Finite Group Databasebeta

← #26389342

Subgroups — #26389342

Order 12032.

1690 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251727C211yesmaximal, characteristic
2#20251694C212yesmaximal
3#20249505C211yesmaximal, characteristic
4#20249504C211yesmaximal, characteristic
5#20249205C212yesmaximal
6#20248798C212yesmaximal, complemented
7#20248797C212yesmaximal, complemented
8#20248784C212yesmaximal, complemented
9#20248782C212yesmaximal, complemented
10#20248082C212yesmaximal, complemented
11#20248074C212yesmaximal, complemented
12#20247376C212yesmaximal, complemented
13#20247368C212yesmaximal, complemented
14#20246123C211yesmaximal, characteristic
15#20246118C211yesmaximal, characteristic
16#20245989C212yesmaximal
17#20245920C212yesmaximal
18C2×C4×C4⋊Dic47C211yesmaximal, characteristic
19C47×#2855C211yesmaximal, characteristic
20C2×#13094014C2212yes—
21C2×#13094003C2211yescharacteristic
22C2×#13094001C2212yes—
23C2×#13093989C2212yes—
24C22×C4⋊Dic47C2211yescharacteristic
25C22×C4⋊Dic47C2211yescharacteristic
26C22×C4×Dic47C2211yescharacteristic
27C22×C4×Dic47C2211yescharacteristic
28#15689065C2212yes—
29#15689065C2212yes—
30#15689057C2212yes—
31#15689057C2212yes—
32#15689057C2212yes—
33#15689056C2212yes—
34#15689055C2212yes—
35#15689055C2212yes—
36#15689054C2212yes—
37#15689053C2212yes—
38#15689044C2212yes—
39#15689044C2212yes—
40#15689044C2212yes—
41#15689043C2212yes—
42#15689043C2212yes—
43#15689042C2212yes—
44#15689030C2212yes—
45#15689029C2211yescharacteristic
46#15689029C2211yescharacteristic
47#15689027C2212yes—
48#15689027C2212yes—
49#15689022C2212yes—
50#15689021C2211yescharacteristic
51#15689021C2211yescharacteristic
52#15689020C2212yes—
53#15689018C2212yes—
54#15689018C2212yes—
55#15689018C2212yes—
56#15689009C2212yes—
57#15689009C2212yes—
58#15689009C2212yes—
59#15689008C2212yes—
60#15689008C2212yes—
61#15689008C2212yes—
62#15689008C2212yes—
63#15689008C2212yes—
64#15689008C2212yes—
65#15689008C2212yes—
66#15689007C2212yes—
67#15689007C2212yes—
68#15689006C2212yes—
69#15689006C2212yes—
70#15689006C2212yes—
71#15689006C2212yes—
72#15689005C2212yes—
73#15689004C2212yes—
74#15689004C2212yes—
75#15689004C2212yes—
76#15688998C2212yes—
77#15688996C2212yes—
78#15688995C2212yes—
79#15688987C2212yes—
80#15688986C2212yes—
81#15688983C2211yescharacteristic
82#15688981C2212yes—
83#15688981C2212yes—
84#15688981C2212yes—
85C4⋊C4×Dic47C2212yes—
86C4×C4⋊Dic47C2212yes—
87C4×C4⋊Dic47C2212yes—
88C4×C4⋊Dic47C2212yes—
89C4×C4⋊Dic47C2212yes—
90#15688974C2212yes—
91#15688974C2212yes—
92C22⋊C4×Dic47C2212yes—
93C22⋊C4×Dic47C2212yes—
94C2×C47⋊#95C2211yescharacteristic
95C2×C47⋊#95C2211yescharacteristic
96C2×C22⋊Q8×C47C2211yescharacteristic
97C22×C42×C47C2211yescharacteristic
98C47×#391C2211yescharacteristic
99C47×#391C2211yescharacteristic
100C47×#389C2211yescharacteristic
101C47×#389C2211yescharacteristic
102C47×#387C2212yes—
103C47×#387C2212yes—
104C47×#385C2212yes—
105C47×#381C2212yes—
106C47×#380C2211yescharacteristic
107C22×Dic94C2311yescharacteristic
108C22×Dic94C2312yes—
109C23×Dic47C2311yescharacteristic
110C23×Dic47C2311yescharacteristic
111C23×Dic47C2311yescharacteristic
112C23×Dic47C2311yescharacteristic
113#13094014—44no—
114#13094003—24no—
115#13094001—28no—
116#13093989—44no—
117C2×C4⋊Dic47—24no—
118C2×C4⋊Dic47Q818yescomplemented
119C2×C4⋊Dic47C2312yes—
120C2×C4⋊Dic47C2312yes—
121C2×C4⋊Dic47C2312yes—
122C2×C4⋊Dic47C2311yescharacteristic
123C2×C4⋊Dic47C2311yescharacteristic
124C2×C4⋊Dic47C2311yescharacteristic
125C2×C4⋊Dic47C2312yes—
126C2×C4⋊Dic47C2312yes—
127C2×C4⋊Dic47C2312yes—
128C2×C4⋊Dic47C2312yes—
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×C22⋊Dic47C2312yes—
143C2×C22⋊Dic47C2312yes—
144C2×C4×Dic47—42no—
145C2×C4×Dic47—42no—
146C2×C4×Dic47C2312yes—
147C2×C4×Dic47C2312yes—
148C2×C4×Dic47C2312yes—
149C2×C4×Dic47C2312yes—
150C2×C4×Dic47C2312yes—
151C2×C4×Dic47C2312yes—
152C2×C4×Dic47C2312yes—
153C2×C4×Dic47C2312yes—
154C47⋊#95C2312yes—
155C47⋊#95C2312yes—
156C47⋊#95C2312yes—
157C47⋊#95C2312yes—
158C47⋊#95C2312yes—
159C47⋊#95C2312yes—
160C47⋊#95C2312yes—
161C47⋊#95C2312yes—
162C47⋊#95C2312yes—
163C47⋊#95C2312yes—
164C47⋊#95C2312yes—
165C47⋊#95C2312yes—
166C47⋊#95C2312yes—
167C47⋊#95C2312yes—
168C47⋊#95C2312yes—
169C47⋊#95C2312yes—
170C47⋊#95C2312yes—
171C47⋊#95C2312yes—
172C47⋊#95C2312yes—
173C47⋊#95C2312yes—
174C47⋊#95C2312yes—
175C47⋊#95C2312yes—
176C47⋊#95C2312yes—
177C47⋊#95C2312yes—
178C47⋊#95C2312yes—
179C22×Q8×C47C2311yescharacteristic
180C23×C4×C47C2311yescharacteristic
181C23×C4×C47C2311yescharacteristic
182C23×C4×C47C2311yescharacteristic
183C22⋊Q8×C47—24no—
184C2×C4⋊C4×C47C2312yes—
185C2×C4⋊C4×C47C2312yes—
186C2×C4⋊C4×C47C2311yescharacteristic
187C2×C4⋊C4×C47C2312yes—
188C2×C4⋊C4×C47C2311yescharacteristic
189C2×C4⋊C4×C47C2311yescharacteristic
190C2×C22⋊C4×C47C2312yes—
191C2×C22⋊C4×C47C2312yes—
192C2×C42×C47—24no—
193C2×C42×C47C2311yescharacteristic
194C2×C42×C47C2311yescharacteristic
195C2×C42×C47C2311yescharacteristic
196C2×C42×C47C2311yescharacteristic
197#95×C47C2312yes—
198#95×C47C2312yes—
199#95×C47C2312yes—
200#95×C47C2312yes—
201#95×C47C2312yes—
202#95×C47C2312yes—
203#95×C47C2312yes—
204C24×C47C2411yescharacteristic
205C2×Q8×C47—22no—
206C2×Q8×C47—41no—
207C2×Q8×C47—41no—
208C22×C4×C47—22no—
209C22×C4×C47—22no—
210C22×C4×C47—22no—
211C22×C4×C47—22no—
212C22×C4×C47—22no—
213C22×C4×C47—41no—
214C22×C4×C47—41no—
215C22×C4×C47C2×Q814yes—
216C22×C4×C47#4114yes—
217C22×C4×C47C2412yes—
218C22×C4×C47C2412yes—
219C22×C4×C47C2412yes—
220C22×C4×C47C2412yes—
221C22×C4×C47C2411yescharacteristic
222C22×C4×C47C2411yescharacteristic
223C22×C4×C47C2411yescharacteristic
224C22×C4×C47C2411yescharacteristic
225C22×C4×C47C2411yescharacteristic
226C22×C4×C47C2411yescharacteristic
227C22×Dic47—22no—
228C22×Dic47—41no—
229C22×Dic47—41no—
230C22×Dic47—41no—
231C22×Dic47—41no—
232C22×Dic47—41no—
233C22×Dic47—41no—
234C22×Dic47—41no—
235C22×Dic47—41no—
236C22×Dic47C2×Q814yes—
237C22×Dic47C2×Q814yes—
238C22×Dic47#4114yes—
239C22×Dic47C2412yes—
240C22×Dic47C2412yes—
241C22×Dic47C2412yes—
242C22×Dic47C2412yes—
243C22×Dic47C2412yes—
244C22×Dic47C2412yes—
245C22×Dic47C2412yes—
246C22×Dic47C2412yes—
247C2×Dic94—24no—
248C2×Dic94—22no—
249C2×Dic94—42no—
250C2×Dic94—42no—
251C2×Dic94—41no—
252C2×Dic94—41no—
253C4⋊C4×C47—22no—
254C4⋊C4×C47—24no—
255C4⋊C4×C47—24no—
256C4⋊C4×C47—24no—
257C4⋊C4×C47—41no—
258C4⋊C4×C47—41no—
259C22⋊C4×C47—24no—
260C22⋊C4×C47—24no—
261C42×C47—22no—
262C42×C47—22no—
263C42×C47—22no—
264C42×C47—22no—
265C22⋊Dic47—24no—
266C22⋊Dic47—24no—
267C4⋊Dic47—22no—
268C4⋊Dic47—24no—
269C4⋊Dic47—24no—
270C4⋊Dic47—24no—
271C4⋊Dic47—41no—
272C4⋊Dic47—42no—
273C4⋊Dic47—41no—
274C4⋊Dic47—42no—
275C4⋊Dic47C2×Q818yes—
276C4⋊Dic47C2×Q818yes—
277Dic47⋊C4—24no—
278Dic47⋊C4—24no—
279Dic47⋊C4—24no—
280Dic47⋊C4—24no—
281Dic47⋊C4—24no—
282Dic47⋊C4—42no—
283Dic47⋊C4—42no—
284Dic47⋊C4—42no—
285Dic47⋊C4—42no—
286Dic47⋊C4—42no—
287Dic47⋊C4—42no—
288Dic47⋊C4—42no—
289Dic47⋊C4—42no—
290C4×Dic47—24no—
291C4×Dic47—24no—
292C4×Dic47—42no—
293C4×Dic47—42no—
294C4×Dic47—42no—
295C4×Dic47—42no—
296C4×Dic47—42no—
297C4×Dic47—42no—
298C23×C47—21no—
299C23×C47—21no—
300C23×C47—21no—
301C23×C47—21no—
302C23×C47C22×Q812yes—
303C23×C47C2×#4112yes—
304C23×C47C2×#4112yes—
305C23×C47C2511yescharacteristic
306Q8×C47—82no—
307C2×C4×C47—28no—
308C2×C4×C47—28no—
309C2×C4×C47—21no—
310C2×C4×C47—21no—
311C2×C4×C47—21no—
312C2×C4×C47—21no—
313C2×C4×C47—21no—
314C2×C4×C47—21no—
315C2×C4×C47—21no—
316C2×C4×C47—21no—
317C2×C4×C47—21no—
318C2×C4×C47—21no—
319C2×C4×C47—21no—
320C2×C4×C47—21no—
321C2×C4×C47—22no—
322C2×C4×C47—22no—
323C2×C4×C47—22no—
324C2×C4×C47—22no—
325C2×C4×C47—22no—
326C2×C4×C47—22no—
327C2×C4×C47—22no—
328C2×C4×C47—22no—
329C2×C4×C47—22no—
330C2×C4×C47—22no—
331C2×C4×C47—22no—
332C2×C4×C47—22no—
333C2×C4×C47—44no—
334C2×C4×C47C22×Q812yes—
335C2×C4×C47C22×Q812yes—
336C2×C4×C47C2×#4112yes—
337C2×C4×C47C2×#4112yes—
338C2×C4×C47H(5,𝔽2)12yes—
339C2×C4×C472−1+412yes—
340C2×Dic47—22no—
341C2×Dic47—22no—
342C2×Dic47—22no—
343C2×Dic47—22no—
344C2×Dic47—22no—
345C2×Dic47—22no—
346C2×Dic47—22no—
347C2×Dic47—22no—
348C2×Dic47—22no—
349C2×Dic47—22no—
350C2×Dic47—22no—
351C2×Dic47—22no—
352C2×Dic47—22no—
353C2×Dic47—22no—
354C2×Dic47—22no—
355C2×Dic47—22no—
356C2×Dic47—22no—
357C2×Dic47—22no—
358C2×Dic47—22no—
359C2×Dic47—22no—
360C2×Dic47—22no—
361C2×Dic47—44no—
362C2×Dic47—44no—
363C2×Dic47—44no—
364C2×Dic47—44no—
365C2×Dic47C22×Q814yes—
366C2×Dic47C22×Q814yes—
367C2×Dic47C2×#4114yes—
368Dic94—48no—
369Dic94—82no—
370#35013—471nomaximal, Sylow
371C22×C47—22no—
372C22×C47—22no—
373C22×C47—22no—
374C22×C47—22no—
375C22×C47—22no—
376C22×C47—22no—
377C22×C47#53314yes—
378C22×C47C23×Q811yescharacteristic
379C22×C47C22×#4111yescharacteristic
380C22×C47C22×#4111yescharacteristic
381C22×C47C2×H(5,𝔽2)11yescharacteristic
382C22×C47C2×2−1+411yescharacteristic
383C22×C47#58511yescharacteristic
384C22×C47#58511yescharacteristic
385C4×C47—22no—
386C4×C47—22no—
387C4×C47—22no—
388C4×C47—22no—
389C4×C47—22no—
390C4×C47—22no—
391C4×C47—42no—
392C4×C47—42no—
393C4×C47—42no—
394C4×C47—42no—
395Dic47—24no—
396Dic47—24no—
397Dic47—24no—
398Dic47—42no—
399Dic47—42no—
400Dic47—42no—
401Dic47—42no—
402Dic47—42no—
403#2855—471no—
404#2855D4711yescharacteristic
405#2851—472no—
406#2659—471no—
407#2659—471no—
408#2627—472no—
409#2586—472no—
410#2586—472no—
411#2585—472no—
412#2585—472no—
413#2520—472no—
414#2520—472no—
415#2462—472no—
416#2462—472no—
417#2329—471no—
418#2329—471no—
419#2313—472no—
420C4×C22⋊Q8—472no—
421C2×C4×C4⋊C4—471no—
422C2×C47—24no—
423C2×C47C2×#53311yescharacteristic
424C2×C47#345911yescharacteristic
425C2×C47#346111yescharacteristic
426C2×C47#349111yescharacteristic
427C2×C47#349211yescharacteristic
428C2×C47#350111yescharacteristic
429C2×C47#350211yescharacteristic
430C2×#125—472no—
431C2×C22⋊Q8—471no—
432C2×C22⋊Q8—472no—
433C2×C22⋊Q8C2×D4711yescharacteristic
434C2×C4×Q8—472no—
435C22×C4⋊C4—471no—
436C22×C4⋊C4—471no—
437C22×C42—471no—
438C22×C42—471no—
439C22×C42C2×D4711yescharacteristic
440#400—472no—
441#400—472no—
442#398—472no—
443#398—472no—
444#398—472no—
445#398—472no—
446#398—472no—
447#398—472no—
448#398—472no—
449#398—472no—
450#395—472no—
451#395—472no—
452#395—472no—
453#395—472no—
454#395—472no—
455#395—472no—
456#391—472no—
457#391—471no—
458#391—471no—
459#391—472no—
460#391—472no—
461#391C2×D4711yescharacteristic
462#391C2×D4711yescharacteristic
463#389—472no—
464#389—472no—
465#389—472no—
466#389—472no—
467#389—471no—
468#389—471no—
469#389—472no—
470#389C2×D4711yescharacteristic
471#389C2×D4711yescharacteristic
472#387—472no—
473#387—472no—
474#387—472no—
475#387—472no—
476#387—472no—
477#387—472no—
478#387—472no—
479#387—472no—
480#387—472no—
481#387—472no—
482#387—472no—
483#387—472no—
484#387—472no—
485#387—472no—
486#387—472no—
487#387—472no—
488#387—472no—
489#387—472no—
490#387—472no—
491#387—472no—
492#387C2×D4712yes—
493#387C2×D4712yes—
494#385—472no—
495#385—472no—
496#385—472no—
497#385C2×D4712yes—
498#382—472no—
499#381—472no—
500#381C2×D4712yes—
501#380—471no—
502#380—472no—
503#380—472no—
504#380—472no—
505#380C2×D4711yescharacteristic
506C4×C4⋊C4—472no—
507C4×C4⋊C4—472no—
508C4×C4⋊C4—472no—
509C4×C4⋊C4—472no—
510C4×C4⋊C4—472no—
511C4×C4⋊C4—472no—
512C4×C4⋊C4—472no—
513C4×C22⋊C4—472no—
514C4×C22⋊C4—472no—
515C2×#95—471no—
516C2×#95—471no—
517C47#3501311yescharacteristic, complemented, Sylow
518C22×Q8—472no—
519C22×Q8—471no—
520C22×Q8C22×D4711yescharacteristic
521C23×C4—471no—
522C23×C4—471no—
523C23×C4—471no—
524C23×C4—471no—
525C23×C4C22×D4711yescharacteristic
526C23×C4C22×D4711yescharacteristic
527C23×C4C22×D4711yescharacteristic
528#125—1884no—
529C22⋊Q8—24no—
530C22⋊Q8—948no—
531C22⋊Q8—944no—
532C4×Q8—1884no—
533C2×C4⋊C4—478no—
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—471no—
544C2×C4⋊C4—472no—
545C2×C4⋊C4—472no—
546C2×C4⋊C4—472no—
547C2×C4⋊C4—472no—
548C2×C4⋊C4—472no—
549C2×C4⋊C4—472no—
550C2×C4⋊C4—472no—
551C2×C4⋊C4—472no—
552C2×C4⋊C4—472no—
553C2×C4⋊C4—472no—
554C2×C4⋊C4—471no—
555C2×C4⋊C4—471no—
556C2×C4⋊C4—472no—
557C2×C4⋊C4—944no—
558C2×C4⋊C4C22×D4712yes—
559C2×C4⋊C4C22×D4711yescharacteristic
560C2×C4⋊C4C22×D4712yes—
561C2×C4⋊C4C22×D4712yes—
562C2×C4⋊C4C22×D4711yescharacteristic
563C2×C4⋊C4C22×D4711yescharacteristic
564C2×C22⋊C4—472no—
565C2×C22⋊C4—472no—
566C2×C22⋊C4C22×D4712yes—
567C2×C22⋊C4C22×D4712yes—
568C2×C42—24no—
569C2×C42—472no—
570C2×C42—472no—
571C2×C42—472no—
572C2×C42—472no—
573C2×C42—472no—
574C2×C42—472no—
575C2×C42—472no—
576C2×C42—472no—
577C2×C42—1882no—
578C2×C42—1882no—
579C2×C42C22×D4711yescharacteristic
580C2×C42C22×D4711yescharacteristic
581C2×C42C22×D4711yescharacteristic
582C2×C42C22×D4711yescharacteristic
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#95—472no—
598#95—472no—
599#95—472no—
600#95—472no—
601#95—472no—
602#95—472no—
603#95—472no—
604#95—472no—
605#95—472no—
606#95—472no—
607#95—472no—
608#95C22×D4712yes—
609#95C22×D4712yes—
610#95C22×D4712yes—
611#95C22×D4712yes—
612#95C22×D4712yes—
613#95C22×D4712yes—
614#95C22×D4712yes—
615C24C23×D4711yescharacteristic
616C2×Q8—22no—
617C2×Q8—41no—
618C2×Q8—41no—
619C2×Q8—944no—
620C2×Q8—942no—
621C2×Q8—1881no—
622C2×Q8—1881no—
623C2×Q8—1882no—
624C2×Q8—1882no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4—472no—
633C22×C4—472no—
634C22×C4—472no—
635C22×C4—474no—
636C22×C4—474no—
637C22×C4—474no—
638C22×C4—472no—
639C22×C4—472no—
640C22×C4—472no—
641C22×C4—472no—
642C22×C4—472no—
643C22×C4—942no—
644C22×C4—1881no—
645C22×C4—1881no—
646C22×C4—1881no—
647C22×C4—1881no—
648C22×C4—1881no—
649C22×C4—1881no—
650C22×C4—1881no—
651C22×C4—1881no—
652C22×C4#1062535214yes—
653C22×C4Q8×D4714yes—
654C22×C4C23×D4712yes—
655C22×C4C23×D4712yes—
656C22×C4C23×D4712yes—
657C22×C4C23×D4712yes—
658C22×C4C23×D4711yescharacteristic
659C22×C4C23×D4711yescharacteristic
660C22×C4C23×D4711yescharacteristic
661C22×C4C23×D4711yescharacteristic
662C22×C4C23×D4711yescharacteristic
663C22×C4C23×D4711yescharacteristic
664C4⋊C4—22no—
665C4⋊C4—24no—
666C4⋊C4—24no—
667C4⋊C4—24no—
668C4⋊C4—41no—
669C4⋊C4—41no—
670C4⋊C4—478no—
671C4⋊C4—478no—
672C4⋊C4—944no—
673C4⋊C4—944no—
674C4⋊C4—944no—
675C4⋊C4—944no—
676C4⋊C4—944no—
677C4⋊C4—944no—
678C4⋊C4—942no—
679C4⋊C4—944no—
680C4⋊C4—944no—
681C4⋊C4—1882no—
682C4⋊C4—1882no—
683C4⋊C4—1882no—
684C4⋊C4—1882no—
685C4⋊C4—1882no—
686C4⋊C4—1882no—
687C4⋊C4—1882no—
688C4⋊C4—1882no—
689C4⋊C4—1881no—
690C4⋊C4—1881no—
691C4⋊C4—1882no—
692C4⋊C4—1882no—
693C22⋊C4—24no—
694C22⋊C4—24no—
695C22⋊C4—944no—
696C22⋊C4—944no—
697C42—22no—
698C42—22no—
699C42—22no—
700C42—22no—
701C42—944no—
702C42—944no—
703C42—1882no—
704C42—1882no—
705C42—1882no—
706C42—1882no—
707C42—1882no—
708C42—1882no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23C2×Q8×D4712yes—
714C23#41×D4712yes—
715C23C2×#1062535212yes—
716C23C24×D4711yescharacteristic
717Q8—82no—
718Q8—3762no—
719Q8—1888no—
720C2×C4—28no—
721C2×C4—28no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—44no—
747C2×C4—474no—
748C2×C4—474no—
749C2×C4—474no—
750C2×C4—942no—
751C2×C4—942no—
752C2×C4—942no—
753C2×C4—942no—
754C2×C4—942no—
755C2×C4—942no—
756C2×C4—942no—
757C2×C4—942no—
758C2×C4—942no—
759C2×C4—942no—
760C2×C4—942no—
761C2×C4—942no—
762C2×C4—942no—
763C2×C4—942no—
764C2×C4—942no—
765C2×C4—942no—
766C2×C4—942no—
767C2×C4—942no—
768C2×C4—942no—
769C2×C4—942no—
770C2×C4—942no—
771C2×C4—1884no—
772C2×C4—1884no—
773C2×C4—1884no—
774C2×C4—1884no—
775C2×C4C2×Q8×D4712yes—
776C2×C4C2×Q8×D4712yes—
777C2×C4C2×#1062535212yes—
778C2×C4C2×#1062535212yes—
779C2×C4#1309407012yes—
780C2×C4#1309407112yes—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22#1568967514yes—
788C22C22×Q8×D4711yescharacteristic
789C22C2×#41×D4711yescharacteristic
790C22C22×#1062535211yescharacteristic
791C22C2×#1309407011yescharacteristic
792C22C2×#1309407111yescharacteristic
793C22#1568995911yescharacteristic
794C22#1568995911yescharacteristic
795C4—22no—
796C4—22no—
797C4—22no—
798C4—22no—
799C4—22no—
800C4—22no—
801C4—42no—
802C4—42no—
803C4—42no—
804C4—42no—
805C4—944no—
806C4—944no—
807C4—944no—
808C4—1882no—
809C4—1882no—
810C4—1882no—
811C4—1882no—
812C4—1882no—
813C2—24no—
814C2C2×#1568967511yescharacteristic
815C2#2025679811yescharacteristic
816C2#2025681711yescharacteristic
817C2#2025708411yescharacteristic
818C2#2025709411yescharacteristic
819C2#2025718911yescharacteristic
820C2#2025719311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2855C2
prime radicalC24×C47C24
hypercenter#2855D47
hypocenterC47#35013
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2855

Complements

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

NH ≅ G/Ntype
6. #20248798C2semidirect
7. #20248797C2semidirect
8. #20248784C2semidirect
9. #20248782C2semidirect
10. #20248082C2semidirect
11. #20248074C2semidirect
12. #20247376C2semidirect
13. #20247368C2semidirect
118. C2×C4⋊Dic47Q8semidirect
517. C47#35013semidirect

Maximal subgroups

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

subgroupindex
#202517272
#202516942
#202495052
#202495042
#202492052
#202487982
#202487972
#202487842
#202487822
#202480822
#202480742
#202473762
#202473682
#202461232
#202461182
#202459892
#202459202
C2×C4×C4⋊Dic472
C47×#28552
#3501347