Finite Group Databasebeta

← #26138649

Subgroups — #26138649

Order 12032.

2458 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic47C211yesmaximal, characteristic
2C2×#15689026C211yesmaximal, characteristic
3C2×#15689021C211yesmaximal, characteristic, complemented
4C2×#15689019C211yesmaximal, characteristic, complemented
5C2×#15688981C212yesmaximal, complemented
6#20241631C212yesmaximal, complemented
7#20241631C212yesmaximal, complemented
8#20241617C211yesmaximal, characteristic, complemented
9#20241610C212yesmaximal, complemented
10C4×C47⋊#95C211yesmaximal, characteristic, complemented
11C2×C47×#390C211yesmaximal, characteristic
12C24×Dic47C2212yes—
13C2×D4×Dic47—24no—
14C2×D4×Dic47—24no—
15C2×D4×Dic47C418yescomplemented
16C22×C4⋊Dic47C2211yescharacteristic
17C22×C4⋊Dic47C2211yescharacteristic
18C22×Dic47⋊C4C2212yes—
19C22×Dic47⋊C4C2212yes—
20C22×C22⋊Dic47C2212yes—
21C22×C22⋊Dic47C2212yes—
22C22×C22⋊Dic47C2212yes—
23C22×C4×Dic47C2211yescharacteristic
24C22×C4×Dic47C2211yescharacteristic
25#15689026—24no—
26#15689021—24no—
27#15689019—24no—
28#15688981—28no—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2211yescharacteristic
32C2×C47⋊#95C2211yescharacteristic
33C2×C47⋊#95C2211yescharacteristic
34C2×C47⋊#95C2212yes—
35C2×C47⋊#95C2212yes—
36C2×C47⋊#95C2211yescharacteristic
37C23×D4×C47C2211yescharacteristic
38C22×C4⋊C4×C47C2211yescharacteristic
39C22×C22⋊C4×C47C2212yes—
40C22×C22⋊C4×C47C2212yes—
41C22×C42×C47C2211yescharacteristic
42C47×#390—24no—
43C23×Dic47—24no—
44C23×Dic47—24no—
45C23×Dic47—24no—
46C23×Dic47—24no—
47C23×Dic47—42no—
48C23×Dic47—42no—
49C23×Dic47C2×C418yes—
50C23×Dic47C2312yes—
51C23×Dic47C2311yescharacteristic
52C23×Dic47C2311yescharacteristic
53C23×Dic47C2311yescharacteristic
54C23×Dic47C2312yes—
55C23×Dic47C2311yescharacteristic
56D4×Dic47—232no—
57C2×C4⋊Dic47—22no—
58C2×C4⋊Dic47—22no—
59C2×C4⋊Dic47—22no—
60C2×C4⋊Dic47C2×C414yes—
61C2×C4⋊Dic47D414yes—
62C2×C4⋊Dic47D414yes—
63C2×Dic47⋊C4—24no—
64C2×Dic47⋊C4—24no—
65C2×Dic47⋊C4—24no—
66C2×Dic47⋊C4—24no—
67C2×Dic47⋊C4—42no—
68C2×Dic47⋊C4—42no—
69C2×C22⋊Dic47—24no—
70C2×C22⋊Dic47—24no—
71C2×C22⋊Dic47—24no—
72C2×C22⋊Dic47—24no—
73C2×C22⋊Dic47—24no—
74C2×C22⋊Dic47—24no—
75C2×C22⋊Dic47—42no—
76C2×C22⋊Dic47—42no—
77C2×C22⋊Dic47C2×C418yes—
78C2×C4×Dic47—22no—
79C2×C4×Dic47—22no—
80C2×C4×Dic47—22no—
81C2×C4×Dic47—22no—
82C2×C4×Dic47—22no—
83C2×C4×Dic47C2×C414yes—
84C47⋊#95—22no—
85C47⋊#95—24no—
86C47⋊#95—24no—
87C47⋊#95—24no—
88C47⋊#95—22no—
89C47⋊#95—22no—
90C47⋊#95—42no—
91C47⋊#95D414yescomplemented
92C25×C47C2312yes—
93C22×D4×C47—22no—
94C22×D4×C47—22no—
95C22×D4×C47—22no—
96C22×D4×C47—22no—
97C22×D4×C47C2×C414yes—
98C22×D4×C47D414yes—
99C22×D4×C47Q814yes—
100C23×C4×C47C2312yes—
101C23×C4×C47C2311yescharacteristic
102C23×C4×C47C2311yescharacteristic
103C23×C4×C47C2311yescharacteristic
104C2×C4⋊C4×C47—22no—
105C2×C4⋊C4×C47—22no—
106C2×C4⋊C4×C47—22no—
107C2×C22⋊C4×C47—24no—
108C2×C22⋊C4×C47—24no—
109C2×C22⋊C4×C47—24no—
110C2×C22⋊C4×C47—24no—
111C2×C22⋊C4×C47—42no—
112C2×C22⋊C4×C47—42no—
113C2×C42×C47—22no—
114C2×C42×C47—22no—
115C2×C42×C47—22no—
116C24×C47—22no—
117C24×C47—22no—
118C24×C47—22no—
119C24×C47—22no—
120C24×C47—22no—
121C24×C47—22no—
122C24×C47—22no—
123C24×C47—22no—
124C24×C47—22no—
125C24×C47—22no—
126C24×C47—22no—
127C24×C47—22no—
128C24×C47C22×C414yes—
129C24×C47C2×D414yes—
130C24×C47C2×Q814yes—
131C24×C47C2411yescharacteristic
132C2×D4×C47—28no—
133C2×D4×C47—28no—
134C2×D4×C47—28no—
135C2×D4×C47—28no—
136C2×D4×C47—28no—
137C2×D4×C47—28no—
138C2×D4×C47C4⋊C4116yescomplemented
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—21no—
147C22×C4×C47—21no—
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—22no—
152C22×C4×C47—22no—
153C22×C4×C47—22no—
154C22×C4×C47—22no—
155C22×C4×C47—22no—
156C22×C4×C47—22no—
157C22×C4×C47—22no—
158C22×C4×C47C22×C412yes—
159C22×C4×C47C2×D412yes—
160C22×C4×C47C2×D412yes—
161C22×C4×C47C2×D412yes—
162C22×C4×C47C2×D412yes—
163C22×C4×C47C2×Q812yes—
164C22×C4×C47#4112yes—
165C22×C4×C47#4112yes—
166C22×C4×C47#4112yes—
167C22×Dic47—21no—
168C22×Dic47—21no—
169C22×Dic47—22no—
170C22×Dic47—22no—
171C22×Dic47—22no—
172C22×Dic47—22no—
173C22×Dic47—21no—
174C22×Dic47—21no—
175C22×Dic47—21no—
176C22×Dic47—21no—
177C22×Dic47—21no—
178C22×Dic47—21no—
179C22×Dic47—21no—
180C22×Dic47—21no—
181C22×Dic47—21no—
182C22×Dic47—21no—
183C22×Dic47—21no—
184C22×Dic47—21no—
185C22×Dic47—21no—
186C22×Dic47—21no—
187C22×Dic47—21no—
188C22×Dic47—21no—
189C22×Dic47—21no—
190C22×Dic47—21no—
191C22×Dic47—21no—
192C22×Dic47—21no—
193C22×Dic47—216no—
194C22×Dic47—216no—
195C22×Dic47—22no—
196C22×Dic47—22no—
197C22×Dic47—22no—
198C22×Dic47—22no—
199C22×Dic47—22no—
200C22×Dic47—22no—
201C22×Dic47—22no—
202C22×Dic47—48no—
203C22×Dic47—48no—
204C22×Dic47—48no—
205C22×Dic47—48no—
206C22×Dic47—48no—
207C22×Dic47C22×C412yes—
208C22×Dic47C22×C414yes—
209C22×Dic47C22×C412yes—
210C22×Dic47C2×D412yes—
211C22×Dic47C2×D414yes—
212C22×Dic47C2×D414yes—
213C22×Dic47C2×D412yes—
214C22×Dic47#4112yes—
215C22×Dic47#4112yes—
216C4⋊C4×C47—44no—
217C22⋊C4×C47—48no—
218C22⋊C4×C47—48no—
219C42×C47—44no—
220C22⋊Dic47—216no—
221C22⋊Dic47—48no—
222C22⋊Dic47—48no—
223C4⋊Dic47—44no—
224C4⋊Dic47C22⋊C4116yescomplemented
225Dic47⋊C4—48no—
226Dic47⋊C4—48no—
227C4×Dic47—28no—
228C4×Dic47—44no—
229C23×C47—24no—
230C23×C47—24no—
231C23×C47—24no—
232C23×C47—24no—
233C23×C47—24no—
234C23×C47—24no—
235C23×C47—24no—
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—24no—
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×C47—42no—
256C23×C47—42no—
257C23×C47—42no—
258C23×C47—42no—
259C23×C47—42no—
260C23×C47—42no—
261C23×C47—42no—
262C23×C47—42no—
263C23×C47C2×C4⋊C418yes—
264C23×C47C23×C411yescharacteristic
265C23×C47C22×D411yescharacteristic
266C23×C47C22×D411yescharacteristic
267C23×C47C22×D411yescharacteristic
268C23×C47C22×D411yescharacteristic
269C23×C47C22×Q811yescharacteristic
270C23×C47C2×#4111yescharacteristic
271C23×C47C2×#4111yescharacteristic
272C23×C47C2×#4111yescharacteristic
273C23×C47C2×#4111yescharacteristic
274C23×C47C2×#4111yescharacteristic
275C23×C47H(5,𝔽2)11yescharacteristic
276C23×C47H(5,𝔽2)11yescharacteristic
277C23×C47H(5,𝔽2)11yescharacteristic
278C23×C472−1+411yescharacteristic
279D4×C47—232no—
280C2×C4×C47—22no—
281C2×C4×C47—22no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—41no—
287C2×C4×C47—41no—
288C2×C4×C47—41no—
289C2×C4×C47—41no—
290C2×C4×C47—41no—
291C2×C4×C47—41no—
292C2×C4×C47—41no—
293C2×C4×C47—41no—
294C2×C4×C47—42no—
295C2×C4×C47—42no—
296C2×C4×C47—42no—
297C2×C4×C47—42no—
298C2×C4×C47—42no—
299C2×C4×C47—42no—
300C2×C4×C47—42no—
301C2×C4×C47C2×C22⋊C414yes—
302C2×C4×C47C2×C4⋊C414yes—
303C2×C4×C47#11714yes—
304C2×C4×C47#12114yes—
305C2×C4×C47#12114yes—
306C2×C4×C47C22⋊Q814yes—
307C2×C4×C47C22⋊Q814yes—
308C2×Dic47—22no—
309C2×Dic47—24no—
310C2×Dic47—22no—
311C2×Dic47—24no—
312C2×Dic47—24no—
313C2×Dic47—24no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—24no—
319C2×Dic47—24no—
320C2×Dic47—22no—
321C2×Dic47—22no—
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—22no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—22no—
328C2×Dic47—22no—
329C2×Dic47—432no—
330C2×Dic47—41no—
331C2×Dic47—41no—
332C2×Dic47—41no—
333C2×Dic47—41no—
334C2×Dic47—41no—
335C2×Dic47—41no—
336C2×Dic47—41no—
337C2×Dic47—41no—
338C2×Dic47—41no—
339C2×Dic47—41no—
340C2×Dic47—41no—
341C2×Dic47—41no—
342C2×Dic47—42no—
343C2×Dic47—42no—
344C2×Dic47—42no—
345C2×Dic47—42no—
346C2×Dic47—42no—
347C2×Dic47—42no—
348C2×Dic47—42no—
349C2×Dic47C2×C22⋊C418yes—
350C2×Dic47C4×D414yes—
351#13920—471nomaximal, Sylow
352C22×C47—28no—
353C22×C47—28no—
354C22×C47—28no—
355C22×C47—44no—
356C22×C47—44no—
357C22×C47—44no—
358C22×C47—44no—
359C22×C47—44no—
360C22×C47—44no—
361C22×C47—44no—
362C22×C47—44no—
363C22×C47—44no—
364C22×C47—44no—
365C22×C47—44no—
366C22×C47—44no—
367C22×C47C22×C22⋊C411yescharacteristic
368C22×C47C22×C4⋊C411yescharacteristic
369C22×C47C2×#11711yescharacteristic
370C22×C47C2×C4×D411yescharacteristic
371C22×C47C4×#4111yescharacteristic
372C22×C47#51811yescharacteristic
373C22×C47#52011yescharacteristic
374C22×C47C2×#12111yescharacteristic
375C22×C47C2×#12111yescharacteristic
376C22×C47C2×C22⋊Q811yescharacteristic
377C22×C47C2×C22⋊Q811yescharacteristic
378C22×C47#52911yescharacteristic
379C22×C47#52911yescharacteristic
380C22×C47#53211yescharacteristic
381C22×C47#53211yescharacteristic
382C22×C47#54011yescharacteristic
383C22×C47#54011yescharacteristic
384C22×C47#54211yescharacteristic
385C22×C47#54211yescharacteristic
386C22×C47D4211yescharacteristic
387C22×C47D4211yescharacteristic
388C22×C47D4211yescharacteristic
389C22×C47#54611yescharacteristic
390C22×C47#54611yescharacteristic
391C22×C47#54611yescharacteristic
392C22×C47#54611yescharacteristic
393C22×C47#54711yescharacteristic
394C22×C47#54811yescharacteristic
395C22×C47#54811yescharacteristic
396C22×C47D4×Q811yescharacteristic
397C22×C47#55011yescharacteristic
398C22×C47#55011yescharacteristic
399C22×C47#55411yescharacteristic
400C22×C47#55411yescharacteristic
401C22×C47#55411yescharacteristic
402C4×C47—42no—
403C4×C47—42no—
404C4×C47—82no—
405C4×C47#38018yescomplemented
406Dic47—24no—
407Dic47—28no—
408Dic47—42no—
409Dic47—42no—
410Dic47—42no—
411Dic47—82no—
412C22×C4×D4—471no—
413C2×#390—471no—
414C2×#390D4711yescharacteristic
415C2×#389—471no—
416C2×#389—471no—
417C2×#380—472no—
418#1439—472no—
419#1439—472no—
420C4⋊#95—471no—
421C22⋊#95—472no—
422C4×#95—471no—
423C2×C47—48no—
424C2×C47C2×#38011yescharacteristic
425C2×C47#229311yescharacteristic
426C2×C47#231911yescharacteristic
427C2×C47D4×C22⋊C411yescharacteristic
428C2×C47#234111yescharacteristic
429C2×C47D4×C4⋊C411yescharacteristic
430C2×C47#234911yescharacteristic
431C2×C47#242711yescharacteristic
432C2×C47#242711yescharacteristic
433C2×C47#242811yescharacteristic
434C2×C47#242811yescharacteristic
435C2×C47#245211yescharacteristic
436C2×C47#245211yescharacteristic
437C2×C47#245411yescharacteristic
438C2×C47#245411yescharacteristic
439C23×D4C2×D4711yescharacteristic
440C24×C4—472no—
441C2×C4×D4—478no—
442C2×C4×D4—944no—
443C2×C4×D4—944no—
444C22×C4⋊C4—471no—
445C22×C4⋊C4—471no—
446C22×C4⋊C4—472no—
447C22×C4⋊C4—472no—
448C22×C4⋊C4C2×D4711yescharacteristic
449C22×C22⋊C4—472no—
450C22×C22⋊C4—472no—
451C22×C22⋊C4—472no—
452C22×C22⋊C4C2×D4712yes—
453C22×C22⋊C4C2×D4712yes—
454C22×C42—471no—
455C22×C42—471no—
456C22×C42C2×D4711yescharacteristic
457#390—24no—
458#390—944no—
459#389—944no—
460#389—944no—
461#380—948no—
462C2×#95—471no—
463C2×#95—471no—
464C2×#95—471no—
465C2×#95—471no—
466C2×#95—472no—
467C2×#95—472no—
468C2×#95—472no—
469C2×#95—472no—
470C47#1392011yescharacteristic, complemented, Sylow
471C25C22×D4712yes—
472C22×D4—22no—
473C22×D4—22no—
474C22×D4—22no—
475C22×D4—22no—
476C22×D4Dic9414yes—
477C22×D4C4×D4714yes—
478C22×D4C22⋊D4714yes—
479C23×C4—472no—
480C23×C4—471no—
481C23×C4—471no—
482C23×C4—471no—
483C23×C4—471no—
484C23×C4—478no—
485C23×C4—472no—
486C23×C4—944no—
487C23×C4—944no—
488C23×C4—944no—
489C23×C4—944no—
490C23×C4—1882no—
491C23×C4—1882no—
492C23×C4C22×D4712yes—
493C23×C4C22×D4711yescharacteristic
494C23×C4C22×D4711yescharacteristic
495C23×C4C22×D4711yescharacteristic
496C4×D4—9432no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—474no—
501C2×C4⋊C4—474no—
502C2×C4⋊C4—474no—
503C2×C4⋊C4—944no—
504C2×C4⋊C4—944no—
505C2×C4⋊C4—944no—
506C2×C4⋊C4—944no—
507C2×C4⋊C4—942no—
508C2×C4⋊C4—942no—
509C2×C4⋊C4—942no—
510C2×C4⋊C4—1882no—
511C2×C4⋊C4—1882no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—42no—
517C2×C22⋊C4—42no—
518C2×C22⋊C4—478no—
519C2×C22⋊C4—944no—
520C2×C22⋊C4—944no—
521C2×C22⋊C4—944no—
522C2×C22⋊C4—944no—
523C2×C22⋊C4—944no—
524C2×C22⋊C4—944no—
525C2×C22⋊C4—1882no—
526C2×C22⋊C4—1882no—
527C2×C42—22no—
528C2×C42—22no—
529C2×C42—22no—
530C2×C42—474no—
531C2×C42—942no—
532C2×C42—942no—
533C2×C42—942no—
534C2×C42—942no—
535C2×C42—942no—
536#95—474no—
537#95—942no—
538#95—942no—
539#95—944no—
540#95—944no—
541#95—944no—
542#95—942no—
543#95—1882no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24C2×Dic9414yes—
557C24C2×C4×D4714yes—
558C24C2×C22⋊D4714yes—
559C24C23×D4711yescharacteristic
560C2×D4—28no—
561C2×D4—28no—
562C2×D4—28no—
563C2×D4—28no—
564C2×D4—28no—
565C2×D4—28no—
566C2×D4Dic47⋊C4116yescomplemented
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—472no—
587C22×C4—474no—
588C22×C4—472no—
589C22×C4—474no—
590C22×C4—474no—
591C22×C4—472no—
592C22×C4—472no—
593C22×C4—472no—
594C22×C4—472no—
595C22×C4—9416no—
596C22×C4—9416no—
597C22×C4—941no—
598C22×C4—941no—
599C22×C4—942no—
600C22×C4—942no—
601C22×C4—942no—
602C22×C4—941no—
603C22×C4—942no—
604C22×C4—941no—
605C22×C4—941no—
606C22×C4—941no—
607C22×C4—941no—
608C22×C4—941no—
609C22×C4—941no—
610C22×C4—941no—
611C22×C4—941no—
612C22×C4—941no—
613C22×C4—941no—
614C22×C4—941no—
615C22×C4—941no—
616C22×C4—941no—
617C22×C4—941no—
618C22×C4—941no—
619C22×C4—941no—
620C22×C4—941no—
621C22×C4—941no—
622C22×C4—941no—
623C22×C4—942no—
624C22×C4—942no—
625C22×C4—942no—
626C22×C4—942no—
627C22×C4—942no—
628C22×C4—942no—
629C22×C4—942no—
630C22×C4—1888no—
631C22×C4—1888no—
632C22×C4—1888no—
633C22×C4—1888no—
634C22×C4—1888no—
635C22×C4C2×Dic9412yes—
636C22×C4C2×C4×D4712yes—
637C22×C4D4×D4712yes—
638C22×C4D4×D4712yes—
639C22×C4D4×D4712yes—
640C22×C4#1062535212yes—
641C22×C4#1062535212yes—
642C22×C4#1062535212yes—
643C22×C4C2×C22⋊D4712yes—
644C4⋊C4—44no—
645C4⋊C4—4716no—
646C4⋊C4—1888no—
647C4⋊C4—1888no—
648C4⋊C4—1884no—
649C22⋊C4—48no—
650C22⋊C4—48no—
651C22⋊C4—9416no—
652C22⋊C4—1888no—
653C22⋊C4—1888no—
654C42—44no—
655C42—948no—
656C42—1884no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23C2×Dic47⋊C418yes—
692C23C22×C4×D4711yescharacteristic
693C23C2×D4×D4711yescharacteristic
694C23C2×D4×D4711yescharacteristic
695C23C2×D4×D4711yescharacteristic
696C23C22×C22⋊D4711yescharacteristic
697C23C22×Dic9411yescharacteristic
698C23#41×D4711yescharacteristic
699C23#41×D4711yescharacteristic
700C23C2×#1062535211yescharacteristic
701C23C2×#1062535211yescharacteristic
702C23C2×#1062535211yescharacteristic
703C23#1309406911yescharacteristic
704C23#1309406911yescharacteristic
705C23#1309407011yescharacteristic
706C23#1309407111yescharacteristic
707D4—232no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—478no—
730C2×C4—474no—
731C2×C4—944no—
732C2×C4—942no—
733C2×C4—944no—
734C2×C4—942no—
735C2×C4—944no—
736C2×C4—942no—
737C2×C4—944no—
738C2×C4—942no—
739C2×C4—942no—
740C2×C4—944no—
741C2×C4—944no—
742C2×C4—942no—
743C2×C4—942no—
744C2×C4—942no—
745C2×C4—942no—
746C2×C4—942no—
747C2×C4—942no—
748C2×C4—942no—
749C2×C4—942no—
750C2×C4—942no—
751C2×C4—942no—
752C2×C4—18832no—
753C2×C4—1882no—
754C2×C4—1882no—
755C2×C4—1882no—
756C2×C4—1882no—
757C2×C4—1882no—
758C2×C4—1882no—
759C2×C4—1882no—
760C2×C4—1881no—
761C2×C4—1881no—
762C2×C4—1881no—
763C2×C4—1881no—
764C2×C4—1881no—
765C2×C4—1881no—
766C2×C4—1881no—
767C2×C4—1881no—
768C2×C4—1881no—
769C2×C4—1881no—
770C2×C4—1881no—
771C2×C4—1881no—
772C2×C4C22⋊C4×D4714yes—
773C2×C4C2×Dic47⋊C414yes—
774C2×C4#1309398014yes—
775C2×C4#1309399614yes—
776C2×C4#1309399614yes—
777C2×C4#1309400114yes—
778C2×C4#1309400114yes—
779C22—28no—
780C22—28no—
781C22—28no—
782C22—44no—
783C22—44no—
784C22—44no—
785C22—44no—
786C22—44no—
787C22—44no—
788C22—44no—
789C22—44no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22C2×C22⋊C4×D4711yescharacteristic
795C22C22×Dic47⋊C411yescharacteristic
796C22C2×#1309398011yescharacteristic
797C22C4×D4×D4711yescharacteristic
798C22C4×#1062535211yescharacteristic
799C22#1568959511yescharacteristic
800C22#1568960211yescharacteristic
801C22C2×#1309399611yescharacteristic
802C22C2×#1309399611yescharacteristic
803C22C2×#1309400111yescharacteristic
804C22C2×#1309400111yescharacteristic
805C22#1568965211yescharacteristic
806C22#1568965411yescharacteristic
807C22#1568966811yescharacteristic
808C22#1568967111yescharacteristic
809C22#1568972611yescharacteristic
810C22#1568972711yescharacteristic
811C22#1568974011yescharacteristic
812C22#1568974211yescharacteristic
813C22D4×C22⋊D4711yescharacteristic
814C22#1568975711yescharacteristic
815C22#1568975811yescharacteristic
816C22#1568976111yescharacteristic
817C22#1568976611yescharacteristic
818C22#1568976711yescharacteristic
819C22#1568977011yescharacteristic
820C22#1568977211yescharacteristic
821C22#1568977911yescharacteristic
822C22#1568978111yescharacteristic
823C22D4×Dic9411yescharacteristic
824C22#1568979111yescharacteristic
825C22#1568979311yescharacteristic
826C22#1568983011yescharacteristic
827C22#1568983211yescharacteristic
828C22#1568983211yescharacteristic
829C4—42no—
830C4—42no—
831C4—82no—
832C4—944no—
833C4—948no—
834C4—3762no—
835C4—1882no—
836C4—1882no—
837C4—1882no—
838C4#1568898118yescomplemented
839C2—48no—
840C2C2×#1568898111yescharacteristic
841C2#2024585011yescharacteristic
842C2#2024602511yescharacteristic
843C2#2024620911yescharacteristic
844C2#2024622711yescharacteristic
845C2D4×Dic47⋊C411yescharacteristic
846C2#2024629311yescharacteristic
847C2#2024696711yescharacteristic
848C2#2024696811yescharacteristic
849C2#2024697811yescharacteristic
850C2#2024697911yescharacteristic
851C2#2024724011yescharacteristic
852C2#2024724111yescharacteristic
853C2#2024726211yescharacteristic
854C2#2024726311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C47×#390C2
socle, cosocleC24×C47C24
prime radicalC23×D4×C47C22
hypercenterC2×#390D47
hypocenterC47#13920
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
3. C2×#15689021C2semidirect
4. C2×#15689019C2semidirect
5. C2×#15688981C2semidirect
6. #20241631C2semidirect
7. #20241631C2semidirect
8. #20241617C2semidirect
9. #20241610C2semidirect
10. C4×C47⋊#95C2semidirect
15. C2×D4×Dic47C4semidirect
91. C47⋊#95D4semidirect
138. C2×D4×C47C4⋊C4semidirect
224. C4⋊Dic47C22⋊C4semidirect
405. C4×C47#380semidirect
470. C47#13920semidirect
566. C2×D4Dic47⋊C4semidirect
838. C4#15688981semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic472
C2×#156890262
C2×#156890212
C2×#156890192
C2×#156889812
#202416312
#202416172
#202416102
C4×C47⋊#952
C2×C47×#3902
#1392047