Finite Group Databasebeta

← C151×#8691 #50313616

Subgroups — C151×#8691 #50313616

Order 38656.

358 conjugacy classes of subgroups.

The subgroup lattice has 298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2966×C151C211yesmaximal, characteristic
2C4×#108×C151C211yesmaximal, characteristic, complemented
3#1568×C151C211yesmaximal, characteristic, complemented
4#1529×C151C212yesmaximal
5#1291×C151C212yesmaximal, complemented
6#529×C151C2211yescharacteristic
7#446×C151C411yescharacteristic
8C8×Q8×C151C411yescharacteristic
9#436×C151C411yescharacteristic
10#435×C151—21no—
11C8×D4×C151—21no—
12C8×D4×C151C411yescharacteristic
13#433×C151—21no—
14#432×C151C2212yes—
15#432×C151C2211yescharacteristic
16C2×#108×C151—21no—
17#405×C151—21no—
18C4×M16×C151C2212yes—
19C2×C4×C8×C151C2211yescharacteristic
20#341×C151—21no—
21#335×C151—21no—
22#334×C151—21no—
23#330×C151—22no—
24#329×C151—22no—
25C2×M16×C151—21no—
26C2×M16×C151—22no—
27C22×C8×C151—21no—
28C22×C8×C151D411yescharacteristic
29C22×C8×C151D411yescharacteristic
30#126×C151—21no—
31#125×C151D411yescharacteristic
32#124×C151D411yescharacteristic
33#123×C151—21no—
34C22⋊Q8×C151Q811yescharacteristic
35#121×C151Q811yescharacteristic
36C4×Q8×C151C2×C411yescharacteristic
37C4×D4×C151—21no—
38C4×D4×C151C2×C411yescharacteristic
39#117×C151—21no—
40C2×C42×C151C2311yescharacteristic
41#108×C151—24no—
42C4⋊C8×C151—21no—
43C4⋊C8×C151—21no—
44C4⋊C8×C151—22no—
45C4⋊C8×C151C2×C411yescharacteristic
46C4⋊C8×C151C2×C411yescharacteristic
47C22⋊C8×C151—21no—
48C22⋊C8×C151—21no—
49C22⋊C8×C151—21no—
50C22⋊C8×C151—22no—
51#97×C151—21no—
52#97×C151—21no—
53#97×C151—22no—
54#97×C151—22no—
55C4×C8×C151—21no—
56C4×C8×C151—22no—
57C4×C8×C151C2×C411yescharacteristic
58C4×C8×C151C2×C411yescharacteristic
59C4×C8×C151D411yescharacteristic
60C4×C8×C151D411yescharacteristic
61C2×Q8×C151C4⋊C411yescharacteristic
62C2×D4×C151—21no—
63C2×D4×C151C4⋊C411yescharacteristic
64C22×C4×C151—21no—
65C22×C4×C151C2×D411yescharacteristic
66C22×C4×C151C2×Q811yescharacteristic
67C22×C4×C151#4111yescharacteristic
68M16×C151—24no—
69M16×C151—42no—
70M16×C151—42no—
71C2×C8×C151—22no—
72C2×C8×C151—21no—
73C2×C8×C151—21no—
74C2×C8×C151—41no—
75C2×C8×C151—42no—
76C2×C8×C151—42no—
77C2×C8×C151—42no—
78C2×C8×C151C22⋊C411yescharacteristic
79C2×C8×C151C22⋊C411yescharacteristic
80C2×C8×C151C22⋊C411yescharacteristic
81C2×C8×C151C22⋊C411yescharacteristic
82C4⋊C4×C151—21no—
83C4⋊C4×C151—21no—
84C4⋊C4×C151—21no—
85C4⋊C4×C151—21no—
86C4⋊C4×C151C4⋊C411yescharacteristic
87C4⋊C4×C151C4⋊C411yescharacteristic
88C22⋊C4×C151—21no—
89C22⋊C4×C151—21no—
90C22⋊C4×C151—21no—
91C22⋊C4×C151—21no—
92C22⋊C4×C151—21no—
93C42×C151—21no—
94C42×C151C22×C411yescharacteristic
95C42×C151C2×D411yescharacteristic
96C42×C151C2×D411yescharacteristic
97C42×C151#4111yescharacteristic
98C23×C151—21no—
99C23×C151C22⋊Q811yescharacteristic
100Q8×C151—41no—
101D4×C151—41no—
102D4×C151—42no—
103C2×C4×C151—21no—
104C2×C4×C151—21no—
105C2×C4×C151—21no—
106C2×C4×C151—21no—
107C2×C4×C151—21no—
108C2×C4×C151—41no—
109C2×C4×C151—41no—
110C2×C4×C151—41no—
111C2×C4×C151—41no—
112C2×C4×C151C2×C22⋊C411yescharacteristic
113C2×C4×C151C2×C4⋊C411yescharacteristic
114C2×C4×C151#11711yescharacteristic
115C2×C4×C151#12111yescharacteristic
116C2×C4×C151#12111yescharacteristic
117C2×C4×C151C22⋊Q811yescharacteristic
118C8×C151—21no—
119C8×C151—21no—
120C8×C151—21no—
121C8×C151—44no—
122C8×C151—41no—
123C8×C151—41no—
124C8×C151—82no—
125C8×C151#10412yes—
126C22×C151—21no—
127C22×C151—21no—
128C22×C151—21no—
129C22×C151—41no—
130C22×C151—41no—
131C22×C151—41no—
132C22×C151#38011yescharacteristic
133C4×C151—21no—
134C4×C151—21no—
135C4×C151—21no—
136C4×C151—21no—
137C4×C151—21no—
138C4×C151—41no—
139C4×C151—41no—
140C4×C151—41no—
141C4×C151C2×#10411yescharacteristic
142C4×C151#42111yescharacteristic
143C2×C151—41no—
144C2×C151—81no—
145C2×C151#180611yescharacteristic
146C2×C151#181311yescharacteristic
147C2×C151#181411yescharacteristic
148#8691C15111yesmaximal, characteristic, direct product factor, Sylow
149C151#869111yescharacteristic, direct product factor, Sylow
150#2966C2×C15111yescharacteristic
151C4×#108C2×C15111yescharacteristic, complemented
152#1568C2×C15111yescharacteristic, complemented
153#1529C2×C15112yes—
154#1291C2×C15112yescomplemented
155#529C22×C15111yescharacteristic
156#446C4×C15111yescharacteristic
157C8×Q8C4×C15111yescharacteristic
158#436C4×C15111yescharacteristic
159#435—21no—
160C8×D4—21no—
161C8×D4C4×C15111yescharacteristic
162#433—21no—
163#432C22×C15112yes—
164#432C22×C15111yescharacteristic
165C2×#108—21no—
166#405—21no—
167C4×M16C22×C15112yes—
168C2×C4×C8C22×C15111yescharacteristic
169#341—21no—
170#335—21no—
171#334—21no—
172#330—22no—
173#329—22no—
174C2×M16—21no—
175C2×M16—22no—
176C22×C8—21no—
177C22×C8D4×C15111yescharacteristic
178C22×C8D4×C15111yescharacteristic
179#126—21no—
180#125D4×C15111yescharacteristic
181#124D4×C15111yescharacteristic
182#123—21no—
183C22⋊Q8Q8×C15111yescharacteristic
184#121Q8×C15111yescharacteristic
185C4×Q8C2×C4×C15111yescharacteristic
186C4×D4—21no—
187C4×D4C2×C4×C15111yescharacteristic
188#117—21no—
189C2×C42C23×C15111yescharacteristic
190#108—24no—
191C4⋊C8—21no—
192C4⋊C8—21no—
193C4⋊C8—22no—
194C4⋊C8C2×C4×C15111yescharacteristic
195C4⋊C8C2×C4×C15111yescharacteristic
196C22⋊C8—21no—
197C22⋊C8—21no—
198C22⋊C8—21no—
199C22⋊C8—22no—
200#97—21no—
201#97—21no—
202#97—22no—
203#97—22no—
204C4×C8—21no—
205C4×C8—22no—
206C4×C8C2×C4×C15111yescharacteristic
207C4×C8C2×C4×C15111yescharacteristic
208C4×C8D4×C15111yescharacteristic
209C4×C8D4×C15111yescharacteristic
210C2×Q8C4⋊C4×C15111yescharacteristic
211C2×D4—21no—
212C2×D4C4⋊C4×C15111yescharacteristic
213C22×C4—21no—
214C22×C4C2×D4×C15111yescharacteristic
215C22×C4C2×Q8×C15111yescharacteristic
216C22×C4#41×C15111yescharacteristic
217M16—24no—
218M16—42no—
219M16—42no—
220C2×C8—22no—
221C2×C8—21no—
222C2×C8—21no—
223C2×C8—41no—
224C2×C8—42no—
225C2×C8—42no—
226C2×C8—42no—
227C2×C8C22⋊C4×C15111yescharacteristic
228C2×C8C22⋊C4×C15111yescharacteristic
229C2×C8C22⋊C4×C15111yescharacteristic
230C2×C8C22⋊C4×C15111yescharacteristic
231C4⋊C4—21no—
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4C4⋊C4×C15111yescharacteristic
236C4⋊C4C4⋊C4×C15111yescharacteristic
237C22⋊C4—21no—
238C22⋊C4—21no—
239C22⋊C4—21no—
240C22⋊C4—21no—
241C22⋊C4—21no—
242C42—21no—
243C42C22×C4×C15111yescharacteristic
244C42C2×D4×C15111yescharacteristic
245C42C2×D4×C15111yescharacteristic
246C42#41×C15111yescharacteristic
247C23—21no—
248C23C22⋊Q8×C15111yescharacteristic
249Q8—41no—
250D4—41no—
251D4—42no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4C2×C22⋊C4×C15111yescharacteristic
262C2×C4C2×C4⋊C4×C15111yescharacteristic
263C2×C4#117×C15111yescharacteristic
264C2×C4#121×C15111yescharacteristic
265C2×C4#121×C15111yescharacteristic
266C2×C4C22⋊Q8×C15111yescharacteristic
267C8—21no—
268C8—21no—
269C8—21no—
270C8—44no—
271C8—41no—
272C8—41no—
273C8—82no—
274C8#104×C15112yes—
275C22—21no—
276C22—21no—
277C22—21no—
278C22—41no—
279C22—41no—
280C22—41no—
281C22#380×C15111yescharacteristic
282C4—21no—
283C4—21no—
284C4—21no—
285C4—21no—
286C4—21no—
287C4—41no—
288C4—41no—
289C4—41no—
290C4C2×#104×C15111yescharacteristic
291C4#421×C15111yescharacteristic
292C2—41no—
293C2—81no—
294C2#1806×C15111yescharacteristic
295C2#1813×C15111yescharacteristic
296C2#1814×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#380
commutatorC42C22×C4×C151
Frattini, cosocleC2×C42C23×C151
prime radical#121×C151Q8
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×#108×C151C2semidirect
3. #1568×C151C2semidirect
5. #1291×C151C2semidirect
148. #8691C151direct (N × H)
149. C151#8691direct (N × H)
151. C4×#108C2×C151semidirect
152. #1568C2×C151semidirect
154. #1291C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2966×C1512
C4×#108×C1512
#1568×C1512
#1529×C1512
#1291×C1512
#8691151