Finite Group Databasebeta

← C151×#9110 #50314035

Subgroups — C151×#9110 #50314035

Order 38656.

560 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2973×C151C211yesmaximal, characteristic
2#2322×C151C211yesmaximal, characteristic
3#1459×C151C211yesmaximal, characteristic
4C2×#324×C151C212yesmaximal, complemented
5#1282×C151C212yesmaximal, complemented
6C2×#123×C151C411yescharacteristic
7C2×C4×D4×C151C2211yescharacteristic
8C22×C4⋊C4×C151C2211yescharacteristic
9#435×C151—24no—
10#432×C151—21no—
11#407×C151—21no—
12C2×C22⋊C8×C151C2212yes—
13C2×C22⋊C8×C151C2212yes—
14#389×C151—21no—
15#388×C151—21no—
16#387×C151—21no—
17#386×C151C411yescharacteristic
18#385×C151—21no—
19#385×C151C411yescharacteristic
20#381×C151C411yescharacteristic
21C4×C22⋊C4×C151C2211yescharacteristic
22#324×C151—21no—
23#324×C151—24no—
24#323×C151—21no—
25C22×D4×C151C2×C411yescharacteristic
26C23×C4×C151C2×C411yescharacteristic
27C23×C4×C151C2×C411yescharacteristic
28C23×C4×C151D411yescharacteristic
29C23×C4×C151C2311yescharacteristic
30C2×M16×C151—22no—
31C22×C8×C151—22no—
32C22×C8×C151—22no—
33#123×C151—22no—
34#123×C151—22no—
35C4×D4×C151—22no—
36C4×D4×C151—22no—
37C2×C4⋊C4×C151—21no—
38C2×C4⋊C4×C151—21no—
39C2×C4⋊C4×C151—21no—
40C2×C4⋊C4×C151—22no—
41C2×C4⋊C4×C151—22no—
42C2×C4⋊C4×C151—21no—
43C2×C4⋊C4×C151D411yescharacteristic
44C2×C22⋊C4×C151—21no—
45C2×C22⋊C4×C151—21no—
46C2×C22⋊C4×C151C2×C411yescharacteristic
47C2×C22⋊C4×C151C2×C411yescharacteristic
48C2×C22⋊C4×C151C2×C411yescharacteristic
49C2×C22⋊C4×C151D411yescharacteristic
50C2×C42×C151—21no—
51C2×C42×C151D411yescharacteristic
52C4⋊C8×C151—22no—
53C22⋊C8×C151—22no—
54C22⋊C8×C151—22no—
55C22⋊C8×C151—22no—
56C22⋊C8×C151—22no—
57C22⋊C8×C151D414yes—
58#97×C151—22no—
59#95×C151—21no—
60#95×C151—21no—
61#95×C151—21no—
62#95×C151—21no—
63#95×C151—21no—
64C24×C151C22⋊C411yescharacteristic
65C24×C151C22×C411yescharacteristic
66C2×D4×C151—22no—
67C2×D4×C151—21no—
68C2×D4×C151—21no—
69C2×D4×C151—22no—
70C22×C4×C151—21no—
71C22×C4×C151—21no—
72C22×C4×C151—22no—
73C22×C4×C151—21no—
74C22×C4×C151—22no—
75C22×C4×C151—21no—
76C22×C4×C151—21no—
77C22×C4×C151—21no—
78C22×C4×C151—21no—
79C22×C4×C151—22no—
80C22×C4×C151—81no—
81C22×C4×C151—81no—
82C22×C4×C151—81no—
83C22×C4×C151C22⋊C411yescharacteristic
84C22×C4×C151C22⋊C411yescharacteristic
85C22×C4×C151C22⋊C411yescharacteristic
86C22×C4×C151M1612yescomplemented
87C22×C4×C151C2×D412yes—
88C22×C4×C151C2×D411yescharacteristic
89C22×C4×C151C2×D411yescharacteristic
90C22×C4×C151#4112yes—
91M16×C151—82no—
92C2×C8×C151—24no—
93C2×C8×C151—42no—
94C2×C8×C151—82no—
95C2×C8×C151—82no—
96C4⋊C4×C151—24no—
97C4⋊C4×C151—22no—
98C4⋊C4×C151—41no—
99C4⋊C4×C151—42no—
100C4⋊C4×C151—41no—
101C4⋊C4×C151—81no—
102C22⋊C4×C151—24no—
103C22⋊C4×C151—22no—
104C22⋊C4×C151—21no—
105C22⋊C4×C151—22no—
106C22⋊C4×C151—22no—
107C22⋊C4×C151—81no—
108C22⋊C4×C151M1612yescomplemented
109C42×C151—21no—
110C42×C151—21no—
111C42×C151—81no—
112C23×C151—21no—
113C23×C151—21no—
114C23×C151—21no—
115C23×C151—41no—
116C23×C151—41no—
117C23×C151—41no—
118C23×C151—41no—
119C23×C151C2×C22⋊C411yescharacteristic
120C23×C151C4×D412yes—
121C23×C151C2×M1611yescharacteristic
122C23×C151C2×M1611yescharacteristic
123C23×C151#13112yes—
124D4×C151—42no—
125D4×C151—42no—
126C2×C4×C151—21no—
127C2×C4×C151—21no—
128C2×C4×C151—21no—
129C2×C4×C151—22no—
130C2×C4×C151—22no—
131C2×C4×C151—21no—
132C2×C4×C151—21no—
133C2×C4×C151—24no—
134C2×C4×C151—41no—
135C2×C4×C151—42no—
136C2×C4×C151—42no—
137C2×C4×C151—41no—
138C2×C4×C151—42no—
139C2×C4×C151—41no—
140C2×C4×C151—41no—
141C2×C4×C151—41no—
142C2×C4×C151—41no—
143C2×C4×C151—42no—
144C2×C4×C151—41no—
145C2×C4×C151—41no—
146C2×C4×C151—41no—
147C2×C4×C151—41no—
148C2×C4×C151—41no—
149C2×C4×C151—41no—
150C2×C4×C151—41no—
151C2×C4×C151—41no—
152C2×C4×C151—81no—
153C2×C4×C151—82no—
154C2×C4×C151#12011yescharacteristic
155C2×C4×C151#12112yes—
156C2×C4×C151#12311yescharacteristic
157C8×C151—44no—
158C8×C151—82no—
159C22×C151—21no—
160C22×C151—22no—
161C22×C151—21no—
162C22×C151—22no—
163C22×C151—41no—
164C22×C151—41no—
165C22×C151—42no—
166C22×C151—42no—
167C22×C151—41no—
168C22×C151—41no—
169C22×C151—41no—
170C22×C151—81no—
171C22×C151#38611yescharacteristic
172C22×C151#40711yescharacteristic
173C22×C151#40811yescharacteristic
174C22×C151#43512yes—
175C22×C151#43612yes—
176C4×C151—21no—
177C4×C151—22no—
178C4×C151—21no—
179C4×C151—42no—
180C4×C151—42no—
181C4×C151—41no—
182C4×C151—41no—
183C4×C151—41no—
184C4×C151—81no—
185C4×C151—81no—
186C2×C151—21no—
187C2×C151—21no—
188C2×C151—22no—
189C2×C151—22no—
190C2×C151—81no—
191C2×C151#187011yescharacteristic
192C2×C151#191311yescharacteristic
193C2×C151#191511yescharacteristic
194#9110C15111yesmaximal, characteristic, direct product factor, Sylow
195C151#911011yescharacteristic, direct product factor, Sylow
196#2973C2×C15111yescharacteristic
197#2322C2×C15111yescharacteristic
198#1459C2×C15111yescharacteristic
199C2×#324C2×C15112yescomplemented
200#1282C2×C15112yescomplemented
201C2×#123C4×C15111yescharacteristic
202C2×C4×D4C22×C15111yescharacteristic
203C22×C4⋊C4C22×C15111yescharacteristic
204#435—24no—
205#432—21no—
206#407—21no—
207C2×C22⋊C8C22×C15112yes—
208C2×C22⋊C8C22×C15112yes—
209#389—21no—
210#388—21no—
211#387—21no—
212#386C4×C15111yescharacteristic
213#385—21no—
214#385C4×C15111yescharacteristic
215#381C4×C15111yescharacteristic
216C4×C22⋊C4C22×C15111yescharacteristic
217#324—21no—
218#324—24no—
219#323—21no—
220C22×D4C2×C4×C15111yescharacteristic
221C23×C4C2×C4×C15111yescharacteristic
222C23×C4C2×C4×C15111yescharacteristic
223C23×C4D4×C15111yescharacteristic
224C23×C4C23×C15111yescharacteristic
225C2×M16—22no—
226C22×C8—22no—
227C22×C8—22no—
228#123—22no—
229#123—22no—
230C4×D4—22no—
231C4×D4—22no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4D4×C15111yescharacteristic
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4C2×C4×C15111yescharacteristic
242C2×C22⋊C4C2×C4×C15111yescharacteristic
243C2×C22⋊C4C2×C4×C15111yescharacteristic
244C2×C22⋊C4D4×C15111yescharacteristic
245C2×C42—21no—
246C2×C42D4×C15111yescharacteristic
247C4⋊C8—22no—
248C22⋊C8—22no—
249C22⋊C8—22no—
250C22⋊C8—22no—
251C22⋊C8—22no—
252C22⋊C8D4×C15114yes—
253#97—22no—
254#95—21no—
255#95—21no—
256#95—21no—
257#95—21no—
258#95—21no—
259C24C22⋊C4×C15111yescharacteristic
260C24C22×C4×C15111yescharacteristic
261C2×D4—22no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—22no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—22no—
268C22×C4—21no—
269C22×C4—22no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—22no—
275C22×C4—81no—
276C22×C4—81no—
277C22×C4—81no—
278C22×C4C22⋊C4×C15111yescharacteristic
279C22×C4C22⋊C4×C15111yescharacteristic
280C22×C4C22⋊C4×C15111yescharacteristic
281C22×C4M16×C15112yescomplemented
282C22×C4C2×D4×C15112yes—
283C22×C4C2×D4×C15111yescharacteristic
284C22×C4C2×D4×C15111yescharacteristic
285C22×C4#41×C15112yes—
286M16—82no—
287C2×C8—24no—
288C2×C8—42no—
289C2×C8—82no—
290C2×C8—82no—
291C4⋊C4—24no—
292C4⋊C4—22no—
293C4⋊C4—41no—
294C4⋊C4—42no—
295C4⋊C4—41no—
296C4⋊C4—81no—
297C22⋊C4—24no—
298C22⋊C4—22no—
299C22⋊C4—21no—
300C22⋊C4—22no—
301C22⋊C4—22no—
302C22⋊C4—81no—
303C22⋊C4M16×C15112yescomplemented
304C42—21no—
305C42—21no—
306C42—81no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23C2×C22⋊C4×C15111yescharacteristic
315C23C4×D4×C15112yes—
316C23C2×M16×C15111yescharacteristic
317C23C2×M16×C15111yescharacteristic
318C23#131×C15112yes—
319D4—42no—
320D4—42no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—24no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—81no—
348C2×C4—82no—
349C2×C4#120×C15111yescharacteristic
350C2×C4#121×C15112yes—
351C2×C4#123×C15111yescharacteristic
352C8—44no—
353C8—82no—
354C22—21no—
355C22—22no—
356C22—21no—
357C22—22no—
358C22—41no—
359C22—41no—
360C22—42no—
361C22—42no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—81no—
366C22#386×C15111yescharacteristic
367C22#407×C15111yescharacteristic
368C22#408×C15111yescharacteristic
369C22#435×C15112yes—
370C22#436×C15112yes—
371C4—21no—
372C4—22no—
373C4—21no—
374C4—42no—
375C4—42no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—81no—
380C4—81no—
381C2—21no—
382C2—21no—
383C2—22no—
384C2—22no—
385C2—81no—
386C2#1870×C15111yescharacteristic
387C2#1913×C15111yescharacteristic
388C2#1915×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#386
commutatorC24C22×C4×C151
Frattini, cosocleC23×C4C23×C151
prime radicalC22×D4×C151C2×C4
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×#324×C151C2semidirect
5. #1282×C151C2semidirect
86. C22×C4×C151M16semidirect
108. C22⋊C4×C151M16semidirect
194. #9110C151direct (N × H)
195. C151#9110direct (N × H)
199. C2×#324C2×C151semidirect
200. #1282C2×C151semidirect
281. C22×C4M16×C151semidirect
303. C22⋊C4M16×C151semidirect

Maximal subgroups

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

subgroupindex
#2973×C1512
#2322×C1512
#1459×C1512
C2×#324×C1512
#1282×C1512
#9110151