Group #33073789 — subgroups

Subgroups — #33073789

Order 18688.

690 conjugacy classes of subgroups; only the 227 normal subgroups are shown.

normal subgroups only

This group has 690 conjugacy classes of subgroups — too many to draw. Only its 227 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	#22620517	C₂	1	4	yes	maximal
2	#22620445	C₂	1	2	yes	maximal
3	#22609608	C₂	1	8	yes	maximal, complemented
4	C₂×#322×C₇₃	C₂	1	1	yes	maximal, characteristic
5	#17989144	C₂²	1	4	yes	—
6	#17988992	C₂²	1	4	yes	—
7	#17988992	C₂²	1	4	yes	—
8	#17988989	—	2	4	no	—
9	#17988985	C₂²	1	4	yes	—
10	#17988967	C₂²	1	4	yes	—
11	#17988938	C₂²	1	8	yes	—
12	#17988828	—	2	8	no	—
13	C₄×Dic₂₉₂	—	2	8	no	—
14	#17988625	—	2	4	no	—
15	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₈×C₇₃	C₂²	1	2	yes	—
17	#322×C₇₃	C₂²	1	4	yes	—
18	C₂×Dic₂₉₂	—	2	8	no	—
19	#14556591	C₂³	1	8	yes	—
20	#14556583	—	2	4	no	—
21	#14556570	—	2	8	no	—
22	C₄×Dic₁₄₆	—	2	8	no	—
23	#14556550	—	2	4	no	—
24	#14556525	—	2	8	no	—
25	#14556525	—	2	8	no	—
26	#14556523	—	2	8	no	—
27	#14556516	—	2	16	no	—
28	C₂²×C₈×C₇₃	D₄	1	4	yes	—
29	C₂²×C₈×C₇₃	D₄	1	2	yes	—
30	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
31	C₄×C₈×C₇₃	D₄	1	4	yes	—
32	C₄×C₈×C₇₃	D₄	1	2	yes	—
33	C₄×C₈×C₇₃	C₂³	1	4	yes	—
34	C₄×C₈×C₇₃	C₂³	1	2	yes	—
35	C₂×Dic₁₄₆	—	2	8	no	—
36	Dic₂₉₂	—	4	16	no	—
37	C₄⋊Dic₇₃	—	2	8	no	—
38	C₄⋊Dic₇₃	—	2	8	no	—
39	#11924007	—	4	8	no	—
40	C₂²⋊Dic₇₃	—	4	4	no	—
41	C₄×Dic₇₃	—	4	4	no	—
42	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
43	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
44	C₂×C₈×C₇₃	—	4	4	no	—
45	C₂×C₈×C₇₃	Q₁₆	1	8	yes	complemented
46	C₂×C₈×C₇₃	C₂×D₄	1	8	yes	—
47	C₂×C₈×C₇₃	C₂×D₄	1	4	yes	—
48	C₄²×C₇₃	C₂×D₄	1	2	yes	—
49	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
50	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
51	C₂³×C₇₃	#127	1	1	yes	characteristic
52	C₂×C₄×C₇₃	—	2	4	no	—
53	C₂×C₄×C₇₃	#127	1	2	yes	—
54	C₂×C₄×C₇₃	#127	1	1	yes	characteristic
55	C₂×C₄×C₇₃	C₂×Q₁₆	1	4	yes	—
56	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
57	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
58	C₂×Dic₇₃	—	4	8	no	—
59	Dic₁₄₆	—	4	16	no	—
60	C₈×C₇₃	—	2	8	no	—
61	C₈×C₇₃	C₂×Q₁₆	1	8	yes	—
62	C₂²×C₇₃	—	2	2	no	—
63	C₂²×C₇₃	#494	1	2	yes	—
64	C₂²×C₇₃	C₂×#127	1	1	yes	characteristic
65	C₄×C₇₃	—	2	2	no	—
66	C₄×C₇₃	#494	1	2	yes	—
67	C₄×C₇₃	C₂²×Q₁₆	1	2	yes	—
68	C₄×C₇₃	#575	1	4	yes	—
69	Dic₇₃	—	8	8	no	—
70	#19618	—	73	1	no	maximal, Sylow
71	C₂×C₇₃	—	2	2	no	—
72	C₂×C₇₃	C₂×#494	1	1	yes	characteristic
73	C₂×C₇₃	#3150	1	2	yes	—
74	#3170	—	73	4	no	—
75	#3160	—	73	2	no	—
76	#1723	—	73	8	no	—
77	C₂×#322	D₇₃	1	1	yes	characteristic
78	C₇₃	#19618	1	1	yes	characteristic, complemented, Sylow
79	#533	—	73	4	no	—
80	#500	—	73	4	no	—
81	#500	—	73	4	no	—
82	#499	—	146	4	no	—
83	#498	—	73	4	no	—
84	#494	—	73	4	no	—
85	#487	—	73	8	no	—
86	#467	—	146	8	no	—
87	C₄×Q₁₆	—	146	8	no	—
88	#427	—	146	4	no	—
89	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
90	C₂×C₄×C₈	C₂×D₇₃	1	2	yes	—
91	#322	C₂×D₇₃	1	4	yes	—
92	C₂×Q₁₆	—	146	8	no	—
93	C₂²×C₈	D₂₉₂	1	4	yes	—
94	C₂²×C₈	D₂₉₂	1	2	yes	—
95	C₄⋊Q₈	—	73	8	no	—
96	#125	—	146	4	no	—
97	C₂²⋊Q₈	—	146	8	no	—
98	C₄×Q₈	—	146	8	no	—
99	#117	—	146	4	no	—
100	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
101	#107	—	146	8	no	—
102	#107	—	146	8	no	—
103	#106	—	146	8	no	—
104	#103	—	146	16	no	—
105	C₄×C₈	D₂₉₂	1	4	yes	—
106	C₄×C₈	D₂₉₂	1	2	yes	—
107	C₄×C₈	C₂²×D₇₃	1	4	yes	—
108	C₄×C₈	C₂²×D₇₃	1	2	yes	—
109	C₂×Q₈	—	146	8	no	—
110	C₂²×C₄	C₂×D₂₉₂	1	2	yes	—
111	C₂²×C₄	C₂×D₂₉₂	1	1	yes	characteristic
112	Q₁₆	—	292	16	no	—
113	C₂×C₈	—	4	4	no	—
114	C₂×C₈	Dic₂₉₂	1	8	yes	complemented
115	C₂×C₈	C₂×D₂₉₂	1	8	yes	—
116	C₂×C₈	C₂×D₂₉₂	1	4	yes	—
117	C₄⋊C₄	—	292	8	no	—
118	C₄⋊C₄	—	146	8	no	—
119	C₄⋊C₄	—	146	8	no	—
120	C₂²⋊C₄	—	292	4	no	—
121	C₄²	—	292	4	no	—
122	C₄²	C₂×D₂₉₂	1	1	yes	characteristic
123	C₄²	C₂×D₂₉₂	1	2	yes	—
124	C₄²	C₂³×D₇₃	1	1	yes	characteristic
125	C₂³	#14556588	1	1	yes	characteristic
126	Q₈	—	292	16	no	—
127	C₂×C₄	—	2	4	no	—
128	C₂×C₄	—	292	8	no	—
129	C₂×C₄	#14556588	1	2	yes	—
130	C₂×C₄	#14556588	1	1	yes	characteristic
131	C₂×C₄	C₂×Dic₂₉₂	1	4	yes	—
132	C₂×C₄	C₂²×D₂₉₂	1	2	yes	—
133	C₂×C₄	C₂²×D₂₉₂	1	1	yes	characteristic
134	C₈	—	2	8	no	—
135	C₈	C₂×Dic₂₉₂	1	8	yes	—
136	C₂²	—	2	2	no	—
137	C₂²	#17988967	1	2	yes	—
138	C₂²	C₂×#14556588	1	1	yes	characteristic
139	C₄	—	2	2	no	—
140	C₄	—	584	8	no	—
141	C₄	#17988967	1	2	yes	—
142	C₄	C₂²×Dic₂₉₂	1	2	yes	—
143	C₄	#17989387	1	4	yes	—
144	C₂	—	2	2	no	—
145	C₂	C₂×#17988967	1	1	yes	characteristic
146	C₂	#22620377	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#22620517

C₂

yes

maximal

#22620445

C₂

yes

maximal

#22609608

C₂

yes

maximal, complemented

C₂×#322×C₇₃

C₂

yes

maximal, characteristic

#17989144

C₂²

yes

—

#17988992

C₂²

yes

—

#17988992

C₂²

yes

—

#17988989

—

#17988985

C₂²

yes

—

#17988967

C₂²

yes

—

#17988938

C₂²

yes

—

#17988828

—

C₄×Dic₂₉₂

—

#17988625

—

C₂×C₄×C₈×C₇₃

C₂²

yes

characteristic

C₂×C₄×C₈×C₇₃

C₂²

yes

—

#322×C₇₃

C₂²

yes

—

C₂×Dic₂₉₂

—

#14556591

C₂³

yes

—

#14556583

—

#14556570

—

C₄×Dic₁₄₆

—

—

—

—

—

—

C₂²×C₈×C₇₃

D₄

yes

—

C₂²×C₈×C₇₃

D₄

yes

—

C₂×C₄²×C₇₃

C₂³

yes

characteristic

C₄×C₈×C₇₃

D₄

yes

—

C₄×C₈×C₇₃

D₄

yes

—

C₄×C₈×C₇₃

C₂³

yes

—

C₄×C₈×C₇₃

C₂³

yes

—

C₂×Dic₁₄₆

—

Dic₂₉₂

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

#11924007

—

C₂²⋊Dic₇₃

—

C₄×Dic₇₃

—

C₂²×C₄×C₇₃

C₂×D₄

yes

—

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

Q₁₆

yes

complemented

C₂×C₈×C₇₃

C₂×D₄

yes

—

C₂×C₈×C₇₃

C₂×D₄

yes

—

C₄²×C₇₃

C₂×D₄

yes

—

C₄²×C₇₃

C₂×D₄

yes

characteristic

C₄²×C₇₃

C₂⁴

yes

characteristic

C₂³×C₇₃

#127

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

#127

yes

—

C₂×C₄×C₇₃

#127

yes

characteristic

C₂×C₄×C₇₃

C₂×Q₁₆

yes

—

C₂×C₄×C₇₃

C₂²×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂²×D₄

yes

—

C₂×Dic₇₃

—

Dic₁₄₆

—

C₈×C₇₃

—

C₈×C₇₃

C₂×Q₁₆

yes

—

C₂²×C₇₃

—

C₂²×C₇₃

#494

yes

—

C₂²×C₇₃

C₂×#127

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

#494

yes

—

C₄×C₇₃

C₂²×Q₁₆

yes

—

C₄×C₇₃

#575

yes

—

Dic₇₃

—

#19618

—

maximal, Sylow

C₂×C₇₃

—

C₂×C₇₃

C₂×#494

yes

characteristic

C₂×C₇₃

#3150

yes

—

—

—

—

D₇₃

yes

characteristic

C₇₃

#19618

yes

characteristic, complemented, Sylow

—

—

—

—

146

—

—

—

—

—

146

—

C₄×Q₁₆

—

146

—

#427

—

146

—

C₂×C₄×C₈

C₂×D₇₃

yes

characteristic

C₂×C₄×C₈

C₂×D₇₃

yes

—

#322

C₂×D₇₃

yes

—

C₂×Q₁₆

—

146

—

C₂²×C₈

D₂₉₂

yes

—

C₂²×C₈

D₂₉₂

yes

—

C₄⋊Q₈

—

#125

—

146

—

C₂²⋊Q₈

—

146

—

C₄×Q₈

—

146

—

#117

—

146

—

100

C₂×C₄²

C₂²×D₇₃

yes

characteristic

101

#107

—

146

—

102

#107

—

146

—

103

#106

—

146

—

104

#103

—

146

—

105

C₄×C₈

D₂₉₂

yes

—

106

C₄×C₈

D₂₉₂

yes

—

107

C₄×C₈

C₂²×D₇₃

yes

—

108

C₄×C₈

C₂²×D₇₃

yes

—

109

C₂×Q₈

—

146

—

110

C₂²×C₄

C₂×D₂₉₂

yes

—

111

C₂²×C₄

C₂×D₂₉₂

yes

characteristic

112

Q₁₆

—

292

—

113

C₂×C₈

—

114

C₂×C₈

Dic₂₉₂

yes

complemented

115

C₂×C₈

C₂×D₂₉₂

yes

—

116

C₂×C₈

C₂×D₂₉₂

yes

—

117

C₄⋊C₄

—

292

—

118

C₄⋊C₄

—

146

—

119

C₄⋊C₄

—

146

—

120

C₂²⋊C₄

—

292

—

121

C₄²

—

292

—

122

C₄²

C₂×D₂₉₂

yes

characteristic

123

C₄²

C₂×D₂₉₂

yes

—

124

C₄²

C₂³×D₇₃

yes

characteristic

125

C₂³

#14556588

yes

characteristic

126

Q₈

—

292

—

127

C₂×C₄

—

128

C₂×C₄

—

292

—

129

C₂×C₄

#14556588

yes

—

130

C₂×C₄

#14556588

yes

characteristic

131

C₂×C₄

C₂×Dic₂₉₂

yes

—

132

C₂×C₄

C₂²×D₂₉₂

yes

—

133

C₂×C₄

C₂²×D₂₉₂

yes

characteristic

134

C₈

—

135

C₈

C₂×Dic₂₉₂

yes

—

136

C₂²

—

137

C₂²

#17988967

yes

—

138

C₂²

C₂×#14556588

yes

characteristic

139

C₄

—

140

C₄

—

584

—

141

C₄

#17988967

yes

—

142

C₄

C₂²×Dic₂₉₂

yes

—

143

C₄

#17989387

yes

—

144

C₂

—

145

C₂

C₂×#17988967

yes

characteristic

146

C₂

#22620377

yes

—

	subgroup	G/H
center	C₂×C₄	#14556588
commutator, cosocle	C₄²×C₇₃	C₂⁴
Frattini	C₄²	C₂³×D₇₃
Fitting	C₂×#322×C₇₃	C₂
socle	C₂²×C₇₃	C₂×#127
prime radical	C₂³×C₇₃	#127
hypercenter	C₂×#322	D₇₃
hypocenter	C₇₃	#19618
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#322

subgroup

G/H

center

C₂×C₄

#14556588

commutator, cosocle

C₄²×C₇₃

C₂⁴

Frattini

C₄²

C₂³×D₇₃

Fitting

C₂×#322×C₇₃

C₂

C₂²×C₇₃

C₂³×C₇₃

D₇₃

C₇₃

G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#322

N	H ≅ G/N	type
3. #22609608	C₂	semidirect
45. C₂×C₈×C₇₃	Q₁₆	semidirect
78. C₇₃	#19618	semidirect
114. C₂×C₈	Dic₂₉₂	semidirect

H ≅ G/N

type

3. #22609608

C₂

semidirect

45. C₂×C₈×C₇₃

Q₁₆

semidirect

78. C₇₃

#19618

semidirect

114. C₂×C₈

Dic₂₉₂

semidirect

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

subgroup	index
#22620517	2
#22620445	2
#22609608	2
C₂×#322×C₇₃	2
#19618	73

subgroup

index

C₂×#322×C₇₃

Subgroups — #33073789

Conjugacy classes of subgroups

Complements

Maximal subgroups