Finite Group Databasebeta

← #26121604

Subgroups — #26121604

Order 12032.

1226 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689889C211yesmaximal, characteristic
2C2×#15689096C211yesmaximal, characteristic
3#20245981C211yesmaximal, characteristic
4#20243107C211yesmaximal, characteristic, complemented
5C2×#15688880C211yesmaximal, characteristic, complemented
6C2×#15688879C211yesmaximal, characteristic, complemented
7C47×#1736C211yesmaximal, characteristic, complemented
8C22×#10625350C2211yescharacteristic
9#15689889—22no—
10#15689889—22no—
11#15689889—22no—
12#15689889C414yescomplemented
13C2×#13094032—22no—
14C2×#13094030—22no—
15C22×#10625329C2211yescharacteristic
16C2×M16×D47—22no—
17C2×#13093983C2211yescharacteristic
18C2×#13093983C2211yescharacteristic
19#15689096—22no—
20#15689096C414yescomplemented
21C2×#13093938—22no—
22#15689028C412yescomplemented
23#15689024C412yescomplemented
24#15689002—22no—
25#15688980—22no—
26#15688885—22no—
27#15688880—22no—
28#15688879—22no—
29C22×M16×C47C2211yescharacteristic
30C2×#117×C47C2211yescharacteristic
31C22×C4⋊C4×C47C2211yescharacteristic
32C47×#340—22no—
33C2×#10625350—21no—
34C2×#10625350—21no—
35C2×#10625350—21no—
36C2×#10625350—21no—
37C2×#10625350—21no—
38C2×#10625350—21no—
39C2×#10625350—21no—
40C2×#10625350—21no—
41C2×#10625350C2×C412yes—
42C2×#10625350C2×C412yes—
43C2×#10625350D412yes—
44C2×#10625350Q812yes—
45C22×Dic94C2×C411yescharacteristic
46C22×D188C2×C411yescharacteristic
47C22×C22⋊D47D412yes—
48C22×C4×D47D412yes—
49#13094032—28no—
50#13094032—28no—
51#13094030—28no—
52#13094030—28no—
53C2×#10625329—21no—
54C2×#10625329—21no—
55C2×#10625329—21no—
56C2×#10625329—21no—
57C2×#10625329C2×C412yes—
58C2×#10625329D412yes—
59C2×#10625324—24no—
60M16×D47—28no—
61M16×D47—28no—
62C22×C47⋊C8D412yes—
63C2×C8×D47—24no—
64#13093983—21no—
65#13093983—21no—
66#13093983—21no—
67#13093983—21no—
68#13093983—21no—
69#13093983—21no—
70#13093983—21no—
71#13093983C2×C412yes—
72C2×C4⋊Dic47—21no—
73C2×C4⋊Dic47—21no—
74C2×C22⋊Dic47—21no—
75C2×C22⋊Dic47—21no—
76C2×(C2×D47)⋊C4—24no—
77C2×C4×Dic47—21no—
78C2×C4×Dic47C2×C412yes—
79#13093938—28no—
80C47⋊#95—24no—
81C23×C4×C47—21no—
82C23×C4×C47C2311yescharacteristic
83C2×M16×C47—21no—
84C2×M16×C47—21no—
85C2×M16×C47—21no—
86C2×M16×C47—21no—
87C2×M16×C47C2×C412yes—
88C2×M16×C47D412yes—
89C22×C8×C47D412yes—
90#117×C47—21no—
91#117×C47—21no—
92#117×C47—21no—
93#117×C47C2×C412yes—
94C2×C4⋊C4×C47—21no—
95C2×C4⋊C4×C47—21no—
96C2×C4⋊C4×C47—21no—
97C2×C4⋊C4×C47—21no—
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47—21no—
100C2×C4⋊C4×C47C2×C412yes—
101C2×C22⋊C4×C47—21no—
102C2×C42×C47—21no—
103C24×C47C2×D411yescharacteristic
104C23×D47C22⋊C412yes—
105C22×C4×C47—22no—
106C22×C4×C47—41no—
107C22×C4×C47—41no—
108C22×C4×C47—41no—
109C22×C4×C47—82no—
110C22×C4×C47C22×C411yescharacteristic
111C22×C4×C47C22×C411yescharacteristic
112C22×C4×C47C22×C411yescharacteristic
113C22×C4×C47C2×D411yescharacteristic
114C22×C4×C47C2×D411yescharacteristic
115C22×C4×C47C2×D411yescharacteristic
116C22×C4×C47C2×D411yescharacteristic
117C22×C4×C47C2×D411yescharacteristic
118C22×C4×C47C2×D411yescharacteristic
119C22×C4×C47C2×Q811yescharacteristic
120C22×C4×C47#4111yescharacteristic
121C22×C4×C47#4111yescharacteristic
122C22×C4×C47#4111yescharacteristic
123C22×C4×C47#4111yescharacteristic
124C2×C22⋊D47—22no—
125C2×C22⋊D47—22no—
126C2×C22⋊D47—22no—
127C2×C22⋊D47—22no—
128C2×C22⋊D47C22⋊C414yes—
129C2×C22⋊D47C4⋊C414yes—
130C22×Dic47—22no—
131C22×Dic47—41no—
132C22×Dic47C22⋊C412yes—
133#10625350—22no—
134#10625350—22no—
135#10625350—22no—
136#10625350—22no—
137#10625350—22no—
138#10625350—22no—
139#10625350—22no—
140#10625350—22no—
141#10625350—22no—
142#10625350—22no—
143#10625350—22no—
144#10625350—22no—
145#10625350—22no—
146#10625350—22no—
147#10625350—22no—
148#10625350—22no—
149C2×D188—21no—
150C2×D188—21no—
151C2×D188—21no—
152C2×D188—21no—
153C2×D188C4212yes—
154C2×D188C4⋊C412yes—
155C2×C4×D47—22no—
156C2×C4×D47—22no—
157C2×C4×D47—22no—
158C2×C4×D47—22no—
159C2×C4×D47C22⋊C414yes—
160C2×C4×D47C4⋊C414yes—
161C2×Dic94—21no—
162C2×Dic94—21no—
163C2×Dic94—21no—
164C2×Dic94—21no—
165C2×Dic94C4212yes—
166C2×Dic94C4⋊C412yes—
167M16×C47—22no—
168M16×C47—22no—
169M16×C47—22no—
170M16×C47—22no—
171C2×C8×C47—22no—
172C2×C8×C47—22no—
173C2×C8×C47C22⋊C414yescomplemented
174C4⋊C4×C47—22no—
175C4⋊C4×C47—22no—
176C4⋊C4×C47—22no—
177C4⋊C4×C47—41no—
178C4⋊C4×C47—41no—
179C4⋊C4×C47—41no—
180C22⋊C4×C47—22no—
181C22⋊C4×C47—41no—
182C42×C47—22no—
183C42×C47—41no—
184C22⋊Dic47—22no—
185C22⋊Dic47—41no—
186C22⋊Dic47—41no—
187C22⋊Dic47—41no—
188(C2×D47)⋊C4—84no—
189C4⋊Dic47—22no—
190C4⋊Dic47—41no—
191C4⋊Dic47—41no—
192C4⋊Dic47—41no—
193C4×Dic47—22no—
194C4×Dic47—22no—
195C4×Dic47—22no—
196C4×Dic47—41no—
197#10625329—22no—
198#10625329—22no—
199#10625329—22no—
200#10625329—22no—
201C2×C47⋊C8—22no—
202C2×C47⋊C8—22no—
203C2×C47⋊C8C22⋊C414yescomplemented
204#10625324—216no—
205C8×D47—216no—
206C23×C47—41no—
207C23×C47—41no—
208C23×C47C2×C22⋊C411yescharacteristic
209C23×C47C2×C22⋊C411yescharacteristic
210C23×C47C2×C4⋊C411yescharacteristic
211C23×C47#12111yescharacteristic
212C23×C47#12111yescharacteristic
213C23×C47#12111yescharacteristic
214C23×C47#12111yescharacteristic
215C22×D47—22no—
216C22×D47—22no—
217C22×D47—42no—
218C22×D47—42no—
219C22×D47#9514yes—
220C2×C4×C47—44no—
221C2×C4×C47—42no—
222C2×C4×C47—42no—
223C2×C4×C47—81no—
224C2×C4×C47—81no—
225C2×C4×C47—82no—
226C2×C4×C47—82no—
227C2×C4×C47C2×C4211yescharacteristic
228C2×C4×C47C2×C22⋊C411yescharacteristic
229C2×C4×C47C2×C22⋊C411yescharacteristic
230C2×C4×C47C2×C22⋊C411yescharacteristic
231C2×C4×C47C2×C4⋊C411yescharacteristic
232C2×C4×C47C2×C4⋊C411yescharacteristic
233C2×C4×C47#11711yescharacteristic
234C2×C4×C47#11711yescharacteristic
235C2×C4×C47C4×D411yescharacteristic
236C2×C4×C47C4×D411yescharacteristic
237C2×C4×C47C4×D411yescharacteristic
238C2×C4×C47C4×D411yescharacteristic
239C2×C4×C47C4×D411yescharacteristic
240C2×C4×C47C4×D411yescharacteristic
241C2×C4×C47C4×D411yescharacteristic
242C2×C4×C47C4×D411yescharacteristic
243C2×C4×C47#12011yescharacteristic
244C2×C4×C47#12011yescharacteristic
245C2×C4×C47#12011yescharacteristic
246C2×C4×C47#12011yescharacteristic
247C2×C4×C47C22⋊Q811yescharacteristic
248C2×C4×C47C22⋊Q811yescharacteristic
249C2×C4×C47C22⋊Q811yescharacteristic
250C2×C4×C47C22⋊Q811yescharacteristic
251C2×C4×C47#12311yescharacteristic
252C2×C4×C47#12311yescharacteristic
253C2×C4×C47#12311yescharacteristic
254C2×C4×C47#12311yescharacteristic
255C22⋊D47—24no—
256C22⋊D47—24no—
257C22⋊D47—24no—
258C22⋊D47—24no—
259C2×Dic47—22no—
260C2×Dic47—22no—
261C2×Dic47—42no—
262C2×Dic47—42no—
263C2×Dic47—42no—
264C2×Dic47—42no—
265C2×Dic47—81no—
266C2×Dic47—81no—
267C2×Dic47#9514yes—
268D188—22no—
269D188—22no—
270D188—22no—
271D188—22no—
272C4×D47—24no—
273C4×D47—24no—
274C4×D47—24no—
275C4×D47—24no—
276Dic94—22no—
277Dic94—22no—
278Dic94—22no—
279Dic94—22no—
280C8×C47—24no—
281C47⋊C8—24no—
282#10742—471nomaximal, Sylow
283C22×C47—21no—
284C22×C47—21no—
285C22×C47—21no—
286C22×C47—21no—
287C22×C47—21no—
288C22×C47—21no—
289C22×C47—41no—
290C22×C47—41no—
291C22×C47—41no—
292C22×C47—41no—
293C22×C47C2×#9511yescharacteristic
294C22×C47#38011yescharacteristic
295C22×C47#38011yescharacteristic
296C22×C47#38611yescharacteristic
297C22×C47#38611yescharacteristic
298C22×C47#38611yescharacteristic
299C22×C47#38611yescharacteristic
300C2×D47—24no—
301C2×D47—42no—
302C2×D47—42no—
303C2×D47—44no—
304C2×D47—82no—
305C4×C47—82no—
306C4×C47—82no—
307C4×C47C4×C22⋊C411yescharacteristic
308C4×C47C4×C22⋊C411yescharacteristic
309C4×C47#37911yescharacteristic
310C4×C47#38111yescharacteristic
311C4×C47#38511yescharacteristic
312C4×C47#38511yescharacteristic
313C4×C47#38511yescharacteristic
314C4×C47#38511yescharacteristic
315Dic47—24no—
316Dic47—82no—
317Dic47—82no—
318C2×#568—471no—
319C2×#410—471no—
320#2311—471no—
321#1736—471no—
322#1736D4711yescharacteristic, complemented
323C2×H(3,ℤ/4)—471no—
324C2×H(3,ℤ/4)—471no—
325C2×C47—21no—
326C2×C47—21no—
327C2×C47—21no—
328C2×C47—21no—
329C2×C47—21no—
330C2×C47—21no—
331C2×C47C22⋊#9511yescharacteristic
332C2×C47#190911yescharacteristic
333C2×C47#191011yescharacteristic
334D47—44no—
335C22×#41—471no—
336#568—474no—
337#568—942no—
338#568—942no—
339#568—942no—
340C2×#131—942no—
341C2×#131—942no—
342C22×M16—471no—
343C22×M16—942no—
344C22×M16C2×D4711yescharacteristic
345C2×#117—471no—
346C2×#117—471no—
347C2×#117C2×D4711yescharacteristic
348C22×C4⋊C4C2×D4711yescharacteristic
349#410—474no—
350#410—942no—
351C2×#99—942no—
352#391—472no—
353#390—472no—
354#386—942no—
355#380—942no—
356#340—22no—
357#340—942no—
358H(3,ℤ/4)—942no—
359H(3,ℤ/4)—942no—
360C47#1074211yescharacteristic, complemented, Sylow
361C2×#41—472no—
362C2×#41—472no—
363C2×#41—472no—
364C2×#41—472no—
365C2×#41—941no—
366C2×#41—941no—
367C2×#41—941no—
368C2×#41—941no—
369C2×#41—941no—
370C2×#41—941no—
371C2×#41—941no—
372C2×#41—941no—
373C22×Q8—471no—
374C22×D4—472no—
375C22×D4—471no—
376C23×C4—21no—
377C23×C4—472no—
378C23×C4C22×D4711yescharacteristic
379#131—948no—
380#131—948no—
381#131—948no—
382#131—948no—
383C2×M16—21no—
384C2×M16—21no—
385C2×M16—21no—
386C2×M16—21no—
387C2×M16—472no—
388C2×M16—472no—
389C2×M16—944no—
390C2×M16—948no—
391C2×M16—948no—
392C2×M16—941no—
393C2×M16—941no—
394C2×M16—941no—
395C2×M16—941no—
396C2×M16C4×D4712yes—
397C2×M16D18812yes—
398C22×C8—472no—
399C22×C8—944no—
400C22×C8C22⋊D4712yes—
401#117—21no—
402#117—21no—
403#117—21no—
404#117—472no—
405#117—941no—
406#117—941no—
407#117—941no—
408#117—941no—
409#117—941no—
410#117—941no—
411#117—941no—
412#117C4×D4712yes—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—941no—
420C2×C4⋊C4—941no—
421C2×C4⋊C4C4×D4712yes—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—941no—
424C2×C22⋊C4—944no—
425C2×C22⋊C4—941no—
426C2×C42—21no—
427C2×C42—472no—
428C2×C42—941no—
429#99—948no—
430#95—944no—
431C24—472no—
432C24D4×D4711yescharacteristic
433#41—942no—
434#41—942no—
435#41—942no—
436#41—942no—
437#41—942no—
438#41—942no—
439#41—942no—
440#41—942no—
441#41—942no—
442#41—942no—
443#41—942no—
444#41—942no—
445#41—942no—
446#41—942no—
447#41—942no—
448#41—942no—
449C2×Q8—472no—
450C2×Q8—472no—
451C2×Q8—941no—
452C2×Q8—941no—
453C2×Q8—941no—
454C2×Q8—941no—
455C2×D4—474no—
456C2×D4—474no—
457C2×D4—472no—
458C2×D4—472no—
459C2×D4—942no—
460C2×D4—942no—
461C2×D4—942no—
462C2×D4—942no—
463C2×D4—941no—
464C2×D4—941no—
465C2×D4—941no—
466C2×D4—941no—
467C22×C4—22no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—82no—
472C22×C4—472no—
473C22×C4—474no—
474C22×C4—474no—
475C22×C4—942no—
476C22×C4—942no—
477C22×C4—942no—
478C22×C4—942no—
479C22×C4—942no—
480C22×C4—1881no—
481C22×C4C2×C4×D4711yescharacteristic
482C22×C4C2×C4×D4711yescharacteristic
483C22×C4C2×C4×D4711yescharacteristic
484C22×C4C2×D18811yescharacteristic
485C22×C4#1062535011yescharacteristic
486C22×C4#1062535011yescharacteristic
487C22×C4D4×D4711yescharacteristic
488C22×C4D4×D4711yescharacteristic
489C22×C4D4×D4711yescharacteristic
490C22×C4D4×D4711yescharacteristic
491C22×C4#1062535211yescharacteristic
492C22×C4Q8×D4711yescharacteristic
493C22×C4#1062535411yescharacteristic
494C22×C4C2×C22⋊D4711yescharacteristic
495M16—22no—
496M16—22no—
497M16—22no—
498M16—22no—
499M16—9416no—
500M16—942no—
501M16—942no—
502M16—942no—
503M16—942no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—474no—
507C2×C8—9416no—
508C2×C8—942no—
509C2×C8—942no—
510C2×C8(C2×D47)⋊C414yescomplemented
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4—41no—
517C4⋊C4—942no—
518C4⋊C4—1881no—
519C4⋊C4—1881no—
520C4⋊C4—1881no—
521C22⋊C4—22no—
522C22⋊C4—41no—
523C22⋊C4—942no—
524C22⋊C4—3764no—
525C22⋊C4—1881no—
526C22⋊C4—1881no—
527C22⋊C4—1881no—
528C42—22no—
529C42—41no—
530C42—942no—
531C42—942no—
532C42—942no—
533C42—1881no—
534C23—41no—
535C23—41no—
536C23—474no—
537C23—942no—
538C23—942no—
539C23—1882no—
540C23—1882no—
541C23C22⋊C4×D4711yescharacteristic
542C23C22⋊C4×D4711yescharacteristic
543C23C4⋊C4×D4711yescharacteristic
544C23#1309399511yescharacteristic
545C23#1309399711yescharacteristic
546C23#1309399711yescharacteristic
547C23#1309399911yescharacteristic
548Q8—942no—
549Q8—942no—
550Q8—942no—
551Q8—942no—
552D4—944no—
553D4—944no—
554D4—944no—
555D4—944no—
556D4—942no—
557D4—942no—
558D4—942no—
559D4—942no—
560C2×C4—44no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—81no—
564C2×C4—81no—
565C2×C4—82no—
566C2×C4—82no—
567C2×C4—474no—
568C2×C4—942no—
569C2×C4—942no—
570C2×C4—944no—
571C2×C4—944no—
572C2×C4—944no—
573C2×C4—944no—
574C2×C4—3761no—
575C2×C4—3761no—
576C2×C4—1882no—
577C2×C4—1882no—
578C2×C4—1882no—
579C2×C4—1882no—
580C2×C4C42×D4711yescharacteristic
581C2×C4C22⋊C4×D4711yescharacteristic
582C2×C4C22⋊C4×D4711yescharacteristic
583C2×C4C2×(C2×D47)⋊C411yescharacteristic
584C2×C4C4⋊C4×D4711yescharacteristic
585C2×C4C4⋊C4×D4711yescharacteristic
586C2×C4#1309398111yescharacteristic
587C2×C4#1309398211yescharacteristic
588C2×C4(C22⋊D47)⋊C411yescharacteristic
589C2×C4(C22⋊D47)⋊C411yescharacteristic
590C2×C4C4×C22⋊D4711yescharacteristic
591C2×C4C4×C22⋊D4711yescharacteristic
592C2×C4#1309398611yescharacteristic
593C2×C4#1309398611yescharacteristic
594C2×C4C4×D18811yescharacteristic
595C2×C4C4×D18811yescharacteristic
596C2×C4#1309399211yescharacteristic
597C2×C4#1309399211yescharacteristic
598C2×C4#1309399411yescharacteristic
599C2×C4#1309399411yescharacteristic
600C2×C4#1309400011yescharacteristic
601C2×C4#1309400211yescharacteristic
602C2×C4#1309400211yescharacteristic
603C2×C4#1309400411yescharacteristic
604C2×C4#1309400611yescharacteristic
605C2×C4#1309400611yescharacteristic
606C2×C4#1309400911yescharacteristic
607C2×C4#1309400911yescharacteristic
608C8—24no—
609C8—944no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—41no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—944no—
621C22—3762no—
622C22—1884no—
623C22—1882no—
624C22—1882no—
625C22#95×D4711yescharacteristic
626C22#1568898011yescharacteristic
627C22#1568898211yescharacteristic
628C22#1568899911yescharacteristic
629C22#1568899911yescharacteristic
630C22#1568900111yescharacteristic
631C22#1568900111yescharacteristic
632C4—82no—
633C4—82no—
634C4—944no—
635C4—3762no—
636C4—3762no—
637C4#1568897011yescharacteristic
638C4C4×(C2×D47)⋊C411yescharacteristic
639C4#1568897811yescharacteristic
640C4#1568898511yescharacteristic
641C4#1568899411yescharacteristic
642C4#1568899411yescharacteristic
643C4#1568899711yescharacteristic
644C4#1568899711yescharacteristic
645C2—21no—
646C2—21no—
647C2—21no—
648C2—21no—
649C2—21no—
650C2—21no—
651C2—1884no—
652C2(C2×D47)⋊#9511yescharacteristic
653C2#2024390711yescharacteristic
654C2#2024391211yescharacteristic
subgroupG/H
centerC22#15688999
commutatorC2×C4×C47C2×C42
FrattiniC23×C4C22×D47
FittingC47×#1736C2
socleC22×C47#386
prime radicalC22×#10625350C22
cosocleC23×C4×C47C23
hypercenter#1736D47
hypocenterC47#10742
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
4. #20243107C2semidirect
5. C2×#15688880C2semidirect
6. C2×#15688879C2semidirect
7. C47×#1736C2semidirect
12. #15689889C4semidirect
20. #15689096C4semidirect
22. #15689028C4semidirect
23. #15689024C4semidirect
173. C2×C8×C47C22⋊C4semidirect
203. C2×C47⋊C8C22⋊C4semidirect
322. #1736D47semidirect
360. C47#10742semidirect
510. C2×C8(C2×D47)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#156898892
C2×#156890962
#202459812
#202431072
C2×#156888802
C2×#156888792
C47×#17362
#1074247