Finite Group Databasebeta

← #2413×C151 #34065745

Subgroups — #2413×C151 #34065745

Order 19328.

610 conjugacy classes of subgroups.

The subgroup lattice has 296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#123×C151C211yesmaximal, characteristic
2C2×#123×C151C211yesmaximal, characteristic
3C2×#117×C151C211yesmaximal, characteristic, complemented
4C22×C4⋊C4×C151C211yesmaximal, characteristic, complemented
5#398×C151C212yesmaximal, complemented
6#396×C151C212yesmaximal, complemented
7#389×C151C212yesmaximal, complemented
8#388×C151C212yesmaximal, complemented
9#386×C151C211yesmaximal, characteristic
10#385×C151C211yesmaximal, characteristic, complemented
11#381×C151C211yesmaximal, characteristic, complemented
12C22×D4×C151C2211yescharacteristic
13C23×C4×C151C2211yescharacteristic
14C23×C4×C151C2211yescharacteristic
15C23×C4×C151C2211yescharacteristic
16#123×C151—24no—
17#123×C151—24no—
18#117×C151—24no—
19C2×C4⋊C4×C151—24no—
20C2×C4⋊C4×C151C2212yes—
21C2×C4⋊C4×C151C2212yes—
22C2×C4⋊C4×C151C2211yescharacteristic
23C2×C4⋊C4×C151C2212yes—
24C2×C4⋊C4×C151C2212yes—
25C2×C4⋊C4×C151C2212yes—
26C2×C4⋊C4×C151C2211yescharacteristic
27C2×C22⋊C4×C151C2211yescharacteristic
28C2×C22⋊C4×C151C2211yescharacteristic
29C2×C22⋊C4×C151C2212yes—
30C2×C22⋊C4×C151C2211yescharacteristic
31C2×C22⋊C4×C151C2212yes—
32C2×C22⋊C4×C151C2211yescharacteristic
33C2×C22⋊C4×C151C2211yescharacteristic
34C2×C42×C151C2212yes—
35#95×C151C2212yes—
36#95×C151C2212yes—
37#95×C151C2212yes—
38#95×C151C2212yes—
39C24×C151C2311yescharacteristic
40C24×C151C2311yescharacteristic
41C2×D4×C151—22no—
42C2×D4×C151—22no—
43C2×D4×C151—22no—
44C22×C4×C151—22no—
45C22×C4×C151—22no—
46C22×C4×C151—22no—
47C22×C4×C151—24no—
48C22×C4×C151—22no—
49C22×C4×C151—22no—
50C22×C4×C151—22no—
51C22×C4×C151D414yes—
52C22×C4×C151C2311yescharacteristic
53C22×C4×C151C2312yes—
54C22×C4×C151C2311yescharacteristic
55C22×C4×C151C2312yes—
56C22×C4×C151C2311yescharacteristic
57C22×C4×C151C2312yes—
58C22×C4×C151C2311yescharacteristic
59C22×C4×C151C2311yescharacteristic
60C22×C4×C151C2312yes—
61C4⋊C4×C151—24no—
62C4⋊C4×C151—24no—
63C4⋊C4×C151—24no—
64C4⋊C4×C151—22no—
65C4⋊C4×C151—22no—
66C4⋊C4×C151—24no—
67C4⋊C4×C151—24no—
68C22⋊C4×C151—22no—
69C22⋊C4×C151—22no—
70C22⋊C4×C151—22no—
71C22⋊C4×C151—22no—
72C22⋊C4×C151—24no—
73C22⋊C4×C151—24no—
74C22⋊C4×C151D414yes—
75C42×C151—24no—
76C23×C151—22no—
77C23×C151—22no—
78C23×C151—21no—
79C23×C151—21no—
80C23×C151—22no—
81C23×C151—21no—
82C23×C151—22no—
83C23×C151C2×D412yes—
84C23×C151C2×D412yes—
85C23×C151#4112yes—
86C23×C151C2411yescharacteristic
87D4×C151—44no—
88C2×C4×C151—28no—
89C2×C4×C151—28no—
90C2×C4×C151—21no—
91C2×C4×C151—21no—
92C2×C4×C151—22no—
93C2×C4×C151—22no—
94C2×C4×C151—21no—
95C2×C4×C151—21no—
96C2×C4×C151—22no—
97C2×C4×C151—22no—
98C2×C4×C151—22no—
99C2×C4×C151—21no—
100C2×C4×C151—21no—
101C2×C4×C151—22no—
102C2×C4×C151—22no—
103C2×C4×C151—21no—
104C2×C4×C151—21no—
105C2×C4×C151—22no—
106C2×C4×C151—22no—
107C2×C4×C151—22no—
108C2×C4×C151—21no—
109C2×C4×C151—22no—
110C2×C4×C151—22no—
111C2×C4×C151—44no—
112C2×C4×C151C2×D414yes—
113C2×C4×C151C2×D412yes—
114C2×C4×C151C2×D412yes—
115C2×C4×C151#4114yes—
116C22×C151—22no—
117C22×C151—22no—
118C22×C151—24no—
119C22×C151—24no—
120C22×C151—41no—
121C22×C151—41no—
122C22×C151—41no—
123C22×C151—42no—
124C22×C151—42no—
125C22×C151#12114yes—
126C22×C151C22×D411yescharacteristic
127C22×C151C22×D411yescharacteristic
128C22×C151C2×#4111yescharacteristic
129C22×C151C2×#4112yes—
130C22×C1512−1+412yes—
131C4×C151—22no—
132C4×C151—22no—
133C4×C151—24no—
134C4×C151—24no—
135C4×C151—42no—
136C4×C151—41no—
137C4×C151—41no—
138C4×C151—41no—
139C4×C151—42no—
140C2×C151—24no—
141C2×C151—81no—
142C2×C151C2×#12111yescharacteristic
143C2×C151#52511yescharacteristic
144C2×C151#53611yescharacteristic
145C2×C151#54712yes—
146C2×C151#55212yes—
147C151#241311yescharacteristic, direct product factor, Sylow
148#2413C15111yesmaximal, characteristic, direct product factor, Sylow
149C2×#123C2×C15111yescharacteristic
150C2×#123C2×C15111yescharacteristic
151C2×#117C2×C15111yescharacteristic, complemented
152C22×C4⋊C4C2×C15111yescharacteristic, complemented
153#398C2×C15112yescomplemented
154#396C2×C15112yescomplemented
155#389C2×C15112yescomplemented
156#388C2×C15112yescomplemented
157#386C2×C15111yescharacteristic
158#385C2×C15111yescharacteristic, complemented
159#381C2×C15111yescharacteristic, complemented
160C22×D4C22×C15111yescharacteristic
161C23×C4C22×C15111yescharacteristic
162C23×C4C22×C15111yescharacteristic
163C23×C4C22×C15111yescharacteristic
164#123—24no—
165#123—24no—
166#117—24no—
167C2×C4⋊C4—24no—
168C2×C4⋊C4C22×C15112yes—
169C2×C4⋊C4C22×C15112yes—
170C2×C4⋊C4C22×C15112yes—
171C2×C4⋊C4C22×C15111yescharacteristic
172C2×C4⋊C4C22×C15112yes—
173C2×C4⋊C4C22×C15111yescharacteristic
174C2×C4⋊C4C22×C15112yes—
175C2×C22⋊C4C22×C15111yescharacteristic
176C2×C22⋊C4C22×C15111yescharacteristic
177C2×C22⋊C4C22×C15111yescharacteristic
178C2×C22⋊C4C22×C15112yes—
179C2×C22⋊C4C22×C15111yescharacteristic
180C2×C22⋊C4C22×C15112yes—
181C2×C22⋊C4C22×C15111yescharacteristic
182C2×C42C22×C15112yes—
183#95C22×C15112yes—
184#95C22×C15112yes—
185#95C22×C15112yes—
186#95C22×C15112yes—
187C24C23×C15111yescharacteristic
188C24C23×C15111yescharacteristic
189C2×D4—22no—
190C2×D4—22no—
191C2×D4—22no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—24no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4D4×C15114yes—
200C22×C4C23×C15111yescharacteristic
201C22×C4C23×C15112yes—
202C22×C4C23×C15111yescharacteristic
203C22×C4C23×C15112yes—
204C22×C4C23×C15111yescharacteristic
205C22×C4C23×C15112yes—
206C22×C4C23×C15112yes—
207C22×C4C23×C15111yescharacteristic
208C22×C4C23×C15111yescharacteristic
209C4⋊C4—24no—
210C4⋊C4—24no—
211C4⋊C4—24no—
212C4⋊C4—24no—
213C4⋊C4—22no—
214C4⋊C4—22no—
215C4⋊C4—24no—
216C22⋊C4—22no—
217C22⋊C4—22no—
218C22⋊C4—24no—
219C22⋊C4—22no—
220C22⋊C4—22no—
221C22⋊C4—24no—
222C22⋊C4D4×C15114yes—
223C42—24no—
224C23—22no—
225C23—22no—
226C23—21no—
227C23—21no—
228C23—22no—
229C23—21no—
230C23—22no—
231C23C2×D4×C15112yes—
232C23C2×D4×C15112yes—
233C23#41×C15112yes—
234C23C24×C15111yescharacteristic
235D4—44no—
236C2×C4—28no—
237C2×C4—28no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—44no—
260C2×C4C2×D4×C15114yes—
261C2×C4C2×D4×C15112yes—
262C2×C4C2×D4×C15112yes—
263C2×C4#41×C15114yes—
264C22—22no—
265C22—22no—
266C22—24no—
267C22—24no—
268C22—41no—
269C22—41no—
270C22—41no—
271C22—42no—
272C22—42no—
273C22#121×C15114yes—
274C22C22×D4×C15111yescharacteristic
275C22C22×D4×C15111yescharacteristic
276C22C2×#41×C15111yescharacteristic
277C22C2×#41×C15112yes—
278C222−1+4×C15112yes—
279C4—22no—
280C4—22no—
281C4—24no—
282C4—24no—
283C4—42no—
284C4—41no—
285C4—41no—
286C4—41no—
287C4—42no—
288C2—24no—
289C2—81no—
290C2C2×#121×C15111yescharacteristic
291C2#525×C15111yescharacteristic
292C2#536×C15111yescharacteristic
293C2#547×C15112yes—
294C2#552×C15112yes—
subgroupG/H
center, socleC23×C151C24
commutator, Frattini, cosocleC23C24×C151
prime radicalC22×D4×C151C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#117×C151C2semidirect
4. C22×C4⋊C4×C151C2semidirect
5. #398×C151C2semidirect
6. #396×C151C2semidirect
7. #389×C151C2semidirect
8. #388×C151C2semidirect
10. #385×C151C2semidirect
11. #381×C151C2semidirect
147. C151#2413direct (N × H)
148. #2413C151direct (N × H)
151. C2×#117C2×C151semidirect
152. C22×C4⋊C4C2×C151semidirect
153. #398C2×C151semidirect
154. #396C2×C151semidirect
155. #389C2×C151semidirect
156. #388C2×C151semidirect
158. #385C2×C151semidirect
159. #381C2×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×#117×C1512
C22×C4⋊C4×C1512
#398×C1512
#396×C1512
#389×C1512
#388×C1512
#386×C1512
#385×C1512
#381×C1512
#2413151