Group #34001940 — subgroups

Subgroups — #34001940

Order 18688.

526 conjugacy classes of subgroups; only the 228 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 228 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	#22625645	C₂	1	2	yes	maximal
2	C₂×#17989429	C₂	1	4	yes	maximal
3	C₄×C₈×Dic₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×#10596833	C₂²	1	4	yes	—
5	#17989453	C₄	1	8	yes	—
6	#17989429	C₄	1	16	yes	complemented
7	C₂×C₄×#10596831	C₄	1	1	yes	characteristic
8	C₂×C₈×Dic₇₃	C₄	1	2	yes	—
9	C₂×C₈×Dic₇₃	C₂²	1	2	yes	—
10	C₄²×Dic₇₃	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₈×C₇₃	C₄	1	1	yes	characteristic
12	C₂²×#10596833	C₂×C₄	1	8	yes	—
13	C₄×#10596833	C₂×C₄	1	16	yes	—
14	C₂²×#10596831	C₂×C₄	1	2	yes	—
15	C₂×C₄×Dic₇₃	C₂×C₄	1	4	yes	—
16	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
18	C₄×#10596831	—	2	2	no	—
19	C₈×Dic₇₃	—	2	4	no	—
20	C₈×Dic₇₃	C₂×C₄	1	8	yes	—
21	C₂²×C₈×C₇₃	C₂×C₄	1	2	yes	—
22	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
23	C₄×C₈×C₇₃	—	2	2	no	—
24	C₂×#10596833	—	2	16	no	—
25	C₂×#10596833	C₄²	1	16	yes	—
26	C₂²×Dic₇₃	C₄²	1	2	yes	—
27	C₂²×Dic₇₃	C₂²×C₄	1	2	yes	—
28	C₂×#10596831	—	2	2	no	—
29	C₂×#10596831	—	2	2	no	—
30	C₂×#10596831	C₄²	1	4	yes	—
31	C₄×Dic₇₃	—	2	8	no	—
32	C₄×Dic₇₃	M₁₆	1	4	yes	—
33	C₄×Dic₇₃	C₂²×C₄	1	4	yes	—
34	C₂²×C₄×C₇₃	C₄²	1	2	yes	—
35	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₈×C₇₃	—	2	2	no	—
37	C₂×C₈×C₇₃	—	2	2	no	—
38	C₂×C₈×C₇₃	C₄²	1	4	yes	—
39	C₄²×C₇₃	M₁₆	1	2	yes	—
40	C₄²×C₇₃	M₁₆	1	2	yes	—
41	C₂³×C₇₃	C₂×C₄²	1	1	yes	characteristic
42	C₂×C₄×C₇₃	—	2	4	no	—
43	C₂×C₄×C₇₃	#97	1	4	yes	—
44	C₂×C₄×C₇₃	C₂×C₄²	1	2	yes	—
45	C₂×C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
46	C₂×C₄×C₇₃	C₂×M₁₆	1	2	yes	—
47	C₂×C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
48	C₂×Dic₇₃	—	2	4	no	—
49	C₂×Dic₇₃	#97	1	4	yes	—
50	C₂×Dic₇₃	C₂×C₄²	1	4	yes	—
51	C₂×Dic₇₃	#131	1	8	yes	—
52	#10596833	—	2	16	no	—
53	C₈×C₇₃	—	2	4	no	—
54	#10596831	—	2	4	no	—
55	C₂²×C₇₃	C₄³	1	1	yes	characteristic
56	C₂²×C₇₃	C₂×#97	1	1	yes	characteristic
57	C₂²×C₇₃	C₂×#97	1	1	yes	characteristic
58	C₂²×C₇₃	#405	1	4	yes	—
59	C₄×C₇₃	—	2	4	no	—
60	C₄×C₇₃	C₄×M₁₆	1	2	yes	—
61	C₄×C₇₃	C₄×M₁₆	1	2	yes	—
62	Dic₇₃	—	2	4	no	—
63	Dic₇₃	#405	1	8	yes	—
64	#7843	—	73	1	no	maximal, Sylow
65	C₂×C₇₃	#1452	1	2	yes	—
66	C₂×C₇₃	#1452	1	2	yes	—
67	C₂×C₇₃	C₄×#97	1	1	yes	characteristic
68	C₂×C₇₃	#1726	1	2	yes	—
69	#1744	—	73	2	no	—
70	C₄²×C₈	—	73	1	no	—
71	C₂×#322	—	73	4	no	—
72	C₇₃	#7843	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₄×C₈	—	73	4	no	—
74	C₂×C₄×C₈	—	73	2	no	—
75	C₂×C₄×C₈	—	73	2	no	—
76	C₂×C₄×C₈	—	73	1	no	—
77	C₂×C₄×C₈	#64408	1	1	yes	characteristic
78	C₄³	—	73	1	no	—
79	#336	—	73	8	no	—
80	#322	—	73	16	no	—
81	C₂²×C₈	—	73	8	no	—
82	C₂²×C₈	—	73	2	no	—
83	C₂²×C₈	C₂×#64408	1	2	yes	—
84	C₂×C₄²	—	73	1	no	—
85	C₂×C₄²	—	73	1	no	—
86	C₂×C₄²	—	73	4	no	—
87	C₂×C₄²	C₂×#64408	1	1	yes	characteristic
88	C₄×C₈	—	2	2	no	—
89	C₄×C₈	—	73	16	no	—
90	C₄×C₈	—	73	8	no	—
91	C₄×C₈	—	146	4	no	—
92	C₄×C₈	—	146	2	no	—
93	C₂²×C₄	—	73	2	no	—
94	C₂²×C₄	—	73	2	no	—
95	C₂²×C₄	C₄×#64408	1	2	yes	—
96	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
97	C₂×C₈	—	2	2	no	—
98	C₂×C₈	—	2	2	no	—
99	C₂×C₈	—	73	16	no	—
100	C₂×C₈	—	73	4	no	—
101	C₂×C₈	—	146	16	no	—
102	C₂×C₈	—	146	2	no	—
103	C₂×C₈	—	146	2	no	—
104	C₂×C₈	C₄×#64408	1	4	yes	—
105	C₄²	—	73	4	no	—
106	C₄²	—	73	4	no	—
107	C₄²	—	146	8	no	—
108	C₄²	#11924037	1	2	yes	—
109	C₄²	#11924038	1	2	yes	—
110	C₂³	C₂×C₄×#64408	1	1	yes	characteristic
111	C₂×C₄	—	2	4	no	—
112	C₂×C₄	—	73	4	no	—
113	C₂×C₄	—	73	8	no	—
114	C₂×C₄	—	73	4	no	—
115	C₂×C₄	—	146	4	no	—
116	C₂×C₄	#14556646	1	4	yes	—
117	C₂×C₄	C₂×C₄×#64408	1	2	yes	—
118	C₂×C₄	C₂×#11924037	1	1	yes	characteristic
119	C₂×C₄	D₇₃⋊M₁₆	1	2	yes	—
120	C₂×C₄	C₂×#11924038	1	1	yes	characteristic
121	C₈	—	2	4	no	—
122	C₈	—	146	16	no	—
123	C₈	—	146	4	no	—
124	C₂²	C₄²×#64408	1	1	yes	characteristic
125	C₂²	C₂×#14556646	1	1	yes	characteristic
126	C₂²	#17989546	1	1	yes	characteristic
127	C₂²	#17989550	1	4	yes	—
128	C₄	—	2	4	no	—
129	C₄	—	73	8	no	—
130	C₄	—	146	4	no	—
131	C₄	C₄×#11924037	1	2	yes	—
132	C₄	C₄×#11924038	1	2	yes	—
133	C₂	#22625144	1	2	yes	—
134	C₂	#22625145	1	2	yes	—
135	C₂	C₄×#14556646	1	1	yes	characteristic
136	C₂	#22625587	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#22625645

C₂

yes

maximal

C₂×#17989429

C₂

yes

maximal

C₄×C₈×Dic₇₃

C₂

yes

maximal, characteristic

C₂×C₄×#10596833

C₂²

yes

—

#17989453

C₄

yes

—

#17989429

C₄

yes

complemented

C₂×C₄×#10596831

C₄

yes

characteristic

C₂×C₈×Dic₇₃

C₄

yes

—

C₂×C₈×Dic₇₃

C₂²

yes

—

C₄²×Dic₇₃

C₂²

yes

characteristic

C₂×C₄×C₈×C₇₃

C₄

yes

characteristic

C₂²×#10596833

C₂×C₄

yes

—

C₄×#10596833

C₂×C₄

yes

—

C₂²×#10596831

C₂×C₄

yes

—

C₂×C₄×Dic₇₃

C₂×C₄

yes

—

C₂×C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₂×C₄×Dic₇₃

C₂³

yes

characteristic

C₄×#10596831

—

C₈×Dic₇₃

—

C₈×Dic₇₃

C₂×C₄

yes

—

C₂²×C₈×C₇₃

C₂×C₄

yes

—

C₂×C₄²×C₇₃

C₂×C₄

yes

characteristic

C₄×C₈×C₇₃

—

C₂×#10596833

—

C₂×#10596833

C₄²

yes

—

C₂²×Dic₇₃

C₄²

yes

—

C₂²×Dic₇₃

C₂²×C₄

yes

—

C₂×#10596831

—

C₂×#10596831

—

C₂×#10596831

C₄²

yes

—

C₄×Dic₇₃

—

C₄×Dic₇₃

M₁₆

yes

—

C₄×Dic₇₃

C₂²×C₄

yes

—

C₂²×C₄×C₇₃

C₄²

yes

—

C₂²×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₄²

yes

—

C₄²×C₇₃

M₁₆

yes

—

C₄²×C₇₃

M₁₆

yes

—

C₂³×C₇₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

#97

yes

—

C₂×C₄×C₇₃

C₂×C₄²

yes

—

C₂×C₄×C₇₃

C₂×M₁₆

yes

characteristic

C₂×C₄×C₇₃

C₂×M₁₆

yes

—

C₂×C₄×C₇₃

C₂×M₁₆

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

#97

yes

—

C₂×Dic₇₃

C₂×C₄²

yes

—

C₂×Dic₇₃

#131

yes

—

#10596833

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

C₄³

yes

characteristic

C₂²×C₇₃

C₂×#97

yes

characteristic

C₂²×C₇₃

C₂×#97

yes

characteristic

C₂²×C₇₃

#405

yes

—

C₄×C₇₃

—

C₄×C₇₃

C₄×M₁₆

yes

—

C₄×C₇₃

C₄×M₁₆

yes

—

Dic₇₃

—

Dic₇₃

#405

yes

—

#7843

—

maximal, Sylow

C₂×C₇₃

#1452

yes

—

C₂×C₇₃

#1452

yes

—

C₂×C₇₃

C₄×#97

yes

characteristic

C₂×C₇₃

#1726

yes

—

#1744

—

C₄²×C₈

—

C₂×#322

—

C₇₃

#7843

yes

characteristic, complemented, Sylow

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

#64408

yes

characteristic

C₄³

—

#336

—

#322

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

C₂×#64408

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×#64408

yes

characteristic

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

146

—

C₄×C₈

—

146

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×#64408

yes

—

C₂²×C₄

C₂²×#64408

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

146

—

102

C₂×C₈

—

146

—

103

C₂×C₈

—

146

—

104

C₂×C₈

C₄×#64408

yes

—

105

C₄²

—

106

C₄²

—

107

C₄²

—

146

—

108

C₄²

#11924037

yes

—

109

C₄²

#11924038

yes

—

110

C₂³

C₂×C₄×#64408

yes

characteristic

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

146

—

116

C₂×C₄

#14556646

yes

—

117

C₂×C₄

C₂×C₄×#64408

yes

—

118

C₂×C₄

C₂×#11924037

yes

characteristic

119

C₂×C₄

D₇₃⋊M₁₆

yes

—

120

C₂×C₄

C₂×#11924038

yes

characteristic

121

C₈

—

122

C₈

—

146

—

123

C₈

—

146

—

124

C₂²

C₄²×#64408

yes

characteristic

125

C₂²

C₂×#14556646

yes

characteristic

126

C₂²

#17989546

yes

characteristic

127

C₂²

#17989550

yes

—

128

C₄

—

129

C₄

—

130

C₄

—

146

—

131

C₄

C₄×#11924037

yes

—

132

C₄

C₄×#11924038

yes

—

133

C₂

#22625144

yes

—

134

C₂

#22625145

yes

—

135

C₂

C₄×#14556646

yes

characteristic

136

C₂

#22625587

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×#64408
commutator	C₂²×C₇₃	C₄³
Fitting	C₂×C₄×C₈×C₇₃	C₄
socle, prime radical	C₂³×C₇₃	C₂×C₄²
cosocle	C₂×C₄×Dic₇₃	C₂³
hypercenter	C₂×C₄×C₈	#64408
hypocenter	C₇₃	#7843
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₈

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×#64408

commutator

C₂²×C₇₃

C₄³

Fitting

C₂×C₄×C₈×C₇₃

C₄

socle, prime radical

C₂³×C₇₃

C₂×C₄²

cosocle

C₂×C₄×Dic₇₃

C₂³

C₂×C₄×C₈

C₇₃

G ▷ C₂²×C₇₃ ▷ C₇₃

C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₈

N	H ≅ G/N	type
6. #17989429	C₄	semidirect
72. C₇₃	#7843	semidirect

H ≅ G/N

type

6. #17989429

C₄

semidirect

72. C₇₃

#7843

semidirect

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

subgroup	index
#22625645	2
C₂×#17989429	2
C₄×C₈×Dic₇₃	2
#7843	73

subgroup

index

#22625645

C₂×#17989429

C₄×C₈×Dic₇₃

#7843

Subgroups — #34001940

Conjugacy classes of subgroups

Complements

Maximal subgroups