Finite Group Databasebeta

← #26389148

Subgroups — #26389148

Order 12032.

3754 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689685C212yesmaximal, complemented
2C22×#13093998C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D47C211yesmaximal, characteristic, complemented
4#20251720C212yesmaximal, complemented
5#20251671C212yesmaximal, complemented
6#20249133C212yesmaximal, complemented
7#20249125C212yesmaximal, complemented
8#20248348C214yesmaximal, complemented
9#20248280C214yesmaximal, complemented
10#20247697C212yesmaximal, complemented
11#20246822C214yesmaximal, complemented
12#20246745C212yesmaximal, complemented
13#20245963C212yesmaximal, complemented
14C2×C47×#380C211yesmaximal, characteristic, complemented
15C23×D188C2211yescharacteristic, complemented
16C23×C22⋊D47C2212yes—
17C23×C22⋊D47C2211yescharacteristic
18C23×C4×D47C2211yescharacteristic, complemented
19#15689685—216no—
20C2×#13094008C2214yes—
21C2×#13094008C2214yescomplemented
22C2×#13093999C2214yescomplemented
23C2×#13093998—28no—
24C2×#13093998C2212yes—
25C2×#13093998C2212yes—
26C2×#13093998C2212yescomplemented
27C2×#13093998C2218yescomplemented
28C2×#13093998C2212yescomplemented
29C2×#13093994C2214yes—
30C2×#13093994C2214yescomplemented
31C2×C4×C22⋊D47—28no—
32C2×C4×C22⋊D47C2212yes—
33C2×C4×C22⋊D47C2212yes—
34C2×C4×C22⋊D47C2212yescomplemented
35C2×C4×C22⋊D47C2212yescomplemented
36C22×C4⋊Dic47C2211yescharacteristic, complemented
37C22×Dic47⋊C4C2211yescharacteristic, complemented
38C22×C22⋊Dic47C2211yescharacteristic
39C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
40C22×(C2×D47)⋊C4C2212yescomplemented
41C22×C4×Dic47C2211yescharacteristic, complemented
42#15689055C2214yescomplemented
43#15689050C2214yescomplemented
44#15689045C2218yescomplemented
45#15689041C2214yescomplemented
46#15689040C2218yescomplemented
47#15689033C2214yescomplemented
48#15689024C2214yescomplemented
49#15689022C2214yescomplemented
50#15689015C2218yescomplemented
51#15689002C2218yescomplemented
52#15689001C2218yescomplemented
53#15689000C2214yescomplemented
54#15689000C2214yescomplemented
55#15688984C2214yescomplemented
56#15688980C2214yescomplemented
57#15688978C2214yescomplemented
58C24×C4×C47C2211yescharacteristic
59C22×C4⋊C4×C47C2212yescomplemented
60C22×C22⋊C4×C47C2212yes—
61C47×#380C2212yescomplemented
62C47×#380C2212yescomplemented
63C47×#380C2212yescomplemented
64C47×#380C2212yescomplemented
65C2×#95×C47C2212yescomplemented
66C24×D47C2312yes—
67C24×D47C2311yescharacteristic
68C22×D188—24no—
69C22×D188—44no—
70C22×D188C2312yes—
71C22×D188C2318yes—
72C22×D188C2312yes—
73C22×C22⋊D47—24no—
74C22×C22⋊D47—24no—
75C22×C22⋊D47—28no—
76C22×C22⋊D47—28no—
77C22×C22⋊D47—28no—
78C22×C22⋊D47D418yescomplemented
79C22×C22⋊D47C2314yes—
80C22×C22⋊D47C2314yes—
81C22×C22⋊D47C2312yes—
82C22×C22⋊D47C2312yes—
83C23×Dic47C2312yes—
84C23×Dic47C2311yescharacteristic
85C23×Dic47C2311yescharacteristic
86C23×Dic47C2311yescharacteristic
87C22×C4×D47—24no—
88C22×C4×D47—44no—
89C22×C4×D47C2312yes—
90C22×C4×D47C2312yes—
91#13094008—216no—
92#13094008—216no—
93#13093999—48no—
94#13093998—28no—
95#13093998—28no—
96#13093998—28no—
97#13093998—28no—
98#13093998—232no—
99#13093994—216no—
100#13093994—216no—
101C4×C22⋊D47—28no—
102C4×C22⋊D47—28no—
103C4×C22⋊D47—28no—
104C4×C22⋊D47—28no—
105C2×C4⋊Dic47—24no—
106C2×C4⋊Dic47C2312yes—
107C2×C4⋊Dic47C2318yes—
108C2×C4⋊Dic47C2312yes—
109C2×Dic47⋊C4—24no—
110C2×Dic47⋊C4C2312yes—
111C2×Dic47⋊C4C2312yes—
112C2×C22⋊Dic47—24no—
113C2×C22⋊Dic47C2312yes—
114C2×C22⋊Dic47C2312yes—
115C2×(C2×D47)⋊C4—24no—
116C2×(C2×D47)⋊C4—28no—
117C2×(C2×D47)⋊C4C2318yes—
118C2×(C2×D47)⋊C4C2314yes—
119C2×(C2×D47)⋊C4C2318yes—
120C2×(C2×D47)⋊C4C2312yes—
121C2×(C2×D47)⋊C4C2312yes—
122C2×(C2×D47)⋊C4C2314yes—
123C2×(C2×D47)⋊C4C2318yes—
124C2×(C2×D47)⋊C4C2318yes—
125C2×C4×Dic47—24no—
126C2×C4×Dic47C2312yes—
127C2×C4×Dic47C2312yes—
128C47⋊#95C2318yes—
129C47⋊#95C2318yes—
130C25×C47C2311yescharacteristic
131C23×C4×C47—44no—
132C23×C4×C47D418yescomplemented
133C23×C4×C47C2311yescharacteristic
134C23×C4×C47C2311yescharacteristic
135C23×C4×C47C2311yescharacteristic
136C23×C4×C47C2314yes—
137C23×C4×C47C2311yescharacteristic
138C23×C4×C47C2311yescharacteristic
139C23×C4×C47C2311yescharacteristic
140C2×C4⋊C4×C47—44no—
141C2×C4⋊C4×C47C2314yes—
142C2×C4⋊C4×C47C2314yes—
143C2×C22⋊C4×C47—28no—
144C2×C22⋊C4×C47C2314yes—
145C2×C22⋊C4×C47C2314yes—
146#95×C47C2314yes—
147#95×C47C2314yes—
148C24×C47—42no—
149C24×C47—42no—
150C24×C47C2×D414yes—
151C24×C47C2×D414yes—
152C24×C47#4114yes—
153C24×C47C2411yescharacteristic
154C24×C47C2411yescharacteristic
155C24×C47C2411yescharacteristic
156C23×D47—22no—
157C23×D47—22no—
158C23×D47—24no—
159C23×D47—24no—
160C23×D47—24no—
161C23×D47—42no—
162C23×D47—42no—
163C23×D47—44no—
164C23×D47—44no—
165C23×D47C2×D414yescomplemented
166C23×D47C2414yes—
167C23×D47C2412yes—
168C22×C4×C47—24no—
169C22×C4×C47—24no—
170C22×C4×C47—24no—
171C22×C4×C47—28no—
172C22×C4×C47—416no—
173C22×C4×C47—42no—
174C22×C4×C47—42no—
175C22×C4×C47—42no—
176C22×C4×C47—44no—
177C22×C4×C47—44no—
178C22×C4×C47C2×D414yes—
179C22×C4×C47C2×D414yes—
180C22×C4×C47C2×D414yes—
181C22×C4×C47C2×D414yes—
182C22×C4×C47C2×D414yes—
183C22×C4×C47C2×D414yes—
184C22×C4×C47C2418yes—
185C22×C4×C47C2411yescharacteristic
186C22×C4×C47C2411yescharacteristic
187C22×C4×C47C2411yescharacteristic
188C22×C4×C47C2411yescharacteristic
189C2×C22⋊D47—232no—
190C2×C22⋊D47—24no—
191C2×C22⋊D47—24no—
192C2×C22⋊D47—24no—
193C2×C22⋊D47—24no—
194C2×C22⋊D47—28no—
195C2×C22⋊D47—28no—
196C2×C22⋊D47—28no—
197C2×C22⋊D47—28no—
198C2×C22⋊D47—28no—
199C2×C22⋊D47—28no—
200C2×C22⋊D47—432no—
201C2×C22⋊D47C2×D418yes—
202C2×C22⋊D47C2×D418yescomplemented
203C22×Dic47—22no—
204C22×Dic47—22no—
205C22×Dic47—22no—
206C22×Dic47—24no—
207C22×Dic47—22no—
208C22×Dic47—24no—
209C22×Dic47—24no—
210C22×Dic47—42no—
211C22×Dic47—42no—
212C22×Dic47C2×D414yescomplemented
213C22×Dic47C2412yes—
214C22×Dic47C2412yes—
215C22×Dic47C2414yes—
216C22×Dic47C2412yes—
217C2×D188—24no—
218C2×D188—24no—
219C2×D188—28no—
220C2×D188—216no—
221C2×D188—44no—
222C2×D188—416no—
223C2×D188—48no—
224C2×D188—48no—
225C2×C4×D47—24no—
226C2×C4×D47—24no—
227C2×C4×D47—28no—
228C2×C4×D47—44no—
229C2×C4×D47—416no—
230C4⋊C4×C47—28no—
231C4⋊C4×C47—44no—
232C22⋊C4×C47—28no—
233C22⋊C4×C47—28no—
234C22⋊Dic47—24no—
235C22⋊Dic47—24no—
236(C2×D47)⋊C4—216no—
237(C2×D47)⋊C4—24no—
238(C2×D47)⋊C4—24no—
239(C2×D47)⋊C4—28no—
240(C2×D47)⋊C4—28no—
241(C2×D47)⋊C4—216no—
242(C2×D47)⋊C4—48no—
243(C2×D47)⋊C4—48no—
244C4⋊Dic47—24no—
245C4⋊Dic47—24no—
246C4⋊Dic47—216no—
247Dic47⋊C4—24no—
248Dic47⋊C4—24no—
249C4×Dic47—24no—
250C4×Dic47—24no—
251C23×C47—22no—
252C23×C47—22no—
253C23×C47—22no—
254C23×C47—22no—
255C23×C47—22no—
256C23×C47—22no—
257C23×C47—44no—
258C23×C47—44no—
259C23×C47—48no—
260C23×C47—48no—
261C23×C47#121116yescomplemented
262C23×C47C22×D412yes—
263C23×C47C22×D412yes—
264C23×C47C22×D412yes—
265C23×C47C22×D412yes—
266C23×C47C22×D412yes—
267C23×C47C22×D412yes—
268C23×C47C2×#4112yes—
269C23×C47C2×#4112yes—
270C23×C47C2×#4112yes—
271C23×C47C2511yescharacteristic
272C22×D47—28no—
273C22×D47—22no—
274C22×D47—22no—
275C22×D47—24no—
276C22×D47—24no—
277C22×D47—24no—
278C22×D47—24no—
279C22×D47—24no—
280C22×D47—28no—
281C22×D47—28no—
282C22×D47—48no—
283C22×D47—44no—
284C22×D47—44no—
285C22×D47—48no—
286C22×D47—48no—
287C22×D47—48no—
288C22×D47—48no—
289C22×D47—88no—
290C22×D47—88no—
291C22×D47C22×D414yes—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—28no—
296C2×C4×C47—28no—
297C2×C4×C47—28no—
298C2×C4×C47—28no—
299C2×C4×C47—28no—
300C2×C4×C47—28no—
301C2×C4×C47—44no—
302C2×C4×C47—44no—
303C2×C4×C47—44no—
304C2×C4×C47—88no—
305C2×C4×C47C22×D412yes—
306C2×C4×C47C22×D412yes—
307C2×C4×C47C22×D412yes—
308C2×C4×C47C22×D412yes—
309C2×C4×C47H(5,𝔽2)14yes—
310C22⋊D47—216no—
311C22⋊D47—216no—
312C22⋊D47—416no—
313C22⋊D47—416no—
314C2×Dic47—28no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—24no—
320C2×Dic47—24no—
321C2×Dic47—24no—
322C2×Dic47—24no—
323C2×Dic47—24no—
324C2×Dic47—44no—
325C2×Dic47—44no—
326C2×Dic47—48no—
327C2×Dic47C22×D414yes—
328D188—48no—
329D188—48no—
330D188—816no—
331C4×D47—48no—
332C4×D47—48no—
333#35000—471nomaximal, Sylow
334C22×C47—22no—
335C22×C47—22no—
336C22×C47—22no—
337C22×C47—22no—
338C22×C47—22no—
339C22×C47—22no—
340C22×C47—24no—
341C22×C47—24no—
342C22×C47—24no—
343C22×C47—24no—
344C22×C47—24no—
345C22×C47—24no—
346C22×C47—416no—
347C22×C47C2×#12114yes—
348C22×C47C2×#12114yes—
349C22×C47C2×#12114yes—
350C22×C47C23×D411yescharacteristic
351C22×C47C23×D411yescharacteristic
352C22×C47C22×#4111yescharacteristic
353C22×C47C2×H(5,𝔽2)12yes—
354C22×C47#58512yes—
355C2×D47—24no—
356C2×D47—28no—
357C2×D47—416no—
358C2×D47—42no—
359C2×D47—42no—
360C2×D47—44no—
361C2×D47—44no—
362C2×D47—44no—
363C2×D47—44no—
364C2×D47—48no—
365C2×D47—48no—
366C2×D47—816no—
367C4×C47—22no—
368C4×C47—22no—
369C4×C47—22no—
370C4×C47—48no—
371C4×C47#53414yescomplemented
372Dic47—24no—
373Dic47—44no—
374Dic47—42no—
375Dic47—42no—
376C2×#534—472no—
377C22×#121—471no—
378C22×C4×D4—471no—
379#2854—472no—
380#2847—472no—
381#2618—472no—
382#2617—472no—
383#2543—474no—
384#2534—474no—
385#2486—472no—
386#2416—474no—
387#2408—472no—
388#2308—472no—
389C2×#380D4711yescharacteristic, complemented
390C2×C47—24no—
391C2×C47—24no—
392C2×C47—24no—
393C2×C47C22×#12111yescharacteristic
394C2×C47C2×#53411yescharacteristic
395C2×C47#344911yescharacteristic
396C2×C47#349612yes—
397C2×C47#350512yes—
398D47—44no—
399D47—84no—
400C23×D4—471no—
401C23×D4—472no—
402C23×D4—471no—
403C24×C4—471no—
404C24×C4C2×D4711yescharacteristic
405#534—9416no—
406C2×#123—474no—
407C2×#123—474no—
408C2×#121—472no—
409C2×#121—472no—
410C2×#121—472no—
411C2×#121—472no—
412C2×#121—478no—
413C2×#121—474no—
414C2×#121—948no—
415C2×#120—474no—
416C2×#120—474no—
417C2×C4×D4—472no—
418C2×C4×D4—472no—
419C2×C4×D4—472no—
420C2×C4×D4—472no—
421C2×C4×D4—948no—
422C22×C4⋊C4—471no—
423C22×C4⋊C4—471no—
424C22×C4⋊C4C2×D4712yescomplemented
425C22×C22⋊C4—471no—
426C22×C22⋊C4—471no—
427C22×C22⋊C4—472no—
428C22×C22⋊C4C2×D4712yes—
429C22×C42—471no—
430#398—474no—
431#397—474no—
432#396—478no—
433#394—478no—
434#394—474no—
435#392—474no—
436#390—474no—
437#389—474no—
438#388—478no—
439#386—478no—
440#386—474no—
441#386—474no—
442#386—478no—
443#381—474no—
444#380—474no—
445#380C2×D4712yescomplemented
446#380C2×D4712yescomplemented
447#380C2×D4712yescomplemented
448#380C2×D4712yescomplemented
449#379—474no—
450C2×#95C2×D4712yescomplemented
451C47#3500011yescharacteristic, complemented, Sylow
452C25—471no—
453C25—472no—
454C25C22×D4711yescharacteristic
455C22×D4—478no—
456C22×D4—472no—
457C22×D4—472no—
458C22×D4—474no—
459C22×D4—474no—
460C22×D4—472no—
461C22×D4—478no—
462C22×D4—472no—
463C22×D4—944no—
464C22×D4—944no—
465C22×D4—948no—
466C22×D4—948no—
467C22×D4—948no—
468C22×D4—944no—
469C22×D4—1884no—
470C23×C4—44no—
471C23×C4—471no—
472C23×C4—472no—
473C23×C4—471no—
474C23×C4—471no—
475C23×C4—472no—
476C23×C4—472no—
477C23×C4—944no—
478C23×C4—1884no—
479C23×C4D18818yescomplemented
480C23×C4C22×D4711yescharacteristic
481C23×C4C22×D4711yescharacteristic
482C23×C4C22×D4711yescharacteristic
483C23×C4C22×D4714yes—
484C23×C4C22×D4711yescharacteristic
485C23×C4C22×D4711yescharacteristic
486C23×C4C22×D4711yescharacteristic
487#123—9416no—
488#123—9416no—
489#121—9432no—
490#121—948no—
491#121—948no—
492#121—948no—
493#121—948no—
494#121—1888no—
495#120—9416no—
496#120—9416no—
497C4×D4—948no—
498C4×D4—948no—
499C4×D4—948no—
500C4×D4—948no—
501C2×C4⋊C4—44no—
502C2×C4⋊C4—472no—
503C2×C4⋊C4—472no—
504C2×C4⋊C4—472no—
505C2×C4⋊C4—472no—
506C2×C4⋊C4—478no—
507C2×C4⋊C4—944no—
508C2×C4⋊C4—944no—
509C2×C4⋊C4C22×D4714yes—
510C2×C4⋊C4C22×D4714yes—
511C2×C22⋊C4—28no—
512C2×C22⋊C4—472no—
513C2×C22⋊C4—472no—
514C2×C22⋊C4—472no—
515C2×C22⋊C4—472no—
516C2×C22⋊C4—474no—
517C2×C22⋊C4—474no—
518C2×C22⋊C4—478no—
519C2×C22⋊C4—478no—
520C2×C22⋊C4—478no—
521C2×C22⋊C4—478no—
522C2×C22⋊C4—944no—
523C2×C22⋊C4—944no—
524C2×C22⋊C4—948no—
525C2×C22⋊C4C22×D4714yes—
526C2×C22⋊C4C22×D4714yes—
527C2×C42—472no—
528C2×C42—472no—
529C2×C42—944no—
530#95—478no—
531#95—478no—
532#95C22×D4714yes—
533#95C22×D4714yes—
534C24—42no—
535C24—42no—
536C24—472no—
537C24—474no—
538C24—474no—
539C24—942no—
540C24—942no—
541C24—944no—
542C24—944no—
543C24—944no—
544C24—1884no—
545C24—1884no—
546C24—1882no—
547C24—1882no—
548C24C2×D18814yes—
549C24D4×D4714yes—
550C24#1062535414yes—
551C24C23×D4711yescharacteristic
552C24C23×D4711yescharacteristic
553C24C23×D4711yescharacteristic
554C2×D4—478no—
555C2×D4—478no—
556C2×D4—9416no—
557C2×D4—9432no—
558C2×D4—944no—
559C2×D4—944no—
560C2×D4—944no—
561C2×D4—944no—
562C2×D4—948no—
563C2×D4—948no—
564C2×D4—948no—
565C2×D4—948no—
566C2×D4—948no—
567C2×D4—948no—
568C2×D4—944no—
569C2×D4—944no—
570C2×D4—948no—
571C2×D4—1888no—
572C2×D4—1888no—
573C2×D4—1884no—
574C2×D4—18816no—
575C2×D4—18832no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—28no—
580C22×C4—416no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—474no—
587C22×C4—472no—
588C22×C4—472no—
589C22×C4—472no—
590C22×C4—474no—
591C22×C4—942no—
592C22×C4—942no—
593C22×C4—944no—
594C22×C4—942no—
595C22×C4—942no—
596C22×C4—944no—
597C22×C4—944no—
598C22×C4—944no—
599C22×C4—944no—
600C22×C4—948no—
601C22×C4—1884no—
602C22×C4—18816no—
603C22×C4—1882no—
604C22×C4—1882no—
605C22×C4C2×D18814yes—
606C22×C4C2×D18814yes—
607C22×C4C2×D18814yes—
608C22×C4C2×D18814yes—
609C22×C4C2×D18814yes—
610C22×C4C2×D18814yes—
611C22×C4C23×D4718yes—
612C22×C4C23×D4711yescharacteristic
613C22×C4C23×D4711yescharacteristic
614C22×C4C23×D4711yescharacteristic
615C22×C4C23×D4711yescharacteristic
616C4⋊C4—28no—
617C4⋊C4—44no—
618C4⋊C4—9416no—
619C4⋊C4—944no—
620C4⋊C4—944no—
621C4⋊C4—944no—
622C4⋊C4—944no—
623C22⋊C4—28no—
624C22⋊C4—28no—
625C22⋊C4—9416no—
626C22⋊C4—9416no—
627C22⋊C4—944no—
628C22⋊C4—944no—
629C22⋊C4—944no—
630C22⋊C4—944no—
631C22⋊C4—948no—
632C22⋊C4—948no—
633C22⋊C4—1888no—
634C22⋊C4—1888no—
635C42—944no—
636C42—944no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—44no—
644C23—44no—
645C23—48no—
646C23—48no—
647C23—474no—
648C23—948no—
649C23—942no—
650C23—942no—
651C23—944no—
652C23—944no—
653C23—944no—
654C23—944no—
655C23—944no—
656C23—948no—
657C23—948no—
658C23—3768no—
659C23—3768no—
660C23—1888no—
661C23—1888no—
662C23—1888no—
663C23—1884no—
664C23—1888no—
665C23—1884no—
666C23—1888no—
667C23#13093999116yescomplemented
668C23C2×D4×D4712yes—
669C23C2×D4×D4712yes—
670C23C2×D4×D4712yes—
671C23C22×D18812yes—
672C23C22×D18812yes—
673C23C22×D18812yes—
674C23C2×#1062535412yes—
675C23C2×#1062535412yes—
676C23C2×#1062535412yes—
677C23C24×D4711yescharacteristic
678D4—9416no—
679D4—9416no—
680D4—37616no—
681D4—1888no—
682D4—18816no—
683D4—18816no—
684D4—1888no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—28no—
689C2×C4—28no—
690C2×C4—28no—
691C2×C4—28no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—88no—
698C2×C4—474no—
699C2×C4—948no—
700C2×C4—942no—
701C2×C4—942no—
702C2×C4—944no—
703C2×C4—942no—
704C2×C4—942no—
705C2×C4—944no—
706C2×C4—944no—
707C2×C4—944no—
708C2×C4—944no—
709C2×C4—1888no—
710C2×C4—1884no—
711C2×C4—1884no—
712C2×C4—1888no—
713C2×C4—1888no—
714C2×C4C22×D18812yes—
715C2×C4C22×D18812yes—
716C2×C4C22×D18812yes—
717C2×C4C22×D18812yes—
718C2×C4#1309406914yes—
719C22—24no—
720C22—24no—
721C22—24no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—24no—
726C22—24no—
727C22—24no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—416no—
732C22—944no—
733C22—948no—
734C22—37616no—
735C22—18816no—
736C22—1884no—
737C22—1888no—
738C22—1884no—
739C22—1888no—
740C22—1884no—
741C22—1882no—
742C22—1884no—
743C22—1882no—
744C22C2×#1309399914yes—
745C22C2×#1309399914yes—
746C22C2×#1309399914yes—
747C22C22×D4×D4711yescharacteristic
748C22C23×D18811yescharacteristic
749C22C22×#1062535411yescharacteristic
750C22C2×#1309406912yes—
751C22#1568995912yes—
752C4—22no—
753C4—22no—
754C4—22no—
755C4—48no—
756C4—944no—
757C4—1884no—
758C4—1882no—
759C4—1882no—
760C4#1568968514yescomplemented
761C2—24no—
762C2—24no—
763C2—24no—
764C2—3764no—
765C2—1884no—
766C2C22×#1309399911yescharacteristic
767C2C2×#1568968511yescharacteristic
768C2#2025672111yescharacteristic
769C2#2025714512yes—
770C2#2025722912yes—
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC2×C47×#380C2
hypercenterC2×#380D47
hypocenterC47#35000
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C2×#15689685C2semidirect
2. C22×#13093998C2semidirect
3. C22×C4×C22⋊D47C2semidirect
4. #20251720C2semidirect
5. #20251671C2semidirect
6. #20249133C2semidirect
7. #20249125C2semidirect
8. #20248348C2semidirect
9. #20248280C2semidirect
10. #20247697C2semidirect
11. #20246822C2semidirect
12. #20246745C2semidirect
13. #20245963C2semidirect
14. C2×C47×#380C2semidirect
15. C23×D188C22semidirect
18. C23×C4×D47C22semidirect
21. C2×#13094008C22semidirect
22. C2×#13093999C22semidirect
26. C2×#13093998C22semidirect
27. C2×#13093998C22semidirect
28. C2×#13093998C22semidirect
30. C2×#13093994C22semidirect
34. C2×C4×C22⋊D47C22semidirect
35. C2×C4×C22⋊D47C22semidirect
36. C22×C4⋊Dic47C22semidirect
37. C22×Dic47⋊C4C22semidirect
39. C22×(C2×D47)⋊C4C22semidirect
40. C22×(C2×D47)⋊C4C22semidirect
41. C22×C4×Dic47C22semidirect
42. #15689055C22semidirect
43. #15689050C22semidirect
44. #15689045C22semidirect
45. #15689041C22semidirect
46. #15689040C22semidirect
47. #15689033C22semidirect
48. #15689024C22semidirect
49. #15689022C22semidirect
50. #15689015C22semidirect
51. #15689002C22semidirect
52. #15689001C22semidirect
53. #15689000C22semidirect
54. #15689000C22semidirect
55. #15688984C22semidirect
56. #15688980C22semidirect
57. #15688978C22semidirect
59. C22×C4⋊C4×C47C22semidirect
61. C47×#380C22semidirect
62. C47×#380C22semidirect
63. C47×#380C22semidirect
64. C47×#380C22semidirect
65. C2×#95×C47C22semidirect
78. C22×C22⋊D47D4semidirect
132. C23×C4×C47D4semidirect
165. C23×D47C2×D4semidirect
202. C2×C22⋊D47C2×D4semidirect
212. C22×Dic47C2×D4semidirect
261. C23×C47#121semidirect
371. C4×C47#534semidirect
389. C2×#380D47semidirect
424. C22×C4⋊C4C2×D47semidirect
445. #380C2×D47semidirect
446. #380C2×D47semidirect
447. #380C2×D47semidirect
448. #380C2×D47semidirect
450. C2×#95C2×D47semidirect
451. C47#35000semidirect
479. C23×C4D188semidirect
667. C23#13093999semidirect
760. C4#15689685semidirect

Maximal subgroups

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

subgroupindex
C2×#156896852
C22×#130939982
C22×C4×C22⋊D472
#202517202
#202516712
#202491332
#202491252
#202483482
#202482802
#202476972
#202468222
#202467452
#202459632
C2×C47×#3802
#3500047