Finite Group Databasebeta

← D4×#13083559 #26031925

Subgroups — D4×#13083559 #26031925

Order 11392.

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

normal subgroups only

This group has 620 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×#13083559C212yesmaximal, complemented
2D4×D356C211yesmaximal, characteristic, complemented
3#19151974C211yesmaximal, characteristic, complemented
4#19151832C212yesmaximal, complemented
5#19151793C211yesmaximal, characteristic, complemented
6#19151790C211yesmaximal, characteristic, complemented
7#19151732C212yesmaximal, complemented
8#19151731C212yesmaximal, complemented
9C4×#13083559C211yesmaximal, characteristic, complemented
10D4×#10623494C211yesmaximal, characteristic, complemented
11D42×C89C211yesmaximal, characteristic, complemented
12C22×D356C2212yescomplemented
13C2×D4×D89—21no—
14C2×#13083559—28no—
15C2×#13083559C2211yescharacteristic
16C2×#13083559C2212yescomplemented
17C2×#13083559C2212yescomplemented
18C2×#13083559C2212yescomplemented
19C2×#13083559C2212yescomplemented
20C22×#10623494C2212yescomplemented
21#15668009C2211yescharacteristic, complemented
22#15667987—21no—
23#15667986C2212yescomplemented
24#15667982—22no—
25C4×D356C2211yescharacteristic, complemented
26#15667945C2211yescharacteristic, complemented
27C4⋊#10623494C2211yescharacteristic, complemented
28#15667933C2211yescharacteristic, complemented
29#15667933C2212yescomplemented
30#15667932C2211yescharacteristic, complemented
31#15667932C2212yescomplemented
32C22⋊#10623494C2212yescomplemented
33C4×#10623494C2211yescharacteristic, complemented
34C22×D4×C89—21no—
35C22×D4×C89C2212yescomplemented
36#127×C89C2211yescharacteristic, complemented
37#121×C89—21no—
38#121×C89C2212yescomplemented
39#120×C89—22no—
40C4×D4×C89C2211yescharacteristic
41C4×D4×C89C2211yescharacteristic, complemented
42C23×D89—22no—
43C2×D356—24no—
44C2×D356—22no—
45C2×D356—21no—
46C2×D356—21no—
47C2×D356—42no—
48C2×D356C2312yes—
49C2×D356C2311yescharacteristic
50C2×C22⋊D89—22no—
51D4×D89—44no—
52C2×C4×D89—21no—
53#13083559—24no—
54#13083559—24no—
55#13083559—24no—
56#13083559—42no—
57#13083559D414yesdirect product factor
58C2×#10623494—24no—
59C2×#10623494C2312yes—
60C2×#10623494C2311yescharacteristic
61C2×#10623494C2311yescharacteristic
62C4⋊Dic89C2311yescharacteristic
63#13083551—21no—
64#13083551—22no—
65C24×C89—22no—
66C2×D4×C89—24no—
67C2×D4×C89—22no—
68C2×D4×C89—22no—
69C2×D4×C89—21no—
70C2×D4×C89—21no—
71C2×D4×C89—42no—
72C2×D4×C89—44no—
73C2×D4×C89D411yescharacteristic
74C2×D4×C89C2312yes—
75C2×D4×C89C2311yescharacteristic
76C22×C4×C89—21no—
77C22×C4×C89C2312yes—
78C4⋊C4×C89D411yescharacteristic
79C4⋊C4×C89C2311yescharacteristic
80C22⋊C4×C89—21no—
81C22⋊C4×C89—22no—
82C22⋊C4×C89D412yes—
83C42×C89C2311yescharacteristic
84C23×C89—21no—
85C23×C89—22no—
86C23×C89—44no—
87C23×C89—44no—
88C23×C89—82no—
89C23×C89C2×D412yes—
90C22×D89—21no—
91C22×D89—22no—
92C22×D89—44no—
93C22×D89—44no—
94C22×D89—82no—
95D4×C89—22no—
96D4×C89—21no—
97D4×C89—22no—
98D4×C89—44no—
99D4×C89—44no—
100D4×C89—42no—
101D4×C89—81no—
102D4×C89D814yescomplemented
103D4×C89C2×D412yescomplemented
104C2×C4×C89—22no—
105C2×C4×C89—22no—
106C2×C4×C89—21no—
107C2×C4×C89—42no—
108C2×C4×C89C2×D411yescharacteristic
109C2×C4×C89C2×D412yes—
110C2×C4×C89C2×D411yescharacteristic
111C2×C4×C89C2411yescharacteristic
112C22⋊D89—44no—
113C2×Dic89—21no—
114D356—22no—
115D356—21no—
116D356—22no—
117D356—44no—
118D356—42no—
119D356—81no—
120D356C2×D412yescomplemented
121C4×D89—42no—
122#10623494—22no—
123#10623494—21no—
124#10623494C2×D412yescomplemented
125C22×C89—22no—
126C22×C89—22no—
127C22×C89—22no—
128C22×C89—41no—
129C22×C89—41no—
130C22×C89—42no—
131C22×C89—42no—
132C22×C89—42no—
133C22×C89—88no—
134C22×C89C2×D814yescomplemented
135C22×C89C22×D411yescharacteristic
136C2×D89—22no—
137C2×D89—41no—
138C2×D89—41no—
139C2×D89—42no—
140C2×D89—42no—
141C2×D89—42no—
142C2×D89—88no—
143C4×C89—22no—
144C4×C89—21no—
145C4×C89—41no—
146C4×C89C2×D812yescomplemented
147C4×C89C22×D411yescharacteristic
148C4×C89H(5,𝔽2)11yescharacteristic
149Dic89—41no—
150C2×C89—24no—
151C2×C89—42no—
152C2×C89—82no—
153C2×C89D4211yescharacteristic
154C2×C89C22×D811yescharacteristic
155C2×C89#57611yescharacteristic
156D89—42no—
157D89—82no—
158D4×D8—891nomaximal, Sylow
159C89D4×D811yescharacteristic, complemented, Sylow
160C22×D8—892no—
161D42—891no—
162D42D8911yescharacteristic, complemented
163#493—891no—
164#466—892no—
165#459—891no—
166#459—891no—
167#447—892no—
168#447—892no—
169C4×D8—891no—
170C8×D4—891no—
171C22×D4—21no—
172C22×D4—892no—
173C22×D4—1781no—
174C22×D4C2×D8912yescomplemented
175C2×D8—891no—
176C2×D8—892no—
177C2×D8—892no—
178C2×D8—892no—
179C2×D8—892no—
180C2×D8—1788no—
181C22×C8—892no—
182#127—891no—
183#127C2×D8911yescharacteristic, complemented
184#121—21no—
185#121—892no—
186#121—1781no—
187#121C2×D8912yescomplemented
188#120—22no—
189#120—1782no—
190C4×D4—891no—
191C4×D4C2×D8911yescharacteristic
192C4×D4C2×D8911yescharacteristic, complemented
193#107—891no—
194C4⋊C8—891no—
195#102—891no—
196#102—892no—
197#102—891no—
198#102—892no—
199C22⋊C8—892no—
200C4×C8—891no—
201C24—22no—
202C24—1782no—
203C2×D4—24no—
204C2×D4—22no—
205C2×D4—22no—
206C2×D4—21no—
207C2×D4—21no—
208C2×D4—42no—
209C2×D4—44no—
210C2×D4—891no—
211C2×D4—892no—
212C2×D4—3562no—
213C2×D4—3564no—
214C2×D4—1784no—
215C2×D4—1782no—
216C2×D4—1782no—
217C2×D4—1781no—
218C2×D4—1781no—
219C2×D4C22⋊D8911yescharacteristic
220C2×D4C22×D8912yes—
221C2×D4C22×D8911yescharacteristic
222C22×C4—21no—
223C22×C4—1781no—
224C22×C4C22×D8912yes—
225D8—894no—
226D8—3562no—
227D8—1784no—
228D8—1784no—
229D8—1784no—
230C2×C8—891no—
231C2×C8—891no—
232C2×C8—892no—
233C2×C8—1784no—
234C4⋊C4—891no—
235C4⋊C4C22⋊D8911yescharacteristic
236C4⋊C4C22×D8911yescharacteristic
237C22⋊C4—21no—
238C22⋊C4—22no—
239C22⋊C4—1781no—
240C22⋊C4—1782no—
241C22⋊C4C22⋊D8912yes—
242C42C22×D8911yescharacteristic
243C23—21no—
244C23—22no—
245C23—44no—
246C23—44no—
247C23—82no—
248C23—3564no—
249C23—3564no—
250C23—1782no—
251C23—1781no—
252C23—7122no—
253C23C2×C22⋊D8912yes—
254D4—22no—
255D4—21no—
256D4—22no—
257D4—44no—
258D4—44no—
259D4—42no—
260D4—81no—
261D4—892no—
262D4—3564no—
263D4—3564no—
264D4—3562no—
265D4—1782no—
266D4—1782no—
267D4—1781no—
268D4—7121no—
269D4#1308355914yesdirect product factor
270D4D4×D8912yescomplemented
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—21no—
274C2×C4—42no—
275C2×C4—3562no—
276C2×C4—1781no—
277C2×C4C2×C22⋊D8911yescharacteristic
278C2×C4C2×C22⋊D8912yes—
279C2×C4C2×C22⋊D8911yescharacteristic
280C2×C4C23×D8911yescharacteristic
281C8—892no—
282C8—1782no—
283C8—1781no—
284C22—22no—
285C22—22no—
286C22—22no—
287C22—41no—
288C22—41no—
289C22—42no—
290C22—42no—
291C22—42no—
292C22—88no—
293C22—3561no—
294C22—3561no—
295C22—3562no—
296C22—3562no—
297C22—3562no—
298C22—1782no—
299C22—7128no—
300C22C2×#1308355914yescomplemented
301C22C22×C22⋊D8911yescharacteristic
302C4—21no—
303C4—22no—
304C4—41no—
305C4—3561no—
306C4C2×#1308355912yescomplemented
307C4C2×D4×D8911yescharacteristic
308C4#1566805711yescharacteristic
309C2—24no—
310C2—42no—
311C2—82no—
312C2—3562no—
313C2—7122no—
314C2D4×C22⋊D8911yescharacteristic
315C2C22×#1308355911yescharacteristic
316C2#1915240111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
FittingD42×C89C2
socleC22×C89C22×D4
hypercenterD42D89
hypocenterC89D4×D8
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×#13083559C2semidirect
2. D4×D356C2semidirect
3. #19151974C2semidirect
4. #19151832C2semidirect
5. #19151793C2semidirect
6. #19151790C2semidirect
7. #19151732C2semidirect
8. #19151731C2semidirect
9. C4×#13083559C2semidirect
10. D4×#10623494C2semidirect
11. D42×C89C2semidirect
12. C22×D356C22semidirect
16. C2×#13083559C22semidirect
17. C2×#13083559C22semidirect
18. C2×#13083559C22semidirect
19. C2×#13083559C22semidirect
20. C22×#10623494C22semidirect
21. #15668009C22semidirect
23. #15667986C22semidirect
25. C4×D356C22semidirect
26. #15667945C22semidirect
27. C4⋊#10623494C22semidirect
28. #15667933C22semidirect
29. #15667933C22semidirect
30. #15667932C22semidirect
31. #15667932C22semidirect
32. C22⋊#10623494C22semidirect
33. C4×#10623494C22semidirect
35. C22×D4×C89C22semidirect
36. #127×C89C22semidirect
38. #121×C89C22semidirect
41. C4×D4×C89C22semidirect
57. #13083559D4direct (N × H)
102. D4×C89D8semidirect
103. D4×C89C2×D4semidirect
120. D356C2×D4semidirect
124. #10623494C2×D4semidirect
134. C22×C89C2×D8semidirect
146. C4×C89C2×D8semidirect
159. C89D4×D8semidirect
162. D42D89semidirect
174. C22×D4C2×D89semidirect
183. #127C2×D89semidirect
187. #121C2×D89semidirect
192. C4×D4C2×D89semidirect
269. D4#13083559direct (N × H)
270. D4D4×D89semidirect
300. C22C2×#13083559semidirect
306. C4C2×#13083559semidirect

Maximal subgroups

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

subgroupindex
C22×#130835592
D4×D3562
#191519742
#191518322
#191517932
#191517902
#191517322
#191517312
C4×#130835592
D4×#106234942
D42×C892
D4×D889