Finite Group Databasebeta

← #26388865

Subgroups — #26388865

Order 12032.

2866 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689749C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D47C211yesmaximal, characteristic
3#20251724C212yesmaximal, complemented
4#20251674C212yesmaximal, complemented
5#20249207C212yesmaximal, complemented
6#20249199C212yesmaximal, complemented
7#20247214C214yesmaximal, complemented
8#20247212C214yesmaximal, complemented
9#20247199C214yesmaximal, complemented
10#20247197C214yesmaximal, complemented
11#20246000C211yesmaximal, characteristic, complemented
12#20245963C211yesmaximal, characteristic
13#20245963C211yesmaximal, characteristic
14C2×#15688996C211yesmaximal, characteristic, complemented
15C2×C47×#385C211yesmaximal, characteristic, complemented
16C23×C22⋊D47C2211yescharacteristic
17C23×C4×D47C2211yescharacteristic
18#15689749—28no—
19C2×#13094003C2212yescomplemented
20C2×#13094003C2212yescomplemented
21C2×#13094002C2214yescomplemented
22C2×#13094001C2212yes—
23C2×#13094001C2212yes—
24C2×#13094001C2212yescomplemented
25C2×#13094001C2212yescomplemented
26C2×C4×C22⋊D47—28no—
27C2×C4×C22⋊D47C2214yes—
28C2×C4×C22⋊D47C2214yes—
29C22×Dic47⋊C4C2211yescharacteristic
30C22×Dic47⋊C4C2212yescomplemented
31C22×C22⋊Dic47C2211yescharacteristic
32C22×C22⋊Dic47C2211yescharacteristic
33C22×C22⋊Dic47C2211yescharacteristic
34C22×(C2×D47)⋊C4C2211yescharacteristic
35C22×C4×Dic47C2211yescharacteristic
36#15689064C2214yescomplemented
37#15689058C2214yescomplemented
38#15689057C2214yescomplemented
39#15689054C2214yescomplemented
40#15689047C2214yescomplemented
41#15689045C2214yescomplemented
42#15689043C2214yescomplemented
43#15689036C2214yescomplemented
44#15689027C2214yescomplemented
45#15689018C2214yescomplemented
46#15689009C2214yescomplemented
47#15689005C2214yescomplemented
48#15689002C2212yes—
49#15689002C2214yes—
50#15689002C2212yes—
51#15689000C2212yes—
52#15689000C2214yes—
53#15689000C2212yes—
54#15688997C2214yescomplemented
55#15688996C2212yes—
56#15688996C2212yes—
57#15688996C2214yescomplemented
58#15688996C2214yescomplemented
59#15688995C2214yescomplemented
60#15688994C2214yescomplemented
61#15688984C2212yes—
62#15688984C2212yes—
63#15688982C2214yescomplemented
64#15688981C2212yes—
65#15688981C2212yes—
66#15688978C2212yes—
67#15688978C2212yes—
68C2×C47⋊#95C2212yescomplemented
69C24×C4×C47C2211yescharacteristic
70C22×C4⋊C4×C47C2212yescomplemented
71C22×C22⋊C4×C47C2211yescharacteristic
72C22×C22⋊C4×C47C2211yescharacteristic
73C47×#385C2212yes—
74C47×#385C2212yes—
75C47×#385C2214yescomplemented
76C2×#95×C47C2212yescomplemented
77C24×D47C2311yescharacteristic
78C22×Dic94C2312yes—
79C22×Dic94C2312yes—
80C22×C22⋊D47—24no—
81C22×C22⋊D47—24no—
82C22×C22⋊D47Q818yescomplemented
83C22×C22⋊D47C2312yes—
84C22×C22⋊D47C2312yes—
85C23×Dic47C2311yescharacteristic
86C23×Dic47C2311yescharacteristic
87C23×Dic47C2312yes—
88C23×Dic47C2311yescharacteristic
89C23×Dic47C2311yescharacteristic
90C23×Dic47C2311yescharacteristic
91C22×C4×D47—24no—
92C22×C4×D47—44no—
93C22×C4×D47C2314yes—
94#13094003—28no—
95#13094003—28no—
96#13094002—48no—
97#13094001—28no—
98#13094001—28no—
99#13094001—28no—
100#13094001—28no—
101C4×C22⋊D47—216no—
102C4×C22⋊D47—216no—
103C2×C4⋊Dic47C2312yes—
104C2×C4⋊Dic47C2312yes—
105C2×Dic47⋊C4—24no—
106C2×Dic47⋊C4—44no—
107C2×Dic47⋊C4C2312yes—
108C2×Dic47⋊C4C2312yes—
109C2×Dic47⋊C4C2314yes—
110C2×Dic47⋊C4C2312yes—
111C2×Dic47⋊C4C2312yes—
112C2×Dic47⋊C4C2314yes—
113C2×Dic47⋊C4C2314yes—
114C2×Dic47⋊C4C2314yes—
115C2×Dic47⋊C4C2314yes—
116C2×C22⋊Dic47—24no—
117C2×C22⋊Dic47—24no—
118C2×C22⋊Dic47D418yes—
119C2×C22⋊Dic47C2312yes—
120C2×C22⋊Dic47C2312yes—
121C2×C22⋊Dic47C2312yes—
122C2×C22⋊Dic47C2312yes—
123C2×C22⋊Dic47C2312yes—
124C2×C22⋊Dic47C2312yes—
125C2×(C2×D47)⋊C4—24no—
126C2×(C2×D47)⋊C4C2314yes—
127C2×(C2×D47)⋊C4C2314yes—
128C2×(C2×D47)⋊C4C2314yes—
129C2×(C2×D47)⋊C4C2314yes—
130C2×(C2×D47)⋊C4C2314yes—
131C2×C4×Dic47—24no—
132C2×C4×Dic47C2314yes—
133C47⋊#95C2314yes—
134C47⋊#95C2314yes—
135C47⋊#95C2314yes—
136C47⋊#95C2314yes—
137C47⋊#95C2314yes—
138C47⋊#95C2314yes—
139C47⋊#95C2314yes—
140C47⋊#95C2314yes—
141C25×C47C2311yescharacteristic
142C23×C4×C47—24no—
143C23×C4×C47—44no—
144C23×C4×C47C2311yescharacteristic
145C23×C4×C47C2312yes—
146C23×C4×C47C2312yes—
147C23×C4×C47C2311yescharacteristic
148C23×C4×C47C2312yes—
149C23×C4×C47C2311yescharacteristic
150C23×C4×C47C2311yescharacteristic
151C2×C4⋊C4×C47—44no—
152C2×C4⋊C4×C47C2314yes—
153C2×C4⋊C4×C47C2314yes—
154C2×C22⋊C4×C47—24no—
155C2×C22⋊C4×C47—24no—
156C2×C22⋊C4×C47C2312yes—
157C2×C22⋊C4×C47C2312yes—
158C2×C22⋊C4×C47C2312yes—
159C2×C22⋊C4×C47C2312yes—
160#95×C47C2314yes—
161#95×C47C2314yes—
162C24×C47—42no—
163C24×C47—42no—
164C24×C47C2×D414yes—
165C24×C47C2×Q814yes—
166C24×C47#4114yes—
167C24×C47C2411yescharacteristic
168C24×C47C2411yescharacteristic
169C24×C47C2411yescharacteristic
170C23×D47—22no—
171C23×D47—22no—
172C23×D47—42no—
173C23×D47—42no—
174C23×D47C2×Q814yes—
175C23×D47C2412yes—
176C22×C4×C47—22no—
177C22×C4×C47—24no—
178C22×C4×C47—22no—
179C22×C4×C47—24no—
180C22×C4×C47—24no—
181C22×C4×C47—24no—
182C22×C4×C47—22no—
183C22×C4×C47—22no—
184C22×C4×C47—24no—
185C22×C4×C47—24no—
186C22×C4×C47—42no—
187C22×C4×C47—42no—
188C22×C4×C47—42no—
189C22×C4×C47—42no—
190C22×C4×C47—42no—
191C22×C4×C47—42no—
192C22×C4×C47—42no—
193C22×C4×C47—416no—
194C22×C4×C47C2412yes—
195C22×C4×C47C2414yes—
196C22×C4×C47C2412yes—
197C22×C4×C47C2412yes—
198C22×C4×C47C2412yes—
199C2×C22⋊D47—232no—
200C2×C22⋊D47—24no—
201C2×C22⋊D47—24no—
202C2×C22⋊D47—24no—
203C2×C22⋊D47—24no—
204C2×C22⋊D47C2×Q818yes—
205C2×C22⋊D47C2×Q818yes—
206C22×Dic47—22no—
207C22×Dic47—22no—
208C22×Dic47—24no—
209C22×Dic47—22no—
210C22×Dic47—22no—
211C22×Dic47—42no—
212C22×Dic47—42no—
213C22×Dic47—42no—
214C22×Dic47—42no—
215C22×Dic47—42no—
216C22×Dic47—42no—
217C22×Dic47C2×D414yes—
218C22×Dic47C2×D414yes—
219C22×Dic47C2×Q814yes—
220C22×Dic47C2414yes—
221C22×Dic47C2412yes—
222C22×Dic47C2412yes—
223C22×Dic47C2412yes—
224C22×Dic47C2412yes—
225C22×Dic47C2412yes—
226C2×C4×D47—28no—
227C2×C4×D47—28no—
228C2×C4×D47—44no—
229C2×C4×D47—416no—
230C2×Dic94—24no—
231C2×Dic94—24no—
232C2×Dic94—44no—
233C2×Dic94—44no—
234C4⋊C4×C47—28no—
235C4⋊C4×C47—44no—
236C22⋊C4×C47—24no—
237C22⋊C4×C47—24no—
238C22⋊C4×C47—24no—
239C22⋊C4×C47—24no—
240C22⋊Dic47—24no—
241C22⋊Dic47—24no—
242C22⋊Dic47—24no—
243C22⋊Dic47—24no—
244C22⋊Dic47C2×D418yes—
245C22⋊Dic47C2×D418yes—
246(C2×D47)⋊C4—28no—
247(C2×D47)⋊C4—44no—
248(C2×D47)⋊C4—44no—
249(C2×D47)⋊C4—44no—
250(C2×D47)⋊C4—44no—
251C4⋊Dic47—24no—
252C4⋊Dic47—24no—
253Dic47⋊C4—28no—
254Dic47⋊C4—28no—
255Dic47⋊C4—24no—
256Dic47⋊C4—24no—
257Dic47⋊C4—24no—
258Dic47⋊C4—24no—
259Dic47⋊C4—44no—
260Dic47⋊C4—44no—
261Dic47⋊C4—44no—
262C4×Dic47—28no—
263C23×C47—22no—
264C23×C47—22no—
265C23×C47—22no—
266C23×C47—22no—
267C23×C47—22no—
268C23×C47—22no—
269C23×C47—44no—
270C23×C47—44no—
271C23×C47—48no—
272C23×C47—48no—
273C23×C47C22⋊Q8116yescomplemented
274C23×C47C22×D412yes—
275C23×C47C22×D412yes—
276C23×C47C22×D412yes—
277C23×C47C22×Q812yes—
278C23×C47C22×Q812yes—
279C23×C47C22×Q812yes—
280C23×C47C2×#4112yes—
281C23×C47C2×#4112yes—
282C23×C47C2×#4112yes—
283C23×C47C2511yescharacteristic
284C22×D47—28no—
285C22×D47—22no—
286C22×D47—22no—
287C22×D47—24no—
288C22×D47—24no—
289C22×D47—48no—
290C22×D47—44no—
291C22×D47—48no—
292C22×D47—44no—
293C22×D47C22×Q814yes—
294C2×C4×C47—28no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47—24no—
301C2×C4×C47—22no—
302C2×C4×C47—24no—
303C2×C4×C47—24no—
304C2×C4×C47—22no—
305C2×C4×C47—24no—
306C2×C4×C47—24no—
307C2×C4×C47—48no—
308C2×C4×C47—48no—
309C2×C4×C47—48no—
310C2×C4×C47—44no—
311C2×C4×C47—82no—
312C2×C4×C47—82no—
313C2×C4×C47H(5,𝔽2)14yes—
314C22⋊D47—216no—
315C22⋊D47—216no—
316C2×Dic47—28no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—24no—
320C2×Dic47—24no—
321C2×Dic47—22no—
322C2×Dic47—22no—
323C2×Dic47—24no—
324C2×Dic47—24no—
325C2×Dic47—24no—
326C2×Dic47—24no—
327C2×Dic47—24no—
328C2×Dic47—44no—
329C2×Dic47—44no—
330C2×Dic47—48no—
331C2×Dic47—82no—
332C2×Dic47—82no—
333C2×Dic47C22×D414yes—
334C2×Dic47C22×D414yes—
335C2×Dic47C22×Q814yes—
336C4×D47—416no—
337Dic94—84no—
338Dic94—84no—
339#34985—471nomaximal, Sylow
340C22×C47—24no—
341C22×C47—24no—
342C22×C47—24no—
343C22×C47—22no—
344C22×C47—22no—
345C22×C47—22no—
346C22×C47—22no—
347C22×C47—22no—
348C22×C47—22no—
349C22×C47—24no—
350C22×C47—24no—
351C22×C47—24no—
352C22×C47—416no—
353C22×C47C2×C22⋊Q814yes—
354C22×C47C2×C22⋊Q814yes—
355C22×C47C2×C22⋊Q814yes—
356C22×C47C23×D411yescharacteristic
357C22×C47C23×Q811yescharacteristic
358C22×C47C22×#4111yescharacteristic
359C22×C47C2×H(5,𝔽2)12yes—
360C22×C47#58512yes—
361C2×D47—24no—
362C2×D47—28no—
363C2×D47—416no—
364C2×D47—44no—
365C2×D47—42no—
366C2×D47—42no—
367C4×C47—24no—
368C4×C47—44no—
369C4×C47—42no—
370C4×C47—42no—
371C4×C47—42no—
372Dic47—24no—
373Dic47—24no—
374Dic47—24no—
375Dic47—44no—
376Dic47—42no—
377Dic47—42no—
378C2×#543—471no—
379C22×C4×D4—471no—
380#2855—472no—
381#2848—472no—
382#2627—472no—
383#2626—472no—
384#2450—474no—
385#2450—474no—
386#2449—474no—
387#2449—474no—
388#2315—471no—
389#2308—471no—
390#2308—471no—
391C2×#385—471no—
392C2×#385D4711yescharacteristic, complemented
393C2×C47—24no—
394C2×C47—24no—
395C2×C47—24no—
396C2×C47C22×C22⋊Q811yescharacteristic
397C2×C47#345912yes—
398C2×C47#348411yescharacteristic
399C2×C47#348511yescharacteristic
400C2×C47#350112yes—
401D47—44no—
402C23×D4—471no—
403C24×C4—471no—
404C24×C4C2×D4711yescharacteristic
405#543—948no—
406C2×C22⋊Q8—472no—
407C2×C22⋊Q8—472no—
408C2×C22⋊Q8—474no—
409C2×C22⋊Q8—472no—
410C2×C22⋊Q8—472no—
411C2×C22⋊Q8—472no—
412C2×C22⋊Q8—472no—
413C2×C4×D4—474no—
414C2×C4×D4—474no—
415C2×C4×D4—948no—
416C22×C4⋊C4—471no—
417C22×C4⋊C4—472no—
418C22×C4⋊C4C2×D4712yescomplemented
419C22×C22⋊C4—471no—
420C22×C22⋊C4—471no—
421C22×C22⋊C4—471no—
422C22×C22⋊C4—471no—
423C22×C22⋊C4C2×D4711yescharacteristic
424C22×C22⋊C4C2×D4711yescharacteristic
425C22×C42—471no—
426#400—474no—
427#399—474no—
428#398—474no—
429#398—474no—
430#396—474no—
431#396—474no—
432#395—474no—
433#393—474no—
434#391—474no—
435#389—474no—
436#387—474no—
437#387—474no—
438#386—472no—
439#386—474no—
440#386—472no—
441#386—472no—
442#386—474no—
443#386—472no—
444#385—474no—
445#385—472no—
446#385—472no—
447#385—474no—
448#385—474no—
449#385—474no—
450#385—474no—
451#385C2×D4712yes—
452#385C2×D4712yes—
453#385C2×D4714yescomplemented
454#381—472no—
455#381—472no—
456#380—472no—
457#380—472no—
458#380—474no—
459#379—472no—
460#379—472no—
461C2×#95—472no—
462C2×#95C2×D4712yescomplemented
463C47#3498511yescharacteristic, complemented, Sylow
464C25—471no—
465C25C22×D4711yescharacteristic
466C22×Q8—472no—
467C22×Q8—472no—
468C22×D4—478no—
469C22×D4—472no—
470C22×D4—472no—
471C22×D4—944no—
472C22×D4—944no—
473C23×C4—24no—
474C23×C4—44no—
475C23×C4—471no—
476C23×C4—471no—
477C23×C4—471no—
478C23×C4—471no—
479C23×C4—472no—
480C23×C4—471no—
481C23×C4—474no—
482C23×C4—944no—
483C23×C4—1884no—
484C23×C4C22×D4711yescharacteristic
485C23×C4C22×D4712yes—
486C23×C4C22×D4712yes—
487C23×C4C22×D4711yescharacteristic
488C23×C4C22×D4711yescharacteristic
489C23×C4C22×D4712yes—
490C23×C4C22×D4711yescharacteristic
491C22⋊Q8—948no—
492C22⋊Q8—948no—
493C22⋊Q8—948no—
494C22⋊Q8—948no—
495C22⋊Q8—948no—
496C22⋊Q8—948no—
497C22⋊Q8—1888no—
498C4×D4—9416no—
499C4×D4—9416no—
500C2×C4⋊C4—44no—
501C2×C4⋊C4—474no—
502C2×C4⋊C4—474no—
503C2×C4⋊C4—472no—
504C2×C4⋊C4—472no—
505C2×C4⋊C4—472no—
506C2×C4⋊C4—472no—
507C2×C4⋊C4—472no—
508C2×C4⋊C4—472no—
509C2×C4⋊C4—474no—
510C2×C4⋊C4—474no—
511C2×C4⋊C4—474no—
512C2×C4⋊C4—944no—
513C2×C4⋊C4—1884no—
514C2×C4⋊C4C22×D4714yes—
515C2×C4⋊C4C22×D4714yes—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—478no—
519C2×C22⋊C4—472no—
520C2×C22⋊C4—472no—
521C2×C22⋊C4—472no—
522C2×C22⋊C4—472no—
523C2×C22⋊C4—472no—
524C2×C22⋊C4—472no—
525C2×C22⋊C4—474no—
526C2×C22⋊C4—474no—
527C2×C22⋊C4—474no—
528C2×C22⋊C4—474no—
529C2×C22⋊C4—474no—
530C2×C22⋊C4—944no—
531C2×C22⋊C4—944no—
532C2×C22⋊C4—944no—
533C2×C22⋊C4C22×D4712yes—
534C2×C22⋊C4C22×D4712yes—
535C2×C22⋊C4C22×D4712yes—
536C2×C22⋊C4C22×D4712yes—
537C2×C42—474no—
538C2×C42—944no—
539#95—474no—
540#95—474no—
541#95—474no—
542#95—474no—
543#95—474no—
544#95—474no—
545#95—474no—
546#95—474no—
547#95C22×D4714yes—
548#95C22×D4714yes—
549C24—42no—
550C24—42no—
551C24—472no—
552C24—474no—
553C24—942no—
554C24—942no—
555C24—1882no—
556C24—1882no—
557C24#1062535014yes—
558C24D4×D4714yes—
559C24Q8×D4714yes—
560C24C23×D4711yescharacteristic
561C24C23×D4711yescharacteristic
562C24C23×D4711yescharacteristic
563C2×Q8—944no—
564C2×Q8—944no—
565C2×Q8—1884no—
566C2×Q8—1884no—
567C2×D4—478no—
568C2×D4—478no—
569C2×D4—9432no—
570C2×D4—944no—
571C2×D4—944no—
572C2×D4—944no—
573C2×D4—944no—
574C22×C4—22no—
575C22×C4—24no—
576C22×C4—22no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—416no—
592C22×C4—474no—
593C22×C4—472no—
594C22×C4—472no—
595C22×C4—472no—
596C22×C4—474no—
597C22×C4—474no—
598C22×C4—474no—
599C22×C4—472no—
600C22×C4—472no—
601C22×C4—948no—
602C22×C4—942no—
603C22×C4—942no—
604C22×C4—942no—
605C22×C4—942no—
606C22×C4—944no—
607C22×C4—948no—
608C22×C4—1884no—
609C22×C4—18816no—
610C22×C4—1882no—
611C22×C4—1882no—
612C22×C4—1882no—
613C22×C4—1882no—
614C22×C4—1882no—
615C22×C4—1882no—
616C22×C4C23×D4714yes—
617C22×C4C23×D4712yes—
618C22×C4C23×D4712yes—
619C22×C4C23×D4712yes—
620C22×C4C23×D4712yes—
621C4⋊C4—28no—
622C4⋊C4—44no—
623C4⋊C4—948no—
624C4⋊C4—944no—
625C4⋊C4—944no—
626C4⋊C4—944no—
627C4⋊C4—944no—
628C4⋊C4—944no—
629C4⋊C4—944no—
630C4⋊C4—948no—
631C4⋊C4—1884no—
632C4⋊C4—1884no—
633C4⋊C4—1884no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—478no—
639C22⋊C4—478no—
640C22⋊C4—948no—
641C22⋊C4—944no—
642C22⋊C4—944no—
643C22⋊C4—944no—
644C22⋊C4—944no—
645C22⋊C4—1884no—
646C22⋊C4—1884no—
647C22⋊C4—1884no—
648C22⋊C4—1884no—
649C42—948no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—44no—
657C23—48no—
658C23—44no—
659C23—48no—
660C23—474no—
661C23—948no—
662C23—942no—
663C23—942no—
664C23—944no—
665C23—944no—
666C23—1888no—
667C23—1884no—
668C23—1884no—
669C23—1888no—
670C23#13094002116yescomplemented
671C23C2×D4×D4712yes—
672C23C2×D4×D4712yes—
673C23C2×D4×D4712yes—
674C23C2×Q8×D4712yes—
675C23C2×Q8×D4712yes—
676C23C2×Q8×D4712yes—
677C23C2×#1062535012yes—
678C23C2×#1062535012yes—
679C23C2×#1062535012yes—
680C23C24×D4711yescharacteristic
681Q8—3764no—
682Q8—3764no—
683D4—9416no—
684D4—9416no—
685C2×C4—28no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—48no—
699C2×C4—48no—
700C2×C4—48no—
701C2×C4—44no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4—474no—
705C2×C4—474no—
706C2×C4—474no—
707C2×C4—948no—
708C2×C4—942no—
709C2×C4—942no—
710C2×C4—944no—
711C2×C4—944no—
712C2×C4—942no—
713C2×C4—942no—
714C2×C4—944no—
715C2×C4—944no—
716C2×C4—944no—
717C2×C4—944no—
718C2×C4—944no—
719C2×C4—3762no—
720C2×C4—3762no—
721C2×C4—18816no—
722C2×C4—1884no—
723C2×C4—1884no—
724C2×C4—1888no—
725C2×C4#1309406914yes—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—24no—
730C22—24no—
731C22—24no—
732C22—24no—
733C22—24no—
734C22—24no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—416no—
739C22—944no—
740C22—948no—
741C22—18816no—
742C22—1882no—
743C22—1884no—
744C22—1882no—
745C22C2×#1309400214yes—
746C22C2×#1309400214yes—
747C22C2×#1309400214yes—
748C22C22×D4×D4711yescharacteristic
749C22C22×Q8×D4711yescharacteristic
750C22C22×#1062535011yescharacteristic
751C22C2×#1309406912yes—
752C22#1568995912yes—
753C4—24no—
754C4—42no—
755C4—44no—
756C4—42no—
757C4—42no—
758C4—944no—
759C4—944no—
760C4—944no—
761C4—1882no—
762C4—1884no—
763C4—1882no—
764C2—24no—
765C2—24no—
766C2—24no—
767C2—1884no—
768C2C22×#1309400211yescharacteristic
769C2#2025679712yes—
770C2#2025701711yescharacteristic
771C2#2025702611yescharacteristic
772C2#2025718412yes—
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC2×C47×#385C2
prime radicalC23×C22⋊D47C22
hypercenterC2×#385D47
hypocenterC47#34985
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C2×#15689749C2semidirect
3. #20251724C2semidirect
4. #20251674C2semidirect
5. #20249207C2semidirect
6. #20249199C2semidirect
7. #20247214C2semidirect
8. #20247212C2semidirect
9. #20247199C2semidirect
10. #20247197C2semidirect
11. #20246000C2semidirect
14. C2×#15688996C2semidirect
15. C2×C47×#385C2semidirect
19. C2×#13094003C22semidirect
20. C2×#13094003C22semidirect
21. C2×#13094002C22semidirect
24. C2×#13094001C22semidirect
25. C2×#13094001C22semidirect
30. C22×Dic47⋊C4C22semidirect
36. #15689064C22semidirect
37. #15689058C22semidirect
38. #15689057C22semidirect
39. #15689054C22semidirect
40. #15689047C22semidirect
41. #15689045C22semidirect
42. #15689043C22semidirect
43. #15689036C22semidirect
44. #15689027C22semidirect
45. #15689018C22semidirect
46. #15689009C22semidirect
47. #15689005C22semidirect
54. #15688997C22semidirect
57. #15688996C22semidirect
58. #15688996C22semidirect
59. #15688995C22semidirect
60. #15688994C22semidirect
63. #15688982C22semidirect
68. C2×C47⋊#95C22semidirect
70. C22×C4⋊C4×C47C22semidirect
75. C47×#385C22semidirect
76. C2×#95×C47C22semidirect
82. C22×C22⋊D47Q8semidirect
273. C23×C47C22⋊Q8semidirect
392. C2×#385D47semidirect
418. C22×C4⋊C4C2×D47semidirect
453. #385C2×D47semidirect
462. C2×#95C2×D47semidirect
463. C47#34985semidirect
670. C23#13094002semidirect

Maximal subgroups

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

subgroupindex
C2×#156897492
C22×C4×C22⋊D472
#202517242
#202516742
#202492072
#202491992
#202472142
#202472122
#202471992
#202471972
#202460002
#202459632
C2×#156889962
C2×C47×#3852
#3498547