Finite Group Databasebeta

← #26137773

Subgroups — #26137773

Order 12032.

2882 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689003C212yesmaximal
2C2×C22⋊C4×Dic47C212yesmaximal, complemented
3C2×C4×C22⋊Dic47C211yesmaximal, characteristic, complemented
4C22×C47⋊#95C211yesmaximal, characteristic, complemented
5#20241625C212yesmaximal, complemented
6#20241620C212yesmaximal, complemented
7#20241615C211yesmaximal, characteristic, complemented
8#20241611C211yesmaximal, characteristic, complemented
9#20241611C211yesmaximal, characteristic, complemented
10C4×C47⋊#95C211yesmaximal, characteristic, complemented
11C22×C4×D4×C47C211yesmaximal, characteristic
12C24×Dic47C2212yes—
13C22×C22⋊Dic47C2212yes—
14C22×C22⋊Dic47C2212yes—
15C22×C22⋊Dic47C2212yes—
16C22×C4×Dic47C2212yes—
17C22×C4×Dic47C2212yes—
18#15689003C4116yescomplemented
19C22⋊C4×Dic47—28no—
20C4×C22⋊Dic47—24no—
21C2×C47⋊#95—24no—
22C2×C47⋊#95C2211yescharacteristic
23C2×C47⋊#95C2211yescharacteristic
24C2×C47⋊#95C2211yescharacteristic
25C2×C47⋊#95C2212yes—
26C2×C47⋊#95C2212yes—
27C2×C47⋊#95C2212yes—
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2211yescharacteristic
32C23×D4×C47C2211yescharacteristic
33C24×C4×C47C2211yescharacteristic
34C24×C4×C47C2211yescharacteristic
35C2×C4×D4×C47—28no—
36C2×C4×D4×C47C418yescomplemented
37C22×C4⋊C4×C47C2211yescharacteristic
38C22×C22⋊C4×C47C2211yescharacteristic
39C22×C22⋊C4×C47C2211yescharacteristic
40C22×C42×C47C2211yescharacteristic
41C23×Dic47—24no—
42C23×Dic47—24no—
43C23×Dic47—24no—
44C23×Dic47—24no—
45C23×Dic47—42no—
46C23×Dic47—42no—
47C23×Dic47C2×C418yescomplemented
48C23×Dic47C2312yes—
49C23×Dic47C2312yes—
50C23×Dic47C2312yes—
51C23×Dic47C2312yes—
52C2×C22⋊Dic47—24no—
53C2×C22⋊Dic47—24no—
54C2×C22⋊Dic47—24no—
55C2×C22⋊Dic47—24no—
56C2×C22⋊Dic47—42no—
57C2×C22⋊Dic47—42no—
58C2×C22⋊Dic47C2×C418yescomplemented
59C2×C22⋊Dic47C2×C418yescomplemented
60C2×C22⋊Dic47C2×C418yescomplemented
61C2×C4×Dic47—24no—
62C2×C4×Dic47—24no—
63C2×C4×Dic47—24no—
64C2×C4×Dic47—24no—
65C2×C4×Dic47—42no—
66C2×C4×Dic47—42no—
67C47⋊#95—22no—
68C47⋊#95—22no—
69C47⋊#95—24no—
70C47⋊#95—24no—
71C47⋊#95—22no—
72C47⋊#95—24no—
73C47⋊#95—42no—
74C47⋊#95C2×C418yescomplemented
75C47⋊#95C2×C418yescomplemented
76C47⋊#95D414yescomplemented
77C25×C47C2311yescharacteristic
78C25×C47C2311yescharacteristic
79C22×D4×C47—24no—
80C22×D4×C47—22no—
81C22×D4×C47—22no—
82C22×D4×C47C2×C418yes—
83C22×D4×C47C2×C414yes—
84C23×C4×C47—24no—
85C23×C4×C47—22no—
86C23×C4×C47—22no—
87C23×C4×C47—24no—
88C23×C4×C47—22no—
89C23×C4×C47—22no—
90C23×C4×C47—42no—
91C23×C4×C47—42no—
92C23×C4×C47C2×C414yes—
93C23×C4×C47C2×C414yescomplemented
94C23×C4×C47C2311yescharacteristic
95C23×C4×C47C2311yescharacteristic
96C23×C4×C47C2311yescharacteristic
97C23×C4×C47C2311yescharacteristic
98C23×C4×C47C2311yescharacteristic
99C4×D4×C47—232no—
100C2×C4⋊C4×C47—24no—
101C2×C4⋊C4×C47C2×C414yescomplemented
102C2×C22⋊C4×C47—24no—
103C2×C22⋊C4×C47C2×C414yes—
104C2×C22⋊C4×C47C2×C414yescomplemented
105C2×C22⋊C4×C47D418yes—
106C2×C42×C47—24no—
107C2×C42×C47C2×C414yescomplemented
108C24×C47—21no—
109C24×C47—21no—
110C24×C47—22no—
111C24×C47—22no—
112C24×C47—21no—
113C24×C47—21no—
114C24×C47—22no—
115C24×C47—21no—
116C24×C47—21no—
117C24×C47—21no—
118C24×C47—21no—
119C24×C47—22no—
120C24×C47—22no—
121C24×C47—21no—
122C24×C47—21no—
123C24×C47C22×C414yes—
124C24×C47C22×C412yes—
125C24×C47C22×C412yes—
126C24×C47C22×C414yes—
127C24×C47C2×D414yes—
128C24×C47#4112yes—
129C24×C47#4112yes—
130C24×C47C2411yescharacteristic
131C2×D4×C47—28no—
132C2×D4×C47—28no—
133C2×D4×C47—216no—
134C2×D4×C47—216no—
135C2×D4×C47C42116yescomplemented
136C22×C4×C47—22no—
137C22×C4×C47—22no—
138C22×C4×C47—21no—
139C22×C4×C47—21no—
140C22×C4×C47—21no—
141C22×C4×C47—21no—
142C22×C4×C47—22no—
143C22×C4×C47—22no—
144C22×C4×C47—22no—
145C22×C4×C47—21no—
146C22×C4×C47—21no—
147C22×C4×C47—28no—
148C22×C4×C47—22no—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—22no—
152C22×C4×C47—28no—
153C22×C4×C47—28no—
154C22×C4×C47—28no—
155C22×C4×C47—44no—
156C22×C4×C47—44no—
157C22×C4×C47—48no—
158C22×C4×C47—48no—
159C22×C4×C47—48no—
160C22×C4×C47—48no—
161C22×C4×C47C22×C412yes—
162C22×C4×C47C22×C414yes—
163C22×C4×C47C22×C412yes—
164C22×C4×C47C22×C412yes—
165C22×C4×C47C22×C412yes—
166C22×C4×C47C22×C412yes—
167C22×C4×C47C2×D414yes—
168C22×C4×C47C2×D414yes—
169C22×C4×C47C2×D412yes—
170C22×C4×C47#4112yes—
171C22×Dic47—22no—
172C22×Dic47—22no—
173C22×Dic47—22no—
174C22×Dic47—22no—
175C22×Dic47—216no—
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×Dic47—22no—
194C22×Dic47—216no—
195C22×Dic47—48no—
196C22×Dic47—48no—
197C22×Dic47—48no—
198C22×Dic47—48no—
199C22×Dic47—48no—
200C22×Dic47C22×C414yes—
201C22×Dic47C22×C414yes—
202C22×Dic47C22×C414yes—
203C22×Dic47C22×C414yes—
204C22×Dic47C2×D414yes—
205C22×Dic47#4114yes—
206C4⋊C4×C47—28no—
207C22⋊C4×C47—28no—
208C22⋊C4×C47C22⋊C4116yescomplemented
209C42×C47—28no—
210C22⋊Dic47—216no—
211C22⋊Dic47—216no—
212C22⋊Dic47—48no—
213C4×Dic47—48no—
214C4×Dic47—48no—
215C23×C47—24no—
216C23×C47—22no—
217C23×C47—24no—
218C23×C47—22no—
219C23×C47—24no—
220C23×C47—22no—
221C23×C47—24no—
222C23×C47—22no—
223C23×C47—24no—
224C23×C47—22no—
225C23×C47—24no—
226C23×C47—24no—
227C23×C47—24no—
228C23×C47—22no—
229C23×C47—24no—
230C23×C47—22no—
231C23×C47—22no—
232C23×C47—24no—
233C23×C47—22no—
234C23×C47—22no—
235C23×C47—24no—
236C23×C47—22no—
237C23×C47—24no—
238C23×C47—24no—
239C23×C47—24no—
240C23×C47—22no—
241C23×C47—24no—
242C23×C47—22no—
243C23×C47—24no—
244C23×C47—22no—
245C23×C47—42no—
246C23×C47—42no—
247C23×C47—42no—
248C23×C47—41no—
249C23×C47—42no—
250C23×C47—41no—
251C23×C47—42no—
252C23×C47—41no—
253C23×C47—41no—
254C23×C47—42no—
255C23×C47C2×C4214yes—
256C23×C47C2×C4214yes—
257C23×C47C2×C22⋊C414yes—
258C23×C47#11714yes—
259C23×C47C4×D418yes—
260C23×C47C4×D418yes—
261C23×C47C23×C412yes—
262C23×C47C23×C411yescharacteristic
263C23×C47C22×D411yescharacteristic
264C23×C47C22×D412yes—
265C23×C47C2×#4112yes—
266C23×C47C2×#4111yescharacteristic
267C23×C47C2×#4111yescharacteristic
268C23×C47C2×#4111yescharacteristic
269C23×C47H(5,𝔽2)12yes—
270C23×C47H(5,𝔽2)11yescharacteristic
271C23×C472−1+411yescharacteristic
272D4×C47—232no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—22no—
276C2×C4×C47—22no—
277C2×C4×C47—24no—
278C2×C4×C47—24no—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—22no—
282C2×C4×C47—22no—
283C2×C4×C47—24no—
284C2×C4×C47—24no—
285C2×C4×C47—24no—
286C2×C4×C47—24no—
287C2×C4×C47—24no—
288C2×C4×C47—24no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—416no—
293C2×C4×C47—416no—
294C2×C4×C47—42no—
295C2×C4×C47—42no—
296C2×C4×C47C2×C4214yes—
297C2×C4×C47C2×C22⋊C414yes—
298C2×C4×C47C2×C22⋊C414yes—
299C2×C4×C47C4×D414yes—
300C2×Dic47—24no—
301C2×Dic47—24no—
302C2×Dic47—24no—
303C2×Dic47—24no—
304C2×Dic47—24no—
305C2×Dic47—24no—
306C2×Dic47—24no—
307C2×Dic47—24no—
308C2×Dic47—24no—
309C2×Dic47—24no—
310C2×Dic47—24no—
311C2×Dic47—24no—
312C2×Dic47—24no—
313C2×Dic47—24no—
314C2×Dic47—24no—
315C2×Dic47—432no—
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—
327C2×Dic47—42no—
328C2×Dic47C4×D418yescomplemented
329#13813—471nomaximal, Sylow
330C22×C47—24no—
331C22×C47—24no—
332C22×C47—24no—
333C22×C47—24no—
334C22×C47—28no—
335C22×C47—28no—
336C22×C47—28no—
337C22×C47—28no—
338C22×C47—24no—
339C22×C47—24no—
340C22×C47—24no—
341C22×C47—24no—
342C22×C47—24no—
343C22×C47—42no—
344C22×C47—42no—
345C22×C47—42no—
346C22×C47—42no—
347C22×C47—44no—
348C22×C47—44no—
349C22×C47—44no—
350C22×C47—44no—
351C22×C47C4×C22⋊C418yescomplemented
352C22×C47C22×C4211yescharacteristic
353C22×C47C22×C22⋊C411yescharacteristic
354C22×C47C2×#11711yescharacteristic
355C22×C47C2×C4×D412yes—
356C22×C47C2×C4×D412yes—
357C22×C47C2×C4×D412yes—
358C22×C47C2×C4×D411yescharacteristic
359C22×C47C4×#4112yes—
360C22×C47C4×#4111yescharacteristic
361C22×C47#51812yes—
362C22×C47#51811yescharacteristic
363C22×C47#52012yes—
364C22×C47#52011yescharacteristic
365C22×C47D4212yes—
366C22×C47#54612yes—
367C22×C47#54612yes—
368C22×C47#54611yescharacteristic
369C22×C47#54712yes—
370C22×C47#54811yescharacteristic
371C22×C47#55112yes—
372C22×C47#55211yescharacteristic
373C22×C47#55311yescharacteristic
374C22×C47#55312yes—
375C4×C47—24no—
376C4×C47—24no—
377C4×C47—24no—
378C4×C47—24no—
379C4×C47—42no—
380Dic47—28no—
381Dic47—44no—
382Dic47—44no—
383Dic47—44no—
384C22×C4×D4D4711yescharacteristic
385C2×#386—472no—
386C2×C4×C22⋊C4—471no—
387C2×C4×C22⋊C4—472no—
388C22×#95—471no—
389#1437—472no—
390#1436—472no—
391#1434—471no—
392C22⋊#95—471no—
393C22⋊#95—471no—
394C4×#95—471no—
395C2×C47—28no—
396C2×C47—44no—
397C2×C47C2×C4×C22⋊C411yescharacteristic
398C2×C47C42×D411yescharacteristic
399C2×C47#227511yescharacteristic
400C2×C47D4×C22⋊C411yescharacteristic
401C2×C47#233911yescharacteristic
402C2×C47#235211yescharacteristic
403C2×C47#235311yescharacteristic
404C2×C47#235812yes—
405C2×C47#235912yes—
406C2×C47#236112yes—
407C2×C47#236412yes—
408C23×D4C2×D4711yescharacteristic
409C24×C4—472no—
410C24×C4C2×D4711yescharacteristic
411C24×C4C2×D4711yescharacteristic
412C2×C4×D4—28no—
413C2×C4×D4Dic4718yescomplemented
414C22×C4⋊C4C2×D4711yescharacteristic
415C22×C22⋊C4—472no—
416C22×C22⋊C4—472no—
417C22×C22⋊C4—472no—
418C22×C22⋊C4C2×D4711yescharacteristic
419C22×C22⋊C4C2×D4711yescharacteristic
420C22×C42—472no—
421C22×C42—472no—
422C22×C42C2×D4711yescharacteristic
423#386—4716no—
424C4×C22⋊C4—944no—
425C4×C22⋊C4—948no—
426C2×#95—472no—
427C2×#95—471no—
428C2×#95—472no—
429C2×#95—471no—
430C2×#95—471no—
431C2×#95—471no—
432C2×#95—472no—
433C2×#95—472no—
434C2×#95—472no—
435C2×#95—472no—
436C2×#95—944no—
437C47#1381311yescharacteristic, complemented, Sylow
438C25C22×D4711yescharacteristic
439C25C22×D4711yescharacteristic
440C22×D4—22no—
441C22×D4—22no—
442C22×D4—24no—
443C22×D4C4×D4718yes—
444C22×D4C2×Dic4714yes—
445C23×C4—24no—
446C23×C4—22no—
447C23×C4—22no—
448C23×C4—22no—
449C23×C4—22no—
450C23×C4—24no—
451C23×C4—42no—
452C23×C4—42no—
453C23×C4—472no—
454C23×C4—472no—
455C23×C4—472no—
456C23×C4—472no—
457C23×C4—478no—
458C23×C4—944no—
459C23×C4—944no—
460C23×C4—944no—
461C23×C4—944no—
462C23×C4—1882no—
463C23×C4—1882no—
464C23×C4C2×Dic4714yes—
465C23×C4C2×Dic4714yescomplemented
466C23×C4C22×D4711yescharacteristic
467C23×C4C22×D4711yescharacteristic
468C23×C4C22×D4711yescharacteristic
469C23×C4C22×D4711yescharacteristic
470C23×C4C22×D4711yescharacteristic
471C4×D4—232no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4C2×Dic4714yescomplemented
474C2×C22⋊C4—24no—
475C2×C22⋊C4—478no—
476C2×C22⋊C4—478no—
477C2×C22⋊C4—478no—
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×Dic4714yescomplemented
486C2×C22⋊C4C22⋊D4718yes—
487C2×C42—24no—
488C2×C42—944no—
489C2×C42—944no—
490C2×C42—944no—
491C2×C42—944no—
492C2×C42—1882no—
493C2×C42—1882no—
494C2×C42C2×Dic4714yescomplemented
495#95—478no—
496#95—478no—
497#95—474no—
498#95—944no—
499#95—942no—
500#95—942no—
501#95—942no—
502#95—944no—
503#95—944no—
504#95—1882no—
505C24—21no—
506C24—22no—
507C24—21no—
508C24—22no—
509C24—21no—
510C24—21no—
511C24—21no—
512C24—22no—
513C24—22no—
514C24—21no—
515C24—21no—
516C24—21no—
517C24—22no—
518C24—21no—
519C24—21no—
520C24C2×C4×D4714yes—
521C24C2×C4×D4714yes—
522C24#1062535012yes—
523C24#1062535012yes—
524C24C22×Dic4712yes—
525C24C22×Dic4712yes—
526C24C2×C22⋊D4714yes—
527C24C23×D4711yescharacteristic
528C2×D4—28no—
529C2×D4—28no—
530C2×D4—216no—
531C2×D4—216no—
532C2×D4C4×Dic47116yescomplemented
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—28no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—28no—
550C22×C4—28no—
551C22×C4—28no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—48no—
555C22×C4—48no—
556C22×C4—48no—
557C22×C4—48no—
558C22×C4—474no—
559C22×C4—474no—
560C22×C4—474no—
561C22×C4—474no—
562C22×C4—474no—
563C22×C4—474no—
564C22×C4—9416no—
565C22×C4—942no—
566C22×C4—942no—
567C22×C4—942no—
568C22×C4—942no—
569C22×C4—9416no—
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—942no—
586C22×C4—942no—
587C22×C4—942no—
588C22×C4—1888no—
589C22×C4—1888no—
590C22×C4—1888no—
591C22×C4—1888no—
592C22×C4—1888no—
593C22×C4C2×C4×D4714yes—
594C22×C4D4×D4712yes—
595C22×C4#1062535212yes—
596C22×C4C22×Dic4712yes—
597C22×C4C22×Dic4712yes—
598C22×C4C22×Dic4712yes—
599C22×C4C22×Dic4712yes—
600C22×C4C22×Dic4712yes—
601C22×C4C2×C22⋊D4714yes—
602C22×C4C2×C22⋊D4714yes—
603C4⋊C4—28no—
604C22⋊C4—28no—
605C22⋊C4—9416no—
606C22⋊C4—9416no—
607C22⋊C4—1888no—
608C22⋊C4C22⋊Dic47116yescomplemented
609C42—28no—
610C42—1888no—
611C42—1888no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—22no—
616C23—24no—
617C23—22no—
618C23—24no—
619C23—22no—
620C23—22no—
621C23—24no—
622C23—24no—
623C23—22no—
624C23—24no—
625C23—22no—
626C23—24no—
627C23—22no—
628C23—24no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—22no—
636C23—24no—
637C23—22no—
638C23—24no—
639C23—22no—
640C23—24no—
641C23—22no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—41no—
646C23—42no—
647C23—41no—
648C23—42no—
649C23—41no—
650C23—41no—
651C23—42no—
652C23C2×C4×Dic4714yes—
653C23C2×C4×Dic4714yes—
654C23C2×C22⋊Dic4714yes—
655C23#1309398314yes—
656C23C4×C22⋊D4718yes—
657C23C4×C22⋊D4718yes—
658C23C22×C4×D4712yes—
659C23C23×Dic4711yescharacteristic
660C23C2×D4×D4711yescharacteristic
661C23C22×C22⋊D4712yes—
662C23#41×D4712yes—
663C23C2×#1062535211yescharacteristic
664C23C2×#1062535011yescharacteristic
665C23C2×#1062535011yescharacteristic
666C23#1309406912yes—
667C23#1309407011yescharacteristic
668C23#1309407111yescharacteristic
669D4—232no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—416no—
690C2×C4—416no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—478no—
694C2×C4—944no—
695C2×C4—944no—
696C2×C4—944no—
697C2×C4—944no—
698C2×C4—944no—
699C2×C4—944no—
700C2×C4—944no—
701C2×C4—944no—
702C2×C4—944no—
703C2×C4—944no—
704C2×C4—944no—
705C2×C4—944no—
706C2×C4—944no—
707C2×C4—944no—
708C2×C4—944no—
709C2×C4—18832no—
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×C4C2×C4×Dic4714yes—
723C2×C4C2×C22⋊Dic4714yes—
724C2×C4C2×C22⋊Dic4714yes—
725C2×C4D4×Dic4714yes—
726C22—24no—
727C22—24no—
728C22—28no—
729C22—28no—
730C22—28no—
731C22—28no—
732C22—24no—
733C22—24no—
734C22—24no—
735C22—24no—
736C22—24no—
737C22—24no—
738C22—24no—
739C22—42no—
740C22—42no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—44no—
745C22—42no—
746C22—42no—
747C22C4×C22⋊Dic4718yescomplemented
748C22C22×C4×Dic4711yescharacteristic
749C22C22×C22⋊Dic4711yescharacteristic
750C22C2×#1309398311yescharacteristic
751C22C4×D4×D4712yes—
752C22C2×C4×C22⋊D4712yes—
753C22C2×C4×C22⋊D4712yes—
754C22C2×D4×Dic4711yescharacteristic
755C22C4×#1062535212yes—
756C22#41×Dic4711yescharacteristic
757C22#1568959512yes—
758C22#1568959811yescharacteristic
759C22#1568960212yes—
760C22#1568960611yescharacteristic
761C22D4×C22⋊D4712yes—
762C22#1568976112yes—
763C22#1568976712yes—
764C22#1568976911yescharacteristic
765C22#1568977212yes—
766C22#1568978211yescharacteristic
767C22#1568980212yes—
768C22#1568981311yescharacteristic
769C22#1568981911yescharacteristic
770C22#1568982212yes—
771C4—24no—
772C4—24no—
773C4—24no—
774C4—24no—
775C4—42no—
776C4—948no—
777C4—1884no—
778C4—1884no—
779C4—1884no—
780C2—28no—
781C2—44no—
782C2C2×C4×C22⋊Dic4711yescharacteristic
783C2C4×D4×Dic4711yescharacteristic
784C2#2024574911yescharacteristic
785C2D4×C22⋊Dic4711yescharacteristic
786C2#2024621811yescharacteristic
787C2#2024631711yescharacteristic
788C2#2024632811yescharacteristic
789C2#2024636512yes—
790C2#2024637412yes—
791C2#2024640512yes—
792C2#2024643312yes—
subgroupG/H
center, FrattiniC24C23×D47
commutatorC22×C47C22×C42
FittingC22×C4×D4×C47C2
socle, cosocleC24×C47C24
prime radicalC23×D4×C47C22
hypercenterC22×C4×D4D47
hypocenterC47#13813
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊C4×Dic47C2semidirect
3. C2×C4×C22⋊Dic47C2semidirect
4. C22×C47⋊#95C2semidirect
5. #20241625C2semidirect
6. #20241620C2semidirect
7. #20241615C2semidirect
8. #20241611C2semidirect
9. #20241611C2semidirect
10. C4×C47⋊#95C2semidirect
18. #15689003C4semidirect
36. C2×C4×D4×C47C4semidirect
47. C23×Dic47C2×C4semidirect
58. C2×C22⋊Dic47C2×C4semidirect
59. C2×C22⋊Dic47C2×C4semidirect
60. C2×C22⋊Dic47C2×C4semidirect
74. C47⋊#95C2×C4semidirect
75. C47⋊#95C2×C4semidirect
76. C47⋊#95D4semidirect
93. C23×C4×C47C2×C4semidirect
101. C2×C4⋊C4×C47C2×C4semidirect
104. C2×C22⋊C4×C47C2×C4semidirect
107. C2×C42×C47C2×C4semidirect
135. C2×D4×C47C42semidirect
208. C22⋊C4×C47C22⋊C4semidirect
328. C2×Dic47C4×D4semidirect
351. C22×C47C4×C22⋊C4semidirect
413. C2×C4×D4Dic47semidirect
437. C47#13813semidirect
465. C23×C4C2×Dic47semidirect
473. C2×C4⋊C4C2×Dic47semidirect
485. C2×C22⋊C4C2×Dic47semidirect
494. C2×C42C2×Dic47semidirect
532. C2×D4C4×Dic47semidirect
608. C22⋊C4C22⋊Dic47semidirect
747. C22C4×C22⋊Dic47semidirect

Maximal subgroups

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

subgroupindex
C2×#156890032
C2×C22⋊C4×Dic472
C2×C4×C22⋊Dic472
C22×C47⋊#952
#202416252
#202416202
#202416152
#202416112
C4×C47⋊#952
C22×C4×D4×C472
#1381347