Finite Group Databasebeta

← D8×C22⋊D181 #37545392

Subgroups — D8×C22⋊D181 #37545392

Order 23168.

620 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 141 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
2D4×C22⋊D181C212yesmaximal, complemented
3#26041654C211yesmaximal, characteristic, complemented
4#26041515C211yesmaximal, characteristic, complemented
5#26041512C211yesmaximal, characteristic, complemented
6#26041472C212yesmaximal, complemented
7#26041413C212yesmaximal, complemented
8#26041411C212yesmaximal, complemented
9D8×Dic181C211yesmaximal, characteristic, complemented
10C8×C22⋊D181C211yesmaximal, characteristic, complemented
11C22×D8×C181C211yesmaximal, characteristic, complemented
12C22×C22⋊D181—22no—
13C2×D4×D181C2212yescomplemented
14C2×D1448C2211yescharacteristic, complemented
15C2×#15668434C2212yescomplemented
16C2×#15668434C2212yescomplemented
17D8×D181—24no—
18C2×C8×D181C2211yescharacteristic, complemented
19#19153812C2212yescomplemented
20#19153790C2212yescomplemented
21#19153788—22no—
22#19153787C2212yescomplemented
23#19153785—22no—
24#19153784—22no—
25D4×Dic181C2212yescomplemented
26C4×C22⋊D181C2211yescharacteristic
27#19153750C2211yescharacteristic, complemented
28#19153745C2211yescharacteristic, complemented
29#19153738C2212yescomplemented
30#19153737C2212yescomplemented
31#19153737C2212yescomplemented
32C22⋊#13089678C2211yescharacteristic, complemented
33#19153728C2211yescharacteristic, complemented
34C8×Dic181C2211yescharacteristic, complemented
35C22×D4×C181C2212yescomplemented
36C2×D8×C181—24no—
37C2×D8×C181C2211yescharacteristic
38C2×D8×C181C2211yescharacteristic, complemented
39C2×D8×C181C2212yescomplemented
40C22×C8×C181C2211yescharacteristic, complemented
41C23×D181—22no—
42C2×D724C2312yes—
43C2×C22⋊D181—22no—
44C2×C22⋊D181—22no—
45C2×C22⋊D181—22no—
46C2×C22⋊D181—22no—
47C2×C22⋊D181—22no—
48C2×C22⋊D181—48no—
49C2×C22⋊D181D411yescharacteristic
50D4×D181—24no—
51D4×D181—42no—
52C22×Dic181—22no—
53C2×C4×D181C2311yescharacteristic
54D1448—22no—
55#15668434—24no—
56#15668434—42no—
57C2×#13089678C2311yescharacteristic
58C2×#13089678C2311yescharacteristic
59C8×D181—22no—
60C4⋊Dic181C2312yes—
61#15668428D411yescharacteristic
62C22⋊Dic181—22no—
63C22⋊Dic181—22no—
64C22⋊Dic181D411yescharacteristic
65#15668426—22no—
66#15668426D411yescharacteristic
67C4×Dic181C2311yescharacteristic
68C24×C181—22no—
69C2×D4×C181—24no—
70C2×D4×C181—22no—
71C2×D4×C181—42no—
72C2×D4×C181C2312yes—
73C2×D4×C181C2312yes—
74C22×C4×C181C2311yescharacteristic
75D8×C181—24no—
76D8×C181—22no—
77D8×C181D414yescomplemented
78C2×C8×C181—22no—
79C2×C8×C181C2311yescharacteristic
80C2×C8×C181C2311yescharacteristic
81C22×D181—22no—
82C22×D181—44no—
83C22×D181—44no—
84C22×D181—82no—
85C22×D181C2×D411yescharacteristic
86D724—22no—
87D724—22no—
88C22⋊D181—44no—
89C22⋊D181—44no—
90C22⋊D181—44no—
91C22⋊D181—44no—
92C22⋊D181—82no—
93C22⋊D181D814yesdirect product factor
94C2×Dic181—22no—
95C2×Dic181—44no—
96C2×Dic181C2×D411yescharacteristic
97C2×Dic181C2×D411yescharacteristic
98C2×Dic181C2×D411yescharacteristic
99C4×D181—21no—
100C4×D181—21no—
101#13089678—21no—
102#13089678—21no—
103C23×C181—22no—
104C23×C181—22no—
105C23×C181—44no—
106C23×C181—44no—
107C23×C181—82no—
108C23×C181C2×D411yescharacteristic
109D4×C181—22no—
110D4×C181—22no—
111D4×C181—22no—
112D4×C181—44no—
113D4×C181C2×D414yescomplemented
114C2×C4×C181—21no—
115C2×C4×C181—21no—
116C2×C4×C181C2×D411yescharacteristic
117C2×C4×C181C2411yescharacteristic
118C8×C181—21no—
119C8×C181C2×D412yescomplemented
120C22×C181—21no—
121C22×C181—21no—
122C22×C181—24no—
123C22×C181—42no—
124C22×C181—42no—
125C22×C181—42no—
126C22×C181—42no—
127C22×C181—42no—
128C22×C181—88no—
129C22×C181C2×D812yescomplemented
130C22×C181C22×D411yescharacteristic
131C2×D181—21no—
132C2×D181—21no—
133C2×D181—42no—
134C2×D181—42no—
135C2×D181—42no—
136C2×D181—88no—
137C2×D181C2×D812yescomplemented
138C4×C181—21no—
139C4×C181C22×D411yescharacteristic
140C4×C181H(5,𝔽2)11yescharacteristic
141Dic181—21no—
142Dic181—21no—
143Dic181—42no—
144Dic181C2×D812yescomplemented
145C2×C181—22no—
146C2×C181—44no—
147C2×C181—82no—
148C2×C181D4211yescharacteristic
149C2×C181C22×D811yescharacteristic
150C2×C181#57611yescharacteristic
151D181—22no—
152D181—82no—
153C181D4×D811yescharacteristic, complemented, Sylow
154D4×D8—1811nomaximal, Sylow
155C22×D8—1811no—
156C22×D8D18111yescharacteristic, complemented
157D42—1812no—
158#493—1811no—
159#466—1811no—
160#466—1811no—
161#459—1812no—
162#447—1812no—
163#447—1812no—
164C4×D8—1811no—
165C8×D4—1811no—
166C22×D4—3622no—
167C22×D4—1812no—
168C22×D4C2×D18112yescomplemented
169C2×D8—24no—
170C2×D8—3624no—
171C2×D8—1812no—
172C2×D8—1812no—
173C2×D8—1811no—
174C2×D8C2×D18111yescharacteristic
175C2×D8C2×D18112yescomplemented
176C2×D8C2×D18111yescharacteristic, complemented
177C22×C8—1811no—
178C22×C8C2×D18111yescharacteristic, complemented
179#127—1812no—
180#121—3622no—
181#121—1812no—
182#121—1812no—
183#120—3622no—
184#120—3622no—
185C4×D4—1812no—
186C4×D4—1811no—
187#107—1811no—
188C4⋊C8—1811no—
189#102—1812no—
190#102—1812no—
191#102—1812no—
192C22⋊C8—1811no—
193C22⋊C8—1811no—
194C4×C8—1811no—
195C24—22no—
196C24—3622no—
197C2×D4—24no—
198C2×D4—22no—
199C2×D4—42no—
200C2×D4—3624no—
201C2×D4—3622no—
202C2×D4—3622no—
203C2×D4—3622no—
204C2×D4—3622no—
205C2×D4—3622no—
206C2×D4—1811no—
207C2×D4—1812no—
208C2×D4—7242no—
209C2×D4—7248no—
210C2×D4C22×D18112yes—
211C2×D4C22×D18112yes—
212C22×C4—3622no—
213C22×C4—1811no—
214C22×C4C22×D18111yescharacteristic
215D8—24no—
216D8—22no—
217D8—3624no—
218D8—3622no—
219D8—7242no—
220D8C22⋊D18114yesdirect product factor
221C2×C8—22no—
222C2×C8—3622no—
223C2×C8—1811no—
224C2×C8—1811no—
225C2×C8C22×D18111yescharacteristic
226C2×C8C22×D18111yescharacteristic
227C4⋊C4—1812no—
228C4⋊C4—1811no—
229C22⋊C4—3622no—
230C22⋊C4—3622no—
231C22⋊C4—3622no—
232C22⋊C4—1811no—
233C22⋊C4—1811no—
234C42—1811no—
235C23—22no—
236C23—22no—
237C23—44no—
238C23—44no—
239C23—82no—
240C23—3622no—
241C23—14482no—
242C23—1811no—
243C23—7244no—
244C23—7244no—
245C23D4×D18111yescharacteristic
246D4—22no—
247D4—22no—
248D4—22no—
249D4—44no—
250D4—3622no—
251D4—3622no—
252D4—14482no—
253D4—1814no—
254D4—7244no—
255D4—7244no—
256D4—7244no—
257D4—7244no—
258D4C2×C22⋊D18114yescomplemented
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—3621no—
262C2×C4—3621no—
263C2×C4—3622no—
264C2×C4—1811no—
265C2×C4—1811no—
266C2×C4—1811no—
267C2×C4—7244no—
268C2×C4D4×D18111yescharacteristic
269C2×C4C23×D18111yescharacteristic
270C8—21no—
271C8—3621no—
272C8—3621no—
273C8C2×C22⋊D18112yescomplemented
274C22—21no—
275C22—21no—
276C22—24no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—42no—
282C22—88no—
283C22—3621no—
284C22—3621no—
285C22—14488no—
286C22—1812no—
287C22—7242no—
288C22—7242no—
289C22—7242no—
290C22D8×D18112yescomplemented
291C22C2×D4×D18111yescharacteristic
292C4—21no—
293C4—3621no—
294C4—3621no—
295C4—1812no—
296C4—7242no—
297C4C22×C22⋊D18111yescharacteristic
298C4#1915386111yescharacteristic
299C2—22no—
300C2—44no—
301C2—82no—
302C2—3622no—
303C2—14482no—
304C2D4×C22⋊D18111yescharacteristic
305C2C2×D8×D18111yescharacteristic
306C2#2604208011yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
FittingC22×D8×C181C2
socleC22×C181C22×D4
hypercenterC22×D8D181
hypocenterC181D4×D8
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C2×D8×D181C2semidirect
2. D4×C22⋊D181C2semidirect
3. #26041654C2semidirect
4. #26041515C2semidirect
5. #26041512C2semidirect
6. #26041472C2semidirect
7. #26041413C2semidirect
8. #26041411C2semidirect
9. D8×Dic181C2semidirect
10. C8×C22⋊D181C2semidirect
11. C22×D8×C181C2semidirect
13. C2×D4×D181C22semidirect
14. C2×D1448C22semidirect
15. C2×#15668434C22semidirect
16. C2×#15668434C22semidirect
18. C2×C8×D181C22semidirect
19. #19153812C22semidirect
20. #19153790C22semidirect
22. #19153787C22semidirect
25. D4×Dic181C22semidirect
27. #19153750C22semidirect
28. #19153745C22semidirect
29. #19153738C22semidirect
30. #19153737C22semidirect
31. #19153737C22semidirect
32. C22⋊#13089678C22semidirect
33. #19153728C22semidirect
34. C8×Dic181C22semidirect
35. C22×D4×C181C22semidirect
38. C2×D8×C181C22semidirect
39. C2×D8×C181C22semidirect
40. C22×C8×C181C22semidirect
77. D8×C181D4semidirect
93. C22⋊D181D8direct (N × H)
113. D4×C181C2×D4semidirect
119. C8×C181C2×D4semidirect
129. C22×C181C2×D8semidirect
137. C2×D181C2×D8semidirect
144. Dic181C2×D8semidirect
153. C181D4×D8semidirect
156. C22×D8D181semidirect
168. C22×D4C2×D181semidirect
175. C2×D8C2×D181semidirect
176. C2×D8C2×D181semidirect
178. C22×C8C2×D181semidirect
220. D8C22⋊D181direct (N × H)
258. D4C2×C22⋊D181semidirect
273. C8C2×C22⋊D181semidirect
290. C22D8×D181semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1812
D4×C22⋊D1812
#260416542
#260415152
#260415122
#260414722
#260414132
#260414112
D8×Dic1812
C8×C22⋊D1812
C22×D8×C1812
D4×D8181