Subgroups — #27196546

Order 13184.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20267839	C₂	1	3	yes	maximal
2	C₂×#15692939	C₂	1	3	yes	maximal
3	#338×C₁₀₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₂₀₆	C₂²	1	1	yes	characteristic
5	C₂×#13110089	C₂²	1	3	yes	—
6	#15692956	—	2	6	no	—
7	#15692939	—	2	6	no	—
8	C₂×M₁₆×C₁₀₃	C₂²	1	3	yes	—
9	C₂×Dic₂₀₆	—	2	3	no	—
10	C₂×Dic₂₀₆	—	2	3	no	—
11	C₂²×Dic₁₀₃	Q₈	1	2	yes	—
12	#13110089	—	2	3	no	—
13	#13110089	D₄	1	6	yes	—
14	C₂×C₁₀₃⋊C₈	—	2	3	no	—
15	C₂²×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
16	M₁₆×C₁₀₃	—	2	3	no	—
17	M₁₆×C₁₀₃	—	2	3	no	—
18	C₂×C₈×C₁₀₃	—	2	3	no	—
19	C₂³×C₁₀₃	C₂×Q₈	1	1	yes	characteristic
20	C₂×C₄×C₁₀₃	C₂×D₄	1	3	yes	—
21	C₂×C₄×C₁₀₃	#41	1	3	yes	—
22	C₂×Dic₁₀₃	—	2	6	no	—
23	Dic₂₀₆	—	4	3	no	—
24	Dic₂₀₆	—	4	1	no	—
25	C₈×C₁₀₃	—	4	3	no	—
26	C₁₀₃⋊C₈	—	2	6	no	—
27	C₂²×C₁₀₃	—	4	1	no	—
28	C₂²×C₁₀₃	C₂²⋊Q₈	1	3	yes	—
29	C₄×C₁₀₃	#121	1	3	yes	—
30	C₄×C₁₀₃	#126	1	1	yes	characteristic
31	Dic₁₀₃	—	4	2	no	—
32	C₂×C₁₀₃	—	2	3	no	—
33	C₂×C₁₀₃	#396	1	1	yes	characteristic
34	#2070	—	103	1	no	maximal, Sylow
35	C₁₀₃	#2070	1	1	yes	characteristic, complemented, Sylow
36	#430	—	103	3	no	—
37	C₂×#101	—	103	3	no	—
38	#338	D₁₀₃	1	1	yes	characteristic
39	C₂²×Q₈	—	103	1	no	—
40	C₂×M₁₆	—	103	3	no	—
41	C₂×M₁₆	C₂×D₁₀₃	1	3	yes	—
42	#108	—	206	6	no	—
43	#101	—	206	6	no	—
44	C₂×Q₈	—	206	3	no	—
45	C₂×Q₈	—	206	3	no	—
46	C₂²×C₄	—	103	2	no	—
47	C₂²×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
48	M₁₆	—	2	3	no	—
49	M₁₆	—	2	3	no	—
50	M₁₆	—	103	6	no	—
51	M₁₆	—	206	3	no	—
52	C₂×C₈	—	2	3	no	—
53	C₂×C₈	—	206	3	no	—
54	C₂³	Q₈×D₁₀₃	1	1	yes	characteristic
55	Q₈	—	412	3	no	—
56	Q₈	—	412	1	no	—
57	C₂×C₄	—	206	6	no	—
58	C₂×C₄	D₄×D₁₀₃	1	3	yes	—
59	C₂×C₄	#13110105	1	3	yes	—
60	C₈	—	4	3	no	—
61	C₈	—	206	6	no	—
62	C₂²	—	4	1	no	—
63	C₂²	#15692999	1	3	yes	—
64	C₄	—	412	2	no	—
65	C₄	#15692994	1	3	yes	—
66	C₄	#15693015	1	1	yes	characteristic
67	C₂	—	2	3	no	—
68	C₂	#20267715	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#20267715
commutator, cosocle	C₂²×C₄×C₁₀₃	C₂³
Frattini	C₂²×C₄	C₂²×D₁₀₃
Fitting	#338×C₁₀₃	C₂
socle	C₂×C₁₀₃	#396
prime radical	C₂³×C₁₀₃	C₂×Q₈
hypercenter	#338	D₁₀₃
hypocenter	C₁₀₃	#2070
LCS	G ▷ C₂²×C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #338

Complements

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

N	H ≅ G/N	type
35. C₁₀₃	#2070	semidirect

Maximal subgroups

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

subgroup	index
#20267839	2
C₂×#15692939	2
#338×C₁₀₃	2
#2070	103