Subgroups — #20266201

Order 6464.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15692322	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄⋊#11717581	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊#11717581	C₂	1	1	yes	maximal, characteristic
4	C₂²⋊#11717581	C₂	1	1	yes	maximal, characteristic
5	#15692310	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×#11717581	C₂	1	1	yes	maximal, characteristic, complemented
7	#15692211	C₂	1	1	yes	maximal, characteristic
8	C₂×#11717581	C₂²	1	1	yes	characteristic
9	C₂×#11717581	C₂²	1	1	yes	characteristic
10	C₂×#11717581	C₂²	1	1	yes	characteristic
11	C₂×#11717581	C₂²	1	1	yes	characteristic
12	C₂²×Dic₁₀₁	C₂²	1	1	yes	characteristic
13	#13108053	C₄	1	1	yes	characteristic
14	#13108053	C₄	1	1	yes	characteristic
15	C₂²⋊Dic₁₀₁	C₄	1	1	yes	characteristic
16	C₄×Dic₁₀₁	C₂²	1	1	yes	characteristic
17	C₄×Dic₁₀₁	C₂²	1	1	yes	characteristic
18	C₂²⋊C₄×C₁₀₁	C₄	1	1	yes	characteristic
19	C₂³×C₁₀₁	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
22	C₂×Dic₁₀₁	—	2	1	no	—
23	C₂×Dic₁₀₁	—	2	1	no	—
24	C₂×Dic₁₀₁	C₂×C₄	1	1	yes	characteristic
25	C₂×Dic₁₀₁	C₂×C₄	1	1	yes	characteristic
26	C₂×Dic₁₀₁	C₂×C₄	1	1	yes	characteristic
27	C₂×Dic₁₀₁	C₂³	1	1	yes	characteristic
28	#11717581	—	2	1	no	—
29	#11717581	—	2	1	no	—
30	#11717581	—	2	1	no	—
31	#11717581	—	2	1	no	—
32	C₂²×C₁₀₁	—	2	1	no	—
33	C₂²×C₁₀₁	—	2	1	no	—
34	C₂²×C₁₀₁	—	2	1	no	—
35	C₂²×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
36	C₄×C₁₀₁	—	2	1	no	—
37	C₄×C₁₀₁	—	2	1	no	—
38	Dic₁₀₁	—	2	1	no	—
39	Dic₁₀₁	—	2	1	no	—
40	Dic₁₀₁	—	2	1	no	—
41	Dic₁₀₁	#41	1	1	yes	characteristic
42	Dic₁₀₁	#41	1	1	yes	characteristic
43	C₂×C₁₀₁	—	4	1	no	—
44	C₂×C₁₀₁	#117	1	1	yes	characteristic
45	C₂×C₁₀₁	#131	1	1	yes	characteristic
46	C₂×C₁₀₁	#131	1	1	yes	characteristic
47	C₁₀₁	#433	1	1	yes	characteristic, complemented, Sylow
48	#433	—	101	1	no	maximal, Sylow
49	#117	—	101	1	no	—
50	C₄⋊C₈	—	101	1	no	—
51	C₄⋊C₈	—	101	1	no	—
52	C₂²⋊C₈	—	101	1	no	—
53	C₂²⋊C₈	—	101	1	no	—
54	#97	—	101	1	no	—
55	C₄×C₈	—	101	1	no	—
56	C₂²×C₄	—	101	1	no	—
57	C₂×C₈	—	101	1	no	—
58	C₂×C₈	—	101	1	no	—
59	C₂×C₈	—	101	1	no	—
60	C₂×C₈	—	101	1	no	—
61	C₄⋊C₄	—	101	1	no	—
62	C₄⋊C₄	—	101	1	no	—
63	C₂²⋊C₄	—	101	1	no	—
64	C₂²⋊C₄	#87938	1	1	yes	characteristic
65	C₄²	—	101	1	no	—
66	C₄²	—	101	1	no	—
67	C₂³	C₂×#87938	1	1	yes	characteristic
68	C₂×C₄	—	101	1	no	—
69	C₂×C₄	—	101	1	no	—
70	C₂×C₄	—	101	1	no	—
71	C₂×C₄	—	101	1	no	—
72	C₂×C₄	—	202	1	no	—
73	C₂×C₄	—	202	1	no	—
74	C₂×C₄	C₂×#87938	1	1	yes	characteristic
75	C₂×C₄	C₂×#87938	1	1	yes	characteristic
76	C₈	—	202	1	no	—
77	C₈	—	202	1	no	—
78	C₈	—	202	1	no	—
79	C₈	—	202	1	no	—
80	C₂²	—	2	1	no	—
81	C₂²	—	2	1	no	—
82	C₂²	—	2	1	no	—
83	C₂²	C₂²×#87938	1	1	yes	characteristic
84	C₄	—	2	1	no	—
85	C₄	—	2	1	no	—
86	C₄	—	101	1	no	—
87	C₄	—	101	1	no	—
88	C₄	—	202	1	no	—
89	C₄	—	202	1	no	—
90	C₄	—	202	1	no	—
91	C₂	—	4	1	no	—
92	C₂	#15692334	1	1	yes	characteristic
93	C₂	#15692342	1	1	yes	characteristic
94	C₂	#15692342	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×#87938
commutator, socle	C₂²×C₁₀₁	C₂²×C₄
Fitting	C₂²⋊C₄×C₁₀₁	C₄
hypercenter	C₂²⋊C₄	#87938
hypocenter	C₁₀₁	#433
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
1. #15692322	C₂	semidirect
2. C₄⋊#11717581	C₂	semidirect
5. #15692310	C₂	semidirect
6. C₄×#11717581	C₂	semidirect
47. C₁₀₁	#433	semidirect