Finite Group Databasebeta

← D4×#13083562 #26031944

Subgroups — D4×#13083562 #26031944

Order 11392.

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×#13083562C212yesmaximal, complemented
2D4×Dic178C211yesmaximal, characteristic, complemented
3#19151970C211yesmaximal, characteristic, complemented
4#19151825C212yesmaximal, complemented
5#19151803C211yesmaximal, characteristic, complemented
6#19151795C211yesmaximal, characteristic, complemented
7#19151749C212yesmaximal, complemented
8#19151736C212yesmaximal, complemented
9C4×#13083562C211yesmaximal, characteristic, complemented
10D4×#10623494C211yesmaximal, characteristic, complemented
11D42×C89C211yesmaximal, characteristic
12C22×Dic178C2212yescomplemented
13C2×#13083562—28no—
14C2×#13083562C2212yes—
15C2×#13083562C2211yescharacteristic
16C2×#13083562C2212yescomplemented
17C2×#13083562C2212yescomplemented
18C2×#13083562C2212yescomplemented
19C22×#10623494C2212yescomplemented
20#15668012C2211yescharacteristic, complemented
21#15668011—21no—
22#15667991C2212yescomplemented
23#15667989—22no—
24C4×Dic178C2211yescharacteristic, complemented
25D4×Dic89—21no—
26#15667943C2211yescharacteristic, complemented
27C4⋊#10623494C2211yescharacteristic, complemented
28#15667935C2211yescharacteristic, complemented
29#15667935C2212yescomplemented
30#15667933C2211yescharacteristic
31#15667933C2212yescomplemented
32C22⋊#10623494C2212yescomplemented
33C4×#10623494C2211yescharacteristic, complemented
34C22×D4×C89—21no—
35C22×D4×C89C2212yes—
36#127×C89C2211yescharacteristic
37#121×C89—21no—
38#121×C89C2212yes—
39#120×C89—22no—
40C4×D4×C89C2211yescharacteristic
41C4×D4×C89C2211yescharacteristic
42C2×Dic178—24no—
43C2×Dic178—22no—
44C2×Dic178—42no—
45C2×Dic178C2312yes—
46C2×Dic178C2311yescharacteristic
47C22×Dic89—22no—
48#13083562—24no—
49#13083562—24no—
50#13083562—24no—
51#13083562—42no—
52#13083562D414yesdirect product factor
53C2×#10623494—24no—
54C2×#10623494C2312yes—
55C2×#10623494C2311yescharacteristic
56C2×#10623494C2311yescharacteristic
57C4⋊Dic89—21no—
58C4⋊Dic89—21no—
59C4⋊Dic89C2311yescharacteristic
60#13083553—21no—
61#13083553—22no—
62C22⋊Dic89—22no—
63C4×Dic89—21no—
64C24×C89—22no—
65C2×D4×C89—24no—
66C2×D4×C89—22no—
67C2×D4×C89—22no—
68C2×D4×C89—21no—
69C2×D4×C89—21no—
70C2×D4×C89—42no—
71C2×D4×C89—44no—
72C2×D4×C89D411yescharacteristic
73C2×D4×C89C2312yes—
74C2×D4×C89C2311yescharacteristic
75C22×C4×C89—21no—
76C22×C4×C89C2312yes—
77C4⋊C4×C89D411yescharacteristic
78C4⋊C4×C89C2311yescharacteristic
79C22⋊C4×C89—21no—
80C22⋊C4×C89—22no—
81C22⋊C4×C89D412yes—
82C42×C89C2311yescharacteristic
83C23×C89—21no—
84C23×C89—22no—
85C23×C89—44no—
86C23×C89—44no—
87C23×C89—82no—
88C23×C89C2×D412yes—
89D4×C89—22no—
90D4×C89—21no—
91D4×C89—22no—
92D4×C89—44no—
93D4×C89—44no—
94D4×C89—42no—
95D4×C89—81no—
96D4×C89SD1614yescomplemented
97D4×C89C2×D412yes—
98C2×C4×C89—22no—
99C2×C4×C89—22no—
100C2×C4×C89—21no—
101C2×C4×C89—42no—
102C2×C4×C89C2×D411yescharacteristic
103C2×C4×C89C2×D412yes—
104C2×C4×C89C2×D411yescharacteristic
105C2×C4×C89C2411yescharacteristic
106C2×Dic89—21no—
107C2×Dic89—21no—
108C2×Dic89—22no—
109C2×Dic89—44no—
110Dic178—21no—
111Dic178—22no—
112Dic178—22no—
113Dic178—44no—
114Dic178C2×D412yescomplemented
115#10623494—22no—
116#10623494—21no—
117#10623494C2×D412yescomplemented
118C22×C89—22no—
119C22×C89—22no—
120C22×C89—22no—
121C22×C89—41no—
122C22×C89—41no—
123C22×C89—42no—
124C22×C89—42no—
125C22×C89—42no—
126C22×C89—88no—
127C22×C89C2×SD1614yescomplemented
128C22×C89C22×D411yescharacteristic
129C4×C89—22no—
130C4×C89—21no—
131C4×C89—41no—
132C4×C89C2×SD1612yescomplemented
133C4×C89C22×D411yescharacteristic
134C4×C89H(5,𝔽2)11yescharacteristic
135Dic89—22no—
136Dic89—42no—
137Dic89—41no—
138C2×C89—24no—
139C2×C89—42no—
140C2×C89—82no—
141C2×C89D4211yescharacteristic
142C2×C89C22×SD1611yescharacteristic
143C2×C89#57711yescharacteristic
144D4×SD16—891nomaximal, Sylow
145C89D4×SD1611yescharacteristic, complemented, Sylow
146C22×SD16—892no—
147D4×Q8—891no—
148D42D8911yescharacteristic
149#492—891no—
150#465—892no—
151#461—891no—
152#460—891no—
153#450—892no—
154#448—892no—
155C4×SD16—891no—
156C8×D4—891no—
157C22×Q8—892no—
158C22×D4—21no—
159C22×D4C2×D8912yes—
160C2×SD16—891no—
161C2×SD16—892no—
162C2×SD16—892no—
163C2×SD16—892no—
164C2×SD16—892no—
165C2×SD16—1788no—
166C22×C8—892no—
167C4⋊Q8—891no—
168C4⋊Q8—1781no—
169#127C2×D8911yescharacteristic
170C22⋊Q8—892no—
171C22⋊Q8—1782no—
172#121—21no—
173#121C2×D8912yes—
174#120—22no—
175C4×Q8—891no—
176C4×D4—1781no—
177C4×D4C2×D8911yescharacteristic
178C4×D4C2×D8911yescharacteristic
179#106—891no—
180C4⋊C8—891no—
181#103—891no—
182#103—892no—
183#102—891no—
184#102—892no—
185C22⋊C8—892no—
186C4×C8—891no—
187C24—22no—
188C2×Q8—891no—
189C2×Q8—892no—
190C2×Q8—3562no—
191C2×Q8—1784no—
192C2×Q8—1782no—
193C2×D4—24no—
194C2×D4—22no—
195C2×D4—22no—
196C2×D4—21no—
197C2×D4—21no—
198C2×D4—42no—
199C2×D4—44no—
200C2×D4C22⋊D8911yescharacteristic
201C2×D4C22×D8912yes—
202C2×D4C22×D8911yescharacteristic
203C22×C4—21no—
204C22×C4—1782no—
205C22×C4C22×D8912yes—
206SD16—894no—
207SD16—3562no—
208SD16—1784no—
209SD16—1784no—
210SD16—1784no—
211C2×C8—891no—
212C2×C8—891no—
213C2×C8—892no—
214C2×C8—1784no—
215C4⋊C4—891no—
216C4⋊C4—1781no—
217C4⋊C4—1781no—
218C4⋊C4—1782no—
219C4⋊C4—1781no—
220C4⋊C4C22⋊D8911yescharacteristic
221C4⋊C4C22×D8911yescharacteristic
222C22⋊C4—21no—
223C22⋊C4—22no—
224C22⋊C4—1782no—
225C22⋊C4C22⋊D8912yes—
226C42—1781no—
227C42C22×D8911yescharacteristic
228C23—21no—
229C23—22no—
230C23—44no—
231C23—44no—
232C23—82no—
233C23C2×C22⋊D8912yes—
234Q8—892no—
235Q8—3564no—
236Q8—1782no—
237Q8—1782no—
238Q8—1781no—
239D4—22no—
240D4—21no—
241D4—22no—
242D4—44no—
243D4—44no—
244D4—42no—
245D4—81no—
246D4#1308356214yesdirect product factor
247D4D4×D8912yes—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—42no—
252C2×C4—3564no—
253C2×C4—1781no—
254C2×C4—1782no—
255C2×C4—1781no—
256C2×C4C2×C22⋊D8911yescharacteristic
257C2×C4C2×C22⋊D8912yes—
258C2×C4C2×C22⋊D8911yescharacteristic
259C2×C4C23×D8911yescharacteristic
260C8—892no—
261C8—1782no—
262C8—1781no—
263C22—22no—
264C22—22no—
265C22—22no—
266C22—41no—
267C22—41no—
268C22—42no—
269C22—42no—
270C22—42no—
271C22—88no—
272C22C2×#1308356214yescomplemented
273C22C22×C22⋊D8911yescharacteristic
274C4—21no—
275C4—22no—
276C4—41no—
277C4—3561no—
278C4—3562no—
279C4—1782no—
280C4C2×#1308356212yescomplemented
281C4C2×D4×D8911yescharacteristic
282C4#1566805711yescharacteristic
283C2—24no—
284C2—42no—
285C2—82no—
286C2D4×C22⋊D8911yescharacteristic
287C2C22×#1308356211yescharacteristic
288C2#1915240911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting, prime radicalD42×C89C2
socleC22×C89C22×D4
hypercenterD42D89
hypocenterC89D4×SD16
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C22×#13083562C2semidirect
2. D4×Dic178C2semidirect
3. #19151970C2semidirect
4. #19151825C2semidirect
5. #19151803C2semidirect
6. #19151795C2semidirect
7. #19151749C2semidirect
8. #19151736C2semidirect
9. C4×#13083562C2semidirect
10. D4×#10623494C2semidirect
12. C22×Dic178C22semidirect
16. C2×#13083562C22semidirect
17. C2×#13083562C22semidirect
18. C2×#13083562C22semidirect
19. C22×#10623494C22semidirect
20. #15668012C22semidirect
22. #15667991C22semidirect
24. C4×Dic178C22semidirect
26. #15667943C22semidirect
27. C4⋊#10623494C22semidirect
28. #15667935C22semidirect
29. #15667935C22semidirect
31. #15667933C22semidirect
32. C22⋊#10623494C22semidirect
33. C4×#10623494C22semidirect
52. #13083562D4direct (N × H)
96. D4×C89SD16semidirect
114. Dic178C2×D4semidirect
117. #10623494C2×D4semidirect
127. C22×C89C2×SD16semidirect
132. C4×C89C2×SD16semidirect
145. C89D4×SD16semidirect
246. D4#13083562direct (N × H)
272. C22C2×#13083562semidirect
280. C4C2×#13083562semidirect

Maximal subgroups

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

subgroupindex
C22×#130835622
D4×Dic1782
#191519702
#191518252
#191518032
#191517952
#191517492
#191517362
C4×#130835622
D4×#106234942
D42×C892
D4×SD1689