Finite Group Databasebeta

← #26215684

Subgroups — #26215684

Order 12032.

1462 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689602C211yesmaximal, characteristic
2C2×#15689095C212yesmaximal
3#20246005C212yesmaximal, complemented
4#20243376C211yesmaximal, characteristic, complemented
5#20243375C212yesmaximal, complemented
6#20243374C212yesmaximal, complemented
7#20243373C212yesmaximal, complemented
8#20243119C212yesmaximal, complemented
9C47×#1799C211yesmaximal, characteristic, complemented
10C22×#10625352C2211yescharacteristic
11#15689602—24no—
12#15689602—24no—
13C2×C4×Dic94C411yescharacteristic, complemented
14C2×#13093989C411yescharacteristic, complemented
15C2×D4×Dic47C2211yescharacteristic
16C2×C4×C22⋊D47C411yescharacteristic, complemented
17C2×C4×C22⋊D47C2211yescharacteristic
18C2×(C22⋊D47)⋊C4C411yescharacteristic, complemented
19C2×(C22⋊D47)⋊C4C2211yescharacteristic
20C2×#13093981C411yescharacteristic, complemented
21C2×#13093980C411yescharacteristic, complemented
22C2×#13093980C2214yes—
23C2×#13093980C2211yescharacteristic
24C22×Dic47⋊C4C411yescharacteristic, complemented
25C22×Dic47⋊C4C2211yescharacteristic
26C2×C4⋊C4×D47C411yescharacteristic, complemented
27#15689095—28no—
28C2×#13093939C2212yes—
29C2×#13093938C2214yes—
30#15689020—24no—
31#15689018—24no—
32#15688983C2212yes—
33#15688981C2214yes—
34#15688890C2212yes—
35#15688889C2214yes—
36C2×C4×D4×C47C2211yescharacteristic
37C2×#99×C47C2212yes—
38C47×#380C2212yes—
39C47×#342C2212yes—
40C2×#10625352—24no—
41C2×#10625352—24no—
42C2×#10625352D414yes—
43C2×#10625352Q814yes—
44C22×Dic94C2×C411yescharacteristic
45C22×C22⋊D47C2×C411yescharacteristic
46C22×C22⋊D47C2311yescharacteristic
47C23×Dic47C2×C411yescharacteristic
48C23×Dic47C2×C411yescharacteristic
49C23×Dic47C2311yescharacteristic
50C23×Dic47C2311yescharacteristic
51C22×C4×D47C2×C411yescharacteristic
52C22×C4×D47C2×C411yescharacteristic
53C22×C4×D47C2×C411yescharacteristic
54C4×Dic94—22no—
55C4×Dic94—22no—
56#13093989—24no—
57D4×Dic47—24no—
58C4×C22⋊D47—22no—
59C4×C22⋊D47—22no—
60C4×C22⋊D47—22no—
61C4×C22⋊D47—22no—
62(C22⋊D47)⋊C4—24no—
63(C22⋊D47)⋊C4—24no—
64#13093981—22no—
65#13093981—22no—
66#13093980—24no—
67#13093980—24no—
68#13093980—28no—
69#13093980—28no—
70C2×C4⋊Dic47—22no—
71C2×C4⋊Dic47C2×C411yescharacteristic
72C2×Dic47⋊C4—22no—
73C2×Dic47⋊C4—22no—
74C2×Dic47⋊C4—24no—
75C2×Dic47⋊C4—24no—
76C2×Dic47⋊C4C2×C411yescharacteristic
77C2×Dic47⋊C4C2×C411yescharacteristic
78C2×Dic47⋊C4C2×C411yescharacteristic
79C2×Dic47⋊C4C2×C411yescharacteristic
80C2×Dic47⋊C4C2×C411yescharacteristic
81C2×Dic47⋊C4C2×C411yescharacteristic
82C2×Dic47⋊C4C2×C411yescharacteristic
83C2×Dic47⋊C4C2×C411yescharacteristic
84C2×Dic47⋊C4D414yes—
85C2×Dic47⋊C4D414yes—
86C4⋊C4×D47—24no—
87C2×C22⋊Dic47C2×C411yescharacteristic
88C2×C22⋊Dic47C2314yes—
89C2×C22⋊Dic47C2311yescharacteristic
90C2×(C2×D47)⋊C4C2×C411yescharacteristic
91C2×(C2×D47)⋊C4C2×C411yescharacteristic
92C2×C4×Dic47—24no—
93C2×C4×Dic47C2×C411yescharacteristic
94C2×C4×Dic47C2×C411yescharacteristic
95C2×C4×Dic47C2×C411yescharacteristic
96C2×C4×Dic47C2×C411yescharacteristic
97C2×C4×Dic47C2×C411yescharacteristic
98#13093939—24no—
99#13093938—28no—
100C47⋊#95—22no—
101C47⋊#95—24no—
102C22×D4×C47C2311yescharacteristic
103C23×C4×C47C2×C411yescharacteristic
104C23×C4×C47C2311yescharacteristic
105C4×D4×C47—22no—
106C4×D4×C47—22no—
107C2×C4⋊C4×C47—22no—
108C2×C4⋊C4×C47C2×C411yescharacteristic
109C2×C22⋊C4×C47C2×C411yescharacteristic
110C2×C22⋊C4×C47C2314yes—
111C2×C22⋊C4×C47C2311yescharacteristic
112C2×C42×C47C2×C411yescharacteristic
113#99×C47—24no—
114#95×C47—22no—
115C24×C47C22×C411yescharacteristic
116C24×C47C2411yescharacteristic
117C23×D47C22×C411yescharacteristic
118C2×D4×C47—22no—
119C2×D4×C47—22no—
120C2×D4×C47C2×D412yes—
121C2×D4×C47C2×Q812yes—
122C22×C4×C47—21no—
123C22×C4×C47—21no—
124C22×C4×C47—24no—
125C22×C4×C47—81no—
126C22×C4×C47—81no—
127C22×C4×C47C22×C411yescharacteristic
128C22×C4×C47C22×C411yescharacteristic
129C22×C4×C47C22×C411yescharacteristic
130C22×C4×C47C22×C411yescharacteristic
131C22×C4×C47C22×C411yescharacteristic
132C22×C4×C47C2×D412yes—
133C22×C4×C47C2×D412yes—
134C2×C22⋊D47—22no—
135C2×C22⋊D47—22no—
136C2×C22⋊D47—22no—
137C2×C22⋊D47—22no—
138C2×C22⋊D47C4⋊C414yescomplemented
139C2×C22⋊D47C2×D412yes—
140C2×C22⋊D47C2×Q812yes—
141C22×Dic47—22no—
142C22×Dic47—22no—
143C22×Dic47—22no—
144C22×Dic47—24no—
145C22×Dic47—81no—
146C22×Dic47—81no—
147C22×Dic47C4⋊C414yescomplemented
148C22×Dic47C22×C411yescharacteristic
149C22×Dic47C22×C411yescharacteristic
150C22×Dic47C22×C411yescharacteristic
151C22×Dic47C22×C411yescharacteristic
152C22×Dic47C22×C411yescharacteristic
153C22×Dic47C22×C411yescharacteristic
154C22×Dic47C22×C411yescharacteristic
155C22×Dic47C2×D414yes—
156C22×Dic47C2×D414yes—
157C22×Dic47C2×D412yes—
158C22×Dic47C2×Q812yes—
159C22×Dic47#4114yes—
160#10625352—216no—
161#10625352—216no—
162C2×C4×D47—22no—
163C2×C4×D47—22no—
164C2×C4×D47—22no—
165C2×C4×D47—22no—
166C2×C4×D47—81no—
167C2×C4×D47—81no—
168C2×C4×D47C4⋊C414yescomplemented
169C2×Dic94—22no—
170C2×Dic94—22no—
171C2×Dic94C4⋊C414yescomplemented
172C4⋊C4×C47—22no—
173C4⋊C4×C47—82no—
174C22⋊C4×C47—22no—
175C22⋊C4×C47—22no—
176C22⋊C4×C47—24no—
177C22⋊C4×C47—24no—
178C42×C47—21no—
179C42×C47—21no—
180C22⋊Dic47—22no—
181C22⋊Dic47—22no—
182C22⋊Dic47—24no—
183C22⋊Dic47—24no—
184(C2×D47)⋊C4—21no—
185(C2×D47)⋊C4—21no—
186(C2×D47)⋊C4—22no—
187C4⋊Dic47—22no—
188C4⋊Dic47—82no—
189Dic47⋊C4—21no—
190Dic47⋊C4—21no—
191Dic47⋊C4—22no—
192Dic47⋊C4—22no—
193Dic47⋊C4—22no—
194Dic47⋊C4—48no—
195Dic47⋊C4—84no—
196Dic47⋊C4C22⋊C414yes—
197Dic47⋊C4C22⋊C412yes—
198Dic47⋊C4C22⋊C412yes—
199Dic47⋊C4C22⋊C414yes—
200Dic47⋊C4C22⋊C412yes—
201Dic47⋊C4C22⋊C412yes—
202C4×Dic47—22no—
203C4×Dic47—22no—
204C4×Dic47—22no—
205C4×Dic47—22no—
206C4×Dic47—22no—
207C4×Dic47—48no—
208C23×C47—21no—
209C23×C47—21no—
210C23×C47—41no—
211C23×C47—41no—
212C23×C47—41no—
213C23×C47—41no—
214C23×C47C2×C4⋊C412yes—
215C23×C47C23×C411yescharacteristic
216C23×C47C22×D412yes—
217C23×C47C22×D411yescharacteristic
218C23×C47C22×Q811yescharacteristic
219C23×C47C2×#4112yes—
220C22×D47—21no—
221C22×D47—21no—
222C22×D47—41no—
223C22×D47—41no—
224C22×D47C2×C4⋊C412yes—
225D4×C47—24no—
226D4×C47—24no—
227C2×C4×C47—21no—
228C2×C4×C47—21no—
229C2×C4×C47—21no—
230C2×C4×C47—21no—
231C2×C4×C47—42no—
232C2×C4×C47—42no—
233C2×C4×C47—41no—
234C2×C4×C47—41no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47—44no—
238C2×C4×C47—44no—
239C2×C4×C47—44no—
240C2×C4×C47—81no—
241C2×C4×C47—81no—
242C2×C4×C47C2×C22⋊C412yes—
243C2×C4×C47C2×C22⋊C411yescharacteristic
244C2×C4×C47C2×C22⋊C411yescharacteristic
245C2×C4×C47C2×C4⋊C412yes—
246C22⋊D47—24no—
247C22⋊D47—24no—
248C22⋊D47—28no—
249C2×Dic47—21no—
250C2×Dic47—21no—
251C2×Dic47—28no—
252C2×Dic47—21no—
253C2×Dic47—21no—
254C2×Dic47—44no—
255C2×Dic47—41no—
256C2×Dic47—41no—
257C2×Dic47—41no—
258C2×Dic47—41no—
259C2×Dic47—44no—
260C2×Dic47—44no—
261C2×Dic47—44no—
262C2×Dic47—82no—
263C2×Dic47C2×C22⋊C412yes—
264C2×Dic47C2×C22⋊C412yes—
265C2×Dic47C2×C22⋊C412yes—
266C2×Dic47C2×C22⋊C412yes—
267C2×Dic47C2×C4⋊C412yes—
268C2×Dic47C2×C4⋊C412yes—
269C2×Dic47C2×C4⋊C412yes—
270C2×Dic47#11712yes—
271C2×Dic47#11712yes—
272C2×Dic47#12118yes—
273C2×Dic47C22⋊Q818yes—
274C4×D47—28no—
275C4×D47—82no—
276C4×D47—82no—
277Dic94—28no—
278#20634—471nomaximal, Sylow
279C22×C47—22no—
280C22×C47—21no—
281C22×C47—22no—
282C22×C47—21no—
283C22×C47—22no—
284C22×C47—41no—
285C22×C47—41no—
286C22×C47—42no—
287C22×C47—42no—
288C22×C47—42no—
289C22×C47—41no—
290C22×C47—41no—
291C22×C47C22×C22⋊C411yescharacteristic
292C22×C47C22×C4⋊C411yescharacteristic
293C22×C47C2×#11711yescharacteristic
294C22×C47C2×#12112yes—
295C22×C47C2×C22⋊Q812yes—
296C2×D47—22no—
297C2×D47—42no—
298C2×D47—41no—
299C2×D47—41no—
300C2×D47—42no—
301C4×C47—22no—
302C4×C47—21no—
303C4×C47—21no—
304C4×C47—22no—
305C4×C47—41no—
306C4×C47—41no—
307C4×C47—84no—
308Dic47—22no—
309Dic47—22no—
310Dic47—22no—
311Dic47—41no—
312Dic47—41no—
313Dic47—84no—
314Dic47#38014yes—
315Dic47#38014yes—
316C2×#520—471no—
317C2×#410—472no—
318#2316—472no—
319#1799—472no—
320#1799—472no—
321#1799—472no—
322#1799—471no—
323#1799D4711yescharacteristic, complemented
324#1740—472no—
325C2×C47—22no—
326C2×C47—21no—
327C2×C47—21no—
328C2×C47—22no—
329C2×C47—42no—
330C2×C47C2×#38011yescharacteristic
331C2×C47#288311yescharacteristic
332C2×C47#288411yescharacteristic
333D47—42no—
334C22×#41—471no—
335#520—944no—
336#520—944no—
337C2×C4×Q8—471no—
338C2×C4×Q8—471no—
339C2×C4×D4—471no—
340C2×C4×D4—471no—
341C2×C4×D4—471no—
342C2×C4×D4—471no—
343C2×C4×D4—471no—
344C2×C4×D4C2×D4711yescharacteristic
345C2×#117—471no—
346C2×#117—471no—
347C2×#117—471no—
348C2×#117—474no—
349C22×C4⋊C4—471no—
350C22×C4⋊C4—471no—
351C22×C4⋊C4—471no—
352#410—948no—
353C2×#99—472no—
354C2×#99—474no—
355C2×#99C2×D4712yes—
356#389—944no—
357#389—944no—
358#380—472no—
359#380—474no—
360#380C2×D4712yes—
361#342—474no—
362#342—472no—
363#342C2×D4712yes—
364C47#2063411yescharacteristic, complemented, Sylow
365C2×#41—474no—
366C2×#41—474no—
367C2×#41—944no—
368C2×#41—944no—
369C22×Q8—471no—
370C22×D4—471no—
371C22×D4—471no—
372C22×D4C22×D4711yescharacteristic
373C23×C4—471no—
374C23×C4—471no—
375C23×C4—471no—
376C23×C4—471no—
377C23×C4—471no—
378C23×C4—471no—
379C23×C4—471no—
380C23×C4C4×D4711yescharacteristic
381C23×C4C22×D4711yescharacteristic
382C4×Q8—942no—
383C4×Q8—942no—
384C4×Q8—944no—
385C4×D4—22no—
386C4×D4—22no—
387C4×D4—944no—
388C4×D4—944no—
389C4×D4—942no—
390C4×D4—942no—
391C4×D4—944no—
392C4×D4—942no—
393C4×D4—942no—
394#117—942no—
395#117—942no—
396#117—944no—
397#117—944no—
398#117—948no—
399#117—948no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—471no—
402C2×C4⋊C4—471no—
403C2×C4⋊C4—471no—
404C2×C4⋊C4—471no—
405C2×C4⋊C4—474no—
406C2×C4⋊C4—474no—
407C2×C4⋊C4—471no—
408C2×C4⋊C4—471no—
409C2×C4⋊C4—471no—
410C2×C4⋊C4—471no—
411C2×C4⋊C4—471no—
412C2×C4⋊C4—944no—
413C2×C4⋊C4—942no—
414C2×C4⋊C4—942no—
415C2×C4⋊C4—944no—
416C2×C4⋊C4—942no—
417C2×C4⋊C4—944no—
418C2×C4⋊C4C4×D4711yescharacteristic
419C2×C22⋊C4—471no—
420C2×C22⋊C4—471no—
421C2×C22⋊C4—471no—
422C2×C22⋊C4—471no—
423C2×C22⋊C4—474no—
424C2×C22⋊C4C4×D4711yescharacteristic
425C2×C22⋊C4C22×D4714yes—
426C2×C22⋊C4C22×D4711yescharacteristic
427C2×C42—471no—
428C2×C42—471no—
429C2×C42—471no—
430C2×C42—471no—
431C2×C42—471no—
432C2×C42—944no—
433C2×C42C4×D4711yescharacteristic
434#99—24no—
435#99—948no—
436#99—944no—
437#95—22no—
438#95—944no—
439#95—942no—
440C24—471no—
441C24C2×C4×D4711yescharacteristic
442C24C23×D4711yescharacteristic
443#41—9416no—
444#41—9416no—
445C2×Q8—474no—
446C2×Q8—942no—
447C2×Q8—942no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—474no—
451C2×D4—472no—
452C2×D4—472no—
453C2×D4—942no—
454C2×D4—942no—
455C2×D4—942no—
456C2×D4—942no—
457C2×D4D4×D4712yes—
458C2×D4Q8×D4712yes—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—24no—
462C22×C4—81no—
463C22×C4—81no—
464C22×C4—471no—
465C22×C4—471no—
466C22×C4—474no—
467C22×C4—472no—
468C22×C4—472no—
469C22×C4—474no—
470C22×C4—474no—
471C22×C4—471no—
472C22×C4—471no—
473C22×C4—471no—
474C22×C4—474no—
475C22×C4—474no—
476C22×C4—471no—
477C22×C4—471no—
478C22×C4—942no—
479C22×C4—942no—
480C22×C4—942no—
481C22×C4—942no—
482C22×C4—942no—
483C22×C4—942no—
484C22×C4—942no—
485C22×C4—944no—
486C22×C4—3761no—
487C22×C4—3761no—
488C22×C4—3761no—
489C22×C4—3761no—
490C22×C4C2×C4×D4711yescharacteristic
491C22×C4C2×C4×D4711yescharacteristic
492C22×C4C2×C4×D4711yescharacteristic
493C22×C4C2×C4×D4711yescharacteristic
494C22×C4C2×C4×D4711yescharacteristic
495C22×C4D4×D4712yes—
496C22×C4D4×D4712yes—
497C4⋊C4—22no—
498C4⋊C4—82no—
499C4⋊C4—472no—
500C4⋊C4—472no—
501C4⋊C4—474no—
502C4⋊C4—472no—
503C4⋊C4—472no—
504C4⋊C4—474no—
505C4⋊C4—942no—
506C4⋊C4—942no—
507C4⋊C4—942no—
508C4⋊C4—942no—
509C4⋊C4—941no—
510C4⋊C4—941no—
511C4⋊C4—3764no—
512C4⋊C4—3762no—
513C4⋊C4—1888no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—24no—
517C22⋊C4—24no—
518C22⋊C4—942no—
519C22⋊C4—942no—
520C22⋊C4—942no—
521C22⋊C4—941no—
522C22⋊C4—941no—
523C22⋊C4—944no—
524C22⋊C4—944no—
525C42—21no—
526C42—21no—
527C42—942no—
528C42—942no—
529C42—942no—
530C42—942no—
531C42—942no—
532C42—1888no—
533C23—21no—
534C23—21no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—472no—
540C23—941no—
541C23—941no—
542C23—1881no—
543C23—1881no—
544C23C4⋊C4×D4712yes—
545C23C22×C4×D4711yescharacteristic
546C23C2×D4×D4712yes—
547C23C2×D4×D4711yescharacteristic
548C23C2×Q8×D4711yescharacteristic
549C23#41×D4712yes—
550Q8—948no—
551D4—24no—
552D4—24no—
553D4—948no—
554D4—944no—
555D4—944no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—44no—
567C2×C4—44no—
568C2×C4—44no—
569C2×C4—81no—
570C2×C4—81no—
571C2×C4—472no—
572C2×C4—472no—
573C2×C4—472no—
574C2×C4—472no—
575C2×C4—472no—
576C2×C4—472no—
577C2×C4—478no—
578C2×C4—478no—
579C2×C4—472no—
580C2×C4—472no—
581C2×C4—472no—
582C2×C4—948no—
583C2×C4—948no—
584C2×C4—941no—
585C2×C4—941no—
586C2×C4—941no—
587C2×C4—941no—
588C2×C4—3762no—
589C2×C4—3762no—
590C2×C4—3762no—
591C2×C4—1884no—
592C2×C4—1881no—
593C2×C4—1881no—
594C2×C4—1884no—
595C2×C4—1884no—
596C2×C4—1884no—
597C2×C4—1881no—
598C2×C4—1881no—
599C2×C4C22⋊C4×D4711yescharacteristic
600C2×C4C22⋊C4×D4711yescharacteristic
601C2×C4C22⋊C4×D4712yes—
602C2×C4C4⋊C4×D4712yes—
603C22—22no—
604C22—21no—
605C22—22no—
606C22—21no—
607C22—22no—
608C22—41no—
609C22—41no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22—41no—
614C22—41no—
615C22—942no—
616C22—1882no—
617C22—1882no—
618C22—1881no—
619C22—1881no—
620C22C2×C22⋊C4×D4711yescharacteristic
621C22C2×C4⋊C4×D4711yescharacteristic
622C22#117×D4711yescharacteristic
623C22#121×D4712yes—
624C22C22⋊Q8×D4712yes—
625C4—21no—
626C4—21no—
627C4—22no—
628C4—22no—
629C4—41no—
630C4—41no—
631C4—84no—
632C4—474no—
633C4—474no—
634C4—942no—
635C4—942no—
636C4—942no—
637C4—3764no—
638C4—1881no—
639C4—1881no—
640C2—22no—
641C2—21no—
642C2—21no—
643C2—22no—
644C2—42no—
645C2—1882no—
646C2#380×D4711yescharacteristic
647C2#2025184611yescharacteristic
648C2#2025185011yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D47
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC47×#1799C2
socleC22×C47C22×C22⋊C4
prime radicalC22×#10625352C22
cosocleC24×C47C24
hypercenter#1799D47
hypocenterC47#20634
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
3. #20246005C2semidirect
4. #20243376C2semidirect
5. #20243375C2semidirect
6. #20243374C2semidirect
7. #20243373C2semidirect
8. #20243119C2semidirect
9. C47×#1799C2semidirect
13. C2×C4×Dic94C4semidirect
14. C2×#13093989C4semidirect
16. C2×C4×C22⋊D47C4semidirect
18. C2×(C22⋊D47)⋊C4C4semidirect
20. C2×#13093981C4semidirect
21. C2×#13093980C4semidirect
24. C22×Dic47⋊C4C4semidirect
26. C2×C4⋊C4×D47C4semidirect
138. C2×C22⋊D47C4⋊C4semidirect
147. C22×Dic47C4⋊C4semidirect
168. C2×C4×D47C4⋊C4semidirect
171. C2×Dic94C4⋊C4semidirect
323. #1799D47semidirect
364. C47#20634semidirect

Maximal subgroups

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

subgroupindex
C2×#156896022
C2×#156890952
#202460052
#202433762
#202433752
#202433742
#202433732
#202431192
C47×#17992
#2063447