Finite Group Databasebeta

← #26139412

Subgroups — #26139412

Order 12032.

2106 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094003C211yesmaximal, characteristic
2C2×#15689029C211yesmaximal, characteristic, complemented
3C2×#15689029C211yesmaximal, characteristic, complemented
4C2×#15689021C211yesmaximal, characteristic, complemented
5C2×#15688983C211yesmaximal, characteristic
6C2×C4×C4⋊Dic47C211yesmaximal, characteristic, complemented
7#20241654C212yesmaximal, complemented
8#20241631C212yesmaximal
9#20241625C212yesmaximal
10Dic47⋊#95C212yesmaximal, complemented
11C2×C4×C22⋊C4×C47C211yesmaximal, characteristic
12C23×Dic94C2211yescharacteristic
13C2×#13094003—24no—
14C2×#13094003—24no—
15C2×#13094003C418yescomplemented
16C22×C4⋊Dic47C2211yescharacteristic
17C22×C4⋊Dic47C2211yescharacteristic
18C22×C4⋊Dic47C2211yescharacteristic
19C22×Dic47⋊C4C2212yes—
20C22×Dic47⋊C4C2212yes—
21C22×C22⋊Dic47C2212yes—
22C22×C22⋊Dic47C2212yes—
23C22×C4×Dic47C2212yes—
24#15689029—24no—
25#15689029—24no—
26#15689021—24no—
27#15688983—24no—
28C4×C4⋊Dic47—24no—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2212yes—
35C2×C47⋊#95C2212yes—
36C24×C4×C47C2211yescharacteristic
37C22×C22⋊C4×C47C2211yescharacteristic
38C22×C22⋊C4×C47C2211yescharacteristic
39C22×C42×C47C2211yescharacteristic
40C22×C42×C47C2211yescharacteristic
41C4×C22⋊C4×C47—24no—
42C2×#95×C47C2211yescharacteristic
43C2×#95×C47C2211yescharacteristic
44C22×Dic94—22no—
45C22×Dic94—22no—
46C22×Dic94—22no—
47C22×Dic94—22no—
48C22×Dic94—22no—
49C22×Dic94—22no—
50C22×Dic94C2×C414yes—
51C23×Dic47C2312yes—
52C23×Dic47C2312yes—
53C23×Dic47C2312yes—
54C23×Dic47C2312yes—
55#13094003—232no—
56C2×C4⋊Dic47—22no—
57C2×C4⋊Dic47—22no—
58C2×C4⋊Dic47—22no—
59C2×C4⋊Dic47—22no—
60C2×C4⋊Dic47—22no—
61C2×C4⋊Dic47C2×C414yes—
62C2×C4⋊Dic47D414yes—
63C2×C4⋊Dic47D414yes—
64C2×C4⋊Dic47D414yes—
65C2×Dic47⋊C4—24no—
66C2×Dic47⋊C4—24no—
67C2×Dic47⋊C4—24no—
68C2×Dic47⋊C4—24no—
69C2×Dic47⋊C4—42no—
70C2×Dic47⋊C4C2×C418yes—
71C2×C22⋊Dic47—24no—
72C2×C22⋊Dic47—24no—
73C2×C22⋊Dic47—24no—
74C2×C22⋊Dic47—24no—
75C2×C22⋊Dic47—42no—
76C2×C22⋊Dic47C2×C418yes—
77C2×C4×Dic47—24no—
78C2×C4×Dic47—24no—
79C2×C4×Dic47—42no—
80C47⋊#95—24no—
81C47⋊#95—24no—
82C47⋊#95—24no—
83C47⋊#95—24no—
84C47⋊#95—24no—
85C47⋊#95—24no—
86C47⋊#95—24no—
87C25×C47C2311yescharacteristic
88C23×C4×C47—22no—
89C23×C4×C47—22no—
90C23×C4×C47—22no—
91C23×C4×C47—22no—
92C23×C4×C47—22no—
93C23×C4×C47—22no—
94C23×C4×C47C2×C414yes—
95C23×C4×C47C2311yescharacteristic
96C23×C4×C47C2311yescharacteristic
97C23×C4×C47C2311yescharacteristic
98C23×C4×C47C2311yescharacteristic
99C23×C4×C47C2311yescharacteristic
100C23×C4×C47C2311yescharacteristic
101C2×C22⋊C4×C47—22no—
102C2×C22⋊C4×C47—22no—
103C2×C22⋊C4×C47—22no—
104C2×C22⋊C4×C47—22no—
105C2×C22⋊C4×C47—22no—
106C2×C22⋊C4×C47Q814yescomplemented
107C2×C42×C47—22no—
108C2×C42×C47—22no—
109C2×C42×C47—22no—
110C2×C42×C47—22no—
111C2×C42×C47—22no—
112C2×C42×C47D414yes—
113#95×C47—22no—
114#95×C47—22no—
115C24×C47—21no—
116C24×C47—21no—
117C24×C47—21no—
118C24×C47—21no—
119C24×C47—21no—
120C24×C47—21no—
121C24×C47—21no—
122C24×C47—21no—
123C24×C47—21no—
124C24×C47—21no—
125C24×C47—21no—
126C24×C47—21no—
127C24×C47C22×C412yes—
128C24×C47C2×Q812yes—
129C24×C47#4112yes—
130C24×C47C2411yescharacteristic
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—21no—
147C22×C4×C47—21no—
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
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—21no—
158C22×C4×C47—21no—
159C22×C4×C47—28no—
160C22×C4×C47—28no—
161C22×C4×C47—28no—
162C22×C4×C47—44no—
163C22×C4×C47—44no—
164C22×C4×C47—44no—
165C22×C4×C47—44no—
166C22×C4×C47C22×C412yes—
167C22×C4×C47C22×C412yes—
168C22×C4×C47C2×D412yes—
169C22×C4×C47C2×D412yes—
170C22×C4×C47C2×D412yes—
171C22×C4×C47C2×D412yes—
172C22×C4×C47C2×D412yes—
173C22×C4×C47C2×D412yes—
174C22×C4×C47C2×Q812yes—
175C22×C4×C47C2×Q812yes—
176C22×C4×C47#4112yes—
177C22×C4×C47#4112yes—
178C22×C4×C47#4112yes—
179C22×C4×C47#4112yes—
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—22no—
199C22×Dic47—22no—
200C22×Dic47—22no—
201C22×Dic47—22no—
202C22×Dic47—22no—
203C22×Dic47C22×C414yes—
204C22×Dic47C22×C414yes—
205C22×Dic47C2×D414yes—
206C22×Dic47C2×D414yes—
207C22×Dic47C2×D414yes—
208C2×Dic94—28no—
209C2×Dic94—28no—
210C2×Dic94—28no—
211C2×Dic94—44no—
212C2×Dic94—44no—
213C2×Dic94—44no—
214C2×Dic94—44no—
215C22⋊C4×C47—28no—
216C22⋊C4×C47—28no—
217C42×C47—28no—
218C42×C47—44no—
219C22⋊Dic47—216no—
220C22⋊Dic47—48no—
221C4⋊Dic47—28no—
222C4⋊Dic47—44no—
223C4⋊Dic47C22⋊C4116yescomplemented
224Dic47⋊C4—216no—
225Dic47⋊C4—48no—
226C4×Dic47—48no—
227C23×C47—22no—
228C23×C47—22no—
229C23×C47—22no—
230C23×C47—22no—
231C23×C47—22no—
232C23×C47—22no—
233C23×C47—22no—
234C23×C47—22no—
235C23×C47—22no—
236C23×C47—22no—
237C23×C47—22no—
238C23×C47—22no—
239C23×C47—22no—
240C23×C47—22no—
241C23×C47—22no—
242C23×C47—22no—
243C23×C47—22no—
244C23×C47—22no—
245C23×C47—41no—
246C23×C47—41no—
247C23×C47—41no—
248C23×C47—41no—
249C23×C47—41no—
250C23×C47—41no—
251C23×C47—41no—
252C23×C47—41no—
253C23×C47—41no—
254C23×C47—41no—
255C23×C47—41no—
256C23×C47—41no—
257C23×C47—41no—
258C23×C47—41no—
259C23×C47—41no—
260C23×C47—41no—
261C23×C47C4×Q814yes—
262C23×C47C23×C411yescharacteristic
263C23×C47C22×D411yescharacteristic
264C23×C47C22×D411yescharacteristic
265C23×C47C22×D411yescharacteristic
266C23×C47C22×D411yescharacteristic
267C23×C47C22×Q811yescharacteristic
268C23×C47C2×#4111yescharacteristic
269C23×C47C2×#4111yescharacteristic
270C23×C47C2×#4111yescharacteristic
271C23×C47C2×#4111yescharacteristic
272C23×C47C2×#4111yescharacteristic
273C23×C47H(5,𝔽2)11yescharacteristic
274C23×C472−1+411yescharacteristic
275C23×C472−1+411yescharacteristic
276C23×C472−1+411yescharacteristic
277C2×C4×C47—22no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
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—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—41no—
296C2×C4×C47—41no—
297C2×C4×C47—41no—
298C2×C4×C47—41no—
299C2×C4×C47—41no—
300C2×C4×C47—41no—
301C2×C4×C47—41no—
302C2×C4×C47—41no—
303C2×C4×C47—41no—
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—41no—
311C2×C4×C47—416no—
312C2×C4×C47C2×C22⋊C414yes—
313C2×C4×C47C4×D414yes—
314C2×C4×C47C4×D414yes—
315C2×C4×C47#12114yes—
316C2×C4×C47#12114yes—
317C2×C4×C47C22⋊Q814yescomplemented
318C2×C4×C47#12414yes—
319C2×C4×C47#12714yes—
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—24no—
331C2×Dic47—24no—
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—42no—
344C2×Dic47—42no—
345C2×Dic47—42no—
346C2×Dic47—42no—
347C2×Dic47C2×C22⋊C418yes—
348Dic94—416no—
349#13997—471nomaximal, Sylow
350C22×C47—24no—
351C22×C47—24no—
352C22×C47—24no—
353C22×C47—42no—
354C22×C47—42no—
355C22×C47—42no—
356C22×C47—42no—
357C22×C47—42no—
358C22×C47—42no—
359C22×C47—42no—
360C22×C47—42no—
361C22×C47—42no—
362C22×C47—42no—
363C22×C47—42no—
364C22×C47—42no—
365C22×C47C22×C22⋊C411yescharacteristic
366C22×C47C2×C4×D411yescharacteristic
367C22×C47C2×C4×D411yescharacteristic
368C22×C47C2×C4×Q811yescharacteristic
369C22×C47C4×#4111yescharacteristic
370C22×C47#51911yescharacteristic
371C22×C47#52011yescharacteristic
372C22×C47C2×#12111yescharacteristic
373C22×C47C2×#12111yescharacteristic
374C22×C47C2×C22⋊Q811yescharacteristic
375C22×C47#52511yescharacteristic
376C22×C47C2×#12411yescharacteristic
377C22×C47#52911yescharacteristic
378C22×C47C2×#12711yescharacteristic
379C22×C47#53311yescharacteristic
380C22×C47#53611yescharacteristic
381C22×C47#53711yescharacteristic
382C22×C47#54111yescharacteristic
383C22×C47#54211yescharacteristic
384C22×C47#54611yescharacteristic
385C22×C47#54611yescharacteristic
386C22×C47#54611yescharacteristic
387C22×C47#54711yescharacteristic
388C22×C47#54711yescharacteristic
389C22×C47#54711yescharacteristic
390C22×C47#54811yescharacteristic
391C22×C47#54811yescharacteristic
392C22×C47#54811yescharacteristic
393C22×C47D4×Q811yescharacteristic
394C22×C47D4×Q811yescharacteristic
395C22×C47D4×Q811yescharacteristic
396C22×C47#55211yescharacteristic
397C22×C47#55211yescharacteristic
398C22×C47#55411yescharacteristic
399C22×C47#55611yescharacteristic
400C4×C47—24no—
401C4×C47—42no—
402C4×C47—42no—
403C4×C47—42no—
404C4×C47—42no—
405C4×C47#39018yes—
406Dic47—28no—
407Dic47—44no—
408Dic47—44no—
409Dic47—82no—
410C22×C22⋊Q8—471no—
411C2×#391—471no—
412C2×#391—471no—
413C2×#389—471no—
414C2×#380—471no—
415C2×C4×C4⋊C4—471no—
416C2×C4×C22⋊C4D4711yescharacteristic
417#1445—472no—
418#1439—472no—
419#1437—472no—
420C4⋊#95—472no—
421C2×C47—44no—
422C2×C47C2×#39011yescharacteristic
423C2×C47C4×C22⋊Q811yescharacteristic
424C2×C47#232311yescharacteristic
425C2×C47#233911yescharacteristic
426C2×C47Q8×C22⋊C411yescharacteristic
427C2×C47#236011yescharacteristic
428C2×C47#236211yescharacteristic
429C2×C47#241511yescharacteristic
430C2×C47#241711yescharacteristic
431C2×C47#242711yescharacteristic
432C2×C47#242911yescharacteristic
433C2×C47#248911yescharacteristic
434C2×C47#249211yescharacteristic
435C2×C47#254011yescharacteristic
436C2×C47#254211yescharacteristic
437C23×Q8—471no—
438C24×C4C2×D4711yescharacteristic
439C2×C22⋊Q8—478no—
440C2×C22⋊Q8—944no—
441C2×C22⋊Q8—944no—
442C22×C4⋊C4—471no—
443C22×C4⋊C4—472no—
444C22×C4⋊C4—471no—
445C22×C4⋊C4—471no—
446C22×C4⋊C4—472no—
447C22×C22⋊C4—472no—
448C22×C22⋊C4—472no—
449C22×C22⋊C4C2×D4711yescharacteristic
450C22×C22⋊C4C2×D4711yescharacteristic
451C22×C42—472no—
452C22×C42C2×D4711yescharacteristic
453C22×C42C2×D4711yescharacteristic
454#391—944no—
455#391—944no—
456#389—944no—
457#380—944no—
458C4×C4⋊C4—944no—
459C4×C22⋊C4—24no—
460C2×#95—472no—
461C2×#95—472no—
462C2×#95—472no—
463C2×#95—472no—
464C2×#95—472no—
465C2×#95—472no—
466C2×#95—472no—
467C2×#95C2×D4711yescharacteristic
468C2×#95C2×D4711yescharacteristic
469C47#1399711yescharacteristic, complemented, Sylow
470C25C22×D4711yescharacteristic
471C22×Q8—474no—
472C22×Q8—942no—
473C22×Q8—942no—
474C22×Q8—942no—
475C22×Q8—942no—
476C22×Q8—942no—
477C22×Q8—942no—
478C23×C4—22no—
479C23×C4—22no—
480C23×C4—22no—
481C23×C4—22no—
482C23×C4—22no—
483C23×C4—22no—
484C23×C4—472no—
485C23×C4—472no—
486C23×C4—472no—
487C23×C4—472no—
488C23×C4C4×D4714yes—
489C23×C4C22×D4711yescharacteristic
490C23×C4C22×D4711yescharacteristic
491C23×C4C22×D4711yescharacteristic
492C23×C4C22×D4711yescharacteristic
493C23×C4C22×D4711yescharacteristic
494C23×C4C22×D4711yescharacteristic
495C22⋊Q8—9432no—
496C2×C4⋊C4—474no—
497C2×C4⋊C4—474no—
498C2×C4⋊C4—474no—
499C2×C4⋊C4—478no—
500C2×C4⋊C4—474no—
501C2×C4⋊C4—944no—
502C2×C4⋊C4—944no—
503C2×C4⋊C4—942no—
504C2×C4⋊C4—942no—
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×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—478no—
517C2×C22⋊C4—944no—
518C2×C22⋊C4—944no—
519C2×C22⋊C4—944no—
520C2×C22⋊C4—944no—
521C2×C22⋊C4—1882no—
522C2×C22⋊C4Dic9414yescomplemented
523C2×C42—22no—
524C2×C42—22no—
525C2×C42—22no—
526C2×C42—22no—
527C2×C42—22no—
528C2×C42—944no—
529C2×C42—944no—
530C2×C42—1882no—
531C2×C42C22⋊D4714yes—
532#95—22no—
533#95—22no—
534#95—944no—
535#95—944no—
536#95—944no—
537#95—944no—
538#95—944no—
539#95—944no—
540#95—944no—
541C24—21no—
542C24—21no—
543C24—21no—
544C24—21no—
545C24—21no—
546C24—21no—
547C24—21no—
548C24—21no—
549C24—21no—
550C24—21no—
551C24—21no—
552C24—21no—
553C24C2×Dic9412yes—
554C24C2×C4×D4712yes—
555C24#1062535012yes—
556C24C23×D4711yescharacteristic
557C2×Q8—948no—
558C2×Q8—948no—
559C2×Q8—948no—
560C2×Q8—1884no—
561C2×Q8—1884no—
562C2×Q8—1884no—
563C2×Q8—1884no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
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—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—28no—
593C22×C4—28no—
594C22×C4—28no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—474no—
600C22×C4—474no—
601C22×C4—474no—
602C22×C4—474no—
603C22×C4—474no—
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—942no—
621C22×C4—942no—
622C22×C4—942no—
623C22×C4—942no—
624C22×C4—942no—
625C22×C4—942no—
626C22×C4—942no—
627C22×C4C2×Dic9412yes—
628C22×C4C2×Dic9412yes—
629C22×C4C2×C4×D4712yes—
630C22×C4C2×C4×D4712yes—
631C22×C4#1062535012yes—
632C22×C4#1062535012yes—
633C22×C4#1062535012yes—
634C22×C4D4×D4712yes—
635C22×C4D4×D4712yes—
636C22×C4D4×D4712yes—
637C22×C4#1062535212yes—
638C22×C4C2×C22⋊D4712yes—
639C22×C4C2×C22⋊D4712yes—
640C22×C4C2×C22⋊D4712yes—
641C4⋊C4—4716no—
642C4⋊C4—9416no—
643C4⋊C4—948no—
644C4⋊C4—1888no—
645C4⋊C4—1884no—
646C22⋊C4—28no—
647C22⋊C4—28no—
648C22⋊C4—9416no—
649C22⋊C4—1888no—
650C42—28no—
651C42—44no—
652C42—1888no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23C4×Dic9414yes—
688C23C22×C4×D4711yescharacteristic
689C23C2×D4×D4711yescharacteristic
690C23C2×D4×D4711yescharacteristic
691C23C2×D4×D4711yescharacteristic
692C23C22×C22⋊D4711yescharacteristic
693C23C22×Dic9411yescharacteristic
694C23C2×#1062535211yescharacteristic
695C23C2×#1062535011yescharacteristic
696C23C2×#1062535011yescharacteristic
697C23C2×#1062535011yescharacteristic
698C23C2×#1062535011yescharacteristic
699C23#1309407011yescharacteristic
700C23#1309407111yescharacteristic
701C23#1309407111yescharacteristic
702C23#1309407111yescharacteristic
703Q8—18816no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—416no—
739C2×C4—478no—
740C2×C4—944no—
741C2×C4—944no—
742C2×C4—944no—
743C2×C4—944no—
744C2×C4—944no—
745C2×C4—944no—
746C2×C4—944no—
747C2×C4—944no—
748C2×C4—944no—
749C2×C4—944no—
750C2×C4—944no—
751C2×C4—944no—
752C2×C4—1882no—
753C2×C4—1882no—
754C2×C4—1882no—
755C2×C4—1882no—
756C2×C4—1882no—
757C2×C4—1882no—
758C2×C4—1882no—
759C2×C4—1882no—
760C2×C4—1882no—
761C2×C4—1882no—
762C2×C4—1882no—
763C2×C4—1882no—
764C2×C4—1882no—
765C2×C4—1882no—
766C2×C4—1882no—
767C2×C4C22⋊C4×D4714yes—
768C2×C4(C22⋊D47)⋊C414yes—
769C2×C4C4×C22⋊D4714yes—
770C2×C4#1309399614yes—
771C2×C4#1309399714yes—
772C2×C4#1309400314yescomplemented
773C2×C4#1309401014yes—
774C2×C4#1309402014yes—
775C22—24no—
776C22—24no—
777C22—24no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22C2×C22⋊C4×D4711yescharacteristic
791C22C2×(C22⋊D47)⋊C411yescharacteristic
792C22C2×C4×C22⋊D4711yescharacteristic
793C22C2×C4×Dic9411yescharacteristic
794C22C4×#1062535011yescharacteristic
795C22#1568960011yescharacteristic
796C22#1568960311yescharacteristic
797C22C2×#1309399611yescharacteristic
798C22C2×#1309399711yescharacteristic
799C22C2×#1309400311yescharacteristic
800C22#1568963411yescharacteristic
801C22C2×#1309401011yescharacteristic
802C22#1568965711yescharacteristic
803C22C2×#1309402011yescharacteristic
804C22#1568968011yescharacteristic
805C22#1568969411yescharacteristic
806C22#1568970111yescharacteristic
807C22#1568973511yescharacteristic
808C22#1568974411yescharacteristic
809C22#1568976911yescharacteristic
810C22#1568976911yescharacteristic
811C22#1568976911yescharacteristic
812C22#1568977811yescharacteristic
813C22#1568977811yescharacteristic
814C22#1568977811yescharacteristic
815C22#1568978211yescharacteristic
816C22#1568978211yescharacteristic
817C22#1568978211yescharacteristic
818C22D4×Dic9411yescharacteristic
819C22D4×Dic9411yescharacteristic
820C22D4×Dic9411yescharacteristic
821C22#1568981311yescharacteristic
822C22#1568981311yescharacteristic
823C22#1568983011yescharacteristic
824C22#1568984311yescharacteristic
825C4—24no—
826C4—42no—
827C4—42no—
828C4—42no—
829C4—42no—
830C4—948no—
831C4—3762no—
832C4—1884no—
833C4—1884no—
834C4#1568902318yes—
835C2—44no—
836C2C2×#1568902311yescharacteristic
837C2C4×#1309400311yescharacteristic
838C2#2024607011yescharacteristic
839C2#2024621911yescharacteristic
840C2C22⋊C4×Dic9411yescharacteristic
841C2#2024639111yescharacteristic
842C2#2024641311yescharacteristic
843C2#2024681711yescharacteristic
844C2#2024683911yescharacteristic
845C2#2024696511yescharacteristic
846C2#2024698711yescharacteristic
847C2#2024772911yescharacteristic
848C2#2024776211yescharacteristic
849C2#2024832711yescharacteristic
850C2#2024834111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C4×C22⋊C4×C47C2
socle, cosocleC24×C47C24
prime radicalC25×C47C23
hypercenterC2×C4×C22⋊C4D47
hypocenterC47#13997
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#15689029C2semidirect
3. C2×#15689029C2semidirect
4. C2×#15689021C2semidirect
6. C2×C4×C4⋊Dic47C2semidirect
7. #20241654C2semidirect
10. Dic47⋊#95C2semidirect
15. C2×#13094003C4semidirect
106. C2×C22⋊C4×C47Q8semidirect
223. C4⋊Dic47C22⋊C4semidirect
317. C2×C4×C47C22⋊Q8semidirect
469. C47#13997semidirect
522. C2×C22⋊C4Dic94semidirect
772. C2×C4#13094003semidirect

Maximal subgroups

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

subgroupindex
C22×#130940032
C2×#156890292
C2×#156890212
C2×#156889832
C2×C4×C4⋊Dic472
#202416542
#202416312
#202416252
Dic47⋊#952
C2×C4×C22⋊C4×C472
#1399747