Finite Group Databasebeta

← C151×#24087 #50329012

Subgroups — C151×#24087 #50329012

Order 38656.

984 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3495×C151C211yesmaximal, characteristic
2#3093×C151C211yesmaximal, characteristic
3#2911×C151C211yesmaximal, characteristic, complemented
4#2499×C151C211yesmaximal, characteristic, complemented
5#2061×C151C211yesmaximal, characteristic, complemented
6#2060×C151C211yesmaximal, characteristic, complemented
7#2038×C151C211yesmaximal, characteristic, complemented
8#2038×C151C211yesmaximal, characteristic, complemented
9#1901×C151C211yesmaximal, characteristic, complemented
10#1871×C151C211yesmaximal, characteristic
11#1860×C151C211yesmaximal, characteristic, complemented
12#1859×C151C211yesmaximal, characteristic, complemented
13#1857×C151C211yesmaximal, characteristic, complemented
14#1857×C151C211yesmaximal, characteristic, complemented
15#1826×C151C211yesmaximal, characteristic, complemented
16C22×M16×C151C2211yescharacteristic
17#556×C151—21no—
18#554×C151—21no—
19#552×C151—21no—
20#552×C151—22no—
21#552×C151—21no—
22#551×C151—22no—
23#544×C151C2211yescharacteristic
24#542×C151—21no—
25#541×C151—21no—
26#536×C151C2211yescharacteristic
27#533×C151—21no—
28#529×C151—21no—
29#525×C151C2211yescharacteristic
30C2×C22⋊Q8×C151C2211yescharacteristic
31#520×C151C2211yescharacteristic
32#519×C151C2211yescharacteristic
33C2×#117×C151C2211yescharacteristic
34C2×#117×C151C2211yescharacteristic
35#485×C151—21no—
36#485×C151—21no—
37#482×C151—21no—
38#482×C151—21no—
39#428×C151—21no—
40#428×C151—21no—
41#428×C151C2211yescharacteristic
42#428×C151C2211yescharacteristic
43#428×C151C2211yescharacteristic
44#428×C151C2211yescharacteristic
45#428×C151C2211yescharacteristic
46#428×C151C2211yescharacteristic
47#427×C151—21no—
48#427×C151—21no—
49C2×#104×C151C2211yescharacteristic
50C2×#104×C151C2211yescharacteristic
51#417×C151C2211yescharacteristic
52#417×C151C2211yescharacteristic
53C2×#101×C151C2211yescharacteristic
54C2×#101×C151C2211yescharacteristic
55#407×C151C2211yescharacteristic
56#397×C151—22no—
57#391×C151C2211yescharacteristic
58#391×C151C2211yescharacteristic
59#387×C151—22no—
60#384×C151C2211yescharacteristic
61#382×C151C2211yescharacteristic
62C4×C22⋊C4×C151C2211yescharacteristic
63#343×C151C2211yescharacteristic
64#343×C151C2211yescharacteristic
65#339×C151C2211yescharacteristic
66#339×C151C2211yescharacteristic
67#339×C151C2211yescharacteristic
68#339×C151C2211yescharacteristic
69#339×C151C2211yescharacteristic
70#339×C151C2211yescharacteristic
71C2×#41×C151C2311yescharacteristic
72C22×Q8×C151C2311yescharacteristic
73C23×C4×C151C2311yescharacteristic
74C2×M16×C151—21no—
75C2×M16×C151—22no—
76C2×M16×C151—22no—
77C2×M16×C151C2311yescharacteristic
78C2×M16×C151C2311yescharacteristic
79C2×M16×C151C2311yescharacteristic
80C2×M16×C151C2311yescharacteristic
81C22×C8×C151—21no—
82C4⋊Q8×C151—21no—
83C4⋊Q8×C151—21no—
84C4⋊Q8×C151—21no—
85#126×C151—22no—
86#126×C151—22no—
87#126×C151—22no—
88#126×C151—22no—
89#125×C151—22no—
90#125×C151—22no—
91#125×C151—22no—
92#125×C151—21no—
93#125×C151—21no—
94#124×C151—22no—
95#124×C151—21no—
96#123×C151—22no—
97#123×C151—22no—
98#123×C151—21no—
99#123×C151—22no—
100C22⋊Q8×C151—22no—
101C22⋊Q8×C151—22no—
102C22⋊Q8×C151—21no—
103C22⋊Q8×C151—21no—
104C22⋊Q8×C151—21no—
105C22⋊Q8×C151—21no—
106C22⋊Q8×C151—22no—
107C22⋊Q8×C151—21no—
108C22⋊Q8×C151—21no—
109C22⋊Q8×C151D411yescharacteristic
110C22⋊Q8×C151D411yescharacteristic
111#121×C151D411yescharacteristic
112#121×C151D411yescharacteristic
113#120×C151—21no—
114C4×Q8×C151—22no—
115C4×Q8×C151—21no—
116C4×Q8×C151—21no—
117C4×Q8×C151—21no—
118C4×Q8×C151—21no—
119C4×Q8×C151—21no—
120C4×D4×C151—22no—
121C4×D4×C151—21no—
122C4×D4×C151—22no—
123C4×D4×C151—21no—
124C4×D4×C151—21no—
125#117×C151—22no—
126#117×C151—22no—
127#117×C151—21no—
128#117×C151—21no—
129#117×C151—22no—
130#117×C151—21no—
131#117×C151—21no—
132#117×C151—21no—
133#117×C151—21no—
134#117×C151—21no—
135#117×C151D411yescharacteristic
136#117×C151D411yescharacteristic
137#117×C151C2311yescharacteristic
138#117×C151C2311yescharacteristic
139#117×C151C2311yescharacteristic
140C2×C4⋊C4×C151—21no—
141C2×C4⋊C4×C151—22no—
142C2×C4⋊C4×C151D412yes—
143C2×C4⋊C4×C151D411yescharacteristic
144C2×C4⋊C4×C151D411yescharacteristic
145C2×C4⋊C4×C151C2311yescharacteristic
146C2×C4⋊C4×C151C2311yescharacteristic
147C2×C4⋊C4×C151C2311yescharacteristic
148C2×C22⋊C4×C151—21no—
149C2×C22⋊C4×C151—21no—
150C2×C22⋊C4×C151—21no—
151C2×C22⋊C4×C151D412yes—
152C2×C42×C151—21no—
153C2×C42×C151—21no—
154C2×C42×C151C2311yescharacteristic
155C2×C42×C151C2311yescharacteristic
156#107×C151—21no—
157#107×C151—21no—
158#107×C151—21no—
159#107×C151—21no—
160#107×C151—21no—
161#107×C151—21no—
162#106×C151—21no—
163#106×C151—21no—
164#106×C151—21no—
165#106×C151—21no—
166#106×C151—21no—
167#106×C151—21no—
168#104×C151—22no—
169#104×C151—22no—
170#103×C151—21no—
171#103×C151—21no—
172#102×C151—21no—
173#102×C151—21no—
174#101×C151—22no—
175#101×C151—22no—
176C22⋊C8×C151—21no—
177C22⋊C8×C151—21no—
178#95×C151—21no—
179#95×C151—22no—
180#95×C151—22no—
181#95×C151—22no—
182C24×C151C2×D411yescharacteristic
183#41×C151—21no—
184#41×C151—21no—
185#41×C151—21no—
186#41×C151—21no—
187C2×Q8×C151—22no—
188C2×Q8×C151—21no—
189C2×Q8×C151—21no—
190C2×Q8×C151—21no—
191C2×Q8×C151—21no—
192C2×Q8×C151—21no—
193C2×Q8×C151—21no—
194C2×Q8×C151C2×D411yescharacteristic
195C2×D4×C151—21no—
196C2×D4×C151—21no—
197C2×D4×C151—21no—
198C2×D4×C151C2×D411yescharacteristic
199C22×C4×C151—21no—
200C22×C4×C151—21no—
201C22×C4×C151—21no—
202C22×C4×C151—21no—
203C22×C4×C151—21no—
204C22×C4×C151—21no—
205C22×C4×C151—22no—
206C22×C4×C151—21no—
207C22×C4×C151—21no—
208C22×C4×C151—21no—
209C22×C4×C151—21no—
210C22×C4×C151—21no—
211C22×C4×C151C2×D412yes—
212C22×C4×C151C2×D411yescharacteristic
213C22×C4×C151C2×D411yescharacteristic
214C22×C4×C151C2×D411yescharacteristic
215C22×C4×C151C2×D411yescharacteristic
216C22×C4×C151C2×D411yescharacteristic
217C22×C4×C151C2×D412yes—
218C22×C4×C151C2411yescharacteristic
219M16×C151—24no—
220M16×C151—21no—
221M16×C151—21no—
222M16×C151—21no—
223M16×C151—21no—
224M16×C151—21no—
225M16×C151—21no—
226M16×C151#4112yes—
227M16×C151#4112yes—
228C2×C8×C151—24no—
229C2×C8×C151—21no—
230C2×C8×C151—21no—
231C2×C8×C151—21no—
232C2×C8×C151—21no—
233C4⋊C4×C151—22no—
234C4⋊C4×C151—22no—
235C4⋊C4×C151—22no—
236C4⋊C4×C151—22no—
237C4⋊C4×C151—22no—
238C4⋊C4×C151—22no—
239C4⋊C4×C151—22no—
240C4⋊C4×C151—22no—
241C4⋊C4×C151—21no—
242C4⋊C4×C151—21no—
243C4⋊C4×C151—22no—
244C4⋊C4×C151—22no—
245C4⋊C4×C151—21no—
246C4⋊C4×C151—21no—
247C4⋊C4×C151—21no—
248C4⋊C4×C151—21no—
249C4⋊C4×C151—21no—
250C4⋊C4×C151—21no—
251C4⋊C4×C151—21no—
252C4⋊C4×C151—21no—
253C4⋊C4×C151—44no—
254C4⋊C4×C151C2×D411yescharacteristic
255C4⋊C4×C151C2×D411yescharacteristic
256C4⋊C4×C151C2×D411yescharacteristic
257C4⋊C4×C151C2×D411yescharacteristic
258C4⋊C4×C151C2×D411yescharacteristic
259C4⋊C4×C151C2×D411yescharacteristic
260C22⋊C4×C151—22no—
261C22⋊C4×C151—22no—
262C22⋊C4×C151—22no—
263C22⋊C4×C151—21no—
264C22⋊C4×C151—21no—
265C22⋊C4×C151—22no—
266C22⋊C4×C151—22no—
267C22⋊C4×C151—21no—
268C22⋊C4×C151—21no—
269C22⋊C4×C151—21no—
270C22⋊C4×C151—21no—
271C22⋊C4×C151—21no—
272C22⋊C4×C151—21no—
273C22⋊C4×C151—21no—
274C22⋊C4×C151—42no—
275C22⋊C4×C151—41no—
276C22⋊C4×C151—41no—
277C42×C151—22no—
278C42×C151—22no—
279C42×C151—22no—
280C42×C151—21no—
281C42×C151—21no—
282C42×C151—21no—
283C42×C151—21no—
284C42×C151—21no—
285C42×C151—21no—
286C42×C151—21no—
287C42×C151—21no—
288C42×C151—21no—
289C42×C151—41no—
290C42×C151—41no—
291C23×C151—21no—
292C23×C151—21no—
293C23×C151—21no—
294C23×C151—41no—
295C23×C151—41no—
296C23×C151#12011yescharacteristic
297C23×C151#12011yescharacteristic
298C23×C151C22×D411yescharacteristic
299Q8×C151—21no—
300Q8×C151—21no—
301Q8×C151—41no—
302Q8×C151—41no—
303Q8×C151—41no—
304Q8×C151—41no—
305Q8×C151—82no—
306D4×C151—21no—
307D4×C151—21no—
308D4×C151—42no—
309D4×C151—41no—
310D4×C151—41no—
311D4×C151—81no—
312C2×C4×C151—21no—
313C2×C4×C151—21no—
314C2×C4×C151—21no—
315C2×C4×C151—21no—
316C2×C4×C151—21no—
317C2×C4×C151—21no—
318C2×C4×C151—21no—
319C2×C4×C151—21no—
320C2×C4×C151—21no—
321C2×C4×C151—21no—
322C2×C4×C151—22no—
323C2×C4×C151—21no—
324C2×C4×C151—22no—
325C2×C4×C151—21no—
326C2×C4×C151—22no—
327C2×C4×C151—21no—
328C2×C4×C151—21no—
329C2×C4×C151—21no—
330C2×C4×C151—21no—
331C2×C4×C151—21no—
332C2×C4×C151—22no—
333C2×C4×C151—22no—
334C2×C4×C151—41no—
335C2×C4×C151—42no—
336C2×C4×C151—41no—
337C2×C4×C151—41no—
338C2×C4×C151—41no—
339C2×C4×C151—42no—
340C2×C4×C151—41no—
341C2×C4×C151—42no—
342C2×C4×C151—41no—
343C2×C4×C151—42no—
344C2×C4×C151—41no—
345C2×C4×C151—41no—
346C2×C4×C151—41no—
347C2×C4×C151—81no—
348C2×C4×C151—82no—
349C2×C4×C151#12011yescharacteristic
350C2×C4×C151#12011yescharacteristic
351C2×C4×C151C22×D411yescharacteristic
352C2×C4×C151C22×D411yescharacteristic
353C2×C4×C151C2×#4111yescharacteristic
354C2×C4×C151C2×#4111yescharacteristic
355C2×C4×C1512−1+411yescharacteristic
356C2×C4×C1512−1+411yescharacteristic
357C8×C151—22no—
358C8×C151—22no—
359C8×C151—41no—
360C8×C151—41no—
361C22×C151—21no—
362C22×C151—21no—
363C22×C151—21no—
364C22×C151—21no—
365C22×C151—21no—
366C22×C151—21no—
367C22×C151—21no—
368C22×C151—21no—
369C22×C151—41no—
370C22×C151—41no—
371C22×C151—41no—
372C22×C151—81no—
373C22×C151—81no—
374C22×C151C2×#12011yescharacteristic
375C22×C151#54711yescharacteristic
376C22×C151#54711yescharacteristic
377C4×C151—21no—
378C4×C151—21no—
379C4×C151—42no—
380C4×C151—42no—
381C4×C151—41no—
382C4×C151—42no—
383C4×C151—41no—
384C4×C151—41no—
385C4×C151—41no—
386C4×C151—41no—
387C4×C151—41no—
388C4×C151—41no—
389C4×C151—81no—
390C4×C151—81no—
391C4×C151—81no—
392C4×C151#52511yescharacteristic
393C4×C151#53611yescharacteristic
394C4×C151#54711yescharacteristic
395C4×C151#54711yescharacteristic
396C2×C151—21no—
397C2×C151—21no—
398C2×C151—41no—
399C2×C151—41no—
400C2×C151—81no—
401C2×C151#240611yescharacteristic
402C2×C151#301811yescharacteristic
403C2×C151#302011yescharacteristic
404#24087C15111yesmaximal, characteristic, direct product factor, Sylow
405C151#2408711yescharacteristic, direct product factor, Sylow
406#3495C2×C15111yescharacteristic
407#3093C2×C15111yescharacteristic
408#2911C2×C15111yescharacteristic, complemented
409#2499C2×C15111yescharacteristic, complemented
410#2061C2×C15111yescharacteristic, complemented
411#2060C2×C15111yescharacteristic, complemented
412#2038C2×C15111yescharacteristic, complemented
413#2038C2×C15111yescharacteristic, complemented
414#1901C2×C15111yescharacteristic, complemented
415#1871C2×C15111yescharacteristic
416#1860C2×C15111yescharacteristic, complemented
417#1859C2×C15111yescharacteristic, complemented
418#1857C2×C15111yescharacteristic, complemented
419#1857C2×C15111yescharacteristic, complemented
420#1826C2×C15111yescharacteristic, complemented
421C22×M16C22×C15111yescharacteristic
422#556—21no—
423#554—21no—
424#552—21no—
425#552—22no—
426#552—21no—
427#551—22no—
428#544C22×C15111yescharacteristic
429#542—21no—
430#541—21no—
431#536C22×C15111yescharacteristic
432#533—21no—
433#529—21no—
434#525C22×C15111yescharacteristic
435C2×C22⋊Q8C22×C15111yescharacteristic
436#520C22×C15111yescharacteristic
437#519C22×C15111yescharacteristic
438C2×#117C22×C15111yescharacteristic
439C2×#117C22×C15111yescharacteristic
440#485—21no—
441#485—21no—
442#482—21no—
443#482—21no—
444#428—21no—
445#428—21no—
446#428C22×C15111yescharacteristic
447#428C22×C15111yescharacteristic
448#428C22×C15111yescharacteristic
449#428C22×C15111yescharacteristic
450#428C22×C15111yescharacteristic
451#428C22×C15111yescharacteristic
452#427—21no—
453#427—21no—
454C2×#104C22×C15111yescharacteristic
455C2×#104C22×C15111yescharacteristic
456#417C22×C15111yescharacteristic
457#417C22×C15111yescharacteristic
458C2×#101C22×C15111yescharacteristic
459C2×#101C22×C15111yescharacteristic
460#407C22×C15111yescharacteristic
461#397—22no—
462#391C22×C15111yescharacteristic
463#391C22×C15111yescharacteristic
464#387—22no—
465#384C22×C15111yescharacteristic
466#382C22×C15111yescharacteristic
467C4×C22⋊C4C22×C15111yescharacteristic
468#343C22×C15111yescharacteristic
469#343C22×C15111yescharacteristic
470#339C22×C15111yescharacteristic
471#339C22×C15111yescharacteristic
472#339C22×C15111yescharacteristic
473#339C22×C15111yescharacteristic
474#339C22×C15111yescharacteristic
475#339C22×C15111yescharacteristic
476C2×#41C23×C15111yescharacteristic
477C22×Q8C23×C15111yescharacteristic
478C23×C4C23×C15111yescharacteristic
479C2×M16—21no—
480C2×M16—22no—
481C2×M16—22no—
482C2×M16C23×C15111yescharacteristic
483C2×M16C23×C15111yescharacteristic
484C2×M16C23×C15111yescharacteristic
485C2×M16C23×C15111yescharacteristic
486C22×C8—21no—
487C4⋊Q8—21no—
488C4⋊Q8—21no—
489C4⋊Q8—21no—
490#126—22no—
491#126—22no—
492#126—22no—
493#126—22no—
494#125—22no—
495#125—22no—
496#125—22no—
497#125—21no—
498#125—21no—
499#124—22no—
500#124—21no—
501#123—22no—
502#123—22no—
503#123—21no—
504#123—22no—
505C22⋊Q8—22no—
506C22⋊Q8—22no—
507C22⋊Q8—21no—
508C22⋊Q8—21no—
509C22⋊Q8—21no—
510C22⋊Q8—21no—
511C22⋊Q8—22no—
512C22⋊Q8—21no—
513C22⋊Q8—21no—
514C22⋊Q8D4×C15111yescharacteristic
515C22⋊Q8D4×C15111yescharacteristic
516#121D4×C15111yescharacteristic
517#121D4×C15111yescharacteristic
518#120—21no—
519C4×Q8—22no—
520C4×Q8—21no—
521C4×Q8—21no—
522C4×Q8—21no—
523C4×Q8—21no—
524C4×Q8—21no—
525C4×D4—22no—
526C4×D4—21no—
527C4×D4—22no—
528C4×D4—21no—
529C4×D4—21no—
530#117—22no—
531#117—22no—
532#117—21no—
533#117—21no—
534#117—22no—
535#117—21no—
536#117—21no—
537#117—21no—
538#117—21no—
539#117—21no—
540#117D4×C15111yescharacteristic
541#117D4×C15111yescharacteristic
542#117C23×C15111yescharacteristic
543#117C23×C15111yescharacteristic
544#117C23×C15111yescharacteristic
545C2×C4⋊C4—21no—
546C2×C4⋊C4—22no—
547C2×C4⋊C4D4×C15112yes—
548C2×C4⋊C4D4×C15111yescharacteristic
549C2×C4⋊C4D4×C15111yescharacteristic
550C2×C4⋊C4C23×C15111yescharacteristic
551C2×C4⋊C4C23×C15111yescharacteristic
552C2×C4⋊C4C23×C15111yescharacteristic
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4D4×C15112yes—
557C2×C42—21no—
558C2×C42—21no—
559C2×C42C23×C15111yescharacteristic
560C2×C42C23×C15111yescharacteristic
561#107—21no—
562#107—21no—
563#107—21no—
564#107—21no—
565#107—21no—
566#107—21no—
567#106—21no—
568#106—21no—
569#106—21no—
570#106—21no—
571#106—21no—
572#106—21no—
573#104—22no—
574#104—22no—
575#103—21no—
576#103—21no—
577#102—21no—
578#102—21no—
579#101—22no—
580#101—22no—
581C22⋊C8—21no—
582C22⋊C8—21no—
583#95—21no—
584#95—22no—
585#95—22no—
586#95—22no—
587C24C2×D4×C15111yescharacteristic
588#41—21no—
589#41—21no—
590#41—21no—
591#41—21no—
592C2×Q8—22no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8C2×D4×C15111yescharacteristic
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4C2×D4×C15111yescharacteristic
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—22no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4C2×D4×C15112yes—
617C22×C4C2×D4×C15111yescharacteristic
618C22×C4C2×D4×C15111yescharacteristic
619C22×C4C2×D4×C15111yescharacteristic
620C22×C4C2×D4×C15111yescharacteristic
621C22×C4C2×D4×C15111yescharacteristic
622C22×C4C2×D4×C15112yes—
623C22×C4C24×C15111yescharacteristic
624M16—24no—
625M16—21no—
626M16—21no—
627M16—21no—
628M16—21no—
629M16—21no—
630M16—21no—
631M16#41×C15112yes—
632M16#41×C15112yes—
633C2×C8—24no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—44no—
659C4⋊C4C2×D4×C15111yescharacteristic
660C4⋊C4C2×D4×C15111yescharacteristic
661C4⋊C4C2×D4×C15111yescharacteristic
662C4⋊C4C2×D4×C15111yescharacteristic
663C4⋊C4C2×D4×C15111yescharacteristic
664C4⋊C4C2×D4×C15111yescharacteristic
665C22⋊C4—22no—
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—21no—
676C22⋊C4—21no—
677C22⋊C4—21no—
678C22⋊C4—21no—
679C22⋊C4—42no—
680C22⋊C4—41no—
681C22⋊C4—41no—
682C42—22no—
683C42—22no—
684C42—22no—
685C42—21no—
686C42—21no—
687C42—21no—
688C42—21no—
689C42—21no—
690C42—21no—
691C42—21no—
692C42—21no—
693C42—21no—
694C42—41no—
695C42—41no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—41no—
700C23—41no—
701C23#120×C15111yescharacteristic
702C23#120×C15111yescharacteristic
703C23C22×D4×C15111yescharacteristic
704Q8—21no—
705Q8—21no—
706Q8—41no—
707Q8—41no—
708Q8—41no—
709Q8—41no—
710Q8—82no—
711D4—21no—
712D4—21no—
713D4—42no—
714D4—41no—
715D4—41no—
716D4—81no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—41no—
746C2×C4—42no—
747C2×C4—41no—
748C2×C4—42no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—81no—
753C2×C4—82no—
754C2×C4#120×C15111yescharacteristic
755C2×C4#120×C15111yescharacteristic
756C2×C4C22×D4×C15111yescharacteristic
757C2×C4C22×D4×C15111yescharacteristic
758C2×C4C2×#41×C15111yescharacteristic
759C2×C4C2×#41×C15111yescharacteristic
760C2×C42−1+4×C15111yescharacteristic
761C2×C42−1+4×C15111yescharacteristic
762C8—22no—
763C8—22no—
764C8—41no—
765C8—41no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—81no—
778C22—81no—
779C22C2×#120×C15111yescharacteristic
780C22#547×C15111yescharacteristic
781C22#547×C15111yescharacteristic
782C4—21no—
783C4—21no—
784C4—42no—
785C4—42no—
786C4—41no—
787C4—42no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—41no—
792C4—41no—
793C4—41no—
794C4—81no—
795C4—81no—
796C4—81no—
797C4#525×C15111yescharacteristic
798C4#536×C15111yescharacteristic
799C4#547×C15111yescharacteristic
800C4#547×C15111yescharacteristic
801C2—21no—
802C2—21no—
803C2—41no—
804C2—41no—
805C2—81no—
806C2#2406×C15111yescharacteristic
807C2#3018×C15111yescharacteristic
808C2#3020×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#525×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #2911×C151C2semidirect
4. #2499×C151C2semidirect
5. #2061×C151C2semidirect
6. #2060×C151C2semidirect
7. #2038×C151C2semidirect
8. #2038×C151C2semidirect
9. #1901×C151C2semidirect
11. #1860×C151C2semidirect
12. #1859×C151C2semidirect
13. #1857×C151C2semidirect
14. #1857×C151C2semidirect
15. #1826×C151C2semidirect
404. #24087C151direct (N × H)
405. C151#24087direct (N × H)
408. #2911C2×C151semidirect
409. #2499C2×C151semidirect
410. #2061C2×C151semidirect
411. #2060C2×C151semidirect
412. #2038C2×C151semidirect
413. #2038C2×C151semidirect
414. #1901C2×C151semidirect
416. #1860C2×C151semidirect
417. #1859C2×C151semidirect
418. #1857C2×C151semidirect
419. #1857C2×C151semidirect
420. #1826C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3495×C1512
#3093×C1512
#2911×C1512
#2499×C1512
#2061×C1512
#2060×C1512
#2038×C1512
#1901×C1512
#1871×C1512
#1860×C1512
#1859×C1512
#1857×C1512
#1826×C1512
#24087151