Finite Group Databasebeta

← C151×#9330 #50314255

Subgroups — C151×#9330 #50314255

Order 38656.

482 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3112×C151C211yesmaximal, characteristic
2#2320×C151C211yesmaximal, characteristic, complemented
3#1980×C151C211yesmaximal, characteristic
4#1505×C151C211yesmaximal, characteristic
5#1491×C151C211yesmaximal, characteristic, complemented
6#1300×C151C211yesmaximal, characteristic, complemented
7#1285×C151C211yesmaximal, characteristic, complemented
8#532×C151C2211yescharacteristic
9C2×C4×Q8×C151C2211yescharacteristic
10#480×C151—21no—
11#477×C151C412yescomplemented
12#460×C151C412yescomplemented
13#448×C151—21no—
14#440×C151—22no—
15#432×C151C2211yescharacteristic
16#432×C151C2211yescharacteristic
17C2×#104×C151—22no—
18C4×M16×C151C2211yescharacteristic
19#391×C151—21no—
20#389×C151—21no—
21#387×C151—22no—
22#383×C151—21no—
23#382×C151—21no—
24C4×C4⋊C4×C151C2211yescharacteristic
25#376×C151C2211yescharacteristic
26#327×C151—21no—
27#327×C151—21no—
28Q8⋊C8×C151—22no—
29C2×#41×C151—21no—
30C22×Q8×C151D411yescharacteristic
31C2×SD16×C151—22no—
32C2×M16×C151—21no—
33C4⋊Q8×C151C2×C411yescharacteristic
34#127×C151C2×C411yescharacteristic
35#124×C151—21no—
36#121×C151—21no—
37#121×C151—21no—
38C4×Q8×C151—21no—
39C4×Q8×C151—21no—
40C4×Q8×C151C2×C412yes—
41C4×Q8×C151D412yes—
42C4×D4×C151—21no—
43C4×D4×C151—21no—
44C2×C4⋊C4×C151—21no—
45C2×C4⋊C4×C151—21no—
46C2×C4⋊C4×C151—22no—
47C2×C4⋊C4×C151D411yescharacteristic
48C2×C42×C151—21no—
49C2×C42×C151—21no—
50C2×C42×C151D412yes—
51C2×C42×C151C2311yescharacteristic
52#107×C151—22no—
53C4⋊C8×C151—21no—
54C4⋊C8×C151C2×C412yes—
55#104×C151—44no—
56#103×C151—22no—
57#102×C151—22no—
58C22⋊C8×C151—21no—
59C22⋊C8×C151—21no—
60#97×C151—21no—
61#97×C151—21no—
62#97×C151—21no—
63C4×C8×C151—21no—
64#95×C151—22no—
65#95×C151—22no—
66#95×C151—22no—
67#95×C151—21no—
68#95×C151—21no—
69#95×C151D411yescharacteristic
70#95×C151D411yescharacteristic
71#41×C151—42no—
72#41×C151—42no—
73C2×Q8×C151—21no—
74C2×Q8×C151—21no—
75C2×Q8×C151—42no—
76C2×Q8×C151C22⋊C412yes—
77C2×D4×C151—21no—
78C2×D4×C151—21no—
79C2×D4×C151—21no—
80C2×D4×C151—41no—
81C22×C4×C151—21no—
82C22×C4×C151—21no—
83C22×C4×C151—21no—
84C22×C4×C151—22no—
85C22×C4×C151—21no—
86C22×C4×C151—41no—
87C22×C4×C151C2×D411yescharacteristic
88C22×C4×C151C2×D411yescharacteristic
89C22×C4×C151C2×D411yescharacteristic
90SD16×C151—44no—
91M16×C151—22no—
92M16×C151—41no—
93C2×C8×C151—22no—
94C2×C8×C151—41no—
95C2×C8×C151—41no—
96C4⋊C4×C151—22no—
97C4⋊C4×C151—22no—
98C4⋊C4×C151—21no—
99C4⋊C4×C151—21no—
100C4⋊C4×C151—21no—
101C4⋊C4×C151—42no—
102C4⋊C4×C151—82no—
103C4⋊C4×C151C22⋊C412yes—
104C22⋊C4×C151—41no—
105C22⋊C4×C151—41no—
106C42×C151—22no—
107C42×C151—22no—
108C42×C151—42no—
109C42×C151—42no—
110C42×C151C22×C411yescharacteristic
111C42×C151C2×D411yescharacteristic
112C42×C151#4111yescharacteristic
113C42×C151#4111yescharacteristic
114C23×C151—41no—
115C23×C151#12011yescharacteristic
116Q8×C151—22no—
117Q8×C151—22no—
118Q8×C151—42no—
119Q8×C151—42no—
120D4×C151—42no—
121D4×C151—42no—
122D4×C151—81no—
123D4×C151—81no—
124D4×C151—81no—
125C2×C4×C151—21no—
126C2×C4×C151—21no—
127C2×C4×C151—22no—
128C2×C4×C151—22no—
129C2×C4×C151—22no—
130C2×C4×C151—41no—
131C2×C4×C151—42no—
132C2×C4×C151—41no—
133C2×C4×C151—41no—
134C2×C4×C151—41no—
135C2×C4×C151—41no—
136C2×C4×C151—42no—
137C2×C4×C151—41no—
138C2×C4×C151—42no—
139C2×C4×C151—41no—
140C2×C4×C151—41no—
141C2×C4×C151—42no—
142C2×C4×C151—41no—
143C2×C4×C151—41no—
144C2×C4×C151—82no—
145C2×C4×C151C2×C22⋊C411yescharacteristic
146C2×C4×C151C4×D411yescharacteristic
147C2×C4×C151C4×D411yescharacteristic
148C2×C4×C151#12111yescharacteristic
149C2×C4×C151#12111yescharacteristic
150C2×C4×C151#12311yescharacteristic
151C8×C151—42no—
152C8×C151—42no—
153C8×C151—81no—
154C22×C151—21no—
155C22×C151—21no—
156C22×C151—81no—
157C22×C151—81no—
158C22×C151—81no—
159C22×C151#38611yescharacteristic
160C22×C151#45311yescharacteristic
161C22×C151#45411yescharacteristic
162C4×C151—21no—
163C4×C151—21no—
164C4×C151—21no—
165C4×C151—21no—
166C4×C151—21no—
167C4×C151—42no—
168C4×C151—42no—
169C4×C151—81no—
170C4×C151—82no—
171C4×C151—81no—
172C4×C151—81no—
173C4×C151#42112yes—
174C2×C151—21no—
175C2×C151—21no—
176C2×C151—161no—
177C2×C151#188311yescharacteristic
178C2×C151#189711yescharacteristic
179C2×C151#190511yescharacteristic
180#9330C15111yesmaximal, characteristic, direct product factor, Sylow
181C151#933011yescharacteristic, direct product factor, Sylow
182#3112C2×C15111yescharacteristic
183#2320C2×C15111yescharacteristic, complemented
184#1980C2×C15111yescharacteristic
185#1505C2×C15111yescharacteristic
186#1491C2×C15111yescharacteristic, complemented
187#1300C2×C15111yescharacteristic, complemented
188#1285C2×C15111yescharacteristic, complemented
189#532C22×C15111yescharacteristic
190C2×C4×Q8C22×C15111yescharacteristic
191#480—21no—
192#477C4×C15112yescomplemented
193#460C4×C15112yescomplemented
194#448—21no—
195#440—22no—
196#432C22×C15111yescharacteristic
197#432C22×C15111yescharacteristic
198C2×#104—22no—
199C4×M16C22×C15111yescharacteristic
200#391—21no—
201#389—21no—
202#387—22no—
203#383—21no—
204#382—21no—
205C4×C4⋊C4C22×C15111yescharacteristic
206#376C22×C15111yescharacteristic
207#327—21no—
208#327—21no—
209Q8⋊C8—22no—
210C2×#41—21no—
211C22×Q8D4×C15111yescharacteristic
212C2×SD16—22no—
213C2×M16—21no—
214C4⋊Q8C2×C4×C15111yescharacteristic
215#127C2×C4×C15111yescharacteristic
216#124—21no—
217#121—21no—
218#121—21no—
219C4×Q8—21no—
220C4×Q8—21no—
221C4×Q8C2×C4×C15112yes—
222C4×Q8D4×C15112yes—
223C4×D4—21no—
224C4×D4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4D4×C15111yescharacteristic
229C2×C42—21no—
230C2×C42—21no—
231C2×C42D4×C15112yes—
232C2×C42C23×C15111yescharacteristic
233#107—22no—
234C4⋊C8—21no—
235C4⋊C8C2×C4×C15112yes—
236#104—44no—
237#103—22no—
238#102—22no—
239C22⋊C8—21no—
240C22⋊C8—21no—
241#97—21no—
242#97—21no—
243#97—21no—
244C4×C8—21no—
245#95—22no—
246#95—22no—
247#95—22no—
248#95—21no—
249#95—21no—
250#95D4×C15111yescharacteristic
251#95D4×C15111yescharacteristic
252#41—42no—
253#41—42no—
254C2×Q8—21no—
255C2×Q8—21no—
256C2×Q8—42no—
257C2×Q8C22⋊C4×C15112yes—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—41no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—22no—
266C22×C4—21no—
267C22×C4—41no—
268C22×C4C2×D4×C15111yescharacteristic
269C22×C4C2×D4×C15111yescharacteristic
270C22×C4C2×D4×C15111yescharacteristic
271SD16—44no—
272M16—22no—
273M16—41no—
274C2×C8—22no—
275C2×C8—41no—
276C2×C8—41no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—42no—
283C4⋊C4—82no—
284C4⋊C4C22⋊C4×C15112yes—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C42—22no—
288C42—22no—
289C42—42no—
290C42—42no—
291C42C22×C4×C15111yescharacteristic
292C42C2×D4×C15111yescharacteristic
293C42#41×C15111yescharacteristic
294C42#41×C15111yescharacteristic
295C23—41no—
296C23#120×C15111yescharacteristic
297Q8—22no—
298Q8—22no—
299Q8—42no—
300Q8—42no—
301D4—42no—
302D4—42no—
303D4—81no—
304D4—81no—
305D4—81no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—82no—
326C2×C4C2×C22⋊C4×C15111yescharacteristic
327C2×C4C4×D4×C15111yescharacteristic
328C2×C4C4×D4×C15111yescharacteristic
329C2×C4#121×C15111yescharacteristic
330C2×C4#121×C15111yescharacteristic
331C2×C4#123×C15111yescharacteristic
332C8—42no—
333C8—42no—
334C8—81no—
335C22—21no—
336C22—21no—
337C22—81no—
338C22—81no—
339C22—81no—
340C22#386×C15111yescharacteristic
341C22#453×C15111yescharacteristic
342C22#454×C15111yescharacteristic
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—42no—
349C4—42no—
350C4—81no—
351C4—82no—
352C4—81no—
353C4—81no—
354C4#421×C15112yes—
355C2—21no—
356C2—21no—
357C2—161no—
358C2#1883×C15111yescharacteristic
359C2#1897×C15111yescharacteristic
360C2#1905×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#386
commutatorC42C22×C4×C151
Frattini, cosocleC2×C42C23×C151
prime radical#532×C151C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2320×C151C2semidirect
5. #1491×C151C2semidirect
6. #1300×C151C2semidirect
7. #1285×C151C2semidirect
11. #477×C151C4semidirect
12. #460×C151C4semidirect
180. #9330C151direct (N × H)
181. C151#9330direct (N × H)
183. #2320C2×C151semidirect
186. #1491C2×C151semidirect
187. #1300C2×C151semidirect
188. #1285C2×C151semidirect
192. #477C4×C151semidirect
193. #460C4×C151semidirect

Maximal subgroups

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

subgroupindex
#3112×C1512
#2320×C1512
#1980×C1512
#1505×C1512
#1491×C1512
#1300×C1512
#1285×C1512
#9330151