Finite Group Databasebeta

← #26217239

Subgroups — #26217239

Order 12032.

1446 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D47C211yesmaximal, characteristic
2C2×#15689164C211yesmaximal, characteristic
3C2×#15689130C211yesmaximal, characteristic
4C2×#15689130C211yesmaximal, characteristic
5#20245869C211yesmaximal, characteristic
6#20243659C211yesmaximal, characteristic, complemented
7#20243658C211yesmaximal, characteristic, complemented
8#20243657C211yesmaximal, characteristic, complemented
9#20243656C211yesmaximal, characteristic, complemented
10#20243641C211yesmaximal, characteristic, complemented
11#20243640C211yesmaximal, characteristic, complemented
12#20243639C211yesmaximal, characteristic, complemented
13#20243106C211yesmaximal, characteristic
14#20243080C211yesmaximal, characteristic
15C47×#1863C211yesmaximal, characteristic, complemented
16C22×Q8×D47C2211yescharacteristic
17C22×#10625324C2211yescharacteristic
18C22×#10625324C2211yescharacteristic
19C2×Q8×Dic47C2211yescharacteristic
20C2×C4×Dic94—21no—
21C2×C4×Dic94C2211yescharacteristic
22C2×#13093989—21no—
23C2×#13093989C2211yescharacteristic
24C4×Q8×D47—24no—
25C4×Q8×D47—24no—
26C2×#13093982C2211yescharacteristic
27C2×#13093982C2211yescharacteristic
28C2×C4⋊C4×D47—21no—
29C2×C4⋊C4×D47C2211yescharacteristic
30C2×C42×D47—21no—
31C2×C42×D47C2211yescharacteristic
32#15689164—24no—
33C2×#13093957C2211yescharacteristic
34C2×#13093956C2211yescharacteristic
35C2×#13093955C2211yescharacteristic
36#15689130—24no—
37#15689130C418yescomplemented
38C2×#13093949C2211yescharacteristic
39C2×#13093949C2211yescharacteristic
40C2×#13093948C2211yescharacteristic
41C2×#13093948C2211yescharacteristic
42C2×#13093947C2211yescharacteristic
43C2×#13093947C2211yescharacteristic
44#15689022C2211yescharacteristic
45#15689021C2211yescharacteristic
46#15689019C2211yescharacteristic
47#15688997—21no—
48#15688994—21no—
49C4⋊C4×Dic47—21no—
50#15688974—21no—
51#15688886C2211yescharacteristic
52#15688885C2211yescharacteristic
53#15688885C2211yescharacteristic
54#15688878C2211yescharacteristic
55#15688877C2211yescharacteristic
56#15688877C2211yescharacteristic
57C2×C4×Q8×C47C2211yescharacteristic
58C2×#107×C47C2211yescharacteristic
59C2×#103×C47C2211yescharacteristic
60C2×#103×C47C2211yescharacteristic
61C47×#389C2211yescharacteristic
62C47×#340C2211yescharacteristic
63C47×#336C2211yescharacteristic
64C22×Dic94—21no—
65C22×Dic94C2311yescharacteristic
66C2×Q8×D47—22no—
67C2×Q8×D47—22no—
68C2×Q8×D47—22no—
69C2×Q8×D47C2×C414yes—
70C2×Q8×D47D414yes—
71C2×Q8×D47Q814yes—
72C22×C4×D47—21no—
73C22×C4×D47—21no—
74C22×C4×D47D411yescharacteristic
75C22×C4×D47D411yescharacteristic
76C22×C4×D47C2311yescharacteristic
77C2×#10625324—22no—
78C2×#10625324—22no—
79C2×#10625324—22no—
80C2×#10625324—22no—
81C2×#10625324—22no—
82C2×#10625324C2×C414yes—
83C22×C47⋊C8C2311yescharacteristic
84C22×C47⋊C8C2311yescharacteristic
85Q8×Dic47—22no—
86Q8×Dic47—22no—
87C4×Dic94—28no—
88C4×Dic94—22no—
89C4×Dic94—22no—
90#13093989—28no—
91#13093989—22no—
92#13093989—22no—
93#13093982—22no—
94#13093982—22no—
95#13093982—22no—
96#13093982C2×C414yes—
97C2×C4⋊Dic47—21no—
98C2×C4⋊Dic47—21no—
99C2×C4⋊Dic47C2311yescharacteristic
100C2×C4⋊Dic47C2311yescharacteristic
101C2×C4⋊Dic47C2311yescharacteristic
102C2×Dic47⋊C4—21no—
103C2×Dic47⋊C4—21no—
104C2×Dic47⋊C4—21no—
105C2×Dic47⋊C4—21no—
106C2×Dic47⋊C4—21no—
107C4⋊C4×D47—28no—
108C4⋊C4×D47—22no—
109C4⋊C4×D47D414yes—
110C2×(C2×D47)⋊C4—21no—
111C2×(C2×D47)⋊C4—21no—
112C2×C4×Dic47—21no—
113C2×C4×Dic47—21no—
114C2×C4×Dic47—21no—
115C2×C4×Dic47—21no—
116C2×C4×Dic47—21no—
117C2×C4×Dic47D411yescharacteristic
118C2×C4×Dic47D411yescharacteristic
119C2×C4×Dic47C2311yescharacteristic
120C42×D47—28no—
121C42×D47—22no—
122C42×D47—22no—
123#13093957—22no—
124#13093956—22no—
125#13093955—22no—
126#13093949—22no—
127#13093949C2×C414yescomplemented
128#13093948—22no—
129#13093948C2×C414yescomplemented
130#13093947—22no—
131#13093947C2×C414yescomplemented
132C47⋊#95—21no—
133C47⋊#95—21no—
134C47⋊#95—21no—
135C22×Q8×C47C2311yescharacteristic
136C22×C8×C47C2311yescharacteristic
137C22×C8×C47C2311yescharacteristic
138C4×Q8×C47—22no—
139C4×Q8×C47—22no—
140C2×C4⋊C4×C47—21no—
141C2×C4⋊C4×C47—21no—
142C2×C4⋊C4×C47C2311yescharacteristic
143C2×C4⋊C4×C47C2311yescharacteristic
144C2×C4⋊C4×C47C2311yescharacteristic
145C2×C42×C47—21no—
146C2×C42×C47C2311yescharacteristic
147#107×C47—22no—
148#103×C47—22no—
149#103×C47C2×C414yescomplemented
150#95×C47—21no—
151C23×D47C2×D411yescharacteristic
152C2×Q8×C47—21no—
153C2×Q8×C47—21no—
154C2×Q8×C47—21no—
155C2×Q8×C47C22×C412yes—
156C2×Q8×C47C2×D412yes—
157C2×Q8×C47C2×Q812yes—
158C22×C4×C47—21no—
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47—21no—
162C22×C4×C47C2×D411yescharacteristic
163C22×C4×C47C2×D411yescharacteristic
164C22×C4×C47C2411yescharacteristic
165C22×Dic47—21no—
166C22×Dic47—21no—
167C22×Dic47—21no—
168C22×Dic47—21no—
169C22×Dic47C2×D411yescharacteristic
170C22×Dic47C2×D411yescharacteristic
171C22×Dic47C2×D411yescharacteristic
172Q8×D47—28no—
173Q8×D47—28no—
174Q8×D47—28no—
175Q8×D47C4⋊C4116yescomplemented
176C2×C4×D47—24no—
177C2×C4×D47—22no—
178C2×C4×D47—24no—
179C2×C4×D47—24no—
180C2×C4×D47—22no—
181C2×C4×D47—22no—
182C2×C4×D47—22no—
183C2×C4×D47—24no—
184C2×C4×D47—41no—
185C2×C4×D47—41no—
186C2×C4×D47—42no—
187C2×C4×D47—42no—
188C2×C4×D47C22×C412yes—
189C2×C4×D47C2×D412yes—
190C2×C4×D47C2×D412yes—
191C2×C4×D47C2×Q812yes—
192C2×C4×D47#4112yes—
193C2×C4×D47#4112yes—
194C2×Dic94—21no—
195C2×Dic94—21no—
196C2×Dic94—21no—
197C2×Dic94—24no—
198C2×Dic94—24no—
199C2×Dic94—24no—
200C2×Dic94C22×C412yes—
201C2×Dic94C2×D412yes—
202C2×Dic94C2×Q812yes—
203C2×C8×C47—21no—
204C2×C8×C47—21no—
205C2×C8×C47—21no—
206C2×C8×C47—21no—
207C2×C8×C47—21no—
208C2×C8×C47C22×C412yes—
209C4⋊C4×C47—24no—
210C4⋊C4×C47—21no—
211C4⋊C4×C47—21no—
212C4⋊C4×C47—21no—
213C4⋊C4×C47—21no—
214C4⋊C4×C47—42no—
215C4⋊C4×C47C22×C412yes—
216C4⋊C4×C47C2×D412yes—
217C42×C47—24no—
218C42×C47—21no—
219C42×C47—21no—
220(C2×D47)⋊C4—24no—
221(C2×D47)⋊C4—42no—
222C4⋊Dic47—24no—
223C4⋊Dic47—21no—
224C4⋊Dic47—21no—
225C4⋊Dic47—21no—
226C4⋊Dic47—21no—
227C4⋊Dic47—42no—
228C4⋊Dic47C22×C412yes—
229C4⋊Dic47C2×D412yes—
230Dic47⋊C4—24no—
231Dic47⋊C4—24no—
232Dic47⋊C4—24no—
233Dic47⋊C4—42no—
234Dic47⋊C4—42no—
235C4×Dic47—24no—
236C4×Dic47—24no—
237C4×Dic47—24no—
238C4×Dic47—21no—
239C4×Dic47—21no—
240C4×Dic47—24no—
241C4×Dic47—22no—
242C4×Dic47—22no—
243C4×Dic47—42no—
244C2×C47⋊C8—21no—
245C2×C47⋊C8—21no—
246C2×C47⋊C8—21no—
247C2×C47⋊C8—21no—
248C2×C47⋊C8—21no—
249C2×C47⋊C8C22×C412yes—
250#10625324—28no—
251#10625324—44no—
252C23×C47C22×D411yescharacteristic
253C22×D47—21no—
254C22×D47—21no—
255C22×D47—21no—
256C22×D47—21no—
257C22×D47C4×D412yes—
258C22×D47#12012yes—
259C22×D47C22⋊Q812yes—
260Q8×C47—22no—
261Q8×C47—22no—
262Q8×C47—22no—
263Q8×C47C2×C4⋊C414yes—
264C2×C4×C47—22no—
265C2×C4×C47—21no—
266C2×C4×C47—22no—
267C2×C4×C47—22no—
268C2×C4×C47—21no—
269C2×C4×C47—22no—
270C2×C4×C47—21no—
271C2×C4×C47—22no—
272C2×C4×C47—21no—
273C2×C4×C47—21no—
274C2×C4×C47—41no—
275C2×C4×C47—41no—
276C2×C4×C47—41no—
277C2×C4×C47—41no—
278C2×C4×C47—41no—
279C2×C4×C47—41no—
280C2×C4×C47—41no—
281C2×C4×C47#13712yes—
282C2×C4×C47C23×C411yescharacteristic
283C2×C4×C47C22×D411yescharacteristic
284C2×C4×C47C22×D411yescharacteristic
285C2×C4×C47C22×Q811yescharacteristic
286C2×C4×C47C2×#4111yescharacteristic
287C2×C4×C47C2×#4111yescharacteristic
288C2×Dic47—22no—
289C2×Dic47—21no—
290C2×Dic47—22no—
291C2×Dic47—22no—
292C2×Dic47—21no—
293C2×Dic47—22no—
294C2×Dic47—21no—
295C2×Dic47—22no—
296C2×Dic47—21no—
297C2×Dic47—21no—
298C2×Dic47—41no—
299C2×Dic47—41no—
300C2×Dic47—41no—
301C2×Dic47—41no—
302C2×Dic47—41no—
303C2×Dic47—41no—
304C2×Dic47—41no—
305C2×Dic47C4×D412yes—
306C2×Dic47#12012yes—
307C2×Dic47C22⋊Q812yes—
308C2×Dic47#13712yes—
309C4×D47—28no—
310C4×D47—216no—
311C4×D47—44no—
312C4×D47—48no—
313C4×D47C2×C4⋊C414yes—
314C4×D47C4×D414yes—
315C4×D47C22⋊Q814yes—
316C4×D47#12314yes—
317Dic94—22no—
318Dic94—22no—
319Dic94—22no—
320Dic94—216no—
321Dic94C2×C4⋊C414yes—
322C8×C47—22no—
323C8×C47—41no—
324C47⋊C8—22no—
325C47⋊C8—41no—
326#20874—471nomaximal, Sylow
327C22×C47C2×C4×D411yescharacteristic
328C22×C47C2×#12011yescharacteristic
329C22×C47C2×C22⋊Q811yescharacteristic
330C22×C47C2×#13711yescharacteristic
331C22×C47C2×#13711yescharacteristic
332C22×C47#57511yescharacteristic
333C22×C47#57511yescharacteristic
334C2×D47—22no—
335C2×D47—22no—
336C2×D47—22no—
337C2×D47—22no—
338C2×D47—22no—
339C2×D47—22no—
340C2×D47#38514yes—
341C4×C47—22no—
342C4×C47—24no—
343C4×C47—42no—
344C4×C47—41no—
345C4×C47—42no—
346C4×C47—81no—
347C4×C47C22×C4⋊C411yescharacteristic
348C4×C47C2×C4×D411yescharacteristic
349C4×C47C2×C22⋊Q811yescharacteristic
350C4×C47C2×#12311yescharacteristic
351Dic47—22no—
352Dic47—24no—
353Dic47—42no—
354Dic47—41no—
355Dic47—42no—
356Dic47—81no—
357Dic47#38514yes—
358C22×C4×Q8—471no—
359C2×#428—471no—
360C2×#419—471no—
361C2×#419—471no—
362#2296—471no—
363#1865—471no—
364#1865—471no—
365#1865—471no—
366#1865—471no—
367#1863—471no—
368#1863—471no—
369#1863—471no—
370#1863D4711yescharacteristic, complemented
371#1736—471no—
372#1728—471no—
373C2×C47C2×#38511yescharacteristic
374C2×C47C4×#13711yescharacteristic
375C2×C47C4×#13711yescharacteristic
376C2×C47#300411yescharacteristic
377C2×C47#300511yescharacteristic
378C2×C47#307811yescharacteristic
379C2×C47#307811yescharacteristic
380D47—24no—
381C23×Q8—471no—
382C22×M16—471no—
383C22×M16—471no—
384C2×C4×Q8—471no—
385C2×C4×Q8—471no—
386C2×C4×Q8—471no—
387C2×C4×Q8—941no—
388C2×C4×Q8—941no—
389C2×C4×Q8—944no—
390C2×C4×Q8—944no—
391C2×C4×Q8C2×D4711yescharacteristic
392C2×#117—471no—
393C2×#117—471no—
394C22×C4⋊C4—471no—
395C22×C4⋊C4—941no—
396C22×C42—471no—
397C22×C42—941no—
398#428—944no—
399C2×#107—471no—
400C2×#107C2×D4711yescharacteristic
401C2×#106—471no—
402C2×#106—471no—
403#419—478no—
404#419—944no—
405C2×#103—471no—
406C2×#103—471no—
407C2×#103—471no—
408C2×#103—471no—
409C2×#103—471no—
410C2×#103—471no—
411C2×#103C2×D4711yescharacteristic
412C2×#103C2×D4711yescharacteristic
413#389—471no—
414#389—471no—
415#389—471no—
416#389C2×D4711yescharacteristic
417#385—941no—
418#385—941no—
419C4×C4⋊C4—941no—
420C4×C4⋊C4—941no—
421#340—471no—
422#340—471no—
423#340—471no—
424#340C2×D4711yescharacteristic
425#336—471no—
426#336—471no—
427#336—471no—
428#336C2×D4711yescharacteristic
429C47#2087411yescharacteristic, complemented, Sylow
430C22×Q8—474no—
431C22×Q8—474no—
432C22×Q8—474no—
433C22×Q8—471no—
434C22×Q8—941no—
435C22×Q8—942no—
436C22×Q8—942no—
437C22×Q8—942no—
438C22×Q8C22×D4711yescharacteristic
439C23×C4—471no—
440C23×C4—471no—
441C23×C4—471no—
442C23×C4—941no—
443C23×C4—941no—
444C2×M16—474no—
445C2×M16—942no—
446C2×M16—942no—
447C2×M16—942no—
448C2×M16—942no—
449C2×M16—942no—
450C22×C8—471no—
451C22×C8—471no—
452C22×C8C22×D4711yescharacteristic
453C22×C8C22×D4711yescharacteristic
454C4×Q8—22no—
455C4×Q8—22no—
456C4×Q8—942no—
457C4×Q8—942no—
458C4×Q8—948no—
459C4×Q8—942no—
460C4×Q8—948no—
461C4×Q8—942no—
462C4×Q8—942no—
463C4×Q8—942no—
464#117—474no—
465#117—942no—
466#117—942no—
467#117—942no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—471no—
471C2×C4⋊C4—471no—
472C2×C4⋊C4—474no—
473C2×C4⋊C4—471no—
474C2×C4⋊C4—942no—
475C2×C4⋊C4—948no—
476C2×C4⋊C4—941no—
477C2×C4⋊C4—941no—
478C2×C4⋊C4—941no—
479C2×C4⋊C4—941no—
480C2×C4⋊C4—941no—
481C2×C4⋊C4—941no—
482C2×C4⋊C4—941no—
483C2×C4⋊C4C22×D4711yescharacteristic
484C2×C4⋊C4C22×D4711yescharacteristic
485C2×C4⋊C4C22×D4711yescharacteristic
486C2×C22⋊C4—941no—
487C2×C22⋊C4—941no—
488C2×C42—21no—
489C2×C42—471no—
490C2×C42—471no—
491C2×C42—471no—
492C2×C42—942no—
493C2×C42—942no—
494C2×C42—948no—
495C2×C42—941no—
496C2×C42—941no—
497C2×C42—941no—
498C2×C42—941no—
499C2×C42—941no—
500C2×C42C22×D4711yescharacteristic
501#107—22no—
502#107—942no—
503#106—942no—
504#106—942no—
505#103—22no—
506#103—474no—
507#103—474no—
508#103—474no—
509#103—942no—
510#103—942no—
511#103—942no—
512#103C4×D4714yescomplemented
513#95—21no—
514#95—941no—
515#95—941no—
516#95—941no—
517C24—471no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—4716no—
522C2×Q8—472no—
523C2×Q8—472no—
524C2×Q8—472no—
525C2×Q8—944no—
526C2×Q8—944no—
527C2×Q8—944no—
528C2×Q8—948no—
529C2×Q8—948no—
530C2×Q8—948no—
531C2×Q8—941no—
532C2×Q8—941no—
533C2×Q8—941no—
534C2×Q8C2×C4×D4712yes—
535C2×Q8D4×D4712yes—
536C2×Q8Q8×D4712yes—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—471no—
542C22×C4—472no—
543C22×C4—472no—
544C22×C4—472no—
545C22×C4—472no—
546C22×C4—472no—
547C22×C4—472no—
548C22×C4—471no—
549C22×C4—471no—
550C22×C4—942no—
551C22×C4—942no—
552C22×C4—944no—
553C22×C4—944no—
554C22×C4—944no—
555C22×C4—944no—
556C22×C4—942no—
557C22×C4—941no—
558C22×C4—942no—
559C22×C4—941no—
560C22×C4—941no—
561C22×C4—941no—
562C22×C4—1881no—
563C22×C4—1881no—
564C22×C4—1882no—
565C22×C4—1882no—
566C22×C4D4×D4711yescharacteristic
567C22×C4D4×D4711yescharacteristic
568C22×C4C23×D4711yescharacteristic
569M16—948no—
570M16—1884no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—472no—
577C2×C8—941no—
578C2×C8—941no—
579C2×C8—941no—
580C2×C8—941no—
581C2×C8—941no—
582C2×C8C2×C4×D4712yes—
583C4⋊C4—24no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—42no—
589C4⋊C4—472no—
590C4⋊C4—472no—
591C4⋊C4—944no—
592C4⋊C4—944no—
593C4⋊C4—944no—
594C4⋊C4—944no—
595C4⋊C4—941no—
596C4⋊C4—941no—
597C4⋊C4—941no—
598C4⋊C4—941no—
599C4⋊C4—1882no—
600C4⋊C4—1882no—
601C4⋊C4—1882no—
602C4⋊C4C2×C4×D4712yes—
603C4⋊C4D4×D4712yes—
604C22⋊C4—944no—
605C22⋊C4—1882no—
606C42—24no—
607C42—21no—
608C42—21no—
609C42—942no—
610C42—942no—
611C42—944no—
612C42—944no—
613C42—944no—
614C42—944no—
615C42—941no—
616C42—941no—
617C42—1882no—
618C23—472no—
619C23—472no—
620C23—472no—
621C23—941no—
622C23—941no—
623C23—941no—
624C23—941no—
625C23C2×D4×D4711yescharacteristic
626Q8—22no—
627Q8—22no—
628Q8—22no—
629Q8—474no—
630Q8—9416no—
631Q8—942no—
632Q8—942no—
633Q8—942no—
634Q8C4⋊C4×D4714yes—
635C2×C4—22no—
636C2×C4—21no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—21no—
640C2×C4—22no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—472no—
653C2×C4—472no—
654C2×C4—472no—
655C2×C4—474no—
656C2×C4—474no—
657C2×C4—474no—
658C2×C4—474no—
659C2×C4—472no—
660C2×C4—9416no—
661C2×C4—948no—
662C2×C4—942no—
663C2×C4—941no—
664C2×C4—942no—
665C2×C4—942no—
666C2×C4—941no—
667C2×C4—942no—
668C2×C4—942no—
669C2×C4—941no—
670C2×C4—941no—
671C2×C4—941no—
672C2×C4—1884no—
673C2×C4—1888no—
674C2×C4—1881no—
675C2×C4—1881no—
676C2×C4—1881no—
677C2×C4—1881no—
678C2×C4—1881no—
679C2×C4—1881no—
680C2×C4—1881no—
681C2×C4#1309405612yes—
682C2×C4C22×C4×D4711yescharacteristic
683C2×C4C2×D4×D4711yescharacteristic
684C2×C4C2×D4×D4711yescharacteristic
685C2×C4C2×Q8×D4711yescharacteristic
686C2×C4#41×D4711yescharacteristic
687C2×C4#41×D4711yescharacteristic
688C8—22no—
689C8—41no—
690C8—942no—
691C8—1881no—
692C22—474no—
693C22—942no—
694C22—942no—
695C22—942no—
696C22—942no—
697C22—942no—
698C22—942no—
699C22C4×D4×D4711yescharacteristic
700C22#120×D4711yescharacteristic
701C22C22⋊Q8×D4711yescharacteristic
702C22#137×D4711yescharacteristic
703C22C2×#1309405611yescharacteristic
704C22#1568991911yescharacteristic
705C22#1568992011yescharacteristic
706C4—24no—
707C4—22no—
708C4—42no—
709C4—41no—
710C4—42no—
711C4—81no—
712C4—474no—
713C4—944no—
714C4—942no—
715C4—3761no—
716C4—1882no—
717C4—1881no—
718C4—1882no—
719C4C2×C4⋊C4×D4711yescharacteristic
720C4C4×D4×D4711yescharacteristic
721C4C22⋊Q8×D4711yescharacteristic
722C4#123×D4711yescharacteristic
723C2—944no—
724C2#385×D4711yescharacteristic
725C2C4×#1309405611yescharacteristic
726C2#2025221011yescharacteristic
727C2#2025262311yescharacteristic
728C2#2025262611yescharacteristic
729C2#2025319111yescharacteristic
730C2#2025319411yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1863C2
socleC23×C47C22×D4
prime radicalC23×D47C2×D4
cosocleC22×C4×C47C24
hypercenter#1863D47
hypocenterC47#20874
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1863

Complements

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

NH ≅ G/Ntype
6. #20243659C2semidirect
7. #20243658C2semidirect
8. #20243657C2semidirect
9. #20243656C2semidirect
10. #20243641C2semidirect
11. #20243640C2semidirect
12. #20243639C2semidirect
15. C47×#1863C2semidirect
37. #15689130C4semidirect
127. #13093949C2×C4semidirect
129. #13093948C2×C4semidirect
131. #13093947C2×C4semidirect
149. #103×C47C2×C4semidirect
175. Q8×D47C4⋊C4semidirect
370. #1863D47semidirect
429. C47#20874semidirect
512. #103C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D472
C2×#156891642
C2×#156891302
#202458692
#202436592
#202436582
#202436572
#202436562
#202436412
#202436402
#202436392
#202431062
#202430802
C47×#18632
#2087447