Finite Group Databasebeta

← C151×#18552 #50323477

Subgroups — C151×#18552 #50323477

Order 38656.

982 conjugacy classes of subgroups; only the 230 normal subgroups are shown.

normal subgroups only

This group has 982 conjugacy classes of subgroups — too many to draw. Only its 230 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×#555×C151C211yesmaximal, characteristic
2#3139×C151C211yesmaximal, characteristic, complemented
3#3110×C151C212yesmaximal, complemented
4#1646×C151C218yesmaximal, complemented
5#1558×C151C211yesmaximal, characteristic, complemented
6#1490×C151C212yesmaximal, complemented
7#555×C151—22no—
8#555×C151—24no—
9#555×C151C2214yes—
10#533×C151C2211yescharacteristic
11C2×C4⋊Q8×C151C2211yescharacteristic
12C2×#124×C151—22no—
13C2×#121×C151—22no—
14C2×C4×D4×C151C2212yes—
15C2×#117×C151—22no—
16#491×C151—22no—
17#487×C151C2214yescomplemented
18#484×C151—22no—
19#474×C151C2214yescomplemented
20#461×C151C2214yescomplemented
21#450×C151—22no—
22#440×C151—24no—
23#432×C151C2212yes—
24#419×C151—22no—
25C4×M16×C151C2211yescharacteristic
26#333×C151C2214yescomplemented
27D4⋊C8×C151C2218yescomplemented
28C22×Q8×C151D412yes—
29C22×D4×C151—22no—
30C22×D4×C151D412yes—
31C23×C4×C151—22no—
32C2×SD16×C151—24no—
33C2×M16×C151—21no—
34C4⋊Q8×C151—22no—
35C4⋊Q8×C151D412yes—
36C4⋊Q8×C151C2312yes—
37C4⋊Q8×C151C2312yes—
38#125×C151—21no—
39#124×C151—28no—
40#124×C151—28no—
41C22⋊Q8×C151—22no—
42#121×C151—28no—
43#121×C151—28no—
44C4×Q8×C151—22no—
45C4×D4×C151—22no—
46C4×D4×C151—22no—
47C4×D4×C151D414yes—
48C4×D4×C151C2314yes—
49#117×C151—28no—
50#117×C151—28no—
51#117×C151—21no—
52C2×C4⋊C4×C151—22no—
53C2×C4⋊C4×C151D412yes—
54C2×C22⋊C4×C151—24no—
55C2×C22⋊C4×C151—22no—
56C2×C42×C151—22no—
57C2×C42×C151C2311yescharacteristic
58#107×C151—24no—
59C4⋊C8×C151C2314yes—
60#103×C151—24no—
61#103×C151—28no—
62#102×C151—24no—
63C22⋊C8×C151—22no—
64#97×C151—21no—
65#97×C151—22no—
66C4×C8×C151C2312yes—
67C24×C151—22no—
68C2×Q8×C151—22no—
69C2×Q8×C151—22no—
70C2×Q8×C151—44no—
71C2×Q8×C151C2×D414yes—
72C2×D4×C151—28no—
73C2×D4×C151—22no—
74C2×D4×C151—44no—
75C2×D4×C151—84no—
76C2×D4×C151C2×D414yes—
77C22×C4×C151—22no—
78C22×C4×C151—22no—
79C22×C4×C151—24no—
80C22×C4×C151—24no—
81C22×C4×C151—48no—
82C22×C4×C151C2×D412yes—
83C22×C4×C151C2×D411yescharacteristic
84SD16×C151—48no—
85M16×C151—42no—
86C2×C8×C151—22no—
87C2×C8×C151—24no—
88C4⋊C4×C151—24no—
89C4⋊C4×C151—22no—
90C4⋊C4×C151—24no—
91C4⋊C4×C151—22no—
92C4⋊C4×C151—22no—
93C4⋊C4×C151—42no—
94C4⋊C4×C151C2×D414yes—
95C22⋊C4×C151—216no—
96C22⋊C4×C151—24no—
97C22⋊C4×C151—24no—
98C22⋊C4×C151—41no—
99C42×C151—28no—
100C42×C151—41no—
101C42×C151C2×D411yescharacteristic
102C42×C151C2×D412yes—
103C42×C151C2411yescharacteristic
104C23×C151—24no—
105C23×C151—44no—
106C23×C151—44no—
107C23×C151—44no—
108C23×C151#12011yescharacteristic
109Q8×C151—44no—
110Q8×C151—44no—
111Q8×C151—82no—
112D4×C151—24no—
113D4×C151—24no—
114D4×C151—44no—
115D4×C151—88no—
116C2×C4×C151—22no—
117C2×C4×C151—24no—
118C2×C4×C151—24no—
119C2×C4×C151—24no—
120C2×C4×C151—48no—
121C2×C4×C151—44no—
122C2×C4×C151—44no—
123C2×C4×C151—48no—
124C2×C4×C151—42no—
125C2×C4×C151#12011yescharacteristic
126C2×C4×C151#12012yes—
127C2×C4×C151C22×D411yescharacteristic
128C2×C4×C151C22×D412yes—
129C8×C151—42no—
130C8×C151—44no—
131C22×C151—22no—
132C22×C151—44no—
133C22×C151—44no—
134C22×C151—44no—
135C22×C151—88no—
136C22×C151#45512yes—
137C22×C151C2×#12011yescharacteristic
138C4×C151—22no—
139C4×C151—21no—
140C4×C151—21no—
141C4×C151—44no—
142C4×C151—44no—
143C4×C151—82no—
144C4×C151#57514yes—
145C2×C151—22no—
146C2×C151—84no—
147C2×C151#300512yes—
148C2×C151C2×#45511yescharacteristic
149#18552C15111yesmaximal, characteristic, direct product factor, Sylow
150C151#1855211yescharacteristic, direct product factor, Sylow
151C2×#555C2×C15111yescharacteristic
152#3139C2×C15111yescharacteristic, complemented
153#3110C2×C15112yescomplemented
154#1646C2×C15118yescomplemented
155#1558C2×C15111yescharacteristic, complemented
156#1490C2×C15112yescomplemented
157#555—22no—
158#555—24no—
159#555C22×C15114yes—
160#533C22×C15111yescharacteristic
161C2×C4⋊Q8C22×C15111yescharacteristic
162C2×#124—22no—
163C2×#121—22no—
164C2×C4×D4C22×C15112yes—
165C2×#117—22no—
166#491—22no—
167#487C22×C15114yescomplemented
168#484—22no—
169#474C22×C15114yescomplemented
170#461C22×C15114yescomplemented
171#450—22no—
172#440—24no—
173#432C22×C15112yes—
174#419—22no—
175C4×M16C22×C15111yescharacteristic
176#333C22×C15114yescomplemented
177D4⋊C8C22×C15118yescomplemented
178C22×Q8D4×C15112yes—
179C22×D4—22no—
180C22×D4D4×C15112yes—
181C23×C4—22no—
182C2×SD16—24no—
183C2×M16—21no—
184C4⋊Q8—22no—
185C4⋊Q8D4×C15112yes—
186C4⋊Q8C23×C15112yes—
187C4⋊Q8C23×C15112yes—
188#125—21no—
189#124—28no—
190#124—28no—
191C22⋊Q8—22no—
192#121—28no—
193#121—28no—
194C4×Q8—22no—
195C4×D4—22no—
196C4×D4—22no—
197C4×D4D4×C15114yes—
198C4×D4C23×C15114yes—
199#117—28no—
200#117—28no—
201#117—21no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4D4×C15112yes—
204C2×C22⋊C4—24no—
205C2×C22⋊C4—22no—
206C2×C42—22no—
207C2×C42C23×C15111yescharacteristic
208#107—24no—
209C4⋊C8C23×C15114yes—
210#103—28no—
211#103—24no—
212#102—24no—
213C22⋊C8—22no—
214#97—21no—
215#97—22no—
216C4×C8C23×C15112yes—
217C24—22no—
218C2×Q8—22no—
219C2×Q8—22no—
220C2×Q8—44no—
221C2×Q8C2×D4×C15114yes—
222C2×D4—28no—
223C2×D4—22no—
224C2×D4—44no—
225C2×D4—84no—
226C2×D4C2×D4×C15114yes—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—24no—
230C22×C4—24no—
231C22×C4—48no—
232C22×C4C2×D4×C15112yes—
233C22×C4C2×D4×C15111yescharacteristic
234SD16—48no—
235M16—42no—
236C2×C8—22no—
237C2×C8—24no—
238C4⋊C4—24no—
239C4⋊C4—22no—
240C4⋊C4—24no—
241C4⋊C4—22no—
242C4⋊C4—22no—
243C4⋊C4—42no—
244C4⋊C4C2×D4×C15114yes—
245C22⋊C4—216no—
246C22⋊C4—24no—
247C22⋊C4—24no—
248C22⋊C4—41no—
249C42—28no—
250C42—41no—
251C42C2×D4×C15111yescharacteristic
252C42C2×D4×C15112yes—
253C42C24×C15111yescharacteristic
254C23—24no—
255C23—44no—
256C23—44no—
257C23—44no—
258C23#120×C15111yescharacteristic
259Q8—44no—
260Q8—44no—
261Q8—82no—
262D4—24no—
263D4—24no—
264D4—44no—
265D4—88no—
266C2×C4—22no—
267C2×C4—24no—
268C2×C4—24no—
269C2×C4—24no—
270C2×C4—48no—
271C2×C4—44no—
272C2×C4—44no—
273C2×C4—48no—
274C2×C4—42no—
275C2×C4#120×C15111yescharacteristic
276C2×C4#120×C15112yes—
277C2×C4C22×D4×C15111yescharacteristic
278C2×C4C22×D4×C15112yes—
279C8—42no—
280C8—44no—
281C22—22no—
282C22—44no—
283C22—44no—
284C22—44no—
285C22—88no—
286C22#455×C15112yes—
287C22C2×#120×C15111yescharacteristic
288C4—22no—
289C4—21no—
290C4—21no—
291C4—44no—
292C4—44no—
293C4—82no—
294C4#575×C15114yes—
295C2—22no—
296C2—84no—
297C2#3005×C15112yes—
298C2C2×#455×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radicalC2×#555×C151C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3139×C151C2semidirect
3. #3110×C151C2semidirect
4. #1646×C151C2semidirect
5. #1558×C151C2semidirect
6. #1490×C151C2semidirect
17. #487×C151C22semidirect
19. #474×C151C22semidirect
20. #461×C151C22semidirect
26. #333×C151C22semidirect
27. D4⋊C8×C151C22semidirect
149. #18552C151direct (N × H)
150. C151#18552direct (N × H)
152. #3139C2×C151semidirect
153. #3110C2×C151semidirect
154. #1646C2×C151semidirect
155. #1558C2×C151semidirect
156. #1490C2×C151semidirect
167. #487C22×C151semidirect
169. #474C22×C151semidirect
170. #461C22×C151semidirect
176. #333C22×C151semidirect
177. D4⋊C8C22×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#555×C1512
#3139×C1512
#3110×C1512
#1646×C1512
#1558×C1512
#1490×C1512
#18552151