Group #32973545 — subgroups

Subgroups — #32973545

Order 18688.

150 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 47 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	C₂²⋊#14556497	C₂	1	1	yes	maximal, characteristic, complemented
2	#22608025	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#2215	C₂	1	1	yes	maximal, characteristic
4	C₂×#14556527	—	2	1	no	—
5	C₂×#14556497	—	2	1	no	—
6	C₂×D₁₆×C₇₃	C₄	1	1	yes	characteristic
7	C₂²×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
8	#466×C₇₃	—	2	1	no	—
9	#366×C₇₃	C₄	1	1	yes	characteristic
10	#357×C₇₃	—	2	1	no	—
11	C₂×#11924012	—	4	1	no	—
12	#14556527	—	2	2	no	—
13	#14556527	—	4	1	no	—
14	#14556497	—	4	1	no	—
15	C₂×D₈×C₇₃	—	2	1	no	—
16	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
17	#121×C₇₃	—	4	1	no	—
18	D₁₆×C₇₃	—	4	1	no	—
19	C₂×C₁₆×C₇₃	—	4	1	no	—
20	C₂×C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₁₆×C₇₃	D₄	1	1	yes	characteristic
22	#107×C₇₃	—	2	1	no	—
23	#102×C₇₃	—	4	1	no	—
24	#11924012	—	4	2	no	—
25	#11924012	—	8	1	no	—
26	C₂×#10596831	—	8	1	no	—
27	C₂×D₄×C₇₃	—	4	1	no	—
28	C₂×D₄×C₇₃	—	8	1	no	—
29	C₂²×C₄×C₇₃	D₈	1	1	yes	characteristic
30	D₈×C₇₃	—	4	1	no	—
31	D₈×C₇₃	—	4	1	no	—
32	C₂×C₈×C₇₃	—	2	1	no	—
33	C₂×C₈×C₇₃	—	2	1	no	—
34	C₂×C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×C₈×C₇₃	SD₁₆	1	1	yes	characteristic
36	C₄⋊C₄×C₇₃	—	4	1	no	—
37	C₂²⋊C₄×C₇₃	—	8	1	no	—
38	C₁₆×C₇₃	—	2	1	no	—
39	C₁₆×C₇₃	—	2	1	no	—
40	C₂³×C₇₃	—	8	1	no	—
41	C₂³×C₇₃	SD₃₂	1	1	yes	characteristic
42	D₄×C₇₃	—	8	1	no	—
43	D₄×C₇₃	—	8	1	no	—
44	D₄×C₇₃	—	16	2	no	—
45	C₂×C₄×C₇₃	—	2	1	no	—
46	C₂×C₄×C₇₃	—	2	1	no	—
47	C₂×C₄×C₇₃	—	8	1	no	—
48	C₂×C₄×C₇₃	#102	1	1	yes	characteristic
49	C₂×C₄×C₇₃	D₁₆	1	1	yes	characteristic
50	C₈×C₇₃	—	2	1	no	—
51	C₈×C₇₃	#99	1	1	yes	characteristic
52	C₈×C₇₃	#104	1	1	yes	characteristic
53	#10596831	—	8	2	no	—
54	C₂²×C₇₃	—	2	1	no	—
55	C₂²×C₇₃	—	2	1	no	—
56	C₂²×C₇₃	—	2	1	no	—
57	C₂²×C₇₃	—	16	1	no	—
58	C₂²×C₇₃	—	16	1	no	—
59	C₂²×C₇₃	—	16	1	no	—
60	C₂²×C₇₃	#357	1	1	yes	characteristic
61	C₄×C₇₃	—	2	1	no	—
62	C₄×C₇₃	—	16	1	no	—
63	C₄×C₇₃	#327	1	1	yes	characteristic
64	C₄×C₇₃	#360	1	1	yes	characteristic
65	#7420	—	73	1	no	maximal, Sylow
66	C₂×C₇₃	—	4	1	no	—
67	C₂×C₇₃	—	32	1	no	—
68	C₂×C₇₃	#1347	1	1	yes	characteristic
69	C₂×C₇₃	#1417	1	1	yes	characteristic
70	C₂×C₇₃	#1419	1	1	yes	characteristic
71	#2215	D₇₃	1	1	yes	characteristic
72	C₂²⋊C₃₂	—	73	1	no	—
73	#1381	—	73	1	no	—
74	C₇₃	#7420	1	1	yes	characteristic, complemented, Sylow
75	C₂×D₁₆	Dic₇₃	1	1	yes	characteristic
76	C₂²×C₁₆	C₂×D₇₃	1	1	yes	characteristic
77	#466	—	2	1	no	—
78	C₂×#108	—	146	1	no	—
79	C₂×C₃₂	—	146	1	no	—
80	#366	Dic₇₃	1	1	yes	characteristic
81	#357	—	2	1	no	—
82	C₂×D₈	—	2	1	no	—
83	C₂×M₁₆	—	292	1	no	—
84	C₂²×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
85	#121	—	4	1	no	—
86	D₁₆	—	4	1	no	—
87	C₂×C₁₆	—	4	1	no	—
88	C₂×C₁₆	C₂×Dic₇₃	1	1	yes	characteristic
89	C₂×C₁₆	C₂²⋊D₇₃	1	1	yes	characteristic
90	#108	—	292	1	no	—
91	#108	—	146	2	no	—
92	#107	—	2	1	no	—
93	#102	—	4	1	no	—
94	C₃₂	—	292	1	no	—
95	C₂×D₄	—	4	1	no	—
96	C₂×D₄	—	8	1	no	—
97	C₂²×C₄	#11924013	1	1	yes	characteristic
98	D₈	—	4	1	no	—
99	D₈	—	4	1	no	—
100	M₁₆	—	292	2	no	—
101	M₁₆	—	584	1	no	—
102	C₂×C₈	—	2	1	no	—
103	C₂×C₈	—	2	1	no	—
104	C₂×C₈	—	584	1	no	—
105	C₂×C₈	C₂²⋊Dic₇₃	1	1	yes	characteristic
106	C₂×C₈	#11924016	1	1	yes	characteristic
107	C₄⋊C₄	—	4	1	no	—
108	C₂²⋊C₄	—	8	1	no	—
109	C₁₆	—	2	1	no	—
110	C₁₆	—	2	1	no	—
111	C₂³	—	8	1	no	—
112	C₂³	#14556535	1	1	yes	characteristic
113	D₄	—	8	1	no	—
114	D₄	—	8	1	no	—
115	D₄	—	16	2	no	—
116	C₂×C₄	—	2	1	no	—
117	C₂×C₄	—	2	1	no	—
118	C₂×C₄	—	8	1	no	—
119	C₂×C₄	#14556512	1	1	yes	characteristic
120	C₂×C₄	#14556532	1	1	yes	characteristic
121	C₈	—	2	1	no	—
122	C₈	—	584	2	no	—
123	C₈	#14556506	1	1	yes	characteristic
124	C₈	#14556518	1	1	yes	characteristic
125	C₂²	—	2	1	no	—
126	C₂²	—	2	1	no	—
127	C₂²	—	2	1	no	—
128	C₂²	—	16	1	no	—
129	C₂²	—	16	1	no	—
130	C₂²	—	16	1	no	—
131	C₂²	#17988388	1	1	yes	characteristic
132	C₄	—	2	1	no	—
133	C₄	—	16	1	no	—
134	C₄	#17988321	1	1	yes	characteristic
135	C₄	#17988397	1	1	yes	characteristic
136	C₂	—	4	1	no	—
137	C₂	—	32	1	no	—
138	C₂	#22607940	1	1	yes	characteristic
139	C₂	#22608115	1	1	yes	characteristic
140	C₂	#22608121	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²⋊#14556497

C₂

yes

maximal, characteristic, complemented

#22608025

C₂

yes

maximal, characteristic, complemented

C₇₃×#2215

C₂

yes

maximal, characteristic

C₂×#14556527

—

C₂×#14556497

—

C₂×D₁₆×C₇₃

C₄

yes

characteristic

C₂²×C₁₆×C₇₃

C₂²

yes

characteristic

#466×C₇₃

—

#366×C₇₃

C₄

yes

characteristic

#357×C₇₃

—

—

—

—

—

C₂×D₈×C₇₃

—

C₂²×C₈×C₇₃

D₄

yes

characteristic

#121×C₇₃

—

D₁₆×C₇₃

—

C₂×C₁₆×C₇₃

—

C₂×C₁₆×C₇₃

C₂×C₄

yes

characteristic

C₂×C₁₆×C₇₃

D₄

yes

characteristic

#107×C₇₃

—

#102×C₇₃

—

#11924012

—

#11924012

—

C₂×#10596831

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂²×C₄×C₇₃

D₈

yes

characteristic

D₈×C₇₃

—

D₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₃

SD₁₆

yes

characteristic

C₄⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₁₆×C₇₃

—

C₁₆×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

SD₃₂

yes

characteristic

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

#102

yes

characteristic

C₂×C₄×C₇₃

D₁₆

yes

characteristic

C₈×C₇₃

—

C₈×C₇₃

yes

C₈×C₇₃

yes

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

#357

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

yes

C₄×C₇₃

yes

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

D₇₃

yes

characteristic

C₂²⋊C₃₂

—

#1381

—

C₇₃

#7420

yes

characteristic, complemented, Sylow

C₂×D₁₆

Dic₇₃

yes

characteristic

C₂²×C₁₆

C₂×D₇₃

yes

characteristic

#466

—

C₂×#108

—

146

—

C₂×C₃₂

—

146

—

#366

Dic₇₃

yes

characteristic

#357

—

C₂×D₈

—

C₂×M₁₆

—

292

—

C₂²×C₈

C₂²⋊D₇₃

yes

characteristic

#121

—

D₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×Dic₇₃

yes

characteristic

C₂×C₁₆

C₂²⋊D₇₃

yes

characteristic

#108

—

292

—

#108

—

146

—

#107

—

#102

—

C₃₂

—

292

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

#11924013

yes

characteristic

D₈

—

D₈

—

100

M₁₆

—

292

—

101

M₁₆

—

584

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

584

—

105

C₂×C₈

C₂²⋊Dic₇₃

yes

characteristic

106

C₂×C₈

#11924016

yes

characteristic

107

C₄⋊C₄

—

108

C₂²⋊C₄

—

109

C₁₆

—

110

C₁₆

—

111

C₂³

—

112

C₂³

#14556535

yes

characteristic

113

D₄

—

114

D₄

—

115

D₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

#14556512

yes

characteristic

120

C₂×C₄

#14556532

yes

characteristic

121

C₈

—

122

C₈

—

584

—

123

C₈

#14556506

yes

characteristic

124

C₈

#14556518

yes

characteristic

125

C₂²

—

126

C₂²

—

127

C₂²

—

128

C₂²

—

129

C₂²

—

130

C₂²

—

131

C₂²

#17988388

yes

characteristic

132

C₄

—

133

C₄

—

134

C₄

#17988321

yes

characteristic

135

C₄

#17988397

yes

characteristic

136

C₂

—

137

C₂

—

138

C₂

#22607940

yes

characteristic

139

C₂

#22608115

yes

characteristic

140

C₂

#22608121

yes

characteristic

	subgroup	G/H
center	C₂²	#17988388
commutator	C₂×C₁₆×C₇₃	C₂×C₄
Frattini	C₂²×C₁₆	C₂×D₇₃
Fitting, prime radical	C₇₃×#2215	C₂
socle	C₂²×C₇₃	#357
cosocle	C₂²×C₁₆×C₇₃	C₂²
hypercenter	#2215	D₇₃
hypocenter	C₇₃	#7420
LCS	G ▷ C₂×C₁₆×C₇₃ ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆ ◁ #2215

subgroup

G/H

center

C₂²

#17988388

commutator

C₂×C₁₆×C₇₃

C₂×C₄

Frattini

C₂²×C₁₆

C₂×D₇₃

Fitting, prime radical

C₇₃×#2215

C₂

socle

C₂²×C₇₃

#357

cosocle

C₂²×C₁₆×C₇₃

C₂²

D₇₃

C₇₃

G ▷ C₂×C₁₆×C₇₃ ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆ ◁ #2215

N	H ≅ G/N	type
1. C₂²⋊#14556497	C₂	semidirect
2. #22608025	C₂	semidirect
74. C₇₃	#7420	semidirect

H ≅ G/N

type

1. C₂²⋊#14556497

C₂

semidirect

2. #22608025

C₂

semidirect

74. C₇₃

#7420

semidirect

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

subgroup	index
C₂²⋊#14556497	2
#22608025	2
C₇₃×#2215	2
#7420	73

subgroup

index

C₂²⋊#14556497

#22608025

C₇₃×#2215

#7420

Subgroups — #32973545

Conjugacy classes of subgroups

Complements

Maximal subgroups