Finite Group Databasebeta

← #469×D151 #34078702

Subgroups — #469×D151 #34078702

Order 19328.

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

normal subgroups only

This group has 596 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
1C2×D8×D151C211yesmaximal, characteristic, complemented
2C2×M16×D151C211yesmaximal, characteristic, complemented
3#121×D151C212yesmaximal, complemented
4#23752466C211yesmaximal, characteristic, complemented
5#23752465C211yesmaximal, characteristic, complemented
6#23752464C212yesmaximal, complemented
7#23752463C212yesmaximal, complemented
8#23752462C211yesmaximal, characteristic, complemented
9#106×D151C211yesmaximal, characteristic, complemented
10#102×D151C212yesmaximal, complemented
11#469×C151C211yesmaximal, characteristic, complemented
12C2×D4×D151—22no—
13C2×D4×D151C2212yes—
14C22×C4×D151C2211yescharacteristic
15C2×D1208C2211yescharacteristic, complemented
16C2×#14558989C2212yescomplemented
17D8×D151—24no—
18C2×#14558988C2211yescharacteristic, complemented
19C2×#14558987C2211yescharacteristic, complemented
20C2×#14558987C2211yescharacteristic, complemented
21M16×D151—24no—
22C2×C8×D151C2211yescharacteristic
23C2×C8×D151C2211yescharacteristic
24#18012714C2212yescomplemented
25#18012713C2212yescomplemented
26#18012712—22no—
27#18012711—22no—
28#18012710C2212yescomplemented
29C4⋊C4×D151C2212yes—
30C22⋊C4×D151—22no—
31#18012671C2211yescharacteristic, complemented
32#18012670C2212yescomplemented
33#18012661C2212yescomplemented
34#18012660C2212yescomplemented
35#18012659C2212yescomplemented
36C2×D8×C151C2211yescharacteristic, complemented
37C2×M16×C151C2211yescharacteristic, complemented
38#121×C151C2212yescomplemented
39#106×C151C2211yescharacteristic, complemented
40#102×C151C2212yescomplemented
41C23×D151—22no—
42C23×D151D411yescharacteristic
43C2×D604—22no—
44C2×D604C2312yes—
45C2×C22⋊D151—22no—
46C2×C22⋊D151—22no—
47C2×C22⋊D151—22no—
48D4×D151—24no—
49D4×D151—24no—
50D4×D151—48no—
51C22×Dic151D411yescharacteristic
52C2×C4×D151—22no—
53C2×C4×D151—22no—
54C2×C4×D151—22no—
55C2×C4×D151D411yescharacteristic
56C2×C4×D151D411yescharacteristic
57C2×C4×D151C2311yescharacteristic
58C2×C4×D151C2311yescharacteristic
59D1208—22no—
60#14558989—24no—
61#14558988—22no—
62#14558987—22no—
63#14558987—22no—
64C2×C151⋊C8C2311yescharacteristic
65C2×C151⋊C8C2311yescharacteristic
66C8×D151—22no—
67C8×D151D414yescomplemented
68C4⋊Dic151C2312yes—
69Dic151⋊C4—22no—
70C22⋊Dic151—22no—
71(C2×D151)⋊C4—22no—
72(C2×D151)⋊C4—22no—
73C2×D4×C151—22no—
74C2×D4×C151C2312yes—
75C22×C4×C151C2311yescharacteristic
76D8×C151—22no—
77M16×C151—22no—
78C2×C8×C151C2311yescharacteristic
79C2×C8×C151C2311yescharacteristic
80C4⋊C4×C151C2312yes—
81C22⋊C4×C151—22no—
82C22×D151—22no—
83C22×D151—24no—
84C22×D151—22no—
85C22×D151—44no—
86C22×D151—44no—
87C22×D151—44no—
88C22×D151C2×D411yescharacteristic
89C22×D151C2×D411yescharacteristic
90D604—22no—
91D604—22no—
92D604—44no—
93C22⋊D151—44no—
94C22⋊D151—44no—
95C22⋊D151—44no—
96C2×Dic151—22no—
97C2×Dic151—22no—
98C2×Dic151C2×D411yescharacteristic
99C2×Dic151C2×D411yescharacteristic
100C4×D151—22no—
101C4×D151—21no—
102C4×D151—21no—
103C4×D151—22no—
104C4×D151—44no—
105C4×D151C2×D412yes—
106C4×D151#4112yes—
107C151⋊C8—21no—
108C151⋊C8C2×D412yescomplemented
109C23×C151—22no—
110C23×C151C2×D411yescharacteristic
111D4×C151—22no—
112D4×C151—22no—
113D4×C151—44no—
114C2×C4×C151—21no—
115C2×C4×C151—21no—
116C2×C4×C151—22no—
117C2×C4×C151C2×D411yescharacteristic
118C2×C4×C151C2411yescharacteristic
119C8×C151—21no—
120C8×C151C2×D412yescomplemented
121C22×C151—21no—
122C22×C151—22no—
123C22×C151—42no—
124C22×C151—42no—
125C22×C151—42no—
126C22×C151C22×D411yescharacteristic
127C2×D151—21no—
128C2×D151—22no—
129C2×D151—44no—
130C2×D151—42no—
131C2×D151—42no—
132C2×D151—42no—
133C2×D151—88no—
134C2×D151#12112yes—
135C2×D151AGL(1,ℤ/8)14yes—
136C4×C151—21no—
137C4×C151—42no—
138C4×C151C22×D411yescharacteristic
139C4×C151C2×#4111yescharacteristic
140Dic151—21no—
141Dic151—42no—
142Dic151#12112yes—
143C2×C151—41no—
144C2×C151—82no—
145C2×C151C2×#12111yescharacteristic
146C2×C151C2×AGL(1,ℤ/8)12yes—
147D151—41no—
148D151—82no—
149D151#46914yesdirect product factor
150C151C2×#46911yescharacteristic, complemented, Sylow
151C2×#469—1511nomaximal, Sylow
152C22×D8—1511no—
153C22×M16—1511no—
154C2×#121—1512no—
155#469—1511no—
156#469—1511no—
157#469—1512no—
158#469—1511no—
159#469—1512no—
160#469D15111yescharacteristic, direct product factor
161C2×#106—1511no—
162C2×#102—1512no—
163C22×D4—3022no—
164C22×D4—1512no—
165C23×C4—1511no—
166C2×D8—3024no—
167C2×D8—1512no—
168C2×D8—1511no—
169C2×D8C2×D15111yescharacteristic, complemented
170C2×M16—3024no—
171C2×M16—1511no—
172C2×M16—1511no—
173C2×M16—1511no—
174C2×M16C2×D15111yescharacteristic, complemented
175C22×C8—1511no—
176C22×C8—1511no—
177#121—3022no—
178#121—3022no—
179#121—1512no—
180#121—1512no—
181#121—1512no—
182#121C2×D15112yescomplemented
183C2×C4⋊C4—1512no—
184C2×C22⋊C4—3022no—
185#106—1511no—
186#106—1512no—
187#106C2×D15111yescharacteristic, complemented
188#102—1512no—
189#102—1512no—
190#102—1512no—
191#102C2×D15112yescomplemented
192C24—3022no—
193C24—1511no—
194C2×D4—22no—
195C2×D4—3022no—
196C2×D4—3022no—
197C2×D4—3022no—
198C2×D4—3024no—
199C2×D4—3024no—
200C2×D4—3022no—
201C2×D4—6048no—
202C2×D4—1512no—
203C2×D4C22×D15112yes—
204C22×C4—3022no—
205C22×C4—3022no—
206C22×C4—3022no—
207C22×C4—1511no—
208C22×C4—1511no—
209C22×C4—1511no—
210C22×C4—1511no—
211C22×C4—1511no—
212C22×C4C22×D15111yescharacteristic
213D8—22no—
214D8—3024no—
215D8—3022no—
216M16—22no—
217M16—3022no—
218M16—3022no—
219M16—3022no—
220C2×C8—3022no—
221C2×C8—1511no—
222C2×C8—1511no—
223C2×C8—1514no—
224C2×C8C22×D15111yescharacteristic
225C2×C8C22×D15111yescharacteristic
226C4⋊C4—3022no—
227C4⋊C4—1512no—
228C4⋊C4C22×D15112yes—
229C22⋊C4—22no—
230C22⋊C4—3022no—
231C22⋊C4—3022no—
232C22⋊C4—3022no—
233C23—22no—
234C23—3022no—
235C23—3024no—
236C23—3022no—
237C23—6044no—
238C23—6044no—
239C23—6044no—
240C23—1511no—
241C23—1511no—
242C23D4×D15111yescharacteristic
243D4—22no—
244D4—22no—
245D4—44no—
246D4—3022no—
247D4—3022no—
248D4—6044no—
249D4—6044no—
250D4—6044no—
251D4—6044no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—3022no—
256C2×C4—3022no—
257C2×C4—3022no—
258C2×C4—3021no—
259C2×C4—3021no—
260C2×C4—3022no—
261C2×C4—6044no—
262C2×C4—1511no—
263C2×C4—1511no—
264C2×C4—1512no—
265C2×C4—1512no—
266C2×C4D4×D15111yescharacteristic
267C2×C4C23×D15111yescharacteristic
268C8—21no—
269C8—3021no—
270C8—1512no—
271C8D4×D15112yescomplemented
272C22—22no—
273C22—21no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—3022no—
278C22—3021no—
279C22—6044no—
280C22—6042no—
281C22—6042no—
282C22—6042no—
283C22—1514no—
284C22—1512no—
285C22—12088no—
286C22C2×D4×D15111yescharacteristic
287C4—21no—
288C4—42no—
289C4—3021no—
290C4—6042no—
291C4—1512no—
292C4C2×D4×D15111yescharacteristic
293C4#41×D15111yescharacteristic
294C2—41no—
295C2—82no—
296C2—6041no—
297C2—1514no—
298C2—12082no—
299C2#121×D15111yescharacteristic
300C2AGL(1,ℤ/8)×D15112yes—
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#469×C151C2
socleC22×C151C22×D4
hypercenter#469D151
hypocenterC151C2×#469
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. C2×D8×D151C2semidirect
2. C2×M16×D151C2semidirect
3. #121×D151C2semidirect
4. #23752466C2semidirect
5. #23752465C2semidirect
6. #23752464C2semidirect
7. #23752463C2semidirect
8. #23752462C2semidirect
9. #106×D151C2semidirect
10. #102×D151C2semidirect
11. #469×C151C2semidirect
15. C2×D1208C22semidirect
16. C2×#14558989C22semidirect
18. C2×#14558988C22semidirect
19. C2×#14558987C22semidirect
20. C2×#14558987C22semidirect
24. #18012714C22semidirect
25. #18012713C22semidirect
28. #18012710C22semidirect
31. #18012671C22semidirect
32. #18012670C22semidirect
33. #18012661C22semidirect
34. #18012660C22semidirect
35. #18012659C22semidirect
36. C2×D8×C151C22semidirect
37. C2×M16×C151C22semidirect
38. #121×C151C22semidirect
39. #106×C151C22semidirect
40. #102×C151C22semidirect
67. C8×D151D4semidirect
108. C151⋊C8C2×D4semidirect
120. C8×C151C2×D4semidirect
149. D151#469direct (N × H)
150. C151C2×#469semidirect
160. #469D151direct (N × H)
169. C2×D8C2×D151semidirect
174. C2×M16C2×D151semidirect
182. #121C2×D151semidirect
187. #106C2×D151semidirect
191. #102C2×D151semidirect
271. C8D4×D151semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1512
C2×M16×D1512
#121×D1512
#237524662
#237524652
#237524642
#237524632
#237524622
#106×D1512
#102×D1512
#469×C1512
C2×#469151