Group #29680258 — subgroups

Subgroups — D₆₁×#1840 #29680258

Order 15616.

894 conjugacy classes of subgroups; only the 283 normal subgroups are shown.

normal subgroups only

This group has 894 conjugacy classes of subgroups — too many to draw. Only its 283 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	#376×D₆₁	C₂	1	1	yes	maximal, characteristic
2	#21445964	C₂	1	1	yes	maximal, characteristic, complemented
3	#21445963	C₂	1	6	yes	maximal, complemented
4	#336×D₆₁	C₂	1	6	yes	maximal
5	C₆₁×#1840	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₈×D₆₁	C₂²	1	4	yes	—
7	C₂×C₄²×D₆₁	C₂²	1	3	yes	—
8	#16839608	C₂²	1	3	yes	—
9	#16839607	C₄	1	4	yes	—
10	#95×D₆₁	C₄	1	4	yes	—
11	#16839517	C₂²	1	6	yes	—
12	#16839516	C₂²	1	12	yes	—
13	C₆₁×#376	C₂²	1	1	yes	characteristic
14	C₆₁×#336	C₂²	1	6	yes	—
15	C₂²×C₄×D₆₁	C₂×C₄	1	6	yes	—
16	C₂²×C₄×D₆₁	C₂³	1	1	yes	characteristic
17	C₂²×#92418	C₂³	1	4	yes	—
18	C₂×C₈×D₆₁	—	2	24	no	—
19	C₂×C₄×Dic₆₁	C₂×C₄	1	6	yes	—
20	C₂×C₄×Dic₆₁	C₂³	1	3	yes	—
21	C₄²×D₆₁	—	2	12	no	—
22	#14519684	C₂×C₄	1	12	yes	—
23	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
24	C₂×C₄²×C₆₁	C₂³	1	3	yes	—
25	#95×C₆₁	C₂×C₄	1	4	yes	—
26	C₂³×D₆₁	C₂²×C₄	1	1	yes	characteristic
27	C₂²×C₄×C₆₁	C₂²×C₄	1	6	yes	—
28	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
29	C₂²×Dic₆₁	C₂²×C₄	1	6	yes	—
30	C₂²×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄×D₆₁	—	2	12	no	—
32	C₂×C₄×D₆₁	—	2	24	no	—
33	C₂×C₄×D₆₁	#41	1	12	yes	—
34	C₂×C₈×C₆₁	—	2	12	no	—
35	C₄²×C₆₁	—	2	6	no	—
36	C₄×Dic₆₁	—	2	6	no	—
37	C₄×Dic₆₁	—	2	12	no	—
38	C₂×#92418	—	2	12	no	—
39	C₈×D₆₁	—	4	16	no	—
40	C₂³×C₆₁	C₂³×C₄	1	1	yes	characteristic
41	C₂²×D₆₁	#117	1	6	yes	—
42	C₂²×D₆₁	#131	1	8	yes	—
43	C₂×C₄×C₆₁	—	2	6	no	—
44	C₂×C₄×C₆₁	—	2	12	no	—
45	C₂×C₄×C₆₁	C₂×#41	1	6	yes	—
46	C₂×Dic₆₁	—	2	6	no	—
47	C₂×Dic₆₁	—	2	12	no	—
48	C₂×Dic₆₁	#117	1	6	yes	—
49	C₄×D₆₁	—	4	24	no	—
50	C₄×D₆₁	#126	1	16	yes	—
51	C₈×C₆₁	—	4	4	no	—
52	#92418	—	4	4	no	—
53	C₂×#1840	—	61	1	no	maximal, Sylow
54	C₂²×C₆₁	C₂×#117	1	3	yes	—
55	C₂²×C₆₁	C₂×#131	1	4	yes	—
56	C₂×D₆₁	#383	1	4	yes	—
57	C₂×D₆₁	#433	1	24	yes	—
58	C₄×C₆₁	—	4	6	no	—
59	C₄×C₆₁	C₂×#126	1	4	yes	—
60	Dic₆₁	—	4	6	no	—
61	Dic₆₁	#383	1	4	yes	—
62	C₂×#376	—	61	1	no	—
63	#1840	—	61	1	no	—
64	#1840	—	61	6	no	—
65	#1840	D₆₁	1	1	yes	characteristic, direct product factor
66	C₂×#336	—	61	6	no	—
67	C₂×C₆₁	C₂×#383	1	1	yes	characteristic
68	C₂×C₆₁	C₂×#433	1	6	yes	—
69	D₆₁	#1840	1	8	yes	direct product factor
70	C₂³×C₈	—	61	4	no	—
71	C₂²×C₄²	—	61	3	no	—
72	#376	—	61	3	no	—
73	#376	—	61	4	no	—
74	#376	C₂×D₆₁	1	1	yes	characteristic
75	C₂×#95	—	61	4	no	—
76	#336	—	61	12	no	—
77	#336	—	61	6	no	—
78	#336	C₂×D₆₁	1	6	yes	—
79	C₆₁	C₂×#1840	1	1	yes	characteristic, complemented, Sylow
80	C₂³×C₄	—	61	1	no	—
81	C₂³×C₄	—	61	6	no	—
82	C₂²×C₈	—	61	4	no	—
83	C₂²×C₈	—	122	24	no	—
84	C₂²×C₈	C₂²×D₆₁	1	4	yes	—
85	C₂×C₄²	—	61	6	no	—
86	C₂×C₄²	—	61	3	no	—
87	C₂×C₄²	—	122	12	no	—
88	C₂×C₄²	C₂²×D₆₁	1	3	yes	—
89	#95	—	61	12	no	—
90	#95	C₄×D₆₁	1	4	yes	—
91	C₂⁴	—	61	1	no	—
92	C₂²×C₄	—	61	1	no	—
93	C₂²×C₄	—	61	12	no	—
94	C₂²×C₄	—	61	6	no	—
95	C₂²×C₄	—	122	12	no	—
96	C₂²×C₄	—	122	24	no	—
97	C₂²×C₄	C₂×C₄×D₆₁	1	6	yes	—
98	C₂²×C₄	C₂³×D₆₁	1	1	yes	characteristic
99	C₂×C₈	—	2	12	no	—
100	C₂×C₈	—	122	12	no	—
101	C₂×C₈	—	244	16	no	—
102	C₄²	—	2	6	no	—
103	C₄²	—	122	12	no	—
104	C₄²	—	122	6	no	—
105	C₂³	—	61	6	no	—
106	C₂³	—	61	8	no	—
107	C₂³	C₂²×C₄×D₆₁	1	1	yes	characteristic
108	C₂×C₄	—	2	6	no	—
109	C₂×C₄	—	2	12	no	—
110	C₂×C₄	—	61	6	no	—
111	C₂×C₄	—	61	16	no	—
112	C₂×C₄	—	122	6	no	—
113	C₂×C₄	—	122	12	no	—
114	C₂×C₄	—	244	24	no	—
115	C₂×C₄	#41×D₆₁	1	6	yes	—
116	C₈	—	4	4	no	—
117	C₈	—	244	4	no	—
118	C₂²	—	61	4	no	—
119	C₂²	—	61	24	no	—
120	C₂²	#117×D₆₁	1	3	yes	—
121	C₂²	#131×D₆₁	1	4	yes	—
122	C₄	—	4	6	no	—
123	C₄	—	61	4	no	—
124	C₄	—	244	6	no	—
125	C₄	#126×D₆₁	1	4	yes	—
126	C₂	—	61	8	no	—
127	C₂	#383×D₆₁	1	1	yes	characteristic
128	C₂	#433×D₆₁	1	6	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#376×D₆₁

C₂

yes

maximal, characteristic

#21445964

C₂

yes

maximal, characteristic, complemented

#21445963

C₂

yes

maximal, complemented

#336×D₆₁

C₂

yes

maximal

C₆₁×#1840

C₂

yes

maximal, characteristic, complemented

C₂²×C₈×D₆₁

C₂²

yes

—

C₂×C₄²×D₆₁

C₂²

yes

—

#16839608

C₂²

yes

—

#16839607

C₄

yes

—

#95×D₆₁

C₄

yes

—

#16839517

C₂²

yes

—

#16839516

C₂²

yes

—

C₆₁×#376

C₂²

yes

characteristic

C₆₁×#336

C₂²

yes

—

C₂²×C₄×D₆₁

C₂×C₄

yes

—

C₂²×C₄×D₆₁

C₂³

yes

characteristic

C₂²×#92418

C₂³

yes

—

C₂×C₈×D₆₁

—

C₂×C₄×Dic₆₁

C₂×C₄

yes

—

C₂×C₄×Dic₆₁

C₂³

yes

—

C₄²×D₆₁

—

#14519684

C₂×C₄

yes

—

C₂²×C₈×C₆₁

C₂³

yes

—

C₂×C₄²×C₆₁

C₂³

yes

—

#95×C₆₁

C₂×C₄

yes

—

C₂³×D₆₁

C₂²×C₄

yes

characteristic

C₂²×C₄×C₆₁

C₂²×C₄

yes

—

C₂²×C₄×C₆₁

C₂⁴

yes

characteristic

C₂²×Dic₆₁

C₂²×C₄

yes

—

C₂²×Dic₆₁

C₂²×C₄

yes

characteristic

C₂×C₄×D₆₁

—

C₂×C₄×D₆₁

—

C₂×C₄×D₆₁

#41

yes

—

C₂×C₈×C₆₁

—

C₄²×C₆₁

—

C₄×Dic₆₁

—

C₄×Dic₆₁

—

C₂×#92418

—

C₈×D₆₁

—

C₂³×C₆₁

C₂³×C₄

yes

characteristic

C₂²×D₆₁

#117

yes

—

C₂²×D₆₁

#131

yes

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂×#41

yes

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

#117

yes

—

C₄×D₆₁

—

C₄×D₆₁

#126

yes

—

C₈×C₆₁

—

—

—

C₂²×C₆₁

yes

—

C₂²×C₆₁

C₂×#131

yes

—

C₂×D₆₁

#383

yes

—

C₂×D₆₁

#433

yes

—

C₄×C₆₁

—

C₄×C₆₁

C₂×#126

yes

—

Dic₆₁

—

Dic₆₁

#383

yes

—

—

—

—

D₆₁

yes

characteristic, direct product factor

C₂×#336

—

C₂×C₆₁

C₂×#383

yes

characteristic

C₂×C₆₁

C₂×#433

yes

—

D₆₁

#1840

yes

direct product factor

C₂³×C₈

—

C₂²×C₄²

—

#376

—

#376

—

#376

C₂×D₆₁

yes

characteristic

C₂×#95

—

#336

—

#336

—

#336

C₂×D₆₁

yes

—

C₆₁

C₂×#1840

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂³×C₄

—

C₂²×C₈

—

C₂²×C₈

—

122

—

C₂²×C₈

C₂²×D₆₁

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

122

—

C₂×C₄²

C₂²×D₆₁

yes

—

#95

—

#95

C₄×D₆₁

yes

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

122

—

C₂²×C₄

—

122

—

C₂²×C₄

C₂×C₄×D₆₁

yes

—

C₂²×C₄

C₂³×D₆₁

yes

characteristic

C₂×C₈

—

100

C₂×C₈

—

122

—

101

C₂×C₈

—

244

—

102

C₄²

—

103

C₄²

—

122

—

104

C₄²

—

122

—

105

C₂³

—

106

C₂³

—

107

C₂³

C₂²×C₄×D₆₁

yes

characteristic

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

122

—

113

C₂×C₄

—

122

—

114

C₂×C₄

—

244

—

115

C₂×C₄

#41×D₆₁

yes

—

116

C₈

—

117

C₈

—

244

—

118

C₂²

—

119

C₂²

—

120

C₂²

#117×D₆₁

yes

—

121

C₂²

#131×D₆₁

yes

—

122

C₄

—

123

C₄

—

124

C₄

—

244

—

125

C₄

#126×D₆₁

yes

—

126

C₂

—

127

C₂

#383×D₆₁

yes

characteristic

128

C₂

#433×D₆₁

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₆₁
commutator, socle	C₂³×C₆₁	C₂³×C₄
Fitting	C₆₁×#1840	C₂
prime radical	C₂³×D₆₁	C₂²×C₄
cosocle	C₂²×C₄×C₆₁	C₂⁴
hypercenter	#1840	D₆₁
hypocenter	C₆₁	C₂×#1840
LCS	G ▷ C₂³×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂²×C₄ ◁ #1840

subgroup

G/H

center, Frattini

C₂²×C₄

C₂³×D₆₁

commutator, socle

C₂³×C₆₁

C₂³×C₄

Fitting

C₆₁×#1840

C₂

prime radical

C₂³×D₆₁

C₂²×C₄

cosocle

C₂²×C₄×C₆₁

C₂⁴

D₆₁

C₆₁

G ▷ C₂³×C₆₁ ▷ C₆₁

C₁ ◁ C₂²×C₄ ◁ #1840

N	H ≅ G/N	type
2. #21445964	C₂	semidirect
3. #21445963	C₂	semidirect
5. C₆₁×#1840	C₂	semidirect
65. #1840	D₆₁	direct (N × H)
69. D₆₁	#1840	direct (N × H)
79. C₆₁	C₂×#1840	semidirect

H ≅ G/N

type

2. #21445964

C₂

semidirect

3. #21445963

C₂

semidirect

5. C₆₁×#1840

C₂

semidirect

65. #1840

D₆₁

direct (N × H)

69. D₆₁

#1840

direct (N × H)

79. C₆₁

C₂×#1840

semidirect

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

subgroup	index
#376×D₆₁	2
#21445964	2
#21445963	2
#336×D₆₁	2
C₆₁×#1840	2
C₂×#1840	61

subgroup

index

#376×D₆₁

#21445964

#21445963

#336×D₆₁

C₆₁×#1840

C₂×#1840

Subgroups — D₆₁×#1840 #29680258

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D61×#1840 #29680258

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₆₁×#1840 #29680258