Subgroups — #27187507

Order 12928.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20266099	C₂	1	2	yes	maximal, complemented
2	#20266074	C₂	1	2	yes	maximal
3	#20266069	C₂	1	2	yes	maximal, complemented
4	#20265131	C₂	1	1	yes	maximal, characteristic
5	#15692329	C₂²	1	4	yes	—
6	C₂×#13108057	C₂²	1	1	yes	characteristic
7	C₂×C₈×D₁₀₁	C₄	1	1	yes	characteristic
8	#15692212	C₄	1	1	yes	characteristic
9	#15692166	C₂²	1	1	yes	characteristic
10	#15692165	C₄	1	1	yes	characteristic
11	C₈×Dic₁₀₁	C₂²	1	1	yes	characteristic
12	C₄×C₈×C₁₀₁	C₄	1	1	yes	characteristic
13	#13108077	—	2	4	no	—
14	C₂×C₄×D₁₀₁	C₂×C₄	1	1	yes	characteristic
15	#13108057	—	2	2	no	—
16	C₂×#11717579	C₂×C₄	1	1	yes	characteristic
17	C₂×#11717579	C₂³	1	1	yes	characteristic
18	C₈×D₁₀₁	—	2	2	no	—
19	#13108053	—	2	1	no	—
20	#13108051	—	2	1	no	—
21	C₄×Dic₁₀₁	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
23	C₂×C₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
24	C₄²×C₁₀₁	C₂×C₄	1	1	yes	characteristic
25	C₂²×D₁₀₁	M₁₆	1	1	yes	characteristic
26	C₂×C₄×C₁₀₁	—	2	1	no	—
27	C₂×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
28	C₂×Dic₁₀₁	—	2	1	no	—
29	C₂×Dic₁₀₁	M₁₆	1	1	yes	characteristic
30	C₄×D₁₀₁	—	2	1	no	—
31	C₄×D₁₀₁	—	2	1	no	—
32	C₈×C₁₀₁	—	2	1	no	—
33	C₈×C₁₀₁	M₁₆	1	2	yes	—
34	#11717579	—	2	1	no	—
35	#11717579	#41	1	2	yes	—
36	C₂²×C₁₀₁	C₂×M₁₆	1	1	yes	characteristic
37	C₂×D₁₀₁	—	2	1	no	—
38	C₂×D₁₀₁	—	4	1	no	—
39	C₄×C₁₀₁	—	4	1	no	—
40	C₄×C₁₀₁	#117	1	1	yes	characteristic
41	C₄×C₁₀₁	C₂×M₁₆	1	1	yes	characteristic
42	Dic₁₀₁	—	2	1	no	—
43	Dic₁₀₁	—	4	1	no	—
44	C₂×C₁₀₁	—	2	1	no	—
45	C₂×C₁₀₁	#432	1	1	yes	characteristic
46	D₁₀₁	—	4	1	no	—
47	#2166	—	101	1	no	maximal, Sylow
48	C₁₀₁	#2166	1	1	yes	characteristic, complemented, Sylow
49	#405	—	101	1	no	—
50	#364	—	101	2	no	—
51	#349	—	101	2	no	—
52	#347	—	101	2	no	—
53	C₂×M₁₆	—	101	1	no	—
54	C₂²×C₈	—	101	1	no	—
55	#117	—	101	1	no	—
56	M₃₂	—	101	4	no	—
57	#97	—	101	1	no	—
58	#97	—	101	1	no	—
59	C₄×C₈	—	101	1	no	—
60	C₄×C₈	#87938	1	1	yes	characteristic
61	C₂²×C₄	—	101	1	no	—
62	M₁₆	—	202	2	no	—
63	C₂×C₈	—	101	1	no	—
64	C₂×C₈	—	101	1	no	—
65	C₂×C₈	—	202	2	no	—
66	C₂×C₈	C₂×#87938	1	1	yes	characteristic
67	C₂×C₈	C₂×#87938	1	1	yes	characteristic
68	C₄⋊C₄	—	202	1	no	—
69	C₂²⋊C₄	—	202	1	no	—
70	C₄²	—	101	1	no	—
71	C₄²	C₂×#87938	1	1	yes	characteristic
72	C₁₆	—	202	4	no	—
73	C₂³	—	101	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	101	1	no	—
76	C₂×C₄	—	202	1	no	—
77	C₂×C₄	—	202	1	no	—
78	C₂×C₄	—	202	1	no	—
79	C₂×C₄	C₂²×#87938	1	1	yes	characteristic
80	C₈	—	2	1	no	—
81	C₈	—	101	2	no	—
82	C₈	—	202	1	no	—
83	C₈	#13108084	1	2	yes	—
84	C₂²	—	404	1	no	—
85	C₂²	—	202	1	no	—
86	C₂²	D₁₀₁⋊M₁₆	1	1	yes	characteristic
87	C₄	—	4	1	no	—
88	C₄	—	404	1	no	—
89	C₄	—	202	1	no	—
90	C₄	#15692334	1	1	yes	characteristic
91	C₄	C₂×#13108084	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	404	1	no	—
94	C₂	#20266199	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#15692334
commutator	C₂×C₄×C₁₀₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×#87938
Fitting	C₄×C₈×C₁₀₁	C₄
socle	C₂×C₁₀₁	#432
prime radical	C₂²×D₁₀₁	M₁₆
cosocle	C₂×#11717579	C₂³
hypercenter	C₄×C₈	#87938
hypocenter	C₁₀₁	#2166
LCS	G ▷ C₂×C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₄ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
1. #20266099	C₂	semidirect
3. #20266069	C₂	semidirect
48. C₁₀₁	#2166	semidirect

Maximal subgroups

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

subgroup	index
#20266099	2
#20266074	2
#20266069	2
#20265131	2
#2166	101