Group #32979760 — subgroups

Subgroups — #32979760

Order 18688.

422 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 203 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	#22610091	C₂	1	1	yes	maximal, characteristic
2	#22610058	C₂	1	4	yes	maximal
3	C₂×C₈×#10596831	C₂	1	1	yes	maximal, characteristic
4	C₇₃×#1845	C₂	1	1	yes	maximal, characteristic
5	C₂×#14556525	—	2	2	no	—
6	C₂×C₄×#10596831	C₂²	1	2	yes	—
7	#17988457	C₂²	1	2	yes	—
8	#17988349	—	2	8	no	—
9	C₈×#10596831	C₄	1	4	yes	complemented
10	C₂×#107×C₇₃	—	2	2	no	—
11	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
12	#384×C₇₃	C₂²	1	2	yes	—
13	C₂²×#10596831	D₄	1	4	yes	—
14	C₂×C₄⋊Dic₇₃	—	2	2	no	—
15	C₂×C₄⋊Dic₇₃	—	2	4	no	—
16	#14556525	—	4	4	no	—
17	C₄×#10596831	C₂×C₄	1	4	yes	—
18	C₄×#10596831	Q₈	1	4	yes	—
19	C₂²×C₈×C₇₃	D₄	1	2	yes	—
20	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
21	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
22	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
23	#107×C₇₃	—	4	4	no	—
24	C₄×C₈×C₇₃	C₂×C₄	1	2	yes	—
25	C₄×C₈×C₇₃	Q₈	1	2	yes	—
26	C₂²×Dic₇₃	—	4	2	no	—
27	C₂×#10596831	—	2	4	no	—
28	C₂×#10596831	—	2	4	no	—
29	C₂×#10596831	C₄⋊C₄	1	8	yes	—
30	C₄⋊Dic₇₃	—	4	4	no	—
31	C₄⋊Dic₇₃	—	4	8	no	—
32	C₂²×C₄×C₇₃	—	4	2	no	—
33	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
34	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
35	C₂×C₈×C₇₃	C₄⋊C₄	1	4	yes	—
36	C₂×C₈×C₇₃	D₈	1	4	yes	—
37	C₂×C₈×C₇₃	Q₁₆	1	4	yes	—
38	C₄⋊C₄×C₇₃	—	4	4	no	—
39	C₄⋊C₄×C₇₃	—	4	8	no	—
40	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
41	C₄²×C₇₃	C₂×Q₈	1	2	yes	—
42	C₄²×C₇₃	C₂×Q₈	1	1	yes	characteristic
43	C₂³×C₇₃	#127	1	1	yes	characteristic
44	C₂×C₄×C₇₃	—	8	2	no	—
45	C₂×C₄×C₇₃	—	8	4	no	—
46	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
47	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
48	C₂×C₄×C₇₃	C₄⋊Q₈	1	1	yes	characteristic
49	C₂×C₄×C₇₃	C₄⋊Q₈	1	2	yes	—
50	C₂×C₄×C₇₃	C₂×D₈	1	2	yes	—
51	C₂×C₄×C₇₃	C₂×Q₁₆	1	2	yes	—
52	C₂×C₄×C₇₃	#135	1	4	yes	—
53	C₂×C₄×C₇₃	#135	1	4	yes	—
54	C₂×Dic₇₃	—	8	2	no	—
55	C₂×Dic₇₃	—	8	4	no	—
56	C₈×C₇₃	#107	1	8	yes	—
57	#10596831	—	2	8	no	—
58	C₂²×C₇₃	#384	1	1	yes	characteristic
59	C₂²×C₇₃	#493	1	1	yes	characteristic
60	C₂²×C₇₃	#494	1	1	yes	characteristic
61	C₂²×C₇₃	#495	1	2	yes	—
62	C₂²×C₇₃	#495	1	2	yes	—
63	C₄×C₇₃	—	16	2	no	—
64	C₄×C₇₃	C₂×#107	1	2	yes	—
65	C₄×C₇₃	#427	1	4	yes	—
66	C₄×C₇₃	#499	1	4	yes	—
67	C₄×C₇₃	#500	1	2	yes	—
68	Dic₇₃	—	16	2	no	—
69	#8816	—	73	1	no	maximal, Sylow
70	C₂×C₇₃	#1709	1	1	yes	characteristic
71	C₂×C₇₃	#1709	1	1	yes	characteristic
72	C₂×C₇₃	#1710	1	2	yes	—
73	C₂×C₇₃	#1845	1	1	yes	characteristic
74	C₂×C₇₃	#1846	1	2	yes	—
75	#1845	—	73	1	no	—
76	#1845	D₇₃	1	1	yes	characteristic
77	#1834	—	73	4	no	—
78	C₂×C₈²	—	73	1	no	—
79	C₇₃	#8816	1	1	yes	characteristic, complemented, Sylow
80	C₂×#107	—	2	2	no	—
81	C₂×#107	—	146	2	no	—
82	C₂×C₄×C₈	—	73	2	no	—
83	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
84	#384	—	73	2	no	—
85	#384	C₂×D₇₃	1	2	yes	—
86	#340	—	146	8	no	—
87	C₈²	—	73	4	no	—
88	C₂²×C₈	—	73	4	no	—
89	C₂²×C₈	C₂²⋊D₇₃	1	2	yes	—
90	C₂×C₄⋊C₄	—	2	4	no	—
91	C₂×C₄⋊C₄	—	2	2	no	—
92	C₂×C₄⋊C₄	—	146	4	no	—
93	C₂×C₄⋊C₄	—	146	2	no	—
94	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
95	#107	—	4	4	no	—
96	#107	—	292	4	no	—
97	C₄×C₈	—	73	4	no	—
98	C₄×C₈	—	73	4	no	—
99	C₄×C₈	Dic₁₄₆	1	2	yes	—
100	C₄×C₈	C₄×D₇₃	1	2	yes	—
101	C₂²×C₄	—	4	2	no	—
102	C₂²×C₄	—	292	2	no	—
103	C₂²×C₄	D₄×D₇₃	1	2	yes	—
104	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
105	C₂×C₈	—	73	8	no	—
106	C₂×C₈	—	146	4	no	—
107	C₂×C₈	—	146	4	no	—
108	C₂×C₈	#11924007	1	4	yes	—
109	C₂×C₈	#11924013	1	4	yes	—
110	C₂×C₈	#11924018	1	4	yes	—
111	C₄⋊C₄	—	4	4	no	—
112	C₄⋊C₄	—	4	8	no	—
113	C₄⋊C₄	—	292	4	no	—
114	C₄⋊C₄	—	292	8	no	—
115	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
116	C₄²	Q₈×D₇₃	1	2	yes	—
117	C₄²	C₂×Dic₁₄₆	1	1	yes	characteristic
118	C₂³	#14556587	1	1	yes	characteristic
119	C₂×C₄	—	8	2	no	—
120	C₂×C₄	—	8	4	no	—
121	C₂×C₄	—	584	2	no	—
122	C₂×C₄	—	584	4	no	—
123	C₂×C₄	C₄⋊C₄×D₇₃	1	2	yes	—
124	C₂×C₄	C₂×#11924007	1	1	yes	characteristic
125	C₂×C₄	#14556589	1	1	yes	characteristic
126	C₂×C₄	#14556590	1	2	yes	—
127	C₂×C₄	C₂×#11924013	1	2	yes	—
128	C₂×C₄	C₂×#11924018	1	2	yes	—
129	C₂×C₄	#14556610	1	4	yes	—
130	C₂×C₄	#14556614	1	4	yes	—
131	C₈	—	146	8	no	—
132	C₈	#14556524	1	8	yes	—
133	C₂²	#17988456	1	1	yes	characteristic
134	C₂²	#17988963	1	1	yes	characteristic
135	C₂²	#17988966	1	1	yes	characteristic
136	C₂²	#17988970	1	2	yes	—
137	C₂²	#17988972	1	2	yes	—
138	C₄	—	16	2	no	—
139	C₄	—	1168	2	no	—
140	C₄	C₂×#14556524	1	2	yes	—
141	C₄	#17988624	1	4	yes	—
142	C₄	#17988988	1	4	yes	—
143	C₄	#17988990	1	2	yes	—
144	C₂	#22609536	1	1	yes	characteristic
145	C₂	#22609538	1	1	yes	characteristic
146	C₂	#22609540	1	2	yes	—
147	C₂	#22610090	1	1	yes	characteristic
148	C₂	#22610094	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#22610091

C₂

yes

maximal, characteristic

#22610058

C₂

yes

maximal

C₂×C₈×#10596831

C₂

yes

maximal, characteristic

C₇₃×#1845

C₂

yes

maximal, characteristic

C₂×#14556525

—

C₂×C₄×#10596831

C₂²

yes

—

#17988457

C₂²

yes

—

#17988349

—

C₈×#10596831

C₄

yes

complemented

C₂×#107×C₇₃

—

C₂×C₄×C₈×C₇₃

C₂²

yes

characteristic

#384×C₇₃

C₂²

yes

—

C₂²×#10596831

D₄

yes

—

C₂×C₄⋊Dic₇₃

—

C₂×C₄⋊Dic₇₃

—

#14556525

—

C₄×#10596831

C₂×C₄

yes

—

C₄×#10596831

Q₈

yes

—

C₂²×C₈×C₇₃

D₄

yes

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄²×C₇₃

C₂³

yes

characteristic

#107×C₇₃

—

C₄×C₈×C₇₃

C₂×C₄

yes

—

C₄×C₈×C₇₃

Q₈

yes

—

C₂²×Dic₇₃

—

C₂×#10596831

—

C₂×#10596831

—

C₂×#10596831

C₄⋊C₄

yes

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂×D₄

yes

—

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₈×C₇₃

C₄⋊C₄

yes

—

C₂×C₈×C₇₃

D₈

yes

—

C₂×C₈×C₇₃

Q₁₆

yes

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄²×C₇₃

C₂²×C₄

yes

characteristic

C₄²×C₇₃

C₂×Q₈

yes

—

C₄²×C₇₃

C₂×Q₈

yes

characteristic

C₂³×C₇₃

#127

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₇₃

C₄⋊Q₈

yes

—

C₂×C₄×C₇₃

C₂×D₈

yes

—

C₂×C₄×C₇₃

C₂×Q₁₆

yes

—

C₂×C₄×C₇₃

#135

yes

—

C₂×C₄×C₇₃

#135

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₈×C₇₃

#107

yes

—

#10596831

—

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

—

C₂²×C₇₃

#495

yes

—

C₄×C₇₃

—

C₄×C₇₃

C₂×#107

yes

—

C₄×C₇₃

#427

yes

—

C₄×C₇₃

#499

yes

—

C₄×C₇₃

#500

yes

—

Dic₇₃

—

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₂×C₇₃

#1845

yes

characteristic

C₂×C₇₃

#1846

yes

—

#1845

—

#1845

D₇₃

yes

characteristic

#1834

—

C₂×C₈²

—

C₇₃

#8816

yes

characteristic, complemented, Sylow

C₂×#107

—

C₂×#107

—

146

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₇₃

yes

characteristic

#384

—

#384

C₂×D₇₃

yes

—

#340

—

146

—

C₈²

—

C₂²×C₈

—

C₂²×C₈

C₂²⋊D₇₃

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

146

—

C₂×C₄⋊C₄

—

146

—

C₂×C₄²

C₂²×D₇₃

yes

characteristic

#107

—

#107

—

292

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

Dic₁₄₆

yes

—

100

C₄×C₈

C₄×D₇₃

yes

—

101

C₂²×C₄

—

102

C₂²×C₄

—

292

—

103

C₂²×C₄

D₄×D₇₃

yes

—

104

C₂²×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

105

C₂×C₈

—

106

C₂×C₈

—

146

—

107

C₂×C₈

—

146

—

108

C₂×C₈

#11924007

yes

—

109

C₂×C₈

#11924013

yes

—

110

C₂×C₈

#11924018

yes

—

111

C₄⋊C₄

—

112

C₄⋊C₄

—

113

C₄⋊C₄

—

292

—

114

C₄⋊C₄

—

292

—

115

C₄²

C₂×C₄×D₇₃

yes

characteristic

116

C₄²

Q₈×D₇₃

yes

—

117

C₄²

C₂×Dic₁₄₆

yes

characteristic

118

C₂³

#14556587

yes

characteristic

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

584

—

122

C₂×C₄

—

584

—

123

C₂×C₄

C₄⋊C₄×D₇₃

yes

—

124

C₂×C₄

C₂×#11924007

yes

characteristic

125

C₂×C₄

#14556589

yes

characteristic

126

C₂×C₄

#14556590

yes

—

127

C₂×C₄

C₂×#11924013

yes

—

128

C₂×C₄

C₂×#11924018

yes

—

129

C₂×C₄

#14556610

yes

—

130

C₂×C₄

#14556614

yes

—

131

C₈

—

146

—

132

C₈

#14556524

yes

—

133

C₂²

#17988456

yes

characteristic

134

C₂²

#17988963

yes

characteristic

135

C₂²

#17988966

yes

characteristic

136

C₂²

#17988970

yes

—

137

C₂²

#17988972

yes

—

138

C₄

—

139

C₄

—

1168

—

140

C₄

C₂×#14556524

yes

—

141

C₄

#17988624

yes

—

142

C₄

#17988988

yes

—

143

C₄

#17988990

yes

—

144

C₂

#22609536

yes

characteristic

145

C₂

#22609538

yes

characteristic

146

C₂

#22609540

yes

—

147

C₂

#22610090

yes

characteristic

148

C₂

#22610094

yes

—

	subgroup	G/H
center	C₂³	#14556587
commutator	C₄²×C₇₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₃
Fitting	C₇₃×#1845	C₂
socle, prime radical	C₂³×C₇₃	#127
cosocle	C₂×C₄²×C₇₃	C₂³
hypercenter	#1845	D₇₃
hypocenter	C₇₃	#8816
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1845

subgroup

G/H

center

C₂³

#14556587

commutator

C₄²×C₇₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₃

Fitting

C₇₃×#1845

C₂

socle, prime radical

C₂³×C₇₃

#127

cosocle

C₂×C₄²×C₇₃

C₂³

D₇₃

C₇₃

G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1845

N	H ≅ G/N	type
9. C₈×#10596831	C₄	semidirect
79. C₇₃	#8816	semidirect

H ≅ G/N

type

9. C₈×#10596831

C₄

semidirect

79. C₇₃

#8816

semidirect

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

subgroup	index
#22610091	2
#22610058	2
C₂×C₈×#10596831	2
C₇₃×#1845	2
#8816	73

subgroup

index

C₇₃×#1845

Subgroups — #32979760

Conjugacy classes of subgroups

Complements

Maximal subgroups