Finite Group Databasebeta

← D8×C22⋊D113 #28402245

Subgroups — D8×C22⋊D113 #28402245

Order 14464.

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×D113C211yesmaximal, characteristic, complemented
2D4×C22⋊D113C212yesmaximal, complemented
3#20298973C211yesmaximal, characteristic, complemented
4#20298834C211yesmaximal, characteristic, complemented
5#20298831C211yesmaximal, characteristic, complemented
6#20298791C212yesmaximal, complemented
7#20298732C212yesmaximal, complemented
8#20298730C212yesmaximal, complemented
9D8×Dic113C211yesmaximal, characteristic, complemented
10C8×C22⋊D113C211yesmaximal, characteristic, complemented
11C22×D8×C113C211yesmaximal, characteristic, complemented
12C22×C22⋊D113—22no—
13C2×D4×D113C2212yescomplemented
14C2×D904C2211yescharacteristic, complemented
15C2×#14268632C2212yescomplemented
16C2×#14268632C2212yescomplemented
17D8×D113—24no—
18C2×C8×D113C2211yescharacteristic, complemented
19#16813618C2212yescomplemented
20#16813596C2212yescomplemented
21#16813594—22no—
22#16813593C2212yescomplemented
23#16813591—22no—
24#16813590—22no—
25D4×Dic113C2212yescomplemented
26C4×C22⋊D113C2211yescharacteristic
27#16813556C2211yescharacteristic, complemented
28#16813551C2211yescharacteristic, complemented
29#16813544C2212yescomplemented
30#16813543C2212yescomplemented
31#16813543C2212yescomplemented
32C22⋊#11744751C2211yescharacteristic, complemented
33#16813534C2211yescharacteristic, complemented
34C8×Dic113C2211yescharacteristic, complemented
35C22×D4×C113C2212yescomplemented
36C2×D8×C113—24no—
37C2×D8×C113C2211yescharacteristic
38C2×D8×C113C2212yescomplemented
39C2×D8×C113C2211yescharacteristic, complemented
40C22×C8×C113C2211yescharacteristic, complemented
41C23×D113—22no—
42C2×D452C2312yes—
43C2×C22⋊D113—22no—
44C2×C22⋊D113—22no—
45C2×C22⋊D113—22no—
46C2×C22⋊D113—22no—
47C2×C22⋊D113—22no—
48C2×C22⋊D113—48no—
49C2×C22⋊D113D411yescharacteristic
50D4×D113—24no—
51D4×D113—42no—
52C22×Dic113—22no—
53C2×C4×D113C2311yescharacteristic
54D904—22no—
55#14268632—24no—
56#14268632—42no—
57C2×#11744751C2311yescharacteristic
58C2×#11744751C2311yescharacteristic
59C8×D113—22no—
60C4⋊Dic113C2312yes—
61#14268626D411yescharacteristic
62C22⋊Dic113—22no—
63C22⋊Dic113—22no—
64C22⋊Dic113D411yescharacteristic
65#14268624—22no—
66#14268624D411yescharacteristic
67C4×Dic113C2311yescharacteristic
68C24×C113—22no—
69C2×D4×C113—24no—
70C2×D4×C113—22no—
71C2×D4×C113—42no—
72C2×D4×C113C2312yes—
73C2×D4×C113C2312yes—
74C22×C4×C113C2311yescharacteristic
75D8×C113—24no—
76D8×C113—22no—
77D8×C113D414yescomplemented
78C2×C8×C113—22no—
79C2×C8×C113C2311yescharacteristic
80C2×C8×C113C2311yescharacteristic
81C23×C113—22no—
82C23×C113—22no—
83C23×C113—44no—
84C23×C113—44no—
85C23×C113—82no—
86C23×C113C2×D411yescharacteristic
87C22×D113—22no—
88C22×D113—44no—
89C22×D113—44no—
90C22×D113—82no—
91C22×D113C2×D411yescharacteristic
92D4×C113—22no—
93D4×C113—22no—
94D4×C113—22no—
95D4×C113—44no—
96D4×C113C2×D414yescomplemented
97C2×C4×C113—21no—
98C2×C4×C113—21no—
99C2×C4×C113C2×D411yescharacteristic
100C2×C4×C113C2411yescharacteristic
101C22⋊D113—44no—
102C22⋊D113—44no—
103C22⋊D113—44no—
104C22⋊D113—44no—
105C22⋊D113—82no—
106C22⋊D113D814yesdirect product factor
107C2×Dic113—22no—
108C2×Dic113—44no—
109C2×Dic113C2×D411yescharacteristic
110C2×Dic113C2×D411yescharacteristic
111C2×Dic113C2×D411yescharacteristic
112D452—22no—
113D452—22no—
114C4×D113—21no—
115C4×D113—21no—
116C8×C113—21no—
117C8×C113C2×D412yescomplemented
118#11744751—21no—
119#11744751—21no—
120C22×C113—21no—
121C22×C113—21no—
122C22×C113—24no—
123C22×C113—42no—
124C22×C113—42no—
125C22×C113—42no—
126C22×C113—42no—
127C22×C113—42no—
128C22×C113—88no—
129C22×C113C2×D812yescomplemented
130C22×C113C22×D411yescharacteristic
131C2×D113—21no—
132C2×D113—21no—
133C2×D113—42no—
134C2×D113—42no—
135C2×D113—42no—
136C2×D113—88no—
137C2×D113C2×D812yescomplemented
138C4×C113—21no—
139C4×C113C22×D411yescharacteristic
140C4×C113H(5,𝔽2)11yescharacteristic
141Dic113—21no—
142Dic113—21no—
143Dic113—42no—
144Dic113C2×D812yescomplemented
145C2×C113—22no—
146C2×C113—44no—
147C2×C113—82no—
148C2×C113D4211yescharacteristic
149C2×C113C22×D811yescharacteristic
150C2×C113#57611yescharacteristic
151D113—22no—
152D113—82no—
153D4×D8—1131nomaximal, Sylow
154C113D4×D811yescharacteristic, complemented, Sylow
155C22×D8—1131no—
156C22×D8D11311yescharacteristic, complemented
157D42—1132no—
158#493—1131no—
159#466—1131no—
160#466—1131no—
161#459—1132no—
162#447—1132no—
163#447—1132no—
164C4×D8—1131no—
165C8×D4—1131no—
166C22×D4—1132no—
167C22×D4—2262no—
168C22×D4C2×D11312yescomplemented
169C2×D8—24no—
170C2×D8—1132no—
171C2×D8—1132no—
172C2×D8—1131no—
173C2×D8—2264no—
174C2×D8C2×D11311yescharacteristic
175C2×D8C2×D11312yescomplemented
176C2×D8C2×D11311yescharacteristic, complemented
177C22×C8—1131no—
178C22×C8C2×D11311yescharacteristic, complemented
179#127—1132no—
180#121—1132no—
181#121—1132no—
182#121—2262no—
183#120—2262no—
184#120—2262no—
185C4×D4—1131no—
186C4×D4—1132no—
187#107—1131no—
188C4⋊C8—1131no—
189#102—1132no—
190#102—1132no—
191#102—1132no—
192C22⋊C8—1131no—
193C22⋊C8—1131no—
194C4×C8—1131no—
195C24—22no—
196C24—2262no—
197C2×D4—24no—
198C2×D4—22no—
199C2×D4—42no—
200C2×D4—1131no—
201C2×D4—1132no—
202C2×D4—4528no—
203C2×D4—4522no—
204C2×D4—2262no—
205C2×D4—2262no—
206C2×D4—2262no—
207C2×D4—2262no—
208C2×D4—2262no—
209C2×D4—2264no—
210C2×D4C22×D11312yes—
211C2×D4C22×D11312yes—
212C22×C4—1131no—
213C22×C4—2262no—
214C22×C4C22×D11311yescharacteristic
215D8—24no—
216D8—22no—
217D8—4522no—
218D8—2264no—
219D8—2262no—
220D8C22⋊D11314yesdirect product factor
221C2×C8—22no—
222C2×C8—1131no—
223C2×C8—1131no—
224C2×C8—2262no—
225C2×C8C22×D11311yescharacteristic
226C2×C8C22×D11311yescharacteristic
227C4⋊C4—1131no—
228C4⋊C4—1132no—
229C22⋊C4—1131no—
230C22⋊C4—1131no—
231C22⋊C4—2262no—
232C22⋊C4—2262no—
233C22⋊C4—2262no—
234C42—1131no—
235C23—22no—
236C23—22no—
237C23—44no—
238C23—44no—
239C23—82no—
240C23—1131no—
241C23—9042no—
242C23—4524no—
243C23—4524no—
244C23—2262no—
245C23D4×D11311yescharacteristic
246D4—22no—
247D4—22no—
248D4—22no—
249D4—44no—
250D4—1134no—
251D4—9042no—
252D4—4524no—
253D4—4524no—
254D4—4524no—
255D4—4524no—
256D4—2262no—
257D4—2262no—
258D4C2×C22⋊D11314yescomplemented
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—1131no—
262C2×C4—1131no—
263C2×C4—1131no—
264C2×C4—4524no—
265C2×C4—2262no—
266C2×C4—2261no—
267C2×C4—2261no—
268C2×C4D4×D11311yescharacteristic
269C2×C4C23×D11311yescharacteristic
270C8—21no—
271C8—2261no—
272C8—2261no—
273C8C2×C22⋊D11312yescomplemented
274C22—21no—
275C22—21no—
276C22—24no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—42no—
282C22—88no—
283C22—1132no—
284C22—9048no—
285C22—4522no—
286C22—4522no—
287C22—4522no—
288C22—2261no—
289C22—2261no—
290C22D8×D11312yescomplemented
291C22C2×D4×D11311yescharacteristic
292C4—21no—
293C4—1132no—
294C4—4522no—
295C4—2261no—
296C4—2261no—
297C4C22×C22⋊D11311yescharacteristic
298C4#1681366711yescharacteristic
299C2—22no—
300C2—44no—
301C2—82no—
302C2—9042no—
303C2—2262no—
304C2D4×C22⋊D11311yescharacteristic
305C2C2×D8×D11311yescharacteristic
306C2#2029939911yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC22×D8×C113C2
socleC22×C113C22×D4
hypercenterC22×D8D113
hypocenterC113D4×D8
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C2×D8×D113C2semidirect
2. D4×C22⋊D113C2semidirect
3. #20298973C2semidirect
4. #20298834C2semidirect
5. #20298831C2semidirect
6. #20298791C2semidirect
7. #20298732C2semidirect
8. #20298730C2semidirect
9. D8×Dic113C2semidirect
10. C8×C22⋊D113C2semidirect
11. C22×D8×C113C2semidirect
13. C2×D4×D113C22semidirect
14. C2×D904C22semidirect
15. C2×#14268632C22semidirect
16. C2×#14268632C22semidirect
18. C2×C8×D113C22semidirect
19. #16813618C22semidirect
20. #16813596C22semidirect
22. #16813593C22semidirect
25. D4×Dic113C22semidirect
27. #16813556C22semidirect
28. #16813551C22semidirect
29. #16813544C22semidirect
30. #16813543C22semidirect
31. #16813543C22semidirect
32. C22⋊#11744751C22semidirect
33. #16813534C22semidirect
34. C8×Dic113C22semidirect
35. C22×D4×C113C22semidirect
38. C2×D8×C113C22semidirect
39. C2×D8×C113C22semidirect
40. C22×C8×C113C22semidirect
77. D8×C113D4semidirect
96. D4×C113C2×D4semidirect
106. C22⋊D113D8direct (N × H)
117. C8×C113C2×D4semidirect
129. C22×C113C2×D8semidirect
137. C2×D113C2×D8semidirect
144. Dic113C2×D8semidirect
154. C113D4×D8semidirect
156. C22×D8D113semidirect
168. C22×D4C2×D113semidirect
175. C2×D8C2×D113semidirect
176. C2×D8C2×D113semidirect
178. C22×C8C2×D113semidirect
220. D8C22⋊D113direct (N × H)
258. D4C2×C22⋊D113semidirect
273. C8C2×C22⋊D113semidirect
290. C22D8×D113semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1132
D4×C22⋊D1132
#202989732
#202988342
#202988312
#202987912
#202987322
#202987302
D8×Dic1132
C8×C22⋊D1132
C22×D8×C1132
D4×D8113