Finite Group Databasebeta

← C151×#24130 #50329055

Subgroups — C151×#24130 #50329055

Order 38656.

1184 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#554×C151C211yesmaximal, characteristic, complemented
2C2×#474×C151C211yesmaximal, characteristic, complemented
3C2×#440×C151C211yesmaximal, characteristic, complemented
4#2535×C151C211yesmaximal, characteristic
5#2036×C151C212yesmaximal, complemented
6#2000×C151C212yesmaximal, complemented
7#1993×C151C211yesmaximal, characteristic, complemented
8#1955×C151C211yesmaximal, characteristic, complemented
9#1874×C151C212yesmaximal, complemented
10#1852×C151C212yesmaximal, complemented
11#1805×C151C211yesmaximal, characteristic, complemented
12C22×SD16×C151C2211yescharacteristic
13#554×C151—24no—
14#554×C151—24no—
15C2×C4⋊Q8×C151C2211yescharacteristic
16C2×#125×C151—21no—
17C2×C22⋊Q8×C151—22no—
18C2×C22⋊Q8×C151C2212yes—
19C2×#121×C151C2212yes—
20C2×C4×Q8×C151C2211yescharacteristic
21C2×C4×D4×C151—21no—
22C2×C4×D4×C151C2211yescharacteristic
23C2×C4×D4×C151C2211yescharacteristic
24C22×C4⋊C4×C151C2212yes—
25#474×C151—24no—
26#440×C151—24no—
27C2×#107×C151C2211yescharacteristic
28C2×#107×C151C2212yes—
29C2×C4⋊C8×C151C2211yescharacteristic
30C2×#103×C151C2211yescharacteristic
31C2×#103×C151C2212yes—
32C2×#102×C151C2211yescharacteristic
33C2×#102×C151C2212yes—
34C2×C22⋊C8×C151C2212yes—
35C2×C22⋊C8×C151C2212yes—
36C2×#97×C151C2211yescharacteristic
37#397×C151—21no—
38#392×C151—21no—
39#386×C151—22no—
40#382×C151C2211yescharacteristic
41#380×C151C2212yes—
42#340×C151C2212yes—
43#340×C151C2212yes—
44#340×C151C2212yes—
45C22×Q8×C151—21no—
46C22×Q8×C151C2311yescharacteristic
47C22×D4×C151—22no—
48C22×D4×C151D411yescharacteristic
49C22×D4×C151C2311yescharacteristic
50C23×C4×C151—21no—
51C23×C4×C151—22no—
52C23×C4×C151C2312yes—
53C2×SD16×C151—22no—
54C2×SD16×C151—22no—
55C2×SD16×C151—22no—
56C22×C8×C151C2311yescharacteristic
57C22×C8×C151C2312yes—
58C22×C8×C151C2311yescharacteristic
59C4⋊Q8×C151—22no—
60C4⋊Q8×C151D414yescomplemented
61#125×C151—28no—
62C22⋊Q8×C151—216no—
63C22⋊Q8×C151—24no—
64C22⋊Q8×C151—24no—
65#121×C151—24no—
66#121×C151—42no—
67C4×Q8×C151—22no—
68C4×Q8×C151D414yescomplemented
69C4×D4×C151—28no—
70C4×D4×C151—22no—
71C4×D4×C151—22no—
72C4×D4×C151—22no—
73C4×D4×C151—22no—
74C2×C4⋊C4×C151—22no—
75C2×C4⋊C4×C151—21no—
76C2×C4⋊C4×C151—21no—
77C2×C4⋊C4×C151—22no—
78C2×C4⋊C4×C151—24no—
79C2×C4⋊C4×C151—24no—
80C2×C4⋊C4×C151D411yescharacteristic
81C2×C4⋊C4×C151C2312yes—
82C2×C4⋊C4×C151C2311yescharacteristic
83C2×C4⋊C4×C151C2311yescharacteristic
84C2×C4⋊C4×C151C2312yes—
85C2×C22⋊C4×C151—22no—
86C2×C22⋊C4×C151—21no—
87C2×C22⋊C4×C151—22no—
88C2×C22⋊C4×C151—22no—
89C2×C22⋊C4×C151D412yes—
90C2×C42×C151—21no—
91C2×C42×C151C2311yescharacteristic
92#107×C151—22no—
93#107×C151—24no—
94C4⋊C8×C151—22no—
95#103×C151—22no—
96#103×C151—42no—
97#102×C151—22no—
98#102×C151—24no—
99C22⋊C8×C151—24no—
100C22⋊C8×C151—42no—
101#97×C151—22no—
102#95×C151—22no—
103#95×C151—21no—
104#95×C151—21no—
105C24×C151—21no—
106C24×C151C2×D412yes—
107C2×Q8×C151—24no—
108C2×Q8×C151—21no—
109C2×Q8×C151—21no—
110C2×Q8×C151—21no—
111C2×Q8×C151—21no—
112C2×Q8×C151—21no—
113C2×Q8×C151—82no—
114C2×Q8×C151C2×D412yes—
115C2×D4×C151—24no—
116C2×D4×C151—22no—
117C2×D4×C151—21no—
118C2×D4×C151—21no—
119C2×D4×C151—21no—
120C2×D4×C151—21no—
121C2×D4×C151—21no—
122C2×D4×C151—44no—
123C2×D4×C151—44no—
124C2×D4×C151—82no—
125C2×D4×C151#4112yes—
126C22×C4×C151—21no—
127C22×C4×C151—21no—
128C22×C4×C151—22no—
129C22×C4×C151—28no—
130C22×C4×C151—22no—
131C22×C4×C151—22no—
132C22×C4×C151—22no—
133C22×C4×C151—22no—
134C22×C4×C151—22no—
135C22×C4×C151—22no—
136C22×C4×C151—22no—
137C22×C4×C151—21no—
138C22×C4×C151—42no—
139C22×C4×C151—82no—
140C22×C4×C151—82no—
141C22×C4×C151—82no—
142C22×C4×C151C2×D412yes—
143C22×C4×C151C2×D411yescharacteristic
144C22×C4×C151C2×D411yescharacteristic
145C22×C4×C151C2411yescharacteristic
146SD16×C151—28no—
147C2×C8×C151—21no—
148C2×C8×C151—21no—
149C2×C8×C151—21no—
150C2×C8×C151—22no—
151C2×C8×C151—22no—
152C2×C8×C151—21no—
153C2×C8×C151—22no—
154C2×C8×C151—21no—
155C2×C8×C151#4112yes—
156C4⋊C4×C151—28no—
157C4⋊C4×C151—28no—
158C4⋊C4×C151—24no—
159C4⋊C4×C151—24no—
160C4⋊C4×C151—22no—
161C4⋊C4×C151—21no—
162C4⋊C4×C151—22no—
163C4⋊C4×C151—21no—
164C4⋊C4×C151—21no—
165C4⋊C4×C151—22no—
166C4⋊C4×C151—22no—
167C4⋊C4×C151C2×D412yes—
168C4⋊C4×C151C2×D414yes—
169C22⋊C4×C151—28no—
170C22⋊C4×C151—24no—
171C22⋊C4×C151—44no—
172C22⋊C4×C151—42no—
173C22⋊C4×C151—82no—
174C42×C151—24no—
175C42×C151C2×D412yes—
176C42×C151C2×D412yes—
177C23×C151—22no—
178C23×C151—22no—
179C23×C151—22no—
180C23×C151—22no—
181C23×C151—22no—
182C23×C151—22no—
183C23×C151—22no—
184C23×C151—41no—
185C23×C151—41no—
186C23×C151—42no—
187C23×C151—42no—
188C23×C151#13714yes—
189C23×C151C22×D411yescharacteristic
190Q8×C151—22no—
191Q8×C151—22no—
192Q8×C151—41no—
193Q8×C151—41no—
194Q8×C151—84no—
195D4×C151—28no—
196D4×C151—22no—
197D4×C151—22no—
198D4×C151—41no—
199D4×C151—41no—
200D4×C151—88no—
201C2×C4×C151—22no—
202C2×C4×C151—22no—
203C2×C4×C151—24no—
204C2×C4×C151—22no—
205C2×C4×C151—22no—
206C2×C4×C151—22no—
207C2×C4×C151—22no—
208C2×C4×C151—22no—
209C2×C4×C151—41no—
210C2×C4×C151—41no—
211C2×C4×C151—42no—
212C2×C4×C151—42no—
213C2×C4×C151—42no—
214C2×C4×C151—42no—
215C2×C4×C151—42no—
216C2×C4×C151—42no—
217C2×C4×C151—42no—
218C2×C4×C151—41no—
219C2×C4×C151—42no—
220C2×C4×C151—42no—
221C2×C4×C151—42no—
222C2×C4×C151—42no—
223C2×C4×C151—84no—
224C2×C4×C151—88no—
225C2×C4×C151#12012yes—
226C2×C4×C151#12012yes—
227C2×C4×C151C22×D411yescharacteristic
228C2×C4×C151C22×D411yescharacteristic
229C2×C4×C151C2×#4111yescharacteristic
230C2×C4×C151C2×#4111yescharacteristic
231C2×C4×C151H(5,𝔽2)11yescharacteristic
232C2×C4×C1512−1+411yescharacteristic
233C8×C151—22no—
234C8×C151—41no—
235C8×C151—42no—
236C22×C151—24no—
237C22×C151—24no—
238C22×C151—24no—
239C22×C151—42no—
240C22×C151—42no—
241C22×C151—42no—
242C22×C151—42no—
243C22×C151—42no—
244C22×C151—44no—
245C22×C151—82no—
246C22×C151—81no—
247C22×C151—81no—
248C22×C151C2×#12011yescharacteristic
249C22×C151#54611yescharacteristic
250C22×C151#54711yescharacteristic
251C22×C151C2×#13712yes—
252C22×C151#57612yes—
253C4×C151—22no—
254C4×C151—22no—
255C4×C151—42no—
256C4×C151—42no—
257C4×C151—42no—
258C4×C151—44no—
259C4×C151—81no—
260C4×C151—82no—
261C4×C151#52511yescharacteristic
262C4×C151#53711yescharacteristic
263C4×C151#54811yescharacteristic
264C4×C151#55011yescharacteristic
265C2×C151—44no—
266C2×C151—82no—
267C2×C151#240711yescharacteristic
268C2×C151#300411yescharacteristic
269C2×C151#300811yescharacteristic
270C2×C151#331412yes—
271C2×C151#334612yes—
272#24130C15111yesmaximal, characteristic, direct product factor, Sylow
273C151#2413011yescharacteristic, direct product factor, Sylow
274C2×#554C2×C15111yescharacteristic, complemented
275C2×#474C2×C15111yescharacteristic, complemented
276C2×#440C2×C15111yescharacteristic, complemented
277#2535C2×C15111yescharacteristic
278#2036C2×C15112yescomplemented
279#2000C2×C15112yescomplemented
280#1993C2×C15111yescharacteristic, complemented
281#1955C2×C15111yescharacteristic, complemented
282#1874C2×C15112yescomplemented
283#1852C2×C15112yescomplemented
284#1805C2×C15111yescharacteristic, complemented
285C22×SD16C22×C15111yescharacteristic
286#554—24no—
287#554—24no—
288C2×C4⋊Q8C22×C15111yescharacteristic
289C2×#125—21no—
290C2×C22⋊Q8—22no—
291C2×C22⋊Q8C22×C15112yes—
292C2×#121C22×C15112yes—
293C2×C4×Q8C22×C15111yescharacteristic
294C2×C4×D4—21no—
295C2×C4×D4C22×C15111yescharacteristic
296C2×C4×D4C22×C15111yescharacteristic
297C22×C4⋊C4C22×C15112yes—
298#474—24no—
299#440—24no—
300C2×#107C22×C15111yescharacteristic
301C2×#107C22×C15112yes—
302C2×C4⋊C8C22×C15111yescharacteristic
303C2×#103C22×C15111yescharacteristic
304C2×#103C22×C15112yes—
305C2×#102C22×C15111yescharacteristic
306C2×#102C22×C15112yes—
307C2×C22⋊C8C22×C15112yes—
308C2×C22⋊C8C22×C15112yes—
309C2×#97C22×C15111yescharacteristic
310#397—21no—
311#392—21no—
312#386—22no—
313#382C22×C15111yescharacteristic
314#380C22×C15112yes—
315#340C22×C15112yes—
316#340C22×C15112yes—
317#340C22×C15112yes—
318C22×Q8—21no—
319C22×Q8C23×C15111yescharacteristic
320C22×D4—22no—
321C22×D4D4×C15111yescharacteristic
322C22×D4C23×C15111yescharacteristic
323C23×C4—22no—
324C23×C4—21no—
325C23×C4C23×C15112yes—
326C2×SD16—22no—
327C2×SD16—22no—
328C2×SD16—22no—
329C22×C8C23×C15111yescharacteristic
330C22×C8C23×C15112yes—
331C22×C8C23×C15111yescharacteristic
332C4⋊Q8—22no—
333C4⋊Q8D4×C15114yescomplemented
334#125—28no—
335C22⋊Q8—216no—
336C22⋊Q8—24no—
337C22⋊Q8—24no—
338#121—24no—
339#121—42no—
340C4×Q8—22no—
341C4×Q8D4×C15114yescomplemented
342C4×D4—28no—
343C4×D4—22no—
344C4×D4—22no—
345C4×D4—22no—
346C4×D4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4D4×C15111yescharacteristic
354C2×C4⋊C4C23×C15111yescharacteristic
355C2×C4⋊C4C23×C15112yes—
356C2×C4⋊C4C23×C15111yescharacteristic
357C2×C4⋊C4C23×C15112yes—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4D4×C15112yes—
363C2×C42—21no—
364C2×C42C23×C15111yescharacteristic
365#107—22no—
366#107—24no—
367C4⋊C8—22no—
368#103—22no—
369#103—42no—
370#102—22no—
371#102—24no—
372C22⋊C8—24no—
373C22⋊C8—42no—
374#97—22no—
375#95—22no—
376#95—21no—
377#95—21no—
378C24—21no—
379C24C2×D4×C15112yes—
380C2×Q8—24no—
381C2×Q8—21no—
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—82no—
387C2×Q8C2×D4×C15112yes—
388C2×D4—24no—
389C2×D4—22no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—44no—
396C2×D4—44no—
397C2×D4—82no—
398C2×D4#41×C15112yes—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—28no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—42no—
412C22×C4—82no—
413C22×C4—82no—
414C22×C4—82no—
415C22×C4C2×D4×C15112yes—
416C22×C4C2×D4×C15111yescharacteristic
417C22×C4C2×D4×C15111yescharacteristic
418C22×C4C24×C15111yescharacteristic
419SD16—28no—
420C2×C8—21no—
421C2×C8—21no—
422C2×C8—21no—
423C2×C8—22no—
424C2×C8—22no—
425C2×C8—21no—
426C2×C8—22no—
427C2×C8—21no—
428C2×C8#41×C15112yes—
429C4⋊C4—28no—
430C4⋊C4—28no—
431C4⋊C4—24no—
432C4⋊C4—24no—
433C4⋊C4—22no—
434C4⋊C4—21no—
435C4⋊C4—22no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4C2×D4×C15112yes—
441C4⋊C4C2×D4×C15114yes—
442C22⋊C4—28no—
443C22⋊C4—24no—
444C22⋊C4—44no—
445C22⋊C4—42no—
446C22⋊C4—82no—
447C42—24no—
448C42C2×D4×C15112yes—
449C42C2×D4×C15112yes—
450C23—22no—
451C23—22no—
452C23—22no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—22no—
457C23—41no—
458C23—41no—
459C23—42no—
460C23—42no—
461C23#137×C15114yes—
462C23C22×D4×C15111yescharacteristic
463Q8—22no—
464Q8—22no—
465Q8—41no—
466Q8—41no—
467Q8—84no—
468D4—28no—
469D4—22no—
470D4—22no—
471D4—41no—
472D4—41no—
473D4—88no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—24no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—84no—
497C2×C4—88no—
498C2×C4#120×C15112yes—
499C2×C4#120×C15112yes—
500C2×C4C22×D4×C15111yescharacteristic
501C2×C4C22×D4×C15111yescharacteristic
502C2×C4C2×#41×C15111yescharacteristic
503C2×C4C2×#41×C15111yescharacteristic
504C2×C4H(5,𝔽2)×C15111yescharacteristic
505C2×C42−1+4×C15111yescharacteristic
506C8—22no—
507C8—41no—
508C8—42no—
509C22—24no—
510C22—24no—
511C22—24no—
512C22—42no—
513C22—42no—
514C22—42no—
515C22—42no—
516C22—42no—
517C22—44no—
518C22—81no—
519C22—81no—
520C22—82no—
521C22C2×#120×C15111yescharacteristic
522C22#546×C15111yescharacteristic
523C22#547×C15111yescharacteristic
524C22C2×#137×C15112yes—
525C22#576×C15112yes—
526C4—22no—
527C4—22no—
528C4—42no—
529C4—42no—
530C4—42no—
531C4—44no—
532C4—81no—
533C4—82no—
534C4#525×C15111yescharacteristic
535C4#537×C15111yescharacteristic
536C4#548×C15111yescharacteristic
537C4#550×C15111yescharacteristic
538C2—44no—
539C2—82no—
540C2#2407×C15111yescharacteristic
541C2#3004×C15111yescharacteristic
542C2#3008×C15111yescharacteristic
543C2#3314×C15112yes—
544C2#3346×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#2535×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#554×C151C2semidirect
2. C2×#474×C151C2semidirect
3. C2×#440×C151C2semidirect
5. #2036×C151C2semidirect
6. #2000×C151C2semidirect
7. #1993×C151C2semidirect
8. #1955×C151C2semidirect
9. #1874×C151C2semidirect
10. #1852×C151C2semidirect
11. #1805×C151C2semidirect
60. C4⋊Q8×C151D4semidirect
68. C4×Q8×C151D4semidirect
272. #24130C151direct (N × H)
273. C151#24130direct (N × H)
274. C2×#554C2×C151semidirect
275. C2×#474C2×C151semidirect
276. C2×#440C2×C151semidirect
278. #2036C2×C151semidirect
279. #2000C2×C151semidirect
280. #1993C2×C151semidirect
281. #1955C2×C151semidirect
282. #1874C2×C151semidirect
283. #1852C2×C151semidirect
284. #1805C2×C151semidirect
333. C4⋊Q8D4×C151semidirect
341. C4×Q8D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#554×C1512
C2×#474×C1512
C2×#440×C1512
#2535×C1512
#2036×C1512
#2000×C1512
#1993×C1512
#1955×C1512
#1874×C1512
#1852×C1512
#1805×C1512
#24130151