Finite Group Databasebeta

← #26138412

Subgroups — #26138412

Order 12032.

2546 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D47C211yesmaximal, characteristic
2C2×#15689000C212yesmaximal
3C2×#15688985C211yesmaximal, characteristic, complemented
4C22×C47⋊#95C211yesmaximal, characteristic, complemented
5#20241654C212yesmaximal, complemented
6#20241636C212yesmaximal, complemented
7#20241614C211yesmaximal, characteristic, complemented
8#20241613C211yesmaximal, characteristic, complemented
9#20241610C212yesmaximal, complemented
10(C2×D47)⋊#95C211yesmaximal, characteristic, complemented
11C47×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×C22⋊D47C2211yescharacteristic
13C24×Dic47C2212yes—
14C23×C4×D47C2211yescharacteristic
15C2×C4×C22⋊D47—28no—
16C2×C4×C22⋊D47C418yescomplemented
17C22×Dic47⋊C4C2211yescharacteristic
18C22×C22⋊Dic47C2211yescharacteristic
19C22×(C2×D47)⋊C4C2212yes—
20C22×(C2×D47)⋊C4C2212yes—
21C22×(C2×D47)⋊C4C2211yescharacteristic
22C22×C4×Dic47C2211yescharacteristic
23#15689000—28no—
24#15688985—24no—
25C2×C47⋊#95—24no—
26C2×C47⋊#95C2212yes—
27C2×C47⋊#95C2212yes—
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2211yescharacteristic
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2211yescharacteristic
35C24×C4×C47C2211yescharacteristic
36C22×C22⋊C4×C47C2212yes—
37C2×#95×C47C2211yescharacteristic
38C2×#95×C47C2211yescharacteristic
39C2×#95×C47C2212yes—
40C24×D47C2311yescharacteristic
41C22×C22⋊D47—24no—
42C22×C22⋊D47—22no—
43C22×C22⋊D47—22no—
44C22×C22⋊D47C2×C414yes—
45C22×C22⋊D47D418yes—
46C23×Dic47—24no—
47C23×Dic47—24no—
48C23×Dic47—24no—
49C23×Dic47—24no—
50C23×Dic47—24no—
51C23×Dic47—42no—
52C23×Dic47—42no—
53C23×Dic47C2311yescharacteristic
54C23×Dic47C2311yescharacteristic
55C23×Dic47C2312yes—
56C23×Dic47C2312yes—
57C23×Dic47C2311yescharacteristic
58C22×C4×D47—24no—
59C22×C4×D47—22no—
60C22×C4×D47—22no—
61C22×C4×D47—42no—
62C22×C4×D47C2×C414yescomplemented
63C4×C22⋊D47—232no—
64C2×Dic47⋊C4—24no—
65C2×Dic47⋊C4C2×C414yescomplemented
66C2×C22⋊Dic47—24no—
67C2×C22⋊Dic47C2×C414yes—
68C2×(C2×D47)⋊C4—24no—
69C2×(C2×D47)⋊C4—24no—
70C2×(C2×D47)⋊C4—24no—
71C2×(C2×D47)⋊C4—24no—
72C2×(C2×D47)⋊C4—24no—
73C2×(C2×D47)⋊C4—42no—
74C2×(C2×D47)⋊C4—42no—
75C2×(C2×D47)⋊C4C2×C414yescomplemented
76C2×C4×Dic47—24no—
77C2×C4×Dic47C2×C414yescomplemented
78C47⋊#95—22no—
79C47⋊#95—24no—
80C47⋊#95—24no—
81C47⋊#95—24no—
82C47⋊#95—24no—
83C47⋊#95—24no—
84C47⋊#95—42no—
85C47⋊#95—42no—
86C47⋊#95D414yescomplemented
87C25×C47C2311yescharacteristic
88C23×C4×C47—24no—
89C23×C4×C47—22no—
90C23×C4×C47—22no—
91C23×C4×C47—42no—
92C23×C4×C47C2×C414yes—
93C23×C4×C47C2312yes—
94C23×C4×C47C2312yes—
95C23×C4×C47C2311yescharacteristic
96C23×C4×C47C2311yescharacteristic
97C2×C22⋊C4×C47—24no—
98C2×C22⋊C4×C47—24no—
99C2×C22⋊C4×C47—24no—
100#95×C47—22no—
101#95×C47—22no—
102#95×C47—42no—
103C24×C47—21no—
104C24×C47—21no—
105C24×C47—22no—
106C24×C47—22no—
107C24×C47—21no—
108C24×C47—21no—
109C24×C47C22×C412yes—
110C24×C47C2×D414yes—
111C24×C47#4114yes—
112C24×C47#4112yes—
113C24×C47#4112yes—
114C24×C47C2411yescharacteristic
115C23×D47—21no—
116C23×D47—22no—
117C23×D47—21no—
118C23×D47—22no—
119C23×D47—21no—
120C23×D47—21no—
121C23×D47—21no—
122C23×D47—22no—
123C23×D47—21no—
124C23×D47C22×C412yes—
125C23×D47C2×D414yes—
126C22×C4×C47—22no—
127C22×C4×C47—22no—
128C22×C4×C47—28no—
129C22×C4×C47—21no—
130C22×C4×C47—22no—
131C22×C4×C47—21no—
132C22×C4×C47—22no—
133C22×C4×C47—28no—
134C22×C4×C47—22no—
135C22×C4×C47—22no—
136C22×C4×C47—22no—
137C22×C4×C47—22no—
138C22×C4×C47—22no—
139C22×C4×C47—22no—
140C22×C4×C47—22no—
141C22×C4×C47—22no—
142C22×C4×C47—22no—
143C22×C4×C47—22no—
144C22×C4×C47—22no—
145C22×C4×C47—22no—
146C22×C4×C47—22no—
147C22×C4×C47—22no—
148C22×C4×C47—44no—
149C22×C4×C47—48no—
150C22×C4×C47—48no—
151C22×C4×C47C22×C412yes—
152C22×C4×C47C22×C412yes—
153C22×C4×C47C2×D412yes—
154C22×C4×C47#4112yes—
155C2×C22⋊D47—28no—
156C2×C22⋊D47—28no—
157C2×C22⋊D47—216no—
158C2×C22⋊D47—216no—
159C2×C22⋊D47C22⋊C4116yes—
160C22×Dic47—21no—
161C22×Dic47—22no—
162C22×Dic47—21no—
163C22×Dic47—216no—
164C22×Dic47—21no—
165C22×Dic47—22no—
166C22×Dic47—22no—
167C22×Dic47—22no—
168C22×Dic47—22no—
169C22×Dic47—22no—
170C22×Dic47—22no—
171C22×Dic47—21no—
172C22×Dic47—22no—
173C22×Dic47—22no—
174C22×Dic47—22no—
175C22×Dic47—22no—
176C22×Dic47—22no—
177C22×Dic47—21no—
178C22×Dic47—22no—
179C22×Dic47—22no—
180C22×Dic47—22no—
181C22×Dic47—22no—
182C22×Dic47—22no—
183C22×Dic47—21no—
184C22×Dic47—48no—
185C22×Dic47—48no—
186C22×Dic47—48no—
187C22×Dic47—48no—
188C22×Dic47—48no—
189C22×Dic47—48no—
190C22×Dic47C22×C412yes—
191C22×Dic47C22×C412yes—
192C22×Dic47C22×C412yes—
193C22×Dic47C2×D414yes—
194C22×Dic47C2×D414yes—
195C22×Dic47#4114yes—
196C2×C4×D47—28no—
197C2×C4×D47—28no—
198C2×C4×D47—44no—
199C2×C4×D47—48no—
200C2×C4×D47—48no—
201C22⋊C4×C47—48no—
202C22⋊Dic47—28no—
203(C2×D47)⋊C4—28no—
204(C2×D47)⋊C4—48no—
205(C2×D47)⋊C4—48no—
206Dic47⋊C4—28no—
207C4×Dic47—28no—
208C23×C47—22no—
209C23×C47—22no—
210C23×C47—22no—
211C23×C47—22no—
212C23×C47—24no—
213C23×C47—24no—
214C23×C47—24no—
215C23×C47—24no—
216C23×C47—24no—
217C23×C47—22no—
218C23×C47—24no—
219C23×C47—24no—
220C23×C47—24no—
221C23×C47—22no—
222C23×C47—24no—
223C23×C47—22no—
224C23×C47—24no—
225C23×C47—22no—
226C23×C47C2×C22⋊C414yes—
227C23×C47#11714yes—
228C23×C47#11714yes—
229C23×C47#12318yes—
230C23×C47#12318yes—
231C23×C47C23×C411yescharacteristic
232C23×C47C22×D412yes—
233C23×C47C22×D411yescharacteristic
234C23×C47C2×#4112yes—
235C23×C47C2×#4111yescharacteristic
236C23×C47C2×#4111yescharacteristic
237C23×C47C2×#4112yes—
238C23×C47C2×#4111yescharacteristic
239C23×C47H(5,𝔽2)12yes—
240C23×C47H(5,𝔽2)11yescharacteristic
241C23×C472−1+411yescharacteristic
242C22×D47—22no—
243C22×D47—22no—
244C22×D47—22no—
245C22×D47—22no—
246C22×D47—22no—
247C22×D47—22no—
248C22×D47—24no—
249C22×D47—24no—
250C22×D47—24no—
251C22×D47—24no—
252C22×D47—24no—
253C22×D47—24no—
254C22×D47—42no—
255C22×D47—42no—
256C22×D47—42no—
257C22×D47—42no—
258C22×D47—41no—
259C22×D47—41no—
260C22×D47—42no—
261C22×D47—41no—
262C22×D47—42no—
263C22×D47—41no—
264C22×D47C2×C22⋊C414yes—
265C2×C4×C47—22no—
266C2×C4×C47—22no—
267C2×C4×C47—24no—
268C2×C4×C47—24no—
269C2×C4×C47—22no—
270C2×C4×C47—22no—
271C2×C4×C47—22no—
272C2×C4×C47—416no—
273C2×C4×C47—42no—
274C2×C4×C47—42no—
275C2×C4×C47—42no—
276C2×C4×C47—42no—
277C2×C4×C47—42no—
278C2×C4×C47—42no—
279C2×C4×C47—42no—
280C2×C4×C47—42no—
281C2×C4×C47—42no—
282C2×C4×C47—42no—
283C2×C4×C47—42no—
284C2×C4×C47—42no—
285C2×C4×C47—42no—
286C2×C4×C47—42no—
287C2×C4×C47—42no—
288C2×C4×C47—42no—
289C2×C4×C47C4×D414yes—
290C22⋊D47—232no—
291C2×Dic47—22no—
292C2×Dic47—22no—
293C2×Dic47—24no—
294C2×Dic47—24no—
295C2×Dic47—22no—
296C2×Dic47—22no—
297C2×Dic47—22no—
298C2×Dic47—22no—
299C2×Dic47—22no—
300C2×Dic47—22no—
301C2×Dic47—24no—
302C2×Dic47—24no—
303C2×Dic47—24no—
304C2×Dic47—24no—
305C2×Dic47—24no—
306C2×Dic47—24no—
307C2×Dic47—432no—
308C2×Dic47—42no—
309C2×Dic47—42no—
310C2×Dic47—42no—
311C2×Dic47—42no—
312C2×Dic47—42no—
313C2×Dic47—42no—
314C2×Dic47—42no—
315C2×Dic47—42no—
316C2×Dic47—42no—
317C2×Dic47—42no—
318C2×Dic47—42no—
319C2×Dic47—42no—
320C2×Dic47C2×C22⋊C414yes—
321C4×D47—416no—
322#13894—471nomaximal, Sylow
323C22×C47—24no—
324C22×C47—24no—
325C22×C47—24no—
326C22×C47—24no—
327C22×C47—24no—
328C22×C47—28no—
329C22×C47—28no—
330C22×C47—28no—
331C22×C47—28no—
332C22×C47—24no—
333C22×C47#38118yescomplemented
334C22×C47C22×C22⋊C411yescharacteristic
335C22×C47C2×#11711yescharacteristic
336C22×C47C2×#11711yescharacteristic
337C22×C47C2×C4×D411yescharacteristic
338C22×C47C4×#4111yescharacteristic
339C22×C47#51811yescharacteristic
340C22×C47#52011yescharacteristic
341C22×C47C2×#12312yes—
342C22×C47C2×#12312yes—
343C22×C47#52512yes—
344C22×C47#52912yes—
345C22×C47#53812yes—
346C22×C47#53912yes—
347C22×C47D4212yes—
348C22×C47#54612yes—
349C22×C47#54611yescharacteristic
350C22×C47#54612yes—
351C22×C47#54712yes—
352C22×C47#54811yescharacteristic
353C22×C47#55112yes—
354C22×C47#55211yescharacteristic
355C22×C47#55312yes—
356C22×C47#55311yescharacteristic
357C2×D47—24no—
358C2×D47—24no—
359C2×D47—24no—
360C2×D47—42no—
361C2×D47—42no—
362C2×D47—42no—
363C2×D47—44no—
364C2×D47—44no—
365C2×D47—44no—
366C2×D47—44no—
367C2×D47—42no—
368C4×C47—24no—
369C4×C47—42no—
370C4×C47—82no—
371C4×C47—82no—
372Dic47—24no—
373Dic47—42no—
374Dic47—42no—
375Dic47—44no—
376Dic47—44no—
377C22×C4×D4—471no—
378C2×#386—472no—
379C2×#381—471no—
380C22×#95—471no—
381#1445—472no—
382#1440—472no—
383#1434—471no—
384#1434—471no—
385C22⋊#95—471no—
386C22⋊#95—472no—
387C22⋊#95D4711yescharacteristic, complemented
388C2×C47—28no—
389C2×C47C2×#38111yescharacteristic
390C2×C47#229011yescharacteristic
391C2×C47#231811yescharacteristic
392C2×C47D4×C22⋊C411yescharacteristic
393C2×C47#233911yescharacteristic
394C2×C47#235211yescharacteristic
395C2×C47#235311yescharacteristic
396C2×C47#241812yes—
397C2×C47#241912yes—
398C2×C47#244312yes—
399C2×C47#244412yes—
400D47—44no—
401C23×D4—471no—
402C24×C4—471no—
403C24×C4—472no—
404C24×C4C2×D4711yescharacteristic
405C2×C4×D4—478no—
406C2×C4×D4—948no—
407C22×C4⋊C4—471no—
408C22×C22⋊C4—471no—
409C22×C22⋊C4—471no—
410C22×C22⋊C4—472no—
411C22×C22⋊C4—472no—
412C22×C22⋊C4C2×D4712yes—
413C22×C42—471no—
414#386—948no—
415#381—944no—
416C2×#95—471no—
417C2×#95—472no—
418C2×#95—471no—
419C2×#95—472no—
420C2×#95—472no—
421C2×#95—472no—
422C2×#95—472no—
423C2×#95—472no—
424C2×#95—472no—
425C2×#95—944no—
426C2×#95C2×D4711yescharacteristic
427C2×#95C2×D4711yescharacteristic
428C2×#95C2×D4712yes—
429C47#1389411yescharacteristic, complemented, Sylow
430C25—471no—
431C25C22×D4711yescharacteristic
432C22×D4—474no—
433C22×D4—478no—
434C22×D4—944no—
435C22×D4—942no—
436C22×D4—942no—
437C23×C4—24no—
438C23×C4—22no—
439C23×C4—22no—
440C23×C4—42no—
441C23×C4—471no—
442C23×C4—471no—
443C23×C4—471no—
444C23×C4—472no—
445C23×C4—472no—
446C23×C4—474no—
447C23×C4—944no—
448C23×C4—944no—
449C23×C4—944no—
450C23×C4—944no—
451C23×C4—942no—
452C23×C4—942no—
453C23×C4—944no—
454C23×C4—944no—
455C23×C4—1882no—
456C23×C4—1882no—
457C23×C4—1882no—
458C23×C4C4×D4714yes—
459C23×C4C22×D4712yes—
460C23×C4C22×D4712yes—
461C23×C4C22×D4711yescharacteristic
462C23×C4C22×D4711yescharacteristic
463C4×D4—9432no—
464C2×C4⋊C4—474no—
465C2×C4⋊C4—944no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—474no—
470C2×C22⋊C4—474no—
471C2×C22⋊C4—944no—
472C2×C22⋊C4—944no—
473C2×C22⋊C4—944no—
474C2×C22⋊C4—944no—
475C2×C22⋊C4—944no—
476C2×C22⋊C4—944no—
477C2×C22⋊C4—1882no—
478C2×C22⋊C4—1882no—
479C2×C42—474no—
480C2×C42—944no—
481#95—22no—
482#95—22no—
483#95—42no—
484#95—474no—
485#95—944no—
486#95—944no—
487#95—944no—
488#95—944no—
489#95—944no—
490#95—942no—
491#95—1882no—
492#95—1882no—
493C24—21no—
494C24—22no—
495C24—21no—
496C24—22no—
497C24—21no—
498C24—21no—
499C24—472no—
500C24—474no—
501C24—941no—
502C24—942no—
503C24—941no—
504C24—941no—
505C24—942no—
506C24—941no—
507C24—942no—
508C24—941no—
509C24—941no—
510C24C2×C4×D4712yes—
511C24#1062535014yes—
512C24D4×D4714yes—
513C24#1062535212yes—
514C24#1062535412yes—
515C24C23×D4711yescharacteristic
516C2×D4—4716no—
517C2×D4—948no—
518C2×D4—948no—
519C2×D4—9416no—
520C2×D4—9416no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—28no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—28no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—44no—
544C22×C4—48no—
545C22×C4—48no—
546C22×C4—472no—
547C22×C4—474no—
548C22×C4—472no—
549C22×C4—472no—
550C22×C4—474no—
551C22×C4—474no—
552C22×C4—948no—
553C22×C4—941no—
554C22×C4—942no—
555C22×C4—941no—
556C22×C4—9416no—
557C22×C4—941no—
558C22×C4—942no—
559C22×C4—942no—
560C22×C4—942no—
561C22×C4—942no—
562C22×C4—942no—
563C22×C4—942no—
564C22×C4—942no—
565C22×C4—941no—
566C22×C4—942no—
567C22×C4—942no—
568C22×C4—942no—
569C22×C4—942no—
570C22×C4—942no—
571C22×C4—942no—
572C22×C4—942no—
573C22×C4—941no—
574C22×C4—942no—
575C22×C4—942no—
576C22×C4—941no—
577C22×C4—948no—
578C22×C4—1884no—
579C22×C4—1888no—
580C22×C4—1888no—
581C22×C4—1888no—
582C22×C4—1888no—
583C22×C4—1888no—
584C22×C4—1888no—
585C22×C4—1888no—
586C22×C4—1888no—
587C22×C4C2×C4×D4712yes—
588C22×C4C2×C4×D4712yes—
589C22×C4D4×D4712yes—
590C22×C4#1062535212yes—
591C4⋊C4—948no—
592C22⋊C4—48no—
593C22⋊C4—948no—
594C22⋊C4—948no—
595C22⋊C4—1888no—
596C22⋊C4—1888no—
597C42—948no—
598C23—24no—
599C23—24no—
600C23—22no—
601C23—24no—
602C23—24no—
603C23—22no—
604C23—24no—
605C23—22no—
606C23—24no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—474no—
617C23—944no—
618C23—944no—
619C23—944no—
620C23—944no—
621C23—942no—
622C23—942no—
623C23—942no—
624C23—942no—
625C23—942no—
626C23—942no—
627C23—944no—
628C23—944no—
629C23—1881no—
630C23—1881no—
631C23—1882no—
632C23—1881no—
633C23—1882no—
634C23—1881no—
635C23—1882no—
636C23—1882no—
637C23—1882no—
638C23—1882no—
639C23C22⋊C4×D4714yes—
640C23#1309398114yes—
641C23#1309398214yes—
642C23#1309400618yes—
643C23#1309400918yes—
644C23C22×C4×D4711yescharacteristic
645C23C2×D4×D4711yescharacteristic
646C23C2×D4×D4712yes—
647C23#41×D4712yes—
648C23C2×#1062535211yescharacteristic
649C23C2×#1062535211yescharacteristic
650C23C2×#1062535012yes—
651C23C2×#1062535411yescharacteristic
652C23#1309406912yes—
653C23#1309407011yescharacteristic
654C23#1309407111yescharacteristic
655D4—9432no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—416no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—474no—
681C2×C4—942no—
682C2×C4—942no—
683C2×C4—944no—
684C2×C4—944no—
685C2×C4—944no—
686C2×C4—944no—
687C2×C4—944no—
688C2×C4—944no—
689C2×C4—942no—
690C2×C4—942no—
691C2×C4—942no—
692C2×C4—942no—
693C2×C4—942no—
694C2×C4—942no—
695C2×C4—944no—
696C2×C4—944no—
697C2×C4—18816no—
698C2×C4—18832no—
699C2×C4—1882no—
700C2×C4—1882no—
701C2×C4—1882no—
702C2×C4—1882no—
703C2×C4—1882no—
704C2×C4—1882no—
705C2×C4—1882no—
706C2×C4—1882no—
707C2×C4—1882no—
708C2×C4—1882no—
709C2×C4—1882no—
710C2×C4—1882no—
711C2×C4(C22⋊D47)⋊C414yes—
712C22—24no—
713C22—24no—
714C22—24no—
715C22—28no—
716C22—28no—
717C22—28no—
718C22—28no—
719C22—24no—
720C22—24no—
721C22—24no—
722C22—944no—
723C22—944no—
724C22—944no—
725C22—1882no—
726C22—1882no—
727C22—1882no—
728C22—1884no—
729C22—1884no—
730C22—1884no—
731C22—1884no—
732C22—1882no—
733C22#1568898518yescomplemented
734C22C2×C22⋊C4×D4711yescharacteristic
735C22C2×#1309398111yescharacteristic
736C22C2×#1309398211yescharacteristic
737C22C2×(C22⋊D47)⋊C411yescharacteristic
738C22#1568959111yescharacteristic
739C22#1568959611yescharacteristic
740C22#1568960311yescharacteristic
741C22C2×#1309400612yes—
742C22C2×#1309400912yes—
743C22#1568963212yes—
744C22#1568965312yes—
745C22#1568970612yes—
746C22#1568971512yes—
747C22#1568975512yes—
748C22#1568976012yes—
749C22#1568976411yescharacteristic
750C22#1568976512yes—
751C22#1568977112yes—
752C22#1568977911yescharacteristic
753C22#1568980012yes—
754C22#1568981511yescharacteristic
755C22#1568981612yes—
756C22#1568982511yescharacteristic
757C4—24no—
758C4—42no—
759C4—82no—
760C4—82no—
761C4—944no—
762C4—1884no—
763C4—1884no—
764C4—1882no—
765C4—1882no—
766C2—28no—
767C2—1884no—
768C2C2×#1568898511yescharacteristic
769C2#2024582711yescharacteristic
770C2#2024601511yescharacteristic
771C2#2024620411yescharacteristic
772C2#2024621211yescharacteristic
773C2#2024631911yescharacteristic
774C2#2024633011yescharacteristic
775C2#2024685212yes—
776C2#2024686712yes—
777C2#2024712512yes—
778C2#2024714012yes—
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC47×C22⋊#95C2
socle, cosocleC24×C47C24
prime radicalC23×C22⋊D47C22
hypercenterC22⋊#95D47
hypocenterC47#13894
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#15688985C2semidirect
4. C22×C47⋊#95C2semidirect
5. #20241654C2semidirect
6. #20241636C2semidirect
7. #20241614C2semidirect
8. #20241613C2semidirect
9. #20241610C2semidirect
10. (C2×D47)⋊#95C2semidirect
11. C47×C22⋊#95C2semidirect
16. C2×C4×C22⋊D47C4semidirect
62. C22×C4×D47C2×C4semidirect
65. C2×Dic47⋊C4C2×C4semidirect
75. C2×(C2×D47)⋊C4C2×C4semidirect
77. C2×C4×Dic47C2×C4semidirect
86. C47⋊#95D4semidirect
333. C22×C47#381semidirect
387. C22⋊#95D47semidirect
429. C47#13894semidirect
733. C22#15688985semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D472
C2×#156890002
C2×#156889852
C22×C47⋊#952
#202416542
#202416362
#202416142
#202416132
#202416102
(C2×D47)⋊#952
C47×C22⋊#952
#1389447