Finite Group Databasebeta

← C151×#18791 #50323716

Subgroups — C151×#18791 #50323716

Order 38656.

938 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3480×C151C211yesmaximal, characteristic
2#3206×C151C211yesmaximal, characteristic, complemented
3#3079×C151C211yesmaximal, characteristic, complemented
4C2×#477×C151C211yesmaximal, characteristic, complemented
5#1638×C151C212yesmaximal, complemented
6#1636×C151C212yesmaximal, complemented
7#1631×C151C212yesmaximal, complemented
8#1630×C151C212yesmaximal, complemented
9#1547×C151C211yesmaximal, characteristic, complemented
10#1487×C151C211yesmaximal, characteristic, complemented
11#1477×C151C211yesmaximal, characteristic, complemented
12#559×C151—21no—
13#559×C151C2211yescharacteristic
14#557×C151C2211yescharacteristic
15#556×C151—21no—
16#556×C151C2211yescharacteristic
17#553×C151—22no—
18#553×C151—21no—
19#550×C151C2211yescharacteristic
20#548×C151—21no—
21#532×C151—21no—
22#532×C151C2211yescharacteristic
23C2×C4⋊Q8×C151C2211yescharacteristic
24#529×C151—21no—
25#529×C151—22no—
26C4×#41×C151—21no—
27C4×#41×C151—21no—
28C4×#41×C151C2211yescharacteristic
29C2×C4×Q8×C151C2211yescharacteristic
30#492×C151C2212yes—
31#487×C151C2212yes—
32#477×C151—21no—
33#477×C151—21no—
34#477×C151C2212yes—
35#477×C151C2212yes—
36#477×C151C2212yes—
37#476×C151C2212yes—
38#475×C151—21no—
39#474×C151—21no—
40#461×C151—22no—
41#448×C151—22no—
42#431×C151C2211yescharacteristic
43#428×C151—21no—
44C2×#107×C151—21no—
45#423×C151C2211yescharacteristic
46C2×C4⋊C8×C151C2211yescharacteristic
47#417×C151—21no—
48C2×#103×C151—21no—
49#332×C151C2212yes—
50#331×C151C2212yes—
51Q8⋊C8×C151C2212yes—
52Q8⋊C8×C151C2212yes—
53Q8⋊C8×C151C2212yes—
54D4⋊C8×C151C2212yes—
55C2×#41×C151—21no—
56C2×#41×C151—21no—
57C2×#41×C151D411yescharacteristic
58C22×Q8×C151—21no—
59C22×Q8×C151D411yescharacteristic
60C2×SD16×C151—24no—
61C2×M16×C151—21no—
62C22×C8×C151—21no—
63C4⋊Q8×C151—21no—
64C4⋊Q8×C151—21no—
65C4⋊Q8×C151—21no—
66C4⋊Q8×C151—21no—
67C4⋊Q8×C151C2312yes—
68C4⋊Q8×C151C2311yescharacteristic
69#127×C151—21no—
70#127×C151C2311yescharacteristic
71#126×C151—22no—
72#126×C151—22no—
73#126×C151—22no—
74#125×C151—22no—
75#125×C151—21no—
76#124×C151—22no—
77#124×C151—21no—
78#124×C151—21no—
79#124×C151—21no—
80#124×C151—21no—
81#123×C151—22no—
82#123×C151—22no—
83#123×C151—22no—
84C22⋊Q8×C151—22no—
85C22⋊Q8×C151—21no—
86#121×C151—22no—
87#121×C151—22no—
88#121×C151—22no—
89#121×C151—21no—
90#121×C151—21no—
91#121×C151D412yes—
92C4×Q8×C151—21no—
93C4×Q8×C151—21no—
94C4×Q8×C151—21no—
95C4×Q8×C151—21no—
96C4×Q8×C151—21no—
97C4×Q8×C151D411yescharacteristic
98C4×Q8×C151D411yescharacteristic
99C4×Q8×C151D411yescharacteristic
100C4×Q8×C151C2311yescharacteristic
101C4×Q8×C151C2311yescharacteristic
102C4×Q8×C151C2311yescharacteristic
103C4×D4×C151—22no—
104C4×D4×C151—22no—
105C4×D4×C151—22no—
106C4×D4×C151—22no—
107C4×D4×C151—22no—
108C4×D4×C151—21no—
109C4×D4×C151—21no—
110C4×D4×C151—21no—
111C4×D4×C151—21no—
112C4×D4×C151—21no—
113C4×D4×C151—21no—
114C4×D4×C151D412yes—
115C4×D4×C151D411yescharacteristic
116C4×D4×C151C2311yescharacteristic
117#117×C151—22no—
118#117×C151—22no—
119#117×C151—21no—
120#117×C151—21no—
121#117×C151D411yescharacteristic
122C2×C4⋊C4×C151—21no—
123C2×C4⋊C4×C151—21no—
124C2×C4⋊C4×C151—21no—
125C2×C4⋊C4×C151D411yescharacteristic
126C2×C42×C151—22no—
127C2×C42×C151—21no—
128C2×C42×C151—21no—
129C2×C42×C151C2311yescharacteristic
130#107×C151—22no—
131#107×C151—22no—
132#107×C151—22no—
133#106×C151—22no—
134C4⋊C8×C151—21no—
135C4⋊C8×C151—21no—
136C4⋊C8×C151—21no—
137C4⋊C8×C151C2312yes—
138C4⋊C8×C151C2312yes—
139#103×C151—24no—
140#103×C151—22no—
141#103×C151—22no—
142#103×C151—22no—
143#102×C151—22no—
144C22⋊C8×C151—21no—
145C4×C8×C151C2312yes—
146#41×C151—22no—
147#41×C151—22no—
148#41×C151—42no—
149#41×C151—42no—
150#41×C151—42no—
151#41×C151—42no—
152C2×Q8×C151—21no—
153C2×Q8×C151—21no—
154C2×Q8×C151—22no—
155C2×Q8×C151—22no—
156C2×Q8×C151—41no—
157C2×Q8×C151—41no—
158C2×Q8×C151—82no—
159C2×Q8×C151C2×D411yescharacteristic
160C2×Q8×C151C2×D411yescharacteristic
161C2×Q8×C151C2×D411yescharacteristic
162C2×D4×C151—22no—
163C2×D4×C151—21no—
164C2×D4×C151—22no—
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—22no—
173C22×C4×C151—21no—
174C22×C4×C151—21no—
175C22×C4×C151—22no—
176C22×C4×C151—21no—
177C22×C4×C151—21no—
178C22×C4×C151—41no—
179C22×C4×C151C2×D411yescharacteristic
180C22×C4×C151C2×D411yescharacteristic
181C22×C4×C151C2×D411yescharacteristic
182SD16×C151—84no—
183M16×C151—42no—
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—22no—
201C4⋊C4×C151—22no—
202C4⋊C4×C151—41no—
203C4⋊C4×C151—41no—
204C4⋊C4×C151C2×D412yes—
205C4⋊C4×C151C2×D411yescharacteristic
206C4⋊C4×C151C2×D411yescharacteristic
207C4⋊C4×C151C2×D411yescharacteristic
208C4⋊C4×C151C2×D411yescharacteristic
209C22⋊C4×C151—22no—
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—22no—
219C22⋊C4×C151—21no—
220C42×C151—22no—
221C42×C151—22no—
222C42×C151—21no—
223C42×C151—21no—
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—21no—
240Q8×C151—21no—
241Q8×C151—42no—
242Q8×C151—44no—
243Q8×C151—41no—
244Q8×C151—41no—
245Q8×C151—82no—
246Q8×C151#13712yes—
247D4×C151—21no—
248D4×C151—21no—
249D4×C151—42no—
250D4×C151—44no—
251D4×C151—42no—
252D4×C151—44no—
253D4×C151—41no—
254D4×C151—41no—
255D4×C151—41no—
256D4×C151—41no—
257D4×C151—82no—
258C2×C4×C151—21no—
259C2×C4×C151—21no—
260C2×C4×C151—21no—
261C2×C4×C151—21no—
262C2×C4×C151—22no—
263C2×C4×C151—21no—
264C2×C4×C151—21no—
265C2×C4×C151—21no—
266C2×C4×C151—21no—
267C2×C4×C151—21no—
268C2×C4×C151—41no—
269C2×C4×C151—42no—
270C2×C4×C151—44no—
271C2×C4×C151—41no—
272C2×C4×C151—41no—
273C2×C4×C151—42no—
274C2×C4×C151—44no—
275C2×C4×C151—42no—
276C2×C4×C151—81no—
277C2×C4×C151—81no—
278C2×C4×C151—82no—
279C2×C4×C151—82no—
280C2×C4×C151#12011yescharacteristic
281C2×C4×C151#12011yescharacteristic
282C2×C4×C151#12011yescharacteristic
283C2×C4×C151#13512yes—
284C2×C4×C151#13712yes—
285C2×C4×C151C22×D411yescharacteristic
286C2×C4×C151C22×D411yescharacteristic
287C2×C4×C151C22×D411yescharacteristic
288C8×C151—42no—
289C8×C151—42no—
290C8×C151—42no—
291C22×C151—21no—
292C22×C151—21no—
293C22×C151—41no—
294C22×C151—42no—
295C22×C151—42no—
296C22×C151—41no—
297C22×C151—42no—
298C22×C151—41no—
299C22×C151#45212yes—
300C22×C151C2×#12011yescharacteristic
301C4×C151—21no—
302C4×C151—22no—
303C4×C151—21no—
304C4×C151—21no—
305C4×C151—41no—
306C4×C151—42no—
307C4×C151—41no—
308C4×C151—41no—
309C4×C151—41no—
310C4×C151—41no—
311C4×C151—41no—
312C4×C151—82no—
313C4×C151#45212yes—
314C4×C151C2×#13511yescharacteristic
315C4×C151C2×#13711yescharacteristic
316C4×C151C2×#13711yescharacteristic
317C4×C151#57511yescharacteristic
318C2×C151—22no—
319C2×C151—81no—
320C2×C151—82no—
321C2×C151C2×#45211yescharacteristic
322C2×C151#300711yescharacteristic
323C2×C151#302111yescharacteristic
324#18791C15111yesmaximal, characteristic, direct product factor, Sylow
325C151#1879111yescharacteristic, direct product factor, Sylow
326#3480C2×C15111yescharacteristic
327#3206C2×C15111yescharacteristic, complemented
328#3079C2×C15111yescharacteristic, complemented
329C2×#477C2×C15111yescharacteristic, complemented
330#1638C2×C15112yescomplemented
331#1636C2×C15112yescomplemented
332#1631C2×C15112yescomplemented
333#1630C2×C15112yescomplemented
334#1547C2×C15111yescharacteristic, complemented
335#1487C2×C15111yescharacteristic, complemented
336#1477C2×C15111yescharacteristic, complemented
337#559—21no—
338#559C22×C15111yescharacteristic
339#557C22×C15111yescharacteristic
340#556—21no—
341#556C22×C15111yescharacteristic
342#553—22no—
343#553—21no—
344#550C22×C15111yescharacteristic
345#548—21no—
346#532—21no—
347#532C22×C15111yescharacteristic
348C2×C4⋊Q8C22×C15111yescharacteristic
349#529—21no—
350#529—22no—
351C4×#41—21no—
352C4×#41—21no—
353C4×#41C22×C15111yescharacteristic
354C2×C4×Q8C22×C15111yescharacteristic
355#492C22×C15112yes—
356#487C22×C15112yes—
357#477—21no—
358#477—21no—
359#477C22×C15112yes—
360#477C22×C15112yes—
361#477C22×C15112yes—
362#476C22×C15112yes—
363#475—21no—
364#474—21no—
365#461—22no—
366#448—22no—
367#431C22×C15111yescharacteristic
368#428—21no—
369C2×#107—21no—
370#423C22×C15111yescharacteristic
371C2×C4⋊C8C22×C15111yescharacteristic
372#417—21no—
373C2×#103—21no—
374#332C22×C15112yes—
375#331C22×C15112yes—
376Q8⋊C8C22×C15112yes—
377Q8⋊C8C22×C15112yes—
378Q8⋊C8C22×C15112yes—
379D4⋊C8C22×C15112yes—
380C2×#41—21no—
381C2×#41—21no—
382C2×#41D4×C15111yescharacteristic
383C22×Q8—21no—
384C22×Q8D4×C15111yescharacteristic
385C2×SD16—24no—
386C2×M16—21no—
387C22×C8—21no—
388C4⋊Q8—21no—
389C4⋊Q8—21no—
390C4⋊Q8—21no—
391C4⋊Q8—21no—
392C4⋊Q8C23×C15112yes—
393C4⋊Q8C23×C15111yescharacteristic
394#127—21no—
395#127C23×C15111yescharacteristic
396#126—22no—
397#126—22no—
398#126—22no—
399#125—22no—
400#125—21no—
401#124—22no—
402#124—21no—
403#124—21no—
404#124—21no—
405#124—21no—
406#123—22no—
407#123—22no—
408#123—22no—
409C22⋊Q8—22no—
410C22⋊Q8—21no—
411#121—22no—
412#121—22no—
413#121—22no—
414#121—21no—
415#121—21no—
416#121D4×C15112yes—
417C4×Q8—21no—
418C4×Q8—21no—
419C4×Q8—21no—
420C4×Q8—21no—
421C4×Q8—21no—
422C4×Q8D4×C15111yescharacteristic
423C4×Q8D4×C15111yescharacteristic
424C4×Q8D4×C15111yescharacteristic
425C4×Q8C23×C15111yescharacteristic
426C4×Q8C23×C15111yescharacteristic
427C4×Q8C23×C15111yescharacteristic
428C4×D4—22no—
429C4×D4—22no—
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×D4D4×C15111yescharacteristic
440C4×D4D4×C15112yes—
441C4×D4C23×C15111yescharacteristic
442#117—22no—
443#117—22no—
444#117—21no—
445#117—21no—
446#117D4×C15111yescharacteristic
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4D4×C15111yescharacteristic
451C2×C42—22no—
452C2×C42—21no—
453C2×C42—21no—
454C2×C42C23×C15111yescharacteristic
455#107—22no—
456#107—22no—
457#107—22no—
458#106—22no—
459C4⋊C8—21no—
460C4⋊C8—21no—
461C4⋊C8—21no—
462C4⋊C8C23×C15112yes—
463C4⋊C8C23×C15112yes—
464#103—22no—
465#103—22no—
466#103—22no—
467#103—24no—
468#102—22no—
469C22⋊C8—21no—
470C4×C8C23×C15112yes—
471#41—22no—
472#41—22no—
473#41—42no—
474#41—42no—
475#41—42no—
476#41—42no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—22no—
480C2×Q8—22no—
481C2×Q8—41no—
482C2×Q8—41no—
483C2×Q8—82no—
484C2×Q8C2×D4×C15111yescharacteristic
485C2×Q8C2×D4×C15111yescharacteristic
486C2×Q8C2×D4×C15111yescharacteristic
487C2×D4—22no—
488C2×D4—21no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4C2×D4×C15111yescharacteristic
494C2×D4C2×D4×C15112yes—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—41no—
504C22×C4C2×D4×C15111yescharacteristic
505C22×C4C2×D4×C15111yescharacteristic
506C22×C4C2×D4×C15111yescharacteristic
507SD16—84no—
508M16—42no—
509C2×C8—22no—
510C2×C8—22no—
511C2×C8—22no—
512C2×C8—42no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—41no—
528C4⋊C4—41no—
529C4⋊C4C2×D4×C15112yes—
530C4⋊C4C2×D4×C15111yescharacteristic
531C4⋊C4C2×D4×C15111yescharacteristic
532C4⋊C4C2×D4×C15111yescharacteristic
533C4⋊C4C2×D4×C15111yescharacteristic
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—21no—
541C22⋊C4—22no—
542C22⋊C4—21no—
543C22⋊C4—22no—
544C22⋊C4—21no—
545C42—22no—
546C42—22no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—21no—
551C42—21no—
552C42—21no—
553C42—21no—
554C42C2×D4×C15111yescharacteristic
555C42C2×D4×C15111yescharacteristic
556C42C2×D4×C15111yescharacteristic
557C42C24×C15111yescharacteristic
558C23—21no—
559C23—22no—
560C23#120×C15111yescharacteristic
561Q8—21no—
562Q8—21no—
563Q8—21no—
564Q8—21no—
565Q8—21no—
566Q8—42no—
567Q8—44no—
568Q8—41no—
569Q8—41no—
570Q8—82no—
571Q8#137×C15112yes—
572D4—21no—
573D4—21no—
574D4—42no—
575D4—44no—
576D4—42no—
577D4—44no—
578D4—41no—
579D4—41no—
580D4—41no—
581D4—41no—
582D4—82no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—41no—
594C2×C4—42no—
595C2×C4—44no—
596C2×C4—42no—
597C2×C4—44no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—42no—
601C2×C4—81no—
602C2×C4—81no—
603C2×C4—82no—
604C2×C4—82no—
605C2×C4#120×C15111yescharacteristic
606C2×C4#120×C15111yescharacteristic
607C2×C4#120×C15111yescharacteristic
608C2×C4#135×C15112yes—
609C2×C4#137×C15112yes—
610C2×C4C22×D4×C15111yescharacteristic
611C2×C4C22×D4×C15111yescharacteristic
612C2×C4C22×D4×C15111yescharacteristic
613C8—42no—
614C8—42no—
615C8—42no—
616C22—21no—
617C22—21no—
618C22—41no—
619C22—42no—
620C22—42no—
621C22—41no—
622C22—42no—
623C22—41no—
624C22#452×C15112yes—
625C22C2×#120×C15111yescharacteristic
626C4—21no—
627C4—22no—
628C4—21no—
629C4—21no—
630C4—41no—
631C4—42no—
632C4—41no—
633C4—41no—
634C4—41no—
635C4—41no—
636C4—41no—
637C4—82no—
638C4#452×C15112yes—
639C4C2×#135×C15111yescharacteristic
640C4C2×#137×C15111yescharacteristic
641C4C2×#137×C15111yescharacteristic
642C4#575×C15111yescharacteristic
643C2—22no—
644C2—81no—
645C2—82no—
646C2C2×#452×C15111yescharacteristic
647C2#3007×C15111yescharacteristic
648C2#3021×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3480×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. #3206×C151C2semidirect
3. #3079×C151C2semidirect
4. C2×#477×C151C2semidirect
5. #1638×C151C2semidirect
6. #1636×C151C2semidirect
7. #1631×C151C2semidirect
8. #1630×C151C2semidirect
9. #1547×C151C2semidirect
10. #1487×C151C2semidirect
11. #1477×C151C2semidirect
324. #18791C151direct (N × H)
325. C151#18791direct (N × H)
327. #3206C2×C151semidirect
328. #3079C2×C151semidirect
329. C2×#477C2×C151semidirect
330. #1638C2×C151semidirect
331. #1636C2×C151semidirect
332. #1631C2×C151semidirect
333. #1630C2×C151semidirect
334. #1547C2×C151semidirect
335. #1487C2×C151semidirect
336. #1477C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3480×C1512
#3206×C1512
#3079×C1512
C2×#477×C1512
#1638×C1512
#1636×C1512
#1631×C1512
#1630×C1512
#1547×C1512
#1487×C1512
#1477×C1512
#18791151