Finite Group Databasebeta

← C151×#7588 #50312513

Subgroups — C151×#7588 #50312513

Order 38656.

478 conjugacy classes of subgroups.

The subgroup lattice has 280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C4⋊Q8×C151C211yesmaximal, characteristic
2#1831×C151C211yesmaximal, characteristic
3#1744×C151C211yesmaximal, characteristic
4#1271×C151C214yesmaximal
5C2×C4⋊Q8×C151C411yescharacteristic
6C2×C4×Q8×C151—21no—
7C2×C4⋊C8×C151—21no—
8C2×C4×C8×C151—21no—
9#391×C151—21no—
10#389×C151—21no—
11#389×C151C2212yes—
12#384×C151C411yescharacteristic
13C4×C4⋊C4×C151—21no—
14C4×C4⋊C4×C151C412yes—
15C43×C151C2211yescharacteristic
16#336×C151—21no—
17#336×C151—21no—
18#336×C151C2212yes—
19#336×C151C2212yes—
20C22×Q8×C151—21no—
21C22×C8×C151—22no—
22C22×C8×C151—22no—
23C4⋊Q8×C151—22no—
24C4⋊Q8×C151C814yescomplemented
25C4×Q8×C151—42no—
26C4×Q8×C151—42no—
27C2×C4⋊C4×C151—21no—
28C2×C4⋊C4×C151—21no—
29C2×C4⋊C4×C151—21no—
30C2×C4⋊C4×C151—22no—
31C2×C4⋊C4×C151C2×C412yes—
32C2×C4⋊C4×C151C2×C412yes—
33C2×C42×C151—22no—
34C2×C42×C151C2×C411yescharacteristic
35C2×C42×C151C2×C411yescharacteristic
36C2×C42×C151D411yescharacteristic
37C2×C42×C151D411yescharacteristic
38C2×C42×C151D411yescharacteristic
39C2×C42×C151D411yescharacteristic
40C2×C42×C151C2311yescharacteristic
41C4⋊C8×C151—42no—
42C4×C8×C151—24no—
43#95×C151—22no—
44#95×C151—22no—
45C2×Q8×C151—24no—
46C2×Q8×C151—42no—
47C2×Q8×C151—42no—
48C22×C4×C151—22no—
49C22×C4×C151—22no—
50C22×C4×C151C22⋊C411yescharacteristic
51C22×C4×C151C22⋊C411yescharacteristic
52C22×C4×C151C22⋊C411yescharacteristic
53C22×C4×C151C22⋊C411yescharacteristic
54C22×C4×C151C22×C411yescharacteristic
55C22×C4×C151C2×D411yescharacteristic
56C22×C4×C151C2×D411yescharacteristic
57C2×C8×C151—24no—
58C2×C8×C151—42no—
59C2×C8×C151—42no—
60C2×C8×C151—42no—
61C2×C8×C151—42no—
62C2×C8×C151—42no—
63C4⋊C4×C151—24no—
64C4⋊C4×C151—22no—
65C4⋊C4×C151—42no—
66C4⋊C4×C151—42no—
67C4⋊C4×C151—42no—
68C4⋊C4×C151—42no—
69C4⋊C4×C151—42no—
70C4⋊C4×C151C2×C814yes—
71C42×C151—22no—
72C42×C151—22no—
73C42×C151—22no—
74C42×C151—41no—
75C42×C151—41no—
76C42×C151—44no—
77C42×C151C2×C812yes—
78C42×C151M1612yes—
79C42×C151D812yes—
80C42×C151SD1612yes—
81C23×C151C2×C22⋊C411yescharacteristic
82Q8×C151—48no—
83C2×C4×C151—21no—
84C2×C4×C151—21no—
85C2×C4×C151—21no—
86C2×C4×C151—21no—
87C2×C4×C151—21no—
88C2×C4×C151—21no—
89C2×C4×C151—21no—
90C2×C4×C151—21no—
91C2×C4×C151—21no—
92C2×C4×C151—21no—
93C2×C4×C151—21no—
94C2×C4×C151—21no—
95C2×C4×C151—24no—
96C2×C4×C151—42no—
97C2×C4×C151—42no—
98C2×C4×C151—42no—
99C2×C4×C151—42no—
100C2×C4×C151—42no—
101C2×C4×C151C22⋊C812yes—
102C2×C4×C151C22⋊C812yes—
103C2×C4×C151#10112yes—
104C2×C4×C151#10212yes—
105C2×C4×C151#10212yes—
106C2×C4×C151#10412yes—
107C2×C4×C151C22×C811yescharacteristic
108C2×C4×C151C2×M1611yescharacteristic
109C2×C4×C151C2×D811yescharacteristic
110C2×C4×C151C2×SD1611yescharacteristic
111C2×C4×C151#13712yes—
112C8×C151—44no—
113C8×C151—82no—
114C22×C151C2×C22⋊C811yescharacteristic
115C22×C151#41011yescharacteristic
116C22×C151C2×#10111yescharacteristic
117C22×C151C2×#10211yescharacteristic
118C22×C151#41911yescharacteristic
119C22×C151C2×#10411yescharacteristic
120C22×C151#42111yescharacteristic
121C4×C151—22no—
122C4×C151—21no—
123C4×C151—21no—
124C4×C151—22no—
125C4×C151—22no—
126C4×C151—21no—
127C4×C151—21no—
128C4×C151—22no—
129C4×C151—44no—
130C4×C151—82no—
131C4×C151D4⋊C814yes—
132C2×C151#146111yescharacteristic
133C2×C151C2×D4⋊C811yescharacteristic
134C2×C151#147911yescharacteristic
135C2×C151#150611yescharacteristic
136C2×C151#151711yescharacteristic
137C2×C151#153111yescharacteristic
138C2×C151#154611yescharacteristic
139#7588C15111yesmaximal, characteristic, direct product factor, Sylow
140C151#758811yescharacteristic, direct product factor, Sylow
141C4×C4⋊Q8C2×C15111yescharacteristic
142#1831C2×C15111yescharacteristic
143#1744C2×C15111yescharacteristic
144#1271C2×C15114yes—
145C2×C4⋊Q8C4×C15111yescharacteristic
146C2×C4×Q8—21no—
147C2×C4⋊C8—21no—
148C2×C4×C8—21no—
149#391—21no—
150#389—21no—
151#389C22×C15112yes—
152#384C4×C15111yescharacteristic
153C4×C4⋊C4—21no—
154C4×C4⋊C4C4×C15112yes—
155C43C22×C15111yescharacteristic
156#336—21no—
157#336—21no—
158#336C22×C15112yes—
159#336C22×C15112yes—
160C22×Q8—21no—
161C22×C8—22no—
162C22×C8—22no—
163C4⋊Q8—22no—
164C4⋊Q8C8×C15114yescomplemented
165C4×Q8—42no—
166C4×Q8—42no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4C2×C4×C15112yes—
172C2×C4⋊C4C2×C4×C15112yes—
173C2×C42—22no—
174C2×C42C2×C4×C15111yescharacteristic
175C2×C42C2×C4×C15111yescharacteristic
176C2×C42D4×C15111yescharacteristic
177C2×C42D4×C15111yescharacteristic
178C2×C42D4×C15111yescharacteristic
179C2×C42D4×C15111yescharacteristic
180C2×C42C23×C15111yescharacteristic
181C4⋊C8—42no—
182C4×C8—24no—
183#95—22no—
184#95—22no—
185C2×Q8—24no—
186C2×Q8—42no—
187C2×Q8—42no—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4C22⋊C4×C15111yescharacteristic
191C22×C4C22⋊C4×C15111yescharacteristic
192C22×C4C22⋊C4×C15111yescharacteristic
193C22×C4C22⋊C4×C15111yescharacteristic
194C22×C4C22×C4×C15111yescharacteristic
195C22×C4C2×D4×C15111yescharacteristic
196C22×C4C2×D4×C15111yescharacteristic
197C2×C8—24no—
198C2×C8—42no—
199C2×C8—42no—
200C2×C8—42no—
201C2×C8—42no—
202C2×C8—42no—
203C4⋊C4—24no—
204C4⋊C4—22no—
205C4⋊C4—42no—
206C4⋊C4—42no—
207C4⋊C4—42no—
208C4⋊C4—42no—
209C4⋊C4—42no—
210C4⋊C4C2×C8×C15114yes—
211C42—22no—
212C42—22no—
213C42—22no—
214C42—41no—
215C42—41no—
216C42—44no—
217C42C2×C8×C15112yes—
218C42M16×C15112yes—
219C42D8×C15112yes—
220C42SD16×C15112yes—
221C23C2×C22⋊C4×C15111yescharacteristic
222Q8—48no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—24no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4C22⋊C8×C15112yes—
242C2×C4C22⋊C8×C15112yes—
243C2×C4#101×C15112yes—
244C2×C4#102×C15112yes—
245C2×C4#102×C15112yes—
246C2×C4#104×C15112yes—
247C2×C4C22×C8×C15111yescharacteristic
248C2×C4C2×M16×C15111yescharacteristic
249C2×C4C2×D8×C15111yescharacteristic
250C2×C4C2×SD16×C15111yescharacteristic
251C2×C4#137×C15112yes—
252C8—44no—
253C8—82no—
254C22C2×C22⋊C8×C15111yescharacteristic
255C22#410×C15111yescharacteristic
256C22C2×#101×C15111yescharacteristic
257C22C2×#102×C15111yescharacteristic
258C22#419×C15111yescharacteristic
259C22C2×#104×C15111yescharacteristic
260C22#421×C15111yescharacteristic
261C4—21no—
262C4—21no—
263C4—22no—
264C4—22no—
265C4—21no—
266C4—21no—
267C4—22no—
268C4—22no—
269C4—44no—
270C4—82no—
271C4D4⋊C8×C15114yes—
272C2#1461×C15111yescharacteristic
273C2C2×D4⋊C8×C15111yescharacteristic
274C2#1479×C15111yescharacteristic
275C2#1506×C15111yescharacteristic
276C2#1517×C15111yescharacteristic
277C2#1531×C15111yescharacteristic
278C2#1546×C15111yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C151C2×C22⋊C4
commutatorC2×C4C22×C8×C151
Frattini, cosocleC2×C42C23×C151
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C151 ◁ C43×C151 ◁ G

Complements

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

NH ≅ G/Ntype
24. C4⋊Q8×C151C8semidirect
139. #7588C151direct (N × H)
140. C151#7588direct (N × H)
164. C4⋊Q8C8×C151semidirect

Maximal subgroups

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

subgroupindex
C4×C4⋊Q8×C1512
#1831×C1512
#1744×C1512
#1271×C1512
#7588151