Finite Group Databasebeta

← C151×#8720 #50313645

Subgroups — C151×#8720 #50313645

Order 38656.

482 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2283×C151C211yesmaximal, characteristic
2#1749×C151C211yesmaximal, characteristic
3#1749×C151C211yesmaximal, characteristic
4#1295×C151C212yesmaximal, complemented
5#1295×C151C212yesmaximal, complemented
6C22×C42×C151C2211yescharacteristic
7C2×C22⋊C8×C151—21no—
8C2×C22⋊C8×C151—21no—
9C2×#97×C151C2212yes—
10C2×#97×C151C2212yes—
11#383×C151—21no—
12#382×C151C2211yescharacteristic
13#382×C151C2211yescharacteristic
14#381×C151—21no—
15#380×C151C411yescharacteristic
16#380×C151C411yescharacteristic
17C4×C4⋊C4×C151C411yescharacteristic
18C4×C4⋊C4×C151C411yescharacteristic
19C4×C22⋊C4×C151—21no—
20#376×C151—21no—
21#336×C151—21no—
22#336×C151—21no—
23C23×C4×C151C2×C411yescharacteristic
24C23×C4×C151D411yescharacteristic
25C23×C4×C151D411yescharacteristic
26C22×C8×C151—22no—
27C22×C8×C151—22no—
28C2×C4⋊C4×C151C2×C411yescharacteristic
29C2×C4⋊C4×C151C2×C411yescharacteristic
30C2×C4⋊C4×C151C2×C411yescharacteristic
31C2×C4⋊C4×C151C2×C411yescharacteristic
32C2×C22⋊C4×C151—21no—
33C2×C22⋊C4×C151—21no—
34C2×C42×C151—24no—
35C2×C42×C151—21no—
36C2×C42×C151—21no—
37C2×C42×C151C2×C411yescharacteristic
38C2×C42×C151D411yescharacteristic
39C2×C42×C151D411yescharacteristic
40C2×C42×C151C2311yescharacteristic
41C22⋊C8×C151—24no—
42C22⋊C8×C151—24no—
43#97×C151—24no—
44#97×C151—24no—
45#95×C151—21no—
46#95×C151—21no—
47#95×C151—21no—
48#95×C151—21no—
49#95×C151—21no—
50#95×C151—21no—
51#95×C151—21no—
52#95×C151—21no—
53C24×C151C22⋊C411yescharacteristic
54C22×C4×C151—22no—
55C22×C4×C151—22no—
56C22×C4×C151—22no—
57C22×C4×C151—22no—
58C22×C4×C151—22no—
59C22×C4×C151—21no—
60C22×C4×C151—21no—
61C22×C4×C151—21no—
62C22×C4×C151—21no—
63C22×C4×C151—41no—
64C22×C4×C151—41no—
65C22×C4×C151—41no—
66C22×C4×C151—41no—
67C22×C4×C151C22⋊C411yescharacteristic
68C22×C4×C151C22⋊C411yescharacteristic
69C22×C4×C151C22⋊C411yescharacteristic
70C22×C4×C151C22×C411yescharacteristic
71C22×C4×C151C2×D411yescharacteristic
72C22×C4×C151C2×D411yescharacteristic
73C2×C8×C151—24no—
74C2×C8×C151—24no—
75C2×C8×C151—42no—
76C2×C8×C151—42no—
77C2×C8×C151—42no—
78C2×C8×C151—42no—
79C4⋊C4×C151—41no—
80C4⋊C4×C151—41no—
81C4⋊C4×C151—41no—
82C4⋊C4×C151—41no—
83C22⋊C4×C151—42no—
84C22⋊C4×C151—42no—
85C42×C151—22no—
86C42×C151—22no—
87C42×C151—22no—
88C42×C151—42no—
89C42×C151—42no—
90C42×C151#4114yes—
91C23×C151—21no—
92C23×C151—21no—
93C23×C151—21no—
94C23×C151—21no—
95C23×C151—21no—
96C23×C151—21no—
97C23×C151#10412yes—
98C23×C151C2×C22⋊C411yescharacteristic
99C2×C4×C151—21no—
100C2×C4×C151—21no—
101C2×C4×C151—21no—
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—21no—
110C2×C4×C151—21no—
111C2×C4×C151—21no—
112C2×C4×C151—21no—
113C2×C4×C151—44no—
114C2×C4×C151—44no—
115C2×C4×C151—44no—
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—41no—
127C2×C4×C151—41no—
128C2×C4×C151#10412yes—
129C2×C4×C151#11712yes—
130C2×C4×C151#12312yes—
131C2×C4×C151#12312yes—
132C8×C151—44no—
133C8×C151—44no—
134C22×C151—22no—
135C22×C151—22no—
136C22×C151—22no—
137C22×C151—41no—
138C22×C151—41no—
139C22×C151—41no—
140C22×C151—41no—
141C22×C151#38111yescharacteristic
142C22×C151#41311yescharacteristic
143C22×C151#41311yescharacteristic
144C22×C151C2×#10411yescharacteristic
145C22×C151C2×#10411yescharacteristic
146C22×C151#42111yescharacteristic
147C22×C151#42111yescharacteristic
148C4×C151—22no—
149C4×C151—22no—
150C4×C151—22no—
151C4×C151—22no—
152C4×C151—41no—
153C4×C151—41no—
154C4×C151—81no—
155C4×C151—81no—
156C4×C151—81no—
157C4×C151—81no—
158C2×C151—42no—
159C2×C151#152411yescharacteristic
160C2×C151#152911yescharacteristic
161C2×C151#153211yescharacteristic
162C2×C151#153511yescharacteristic
163C2×C151#182211yescharacteristic
164C2×C151#182611yescharacteristic
165C2×C151#182611yescharacteristic
166#8720C15111yesmaximal, characteristic, direct product factor, Sylow
167C151#872011yescharacteristic, direct product factor, Sylow
168#2283C2×C15111yescharacteristic
169#1749C2×C15111yescharacteristic
170#1749C2×C15111yescharacteristic
171#1295C2×C15112yescomplemented
172#1295C2×C15112yescomplemented
173C22×C42C22×C15111yescharacteristic
174C2×C22⋊C8—21no—
175C2×C22⋊C8—21no—
176C2×#97C22×C15112yes—
177C2×#97C22×C15112yes—
178#383—21no—
179#382C22×C15111yescharacteristic
180#382C22×C15111yescharacteristic
181#381—21no—
182#380C4×C15111yescharacteristic
183#380C4×C15111yescharacteristic
184C4×C4⋊C4C4×C15111yescharacteristic
185C4×C4⋊C4C4×C15111yescharacteristic
186C4×C22⋊C4—21no—
187#376—21no—
188#336—21no—
189#336—21no—
190C23×C4C2×C4×C15111yescharacteristic
191C23×C4D4×C15111yescharacteristic
192C23×C4D4×C15111yescharacteristic
193C22×C8—22no—
194C22×C8—22no—
195C2×C4⋊C4C2×C4×C15111yescharacteristic
196C2×C4⋊C4C2×C4×C15111yescharacteristic
197C2×C4⋊C4C2×C4×C15111yescharacteristic
198C2×C4⋊C4C2×C4×C15111yescharacteristic
199C2×C22⋊C4—21no—
200C2×C22⋊C4—21no—
201C2×C42—24no—
202C2×C42—21no—
203C2×C42—21no—
204C2×C42C2×C4×C15111yescharacteristic
205C2×C42D4×C15111yescharacteristic
206C2×C42D4×C15111yescharacteristic
207C2×C42C23×C15111yescharacteristic
208C22⋊C8—24no—
209C22⋊C8—24no—
210#97—24no—
211#97—24no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95—21no—
220C24C22⋊C4×C15111yescharacteristic
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—41no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4C22⋊C4×C15111yescharacteristic
235C22×C4C22⋊C4×C15111yescharacteristic
236C22×C4C22⋊C4×C15111yescharacteristic
237C22×C4C22×C4×C15111yescharacteristic
238C22×C4C2×D4×C15111yescharacteristic
239C22×C4C2×D4×C15111yescharacteristic
240C2×C8—24no—
241C2×C8—24no—
242C2×C8—42no—
243C2×C8—42no—
244C2×C8—42no—
245C2×C8—42no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C22⋊C4—42no—
251C22⋊C4—42no—
252C42—22no—
253C42—22no—
254C42—22no—
255C42—42no—
256C42—42no—
257C42#41×C15114yes—
258C23—21no—
259C23—21no—
260C23—21no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23#104×C15112yes—
265C23C2×C22⋊C4×C15111yescharacteristic
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—44no—
281C2×C4—44no—
282C2×C4—44no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4#104×C15112yes—
296C2×C4#117×C15112yes—
297C2×C4#123×C15112yes—
298C2×C4#123×C15112yes—
299C8—44no—
300C8—44no—
301C22—22no—
302C22—22no—
303C22—22no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22#381×C15111yescharacteristic
309C22#413×C15111yescharacteristic
310C22#413×C15111yescharacteristic
311C22C2×#104×C15111yescharacteristic
312C22C2×#104×C15111yescharacteristic
313C22#421×C15111yescharacteristic
314C22#421×C15111yescharacteristic
315C4—22no—
316C4—22no—
317C4—22no—
318C4—22no—
319C4—41no—
320C4—41no—
321C4—81no—
322C4—81no—
323C4—81no—
324C4—81no—
325C2—42no—
326C2#1524×C15111yescharacteristic
327C2#1529×C15111yescharacteristic
328C2#1532×C15111yescharacteristic
329C2#1535×C15111yescharacteristic
330C2#1822×C15111yescharacteristic
331C2#1826×C15111yescharacteristic
332C2#1826×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C2×C22⋊C4
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×C42C23×C151
prime radicalC24×C151C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1295×C151C2semidirect
5. #1295×C151C2semidirect
166. #8720C151direct (N × H)
167. C151#8720direct (N × H)
171. #1295C2×C151semidirect
172. #1295C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2283×C1512
#1749×C1512
#1295×C1512
#8720151