Group #35404649 — subgroups

Subgroups — #1840×D₈₃ #35404649

Order 21248.

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×D₈₃	C₂	1	1	yes	maximal, characteristic
2	#24907608	C₂	1	1	yes	maximal, characteristic, complemented
3	#24907607	C₂	1	6	yes	maximal, complemented
4	#336×D₈₃	C₂	1	6	yes	maximal
5	C₈₃×#1840	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₈×D₈₃	C₂²	1	4	yes	—
7	C₂×C₄²×D₈₃	C₂²	1	3	yes	—
8	#19127547	C₂²	1	3	yes	—
9	#19127546	C₄	1	4	yes	—
10	#95×D₈₃	C₄	1	4	yes	—
11	#19127456	C₂²	1	6	yes	—
12	#19127455	C₂²	1	12	yes	—
13	#376×C₈₃	C₂²	1	1	yes	characteristic
14	#336×C₈₃	C₂²	1	6	yes	—
15	C₂²×C₄×D₈₃	C₂×C₄	1	6	yes	—
16	C₂²×C₄×D₈₃	C₂³	1	1	yes	characteristic
17	C₂²×C₈₃⋊C₈	C₂³	1	4	yes	—
18	C₂×C₈×D₈₃	—	2	24	no	—
19	C₂×C₄×Dic₈₃	C₂×C₄	1	6	yes	—
20	C₂×C₄×Dic₈₃	C₂³	1	3	yes	—
21	C₄²×D₈₃	—	2	12	no	—
22	C₈₃⋊#95	C₂×C₄	1	12	yes	—
23	C₂²×C₈×C₈₃	C₂³	1	4	yes	—
24	C₂×C₄²×C₈₃	C₂³	1	3	yes	—
25	#95×C₈₃	C₂×C₄	1	4	yes	—
26	C₂³×D₈₃	C₂²×C₄	1	1	yes	characteristic
27	C₂²×Dic₈₃	C₂²×C₄	1	6	yes	—
28	C₂²×Dic₈₃	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×D₈₃	—	2	12	no	—
30	C₂×C₄×D₈₃	—	2	24	no	—
31	C₂×C₄×D₈₃	#41	1	12	yes	—
32	C₂×C₈₃⋊C₈	—	2	12	no	—
33	C₈×D₈₃	—	4	16	no	—
34	C₄×Dic₈₃	—	2	6	no	—
35	C₄×Dic₈₃	—	2	12	no	—
36	C₂²×C₄×C₈₃	C₂²×C₄	1	6	yes	—
37	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
38	C₂×C₈×C₈₃	—	2	12	no	—
39	C₄²×C₈₃	—	2	6	no	—
40	C₂³×C₈₃	C₂³×C₄	1	1	yes	characteristic
41	C₂²×D₈₃	#117	1	6	yes	—
42	C₂²×D₈₃	#131	1	8	yes	—
43	C₂×C₄×C₈₃	—	2	6	no	—
44	C₂×C₄×C₈₃	—	2	12	no	—
45	C₂×C₄×C₈₃	C₂×#41	1	6	yes	—
46	C₂×Dic₈₃	—	2	6	no	—
47	C₂×Dic₈₃	—	2	12	no	—
48	C₂×Dic₈₃	#117	1	6	yes	—
49	C₄×D₈₃	—	4	24	no	—
50	C₄×D₈₃	#126	1	16	yes	—
51	C₈×C₈₃	—	4	4	no	—
52	C₈₃⋊C₈	—	4	4	no	—
53	C₂²×C₈₃	C₂×#117	1	3	yes	—
54	C₂²×C₈₃	C₂×#131	1	4	yes	—
55	C₂×D₈₃	#383	1	4	yes	—
56	C₂×D₈₃	#433	1	24	yes	—
57	C₄×C₈₃	—	4	6	no	—
58	C₄×C₈₃	C₂×#126	1	4	yes	—
59	Dic₈₃	—	4	6	no	—
60	Dic₈₃	#383	1	4	yes	—
61	C₂×#1840	—	83	1	no	maximal, Sylow
62	C₂×C₈₃	C₂×#383	1	1	yes	characteristic
63	C₂×C₈₃	C₂×#433	1	6	yes	—
64	D₈₃	#1840	1	8	yes	direct product factor
65	C₂×#376	—	83	1	no	—
66	#1840	—	83	1	no	—
67	#1840	—	83	6	no	—
68	#1840	D₈₃	1	1	yes	characteristic, direct product factor
69	C₂×#336	—	83	6	no	—
70	C₈₃	C₂×#1840	1	1	yes	characteristic, complemented, Sylow
71	C₂³×C₈	—	83	4	no	—
72	C₂²×C₄²	—	83	3	no	—
73	#376	—	83	3	no	—
74	#376	—	83	4	no	—
75	#376	C₂×D₈₃	1	1	yes	characteristic
76	C₂×#95	—	83	4	no	—
77	#336	—	83	12	no	—
78	#336	—	83	6	no	—
79	#336	C₂×D₈₃	1	6	yes	—
80	C₂³×C₄	—	83	1	no	—
81	C₂³×C₄	—	83	6	no	—
82	C₂²×C₈	—	83	4	no	—
83	C₂²×C₈	—	166	24	no	—
84	C₂²×C₈	C₂²×D₈₃	1	4	yes	—
85	C₂×C₄²	—	83	6	no	—
86	C₂×C₄²	—	83	3	no	—
87	C₂×C₄²	—	166	12	no	—
88	C₂×C₄²	C₂²×D₈₃	1	3	yes	—
89	#95	—	83	12	no	—
90	#95	C₄×D₈₃	1	4	yes	—
91	C₂⁴	—	83	1	no	—
92	C₂²×C₄	—	83	1	no	—
93	C₂²×C₄	—	83	12	no	—
94	C₂²×C₄	—	83	6	no	—
95	C₂²×C₄	—	166	12	no	—
96	C₂²×C₄	—	166	24	no	—
97	C₂²×C₄	C₂×C₄×D₈₃	1	6	yes	—
98	C₂²×C₄	C₂³×D₈₃	1	1	yes	characteristic
99	C₂×C₈	—	2	12	no	—
100	C₂×C₈	—	332	16	no	—
101	C₂×C₈	—	166	12	no	—
102	C₄²	—	2	6	no	—
103	C₄²	—	166	12	no	—
104	C₄²	—	166	6	no	—
105	C₂³	—	83	6	no	—
106	C₂³	—	83	8	no	—
107	C₂³	C₂²×C₄×D₈₃	1	1	yes	characteristic
108	C₂×C₄	—	2	6	no	—
109	C₂×C₄	—	2	12	no	—
110	C₂×C₄	—	332	24	no	—
111	C₂×C₄	—	83	6	no	—
112	C₂×C₄	—	83	16	no	—
113	C₂×C₄	—	166	6	no	—
114	C₂×C₄	—	166	12	no	—
115	C₂×C₄	#41×D₈₃	1	6	yes	—
116	C₈	—	4	4	no	—
117	C₈	—	332	4	no	—
118	C₂²	—	83	4	no	—
119	C₂²	—	83	24	no	—
120	C₂²	#117×D₈₃	1	3	yes	—
121	C₂²	#131×D₈₃	1	4	yes	—
122	C₄	—	4	6	no	—
123	C₄	—	332	6	no	—
124	C₄	—	83	4	no	—
125	C₄	#126×D₈₃	1	4	yes	—
126	C₂	—	83	8	no	—
127	C₂	#383×D₈₃	1	1	yes	characteristic
128	C₂	#433×D₈₃	1	6	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#376×D₈₃

C₂

yes

maximal, characteristic

#24907608

C₂

yes

maximal, characteristic, complemented

#24907607

C₂

yes

maximal, complemented

#336×D₈₃

C₂

yes

maximal

C₈₃×#1840

C₂

yes

maximal, characteristic, complemented

C₂²×C₈×D₈₃

C₂²

yes

—

C₂×C₄²×D₈₃

C₂²

yes

—

#19127547

C₂²

yes

—

#19127546

C₄

yes

—

#95×D₈₃

C₄

yes

—

#19127456

C₂²

yes

—

#19127455

C₂²

yes

—

#376×C₈₃

C₂²

yes

characteristic

#336×C₈₃

C₂²

yes

—

C₂²×C₄×D₈₃

C₂×C₄

yes

—

C₂²×C₄×D₈₃

C₂³

yes

characteristic

C₂²×C₈₃⋊C₈

C₂³

yes

—

C₂×C₈×D₈₃

—

C₂×C₄×Dic₈₃

C₂×C₄

yes

—

C₂×C₄×Dic₈₃

C₂³

yes

—

C₄²×D₈₃

—

C₈₃⋊#95

C₂×C₄

yes

—

C₂²×C₈×C₈₃

C₂³

yes

—

C₂×C₄²×C₈₃

C₂³

yes

—

#95×C₈₃

C₂×C₄

yes

—

C₂³×D₈₃

C₂²×C₄

yes

characteristic

C₂²×Dic₈₃

C₂²×C₄

yes

—

C₂²×Dic₈₃

C₂²×C₄

yes

characteristic

C₂×C₄×D₈₃

—

C₂×C₄×D₈₃

—

C₂×C₄×D₈₃

#41

yes

—

C₂×C₈₃⋊C₈

—

C₈×D₈₃

—

C₄×Dic₈₃

—

C₄×Dic₈₃

—

C₂²×C₄×C₈₃

C₂²×C₄

yes

—

C₂²×C₄×C₈₃

C₂⁴

yes

characteristic

C₂×C₈×C₈₃

—

C₄²×C₈₃

—

C₂³×C₈₃

C₂³×C₄

yes

characteristic

C₂²×D₈₃

#117

yes

—

C₂²×D₈₃

#131

yes

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

C₂×#41

yes

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

#117

yes

—

C₄×D₈₃

—

C₄×D₈₃

#126

yes

—

C₈×C₈₃

—

C₈₃⋊C₈

—

C₂²×C₈₃

C₂×#117

yes

—

C₂²×C₈₃

C₂×#131

yes

—

C₂×D₈₃

#383

yes

—

C₂×D₈₃

#433

yes

—

C₄×C₈₃

—

C₄×C₈₃

C₂×#126

yes

—

Dic₈₃

—

Dic₈₃

#383

yes

—

—

C₂×C₈₃

yes

C₂×C₈₃

yes

—

D₈₃

#1840

yes

direct product factor

—

—

—

D₈₃

yes

characteristic, direct product factor

C₂×#336

—

C₈₃

C₂×#1840

yes

characteristic, complemented, Sylow

C₂³×C₈

—

C₂²×C₄²

—

#376

—

#376

—

#376

C₂×D₈₃

yes

characteristic

C₂×#95

—

#336

—

#336

—

#336

C₂×D₈₃

yes

—

C₂³×C₄

—

C₂³×C₄

—

C₂²×C₈

—

C₂²×C₈

—

166

—

C₂²×C₈

C₂²×D₈₃

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

166

—

C₂×C₄²

C₂²×D₈₃

yes

—

#95

—

#95

C₄×D₈₃

yes

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

166

—

C₂²×C₄

—

166

—

C₂²×C₄

C₂×C₄×D₈₃

yes

—

C₂²×C₄

C₂³×D₈₃

yes

characteristic

C₂×C₈

—

100

C₂×C₈

—

332

—

101

C₂×C₈

—

166

—

102

C₄²

—

103

C₄²

—

166

—

104

C₄²

—

166

—

105

C₂³

—

106

C₂³

—

107

C₂³

C₂²×C₄×D₈₃

yes

characteristic

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

332

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

166

—

114

C₂×C₄

—

166

—

115

C₂×C₄

#41×D₈₃

yes

—

116

C₈

—

117

C₈

—

332

—

118

C₂²

—

119

C₂²

—

120

C₂²

#117×D₈₃

yes

—

121

C₂²

#131×D₈₃

yes

—

122

C₄

—

123

C₄

—

332

—

124

C₄

—

125

C₄

#126×D₈₃

yes

—

126

C₂

—

127

C₂

#383×D₈₃

yes

characteristic

128

C₂

#433×D₈₃

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₈₃
commutator, socle	C₂³×C₈₃	C₂³×C₄
Fitting	C₈₃×#1840	C₂
prime radical	C₂³×D₈₃	C₂²×C₄
cosocle	C₂²×C₄×C₈₃	C₂⁴
hypercenter	#1840	D₈₃
hypocenter	C₈₃	C₂×#1840
LCS	G ▷ C₂³×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1840

subgroup

G/H

center, Frattini

C₂²×C₄

C₂³×D₈₃

commutator, socle

C₂³×C₈₃

C₂³×C₄

Fitting

C₈₃×#1840

C₂

prime radical

C₂³×D₈₃

C₂²×C₄

cosocle

C₂²×C₄×C₈₃

C₂⁴

D₈₃

C₈₃

G ▷ C₂³×C₈₃ ▷ C₈₃

C₁ ◁ C₂²×C₄ ◁ #1840

N	H ≅ G/N	type
2. #24907608	C₂	semidirect
3. #24907607	C₂	semidirect
5. C₈₃×#1840	C₂	semidirect
64. D₈₃	#1840	direct (N × H)
68. #1840	D₈₃	direct (N × H)
70. C₈₃	C₂×#1840	semidirect

H ≅ G/N

type

2. #24907608

C₂

semidirect

3. #24907607

C₂

semidirect

5. C₈₃×#1840

C₂

semidirect

64. D₈₃

#1840

direct (N × H)

68. #1840

D₈₃

direct (N × H)

70. C₈₃

C₂×#1840

semidirect

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

subgroup	index
#376×D₈₃	2
#24907608	2
#24907607	2
#336×D₈₃	2
C₈₃×#1840	2
C₂×#1840	83

subgroup

index

#376×D₈₃

#24907608

#24907607

#336×D₈₃

C₈₃×#1840

C₂×#1840

Subgroups — #1840×D₈₃ #35404649

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1840×D83 #35404649

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1840×D₈₃ #35404649