Finite Group Databasebeta

← C151×#8899 #50313824

Subgroups — C151×#8899 #50313824

Order 38656.

388 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2991×C151C211yesmaximal, characteristic
2#1848×C151C211yesmaximal, characteristic, complemented
3#1574×C151C211yesmaximal, characteristic, complemented
4#1489×C151C211yesmaximal, characteristic
5#1476×C151C211yesmaximal, characteristic
6#1299×C151C211yesmaximal, characteristic, complemented
7#1278×C151C211yesmaximal, characteristic, complemented
8C4×#41×C151C2211yescharacteristic
9C8×Q8×C151—21no—
10#436×C151—22no—
11#436×C151—21no—
12#431×C151—21no—
13#431×C151C2211yescharacteristic
14#431×C151C2211yescharacteristic
15C2×#108×C151—22no—
16#423×C151—21no—
17#423×C151C2211yescharacteristic
18#423×C151C2211yescharacteristic
19C4×M16×C151C2211yescharacteristic
20C2×C4×C8×C151C2211yescharacteristic
21#335×C151—21no—
22#334×C151—21no—
23Q8⋊C8×C151—21no—
24Q8⋊C8×C151C411yescharacteristic
25Q8⋊C8×C151C411yescharacteristic
26D4⋊C8×C151—21no—
27D4⋊C8×C151C411yescharacteristic
28D4⋊C8×C151C411yescharacteristic
29C2×#41×C151Q811yescharacteristic
30C2×M16×C151—22no—
31C2×M16×C151—21no—
32C2×M16×C151—21no—
33C2×M16×C151D412yes—
34C22×C8×C151—21no—
35C4×Q8×C151C2×C411yescharacteristic
36C4×Q8×C151D411yescharacteristic
37C4×D4×C151—21no—
38C4×D4×C151—21no—
39C4×D4×C151C2×C411yescharacteristic
40C4×D4×C151D411yescharacteristic
41#117×C151—21no—
42#117×C151Q811yescharacteristic
43C2×C42×C151—21no—
44C2×C42×C151C2311yescharacteristic
45#108×C151—44no—
46C4⋊C8×C151—22no—
47C4⋊C8×C151—21no—
48C4⋊C8×C151—21no—
49C4⋊C8×C151—21no—
50C4⋊C8×C151—21no—
51C4⋊C8×C151C2×C411yescharacteristic
52C4⋊C8×C151C2×C411yescharacteristic
53C4⋊C8×C151D411yescharacteristic
54C4⋊C8×C151D411yescharacteristic
55C22⋊C8×C151—22no—
56C22⋊C8×C151—21no—
57C22⋊C8×C151—21no—
58#97×C151—21no—
59C4×C8×C151—22no—
60C4×C8×C151—21no—
61C4×C8×C151—21no—
62C4×C8×C151—21no—
63C4×C8×C151—21no—
64C4×C8×C151C2×C411yescharacteristic
65C4×C8×C151C2×C411yescharacteristic
66#41×C151—22no—
67#41×C151—41no—
68C2×Q8×C151C4⋊C411yescharacteristic
69C2×D4×C151—21no—
70C2×D4×C151C4⋊C411yescharacteristic
71C22×C4×C151—21no—
72C22×C4×C151—21no—
73C22×C4×C151—21no—
74C22×C4×C151C2×D411yescharacteristic
75C22×C4×C151C2×Q811yescharacteristic
76C22×C4×C151#4111yescharacteristic
77M16×C151—22no—
78M16×C151—41no—
79M16×C151—42no—
80M16×C151—42no—
81M16×C151—82no—
82C2×C8×C151—22no—
83C2×C8×C151—22no—
84C2×C8×C151—21no—
85C2×C8×C151—21no—
86C2×C8×C151—21no—
87C2×C8×C151—21no—
88C2×C8×C151—21no—
89C2×C8×C151—22no—
90C2×C8×C151—21no—
91C2×C8×C151—41no—
92C2×C8×C151—41no—
93C4⋊C4×C151—21no—
94C4⋊C4×C151—21no—
95C4⋊C4×C151C4⋊C411yescharacteristic
96C4⋊C4×C151C4⋊C411yescharacteristic
97C22⋊C4×C151—21no—
98C22⋊C4×C151—21no—
99C22⋊C4×C151—21no—
100C42×C151—21no—
101C42×C151—21no—
102C42×C151—21no—
103C42×C151C22×C411yescharacteristic
104C42×C151C2×D411yescharacteristic
105C42×C151C2×D411yescharacteristic
106C42×C151#4111yescharacteristic
107C23×C151—21no—
108C23×C151C22⋊Q811yescharacteristic
109Q8×C151—21no—
110Q8×C151#10812yescomplemented
111D4×C151—21no—
112D4×C151—21no—
113D4×C151—42no—
114C2×C4×C151—21no—
115C2×C4×C151—21no—
116C2×C4×C151—21no—
117C2×C4×C151—21no—
118C2×C4×C151—21no—
119C2×C4×C151—21no—
120C2×C4×C151—21no—
121C2×C4×C151—21no—
122C2×C4×C151—21no—
123C2×C4×C151—42no—
124C2×C4×C151—41no—
125C2×C4×C151—41no—
126C2×C4×C151—41no—
127C2×C4×C151—41no—
128C2×C4×C151C2×C4⋊C411yescharacteristic
129C2×C4×C151C4×D411yescharacteristic
130C2×C4×C151C4×D411yescharacteristic
131C2×C4×C151#12011yescharacteristic
132C2×C4×C151C22⋊Q811yescharacteristic
133C2×C4×C151#12311yescharacteristic
134C8×C151—22no—
135C8×C151—22no—
136C8×C151—42no—
137C8×C151—41no—
138C8×C151—41no—
139C8×C151—42no—
140C8×C151—41no—
141C8×C151—41no—
142C8×C151—81no—
143C22×C151—21no—
144C22×C151—21no—
145C22×C151—21no—
146C22×C151—41no—
147C22×C151—41no—
148C22×C151—41no—
149C22×C151#38511yescharacteristic
150C4×C151—21no—
151C4×C151—22no—
152C4×C151—21no—
153C4×C151—21no—
154C4×C151—41no—
155C4×C151—41no—
156C4×C151C2×#10811yescharacteristic
157C4×C151#43011yescharacteristic
158C4×C151#44311yescharacteristic
159C4×C151#44411yescharacteristic
160C4×C151#45311yescharacteristic
161C4×C151#45611yescharacteristic
162C2×C151—41no—
163C2×C151—81no—
164C2×C151#185511yescharacteristic
165C2×C151#185911yescharacteristic
166C2×C151#186611yescharacteristic
167#8899C15111yesmaximal, characteristic, direct product factor, Sylow
168C151#889911yescharacteristic, direct product factor, Sylow
169#2991C2×C15111yescharacteristic
170#1848C2×C15111yescharacteristic, complemented
171#1574C2×C15111yescharacteristic, complemented
172#1489C2×C15111yescharacteristic
173#1476C2×C15111yescharacteristic
174#1299C2×C15111yescharacteristic, complemented
175#1278C2×C15111yescharacteristic, complemented
176C4×#41C22×C15111yescharacteristic
177C8×Q8—21no—
178#436—22no—
179#436—21no—
180#431—21no—
181#431C22×C15111yescharacteristic
182#431C22×C15111yescharacteristic
183C2×#108—22no—
184#423—21no—
185#423C22×C15111yescharacteristic
186#423C22×C15111yescharacteristic
187C4×M16C22×C15111yescharacteristic
188C2×C4×C8C22×C15111yescharacteristic
189#335—21no—
190#334—21no—
191Q8⋊C8—21no—
192Q8⋊C8C4×C15111yescharacteristic
193Q8⋊C8C4×C15111yescharacteristic
194D4⋊C8—21no—
195D4⋊C8C4×C15111yescharacteristic
196D4⋊C8C4×C15111yescharacteristic
197C2×#41Q8×C15111yescharacteristic
198C2×M16—22no—
199C2×M16—21no—
200C2×M16—21no—
201C2×M16D4×C15112yes—
202C22×C8—21no—
203C4×Q8C2×C4×C15111yescharacteristic
204C4×Q8D4×C15111yescharacteristic
205C4×D4—21no—
206C4×D4—21no—
207C4×D4C2×C4×C15111yescharacteristic
208C4×D4D4×C15111yescharacteristic
209#117—21no—
210#117Q8×C15111yescharacteristic
211C2×C42—21no—
212C2×C42C23×C15111yescharacteristic
213#108—44no—
214C4⋊C8—22no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8C2×C4×C15111yescharacteristic
220C4⋊C8C2×C4×C15111yescharacteristic
221C4⋊C8D4×C15111yescharacteristic
222C4⋊C8D4×C15111yescharacteristic
223C22⋊C8—22no—
224C22⋊C8—21no—
225C22⋊C8—21no—
226#97—21no—
227C4×C8—22no—
228C4×C8—21no—
229C4×C8—21no—
230C4×C8—21no—
231C4×C8—21no—
232C4×C8C2×C4×C15111yescharacteristic
233C4×C8C2×C4×C15111yescharacteristic
234#41—22no—
235#41—41no—
236C2×Q8C4⋊C4×C15111yescharacteristic
237C2×D4—21no—
238C2×D4C4⋊C4×C15111yescharacteristic
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4C2×D4×C15111yescharacteristic
243C22×C4C2×Q8×C15111yescharacteristic
244C22×C4#41×C15111yescharacteristic
245M16—22no—
246M16—41no—
247M16—42no—
248M16—42no—
249M16—82no—
250C2×C8—22no—
251C2×C8—22no—
252C2×C8—21no—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—22no—
258C2×C8—21no—
259C2×C8—41no—
260C2×C8—41no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4C4⋊C4×C15111yescharacteristic
264C4⋊C4C4⋊C4×C15111yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C42—21no—
269C42—21no—
270C42—21no—
271C42C22×C4×C15111yescharacteristic
272C42C2×D4×C15111yescharacteristic
273C42C2×D4×C15111yescharacteristic
274C42#41×C15111yescharacteristic
275C23—21no—
276C23C22⋊Q8×C15111yescharacteristic
277Q8—21no—
278Q8#108×C15112yescomplemented
279D4—21no—
280D4—21no—
281D4—42no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4C2×C4⋊C4×C15111yescharacteristic
297C2×C4C4×D4×C15111yescharacteristic
298C2×C4C4×D4×C15111yescharacteristic
299C2×C4#120×C15111yescharacteristic
300C2×C4C22⋊Q8×C15111yescharacteristic
301C2×C4#123×C15111yescharacteristic
302C8—22no—
303C8—22no—
304C8—42no—
305C8—41no—
306C8—41no—
307C8—42no—
308C8—41no—
309C8—41no—
310C8—81no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22#385×C15111yescharacteristic
318C4—21no—
319C4—22no—
320C4—21no—
321C4—21no—
322C4—41no—
323C4—41no—
324C4C2×#108×C15111yescharacteristic
325C4#430×C15111yescharacteristic
326C4#443×C15111yescharacteristic
327C4#444×C15111yescharacteristic
328C4#453×C15111yescharacteristic
329C4#456×C15111yescharacteristic
330C2—41no—
331C2—81no—
332C2#1855×C15111yescharacteristic
333C2#1859×C15111yescharacteristic
334C2#1866×C15111yescharacteristic
subgroupG/H
centerC2×C4×C151#120
commutatorC42C22×C4×C151
Frattini, cosocleC2×C42C23×C151
socleC22×C151#385
prime radicalC2×#41×C151Q8
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1848×C151C2semidirect
3. #1574×C151C2semidirect
6. #1299×C151C2semidirect
7. #1278×C151C2semidirect
110. Q8×C151#108semidirect
167. #8899C151direct (N × H)
168. C151#8899direct (N × H)
170. #1848C2×C151semidirect
171. #1574C2×C151semidirect
174. #1299C2×C151semidirect
175. #1278C2×C151semidirect
278. Q8#108×C151semidirect

Maximal subgroups

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

subgroupindex
#2991×C1512
#1848×C1512
#1574×C1512
#1489×C1512
#1476×C1512
#1299×C1512
#1278×C1512
#8899151