Finite Group Databasebeta

← C151×#18565 #50323490

Subgroups — C151×#18565 #50323490

Order 38656.

986 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3522×C151C211yesmaximal, characteristic
2#3238×C151C211yesmaximal, characteristic, complemented
3#3152×C151C211yesmaximal, characteristic, complemented
4C2×#477×C151C211yesmaximal, characteristic, complemented
5#1633×C151C212yesmaximal, complemented
6#1632×C151C212yesmaximal, complemented
7#1631×C151C212yesmaximal, complemented
8#1630×C151C212yesmaximal, complemented
9#1551×C151C211yesmaximal, characteristic, complemented
10#1491×C151C211yesmaximal, characteristic, complemented
11#1483×C151C211yesmaximal, characteristic, complemented
12C2×#137×C151—22no—
13#559×C151—21no—
14#559×C151C2211yescharacteristic
15Q82×C151C2211yescharacteristic
16#554×C151—21no—
17#554×C151C2211yescharacteristic
18#550×C151C2211yescharacteristic
19#548×C151—21no—
20#547×C151—22no—
21#547×C151—21no—
22#542×C151—22no—
23#542×C151—21no—
24#532×C151—21no—
25#532×C151C2211yescharacteristic
26C2×C4⋊Q8×C151C2211yescharacteristic
27#529×C151—21no—
28#529×C151C2211yescharacteristic
29#520×C151—21no—
30C2×C4×Q8×C151C2211yescharacteristic
31#501×C151—21no—
32#497×C151—22no—
33#494×C151C2212yes—
34#492×C151C2212yes—
35#489×C151—21no—
36#483×C151—21no—
37#480×C151—21no—
38#477×C151—21no—
39#477×C151—21no—
40#477×C151C2212yes—
41#477×C151C2212yes—
42#477×C151C2212yes—
43#476×C151C2212yes—
44#432×C151C2211yescharacteristic
45C2×#107×C151—21no—
46C2×C4⋊C8×C151C2211yescharacteristic
47C2×#103×C151—21no—
48C4×M16×C151C2211yescharacteristic
49#333×C151C2212yes—
50#331×C151C2212yes—
51Q8⋊C8×C151C2212yes—
52Q8⋊C8×C151C2212yes—
53Q8⋊C8×C151C2212yes—
54D4⋊C8×C151C2212yes—
55C2×#41×C151—22no—
56C2×#41×C151—21no—
57C2×#41×C151D412yes—
58C22×Q8×C151—21no—
59C22×Q8×C151D411yescharacteristic
60#137×C151—48no—
61C2×Q16×C151—24no—
62C2×SD16×C151—24no—
63C2×M16×C151—21no—
64C22×C8×C151—21no—
65C4⋊Q8×C151—21no—
66C4⋊Q8×C151—21no—
67C4⋊Q8×C151—21no—
68C4⋊Q8×C151—22no—
69C4⋊Q8×C151—21no—
70C4⋊Q8×C151—21no—
71C4⋊Q8×C151C2312yes—
72C4⋊Q8×C151C2311yescharacteristic
73#127×C151—21no—
74#127×C151C2311yescharacteristic
75#126×C151—22no—
76#126×C151—21no—
77#125×C151—21no—
78#125×C151D411yescharacteristic
79#124×C151—22no—
80#124×C151—22no—
81#124×C151—21no—
82#124×C151—21no—
83#124×C151D411yescharacteristic
84#124×C151D412yes—
85#123×C151—22no—
86#123×C151—22no—
87#123×C151—22no—
88#123×C151—22no—
89#123×C151—21no—
90C22⋊Q8×C151—22no—
91C22⋊Q8×C151—22no—
92C22⋊Q8×C151—22no—
93C22⋊Q8×C151—22no—
94C22⋊Q8×C151—21no—
95C22⋊Q8×C151D411yescharacteristic
96#121×C151—22no—
97#121×C151—22no—
98#121×C151—21no—
99#121×C151—21no—
100#121×C151—21no—
101#121×C151D411yescharacteristic
102C4×Q8×C151—21no—
103C4×Q8×C151—21no—
104C4×Q8×C151—21no—
105C4×Q8×C151—21no—
106C4×Q8×C151D411yescharacteristic
107C4×Q8×C151D411yescharacteristic
108C4×Q8×C151C2311yescharacteristic
109C4×Q8×C151C2311yescharacteristic
110C4×Q8×C151C2311yescharacteristic
111C4×D4×C151—22no—
112C4×D4×C151—22no—
113C4×D4×C151—22no—
114C4×D4×C151—21no—
115C4×D4×C151—21no—
116C4×D4×C151—21no—
117C4×D4×C151—21no—
118C4×D4×C151—21no—
119C4×D4×C151—21no—
120C4×D4×C151—21no—
121C4×D4×C151C2311yescharacteristic
122#117×C151—22no—
123#117×C151—21no—
124C2×C4⋊C4×C151—22no—
125C2×C4⋊C4×C151—21no—
126C2×C4⋊C4×C151—21no—
127C2×C4⋊C4×C151—21no—
128C2×C4⋊C4×C151—21no—
129C2×C4⋊C4×C151D411yescharacteristic
130C2×C42×C151—21no—
131C2×C42×C151C2311yescharacteristic
132#107×C151—22no—
133#107×C151—22no—
134#107×C151—22no—
135#106×C151—22no—
136C4⋊C8×C151—21no—
137C4⋊C8×C151C2312yes—
138C4⋊C8×C151C2312yes—
139#103×C151—22no—
140#103×C151—22no—
141#103×C151—22no—
142#102×C151—22no—
143C22⋊C8×C151—21no—
144#97×C151—21no—
145#97×C151—21no—
146C4×C8×C151C2312yes—
147#41×C151—44no—
148#41×C151—42no—
149#41×C151—42no—
150#41×C151—84no—
151C2×Q8×C151—22no—
152C2×Q8×C151—21no—
153C2×Q8×C151—22no—
154C2×Q8×C151—22no—
155C2×Q8×C151—41no—
156C2×Q8×C151—44no—
157C2×Q8×C151—41no—
158C2×Q8×C151C2×D411yescharacteristic
159C2×Q8×C151C2×D411yescharacteristic
160C2×Q8×C151C2×D411yescharacteristic
161C2×Q8×C151C2×D412yes—
162C2×D4×C151—22no—
163C2×D4×C151—22no—
164C2×D4×C151—21no—
165C2×D4×C151—22no—
166C2×D4×C151—21no—
167C2×D4×C151—21no—
168C2×D4×C151C2×D411yescharacteristic
169C2×D4×C151C2×D412yes—
170C22×C4×C151—22no—
171C22×C4×C151—21no—
172C22×C4×C151—21no—
173C22×C4×C151—22no—
174C22×C4×C151—22no—
175C22×C4×C151—21no—
176C22×C4×C151—22no—
177C22×C4×C151—41no—
178C22×C4×C151C2×D411yescharacteristic
179C22×C4×C151C2×D411yescharacteristic
180C22×C4×C151C2×D411yescharacteristic
181Q16×C151—48no—
182SD16×C151—48no—
183M16×C151—24no—
184C2×C8×C151—22no—
185C2×C8×C151—22no—
186C2×C8×C151—22no—
187C2×C8×C151—42no—
188C4⋊C4×C151—22no—
189C4⋊C4×C151—22no—
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—21no—
197C4⋊C4×C151—21no—
198C4⋊C4×C151—21no—
199C4⋊C4×C151—21no—
200C4⋊C4×C151—21no—
201C4⋊C4×C151—21no—
202C4⋊C4×C151—21no—
203C4⋊C4×C151—22no—
204C4⋊C4×C151—22no—
205C4⋊C4×C151—41no—
206C4⋊C4×C151—41no—
207C4⋊C4×C151C2×D411yescharacteristic
208C4⋊C4×C151C2×D411yescharacteristic
209C4⋊C4×C151C2×D411yescharacteristic
210C4⋊C4×C151C2×D411yescharacteristic
211C22⋊C4×C151—22no—
212C22⋊C4×C151—22no—
213C22⋊C4×C151—22no—
214C22⋊C4×C151—22no—
215C22⋊C4×C151—22no—
216C22⋊C4×C151—21no—
217C22⋊C4×C151—22no—
218C22⋊C4×C151—21no—
219C22⋊C4×C151—21no—
220C22⋊C4×C151—22no—
221C22⋊C4×C151—21no—
222C22⋊C4×C151—21no—
223C42×C151—22no—
224C42×C151—21no—
225C42×C151—21no—
226C42×C151—21no—
227C42×C151—21no—
228C42×C151—21no—
229C42×C151C2×D411yescharacteristic
230C42×C151C2×D411yescharacteristic
231C42×C151C2×D411yescharacteristic
232C42×C151C2411yescharacteristic
233C23×C151—21no—
234C23×C151—22no—
235C23×C151#12011yescharacteristic
236Q8×C151—21no—
237Q8×C151—21no—
238Q8×C151—21no—
239Q8×C151—22no—
240Q8×C151—42no—
241Q8×C151—42no—
242Q8×C151—44no—
243Q8×C151—82no—
244Q8×C151—82no—
245Q8×C151#13712yescomplemented
246D4×C151—22no—
247D4×C151—42no—
248D4×C151—44no—
249D4×C151—44no—
250D4×C151—42no—
251D4×C151—41no—
252D4×C151—41no—
253D4×C151—42no—
254D4×C151—82no—
255C2×C4×C151—21no—
256C2×C4×C151—22no—
257C2×C4×C151—21no—
258C2×C4×C151—21no—
259C2×C4×C151—22no—
260C2×C4×C151—21no—
261C2×C4×C151—21no—
262C2×C4×C151—21no—
263C2×C4×C151—22no—
264C2×C4×C151—21no—
265C2×C4×C151—21no—
266C2×C4×C151—21no—
267C2×C4×C151—42no—
268C2×C4×C151—44no—
269C2×C4×C151—42no—
270C2×C4×C151—41no—
271C2×C4×C151—41no—
272C2×C4×C151—42no—
273C2×C4×C151—82no—
274C2×C4×C151—82no—
275C2×C4×C151—82no—
276C2×C4×C151—82no—
277C2×C4×C151#12011yescharacteristic
278C2×C4×C151#12011yescharacteristic
279C2×C4×C151#12011yescharacteristic
280C2×C4×C151C22×D411yescharacteristic
281C2×C4×C151C22×D411yescharacteristic
282C2×C4×C151C22×D411yescharacteristic
283C8×C151—24no—
284C8×C151—42no—
285C8×C151—42no—
286C22×C151—21no—
287C22×C151—21no—
288C22×C151—42no—
289C22×C151—41no—
290C22×C151—41no—
291C22×C151—42no—
292C22×C151—42no—
293C22×C151—41no—
294C22×C151#45312yes—
295C22×C151C2×#12011yescharacteristic
296C4×C151—21no—
297C4×C151—22no—
298C4×C151—21no—
299C4×C151—21no—
300C4×C151—21no—
301C4×C151—41no—
302C4×C151—41no—
303C4×C151—41no—
304C4×C151—41no—
305C4×C151—41no—
306C4×C151—42no—
307C4×C151—41no—
308C4×C151—82no—
309C4×C151C2×#13711yescharacteristic
310C4×C151#57511yescharacteristic
311C4×C151#57812yes—
312C2×C151—22no—
313C2×C151—81no—
314C2×C151—82no—
315C2×C151#300711yescharacteristic
316C2×C151#301111yescharacteristic
317C2×C151C2×#45311yescharacteristic
318#18565C15111yesmaximal, characteristic, direct product factor, Sylow
319C151#1856511yescharacteristic, direct product factor, Sylow
320#3522C2×C15111yescharacteristic
321#3238C2×C15111yescharacteristic, complemented
322#3152C2×C15111yescharacteristic, complemented
323C2×#477C2×C15111yescharacteristic, complemented
324#1633C2×C15112yescomplemented
325#1632C2×C15112yescomplemented
326#1631C2×C15112yescomplemented
327#1630C2×C15112yescomplemented
328#1551C2×C15111yescharacteristic, complemented
329#1491C2×C15111yescharacteristic, complemented
330#1483C2×C15111yescharacteristic, complemented
331C2×#137—22no—
332#559—21no—
333#559C22×C15111yescharacteristic
334Q82C22×C15111yescharacteristic
335#554—21no—
336#554C22×C15111yescharacteristic
337#550C22×C15111yescharacteristic
338#548—21no—
339#547—22no—
340#547—21no—
341#542—22no—
342#542—21no—
343#532—21no—
344#532C22×C15111yescharacteristic
345C2×C4⋊Q8C22×C15111yescharacteristic
346#529—21no—
347#529C22×C15111yescharacteristic
348#520—21no—
349C2×C4×Q8C22×C15111yescharacteristic
350#501—21no—
351#497—22no—
352#494C22×C15112yes—
353#492C22×C15112yes—
354#489—21no—
355#483—21no—
356#480—21no—
357#477—21no—
358#477—21no—
359#477C22×C15112yes—
360#477C22×C15112yes—
361#477C22×C15112yes—
362#476C22×C15112yes—
363#432C22×C15111yescharacteristic
364C2×#107—21no—
365C2×C4⋊C8C22×C15111yescharacteristic
366C2×#103—21no—
367C4×M16C22×C15111yescharacteristic
368#333C22×C15112yes—
369#331C22×C15112yes—
370Q8⋊C8C22×C15112yes—
371Q8⋊C8C22×C15112yes—
372Q8⋊C8C22×C15112yes—
373D4⋊C8C22×C15112yes—
374C2×#41—22no—
375C2×#41—21no—
376C2×#41D4×C15112yes—
377C22×Q8—21no—
378C22×Q8D4×C15111yescharacteristic
379#137—48no—
380C2×Q16—24no—
381C2×SD16—24no—
382C2×M16—21no—
383C22×C8—21no—
384C4⋊Q8—22no—
385C4⋊Q8—21no—
386C4⋊Q8—21no—
387C4⋊Q8—21no—
388C4⋊Q8—21no—
389C4⋊Q8—21no—
390C4⋊Q8C23×C15112yes—
391C4⋊Q8C23×C15111yescharacteristic
392#127—21no—
393#127C23×C15111yescharacteristic
394#126—22no—
395#126—21no—
396#125—21no—
397#125D4×C15111yescharacteristic
398#124—22no—
399#124—22no—
400#124—21no—
401#124—21no—
402#124D4×C15111yescharacteristic
403#124D4×C15112yes—
404#123—22no—
405#123—22no—
406#123—22no—
407#123—22no—
408#123—21no—
409C22⋊Q8—22no—
410C22⋊Q8—22no—
411C22⋊Q8—22no—
412C22⋊Q8—22no—
413C22⋊Q8—21no—
414C22⋊Q8D4×C15111yescharacteristic
415#121—22no—
416#121—22no—
417#121—21no—
418#121—21no—
419#121—21no—
420#121D4×C15111yescharacteristic
421C4×Q8—21no—
422C4×Q8—21no—
423C4×Q8—21no—
424C4×Q8—21no—
425C4×Q8D4×C15111yescharacteristic
426C4×Q8D4×C15111yescharacteristic
427C4×Q8C23×C15111yescharacteristic
428C4×Q8C23×C15111yescharacteristic
429C4×Q8C23×C15111yescharacteristic
430C4×D4—22no—
431C4×D4—22no—
432C4×D4—22no—
433C4×D4—21no—
434C4×D4—21no—
435C4×D4—21no—
436C4×D4—21no—
437C4×D4—21no—
438C4×D4—21no—
439C4×D4—21no—
440C4×D4C23×C15111yescharacteristic
441#117—22no—
442#117—21no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4D4×C15111yescharacteristic
449C2×C42—21no—
450C2×C42C23×C15111yescharacteristic
451#107—22no—
452#107—22no—
453#107—22no—
454#106—22no—
455C4⋊C8—21no—
456C4⋊C8C23×C15112yes—
457C4⋊C8C23×C15112yes—
458#103—22no—
459#103—22no—
460#103—22no—
461#102—22no—
462C22⋊C8—21no—
463#97—21no—
464#97—21no—
465C4×C8C23×C15112yes—
466#41—44no—
467#41—42no—
468#41—42no—
469#41—84no—
470C2×Q8—22no—
471C2×Q8—21no—
472C2×Q8—22no—
473C2×Q8—22no—
474C2×Q8—41no—
475C2×Q8—44no—
476C2×Q8—41no—
477C2×Q8C2×D4×C15111yescharacteristic
478C2×Q8C2×D4×C15111yescharacteristic
479C2×Q8C2×D4×C15111yescharacteristic
480C2×Q8C2×D4×C15112yes—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—21no—
484C2×D4—22no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4C2×D4×C15111yescharacteristic
488C2×D4C2×D4×C15112yes—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—41no—
497C22×C4C2×D4×C15111yescharacteristic
498C22×C4C2×D4×C15111yescharacteristic
499C22×C4C2×D4×C15111yescharacteristic
500Q16—48no—
501SD16—48no—
502M16—24no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—42no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—41no—
525C4⋊C4—41no—
526C4⋊C4C2×D4×C15111yescharacteristic
527C4⋊C4C2×D4×C15111yescharacteristic
528C4⋊C4C2×D4×C15111yescharacteristic
529C4⋊C4C2×D4×C15111yescharacteristic
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—21no—
536C22⋊C4—22no—
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—22no—
540C22⋊C4—21no—
541C22⋊C4—21no—
542C42—22no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42C2×D4×C15111yescharacteristic
549C42C2×D4×C15111yescharacteristic
550C42C2×D4×C15111yescharacteristic
551C42C24×C15111yescharacteristic
552C23—21no—
553C23—22no—
554C23#120×C15111yescharacteristic
555Q8—21no—
556Q8—21no—
557Q8—21no—
558Q8—22no—
559Q8—42no—
560Q8—42no—
561Q8—44no—
562Q8—82no—
563Q8—82no—
564Q8#137×C15112yescomplemented
565D4—22no—
566D4—42no—
567D4—44no—
568D4—44no—
569D4—42no—
570D4—41no—
571D4—41no—
572D4—42no—
573D4—82no—
574C2×C4—22no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—42no—
587C2×C4—44no—
588C2×C4—42no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—42no—
592C2×C4—82no—
593C2×C4—82no—
594C2×C4—82no—
595C2×C4—82no—
596C2×C4#120×C15111yescharacteristic
597C2×C4#120×C15111yescharacteristic
598C2×C4#120×C15111yescharacteristic
599C2×C4C22×D4×C15111yescharacteristic
600C2×C4C22×D4×C15111yescharacteristic
601C2×C4C22×D4×C15111yescharacteristic
602C8—24no—
603C8—42no—
604C8—42no—
605C22—21no—
606C22—21no—
607C22—42no—
608C22—41no—
609C22—41no—
610C22—42no—
611C22—42no—
612C22—41no—
613C22#453×C15112yes—
614C22C2×#120×C15111yescharacteristic
615C4—21no—
616C4—22no—
617C4—21no—
618C4—21no—
619C4—21no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—41no—
624C4—41no—
625C4—42no—
626C4—41no—
627C4—82no—
628C4C2×#137×C15111yescharacteristic
629C4#575×C15111yescharacteristic
630C4#578×C15112yes—
631C2—22no—
632C2—81no—
633C2—82no—
634C2#3007×C15111yescharacteristic
635C2#3011×C15111yescharacteristic
636C2C2×#453×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3522×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. #3238×C151C2semidirect
3. #3152×C151C2semidirect
4. C2×#477×C151C2semidirect
5. #1633×C151C2semidirect
6. #1632×C151C2semidirect
7. #1631×C151C2semidirect
8. #1630×C151C2semidirect
9. #1551×C151C2semidirect
10. #1491×C151C2semidirect
11. #1483×C151C2semidirect
245. Q8×C151#137semidirect
318. #18565C151direct (N × H)
319. C151#18565direct (N × H)
321. #3238C2×C151semidirect
322. #3152C2×C151semidirect
323. C2×#477C2×C151semidirect
324. #1633C2×C151semidirect
325. #1632C2×C151semidirect
326. #1631C2×C151semidirect
327. #1630C2×C151semidirect
328. #1551C2×C151semidirect
329. #1491C2×C151semidirect
330. #1483C2×C151semidirect
564. Q8#137×C151semidirect

Maximal subgroups

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

subgroupindex
#3522×C1512
#3238×C1512
#3152×C1512
C2×#477×C1512
#1633×C1512
#1632×C1512
#1631×C1512
#1630×C1512
#1551×C1512
#1491×C1512
#1483×C1512
#18565151