Finite Group Databasebeta

← C151×#24627 #50329552

Subgroups — C151×#24627 #50329552

Order 38656.

938 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#461×C151C211yesmaximal, characteristic, complemented
2C2×C4×D8×C151C211yesmaximal, characteristic
3#2547×C151C211yesmaximal, characteristic, complemented
4#2354×C151C211yesmaximal, characteristic, complemented
5#2055×C151C212yesmaximal, complemented
6#2012×C151C212yesmaximal
7#1983×C151C212yesmaximal, complemented
8#1956×C151C211yesmaximal, characteristic, complemented
9#1939×C151C211yesmaximal, characteristic, complemented
10#1928×C151C212yesmaximal, complemented
11#1802×C151C211yesmaximal, characteristic, complemented
12C22×SD16×C151C2212yes—
13C22×D8×C151C2211yescharacteristic
14C2×C4⋊Q8×C151C2211yescharacteristic
15C2×#124×C151C2212yes—
16C2×C4×D4×C151C2211yescharacteristic
17C2×C4×D4×C151C2211yescharacteristic
18C2×#117×C151—21no—
19#461×C151—24no—
20C4×D8×C151—24no—
21C2×#107×C151C2211yescharacteristic
22C2×C4⋊C8×C151C2211yescharacteristic
23C2×C4⋊C8×C151C2212yes—
24C2×#103×C151C2212yes—
25C2×#103×C151C2212yes—
26C2×#103×C151C2212yes—
27C2×#102×C151C2211yescharacteristic
28C2×#102×C151C2211yescharacteristic
29C2×#102×C151C2212yes—
30C2×C4×C8×C151C2211yescharacteristic
31#397×C151—22no—
32#391×C151C2212yes—
33#390×C151C2212yes—
34#388×C151—22no—
35#384×C151C2211yescharacteristic
36#380×C151—21no—
37#380×C151—21no—
38#380×C151—21no—
39C4×C4⋊C4×C151C2212yes—
40C4×C4⋊C4×C151C2211yescharacteristic
41#340×C151C2212yes—
42#336×C151C2212yes—
43C22×Q8×C151C2312yes—
44C22×D4×C151C2311yescharacteristic
45C22×D4×C151C2311yescharacteristic
46C23×C4×C151—21no—
47C23×C4×C151—21no—
48C2×SD16×C151—24no—
49C2×SD16×C151—42no—
50C2×SD16×C151—42no—
51C2×D8×C151—22no—
52C2×D8×C151—22no—
53C2×D8×C151—22no—
54C22×C8×C151C2312yes—
55C22×C8×C151C2311yescharacteristic
56C22×C8×C151C2311yescharacteristic
57C4⋊Q8×C151—22no—
58C4⋊Q8×C151—22no—
59#124×C151—24no—
60#124×C151—42no—
61C4×D4×C151—22no—
62C4×D4×C151—22no—
63C4×D4×C151—22no—
64C4×D4×C151D414yes—
65#117×C151—44no—
66C2×C4⋊C4×C151—21no—
67C2×C4⋊C4×C151—21no—
68C2×C4⋊C4×C151—21no—
69C2×C4⋊C4×C151—21no—
70C2×C4⋊C4×C151D411yescharacteristic
71C2×C4⋊C4×C151D411yescharacteristic
72C2×C4⋊C4×C151C2311yescharacteristic
73C2×C4⋊C4×C151C2312yes—
74C2×C4⋊C4×C151C2311yescharacteristic
75C2×C22⋊C4×C151—21no—
76C2×C22⋊C4×C151—22no—
77C2×C22⋊C4×C151—22no—
78C2×C22⋊C4×C151—22no—
79C2×C22⋊C4×C151—21no—
80C2×C22⋊C4×C151—22no—
81C2×C42×C151—22no—
82C2×C42×C151C2312yes—
83C2×C42×C151C2311yescharacteristic
84#107×C151—22no—
85C4⋊C8×C151—22no—
86C4⋊C8×C151—42no—
87#103×C151—24no—
88#103×C151—24no—
89#103×C151—42no—
90#102×C151—22no—
91#102×C151—22no—
92#102×C151—42no—
93C4×C8×C151—22no—
94#95×C151—22no—
95#95×C151—22no—
96#95×C151—22no—
97#95×C151D412yes—
98C24×C151—21no—
99C24×C151—21no—
100C2×Q8×C151—22no—
101C2×Q8×C151—22no—
102C2×Q8×C151—22no—
103C2×Q8×C151—22no—
104C2×Q8×C151—22no—
105C2×Q8×C151—22no—
106C2×D4×C151—21no—
107C2×D4×C151—21no—
108C2×D4×C151—21no—
109C2×D4×C151—21no—
110C2×D4×C151—21no—
111C2×D4×C151—21no—
112C2×D4×C151—21no—
113C2×D4×C151—21no—
114C2×D4×C151—21no—
115C2×D4×C151—21no—
116C2×D4×C151C2×D412yes—
117C2×D4×C151#4112yes—
118C22×C4×C151—21no—
119C22×C4×C151—24no—
120C22×C4×C151—21no—
121C22×C4×C151—22no—
122C22×C4×C151—22no—
123C22×C4×C151—42no—
124C22×C4×C151—42no—
125C22×C4×C151—42no—
126C22×C4×C151—42no—
127C22×C4×C151—42no—
128C22×C4×C151C2×D412yes—
129C22×C4×C151C2×D412yes—
130C22×C4×C151C2×D411yescharacteristic
131C22×C4×C151C2×D411yescharacteristic
132C22×C4×C151C2411yescharacteristic
133SD16×C151—48no—
134D8×C151—28no—
135C2×C8×C151—21no—
136C2×C8×C151—21no—
137C2×C8×C151—21no—
138C2×C8×C151—22no—
139C2×C8×C151—22no—
140C2×C8×C151—21no—
141C2×C8×C151—21no—
142C2×C8×C151—22no—
143C2×C8×C151#4112yes—
144C4⋊C4×C151—22no—
145C4⋊C4×C151—22no—
146C4⋊C4×C151—21no—
147C4⋊C4×C151—21no—
148C4⋊C4×C151—22no—
149C4⋊C4×C151—21no—
150C4⋊C4×C151—22no—
151C4⋊C4×C151—42no—
152C4⋊C4×C151—42no—
153C4⋊C4×C151—42no—
154C4⋊C4×C151—81no—
155C4⋊C4×C151C2×D412yes—
156C22⋊C4×C151—24no—
157C22⋊C4×C151—44no—
158C22⋊C4×C151—44no—
159C22⋊C4×C151—44no—
160C22⋊C4×C151—42no—
161C22⋊C4×C151—82no—
162C42×C151—22no—
163C42×C151—22no—
164C42×C151—44no—
165C42×C151C2×D412yes—
166C42×C151#4112yes—
167C23×C151—22no—
168C23×C151—22no—
169C23×C151—41no—
170C23×C151—41no—
171C23×C151—41no—
172C23×C151—41no—
173C23×C151—41no—
174C23×C151—41no—
175C23×C151—41no—
176C23×C151—41no—
177C23×C151—41no—
178C23×C151—41no—
179C23×C151—41no—
180C23×C151—41no—
181C23×C151C22×D411yescharacteristic
182Q8×C151—42no—
183Q8×C151—42no—
184Q8×C151—42no—
185Q8×C151—42no—
186D4×C151—22no—
187D4×C151—22no—
188D4×C151—22no—
189D4×C151—22no—
190D4×C151—41no—
191D4×C151—41no—
192D4×C151—41no—
193D4×C151—41no—
194C2×C4×C151—21no—
195C2×C4×C151—21no—
196C2×C4×C151—22no—
197C2×C4×C151—22no—
198C2×C4×C151—22no—
199C2×C4×C151—22no—
200C2×C4×C151—22no—
201C2×C4×C151—22no—
202C2×C4×C151—22no—
203C2×C4×C151—41no—
204C2×C4×C151—41no—
205C2×C4×C151—48no—
206C2×C4×C151—42no—
207C2×C4×C151—41no—
208C2×C4×C151—42no—
209C2×C4×C151—42no—
210C2×C4×C151—42no—
211C2×C4×C151—41no—
212C2×C4×C151—42no—
213C2×C4×C151—41no—
214C2×C4×C151—42no—
215C2×C4×C151—84no—
216C2×C4×C151#12112yes—
217C2×C4×C151#12112yes—
218C2×C4×C151#13512yes—
219C2×C4×C151AGL(1,ℤ/8)12yes—
220C2×C4×C151C22×D411yescharacteristic
221C2×C4×C151C2×#4111yescharacteristic
222C2×C4×C151C2×#4111yescharacteristic
223C2×C4×C151C2×#4111yescharacteristic
224C2×C4×C151H(5,𝔽2)11yescharacteristic
225C2×C4×C151H(5,𝔽2)11yescharacteristic
226C8×C151—22no—
227C8×C151—41no—
228C8×C151—42no—
229C22×C151—42no—
230C22×C151—42no—
231C22×C151—42no—
232C22×C151—42no—
233C22×C151—42no—
234C22×C151—42no—
235C22×C151—81no—
236C22×C151—81no—
237C22×C151—81no—
238C22×C151—81no—
239C22×C151—81no—
240C22×C151—81no—
241C22×C151—81no—
242C22×C151—81no—
243C22×C151C2×#12111yescharacteristic
244C22×C151#54611yescharacteristic
245C22×C151#55011yescharacteristic
246C22×C151C2×#13511yescharacteristic
247C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
248C22×C151#57711yescharacteristic
249C22×C151#57811yescharacteristic
250C4×C151—22no—
251C4×C151—42no—
252C4×C151—42no—
253C4×C151—42no—
254C4×C151—82no—
255C4×C151—82no—
256C4×C151—81no—
257C4×C151#46314yes—
258C4×C151#52511yescharacteristic
259C4×C151#53511yescharacteristic
260C4×C151#55311yescharacteristic
261C4×C151#55511yescharacteristic
262C2×C151—82no—
263C2×C151—82no—
264C2×C151#241411yescharacteristic
265C2×C151C2×#46311yescharacteristic
266C2×C151#304611yescharacteristic
267C2×C151#330311yescharacteristic
268C2×C151#333011yescharacteristic
269C2×C151#339311yescharacteristic
270C2×C151#339711yescharacteristic
271#24627C15111yesmaximal, characteristic, direct product factor, Sylow
272C151#2462711yescharacteristic, direct product factor, Sylow
273C2×#461C2×C15111yescharacteristic, complemented
274C2×C4×D8C2×C15111yescharacteristic
275#2547C2×C15111yescharacteristic, complemented
276#2354C2×C15111yescharacteristic, complemented
277#2055C2×C15112yescomplemented
278#2012C2×C15112yes—
279#1983C2×C15112yescomplemented
280#1956C2×C15111yescharacteristic, complemented
281#1939C2×C15111yescharacteristic, complemented
282#1928C2×C15112yescomplemented
283#1802C2×C15111yescharacteristic, complemented
284C22×SD16C22×C15112yes—
285C22×D8C22×C15111yescharacteristic
286C2×C4⋊Q8C22×C15111yescharacteristic
287C2×#124C22×C15112yes—
288C2×C4×D4C22×C15111yescharacteristic
289C2×C4×D4C22×C15111yescharacteristic
290C2×#117—21no—
291#461—24no—
292C4×D8—24no—
293C2×#107C22×C15111yescharacteristic
294C2×C4⋊C8C22×C15111yescharacteristic
295C2×C4⋊C8C22×C15112yes—
296C2×#103C22×C15112yes—
297C2×#103C22×C15112yes—
298C2×#103C22×C15112yes—
299C2×#102C22×C15111yescharacteristic
300C2×#102C22×C15111yescharacteristic
301C2×#102C22×C15112yes—
302C2×C4×C8C22×C15111yescharacteristic
303#397—22no—
304#391C22×C15112yes—
305#390C22×C15112yes—
306#388—22no—
307#384C22×C15111yescharacteristic
308#380—21no—
309#380—21no—
310#380—21no—
311C4×C4⋊C4C22×C15112yes—
312C4×C4⋊C4C22×C15111yescharacteristic
313#340C22×C15112yes—
314#336C22×C15112yes—
315C22×Q8C23×C15112yes—
316C22×D4C23×C15111yescharacteristic
317C22×D4C23×C15111yescharacteristic
318C23×C4—21no—
319C23×C4—21no—
320C2×SD16—24no—
321C2×SD16—42no—
322C2×SD16—42no—
323C2×D8—22no—
324C2×D8—22no—
325C2×D8—22no—
326C22×C8C23×C15112yes—
327C22×C8C23×C15111yescharacteristic
328C22×C8C23×C15111yescharacteristic
329C4⋊Q8—22no—
330C4⋊Q8—22no—
331#124—24no—
332#124—42no—
333C4×D4—22no—
334C4×D4—22no—
335C4×D4—22no—
336C4×D4D4×C15114yes—
337#117—44no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4D4×C15111yescharacteristic
343C2×C4⋊C4D4×C15111yescharacteristic
344C2×C4⋊C4C23×C15111yescharacteristic
345C2×C4⋊C4C23×C15112yes—
346C2×C4⋊C4C23×C15111yescharacteristic
347C2×C22⋊C4—21no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C42—22no—
354C2×C42C23×C15112yes—
355C2×C42C23×C15111yescharacteristic
356#107—22no—
357C4⋊C8—22no—
358C4⋊C8—42no—
359#103—24no—
360#103—24no—
361#103—42no—
362#102—22no—
363#102—22no—
364#102—42no—
365C4×C8—22no—
366#95—22no—
367#95—22no—
368#95—22no—
369#95D4×C15112yes—
370C24—21no—
371C24—21no—
372C2×Q8—22no—
373C2×Q8—22no—
374C2×Q8—22no—
375C2×Q8—22no—
376C2×Q8—22no—
377C2×Q8—22no—
378C2×D4—21no—
379C2×D4—21no—
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4C2×D4×C15112yes—
389C2×D4#41×C15112yes—
390C22×C4—21no—
391C22×C4—24no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—42no—
396C22×C4—42no—
397C22×C4—42no—
398C22×C4—42no—
399C22×C4—42no—
400C22×C4C2×D4×C15112yes—
401C22×C4C2×D4×C15112yes—
402C22×C4C2×D4×C15111yescharacteristic
403C22×C4C2×D4×C15111yescharacteristic
404C22×C4C24×C15111yescharacteristic
405SD16—48no—
406D8—28no—
407C2×C8—21no—
408C2×C8—21no—
409C2×C8—21no—
410C2×C8—22no—
411C2×C8—22no—
412C2×C8—21no—
413C2×C8—21no—
414C2×C8—22no—
415C2×C8#41×C15112yes—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—22no—
421C4⋊C4—21no—
422C4⋊C4—22no—
423C4⋊C4—42no—
424C4⋊C4—42no—
425C4⋊C4—42no—
426C4⋊C4—81no—
427C4⋊C4C2×D4×C15112yes—
428C22⋊C4—24no—
429C22⋊C4—44no—
430C22⋊C4—44no—
431C22⋊C4—44no—
432C22⋊C4—42no—
433C22⋊C4—82no—
434C42—22no—
435C42—22no—
436C42—44no—
437C42C2×D4×C15112yes—
438C42#41×C15112yes—
439C23—22no—
440C23—22no—
441C23—41no—
442C23—41no—
443C23—41no—
444C23—41no—
445C23—41no—
446C23—41no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23—41no—
451C23—41no—
452C23—41no—
453C23C22×D4×C15111yescharacteristic
454Q8—42no—
455Q8—42no—
456Q8—42no—
457Q8—42no—
458D4—22no—
459D4—22no—
460D4—22no—
461D4—22no—
462D4—41no—
463D4—41no—
464D4—41no—
465D4—41no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—48no—
478C2×C4—41no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4—41no—
486C2×C4—42no—
487C2×C4—84no—
488C2×C4#121×C15112yes—
489C2×C4#121×C15112yes—
490C2×C4#135×C15112yes—
491C2×C4AGL(1,ℤ/8)×C15112yes—
492C2×C4C22×D4×C15111yescharacteristic
493C2×C4C2×#41×C15111yescharacteristic
494C2×C4C2×#41×C15111yescharacteristic
495C2×C4C2×#41×C15111yescharacteristic
496C2×C4H(5,𝔽2)×C15111yescharacteristic
497C2×C4H(5,𝔽2)×C15111yescharacteristic
498C8—22no—
499C8—42no—
500C8—41no—
501C22—42no—
502C22—42no—
503C22—42no—
504C22—42no—
505C22—42no—
506C22—42no—
507C22—81no—
508C22—81no—
509C22—81no—
510C22—81no—
511C22—81no—
512C22—81no—
513C22—81no—
514C22—81no—
515C22C2×#121×C15111yescharacteristic
516C22#546×C15111yescharacteristic
517C22#550×C15111yescharacteristic
518C22C2×#135×C15111yescharacteristic
519C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
520C22#577×C15111yescharacteristic
521C22#578×C15111yescharacteristic
522C4—22no—
523C4—42no—
524C4—42no—
525C4—42no—
526C4—82no—
527C4—82no—
528C4—81no—
529C4#463×C15114yes—
530C4#525×C15111yescharacteristic
531C4#535×C15111yescharacteristic
532C4#553×C15111yescharacteristic
533C4#555×C15111yescharacteristic
534C2—82no—
535C2—82no—
536C2#2414×C15111yescharacteristic
537C2C2×#463×C15111yescharacteristic
538C2#3046×C15111yescharacteristic
539C2#3303×C15111yescharacteristic
540C2#3330×C15111yescharacteristic
541C2#3393×C15111yescharacteristic
542C2#3397×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D8×C151C22
LCSG ▷ C22×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
1. C2×#461×C151C2semidirect
3. #2547×C151C2semidirect
4. #2354×C151C2semidirect
5. #2055×C151C2semidirect
7. #1983×C151C2semidirect
8. #1956×C151C2semidirect
9. #1939×C151C2semidirect
10. #1928×C151C2semidirect
11. #1802×C151C2semidirect
271. #24627C151direct (N × H)
272. C151#24627direct (N × H)
273. C2×#461C2×C151semidirect
275. #2547C2×C151semidirect
276. #2354C2×C151semidirect
277. #2055C2×C151semidirect
279. #1983C2×C151semidirect
280. #1956C2×C151semidirect
281. #1939C2×C151semidirect
282. #1928C2×C151semidirect
283. #1802C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#461×C1512
C2×C4×D8×C1512
#2547×C1512
#2354×C1512
#2055×C1512
#2012×C1512
#1983×C1512
#1956×C1512
#1939×C1512
#1928×C1512
#1802×C1512
#24627151