Finite Group Databasebeta

← D4×#14268635 #28402266

Subgroups — D4×#14268635 #28402266

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×#14268635C212yesmaximal, complemented
2D4×Dic226C211yesmaximal, characteristic, complemented
3#20298970C211yesmaximal, characteristic, complemented
4#20298825C212yesmaximal, complemented
5#20298803C211yesmaximal, characteristic, complemented
6#20298795C211yesmaximal, characteristic, complemented
7#20298749C212yesmaximal, complemented
8#20298736C212yesmaximal, complemented
9C4×#14268635C211yesmaximal, characteristic, complemented
10D4×#11744751C211yesmaximal, characteristic, complemented
11D42×C113C211yesmaximal, characteristic
12C22×Dic226C2212yescomplemented
13C2×#14268635—28no—
14C2×#14268635C2212yes—
15C2×#14268635C2211yescharacteristic
16C2×#14268635C2212yescomplemented
17C2×#14268635C2212yescomplemented
18C2×#14268635C2212yescomplemented
19C22×#11744751C2212yescomplemented
20#16813622C2211yescharacteristic, complemented
21#16813621—21no—
22#16813601C2212yescomplemented
23#16813599—22no—
24C4×Dic226C2211yescharacteristic, complemented
25D4×Dic113—21no—
26#16813553C2211yescharacteristic, complemented
27C4⋊#11744751C2211yescharacteristic, complemented
28#16813545C2212yescomplemented
29#16813545C2211yescharacteristic, complemented
30#16813543C2211yescharacteristic
31#16813543C2212yescomplemented
32C22⋊#11744751C2212yescomplemented
33C4×#11744751C2211yescharacteristic, complemented
34C22×D4×C113—21no—
35C22×D4×C113C2212yes—
36#127×C113C2211yescharacteristic
37#121×C113—21no—
38#121×C113C2212yes—
39#120×C113—22no—
40C4×D4×C113C2211yescharacteristic
41C4×D4×C113C2211yescharacteristic
42C2×Dic226—24no—
43C2×Dic226—22no—
44C2×Dic226—42no—
45C2×Dic226C2312yes—
46C2×Dic226C2311yescharacteristic
47C22×Dic113—22no—
48#14268635—24no—
49#14268635—24no—
50#14268635—24no—
51#14268635—42no—
52#14268635D414yesdirect product factor
53C2×#11744751—24no—
54C2×#11744751C2312yes—
55C2×#11744751C2311yescharacteristic
56C2×#11744751C2311yescharacteristic
57C4⋊Dic113—21no—
58C4⋊Dic113—21no—
59C4⋊Dic113C2311yescharacteristic
60#14268626—21no—
61#14268626—22no—
62C22⋊Dic113—22no—
63C4×Dic113—21no—
64C24×C113—22no—
65C2×D4×C113—24no—
66C2×D4×C113—22no—
67C2×D4×C113—22no—
68C2×D4×C113—21no—
69C2×D4×C113—21no—
70C2×D4×C113—42no—
71C2×D4×C113—44no—
72C2×D4×C113D411yescharacteristic
73C2×D4×C113C2312yes—
74C2×D4×C113C2311yescharacteristic
75C22×C4×C113—21no—
76C22×C4×C113C2312yes—
77C4⋊C4×C113D411yescharacteristic
78C4⋊C4×C113C2311yescharacteristic
79C22⋊C4×C113—21no—
80C22⋊C4×C113—22no—
81C22⋊C4×C113D412yes—
82C42×C113C2311yescharacteristic
83C23×C113—21no—
84C23×C113—22no—
85C23×C113—44no—
86C23×C113—44no—
87C23×C113—82no—
88C23×C113C2×D412yes—
89D4×C113—22no—
90D4×C113—21no—
91D4×C113—22no—
92D4×C113—44no—
93D4×C113—44no—
94D4×C113—42no—
95D4×C113—81no—
96D4×C113SD1614yescomplemented
97D4×C113C2×D412yes—
98C2×C4×C113—22no—
99C2×C4×C113—22no—
100C2×C4×C113—21no—
101C2×C4×C113—42no—
102C2×C4×C113C2×D411yescharacteristic
103C2×C4×C113C2×D412yes—
104C2×C4×C113C2×D411yescharacteristic
105C2×C4×C113C2411yescharacteristic
106C2×Dic113—21no—
107C2×Dic113—21no—
108C2×Dic113—22no—
109C2×Dic113—44no—
110Dic226—21no—
111Dic226—22no—
112Dic226—22no—
113Dic226—44no—
114Dic226C2×D412yescomplemented
115#11744751—22no—
116#11744751—21no—
117#11744751C2×D412yescomplemented
118C22×C113—22no—
119C22×C113—22no—
120C22×C113—22no—
121C22×C113—41no—
122C22×C113—41no—
123C22×C113—42no—
124C22×C113—42no—
125C22×C113—42no—
126C22×C113—88no—
127C22×C113C2×SD1614yescomplemented
128C22×C113C22×D411yescharacteristic
129C4×C113—22no—
130C4×C113—21no—
131C4×C113—41no—
132C4×C113C2×SD1612yescomplemented
133C4×C113C22×D411yescharacteristic
134C4×C113H(5,𝔽2)11yescharacteristic
135Dic113—22no—
136Dic113—42no—
137Dic113—41no—
138C2×C113—24no—
139C2×C113—42no—
140C2×C113—82no—
141C2×C113D4211yescharacteristic
142C2×C113C22×SD1611yescharacteristic
143C2×C113#57711yescharacteristic
144D4×SD16—1131nomaximal, Sylow
145C113D4×SD1611yescharacteristic, complemented, Sylow
146C22×SD16—1132no—
147D4×Q8—1131no—
148D42D11311yescharacteristic
149#492—1131no—
150#465—1132no—
151#461—1131no—
152#460—1131no—
153#450—1132no—
154#448—1132no—
155C4×SD16—1131no—
156C8×D4—1131no—
157C22×Q8—1132no—
158C22×D4—21no—
159C22×D4C2×D11312yes—
160C2×SD16—1131no—
161C2×SD16—1132no—
162C2×SD16—1132no—
163C2×SD16—1132no—
164C2×SD16—1132no—
165C2×SD16—2268no—
166C22×C8—1132no—
167C4⋊Q8—1131no—
168C4⋊Q8—2261no—
169#127C2×D11311yescharacteristic
170C22⋊Q8—1132no—
171C22⋊Q8—2262no—
172#121—21no—
173#121C2×D11312yes—
174#120—22no—
175C4×Q8—1131no—
176C4×D4—2261no—
177C4×D4C2×D11311yescharacteristic
178C4×D4C2×D11311yescharacteristic
179#106—1131no—
180C4⋊C8—1131no—
181#103—1131no—
182#103—1132no—
183#102—1131no—
184#102—1132no—
185C22⋊C8—1132no—
186C4×C8—1131no—
187C24—22no—
188C2×Q8—1131no—
189C2×Q8—1132no—
190C2×Q8—4522no—
191C2×Q8—2264no—
192C2×Q8—2262no—
193C2×D4—24no—
194C2×D4—22no—
195C2×D4—22no—
196C2×D4—21no—
197C2×D4—21no—
198C2×D4—42no—
199C2×D4—44no—
200C2×D4C22⋊D11311yescharacteristic
201C2×D4C22×D11312yes—
202C2×D4C22×D11311yescharacteristic
203C22×C4—21no—
204C22×C4—2262no—
205C22×C4C22×D11312yes—
206SD16—1134no—
207SD16—4522no—
208SD16—2264no—
209SD16—2264no—
210SD16—2264no—
211C2×C8—1131no—
212C2×C8—1131no—
213C2×C8—1132no—
214C2×C8—2264no—
215C4⋊C4—1131no—
216C4⋊C4—2261no—
217C4⋊C4—2261no—
218C4⋊C4—2262no—
219C4⋊C4—2261no—
220C4⋊C4C22⋊D11311yescharacteristic
221C4⋊C4C22×D11311yescharacteristic
222C22⋊C4—21no—
223C22⋊C4—22no—
224C22⋊C4—2262no—
225C22⋊C4C22⋊D11312yes—
226C42—2261no—
227C42C22×D11311yescharacteristic
228C23—21no—
229C23—22no—
230C23—44no—
231C23—44no—
232C23—82no—
233C23C2×C22⋊D11312yes—
234Q8—1132no—
235Q8—4524no—
236Q8—2262no—
237Q8—2262no—
238Q8—2261no—
239D4—22no—
240D4—21no—
241D4—22no—
242D4—44no—
243D4—44no—
244D4—42no—
245D4—81no—
246D4#1426863514yesdirect product factor
247D4D4×D11312yes—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—42no—
252C2×C4—4524no—
253C2×C4—2261no—
254C2×C4—2262no—
255C2×C4—2261no—
256C2×C4C2×C22⋊D11311yescharacteristic
257C2×C4C2×C22⋊D11312yes—
258C2×C4C2×C22⋊D11311yescharacteristic
259C2×C4C23×D11311yescharacteristic
260C8—1132no—
261C8—2262no—
262C8—2261no—
263C22—22no—
264C22—22no—
265C22—22no—
266C22—41no—
267C22—41no—
268C22—42no—
269C22—42no—
270C22—42no—
271C22—88no—
272C22C2×#1426863514yescomplemented
273C22C22×C22⋊D11311yescharacteristic
274C4—21no—
275C4—22no—
276C4—41no—
277C4—4521no—
278C4—4522no—
279C4—2262no—
280C4C2×#1426863512yescomplemented
281C4C2×D4×D11311yescharacteristic
282C4#1681366711yescharacteristic
283C2—24no—
284C2—42no—
285C2—82no—
286C2D4×C22⋊D11311yescharacteristic
287C2C22×#1426863511yescharacteristic
288C2#2029940911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting, prime radicalD42×C113C2
socleC22×C113C22×D4
hypercenterD42D113
hypocenterC113D4×SD16
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C22×#14268635C2semidirect
2. D4×Dic226C2semidirect
3. #20298970C2semidirect
4. #20298825C2semidirect
5. #20298803C2semidirect
6. #20298795C2semidirect
7. #20298749C2semidirect
8. #20298736C2semidirect
9. C4×#14268635C2semidirect
10. D4×#11744751C2semidirect
12. C22×Dic226C22semidirect
16. C2×#14268635C22semidirect
17. C2×#14268635C22semidirect
18. C2×#14268635C22semidirect
19. C22×#11744751C22semidirect
20. #16813622C22semidirect
22. #16813601C22semidirect
24. C4×Dic226C22semidirect
26. #16813553C22semidirect
27. C4⋊#11744751C22semidirect
28. #16813545C22semidirect
29. #16813545C22semidirect
31. #16813543C22semidirect
32. C22⋊#11744751C22semidirect
33. C4×#11744751C22semidirect
52. #14268635D4direct (N × H)
96. D4×C113SD16semidirect
114. Dic226C2×D4semidirect
117. #11744751C2×D4semidirect
127. C22×C113C2×SD16semidirect
132. C4×C113C2×SD16semidirect
145. C113D4×SD16semidirect
246. D4#14268635direct (N × H)
272. C22C2×#14268635semidirect
280. C4C2×#14268635semidirect

Maximal subgroups

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

subgroupindex
C22×#142686352
D4×Dic2262
#202989702
#202988252
#202988032
#202987952
#202987492
#202987362
C4×#142686352
D4×#117447512
D42×C1132
D4×SD16113