Finite Group Databasebeta

← C151×#23941 #50328866

Subgroups — C151×#23941 #50328866

Order 38656.

1334 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#540×C151C211yesmaximal, characteristic, complemented
2C2×#449×C151C212yesmaximal, complemented
3#2311×C151C211yesmaximal, characteristic, complemented
4#2026×C151C211yesmaximal, characteristic, complemented
5#2025×C151C211yesmaximal, characteristic, complemented
6#2014×C151C211yesmaximal, characteristic, complemented
7#2011×C151C211yesmaximal, characteristic, complemented
8#1879×C151C212yesmaximal, complemented
9#1877×C151C212yesmaximal, complemented
10#1874×C151C212yesmaximal, complemented
11#1818×C151C211yesmaximal, characteristic, complemented
12C22×#41×C151C2211yescharacteristic
13C22×SD16×C151C2212yes—
14C22×D8×C151C2212yes—
15#540×C151—28no—
16C2×#127×C151C2211yescharacteristic
17C2×#125×C151C2211yescharacteristic
18C2×#123×C151—22no—
19C2×#121×C151—22no—
20C2×#121×C151C2212yes—
21C2×C4×D4×C151C2212yes—
22C2×#117×C151C2211yescharacteristic
23C22×C4⋊C4×C151C2211yescharacteristic
24#449×C151—28no—
25C2×#103×C151C2212yes—
26C2×#102×C151C2212yes—
27C2×#102×C151C2212yes—
28C2×#102×C151C2212yes—
29C2×C22⋊C8×C151C2212yes—
30#391×C151C2211yescharacteristic
31#391×C151C2211yescharacteristic
32#390×C151C2211yescharacteristic
33#390×C151C2211yescharacteristic
34#386×C151—22no—
35#380×C151—22no—
36#340×C151C2212yes—
37#340×C151C2212yes—
38#336×C151C2212yes—
39#336×C151C2211yescharacteristic
40#336×C151C2211yescharacteristic
41C2×#41×C151—22no—
42C2×#41×C151—24no—
43C2×#41×C151—22no—
44C2×#41×C151—42no—
45C22×Q8×C151C2311yescharacteristic
46C22×D4×C151—22no—
47C22×D4×C151—21no—
48C22×D4×C151—22no—
49C22×D4×C151C2312yes—
50C22×D4×C151C2311yescharacteristic
51C23×C4×C151—21no—
52C23×C4×C151—22no—
53C23×C4×C151—21no—
54C23×C4×C151C2311yescharacteristic
55C2×SD16×C151—24no—
56C2×SD16×C151—24no—
57C2×SD16×C151—42no—
58C2×D8×C151—24no—
59C2×D8×C151—24no—
60C2×D8×C151—42no—
61C22×C8×C151C2312yes—
62C22×C8×C151C2312yes—
63#127×C151—24no—
64#125×C151—24no—
65#123×C151—216no—
66#121×C151—216no—
67#121×C151—24no—
68#121×C151D418yes—
69C4×D4×C151—24no—
70C4×D4×C151—24no—
71#117×C151—24no—
72C2×C4⋊C4×C151—22no—
73C2×C4⋊C4×C151—21no—
74C2×C4⋊C4×C151—42no—
75C2×C4⋊C4×C151D412yes—
76C2×C4⋊C4×C151C2311yescharacteristic
77C2×C4⋊C4×C151C2311yescharacteristic
78C2×C4⋊C4×C151C2312yes—
79C2×C22⋊C4×C151—22no—
80C2×C22⋊C4×C151—22no—
81C2×C22⋊C4×C151—22no—
82C2×C22⋊C4×C151—22no—
83C2×C22⋊C4×C151D412yes—
84C2×C42×C151C2311yescharacteristic
85C2×C42×C151C2311yescharacteristic
86#103×C151—24no—
87#102×C151—24no—
88#102×C151—42no—
89#102×C151—42no—
90C22⋊C8×C151—24no—
91#95×C151—22no—
92#95×C151—22no—
93C24×C151—21no—
94C24×C151—22no—
95C24×C151C2×D411yescharacteristic
96#41×C151—48no—
97#41×C151—48no—
98C2×Q8×C151—21no—
99C2×Q8×C151—22no—
100C2×Q8×C151—22no—
101C2×Q8×C151#4112yes—
102C2×D4×C151—24no—
103C2×D4×C151—28no—
104C2×D4×C151—28no—
105C2×D4×C151—22no—
106C2×D4×C151—22no—
107C2×D4×C151—22no—
108C2×D4×C151—22no—
109C2×D4×C151—21no—
110C2×D4×C151—22no—
111C2×D4×C151—22no—
112C2×D4×C151—22no—
113C2×D4×C151—42no—
114C2×D4×C151—42no—
115C2×D4×C151—82no—
116C2×D4×C151—82no—
117C2×D4×C151—82no—
118C2×D4×C151—82no—
119C2×D4×C151C2×D414yes—
120C2×D4×C151#4112yes—
121C22×C4×C151—21no—
122C22×C4×C151—21no—
123C22×C4×C151—22no—
124C22×C4×C151—24no—
125C22×C4×C151—21no—
126C22×C4×C151—22no—
127C22×C4×C151—28no—
128C22×C4×C151—21no—
129C22×C4×C151—21no—
130C22×C4×C151—42no—
131C22×C4×C151—42no—
132C22×C4×C151—42no—
133C22×C4×C151—82no—
134C22×C4×C151—82no—
135C22×C4×C151—82no—
136C22×C4×C151C2×D412yes—
137C22×C4×C151C2×D412yes—
138C22×C4×C151C2×D411yescharacteristic
139C22×C4×C151C2×D414yes—
140C22×C4×C151C2411yescharacteristic
141SD16×C151—48no—
142D8×C151—48no—
143C2×C8×C151—22no—
144C2×C8×C151—22no—
145C2×C8×C151—22no—
146C2×C8×C151—22no—
147C2×C8×C151—22no—
148C2×C8×C151—22no—
149C4⋊C4×C151—28no—
150C4⋊C4×C151—24no—
151C4⋊C4×C151—22no—
152C4⋊C4×C151—22no—
153C4⋊C4×C151—22no—
154C4⋊C4×C151—42no—
155C4⋊C4×C151C2×D414yes—
156C22⋊C4×C151—28no—
157C22⋊C4×C151—24no—
158C22⋊C4×C151—28no—
159C22⋊C4×C151—82no—
160C22⋊C4×C151—82no—
161C42×C151—22no—
162C42×C151—22no—
163C23×C151—21no—
164C23×C151—21no—
165C23×C151—22no—
166C23×C151—22no—
167C23×C151—24no—
168C23×C151—22no—
169C23×C151—41no—
170C23×C151—42no—
171C23×C151—41no—
172C23×C151—42no—
173C23×C151—42no—
174C23×C151—42no—
175C23×C151—42no—
176C23×C151—42no—
177C23×C151—42no—
178C23×C151—42no—
179C23×C151#12012yes—
180C23×C151C22×D411yescharacteristic
181Q8×C151—24no—
182Q8×C151—42no—
183D4×C151—24no—
184D4×C151—24no—
185D4×C151—24no—
186D4×C151—48no—
187D4×C151—42no—
188D4×C151—42no—
189D4×C151—42no—
190D4×C151—88no—
191D4×C151—88no—
192C2×C4×C151—21no—
193C2×C4×C151—21no—
194C2×C4×C151—24no—
195C2×C4×C151—24no—
196C2×C4×C151—22no—
197C2×C4×C151—22no—
198C2×C4×C151—24no—
199C2×C4×C151—22no—
200C2×C4×C151—22no—
201C2×C4×C151—22no—
202C2×C4×C151—22no—
203C2×C4×C151—22no—
204C2×C4×C151—48no—
205C2×C4×C151—41no—
206C2×C4×C151—41no—
207C2×C4×C151—42no—
208C2×C4×C151—42no—
209C2×C4×C151—41no—
210C2×C4×C151—41no—
211C2×C4×C151—42no—
212C2×C4×C151—42no—
213C2×C4×C151—88no—
214C2×C4×C151—84no—
215C2×C4×C151#12012yes—
216C2×C4×C151C22×D412yes—
217C2×C4×C151C2×#4111yescharacteristic
218C2×C4×C151C2×#4111yescharacteristic
219C2×C4×C151H(5,𝔽2)12yes—
220C8×C151—42no—
221C8×C151—42no—
222C22×C151—22no—
223C22×C151—24no—
224C22×C151—42no—
225C22×C151—41no—
226C22×C151—41no—
227C22×C151—44no—
228C22×C151—42no—
229C22×C151—44no—
230C22×C151—44no—
231C22×C151—44no—
232C22×C151—82no—
233C22×C151—82no—
234C22×C151—81no—
235C22×C151—82no—
236C22×C151—81no—
237C22×C151—82no—
238C22×C151—82no—
239C22×C151C2×#12011yescharacteristic
240C22×C151#52511yescharacteristic
241C22×C151#53511yescharacteristic
242C22×C151#57612yes—
243C22×C151#57712yes—
244C4×C151—22no—
245C4×C151—42no—
246C4×C151—42no—
247C4×C151—42no—
248C4×C151—44no—
249C4×C151—81no—
250C4×C151—81no—
251C4×C151#54612yes—
252C4×C151#54612yes—
253C2×C151—42no—
254C2×C151—82no—
255C2×C151—84no—
256C2×C151#240411yescharacteristic
257C2×C151#301212yes—
258C2×C151#311912yes—
259C2×C151#322011yescharacteristic
260C2×C151#322111yescharacteristic
261#23941C15111yesmaximal, characteristic, direct product factor, Sylow
262C151#2394111yescharacteristic, direct product factor, Sylow
263C2×#540C2×C15111yescharacteristic, complemented
264C2×#449C2×C15112yescomplemented
265#2311C2×C15111yescharacteristic, complemented
266#2026C2×C15111yescharacteristic, complemented
267#2025C2×C15111yescharacteristic, complemented
268#2014C2×C15111yescharacteristic, complemented
269#2011C2×C15111yescharacteristic, complemented
270#1879C2×C15112yescomplemented
271#1877C2×C15112yescomplemented
272#1874C2×C15112yescomplemented
273#1818C2×C15111yescharacteristic, complemented
274C22×#41C22×C15111yescharacteristic
275C22×SD16C22×C15112yes—
276C22×D8C22×C15112yes—
277#540—28no—
278C2×#127C22×C15111yescharacteristic
279C2×#125C22×C15111yescharacteristic
280C2×#123—22no—
281C2×#121—22no—
282C2×#121C22×C15112yes—
283C2×C4×D4C22×C15112yes—
284C2×#117C22×C15111yescharacteristic
285C22×C4⋊C4C22×C15111yescharacteristic
286#449—28no—
287C2×#103C22×C15112yes—
288C2×#102C22×C15112yes—
289C2×#102C22×C15112yes—
290C2×#102C22×C15112yes—
291C2×C22⋊C8C22×C15112yes—
292#391C22×C15111yescharacteristic
293#391C22×C15111yescharacteristic
294#390C22×C15111yescharacteristic
295#390C22×C15111yescharacteristic
296#386—22no—
297#380—22no—
298#340C22×C15112yes—
299#340C22×C15112yes—
300#336C22×C15112yes—
301#336C22×C15111yescharacteristic
302#336C22×C15111yescharacteristic
303C2×#41—22no—
304C2×#41—22no—
305C2×#41—24no—
306C2×#41—42no—
307C22×Q8C23×C15111yescharacteristic
308C22×D4—21no—
309C22×D4—22no—
310C22×D4—22no—
311C22×D4C23×C15111yescharacteristic
312C22×D4C23×C15112yes—
313C23×C4—21no—
314C23×C4—22no—
315C23×C4—21no—
316C23×C4C23×C15111yescharacteristic
317C2×SD16—24no—
318C2×SD16—24no—
319C2×SD16—42no—
320C2×D8—24no—
321C2×D8—24no—
322C2×D8—42no—
323C22×C8C23×C15112yes—
324C22×C8C23×C15112yes—
325#127—24no—
326#125—24no—
327#123—216no—
328#121—216no—
329#121—24no—
330#121D4×C15118yes—
331C4×D4—24no—
332C4×D4—24no—
333#117—24no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4D4×C15112yes—
338C2×C4⋊C4C23×C15111yescharacteristic
339C2×C4⋊C4C23×C15111yescharacteristic
340C2×C4⋊C4C23×C15112yes—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4D4×C15112yes—
346C2×C42C23×C15111yescharacteristic
347C2×C42C23×C15111yescharacteristic
348#103—24no—
349#102—24no—
350#102—42no—
351#102—42no—
352C22⋊C8—24no—
353#95—22no—
354#95—22no—
355C24—21no—
356C24—22no—
357C24C2×D4×C15111yescharacteristic
358#41—48no—
359#41—48no—
360C2×Q8—21no—
361C2×Q8—22no—
362C2×Q8—22no—
363C2×Q8#41×C15112yes—
364C2×D4—24no—
365C2×D4—28no—
366C2×D4—28no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4—21no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—42no—
376C2×D4—42no—
377C2×D4—82no—
378C2×D4—82no—
379C2×D4—82no—
380C2×D4—82no—
381C2×D4C2×D4×C15114yes—
382C2×D4#41×C15112yes—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—24no—
387C22×C4—21no—
388C22×C4—22no—
389C22×C4—28no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—42no—
393C22×C4—42no—
394C22×C4—42no—
395C22×C4—82no—
396C22×C4—82no—
397C22×C4—82no—
398C22×C4C2×D4×C15112yes—
399C22×C4C2×D4×C15112yes—
400C22×C4C2×D4×C15111yescharacteristic
401C22×C4C2×D4×C15114yes—
402C22×C4C24×C15111yescharacteristic
403SD16—48no—
404D8—48no—
405C2×C8—22no—
406C2×C8—22no—
407C2×C8—22no—
408C2×C8—22no—
409C2×C8—22no—
410C2×C8—22no—
411C4⋊C4—28no—
412C4⋊C4—24no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—42no—
417C4⋊C4C2×D4×C15114yes—
418C22⋊C4—28no—
419C22⋊C4—24no—
420C22⋊C4—28no—
421C22⋊C4—82no—
422C22⋊C4—82no—
423C42—22no—
424C42—22no—
425C23—21no—
426C23—21no—
427C23—22no—
428C23—22no—
429C23—24no—
430C23—22no—
431C23—41no—
432C23—42no—
433C23—41no—
434C23—42no—
435C23—42no—
436C23—42no—
437C23—42no—
438C23—42no—
439C23—42no—
440C23—42no—
441C23#120×C15112yes—
442C23C22×D4×C15111yescharacteristic
443Q8—24no—
444Q8—42no—
445D4—24no—
446D4—24no—
447D4—24no—
448D4—48no—
449D4—42no—
450D4—42no—
451D4—42no—
452D4—88no—
453D4—88no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—24no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—48no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—88no—
476C2×C4—84no—
477C2×C4#120×C15112yes—
478C2×C4C22×D4×C15112yes—
479C2×C4C2×#41×C15111yescharacteristic
480C2×C4C2×#41×C15111yescharacteristic
481C2×C4H(5,𝔽2)×C15112yes—
482C8—42no—
483C8—42no—
484C22—22no—
485C22—24no—
486C22—42no—
487C22—41no—
488C22—41no—
489C22—44no—
490C22—42no—
491C22—44no—
492C22—44no—
493C22—44no—
494C22—82no—
495C22—82no—
496C22—81no—
497C22—82no—
498C22—81no—
499C22—82no—
500C22—82no—
501C22C2×#120×C15111yescharacteristic
502C22#525×C15111yescharacteristic
503C22#535×C15111yescharacteristic
504C22#576×C15112yes—
505C22#577×C15112yes—
506C4—22no—
507C4—42no—
508C4—42no—
509C4—42no—
510C4—44no—
511C4—81no—
512C4—81no—
513C4#546×C15112yes—
514C4#546×C15112yes—
515C2—42no—
516C2—82no—
517C2—84no—
518C2#2404×C15111yescharacteristic
519C2#3012×C15112yes—
520C2#3119×C15112yes—
521C2#3220×C15111yescharacteristic
522C2#3221×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×#117×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#540×C151C2semidirect
2. C2×#449×C151C2semidirect
3. #2311×C151C2semidirect
4. #2026×C151C2semidirect
5. #2025×C151C2semidirect
6. #2014×C151C2semidirect
7. #2011×C151C2semidirect
8. #1879×C151C2semidirect
9. #1877×C151C2semidirect
10. #1874×C151C2semidirect
11. #1818×C151C2semidirect
261. #23941C151direct (N × H)
262. C151#23941direct (N × H)
263. C2×#540C2×C151semidirect
264. C2×#449C2×C151semidirect
265. #2311C2×C151semidirect
266. #2026C2×C151semidirect
267. #2025C2×C151semidirect
268. #2014C2×C151semidirect
269. #2011C2×C151semidirect
270. #1879C2×C151semidirect
271. #1877C2×C151semidirect
272. #1874C2×C151semidirect
273. #1818C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#540×C1512
C2×#449×C1512
#2311×C1512
#2026×C1512
#2025×C1512
#2014×C1512
#2011×C1512
#1879×C1512
#1877×C1512
#1874×C1512
#1818×C1512
#23941151