Group #21444115 — subgroups

Subgroups — #21444115

Order 7808.

190 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16839813	C₂	1	1	yes	maximal, characteristic
2	#16839813	C₂	1	1	yes	maximal, characteristic
3	C₄×#11758189	C₂	1	1	yes	maximal, characteristic
4	#16839484	C₂	1	1	yes	maximal, characteristic, complemented
5	#16839484	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×#92418	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#322	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#11758189	C₄	1	2	yes	—
9	C₄²×D₆₁	C₂²	1	1	yes	characteristic
10	#14519706	C₄	1	2	yes	—
11	#14519706	C₄	1	2	yes	—
12	#14519689	C₄	1	2	yes	—
13	#14519689	C₄	1	2	yes	—
14	#14519687	C₄	1	2	yes	—
15	C₄×#92418	C₂²	1	1	yes	characteristic
16	C₄×#92418	C₂²	1	1	yes	characteristic
17	C₄×#92418	C₂²	1	1	yes	characteristic
18	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
19	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
20	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
25	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
26	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
27	C₄²×C₆₁	C₂³	1	1	yes	characteristic
28	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
29	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
30	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
31	C₂×#92418	C₂×C₄	1	2	yes	—
32	C₂×#92418	C₂×C₄	1	2	yes	—
33	C₂×#92418	C₂×C₄	1	2	yes	—
34	#11758189	—	2	4	no	—
35	C₂²×D₆₁	C₄²	1	1	yes	characteristic
36	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
39	C₂×Dic₆₁	C₄²	1	1	yes	characteristic
40	C₂×Dic₆₁	C₄²	1	1	yes	characteristic
41	C₂×Dic₆₁	C₄²	1	1	yes	characteristic
42	C₄×D₆₁	—	2	2	no	—
43	C₄×D₆₁	—	2	2	no	—
44	C₄×D₆₁	—	2	2	no	—
45	C₈×C₆₁	—	2	2	no	—
46	C₈×C₆₁	—	2	2	no	—
47	C₈×C₆₁	—	2	2	no	—
48	#92418	—	2	2	no	—
49	#92418	—	2	2	no	—
50	#92418	M₁₆	1	4	yes	—
51	C₂²×C₆₁	C₂×C₄²	1	1	yes	characteristic
52	C₂×D₆₁	—	2	1	no	—
53	C₂×D₆₁	—	2	1	no	—
54	C₂×D₆₁	—	2	1	no	—
55	C₄×C₆₁	C₂×M₁₆	1	2	yes	—
56	C₄×C₆₁	#131	1	2	yes	—
57	C₄×C₆₁	#131	1	2	yes	—
58	Dic₆₁	—	2	1	no	—
59	Dic₆₁	—	2	1	no	—
60	Dic₆₁	—	2	1	no	—
61	#1453	—	61	1	no	maximal, Sylow
62	C₂×C₆₁	C₄×M₁₆	1	1	yes	characteristic
63	C₂×C₆₁	#405	1	1	yes	characteristic
64	C₂×C₆₁	#405	1	1	yes	characteristic
65	D₆₁	—	4	1	no	—
66	#431	—	61	1	no	—
67	#431	—	61	1	no	—
68	C₄×M₁₆	—	61	1	no	—
69	#322	—	61	1	no	—
70	#322	—	61	1	no	—
71	#322	D₆₁	1	1	yes	characteristic, complemented
72	C₈²	—	61	1	no	—
73	C₆₁	#1453	1	1	yes	characteristic, complemented, Sylow
74	C₂×M₁₆	—	61	2	no	—
75	C₂×C₄²	—	61	1	no	—
76	C₄⋊C₈	—	61	2	no	—
77	C₄⋊C₈	—	61	2	no	—
78	C₂²⋊C₈	—	61	2	no	—
79	C₂²⋊C₈	—	61	2	no	—
80	#97	—	61	2	no	—
81	C₄×C₈	—	61	1	no	—
82	C₄×C₈	—	61	1	no	—
83	C₄×C₈	—	61	1	no	—
84	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
85	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
86	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
87	C₂²×C₄	—	61	1	no	—
88	C₂²×C₄	—	61	1	no	—
89	C₂²×C₄	—	61	1	no	—
90	M₁₆	—	122	4	no	—
91	C₂×C₈	—	61	2	no	—
92	C₂×C₈	—	61	2	no	—
93	C₂×C₈	—	61	2	no	—
94	C₂×C₈	C₄×D₆₁	1	2	yes	—
95	C₂×C₈	C₄×D₆₁	1	2	yes	—
96	C₂×C₈	C₄×D₆₁	1	2	yes	—
97	C₄²	—	61	1	no	—
98	C₄²	—	61	1	no	—
99	C₄²	—	61	1	no	—
100	C₄²	C₂²×D₆₁	1	1	yes	characteristic
101	C₂³	—	61	1	no	—
102	C₂×C₄	—	61	1	no	—
103	C₂×C₄	—	61	1	no	—
104	C₂×C₄	—	61	1	no	—
105	C₂×C₄	—	122	2	no	—
106	C₂×C₄	—	122	2	no	—
107	C₂×C₄	—	122	2	no	—
108	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
109	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
110	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
111	C₈	—	2	2	no	—
112	C₈	—	2	2	no	—
113	C₈	—	2	2	no	—
114	C₈	—	61	4	no	—
115	C₈	—	122	2	no	—
116	C₈	—	122	2	no	—
117	C₂²	—	122	1	no	—
118	C₂²	—	122	1	no	—
119	C₂²	—	122	1	no	—
120	C₂²	C₄²×D₆₁	1	1	yes	characteristic
121	C₄	—	122	1	no	—
122	C₄	—	122	1	no	—
123	C₄	—	122	1	no	—
124	C₄	M₁₆×D₆₁	1	2	yes	—
125	C₄	#14519783	1	2	yes	—
126	C₄	#14519785	1	2	yes	—
127	C₂	—	244	1	no	—
128	C₂	#16839714	1	1	yes	characteristic
129	C₂	#16839716	1	1	yes	characteristic
130	C₂	#16839719	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16839813

C₂

yes

maximal, characteristic

#16839813

C₂

yes

maximal, characteristic

C₄×#11758189

C₂

yes

maximal, characteristic

#16839484

C₂

yes

maximal, characteristic, complemented

#16839484

C₂

yes

maximal, characteristic, complemented

C₈×#92418

C₂

yes

maximal, characteristic, complemented

C₆₁×#322

C₂

yes

maximal, characteristic, complemented

C₂×#11758189

C₄

yes

—

C₄²×D₆₁

C₂²

yes

characteristic

#14519706

C₄

yes

—

#14519706

C₄

yes

—

#14519689

C₄

yes

—

#14519689

C₄

yes

—

#14519687

C₄

yes

—

C₄×#92418

C₂²

yes

characteristic

C₄×#92418

C₂²

yes

characteristic

C₄×#92418

C₂²

yes

characteristic

C₄×C₈×C₆₁

C₂²

yes

characteristic

C₄×C₈×C₆₁

C₂²

yes

characteristic

C₄×C₈×C₆₁

C₂²

yes

characteristic

C₂×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₄²×C₆₁

C₂³

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

—

C₂×#92418

C₂×C₄

yes

—

C₂×#92418

C₂×C₄

yes

—

#11758189

—

C₂²×D₆₁

C₄²

yes

characteristic

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

C₄²

yes

characteristic

C₂×Dic₆₁

C₄²

yes

characteristic

C₂×Dic₆₁

C₄²

yes

characteristic

C₄×D₆₁

—

C₄×D₆₁

—

C₄×D₆₁

—

C₈×C₆₁

—

C₈×C₆₁

—

C₈×C₆₁

—

#92418

—

#92418

—

#92418

M₁₆

yes

—

C₂²×C₆₁

C₂×C₄²

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

—

C₄×C₆₁

C₂×M₁₆

yes

—

C₄×C₆₁

#131

yes

—

C₄×C₆₁

#131

yes

—

Dic₆₁

—

Dic₆₁

—

Dic₆₁

—

#1453

—

maximal, Sylow

C₂×C₆₁

C₄×M₁₆

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

D₆₁

—

#431

—

#431

—

C₄×M₁₆

—

#322

—

#322

—

#322

D₆₁

yes

characteristic, complemented

C₈²

—

C₆₁

#1453

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₆₁

yes

characteristic

C₄×C₈

C₂×D₆₁

yes

characteristic

C₄×C₈

C₂×D₆₁

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

122

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₆₁

yes

—

C₂×C₈

C₄×D₆₁

yes

—

C₂×C₈

C₄×D₆₁

yes

—

C₄²

—

C₄²

—

C₄²

—

100

C₄²

C₂²×D₆₁

yes

characteristic

101

C₂³

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

122

—

106

C₂×C₄

—

122

—

107

C₂×C₄

—

122

—

108

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

109

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

110

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

111

C₈

—

112

C₈

—

113

C₈

—

114

C₈

—

115

C₈

—

122

—

116

C₈

—

122

—

117

C₂²

—

122

—

118

C₂²

—

122

—

119

C₂²

—

122

—

120

C₂²

C₄²×D₆₁

yes

characteristic

121

C₄

—

122

—

122

C₄

—

122

—

123

C₄

—

122

—

124

C₄

M₁₆×D₆₁

yes

—

125

C₄

#14519783

yes

—

126

C₄

#14519785

yes

—

127

C₂

—

244

—

128

C₂

#16839714

yes

characteristic

129

C₂

#16839716

yes

characteristic

130

C₂

#16839719

yes

characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂²×D₆₁
commutator, socle	C₂²×C₆₁	C₂×C₄²
Fitting	C₆₁×#322	C₂
hypercenter	#322	D₆₁
hypocenter	C₆₁	#1453
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄² ◁ #322

subgroup

G/H

center, Frattini

C₄²

C₂²×D₆₁

commutator, socle

C₂²×C₆₁

C₂×C₄²

Fitting

C₆₁×#322

C₂

D₆₁

C₆₁

G ▷ C₂²×C₆₁ ▷ C₆₁

C₁ ◁ C₄² ◁ #322

N	H ≅ G/N	type
4. #16839484	C₂	semidirect
5. #16839484	C₂	semidirect
6. C₈×#92418	C₂	semidirect
7. C₆₁×#322	C₂	semidirect
71. #322	D₆₁	semidirect
73. C₆₁	#1453	semidirect

H ≅ G/N

type

4. #16839484

C₂

semidirect

5. #16839484

C₂

semidirect

6. C₈×#92418

C₂

semidirect

7. C₆₁×#322

C₂

semidirect

71. #322

D₆₁

semidirect

73. C₆₁

#1453

semidirect

Subgroups — #21444115

Conjugacy classes of subgroups

Complements