Finite Group Databasebeta

← #26379048

Subgroups — #26379048

Order 12032.

2714 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689634C211yesmaximal, characteristic
2#20246532C214yesmaximal, complemented
3#20246367C214yesmaximal, complemented
4#20246319C212yesmaximal, complemented
5#20246313C212yesmaximal, complemented
6C4⋊C4×C22⋊D47C212yesmaximal, complemented
7#20246284C212yesmaximal, complemented
8#20246121C212yesmaximal, complemented
9#20246118C212yesmaximal, complemented
10#20246091C212yesmaximal, complemented
11#20246088C212yesmaximal, complemented
12#20245995C212yesmaximal, complemented
13#20245977C212yesmaximal, complemented
14C2×#15688983C211yesmaximal, characteristic, complemented
15C2×C47×#380C211yesmaximal, characteristic, complemented
16C22×#10625350C2211yescharacteristic
17#15689634C4116yescomplemented
18C2×#13094007C2212yes—
19C2×#13094003C2211yescharacteristic
20C2×#13094003C2211yescharacteristic
21C2×#13093998C2211yescharacteristic
22C2×#13093998C2211yescharacteristic
23C2×#13093993C2212yes—
24C2×C4×C22⋊D47C2214yes—
25C2×C4×C22⋊D47C2212yes—
26C2×C4×C22⋊D47C2212yes—
27C2×(C22⋊D47)⋊C4C2214yes—
28C2×#13093983C2211yescharacteristic
29C2×#13093982C2212yescomplemented
30C22×C4⋊Dic47C2211yescharacteristic
31C22×C4⋊Dic47C2211yescharacteristic
32C2×C4⋊C4×D47C2212yescomplemented
33C22×C22⋊Dic47C2212yes—
34#15689027C2214yescomplemented
35#15689023C2214yes—
36#15689020C2214yescomplemented
37#15689018C2214yescomplemented
38#15689017C2214yes—
39#15689015C2214yescomplemented
40#15689013C2214yescomplemented
41#15689011C2214yes—
42#15689010C2214yescomplemented
43#15689008C2214yescomplemented
44#15689006C2214yescomplemented
45#15689004C2214yescomplemented
46#15689002C2214yes—
47#15689001C2214yescomplemented
48#15689000C2214yes—
49#15688999C2214yes—
50#15688997C2214yescomplemented
51#15688996C2214yes—
52#15688995C2214yes—
53#15688994C2214yescomplemented
54#15688992C2212yescomplemented
55#15688988C2212yescomplemented
56#15688983C2212yes—
57#15688983C2212yes—
58#15688983C2212yes—
59#15688983C2212yes—
60#15688980C2212yescomplemented
61#15688980C2212yescomplemented
62C4⋊C4×Dic47C2212yescomplemented
63C4⋊C4×Dic47C2212yescomplemented
64C22⋊C4×Dic47C2214yes—
65C4×C22⋊Dic47C2214yes—
66C2×C47⋊#95C2212yes—
67C24×C4×C47C2211yescharacteristic
68C22×C4⋊C4×C47C2211yescharacteristic
69C22×C4⋊C4×C47C2211yescharacteristic
70C22×C22⋊C4×C47C2212yes—
71C47×#380C2212yes—
72C47×#380C2212yes—
73C47×#380C2212yes—
74C47×#380C2212yes—
75C2×#95×C47C2212yes—
76C2×#10625350—42no—
77C2×#10625350—42no—
78C2×#10625350C2×C418yescomplemented
79C22×Dic94C2311yescharacteristic
80C22×D188C2311yescharacteristic
81C22×C22⋊D47C2312yes—
82C22×C22⋊D47C2312yes—
83C22×C22⋊D47C2312yes—
84C23×Dic47C2312yes—
85C23×Dic47C2312yes—
86C22×C4×D47C2312yes—
87C22×C4×D47C2314yes—
88#13094007C2×C4116yescomplemented
89#13094003C2×C418yescomplemented
90#13094003C2×C418yescomplemented
91#13093998C2×C418yescomplemented
92#13093998C2×C418yescomplemented
93#13093993C2×C4116yescomplemented
94C4×C22⋊D47—48no—
95C4×C22⋊D47C2×C4116yescomplemented
96C4×C22⋊D47C2×C4116yescomplemented
97(C22⋊D47)⋊C4—48no—
98#13093983C2×C418yescomplemented
99#13093982—44no—
100C2×C4⋊Dic47—42no—
101C2×C4⋊Dic47—42no—
102C2×C4⋊Dic47C2312yes—
103C2×C4⋊Dic47C2312yes—
104C2×C4⋊Dic47C2312yes—
105C2×C4⋊Dic47C2312yes—
106C2×C4⋊Dic47C2311yescharacteristic
107C2×C4⋊Dic47C2311yescharacteristic
108C2×Dic47⋊C4C2314yes—
109C2×Dic47⋊C4C2314yes—
110C2×Dic47⋊C4C2314yes—
111C2×Dic47⋊C4C2312yes—
112C2×Dic47⋊C4C2312yes—
113C4⋊C4×D47—44no—
114C2×C22⋊Dic47—44no—
115C2×C22⋊Dic47C2314yes—
116C2×C22⋊Dic47C2314yes—
117C2×C22⋊Dic47C2312yes—
118C2×C22⋊Dic47C2312yes—
119C2×C22⋊Dic47C2312yes—
120C2×(C2×D47)⋊C4C2314yes—
121C2×(C2×D47)⋊C4C2314yes—
122C2×(C2×D47)⋊C4C2314yes—
123C2×(C2×D47)⋊C4C2312yes—
124C2×(C2×D47)⋊C4C2312yes—
125C2×C4×Dic47C2314yes—
126C2×C4×Dic47C2314yes—
127C2×C4×Dic47C2314yes—
128C2×C4×Dic47C2312yes—
129C47⋊#95C2314yes—
130C47⋊#95C2314yes—
131C47⋊#95C2314yes—
132C47⋊#95C2314yes—
133C47⋊#95C2314yes—
134C47⋊#95C2314yes—
135C47⋊#95C2314yes—
136C47⋊#95C2314yes—
137C25×C47C2311yescharacteristic
138C23×C4×C47—42no—
139C23×C4×C47—42no—
140C23×C4×C47C2×C418yescomplemented
141C23×C4×C47C2311yescharacteristic
142C23×C4×C47C2311yescharacteristic
143C23×C4×C47C2311yescharacteristic
144C23×C4×C47C2312yes—
145C23×C4×C47C2312yes—
146C23×C4×C47C2311yescharacteristic
147C23×C4×C47C2311yescharacteristic
148C23×C4×C47C2311yescharacteristic
149C2×C4⋊C4×C47—42no—
150C2×C4⋊C4×C47—42no—
151C2×C4⋊C4×C47C2312yes—
152C2×C4⋊C4×C47C2312yes—
153C2×C4⋊C4×C47C2312yes—
154C2×C4⋊C4×C47C2312yes—
155C2×C22⋊C4×C47—44no—
156C2×C22⋊C4×C47C2314yes—
157C2×C22⋊C4×C47C2314yes—
158#95×C47C2314yes—
159#95×C47C2314yes—
160C24×C47—22no—
161C24×C47—22no—
162C24×C47—22no—
163C24×C47—22no—
164C24×C47—41no—
165C24×C47—41no—
166C24×C47C22×C414yes—
167C24×C47C2411yescharacteristic
168C24×C47C2411yescharacteristic
169C24×C47C2411yescharacteristic
170C23×D47C2412yes—
171C22×C4×C47—22no—
172C22×C4×C47—22no—
173C22×C4×C47—22no—
174C22×C4×C47—22no—
175C22×C4×C47—22no—
176C22×C4×C47—22no—
177C22×C4×C47—24no—
178C22×C4×C47—24no—
179C22×C4×C47—416no—
180C22×C4×C47—41no—
181C22×C4×C47—41no—
182C22×C4×C47—41no—
183C22×C4×C47—41no—
184C22×C4×C47—41no—
185C22×C4×C47—41no—
186C22×C4×C47—42no—
187C22×C4×C47—42no—
188C22×C4×C47—42no—
189C22×C4×C47—42no—
190C22×C4×C47C22×C414yes—
191C22×C4×C47C22×C414yes—
192C22×C4×C47C22×C414yes—
193C22×C4×C47C22×C414yes—
194C22×C4×C47C22×C414yes—
195C22×C4×C47C22×C414yes—
196C22×C4×C47C2414yes—
197C22×C4×C47C2414yes—
198C22×C4×C47C2411yescharacteristic
199C22×C4×C47C2411yescharacteristic
200C22×C4×C47C2411yescharacteristic
201C22×C4×C47C2411yescharacteristic
202C2×C22⋊D47—24no—
203C2×C22⋊D47—24no—
204C2×C22⋊D47—24no—
205C2×C22⋊D47—24no—
206C2×C22⋊D47—42no—
207C2×C22⋊D47—42no—
208C2×C22⋊D47C22×C418yes—
209C2×C22⋊D47C22×C418yes—
210C2×C22⋊D47C22×C418yes—
211C22×Dic47—24no—
212C22×Dic47—24no—
213C22×Dic47—42no—
214C22×Dic47—42no—
215C22×Dic47—42no—
216C22×Dic47—42no—
217C22×Dic47C2414yes—
218C22×Dic47C2414yes—
219C22×Dic47C2412yes—
220C22×Dic47C2412yes—
221C22×Dic47C2412yes—
222#10625350—416no—
223C2×D188—41no—
224C2×D188—41no—
225C2×D188C22×C414yes—
226C2×C4×D47—24no—
227C2×C4×D47—24no—
228C2×C4×D47—44no—
229C2×C4×D47—44no—
230C2×C4×D47—44no—
231C2×C4×D47C22×C418yes—
232C2×Dic94—41no—
233C2×Dic94—41no—
234C2×Dic94C22×C414yes—
235C4⋊C4×C47—24no—
236C4⋊C4×C47—24no—
237C4⋊C4×C47—42no—
238C4⋊C4×C47—42no—
239C22⋊C4×C47—28no—
240C22⋊C4×C47—44no—
241C22⋊Dic47—28no—
242C22⋊Dic47—44no—
243C22⋊Dic47C22×C418yes—
244C22⋊Dic47C22×C418yes—
245C22⋊Dic47C22×C418yes—
246(C2×D47)⋊C4—44no—
247(C2×D47)⋊C4—44no—
248(C2×D47)⋊C4—44no—
249(C2×D47)⋊C4C22×C418yes—
250(C2×D47)⋊C4C22×C418yes—
251C4⋊Dic47—24no—
252C4⋊Dic47—24no—
253C4⋊Dic47—42no—
254C4⋊Dic47—42no—
255C4⋊Dic47C22×C414yes—
256C4⋊Dic47C22×C414yes—
257Dic47⋊C4—44no—
258Dic47⋊C4—44no—
259Dic47⋊C4—44no—
260Dic47⋊C4C22×C418yes—
261Dic47⋊C4C22×C418yes—
262C4×Dic47—44no—
263C4×Dic47—44no—
264C4×Dic47—44no—
265C4×Dic47C22×C418yes—
266C23×C47—21no—
267C23×C47—21no—
268C23×C47—21no—
269C23×C47—21no—
270C23×C47—21no—
271C23×C47—21no—
272C23×C47—21no—
273C23×C47—21no—
274C23×C47—28no—
275C23×C47—28no—
276C23×C47—21no—
277C23×C47—21no—
278C23×C47—21no—
279C23×C47—21no—
280C23×C47—21no—
281C23×C47—21no—
282C23×C47—44no—
283C23×C47—44no—
284C23×C47—44no—
285C23×C47—44no—
286C23×C47—44no—
287C23×C47C23×C412yes—
288C23×C47C23×C412yes—
289C23×C47C23×C412yes—
290C23×C47H(5,𝔽2)12yes—
291C23×C47H(5,𝔽2)12yes—
292C23×C472−1+412yes—
293C23×C472−1+412yes—
294C23×C47C2511yescharacteristic
295C22×D47—22no—
296C22×D47—22no—
297C22×D47—22no—
298C22×D47—22no—
299C22×D47—22no—
300C22×D47—22no—
301C22×D47C23×C414yes—
302C2×C4×C47—21no—
303C2×C4×C47—21no—
304C2×C4×C47—21no—
305C2×C4×C47—21no—
306C2×C4×C47—21no—
307C2×C4×C47—21no—
308C2×C4×C47—28no—
309C2×C4×C47—28no—
310C2×C4×C47—28no—
311C2×C4×C47—24no—
312C2×C4×C47—24no—
313C2×C4×C47—24no—
314C2×C4×C47—24no—
315C2×C4×C47—24no—
316C2×C4×C47—24no—
317C2×C4×C47—44no—
318C2×C4×C47—44no—
319C2×C4×C47—44no—
320C2×C4×C47—84no—
321C2×C4×C47—84no—
322C2×C4×C47C23×C412yes—
323C2×C4×C47C23×C412yes—
324C2×C4×C47C23×C412yes—
325C2×C4×C47C23×C412yes—
326C2×C4×C47H(5,𝔽2)12yes—
327C2×C4×C47H(5,𝔽2)12yes—
328C22⋊D47—216no—
329C22⋊D47—216no—
330C22⋊D47—48no—
331C2×Dic47—22no—
332C2×Dic47—22no—
333C2×Dic47—22no—
334C2×Dic47—22no—
335C2×Dic47—22no—
336C2×Dic47—22no—
337C2×Dic47—24no—
338C2×Dic47—24no—
339C2×Dic47—24no—
340C2×Dic47—24no—
341C2×Dic47—24no—
342C2×Dic47—24no—
343C2×Dic47—84no—
344C2×Dic47—84no—
345C2×Dic47C23×C414yes—
346C2×Dic47C23×C414yes—
347C2×Dic47C23×C414yes—
348D188—44no—
349C4×D47—216no—
350C4×D47—88no—
351Dic94—44no—
352#34360—471nomaximal, Sylow
353C22×C47—22no—
354C22×C47—22no—
355C22×C47—22no—
356C22×C47—22no—
357C22×C47—22no—
358C22×C47—22no—
359C22×C47—22no—
360C22×C47—22no—
361C22×C47—22no—
362C22×C47—22no—
363C22×C47—22no—
364C22×C47—22no—
365C22×C47—22no—
366C22×C47—22no—
367C22×C47—22no—
368C22×C47—416no—
369C22×C47—41no—
370C22×C47—41no—
371C22×C47—41no—
372C22×C47—41no—
373C22×C47#52014yes—
374C22×C47#52014yes—
375C22×C47C24×C411yescharacteristic
376C22×C47C2×H(5,𝔽2)11yescharacteristic
377C22×C47C2×H(5,𝔽2)11yescharacteristic
378C22×C47C2×H(5,𝔽2)11yescharacteristic
379C22×C47C2×H(5,𝔽2)11yescharacteristic
380C22×C47C2×2−1+411yescharacteristic
381C22×C47C2×2−1+411yescharacteristic
382C2×D47—24no—
383C2×D47—24no—
384C2×D47—24no—
385C2×D47—42no—
386C2×D47—42no—
387C2×D47—42no—
388C2×D47—42no—
389C4×C47—22no—
390C4×C47—22no—
391C4×C47—22no—
392C4×C47—44no—
393C4×C47—44no—
394C4×C47#51814yes—
395Dic47—24no—
396Dic47—24no—
397Dic47—24no—
398Dic47—44no—
399Dic47—44no—
400C2×#525—471no—
401#2376—474no—
402#2358—474no—
403#2352—472no—
404#2352—472no—
405D4×C4⋊C4—472no—
406D4×C4⋊C4—472no—
407#2329—472no—
408#2329—472no—
409#2325—472no—
410#2325—472no—
411#2314—472no—
412#2311—472no—
413C2×#380—471no—
414C2×#380D4711yescharacteristic, complemented
415C2×C47—24no—
416C2×C47—24no—
417C2×C47—42no—
418C2×C47C2×#51811yescharacteristic
419C2×C47C2×#52011yescharacteristic
420C2×C47C2×#52011yescharacteristic
421C2×C47#353611yescharacteristic
422C2×C47#353611yescharacteristic
423C2×C47#353711yescharacteristic
424C2×C47#353811yescharacteristic
425D47—44no—
426C22×#41—471no—
427C24×C4C2×D4711yescharacteristic
428#525—4716no—
429C2×#123—472no—
430C2×C22⋊Q8—471no—
431C2×C22⋊Q8—471no—
432C2×#121—471no—
433C2×#121—471no—
434C2×#120—472no—
435C2×C4×D4—472no—
436C2×C4×D4—472no—
437C2×C4×D4—474no—
438C2×C4×D4—474no—
439C2×#117—471no—
440C2×#117—472no—
441C22×C4⋊C4—471no—
442C22×C4⋊C4—471no—
443C22×C4⋊C4—472no—
444C22×C4⋊C4C2×D4711yescharacteristic
445C22×C4⋊C4C2×D4711yescharacteristic
446C22×C22⋊C4—472no—
447C22×C22⋊C4C2×D4712yes—
448#391—474no—
449#390—474no—
450#389—474no—
451#389—474no—
452#388—474no—
453#388—474no—
454#388—474no—
455#388—474no—
456#387—474no—
457#387—474no—
458#387—474no—
459#387—474no—
460#386—474no—
461#386—474no—
462#386—474no—
463#386—474no—
464#385—474no—
465#385—474no—
466#385—474no—
467#385—474no—
468#384—472no—
469#382—472no—
470#380—472no—
471#380—472no—
472#380—472no—
473#380—472no—
474#380—472no—
475#380—472no—
476#380C2×D4712yes—
477#380C2×D4712yes—
478#380C2×D4712yes—
479#380C2×D4712yes—
480C4×C4⋊C4—472no—
481C4×C4⋊C4—472no—
482C4×C22⋊C4—474no—
483C4×C22⋊C4—474no—
484C2×#95—472no—
485C2×#95C2×D4712yes—
486C47#3436011yescharacteristic, complemented, Sylow
487C25C22×D4711yescharacteristic
488C2×#41—478no—
489C2×#41—1882no—
490C2×#41—1882no—
491C22×Q8—471no—
492C22×D4—472no—
493C22×D4—472no—
494C22×D4—472no—
495C22×D4—471no—
496C23×C4—42no—
497C23×C4—42no—
498C23×C4—472no—
499C23×C4—472no—
500C23×C4—472no—
501C23×C4—474no—
502C23×C4C4×D4718yescomplemented
503C23×C4C22×D4711yescharacteristic
504C23×C4C22×D4711yescharacteristic
505C23×C4C22×D4711yescharacteristic
506C23×C4C22×D4712yes—
507C23×C4C22×D4712yes—
508C23×C4C22×D4711yescharacteristic
509C23×C4C22×D4711yescharacteristic
510C23×C4C22×D4711yescharacteristic
511#123—4716no—
512C22⋊Q8—478no—
513C22⋊Q8—478no—
514#121—478no—
515#121—478no—
516#120—4716no—
517C4×D4—4716no—
518C4×D4—4716no—
519C4×D4—1888no—
520C4×D4—1888no—
521#117—478no—
522#117—1884no—
523C2×C4⋊C4—42no—
524C2×C4⋊C4—42no—
525C2×C4⋊C4—471no—
526C2×C4⋊C4—471no—
527C2×C4⋊C4—472no—
528C2×C4⋊C4—472no—
529C2×C4⋊C4—472no—
530C2×C4⋊C4—472no—
531C2×C4⋊C4—474no—
532C2×C4⋊C4—472no—
533C2×C4⋊C4—472no—
534C2×C4⋊C4—474no—
535C2×C4⋊C4—474no—
536C2×C4⋊C4—1884no—
537C2×C4⋊C4—1882no—
538C2×C4⋊C4—1882no—
539C2×C4⋊C4C22×D4712yes—
540C2×C4⋊C4C22×D4712yes—
541C2×C4⋊C4C22×D4712yes—
542C2×C4⋊C4C22×D4712yes—
543C2×C22⋊C4—44no—
544C2×C22⋊C4—472no—
545C2×C22⋊C4—472no—
546C2×C22⋊C4—472no—
547C2×C22⋊C4—472no—
548C2×C22⋊C4—472no—
549C2×C22⋊C4—474no—
550C2×C22⋊C4—474no—
551C2×C22⋊C4—474no—
552C2×C22⋊C4—474no—
553C2×C22⋊C4—474no—
554C2×C22⋊C4—1884no—
555C2×C22⋊C4C22×D4714yes—
556C2×C22⋊C4C22×D4714yes—
557C2×C42—472no—
558C2×C42—474no—
559C2×C42—474no—
560C2×C42—474no—
561#95—474no—
562#95—474no—
563#95—474no—
564#95—474no—
565#95—474no—
566#95—474no—
567#95—474no—
568#95—474no—
569#95C22×D4714yes—
570#95C22×D4714yes—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—41no—
576C24—41no—
577C24—472no—
578C24C2×C4×D4714yes—
579C24C23×D4711yescharacteristic
580C24C23×D4711yescharacteristic
581C24C23×D4711yescharacteristic
582#41—18816no—
583C2×Q8—474no—
584C2×Q8—1881no—
585C2×Q8—1881no—
586C2×D4—478no—
587C2×D4—478no—
588C2×D4—478no—
589C2×D4—474no—
590C2×D4—944no—
591C2×D4—944no—
592C2×D4—944no—
593C2×D4—944no—
594C2×D4—1881no—
595C2×D4—1881no—
596C2×D4—1882no—
597C2×D4—1882no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—416no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—472no—
618C22×C4—472no—
619C22×C4—472no—
620C22×C4—478no—
621C22×C4—474no—
622C22×C4—474no—
623C22×C4—944no—
624C22×C4—944no—
625C22×C4—944no—
626C22×C4—944no—
627C22×C4—1884no—
628C22×C4—1884no—
629C22×C4—1884no—
630C22×C4—1882no—
631C22×C4—1882no—
632C22×C4—1882no—
633C22×C4—1882no—
634C22×C4C2×C4×D4714yes—
635C22×C4C2×C4×D4714yes—
636C22×C4C2×C4×D4714yes—
637C22×C4C2×C4×D4714yes—
638C22×C4C2×C4×D4714yes—
639C22×C4C2×C4×D4714yes—
640C22×C4C23×D4714yes—
641C22×C4C23×D4714yes—
642C22×C4C23×D4711yescharacteristic
643C22×C4C23×D4711yescharacteristic
644C22×C4C23×D4711yescharacteristic
645C22×C4C23×D4711yescharacteristic
646C4⋊C4—24no—
647C4⋊C4—24no—
648C4⋊C4—42no—
649C4⋊C4—42no—
650C4⋊C4—478no—
651C4⋊C4—478no—
652C4⋊C4—474no—
653C4⋊C4—474no—
654C4⋊C4—944no—
655C4⋊C4—944no—
656C4⋊C4—1884no—
657C4⋊C4—1884no—
658C4⋊C4—1884no—
659C4⋊C4—1882no—
660C4⋊C4—1882no—
661C22⋊C4—28no—
662C22⋊C4—44no—
663C22⋊C4—478no—
664C22⋊C4—478no—
665C22⋊C4—478no—
666C22⋊C4—478no—
667C22⋊C4—478no—
668C22⋊C4—948no—
669C22⋊C4—1884no—
670C22⋊C4—1884no—
671C22⋊C4—1884no—
672C22⋊C4—1884no—
673C42—478no—
674C42—1884no—
675C42—1884no—
676C42—1884no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—28no—
686C23—28no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23—44no—
697C23—44no—
698C23—474no—
699C23—942no—
700C23—942no—
701C23—942no—
702C23—942no—
703C23—942no—
704C23—942no—
705C23C22×C4×D4712yes—
706C23C22×C4×D4712yes—
707C23C22×C4×D4712yes—
708C23#1309406912yes—
709C23#1309407012yes—
710C23#1309407112yes—
711C23#1309407212yes—
712C23C24×D4711yescharacteristic
713Q8—1884no—
714D4—9416no—
715D4—9416no—
716D4—1884no—
717D4—1888no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—28no—
725C2×C4—28no—
726C2×C4—28no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—84no—
737C2×C4—84no—
738C2×C4—474no—
739C2×C4—474no—
740C2×C4—474no—
741C2×C4—942no—
742C2×C4—942no—
743C2×C4—942no—
744C2×C4—942no—
745C2×C4—942no—
746C2×C4—942no—
747C2×C4—9416no—
748C2×C4—944no—
749C2×C4—944no—
750C2×C4—944no—
751C2×C4—944no—
752C2×C4—944no—
753C2×C4—944no—
754C2×C4—3768no—
755C2×C4—3764no—
756C2×C4—3764no—
757C2×C4C22×C4×D4712yes—
758C2×C4C22×C4×D4712yes—
759C2×C4C22×C4×D4712yes—
760C2×C4C22×C4×D4712yes—
761C2×C4#1309406912yes—
762C2×C4#1309406912yes—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—416no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—944no—
784C22—944no—
785C22—944no—
786C22—1882no—
787C22—1882no—
788C22—1882no—
789C22—1882no—
790C22#1568960314yes—
791C22#1568960414yes—
792C22C23×C4×D4711yescharacteristic
793C22C2×#1309406911yescharacteristic
794C22C2×#1309406911yescharacteristic
795C22C2×#1309406911yescharacteristic
796C22C2×#1309407011yescharacteristic
797C22C2×#1309407111yescharacteristic
798C22C2×#1309407211yescharacteristic
799C4—22no—
800C4—22no—
801C4—22no—
802C4—44no—
803C4—44no—
804C4—944no—
805C4—944no—
806C4—944no—
807C4—1884no—
808C4—1884no—
809C4#1568959614yes—
810C2—24no—
811C2—24no—
812C2—42no—
813C2—1884no—
814C2C2×#1568959611yescharacteristic
815C2C2×#1568960311yescharacteristic
816C2C2×#1568960411yescharacteristic
817C2#2025761011yescharacteristic
818C2#2025761711yescharacteristic
819C2#2025762311yescharacteristic
820C2#2025763311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC2×C47×#380C2
socle, cosocleC23×C47C25
prime radicalC2×#15689634C2
hypercenterC2×#380D47
hypocenterC47#34360
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. #20246532C2semidirect
3. #20246367C2semidirect
4. #20246319C2semidirect
5. #20246313C2semidirect
6. C4⋊C4×C22⋊D47C2semidirect
7. #20246284C2semidirect
8. #20246121C2semidirect
9. #20246118C2semidirect
10. #20246091C2semidirect
11. #20246088C2semidirect
12. #20245995C2semidirect
13. #20245977C2semidirect
14. C2×#15688983C2semidirect
15. C2×C47×#380C2semidirect
17. #15689634C4semidirect
29. C2×#13093982C22semidirect
32. C2×C4⋊C4×D47C22semidirect
34. #15689027C22semidirect
36. #15689020C22semidirect
37. #15689018C22semidirect
39. #15689015C22semidirect
40. #15689013C22semidirect
42. #15689010C22semidirect
43. #15689008C22semidirect
44. #15689006C22semidirect
45. #15689004C22semidirect
47. #15689001C22semidirect
50. #15688997C22semidirect
53. #15688994C22semidirect
54. #15688992C22semidirect
55. #15688988C22semidirect
60. #15688980C22semidirect
61. #15688980C22semidirect
62. C4⋊C4×Dic47C22semidirect
63. C4⋊C4×Dic47C22semidirect
78. C2×#10625350C2×C4semidirect
88. #13094007C2×C4semidirect
89. #13094003C2×C4semidirect
90. #13094003C2×C4semidirect
91. #13093998C2×C4semidirect
92. #13093998C2×C4semidirect
93. #13093993C2×C4semidirect
95. C4×C22⋊D47C2×C4semidirect
96. C4×C22⋊D47C2×C4semidirect
98. #13093983C2×C4semidirect
140. C23×C4×C47C2×C4semidirect
414. C2×#380D47semidirect
486. C47#34360semidirect
502. C23×C4C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156896342
#202465322
#202463672
#202463192
#202463132
C4⋊C4×C22⋊D472
#202462842
#202461212
#202461182
#202460912
#202460882
#202459952
#202459772
C2×#156889832
C2×C47×#3802
#3436047