Finite Group Databasebeta

← #26389370

Subgroups — #26389370

Order 12032.

1690 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251738C211yesmaximal, characteristic
2#20251736C211yesmaximal, characteristic
3#20251724C212yesmaximal
4#20249360C212yesmaximal
5#20249204C211yesmaximal, characteristic
6#20249203C211yesmaximal, characteristic
7#20248860C212yesmaximal, complemented
8#20248858C212yesmaximal, complemented
9#20248830C212yesmaximal, complemented
10#20248828C212yesmaximal, complemented
11#20247960C212yesmaximal, complemented
12#20247912C212yesmaximal, complemented
13#20247224C212yesmaximal, complemented
14#20247161C212yesmaximal, complemented
15#20246121C211yesmaximal, characteristic
16#20245988C212yesmaximal
17C4×#13094001C212yesmaximal
18C2×#15688974C211yesmaximal, characteristic
19C47×#2329C211yesmaximal, characteristic
20C2×#13094023C2211yescharacteristic
21C2×#13094022C2211yescharacteristic
22C2×#13094003C2211yescharacteristic
23C2×#13094001C2212yes—
24C2×C4×Dic94C2212yes—
25C22×Dic47⋊C4C2211yescharacteristic
26C22×Dic47⋊C4C2211yescharacteristic
27C22×C4×Dic47C2211yescharacteristic
28C22×C4×Dic47C2211yescharacteristic
29C22×C4×Dic47C2211yescharacteristic
30#15689064C2212yes—
31#15689064C2212yes—
32#15689063C2212yes—
33#15689063C2212yes—
34#15689061C2212yes—
35#15689061C2212yes—
36#15689057C2212yes—
37#15689056C2212yes—
38#15689056C2212yes—
39#15689056C2212yes—
40#15689054C2212yes—
41#15689053C2212yes—
42#15689053C2212yes—
43#15689053C2212yes—
44#15689044C2212yes—
45#15689042C2212yes—
46#15689030C2211yescharacteristic
47#15689028C2211yescharacteristic
48#15689027C2212yes—
49#15689027C2212yes—
50#15689027C2212yes—
51#15689027C2212yes—
52#15689027C2212yes—
53#15689022C2211yescharacteristic
54#15689020C2212yes—
55#15689020C2212yes—
56#15689020C2212yes—
57#15689019C2211yescharacteristic
58#15689018C2212yes—
59#15689018C2212yes—
60#15689018C2212yes—
61#15689018C2212yes—
62#15689010C2212yes—
63#15689010C2212yes—
64#15689009C2212yes—
65#15689009C2212yes—
66#15689007C2212yes—
67#15689007C2212yes—
68#15689007C2212yes—
69#15689007C2212yes—
70#15689006C2212yes—
71#15689006C2212yes—
72#15689005C2212yes—
73#15689005C2212yes—
74#15689005C2212yes—
75#15689005C2212yes—
76#15689005C2212yes—
77#15689005C2212yes—
78#15688998C2212yes—
79#15688996C2212yes—
80#15688995C2212yes—
81#15688992C2211yescharacteristic
82#15688992C2211yescharacteristic
83#15688984C2212yes—
84#15688984C2212yes—
85#15688983C2211yescharacteristic
86#15688981C2212yes—
87#15688981C2212yes—
88#15688981C2212yes—
89C4×Dic47⋊C4C2212yes—
90C4×Dic47⋊C4C2212yes—
91C4×C4⋊Dic47C2212yes—
92#15688974C2212yes—
93#15688974C2212yes—
94#15688974C2212yes—
95#15688974C2212yes—
96C4×C22⋊Dic47C2212yes—
97C2×C47⋊#95C2211yescharacteristic
98C2×C22⋊Q8×C47C2211yescharacteristic
99C47×#391C2212yes—
100C47×#389C2212yes—
101C47×#387C2212yes—
102C47×#387C2212yes—
103C47×#385C2212yes—
104C47×#380C2211yescharacteristic
105C4×C22⋊C4×C47C2212yes—
106C2×#95×C47C2211yescharacteristic
107C22×Dic94C2312yes—
108C22×Dic94C2311yescharacteristic
109C23×Dic47C2311yescharacteristic
110C23×Dic47C2311yescharacteristic
111C23×Dic47C2311yescharacteristic
112C23×Dic47C2311yescharacteristic
113#13094023—42no—
114#13094022—42no—
115#13094003—24no—
116#13094001—28no—
117C4×Dic94—44no—
118C2×C4⋊Dic47C2312yes—
119C2×C4⋊Dic47C2311yescharacteristic
120C2×C4⋊Dic47C2312yes—
121C2×C4⋊Dic47C2311yescharacteristic
122C2×C4⋊Dic47C2311yescharacteristic
123C2×C4⋊Dic47C2312yes—
124C2×Dic47⋊C4—24no—
125C2×Dic47⋊C4Q818yescomplemented
126C2×Dic47⋊C4C2312yes—
127C2×Dic47⋊C4C2312yes—
128C2×Dic47⋊C4C2312yes—
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×C22⋊Dic47C2312yes—
144C2×C22⋊Dic47C2312yes—
145C2×C4×Dic47—24no—
146C2×C4×Dic47—42no—
147C2×C4×Dic47—42no—
148C2×C4×Dic47C2312yes—
149C2×C4×Dic47C2311yescharacteristic
150C2×C4×Dic47C2311yescharacteristic
151C2×C4×Dic47C2312yes—
152C2×C4×Dic47C2312yes—
153C2×C4×Dic47C2312yes—
154C2×C4×Dic47C2312yes—
155C2×C4×Dic47C2312yes—
156C2×C4×Dic47C2311yescharacteristic
157C2×C4×Dic47C2311yescharacteristic
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—
179C47⋊#95C2312yes—
180C47⋊#95C2312yes—
181C47⋊#95C2312yes—
182C47⋊#95C2312yes—
183C22×Q8×C47C2311yescharacteristic
184C23×C4×C47C2311yescharacteristic
185C23×C4×C47C2311yescharacteristic
186C23×C4×C47C2311yescharacteristic
187C22⋊Q8×C47—24no—
188C2×C4⋊C4×C47C2311yescharacteristic
189C2×C4⋊C4×C47C2312yes—
190C2×C4⋊C4×C47C2311yescharacteristic
191C2×C4⋊C4×C47C2312yes—
192C2×C4⋊C4×C47C2312yes—
193C2×C4⋊C4×C47C2311yescharacteristic
194C2×C22⋊C4×C47C2312yes—
195C2×C22⋊C4×C47C2312yes—
196C2×C42×C47C2312yes—
197C2×C42×C47C2312yes—
198#95×C47C2312yes—
199#95×C47C2312yes—
200#95×C47C2312yes—
201#95×C47C2312yes—
202#95×C47C2312yes—
203#95×C47C2312yes—
204#95×C47C2312yes—
205C24×C47C2411yescharacteristic
206C2×Q8×C47—22no—
207C2×Q8×C47—41no—
208C2×Q8×C47—41no—
209C22×C4×C47—22no—
210C22×C4×C47—41no—
211C22×C4×C47—41no—
212C22×C4×C47—41no—
213C22×C4×C47—41no—
214C22×C4×C47—41no—
215C22×C4×C47—41no—
216C22×C4×C47C2×Q814yes—
217C22×C4×C47#4114yes—
218C22×C4×C47C2412yes—
219C22×C4×C47C2412yes—
220C22×C4×C47C2412yes—
221C22×C4×C47C2412yes—
222C22×C4×C47C2412yes—
223C22×C4×C47C2412yes—
224C22×C4×C47C2411yescharacteristic
225C22×C4×C47C2411yescharacteristic
226C22×Dic47—22no—
227C22×Dic47—22no—
228C22×Dic47—22no—
229C22×Dic47—22no—
230C22×Dic47—22no—
231C22×Dic47—41no—
232C22×Dic47—41no—
233C22×Dic47—41no—
234C22×Dic47—41no—
235C22×Dic47C2×Q814yes—
236C22×Dic47C2×Q814yes—
237C22×Dic47#4114yes—
238C22×Dic47C2412yes—
239C22×Dic47C2412yes—
240C22×Dic47C2412yes—
241C22×Dic47C2412yes—
242C22×Dic47C2412yes—
243C22×Dic47C2412yes—
244C22×Dic47C2411yescharacteristic
245C22×Dic47C2411yescharacteristic
246C22×Dic47C2411yescharacteristic
247C22×Dic47C2411yescharacteristic
248C2×Dic94—24no—
249C2×Dic94—24no—
250C2×Dic94—24no—
251C2×Dic94—22no—
252C2×Dic94—41no—
253C2×Dic94—41no—
254C4⋊C4×C47—22no—
255C4⋊C4×C47—24no—
256C4⋊C4×C47—41no—
257C4⋊C4×C47—42no—
258C4⋊C4×C47—42no—
259C4⋊C4×C47—41no—
260C22⋊C4×C47—24no—
261C22⋊C4×C47—24no—
262C42×C47—42no—
263C42×C47—42no—
264C22⋊Dic47—24no—
265C22⋊Dic47—24no—
266C4⋊Dic47—22no—
267C4⋊Dic47—24no—
268C4⋊Dic47—41no—
269C4⋊Dic47—42no—
270C4⋊Dic47—42no—
271C4⋊Dic47—41no—
272Dic47⋊C4—24no—
273Dic47⋊C4—24no—
274Dic47⋊C4—24no—
275Dic47⋊C4—24no—
276Dic47⋊C4—24no—
277Dic47⋊C4—24no—
278Dic47⋊C4—24no—
279Dic47⋊C4—42no—
280Dic47⋊C4—42no—
281Dic47⋊C4—42no—
282Dic47⋊C4—42no—
283Dic47⋊C4—42no—
284Dic47⋊C4—42no—
285Dic47⋊C4—42no—
286Dic47⋊C4—42no—
287Dic47⋊C4C2×Q818yes—
288Dic47⋊C4C2×Q818yes—
289C4×Dic47—24no—
290C4×Dic47—24no—
291C4×Dic47—24no—
292C4×Dic47—22no—
293C4×Dic47—22no—
294C4×Dic47—41no—
295C4×Dic47—41no—
296C4×Dic47—42no—
297C4×Dic47—42no—
298C4×Dic47—42no—
299C23×C47—21no—
300C23×C47—21no—
301C23×C47—21no—
302C23×C47—21no—
303C23×C47C22×Q812yes—
304C23×C47C2×#4112yes—
305C23×C47C2×#4112yes—
306C23×C47C2511yescharacteristic
307Q8×C47—82no—
308C2×C4×C47—22no—
309C2×C4×C47—21no—
310C2×C4×C47—21no—
311C2×C4×C47—22no—
312C2×C4×C47—21no—
313C2×C4×C47—21no—
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—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—44no—
330C2×C4×C47—44no—
331C2×C4×C47—44no—
332C2×C4×C47C22×Q814yes—
333C2×C4×C47C2×#4112yes—
334C2×C4×C47C2×#4112yes—
335C2×Dic47—28no—
336C2×Dic47—22no—
337C2×Dic47—22no—
338C2×Dic47—21no—
339C2×Dic47—21no—
340C2×Dic47—21no—
341C2×Dic47—21no—
342C2×Dic47—21no—
343C2×Dic47—21no—
344C2×Dic47—28no—
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—44no—
361C2×Dic47—44no—
362C2×Dic47C22×Q814yes—
363C2×Dic47C22×Q812yes—
364C2×Dic47C22×Q812yes—
365C2×Dic47C2×#4112yes—
366C2×Dic47C2×#4112yes—
367C2×Dic47H(5,𝔽2)12yes—
368C2×Dic472−1+412yes—
369Dic94—48no—
370Dic94—82no—
371#35015—471nomaximal, Sylow
372C22×C47—22no—
373C22×C47—22no—
374C22×C47—22no—
375C22×C47—22no—
376C22×C47—22no—
377C22×C47—22no—
378C22×C47#53314yes—
379C22×C47C23×Q811yescharacteristic
380C22×C47C22×#4111yescharacteristic
381C22×C47C22×#4111yescharacteristic
382C22×C47C2×H(5,𝔽2)11yescharacteristic
383C22×C47C2×2−1+411yescharacteristic
384C22×C47#58511yescharacteristic
385C22×C47#58511yescharacteristic
386C4×C47—24no—
387C4×C47—22no—
388C4×C47—22no—
389C4×C47—42no—
390C4×C47—42no—
391C4×C47—42no—
392C4×C47—42no—
393C4×C47—42no—
394Dic47—24no—
395Dic47—22no—
396Dic47—22no—
397Dic47—22no—
398Dic47—42no—
399Dic47—42no—
400Dic47—42no—
401Dic47—42no—
402Dic47—42no—
403Dic47#53914yes—
404#2857—471no—
405#2857—471no—
406#2855—472no—
407#2646—472no—
408#2627—471no—
409#2627—471no—
410#2590—472no—
411#2590—472no—
412#2588—472no—
413#2588—472no—
414#2511—472no—
415#2507—472no—
416#2451—472no—
417#2446—472no—
418#2329—471no—
419#2329D4711yescharacteristic
420#2313—472no—
421C4×C22⋊Q8—472no—
422C2×C4×C4⋊C4—471no—
423C2×C47—24no—
424C2×C47C2×#53311yescharacteristic
425C2×C47C2×#53911yescharacteristic
426C2×C47#345511yescharacteristic
427C2×C47#350111yescharacteristic
428C2×C47#350211yescharacteristic
429C2×C47#350511yescharacteristic
430C2×C47#350711yescharacteristic
431C2×C4⋊Q8—471no—
432C2×C4⋊Q8—471no—
433C2×C22⋊Q8—471no—
434C2×C22⋊Q8—472no—
435C2×C22⋊Q8C2×D4711yescharacteristic
436C2×C4×Q8—472no—
437C22×C4⋊C4—471no—
438C22×C4⋊C4—471no—
439C22×C42—471no—
440C22×C42—471no—
441C22×C42—471no—
442#400—472no—
443#400—472no—
444#400—472no—
445#400—472no—
446#400—472no—
447#400—472no—
448#398—472no—
449#398—472no—
450#398—472no—
451#398—472no—
452#398—472no—
453#398—472no—
454#398—472no—
455#398—472no—
456#395—472no—
457#395—472no—
458#391—471no—
459#391—471no—
460#391—472no—
461#391—472no—
462#391—472no—
463#391—472no—
464#391—472no—
465#391C2×D4712yes—
466#389—472no—
467#389—471no—
468#389—471no—
469#389—472no—
470#389—472no—
471#389—472no—
472#389—472no—
473#389—472no—
474#389—472no—
475#389C2×D4712yes—
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#384—471no—
499#384—471no—
500#381—472no—
501#381—472no—
502#380—471no—
503#380—472no—
504#380—472no—
505#380—472no—
506#380C2×D4711yescharacteristic
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×C4⋊C4—472no—
514C4×C22⋊C4—472no—
515C4×C22⋊C4C2×D4712yes—
516C2×#95—471no—
517C2×#95C2×D4711yescharacteristic
518C47#3501511yescharacteristic, complemented, Sylow
519C22×Q8—472no—
520C22×Q8—471no—
521C22×Q8C22×D4711yescharacteristic
522C23×C4—471no—
523C23×C4—471no—
524C23×C4—471no—
525C23×C4—471no—
526C23×C4C22×D4711yescharacteristic
527C23×C4C22×D4711yescharacteristic
528C23×C4C22×D4711yescharacteristic
529C4⋊Q8—1882no—
530C4⋊Q8—1882no—
531C22⋊Q8—24no—
532C22⋊Q8—948no—
533C22⋊Q8—944no—
534C4×Q8—1884no—
535C2×C4⋊C4—478no—
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—472no—
544C2×C4⋊C4—472no—
545C2×C4⋊C4—471no—
546C2×C4⋊C4—472no—
547C2×C4⋊C4—472no—
548C2×C4⋊C4—472no—
549C2×C4⋊C4—472no—
550C2×C4⋊C4—472no—
551C2×C4⋊C4—471no—
552C2×C4⋊C4—472no—
553C2×C4⋊C4—472no—
554C2×C4⋊C4—472no—
555C2×C4⋊C4—472no—
556C2×C4⋊C4—472no—
557C2×C4⋊C4—472no—
558C2×C4⋊C4—471no—
559C2×C4⋊C4—944no—
560C2×C4⋊C4C22×D4711yescharacteristic
561C2×C4⋊C4C22×D4712yes—
562C2×C4⋊C4C22×D4711yescharacteristic
563C2×C4⋊C4C22×D4711yescharacteristic
564C2×C4⋊C4C22×D4712yes—
565C2×C4⋊C4C22×D4712yes—
566C2×C22⋊C4—472no—
567C2×C22⋊C4—472no—
568C2×C22⋊C4C22×D4712yes—
569C2×C22⋊C4C22×D4712yes—
570C2×C42—472no—
571C2×C42—471no—
572C2×C42—471no—
573C2×C42—472no—
574C2×C42—472no—
575C2×C42—472no—
576C2×C42—472no—
577C2×C42—472no—
578C2×C42—471no—
579C2×C42—471no—
580C2×C42—944no—
581C2×C42—1882no—
582C2×C42—1882no—
583C2×C42C22×D4712yes—
584C2×C42C22×D4712yes—
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#95—472no—
609#95—472no—
610#95C22×D4712yes—
611#95C22×D4712yes—
612#95C22×D4712yes—
613#95C22×D4712yes—
614#95C22×D4712yes—
615#95C22×D4712yes—
616#95C22×D4712yes—
617C24C23×D4711yescharacteristic
618C2×Q8—22no—
619C2×Q8—41no—
620C2×Q8—41no—
621C2×Q8—944no—
622C2×Q8—944no—
623C2×Q8—944no—
624C2×Q8—942no—
625C2×Q8—1881no—
626C2×Q8—1881no—
627C22×C4—22no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4—471no—
635C22×C4—474no—
636C22×C4—474no—
637C22×C4—472no—
638C22×C4—471no—
639C22×C4—471no—
640C22×C4—471no—
641C22×C4—474no—
642C22×C4—472no—
643C22×C4—472no—
644C22×C4—472no—
645C22×C4—472no—
646C22×C4—472no—
647C22×C4—942no—
648C22×C4—942no—
649C22×C4—942no—
650C22×C4—942no—
651C22×C4—942no—
652C22×C4—1881no—
653C22×C4—1881no—
654C22×C4—1881no—
655C22×C4—1881no—
656C22×C4#1062535014yes—
657C22×C4Q8×D4714yes—
658C22×C4C23×D4712yes—
659C22×C4C23×D4712yes—
660C22×C4C23×D4712yes—
661C22×C4C23×D4712yes—
662C22×C4C23×D4712yes—
663C22×C4C23×D4712yes—
664C22×C4C23×D4711yescharacteristic
665C22×C4C23×D4711yescharacteristic
666C4⋊C4—22no—
667C4⋊C4—24no—
668C4⋊C4—41no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—41no—
672C4⋊C4—478no—
673C4⋊C4—478no—
674C4⋊C4—944no—
675C4⋊C4—944no—
676C4⋊C4—944no—
677C4⋊C4—944no—
678C4⋊C4—944no—
679C4⋊C4—944no—
680C4⋊C4—944no—
681C4⋊C4—944no—
682C4⋊C4—942no—
683C4⋊C4—1882no—
684C4⋊C4—1882no—
685C4⋊C4—1882no—
686C4⋊C4—1882no—
687C4⋊C4—1882no—
688C4⋊C4—1882no—
689C4⋊C4—1882no—
690C4⋊C4—1882no—
691C4⋊C4—1881no—
692C4⋊C4—1882no—
693C4⋊C4—1882no—
694C4⋊C4—1881no—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—944no—
698C22⋊C4—944no—
699C42—42no—
700C42—42no—
701C42—944no—
702C42—944no—
703C42—944no—
704C42—942no—
705C42—942no—
706C42—1882no—
707C42—1882no—
708C42—1881no—
709C42—1881no—
710C42—1882no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23C2×Q8×D4712yes—
716C23#41×D4712yes—
717C23C2×#1062535012yes—
718C23C24×D4711yescharacteristic
719Q8—82no—
720Q8—3762no—
721Q8—1888no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
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—44no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—472no—
747C2×C4—472no—
748C2×C4—472no—
749C2×C4—474no—
750C2×C4—472no—
751C2×C4—472no—
752C2×C4—472no—
753C2×C4—948no—
754C2×C4—948no—
755C2×C4—942no—
756C2×C4—942no—
757C2×C4—941no—
758C2×C4—941no—
759C2×C4—941no—
760C2×C4—941no—
761C2×C4—941no—
762C2×C4—941no—
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—942no—
772C2×C4—942no—
773C2×C4—942no—
774C2×C4—942no—
775C2×C4—942no—
776C2×C4—942no—
777C2×C4—942no—
778C2×C4—1884no—
779C2×C4—1884no—
780C2×C4C2×Q8×D4714yes—
781C2×C4C2×#1062535012yes—
782C2×C4C2×#1062535012yes—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22#1568967714yes—
790C22C22×Q8×D4711yescharacteristic
791C22C2×#41×D4711yescharacteristic
792C22C22×#1062535011yescharacteristic
793C22H(5,𝔽2)×D4711yescharacteristic
794C222−1+4×D4711yescharacteristic
795C22#1568995811yescharacteristic
796C22#1568995811yescharacteristic
797C4—24no—
798C4—22no—
799C4—22no—
800C4—42no—
801C4—42no—
802C4—42no—
803C4—42no—
804C4—42no—
805C4—474no—
806C4—944no—
807C4—942no—
808C4—942no—
809C4—942no—
810C4—1882no—
811C4—1882no—
812C4—1882no—
813C4—1882no—
814C4—1882no—
815C2—24no—
816C2C2×#1568967711yescharacteristic
817C2#539×D4711yescharacteristic
818C2#2025677011yescharacteristic
819C2#2025718811yescharacteristic
820C2#2025719611yescharacteristic
821C2#2025721811yescharacteristic
822C2#2025724611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2329C2
prime radicalC24×C47C24
hypercenter#2329D47
hypocenterC47#35015
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2329

Complements

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

NH ≅ G/Ntype
7. #20248860C2semidirect
8. #20248858C2semidirect
9. #20248830C2semidirect
10. #20248828C2semidirect
11. #20247960C2semidirect
12. #20247912C2semidirect
13. #20247224C2semidirect
14. #20247161C2semidirect
125. C2×Dic47⋊C4Q8semidirect
518. C47#35015semidirect

Maximal subgroups

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

subgroupindex
#202517382
#202517362
#202517242
#202493602
#202492042
#202492032
#202488602
#202488582
#202488302
#202488282
#202479602
#202479122
#202472242
#202471612
#202461212
#202459882
C4×#130940012
C2×#156889742
C47×#23292
#3501547