Finite Group Databasebeta

← C151×#9211 #50314136

Subgroups — C151×#9211 #50314136

Order 38656.

536 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3106×C151C211yesmaximal, characteristic
2C4×#131×C151C211yesmaximal, characteristic, complemented
3#1525×C151C211yesmaximal, characteristic, complemented
4#1492×C151C211yesmaximal, characteristic, complemented
5#1489×C151C211yesmaximal, characteristic, complemented
6#1299×C151C211yesmaximal, characteristic, complemented
7#1278×C151C211yesmaximal, characteristic, complemented
8C2×#131×C151—21no—
9#532×C151C2211yescharacteristic
10C4×#41×C151C2211yescharacteristic
11#482×C151—21no—
12#477×C151C411yescharacteristic
13#476×C151C411yescharacteristic
14#460×C151C411yescharacteristic
15#459×C151C411yescharacteristic
16#449×C151—21no—
17C4×SD16×C151—21no—
18C4×D8×C151—21no—
19#431×C151C2211yescharacteristic
20#423×C151C2211yescharacteristic
21#405×C151—21no—
22#405×C151—22no—
23C4×M16×C151—21no—
24C4×M16×C151C2211yescharacteristic
25C4×M16×C151C2211yescharacteristic
26C2×C4×C8×C151—21no—
27C2×C4×C8×C151C2211yescharacteristic
28#329×C151—22no—
29Q8⋊C8×C151—21no—
30D4⋊C8×C151—21no—
31D4⋊C8×C151—21no—
32D4⋊C8×C151—21no—
33C2×#41×C151—21no—
34C2×#41×C151D411yescharacteristic
35C2×SD16×C151—21no—
36C2×D8×C151—21no—
37#131×C151—24no—
38#131×C151—24no—
39C2×M16×C151—22no—
40C2×M16×C151—21no—
41C2×M16×C151—21no—
42C2×M16×C151—21no—
43C22×C8×C151—22no—
44C22×C8×C151—21no—
45C4⋊Q8×C151C2×C411yescharacteristic
46#127×C151C2×C411yescharacteristic
47#124×C151—21no—
48#121×C151—21no—
49#121×C151—21no—
50C4×Q8×C151C2×C411yescharacteristic
51C4×Q8×C151D411yescharacteristic
52C4×D4×C151—21no—
53C4×D4×C151—21no—
54C4×D4×C151—21no—
55C4×D4×C151—21no—
56C4×D4×C151C2×C411yescharacteristic
57C4×D4×C151D411yescharacteristic
58#117×C151—21no—
59#117×C151D411yescharacteristic
60C2×C42×C151—21no—
61C2×C42×C151C2311yescharacteristic
62#107×C151—21no—
63#106×C151—21no—
64C4⋊C8×C151—21no—
65C4⋊C8×C151—21no—
66C4⋊C8×C151C2×C411yescharacteristic
67C4⋊C8×C151C2×C411yescharacteristic
68#103×C151—21no—
69#102×C151—21no—
70#102×C151—21no—
71#102×C151—21no—
72C22⋊C8×C151—21no—
73#97×C151—22no—
74#97×C151—21no—
75#97×C151D412yes—
76C4×C8×C151—22no—
77C4×C8×C151—21no—
78C4×C8×C151—21no—
79C4×C8×C151—21no—
80C4×C8×C151—21no—
81C4×C8×C151D411yescharacteristic
82C4×C8×C151D411yescharacteristic
83#41×C151—22no—
84#41×C151—22no—
85#41×C151—81no—
86#41×C151—81no—
87C2×Q8×C151—21no—
88C2×Q8×C151C22⋊C411yescharacteristic
89C2×D4×C151—21no—
90C2×D4×C151—21no—
91C2×D4×C151—21no—
92C2×D4×C151—21no—
93C2×D4×C151—41no—
94C2×D4×C151C22⋊C411yescharacteristic
95C22×C4×C151—21no—
96C22×C4×C151—21no—
97C22×C4×C151—21no—
98C22×C4×C151—41no—
99C22×C4×C151C2×D411yescharacteristic
100C22×C4×C151#4111yescharacteristic
101C22×C4×C151#4111yescharacteristic
102SD16×C151—42no—
103D8×C151—42no—
104M16×C151—28no—
105M16×C151—22no—
106M16×C151—22no—
107M16×C151—22no—
108M16×C151—41no—
109M16×C151—81no—
110C2×C8×C151—28no—
111C2×C8×C151—22no—
112C2×C8×C151—22no—
113C2×C8×C151—21no—
114C2×C8×C151—22no—
115C2×C8×C151—21no—
116C2×C8×C151—21no—
117C2×C8×C151—21no—
118C2×C8×C151—41no—
119C2×C8×C151—41no—
120C4⋊C4×C151—21no—
121C4⋊C4×C151—21no—
122C4⋊C4×C151—21no—
123C4⋊C4×C151—21no—
124C4⋊C4×C151C22⋊C411yescharacteristic
125C4⋊C4×C151C22⋊C411yescharacteristic
126C22⋊C4×C151—21no—
127C22⋊C4×C151—21no—
128C22⋊C4×C151—21no—
129C22⋊C4×C151—41no—
130C22⋊C4×C151—41no—
131C42×C151—21no—
132C42×C151—21no—
133C42×C151—21no—
134C42×C151C22×C411yescharacteristic
135C42×C151C2×D411yescharacteristic
136C42×C151C2×D411yescharacteristic
137C42×C151C2×D411yescharacteristic
138C23×C151—21no—
139C23×C151—41no—
140C23×C151#12311yescharacteristic
141Q8×C151—21no—
142Q8×C151—81no—
143Q8×C151#10412yes—
144D4×C151—24no—
145D4×C151—21no—
146D4×C151—41no—
147D4×C151—41no—
148D4×C151—41no—
149D4×C151—41no—
150D4×C151—81no—
151D4×C151—82no—
152D4×C151#10412yes—
153C2×C4×C151—24no—
154C2×C4×C151—21no—
155C2×C4×C151—21no—
156C2×C4×C151—21no—
157C2×C4×C151—21no—
158C2×C4×C151—21no—
159C2×C4×C151—21no—
160C2×C4×C151—21no—
161C2×C4×C151—21no—
162C2×C4×C151—21no—
163C2×C4×C151—41no—
164C2×C4×C151—41no—
165C2×C4×C151—41no—
166C2×C4×C151—41no—
167C2×C4×C151—41no—
168C2×C4×C151—81no—
169C2×C4×C151—81no—
170C2×C4×C151C2×C22⋊C411yescharacteristic
171C2×C4×C151C4×D411yescharacteristic
172C2×C4×C151C4×D411yescharacteristic
173C2×C4×C151#12011yescharacteristic
174C2×C4×C151#12111yescharacteristic
175C2×C4×C151#12111yescharacteristic
176C8×C151—22no—
177C8×C151—24no—
178C8×C151—22no—
179C8×C151—42no—
180C8×C151—41no—
181C8×C151—41no—
182C8×C151—81no—
183C22×C151—21no—
184C22×C151—21no—
185C22×C151—22no—
186C22×C151—21no—
187C22×C151—41no—
188C22×C151—41no—
189C22×C151—81no—
190C22×C151—81no—
191C22×C151—81no—
192C22×C151#38611yescharacteristic
193C4×C151—21no—
194C4×C151—21no—
195C4×C151—22no—
196C4×C151—21no—
197C4×C151—41no—
198C4×C151—41no—
199C4×C151—81no—
200C4×C151C2×#10411yescharacteristic
201C4×C151C2×#10411yescharacteristic
202C4×C151#44311yescharacteristic
203C4×C151#44411yescharacteristic
204C4×C151#47111yescharacteristic
205C4×C151#47211yescharacteristic
206C2×C151—41no—
207C2×C151—42no—
208C2×C151—161no—
209C2×C151#187611yescharacteristic
210C2×C151#189611yescharacteristic
211C2×C151#190711yescharacteristic
212#9211C15111yesmaximal, characteristic, direct product factor, Sylow
213C151#921111yescharacteristic, direct product factor, Sylow
214#3106C2×C15111yescharacteristic
215C4×#131C2×C15111yescharacteristic, complemented
216#1525C2×C15111yescharacteristic, complemented
217#1492C2×C15111yescharacteristic, complemented
218#1489C2×C15111yescharacteristic, complemented
219#1299C2×C15111yescharacteristic, complemented
220#1278C2×C15111yescharacteristic, complemented
221C2×#131—21no—
222#532C22×C15111yescharacteristic
223C4×#41C22×C15111yescharacteristic
224#482—21no—
225#477C4×C15111yescharacteristic
226#476C4×C15111yescharacteristic
227#460C4×C15111yescharacteristic
228#459C4×C15111yescharacteristic
229#449—21no—
230C4×SD16—21no—
231C4×D8—21no—
232#431C22×C15111yescharacteristic
233#423C22×C15111yescharacteristic
234#405—21no—
235#405—22no—
236C4×M16—21no—
237C4×M16C22×C15111yescharacteristic
238C4×M16C22×C15111yescharacteristic
239C2×C4×C8—21no—
240C2×C4×C8C22×C15111yescharacteristic
241#329—22no—
242Q8⋊C8—21no—
243D4⋊C8—21no—
244D4⋊C8—21no—
245D4⋊C8—21no—
246C2×#41—21no—
247C2×#41D4×C15111yescharacteristic
248C2×SD16—21no—
249C2×D8—21no—
250#131—24no—
251#131—24no—
252C2×M16—22no—
253C2×M16—21no—
254C2×M16—21no—
255C2×M16—21no—
256C22×C8—22no—
257C22×C8—21no—
258C4⋊Q8C2×C4×C15111yescharacteristic
259#127C2×C4×C15111yescharacteristic
260#124—21no—
261#121—21no—
262#121—21no—
263C4×Q8C2×C4×C15111yescharacteristic
264C4×Q8D4×C15111yescharacteristic
265C4×D4—21no—
266C4×D4—21no—
267C4×D4—21no—
268C4×D4—21no—
269C4×D4C2×C4×C15111yescharacteristic
270C4×D4D4×C15111yescharacteristic
271#117—21no—
272#117D4×C15111yescharacteristic
273C2×C42—21no—
274C2×C42C23×C15111yescharacteristic
275#107—21no—
276#106—21no—
277C4⋊C8—21no—
278C4⋊C8—21no—
279C4⋊C8C2×C4×C15111yescharacteristic
280C4⋊C8C2×C4×C15111yescharacteristic
281#103—21no—
282#102—21no—
283#102—21no—
284#102—21no—
285C22⋊C8—21no—
286#97—22no—
287#97—21no—
288#97D4×C15112yes—
289C4×C8—22no—
290C4×C8—21no—
291C4×C8—21no—
292C4×C8—21no—
293C4×C8—21no—
294C4×C8D4×C15111yescharacteristic
295C4×C8D4×C15111yescharacteristic
296#41—22no—
297#41—22no—
298#41—81no—
299#41—81no—
300C2×Q8—21no—
301C2×Q8C22⋊C4×C15111yescharacteristic
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—41no—
307C2×D4C22⋊C4×C15111yescharacteristic
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—41no—
312C22×C4C2×D4×C15111yescharacteristic
313C22×C4#41×C15111yescharacteristic
314C22×C4#41×C15111yescharacteristic
315SD16—42no—
316D8—42no—
317M16—28no—
318M16—22no—
319M16—22no—
320M16—22no—
321M16—41no—
322M16—81no—
323C2×C8—28no—
324C2×C8—22no—
325C2×C8—22no—
326C2×C8—21no—
327C2×C8—22no—
328C2×C8—21no—
329C2×C8—21no—
330C2×C8—21no—
331C2×C8—41no—
332C2×C8—41no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4C22⋊C4×C15111yescharacteristic
338C4⋊C4C22⋊C4×C15111yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—21no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C42—21no—
345C42—21no—
346C42—21no—
347C42C22×C4×C15111yescharacteristic
348C42C2×D4×C15111yescharacteristic
349C42C2×D4×C15111yescharacteristic
350C42C2×D4×C15111yescharacteristic
351C23—21no—
352C23—41no—
353C23#123×C15111yescharacteristic
354Q8—21no—
355Q8—81no—
356Q8#104×C15112yes—
357D4—24no—
358D4—21no—
359D4—41no—
360D4—41no—
361D4—41no—
362D4—41no—
363D4—81no—
364D4—82no—
365D4#104×C15112yes—
366C2×C4—24no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4C2×C22⋊C4×C15111yescharacteristic
384C2×C4C4×D4×C15111yescharacteristic
385C2×C4C4×D4×C15111yescharacteristic
386C2×C4#120×C15111yescharacteristic
387C2×C4#121×C15111yescharacteristic
388C2×C4#121×C15111yescharacteristic
389C8—22no—
390C8—24no—
391C8—22no—
392C8—42no—
393C8—41no—
394C8—41no—
395C8—81no—
396C22—21no—
397C22—21no—
398C22—22no—
399C22—21no—
400C22—41no—
401C22—41no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22#386×C15111yescharacteristic
406C4—21no—
407C4—21no—
408C4—22no—
409C4—21no—
410C4—41no—
411C4—41no—
412C4—81no—
413C4C2×#104×C15111yescharacteristic
414C4C2×#104×C15111yescharacteristic
415C4#443×C15111yescharacteristic
416C4#444×C15111yescharacteristic
417C4#471×C15111yescharacteristic
418C4#472×C15111yescharacteristic
419C2—41no—
420C2—42no—
421C2—161no—
422C2#1876×C15111yescharacteristic
423C2#1896×C15111yescharacteristic
424C2#1907×C15111yescharacteristic
subgroupG/H
centerC2×C4×C151#121
commutatorC42C22×C4×C151
Frattini, cosocleC2×C42C23×C151
socleC22×C151#386
prime radical#3106×C151C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×#131×C151C2semidirect
3. #1525×C151C2semidirect
4. #1492×C151C2semidirect
5. #1489×C151C2semidirect
6. #1299×C151C2semidirect
7. #1278×C151C2semidirect
212. #9211C151direct (N × H)
213. C151#9211direct (N × H)
215. C4×#131C2×C151semidirect
216. #1525C2×C151semidirect
217. #1492C2×C151semidirect
218. #1489C2×C151semidirect
219. #1299C2×C151semidirect
220. #1278C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3106×C1512
C4×#131×C1512
#1525×C1512
#1492×C1512
#1489×C1512
#1299×C1512
#1278×C1512
#9211151