Subgroups — #27197425

Order 13184.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20268195	C₂	1	2	yes	maximal
2	#20267619	C₂	1	1	yes	maximal, characteristic
3	#20267618	C₂	1	2	yes	maximal
4	C₁₆×Dic₁₀₃	C₂	1	1	yes	maximal, characteristic
5	#367×C₁₀₃	C₂	1	1	yes	maximal, characteristic
6	#15693020	—	2	2	no	—
7	C₂×C₁₀₃⋊C₁₆	C₂²	1	1	yes	characteristic
8	#15692955	C₂²	1	2	yes	—
9	#15692954	—	2	2	no	—
10	C₈×Dic₁₀₃	C₂²	1	1	yes	characteristic
11	C₂×C₁₆×C₁₀₃	C₂²	1	1	yes	characteristic
12	#107×C₁₀₃	C₂²	1	2	yes	—
13	C₂×Dic₂₀₆	—	4	2	no	—
14	C₂×C₁₀₃⋊C₈	D₄	1	1	yes	characteristic
15	C₄⋊Dic₁₀₃	—	2	2	no	—
16	Dic₁₀₃⋊C₄	—	4	2	no	—
17	C₄×Dic₁₀₃	D₄	1	1	yes	characteristic
18	C₁₀₃⋊C₁₆	Q₈	1	2	yes	complemented
19	C₂×C₈×C₁₀₃	C₂³	1	1	yes	characteristic
20	C₄⋊C₄×C₁₀₃	—	2	2	no	—
21	C₁₆×C₁₀₃	Q₈	1	2	yes	complemented
22	C₂×C₄×C₁₀₃	—	4	2	no	—
23	C₂×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
24	C₂×Dic₁₀₃	—	4	2	no	—
25	C₂×Dic₁₀₃	D₈	1	2	yes	—
26	Dic₂₀₆	—	8	4	no	—
27	C₈×C₁₀₃	C₂×Q₈	1	1	yes	characteristic
28	C₈×C₁₀₃	C₂×Q₈	1	1	yes	characteristic
29	C₁₀₃⋊C₈	Q₁₆	1	2	yes	—
30	C₂²×C₁₀₃	C₂×D₈	1	1	yes	characteristic
31	C₄×C₁₀₃	—	8	2	no	—
32	C₄×C₁₀₃	C₄⋊Q₈	1	1	yes	characteristic
33	C₄×C₁₀₃	C₂×Q₁₆	1	1	yes	characteristic
34	Dic₁₀₃	—	8	2	no	—
35	Dic₁₀₃	SD₃₂	1	4	yes	—
36	C₂×C₁₀₃	#500	1	1	yes	characteristic
37	C₂×C₁₀₃	C₂×SD₃₂	1	2	yes	—
38	#2254	—	103	1	no	maximal, Sylow
39	C₁₀₃	#2254	1	1	yes	characteristic, complemented, Sylow
40	#500	—	103	2	no	—
41	#367	—	103	1	no	—
42	#367	—	103	2	no	—
43	#367	D₁₀₃	1	1	yes	characteristic
44	C₄×C₁₆	—	103	1	no	—
45	C₄⋊Q₈	—	206	2	no	—
46	C₂×C₁₆	—	103	1	no	—
47	C₂×C₁₆	C₂×D₁₀₃	1	1	yes	characteristic
48	#107	—	103	2	no	—
49	#107	—	206	2	no	—
50	#107	C₂×D₁₀₃	1	2	yes	—
51	C₄×C₈	—	103	1	no	—
52	C₂×Q₈	—	412	2	no	—
53	C₂×C₈	—	103	1	no	—
54	C₂×C₈	C₂²×D₁₀₃	1	1	yes	characteristic
55	C₄⋊C₄	—	2	2	no	—
56	C₄⋊C₄	—	412	2	no	—
57	C₄⋊C₄	—	206	2	no	—
58	C₄²	—	103	1	no	—
59	C₁₆	—	103	2	no	—
60	C₁₆	Dic₂₀₆	1	2	yes	complemented
61	Q₈	—	824	4	no	—
62	C₂×C₄	—	4	2	no	—
63	C₂×C₄	—	103	2	no	—
64	C₂×C₄	—	412	2	no	—
65	C₂×C₄	D₄×D₁₀₃	1	1	yes	characteristic
66	C₈	—	103	2	no	—
67	C₈	Q₈×D₁₀₃	1	1	yes	characteristic
68	C₈	C₂×Dic₂₀₆	1	1	yes	characteristic
69	C₂²	D₈×D₁₀₃	1	1	yes	characteristic
70	C₄	—	8	2	no	—
71	C₄	—	824	2	no	—
72	C₄	—	103	4	no	—
73	C₄	#15693020	1	1	yes	characteristic
74	C₄	Q₁₆×D₁₀₃	1	1	yes	characteristic
75	C₂	#20268195	1	1	yes	characteristic
76	C₂	SD₃₂×D₁₀₃	1	2	yes	—

	subgroup	G/H
center	C₂²	D₈×D₁₀₃
commutator, cosocle	C₂×C₈×C₁₀₃	C₂³
Frattini	C₂×C₈	C₂²×D₁₀₃
Fitting	#367×C₁₀₃	C₂
socle, prime radical	C₂²×C₁₀₃	C₂×D₈
hypercenter	#367	D₁₀₃
hypocenter	C₁₀₃	#2254
LCS	G ▷ C₂×C₈×C₁₀₃ ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #367

Complements

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

N	H ≅ G/N	type
18. C₁₀₃⋊C₁₆	Q₈	semidirect
21. C₁₆×C₁₀₃	Q₈	semidirect
39. C₁₀₃	#2254	semidirect
60. C₁₆	Dic₂₀₆	semidirect

Maximal subgroups

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

subgroup	index
#20268195	2
#20267619	2
#20267618	2
C₁₆×Dic₁₀₃	2
#367×C₁₀₃	2
#2254	103