Group #32985483 — subgroups

Subgroups — #32985483

Order 18688.

454 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 119 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×#17988967	C₂	1	1	yes	maximal, characteristic
2	#22608604	C₂	1	4	yes	maximal
3	#22608223	C₂	1	1	yes	maximal, characteristic
4	C₇₃×#1837	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₂₉₂	—	2	2	no	—
6	C₂×#14556591	C₂²	1	2	yes	—
7	#17988967	—	2	2	no	—
8	#17988967	C₄	1	4	yes	—
9	#17988640	C₂²	1	2	yes	—
10	#17988334	—	2	8	no	—
11	#17988309	—	2	2	no	—
12	#423×C₇₃	C₂²	1	2	yes	—
13	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
14	#341×C₇₃	—	2	2	no	—
15	C₂²×Dic₁₄₆	—	2	2	no	—
16	C₂×Dic₂₉₂	—	2	8	no	—
17	C₂×Dic₂₉₂	—	4	8	no	—
18	#14556591	—	2	4	no	—
19	#14556591	—	2	2	no	—
20	#14556591	C₂×C₄	1	4	yes	—
21	C₂×C₄⋊Dic₇₃	—	2	4	no	—
22	C₄⋊#10596831	D₄	1	4	yes	—
23	C₂²⋊#10596831	—	2	2	no	—
24	C₄×#10596831	—	2	2	no	—
25	C₂×M₁₆×C₇₃	—	2	2	no	—
26	C₂²×C₈×C₇₃	D₄	1	2	yes	—
27	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
28	C₄⋊C₈×C₇₃	—	2	4	no	—
29	C₄×C₈×C₇₃	C₂×C₄	1	2	yes	—
30	C₄×C₈×C₇₃	D₄	1	2	yes	—
31	C₂×Dic₁₄₆	—	2	4	no	—
32	C₂×Dic₁₄₆	—	4	8	no	—
33	C₂×Dic₁₄₆	—	4	2	no	—
34	C₂²×Dic₇₃	—	4	2	no	—
35	Dic₂₉₂	—	4	16	no	—
36	C₂×#10596831	—	2	4	no	—
37	C₄⋊Dic₇₃	—	2	8	no	—
38	C₄⋊Dic₇₃	—	4	4	no	—
39	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
40	C₂²×C₄×C₇₃	#41	1	2	yes	—
41	M₁₆×C₇₃	—	4	4	no	—
42	C₂×C₈×C₇₃	—	2	4	no	—
43	C₂×C₈×C₇₃	—	4	2	no	—
44	C₂×C₈×C₇₃	C₂²⋊C₄	1	4	yes	—
45	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
46	C₄²×C₇₃	C₂×D₄	1	2	yes	—
47	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
48	C₂³×C₇₃	#124	1	1	yes	characteristic
49	C₂×C₄×C₇₃	—	2	4	no	—
50	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
51	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
52	C₂×C₄×C₇₃	#121	1	2	yes	—
53	C₂×C₄×C₇₃	#127	1	1	yes	characteristic
54	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	4	yes	—
55	C₂×Dic₇₃	—	4	4	no	—
56	C₂×Dic₇₃	—	8	4	no	—
57	Dic₁₄₆	—	4	8	no	—
58	Dic₁₄₆	—	8	4	no	—
59	C₈×C₇₃	—	2	4	no	—
60	C₈×C₇₃	—	8	2	no	—
61	#10596831	—	4	4	no	—
62	C₂²×C₇₃	—	2	2	no	—
63	C₂²×C₇₃	#390	1	1	yes	characteristic
64	C₂²×C₇₃	#490	1	2	yes	—
65	C₄×C₇₃	—	2	2	no	—
66	C₄×C₇₃	#418	1	2	yes	—
67	C₄×C₇₃	#473	1	4	yes	—
68	C₄×C₇₃	#496	1	2	yes	—
69	Dic₇₃	—	8	4	no	—
70	#9779	—	73	1	no	maximal, Sylow
71	C₂×C₇₃	—	2	2	no	—
72	C₂×C₇₃	#1961	1	1	yes	characteristic
73	C₂×C₇₃	#1979	1	2	yes	—
74	C₂×#494	—	73	1	no	—
75	#1837	D₇₃	1	1	yes	characteristic
76	#1546	—	73	4	no	—
77	#1452	—	73	1	no	—
78	C₇₃	#9779	1	1	yes	characteristic, complemented, Sylow
79	C₂²×Q₁₆	—	146	2	no	—
80	C₂×C₄⋊Q₈	—	73	2	no	—
81	#494	—	73	4	no	—
82	#494	—	146	2	no	—
83	#431	—	73	2	no	—
84	#423	C₂×D₇₃	1	2	yes	—
85	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
86	#341	—	2	2	no	—
87	#332	—	146	8	no	—
88	#322	—	146	2	no	—
89	C₂²×Q₈	—	146	2	no	—
90	C₂×Q₁₆	—	292	8	no	—
91	C₂×Q₁₆	—	146	8	no	—
92	C₂×M₁₆	—	2	2	no	—
93	C₂²×C₈	C₂²⋊D₇₃	1	2	yes	—
94	C₄⋊Q₈	—	73	4	no	—
95	C₄⋊Q₈	—	146	4	no	—
96	C₄⋊Q₈	—	146	2	no	—
97	C₂×C₄⋊C₄	—	146	4	no	—
98	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
99	C₄⋊C₈	—	2	4	no	—
100	C₄⋊C₈	—	73	4	no	—
101	C₂²⋊C₈	—	146	2	no	—
102	C₄×C₈	—	146	2	no	—
103	C₄×C₈	C₄×D₇₃	1	2	yes	—
104	C₄×C₈	D₂₉₂	1	2	yes	—
105	C₂×Q₈	—	292	2	no	—
106	C₂×Q₈	—	292	8	no	—
107	C₂×Q₈	—	146	4	no	—
108	C₂²×C₄	—	292	2	no	—
109	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
110	C₂²×C₄	#11924029	1	2	yes	—
111	Q₁₆	—	292	16	no	—
112	M₁₆	—	4	4	no	—
113	C₂×C₈	—	2	4	no	—
114	C₂×C₈	—	4	2	no	—
115	C₂×C₈	—	146	4	no	—
116	C₂×C₈	#11924005	1	4	yes	—
117	C₄⋊C₄	—	292	4	no	—
118	C₄⋊C₄	—	146	8	no	—
119	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
120	C₄²	D₄×D₇₃	1	2	yes	—
121	C₄²	C₂×D₂₉₂	1	1	yes	characteristic
122	C₂³	#14556580	1	1	yes	characteristic
123	Q₈	—	292	8	no	—
124	Q₈	—	584	4	no	—
125	C₂×C₄	—	2	4	no	—
126	C₂×C₄	—	292	4	no	—
127	C₂×C₄	—	584	4	no	—
128	C₂×C₄	C₂×#11924005	1	1	yes	characteristic
129	C₂×C₄	#14556553	1	2	yes	—
130	C₂×C₄	#14556566	1	2	yes	—
131	C₂×C₄	#14556587	1	1	yes	characteristic
132	C₂×C₄	#14556616	1	4	yes	—
133	C₈	—	2	4	no	—
134	C₈	—	8	2	no	—
135	C₈	—	292	4	no	—
136	C₂²	—	2	2	no	—
137	C₂²	#17988488	1	1	yes	characteristic
138	C₂²	#17988953	1	2	yes	—
139	C₄	—	2	2	no	—
140	C₄	—	584	4	no	—
141	C₄	#17988591	1	2	yes	—
142	C₄	#17988863	1	4	yes	—
143	C₄	#17988977	1	2	yes	—
144	C₂	—	2	2	no	—
145	C₂	#22610754	1	1	yes	characteristic
146	C₂	#22610844	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#17988967

C₂

yes

maximal, characteristic

#22608604

C₂

yes

maximal

#22608223

C₂

yes

maximal, characteristic

C₇₃×#1837

C₂

yes

maximal, characteristic

C₂²×Dic₂₉₂

—

C₂×#14556591

C₂²

yes

—

#17988967

—

#17988967

C₄

yes

—

#17988640

C₂²

yes

—

#17988334

—

#17988309

—

#423×C₇₃

C₂²

yes

—

C₂×C₄×C₈×C₇₃

C₂²

yes

characteristic

#341×C₇₃

—

C₂²×Dic₁₄₆

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

#14556591

—

#14556591

—

#14556591

C₂×C₄

yes

—

C₂×C₄⋊Dic₇₃

—

C₄⋊#10596831

D₄

yes

—

C₂²⋊#10596831

—

C₄×#10596831

—

C₂×M₁₆×C₇₃

—

C₂²×C₈×C₇₃

D₄

yes

—

C₂×C₄²×C₇₃

C₂³

yes

characteristic

C₄⋊C₈×C₇₃

—

C₄×C₈×C₇₃

C₂×C₄

yes

—

C₄×C₈×C₇₃

D₄

yes

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂²×Dic₇₃

—

Dic₂₉₂

—

C₂×#10596831

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₃

#41

yes

—

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂²⋊C₄

yes

—

C₄²×C₇₃

C₂²×C₄

yes

characteristic

C₄²×C₇₃

C₂×D₄

yes

—

C₄²×C₇₃

C₂×D₄

yes

characteristic

C₂³×C₇₃

#124

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₄×D₄

yes

—

C₂×C₄×C₇₃

#121

yes

—

C₂×C₄×C₇₃

#127

yes

characteristic

C₂×C₄×C₇₃

AGL(1,ℤ/8)

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

#390

yes

characteristic

C₂²×C₇₃

#490

yes

—

C₄×C₇₃

—

C₄×C₇₃

#418

yes

—

C₄×C₇₃

#473

yes

—

C₄×C₇₃

#496

yes

—

Dic₇₃

—

#9779

—

maximal, Sylow

C₂×C₇₃

—

C₂×C₇₃

#1961

yes

characteristic

C₂×C₇₃

#1979

yes

—

C₂×#494

—

#1837

D₇₃

yes

characteristic

#1546

—

#1452

—

C₇₃

#9779

yes

characteristic, complemented, Sylow

C₂²×Q₁₆

—

146

—

C₂×C₄⋊Q₈

—

#494

—

#494

—

146

—

#431

—

#423

C₂×D₇₃

yes

—

C₂×C₄×C₈

C₂×D₇₃

yes

characteristic

#341

—

#332

—

146

—

#322

—

146

—

C₂²×Q₈

—

146

—

C₂×Q₁₆

—

292

—

C₂×Q₁₆

—

146

—

C₂×M₁₆

—

C₂²×C₈

C₂²⋊D₇₃

yes

—

C₄⋊Q₈

—

C₄⋊Q₈

—

146

—

C₄⋊Q₈

—

146

—

C₂×C₄⋊C₄

—

146

—

C₂×C₄²

C₂²×D₇₃

yes

characteristic

C₄⋊C₈

—

100

C₄⋊C₈

—

101

C₂²⋊C₈

—

146

—

102

C₄×C₈

—

146

—

103

C₄×C₈

C₄×D₇₃

yes

—

104

C₄×C₈

D₂₉₂

yes

—

105

C₂×Q₈

—

292

—

106

C₂×Q₈

—

292

—

107

C₂×Q₈

—

146

—

108

C₂²×C₄

—

292

—

109

C₂²×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

110

C₂²×C₄

#11924029

yes

—

111

Q₁₆

—

292

—

112

M₁₆

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

146

—

116

C₂×C₈

#11924005

yes

—

117

C₄⋊C₄

—

292

—

118

C₄⋊C₄

—

146

—

119

C₄²

C₂×C₄×D₇₃

yes

characteristic

120

C₄²

D₄×D₇₃

yes

—

121

C₄²

C₂×D₂₉₂

yes

characteristic

122

C₂³

#14556580

yes

characteristic

123

Q₈

—

292

—

124

Q₈

—

584

—

125

C₂×C₄

—

126

C₂×C₄

—

292

—

127

C₂×C₄

—

584

—

128

C₂×C₄

C₂×#11924005

yes

characteristic

129

C₂×C₄

#14556553

yes

—

130

C₂×C₄

#14556566

yes

—

131

C₂×C₄

#14556587

yes

characteristic

132

C₂×C₄

#14556616

yes

—

133

C₈

—

134

C₈

—

135

C₈

—

292

—

136

C₂²

—

137

C₂²

#17988488

yes

characteristic

138

C₂²

#17988953

yes

—

139

C₄

—

140

C₄

—

584

—

141

C₄

#17988591

yes

—

142

C₄

#17988863

yes

—

143

C₄

#17988977

yes

—

144

C₂

—

145

C₂

#22610754

yes

characteristic

146

C₂

#22610844

yes

—

	subgroup	G/H
center	C₂²	#17988488
commutator	C₄²×C₇₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₃
Fitting	C₇₃×#1837	C₂
socle	C₂²×C₇₃	#390
prime radical	C₂³×C₇₃	#124
cosocle	C₂×C₄²×C₇₃	C₂³
hypercenter	#1837	D₇₃
hypocenter	C₇₃	#9779
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1837

subgroup

G/H

center

C₂²

#17988488

commutator

C₄²×C₇₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₃

Fitting

C₇₃×#1837

C₂

C₂²×C₇₃

C₂³×C₇₃

C₂×C₄²×C₇₃

C₂³

D₇₃

C₇₃

G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1837

N	H ≅ G/N	type
78. C₇₃	#9779	semidirect

H ≅ G/N

type

78. C₇₃

#9779

semidirect

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

subgroup	index
C₂×#17988967	2
#22608604	2
#22608223	2
C₇₃×#1837	2
#9779	73

subgroup

index

C₇₃×#1837

Subgroups — #32985483

Conjugacy classes of subgroups

Complements

Maximal subgroups