Finite Group Databasebeta

← C151×#24115 #50329040

Subgroups — C151×#24115 #50329040

Order 38656.

1078 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3491×C151C211yesmaximal, characteristic
2#2623×C151C212yesmaximal, complemented
3#2317×C151C211yesmaximal, characteristic, complemented
4#2062×C151C212yesmaximal, complemented
5#2044×C151C212yesmaximal
6#1899×C151C212yesmaximal, complemented
7#1867×C151C214yesmaximal, complemented
8#1820×C151C211yesmaximal, characteristic, complemented
9#552×C151—22no—
10#552×C151—22no—
11#551×C151—22no—
12#551×C151—22no—
13#543×C151C2211yescharacteristic
14#539×C151—21no—
15#539×C151—21no—
16#534×C151C2211yescharacteristic
17#529×C151—21no—
18#529×C151—21no—
19C2×#123×C151C2212yes—
20#518×C151C2212yes—
21C2×#117×C151C2211yescharacteristic
22C2×#117×C151C2211yescharacteristic
23C22×C4⋊C4×C151C2211yescharacteristic
24C2×#99×C151C2214yes—
25#400×C151—22no—
26#399×C151—22no—
27#398×C151—22no—
28#397×C151—22no—
29#389×C151—21no—
30#389×C151—21no—
31#386×C151C2214yes—
32#385×C151C2214yes—
33#385×C151C2212yes—
34#385×C151C2212yes—
35#384×C151—21no—
36#382×C151—21no—
37#381×C151C2212yes—
38#342×C151C2212yes—
39#342×C151C2212yes—
40#342×C151C2214yes—
41C22×D4×C151C2312yes—
42C23×C4×C151C2312yes—
43C23×C4×C151C2311yescharacteristic
44#126×C151—22no—
45#126×C151—22no—
46#126×C151—22no—
47#126×C151—22no—
48#125×C151—21no—
49#125×C151—21no—
50#125×C151—22no—
51#125×C151—22no—
52#124×C151—21no—
53#124×C151—21no—
54#123×C151—22no—
55#123×C151—22no—
56#123×C151—22no—
57#123×C151—22no—
58#123×C151—22no—
59#123×C151—22no—
60#123×C151—22no—
61C22⋊Q8×C151—22no—
62C22⋊Q8×C151—22no—
63C22⋊Q8×C151—21no—
64C22⋊Q8×C151—21no—
65C22⋊Q8×C151—22no—
66C22⋊Q8×C151—22no—
67#121×C151—21no—
68#121×C151—21no—
69#120×C151—22no—
70C4×Q8×C151—21no—
71C4×Q8×C151—21no—
72C4×D4×C151—21no—
73C4×D4×C151—21no—
74C4×D4×C151—22no—
75C4×D4×C151—22no—
76C4×D4×C151—22no—
77C4×D4×C151—22no—
78#117×C151—22no—
79#117×C151—22no—
80#117×C151—22no—
81#117×C151—22no—
82#117×C151—22no—
83#117×C151—24no—
84C2×C4⋊C4×C151—21no—
85C2×C4⋊C4×C151—21no—
86C2×C4⋊C4×C151—21no—
87C2×C4⋊C4×C151—22no—
88C2×C4⋊C4×C151—22no—
89C2×C4⋊C4×C151—22no—
90C2×C4⋊C4×C151—22no—
91C2×C4⋊C4×C151—24no—
92C2×C4⋊C4×C151D411yescharacteristic
93C2×C4⋊C4×C151D411yescharacteristic
94C2×C4⋊C4×C151D412yes—
95C2×C4⋊C4×C151D412yes—
96C2×C22⋊C4×C151—22no—
97C2×C22⋊C4×C151—24no—
98C2×C22⋊C4×C151D412yes—
99C2×C22⋊C4×C151D412yes—
100C2×C22⋊C4×C151C2314yes—
101C2×C22⋊C4×C151C2311yescharacteristic
102C2×C22⋊C4×C151C2311yescharacteristic
103C2×C22⋊C4×C151C2312yes—
104C2×C22⋊C4×C151C2312yes—
105C2×C42×C151—21no—
106C2×C42×C151D411yescharacteristic
107C2×C42×C151D411yescharacteristic
108#99×C151—28no—
109#95×C151—22no—
110#95×C151—22no—
111#95×C151—22no—
112#95×C151—22no—
113#95×C151—24no—
114#95×C151—24no—
115C24×C151C2×D412yes—
116C24×C151C2411yescharacteristic
117C2×Q8×C151—21no—
118C2×Q8×C151—21no—
119C2×D4×C151—22no—
120C2×D4×C151—22no—
121C2×D4×C151—24no—
122C2×D4×C151—24no—
123C2×D4×C151—21no—
124C2×D4×C151—21no—
125C22×C4×C151—22no—
126C22×C4×C151—22no—
127C22×C4×C151—22no—
128C22×C4×C151—22no—
129C22×C4×C151—22no—
130C22×C4×C151—24no—
131C22×C4×C151—24no—
132C22×C4×C151—22no—
133C22×C4×C151—82no—
134C22×C4×C151C2×D412yes—
135C22×C4×C151C2×D412yes—
136C22×C4×C151C2×D412yes—
137C22×C4×C151C2×D411yescharacteristic
138C22×C4×C151C2×D411yescharacteristic
139C22×C4×C151C2×D411yescharacteristic
140C22×C4×C151C2×D411yescharacteristic
141C22×C4×C151C2×D412yes—
142C22×C4×C151C2×D411yescharacteristic
143C22×C4×C151C2×D411yescharacteristic
144C22×C4×C151C2×D412yes—
145C4⋊C4×C151—24no—
146C4⋊C4×C151—22no—
147C4⋊C4×C151—22no—
148C4⋊C4×C151—22no—
149C4⋊C4×C151—22no—
150C4⋊C4×C151—21no—
151C4⋊C4×C151—21no—
152C4⋊C4×C151—21no—
153C4⋊C4×C151—21no—
154C4⋊C4×C151—22no—
155C4⋊C4×C151—22no—
156C4⋊C4×C151—22no—
157C4⋊C4×C151—22no—
158C4⋊C4×C151—22no—
159C4⋊C4×C151—22no—
160C4⋊C4×C151—41no—
161C4⋊C4×C151—41no—
162C4⋊C4×C151—42no—
163C4⋊C4×C151—82no—
164C4⋊C4×C151—82no—
165C4⋊C4×C151—84no—
166C22⋊C4×C151—22no—
167C22⋊C4×C151—22no—
168C22⋊C4×C151—22no—
169C22⋊C4×C151—22no—
170C22⋊C4×C151—22no—
171C22⋊C4×C151—22no—
172C22⋊C4×C151—22no—
173C22⋊C4×C151—22no—
174C22⋊C4×C151—22no—
175C22⋊C4×C151—22no—
176C22⋊C4×C151—22no—
177C22⋊C4×C151—22no—
178C22⋊C4×C151—22no—
179C22⋊C4×C151—24no—
180C22⋊C4×C151—24no—
181C22⋊C4×C151—84no—
182C22⋊C4×C151#4114yes—
183C42×C151—24no—
184C42×C151—22no—
185C42×C151—22no—
186C42×C151—21no—
187C42×C151—21no—
188C42×C151—21no—
189C42×C151—21no—
190C23×C151—22no—
191C23×C151—24no—
192C23×C151—41no—
193C23×C151—41no—
194C23×C151—42no—
195C23×C151—42no—
196C23×C151C22×D411yescharacteristic
197C23×C151C22×D412yes—
198C23×C151C2×#4112yes—
199C23×C1512−1+412yes—
200Q8×C151—81no—
201Q8×C151—81no—
202D4×C151—42no—
203D4×C151—42no—
204D4×C151—44no—
205D4×C151—81no—
206D4×C151—81no—
207C2×C4×C151—21no—
208C2×C4×C151—21no—
209C2×C4×C151—21no—
210C2×C4×C151—21no—
211C2×C4×C151—24no—
212C2×C4×C151—24no—
213C2×C4×C151—21no—
214C2×C4×C151—21no—
215C2×C4×C151—22no—
216C2×C4×C151—22no—
217C2×C4×C151—21no—
218C2×C4×C151—21no—
219C2×C4×C151—22no—
220C2×C4×C151—24no—
221C2×C4×C151—24no—
222C2×C4×C151—42no—
223C2×C4×C151—42no—
224C2×C4×C151—41no—
225C2×C4×C151—42no—
226C2×C4×C151—41no—
227C2×C4×C151—41no—
228C2×C4×C151—42no—
229C2×C4×C151—41no—
230C2×C4×C151—44no—
231C2×C4×C151—44no—
232C2×C4×C151—42no—
233C2×C4×C151—42no—
234C2×C4×C151—44no—
235C2×C4×C151—44no—
236C2×C4×C151—42no—
237C2×C4×C151—44no—
238C2×C4×C151—82no—
239C2×C4×C151—82no—
240C2×C4×C151#12011yescharacteristic
241C2×C4×C151#12011yescharacteristic
242C2×C4×C151#12012yes—
243C22×C151—21no—
244C22×C151—22no—
245C22×C151—21no—
246C22×C151—22no—
247C22×C151—42no—
248C22×C151—42no—
249C22×C151—42no—
250C22×C151—42no—
251C22×C151—42no—
252C22×C151—84no—
253C22×C151C2×#12011yescharacteristic
254C22×C151#52511yescharacteristic
255C22×C151#53611yescharacteristic
256C22×C151#54714yes—
257C4×C151—22no—
258C4×C151—21no—
259C4×C151—21no—
260C4×C151—44no—
261C4×C151—42no—
262C4×C151—41no—
263C4×C151—42no—
264C4×C151—41no—
265C4×C151—41no—
266C4×C151—42no—
267C4×C151—41no—
268C4×C151—84no—
269C4×C151—82no—
270C2×C151—21no—
271C2×C151—24no—
272C2×C151—21no—
273C2×C151—82no—
274C2×C151#240611yescharacteristic
275C2×C151#302711yescharacteristic
276C2×C151#302811yescharacteristic
277#24115C15111yesmaximal, characteristic, direct product factor, Sylow
278C151#2411511yescharacteristic, direct product factor, Sylow
279#3491C2×C15111yescharacteristic
280#2623C2×C15112yescomplemented
281#2317C2×C15111yescharacteristic, complemented
282#2062C2×C15112yescomplemented
283#2044C2×C15112yes—
284#1899C2×C15112yescomplemented
285#1867C2×C15114yescomplemented
286#1820C2×C15111yescharacteristic, complemented
287#552—22no—
288#552—22no—
289#551—22no—
290#551—22no—
291#543C22×C15111yescharacteristic
292#539—21no—
293#539—21no—
294#534C22×C15111yescharacteristic
295#529—21no—
296#529—21no—
297C2×#123C22×C15112yes—
298#518C22×C15112yes—
299C2×#117C22×C15111yescharacteristic
300C2×#117C22×C15111yescharacteristic
301C22×C4⋊C4C22×C15111yescharacteristic
302C2×#99C22×C15114yes—
303#400—22no—
304#399—22no—
305#398—22no—
306#397—22no—
307#389—21no—
308#389—21no—
309#386C22×C15114yes—
310#385C22×C15112yes—
311#385C22×C15112yes—
312#385C22×C15114yes—
313#384—21no—
314#382—21no—
315#381C22×C15112yes—
316#342C22×C15112yes—
317#342C22×C15114yes—
318#342C22×C15112yes—
319C22×D4C23×C15112yes—
320C23×C4C23×C15111yescharacteristic
321C23×C4C23×C15112yes—
322#126—22no—
323#126—22no—
324#126—22no—
325#126—22no—
326#125—21no—
327#125—21no—
328#125—22no—
329#125—22no—
330#124—21no—
331#124—21no—
332#123—22no—
333#123—22no—
334#123—22no—
335#123—22no—
336#123—22no—
337#123—22no—
338#123—22no—
339C22⋊Q8—22no—
340C22⋊Q8—22no—
341C22⋊Q8—21no—
342C22⋊Q8—21no—
343C22⋊Q8—22no—
344C22⋊Q8—22no—
345#121—21no—
346#121—21no—
347#120—22no—
348C4×Q8—21no—
349C4×Q8—21no—
350C4×D4—21no—
351C4×D4—21no—
352C4×D4—22no—
353C4×D4—22no—
354C4×D4—22no—
355C4×D4—22no—
356#117—22no—
357#117—22no—
358#117—22no—
359#117—22no—
360#117—22no—
361#117—24no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4D4×C15111yescharacteristic
371C2×C4⋊C4D4×C15111yescharacteristic
372C2×C4⋊C4D4×C15112yes—
373C2×C4⋊C4D4×C15112yes—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4D4×C15112yes—
377C2×C22⋊C4D4×C15112yes—
378C2×C22⋊C4C23×C15114yes—
379C2×C22⋊C4C23×C15111yescharacteristic
380C2×C22⋊C4C23×C15111yescharacteristic
381C2×C22⋊C4C23×C15112yes—
382C2×C22⋊C4C23×C15112yes—
383C2×C42—21no—
384C2×C42D4×C15111yescharacteristic
385C2×C42D4×C15111yescharacteristic
386#99—28no—
387#95—22no—
388#95—22no—
389#95—22no—
390#95—22no—
391#95—24no—
392#95—24no—
393C24C2×D4×C15112yes—
394C24C24×C15111yescharacteristic
395C2×Q8—21no—
396C2×Q8—21no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—24no—
400C2×D4—24no—
401C2×D4—21no—
402C2×D4—21no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—24no—
409C22×C4—24no—
410C22×C4—22no—
411C22×C4—82no—
412C22×C4C2×D4×C15112yes—
413C22×C4C2×D4×C15112yes—
414C22×C4C2×D4×C15112yes—
415C22×C4C2×D4×C15111yescharacteristic
416C22×C4C2×D4×C15111yescharacteristic
417C22×C4C2×D4×C15111yescharacteristic
418C22×C4C2×D4×C15111yescharacteristic
419C22×C4C2×D4×C15112yes—
420C22×C4C2×D4×C15111yescharacteristic
421C22×C4C2×D4×C15111yescharacteristic
422C22×C4C2×D4×C15112yes—
423C4⋊C4—24no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—41no—
439C4⋊C4—41no—
440C4⋊C4—42no—
441C4⋊C4—82no—
442C4⋊C4—82no—
443C4⋊C4—84no—
444C22⋊C4—22no—
445C22⋊C4—22no—
446C22⋊C4—22no—
447C22⋊C4—22no—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—22no—
451C22⋊C4—22no—
452C22⋊C4—22no—
453C22⋊C4—22no—
454C22⋊C4—22no—
455C22⋊C4—22no—
456C22⋊C4—22no—
457C22⋊C4—24no—
458C22⋊C4—24no—
459C22⋊C4—84no—
460C22⋊C4#41×C15114yes—
461C42—24no—
462C42—22no—
463C42—22no—
464C42—21no—
465C42—21no—
466C42—21no—
467C42—21no—
468C23—22no—
469C23—24no—
470C23—41no—
471C23—41no—
472C23—42no—
473C23—42no—
474C23C22×D4×C15111yescharacteristic
475C23C22×D4×C15112yes—
476C23C2×#41×C15112yes—
477C232−1+4×C15112yes—
478Q8—81no—
479Q8—81no—
480D4—42no—
481D4—42no—
482D4—44no—
483D4—81no—
484D4—81no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—41no—
508C2×C4—44no—
509C2×C4—44no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—44no—
513C2×C4—44no—
514C2×C4—42no—
515C2×C4—44no—
516C2×C4—82no—
517C2×C4—82no—
518C2×C4#120×C15111yescharacteristic
519C2×C4#120×C15111yescharacteristic
520C2×C4#120×C15112yes—
521C22—21no—
522C22—22no—
523C22—21no—
524C22—22no—
525C22—42no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—84no—
531C22C2×#120×C15111yescharacteristic
532C22#525×C15111yescharacteristic
533C22#536×C15111yescharacteristic
534C22#547×C15114yes—
535C4—22no—
536C4—21no—
537C4—21no—
538C4—44no—
539C4—42no—
540C4—41no—
541C4—42no—
542C4—41no—
543C4—41no—
544C4—42no—
545C4—41no—
546C4—84no—
547C4—82no—
548C2—21no—
549C2—24no—
550C2—21no—
551C2—82no—
552C2#2406×C15111yescharacteristic
553C2#3027×C15111yescharacteristic
554C2#3028×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC24C24×C151
prime radical#534×C151C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2623×C151C2semidirect
3. #2317×C151C2semidirect
4. #2062×C151C2semidirect
6. #1899×C151C2semidirect
7. #1867×C151C2semidirect
8. #1820×C151C2semidirect
277. #24115C151direct (N × H)
278. C151#24115direct (N × H)
280. #2623C2×C151semidirect
281. #2317C2×C151semidirect
282. #2062C2×C151semidirect
284. #1899C2×C151semidirect
285. #1867C2×C151semidirect
286. #1820C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3491×C1512
#2623×C1512
#2317×C1512
#2062×C1512
#2044×C1512
#1899×C1512
#1867×C1512
#1820×C1512
#24115151