Finite Group Databasebeta

← #37545400

Subgroups — #37545400

Order 23168.

526 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 131 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
1C2×D8×D181C211yesmaximal, characteristic, complemented
2#26041917C212yesmaximal, complemented
3#26041664C211yesmaximal, characteristic, complemented
4#26041517C211yesmaximal, characteristic, complemented
5#26041515C211yesmaximal, characteristic, complemented
6#26041496C212yesmaximal, complemented
7#26041428C212yesmaximal, complemented
8#26041424C212yesmaximal, complemented
9D8×Dic181C211yesmaximal, characteristic, complemented
10C8×C22⋊D181C211yesmaximal, characteristic, complemented
11C2×#135×C181C211yesmaximal, characteristic, complemented
12C2×D4×D181C2212yes—
13C2×#15668436C2212yescomplemented
14C2×D1448C2211yescharacteristic
15C2×#15668434C2212yes—
16D8×D181—24no—
17C2×C8×D181C2211yescharacteristic
18#19153805C2212yescomplemented
19#19153799—22no—
20#19153792C2212yes—
21#19153790C2212yescomplemented
22#19153788—22no—
23#19153784—22no—
24D4×Dic181C2212yescomplemented
25C4×C22⋊D181C2211yescharacteristic
26C2×#15668426—22no—
27#19153750C2211yescharacteristic, complemented
28#19153745C2211yescharacteristic, complemented
29#19153740C2212yescomplemented
30#19153738C2212yescomplemented
31#19153737C2212yescomplemented
32C22⋊#13089678C2211yescharacteristic, complemented
33#19153728C2211yescharacteristic
34C8×Dic181C2211yescharacteristic, complemented
35C2×#41×C181C2212yescomplemented
36#135×C181—24no—
37C2×Q16×C181C2211yescharacteristic, complemented
38C2×SD16×C181C2212yescomplemented
39C2×D8×C181C2211yescharacteristic
40C22×C8×C181C2211yescharacteristic, complemented
41C23×D181—22no—
42C2×D724C2312yes—
43C2×C22⋊D181—22no—
44C2×C22⋊D181—22no—
45C2×C22⋊D181D411yescharacteristic
46D4×D181—24no—
47D4×D181—42no—
48C22×Dic181—22no—
49C2×C4×D181C2311yescharacteristic
50#15668436—42no—
51D1448—22no—
52#15668434—24no—
53C2×#13089678C2311yescharacteristic
54C2×#13089678C2311yescharacteristic
55C8×D181—22no—
56C4⋊Dic181C2312yes—
57#15668428—22no—
58#15668428D411yescharacteristic
59C22⋊Dic181—22no—
60C22⋊Dic181D411yescharacteristic
61#15668426—22no—
62#15668426—22no—
63#15668426—22no—
64#15668426—22no—
65#15668426D411yescharacteristic
66C4×Dic181C2311yescharacteristic
67#41×C181—24no—
68#41×C181—42no—
69C2×Q8×C181C2312yes—
70C2×D4×C181—22no—
71C2×D4×C181C2312yes—
72C22×C4×C181—22no—
73C22×C4×C181C2311yescharacteristic
74Q16×C181—22no—
75SD16×C181—24no—
76D8×C181D414yescomplemented
77C2×C8×C181—22no—
78C2×C8×C181C2311yescharacteristic
79C2×C8×C181C2311yescharacteristic
80C22×D181—22no—
81C22×D181—44no—
82C22×D181—44no—
83C22×D181—82no—
84C22×D181C2×D411yescharacteristic
85D724—22no—
86D724—22no—
87C22⋊D181—22no—
88C22⋊D181—44no—
89C22⋊D181—82no—
90C2×Dic181—22no—
91C2×Dic181—82no—
92C2×Dic181C2×D411yescharacteristic
93C2×Dic181C2×D411yescharacteristic
94C2×Dic181C2×D411yescharacteristic
95C4×D181—21no—
96C4×D181—21no—
97#13089678—21no—
98#13089678—21no—
99C23×C181—22no—
100C23×C181C2×D411yescharacteristic
101Q8×C181—22no—
102Q8×C181—22no—
103D4×C181—22no—
104D4×C181—44no—
105D4×C181C2×D414yes—
106C2×C4×C181—21no—
107C2×C4×C181—21no—
108C2×C4×C181—22no—
109C2×C4×C181—44no—
110C2×C4×C181C2×D411yescharacteristic
111C2×C4×C181C2411yescharacteristic
112C8×C181—21no—
113C8×C181C2×D412yes—
114C22×C181—21no—
115C22×C181—24no—
116C22×C181—21no—
117C22×C181—21no—
118C22×C181—42no—
119C22×C181—42no—
120C22×C181C22×D411yescharacteristic
121C2×D181—21no—
122C2×D181—21no—
123C2×D181—42no—
124C2×D181—42no—
125C2×D181—42no—
126C2×D181—88no—
127C2×D181#13512yescomplemented
128C4×C181—21no—
129C4×C181—42no—
130C4×C181C22×D411yescharacteristic
131C4×C181H(5,𝔽2)11yescharacteristic
132Dic181—21no—
133Dic181—21no—
134Dic181—21no—
135Dic181—42no—
136C2×C181—44no—
137C2×C181—41no—
138C2×C181D4211yescharacteristic
139C2×C181C2×#13511yescharacteristic
140C2×C181#57611yescharacteristic
141D181—22no—
142D181—82no—
143C181#328011yescharacteristic, complemented, Sylow
144#3280—1811nomaximal, Sylow
145C2×#135D18111yescharacteristic, complemented
146C22×D8—1811no—
147#546—1812no—
148#495—1811no—
149#467—1811no—
150#466—1811no—
151#463—1812no—
152#450—1812no—
153#449—1812no—
154C4×D8—1811no—
155C8×D4—1811no—
156C2×#41C2×D18112yescomplemented
157C22×D4—1812no—
158#135—24no—
159C2×Q16C2×D18111yescharacteristic, complemented
160C2×SD16—1812no—
161C2×SD16C2×D18112yescomplemented
162C2×D8—3624no—
163C2×D8—1812no—
164C2×D8—1811no—
165C2×D8C2×D18111yescharacteristic
166C22×C8—1811no—
167C22×C8C2×D18111yescharacteristic, complemented
168#124—1812no—
169#123—3622no—
170C22⋊Q8—1812no—
171#121—3622no—
172#121—1812no—
173#120—3622no—
174C4×D4—1812no—
175C4×D4—1811no—
176C2×C22⋊C4—3622no—
177#107—1811no—
178C4⋊C8—1811no—
179#103—1812no—
180#102—1812no—
181#102—1812no—
182C22⋊C8—1811no—
183C22⋊C8—1811no—
184C4×C8—1811no—
185C24—3622no—
186#41—24no—
187#41—42no—
188C2×Q8C22×D18112yes—
189C2×D4—22no—
190C2×D4—3624no—
191C2×D4—3622no—
192C2×D4—3622no—
193C2×D4—1811no—
194C2×D4—1812no—
195C2×D4—7242no—
196C2×D4C22×D18112yes—
197C22×C4—22no—
198C22×C4—3622no—
199C22×C4—1811no—
200C22×C4C22×D18111yescharacteristic
201Q16—22no—
202SD16—24no—
203SD16—7242no—
204D8—3624no—
205D8—3622no—
206D8C22⋊D18114yescomplemented
207C2×C8—22no—
208C2×C8—3622no—
209C2×C8—1811no—
210C2×C8—1811no—
211C2×C8C22×D18111yescharacteristic
212C2×C8C22×D18111yescharacteristic
213C4⋊C4—3622no—
214C4⋊C4—1812no—
215C4⋊C4—1811no—
216C22⋊C4—3622no—
217C22⋊C4—3622no—
218C22⋊C4—3622no—
219C22⋊C4—3622no—
220C22⋊C4—3622no—
221C22⋊C4—1811no—
222C22⋊C4—1811no—
223C42—1811no—
224C23—22no—
225C23—3622no—
226C23—14482no—
227C23—1811no—
228C23—7244no—
229C23—7244no—
230C23D4×D18111yescharacteristic
231Q8—22no—
232Q8—22no—
233D4—22no—
234D4—44no—
235D4—3622no—
236D4—3622no—
237D4—3622no—
238D4—14482no—
239D4—7244no—
240D4C2×C22⋊D18114yes—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—44no—
245C2×C4—3621no—
246C2×C4—3621no—
247C2×C4—3622no—
248C2×C4—14482no—
249C2×C4—1811no—
250C2×C4—1811no—
251C2×C4—1811no—
252C2×C4D4×D18111yescharacteristic
253C2×C4C23×D18111yescharacteristic
254C8—21no—
255C8—3621no—
256C8—3621no—
257C8C2×C22⋊D18112yes—
258C22—21no—
259C22—24no—
260C22—21no—
261C22—21no—
262C22—42no—
263C22—42no—
264C22—3621no—
265C22—3621no—
266C22—14488no—
267C22—1812no—
268C22—7242no—
269C22—7242no—
270C22—7242no—
271C22C2×D4×D18111yescharacteristic
272C4—21no—
273C4—42no—
274C4—3621no—
275C4—3621no—
276C4—3621no—
277C4—7242no—
278C4C22×C22⋊D18111yescharacteristic
279C4#1915386111yescharacteristic
280C2—41no—
281C2—44no—
282C2—3622no—
283C2—14482no—
284C2D4×C22⋊D18111yescharacteristic
285C2#135×D18111yescharacteristic
286C2#2604208111yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
FittingC2×#135×C181C2
socleC22×C181C22×D4
hypercenterC2×#135D181
hypocenterC181#3280
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×D8×D181C2semidirect
2. #26041917C2semidirect
3. #26041664C2semidirect
4. #26041517C2semidirect
5. #26041515C2semidirect
6. #26041496C2semidirect
7. #26041428C2semidirect
8. #26041424C2semidirect
9. D8×Dic181C2semidirect
10. C8×C22⋊D181C2semidirect
11. C2×#135×C181C2semidirect
13. C2×#15668436C22semidirect
18. #19153805C22semidirect
21. #19153790C22semidirect
24. D4×Dic181C22semidirect
27. #19153750C22semidirect
28. #19153745C22semidirect
29. #19153740C22semidirect
30. #19153738C22semidirect
31. #19153737C22semidirect
32. C22⋊#13089678C22semidirect
34. C8×Dic181C22semidirect
35. C2×#41×C181C22semidirect
37. C2×Q16×C181C22semidirect
38. C2×SD16×C181C22semidirect
40. C22×C8×C181C22semidirect
76. D8×C181D4semidirect
127. C2×D181#135semidirect
143. C181#3280semidirect
145. C2×#135D181semidirect
156. C2×#41C2×D181semidirect
159. C2×Q16C2×D181semidirect
161. C2×SD16C2×D181semidirect
167. C22×C8C2×D181semidirect
206. D8C22⋊D181semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1812
#260419172
#260416642
#260415172
#260415152
#260414962
#260414282
#260414242
D8×Dic1812
C8×C22⋊D1812
C2×#135×C1812
#3280181