Finite Group Databasebeta

← C151×#9472 #50314397

Subgroups — C151×#9472 #50314397

Order 38656.

912 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2973×C151C211yesmaximal, characteristic, complemented
2#2408×C151C211yesmaximal, characteristic
3#1799×C151C211yesmaximal, characteristic, complemented
4#1786×C151C212yesmaximal, complemented
5#1289×C151C212yesmaximal, complemented
6C23×D4×C151C2211yescharacteristic
7C2×#121×C151—21no—
8C2×#120×C151—21no—
9C2×C4×D4×C151C2211yescharacteristic
10#435×C151—24no—
11#432×C151—21no—
12C2×#102×C151—24no—
13C2×#99×C151—21no—
14#407×C151—21no—
15C2×C22⋊C8×C151C2212yes—
16#394×C151C412yescomplemented
17#392×C151C412yescomplemented
18#390×C151—21no—
19#380×C151C2212yes—
20#380×C151C2211yescharacteristic
21#379×C151—21no—
22#342×C151—21no—
23C25×C151—21no—
24C22×D4×C151—21no—
25C22×D4×C151—22no—
26C22×D4×C151—22no—
27C22×D4×C151—22no—
28C22×D4×C151—44no—
29C22×D4×C151C2×C412yes—
30C22×D4×C151D411yescharacteristic
31C23×C4×C151D411yescharacteristic
32C23×C4×C151C2311yescharacteristic
33C2×M16×C151—22no—
34C22×C8×C151D414yescomplemented
35#121×C151—44no—
36#120×C151—44no—
37C4×D4×C151—22no—
38C4×D4×C151—22no—
39C2×C4⋊C4×C151—21no—
40C2×C4⋊C4×C151—22no—
41C2×C4⋊C4×C151C2×C411yescharacteristic
42C2×C22⋊C4×C151—22no—
43C2×C22⋊C4×C151—22no—
44C2×C22⋊C4×C151—22no—
45C2×C22⋊C4×C151—21no—
46C2×C22⋊C4×C151—22no—
47C2×C22⋊C4×C151C2×C411yescharacteristic
48C2×C22⋊C4×C151D411yescharacteristic
49C2×C42×C151D411yescharacteristic
50C4⋊C8×C151—22no—
51#102×C151—48no—
52#99×C151—42no—
53C22⋊C8×C151—22no—
54C22⋊C8×C151—22no—
55C22⋊C8×C151—22no—
56#97×C151—22no—
57#95×C151—22no—
58#95×C151C2×C412yes—
59C24×C151—22no—
60C24×C151—44no—
61C24×C151—42no—
62C24×C151—42no—
63C24×C151—41no—
64C24×C151—41no—
65C24×C151—82no—
66C24×C151C22⋊C411yescharacteristic
67C24×C151C2×D411yescharacteristic
68C2×D4×C151—28no—
69C2×D4×C151—24no—
70C2×D4×C151—22no—
71C2×D4×C151—21no—
72C2×D4×C151—22no—
73C2×D4×C151—21no—
74C2×D4×C151—24no—
75C2×D4×C151—44no—
76C2×D4×C151—42no—
77C2×D4×C151—44no—
78C2×D4×C151—48no—
79C2×D4×C151—44no—
80C2×D4×C151—44no—
81C2×D4×C151—41no—
82C2×D4×C151—41no—
83C2×D4×C151—82no—
84C22×C4×C151—21no—
85C22×C4×C151—21no—
86C22×C4×C151—22no—
87C22×C4×C151—42no—
88C22×C4×C151—42no—
89C22×C4×C151—42no—
90C22×C4×C151C22⋊C411yescharacteristic
91C22×C4×C151C22⋊C411yescharacteristic
92C22×C4×C151C22⋊C411yescharacteristic
93C22×C4×C151C22×C411yescharacteristic
94C22×C4×C151C2×D412yes—
95C22×C4×C151C2×D411yescharacteristic
96C22×C4×C151#4112yes—
97M16×C151—82no—
98C2×C8×C151—24no—
99C2×C8×C151—44no—
100C4⋊C4×C151—22no—
101C4⋊C4×C151—42no—
102C4⋊C4×C151—44no—
103C22⋊C4×C151—22no—
104C22⋊C4×C151—22no—
105C22⋊C4×C151—44no—
106C22⋊C4×C151—44no—
107C22⋊C4×C151—42no—
108C22⋊C4×C151—42no—
109C22⋊C4×C151—42no—
110C22⋊C4×C151—82no—
111C42×C151—21no—
112C42×C151—21no—
113C23×C151—24no—
114C23×C151—21no—
115C23×C151—21no—
116C23×C151—21no—
117C23×C151—41no—
118C23×C151—41no—
119C23×C151—41no—
120C23×C151—41no—
121C23×C151—42no—
122C23×C151—42no—
123C23×C151—42no—
124C23×C151—48no—
125C23×C151—42no—
126C23×C151—42no—
127C23×C151—42no—
128C23×C151—84no—
129C23×C151—88no—
130C23×C151—84no—
131C23×C151—84no—
132C23×C151—82no—
133C23×C151—82no—
134C23×C151C2×C22⋊C411yescharacteristic
135C23×C151#12112yes—
136C23×C151AGL(1,ℤ/8)11yescharacteristic
137C23×C151AGL(1,ℤ/8)12yes—
138C23×C151#13711yescharacteristic
139D4×C151—28no—
140D4×C151—44no—
141D4×C151—44no—
142D4×C151—42no—
143D4×C151—42no—
144D4×C151—44no—
145D4×C151—88no—
146C2×C4×C151—24no—
147C2×C4×C151—22no—
148C2×C4×C151—21no—
149C2×C4×C151—21no—
150C2×C4×C151—21no—
151C2×C4×C151—21no—
152C2×C4×C151—21no—
153C2×C4×C151—41no—
154C2×C4×C151—42no—
155C2×C4×C151—42no—
156C2×C4×C151—41no—
157C2×C4×C151—41no—
158C2×C4×C151—42no—
159C2×C4×C151—42no—
160C2×C4×C151—42no—
161C2×C4×C151—81no—
162C2×C4×C151—82no—
163C2×C4×C151—82no—
164C2×C4×C151—82no—
165C2×C4×C151C4×D412yes—
166C2×C4×C151#12011yescharacteristic
167C2×C4×C151#12311yescharacteristic
168C8×C151—44no—
169C22×C151—21no—
170C22×C151—22no—
171C22×C151—21no—
172C22×C151—22no—
173C22×C151—42no—
174C22×C151—41no—
175C22×C151—41no—
176C22×C151—42no—
177C22×C151—44no—
178C22×C151—44no—
179C22×C151—41no—
180C22×C151—44no—
181C22×C151—41no—
182C22×C151—41no—
183C22×C151—81no—
184C22×C151—82no—
185C22×C151—82no—
186C22×C151—88no—
187C22×C151—88no—
188C22×C151—82no—
189C22×C151—82no—
190C22×C151#38611yescharacteristic
191C22×C151#41711yescharacteristic
192C22×C151#41811yescharacteristic
193C22×C151#46812yes—
194C22×C151#46912yes—
195C4×C151—21no—
196C4×C151—22no—
197C4×C151—41no—
198C4×C151—41no—
199C4×C151—41no—
200C4×C151—82no—
201C4×C151—162no—
202C4×C151B(4,𝔽2)12yes—
203C2×C151—21no—
204C2×C151—22no—
205C2×C151—21no—
206C2×C151—22no—
207C2×C151—81no—
208C2×C151—84no—
209C2×C151#188911yescharacteristic
210C2×C151#189511yescharacteristic
211C2×C151#191011yescharacteristic
212#9472C15111yesmaximal, characteristic, direct product factor, Sylow
213C151#947211yescharacteristic, direct product factor, Sylow
214#2973C2×C15111yescharacteristic, complemented
215#2408C2×C15111yescharacteristic
216#1799C2×C15111yescharacteristic, complemented
217#1786C2×C15112yescomplemented
218#1289C2×C15112yescomplemented
219C23×D4C22×C15111yescharacteristic
220C2×#121—21no—
221C2×#120—21no—
222C2×C4×D4C22×C15111yescharacteristic
223#435—24no—
224#432—21no—
225C2×#102—24no—
226C2×#99—21no—
227#407—21no—
228C2×C22⋊C8C22×C15112yes—
229#394C4×C15112yescomplemented
230#392C4×C15112yescomplemented
231#390—21no—
232#380C22×C15112yes—
233#380C22×C15111yescharacteristic
234#379—21no—
235#342—21no—
236C25—21no—
237C22×D4—22no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—21no—
241C22×D4—44no—
242C22×D4C2×C4×C15112yes—
243C22×D4D4×C15111yescharacteristic
244C23×C4D4×C15111yescharacteristic
245C23×C4C23×C15111yescharacteristic
246C2×M16—22no—
247C22×C8D4×C15114yescomplemented
248#121—44no—
249#120—44no—
250C4×D4—22no—
251C4×D4—22no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4C2×C4×C15111yescharacteristic
255C2×C22⋊C4—21no—
256C2×C22⋊C4—22no—
257C2×C22⋊C4—22no—
258C2×C22⋊C4—22no—
259C2×C22⋊C4—22no—
260C2×C22⋊C4C2×C4×C15111yescharacteristic
261C2×C22⋊C4D4×C15111yescharacteristic
262C2×C42D4×C15111yescharacteristic
263C4⋊C8—22no—
264#102—48no—
265#99—42no—
266C22⋊C8—22no—
267C22⋊C8—22no—
268C22⋊C8—22no—
269#97—22no—
270#95—22no—
271#95C2×C4×C15112yes—
272C24—22no—
273C24—44no—
274C24—42no—
275C24—42no—
276C24—41no—
277C24—41no—
278C24—82no—
279C24C22⋊C4×C15111yescharacteristic
280C24C2×D4×C15111yescharacteristic
281C2×D4—28no—
282C2×D4—24no—
283C2×D4—22no—
284C2×D4—21no—
285C2×D4—22no—
286C2×D4—21no—
287C2×D4—24no—
288C2×D4—44no—
289C2×D4—42no—
290C2×D4—44no—
291C2×D4—48no—
292C2×D4—44no—
293C2×D4—44no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—82no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—22no—
300C22×C4—42no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4C22⋊C4×C15111yescharacteristic
304C22×C4C22⋊C4×C15111yescharacteristic
305C22×C4C22⋊C4×C15111yescharacteristic
306C22×C4C22×C4×C15111yescharacteristic
307C22×C4C2×D4×C15112yes—
308C22×C4C2×D4×C15111yescharacteristic
309C22×C4#41×C15112yes—
310M16—82no—
311C2×C8—24no—
312C2×C8—44no—
313C4⋊C4—22no—
314C4⋊C4—42no—
315C4⋊C4—44no—
316C22⋊C4—22no—
317C22⋊C4—22no—
318C22⋊C4—44no—
319C22⋊C4—44no—
320C22⋊C4—42no—
321C22⋊C4—42no—
322C22⋊C4—42no—
323C22⋊C4—82no—
324C42—21no—
325C42—21no—
326C23—24no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—42no—
335C23—48no—
336C23—42no—
337C23—42no—
338C23—42no—
339C23—42no—
340C23—42no—
341C23—84no—
342C23—88no—
343C23—84no—
344C23—84no—
345C23—82no—
346C23—82no—
347C23C2×C22⋊C4×C15111yescharacteristic
348C23#121×C15112yes—
349C23AGL(1,ℤ/8)×C15111yescharacteristic
350C23AGL(1,ℤ/8)×C15112yes—
351C23#137×C15111yescharacteristic
352D4—28no—
353D4—44no—
354D4—44no—
355D4—42no—
356D4—42no—
357D4—44no—
358D4—88no—
359C2×C4—24no—
360C2×C4—22no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—42no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—81no—
375C2×C4—82no—
376C2×C4—82no—
377C2×C4—82no—
378C2×C4C4×D4×C15112yes—
379C2×C4#120×C15111yescharacteristic
380C2×C4#123×C15111yescharacteristic
381C8—44no—
382C22—21no—
383C22—22no—
384C22—21no—
385C22—22no—
386C22—42no—
387C22—41no—
388C22—41no—
389C22—42no—
390C22—44no—
391C22—44no—
392C22—41no—
393C22—44no—
394C22—41no—
395C22—41no—
396C22—81no—
397C22—82no—
398C22—82no—
399C22—88no—
400C22—88no—
401C22—82no—
402C22—82no—
403C22#386×C15111yescharacteristic
404C22#417×C15111yescharacteristic
405C22#418×C15111yescharacteristic
406C22#468×C15112yes—
407C22#469×C15112yes—
408C4—21no—
409C4—22no—
410C4—41no—
411C4—41no—
412C4—41no—
413C4—82no—
414C4—162no—
415C4B(4,𝔽2)×C15112yes—
416C2—21no—
417C2—22no—
418C2—21no—
419C2—22no—
420C2—81no—
421C2—84no—
422C2#1889×C15111yescharacteristic
423C2#1895×C15111yescharacteristic
424C2#1910×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#386
commutatorC22×C4C22×C4×C151
Frattini, cosocleC23×C4C23×C151
prime radical#2408×C151C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2973×C151C2semidirect
3. #1799×C151C2semidirect
4. #1786×C151C2semidirect
5. #1289×C151C2semidirect
16. #394×C151C4semidirect
17. #392×C151C4semidirect
34. C22×C8×C151D4semidirect
212. #9472C151direct (N × H)
213. C151#9472direct (N × H)
214. #2973C2×C151semidirect
216. #1799C2×C151semidirect
217. #1786C2×C151semidirect
218. #1289C2×C151semidirect
229. #394C4×C151semidirect
230. #392C4×C151semidirect
247. C22×C8D4×C151semidirect

Maximal subgroups

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

subgroupindex
#2973×C1512
#2408×C1512
#1799×C1512
#1786×C1512
#1289×C1512
#9472151