Finite Group Databasebeta

← C151×#23952 #50328877

Subgroups — C151×#23952 #50328877

Order 38656.

1326 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3493×C151C211yesmaximal, characteristic, complemented
2#3003×C151C212yesmaximal, complemented
3#2309×C151C211yesmaximal, characteristic, complemented
4#2027×C151C212yesmaximal, complemented
5#2006×C151C212yesmaximal, complemented
6#1897×C151C212yesmaximal, complemented
7#1883×C151C214yesmaximal, complemented
8#1822×C151C211yesmaximal, characteristic, complemented
9C23×D4×C151C2211yescharacteristic
10C2×AGL(1,ℤ/8)×C151C2214yes—
11#556×C151—22no—
12#555×C151—22no—
13#553×C151—22no—
14#552×C151—22no—
15#544×C151C2211yescharacteristic, complemented
16#538×C151—22no—
17#537×C151C2211yescharacteristic, complemented
18#529×C151—22no—
19#525×C151C2212yes—
20#520×C151C2212yescomplemented
21C2×#117×C151C2211yescharacteristic
22C2×#117×C151C2211yescharacteristic
23#450×C151—22no—
24#450×C151—22no—
25#447×C151—22no—
26#447×C151—22no—
27C2×#104×C151C2214yescomplemented
28#418×C151C2214yes—
29#407×C151C2212yes—
30#390×C151—22no—
31#390×C151C2212yes—
32#390×C151C2212yes—
33#379×C151—22no—
34#343×C151C2212yescomplemented
35#343×C151C2212yescomplemented
36#339×C151C2214yescomplemented
37C25×C151—21no—
38C2×#41×C151C2312yes—
39C22×D4×C151—24no—
40C22×D4×C151—21no—
41C22×D4×C151—22no—
42C22×D4×C151—22no—
43C22×D4×C151—42no—
44C22×D4×C151C2312yes—
45C23×C4×C151C2311yescharacteristic
46AGL(1,ℤ/8)×C151—28no—
47AGL(1,ℤ/8)×C151—44no—
48C2×SD16×C151—24no—
49C2×D8×C151—24no—
50C2×M16×C151C2314yes—
51C4⋊Q8×C151—22no—
52#126×C151—24no—
53#126×C151—24no—
54#125×C151—22no—
55#125×C151—22no—
56#124×C151—22no—
57#124×C151—24no—
58#123×C151—24no—
59#123×C151—22no—
60C22⋊Q8×C151—22no—
61C22⋊Q8×C151—22no—
62C22⋊Q8×C151D412yes—
63C22⋊Q8×C151D412yes—
64#121×C151—24no—
65#121×C151—22no—
66#121×C151—22no—
67#121×C151D412yes—
68#121×C151D412yes—
69#120×C151—22no—
70C4×Q8×C151—22no—
71C4×Q8×C151—22no—
72C4×D4×C151—22no—
73C4×D4×C151—22no—
74C4×D4×C151—24no—
75C4×D4×C151—22no—
76C4×D4×C151—22no—
77#117×C151—24no—
78#117×C151—22no—
79#117×C151—22no—
80#117×C151—22no—
81#117×C151—42no—
82#117×C151C2312yes—
83C2×C4⋊C4×C151—22no—
84C2×C4⋊C4×C151—21no—
85C2×C4⋊C4×C151C2311yescharacteristic
86C2×C4⋊C4×C151C2311yescharacteristic
87C2×C22⋊C4×C151—24no—
88C2×C22⋊C4×C151—24no—
89C2×C22⋊C4×C151—21no—
90C2×C22⋊C4×C151D412yes—
91C2×C42×C151D412yes—
92C2×C42×C151C2312yes—
93#104×C151—44no—
94#102×C151—24no—
95#102×C151—24no—
96C22⋊C8×C151—22no—
97C22⋊C8×C151—22no—
98C24×C151—24no—
99C24×C151—22no—
100C24×C151—42no—
101C24×C151—42no—
102C24×C151—82no—
103C24×C151—82no—
104C24×C151C2×D411yescharacteristic
105#41×C151—24no—
106#41×C151—24no—
107C2×Q8×C151—22no—
108C2×Q8×C151C2×D412yes—
109C2×D4×C151—24no—
110C2×D4×C151—22no—
111C2×D4×C151—22no—
112C2×D4×C151—22no—
113C2×D4×C151—22no—
114C2×D4×C151—24no—
115C2×D4×C151—22no—
116C2×D4×C151—24no—
117C2×D4×C151—48no—
118C2×D4×C151—48no—
119C2×D4×C151—42no—
120C2×D4×C151—41no—
121C2×D4×C151—41no—
122C2×D4×C151C2×D412yes—
123C2×D4×C151#4114yes—
124C22×C4×C151—22no—
125C22×C4×C151—22no—
126C22×C4×C151—24no—
127C22×C4×C151—22no—
128C22×C4×C151—22no—
129C22×C4×C151C2×D411yescharacteristic
130C22×C4×C151C2×D412yes—
131C22×C4×C151C2×D412yes—
132C22×C4×C151C2×D412yes—
133C22×C4×C151C2×D412yes—
134C22×C4×C151C2411yescharacteristic
135SD16×C151—48no—
136D8×C151—48no—
137M16×C151—24no—
138M16×C151—24no—
139C2×C8×C151—24no—
140C4⋊C4×C151—24no—
141C4⋊C4×C151—24no—
142C4⋊C4×C151—22no—
143C4⋊C4×C151—22no—
144C4⋊C4×C151—22no—
145C4⋊C4×C151—22no—
146C4⋊C4×C151—22no—
147C4⋊C4×C151—22no—
148C4⋊C4×C151—42no—
149C4⋊C4×C151C2×D412yes—
150C4⋊C4×C151C2×D412yes—
151C22⋊C4×C151—24no—
152C22⋊C4×C151—24no—
153C22⋊C4×C151—24no—
154C22⋊C4×C151—22no—
155C22⋊C4×C151—22no—
156C22⋊C4×C151—22no—
157C22⋊C4×C151—22no—
158C22⋊C4×C151—22no—
159C22⋊C4×C151—42no—
160C22⋊C4×C151—84no—
161C22⋊C4×C151—84no—
162C42×C151—24no—
163C42×C151—22no—
164C42×C151—22no—
165C42×C151—22no—
166C42×C151—24no—
167C23×C151—21no—
168C23×C151—21no—
169C23×C151—22no—
170C23×C151—24no—
171C23×C151—41no—
172C23×C151—41no—
173C23×C151—48no—
174C23×C151—44no—
175C23×C151—44no—
176C23×C151—42no—
177C23×C151—42no—
178C23×C151—84no—
179C23×C151—84no—
180C23×C151—88no—
181C23×C151—88no—
182C23×C151#12012yes—
183C23×C151C22×D411yescharacteristic
184Q8×C151—24no—
185Q8×C151—82no—
186D4×C151—24no—
187D4×C151—28no—
188D4×C151—44no—
189D4×C151—44no—
190D4×C151—42no—
191D4×C151—42no—
192D4×C151—44no—
193D4×C151—82no—
194D4×C151—82no—
195D4×C151—82no—
196C2×C4×C151—21no—
197C2×C4×C151—21no—
198C2×C4×C151—24no—
199C2×C4×C151—24no—
200C2×C4×C151—22no—
201C2×C4×C151—22no—
202C2×C4×C151—22no—
203C2×C4×C151—22no—
204C2×C4×C151—22no—
205C2×C4×C151—44no—
206C2×C4×C151—42no—
207C2×C4×C151—42no—
208C2×C4×C151—42no—
209C2×C4×C151—42no—
210C2×C4×C151—42no—
211C2×C4×C151—84no—
212C2×C4×C151#12011yescharacteristic
213C2×C4×C151#12011yescharacteristic
214C2×C4×C151C22×D412yes—
215C2×C4×C151C2×#4112yes—
216C2×C4×C151H(5,𝔽2)12yes—
217C8×C151—44no—
218C22×C151—21no—
219C22×C151—21no—
220C22×C151—22no—
221C22×C151—22no—
222C22×C151—22no—
223C22×C151—42no—
224C22×C151—42no—
225C22×C151—48no—
226C22×C151—42no—
227C22×C151—44no—
228C22×C151—42no—
229C22×C151—42no—
230C22×C151—84no—
231C22×C151—816no—
232C22×C151—82no—
233C22×C151—82no—
234C22×C151C2×#12011yescharacteristic
235C22×C151#52511yescharacteristic
236C22×C151#53511yescharacteristic
237C4×C151—21no—
238C4×C151—21no—
239C4×C151—42no—
240C4×C151—42no—
241C4×C151—42no—
242C4×C151—42no—
243C4×C151—42no—
244C4×C151—82no—
245C4×C151#54614yes—
246C2×C151—21no—
247C2×C151—21no—
248C2×C151—42no—
249C2×C151—82no—
250C2×C151—84no—
251C2×C151#240411yescharacteristic
252C2×C151#302111yescharacteristic
253C2×C151#302111yescharacteristic
254#23952C15111yesmaximal, characteristic, direct product factor, Sylow
255C151#2395211yescharacteristic, direct product factor, Sylow
256#3493C2×C15111yescharacteristic, complemented
257#3003C2×C15112yescomplemented
258#2309C2×C15111yescharacteristic, complemented
259#2027C2×C15112yescomplemented
260#2006C2×C15112yescomplemented
261#1897C2×C15112yescomplemented
262#1883C2×C15114yescomplemented
263#1822C2×C15111yescharacteristic, complemented
264C23×D4C22×C15111yescharacteristic
265C2×AGL(1,ℤ/8)C22×C15114yes—
266#556—22no—
267#555—22no—
268#553—22no—
269#552—22no—
270#544C22×C15111yescharacteristic, complemented
271#538—22no—
272#537C22×C15111yescharacteristic, complemented
273#529—22no—
274#525C22×C15112yes—
275#520C22×C15112yescomplemented
276C2×#117C22×C15111yescharacteristic
277C2×#117C22×C15111yescharacteristic
278#450—22no—
279#450—22no—
280#447—22no—
281#447—22no—
282C2×#104C22×C15114yescomplemented
283#418C22×C15114yes—
284#407C22×C15112yes—
285#390—22no—
286#390C22×C15112yes—
287#390C22×C15112yes—
288#379—22no—
289#343C22×C15112yescomplemented
290#343C22×C15112yescomplemented
291#339C22×C15114yescomplemented
292C25—21no—
293C2×#41C23×C15112yes—
294C22×D4—24no—
295C22×D4—21no—
296C22×D4—22no—
297C22×D4—22no—
298C22×D4—42no—
299C22×D4C23×C15112yes—
300C23×C4C23×C15111yescharacteristic
301AGL(1,ℤ/8)—28no—
302AGL(1,ℤ/8)—44no—
303C2×SD16—24no—
304C2×D8—24no—
305C2×M16C23×C15114yes—
306C4⋊Q8—22no—
307#126—24no—
308#126—24no—
309#125—22no—
310#125—22no—
311#124—22no—
312#124—24no—
313#123—24no—
314#123—22no—
315C22⋊Q8—22no—
316C22⋊Q8—22no—
317C22⋊Q8D4×C15112yes—
318C22⋊Q8D4×C15112yes—
319#121—24no—
320#121—22no—
321#121—22no—
322#121D4×C15112yes—
323#121D4×C15112yes—
324#120—22no—
325C4×Q8—22no—
326C4×Q8—22no—
327C4×D4—22no—
328C4×D4—22no—
329C4×D4—24no—
330C4×D4—22no—
331C4×D4—22no—
332#117—24no—
333#117—22no—
334#117—22no—
335#117—22no—
336#117—42no—
337#117C23×C15112yes—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4C23×C15111yescharacteristic
341C2×C4⋊C4C23×C15111yescharacteristic
342C2×C22⋊C4—21no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4D4×C15112yes—
346C2×C42D4×C15112yes—
347C2×C42C23×C15112yes—
348#104—44no—
349#102—24no—
350#102—24no—
351C22⋊C8—22no—
352C22⋊C8—22no—
353C24—24no—
354C24—22no—
355C24—42no—
356C24—42no—
357C24—82no—
358C24—82no—
359C24C2×D4×C15111yescharacteristic
360#41—24no—
361#41—24no—
362C2×Q8—22no—
363C2×Q8C2×D4×C15112yes—
364C2×D4—24no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—24no—
370C2×D4—22no—
371C2×D4—24no—
372C2×D4—48no—
373C2×D4—48no—
374C2×D4—42no—
375C2×D4—41no—
376C2×D4—41no—
377C2×D4C2×D4×C15112yes—
378C2×D4#41×C15114yes—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—24no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4C2×D4×C15111yescharacteristic
385C22×C4C2×D4×C15112yes—
386C22×C4C2×D4×C15112yes—
387C22×C4C2×D4×C15112yes—
388C22×C4C2×D4×C15112yes—
389C22×C4C24×C15111yescharacteristic
390SD16—48no—
391D8—48no—
392M16—24no—
393M16—24no—
394C2×C8—24no—
395C4⋊C4—24no—
396C4⋊C4—24no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—42no—
404C4⋊C4C2×D4×C15112yes—
405C4⋊C4C2×D4×C15112yes—
406C22⋊C4—24no—
407C22⋊C4—24no—
408C22⋊C4—24no—
409C22⋊C4—22no—
410C22⋊C4—22no—
411C22⋊C4—22no—
412C22⋊C4—22no—
413C22⋊C4—22no—
414C22⋊C4—42no—
415C22⋊C4—84no—
416C22⋊C4—84no—
417C42—24no—
418C42—22no—
419C42—22no—
420C42—22no—
421C42—24no—
422C23—21no—
423C23—21no—
424C23—22no—
425C23—24no—
426C23—41no—
427C23—41no—
428C23—44no—
429C23—44no—
430C23—48no—
431C23—42no—
432C23—42no—
433C23—84no—
434C23—84no—
435C23—88no—
436C23—88no—
437C23#120×C15112yes—
438C23C22×D4×C15111yescharacteristic
439Q8—24no—
440Q8—82no—
441D4—24no—
442D4—28no—
443D4—44no—
444D4—44no—
445D4—42no—
446D4—42no—
447D4—44no—
448D4—82no—
449D4—82no—
450D4—82no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—24no—
454C2×C4—24no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—44no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—84no—
467C2×C4#120×C15111yescharacteristic
468C2×C4#120×C15111yescharacteristic
469C2×C4C22×D4×C15112yes—
470C2×C4C2×#41×C15112yes—
471C2×C4H(5,𝔽2)×C15112yes—
472C8—44no—
473C22—21no—
474C22—21no—
475C22—22no—
476C22—22no—
477C22—22no—
478C22—42no—
479C22—42no—
480C22—48no—
481C22—42no—
482C22—44no—
483C22—42no—
484C22—42no—
485C22—84no—
486C22—816no—
487C22—82no—
488C22—82no—
489C22C2×#120×C15111yescharacteristic
490C22#525×C15111yescharacteristic
491C22#535×C15111yescharacteristic
492C4—21no—
493C4—21no—
494C4—42no—
495C4—42no—
496C4—42no—
497C4—42no—
498C4—42no—
499C4—82no—
500C4#546×C15114yes—
501C2—21no—
502C2—21no—
503C2—42no—
504C2—84no—
505C2—82no—
506C2#2404×C15111yescharacteristic
507C2#3021×C15111yescharacteristic
508C2#3021×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3493×C151C2semidirect
2. #3003×C151C2semidirect
3. #2309×C151C2semidirect
4. #2027×C151C2semidirect
5. #2006×C151C2semidirect
6. #1897×C151C2semidirect
7. #1883×C151C2semidirect
8. #1822×C151C2semidirect
15. #544×C151C22semidirect
17. #537×C151C22semidirect
20. #520×C151C22semidirect
27. C2×#104×C151C22semidirect
34. #343×C151C22semidirect
35. #343×C151C22semidirect
36. #339×C151C22semidirect
254. #23952C151direct (N × H)
255. C151#23952direct (N × H)
256. #3493C2×C151semidirect
257. #3003C2×C151semidirect
258. #2309C2×C151semidirect
259. #2027C2×C151semidirect
260. #2006C2×C151semidirect
261. #1897C2×C151semidirect
262. #1883C2×C151semidirect
263. #1822C2×C151semidirect
270. #544C22×C151semidirect
272. #537C22×C151semidirect
275. #520C22×C151semidirect
282. C2×#104C22×C151semidirect
289. #343C22×C151semidirect
290. #343C22×C151semidirect
291. #339C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3493×C1512
#3003×C1512
#2309×C1512
#2027×C1512
#2006×C1512
#1897×C1512
#1883×C1512
#1822×C1512
#23952151