Finite Group Databasebeta

← C151×#19096 #50324021

Subgroups — C151×#19096 #50324021

Order 38656.

906 conjugacy classes of subgroups; only the 218 normal subgroups are shown.

normal subgroups only

This group has 906 conjugacy classes of subgroups — too many to draw. Only its 218 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#3567×C151C211yesmaximal, characteristic, complemented
2#3217×C151C213yesmaximal, complemented
3#1658×C151C212yesmaximal, complemented
4#1656×C151C216yesmaximal, complemented
5#1535×C151C213yesmaximal, complemented
6#564×C151C2211yescharacteristic, complemented
7#562×C151C2213yescomplemented
8#553×C151—23no—
9#552×C151—23no—
10#540×C151—23no—
11#539×C151—23no—
12C2×#127×C151C2211yescharacteristic
13#529×C151C2213yes—
14#496×C151C2216yes—
15#490×C151C2216yes—
16#460×C151—23no—
17#459×C151—23no—
18#450×C151—23no—
19#447×C151—23no—
20#432×C151C2213yes—
21#330×C151C2216yescomplemented
22#329×C151C2216yescomplemented
23C22×D4×C151—23no—
24C2×SD16×C151—26no—
25C2×D8×C151—26no—
26#127×C151—21no—
27#127×C151—23no—
28#127×C151C2312yes—
29#126×C151—21no—
30#126×C151—23no—
31#126×C151—23no—
32#125×C151—23no—
33#125×C151—23no—
34#125×C151—23no—
35#125×C151C2313yes—
36#124×C151C2313yes—
37#123×C151—23no—
38#123×C151—23no—
39#123×C151—23no—
40#123×C151—23no—
41#123×C151—23no—
42C22⋊Q8×C151—23no—
43C22⋊Q8×C151—23no—
44C22⋊Q8×C151D413yes—
45#121×C151—23no—
46#121×C151—23no—
47#121×C151—23no—
48#121×C151—23no—
49#121×C151D413yes—
50C4×Q8×C151D413yes—
51C4×D4×C151—23no—
52C4×D4×C151—23no—
53C4×D4×C151—23no—
54C4×D4×C151D413yes—
55#117×C151—23no—
56#117×C151—23no—
57C2×C4⋊C4×C151—23no—
58C2×C42×C151C2311yescharacteristic
59C4⋊C8×C151—23no—
60#102×C151—26no—
61#102×C151—26no—
62C22⋊C8×C151—23no—
63#97×C151C2316yes—
64C24×C151—41no—
65C2×Q8×C151C2×D413yes—
66C2×D4×C151—23no—
67C2×D4×C151—23no—
68C2×D4×C151—23no—
69C2×D4×C151—26no—
70C2×D4×C151—43no—
71C2×D4×C151—86no—
72C2×D4×C151C2×D413yes—
73C22×C4×C151—23no—
74C22×C4×C151—23no—
75C22×C4×C151—23no—
76C22×C4×C151C2×D413yes—
77SD16×C151—86no—
78D8×C151—86no—
79C2×C8×C151—26no—
80C4⋊C4×C151—23no—
81C4⋊C4×C151—23no—
82C4⋊C4×C151—23no—
83C4⋊C4×C151—23no—
84C4⋊C4×C151—23no—
85C4⋊C4×C151—23no—
86C4⋊C4×C151—23no—
87C4⋊C4×C151—23no—
88C4⋊C4×C151C2×D413yes—
89C4⋊C4×C151C2×D413yes—
90C22⋊C4×C151—23no—
91C22⋊C4×C151—23no—
92C22⋊C4×C151—23no—
93C22⋊C4×C151—23no—
94C22⋊C4×C151—23no—
95C22⋊C4×C151—23no—
96C22⋊C4×C151—23no—
97C42×C151—21no—
98C42×C151—21no—
99C42×C151—23no—
100C42×C151C2×D413yes—
101C42×C151C2411yescharacteristic
102C23×C151—23no—
103C23×C151—42no—
104C23×C151—86no—
105C23×C151#12011yescharacteristic
106Q8×C151—43no—
107D4×C151—43no—
108D4×C151—46no—
109D4×C151—46no—
110D4×C151—86no—
111D4×C151—83no—
112D4×C151—83no—
113D4×C151—83no—
114C2×C4×C151—23no—
115C2×C4×C151—23no—
116C2×C4×C151—23no—
117C2×C4×C151—43no—
118C2×C4×C151—83no—
119C2×C4×C151—83no—
120C2×C4×C151—83no—
121C2×C4×C151#12013yes—
122C2×C4×C151C22×D413yes—
123C8×C151—46no—
124C22×C151—23no—
125C22×C151—43no—
126C22×C151—43no—
127C22×C151—43no—
128C22×C151—86no—
129C22×C151—164no—
130C22×C151C2×#12011yescharacteristic
131C4×C151—23no—
132C4×C151—23no—
133C4×C151—43no—
134C4×C151—43no—
135C4×C151—43no—
136C2×C151—41no—
137C2×C151—83no—
138C2×C151—162no—
139C2×C151#302113yes—
140#19096C15111yesmaximal, characteristic, direct product factor, Sylow
141C151#1909611yescharacteristic, direct product factor, Sylow
142#3567C2×C15111yescharacteristic, complemented
143#3217C2×C15113yescomplemented
144#1658C2×C15112yescomplemented
145#1656C2×C15116yescomplemented
146#1535C2×C15113yescomplemented
147#564C22×C15111yescharacteristic, complemented
148#562C22×C15113yescomplemented
149#553—23no—
150#552—23no—
151#540—23no—
152#539—23no—
153C2×#127C22×C15111yescharacteristic
154#529C22×C15113yes—
155#496C22×C15116yes—
156#490C22×C15116yes—
157#460—23no—
158#459—23no—
159#450—23no—
160#447—23no—
161#432C22×C15113yes—
162#330C22×C15116yescomplemented
163#329C22×C15116yescomplemented
164C22×D4—23no—
165C2×SD16—26no—
166C2×D8—26no—
167#127—21no—
168#127—23no—
169#127C23×C15112yes—
170#126—21no—
171#126—23no—
172#126—23no—
173#125—23no—
174#125—23no—
175#125—23no—
176#125C23×C15113yes—
177#124C23×C15113yes—
178#123—23no—
179#123—23no—
180#123—23no—
181#123—23no—
182#123—23no—
183C22⋊Q8—23no—
184C22⋊Q8—23no—
185C22⋊Q8D4×C15113yes—
186#121—23no—
187#121—23no—
188#121—23no—
189#121—23no—
190#121D4×C15113yes—
191C4×Q8D4×C15113yes—
192C4×D4—23no—
193C4×D4—23no—
194C4×D4—23no—
195C4×D4D4×C15113yes—
196#117—23no—
197#117—23no—
198C2×C4⋊C4—23no—
199C2×C42C23×C15111yescharacteristic
200C4⋊C8—23no—
201#102—26no—
202#102—26no—
203C22⋊C8—23no—
204#97C23×C15116yes—
205C24—41no—
206C2×Q8C2×D4×C15113yes—
207C2×D4—23no—
208C2×D4—23no—
209C2×D4—23no—
210C2×D4—26no—
211C2×D4—43no—
212C2×D4—86no—
213C2×D4C2×D4×C15113yes—
214C22×C4—23no—
215C22×C4—23no—
216C22×C4—23no—
217C22×C4C2×D4×C15113yes—
218SD16—86no—
219D8—86no—
220C2×C8—26no—
221C4⋊C4—23no—
222C4⋊C4—23no—
223C4⋊C4—23no—
224C4⋊C4—23no—
225C4⋊C4—23no—
226C4⋊C4—23no—
227C4⋊C4—23no—
228C4⋊C4—23no—
229C4⋊C4C2×D4×C15113yes—
230C4⋊C4C2×D4×C15113yes—
231C22⋊C4—23no—
232C22⋊C4—23no—
233C22⋊C4—23no—
234C22⋊C4—23no—
235C22⋊C4—23no—
236C22⋊C4—23no—
237C22⋊C4—23no—
238C42—21no—
239C42—21no—
240C42—23no—
241C42C2×D4×C15113yes—
242C42C24×C15111yescharacteristic
243C23—23no—
244C23—42no—
245C23—86no—
246C23#120×C15111yescharacteristic
247Q8—43no—
248D4—43no—
249D4—46no—
250D4—46no—
251D4—86no—
252D4—83no—
253D4—83no—
254D4—83no—
255C2×C4—23no—
256C2×C4—23no—
257C2×C4—23no—
258C2×C4—43no—
259C2×C4—83no—
260C2×C4—83no—
261C2×C4—83no—
262C2×C4#120×C15113yes—
263C2×C4C22×D4×C15113yes—
264C8—46no—
265C22—23no—
266C22—43no—
267C22—43no—
268C22—43no—
269C22—86no—
270C22—164no—
271C22C2×#120×C15111yescharacteristic
272C4—23no—
273C4—23no—
274C4—43no—
275C4—43no—
276C4—43no—
277C2—41no—
278C2—83no—
279C2—162no—
280C2#3021×C15113yes—
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
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
1. #3567×C151C2semidirect
2. #3217×C151C2semidirect
3. #1658×C151C2semidirect
4. #1656×C151C2semidirect
5. #1535×C151C2semidirect
6. #564×C151C22semidirect
7. #562×C151C22semidirect
21. #330×C151C22semidirect
22. #329×C151C22semidirect
140. #19096C151direct (N × H)
141. C151#19096direct (N × H)
142. #3567C2×C151semidirect
143. #3217C2×C151semidirect
144. #1658C2×C151semidirect
145. #1656C2×C151semidirect
146. #1535C2×C151semidirect
147. #564C22×C151semidirect
148. #562C22×C151semidirect
162. #330C22×C151semidirect
163. #329C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3567×C1512
#3217×C1512
#1658×C1512
#1656×C1512
#1535×C1512
#19096151