Finite Group Databasebeta

← C151×#25016 #50329941

Subgroups — C151×#25016 #50329941

Order 38656.

898 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#484×C151C212yesmaximal, complemented
2#2538×C151C211yesmaximal, characteristic
3D4×C4⋊C4×C151C211yesmaximal, characteristic
4#2076×C151C212yesmaximal, complemented
5#2036×C151C212yesmaximal, complemented
6#1954×C151C211yesmaximal, characteristic
7#1947×C151C211yesmaximal, characteristic, complemented
8#1852×C151C212yesmaximal, complemented
9#1845×C151C211yesmaximal, characteristic, complemented
10#1803×C151C211yesmaximal, characteristic, complemented
11C4×#103×C151C211yesmaximal, characteristic, complemented
12C2×C22⋊Q8×C151C2212yes—
13C2×C4×Q8×C151C2211yescharacteristic
14C2×C4×D4×C151—21no—
15C2×C4×D4×C151C2211yescharacteristic
16C22×C4⋊C4×C151C2212yes—
17#484×C151—28no—
18C2×#107×C151C2212yes—
19C2×#107×C151C2212yes—
20C2×#107×C151C2212yes—
21C2×C4⋊C8×C151C2211yescharacteristic
22C2×#103×C151C2211yescharacteristic
23C2×#103×C151C2212yes—
24C2×#103×C151C2211yescharacteristic
25C2×C22⋊C8×C151C2212yes—
26C2×C22⋊C8×C151C2212yes—
27C2×C4×C8×C151C2211yescharacteristic
28#396×C151—22no—
29#390×C151—21no—
30#389×C151—21no—
31#389×C151—21no—
32#385×C151—22no—
33#384×C151C2211yescharacteristic
34#384×C151C2211yescharacteristic
35#380×C151C2212yes—
36#380×C151C2212yes—
37C4×C4⋊C4×C151C2211yescharacteristic
38#340×C151C2211yescharacteristic
39#340×C151C2212yes—
40#340×C151C2212yes—
41#340×C151C2211yescharacteristic
42C22×Q8×C151C2311yescharacteristic
43C22×D4×C151D411yescharacteristic
44C23×C4×C151—22no—
45C23×C4×C151C2312yes—
46C22×C8×C151C2312yes—
47C22×C8×C151C2311yescharacteristic
48C22×C8×C151C2311yescharacteristic
49C22⋊Q8×C151—24no—
50C22⋊Q8×C151—42no—
51C4×Q8×C151—22no—
52C4×Q8×C151—22no—
53C4×D4×C151—22no—
54C4×D4×C151—22no—
55C4×D4×C151—44no—
56C2×C4⋊C4×C151—24no—
57C2×C4⋊C4×C151—21no—
58C2×C4⋊C4×C151—21no—
59C2×C4⋊C4×C151—22no—
60C2×C4⋊C4×C151—22no—
61C2×C4⋊C4×C151—21no—
62C2×C4⋊C4×C151—21no—
63C2×C4⋊C4×C151—21no—
64C2×C4⋊C4×C151—42no—
65C2×C4⋊C4×C151D411yescharacteristic
66C2×C4⋊C4×C151C2311yescharacteristic
67C2×C4⋊C4×C151C2311yescharacteristic
68C2×C4⋊C4×C151C2312yes—
69C2×C4⋊C4×C151C2312yes—
70C2×C4⋊C4×C151C2311yescharacteristic
71C2×C22⋊C4×C151—22no—
72C2×C22⋊C4×C151—22no—
73C2×C22⋊C4×C151—22no—
74C2×C22⋊C4×C151D412yes—
75C2×C42×C151—21no—
76C2×C42×C151—21no—
77C2×C42×C151C2311yescharacteristic
78#107×C151—24no—
79#107×C151—24no—
80#107×C151—42no—
81C4⋊C8×C151—22no—
82#103×C151—22no—
83#103×C151—24no—
84#103×C151D414yescomplemented
85C22⋊C8×C151—24no—
86C22⋊C8×C151—24no—
87C4×C8×C151—22no—
88#95×C151—21no—
89#95×C151—22no—
90#95×C151—22no—
91C24×C151C2×D412yes—
92C2×Q8×C151—21no—
93C2×Q8×C151—21no—
94C2×Q8×C151—21no—
95C2×Q8×C151—21no—
96C2×Q8×C151—21no—
97C2×Q8×C151C2×D412yes—
98C2×D4×C151—22no—
99C2×D4×C151—22no—
100C2×D4×C151Q1614yes—
101C22×C4×C151—21no—
102C22×C4×C151—21no—
103C22×C4×C151—22no—
104C22×C4×C151—22no—
105C22×C4×C151—22no—
106C22×C4×C151—22no—
107C22×C4×C151—22no—
108C22×C4×C151—22no—
109C22×C4×C151—21no—
110C22×C4×C151—21no—
111C22×C4×C151—22no—
112C22×C4×C151—22no—
113C22×C4×C151—44no—
114C22×C4×C151—44no—
115C22×C4×C151—82no—
116C22×C4×C151C2×D412yes—
117C22×C4×C151C2×D411yescharacteristic
118C22×C4×C151C2×D411yescharacteristic
119C22×C4×C151C2411yescharacteristic
120C2×C8×C151—21no—
121C2×C8×C151—21no—
122C2×C8×C151—21no—
123C2×C8×C151—21no—
124C2×C8×C151—22no—
125C2×C8×C151—22no—
126C2×C8×C151—22no—
127C2×C8×C151C2×D412yes—
128C2×C8×C151#4112yes—
129C4⋊C4×C151—22no—
130C4⋊C4×C151—21no—
131C4⋊C4×C151—22no—
132C4⋊C4×C151—22no—
133C4⋊C4×C151—21no—
134C4⋊C4×C151—21no—
135C4⋊C4×C151—21no—
136C4⋊C4×C151—22no—
137C4⋊C4×C151—22no—
138C4⋊C4×C151—21no—
139C4⋊C4×C151—44no—
140C4⋊C4×C151—44no—
141C4⋊C4×C151—42no—
142C4⋊C4×C151—42no—
143C4⋊C4×C151—42no—
144C4⋊C4×C151—81no—
145C4⋊C4×C151—81no—
146C4⋊C4×C151C2×D412yes—
147C22⋊C4×C151—24no—
148C22⋊C4×C151—44no—
149C22⋊C4×C151—44no—
150C22⋊C4×C151—82no—
151C42×C151—42no—
152C42×C151—42no—
153C42×C151#4112yes—
154C42×C151#4112yes—
155C23×C151—22no—
156C23×C151—22no—
157C23×C151—22no—
158C23×C151—22no—
159C23×C151—22no—
160C23×C151—22no—
161C23×C151C2×Q1614yes—
162C23×C151C22×D411yescharacteristic
163Q8×C151—22no—
164Q8×C151—22no—
165Q8×C151—41no—
166Q8×C151—41no—
167D4×C151—28no—
168C2×C4×C151—21no—
169C2×C4×C151—21no—
170C2×C4×C151—22no—
171C2×C4×C151—22no—
172C2×C4×C151—22no—
173C2×C4×C151—22no—
174C2×C4×C151—22no—
175C2×C4×C151—41no—
176C2×C4×C151—41no—
177C2×C4×C151—41no—
178C2×C4×C151—41no—
179C2×C4×C151—42no—
180C2×C4×C151—42no—
181C2×C4×C151—42no—
182C2×C4×C151—42no—
183C2×C4×C151—41no—
184C2×C4×C151—42no—
185C2×C4×C151—42no—
186C2×C4×C151—41no—
187C2×C4×C151—41no—
188C2×C4×C151—42no—
189C2×C4×C151—42no—
190C2×C4×C151—41no—
191C2×C4×C151—42no—
192C2×C4×C151—42no—
193C2×C4×C151—41no—
194C2×C4×C151—41no—
195C2×C4×C151—88no—
196C2×C4×C151#12312yes—
197C2×C4×C151#12312yes—
198C2×C4×C151C2×Q1612yes—
199C2×C4×C151AGL(1,ℤ/8)12yes—
200C2×C4×C151C22×D411yescharacteristic
201C2×C4×C151C2×#4111yescharacteristic
202C2×C4×C151C2×#4111yescharacteristic
203C2×C4×C151C2×#4111yescharacteristic
204C2×C4×C151H(5,𝔽2)11yescharacteristic
205C2×C4×C1512−1+411yescharacteristic
206C8×C151—22no—
207C8×C151—22no—
208C8×C151—42no—
209C22×C151—24no—
210C22×C151—24no—
211C22×C151—24no—
212C22×C151—42no—
213C22×C151—42no—
214C22×C151—42no—
215C22×C151—42no—
216C22×C151C2×#12311yescharacteristic
217C22×C151D4211yescharacteristic
218C22×C151#54711yescharacteristic
219C22×C151C22×Q1611yescharacteristic
220C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
221C22×C151#57611yescharacteristic
222C22×C151#57811yescharacteristic
223C4×C151—22no—
224C4×C151—42no—
225C4×C151—42no—
226C4×C151—42no—
227C4×C151—81no—
228C4×C151—81no—
229C4×C151—82no—
230C4×C151—82no—
231C4×C151#48414yescomplemented
232C4×C151#53211yescharacteristic
233C4×C151#54211yescharacteristic
234C4×C151#54711yescharacteristic
235C4×C151#55311yescharacteristic
236C2×C151—44no—
237C2×C151#242211yescharacteristic
238C2×C151C2×#48411yescharacteristic
239C2×C151#309811yescharacteristic
240C2×C151#327411yescharacteristic
241C2×C151D4×Q1611yescharacteristic
242C2×C151#333811yescharacteristic
243C2×C151#335311yescharacteristic
244#25016C15111yesmaximal, characteristic, direct product factor, Sylow
245C151#2501611yescharacteristic, direct product factor, Sylow
246C2×#484C2×C15112yescomplemented
247#2538C2×C15111yescharacteristic
248D4×C4⋊C4C2×C15111yescharacteristic
249#2076C2×C15112yescomplemented
250#2036C2×C15112yescomplemented
251#1954C2×C15111yescharacteristic
252#1947C2×C15111yescharacteristic, complemented
253#1852C2×C15112yescomplemented
254#1845C2×C15111yescharacteristic, complemented
255#1803C2×C15111yescharacteristic, complemented
256C4×#103C2×C15111yescharacteristic, complemented
257C2×C22⋊Q8C22×C15112yes—
258C2×C4×Q8C22×C15111yescharacteristic
259C2×C4×D4—21no—
260C2×C4×D4C22×C15111yescharacteristic
261C22×C4⋊C4C22×C15112yes—
262#484—28no—
263C2×#107C22×C15112yes—
264C2×#107C22×C15112yes—
265C2×#107C22×C15112yes—
266C2×C4⋊C8C22×C15111yescharacteristic
267C2×#103C22×C15112yes—
268C2×#103C22×C15111yescharacteristic
269C2×#103C22×C15111yescharacteristic
270C2×C22⋊C8C22×C15112yes—
271C2×C22⋊C8C22×C15112yes—
272C2×C4×C8C22×C15111yescharacteristic
273#396—22no—
274#390—21no—
275#389—21no—
276#389—21no—
277#385—22no—
278#384C22×C15111yescharacteristic
279#384C22×C15111yescharacteristic
280#380C22×C15112yes—
281#380C22×C15112yes—
282C4×C4⋊C4C22×C15111yescharacteristic
283#340C22×C15112yes—
284#340C22×C15111yescharacteristic
285#340C22×C15112yes—
286#340C22×C15111yescharacteristic
287C22×Q8C23×C15111yescharacteristic
288C22×D4D4×C15111yescharacteristic
289C23×C4—22no—
290C23×C4C23×C15112yes—
291C22×C8C23×C15112yes—
292C22×C8C23×C15111yescharacteristic
293C22×C8C23×C15111yescharacteristic
294C22⋊Q8—24no—
295C22⋊Q8—42no—
296C4×Q8—22no—
297C4×Q8—22no—
298C4×D4—22no—
299C4×D4—22no—
300C4×D4—44no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4D4×C15111yescharacteristic
311C2×C4⋊C4C23×C15112yes—
312C2×C4⋊C4C23×C15111yescharacteristic
313C2×C4⋊C4C23×C15112yes—
314C2×C4⋊C4C23×C15111yescharacteristic
315C2×C4⋊C4C23×C15111yescharacteristic
316C2×C22⋊C4—22no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4D4×C15112yes—
320C2×C42—21no—
321C2×C42—21no—
322C2×C42C23×C15111yescharacteristic
323#107—24no—
324#107—24no—
325#107—42no—
326C4⋊C8—22no—
327#103—24no—
328#103—22no—
329#103D4×C15114yescomplemented
330C22⋊C8—24no—
331C22⋊C8—24no—
332C4×C8—22no—
333#95—21no—
334#95—22no—
335#95—22no—
336C24C2×D4×C15112yes—
337C2×Q8—21no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8C2×D4×C15112yes—
343C2×D4—22no—
344C2×D4—22no—
345C2×D4Q16×C15114yes—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—44no—
359C22×C4—44no—
360C22×C4—82no—
361C22×C4C2×D4×C15112yes—
362C22×C4C2×D4×C15111yescharacteristic
363C22×C4C2×D4×C15111yescharacteristic
364C22×C4C24×C15111yescharacteristic
365C2×C8—21no—
366C2×C8—21no—
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—22no—
370C2×C8—22no—
371C2×C8—22no—
372C2×C8C2×D4×C15112yes—
373C2×C8#41×C15112yes—
374C4⋊C4—22no—
375C4⋊C4—21no—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—21no—
384C4⋊C4—44no—
385C4⋊C4—44no—
386C4⋊C4—42no—
387C4⋊C4—42no—
388C4⋊C4—42no—
389C4⋊C4—81no—
390C4⋊C4—81no—
391C4⋊C4C2×D4×C15112yes—
392C22⋊C4—24no—
393C22⋊C4—44no—
394C22⋊C4—44no—
395C22⋊C4—82no—
396C42—42no—
397C42—42no—
398C42#41×C15112yes—
399C42#41×C15112yes—
400C23—22no—
401C23—22no—
402C23—22no—
403C23—22no—
404C23—22no—
405C23—22no—
406C23C2×Q16×C15114yes—
407C23C22×D4×C15111yescharacteristic
408Q8—22no—
409Q8—22no—
410Q8—41no—
411Q8—41no—
412D4—28no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—88no—
441C2×C4#123×C15112yes—
442C2×C4#123×C15112yes—
443C2×C4C2×Q16×C15112yes—
444C2×C4AGL(1,ℤ/8)×C15112yes—
445C2×C4C22×D4×C15111yescharacteristic
446C2×C4C2×#41×C15111yescharacteristic
447C2×C4C2×#41×C15111yescharacteristic
448C2×C4C2×#41×C15111yescharacteristic
449C2×C4H(5,𝔽2)×C15111yescharacteristic
450C2×C42−1+4×C15111yescharacteristic
451C8—22no—
452C8—22no—
453C8—42no—
454C22—24no—
455C22—24no—
456C22—24no—
457C22—42no—
458C22—42no—
459C22—42no—
460C22—42no—
461C22C2×#123×C15111yescharacteristic
462C22D42×C15111yescharacteristic
463C22#547×C15111yescharacteristic
464C22C22×Q16×C15111yescharacteristic
465C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
466C22#576×C15111yescharacteristic
467C22#578×C15111yescharacteristic
468C4—22no—
469C4—42no—
470C4—42no—
471C4—42no—
472C4—82no—
473C4—82no—
474C4—81no—
475C4—81no—
476C4#484×C15114yescomplemented
477C4#532×C15111yescharacteristic
478C4#542×C15111yescharacteristic
479C4#547×C15111yescharacteristic
480C4#553×C15111yescharacteristic
481C2—44no—
482C2#2422×C15111yescharacteristic
483C2C2×#484×C15111yescharacteristic
484C2#3098×C15111yescharacteristic
485C2#3274×C15111yescharacteristic
486C2D4×Q16×C15111yescharacteristic
487C2#3338×C15111yescharacteristic
488C2#3353×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#484×C151C2semidirect
4. #2076×C151C2semidirect
5. #2036×C151C2semidirect
7. #1947×C151C2semidirect
8. #1852×C151C2semidirect
9. #1845×C151C2semidirect
10. #1803×C151C2semidirect
11. C4×#103×C151C2semidirect
84. #103×C151D4semidirect
231. C4×C151#484semidirect
244. #25016C151direct (N × H)
245. C151#25016direct (N × H)
246. C2×#484C2×C151semidirect
249. #2076C2×C151semidirect
250. #2036C2×C151semidirect
252. #1947C2×C151semidirect
253. #1852C2×C151semidirect
254. #1845C2×C151semidirect
255. #1803C2×C151semidirect
256. C4×#103C2×C151semidirect
329. #103D4×C151semidirect
476. C4#484×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#484×C1512
#2538×C1512
D4×C4⋊C4×C1512
#2076×C1512
#2036×C1512
#1954×C1512
#1947×C1512
#1852×C1512
#1845×C1512
#1803×C1512
C4×#103×C1512
#25016151