Finite Group Databasebeta

← C151×#11846 #50316771

Subgroups — C151×#11846 #50316771

Order 38656.

382 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 98 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#2611×C151C211yesmaximal, characteristic
2#1820×C151C211yesmaximal, characteristic
3#1458×C151C211yesmaximal, characteristic
4#1352×C151C212yesmaximal
5#1344×C151C212yesmaximal
6C2×#125×C151C411yescharacteristic, complemented
7C2×#117×C151C2211yescharacteristic
8#431×C151—21no—
9#400×C151C411yescharacteristic, complemented
10#399×C151C2211yescharacteristic
11#398×C151C411yescharacteristic, complemented
12#397×C151C2211yescharacteristic
13#389×C151—21no—
14#388×C151—21no—
15#387×C151—21no—
16#385×C151—21no—
17#381×C151—21no—
18#376×C151C411yescharacteristic, complemented
19#342×C151—21no—
20#342×C151C2212yes—
21#324×C151—21no—
22#323×C151C2212yes—
23C23×C4×C151D411yescharacteristic
24#125×C151—41no—
25#125×C151—41no—
26#117×C151—41no—
27#117×C151—41no—
28C2×C4⋊C4×C151—21no—
29C2×C4⋊C4×C151—21no—
30C2×C4⋊C4×C151—21no—
31C2×C4⋊C4×C151—21no—
32C2×C4⋊C4×C151C2×C411yescharacteristic
33C2×C4⋊C4×C151C2×C411yescharacteristic
34C2×C4⋊C4×C151C2×C411yescharacteristic
35C2×C4⋊C4×C151D411yescharacteristic
36C2×C22⋊C4×C151—21no—
37C2×C22⋊C4×C151—21no—
38C2×C22⋊C4×C151—22no—
39C2×C22⋊C4×C151D411yescharacteristic
40C2×C22⋊C4×C151C2311yescharacteristic
41C2×C42×C151—21no—
42C2×C42×C151C2×C411yescharacteristic
43C2×C42×C151D411yescharacteristic
44C4⋊C8×C151—41no—
45C22⋊C8×C151—22no—
46C4×C8×C151—41no—
47#95×C151—21no—
48#95×C151—21no—
49#95×C151—21no—
50#95×C151—21no—
51#95×C151—21no—
52#95×C151—41no—
53#95×C151—41no—
54#95×C151C2×C411yescharacteristic
55#95×C151C2×C411yescharacteristic
56C24×C151C2×D411yescharacteristic
57C22×C4×C151—21no—
58C22×C4×C151—22no—
59C22×C4×C151—21no—
60C22×C4×C151—21no—
61C22×C4×C151—21no—
62C22×C4×C151—21no—
63C22×C4×C151—21no—
64C22×C4×C151—41no—
65C22×C4×C151—42no—
66C22×C4×C151C22⋊C411yescharacteristic
67C22×C4×C151C22⋊C411yescharacteristic
68C22×C4×C151C22⋊C411yescharacteristic
69C22×C4×C151C22⋊C411yescharacteristic
70C22×C4×C151C22×C411yescharacteristic
71C22×C4×C151C2×D411yescharacteristic
72C2×C8×C151—42no—
73C4⋊C4×C151—41no—
74C4⋊C4×C151—41no—
75C4⋊C4×C151—41no—
76C4⋊C4×C151—41no—
77C4⋊C4×C151—42no—
78C4⋊C4×C151—42no—
79C4⋊C4×C151—42no—
80C4⋊C4×C151—41no—
81C4⋊C4×C151—41no—
82C22⋊C4×C151—41no—
83C22⋊C4×C151—41no—
84C22⋊C4×C151—42no—
85C22⋊C4×C151—42no—
86C22⋊C4×C151—42no—
87C22⋊C4×C151—42no—
88C42×C151—21no—
89C42×C151—21no—
90C42×C151—21no—
91C42×C151—21no—
92C42×C151—42no—
93C23×C151—21no—
94C23×C151—21no—
95C23×C151—41no—
96C23×C151—41no—
97C23×C151C2×C22⋊C411yescharacteristic
98C23×C151#13512yes—
99C2×C4×C151—21no—
100C2×C4×C151—21no—
101C2×C4×C151—22no—
102C2×C4×C151—21no—
103C2×C4×C151—21no—
104C2×C4×C151—21no—
105C2×C4×C151—21no—
106C2×C4×C151—21no—
107C2×C4×C151—21no—
108C2×C4×C151—21no—
109C2×C4×C151—42no—
110C2×C4×C151—42no—
111C2×C4×C151—41no—
112C2×C4×C151—41no—
113C2×C4×C151—41no—
114C2×C4×C151—41no—
115C2×C4×C151—41no—
116C2×C4×C151—41no—
117C2×C4×C151—41no—
118C2×C4×C151—41no—
119C2×C4×C151—41no—
120C2×C4×C151—41no—
121C2×C4×C151—41no—
122C2×C4×C151—41no—
123C2×C4×C151—41no—
124C2×C4×C151—41no—
125C2×C4×C151—41no—
126C2×C4×C151—82no—
127C2×C4×C151—82no—
128C2×C4×C151—82no—
129C2×C4×C151#9911yescharacteristic
130C2×C4×C151#9911yescharacteristic
131C8×C151—82no—
132C22×C151—21no—
133C22×C151—21no—
134C22×C151—22no—
135C22×C151—42no—
136C22×C151—41no—
137C22×C151—41no—
138C22×C151—81no—
139C22×C151C2×#9911yescharacteristic
140C22×C151#41611yescharacteristic
141C22×C151#42111yescharacteristic
142C4×C151—21no—
143C4×C151—21no—
144C4×C151—42no—
145C4×C151—41no—
146C4×C151—41no—
147C4×C151—41no—
148C4×C151—41no—
149C4×C151—41no—
150C4×C151—81no—
151C4×C151—81no—
152C4×C151—81no—
153C4×C151—162no—
154C2×C151—21no—
155C2×C151—21no—
156C2×C151—42no—
157C2×C151#151611yescharacteristic
158C2×C151#212311yescharacteristic
159C2×C151#212611yescharacteristic
160#11846C15111yesmaximal, characteristic, direct product factor, Sylow
161C151#1184611yescharacteristic, direct product factor, Sylow
162#2611C2×C15111yescharacteristic
163#1820C2×C15111yescharacteristic
164#1458C2×C15111yescharacteristic
165#1352C2×C15112yes—
166#1344C2×C15112yes—
167C2×#125C4×C15111yescharacteristic, complemented
168C2×#117C22×C15111yescharacteristic
169#431—21no—
170#400C4×C15111yescharacteristic, complemented
171#399C22×C15111yescharacteristic
172#398C4×C15111yescharacteristic, complemented
173#397C22×C15111yescharacteristic
174#389—21no—
175#388—21no—
176#387—21no—
177#385—21no—
178#381—21no—
179#376C4×C15111yescharacteristic, complemented
180#342—21no—
181#342C22×C15112yes—
182#324—21no—
183#323C22×C15112yes—
184C23×C4D4×C15111yescharacteristic
185#125—41no—
186#125—41no—
187#117—41no—
188#117—41no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4C2×C4×C15111yescharacteristic
194C2×C4⋊C4C2×C4×C15111yescharacteristic
195C2×C4⋊C4C2×C4×C15111yescharacteristic
196C2×C4⋊C4D4×C15111yescharacteristic
197C2×C22⋊C4—21no—
198C2×C22⋊C4—21no—
199C2×C22⋊C4—22no—
200C2×C22⋊C4D4×C15111yescharacteristic
201C2×C22⋊C4C23×C15111yescharacteristic
202C2×C42—21no—
203C2×C42C2×C4×C15111yescharacteristic
204C2×C42D4×C15111yescharacteristic
205C4⋊C8—41no—
206C22⋊C8—22no—
207C4×C8—41no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—41no—
214#95—41no—
215#95C2×C4×C15111yescharacteristic
216#95C2×C4×C15111yescharacteristic
217C24C2×D4×C15111yescharacteristic
218C22×C4—21no—
219C22×C4—22no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—41no—
226C22×C4—42no—
227C22×C4C22⋊C4×C15111yescharacteristic
228C22×C4C22⋊C4×C15111yescharacteristic
229C22×C4C22⋊C4×C15111yescharacteristic
230C22×C4C22⋊C4×C15111yescharacteristic
231C22×C4C22×C4×C15111yescharacteristic
232C22×C4C2×D4×C15111yescharacteristic
233C2×C8—42no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C4⋊C4—42no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C22⋊C4—41no—
244C22⋊C4—41no—
245C22⋊C4—42no—
246C22⋊C4—42no—
247C22⋊C4—42no—
248C22⋊C4—42no—
249C42—21no—
250C42—21no—
251C42—21no—
252C42—21no—
253C42—42no—
254C23—21no—
255C23—21no—
256C23—41no—
257C23—41no—
258C23C2×C22⋊C4×C15111yescharacteristic
259C23#135×C15112yes—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—82no—
288C2×C4—82no—
289C2×C4—82no—
290C2×C4#99×C15111yescharacteristic
291C2×C4#99×C15111yescharacteristic
292C8—82no—
293C22—21no—
294C22—21no—
295C22—22no—
296C22—42no—
297C22—41no—
298C22—41no—
299C22—81no—
300C22C2×#99×C15111yescharacteristic
301C22#416×C15111yescharacteristic
302C22#421×C15111yescharacteristic
303C4—21no—
304C4—21no—
305C4—42no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—81no—
312C4—81no—
313C4—81no—
314C4—162no—
315C2—21no—
316C2—21no—
317C2—42no—
318C2#1516×C15111yescharacteristic
319C2#2123×C15111yescharacteristic
320C2#2126×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#99
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×C22⋊C4C23×C151
prime radicalC24×C151C2×D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C22×C4×C151 ◁ C2×#117×C151 ◁ G

Complements

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

NH ≅ G/Ntype
6. C2×#125×C151C4semidirect
9. #400×C151C4semidirect
11. #398×C151C4semidirect
18. #376×C151C4semidirect
160. #11846C151direct (N × H)
161. C151#11846direct (N × H)
167. C2×#125C4×C151semidirect
170. #400C4×C151semidirect
172. #398C4×C151semidirect
179. #376C4×C151semidirect

Maximal subgroups

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

subgroupindex
#2611×C1512
#1820×C1512
#1458×C1512
#1352×C1512
#1344×C1512
#11846151