Finite Group Databasebeta

← #34079245

Subgroups — #34079245

Order 19328.

450 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 117 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#23752743C211yesmaximal, characteristic, complemented
2C2×#18012701C211yesmaximal, characteristic, complemented
3#23752542C211yesmaximal, characteristic, complemented
4#23752515C212yesmaximal, complemented
5#23752426C212yesmaximal, complemented
6#23752365C211yesmaximal, characteristic, complemented
7#23752345C211yesmaximal, characteristic
8#23752321C212yesmaximal, complemented
9#23752311C212yesmaximal, complemented
10#23752266C211yesmaximal, characteristic, complemented
11#480×C151C211yesmaximal, characteristic, complemented
12C22×D604C2211yescharacteristic
13C22×C4×D151—21no—
14C2×#14558993C2212yes—
15C2×#14558989C2212yes—
16#18012732—21no—
17#18012730C2211yescharacteristic, complemented
18#18012726C2211yescharacteristic, complemented
19#18012720—21no—
20#18012718C2211yescharacteristic
21#18012704C2211yescharacteristic, complemented
22D4×Dic151—21no—
23D4×Dic151C2211yescharacteristic, complemented
24#18012701—21no—
25#18012701—21no—
26#18012701C2212yes—
27#18012701C2212yes—
28#18012695—21no—
29C2×(C2×D151)⋊C4—21no—
30C2×C4×Dic151C2211yescharacteristic
31#18012670C2212yescomplemented
32Dic151⋊C8C2212yescomplemented
33#18012662C2212yescomplemented
34#18012661C2212yes—
35#18012659C2212yes—
36C22⋊(C151⋊C8)C2211yescharacteristic
37#18012649C2212yescomplemented
38#121×C151C2211yescharacteristic
39C2×C4⋊C4×C151C2211yescharacteristic
40#107×C151C2212yescomplemented
41#102×C151C2212yescomplemented
42C22⋊C8×C151C2211yescharacteristic
43C23×D151—21no—
44C2×Dic302C2311yescharacteristic
45C2×D604—24no—
46C2×D604—21no—
47C2×D604C2312yes—
48C22×Dic151—21no—
49C22×Dic151D411yescharacteristic
50C22×Dic151D411yescharacteristic
51C2×C4×D151—22no—
52C2×C4×D151—22no—
53C2×C4×D151—44no—
54#14558993—24no—
55#14558989—24no—
56C2×C151⋊C8C2312yes—
57C4⋊Dic151—21no—
58C4⋊Dic151C2311yescharacteristic
59Dic151⋊C4—21no—
60Dic151⋊C4—21no—
61Dic151⋊C4—21no—
62C22⋊Dic151—21no—
63C22⋊Dic151—21no—
64C22⋊Dic151—21no—
65C22⋊Dic151—21no—
66(C2×D151)⋊C4—22no—
67(C2×D151)⋊C4—22no—
68C4×Dic151—21no—
69C4×Dic151D411yescharacteristic
70C4×Dic151D411yescharacteristic
71C4×Dic151C2311yescharacteristic
72C4×Dic151C2311yescharacteristic
73C2×D4×C151—21no—
74C2×D4×C151C2311yescharacteristic
75C22×C4×C151—21no—
76C22×C4×C151C2311yescharacteristic
77C2×C8×C151C2312yes—
78C4⋊C4×C151—21no—
79C4⋊C4×C151C2312yes—
80C4⋊C4×C151C2311yescharacteristic
81C22⋊C4×C151—21no—
82C22×D151—24no—
83C22×D151—22no—
84C22×D151—42no—
85C22×D151—42no—
86Dic302—22no—
87D604—24no—
88D604—22no—
89D604#4114yes—
90C2×Dic151—22no—
91C2×Dic151—21no—
92C2×Dic151—21no—
93C2×Dic151—41no—
94C2×Dic151—42no—
95C2×Dic151C2×D411yescharacteristic
96C2×Dic151C2×D411yescharacteristic
97C2×Dic151C2×D411yescharacteristic
98C2×Dic151C2×D411yescharacteristic
99C4×D151—44no—
100C4×D151—44no—
101C151⋊C8—22no—
102C23×C151—21no—
103C23×C151C2×D411yescharacteristic
104D4×C151—22no—
105D4×C151—42no—
106C2×C4×C151—22no—
107C2×C4×C151—21no—
108C2×C4×C151—22no—
109C2×C4×C151—42no—
110C2×C4×C151C2×D411yescharacteristic
111C2×C4×C151C2411yescharacteristic
112C8×C151—22no—
113C22×C151—21no—
114C22×C151—21no—
115C22×C151—41no—
116C22×C151—41no—
117C22×C151—41no—
118C22×C151AGL(1,ℤ/8)12yes—
119C22×C151C22×D411yescharacteristic
120C2×D151—24no—
121C2×D151—48no—
122C2×D151—42no—
123C2×D151—42no—
124C4×C151—21no—
125C4×C151—42no—
126C4×C151—41no—
127C4×C151C2×#4112yes—
128Dic151—21no—
129Dic151—21no—
130Dic151—21no—
131Dic151—21no—
132Dic151—41no—
133Dic151—41no—
134C2×C151—22no—
135C2×C151—81no—
136C2×C151#52511yescharacteristic
137C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
138C2×C151#57511yescharacteristic
139D151—44no—
140C151#311411yescharacteristic, complemented, Sylow
141#3114—1511nomaximal, Sylow
142#529—1511no—
143C2×C4×D4—1511no—
144#483—1511no—
145#480D15111yescharacteristic, complemented
146#478—1512no—
147#463—1512no—
148#450—1511no—
149#447—1511no—
150#442—1512no—
151#440—1512no—
152#432—1511no—
153C22×D4—1511no—
154C23×C4—3021no—
155C2×SD16—1512no—
156C2×D8—1512no—
157#126—3021no—
158#125—1511no—
159#124—1511no—
160#123—3021no—
161C22⋊Q8—1511no—
162#121C2×D15111yescharacteristic
163C4×Q8—1511no—
164C4×D4—3021no—
165C4×D4—3021no—
166C4×D4—3021no—
167C4×D4—1511no—
168C4×D4—1512no—
169C4×D4—1512no—
170#117—3021no—
171C2×C4⋊C4C2×D15111yescharacteristic
172C2×C22⋊C4—3021no—
173C2×C42—1511no—
174#107C2×D15112yescomplemented
175#106—1512no—
176C4⋊C8—1512no—
177#103—1512no—
178#102—1512no—
179#102—1512no—
180#102C2×D15112yescomplemented
181C22⋊C8—1511no—
182C22⋊C8C2×D15111yescharacteristic
183#97—1512no—
184C24—3021no—
185C2×Q8—1511no—
186C2×D4—21no—
187C2×D4—3024no—
188C2×D4—3021no—
189C2×D4—1512no—
190C2×D4C22×D15111yescharacteristic
191C22×C4—21no—
192C22×C4—3022no—
193C22×C4—3022no—
194C22×C4—3021no—
195C22×C4—6044no—
196C22×C4—1511no—
197C22×C4—1511no—
198C22×C4C22×D15111yescharacteristic
199SD16—3024no—
200D8—3024no—
201C2×C8—1512no—
202C2×C8C22×D15112yes—
203C4⋊C4—21no—
204C4⋊C4—3021no—
205C4⋊C4—3021no—
206C4⋊C4—3021no—
207C4⋊C4—3021no—
208C4⋊C4—1511no—
209C4⋊C4C22×D15111yescharacteristic
210C4⋊C4C22×D15112yes—
211C22⋊C4—21no—
212C22⋊C4—3022no—
213C22⋊C4—3022no—
214C22⋊C4—3021no—
215C22⋊C4—3021no—
216C22⋊C4—3021no—
217C22⋊C4—3021no—
218C42—3021no—
219C42—1511no—
220C42—1511no—
221C42—1511no—
222C42—1511no—
223C23—21no—
224C23—3024no—
225C23—3022no—
226C23—6042no—
227C23—6042no—
228C23D4×D15111yescharacteristic
229Q8—3022no—
230D4—22no—
231D4—42no—
232D4—3024no—
233D4—3022no—
234D4—1514no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—42no—
239C2×C4—3022no—
240C2×C4—3021no—
241C2×C4—3021no—
242C2×C4—6044no—
243C2×C4—6044no—
244C2×C4—6041no—
245C2×C4—6042no—
246C2×C4—1511no—
247C2×C4—1511no—
248C2×C4—1511no—
249C2×C4—1511no—
250C2×C4D4×D15111yescharacteristic
251C2×C4C23×D15111yescharacteristic
252C8—22no—
253C8—3022no—
254C22—21no—
255C22—21no—
256C22—41no—
257C22—41no—
258C22—41no—
259C22—3024no—
260C22—6048no—
261C22—6042no—
262C22—6042no—
263C22#1801276312yes—
264C22C2×D4×D15111yescharacteristic
265C4—21no—
266C4—42no—
267C4—41no—
268C4—3021no—
269C4—3021no—
270C4—3021no—
271C4—3021no—
272C4—6041no—
273C4—6041no—
274C4#41×D15112yes—
275C2—22no—
276C2—81no—
277C2—6044no—
278C2#2375272011yescharacteristic
279C2C2×#1801276311yescharacteristic
280C2#2375301111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#480×C151C2
socleC22×C151C22×D4
prime radical#23752345C2
hypercenter#480D151
hypocenterC151#3114
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #23752743C2semidirect
2. C2×#18012701C2semidirect
3. #23752542C2semidirect
4. #23752515C2semidirect
5. #23752426C2semidirect
6. #23752365C2semidirect
8. #23752321C2semidirect
9. #23752311C2semidirect
10. #23752266C2semidirect
11. #480×C151C2semidirect
17. #18012730C22semidirect
18. #18012726C22semidirect
21. #18012704C22semidirect
23. D4×Dic151C22semidirect
31. #18012670C22semidirect
32. Dic151⋊C8C22semidirect
33. #18012662C22semidirect
37. #18012649C22semidirect
40. #107×C151C22semidirect
41. #102×C151C22semidirect
140. C151#3114semidirect
145. #480D151semidirect
174. #107C2×D151semidirect
180. #102C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527432
C2×#180127012
#237525422
#237525152
#237524262
#237523652
#237523452
#237523212
#237523112
#237522662
#480×C1512
#3114151