Finite Group Databasebeta

← C151×#24190 #50329115

Subgroups — C151×#24190 #50329115

Order 38656.

1146 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#559×C151C211yesmaximal, characteristic
2C2×#460×C151C211yesmaximal, characteristic
3C2×C4×Q16×C151C211yesmaximal, characteristic, complemented
4#2582×C151C211yesmaximal, characteristic, complemented
5#2042×C151C212yesmaximal, complemented
6#2015×C151C212yesmaximal, complemented
7#1984×C151C211yesmaximal, characteristic, complemented
8#1957×C151C211yesmaximal, characteristic
9#1877×C151C212yesmaximal, complemented
10#1862×C151C212yesmaximal, complemented
11#1803×C151C211yesmaximal, characteristic, complemented
12C22×Q16×C151C2211yescharacteristic
13C22×SD16×C151C2212yes—
14#559×C151—24no—
15#559×C151—24no—
16C2×#127×C151C2211yescharacteristic
17C2×#124×C151—21no—
18C2×#124×C151C2212yes—
19C2×#123×C151—22no—
20C2×C4×Q8×C151C2211yescharacteristic
21C2×C4×Q8×C151C2211yescharacteristic
22C2×C4×Q8×C151C2211yescharacteristic
23C2×C4×D4×C151—21no—
24C2×C4×D4×C151C2212yes—
25#460×C151—24no—
26C4×Q16×C151—24no—
27C2×#107×C151C2211yescharacteristic
28C2×C4⋊C8×C151C2211yescharacteristic
29C2×#103×C151C2211yescharacteristic
30C2×#103×C151C2211yescharacteristic
31C2×#103×C151C2212yes—
32C2×#102×C151C2212yes—
33C2×#102×C151C2212yes—
34C2×#102×C151C2212yes—
35C2×C4×C8×C151C2211yescharacteristic
36#398×C151—22no—
37#391×C151—21no—
38#391×C151C2212yes—
39#389×C151—21no—
40#389×C151C2212yes—
41#384×C151C2211yescharacteristic
42#340×C151C2212yes—
43#336×C151C2212yes—
44#336×C151C2212yes—
45C22×Q8×C151D411yescharacteristic
46C22×Q8×C151C2311yescharacteristic
47C22×Q8×C151C2311yescharacteristic
48C22×D4×C151—21no—
49C22×D4×C151—21no—
50C22×D4×C151C2312yes—
51C23×C4×C151—22no—
52C2×Q16×C151—22no—
53C2×Q16×C151—22no—
54C2×Q16×C151—22no—
55C2×SD16×C151—24no—
56C2×SD16×C151—24no—
57C2×SD16×C151—42no—
58C22×C8×C151C2312yes—
59C22×C8×C151C2311yescharacteristic
60C22×C8×C151C2311yescharacteristic
61#127×C151—22no—
62#127×C151D414yes—
63#124×C151—28no—
64#124×C151—24no—
65#124×C151—24no—
66#123×C151—216no—
67C4×Q8×C151—22no—
68C4×Q8×C151—22no—
69C4×Q8×C151—22no—
70C4×Q8×C151—22no—
71C4×Q8×C151—22no—
72C4×Q8×C151D414yes—
73C4×D4×C151—28no—
74C4×D4×C151—24no—
75C4×D4×C151—24no—
76C2×C4⋊C4×C151—21no—
77C2×C4⋊C4×C151—21no—
78C2×C4⋊C4×C151—21no—
79C2×C4⋊C4×C151—21no—
80C2×C4⋊C4×C151—22no—
81C2×C4⋊C4×C151D411yescharacteristic
82C2×C4⋊C4×C151D412yes—
83C2×C4⋊C4×C151C2312yes—
84C2×C4⋊C4×C151C2311yescharacteristic
85C2×C4⋊C4×C151C2311yescharacteristic
86C2×C22⋊C4×C151—22no—
87C2×C22⋊C4×C151—22no—
88C2×C22⋊C4×C151—22no—
89C2×C42×C151—21no—
90C2×C42×C151—21no—
91C2×C42×C151C2312yes—
92C2×C42×C151C2311yescharacteristic
93#107×C151—22no—
94C4⋊C8×C151—22no—
95#103×C151—22no—
96#103×C151—22no—
97#103×C151—42no—
98#102×C151—24no—
99#102×C151—24no—
100#102×C151—42no—
101C4×C8×C151—22no—
102#95×C151—22no—
103#95×C151—22no—
104#95×C151—22no—
105C24×C151—22no—
106C2×Q8×C151—22no—
107C2×Q8×C151—22no—
108C2×Q8×C151—22no—
109C2×Q8×C151—21no—
110C2×Q8×C151—21no—
111C2×Q8×C151—21no—
112C2×Q8×C151—21no—
113C2×Q8×C151—21no—
114C2×Q8×C151—21no—
115C2×Q8×C151—21no—
116C2×Q8×C151—21no—
117C2×Q8×C151—21no—
118C2×Q8×C151—21no—
119C2×Q8×C151C2×D412yes—
120C2×Q8×C151#4112yes—
121C2×D4×C151—24no—
122C2×D4×C151—24no—
123C2×D4×C151—22no—
124C2×D4×C151—22no—
125C2×D4×C151—22no—
126C2×D4×C151—22no—
127C2×D4×C151—22no—
128C2×D4×C151—42no—
129C2×D4×C151—42no—
130C2×D4×C151—81no—
131C2×D4×C151—81no—
132C2×D4×C151C2×D414yes—
133C22×C4×C151—21no—
134C22×C4×C151—21no—
135C22×C4×C151—21no—
136C22×C4×C151—28no—
137C22×C4×C151—22no—
138C22×C4×C151—21no—
139C22×C4×C151—82no—
140C22×C4×C151—82no—
141C22×C4×C151C2×D412yes—
142C22×C4×C151C2×D412yes—
143C22×C4×C151C2×D411yescharacteristic
144C22×C4×C151C2×D411yescharacteristic
145C22×C4×C151C2411yescharacteristic
146Q16×C151—28no—
147SD16×C151—48no—
148C2×C8×C151—21no—
149C2×C8×C151—21no—
150C2×C8×C151—21no—
151C2×C8×C151—22no—
152C2×C8×C151—22no—
153C2×C8×C151—21no—
154C2×C8×C151—22no—
155C2×C8×C151—21no—
156C2×C8×C151#4112yes—
157C4⋊C4×C151—24no—
158C4⋊C4×C151—22no—
159C4⋊C4×C151—24no—
160C4⋊C4×C151—21no—
161C4⋊C4×C151—21no—
162C4⋊C4×C151—21no—
163C4⋊C4×C151—22no—
164C4⋊C4×C151—22no—
165C4⋊C4×C151—42no—
166C4⋊C4×C151—42no—
167C4⋊C4×C151—81no—
168C4⋊C4×C151—82no—
169C4⋊C4×C151C2×D412yes—
170C22⋊C4×C151—28no—
171C22⋊C4×C151—28no—
172C22⋊C4×C151—28no—
173C42×C151—24no—
174C42×C151—22no—
175C42×C151—22no—
176C42×C151—42no—
177C42×C151C2×D412yes—
178C42×C151C2×D412yes—
179C23×C151—24no—
180C23×C151—42no—
181C23×C151—42no—
182C23×C151—42no—
183C23×C151—42no—
184C23×C151—42no—
185C23×C151—42no—
186C23×C151C22×D411yescharacteristic
187Q8×C151—22no—
188Q8×C151—22no—
189Q8×C151—22no—
190Q8×C151—22no—
191Q8×C151—41no—
192Q8×C151—41no—
193Q8×C151—41no—
194Q8×C151—41no—
195Q8×C151—44no—
196D4×C151—24no—
197D4×C151—24no—
198D4×C151—42no—
199D4×C151—42no—
200D4×C151—48no—
201D4×C151—84no—
202C2×C4×C151—21no—
203C2×C4×C151—21no—
204C2×C4×C151—22no—
205C2×C4×C151—22no—
206C2×C4×C151—22no—
207C2×C4×C151—22no—
208C2×C4×C151—22no—
209C2×C4×C151—22no—
210C2×C4×C151—22no—
211C2×C4×C151—22no—
212C2×C4×C151—22no—
213C2×C4×C151—41no—
214C2×C4×C151—41no—
215C2×C4×C151—41no—
216C2×C4×C151—41no—
217C2×C4×C151—41no—
218C2×C4×C151—41no—
219C2×C4×C151—41no—
220C2×C4×C151—42no—
221C2×C4×C151—42no—
222C2×C4×C151—42no—
223C2×C4×C151—41no—
224C2×C4×C151—41no—
225C2×C4×C151—88no—
226C2×C4×C151#12012yes—
227C2×C4×C151#12012yes—
228C2×C4×C151#13512yes—
229C2×C4×C151#13712yes—
230C2×C4×C151C22×D411yescharacteristic
231C2×C4×C151C22×D411yescharacteristic
232C2×C4×C151C2×#4111yescharacteristic
233C2×C4×C151C2×#4111yescharacteristic
234C2×C4×C151H(5,𝔽2)11yescharacteristic
235C2×C4×C1512−1+411yescharacteristic
236C8×C151—22no—
237C8×C151—41no—
238C8×C151—42no—
239C22×C151—44no—
240C22×C151—44no—
241C22×C151—44no—
242C22×C151—82no—
243C22×C151—82no—
244C22×C151—82no—
245C22×C151—82no—
246C22×C151C2×#12011yescharacteristic
247C22×C151#54811yescharacteristic
248C22×C151#55011yescharacteristic
249C22×C151C2×#13511yescharacteristic
250C22×C151C2×#13711yescharacteristic
251C22×C151#57611yescharacteristic
252C22×C151#57711yescharacteristic
253C4×C151—22no—
254C4×C151—42no—
255C4×C151—42no—
256C4×C151—42no—
257C4×C151—42no—
258C4×C151—42no—
259C4×C151—82no—
260C4×C151—81no—
261C4×C151#45214yes—
262C4×C151#52511yescharacteristic
263C4×C151#53711yescharacteristic
264C4×C151#54611yescharacteristic
265C4×C151#54711yescharacteristic
266C2×C151—84no—
267C2×C151#240711yescharacteristic
268C2×C151C2×#45211yescharacteristic
269C2×C151#301211yescharacteristic
270C2×C151#336511yescharacteristic
271C2×C151#337511yescharacteristic
272C2×C151#339611yescharacteristic
273C2×C151#340011yescharacteristic
274#24190C15111yesmaximal, characteristic, direct product factor, Sylow
275C151#2419011yescharacteristic, direct product factor, Sylow
276C2×#559C2×C15111yescharacteristic
277C2×#460C2×C15111yescharacteristic
278C2×C4×Q16C2×C15111yescharacteristic, complemented
279#2582C2×C15111yescharacteristic, complemented
280#2042C2×C15112yescomplemented
281#2015C2×C15112yescomplemented
282#1984C2×C15111yescharacteristic, complemented
283#1957C2×C15111yescharacteristic
284#1877C2×C15112yescomplemented
285#1862C2×C15112yescomplemented
286#1803C2×C15111yescharacteristic, complemented
287C22×Q16C22×C15111yescharacteristic
288C22×SD16C22×C15112yes—
289#559—24no—
290#559—24no—
291C2×#127C22×C15111yescharacteristic
292C2×#124—21no—
293C2×#124C22×C15112yes—
294C2×#123—22no—
295C2×C4×Q8C22×C15111yescharacteristic
296C2×C4×Q8C22×C15111yescharacteristic
297C2×C4×Q8C22×C15111yescharacteristic
298C2×C4×D4—21no—
299C2×C4×D4C22×C15112yes—
300#460—24no—
301C4×Q16—24no—
302C2×#107C22×C15111yescharacteristic
303C2×C4⋊C8C22×C15111yescharacteristic
304C2×#103C22×C15111yescharacteristic
305C2×#103C22×C15111yescharacteristic
306C2×#103C22×C15112yes—
307C2×#102C22×C15112yes—
308C2×#102C22×C15112yes—
309C2×#102C22×C15112yes—
310C2×C4×C8C22×C15111yescharacteristic
311#398—22no—
312#391—21no—
313#391C22×C15112yes—
314#389—21no—
315#389C22×C15112yes—
316#384C22×C15111yescharacteristic
317#340C22×C15112yes—
318#336C22×C15112yes—
319#336C22×C15112yes—
320C22×Q8D4×C15111yescharacteristic
321C22×Q8C23×C15111yescharacteristic
322C22×Q8C23×C15111yescharacteristic
323C22×D4—21no—
324C22×D4—21no—
325C22×D4C23×C15112yes—
326C23×C4—22no—
327C2×Q16—22no—
328C2×Q16—22no—
329C2×Q16—22no—
330C2×SD16—24no—
331C2×SD16—24no—
332C2×SD16—42no—
333C22×C8C23×C15112yes—
334C22×C8C23×C15111yescharacteristic
335C22×C8C23×C15111yescharacteristic
336#127—22no—
337#127D4×C15114yes—
338#124—28no—
339#124—24no—
340#124—24no—
341#123—216no—
342C4×Q8—22no—
343C4×Q8—22no—
344C4×Q8—22no—
345C4×Q8—22no—
346C4×Q8—22no—
347C4×Q8D4×C15114yes—
348C4×D4—28no—
349C4×D4—24no—
350C4×D4—24no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4D4×C15111yescharacteristic
357C2×C4⋊C4D4×C15112yes—
358C2×C4⋊C4C23×C15111yescharacteristic
359C2×C4⋊C4C23×C15112yes—
360C2×C4⋊C4C23×C15111yescharacteristic
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C42—21no—
365C2×C42—21no—
366C2×C42C23×C15112yes—
367C2×C42C23×C15111yescharacteristic
368#107—22no—
369C4⋊C8—22no—
370#103—22no—
371#103—22no—
372#103—42no—
373#102—24no—
374#102—24no—
375#102—42no—
376C4×C8—22no—
377#95—22no—
378#95—22no—
379#95—22no—
380C24—22no—
381C2×Q8—22no—
382C2×Q8—22no—
383C2×Q8—22no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—21no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—21no—
393C2×Q8—21no—
394C2×Q8C2×D4×C15112yes—
395C2×Q8#41×C15112yes—
396C2×D4—24no—
397C2×D4—24no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—42no—
404C2×D4—42no—
405C2×D4—81no—
406C2×D4—81no—
407C2×D4C2×D4×C15114yes—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—28no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—82no—
415C22×C4—82no—
416C22×C4C2×D4×C15112yes—
417C22×C4C2×D4×C15112yes—
418C22×C4C2×D4×C15111yescharacteristic
419C22×C4C2×D4×C15111yescharacteristic
420C22×C4C24×C15111yescharacteristic
421Q16—28no—
422SD16—48no—
423C2×C8—21no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—22no—
427C2×C8—22no—
428C2×C8—21no—
429C2×C8—22no—
430C2×C8—21no—
431C2×C8#41×C15112yes—
432C4⋊C4—24no—
433C4⋊C4—22no—
434C4⋊C4—24no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—42no—
441C4⋊C4—42no—
442C4⋊C4—81no—
443C4⋊C4—82no—
444C4⋊C4C2×D4×C15112yes—
445C22⋊C4—28no—
446C22⋊C4—28no—
447C22⋊C4—28no—
448C42—24no—
449C42—22no—
450C42—22no—
451C42—42no—
452C42C2×D4×C15112yes—
453C42C2×D4×C15112yes—
454C23—24no—
455C23—42no—
456C23—42no—
457C23—42no—
458C23—42no—
459C23—42no—
460C23—42no—
461C23C22×D4×C15111yescharacteristic
462Q8—22no—
463Q8—22no—
464Q8—22no—
465Q8—22no—
466Q8—44no—
467Q8—41no—
468Q8—41no—
469Q8—41no—
470Q8—41no—
471D4—24no—
472D4—24no—
473D4—48no—
474D4—42no—
475D4—42no—
476D4—84no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—88no—
501C2×C4#120×C15112yes—
502C2×C4#120×C15112yes—
503C2×C4#135×C15112yes—
504C2×C4#137×C15112yes—
505C2×C4C22×D4×C15111yescharacteristic
506C2×C4C22×D4×C15111yescharacteristic
507C2×C4C2×#41×C15111yescharacteristic
508C2×C4C2×#41×C15111yescharacteristic
509C2×C4H(5,𝔽2)×C15111yescharacteristic
510C2×C42−1+4×C15111yescharacteristic
511C8—22no—
512C8—41no—
513C8—42no—
514C22—44no—
515C22—44no—
516C22—44no—
517C22—82no—
518C22—82no—
519C22—82no—
520C22—82no—
521C22C2×#120×C15111yescharacteristic
522C22#548×C15111yescharacteristic
523C22#550×C15111yescharacteristic
524C22C2×#135×C15111yescharacteristic
525C22C2×#137×C15111yescharacteristic
526C22#576×C15111yescharacteristic
527C22#577×C15111yescharacteristic
528C4—22no—
529C4—42no—
530C4—42no—
531C4—42no—
532C4—42no—
533C4—42no—
534C4—82no—
535C4—81no—
536C4#452×C15114yes—
537C4#525×C15111yescharacteristic
538C4#537×C15111yescharacteristic
539C4#546×C15111yescharacteristic
540C4#547×C15111yescharacteristic
541C2—84no—
542C2#2407×C15111yescharacteristic
543C2C2×#452×C15111yescharacteristic
544C2#3012×C15111yescharacteristic
545C2#3365×C15111yescharacteristic
546C2#3375×C15111yescharacteristic
547C2#3396×C15111yescharacteristic
548C2#3400×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#127×C151C22
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
3. C2×C4×Q16×C151C2semidirect
4. #2582×C151C2semidirect
5. #2042×C151C2semidirect
6. #2015×C151C2semidirect
7. #1984×C151C2semidirect
9. #1877×C151C2semidirect
10. #1862×C151C2semidirect
11. #1803×C151C2semidirect
274. #24190C151direct (N × H)
275. C151#24190direct (N × H)
278. C2×C4×Q16C2×C151semidirect
279. #2582C2×C151semidirect
280. #2042C2×C151semidirect
281. #2015C2×C151semidirect
282. #1984C2×C151semidirect
284. #1877C2×C151semidirect
285. #1862C2×C151semidirect
286. #1803C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#559×C1512
C2×#460×C1512
C2×C4×Q16×C1512
#2582×C1512
#2042×C1512
#2015×C1512
#1984×C1512
#1957×C1512
#1877×C1512
#1862×C1512
#1803×C1512
#24190151