Finite Group Databasebeta

← C151×#9135 #50314060

Subgroups — C151×#9135 #50314060

Order 38656.

612 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#423×C151C211yesmaximal, characteristic
2#2857×C151C211yesmaximal, characteristic
3#1797×C151C211yesmaximal, characteristic
4C2×#333×C151C212yesmaximal, complemented
5#1296×C151C212yesmaximal, complemented
6C22×M16×C151—21no—
7C2×C4⋊Q8×C151C2211yescharacteristic
8C2×C22⋊Q8×C151C412yes—
9C22×C42×C151C2211yescharacteristic
10#423×C151—24no—
11C2×C4⋊C8×C151—21no—
12C2×C4⋊C8×C151C2212yes—
13C2×C4⋊C8×C151C2212yes—
14C2×C22⋊C8×C151—21no—
15#391×C151C412yes—
16#389×C151—21no—
17#389×C151—21no—
18#384×C151C2211yescharacteristic
19#380×C151—21no—
20#380×C151—21no—
21#336×C151—21no—
22#333×C151—24no—
23C22×Q8×C151C2×C412yes—
24C23×C4×C151C2×C411yescharacteristic
25C23×C4×C151D411yescharacteristic
26C23×C4×C151D411yescharacteristic
27C2×M16×C151—24no—
28C2×M16×C151—42no—
29C2×M16×C151—42no—
30C22×C8×C151—22no—
31C22×C8×C151—22no—
32C4⋊Q8×C151—22no—
33C4⋊Q8×C151—22no—
34C22⋊Q8×C151—44no—
35C2×C4⋊C4×C151—22no—
36C2×C4⋊C4×C151—21no—
37C2×C4⋊C4×C151—21no—
38C2×C4⋊C4×C151—21no—
39C2×C4⋊C4×C151—21no—
40C2×C4⋊C4×C151C2×C412yes—
41C2×C22⋊C4×C151—22no—
42C2×C42×C151—22no—
43C2×C42×C151—22no—
44C2×C42×C151C2×C411yescharacteristic
45C2×C42×C151D411yescharacteristic
46C2×C42×C151D411yescharacteristic
47C2×C42×C151C2311yescharacteristic
48C4⋊C8×C151—24no—
49C4⋊C8×C151—22no—
50C4⋊C8×C151—22no—
51C4⋊C8×C151—22no—
52C4⋊C8×C151D414yes—
53C22⋊C8×C151—42no—
54#95×C151—22no—
55#95×C151—22no—
56C24×C151C22⋊C411yescharacteristic
57C2×Q8×C151—24no—
58C2×Q8×C151—42no—
59C2×Q8×C151—42no—
60C22×C4×C151—21no—
61C22×C4×C151—21no—
62C22×C4×C151—21no—
63C22×C4×C151—21no—
64C22×C4×C151—22no—
65C22×C4×C151—22no—
66C22×C4×C151—22no—
67C22×C4×C151—21no—
68C22×C4×C151—21no—
69C22×C4×C151—22no—
70C22×C4×C151—22no—
71C22×C4×C151—22no—
72C22×C4×C151—41no—
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×D411yescharacteristic
81M16×C151—48no—
82C2×C8×C151—24no—
83C2×C8×C151—42no—
84C2×C8×C151—42no—
85C2×C8×C151—42no—
86C2×C8×C151—42no—
87C2×C8×C151—42no—
88C4⋊C4×C151—42no—
89C4⋊C4×C151—44no—
90C4⋊C4×C151—41no—
91C4⋊C4×C151—42no—
92C4⋊C4×C151—41no—
93C4⋊C4×C151—41no—
94C4⋊C4×C151—41no—
95C4⋊C4×C151—41no—
96C4⋊C4×C151—41no—
97C22⋊C4×C151—44no—
98C42×C151—22no—
99C42×C151—21no—
100C42×C151—22no—
101C42×C151—21no—
102C42×C151C2×D412yes—
103C42×C151#4112yes—
104C23×C151—21no—
105C23×C151—21no—
106C23×C151—21no—
107C23×C151—21no—
108C23×C151—21no—
109C23×C151—21no—
110C23×C151#10312yes—
111C23×C151C2×C22⋊C411yescharacteristic
112Q8×C151—84no—
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—22no—
120C2×C4×C151—22no—
121C2×C4×C151—22no—
122C2×C4×C151—22no—
123C2×C4×C151—21no—
124C2×C4×C151—21no—
125C2×C4×C151—21no—
126C2×C4×C151—44no—
127C2×C4×C151—42no—
128C2×C4×C151—42no—
129C2×C4×C151—42no—
130C2×C4×C151—42no—
131C2×C4×C151—42no—
132C2×C4×C151—42no—
133C2×C4×C151—42no—
134C2×C4×C151—42no—
135C2×C4×C151#10012yes—
136C2×C4×C151#10312yes—
137C2×C4×C151C4×D412yes—
138C2×C4×C151#12011yescharacteristic
139C2×C4×C151#12112yes—
140C2×C4×C151#12311yescharacteristic
141C2×C4×C151C2×SD1611yescharacteristic
142C2×C4×C151C2×Q1611yescharacteristic
143C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C151#13711yescharacteristic
146C2×C4×C151#13712yes—
147C2×C4×C151#13711yescharacteristic
148C8×C151—44no—
149C8×C151—82no—
150C22×C151—22no—
151C22×C151—22no—
152C22×C151—22no—
153C22×C151—41no—
154C22×C151—41no—
155C22×C151—41no—
156C22×C151—41no—
157C22×C151#38611yescharacteristic
158C22×C151C2×#10011yescharacteristic
159C22×C151#41311yescharacteristic
160C22×C151C2×#10311yescharacteristic
161C22×C151#41711yescharacteristic
162C22×C151#41711yescharacteristic
163C22×C151#41911yescharacteristic
164C4×C151—22no—
165C4×C151—22no—
166C4×C151—22no—
167C4×C151—41no—
168C4×C151—82no—
169C4×C151—82no—
170C4×C151#45011yescharacteristic
171C4×C151#45111yescharacteristic
172C4×C151#46812yes—
173C4×C151#47012yes—
174C4×C151#48311yescharacteristic
175C4×C151#48411yescharacteristic
176C2×C151—42no—
177C2×C151#154811yescharacteristic
178C2×C151#155011yescharacteristic
179C2×C151#155911yescharacteristic
180C2×C151#156011yescharacteristic
181C2×C151#187211yescharacteristic
182C2×C151#189411yescharacteristic
183C2×C151#190011yescharacteristic
184#9135C15111yesmaximal, characteristic, direct product factor, Sylow
185C151#913511yescharacteristic, direct product factor, Sylow
186C2×#423C2×C15111yescharacteristic
187#2857C2×C15111yescharacteristic
188#1797C2×C15111yescharacteristic
189C2×#333C2×C15112yescomplemented
190#1296C2×C15112yescomplemented
191C22×M16—21no—
192C2×C4⋊Q8C22×C15111yescharacteristic
193C2×C22⋊Q8C4×C15112yes—
194C22×C42C22×C15111yescharacteristic
195#423—24no—
196C2×C4⋊C8—21no—
197C2×C4⋊C8C22×C15112yes—
198C2×C4⋊C8C22×C15112yes—
199C2×C22⋊C8—21no—
200#391C4×C15112yes—
201#389—21no—
202#389—21no—
203#384C22×C15111yescharacteristic
204#380—21no—
205#380—21no—
206#336—21no—
207#333—24no—
208C22×Q8C2×C4×C15112yes—
209C23×C4C2×C4×C15111yescharacteristic
210C23×C4D4×C15111yescharacteristic
211C23×C4D4×C15111yescharacteristic
212C2×M16—24no—
213C2×M16—42no—
214C2×M16—42no—
215C22×C8—22no—
216C22×C8—22no—
217C4⋊Q8—22no—
218C4⋊Q8—22no—
219C22⋊Q8—44no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4C2×C4×C15112yes—
226C2×C22⋊C4—22no—
227C2×C42—22no—
228C2×C42—22no—
229C2×C42C2×C4×C15111yescharacteristic
230C2×C42D4×C15111yescharacteristic
231C2×C42D4×C15111yescharacteristic
232C2×C42C23×C15111yescharacteristic
233C4⋊C8—24no—
234C4⋊C8—22no—
235C4⋊C8—22no—
236C4⋊C8—22no—
237C4⋊C8D4×C15114yes—
238C22⋊C8—42no—
239#95—22no—
240#95—22no—
241C24C22⋊C4×C15111yescharacteristic
242C2×Q8—24no—
243C2×Q8—42no—
244C2×Q8—42no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—41no—
258C22×C4C22⋊C4×C15111yescharacteristic
259C22×C4C22⋊C4×C15111yescharacteristic
260C22×C4C22⋊C4×C15111yescharacteristic
261C22×C4SD16×C15112yes—
262C22×C4Q16×C15112yes—
263C22×C4C22×C4×C15111yescharacteristic
264C22×C4C2×D4×C15111yescharacteristic
265C22×C4C2×D4×C15111yescharacteristic
266M16—48no—
267C2×C8—24no—
268C2×C8—42no—
269C2×C8—42no—
270C2×C8—42no—
271C2×C8—42no—
272C2×C8—42no—
273C4⋊C4—42no—
274C4⋊C4—44no—
275C4⋊C4—41no—
276C4⋊C4—42no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C22⋊C4—44no—
283C42—22no—
284C42—21no—
285C42—22no—
286C42—21no—
287C42C2×D4×C15112yes—
288C42#41×C15112yes—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23#103×C15112yes—
296C23C2×C22⋊C4×C15111yescharacteristic
297Q8—84no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—44no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4#100×C15112yes—
321C2×C4#103×C15112yes—
322C2×C4C4×D4×C15112yes—
323C2×C4#120×C15111yescharacteristic
324C2×C4#121×C15112yes—
325C2×C4#123×C15111yescharacteristic
326C2×C4C2×SD16×C15111yescharacteristic
327C2×C4C2×Q16×C15111yescharacteristic
328C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
329C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
330C2×C4#137×C15111yescharacteristic
331C2×C4#137×C15112yes—
332C2×C4#137×C15111yescharacteristic
333C8—44no—
334C8—82no—
335C22—22no—
336C22—22no—
337C22—22no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22#386×C15111yescharacteristic
343C22C2×#100×C15111yescharacteristic
344C22#413×C15111yescharacteristic
345C22C2×#103×C15111yescharacteristic
346C22#417×C15111yescharacteristic
347C22#417×C15111yescharacteristic
348C22#419×C15111yescharacteristic
349C4—22no—
350C4—22no—
351C4—22no—
352C4—41no—
353C4—82no—
354C4—82no—
355C4#450×C15111yescharacteristic
356C4#451×C15111yescharacteristic
357C4#468×C15112yes—
358C4#470×C15112yes—
359C4#483×C15111yescharacteristic
360C4#484×C15111yescharacteristic
361C2—42no—
362C2#1548×C15111yescharacteristic
363C2#1550×C15111yescharacteristic
364C2#1559×C15111yescharacteristic
365C2#1560×C15111yescharacteristic
366C2#1872×C15111yescharacteristic
367C2#1894×C15111yescharacteristic
368C2#1900×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C2×C22⋊C4
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×C42C23×C151
prime radicalC24×C151C22⋊C4
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
4. C2×#333×C151C2semidirect
5. #1296×C151C2semidirect
184. #9135C151direct (N × H)
185. C151#9135direct (N × H)
189. C2×#333C2×C151semidirect
190. #1296C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#423×C1512
#2857×C1512
#1797×C1512
C2×#333×C1512
#1296×C1512
#9135151