Finite Group Databasebeta

← C151×#24525 #50329450

Subgroups — C151×#24525 #50329450

Order 38656.

858 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3095×C151C211yesmaximal, characteristic, complemented
2C2×#452×C151C211yesmaximal, characteristic
3#2924×C151C211yesmaximal, characteristic, complemented
4#2896×C151C211yesmaximal, characteristic
5#2064×C151C211yesmaximal, characteristic, complemented
6#2063×C151C211yesmaximal, characteristic, complemented
7#2047×C151C211yesmaximal, characteristic, complemented
8#2046×C151C211yesmaximal, characteristic, complemented
9#1979×C151C211yesmaximal, characteristic, complemented
10#1977×C151C211yesmaximal, characteristic, complemented
11#1931×C151C211yesmaximal, characteristic, complemented
12#1930×C151C211yesmaximal, characteristic, complemented
13#1901×C151C211yesmaximal, characteristic, complemented
14#1855×C151C211yesmaximal, characteristic, complemented
15#1785×C151C211yesmaximal, characteristic
16C22×#41×C151C2211yescharacteristic
17C22×Q16×C151C2211yescharacteristic
18C22×SD16×C151C2211yescharacteristic
19C22×M16×C151C2211yescharacteristic
20C2×C22⋊Q8×C151C2211yescharacteristic
21C2×#117×C151C2211yescharacteristic
22#485×C151—21no—
23#485×C151—21no—
24#484×C151—21no—
25#483×C151—21no—
26#452×C151—21no—
27#452×C151—21no—
28#452×C151—21no—
29#452×C151—21no—
30#433×C151—21no—
31#433×C151—21no—
32#432×C151—21no—
33#431×C151—21no—
34C2×#108×C151C2211yescharacteristic
35C2×#108×C151C2211yescharacteristic
36#428×C151C2211yescharacteristic
37#428×C151C2211yescharacteristic
38#424×C151C2211yescharacteristic
39#424×C151C2211yescharacteristic
40#419×C151C2211yescharacteristic
41#419×C151C2211yescharacteristic
42#419×C151C2211yescharacteristic
43#419×C151C2211yescharacteristic
44#418×C151C2211yescharacteristic
45#418×C151C2211yescharacteristic
46#417×C151—21no—
47#417×C151—21no—
48#416×C151—21no—
49#416×C151—21no—
50C2×#103×C151C2211yescharacteristic
51C2×#102×C151C2211yescharacteristic
52C2×#101×C151C2211yescharacteristic
53C2×#101×C151C2211yescharacteristic
54C2×#101×C151C2211yescharacteristic
55C2×#101×C151C2211yescharacteristic
56C2×#100×C151C2211yescharacteristic
57C2×#100×C151C2211yescharacteristic
58#407×C151C2211yescharacteristic
59#407×C151C2211yescharacteristic
60C2×C22⋊C8×C151C2211yescharacteristic
61#405×C151C2211yescharacteristic
62#405×C151C2211yescharacteristic
63#343×C151C2211yescharacteristic
64#343×C151C2211yescharacteristic
65#341×C151C2211yescharacteristic
66#341×C151C2211yescharacteristic
67C2×#41×C151—22no—
68C2×#41×C151—21no—
69C2×#41×C151—21no—
70C2×#41×C151—21no—
71C2×#41×C151—21no—
72C2×#41×C151—22no—
73C2×#41×C151—41no—
74C2×#41×C151—41no—
75C22×Q8×C151C2311yescharacteristic
76C22×Q8×C151C2311yescharacteristic
77C22×D4×C151—21no—
78C22×D4×C151C2311yescharacteristic
79C23×C4×C151—21no—
80C23×C4×C151C2311yescharacteristic
81C2×Q16×C151—21no—
82C2×Q16×C151—21no—
83C2×Q16×C151—22no—
84C2×Q16×C151—41no—
85C2×SD16×C151—22no—
86C2×SD16×C151—21no—
87C2×SD16×C151—21no—
88C2×SD16×C151—41no—
89C2×M16×C151—21no—
90C2×M16×C151—41no—
91C2×M16×C151—41no—
92C2×M16×C151C2311yescharacteristic
93C2×M16×C151C2311yescharacteristic
94C2×M16×C151C2311yescharacteristic
95C2×M16×C151C2311yescharacteristic
96C2×M16×C151C2311yescharacteristic
97C2×M16×C151C2311yescharacteristic
98C22×C8×C151—21no—
99C22×C8×C151C2311yescharacteristic
100C22×C8×C151C2311yescharacteristic
101C22⋊Q8×C151—21no—
102C22⋊Q8×C151—21no—
103C22⋊Q8×C151—21no—
104C22⋊Q8×C151—21no—
105#117×C151—21no—
106#117×C151—21no—
107#117×C151D411yescharacteristic
108#117×C151D411yescharacteristic
109#117×C151C2311yescharacteristic
110#117×C151C2311yescharacteristic
111C2×C4⋊C4×C151—21no—
112C2×C4⋊C4×C151D411yescharacteristic
113C2×C4⋊C4×C151D411yescharacteristic
114C2×C4⋊C4×C151C2311yescharacteristic
115C2×C22⋊C4×C151—21no—
116C2×C22⋊C4×C151—21no—
117C2×C42×C151—21no—
118#108×C151—41no—
119#108×C151—41no—
120#107×C151—21no—
121#107×C151—21no—
122#106×C151—21no—
123#106×C151—21no—
124C4⋊C8×C151—21no—
125C4⋊C8×C151—21no—
126C4⋊C8×C151—21no—
127C4⋊C8×C151—21no—
128#103×C151—21no—
129#103×C151—21no—
130#103×C151—21no—
131#103×C151—21no—
132#103×C151—21no—
133#103×C151—21no—
134#103×C151—21no—
135#103×C151—21no—
136#103×C151—21no—
137#103×C151—21no—
138#102×C151—21no—
139#102×C151—21no—
140#102×C151—21no—
141#102×C151—21no—
142#102×C151—21no—
143#102×C151—21no—
144#101×C151—22no—
145#101×C151—41no—
146#101×C151—41no—
147#101×C151—41no—
148#100×C151—22no—
149#100×C151—41no—
150C22⋊C8×C151—21no—
151C22⋊C8×C151—21no—
152C22⋊C8×C151—21no—
153C22⋊C8×C151—21no—
154C22⋊C8×C151D411yescharacteristic
155C22⋊C8×C151D411yescharacteristic
156C22⋊C8×C151D411yescharacteristic
157C22⋊C8×C151D411yescharacteristic
158#97×C151—21no—
159#97×C151—21no—
160C4×C8×C151—21no—
161C4×C8×C151—21no—
162C24×C151—21no—
163C24×C151#4111yescharacteristic
164#41×C151—24no—
165#41×C151—24no—
166#41×C151—42no—
167#41×C151—42no—
168#41×C151—42no—
169#41×C151—42no—
170#41×C151—42no—
171#41×C151—42no—
172C2×Q8×C151—21no—
173C2×Q8×C151—21no—
174C2×Q8×C151—21no—
175C2×Q8×C151—21no—
176C2×Q8×C151—21no—
177C2×Q8×C151—21no—
178C2×Q8×C151—21no—
179C2×Q8×C151—21no—
180C2×Q8×C151—21no—
181C2×Q8×C151—21no—
182C2×Q8×C151—21no—
183C2×Q8×C151#4112yes—
184C2×D4×C151—21no—
185C2×D4×C151—21no—
186C2×D4×C151—21no—
187C2×D4×C151—21no—
188C2×D4×C151—21no—
189C2×D4×C151—42no—
190C2×D4×C151—42no—
191C2×D4×C151—41no—
192C2×D4×C151—41no—
193C2×D4×C151#4112yes—
194C22×C4×C151—21no—
195C22×C4×C151—21no—
196C22×C4×C151—21no—
197C22×C4×C151—21no—
198C22×C4×C151—21no—
199C22×C4×C151—21no—
200C22×C4×C151—21no—
201C22×C4×C151—21no—
202C22×C4×C151—21no—
203C22×C4×C151—42no—
204C22×C4×C151—42no—
205C22×C4×C151—41no—
206C22×C4×C151—41no—
207C22×C4×C151C2×D411yescharacteristic
208C22×C4×C151C2×D411yescharacteristic
209C22×C4×C151C2×D411yescharacteristic
210C22×C4×C151C2×D411yescharacteristic
211C22×C4×C151#4111yescharacteristic
212C22×C4×C151C2411yescharacteristic
213Q16×C151—42no—
214Q16×C151—42no—
215SD16×C151—42no—
216SD16×C151—42no—
217M16×C151—21no—
218M16×C151—21no—
219M16×C151—21no—
220M16×C151—21no—
221M16×C151—21no—
222M16×C151—21no—
223M16×C151—21no—
224M16×C151—21no—
225M16×C151—21no—
226M16×C151—21no—
227M16×C151—21no—
228M16×C151—21no—
229M16×C151—42no—
230C2×C8×C151—21no—
231C2×C8×C151—21no—
232C2×C8×C151—21no—
233C2×C8×C151—21no—
234C2×C8×C151—21no—
235C2×C8×C151—21no—
236C2×C8×C151—21no—
237C2×C8×C151—21no—
238C2×C8×C151—21no—
239C2×C8×C151—21no—
240C2×C8×C151—42no—
241C2×C8×C151C2×D411yescharacteristic
242C2×C8×C151C2×D411yescharacteristic
243C2×C8×C151C2×D411yescharacteristic
244C2×C8×C151C2×D411yescharacteristic
245C4⋊C4×C151—21no—
246C4⋊C4×C151—21no—
247C4⋊C4×C151—21no—
248C4⋊C4×C151—21no—
249C4⋊C4×C151—41no—
250C4⋊C4×C151—41no—
251C4⋊C4×C151C2×D411yescharacteristic
252C4⋊C4×C151C2×D411yescharacteristic
253C4⋊C4×C151C2×D411yescharacteristic
254C4⋊C4×C151C2×D411yescharacteristic
255C22⋊C4×C151—21no—
256C22⋊C4×C151—21no—
257C22⋊C4×C151—21no—
258C22⋊C4×C151—21no—
259C22⋊C4×C151—41no—
260C22⋊C4×C151—41no—
261C42×C151—21no—
262C42×C151—21no—
263C42×C151—21no—
264C42×C151—21no—
265C23×C151—21no—
266C23×C151—21no—
267C23×C151—22no—
268C23×C151—41no—
269C23×C151—41no—
270C23×C151—41no—
271C23×C151—41no—
272C23×C151—81no—
273C23×C151—81no—
274C23×C151#12111yescharacteristic
275C23×C151#12111yescharacteristic
276C23×C151C2×#4111yescharacteristic
277Q8×C151—22no—
278Q8×C151—22no—
279Q8×C151—41no—
280Q8×C151—41no—
281Q8×C151—41no—
282Q8×C151—41no—
283Q8×C151—41no—
284Q8×C151—41no—
285D4×C151—22no—
286D4×C151—22no—
287D4×C151—44no—
288D4×C151—44no—
289D4×C151—41no—
290D4×C151—41no—
291C2×C4×C151—21no—
292C2×C4×C151—21no—
293C2×C4×C151—21no—
294C2×C4×C151—21no—
295C2×C4×C151—21no—
296C2×C4×C151—21no—
297C2×C4×C151—21no—
298C2×C4×C151—21no—
299C2×C4×C151—21no—
300C2×C4×C151—21no—
301C2×C4×C151—21no—
302C2×C4×C151—21no—
303C2×C4×C151—21no—
304C2×C4×C151—21no—
305C2×C4×C151—22no—
306C2×C4×C151—44no—
307C2×C4×C151—44no—
308C2×C4×C151—42no—
309C2×C4×C151—41no—
310C2×C4×C151—41no—
311C2×C4×C151—41no—
312C2×C4×C151—41no—
313C2×C4×C151—41no—
314C2×C4×C151—41no—
315C2×C4×C151—81no—
316C2×C4×C151—81no—
317C2×C4×C151#12111yescharacteristic
318C2×C4×C151#12111yescharacteristic
319C2×C4×C151C22×D411yescharacteristic
320C2×C4×C151C22×D411yescharacteristic
321C2×C4×C151C2×#4111yescharacteristic
322C2×C4×C151C2×#4111yescharacteristic
323C2×C4×C151H(5,𝔽2)11yescharacteristic
324C2×C4×C151H(5,𝔽2)11yescharacteristic
325C8×C151—21no—
326C8×C151—21no—
327C8×C151—21no—
328C8×C151—21no—
329C8×C151—41no—
330C8×C151—41no—
331C8×C151—41no—
332C8×C151—41no—
333C8×C151—41no—
334C8×C151—41no—
335C22×C151—21no—
336C22×C151—21no—
337C22×C151—21no—
338C22×C151—21no—
339C22×C151—21no—
340C22×C151—21no—
341C22×C151—21no—
342C22×C151—21no—
343C22×C151—42no—
344C22×C151—81no—
345C22×C151—81no—
346C22×C151—82no—
347C22×C151—82no—
348C22×C151—81no—
349C22×C151—81no—
350C22×C151C2×#12111yescharacteristic
351C22×C151#55111yescharacteristic
352C22×C151#55111yescharacteristic
353C4×C151—21no—
354C4×C151—21no—
355C4×C151—42no—
356C4×C151—41no—
357C4×C151—41no—
358C4×C151—41no—
359C4×C151—41no—
360C4×C151—81no—
361C4×C151—81no—
362C4×C151#52511yescharacteristic
363C4×C151#53511yescharacteristic
364C4×C151#54611yescharacteristic
365C4×C151#54611yescharacteristic
366C2×C151—21no—
367C2×C151—21no—
368C2×C151—41no—
369C2×C151—41no—
370C2×C151—82no—
371C2×C151#241111yescharacteristic
372C2×C151#306711yescharacteristic
373C2×C151#306911yescharacteristic
374#24525C15111yesmaximal, characteristic, direct product factor, Sylow
375C151#2452511yescharacteristic, direct product factor, Sylow
376#3095C2×C15111yescharacteristic, complemented
377C2×#452C2×C15111yescharacteristic
378#2924C2×C15111yescharacteristic, complemented
379#2896C2×C15111yescharacteristic
380#2064C2×C15111yescharacteristic, complemented
381#2063C2×C15111yescharacteristic, complemented
382#2047C2×C15111yescharacteristic, complemented
383#2046C2×C15111yescharacteristic, complemented
384#1979C2×C15111yescharacteristic, complemented
385#1977C2×C15111yescharacteristic, complemented
386#1931C2×C15111yescharacteristic, complemented
387#1930C2×C15111yescharacteristic, complemented
388#1901C2×C15111yescharacteristic, complemented
389#1855C2×C15111yescharacteristic, complemented
390#1785C2×C15111yescharacteristic
391C22×#41C22×C15111yescharacteristic
392C22×Q16C22×C15111yescharacteristic
393C22×SD16C22×C15111yescharacteristic
394C22×M16C22×C15111yescharacteristic
395C2×C22⋊Q8C22×C15111yescharacteristic
396C2×#117C22×C15111yescharacteristic
397#485—21no—
398#485—21no—
399#484—21no—
400#483—21no—
401#452—21no—
402#452—21no—
403#452—21no—
404#452—21no—
405#433—21no—
406#433—21no—
407#432—21no—
408#431—21no—
409C2×#108C22×C15111yescharacteristic
410C2×#108C22×C15111yescharacteristic
411#428C22×C15111yescharacteristic
412#428C22×C15111yescharacteristic
413#424C22×C15111yescharacteristic
414#424C22×C15111yescharacteristic
415#419C22×C15111yescharacteristic
416#419C22×C15111yescharacteristic
417#419C22×C15111yescharacteristic
418#419C22×C15111yescharacteristic
419#418C22×C15111yescharacteristic
420#418C22×C15111yescharacteristic
421#417—21no—
422#417—21no—
423#416—21no—
424#416—21no—
425C2×#103C22×C15111yescharacteristic
426C2×#102C22×C15111yescharacteristic
427C2×#101C22×C15111yescharacteristic
428C2×#101C22×C15111yescharacteristic
429C2×#101C22×C15111yescharacteristic
430C2×#101C22×C15111yescharacteristic
431C2×#100C22×C15111yescharacteristic
432C2×#100C22×C15111yescharacteristic
433#407C22×C15111yescharacteristic
434#407C22×C15111yescharacteristic
435C2×C22⋊C8C22×C15111yescharacteristic
436#405C22×C15111yescharacteristic
437#405C22×C15111yescharacteristic
438#343C22×C15111yescharacteristic
439#343C22×C15111yescharacteristic
440#341C22×C15111yescharacteristic
441#341C22×C15111yescharacteristic
442C2×#41—22no—
443C2×#41—22no—
444C2×#41—21no—
445C2×#41—21no—
446C2×#41—21no—
447C2×#41—21no—
448C2×#41—41no—
449C2×#41—41no—
450C22×Q8C23×C15111yescharacteristic
451C22×Q8C23×C15111yescharacteristic
452C22×D4—21no—
453C22×D4C23×C15111yescharacteristic
454C23×C4—21no—
455C23×C4C23×C15111yescharacteristic
456C2×Q16—22no—
457C2×Q16—21no—
458C2×Q16—21no—
459C2×Q16—41no—
460C2×SD16—22no—
461C2×SD16—21no—
462C2×SD16—21no—
463C2×SD16—41no—
464C2×M16—21no—
465C2×M16—41no—
466C2×M16—41no—
467C2×M16C23×C15111yescharacteristic
468C2×M16C23×C15111yescharacteristic
469C2×M16C23×C15111yescharacteristic
470C2×M16C23×C15111yescharacteristic
471C2×M16C23×C15111yescharacteristic
472C2×M16C23×C15111yescharacteristic
473C22×C8—21no—
474C22×C8C23×C15111yescharacteristic
475C22×C8C23×C15111yescharacteristic
476C22⋊Q8—21no—
477C22⋊Q8—21no—
478C22⋊Q8—21no—
479C22⋊Q8—21no—
480#117—21no—
481#117—21no—
482#117D4×C15111yescharacteristic
483#117D4×C15111yescharacteristic
484#117C23×C15111yescharacteristic
485#117C23×C15111yescharacteristic
486C2×C4⋊C4—21no—
487C2×C4⋊C4D4×C15111yescharacteristic
488C2×C4⋊C4D4×C15111yescharacteristic
489C2×C4⋊C4C23×C15111yescharacteristic
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C42—21no—
493#108—41no—
494#108—41no—
495#107—21no—
496#107—21no—
497#106—21no—
498#106—21no—
499C4⋊C8—21no—
500C4⋊C8—21no—
501C4⋊C8—21no—
502C4⋊C8—21no—
503#103—21no—
504#103—21no—
505#103—21no—
506#103—21no—
507#103—21no—
508#103—21no—
509#103—21no—
510#103—21no—
511#103—21no—
512#103—21no—
513#102—21no—
514#102—21no—
515#102—21no—
516#102—21no—
517#102—21no—
518#102—21no—
519#101—22no—
520#101—41no—
521#101—41no—
522#101—41no—
523#100—22no—
524#100—41no—
525C22⋊C8—21no—
526C22⋊C8—21no—
527C22⋊C8—21no—
528C22⋊C8—21no—
529C22⋊C8D4×C15111yescharacteristic
530C22⋊C8D4×C15111yescharacteristic
531C22⋊C8D4×C15111yescharacteristic
532C22⋊C8D4×C15111yescharacteristic
533#97—21no—
534#97—21no—
535C4×C8—21no—
536C4×C8—21no—
537C24—21no—
538C24#41×C15111yescharacteristic
539#41—24no—
540#41—24no—
541#41—42no—
542#41—42no—
543#41—42no—
544#41—42no—
545#41—42no—
546#41—42no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8#41×C15112yes—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—41no—
567C2×D4—41no—
568C2×D4#41×C15112yes—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4C2×D4×C15111yescharacteristic
583C22×C4C2×D4×C15111yescharacteristic
584C22×C4C2×D4×C15111yescharacteristic
585C22×C4C2×D4×C15111yescharacteristic
586C22×C4#41×C15111yescharacteristic
587C22×C4C24×C15111yescharacteristic
588Q16—42no—
589Q16—42no—
590SD16—42no—
591SD16—42no—
592M16—21no—
593M16—21no—
594M16—21no—
595M16—21no—
596M16—21no—
597M16—21no—
598M16—21no—
599M16—21no—
600M16—21no—
601M16—21no—
602M16—21no—
603M16—21no—
604M16—42no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—42no—
616C2×C8C2×D4×C15111yescharacteristic
617C2×C8C2×D4×C15111yescharacteristic
618C2×C8C2×D4×C15111yescharacteristic
619C2×C8C2×D4×C15111yescharacteristic
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—41no—
625C4⋊C4—41no—
626C4⋊C4C2×D4×C15111yescharacteristic
627C4⋊C4C2×D4×C15111yescharacteristic
628C4⋊C4C2×D4×C15111yescharacteristic
629C4⋊C4C2×D4×C15111yescharacteristic
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—41no—
635C22⋊C4—41no—
636C42—21no—
637C42—21no—
638C42—21no—
639C42—21no—
640C23—21no—
641C23—21no—
642C23—22no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—81no—
648C23—81no—
649C23#121×C15111yescharacteristic
650C23#121×C15111yescharacteristic
651C23C2×#41×C15111yescharacteristic
652Q8—22no—
653Q8—22no—
654Q8—41no—
655Q8—41no—
656Q8—41no—
657Q8—41no—
658Q8—41no—
659Q8—41no—
660D4—22no—
661D4—22no—
662D4—44no—
663D4—44no—
664D4—41no—
665D4—41no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—44no—
682C2×C4—44no—
683C2×C4—42no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—81no—
691C2×C4—81no—
692C2×C4#121×C15111yescharacteristic
693C2×C4#121×C15111yescharacteristic
694C2×C4C22×D4×C15111yescharacteristic
695C2×C4C22×D4×C15111yescharacteristic
696C2×C4C2×#41×C15111yescharacteristic
697C2×C4C2×#41×C15111yescharacteristic
698C2×C4H(5,𝔽2)×C15111yescharacteristic
699C2×C4H(5,𝔽2)×C15111yescharacteristic
700C8—21no—
701C8—21no—
702C8—21no—
703C8—21no—
704C8—41no—
705C8—41no—
706C8—41no—
707C8—41no—
708C8—41no—
709C8—41no—
710C22—21no—
711C22—21no—
712C22—21no—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—42no—
719C22—81no—
720C22—81no—
721C22—82no—
722C22—82no—
723C22—81no—
724C22—81no—
725C22C2×#121×C15111yescharacteristic
726C22#551×C15111yescharacteristic
727C22#551×C15111yescharacteristic
728C4—21no—
729C4—21no—
730C4—42no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—41no—
735C4—81no—
736C4—81no—
737C4#525×C15111yescharacteristic
738C4#535×C15111yescharacteristic
739C4#546×C15111yescharacteristic
740C4#546×C15111yescharacteristic
741C2—21no—
742C2—21no—
743C2—41no—
744C2—41no—
745C2—82no—
746C2#2411×C15111yescharacteristic
747C2#3067×C15111yescharacteristic
748C2#3069×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×#41×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
1. #3095×C151C2semidirect
3. #2924×C151C2semidirect
5. #2064×C151C2semidirect
6. #2063×C151C2semidirect
7. #2047×C151C2semidirect
8. #2046×C151C2semidirect
9. #1979×C151C2semidirect
10. #1977×C151C2semidirect
11. #1931×C151C2semidirect
12. #1930×C151C2semidirect
13. #1901×C151C2semidirect
14. #1855×C151C2semidirect
374. #24525C151direct (N × H)
375. C151#24525direct (N × H)
376. #3095C2×C151semidirect
378. #2924C2×C151semidirect
380. #2064C2×C151semidirect
381. #2063C2×C151semidirect
382. #2047C2×C151semidirect
383. #2046C2×C151semidirect
384. #1979C2×C151semidirect
385. #1977C2×C151semidirect
386. #1931C2×C151semidirect
387. #1930C2×C151semidirect
388. #1901C2×C151semidirect
389. #1855C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3095×C1512
C2×#452×C1512
#2924×C1512
#2896×C1512
#2064×C1512
#2063×C1512
#2047×C1512
#2046×C1512
#1979×C1512
#1977×C1512
#1931×C1512
#1930×C1512
#1901×C1512
#1855×C1512
#1785×C1512
#24525151