Subgroups — #27193115

Order 13184.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Dic₄₁₂	C₂	1	1	yes	maximal, characteristic
2	#20267542	C₂	1	1	yes	maximal, characteristic
3	#346×C₁₀₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₄₁₂	C₄	1	1	yes	characteristic
5	C₄×Dic₂₀₆	—	2	1	no	—
6	#15692955	C₄	1	1	yes	characteristic
7	C₄⋊(C₁₀₃⋊C₈)	—	2	1	no	—
8	#15692946	—	2	1	no	—
9	C₂×C₁₆×C₁₀₃	—	2	1	no	—
10	C₄×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
11	C₂×Dic₂₀₆	—	2	1	no	—
12	Dic₄₁₂	—	2	1	no	—
13	Dic₄₁₂	C₈	1	2	yes	complemented
14	C₂×C₁₀₃⋊C₈	—	4	1	no	—
15	C₄⋊Dic₁₀₃	—	2	1	no	—
16	Dic₁₀₃⋊C₄	—	4	1	no	—
17	C₄×Dic₁₀₃	—	4	1	no	—
18	C₂×C₈×C₁₀₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₁₀₃	D₄	1	1	yes	characteristic
20	C₄²×C₁₀₃	D₄	1	1	yes	characteristic
21	C₁₆×C₁₀₃	—	2	2	no	—
22	C₂×C₄×C₁₀₃	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₄×C₁₀₃	D₈	1	1	yes	characteristic
24	C₂×C₄×C₁₀₃	SD₁₆	1	1	yes	characteristic
25	C₂×Dic₁₀₃	—	4	1	no	—
26	C₂×Dic₁₀₃	—	4	1	no	—
27	Dic₂₀₆	—	2	2	no	—
28	Dic₂₀₆	—	4	1	no	—
29	C₈×C₁₀₃	—	2	1	no	—
30	C₈×C₁₀₃	C₂×C₈	1	1	yes	characteristic
31	C₈×C₁₀₃	M₁₆	1	1	yes	characteristic
32	C₁₀₃⋊C₈	—	8	1	no	—
33	C₂²×C₁₀₃	#102	1	1	yes	characteristic
34	C₄×C₁₀₃	—	2	1	no	—
35	C₄×C₁₀₃	—	2	1	no	—
36	C₄×C₁₀₃	C₂²⋊C₈	1	1	yes	characteristic
37	C₄×C₁₀₃	#104	1	1	yes	characteristic
38	Dic₁₀₃	—	4	2	no	—
39	Dic₁₀₃	—	8	1	no	—
40	C₂×C₁₀₃	D₄⋊C₈	1	1	yes	characteristic
41	C₂×C₁₀₃	#360	1	1	yes	characteristic
42	C₂×C₁₀₃	#362	1	1	yes	characteristic
43	#1334	—	103	1	no	maximal, Sylow
44	C₁₀₃	#1334	1	1	yes	characteristic, complemented, Sylow
45	C₄×Q₁₆	—	103	1	no	—
46	#346	D₁₀₃	1	1	yes	characteristic
47	#334	—	103	1	no	—
48	C₂×Q₁₆	—	103	1	no	—
49	C₄×Q₈	—	206	1	no	—
50	C₂×C₁₆	—	2	1	no	—
51	#107	—	103	1	no	—
52	C₄⋊C₈	—	206	1	no	—
53	#103	—	206	1	no	—
54	C₄×C₈	C₂×D₁₀₃	1	1	yes	characteristic
55	C₂×Q₈	—	206	1	no	—
56	Q₁₆	—	103	2	no	—
57	Q₁₆	—	206	1	no	—
58	C₂×C₈	—	412	1	no	—
59	C₂×C₈	C₄×D₁₀₃	1	1	yes	characteristic
60	C₂×C₈	C₂²⋊D₁₀₃	1	1	yes	characteristic
61	C₄⋊C₄	—	412	1	no	—
62	C₄⋊C₄	—	206	1	no	—
63	C₄²	—	412	1	no	—
64	C₄²	D₄₁₂	1	1	yes	characteristic
65	C₁₆	—	2	2	no	—
66	Q₈	—	412	1	no	—
67	Q₈	—	206	2	no	—
68	C₂×C₄	—	412	1	no	—
69	C₂×C₄	—	412	1	no	—
70	C₂×C₄	(C₂×D₁₀₃)⋊C₄	1	1	yes	characteristic
71	C₂×C₄	D₈₂₄	1	1	yes	characteristic
72	C₂×C₄	#13110094	1	1	yes	characteristic
73	C₈	—	2	1	no	—
74	C₈	—	824	1	no	—
75	C₈	C₈×D₁₀₃	1	1	yes	characteristic
76	C₈	#13110088	1	1	yes	characteristic
77	C₂²	#15692943	1	1	yes	characteristic
78	C₄	—	2	1	no	—
79	C₄	—	2	1	no	—
80	C₄	—	824	1	no	—
81	C₄	—	412	2	no	—
82	C₄	(C₂×D₁₀₃)⋊C₈	1	1	yes	characteristic
83	C₄	#15692949	1	1	yes	characteristic
84	C₂	#20267520	1	1	yes	characteristic
85	C₂	#20267602	1	1	yes	characteristic
86	C₂	#20267608	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#15692943
commutator	C₈×C₁₀₃	C₂×C₈
Frattini	C₄×C₈	C₂×D₁₀₃
Fitting	#346×C₁₀₃	C₂
socle, prime radical	C₂²×C₁₀₃	#102
cosocle	C₄×C₈×C₁₀₃	C₂²
hypercenter	#346	D₁₀₃
hypocenter	C₁₀₃	#1334
LCS	G ▷ C₈×C₁₀₃ ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
13. Dic₄₁₂	C₈	semidirect
44. C₁₀₃	#1334	semidirect

Maximal subgroups

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

subgroup	index
C₄×Dic₄₁₂	2
#20267542	2
#346×C₁₀₃	2
#1334	103