Finite Group Databasebeta

← C151×#18581 #50323506

Subgroups — C151×#18581 #50323506

Order 38656.

866 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3523×C151C211yesmaximal, characteristic
2#3238×C151C211yesmaximal, characteristic
3#3139×C151C211yesmaximal, characteristic, complemented
4C2×#477×C151C211yesmaximal, characteristic, complemented
5#1638×C151C212yesmaximal, complemented
6#1637×C151C212yesmaximal, complemented
7#1636×C151C212yesmaximal, complemented
8#1636×C151C212yesmaximal, complemented
9#1552×C151C211yesmaximal, characteristic, complemented
10#1491×C151C211yesmaximal, characteristic, complemented
11#1483×C151C211yesmaximal, characteristic
12#557×C151—21no—
13#557×C151C2211yescharacteristic
14#557×C151C2211yescharacteristic
15#556×C151—21no—
16#556×C151C2211yescharacteristic
17#552×C151—22no—
18#552×C151—21no—
19D4×Q8×C151—21no—
20D4×Q8×C151C2211yescharacteristic
21#541×C151—22no—
22#541×C151—21no—
23#533×C151—21no—
24#533×C151C2211yescharacteristic
25C2×C4⋊Q8×C151C2211yescharacteristic
26#529×C151—21no—
27#529×C151C2211yescharacteristic
28#519×C151—21no—
29C2×C4×Q8×C151C2211yescharacteristic
30#501×C151—21no—
31#491×C151—22no—
32#489×C151—21no—
33#487×C151C2212yes—
34#487×C151C2212yes—
35#483×C151—21no—
36#480×C151—21no—
37#477×C151—21no—
38#477×C151—21no—
39#477×C151C2212yes—
40#477×C151C2212yes—
41#477×C151C2212yes—
42#476×C151C2212yes—
43#432×C151C2211yescharacteristic
44C2×#107×C151—21no—
45C2×C4⋊C8×C151C2211yescharacteristic
46#419×C151—22no—
47C2×#103×C151—21no—
48C4×M16×C151C2211yescharacteristic
49#332×C151C2212yes—
50#332×C151C2212yes—
51Q8⋊C8×C151C2212yes—
52Q8⋊C8×C151C2212yes—
53Q8⋊C8×C151C2212yes—
54D4⋊C8×C151C2212yes—
55C22×Q8×C151—21no—
56C22×Q8×C151—21no—
57C22×Q8×C151D411yescharacteristic
58C2×M16×C151—21no—
59C22×C8×C151—21no—
60C4⋊Q8×C151—22no—
61C4⋊Q8×C151—21no—
62C4⋊Q8×C151—21no—
63C4⋊Q8×C151—21no—
64C4⋊Q8×C151—21no—
65C4⋊Q8×C151—21no—
66C4⋊Q8×C151—21no—
67C4⋊Q8×C151C2312yes—
68C4⋊Q8×C151C2311yescharacteristic
69C4⋊Q8×C151C2311yescharacteristic
70#126×C151—22no—
71#126×C151—22no—
72#126×C151—22no—
73#126×C151—22no—
74#126×C151—21no—
75#125×C151—22no—
76#125×C151—22no—
77#125×C151—22no—
78#125×C151—21no—
79#125×C151—22no—
80#125×C151—22no—
81#125×C151—21no—
82#125×C151D412yes—
83#125×C151D411yescharacteristic
84#124×C151—21no—
85#124×C151D411yescharacteristic
86#123×C151—22no—
87#123×C151—21no—
88C22⋊Q8×C151—22no—
89C22⋊Q8×C151—22no—
90C22⋊Q8×C151—21no—
91C22⋊Q8×C151—21no—
92C22⋊Q8×C151—22no—
93C22⋊Q8×C151—21no—
94C22⋊Q8×C151—21no—
95C22⋊Q8×C151D411yescharacteristic
96#121×C151D411yescharacteristic
97C4×Q8×C151—22no—
98C4×Q8×C151—22no—
99C4×Q8×C151—21no—
100C4×Q8×C151—21no—
101C4×Q8×C151—21no—
102C4×Q8×C151—21no—
103C4×Q8×C151—21no—
104C4×Q8×C151—21no—
105C4×Q8×C151—21no—
106C4×Q8×C151—21no—
107C4×Q8×C151—21no—
108C4×Q8×C151D411yescharacteristic
109C4×Q8×C151D411yescharacteristic
110C4×Q8×C151C2311yescharacteristic
111C4×Q8×C151C2311yescharacteristic
112C4×Q8×C151C2311yescharacteristic
113C4×D4×C151—22no—
114C4×D4×C151—21no—
115C4×D4×C151—21no—
116C4×D4×C151C2311yescharacteristic
117#117×C151—22no—
118#117×C151—22no—
119#117×C151—22no—
120#117×C151—21no—
121#117×C151—21no—
122#117×C151D412yes—
123C2×C4⋊C4×C151—21no—
124C2×C4⋊C4×C151—21no—
125C2×C4⋊C4×C151—21no—
126C2×C4⋊C4×C151D411yescharacteristic
127C2×C42×C151—21no—
128C2×C42×C151C2311yescharacteristic
129#107×C151—22no—
130#107×C151—22no—
131#107×C151—22no—
132#106×C151—22no—
133C4⋊C8×C151—21no—
134C4⋊C8×C151C2312yes—
135C4⋊C8×C151C2312yes—
136#103×C151—24no—
137#103×C151—24no—
138#103×C151—22no—
139#103×C151—22no—
140#103×C151—22no—
141#102×C151—22no—
142C22⋊C8×C151—21no—
143#97×C151—21no—
144#97×C151—21no—
145C4×C8×C151C2312yes—
146C2×Q8×C151—22no—
147C2×Q8×C151—21no—
148C2×Q8×C151—21no—
149C2×Q8×C151—21no—
150C2×Q8×C151—22no—
151C2×Q8×C151—22no—
152C2×Q8×C151—41no—
153C2×Q8×C151—44no—
154C2×Q8×C151—42no—
155C2×Q8×C151—42no—
156C2×Q8×C151—41no—
157C2×Q8×C151C2×D411yescharacteristic
158C2×Q8×C151C2×D411yescharacteristic
159C2×Q8×C151C2×D411yescharacteristic
160C2×D4×C151—21no—
161C2×D4×C151C2×D411yescharacteristic
162C22×C4×C151—22no—
163C22×C4×C151—21no—
164C22×C4×C151—21no—
165C22×C4×C151—21no—
166C22×C4×C151—41no—
167C22×C4×C151C2×D411yescharacteristic
168C22×C4×C151C2×D411yescharacteristic
169C22×C4×C151C2×D411yescharacteristic
170M16×C151—42no—
171C2×C8×C151—22no—
172C2×C8×C151—22no—
173C2×C8×C151—22no—
174C2×C8×C151—42no—
175C4⋊C4×C151—22no—
176C4⋊C4×C151—22no—
177C4⋊C4×C151—22no—
178C4⋊C4×C151—22no—
179C4⋊C4×C151—22no—
180C4⋊C4×C151—22no—
181C4⋊C4×C151—22no—
182C4⋊C4×C151—22no—
183C4⋊C4×C151—21no—
184C4⋊C4×C151—21no—
185C4⋊C4×C151—21no—
186C4⋊C4×C151—22no—
187C4⋊C4×C151—21no—
188C4⋊C4×C151—21no—
189C4⋊C4×C151—21no—
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—22no—
197C4⋊C4×C151—22no—
198C4⋊C4×C151—41no—
199C4⋊C4×C151—41no—
200C4⋊C4×C151C2×D412yes—
201C4⋊C4×C151C2×D412yes—
202C4⋊C4×C151C2×D411yescharacteristic
203C4⋊C4×C151C2×D411yescharacteristic
204C4⋊C4×C151C2×D411yescharacteristic
205C4⋊C4×C151C2×D411yescharacteristic
206C22⋊C4×C151—22no—
207C22⋊C4×C151—22no—
208C22⋊C4×C151—22no—
209C22⋊C4×C151—21no—
210C22⋊C4×C151—22no—
211C22⋊C4×C151—21no—
212C22⋊C4×C151—21no—
213C22⋊C4×C151—21no—
214C22⋊C4×C151—21no—
215C42×C151—22no—
216C42×C151—22no—
217C42×C151—22no—
218C42×C151—21no—
219C42×C151—21no—
220C42×C151—22no—
221C42×C151—21no—
222C42×C151—21no—
223C42×C151—21no—
224C42×C151C2×D411yescharacteristic
225C42×C151C2×D411yescharacteristic
226C42×C151C2×D411yescharacteristic
227C42×C151C2411yescharacteristic
228C23×C151—21no—
229C23×C151#12011yescharacteristic
230Q8×C151—21no—
231Q8×C151—21no—
232Q8×C151—21no—
233Q8×C151—22no—
234Q8×C151—42no—
235Q8×C151—44no—
236Q8×C151—44no—
237Q8×C151—41no—
238Q8×C151—41no—
239Q8×C151—42no—
240Q8×C151—82no—
241Q8×C151#13712yes—
242D4×C151—22no—
243D4×C151—42no—
244C2×C4×C151—21no—
245C2×C4×C151—22no—
246C2×C4×C151—21no—
247C2×C4×C151—21no—
248C2×C4×C151—22no—
249C2×C4×C151—21no—
250C2×C4×C151—22no—
251C2×C4×C151—21no—
252C2×C4×C151—22no—
253C2×C4×C151—21no—
254C2×C4×C151—21no—
255C2×C4×C151—21no—
256C2×C4×C151—21no—
257C2×C4×C151—42no—
258C2×C4×C151—44no—
259C2×C4×C151—42no—
260C2×C4×C151—41no—
261C2×C4×C151—41no—
262C2×C4×C151—42no—
263C2×C4×C151—82no—
264C2×C4×C151#12011yescharacteristic
265C2×C4×C151#12011yescharacteristic
266C2×C4×C151#12011yescharacteristic
267C2×C4×C151C22×D411yescharacteristic
268C2×C4×C151C22×D411yescharacteristic
269C2×C4×C151C22×D411yescharacteristic
270C8×C151—42no—
271C8×C151—42no—
272C8×C151—42no—
273C22×C151—21no—
274C22×C151—21no—
275C22×C151—41no—
276C22×C151—41no—
277C22×C151—41no—
278C22×C151#45412yes—
279C22×C151C2×#12011yescharacteristic
280C4×C151—21no—
281C4×C151—22no—
282C4×C151—21no—
283C4×C151—21no—
284C4×C151—21no—
285C4×C151—41no—
286C4×C151—42no—
287C4×C151—41no—
288C4×C151—41no—
289C4×C151—42no—
290C4×C151—41no—
291C4×C151—41no—
292C4×C151—41no—
293C4×C151—82no—
294C4×C151C2×#13711yescharacteristic
295C4×C151#57511yescharacteristic
296C4×C151#57812yes—
297C2×C151—22no—
298C2×C151—81no—
299C2×C151#300711yescharacteristic
300C2×C151#301111yescharacteristic
301C2×C151C2×#45411yescharacteristic
302#18581C15111yesmaximal, characteristic, direct product factor, Sylow
303C151#1858111yescharacteristic, direct product factor, Sylow
304#3523C2×C15111yescharacteristic
305#3238C2×C15111yescharacteristic
306#3139C2×C15111yescharacteristic, complemented
307C2×#477C2×C15111yescharacteristic, complemented
308#1638C2×C15112yescomplemented
309#1637C2×C15112yescomplemented
310#1636C2×C15112yescomplemented
311#1636C2×C15112yescomplemented
312#1552C2×C15111yescharacteristic, complemented
313#1491C2×C15111yescharacteristic, complemented
314#1483C2×C15111yescharacteristic
315#557—21no—
316#557C22×C15111yescharacteristic
317#557C22×C15111yescharacteristic
318#556—21no—
319#556C22×C15111yescharacteristic
320#552—22no—
321#552—21no—
322D4×Q8—21no—
323D4×Q8C22×C15111yescharacteristic
324#541—22no—
325#541—21no—
326#533—21no—
327#533C22×C15111yescharacteristic
328C2×C4⋊Q8C22×C15111yescharacteristic
329#529—21no—
330#529C22×C15111yescharacteristic
331#519—21no—
332C2×C4×Q8C22×C15111yescharacteristic
333#501—21no—
334#491—22no—
335#489—21no—
336#487C22×C15112yes—
337#487C22×C15112yes—
338#483—21no—
339#480—21no—
340#477—21no—
341#477—21no—
342#477C22×C15112yes—
343#477C22×C15112yes—
344#477C22×C15112yes—
345#476C22×C15112yes—
346#432C22×C15111yescharacteristic
347C2×#107—21no—
348C2×C4⋊C8C22×C15111yescharacteristic
349#419—22no—
350C2×#103—21no—
351C4×M16C22×C15111yescharacteristic
352#332C22×C15112yes—
353#332C22×C15112yes—
354Q8⋊C8C22×C15112yes—
355Q8⋊C8C22×C15112yes—
356Q8⋊C8C22×C15112yes—
357D4⋊C8C22×C15112yes—
358C22×Q8—21no—
359C22×Q8—21no—
360C22×Q8D4×C15111yescharacteristic
361C2×M16—21no—
362C22×C8—21no—
363C4⋊Q8—22no—
364C4⋊Q8—21no—
365C4⋊Q8—21no—
366C4⋊Q8—21no—
367C4⋊Q8—21no—
368C4⋊Q8—21no—
369C4⋊Q8—21no—
370C4⋊Q8C23×C15112yes—
371C4⋊Q8C23×C15111yescharacteristic
372C4⋊Q8C23×C15111yescharacteristic
373#126—22no—
374#126—22no—
375#126—22no—
376#126—22no—
377#126—21no—
378#125—22no—
379#125—22no—
380#125—22no—
381#125—21no—
382#125—22no—
383#125—22no—
384#125—21no—
385#125D4×C15111yescharacteristic
386#125D4×C15112yes—
387#124—21no—
388#124D4×C15111yescharacteristic
389#123—22no—
390#123—21no—
391C22⋊Q8—22no—
392C22⋊Q8—22no—
393C22⋊Q8—21no—
394C22⋊Q8—21no—
395C22⋊Q8—21no—
396C22⋊Q8—21no—
397C22⋊Q8—22no—
398C22⋊Q8D4×C15111yescharacteristic
399#121D4×C15111yescharacteristic
400C4×Q8—22no—
401C4×Q8—22no—
402C4×Q8—21no—
403C4×Q8—21no—
404C4×Q8—21no—
405C4×Q8—21no—
406C4×Q8—21no—
407C4×Q8—21no—
408C4×Q8—21no—
409C4×Q8—21no—
410C4×Q8—21no—
411C4×Q8D4×C15111yescharacteristic
412C4×Q8D4×C15111yescharacteristic
413C4×Q8C23×C15111yescharacteristic
414C4×Q8C23×C15111yescharacteristic
415C4×Q8C23×C15111yescharacteristic
416C4×D4—22no—
417C4×D4—21no—
418C4×D4—21no—
419C4×D4C23×C15111yescharacteristic
420#117—22no—
421#117—22no—
422#117—22no—
423#117—21no—
424#117—21no—
425#117D4×C15112yes—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4D4×C15111yescharacteristic
430C2×C42—21no—
431C2×C42C23×C15111yescharacteristic
432#107—22no—
433#107—22no—
434#107—22no—
435#106—22no—
436C4⋊C8—21no—
437C4⋊C8C23×C15112yes—
438C4⋊C8C23×C15112yes—
439#103—22no—
440#103—22no—
441#103—22no—
442#103—24no—
443#103—24no—
444#102—22no—
445C22⋊C8—21no—
446#97—21no—
447#97—21no—
448C4×C8C23×C15112yes—
449C2×Q8—22no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—22no—
454C2×Q8—22no—
455C2×Q8—41no—
456C2×Q8—44no—
457C2×Q8—42no—
458C2×Q8—42no—
459C2×Q8—41no—
460C2×Q8C2×D4×C15111yescharacteristic
461C2×Q8C2×D4×C15111yescharacteristic
462C2×Q8C2×D4×C15111yescharacteristic
463C2×D4—21no—
464C2×D4C2×D4×C15111yescharacteristic
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—41no—
470C22×C4C2×D4×C15111yescharacteristic
471C22×C4C2×D4×C15111yescharacteristic
472C22×C4C2×D4×C15111yescharacteristic
473M16—42no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—42no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—22no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—22no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—41no—
502C4⋊C4—41no—
503C4⋊C4C2×D4×C15112yes—
504C4⋊C4C2×D4×C15112yes—
505C4⋊C4C2×D4×C15111yescharacteristic
506C4⋊C4C2×D4×C15111yescharacteristic
507C4⋊C4C2×D4×C15111yescharacteristic
508C4⋊C4C2×D4×C15111yescharacteristic
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—21no—
513C22⋊C4—22no—
514C22⋊C4—21no—
515C22⋊C4—21no—
516C22⋊C4—21no—
517C22⋊C4—21no—
518C42—22no—
519C42—22no—
520C42—22no—
521C42—21no—
522C42—21no—
523C42—22no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42C2×D4×C15111yescharacteristic
528C42C2×D4×C15111yescharacteristic
529C42C2×D4×C15111yescharacteristic
530C42C24×C15111yescharacteristic
531C23—21no—
532C23#120×C15111yescharacteristic
533Q8—21no—
534Q8—21no—
535Q8—21no—
536Q8—22no—
537Q8—42no—
538Q8—44no—
539Q8—44no—
540Q8—41no—
541Q8—41no—
542Q8—42no—
543Q8—82no—
544Q8#137×C15112yes—
545D4—22no—
546D4—42no—
547C2×C4—22no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—42no—
561C2×C4—44no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—42no—
566C2×C4—82no—
567C2×C4#120×C15111yescharacteristic
568C2×C4#120×C15111yescharacteristic
569C2×C4#120×C15111yescharacteristic
570C2×C4C22×D4×C15111yescharacteristic
571C2×C4C22×D4×C15111yescharacteristic
572C2×C4C22×D4×C15111yescharacteristic
573C8—42no—
574C8—42no—
575C8—42no—
576C22—21no—
577C22—21no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22#454×C15112yes—
582C22C2×#120×C15111yescharacteristic
583C4—21no—
584C4—22no—
585C4—21no—
586C4—21no—
587C4—21no—
588C4—41no—
589C4—42no—
590C4—41no—
591C4—41no—
592C4—42no—
593C4—41no—
594C4—41no—
595C4—41no—
596C4—82no—
597C4C2×#137×C15111yescharacteristic
598C4#575×C15111yescharacteristic
599C4#578×C15112yes—
600C2—22no—
601C2—81no—
602C2#3007×C15111yescharacteristic
603C2#3011×C15111yescharacteristic
604C2C2×#454×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#121×C151D4
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
3. #3139×C151C2semidirect
4. C2×#477×C151C2semidirect
5. #1638×C151C2semidirect
6. #1637×C151C2semidirect
7. #1636×C151C2semidirect
8. #1636×C151C2semidirect
9. #1552×C151C2semidirect
10. #1491×C151C2semidirect
302. #18581C151direct (N × H)
303. C151#18581direct (N × H)
306. #3139C2×C151semidirect
307. C2×#477C2×C151semidirect
308. #1638C2×C151semidirect
309. #1637C2×C151semidirect
310. #1636C2×C151semidirect
311. #1636C2×C151semidirect
312. #1552C2×C151semidirect
313. #1491C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3523×C1512
#3238×C1512
#3139×C1512
C2×#477×C1512
#1638×C1512
#1637×C1512
#1636×C1512
#1552×C1512
#1491×C1512
#1483×C1512
#18581151