Finite Group Databasebeta

← C151×#25947 #50330872

Subgroups — C151×#25947 #50330872

Order 38656.

1490 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
1#3501×C151C211yesmaximal, characteristic, complemented
2#2435×C151C212yesmaximal, complemented
3#2408×C151C211yesmaximal, characteristic
4#2029×C151C214yesmaximal, complemented
5#1996×C151C212yesmaximal, complemented
6#1889×C151C214yesmaximal, complemented
7C4×#99×C151C211yesmaximal, characteristic, complemented
8C23×D4×C151C2211yescharacteristic
9#554×C151—22no—
10#554×C151—24no—
11D4×Q8×C151—22no—
12#544×C151—21no—
13#543×C151—21no—
14#543×C151C2212yes—
15#533×C151—21no—
16C2×#124×C151—22no—
17C2×C22⋊Q8×C151—21no—
18C2×C22⋊Q8×C151C2212yes—
19C2×#121×C151—21no—
20C2×#120×C151C2212yes—
21#518×C151C2212yes—
22C2×C4×D4×C151C2211yescharacteristic
23C2×#99×C151C2212yes—
24#394×C151—21no—
25#394×C151—24no—
26#392×C151—21no—
27#390×C151—22no—
28#390×C151—21no—
29#380×C151C2211yescharacteristic
30#379×C151C2218yes—
31#379×C151C2212yes—
32C4×C22⋊C4×C151C2212yes—
33#342×C151C2218yes—
34#342×C151C2212yes—
35C25×C151C2312yes—
36C22×Q8×C151—21no—
37C22×Q8×C151D412yescomplemented
38C22×D4×C151—21no—
39C22×D4×C151—22no—
40C22×D4×C151—21no—
41C22×D4×C151—22no—
42C22×D4×C151—22no—
43C22×D4×C151—44no—
44C22×D4×C151C2311yescharacteristic
45C23×C4×C151D411yescharacteristic
46C23×C4×C151C2311yescharacteristic
47C4⋊Q8×C151—21no—
48C4⋊Q8×C151—21no—
49C4⋊Q8×C151—24no—
50#125×C151—22no—
51#125×C151—24no—
52#124×C151—48no—
53C22⋊Q8×C151—22no—
54C22⋊Q8×C151—22no—
55C22⋊Q8×C151—24no—
56C22⋊Q8×C151—24no—
57C22⋊Q8×C151—22no—
58C22⋊Q8×C151—22no—
59C22⋊Q8×C151—22no—
60C22⋊Q8×C151—22no—
61C22⋊Q8×C151—22no—
62C22⋊Q8×C151—22no—
63C22⋊Q8×C151—24no—
64C22⋊Q8×C151—24no—
65#121×C151—44no—
66#120×C151—28no—
67C4×Q8×C151—22no—
68C4×Q8×C151—22no—
69C4×D4×C151—22no—
70C4×D4×C151—22no—
71C4×D4×C151—24no—
72C4×D4×C151—24no—
73#117×C151—22no—
74C2×C4⋊C4×C151—21no—
75C2×C4⋊C4×C151—22no—
76C2×C4⋊C4×C151—21no—
77C2×C4⋊C4×C151D411yescharacteristic
78C2×C4⋊C4×C151D412yescomplemented
79C2×C4⋊C4×C151D414yescomplemented
80C2×C22⋊C4×C151—22no—
81C2×C22⋊C4×C151—28no—
82C2×C22⋊C4×C151—22no—
83C2×C22⋊C4×C151—22no—
84C2×C22⋊C4×C151—28no—
85C2×C22⋊C4×C151—22no—
86C2×C22⋊C4×C151D411yescharacteristic
87C2×C22⋊C4×C151C2312yes—
88C2×C22⋊C4×C151C2314yes—
89C2×C22⋊C4×C151C2311yescharacteristic
90C2×C22⋊C4×C151C2314yes—
91C2×C42×C151—22no—
92C2×C42×C151D411yescharacteristic
93#99×C151—24no—
94#95×C151—22no—
95#95×C151—21no—
96C24×C151—24no—
97C24×C151—22no—
98C24×C151—24no—
99C24×C151—24no—
100C24×C151—44no—
101C24×C151—82no—
102C24×C151C2×D411yescharacteristic
103C24×C151C2411yescharacteristic
104C2×Q8×C151—22no—
105C2×Q8×C151—22no—
106C2×Q8×C151—22no—
107C2×Q8×C151—22no—
108C2×Q8×C151—44no—
109C2×Q8×C151—82no—
110C2×D4×C151—22no—
111C2×D4×C151—22no—
112C2×D4×C151—24no—
113C2×D4×C151—28no—
114C2×D4×C151—44no—
115C2×D4×C151—42no—
116C2×D4×C151—48no—
117C2×D4×C151—44no—
118C2×D4×C151—44no—
119C2×D4×C151—44no—
120C2×D4×C151—42no—
121C2×D4×C151—41no—
122C2×D4×C151—41no—
123C2×D4×C151—82no—
124C2×D4×C151#4114yes—
125C22×C4×C151—22no—
126C22×C4×C151—22no—
127C22×C4×C151—21no—
128C22×C4×C151—21no—
129C22×C4×C151—24no—
130C22×C4×C151—22no—
131C22×C4×C151—42no—
132C22×C4×C151—42no—
133C22×C4×C151C2×D412yes—
134C22×C4×C151C2×D411yescharacteristic
135C22×C4×C151C2×D411yescharacteristic
136C22×C4×C151C2×D411yescharacteristic
137C22×C4×C151C2×D411yescharacteristic
138C22×C4×C151C2×D414yes—
139C22×C4×C151C2×D414yes—
140C22×C4×C151C2×D411yescharacteristic
141C22×C4×C151C2×D412yes—
142C4⋊C4×C151—22no—
143C4⋊C4×C151—24no—
144C4⋊C4×C151—22no—
145C4⋊C4×C151—22no—
146C4⋊C4×C151—24no—
147C4⋊C4×C151—22no—
148C4⋊C4×C151—24no—
149C4⋊C4×C151—22no—
150C4⋊C4×C151—22no—
151C4⋊C4×C151—22no—
152C4⋊C4×C151—24no—
153C4⋊C4×C151—42no—
154C22⋊C4×C151—24no—
155C22⋊C4×C151—24no—
156C22⋊C4×C151—24no—
157C22⋊C4×C151—22no—
158C22⋊C4×C151—22no—
159C22⋊C4×C151—24no—
160C22⋊C4×C151—24no—
161C22⋊C4×C151—24no—
162C22⋊C4×C151—44no—
163C22⋊C4×C151—416no—
164C22⋊C4×C151—44no—
165C22⋊C4×C151—88no—
166C22⋊C4×C151—82no—
167C42×C151—24no—
168C42×C151—21no—
169C42×C151—21no—
170C42×C151—44no—
171C23×C151—21no—
172C23×C151—21no—
173C23×C151—28no—
174C23×C151—24no—
175C23×C151—41no—
176C23×C151—41no—
177C23×C151—41no—
178C23×C151—41no—
179C23×C151—44no—
180C23×C151—42no—
181C23×C151—48no—
182C23×C151—42no—
183C23×C151—42no—
184C23×C151—42no—
185C23×C151—42no—
186C23×C151—42no—
187C23×C151—48no—
188C23×C151—88no—
189C23×C151—88no—
190C23×C151#12412yescomplemented
191C23×C151C22×D411yescharacteristic
192C23×C151C22×D412yes—
193C23×C151C2×#4112yes—
194C23×C1512−1+412yes—
195Q8×C151—44no—
196Q8×C151—82no—
197Q8×C151—82no—
198Q8×C151—82no—
199D4×C151—28no—
200D4×C151—44no—
201D4×C151—48no—
202D4×C151—44no—
203D4×C151—88no—
204C2×C4×C151—21no—
205C2×C4×C151—21no—
206C2×C4×C151—24no—
207C2×C4×C151—22no—
208C2×C4×C151—24no—
209C2×C4×C151—21no—
210C2×C4×C151—21no—
211C2×C4×C151—24no—
212C2×C4×C151—42no—
213C2×C4×C151—41no—
214C2×C4×C151—42no—
215C2×C4×C151—44no—
216C2×C4×C151—41no—
217C2×C4×C151—44no—
218C2×C4×C151—41no—
219C2×C4×C151—44no—
220C2×C4×C151—42no—
221C2×C4×C151—44no—
222C2×C4×C151—42no—
223C2×C4×C151—42no—
224C2×C4×C151—44no—
225C2×C4×C151—81no—
226C2×C4×C151—82no—
227C2×C4×C151—82no—
228C2×C4×C151#12012yes—
229C2×C4×C151#12011yescharacteristic
230C2×C4×C151#12011yescharacteristic
231C2×C4×C151#12412yescomplemented
232C22×C151—22no—
233C22×C151—21no—
234C22×C151—22no—
235C22×C151—21no—
236C22×C151—22no—
237C22×C151—42no—
238C22×C151—42no—
239C22×C151—42no—
240C22×C151—44no—
241C22×C151—416no—
242C22×C151—44no—
243C22×C151—41no—
244C22×C151—41no—
245C22×C151—44no—
246C22×C151—81no—
247C22×C151—82no—
248C22×C151—88no—
249C22×C151—82no—
250C22×C151—82no—
251C22×C151—82no—
252C22×C151C2×#12011yescharacteristic
253C22×C151C2×#12411yescharacteristic
254C22×C151#53611yescharacteristic
255C22×C151#54814yes—
256C4×C151—22no—
257C4×C151—21no—
258C4×C151—22no—
259C4×C151—41no—
260C4×C151—44no—
261C4×C151—44no—
262C4×C151—41no—
263C4×C151—84no—
264C4×C151—82no—
265C4×C151B(4,𝔽2)12yes—
266C2×C151—21no—
267C2×C151—24no—
268C2×C151—21no—
269C2×C151—42no—
270C2×C151—84no—
271C2×C151#243611yescharacteristic
272C2×C151C2×B(4,𝔽2)11yescharacteristic
273C2×C151#302711yescharacteristic
274#25947C15111yesmaximal, characteristic, direct product factor, Sylow
275C151#2594711yescharacteristic, direct product factor, Sylow
276#3501C2×C15111yescharacteristic, complemented
277#2435C2×C15112yescomplemented
278#2408C2×C15111yescharacteristic
279#2029C2×C15114yescomplemented
280#1996C2×C15112yescomplemented
281#1889C2×C15114yescomplemented
282C4×#99C2×C15111yescharacteristic, complemented
283C23×D4C22×C15111yescharacteristic
284#554—22no—
285#554—24no—
286D4×Q8—22no—
287#544—21no—
288#543—21no—
289#543C22×C15112yes—
290#533—21no—
291C2×#124—22no—
292C2×C22⋊Q8—21no—
293C2×C22⋊Q8C22×C15112yes—
294C2×#121—21no—
295C2×#120C22×C15112yes—
296#518C22×C15112yes—
297C2×C4×D4C22×C15111yescharacteristic
298C2×#99C22×C15112yes—
299#394—21no—
300#394—24no—
301#392—21no—
302#390—22no—
303#390—21no—
304#380C22×C15111yescharacteristic
305#379C22×C15118yes—
306#379C22×C15112yes—
307C4×C22⋊C4C22×C15112yes—
308#342C22×C15118yes—
309#342C22×C15112yes—
310C25C23×C15112yes—
311C22×Q8—21no—
312C22×Q8D4×C15112yescomplemented
313C22×D4—22no—
314C22×D4—21no—
315C22×D4—22no—
316C22×D4—21no—
317C22×D4—22no—
318C22×D4—44no—
319C22×D4C23×C15111yescharacteristic
320C23×C4D4×C15111yescharacteristic
321C23×C4C23×C15111yescharacteristic
322C4⋊Q8—21no—
323C4⋊Q8—21no—
324C4⋊Q8—24no—
325#125—22no—
326#125—24no—
327#124—48no—
328C22⋊Q8—22no—
329C22⋊Q8—22no—
330C22⋊Q8—24no—
331C22⋊Q8—24no—
332C22⋊Q8—22no—
333C22⋊Q8—22no—
334C22⋊Q8—22no—
335C22⋊Q8—22no—
336C22⋊Q8—22no—
337C22⋊Q8—22no—
338C22⋊Q8—24no—
339C22⋊Q8—24no—
340#121—44no—
341#120—28no—
342C4×Q8—22no—
343C4×Q8—22no—
344C4×D4—22no—
345C4×D4—22no—
346C4×D4—24no—
347C4×D4—24no—
348#117—22no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4D4×C15111yescharacteristic
353C2×C4⋊C4D4×C15112yescomplemented
354C2×C4⋊C4D4×C15114yescomplemented
355C2×C22⋊C4—22no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4D4×C15111yescharacteristic
362C2×C22⋊C4C23×C15112yes—
363C2×C22⋊C4C23×C15114yes—
364C2×C22⋊C4C23×C15111yescharacteristic
365C2×C22⋊C4C23×C15114yes—
366C2×C42—22no—
367C2×C42D4×C15111yescharacteristic
368#99—24no—
369#95—22no—
370#95—21no—
371C24—24no—
372C24—22no—
373C24—24no—
374C24—24no—
375C24—44no—
376C24—82no—
377C24C2×D4×C15111yescharacteristic
378C24C24×C15111yescharacteristic
379C2×Q8—22no—
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8—22no—
383C2×Q8—44no—
384C2×Q8—82no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—24no—
388C2×D4—28no—
389C2×D4—44no—
390C2×D4—42no—
391C2×D4—48no—
392C2×D4—44no—
393C2×D4—44no—
394C2×D4—44no—
395C2×D4—41no—
396C2×D4—42no—
397C2×D4—41no—
398C2×D4—82no—
399C2×D4#41×C15114yes—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—24no—
405C22×C4—22no—
406C22×C4—42no—
407C22×C4—42no—
408C22×C4C2×D4×C15112yes—
409C22×C4C2×D4×C15111yescharacteristic
410C22×C4C2×D4×C15111yescharacteristic
411C22×C4C2×D4×C15111yescharacteristic
412C22×C4C2×D4×C15111yescharacteristic
413C22×C4C2×D4×C15114yes—
414C22×C4C2×D4×C15114yes—
415C22×C4C2×D4×C15111yescharacteristic
416C22×C4C2×D4×C15112yes—
417C4⋊C4—22no—
418C4⋊C4—24no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—24no—
422C4⋊C4—22no—
423C4⋊C4—24no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—24no—
428C4⋊C4—42no—
429C22⋊C4—24no—
430C22⋊C4—24no—
431C22⋊C4—22no—
432C22⋊C4—24no—
433C22⋊C4—22no—
434C22⋊C4—24no—
435C22⋊C4—24no—
436C22⋊C4—24no—
437C22⋊C4—44no—
438C22⋊C4—416no—
439C22⋊C4—44no—
440C22⋊C4—88no—
441C22⋊C4—82no—
442C42—24no—
443C42—21no—
444C42—21no—
445C42—44no—
446C23—21no—
447C23—21no—
448C23—28no—
449C23—24no—
450C23—41no—
451C23—41no—
452C23—41no—
453C23—41no—
454C23—48no—
455C23—42no—
456C23—44no—
457C23—42no—
458C23—42no—
459C23—42no—
460C23—42no—
461C23—42no—
462C23—48no—
463C23—88no—
464C23—88no—
465C23#124×C15112yescomplemented
466C23C22×D4×C15111yescharacteristic
467C23C22×D4×C15112yes—
468C23C2×#41×C15112yes—
469C232−1+4×C15112yes—
470Q8—44no—
471Q8—82no—
472Q8—82no—
473Q8—82no—
474D4—28no—
475D4—44no—
476D4—48no—
477D4—44no—
478D4—88no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—24no—
482C2×C4—22no—
483C2×C4—21no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—21no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4—44no—
492C2×C4—44no—
493C2×C4—41no—
494C2×C4—44no—
495C2×C4—42no—
496C2×C4—44no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—44no—
500C2×C4—81no—
501C2×C4—82no—
502C2×C4—82no—
503C2×C4#120×C15111yescharacteristic
504C2×C4#120×C15112yes—
505C2×C4#120×C15111yescharacteristic
506C2×C4#124×C15112yescomplemented
507C22—22no—
508C22—21no—
509C22—22no—
510C22—21no—
511C22—22no—
512C22—42no—
513C22—42no—
514C22—42no—
515C22—44no—
516C22—416no—
517C22—44no—
518C22—41no—
519C22—41no—
520C22—44no—
521C22—81no—
522C22—82no—
523C22—88no—
524C22—82no—
525C22—82no—
526C22—82no—
527C22C2×#120×C15111yescharacteristic
528C22C2×#124×C15111yescharacteristic
529C22#536×C15111yescharacteristic
530C22#548×C15114yes—
531C4—22no—
532C4—21no—
533C4—22no—
534C4—41no—
535C4—44no—
536C4—44no—
537C4—41no—
538C4—82no—
539C4—84no—
540C4B(4,𝔽2)×C15112yes—
541C2—21no—
542C2—24no—
543C2—21no—
544C2—42no—
545C2—84no—
546C2#2436×C15111yescharacteristic
547C2C2×B(4,𝔽2)×C15111yescharacteristic
548C2#3027×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC24C24×C151
prime radical#2408×C151C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3501×C151C2semidirect
2. #2435×C151C2semidirect
4. #2029×C151C2semidirect
5. #1996×C151C2semidirect
6. #1889×C151C2semidirect
7. C4×#99×C151C2semidirect
37. C22×Q8×C151D4semidirect
78. C2×C4⋊C4×C151D4semidirect
79. C2×C4⋊C4×C151D4semidirect
190. C23×C151#124semidirect
231. C2×C4×C151#124semidirect
274. #25947C151direct (N × H)
275. C151#25947direct (N × H)
276. #3501C2×C151semidirect
277. #2435C2×C151semidirect
279. #2029C2×C151semidirect
280. #1996C2×C151semidirect
281. #1889C2×C151semidirect
282. C4×#99C2×C151semidirect
312. C22×Q8D4×C151semidirect
353. C2×C4⋊C4D4×C151semidirect
354. C2×C4⋊C4D4×C151semidirect
465. C23#124×C151semidirect
506. C2×C4#124×C151semidirect

Maximal subgroups

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

subgroupindex
#3501×C1512
#2435×C1512
#2408×C1512
#2029×C1512
#1996×C1512
#1889×C1512
C4×#99×C1512
#25947151