Finite Group Databasebeta

← #26121869

Subgroups — #26121869

Order 12032.

1204 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256589C211yesmaximal, characteristic
2C2×#15689141C211yesmaximal, characteristic
3#20251908C211yesmaximal, characteristic
4C2×#15688894C211yesmaximal, characteristic, complemented
5#20243121C211yesmaximal, characteristic, complemented
6C2×#15688879C211yesmaximal, characteristic, complemented
7C2×C47×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
8C22×#10625350C2211yescharacteristic
9C22×#10625329C2211yescharacteristic
10#15689604—22no—
11#15689603—22no—
12#15689600—21no—
13#15689597—21no—
14#15689596—22no—
15C4×#10625350C414yescomplemented
16#15689591—22no—
17C2×#13093983C2211yescharacteristic
18C2×#13093983C2211yescharacteristic
19#117×D47—22no—
20#15689141—22no—
21#15689141—22no—
22C2×#13093952C414yescomplemented
23#15689133—21no—
24#15689129—21no—
25#15689125—22no—
26#15689120C414yescomplemented
27#15688894—22no—
28#15688890—22no—
29#15688879—22no—
30C22×M16×C47C2211yescharacteristic
31C2×#117×C47C2211yescharacteristic
32C2×#117×C47C2211yescharacteristic
33C47×H(3,ℤ/4)—22no—
34C2×#10625350—21no—
35C2×#10625350—21no—
36C2×#10625350—21no—
37C2×#10625350—21no—
38C2×#10625350—21no—
39C2×#10625350—21no—
40C2×#10625350C2×C412yes—
41C2×#10625350C2×C412yes—
42C2×#10625350C2×C412yes—
43C2×#10625350D412yes—
44C2×#10625350D412yes—
45C2×#10625350Q812yes—
46C22×Dic94D411yescharacteristic
47C22×D188D411yescharacteristic
48C22×C22⋊D47—21no—
49C22×C4×D47—21no—
50C2×#10625329—21no—
51C2×#10625329—21no—
52C2×#10625329—21no—
53C2×#10625329—21no—
54C2×#10625329—21no—
55C2×#10625329C2×C412yescomplemented
56C22×C47⋊C8—21no—
57C4×Dic94—24no—
58#13093989—24no—
59C4×D188—24no—
60#13093986—24no—
61C4×C22⋊D47—28no—
62(C22⋊D47)⋊C4—28no—
63#13093983—21no—
64#13093983—21no—
65#13093983—21no—
66#13093983—21no—
67#13093983—21no—
68#13093983C2×C412yes—
69#13093983C2×C412yescomplemented
70#13093983D412yes—
71#13093982—24no—
72#13093981—24no—
73#13093980—24no—
74C2×C4⋊Dic47—21no—
75C2×C4⋊Dic47—21no—
76C4⋊C4×D47—24no—
77C2×C22⋊Dic47—21no—
78C2×C22⋊Dic47D412yes—
79C22⋊C4×D47—24no—
80C2×C4×Dic47—21no—
81C2×C4×Dic47—21no—
82C42×D47—24no—
83#13093952—28no—
84#13093949—24no—
85#13093946—24no—
86C23×C4×C47C2311yescharacteristic
87C2×M16×C47—21no—
88C2×M16×C47—21no—
89C2×M16×C47—21no—
90C2×M16×C47—21no—
91C2×M16×C47—21no—
92C2×M16×C47—21no—
93C22×C8×C47C2×C412yescomplemented
94#117×C47—21no—
95#117×C47—21no—
96#117×C47—21no—
97#117×C47—21no—
98#117×C47—21no—
99#117×C47—21no—
100#117×C47D412yes—
101#117×C47D412yes—
102C2×C4⋊C4×C47—21no—
103C2×C4⋊C4×C47—21no—
104C2×C22⋊C4×C47—21no—
105C2×C22⋊C4×C47—21no—
106C2×C42×C47C2×C412yes—
107C2×C42×C47C2×C412yescomplemented
108C24×C47C2×D411yescharacteristic
109C23×D47—21no—
110C22×C4×C47—22no—
111C22×C4×C47—22no—
112C22×C4×C47C22×C411yescharacteristic
113C22×C4×C47C22×C411yescharacteristic
114C22×C4×C47C22×C411yescharacteristic
115C22×C4×C47C2×D411yescharacteristic
116C22×C4×C47C2×D411yescharacteristic
117C22×C4×C47C2×D411yescharacteristic
118C22×C4×C47C2×D411yescharacteristic
119C22×C4×C47C2×D411yescharacteristic
120C22×C4×C47C2×D411yescharacteristic
121C22×C4×C47C2×Q811yescharacteristic
122C22×C4×C47#4111yescharacteristic
123C22×C4×C47#4111yescharacteristic
124C22×C4×C47#4111yescharacteristic
125C22×C4×C47#4111yescharacteristic
126C2×C22⋊D47—22no—
127C2×C22⋊D47—22no—
128C2×C22⋊D47—22no—
129C2×C22⋊D47—22no—
130C2×C22⋊D47—22no—
131C2×C22⋊D47—22no—
132C22×Dic47—21no—
133C22×Dic47—22no—
134C22×Dic47—41no—
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#10625350C4214yes—
148#10625350C22⋊C414yes—
149#10625350C4⋊C414yes—
150#10625350C4⋊C414yes—
151C2×D188—21no—
152C2×D188—21no—
153C2×D188—21no—
154C2×D188C22⋊C412yes—
155C2×D188C22⋊C412yes—
156C2×D188C4⋊C412yes—
157C2×C4×D47—22no—
158C2×C4×D47—22no—
159C2×C4×D47—22no—
160C2×C4×D47—22no—
161C2×C4×D47—22no—
162C2×C4×D47—22no—
163C2×C4×D47—28no—
164C2×Dic94—21no—
165C2×Dic94—21no—
166C2×Dic94—21no—
167C2×Dic94C22⋊C412yes—
168C2×Dic94C22⋊C412yes—
169C2×Dic94C4⋊C412yes—
170M16×C47—41no—
171M16×C47—41no—
172M16×C47—41no—
173M16×C47—41no—
174C2×C8×C47—22no—
175C2×C8×C47—22no—
176C2×C8×C47—22no—
177C4⋊C4×C47—22no—
178C4⋊C4×C47—22no—
179C4⋊C4×C47—41no—
180C4⋊C4×C47—41no—
181C22⋊C4×C47—22no—
182C22⋊C4×C47—22no—
183C22⋊C4×C47—41no—
184C22⋊C4×C47—41no—
185C42×C47—22no—
186C42×C47—22no—
187C42×C47—22no—
188C42×C47C22⋊C414yes—
189C22⋊Dic47—22no—
190C22⋊Dic47—22no—
191C22⋊Dic47—41no—
192C22⋊Dic47C22⋊C414yes—
193(C2×D47)⋊C4—28no—
194C4⋊Dic47—22no—
195C4⋊Dic47—22no—
196C4⋊Dic47—22no—
197C4⋊Dic47—41no—
198Dic47⋊C4—28no—
199C4×Dic47—28no—
200C4×Dic47—22no—
201C4×Dic47—22no—
202C4×Dic47—22no—
203C4×Dic47—41no—
204#10625329—22no—
205#10625329—22no—
206#10625329—41no—
207#10625329—41no—
208C2×C47⋊C8—22no—
209C2×C47⋊C8—41no—
210C2×C47⋊C8—41no—
211C23×C47—81no—
212C23×C47C2×C22⋊C411yescharacteristic
213C23×C47C4×D411yescharacteristic
214C23×C47C4×D411yescharacteristic
215C23×C47#12011yescharacteristic
216C23×C47#12011yescharacteristic
217C23×C47#12111yescharacteristic
218C23×C47C22⋊Q811yescharacteristic
219C22×D47—22no—
220C22×D47—22no—
221C22×D47—22no—
222C22×D47—82no—
223C2×C4×C47—24no—
224C2×C4×C47—42no—
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×C22⋊C411yescharacteristic
232C2×C4×C47C2×C4⋊C411yescharacteristic
233C2×C4×C47C2×C4⋊C411yescharacteristic
234C2×C4×C47C2×C4⋊C411yescharacteristic
235C2×C4×C47#11711yescharacteristic
236C2×C4×C47#11711yescharacteristic
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#12111yescharacteristic
246C2×C4×C47#12111yescharacteristic
247C2×C4×C47#12111yescharacteristic
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—22no—
262C2×Dic47—24no—
263C2×Dic47—42no—
264C2×Dic47—82no—
265C2×Dic47—82no—
266D188—22no—
267D188—22no—
268D188—22no—
269D188#9514yes—
270C4×D47—24no—
271C4×D47—24no—
272C4×D47—24no—
273C4×D47—24no—
274C4×D47—88no—
275Dic94—22no—
276Dic94—22no—
277Dic94—22no—
278Dic94#9514yes—
279C8×C47—42no—
280C47⋊C8—42no—
281#10792—471nomaximal, Sylow
282C22×C47—41no—
283C22×C47—41no—
284C22×C47—41no—
285C22×C47—41no—
286C22×C47—41no—
287C22×C47—41no—
288C22×C47—41no—
289C22×C47C4×C22⋊C411yescharacteristic
290C22×C47#37911yescharacteristic
291C22×C47#38011yescharacteristic
292C22×C47#38511yescharacteristic
293C22×C47#38511yescharacteristic
294C22×C47#38611yescharacteristic
295C22×C47#38611yescharacteristic
296C2×D47—24no—
297C2×D47—44no—
298C2×D47—82no—
299C2×D47—82no—
300C4×C47—44no—
301C4×C47—82no—
302C4×C47C2×#9511yescharacteristic
303C4×C47C4×C22⋊C411yescharacteristic
304C4×C47#38011yescharacteristic
305C4×C47#38111yescharacteristic
306C4×C47#38511yescharacteristic
307C4×C47#38511yescharacteristic
308C4×C47#38611yescharacteristic
309C4×C47#38611yescharacteristic
310Dic47—24no—
311Dic47—44no—
312Dic47—82no—
313#3428—471no—
314C2×#421—471no—
315#2896—471no—
316C2×#344—471no—
317#1740—471no—
318C2×H(3,ℤ/4)—471no—
319C2×H(3,ℤ/4)D4711yescharacteristic, complemented
320C2×C47—21no—
321C2×C47—21no—
322C2×C47—21no—
323C2×C47—21no—
324C2×C47—21no—
325C2×C47—21no—
326C2×C47—21no—
327C2×C47C22⋊#9511yescharacteristic
328D47—44no—
329C22×#41—471no—
330C22×M16—471no—
331C22×M16C2×D4711yescharacteristic
332#520—942no—
333#520—942no—
334#519—941no—
335#518—942no—
336#518—941no—
337C4×#41—474no—
338C4×#41—942no—
339C2×#117—471no—
340C2×#117—471no—
341C2×#117—942no—
342C2×#117C2×D4711yescharacteristic
343C2×#117C2×D4711yescharacteristic
344#421—942no—
345#421—942no—
346C2×#104—474no—
347#419—941no—
348#418—941no—
349#417—942no—
350#416—474no—
351#344—942no—
352#342—942no—
353H(3,ℤ/4)—22no—
354H(3,ℤ/4)—942no—
355C47#1079211yescharacteristic, complemented, Sylow
356C2×#41—472no—
357C2×#41—472no—
358C2×#41—472no—
359C2×#41—472no—
360C2×#41—472no—
361C2×#41—472no—
362C2×#41—941no—
363C2×#41—941no—
364C2×#41—941no—
365C2×#41—941no—
366C2×#41—941no—
367C2×#41—941no—
368C22×Q8—471no—
369C22×D4—471no—
370C22×D4—941no—
371C23×C4—941no—
372C23×C4C22×D4711yescharacteristic
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—21no—
376C2×M16—21no—
377C2×M16—21no—
378C2×M16—21no—
379C2×M16—472no—
380C2×M16—941no—
381C2×M16—941no—
382C2×M16—941no—
383C2×M16—941no—
384C2×M16—941no—
385C22×C8—941no—
386C22×C8C4×D4712yescomplemented
387C4×Q8—944no—
388C4×Q8—944no—
389C4×D4—944no—
390C4×D4—948no—
391C4×D4—948no—
392C4×D4—944no—
393#117—21no—
394#117—21no—
395#117—21no—
396#117—21no—
397#117—21no—
398#117—21no—
399#117—472no—
400#117—472no—
401#117—472no—
402#117—944no—
403#117—944no—
404#117—941no—
405#117—941no—
406#117—941no—
407#117—944no—
408#117—941no—
409#117—941no—
410#117D18812yes—
411#117C22⋊D4712yes—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—944no—
415C2×C4⋊C4—941no—
416C2×C4⋊C4—941no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—472no—
420C2×C22⋊C4—944no—
421C2×C22⋊C4—941no—
422C2×C42—941no—
423C2×C42—944no—
424C2×C42—941no—
425C2×C42C4×D4712yes—
426C2×C42C4×D4712yescomplemented
427#104—948no—
428#103—944no—
429#102—944no—
430C24—941no—
431C24D4×D4711yescharacteristic
432#41—474no—
433#41—474no—
434#41—474no—
435#41—474no—
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—
448C2×Q8—472no—
449C2×Q8—472no—
450C2×Q8—472no—
451C2×Q8—941no—
452C2×Q8—941no—
453C2×Q8—941no—
454C2×D4—472no—
455C2×D4—472no—
456C2×D4—472no—
457C2×D4—942no—
458C2×D4—942no—
459C2×D4—942no—
460C2×D4—942no—
461C2×D4—942no—
462C2×D4—942no—
463C2×D4—941no—
464C2×D4—941no—
465C2×D4—941no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—948no—
469C22×C4—941no—
470C22×C4—942no—
471C22×C4—942no—
472C22×C4—942no—
473C22×C4—942no—
474C22×C4—942no—
475C22×C4—942no—
476C22×C4—942no—
477C22×C4—1881no—
478C22×C4C2×C4×D4711yescharacteristic
479C22×C4C2×C4×D4711yescharacteristic
480C22×C4C2×C4×D4711yescharacteristic
481C22×C4C2×D18811yescharacteristic
482C22×C4#1062535011yescharacteristic
483C22×C4#1062535011yescharacteristic
484C22×C4D4×D4711yescharacteristic
485C22×C4D4×D4711yescharacteristic
486C22×C4D4×D4711yescharacteristic
487C22×C4D4×D4711yescharacteristic
488C22×C4#1062535211yescharacteristic
489C22×C4Q8×D4711yescharacteristic
490C22×C4#1062535411yescharacteristic
491C22×C4C2×C22⋊D4711yescharacteristic
492M16—41no—
493M16—41no—
494M16—41no—
495M16—41no—
496M16—942no—
497M16—942no—
498M16—1881no—
499M16—1881no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—942no—
504C2×C8—1881no—
505C2×C8—1881no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—41no—
509C4⋊C4—41no—
510C4⋊C4—948no—
511C4⋊C4—942no—
512C4⋊C4—942no—
513C4⋊C4—942no—
514C4⋊C4—1881no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C22⋊C4—474no—
520C22⋊C4—948no—
521C22⋊C4—942no—
522C22⋊C4—942no—
523C22⋊C4—1881no—
524C42—22no—
525C42—22no—
526C42—22no—
527C42—948no—
528C42—942no—
529C42—942no—
530C42—942no—
531C42—1881no—
532C42(C2×D47)⋊C414yes—
533C23—81no—
534C23—942no—
535C23—942no—
536C23—942no—
537C23—3762no—
538C23C22⋊C4×D4711yescharacteristic
539C23(C22⋊D47)⋊C411yescharacteristic
540C23#1309398611yescharacteristic
541C23#1309399211yescharacteristic
542C23#1309399411yescharacteristic
543C23#1309399711yescharacteristic
544C23#1309400211yescharacteristic
545Q8—474no—
546Q8—942no—
547Q8—942no—
548Q8—942no—
549D4—474no—
550D4—944no—
551D4—944no—
552D4—944no—
553D4—944no—
554D4—942no—
555D4—942no—
556D4—942no—
557C2×C4—24no—
558C2×C4—42no—
559C2×C4—82no—
560C2×C4—82no—
561C2×C4—942no—
562C2×C4—942no—
563C2×C4—942no—
564C2×C4—944no—
565C2×C4—944no—
566C2×C4—944no—
567C2×C4—944no—
568C2×C4—944no—
569C2×C4—3768no—
570C2×C4—3762no—
571C2×C4—3762no—
572C2×C4—1882no—
573C2×C4C42×D4711yescharacteristic
574C2×C4C22⋊C4×D4711yescharacteristic
575C2×C4C22⋊C4×D4711yescharacteristic
576C2×C4C22⋊C4×D4711yescharacteristic
577C2×C4C2×(C2×D47)⋊C411yescharacteristic
578C2×C4C4⋊C4×D4711yescharacteristic
579C2×C4C4⋊C4×D4711yescharacteristic
580C2×C4C4⋊C4×D4711yescharacteristic
581C2×C4#1309398111yescharacteristic
582C2×C4#1309398211yescharacteristic
583C2×C4(C22⋊D47)⋊C411yescharacteristic
584C2×C4C4×C22⋊D4711yescharacteristic
585C2×C4C4×C22⋊D4711yescharacteristic
586C2×C4#1309398611yescharacteristic
587C2×C4C4×D18811yescharacteristic
588C2×C4C4×D18811yescharacteristic
589C2×C4#1309399211yescharacteristic
590C2×C4#1309399411yescharacteristic
591C2×C4#1309399511yescharacteristic
592C2×C4#1309399711yescharacteristic
593C2×C4#1309399911yescharacteristic
594C2×C4#1309400011yescharacteristic
595C2×C4#1309400211yescharacteristic
596C2×C4#1309400411yescharacteristic
597C2×C4#1309400611yescharacteristic
598C2×C4#1309400611yescharacteristic
599C2×C4#1309400911yescharacteristic
600C2×C4#1309400911yescharacteristic
601C8—42no—
602C8—1882no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—944no—
611C22—3762no—
612C22—3762no—
613C22—1884no—
614C22#1568897011yescharacteristic
615C22#1568897811yescharacteristic
616C22#1568898211yescharacteristic
617C22#1568899411yescharacteristic
618C22#1568899711yescharacteristic
619C22#1568899911yescharacteristic
620C22#1568900111yescharacteristic
621C4—44no—
622C4—82no—
623C4—944no—
624C4—3762no—
625C4—1884no—
626C4#95×D4711yescharacteristic
627C4C4×(C2×D47)⋊C411yescharacteristic
628C4#1568898011yescharacteristic
629C4#1568898511yescharacteristic
630C4#1568899411yescharacteristic
631C4#1568899711yescharacteristic
632C4#1568899911yescharacteristic
633C4#1568900111yescharacteristic
634C2—21no—
635C2—21no—
636C2—21no—
637C2—21no—
638C2—21no—
639C2—21no—
640C2—21no—
641C2—1884no—
642C2(C2×D47)⋊#9511yescharacteristic
subgroupG/H
centerC4C4×(C2×D47)⋊C4
commutatorC2×C4×C47C2×C42
FrattiniC23×C4C22×D47
FittingC2×C47×H(3,ℤ/4)C2
socleC2×C47C22⋊#95
prime radicalC22×#10625350C22
cosocleC23×C4×C47C23
hypercenterC2×H(3,ℤ/4)D47
hypocenterC47#10792
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C2×#117 ◁ C2×H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
4. C2×#15688894C2semidirect
5. #20243121C2semidirect
6. C2×#15688879C2semidirect
7. C2×C47×H(3,ℤ/4)C2semidirect
15. C4×#10625350C4semidirect
22. C2×#13093952C4semidirect
26. #15689120C4semidirect
55. C2×#10625329C2×C4semidirect
69. #13093983C2×C4semidirect
93. C22×C8×C47C2×C4semidirect
107. C2×C42×C47C2×C4semidirect
319. C2×H(3,ℤ/4)D47semidirect
355. C47#10792semidirect
386. C22×C8C4×D47semidirect
426. C2×C42C4×D47semidirect

Maximal subgroups

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

subgroupindex
#202565892
C2×#156891412
#202519082
C2×#156888942
#202431212
C2×#156888792
C2×C47×H(3,ℤ/4)2
#1079247