Finite Group Databasebeta

← C151×#19040 #50323965

Subgroups — C151×#19040 #50323965

Order 38656.

872 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3567×C151C211yesmaximal, characteristic, complemented
2#3219×C151C211yesmaximal, characteristic, complemented
3#3180×C151C211yesmaximal, characteristic, complemented
4#3171×C151C211yesmaximal, characteristic, complemented
5#1663×C151C211yesmaximal, characteristic, complemented
6#1662×C151C211yesmaximal, characteristic, complemented
7#1661×C151C211yesmaximal, characteristic, complemented
8#1661×C151C211yesmaximal, characteristic, complemented
9#1658×C151C211yesmaximal, characteristic, complemented
10#1656×C151C211yesmaximal, characteristic, complemented
11#1656×C151C211yesmaximal, characteristic, complemented
12#1656×C151C211yesmaximal, characteristic, complemented
13#1532×C151C211yesmaximal, characteristic, complemented
14#1529×C151C211yesmaximal, characteristic, complemented
15#1524×C151C211yesmaximal, characteristic, complemented
16#564×C151C2211yescharacteristic
17#562×C151C2211yescharacteristic
18#562×C151C2211yescharacteristic
19#562×C151C2211yescharacteristic
20#553×C151—21no—
21#553×C151—21no—
22#553×C151—21no—
23#552×C151—21no—
24#552×C151—21no—
25#552×C151—21no—
26#540×C151—21no—
27#540×C151—21no—
28#540×C151—21no—
29#539×C151—21no—
30#539×C151—21no—
31#539×C151—21no—
32#532×C151C2211yescharacteristic
33#529×C151C2211yescharacteristic
34#529×C151C2211yescharacteristic
35#529×C151C2211yescharacteristic
36#501×C151C2211yescharacteristic
37#501×C151C2211yescharacteristic
38#497×C151C2211yescharacteristic
39#496×C151C2211yescharacteristic
40#496×C151C2211yescharacteristic
41#496×C151C2211yescharacteristic
42#491×C151C2211yescharacteristic
43#490×C151C2211yescharacteristic
44#490×C151C2211yescharacteristic
45#490×C151C2211yescharacteristic
46#489×C151C2211yescharacteristic
47#489×C151C2211yescharacteristic
48#469×C151—21no—
49#468×C151—21no—
50#466×C151—21no—
51#465×C151—21no—
52#464×C151—21no—
53#463×C151—21no—
54#452×C151—21no—
55#449×C151—21no—
56#442×C151—21no—
57#440×C151—21no—
58C4×SD16×C151—21no—
59C4×D8×C151—21no—
60#432×C151C2211yescharacteristic
61C4×M16×C151C2211yescharacteristic
62C2×#97×C151C2211yescharacteristic
63#330×C151C2211yescharacteristic
64#330×C151C2211yescharacteristic
65#330×C151C2211yescharacteristic
66#330×C151C2211yescharacteristic
67#330×C151C2211yescharacteristic
68#330×C151C2211yescharacteristic
69#329×C151C2211yescharacteristic
70#329×C151C2211yescharacteristic
71#329×C151C2211yescharacteristic
72#329×C151C2211yescharacteristic
73#329×C151C2211yescharacteristic
74#329×C151C2211yescharacteristic
75C2×#41×C151—21no—
76C2×Q16×C151—21no—
77C2×SD16×C151—21no—
78C2×SD16×C151—21no—
79C2×SD16×C151—21no—
80C2×SD16×C151—21no—
81C2×D8×C151—21no—
82C2×D8×C151—21no—
83C2×D8×C151—21no—
84C2×M16×C151—21no—
85C22×C8×C151—21no—
86C4⋊Q8×C151C2311yescharacteristic
87#127×C151—21no—
88#127×C151C2311yescharacteristic
89#126×C151—21no—
90#126×C151—21no—
91#126×C151—21no—
92#126×C151—21no—
93#126×C151—21no—
94#126×C151—21no—
95#126×C151—21no—
96#125×C151—21no—
97#125×C151—21no—
98#125×C151—21no—
99#125×C151—21no—
100#125×C151—21no—
101#125×C151—21no—
102#125×C151—21no—
103#125×C151—21no—
104#125×C151—21no—
105#125×C151C2311yescharacteristic
106#125×C151C2311yescharacteristic
107#125×C151C2311yescharacteristic
108#124×C151—21no—
109#124×C151C2311yescharacteristic
110#124×C151C2311yescharacteristic
111#124×C151C2311yescharacteristic
112#123×C151—21no—
113#123×C151—21no—
114#123×C151—21no—
115#123×C151—21no—
116#123×C151—21no—
117#123×C151—21no—
118#123×C151—21no—
119#123×C151—21no—
120#123×C151—21no—
121#123×C151—21no—
122#123×C151—21no—
123#123×C151—21no—
124#123×C151—21no—
125#123×C151—21no—
126#123×C151—21no—
127C22⋊Q8×C151—21no—
128C22⋊Q8×C151—21no—
129C22⋊Q8×C151—21no—
130C22⋊Q8×C151—21no—
131C22⋊Q8×C151—21no—
132C22⋊Q8×C151—21no—
133C22⋊Q8×C151D411yescharacteristic
134C22⋊Q8×C151D411yescharacteristic
135C22⋊Q8×C151D411yescharacteristic
136#121×C151—21no—
137#121×C151—21no—
138#121×C151—21no—
139#121×C151—21no—
140#121×C151—21no—
141#121×C151—21no—
142#121×C151—21no—
143#121×C151—21no—
144#121×C151—21no—
145#121×C151—21no—
146#121×C151—21no—
147#121×C151—21no—
148#121×C151—21no—
149#121×C151—21no—
150#121×C151D411yescharacteristic
151#121×C151D411yescharacteristic
152#121×C151D411yescharacteristic
153C4×Q8×C151D411yescharacteristic
154C4×Q8×C151D411yescharacteristic
155C4×Q8×C151D411yescharacteristic
156C4×D4×C151—21no—
157C4×D4×C151—21no—
158C4×D4×C151—21no—
159C4×D4×C151—21no—
160C4×D4×C151—21no—
161C4×D4×C151—21no—
162C4×D4×C151—21no—
163C4×D4×C151—21no—
164C4×D4×C151—21no—
165C4×D4×C151—21no—
166C4×D4×C151—21no—
167C4×D4×C151D411yescharacteristic
168C4×D4×C151D411yescharacteristic
169C4×D4×C151D411yescharacteristic
170#117×C151—21no—
171#117×C151—21no—
172#117×C151—21no—
173#117×C151—21no—
174#117×C151—21no—
175#117×C151—21no—
176C2×C4⋊C4×C151—21no—
177C2×C4⋊C4×C151—21no—
178C2×C4⋊C4×C151—21no—
179C2×C42×C151C2311yescharacteristic
180#107×C151—21no—
181#107×C151—21no—
182#106×C151—21no—
183#106×C151—21no—
184C4⋊C8×C151—21no—
185#103×C151—21no—
186#103×C151—21no—
187#103×C151—21no—
188#103×C151—21no—
189#102×C151—21no—
190#102×C151—21no—
191#102×C151—21no—
192#102×C151—21no—
193#102×C151—21no—
194#102×C151—21no—
195#102×C151—21no—
196#102×C151—21no—
197C22⋊C8×C151—21no—
198#97×C151—21no—
199#97×C151C2311yescharacteristic
200#97×C151C2311yescharacteristic
201#97×C151C2311yescharacteristic
202#97×C151C2311yescharacteristic
203#97×C151C2311yescharacteristic
204#97×C151C2311yescharacteristic
205C4×C8×C151—21no—
206#41×C151—81no—
207#41×C151—81no—
208C2×Q8×C151—21no—
209C2×Q8×C151C2×D411yescharacteristic
210C2×Q8×C151C2×D411yescharacteristic
211C2×Q8×C151C2×D411yescharacteristic
212C2×D4×C151—21no—
213C2×D4×C151—21no—
214C2×D4×C151—21no—
215C2×D4×C151—21no—
216C2×D4×C151—21no—
217C2×D4×C151—21no—
218C2×D4×C151—21no—
219C2×D4×C151—21no—
220C2×D4×C151—21no—
221C2×D4×C151—21no—
222C2×D4×C151—21no—
223C2×D4×C151—21no—
224C2×D4×C151—41no—
225C2×D4×C151C2×D411yescharacteristic
226C2×D4×C151C2×D411yescharacteristic
227C2×D4×C151C2×D411yescharacteristic
228C22×C4×C151—21no—
229C22×C4×C151—21no—
230C22×C4×C151—21no—
231C22×C4×C151—21no—
232C22×C4×C151—21no—
233C22×C4×C151—21no—
234C22×C4×C151—21no—
235C22×C4×C151—21no—
236C22×C4×C151—21no—
237C22×C4×C151—41no—
238C22×C4×C151C2×D411yescharacteristic
239C22×C4×C151C2×D411yescharacteristic
240C22×C4×C151C2×D411yescharacteristic
241Q16×C151—81no—
242SD16×C151—42no—
243SD16×C151—42no—
244SD16×C151—81no—
245SD16×C151—81no—
246D8×C151—42no—
247D8×C151—42no—
248D8×C151—81no—
249M16×C151—42no—
250C2×C8×C151—21no—
251C2×C8×C151—21no—
252C2×C8×C151—21no—
253C2×C8×C151—21no—
254C2×C8×C151—21no—
255C2×C8×C151—21no—
256C2×C8×C151—42no—
257C4⋊C4×C151—21no—
258C4⋊C4×C151—21no—
259C4⋊C4×C151—21no—
260C4⋊C4×C151—21no—
261C4⋊C4×C151—21no—
262C4⋊C4×C151—21no—
263C4⋊C4×C151—21no—
264C4⋊C4×C151—21no—
265C4⋊C4×C151—21no—
266C4⋊C4×C151—21no—
267C4⋊C4×C151—21no—
268C4⋊C4×C151—21no—
269C4⋊C4×C151—21no—
270C4⋊C4×C151—21no—
271C4⋊C4×C151—21no—
272C4⋊C4×C151—21no—
273C4⋊C4×C151—21no—
274C4⋊C4×C151—21no—
275C4⋊C4×C151—21no—
276C4⋊C4×C151—21no—
277C4⋊C4×C151—21no—
278C4⋊C4×C151—21no—
279C4⋊C4×C151—21no—
280C4⋊C4×C151—21no—
281C4⋊C4×C151—21no—
282C4⋊C4×C151—21no—
283C4⋊C4×C151C2×D411yescharacteristic
284C4⋊C4×C151C2×D411yescharacteristic
285C4⋊C4×C151C2×D411yescharacteristic
286C4⋊C4×C151C2×D411yescharacteristic
287C4⋊C4×C151C2×D411yescharacteristic
288C4⋊C4×C151C2×D411yescharacteristic
289C22⋊C4×C151—21no—
290C22⋊C4×C151—21no—
291C22⋊C4×C151—21no—
292C22⋊C4×C151—21no—
293C22⋊C4×C151—21no—
294C22⋊C4×C151—21no—
295C22⋊C4×C151—21no—
296C22⋊C4×C151—21no—
297C22⋊C4×C151—21no—
298C22⋊C4×C151—21no—
299C22⋊C4×C151—21no—
300C22⋊C4×C151—21no—
301C22⋊C4×C151—21no—
302C22⋊C4×C151—21no—
303C22⋊C4×C151—21no—
304C22⋊C4×C151—21no—
305C22⋊C4×C151—21no—
306C22⋊C4×C151—21no—
307C22⋊C4×C151—21no—
308C22⋊C4×C151—21no—
309C22⋊C4×C151—21no—
310C22⋊C4×C151—41no—
311C22⋊C4×C151—41no—
312C42×C151—21no—
313C42×C151—21no—
314C42×C151—21no—
315C42×C151—21no—
316C42×C151—21no—
317C42×C151C2×D411yescharacteristic
318C42×C151C2×D411yescharacteristic
319C42×C151C2×D411yescharacteristic
320C42×C151C2411yescharacteristic
321C23×C151—21no—
322C23×C151—21no—
323C23×C151—21no—
324C23×C151—41no—
325C23×C151#12011yescharacteristic
326Q8×C151—41no—
327Q8×C151—41no—
328Q8×C151—41no—
329Q8×C151—41no—
330Q8×C151—41no—
331D4×C151—41no—
332D4×C151—41no—
333D4×C151—41no—
334D4×C151—41no—
335D4×C151—41no—
336D4×C151—41no—
337D4×C151—41no—
338D4×C151—41no—
339D4×C151—41no—
340D4×C151—81no—
341D4×C151—81no—
342D4×C151—81no—
343D4×C151—81no—
344D4×C151—81no—
345D4×C151—81no—
346D4×C151—81no—
347D4×C151—81no—
348D4×C151—81no—
349D4×C151—82no—
350C2×C4×C151—21no—
351C2×C4×C151—21no—
352C2×C4×C151—21no—
353C2×C4×C151—21no—
354C2×C4×C151—21no—
355C2×C4×C151—21no—
356C2×C4×C151—21no—
357C2×C4×C151—21no—
358C2×C4×C151—21no—
359C2×C4×C151—41no—
360C2×C4×C151—41no—
361C2×C4×C151—41no—
362C2×C4×C151—41no—
363C2×C4×C151—81no—
364C2×C4×C151—81no—
365C2×C4×C151—81no—
366C2×C4×C151—82no—
367C2×C4×C151—81no—
368C2×C4×C151—81no—
369C2×C4×C151—81no—
370C2×C4×C151—81no—
371C2×C4×C151—81no—
372C2×C4×C151—81no—
373C2×C4×C151#12011yescharacteristic
374C2×C4×C151#12011yescharacteristic
375C2×C4×C151#12011yescharacteristic
376C2×C4×C151C22×D411yescharacteristic
377C2×C4×C151C22×D411yescharacteristic
378C2×C4×C151C22×D411yescharacteristic
379C8×C151—22no—
380C8×C151—22no—
381C8×C151—41no—
382C8×C151—41no—
383C8×C151—41no—
384C8×C151—41no—
385C22×C151—21no—
386C22×C151—21no—
387C22×C151—21no—
388C22×C151—41no—
389C22×C151—41no—
390C22×C151—41no—
391C22×C151—41no—
392C22×C151—41no—
393C22×C151—41no—
394C22×C151—41no—
395C22×C151—41no—
396C22×C151—41no—
397C22×C151—81no—
398C22×C151—81no—
399C22×C151—81no—
400C22×C151C2×#12011yescharacteristic
401C4×C151—21no—
402C4×C151—21no—
403C4×C151—21no—
404C4×C151—21no—
405C4×C151—21no—
406C4×C151—21no—
407C4×C151—41no—
408C4×C151—41no—
409C4×C151—41no—
410C4×C151—41no—
411C4×C151—41no—
412C4×C151—41no—
413C4×C151—41no—
414C4×C151—41no—
415C4×C151—41no—
416C4×C151—81no—
417C2×C151—41no—
418C2×C151—81no—
419C2×C151—81no—
420C2×C151—81no—
421C2×C151—161no—
422C2×C151#301811yescharacteristic
423C2×C151#301811yescharacteristic
424C2×C151#302111yescharacteristic
425#19040C15111yesmaximal, characteristic, direct product factor, Sylow
426C151#1904011yescharacteristic, direct product factor, Sylow
427#3567C2×C15111yescharacteristic, complemented
428#3219C2×C15111yescharacteristic, complemented
429#3180C2×C15111yescharacteristic, complemented
430#3171C2×C15111yescharacteristic, complemented
431#1663C2×C15111yescharacteristic, complemented
432#1662C2×C15111yescharacteristic, complemented
433#1661C2×C15111yescharacteristic, complemented
434#1661C2×C15111yescharacteristic, complemented
435#1658C2×C15111yescharacteristic, complemented
436#1656C2×C15111yescharacteristic, complemented
437#1656C2×C15111yescharacteristic, complemented
438#1656C2×C15111yescharacteristic, complemented
439#1532C2×C15111yescharacteristic, complemented
440#1529C2×C15111yescharacteristic, complemented
441#1524C2×C15111yescharacteristic, complemented
442#564C22×C15111yescharacteristic
443#562C22×C15111yescharacteristic
444#562C22×C15111yescharacteristic
445#562C22×C15111yescharacteristic
446#553—21no—
447#553—21no—
448#553—21no—
449#552—21no—
450#552—21no—
451#552—21no—
452#540—21no—
453#540—21no—
454#540—21no—
455#539—21no—
456#539—21no—
457#539—21no—
458#532C22×C15111yescharacteristic
459#529C22×C15111yescharacteristic
460#529C22×C15111yescharacteristic
461#529C22×C15111yescharacteristic
462#501C22×C15111yescharacteristic
463#501C22×C15111yescharacteristic
464#497C22×C15111yescharacteristic
465#496C22×C15111yescharacteristic
466#496C22×C15111yescharacteristic
467#496C22×C15111yescharacteristic
468#491C22×C15111yescharacteristic
469#490C22×C15111yescharacteristic
470#490C22×C15111yescharacteristic
471#490C22×C15111yescharacteristic
472#489C22×C15111yescharacteristic
473#489C22×C15111yescharacteristic
474#469—21no—
475#468—21no—
476#466—21no—
477#465—21no—
478#464—21no—
479#463—21no—
480#452—21no—
481#449—21no—
482#442—21no—
483#440—21no—
484C4×SD16—21no—
485C4×D8—21no—
486#432C22×C15111yescharacteristic
487C4×M16C22×C15111yescharacteristic
488C2×#97C22×C15111yescharacteristic
489#330C22×C15111yescharacteristic
490#330C22×C15111yescharacteristic
491#330C22×C15111yescharacteristic
492#330C22×C15111yescharacteristic
493#330C22×C15111yescharacteristic
494#330C22×C15111yescharacteristic
495#329C22×C15111yescharacteristic
496#329C22×C15111yescharacteristic
497#329C22×C15111yescharacteristic
498#329C22×C15111yescharacteristic
499#329C22×C15111yescharacteristic
500#329C22×C15111yescharacteristic
501C2×#41—21no—
502C2×Q16—21no—
503C2×SD16—21no—
504C2×SD16—21no—
505C2×SD16—21no—
506C2×SD16—21no—
507C2×D8—21no—
508C2×D8—21no—
509C2×D8—21no—
510C2×M16—21no—
511C22×C8—21no—
512C4⋊Q8C23×C15111yescharacteristic
513#127—21no—
514#127C23×C15111yescharacteristic
515#126—21no—
516#126—21no—
517#126—21no—
518#126—21no—
519#126—21no—
520#126—21no—
521#126—21no—
522#125—21no—
523#125—21no—
524#125—21no—
525#125—21no—
526#125—21no—
527#125—21no—
528#125—21no—
529#125—21no—
530#125—21no—
531#125C23×C15111yescharacteristic
532#125C23×C15111yescharacteristic
533#125C23×C15111yescharacteristic
534#124—21no—
535#124C23×C15111yescharacteristic
536#124C23×C15111yescharacteristic
537#124C23×C15111yescharacteristic
538#123—21no—
539#123—21no—
540#123—21no—
541#123—21no—
542#123—21no—
543#123—21no—
544#123—21no—
545#123—21no—
546#123—21no—
547#123—21no—
548#123—21no—
549#123—21no—
550#123—21no—
551#123—21no—
552#123—21no—
553C22⋊Q8—21no—
554C22⋊Q8—21no—
555C22⋊Q8—21no—
556C22⋊Q8—21no—
557C22⋊Q8—21no—
558C22⋊Q8—21no—
559C22⋊Q8D4×C15111yescharacteristic
560C22⋊Q8D4×C15111yescharacteristic
561C22⋊Q8D4×C15111yescharacteristic
562#121—21no—
563#121—21no—
564#121—21no—
565#121—21no—
566#121—21no—
567#121—21no—
568#121—21no—
569#121—21no—
570#121—21no—
571#121—21no—
572#121—21no—
573#121—21no—
574#121—21no—
575#121—21no—
576#121D4×C15111yescharacteristic
577#121D4×C15111yescharacteristic
578#121D4×C15111yescharacteristic
579C4×Q8D4×C15111yescharacteristic
580C4×Q8D4×C15111yescharacteristic
581C4×Q8D4×C15111yescharacteristic
582C4×D4—21no—
583C4×D4—21no—
584C4×D4—21no—
585C4×D4—21no—
586C4×D4—21no—
587C4×D4—21no—
588C4×D4—21no—
589C4×D4—21no—
590C4×D4—21no—
591C4×D4—21no—
592C4×D4—21no—
593C4×D4D4×C15111yescharacteristic
594C4×D4D4×C15111yescharacteristic
595C4×D4D4×C15111yescharacteristic
596#117—21no—
597#117—21no—
598#117—21no—
599#117—21no—
600#117—21no—
601#117—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C42C23×C15111yescharacteristic
606#107—21no—
607#107—21no—
608#106—21no—
609#106—21no—
610C4⋊C8—21no—
611#103—21no—
612#103—21no—
613#103—21no—
614#103—21no—
615#102—21no—
616#102—21no—
617#102—21no—
618#102—21no—
619#102—21no—
620#102—21no—
621#102—21no—
622#102—21no—
623C22⋊C8—21no—
624#97—21no—
625#97C23×C15111yescharacteristic
626#97C23×C15111yescharacteristic
627#97C23×C15111yescharacteristic
628#97C23×C15111yescharacteristic
629#97C23×C15111yescharacteristic
630#97C23×C15111yescharacteristic
631C4×C8—21no—
632#41—81no—
633#41—81no—
634C2×Q8—21no—
635C2×Q8C2×D4×C15111yescharacteristic
636C2×Q8C2×D4×C15111yescharacteristic
637C2×Q8C2×D4×C15111yescharacteristic
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—41no—
651C2×D4C2×D4×C15111yescharacteristic
652C2×D4C2×D4×C15111yescharacteristic
653C2×D4C2×D4×C15111yescharacteristic
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—41no—
664C22×C4C2×D4×C15111yescharacteristic
665C22×C4C2×D4×C15111yescharacteristic
666C22×C4C2×D4×C15111yescharacteristic
667Q16—81no—
668SD16—42no—
669SD16—42no—
670SD16—81no—
671SD16—81no—
672D8—42no—
673D8—42no—
674D8—81no—
675M16—42no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—42no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4C2×D4×C15111yescharacteristic
710C4⋊C4C2×D4×C15111yescharacteristic
711C4⋊C4C2×D4×C15111yescharacteristic
712C4⋊C4C2×D4×C15111yescharacteristic
713C4⋊C4C2×D4×C15111yescharacteristic
714C4⋊C4C2×D4×C15111yescharacteristic
715C22⋊C4—21no—
716C22⋊C4—21no—
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—21no—
727C22⋊C4—21no—
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—21no—
731C22⋊C4—21no—
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—41no—
737C22⋊C4—41no—
738C42—21no—
739C42—21no—
740C42—21no—
741C42—21no—
742C42—21no—
743C42C2×D4×C15111yescharacteristic
744C42C2×D4×C15111yescharacteristic
745C42C2×D4×C15111yescharacteristic
746C42C24×C15111yescharacteristic
747C23—21no—
748C23—21no—
749C23—21no—
750C23—41no—
751C23#120×C15111yescharacteristic
752Q8—41no—
753Q8—41no—
754Q8—41no—
755Q8—41no—
756Q8—41no—
757D4—41no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—41no—
763D4—41no—
764D4—41no—
765D4—41no—
766D4—81no—
767D4—81no—
768D4—81no—
769D4—81no—
770D4—81no—
771D4—81no—
772D4—81no—
773D4—81no—
774D4—81no—
775D4—82no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—81no—
790C2×C4—81no—
791C2×C4—81no—
792C2×C4—82no—
793C2×C4—81no—
794C2×C4—81no—
795C2×C4—81no—
796C2×C4—81no—
797C2×C4—81no—
798C2×C4—81no—
799C2×C4#120×C15111yescharacteristic
800C2×C4#120×C15111yescharacteristic
801C2×C4#120×C15111yescharacteristic
802C2×C4C22×D4×C15111yescharacteristic
803C2×C4C22×D4×C15111yescharacteristic
804C2×C4C22×D4×C15111yescharacteristic
805C8—22no—
806C8—22no—
807C8—41no—
808C8—41no—
809C8—41no—
810C8—41no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22C2×#120×C15111yescharacteristic
827C4—21no—
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—21no—
833C4—41no—
834C4—41no—
835C4—41no—
836C4—41no—
837C4—41no—
838C4—41no—
839C4—41no—
840C4—41no—
841C4—41no—
842C4—81no—
843C2—41no—
844C2—81no—
845C2—81no—
846C2—81no—
847C2—161no—
848C2#3018×C15111yescharacteristic
849C2#3018×C15111yescharacteristic
850C2#3021×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
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
1. #3567×C151C2semidirect
2. #3219×C151C2semidirect
3. #3180×C151C2semidirect
4. #3171×C151C2semidirect
5. #1663×C151C2semidirect
6. #1662×C151C2semidirect
7. #1661×C151C2semidirect
8. #1661×C151C2semidirect
9. #1658×C151C2semidirect
10. #1656×C151C2semidirect
11. #1656×C151C2semidirect
12. #1656×C151C2semidirect
13. #1532×C151C2semidirect
14. #1529×C151C2semidirect
15. #1524×C151C2semidirect
425. #19040C151direct (N × H)
426. C151#19040direct (N × H)
427. #3567C2×C151semidirect
428. #3219C2×C151semidirect
429. #3180C2×C151semidirect
430. #3171C2×C151semidirect
431. #1663C2×C151semidirect
432. #1662C2×C151semidirect
433. #1661C2×C151semidirect
434. #1661C2×C151semidirect
435. #1658C2×C151semidirect
436. #1656C2×C151semidirect
437. #1656C2×C151semidirect
438. #1656C2×C151semidirect
439. #1532C2×C151semidirect
440. #1529C2×C151semidirect
441. #1524C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3567×C1512
#3219×C1512
#3180×C1512
#3171×C1512
#1663×C1512
#1662×C1512
#1661×C1512
#1658×C1512
#1656×C1512
#1532×C1512
#1529×C1512
#1524×C1512
#19040151