Group #32979783 — subgroups

Subgroups — #32979783

Order 18688.

354 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 171 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	#22610103	C₂	1	1	yes	maximal, characteristic
2	#22608686	C₂	1	4	yes	maximal
3	C₂×C₈×#10596831	C₂	1	1	yes	maximal, characteristic
4	C₇₃×#1848	C₂	1	1	yes	maximal, characteristic
5	C₂×#14556527	—	2	2	no	—
6	#17988611	C₂²	1	2	yes	—
7	C₂×C₄×#10596831	C₂²	1	2	yes	—
8	#17988337	—	2	8	no	—
9	C₈×#10596831	C₄	1	1	yes	characteristic
10	C₈×#10596831	C₄	1	2	yes	—
11	C₈×#10596831	C₄	1	1	yes	characteristic
12	C₂×#108×C₇₃	—	2	2	no	—
13	#423×C₇₃	C₂²	1	2	yes	—
14	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×#11924012	—	2	2	no	—
16	C₂²×#10596831	Q₈	1	4	yes	—
17	#14556527	—	4	4	no	—
18	C₄⋊#10596831	—	2	4	no	—
19	C₄×#10596831	C₂×C₄	1	2	yes	—
20	C₄×#10596831	C₂×C₄	1	2	yes	—
21	C₄×#10596831	D₄	1	4	yes	—
22	C₂×M₁₆×C₇₃	—	2	2	no	—
23	C₂²×C₈×C₇₃	D₄	1	2	yes	—
24	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
25	#108×C₇₃	—	4	4	no	—
26	C₄⋊C₈×C₇₃	—	2	4	no	—
27	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
28	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
29	C₄×C₈×C₇₃	Q₈	1	2	yes	—
30	#11924012	—	4	4	no	—
31	C₂×#10596831	—	2	8	no	—
32	C₂×#10596831	—	4	2	no	—
33	C₂×#10596831	C₄⋊C₄	1	4	yes	—
34	C₂×#10596831	C₄⋊C₄	1	4	yes	—
35	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
36	C₂²×C₄×C₇₃	C₂×Q₈	1	2	yes	—
37	M₁₆×C₇₃	—	4	4	no	—
38	C₂×C₈×C₇₃	—	4	2	no	—
39	C₂×C₈×C₇₃	C₄⋊C₄	1	2	yes	—
40	C₂×C₈×C₇₃	C₄⋊C₄	1	2	yes	—
41	C₂×C₈×C₇₃	SD₁₆	1	4	yes	—
42	C₂×C₈×C₇₃	SD₁₆	1	4	yes	—
43	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
44	C₄²×C₇₃	C₂×D₄	1	2	yes	—
45	C₄²×C₇₃	C₂×Q₈	1	1	yes	characteristic
46	C₂³×C₇₃	C₄⋊Q₈	1	1	yes	characteristic
47	C₂×C₄×C₇₃	—	2	4	no	—
48	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
49	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
50	C₂×C₄×C₇₃	#127	1	1	yes	characteristic
51	C₂×C₄×C₇₃	C₄⋊Q₈	1	2	yes	—
52	C₂×C₄×C₇₃	C₂×SD₁₆	1	2	yes	—
53	C₂×C₄×C₇₃	C₂×SD₁₆	1	2	yes	—
54	C₈×C₇₃	—	8	2	no	—
55	C₈×C₇₃	#106	1	4	yes	—
56	C₈×C₇₃	#106	1	4	yes	—
57	#10596831	—	2	4	no	—
58	#10596831	—	8	2	no	—
59	#10596831	#108	1	8	yes	complemented
60	C₂²×C₇₃	—	2	2	no	—
61	C₂²×C₇₃	#384	1	1	yes	characteristic
62	C₂²×C₇₃	#498	1	2	yes	—
63	C₄×C₇₃	—	2	2	no	—
64	C₄×C₇₃	C₂×#106	1	2	yes	—
65	C₄×C₇₃	C₂×#108	1	4	yes	—
66	C₄×C₇₃	#492	1	1	yes	characteristic
67	C₄×C₇₃	#492	1	1	yes	characteristic
68	#8822	—	73	1	no	maximal, Sylow
69	C₂×C₇₃	—	2	2	no	—
70	C₂×C₇₃	#1844	1	1	yes	characteristic
71	C₂×C₇₃	#1848	1	2	yes	—
72	#1848	—	73	1	no	—
73	#1848	D₇₃	1	1	yes	characteristic
74	#1566	—	73	4	no	—
75	C₂×C₈²	—	73	1	no	—
76	C₇₃	#8822	1	1	yes	characteristic, complemented, Sylow
77	C₂×#108	—	2	2	no	—
78	C₂×#108	—	146	2	no	—
79	#423	—	73	2	no	—
80	#423	C₂×D₇₃	1	2	yes	—
81	C₂×C₄×C₈	—	73	2	no	—
82	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
83	#334	—	146	8	no	—
84	C₈²	—	73	1	no	—
85	C₈²	—	73	2	no	—
86	C₈²	—	73	1	no	—
87	C₂×M₁₆	—	2	2	no	—
88	C₂×M₁₆	—	146	2	no	—
89	C₂²×C₈	—	73	4	no	—
90	C₂²×C₈	C₂²⋊D₇₃	1	2	yes	—
91	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
92	#108	—	4	4	no	—
93	#108	—	292	4	no	—
94	C₄⋊C₈	—	2	4	no	—
95	C₄⋊C₈	—	146	4	no	—
96	C₄×C₈	—	73	2	no	—
97	C₄×C₈	—	73	2	no	—
98	C₄×C₈	—	73	4	no	—
99	C₄×C₈	Dic₁₄₆	1	2	yes	—
100	C₄×C₈	C₄×D₇₃	1	1	yes	characteristic
101	C₄×C₈	C₄×D₇₃	1	1	yes	characteristic
102	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
103	C₂²×C₄	Q₈×D₇₃	1	2	yes	—
104	M₁₆	—	4	4	no	—
105	M₁₆	—	292	4	no	—
106	C₂×C₈	—	4	2	no	—
107	C₂×C₈	—	292	2	no	—
108	C₂×C₈	—	73	4	no	—
109	C₂×C₈	—	73	4	no	—
110	C₂×C₈	—	146	8	no	—
111	C₂×C₈	#11924007	1	2	yes	—
112	C₂×C₈	#11924007	1	2	yes	—
113	C₂×C₈	#11924015	1	4	yes	—
114	C₂×C₈	#11924016	1	4	yes	—
115	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
116	C₄²	D₄×D₇₃	1	2	yes	—
117	C₄²	C₂×Dic₁₄₆	1	1	yes	characteristic
118	C₂³	#14556589	1	1	yes	characteristic
119	C₂×C₄	—	2	4	no	—
120	C₂×C₄	C₄⋊C₄×D₇₃	1	2	yes	—
121	C₂×C₄	C₂×#11924007	1	1	yes	characteristic
122	C₂×C₄	#14556587	1	1	yes	characteristic
123	C₂×C₄	#14556590	1	2	yes	—
124	C₂×C₄	C₂×#11924015	1	2	yes	—
125	C₂×C₄	C₂×#11924016	1	2	yes	—
126	C₈	—	8	2	no	—
127	C₈	—	584	2	no	—
128	C₈	—	73	8	no	—
129	C₈	—	146	4	no	—
130	C₈	#14556522	1	4	yes	—
131	C₈	#14556522	1	4	yes	—
132	C₂²	—	2	2	no	—
133	C₂²	#17988456	1	1	yes	characteristic
134	C₂²	#17988983	1	2	yes	—
135	C₄	—	2	2	no	—
136	C₄	C₂×#14556522	1	2	yes	—
137	C₄	#108×D₇₃	1	4	yes	—
138	C₄	#17988959	1	1	yes	characteristic
139	C₄	#17988961	1	1	yes	characteristic
140	C₂	—	2	2	no	—
141	C₂	#22610087	1	1	yes	characteristic
142	C₂	#22610101	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#22610103

C₂

yes

maximal, characteristic

#22608686

C₂

yes

maximal

C₂×C₈×#10596831

C₂

yes

maximal, characteristic

C₇₃×#1848

C₂

yes

maximal, characteristic

C₂×#14556527

—

#17988611

C₂²

yes

—

C₂×C₄×#10596831

C₂²

yes

—

#17988337

—

C₈×#10596831

C₄

yes

characteristic

C₈×#10596831

C₄

yes

—

C₈×#10596831

C₄

yes

characteristic

C₂×#108×C₇₃

—

#423×C₇₃

C₂²

yes

—

C₂×C₄×C₈×C₇₃

C₂²

yes

characteristic

C₂×#11924012

—

C₂²×#10596831

Q₈

yes

—

#14556527

—

C₄⋊#10596831

—

C₄×#10596831

C₂×C₄

yes

—

C₄×#10596831

C₂×C₄

yes

—

C₄×#10596831

D₄

yes

—

C₂×M₁₆×C₇₃

—

C₂²×C₈×C₇₃

D₄

yes

—

C₂×C₄²×C₇₃

C₂³

yes

characteristic

#108×C₇₃

—

C₄⋊C₈×C₇₃

—

C₄×C₈×C₇₃

C₂×C₄

yes

characteristic

C₄×C₈×C₇₃

C₂×C₄

yes

characteristic

C₄×C₈×C₇₃

Q₈

yes

—

—

—

—

C₄⋊C₄

yes

—

C₂×#10596831

C₄⋊C₄

yes

—

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₃

C₂×Q₈

yes

—

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₄⋊C₄

yes

—

C₂×C₈×C₇₃

C₄⋊C₄

yes

—

C₂×C₈×C₇₃

SD₁₆

yes

—

C₂×C₈×C₇₃

SD₁₆

yes

—

C₄²×C₇₃

C₂²×C₄

yes

characteristic

C₄²×C₇₃

C₂×D₄

yes

—

C₄²×C₇₃

C₂×Q₈

yes

characteristic

C₂³×C₇₃

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

#127

yes

characteristic

C₂×C₄×C₇₃

C₄⋊Q₈

yes

—

C₂×C₄×C₇₃

C₂×SD₁₆

yes

—

C₂×C₄×C₇₃

C₂×SD₁₆

yes

—

C₈×C₇₃

—

C₈×C₇₃

#106

yes

—

C₈×C₇₃

#106

yes

—

—

—

yes

C₂²×C₇₃

—

C₂²×C₇₃

#384

yes

characteristic

C₂²×C₇₃

#498

yes

—

C₄×C₇₃

—

C₄×C₇₃

C₂×#106

yes

—

C₄×C₇₃

C₂×#108

yes

—

C₄×C₇₃

yes

C₄×C₇₃

yes

—

C₂×C₇₃

—

C₂×C₇₃

#1844

yes

characteristic

C₂×C₇₃

#1848

yes

—

#1848

—

#1848

D₇₃

yes

characteristic

#1566

—

C₂×C₈²

—

C₇₃

#8822

yes

characteristic, complemented, Sylow

C₂×#108

—

C₂×#108

—

146

—

#423

—

#423

C₂×D₇₃

yes

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₇₃

yes

characteristic

#334

—

146

—

C₈²

—

C₈²

—

C₈²

—

C₂×M₁₆

—

C₂×M₁₆

—

146

—

C₂²×C₈

—

C₂²×C₈

C₂²⋊D₇₃

yes

—

C₂×C₄²

C₂²×D₇₃

yes

characteristic

#108

—

#108

—

292

—

C₄⋊C₈

—

C₄⋊C₈

—

146

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

Dic₁₄₆

yes

—

100

C₄×C₈

C₄×D₇₃

yes

characteristic

101

C₄×C₈

C₄×D₇₃

yes

characteristic

102

C₂²×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

103

C₂²×C₄

Q₈×D₇₃

yes

—

104

M₁₆

—

105

M₁₆

—

292

—

106

C₂×C₈

—

107

C₂×C₈

—

292

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

146

—

111

C₂×C₈

#11924007

yes

—

112

C₂×C₈

#11924007

yes

—

113

C₂×C₈

#11924015

yes

—

114

C₂×C₈

#11924016

yes

—

115

C₄²

C₂×C₄×D₇₃

yes

characteristic

116

C₄²

D₄×D₇₃

yes

—

117

C₄²

C₂×Dic₁₄₆

yes

characteristic

118

C₂³

#14556589

yes

characteristic

119

C₂×C₄

—

120

C₂×C₄

C₄⋊C₄×D₇₃

yes

—

121

C₂×C₄

C₂×#11924007

yes

characteristic

122

C₂×C₄

#14556587

yes

characteristic

123

C₂×C₄

#14556590

yes

—

124

C₂×C₄

C₂×#11924015

yes

—

125

C₂×C₄

C₂×#11924016

yes

—

126

C₈

—

127

C₈

—

584

—

128

C₈

—

129

C₈

—

146

—

130

C₈

#14556522

yes

—

131

C₈

#14556522

yes

—

132

C₂²

—

133

C₂²

#17988456

yes

characteristic

134

C₂²

#17988983

yes

—

135

C₄

—

136

C₄

C₂×#14556522

yes

—

137

C₄

#108×D₇₃

yes

—

138

C₄

#17988959

yes

characteristic

139

C₄

#17988961

yes

characteristic

140

C₂

—

141

C₂

#22610087

yes

characteristic

142

C₂

#22610101

yes

—

	subgroup	G/H
center	C₂×C₄	#14556587
commutator	C₄²×C₇₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₃
Fitting	C₇₃×#1848	C₂
socle	C₂²×C₇₃	#384
prime radical	C₂³×C₇₃	C₄⋊Q₈
cosocle	C₂×C₄²×C₇₃	C₂³
hypercenter	#1848	D₇₃
hypocenter	C₇₃	#8822
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1848

subgroup

G/H

center

C₂×C₄

#14556587

commutator

C₄²×C₇₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₃

Fitting

C₇₃×#1848

C₂

socle

C₂²×C₇₃

#384

prime radical

C₂³×C₇₃

C₄⋊Q₈

cosocle

C₂×C₄²×C₇₃

C₂³

D₇₃

C₇₃

G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1848

N	H ≅ G/N	type
59. #10596831	#108	semidirect
76. C₇₃	#8822	semidirect

H ≅ G/N

type

59. #10596831

#108

semidirect

76. C₇₃

#8822

semidirect

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

subgroup	index
#22610103	2
#22608686	2
C₂×C₈×#10596831	2
C₇₃×#1848	2
#8822	73

subgroup

index

C₇₃×#1848

Subgroups — #32979783

Conjugacy classes of subgroups

Complements

Maximal subgroups