Finite Group Databasebeta

← C151×#8049 #50312974

Subgroups — C151×#8049 #50312974

Order 38656.

954 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#407×C151C211yesmaximal, characteristic
2#2280×C151C212yesmaximal
3#1297×C151C214yesmaximal, complemented
4C24×C4×C151C2211yescharacteristic
5C22×M16×C151C412yescomplemented
6C2×#117×C151—22no—
7#407×C151—22no—
8#407×C151C412yescomplemented
9#407×C151C2212yes—
10C2×C22⋊C8×C151—22no—
11#381×C151C414yescomplemented
12#380×C151—22no—
13#380×C151C414yescomplemented
14#379×C151—22no—
15C4×C22⋊C4×C151—22no—
16C4×C22⋊C4×C151C2214yes—
17C25×C151D411yescharacteristic
18C23×C4×C151—44no—
19C23×C4×C151C2×C412yes—
20C23×C4×C151C2×C412yes—
21C23×C4×C151C2×C411yescharacteristic
22C23×C4×C151C2×C411yescharacteristic
23C23×C4×C151D412yes—
24C23×C4×C151D412yes—
25C23×C4×C151D411yescharacteristic
26C23×C4×C151Q811yescharacteristic
27C23×C4×C151Q811yescharacteristic
28C23×C4×C151C2311yescharacteristic
29C2×M16×C151—22no—
30C2×M16×C151—44no—
31C2×M16×C151C2×C414yes—
32C22×C8×C151—22no—
33#117×C151—48no—
34C2×C4⋊C4×C151—24no—
35C2×C22⋊C4×C151—24no—
36C2×C22⋊C4×C151—24no—
37C2×C22⋊C4×C151—24no—
38C2×C42×C151—24no—
39C22⋊C8×C151—24no—
40C22⋊C8×C151—24no—
41#95×C151—24no—
42#95×C151C2×C418yes—
43C24×C151—42no—
44C24×C151—44no—
45C24×C151C22⋊C412yes—
46C24×C151C22⋊C412yes—
47C24×C151C4⋊C411yescharacteristic
48C24×C151C4⋊C411yescharacteristic
49C24×C151C2×D411yescharacteristic
50C22×C4×C151—28no—
51C22×C4×C151—24no—
52C22×C4×C151—28no—
53C22×C4×C151—44no—
54C22×C4×C151—42no—
55C22×C4×C151—42no—
56C22×C4×C151—44no—
57C22×C4×C151—42no—
58C22×C4×C151—42no—
59C22×C4×C151—44no—
60C22×C4×C151—42no—
61C22×C4×C151C4211yescharacteristic
62C22×C4×C151C4211yescharacteristic
63C22×C4×C151C4212yes—
64C22×C4×C151C22⋊C412yes—
65C22×C4×C151C22⋊C412yes—
66C22×C4×C151C22⋊C411yescharacteristic
67C22×C4×C151C22⋊C412yes—
68C22×C4×C151C22⋊C411yescharacteristic
69C22×C4×C151C4⋊C411yescharacteristic
70C22×C4×C151C4⋊C412yes—
71C22×C4×C151C4⋊C412yes—
72C22×C4×C151C4⋊C411yescharacteristic
73C22×C4×C151C4⋊C412yes—
74C22×C4×C151C4⋊C412yes—
75C22×C4×C151C22×C411yescharacteristic
76C22×C4×C151C22×C412yes—
77C22×C4×C151C2×D412yes—
78C22×C4×C151C2×Q811yescharacteristic
79M16×C151—44no—
80M16×C151—44no—
81C2×C8×C151—24no—
82C2×C8×C151—44no—
83C4⋊C4×C151—48no—
84C22⋊C4×C151—48no—
85C22⋊C4×C151—48no—
86C22⋊C4×C151—48no—
87C42×C151—48no—
88C23×C151—24no—
89C23×C151—22no—
90C23×C151—24no—
91C23×C151—24no—
92C23×C151—24no—
93C23×C151—42no—
94C23×C151—42no—
95C23×C151—42no—
96C23×C151—42no—
97C23×C151—42no—
98C23×C151—41no—
99C23×C151—41no—
100C23×C151—416no—
101C23×C151#9512yes—
102C23×C151#9511yescharacteristic
103C23×C151#9511yescharacteristic
104C23×C151C2×C22⋊C412yes—
105C23×C151C2×C4⋊C411yescharacteristic
106C2×C4×C151—22no—
107C2×C4×C151—24no—
108C2×C4×C151—24no—
109C2×C4×C151—22no—
110C2×C4×C151—22no—
111C2×C4×C151—24no—
112C2×C4×C151—24no—
113C2×C4×C151—22no—
114C2×C4×C151—22no—
115C2×C4×C151—24no—
116C2×C4×C151—42no—
117C2×C4×C151—42no—
118C2×C4×C151—41no—
119C2×C4×C151—42no—
120C2×C4×C151—42no—
121C2×C4×C151—42no—
122C2×C4×C151—41no—
123C2×C4×C151—48no—
124C2×C4×C151—48no—
125C2×C4×C151—48no—
126C2×C4×C151#9511yescharacteristic
127C2×C4×C151#9512yes—
128C2×C4×C151#9511yescharacteristic
129C2×C4×C151#9914yes—
130C2×C4×C151C2×C4211yescharacteristic
131C2×C4×C151C2×C22⋊C411yescharacteristic
132C2×C4×C151C2×C4⋊C412yes—
133C8×C151—44no—
134C22×C151—22no—
135C22×C151—22no—
136C22×C151—22no—
137C22×C151—22no—
138C22×C151—22no—
139C22×C151—22no—
140C22×C151—22no—
141C22×C151—21no—
142C22×C151—22no—
143C22×C151—21no—
144C22×C151—44no—
145C22×C151—48no—
146C22×C151—48no—
147C22×C151—44no—
148C22×C151—44no—
149C22×C151#34212yes—
150C22×C151C2×#9511yescharacteristic
151C22×C151#42114yes—
152C4×C151—21no—
153C4×C151—22no—
154C4×C151—21no—
155C4×C151—22no—
156C4×C151—88no—
157C4×C151#34212yes—
158C4×C151C2×#9912yes—
159C2×C151—24no—
160C2×C151—22no—
161C2×C151—42no—
162C2×C151—41no—
163C2×C151—41no—
164C2×C151#173312yes—
165C2×C151C2×#34211yescharacteristic
166#8049C15111yesmaximal, characteristic, direct product factor, Sylow
167C151#804911yescharacteristic, direct product factor, Sylow
168C2×#407C2×C15111yescharacteristic
169#2280C2×C15112yes—
170#1297C2×C15114yescomplemented
171C24×C4C22×C15111yescharacteristic
172C22×M16C4×C15112yescomplemented
173C2×#117—22no—
174#407—22no—
175#407C4×C15112yescomplemented
176#407C22×C15112yes—
177C2×C22⋊C8—22no—
178#381C4×C15114yescomplemented
179#380—22no—
180#380C4×C15114yescomplemented
181#379—22no—
182C4×C22⋊C4—22no—
183C4×C22⋊C4C22×C15114yes—
184C25D4×C15111yescharacteristic
185C23×C4—44no—
186C23×C4C2×C4×C15111yescharacteristic
187C23×C4C2×C4×C15111yescharacteristic
188C23×C4C2×C4×C15112yes—
189C23×C4C2×C4×C15112yes—
190C23×C4D4×C15112yes—
191C23×C4D4×C15111yescharacteristic
192C23×C4D4×C15112yes—
193C23×C4Q8×C15111yescharacteristic
194C23×C4Q8×C15111yescharacteristic
195C23×C4C23×C15111yescharacteristic
196C2×M16—22no—
197C2×M16—44no—
198C2×M16C2×C4×C15114yes—
199C22×C8—22no—
200#117—48no—
201C2×C4⋊C4—24no—
202C2×C22⋊C4—24no—
203C2×C22⋊C4—24no—
204C2×C22⋊C4—24no—
205C2×C42—24no—
206C22⋊C8—24no—
207C22⋊C8—24no—
208#95—24no—
209#95C2×C4×C15118yes—
210C24—42no—
211C24—44no—
212C24C22⋊C4×C15112yes—
213C24C22⋊C4×C15112yes—
214C24C4⋊C4×C15111yescharacteristic
215C24C4⋊C4×C15111yescharacteristic
216C24C2×D4×C15111yescharacteristic
217C22×C4—28no—
218C22×C4—24no—
219C22×C4—28no—
220C22×C4—44no—
221C22×C4—42no—
222C22×C4—42no—
223C22×C4—44no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4—44no—
227C22×C4—42no—
228C22×C4C42×C15111yescharacteristic
229C22×C4C42×C15111yescharacteristic
230C22×C4C42×C15112yes—
231C22×C4C22⋊C4×C15112yes—
232C22×C4C22⋊C4×C15112yes—
233C22×C4C22⋊C4×C15111yescharacteristic
234C22×C4C22⋊C4×C15112yes—
235C22×C4C22⋊C4×C15111yescharacteristic
236C22×C4C4⋊C4×C15111yescharacteristic
237C22×C4C4⋊C4×C15112yes—
238C22×C4C4⋊C4×C15112yes—
239C22×C4C4⋊C4×C15111yescharacteristic
240C22×C4C4⋊C4×C15112yes—
241C22×C4C4⋊C4×C15112yes—
242C22×C4C22×C4×C15111yescharacteristic
243C22×C4C22×C4×C15112yes—
244C22×C4C2×D4×C15112yes—
245C22×C4C2×Q8×C15111yescharacteristic
246M16—44no—
247M16—44no—
248C2×C8—24no—
249C2×C8—44no—
250C4⋊C4—48no—
251C22⋊C4—48no—
252C22⋊C4—48no—
253C22⋊C4—48no—
254C42—48no—
255C23—24no—
256C23—22no—
257C23—24no—
258C23—24no—
259C23—24no—
260C23—42no—
261C23—41no—
262C23—41no—
263C23—42no—
264C23—42no—
265C23—42no—
266C23—42no—
267C23—416no—
268C23#95×C15111yescharacteristic
269C23#95×C15112yes—
270C23#95×C15111yescharacteristic
271C23C2×C22⋊C4×C15112yes—
272C23C2×C4⋊C4×C15111yescharacteristic
273C2×C4—22no—
274C2×C4—24no—
275C2×C4—24no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—24no—
279C2×C4—24no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—24no—
283C2×C4—41no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—41no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—48no—
291C2×C4—48no—
292C2×C4—48no—
293C2×C4#95×C15111yescharacteristic
294C2×C4#95×C15112yes—
295C2×C4#95×C15111yescharacteristic
296C2×C4#99×C15114yes—
297C2×C4C2×C42×C15111yescharacteristic
298C2×C4C2×C22⋊C4×C15111yescharacteristic
299C2×C4C2×C4⋊C4×C15112yes—
300C8—44no—
301C22—22no—
302C22—22no—
303C22—22no—
304C22—22no—
305C22—22no—
306C22—22no—
307C22—22no—
308C22—21no—
309C22—22no—
310C22—21no—
311C22—44no—
312C22—48no—
313C22—48no—
314C22—44no—
315C22—44no—
316C22#342×C15112yes—
317C22C2×#95×C15111yescharacteristic
318C22#421×C15114yes—
319C4—21no—
320C4—22no—
321C4—21no—
322C4—22no—
323C4—88no—
324C4#342×C15112yes—
325C4C2×#99×C15112yes—
326C2—24no—
327C2—22no—
328C2—42no—
329C2—41no—
330C2—41no—
331C2#1733×C15112yes—
332C2C2×#342×C15111yescharacteristic
subgroupG/H
centerC2×C4×C151C2×C22⋊C4
commutatorC2×C4C2×C42×C151
Frattini, cosocleC23×C4C23×C151
socleC22×C151C2×#95
prime radicalC25×C151D4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C151 ◁ C24×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1297×C151C2semidirect
5. C22×M16×C151C4semidirect
8. #407×C151C4semidirect
11. #381×C151C4semidirect
13. #380×C151C4semidirect
166. #8049C151direct (N × H)
167. C151#8049direct (N × H)
170. #1297C2×C151semidirect
172. C22×M16C4×C151semidirect
175. #407C4×C151semidirect
178. #381C4×C151semidirect
180. #380C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#407×C1512
#2280×C1512
#1297×C1512
#8049151