Finite Group Databasebeta

← C151×#24967 #50329892

Subgroups — C151×#24967 #50329892

Order 38656.

926 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2537×C151C211yesmaximal, characteristic
2D4×C4⋊C4×C151C211yesmaximal, characteristic, complemented
3#2077×C151C212yesmaximal, complemented
4#2034×C151C212yesmaximal, complemented
5#1954×C151C211yesmaximal, characteristic, complemented
6#1948×C151C211yesmaximal, characteristic, complemented
7#1874×C151C212yesmaximal, complemented
8#1834×C151C211yesmaximal, characteristic, complemented
9#1824×C151C212yesmaximal, complemented
10#1802×C151C211yesmaximal, characteristic, complemented
11C4×#102×C151C211yesmaximal, characteristic, complemented
12C2×#121×C151—21no—
13C2×#121×C151C2212yes—
14C2×C4×D4×C151—21no—
15C2×C4×D4×C151C2211yescharacteristic
16C2×C4×D4×C151C2211yescharacteristic
17C22×C4⋊C4×C151C2212yes—
18C2×#106×C151C2212yes—
19C2×C4⋊C8×C151C2211yescharacteristic
20C2×#102×C151C2211yescharacteristic
21C2×#102×C151C2211yescharacteristic
22C2×#102×C151C2212yes—
23C2×C22⋊C8×C151C2212yes—
24C2×C22⋊C8×C151C2212yes—
25C2×C4×C8×C151C2211yescharacteristic
26#394×C151—22no—
27#389×C151—21no—
28#385×C151—22no—
29#384×C151C2211yescharacteristic
30#384×C151C2211yescharacteristic
31#380×C151—21no—
32#380×C151C2212yes—
33#380×C151C2212yes—
34C4×C4⋊C4×C151C2211yescharacteristic
35#340×C151C2211yescharacteristic
36#340×C151C2212yes—
37#340×C151C2212yes—
38#340×C151C2211yescharacteristic
39#340×C151C2212yes—
40#340×C151C2212yes—
41C22×D4×C151—22no—
42C22×D4×C151D411yescharacteristic
43C22×D4×C151C2311yescharacteristic
44C23×C4×C151—21no—
45C23×C4×C151—22no—
46C23×C4×C151C2312yes—
47C22×C8×C151C2311yescharacteristic
48C22×C8×C151C2311yescharacteristic
49C22×C8×C151C2312yes—
50#121×C151—24no—
51#121×C151—42no—
52#121×C151—44no—
53C4×D4×C151—22no—
54C4×D4×C151—22no—
55C4×D4×C151—22no—
56C4×D4×C151—22no—
57C4×D4×C151—44no—
58C2×C4⋊C4×C151—24no—
59C2×C4⋊C4×C151—21no—
60C2×C4⋊C4×C151—21no—
61C2×C4⋊C4×C151—22no—
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×C151C2312yes—
68C2×C4⋊C4×C151C2312yes—
69C2×C4⋊C4×C151C2311yescharacteristic
70C2×C4⋊C4×C151C2311yescharacteristic
71C2×C22⋊C4×C151—22no—
72C2×C22⋊C4×C151—21no—
73C2×C22⋊C4×C151—22no—
74C2×C22⋊C4×C151—22no—
75C2×C22⋊C4×C151D412yes—
76C2×C42×C151—21no—
77C2×C42×C151C2311yescharacteristic
78#106×C151—42no—
79C4⋊C8×C151—22no—
80#102×C151—22no—
81#102×C151—22no—
82#102×C151—42no—
83C22⋊C8×C151—42no—
84C22⋊C8×C151—42no—
85C4×C8×C151—22no—
86#95×C151—21no—
87#95×C151—22no—
88#95×C151—22no—
89C24×C151—21no—
90C24×C151C2×D412yes—
91C2×D4×C151—22no—
92C2×D4×C151—22no—
93C2×D4×C151—21no—
94C2×D4×C151—21no—
95C2×D4×C151—21no—
96C2×D4×C151—21no—
97C2×D4×C151—21no—
98C2×D4×C151—44no—
99C2×D4×C151—44no—
100C2×D4×C151—82no—
101C2×D4×C151SD1614yes—
102C2×D4×C151#4112yes—
103C22×C4×C151—21no—
104C22×C4×C151—22no—
105C22×C4×C151—22no—
106C22×C4×C151—22no—
107C22×C4×C151—22no—
108C22×C4×C151—22no—
109C22×C4×C151—22no—
110C22×C4×C151—21no—
111C22×C4×C151—21no—
112C22×C4×C151—22no—
113C22×C4×C151—22no—
114C22×C4×C151—44no—
115C22×C4×C151—44no—
116C22×C4×C151—42no—
117C22×C4×C151—42no—
118C22×C4×C151—42no—
119C22×C4×C151—82no—
120C22×C4×C151C2×D412yes—
121C22×C4×C151C2×D411yescharacteristic
122C22×C4×C151C2×D411yescharacteristic
123C22×C4×C151C2411yescharacteristic
124C2×C8×C151—21no—
125C2×C8×C151—21no—
126C2×C8×C151—21no—
127C2×C8×C151—21no—
128C2×C8×C151—22no—
129C2×C8×C151—21no—
130C2×C8×C151—21no—
131C2×C8×C151—22no—
132C2×C8×C151—22no—
133C4⋊C4×C151—22no—
134C4⋊C4×C151—21no—
135C4⋊C4×C151—21no—
136C4⋊C4×C151—22no—
137C4⋊C4×C151—21no—
138C4⋊C4×C151—21no—
139C4⋊C4×C151—22no—
140C4⋊C4×C151—22no—
141C4⋊C4×C151—21no—
142C4⋊C4×C151—22no—
143C4⋊C4×C151—44no—
144C4⋊C4×C151—42no—
145C4⋊C4×C151—42no—
146C4⋊C4×C151—81no—
147C4⋊C4×C151—81no—
148C4⋊C4×C151#4112yes—
149C22⋊C4×C151—24no—
150C22⋊C4×C151—44no—
151C22⋊C4×C151—44no—
152C22⋊C4×C151—44no—
153C22⋊C4×C151—42no—
154C42×C151—42no—
155C42×C151#4112yes—
156C42×C151#4112yes—
157C23×C151—22no—
158C23×C151—22no—
159C23×C151—22no—
160C23×C151—22no—
161C23×C151—22no—
162C23×C151—22no—
163C23×C151—22no—
164C23×C151—41no—
165C23×C151—41no—
166C23×C151—41no—
167C23×C151—41no—
168C23×C151—41no—
169C23×C151—41no—
170C23×C151C2×SD1614yes—
171C23×C151C22×D411yescharacteristic
172D4×C151—22no—
173D4×C151—22no—
174D4×C151—28no—
175D4×C151—41no—
176D4×C151—41no—
177D4×C151—88no—
178C2×C4×C151—21no—
179C2×C4×C151—21no—
180C2×C4×C151—22no—
181C2×C4×C151—22no—
182C2×C4×C151—22no—
183C2×C4×C151—22no—
184C2×C4×C151—41no—
185C2×C4×C151—41no—
186C2×C4×C151—42no—
187C2×C4×C151—42no—
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—42no—
196C2×C4×C151—41no—
197C2×C4×C151—42no—
198C2×C4×C151—41no—
199C2×C4×C151—42no—
200C2×C4×C151—42no—
201C2×C4×C151—41no—
202C2×C4×C151—88no—
203C2×C4×C151—84no—
204C2×C4×C151#12312yes—
205C2×C4×C151#12312yes—
206C2×C4×C151C2×SD1612yes—
207C2×C4×C151AGL(1,ℤ/8)12yes—
208C2×C4×C151C2×#4111yescharacteristic
209C2×C4×C151C2×#4111yescharacteristic
210C2×C4×C151C2×#4111yescharacteristic
211C2×C4×C151C2×#4111yescharacteristic
212C2×C4×C151H(5,𝔽2)11yescharacteristic
213C2×C4×C151H(5,𝔽2)11yescharacteristic
214C8×C151—42no—
215C8×C151—41no—
216C8×C151—41no—
217C22×C151—24no—
218C22×C151—24no—
219C22×C151—24no—
220C22×C151—42no—
221C22×C151—42no—
222C22×C151—42no—
223C22×C151—42no—
224C22×C151—42no—
225C22×C151—42no—
226C22×C151—42no—
227C22×C151—81no—
228C22×C151—81no—
229C22×C151—81no—
230C22×C151—81no—
231C22×C151C2×#12311yescharacteristic
232C22×C151#54611yescharacteristic
233C22×C151#54611yescharacteristic
234C22×C151C22×SD1611yescharacteristic
235C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
236C22×C151#57611yescharacteristic
237C22×C151#57811yescharacteristic
238C4×C151—22no—
239C4×C151—42no—
240C4×C151—42no—
241C4×C151—81no—
242C4×C151—81no—
243C4×C151—82no—
244C4×C151—82no—
245C4×C151#48114yes—
246C4×C151#52911yescharacteristic
247C4×C151#54011yescharacteristic
248C4×C151#55311yescharacteristic
249C4×C151#55511yescharacteristic
250C2×C151—44no—
251C2×C151—82no—
252C2×C151#242011yescharacteristic
253C2×C151C2×#48111yescharacteristic
254C2×C151#309811yescharacteristic
255C2×C151#329511yescharacteristic
256C2×C151#329811yescharacteristic
257C2×C151#332511yescharacteristic
258C2×C151#333011yescharacteristic
259#24967C15111yesmaximal, characteristic, direct product factor, Sylow
260C151#2496711yescharacteristic, direct product factor, Sylow
261#2537C2×C15111yescharacteristic
262D4×C4⋊C4C2×C15111yescharacteristic, complemented
263#2077C2×C15112yescomplemented
264#2034C2×C15112yescomplemented
265#1954C2×C15111yescharacteristic, complemented
266#1948C2×C15111yescharacteristic, complemented
267#1874C2×C15112yescomplemented
268#1834C2×C15111yescharacteristic, complemented
269#1824C2×C15112yescomplemented
270#1802C2×C15111yescharacteristic, complemented
271C4×#102C2×C15111yescharacteristic, complemented
272C2×#121—21no—
273C2×#121C22×C15112yes—
274C2×C4×D4—21no—
275C2×C4×D4C22×C15111yescharacteristic
276C2×C4×D4C22×C15111yescharacteristic
277C22×C4⋊C4C22×C15112yes—
278C2×#106C22×C15112yes—
279C2×C4⋊C8C22×C15111yescharacteristic
280C2×#102C22×C15111yescharacteristic
281C2×#102C22×C15111yescharacteristic
282C2×#102C22×C15112yes—
283C2×C22⋊C8C22×C15112yes—
284C2×C22⋊C8C22×C15112yes—
285C2×C4×C8C22×C15111yescharacteristic
286#394—22no—
287#389—21no—
288#385—22no—
289#384C22×C15111yescharacteristic
290#384C22×C15111yescharacteristic
291#380—21no—
292#380C22×C15112yes—
293#380C22×C15112yes—
294C4×C4⋊C4C22×C15111yescharacteristic
295#340C22×C15112yes—
296#340C22×C15111yescharacteristic
297#340C22×C15112yes—
298#340C22×C15111yescharacteristic
299#340C22×C15112yes—
300#340C22×C15112yes—
301C22×D4—22no—
302C22×D4D4×C15111yescharacteristic
303C22×D4C23×C15111yescharacteristic
304C23×C4—22no—
305C23×C4—21no—
306C23×C4C23×C15112yes—
307C22×C8C23×C15111yescharacteristic
308C22×C8C23×C15111yescharacteristic
309C22×C8C23×C15112yes—
310#121—24no—
311#121—42no—
312#121—44no—
313C4×D4—22no—
314C4×D4—22no—
315C4×D4—22no—
316C4×D4—22no—
317C4×D4—44no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4D4×C15111yescharacteristic
326C2×C4⋊C4C23×C15112yes—
327C2×C4⋊C4C23×C15111yescharacteristic
328C2×C4⋊C4C23×C15112yes—
329C2×C4⋊C4C23×C15111yescharacteristic
330C2×C4⋊C4C23×C15111yescharacteristic
331C2×C22⋊C4—22no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4D4×C15112yes—
336C2×C42—21no—
337C2×C42C23×C15111yescharacteristic
338#106—42no—
339C4⋊C8—22no—
340#102—22no—
341#102—22no—
342#102—42no—
343C22⋊C8—42no—
344C22⋊C8—42no—
345C4×C8—22no—
346#95—21no—
347#95—22no—
348#95—22no—
349C24—21no—
350C24C2×D4×C15112yes—
351C2×D4—22no—
352C2×D4—22no—
353C2×D4—21no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—44no—
359C2×D4—44no—
360C2×D4—82no—
361C2×D4SD16×C15114yes—
362C2×D4#41×C15112yes—
363C22×C4—21no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—44no—
375C22×C4—44no—
376C22×C4—42no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4—82no—
380C22×C4C2×D4×C15112yes—
381C22×C4C2×D4×C15111yescharacteristic
382C22×C4C2×D4×C15111yescharacteristic
383C22×C4C24×C15111yescharacteristic
384C2×C8—21no—
385C2×C8—21no—
386C2×C8—21no—
387C2×C8—21no—
388C2×C8—22no—
389C2×C8—21no—
390C2×C8—21no—
391C2×C8—22no—
392C2×C8—22no—
393C4⋊C4—22no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—22no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—21no—
402C4⋊C4—22no—
403C4⋊C4—44no—
404C4⋊C4—42no—
405C4⋊C4—42no—
406C4⋊C4—81no—
407C4⋊C4—81no—
408C4⋊C4#41×C15112yes—
409C22⋊C4—24no—
410C22⋊C4—44no—
411C22⋊C4—44no—
412C22⋊C4—44no—
413C22⋊C4—42no—
414C42—42no—
415C42#41×C15112yes—
416C42#41×C15112yes—
417C23—22no—
418C23—22no—
419C23—22no—
420C23—22no—
421C23—22no—
422C23—22no—
423C23—22no—
424C23—41no—
425C23—41no—
426C23—41no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23C2×SD16×C15114yes—
431C23C22×D4×C15111yescharacteristic
432D4—28no—
433D4—22no—
434D4—22no—
435D4—41no—
436D4—41no—
437D4—88no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4—41no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—41no—
462C2×C4—88no—
463C2×C4—84no—
464C2×C4#123×C15112yes—
465C2×C4#123×C15112yes—
466C2×C4C2×SD16×C15112yes—
467C2×C4AGL(1,ℤ/8)×C15112yes—
468C2×C4C2×#41×C15111yescharacteristic
469C2×C4C2×#41×C15111yescharacteristic
470C2×C4C2×#41×C15111yescharacteristic
471C2×C4C2×#41×C15111yescharacteristic
472C2×C4H(5,𝔽2)×C15111yescharacteristic
473C2×C4H(5,𝔽2)×C15111yescharacteristic
474C8—42no—
475C8—41no—
476C8—41no—
477C22—24no—
478C22—24no—
479C22—24no—
480C22—42no—
481C22—42no—
482C22—42no—
483C22—42no—
484C22—42no—
485C22—42no—
486C22—42no—
487C22—81no—
488C22—81no—
489C22—81no—
490C22—81no—
491C22C2×#123×C15111yescharacteristic
492C22#546×C15111yescharacteristic
493C22#546×C15111yescharacteristic
494C22C22×SD16×C15111yescharacteristic
495C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
496C22#576×C15111yescharacteristic
497C22#578×C15111yescharacteristic
498C4—22no—
499C4—42no—
500C4—42no—
501C4—82no—
502C4—82no—
503C4—81no—
504C4—81no—
505C4#481×C15114yes—
506C4#529×C15111yescharacteristic
507C4#540×C15111yescharacteristic
508C4#553×C15111yescharacteristic
509C4#555×C15111yescharacteristic
510C2—44no—
511C2—82no—
512C2#2420×C15111yescharacteristic
513C2C2×#481×C15111yescharacteristic
514C2#3098×C15111yescharacteristic
515C2#3295×C15111yescharacteristic
516C2#3298×C15111yescharacteristic
517C2#3325×C15111yescharacteristic
518C2#3330×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#2537×C151C2
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
2. D4×C4⋊C4×C151C2semidirect
3. #2077×C151C2semidirect
4. #2034×C151C2semidirect
5. #1954×C151C2semidirect
6. #1948×C151C2semidirect
7. #1874×C151C2semidirect
8. #1834×C151C2semidirect
9. #1824×C151C2semidirect
10. #1802×C151C2semidirect
11. C4×#102×C151C2semidirect
259. #24967C151direct (N × H)
260. C151#24967direct (N × H)
262. D4×C4⋊C4C2×C151semidirect
263. #2077C2×C151semidirect
264. #2034C2×C151semidirect
265. #1954C2×C151semidirect
266. #1948C2×C151semidirect
267. #1874C2×C151semidirect
268. #1834C2×C151semidirect
269. #1824C2×C151semidirect
270. #1802C2×C151semidirect
271. C4×#102C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2537×C1512
D4×C4⋊C4×C1512
#2077×C1512
#2034×C1512
#1954×C1512
#1948×C1512
#1874×C1512
#1834×C1512
#1824×C1512
#1802×C1512
C4×#102×C1512
#24967151