Subgroups — #27193236

Order 13184.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15692955	C₂	1	2	yes	maximal
2	C₂²×C₁₆×C₁₀₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊Dic₁₀₃	—	2	2	no	—
4	#15692955	—	2	2	no	—
5	#15692955	C₄	1	4	yes	complemented
6	C₂²×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
7	C₂×C₁₆×C₁₀₃	—	2	2	no	—
8	C₂×C₁₆×C₁₀₃	C₄	1	2	yes	complemented
9	C₂²×Dic₁₀₃	—	4	2	no	—
10	C₄⋊Dic₁₀₃	—	2	4	no	—
11	C₄⋊Dic₁₀₃	—	4	2	no	—
12	C₂²×C₄×C₁₀₃	D₄	1	1	yes	characteristic
13	C₂×C₈×C₁₀₃	C₂×C₄	1	2	yes	—
14	C₂×C₈×C₁₀₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₁₀₃	D₄	1	2	yes	—
16	C₂×C₈×C₁₀₃	Q₈	1	1	yes	characteristic
17	C₁₆×C₁₀₃	—	2	2	no	—
18	C₂³×C₁₀₃	D₈	1	1	yes	characteristic
19	C₂×C₄×C₁₀₃	C₂²⋊C₄	1	2	yes	—
20	C₂×C₄×C₁₀₃	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₄×C₁₀₃	SD₁₆	1	2	yes	—
22	C₂×C₄×C₁₀₃	Q₁₆	1	1	yes	characteristic
23	C₂×Dic₁₀₃	—	4	4	no	—
24	C₂×Dic₁₀₃	—	8	2	no	—
25	C₂×Dic₁₀₃	—	8	2	no	—
26	C₈×C₁₀₃	C₄²	1	1	yes	characteristic
27	C₈×C₁₀₃	C₂²⋊C₄	1	1	yes	characteristic
28	C₈×C₁₀₃	C₄⋊C₄	1	2	yes	—
29	C₂²×C₁₀₃	#102	1	2	yes	—
30	C₂²×C₁₀₃	#107	1	1	yes	characteristic
31	C₂²×C₁₀₃	D₁₆	1	1	yes	characteristic
32	C₂²×C₁₀₃	SD₃₂	1	2	yes	—
33	C₂²×C₁₀₃	Q₃₂	1	1	yes	characteristic
34	C₄×C₁₀₃	#95	1	1	yes	characteristic
35	C₄×C₁₀₃	#103	1	2	yes	—
36	C₄×C₁₀₃	#106	1	1	yes	characteristic
37	Dic₁₀₃	—	8	4	no	—
38	C₂×C₁₀₃	#340	1	1	yes	characteristic
39	C₂×C₁₀₃	#357	1	2	yes	—
40	C₂×C₁₀₃	#358	1	2	yes	—
41	C₂×C₁₀₃	#366	1	1	yes	characteristic
42	C₂×C₁₀₃	#367	1	1	yes	characteristic
43	#1380	—	103	1	no	maximal, Sylow
44	C₁₀₃	#1380	1	1	yes	characteristic, complemented, Sylow
45	C₂²×C₁₆	D₁₀₃	1	1	yes	characteristic
46	C₂×#107	—	103	2	no	—
47	C₂²×C₈	C₂×D₁₀₃	1	1	yes	characteristic
48	C₂×C₄⋊C₄	—	206	2	no	—
49	C₂×C₁₆	—	2	2	no	—
50	C₂×C₁₆	Dic₁₀₃	1	2	yes	complemented
51	#107	—	103	4	no	—
52	#107	—	206	2	no	—
53	C₂²×C₄	—	412	2	no	—
54	C₂²×C₄	D₄₁₂	1	1	yes	characteristic
55	C₂×C₈	Dic₂₀₆	1	1	yes	characteristic
56	C₂×C₈	C₄×D₁₀₃	1	2	yes	—
57	C₂×C₈	C₂×Dic₁₀₃	1	1	yes	characteristic
58	C₂×C₈	C₂²⋊D₁₀₃	1	2	yes	—
59	C₄⋊C₄	—	412	2	no	—
60	C₄⋊C₄	—	206	4	no	—
61	C₁₆	—	2	2	no	—
62	C₂³	D₈₂₄	1	1	yes	characteristic
63	C₂×C₄	—	824	2	no	—
64	C₂×C₄	—	824	2	no	—
65	C₂×C₄	—	412	4	no	—
66	C₂×C₄	(C₂×D₁₀₃)⋊C₄	1	2	yes	—
67	C₂×C₄	C₄⋊Dic₁₀₃	1	1	yes	characteristic
68	C₂×C₄	#13110094	1	2	yes	—
69	C₂×C₄	Dic₄₁₂	1	1	yes	characteristic
70	C₈	C₄×Dic₁₀₃	1	1	yes	characteristic
71	C₈	C₂²⋊Dic₁₀₃	1	1	yes	characteristic
72	C₈	Dic₁₀₃⋊C₄	1	2	yes	—
73	C₂²	#15692943	1	2	yes	—
74	C₂²	#15692955	1	1	yes	characteristic
75	C₂²	D₁₆₄₈	1	1	yes	characteristic
76	C₂²	#15692966	1	2	yes	—
77	C₂²	Dic₈₂₄	1	1	yes	characteristic
78	C₄	—	824	4	no	—
79	C₄	C₁₀₃⋊#95	1	1	yes	characteristic
80	C₄	#15692946	1	2	yes	—
81	C₄	#15692953	1	1	yes	characteristic
82	C₂	#20267554	1	1	yes	characteristic
83	C₂	#20267593	1	2	yes	—
84	C₂	#20267596	1	2	yes	—
85	C₂	#20267617	1	1	yes	characteristic
86	C₂	#20267619	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₈₂₄
commutator	C₈×C₁₀₃	C₄²
Frattini	C₂²×C₈	C₂×D₁₀₃
Fitting	C₂²×C₁₆×C₁₀₃	C₂
socle, prime radical	C₂³×C₁₀₃	D₈
cosocle	C₂²×C₈×C₁₀₃	C₂²
hypercenter	C₂²×C₁₆	D₁₀₃
hypocenter	C₁₀₃	#1380
LCS	G ▷ C₈×C₁₀₃ ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
5. #15692955	C₄	semidirect
8. C₂×C₁₆×C₁₀₃	C₄	semidirect
44. C₁₀₃	#1380	semidirect
50. C₂×C₁₆	Dic₁₀₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#15692955	2
C₂²×C₁₆×C₁₀₃	2
#1380	103