Group #21444573 — subgroups

Subgroups — #21444573

Order 7808.

184 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 81 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	#16839784	C₂	1	2	yes	maximal
2	C₄×C₈×D₆₁	C₂	1	1	yes	maximal, characteristic
3	#16839513	C₂	1	1	yes	maximal, characteristic, complemented
4	#16839512	C₂	1	2	yes	maximal, complemented
5	C₆₁×#334	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11758189	—	2	2	no	—
7	C₂×C₈×D₆₁	C₄	1	1	yes	characteristic
8	C₂×C₈×D₆₁	C₄	1	1	yes	characteristic
9	C₄²×D₆₁	C₂²	1	1	yes	characteristic
10	C₄⋊#92418	C₂²	1	2	yes	—
11	#14519706	—	2	2	no	—
12	C₄×#92418	C₂²	1	1	yes	characteristic
13	C₈×Dic₆₁	C₄	1	1	yes	characteristic
14	C₈×Dic₆₁	C₄	1	1	yes	characteristic
15	C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
16	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×D₆₁	D₄	1	1	yes	characteristic
19	C₂×C₄×D₆₁	Q₈	1	1	yes	characteristic
20	C₂×C₈×C₆₁	—	2	2	no	—
21	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
23	C₄²×C₆₁	C₂³	1	1	yes	characteristic
24	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
25	C₄×Dic₆₁	D₄	1	1	yes	characteristic
26	C₄×Dic₆₁	Q₈	1	1	yes	characteristic
27	C₂×#92418	—	2	2	no	—
28	C₂×#92418	C₂×C₄	1	1	yes	characteristic
29	C₂×#92418	C₂×C₄	1	1	yes	characteristic
30	#11758189	—	4	4	no	—
31	C₈×D₆₁	—	2	2	no	—
32	C₈×D₆₁	—	2	2	no	—
33	C₂²×D₆₁	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
37	C₂×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
38	C₂×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
39	C₂×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
40	C₄×D₆₁	—	2	1	no	—
41	C₄×D₆₁	—	2	1	no	—
42	C₄×D₆₁	—	2	2	no	—
43	C₄×D₆₁	SD₁₆	1	4	yes	—
44	C₈×C₆₁	—	2	1	no	—
45	C₈×C₆₁	—	4	2	no	—
46	C₈×C₆₁	M₁₆	1	2	yes	complemented
47	#92418	—	2	1	no	—
48	#92418	—	4	2	no	—
49	#92418	M₁₆	1	2	yes	complemented
50	C₂²×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
51	C₂×D₆₁	—	2	1	no	—
52	C₂×D₆₁	—	2	1	no	—
53	C₂×D₆₁	#106	1	2	yes	—
54	C₄×C₆₁	—	2	1	no	—
55	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
56	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
57	C₄×C₆₁	C₂×SD₁₆	1	2	yes	—
58	Dic₆₁	—	2	1	no	—
59	Dic₆₁	#106	1	2	yes	—
60	Dic₆₁	#108	1	2	yes	—
61	#1566	—	61	1	no	maximal, Sylow
62	C₂×C₆₁	#423	1	1	yes	characteristic
63	C₂×C₆₁	C₂×#106	1	1	yes	characteristic
64	C₂×C₆₁	C₂×#108	1	1	yes	characteristic
65	D₆₁	—	2	2	no	—
66	#423	—	61	2	no	—
67	C₂×C₄×C₈	—	61	1	no	—
68	#334	—	61	2	no	—
69	#334	—	61	1	no	—
70	#334	D₆₁	1	1	yes	characteristic, complemented
71	C₆₁	#1566	1	1	yes	characteristic, complemented, Sylow
72	C₂×M₁₆	—	122	2	no	—
73	C₂²×C₈	—	61	1	no	—
74	C₂²×C₈	—	61	1	no	—
75	C₂×C₄²	—	61	1	no	—
76	C₄⋊C₈	—	61	2	no	—
77	C₄⋊C₈	—	122	2	no	—
78	C₄⋊C₈	C₂×D₆₁	1	2	yes	—
79	C₄×C₈	—	61	1	no	—
80	C₄×C₈	—	61	1	no	—
81	C₄×C₈	—	61	1	no	—
82	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
83	C₂²×C₄	—	61	1	no	—
84	C₂²×C₄	—	61	1	no	—
85	C₂²×C₄	—	61	1	no	—
86	M₁₆	—	244	4	no	—
87	C₂×C₈	—	2	2	no	—
88	C₂×C₈	—	61	1	no	—
89	C₂×C₈	—	61	1	no	—
90	C₂×C₈	—	122	2	no	—
91	C₂×C₈	—	122	2	no	—
92	C₂×C₈	—	122	2	no	—
93	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
94	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
95	C₄²	—	61	1	no	—
96	C₄²	—	61	1	no	—
97	C₄²	—	61	1	no	—
98	C₄²	C₂²×D₆₁	1	1	yes	characteristic
99	C₂³	—	61	1	no	—
100	C₂×C₄	—	61	1	no	—
101	C₂×C₄	—	61	1	no	—
102	C₂×C₄	—	61	4	no	—
103	C₂×C₄	—	61	1	no	—
104	C₂×C₄	—	122	2	no	—
105	C₂×C₄	—	122	1	no	—
106	C₂×C₄	—	122	1	no	—
107	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
108	C₂×C₄	D₄×D₆₁	1	1	yes	characteristic
109	C₂×C₄	Q₈×D₆₁	1	1	yes	characteristic
110	C₈	—	2	1	no	—
111	C₈	—	4	2	no	—
112	C₈	—	61	2	no	—
113	C₈	—	122	1	no	—
114	C₈	—	244	2	no	—
115	C₈	#11758189	1	2	yes	complemented
116	C₂²	—	61	2	no	—
117	C₂²	—	122	1	no	—
118	C₂²	—	122	1	no	—
119	C₂²	C₄⋊C₄×D₆₁	1	1	yes	characteristic
120	C₄	—	2	1	no	—
121	C₄	—	61	2	no	—
122	C₄	—	61	2	no	—
123	C₄	—	122	1	no	—
124	C₄	M₁₆×D₆₁	1	1	yes	characteristic
125	C₄	C₂×#11758189	1	1	yes	characteristic
126	C₄	SD₁₆×D₆₁	1	2	yes	—
127	C₂	—	122	2	no	—
128	C₂	#16839784	1	1	yes	characteristic
129	C₂	#106×D₆₁	1	1	yes	characteristic
130	C₂	#108×D₆₁	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16839784

C₂

yes

maximal

C₄×C₈×D₆₁

C₂

yes

maximal, characteristic

#16839513

C₂

yes

maximal, characteristic, complemented

#16839512

C₂

yes

maximal, complemented

C₆₁×#334

C₂

yes

maximal, characteristic, complemented

C₂×#11758189

—

C₂×C₈×D₆₁

C₄

yes

characteristic

C₂×C₈×D₆₁

C₄

yes

characteristic

C₄²×D₆₁

C₂²

yes

characteristic

C₄⋊#92418

C₂²

yes

—

#14519706

—

C₄×#92418

C₂²

yes

characteristic

C₈×Dic₆₁

C₄

yes

characteristic

C₈×Dic₆₁

C₄

yes

characteristic

C₄⋊C₈×C₆₁

C₂²

yes

—

C₄×C₈×C₆₁

C₂²

yes

characteristic

C₂×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂×C₄×D₆₁

D₄

yes

characteristic

C₂×C₄×D₆₁

Q₈

yes

characteristic

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₄²×C₆₁

C₂³

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

D₄

yes

characteristic

C₄×Dic₆₁

Q₈

yes

characteristic

C₂×#92418

—

C₂×#92418

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

#11758189

—

C₈×D₆₁

—

C₈×D₆₁

—

C₂²×D₆₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

C₂×Q₈

yes

characteristic

C₂×Dic₆₁

C₄⋊C₄

yes

characteristic

C₂×Dic₆₁

C₄⋊C₄

yes

characteristic

C₂×Dic₆₁

C₄⋊C₄

yes

characteristic

C₄×D₆₁

—

C₄×D₆₁

—

C₄×D₆₁

—

C₄×D₆₁

SD₁₆

yes

—

C₈×C₆₁

—

C₈×C₆₁

—

C₈×C₆₁

M₁₆

yes

—

—

M₁₆

yes

complemented

C₂²×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

#106

yes

—

C₄×C₆₁

—

C₄×C₆₁

C₂×M₁₆

yes

characteristic

C₄×C₆₁

C₂×M₁₆

yes

characteristic

C₄×C₆₁

C₂×SD₁₆

yes

—

Dic₆₁

—

Dic₆₁

#106

yes

—

Dic₆₁

#108

yes

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

D₆₁

—

#423

—

C₂×C₄×C₈

—

#334

—

#334

—

#334

D₆₁

yes

characteristic, complemented

C₆₁

#1566

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

122

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

122

—

C₄⋊C₈

C₂×D₆₁

yes

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₆₁

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

244

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

C₄×D₆₁

yes

characteristic

C₂×C₈

C₄×D₆₁

yes

characteristic

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂²×D₆₁

yes

characteristic

C₂³

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

122

—

105

C₂×C₄

—

122

—

106

C₂×C₄

—

122

—

107

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

108

C₂×C₄

D₄×D₆₁

yes

characteristic

109

C₂×C₄

Q₈×D₆₁

yes

characteristic

110

C₈

—

111

C₈

—

112

C₈

—

113

C₈

—

122

—

114

C₈

—

244

—

115

C₈

#11758189

yes

complemented

116

C₂²

—

117

C₂²

—

122

—

118

C₂²

—

122

—

119

C₂²

C₄⋊C₄×D₆₁

yes

characteristic

120

C₄

—

121

C₄

—

122

C₄

—

123

C₄

—

122

—

124

C₄

M₁₆×D₆₁

yes

characteristic

125

C₄

C₂×#11758189

yes

characteristic

126

C₄

SD₁₆×D₆₁

yes

—

127

C₂

—

122

—

128

C₂

#16839784

yes

characteristic

129

C₂

#106×D₆₁

yes

characteristic

130

C₂

#108×D₆₁

yes

characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₆₁
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₄²	C₂²×D₆₁
Fitting	C₆₁×#334	C₂
socle	C₂²×C₆₁	C₂×C₄⋊C₄
hypercenter	#334	D₆₁
hypocenter	C₆₁	#1566
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ #334

subgroup

G/H

center

C₂×C₄

D₄×D₆₁

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₄²

C₂²×D₆₁

Fitting

C₆₁×#334

C₂

socle

C₂²×C₆₁

C₂×C₄⋊C₄

D₆₁

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ #334

N	H ≅ G/N	type
3. #16839513	C₂	semidirect
4. #16839512	C₂	semidirect
5. C₆₁×#334	C₂	semidirect
46. C₈×C₆₁	M₁₆	semidirect
49. #92418	M₁₆	semidirect
70. #334	D₆₁	semidirect
71. C₆₁	#1566	semidirect
115. C₈	#11758189	semidirect

H ≅ G/N

type

3. #16839513

C₂

semidirect

4. #16839512

C₂

semidirect

5. C₆₁×#334

C₂

semidirect

46. C₈×C₆₁

M₁₆

semidirect

49. #92418

M₁₆

semidirect

70. #334

D₆₁

semidirect

71. C₆₁

#1566

semidirect

115. C₈

#11758189

semidirect

Subgroups — #21444573

Conjugacy classes of subgroups

Complements