Finite Group Databasebeta

← #26379725

Subgroups — #26379725

Order 12032.

2766 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689687C211yesmaximal, characteristic
2#20246563C212yesmaximal, complemented
3#20246525C212yesmaximal, complemented
4#20246451C212yesmaximal, complemented
5#20246426C212yesmaximal, complemented
6#20246404C212yesmaximal, complemented
7#20246369C212yesmaximal, complemented
8#20246283C212yesmaximal, complemented
9#20246208C212yesmaximal, complemented
10#20246200C214yesmaximal, complemented
11#20246077C212yesmaximal, complemented
12#20246044C214yesmaximal, complemented
13#20245894C212yesmaximal, complemented
14#20245879C211yesmaximal, characteristic, complemented
15C47×#2311C211yesmaximal, characteristic, complemented
16C23×D188C2211yescharacteristic
17#15689687C4116yescomplemented
18C2×#13094020C2212yes—
19C2×#13094013C2212yes—
20C2×#13093998C2212yes—
21C2×#13093998C2212yes—
22C2×#13093992C2212yes—
23C2×#13093992C2212yes—
24C2×#13093986C2212yes—
25C2×#13093986C2212yes—
26C2×C4×C22⋊D47C2214yescomplemented
27C2×(C22⋊D47)⋊C4C2214yescomplemented
28C2×#13093983C2211yescharacteristic
29C2×#13093983C2211yescharacteristic, complemented
30C2×C22⋊C4×D47C2214yes—
31C22×C4×Dic47C2211yescharacteristic, complemented
32#15689030C2212yescomplemented
33#15689026C2212yes—
34#15689024C2212yes—
35#15689024C2212yes—
36#15689023C2214yescomplemented
37#15689023C2214yescomplemented
38#15689019C2212yescomplemented
39#15689019C2212yescomplemented
40#15689015C2214yescomplemented
41#15689014C2214yescomplemented
42#15689013C2214yescomplemented
43#15689012C2214yescomplemented
44#15689011C2214yes—
45#15689011C2214yes—
46#15689003C2211yescharacteristic
47#15689003C2211yescharacteristic
48#15689003C2211yescharacteristic, complemented
49#15689003C2211yescharacteristic, complemented
50#15689002C2214yescomplemented
51#15689001C2214yes—
52#15689001C2214yes—
53#15689000C2214yescomplemented
54#15688999C2214yescomplemented
55#15688999C2214yescomplemented
56#15688997C2214yescomplemented
57#15688994C2214yescomplemented
58#15688990C2214yescomplemented
59#15688978C2214yes—
60C4⋊C4×Dic47C2212yescomplemented
61C4⋊C4×Dic47C2212yescomplemented
62#15688974C2214yescomplemented
63C4×(C2×D47)⋊C4C2214yescomplemented
64C4×C22⋊Dic47C2212yes—
65C4×C22⋊Dic47C2212yescomplemented
66#15688970C2214yescomplemented
67C22×#41×C47C2211yescharacteristic
68C2×#117×C47C2211yescharacteristic, complemented
69C22×C4⋊C4×C47C2211yescharacteristic, complemented
70C47×#391C2212yescomplemented
71C47×#390C2212yes—
72C47×#386C2212yes—
73C47×#386C2212yescomplemented
74C47×#380C2212yes—
75C47×#380C2212yescomplemented
76C24×D47C2312yes—
77C22×D188—42no—
78C22×D188—42no—
79C22×D188C2×C418yescomplemented
80C22×D188C2312yes—
81C22×D188C2312yes—
82C22×C22⋊D47C2314yes—
83C22×C22⋊D47C2314yes—
84C23×Dic47C2311yescharacteristic
85C23×Dic47C2311yescharacteristic
86C22×C4×D47C2314yes—
87C22×C4×D47C2314yes—
88#13094020C2×C4116yescomplemented
89#13094013C2×C4116yescomplemented
90#13093998C2×C4116yescomplemented
91#13093998C2×C4116yescomplemented
92#13093992C2×C4116yescomplemented
93#13093992C2×C4116yescomplemented
94#13093986—44no—
95#13093986—44no—
96C4×C22⋊D47—48no—
97(C22⋊D47)⋊C4—48no—
98#13093983—42no—
99#13093983C2×C418yescomplemented
100C2×C4⋊Dic47C2312yes—
101C2×C4⋊Dic47C2312yes—
102C2×Dic47⋊C4C2314yes—
103C2×Dic47⋊C4C2314yes—
104C2×C22⋊Dic47C2312yes—
105C2×C22⋊Dic47C2312yes—
106C2×C22⋊Dic47C2312yes—
107C2×C22⋊Dic47C2312yes—
108C2×C22⋊Dic47C2311yescharacteristic
109C2×C22⋊Dic47C2311yescharacteristic
110C2×C22⋊Dic47C2312yes—
111C2×(C2×D47)⋊C4C2314yes—
112C2×(C2×D47)⋊C4C2314yes—
113C2×(C2×D47)⋊C4C2314yes—
114C2×(C2×D47)⋊C4C2314yes—
115C2×(C2×D47)⋊C4C2314yes—
116C2×(C2×D47)⋊C4C2314yes—
117C2×(C2×D47)⋊C4C2314yes—
118C2×(C2×D47)⋊C4C2314yes—
119C22⋊C4×D47—48no—
120C2×C4×Dic47—42no—
121C2×C4×Dic47C2312yes—
122C2×C4×Dic47C2312yes—
123C2×C4×Dic47C2312yes—
124C2×C4×Dic47C2314yes—
125C2×C4×Dic47C2314yes—
126C2×C4×Dic47C2312yes—
127C47⋊#95C2314yes—
128C47⋊#95C2312yes—
129C47⋊#95C2312yes—
130C47⋊#95C2312yes—
131C47⋊#95C2312yes—
132C47⋊#95C2314yes—
133C47⋊#95C2314yes—
134C47⋊#95C2314yes—
135C2×#41×C47—42no—
136C2×#41×C47—42no—
137C2×#41×C47C2×C418yescomplemented
138C22×Q8×C47C2311yescharacteristic
139C22×D4×C47C2311yescharacteristic
140C22×D4×C47C2311yescharacteristic
141C22×D4×C47C2311yescharacteristic
142C23×C4×C47C2311yescharacteristic
143C23×C4×C47C2311yescharacteristic
144C23×C4×C47C2311yescharacteristic
145C23×C4×C47C2312yes—
146#117×C47—42no—
147C2×C4⋊C4×C47—42no—
148C2×C4⋊C4×C47C2312yes—
149C2×C4⋊C4×C47C2312yes—
150C2×C4⋊C4×C47C2312yes—
151C2×C22⋊C4×C47C2314yes—
152C2×C22⋊C4×C47C2312yes—
153C2×C22⋊C4×C47C2314yes—
154C2×C42×C47C2312yes—
155#95×C47C2314yes—
156#95×C47C2314yes—
157C24×C47C2411yescharacteristic
158C24×C47C2411yescharacteristic
159C24×C47C2411yescharacteristic
160C23×D47—44no—
161C23×D47—42no—
162C23×D47—42no—
163C23×D47—44no—
164C23×D47C22×C418yes—
165C23×D47C2414yes—
166#41×C47—416no—
167C2×Q8×C47—41no—
168C2×Q8×C47—41no—
169C2×Q8×C47C22×C414yes—
170C2×D4×C47—41no—
171C2×D4×C47—41no—
172C2×D4×C47—41no—
173C2×D4×C47—41no—
174C2×D4×C47—41no—
175C2×D4×C47—41no—
176C2×D4×C47C22×C414yes—
177C2×D4×C47C22×C414yes—
178C2×D4×C47C22×C414yes—
179C22×C4×C47—22no—
180C22×C4×C47—22no—
181C22×C4×C47—22no—
182C22×C4×C47—22no—
183C22×C4×C47—22no—
184C22×C4×C47—22no—
185C22×C4×C47—42no—
186C22×C4×C47—44no—
187C22×C4×C47C22×C414yes—
188C22×C4×C47C22×C414yes—
189C22×C4×C47C22×C414yes—
190C22×C4×C47C2414yes—
191C22×C4×C47C2414yes—
192C22×C4×C47C2411yescharacteristic
193C22×C4×C47C2411yescharacteristic
194C22×C4×C47C2411yescharacteristic
195C22×C4×C47C2411yescharacteristic
196C2×C22⋊D47—44no—
197C2×C22⋊D47—44no—
198C2×C22⋊D47—44no—
199C2×C22⋊D47—44no—
200C2×C22⋊D47C22×C4116yes—
201C2×C22⋊D47C22×C4116yes—
202C22×Dic47—24no—
203C22×Dic47—41no—
204C22×Dic47—41no—
205C22×Dic47—42no—
206C22×Dic47C2412yes—
207C22×Dic47C2412yes—
208C22×Dic47C2412yes—
209C22×Dic47C2414yes—
210C22×Dic47C2412yes—
211C2×D188—24no—
212C2×D188—24no—
213C2×D188—416no—
214C2×D188—42no—
215C2×D188—42no—
216C2×D188C22×C418yes—
217C2×D188C22×C418yes—
218C2×C4×D47—28no—
219C2×C4×D47—44no—
220C2×C4×D47—44no—
221C2×C4×D47—44no—
222C2×C4×D47—44no—
223C2×C4×D47—44no—
224C4⋊C4×C47—24no—
225C4⋊C4×C47—24no—
226C4⋊C4×C47—42no—
227C22⋊C4×C47—42no—
228C22⋊C4×C47—44no—
229C22⋊C4×C47—44no—
230C42×C47—42no—
231C22⋊Dic47—24no—
232C22⋊Dic47—24no—
233C22⋊Dic47—42no—
234C22⋊Dic47—42no—
235C22⋊Dic47—41no—
236C22⋊Dic47—41no—
237C22⋊Dic47C22×C418yes—
238(C2×D47)⋊C4—28no—
239(C2×D47)⋊C4—44no—
240(C2×D47)⋊C4—44no—
241(C2×D47)⋊C4—44no—
242(C2×D47)⋊C4—44no—
243(C2×D47)⋊C4—44no—
244(C2×D47)⋊C4C22×C4116yes—
245(C2×D47)⋊C4C22×C4116yes—
246C4⋊Dic47—42no—
247C4⋊Dic47C22×C418yes—
248Dic47⋊C4—28no—
249Dic47⋊C4—44no—
250C4×Dic47—24no—
251C4×Dic47—24no—
252C4×Dic47—42no—
253C4×Dic47—44no—
254C4×Dic47—44no—
255C4×Dic47C22×C418yes—
256C23×C47—22no—
257C23×C47—22no—
258C23×C47—21no—
259C23×C47—22no—
260C23×C47—21no—
261C23×C47—21no—
262C23×C47—21no—
263C23×C47—21no—
264C23×C47—21no—
265C23×C47—22no—
266C23×C47—22no—
267C23×C47—22no—
268C23×C47C23×C412yes—
269C23×C47C23×C412yes—
270C23×C47C23×C412yes—
271C23×C47C2511yescharacteristic
272C22×D47—24no—
273C22×D47—24no—
274C22×D47—24no—
275C22×D47—24no—
276C22×D47—24no—
277C22×D47—24no—
278C22×D47—48no—
279C22×D47—416no—
280C22×D47—84no—
281C22×D47—84no—
282C22×D47—88no—
283C22×D47C23×C418yes—
284Q8×C47—44no—
285D4×C47—44no—
286D4×C47—44no—
287D4×C47—44no—
288C2×C4×C47—21no—
289C2×C4×C47—21no—
290C2×C4×C47—21no—
291C2×C4×C47—21no—
292C2×C4×C47—21no—
293C2×C4×C47—21no—
294C2×C4×C47—28no—
295C2×C4×C47—28no—
296C2×C4×C47—28no—
297C2×C4×C47—24no—
298C2×C4×C47—24no—
299C2×C4×C47—24no—
300C2×C4×C47—24no—
301C2×C4×C47—24no—
302C2×C4×C47—24no—
303C2×C4×C47—84no—
304C2×C4×C47C23×C412yes—
305C2×C4×C47C23×C412yes—
306C2×C4×C47C23×C412yes—
307C2×C4×C47C23×C412yes—
308C2×C4×C47H(5,𝔽2)12yes—
309C2×C4×C47H(5,𝔽2)12yes—
310C22⋊D47—416no—
311C22⋊D47—416no—
312C2×Dic47—22no—
313C2×Dic47—24no—
314C2×Dic47—22no—
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—22no—
325C2×Dic47—44no—
326C2×Dic47—44no—
327C2×Dic47C23×C418yes—
328C2×Dic47H(5,𝔽2)14yes—
329D188—216no—
330D188—48no—
331C4×D47—88no—
332C4×D47—88no—
333#34411—471nomaximal, Sylow
334C22×C47—22no—
335C22×C47—22no—
336C22×C47—22no—
337C22×C47—24no—
338C22×C47—24no—
339C22×C47—24no—
340C22×C47—41no—
341C22×C47—41no—
342C22×C47—41no—
343C22×C47—41no—
344C22×C47—41no—
345C22×C47—41no—
346C22×C47—42no—
347C22×C47—42no—
348C22×C47—42no—
349C22×C47C24×C411yescharacteristic
350C22×C47C2×H(5,𝔽2)12yes—
351C22×C47C2×H(5,𝔽2)11yescharacteristic
352C22×C47C2×H(5,𝔽2)11yescharacteristic
353C22×C47#58512yes—
354C2×D47—28no—
355C2×D47—28no—
356C2×D47—28no—
357C2×D47—44no—
358C2×D47—44no—
359C2×D47—44no—
360C2×D47—44no—
361C2×D47—816no—
362C4×C47—22no—
363C4×C47—22no—
364C4×C47—22no—
365C4×C47—44no—
366C4×C47—44no—
367C4×C47#51814yes—
368Dic47—28no—
369Dic47—24no—
370Dic47—42no—
371Dic47—42no—
372Dic47—42no—
373C2×#535—471no—
374#2380—472no—
375#2375—472no—
376#2366—472no—
377#2363—472no—
378#2361—472no—
379#2358—472no—
380#2347—472no—
381D4×C22⋊C4—472no—
382#2337—474no—
383#2324—472no—
384#2321—474no—
385#2311D4711yescharacteristic, complemented
386C4×#121—472no—
387#2297—471no—
388C2×C47—42no—
389C2×C47—42no—
390C2×C47—42no—
391C2×C47C2×#51811yescharacteristic
392C2×C47C4×H(5,𝔽2)12yes—
393C2×C47#353711yescharacteristic
394C2×C47#354011yescharacteristic
395C2×C47#354612yes—
396D47—48no—
397C22×#41C2×D4711yescharacteristic
398C23×D4—471no—
399#535—4716no—
400C2×#127—472no—
401C2×#124—472no—
402C2×#121—472no—
403C2×#121—472no—
404C2×#120—472no—
405C2×#120—472no—
406C2×C4×D4—474no—
407C2×C4×D4—472no—
408C2×C4×D4—472no—
409C2×C4×D4—474no—
410C2×#117—471no—
411C2×#117—471no—
412C2×#117C2×D4711yescharacteristic, complemented
413C22×C4⋊C4C2×D4711yescharacteristic, complemented
414C22×C22⋊C4—474no—
415C22×C42—471no—
416#391—472no—
417#391C2×D4712yescomplemented
418#390—472no—
419#390—472no—
420#390—472no—
421#390—474no—
422#390—474no—
423#390C2×D4712yes—
424#389—472no—
425#389—472no—
426#388—474no—
427#388—474no—
428#388—474no—
429#388—474no—
430#388—474no—
431#388—474no—
432#386—471no—
433#386—471no—
434#386—471no—
435#386—471no—
436#386—474no—
437#386—474no—
438#386—474no—
439#386—474no—
440#386—474no—
441#386—474no—
442#386C2×D4712yes—
443#386C2×D4712yescomplemented
444#385—474no—
445#385—474no—
446#383—474no—
447#380C2×D4712yes—
448#380C2×D4712yescomplemented
449#379—474no—
450C4×C4⋊C4—472no—
451C4×C4⋊C4—472no—
452C4×C4⋊C4—474no—
453C4×C22⋊C4—472no—
454C4×C22⋊C4—472no—
455C4×C22⋊C4—474no—
456C4×C22⋊C4—474no—
457C47#3441111yescharacteristic, complemented, Sylow
458C25—472no—
459C2×#41—42no—
460C2×#41—42no—
461C2×#41C4×D4718yescomplemented
462C22×Q8C22×D4711yescharacteristic
463C22×D4—474no—
464C22×D4—474no—
465C22×D4—478no—
466C22×D4—472no—
467C22×D4—472no—
468C22×D4—1882no—
469C22×D4—1882no—
470C22×D4C22×D4711yescharacteristic
471C22×D4C22×D4711yescharacteristic
472C22×D4C22×D4711yescharacteristic
473C23×C4—471no—
474C23×C4—471no—
475C23×C4—474no—
476C23×C4—474no—
477C23×C4C22×D4711yescharacteristic
478C23×C4C22×D4711yescharacteristic
479C23×C4C22×D4711yescharacteristic
480C23×C4C22×D4712yes—
481#127—4716no—
482#124—4716no—
483#121—4716no—
484#121—4716no—
485#120—4716no—
486#120—4716no—
487C4×D4—1884no—
488C4×D4—1884no—
489C4×D4—1888no—
490C4×D4—1888no—
491#117—42no—
492#117—478no—
493#117—1882no—
494C2×C4⋊C4—42no—
495C2×C4⋊C4—472no—
496C2×C4⋊C4—474no—
497C2×C4⋊C4—472no—
498C2×C4⋊C4—474no—
499C2×C4⋊C4C22×D4712yes—
500C2×C4⋊C4C22×D4712yes—
501C2×C4⋊C4C22×D4712yes—
502C2×C22⋊C4—472no—
503C2×C22⋊C4—474no—
504C2×C22⋊C4—474no—
505C2×C22⋊C4—472no—
506C2×C22⋊C4—472no—
507C2×C22⋊C4—474no—
508C2×C22⋊C4—471no—
509C2×C22⋊C4—471no—
510C2×C22⋊C4—472no—
511C2×C22⋊C4—472no—
512C2×C22⋊C4—474no—
513C2×C22⋊C4—474no—
514C2×C22⋊C4—474no—
515C2×C22⋊C4—474no—
516C2×C22⋊C4—474no—
517C2×C22⋊C4—1888no—
518C2×C22⋊C4C22×D4714yes—
519C2×C22⋊C4C22×D4712yes—
520C2×C22⋊C4C22×D4714yes—
521C2×C42—472no—
522C2×C42—472no—
523C2×C42—472no—
524C2×C42—474no—
525C2×C42—474no—
526C2×C42—472no—
527C2×C42—1882no—
528C2×C42C22×D4712yes—
529#95—472no—
530#95—472no—
531#95—472no—
532#95—474no—
533#95—474no—
534#95—472no—
535#95—474no—
536#95—474no—
537#95C22×D4714yes—
538#95C22×D4714yes—
539C24—474no—
540C24—478no—
541C24—1884no—
542C24—1882no—
543C24—1882no—
544C24—1884no—
545C24C23×D4711yescharacteristic
546C24C23×D4711yescharacteristic
547C24C23×D4711yescharacteristic
548#41—416no—
549C2×Q8—41no—
550C2×Q8—41no—
551C2×Q8C2×C4×D4714yes—
552C2×D4—41no—
553C2×D4—41no—
554C2×D4—41no—
555C2×D4—41no—
556C2×D4—41no—
557C2×D4—41no—
558C2×D4—4716no—
559C2×D4—4716no—
560C2×D4—478no—
561C2×D4—478no—
562C2×D4—944no—
563C2×D4—944no—
564C2×D4—18816no—
565C2×D4—1882no—
566C2×D4—1882no—
567C2×D4—1884no—
568C2×D4—1884no—
569C2×D4—1884no—
570C2×D4—1884no—
571C2×D4C2×C4×D4714yes—
572C2×D4C2×C4×D4714yes—
573C2×D4C2×C4×D4714yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—42no—
581C22×C4—44no—
582C22×C4—474no—
583C22×C4—472no—
584C22×C4—472no—
585C22×C4—472no—
586C22×C4—472no—
587C22×C4—948no—
588C22×C4—944no—
589C22×C4—1884no—
590C22×C4—1884no—
591C22×C4—1884no—
592C22×C4—1884no—
593C22×C4—1884no—
594C22×C4—1881no—
595C22×C4—1881no—
596C22×C4—1882no—
597C22×C4C2×C4×D4714yes—
598C22×C4C2×C4×D4714yes—
599C22×C4C2×C4×D4714yes—
600C22×C4C23×D4714yes—
601C22×C4C23×D4714yes—
602C22×C4C23×D4711yescharacteristic
603C22×C4C23×D4711yescharacteristic
604C22×C4C23×D4711yescharacteristic
605C22×C4C23×D4711yescharacteristic
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—42no—
609C4⋊C4—478no—
610C4⋊C4—948no—
611C4⋊C4—1884no—
612C4⋊C4—1882no—
613C22⋊C4—44no—
614C22⋊C4—42no—
615C22⋊C4—44no—
616C22⋊C4—478no—
617C22⋊C4—4716no—
618C22⋊C4—4716no—
619C22⋊C4—948no—
620C22⋊C4—944no—
621C22⋊C4—944no—
622C22⋊C4—1884no—
623C22⋊C4—1884no—
624C22⋊C4—1884no—
625C22⋊C4—1884no—
626C22⋊C4—1884no—
627C22⋊C4—1882no—
628C22⋊C4—1882no—
629C22⋊C4—1881no—
630C22⋊C4—1881no—
631C42—42no—
632C42—478no—
633C42—944no—
634C42—944no—
635C42—1882no—
636C42—1884no—
637C42—1884no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—478no—
651C23—944no—
652C23—944no—
653C23—944no—
654C23—944no—
655C23—944no—
656C23—944no—
657C23—3764no—
658C23—3764no—
659C23—3768no—
660C23—1888no—
661C23—18816no—
662C23C22×C4×D4712yes—
663C23C22×C4×D4712yes—
664C23C22×C4×D4712yes—
665C23C24×D4711yescharacteristic
666Q8—44no—
667D4—44no—
668D4—44no—
669D4—44no—
670D4—9416no—
671D4—1888no—
672D4—18816no—
673D4—18816no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—28no—
681C2×C4—28no—
682C2×C4—28no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—84no—
690C2×C4—478no—
691C2×C4—474no—
692C2×C4—944no—
693C2×C4—942no—
694C2×C4—942no—
695C2×C4—944no—
696C2×C4—942no—
697C2×C4—942no—
698C2×C4—942no—
699C2×C4—942no—
700C2×C4—942no—
701C2×C4—942no—
702C2×C4—942no—
703C2×C4—942no—
704C2×C4—942no—
705C2×C4—3768no—
706C2×C4—3768no—
707C2×C4—1884no—
708C2×C4—1884no—
709C2×C4C22×C4×D4712yes—
710C2×C4C22×C4×D4712yes—
711C2×C4C22×C4×D4712yes—
712C2×C4C22×C4×D4712yes—
713C2×C4#1309406912yes—
714C2×C4#1309406912yes—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—24no—
719C22—24no—
720C22—24no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—948no—
731C22—948no—
732C22—948no—
733C22—37616no—
734C22—1884no—
735C22—1884no—
736C22—1884no—
737C22—1884no—
738C22C23×C4×D4711yescharacteristic
739C22H(5,𝔽2)×D4712yes—
740C22C2×#1309406911yescharacteristic
741C22C2×#1309406911yescharacteristic
742C22#1568996012yes—
743C4—22no—
744C4—22no—
745C4—22no—
746C4—44no—
747C4—44no—
748C4—948no—
749C4—944no—
750C4—1882no—
751C4—1882no—
752C4—1882no—
753C4#1568959614yes—
754C2—42no—
755C2—42no—
756C2—42no—
757C2—1888no—
758C2C2×#1568959611yescharacteristic
759C2#2025659412yes—
760C2#2025762111yescharacteristic
761C2#2025766511yescharacteristic
762C2#2025775012yes—
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC47×#2311C2
socle, cosocleC23×C47C25
prime radicalC2×#15689687C2
hypercenter#2311D47
hypocenterC47#34411
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2311

Complements

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

NH ≅ G/Ntype
2. #20246563C2semidirect
3. #20246525C2semidirect
4. #20246451C2semidirect
5. #20246426C2semidirect
6. #20246404C2semidirect
7. #20246369C2semidirect
8. #20246283C2semidirect
9. #20246208C2semidirect
10. #20246200C2semidirect
11. #20246077C2semidirect
12. #20246044C2semidirect
13. #20245894C2semidirect
14. #20245879C2semidirect
15. C47×#2311C2semidirect
17. #15689687C4semidirect
26. C2×C4×C22⋊D47C22semidirect
27. C2×(C22⋊D47)⋊C4C22semidirect
29. C2×#13093983C22semidirect
31. C22×C4×Dic47C22semidirect
32. #15689030C22semidirect
36. #15689023C22semidirect
37. #15689023C22semidirect
38. #15689019C22semidirect
39. #15689019C22semidirect
40. #15689015C22semidirect
41. #15689014C22semidirect
42. #15689013C22semidirect
43. #15689012C22semidirect
48. #15689003C22semidirect
49. #15689003C22semidirect
50. #15689002C22semidirect
53. #15689000C22semidirect
54. #15688999C22semidirect
55. #15688999C22semidirect
56. #15688997C22semidirect
57. #15688994C22semidirect
58. #15688990C22semidirect
60. C4⋊C4×Dic47C22semidirect
61. C4⋊C4×Dic47C22semidirect
62. #15688974C22semidirect
63. C4×(C2×D47)⋊C4C22semidirect
65. C4×C22⋊Dic47C22semidirect
66. #15688970C22semidirect
68. C2×#117×C47C22semidirect
69. C22×C4⋊C4×C47C22semidirect
70. C47×#391C22semidirect
73. C47×#386C22semidirect
75. C47×#380C22semidirect
79. C22×D188C2×C4semidirect
88. #13094020C2×C4semidirect
89. #13094013C2×C4semidirect
90. #13093998C2×C4semidirect
91. #13093998C2×C4semidirect
92. #13093992C2×C4semidirect
93. #13093992C2×C4semidirect
99. #13093983C2×C4semidirect
137. C2×#41×C47C2×C4semidirect
385. #2311D47semidirect
412. C2×#117C2×D47semidirect
413. C22×C4⋊C4C2×D47semidirect
417. #391C2×D47semidirect
443. #386C2×D47semidirect
448. #380C2×D47semidirect
457. C47#34411semidirect
461. C2×#41C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156896872
#202465632
#202465252
#202464512
#202464262
#202464042
#202463692
#202462832
#202462082
#202462002
#202460772
#202460442
#202458942
#202458792
C47×#23112
#3441147