Finite Group Databasebeta

← #34079045

Subgroups — #34079045

Order 19328.

462 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 121 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×D151C211yesmaximal, characteristic
2C2×#18012697C211yesmaximal, characteristic, complemented
3#23752539C212yesmaximal, complemented
4#23752535C212yesmaximal, complemented
5#23752531C211yesmaximal, characteristic, complemented
6#23752528C211yesmaximal, characteristic, complemented
7#23752525C211yesmaximal, characteristic, complemented
8#23752253C212yesmaximal, complemented
9#23752215C212yesmaximal, complemented
10#23752174C211yesmaximal, characteristic, complemented
11#480×C151C211yesmaximal, characteristic, complemented
12C2×D4×D151—21no—
13C2×D4×D151C2211yescharacteristic
14C22×C4×D151C2211yescharacteristic
15C2×#14558987C2212yes—
16#18012714C2211yescharacteristic
17#18012713C2211yescharacteristic
18#18012712—21no—
19#18012711—21no—
20#18012710C2211yescharacteristic
21#18012697—21no—
22#18012697—21no—
23#18012697C2212yes—
24#18012697C2212yescomplemented
25C2×C4⋊Dic151C2211yescharacteristic, complemented
26C4⋊C4×D151C2211yescharacteristic
27C2×(C2×D151)⋊C4—21no—
28C22⋊C4×D151—21no—
29C2×C4×Dic151—21no—
30#18012672C2212yescomplemented
31#18012671C2212yescomplemented
32#18012670C2212yescomplemented
33#18012661C2212yescomplemented
34#18012660C2212yescomplemented
35#18012659C2212yescomplemented
36C22⋊(C151⋊C8)C2211yescharacteristic, complemented
37(C2×D151)⋊C8C2212yescomplemented
38#121×C151C2211yescharacteristic
39C2×C4⋊C4×C151C2211yescharacteristic, complemented
40#107×C151C2212yescomplemented
41#102×C151C2212yescomplemented
42C22⋊C8×C151C2211yescharacteristic, complemented
43C23×D151—21no—
44C23×D151D411yescharacteristic
45C2×D604—21no—
46C2×D604C2311yescharacteristic
47C2×C22⋊D151—21no—
48C2×C22⋊D151—21no—
49C2×C22⋊D151—21no—
50D4×D151—24no—
51D4×D151—44no—
52C22×Dic151—21no—
53C22×Dic151D411yescharacteristic
54C2×C4×D151—24no—
55C2×C4×D151—21no—
56C2×C4×D151D411yescharacteristic
57C2×C4×D151D411yescharacteristic
58C2×C4×D151C2311yescharacteristic
59C2×C4×D151C2311yescharacteristic
60#14558987—24no—
61C2×C151⋊C8C2312yes—
62C4⋊Dic151—21no—
63C4⋊Dic151C2311yescharacteristic
64C4⋊Dic151C2312yes—
65Dic151⋊C4—21no—
66C22⋊Dic151—21no—
67(C2×D151)⋊C4—22no—
68(C2×D151)⋊C4—22no—
69(C2×D151)⋊C4—21no—
70(C2×D151)⋊C4—21no—
71C4×Dic151—22no—
72C4×Dic151—22no—
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—22no—
83C22×D151—22no—
84C22×D151—21no—
85C22×D151—41no—
86C22×D151—42no—
87C22×D151—42no—
88C22×D151—42no—
89C22×D151C2×D411yescharacteristic
90C22×D151C2×D411yescharacteristic
91D604—22no—
92D604—42no—
93C22⋊D151—42no—
94C22⋊D151—42no—
95C22⋊D151—42no—
96C2×Dic151—22no—
97C2×Dic151—22no—
98C2×Dic151—21no—
99C2×Dic151—42no—
100C2×Dic151C2×D411yescharacteristic
101C2×Dic151C2×D411yescharacteristic
102C4×D151—22no—
103C4×D151—22no—
104C4×D151—22no—
105C4×D151—42no—
106C4×D151#4114yes—
107C151⋊C8—22no—
108C23×C151—21no—
109C23×C151C2×D411yescharacteristic
110D4×C151—22no—
111D4×C151—42no—
112C2×C4×C151—22no—
113C2×C4×C151—22no—
114C2×C4×C151—21no—
115C2×C4×C151—42no—
116C2×C4×C151C2×D411yescharacteristic
117C2×C4×C151C2411yescharacteristic
118C8×C151—22no—
119C22×C151—21no—
120C22×C151—21no—
121C22×C151—41no—
122C22×C151—41no—
123C22×C151—41no—
124C22×C151AGL(1,ℤ/8)12yes—
125C22×C151C22×D411yescharacteristic
126C2×D151—21no—
127C2×D151—21no—
128C2×D151—21no—
129C2×D151—21no—
130C2×D151—21no—
131C2×D151—44no—
132C2×D151—41no—
133C2×D151—41no—
134C2×D151—41no—
135C2×D151—84no—
136C2×D151#12312yes—
137C4×C151—21no—
138C4×C151—42no—
139C4×C151—41no—
140C4×C151C2×#4112yes—
141Dic151—21no—
142Dic151—41no—
143Dic151—42no—
144Dic151#12312yes—
145C2×C151—22no—
146C2×C151—81no—
147C2×C151C2×#12311yescharacteristic
148C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
149C2×C151#57511yescharacteristic
150D151—22no—
151D151—41no—
152D151—81no—
153C151#309411yescharacteristic, complemented, Sylow
154#3094—1511nomaximal, Sylow
155C2×#121—1511no—
156C2×#117—1511no—
157#482—1512no—
158#482—1512no—
159#481—1511no—
160#481—1511no—
161#480—1511no—
162#480D15111yescharacteristic, complemented
163#428—1512no—
164#418—1512no—
165#407—1511no—
166C22×D4—3021no—
167C22×D4—1511no—
168C23×C4—1511no—
169C2×M16—1512no—
170#121—3021no—
171#121—3021no—
172#121—1511no—
173#121—1511no—
174#121—1511no—
175#121C2×D15111yescharacteristic
176#117—3021no—
177#117—3021no—
178#117—1512no—
179#117—1512no—
180C2×C4⋊C4—1511no—
181C2×C4⋊C4—1511no—
182C2×C4⋊C4C2×D15111yescharacteristic, complemented
183C2×C22⋊C4—3021no—
184C2×C22⋊C4—3021no—
185C2×C42—3021no—
186#107—1512no—
187#107C2×D15112yescomplemented
188#106—1512no—
189#106—1512no—
190#102—1512no—
191#102—1512no—
192#102—1512no—
193#102C2×D15112yescomplemented
194C22⋊C8—1511no—
195C22⋊C8—1512no—
196C22⋊C8C2×D15111yescharacteristic, complemented
197C24—3021no—
198C24—1511no—
199C2×D4—21no—
200C2×D4—3021no—
201C2×D4—3021no—
202C2×D4—3021no—
203C2×D4—3024no—
204C2×D4—3021no—
205C2×D4—6044no—
206C2×D4—1511no—
207C2×D4C22×D15111yescharacteristic
208C22×C4—21no—
209C22×C4—3024no—
210C22×C4—3021no—
211C22×C4—3021no—
212C22×C4—1511no—
213C22×C4—1511no—
214C22×C4—1511no—
215C22×C4—1511no—
216C22×C4—1511no—
217C22×C4C22×D15111yescharacteristic
218M16—3024no—
219C2×C8—1512no—
220C2×C8C22×D15112yes—
221C4⋊C4—21no—
222C4⋊C4—3021no—
223C4⋊C4—3021no—
224C4⋊C4—1512no—
225C4⋊C4—1511no—
226C4⋊C4C22×D15112yes—
227C4⋊C4C22×D15111yescharacteristic
228C22⋊C4—21no—
229C22⋊C4—3022no—
230C22⋊C4—3022no—
231C22⋊C4—3021no—
232C22⋊C4—3021no—
233C22⋊C4—3021no—
234C42—3022no—
235C42—3022no—
236C23—21no—
237C23—3022no—
238C23—3022no—
239C23—3021no—
240C23—6041no—
241C23—6042no—
242C23—6042no—
243C23—6042no—
244C23—1511no—
245C23—1511no—
246C23D4×D15111yescharacteristic
247D4—22no—
248D4—42no—
249D4—3022no—
250D4—6042no—
251D4—6042no—
252D4—6042no—
253D4—6042no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—42no—
258C2×C4—3022no—
259C2×C4—3022no—
260C2×C4—3022no—
261C2×C4—3022no—
262C2×C4—3022no—
263C2×C4—3021no—
264C2×C4—6042no—
265C2×C4—6042no—
266C2×C4—1511no—
267C2×C4—1511no—
268C2×C4—1514no—
269C2×C4D4×D15111yescharacteristic
270C2×C4C23×D15111yescharacteristic
271C8—22no—
272C8—3022no—
273C22—21no—
274C22—21no—
275C22—41no—
276C22—41no—
277C22—41no—
278C22—3021no—
279C22—3021no—
280C22—3021no—
281C22—3021no—
282C22—3021no—
283C22—6044no—
284C22—6041no—
285C22—6041no—
286C22—6041no—
287C22—1512no—
288C22—12084no—
289C22#1801276312yes—
290C22C2×D4×D15111yescharacteristic
291C4—21no—
292C4—42no—
293C4—41no—
294C4—3021no—
295C4—6041no—
296C4—6042no—
297C4—1512no—
298C4#41×D15112yes—
299C2—22no—
300C2—81no—
301C2—3022no—
302C2—6041no—
303C2—12081no—
304C2#123×D15111yescharacteristic
305C2C2×#1801276311yescharacteristic
306C2#2375301111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#480×C151C2
socleC22×C151C22×D4
prime radical#121×D151C2
hypercenter#480D151
hypocenterC151#3094
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
2. C2×#18012697C2semidirect
3. #23752539C2semidirect
4. #23752535C2semidirect
5. #23752531C2semidirect
6. #23752528C2semidirect
7. #23752525C2semidirect
8. #23752253C2semidirect
9. #23752215C2semidirect
10. #23752174C2semidirect
11. #480×C151C2semidirect
24. #18012697C22semidirect
25. C2×C4⋊Dic151C22semidirect
30. #18012672C22semidirect
31. #18012671C22semidirect
32. #18012670C22semidirect
33. #18012661C22semidirect
34. #18012660C22semidirect
35. #18012659C22semidirect
36. C22⋊(C151⋊C8)C22semidirect
37. (C2×D151)⋊C8C22semidirect
39. C2×C4⋊C4×C151C22semidirect
40. #107×C151C22semidirect
41. #102×C151C22semidirect
42. C22⋊C8×C151C22semidirect
153. C151#3094semidirect
162. #480D151semidirect
182. C2×C4⋊C4C2×D151semidirect
187. #107C2×D151semidirect
193. #102C2×D151semidirect
196. C22⋊C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
#121×D1512
C2×#180126972
#237525392
#237525352
#237525312
#237525282
#237525252
#237522532
#237522152
#237521742
#480×C1512
#3094151