Finite Group Databasebeta

← C151×#9711 #50314636

Subgroups — C151×#9711 #50314636

Order 38656.

716 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2857×C151C211yesmaximal, characteristic
2#1797×C151C211yesmaximal, characteristic
3C2×#328×C151C214yesmaximal
4C4×#95×C151C211yesmaximal, characteristic
5C2×C4⋊Q8×C151C411yescharacteristic, complemented
6C2×C22⋊Q8×C151C2212yes—
7C22×C42×C151—21no—
8C22×C42×C151C2211yescharacteristic
9C2×C4⋊C8×C151—21no—
10C2×C22⋊C8×C151C2212yes—
11#391×C151C412yescomplemented
12#389×C151—21no—
13#389×C151—21no—
14#384×C151C411yescharacteristic, complemented
15#380×C151—21no—
16#380×C151—21no—
17C2×#95×C151—21no—
18C2×#95×C151C2212yes—
19#336×C151—21no—
20#328×C151—28no—
21C22×Q8×C151C2×C412yes—
22C23×C4×C151—22no—
23C23×C4×C151D411yescharacteristic
24C23×C4×C151D411yescharacteristic
25C23×C4×C151C2311yescharacteristic
26C22×C8×C151—22no—
27C4⋊Q8×C151—42no—
28C22⋊Q8×C151—24no—
29C22⋊Q8×C151—24no—
30C2×C4⋊C4×C151—21no—
31C2×C4⋊C4×C151—21no—
32C2×C4⋊C4×C151—21no—
33C2×C4⋊C4×C151—21no—
34C2×C4⋊C4×C151—22no—
35C2×C4⋊C4×C151C2×C412yes—
36C2×C22⋊C4×C151—22no—
37C2×C42×C151—24no—
38C2×C42×C151—42no—
39C2×C42×C151—42no—
40C2×C42×C151—42no—
41C2×C42×C151C2×C411yescharacteristic
42C2×C42×C151C2×C411yescharacteristic
43C2×C42×C151D411yescharacteristic
44C2×C42×C151D411yescharacteristic
45C4⋊C8×C151—42no—
46C22⋊C8×C151—24no—
47#95×C151—24no—
48#95×C151—22no—
49#95×C151—22no—
50#95×C151—22no—
51#95×C151D414yes—
52C24×C151C2×D411yescharacteristic
53C2×Q8×C151—24no—
54C2×Q8×C151—42no—
55C2×Q8×C151—42no—
56C22×C4×C151—22no—
57C22×C4×C151—22no—
58C22×C4×C151—24no—
59C22×C4×C151—24no—
60C22×C4×C151—24no—
61C22×C4×C151—22no—
62C22×C4×C151—22no—
63C22×C4×C151—22no—
64C22×C4×C151—22no—
65C22×C4×C151—41no—
66C22×C4×C151—41no—
67C22×C4×C151—41no—
68C22×C4×C151—42no—
69C22×C4×C151—42no—
70C22×C4×C151—42no—
71C22×C4×C151—42no—
72C22×C4×C151C22⋊C411yescharacteristic
73C22×C4×C151C22⋊C411yescharacteristic
74C22×C4×C151C22⋊C411yescharacteristic
75C22×C4×C151C22⋊C411yescharacteristic
76C22×C4×C151SD1612yes—
77C22×C4×C151Q1612yes—
78C22×C4×C151C22×C411yescharacteristic
79C22×C4×C151C2×D411yescharacteristic
80C22×C4×C151C2×D412yes—
81C22×C4×C151#4112yes—
82C2×C8×C151—42no—
83C2×C8×C151—42no—
84C2×C8×C151—42no—
85C4⋊C4×C151—24no—
86C4⋊C4×C151—42no—
87C4⋊C4×C151—42no—
88C4⋊C4×C151—42no—
89C4⋊C4×C151—42no—
90C4⋊C4×C151—42no—
91C4⋊C4×C151—42no—
92C22⋊C4×C151—44no—
93C42×C151—22no—
94C42×C151—22no—
95C42×C151—41no—
96C42×C151—41no—
97C42×C151—48no—
98C23×C151—21no—
99C23×C151—21no—
100C23×C151—21no—
101C23×C151—21no—
102C23×C151C2×C22⋊C411yescharacteristic
103C23×C151#12112yes—
104C23×C151C2×SD1611yescharacteristic
105C23×C151C2×Q1611yescharacteristic
106C23×C151#13712yes—
107Q8×C151—84no—
108C2×C4×C151—21no—
109C2×C4×C151—21no—
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—24no—
117C2×C4×C151—24no—
118C2×C4×C151—28no—
119C2×C4×C151—21no—
120C2×C4×C151—21no—
121C2×C4×C151—21no—
122C2×C4×C151—42no—
123C2×C4×C151—42no—
124C2×C4×C151—44no—
125C2×C4×C151—44no—
126C2×C4×C151—44no—
127C2×C4×C151—44no—
128C2×C4×C151—44no—
129C2×C4×C151—44no—
130C2×C4×C151—44no—
131C2×C4×C151—42no—
132C2×C4×C151—42no—
133C2×C4×C151—42no—
134C2×C4×C151—42no—
135C2×C4×C151—42no—
136C2×C4×C151—42no—
137C2×C4×C151#9912yes—
138C2×C4×C151#10312yes—
139C2×C4×C151#10312yes—
140C2×C4×C151#10412yes—
141C2×C4×C151#10412yes—
142C2×C4×C151C4×D412yes—
143C2×C4×C151#12411yescharacteristic
144C2×C4×C151#12711yescharacteristic
145C8×C151—82no—
146C22×C151—22no—
147C22×C151—22no—
148C22×C151—21no—
149C22×C151—21no—
150C22×C151—21no—
151C22×C151—21no—
152C22×C151—22no—
153C22×C151—22no—
154C22×C151#39011yescharacteristic
155C22×C151C2×#9911yescharacteristic
156C22×C151#41011yescharacteristic
157C22×C151C2×#10311yescharacteristic
158C22×C151#41911yescharacteristic
159C22×C151C2×#10411yescharacteristic
160C22×C151C2×#10411yescharacteristic
161C22×C151#46112yes—
162C22×C151#46212yes—
163C4×C151—21no—
164C4×C151—22no—
165C4×C151—21no—
166C4×C151—22no—
167C4×C151—22no—
168C4×C151—48no—
169C4×C151—41no—
170C4×C151—82no—
171C4×C151—82no—
172C4×C151#32814yescomplemented
173C2×C151—22no—
174C2×C151—22no—
175C2×C151C2×#32811yescharacteristic
176C2×C151#150311yescharacteristic
177C2×C151#150611yescharacteristic
178C2×C151#150811yescharacteristic
179C2×C151#196211yescharacteristic
180C2×C151#196411yescharacteristic
181C2×C151#198111yescharacteristic
182#9711C15111yesmaximal, characteristic, direct product factor, Sylow
183C151#971111yescharacteristic, direct product factor, Sylow
184#2857C2×C15111yescharacteristic
185#1797C2×C15111yescharacteristic
186C2×#328C2×C15114yes—
187C4×#95C2×C15111yescharacteristic
188C2×C4⋊Q8C4×C15111yescharacteristic, complemented
189C2×C22⋊Q8C22×C15112yes—
190C22×C42—21no—
191C22×C42C22×C15111yescharacteristic
192C2×C4⋊C8—21no—
193C2×C22⋊C8C22×C15112yes—
194#391C4×C15112yescomplemented
195#389—21no—
196#389—21no—
197#384C4×C15111yescharacteristic, complemented
198#380—21no—
199#380—21no—
200C2×#95—21no—
201C2×#95C22×C15112yes—
202#336—21no—
203#328—28no—
204C22×Q8C2×C4×C15112yes—
205C23×C4—22no—
206C23×C4D4×C15111yescharacteristic
207C23×C4D4×C15111yescharacteristic
208C23×C4C23×C15111yescharacteristic
209C22×C8—22no—
210C4⋊Q8—42no—
211C22⋊Q8—24no—
212C22⋊Q8—24no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—22no—
218C2×C4⋊C4C2×C4×C15112yes—
219C2×C22⋊C4—22no—
220C2×C42—24no—
221C2×C42—42no—
222C2×C42—42no—
223C2×C42—42no—
224C2×C42C2×C4×C15111yescharacteristic
225C2×C42C2×C4×C15111yescharacteristic
226C2×C42D4×C15111yescharacteristic
227C2×C42D4×C15111yescharacteristic
228C4⋊C8—42no—
229C22⋊C8—24no—
230#95—24no—
231#95—22no—
232#95—22no—
233#95—22no—
234#95D4×C15114yes—
235C24C2×D4×C15111yescharacteristic
236C2×Q8—24no—
237C2×Q8—42no—
238C2×Q8—42no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—24no—
242C22×C4—24no—
243C22×C4—24no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—42no—
252C22×C4—42no—
253C22×C4—42no—
254C22×C4—42no—
255C22×C4C22⋊C4×C15111yescharacteristic
256C22×C4C22⋊C4×C15111yescharacteristic
257C22×C4C22⋊C4×C15111yescharacteristic
258C22×C4C22⋊C4×C15111yescharacteristic
259C22×C4SD16×C15112yes—
260C22×C4Q16×C15112yes—
261C22×C4C22×C4×C15111yescharacteristic
262C22×C4C2×D4×C15111yescharacteristic
263C22×C4C2×D4×C15112yes—
264C22×C4#41×C15112yes—
265C2×C8—42no—
266C2×C8—42no—
267C2×C8—42no—
268C4⋊C4—24no—
269C4⋊C4—42no—
270C4⋊C4—42no—
271C4⋊C4—42no—
272C4⋊C4—42no—
273C4⋊C4—42no—
274C4⋊C4—42no—
275C22⋊C4—44no—
276C42—22no—
277C42—22no—
278C42—41no—
279C42—41no—
280C42—48no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23C2×C22⋊C4×C15111yescharacteristic
286C23#121×C15112yes—
287C23C2×SD16×C15111yescharacteristic
288C23C2×Q16×C15111yescharacteristic
289C23#137×C15112yes—
290Q8—84no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—24no—
300C2×C4—24no—
301C2×C4—28no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—44no—
308C2×C4—44no—
309C2×C4—44no—
310C2×C4—44no—
311C2×C4—44no—
312C2×C4—44no—
313C2×C4—44no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4#99×C15112yes—
321C2×C4#103×C15112yes—
322C2×C4#103×C15112yes—
323C2×C4#104×C15112yes—
324C2×C4#104×C15112yes—
325C2×C4C4×D4×C15112yes—
326C2×C4#124×C15111yescharacteristic
327C2×C4#127×C15111yescharacteristic
328C8—82no—
329C22—22no—
330C22—22no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—22no—
336C22—22no—
337C22#390×C15111yescharacteristic
338C22C2×#99×C15111yescharacteristic
339C22#410×C15111yescharacteristic
340C22C2×#103×C15111yescharacteristic
341C22#419×C15111yescharacteristic
342C22C2×#104×C15111yescharacteristic
343C22C2×#104×C15111yescharacteristic
344C22#461×C15112yes—
345C22#462×C15112yes—
346C4—21no—
347C4—22no—
348C4—21no—
349C4—22no—
350C4—22no—
351C4—48no—
352C4—41no—
353C4—82no—
354C4—82no—
355C4#328×C15114yescomplemented
356C2—22no—
357C2—22no—
358C2C2×#328×C15111yescharacteristic
359C2#1503×C15111yescharacteristic
360C2#1506×C15111yescharacteristic
361C2#1508×C15111yescharacteristic
362C2#1962×C15111yescharacteristic
363C2#1964×C15111yescharacteristic
364C2#1981×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
5. C2×C4⋊Q8×C151C4semidirect
11. #391×C151C4semidirect
14. #384×C151C4semidirect
172. C4×C151#328semidirect
182. #9711C151direct (N × H)
183. C151#9711direct (N × H)
188. C2×C4⋊Q8C4×C151semidirect
194. #391C4×C151semidirect
197. #384C4×C151semidirect
355. C4#328×C151semidirect

Maximal subgroups

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

subgroupindex
#2857×C1512
#1797×C1512
C2×#328×C1512
C4×#95×C1512
#9711151