Finite Group Databasebeta

← C151×#14487 #50319412

Subgroups — C151×#14487 #50319412

Order 38656.

1246 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#389×C151C211yesmaximal, characteristic
2C2×#387×C151C212yesmaximal
3#1442×C151C212yesmaximal
4#1441×C151C212yesmaximal
5#1441×C151C212yesmaximal
6#1436×C151C212yesmaximal
7C4⋊#95×C151C212yesmaximal
8#1434×C151C211yesmaximal, characteristic
9#1434×C151C211yesmaximal, characteristic
10C22×C4⋊C4×C151C2212yes—
11C22×C4⋊C4×C151C2212yes—
12C22×C4⋊C4×C151C2212yes—
13C22×C4⋊C4×C151C2211yescharacteristic
14C22×C4⋊C4×C151C2211yescharacteristic
15C22×C42×C151C2212yes—
16C22×C42×C151C2211yescharacteristic
17#389×C151C418yescomplemented
18#387×C151—28no—
19C2×#95×C151C2212yes—
20C2×#95×C151C2212yes—
21C2×#95×C151C2212yes—
22C2×#95×C151C2212yes—
23C2×#95×C151C2212yes—
24C2×#95×C151C2212yes—
25C2×#95×C151C2212yes—
26C2×#95×C151C2211yescharacteristic
27C2×#95×C151C2211yescharacteristic
28C2×#95×C151C2211yescharacteristic
29C2×#95×C151C2211yescharacteristic
30C2×#95×C151C2212yes—
31C2×#95×C151C2212yes—
32C2×#95×C151C2212yes—
33C23×C4×C151C2312yes—
34C23×C4×C151C2312yes—
35C23×C4×C151C2311yescharacteristic
36C23×C4×C151C2311yescharacteristic
37C23×C4×C151C2312yes—
38C23×C4×C151C2312yes—
39C23×C4×C151C2312yes—
40C23×C4×C151C2311yescharacteristic
41C23×C4×C151C2312yes—
42C2×C4⋊C4×C151—24no—
43C2×C4⋊C4×C151—24no—
44C2×C4⋊C4×C151—24no—
45C2×C4⋊C4×C151—41no—
46C2×C4⋊C4×C151—42no—
47C2×C4⋊C4×C151—41no—
48C2×C4⋊C4×C151—42no—
49C2×C4⋊C4×C151—42no—
50C2×C4⋊C4×C151—42no—
51C2×C4⋊C4×C151—42no—
52C2×C4⋊C4×C151C2×C414yes—
53C2×C4⋊C4×C151C2×C418yes—
54C2×C4⋊C4×C151C2×C414yes—
55C2×C4⋊C4×C151D414yes—
56C2×C4⋊C4×C151Q814yes—
57C2×C42×C151—24no—
58C2×C42×C151—24no—
59C2×C42×C151—41no—
60C2×C42×C151—41no—
61C2×C42×C151—42no—
62C2×C42×C151C2×C414yes—
63#95×C151—24no—
64#95×C151—24no—
65#95×C151—24no—
66#95×C151—24no—
67#95×C151—24no—
68#95×C151—24no—
69#95×C151—24no—
70#95×C151—41no—
71#95×C151—42no—
72#95×C151—41no—
73#95×C151—41no—
74#95×C151—41no—
75#95×C151—42no—
76#95×C151C2×C418yes—
77C24×C151C2411yescharacteristic
78C22×C4×C151—22no—
79C22×C4×C151—22no—
80C22×C4×C151—21no—
81C22×C4×C151—21no—
82C22×C4×C151—22no—
83C22×C4×C151—22no—
84C22×C4×C151—21no—
85C22×C4×C151—21no—
86C22×C4×C151—22no—
87C22×C4×C151—22no—
88C22×C4×C151—22no—
89C22×C4×C151—22no—
90C22×C4×C151—22no—
91C22×C4×C151—22no—
92C22×C4×C151—22no—
93C22×C4×C151—22no—
94C22×C4×C151—22no—
95C22×C4×C151—21no—
96C22×C4×C151—21no—
97C22×C4×C151—21no—
98C22×C4×C151—21no—
99C22×C4×C151—22no—
100C22×C4×C151—22no—
101C22×C4×C151—22no—
102C22×C4×C151—22no—
103C22×C4×C151—22no—
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—22no—
111C22×C4×C151—22no—
112C22×C4×C151—22no—
113C22×C4×C151—22no—
114C22×C4×C151—22no—
115C22×C4×C151—22no—
116C22×C4×C151—22no—
117C22×C4×C151—22no—
118C22×C4×C151—22no—
119C22×C4×C151—22no—
120C22×C4×C151—22no—
121C22×C4×C151—22no—
122C22×C4×C151—22no—
123C22×C4×C151—22no—
124C22×C4×C151—22no—
125C22×C4×C151—22no—
126C22×C4×C151C22×C412yes—
127C22×C4×C151C22×C414yes—
128C22×C4×C151C22×C412yes—
129C22×C4×C151C22×C414yes—
130C22×C4×C151C22×C412yes—
131C22×C4×C151C2×D412yes—
132C22×C4×C151C2×D414yes—
133C22×C4×C151C2×Q812yes—
134C22×C4×C151C2×Q814yes—
135C22×C4×C151#4114yes—
136C22×C4×C151#4114yes—
137C4⋊C4×C151—44no—
138C4⋊C4×C151—48no—
139C4⋊C4×C151—48no—
140C4⋊C4×C151—48no—
141C4⋊C4×C151C4⋊C4116yescomplemented
142C42×C151—44no—
143C42×C151—48no—
144C23×C151C23×C411yescharacteristic
145C23×C151C22×D411yescharacteristic
146C23×C151C22×Q811yescharacteristic
147C23×C151C2×#4112yes—
148C23×C151C2×#4112yes—
149C23×C151H(5,𝔽2)11yescharacteristic
150C23×C151H(5,𝔽2)11yescharacteristic
151C23×C151H(5,𝔽2)12yes—
152C23×C1512−1+411yescharacteristic
153C23×C1512−1+411yescharacteristic
154C23×C1512−1+412yes—
155C2×C4×C151—24no—
156C2×C4×C151—22no—
157C2×C4×C151—24no—
158C2×C4×C151—22no—
159C2×C4×C151—22no—
160C2×C4×C151—22no—
161C2×C4×C151—22no—
162C2×C4×C151—22no—
163C2×C4×C151—24no—
164C2×C4×C151—24no—
165C2×C4×C151—24no—
166C2×C4×C151—24no—
167C2×C4×C151—22no—
168C2×C4×C151—22no—
169C2×C4×C151—24no—
170C2×C4×C151—22no—
171C2×C4×C151—22no—
172C2×C4×C151—22no—
173C2×C4×C151—24no—
174C2×C4×C151—24no—
175C2×C4×C151—22no—
176C2×C4×C151—24no—
177C2×C4×C151—24no—
178C2×C4×C151—24no—
179C2×C4×C151—24no—
180C2×C4×C151—24no—
181C2×C4×C151—24no—
182C2×C4×C151—42no—
183C2×C4×C151—42no—
184C2×C4×C151—42no—
185C2×C4×C151—42no—
186C2×C4×C151—42no—
187C2×C4×C151—42no—
188C2×C4×C151—42no—
189C2×C4×C151—42no—
190C2×C4×C151—42no—
191C2×C4×C151—42no—
192C2×C4×C151—42no—
193C2×C4×C151—42no—
194C2×C4×C151—42no—
195C2×C4×C151—42no—
196C2×C4×C151—42no—
197C2×C4×C151—42no—
198C2×C4×C151—42no—
199C2×C4×C151—42no—
200C2×C4×C151—42no—
201C2×C4×C151—42no—
202C2×C4×C151—42no—
203C2×C4×C151—42no—
204C2×C4×C151—42no—
205C2×C4×C151—42no—
206C2×C4×C151—42no—
207C2×C4×C151—42no—
208C2×C4×C151—42no—
209C2×C4×C151—42no—
210C2×C4×C151—42no—
211C2×C4×C151—42no—
212C2×C4×C151C2×C4⋊C414yes—
213C2×C4×C151C2×C4⋊C418yes—
214C22×C151C22×C4⋊C411yescharacteristic
215C22×C151C4×#4111yescharacteristic
216C22×C151C4×#4111yescharacteristic
217C22×C151#51811yescharacteristic
218C22×C151#51811yescharacteristic
219C22×C151#51911yescharacteristic
220C22×C151#51911yescharacteristic
221C22×C151#53711yescharacteristic
222C22×C151#53711yescharacteristic
223C22×C151#53812yes—
224C22×C151#53912yes—
225C22×C151#54012yes—
226C22×C151#54212yes—
227C22×C151#54411yescharacteristic
228C22×C151#54411yescharacteristic
229C22×C151#54612yes—
230C22×C151#54812yes—
231C22×C151#55212yes—
232C22×C151#55212yes—
233C22×C151#55412yes—
234C22×C151#55712yes—
235C22×C151#56312yes—
236C22×C151#56312yes—
237C4×C151—24no—
238C4×C151—28no—
239C4×C151—42no—
240C4×C151—42no—
241C4×C151—44no—
242C4×C151—44no—
243C4×C151—44no—
244C4×C151—82no—
245C4×C151—82no—
246C2×C151#231611yescharacteristic
247C2×C151#233211yescharacteristic
248C2×C151#233311yescharacteristic
249C2×C151#234911yescharacteristic
250C2×C151#235111yescharacteristic
251C2×C151#237111yescharacteristic
252C2×C151#238111yescharacteristic
253C2×C151#270212yes—
254C2×C151#270712yes—
255C2×C151#277412yes—
256C2×C151#279112yes—
257#14487C15111yesmaximal, characteristic, direct product factor, Sylow
258C151#1448711yescharacteristic, direct product factor, Sylow
259C2×#389C2×C15111yescharacteristic
260C2×#387C2×C15112yes—
261#1442C2×C15112yes—
262#1441C2×C15112yes—
263#1441C2×C15112yes—
264#1436C2×C15112yes—
265C4⋊#95C2×C15112yes—
266#1434C2×C15111yescharacteristic
267#1434C2×C15111yescharacteristic
268C22×C4⋊C4C22×C15112yes—
269C22×C4⋊C4C22×C15112yes—
270C22×C4⋊C4C22×C15112yes—
271C22×C4⋊C4C22×C15111yescharacteristic
272C22×C4⋊C4C22×C15111yescharacteristic
273C22×C42C22×C15112yes—
274C22×C42C22×C15111yescharacteristic
275#389C4×C15118yescomplemented
276#387—28no—
277C2×#95C22×C15112yes—
278C2×#95C22×C15112yes—
279C2×#95C22×C15112yes—
280C2×#95C22×C15112yes—
281C2×#95C22×C15112yes—
282C2×#95C22×C15112yes—
283C2×#95C22×C15112yes—
284C2×#95C22×C15111yescharacteristic
285C2×#95C22×C15111yescharacteristic
286C2×#95C22×C15111yescharacteristic
287C2×#95C22×C15111yescharacteristic
288C2×#95C22×C15112yes—
289C2×#95C22×C15112yes—
290C2×#95C22×C15112yes—
291C23×C4C23×C15112yes—
292C23×C4C23×C15112yes—
293C23×C4C23×C15112yes—
294C23×C4C23×C15112yes—
295C23×C4C23×C15112yes—
296C23×C4C23×C15111yescharacteristic
297C23×C4C23×C15111yescharacteristic
298C23×C4C23×C15112yes—
299C23×C4C23×C15111yescharacteristic
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—41no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—41no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4C2×C4×C15114yes—
311C2×C4⋊C4C2×C4×C15118yes—
312C2×C4⋊C4C2×C4×C15114yes—
313C2×C4⋊C4D4×C15114yes—
314C2×C4⋊C4Q8×C15114yes—
315C2×C42—24no—
316C2×C42—24no—
317C2×C42—41no—
318C2×C42—41no—
319C2×C42—42no—
320C2×C42C2×C4×C15114yes—
321#95—24no—
322#95—24no—
323#95—24no—
324#95—24no—
325#95—24no—
326#95—24no—
327#95—24no—
328#95—41no—
329#95—42no—
330#95—41no—
331#95—41no—
332#95—41no—
333#95—42no—
334#95C2×C4×C15118yes—
335C24C24×C15111yescharacteristic
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4C22×C4×C15112yes—
385C22×C4C22×C4×C15114yes—
386C22×C4C22×C4×C15112yes—
387C22×C4C22×C4×C15114yes—
388C22×C4C22×C4×C15112yes—
389C22×C4C2×D4×C15112yes—
390C22×C4C2×D4×C15114yes—
391C22×C4C2×Q8×C15112yes—
392C22×C4C2×Q8×C15114yes—
393C22×C4#41×C15114yes—
394C22×C4#41×C15114yes—
395C4⋊C4—44no—
396C4⋊C4—48no—
397C4⋊C4—48no—
398C4⋊C4—48no—
399C4⋊C4C4⋊C4×C151116yescomplemented
400C42—44no—
401C42—48no—
402C23C23×C4×C15111yescharacteristic
403C23C22×D4×C15111yescharacteristic
404C23C22×Q8×C15111yescharacteristic
405C23C2×#41×C15112yes—
406C23C2×#41×C15112yes—
407C23H(5,𝔽2)×C15111yescharacteristic
408C23H(5,𝔽2)×C15111yescharacteristic
409C23H(5,𝔽2)×C15112yes—
410C232−1+4×C15111yescharacteristic
411C232−1+4×C15111yescharacteristic
412C232−1+4×C15112yes—
413C2×C4—24no—
414C2×C4—22no—
415C2×C4—24no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—24no—
424C2×C4—24no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—24no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—22no—
434C2×C4—24no—
435C2×C4—24no—
436C2×C4—24no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—24no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4C2×C4⋊C4×C15118yes—
471C2×C4C2×C4⋊C4×C15114yes—
472C22C22×C4⋊C4×C15111yescharacteristic
473C22C4×#41×C15111yescharacteristic
474C22C4×#41×C15111yescharacteristic
475C22#518×C15111yescharacteristic
476C22#518×C15111yescharacteristic
477C22#519×C15111yescharacteristic
478C22#519×C15111yescharacteristic
479C22#537×C15111yescharacteristic
480C22#537×C15111yescharacteristic
481C22#538×C15112yes—
482C22#539×C15112yes—
483C22#540×C15112yes—
484C22#542×C15112yes—
485C22#544×C15111yescharacteristic
486C22#544×C15111yescharacteristic
487C22#546×C15112yes—
488C22#548×C15112yes—
489C22#552×C15112yes—
490C22#552×C15112yes—
491C22#554×C15112yes—
492C22#557×C15112yes—
493C22#563×C15112yes—
494C22#563×C15112yes—
495C4—28no—
496C4—24no—
497C4—42no—
498C4—42no—
499C4—44no—
500C4—44no—
501C4—44no—
502C4—82no—
503C4—82no—
504C2#2316×C15111yescharacteristic
505C2#2332×C15111yescharacteristic
506C2#2333×C15111yescharacteristic
507C2#2349×C15111yescharacteristic
508C2#2351×C15111yescharacteristic
509C2#2371×C15111yescharacteristic
510C2#2381×C15111yescharacteristic
511C2#2702×C15112yes—
512C2#2707×C15112yes—
513C2#2774×C15112yes—
514C2#2791×C15112yes—
subgroupG/H
center, socle, prime radicalC24×C151C24
commutatorC23C23×C4×C151
Frattini, cosocleC24C24×C151
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C151 ◁ G

Complements

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

NH ≅ G/Ntype
17. #389×C151C4semidirect
141. C4⋊C4×C151C4⋊C4semidirect
257. #14487C151direct (N × H)
258. C151#14487direct (N × H)
275. #389C4×C151semidirect
399. C4⋊C4C4⋊C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#389×C1512
C2×#387×C1512
#1442×C1512
#1441×C1512
#1436×C1512
C4⋊#95×C1512
#1434×C1512
#14487151