Finite Group Databasebeta

← C151×#22765 #50327690

Subgroups — C151×#22765 #50327690

Order 38656.

830 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×SD16×C151C211yesmaximal, characteristic
2#2357×C151C211yesmaximal, characteristic
3#2351×C151C211yesmaximal, characteristic, complemented
4#1936×C151C212yesmaximal
5#1920×C151C212yesmaximal, complemented
6#1880×C151C212yesmaximal
7#1835×C151C211yesmaximal, characteristic, complemented
8#1805×C151C211yesmaximal, characteristic, complemented
9#1804×C151C211yesmaximal, characteristic
10#1770×C151C211yesmaximal, characteristic, complemented
11#1763×C151C212yesmaximal, complemented
12C22×SD16×C151C2211yescharacteristic
13C2×C4×Q8×C151C2212yes—
14C2×C4×Q8×C151C2211yescharacteristic
15C2×C4×D4×C151C2211yescharacteristic
16C4×SD16×C151C418yescomplemented
17C2×#106×C151C2211yescharacteristic
18C2×C4⋊C8×C151C2211yescharacteristic
19C2×#103×C151C2212yes—
20C2×#103×C151C2211yescharacteristic
21C2×#102×C151C2212yes—
22C2×#102×C151C2211yescharacteristic
23C2×#97×C151C2212yes—
24C2×C4×C8×C151C2211yescharacteristic
25#390×C151C2212yes—
26#389×C151—22no—
27#389×C151C2212yes—
28#388×C151—22no—
29#382×C151—21no—
30#382×C151C2211yescharacteristic
31#382×C151C2211yescharacteristic
32#381×C151—21no—
33C4×C4⋊C4×C151—21no—
34C4×C4⋊C4×C151C2212yes—
35C4×C4⋊C4×C151C2211yescharacteristic
36C4×C22⋊C4×C151—21no—
37#340×C151C2212yes—
38#340×C151C2212yes—
39#340×C151C2212yes—
40#340×C151C2212yes—
41#336×C151C2212yes—
42C22×Q8×C151C2311yescharacteristic
43C22×D4×C151C2311yescharacteristic
44C23×C4×C151—21no—
45C2×SD16×C151—22no—
46C2×SD16×C151—22no—
47C2×SD16×C151C2×C414yes—
48C22×C8×C151C2312yes—
49C22×C8×C151C2311yescharacteristic
50C22×C8×C151C2311yescharacteristic
51C4×Q8×C151—22no—
52C4×Q8×C151—24no—
53C4×Q8×C151—42no—
54C4×Q8×C151C2×C414yes—
55C4×D4×C151—22no—
56C4×D4×C151C2×C414yes—
57C2×C4⋊C4×C151—21no—
58C2×C4⋊C4×C151—22no—
59C2×C4⋊C4×C151—22no—
60C2×C4⋊C4×C151D412yes—
61C2×C4⋊C4×C151C2312yes—
62C2×C4⋊C4×C151C2312yes—
63C2×C4⋊C4×C151C2311yescharacteristic
64C2×C4⋊C4×C151C2311yescharacteristic
65C2×C22⋊C4×C151—21no—
66C2×C22⋊C4×C151—22no—
67C2×C22⋊C4×C151—22no—
68C2×C42×C151—21no—
69C2×C42×C151—22no—
70C2×C42×C151—22no—
71C2×C42×C151C2312yes—
72C2×C42×C151C2311yescharacteristic
73#106×C151C2×C414yes—
74C4⋊C8×C151—22no—
75#103×C151—24no—
76#103×C151C2×C414yes—
77#102×C151—42no—
78#102×C151C2×C414yes—
79#97×C151—42no—
80C4×C8×C151C2×C414yes—
81#95×C151—21no—
82#95×C151—21no—
83#95×C151—22no—
84#95×C151—22no—
85#95×C151—21no—
86#95×C151—21no—
87#95×C151D411yescharacteristic
88#95×C151D411yescharacteristic
89C24×C151—21no—
90C2×Q8×C151—21no—
91C2×Q8×C151—21no—
92C2×Q8×C151—21no—
93C2×Q8×C151C22×C412yes—
94C2×Q8×C151#4112yes—
95C2×Q8×C151#4112yes—
96C2×D4×C151—21no—
97C2×D4×C151—21no—
98C2×D4×C151—21no—
99C2×D4×C151—21no—
100C2×D4×C151—21no—
101C2×D4×C151C22×C412yes—
102C22×C4×C151—21no—
103C22×C4×C151—21no—
104C22×C4×C151—21no—
105C22×C4×C151—24no—
106C22×C4×C151—22no—
107C22×C4×C151—22no—
108C22×C4×C151—82no—
109C22×C4×C151C2×D412yes—
110C22×C4×C151C2×D412yes—
111C22×C4×C151C2×D411yescharacteristic
112C22×C4×C151C2×D411yescharacteristic
113C22×C4×C151C2411yescharacteristic
114SD16×C151—28no—
115C2×C8×C151—21no—
116C2×C8×C151—21no—
117C2×C8×C151—21no—
118C2×C8×C151—21no—
119C2×C8×C151—22no—
120C2×C8×C151—22no—
121C2×C8×C151—22no—
122C2×C8×C151C22×C412yes—
123C2×C8×C151C22×C412yes—
124C4⋊C4×C151—24no—
125C4⋊C4×C151—21no—
126C4⋊C4×C151—21no—
127C4⋊C4×C151—22no—
128C4⋊C4×C151—22no—
129C4⋊C4×C151—22no—
130C4⋊C4×C151—22no—
131C4⋊C4×C151—42no—
132C4⋊C4×C151—44no—
133C4⋊C4×C151—44no—
134C4⋊C4×C151C22×C412yes—
135C4⋊C4×C151C22×C412yes—
136C22⋊C4×C151—24no—
137C22⋊C4×C151—44no—
138C22⋊C4×C151—82no—
139C42×C151—24no—
140C42×C151—22no—
141C42×C151—22no—
142C42×C151—44no—
143C42×C151—82no—
144C42×C151C22×C412yes—
145C42×C151#4112yes—
146C23×C151—22no—
147C23×C151—41no—
148C23×C151—41no—
149C23×C151—42no—
150C23×C151—42no—
151C23×C151C22×D411yescharacteristic
152Q8×C151—22no—
153Q8×C151—22no—
154Q8×C151—22no—
155Q8×C151#11714yes—
156D4×C151—22no—
157D4×C151—22no—
158D4×C151—41no—
159D4×C151—41no—
160C2×C4×C151—22no—
161C2×C4×C151—22no—
162C2×C4×C151—22no—
163C2×C4×C151—22no—
164C2×C4×C151—22no—
165C2×C4×C151—22no—
166C2×C4×C151—22no—
167C2×C4×C151—22no—
168C2×C4×C151—22no—
169C2×C4×C151—22no—
170C2×C4×C151—22no—
171C2×C4×C151—22no—
172C2×C4×C151—22no—
173C2×C4×C151—42no—
174C2×C4×C151—42no—
175C2×C4×C151—42no—
176C2×C4×C151—42no—
177C2×C4×C151—42no—
178C2×C4×C151—42no—
179C2×C4×C151—42no—
180C2×C4×C151—42no—
181C2×C4×C151—84no—
182C2×C4×C151C4×D412yes—
183C2×C4×C151C4×D412yes—
184C2×C4×C151C23×C411yescharacteristic
185C2×C4×C151C2×#4111yescharacteristic
186C2×C4×C151C2×#4111yescharacteristic
187C2×C4×C151C2×#4111yescharacteristic
188C2×C4×C151H(5,𝔽2)11yescharacteristic
189C2×C4×C1512−1+411yescharacteristic
190C8×C151—22no—
191C8×C151—22no—
192C8×C151—42no—
193C22×C151—42no—
194C22×C151—42no—
195C22×C151—42no—
196C22×C151—82no—
197C22×C151—82no—
198C22×C151C2×C4×D411yescharacteristic
199C22×C151#54611yescharacteristic
200C22×C151#54811yescharacteristic
201C22×C151#57512yes—
202C22×C151#57712yes—
203C4×C151—24no—
204C4×C151—22no—
205C4×C151—22no—
206C4×C151—42no—
207C4×C151—42no—
208C4×C151—42no—
209C4×C151—42no—
210C4×C151—82no—
211C4×C151—82no—
212C4×C151C2×#11711yescharacteristic
213C4×C151#52011yescharacteristic
214C4×C151#55211yescharacteristic
215C4×C151#55311yescharacteristic
216C2×C151—82no—
217C2×C151#235211yescharacteristic
218C2×C151#294311yescharacteristic
219C2×C151#294911yescharacteristic
220C2×C151#332612yes—
221C2×C151#337112yes—
222#22765C15111yesmaximal, characteristic, direct product factor, Sylow
223C151#2276511yescharacteristic, direct product factor, Sylow
224C2×C4×SD16C2×C15111yescharacteristic
225#2357C2×C15111yescharacteristic
226#2351C2×C15111yescharacteristic, complemented
227#1936C2×C15112yes—
228#1920C2×C15112yescomplemented
229#1880C2×C15112yes—
230#1835C2×C15111yescharacteristic, complemented
231#1805C2×C15111yescharacteristic, complemented
232#1804C2×C15111yescharacteristic
233#1770C2×C15111yescharacteristic, complemented
234#1763C2×C15112yescomplemented
235C22×SD16C22×C15111yescharacteristic
236C2×C4×Q8C22×C15112yes—
237C2×C4×Q8C22×C15111yescharacteristic
238C2×C4×D4C22×C15111yescharacteristic
239C4×SD16C4×C15118yescomplemented
240C2×#106C22×C15111yescharacteristic
241C2×C4⋊C8C22×C15111yescharacteristic
242C2×#103C22×C15112yes—
243C2×#103C22×C15111yescharacteristic
244C2×#102C22×C15112yes—
245C2×#102C22×C15111yescharacteristic
246C2×#97C22×C15112yes—
247C2×C4×C8C22×C15111yescharacteristic
248#390C22×C15112yes—
249#389—22no—
250#389C22×C15112yes—
251#388—22no—
252#382—21no—
253#382C22×C15111yescharacteristic
254#382C22×C15111yescharacteristic
255#381—21no—
256C4×C4⋊C4—21no—
257C4×C4⋊C4C22×C15112yes—
258C4×C4⋊C4C22×C15111yescharacteristic
259C4×C22⋊C4—21no—
260#340C22×C15112yes—
261#340C22×C15112yes—
262#340C22×C15112yes—
263#340C22×C15112yes—
264#336C22×C15112yes—
265C22×Q8C23×C15111yescharacteristic
266C22×D4C23×C15111yescharacteristic
267C23×C4—21no—
268C2×SD16—22no—
269C2×SD16—22no—
270C2×SD16C2×C4×C15114yes—
271C22×C8C23×C15112yes—
272C22×C8C23×C15111yescharacteristic
273C22×C8C23×C15111yescharacteristic
274C4×Q8—22no—
275C4×Q8—24no—
276C4×Q8—42no—
277C4×Q8C2×C4×C15114yes—
278C4×D4—22no—
279C4×D4C2×C4×C15114yes—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4D4×C15112yes—
284C2×C4⋊C4C23×C15112yes—
285C2×C4⋊C4C23×C15112yes—
286C2×C4⋊C4C23×C15111yescharacteristic
287C2×C4⋊C4C23×C15111yescharacteristic
288C2×C22⋊C4—21no—
289C2×C22⋊C4—22no—
290C2×C22⋊C4—22no—
291C2×C42—21no—
292C2×C42—22no—
293C2×C42—22no—
294C2×C42C23×C15112yes—
295C2×C42C23×C15111yescharacteristic
296#106C2×C4×C15114yes—
297C4⋊C8—22no—
298#103—24no—
299#103C2×C4×C15114yes—
300#102—42no—
301#102C2×C4×C15114yes—
302#97—42no—
303C4×C8C2×C4×C15114yes—
304#95—21no—
305#95—21no—
306#95—22no—
307#95—22no—
308#95—21no—
309#95—21no—
310#95D4×C15111yescharacteristic
311#95D4×C15111yescharacteristic
312C24—21no—
313C2×Q8—21no—
314C2×Q8—21no—
315C2×Q8—21no—
316C2×Q8C22×C4×C15112yes—
317C2×Q8#41×C15112yes—
318C2×Q8#41×C15112yes—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—21no—
324C2×D4C22×C4×C15112yes—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—24no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—82no—
332C22×C4C2×D4×C15112yes—
333C22×C4C2×D4×C15112yes—
334C22×C4C2×D4×C15111yescharacteristic
335C22×C4C2×D4×C15111yescharacteristic
336C22×C4C24×C15111yescharacteristic
337SD16—28no—
338C2×C8—21no—
339C2×C8—21no—
340C2×C8—21no—
341C2×C8—21no—
342C2×C8—22no—
343C2×C8—22no—
344C2×C8—22no—
345C2×C8C22×C4×C15112yes—
346C2×C8C22×C4×C15112yes—
347C4⋊C4—24no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—22no—
351C4⋊C4—22no—
352C4⋊C4—22no—
353C4⋊C4—22no—
354C4⋊C4—42no—
355C4⋊C4—44no—
356C4⋊C4—44no—
357C4⋊C4C22×C4×C15112yes—
358C4⋊C4C22×C4×C15112yes—
359C22⋊C4—24no—
360C22⋊C4—44no—
361C22⋊C4—82no—
362C42—24no—
363C42—22no—
364C42—22no—
365C42—44no—
366C42—82no—
367C42C22×C4×C15112yes—
368C42#41×C15112yes—
369C23—22no—
370C23—41no—
371C23—41no—
372C23—42no—
373C23—42no—
374C23C22×D4×C15111yescharacteristic
375Q8—22no—
376Q8—22no—
377Q8—22no—
378Q8#117×C15114yes—
379D4—22no—
380D4—22no—
381D4—41no—
382D4—41no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—84no—
405C2×C4C4×D4×C15112yes—
406C2×C4C4×D4×C15112yes—
407C2×C4C23×C4×C15111yescharacteristic
408C2×C4C2×#41×C15111yescharacteristic
409C2×C4C2×#41×C15111yescharacteristic
410C2×C4C2×#41×C15111yescharacteristic
411C2×C4H(5,𝔽2)×C15111yescharacteristic
412C2×C42−1+4×C15111yescharacteristic
413C8—22no—
414C8—22no—
415C8—42no—
416C22—42no—
417C22—42no—
418C22—42no—
419C22—82no—
420C22—82no—
421C22C2×C4×D4×C15111yescharacteristic
422C22#546×C15111yescharacteristic
423C22#548×C15111yescharacteristic
424C22#575×C15112yes—
425C22#577×C15112yes—
426C4—24no—
427C4—22no—
428C4—22no—
429C4—42no—
430C4—42no—
431C4—42no—
432C4—42no—
433C4—82no—
434C4—82no—
435C4C2×#117×C15111yescharacteristic
436C4#520×C15111yescharacteristic
437C4#552×C15111yescharacteristic
438C4#553×C15111yescharacteristic
439C2—82no—
440C2#2352×C15111yescharacteristic
441C2#2943×C15111yescharacteristic
442C2#2949×C15111yescharacteristic
443C2#3326×C15112yes—
444C2#3371×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C4⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. #2351×C151C2semidirect
5. #1920×C151C2semidirect
7. #1835×C151C2semidirect
8. #1805×C151C2semidirect
10. #1770×C151C2semidirect
11. #1763×C151C2semidirect
16. C4×SD16×C151C4semidirect
222. #22765C151direct (N × H)
223. C151#22765direct (N × H)
226. #2351C2×C151semidirect
228. #1920C2×C151semidirect
230. #1835C2×C151semidirect
231. #1805C2×C151semidirect
233. #1770C2×C151semidirect
234. #1763C2×C151semidirect
239. C4×SD16C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×C4×SD16×C1512
#2357×C1512
#2351×C1512
#1936×C1512
#1920×C1512
#1880×C1512
#1835×C1512
#1805×C1512
#1804×C1512
#1770×C1512
#1763×C1512
#22765151