Subgroups — #27193063

Order 13184.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₀₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₈×C₁₀₃⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₆×C₁₀₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₀₃⋊C₁₆	C₄	1	2	yes	—
5	C₄×C₁₀₃⋊C₈	C₄	1	1	yes	characteristic
6	C₄×C₁₀₃⋊C₈	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₁₀₃	C₄	1	2	yes	—
8	C₄×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
9	C₂×C₁₀₃⋊C₈	C₈	1	2	yes	—
10	C₂×C₁₀₃⋊C₈	C₈	1	2	yes	—
11	C₁₀₃⋊C₁₆	—	2	2	no	—
12	C₂×C₈×C₁₀₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₁₀₃	C₂×C₄	1	1	yes	characteristic
14	C₄²×C₁₀₃	C₂×C₄	1	1	yes	characteristic
15	C₁₆×C₁₀₃	—	2	2	no	—
16	C₂×C₄×C₁₀₃	C₄²	1	1	yes	characteristic
17	C₂×C₄×C₁₀₃	C₂×C₈	1	1	yes	characteristic
18	C₂×C₄×C₁₀₃	C₂×C₈	1	1	yes	characteristic
19	C₈×C₁₀₃	M₁₆	1	2	yes	—
20	C₈×C₁₀₃	M₁₆	1	2	yes	—
21	C₁₀₃⋊C₈	—	2	2	no	—
22	C₁₀₃⋊C₈	C₁₆	1	4	yes	complemented
23	C₂²×C₁₀₃	C₄×C₈	1	1	yes	characteristic
24	C₄×C₁₀₃	#97	1	1	yes	characteristic
25	C₄×C₁₀₃	#97	1	1	yes	characteristic
26	C₄×C₁₀₃	C₂×C₁₆	1	2	yes	—
27	C₄×C₁₀₃	M₃₂	1	2	yes	—
28	C₂×C₁₀₃	#322	1	1	yes	characteristic
29	C₂×C₁₀₃	C₄×C₁₆	1	1	yes	characteristic
30	C₂×C₁₀₃	#346	1	1	yes	characteristic
31	#1312	—	103	1	no	maximal, Sylow
32	C₁₀₃	#1312	1	1	yes	characteristic, complemented, Sylow
33	C₄×C₁₆	—	103	1	no	—
34	C₄×C₁₆	D₁₀₃	1	1	yes	characteristic
35	C₈²	—	103	1	no	—
36	C₂×C₁₆	—	103	2	no	—
37	C₂×C₁₆	Dic₁₀₃	1	2	yes	—
38	C₄×C₈	—	103	1	no	—
39	C₄×C₈	—	103	1	no	—
40	C₄×C₈	C₂×D₁₀₃	1	1	yes	characteristic
41	C₂×C₈	—	103	2	no	—
42	C₂×C₈	—	103	2	no	—
43	C₂×C₈	C₄×D₁₀₃	1	1	yes	characteristic
44	C₂×C₈	C₂×Dic₁₀₃	1	1	yes	characteristic
45	C₄²	C₄×D₁₀₃	1	1	yes	characteristic
46	C₁₆	—	2	2	no	—
47	C₁₆	—	206	2	no	—
48	C₂×C₄	C₄×Dic₁₀₃	1	1	yes	characteristic
49	C₂×C₄	C₈×D₁₀₃	1	1	yes	characteristic
50	C₂×C₄	C₈×D₁₀₃	1	1	yes	characteristic
51	C₈	—	103	4	no	—
52	C₈	—	206	2	no	—
53	C₈	#13110088	1	2	yes	—
54	C₈	#13110089	1	2	yes	—
55	C₂²	C₈×Dic₁₀₃	1	1	yes	characteristic
56	C₄	#15692931	1	1	yes	characteristic
57	C₄	#15692932	1	1	yes	characteristic
58	C₄	C₁₆×D₁₀₃	1	2	yes	—
59	C₄	#15692960	1	2	yes	—
60	C₂	#20267513	1	1	yes	characteristic
61	C₂	C₁₆×Dic₁₀₃	1	1	yes	characteristic
62	C₂	#20267566	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄×C₈	C₂×D₁₀₃
commutator	C₂×C₁₀₃	C₄×C₁₆
Fitting	C₄×C₁₆×C₁₀₃	C₂
socle, prime radical	C₂²×C₁₀₃	C₄×C₈
cosocle	C₄×C₈×C₁₀₃	C₂²
hypercenter	C₄×C₁₆	D₁₀₃
hypocenter	C₁₀₃	#1312
LCS	G ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
22. C₁₀₃⋊C₈	C₁₆	semidirect
32. C₁₀₃	#1312	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₁₀₃⋊C₁₆	2
C₈×C₁₀₃⋊C₈	2
C₄×C₁₆×C₁₀₃	2
#1312	103