Finite Group Databasebeta

← #26139406

Subgroups — #26139406

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×#13094004C211yesmaximal, characteristic
2C2×#15689029C211yesmaximal, characteristic, complemented
3C2×#15689028C211yesmaximal, characteristic, complemented
4C2×#15689022C211yesmaximal, characteristic, complemented
5C2×#15688980C211yesmaximal, characteristic
6C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic
7#20241655C212yesmaximal, complemented
8#20241634C212yesmaximal
9#20241626C212yesmaximal
10#20241618C212yesmaximal, complemented
11C2×C4×C4⋊C4×C47C211yesmaximal, characteristic, complemented
12C23×Dic94C2211yescharacteristic
13C23×C4×D47C2211yescharacteristic
14C2×#13094004—24no—
15C2×#13094004—24no—
16C2×#13094004C418yescomplemented
17C22×C4⋊Dic47C2211yescharacteristic
18C22×C4⋊Dic47C2212yes—
19C22×C4⋊Dic47C2212yes—
20C22×(C2×D47)⋊C4C2211yescharacteristic
21C22×(C2×D47)⋊C4C2212yes—
22C22×(C2×D47)⋊C4C2212yes—
23C22×(C2×D47)⋊C4C2211yescharacteristic
24C22×C4×Dic47C2211yescharacteristic
25#15689029—24no—
26#15689028—24no—
27#15689022—24no—
28#15688980—24no—
29C4×(C2×D47)⋊C4—24no—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2212yes—
35C2×C47⋊#95C2211yescharacteristic
36C2×C47⋊#95C2212yes—
37C2×C47⋊#95C2211yescharacteristic
38C22×C4⋊C4×C47C2211yescharacteristic
39C22×C4⋊C4×C47C2211yescharacteristic
40C22×C42×C47C2212yes—
41C22×C42×C47C2211yescharacteristic
42C4×C4⋊C4×C47—24no—
43C2×#95×C47C2212yes—
44C24×D47C2311yescharacteristic
45C22×Dic94—22no—
46C22×Dic94—22no—
47C22×Dic94—22no—
48C22×Dic94—22no—
49C22×Dic94—22no—
50C22×Dic94—22no—
51C22×Dic94C2×C414yes—
52C23×Dic47C2312yes—
53C23×Dic47C2312yes—
54C23×Dic47C2311yescharacteristic
55C23×Dic47C2311yescharacteristic
56C23×Dic47C2311yescharacteristic
57C22×C4×D47—22no—
58C22×C4×D47—22no—
59C22×C4×D47—22no—
60C22×C4×D47—22no—
61C22×C4×D47—22no—
62C22×C4×D47—22no—
63C22×C4×D47C2×C414yes—
64#13094004—232no—
65C2×C4⋊Dic47—24no—
66C2×C4⋊Dic47—24no—
67C2×C4⋊Dic47—22no—
68C2×C4⋊Dic47—24no—
69C2×C4⋊Dic47—22no—
70C2×C4⋊Dic47—22no—
71C2×C4⋊Dic47—24no—
72C2×C4⋊Dic47—42no—
73C2×C4⋊Dic47C2×C418yes—
74C2×(C2×D47)⋊C4—22no—
75C2×(C2×D47)⋊C4—22no—
76C2×(C2×D47)⋊C4—22no—
77C2×(C2×D47)⋊C4—24no—
78C2×(C2×D47)⋊C4—24no—
79C2×(C2×D47)⋊C4—22no—
80C2×(C2×D47)⋊C4—22no—
81C2×(C2×D47)⋊C4—24no—
82C2×(C2×D47)⋊C4—24no—
83C2×(C2×D47)⋊C4—42no—
84C2×(C2×D47)⋊C4C2×C418yes—
85C2×(C2×D47)⋊C4Q814yescomplemented
86C2×C4×Dic47—22no—
87C2×C4×Dic47—22no—
88C2×C4×Dic47—22no—
89C47⋊#95—22no—
90C47⋊#95—22no—
91C47⋊#95—24no—
92C47⋊#95—24no—
93C47⋊#95—24no—
94C47⋊#95—24no—
95C47⋊#95—24no—
96C47⋊#95—24no—
97C23×C4×C47C2312yes—
98C23×C4×C47C2311yescharacteristic
99C23×C4×C47C2312yes—
100C23×C4×C47C2311yescharacteristic
101C23×C4×C47C2311yescharacteristic
102C2×C4⋊C4×C47—22no—
103C2×C4⋊C4×C47—22no—
104C2×C4⋊C4×C47C2×C414yes—
105C2×C4⋊C4×C47D414yes—
106C2×C4⋊C4×C47D414yes—
107C2×C4⋊C4×C47D414yes—
108C2×C42×C47—22no—
109C2×C42×C47—22no—
110C2×C42×C47—24no—
111C2×C42×C47—24no—
112C2×C42×C47—42no—
113C2×C42×C47D414yes—
114#95×C47—24no—
115C24×C47C2411yescharacteristic
116C23×D47—21no—
117C23×D47—21no—
118C23×D47—21no—
119C23×D47—21no—
120C23×D47—21no—
121C23×D47—21no—
122C23×D47—21no—
123C23×D47—21no—
124C23×D47—21no—
125C23×D47—21no—
126C23×D47—21no—
127C23×D47—21no—
128C23×D47C22×C412yes—
129C23×D47C2×Q812yes—
130C23×D47#4112yes—
131C22×C4×C47—21no—
132C22×C4×C47—22no—
133C22×C4×C47—21no—
134C22×C4×C47—22no—
135C22×C4×C47—21no—
136C22×C4×C47—22no—
137C22×C4×C47—22no—
138C22×C4×C47—21no—
139C22×C4×C47—22no—
140C22×C4×C47—21no—
141C22×C4×C47—21no—
142C22×C4×C47—22no—
143C22×C4×C47—22no—
144C22×C4×C47—21no—
145C22×C4×C47—21no—
146C22×C4×C47—22no—
147C22×C4×C47—22no—
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47—22no—
151C22×C4×C47C22×C414yes—
152C22×C4×C47C22×C412yes—
153C22×C4×C47C2×D412yes—
154C22×C4×C47C2×D414yes—
155C22×C4×C47C2×D414yes—
156C22×C4×C47C2×D414yes—
157C22×C4×C47C2×D412yes—
158C22×C4×C47C2×D412yes—
159C22×C4×C47C2×D412yes—
160C22×C4×C47C2×D412yes—
161C22×C4×C47C2×D412yes—
162C22×C4×C47C2×Q812yes—
163C22×C4×C47#4112yes—
164C22×C4×C47#4112yes—
165C22×C4×C47#4112yes—
166C22×Dic47—21no—
167C22×Dic47—21no—
168C22×Dic47—21no—
169C22×Dic47—21no—
170C22×Dic47—21no—
171C22×Dic47—22no—
172C22×Dic47—22no—
173C22×Dic47—21no—
174C22×Dic47—21no—
175C22×Dic47—21no—
176C22×Dic47—22no—
177C22×Dic47—22no—
178C22×Dic47—21no—
179C22×Dic47—21no—
180C22×Dic47—21no—
181C22×Dic47—21no—
182C22×Dic47—21no—
183C22×Dic47—21no—
184C22×Dic47—22no—
185C22×Dic47—22no—
186C22×Dic47—21no—
187C22×Dic47—21no—
188C22×Dic47—21no—
189C22×Dic47—21no—
190C22×Dic47—22no—
191C22×Dic47—22no—
192C22×Dic47—22no—
193C22×Dic47—22no—
194C22×Dic47—22no—
195C22×Dic47—22no—
196C22×Dic47—22no—
197C22×Dic47C22×C414yes—
198C22×Dic47C22×C412yes—
199C22×Dic47C2×Q812yes—
200C22×Dic47#4112yes—
201C2×C4×D47—28no—
202C2×C4×D47—28no—
203C2×C4×D47—28no—
204C2×C4×D47—44no—
205C2×C4×D47—44no—
206C2×C4×D47—44no—
207C2×C4×D47—44no—
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×C47C22⋊C4116yescomplemented
217C42×C47—28no—
218C42×C47—48no—
219(C2×D47)⋊C4—28no—
220(C2×D47)⋊C4—216no—
221(C2×D47)⋊C4—28no—
222(C2×D47)⋊C4—48no—
223C4⋊Dic47—216no—
224C4⋊Dic47—48no—
225C4⋊Dic47—44no—
226C4×Dic47—44no—
227C23×C47C23×C411yescharacteristic
228C23×C47C22×D411yescharacteristic
229C23×C47C22×D411yescharacteristic
230C23×C47C22×D411yescharacteristic
231C23×C47C22×D411yescharacteristic
232C23×C47C22×Q811yescharacteristic
233C23×C47C2×#4111yescharacteristic
234C23×C47C2×#4111yescharacteristic
235C23×C47C2×#4111yescharacteristic
236C23×C47C2×#4111yescharacteristic
237C23×C47C2×#4111yescharacteristic
238C23×C47H(5,𝔽2)11yescharacteristic
239C23×C472−1+411yescharacteristic
240C23×C472−1+411yescharacteristic
241C23×C472−1+411yescharacteristic
242C22×D47—22no—
243C22×D47—22no—
244C22×D47—22no—
245C22×D47—22no—
246C22×D47—22no—
247C22×D47—22no—
248C22×D47—22no—
249C22×D47—22no—
250C22×D47—22no—
251C22×D47—22no—
252C22×D47—22no—
253C22×D47—22no—
254C22×D47—22no—
255C22×D47—22no—
256C22×D47—22no—
257C22×D47—22no—
258C22×D47—22no—
259C22×D47—22no—
260C22×D47—41no—
261C22×D47—41no—
262C22×D47—41no—
263C22×D47—41no—
264C22×D47—41no—
265C22×D47—41no—
266C22×D47—41no—
267C22×D47—41no—
268C22×D47—41no—
269C22×D47—41no—
270C22×D47—41no—
271C22×D47—41no—
272C22×D47—41no—
273C22×D47—41no—
274C22×D47—41no—
275C22×D47—41no—
276C22×D47C4×Q814yes—
277C2×C4×C47—24no—
278C2×C4×C47—24no—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—24no—
282C2×C4×C47—22no—
283C2×C4×C47—24no—
284C2×C4×C47—24no—
285C2×C4×C47—24no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—24no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—24no—
294C2×C4×C47—24no—
295C2×C4×C47—42no—
296C2×C4×C47—42no—
297C2×C4×C47—42no—
298C2×C4×C47—41no—
299C2×C4×C47—41no—
300C2×C4×C47—42no—
301C2×C4×C47—41no—
302C2×C4×C47—41no—
303C2×C4×C47C2×C22⋊C418yes—
304C2×C4×C47C2×C22⋊C414yes—
305C2×C4×C47C4×D414yes—
306C2×C4×C47C4×D414yes—
307C2×C4×C47#12114yes—
308C2×C4×C47#12114yes—
309C2×C4×C47C22⋊Q814yescomplemented
310C2×C4×C47#12414yes—
311C2×C4×C47#12714yes—
312C2×Dic47—22no—
313C2×Dic47—24no—
314C2×Dic47—24no—
315C2×Dic47—24no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—22no—
321C2×Dic47—22no—
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—42no—
325C2×Dic47—42no—
326C2×Dic47—41no—
327C2×Dic47—41no—
328C2×Dic47—42no—
329C2×Dic47—41no—
330C2×Dic47—41no—
331C2×Dic47—41no—
332C2×Dic47—42no—
333C2×Dic47—41no—
334C2×Dic47—41no—
335C2×Dic47—41no—
336C2×Dic47—41no—
337C2×Dic47—41no—
338C2×Dic47—41no—
339C2×Dic47—41no—
340C2×Dic47—42no—
341C2×Dic47—42no—
342C2×Dic47—42no—
343C2×Dic47—42no—
344C2×Dic47—42no—
345C2×Dic47—42no—
346C2×Dic47—42no—
347C4×D47—416no—
348Dic94—416no—
349#13997—471nomaximal, Sylow
350C22×C47C22×C22⋊C411yescharacteristic
351C22×C47C2×C4×D411yescharacteristic
352C22×C47C2×C4×D411yescharacteristic
353C22×C47C2×C4×Q811yescharacteristic
354C22×C47C4×#4111yescharacteristic
355C22×C47#51911yescharacteristic
356C22×C47#52011yescharacteristic
357C22×C47C2×#12111yescharacteristic
358C22×C47C2×#12111yescharacteristic
359C22×C47C2×C22⋊Q811yescharacteristic
360C22×C47#52511yescharacteristic
361C22×C47C2×#12411yescharacteristic
362C22×C47#52911yescharacteristic
363C22×C47C2×#12711yescharacteristic
364C22×C47#53311yescharacteristic
365C22×C47#53611yescharacteristic
366C22×C47#53711yescharacteristic
367C22×C47#54111yescharacteristic
368C22×C47#54211yescharacteristic
369C22×C47#54611yescharacteristic
370C22×C47#54611yescharacteristic
371C22×C47#54611yescharacteristic
372C22×C47#54711yescharacteristic
373C22×C47#54711yescharacteristic
374C22×C47#54711yescharacteristic
375C22×C47#54811yescharacteristic
376C22×C47#54811yescharacteristic
377C22×C47#54811yescharacteristic
378C22×C47D4×Q811yescharacteristic
379C22×C47D4×Q811yescharacteristic
380C22×C47D4×Q811yescharacteristic
381C22×C47#55211yescharacteristic
382C22×C47#55211yescharacteristic
383C22×C47#55411yescharacteristic
384C22×C47#55611yescharacteristic
385C2×D47—24no—
386C2×D47—24no—
387C2×D47—24no—
388C2×D47—42no—
389C2×D47—42no—
390C2×D47—42no—
391C2×D47—42no—
392C2×D47—42no—
393C2×D47—42no—
394C2×D47—42no—
395C2×D47—42no—
396C2×D47—42no—
397C2×D47—42no—
398C2×D47—42no—
399C2×D47—42no—
400C4×C47—28no—
401C4×C47—24no—
402C4×C47—42no—
403C4×C47—44no—
404C4×C47#39018yes—
405Dic47—42no—
406Dic47—42no—
407Dic47—44no—
408Dic47—42no—
409Dic47—82no—
410C22×C22⋊Q8—471no—
411C2×#391—471no—
412C2×#391—471no—
413C2×#389—471no—
414C2×#380—471no—
415C2×C4×C4⋊C4D4711yescharacteristic, complemented
416C2×C4×C22⋊C4—471no—
417#1445—472no—
418#1439—472no—
419#1437—472no—
420C4⋊#95—472no—
421C2×C47C2×#39011yescharacteristic
422C2×C47C4×C22⋊Q811yescharacteristic
423C2×C47#232311yescharacteristic
424C2×C47#233911yescharacteristic
425C2×C47Q8×C22⋊C411yescharacteristic
426C2×C47#236011yescharacteristic
427C2×C47#236211yescharacteristic
428C2×C47#241511yescharacteristic
429C2×C47#241711yescharacteristic
430C2×C47#242711yescharacteristic
431C2×C47#242911yescharacteristic
432C2×C47#248911yescharacteristic
433C2×C47#249211yescharacteristic
434C2×C47#254011yescharacteristic
435C2×C47#254211yescharacteristic
436D47—44no—
437C23×Q8—471no—
438C24×C4—471no—
439C2×C22⋊Q8—478no—
440C2×C22⋊Q8—944no—
441C2×C22⋊Q8—944no—
442C22×C4⋊C4—472no—
443C22×C4⋊C4—471no—
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⋊C4—472no—
451C22×C42—471no—
452C22×C42C2×D4712yes—
453C22×C42C2×D4711yescharacteristic
454#391—944no—
455#391—944no—
456#389—944no—
457#380—944no—
458C4×C4⋊C4—24no—
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
470C25—471no—
471C22×Q8—474no—
472C22×Q8—942no—
473C22×Q8—942no—
474C22×Q8—942no—
475C22×Q8—942no—
476C22×Q8—942no—
477C22×Q8—942no—
478C23×C4—471no—
479C23×C4—472no—
480C23×C4—471no—
481C23×C4—471no—
482C23×C4—474no—
483C23×C4—472no—
484C23×C4—942no—
485C23×C4—942no—
486C23×C4—942no—
487C23×C4—942no—
488C23×C4—942no—
489C23×C4—942no—
490C23×C4C22×D4712yes—
491C23×C4C22×D4711yescharacteristic
492C23×C4C22×D4712yes—
493C23×C4C22×D4711yescharacteristic
494C23×C4C22×D4711yescharacteristic
495C22⋊Q8—9432no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—478no—
499C2×C4⋊C4—944no—
500C2×C4⋊C4—944no—
501C2×C4⋊C4—944no—
502C2×C4⋊C4—942no—
503C2×C4⋊C4—944no—
504C2×C4⋊C4—942no—
505C2×C4⋊C4—942no—
506C2×C4⋊C4—1882no—
507C2×C4⋊C4C4×D4714yes—
508C2×C4⋊C4D18814yes—
509C2×C4⋊C4D18814yes—
510C2×C4⋊C4C22⋊D4714yes—
511C2×C22⋊C4—478no—
512C2×C22⋊C4—474no—
513C2×C22⋊C4—942no—
514C2×C22⋊C4—942no—
515C2×C22⋊C4—944no—
516C2×C22⋊C4—942no—
517C2×C22⋊C4—942no—
518C2×C22⋊C4—942no—
519C2×C22⋊C4—944no—
520C2×C22⋊C4—944no—
521C2×C22⋊C4—944no—
522C2×C22⋊C4—1882no—
523C2×C42—22no—
524C2×C42—22no—
525C2×C42—24no—
526C2×C42—24no—
527C2×C42—42no—
528C2×C42—942no—
529C2×C42—942no—
530C2×C42—942no—
531C2×C42D18814yes—
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—472no—
542C24—472no—
543C24—472no—
544C24—941no—
545C24—941no—
546C24—941no—
547C24—941no—
548C24—941no—
549C24—941no—
550C24—941no—
551C24—941no—
552C24—941no—
553C24—941no—
554C24—941no—
555C24—941no—
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—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—474no—
585C22×C4—472no—
586C22×C4—472no—
587C22×C4—472no—
588C22×C4—942no—
589C22×C4—941no—
590C22×C4—941no—
591C22×C4—941no—
592C22×C4—941no—
593C22×C4—941no—
594C22×C4—941no—
595C22×C4—942no—
596C22×C4—942no—
597C22×C4—941no—
598C22×C4—941no—
599C22×C4—941no—
600C22×C4—942no—
601C22×C4—941no—
602C22×C4—941no—
603C22×C4—941no—
604C22×C4—941no—
605C22×C4—941no—
606C22×C4—942no—
607C22×C4—942no—
608C22×C4—941no—
609C22×C4—941no—
610C22×C4—941no—
611C22×C4—941no—
612C22×C4—948no—
613C22×C4—948no—
614C22×C4—948no—
615C22×C4—942no—
616C22×C4—942no—
617C22×C4—942no—
618C22×C4—942no—
619C22×C4—942no—
620C22×C4—942no—
621C22×C4—942no—
622C22×C4—1884no—
623C22×C4—1884no—
624C22×C4—1884no—
625C22×C4—1884no—
626C22×C4C2×C4×D4714yes—
627C22×C4C2×C4×D4712yes—
628C22×C4C2×D18812yes—
629C22×C4C2×D18814yes—
630C22×C4C2×D18814yes—
631C22×C4C2×D18812yes—
632C22×C4C2×D18812yes—
633C22×C4C2×D18812yes—
634C22×C4C2×D18812yes—
635C22×C4#1062535012yes—
636C22×C4#1062535012yes—
637C22×C4#1062535212yes—
638C22×C4Q8×D4712yes—
639C22×C4C2×C22⋊D4714yes—
640C22×C4C2×C22⋊D4712yes—
641C4⋊C4—28no—
642C4⋊C4—9416no—
643C4⋊C4—1888no—
644C4⋊C4—1884no—
645C4⋊C4(C2×D47)⋊C4116yescomplemented
646C22⋊C4—948no—
647C22⋊C4—9416no—
648C22⋊C4—948no—
649C22⋊C4—1888no—
650C42—28no—
651C42—48no—
652C42—1884no—
653C23—474no—
654C23—942no—
655C23—942no—
656C23—942no—
657C23—942no—
658C23—942no—
659C23—942no—
660C23—942no—
661C23—942no—
662C23—942no—
663C23—942no—
664C23—942no—
665C23—942no—
666C23—942no—
667C23—942no—
668C23—942no—
669C23—942no—
670C23—942no—
671C23—942no—
672C23—1881no—
673C23—1881no—
674C23—1881no—
675C23—1881no—
676C23—1881no—
677C23—1881no—
678C23—1881no—
679C23—1881no—
680C23—1881no—
681C23—1881no—
682C23—1881no—
683C23—1881no—
684C23—1881no—
685C23—1881no—
686C23—1881no—
687C23—1881no—
688C23C22×C4×D4711yescharacteristic
689C23C22×C22⋊D4711yescharacteristic
690C23C22×D18811yescharacteristic
691C23C22×D18811yescharacteristic
692C23C22×D18811yescharacteristic
693C23C2×Q8×D4711yescharacteristic
694C23#41×D4711yescharacteristic
695C23#41×D4711yescharacteristic
696C23C2×#1062535211yescharacteristic
697C23C2×#1062535011yescharacteristic
698C23C2×#1062535011yescharacteristic
699C23#1309406911yescharacteristic
700C23#1309407111yescharacteristic
701C23#1309407111yescharacteristic
702C23#1309407211yescharacteristic
703Q8—18816no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—942no—
731C2×C4—942no—
732C2×C4—942no—
733C2×C4—942no—
734C2×C4—944no—
735C2×C4—942no—
736C2×C4—942no—
737C2×C4—942no—
738C2×C4—944no—
739C2×C4—944no—
740C2×C4—942no—
741C2×C4—942no—
742C2×C4—1882no—
743C2×C4—1882no—
744C2×C4—1882no—
745C2×C4—1882no—
746C2×C4—1882no—
747C2×C4—1882no—
748C2×C4—1882no—
749C2×C4—1881no—
750C2×C4—1881no—
751C2×C4—1881no—
752C2×C4—1881no—
753C2×C4—1881no—
754C2×C4—1881no—
755C2×C4—1882no—
756C2×C4—1882no—
757C2×C4—1881no—
758C2×C4—1882no—
759C2×C4—1881no—
760C2×C4—1881no—
761C2×C4—1881no—
762C2×C4—1882no—
763C2×C4—1881no—
764C2×C4—1881no—
765C2×C4—18816no—
766C2×C4C2×(C2×D47)⋊C418yes—
767C2×C4C2×(C2×D47)⋊C414yes—
768C2×C4C4×D18814yes—
769C2×C4C4×D18814yes—
770C2×C4#1309399814yes—
771C2×C4#1309399814yes—
772C2×C4#1309400414yescomplemented
773C2×C4#1309401214yes—
774C2×C4#1309402114yes—
775C22—944no—
776C22—944no—
777C22—944no—
778C22—1882no—
779C22—1882no—
780C22—1882no—
781C22—1882no—
782C22—1882no—
783C22—1882no—
784C22—1882no—
785C22—1882no—
786C22—1882no—
787C22—1882no—
788C22—1882no—
789C22—1882no—
790C22C22×(C2×D47)⋊C411yescharacteristic
791C22C2×C4×D18811yescharacteristic
792C22C2×C4×D18811yescharacteristic
793C22C4×Q8×D4711yescharacteristic
794C22C4×#1062535211yescharacteristic
795C22#1568959911yescharacteristic
796C22#1568960211yescharacteristic
797C22C2×#1309399811yescharacteristic
798C22C2×#1309399811yescharacteristic
799C22C2×#1309400411yescharacteristic
800C22#1568963511yescharacteristic
801C22C2×#1309401211yescharacteristic
802C22#1568965511yescharacteristic
803C22C2×#1309402111yescharacteristic
804C22#1568967711yescharacteristic
805C22#1568969911yescharacteristic
806C22#1568970411yescharacteristic
807C22#1568973111yescharacteristic
808C22#1568973811yescharacteristic
809C22#1568976711yescharacteristic
810C22#1568976811yescharacteristic
811C22#1568976811yescharacteristic
812C22#1568977211yescharacteristic
813C22#1568977711yescharacteristic
814C22#1568977711yescharacteristic
815C22#1568978011yescharacteristic
816C22#1568978511yescharacteristic
817C22#1568978511yescharacteristic
818C22Q8×C22⋊D4711yescharacteristic
819C22Q8×D18811yescharacteristic
820C22Q8×D18811yescharacteristic
821C22#1568980811yescharacteristic
822C22#1568981211yescharacteristic
823C22#1568982811yescharacteristic
824C22#1568984111yescharacteristic
825C4—24no—
826C4—28no—
827C4—42no—
828C4—44no—
829C4—3762no—
830C4—1882no—
831C4—1882no—
832C4—1882no—
833C4—1884no—
834C4#1568902518yes—
835C2—1884no—
836C2C2×#1568902511yescharacteristic
837C2C4×#1309400411yescharacteristic
838C2#2024607111yescharacteristic
839C2#2024621311yescharacteristic
840C2Q8×(C2×D47)⋊C411yescharacteristic
841C2#2024639511yescharacteristic
842C2#2024641711yescharacteristic
843C2#2024681111yescharacteristic
844C2#2024683311yescharacteristic
845C2#2024695911yescharacteristic
846C2#2024698111yescharacteristic
847C2#2024772311yescharacteristic
848C2#2024775611yescharacteristic
849C2#2024832211yescharacteristic
850C2#2024833711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C4×C4⋊C4×C47C2
socle, cosocleC24×C47C24
prime radicalC24×D47C23
hypercenterC2×C4×C4⋊C4D47
hypocenterC47#13997
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#15689029C2semidirect
3. C2×#15689028C2semidirect
4. C2×#15689022C2semidirect
7. #20241655C2semidirect
10. #20241618C2semidirect
11. C2×C4×C4⋊C4×C47C2semidirect
16. C2×#13094004C4semidirect
85. C2×(C2×D47)⋊C4Q8semidirect
216. C4⋊C4×C47C22⋊C4semidirect
309. C2×C4×C47C22⋊Q8semidirect
415. C2×C4×C4⋊C4D47semidirect
469. C47#13997semidirect
645. C4⋊C4(C2×D47)⋊C4semidirect
772. C2×C4#13094004semidirect

Maximal subgroups

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

subgroupindex
C22×#130940042
C2×#156890292
C2×#156890282
C2×#156890222
C2×#156889802
C2×C4×(C2×D47)⋊C42
#202416552
#202416342
#202416262
#202416182
C2×C4×C4⋊C4×C472
#1399747