Finite Group Databasebeta

← #26138466

Subgroups — #26138466

Order 12032.

2690 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×#15688998C212yesmaximal, complemented
3C2×#15688983C211yesmaximal, characteristic, complemented
4C22×C47⋊#95C211yesmaximal, characteristic, complemented
5#20241641C212yesmaximal, complemented
6#20241633C212yesmaximal, complemented
7#20241618C211yesmaximal, characteristic, complemented
8#20241615C211yesmaximal, characteristic, complemented
9#20241611C211yesmaximal, characteristic, complemented
10#20241611C211yesmaximal, characteristic, complemented
11C22×C4×D4×C47C211yesmaximal, characteristic
12C24×Dic47C2212yes—
13C22×C4⋊Dic47C2212yes—
14C22×C4⋊Dic47C2212yes—
15C22×C22⋊Dic47C2212yes—
16C22×C22⋊Dic47C2212yes—
17C22×C22⋊Dic47C2212yes—
18#15689003—28no—
19#15688998—28no—
20#15688983—24no—
21C2×C47⋊#95—24no—
22C2×C47⋊#95C2211yescharacteristic
23C2×C47⋊#95C2212yes—
24C2×C47⋊#95C2212yes—
25C2×C47⋊#95C2212yes—
26C2×C47⋊#95C2212yes—
27C2×C47⋊#95C2211yescharacteristic
28C2×C47⋊#95C2211yescharacteristic
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—24no—
46C23×Dic47—42no—
47C23×Dic47—42no—
48C23×Dic47C2312yes—
49C23×Dic47C2312yes—
50C23×Dic47C2312yes—
51C23×Dic47C2312yes—
52C2×C4⋊Dic47—24no—
53C2×C4⋊Dic47—24no—
54C2×C4⋊Dic47—24no—
55C2×C4⋊Dic47—24no—
56C2×C4⋊Dic47—42no—
57C2×C4⋊Dic47—42no—
58C2×C22⋊Dic47—24no—
59C2×C22⋊Dic47—24no—
60C2×C22⋊Dic47—24no—
61C2×C22⋊Dic47—24no—
62C2×C22⋊Dic47—24no—
63C2×C22⋊Dic47—24no—
64C2×C22⋊Dic47—24no—
65C2×C22⋊Dic47—42no—
66C2×C22⋊Dic47—42no—
67C47⋊#95—22no—
68C47⋊#95—22no—
69C47⋊#95—24no—
70C47⋊#95—24no—
71C47⋊#95—24no—
72C47⋊#95—24no—
73C47⋊#95—22no—
74C47⋊#95—24no—
75C47⋊#95—42no—
76C47⋊#95D414yescomplemented
77C25×C47C2311yescharacteristic
78C25×C47C2311yescharacteristic
79C22×D4×C47—24no—
80C22×D4×C47—24no—
81C22×D4×C47C2×C414yes—
82C22×D4×C47D414yes—
83C22×D4×C47Q814yes—
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—22no—
118C24×C47—22no—
119C24×C47—22no—
120C24×C47—21no—
121C24×C47—21no—
122C24×C47C22×C412yes—
123C24×C47C22×C412yes—
124C24×C47C2×D412yes—
125C24×C47C2×D414yes—
126C24×C47C2×D412yes—
127C24×C47C2×Q812yes—
128C24×C47C2×Q812yes—
129C24×C47#4114yes—
130C24×C47C2411yescharacteristic
131C2×D4×C47—28no—
132C2×D4×C47—28no—
133C2×D4×C47—216no—
134C2×D4×C47—216no—
135C2×D4×C47C4⋊C4116yescomplemented
136C22×C4×C47—22no—
137C22×C4×C47—22no—
138C22×C4×C47—21no—
139C22×C4×C47—21no—
140C22×C4×C47—22no—
141C22×C4×C47—22no—
142C22×C4×C47—22no—
143C22×C4×C47—22no—
144C22×C4×C47—21no—
145C22×C4×C47—21no—
146C22×C4×C47—28no—
147C22×C4×C47—22no—
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47—22no—
151C22×C4×C47—28no—
152C22×C4×C47—28no—
153C22×C4×C47—28no—
154C22×C4×C47—44no—
155C22×C4×C47—44no—
156C22×C4×C47—48no—
157C22×C4×C47—48no—
158C22×C4×C47—48no—
159C22×C4×C47—48no—
160C22×C4×C47C22×C412yes—
161C22×C4×C47C22×C412yes—
162C22×C4×C47C22×C412yes—
163C22×C4×C47C22×C412yes—
164C22×C4×C47C22×C412yes—
165C22×C4×C47C2×D414yes—
166C22×C4×C47C2×D414yes—
167C22×C4×C47C2×D412yes—
168C22×C4×C47C2×D412yes—
169C22×C4×C47C2×Q812yes—
170C22×C4×C47#4112yes—
171C22×Dic47—216no—
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×Dic47—22no—
194C22×Dic47—22no—
195C22×Dic47—22no—
196C22×Dic47—22no—
197C22×Dic47—22no—
198C22×Dic47—48no—
199C22×Dic47—48no—
200C22×Dic47—48no—
201C22×Dic47—48no—
202C22×Dic47—48no—
203C22×Dic47—48no—
204C22×Dic47C2×D414yes—
205C22×Dic47#4114yes—
206C4⋊C4×C47—28no—
207C22⋊C4×C47—28no—
208C22⋊C4×C47C22⋊C4116yescomplemented
209C42×C47—28no—
210C22⋊Dic47—48no—
211C22⋊Dic47—48no—
212C22⋊Dic47—48no—
213C4⋊Dic47—48no—
214C4⋊Dic47—48no—
215C23×C47—22no—
216C23×C47—22no—
217C23×C47—22no—
218C23×C47—22no—
219C23×C47—24no—
220C23×C47—24no—
221C23×C47—24no—
222C23×C47—24no—
223C23×C47—22no—
224C23×C47—24no—
225C23×C47—24no—
226C23×C47—24no—
227C23×C47—24no—
228C23×C47—24no—
229C23×C47—22no—
230C23×C47—22no—
231C23×C47—22no—
232C23×C47—24no—
233C23×C47—22no—
234C23×C47—22no—
235C23×C47—22no—
236C23×C47—22no—
237C23×C47—22no—
238C23×C47—22no—
239C23×C47—24no—
240C23×C47—24no—
241C23×C47—22no—
242C23×C47—24no—
243C23×C47—22no—
244C23×C47—22no—
245C23×C47—22no—
246C23×C47—24no—
247C23×C47—42no—
248C23×C47—42no—
249C23×C47—42no—
250C23×C47—42no—
251C23×C47—42no—
252C23×C47—42no—
253C23×C47—42no—
254C23×C47—42no—
255C23×C47C2×C22⋊C414yes—
256C23×C47C2×C4⋊C414yes—
257C23×C47C2×C4⋊C414yes—
258C23×C47#11714yes—
259C23×C47#12118yes—
260C23×C47C22⋊Q818yes—
261C23×C47C23×C411yescharacteristic
262C23×C47C22×D411yescharacteristic
263C23×C47C22×D412yes—
264C23×C47C22×D411yescharacteristic
265C23×C47C22×Q811yescharacteristic
266C23×C47C2×#4112yes—
267C23×C47C2×#4111yescharacteristic
268C23×C47C2×#4112yes—
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—22no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—24no—
282C2×C4×C47—24no—
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×C22⋊C414yes—
297C2×C4×C47C2×C22⋊C414yes—
298C2×C4×C47C2×C4⋊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—432no—
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—
327C2×Dic47—42no—
328C2×Dic47—42no—
329#13899—471nomaximal, Sylow
330C22×C47—24no—
331C22×C47—24no—
332C22×C47—24no—
333C22×C47—24no—
334C22×C47—24no—
335C22×C47—28no—
336C22×C47—28no—
337C22×C47—28no—
338C22×C47—28no—
339C22×C47—24no—
340C22×C47—24no—
341C22×C47—24no—
342C22×C47—24no—
343C22×C47—42no—
344C22×C47—42no—
345C22×C47—42no—
346C22×C47—44no—
347C22×C47—44no—
348C22×C47—44no—
349C22×C47—44no—
350C22×C47—42no—
351C22×C47#38018yescomplemented
352C22×C47C22×C22⋊C411yescharacteristic
353C22×C47C22×C4⋊C411yescharacteristic
354C22×C47C2×#11711yescharacteristic
355C22×C47C2×C4×D411yescharacteristic
356C22×C47C4×#4111yescharacteristic
357C22×C47#51811yescharacteristic
358C22×C47#52011yescharacteristic
359C22×C47C2×#12112yes—
360C22×C47C2×C22⋊Q812yes—
361C22×C47#52512yes—
362C22×C47#52912yes—
363C22×C47#53812yes—
364C22×C47#53912yes—
365C22×C47D4212yes—
366C22×C47D4211yescharacteristic
367C22×C47#54612yes—
368C22×C47#54612yes—
369C22×C47#54612yes—
370C22×C47#54712yes—
371C22×C47#54711yescharacteristic
372C22×C47D4×Q811yescharacteristic
373C22×C47#55411yescharacteristic
374C22×C47#55412yes—
375C4×C47—24no—
376C4×C47—24no—
377C4×C47—24no—
378C4×C47—24no—
379C4×C47—42no—
380Dic47—44no—
381Dic47—44no—
382Dic47—82no—
383Dic47—82no—
384C22×C4×D4D4711yescharacteristic
385C2×#386—472no—
386C2×#385—472no—
387C2×#380—471no—
388C22×#95—471no—
389#1441—472no—
390#1439—472no—
391C4⋊#95—471no—
392#1434—471no—
393C22⋊#95—471no—
394C22⋊#95—471no—
395C2×C47—28no—
396C2×C47—44no—
397C2×C47C2×#38011yescharacteristic
398C2×C47#229011yescharacteristic
399C2×C47#231811yescharacteristic
400C2×C47D4×C22⋊C411yescharacteristic
401C2×C47#233911yescharacteristic
402C2×C47D4×C4⋊C411yescharacteristic
403C2×C47#234911yescharacteristic
404C2×C47#242412yes—
405C2×C47#242512yes—
406C2×C47#244912yes—
407C2×C47#245012yes—
408C23×D4C2×D4711yescharacteristic
409C24×C4—472no—
410C24×C4C2×D4711yescharacteristic
411C24×C4C2×D4711yescharacteristic
412C2×C4×D4—28no—
413C2×C4×D4Dic4718yescomplemented
414C22×C4⋊C4—472no—
415C22×C4⋊C4—472no—
416C22×C4⋊C4C2×D4711yescharacteristic
417C22×C22⋊C4—472no—
418C22×C22⋊C4—472no—
419C22×C22⋊C4—472no—
420C22×C22⋊C4C2×D4711yescharacteristic
421C22×C22⋊C4C2×D4711yescharacteristic
422C22×C42C2×D4711yescharacteristic
423#386—948no—
424#385—948no—
425#380—944no—
426C2×#95—471no—
427C2×#95—471no—
428C2×#95—471no—
429C2×#95—471no—
430C2×#95—472no—
431C2×#95—472no—
432C2×#95—472no—
433C2×#95—472no—
434C2×#95—472no—
435C2×#95—472no—
436C2×#95—944no—
437C47#1389911yescharacteristic, complemented, Sylow
438C25C22×D4711yescharacteristic
439C25C22×D4711yescharacteristic
440C22×D4—24no—
441C22×D4—24no—
442C22×D4Dic9414yes—
443C22×D4D18814yes—
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—944no—
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⋊C4—944no—
474C2×C4⋊C4—944no—
475C2×C4⋊C4—944no—
476C2×C4⋊C4—944no—
477C2×C4⋊C4—1882no—
478C2×C4⋊C4—1882no—
479C2×C4⋊C4C2×Dic4714yescomplemented
480C2×C22⋊C4—24no—
481C2×C22⋊C4—944no—
482C2×C22⋊C4—944no—
483C2×C22⋊C4—944no—
484C2×C22⋊C4—944no—
485C2×C22⋊C4—944no—
486C2×C22⋊C4—944no—
487C2×C22⋊C4—944no—
488C2×C22⋊C4—1882no—
489C2×C22⋊C4—1882no—
490C2×C22⋊C4C2×Dic4714yes—
491C2×C22⋊C4C2×Dic4714yescomplemented
492C2×C22⋊C4C22⋊D4718yes—
493C2×C42—24no—
494C2×C42C2×Dic4714yescomplemented
495#95—474no—
496#95—944no—
497#95—944no—
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—22no—
516C24—22no—
517C24—21no—
518C24—21no—
519C24C2×Dic9412yes—
520C24C2×Dic9412yes—
521C24C2×D18812yes—
522C24C2×D18812yes—
523C24#1062535014yes—
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—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—28no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—28no—
549C22×C4—28no—
550C22×C4—28no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—48no—
554C22×C4—48no—
555C22×C4—48no—
556C22×C4—48no—
557C22×C4—474no—
558C22×C4—474no—
559C22×C4—9416no—
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—942no—
586C22×C4—1888no—
587C22×C4—1888no—
588C22×C4—1888no—
589C22×C4—1888no—
590C22×C4—1888no—
591C22×C4—1888no—
592C22×C4C2×Dic9412yes—
593C22×C4C2×D18812yes—
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—
604C4⋊C4—1888no—
605C4⋊C4—1888no—
606C22⋊C4—28no—
607C22⋊C4—1888no—
608C22⋊C4—1888no—
609C22⋊C4—1888no—
610C22⋊C4C22⋊Dic47116yescomplemented
611C42—28no—
612C23—24no—
613C23—22no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—24no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—24no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—22no—
631C23—24no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—24no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—24no—
643C23—24no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23C2×C22⋊Dic4714yes—
653C23C2×C4⋊Dic4714yes—
654C23C2×C4⋊Dic4714yes—
655C23#1309398314yes—
656C23#1309399818yes—
657C23#1309400318yes—
658C23C23×Dic4711yescharacteristic
659C23C2×D4×D4711yescharacteristic
660C23C22×C22⋊D4712yes—
661C23C22×D18811yescharacteristic
662C23C22×Dic9411yescharacteristic
663C23#41×D4712yes—
664C23C2×#1062535211yescharacteristic
665C23C2×#1062535012yes—
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—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—416no—
690C2×C4—416no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—944no—
694C2×C4—944no—
695C2×C4—944no—
696C2×C4—944no—
697C2×C4—944no—
698C2×C4—944no—
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—1882no—
712C2×C4—1882no—
713C2×C4—18832no—
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×C22⋊Dic4714yes—
723C2×C4C2×C22⋊Dic4714yes—
724C2×C4C2×C4⋊Dic4714yes—
725C2×C4D4×Dic4714yes—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—24no—
730C22—28no—
731C22—28no—
732C22—28no—
733C22—28no—
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—
747C22#1568898318yescomplemented
748C22C22×C22⋊Dic4711yescharacteristic
749C22C22×C4⋊Dic4711yescharacteristic
750C22C2×#1309398311yescharacteristic
751C22C2×D4×Dic4711yescharacteristic
752C22#41×Dic4711yescharacteristic
753C22#1568959811yescharacteristic
754C22#1568960611yescharacteristic
755C22C2×#1309399812yes—
756C22C2×#1309400312yes—
757C22#1568963212yes—
758C22#1568965312yes—
759C22#1568970612yes—
760C22#1568971512yes—
761C22D4×C22⋊D4712yes—
762C22D4×D18811yescharacteristic
763C22#1568976112yes—
764C22#1568976712yes—
765C22#1568976812yes—
766C22#1568977212yes—
767C22#1568977711yescharacteristic
768C22D4×Dic9411yescharacteristic
769C22#1568983011yescharacteristic
770C22#1568983212yes—
771C4—24no—
772C4—24no—
773C4—24no—
774C4—24no—
775C4—42no—
776C4—3762no—
777C4—3762no—
778C4—1884no—
779C4—1884no—
780C2—28no—
781C2—44no—
782C2C2×#1568898311yescharacteristic
783C2#2024583311yescharacteristic
784C2#2024602111yescharacteristic
785C2D4×C22⋊Dic4711yescharacteristic
786C2#2024621811yescharacteristic
787C2D4×C4⋊Dic4711yescharacteristic
788C2#2024629811yescharacteristic
789C2#2024691812yes—
790C2#2024693312yes—
791C2#2024719112yes—
792C2#2024720612yes—
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC22×C4×D4×C47C2
socle, cosocleC24×C47C24
prime radicalC23×D4×C47C22
hypercenterC22×C4×D4D47
hypocenterC47#13899
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×#15688998C2semidirect
3. C2×#15688983C2semidirect
4. C22×C47⋊#95C2semidirect
5. #20241641C2semidirect
6. #20241633C2semidirect
7. #20241618C2semidirect
8. #20241615C2semidirect
9. #20241611C2semidirect
10. #20241611C2semidirect
36. C2×C4×D4×C47C4semidirect
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×C47C4⋊C4semidirect
208. C22⋊C4×C47C22⋊C4semidirect
351. C22×C47#380semidirect
413. C2×C4×D4Dic47semidirect
437. C47#13899semidirect
465. C23×C4C2×Dic47semidirect
479. C2×C4⋊C4C2×Dic47semidirect
491. C2×C22⋊C4C2×Dic47semidirect
494. C2×C42C2×Dic47semidirect
532. C2×D4C4⋊Dic47semidirect
610. C22⋊C4C22⋊Dic47semidirect
747. C22#15688983semidirect

Maximal subgroups

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

subgroupindex
C2×#156890032
C2×#156889982
C2×#156889832
C22×C47⋊#952
#202416412
#202416332
#202416182
#202416152
#202416112
C22×C4×D4×C472
#1389947