Finite Group Databasebeta

← #26376731

Subgroups — #26376731

Order 12032.

2110 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689675C211yesmaximal, characteristic
2#20246473C211yesmaximal, characteristic
3#20246471C211yesmaximal, characteristic
4#20246469C212yesmaximal
5#20246468C211yesmaximal, characteristic
6#20246466C212yesmaximal
7#20246344C212yesmaximal, complemented
8#20246342C212yesmaximal, complemented
9#20246342C212yesmaximal, complemented
10#20246341C212yesmaximal, complemented
11#20246133C212yesmaximal, complemented
12#20246131C212yesmaximal, complemented
13#20246007C212yesmaximal
14#20245945C212yesmaximal, complemented
15C4×#13094014C212yesmaximal, complemented
16C2×#15688987C211yesmaximal, characteristic
17#20245743C212yesmaximal
18C4×#13093980C211yesmaximal, characteristic
19C47×#2368C211yesmaximal, characteristic
20#15689675C4116yescomplemented
21C2×#13094023C2211yescharacteristic
22C2×#13094022C2211yescharacteristic
23C2×#13094014C2212yes—
24C2×#13094003C2211yescharacteristic
25C2×#13094001C2212yes—
26C2×Q8×Dic47C2211yescharacteristic
27C2×#13093989C2212yes—
28C2×#13093989C2211yescharacteristic
29C2×#13093980C2211yescharacteristic
30C2×#13093980C2212yes—
31C2×#13093980C2211yescharacteristic
32C22×Dic47⋊C4C2212yes—
33C22×C4×Dic47C2211yescharacteristic
34#15689030C2212yes—
35#15689029C2212yes—
36#15689028C2212yes—
37#15689027C2212yes—
38#15689027C2212yes—
39#15689027C2212yes—
40#15689027C2212yes—
41#15689020C2212yes—
42#15689020C2212yes—
43#15689018C2212yes—
44#15689018C2212yes—
45#15689010C2212yes—
46#15689010C2212yes—
47#15689009C2212yes—
48#15689009C2212yes—
49#15689008C2212yes—
50#15689008C2212yes—
51#15689007C2212yes—
52#15689007C2212yes—
53#15689006C2212yes—
54#15689006C2212yes—
55#15689005C2212yes—
56#15689005C2212yes—
57#15689004C2212yes—
58#15689004C2212yes—
59#15688998C2212yes—
60#15688996C2212yes—
61#15688995C2212yes—
62#15688992C2212yes—
63#15688992C2212yes—
64#15688987C2211yescharacteristic
65#15688987C2211yescharacteristic
66#15688987C2212yes—
67#15688987C2212yes—
68#15688987C2211yescharacteristic
69#15688987C2211yescharacteristic
70#15688987C2212yes—
71#15688987C2212yes—
72C4⋊C4×Dic47C2212yes—
73C4⋊C4×Dic47C2212yes—
74C4×Dic47⋊C4C2212yes—
75C4×Dic47⋊C4C2212yes—
76C4×Dic47⋊C4C2212yes—
77C4×Dic47⋊C4C2212yes—
78C4×Dic47⋊C4C2212yes—
79C4×Dic47⋊C4C2212yes—
80C4×Dic47⋊C4C2212yes—
81C4×C4⋊Dic47C2212yes—
82#15688974C2212yes—
83#15688974C2212yes—
84#15688974C2212yes—
85#15688974C2212yes—
86#15688974C2212yes—
87#15688974C2212yes—
88#15688974C2212yes—
89C22⋊C4×Dic47C2211yescharacteristic
90C22⋊C4×Dic47C2212yes—
91C22⋊C4×Dic47C2211yescharacteristic
92C22⋊C4×Dic47C2212yes—
93C4×C22⋊Dic47C2212yes—
94C4×C22⋊Dic47C2211yescharacteristic
95#15688968C2212yes—
96C2×C47⋊#95C2212yes—
97C2×C47⋊#95C2211yescharacteristic
98C42×Dic47C2212yes—
99C2×C22⋊Q8×C47C2211yescharacteristic
100C47×#391C2212yes—
101C47×#387C2212yes—
102C47×#387C2212yes—
103C47×#385C2212yes—
104C4×C4⋊C4×C47C2212yes—
105C4×C22⋊C4×C47C2212yes—
106C4×C22⋊C4×C47C2211yescharacteristic
107C2×#95×C47C2211yescharacteristic
108C22×Dic94C2311yescharacteristic
109C22×Dic94C2312yes—
110C23×Dic47C2312yes—
111C23×Dic47C2311yescharacteristic
112C23×Dic47C2311yescharacteristic
113#13094023C2×C418yescomplemented
114#13094022C2×C418yescomplemented
115#13094014C2×C4116yescomplemented
116#13094003C2×C418yes—
117#13094001C2×C4116yes—
118Q8×Dic47C2×C418yescomplemented
119#13093989C2×C4116yescomplemented
120#13093989C2×C418yescomplemented
121#13093980—24no—
122#13093980C2×C4116yes—
123#13093980Q818yescomplemented
124C2×C4⋊Dic47C2312yes—
125C2×C4⋊Dic47C2312yes—
126C2×C4⋊Dic47C2312yes—
127C2×C4⋊Dic47C2311yescharacteristic
128C2×Dic47⋊C4—28no—
129C2×Dic47⋊C4C2312yes—
130C2×Dic47⋊C4C2312yes—
131C2×Dic47⋊C4C2312yes—
132C2×Dic47⋊C4C2312yes—
133C2×Dic47⋊C4C2312yes—
134C2×Dic47⋊C4C2312yes—
135C2×Dic47⋊C4C2312yes—
136C2×Dic47⋊C4C2312yes—
137C2×Dic47⋊C4C2312yes—
138C2×Dic47⋊C4C2312yes—
139C2×Dic47⋊C4C2312yes—
140C2×Dic47⋊C4C2312yes—
141C2×Dic47⋊C4C2312yes—
142C2×Dic47⋊C4C2312yes—
143C2×Dic47⋊C4C2312yes—
144C2×C22⋊Dic47C2311yescharacteristic
145C2×C22⋊Dic47C2312yes—
146C2×C22⋊Dic47C2311yescharacteristic
147C2×C4×Dic47C2×C418yes—
148C2×C4×Dic47C2312yes—
149C2×C4×Dic47C2312yes—
150C2×C4×Dic47C2312yes—
151C2×C4×Dic47C2312yes—
152C2×C4×Dic47C2312yes—
153C2×C4×Dic47C2312yes—
154C2×C4×Dic47C2312yes—
155C2×C4×Dic47C2312yes—
156C2×C4×Dic47C2312yes—
157C2×C4×Dic47C2312yes—
158C2×C4×Dic47C2311yescharacteristic
159C2×C4×Dic47C2311yescharacteristic
160C2×C4×Dic47C2311yescharacteristic
161C2×C4×Dic47C2312yes—
162C2×C4×Dic47C2312yes—
163C2×C4×Dic47C2311yescharacteristic
164C2×C4×Dic47C2312yes—
165C47⋊#95C2312yes—
166C47⋊#95C2312yes—
167C47⋊#95C2311yescharacteristic
168C47⋊#95C2311yescharacteristic
169C47⋊#95C2312yes—
170C47⋊#95C2312yes—
171C47⋊#95C2312yes—
172C47⋊#95C2312yes—
173C47⋊#95C2312yes—
174C47⋊#95C2312yes—
175C47⋊#95C2312yes—
176C47⋊#95C2312yes—
177C47⋊#95C2312yes—
178C47⋊#95C2312yes—
179C47⋊#95C2312yes—
180C47⋊#95C2312yes—
181C47⋊#95C2312yes—
182C47⋊#95C2312yes—
183C47⋊#95C2312yes—
184C47⋊#95C2312yes—
185C47⋊#95C2312yes—
186C47⋊#95C2312yes—
187C22×Q8×C47C2311yescharacteristic
188C23×C4×C47C2312yes—
189C23×C4×C47C2311yescharacteristic
190C22⋊Q8×C47C2×C418yes—
191C2×C4⋊C4×C47C2312yes—
192C2×C4⋊C4×C47C2312yes—
193C2×C4⋊C4×C47C2312yes—
194C2×C4⋊C4×C47C2311yescharacteristic
195C2×C22⋊C4×C47C2311yescharacteristic
196C2×C22⋊C4×C47C2312yes—
197C2×C22⋊C4×C47C2311yescharacteristic
198C2×C42×C47C2312yes—
199C2×C42×C47C2312yes—
200C2×C42×C47C2312yes—
201#95×C47C2312yes—
202#95×C47C2311yescharacteristic
203#95×C47C2312yes—
204#95×C47C2312yes—
205#95×C47C2312yes—
206#95×C47C2311yescharacteristic
207#95×C47C2312yes—
208#95×C47C2312yes—
209C24×C47C2411yescharacteristic
210C2×Q8×C47—42no—
211C2×Q8×C47C22×C414yes—
212C22×C4×C47—24no—
213C22×C4×C47—42no—
214C22×C4×C47—42no—
215C22×C4×C47—42no—
216C22×C4×C47C22×C414yes—
217C22×C4×C47C2412yes—
218C22×C4×C47C2412yes—
219C22×C4×C47C2412yes—
220C22×C4×C47C2411yescharacteristic
221C22×C4×C47C2412yes—
222C22×C4×C47C2412yes—
223C22×C4×C47C2411yescharacteristic
224C22×C4×C47C2412yes—
225C22×Dic47—24no—
226C22×Dic47—42no—
227C22×Dic47—42no—
228C22×Dic47—42no—
229C22×Dic47C22×C414yes—
230C22×Dic47C22×C414yes—
231C22×Dic47C2×Q814yes—
232C22×Dic47#4114yes—
233C22×Dic47C2412yes—
234C22×Dic47C2412yes—
235C22×Dic47C2412yes—
236C22×Dic47C2411yescharacteristic
237C22×Dic47C2411yescharacteristic
238C22×Dic47C2412yes—
239C22×Dic47C2412yes—
240C22×Dic47C2412yes—
241C22×Dic47C2411yescharacteristic
242C22×Dic47C2411yescharacteristic
243C2×Dic94—42no—
244C2×Dic94—42no—
245C2×Dic94—42no—
246C2×Dic94C22×C418yes—
247C2×Dic94C22×C414yes—
248C4⋊C4×C47—42no—
249C4⋊C4×C47—42no—
250C4⋊C4×C47C22×C418yes—
251C4⋊C4×C47C22×C414yes—
252C22⋊C4×C47—22no—
253C22⋊C4×C47C22×C418yes—
254C22⋊C4×C47C2×Q814yes—
255C42×C47—42no—
256C42×C47—42no—
257C42×C47—42no—
258C22⋊Dic47—22no—
259C22⋊Dic47C22×C418yes—
260C22⋊Dic47C2×Q814yes—
261C4⋊Dic47—42no—
262C4⋊Dic47—42no—
263C4⋊Dic47C22×C418yes—
264C4⋊Dic47C22×C414yes—
265Dic47⋊C4—24no—
266Dic47⋊C4—24no—
267Dic47⋊C4—24no—
268Dic47⋊C4—24no—
269Dic47⋊C4—24no—
270Dic47⋊C4—42no—
271Dic47⋊C4—42no—
272Dic47⋊C4—42no—
273Dic47⋊C4—42no—
274Dic47⋊C4C22×C418yes—
275Dic47⋊C4C22×C418yes—
276Dic47⋊C4C22×C418yes—
277Dic47⋊C4C22×C418yes—
278Dic47⋊C4C22×C418yes—
279Dic47⋊C4C2×Q818yes—
280C4×Dic47—24no—
281C4×Dic47—42no—
282C4×Dic47—42no—
283C4×Dic47—42no—
284C4×Dic47—42no—
285C4×Dic47—42no—
286C4×Dic47—42no—
287C4×Dic47—42no—
288C4×Dic47—42no—
289C4×Dic47—42no—
290C4×Dic47C22×C414yes—
291C4×Dic47C22×C414yes—
292C4×Dic47C22×C414yes—
293C4×Dic47C22×C414yes—
294C4×Dic47C22×C418yes—
295C4×Dic47C22×C418yes—
296C4×Dic47C2×Q818yes—
297C23×C47—22no—
298C23×C47—22no—
299C23×C47C23×C412yes—
300C23×C47C22×Q812yes—
301C23×C47C2×#4112yes—
302C23×C47C2511yescharacteristic
303Q8×C47—44no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—22no—
310C2×C4×C47—22no—
311C2×C4×C47—22no—
312C2×C4×C47—22no—
313C2×C4×C47—22no—
314C2×C4×C47—22no—
315C2×C4×C47—22no—
316C2×C4×C47—22no—
317C2×C4×C47—22no—
318C2×C4×C47—22no—
319C2×C4×C47—22no—
320C2×C4×C47—22no—
321C2×C4×C47—44no—
322C2×C4×C47—84no—
323C2×C4×C47C23×C412yes—
324C2×C4×C47C23×C412yes—
325C2×C4×C47C23×C414yes—
326C2×C4×C47C23×C414yes—
327C2×C4×C47C22×Q814yes—
328C2×Dic47—22no—
329C2×Dic47—22no—
330C2×Dic47—22no—
331C2×Dic47—22no—
332C2×Dic47—22no—
333C2×Dic47—22no—
334C2×Dic47—22no—
335C2×Dic47—22no—
336C2×Dic47—22no—
337C2×Dic47—22no—
338C2×Dic47—22no—
339C2×Dic47—22no—
340C2×Dic47—22no—
341C2×Dic47—22no—
342C2×Dic47—22no—
343C2×Dic47—22no—
344C2×Dic47—22no—
345C2×Dic47—44no—
346C2×Dic47—84no—
347C2×Dic47C4×Q8116yes—
348C2×Dic47C23×C412yes—
349C2×Dic47C23×C412yes—
350C2×Dic47C23×C414yes—
351C2×Dic47C23×C414yes—
352C2×Dic47C23×C412yes—
353C2×Dic47C23×C412yes—
354C2×Dic47C22×Q814yes—
355C2×Dic47C22×Q812yes—
356C2×Dic47C22×Q812yes—
357C2×Dic47C2×#4112yes—
358C2×Dic47C2×#4112yes—
359Dic94—48no—
360Dic94—44no—
361#34215—471nomaximal, Sylow
362C22×C47—22no—
363C22×C47—22no—
364C22×C47—24no—
365C22×C47—24no—
366C22×C47C2×C4×Q814yes—
367C22×C47C24×C411yescharacteristic
368C22×C47C23×Q811yescharacteristic
369C22×C47C22×#4111yescharacteristic
370C22×C47#58512yes—
371C22×C47#58512yes—
372C4×C47—22no—
373C4×C47—24no—
374C4×C47—22no—
375C4×C47—24no—
376C4×C47—24no—
377C4×C47—42no—
378C4×C47—42no—
379C4×C47—42no—
380Dic47—22no—
381Dic47—24no—
382Dic47—24no—
383Dic47—22no—
384Dic47—24no—
385Dic47—42no—
386Dic47—42no—
387Dic47—42no—
388Dic47C2×C4×Q814yes—
389Dic47C2×C4×Q814yes—
390C2×#533—471no—
391#2368—472no—
392#2368—472no—
393#2368—471no—
394#2368—471no—
395#2368—471no—
396#2368D4711yescharacteristic
397#2355—472no—
398#2355—472no—
399#2355—472no—
400#2355—472no—
401#2331—472no—
402#2331—472no—
403#2317—472no—
404C4×#125—472no—
405C4×#125—472no—
406C2×#382—471no—
407#2274—472no—
408C4×#117—471no—
409C2×C47—24no—
410C2×C47C22×C4×Q811yescharacteristic
411C2×C47#342811yescharacteristic
412C2×C47#342811yescharacteristic
413C2×C47#350412yes—
414C2×C47#351012yes—
415#533—4716no—
416C2×C4⋊Q8—471no—
417C2×C4⋊Q8—471no—
418C2×#125—472no—
419C2×C22⋊Q8—471no—
420C2×C22⋊Q8—472no—
421C2×C22⋊Q8C2×D4711yescharacteristic
422C2×C4×Q8—471no—
423C2×C4×Q8—471no—
424C2×C4×Q8—472no—
425C2×#117—472no—
426C2×#117—471no—
427C2×#117—471no—
428C22×C4⋊C4—472no—
429C22×C42—471no—
430#391—472no—
431#391—472no—
432#391—472no—
433#391—472no—
434#391—472no—
435#391—472no—
436#391—472no—
437#391C2×D4712yes—
438#389—472no—
439#389—472no—
440#389—472no—
441#389—472no—
442#387—472no—
443#387—472no—
444#387—472no—
445#387—472no—
446#387—472no—
447#387—472no—
448#387—472no—
449#387—472no—
450#387—472no—
451#387—472no—
452#387—472no—
453#387—472no—
454#387—472no—
455#387—472no—
456#387C2×D4712yes—
457#387C2×D4712yes—
458#385—472no—
459#385—472no—
460#385—472no—
461#385C2×D4712yes—
462#384—472no—
463#384—472no—
464#382—471no—
465#382—471no—
466#382—472no—
467#382—472no—
468#382—472no—
469#382—472no—
470#382—471no—
471#382—471no—
472C4×C4⋊C4—472no—
473C4×C4⋊C4—472no—
474C4×C4⋊C4—472no—
475C4×C4⋊C4—472no—
476C4×C4⋊C4—472no—
477C4×C4⋊C4—472no—
478C4×C4⋊C4—472no—
479C4×C4⋊C4—472no—
480C4×C4⋊C4—472no—
481C4×C4⋊C4—472no—
482C4×C4⋊C4—472no—
483C4×C4⋊C4—472no—
484C4×C4⋊C4—472no—
485C4×C4⋊C4—472no—
486C4×C4⋊C4—472no—
487C4×C4⋊C4—472no—
488C4×C4⋊C4—472no—
489C4×C4⋊C4C2×D4712yes—
490C4×C22⋊C4—471no—
491C4×C22⋊C4—472no—
492C4×C22⋊C4—471no—
493C4×C22⋊C4—471no—
494C4×C22⋊C4—472no—
495C4×C22⋊C4—472no—
496C4×C22⋊C4C2×D4711yescharacteristic
497C4×C22⋊C4C2×D4712yes—
498#376—472no—
499C2×#95—472no—
500C2×#95—471no—
501C2×#95C2×D4711yescharacteristic
502C43—472no—
503C47#3421511yescharacteristic, complemented, Sylow
504C22×Q8—472no—
505C22×Q8—471no—
506C22×Q8C22×D4711yescharacteristic
507C23×C4—471no—
508C23×C4—471no—
509C23×C4—472no—
510C23×C4C22×D4712yes—
511C23×C4C22×D4711yescharacteristic
512C4⋊Q8—478no—
513C4⋊Q8—478no—
514#125—4716no—
515C22⋊Q8—478no—
516C22⋊Q8—4716no—
517C22⋊Q8C4×D4718yes—
518C4×Q8—478no—
519C4×Q8—478no—
520C4×Q8—4716no—
521#117—4716no—
522#117—478no—
523#117—944no—
524C2×C4⋊C4—472no—
525C2×C4⋊C4—472no—
526C2×C4⋊C4—472no—
527C2×C4⋊C4—472no—
528C2×C4⋊C4—472no—
529C2×C4⋊C4—472no—
530C2×C4⋊C4—472no—
531C2×C4⋊C4—471no—
532C2×C4⋊C4—472no—
533C2×C4⋊C4—472no—
534C2×C4⋊C4—472no—
535C2×C4⋊C4—472no—
536C2×C4⋊C4—472no—
537C2×C4⋊C4—472no—
538C2×C4⋊C4—472no—
539C2×C4⋊C4—472no—
540C2×C4⋊C4—472no—
541C2×C4⋊C4—472no—
542C2×C4⋊C4—472no—
543C2×C4⋊C4—948no—
544C2×C4⋊C4C22×D4712yes—
545C2×C4⋊C4C22×D4712yes—
546C2×C4⋊C4C22×D4712yes—
547C2×C4⋊C4C22×D4711yescharacteristic
548C2×C22⋊C4—472no—
549C2×C22⋊C4—471no—
550C2×C22⋊C4—471no—
551C2×C22⋊C4C22×D4711yescharacteristic
552C2×C22⋊C4C22×D4712yes—
553C2×C22⋊C4C22×D4711yescharacteristic
554C2×C42—478no—
555C2×C42—472no—
556C2×C42—472no—
557C2×C42—472no—
558C2×C42—471no—
559C2×C42—471no—
560C2×C42—471no—
561C2×C42—471no—
562C2×C42—472no—
563C2×C42—472no—
564C2×C42—472no—
565C2×C42—472no—
566C2×C42—472no—
567C2×C42—472no—
568C2×C42—472no—
569C2×C42—472no—
570C2×C42—472no—
571C2×C42—472no—
572C2×C42C22×D4712yes—
573C2×C42C22×D4712yes—
574C2×C42C22×D4712yes—
575#95—472no—
576#95—472no—
577#95—471no—
578#95—471no—
579#95—472no—
580#95—472no—
581#95—472no—
582#95—472no—
583#95—472no—
584#95—472no—
585#95—472no—
586#95—472no—
587#95—472no—
588#95—472no—
589#95—472no—
590#95—472no—
591#95—472no—
592#95—472no—
593#95—472no—
594#95—472no—
595#95—472no—
596#95—472no—
597#95C22×D4711yescharacteristic
598#95C22×D4711yescharacteristic
599#95C22×D4712yes—
600#95C22×D4712yes—
601#95C22×D4712yes—
602#95C22×D4712yes—
603#95C22×D4712yes—
604#95C22×D4712yes—
605C24C23×D4711yescharacteristic
606C2×Q8—42no—
607C2×Q8—478no—
608C2×Q8—474no—
609C2×Q8—1882no—
610C2×Q8—1882no—
611C2×Q8—1882no—
612C2×Q8C2×C4×D4714yes—
613C22×C4—24no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—474no—
618C22×C4—474no—
619C22×C4—474no—
620C22×C4—471no—
621C22×C4—471no—
622C22×C4—471no—
623C22×C4—472no—
624C22×C4—471no—
625C22×C4—472no—
626C22×C4—472no—
627C22×C4—474no—
628C22×C4—472no—
629C22×C4—472no—
630C22×C4—472no—
631C22×C4—944no—
632C22×C4—1882no—
633C22×C4—1882no—
634C22×C4—1882no—
635C22×C4C2×C4×D4714yes—
636C22×C4C23×D4712yes—
637C22×C4C23×D4712yes—
638C22×C4C23×D4712yes—
639C22×C4C23×D4711yescharacteristic
640C22×C4C23×D4711yescharacteristic
641C22×C4C23×D4712yes—
642C22×C4C23×D4712yes—
643C22×C4C23×D4712yes—
644C4⋊C4—42no—
645C4⋊C4—42no—
646C4⋊C4—478no—
647C4⋊C4—478no—
648C4⋊C4—478no—
649C4⋊C4—478no—
650C4⋊C4—478no—
651C4⋊C4—478no—
652C4⋊C4—474no—
653C4⋊C4—478no—
654C4⋊C4—944no—
655C4⋊C4—944no—
656C4⋊C4—944no—
657C4⋊C4—944no—
658C4⋊C4—944no—
659C4⋊C4—1882no—
660C4⋊C4—1882no—
661C4⋊C4—1882no—
662C4⋊C4—1882no—
663C4⋊C4—1882no—
664C4⋊C4—1882no—
665C4⋊C4C2×C4×D4718yes—
666C4⋊C4C2×C4×D4714yes—
667C22⋊C4—22no—
668C22⋊C4—478no—
669C22⋊C4—474no—
670C22⋊C4—942no—
671C22⋊C4C2×C4×D4718yes—
672C22⋊C4Q8×D4714yes—
673C42—42no—
674C42—42no—
675C42—42no—
676C42—474no—
677C42—474no—
678C42—474no—
679C42—474no—
680C42—478no—
681C42—478no—
682C42—478no—
683C42—944no—
684C42—1882no—
685C42—1882no—
686C42—1882no—
687C42—1882no—
688C42—1882no—
689C42—1882no—
690C42—1882no—
691C42—1882no—
692C42—1882no—
693C23—22no—
694C23—22no—
695C23C22×C4×D4712yes—
696C23C2×Q8×D4712yes—
697C23#41×D4712yes—
698C23C24×D4711yescharacteristic
699Q8—44no—
700Q8—1884no—
701Q8—1888no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—44no—
720C2×C4—84no—
721C2×C4—4716no—
722C2×C4—472no—
723C2×C4—472no—
724C2×C4—472no—
725C2×C4—472no—
726C2×C4—472no—
727C2×C4—472no—
728C2×C4—472no—
729C2×C4—472no—
730C2×C4—474no—
731C2×C4—474no—
732C2×C4—474no—
733C2×C4—942no—
734C2×C4—942no—
735C2×C4—942no—
736C2×C4—942no—
737C2×C4—942no—
738C2×C4—942no—
739C2×C4—942no—
740C2×C4—942no—
741C2×C4—942no—
742C2×C4—942no—
743C2×C4—942no—
744C2×C4—942no—
745C2×C4—942no—
746C2×C4—942no—
747C2×C4—942no—
748C2×C4—942no—
749C2×C4—942no—
750C2×C4—3764no—
751C2×C4—1884no—
752C2×C4C22×C4×D4712yes—
753C2×C4C22×C4×D4712yes—
754C2×C4C22×C4×D4714yes—
755C2×C4C22×C4×D4714yes—
756C2×C4C2×Q8×D4714yes—
757C22—22no—
758C22—22no—
759C22—24no—
760C22—24no—
761C22C4×Q8×D4714yes—
762C22C23×C4×D4711yescharacteristic
763C22C22×Q8×D4711yescharacteristic
764C22C2×#41×D4711yescharacteristic
765C22#1568995812yes—
766C22#1568995912yes—
767C4—22no—
768C4—22no—
769C4—24no—
770C4—24no—
771C4—24no—
772C4—42no—
773C4—42no—
774C4—42no—
775C4—474no—
776C4—474no—
777C4—944no—
778C4—942no—
779C4—942no—
780C4—944no—
781C4—944no—
782C4—1882no—
783C4—1882no—
784C4—1882no—
785C2—24no—
786C2C2×C4×Q8×D4711yescharacteristic
787C2#2025658611yescharacteristic
788C2#2025658711yescharacteristic
789C2#2025720812yes—
790C2#2025727612yes—
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC47×#2368C2
socle, cosocleC23×C47C25
prime radicalC24×C47C24
hypercenter#2368D47
hypocenterC47#34215
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2368

Complements

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

NH ≅ G/Ntype
7. #20246344C2semidirect
8. #20246342C2semidirect
9. #20246342C2semidirect
10. #20246341C2semidirect
11. #20246133C2semidirect
12. #20246131C2semidirect
14. #20245945C2semidirect
15. C4×#13094014C2semidirect
20. #15689675C4semidirect
113. #13094023C2×C4semidirect
114. #13094022C2×C4semidirect
115. #13094014C2×C4semidirect
118. Q8×Dic47C2×C4semidirect
119. #13093989C2×C4semidirect
120. #13093989C2×C4semidirect
123. #13093980Q8semidirect
503. C47#34215semidirect

Maximal subgroups

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

subgroupindex
C2×#156896752
#202464732
#202464712
#202464692
#202464682
#202464662
#202463442
#202463422
#202463412
#202461332
#202461312
#202460072
#202459452
C4×#130940142
C2×#156889872
#202457432
C4×#130939802
C47×#23682
#3421547