Finite Group Databasebeta

← #2422×C151 #34065754

Subgroups — #2422×C151 #34065754

Order 19328.

652 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#123×C151C212yesmaximal, complemented
2C2×#121×C151C211yesmaximal, characteristic
3C2×C4×D4×C151C211yesmaximal, characteristic, complemented
4#397×C151C212yesmaximal, complemented
5#394×C151C212yesmaximal, complemented
6#390×C151C211yesmaximal, characteristic, complemented
7#389×C151C211yesmaximal, characteristic, complemented
8#385×C151C212yesmaximal, complemented
9#384×C151C211yesmaximal, characteristic, complemented
10#380×C151C211yesmaximal, characteristic, complemented
11C4×C22⋊C4×C151C211yesmaximal, characteristic, complemented
12C22×D4×C151C2212yes—
13C22×D4×C151C2211yescharacteristic
14C23×C4×C151C2211yescharacteristic
15C23×C4×C151C2212yes—
16#123×C151—28no—
17#121×C151—24no—
18C4×D4×C151—24no—
19C2×C4⋊C4×C151C2211yescharacteristic
20C2×C4⋊C4×C151C2211yescharacteristic
21C2×C4⋊C4×C151C2211yescharacteristic
22C2×C4⋊C4×C151C2212yes—
23C2×C4⋊C4×C151C2212yes—
24C2×C4⋊C4×C151C2212yes—
25C2×C22⋊C4×C151C2211yescharacteristic
26C2×C22⋊C4×C151C2212yes—
27C2×C22⋊C4×C151C2212yes—
28C2×C22⋊C4×C151C2212yes—
29C2×C22⋊C4×C151C2212yes—
30C2×C22⋊C4×C151C2212yes—
31C2×C22⋊C4×C151C2211yescharacteristic
32C2×C42×C151C2211yescharacteristic
33C2×C42×C151C2211yescharacteristic
34#95×C151C2211yescharacteristic
35#95×C151C2211yescharacteristic
36#95×C151C2212yes—
37#95×C151C2212yes—
38C24×C151C2312yes—
39C24×C151C2311yescharacteristic
40C2×D4×C151—24no—
41C2×D4×C151—24no—
42C2×D4×C151—22no—
43C2×D4×C151—22no—
44C2×D4×C151—42no—
45C2×D4×C151D414yes—
46C22×C4×C151—24no—
47C22×C4×C151—22no—
48C22×C4×C151—24no—
49C22×C4×C151—22no—
50C22×C4×C151—22no—
51C22×C4×C151—42no—
52C22×C4×C151C2311yescharacteristic
53C22×C4×C151C2311yescharacteristic
54C22×C4×C151C2312yes—
55C22×C4×C151C2312yes—
56C22×C4×C151C2312yes—
57C22×C4×C151C2311yescharacteristic
58C22×C4×C151C2311yescharacteristic
59C22×C4×C151C2311yescharacteristic
60C22×C4×C151C2311yescharacteristic
61C4⋊C4×C151—22no—
62C4⋊C4×C151—22no—
63C4⋊C4×C151—24no—
64C4⋊C4×C151—24no—
65C4⋊C4×C151—22no—
66C4⋊C4×C151—42no—
67C22⋊C4×C151—24no—
68C22⋊C4×C151—24no—
69C22⋊C4×C151—24no—
70C22⋊C4×C151—24no—
71C22⋊C4×C151—22no—
72C22⋊C4×C151—24no—
73C22⋊C4×C151D414yescomplemented
74C42×C151—22no—
75C42×C151—22no—
76C23×C151—22no—
77C23×C151—21no—
78C23×C151—21no—
79C23×C151—22no—
80C23×C151—21no—
81C23×C151—21no—
82C23×C151—22no—
83C23×C151—22no—
84C23×C151—22no—
85C23×C151—21no—
86C23×C151—21no—
87C23×C151—22no—
88C23×C151C2×D412yes—
89C23×C151C2×D414yes—
90C23×C151C2411yescharacteristic
91D4×C151—28no—
92D4×C151—48no—
93C2×C4×C151—21no—
94C2×C4×C151—21no—
95C2×C4×C151—21no—
96C2×C4×C151—21no—
97C2×C4×C151—21no—
98C2×C4×C151—21no—
99C2×C4×C151—21no—
100C2×C4×C151—22no—
101C2×C4×C151—21no—
102C2×C4×C151—22no—
103C2×C4×C151—22no—
104C2×C4×C151—22no—
105C2×C4×C151—22no—
106C2×C4×C151—22no—
107C2×C4×C151—21no—
108C2×C4×C151—22no—
109C2×C4×C151—21no—
110C2×C4×C151—21no—
111C2×C4×C151—22no—
112C2×C4×C151—22no—
113C2×C4×C151—21no—
114C2×C4×C151—48no—
115C2×C4×C151—44no—
116C2×C4×C151C2×D412yes—
117C2×C4×C151C2×D412yes—
118C2×C4×C151C2×D412yes—
119C2×C4×C151#4112yes—
120C2×C4×C151#4112yes—
121C2×C4×C151#4112yes—
122C22×C151—24no—
123C22×C151—22no—
124C22×C151—24no—
125C22×C151—22no—
126C22×C151—22no—
127C22×C151—24no—
128C22×C151—41no—
129C22×C151—42no—
130C22×C151—41no—
131C22×C151—42no—
132C22×C151—42no—
133C22×C151—41no—
134C22×C151—41no—
135C22×C151—42no—
136C22×C151C22×D411yescharacteristic
137C22×C151C22×D411yescharacteristic
138C22×C151C2×#4111yescharacteristic
139C22×C151C2×#4111yescharacteristic
140C22×C151C2×#4111yescharacteristic
141C22×C151H(5,𝔽2)11yescharacteristic
142C22×C1512−1+411yescharacteristic
143C4×C151—22no—
144C4×C151—22no—
145C4×C151—22no—
146C4×C151—41no—
147C4×C151—42no—
148C4×C151—42no—
149C4×C151—42no—
150C4×C151—41no—
151C4×C151#12314yescomplemented
152C2×C151—44no—
153C2×C151—42no—
154C2×C151C2×#12311yescharacteristic
155C2×C151#53211yescharacteristic
156C2×C151#54211yescharacteristic
157C2×C151D4211yescharacteristic
158C2×C151#54711yescharacteristic
159C2×C151#54711yescharacteristic
160C2×C151#55311yescharacteristic
161C151#242211yescharacteristic, direct product factor, Sylow
162#2422C15111yesmaximal, characteristic, direct product factor, Sylow
163C2×#123C2×C15112yescomplemented
164C2×#121C2×C15111yescharacteristic
165C2×C4×D4C2×C15111yescharacteristic, complemented
166#397C2×C15112yescomplemented
167#394C2×C15112yescomplemented
168#390C2×C15111yescharacteristic, complemented
169#389C2×C15111yescharacteristic, complemented
170#385C2×C15112yescomplemented
171#384C2×C15111yescharacteristic, complemented
172#380C2×C15111yescharacteristic, complemented
173C4×C22⋊C4C2×C15111yescharacteristic, complemented
174C22×D4C22×C15112yes—
175C22×D4C22×C15111yescharacteristic
176C23×C4C22×C15111yescharacteristic
177C23×C4C22×C15112yes—
178#123—28no—
179#121—24no—
180C4×D4—24no—
181C2×C4⋊C4C22×C15111yescharacteristic
182C2×C4⋊C4C22×C15111yescharacteristic
183C2×C4⋊C4C22×C15112yes—
184C2×C4⋊C4C22×C15112yes—
185C2×C4⋊C4C22×C15111yescharacteristic
186C2×C4⋊C4C22×C15112yes—
187C2×C22⋊C4C22×C15112yes—
188C2×C22⋊C4C22×C15112yes—
189C2×C22⋊C4C22×C15112yes—
190C2×C22⋊C4C22×C15112yes—
191C2×C22⋊C4C22×C15111yescharacteristic
192C2×C22⋊C4C22×C15112yes—
193C2×C22⋊C4C22×C15111yescharacteristic
194C2×C42C22×C15111yescharacteristic
195C2×C42C22×C15111yescharacteristic
196#95C22×C15111yescharacteristic
197#95C22×C15111yescharacteristic
198#95C22×C15112yes—
199#95C22×C15112yes—
200C24C23×C15112yes—
201C24C23×C15111yescharacteristic
202C2×D4—24no—
203C2×D4—24no—
204C2×D4—22no—
205C2×D4—22no—
206C2×D4—42no—
207C2×D4D4×C15114yes—
208C22×C4—24no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—24no—
213C22×C4—42no—
214C22×C4C23×C15111yescharacteristic
215C22×C4C23×C15111yescharacteristic
216C22×C4C23×C15112yes—
217C22×C4C23×C15112yes—
218C22×C4C23×C15112yes—
219C22×C4C23×C15111yescharacteristic
220C22×C4C23×C15111yescharacteristic
221C22×C4C23×C15111yescharacteristic
222C22×C4C23×C15111yescharacteristic
223C4⋊C4—22no—
224C4⋊C4—22no—
225C4⋊C4—22no—
226C4⋊C4—24no—
227C4⋊C4—24no—
228C4⋊C4—42no—
229C22⋊C4—24no—
230C22⋊C4—24no—
231C22⋊C4—24no—
232C22⋊C4—22no—
233C22⋊C4—24no—
234C22⋊C4—24no—
235C22⋊C4D4×C15114yescomplemented
236C42—22no—
237C42—22no—
238C23—22no—
239C23—21no—
240C23—21no—
241C23—22no—
242C23—21no—
243C23—21no—
244C23—22no—
245C23—22no—
246C23—22no—
247C23—21no—
248C23—21no—
249C23—22no—
250C23C2×D4×C15112yes—
251C23C2×D4×C15114yes—
252C23C24×C15111yescharacteristic
253D4—28no—
254D4—48no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—21no—
276C2×C4—48no—
277C2×C4—44no—
278C2×C4C2×D4×C15112yes—
279C2×C4C2×D4×C15112yes—
280C2×C4C2×D4×C15112yes—
281C2×C4#41×C15112yes—
282C2×C4#41×C15112yes—
283C2×C4#41×C15112yes—
284C22—24no—
285C22—22no—
286C22—24no—
287C22—22no—
288C22—22no—
289C22—24no—
290C22—41no—
291C22—42no—
292C22—41no—
293C22—42no—
294C22—42no—
295C22—41no—
296C22—41no—
297C22—42no—
298C22C22×D4×C15111yescharacteristic
299C22C22×D4×C15111yescharacteristic
300C22C2×#41×C15111yescharacteristic
301C22C2×#41×C15111yescharacteristic
302C22C2×#41×C15111yescharacteristic
303C22H(5,𝔽2)×C15111yescharacteristic
304C222−1+4×C15111yescharacteristic
305C4—22no—
306C4—22no—
307C4—22no—
308C4—41no—
309C4—42no—
310C4—42no—
311C4—42no—
312C4—41no—
313C4#123×C15114yescomplemented
314C2—44no—
315C2—42no—
316C2C2×#123×C15111yescharacteristic
317C2#532×C15111yescharacteristic
318C2#542×C15111yescharacteristic
319C2D42×C15111yescharacteristic
320C2#547×C15111yescharacteristic
321C2#547×C15111yescharacteristic
322C2#553×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C24
commutator, Frattini, cosocleC23C24×C151
prime radicalC2×#121×C151C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#123×C151C2semidirect
3. C2×C4×D4×C151C2semidirect
4. #397×C151C2semidirect
5. #394×C151C2semidirect
6. #390×C151C2semidirect
7. #389×C151C2semidirect
8. #385×C151C2semidirect
9. #384×C151C2semidirect
10. #380×C151C2semidirect
11. C4×C22⋊C4×C151C2semidirect
73. C22⋊C4×C151D4semidirect
151. C4×C151#123semidirect
161. C151#2422direct (N × H)
162. #2422C151direct (N × H)
163. C2×#123C2×C151semidirect
165. C2×C4×D4C2×C151semidirect
166. #397C2×C151semidirect
167. #394C2×C151semidirect
168. #390C2×C151semidirect
169. #389C2×C151semidirect
170. #385C2×C151semidirect
171. #384C2×C151semidirect
172. #380C2×C151semidirect
173. C4×C22⋊C4C2×C151semidirect
235. C22⋊C4D4×C151semidirect
313. C4#123×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#123×C1512
C2×#121×C1512
C2×C4×D4×C1512
#397×C1512
#394×C1512
#390×C1512
#389×C1512
#385×C1512
#384×C1512
#380×C1512
C4×C22⋊C4×C1512
#2422151