	no	—
52	C₄⋊C₈	—	103	1	no	—
53	#102	—	103	1	no	—
54	#102	—	103	1	no	—
55	C₂×D₄	—	103	1	no	—
56	C₂²×C₄	—	206	1	no	—
57	C₂×C₈	—	103	1	no	—
58	C₂×C₈	—	103	1	no	—
59	C₄⋊C₄	—	2	1	no	—
60	C₄⋊C₄	—	2	1	no	—
61	C₄⋊C₄	—	103	1	no	—
62	C₄⋊C₄	C₂×D₁₀₃	1	1	yes	characteristic
63	C₄⋊C₄	C₂×D₁₀₃	1	1	yes	characteristic
64	C₂²⋊C₄	—	206	1	no	—
65	C₄²	C₂×D₁₀₃	1	1	yes	characteristic
66	C₂³	—	206	1	no	—
67	D₄	—	103	2	no	—
68	D₄	—	206	1	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	412	2	no	—
72	C₂×C₄	—	206	1	no	—
73	C₂×C₄	C₂²⋊D₁₀₃	1	1	yes	characteristic
74	C₂×C₄	C₂²⋊D₁₀₃	1	1	yes	characteristic
75	C₂×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
76	C₈	—	206	1	no	—
77	C₈	—	206	1	no	—
78	C₂²	—	412	1	no	—
79	C₂²	—	412	1	no	—
80	C₂²	—	206	2	no	—
81	C₂²	C₂×C₂²⋊D₁₀₃	1	1	yes	characteristic
82	C₄	—	2	1	no	—
83	C₄	—	2	1	no	—
84	C₄	—	4	1	no	—
85	C₄	—	4	1	no	—
86	C₄	—	412	1	no	—
87	C₄	Q₈×D₁₀₃	1	1	yes	characteristic
88	C₄	#13110106	1	1	yes	characteristic
89	C₂	—	412	2	no	—
90	C₂	#15692997	1	1	yes	characteristic
91	C₂	#15693041	1	1	yes	characteristic
92	C₂	#15693046	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₁₀₃
commutator	C₂×C₄×C₁₀₃	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₃
Fitting	#125×C₁₀₃	C₂
socle	C₂²×C₁₀₃	C₂×D₄
hypercenter	#125	D₁₀₃
hypocenter	C₁₀₃	#478
LCS	G ▷ C₂×C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #125

Complements

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

N	H ≅ G/N	type
2. #15692954	C₂	semidirect
3. #15692952	C₂	semidirect
4. C₄⋊(C₁₀₃⋊C₈)	C₂	semidirect
7. #125×C₁₀₃	C₂	semidirect
46. C₁₀₃	#478	semidirect
48. #125	D₁₀₃	semidirect