Group #32973151 — subgroups

Subgroups — #32973151

Order 18688.

218 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 79 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	C₂×#17988365	C₂	1	2	yes	maximal
2	C₇₃×#1836	C₂	1	1	yes	maximal, characteristic
3	C₂×#14556531	—	2	2	no	—
4	#17988365	—	2	2	no	—
5	#17988365	C₄	1	4	yes	complemented
6	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
7	#384×C₇₃	C₄	1	1	yes	characteristic
8	#382×C₇₃	C₄	1	1	yes	characteristic
9	#340×C₇₃	—	2	2	no	—
10	#14556531	—	2	4	no	—
11	#14556531	—	2	4	no	—
12	C₂×#11924003	—	2	4	no	—
13	C₂²×C₈×C₇₃	D₄	1	2	yes	—
14	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
15	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
16	C₂×C₄⋊C₄×C₇₃	—	4	1	no	—
17	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
18	#97×C₇₃	C₂×C₄	1	2	yes	—
19	#97×C₇₃	D₄	1	1	yes	characteristic
20	#97×C₇₃	Q₈	1	1	yes	characteristic
21	#95×C₇₃	—	4	1	no	—
22	#11924003	—	2	8	no	—
23	C₂²×C₄×C₇₃	—	2	1	no	—
24	C₂²×C₄×C₇₃	—	4	1	no	—
25	C₂²×C₄×C₇₃	—	4	1	no	—
26	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₈×C₇₃	—	2	2	no	—
28	C₂×C₈×C₇₃	—	2	2	no	—
29	C₂×C₈×C₇₃	C₂²⋊C₄	1	2	yes	—
30	C₂×C₈×C₇₃	C₄⋊C₄	1	2	yes	—
31	C₄⋊C₄×C₇₃	—	4	2	no	—
32	C₄⋊C₄×C₇₃	—	4	2	no	—
33	C₄⋊C₄×C₇₃	—	8	2	no	—
34	C₄²×C₇₃	—	2	1	no	—
35	C₄²×C₇₃	C₄²	1	1	yes	characteristic
36	C₄²×C₇₃	C₄⋊C₄	1	1	yes	characteristic
37	C₂³×C₇₃	#100	1	1	yes	characteristic
38	C₂×C₄×C₇₃	—	2	1	no	—
39	C₂×C₄×C₇₃	—	2	1	no	—
40	C₂×C₄×C₇₃	—	4	1	no	—
41	C₂×C₄×C₇₃	—	4	1	no	—
42	C₂×C₄×C₇₃	—	8	2	no	—
43	C₂×C₄×C₇₃	—	8	1	no	—
44	C₂×C₄×C₇₃	—	8	1	no	—
45	C₂×C₄×C₇₃	—	8	1	no	—
46	C₂×C₄×C₇₃	—	8	1	no	—
47	C₂×C₄×C₇₃	#95	1	1	yes	characteristic
48	C₂×C₄×C₇₃	#101	1	1	yes	characteristic
49	C₂×C₄×C₇₃	#104	1	2	yes	—
50	C₂×C₄×C₇₃	#104	1	2	yes	—
51	C₈×C₇₃	—	2	2	no	—
52	C₈×C₇₃	—	2	2	no	—
53	C₂²×C₇₃	—	2	1	no	—
54	C₂²×C₇₃	—	2	1	no	—
55	C₂²×C₇₃	#329	1	1	yes	characteristic
56	C₂²×C₇₃	#329	1	1	yes	characteristic
57	C₂²×C₇₃	#343	1	1	yes	characteristic
58	C₄×C₇₃	—	4	1	no	—
59	C₄×C₇₃	—	4	1	no	—
60	C₄×C₇₃	—	16	1	no	—
61	C₄×C₇₃	—	16	1	no	—
62	C₄×C₇₃	#330	1	2	yes	—
63	C₄×C₇₃	#339	1	2	yes	—
64	#7266	—	73	1	no	maximal, Sylow
65	C₂×C₇₃	—	2	1	no	—
66	C₂×C₇₃	—	2	1	no	—
67	C₂×C₇₃	#1295	1	1	yes	characteristic
68	C₂×C₇₃	#1355	1	1	yes	characteristic
69	C₂×C₇₃	#1356	1	1	yes	characteristic
70	C₂×#347	—	73	2	no	—
71	#1836	D₇₃	1	1	yes	characteristic
72	C₇₃	#7266	1	1	yes	characteristic, complemented, Sylow
73	C₂×M₃₂	—	146	2	no	—
74	C₂×#97	C₂×D₇₃	1	1	yes	characteristic
75	#384	Dic₇₃	1	1	yes	characteristic
76	#382	Dic₇₃	1	1	yes	characteristic
77	#347	—	73	4	no	—
78	#347	—	146	2	no	—
79	#340	—	2	2	no	—
80	C₂²×C₈	C₂²⋊D₇₃	1	2	yes	—
81	C₂×C₄⋊C₄	—	2	1	no	—
82	C₂×C₄⋊C₄	—	2	1	no	—
83	C₂×C₄⋊C₄	—	4	1	no	—
84	C₂×C₄²	C₂×Dic₇₃	1	1	yes	characteristic
85	M₃₂	—	146	4	no	—
86	M₃₂	—	146	4	no	—
87	C₂×C₁₆	—	146	4	no	—
88	#97	Dic₁₄₆	1	1	yes	characteristic
89	#97	C₄×D₇₃	1	2	yes	—
90	#97	D₂₉₂	1	1	yes	characteristic
91	#95	—	4	1	no	—
92	C₂²×C₄	—	2	1	no	—
93	C₂²×C₄	—	4	1	no	—
94	C₂²×C₄	—	4	1	no	—
95	C₂²×C₄	C₂²⋊Dic₇₃	1	1	yes	characteristic
96	C₂×C₈	—	2	2	no	—
97	C₂×C₈	—	2	2	no	—
98	C₂×C₈	#11924005	1	2	yes	—
99	C₂×C₈	#11924007	1	2	yes	—
100	C₄⋊C₄	—	4	2	no	—
101	C₄⋊C₄	—	4	2	no	—
102	C₄⋊C₄	—	8	2	no	—
103	C₄²	—	2	1	no	—
104	C₄²	C₄×Dic₇₃	1	1	yes	characteristic
105	C₄²	C₄⋊Dic₇₃	1	1	yes	characteristic
106	C₁₆	—	146	8	no	—
107	C₂³	#14556508	1	1	yes	characteristic
108	C₂×C₄	—	2	1	no	—
109	C₂×C₄	—	2	1	no	—
110	C₂×C₄	—	4	1	no	—
111	C₂×C₄	—	4	1	no	—
112	C₂×C₄	—	8	2	no	—
113	C₂×C₄	—	8	1	no	—
114	C₂×C₄	—	8	1	no	—
115	C₂×C₄	—	8	1	no	—
116	C₂×C₄	—	8	1	no	—
117	C₂×C₄	#14556498	1	1	yes	characteristic
118	C₂×C₄	#14556510	1	1	yes	characteristic
119	C₂×C₄	#14556518	1	2	yes	—
120	C₂×C₄	#14556518	1	2	yes	—
121	C₈	—	2	2	no	—
122	C₈	—	2	2	no	—
123	C₂²	—	2	1	no	—
124	C₂²	—	2	1	no	—
125	C₂²	#17988327	1	1	yes	characteristic
126	C₂²	#17988327	1	1	yes	characteristic
127	C₂²	#17988356	1	1	yes	characteristic
128	C₄	—	4	1	no	—
129	C₄	—	4	1	no	—
130	C₄	—	16	1	no	—
131	C₄	—	16	1	no	—
132	C₄	#17988329	1	2	yes	—
133	C₄	#17988346	1	2	yes	—
134	C₂	—	2	1	no	—
135	C₂	—	2	1	no	—
136	C₂	#22607812	1	1	yes	characteristic
137	C₂	#22607964	1	1	yes	characteristic
138	C₂	#22607966	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#17988365

C₂

yes

maximal

C₇₃×#1836

C₂

yes

maximal, characteristic

C₂×#14556531

—

#17988365

—

#17988365

C₄

yes

complemented

C₂×#97×C₇₃

C₂²

yes

characteristic

#384×C₇₃

C₄

yes

characteristic

#382×C₇₃

C₄

yes

characteristic

#340×C₇₃

—

#14556531

—

#14556531

—

C₂×#11924003

—

C₂²×C₈×C₇₃

D₄

yes

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄²×C₇₃

C₂×C₄

yes

characteristic

#97×C₇₃

C₂×C₄

yes

—

#97×C₇₃

D₄

yes

characteristic

#97×C₇₃

Q₈

yes

characteristic

#95×C₇₃

—

#11924003

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂²⋊C₄

yes

—

C₂×C₈×C₇₃

C₄⋊C₄

yes

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄²×C₇₃

—

C₄²×C₇₃

C₄²

yes

characteristic

C₄²×C₇₃

C₄⋊C₄

yes

characteristic

C₂³×C₇₃

#100

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

—

C₂×C₄×C₇₃

#104

yes

—

C₈×C₇₃

—

C₈×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

#330

yes

—

C₄×C₇₃

#339

yes

—

#7266

—

maximal, Sylow

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

D₇₃

yes

characteristic

C₇₃

#7266

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

146

—

C₂×#97

C₂×D₇₃

yes

characteristic

#384

Dic₇₃

yes

characteristic

#382

Dic₇₃

yes

characteristic

#347

—

#347

—

146

—

#340

—

C₂²×C₈

C₂²⋊D₇₃

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×Dic₇₃

yes

characteristic

M₃₂

—

146

—

M₃₂

—

146

—

C₂×C₁₆

—

146

—

#97

Dic₁₄₆

yes

characteristic

#97

C₄×D₇₃

yes

—

#97

D₂₉₂

yes

characteristic

#95

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊Dic₇₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

#11924005

yes

—

C₂×C₈

#11924007

yes

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄²

—

104

C₄²

C₄×Dic₇₃

yes

characteristic

105

C₄²

C₄⋊Dic₇₃

yes

characteristic

106

C₁₆

—

146

—

107

C₂³

#14556508

yes

characteristic

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

#14556498

yes

characteristic

118

C₂×C₄

#14556510

yes

characteristic

119

C₂×C₄

#14556518

yes

—

120

C₂×C₄

#14556518

yes

—

121

C₈

—

122

C₈

—

123

C₂²

—

124

C₂²

—

125

C₂²

#17988327

yes

characteristic

126

C₂²

#17988327

yes

characteristic

127

C₂²

#17988356

yes

characteristic

128

C₄

—

129

C₄

—

130

C₄

—

131

C₄

—

132

C₄

#17988329

yes

—

133

C₄

#17988346

yes

—

134

C₂

—

135

C₂

—

136

C₂

#22607812

yes

characteristic

137

C₂

#22607964

yes

characteristic

138

C₂

#22607966

yes

characteristic

	subgroup	G/H
center	C₂²	#17988327
commutator	C₄²×C₇₃	C₄²
Frattini	C₂×#97	C₂×D₇₃
Fitting	C₇₃×#1836	C₂
socle	C₂²×C₇₃	#329
prime radical	C₂³×C₇₃	#100
cosocle	C₂×#97×C₇₃	C₂²
hypercenter	#1836	D₇₃
hypocenter	C₇₃	#7266
LCS	G ▷ C₄²×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#97 ◁ #1836

subgroup

G/H

center

C₂²

#17988327

commutator

C₄²×C₇₃

C₄²

Frattini

C₂×#97

C₂×D₇₃

Fitting

C₇₃×#1836

C₂

C₂²×C₇₃

C₂³×C₇₃

C₂×#97×C₇₃

C₂²

D₇₃

C₇₃

G ▷ C₄²×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#97 ◁ #1836

N	H ≅ G/N	type
5. #17988365	C₄	semidirect
72. C₇₃	#7266	semidirect

H ≅ G/N

type

5. #17988365

C₄

semidirect

72. C₇₃

#7266

semidirect

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

subgroup	index
C₂×#17988365	2
C₇₃×#1836	2
#7266	73

subgroup

index

C₂×#17988365

C₇₃×#1836

#7266

Subgroups — #32973151

Conjugacy classes of subgroups

Complements

Maximal subgroups