Finite Group Databasebeta

← #37544094

Subgroups — #37544094

Order 23168.

484 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041835C211yesmaximal, characteristic, complemented
2#127×D181C211yesmaximal, characteristic
3#26041645C211yesmaximal, characteristic, complemented
4#26041644C211yesmaximal, characteristic, complemented
5#26041643C211yesmaximal, characteristic, complemented
6#26041624C214yesmaximal, complemented
7#26041282C214yesmaximal, complemented
8#26041231C211yesmaximal, characteristic, complemented
9#490×C181C211yesmaximal, characteristic, complemented
10C2×D4×D181—22no—
11C2×D4×D181C2212yes—
12C2×#15668432C2212yes—
13#19153815C2212yescomplemented
14#19153813C2211yescharacteristic
15#19153812—22no—
16#19153812C2212yes—
17#19153808C2211yescharacteristic, complemented
18#19153794—22no—
19#19153781—22no—
20#19153774C2212yes—
21C42×D181C2211yescharacteristic
22#19153738C2214yescomplemented
23#19153737C2214yescomplemented
24#19153736C2214yescomplemented
25#19153727C2211yescharacteristic, complemented
26C8×Dic181C2212yescomplemented
27#127×C181C2211yescharacteristic
28#125×C181C2211yescharacteristic, complemented
29#102×C181C2214yescomplemented
30#97×C181C2211yescharacteristic, complemented
31C23×D181—22no—
32C2×Dic362—22no—
33C2×D724—22no—
34C2×D724C2312yes—
35C2×C22⋊D181—22no—
36C2×C22⋊D181—24no—
37D4×D181—28no—
38D4×D181—48no—
39C2×C4×D181D412yes—
40C2×C4×D181C2311yescharacteristic
41#15668432—24no—
42C2×#13089678C2312yes—
43C4⋊Dic181C2312yes—
44#15668428—22no—
45#15668428—22no—
46#15668426—22no—
47C4×Dic181—22no—
48C4×Dic181D412yes—
49C4×Dic181C2311yescharacteristic
50C2×D4×C181—22no—
51C2×D4×C181C2312yes—
52C2×C8×C181C2312yes—
53C4⋊C4×C181—22no—
54C4⋊C4×C181C2312yes—
55C42×C181C2311yescharacteristic
56C22×D181—22no—
57C22×D181—48no—
58C22×D181—44no—
59C22×D181C2×D411yescharacteristic
60Dic362—44no—
61D724—24no—
62D724—44no—
63C22⋊D181—44no—
64C22⋊D181—48no—
65C2×Dic181—22no—
66C2×Dic181C2×D411yescharacteristic
67C2×Dic181C2×D412yes—
68C4×D181—24no—
69C4×D181#4114yes—
70#13089678—22no—
71C23×C181—22no—
72D4×C181—24no—
73D4×C181—44no—
74C2×C4×C181—22no—
75C2×C4×C181C2×D412yes—
76C2×C4×C181C2411yescharacteristic
77C8×C181—22no—
78C22×C181—42no—
79C22×C181—44no—
80C22×C181C22×D411yescharacteristic
81C2×D181—22no—
82C2×D181—42no—
83C2×D181—44no—
84C2×D181—88no—
85C2×D181#12412yes—
86C4×C181—22no—
87C4×C181—42no—
88C4×C181C2×#4112yes—
89Dic181—42no—
90Dic181#12412yes—
91Dic181AGL(1,ℤ/8)14yes—
92C2×C181—82no—
93C2×C181C2×#12411yescharacteristic
94C2×C181C2×AGL(1,ℤ/8)12yes—
95D181—22no—
96D181—82no—
97C181#313811yescharacteristic, complemented, Sylow
98#3138—1811nomaximal, Sylow
99#533—1811no—
100C2×#127—1811no—
101#490—1811no—
102#490—1811no—
103#490—1811no—
104#490D18111yescharacteristic, complemented
105#486—1814no—
106#418—1814no—
107C4×M16—1811no—
108C22×D4—3622no—
109C22×D4—1812no—
110C2×M16—1812no—
111C4⋊Q8—1812no—
112#127—3622no—
113#127—1812no—
114#127—1811no—
115#127C2×D18111yescharacteristic
116#125—1811no—
117#125C2×D18111yescharacteristic, complemented
118C22⋊Q8—3622no—
119C4×Q8—3622no—
120#117—1812no—
121C2×C42—1811no—
122#102—1814no—
123#102—1814no—
124#102—1814no—
125#102C2×D18114yescomplemented
126#97—1811no—
127#97C2×D18111yescharacteristic, complemented
128C4×C8—1812no—
129C24—3622no—
130C2×Q8—3622no—
131C2×D4—22no—
132C2×D4—3628no—
133C2×D4—3622no—
134C2×D4—3624no—
135C2×D4—3622no—
136C2×D4—1812no—
137C2×D4—7248no—
138C2×D4C22×D18112yes—
139C22×C4—1812no—
140C22×C4—1811no—
141M16—3624no—
142C2×C8—1812no—
143C2×C8C22×D18112yes—
144C4⋊C4—22no—
145C4⋊C4—3622no—
146C4⋊C4—3622no—
147C4⋊C4—1812no—
148C4⋊C4C22×D18112yes—
149C22⋊C4—3622no—
150C42—3622no—
151C42—1812no—
152C42—1811no—
153C42C22×D18111yescharacteristic
154C23—22no—
155C23—3622no—
156C23—1811no—
157C23—7248no—
158C23—7244no—
159Q8—7244no—
160D4—24no—
161D4—44no—
162D4—3624no—
163D4—7244no—
164D4—7244no—
165D4—7248no—
166C2×C4—22no—
167C2×C4—3624no—
168C2×C4—3622no—
169C2×C4—1811no—
170C2×C4—1812no—
171C2×C4—1814no—
172C2×C4D4×D18112yes—
173C2×C4C23×D18111yescharacteristic
174C8—22no—
175C8—3622no—
176C22—42no—
177C22—44no—
178C22—3622no—
179C22—14488no—
180C22—1812no—
181C22—7242no—
182C22—7244no—
183C22C2×D4×D18111yescharacteristic
184C4—22no—
185C4—42no—
186C4—1812no—
187C4—1814no—
188C4—7242no—
189C4#41×D18112yes—
190C2—82no—
191C2—3622no—
192C2—14482no—
193C2#124×D18111yescharacteristic
194C2AGL(1,ℤ/8)×D18112yes—
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#490×C181C2
socleC22×C181C22×D4
prime radical#127×D181C2
hypercenter#490D181
hypocenterC181#3138
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #26041835C2semidirect
3. #26041645C2semidirect
4. #26041644C2semidirect
5. #26041643C2semidirect
6. #26041624C2semidirect
7. #26041282C2semidirect
8. #26041231C2semidirect
9. #490×C181C2semidirect
13. #19153815C22semidirect
17. #19153808C22semidirect
22. #19153738C22semidirect
23. #19153737C22semidirect
24. #19153736C22semidirect
25. #19153727C22semidirect
26. C8×Dic181C22semidirect
28. #125×C181C22semidirect
29. #102×C181C22semidirect
30. #97×C181C22semidirect
97. C181#3138semidirect
104. #490D181semidirect
117. #125C2×D181semidirect
125. #102C2×D181semidirect
127. #97C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260418352
#127×D1812
#260416452
#260416442
#260416432
#260416242
#260412822
#260412312
#490×C1812
#3138181