Finite Group Databasebeta

← #481×D89 #26030148

Subgroups — #481×D89 #26030148

Order 11392.

512 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 135 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
1#121×D89C211yesmaximal, characteristic
2C2×C4⋊C4×D89C211yesmaximal, characteristic, complemented
3#19151918C212yesmaximal, complemented
4#19151917C211yesmaximal, characteristic, complemented
5#19151916C211yesmaximal, characteristic, complemented
6#19151915C212yesmaximal, complemented
7#19151914C211yesmaximal, characteristic, complemented
8#106×D89C212yesmaximal, complemented
9#102×D89C212yesmaximal, complemented
10C22⋊C8×D89C211yesmaximal, characteristic, complemented
11#481×C89C211yesmaximal, characteristic, complemented
12C2×D4×D89—21no—
13C2×D4×D89C2211yescharacteristic
14C22×C4×D89—21no—
15C22×C4×D89C2211yescharacteristic
16C2×C8×D89C2212yes—
17#15667987C2211yescharacteristic
18#15667986C2211yescharacteristic
19#15667985—21no—
20#15667984—21no—
21#15667983C2211yescharacteristic
22C2×C4⋊Dic89C2211yescharacteristic, complemented
23C2×#13083553—21no—
24C4⋊C4×D89—21no—
25C4⋊C4×D89—21no—
26C4⋊C4×D89C2211yescharacteristic
27C4⋊C4×D89C2212yes—
28C4⋊C4×D89C2212yescomplemented
29C22⋊C4×D89—21no—
30#15667944C2212yescomplemented
31#15667943C2212yescomplemented
32#15667943C2212yescomplemented
33#15667934C2212yescomplemented
34#15667933C2212yescomplemented
35#15667932C2212yescomplemented
36C22⋊#10623494C2211yescharacteristic, complemented
37#15667924C2212yescomplemented
38#121×C89C2211yescharacteristic
39C2×C4⋊C4×C89C2211yescharacteristic, complemented
40#106×C89C2212yescomplemented
41#102×C89C2212yescomplemented
42C22⋊C8×C89C2211yescharacteristic, complemented
43C23×D89—21no—
44C23×D89D411yescharacteristic
45C2×D356—21no—
46C2×D356C2311yescharacteristic
47C2×C22⋊D89—21no—
48C2×C22⋊D89—21no—
49C2×C22⋊D89—21no—
50D4×D89—24no—
51D4×D89—44no—
52C22×Dic89—21no—
53C22×Dic89D411yescharacteristic
54C2×C4×D89—24no—
55C2×C4×D89—22no—
56C2×C4×D89—22no—
57C2×C4×D89—21no—
58C2×C4×D89—44no—
59C2×C4×D89D411yescharacteristic
60C2×C4×D89D411yescharacteristic
61C2×C4×D89C2311yescharacteristic
62C2×C4×D89C2311yescharacteristic
63C2×#10623494C2312yes—
64C8×D89—24no—
65C4⋊Dic89—21no—
66C4⋊Dic89C2311yescharacteristic
67C4⋊Dic89C2312yes—
68#13083553—21no—
69#13083553—22no—
70#13083553—22no—
71C22⋊Dic89—21no—
72#13083551—21no—
73#13083551—21no—
74C2×D4×C89—21no—
75C2×D4×C89C2311yescharacteristic
76C22×C4×C89—21no—
77C22×C4×C89C2311yescharacteristic
78C2×C8×C89C2312yes—
79C4⋊C4×C89—21no—
80C4⋊C4×C89C2311yescharacteristic
81C4⋊C4×C89C2312yes—
82C22⋊C4×C89—21no—
83C23×C89—21no—
84C23×C89C2×D411yescharacteristic
85C22×D89—22no—
86C22×D89—22no—
87C22×D89—21no—
88C22×D89—42no—
89C22×D89—42no—
90C22×D89—42no—
91C22×D89SD1614yes—
92C22×D89C2×D411yescharacteristic
93C22×D89C2×D411yescharacteristic
94D4×C89—22no—
95D4×C89—42no—
96C2×C4×C89—22no—
97C2×C4×C89—21no—
98C2×C4×C89—22no—
99C2×C4×C89—42no—
100C2×C4×C89C2×D411yescharacteristic
101C2×C4×C89C2411yescharacteristic
102C22⋊D89—42no—
103C22⋊D89—42no—
104C22⋊D89—42no—
105C2×Dic89—22no—
106C2×Dic89—21no—
107C2×Dic89—22no—
108C2×Dic89—42no—
109C2×Dic89C2×D411yescharacteristic
110C2×Dic89C2×D411yescharacteristic
111D356—22no—
112D356—42no—
113C4×D89—22no—
114C4×D89—22no—
115C4×D89—22no—
116C4×D89—44no—
117C4×D89—42no—
118C4×D89—44no—
119C4×D89#4114yes—
120C8×C89—22no—
121#10623494—22no—
122C22×C89—21no—
123C22×C89—21no—
124C22×C89—41no—
125C22×C89—41no—
126C22×C89—41no—
127C22×C89C2×SD1612yes—
128C22×C89C22×D411yescharacteristic
129C2×D89—21no—
130C2×D89—21no—
131C2×D89—28no—
132C2×D89—41no—
133C2×D89—41no—
134C2×D89—41no—
135C2×D89—84no—
136C2×D89#12312yes—
137C2×D89C2×SD1612yes—
138C2×D89C2×SD1612yes—
139C2×D89AGL(1,ℤ/8)12yes—
140C4×C89—21no—
141C4×C89—41no—
142C4×C89—42no—
143C4×C89C2×#4112yes—
144Dic89—21no—
145Dic89—41no—
146Dic89—42no—
147Dic89#12312yes—
148C2×C89—22no—
149C2×C89—81no—
150C2×C89C2×#12311yescharacteristic
151C2×C89C22×SD1611yescharacteristic
152C2×C89C2×AGL(1,ℤ/8)11yescharacteristic
153D89—22no—
154D89—81no—
155D89#48114yesdirect product factor
156C2×#481—891nomaximal, Sylow
157C89C2×#48111yescharacteristic, complemented, Sylow
158C2×#121—891no—
159C22×C4⋊C4—891no—
160#481—891no—
161#481—891no—
162#481—892no—
163#481—892no—
164#481—891no—
165#481D8911yescharacteristic, direct product factor
166C2×#106—892no—
167C2×#102—892no—
168C2×C22⋊C8—891no—
169C22×D4—891no—
170C22×D4—1781no—
171C23×C4—891no—
172C23×C4—1781no—
173C22×C8—892no—
174#121—891no—
175#121—891no—
176#121—891no—
177#121—1781no—
178#121—1781no—
179#121C2×D8911yescharacteristic
180C2×C4⋊C4—891no—
181C2×C4⋊C4—892no—
182C2×C4⋊C4—892no—
183C2×C4⋊C4—891no—
184C2×C4⋊C4—1781no—
185C2×C4⋊C4—1781no—
186C2×C4⋊C4—1781no—
187C2×C4⋊C4C2×D8911yescharacteristic, complemented
188C2×C22⋊C4—1781no—
189#106—892no—
190#106—892no—
191#106—892no—
192#106C2×D8912yescomplemented
193#102—892no—
194#102—892no—
195#102—892no—
196#102C2×D8912yescomplemented
197C22⋊C8—891no—
198C22⋊C8—892no—
199C22⋊C8C2×D8911yescharacteristic, complemented
200C24—891no—
201C24—1781no—
202C2×D4—21no—
203C2×D4—891no—
204C2×D4—3564no—
205C2×D4—1781no—
206C2×D4—1784no—
207C2×D4—1781no—
208C2×D4—1781no—
209C2×D4—1781no—
210C2×D4C22×D8911yescharacteristic
211C22×C4—21no—
212C22×C4—891no—
213C22×C4—891no—
214C22×C4—891no—
215C22×C4—891no—
216C22×C4—891no—
217C22×C4—3564no—
218C22×C4—1784no—
219C22×C4—1781no—
220C22×C4—1782no—
221C22×C4—1782no—
222C22×C4—1781no—
223C22×C4C22×D8911yescharacteristic
224C2×C8—892no—
225C2×C8—1784no—
226C2×C8C22×D8912yes—
227C4⋊C4—21no—
228C4⋊C4—892no—
229C4⋊C4—891no—
230C4⋊C4—1782no—
231C4⋊C4—1782no—
232C4⋊C4—1781no—
233C4⋊C4—1781no—
234C4⋊C4C22×D8912yes—
235C4⋊C4C22×D8911yescharacteristic
236C22⋊C4—21no—
237C22⋊C4—1781no—
238C22⋊C4—1781no—
239C22⋊C4—1781no—
240C23—21no—
241C23—891no—
242C23—894no—
243C23—891no—
244C23—3562no—
245C23—3562no—
246C23—3562no—
247C23—1782no—
248C23—1782no—
249C23—1781no—
250C23D4×D8911yescharacteristic
251D4—22no—
252D4—42no—
253D4—3562no—
254D4—3562no—
255D4—3562no—
256D4—3562no—
257D4—1782no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—42no—
262C2×C4—891no—
263C2×C4—894no—
264C2×C4—891no—
265C2×C4—3564no—
266C2×C4—3562no—
267C2×C4—3564no—
268C2×C4—3562no—
269C2×C4—1782no—
270C2×C4—1782no—
271C2×C4—1782no—
272C2×C4—1781no—
273C2×C4—1782no—
274C2×C4—1782no—
275C2×C4D4×D8911yescharacteristic
276C2×C4C23×D8911yescharacteristic
277C8—22no—
278C8—1782no—
279C22—21no—
280C22—21no—
281C22—41no—
282C22—41no—
283C22—41no—
284C22—892no—
285C22—892no—
286C22—892no—
287C22—892no—
288C22—3561no—
289C22—3561no—
290C22—3561no—
291C22—1788no—
292C22—1781no—
293C22—1781no—
294C22—7124no—
295C22SD16×D8912yes—
296C22C2×D4×D8911yescharacteristic
297C4—21no—
298C4—41no—
299C4—42no—
300C4—892no—
301C4—3561no—
302C4—3562no—
303C4—1781no—
304C4#41×D8912yes—
305C2—22no—
306C2—81no—
307C2—894no—
308C2—1782no—
309C2—7121no—
310C2#123×D8911yescharacteristic
311C2C2×SD16×D8911yescharacteristic
312C2AGL(1,ℤ/8)×D8911yescharacteristic
subgroupG/H
centerC22C2×D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#481×C89C2
socleC22×C89C22×D4
prime radical#121×D89C2
hypercenter#481D89
hypocenterC89C2×#481
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D89C2semidirect
3. #19151918C2semidirect
4. #19151917C2semidirect
5. #19151916C2semidirect
6. #19151915C2semidirect
7. #19151914C2semidirect
8. #106×D89C2semidirect
9. #102×D89C2semidirect
10. C22⋊C8×D89C2semidirect
11. #481×C89C2semidirect
22. C2×C4⋊Dic89C22semidirect
28. C4⋊C4×D89C22semidirect
30. #15667944C22semidirect
31. #15667943C22semidirect
32. #15667943C22semidirect
33. #15667934C22semidirect
34. #15667933C22semidirect
35. #15667932C22semidirect
36. C22⋊#10623494C22semidirect
37. #15667924C22semidirect
39. C2×C4⋊C4×C89C22semidirect
40. #106×C89C22semidirect
41. #102×C89C22semidirect
42. C22⋊C8×C89C22semidirect
155. D89#481direct (N × H)
157. C89C2×#481semidirect
165. #481D89direct (N × H)
187. C2×C4⋊C4C2×D89semidirect
192. #106C2×D89semidirect
196. #102C2×D89semidirect
199. C22⋊C8C2×D89semidirect

Maximal subgroups

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

subgroupindex
#121×D892
C2×C4⋊C4×D892
#191519182
#191519172
#191519162
#191519152
#191519142
#106×D892
#102×D892
C22⋊C8×D892
#481×C892
C2×#48189