Finite Group Databasebeta

← C151×#11882 #50316807

Subgroups — C151×#11882 #50316807

Order 38656.

476 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 118 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#2548×C151C211yesmaximal, characteristic
2#1801×C151C211yesmaximal, characteristic, complemented
3#1461×C151C211yesmaximal, characteristic, complemented
4#1345×C151C214yesmaximal, complemented
5C2×#127×C151C411yescharacteristic
6C2×#124×C151—21no—
7C2×C4×Q8×C151C2211yescharacteristic
8#431×C151—21no—
9#423×C151—21no—
10C2×#101×C151—21no—
11#394×C151C412yes—
12#394×C151C2212yes—
13#390×C151—21no—
14#390×C151—21no—
15#390×C151—21no—
16C4×C4⋊C4×C151C411yescharacteristic
17#343×C151C2212yes—
18#324×C151—21no—
19#324×C151C2212yes—
20C22×Q8×C151D411yescharacteristic
21C22×D4×C151—21no—
22C22×D4×C151—21no—
23C22×D4×C151C2×C412yes—
24C2×M16×C151—22no—
25#127×C151—41no—
26#127×C151—41no—
27#124×C151—42no—
28#124×C151—42no—
29C4×Q8×C151—41no—
30C4×Q8×C151—41no—
31C2×C4⋊C4×C151—21no—
32C2×C4⋊C4×C151C2×C411yescharacteristic
33C2×C4⋊C4×C151D411yescharacteristic
34C2×C4⋊C4×C151C2311yescharacteristic
35C2×C22⋊C4×C151—22no—
36C2×C22⋊C4×C151—22no—
37C2×C22⋊C4×C151—22no—
38C2×C22⋊C4×C151—22no—
39C2×C42×C151—21no—
40C2×C42×C151C2×C411yescharacteristic
41C2×C42×C151D411yescharacteristic
42C2×C42×C151D411yescharacteristic
43C4⋊C8×C151—41no—
44C4⋊C8×C151—41no—
45C4⋊C8×C151—41no—
46#101×C151—42no—
47C22⋊C8×C151—22no—
48C4×C8×C151—41no—
49#95×C151C2×C412yes—
50C24×C151—22no—
51C2×Q8×C151—41no—
52C2×Q8×C151—41no—
53C2×Q8×C151D812yes—
54C2×Q8×C151SD1612yes—
55C2×D4×C151—42no—
56C2×D4×C151—42no—
57C2×D4×C151—42no—
58C2×D4×C151—42no—
59C2×D4×C151—42no—
60C2×D4×C151—41no—
61C2×D4×C151—41no—
62C2×D4×C151—42no—
63C2×D4×C151—82no—
64C22×C4×C151—22no—
65C22×C4×C151C22⋊C411yescharacteristic
66C22×C4×C151C22⋊C411yescharacteristic
67C22×C4×C151C22⋊C411yescharacteristic
68C22×C4×C151C22⋊C411yescharacteristic
69C22×C4×C151C22×C411yescharacteristic
70C22×C4×C151C2×D411yescharacteristic
71C22×C4×C151C2×D411yescharacteristic
72M16×C151—42no—
73M16×C151—42no—
74C2×C8×C151—42no—
75C2×C8×C151—42no—
76C4⋊C4×C151—41no—
77C4⋊C4×C151—41no—
78C4⋊C4×C151—41no—
79C4⋊C4×C151—42no—
80C22⋊C4×C151—44no—
81C22⋊C4×C151—42no—
82C22⋊C4×C151—42no—
83C22⋊C4×C151—82no—
84C22⋊C4×C151—82no—
85C42×C151—21no—
86C42×C151—21no—
87C42×C151—21no—
88C42×C151—21no—
89C42×C151—21no—
90C42×C151—21no—
91C42×C151—42no—
92C23×C151—42no—
93C23×C151—42no—
94C23×C151—42no—
95C23×C151—42no—
96C23×C151—42no—
97C23×C151—42no—
98C23×C151—42no—
99C23×C151C2×C22⋊C411yescharacteristic
100Q8×C151—42no—
101Q8×C151—42no—
102D4×C151—82no—
103D4×C151—84no—
104D4×C151—84no—
105D4×C151—82no—
106C2×C4×C151—21no—
107C2×C4×C151—21no—
108C2×C4×C151—21no—
109C2×C4×C151—21no—
110C2×C4×C151—21no—
111C2×C4×C151—21no—
112C2×C4×C151—22no—
113C2×C4×C151—21no—
114C2×C4×C151—21no—
115C2×C4×C151—21no—
116C2×C4×C151—41no—
117C2×C4×C151—41no—
118C2×C4×C151—41no—
119C2×C4×C151—42no—
120C2×C4×C151—42no—
121C2×C4×C151—42no—
122C2×C4×C151#9911yescharacteristic
123C2×C4×C151#9911yescharacteristic
124C2×C4×C151#10212yes—
125C2×C4×C151#10212yes—
126C2×C4×C151C2×D811yescharacteristic
127C2×C4×C151C2×SD1611yescharacteristic
128C8×C151—82no—
129C8×C151—82no—
130C22×C151—21no—
131C22×C151—21no—
132C22×C151—82no—
133C22×C151—82no—
134C22×C151—82no—
135C22×C151—82no—
136C22×C151—82no—
137C22×C151—82no—
138C22×C151—82no—
139C22×C151C2×#9911yescharacteristic
140C22×C151C2×#10211yescharacteristic
141C22×C151#42111yescharacteristic
142C4×C151—21no—
143C4×C151—21no—
144C4×C151—22no—
145C4×C151—22no—
146C4×C151—21no—
147C4×C151—41no—
148C4×C151—41no—
149C4×C151—41no—
150C4×C151—82no—
151C4×C151#35512yes—
152C2×C151—21no—
153C2×C151—21no—
154C2×C151—162no—
155C2×C151#151911yescharacteristic
156C2×C151#212211yescharacteristic
157C2×C151C2×#35511yescharacteristic
158#11882C15111yesmaximal, characteristic, direct product factor, Sylow
159C151#1188211yescharacteristic, direct product factor, Sylow
160#2548C2×C15111yescharacteristic
161#1801C2×C15111yescharacteristic, complemented
162#1461C2×C15111yescharacteristic, complemented
163#1345C2×C15114yescomplemented
164C2×#127C4×C15111yescharacteristic
165C2×#124—21no—
166C2×C4×Q8C22×C15111yescharacteristic
167#431—21no—
168#423—21no—
169C2×#101—21no—
170#394C4×C15112yes—
171#394C22×C15112yes—
172#390—21no—
173#390—21no—
174#390—21no—
175C4×C4⋊C4C4×C15111yescharacteristic
176#343C22×C15112yes—
177#324—21no—
178#324C22×C15112yes—
179C22×Q8D4×C15111yescharacteristic
180C22×D4—21no—
181C22×D4—21no—
182C22×D4C2×C4×C15112yes—
183C2×M16—22no—
184#127—41no—
185#127—41no—
186#124—42no—
187#124—42no—
188C4×Q8—41no—
189C4×Q8—41no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4C2×C4×C15111yescharacteristic
192C2×C4⋊C4D4×C15111yescharacteristic
193C2×C4⋊C4C23×C15111yescharacteristic
194C2×C22⋊C4—22no—
195C2×C22⋊C4—22no—
196C2×C22⋊C4—22no—
197C2×C22⋊C4—22no—
198C2×C42—21no—
199C2×C42C2×C4×C15111yescharacteristic
200C2×C42D4×C15111yescharacteristic
201C2×C42D4×C15111yescharacteristic
202C4⋊C8—41no—
203C4⋊C8—41no—
204C4⋊C8—41no—
205#101—42no—
206C22⋊C8—22no—
207C4×C8—41no—
208#95C2×C4×C15112yes—
209C24—22no—
210C2×Q8—41no—
211C2×Q8—41no—
212C2×Q8D8×C15112yes—
213C2×Q8SD16×C15112yes—
214C2×D4—42no—
215C2×D4—42no—
216C2×D4—42no—
217C2×D4—42no—
218C2×D4—42no—
219C2×D4—41no—
220C2×D4—41no—
221C2×D4—42no—
222C2×D4—82no—
223C22×C4—22no—
224C22×C4C22⋊C4×C15111yescharacteristic
225C22×C4C22⋊C4×C15111yescharacteristic
226C22×C4C22⋊C4×C15111yescharacteristic
227C22×C4C22⋊C4×C15111yescharacteristic
228C22×C4C22×C4×C15111yescharacteristic
229C22×C4C2×D4×C15111yescharacteristic
230C22×C4C2×D4×C15111yescharacteristic
231M16—42no—
232M16—42no—
233C2×C8—42no—
234C2×C8—42no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—42no—
239C22⋊C4—44no—
240C22⋊C4—42no—
241C22⋊C4—42no—
242C22⋊C4—82no—
243C22⋊C4—82no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—21no—
248C42—21no—
249C42—21no—
250C42—42no—
251C23—42no—
252C23—42no—
253C23—42no—
254C23—42no—
255C23—42no—
256C23—42no—
257C23—42no—
258C23C2×C22⋊C4×C15111yescharacteristic
259Q8—42no—
260Q8—42no—
261D4—82no—
262D4—84no—
263D4—84no—
264D4—82no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—22no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4#99×C15111yescharacteristic
282C2×C4#99×C15111yescharacteristic
283C2×C4#102×C15112yes—
284C2×C4#102×C15112yes—
285C2×C4C2×D8×C15111yescharacteristic
286C2×C4C2×SD16×C15111yescharacteristic
287C8—82no—
288C8—82no—
289C22—21no—
290C22—21no—
291C22—82no—
292C22—82no—
293C22—82no—
294C22—82no—
295C22—82no—
296C22—82no—
297C22—82no—
298C22C2×#99×C15111yescharacteristic
299C22C2×#102×C15111yescharacteristic
300C22#421×C15111yescharacteristic
301C4—21no—
302C4—21no—
303C4—22no—
304C4—22no—
305C4—21no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—82no—
310C4#355×C15112yes—
311C2—21no—
312C2—21no—
313C2—162no—
314C2#1519×C15111yescharacteristic
315C2#2122×C15111yescharacteristic
316C2C2×#355×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#99
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×C4⋊C4C23×C151
prime radicalC2×#127×C151C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C22×C4×C151 ◁ C2×C4×Q8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1801×C151C2semidirect
3. #1461×C151C2semidirect
4. #1345×C151C2semidirect
158. #11882C151direct (N × H)
159. C151#11882direct (N × H)
161. #1801C2×C151semidirect
162. #1461C2×C151semidirect
163. #1345C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2548×C1512
#1801×C1512
#1461×C1512
#1345×C1512
#11882151