Finite Group Databasebeta

← C151×#24524 #50329449

Subgroups — C151×#24524 #50329449

Order 38656.

884 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3094×C151C211yesmaximal, characteristic, complemented
2C2×#449×C151C211yesmaximal, characteristic
3#2924×C151C211yesmaximal, characteristic, complemented
4#2896×C151C211yesmaximal, characteristic, complemented
5#2064×C151C211yesmaximal, characteristic, complemented
6#2063×C151C211yesmaximal, characteristic, complemented
7#2046×C151C211yesmaximal, characteristic, complemented
8#2045×C151C211yesmaximal, characteristic, complemented
9#1978×C151C211yesmaximal, characteristic, complemented
10#1977×C151C211yesmaximal, characteristic, complemented
11#1931×C151C211yesmaximal, characteristic, complemented
12#1930×C151C211yesmaximal, characteristic, complemented
13#1900×C151C211yesmaximal, characteristic, complemented
14#1855×C151C211yesmaximal, characteristic, complemented
15#1785×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C22×SD16×C151C2211yescharacteristic
18C22×D8×C151C2211yescharacteristic
19C22×M16×C151C2211yescharacteristic
20C2×#121×C151C2211yescharacteristic
21C2×#117×C151C2211yescharacteristic
22#482×C151—21no—
23#482×C151—21no—
24#481×C151—21no—
25#480×C151—21no—
26#449×C151—21no—
27#449×C151—21no—
28#449×C151—21no—
29#449×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#418×C151C2211yescharacteristic
43#418×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×#100×C151C2211yescharacteristic
55C2×#100×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×D4×C151—21no—
77C22×D4×C151—21no—
78C22×D4×C151C2311yescharacteristic
79C22×D4×C151C2311yescharacteristic
80C23×C4×C151—21no—
81C23×C4×C151C2311yescharacteristic
82C2×SD16×C151—21no—
83C2×SD16×C151—21no—
84C2×SD16×C151—22no—
85C2×SD16×C151—41no—
86C2×D8×C151—22no—
87C2×D8×C151—21no—
88C2×D8×C151—21no—
89C2×D8×C151—41no—
90C2×M16×C151—21no—
91C2×M16×C151—41no—
92C2×M16×C151—41no—
93C2×M16×C151C2311yescharacteristic
94C2×M16×C151C2311yescharacteristic
95C2×M16×C151C2311yescharacteristic
96C2×M16×C151C2311yescharacteristic
97C2×M16×C151C2311yescharacteristic
98C2×M16×C151C2311yescharacteristic
99C22×C8×C151—21no—
100C22×C8×C151C2311yescharacteristic
101C22×C8×C151C2311yescharacteristic
102#121×C151—21no—
103#121×C151—21no—
104#121×C151—21no—
105#121×C151—21no—
106#117×C151—21no—
107#117×C151—21no—
108#117×C151D411yescharacteristic
109#117×C151D411yescharacteristic
110#117×C151C2311yescharacteristic
111#117×C151C2311yescharacteristic
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#102×C151—21no—
135#102×C151—21no—
136#102×C151—21no—
137#102×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#100×C151—22no—
147#100×C151—41no—
148#100×C151—41no—
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—21no—
164C24×C151#4111yescharacteristic
165#41×C151—24no—
166#41×C151—24no—
167#41×C151—42no—
168#41×C151—42no—
169#41×C151—42no—
170#41×C151—42no—
171#41×C151—42no—
172#41×C151—42no—
173C2×Q8×C151—21no—
174C2×Q8×C151—21no—
175C2×Q8×C151—21no—
176C2×Q8×C151—21no—
177C2×Q8×C151—21no—
178C2×Q8×C151#4112yes—
179C2×D4×C151—21no—
180C2×D4×C151—21no—
181C2×D4×C151—21no—
182C2×D4×C151—21no—
183C2×D4×C151—21no—
184C2×D4×C151—21no—
185C2×D4×C151—21no—
186C2×D4×C151—21no—
187C2×D4×C151—21no—
188C2×D4×C151—21no—
189C2×D4×C151—21no—
190C2×D4×C151—42no—
191C2×D4×C151—42no—
192C2×D4×C151—41no—
193C2×D4×C151—41no—
194C2×D4×C151—41no—
195C2×D4×C151—41no—
196C2×D4×C151—82no—
197C2×D4×C151#4112yes—
198C22×C4×C151—21no—
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—21no—
206C22×C4×C151—42no—
207C22×C4×C151—42no—
208C22×C4×C151—41no—
209C22×C4×C151—41no—
210C22×C4×C151C2×D411yescharacteristic
211C22×C4×C151C2×D411yescharacteristic
212C22×C4×C151C2×D411yescharacteristic
213C22×C4×C151C2×D411yescharacteristic
214C22×C4×C151#4111yescharacteristic
215C22×C4×C151C2411yescharacteristic
216SD16×C151—42no—
217SD16×C151—42no—
218D8×C151—42no—
219D8×C151—42no—
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—21no—
230M16×C151—21no—
231M16×C151—21no—
232M16×C151—42no—
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—21no—
241C2×C8×C151—21no—
242C2×C8×C151—21no—
243C2×C8×C151—42no—
244C2×C8×C151C2×D411yescharacteristic
245C2×C8×C151C2×D411yescharacteristic
246C2×C8×C151C2×D411yescharacteristic
247C2×C8×C151C2×D411yescharacteristic
248C4⋊C4×C151—21no—
249C4⋊C4×C151—21no—
250C4⋊C4×C151—21no—
251C4⋊C4×C151—21no—
252C4⋊C4×C151C2×D411yescharacteristic
253C4⋊C4×C151C2×D411yescharacteristic
254C4⋊C4×C151C2×D411yescharacteristic
255C4⋊C4×C151C2×D411yescharacteristic
256C22⋊C4×C151—21no—
257C22⋊C4×C151—21no—
258C22⋊C4×C151—21no—
259C22⋊C4×C151—21no—
260C22⋊C4×C151—41no—
261C22⋊C4×C151—41no—
262C42×C151—21no—
263C42×C151—21no—
264C42×C151—21no—
265C42×C151—21no—
266C23×C151—21no—
267C23×C151—21no—
268C23×C151—22no—
269C23×C151—41no—
270C23×C151—41no—
271C23×C151—41no—
272C23×C151—41no—
273C23×C151—41no—
274C23×C151—41no—
275C23×C151—41no—
276C23×C151—81no—
277C23×C151—81no—
278C23×C151—81no—
279C23×C151—81no—
280C23×C151#12111yescharacteristic
281C23×C151#12111yescharacteristic
282C23×C151C2×#4111yescharacteristic
283Q8×C151—22no—
284Q8×C151—22no—
285Q8×C151—41no—
286Q8×C151—41no—
287D4×C151—22no—
288D4×C151—22no—
289D4×C151—44no—
290D4×C151—44no—
291D4×C151—41no—
292D4×C151—41no—
293D4×C151—41no—
294D4×C151—41no—
295D4×C151—41no—
296D4×C151—41no—
297D4×C151—82no—
298D4×C151—82no—
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—21no—
306C2×C4×C151—21no—
307C2×C4×C151—21no—
308C2×C4×C151—21no—
309C2×C4×C151—21no—
310C2×C4×C151—21no—
311C2×C4×C151—21no—
312C2×C4×C151—21no—
313C2×C4×C151—22no—
314C2×C4×C151—44no—
315C2×C4×C151—44no—
316C2×C4×C151—42no—
317C2×C4×C151—41no—
318C2×C4×C151—41no—
319C2×C4×C151—41no—
320C2×C4×C151—81no—
321C2×C4×C151—81no—
322C2×C4×C151#12111yescharacteristic
323C2×C4×C151#12111yescharacteristic
324C2×C4×C151C22×D411yescharacteristic
325C2×C4×C151C22×D411yescharacteristic
326C2×C4×C151C2×#4111yescharacteristic
327C2×C4×C151C2×#4111yescharacteristic
328C2×C4×C151H(5,𝔽2)11yescharacteristic
329C2×C4×C151H(5,𝔽2)11yescharacteristic
330C8×C151—21no—
331C8×C151—21no—
332C8×C151—21no—
333C8×C151—21no—
334C8×C151—41no—
335C8×C151—41no—
336C8×C151—41no—
337C8×C151—41no—
338C8×C151—41no—
339C8×C151—41no—
340C22×C151—21no—
341C22×C151—21no—
342C22×C151—21no—
343C22×C151—21no—
344C22×C151—21no—
345C22×C151—21no—
346C22×C151—21no—
347C22×C151—21no—
348C22×C151—42no—
349C22×C151—81no—
350C22×C151—81no—
351C22×C151—82no—
352C22×C151—82no—
353C22×C151—81no—
354C22×C151—81no—
355C22×C151—81no—
356C22×C151—81no—
357C22×C151—81no—
358C22×C151—161no—
359C22×C151—161no—
360C22×C151C2×#12111yescharacteristic
361C22×C151#55111yescharacteristic
362C22×C151#55111yescharacteristic
363C4×C151—21no—
364C4×C151—21no—
365C4×C151—42no—
366C4×C151—41no—
367C4×C151—41no—
368C4×C151—41no—
369C4×C151—41no—
370C4×C151—81no—
371C4×C151#52511yescharacteristic
372C4×C151#53511yescharacteristic
373C4×C151#54611yescharacteristic
374C4×C151#54611yescharacteristic
375C2×C151—21no—
376C2×C151—21no—
377C2×C151—41no—
378C2×C151—41no—
379C2×C151—82no—
380C2×C151—161no—
381C2×C151#241111yescharacteristic
382C2×C151#306711yescharacteristic
383C2×C151#306811yescharacteristic
384#24524C15111yesmaximal, characteristic, direct product factor, Sylow
385C151#2452411yescharacteristic, direct product factor, Sylow
386#3094C2×C15111yescharacteristic, complemented
387C2×#449C2×C15111yescharacteristic
388#2924C2×C15111yescharacteristic, complemented
389#2896C2×C15111yescharacteristic, complemented
390#2064C2×C15111yescharacteristic, complemented
391#2063C2×C15111yescharacteristic, complemented
392#2046C2×C15111yescharacteristic, complemented
393#2045C2×C15111yescharacteristic, complemented
394#1978C2×C15111yescharacteristic, complemented
395#1977C2×C15111yescharacteristic, complemented
396#1931C2×C15111yescharacteristic, complemented
397#1930C2×C15111yescharacteristic, complemented
398#1900C2×C15111yescharacteristic, complemented
399#1855C2×C15111yescharacteristic, complemented
400#1785C2×C15111yescharacteristic, complemented
401C22×#41C22×C15111yescharacteristic
402C22×SD16C22×C15111yescharacteristic
403C22×D8C22×C15111yescharacteristic
404C22×M16C22×C15111yescharacteristic
405C2×#121C22×C15111yescharacteristic
406C2×#117C22×C15111yescharacteristic
407#482—21no—
408#482—21no—
409#481—21no—
410#480—21no—
411#449—21no—
412#449—21no—
413#449—21no—
414#449—21no—
415#433—21no—
416#433—21no—
417#432—21no—
418#431—21no—
419C2×#108C22×C15111yescharacteristic
420C2×#108C22×C15111yescharacteristic
421#428C22×C15111yescharacteristic
422#428C22×C15111yescharacteristic
423#424C22×C15111yescharacteristic
424#424C22×C15111yescharacteristic
425#419C22×C15111yescharacteristic
426#419C22×C15111yescharacteristic
427#418C22×C15111yescharacteristic
428#418C22×C15111yescharacteristic
429#418C22×C15111yescharacteristic
430#418C22×C15111yescharacteristic
431#417—21no—
432#417—21no—
433#416—21no—
434#416—21no—
435C2×#103C22×C15111yescharacteristic
436C2×#102C22×C15111yescharacteristic
437C2×#101C22×C15111yescharacteristic
438C2×#101C22×C15111yescharacteristic
439C2×#100C22×C15111yescharacteristic
440C2×#100C22×C15111yescharacteristic
441C2×#100C22×C15111yescharacteristic
442C2×#100C22×C15111yescharacteristic
443#407C22×C15111yescharacteristic
444#407C22×C15111yescharacteristic
445C2×C22⋊C8C22×C15111yescharacteristic
446#405C22×C15111yescharacteristic
447#405C22×C15111yescharacteristic
448#343C22×C15111yescharacteristic
449#343C22×C15111yescharacteristic
450#341C22×C15111yescharacteristic
451#341C22×C15111yescharacteristic
452C2×#41—22no—
453C2×#41—22no—
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—41no—
459C2×#41—41no—
460C22×Q8C23×C15111yescharacteristic
461C22×D4—21no—
462C22×D4—21no—
463C22×D4C23×C15111yescharacteristic
464C22×D4C23×C15111yescharacteristic
465C23×C4—21no—
466C23×C4C23×C15111yescharacteristic
467C2×SD16—22no—
468C2×SD16—21no—
469C2×SD16—21no—
470C2×SD16—41no—
471C2×D8—22no—
472C2×D8—21no—
473C2×D8—21no—
474C2×D8—41no—
475C2×M16—21no—
476C2×M16—41no—
477C2×M16—41no—
478C2×M16C23×C15111yescharacteristic
479C2×M16C23×C15111yescharacteristic
480C2×M16C23×C15111yescharacteristic
481C2×M16C23×C15111yescharacteristic
482C2×M16C23×C15111yescharacteristic
483C2×M16C23×C15111yescharacteristic
484C22×C8—21no—
485C22×C8C23×C15111yescharacteristic
486C22×C8C23×C15111yescharacteristic
487#121—21no—
488#121—21no—
489#121—21no—
490#121—21no—
491#117—21no—
492#117—21no—
493#117D4×C15111yescharacteristic
494#117D4×C15111yescharacteristic
495#117C23×C15111yescharacteristic
496#117C23×C15111yescharacteristic
497C2×C4⋊C4D4×C15111yescharacteristic
498C2×C4⋊C4D4×C15111yescharacteristic
499C2×C4⋊C4C23×C15111yescharacteristic
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C42—21no—
503#108—41no—
504#108—41no—
505#107—21no—
506#107—21no—
507#106—21no—
508#106—21no—
509C4⋊C8—21no—
510C4⋊C8—21no—
511C4⋊C8—21no—
512C4⋊C8—21no—
513#103—21no—
514#103—21no—
515#103—21no—
516#103—21no—
517#103—21no—
518#103—21no—
519#102—21no—
520#102—21no—
521#102—21no—
522#102—21no—
523#102—21no—
524#102—21no—
525#102—21no—
526#102—21no—
527#102—21no—
528#102—21no—
529#101—22no—
530#101—41no—
531#100—22no—
532#100—41no—
533#100—41no—
534#100—41no—
535C22⋊C8—21no—
536C22⋊C8—21no—
537C22⋊C8—21no—
538C22⋊C8—21no—
539C22⋊C8D4×C15111yescharacteristic
540C22⋊C8D4×C15111yescharacteristic
541C22⋊C8D4×C15111yescharacteristic
542C22⋊C8D4×C15111yescharacteristic
543#97—21no—
544#97—21no—
545C4×C8—21no—
546C4×C8—21no—
547C24—21no—
548C24—21no—
549C24#41×C15111yescharacteristic
550#41—24no—
551#41—24no—
552#41—42no—
553#41—42no—
554#41—42no—
555#41—42no—
556#41—42no—
557#41—42no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8#41×C15112yes—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—41no—
578C2×D4—41no—
579C2×D4—41no—
580C2×D4—41no—
581C2×D4—82no—
582C2×D4#41×C15112yes—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4C2×D4×C15111yescharacteristic
596C22×C4C2×D4×C15111yescharacteristic
597C22×C4C2×D4×C15111yescharacteristic
598C22×C4C2×D4×C15111yescharacteristic
599C22×C4#41×C15111yescharacteristic
600C22×C4C24×C15111yescharacteristic
601SD16—42no—
602SD16—42no—
603D8—42no—
604D8—42no—
605M16—21no—
606M16—21no—
607M16—21no—
608M16—21no—
609M16—21no—
610M16—21no—
611M16—21no—
612M16—21no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—21no—
617M16—42no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—42no—
629C2×C8C2×D4×C15111yescharacteristic
630C2×C8C2×D4×C15111yescharacteristic
631C2×C8C2×D4×C15111yescharacteristic
632C2×C8C2×D4×C15111yescharacteristic
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4C2×D4×C15111yescharacteristic
638C4⋊C4C2×D4×C15111yescharacteristic
639C4⋊C4C2×D4×C15111yescharacteristic
640C4⋊C4C2×D4×C15111yescharacteristic
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—41no—
646C22⋊C4—41no—
647C42—21no—
648C42—21no—
649C42—21no—
650C42—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—81no—
662C23—81no—
663C23—81no—
664C23—81no—
665C23#121×C15111yescharacteristic
666C23#121×C15111yescharacteristic
667C23C2×#41×C15111yescharacteristic
668Q8—22no—
669Q8—22no—
670Q8—41no—
671Q8—41no—
672D4—22no—
673D4—22no—
674D4—44no—
675D4—44no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—82no—
683D4—82no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—81no—
706C2×C4—81no—
707C2×C4#121×C15111yescharacteristic
708C2×C4#121×C15111yescharacteristic
709C2×C4C22×D4×C15111yescharacteristic
710C2×C4C22×D4×C15111yescharacteristic
711C2×C4C2×#41×C15111yescharacteristic
712C2×C4C2×#41×C15111yescharacteristic
713C2×C4H(5,𝔽2)×C15111yescharacteristic
714C2×C4H(5,𝔽2)×C15111yescharacteristic
715C8—21no—
716C8—21no—
717C8—21no—
718C8—21no—
719C8—41no—
720C8—41no—
721C8—41no—
722C8—41no—
723C8—41no—
724C8—41no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—42no—
734C22—81no—
735C22—81no—
736C22—82no—
737C22—82no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—161no—
744C22—161no—
745C22C2×#121×C15111yescharacteristic
746C22#551×C15111yescharacteristic
747C22#551×C15111yescharacteristic
748C4—21no—
749C4—21no—
750C4—42no—
751C4—41no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—81no—
756C4#525×C15111yescharacteristic
757C4#535×C15111yescharacteristic
758C4#546×C15111yescharacteristic
759C4#546×C15111yescharacteristic
760C2—21no—
761C2—21no—
762C2—41no—
763C2—41no—
764C2—82no—
765C2—161no—
766C2#2411×C15111yescharacteristic
767C2#3067×C15111yescharacteristic
768C2#3068×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#449×C151C2
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. #3094×C151C2semidirect
3. #2924×C151C2semidirect
4. #2896×C151C2semidirect
5. #2064×C151C2semidirect
6. #2063×C151C2semidirect
7. #2046×C151C2semidirect
8. #2045×C151C2semidirect
9. #1978×C151C2semidirect
10. #1977×C151C2semidirect
11. #1931×C151C2semidirect
12. #1930×C151C2semidirect
13. #1900×C151C2semidirect
14. #1855×C151C2semidirect
15. #1785×C151C2semidirect
384. #24524C151direct (N × H)
385. C151#24524direct (N × H)
386. #3094C2×C151semidirect
388. #2924C2×C151semidirect
389. #2896C2×C151semidirect
390. #2064C2×C151semidirect
391. #2063C2×C151semidirect
392. #2046C2×C151semidirect
393. #2045C2×C151semidirect
394. #1978C2×C151semidirect
395. #1977C2×C151semidirect
396. #1931C2×C151semidirect
397. #1930C2×C151semidirect
398. #1900C2×C151semidirect
399. #1855C2×C151semidirect
400. #1785C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3094×C1512
C2×#449×C1512
#2924×C1512
#2896×C1512
#2064×C1512
#2063×C1512
#2046×C1512
#2045×C1512
#1978×C1512
#1977×C1512
#1931×C1512
#1930×C1512
#1900×C1512
#1855×C1512
#1785×C1512
#24524151