Group #33002353 — subgroups

Subgroups — #33002353

Order 18688.

234 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 103 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	#22611690	C₂	1	1	yes	maximal, characteristic
2	#22609686	C₂	1	1	yes	maximal, characteristic
3	#22608021	C₂	1	2	yes	maximal
4	#22608016	C₂	1	2	yes	maximal
5	C₇₃×#2153	C₂	1	1	yes	maximal, characteristic
6	C₂×#14556531	C₂²	1	1	yes	characteristic
7	C₂²×#11924003	C₂²	1	1	yes	characteristic
8	#17988542	C₂²	1	2	yes	—
9	C₄⋊#11924003	—	2	2	no	—
10	#17988345	C₄	1	1	yes	characteristic
11	#17988344	C₄	1	1	yes	characteristic
12	#17988343	C₄	1	2	yes	—
13	C₂×M₃₂×C₇₃	C₂²	1	2	yes	—
14	#405×C₇₃	C₂²	1	1	yes	characteristic
15	#364×C₇₃	—	2	2	no	—
16	C₂×#11924012	C₂×C₄	1	2	yes	—
17	#14556550	C₂×C₄	1	2	yes	—
18	#14556531	—	2	2	no	—
19	C₂×#11924003	—	2	1	no	—
20	C₂×#11924003	—	2	1	no	—
21	C₂×#11924003	—	2	2	no	—
22	#14556501	—	2	2	no	—
23	C₈×Dic₇₃	—	2	2	no	—
24	C₂×M₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
26	#117×C₇₃	C₂×C₄	1	1	yes	characteristic
27	M₃₂×C₇₃	—	2	2	no	—
28	M₃₂×C₇₃	—	2	2	no	—
29	C₂×C₁₆×C₇₃	—	2	2	no	—
30	#97×C₇₃	Q₈	1	2	yes	—
31	C₄×C₈×C₇₃	D₄	1	2	yes	—
32	#11924012	—	2	2	no	—
33	#11924012	—	2	2	no	—
34	C₂×#10596831	—	2	2	no	—
35	C₄⋊Dic₇₃	—	2	2	no	—
36	C₂²⋊Dic₇₃	—	2	2	no	—
37	C₄×Dic₇₃	—	2	2	no	—
38	#11924003	—	4	1	no	—
39	#11924003	—	4	1	no	—
40	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
41	M₁₆×C₇₃	—	2	2	no	—
42	C₂×C₈×C₇₃	C₄⋊C₄	1	2	yes	—
43	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
44	C₂×C₈×C₇₃	C₂×Q₈	1	1	yes	characteristic
45	C₂×C₈×C₇₃	#41	1	2	yes	—
46	C₂×C₈×C₇₃	#41	1	2	yes	—
47	C₄⋊C₄×C₇₃	—	2	1	no	—
48	C₂²⋊C₄×C₇₃	—	2	1	no	—
49	C₄²×C₇₃	C₄⋊C₄	1	2	yes	—
50	C₁₆×C₇₃	—	4	2	no	—
51	C₂³×C₇₃	#131	1	1	yes	characteristic
52	C₂×C₄×C₇₃	—	2	2	no	—
53	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
54	C₂×C₄×C₇₃	#117	1	2	yes	—
55	C₂×C₄×C₇₃	#131	1	2	yes	—
56	C₂×C₄×C₇₃	#131	1	1	yes	characteristic
57	C₂×Dic₇₃	—	4	2	no	—
58	C₈×C₇₃	—	2	2	no	—
59	C₈×C₇₃	#124	1	1	yes	characteristic
60	C₈×C₇₃	#124	1	1	yes	characteristic
61	C₈×C₇₃	#125	1	2	yes	—
62	#10596831	—	4	2	no	—
63	C₂²×C₇₃	—	4	1	no	—
64	C₂²×C₇₃	#424	1	1	yes	characteristic
65	C₂²×C₇₃	#433	1	2	yes	—
66	C₄×C₇₃	—	4	2	no	—
67	C₄×C₇₃	#382	1	1	yes	characteristic
68	C₄×C₇₃	#424	1	1	yes	characteristic
69	C₄×C₇₃	#433	1	2	yes	—
70	Dic₇₃	—	8	2	no	—
71	#12885	—	73	1	no	maximal, Sylow
72	C₂×C₇₃	—	2	2	no	—
73	C₂×C₇₃	—	2	1	no	—
74	C₂×C₇₃	#1832	1	1	yes	characteristic
75	#2153	D₇₃	1	1	yes	characteristic
76	#2151	—	73	1	no	—
77	#1747	—	73	1	no	—
78	#1379	—	73	2	no	—
79	#1378	—	73	2	no	—
80	C₇₃	#12885	1	1	yes	characteristic, complemented, Sylow
81	C₂×M₃₂	—	73	1	no	—
82	C₂×M₃₂	C₂×D₇₃	1	2	yes	—
83	C₂²×C₁₆	—	73	1	no	—
84	#405	—	73	2	no	—
85	#405	C₂×D₇₃	1	1	yes	characteristic
86	#364	—	2	2	no	—
87	C₄⋊C₁₆	—	146	2	no	—
88	#338	—	73	1	no	—
89	H(3,ℤ/4)	—	73	1	no	—
90	H(3,ℤ/4)	—	73	2	no	—
91	C₂×M₁₆	—	73	2	no	—
92	C₂×M₁₆	C₄×D₇₃	1	1	yes	characteristic
93	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
94	#117	—	73	2	no	—
95	#117	C₄×D₇₃	1	1	yes	characteristic
96	M₃₂	—	2	2	no	—
97	M₃₂	—	2	2	no	—
98	M₃₂	—	146	2	no	—
99	C₂×C₁₆	—	2	2	no	—
100	C₂×C₁₆	—	146	1	no	—
101	C₂×C₁₆	—	146	1	no	—
102	C₂×C₁₆	—	146	2	no	—
103	#97	—	146	2	no	—
104	#97	Dic₁₄₆	1	2	yes	—
105	C₄×C₈	—	146	2	no	—
106	C₄×C₈	C₂²⋊D₇₃	1	2	yes	—
107	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
108	M₁₆	—	2	2	no	—
109	M₁₆	—	146	2	no	—
110	M₁₆	—	146	2	no	—
111	C₂×C₈	—	146	2	no	—
112	C₂×C₈	#11924007	1	2	yes	—
113	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
114	C₂×C₈	C₂×Dic₁₄₆	1	1	yes	characteristic
115	C₂×C₈	#11924027	1	2	yes	—
116	C₂×C₈	#11924029	1	2	yes	—
117	C₄⋊C₄	—	2	1	no	—
118	C₄⋊C₄	—	146	2	no	—
119	C₂²⋊C₄	—	2	1	no	—
120	C₂²⋊C₄	—	146	2	no	—
121	C₄²	—	146	2	no	—
122	C₄²	#11924007	1	2	yes	—
123	C₁₆	—	4	2	no	—
124	C₁₆	—	292	1	no	—
125	C₁₆	—	292	1	no	—
126	C₂³	#14556599	1	1	yes	characteristic
127	C₂×C₄	—	2	2	no	—
128	C₂×C₄	—	292	2	no	—
129	C₂×C₄	C₂×#11924007	1	1	yes	characteristic
130	C₂×C₄	#14556549	1	2	yes	—
131	C₂×C₄	#14556597	1	2	yes	—
132	C₂×C₄	#14556599	1	1	yes	characteristic
133	C₈	—	2	2	no	—
134	C₈	—	292	2	no	—
135	C₈	#14556578	1	1	yes	characteristic
136	C₈	#14556580	1	1	yes	characteristic
137	C₈	#14556582	1	2	yes	—
138	C₂²	—	4	1	no	—
139	C₂²	#17988615	1	1	yes	characteristic
140	C₂²	#17988647	1	2	yes	—
141	C₄	—	4	2	no	—
142	C₄	—	584	2	no	—
143	C₄	#17988452	1	1	yes	characteristic
144	C₄	#17988613	1	1	yes	characteristic
145	C₄	#17988647	1	2	yes	—
146	C₂	—	2	1	no	—
147	C₂	—	2	2	no	—
148	C₂	#22610050	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22611690

C₂

yes

maximal, characteristic

#22609686

C₂

yes

maximal, characteristic

#22608021

C₂

yes

maximal

#22608016

C₂

yes

maximal

C₇₃×#2153

C₂

yes

maximal, characteristic

C₂×#14556531

C₂²

yes

characteristic

C₂²×#11924003

C₂²

yes

characteristic

#17988542

C₂²

yes

—

C₄⋊#11924003

—

#17988345

C₄

yes

characteristic

#17988344

C₄

yes

characteristic

#17988343

C₄

yes

—

C₂×M₃₂×C₇₃

C₂²

yes

—

#405×C₇₃

C₂²

yes

characteristic

#364×C₇₃

—

C₂×#11924012

C₂×C₄

yes

—

#14556550

C₂×C₄

yes

—

—

—

—

—

—

C₈×Dic₇₃

—

C₂×M₁₆×C₇₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₇₃

C₂³

yes

characteristic

#117×C₇₃

C₂×C₄

yes

characteristic

M₃₂×C₇₃

—

M₃₂×C₇₃

—

C₂×C₁₆×C₇₃

—

#97×C₇₃

Q₈

yes

—

C₄×C₈×C₇₃

D₄

yes

—

#11924012

—

#11924012

—

C₂×#10596831

—

C₄⋊Dic₇₃

—

C₂²⋊Dic₇₃

—

C₄×Dic₇₃

—

#11924003

—

#11924003

—

C₂²×C₄×C₇₃

C₂²×C₄

yes

characteristic

M₁₆×C₇₃

—

C₂×C₈×C₇₃

C₄⋊C₄

yes

—

C₂×C₈×C₇₃

C₂×D₄

yes

characteristic

C₂×C₈×C₇₃

C₂×Q₈

yes

characteristic

C₂×C₈×C₇₃

#41

yes

—

C₂×C₈×C₇₃

#41

yes

—

C₄⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₄²×C₇₃

C₄⋊C₄

yes

—

C₁₆×C₇₃

—

C₂³×C₇₃

#131

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

#117

yes

—

C₂×C₄×C₇₃

#131

yes

—

C₂×C₄×C₇₃

#131

yes

characteristic

C₂×Dic₇₃

—

C₈×C₇₃

—

C₈×C₇₃

yes

C₈×C₇₃

yes

C₈×C₇₃

yes

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

#424

yes

characteristic

C₂²×C₇₃

#433

yes

—

C₄×C₇₃

—

C₄×C₇₃

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

—

Dic₇₃

—

#12885

—

maximal, Sylow

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#1832

yes

characteristic

#2153

D₇₃

yes

—

—

—

—

C₇₃

#12885

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₂×M₃₂

C₂×D₇₃

yes

—

C₂²×C₁₆

—

#405

—

#405

C₂×D₇₃

yes

characteristic

#364

—

C₄⋊C₁₆

—

146

—

#338

—

H(3,ℤ/4)

—

H(3,ℤ/4)

—

C₂×M₁₆

—

C₂×M₁₆

C₄×D₇₃

yes

characteristic

C₂²×C₈

C₂²×D₇₃

yes

characteristic

#117

—

#117

C₄×D₇₃

yes

characteristic

M₃₂

—

M₃₂

—

M₃₂

—

146

—

C₂×C₁₆

—

100

C₂×C₁₆

—

146

—

101

C₂×C₁₆

—

146

—

102

C₂×C₁₆

—

146

—

103

#97

—

146

—

104

#97

Dic₁₄₆

yes

—

105

C₄×C₈

—

146

—

106

C₄×C₈

C₂²⋊D₇₃

yes

—

107

C₂²×C₄

C₂×C₄×D₇₃

yes

characteristic

108

M₁₆

—

109

M₁₆

—

146

—

110

M₁₆

—

146

—

111

C₂×C₈

—

146

—

112

C₂×C₈

#11924007

yes

—

113

C₂×C₈

C₂×C₂²⋊D₇₃

yes

characteristic

114

C₂×C₈

C₂×Dic₁₄₆

yes

characteristic

115

C₂×C₈

#11924027

yes

—

116

C₂×C₈

#11924029

yes

—

117

C₄⋊C₄

—

118

C₄⋊C₄

—

146

—

119

C₂²⋊C₄

—

120

C₂²⋊C₄

—

146

—

121

C₄²

—

146

—

122

C₄²

#11924007

yes

—

123

C₁₆

—

124

C₁₆

—

292

—

125

C₁₆

—

292

—

126

C₂³

#14556599

yes

characteristic

127

C₂×C₄

—

128

C₂×C₄

—

292

—

129

C₂×C₄

C₂×#11924007

yes

characteristic

130

C₂×C₄

#14556549

yes

—

131

C₂×C₄

#14556597

yes

—

132

C₂×C₄

#14556599

yes

characteristic

133

C₈

—

134

C₈

—

292

—

135

C₈

#14556578

yes

characteristic

136

C₈

#14556580

yes

characteristic

137

C₈

#14556582

yes

—

138

C₂²

—

139

C₂²

#17988615

yes

characteristic

140

C₂²

#17988647

yes

—

141

C₄

—

142

C₄

—

584

—

143

C₄

#17988452

yes

characteristic

144

C₄

#17988613

yes

characteristic

145

C₄

#17988647

yes

—

146

C₂

—

147

C₂

—

148

C₂

#22610050

yes

characteristic

	subgroup	G/H
center	C₈	#14556578
commutator	C₂²×C₄×C₇₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₇₃
Fitting	C₇₃×#2153	C₂
socle	C₂×C₇₃	#1832
prime radical	C₂³×C₇₃	#131
cosocle	C₂²×C₈×C₇₃	C₂³
hypercenter	#2153	D₇₃
hypocenter	C₇₃	#12885
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #2153

subgroup

G/H

center

C₈

#14556578

commutator

C₂²×C₄×C₇₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₇₃

Fitting

C₇₃×#2153

C₂

C₂×C₇₃

C₂³×C₇₃

C₂²×C₈×C₇₃

C₂³

D₇₃

C₇₃

G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #2153

N	H ≅ G/N	type
80. C₇₃	#12885	semidirect

H ≅ G/N

type

80. C₇₃

#12885

semidirect

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

subgroup	index
#22611690	2
#22609686	2
#22608021	2
#22608016	2
C₇₃×#2153	2
#12885	73

subgroup

index

C₇₃×#2153

Subgroups — #33002353

Conjugacy classes of subgroups

Complements

Maximal subgroups