Finite Group Databasebeta

← C151×#18728 #50323653

Subgroups — C151×#18728 #50323653

Order 38656.

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

normal subgroups only

This group has 920 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#3548×C151C211yesmaximal, characteristic
2#3227×C151C212yesmaximal, complemented
3#3139×C151C211yesmaximal, characteristic, complemented
4#1635×C151C218yesmaximal, complemented
5#1544×C151C211yesmaximal, characteristic, complemented
6#1484×C151C212yesmaximal, complemented
7#562×C151—22no—
8#554×C151—22no—
9#550×C151—22no—
10#547×C151C2214yes—
11#540×C151—22no—
12#537×C151—24no—
13#533×C151C2211yescharacteristic
14#532×C151C2212yes—
15C2×C4⋊Q8×C151C2211yescharacteristic
16#498×C151—22no—
17#491×C151—22no—
18#487×C151C2214yes—
19#486×C151—22no—
20#481×C151—24no—
21#476×C151C2218yes—
22#431×C151C2212yes—
23#419×C151—22no—
24C4×M16×C151C2211yescharacteristic
25#332×C151C2214yes—
26D4⋊C8×C151C2218yes—
27C2×#41×C151—24no—
28C2×#41×C151—22no—
29C22×Q8×C151—21no—
30C2×M16×C151—21no—
31C4⋊Q8×C151—21no—
32C4⋊Q8×C151—22no—
33C4⋊Q8×C151D412yes—
34C4⋊Q8×C151C2312yes—
35C4⋊Q8×C151C2312yes—
36#127×C151—22no—
37#127×C151D412yes—
38#125×C151—22no—
39#125×C151D412yes—
40#124×C151—22no—
41#123×C151—28no—
42C22⋊Q8×C151—28no—
43C22⋊Q8×C151—22no—
44C22⋊Q8×C151—24no—
45#121×C151—28no—
46#121×C151—28no—
47#121×C151—24no—
48#121×C151—22no—
49#121×C151D414yes—
50C4×Q8×C151—22no—
51C4×D4×C151—24no—
52C4×D4×C151—22no—
53C4×D4×C151C2314yes—
54#117×C151D412yes—
55C2×C4⋊C4×C151—24no—
56C2×C4⋊C4×C151—22no—
57C2×C42×C151C2311yescharacteristic
58#106×C151—28no—
59C4⋊C8×C151C2314yes—
60#103×C151—28no—
61#102×C151—28no—
62C22⋊C8×C151—22no—
63#97×C151—21no—
64C4×C8×C151—22no—
65C4×C8×C151C2312yes—
66#41×C151—84no—
67#41×C151—88no—
68C2×Q8×C151—22no—
69C2×Q8×C151—22no—
70C2×Q8×C151—22no—
71C2×Q8×C151—44no—
72C2×Q8×C151—41no—
73C2×D4×C151—28no—
74C2×D4×C151—24no—
75C2×D4×C151—22no—
76C2×D4×C151—22no—
77C2×D4×C151C2×D414yes—
78C22×C4×C151—28no—
79C22×C4×C151—24no—
80C22×C4×C151—41no—
81C22×C4×C151C2×D412yes—
82C22×C4×C151C2×D411yescharacteristic
83M16×C151—42no—
84C2×C8×C151—24no—
85C2×C8×C151—22no—
86C4⋊C4×C151—28no—
87C4⋊C4×C151—22no—
88C4⋊C4×C151—24no—
89C4⋊C4×C151—22no—
90C4⋊C4×C151—24no—
91C4⋊C4×C151—42no—
92C4⋊C4×C151C2×D414yes—
93C4⋊C4×C151C2×D414yes—
94C22⋊C4×C151—28no—
95C22⋊C4×C151—22no—
96C22⋊C4×C151—24no—
97C22⋊C4×C151—24no—
98C42×C151—22no—
99C42×C151C2×D412yes—
100C42×C151C2×D411yescharacteristic
101C42×C151C2411yescharacteristic
102C23×C151—24no—
103C23×C151#12011yescharacteristic
104Q8×C151—44no—
105Q8×C151—44no—
106Q8×C151—82no—
107Q8×C151—82no—
108D4×C151—28no—
109D4×C151—44no—
110D4×C151—82no—
111D4×C151—84no—
112D4×C151—88no—
113C2×C4×C151—24no—
114C2×C4×C151—22no—
115C2×C4×C151—24no—
116C2×C4×C151—24no—
117C2×C4×C151—48no—
118C2×C4×C151—42no—
119C2×C4×C151—88no—
120C2×C4×C151—82no—
121C2×C4×C151#12012yes—
122C2×C4×C151#12011yescharacteristic
123C2×C4×C151C22×D411yescharacteristic
124C2×C4×C151C22×D412yes—
125C8×C151—42no—
126C8×C151—44no—
127C22×C151—22no—
128C22×C151—21no—
129C22×C151—44no—
130C22×C151—44no—
131C22×C151—44no—
132C22×C151C2×#12011yescharacteristic
133C4×C151—22no—
134C4×C151—21no—
135C4×C151—44no—
136C4×C151—44no—
137C4×C151—82no—
138C4×C151#45412yes—
139C4×C151#57714yes—
140C2×C151—41no—
141C2×C151—84no—
142C2×C151#300912yes—
143C2×C151C2×#45411yescharacteristic
144#18728C15111yesmaximal, characteristic, direct product factor, Sylow
145C151#1872811yescharacteristic, direct product factor, Sylow
146#3548C2×C15111yescharacteristic
147#3227C2×C15112yescomplemented
148#3139C2×C15111yescharacteristic, complemented
149#1635C2×C15118yescomplemented
150#1544C2×C15111yescharacteristic, complemented
151#1484C2×C15112yescomplemented
152#562—22no—
153#554—22no—
154#550—22no—
155#547C22×C15114yes—
156#540—22no—
157#537—24no—
158#533C22×C15111yescharacteristic
159#532C22×C15112yes—
160C2×C4⋊Q8C22×C15111yescharacteristic
161#498—22no—
162#491—22no—
163#487C22×C15114yes—
164#486—22no—
165#481—24no—
166#476C22×C15118yes—
167#431C22×C15112yes—
168#419—22no—
169C4×M16C22×C15111yescharacteristic
170#332C22×C15114yes—
171D4⋊C8C22×C15118yes—
172C2×#41—24no—
173C2×#41—22no—
174C22×Q8—21no—
175C2×M16—21no—
176C4⋊Q8—22no—
177C4⋊Q8—21no—
178C4⋊Q8D4×C15112yes—
179C4⋊Q8C23×C15112yes—
180C4⋊Q8C23×C15112yes—
181#127—22no—
182#127D4×C15112yes—
183#125—22no—
184#125D4×C15112yes—
185#124—22no—
186#123—28no—
187C22⋊Q8—28no—
188C22⋊Q8—22no—
189C22⋊Q8—24no—
190#121—28no—
191#121—28no—
192#121—24no—
193#121—22no—
194#121D4×C15114yes—
195C4×Q8—22no—
196C4×D4—24no—
197C4×D4—22no—
198C4×D4C23×C15114yes—
199#117D4×C15112yes—
200C2×C4⋊C4—24no—
201C2×C4⋊C4—22no—
202C2×C42C23×C15111yescharacteristic
203#106—28no—
204C4⋊C8C23×C15114yes—
205#103—28no—
206#102—28no—
207C22⋊C8—22no—
208#97—21no—
209C4×C8—22no—
210C4×C8C23×C15112yes—
211#41—84no—
212#41—88no—
213C2×Q8—22no—
214C2×Q8—22no—
215C2×Q8—22no—
216C2×Q8—44no—
217C2×Q8—41no—
218C2×D4—28no—
219C2×D4—24no—
220C2×D4—22no—
221C2×D4—22no—
222C2×D4C2×D4×C15114yes—
223C22×C4—28no—
224C22×C4—24no—
225C22×C4—41no—
226C22×C4C2×D4×C15112yes—
227C22×C4C2×D4×C15111yescharacteristic
228M16—42no—
229C2×C8—24no—
230C2×C8—22no—
231C4⋊C4—28no—
232C4⋊C4—22no—
233C4⋊C4—24no—
234C4⋊C4—22no—
235C4⋊C4—24no—
236C4⋊C4—42no—
237C4⋊C4C2×D4×C15114yes—
238C4⋊C4C2×D4×C15114yes—
239C22⋊C4—28no—
240C22⋊C4—22no—
241C22⋊C4—24no—
242C22⋊C4—24no—
243C42—22no—
244C42C2×D4×C15112yes—
245C42C2×D4×C15111yescharacteristic
246C42C24×C15111yescharacteristic
247C23—24no—
248C23#120×C15111yescharacteristic
249Q8—44no—
250Q8—44no—
251Q8—82no—
252Q8—82no—
253D4—28no—
254D4—44no—
255D4—82no—
256D4—84no—
257D4—88no—
258C2×C4—22no—
259C2×C4—24no—
260C2×C4—24no—
261C2×C4—24no—
262C2×C4—48no—
263C2×C4—42no—
264C2×C4—88no—
265C2×C4—82no—
266C2×C4#120×C15112yes—
267C2×C4#120×C15111yescharacteristic
268C2×C4C22×D4×C15111yescharacteristic
269C2×C4C22×D4×C15112yes—
270C8—42no—
271C8—44no—
272C22—22no—
273C22—21no—
274C22—44no—
275C22—44no—
276C22—44no—
277C22C2×#120×C15111yescharacteristic
278C4—22no—
279C4—21no—
280C4—44no—
281C4—44no—
282C4—82no—
283C4#454×C15112yes—
284C4#577×C15114yes—
285C2—41no—
286C2—84no—
287C2#3009×C15112yes—
288C2C2×#454×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3548×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. #3227×C151C2semidirect
3. #3139×C151C2semidirect
4. #1635×C151C2semidirect
5. #1544×C151C2semidirect
6. #1484×C151C2semidirect
144. #18728C151direct (N × H)
145. C151#18728direct (N × H)
147. #3227C2×C151semidirect
148. #3139C2×C151semidirect
149. #1635C2×C151semidirect
150. #1544C2×C151semidirect
151. #1484C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3548×C1512
#3227×C1512
#3139×C1512
#1635×C1512
#1544×C1512
#1484×C1512
#18728151