Finite Group Databasebeta

← #26139402

Subgroups — #26139402

Order 12032.

2474 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094005C211yesmaximal, characteristic
2C2×#15689003C211yesmaximal, characteristic
3C2×#15688995C211yesmaximal, characteristic, complemented
4C2×#15688984C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊Dic47C211yesmaximal, characteristic, complemented
6C22×C47⋊#95C211yesmaximal, characteristic, complemented
7#20241654C212yesmaximal, complemented
8#20241631C212yesmaximal, complemented
9#20241625C212yesmaximal, complemented
10Dic47⋊#95C212yesmaximal, complemented
11C2×C47×#386C211yesmaximal, characteristic
12C24×Dic47C2211yescharacteristic
13C24×Dic47C2211yescharacteristic
14C2×#13094005—24no—
15C2×#13094005—24no—
16C2×#13094005C418yescomplemented
17C22×Dic47⋊C4C2212yes—
18C22×Dic47⋊C4C2212yes—
19C22×C22⋊Dic47C2212yes—
20C22×C22⋊Dic47C2212yes—
21C22×C22⋊Dic47C2211yescharacteristic
22C22×C22⋊Dic47C2211yescharacteristic
23C22×C4×Dic47C2212yes—
24#15689003—24no—
25#15688995—24no—
26#15688984—24no—
27C4×C22⋊Dic47—24no—
28C2×C47⋊#95—24no—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2212yes—
35C2×C47⋊#95C2212yes—
36C23×D4×C47C2211yescharacteristic
37C24×C4×C47C2211yescharacteristic
38C22×C22⋊C4×C47C2211yescharacteristic
39C22×C22⋊C4×C47C2211yescharacteristic
40C22×C22⋊C4×C47C2211yescharacteristic
41C47×#386—24no—
42C2×#95×C47C2211yescharacteristic
43C2×#95×C47C2211yescharacteristic
44C23×Dic47—22no—
45C23×Dic47—22no—
46C23×Dic47—22no—
47C23×Dic47—22no—
48C23×Dic47—22no—
49C23×Dic47—22no—
50C23×Dic47—22no—
51C23×Dic47—24no—
52C23×Dic47—22no—
53C23×Dic47—22no—
54C23×Dic47—42no—
55C23×Dic47C2×C414yes—
56C23×Dic47C2312yes—
57C23×Dic47C2312yes—
58C23×Dic47C2312yes—
59C23×Dic47C2312yes—
60#13094005—232no—
61C2×Dic47⋊C4—24no—
62C2×Dic47⋊C4—24no—
63C2×Dic47⋊C4—24no—
64C2×Dic47⋊C4—24no—
65C2×Dic47⋊C4—42no—
66C2×Dic47⋊C4C2×C418yescomplemented
67C2×C22⋊Dic47—22no—
68C2×C22⋊Dic47—22no—
69C2×C22⋊Dic47—24no—
70C2×C22⋊Dic47—24no—
71C2×C22⋊Dic47—24no—
72C2×C22⋊Dic47—24no—
73C2×C22⋊Dic47—42no—
74C2×C22⋊Dic47C2×C414yes—
75C2×C22⋊Dic47C2×C418yescomplemented
76C2×C22⋊Dic47D414yes—
77C2×C22⋊Dic47D414yes—
78C2×C22⋊Dic47D414yes—
79C2×C4×Dic47—24no—
80C2×C4×Dic47—24no—
81C2×C4×Dic47—42no—
82C47⋊#95—24no—
83C47⋊#95—24no—
84C47⋊#95—24no—
85C47⋊#95—24no—
86C47⋊#95—24no—
87C47⋊#95—24no—
88C47⋊#95—24no—
89C25×C47C2311yescharacteristic
90C25×C47C2311yescharacteristic
91C22×D4×C47—22no—
92C22×D4×C47—22no—
93C22×D4×C47—22no—
94C22×D4×C47—22no—
95C22×D4×C47—22no—
96C22×D4×C47—22no—
97C22×D4×C47C2×C414yes—
98C23×C4×C47—22no—
99C23×C4×C47—22no—
100C23×C4×C47—24no—
101C23×C4×C47—42no—
102C23×C4×C47D414yes—
103C23×C4×C47C2311yescharacteristic
104C23×C4×C47C2311yescharacteristic
105C23×C4×C47C2311yescharacteristic
106C23×C4×C47C2311yescharacteristic
107C23×C4×C47C2311yescharacteristic
108C2×C22⋊C4×C47—22no—
109C2×C22⋊C4×C47—22no—
110C2×C22⋊C4×C47—22no—
111C2×C22⋊C4×C47—22no—
112C2×C22⋊C4×C47—22no—
113C2×C22⋊C4×C47—24no—
114C2×C22⋊C4×C47—42no—
115#95×C47—22no—
116#95×C47—22no—
117C24×C47—22no—
118C24×C47—22no—
119C24×C47—22no—
120C24×C47—22no—
121C24×C47—21no—
122C24×C47—21no—
123C24×C47—21no—
124C24×C47—21no—
125C24×C47—22no—
126C24×C47—21no—
127C24×C47—21no—
128C24×C47—22no—
129C24×C47—22no—
130C24×C47—22no—
131C24×C47C22×C412yes—
132C24×C47C22×C412yes—
133C24×C47C2×D412yes—
134C24×C47C2×D412yes—
135C24×C47C2×D412yes—
136C24×C47C2×D412yes—
137C24×C47#4112yes—
138C24×C47#4112yes—
139C24×C47C2411yescharacteristic
140C2×D4×C47—28no—
141C2×D4×C47—28no—
142C2×D4×C47—28no—
143C2×D4×C47—44no—
144C2×D4×C47—44no—
145C2×D4×C47—44no—
146C2×D4×C47—44no—
147C22×C4×C47—21no—
148C22×C4×C47—21no—
149C22×C4×C47—22no—
150C22×C4×C47—28no—
151C22×C4×C47—21no—
152C22×C4×C47—21no—
153C22×C4×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47—21no—
156C22×C4×C47—21no—
157C22×C4×C47—22no—
158C22×C4×C47—21no—
159C22×C4×C47—21no—
160C22×C4×C47—22no—
161C22×C4×C47—28no—
162C22×C4×C47—21no—
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—22no—
169C22×C4×C47—22no—
170C22×C4×C47—22no—
171C22×C4×C47—22no—
172C22×C4×C47—44no—
173C22×C4×C47—48no—
174C22×C4×C47—48no—
175C22×C4×C47C22×C412yes—
176C22×C4×C47C2×D412yes—
177C22×C4×C47C2×D412yes—
178C22×C4×C47#4114yes—
179C22×Dic47—22no—
180C22×Dic47—22no—
181C22×Dic47—22no—
182C22×Dic47—22no—
183C22×Dic47—28no—
184C22×Dic47—28no—
185C22×Dic47—28no—
186C22×Dic47—28no—
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—22no—
199C22×Dic47—22no—
200C22×Dic47—22no—
201C22×Dic47—22no—
202C22×Dic47—22no—
203C22×Dic47—22no—
204C22×Dic47—22no—
205C22×Dic47—48no—
206C22×Dic47—48no—
207C22×Dic47—44no—
208C22×Dic47—44no—
209C22×Dic47—44no—
210C22×Dic47—44no—
211C22×Dic47—44no—
212C22×Dic47—44no—
213C22×Dic47C22×C414yes—
214C22×Dic47C22×C414yes—
215C22×Dic47C2×D414yes—
216C22×Dic47C2×D414yes—
217C22×Dic47C2×D414yes—
218C22×Dic47#4114yes—
219C22⋊C4×C47—44no—
220C22⋊C4×C47—44no—
221C22⋊C4×C47—44no—
222C22⋊Dic47—28no—
223C22⋊Dic47—216no—
224C22⋊Dic47—48no—
225C22⋊Dic47C22⋊C4116yescomplemented
226Dic47⋊C4—216no—
227Dic47⋊C4—48no—
228C4×Dic47—48no—
229C23×C47—24no—
230C23×C47—24no—
231C23×C47—22no—
232C23×C47—22no—
233C23×C47—24no—
234C23×C47—22no—
235C23×C47—22no—
236C23×C47—24no—
237C23×C47—24no—
238C23×C47—24no—
239C23×C47—24no—
240C23×C47—24no—
241C23×C47—24no—
242C23×C47—24no—
243C23×C47—24no—
244C23×C47—24no—
245C23×C47—22no—
246C23×C47—22no—
247C23×C47—22no—
248C23×C47—24no—
249C23×C47—24no—
250C23×C47—41no—
251C23×C47—41no—
252C23×C47—41no—
253C23×C47—41no—
254C23×C47—41no—
255C23×C47—42no—
256C23×C47—41no—
257C23×C47—41no—
258C23×C47—41no—
259C23×C47—42no—
260C23×C47—42no—
261C23×C47—42no—
262C23×C47—42no—
263C23×C47—42no—
264C23×C47—42no—
265C23×C47—42no—
266C23×C47—42no—
267C23×C47—42no—
268C23×C47C2×C22⋊C414yes—
269C23×C47C4×D414yes—
270C23×C47C4×D414yes—
271C23×C47#12114yes—
272C23×C47#12114yes—
273C23×C47#12414yes—
274C23×C47#12714yes—
275C23×C47C23×C411yescharacteristic
276C23×C47C22×D411yescharacteristic
277C23×C47C22×D411yescharacteristic
278C23×C47C22×D411yescharacteristic
279C23×C47C22×D411yescharacteristic
280C23×C47C2×#4112yes—
281C23×C47C2×#4111yescharacteristic
282C23×C47C2×#4112yes—
283C23×C47C2×#4111yescharacteristic
284C23×C47H(5,𝔽2)12yes—
285C23×C472−1+412yes—
286D4×C47—416no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—24no—
290C2×C4×C47—24no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—416no—
298C2×C4×C47—41no—
299C2×C4×C47—41no—
300C2×C4×C47—41no—
301C2×C4×C47—41no—
302C2×C4×C47—42no—
303C2×C4×C47—42no—
304C2×C4×C47—41no—
305C2×C4×C47—41no—
306C2×C4×C47—41no—
307C2×C4×C47—41no—
308C2×C4×C47—41no—
309C2×C4×C47—41no—
310C2×C4×C47—42no—
311C2×C4×C47—42no—
312C2×C4×C47—42no—
313C2×C4×C47—42no—
314C2×C4×C47#12314yescomplemented
315C2×Dic47—24no—
316C2×Dic47—24no—
317C2×Dic47—24no—
318C2×Dic47—24no—
319C2×Dic47—24no—
320C2×Dic47—24no—
321C2×Dic47—24no—
322C2×Dic47—24no—
323C2×Dic47—24no—
324C2×Dic47—24no—
325C2×Dic47—24no—
326C2×Dic47—24no—
327C2×Dic47—24no—
328C2×Dic47—24no—
329C2×Dic47—24no—
330C2×Dic47—416no—
331C2×Dic47—42no—
332C2×Dic47—42no—
333C2×Dic47—42no—
334C2×Dic47—42no—
335C2×Dic47—42no—
336C2×Dic47—42no—
337C2×Dic47—42no—
338C2×Dic47—42no—
339C2×Dic47—42no—
340C2×Dic47—42no—
341C2×Dic47—42no—
342C2×Dic47—42no—
343C2×Dic47—416no—
344C2×Dic47C2×C22⋊C418yes—
345#13996—471nomaximal, Sylow
346C22×C47—24no—
347C22×C47—28no—
348C22×C47—28no—
349C22×C47—24no—
350C22×C47—24no—
351C22×C47—28no—
352C22×C47—28no—
353C22×C47—24no—
354C22×C47—24no—
355C22×C47—24no—
356C22×C47—42no—
357C22×C47—44no—
358C22×C47—44no—
359C22×C47—42no—
360C22×C47—42no—
361C22×C47—81no—
362C22×C47—81no—
363C22×C47—82no—
364C22×C47—82no—
365C22×C47—81no—
366C22×C47—81no—
367C22×C47#39018yes—
368C22×C47C22×C22⋊C411yescharacteristic
369C22×C47C2×C4×D411yescharacteristic
370C22×C47C2×C4×D411yescharacteristic
371C22×C47C4×#4112yes—
372C22×C47#52012yes—
373C22×C47C2×#12111yescharacteristic
374C22×C47C2×#12111yescharacteristic
375C22×C47C2×#12311yescharacteristic
376C22×C47#52511yescharacteristic
377C22×C47C2×#12411yescharacteristic
378C22×C47#52912yes—
379C22×C47C2×#12711yescharacteristic
380C22×C47#53411yescharacteristic
381C22×C47#53611yescharacteristic
382C22×C47#53912yes—
383C22×C47#54612yes—
384C22×C47#54612yes—
385C22×C47#54612yes—
386C22×C47#54712yes—
387C22×C47#54712yes—
388C22×C47#54712yes—
389C22×C47#55112yes—
390C22×C47#55212yes—
391C4×C47—24no—
392C4×C47—42no—
393C4×C47—42no—
394C4×C47—81no—
395C4×C47—81no—
396Dic47—28no—
397Dic47—44no—
398Dic47—44no—
399Dic47—44no—
400C22×#123—471no—
401C2×#386—471no—
402C2×#386D4711yescharacteristic
403C2×#385—471no—
404C2×#381—471no—
405C2×C4×C22⋊C4—471no—
406C22×#95—471no—
407#1445—472no—
408#1439—472no—
409#1437—472no—
410C4⋊#95—472no—
411C2×C47—28no—
412C2×C47—82no—
413C2×C47C2×#39011yescharacteristic
414C2×C47C4×#12311yescharacteristic
415C2×C47#232211yescharacteristic
416C2×C47#233912yes—
417C2×C47#235912yes—
418C2×C47#241211yescharacteristic
419C2×C47#241311yescharacteristic
420C2×C47#242512yes—
421C2×C47#248812yes—
422C2×C47#250111yescharacteristic
423C2×C47#253911yescharacteristic
424C23×D4C2×D4711yescharacteristic
425C24×C4—471no—
426C24×C4—471no—
427C24×C4C2×D4711yescharacteristic
428C2×#123—478no—
429C2×#123—944no—
430C2×#123—944no—
431C22×C4⋊C4—472no—
432C22×C4⋊C4—472no—
433C22×C22⋊C4—471no—
434C22×C22⋊C4—472no—
435C22×C22⋊C4—471no—
436C22×C22⋊C4—472no—
437C22×C22⋊C4C2×D4711yescharacteristic
438C22×C22⋊C4C2×D4711yescharacteristic
439C22×C22⋊C4C2×D4711yescharacteristic
440C22×C42—472no—
441#386—24no—
442#386—944no—
443#385—944no—
444#381—944no—
445C4×C22⋊C4—944no—
446C2×#95—472no—
447C2×#95—472no—
448C2×#95—472no—
449C2×#95—472no—
450C2×#95—472no—
451C2×#95—472no—
452C2×#95—472no—
453C2×#95—944no—
454C2×#95C2×D4711yescharacteristic
455C2×#95C2×D4711yescharacteristic
456C47#1399611yescharacteristic, complemented, Sylow
457C25C22×D4711yescharacteristic
458C25C22×D4711yescharacteristic
459C22×D4—22no—
460C22×D4—22no—
461C22×D4—22no—
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—22no—
465C22×D4C4×D4714yes—
466C23×C4—22no—
467C23×C4—22no—
468C23×C4—24no—
469C23×C4—42no—
470C23×C4—472no—
471C23×C4—474no—
472C23×C4—472no—
473C23×C4—472no—
474C23×C4—472no—
475C23×C4—944no—
476C23×C4—942no—
477C23×C4—942no—
478C23×C4—942no—
479C23×C4—942no—
480C23×C4—942no—
481C23×C4—942no—
482C23×C4—942no—
483C23×C4—942no—
484C23×C4—942no—
485C23×C4—1882no—
486C23×C4C22⋊D4714yes—
487C23×C4C22×D4711yescharacteristic
488C23×C4C22×D4711yescharacteristic
489C23×C4C22×D4711yescharacteristic
490C23×C4C22×D4711yescharacteristic
491C23×C4C22×D4711yescharacteristic
492#123—9432no—
493C2×C4⋊C4—478no—
494C2×C4⋊C4—944no—
495C2×C4⋊C4—944no—
496C2×C4⋊C4—944no—
497C2×C4⋊C4—944no—
498C2×C4⋊C4—1882no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—42no—
506C2×C22⋊C4—474no—
507C2×C22⋊C4—474no—
508C2×C22⋊C4—474no—
509C2×C22⋊C4—478no—
510C2×C22⋊C4—474no—
511C2×C22⋊C4—944no—
512C2×C22⋊C4—944no—
513C2×C22⋊C4—942no—
514C2×C22⋊C4—942no—
515C2×C22⋊C4—944no—
516C2×C22⋊C4—944no—
517C2×C22⋊C4—1882no—
518C2×C42—944no—
519C2×C42—944no—
520C2×C42—1882no—
521#95—22no—
522#95—22no—
523#95—944no—
524#95—944no—
525#95—944no—
526#95—944no—
527#95—944no—
528#95—944no—
529#95—944no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—21no—
535C24—21no—
536C24—21no—
537C24—21no—
538C24—22no—
539C24—22no—
540C24—21no—
541C24—21no—
542C24—22no—
543C24—22no—
544C24C2×C4×D4712yes—
545C24C2×C4×D4712yes—
546C24#1062535012yes—
547C24D4×D4712yes—
548C24D4×D4712yes—
549C24D4×D4712yes—
550C24#1062535212yes—
551C24C2×C22⋊D4712yes—
552C24C23×D4711yescharacteristic
553C2×D4—28no—
554C2×D4—28no—
555C2×D4—28no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—44no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—28no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—28no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—44no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—474no—
589C22×C4—474no—
590C22×C4—474no—
591C22×C4—474no—
592C22×C4—474no—
593C22×C4—474no—
594C22×C4—942no—
595C22×C4—942no—
596C22×C4—942no—
597C22×C4—942no—
598C22×C4—948no—
599C22×C4—948no—
600C22×C4—948no—
601C22×C4—948no—
602C22×C4—942no—
603C22×C4—942no—
604C22×C4—942no—
605C22×C4—942no—
606C22×C4—942no—
607C22×C4—942no—
608C22×C4—942no—
609C22×C4—942no—
610C22×C4—942no—
611C22×C4—942no—
612C22×C4—942no—
613C22×C4—942no—
614C22×C4—942no—
615C22×C4—942no—
616C22×C4—942no—
617C22×C4—942no—
618C22×C4—942no—
619C22×C4—942no—
620C22×C4—1888no—
621C22×C4—1888no—
622C22×C4—1884no—
623C22×C4—1884no—
624C22×C4—1884no—
625C22×C4—1884no—
626C22×C4—1884no—
627C22×C4—1884no—
628C22×C4C2×C4×D4712yes—
629C22×C4#1062535214yes—
630C22×C4C2×C22⋊D4712yes—
631C22×C4C2×C22⋊D4712yes—
632C4⋊C4—9416no—
633C4⋊C4—1888no—
634C22⋊C4—44no—
635C22⋊C4—44no—
636C22⋊C4—44no—
637C22⋊C4—4716no—
638C22⋊C4—9416no—
639C22⋊C4—948no—
640C22⋊C4—1888no—
641C42—1888no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—22no—
653C23—22no—
654C23—24no—
655C23—22no—
656C23—22no—
657C23—24no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—24no—
662C23—24no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—42no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—42no—
681C23C22⋊C4×D4714yes—
682C23(C22⋊D47)⋊C414yes—
683C23C4×C22⋊D4714yes—
684C23#1309399614yes—
685C23#1309399714yes—
686C23#1309401014yes—
687C23#1309402014yes—
688C23C22×C4×D4711yescharacteristic
689C23C2×D4×D4711yescharacteristic
690C23C2×D4×D4711yescharacteristic
691C23C2×D4×D4711yescharacteristic
692C23C22×C22⋊D4711yescharacteristic
693C23#41×D4712yes—
694C23C2×#1062535212yes—
695C23C2×#1062535211yescharacteristic
696C23C2×#1062535011yescharacteristic
697C23#1309406912yes—
698C23#1309407112yes—
699D4—416no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—416no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—478no—
728C2×C4—944no—
729C2×C4—944no—
730C2×C4—944no—
731C2×C4—944no—
732C2×C4—944no—
733C2×C4—944no—
734C2×C4—944no—
735C2×C4—944no—
736C2×C4—944no—
737C2×C4—944no—
738C2×C4—944no—
739C2×C4—944no—
740C2×C4—944no—
741C2×C4—944no—
742C2×C4—944no—
743C2×C4—18816no—
744C2×C4—1882no—
745C2×C4—1882no—
746C2×C4—1882no—
747C2×C4—1882no—
748C2×C4—18816no—
749C2×C4—1882no—
750C2×C4—1882no—
751C2×C4—1882no—
752C2×C4—1882no—
753C2×C4—1882no—
754C2×C4—1882no—
755C2×C4—1882no—
756C2×C4—1882no—
757C2×C4#1309400514yescomplemented
758C22—24no—
759C22—24no—
760C22—24no—
761C22—24no—
762C22—24no—
763C22—28no—
764C22—24no—
765C22—28no—
766C22—28no—
767C22—28no—
768C22—42no—
769C22—42no—
770C22—44no—
771C22—42no—
772C22—44no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—82no—
778C22—82no—
779C22#1568902318yes—
780C22C2×C22⋊C4×D4711yescharacteristic
781C22C2×(C22⋊D47)⋊C411yescharacteristic
782C22C2×C4×C22⋊D4711yescharacteristic
783C22C4×#1062535212yes—
784C22#1568960212yes—
785C22C2×#1309399611yescharacteristic
786C22C2×#1309399711yescharacteristic
787C22C2×#1309400511yescharacteristic
788C22#1568963011yescharacteristic
789C22C2×#1309401011yescharacteristic
790C22#1568965312yes—
791C22C2×#1309402011yescharacteristic
792C22#1568968211yescharacteristic
793C22#1568969411yescharacteristic
794C22#1568971512yes—
795C22#1568976012yes—
796C22#1568976212yes—
797C22#1568976212yes—
798C22#1568977112yes—
799C22#1568977312yes—
800C22#1568977312yes—
801C22#1568980412yes—
802C22#1568981012yes—
803C4—24no—
804C4—42no—
805C4—42no—
806C4—81no—
807C4—81no—
808C4—948no—
809C4—1884no—
810C4—1884no—
811C4—1884no—
812C2—28no—
813C2—82no—
814C2C2×#1568902311yescharacteristic
815C2C4×#1309400511yescharacteristic
816C2#2024605311yescharacteristic
817C2#2024621412yes—
818C2#2024638612yes—
819C2#2024678511yescharacteristic
820C2#2024679611yescharacteristic
821C2#2024694112yes—
822C2#2024771612yes—
823C2#2024786011yescharacteristic
824C2#2024832011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C47×#386C2
socle, cosocleC24×C47C24
prime radicalC23×D4×C47C22
hypercenterC2×#386D47
hypocenterC47#13996
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
3. C2×#15688995C2semidirect
4. C2×#15688984C2semidirect
5. C2×C4×C22⋊Dic47C2semidirect
6. C22×C47⋊#95C2semidirect
7. #20241654C2semidirect
8. #20241631C2semidirect
9. #20241625C2semidirect
10. Dic47⋊#95C2semidirect
16. C2×#13094005C4semidirect
66. C2×Dic47⋊C4C2×C4semidirect
75. C2×C22⋊Dic47C2×C4semidirect
225. C22⋊Dic47C22⋊C4semidirect
314. C2×C4×C47#123semidirect
456. C47#13996semidirect
757. C2×C4#13094005semidirect

Maximal subgroups

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

subgroupindex
C22×#130940052
C2×#156890032
C2×#156889952
C2×#156889842
C2×C4×C22⋊Dic472
C22×C47⋊#952
#202416542
#202416312
#202416252
Dic47⋊#952
C2×C47×#3862
#1399647