Finite Group Databasebeta

← C151×#9886 #50314811

Subgroups — C151×#9886 #50314811

Order 38656.

566 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2851×C151C211yesmaximal, characteristic
2C4×C22⋊C8×C151C211yesmaximal, characteristic
3#1434×C151C211yesmaximal, characteristic
4#1294×C151C212yesmaximal
5#1294×C151C212yesmaximal
6C2×#125×C151C411yescharacteristic, complemented
7C22×C42×C151C2211yescharacteristic
8C2×C22⋊C8×C151C2212yes—
9C2×C4×C8×C151—21no—
10#389×C151C411yescharacteristic, complemented
11#389×C151C411yescharacteristic, complemented
12#387×C151—21no—
13#387×C151—21no—
14#385×C151—21no—
15#385×C151—21no—
16#382×C151C411yescharacteristic, complemented
17#380×C151C2211yescharacteristic
18#380×C151C2211yescharacteristic
19C2×#95×C151—21no—
20C2×#95×C151—21no—
21C2×#95×C151C2212yes—
22#336×C151—21no—
23C23×C4×C151—22no—
24C23×C4×C151D411yescharacteristic
25C23×C4×C151D411yescharacteristic
26C23×C4×C151C2311yescharacteristic
27C22×C8×C151—22no—
28#125×C151—42no—
29C2×C4⋊C4×C151—21no—
30C2×C4⋊C4×C151—21no—
31C2×C4⋊C4×C151—21no—
32C2×C4⋊C4×C151—21no—
33C2×C4⋊C4×C151C2×C411yescharacteristic
34C2×C4⋊C4×C151C2×C411yescharacteristic
35C2×C4⋊C4×C151C2×C411yescharacteristic
36C2×C4⋊C4×C151C2×C411yescharacteristic
37C2×C22⋊C4×C151—21no—
38C2×C22⋊C4×C151—21no—
39C2×C42×C151—42no—
40C2×C42×C151C2×C411yescharacteristic
41C2×C42×C151C2×C411yescharacteristic
42C2×C42×C151D411yescharacteristic
43C2×C42×C151D411yescharacteristic
44C22⋊C8×C151—22no—
45C22⋊C8×C151Q814yes—
46C4×C8×C151—42no—
47#95×C151—24no—
48#95×C151—21no—
49#95×C151—21no—
50#95×C151—21no—
51#95×C151—21no—
52#95×C151—21no—
53#95×C151—21no—
54#95×C151—24no—
55#95×C151—42no—
56C24×C151C2×D411yescharacteristic
57C22×C4×C151—22no—
58C22×C4×C151—22no—
59C22×C4×C151—22no—
60C22×C4×C151—22no—
61C22×C4×C151—24no—
62C22×C4×C151—21no—
63C22×C4×C151—21no—
64C22×C4×C151—21no—
65C22×C4×C151—21no—
66C22×C4×C151—41no—
67C22×C4×C151—41no—
68C22×C4×C151—41no—
69C22×C4×C151—41no—
70C22×C4×C151—42no—
71C22×C4×C151—42no—
72C22×C4×C151—42no—
73C22×C4×C151—42no—
74C22×C4×C151—42no—
75C22×C4×C151—42no—
76C22×C4×C151C22⋊C411yescharacteristic
77C22×C4×C151C22⋊C411yescharacteristic
78C22×C4×C151C22⋊C411yescharacteristic
79C22×C4×C151C22⋊C411yescharacteristic
80C22×C4×C151C22×C411yescharacteristic
81C22×C4×C151C2×D411yescharacteristic
82C22×C4×C151C2×Q812yes—
83C22×C4×C151#4112yes—
84C2×C8×C151—24no—
85C2×C8×C151—42no—
86C2×C8×C151—42no—
87C4⋊C4×C151—41no—
88C4⋊C4×C151—41no—
89C4⋊C4×C151—41no—
90C4⋊C4×C151—41no—
91C4⋊C4×C151—42no—
92C4⋊C4×C151—42no—
93C4⋊C4×C151—42no—
94C4⋊C4×C151—42no—
95C22⋊C4×C151—42no—
96C22⋊C4×C151—42no—
97C42×C151—22no—
98C42×C151—22no—
99C42×C151—41no—
100C42×C151—41no—
101C23×C151—21no—
102C23×C151—21no—
103C23×C151—21no—
104C23×C151—21no—
105C23×C151C2×C22⋊C411yescharacteristic
106C23×C151#12411yescharacteristic
107C23×C151C4⋊Q811yescharacteristic
108C23×C151#13512yes—
109C23×C151#13512yes—
110C2×C4×C151—21no—
111C2×C4×C151—21no—
112C2×C4×C151—21no—
113C2×C4×C151—21no—
114C2×C4×C151—21no—
115C2×C4×C151—21no—
116C2×C4×C151—21no—
117C2×C4×C151—21no—
118C2×C4×C151—21no—
119C2×C4×C151—21no—
120C2×C4×C151—21no—
121C2×C4×C151—21no—
122C2×C4×C151—21no—
123C2×C4×C151—21no—
124C2×C4×C151—42no—
125C2×C4×C151—42no—
126C2×C4×C151—44no—
127C2×C4×C151—44no—
128C2×C4×C151—44no—
129C2×C4×C151—44no—
130C2×C4×C151—44no—
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—41no—
139C2×C4×C151—41no—
140C2×C4×C151—41no—
141C2×C4×C151—41no—
142C2×C4×C151—41no—
143C2×C4×C151—82no—
144C2×C4×C151—82no—
145C2×C4×C151—82no—
146C2×C4×C151—82no—
147C2×C4×C151#9912yes—
148C2×C4×C151#10412yes—
149C2×C4×C151C4×Q812yes—
150C2×C4×C151C22⋊Q812yes—
151C8×C151—44no—
152C22×C151—21no—
153C22×C151—21no—
154C22×C151—21no—
155C22×C151—21no—
156C22×C151—22no—
157C22×C151—22no—
158C22×C151—22no—
159C22×C151—22no—
160C22×C151#39111yescharacteristic
161C22×C151C2×#9911yescharacteristic
162C22×C151#41011yescharacteristic
163C22×C151#41611yescharacteristic
164C22×C151#41611yescharacteristic
165C22×C151C2×#10411yescharacteristic
166C22×C151#42111yescharacteristic
167C22×C151#48812yes—
168C22×C151#49912yes—
169C4×C151—22no—
170C4×C151—22no—
171C4×C151—22no—
172C4×C151—22no—
173C4×C151—41no—
174C4×C151—41no—
175C4×C151—84no—
176C4×C151—81no—
177C4×C151—81no—
178C4×C151—81no—
179C4×C151—81no—
180C2×C151—22no—
181C2×C151—22no—
182C2×C151#150011yescharacteristic
183C2×C151#150111yescharacteristic
184C2×C151#151611yescharacteristic
185C2×C151#152111yescharacteristic
186C2×C151#198611yescharacteristic
187C2×C151#199111yescharacteristic
188C2×C151#199611yescharacteristic
189#9886C15111yesmaximal, characteristic, direct product factor, Sylow
190C151#988611yescharacteristic, direct product factor, Sylow
191#2851C2×C15111yescharacteristic
192C4×C22⋊C8C2×C15111yescharacteristic
193#1434C2×C15111yescharacteristic
194#1294C2×C15112yes—
195#1294C2×C15112yes—
196C2×#125C4×C15111yescharacteristic, complemented
197C22×C42C22×C15111yescharacteristic
198C2×C22⋊C8C22×C15112yes—
199C2×C4×C8—21no—
200#389C4×C15111yescharacteristic, complemented
201#389C4×C15111yescharacteristic, complemented
202#387—21no—
203#387—21no—
204#385—21no—
205#385—21no—
206#382C4×C15111yescharacteristic, complemented
207#380C22×C15111yescharacteristic
208#380C22×C15111yescharacteristic
209C2×#95—21no—
210C2×#95—21no—
211C2×#95C22×C15112yes—
212#336—21no—
213C23×C4—22no—
214C23×C4D4×C15111yescharacteristic
215C23×C4D4×C15111yescharacteristic
216C23×C4C23×C15111yescharacteristic
217C22×C8—22no—
218#125—42no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4C2×C4×C15111yescharacteristic
224C2×C4⋊C4C2×C4×C15111yescharacteristic
225C2×C4⋊C4C2×C4×C15111yescharacteristic
226C2×C4⋊C4C2×C4×C15111yescharacteristic
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C42—42no—
230C2×C42C2×C4×C15111yescharacteristic
231C2×C42C2×C4×C15111yescharacteristic
232C2×C42D4×C15111yescharacteristic
233C2×C42D4×C15111yescharacteristic
234C22⋊C8—22no—
235C22⋊C8Q8×C15114yes—
236C4×C8—42no—
237#95—24no—
238#95—21no—
239#95—21no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95—21no—
244#95—24no—
245#95—42no—
246C24C2×D4×C15111yescharacteristic
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—24no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—42no—
263C22×C4—42no—
264C22×C4—42no—
265C22×C4—42no—
266C22×C4C22⋊C4×C15111yescharacteristic
267C22×C4C22⋊C4×C15111yescharacteristic
268C22×C4C22⋊C4×C15111yescharacteristic
269C22×C4C22⋊C4×C15111yescharacteristic
270C22×C4C22×C4×C15111yescharacteristic
271C22×C4C2×D4×C15111yescharacteristic
272C22×C4C2×Q8×C15112yes—
273C22×C4#41×C15112yes—
274C2×C8—24no—
275C2×C8—42no—
276C2×C8—42no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C4⋊C4—42no—
284C4⋊C4—42no—
285C22⋊C4—42no—
286C22⋊C4—42no—
287C42—22no—
288C42—22no—
289C42—41no—
290C42—41no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23C2×C22⋊C4×C15111yescharacteristic
296C23#124×C15111yescharacteristic
297C23C4⋊Q8×C15111yescharacteristic
298C23#135×C15112yes—
299C23#135×C15112yes—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—44no—
317C2×C4—44no—
318C2×C4—44no—
319C2×C4—44no—
320C2×C4—44no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—82no—
334C2×C4—82no—
335C2×C4—82no—
336C2×C4—82no—
337C2×C4#99×C15112yes—
338C2×C4#104×C15112yes—
339C2×C4C4×Q8×C15112yes—
340C2×C4C22⋊Q8×C15112yes—
341C8—44no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—22no—
347C22—22no—
348C22—22no—
349C22—22no—
350C22#391×C15111yescharacteristic
351C22C2×#99×C15111yescharacteristic
352C22#410×C15111yescharacteristic
353C22#416×C15111yescharacteristic
354C22#416×C15111yescharacteristic
355C22C2×#104×C15111yescharacteristic
356C22#421×C15111yescharacteristic
357C22#488×C15112yes—
358C22#499×C15112yes—
359C4—22no—
360C4—22no—
361C4—22no—
362C4—22no—
363C4—41no—
364C4—41no—
365C4—84no—
366C4—81no—
367C4—81no—
368C4—81no—
369C4—81no—
370C2—22no—
371C2—22no—
372C2#1500×C15111yescharacteristic
373C2#1501×C15111yescharacteristic
374C2#1516×C15111yescharacteristic
375C2#1521×C15111yescharacteristic
376C2#1986×C15111yescharacteristic
377C2#1991×C15111yescharacteristic
378C2#1996×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C2×C22⋊C4
commutatorC22×C4C22×C4×C151
Frattini, cosocleC23×C4C23×C151
prime radicalC24×C151C2×D4
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
6. C2×#125×C151C4semidirect
10. #389×C151C4semidirect
11. #389×C151C4semidirect
16. #382×C151C4semidirect
189. #9886C151direct (N × H)
190. C151#9886direct (N × H)
196. C2×#125C4×C151semidirect
200. #389C4×C151semidirect
201. #389C4×C151semidirect
206. #382C4×C151semidirect

Maximal subgroups

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

subgroupindex
#2851×C1512
C4×C22⋊C8×C1512
#1434×C1512
#1294×C1512
#9886151