Finite Group Databasebeta

← C151×#14604 #50319529

Subgroups — C151×#14604 #50319529

Order 38656.

1138 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
1C2×#400×C151C211yesmaximal, characteristic
2#1442×C151C212yesmaximal
3#1442×C151C212yesmaximal
4#1441×C151C211yesmaximal, characteristic
5#1436×C151C212yesmaximal
6#1436×C151C212yesmaximal
7#1436×C151C212yesmaximal
8#1436×C151C212yesmaximal
9C4⋊#95×C151C211yesmaximal, characteristic
10C22×C4⋊C4×C151C2211yescharacteristic
11C22×C4⋊C4×C151C2212yes—
12C22×C4⋊C4×C151C2211yescharacteristic
13C22×C4⋊C4×C151C2211yescharacteristic
14C22×C4⋊C4×C151C2211yescharacteristic
15C22×C42×C151C2211yescharacteristic
16C22×C42×C151C2212yes—
17#400×C151C418yescomplemented
18C2×#95×C151C2212yes—
19C2×#95×C151C2212yes—
20C2×#95×C151C2212yes—
21C2×#95×C151C2212yes—
22C2×#95×C151C2212yes—
23C2×#95×C151C2212yes—
24C2×#95×C151C2212yes—
25C2×#95×C151C2212yes—
26C2×#95×C151C2212yes—
27C2×#95×C151C2212yes—
28C2×#95×C151C2211yescharacteristic
29C2×#95×C151C2212yes—
30C2×#95×C151C2212yes—
31C2×#95×C151C2211yescharacteristic
32C23×C4×C151C2312yes—
33C23×C4×C151C2312yes—
34C23×C4×C151C2312yes—
35C23×C4×C151C2311yescharacteristic
36C23×C4×C151C2311yescharacteristic
37C23×C4×C151C2312yes—
38C23×C4×C151C2312yes—
39C23×C4×C151C2312yes—
40C23×C4×C151C2311yescharacteristic
41C2×C4⋊C4×C151—24no—
42C2×C4⋊C4×C151—24no—
43C2×C4⋊C4×C151—41no—
44C2×C4⋊C4×C151—41no—
45C2×C4⋊C4×C151—41no—
46C2×C4⋊C4×C151—41no—
47C2×C4⋊C4×C151—41no—
48C2×C4⋊C4×C151—41no—
49C2×C4⋊C4×C151—41no—
50C2×C4⋊C4×C151—42no—
51C2×C4⋊C4×C151—42no—
52C2×C4⋊C4×C151C2×C414yes—
53C2×C4⋊C4×C151C2×C414yes—
54C2×C4⋊C4×C151Q814yes—
55C2×C42×C151—22no—
56C2×C42×C151—41no—
57C2×C42×C151—41no—
58C2×C42×C151—42no—
59C2×C42×C151—42no—
60C2×C42×C151—42no—
61#95×C151—24no—
62#95×C151—24no—
63#95×C151—24no—
64#95×C151—24no—
65#95×C151—24no—
66#95×C151—42no—
67#95×C151—42no—
68#95×C151—42no—
69#95×C151—42no—
70#95×C151—42no—
71#95×C151—41no—
72#95×C151C2×C414yes—
73#95×C151C2×C418yes—
74#95×C151C2×C418yes—
75C24×C151C2411yescharacteristic
76C22×C4×C151—21no—
77C22×C4×C151—21no—
78C22×C4×C151—21no—
79C22×C4×C151—21no—
80C22×C4×C151—22no—
81C22×C4×C151—22no—
82C22×C4×C151—22no—
83C22×C4×C151—22no—
84C22×C4×C151—22no—
85C22×C4×C151—22no—
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—22no—
96C22×C4×C151—22no—
97C22×C4×C151—22no—
98C22×C4×C151—22no—
99C22×C4×C151—21no—
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—21no—
110C22×C4×C151—21no—
111C22×C4×C151—21no—
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×C151C22×C414yes—
126C22×C4×C151C22×C412yes—
127C22×C4×C151C22×C414yes—
128C22×C4×C151C22×C412yes—
129C22×C4×C151C22×C412yes—
130C22×C4×C151C2×Q814yes—
131C22×C4×C151C2×Q812yes—
132C22×C4×C151#4114yes—
133C22×C4×C151#4114yes—
134C22×C4×C151#4112yes—
135C4⋊C4×C151—44no—
136C4⋊C4×C151—44no—
137C4⋊C4×C151—44no—
138C4⋊C4×C151—44no—
139C4⋊C4×C151—48no—
140C42×C151—44no—
141C42×C151—48no—
142C23×C151C23×C411yescharacteristic
143C23×C151C22×Q811yescharacteristic
144C23×C151C2×#4111yescharacteristic
145C23×C151C2×#4112yes—
146C23×C151C2×#4112yes—
147C23×C151H(5,𝔽2)11yescharacteristic
148C23×C151H(5,𝔽2)11yescharacteristic
149C23×C151H(5,𝔽2)11yescharacteristic
150C23×C151H(5,𝔽2)12yes—
151C23×C1512−1+411yescharacteristic
152C23×C1512−1+412yes—
153C2×C4×C151—22no—
154C2×C4×C151—22no—
155C2×C4×C151—22no—
156C2×C4×C151—22no—
157C2×C4×C151—22no—
158C2×C4×C151—22no—
159C2×C4×C151—24no—
160C2×C4×C151—24no—
161C2×C4×C151—24no—
162C2×C4×C151—22no—
163C2×C4×C151—22no—
164C2×C4×C151—24no—
165C2×C4×C151—24no—
166C2×C4×C151—24no—
167C2×C4×C151—24no—
168C2×C4×C151—24no—
169C2×C4×C151—24no—
170C2×C4×C151—24no—
171C2×C4×C151—24no—
172C2×C4×C151—24no—
173C2×C4×C151—24no—
174C2×C4×C151—24no—
175C2×C4×C151—24no—
176C2×C4×C151—24no—
177C2×C4×C151—24no—
178C2×C4×C151—42no—
179C2×C4×C151—42no—
180C2×C4×C151—42no—
181C2×C4×C151—42no—
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—41no—
189C2×C4×C151—41no—
190C2×C4×C151—42no—
191C2×C4×C151—42no—
192C2×C4×C151—42no—
193C2×C4×C151—42no—
194C2×C4×C151—41no—
195C2×C4×C151—41no—
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×C151C4×Q814yes—
212C22×C151C2×C4×Q811yescharacteristic
213C22×C151C4×#4112yes—
214C22×C151#51811yescharacteristic
215C22×C151#52011yescharacteristic
216C22×C151#52012yes—
217C22×C151#53811yescharacteristic
218C22×C151#53812yes—
219C22×C151#53911yescharacteristic
220C22×C151#53912yes—
221C22×C151#54112yes—
222C22×C151#54212yes—
223C22×C151#54311yescharacteristic
224C22×C151#54411yescharacteristic
225C22×C151#55111yescharacteristic
226C22×C151#55212yes—
227C22×C151#55312yes—
228C22×C151#55312yes—
229C22×C151#55412yes—
230C22×C151#55712yes—
231C22×C151#55911yescharacteristic
232C22×C151H(3,𝔽4)11yescharacteristic
233C22×C151#56212yes—
234C22×C151#56311yescharacteristic
235C4×C151—24no—
236C4×C151—44no—
237C4×C151—42no—
238C4×C151—42no—
239C4×C151—44no—
240C4×C151—44no—
241C4×C151—44no—
242C4×C151—44no—
243C4×C151—82no—
244C2×C151#232911yescharacteristic
245C2×C151#233412yes—
246C2×C151#237012yes—
247C2×C151#237411yescharacteristic
248C2×C151#237911yescharacteristic
249C2×C151#277912yes—
250C2×C151#278211yescharacteristic
251C2×C151#279411yescharacteristic
252C2×C151#279911yescharacteristic
253C2×C151#280212yes—
254C2×C151#280411yescharacteristic
255#14604C15111yesmaximal, characteristic, direct product factor, Sylow
256C151#1460411yescharacteristic, direct product factor, Sylow
257C2×#400C2×C15111yescharacteristic
258#1442C2×C15112yes—
259#1442C2×C15112yes—
260#1441C2×C15111yescharacteristic
261#1436C2×C15112yes—
262#1436C2×C15112yes—
263#1436C2×C15112yes—
264#1436C2×C15112yes—
265C4⋊#95C2×C15111yescharacteristic
266C22×C4⋊C4C22×C15111yescharacteristic
267C22×C4⋊C4C22×C15112yes—
268C22×C4⋊C4C22×C15111yescharacteristic
269C22×C4⋊C4C22×C15111yescharacteristic
270C22×C4⋊C4C22×C15111yescharacteristic
271C22×C42C22×C15111yescharacteristic
272C22×C42C22×C15112yes—
273#400C4×C15118yescomplemented
274C2×#95C22×C15112yes—
275C2×#95C22×C15112yes—
276C2×#95C22×C15112yes—
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×C15112yes—
286C2×#95C22×C15112yes—
287C2×#95C22×C15111yescharacteristic
288C23×C4C23×C15112yes—
289C23×C4C23×C15112yes—
290C23×C4C23×C15112yes—
291C23×C4C23×C15112yes—
292C23×C4C23×C15111yescharacteristic
293C23×C4C23×C15111yescharacteristic
294C23×C4C23×C15112yes—
295C23×C4C23×C15112yes—
296C23×C4C23×C15111yescharacteristic
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—41no—
300C2×C4⋊C4—41no—
301C2×C4⋊C4—41no—
302C2×C4⋊C4—41no—
303C2×C4⋊C4—41no—
304C2×C4⋊C4—41no—
305C2×C4⋊C4—41no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4C2×C4×C15114yes—
309C2×C4⋊C4C2×C4×C15114yes—
310C2×C4⋊C4Q8×C15114yes—
311C2×C42—22no—
312C2×C42—41no—
313C2×C42—41no—
314C2×C42—42no—
315C2×C42—42no—
316C2×C42—42no—
317#95—24no—
318#95—24no—
319#95—24no—
320#95—24no—
321#95—24no—
322#95—42no—
323#95—42no—
324#95—42no—
325#95—42no—
326#95—42no—
327#95—41no—
328#95C2×C4×C15114yes—
329#95C2×C4×C15118yes—
330#95C2×C4×C15118yes—
331C24C24×C15111yescharacteristic
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
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—22no—
354C22×C4—22no—
355C22×C4—21no—
356C22×C4—22no—
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—21no—
366C22×C4—21no—
367C22×C4—21no—
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×C4C22×C4×C15114yes—
382C22×C4C22×C4×C15112yes—
383C22×C4C22×C4×C15114yes—
384C22×C4C22×C4×C15112yes—
385C22×C4C22×C4×C15112yes—
386C22×C4C2×Q8×C15114yes—
387C22×C4C2×Q8×C15112yes—
388C22×C4#41×C15114yes—
389C22×C4#41×C15114yes—
390C22×C4#41×C15112yes—
391C4⋊C4—44no—
392C4⋊C4—44no—
393C4⋊C4—44no—
394C4⋊C4—44no—
395C4⋊C4—48no—
396C42—44no—
397C42—48no—
398C23C23×C4×C15111yescharacteristic
399C23C22×Q8×C15111yescharacteristic
400C23C2×#41×C15111yescharacteristic
401C23C2×#41×C15112yes—
402C23C2×#41×C15112yes—
403C23H(5,𝔽2)×C15111yescharacteristic
404C23H(5,𝔽2)×C15111yescharacteristic
405C23H(5,𝔽2)×C15111yescharacteristic
406C23H(5,𝔽2)×C15112yes—
407C232−1+4×C15111yescharacteristic
408C232−1+4×C15112yes—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—24no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—24no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—24no—
424C2×C4—24no—
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—24no—
428C2×C4—24no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4—41no—
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×C4C4×Q8×C15114yes—
468C22C2×C4×Q8×C15111yescharacteristic
469C22C4×#41×C15112yes—
470C22#518×C15111yescharacteristic
471C22#520×C15111yescharacteristic
472C22#520×C15112yes—
473C22#538×C15112yes—
474C22#538×C15111yescharacteristic
475C22#539×C15112yes—
476C22#539×C15111yescharacteristic
477C22#541×C15112yes—
478C22#542×C15112yes—
479C22#543×C15111yescharacteristic
480C22#544×C15111yescharacteristic
481C22#551×C15111yescharacteristic
482C22#552×C15112yes—
483C22#553×C15112yes—
484C22#553×C15112yes—
485C22#554×C15112yes—
486C22#557×C15112yes—
487C22#559×C15111yescharacteristic
488C22H(3,𝔽4)×C15111yescharacteristic
489C22#562×C15112yes—
490C22#563×C15111yescharacteristic
491C4—24no—
492C4—44no—
493C4—42no—
494C4—42no—
495C4—44no—
496C4—44no—
497C4—44no—
498C4—44no—
499C4—82no—
500C2#2329×C15111yescharacteristic
501C2#2334×C15112yes—
502C2#2370×C15112yes—
503C2#2374×C15111yescharacteristic
504C2#2379×C15111yescharacteristic
505C2#2779×C15112yes—
506C2#2782×C15111yescharacteristic
507C2#2794×C15111yescharacteristic
508C2#2799×C15111yescharacteristic
509C2#2802×C15112yes—
510C2#2804×C15111yescharacteristic
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. #400×C151C4semidirect
255. #14604C151direct (N × H)
256. C151#14604direct (N × H)
273. #400C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#400×C1512
#1442×C1512
#1441×C1512
#1436×C1512
C4⋊#95×C1512
#14604151