Finite Group Databasebeta

← D4×#14268636 #28402272

Subgroups — D4×#14268636 #28402272

Order 14464.

546 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C22×#14268636C212yesmaximal, complemented
2D4×Dic226C211yesmaximal, characteristic, complemented
3D4×D452C211yesmaximal, characteristic
4#20298971C211yesmaximal, characteristic, complemented
5#20298827C212yesmaximal, complemented
6#20298804C211yesmaximal, characteristic, complemented
7#20298799C211yesmaximal, characteristic, complemented
8#20298751C212yesmaximal, complemented
9#20298739C212yesmaximal, complemented
10C4×#14268636C211yesmaximal, characteristic, complemented
11C8×D4×C113C211yesmaximal, characteristic, complemented
12C22×Dic226C2212yescomplemented
13C22×D452C2212yes—
14C2×D4×D113—21no—
15C2×#14268636—28no—
16C2×#14268636C2212yes—
17C2×#14268636C2211yescharacteristic
18C2×#14268636C2212yescomplemented
19C2×#14268636C2212yescomplemented
20C2×#14268636C2212yescomplemented
21#16813622C2211yescharacteristic, complemented
22#16813621—21no—
23#16813619C2211yescharacteristic
24#16813601C2212yescomplemented
25#16813599—22no—
26#16813597—21no—
27#16813596C2212yes—
28#16813592—22no—
29C4×Dic226C2211yescharacteristic, complemented
30C4×D452C2211yescharacteristic
31D4×Dic113—21no—
32#16813554C2211yescharacteristic, complemented
33#16813547C2212yescomplemented
34#16813547C2211yescharacteristic, complemented
35#16813544C2211yescharacteristic
36#16813544C2212yescomplemented
37C22×C8×C113C2212yescomplemented
38C4×D4×C113C2211yescharacteristic
39C4⋊C8×C113C2211yescharacteristic, complemented
40C22⋊C8×C113C2212yescomplemented
41C4×C8×C113C2211yescharacteristic, complemented
42C23×D113—22no—
43C2×Dic226—24no—
44C2×Dic226—22no—
45C2×Dic226—42no—
46C2×Dic226C2312yes—
47C2×Dic226C2311yescharacteristic
48C2×D452—24no—
49C2×D452—22no—
50C2×D452—21no—
51C2×D452—21no—
52C2×D452—42no—
53C2×D452C2312yes—
54C2×D452C2311yescharacteristic
55C2×C22⋊D113—22no—
56D4×D113—44no—
57C22×Dic113—22no—
58C2×C4×D113—21no—
59#14268636—24no—
60#14268636—24no—
61#14268636—24no—
62#14268636—42no—
63#14268636D414yesdirect product factor
64C4⋊Dic113—21no—
65C4⋊Dic113—21no—
66C4⋊Dic113C2311yescharacteristic
67C4⋊Dic113C2311yescharacteristic
68#14268626—21no—
69#14268626—22no—
70C22⋊Dic113—22no—
71#14268624—21no—
72#14268624—22no—
73C4×Dic113—21no—
74C2×D4×C113D411yescharacteristic
75C22×C4×C113C2312yes—
76C2×C8×C113—24no—
77C2×C8×C113C2312yes—
78C2×C8×C113C2311yescharacteristic
79C2×C8×C113C2311yescharacteristic
80C4⋊C4×C113D411yescharacteristic
81C22⋊C4×C113D412yes—
82C42×C113C2311yescharacteristic
83C23×C113C2×D412yes—
84C22×D113—21no—
85C22×D113—22no—
86C22×D113—44no—
87C22×D113—44no—
88C22×D113—82no—
89D4×C113SD1614yescomplemented
90C2×C4×C113—22no—
91C2×C4×C113—22no—
92C2×C4×C113C2×D411yescharacteristic
93C2×C4×C113C2×D412yes—
94C2×C4×C113C2×D411yescharacteristic
95C2×C4×C113C2411yescharacteristic
96C22⋊D113—44no—
97C2×Dic113—21no—
98C2×Dic113—21no—
99C2×Dic113—21no—
100C2×Dic113—22no—
101C2×Dic113—44no—
102D452—22no—
103D452—21no—
104D452—22no—
105D452—44no—
106D452—42no—
107D452—81no—
108D452C2×D412yes—
109C4×D113—42no—
110Dic226—21no—
111Dic226—22no—
112Dic226—22no—
113Dic226—44no—
114Dic226C2×D412yescomplemented
115C8×C113—22no—
116C8×C113—21no—
117C8×C113C2×D412yescomplemented
118C22×C113—22no—
119C22×C113—22no—
120C22×C113C2×SD1614yescomplemented
121C22×C113C22×D411yescharacteristic
122C2×D113—22no—
123C2×D113—41no—
124C2×D113—41no—
125C2×D113—42no—
126C2×D113—42no—
127C2×D113—42no—
128C2×D113—88no—
129C4×C113—22no—
130C4×C113—21no—
131C4×C113C2×SD1612yescomplemented
132C4×C113C22×D411yescharacteristic
133C4×C113H(5,𝔽2)11yescharacteristic
134Dic113—22no—
135Dic113—42no—
136Dic113—41no—
137Dic113—41no—
138C2×C113—24no—
139C2×C113D4211yescharacteristic
140C2×C113C22×SD1611yescharacteristic
141C2×C113#57711yescharacteristic
142D113—42no—
143D113—82no—
144D4×SD16—1131nomaximal, Sylow
145C113D4×SD1611yescharacteristic, complemented, Sylow
146C22×SD16—1132no—
147D4×Q8—1131no—
148D42—1131no—
149#492—1131no—
150#465—1132no—
151#461—1131no—
152#460—1131no—
153#450—1132no—
154#448—1132no—
155C4×SD16—1131no—
156C8×D4D11311yescharacteristic, complemented
157C22×Q8—1132no—
158C22×D4—1132no—
159C22×D4—2261no—
160C2×SD16—1131no—
161C2×SD16—1132no—
162C2×SD16—1132no—
163C2×SD16—1132no—
164C2×SD16—1132no—
165C2×SD16—2268no—
166C22×C8C2×D11312yescomplemented
167C4⋊Q8—1131no—
168C4⋊Q8—2261no—
169#127—1131no—
170C22⋊Q8—1132no—
171C22⋊Q8—2262no—
172#121—1132no—
173#121—2261no—
174#120—2262no—
175C4×Q8—1131no—
176C4×D4—1131no—
177C4×D4—2261no—
178C4×D4C2×D11311yescharacteristic
179#106—1131no—
180C4⋊C8C2×D11311yescharacteristic, complemented
181#103—1131no—
182#103—1132no—
183#102—1131no—
184#102—1132no—
185C22⋊C8C2×D11312yescomplemented
186C4×C8C2×D11311yescharacteristic, complemented
187C24—2262no—
188C2×Q8—1131no—
189C2×Q8—1132no—
190C2×Q8—4522no—
191C2×Q8—2264no—
192C2×Q8—2262no—
193C2×D4—1131no—
194C2×D4—1132no—
195C2×D4—4522no—
196C2×D4—4524no—
197C2×D4—2264no—
198C2×D4—2262no—
199C2×D4—2261no—
200C2×D4—2262no—
201C2×D4—2261no—
202C2×D4D45211yescharacteristic
203C22×C4—2262no—
204C22×C4—2261no—
205C22×C4C22×D11312yes—
206SD16—1134no—
207SD16—4522no—
208SD16—2264no—
209SD16—2264no—
210SD16—2264no—
211C2×C8—24no—
212C2×C8C22×D11311yescharacteristic
213C2×C8C22×D11312yes—
214C2×C8C22×D11311yescharacteristic
215C4⋊C4—1131no—
216C4⋊C4—1131no—
217C4⋊C4—2261no—
218C4⋊C4—2261no—
219C4⋊C4—2262no—
220C4⋊C4—2261no—
221C4⋊C4D45211yescharacteristic
222C22⋊C4—2262no—
223C22⋊C4—2261no—
224C22⋊C4—2262no—
225C22⋊C4D45212yes—
226C42—2261no—
227C42C22×D11311yescharacteristic
228C23—9042no—
229C23—4524no—
230C23—4524no—
231C23—2262no—
232C23—2261no—
233C23C2×D45212yes—
234Q8—1132no—
235Q8—4524no—
236Q8—2262no—
237Q8—2262no—
238Q8—2261no—
239D4—1132no—
240D4—9041no—
241D4—4524no—
242D4—4524no—
243D4—4522no—
244D4—2262no—
245D4—2262no—
246D4—2261no—
247D4#1426863614yesdirect product factor
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—4524no—
251C2×C4—4522no—
252C2×C4—2261no—
253C2×C4—2261no—
254C2×C4—2262no—
255C2×C4—2261no—
256C2×C4C2×D45211yescharacteristic
257C2×C4C2×D45212yes—
258C2×C4C2×D45211yescharacteristic
259C2×C4C23×D11311yescharacteristic
260C8—22no—
261C8—21no—
262C8D4×D11312yescomplemented
263C22—22no—
264C22—22no—
265C22—9048no—
266C22—4522no—
267C22—4522no—
268C22—4522no—
269C22—4521no—
270C22—4521no—
271C22—2262no—
272C22C2×#1426863614yescomplemented
273C22C22×D45211yescharacteristic
274C4—21no—
275C4—22no—
276C4—4521no—
277C4—4521no—
278C4—4522no—
279C4—2262no—
280C4C2×#1426863612yescomplemented
281C4C2×D4×D11311yescharacteristic
282C4#1681366811yescharacteristic
283C2—24no—
284C2—9042no—
285C2—4522no—
286C2D4×D45211yescharacteristic
287C2C22×#1426863611yescharacteristic
288C2#2029941011yescharacteristic
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC8×D4×C113C2
socleC22×C113C22×D4
prime radicalD4×D452C2
hypercenterC8×D4D113
hypocenterC113D4×SD16
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. C22×#14268636C2semidirect
2. D4×Dic226C2semidirect
4. #20298971C2semidirect
5. #20298827C2semidirect
6. #20298804C2semidirect
7. #20298799C2semidirect
8. #20298751C2semidirect
9. #20298739C2semidirect
10. C4×#14268636C2semidirect
11. C8×D4×C113C2semidirect
12. C22×Dic226C22semidirect
18. C2×#14268636C22semidirect
19. C2×#14268636C22semidirect
20. C2×#14268636C22semidirect
21. #16813622C22semidirect
24. #16813601C22semidirect
29. C4×Dic226C22semidirect
32. #16813554C22semidirect
33. #16813547C22semidirect
34. #16813547C22semidirect
36. #16813544C22semidirect
37. C22×C8×C113C22semidirect
39. C4⋊C8×C113C22semidirect
40. C22⋊C8×C113C22semidirect
41. C4×C8×C113C22semidirect
63. #14268636D4direct (N × H)
89. D4×C113SD16semidirect
114. Dic226C2×D4semidirect
117. C8×C113C2×D4semidirect
120. C22×C113C2×SD16semidirect
131. C4×C113C2×SD16semidirect
145. C113D4×SD16semidirect
156. C8×D4D113semidirect
166. C22×C8C2×D113semidirect
180. C4⋊C8C2×D113semidirect
185. C22⋊C8C2×D113semidirect
186. C4×C8C2×D113semidirect
247. D4#14268636direct (N × H)
262. C8D4×D113semidirect
272. C22C2×#14268636semidirect
280. C4C2×#14268636semidirect

Maximal subgroups

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

subgroupindex
C22×#142686362
D4×Dic2262
D4×D4522
#202989712
#202988272
#202988042
#202987992
#202987512
#202987392
C4×#142686362
C8×D4×C1132
D4×SD16113