Finite Group Databasebeta

← C151×#18732 #50323657

Subgroups — C151×#18732 #50323657

Order 38656.

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

normal subgroups only

This group has 808 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
1#3556×C151C211yesmaximal, characteristic
2#3230×C151C212yesmaximal
3#3139×C151C211yesmaximal, characteristic
4#1636×C151C218yesmaximal, complemented
5#1544×C151C211yesmaximal, characteristic
6#1485×C151C212yesmaximal
7#564×C151—22no—
8#557×C151—22no—
9#557×C151—22no—
10#557×C151C2214yes—
11#541×C151—24no—
12#541×C151—22no—
13#533×C151C2212yes—
14#533×C151C2211yescharacteristic
15C2×C4⋊Q8×C151C2211yescharacteristic
16#500×C151—22no—
17#491×C151—22no—
18#487×C151—22no—
19#487×C151C2214yes—
20#484×C151—24no—
21#477×C151C2218yes—
22#431×C151C2212yes—
23#419×C151—22no—
24C4×M16×C151C2211yescharacteristic
25#332×C151C2214yes—
26Q8⋊C8×C151C2218yes—
27C22×Q8×C151—21no—
28C2×M16×C151—21no—
29C4⋊Q8×C151—22no—
30C4⋊Q8×C151—21no—
31C4⋊Q8×C151—24no—
32C4⋊Q8×C151—22no—
33C4⋊Q8×C151D412yes—
34C4⋊Q8×C151D412yes—
35C4⋊Q8×C151C2312yes—
36C4⋊Q8×C151C2312yes—
37#126×C151—28no—
38#125×C151—22no—
39#125×C151—28no—
40#125×C151—28no—
41#125×C151—24no—
42#125×C151—28no—
43#125×C151—22no—
44#125×C151D412yes—
45C22⋊Q8×C151—22no—
46C22⋊Q8×C151—22no—
47C22⋊Q8×C151D414yes—
48C4×Q8×C151—24no—
49C4×Q8×C151—24no—
50C4×Q8×C151—22no—
51C4×Q8×C151—22no—
52C4×Q8×C151—24no—
53C4×Q8×C151C2314yes—
54#117×C151—22no—
55#117×C151D412yes—
56C2×C4⋊C4×C151—22no—
57C2×C42×C151C2311yescharacteristic
58#107×C151—28no—
59C4⋊C8×C151C2314yes—
60#103×C151—28no—
61#103×C151—28no—
62C22⋊C8×C151—22no—
63#97×C151—21no—
64C4×C8×C151—22no—
65C4×C8×C151C2312yes—
66C2×Q8×C151—22no—
67C2×Q8×C151—22no—
68C2×Q8×C151—22no—
69C2×Q8×C151—44no—
70C2×Q8×C151—41no—
71C2×Q8×C151C2×D414yes—
72C22×C4×C151—41no—
73C22×C4×C151C2×D412yes—
74C22×C4×C151C2×D411yescharacteristic
75M16×C151—42no—
76C2×C8×C151—24no—
77C2×C8×C151—22no—
78C4⋊C4×C151—28no—
79C4⋊C4×C151—28no—
80C4⋊C4×C151—28no—
81C4⋊C4×C151—22no—
82C4⋊C4×C151—22no—
83C4⋊C4×C151—22no—
84C4⋊C4×C151—24no—
85C4⋊C4×C151—24no—
86C4⋊C4×C151—22no—
87C4⋊C4×C151—24no—
88C4⋊C4×C151—24no—
89C4⋊C4×C151—42no—
90C4⋊C4×C151C2×D414yes—
91C4⋊C4×C151C2×D414yes—
92C22⋊C4×C151—24no—
93C22⋊C4×C151—22no—
94C42×C151—28no—
95C42×C151—22no—
96C42×C151—24no—
97C42×C151C2×D412yes—
98C42×C151C2×D411yescharacteristic
99C42×C151C2411yescharacteristic
100C23×C151#12011yescharacteristic
101Q8×C151—28no—
102Q8×C151—44no—
103Q8×C151—44no—
104Q8×C151—44no—
105Q8×C151—82no—
106C2×C4×C151—24no—
107C2×C4×C151—22no—
108C2×C4×C151—24no—
109C2×C4×C151—24no—
110C2×C4×C151—24no—
111C2×C4×C151—42no—
112C2×C4×C151—82no—
113C2×C4×C151#12012yes—
114C2×C4×C151#12011yescharacteristic
115C2×C4×C151C22×D411yescharacteristic
116C2×C4×C151C22×D412yes—
117C8×C151—42no—
118C8×C151—44no—
119C22×C151—22no—
120C22×C151—21no—
121C22×C151C2×#12011yescharacteristic
122C4×C151—22no—
123C4×C151—21no—
124C4×C151—44no—
125C4×C151—44no—
126C4×C151—44no—
127C4×C151—82no—
128C4×C151#45412yes—
129C4×C151#57814yes—
130C2×C151—41no—
131C2×C151#301112yes—
132C2×C151C2×#45411yescharacteristic
133#18732C15111yesmaximal, characteristic, direct product factor, Sylow
134C151#1873211yescharacteristic, direct product factor, Sylow
135#3556C2×C15111yescharacteristic
136#3230C2×C15112yes—
137#3139C2×C15111yescharacteristic
138#1636C2×C15118yescomplemented
139#1544C2×C15111yescharacteristic
140#1485C2×C15112yes—
141#564—22no—
142#557—22no—
143#557—22no—
144#557C22×C15114yes—
145#541—24no—
146#541—22no—
147#533C22×C15112yes—
148#533C22×C15111yescharacteristic
149C2×C4⋊Q8C22×C15111yescharacteristic
150#500—22no—
151#491—22no—
152#487—22no—
153#487C22×C15114yes—
154#484—24no—
155#477C22×C15118yes—
156#431C22×C15112yes—
157#419—22no—
158C4×M16C22×C15111yescharacteristic
159#332C22×C15114yes—
160Q8⋊C8C22×C15118yes—
161C22×Q8—21no—
162C2×M16—21no—
163C4⋊Q8—22no—
164C4⋊Q8—24no—
165C4⋊Q8—22no—
166C4⋊Q8—21no—
167C4⋊Q8D4×C15112yes—
168C4⋊Q8D4×C15112yes—
169C4⋊Q8C23×C15112yes—
170C4⋊Q8C23×C15112yes—
171#126—28no—
172#125—22no—
173#125—28no—
174#125—28no—
175#125—24no—
176#125—28no—
177#125—22no—
178#125D4×C15112yes—
179C22⋊Q8—22no—
180C22⋊Q8—22no—
181C22⋊Q8D4×C15114yes—
182C4×Q8—24no—
183C4×Q8—24no—
184C4×Q8—24no—
185C4×Q8—22no—
186C4×Q8—22no—
187C4×Q8C23×C15114yes—
188#117—22no—
189#117D4×C15112yes—
190C2×C4⋊C4—22no—
191C2×C42C23×C15111yescharacteristic
192#107—28no—
193C4⋊C8C23×C15114yes—
194#103—28no—
195#103—28no—
196C22⋊C8—22no—
197#97—21no—
198C4×C8—22no—
199C4×C8C23×C15112yes—
200C2×Q8—22no—
201C2×Q8—22no—
202C2×Q8—22no—
203C2×Q8—44no—
204C2×Q8—41no—
205C2×Q8C2×D4×C15114yes—
206C22×C4—41no—
207C22×C4C2×D4×C15112yes—
208C22×C4C2×D4×C15111yescharacteristic
209M16—42no—
210C2×C8—24no—
211C2×C8—22no—
212C4⋊C4—28no—
213C4⋊C4—28no—
214C4⋊C4—28no—
215C4⋊C4—22no—
216C4⋊C4—22no—
217C4⋊C4—22no—
218C4⋊C4—24no—
219C4⋊C4—24no—
220C4⋊C4—22no—
221C4⋊C4—24no—
222C4⋊C4—24no—
223C4⋊C4—42no—
224C4⋊C4C2×D4×C15114yes—
225C4⋊C4C2×D4×C15114yes—
226C22⋊C4—24no—
227C22⋊C4—22no—
228C42—28no—
229C42—22no—
230C42—24no—
231C42C2×D4×C15112yes—
232C42C2×D4×C15111yescharacteristic
233C42C24×C15111yescharacteristic
234C23#120×C15111yescharacteristic
235Q8—28no—
236Q8—44no—
237Q8—44no—
238Q8—44no—
239Q8—82no—
240C2×C4—22no—
241C2×C4—24no—
242C2×C4—24no—
243C2×C4—24no—
244C2×C4—24no—
245C2×C4—42no—
246C2×C4—82no—
247C2×C4#120×C15112yes—
248C2×C4#120×C15111yescharacteristic
249C2×C4C22×D4×C15111yescharacteristic
250C2×C4C22×D4×C15112yes—
251C8—42no—
252C8—44no—
253C22—22no—
254C22—21no—
255C22C2×#120×C15111yescharacteristic
256C4—22no—
257C4—21no—
258C4—44no—
259C4—44no—
260C4—44no—
261C4—82no—
262C4#454×C15112yes—
263C4#578×C15114yes—
264C2—41no—
265C2#3011×C15112yes—
266C2C2×#454×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radicalC23×C151#120
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
4. #1636×C151C2semidirect
133. #18732C151direct (N × H)
134. C151#18732direct (N × H)
138. #1636C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3556×C1512
#3230×C1512
#3139×C1512
#1636×C1512
#1544×C1512
#1485×C1512
#18732151