Finite Group Databasebeta

← C151×#24329 #50329254

Subgroups — C151×#24329 #50329254

Order 38656.

1102 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q82×C151C211yesmaximal, characteristic, complemented
2C2×#476×C151C211yesmaximal, characteristic
3C2×C4×SD16×C151C211yesmaximal, characteristic
4#2538×C151C211yesmaximal, characteristic
5#2058×C151C212yesmaximal, complemented
6#2023×C151C212yesmaximal
7#1990×C151C211yesmaximal, characteristic, complemented
8#1984×C151C211yesmaximal, characteristic, complemented
9#1880×C151C212yesmaximal
10#1865×C151C212yesmaximal, complemented
11#1803×C151C211yesmaximal, characteristic, complemented
12C22×SD16×C151C2211yescharacteristic
13Q82×C151—24no—
14Q82×C151—24no—
15C2×C4⋊Q8×C151—21no—
16C2×C4⋊Q8×C151—22no—
17C2×C4⋊Q8×C151C2212yes—
18C2×C4⋊Q8×C151C2211yescharacteristic
19C2×C22⋊Q8×C151—21no—
20C2×C4×Q8×C151—21no—
21C2×C4×Q8×C151C2212yes—
22C2×C4×Q8×C151C2211yescharacteristic
23C2×C4×Q8×C151C2211yescharacteristic
24C2×C4×D4×C151C2211yescharacteristic
25#476×C151—24no—
26C4×SD16×C151—24no—
27C2×#106×C151C2212yes—
28C2×#106×C151C2211yescharacteristic
29C2×C4⋊C8×C151C2211yescharacteristic
30C2×#103×C151C2211yescharacteristic
31C2×#103×C151C2212yes—
32C2×#102×C151C2212yes—
33C2×#102×C151C2211yescharacteristic
34C2×C4×C8×C151C2211yescharacteristic
35#396×C151—22no—
36#390×C151C2212yes—
37#389×C151C2212yes—
38#384×C151C2211yescharacteristic
39#380×C151—21no—
40#340×C151C2212yes—
41#340×C151C2212yes—
42#340×C151C2212yes—
43#336×C151C2212yes—
44#336×C151C2212yes—
45C22×Q8×C151—22no—
46C22×Q8×C151—21no—
47C22×Q8×C151D411yescharacteristic
48C22×Q8×C151C2311yescharacteristic
49C22×D4×C151C2311yescharacteristic
50C23×C4×C151—21no—
51C2×SD16×C151—22no—
52C2×SD16×C151—22no—
53C2×SD16×C151Q814yescomplemented
54C22×C8×C151C2311yescharacteristic
55C22×C8×C151C2312yes—
56C22×C8×C151C2311yescharacteristic
57C4⋊Q8×C151—28no—
58C4⋊Q8×C151—216no—
59C4⋊Q8×C151—24no—
60C4⋊Q8×C151—24no—
61C4⋊Q8×C151—22no—
62C4⋊Q8×C151D414yes—
63C22⋊Q8×C151—44no—
64C4×Q8×C151—28no—
65C4×Q8×C151—24no—
66C4×Q8×C151—22no—
67C4×Q8×C151—22no—
68C4×Q8×C151—22no—
69C4×Q8×C151—24no—
70C4×Q8×C151D414yes—
71C4×D4×C151—22no—
72C4×D4×C151—22no—
73C2×C4⋊C4×C151—22no—
74C2×C4⋊C4×C151—21no—
75C2×C4⋊C4×C151—22no—
76C2×C4⋊C4×C151—21no—
77C2×C4⋊C4×C151—21no—
78C2×C4⋊C4×C151—22no—
79C2×C4⋊C4×C151—21no—
80C2×C4⋊C4×C151D411yescharacteristic
81C2×C4⋊C4×C151D412yes—
82C2×C4⋊C4×C151C2312yes—
83C2×C4⋊C4×C151C2311yescharacteristic
84C2×C4⋊C4×C151C2312yes—
85C2×C4⋊C4×C151C2311yescharacteristic
86C2×C22⋊C4×C151—22no—
87C2×C22⋊C4×C151—21no—
88C2×C22⋊C4×C151—22no—
89C2×C42×C151—22no—
90C2×C42×C151—21no—
91C2×C42×C151C2312yes—
92C2×C42×C151C2311yescharacteristic
93#106×C151—22no—
94#106×C151—24no—
95C4⋊C8×C151—22no—
96#103×C151—22no—
97#103×C151—24no—
98#102×C151—22no—
99#102×C151—24no—
100C4×C8×C151—22no—
101#95×C151—22no—
102C24×C151—21no—
103C2×Q8×C151—28no—
104C2×Q8×C151—22no—
105C2×Q8×C151—24no—
106C2×Q8×C151—22no—
107C2×Q8×C151—21no—
108C2×Q8×C151—21no—
109C2×Q8×C151—21no—
110C2×Q8×C151—81no—
111C2×Q8×C151—81no—
112C2×Q8×C151—82no—
113C2×Q8×C151—82no—
114C2×Q8×C151SD1614yescomplemented
115C2×Q8×C151C2×D412yes—
116C2×Q8×C151C2×Q812yes—
117C2×Q8×C151#4112yes—
118C2×D4×C151—21no—
119C2×D4×C151—21no—
120C2×D4×C151—21no—
121C2×D4×C151—21no—
122C2×D4×C151—21no—
123C2×D4×C151C2×Q812yes—
124C22×C4×C151—21no—
125C22×C4×C151—21no—
126C22×C4×C151—22no—
127C22×C4×C151—21no—
128C22×C4×C151—22no—
129C22×C4×C151—42no—
130C22×C4×C151—42no—
131C22×C4×C151—42no—
132C22×C4×C151C2×D412yes—
133C22×C4×C151C2×D411yescharacteristic
134C22×C4×C151C2×D412yes—
135C22×C4×C151C2×D411yescharacteristic
136C22×C4×C151C2411yescharacteristic
137SD16×C151—28no—
138C2×C8×C151—21no—
139C2×C8×C151—21no—
140C2×C8×C151—21no—
141C2×C8×C151—22no—
142C2×C8×C151—22no—
143C2×C8×C151—21no—
144C2×C8×C151—21no—
145C2×C8×C151—22no—
146C2×C8×C151C2×Q812yes—
147C4⋊C4×C151—28no—
148C4⋊C4×C151—28no—
149C4⋊C4×C151—24no—
150C4⋊C4×C151—24no—
151C4⋊C4×C151—24no—
152C4⋊C4×C151—22no—
153C4⋊C4×C151—22no—
154C4⋊C4×C151—21no—
155C4⋊C4×C151—21no—
156C4⋊C4×C151—21no—
157C4⋊C4×C151—22no—
158C4⋊C4×C151—22no—
159C4⋊C4×C151—42no—
160C4⋊C4×C151—44no—
161C4⋊C4×C151—81no—
162C4⋊C4×C151C2×D414yes—
163C4⋊C4×C151C2×D412yes—
164C22⋊C4×C151—42no—
165C22⋊C4×C151—44no—
166C22⋊C4×C151—82no—
167C42×C151—28no—
168C42×C151—24no—
169C42×C151—22no—
170C42×C151—22no—
171C42×C151C2×D412yes—
172C42×C151C2×D412yes—
173C23×C151—22no—
174C23×C151—41no—
175C23×C151—41no—
176C23×C151—41no—
177C23×C151—41no—
178C23×C151—41no—
179C23×C151—41no—
180C23×C151C22×D411yescharacteristic
181Q8×C151—22no—
182Q8×C151—22no—
183Q8×C151—22no—
184Q8×C151—28no—
185Q8×C151—84no—
186Q8×C151—88no—
187Q8×C151C22⋊Q814yescomplemented
188D4×C151—22no—
189D4×C151—22no—
190D4×C151—41no—
191D4×C151—41no—
192C2×C4×C151—22no—
193C2×C4×C151—22no—
194C2×C4×C151—22no—
195C2×C4×C151—22no—
196C2×C4×C151—22no—
197C2×C4×C151—21no—
198C2×C4×C151—21no—
199C2×C4×C151—22no—
200C2×C4×C151—22no—
201C2×C4×C151—24no—
202C2×C4×C151—22no—
203C2×C4×C151—22no—
204C2×C4×C151—42no—
205C2×C4×C151—41no—
206C2×C4×C151—42no—
207C2×C4×C151—41no—
208C2×C4×C151—41no—
209C2×C4×C151—42no—
210C2×C4×C151—42no—
211C2×C4×C151—41no—
212C2×C4×C151—41no—
213C2×C4×C151—42no—
214C2×C4×C151—84no—
215C2×C4×C151#12012yes—
216C2×C4×C151#12012yes—
217C2×C4×C151C2×SD1614yes—
218C2×C4×C151C2×SD1612yes—
219C2×C4×C151#13712yes—
220C2×C4×C151C22×D411yescharacteristic
221C2×C4×C151C22×D411yescharacteristic
222C2×C4×C151C22×Q811yescharacteristic
223C2×C4×C151C2×#4111yescharacteristic
224C2×C4×C1512−1+411yescharacteristic
225C2×C4×C1512−1+411yescharacteristic
226C8×C151—22no—
227C8×C151—41no—
228C8×C151—42no—
229C22×C151—42no—
230C22×C151—42no—
231C22×C151—42no—
232C22×C151—81no—
233C22×C151—81no—
234C22×C151—81no—
235C22×C151—81no—
236C22×C151C2×#12011yescharacteristic
237C22×C151#54811yescharacteristic
238C22×C151D4×Q811yescharacteristic
239C22×C151C22×SD1611yescharacteristic
240C22×C151C2×#13711yescharacteristic
241C22×C151#57611yescharacteristic
242C22×C151#57711yescharacteristic
243C4×C151—24no—
244C4×C151—24no—
245C4×C151—22no—
246C4×C151—42no—
247C4×C151—44no—
248C4×C151—42no—
249C4×C151—82no—
250C4×C151—81no—
251C4×C151#44814yes—
252C4×C151C2×C22⋊Q811yescharacteristic
253C4×C151#53611yescharacteristic
254C4×C151#54811yescharacteristic
255C4×C151D4×Q811yescharacteristic
256C2×C151—82no—
257C2×C151#240911yescharacteristic
258C2×C151C2×#44811yescharacteristic
259C2×C151#301211yescharacteristic
260C2×C151#336211yescharacteristic
261C2×C151#336911yescharacteristic
262C2×C151Q8×SD1611yescharacteristic
263C2×C151#338511yescharacteristic
264#24329C15111yesmaximal, characteristic, direct product factor, Sylow
265C151#2432911yescharacteristic, direct product factor, Sylow
266C2×Q82C2×C15111yescharacteristic, complemented
267C2×#476C2×C15111yescharacteristic
268C2×C4×SD16C2×C15111yescharacteristic
269#2538C2×C15111yescharacteristic
270#2058C2×C15112yescomplemented
271#2023C2×C15112yes—
272#1990C2×C15111yescharacteristic, complemented
273#1984C2×C15111yescharacteristic, complemented
274#1880C2×C15112yes—
275#1865C2×C15112yescomplemented
276#1803C2×C15111yescharacteristic, complemented
277C22×SD16C22×C15111yescharacteristic
278Q82—24no—
279Q82—24no—
280C2×C4⋊Q8—21no—
281C2×C4⋊Q8—22no—
282C2×C4⋊Q8C22×C15112yes—
283C2×C4⋊Q8C22×C15111yescharacteristic
284C2×C22⋊Q8—21no—
285C2×C4×Q8—21no—
286C2×C4×Q8C22×C15112yes—
287C2×C4×Q8C22×C15111yescharacteristic
288C2×C4×Q8C22×C15111yescharacteristic
289C2×C4×D4C22×C15111yescharacteristic
290#476—24no—
291C4×SD16—24no—
292C2×#106C22×C15111yescharacteristic
293C2×#106C22×C15112yes—
294C2×C4⋊C8C22×C15111yescharacteristic
295C2×#103C22×C15112yes—
296C2×#103C22×C15111yescharacteristic
297C2×#102C22×C15112yes—
298C2×#102C22×C15111yescharacteristic
299C2×C4×C8C22×C15111yescharacteristic
300#396—22no—
301#390C22×C15112yes—
302#389C22×C15112yes—
303#384C22×C15111yescharacteristic
304#380—21no—
305#340C22×C15112yes—
306#340C22×C15112yes—
307#340C22×C15112yes—
308#336C22×C15112yes—
309#336C22×C15112yes—
310C22×Q8—22no—
311C22×Q8—21no—
312C22×Q8D4×C15111yescharacteristic
313C22×Q8C23×C15111yescharacteristic
314C22×D4C23×C15111yescharacteristic
315C23×C4—21no—
316C2×SD16—22no—
317C2×SD16—22no—
318C2×SD16Q8×C15114yescomplemented
319C22×C8C23×C15111yescharacteristic
320C22×C8C23×C15112yes—
321C22×C8C23×C15111yescharacteristic
322C4⋊Q8—216no—
323C4⋊Q8—28no—
324C4⋊Q8—24no—
325C4⋊Q8—24no—
326C4⋊Q8—22no—
327C4⋊Q8D4×C15114yes—
328C22⋊Q8—44no—
329C4×Q8—28no—
330C4×Q8—24no—
331C4×Q8—24no—
332C4×Q8—22no—
333C4×Q8—22no—
334C4×Q8—22no—
335C4×Q8D4×C15114yes—
336C4×D4—22no—
337C4×D4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4D4×C15111yescharacteristic
346C2×C4⋊C4D4×C15112yes—
347C2×C4⋊C4C23×C15111yescharacteristic
348C2×C4⋊C4C23×C15112yes—
349C2×C4⋊C4C23×C15112yes—
350C2×C4⋊C4C23×C15111yescharacteristic
351C2×C22⋊C4—21no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C42—22no—
355C2×C42—21no—
356C2×C42C23×C15112yes—
357C2×C42C23×C15111yescharacteristic
358#106—22no—
359#106—24no—
360C4⋊C8—22no—
361#103—24no—
362#103—22no—
363#102—22no—
364#102—24no—
365C4×C8—22no—
366#95—22no—
367C24—21no—
368C2×Q8—28no—
369C2×Q8—22no—
370C2×Q8—24no—
371C2×Q8—22no—
372C2×Q8—21no—
373C2×Q8—21no—
374C2×Q8—21no—
375C2×Q8—81no—
376C2×Q8—81no—
377C2×Q8—82no—
378C2×Q8—82no—
379C2×Q8SD16×C15114yescomplemented
380C2×Q8C2×D4×C15112yes—
381C2×Q8C2×Q8×C15112yes—
382C2×Q8#41×C15112yes—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4C2×Q8×C15112yes—
389C22×C4—21no—
390C22×C4—22no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—42no—
395C22×C4—42no—
396C22×C4—42no—
397C22×C4C2×D4×C15112yes—
398C22×C4C2×D4×C15111yescharacteristic
399C22×C4C2×D4×C15112yes—
400C22×C4C2×D4×C15111yescharacteristic
401C22×C4C24×C15111yescharacteristic
402SD16—28no—
403C2×C8—21no—
404C2×C8—21no—
405C2×C8—21no—
406C2×C8—22no—
407C2×C8—22no—
408C2×C8—21no—
409C2×C8—21no—
410C2×C8—22no—
411C2×C8C2×Q8×C15112yes—
412C4⋊C4—28no—
413C4⋊C4—28no—
414C4⋊C4—24no—
415C4⋊C4—24no—
416C4⋊C4—24no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—42no—
425C4⋊C4—44no—
426C4⋊C4—81no—
427C4⋊C4C2×D4×C15114yes—
428C4⋊C4C2×D4×C15112yes—
429C22⋊C4—42no—
430C22⋊C4—44no—
431C22⋊C4—82no—
432C42—28no—
433C42—24no—
434C42—22no—
435C42—22no—
436C42C2×D4×C15112yes—
437C42C2×D4×C15112yes—
438C23—22no—
439C23—41no—
440C23—41no—
441C23—41no—
442C23—41no—
443C23—41no—
444C23—41no—
445C23C22×D4×C15111yescharacteristic
446Q8—28no—
447Q8—22no—
448Q8—22no—
449Q8—22no—
450Q8—84no—
451Q8—88no—
452Q8C22⋊Q8×C15114yescomplemented
453D4—22no—
454D4—22no—
455D4—41no—
456D4—41no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—22no—
465C2×C4—24no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—42no—
479C2×C4—84no—
480C2×C4#120×C15112yes—
481C2×C4#120×C15112yes—
482C2×C4C2×SD16×C15114yes—
483C2×C4C2×SD16×C15112yes—
484C2×C4#137×C15112yes—
485C2×C4C22×D4×C15111yescharacteristic
486C2×C4C22×D4×C15111yescharacteristic
487C2×C4C22×Q8×C15111yescharacteristic
488C2×C4C2×#41×C15111yescharacteristic
489C2×C42−1+4×C15111yescharacteristic
490C2×C42−1+4×C15111yescharacteristic
491C8—22no—
492C8—41no—
493C8—42no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22—81no—
498C22—81no—
499C22—81no—
500C22—81no—
501C22C2×#120×C15111yescharacteristic
502C22#548×C15111yescharacteristic
503C22D4×Q8×C15111yescharacteristic
504C22C22×SD16×C15111yescharacteristic
505C22C2×#137×C15111yescharacteristic
506C22#576×C15111yescharacteristic
507C22#577×C15111yescharacteristic
508C4—24no—
509C4—24no—
510C4—22no—
511C4—42no—
512C4—44no—
513C4—42no—
514C4—82no—
515C4—81no—
516C4#448×C15114yes—
517C4C2×C22⋊Q8×C15111yescharacteristic
518C4#536×C15111yescharacteristic
519C4#548×C15111yescharacteristic
520C4D4×Q8×C15111yescharacteristic
521C2—82no—
522C2#2409×C15111yescharacteristic
523C2C2×#448×C15111yescharacteristic
524C2#3012×C15111yescharacteristic
525C2#3362×C15111yescharacteristic
526C2#3369×C15111yescharacteristic
527C2Q8×SD16×C15111yescharacteristic
528C2#3385×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×Q8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×Q82×C151C2semidirect
5. #2058×C151C2semidirect
7. #1990×C151C2semidirect
8. #1984×C151C2semidirect
10. #1865×C151C2semidirect
11. #1803×C151C2semidirect
53. C2×SD16×C151Q8semidirect
114. C2×Q8×C151SD16semidirect
187. Q8×C151C22⋊Q8semidirect
264. #24329C151direct (N × H)
265. C151#24329direct (N × H)
266. C2×Q82C2×C151semidirect
270. #2058C2×C151semidirect
272. #1990C2×C151semidirect
273. #1984C2×C151semidirect
275. #1865C2×C151semidirect
276. #1803C2×C151semidirect
318. C2×SD16Q8×C151semidirect
379. C2×Q8SD16×C151semidirect
452. Q8C22⋊Q8×C151semidirect

Maximal subgroups

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

subgroupindex
C2×Q82×C1512
C2×#476×C1512
C2×C4×SD16×C1512
#2538×C1512
#2058×C1512
#2023×C1512
#1990×C1512
#1984×C1512
#1880×C1512
#1865×C1512
#1803×C1512
#24329151