Subgroups — #27186088

Order 12928.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20266063	C₂	1	1	yes	maximal, characteristic
2	#20266040	C₂	1	1	yes	maximal, characteristic
3	Q₁₆×Dic₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#13108077	—	2	1	no	—
5	C₄⋊#11717581	—	2	1	no	—
6	Q₈×Dic₁₀₁	—	2	1	no	—
7	#15692189	C₄	1	1	yes	characteristic
8	#15692179	—	2	1	no	—
9	C₈×Dic₁₀₁	C₂²	1	1	yes	characteristic
10	C₂×Q₁₆×C₁₀₁	C₄	1	1	yes	characteristic
11	C₂×#11717581	—	4	1	no	—
12	#13108077	—	2	2	no	—
13	C₂×#11717579	D₄	1	1	yes	characteristic
14	C₄⋊Dic₁₀₁	—	2	1	no	—
15	C₄⋊Dic₁₀₁	—	4	1	no	—
16	C₄×Dic₁₀₁	—	4	1	no	—
17	C₄×Dic₁₀₁	D₄	1	1	yes	characteristic
18	C₂×Q₈×C₁₀₁	—	2	1	no	—
19	Q₁₆×C₁₀₁	—	2	1	no	—
20	Q₁₆×C₁₀₁	C₈	1	2	yes	complemented
21	C₂×C₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
22	Q₈×C₁₀₁	—	2	2	no	—
23	Q₈×C₁₀₁	—	4	1	no	—
24	C₂×C₄×C₁₀₁	—	4	1	no	—
25	C₂×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×Dic₁₀₁	—	4	1	no	—
27	C₂×Dic₁₀₁	D₈	1	1	yes	characteristic
28	C₂×Dic₁₀₁	SD₁₆	1	1	yes	characteristic
29	#11717581	—	8	1	no	—
30	C₈×C₁₀₁	C₂×C₈	1	1	yes	characteristic
31	C₈×C₁₀₁	M₁₆	1	1	yes	characteristic
32	#11717579	—	2	1	no	—
33	C₂²×C₁₀₁	#102	1	1	yes	characteristic
34	C₄×C₁₀₁	—	4	2	no	—
35	C₄×C₁₀₁	C₂²⋊C₈	1	1	yes	characteristic
36	C₄×C₁₀₁	#104	1	1	yes	characteristic
37	Dic₁₀₁	—	2	1	no	—
38	Dic₁₀₁	—	8	1	no	—
39	Dic₁₀₁	SD₃₂	1	1	yes	characteristic
40	Dic₁₀₁	Q₃₂	1	1	yes	characteristic
41	C₂×C₁₀₁	D₄⋊C₈	1	1	yes	characteristic
42	C₂×C₁₀₁	#358	1	1	yes	characteristic
43	C₂×C₁₀₁	#359	1	1	yes	characteristic
44	#1332	—	101	1	no	maximal, Sylow
45	C₁₀₁	#1332	1	1	yes	characteristic, complemented, Sylow
46	C₄×Q₁₆	—	101	1	no	—
47	C₄×C₁₆	—	101	1	no	—
48	#335	—	101	1	no	—
49	C₂×Q₁₆	#87938	1	1	yes	characteristic
50	C₄×Q₈	—	202	1	no	—
51	C₂×C₁₆	—	202	1	no	—
52	#107	—	101	1	no	—
53	C₄⋊C₈	—	202	1	no	—
54	#103	—	202	1	no	—
55	C₄×C₈	—	101	1	no	—
56	C₂×Q₈	—	2	1	no	—
57	Q₁₆	—	2	1	no	—
58	Q₁₆	#11717581	1	2	yes	complemented
59	C₂×C₈	—	101	1	no	—
60	C₂×C₈	—	404	1	no	—
61	C₂×C₈	C₂×#87938	1	1	yes	characteristic
62	C₄⋊C₄	—	404	1	no	—
63	C₄⋊C₄	—	202	1	no	—
64	C₄²	—	101	1	no	—
65	C₄²	—	404	1	no	—
66	C₁₆	—	202	2	no	—
67	Q₈	—	2	2	no	—
68	Q₈	—	4	1	no	—
69	C₂×C₄	—	4	1	no	—
70	C₂×C₄	—	101	1	no	—
71	C₂×C₄	—	101	1	no	—
72	C₂×C₄	—	404	1	no	—
73	C₂×C₄	C₂²⋊#87938	1	1	yes	characteristic
74	C₈	—	808	1	no	—
75	C₈	—	202	1	no	—
76	C₈	C₂×#11717581	1	1	yes	characteristic
77	C₈	#13108083	1	1	yes	characteristic
78	C₂²	#15692317	1	1	yes	characteristic
79	C₄	—	4	2	no	—
80	C₄	—	808	1	no	—
81	C₄	—	101	1	no	—
82	C₄	—	101	1	no	—
83	C₄	—	202	1	no	—
84	C₄	C₂²⋊#11717581	1	1	yes	characteristic
85	C₄	#15692319	1	1	yes	characteristic
86	C₂	D₄⋊#11717581	1	1	yes	characteristic
87	C₂	#20266090	1	1	yes	characteristic
88	C₂	#20266092	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#15692317
commutator	C₈×C₁₀₁	C₂×C₈
Frattini	C₂×C₈	C₂×#87938
Fitting	C₂×Q₁₆×C₁₀₁	C₄
socle, prime radical	C₂²×C₁₀₁	#102
cosocle	C₈×Dic₁₀₁	C₂²
hypercenter	C₂×Q₁₆	#87938
hypocenter	C₁₀₁	#1332
LCS	G ▷ C₈×C₁₀₁ ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
20. Q₁₆×C₁₀₁	C₈	semidirect
45. C₁₀₁	#1332	semidirect
58. Q₁₆	#11717581	semidirect

Maximal subgroups

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

subgroup	index
#20266063	2
#20266040	2
Q₁₆×Dic₁₀₁	2
#1332	101