Subgroups — #27186104

Order 12928.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20266074	C₂	1	1	yes	maximal, characteristic
2	#20266045	C₂	1	1	yes	maximal, characteristic
3	#20265432	C₂	1	1	yes	maximal, characteristic
4	#15692334	—	2	1	no	—
5	#15692329	—	2	1	no	—
6	C₂×#13108057	C₂²	1	1	yes	characteristic
7	#15692231	—	2	1	no	—
8	#15692187	C₄	1	1	yes	characteristic, complemented
9	#15692179	—	2	1	no	—
10	C₂×Q₁₆×C₁₀₁	C₄	1	1	yes	characteristic, complemented
11	C₄⋊#87938	—	4	1	no	—
12	C₂²⋊#87938	—	4	1	no	—
13	C₄×#87938	—	2	2	no	—
14	#13108077	—	4	1	no	—
15	C₂×C₄×D₁₀₁	D₄	1	1	yes	characteristic
16	#13108057	—	4	1	no	—
17	C₂×#11717579	D₄	1	1	yes	characteristic
18	C₄⋊Dic₁₀₁	—	2	1	no	—
19	#13108053	—	4	1	no	—
20	#13108051	—	4	1	no	—
21	C₂×Q₈×C₁₀₁	—	2	1	no	—
22	Q₁₆×C₁₀₁	—	4	1	no	—
23	C₂×C₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
24	C₂²×D₁₀₁	D₈	1	1	yes	characteristic
25	C₂×#87938	—	4	2	no	—
26	Q₈×C₁₀₁	—	4	1	no	—
27	Q₈×C₁₀₁	—	4	1	no	—
28	C₂×C₄×C₁₀₁	—	4	1	no	—
29	C₂×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×Dic₁₀₁	—	4	1	no	—
31	C₂×Dic₁₀₁	SD₁₆	1	1	yes	characteristic
32	C₄×D₁₀₁	—	2	1	no	—
33	C₄×D₁₀₁	—	2	1	no	—
34	C₈×C₁₀₁	—	2	1	no	—
35	#11717579	—	2	1	no	—
36	C₂²×C₁₀₁	#102	1	1	yes	characteristic
37	C₂×D₁₀₁	—	2	1	no	—
38	C₂×D₁₀₁	—	4	1	no	—
39	#87938	—	8	2	no	—
40	C₄×C₁₀₁	—	8	1	no	—
41	C₄×C₁₀₁	#99	1	1	yes	characteristic
42	C₄×C₁₀₁	#104	1	1	yes	characteristic
43	Dic₁₀₁	—	2	1	no	—
44	Dic₁₀₁	—	8	1	no	—
45	C₂×C₁₀₁	—	2	1	no	—
46	C₂×C₁₀₁	#327	1	1	yes	characteristic
47	D₁₀₁	—	4	1	no	—
48	#1340	—	101	1	no	maximal, Sylow
49	C₁₀₁	#1340	1	1	yes	characteristic, complemented, Sylow
50	#470	—	101	1	no	—
51	#349	—	101	1	no	—
52	H(3,ℤ/4)	—	101	1	no	—
53	C₂×Q₁₆	#87938	1	1	yes	characteristic, complemented
54	C₂×M₁₆	—	101	1	no	—
55	C₂²⋊Q₈	—	202	1	no	—
56	#117	—	202	1	no	—
57	M₃₂	—	202	1	no	—
58	#106	—	101	1	no	—
59	#103	—	202	1	no	—
60	C₂×Q₈	—	2	1	no	—
61	C₂²×C₄	—	101	1	no	—
62	Q₁₆	—	4	1	no	—
63	M₁₆	—	404	1	no	—
64	C₂×C₈	—	101	1	no	—
65	C₂×C₈	C₂×#87938	1	1	yes	characteristic
66	C₄⋊C₄	—	404	1	no	—
67	C₄⋊C₄	—	404	1	no	—
68	C₄⋊C₄	—	202	1	no	—
69	C₂²⋊C₄	—	404	1	no	—
70	C₂²⋊C₄	—	404	1	no	—
71	C₄²	—	202	2	no	—
72	C₁₆	—	404	1	no	—
73	C₂³	—	101	1	no	—
74	Q₈	—	4	1	no	—
75	Q₈	—	4	1	no	—
76	C₂×C₄	—	4	1	no	—
77	C₂×C₄	—	101	1	no	—
78	C₂×C₄	—	404	2	no	—
79	C₂×C₄	—	404	1	no	—
80	C₂×C₄	—	202	1	no	—
81	C₂×C₄	—	202	1	no	—
82	C₂×C₄	C₂²⋊#87938	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	202	1	no	—
85	C₂²	—	404	1	no	—
86	C₂²	—	202	1	no	—
87	C₂²	#15692317	1	1	yes	characteristic
88	C₄	—	8	1	no	—
89	C₄	—	808	1	no	—
90	C₄	—	808	2	no	—
91	C₄	—	202	1	no	—
92	C₄	#15692313	1	1	yes	characteristic
93	C₄	#15692319	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	404	1	no	—
96	C₂	#20266028	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#20266028
commutator	C₂×C₈×C₁₀₁	C₂×C₄
Frattini	C₂×C₈	C₂×#87938
Fitting	C₂×Q₁₆×C₁₀₁	C₄
socle	C₂×C₁₀₁	#327
prime radical	C₂²×D₁₀₁	D₈
cosocle	C₂×#13108057	C₂²
hypercenter	C₂×Q₁₆	#87938
hypocenter	C₁₀₁	#1340
LCS	G ▷ C₂×C₈×C₁₀₁ ▷ C₂×C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
8. #15692187	C₄	semidirect
10. C₂×Q₁₆×C₁₀₁	C₄	semidirect
49. C₁₀₁	#1340	semidirect
53. C₂×Q₁₆	#87938	semidirect

Maximal subgroups

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

subgroup	index
#20266074	2
#20266045	2
#20265432	2
#1340	101