Subgroups — #27193109

Order 13184.

98 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	#20267544	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₆×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	C₂²⋊C₈	1	1	yes	characteristic
36	C₄×C₁₀₃	#104	1	1	yes	characteristic
37	C₄×C₁₀₃	SD₃₂	1	1	yes	characteristic
38	C₄×C₁₀₃	Q₃₂	1	1	yes	characteristic
39	Dic₁₀₃	—	4	2	no	—
40	Dic₁₀₃	—	8	1	no	—
41	C₂×C₁₀₃	D₄⋊C₈	1	1	yes	characteristic
42	C₂×C₁₀₃	#358	1	1	yes	characteristic
43	C₂×C₁₀₃	#359	1	1	yes	characteristic
44	#1332	—	103	1	no	maximal, Sylow
45	C₁₀₃	#1332	1	1	yes	characteristic, complemented, Sylow
46	C₄×Q₁₆	—	103	1	no	—
47	C₄×C₁₆	D₁₀₃	1	1	yes	characteristic
48	#335	—	103	1	no	—
49	C₂×Q₁₆	—	103	1	no	—
50	C₄×Q₈	—	206	1	no	—
51	C₂×C₁₆	—	2	1	no	—
52	#107	—	103	1	no	—
53	C₄⋊C₈	—	206	1	no	—
54	#103	—	206	1	no	—
55	C₄×C₈	C₂×D₁₀₃	1	1	yes	characteristic
56	C₂×Q₈	—	206	1	no	—
57	Q₁₆	—	103	2	no	—
58	Q₁₆	—	206	1	no	—
59	C₂×C₈	—	412	1	no	—
60	C₂×C₈	C₄×D₁₀₃	1	1	yes	characteristic
61	C₂×C₈	C₂²⋊D₁₀₃	1	1	yes	characteristic
62	C₄⋊C₄	—	412	1	no	—
63	C₄⋊C₄	—	206	1	no	—
64	C₄²	—	412	1	no	—
65	C₄²	D₄₁₂	1	1	yes	characteristic
66	C₁₆	—	2	2	no	—
67	Q₈	—	412	1	no	—
68	Q₈	—	206	2	no	—
69	C₂×C₄	—	412	1	no	—
70	C₂×C₄	—	412	1	no	—
71	C₂×C₄	(C₂×D₁₀₃)⋊C₄	1	1	yes	characteristic
72	C₂×C₄	D₈₂₄	1	1	yes	characteristic
73	C₂×C₄	#13110094	1	1	yes	characteristic
74	C₈	—	2	1	no	—
75	C₈	—	824	1	no	—
76	C₈	C₈×D₁₀₃	1	1	yes	characteristic
77	C₈	#13110088	1	1	yes	characteristic
78	C₂²	#15692943	1	1	yes	characteristic
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	C₄	#15692966	1	1	yes	characteristic
85	C₄	Dic₈₂₄	1	1	yes	characteristic
86	C₂	#20267520	1	1	yes	characteristic
87	C₂	#20267596	1	1	yes	characteristic
88	C₂	#20267599	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₈₂₄
commutator	C₈×C₁₀₃	C₂×C₈
Frattini	C₄×C₈	C₂×D₁₀₃
Fitting	C₄×C₁₆×C₁₀₃	C₂
socle, prime radical	C₂²×C₁₀₃	#102
cosocle	C₄×C₈×C₁₀₃	C₂²
hypercenter	C₄×C₁₆	D₁₀₃
hypocenter	C₁₀₃	#1332
LCS	G ▷ C₈×C₁₀₃ ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
13. Dic₄₁₂	C₈	semidirect
45. C₁₀₃	#1332	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
#20267544	2
C₄×C₁₆×C₁₀₃	2
#1332	103