Finite Group Databasebeta

← #26139408

Subgroups — #26139408

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×#15689028C211yesmaximal, characteristic, complemented
3C2×#15689028C211yesmaximal, characteristic, complemented
4C2×#15689019C211yesmaximal, characteristic, complemented
5C2×C4⋊C4×Dic47C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊Dic47C211yesmaximal, characteristic
7#20241654C212yesmaximal, complemented
8#20241631C212yesmaximal
9#20241625C212yesmaximal
10Dic47⋊#95C212yesmaximal, complemented
11C2×C47×#380C211yesmaximal, characteristic
12C23×Dic94C2211yescharacteristic
13C2×#13094003—24no—
14C2×#13094003—24no—
15C2×#13094003C418yescomplemented
16C22×C4⋊Dic47C2211yescharacteristic
17C22×Dic47⋊C4C2212yes—
18C22×Dic47⋊C4C2212yes—
19C22×C22⋊Dic47C2211yescharacteristic
20C22×C22⋊Dic47C2212yes—
21C22×C22⋊Dic47C2211yescharacteristic
22C22×C4×Dic47C2211yescharacteristic
23C22×C4×Dic47C2212yes—
24C22×C4×Dic47C2211yescharacteristic
25#15689028—24no—
26#15689028—24no—
27#15689019—24no—
28C4⋊C4×Dic47—24no—
29C4×C22⋊Dic47—24no—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2212yes—
35C2×C47⋊#95C2211yescharacteristic
36C2×C47⋊#95C2211yescharacteristic
37C2×C47⋊#95C2212yes—
38C24×C4×C47C2211yescharacteristic
39C22×C4⋊C4×C47C2211yescharacteristic
40C22×C4⋊C4×C47C2211yescharacteristic
41C22×C22⋊C4×C47C2212yes—
42C47×#380—24no—
43C2×#95×C47C2212yes—
44C22×Dic94—22no—
45C22×Dic94—22no—
46C22×Dic94—22no—
47C22×Dic94—22no—
48C22×Dic94—22no—
49C22×Dic94—22no—
50C22×Dic94C2×C414yes—
51C23×Dic47C2312yes—
52C23×Dic47C2311yescharacteristic
53C23×Dic47C2311yescharacteristic
54C23×Dic47C2311yescharacteristic
55C23×Dic47C2312yes—
56C23×Dic47C2311yescharacteristic
57#13094003—232no—
58C2×C4⋊Dic47C2×C414yes—
59C2×C4⋊Dic47D414yes—
60C2×C4⋊Dic47D414yes—
61C2×Dic47⋊C4—24no—
62C2×Dic47⋊C4—24no—
63C2×Dic47⋊C4—24no—
64C2×Dic47⋊C4—24no—
65C2×Dic47⋊C4—42no—
66C2×Dic47⋊C4C2×C418yes—
67C2×C22⋊Dic47—22no—
68C2×C22⋊Dic47—22no—
69C2×C22⋊Dic47—22no—
70C2×C22⋊Dic47—24no—
71C2×C22⋊Dic47—24no—
72C2×C22⋊Dic47—22no—
73C2×C22⋊Dic47—22no—
74C2×C22⋊Dic47C2×C418yes—
75C2×C22⋊Dic47Q814yescomplemented
76C2×C4×Dic47—22no—
77C2×C4×Dic47—22no—
78C2×C4×Dic47—22no—
79C2×C4×Dic47—22no—
80C2×C4×Dic47—22no—
81C2×C4×Dic47—24no—
82C2×C4×Dic47—24no—
83C2×C4×Dic47—42no—
84C2×C4×Dic47D414yes—
85C47⋊#95—24no—
86C47⋊#95—24no—
87C47⋊#95—22no—
88C47⋊#95—22no—
89C47⋊#95—24no—
90C47⋊#95—24no—
91C47⋊#95—24no—
92C47⋊#95—24no—
93C25×C47C2311yescharacteristic
94C23×C4×C47—22no—
95C23×C4×C47—22no—
96C23×C4×C47—22no—
97C23×C4×C47—22no—
98C23×C4×C47—22no—
99C23×C4×C47—22no—
100C23×C4×C47C2×C414yes—
101C23×C4×C47C2312yes—
102C23×C4×C47C2311yescharacteristic
103C23×C4×C47C2312yes—
104C23×C4×C47C2311yescharacteristic
105C2×C4⋊C4×C47—22no—
106C2×C4⋊C4×C47—22no—
107C2×C4⋊C4×C47—22no—
108C2×C4⋊C4×C47—22no—
109C2×C4⋊C4×C47—22no—
110C2×C4⋊C4×C47D414yes—
111C2×C22⋊C4×C47—24no—
112C2×C22⋊C4×C47—24no—
113C2×C22⋊C4×C47—42no—
114#95×C47—24no—
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—22no—
132C22×C4×C47—21no—
133C22×C4×C47—21no—
134C22×C4×C47—21no—
135C22×C4×C47—21no—
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—28no—
144C22×C4×C47—28no—
145C22×C4×C47—28no—
146C22×C4×C47—22no—
147C22×C4×C47—22no—
148C22×C4×C47—22no—
149C22×C4×C47—22no—
150C22×C4×C47—22no—
151C22×C4×C47—22no—
152C22×C4×C47—22no—
153C22×C4×C47—44no—
154C22×C4×C47—44no—
155C22×C4×C47—44no—
156C22×C4×C47—44no—
157C22×C4×C47C22×C412yes—
158C22×C4×C47C22×C412yes—
159C22×C4×C47C2×D414yes—
160C22×C4×C47C2×D412yes—
161C22×C4×C47C2×D412yes—
162C22×C4×C47C2×D412yes—
163C22×C4×C47C2×D412yes—
164C22×C4×C47#4112yes—
165C22×C4×C47#4112yes—
166C22×Dic47—21no—
167C22×Dic47—22no—
168C22×Dic47—21no—
169C22×Dic47—22no—
170C22×Dic47—21no—
171C22×Dic47—22no—
172C22×Dic47—22no—
173C22×Dic47—21no—
174C22×Dic47—21no—
175C22×Dic47—21no—
176C22×Dic47—21no—
177C22×Dic47—21no—
178C22×Dic47—22no—
179C22×Dic47—22no—
180C22×Dic47—21no—
181C22×Dic47—21no—
182C22×Dic47—21no—
183C22×Dic47—22no—
184C22×Dic47—22no—
185C22×Dic47—21no—
186C22×Dic47—21no—
187C22×Dic47—21no—
188C22×Dic47—21no—
189C22×Dic47—21no—
190C22×Dic47—22no—
191C22×Dic47—22no—
192C22×Dic47—21no—
193C22×Dic47—21no—
194C22×Dic47—21no—
195C22×Dic47—21no—
196C22×Dic47—21no—
197C22×Dic47—21no—
198C22×Dic47C22×C414yes—
199C22×Dic47C22×C414yes—
200C22×Dic47C2×D412yes—
201C22×Dic47C2×D414yes—
202C22×Dic47C2×D414yes—
203C22×Dic47C2×D412yes—
204C22×Dic47C2×Q812yes—
205C22×Dic47C2×Q812yes—
206C22×Dic47#4112yes—
207C22×Dic47#4112yes—
208C2×Dic94—28no—
209C2×Dic94—28no—
210C2×Dic94—28no—
211C2×Dic94—44no—
212C2×Dic94—44no—
213C2×Dic94—44no—
214C2×Dic94—44no—
215C4⋊C4×C47—28no—
216C4⋊C4×C47—44no—
217C22⋊C4×C47—48no—
218C22⋊Dic47—28no—
219C22⋊Dic47—216no—
220C22⋊Dic47—28no—
221C4⋊Dic47C22⋊C4116yescomplemented
222Dic47⋊C4—216no—
223Dic47⋊C4—48no—
224C4×Dic47—28no—
225C4×Dic47—48no—
226C4×Dic47—44no—
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—24no—
281C2×C4×C47—24no—
282C2×C4×C47—24no—
283C2×C4×C47—41no—
284C2×C4×C47—41no—
285C2×C4×C47—41no—
286C2×C4×C47—42no—
287C2×C4×C47—41no—
288C2×C4×C47—42no—
289C2×C4×C47—42no—
290C2×C4×C47—42no—
291C2×C4×C47—416no—
292C2×C4×C47—42no—
293C2×C4×C47—42no—
294C2×C4×C47—42no—
295C2×C4×C47—42no—
296C2×C4×C47—42no—
297C2×C4×C47—42no—
298C2×C4×C47—42no—
299C2×C4×C47C2×C22⋊C414yes—
300C2×C4×C47C4×D414yes—
301C2×C4×C47C4×D414yes—
302C2×C4×C47#12114yes—
303C2×C4×C47#12114yes—
304C2×C4×C47#12414yes—
305C2×C4×C47#12714yes—
306C2×Dic47—24no—
307C2×Dic47—24no—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—24no—
312C2×Dic47—24no—
313C2×Dic47—24no—
314C2×Dic47—24no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—24no—
319C2×Dic47—24no—
320C2×Dic47—24no—
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—22no—
330C2×Dic47—42no—
331C2×Dic47—42no—
332C2×Dic47—42no—
333C2×Dic47—41no—
334C2×Dic47—41no—
335C2×Dic47—42no—
336C2×Dic47—41no—
337C2×Dic47—41no—
338C2×Dic47—41no—
339C2×Dic47—41no—
340C2×Dic47—41no—
341C2×Dic47—41no—
342C2×Dic47—41no—
343C2×Dic47—41no—
344C2×Dic47—41no—
345C2×Dic47—41no—
346C2×Dic47C2×C22⋊C418yes—
347C2×Dic47C22⋊Q814yescomplemented
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—44no—
401C4×C47—42no—
402C4×C47—82no—
403C4×C47#39018yes—
404Dic47—28no—
405Dic47—24no—
406Dic47—42no—
407Dic47—42no—
408Dic47—42no—
409Dic47—44no—
410C22×C22⋊Q8—471no—
411C2×#391—471no—
412C2×#391—471no—
413C2×#389—471no—
414C2×#380D4711yescharacteristic
415C2×C4×C4⋊C4—471no—
416C2×C4×C22⋊C4—471no—
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—472no—
445C22×C4⋊C4C2×D4711yescharacteristic
446C22×C4⋊C4C2×D4711yescharacteristic
447C22×C22⋊C4—472no—
448C22×C22⋊C4—471no—
449C22×C22⋊C4—471no—
450C22×C22⋊C4C2×D4712yes—
451C22×C42—471no—
452C22×C42—471no—
453C22×C42—472no—
454#391—944no—
455#391—944no—
456#389—944no—
457#380—24no—
458C4×C4⋊C4—944no—
459C4×C22⋊C4—944no—
460C2×#95—471no—
461C2×#95—472no—
462C2×#95—472no—
463C2×#95—472no—
464C2×#95—472no—
465C2×#95—472no—
466C2×#95—472no—
467C2×#95—471no—
468C2×#95C2×D4712yes—
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—471no—
486C23×C4—471no—
487C23×C4—472no—
488C23×C4—471no—
489C23×C4—471no—
490C23×C4C4×D4714yes—
491C23×C4C22×D4712yes—
492C23×C4C22×D4711yescharacteristic
493C23×C4C22×D4712yes—
494C23×C4C22×D4711yescharacteristic
495C22⋊Q8—9432no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—474no—
502C2×C4⋊C4—474no—
503C2×C4⋊C4—474no—
504C2×C4⋊C4—478no—
505C2×C4⋊C4—944no—
506C2×C4⋊C4—944no—
507C2×C4⋊C4—944no—
508C2×C4⋊C4—944no—
509C2×C4⋊C4—1882no—
510C2×C4⋊C4C22⋊D4714yes—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—42no—
514C2×C22⋊C4—478no—
515C2×C22⋊C4—474no—
516C2×C22⋊C4—944no—
517C2×C22⋊C4—944no—
518C2×C22⋊C4—942no—
519C2×C22⋊C4—942no—
520C2×C22⋊C4—942no—
521C2×C22⋊C4—942no—
522C2×C22⋊C4—942no—
523C2×C42—474no—
524C2×C42—942no—
525C2×C42—942no—
526C2×C42—944no—
527C2×C42—944no—
528C2×C42—942no—
529C2×C42—942no—
530C2×C42—942no—
531C2×C42—1882no—
532#95—24no—
533#95—942no—
534#95—942no—
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×C4×D4712yes—
554C24#1062535212yes—
555C24Q8×D4712yes—
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—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—28no—
577C22×C4—28no—
578C22×C4—28no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—474no—
591C22×C4—472no—
592C22×C4—474no—
593C22×C4—474no—
594C22×C4—472no—
595C22×C4—472no—
596C22×C4—474no—
597C22×C4—472no—
598C22×C4—472no—
599C22×C4—472no—
600C22×C4—941no—
601C22×C4—942no—
602C22×C4—942no—
603C22×C4—941no—
604C22×C4—941no—
605C22×C4—942no—
606C22×C4—941no—
607C22×C4—942no—
608C22×C4—941no—
609C22×C4—941no—
610C22×C4—942no—
611C22×C4—941no—
612C22×C4—941no—
613C22×C4—941no—
614C22×C4—942no—
615C22×C4—942no—
616C22×C4—941no—
617C22×C4—941no—
618C22×C4—942no—
619C22×C4—941no—
620C22×C4—941no—
621C22×C4—941no—
622C22×C4—941no—
623C22×C4—942no—
624C22×C4—941no—
625C22×C4—942no—
626C22×C4—941no—
627C22×C4—941no—
628C22×C4—941no—
629C22×C4—941no—
630C22×C4—941no—
631C22×C4—941no—
632C22×C4C2×C4×D4712yes—
633C22×C4C2×C4×D4712yes—
634C22×C4#1062535012yes—
635C22×C4D4×D4712yes—
636C22×C4D4×D4712yes—
637C22×C4D4×D4712yes—
638C22×C4#1062535212yes—
639C22×C4C2×C22⋊D4714yes—
640C22×C4C2×C22⋊D4712yes—
641C4⋊C4—28no—
642C4⋊C4—44no—
643C4⋊C4—4716no—
644C4⋊C4—9416no—
645C4⋊C4—1888no—
646C22⋊C4—48no—
647C22⋊C4—948no—
648C22⋊C4—9416no—
649C22⋊C4—948no—
650C42—948no—
651C42—1888no—
652C42—1884no—
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—
687C23#1309398914yes—
688C23C22×C4×D4711yescharacteristic
689C23C2×D4×D4711yescharacteristic
690C23C2×D4×D4711yescharacteristic
691C23C2×D4×D4711yescharacteristic
692C23C22×C22⋊D4711yescharacteristic
693C23C2×Q8×D4711yescharacteristic
694C23#41×D4711yescharacteristic
695C23#41×D4711yescharacteristic
696C23C2×#1062535211yescharacteristic
697C23C2×#1062535211yescharacteristic
698C23C2×#1062535011yescharacteristic
699C23#1309406911yescharacteristic
700C23#1309407111yescharacteristic
701C23#1309407111yescharacteristic
702C23#1309407211yescharacteristic
703Q8—18816no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—416no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—478no—
727C2×C4—474no—
728C2×C4—942no—
729C2×C4—944no—
730C2×C4—944no—
731C2×C4—944no—
732C2×C4—944no—
733C2×C4—942no—
734C2×C4—942no—
735C2×C4—942no—
736C2×C4—944no—
737C2×C4—944no—
738C2×C4—942no—
739C2×C4—942no—
740C2×C4—942no—
741C2×C4—942no—
742C2×C4—942no—
743C2×C4—942no—
744C2×C4—944no—
745C2×C4—944no—
746C2×C4—944no—
747C2×C4—942no—
748C2×C4—942no—
749C2×C4—942no—
750C2×C4—942no—
751C2×C4—942no—
752C2×C4—1881no—
753C2×C4—1881no—
754C2×C4—1881no—
755C2×C4—1881no—
756C2×C4—1881no—
757C2×C4—1881no—
758C2×C4—1881no—
759C2×C4—1881no—
760C2×C4—1882no—
761C2×C4—1882no—
762C2×C4—1882no—
763C2×C4—1881no—
764C2×C4—1881no—
765C2×C4—1882no—
766C2×C4—1881no—
767C2×C4—1881no—
768C2×C4C22⋊C4×D4714yes—
769C2×C4(C22⋊D47)⋊C414yes—
770C2×C4C4×C22⋊D4714yes—
771C2×C4#1309399614yes—
772C2×C4#1309399714yes—
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×#1309398911yescharacteristic
794C22#1568959111yescharacteristic
795C22#1568960011yescharacteristic
796C22#1568960411yescharacteristic
797C22C2×#1309399611yescharacteristic
798C22C2×#1309399711yescharacteristic
799C22C22⋊Q8×D4711yescharacteristic
800C22#1568963311yescharacteristic
801C22C2×#1309401011yescharacteristic
802C22#1568965411yescharacteristic
803C22C2×#1309402011yescharacteristic
804C22#1568967511yescharacteristic
805C22#1568969611yescharacteristic
806C22#1568970211yescharacteristic
807C22#1568973311yescharacteristic
808C22#1568974011yescharacteristic
809C22#1568976711yescharacteristic
810C22#1568977011yescharacteristic
811C22#1568977011yescharacteristic
812C22#1568977211yescharacteristic
813C22#1568977511yescharacteristic
814C22#1568977511yescharacteristic
815C22#1568977911yescharacteristic
816C22#1568977911yescharacteristic
817C22#1568978011yescharacteristic
818C22#1568978611yescharacteristic
819C22#1568978611yescharacteristic
820C22Q8×C22⋊D4711yescharacteristic
821C22#1568980811yescharacteristic
822C22#1568981211yescharacteristic
823C22#1568982811yescharacteristic
824C22#1568984111yescharacteristic
825C4—42no—
826C4—44no—
827C4—82no—
828C4—944no—
829C4—948no—
830C4—1882no—
831C4—1882no—
832C4—1882no—
833C4—1884no—
834C4#1568902318yes—
835C2—44no—
836C2C2×#1568902311yescharacteristic
837C2#2024591611yescharacteristic
838C2#2024606611yescharacteristic
839C2#2024621611yescharacteristic
840C2#2024622011yescharacteristic
841C2#2024639311yescharacteristic
842C2#2024641511yescharacteristic
843C2#2024681911yescharacteristic
844C2#2024684111yescharacteristic
845C2#2024696711yescharacteristic
846C2#2024698911yescharacteristic
847C2#2024772511yescharacteristic
848C2#2024775811yescharacteristic
849C2#2024832411yescharacteristic
850C2#2024833811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C47×#380C2
socle, cosocleC24×C47C24
prime radicalC25×C47C23
hypercenterC2×#380D47
hypocenterC47#13997
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C2×#15689028C2semidirect
3. C2×#15689028C2semidirect
4. C2×#15689019C2semidirect
5. C2×C4⋊C4×Dic47C2semidirect
7. #20241654C2semidirect
10. Dic47⋊#95C2semidirect
15. C2×#13094003C4semidirect
75. C2×C22⋊Dic47Q8semidirect
221. C4⋊Dic47C22⋊C4semidirect
347. C2×Dic47C22⋊Q8semidirect
469. C47#13997semidirect

Maximal subgroups

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

subgroupindex
C22×#130940032
C2×#156890282
C2×#156890192
C2×C4⋊C4×Dic472
C2×C4×C22⋊Dic472
#202416542
#202416312
#202416252
Dic47⋊#952
C2×C47×#3802
#1399747