Finite Group Databasebeta

← C151×#18573 #50323498

Subgroups — C151×#18573 #50323498

Order 38656.

934 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#3218×C151C211yesmaximal, characteristic, complemented
3#3141×C151C211yesmaximal, characteristic, complemented
4C2×#475×C151C211yesmaximal, characteristic, complemented
5#1645×C151C212yesmaximal, complemented
6#1643×C151C212yesmaximal, complemented
7#1642×C151C212yesmaximal, complemented
8#1640×C151C212yesmaximal, complemented
9#1551×C151C211yesmaximal, characteristic, complemented
10#1491×C151C211yesmaximal, characteristic, complemented
11#1483×C151C211yesmaximal, characteristic, complemented
12#559×C151—21no—
13#559×C151C2211yescharacteristic
14Q82×C151C2211yescharacteristic
15#554×C151—21no—
16#554×C151C2211yescharacteristic
17#550×C151C2211yescharacteristic
18#548×C151—21no—
19#547×C151—22no—
20#547×C151—21no—
21#542×C151—22no—
22#542×C151—21no—
23#532×C151—21no—
24#532×C151C2211yescharacteristic
25C2×C4⋊Q8×C151C2211yescharacteristic
26#529×C151—21no—
27#529×C151C2211yescharacteristic
28#520×C151—21no—
29C2×C4×Q8×C151C2211yescharacteristic
30#497×C151—21no—
31#491×C151—21no—
32#489×C151—22no—
33#487×C151C2212yes—
34#486×C151C2212yes—
35#475×C151—21no—
36#475×C151—21no—
37#475×C151C2212yes—
38#475×C151C2212yes—
39#462×C151C2212yes—
40#461×C151C2212yes—
41#451×C151—21no—
42#448×C151—21no—
43#432×C151C2211yescharacteristic
44C2×#106×C151—21no—
45C2×C4⋊C8×C151C2211yescharacteristic
46#417×C151—22no—
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
60C2×Q16×C151—22no—
61C2×SD16×C151—22no—
62C2×M16×C151—21no—
63C22×C8×C151—21no—
64C4⋊Q8×C151—21no—
65C4⋊Q8×C151—21no—
66C4⋊Q8×C151—21no—
67C4⋊Q8×C151—22no—
68C4⋊Q8×C151—21no—
69C4⋊Q8×C151—21no—
70C4⋊Q8×C151C2312yes—
71C4⋊Q8×C151C2311yescharacteristic
72#127×C151—21no—
73#127×C151C2311yescharacteristic
74#126×C151—22no—
75#126×C151—21no—
76#125×C151—21no—
77#125×C151D411yescharacteristic
78#124×C151—22no—
79#124×C151—22no—
80#124×C151—21no—
81#124×C151—21no—
82#124×C151D412yes—
83#124×C151D411yescharacteristic
84#123×C151—22no—
85#123×C151—22no—
86#123×C151—22no—
87#123×C151—22no—
88#123×C151—21no—
89C22⋊Q8×C151—22no—
90C22⋊Q8×C151—22no—
91C22⋊Q8×C151—22no—
92C22⋊Q8×C151—22no—
93C22⋊Q8×C151—21no—
94C22⋊Q8×C151D411yescharacteristic
95#121×C151—22no—
96#121×C151—22no—
97#121×C151—21no—
98#121×C151—21no—
99#121×C151—21no—
100#121×C151D411yescharacteristic
101C4×Q8×C151—21no—
102C4×Q8×C151—21no—
103C4×Q8×C151—21no—
104C4×Q8×C151—21no—
105C4×Q8×C151D411yescharacteristic
106C4×Q8×C151D411yescharacteristic
107C4×Q8×C151C2311yescharacteristic
108C4×Q8×C151C2311yescharacteristic
109C4×Q8×C151C2311yescharacteristic
110C4×D4×C151—22no—
111C4×D4×C151—22no—
112C4×D4×C151—22no—
113C4×D4×C151—21no—
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×C151C2311yescharacteristic
121#117×C151—22no—
122#117×C151—21no—
123C2×C4⋊C4×C151—22no—
124C2×C4⋊C4×C151—21no—
125C2×C4⋊C4×C151—21no—
126C2×C4⋊C4×C151—21no—
127C2×C4⋊C4×C151—21no—
128C2×C4⋊C4×C151D411yescharacteristic
129C2×C42×C151—21no—
130C2×C42×C151C2311yescharacteristic
131#106×C151—22no—
132#106×C151—22no—
133C4⋊C8×C151—21no—
134C4⋊C8×C151C2312yes—
135C4⋊C8×C151C2312yes—
136#103×C151—22no—
137#103×C151—22no—
138#103×C151—22no—
139#103×C151—22no—
140#103×C151—24no—
141#102×C151—24no—
142C22⋊C8×C151—21no—
143#97×C151—21no—
144#97×C151—21no—
145C4×C8×C151C2312yes—
146#41×C151—44no—
147#41×C151—42no—
148#41×C151—42no—
149#41×C151—84no—
150C2×Q8×C151—22no—
151C2×Q8×C151—21no—
152C2×Q8×C151—22no—
153C2×Q8×C151—22no—
154C2×Q8×C151—41no—
155C2×Q8×C151—41no—
156C2×Q8×C151—82no—
157C2×Q8×C151C2×D411yescharacteristic
158C2×Q8×C151C2×D411yescharacteristic
159C2×Q8×C151C2×D411yescharacteristic
160C2×Q8×C151C2×D412yes—
161C2×D4×C151—22no—
162C2×D4×C151—22no—
163C2×D4×C151—21no—
164C2×D4×C151—22no—
165C2×D4×C151—21no—
166C2×D4×C151—21no—
167C2×D4×C151C2×D411yescharacteristic
168C2×D4×C151C2×D412yes—
169C22×C4×C151—22no—
170C22×C4×C151—21no—
171C22×C4×C151—21no—
172C22×C4×C151—22no—
173C22×C4×C151—22no—
174C22×C4×C151—21no—
175C22×C4×C151—22no—
176C22×C4×C151—41no—
177C22×C4×C151C2×D411yescharacteristic
178C22×C4×C151C2×D411yescharacteristic
179C22×C4×C151C2×D411yescharacteristic
180Q16×C151—82no—
181SD16×C151—82no—
182M16×C151—42no—
183C2×C8×C151—22no—
184C2×C8×C151—22no—
185C2×C8×C151—22no—
186C2×C8×C151—42no—
187C4⋊C4×C151—22no—
188C4⋊C4×C151—22no—
189C4⋊C4×C151—22no—
190C4⋊C4×C151—22no—
191C4⋊C4×C151—21no—
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—22no—
203C4⋊C4×C151—22no—
204C4⋊C4×C151—41no—
205C4⋊C4×C151—41no—
206C4⋊C4×C151C2×D411yescharacteristic
207C4⋊C4×C151C2×D411yescharacteristic
208C4⋊C4×C151C2×D411yescharacteristic
209C4⋊C4×C151C2×D411yescharacteristic
210C22⋊C4×C151—22no—
211C22⋊C4×C151—22no—
212C22⋊C4×C151—22no—
213C22⋊C4×C151—22no—
214C22⋊C4×C151—22no—
215C22⋊C4×C151—21no—
216C22⋊C4×C151—22no—
217C22⋊C4×C151—21no—
218C22⋊C4×C151—21no—
219C22⋊C4×C151—22no—
220C22⋊C4×C151—21no—
221C22⋊C4×C151—21no—
222C42×C151—22no—
223C42×C151—21no—
224C42×C151—21no—
225C42×C151—21no—
226C42×C151—21no—
227C42×C151—21no—
228C42×C151C2×D411yescharacteristic
229C42×C151C2×D411yescharacteristic
230C42×C151C2×D411yescharacteristic
231C42×C151C2411yescharacteristic
232C23×C151—21no—
233C23×C151—22no—
234C23×C151#12011yescharacteristic
235Q8×C151—21no—
236Q8×C151—21no—
237Q8×C151—21no—
238Q8×C151—22no—
239Q8×C151—42no—
240Q8×C151—42no—
241Q8×C151—42no—
242Q8×C151—42no—
243Q8×C151—82no—
244Q8×C151—82no—
245Q8×C151#13712yes—
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—42no—
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#45512yes—
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#57712yes—
312C2×C151—22no—
313C2×C151—81no—
314C2×C151—82no—
315C2×C151#300711yescharacteristic
316C2×C151#301011yescharacteristic
317C2×C151C2×#45511yescharacteristic
318#18573C15111yesmaximal, characteristic, direct product factor, Sylow
319C151#1857311yescharacteristic, direct product factor, Sylow
320#3522C2×C15111yescharacteristic
321#3218C2×C15111yescharacteristic, complemented
322#3141C2×C15111yescharacteristic, complemented
323C2×#475C2×C15111yescharacteristic, complemented
324#1645C2×C15112yescomplemented
325#1643C2×C15112yescomplemented
326#1642C2×C15112yescomplemented
327#1640C2×C15112yescomplemented
328#1551C2×C15111yescharacteristic, complemented
329#1491C2×C15111yescharacteristic, complemented
330#1483C2×C15111yescharacteristic, complemented
331#559—21no—
332#559C22×C15111yescharacteristic
333Q82C22×C15111yescharacteristic
334#554—21no—
335#554C22×C15111yescharacteristic
336#550C22×C15111yescharacteristic
337#548—21no—
338#547—22no—
339#547—21no—
340#542—22no—
341#542—21no—
342#532—21no—
343#532C22×C15111yescharacteristic
344C2×C4⋊Q8C22×C15111yescharacteristic
345#529—21no—
346#529C22×C15111yescharacteristic
347#520—21no—
348C2×C4×Q8C22×C15111yescharacteristic
349#497—21no—
350#491—21no—
351#489—22no—
352#487C22×C15112yes—
353#486C22×C15112yes—
354#475—21no—
355#475—21no—
356#475C22×C15112yes—
357#475C22×C15112yes—
358#462C22×C15112yes—
359#461C22×C15112yes—
360#451—21no—
361#448—21no—
362#432C22×C15111yescharacteristic
363C2×#106—21no—
364C2×C4⋊C8C22×C15111yescharacteristic
365#417—22no—
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
379C2×Q16—22no—
380C2×SD16—22no—
381C2×M16—21no—
382C22×C8—21no—
383C4⋊Q8—22no—
384C4⋊Q8—21no—
385C4⋊Q8—21no—
386C4⋊Q8—21no—
387C4⋊Q8—21no—
388C4⋊Q8—21no—
389C4⋊Q8C23×C15112yes—
390C4⋊Q8C23×C15111yescharacteristic
391#127—21no—
392#127C23×C15111yescharacteristic
393#126—22no—
394#126—21no—
395#125—21no—
396#125D4×C15111yescharacteristic
397#124—22no—
398#124—22no—
399#124—21no—
400#124—21no—
401#124D4×C15111yescharacteristic
402#124D4×C15112yes—
403#123—22no—
404#123—22no—
405#123—22no—
406#123—22no—
407#123—21no—
408C22⋊Q8—22no—
409C22⋊Q8—22no—
410C22⋊Q8—22no—
411C22⋊Q8—22no—
412C22⋊Q8—21no—
413C22⋊Q8D4×C15111yescharacteristic
414#121—22no—
415#121—22no—
416#121—21no—
417#121—21no—
418#121—21no—
419#121D4×C15111yescharacteristic
420C4×Q8—21no—
421C4×Q8—21no—
422C4×Q8—21no—
423C4×Q8—21no—
424C4×Q8D4×C15111yescharacteristic
425C4×Q8D4×C15111yescharacteristic
426C4×Q8C23×C15111yescharacteristic
427C4×Q8C23×C15111yescharacteristic
428C4×Q8C23×C15111yescharacteristic
429C4×D4—22no—
430C4×D4—22no—
431C4×D4—22no—
432C4×D4—21no—
433C4×D4—21no—
434C4×D4—21no—
435C4×D4—21no—
436C4×D4—21no—
437C4×D4—21no—
438C4×D4—21no—
439C4×D4C23×C15111yescharacteristic
440#117—22no—
441#117—21no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4D4×C15111yescharacteristic
448C2×C42—21no—
449C2×C42C23×C15111yescharacteristic
450#106—22no—
451#106—22no—
452C4⋊C8—21no—
453C4⋊C8C23×C15112yes—
454C4⋊C8C23×C15112yes—
455#103—22no—
456#103—22no—
457#103—24no—
458#103—22no—
459#103—22no—
460#102—24no—
461C22⋊C8—21no—
462#97—21no—
463#97—21no—
464C4×C8C23×C15112yes—
465#41—44no—
466#41—42no—
467#41—42no—
468#41—84no—
469C2×Q8—22no—
470C2×Q8—21no—
471C2×Q8—22no—
472C2×Q8—22no—
473C2×Q8—41no—
474C2×Q8—41no—
475C2×Q8—82no—
476C2×Q8C2×D4×C15111yescharacteristic
477C2×Q8C2×D4×C15111yescharacteristic
478C2×Q8C2×D4×C15111yescharacteristic
479C2×Q8C2×D4×C15112yes—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—21no—
483C2×D4—22no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4C2×D4×C15111yescharacteristic
487C2×D4C2×D4×C15112yes—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—41no—
496C22×C4C2×D4×C15111yescharacteristic
497C22×C4C2×D4×C15111yescharacteristic
498C22×C4C2×D4×C15111yescharacteristic
499Q16—82no—
500SD16—82no—
501M16—42no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—42no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—21no—
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—22no—
522C4⋊C4—22no—
523C4⋊C4—41no—
524C4⋊C4—41no—
525C4⋊C4C2×D4×C15111yescharacteristic
526C4⋊C4C2×D4×C15111yescharacteristic
527C4⋊C4C2×D4×C15111yescharacteristic
528C4⋊C4C2×D4×C15111yescharacteristic
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—21no—
535C22⋊C4—22no—
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—22no—
539C22⋊C4—21no—
540C22⋊C4—21no—
541C42—22no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42C2×D4×C15111yescharacteristic
548C42C2×D4×C15111yescharacteristic
549C42C2×D4×C15111yescharacteristic
550C42C24×C15111yescharacteristic
551C23—21no—
552C23—22no—
553C23#120×C15111yescharacteristic
554Q8—21no—
555Q8—21no—
556Q8—21no—
557Q8—22no—
558Q8—42no—
559Q8—42no—
560Q8—42no—
561Q8—42no—
562Q8—82no—
563Q8—82no—
564Q8#137×C15112yes—
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—42no—
603C8—42no—
604C8—42no—
605C22—21no—
606C22—21no—
607C22—42no—
608C22—41no—
609C22—41no—
610C22—42no—
611C22—42no—
612C22—41no—
613C22#455×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#577×C15112yes—
631C2—22no—
632C2—81no—
633C2—82no—
634C2#3007×C15111yescharacteristic
635C2#3010×C15111yescharacteristic
636C2C2×#455×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. #3218×C151C2semidirect
3. #3141×C151C2semidirect
4. C2×#475×C151C2semidirect
5. #1645×C151C2semidirect
6. #1643×C151C2semidirect
7. #1642×C151C2semidirect
8. #1640×C151C2semidirect
9. #1551×C151C2semidirect
10. #1491×C151C2semidirect
11. #1483×C151C2semidirect
318. #18573C151direct (N × H)
319. C151#18573direct (N × H)
321. #3218C2×C151semidirect
322. #3141C2×C151semidirect
323. C2×#475C2×C151semidirect
324. #1645C2×C151semidirect
325. #1643C2×C151semidirect
326. #1642C2×C151semidirect
327. #1640C2×C151semidirect
328. #1551C2×C151semidirect
329. #1491C2×C151semidirect
330. #1483C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3522×C1512
#3218×C1512
#3141×C1512
C2×#475×C1512
#1645×C1512
#1643×C1512
#1642×C1512
#1640×C1512
#1551×C1512
#1491×C1512
#1483×C1512
#18573151