Finite Group Databasebeta

← C151×#18968 #50323893

Subgroups — C151×#18968 #50323893

Order 38656.

874 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3547×C151C211yesmaximal, characteristic
2#3239×C151C211yesmaximal, characteristic, complemented
3#3229×C151C211yesmaximal, characteristic, complemented
4#3206×C151C211yesmaximal, characteristic, complemented
5#1654×C151C212yesmaximal, complemented
6#1651×C151C212yesmaximal, complemented
7#1646×C151C212yesmaximal, complemented
8#1643×C151C212yesmaximal, complemented
9#1554×C151C211yesmaximal, characteristic, complemented
10#1496×C151C211yesmaximal, characteristic, complemented
11#1482×C151C211yesmaximal, characteristic, complemented
12#562×C151—22no—
13#555×C151—21no—
14#555×C151C2211yescharacteristic
15#554×C151C2211yescharacteristic
16#553×C151—21no—
17#552×C151—21no—
18D4×Q8×C151C2211yescharacteristic
19#548×C151—21no—
20#547×C151C2211yescharacteristic
21#544×C151—21no—
22#542×C151—22no—
23#540×C151—21no—
24#537×C151—21no—
25#536×C151—21no—
26#533×C151C2211yescharacteristic
27#532×C151C2211yescharacteristic
28C2×C4⋊Q8×C151C2211yescharacteristic
29#529×C151C2211yescharacteristic
30#501×C151—21no—
31#498×C151C2212yes—
32#492×C151—21no—
33#489×C151—21no—
34#487×C151—21no—
35#487×C151C2212yes—
36#484×C151—21no—
37#483×C151—22no—
38#481×C151—21no—
39#475×C151—22no—
40#475×C151C2212yes—
41#474×C151C2212yes—
42#461×C151C2212yes—
43#461×C151C2212yes—
44#448×C151—21no—
45#448×C151—21no—
46#432×C151C2211yescharacteristic
47#431×C151C2211yescharacteristic
48#431×C151C2211yescharacteristic
49#333×C151C2212yes—
50#332×C151C2212yes—
51Q8⋊C8×C151C2212yes—
52D4⋊C8×C151C2212yes—
53D4⋊C8×C151C2212yes—
54D4⋊C8×C151C2212yes—
55C2×#41×C151—21no—
56C2×#41×C151—21no—
57C22×Q8×C151—21no—
58C22×Q8×C151—21no—
59C2×SD16×C151—22no—
60C2×SD16×C151—22no—
61C4⋊Q8×C151—22no—
62C4⋊Q8×C151—21no—
63C4⋊Q8×C151—21no—
64C4⋊Q8×C151—21no—
65C4⋊Q8×C151—21no—
66C4⋊Q8×C151D411yescharacteristic
67C4⋊Q8×C151C2312yes—
68C4⋊Q8×C151C2311yescharacteristic
69C4⋊Q8×C151C2311yescharacteristic
70#127×C151D411yescharacteristic
71#126×C151—22no—
72#126×C151—21no—
73#125×C151—22no—
74#125×C151—21no—
75#125×C151—21no—
76#125×C151D411yescharacteristic
77#124×C151—22no—
78#124×C151—22no—
79#124×C151—21no—
80#124×C151—22no—
81#124×C151D411yescharacteristic
82#123×C151—22no—
83#123×C151—22no—
84#123×C151—22no—
85#123×C151—21no—
86#123×C151—22no—
87C22⋊Q8×C151—22no—
88C22⋊Q8×C151—22no—
89C22⋊Q8×C151—21no—
90C22⋊Q8×C151—21no—
91C22⋊Q8×C151—21no—
92C22⋊Q8×C151—22no—
93C22⋊Q8×C151—21no—
94C22⋊Q8×C151—22no—
95C22⋊Q8×C151D412yes—
96C22⋊Q8×C151D411yescharacteristic
97#121×C151—22no—
98#121×C151—22no—
99#121×C151—22no—
100#121×C151—22no—
101#121×C151—21no—
102#121×C151—21no—
103#121×C151—21no—
104#121×C151—21no—
105#121×C151D411yescharacteristic
106#121×C151D411yescharacteristic
107#121×C151D411yescharacteristic
108C4×Q8×C151—21no—
109C4×Q8×C151D412yes—
110C4×Q8×C151C2311yescharacteristic
111C4×D4×C151—22no—
112C4×D4×C151—21no—
113C4×D4×C151—21no—
114C4×D4×C151—21no—
115C4×D4×C151—21no—
116C4×D4×C151C2311yescharacteristic
117C4×D4×C151C2311yescharacteristic
118C4×D4×C151C2311yescharacteristic
119#117×C151—22no—
120#117×C151—21no—
121#117×C151—21no—
122#117×C151—21no—
123#117×C151—21no—
124C2×C4⋊C4×C151—21no—
125C2×C4⋊C4×C151—21no—
126C2×C4⋊C4×C151—21no—
127C2×C4⋊C4×C151—21no—
128C2×C42×C151C2311yescharacteristic
129#107×C151—22no—
130#106×C151—24no—
131#106×C151—22no—
132C4⋊C8×C151—21no—
133C4⋊C8×C151C2312yes—
134C4⋊C8×C151C2312yes—
135#103×C151—22no—
136#103×C151—22no—
137#103×C151—24no—
138#103×C151—22no—
139#102×C151—22no—
140C22⋊C8×C151—21no—
141C22⋊C8×C151—21no—
142C22⋊C8×C151—21no—
143#97×C151—21no—
144C4×C8×C151—21no—
145C4×C8×C151C2312yes—
146#41×C151—82no—
147#41×C151—82no—
148C2×Q8×C151—22no—
149C2×Q8×C151—21no—
150C2×Q8×C151—21no—
151C2×Q8×C151—22no—
152C2×Q8×C151—41no—
153C2×Q8×C151—82no—
154C2×Q8×C151—82no—
155C2×Q8×C151C2×D411yescharacteristic
156C2×Q8×C151C2×D412yes—
157C2×D4×C151—22no—
158C2×D4×C151—22no—
159C2×D4×C151—21no—
160C2×D4×C151—21no—
161C2×D4×C151—21no—
162C2×D4×C151—21no—
163C2×D4×C151—21no—
164C2×D4×C151C2×D411yescharacteristic
165C2×D4×C151C2×D411yescharacteristic
166C2×D4×C151C2×D411yescharacteristic
167C22×C4×C151—22no—
168C22×C4×C151—22no—
169C22×C4×C151—22no—
170C22×C4×C151—21no—
171C22×C4×C151—21no—
172C22×C4×C151—21no—
173C22×C4×C151—41no—
174C22×C4×C151C2×D411yescharacteristic
175C22×C4×C151C2×D411yescharacteristic
176C22×C4×C151C2×D411yescharacteristic
177SD16×C151—82no—
178SD16×C151—82no—
179C2×C8×C151—22no—
180C2×C8×C151—22no—
181C2×C8×C151—22no—
182C4⋊C4×C151—22no—
183C4⋊C4×C151—22no—
184C4⋊C4×C151—22no—
185C4⋊C4×C151—22no—
186C4⋊C4×C151—21no—
187C4⋊C4×C151—21no—
188C4⋊C4×C151—21no—
189C4⋊C4×C151—21no—
190C4⋊C4×C151—22no—
191C4⋊C4×C151—22no—
192C4⋊C4×C151—21no—
193C4⋊C4×C151—21no—
194C4⋊C4×C151—21no—
195C4⋊C4×C151—21no—
196C4⋊C4×C151—22no—
197C4⋊C4×C151—22no—
198C4⋊C4×C151—41no—
199C4⋊C4×C151—41no—
200C4⋊C4×C151C2×D411yescharacteristic
201C4⋊C4×C151C2×D411yescharacteristic
202C4⋊C4×C151C2×D411yescharacteristic
203C4⋊C4×C151C2×D412yes—
204C4⋊C4×C151C2×D411yescharacteristic
205C22⋊C4×C151—22no—
206C22⋊C4×C151—22no—
207C22⋊C4×C151—22no—
208C22⋊C4×C151—22no—
209C22⋊C4×C151—22no—
210C22⋊C4×C151—22no—
211C22⋊C4×C151—21no—
212C22⋊C4×C151—21no—
213C22⋊C4×C151—21no—
214C22⋊C4×C151—21no—
215C22⋊C4×C151—21no—
216C22⋊C4×C151—21no—
217C22⋊C4×C151—21no—
218C22⋊C4×C151—21no—
219C22⋊C4×C151—21no—
220C42×C151—22no—
221C42×C151—22no—
222C42×C151—21no—
223C42×C151C2×D411yescharacteristic
224C42×C151C2×D411yescharacteristic
225C42×C151C2×D411yescharacteristic
226C42×C151C2411yescharacteristic
227C23×C151—21no—
228C23×C151—21no—
229C23×C151—21no—
230C23×C151#12011yescharacteristic
231Q8×C151—22no—
232Q8×C151—42no—
233Q8×C151—42no—
234Q8×C151—42no—
235Q8×C151—42no—
236Q8×C151—81no—
237Q8×C151—82no—
238Q8×C151—82no—
239D4×C151—22no—
240D4×C151—22no—
241D4×C151—22no—
242D4×C151—81no—
243D4×C151—81no—
244D4×C151—81no—
245D4×C151—81no—
246D4×C151—81no—
247D4×C151—82no—
248D4×C151—82no—
249C2×C4×C151—22no—
250C2×C4×C151—22no—
251C2×C4×C151—21no—
252C2×C4×C151—21no—
253C2×C4×C151—22no—
254C2×C4×C151—21no—
255C2×C4×C151—22no—
256C2×C4×C151—21no—
257C2×C4×C151—21no—
258C2×C4×C151—41no—
259C2×C4×C151—42no—
260C2×C4×C151—42no—
261C2×C4×C151—42no—
262C2×C4×C151—42no—
263C2×C4×C151—82no—
264C2×C4×C151—82no—
265C2×C4×C151—82no—
266C2×C4×C151—82no—
267C2×C4×C151#12011yescharacteristic
268C2×C4×C151#12011yescharacteristic
269C2×C4×C151#12011yescharacteristic
270C2×C4×C151C22×D411yescharacteristic
271C2×C4×C151C22×D411yescharacteristic
272C2×C4×C151C22×D411yescharacteristic
273C8×C151—42no—
274C8×C151—42no—
275C8×C151—42no—
276C22×C151—21no—
277C22×C151—21no—
278C22×C151—21no—
279C22×C151—41no—
280C22×C151—41no—
281C22×C151—41no—
282C22×C151—41no—
283C22×C151—41no—
284C22×C151—41no—
285C22×C151—41no—
286C22×C151—41no—
287C22×C151—41no—
288C22×C151C2×#12011yescharacteristic
289C4×C151—21no—
290C4×C151—21no—
291C4×C151—21no—
292C4×C151—21no—
293C4×C151—41no—
294C4×C151—41no—
295C4×C151—42no—
296C4×C151—41no—
297C4×C151—41no—
298C4×C151—41no—
299C4×C151—42no—
300C4×C151—82no—
301C4×C151#57712yes—
302C4×C151#57712yes—
303C2×C151—41no—
304C2×C151—81no—
305C2×C151—81no—
306C2×C151—81no—
307C2×C151#300911yescharacteristic
308C2×C151#301011yescharacteristic
309C2×C151#302211yescharacteristic
310#18968C15111yesmaximal, characteristic, direct product factor, Sylow
311C151#1896811yescharacteristic, direct product factor, Sylow
312#3547C2×C15111yescharacteristic
313#3239C2×C15111yescharacteristic, complemented
314#3229C2×C15111yescharacteristic, complemented
315#3206C2×C15111yescharacteristic, complemented
316#1654C2×C15112yescomplemented
317#1651C2×C15112yescomplemented
318#1646C2×C15112yescomplemented
319#1643C2×C15112yescomplemented
320#1554C2×C15111yescharacteristic, complemented
321#1496C2×C15111yescharacteristic, complemented
322#1482C2×C15111yescharacteristic, complemented
323#562—22no—
324#555—21no—
325#555C22×C15111yescharacteristic
326#554C22×C15111yescharacteristic
327#553—21no—
328#552—21no—
329D4×Q8C22×C15111yescharacteristic
330#548—21no—
331#547C22×C15111yescharacteristic
332#544—21no—
333#542—22no—
334#540—21no—
335#537—21no—
336#536—21no—
337#533C22×C15111yescharacteristic
338#532C22×C15111yescharacteristic
339C2×C4⋊Q8C22×C15111yescharacteristic
340#529C22×C15111yescharacteristic
341#501—21no—
342#498C22×C15112yes—
343#492—21no—
344#489—21no—
345#487—21no—
346#487C22×C15112yes—
347#484—21no—
348#483—22no—
349#481—21no—
350#475—22no—
351#475C22×C15112yes—
352#474C22×C15112yes—
353#461C22×C15112yes—
354#461C22×C15112yes—
355#448—21no—
356#448—21no—
357#432C22×C15111yescharacteristic
358#431C22×C15111yescharacteristic
359#431C22×C15111yescharacteristic
360#333C22×C15112yes—
361#332C22×C15112yes—
362Q8⋊C8C22×C15112yes—
363D4⋊C8C22×C15112yes—
364D4⋊C8C22×C15112yes—
365D4⋊C8C22×C15112yes—
366C2×#41—21no—
367C2×#41—21no—
368C22×Q8—21no—
369C22×Q8—21no—
370C2×SD16—22no—
371C2×SD16—22no—
372C4⋊Q8—22no—
373C4⋊Q8—21no—
374C4⋊Q8—21no—
375C4⋊Q8—21no—
376C4⋊Q8—21no—
377C4⋊Q8D4×C15111yescharacteristic
378C4⋊Q8C23×C15112yes—
379C4⋊Q8C23×C15111yescharacteristic
380C4⋊Q8C23×C15111yescharacteristic
381#127D4×C15111yescharacteristic
382#126—22no—
383#126—21no—
384#125—22no—
385#125—21no—
386#125—21no—
387#125D4×C15111yescharacteristic
388#124—22no—
389#124—22no—
390#124—22no—
391#124—21no—
392#124D4×C15111yescharacteristic
393#123—22no—
394#123—22no—
395#123—22no—
396#123—21no—
397#123—22no—
398C22⋊Q8—22no—
399C22⋊Q8—22no—
400C22⋊Q8—21no—
401C22⋊Q8—22no—
402C22⋊Q8—21no—
403C22⋊Q8—21no—
404C22⋊Q8—21no—
405C22⋊Q8—22no—
406C22⋊Q8D4×C15111yescharacteristic
407C22⋊Q8D4×C15112yes—
408#121—22no—
409#121—22no—
410#121—22no—
411#121—22no—
412#121—21no—
413#121—21no—
414#121—21no—
415#121—21no—
416#121D4×C15111yescharacteristic
417#121D4×C15111yescharacteristic
418#121D4×C15111yescharacteristic
419C4×Q8—21no—
420C4×Q8D4×C15112yes—
421C4×Q8C23×C15111yescharacteristic
422C4×D4—22no—
423C4×D4—21no—
424C4×D4—21no—
425C4×D4—21no—
426C4×D4—21no—
427C4×D4C23×C15111yescharacteristic
428C4×D4C23×C15111yescharacteristic
429C4×D4C23×C15111yescharacteristic
430#117—22no—
431#117—21no—
432#117—21no—
433#117—21no—
434#117—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C42C23×C15111yescharacteristic
440#107—22no—
441#106—24no—
442#106—22no—
443C4⋊C8—21no—
444C4⋊C8C23×C15112yes—
445C4⋊C8C23×C15112yes—
446#103—24no—
447#103—22no—
448#103—22no—
449#103—22no—
450#102—22no—
451C22⋊C8—21no—
452C22⋊C8—21no—
453C22⋊C8—21no—
454#97—21no—
455C4×C8—21no—
456C4×C8C23×C15112yes—
457#41—82no—
458#41—82no—
459C2×Q8—22no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—22no—
463C2×Q8—41no—
464C2×Q8—82no—
465C2×Q8—82no—
466C2×Q8C2×D4×C15111yescharacteristic
467C2×Q8C2×D4×C15112yes—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4C2×D4×C15111yescharacteristic
476C2×D4C2×D4×C15111yescharacteristic
477C2×D4C2×D4×C15111yescharacteristic
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—41no—
485C22×C4C2×D4×C15111yescharacteristic
486C22×C4C2×D4×C15111yescharacteristic
487C22×C4C2×D4×C15111yescharacteristic
488SD16—82no—
489SD16—82no—
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—41no—
510C4⋊C4—41no—
511C4⋊C4C2×D4×C15111yescharacteristic
512C4⋊C4C2×D4×C15111yescharacteristic
513C4⋊C4C2×D4×C15111yescharacteristic
514C4⋊C4C2×D4×C15112yes—
515C4⋊C4C2×D4×C15111yescharacteristic
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—21no—
525C22⋊C4—21no—
526C22⋊C4—21no—
527C22⋊C4—21no—
528C22⋊C4—21no—
529C22⋊C4—21no—
530C22⋊C4—21no—
531C42—22no—
532C42—22no—
533C42—21no—
534C42C2×D4×C15111yescharacteristic
535C42C2×D4×C15111yescharacteristic
536C42C2×D4×C15111yescharacteristic
537C42C24×C15111yescharacteristic
538C23—21no—
539C23—21no—
540C23—21no—
541C23#120×C15111yescharacteristic
542Q8—22no—
543Q8—42no—
544Q8—42no—
545Q8—42no—
546Q8—42no—
547Q8—81no—
548Q8—82no—
549Q8—82no—
550D4—22no—
551D4—22no—
552D4—22no—
553D4—81no—
554D4—81no—
555D4—81no—
556D4—81no—
557D4—81no—
558D4—82no—
559D4—82no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—82no—
575C2×C4—82no—
576C2×C4—82no—
577C2×C4—82no—
578C2×C4#120×C15111yescharacteristic
579C2×C4#120×C15111yescharacteristic
580C2×C4#120×C15111yescharacteristic
581C2×C4C22×D4×C15111yescharacteristic
582C2×C4C22×D4×C15111yescharacteristic
583C2×C4C22×D4×C15111yescharacteristic
584C8—42no—
585C8—42no—
586C8—42no—
587C22—21no—
588C22—21no—
589C22—21no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22C2×#120×C15111yescharacteristic
600C4—21no—
601C4—21no—
602C4—21no—
603C4—21no—
604C4—41no—
605C4—41no—
606C4—42no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—42no—
611C4—82no—
612C4#577×C15112yes—
613C4#577×C15112yes—
614C2—41no—
615C2—81no—
616C2—81no—
617C2—81no—
618C2#3009×C15111yescharacteristic
619C2#3010×C15111yescharacteristic
620C2#3022×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3547×C151C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3239×C151C2semidirect
3. #3229×C151C2semidirect
4. #3206×C151C2semidirect
5. #1654×C151C2semidirect
6. #1651×C151C2semidirect
7. #1646×C151C2semidirect
8. #1643×C151C2semidirect
9. #1554×C151C2semidirect
10. #1496×C151C2semidirect
11. #1482×C151C2semidirect
310. #18968C151direct (N × H)
311. C151#18968direct (N × H)
313. #3239C2×C151semidirect
314. #3229C2×C151semidirect
315. #3206C2×C151semidirect
316. #1654C2×C151semidirect
317. #1651C2×C151semidirect
318. #1646C2×C151semidirect
319. #1643C2×C151semidirect
320. #1554C2×C151semidirect
321. #1496C2×C151semidirect
322. #1482C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3547×C1512
#3239×C1512
#3229×C1512
#3206×C1512
#1654×C1512
#1651×C1512
#1646×C1512
#1643×C1512
#1554×C1512
#1496×C1512
#1482×C1512
#18968151