Finite Group Databasebeta

← C151×#8052 #50312977

Subgroups — C151×#8052 #50312977

Order 38656.

696 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2920×C151C211yesmaximal, characteristic
2#2283×C151C211yesmaximal, characteristic
3C4×#117×C151C211yesmaximal, characteristic
4#1297×C151C214yesmaximal
5C2×#117×C151—21no—
6C22×C42×C151C2211yescharacteristic
7#432×C151—21no—
8#432×C151—21no—
9#431×C151—21no—
10#431×C151—21no—
11#423×C151C412yescomplemented
12#407×C151C2212yes—
13C4×M16×C151C412yescomplemented
14#383×C151C412yescomplemented
15#382×C151C412yescomplemented
16#381×C151—21no—
17#380×C151—21no—
18C4×C4⋊C4×C151—21no—
19C4×C4⋊C4×C151—21no—
20C4×C4⋊C4×C151C412yescomplemented
21C4×C22⋊C4×C151—21no—
22C4×C22⋊C4×C151C2212yes—
23C4×C22⋊C4×C151C2212yes—
24#376×C151—21no—
25#376×C151C412yescomplemented
26C43×C151—21no—
27C23×C4×C151D411yescharacteristic
28C23×C4×C151D411yescharacteristic
29C23×C4×C151C2311yescharacteristic
30C2×M16×C151C2×C414yes—
31#117×C151—28no—
32C2×C4⋊C4×C151—22no—
33C2×C4⋊C4×C151—22no—
34C2×C22⋊C4×C151—22no—
35C2×C22⋊C4×C151—22no—
36C2×C42×C151—22no—
37C2×C42×C151—22no—
38C2×C42×C151—22no—
39C2×C42×C151—22no—
40C2×C42×C151C2×C411yescharacteristic
41C2×C42×C151C2×C411yescharacteristic
42C2×C42×C151C2×C411yescharacteristic
43C2×C42×C151C2×C411yescharacteristic
44C2×C42×C151C2×C411yescharacteristic
45C2×C42×C151C2×C411yescharacteristic
46C2×C42×C151D411yescharacteristic
47C2×C42×C151D411yescharacteristic
48C2×C42×C151D411yescharacteristic
49C2×C42×C151D411yescharacteristic
50C2×C42×C151Q811yescharacteristic
51C2×C42×C151Q811yescharacteristic
52C4⋊C8×C151—22no—
53C4⋊C8×C151—22no—
54C22⋊C8×C151—22no—
55C22⋊C8×C151—22no—
56#97×C151—22no—
57C4×C8×C151—22no—
58#95×C151—22no—
59#95×C151—22no—
60#95×C151—22no—
61#95×C151—22no—
62#95×C151C2×C414yes—
63#95×C151C2×C414yes—
64C24×C151C2×D411yescharacteristic
65C22×C4×C151—24no—
66C22×C4×C151—24no—
67C22×C4×C151—24no—
68C22×C4×C151—42no—
69C22×C4×C151—42no—
70C22×C4×C151C22⋊C411yescharacteristic
71C22×C4×C151C22⋊C411yescharacteristic
72C22×C4×C151C22⋊C411yescharacteristic
73C22×C4×C151C22⋊C411yescharacteristic
74C22×C4×C151C22⋊C411yescharacteristic
75C22×C4×C151C22⋊C411yescharacteristic
76C22×C4×C151C22⋊C411yescharacteristic
77C22×C4×C151C22⋊C411yescharacteristic
78C22×C4×C151C4⋊C411yescharacteristic
79C22×C4×C151C4⋊C411yescharacteristic
80C22×C4×C151C4⋊C411yescharacteristic
81C22×C4×C151C4⋊C411yescharacteristic
82C22×C4×C151C22×C411yescharacteristic
83C22×C4×C151C22×C411yescharacteristic
84C22×C4×C151C22×C411yescharacteristic
85C22×C4×C151C2×D411yescharacteristic
86C22×C4×C151C2×D411yescharacteristic
87C22×C4×C151C2×Q811yescharacteristic
88M16×C151—44no—
89C2×C8×C151—24no—
90C4⋊C4×C151—28no—
91C4⋊C4×C151—44no—
92C22⋊C4×C151—28no—
93C22⋊C4×C151—44no—
94C42×C151—28no—
95C42×C151—44no—
96C42×C151—44no—
97C42×C151—44no—
98C42×C151C4211yescharacteristic
99C42×C151C4211yescharacteristic
100C42×C151C4211yescharacteristic
101C42×C151C4211yescharacteristic
102C42×C151C22⋊C411yescharacteristic
103C42×C151C22⋊C411yescharacteristic
104C42×C151C22⋊C411yescharacteristic
105C42×C151C22⋊C411yescharacteristic
106C42×C151C4⋊C411yescharacteristic
107C42×C151C4⋊C411yescharacteristic
108C42×C151C4⋊C411yescharacteristic
109C42×C151C4⋊C411yescharacteristic
110C42×C151C4⋊C411yescharacteristic
111C42×C151C4⋊C411yescharacteristic
112C42×C151C4⋊C411yescharacteristic
113C42×C151C4⋊C411yescharacteristic
114C23×C151—22no—
115C23×C151—22no—
116C23×C151—41no—
117C23×C151C2×C22⋊C411yescharacteristic
118C23×C151C2×C22⋊C411yescharacteristic
119C23×C151C2×C4⋊C411yescharacteristic
120C2×C4×C151—22no—
121C2×C4×C151—22no—
122C2×C4×C151—22no—
123C2×C4×C151—22no—
124C2×C4×C151—22no—
125C2×C4×C151—22no—
126C2×C4×C151—22no—
127C2×C4×C151—22no—
128C2×C4×C151—22no—
129C2×C4×C151—22no—
130C2×C4×C151—28no—
131C2×C4×C151—41no—
132C2×C4×C151—41no—
133C2×C4×C151—41no—
134C2×C4×C151—41no—
135C2×C4×C151—41no—
136C2×C4×C151—41no—
137C2×C4×C151—41no—
138C2×C4×C151—44no—
139C2×C4×C151—44no—
140C2×C4×C151—44no—
141C2×C4×C151—44no—
142C2×C4×C151—44no—
143C2×C4×C151#9511yescharacteristic
144C2×C4×C151#9511yescharacteristic
145C2×C4×C151#9511yescharacteristic
146C2×C4×C151#9511yescharacteristic
147C2×C4×C151#9511yescharacteristic
148C2×C4×C151#9511yescharacteristic
149C2×C4×C151#9511yescharacteristic
150C2×C4×C151#9511yescharacteristic
151C2×C4×C151#10414yes—
152C2×C4×C151C2×C4211yescharacteristic
153C2×C4×C151C2×C22⋊C411yescharacteristic
154C2×C4×C151C2×C4⋊C411yescharacteristic
155C2×C4×C151C2×C4⋊C411yescharacteristic
156C8×C151—44no—
157C22×C151—21no—
158C22×C151—21no—
159C22×C151—21no—
160C22×C151—21no—
161C22×C151—21no—
162C22×C151—21no—
163C22×C151—21no—
164C22×C151—44no—
165C22×C151C2×#9511yescharacteristic
166C22×C151C2×#10412yes—
167C22×C151#42112yes—
168C4×C151—21no—
169C4×C151—21no—
170C4×C151—21no—
171C4×C151—21no—
172C4×C151—21no—
173C4×C151—21no—
174C4×C151—21no—
175C4×C151—21no—
176C4×C151—21no—
177C4×C151—48no—
178C4×C151—84no—
179C4×C151#33912yes—
180C4×C151#33912yes—
181C4×C151#41012yes—
182C2×C151—22no—
183C2×C151—22no—
184C2×C151—41no—
185C2×C151C2×#33911yescharacteristic
186C2×C151#173311yescharacteristic
187C2×C151#174011yescharacteristic
188#8052C15111yesmaximal, characteristic, direct product factor, Sylow
189C151#805211yescharacteristic, direct product factor, Sylow
190#2920C2×C15111yescharacteristic
191#2283C2×C15111yescharacteristic
192C4×#117C2×C15111yescharacteristic
193#1297C2×C15114yes—
194C2×#117—21no—
195C22×C42C22×C15111yescharacteristic
196#432—21no—
197#432—21no—
198#431—21no—
199#431—21no—
200#423C4×C15112yescomplemented
201#407C22×C15112yes—
202C4×M16C4×C15112yescomplemented
203#383C4×C15112yescomplemented
204#382C4×C15112yescomplemented
205#381—21no—
206#380—21no—
207C4×C4⋊C4—21no—
208C4×C4⋊C4—21no—
209C4×C4⋊C4C4×C15112yescomplemented
210C4×C22⋊C4—21no—
211C4×C22⋊C4C22×C15112yes—
212C4×C22⋊C4C22×C15112yes—
213#376—21no—
214#376C4×C15112yescomplemented
215C43—21no—
216C23×C4D4×C15111yescharacteristic
217C23×C4D4×C15111yescharacteristic
218C23×C4C23×C15111yescharacteristic
219C2×M16C2×C4×C15114yes—
220#117—28no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—22no—
223C2×C22⋊C4—22no—
224C2×C22⋊C4—22no—
225C2×C42—22no—
226C2×C42—22no—
227C2×C42—22no—
228C2×C42—22no—
229C2×C42C2×C4×C15111yescharacteristic
230C2×C42C2×C4×C15111yescharacteristic
231C2×C42C2×C4×C15111yescharacteristic
232C2×C42C2×C4×C15111yescharacteristic
233C2×C42C2×C4×C15111yescharacteristic
234C2×C42C2×C4×C15111yescharacteristic
235C2×C42D4×C15111yescharacteristic
236C2×C42D4×C15111yescharacteristic
237C2×C42D4×C15111yescharacteristic
238C2×C42D4×C15111yescharacteristic
239C2×C42Q8×C15111yescharacteristic
240C2×C42Q8×C15111yescharacteristic
241C4⋊C8—22no—
242C4⋊C8—22no—
243C22⋊C8—22no—
244C22⋊C8—22no—
245#97—22no—
246C4×C8—22no—
247#95—22no—
248#95—22no—
249#95—22no—
250#95—22no—
251#95C2×C4×C15114yes—
252#95C2×C4×C15114yes—
253C24C2×D4×C15111yescharacteristic
254C22×C4—24no—
255C22×C4—24no—
256C22×C4—24no—
257C22×C4—42no—
258C22×C4—42no—
259C22×C4C22⋊C4×C15111yescharacteristic
260C22×C4C22⋊C4×C15111yescharacteristic
261C22×C4C22⋊C4×C15111yescharacteristic
262C22×C4C22⋊C4×C15111yescharacteristic
263C22×C4C22⋊C4×C15111yescharacteristic
264C22×C4C22⋊C4×C15111yescharacteristic
265C22×C4C22⋊C4×C15111yescharacteristic
266C22×C4C22⋊C4×C15111yescharacteristic
267C22×C4C4⋊C4×C15111yescharacteristic
268C22×C4C4⋊C4×C15111yescharacteristic
269C22×C4C4⋊C4×C15111yescharacteristic
270C22×C4C4⋊C4×C15111yescharacteristic
271C22×C4C22×C4×C15111yescharacteristic
272C22×C4C22×C4×C15111yescharacteristic
273C22×C4C22×C4×C15111yescharacteristic
274C22×C4C2×D4×C15111yescharacteristic
275C22×C4C2×D4×C15111yescharacteristic
276C22×C4C2×Q8×C15111yescharacteristic
277M16—44no—
278C2×C8—24no—
279C4⋊C4—28no—
280C4⋊C4—44no—
281C22⋊C4—28no—
282C22⋊C4—44no—
283C42—28no—
284C42—44no—
285C42—44no—
286C42—44no—
287C42C42×C15111yescharacteristic
288C42C42×C15111yescharacteristic
289C42C42×C15111yescharacteristic
290C42C42×C15111yescharacteristic
291C42C22⋊C4×C15111yescharacteristic
292C42C22⋊C4×C15111yescharacteristic
293C42C22⋊C4×C15111yescharacteristic
294C42C22⋊C4×C15111yescharacteristic
295C42C4⋊C4×C15111yescharacteristic
296C42C4⋊C4×C15111yescharacteristic
297C42C4⋊C4×C15111yescharacteristic
298C42C4⋊C4×C15111yescharacteristic
299C42C4⋊C4×C15111yescharacteristic
300C42C4⋊C4×C15111yescharacteristic
301C42C4⋊C4×C15111yescharacteristic
302C42C4⋊C4×C15111yescharacteristic
303C23—22no—
304C23—22no—
305C23—41no—
306C23C2×C22⋊C4×C15111yescharacteristic
307C23C2×C22⋊C4×C15111yescharacteristic
308C23C2×C4⋊C4×C15111yescharacteristic
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—28no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—44no—
328C2×C4—44no—
329C2×C4—44no—
330C2×C4—44no—
331C2×C4—44no—
332C2×C4#95×C15111yescharacteristic
333C2×C4#95×C15111yescharacteristic
334C2×C4#95×C15111yescharacteristic
335C2×C4#95×C15111yescharacteristic
336C2×C4#95×C15111yescharacteristic
337C2×C4#95×C15111yescharacteristic
338C2×C4#95×C15111yescharacteristic
339C2×C4#95×C15111yescharacteristic
340C2×C4#104×C15114yes—
341C2×C4C2×C42×C15111yescharacteristic
342C2×C4C2×C22⋊C4×C15111yescharacteristic
343C2×C4C2×C4⋊C4×C15111yescharacteristic
344C2×C4C2×C4⋊C4×C15111yescharacteristic
345C8—44no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—44no—
354C22C2×#95×C15111yescharacteristic
355C22C2×#104×C15112yes—
356C22#421×C15112yes—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—48no—
367C4—84no—
368C4#339×C15112yes—
369C4#339×C15112yes—
370C4#410×C15112yes—
371C2—22no—
372C2—22no—
373C2—41no—
374C2C2×#339×C15111yescharacteristic
375C2#1733×C15111yescharacteristic
376C2#1740×C15111yescharacteristic
subgroupG/H
centerC2×C4×C151C2×C22⋊C4
commutatorC2×C4C2×C42×C151
Frattini, cosocleC23×C4C23×C151
socleC22×C151C2×#95
prime radicalC24×C151C2×D4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
11. #423×C151C4semidirect
13. C4×M16×C151C4semidirect
14. #383×C151C4semidirect
15. #382×C151C4semidirect
20. C4×C4⋊C4×C151C4semidirect
25. #376×C151C4semidirect
188. #8052C151direct (N × H)
189. C151#8052direct (N × H)
200. #423C4×C151semidirect
202. C4×M16C4×C151semidirect
203. #383C4×C151semidirect
204. #382C4×C151semidirect
209. C4×C4⋊C4C4×C151semidirect
214. #376C4×C151semidirect

Maximal subgroups

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

subgroupindex
#2920×C1512
#2283×C1512
C4×#117×C1512
#1297×C1512
#8052151