Finite Group Databasebeta

← C151×#24143 #50329068

Subgroups — C151×#24143 #50329068

Order 38656.

1156 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#3505×C151C211yesmaximal, characteristic
2#2627×C151C211yesmaximal, characteristic, complemented
3#2618×C151C211yesmaximal, characteristic, complemented
4#2322×C151C211yesmaximal, characteristic, complemented
5#2044×C151C212yesmaximal, complemented
6#2022×C151C212yesmaximal, complemented
7#1996×C151C211yesmaximal, characteristic, complemented
8#1964×C151C211yesmaximal, characteristic, complemented
9#1890×C151C212yesmaximal, complemented
10#1867×C151C212yesmaximal, complemented
11#1799×C151C211yesmaximal, characteristic, complemented
12#553×C151—22no—
13#553×C151—21no—
14#552×C151—21no—
15#551×C151—22no—
16#548×C151—21no—
17#546×C151—21no—
18#539×C151—21no—
19#538×C151—21no—
20#534×C151C2212yes—
21#529×C151—21no—
22#525×C151—21no—
23C2×#123×C151C2211yescharacteristic
24C2×#123×C151C2212yes—
25C2×C22⋊Q8×C151C2211yescharacteristic
26C2×#121×C151C2211yescharacteristic
27#518×C151C2212yes—
28C2×C4×D4×C151C2211yescharacteristic
29C22×C4⋊C4×C151C2211yescharacteristic
30C2×#99×C151C2212yes—
31C2×#99×C151C2212yes—
32C2×#99×C151C2212yes—
33#400×C151—21no—
34#398×C151—21no—
35#398×C151—22no—
36#396×C151—22no—
37#395×C151—21no—
38#394×C151—21no—
39#389×C151—21no—
40#388×C151—21no—
41#387×C151—21no—
42#386×C151C2212yes—
43#386×C151C2211yescharacteristic
44#385×C151—21no—
45#385×C151C2212yes—
46#385×C151C2211yescharacteristic
47#381×C151C2212yes—
48#381×C151C2211yescharacteristic
49#380×C151C2211yescharacteristic
50#380×C151C2211yescharacteristic
51C4×C22⋊C4×C151C2211yescharacteristic
52#342×C151C2212yes—
53#342×C151C2212yes—
54#342×C151C2212yes—
55C2×#41×C151—21no—
56C22×Q8×C151D411yescharacteristic
57C22×D4×C151D411yescharacteristic
58C22×D4×C151C2311yescharacteristic
59C22×D4×C151C2312yes—
60C23×C4×C151D411yescharacteristic
61C23×C4×C151C2311yescharacteristic
62C23×C4×C151C2311yescharacteristic
63C23×C4×C151C2311yescharacteristic
64#126×C151—22no—
65#126×C151—22no—
66#126×C151—22no—
67#125×C151—21no—
68#125×C151—22no—
69#124×C151—21no—
70#124×C151—22no—
71#123×C151—22no—
72#123×C151—22no—
73#123×C151—22no—
74#123×C151—22no—
75#123×C151—22no—
76#123×C151—22no—
77#123×C151—22no—
78#123×C151—24no—
79#123×C151—42no—
80C22⋊Q8×C151—21no—
81C22⋊Q8×C151—22no—
82C22⋊Q8×C151—21no—
83C22⋊Q8×C151—21no—
84C22⋊Q8×C151—21no—
85C22⋊Q8×C151—21no—
86#121×C151—21no—
87#121×C151—22no—
88#121×C151—21no—
89#121×C151—21no—
90#121×C151—21no—
91#121×C151—21no—
92#121×C151—22no—
93#121×C151—22no—
94#120×C151—22no—
95#120×C151—22no—
96C4×Q8×C151—21no—
97C4×D4×C151—22no—
98C4×D4×C151—21no—
99C4×D4×C151—21no—
100C4×D4×C151—21no—
101C4×D4×C151—21no—
102C4×D4×C151—21no—
103C4×D4×C151—22no—
104C4×D4×C151—22no—
105C4×D4×C151—22no—
106C4×D4×C151—22no—
107#117×C151—21no—
108#117×C151—22no—
109#117×C151—22no—
110C2×C4⋊C4×C151—21no—
111C2×C4⋊C4×C151—21no—
112C2×C4⋊C4×C151—21no—
113C2×C4⋊C4×C151—21no—
114C2×C4⋊C4×C151—21no—
115C2×C4⋊C4×C151—21no—
116C2×C4⋊C4×C151—22no—
117C2×C4⋊C4×C151—21no—
118C2×C4⋊C4×C151—21no—
119C2×C4⋊C4×C151—21no—
120C2×C4⋊C4×C151—21no—
121C2×C4⋊C4×C151—22no—
122C2×C4⋊C4×C151D411yescharacteristic
123C2×C4⋊C4×C151D411yescharacteristic
124C2×C4⋊C4×C151D412yes—
125C2×C4⋊C4×C151D411yescharacteristic
126C2×C22⋊C4×C151—21no—
127C2×C22⋊C4×C151—22no—
128C2×C22⋊C4×C151—22no—
129C2×C22⋊C4×C151—21no—
130C2×C22⋊C4×C151—22no—
131C2×C22⋊C4×C151D411yescharacteristic
132C2×C22⋊C4×C151D412yes—
133C2×C22⋊C4×C151C2312yes—
134C2×C22⋊C4×C151C2311yescharacteristic
135C2×C22⋊C4×C151C2312yes—
136C2×C22⋊C4×C151C2311yescharacteristic
137C2×C22⋊C4×C151C2312yes—
138C2×C22⋊C4×C151C2311yescharacteristic
139C2×C42×C151—21no—
140C2×C42×C151D411yescharacteristic
141#99×C151—24no—
142#99×C151—42no—
143#99×C151—42no—
144#95×C151—21no—
145#95×C151—21no—
146#95×C151—21no—
147#95×C151—21no—
148#95×C151—21no—
149#95×C151—22no—
150#95×C151—22no—
151#95×C151—21no—
152#95×C151—22no—
153#95×C151—21no—
154#95×C151—22no—
155C24×C151C2×D412yes—
156C24×C151C2×D411yescharacteristic
157C24×C151C2411yescharacteristic
158#41×C151—82no—
159C2×Q8×C151—21no—
160C2×Q8×C151—21no—
161C2×Q8×C151—81no—
162C2×D4×C151—21no—
163C2×D4×C151—22no—
164C2×D4×C151—21no—
165C2×D4×C151—22no—
166C2×D4×C151—22no—
167C2×D4×C151—21no—
168C2×D4×C151—21no—
169C2×D4×C151—22no—
170C2×D4×C151—21no—
171C2×D4×C151—22no—
172C2×D4×C151—21no—
173C2×D4×C151—22no—
174C2×D4×C151—22no—
175C2×D4×C151—22no—
176C2×D4×C151—21no—
177C2×D4×C151—21no—
178C2×D4×C151—81no—
179C22×C4×C151—21no—
180C22×C4×C151—21no—
181C22×C4×C151—21no—
182C22×C4×C151—21no—
183C22×C4×C151—21no—
184C22×C4×C151—21no—
185C22×C4×C151—21no—
186C22×C4×C151—22no—
187C22×C4×C151—22no—
188C22×C4×C151—21no—
189C22×C4×C151—21no—
190C22×C4×C151—21no—
191C22×C4×C151—22no—
192C22×C4×C151—22no—
193C22×C4×C151—21no—
194C22×C4×C151—21no—
195C22×C4×C151—21no—
196C22×C4×C151—81no—
197C22×C4×C151—81no—
198C22×C4×C151—81no—
199C22×C4×C151C2×D411yescharacteristic
200C22×C4×C151C2×D412yes—
201C22×C4×C151C2×D411yescharacteristic
202C22×C4×C151C2×D412yes—
203C22×C4×C151C2×D411yescharacteristic
204C22×C4×C151C2×D412yes—
205C22×C4×C151C2×D411yescharacteristic
206C22×C4×C151C2×D411yescharacteristic
207C22×C4×C151C2×D411yescharacteristic
208C22×C4×C151C2×D411yescharacteristic
209C22×C4×C151C2×D411yescharacteristic
210C22×C4×C151C2×D411yescharacteristic
211C22×C4×C151#4112yescomplemented
212C4⋊C4×C151—24no—
213C4⋊C4×C151—22no—
214C4⋊C4×C151—22no—
215C4⋊C4×C151—22no—
216C4⋊C4×C151—22no—
217C4⋊C4×C151—21no—
218C4⋊C4×C151—22no—
219C4⋊C4×C151—21no—
220C4⋊C4×C151—21no—
221C4⋊C4×C151—21no—
222C4⋊C4×C151—21no—
223C4⋊C4×C151—22no—
224C4⋊C4×C151—21no—
225C4⋊C4×C151—44no—
226C4⋊C4×C151—41no—
227C4⋊C4×C151—41no—
228C4⋊C4×C151—41no—
229C4⋊C4×C151—41no—
230C4⋊C4×C151—81no—
231C4⋊C4×C151—81no—
232C4⋊C4×C151—81no—
233C4⋊C4×C151—82no—
234C22⋊C4×C151—22no—
235C22⋊C4×C151—22no—
236C22⋊C4×C151—24no—
237C22⋊C4×C151—22no—
238C22⋊C4×C151—22no—
239C22⋊C4×C151—22no—
240C22⋊C4×C151—22no—
241C22⋊C4×C151—21no—
242C22⋊C4×C151—22no—
243C22⋊C4×C151—21no—
244C22⋊C4×C151—22no—
245C22⋊C4×C151—21no—
246C22⋊C4×C151—22no—
247C22⋊C4×C151—21no—
248C22⋊C4×C151—21no—
249C22⋊C4×C151—22no—
250C22⋊C4×C151—22no—
251C22⋊C4×C151—22no—
252C22⋊C4×C151—21no—
253C22⋊C4×C151—22no—
254C22⋊C4×C151—22no—
255C22⋊C4×C151—21no—
256C22⋊C4×C151—44no—
257C22⋊C4×C151—81no—
258C22⋊C4×C151—82no—
259C22⋊C4×C151#4112yescomplemented
260C42×C151—22no—
261C42×C151—22no—
262C42×C151—21no—
263C42×C151—21no—
264C42×C151—81no—
265C23×C151—21no—
266C23×C151—22no—
267C23×C151—21no—
268C23×C151—21no—
269C23×C151—22no—
270C23×C151—22no—
271C23×C151—41no—
272C23×C151—41no—
273C23×C151—41no—
274C23×C151—41no—
275C23×C151—42no—
276C23×C151—42no—
277C23×C151C22×D411yescharacteristic
278C23×C151C22×D411yescharacteristic
279C23×C151C22×D411yescharacteristic
280C23×C151C2×#4111yescharacteristic
281C23×C151C2×#4111yescharacteristic
282C23×C151H(5,𝔽2)11yescharacteristic
283C23×C1512−1+411yescharacteristic
284Q8×C151—42no—
285Q8×C151—81no—
286D4×C151—42no—
287D4×C151—42no—
288D4×C151—42no—
289D4×C151—41no—
290D4×C151—41no—
291D4×C151—41no—
292D4×C151—42no—
293D4×C151—42no—
294D4×C151—41no—
295D4×C151—81no—
296D4×C151—82no—
297D4×C151—82no—
298C2×C4×C151—22no—
299C2×C4×C151—21no—
300C2×C4×C151—22no—
301C2×C4×C151—21no—
302C2×C4×C151—21no—
303C2×C4×C151—22no—
304C2×C4×C151—22no—
305C2×C4×C151—22no—
306C2×C4×C151—21no—
307C2×C4×C151—21no—
308C2×C4×C151—22no—
309C2×C4×C151—22no—
310C2×C4×C151—22no—
311C2×C4×C151—22no—
312C2×C4×C151—41no—
313C2×C4×C151—41no—
314C2×C4×C151—41no—
315C2×C4×C151—41no—
316C2×C4×C151—41no—
317C2×C4×C151—41no—
318C2×C4×C151—42no—
319C2×C4×C151—41no—
320C2×C4×C151—41no—
321C2×C4×C151—41no—
322C2×C4×C151—41no—
323C2×C4×C151—41no—
324C2×C4×C151—41no—
325C2×C4×C151—42no—
326C2×C4×C151—41no—
327C2×C4×C151—41no—
328C2×C4×C151—42no—
329C2×C4×C151—41no—
330C2×C4×C151—42no—
331C2×C4×C151—41no—
332C2×C4×C151—42no—
333C2×C4×C151—42no—
334C2×C4×C151—42no—
335C2×C4×C151—41no—
336C2×C4×C151—42no—
337C2×C4×C151—41no—
338C2×C4×C151—42no—
339C2×C4×C151—41no—
340C2×C4×C151—41no—
341C2×C4×C151—42no—
342C2×C4×C151—42no—
343C2×C4×C151—81no—
344C2×C4×C151—82no—
345C2×C4×C151—82no—
346C2×C4×C151#12011yescharacteristic
347C2×C4×C151#12011yescharacteristic
348C2×C4×C151#12011yescharacteristic
349C2×C4×C151#12011yescharacteristic
350C22×C151—21no—
351C22×C151—21no—
352C22×C151—21no—
353C22×C151—21no—
354C22×C151—21no—
355C22×C151—21no—
356C22×C151—41no—
357C22×C151—41no—
358C22×C151—41no—
359C22×C151—41no—
360C22×C151—42no—
361C22×C151—41no—
362C22×C151—42no—
363C22×C151—41no—
364C22×C151—42no—
365C22×C151—42no—
366C22×C151—41no—
367C22×C151—82no—
368C22×C151—81no—
369C22×C151—82no—
370C22×C151C2×#12011yescharacteristic
371C22×C151#52511yescharacteristic
372C22×C151#53711yescharacteristic
373C22×C151#54611yescharacteristic
374C22×C151#54711yescharacteristic
375C22×C151#54811yescharacteristic
376C22×C151#55011yescharacteristic
377C4×C151—21no—
378C4×C151—21no—
379C4×C151—21no—
380C4×C151—21no—
381C4×C151—42no—
382C4×C151—42no—
383C4×C151—41no—
384C4×C151—42no—
385C4×C151—41no—
386C4×C151—42no—
387C4×C151—41no—
388C4×C151—42no—
389C4×C151—82no—
390C4×C151—82no—
391C4×C151—81no—
392C4×C151—81no—
393C2×C151—21no—
394C2×C151—21no—
395C2×C151—21no—
396C2×C151—21no—
397C2×C151—21no—
398C2×C151—21no—
399C2×C151—81no—
400C2×C151—82no—
401C2×C151#240711yescharacteristic
402C2×C151#302611yescharacteristic
403C2×C151#302811yescharacteristic
404#24143C15111yesmaximal, characteristic, direct product factor, Sylow
405C151#2414311yescharacteristic, direct product factor, Sylow
406#3505C2×C15111yescharacteristic
407#2627C2×C15111yescharacteristic, complemented
408#2618C2×C15111yescharacteristic, complemented
409#2322C2×C15111yescharacteristic, complemented
410#2044C2×C15112yescomplemented
411#2022C2×C15112yescomplemented
412#1996C2×C15111yescharacteristic, complemented
413#1964C2×C15111yescharacteristic, complemented
414#1890C2×C15112yescomplemented
415#1867C2×C15112yescomplemented
416#1799C2×C15111yescharacteristic, complemented
417#553—22no—
418#553—21no—
419#552—21no—
420#551—22no—
421#548—21no—
422#546—21no—
423#539—21no—
424#538—21no—
425#534C22×C15112yes—
426#529—21no—
427#525—21no—
428C2×#123C22×C15111yescharacteristic
429C2×#123C22×C15112yes—
430C2×C22⋊Q8C22×C15111yescharacteristic
431C2×#121C22×C15111yescharacteristic
432#518C22×C15112yes—
433C2×C4×D4C22×C15111yescharacteristic
434C22×C4⋊C4C22×C15111yescharacteristic
435C2×#99C22×C15112yes—
436C2×#99C22×C15112yes—
437C2×#99C22×C15112yes—
438#400—21no—
439#398—21no—
440#398—22no—
441#396—22no—
442#395—21no—
443#394—21no—
444#389—21no—
445#388—21no—
446#387—21no—
447#386C22×C15111yescharacteristic
448#386C22×C15112yes—
449#385—21no—
450#385C22×C15111yescharacteristic
451#385C22×C15112yes—
452#381C22×C15111yescharacteristic
453#381C22×C15112yes—
454#380C22×C15111yescharacteristic
455#380C22×C15111yescharacteristic
456C4×C22⋊C4C22×C15111yescharacteristic
457#342C22×C15112yes—
458#342C22×C15112yes—
459#342C22×C15112yes—
460C2×#41—21no—
461C22×Q8D4×C15111yescharacteristic
462C22×D4D4×C15111yescharacteristic
463C22×D4C23×C15111yescharacteristic
464C22×D4C23×C15112yes—
465C23×C4D4×C15111yescharacteristic
466C23×C4C23×C15111yescharacteristic
467C23×C4C23×C15111yescharacteristic
468C23×C4C23×C15111yescharacteristic
469#126—22no—
470#126—22no—
471#126—22no—
472#125—21no—
473#125—22no—
474#124—21no—
475#124—22no—
476#123—22no—
477#123—22no—
478#123—22no—
479#123—22no—
480#123—22no—
481#123—22no—
482#123—22no—
483#123—24no—
484#123—42no—
485C22⋊Q8—21no—
486C22⋊Q8—22no—
487C22⋊Q8—21no—
488C22⋊Q8—21no—
489C22⋊Q8—21no—
490C22⋊Q8—21no—
491#121—21no—
492#121—22no—
493#121—21no—
494#121—21no—
495#121—21no—
496#121—21no—
497#121—22no—
498#121—22no—
499#120—22no—
500#120—22no—
501C4×Q8—21no—
502C4×D4—22no—
503C4×D4—21no—
504C4×D4—21no—
505C4×D4—21no—
506C4×D4—21no—
507C4×D4—21no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512#117—21no—
513#117—22no—
514#117—22no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—22no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—22no—
527C2×C4⋊C4D4×C15111yescharacteristic
528C2×C4⋊C4D4×C15111yescharacteristic
529C2×C4⋊C4D4×C15112yes—
530C2×C4⋊C4D4×C15111yescharacteristic
531C2×C22⋊C4—22no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—22no—
536C2×C22⋊C4D4×C15111yescharacteristic
537C2×C22⋊C4D4×C15112yes—
538C2×C22⋊C4C23×C15112yes—
539C2×C22⋊C4C23×C15111yescharacteristic
540C2×C22⋊C4C23×C15112yes—
541C2×C22⋊C4C23×C15111yescharacteristic
542C2×C22⋊C4C23×C15112yes—
543C2×C22⋊C4C23×C15111yescharacteristic
544C2×C42—21no—
545C2×C42D4×C15111yescharacteristic
546#99—24no—
547#99—42no—
548#99—42no—
549#95—21no—
550#95—21no—
551#95—21no—
552#95—21no—
553#95—21no—
554#95—22no—
555#95—22no—
556#95—21no—
557#95—22no—
558#95—21no—
559#95—22no—
560C24C2×D4×C15112yes—
561C24C2×D4×C15111yescharacteristic
562C24C24×C15111yescharacteristic
563#41—82no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—81no—
567C2×D4—21no—
568C2×D4—22no—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—22no—
575C2×D4—21no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—81no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—81no—
602C22×C4—81no—
603C22×C4—81no—
604C22×C4C2×D4×C15111yescharacteristic
605C22×C4C2×D4×C15112yes—
606C22×C4C2×D4×C15111yescharacteristic
607C22×C4C2×D4×C15112yes—
608C22×C4C2×D4×C15111yescharacteristic
609C22×C4C2×D4×C15112yes—
610C22×C4C2×D4×C15111yescharacteristic
611C22×C4C2×D4×C15111yescharacteristic
612C22×C4C2×D4×C15111yescharacteristic
613C22×C4C2×D4×C15111yescharacteristic
614C22×C4C2×D4×C15111yescharacteristic
615C22×C4C2×D4×C15111yescharacteristic
616C22×C4#41×C15112yescomplemented
617C4⋊C4—24no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—21no—
623C4⋊C4—22no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—22no—
629C4⋊C4—21no—
630C4⋊C4—44no—
631C4⋊C4—41no—
632C4⋊C4—41no—
633C4⋊C4—41no—
634C4⋊C4—41no—
635C4⋊C4—81no—
636C4⋊C4—81no—
637C4⋊C4—81no—
638C4⋊C4—82no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—24no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—21no—
647C22⋊C4—22no—
648C22⋊C4—21no—
649C22⋊C4—22no—
650C22⋊C4—21no—
651C22⋊C4—22no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—21no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—21no—
661C22⋊C4—44no—
662C22⋊C4—81no—
663C22⋊C4—82no—
664C22⋊C4#41×C15112yescomplemented
665C42—22no—
666C42—22no—
667C42—21no—
668C42—21no—
669C42—81no—
670C23—21no—
671C23—22no—
672C23—21no—
673C23—21no—
674C23—22no—
675C23—22no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—42no—
681C23—42no—
682C23C22×D4×C15111yescharacteristic
683C23C22×D4×C15111yescharacteristic
684C23C22×D4×C15111yescharacteristic
685C23C2×#41×C15111yescharacteristic
686C23C2×#41×C15111yescharacteristic
687C23H(5,𝔽2)×C15111yescharacteristic
688C232−1+4×C15111yescharacteristic
689Q8—42no—
690Q8—81no—
691D4—42no—
692D4—42no—
693D4—42no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—42no—
698D4—42no—
699D4—41no—
700D4—81no—
701D4—82no—
702D4—82no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—41no—
735C2×C4—42no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—42no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—81no—
749C2×C4—82no—
750C2×C4—82no—
751C2×C4#120×C15111yescharacteristic
752C2×C4#120×C15111yescharacteristic
753C2×C4#120×C15111yescharacteristic
754C2×C4#120×C15111yescharacteristic
755C22—21no—
756C22—21no—
757C22—21no—
758C22—21no—
759C22—21no—
760C22—21no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—42no—
766C22—41no—
767C22—42no—
768C22—41no—
769C22—42no—
770C22—42no—
771C22—41no—
772C22—82no—
773C22—81no—
774C22—82no—
775C22C2×#120×C15111yescharacteristic
776C22#525×C15111yescharacteristic
777C22#537×C15111yescharacteristic
778C22#546×C15111yescharacteristic
779C22#547×C15111yescharacteristic
780C22#548×C15111yescharacteristic
781C22#550×C15111yescharacteristic
782C4—21no—
783C4—21no—
784C4—21no—
785C4—21no—
786C4—42no—
787C4—42no—
788C4—41no—
789C4—42no—
790C4—41no—
791C4—42no—
792C4—41no—
793C4—42no—
794C4—82no—
795C4—82no—
796C4—81no—
797C4—81no—
798C2—21no—
799C2—21no—
800C2—21no—
801C2—21no—
802C2—21no—
803C2—21no—
804C2—81no—
805C2—82no—
806C2#2407×C15111yescharacteristic
807C2#3026×C15111yescharacteristic
808C2#3028×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC24C24×C151
prime radical#3505×C151C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2627×C151C2semidirect
3. #2618×C151C2semidirect
4. #2322×C151C2semidirect
5. #2044×C151C2semidirect
6. #2022×C151C2semidirect
7. #1996×C151C2semidirect
8. #1964×C151C2semidirect
9. #1890×C151C2semidirect
10. #1867×C151C2semidirect
11. #1799×C151C2semidirect
211. C22×C4×C151#41semidirect
259. C22⋊C4×C151#41semidirect
404. #24143C151direct (N × H)
405. C151#24143direct (N × H)
407. #2627C2×C151semidirect
408. #2618C2×C151semidirect
409. #2322C2×C151semidirect
410. #2044C2×C151semidirect
411. #2022C2×C151semidirect
412. #1996C2×C151semidirect
413. #1964C2×C151semidirect
414. #1890C2×C151semidirect
415. #1867C2×C151semidirect
416. #1799C2×C151semidirect
616. C22×C4#41×C151semidirect
664. C22⋊C4#41×C151semidirect

Maximal subgroups

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

subgroupindex
#3505×C1512
#2627×C1512
#2618×C1512
#2322×C1512
#2044×C1512
#2022×C1512
#1996×C1512
#1964×C1512
#1890×C1512
#1867×C1512
#1799×C1512
#24143151