Finite Group Databasebeta

← #496×D151 #34079540

Subgroups — #496×D151 #34079540

Order 19328.

668 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 145 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×SD16×D151C212yesmaximal, complemented
2C2×D8×D151C212yesmaximal, complemented
3#127×D151C211yesmaximal, characteristic, complemented
4#124×D151C211yesmaximal, characteristic, complemented
5#23752602C211yesmaximal, characteristic, complemented
6#23752601C211yesmaximal, characteristic, complemented
7#23752600C212yesmaximal, complemented
8#23752599C211yesmaximal, characteristic, complemented
9#23752598C212yesmaximal, complemented
10#97×D151C211yesmaximal, characteristic, complemented
11#496×C151C211yesmaximal, characteristic, complemented
12C2×Q8×D151C2211yescharacteristic
13C2×D4×D151—22no—
14C2×D4×D151C2211yescharacteristic
15C2×D4×D151C2212yes—
16C2×#14558993C2212yescomplemented
17C2×#14558992C2212yescomplemented
18C2×#14558991C2212yescomplemented
19SD16×D151—28no—
20C2×D1208C2212yescomplemented
21C2×#14558989C2212yescomplemented
22C2×#14558989C2212yescomplemented
23D8×D151—28no—
24C2×C8×D151C2212yes—
25#18012736C2211yescharacteristic, complemented
26#18012735—22no—
27#18012735C2212yescomplemented
28#18012728C2211yescharacteristic, complemented
29#18012727C2211yescharacteristic, complemented
30#18012726C2211yescharacteristic, complemented
31#18012725—22no—
32C22⋊C4×D151—22no—
33C42×D151C2211yescharacteristic
34#18012650C2211yescharacteristic, complemented
35#18012649C2212yescomplemented
36C2×SD16×C151C2212yescomplemented
37C2×D8×C151C2212yescomplemented
38#127×C151C2211yescharacteristic, complemented
39#124×C151C2211yescharacteristic, complemented
40#97×C151C2211yescharacteristic, complemented
41C23×D151—21no—
42C23×D151—22no—
43C2×Dic302—21no—
44C2×Dic302C2311yescharacteristic
45Q8×D151—24no—
46C2×D604—22no—
47C2×D604C2311yescharacteristic
48C2×D604C2312yes—
49C2×C22⋊D151—21no—
50C2×C22⋊D151—22no—
51C2×C22⋊D151—24no—
52D4×D151—24no—
53D4×D151—24no—
54D4×D151—24no—
55D4×D151—48no—
56C2×C4×D151—21no—
57C2×C4×D151D412yes—
58C2×C4×D151C2311yescharacteristic
59#14558993—24no—
60#14558992—24no—
61#14558991—24no—
62D1208—24no—
63#14558989—24no—
64#14558989—24no—
65C2×C151⋊C8C2312yes—
66C8×D151D418yescomplemented
67C22⋊Dic151—22no—
68(C2×D151)⋊C4—22no—
69(C2×D151)⋊C4—22no—
70C4×Dic151D412yes—
71C4×Dic151C2311yescharacteristic
72C2×Q8×C151C2311yescharacteristic
73C2×D4×C151—22no—
74C2×D4×C151C2311yescharacteristic
75C2×D4×C151C2312yes—
76SD16×C151—24no—
77D8×C151—24no—
78C2×C8×C151C2312yes—
79C22⋊C4×C151—22no—
80C42×C151C2311yescharacteristic
81C22×D151—21no—
82C22×D151—22no—
83C22×D151—42no—
84C22×D151—44no—
85C22×D151—48no—
86C22×D151—44no—
87C22×D151C2×D411yescharacteristic
88Dic302—22no—
89Dic302—42no—
90D604—22no—
91D604—22no—
92D604—22no—
93D604—44no—
94C22⋊D151—48no—
95C22⋊D151—42no—
96C22⋊D151—44no—
97C2×Dic151—21no—
98C2×Dic151C2×D412yes—
99C2×Dic151C2×D411yescharacteristic
100C4×D151—24no—
101C4×D151—42no—
102C4×D151C2×D414yes—
103C151⋊C8C2×D414yescomplemented
104C23×C151—21no—
105C23×C151—22no—
106Q8×C151—22no—
107D4×C151—22no—
108D4×C151—22no—
109D4×C151—22no—
110D4×C151—44no—
111C2×C4×C151—21no—
112C2×C4×C151C2×D412yes—
113C2×C4×C151C2411yescharacteristic
114C8×C151C2×D414yescomplemented
115C22×C151—41no—
116C22×C151—42no—
117C22×C151—44no—
118C22×C151—42no—
119C22×C151C22×D411yescharacteristic
120C2×D151—41no—
121C2×D151—42no—
122C2×D151—44no—
123C2×D151—42no—
124C2×D151—88no—
125C2×D151—84no—
126C2×D151#12712yes—
127C2×D151AGL(1,ℤ/8)14yes—
128C4×C151—22no—
129C4×C151—41no—
130C4×C151C22×D412yes—
131Dic151—22no—
132Dic151—41no—
133Dic151#12712yes—
134C2×C151—82no—
135C2×C151—81no—
136C2×C151C2×#12711yescharacteristic
137C2×C151C2×AGL(1,ℤ/8)12yes—
138D151—82no—
139D151—81no—
140D151#49614yesdirect product factor
141C151C2×#49611yescharacteristic, complemented, Sylow
142C2×#496—1511nomaximal, Sylow
143C22×SD16—1512no—
144C22×D8—1512no—
145C2×#127—1511no—
146C2×#124—1511no—
147#496—1512no—
148#496—1512no—
149#496—1511no—
150#496—1511no—
151#496—1511no—
152#496D15111yescharacteristic, direct product factor
153C2×#97—1511no—
154C22×Q8—1511no—
155C22×D4—3022no—
156C22×D4—1511no—
157C22×D4—1512no—
158C2×SD16—3028no—
159C2×SD16—1512no—
160C2×SD16—1512no—
161C2×SD16—1512no—
162C2×SD16C2×D15112yescomplemented
163C2×D8—3028no—
164C2×D8—1512no—
165C2×D8—1512no—
166C2×D8—1512no—
167C2×D8C2×D15112yescomplemented
168C22×C8—1512no—
169#127—3022no—
170#127—1512no—
171#127—1511no—
172#127C2×D15111yescharacteristic, complemented
173#124—3022no—
174#124—1511no—
175#124—1511no—
176#124—1511no—
177#124C2×D15111yescharacteristic, complemented
178C2×C22⋊C4—3022no—
179C2×C42—1511no—
180#97—1512no—
181#97—1511no—
182#97C2×D15111yescharacteristic, complemented
183C24—3021no—
184C24—3022no—
185C2×Q8—3021no—
186C2×Q8—3024no—
187C2×Q8—1511no—
188C2×Q8C22×D15111yescharacteristic
189C2×D4—22no—
190C2×D4—3024no—
191C2×D4—3024no—
192C2×D4—3024no—
193C2×D4—3021no—
194C2×D4—3022no—
195C2×D4—3024no—
196C2×D4—3022no—
197C2×D4—6048no—
198C2×D4—1511no—
199C2×D4—1512no—
200C2×D4C22×D15111yescharacteristic
201C2×D4C22×D15112yes—
202C22×C4—3021no—
203C22×C4—1512no—
204C22×C4—1511no—
205SD16—24no—
206SD16—3024no—
207SD16—3024no—
208SD16—3024no—
209D8—24no—
210D8—3024no—
211D8—3024no—
212D8—3024no—
213C2×C8—1512no—
214C2×C8—1518no—
215C2×C8C22×D15112yes—
216C22⋊C4—22no—
217C22⋊C4—3022no—
218C22⋊C4—3022no—
219C22⋊C4—3022no—
220C42—1512no—
221C42—1511no—
222C42C22×D15111yescharacteristic
223C23—21no—
224C23—22no—
225C23—3021no—
226C23—3022no—
227C23—6042no—
228C23—6044no—
229C23—6048no—
230C23—6044no—
231C23—1511no—
232Q8—22no—
233Q8—3022no—
234Q8—6042no—
235D4—22no—
236D4—22no—
237D4—22no—
238D4—44no—
239D4—3022no—
240D4—3022no—
241D4—3022no—
242D4—6044no—
243D4—6048no—
244D4—6042no—
245D4—6044no—
246C2×C4—21no—
247C2×C4—3024no—
248C2×C4—3021no—
249C2×C4—6042no—
250C2×C4—1512no—
251C2×C4—1511no—
252C2×C4—1514no—
253C2×C4D4×D15112yes—
254C2×C4C23×D15111yescharacteristic
255C8—1514no—
256C8D4×D15114yescomplemented
257C22—44no—
258C22—42no—
259C22—41no—
260C22—42no—
261C22—6044no—
262C22—6042no—
263C22—6041no—
264C22—6042no—
265C22—1514no—
266C22—1512no—
267C22—12088no—
268C22—12084no—
269C22C2×D4×D15111yescharacteristic
270C4—22no—
271C4—41no—
272C4—3022no—
273C4—6041no—
274C4—1512no—
275C4C2×D4×D15112yes—
276C2—82no—
277C2—81no—
278C2—1514no—
279C2—12082no—
280C2—12081no—
281C2#127×D15111yescharacteristic
282C2AGL(1,ℤ/8)×D15112yes—
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#496×C151C2
socleC22×C151C22×D4
hypercenter#496D151
hypocenterC151C2×#496
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D151C2semidirect
2. C2×D8×D151C2semidirect
3. #127×D151C2semidirect
4. #124×D151C2semidirect
5. #23752602C2semidirect
6. #23752601C2semidirect
7. #23752600C2semidirect
8. #23752599C2semidirect
9. #23752598C2semidirect
10. #97×D151C2semidirect
11. #496×C151C2semidirect
16. C2×#14558993C22semidirect
17. C2×#14558992C22semidirect
18. C2×#14558991C22semidirect
20. C2×D1208C22semidirect
21. C2×#14558989C22semidirect
22. C2×#14558989C22semidirect
25. #18012736C22semidirect
27. #18012735C22semidirect
28. #18012728C22semidirect
29. #18012727C22semidirect
30. #18012726C22semidirect
34. #18012650C22semidirect
35. #18012649C22semidirect
36. C2×SD16×C151C22semidirect
37. C2×D8×C151C22semidirect
38. #127×C151C22semidirect
39. #124×C151C22semidirect
40. #97×C151C22semidirect
66. C8×D151D4semidirect
103. C151⋊C8C2×D4semidirect
114. C8×C151C2×D4semidirect
140. D151#496direct (N × H)
141. C151C2×#496semidirect
152. #496D151direct (N × H)
162. C2×SD16C2×D151semidirect
167. C2×D8C2×D151semidirect
172. #127C2×D151semidirect
177. #124C2×D151semidirect
182. #97C2×D151semidirect
256. C8D4×D151semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1512
C2×D8×D1512
#127×D1512
#124×D1512
#237526022
#237526012
#237526002
#237525992
#237525982
#97×D1512
#496×C1512
C2×#496151