Finite Group Databasebeta

← #26379208

Subgroups — #26379208

Order 12032.

2630 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20246536C214yesmaximal, complemented
2#20246384C214yesmaximal, complemented
3#20246265C212yesmaximal, complemented
4#20246237C212yesmaximal, complemented
5#20246237C212yesmaximal, complemented
6D4×C22⋊Dic47C212yesmaximal
7#20246182C214yesmaximal, complemented
8#20246060C214yesmaximal, complemented
9#20246006C211yesmaximal, characteristic, complemented
10#20246002C211yesmaximal, characteristic, complemented
11#20245991C211yesmaximal, characteristic, complemented
12#20245986C211yesmaximal, characteristic, complemented
13#20245771C211yesmaximal, characteristic, complemented
14C2×#15688983C211yesmaximal, characteristic, complemented
15C22×#123×C47C211yesmaximal, characteristic
16C2×D4×Dic47C2214yes—
17C2×#13093983C2212yes—
18C2×#13093983C2212yescomplemented
19C22×C4⋊Dic47C2212yescomplemented
20C22×C22⋊Dic47C2212yes—
21C22×C22⋊Dic47C2212yes—
22#15689026C2214yes—
23#15689022C2214yescomplemented
24#15689022C2214yescomplemented
25#15689022C2214yescomplemented
26#15689016C2214yescomplemented
27#15689016C2214yescomplemented
28#15689016C2214yescomplemented
29#15689016C2214yescomplemented
30#15689016C2214yescomplemented
31#15689016C2214yescomplemented
32#15689009C2214yescomplemented
33#15689009C2214yescomplemented
34#15689009C2214yescomplemented
35#15689009C2214yescomplemented
36#15689003C2214yes—
37#15689003C2214yes—
38#15688998C2214yescomplemented
39#15688998C2214yescomplemented
40#15688998C2214yescomplemented
41#15688998C2214yescomplemented
42#15688986C2212yes—
43#15688986C2212yescomplemented
44#15688983C2212yes—
45#15688983C2211yescharacteristic
46#15688983C2211yescharacteristic
47#15688983C2211yescharacteristic
48#15688983C2211yescharacteristic
49#15688983C2212yes—
50#15688983C2212yes—
51#15688983C2212yescomplemented
52#15688983C2212yescomplemented
53#15688983C2212yescomplemented
54#15688979C2212yes—
55#15688979C2212yes—
56C4⋊C4×Dic47C2214yescomplemented
57C22⋊C4×Dic47C2214yescomplemented
58C22⋊C4×Dic47C2214yescomplemented
59C4×C22⋊Dic47C2212yes—
60C4×C22⋊Dic47C2212yes—
61C4×C22⋊Dic47C2212yes—
62C4×C22⋊Dic47C2212yescomplemented
63C2×C47⋊#95C2212yescomplemented
64C23×D4×C47C2211yescharacteristic
65C24×C4×C47C2211yescharacteristic
66C2×#123×C47C4116yescomplemented
67C2×#123×C47C2212yes—
68C2×#123×C47C2212yes—
69C2×#123×C47C2212yes—
70C2×#123×C47C2212yes—
71C22×C4⋊C4×C47C2211yescharacteristic
72C22×C4⋊C4×C47C2211yescharacteristic
73C22×C22⋊C4×C47C2211yescharacteristic
74C22×C22⋊C4×C47C2211yescharacteristic
75C22×C22⋊C4×C47C2211yescharacteristic
76C23×Dic47C2314yes—
77C23×Dic47C2314yes—
78D4×Dic47—48no—
79#13093983—44no—
80#13093983—44no—
81C2×C4⋊Dic47—44no—
82C2×C4⋊Dic47C2314yes—
83C2×C4⋊Dic47C2312yes—
84C2×C4⋊Dic47C2312yes—
85C2×C4⋊Dic47C2314yes—
86C2×C4⋊Dic47C2312yes—
87C2×C4⋊Dic47C2312yes—
88C2×C4⋊Dic47C2314yes—
89C2×C4⋊Dic47C2314yes—
90C2×C22⋊Dic47—44no—
91C2×C22⋊Dic47—44no—
92C2×C22⋊Dic47C2312yes—
93C2×C22⋊Dic47C2312yes—
94C2×C22⋊Dic47C2312yes—
95C2×C22⋊Dic47C2312yes—
96C2×C22⋊Dic47C2314yes—
97C2×C22⋊Dic47C2314yes—
98C2×C22⋊Dic47C2314yes—
99C2×C22⋊Dic47C2314yes—
100C2×C22⋊Dic47C2314yes—
101C2×C22⋊Dic47C2314yes—
102C2×C4×Dic47C2314yes—
103C2×C4×Dic47C2314yes—
104C2×C4×Dic47C2314yes—
105C2×C4×Dic47C2314yes—
106C47⋊#95C2314yes—
107C47⋊#95C2312yes—
108C47⋊#95C2312yes—
109C47⋊#95C2314yes—
110C47⋊#95C2314yes—
111C47⋊#95C2314yes—
112C47⋊#95C2312yes—
113C47⋊#95C2312yes—
114C47⋊#95C2314yes—
115C47⋊#95C2314yes—
116C47⋊#95C2314yes—
117C47⋊#95C2314yes—
118C25×C47C2311yescharacteristic
119C25×C47C2311yescharacteristic
120C22×D4×C47—44no—
121C22×D4×C47C2×C418yes—
122C22×D4×C47C2312yes—
123C22×D4×C47C2312yes—
124C23×C4×C47—44no—
125C23×C4×C47C2×C418yescomplemented
126C23×C4×C47C2311yescharacteristic
127C23×C4×C47C2311yescharacteristic
128C23×C4×C47C2311yescharacteristic
129C23×C4×C47C2311yescharacteristic
130C23×C4×C47C2311yescharacteristic
131C23×C4×C47C2311yescharacteristic
132C23×C4×C47C2311yescharacteristic
133C23×C4×C47C2311yescharacteristic
134C23×C4×C47C2311yescharacteristic
135#123×C47C2×C4116yescomplemented
136#123×C47C2×C4116yescomplemented
137#123×C47C2×C4116yescomplemented
138#123×C47C2×C4116yescomplemented
139C2×C4⋊C4×C47C2×C418yescomplemented
140C2×C4⋊C4×C47C2×C418yescomplemented
141C2×C4⋊C4×C47C2312yes—
142C2×C4⋊C4×C47C2312yes—
143C2×C4⋊C4×C47C2312yes—
144C2×C4⋊C4×C47C2312yes—
145C2×C22⋊C4×C47C2×C418yescomplemented
146C2×C22⋊C4×C47C2×C418yescomplemented
147C2×C22⋊C4×C47C2×C418yescomplemented
148C2×C22⋊C4×C47C2312yes—
149C2×C22⋊C4×C47C2312yes—
150C2×C22⋊C4×C47C2312yes—
151C2×C22⋊C4×C47C2312yes—
152C2×C22⋊C4×C47C2312yes—
153C2×C22⋊C4×C47C2312yes—
154C24×C47—24no—
155C24×C47—22no—
156C24×C47—22no—
157C24×C47—22no—
158C24×C47—22no—
159C24×C47—42no—
160C24×C47—42no—
161C24×C47—42no—
162C24×C47C22×C414yes—
163C24×C47C22×C414yes—
164C24×C47C2412yes—
165C24×C47C2411yescharacteristic
166C24×C47C2411yescharacteristic
167C24×C47C2411yescharacteristic
168C2×D4×C47—28no—
169C2×D4×C47—44no—
170C2×D4×C47—416no—
171C2×D4×C47C22×C418yes—
172C2×D4×C47C22×C418yes—
173C22×C4×C47—24no—
174C22×C4×C47—24no—
175C22×C4×C47—22no—
176C22×C4×C47—22no—
177C22×C4×C47—416no—
178C22×C4×C47—42no—
179C22×C4×C47—42no—
180C22×C4×C47—42no—
181C22×C4×C47—42no—
182C22×C4×C47—42no—
183C22×C4×C47—42no—
184C22×C4×C47C22×C414yes—
185C22×C4×C47C22×C414yes—
186C22×C4×C47C22×C414yes—
187C22×C4×C47C22×C414yes—
188C22×C4×C47C22×C414yes—
189C22×C4×C47C22×C414yes—
190C22×C4×C47C22×C414yes—
191C22×C4×C47C22×C414yes—
192C22×C4×C47C22×C414yes—
193C22×C4×C47C2412yes—
194C22×C4×C47C2412yes—
195C22×C4×C47C2411yescharacteristic
196C22×C4×C47C2411yescharacteristic
197C22×C4×C47C2411yescharacteristic
198C22×C4×C47C2411yescharacteristic
199C22×C4×C47C2412yes—
200C22×Dic47—28no—
201C22×Dic47—44no—
202C22×Dic47—44no—
203C22×Dic47—44no—
204C22×Dic47—44no—
205C22×Dic47—44no—
206C22×Dic47C2414yes—
207C22×Dic47C2414yes—
208C22×Dic47C2414yes—
209C22×Dic47C2414yes—
210C4⋊C4×C47C22×C418yes—
211C4⋊C4×C47C22×C418yes—
212C4⋊C4×C47C22×C418yes—
213C4⋊C4×C47C22×C418yes—
214C22⋊C4×C47C22×C418yes—
215C22⋊C4×C47C22×C418yes—
216C22⋊C4×C47C22×C418yes—
217C22⋊C4×C47C22×C418yes—
218C22⋊C4×C47C22×C418yes—
219C22⋊C4×C47C22×C418yes—
220C22⋊Dic47—24no—
221C22⋊Dic47—24no—
222C22⋊Dic47—24no—
223C22⋊Dic47—28no—
224C22⋊Dic47—24no—
225C22⋊Dic47—44no—
226C22⋊Dic47—44no—
227C22⋊Dic47—44no—
228C22⋊Dic47—44no—
229C22⋊Dic47—44no—
230C4⋊Dic47—42no—
231C4⋊Dic47—44no—
232C4⋊Dic47—42no—
233C4⋊Dic47—44no—
234C4⋊Dic47—42no—
235C4⋊Dic47—42no—
236C4⋊Dic47—44no—
237C4⋊Dic47—44no—
238C4×Dic47—44no—
239C4×Dic47—44no—
240C4×Dic47—44no—
241C4×Dic47—44no—
242C23×C47—21no—
243C23×C47—22no—
244C23×C47—21no—
245C23×C47—22no—
246C23×C47—22no—
247C23×C47—28no—
248C23×C47—28no—
249C23×C47—21no—
250C23×C47—22no—
251C23×C47—24no—
252C23×C47—22no—
253C23×C47—21no—
254C23×C47—22no—
255C23×C47—22no—
256C23×C47—24no—
257C23×C47—28no—
258C23×C47—44no—
259C23×C47—44no—
260C23×C47—44no—
261C23×C47—48no—
262C23×C47—48no—
263C23×C47—84no—
264C23×C47—84no—
265C23×C47C23×C414yes—
266C23×C47C23×C412yes—
267C23×C47C23×C412yes—
268C23×C47C23×C412yes—
269C23×C47H(5,𝔽2)14yes—
270C23×C47H(5,𝔽2)12yes—
271C23×C472−1+412yes—
272C23×C47C2511yescharacteristic
273D4×C47—216no—
274D4×C47—48no—
275C2×C4×C47—28no—
276C2×C4×C47—28no—
277C2×C4×C47—28no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
280C2×C4×C47—24no—
281C2×C4×C47—22no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—24no—
286C2×C4×C47—44no—
287C2×C4×C47—44no—
288C2×C4×C47—44no—
289C2×C4×C47—44no—
290C2×C4×C47—44no—
291C2×C4×C47—44no—
292C2×C4×C47C23×C414yes—
293C2×C4×C47C23×C414yes—
294C2×C4×C47C23×C412yes—
295C2×C4×C47C23×C412yes—
296C2×C4×C47C23×C412yes—
297C2×C4×C47C23×C412yes—
298C2×C4×C47C23×C414yes—
299C2×Dic47—24no—
300C2×Dic47—24no—
301C2×Dic47—24no—
302C2×Dic47—24no—
303C2×Dic47—24no—
304C2×Dic47—24no—
305C2×Dic47—24no—
306C2×Dic47—24no—
307C2×Dic47—24no—
308C2×Dic47—24no—
309C2×Dic47—24no—
310C2×Dic47—24no—
311C2×Dic47—88no—
312C2×Dic47—88no—
313#34376—471nomaximal, Sylow
314C22×C47—22no—
315C22×C47—22no—
316C22×C47—22no—
317C22×C47—22no—
318C22×C47—24no—
319C22×C47—24no—
320C22×C47—24no—
321C22×C47—24no—
322C22×C47—22no—
323C22×C47—24no—
324C22×C47—22no—
325C22×C47—24no—
326C22×C47—22no—
327C22×C47—24no—
328C22×C47—416no—
329C22×C47—44no—
330C22×C47—42no—
331C22×C47—42no—
332C22×C47—44no—
333C22×C47—88no—
334C22×C47#51814yes—
335C22×C47#52014yes—
336C22×C47C24×C411yescharacteristic
337C22×C47C2×H(5,𝔽2)12yes—
338C22×C47C2×H(5,𝔽2)11yescharacteristic
339C22×C47C2×2−1+411yescharacteristic
340C22×C47#58512yes—
341C4×C47—22no—
342C4×C47—22no—
343C4×C47—22no—
344C4×C47—22no—
345C4×C47—24no—
346C4×C47—24no—
347C4×C47—24no—
348Dic47—44no—
349Dic47—44no—
350Dic47—44no—
351Dic47—44no—
352C22×#123D4711yescharacteristic
353#2376—474no—
354#2359—474no—
355#2345—472no—
356#2342—472no—
357#2342—472no—
358D4×C22⋊C4—472no—
359#2335—474no—
360#2322—474no—
361#2316—471no—
362#2315—471no—
363#2313—471no—
364#2312—471no—
365#2280—471no—
366C2×#380—471no—
367C2×C47—24no—
368C2×C47—24no—
369C2×C47—42no—
370C2×C47—44no—
371C2×C47C2×#51811yescharacteristic
372C2×C47C2×#52011yescharacteristic
373C2×C47#342811yescharacteristic
374C2×C47#353412yes—
375C2×C47#353512yes—
376C23×D4C2×D4711yescharacteristic
377C24×C4C2×D4711yescharacteristic
378C2×#123Dic47116yescomplemented
379C2×#123C2×D4712yes—
380C2×#123C2×D4712yes—
381C2×#123C2×D4712yes—
382C2×#123C2×D4712yes—
383C2×C4×D4—474no—
384C2×#117—472no—
385C2×#117—472no—
386C22×C4⋊C4—472no—
387C22×C4⋊C4C2×D4711yescharacteristic
388C22×C4⋊C4C2×D4711yescharacteristic
389C22×C22⋊C4—472no—
390C22×C22⋊C4—472no—
391C22×C22⋊C4C2×D4711yescharacteristic
392C22×C22⋊C4C2×D4711yescharacteristic
393C22×C22⋊C4C2×D4711yescharacteristic
394#390—474no—
395#389—474no—
396#389—474no—
397#389—474no—
398#388—474no—
399#388—474no—
400#388—474no—
401#388—474no—
402#388—474no—
403#388—474no—
404#387—474no—
405#387—474no—
406#387—474no—
407#387—474no—
408#386—474no—
409#386—474no—
410#385—474no—
411#385—474no—
412#385—474no—
413#385—474no—
414#381—472no—
415#381—472no—
416#380—471no—
417#380—471no—
418#380—471no—
419#380—471no—
420#380—472no—
421#380—472no—
422#380—472no—
423#380—472no—
424#380—472no—
425#380—472no—
426#379—472no—
427#379—472no—
428C4×C4⋊C4—474no—
429C4×C22⋊C4—472no—
430C4×C22⋊C4—472no—
431C4×C22⋊C4—472no—
432C4×C22⋊C4—472no—
433C4×C22⋊C4—474no—
434C4×C22⋊C4—474no—
435C2×#95—472no—
436C47#3437611yescharacteristic, complemented, Sylow
437C25C22×D4711yescharacteristic
438C25C22×D4711yescharacteristic
439C22×D4—44no—
440C22×D4C2×Dic4718yes—
441C22×D4C22×D4712yes—
442C22×D4C22×D4712yes—
443C23×C4—44no—
444C23×C4—474no—
445C23×C4—474no—
446C23×C4C2×Dic4718yescomplemented
447C23×C4C22×D4711yescharacteristic
448C23×C4C22×D4711yescharacteristic
449C23×C4C22×D4711yescharacteristic
450C23×C4C22×D4711yescharacteristic
451C23×C4C22×D4711yescharacteristic
452C23×C4C22×D4711yescharacteristic
453C23×C4C22×D4711yescharacteristic
454C23×C4C22×D4711yescharacteristic
455C23×C4C22×D4711yescharacteristic
456#123C2×Dic47116yescomplemented
457#123C2×Dic47116yescomplemented
458#123C2×Dic47116yescomplemented
459#123C2×Dic47116yescomplemented
460C4×D4—1888no—
461#117—1884no—
462#117—1884no—
463C2×C4⋊C4—472no—
464C2×C4⋊C4—474no—
465C2×C4⋊C4—472no—
466C2×C4⋊C4—472no—
467C2×C4⋊C4—472no—
468C2×C4⋊C4—474no—
469C2×C4⋊C4—474no—
470C2×C4⋊C4—474no—
471C2×C4⋊C4—1884no—
472C2×C4⋊C4C2×Dic4718yescomplemented
473C2×C4⋊C4C2×Dic4718yescomplemented
474C2×C4⋊C4C22×D4712yes—
475C2×C4⋊C4C22×D4712yes—
476C2×C4⋊C4C22×D4712yes—
477C2×C4⋊C4C22×D4712yes—
478C2×C22⋊C4—472no—
479C2×C22⋊C4—472no—
480C2×C22⋊C4—472no—
481C2×C22⋊C4—474no—
482C2×C22⋊C4—472no—
483C2×C22⋊C4—474no—
484C2×C22⋊C4—474no—
485C2×C22⋊C4—474no—
486C2×C22⋊C4—474no—
487C2×C22⋊C4—474no—
488C2×C22⋊C4—1884no—
489C2×C22⋊C4—1884no—
490C2×C22⋊C4C2×Dic4718yescomplemented
491C2×C22⋊C4C2×Dic4718yescomplemented
492C2×C22⋊C4C2×Dic4718yescomplemented
493C2×C22⋊C4C22×D4712yes—
494C2×C22⋊C4C22×D4712yes—
495C2×C22⋊C4C22×D4712yes—
496C2×C22⋊C4C22×D4712yes—
497C2×C22⋊C4C22×D4712yes—
498C2×C22⋊C4C22×D4712yes—
499C2×C42—474no—
500C2×C42—474no—
501C2×C42—474no—
502C2×C42—474no—
503#95—474no—
504#95—472no—
505#95—472no—
506#95—472no—
507#95—474no—
508#95—472no—
509#95—474no—
510#95—474no—
511#95—474no—
512#95—474no—
513#95—474no—
514#95—474no—
515C24—24no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—42no—
521C24—42no—
522C24—42no—
523C24C22×Dic4714yes—
524C24C22×Dic4714yes—
525C24C23×D4711yescharacteristic
526C24C23×D4712yes—
527C24C23×D4711yescharacteristic
528C24C23×D4711yescharacteristic
529C2×D4—28no—
530C2×D4—44no—
531C2×D4—416no—
532C2×D4C22×Dic4718yes—
533C2×D4C22×Dic4718yes—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—416no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—474no—
546C22×C4—474no—
547C22×C4—474no—
548C22×C4—474no—
549C22×C4—948no—
550C22×C4—1884no—
551C22×C4—1884no—
552C22×C4—1884no—
553C22×C4—1884no—
554C22×C4—1884no—
555C22×C4C22×Dic4714yes—
556C22×C4C22×Dic4714yes—
557C22×C4C22×Dic4714yes—
558C22×C4C22×Dic4714yes—
559C22×C4C22×Dic4714yes—
560C22×C4C22×Dic4714yes—
561C22×C4C22×Dic4714yes—
562C22×C4C22×Dic4714yes—
563C22×C4C22×Dic4714yes—
564C22×C4C23×D4711yescharacteristic
565C22×C4C23×D4712yes—
566C22×C4C23×D4712yes—
567C22×C4C23×D4712yes—
568C22×C4C23×D4711yescharacteristic
569C22×C4C23×D4711yescharacteristic
570C22×C4C23×D4711yescharacteristic
571C4⋊C4—1884no—
572C4⋊C4—1882no—
573C4⋊C4—1884no—
574C4⋊C4—1882no—
575C4⋊C4—1882no—
576C4⋊C4—1882no—
577C4⋊C4—1884no—
578C4⋊C4—1884no—
579C4⋊C4C22×Dic4718yes—
580C4⋊C4C22×Dic4718yes—
581C4⋊C4C22×Dic4718yes—
582C4⋊C4C22×Dic4718yes—
583C22⋊C4—948no—
584C22⋊C4—944no—
585C22⋊C4—944no—
586C22⋊C4—944no—
587C22⋊C4—944no—
588C22⋊C4—1884no—
589C22⋊C4—1884no—
590C22⋊C4—1884no—
591C22⋊C4—1884no—
592C22⋊C4—1884no—
593C22⋊C4C22×Dic4718yes—
594C22⋊C4C22×Dic4718yes—
595C22⋊C4C22×Dic4718yes—
596C22⋊C4C22×Dic4718yes—
597C22⋊C4C22×Dic4718yes—
598C22⋊C4C22×Dic4718yes—
599C42—1884no—
600C42—1884no—
601C42—1884no—
602C42—1884no—
603C23—22no—
604C23—21no—
605C23—21no—
606C23—22no—
607C23—22no—
608C23—28no—
609C23—28no—
610C23—24no—
611C23—22no—
612C23—21no—
613C23—22no—
614C23—21no—
615C23—22no—
616C23—22no—
617C23—24no—
618C23—28no—
619C23—44no—
620C23—44no—
621C23—44no—
622C23—48no—
623C23—48no—
624C23—84no—
625C23—84no—
626C23C23×Dic4714yes—
627C23C23×Dic4712yes—
628C23C23×Dic4712yes—
629C23C23×Dic4712yes—
630C23#1309406914yes—
631C23#1309407012yes—
632C23#1309407112yes—
633C23C24×D4711yescharacteristic
634D4—216no—
635D4—48no—
636C2×C4—28no—
637C2×C4—28no—
638C2×C4—28no—
639C2×C4—22no—
640C2×C4—24no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—44no—
648C2×C4—44no—
649C2×C4—44no—
650C2×C4—44no—
651C2×C4—44no—
652C2×C4—44no—
653C2×C4—944no—
654C2×C4—944no—
655C2×C4—944no—
656C2×C4—944no—
657C2×C4—944no—
658C2×C4—944no—
659C2×C4—944no—
660C2×C4—944no—
661C2×C4—944no—
662C2×C4—944no—
663C2×C4—944no—
664C2×C4—944no—
665C2×C4—3768no—
666C2×C4—3768no—
667C2×C4C23×Dic4714yes—
668C2×C4C23×Dic4714yes—
669C2×C4C23×Dic4712yes—
670C2×C4C23×Dic4712yes—
671C2×C4C23×Dic4712yes—
672C2×C4C23×Dic4712yes—
673C2×C4C23×Dic4714yes—
674C22—24no—
675C22—24no—
676C22—22no—
677C22—24no—
678C22—24no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—24no—
684C22—22no—
685C22—24no—
686C22—22no—
687C22—24no—
688C22—416no—
689C22—44no—
690C22—42no—
691C22—42no—
692C22—44no—
693C22—88no—
694C22#1568959814yes—
695C22#1568960614yes—
696C22C24×Dic4711yescharacteristic
697C22C2×#1309406912yes—
698C22C2×#1309407011yescharacteristic
699C22C2×#1309407111yescharacteristic
700C22#1568995912yes—
701C4—22no—
702C4—22no—
703C4—22no—
704C4—22no—
705C4—24no—
706C4—24no—
707C4—24no—
708C4—1884no—
709C4—1884no—
710C4—1884no—
711C4—1884no—
712C2—24no—
713C2—24no—
714C2—42no—
715C2—44no—
716C2C2×#1568959811yescharacteristic
717C2C2×#1568960611yescharacteristic
718C2#2025659111yescharacteristic
719C2#2025758212yes—
720C2#2025760112yes—
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC22×#123×C47C2
socle, cosocleC23×C47C25
prime radicalC23×D4×C47C22
hypercenterC22×#123D47
hypocenterC47#34376
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. #20246536C2semidirect
2. #20246384C2semidirect
3. #20246265C2semidirect
4. #20246237C2semidirect
5. #20246237C2semidirect
7. #20246182C2semidirect
8. #20246060C2semidirect
9. #20246006C2semidirect
10. #20246002C2semidirect
11. #20245991C2semidirect
12. #20245986C2semidirect
13. #20245771C2semidirect
14. C2×#15688983C2semidirect
18. C2×#13093983C22semidirect
19. C22×C4⋊Dic47C22semidirect
23. #15689022C22semidirect
24. #15689022C22semidirect
25. #15689022C22semidirect
26. #15689016C22semidirect
27. #15689016C22semidirect
28. #15689016C22semidirect
29. #15689016C22semidirect
30. #15689016C22semidirect
31. #15689016C22semidirect
32. #15689009C22semidirect
33. #15689009C22semidirect
34. #15689009C22semidirect
35. #15689009C22semidirect
38. #15688998C22semidirect
39. #15688998C22semidirect
40. #15688998C22semidirect
41. #15688998C22semidirect
43. #15688986C22semidirect
51. #15688983C22semidirect
52. #15688983C22semidirect
53. #15688983C22semidirect
56. C4⋊C4×Dic47C22semidirect
57. C22⋊C4×Dic47C22semidirect
58. C22⋊C4×Dic47C22semidirect
62. C4×C22⋊Dic47C22semidirect
63. C2×C47⋊#95C22semidirect
66. C2×#123×C47C4semidirect
125. C23×C4×C47C2×C4semidirect
135. #123×C47C2×C4semidirect
136. #123×C47C2×C4semidirect
137. #123×C47C2×C4semidirect
138. #123×C47C2×C4semidirect
139. C2×C4⋊C4×C47C2×C4semidirect
140. C2×C4⋊C4×C47C2×C4semidirect
145. C2×C22⋊C4×C47C2×C4semidirect
146. C2×C22⋊C4×C47C2×C4semidirect
147. C2×C22⋊C4×C47C2×C4semidirect
378. C2×#123Dic47semidirect
436. C47#34376semidirect
446. C23×C4C2×Dic47semidirect
456. #123C2×Dic47semidirect
457. #123C2×Dic47semidirect
458. #123C2×Dic47semidirect
459. #123C2×Dic47semidirect
472. C2×C4⋊C4C2×Dic47semidirect
473. C2×C4⋊C4C2×Dic47semidirect
490. C2×C22⋊C4C2×Dic47semidirect
491. C2×C22⋊C4C2×Dic47semidirect
492. C2×C22⋊C4C2×Dic47semidirect

Maximal subgroups

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

subgroupindex
#202465362
#202463842
#202462652
#202462372
D4×C22⋊Dic472
#202461822
#202460602
#202460062
#202460022
#202459912
#202459862
#202457712
C2×#156889832
C22×#123×C472
#3437647