Finite Group Databasebeta

← #26246072

Subgroups — #26246072

Order 12032.

1126 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689159C211yesmaximal, characteristic, complemented
2C2×#15689120C211yesmaximal, characteristic
3C2×#15689117C211yesmaximal, characteristic
4#20245876C211yesmaximal, characteristic
5#20245791C211yesmaximal, characteristic, complemented
6#20244937C211yesmaximal, characteristic, complemented
7#20244933C211yesmaximal, characteristic, complemented
8#20244928C211yesmaximal, characteristic, complemented
9#20244923C211yesmaximal, characteristic, complemented
10#20244918C211yesmaximal, characteristic, complemented
11#20244913C211yesmaximal, characteristic, complemented
12#20244910C211yesmaximal, characteristic, complemented
13#20244906C211yesmaximal, characteristic, complemented
14C2×#15688877C211yesmaximal, characteristic, complemented
15C2×C47×#427C211yesmaximal, characteristic, complemented
16C22×#10625350C2211yescharacteristic
17C23×C47⋊C8C2211yescharacteristic
18C2×#13093983C2211yescharacteristic
19C22×C4×Dic47C2211yescharacteristic
20#15689159—24no—
21C2×#13093957C2211yescharacteristic
22C2×#13093957C2211yescharacteristic
23C2×#13093955C2211yescharacteristic
24C2×#13093955C2211yescharacteristic
25#15689120—24no—
26#15689117—24no—
27C2×#13093949C2211yescharacteristic
28C2×#13093949C2211yescharacteristic
29C2×#13093947C2211yescharacteristic
30C2×#13093947C2211yescharacteristic
31C2×#13093946C2211yescharacteristic
32C2×#13093946C2211yescharacteristic
33C2×#13093944C2211yescharacteristic
34C2×#13093944C2211yescharacteristic
35#15689028C2211yescharacteristic
36#15689028C2211yescharacteristic
37#15689024C2211yescharacteristic
38#15689024C2211yescharacteristic
39#15689000—22no—
40#15688992C2211yescharacteristic
41#15688992C2211yescharacteristic
42#15688988C2211yescharacteristic
43#15688988C2211yescharacteristic
44#15688981—22no—
45C4×Dic47⋊C4—22no—
46C4×(C2×D47)⋊C4—22no—
47#15688877C2211yescharacteristic
48#15688877C2211yescharacteristic
49#15688877C2211yescharacteristic
50#15688877C2211yescharacteristic
51C23×C8×C47C2211yescharacteristic
52C2×#117×C47C2211yescharacteristic
53C2×#117×C47C2211yescharacteristic
54C47×#427—24no—
55C2×#107×C47C2211yescharacteristic
56C2×#107×C47C2211yescharacteristic
57C2×#106×C47C2211yescharacteristic
58C2×#106×C47C2211yescharacteristic
59C2×#10625350—22no—
60C2×#10625350—22no—
61C2×#10625350—22no—
62C2×#10625350—22no—
63C2×#10625350—22no—
64C2×#10625350Q814yes—
65C22×Dic94C2311yescharacteristic
66C22×D188C2311yescharacteristic
67C22×C22⋊D47—21no—
68C23×Dic47D412yes—
69C22×C4×D47—21no—
70C22×C47⋊C8—22no—
71C22×C47⋊C8—22no—
72C22×C47⋊C8D414yes—
73C22×C47⋊C8C2311yescharacteristic
74C22×C47⋊C8C2311yescharacteristic
75#13093983—22no—
76#13093983—22no—
77C2×C4⋊Dic47C2311yescharacteristic
78C2×C4⋊Dic47C2311yescharacteristic
79C2×Dic47⋊C4—22no—
80C2×Dic47⋊C4—22no—
81C2×C22⋊Dic47—21no—
82C2×(C2×D47)⋊C4—22no—
83C2×(C2×D47)⋊C4—22no—
84C2×C4×Dic47—22no—
85C2×C4×Dic47—22no—
86C2×C4×Dic47—21no—
87C2×C4×Dic47D412yes—
88C2×C4×Dic47C2311yescharacteristic
89C2×C4×Dic47C2311yescharacteristic
90#13093957—22no—
91#13093957—22no—
92#13093955—22no—
93#13093955—22no—
94#13093949—22no—
95#13093949—22no—
96#13093947—22no—
97#13093947—22no—
98#13093946—22no—
99#13093946—22no—
100#13093944—22no—
101#13093944—22no—
102C47⋊#95—22no—
103C47⋊#95—22no—
104C47⋊#95—22no—
105C47⋊#95—22no—
106C23×C4×C47C2311yescharacteristic
107C22×C8×C47—22no—
108C22×C8×C47—22no—
109C22×C8×C47D414yes—
110C22×C8×C47C2311yescharacteristic
111C22×C8×C47C2311yescharacteristic
112#117×C47—22no—
113#117×C47—22no—
114#117×C47—22no—
115#117×C47—22no—
116C2×C4⋊C4×C47C2311yescharacteristic
117C2×C4⋊C4×C47C2311yescharacteristic
118C2×C4⋊C4×C47C2311yescharacteristic
119C2×C4⋊C4×C47C2311yescharacteristic
120C2×C22⋊C4×C47—21no—
121C2×C22⋊C4×C47—21no—
122C2×C42×C47—21no—
123C2×C42×C47—21no—
124#107×C47—22no—
125#107×C47—22no—
126#106×C47—22no—
127#106×C47—22no—
128C24×C47C2×D411yescharacteristic
129C23×D47—21no—
130C22×C4×C47—21no—
131C22×C4×C47—21no—
132C22×C4×C47—21no—
133C22×C4×C47—21no—
134C22×C4×C47C2×D411yescharacteristic
135C22×C4×C47C2×D412yes—
136C22×C4×C47C2×D412yes—
137C22×C4×C47C2×Q812yes—
138C22×C4×C47#4112yes—
139C22×C4×C47#4112yes—
140C22×C4×C47#4112yes—
141C22×C4×C47C2411yescharacteristic
142C2×C22⋊D47—24no—
143C2×C22⋊D47—42no—
144C2×C22⋊D47—42no—
145C22×Dic47—24no—
146C22×Dic47—21no—
147C22×Dic47—24no—
148C22×Dic47—21no—
149C22×Dic47—21no—
150C22×Dic47—42no—
151C22×Dic47C2×D412yes—
152C22×Dic47C2×D412yes—
153#10625350—28no—
154#10625350—28no—
155#10625350—44no—
156#10625350—44no—
157C2×D188—21no—
158C2×D188—21no—
159C2×D188—21no—
160C2×D188—21no—
161C2×D188—21no—
162C2×D188C2×Q812yes—
163C2×C4×D47—24no—
164C2×C4×D47—42no—
165C2×C4×D47—42no—
166C2×Dic94—21no—
167C2×Dic94—21no—
168C2×Dic94—21no—
169C2×Dic94—21no—
170C2×Dic94—21no—
171C2×Dic94C2×Q812yes—
172C2×C8×C47—28no—
173C2×C8×C47—21no—
174C2×C8×C47—21no—
175C2×C8×C47—21no—
176C2×C8×C47—21no—
177C2×C8×C47C2×D412yes—
178C2×C8×C47C2×D412yes—
179C4⋊C4×C47—21no—
180C4⋊C4×C47—21no—
181C4⋊C4×C47—21no—
182C4⋊C4×C47—21no—
183C4⋊C4×C47—21no—
184C4⋊C4×C47—21no—
185C4⋊C4×C47—21no—
186C4⋊C4×C47—21no—
187C22⋊C4×C47—42no—
188C22⋊C4×C47—42no—
189C42×C47—42no—
190C42×C47—42no—
191C22⋊Dic47—42no—
192(C2×D47)⋊C4—44no—
193(C2×D47)⋊C4—44no—
194C4⋊Dic47—21no—
195C4⋊Dic47—21no—
196C4⋊Dic47—21no—
197C4⋊Dic47—21no—
198Dic47⋊C4—44no—
199Dic47⋊C4—44no—
200C4×Dic47—24no—
201C4×Dic47—21no—
202C4×Dic47—21no—
203C4×Dic47—21no—
204C4×Dic47—21no—
205C4×Dic47—42no—
206C2×C47⋊C8—28no—
207C2×C47⋊C8—21no—
208C2×C47⋊C8—21no—
209C2×C47⋊C8—21no—
210C2×C47⋊C8—21no—
211C2×C47⋊C8C2×D412yes—
212C2×C47⋊C8C2×D412yes—
213C23×C47—22no—
214C23×C47—22no—
215C23×C47C22⋊Q812yes—
216C23×C47#12312yes—
217C23×C47#12712yes—
218C23×C47C22×D411yescharacteristic
219C22×D47—22no—
220C22×D47—41no—
221C22×D47—41no—
222C22×D47—42no—
223C22×D47—42no—
224C2×C4×C47—41no—
225C2×C4×C47—41no—
226C2×C4×C47—41no—
227C2×C4×C47—41no—
228C2×C4×C47—42no—
229C2×C4×C47—42no—
230C2×C4×C47—42no—
231C2×C4×C47—42no—
232C2×C4×C47C22⋊Q814yes—
233C2×C4×C47C22⋊Q814yes—
234C2×C4×C47C22⋊Q812yes—
235C2×C4×C47#12314yes—
236C2×C4×C47#12314yes—
237C2×C4×C47#12312yes—
238C2×C4×C47#12712yes—
239C2×C4×C47C22×D411yescharacteristic
240C2×C4×C47C22×D411yescharacteristic
241C2×C4×C47C22×Q811yescharacteristic
242C2×C4×C47C2×#4111yescharacteristic
243C2×C4×C47C2×#4111yescharacteristic
244C2×C4×C47C2×#4111yescharacteristic
245C22⋊D47—48no—
246C2×Dic47—22no—
247C2×Dic47—22no—
248C2×Dic47—22no—
249C2×Dic47—22no—
250C2×Dic47—22no—
251C2×Dic47—22no—
252C2×Dic47—48no—
253C2×Dic47—41no—
254C2×Dic47—41no—
255C2×Dic47—41no—
256C2×Dic47—41no—
257C2×Dic47—42no—
258C2×Dic47—42no—
259C2×Dic47#13514yes—
260D188—22no—
261D188—22no—
262D188—41no—
263D188—41no—
264C4×D47—48no—
265Dic94—22no—
266Dic94—22no—
267Dic94—41no—
268Dic94—41no—
269C8×C47—22no—
270C8×C47—22no—
271C47⋊C8—22no—
272C47⋊C8—22no—
273#23730—471nomaximal, Sylow
274C22×C47—24no—
275C22×C47—24no—
276C22×C47—22no—
277C22×C47—22no—
278C22×C47#39914yes—
279C22×C47C2×C22⋊Q811yescharacteristic
280C22×C47C2×#12311yescharacteristic
281C22×C47C2×#12711yescharacteristic
282C22×C47C2×#13512yes—
283C22×C47#57512yes—
284C2×D47—44no—
285C2×D47—42no—
286C2×D47—82no—
287C2×D47—81no—
288C2×D47—81no—
289C4×C47—81no—
290C4×C47—81no—
291C4×C47—81no—
292C4×C47—81no—
293C4×C47#39914yes—
294C4×C47C2×C22⋊Q811yescharacteristic
295C4×C47C2×C22⋊Q811yescharacteristic
296C4×C47C2×#12311yescharacteristic
297C4×C47C2×#12311yescharacteristic
298Dic47—24no—
299Dic47—42no—
300Dic47—42no—
301Dic47—81no—
302Dic47—81no—
303C2×#427—471no—
304C2×#427D4711yescharacteristic, complemented
305C2×#416—471no—
306C2×#416—471no—
307#2297—471no—
308#2285—471no—
309#2097—471no—
310#2097—471no—
311#2096—471no—
312#2095—471no—
313#2094—471no—
314#2093—471no—
315#2092—471no—
316#2092—471no—
317C2×#336—471no—
318C2×C47—24no—
319C2×C47C2×#39911yescharacteristic
320C2×C47#307612yes—
321C2×C47#309112yes—
322C2×C47#314711yescharacteristic
323C2×C47#315011yescharacteristic
324D47—82no—
325C22×#41—471no—
326C23×C8—471no—
327C23×C8C2×D4711yescharacteristic
328C2×#117—471no—
329C2×#117C2×D4711yescharacteristic
330C2×#117C2×D4711yescharacteristic
331C22×C42—471no—
332#427—24no—
333#427—944no—
334C2×#107—471no—
335C2×#107—471no—
336C2×#107C2×D4711yescharacteristic
337C2×#107C2×D4711yescharacteristic
338C2×#106—471no—
339C2×#106—471no—
340C2×#106C2×D4711yescharacteristic
341C2×#106C2×D4711yescharacteristic
342#416—944no—
343#416—944no—
344C2×#103—471no—
345C2×#103—471no—
346C2×#103—471no—
347C2×#103—471no—
348C2×#102—471no—
349C2×#102—471no—
350C2×#102—471no—
351C2×#102—471no—
352#391—471no—
353#391—471no—
354#390—471no—
355#390—471no—
356#386—942no—
357#384—471no—
358#384—471no—
359#382—471no—
360#382—471no—
361#380—942no—
362C4×C4⋊C4—942no—
363C4×C22⋊C4—942no—
364#336—471no—
365#336—471no—
366#336—471no—
367#336—471no—
368C47#2373011yescharacteristic, complemented, Sylow
369C2×#41—474no—
370C2×#41—942no—
371C2×#41—942no—
372C2×#41—942no—
373C2×#41—942no—
374C2×#41—942no—
375C22×Q8—471no—
376C22×D4—471no—
377C22×D4—941no—
378C23×C4—472no—
379C23×C4—941no—
380C23×C4C22×D4711yescharacteristic
381C22×C8—22no—
382C22×C8—22no—
383C22×C8—474no—
384C22×C8—471no—
385C22×C8—471no—
386C22×C8—942no—
387C22×C8—942no—
388C22×C8C22⋊D4714yes—
389C22×C8C22×D4711yescharacteristic
390C22×C8C22×D4711yescharacteristic
391#117—22no—
392#117—22no—
393#117—22no—
394#117—22no—
395#117—942no—
396#117—942no—
397C2×C4⋊C4—471no—
398C2×C4⋊C4—471no—
399C2×C4⋊C4—942no—
400C2×C4⋊C4—942no—
401C2×C4⋊C4C22×D4711yescharacteristic
402C2×C4⋊C4C22×D4711yescharacteristic
403C2×C4⋊C4C22×D4711yescharacteristic
404C2×C4⋊C4C22×D4711yescharacteristic
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—942no—
408C2×C22⋊C4—942no—
409C2×C22⋊C4—941no—
410C2×C42—21no—
411C2×C42—21no—
412C2×C42—472no—
413C2×C42—471no—
414C2×C42—471no—
415C2×C42—942no—
416C2×C42—942no—
417C2×C42—941no—
418#107—22no—
419#107—22no—
420#107—942no—
421#107—942no—
422#106—22no—
423#106—22no—
424#106—942no—
425#106—942no—
426#103—942no—
427#103—942no—
428#103—942no—
429#103—942no—
430#102—942no—
431#102—942no—
432#102—942no—
433#102—942no—
434#95—942no—
435#95—942no—
436#95—942no—
437#95—942no—
438C24—941no—
439C24D4×D4711yescharacteristic
440#41—948no—
441#41—948no—
442#41—1884no—
443#41—1884no—
444C2×Q8—472no—
445C2×Q8—941no—
446C2×Q8—941no—
447C2×Q8—941no—
448C2×Q8—941no—
449C2×Q8—941no—
450C2×D4—472no—
451C2×D4—944no—
452C2×D4—941no—
453C2×D4—941no—
454C2×D4—941no—
455C2×D4—941no—
456C2×D4—941no—
457C2×D4—1882no—
458C2×D4—1882no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—472no—
464C22×C4—472no—
465C22×C4—944no—
466C22×C4—944no—
467C22×C4—941no—
468C22×C4—944no—
469C22×C4—941no—
470C22×C4—941no—
471C22×C4—1882no—
472C22×C4—1882no—
473C22×C4—1882no—
474C22×C4#1062535012yes—
475C22×C4#1062535012yes—
476C22×C4D4×D4712yes—
477C22×C4D4×D4711yescharacteristic
478C22×C4Q8×D4712yes—
479C22×C4#1062535412yes—
480C22×C4C2×C22⋊D4712yes—
481C22×C4C23×D4711yescharacteristic
482C2×C8—28no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—472no—
488C2×C8—472no—
489C2×C8—948no—
490C2×C8—941no—
491C2×C8—941no—
492C2×C8—941no—
493C2×C8—941no—
494C2×C8C2×C22⋊D4712yes—
495C2×C8C2×C22⋊D4712yes—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—941no—
505C4⋊C4—941no—
506C4⋊C4—941no—
507C4⋊C4—941no—
508C4⋊C4—1884no—
509C4⋊C4—1884no—
510C22⋊C4—42no—
511C22⋊C4—42no—
512C22⋊C4—1884no—
513C22⋊C4—1884no—
514C22⋊C4—1882no—
515C42—42no—
516C42—42no—
517C42—944no—
518C42—941no—
519C42—941no—
520C42—941no—
521C42—941no—
522C42—1882no—
523C23—22no—
524C23—22no—
525C23—942no—
526C23—1881no—
527C23—1882no—
528C23—1881no—
529C23—1882no—
530C23#1309400212yes—
531C23#1309400912yes—
532C23#1309402012yes—
533C23C2×D4×D4711yescharacteristic
534Q8—942no—
535Q8—942no—
536Q8—1881no—
537Q8—1881no—
538D4—942no—
539D4—942no—
540D4—1888no—
541D4—1881no—
542D4—1881no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—474no—
552C2×C4—942no—
553C2×C4—942no—
554C2×C4—942no—
555C2×C4—942no—
556C2×C4—942no—
557C2×C4—942no—
558C2×C4—1888no—
559C2×C4—1882no—
560C2×C4—1881no—
561C2×C4—1881no—
562C2×C4—1882no—
563C2×C4—1881no—
564C2×C4—1881no—
565C2×C4—1888no—
566C2×C4#1309400014yes—
567C2×C4#1309400212yes—
568C2×C4#1309400214yes—
569C2×C4#1309400714yes—
570C2×C4#1309400912yes—
571C2×C4#1309400914yes—
572C2×C4#1309402012yes—
573C2×C4C2×D4×D4711yescharacteristic
574C2×C4C22×C22⋊D4711yescharacteristic
575C2×C4C2×Q8×D4711yescharacteristic
576C2×C4C2×#1062535011yescharacteristic
577C2×C4C2×#1062535011yescharacteristic
578C2×C4C2×#1062535411yescharacteristic
579C8—22no—
580C8—22no—
581C8—942no—
582C8—942no—
583C22—22no—
584C22—24no—
585C22—22no—
586C22—24no—
587C22—3761no—
588C22—3762no—
589C22—3761no—
590C22—1882no—
591C22—1884no—
592C22#1568905814yes—
593C22C2×#1309400211yescharacteristic
594C22C2×#1309400911yescharacteristic
595C22C2×#1309402011yescharacteristic
596C22#135×D4712yes—
597C22#1568992012yes—
598C4—81no—
599C4—81no—
600C4—81no—
601C4—81no—
602C4—944no—
603C4—3761no—
604C4—3761no—
605C4—1882no—
606C4—1882no—
607C4#1568905814yes—
608C4C2×#1309400011yescharacteristic
609C4C2×#1309400211yescharacteristic
610C4C2×#1309400711yescharacteristic
611C4C2×#1309400911yescharacteristic
612C2—24no—
613C2—3762no—
614C2C2×#1568905811yescharacteristic
615C2#2025317412yes—
616C2#2025330512yes—
617C2#2025381211yescharacteristic
618C2#2025383111yescharacteristic
subgroupG/H
centerC22×C4D4×D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC2×C47×#427C2
socleC23×C47C22×D4
prime radicalC22×#10625350C22
hypercenterC2×#427D47
hypocenterC47#23730
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#427

Complements

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

NH ≅ G/Ntype
1. C2×#15689159C2semidirect
5. #20245791C2semidirect
6. #20244937C2semidirect
7. #20244933C2semidirect
8. #20244928C2semidirect
9. #20244923C2semidirect
10. #20244918C2semidirect
11. #20244913C2semidirect
12. #20244910C2semidirect
13. #20244906C2semidirect
14. C2×#15688877C2semidirect
15. C2×C47×#427C2semidirect
304. C2×#427D47semidirect
368. C47#23730semidirect

Maximal subgroups

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

subgroupindex
C2×#156891592
C2×#156891202
C2×#156891172
#202458762
#202457912
#202449372
#202449332
#202449282
#202449232
#202449182
#202449132
#202449102
#202449062
C2×#156888772
C2×C47×#4272
#2373047