Finite Group Databasebeta

← C151×#9715 #50314640

Subgroups — C151×#9715 #50314640

Order 38656.

764 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2856×C151C211yesmaximal, characteristic
2#1797×C151C211yesmaximal, characteristic, complemented
3C2×#327×C151C214yesmaximal, complemented
4#1434×C151C211yesmaximal, characteristic, complemented
5C2×#127×C151C411yescharacteristic, complemented
6C2×#121×C151—21no—
7C2×#121×C151—21no—
8C2×#121×C151C2212yes—
9C22×C42×C151C2211yescharacteristic
10C2×C4⋊C8×C151—21no—
11C2×C22⋊C8×C151C2212yes—
12#390×C151—21no—
13#390×C151—21no—
14#390×C151C412yescomplemented
15#384×C151C411yescharacteristic, complemented
16C2×#95×C151—21no—
17C2×#95×C151—21no—
18C2×#95×C151C2212yes—
19#336×C151—21no—
20#327×C151—28no—
21C22×D4×C151—21no—
22C22×D4×C151—21no—
23C22×D4×C151—22no—
24C22×D4×C151C2×C412yes—
25C23×C4×C151—22no—
26C23×C4×C151D411yescharacteristic
27C23×C4×C151D411yescharacteristic
28C23×C4×C151C2311yescharacteristic
29C22×C8×C151—22no—
30#127×C151—42no—
31#121×C151—24no—
32#121×C151—24no—
33#121×C151—44no—
34#121×C151—42no—
35#121×C151—42no—
36C2×C4⋊C4×C151—21no—
37C2×C4⋊C4×C151—21no—
38C2×C4⋊C4×C151C2×C412yes—
39C2×C22⋊C4×C151—22no—
40C2×C22⋊C4×C151—22no—
41C2×C22⋊C4×C151—22no—
42C2×C42×C151—42no—
43C2×C42×C151C2×C411yescharacteristic
44C2×C42×C151C2×C411yescharacteristic
45C2×C42×C151D411yescharacteristic
46C2×C42×C151D411yescharacteristic
47C4⋊C8×C151—42no—
48C22⋊C8×C151—24no—
49#95×C151—22no—
50#95×C151—42no—
51#95×C151—42no—
52#95×C151D414yescomplemented
53C24×C151—22no—
54C24×C151C2×D411yescharacteristic
55C2×D4×C151—24no—
56C2×D4×C151—42no—
57C2×D4×C151—42no—
58C2×D4×C151—42no—
59C2×D4×C151—42no—
60C2×D4×C151—42no—
61C2×D4×C151—42no—
62C2×D4×C151—44no—
63C2×D4×C151—42no—
64C2×D4×C151—42no—
65C2×D4×C151—44no—
66C2×D4×C151—42no—
67C2×D4×C151—42no—
68C22×C4×C151—22no—
69C22×C4×C151—22no—
70C22×C4×C151—22no—
71C22×C4×C151—24no—
72C22×C4×C151—41no—
73C22×C4×C151—41no—
74C22×C4×C151—41no—
75C22×C4×C151—41no—
76C22×C4×C151—41no—
77C22×C4×C151—42no—
78C22×C4×C151—42no—
79C22×C4×C151—42no—
80C22×C4×C151—42no—
81C22×C4×C151—42no—
82C22×C4×C151—42no—
83C22×C4×C151C22⋊C411yescharacteristic
84C22×C4×C151C22⋊C411yescharacteristic
85C22×C4×C151C22⋊C411yescharacteristic
86C22×C4×C151C22⋊C411yescharacteristic
87C22×C4×C151D812yes—
88C22×C4×C151SD1612yes—
89C22×C4×C151C22×C411yescharacteristic
90C22×C4×C151C2×D411yescharacteristic
91C22×C4×C151C2×D412yes—
92C22×C4×C151#4112yes—
93C2×C8×C151—42no—
94C2×C8×C151—42no—
95C2×C8×C151—42no—
96C4⋊C4×C151—24no—
97C4⋊C4×C151—42no—
98C4⋊C4×C151—42no—
99C22⋊C4×C151—44no—
100C22⋊C4×C151—44no—
101C22⋊C4×C151—42no—
102C22⋊C4×C151—42no—
103C42×C151—22no—
104C42×C151—22no—
105C42×C151—41no—
106C42×C151—41no—
107C23×C151—21no—
108C23×C151—21no—
109C23×C151—21no—
110C23×C151—21no—
111C23×C151—42no—
112C23×C151—42no—
113C23×C151—42no—
114C23×C151—42no—
115C23×C151—42no—
116C23×C151—42no—
117C23×C151—42no—
118C23×C151C2×C22⋊C411yescharacteristic
119C23×C151#12112yes—
120C23×C151C2×D811yescharacteristic
121C23×C151C2×SD1611yescharacteristic
122C23×C151AGL(1,ℤ/8)12yes—
123D4×C151—84no—
124D4×C151—84no—
125D4×C151—84no—
126D4×C151—84no—
127D4×C151—84no—
128C2×C4×C151—21no—
129C2×C4×C151—21no—
130C2×C4×C151—21no—
131C2×C4×C151—21no—
132C2×C4×C151—21no—
133C2×C4×C151—21no—
134C2×C4×C151—21no—
135C2×C4×C151—21no—
136C2×C4×C151—21no—
137C2×C4×C151—21no—
138C2×C4×C151—21no—
139C2×C4×C151—21no—
140C2×C4×C151—21no—
141C2×C4×C151—42no—
142C2×C4×C151—42no—
143C2×C4×C151—42no—
144C2×C4×C151—42no—
145C2×C4×C151—44no—
146C2×C4×C151—44no—
147C2×C4×C151—44no—
148C2×C4×C151—42no—
149C2×C4×C151—42no—
150C2×C4×C151—42no—
151C2×C4×C151—44no—
152C2×C4×C151—82no—
153C2×C4×C151—82no—
154C2×C4×C151—82no—
155C2×C4×C151—82no—
156C2×C4×C151#9912yes—
157C2×C4×C151#10212yes—
158C2×C4×C151#10212yes—
159C2×C4×C151C4×D412yes—
160C2×C4×C151#12411yescharacteristic
161C2×C4×C151#12711yescharacteristic
162C8×C151—82no—
163C22×C151—22no—
164C22×C151—22no—
165C22×C151—22no—
166C22×C151—22no—
167C22×C151—21no—
168C22×C151—21no—
169C22×C151—21no—
170C22×C151—21no—
171C22×C151—82no—
172C22×C151—82no—
173C22×C151—82no—
174C22×C151—82no—
175C22×C151—82no—
176C22×C151—82no—
177C22×C151—82no—
178C22×C151#39011yescharacteristic
179C22×C151C2×#9911yescharacteristic
180C22×C151#41011yescharacteristic
181C22×C151C2×#10211yescharacteristic
182C22×C151#41811yescharacteristic
183C22×C151#42111yescharacteristic
184C22×C151#42111yescharacteristic
185C22×C151#45912yes—
186C22×C151#46012yes—
187C4×C151—21no—
188C4×C151—22no—
189C4×C151—21no—
190C4×C151—22no—
191C4×C151—22no—
192C4×C151—22no—
193C4×C151—41no—
194C4×C151—84no—
195C4×C151—82no—
196C2×C151—22no—
197C2×C151—22no—
198C2×C151—162no—
199C2×C151#151011yescharacteristic
200C2×C151#151411yescharacteristic
201C2×C151#151711yescharacteristic
202C2×C151#151911yescharacteristic
203C2×C151#196311yescharacteristic
204C2×C151#196411yescharacteristic
205C2×C151#198211yescharacteristic
206#9715C15111yesmaximal, characteristic, direct product factor, Sylow
207C151#971511yescharacteristic, direct product factor, Sylow
208#2856C2×C15111yescharacteristic
209#1797C2×C15111yescharacteristic, complemented
210C2×#327C2×C15114yescomplemented
211#1434C2×C15111yescharacteristic, complemented
212C2×#127C4×C15111yescharacteristic, complemented
213C2×#121—21no—
214C2×#121—21no—
215C2×#121C22×C15112yes—
216C22×C42C22×C15111yescharacteristic
217C2×C4⋊C8—21no—
218C2×C22⋊C8C22×C15112yes—
219#390—21no—
220#390—21no—
221#390C4×C15112yescomplemented
222#384C4×C15111yescharacteristic, complemented
223C2×#95—21no—
224C2×#95—21no—
225C2×#95C22×C15112yes—
226#336—21no—
227#327—28no—
228C22×D4—22no—
229C22×D4—21no—
230C22×D4—21no—
231C22×D4C2×C4×C15112yes—
232C23×C4—22no—
233C23×C4D4×C15111yescharacteristic
234C23×C4D4×C15111yescharacteristic
235C23×C4C23×C15111yescharacteristic
236C22×C8—22no—
237#127—42no—
238#121—24no—
239#121—24no—
240#121—44no—
241#121—42no—
242#121—42no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4C2×C4×C15112yes—
246C2×C22⋊C4—22no—
247C2×C22⋊C4—22no—
248C2×C22⋊C4—22no—
249C2×C42—42no—
250C2×C42C2×C4×C15111yescharacteristic
251C2×C42C2×C4×C15111yescharacteristic
252C2×C42D4×C15111yescharacteristic
253C2×C42D4×C15111yescharacteristic
254C4⋊C8—42no—
255C22⋊C8—24no—
256#95—22no—
257#95—42no—
258#95—42no—
259#95D4×C15114yescomplemented
260C24—22no—
261C24C2×D4×C15111yescharacteristic
262C2×D4—24no—
263C2×D4—42no—
264C2×D4—42no—
265C2×D4—42no—
266C2×D4—42no—
267C2×D4—42no—
268C2×D4—42no—
269C2×D4—44no—
270C2×D4—42no—
271C2×D4—42no—
272C2×D4—44no—
273C2×D4—42no—
274C2×D4—42no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—24no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4C22⋊C4×C15111yescharacteristic
291C22×C4C22⋊C4×C15111yescharacteristic
292C22×C4C22⋊C4×C15111yescharacteristic
293C22×C4C22⋊C4×C15111yescharacteristic
294C22×C4D8×C15112yes—
295C22×C4SD16×C15112yes—
296C22×C4C22×C4×C15111yescharacteristic
297C22×C4C2×D4×C15111yescharacteristic
298C22×C4C2×D4×C15112yes—
299C22×C4#41×C15112yes—
300C2×C8—42no—
301C2×C8—42no—
302C2×C8—42no—
303C4⋊C4—24no—
304C4⋊C4—42no—
305C4⋊C4—42no—
306C22⋊C4—44no—
307C22⋊C4—44no—
308C22⋊C4—42no—
309C22⋊C4—42no—
310C42—22no—
311C42—22no—
312C42—41no—
313C42—41no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—42no—
319C23—42no—
320C23—42no—
321C23—42no—
322C23—42no—
323C23—42no—
324C23—42no—
325C23C2×C22⋊C4×C15111yescharacteristic
326C23#121×C15112yes—
327C23C2×D8×C15111yescharacteristic
328C23C2×SD16×C15111yescharacteristic
329C23AGL(1,ℤ/8)×C15112yes—
330D4—84no—
331D4—84no—
332D4—84no—
333D4—84no—
334D4—84no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—44no—
353C2×C4—44no—
354C2×C4—44no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—44no—
359C2×C4—82no—
360C2×C4—82no—
361C2×C4—82no—
362C2×C4—82no—
363C2×C4#99×C15112yes—
364C2×C4#102×C15112yes—
365C2×C4#102×C15112yes—
366C2×C4C4×D4×C15112yes—
367C2×C4#124×C15111yescharacteristic
368C2×C4#127×C15111yescharacteristic
369C8—82no—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—82no—
379C22—82no—
380C22—82no—
381C22—82no—
382C22—82no—
383C22—82no—
384C22—82no—
385C22#390×C15111yescharacteristic
386C22C2×#99×C15111yescharacteristic
387C22#410×C15111yescharacteristic
388C22C2×#102×C15111yescharacteristic
389C22#418×C15111yescharacteristic
390C22#421×C15111yescharacteristic
391C22#421×C15111yescharacteristic
392C22#459×C15112yes—
393C22#460×C15112yes—
394C4—21no—
395C4—22no—
396C4—21no—
397C4—22no—
398C4—22no—
399C4—22no—
400C4—41no—
401C4—84no—
402C4—82no—
403C2—22no—
404C2—22no—
405C2—162no—
406C2#1510×C15111yescharacteristic
407C2#1514×C15111yescharacteristic
408C2#1517×C15111yescharacteristic
409C2#1519×C15111yescharacteristic
410C2#1963×C15111yescharacteristic
411C2#1964×C15111yescharacteristic
412C2#1982×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C2×C22⋊C4
commutatorC22×C4C22×C4×C151
Frattini, cosocleC23×C4C23×C151
prime radical#2856×C151C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1797×C151C2semidirect
3. C2×#327×C151C2semidirect
4. #1434×C151C2semidirect
5. C2×#127×C151C4semidirect
14. #390×C151C4semidirect
15. #384×C151C4semidirect
52. #95×C151D4semidirect
206. #9715C151direct (N × H)
207. C151#9715direct (N × H)
209. #1797C2×C151semidirect
210. C2×#327C2×C151semidirect
211. #1434C2×C151semidirect
212. C2×#127C4×C151semidirect
221. #390C4×C151semidirect
222. #384C4×C151semidirect
259. #95D4×C151semidirect

Maximal subgroups

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

subgroupindex
#2856×C1512
#1797×C1512
C2×#327×C1512
#1434×C1512
#9715151