Subgroups — #27193246

Order 13184.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20267829	C₂	1	2	yes	maximal
2	C₂×M₃₂×C₁₀₃	C₂	1	1	yes	maximal, characteristic
3	#15692980	—	2	2	no	—
4	#15692955	—	2	2	no	—
5	#15692953	C₄	1	4	yes	complemented
6	C₂²×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
7	M₃₂×C₁₀₃	—	2	2	no	—
8	C₂×C₁₆×C₁₀₃	C₄	1	2	yes	complemented
9	C₄⋊Dic₁₀₃	—	2	4	no	—
10	C₂²⋊Dic₁₀₃	—	4	2	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	C₈×C₁₀₃	C₄²	1	1	yes	characteristic
25	C₈×C₁₀₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₁₀₃	C₄⋊C₄	1	2	yes	—
27	C₂²×C₁₀₃	—	4	1	no	—
28	C₂²×C₁₀₃	#102	1	2	yes	—
29	C₂²×C₁₀₃	#107	1	1	yes	characteristic
30	C₄×C₁₀₃	#95	1	1	yes	characteristic
31	C₄×C₁₀₃	#103	1	2	yes	—
32	C₄×C₁₀₃	#106	1	1	yes	characteristic
33	Dic₁₀₃	—	8	4	no	—
34	C₂×C₁₀₃	—	2	2	no	—
35	C₂×C₁₀₃	—	2	1	no	—
36	C₂×C₁₀₃	#340	1	1	yes	characteristic
37	#1384	—	103	1	no	maximal, Sylow
38	C₁₀₃	#1384	1	1	yes	characteristic, complemented, Sylow
39	C₂×M₃₂	D₁₀₃	1	1	yes	characteristic
40	#427	—	103	2	no	—
41	C₂²×C₈	C₂×D₁₀₃	1	1	yes	characteristic
42	#117	—	206	2	no	—
43	M₃₂	—	2	2	no	—
44	C₂×C₁₆	Dic₁₀₃	1	2	yes	complemented
45	#107	—	206	2	no	—
46	#106	—	103	4	no	—
47	C₂²×C₄	D₄₁₂	1	1	yes	characteristic
48	C₂×C₈	Dic₂₀₆	1	1	yes	characteristic
49	C₂×C₈	C₄×D₁₀₃	1	2	yes	—
50	C₂×C₈	C₂×Dic₁₀₃	1	1	yes	characteristic
51	C₂×C₈	C₂²⋊D₁₀₃	1	2	yes	—
52	C₄⋊C₄	—	206	4	no	—
53	C₂²⋊C₄	—	412	2	no	—
54	C₄²	—	412	2	no	—
55	C₁₆	—	2	2	no	—
56	C₂³	D₈₂₄	1	1	yes	characteristic
57	C₂×C₄	—	412	4	no	—
58	C₂×C₄	(C₂×D₁₀₃)⋊C₄	1	2	yes	—
59	C₂×C₄	C₄⋊Dic₁₀₃	1	1	yes	characteristic
60	C₂×C₄	#13110094	1	2	yes	—
61	C₂×C₄	Dic₄₁₂	1	1	yes	characteristic
62	C₈	C₄×Dic₁₀₃	1	1	yes	characteristic
63	C₈	C₂²⋊Dic₁₀₃	1	1	yes	characteristic
64	C₈	Dic₁₀₃⋊C₄	1	2	yes	—
65	C₂²	—	4	1	no	—
66	C₂²	#15692943	1	2	yes	—
67	C₂²	#15692955	1	1	yes	characteristic
68	C₄	—	824	4	no	—
69	C₄	C₁₀₃⋊#95	1	1	yes	characteristic
70	C₄	#15692946	1	2	yes	—
71	C₄	#15692953	1	1	yes	characteristic
72	C₂	—	2	2	no	—
73	C₂	—	2	1	no	—
74	C₂	#20267554	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#15692953
commutator	C₈×C₁₀₃	C₄²
Frattini	C₂²×C₈	C₂×D₁₀₃
Fitting	C₂×M₃₂×C₁₀₃	C₂
socle	C₂×C₁₀₃	#340
prime radical	C₂³×C₁₀₃	D₈
cosocle	C₂²×C₈×C₁₀₃	C₂²
hypercenter	C₂×M₃₂	D₁₀₃
hypocenter	C₁₀₃	#1384
LCS	G ▷ C₈×C₁₀₃ ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
5. #15692953	C₄	semidirect
8. C₂×C₁₆×C₁₀₃	C₄	semidirect
38. C₁₀₃	#1384	semidirect
44. 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
#20267829	2
C₂×M₃₂×C₁₀₃	2
#1384	103