Finite Group Databasebeta

← C151×#10935 #50315860

Subgroups — C151×#10935 #50315860

Order 38656.

2594 conjugacy classes of subgroups; only the 302 normal subgroups are shown.

normal subgroups only

This group has 2594 conjugacy classes of subgroups — too many to draw. Only its 302 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×#379×C151C213yesmaximal
2#2273×C151C211yesmaximal, characteristic, complemented
3C2×#342×C151C213yesmaximal, complemented
4C26×C151C2211yescharacteristic
5C22×C22⋊C4×C151—26no—
6C22×C22⋊C4×C151C2213yes—
7C22×C22⋊C4×C151C2213yes—
8#379×C151—26no—
9#379×C151C4112yescomplemented
10C4×C22⋊C4×C151—26no—
11#342×C151—26no—
12C25×C151—23no—
13C25×C151—23no—
14C25×C151—26no—
15C25×C151—48no—
16C25×C151C2×C416yes—
17C25×C151C2311yescharacteristic
18C23×C4×C151—23no—
19C23×C4×C151D416yes—
20C2×C22⋊C4×C151—224no—
21C2×C22⋊C4×C151—26no—
22C2×C22⋊C4×C151—26no—
23C2×C22⋊C4×C151—23no—
24C2×C22⋊C4×C151—26no—
25C2×C22⋊C4×C151—26no—
26C2×C22⋊C4×C151—424no—
27C2×C22⋊C4×C151C2×C416yes—
28C2×C22⋊C4×C151C2×C416yes—
29C2×C22⋊C4×C151D416yes—
30C2×C42×C151—24no—
31#95×C151—24no—
32C24×C151—224no—
33C24×C151—26no—
34C24×C151—212no—
35C24×C151—26no—
36C24×C151—212no—
37C24×C151—424no—
38C24×C151—44no—
39C24×C151—412no—
40C24×C151—448no—
41C24×C151—424no—
42C24×C151—41no—
43C24×C151—46no—
44C24×C151—43no—
45C24×C151—43no—
46C24×C151—42no—
47C24×C151—41no—
48C24×C151C4214yescomplemented
49C24×C151C22×C413yes—
50C24×C151C2×D413yes—
51C24×C151C2×D413yes—
52C24×C151#4116yes—
53C22×C4×C151—26no—
54C22×C4×C151—26no—
55C22×C4×C151—26no—
56C22×C4×C151—412no—
57C22×C4×C151—412no—
58C22×C4×C151—46no—
59C22×C4×C151C22⋊C4112yescomplemented
60C22⋊C4×C151—212no—
61C22⋊C4×C151—212no—
62C22⋊C4×C151—212no—
63C22⋊C4×C151—448no—
64C22⋊C4×C151—43no—
65C22⋊C4×C151—43no—
66C42×C151—84no—
67C23×C151—212no—
68C23×C151—248no—
69C23×C151—224no—
70C23×C151—212no—
71C23×C151—48no—
72C23×C151—46no—
73C23×C151—46no—
74C23×C151—412no—
75C23×C151—412no—
76C23×C151—448no—
77C23×C151—424no—
78C23×C151—424no—
79C23×C151—424no—
80C23×C151—448no—
81C23×C151—424no—
82C23×C151—416no—
83C23×C151—48no—
84C23×C151—46no—
85C23×C151—412no—
86C23×C151—46no—
87C23×C151—48no—
88C23×C151C2×C4211yescharacteristic
89C23×C151C2×C22⋊C413yes—
90C23×C151#11713yes—
91C23×C151C4×D416yes—
92C23×C151C4×D416yes—
93C23×C151#12011yescharacteristic
94C23×C151#12116yes—
95C23×C151#12313yes—
96C23×C151#12413yes—
97C23×C151#12612yes—
98C23×C151#12711yescharacteristic
99C2×C4×C151—212no—
100C2×C4×C151—412no—
101C2×C4×C151—412no—
102C2×C4×C151—412no—
103C2×C4×C151—46no—
104C2×C4×C151—86no—
105C2×C4×C151—812no—
106C22×C151—26no—
107C22×C151—212no—
108C22×C151—26no—
109C22×C151—212no—
110C22×C151—224no—
111C22×C151—41no—
112C22×C151—43no—
113C22×C151—46no—
114C22×C151—43no—
115C22×C151—42no—
116C22×C151—41no—
117C22×C151—424no—
118C22×C151—412no—
119C22×C151—448no—
120C22×C151—424no—
121C22×C151—44no—
122C22×C151C4×C22⋊C413yes—
123C22×C151#38613yes—
124C22×C151#38816yes—
125C22×C151#39013yes—
126C22×C151B(4,𝔽2)14yes—
127C4×C151—412no—
128C4×C151—86no—
129C2×C151—23no—
130C2×C151—23no—
131C2×C151—26no—
132C2×C151—48no—
133C2×C151#143711yescharacteristic
134C2×C151#188916yes—
135#10935C15111yesmaximal, characteristic, direct product factor, Sylow
136C151#1093511yescharacteristic, direct product factor, Sylow
137C2×#379C2×C15113yes—
138#2273C2×C15111yescharacteristic, complemented
139C2×#342C2×C15113yescomplemented
140C26C22×C15111yescharacteristic
141C22×C22⋊C4—26no—
142C22×C22⋊C4C22×C15113yes—
143C22×C22⋊C4C22×C15113yes—
144#379—26no—
145#379C4×C151112yescomplemented
146C4×C22⋊C4—26no—
147#342—26no—
148C25—23no—
149C25—26no—
150C25—23no—
151C25—48no—
152C25C2×C4×C15116yes—
153C25C23×C15111yescharacteristic
154C23×C4—23no—
155C23×C4D4×C15116yes—
156C2×C22⋊C4—26no—
157C2×C22⋊C4—26no—
158C2×C22⋊C4—26no—
159C2×C22⋊C4—26no—
160C2×C22⋊C4—23no—
161C2×C22⋊C4—224no—
162C2×C22⋊C4—424no—
163C2×C22⋊C4C2×C4×C15116yes—
164C2×C22⋊C4C2×C4×C15116yes—
165C2×C22⋊C4D4×C15116yes—
166C2×C42—24no—
167#95—24no—
168C24—224no—
169C24—26no—
170C24—212no—
171C24—26no—
172C24—212no—
173C24—424no—
174C24—44no—
175C24—412no—
176C24—424no—
177C24—448no—
178C24—41no—
179C24—46no—
180C24—43no—
181C24—43no—
182C24—42no—
183C24—41no—
184C24C42×C15114yescomplemented
185C24C22×C4×C15113yes—
186C24C2×D4×C15113yes—
187C24C2×D4×C15113yes—
188C24#41×C15116yes—
189C22×C4—26no—
190C22×C4—26no—
191C22×C4—26no—
192C22×C4—412no—
193C22×C4—412no—
194C22×C4—46no—
195C22×C4C22⋊C4×C151112yescomplemented
196C22⋊C4—212no—
197C22⋊C4—212no—
198C22⋊C4—212no—
199C22⋊C4—448no—
200C22⋊C4—43no—
201C22⋊C4—43no—
202C42—84no—
203C23—212no—
204C23—224no—
205C23—248no—
206C23—212no—
207C23—412no—
208C23—48no—
209C23—46no—
210C23—46no—
211C23—412no—
212C23—448no—
213C23—424no—
214C23—424no—
215C23—424no—
216C23—448no—
217C23—424no—
218C23—416no—
219C23—48no—
220C23—46no—
221C23—412no—
222C23—46no—
223C23—48no—
224C23C2×C42×C15111yescharacteristic
225C23C2×C22⋊C4×C15113yes—
226C23#117×C15113yes—
227C23C4×D4×C15116yes—
228C23C4×D4×C15116yes—
229C23#120×C15111yescharacteristic
230C23#121×C15116yes—
231C23#123×C15113yes—
232C23#124×C15113yes—
233C23#126×C15112yes—
234C23#127×C15111yescharacteristic
235C2×C4—212no—
236C2×C4—412no—
237C2×C4—412no—
238C2×C4—412no—
239C2×C4—46no—
240C2×C4—86no—
241C2×C4—812no—
242C22—26no—
243C22—212no—
244C22—26no—
245C22—212no—
246C22—224no—
247C22—41no—
248C22—43no—
249C22—46no—
250C22—43no—
251C22—42no—
252C22—41no—
253C22—424no—
254C22—412no—
255C22—448no—
256C22—424no—
257C22—44no—
258C22C4×C22⋊C4×C15113yes—
259C22#386×C15113yes—
260C22#388×C15116yes—
261C22#390×C15113yes—
262C22B(4,𝔽2)×C15114yes—
263C4—412no—
264C4—86no—
265C2—23no—
266C2—23no—
267C2—26no—
268C2—48no—
269C2#1437×C15111yescharacteristic
270C2#1889×C15116yes—
subgroupG/H
center, socleC23×C151#120
commutatorC23C2×C42×C151
Frattini, cosocleC25C23×C151
prime radicalC26×C151C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C25×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2273×C151C2semidirect
3. C2×#342×C151C2semidirect
9. #379×C151C4semidirect
48. C24×C151C42semidirect
59. C22×C4×C151C22⋊C4semidirect
135. #10935C151direct (N × H)
136. C151#10935direct (N × H)
138. #2273C2×C151semidirect
139. C2×#342C2×C151semidirect
145. #379C4×C151semidirect
184. C24C42×C151semidirect
195. C22×C4C22⋊C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#379×C1512
#2273×C1512
C2×#342×C1512
#10935151