Subgroups — #20267997

Order 6592.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13110094	C₂	1	2	yes	maximal
2	#15693021	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₄₁₂	C₂	1	1	yes	maximal, characteristic
4	#15692946	C₂	1	2	yes	maximal, complemented
5	C₄⋊C₈×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₂₀₆	C₂²	1	2	yes	—
7	C₂×D₄₁₂	C₂²	1	1	yes	characteristic
8	C₂×C₄×D₁₀₃	—	2	1	no	—
9	#13110094	—	2	4	no	—
10	C₄⋊Dic₁₀₃	—	2	1	no	—
11	C₄⋊Dic₁₀₃	—	2	1	no	—
12	C₄⋊Dic₁₀₃	C₂²	1	1	yes	characteristic
13	(C₂×D₁₀₃)⋊C₄	—	2	1	no	—
14	C₂×C₈×C₁₀₃	C₂²	1	2	yes	—
15	C₄²×C₁₀₃	C₂²	1	1	yes	characteristic
16	C₂²×D₁₀₃	—	2	1	no	—
17	C₂×C₄×C₁₀₃	D₄	1	1	yes	characteristic
18	C₂×C₄×C₁₀₃	D₄	1	1	yes	characteristic
19	C₂×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
20	C₂×Dic₁₀₃	—	2	1	no	—
21	C₂×Dic₁₀₃	—	2	2	no	—
22	D₄₁₂	—	2	1	no	—
23	D₄₁₂	D₄	1	2	yes	—
24	C₄×D₁₀₃	—	4	2	no	—
25	Dic₂₀₆	—	2	2	no	—
26	Dic₂₀₆	—	2	2	no	—
27	C₈×C₁₀₃	—	2	2	no	—
28	C₂²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
29	C₂×D₁₀₃	—	2	2	no	—
30	C₂×D₁₀₃	—	4	1	no	—
31	C₂×D₁₀₃	—	4	1	no	—
32	C₄×C₁₀₃	—	2	1	no	—
33	C₄×C₁₀₃	SD₁₆	1	2	yes	complemented
34	C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
35	C₄×C₁₀₃	#41	1	1	yes	characteristic
36	Dic₁₀₃	—	4	2	no	—
37	Dic₁₀₃	—	4	1	no	—
38	C₂×C₁₀₃	#121	1	1	yes	characteristic
39	C₂×C₁₀₃	C₂×SD₁₆	1	1	yes	characteristic
40	C₂×C₁₀₃	#137	1	1	yes	characteristic
41	D₁₀₃	—	4	2	no	—
42	C₁₀₃	#461	1	1	yes	characteristic, complemented, Sylow
43	#461	—	103	1	no	maximal, Sylow
44	C₂×SD₁₆	—	103	2	no	—
45	C₄⋊Q₈	—	103	1	no	—
46	C₄×D₄	—	103	1	no	—
47	C₄⋊C₈	D₁₀₃	1	1	yes	characteristic, complemented
48	#103	—	103	2	no	—
49	C₂×Q₈	—	103	2	no	—
50	C₂×D₄	—	103	1	no	—
51	C₂²×C₄	—	206	1	no	—
52	SD₁₆	—	206	4	no	—
53	C₂×C₈	C₂×D₁₀₃	1	2	yes	—
54	C₄⋊C₄	—	103	1	no	—
55	C₄⋊C₄	—	206	1	no	—
56	C₄⋊C₄	—	206	1	no	—
57	C₂²⋊C₄	—	206	1	no	—
58	C₄²	C₂×D₁₀₃	1	1	yes	characteristic
59	C₂³	—	206	1	no	—
60	Q₈	—	206	2	no	—
61	Q₈	—	206	2	no	—
62	D₄	—	103	2	no	—
63	D₄	—	206	1	no	—
64	C₂×C₄	—	412	2	no	—
65	C₂×C₄	—	206	1	no	—
66	C₂×C₄	—	206	2	no	—
67	C₂×C₄	D₄₁₂	1	1	yes	characteristic
68	C₂×C₄	D₄₁₂	1	1	yes	characteristic
69	C₂×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
70	C₈	—	2	2	no	—
71	C₂²	—	412	1	no	—
72	C₂²	—	412	1	no	—
73	C₂²	—	206	2	no	—
74	C₂²	C₂×D₄₁₂	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	—	412	2	no	—
77	C₄	—	412	1	no	—
78	C₄	#13110094	1	2	yes	complemented
79	C₄	D₄×D₁₀₃	1	1	yes	characteristic
80	C₄	#13110106	1	1	yes	characteristic
81	C₂	—	412	2	no	—
82	C₂	#15692996	1	1	yes	characteristic
83	C₂	C₂×#13110094	1	1	yes	characteristic
84	C₂	#15693054	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄₁₂
commutator	C₂×C₄×C₁₀₃	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₃
Fitting	C₄⋊C₈×C₁₀₃	C₂
socle	C₂²×C₁₀₃	C₂×D₄
hypercenter	C₄⋊C₈	D₁₀₃
hypocenter	C₁₀₃	#461
LCS	G ▷ C₂×C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
2. #15693021	C₂	semidirect
4. #15692946	C₂	semidirect
5. C₄⋊C₈×C₁₀₃	C₂	semidirect
33. C₄×C₁₀₃	SD₁₆	semidirect
42. C₁₀₃	#461	semidirect
47. C₄⋊C₈	D₁₀₃	semidirect
78. C₄	#13110094	semidirect