Finite Group Databasebeta

← #26138218

Subgroups — #26138218

Order 12032.

1702 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15688989C211yesmaximal, characteristic, complemented
2C2×#15688983C211yesmaximal, characteristic
3C2×#15688983C211yesmaximal, characteristic
4C2×C4×C4⋊Dic47C211yesmaximal, characteristic, complemented
5#20241650C212yesmaximal, complemented
6#20241637C212yesmaximal
7#20241625C212yesmaximal
8#20241618C211yesmaximal, characteristic, complemented
9#20241618C211yesmaximal, characteristic, complemented
10#20241613C212yesmaximal, complemented
11C2×C4×C22⋊C4×C47C211yesmaximal, characteristic
12C22×C4⋊Dic47C2211yescharacteristic
13C22×C4⋊Dic47C2211yescharacteristic
14C22×C4⋊Dic47C2211yescharacteristic
15C22×C4⋊Dic47C2211yescharacteristic
16C22×C22⋊Dic47C2212yes—
17C22×C22⋊Dic47C2212yes—
18C22×C4×Dic47C2212yes—
19#15688989—24no—
20#15688983—24no—
21#15688983—24no—
22C4×C4⋊Dic47—24no—
23C2×C47⋊#95C2212yes—
24C2×C47⋊#95C2212yes—
25C2×C47⋊#95C2212yes—
26C2×C47⋊#95C2212yes—
27C2×C47⋊#95C2212yes—
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C24×C4×C47C2211yescharacteristic
33C22×C22⋊C4×C47C2211yescharacteristic
34C22×C22⋊C4×C47C2211yescharacteristic
35C22×C42×C47C2211yescharacteristic
36C22×C42×C47C2211yescharacteristic
37C4×C22⋊C4×C47C418yescomplemented
38C2×#95×C47C2211yescharacteristic
39C2×#95×C47C2211yescharacteristic
40C23×Dic47C2312yes—
41C23×Dic47C2312yes—
42C23×Dic47C2312yes—
43C23×Dic47C2312yes—
44C2×C4⋊Dic47—22no—
45C2×C4⋊Dic47—22no—
46C2×C4⋊Dic47—22no—
47C2×C4⋊Dic47—22no—
48C2×C4⋊Dic47—22no—
49C2×C4⋊Dic47—22no—
50C2×C4⋊Dic47—22no—
51C2×C4⋊Dic47—22no—
52C2×C4⋊Dic47—22no—
53C2×C4⋊Dic47—22no—
54C2×C4⋊Dic47D414yes—
55C2×C4⋊Dic47D414yes—
56C2×C22⋊Dic47—24no—
57C2×C22⋊Dic47—24no—
58C2×C22⋊Dic47—24no—
59C2×C22⋊Dic47—24no—
60C2×C22⋊Dic47—42no—
61C2×C22⋊Dic47—42no—
62C2×C4×Dic47—24no—
63C2×C4×Dic47—24no—
64C2×C4×Dic47—42no—
65C47⋊#95—24no—
66C47⋊#95—24no—
67C47⋊#95—24no—
68C47⋊#95—24no—
69C47⋊#95—24no—
70C47⋊#95—24no—
71C47⋊#95—42no—
72C47⋊#95—42no—
73C47⋊#95—42no—
74C25×C47C2311yescharacteristic
75C23×C4×C47—22no—
76C23×C4×C47—22no—
77C23×C4×C47—22no—
78C23×C4×C47—22no—
79C23×C4×C47—22no—
80C23×C4×C47—22no—
81C23×C4×C47C2×C414yes—
82C23×C4×C47C2311yescharacteristic
83C23×C4×C47C2311yescharacteristic
84C23×C4×C47C2311yescharacteristic
85C23×C4×C47C2311yescharacteristic
86C23×C4×C47C2311yescharacteristic
87C23×C4×C47C2311yescharacteristic
88C2×C22⋊C4×C47—22no—
89C2×C22⋊C4×C47—22no—
90C2×C22⋊C4×C47—22no—
91C2×C22⋊C4×C47—22no—
92C2×C22⋊C4×C47C2×C414yes—
93C2×C22⋊C4×C47C2×C414yes—
94C2×C42×C47—22no—
95C2×C42×C47—22no—
96C2×C42×C47—22no—
97C2×C42×C47—22no—
98C2×C42×C47C2×C414yes—
99C2×C42×C47C2×C414yes—
100#95×C47C2×C414yes—
101#95×C47C2×C414yes—
102C24×C47—21no—
103C24×C47—21no—
104C24×C47—21no—
105C24×C47—21no—
106C24×C47—21no—
107C24×C47—21no—
108C24×C47—21no—
109C24×C47—21no—
110C24×C47—21no—
111C24×C47—21no—
112C24×C47—21no—
113C24×C47—21no—
114C24×C47C22×C412yes—
115C24×C47#4112yes—
116C24×C47#4112yes—
117C24×C47C2411yescharacteristic
118C22×C4×C47—21no—
119C22×C4×C47—21no—
120C22×C4×C47—21no—
121C22×C4×C47—21no—
122C22×C4×C47—21no—
123C22×C4×C47—21no—
124C22×C4×C47—21no—
125C22×C4×C47—21no—
126C22×C4×C47—21no—
127C22×C4×C47—21no—
128C22×C4×C47—21no—
129C22×C4×C47—21no—
130C22×C4×C47—21no—
131C22×C4×C47—21no—
132C22×C4×C47—21no—
133C22×C4×C47—21no—
134C22×C4×C47—21no—
135C22×C4×C47—21no—
136C22×C4×C47—21no—
137C22×C4×C47—21no—
138C22×C4×C47—21no—
139C22×C4×C47—21no—
140C22×C4×C47—21no—
141C22×C4×C47—21no—
142C22×C4×C47—21no—
143C22×C4×C47—21no—
144C22×C4×C47—21no—
145C22×C4×C47—21no—
146C22×C4×C47—28no—
147C22×C4×C47—28no—
148C22×C4×C47—28no—
149C22×C4×C47—44no—
150C22×C4×C47—44no—
151C22×C4×C47—44no—
152C22×C4×C47—44no—
153C22×C4×C47C22×C412yes—
154C22×C4×C47C22×C412yes—
155C22×C4×C47C22×C412yes—
156C22×C4×C47C22×C412yes—
157C22×C4×C47C22×C412yes—
158C22×C4×C47C22×C412yes—
159C22×C4×C47C2×D412yes—
160C22×C4×C47C2×D412yes—
161C22×C4×C47#4112yes—
162C22×C4×C47#4112yes—
163C22×C4×C47#4112yes—
164C22×C4×C47#4112yes—
165C22×C4×C47#4112yes—
166C22×C4×C47#4112yes—
167C22×Dic47—22no—
168C22×Dic47—22no—
169C22×Dic47—22no—
170C22×Dic47—22no—
171C22×Dic47—22no—
172C22×Dic47—22no—
173C22×Dic47—22no—
174C22×Dic47—22no—
175C22×Dic47—22no—
176C22×Dic47—22no—
177C22×Dic47—22no—
178C22×Dic47—22no—
179C22×Dic47—22no—
180C22×Dic47—22no—
181C22×Dic47—22no—
182C22×Dic47—22no—
183C22×Dic47—22no—
184C22×Dic47—22no—
185C22×Dic47—22no—
186C22×Dic47—22no—
187C22×Dic47—22no—
188C22×Dic47—22no—
189C22×Dic47—22no—
190C22×Dic47—22no—
191C22×Dic47—22no—
192C22×Dic47—22no—
193C22×Dic47C2×D414yes—
194C22×Dic47C2×D414yes—
195C22⋊C4×C47—28no—
196C22⋊C4×C47—28no—
197C42×C47—28no—
198C42×C47—28no—
199C22⋊Dic47—48no—
200C22⋊Dic47—48no—
201C4⋊Dic47—28no—
202C4⋊Dic47—28no—
203C4⋊Dic47—44no—
204C4⋊Dic47—44no—
205C4×Dic47—48no—
206C23×C47—22no—
207C23×C47—22no—
208C23×C47—22no—
209C23×C47—22no—
210C23×C47—22no—
211C23×C47—22no—
212C23×C47—22no—
213C23×C47—22no—
214C23×C47—22no—
215C23×C47—22no—
216C23×C47—22no—
217C23×C47—22no—
218C23×C47—22no—
219C23×C47—22no—
220C23×C47—22no—
221C23×C47—22no—
222C23×C47—22no—
223C23×C47—22no—
224C23×C47—41no—
225C23×C47—41no—
226C23×C47—41no—
227C23×C47—41no—
228C23×C47—41no—
229C23×C47—41no—
230C23×C47—41no—
231C23×C47—41no—
232C23×C47—41no—
233C23×C47—41no—
234C23×C47—41no—
235C23×C47—41no—
236C23×C47—41no—
237C23×C47—41no—
238C23×C47—41no—
239C23×C47—41no—
240C23×C47#11714yes—
241C23×C47C23×C411yescharacteristic
242C23×C47C22×D411yescharacteristic
243C23×C47C22×D411yescharacteristic
244C23×C47C2×#4111yescharacteristic
245C23×C47C2×#4111yescharacteristic
246C23×C47C2×#4111yescharacteristic
247C23×C47C2×#4111yescharacteristic
248C23×C47C2×#4111yescharacteristic
249C23×C47C2×#4111yescharacteristic
250C23×C47C2×#4111yescharacteristic
251C23×C47C2×#4111yescharacteristic
252C23×C47H(5,𝔽2)11yescharacteristic
253C23×C47H(5,𝔽2)11yescharacteristic
254C23×C472−1+411yescharacteristic
255C23×C472−1+411yescharacteristic
256C2×C4×C47—22no—
257C2×C4×C47—22no—
258C2×C4×C47—22no—
259C2×C4×C47—22no—
260C2×C4×C47—22no—
261C2×C4×C47—22no—
262C2×C4×C47—22no—
263C2×C4×C47—22no—
264C2×C4×C47—22no—
265C2×C4×C47—22no—
266C2×C4×C47—22no—
267C2×C4×C47—22no—
268C2×C4×C47—22no—
269C2×C4×C47—22no—
270C2×C4×C47—22no—
271C2×C4×C47—22no—
272C2×C4×C47—22no—
273C2×C4×C47—22no—
274C2×C4×C47—41no—
275C2×C4×C47—41no—
276C2×C4×C47—41no—
277C2×C4×C47—41no—
278C2×C4×C47—41no—
279C2×C4×C47—41no—
280C2×C4×C47—41no—
281C2×C4×C47—41no—
282C2×C4×C47—41no—
283C2×C4×C47—41no—
284C2×C4×C47—41no—
285C2×C4×C47—41no—
286C2×C4×C47—41no—
287C2×C4×C47—41no—
288C2×C4×C47—41no—
289C2×C4×C47—41no—
290C2×C4×C47—416no—
291C2×C4×C47#11714yes—
292C2×C4×C47#11714yes—
293C2×C4×C47C4×D414yes—
294C2×C4×C47C4×D414yes—
295C2×C4×C47#12114yes—
296C2×C4×C47#12314yes—
297C2×C4×C47#12414yes—
298C2×C4×C47#12614yes—
299C2×Dic47—24no—
300C2×Dic47—24no—
301C2×Dic47—24no—
302C2×Dic47—24no—
303C2×Dic47—24no—
304C2×Dic47—24no—
305C2×Dic47—42no—
306C2×Dic47—42no—
307C2×Dic47—42no—
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×Dic47—42no—
321C2×Dic47—42no—
322C2×Dic47—42no—
323C2×Dic47—42no—
324C2×Dic47—42no—
325C2×Dic47—42no—
326C2×Dic47—42no—
327#13875—471nomaximal, Sylow
328C22×C47—24no—
329C22×C47—24no—
330C22×C47—24no—
331C22×C47—42no—
332C22×C47—42no—
333C22×C47—42no—
334C22×C47—42no—
335C22×C47—42no—
336C22×C47—42no—
337C22×C47—42no—
338C22×C47—42no—
339C22×C47—42no—
340C22×C47—42no—
341C22×C47—42no—
342C22×C47—42no—
343C22×C47C2×#11711yescharacteristic
344C22×C47C2×#11711yescharacteristic
345C22×C47C2×#11711yescharacteristic
346C22×C47C2×C4×D411yescharacteristic
347C22×C47C2×C4×D411yescharacteristic
348C22×C47#52011yescharacteristic
349C22×C47#52011yescharacteristic
350C22×C47C2×#12111yescharacteristic
351C22×C47C2×#12311yescharacteristic
352C22×C47C2×#12411yescharacteristic
353C22×C47C2×#12611yescharacteristic
354C22×C47#52911yescharacteristic
355C22×C47#52911yescharacteristic
356C22×C47#52911yescharacteristic
357C22×C47#52911yescharacteristic
358C22×C47#54011yescharacteristic
359C22×C47#54111yescharacteristic
360C22×C47#54211yescharacteristic
361C22×C47#54211yescharacteristic
362C22×C47#54611yescharacteristic
363C22×C47#54611yescharacteristic
364C22×C47#54611yescharacteristic
365C22×C47#54711yescharacteristic
366C22×C47#54811yescharacteristic
367C22×C47#54811yescharacteristic
368C22×C47#54811yescharacteristic
369C22×C47#55011yescharacteristic
370C22×C47#55211yescharacteristic
371C22×C47#55211yescharacteristic
372C22×C47#55211yescharacteristic
373C22×C47#55311yescharacteristic
374C22×C47#55311yescharacteristic
375C22×C47#55311yescharacteristic
376C22×C47#55511yescharacteristic
377C22×C47#55611yescharacteristic
378C4×C47—24no—
379C4×C47—42no—
380C4×C47—42no—
381C4×C47—42no—
382C4×C47—42no—
383C4×C47#38818yes—
384Dic47—44no—
385Dic47—44no—
386Dic47—82no—
387Dic47—82no—
388C2×#382—471no—
389C2×#380—471no—
390C2×#380—471no—
391C2×C4×C4⋊C4—471no—
392C2×C4×C22⋊C4D4711yescharacteristic
393#1443—472no—
394#1440—472no—
395#1437—472no—
396C4⋊#95—471no—
397C4⋊#95—471no—
398#1434—472no—
399C2×C47—44no—
400C2×C47#228311yescharacteristic
401C2×C47C2×#38811yescharacteristic
402C2×C47#231411yescharacteristic
403C2×C47#235211yescharacteristic
404C2×C47#235211yescharacteristic
405C2×C47#235211yescharacteristic
406C2×C47#235411yescharacteristic
407C2×C47#242011yescharacteristic
408C2×C47#242111yescharacteristic
409C2×C47#242611yescharacteristic
410C2×C47#242711yescharacteristic
411C2×C47#248911yescharacteristic
412C2×C47#249011yescharacteristic
413C2×C47#249411yescharacteristic
414C2×C47#249511yescharacteristic
415C24×C4C2×D4711yescharacteristic
416C22×C4⋊C4—471no—
417C22×C4⋊C4—471no—
418C22×C4⋊C4—471no—
419C22×C4⋊C4—471no—
420C22×C22⋊C4—472no—
421C22×C22⋊C4—472no—
422C22×C22⋊C4C2×D4711yescharacteristic
423C22×C22⋊C4C2×D4711yescharacteristic
424C22×C42—472no—
425C22×C42C2×D4711yescharacteristic
426C22×C42C2×D4711yescharacteristic
427#382—944no—
428#380—944no—
429#380—944no—
430C4×C4⋊C4—944no—
431C4×C22⋊C4Dic4718yescomplemented
432C2×#95—472no—
433C2×#95—472no—
434C2×#95—472no—
435C2×#95—472no—
436C2×#95—472no—
437C2×#95—472no—
438C2×#95—472no—
439C2×#95—472no—
440C2×#95—472no—
441C2×#95C2×D4711yescharacteristic
442C2×#95C2×D4711yescharacteristic
443C47#1387511yescharacteristic, complemented, Sylow
444C25C22×D4711yescharacteristic
445C23×C4—22no—
446C23×C4—22no—
447C23×C4—22no—
448C23×C4—22no—
449C23×C4—22no—
450C23×C4—22no—
451C23×C4—472no—
452C23×C4—472no—
453C23×C4—472no—
454C23×C4—472no—
455C23×C4C2×Dic4714yes—
456C23×C4C22×D4711yescharacteristic
457C23×C4C22×D4711yescharacteristic
458C23×C4C22×D4711yescharacteristic
459C23×C4C22×D4711yescharacteristic
460C23×C4C22×D4711yescharacteristic
461C23×C4C22×D4711yescharacteristic
462C2×C4⋊C4—474no—
463C2×C4⋊C4—474no—
464C2×C4⋊C4—942no—
465C2×C4⋊C4—942no—
466C2×C4⋊C4—942no—
467C2×C4⋊C4—942no—
468C2×C4⋊C4—942no—
469C2×C4⋊C4—942no—
470C2×C4⋊C4—942no—
471C2×C4⋊C4—942no—
472C2×C4⋊C4—942no—
473C2×C4⋊C4—942no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—944no—
479C2×C22⋊C4—944no—
480C2×C22⋊C4—944no—
481C2×C22⋊C4—944no—
482C2×C22⋊C4—1882no—
483C2×C22⋊C4—1882no—
484C2×C22⋊C4C2×Dic4714yes—
485C2×C22⋊C4C2×Dic4714yes—
486C2×C42—22no—
487C2×C42—22no—
488C2×C42—22no—
489C2×C42—22no—
490C2×C42—944no—
491C2×C42—944no—
492C2×C42—1882no—
493C2×C42C2×Dic4714yes—
494C2×C42C2×Dic4714yes—
495#95—944no—
496#95—944no—
497#95—944no—
498#95—944no—
499#95—944no—
500#95—944no—
501#95—1882no—
502#95—1882no—
503#95—1882no—
504#95C2×Dic4714yes—
505#95C2×Dic4714yes—
506C24—21no—
507C24—21no—
508C24—21no—
509C24—21no—
510C24—21no—
511C24—21no—
512C24—21no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—21no—
517C24—21no—
518C24#1062535012yes—
519C24#1062535012yes—
520C24C22×Dic4712yes—
521C24C23×D4711yescharacteristic
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—28no—
551C22×C4—28no—
552C22×C4—28no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—474no—
558C22×C4—474no—
559C22×C4—942no—
560C22×C4—942no—
561C22×C4—942no—
562C22×C4—942no—
563C22×C4—942no—
564C22×C4—942no—
565C22×C4—942no—
566C22×C4—942no—
567C22×C4—942no—
568C22×C4—942no—
569C22×C4—942no—
570C22×C4—942no—
571C22×C4—942no—
572C22×C4—942no—
573C22×C4—942no—
574C22×C4—942no—
575C22×C4—942no—
576C22×C4—942no—
577C22×C4—942no—
578C22×C4—942no—
579C22×C4—942no—
580C22×C4—942no—
581C22×C4—942no—
582C22×C4—942no—
583C22×C4—942no—
584C22×C4—942no—
585C22×C4#1062535012yes—
586C22×C4#1062535012yes—
587C22×C4#1062535012yes—
588C22×C4#1062535012yes—
589C22×C4D4×D4712yes—
590C22×C4D4×D4712yes—
591C22×C4#1062535212yes—
592C22×C4#1062535212yes—
593C22×C4C22×Dic4712yes—
594C22×C4C22×Dic4712yes—
595C22×C4C22×Dic4712yes—
596C22×C4C22×Dic4712yes—
597C22×C4C22×Dic4712yes—
598C22×C4C22×Dic4712yes—
599C4⋊C4—948no—
600C4⋊C4—948no—
601C4⋊C4—1884no—
602C4⋊C4—1884no—
603C22⋊C4—28no—
604C22⋊C4—28no—
605C22⋊C4—1888no—
606C22⋊C4—1888no—
607C42—28no—
608C42—28no—
609C42—1888no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23#1309398314yes—
645C23C23×Dic4711yescharacteristic
646C23C2×D4×D4711yescharacteristic
647C23C2×D4×D4711yescharacteristic
648C23C2×#1062535211yescharacteristic
649C23C2×#1062535211yescharacteristic
650C23C2×#1062535011yescharacteristic
651C23C2×#1062535011yescharacteristic
652C23C2×#1062535011yescharacteristic
653C23C2×#1062535011yescharacteristic
654C23C2×#1062535011yescharacteristic
655C23C2×#1062535011yescharacteristic
656C23#1309407011yescharacteristic
657C23#1309407011yescharacteristic
658C23#1309407111yescharacteristic
659C23#1309407111yescharacteristic
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—416no—
695C2×C4—944no—
696C2×C4—944no—
697C2×C4—944no—
698C2×C4—944no—
699C2×C4—944no—
700C2×C4—944no—
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—1882no—
712C2×C4—1882no—
713C2×C4—1882no—
714C2×C4—1882no—
715C2×C4—1882no—
716C2×C4—1882no—
717C2×C4—1882no—
718C2×C4—1882no—
719C2×C4—1882no—
720C2×C4—1882no—
721C2×C4—1882no—
722C2×C4—1882no—
723C2×C4#1309398314yes—
724C2×C4#1309398314yes—
725C2×C4D4×Dic4714yes—
726C2×C4D4×Dic4714yes—
727C2×C4#1309399714yes—
728C2×C4#1309400614yes—
729C2×C4#1309401014yes—
730C2×C4#1309401714yes—
731C22—24no—
732C22—24no—
733C22—24no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22C2×#1309398311yescharacteristic
747C22C2×#1309398311yescharacteristic
748C22C2×#1309398311yescharacteristic
749C22C2×D4×Dic4711yescharacteristic
750C22C2×D4×Dic4711yescharacteristic
751C22#1568960611yescharacteristic
752C22#1568960611yescharacteristic
753C22C2×#1309399711yescharacteristic
754C22C2×#1309400611yescharacteristic
755C22C2×#1309401011yescharacteristic
756C22C2×#1309401711yescharacteristic
757C22#1568965711yescharacteristic
758C22#1568965711yescharacteristic
759C22#1568965711yescharacteristic
760C22#1568965711yescharacteristic
761C22#1568972811yescharacteristic
762C22#1568973511yescharacteristic
763C22#1568974411yescharacteristic
764C22#1568974411yescharacteristic
765C22#1568976911yescharacteristic
766C22#1568976911yescharacteristic
767C22#1568976911yescharacteristic
768C22#1568977811yescharacteristic
769C22#1568978211yescharacteristic
770C22#1568978211yescharacteristic
771C22#1568978211yescharacteristic
772C22#1568979411yescharacteristic
773C22#1568981311yescharacteristic
774C22#1568981311yescharacteristic
775C22#1568981311yescharacteristic
776C22#1568981911yescharacteristic
777C22#1568981911yescharacteristic
778C22#1568981911yescharacteristic
779C22#1568983811yescharacteristic
780C22#1568984311yescharacteristic
781C4—24no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—3762no—
787C4—3762no—
788C4—1884no—
789C4—1884no—
790C4#1568901618yes—
791C2—44no—
792C2#2024578611yescharacteristic
793C2C2×#1568901611yescharacteristic
794C2#2024599711yescharacteristic
795C2#2024631711yescharacteristic
796C2#2024631711yescharacteristic
797C2#2024631711yescharacteristic
798C2#2024633711yescharacteristic
799C2#2024688011yescharacteristic
800C2#2024689111yescharacteristic
801C2#2024695411yescharacteristic
802C2#2024696511yescharacteristic
803C2#2024772911yescharacteristic
804C2#2024774011yescharacteristic
805C2#2024778811yescharacteristic
806C2#2024779911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C4×C22⋊C4×C47C2
socle, cosocleC24×C47C24
prime radicalC25×C47C23
hypercenterC2×C4×C22⋊C4D47
hypocenterC47#13875
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#15688989C2semidirect
4. C2×C4×C4⋊Dic47C2semidirect
5. #20241650C2semidirect
8. #20241618C2semidirect
9. #20241618C2semidirect
10. #20241613C2semidirect
37. C4×C22⋊C4×C47C4semidirect
431. C4×C22⋊C4Dic47semidirect
443. C47#13875semidirect

Maximal subgroups

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

subgroupindex
C2×#156889892
C2×#156889832
C2×C4×C4⋊Dic472
#202416502
#202416372
#202416252
#202416182
#202416132
C2×C4×C22⋊C4×C472
#1387547