Finite Group Databasebeta

← C151×#9111 #50314036

Subgroups — C151×#9111 #50314036

Order 38656.

984 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊C8×C151C211yesmaximal, characteristic
2#2848×C151C211yesmaximal, characteristic
3C2×#328×C151C212yesmaximal, complemented
4C22⋊#95×C151C211yesmaximal, characteristic
5#1294×C151C212yesmaximal, complemented
6C24×C4×C151C2211yescharacteristic
7C23×C8×C151—21no—
8C2×C22⋊Q8×C151C411yescharacteristic, complemented
9C2×C22⋊Q8×C151C411yescharacteristic, complemented
10C2×C22⋊Q8×C151C2211yescharacteristic
11C22×C22⋊C4×C151—21no—
12C2×C22⋊C8×C151—21no—
13C2×C22⋊C8×C151—24no—
14C2×C22⋊C8×C151C2212yes—
15#385×C151—21no—
16#385×C151—21no—
17#385×C151—21no—
18#380×C151C411yescharacteristic, complemented
19#380×C151C411yescharacteristic, complemented
20#380×C151C2211yescharacteristic
21#379×C151—21no—
22C2×#95×C151—21no—
23C2×#95×C151C2212yes—
24#328×C151—24no—
25C25×C151D411yescharacteristic
26C22×Q8×C151C2×C411yescharacteristic
27C23×C4×C151—22no—
28C23×C4×C151—22no—
29C23×C4×C151—22no—
30C23×C4×C151—42no—
31C23×C4×C151—42no—
32C23×C4×C151C2×C411yescharacteristic
33C23×C4×C151C2×C411yescharacteristic
34C23×C4×C151D411yescharacteristic
35C23×C4×C151D411yescharacteristic
36C23×C4×C151D411yescharacteristic
37C23×C4×C151C2311yescharacteristic
38C22×C8×C151—24no—
39C22×C8×C151—22no—
40C22×C8×C151—42no—
41C22×C8×C151—42no—
42C22⋊Q8×C151—22no—
43C22⋊Q8×C151—22no—
44C22⋊Q8×C151—42no—
45C22⋊Q8×C151—42no—
46C2×C4⋊C4×C151—21no—
47C2×C4⋊C4×C151—21no—
48C2×C4⋊C4×C151—21no—
49C2×C4⋊C4×C151C2×C411yescharacteristic
50C2×C4⋊C4×C151C2×C411yescharacteristic
51C2×C4⋊C4×C151C2×C411yescharacteristic
52C2×C22⋊C4×C151—24no—
53C2×C22⋊C4×C151—21no—
54C2×C22⋊C4×C151—21no—
55C2×C22⋊C4×C151—21no—
56C2×C22⋊C4×C151—21no—
57C2×C22⋊C4×C151—21no—
58C2×C22⋊C4×C151—21no—
59C2×C22⋊C4×C151—42no—
60C2×C22⋊C4×C151—42no—
61C22⋊C8×C151—24no—
62C22⋊C8×C151—22no—
63C22⋊C8×C151D414yes—
64#95×C151—21no—
65#95×C151—21no—
66#95×C151—21no—
67#95×C151—22no—
68#95×C151—22no—
69#95×C151—42no—
70C24×C151—22no—
71C24×C151—22no—
72C24×C151—22no—
73C24×C151—22no—
74C24×C151—41no—
75C24×C151—41no—
76C24×C151C22⋊C411yescharacteristic
77C24×C151C22⋊C411yescharacteristic
78C24×C151SD1612yes—
79C24×C151Q1612yes—
80C24×C151C2×D411yescharacteristic
81C2×Q8×C151—22no—
82C2×Q8×C151—41no—
83C2×Q8×C151—41no—
84C22×C4×C151—22no—
85C22×C4×C151—22no—
86C22×C4×C151—21no—
87C22×C4×C151—21no—
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—21no—
95C22×C4×C151—21no—
96C22×C4×C151—24no—
97C22×C4×C151—21no—
98C22×C4×C151—21no—
99C22×C4×C151—21no—
100C22×C4×C151—21no—
101C22×C4×C151—41no—
102C22×C4×C151—41no—
103C22×C4×C151—41no—
104C22×C4×C151—41no—
105C22×C4×C151—41no—
106C22×C4×C151—41no—
107C22×C4×C151—41no—
108C22×C4×C151—48no—
109C22×C4×C151—48no—
110C22×C4×C151—42no—
111C22×C4×C151—42no—
112C22×C4×C151—42no—
113C22×C4×C151—42no—
114C22×C4×C151—42no—
115C22×C4×C151—42no—
116C22×C4×C151C22⋊C411yescharacteristic
117C22×C4×C151C22⋊C411yescharacteristic
118C22×C4×C151C22×C411yescharacteristic
119C22×C4×C151C2×D411yescharacteristic
120C22×C4×C151C2×D412yes—
121C22×C4×C151#4112yes—
122C2×C8×C151—24no—
123C2×C8×C151—48no—
124C2×C8×C151—42no—
125C2×C8×C151—42no—
126C4⋊C4×C151—22no—
127C4⋊C4×C151—41no—
128C4⋊C4×C151—41no—
129C4⋊C4×C151—42no—
130C4⋊C4×C151—42no—
131C4⋊C4×C151—41no—
132C4⋊C4×C151—41no—
133C22⋊C4×C151—42no—
134C22⋊C4×C151—48no—
135C22⋊C4×C151—42no—
136C22⋊C4×C151—42no—
137C22⋊C4×C151—42no—
138C22⋊C4×C151—42no—
139C22⋊C4×C151—42no—
140C23×C151—21no—
141C23×C151—21no—
142C23×C151—21no—
143C23×C151—21no—
144C23×C151—21no—
145C23×C151—21no—
146C23×C151—21no—
147C23×C151—21no—
148C23×C151—24no—
149C23×C151—24no—
150C23×C151—21no—
151C23×C151—21no—
152C23×C151—21no—
153C23×C151—21no—
154C23×C151—21no—
155C23×C151—21no—
156C23×C151—24no—
157C23×C151—24no—
158C23×C151—42no—
159C23×C151—42no—
160C23×C151—44no—
161C23×C151—44no—
162C23×C151—44no—
163C23×C151—44no—
164C23×C151#9912yes—
165C23×C151#10312yes—
166C23×C151#10312yes—
167C23×C151#10412yes—
168C23×C151C2×C22⋊C411yescharacteristic
169C23×C151#12112yes—
170C23×C151C2×SD1611yescharacteristic
171C23×C151C2×Q1611yescharacteristic
172C23×C151#13512yes—
173Q8×C151—82no—
174C2×C4×C151—24no—
175C2×C4×C151—24no—
176C2×C4×C151—21no—
177C2×C4×C151—21no—
178C2×C4×C151—21no—
179C2×C4×C151—21no—
180C2×C4×C151—21no—
181C2×C4×C151—21no—
182C2×C4×C151—21no—
183C2×C4×C151—21no—
184C2×C4×C151—21no—
185C2×C4×C151—42no—
186C2×C4×C151—42no—
187C2×C4×C151—44no—
188C2×C4×C151—44no—
189C2×C4×C151—44no—
190C2×C4×C151—42no—
191C2×C4×C151—42no—
192C2×C4×C151—44no—
193C2×C4×C151—44no—
194C2×C4×C151—44no—
195C2×C4×C151—41no—
196C2×C4×C151—41no—
197C2×C4×C151—41no—
198C2×C4×C151—41no—
199C2×C4×C151—41no—
200C2×C4×C151—41no—
201C2×C4×C151—41no—
202C2×C4×C151—41no—
203C2×C4×C151—41no—
204C2×C4×C151—41no—
205C2×C4×C151—41no—
206C2×C4×C151—41no—
207C2×C4×C151—82no—
208C2×C4×C151—82no—
209C2×C4×C151—82no—
210C2×C4×C151—82no—
211C2×C4×C151#9912yes—
212C2×C4×C151C4×D412yes—
213C2×C4×C151#12011yescharacteristic
214C2×C4×C151#12311yescharacteristic
215C8×C151—44no—
216C22×C151—22no—
217C22×C151—22no—
218C22×C151—22no—
219C22×C151—22no—
220C22×C151—22no—
221C22×C151—21no—
222C22×C151—21no—
223C22×C151—22no—
224C22×C151—22no—
225C22×C151—22no—
226C22×C151—22no—
227C22×C151—21no—
228C22×C151—22no—
229C22×C151—21no—
230C22×C151—22no—
231C22×C151—22no—
232C22×C151—22no—
233C22×C151—48no—
234C22×C151—48no—
235C22×C151—41no—
236C22×C151—41no—
237C22×C151—41no—
238C22×C151—41no—
239C22×C151#32814yescomplemented
240C22×C151#38611yescharacteristic
241C22×C151C2×#9911yescharacteristic
242C22×C151C2×#9911yescharacteristic
243C22×C151C2×#10311yescharacteristic
244C22×C151#41611yescharacteristic
245C22×C151C2×#10411yescharacteristic
246C22×C151#42111yescharacteristic
247C22×C151#46512yes—
248C22×C151#46712yes—
249C4×C151—21no—
250C4×C151—22no—
251C4×C151—21no—
252C4×C151—22no—
253C4×C151—41no—
254C4×C151—84no—
255C4×C151—81no—
256C4×C151—81no—
257C4×C151—81no—
258C4×C151—81no—
259C2×C151—22no—
260C2×C151—24no—
261C2×C151—22no—
262C2×C151—42no—
263C2×C151C2×#32811yescharacteristic
264C2×C151#150111yescharacteristic
265C2×C151#151611yescharacteristic
266C2×C151#152011yescharacteristic
267C2×C151#187111yescharacteristic
268C2×C151#189211yescharacteristic
269C2×C151#189811yescharacteristic
270#9111C15111yesmaximal, characteristic, direct product factor, Sylow
271C151#911111yescharacteristic, direct product factor, Sylow
272C22×C22⋊C8C2×C15111yescharacteristic
273#2848C2×C15111yescharacteristic
274C2×#328C2×C15112yescomplemented
275C22⋊#95C2×C15111yescharacteristic
276#1294C2×C15112yescomplemented
277C24×C4C22×C15111yescharacteristic
278C23×C8—21no—
279C2×C22⋊Q8C4×C15111yescharacteristic, complemented
280C2×C22⋊Q8C4×C15111yescharacteristic, complemented
281C2×C22⋊Q8C22×C15111yescharacteristic
282C22×C22⋊C4—21no—
283C2×C22⋊C8—21no—
284C2×C22⋊C8—24no—
285C2×C22⋊C8C22×C15112yes—
286#385—21no—
287#385—21no—
288#385—21no—
289#380C4×C15111yescharacteristic, complemented
290#380C4×C15111yescharacteristic, complemented
291#380C22×C15111yescharacteristic
292#379—21no—
293C2×#95—21no—
294C2×#95C22×C15112yes—
295#328—24no—
296C25D4×C15111yescharacteristic
297C22×Q8C2×C4×C15111yescharacteristic
298C23×C4—22no—
299C23×C4—22no—
300C23×C4—22no—
301C23×C4—42no—
302C23×C4—42no—
303C23×C4C2×C4×C15111yescharacteristic
304C23×C4C2×C4×C15111yescharacteristic
305C23×C4D4×C15111yescharacteristic
306C23×C4D4×C15111yescharacteristic
307C23×C4D4×C15111yescharacteristic
308C23×C4C23×C15111yescharacteristic
309C22×C8—24no—
310C22×C8—22no—
311C22×C8—42no—
312C22×C8—42no—
313C22⋊Q8—22no—
314C22⋊Q8—22no—
315C22⋊Q8—42no—
316C22⋊Q8—42no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4C2×C4×C15111yescharacteristic
321C2×C4⋊C4C2×C4×C15111yescharacteristic
322C2×C4⋊C4C2×C4×C15111yescharacteristic
323C2×C22⋊C4—24no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—42no—
332C22⋊C8—24no—
333C22⋊C8—22no—
334C22⋊C8D4×C15114yes—
335#95—21no—
336#95—21no—
337#95—21no—
338#95—22no—
339#95—22no—
340#95—42no—
341C24—22no—
342C24—22no—
343C24—22no—
344C24—22no—
345C24—41no—
346C24—41no—
347C24C22⋊C4×C15111yescharacteristic
348C24C22⋊C4×C15111yescharacteristic
349C24SD16×C15112yes—
350C24Q16×C15112yes—
351C24C2×D4×C15111yescharacteristic
352C2×Q8—22no—
353C2×Q8—41no—
354C2×Q8—41no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—21no—
358C22×C4—21no—
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—24no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—48no—
380C22×C4—48no—
381C22×C4—42no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4—42no—
385C22×C4—42no—
386C22×C4—42no—
387C22×C4C22⋊C4×C15111yescharacteristic
388C22×C4C22⋊C4×C15111yescharacteristic
389C22×C4C22×C4×C15111yescharacteristic
390C22×C4C2×D4×C15111yescharacteristic
391C22×C4C2×D4×C15112yes—
392C22×C4#41×C15112yes—
393C2×C8—24no—
394C2×C8—48no—
395C2×C8—42no—
396C2×C8—42no—
397C4⋊C4—22no—
398C4⋊C4—41no—
399C4⋊C4—41no—
400C4⋊C4—42no—
401C4⋊C4—42no—
402C4⋊C4—41no—
403C4⋊C4—41no—
404C22⋊C4—48no—
405C22⋊C4—42no—
406C22⋊C4—42no—
407C22⋊C4—42no—
408C22⋊C4—42no—
409C22⋊C4—42no—
410C22⋊C4—42no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23—24no—
426C23—24no—
427C23—24no—
428C23—24no—
429C23—42no—
430C23—42no—
431C23—44no—
432C23—44no—
433C23—44no—
434C23—44no—
435C23#99×C15112yes—
436C23#103×C15112yes—
437C23#103×C15112yes—
438C23#104×C15112yes—
439C23C2×C22⋊C4×C15111yescharacteristic
440C23#121×C15112yes—
441C23C2×SD16×C15111yescharacteristic
442C23C2×Q16×C15111yescharacteristic
443C23#135×C15112yes—
444Q8—82no—
445C2×C4—24no—
446C2×C4—24no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—44no—
459C2×C4—44no—
460C2×C4—44no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—44no—
464C2×C4—44no—
465C2×C4—44no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—82no—
479C2×C4—82no—
480C2×C4—82no—
481C2×C4—82no—
482C2×C4#99×C15112yes—
483C2×C4C4×D4×C15112yes—
484C2×C4#120×C15111yescharacteristic
485C2×C4#123×C15111yescharacteristic
486C8—44no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—22no—
491C22—22no—
492C22—21no—
493C22—21no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22—21no—
499C22—22no—
500C22—21no—
501C22—22no—
502C22—22no—
503C22—22no—
504C22—48no—
505C22—48no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22#328×C15114yescomplemented
511C22#386×C15111yescharacteristic
512C22C2×#99×C15111yescharacteristic
513C22C2×#99×C15111yescharacteristic
514C22C2×#103×C15111yescharacteristic
515C22#416×C15111yescharacteristic
516C22C2×#104×C15111yescharacteristic
517C22#421×C15111yescharacteristic
518C22#465×C15112yes—
519C22#467×C15112yes—
520C4—21no—
521C4—22no—
522C4—21no—
523C4—22no—
524C4—41no—
525C4—84no—
526C4—81no—
527C4—81no—
528C4—81no—
529C4—81no—
530C2—22no—
531C2—22no—
532C2—24no—
533C2—42no—
534C2C2×#328×C15111yescharacteristic
535C2#1501×C15111yescharacteristic
536C2#1516×C15111yescharacteristic
537C2#1520×C15111yescharacteristic
538C2#1871×C15111yescharacteristic
539C2#1892×C15111yescharacteristic
540C2#1898×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C2×C22⋊C4
commutatorC22×C4C22×C4×C151
Frattini, cosocleC23×C4C23×C151
prime radicalC25×C151D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C151 ◁ C24×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#328×C151C2semidirect
5. #1294×C151C2semidirect
8. C2×C22⋊Q8×C151C4semidirect
9. C2×C22⋊Q8×C151C4semidirect
18. #380×C151C4semidirect
19. #380×C151C4semidirect
239. C22×C151#328semidirect
270. #9111C151direct (N × H)
271. C151#9111direct (N × H)
274. C2×#328C2×C151semidirect
276. #1294C2×C151semidirect
279. C2×C22⋊Q8C4×C151semidirect
280. C2×C22⋊Q8C4×C151semidirect
289. #380C4×C151semidirect
290. #380C4×C151semidirect
510. C22#328×C151semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊C8×C1512
#2848×C1512
C2×#328×C1512
C22⋊#95×C1512
#1294×C1512
#9111151