Subgroups — #27193182

Order 13184.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20268171	C₂	1	1	yes	maximal, characteristic
2	#20267612	C₂	1	1	yes	maximal, characteristic
3	#364×C₁₀₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₄₁₂	—	2	1	no	—
5	C₂×Dic₄₁₂	—	2	1	no	—
6	#15693021	C₄	1	2	yes	—
7	#15692961	—	2	1	no	—
8	M₃₂×C₁₀₃	—	2	1	no	—
9	C₄×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
10	C₂×Dic₂₀₆	—	2	2	no	—
11	Dic₄₁₂	—	4	1	no	—
12	Dic₄₁₂	—	4	1	no	—
13	Dic₄₁₂	—	4	1	no	—
14	Dic₄₁₂	—	4	1	no	—
15	C₄⋊Dic₁₀₃	—	4	2	no	—
16	C₁₀₃⋊C₁₆	—	4	1	no	—
17	C₂×C₈×C₁₀₃	D₄	1	1	yes	characteristic
18	C₂×C₈×C₁₀₃	D₄	1	1	yes	characteristic
19	C₄²×C₁₀₃	C₂×C₄	1	1	yes	characteristic
20	C₁₆×C₁₀₃	—	4	1	no	—
21	C₂×C₄×C₁₀₃	—	2	1	no	—
22	C₂×C₄×C₁₀₃	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×Dic₁₀₃	—	4	2	no	—
24	Dic₂₀₆	—	4	2	no	—
25	Dic₂₀₆	—	4	2	no	—
26	C₈×C₁₀₃	D₈	1	1	yes	characteristic
27	C₈×C₁₀₃	D₈	1	1	yes	characteristic
28	C₈×C₁₀₃	SD₁₆	1	1	yes	characteristic
29	C₈×C₁₀₃	SD₁₆	1	1	yes	characteristic
30	C₂²×C₁₀₃	#100	1	1	yes	characteristic
31	C₄×C₁₀₃	—	2	2	no	—
32	C₄×C₁₀₃	#102	1	1	yes	characteristic
33	C₄×C₁₀₃	#102	1	1	yes	characteristic
34	Dic₁₀₃	—	8	2	no	—
35	C₂×C₁₀₃	—	2	1	no	—
36	C₂×C₁₀₃	#331	1	1	yes	characteristic
37	#1358	—	103	1	no	maximal, Sylow
38	C₁₀₃	#1358	1	1	yes	characteristic, complemented, Sylow
39	#494	—	103	1	no	—
40	#364	—	103	1	no	—
41	#364	D₁₀₃	1	1	yes	characteristic
42	C₂×Q₁₆	—	206	1	no	—
43	C₂×Q₁₆	—	206	1	no	—
44	C₄⋊Q₈	—	103	2	no	—
45	M₃₂	—	2	1	no	—
46	M₃₂	—	206	1	no	—
47	C₄×C₈	C₂×D₁₀₃	1	1	yes	characteristic
48	C₂×Q₈	—	206	2	no	—
49	Q₁₆	—	412	1	no	—
50	Q₁₆	—	412	1	no	—
51	Q₁₆	—	412	1	no	—
52	Q₁₆	—	412	1	no	—
53	C₂×C₈	D₄₁₂	1	1	yes	characteristic
54	C₂×C₈	C₂²⋊D₁₀₃	1	1	yes	characteristic
55	C₄⋊C₄	—	412	2	no	—
56	C₄²	C₄×D₁₀₃	1	1	yes	characteristic
57	C₁₆	—	4	1	no	—
58	C₁₆	—	412	1	no	—
59	Q₈	—	412	2	no	—
60	Q₈	—	412	2	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	412	2	no	—
63	C₂×C₄	(C₂×D₁₀₃)⋊C₄	1	1	yes	characteristic
64	C₈	#13110090	1	1	yes	characteristic
65	C₈	D₈₂₄	1	1	yes	characteristic
66	C₈	#13110092	1	1	yes	characteristic
67	C₈	#13110094	1	1	yes	characteristic
68	C₂²	#15692937	1	1	yes	characteristic
69	C₄	—	2	2	no	—
70	C₄	—	824	2	no	—
71	C₄	#15692941	1	1	yes	characteristic
72	C₄	#15692943	1	1	yes	characteristic
73	C₂	—	2	1	no	—
74	C₂	#20267534	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#20267534
commutator	C₄²×C₁₀₃	C₂×C₄
Frattini	C₄×C₈	C₂×D₁₀₃
Fitting	#364×C₁₀₃	C₂
socle	C₂×C₁₀₃	#331
prime radical	C₂²×C₁₀₃	#100
cosocle	C₄×C₈×C₁₀₃	C₂²
hypercenter	#364	D₁₀₃
hypocenter	C₁₀₃	#1358
LCS	G ▷ C₄²×C₁₀₃ ▷ C₂×C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
38. C₁₀₃	#1358	semidirect

Maximal subgroups

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

subgroup	index
#20268171	2
#20267612	2
#364×C₁₀₃	2
#1358	103