Finite Group Databasebeta

← C151×#17410 #50322335

Subgroups — C151×#17410 #50322335

Order 38656.

848 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×#541×C151C211yesmaximal, characteristic
2#2983×C151C212yesmaximal, complemented
3#1473×C151C214yesmaximal
4#1470×C151C214yesmaximal, complemented
5#1467×C151C212yesmaximal, complemented
6#1464×C151C212yesmaximal
7#541×C151—28no—
8C2×C4⋊Q8×C151C411yescharacteristic
9C2×#126×C151C412yes—
10C2×#126×C151C2212yes—
11C2×#125×C151C411yescharacteristic
12C2×#125×C151C412yes—
13C2×#125×C151C2212yes—
14C2×C22⋊Q8×C151C411yescharacteristic
15C2×C22⋊Q8×C151C411yescharacteristic
16C2×C4×Q8×C151C2211yescharacteristic
17C2×C4×Q8×C151C2211yescharacteristic
18C2×#117×C151C2211yescharacteristic
19#446×C151—28no—
20#432×C151C2214yes—
21#432×C151C2214yes—
22#431×C151C2214yes—
23#324×C151C2214yes—
24#324×C151C2218yes—
25#323×C151C2214yes—
26C22×Q8×C151C2×C411yescharacteristic
27C22×Q8×C151C2×C411yescharacteristic
28C23×C4×C151C2×C411yescharacteristic
29C4⋊Q8×C151—24no—
30#126×C151—28no—
31#126×C151—24no—
32#126×C151—24no—
33#125×C151—24no—
34#125×C151—28no—
35#125×C151—24no—
36#125×C151—24no—
37C22⋊Q8×C151—24no—
38C22⋊Q8×C151—24no—
39C4×Q8×C151—24no—
40C4×Q8×C151D418yes—
41#117×C151—24no—
42C2×C4⋊C4×C151C2×C411yescharacteristic
43C2×C4⋊C4×C151C2×C411yescharacteristic
44C2×C4⋊C4×C151C2×C412yes—
45C2×C4⋊C4×C151C2×C412yes—
46C2×C4⋊C4×C151C2×C412yes—
47C2×C4⋊C4×C151C2×C412yes—
48C2×C4⋊C4×C151C2×C412yes—
49C2×C4⋊C4×C151C2×C412yes—
50C2×C4⋊C4×C151C2×C411yescharacteristic
51C2×C4⋊C4×C151C2×C412yes—
52C2×C4⋊C4×C151C2311yescharacteristic
53C2×C4⋊C4×C151C2312yes—
54C2×C22⋊C4×C151C2×C411yescharacteristic
55C2×C22⋊C4×C151C2×C412yes—
56C2×C22⋊C4×C151C2×C412yes—
57C2×C22⋊C4×C151C2311yescharacteristic
58C2×C42×C151C2×C411yescharacteristic
59C2×C42×C151C2×C412yes—
60C2×C42×C151C2312yes—
61C2×C42×C151C2311yescharacteristic
62C4⋊C8×C151—24no—
63C4⋊C8×C151—24no—
64C4⋊C8×C151—24no—
65C22⋊C8×C151C2318yes—
66#97×C151—24no—
67#97×C151—24no—
68C4×C8×C151—24no—
69C24×C151C22×C411yescharacteristic
70C2×Q8×C151—22no—
71C2×Q8×C151—42no—
72C2×Q8×C151—42no—
73C2×Q8×C151C22⋊C414yes—
74C22×C4×C151—22no—
75C22×C4×C151—42no—
76C22×C4×C151C22×C412yes—
77C22×C4×C151C22×C411yescharacteristic
78C22×C4×C151C22×C411yescharacteristic
79C22×C4×C151C22×C412yes—
80C22×C4×C151C22×C411yescharacteristic
81C22×C4×C151C22×C412yes—
82C22×C4×C151C22×C411yescharacteristic
83C22×C4×C151C22×C411yescharacteristic
84C22×C4×C151C22×C412yes—
85C22×C4×C151C2411yescharacteristic
86C2×C8×C151—28no—
87C4⋊C4×C151—22no—
88C4⋊C4×C151—22no—
89C4⋊C4×C151—24no—
90C4⋊C4×C151—24no—
91C4⋊C4×C151—24no—
92C4⋊C4×C151—24no—
93C4⋊C4×C151—24no—
94C4⋊C4×C151—24no—
95C4⋊C4×C151—22no—
96C4⋊C4×C151—22no—
97C4⋊C4×C151—22no—
98C4⋊C4×C151C22⋊C414yes—
99C4⋊C4×C151C22⋊C418yes—
100C22⋊C4×C151—22no—
101C22⋊C4×C151—24no—
102C22⋊C4×C151—24no—
103C22⋊C4×C151—22no—
104C42×C151—22no—
105C42×C151—24no—
106C42×C151C2×D414yes—
107C42×C151C2×D414yes—
108C42×C151C2×D414yes—
109C23×C151—21no—
110C23×C151—22no—
111C23×C151—41no—
112C23×C151—41no—
113C23×C151C23×C411yescharacteristic
114Q8×C151—44no—
115Q8×C151—44no—
116C2×C4×C151—22no—
117C2×C4×C151—24no—
118C2×C4×C151—22no—
119C2×C4×C151—21no—
120C2×C4×C151—22no—
121C2×C4×C151—21no—
122C2×C4×C151—21no—
123C2×C4×C151—24no—
124C2×C4×C151—22no—
125C2×C4×C151—41no—
126C2×C4×C151—42no—
127C2×C4×C151—41no—
128C2×C4×C151—44no—
129C2×C4×C151—41no—
130C2×C4×C151—42no—
131C2×C4×C151—41no—
132C2×C4×C151C2×C22⋊C412yes—
133C2×C4×C151C2×C22⋊C414yes—
134C2×C4×C151C2×C22⋊C412yes—
135C2×C4×C151C2×C22⋊C414yes—
136C2×C4×C151C22×D412yes—
137C8×C151—48no—
138C22×C151—21no—
139C22×C151—21no—
140C22×C151—41no—
141C22×C151—41no—
142C22×C151—41no—
143C22×C151—82no—
144C22×C151C22×C22⋊C411yescharacteristic
145C22×C151#56812yes—
146C4×C151—22no—
147C4×C151—24no—
148C4×C151—22no—
149C4×C151—22no—
150C4×C151—24no—
151C4×C151—41no—
152C4×C151—42no—
153C4×C151—41no—
154C4×C151—42no—
155C4×C151—41no—
156C2×C151—22no—
157C2×C151—81no—
158C2×C151#287911yescharacteristic
159C2×C151#288411yescharacteristic
160C2×C151#288911yescharacteristic
161#17410C15111yesmaximal, characteristic, direct product factor, Sylow
162C151#1741011yescharacteristic, direct product factor, Sylow
163C2×#541C2×C15111yescharacteristic
164#2983C2×C15112yescomplemented
165#1473C2×C15114yes—
166#1470C2×C15114yescomplemented
167#1467C2×C15112yescomplemented
168#1464C2×C15112yes—
169#541—28no—
170C2×C4⋊Q8C4×C15111yescharacteristic
171C2×#126C4×C15112yes—
172C2×#126C22×C15112yes—
173C2×#125C4×C15111yescharacteristic
174C2×#125C4×C15112yes—
175C2×#125C22×C15112yes—
176C2×C22⋊Q8C4×C15111yescharacteristic
177C2×C22⋊Q8C4×C15111yescharacteristic
178C2×C4×Q8C22×C15111yescharacteristic
179C2×C4×Q8C22×C15111yescharacteristic
180C2×#117C22×C15111yescharacteristic
181#446—28no—
182#432C22×C15114yes—
183#432C22×C15114yes—
184#431C22×C15114yes—
185#324C22×C15114yes—
186#324C22×C15118yes—
187#323C22×C15114yes—
188C22×Q8C2×C4×C15111yescharacteristic
189C22×Q8C2×C4×C15111yescharacteristic
190C23×C4C2×C4×C15111yescharacteristic
191C4⋊Q8—24no—
192#126—28no—
193#126—24no—
194#126—24no—
195#125—24no—
196#125—28no—
197#125—24no—
198#125—24no—
199C22⋊Q8—24no—
200C22⋊Q8—24no—
201C4×Q8—24no—
202C4×Q8D4×C15118yes—
203#117—24no—
204C2×C4⋊C4C2×C4×C15111yescharacteristic
205C2×C4⋊C4C2×C4×C15111yescharacteristic
206C2×C4⋊C4C2×C4×C15112yes—
207C2×C4⋊C4C2×C4×C15112yes—
208C2×C4⋊C4C2×C4×C15112yes—
209C2×C4⋊C4C2×C4×C15112yes—
210C2×C4⋊C4C2×C4×C15112yes—
211C2×C4⋊C4C2×C4×C15112yes—
212C2×C4⋊C4C2×C4×C15111yescharacteristic
213C2×C4⋊C4C2×C4×C15112yes—
214C2×C4⋊C4C23×C15111yescharacteristic
215C2×C4⋊C4C23×C15112yes—
216C2×C22⋊C4C2×C4×C15111yescharacteristic
217C2×C22⋊C4C2×C4×C15112yes—
218C2×C22⋊C4C2×C4×C15112yes—
219C2×C22⋊C4C23×C15111yescharacteristic
220C2×C42C2×C4×C15111yescharacteristic
221C2×C42C2×C4×C15112yes—
222C2×C42C23×C15111yescharacteristic
223C2×C42C23×C15112yes—
224C4⋊C8—24no—
225C4⋊C8—24no—
226C4⋊C8—24no—
227C22⋊C8C23×C15118yes—
228#97—24no—
229#97—24no—
230C4×C8—24no—
231C24C22×C4×C15111yescharacteristic
232C2×Q8—22no—
233C2×Q8—42no—
234C2×Q8—42no—
235C2×Q8C22⋊C4×C15114yes—
236C22×C4—22no—
237C22×C4—42no—
238C22×C4C22×C4×C15112yes—
239C22×C4C22×C4×C15111yescharacteristic
240C22×C4C22×C4×C15111yescharacteristic
241C22×C4C22×C4×C15112yes—
242C22×C4C22×C4×C15111yescharacteristic
243C22×C4C22×C4×C15112yes—
244C22×C4C22×C4×C15111yescharacteristic
245C22×C4C22×C4×C15111yescharacteristic
246C22×C4C22×C4×C15112yes—
247C22×C4C24×C15111yescharacteristic
248C2×C8—28no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—24no—
252C4⋊C4—24no—
253C4⋊C4—24no—
254C4⋊C4—24no—
255C4⋊C4—24no—
256C4⋊C4—24no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4C22⋊C4×C15114yes—
261C4⋊C4C22⋊C4×C15118yes—
262C22⋊C4—22no—
263C22⋊C4—24no—
264C22⋊C4—24no—
265C22⋊C4—22no—
266C42—22no—
267C42—24no—
268C42C2×D4×C15114yes—
269C42C2×D4×C15114yes—
270C42C2×D4×C15114yes—
271C23—21no—
272C23—22no—
273C23—41no—
274C23—41no—
275C23C23×C4×C15111yescharacteristic
276Q8—44no—
277Q8—44no—
278C2×C4—22no—
279C2×C4—24no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—21no—
283C2×C4—22no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—24no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—44no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—41no—
294C2×C4C2×C22⋊C4×C15112yes—
295C2×C4C2×C22⋊C4×C15112yes—
296C2×C4C2×C22⋊C4×C15114yes—
297C2×C4C2×C22⋊C4×C15114yes—
298C2×C4C22×D4×C15112yes—
299C8—48no—
300C22—21no—
301C22—21no—
302C22—41no—
303C22—41no—
304C22—41no—
305C22—82no—
306C22C22×C22⋊C4×C15111yescharacteristic
307C22#568×C15112yes—
308C4—22no—
309C4—24no—
310C4—22no—
311C4—22no—
312C4—24no—
313C4—41no—
314C4—42no—
315C4—41no—
316C4—42no—
317C4—41no—
318C2—22no—
319C2—81no—
320C2#2879×C15111yescharacteristic
321C2#2884×C15111yescharacteristic
322C2#2889×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C22×C22⋊C4
commutatorC23C23×C4×C151
Frattini, cosocleC22×C4C24×C151
prime radicalC24×C151C22×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C4×Q8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2983×C151C2semidirect
4. #1470×C151C2semidirect
5. #1467×C151C2semidirect
161. #17410C151direct (N × H)
162. C151#17410direct (N × H)
164. #2983C2×C151semidirect
166. #1470C2×C151semidirect
167. #1467C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#541×C1512
#2983×C1512
#1473×C1512
#1470×C1512
#1467×C1512
#1464×C1512
#17410151