Finite Group Databasebeta

← C151×#24307 #50329232

Subgroups — C151×#24307 #50329232

Order 38656.

1078 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#125×C151C211yesmaximal, characteristic
2C2×#479×C151C212yesmaximal, complemented
3C4×C22⋊Q8×C151C211yesmaximal, characteristic
4#2059×C151C212yesmaximal, complemented
5#2026×C151C212yesmaximal, complemented
6#1989×C151C212yesmaximal, complemented
7#1872×C151C211yesmaximal, characteristic
8#1872×C151C211yesmaximal, characteristic
9#1853×C151C211yesmaximal, characteristic
10#1852×C151C211yesmaximal, characteristic
11#1797×C151C211yesmaximal, characteristic
12C2×#125×C151—28no—
13C2×#125×C151—21no—
14C2×#125×C151—21no—
15C2×#125×C151C2212yes—
16C2×#125×C151C2212yes—
17C2×C22⋊Q8×C151C2211yescharacteristic
18C2×C4×Q8×C151C2211yescharacteristic
19C22×C4⋊C4×C151—21no—
20C22×C4⋊C4×C151—21no—
21C22×C4⋊C4×C151C2211yescharacteristic
22C22×C4⋊C4×C151C2211yescharacteristic
23C22×C42×C151C2211yescharacteristic
24#479×C151—28no—
25C2×#107×C151C2212yes—
26C2×#106×C151C2212yes—
27C2×C4⋊C8×C151C2212yes—
28C2×#103×C151C2212yes—
29C2×#103×C151C2212yes—
30C2×C22⋊C8×C151C2211yescharacteristic
31C2×C22⋊C8×C151C2211yescharacteristic
32#391×C151C2211yescharacteristic
33#389×C151C2211yescharacteristic
34#387×C151—21no—
35#385×C151—21no—
36#380×C151C2211yescharacteristic
37C4×C4⋊C4×C151—21no—
38C4×C4⋊C4×C151C2211yescharacteristic
39C4×C22⋊C4×C151—21no—
40#340×C151C2212yes—
41#340×C151C2212yes—
42#340×C151C2212yes—
43#340×C151C2212yes—
44#336×C151C2212yes—
45C22×Q8×C151C2311yescharacteristic
46C23×C4×C151—21no—
47C23×C4×C151—21no—
48C23×C4×C151D411yescharacteristic
49C23×C4×C151D411yescharacteristic
50C23×C4×C151C2311yescharacteristic
51C22×C8×C151C2312yes—
52C22×C8×C151C2312yes—
53#125×C151—28no—
54#125×C151—28no—
55#125×C151—24no—
56#125×C151—24no—
57#125×C151—24no—
58#125×C151D418yes—
59C22⋊Q8×C151—22no—
60C22⋊Q8×C151Q814yes—
61C4×Q8×C151—24no—
62C2×C4⋊C4×C151—28no—
63C2×C4⋊C4×C151—28no—
64C2×C4⋊C4×C151—21no—
65C2×C4⋊C4×C151—22no—
66C2×C4⋊C4×C151—22no—
67C2×C4⋊C4×C151—22no—
68C2×C4⋊C4×C151—22no—
69C2×C4⋊C4×C151—21no—
70C2×C4⋊C4×C151—21no—
71C2×C4⋊C4×C151—24no—
72C2×C4⋊C4×C151—24no—
73C2×C4⋊C4×C151—21no—
74C2×C4⋊C4×C151—21no—
75C2×C4⋊C4×C151C2311yescharacteristic
76C2×C4⋊C4×C151C2311yescharacteristic
77C2×C4⋊C4×C151C2312yes—
78C2×C4⋊C4×C151C2312yes—
79C2×C4⋊C4×C151C2311yescharacteristic
80C2×C22⋊C4×C151—21no—
81C2×C22⋊C4×C151—21no—
82C2×C42×C151—24no—
83C2×C42×C151—21no—
84C2×C42×C151—21no—
85C2×C42×C151D411yescharacteristic
86C2×C42×C151D411yescharacteristic
87C2×C42×C151C2311yescharacteristic
88C2×C42×C151C2311yescharacteristic
89#107×C151—24no—
90#106×C151—24no—
91C4⋊C8×C151—24no—
92#103×C151—24no—
93#103×C151—24no—
94C22⋊C8×C151—22no—
95C22⋊C8×C151—22no—
96#95×C151—21no—
97#95×C151—21no—
98#95×C151—21no—
99#95×C151—21no—
100#95×C151—21no—
101C24×C151C2×D411yescharacteristic
102C2×Q8×C151—21no—
103C2×Q8×C151—22no—
104C2×Q8×C151—22no—
105C2×Q8×C151C2×Q812yes—
106C22×C4×C151—22no—
107C22×C4×C151—22no—
108C22×C4×C151—24no—
109C22×C4×C151—24no—
110C22×C4×C151—22no—
111C22×C4×C151—22no—
112C22×C4×C151—21no—
113C22×C4×C151—21no—
114C22×C4×C151—22no—
115C22×C4×C151—22no—
116C22×C4×C151—22no—
117C22×C4×C151—22no—
118C22×C4×C151—21no—
119C22×C4×C151—21no—
120C22×C4×C151—41no—
121C22×C4×C151—41no—
122C22×C4×C151—42no—
123C22×C4×C151—42no—
124C22×C4×C151—42no—
125C22×C4×C151—42no—
126C22×C4×C151C2×D411yescharacteristic
127C22×C4×C151C2×D411yescharacteristic
128C22×C4×C151C2×D411yescharacteristic
129C22×C4×C151C2×D411yescharacteristic
130C22×C4×C151C2×D411yescharacteristic
131C22×C4×C151C2×Q812yes—
132C22×C4×C151#4112yes—
133C22×C4×C151C2411yescharacteristic
134C2×C8×C151—22no—
135C2×C8×C151—22no—
136C2×C8×C151—22no—
137C2×C8×C151—22no—
138C2×C8×C151—22no—
139C2×C8×C151—22no—
140C4⋊C4×C151—24no—
141C4⋊C4×C151—24no—
142C4⋊C4×C151—28no—
143C4⋊C4×C151—28no—
144C4⋊C4×C151—28no—
145C4⋊C4×C151—28no—
146C4⋊C4×C151—24no—
147C4⋊C4×C151—22no—
148C4⋊C4×C151—22no—
149C4⋊C4×C151—21no—
150C4⋊C4×C151—22no—
151C4⋊C4×C151—22no—
152C4⋊C4×C151—42no—
153C4⋊C4×C151—42no—
154C4⋊C4×C151C2×D414yes—
155C4⋊C4×C151C2×D414yes—
156C4⋊C4×C151C2×Q812yes—
157C22⋊C4×C151—24no—
158C22⋊C4×C151—42no—
159C42×C151—22no—
160C42×C151—22no—
161C42×C151—22no—
162C42×C151—42no—
163C42×C151—42no—
164C42×C151C2×D414yes—
165C23×C151—21no—
166C23×C151—21no—
167C23×C151—21no—
168C23×C151—21no—
169C23×C151C22⋊Q812yes—
170C23×C151#13512yes—
171C23×C151#13712yes—
172C23×C151C22×D411yescharacteristic
173Q8×C151—24no—
174Q8×C151—42no—
175C2×C4×C151—21no—
176C2×C4×C151—21no—
177C2×C4×C151—21no—
178C2×C4×C151—21no—
179C2×C4×C151—21no—
180C2×C4×C151—21no—
181C2×C4×C151—24no—
182C2×C4×C151—24no—
183C2×C4×C151—21no—
184C2×C4×C151—21no—
185C2×C4×C151—24no—
186C2×C4×C151—24no—
187C2×C4×C151—22no—
188C2×C4×C151—22no—
189C2×C4×C151—21no—
190C2×C4×C151—21no—
191C2×C4×C151—21no—
192C2×C4×C151—21no—
193C2×C4×C151—44no—
194C2×C4×C151—44no—
195C2×C4×C151—48no—
196C2×C4×C151—48no—
197C2×C4×C151—41no—
198C2×C4×C151—41no—
199C2×C4×C151—42no—
200C2×C4×C151—42no—
201C2×C4×C151—41no—
202C2×C4×C151—41no—
203C2×C4×C151—42no—
204C2×C4×C151—42no—
205C2×C4×C151—41no—
206C2×C4×C151—41no—
207C2×C4×C151—41no—
208C2×C4×C151—41no—
209C2×C4×C151—41no—
210C2×C4×C151—41no—
211C2×C4×C151#12012yes—
212C2×C4×C151#12012yes—
213C2×C4×C151C22⋊Q812yes—
214C2×C4×C151C22×D412yes—
215C2×C4×C151C22×Q811yescharacteristic
216C2×C4×C151C2×#4111yescharacteristic
217C2×C4×C1512−1+412yes—
218C8×C151—42no—
219C8×C151—42no—
220C22×C151—22no—
221C22×C151—22no—
222C22×C151—22no—
223C22×C151—22no—
224C22×C151—22no—
225C22×C151—22no—
226C22×C151#47914yescomplemented
227C22×C151C2×#12011yescharacteristic
228C22×C151C2×C22⋊Q811yescharacteristic
229C22×C151#53611yescharacteristic
230C22×C151C2×#13511yescharacteristic
231C22×C151C2×#13711yescharacteristic
232C22×C151#57511yescharacteristic
233C22×C151#57511yescharacteristic
234C4×C151—22no—
235C4×C151—22no—
236C4×C151—22no—
237C4×C151—42no—
238C4×C151—42no—
239C4×C151—41no—
240C4×C151—44no—
241C4×C151—41no—
242C4×C151—44no—
243C4×C151—81no—
244C4×C151—81no—
245C4×C151#54812yes—
246C4×C151D4×Q812yes—
247C2×C151—24no—
248C2×C151#240911yescharacteristic
249C2×C151#300211yescharacteristic
250C2×C151#300711yescharacteristic
251C2×C151C2×#47911yescharacteristic
252C2×C151#308011yescharacteristic
253C2×C151#323211yescharacteristic
254C2×C151#323611yescharacteristic
255#24307C15111yesmaximal, characteristic, direct product factor, Sylow
256C151#2430711yescharacteristic, direct product factor, Sylow
257C22×#125C2×C15111yescharacteristic
258C2×#479C2×C15112yescomplemented
259C4×C22⋊Q8C2×C15111yescharacteristic
260#2059C2×C15112yescomplemented
261#2026C2×C15112yescomplemented
262#1989C2×C15112yescomplemented
263#1872C2×C15111yescharacteristic
264#1872C2×C15111yescharacteristic
265#1853C2×C15111yescharacteristic
266#1852C2×C15111yescharacteristic
267#1797C2×C15111yescharacteristic
268C2×#125—28no—
269C2×#125—21no—
270C2×#125—21no—
271C2×#125C22×C15112yes—
272C2×#125C22×C15112yes—
273C2×C22⋊Q8C22×C15111yescharacteristic
274C2×C4×Q8C22×C15111yescharacteristic
275C22×C4⋊C4—21no—
276C22×C4⋊C4—21no—
277C22×C4⋊C4C22×C15111yescharacteristic
278C22×C4⋊C4C22×C15111yescharacteristic
279C22×C42C22×C15111yescharacteristic
280#479—28no—
281C2×#107C22×C15112yes—
282C2×#106C22×C15112yes—
283C2×C4⋊C8C22×C15112yes—
284C2×#103C22×C15112yes—
285C2×#103C22×C15112yes—
286C2×C22⋊C8C22×C15111yescharacteristic
287C2×C22⋊C8C22×C15111yescharacteristic
288#391C22×C15111yescharacteristic
289#389C22×C15111yescharacteristic
290#387—21no—
291#385—21no—
292#380C22×C15111yescharacteristic
293C4×C4⋊C4—21no—
294C4×C4⋊C4C22×C15111yescharacteristic
295C4×C22⋊C4—21no—
296#340C22×C15112yes—
297#340C22×C15112yes—
298#340C22×C15112yes—
299#340C22×C15112yes—
300#336C22×C15112yes—
301C22×Q8C23×C15111yescharacteristic
302C23×C4—21no—
303C23×C4—21no—
304C23×C4D4×C15111yescharacteristic
305C23×C4D4×C15111yescharacteristic
306C23×C4C23×C15111yescharacteristic
307C22×C8C23×C15112yes—
308C22×C8C23×C15112yes—
309#125—28no—
310#125—28no—
311#125—24no—
312#125—24no—
313#125—24no—
314#125D4×C15118yes—
315C22⋊Q8—22no—
316C22⋊Q8Q8×C15114yes—
317C4×Q8—24no—
318C2×C4⋊C4—28no—
319C2×C4⋊C4—28no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4C23×C15111yescharacteristic
332C2×C4⋊C4C23×C15111yescharacteristic
333C2×C4⋊C4C23×C15111yescharacteristic
334C2×C4⋊C4C23×C15112yes—
335C2×C4⋊C4C23×C15112yes—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C42—24no—
339C2×C42—21no—
340C2×C42—21no—
341C2×C42D4×C15111yescharacteristic
342C2×C42D4×C15111yescharacteristic
343C2×C42C23×C15111yescharacteristic
344C2×C42C23×C15111yescharacteristic
345#107—24no—
346#106—24no—
347C4⋊C8—24no—
348#103—24no—
349#103—24no—
350C22⋊C8—22no—
351C22⋊C8—22no—
352#95—21no—
353#95—21no—
354#95—21no—
355#95—21no—
356#95—21no—
357C24C2×D4×C15111yescharacteristic
358C2×Q8—21no—
359C2×Q8—22no—
360C2×Q8—22no—
361C2×Q8C2×Q8×C15112yes—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—24no—
365C22×C4—24no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—42no—
379C22×C4—42no—
380C22×C4—42no—
381C22×C4—42no—
382C22×C4C2×D4×C15111yescharacteristic
383C22×C4C2×D4×C15111yescharacteristic
384C22×C4C2×D4×C15111yescharacteristic
385C22×C4C2×D4×C15111yescharacteristic
386C22×C4C2×D4×C15111yescharacteristic
387C22×C4C2×Q8×C15112yes—
388C22×C4#41×C15112yes—
389C22×C4C24×C15111yescharacteristic
390C2×C8—22no—
391C2×C8—22no—
392C2×C8—22no—
393C2×C8—22no—
394C2×C8—22no—
395C2×C8—22no—
396C4⋊C4—24no—
397C4⋊C4—24no—
398C4⋊C4—28no—
399C4⋊C4—28no—
400C4⋊C4—28no—
401C4⋊C4—28no—
402C4⋊C4—24no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—21no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—42no—
409C4⋊C4—42no—
410C4⋊C4C2×D4×C15114yes—
411C4⋊C4C2×D4×C15114yes—
412C4⋊C4C2×Q8×C15112yes—
413C22⋊C4—24no—
414C22⋊C4—42no—
415C42—22no—
416C42—22no—
417C42—22no—
418C42—42no—
419C42—42no—
420C42C2×D4×C15114yes—
421C23—21no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23C22⋊Q8×C15112yes—
426C23#135×C15112yes—
427C23#137×C15112yes—
428C23C22×D4×C15111yescharacteristic
429Q8—24no—
430Q8—42no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—24no—
442C2×C4—24no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—44no—
450C2×C4—44no—
451C2×C4—48no—
452C2×C4—48no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4#120×C15112yes—
468C2×C4#120×C15112yes—
469C2×C4C22⋊Q8×C15112yes—
470C2×C4C22×D4×C15112yes—
471C2×C4C22×Q8×C15111yescharacteristic
472C2×C4C2×#41×C15111yescharacteristic
473C2×C42−1+4×C15112yes—
474C8—42no—
475C8—42no—
476C22—22no—
477C22—22no—
478C22—22no—
479C22—22no—
480C22—22no—
481C22—22no—
482C22#479×C15114yescomplemented
483C22C2×#120×C15111yescharacteristic
484C22C2×C22⋊Q8×C15111yescharacteristic
485C22#536×C15111yescharacteristic
486C22C2×#135×C15111yescharacteristic
487C22C2×#137×C15111yescharacteristic
488C22#575×C15111yescharacteristic
489C22#575×C15111yescharacteristic
490C4—22no—
491C4—22no—
492C4—22no—
493C4—42no—
494C4—41no—
495C4—44no—
496C4—41no—
497C4—44no—
498C4—42no—
499C4—81no—
500C4—81no—
501C4#548×C15112yes—
502C4D4×Q8×C15112yes—
503C2—24no—
504C2#2409×C15111yescharacteristic
505C2#3002×C15111yescharacteristic
506C2#3007×C15111yescharacteristic
507C2C2×#479×C15111yescharacteristic
508C2#3080×C15111yescharacteristic
509C2#3232×C15111yescharacteristic
510C2#3236×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC24×C151C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#479×C151C2semidirect
4. #2059×C151C2semidirect
5. #2026×C151C2semidirect
6. #1989×C151C2semidirect
226. C22×C151#479semidirect
255. #24307C151direct (N × H)
256. C151#24307direct (N × H)
258. C2×#479C2×C151semidirect
260. #2059C2×C151semidirect
261. #2026C2×C151semidirect
262. #1989C2×C151semidirect
482. C22#479×C151semidirect

Maximal subgroups

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

subgroupindex
C22×#125×C1512
C2×#479×C1512
C4×C22⋊Q8×C1512
#2059×C1512
#2026×C1512
#1989×C1512
#1872×C1512
#1853×C1512
#1852×C1512
#1797×C1512
#24307151