Finite Group Databasebeta

← C151×#8051 #50312976

Subgroups — C151×#8051 #50312976

Order 38656.

1090 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#407×C151C211yesmaximal, characteristic
2#2280×C151C211yesmaximal, characteristic
3C2×C4×C22⋊C4×C151C211yesmaximal, characteristic
4#1297×C151C214yesmaximal, complemented
5C24×C4×C151C2211yescharacteristic
6C22×M16×C151C412yescomplemented
7C2×#117×C151—21no—
8C22×C22⋊C4×C151—21no—
9C22×C42×C151—21no—
10#407×C151—21no—
11#407×C151—21no—
12#407×C151C412yescomplemented
13#407×C151C2212yes—
14C2×C22⋊C8×C151—21no—
15C2×C22⋊C8×C151—21no—
16#381×C151C412yescomplemented
17#380×C151—21no—
18#380×C151C412yescomplemented
19#379×C151—21no—
20C4×C22⋊C4×C151—21no—
21C4×C22⋊C4×C151—21no—
22C4×C22⋊C4×C151—21no—
23C4×C22⋊C4×C151C412yescomplemented
24C4×C22⋊C4×C151C2212yes—
25C4×C22⋊C4×C151C2212yes—
26C2×#95×C151C412yescomplemented
27C25×C151D411yescharacteristic
28C23×C4×C151—22no—
29C23×C4×C151—44no—
30C23×C4×C151C2×C411yescharacteristic
31C23×C4×C151C2×C411yescharacteristic
32C23×C4×C151C2×C411yescharacteristic
33C23×C4×C151C2×C411yescharacteristic
34C23×C4×C151C2×C411yescharacteristic
35C23×C4×C151C2×C411yescharacteristic
36C23×C4×C151D411yescharacteristic
37C23×C4×C151D411yescharacteristic
38C23×C4×C151D411yescharacteristic
39C23×C4×C151D411yescharacteristic
40C23×C4×C151D411yescharacteristic
41C23×C4×C151Q811yescharacteristic
42C23×C4×C151Q811yescharacteristic
43C23×C4×C151C2311yescharacteristic
44C2×M16×C151—22no—
45C2×M16×C151—44no—
46C2×M16×C151C2×C414yescomplemented
47C22×C8×C151—22no—
48#117×C151—44no—
49C2×C4⋊C4×C151—22no—
50C2×C22⋊C4×C151—28no—
51C2×C22⋊C4×C151—22no—
52C2×C22⋊C4×C151—22no—
53C2×C22⋊C4×C151—22no—
54C2×C22⋊C4×C151—22no—
55C2×C22⋊C4×C151—22no—
56C2×C42×C151—22no—
57C2×C42×C151—22no—
58C2×C42×C151—22no—
59C2×C42×C151—44no—
60C22⋊C8×C151—22no—
61C22⋊C8×C151—22no—
62C22⋊C8×C151—22no—
63C22⋊C8×C151—22no—
64#95×C151—22no—
65#95×C151—22no—
66#95×C151C2×C414yes—
67#95×C151C2×C414yescomplemented
68C24×C151—24no—
69C24×C151—42no—
70C24×C151—42no—
71C24×C151C22⋊C411yescharacteristic
72C24×C151C22⋊C411yescharacteristic
73C24×C151C22⋊C411yescharacteristic
74C24×C151C22⋊C411yescharacteristic
75C24×C151C4⋊C411yescharacteristic
76C24×C151C4⋊C411yescharacteristic
77C24×C151C2×D411yescharacteristic
78C22×C4×C151—24no—
79C22×C4×C151—24no—
80C22×C4×C151—24no—
81C22×C4×C151—28no—
82C22×C4×C151—24no—
83C22×C4×C151—24no—
84C22×C4×C151—42no—
85C22×C4×C151—42no—
86C22×C4×C151—42no—
87C22×C4×C151—42no—
88C22×C4×C151—42no—
89C22×C4×C151—42no—
90C22×C4×C151—42no—
91C22×C4×C151—42no—
92C22×C4×C151—42no—
93C22×C4×C151—42no—
94C22×C4×C151—42no—
95C22×C4×C151—44no—
96C22×C4×C151—44no—
97C22×C4×C151C4211yescharacteristic
98C22×C4×C151C4211yescharacteristic
99C22×C4×C151C4211yescharacteristic
100C22×C4×C151C4211yescharacteristic
101C22×C4×C151C22⋊C411yescharacteristic
102C22×C4×C151C22⋊C411yescharacteristic
103C22×C4×C151C22⋊C411yescharacteristic
104C22×C4×C151C22⋊C411yescharacteristic
105C22×C4×C151C22⋊C411yescharacteristic
106C22×C4×C151C22⋊C411yescharacteristic
107C22×C4×C151C22⋊C411yescharacteristic
108C22×C4×C151C22⋊C411yescharacteristic
109C22×C4×C151C4⋊C411yescharacteristic
110C22×C4×C151C4⋊C411yescharacteristic
111C22×C4×C151C4⋊C411yescharacteristic
112C22×C4×C151C4⋊C411yescharacteristic
113C22×C4×C151C4⋊C411yescharacteristic
114C22×C4×C151C4⋊C411yescharacteristic
115C22×C4×C151C4⋊C411yescharacteristic
116C22×C4×C151C4⋊C411yescharacteristic
117C22×C4×C151C4⋊C411yescharacteristic
118C22×C4×C151C4⋊C411yescharacteristic
119C22×C4×C151C22×C411yescharacteristic
120C22×C4×C151C22×C411yescharacteristic
121C22×C4×C151C22×C411yescharacteristic
122C22×C4×C151C2×D411yescharacteristic
123C22×C4×C151C2×D411yescharacteristic
124C22×C4×C151C2×Q811yescharacteristic
125M16×C151—44no—
126M16×C151—44no—
127C2×C8×C151—24no—
128C2×C8×C151—44no—
129C4⋊C4×C151—44no—
130C22⋊C4×C151—28no—
131C22⋊C4×C151—28no—
132C22⋊C4×C151—44no—
133C22⋊C4×C151—44no—
134C22⋊C4×C151—44no—
135C42×C151—44no—
136C42×C151—44no—
137C42×C151—44no—
138C23×C151—22no—
139C23×C151—22no—
140C23×C151—22no—
141C23×C151—22no—
142C23×C151—22no—
143C23×C151—22no—
144C23×C151—22no—
145C23×C151—22no—
146C23×C151—22no—
147C23×C151—22no—
148C23×C151—22no—
149C23×C151—22no—
150C23×C151—41no—
151C23×C151—41no—
152C23×C151—41no—
153C23×C151—41no—
154C23×C151—41no—
155C23×C151—41no—
156C23×C151—41no—
157C23×C151—41no—
158C23×C151—416no—
159C23×C151#9511yescharacteristic
160C23×C151#9511yescharacteristic
161C23×C151#9511yescharacteristic
162C23×C151#9511yescharacteristic
163C23×C151#10414yes—
164C23×C151C2×C22⋊C411yescharacteristic
165C23×C151C2×C22⋊C411yescharacteristic
166C23×C151C2×C4⋊C411yescharacteristic
167C2×C4×C151—22no—
168C2×C4×C151—22no—
169C2×C4×C151—22no—
170C2×C4×C151—22no—
171C2×C4×C151—22no—
172C2×C4×C151—22no—
173C2×C4×C151—22no—
174C2×C4×C151—22no—
175C2×C4×C151—22no—
176C2×C4×C151—22no—
177C2×C4×C151—22no—
178C2×C4×C151—22no—
179C2×C4×C151—22no—
180C2×C4×C151—22no—
181C2×C4×C151—22no—
182C2×C4×C151—28no—
183C2×C4×C151—41no—
184C2×C4×C151—41no—
185C2×C4×C151—41no—
186C2×C4×C151—41no—
187C2×C4×C151—41no—
188C2×C4×C151—41no—
189C2×C4×C151—41no—
190C2×C4×C151—41no—
191C2×C4×C151—41no—
192C2×C4×C151—41no—
193C2×C4×C151—41no—
194C2×C4×C151—41no—
195C2×C4×C151—44no—
196C2×C4×C151—416no—
197C2×C4×C151—44no—
198C2×C4×C151—44no—
199C2×C4×C151—44no—
200C2×C4×C151—44no—
201C2×C4×C151#9511yescharacteristic
202C2×C4×C151#9511yescharacteristic
203C2×C4×C151#9511yescharacteristic
204C2×C4×C151#9511yescharacteristic
205C2×C4×C151#9914yes—
206C2×C4×C151C2×C4211yescharacteristic
207C2×C4×C151C2×C22⋊C411yescharacteristic
208C2×C4×C151C2×C4⋊C411yescharacteristic
209C2×C4×C151C2×C4⋊C411yescharacteristic
210C8×C151—44no—
211C22×C151—28no—
212C22×C151—21no—
213C22×C151—21no—
214C22×C151—21no—
215C22×C151—21no—
216C22×C151—21no—
217C22×C151—21no—
218C22×C151—21no—
219C22×C151—21no—
220C22×C151—21no—
221C22×C151—21no—
222C22×C151—21no—
223C22×C151—21no—
224C22×C151—21no—
225C22×C151—21no—
226C22×C151—21no—
227C22×C151—21no—
228C22×C151—44no—
229C22×C151—44no—
230C22×C151—44no—
231C22×C151—44no—
232C22×C151—44no—
233C22×C151—44no—
234C22×C151#33912yes—
235C22×C151#33912yes—
236C22×C151#34212yes—
237C22×C151C2×#9511yescharacteristic
238C22×C151C2×#10412yes—
239C22×C151#42112yes—
240C4×C151—21no—
241C4×C151—21no—
242C4×C151—21no—
243C4×C151—21no—
244C4×C151—21no—
245C4×C151—21no—
246C4×C151—48no—
247C4×C151—84no—
248C4×C151#34212yes—
249C4×C151C2×#9912yes—
250C2×C151—22no—
251C2×C151—22no—
252C2×C151—22no—
253C2×C151—22no—
254C2×C151—22no—
255C2×C151—41no—
256C2×C151—41no—
257C2×C151C2×#33911yescharacteristic
258C2×C151#173311yescharacteristic
259C2×C151C2×#34211yescharacteristic
260#8051C15111yesmaximal, characteristic, direct product factor, Sylow
261C151#805111yescharacteristic, direct product factor, Sylow
262C2×#407C2×C15111yescharacteristic
263#2280C2×C15111yescharacteristic
264C2×C4×C22⋊C4C2×C15111yescharacteristic
265#1297C2×C15114yescomplemented
266C24×C4C22×C15111yescharacteristic
267C22×M16C4×C15112yescomplemented
268C2×#117—21no—
269C22×C22⋊C4—21no—
270C22×C42—21no—
271#407—21no—
272#407—21no—
273#407C4×C15112yescomplemented
274#407C22×C15112yes—
275C2×C22⋊C8—21no—
276C2×C22⋊C8—21no—
277#381C4×C15112yescomplemented
278#380—21no—
279#380C4×C15112yescomplemented
280#379—21no—
281C4×C22⋊C4—21no—
282C4×C22⋊C4—21no—
283C4×C22⋊C4—21no—
284C4×C22⋊C4C4×C15112yescomplemented
285C4×C22⋊C4C22×C15112yes—
286C4×C22⋊C4C22×C15112yes—
287C2×#95C4×C15112yescomplemented
288C25D4×C15111yescharacteristic
289C23×C4—22no—
290C23×C4—44no—
291C23×C4C2×C4×C15111yescharacteristic
292C23×C4C2×C4×C15111yescharacteristic
293C23×C4C2×C4×C15111yescharacteristic
294C23×C4C2×C4×C15111yescharacteristic
295C23×C4C2×C4×C15111yescharacteristic
296C23×C4C2×C4×C15111yescharacteristic
297C23×C4D4×C15111yescharacteristic
298C23×C4D4×C15111yescharacteristic
299C23×C4D4×C15111yescharacteristic
300C23×C4D4×C15111yescharacteristic
301C23×C4D4×C15111yescharacteristic
302C23×C4Q8×C15111yescharacteristic
303C23×C4Q8×C15111yescharacteristic
304C23×C4C23×C15111yescharacteristic
305C2×M16—22no—
306C2×M16—44no—
307C2×M16C2×C4×C15114yescomplemented
308C22×C8—22no—
309#117—44no—
310C2×C4⋊C4—22no—
311C2×C22⋊C4—28no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C42—22no—
318C2×C42—22no—
319C2×C42—22no—
320C2×C42—44no—
321C22⋊C8—22no—
322C22⋊C8—22no—
323C22⋊C8—22no—
324C22⋊C8—22no—
325#95—22no—
326#95—22no—
327#95C2×C4×C15114yes—
328#95C2×C4×C15114yescomplemented
329C24—24no—
330C24—42no—
331C24—42no—
332C24C22⋊C4×C15111yescharacteristic
333C24C22⋊C4×C15111yescharacteristic
334C24C22⋊C4×C15111yescharacteristic
335C24C22⋊C4×C15111yescharacteristic
336C24C4⋊C4×C15111yescharacteristic
337C24C4⋊C4×C15111yescharacteristic
338C24C2×D4×C15111yescharacteristic
339C22×C4—24no—
340C22×C4—24no—
341C22×C4—24no—
342C22×C4—28no—
343C22×C4—24no—
344C22×C4—24no—
345C22×C4—42no—
346C22×C4—42no—
347C22×C4—42no—
348C22×C4—42no—
349C22×C4—42no—
350C22×C4—42no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4—42no—
355C22×C4—42no—
356C22×C4—44no—
357C22×C4—44no—
358C22×C4C42×C15111yescharacteristic
359C22×C4C42×C15111yescharacteristic
360C22×C4C42×C15111yescharacteristic
361C22×C4C42×C15111yescharacteristic
362C22×C4C22⋊C4×C15111yescharacteristic
363C22×C4C22⋊C4×C15111yescharacteristic
364C22×C4C22⋊C4×C15111yescharacteristic
365C22×C4C22⋊C4×C15111yescharacteristic
366C22×C4C22⋊C4×C15111yescharacteristic
367C22×C4C22⋊C4×C15111yescharacteristic
368C22×C4C22⋊C4×C15111yescharacteristic
369C22×C4C22⋊C4×C15111yescharacteristic
370C22×C4C4⋊C4×C15111yescharacteristic
371C22×C4C4⋊C4×C15111yescharacteristic
372C22×C4C4⋊C4×C15111yescharacteristic
373C22×C4C4⋊C4×C15111yescharacteristic
374C22×C4C4⋊C4×C15111yescharacteristic
375C22×C4C4⋊C4×C15111yescharacteristic
376C22×C4C4⋊C4×C15111yescharacteristic
377C22×C4C4⋊C4×C15111yescharacteristic
378C22×C4C4⋊C4×C15111yescharacteristic
379C22×C4C4⋊C4×C15111yescharacteristic
380C22×C4C22×C4×C15111yescharacteristic
381C22×C4C22×C4×C15111yescharacteristic
382C22×C4C22×C4×C15111yescharacteristic
383C22×C4C2×D4×C15111yescharacteristic
384C22×C4C2×D4×C15111yescharacteristic
385C22×C4C2×Q8×C15111yescharacteristic
386M16—44no—
387M16—44no—
388C2×C8—24no—
389C2×C8—44no—
390C4⋊C4—44no—
391C22⋊C4—28no—
392C22⋊C4—28no—
393C22⋊C4—44no—
394C22⋊C4—44no—
395C22⋊C4—44no—
396C42—44no—
397C42—44no—
398C42—44no—
399C23—22no—
400C23—22no—
401C23—22no—
402C23—22no—
403C23—22no—
404C23—22no—
405C23—22no—
406C23—22no—
407C23—22no—
408C23—22no—
409C23—22no—
410C23—22no—
411C23—41no—
412C23—41no—
413C23—41no—
414C23—41no—
415C23—41no—
416C23—41no—
417C23—41no—
418C23—41no—
419C23—416no—
420C23#95×C15111yescharacteristic
421C23#95×C15111yescharacteristic
422C23#95×C15111yescharacteristic
423C23#95×C15111yescharacteristic
424C23#104×C15114yes—
425C23C2×C22⋊C4×C15111yescharacteristic
426C23C2×C22⋊C4×C15111yescharacteristic
427C23C2×C4⋊C4×C15111yescharacteristic
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—28no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—44no—
457C2×C4—416no—
458C2×C4—44no—
459C2×C4—44no—
460C2×C4—44no—
461C2×C4—44no—
462C2×C4#95×C15111yescharacteristic
463C2×C4#95×C15111yescharacteristic
464C2×C4#95×C15111yescharacteristic
465C2×C4#95×C15111yescharacteristic
466C2×C4#99×C15114yes—
467C2×C4C2×C42×C15111yescharacteristic
468C2×C4C2×C22⋊C4×C15111yescharacteristic
469C2×C4C2×C4⋊C4×C15111yescharacteristic
470C2×C4C2×C4⋊C4×C15111yescharacteristic
471C8—44no—
472C22—28no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—21no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—44no—
490C22—44no—
491C22—44no—
492C22—44no—
493C22—44no—
494C22—44no—
495C22#339×C15112yes—
496C22#339×C15112yes—
497C22#342×C15112yes—
498C22C2×#95×C15111yescharacteristic
499C22C2×#104×C15112yes—
500C22#421×C15112yes—
501C4—21no—
502C4—21no—
503C4—21no—
504C4—21no—
505C4—21no—
506C4—21no—
507C4—48no—
508C4—84no—
509C4#342×C15112yes—
510C4C2×#99×C15112yes—
511C2—22no—
512C2—22no—
513C2—22no—
514C2—22no—
515C2—22no—
516C2—41no—
517C2—41no—
518C2C2×#339×C15111yescharacteristic
519C2#1733×C15111yescharacteristic
520C2C2×#342×C15111yescharacteristic
subgroupG/H
centerC2×C4×C151C2×C22⋊C4
commutatorC2×C4C2×C42×C151
Frattini, cosocleC23×C4C23×C151
socleC22×C151C2×#95
prime radicalC25×C151D4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C151 ◁ C24×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1297×C151C2semidirect
6. C22×M16×C151C4semidirect
12. #407×C151C4semidirect
16. #381×C151C4semidirect
18. #380×C151C4semidirect
23. C4×C22⋊C4×C151C4semidirect
26. C2×#95×C151C4semidirect
46. C2×M16×C151C2×C4semidirect
67. #95×C151C2×C4semidirect
260. #8051C151direct (N × H)
261. C151#8051direct (N × H)
265. #1297C2×C151semidirect
267. C22×M16C4×C151semidirect
273. #407C4×C151semidirect
277. #381C4×C151semidirect
279. #380C4×C151semidirect
284. C4×C22⋊C4C4×C151semidirect
287. C2×#95C4×C151semidirect
307. C2×M16C2×C4×C151semidirect
328. #95C2×C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#407×C1512
#2280×C1512
C2×C4×C22⋊C4×C1512
#1297×C1512
#8051151