Finite Group Databasebeta

← C151×#19006 #50323931

Subgroups — C151×#19006 #50323931

Order 38656.

938 conjugacy classes of subgroups; only the 222 normal subgroups are shown.

normal subgroups only

This group has 938 conjugacy classes of subgroups — too many to draw. Only its 222 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×#562×C151C211yesmaximal, characteristic
2#3215×C151C212yesmaximal, complemented
3#3166×C151C211yesmaximal, characteristic, complemented
4#1661×C151C218yesmaximal, complemented
5#1534×C151C211yesmaximal, characteristic, complemented
6#1527×C151C212yesmaximal, complemented
7#562×C151—22no—
8#562×C151—24no—
9#562×C151C2214yes—
10#533×C151C2211yescharacteristic
11C2×#125×C151C2211yescharacteristic
12C2×#124×C151C2212yes—
13C2×#123×C151—22no—
14C2×C22⋊Q8×C151—22no—
15C2×#121×C151—22no—
16#501×C151C2214yescomplemented
17#499×C151—22no—
18#497×C151C2214yescomplemented
19#489×C151C2214yescomplemented
20#464×C151—24no—
21#451×C151—22no—
22#450×C151—22no—
23#432×C151C2212yes—
24#428×C151—22no—
25C4×M16×C151C2211yescharacteristic
26#330×C151C2214yescomplemented
27#329×C151C2218yescomplemented
28C22×Q8×C151D412yes—
29C22×D4×C151—22no—
30C22×D4×C151D412yes—
31C23×C4×C151—22no—
32C2×Q16×C151—24no—
33C2×SD16×C151—24no—
34C2×M16×C151—21no—
35C4⋊Q8×C151C2312yes—
36#125×C151—22no—
37#125×C151—21no—
38#125×C151D412yes—
39#125×C151C2312yes—
40#124×C151—22no—
41#124×C151—22no—
42#124×C151D414yes—
43#124×C151C2314yes—
44#123×C151—28no—
45#123×C151—28no—
46C22⋊Q8×C151—28no—
47C22⋊Q8×C151—22no—
48C22⋊Q8×C151—28no—
49#121×C151—28no—
50#121×C151—28no—
51C4×Q8×C151—22no—
52#117×C151—21no—
53C2×C4⋊C4×C151—22no—
54C2×C4⋊C4×C151—22no—
55C2×C4⋊C4×C151D412yes—
56C2×C22⋊C4×C151—22no—
57C2×C22⋊C4×C151—22no—
58C2×C22⋊C4×C151—22no—
59C2×C42×C151C2311yescharacteristic
60#107×C151—24no—
61#106×C151—24no—
62C4⋊C8×C151—22no—
63#103×C151—24no—
64#102×C151—24no—
65C22⋊C8×C151—22no—
66#97×C151C2312yes—
67#97×C151C2314yes—
68C4×C8×C151—21no—
69C24×C151—22no—
70C2×Q8×C151—22no—
71C2×Q8×C151—22no—
72C2×Q8×C151—82no—
73C2×Q8×C151C2×D414yes—
74C2×D4×C151—28no—
75C2×D4×C151—22no—
76C2×D4×C151—82no—
77C2×D4×C151—84no—
78C2×D4×C151C2×D414yes—
79C22×C4×C151—22no—
80C22×C4×C151—22no—
81C22×C4×C151—28no—
82C22×C4×C151—84no—
83C22×C4×C151C2×D411yescharacteristic
84C22×C4×C151C2×D412yes—
85Q16×C151—84no—
86SD16×C151—84no—
87M16×C151—24no—
88C2×C8×C151—22no—
89C2×C8×C151—24no—
90C4⋊C4×C151—28no—
91C4⋊C4×C151—24no—
92C4⋊C4×C151—22no—
93C4⋊C4×C151—24no—
94C4⋊C4×C151—22no—
95C4⋊C4×C151—22no—
96C4⋊C4×C151—42no—
97C4⋊C4×C151C2×D414yes—
98C22⋊C4×C151—28no—
99C22⋊C4×C151—24no—
100C22⋊C4×C151—24no—
101C22⋊C4×C151—24no—
102C22⋊C4×C151—24no—
103C22⋊C4×C151—41no—
104C42×C151—41no—
105C42×C151C2×D411yescharacteristic
106C42×C151C2×D412yes—
107C42×C151C2411yescharacteristic
108C23×C151—24no—
109C23×C151—44no—
110C23×C151—44no—
111C23×C151—44no—
112C23×C151#12011yescharacteristic
113Q8×C151—44no—
114Q8×C151—44no—
115Q8×C151—82no—
116D4×C151—44no—
117D4×C151—82no—
118D4×C151—88no—
119C2×C4×C151—22no—
120C2×C4×C151—24no—
121C2×C4×C151—24no—
122C2×C4×C151—42no—
123C2×C4×C151—44no—
124C2×C4×C151—44no—
125C2×C4×C151—42no—
126C2×C4×C151—88no—
127C2×C4×C151#12012yes—
128C2×C4×C151#12011yescharacteristic
129C2×C4×C151C22×D412yes—
130C2×C4×C151C22×D411yescharacteristic
131C8×C151—24no—
132C8×C151—44no—
133C22×C151—22no—
134C22×C151—44no—
135C22×C151—44no—
136C22×C151—44no—
137C22×C151—88no—
138C22×C151#45612yes—
139C22×C151C2×#12011yescharacteristic
140C4×C151—21no—
141C4×C151—21no—
142C4×C151—22no—
143C4×C151—22no—
144C4×C151—44no—
145C4×C151—44no—
146C4×C151—82no—
147C2×C151—22no—
148C2×C151—84no—
149C2×C151C2×#45611yescharacteristic
150C2×C151#301912yes—
151#19006C15111yesmaximal, characteristic, direct product factor, Sylow
152C151#1900611yescharacteristic, direct product factor, Sylow
153C2×#562C2×C15111yescharacteristic
154#3215C2×C15112yescomplemented
155#3166C2×C15111yescharacteristic, complemented
156#1661C2×C15118yescomplemented
157#1534C2×C15111yescharacteristic, complemented
158#1527C2×C15112yescomplemented
159#562—22no—
160#562—24no—
161#562C22×C15114yes—
162#533C22×C15111yescharacteristic
163C2×#125C22×C15111yescharacteristic
164C2×#124C22×C15112yes—
165C2×#123—22no—
166C2×C22⋊Q8—22no—
167C2×#121—22no—
168#501C22×C15114yescomplemented
169#499—22no—
170#497C22×C15114yescomplemented
171#489C22×C15114yescomplemented
172#464—24no—
173#451—22no—
174#450—22no—
175#432C22×C15112yes—
176#428—22no—
177C4×M16C22×C15111yescharacteristic
178#330C22×C15114yescomplemented
179#329C22×C15118yescomplemented
180C22×Q8D4×C15112yes—
181C22×D4—22no—
182C22×D4D4×C15112yes—
183C23×C4—22no—
184C2×Q16—24no—
185C2×SD16—24no—
186C2×M16—21no—
187C4⋊Q8C23×C15112yes—
188#125—22no—
189#125—21no—
190#125D4×C15112yes—
191#125C23×C15112yes—
192#124—22no—
193#124—22no—
194#124D4×C15114yes—
195#124C23×C15114yes—
196#123—28no—
197#123—28no—
198C22⋊Q8—28no—
199C22⋊Q8—28no—
200C22⋊Q8—22no—
201#121—28no—
202#121—28no—
203C4×Q8—22no—
204#117—21no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—22no—
207C2×C4⋊C4D4×C15112yes—
208C2×C22⋊C4—22no—
209C2×C22⋊C4—22no—
210C2×C22⋊C4—22no—
211C2×C42C23×C15111yescharacteristic
212#107—24no—
213#106—24no—
214C4⋊C8—22no—
215#103—24no—
216#102—24no—
217C22⋊C8—22no—
218#97C23×C15112yes—
219#97C23×C15114yes—
220C4×C8—21no—
221C24—22no—
222C2×Q8—22no—
223C2×Q8—22no—
224C2×Q8—82no—
225C2×Q8C2×D4×C15114yes—
226C2×D4—28no—
227C2×D4—22no—
228C2×D4—82no—
229C2×D4—84no—
230C2×D4C2×D4×C15114yes—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—28no—
234C22×C4—84no—
235C22×C4C2×D4×C15111yescharacteristic
236C22×C4C2×D4×C15112yes—
237Q16—84no—
238SD16—84no—
239M16—24no—
240C2×C8—22no—
241C2×C8—24no—
242C4⋊C4—28no—
243C4⋊C4—24no—
244C4⋊C4—22no—
245C4⋊C4—24no—
246C4⋊C4—22no—
247C4⋊C4—22no—
248C4⋊C4—42no—
249C4⋊C4C2×D4×C15114yes—
250C22⋊C4—28no—
251C22⋊C4—24no—
252C22⋊C4—24no—
253C22⋊C4—24no—
254C22⋊C4—24no—
255C22⋊C4—41no—
256C42—41no—
257C42C2×D4×C15111yescharacteristic
258C42C2×D4×C15112yes—
259C42C24×C15111yescharacteristic
260C23—24no—
261C23—44no—
262C23—44no—
263C23—44no—
264C23#120×C15111yescharacteristic
265Q8—44no—
266Q8—44no—
267Q8—82no—
268D4—44no—
269D4—82no—
270D4—88no—
271C2×C4—22no—
272C2×C4—24no—
273C2×C4—24no—
274C2×C4—42no—
275C2×C4—44no—
276C2×C4—44no—
277C2×C4—42no—
278C2×C4—88no—
279C2×C4#120×C15111yescharacteristic
280C2×C4#120×C15112yes—
281C2×C4C22×D4×C15111yescharacteristic
282C2×C4C22×D4×C15112yes—
283C8—24no—
284C8—44no—
285C22—22no—
286C22—44no—
287C22—44no—
288C22—44no—
289C22—88no—
290C22#456×C15112yes—
291C22C2×#120×C15111yescharacteristic
292C4—21no—
293C4—21no—
294C4—22no—
295C4—22no—
296C4—44no—
297C4—44no—
298C4—82no—
299C2—22no—
300C2—84no—
301C2C2×#456×C15111yescharacteristic
302C2#3019×C15112yes—
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radicalC2×#562×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. #3215×C151C2semidirect
3. #3166×C151C2semidirect
4. #1661×C151C2semidirect
5. #1534×C151C2semidirect
6. #1527×C151C2semidirect
16. #501×C151C22semidirect
18. #497×C151C22semidirect
19. #489×C151C22semidirect
26. #330×C151C22semidirect
27. #329×C151C22semidirect
151. #19006C151direct (N × H)
152. C151#19006direct (N × H)
154. #3215C2×C151semidirect
155. #3166C2×C151semidirect
156. #1661C2×C151semidirect
157. #1534C2×C151semidirect
158. #1527C2×C151semidirect
168. #501C22×C151semidirect
170. #497C22×C151semidirect
171. #489C22×C151semidirect
178. #330C22×C151semidirect
179. #329C22×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#562×C1512
#3215×C1512
#3166×C1512
#1661×C1512
#1534×C1512
#1527×C1512
#19006151