Group #33086370 — subgroups

Subgroups — #33086370

Order 18688.

1118 conjugacy classes of subgroups; only the 387 normal subgroups are shown.

normal subgroups only

This group has 1118 conjugacy classes of subgroups — too many to draw. Only its 387 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×#17988609	C₂	1	6	yes	maximal
2	#376×D₇₃	C₂	1	1	yes	maximal, characteristic
3	#22610085	C₂	1	1	yes	maximal, characteristic, complemented
4	#22610084	C₂	1	6	yes	maximal, complemented
5	C₇₃×#1843	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#11924011	C₂²	1	4	yes	—
7	C₂×C₄²×D₇₃	C₂²	1	3	yes	—
8	#17988609	—	2	24	no	—
9	C₂×C₄⋊#10596831	C₂²	1	6	yes	—
10	C₂×#14556520	C₂²	1	12	yes	—
11	#17988433	C₂²	1	3	yes	—
12	#17988432	C₄	1	4	yes	—
13	#95×D₇₃	C₄	1	4	yes	—
14	C₂×C₄⋊C₈×C₇₃	C₂²	1	6	yes	—
15	#376×C₇₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄×D₇₃	C₂×C₄	1	6	yes	—
17	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
18	C₂×#11924011	—	2	24	no	—
19	C₂²×#10596831	C₂³	1	4	yes	—
20	C₂×C₄×Dic₇₃	C₂×C₄	1	6	yes	—
21	C₂×C₄×Dic₇₃	C₂³	1	3	yes	—
22	C₄²×D₇₃	D₄	1	12	yes	—
23	C₄²×D₇₃	Q₈	1	12	yes	—
24	C₄⋊#10596831	—	2	12	no	—
25	#14556520	—	2	24	no	—
26	#14556498	C₂×C₄	1	12	yes	—
27	C₂²×C₈×C₇₃	C₂³	1	4	yes	—
28	C₂×C₄²×C₇₃	C₂³	1	3	yes	—
29	C₄⋊C₈×C₇₃	—	2	12	no	—
30	#95×C₇₃	C₂×C₄	1	4	yes	—
31	C₂³×D₇₃	C₂²×C₄	1	1	yes	characteristic
32	C₂²×Dic₇₃	C₂²×C₄	1	6	yes	—
33	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₄×D₇₃	—	4	12	no	—
35	C₂×C₄×D₇₃	C₄⋊C₄	1	24	yes	—
36	C₂×C₄×D₇₃	C₂×D₄	1	6	yes	—
37	C₂×C₄×D₇₃	C₂×Q₈	1	6	yes	—
38	#11924011	—	4	16	no	—
39	C₂×#10596831	—	2	12	no	—
40	C₄×Dic₇₃	C₄⋊C₄	1	24	yes	—
41	C₄×Dic₇₃	C₂×D₄	1	6	yes	—
42	C₄×Dic₇₃	C₂×Q₈	1	6	yes	—
43	C₂²×C₄×C₇₃	C₂²×C₄	1	6	yes	—
44	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
45	C₂×C₈×C₇₃	—	2	12	no	—
46	C₄²×C₇₃	C₂×D₄	1	6	yes	—
47	C₄²×C₇₃	C₂×Q₈	1	6	yes	—
48	C₂³×C₇₃	C₂³×C₄	1	1	yes	characteristic
49	C₂²×D₇₃	—	2	4	no	—
50	C₂²×D₇₃	C₂×C₄⋊C₄	1	6	yes	—
51	C₂×C₄×C₇₃	—	2	12	no	—
52	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	12	yes	—
53	C₂×C₄×C₇₃	C₂²×D₄	1	3	yes	—
54	C₂×C₄×C₇₃	C₂²×Q₈	1	3	yes	—
55	C₂×Dic₇₃	—	2	12	no	—
56	C₂×Dic₇₃	C₂×C₄⋊C₄	1	12	yes	—
57	C₂×Dic₇₃	C₂×C₄⋊C₄	1	6	yes	—
58	C₄×D₇₃	—	4	24	no	—
59	C₄×D₇₃	#127	1	4	yes	—
60	C₄×D₇₃	C₄⋊Q₈	1	12	yes	—
61	C₈×C₇₃	—	4	4	no	—
62	#10596831	—	4	4	no	—
63	C₂²×C₇₃	C₂²×C₄⋊C₄	1	3	yes	—
64	C₂²×C₇₃	#568	1	4	yes	—
65	C₂×D₇₃	—	2	12	no	—
66	C₂×D₇₃	#384	1	4	yes	—
67	C₄×C₇₃	—	2	12	no	—
68	C₄×C₇₃	C₂×#127	1	1	yes	characteristic
69	C₄×C₇₃	C₂×C₄⋊Q₈	1	3	yes	—
70	Dic₇₃	—	2	12	no	—
71	Dic₇₃	#384	1	4	yes	—
72	#20792	—	73	1	no	maximal, Sylow
73	C₂×C₇₃	C₂×#384	1	1	yes	characteristic
74	C₂×C₇₃	#2905	1	6	yes	—
75	D₇₃	—	2	4	no	—
76	C₂×#423	—	73	6	no	—
77	C₂×#376	—	73	1	no	—
78	#1843	—	73	6	no	—
79	#1843	—	73	1	no	—
80	#1843	D₇₃	1	1	yes	characteristic, complemented
81	C₇₃	#20792	1	1	yes	characteristic, complemented, Sylow
82	C₂²×M₁₆	—	73	4	no	—
83	C₂²×C₄²	—	73	3	no	—
84	#423	—	146	24	no	—
85	C₂×C₄⋊C₈	—	73	12	no	—
86	C₂×C₄⋊C₈	—	73	6	no	—
87	C₂×C₄⋊C₈	C₂×D₇₃	1	6	yes	—
88	#376	—	73	3	no	—
89	#376	—	73	4	no	—
90	#376	C₂×D₇₃	1	1	yes	characteristic
91	C₂×#95	—	73	4	no	—
92	C₂³×C₄	—	73	6	no	—
93	C₂³×C₄	—	73	1	no	—
94	C₂×M₁₆	—	146	24	no	—
95	C₂²×C₈	—	73	4	no	—
96	C₂²×C₈	C₂²×D₇₃	1	4	yes	—
97	C₂×C₄²	—	73	6	no	—
98	C₂×C₄²	—	73	3	no	—
99	C₂×C₄²	—	73	12	no	—
100	C₂×C₄²	—	73	12	no	—
101	C₂×C₄²	C₂²×D₇₃	1	3	yes	—
102	C₄⋊C₈	—	2	12	no	—
103	C₄⋊C₈	—	146	24	no	—
104	C₄⋊C₈	—	146	12	no	—
105	#95	—	73	12	no	—
106	#95	C₄×D₇₃	1	4	yes	—
107	C₂⁴	—	73	1	no	—
108	C₂²×C₄	—	292	12	no	—
109	C₂²×C₄	—	73	24	no	—
110	C₂²×C₄	—	73	1	no	—
111	C₂²×C₄	—	73	6	no	—
112	C₂²×C₄	—	73	6	no	—
113	C₂²×C₄	—	73	6	no	—
114	C₂²×C₄	C₂×C₄×D₇₃	1	6	yes	—
115	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
116	M₁₆	—	292	16	no	—
117	C₂×C₈	—	2	12	no	—
118	C₂×C₈	—	146	12	no	—
119	C₄²	—	73	24	no	—
120	C₄²	—	73	6	no	—
121	C₄²	—	73	6	no	—
122	C₄²	D₄×D₇₃	1	6	yes	—
123	C₄²	Q₈×D₇₃	1	6	yes	—
124	C₂³	—	73	6	no	—
125	C₂³	—	146	4	no	—
126	C₂³	C₂²×C₄×D₇₃	1	1	yes	characteristic
127	C₂×C₄	—	2	12	no	—
128	C₂×C₄	—	292	24	no	—
129	C₂×C₄	—	73	6	no	—
130	C₂×C₄	—	73	4	no	—
131	C₂×C₄	—	73	12	no	—
132	C₂×C₄	—	73	12	no	—
133	C₂×C₄	—	146	12	no	—
134	C₂×C₄	C₄⋊C₄×D₇₃	1	12	yes	—
135	C₂×C₄	C₂×D₄×D₇₃	1	3	yes	—
136	C₂×C₄	C₂×Q₈×D₇₃	1	3	yes	—
137	C₈	—	4	4	no	—
138	C₈	—	292	4	no	—
139	C₂²	—	73	4	no	—
140	C₂²	—	146	12	no	—
141	C₂²	C₂×C₄⋊C₄×D₇₃	1	3	yes	—
142	C₂²	#17989352	1	4	yes	—
143	C₄	—	2	12	no	—
144	C₄	—	73	4	no	—
145	C₄	—	146	12	no	—
146	C₄	#127×D₇₃	1	1	yes	characteristic
147	C₄	C₄⋊Q₈×D₇₃	1	3	yes	—
148	C₂	—	146	4	no	—
149	C₂	#384×D₇₃	1	1	yes	characteristic
150	C₂	#22618492	1	6	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#17988609

C₂

yes

maximal

#376×D₇₃

C₂

yes

maximal, characteristic

#22610085

C₂

yes

maximal, characteristic, complemented

#22610084

C₂

yes

maximal, complemented

C₇₃×#1843

C₂

yes

maximal, characteristic, complemented

C₂²×#11924011

C₂²

yes

—

C₂×C₄²×D₇₃

C₂²

yes

—

#17988609

—

C₂×C₄⋊#10596831

C₂²

yes

—

C₂×#14556520

C₂²

yes

—

#17988433

C₂²

yes

—

#17988432

C₄

yes

—

#95×D₇₃

C₄

yes

—

C₂×C₄⋊C₈×C₇₃

C₂²

yes

—

#376×C₇₃

C₂²

yes

characteristic

C₂²×C₄×D₇₃

C₂×C₄

yes

—

C₂²×C₄×D₇₃

C₂³

yes

characteristic

C₂×#11924011

—

C₂²×#10596831

C₂³

yes

—

C₂×C₄×Dic₇₃

C₂×C₄

yes

—

C₂×C₄×Dic₇₃

C₂³

yes

—

C₄²×D₇₃

D₄

yes

—

C₄²×D₇₃

Q₈

yes

—

C₄⋊#10596831

—

#14556520

—

#14556498

C₂×C₄

yes

—

C₂²×C₈×C₇₃

C₂³

yes

—

C₂×C₄²×C₇₃

C₂³

yes

—

C₄⋊C₈×C₇₃

—

#95×C₇₃

C₂×C₄

yes

—

C₂³×D₇₃

C₂²×C₄

yes

characteristic

C₂²×Dic₇₃

C₂²×C₄

yes

—

C₂²×Dic₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

C₄⋊C₄

yes

—

C₂×C₄×D₇₃

C₂×D₄

yes

—

C₂×C₄×D₇₃

C₂×Q₈

yes

—

#11924011

—

C₂×#10596831

—

C₄×Dic₇₃

C₄⋊C₄

yes

—

C₄×Dic₇₃

C₂×D₄

yes

—

C₄×Dic₇₃

C₂×Q₈

yes

—

C₂²×C₄×C₇₃

C₂²×C₄

yes

—

C₂²×C₄×C₇₃

C₂⁴

yes

characteristic

C₂×C₈×C₇₃

—

C₄²×C₇₃

C₂×D₄

yes

—

C₄²×C₇₃

C₂×Q₈

yes

—

C₂³×C₇₃

C₂³×C₄

yes

characteristic

C₂²×D₇₃

—

C₂²×D₇₃

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₇₃

C₂²×D₄

yes

—

C₂×C₄×C₇₃

C₂²×Q₈

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂×C₄⋊C₄

yes

—

C₂×Dic₇₃

C₂×C₄⋊C₄

yes

—

C₄×D₇₃

—

C₄×D₇₃

#127

yes

—

C₄×D₇₃

C₄⋊Q₈

yes

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

C₂²×C₄⋊C₄

yes

—

C₂²×C₇₃

#568

yes

—

C₂×D₇₃

—

C₂×D₇₃

#384

yes

—

C₄×C₇₃

—

C₄×C₇₃

C₂×#127

yes

characteristic

C₄×C₇₃

C₂×C₄⋊Q₈

yes

—

Dic₇₃

—

Dic₇₃

#384

yes

—

—

C₂×C₇₃

yes

C₂×C₇₃

yes

—

D₇₃

—

—

—

—

—

D₇₃

yes

characteristic, complemented

C₇₃

#20792

yes

characteristic, complemented, Sylow

C₂²×M₁₆

—

C₂²×C₄²

—

#423

—

146

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

C₂×D₇₃

yes

—

#376

—

#376

—

#376

C₂×D₇₃

yes

characteristic

C₂×#95

—

C₂³×C₄

—

C₂³×C₄

—

C₂×M₁₆

—

146

—

C₂²×C₈

—

C₂²×C₈

C₂²×D₇₃

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

100

C₂×C₄²

—

101

C₂×C₄²

C₂²×D₇₃

yes

—

102

C₄⋊C₈

—

103

C₄⋊C₈

—

146

—

104

C₄⋊C₈

—

146

—

105

#95

—

106

#95

C₄×D₇₃

yes

—

107

C₂⁴

—

108

C₂²×C₄

—

292

—

109

C₂²×C₄

—

110

C₂²×C₄

—

111

C₂²×C₄

—

112

C₂²×C₄

—

113

C₂²×C₄

—

114

C₂²×C₄

C₂×C₄×D₇₃

yes

—

115

C₂²×C₄

C₂³×D₇₃

yes

characteristic

116

M₁₆

—

292

—

117

C₂×C₈

—

118

C₂×C₈

—

146

—

119

C₄²

—

120

C₄²

—

121

C₄²

—

122

C₄²

D₄×D₇₃

yes

—

123

C₄²

Q₈×D₇₃

yes

—

124

C₂³

—

125

C₂³

—

146

—

126

C₂³

C₂²×C₄×D₇₃

yes

characteristic

127

C₂×C₄

—

128

C₂×C₄

—

292

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

146

—

134

C₂×C₄

C₄⋊C₄×D₇₃

yes

—

135

C₂×C₄

C₂×D₄×D₇₃

yes

—

136

C₂×C₄

C₂×Q₈×D₇₃

yes

—

137

C₈

—

138

C₈

—

292

—

139

C₂²

—

140

C₂²

—

146

—

141

C₂²

C₂×C₄⋊C₄×D₇₃

yes

—

142

C₂²

#17989352

yes

—

143

C₄

—

144

C₄

—

145

C₄

—

146

—

146

C₄

#127×D₇₃

yes

characteristic

147

C₄

C₄⋊Q₈×D₇₃

yes

—

148

C₂

—

146

—

149

C₂

#384×D₇₃

yes

characteristic

150

C₂

#22618492

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₃
commutator, socle	C₂³×C₇₃	C₂³×C₄
Fitting	C₇₃×#1843	C₂
prime radical	C₂³×D₇₃	C₂²×C₄
cosocle	C₂²×C₄×C₇₃	C₂⁴
hypercenter	#1843	D₇₃
hypocenter	C₇₃	#20792
LCS	G ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1843

subgroup

G/H

center, Frattini

C₂²×C₄

C₂³×D₇₃

commutator, socle

C₂³×C₇₃

C₂³×C₄

Fitting

C₇₃×#1843

C₂

prime radical

C₂³×D₇₃

C₂²×C₄

cosocle

C₂²×C₄×C₇₃

C₂⁴

D₇₃

C₇₃

G ▷ C₂³×C₇₃ ▷ C₇₃

C₁ ◁ C₂²×C₄ ◁ #1843

N	H ≅ G/N	type
3. #22610085	C₂	semidirect
4. #22610084	C₂	semidirect
5. C₇₃×#1843	C₂	semidirect
80. #1843	D₇₃	semidirect
81. C₇₃	#20792	semidirect

H ≅ G/N

type

3. #22610085

C₂

semidirect

4. #22610084

C₂

semidirect

5. C₇₃×#1843

C₂

semidirect

80. #1843

D₇₃

semidirect

81. C₇₃

#20792

semidirect

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

subgroup	index
C₂×#17988609	2
#376×D₇₃	2
#22610085	2
#22610084	2
C₇₃×#1843	2
#20792	73

subgroup

index

#376×D₇₃

C₇₃×#1843

Subgroups — #33086370

Conjugacy classes of subgroups

Complements

Maximal subgroups