Finite Group Databasebeta

← #26231622

Subgroups — #26231622

Order 12032.

1474 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689777C211yesmaximal, characteristic
2C2×#15689095C212yesmaximal, complemented
3#20246255C212yesmaximal, complemented
4#20244224C212yesmaximal, complemented
5#20243845C214yesmaximal, complemented
6#20243376C211yesmaximal, characteristic, complemented
7#20243304C212yesmaximal, complemented
8C4×#99×C47C211yesmaximal, characteristic, complemented
9C22×#10625352C2212yes—
10#15689777—22no—
11#15689777—24no—
12#15689777—22no—
13C2×#13094024C411yescharacteristic, complemented
14C2×#13094008C412yescomplemented
15C2×#13094008C2212yes—
16C2×#13094004C412yescomplemented
17C2×#13093998C411yescharacteristic, complemented
18C2×#13093998C2211yescharacteristic
19C2×C4×D188C411yescharacteristic, complemented
20C2×#13093980C2214yes—
21C22×C4⋊Dic47C411yescharacteristic, complemented
22C22×C4⋊Dic47C2211yescharacteristic
23#15689095—28no—
24C2×#13093939C2212yes—
25C2×#13093938C2214yes—
26C2×#13093938C2214yes—
27#15689021—22no—
28#15689008—24no—
29#15688984C2214yes—
30#15688983C2212yes—
31C4×C4⋊Dic47—22no—
32#15688890C2212yes—
33C2×C4×D4×C47C2211yescharacteristic
34C2×#99×C47C2211yescharacteristic
35C2×#99×C47C2211yescharacteristic
36C4×C22⋊C4×C47C2212yes—
37C47×#342C2212yes—
38C2×#10625352—24no—
39C2×#10625352—24no—
40C2×#10625352—24no—
41C2×#10625352—24no—
42C2×#10625352—44no—
43C22×Dic94C2×C412yes—
44C22×D188C2×C411yescharacteristic
45C22×C22⋊D47C2×C412yes—
46C22×C22⋊D47C2312yes—
47C23×Dic47C2×C412yes—
48C23×Dic47C2312yes—
49C22×C4×D47C2×C412yes—
50#13094024—22no—
51#13094024—22no—
52#13094008—24no—
53#13094008—24no—
54#13094008—24no—
55#13094008—24no—
56#13094004—24no—
57#13094004—24no—
58#13093998—22no—
59#13093998—22no—
60#13093998—22no—
61#13093998—22no—
62C4×D188—22no—
63C4×D188—21no—
64C4×D188—21no—
65#13093980—28no—
66#13093980—44no—
67C2×C4⋊Dic47—22no—
68C2×C4⋊Dic47—21no—
69C2×C4⋊Dic47—21no—
70C2×C4⋊Dic47—22no—
71C2×C4⋊Dic47C2×C411yescharacteristic
72C2×C4⋊Dic47C2×C412yes—
73C2×C4⋊Dic47C2×C412yes—
74C2×C4⋊Dic47C2×C411yescharacteristic
75C2×C4⋊Dic47C2×C411yescharacteristic
76C2×C4⋊Dic47C2×C412yes—
77C2×C4⋊Dic47D412yes—
78C2×C4⋊Dic47D414yes—
79C2×C4⋊Dic47D412yes—
80C2×Dic47⋊C4—24no—
81C2×C22⋊Dic47C2314yes—
82C2×(C2×D47)⋊C4C2×C412yes—
83C2×(C2×D47)⋊C4C2×C412yes—
84C2×(C2×D47)⋊C4C2×C412yes—
85C2×C4×Dic47—24no—
86#13093939—24no—
87#13093938—28no—
88#13093938—44no—
89C47⋊#95—22no—
90C47⋊#95—24no—
91C47⋊#95—24no—
92C22×D4×C47C2311yescharacteristic
93C23×C4×C47C2×C411yescharacteristic
94C23×C4×C47C2311yescharacteristic
95C4×D4×C47—22no—
96C4×D4×C47—22no—
97C2×C4⋊C4×C47C2×C411yescharacteristic
98C2×C22⋊C4×C47C2×C411yescharacteristic
99C2×C22⋊C4×C47C2312yes—
100C2×C22⋊C4×C47C2311yescharacteristic
101C2×C22⋊C4×C47C2312yes—
102C2×C42×C47—22no—
103C2×C42×C47C2×C411yescharacteristic
104#99×C47—22no—
105#99×C47D414yescomplemented
106#95×C47—22no—
107C24×C47C22×C411yescharacteristic
108C24×C47C2411yescharacteristic
109C23×D47C22×C412yes—
110C2×D4×C47—22no—
111C2×D4×C47—22no—
112C2×D4×C47C2×D412yes—
113C2×D4×C47#4112yes—
114C22×C4×C47—22no—
115C22×C4×C47—21no—
116C22×C4×C47—21no—
117C22×C4×C47—22no—
118C22×C4×C47—42no—
119C22×C4×C47—42no—
120C22×C4×C47C22×C411yescharacteristic
121C22×C4×C47C22×C411yescharacteristic
122C22×C4×C47C22×C411yescharacteristic
123C22×C4×C47C22×C411yescharacteristic
124C22×C4×C47C22×C411yescharacteristic
125C22×C4×C47C2×D412yes—
126C22×C4×C47C2×D412yes—
127C2×C22⋊D47—24no—
128C2×C22⋊D47—22no—
129C2×C22⋊D47—24no—
130C2×C22⋊D47—22no—
131C2×C22⋊D47—24no—
132C2×C22⋊D47—24no—
133C2×C22⋊D47—42no—
134C22×Dic47—22no—
135C22×Dic47—22no—
136C22×Dic47—24no—
137C22×Dic47—24no—
138C22×Dic47—22no—
139C22×Dic47—22no—
140C22×Dic47—24no—
141C22×Dic47—42no—
142C22×Dic47C22×C412yes—
143C22×Dic47C22×C412yes—
144C22×Dic47C22×C412yes—
145C22×Dic47C2×D414yes—
146C22×Dic47C2×D414yes—
147#10625352—48no—
148#10625352—48no—
149#10625352—48no—
150#10625352—48no—
151C2×D188—21no—
152C2×D188—21no—
153C2×D188—42no—
154C2×C4×D47—24no—
155C2×C4×D47—22no—
156C2×C4×D47—22no—
157C2×C4×D47—42no—
158C2×Dic94—24no—
159C2×Dic94—24no—
160C2×Dic94—42no—
161C4⋊C4×C47—22no—
162C22⋊C4×C47—22no—
163C22⋊C4×C47—22no—
164C22⋊C4×C47—22no—
165C22⋊C4×C47—22no—
166C22⋊C4×C47—22no—
167C22⋊C4×C47C2×D414yes—
168C42×C47—21no—
169C42×C47—21no—
170C42×C47—44no—
171C22⋊Dic47—24no—
172C22⋊Dic47—24no—
173(C2×D47)⋊C4—24no—
174(C2×D47)⋊C4—22no—
175(C2×D47)⋊C4—22no—
176(C2×D47)⋊C4—24no—
177C4⋊Dic47—21no—
178C4⋊Dic47—21no—
179C4⋊Dic47—22no—
180C4⋊Dic47—22no—
181C4⋊Dic47—24no—
182C4⋊Dic47—44no—
183C4⋊Dic47C22⋊C412yes—
184C4⋊Dic47C22⋊C411yescharacteristic
185C4⋊Dic47C22⋊C411yescharacteristic
186C4⋊Dic47C22⋊C412yes—
187C4⋊Dic47C22⋊C412yes—
188C4⋊Dic47C22⋊C414yes—
189C4⋊Dic47C22⋊C414yes—
190Dic47⋊C4—48no—
191C4×Dic47—48no—
192C23×C47—21no—
193C23×C47—21no—
194C23×C47—41no—
195C23×C47—41no—
196C23×C47—41no—
197C23×C47—41no—
198C23×C47C4×D412yes—
199C23×C47C23×C411yescharacteristic
200C23×C47C22×D412yes—
201C23×C47C22×D411yescharacteristic
202C23×C47C2×#4111yescharacteristic
203C23×C47H(5,𝔽2)12yes—
204C22×D47—22no—
205C22×D47—22no—
206C22×D47—22no—
207C22×D47—42no—
208C22×D47—42no—
209D4×C47—24no—
210D4×C47—24no—
211C2×C4×C47—21no—
212C2×C4×C47—21no—
213C2×C4×C47—24no—
214C2×C4×C47—22no—
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—24no—
218C2×C4×C47—41no—
219C2×C4×C47—42no—
220C2×C4×C47—42no—
221C2×C4×C47—42no—
222C2×C4×C47—42no—
223C2×C4×C47—42no—
224C2×C4×C47—41no—
225C2×C4×C47—41no—
226C2×C4×C47—42no—
227C2×C4×C47—42no—
228C2×C4×C47—42no—
229C2×C4×C47C2×C22⋊C411yescharacteristic
230C2×C4×C47C2×C22⋊C412yes—
231C2×C4×C47C2×C22⋊C411yescharacteristic
232C2×C4×C47C4×D412yes—
233C22⋊D47—48no—
234C22⋊D47—44no—
235C22⋊D47—44no—
236C2×Dic47—22no—
237C2×Dic47—22no—
238C2×Dic47—22no—
239C2×Dic47—22no—
240C2×Dic47—24no—
241C2×Dic47—24no—
242C2×Dic47—24no—
243C2×Dic47—24no—
244C2×Dic47—22no—
245C2×Dic47—22no—
246C2×Dic47—22no—
247C2×Dic47—44no—
248C2×Dic47—44no—
249C2×Dic47—44no—
250C2×Dic47—44no—
251C2×Dic47—44no—
252C2×Dic47C2×C22⋊C414yes—
253C2×Dic47C2×C22⋊C412yes—
254C2×Dic47C2×C22⋊C412yes—
255D188—42no—
256D188—42no—
257C4×D47—44no—
258C4×D47—44no—
259Dic94—48no—
260#22406—471nomaximal, Sylow
261C22×C47—22no—
262C22×C47—21no—
263C22×C47—22no—
264C22×C47—21no—
265C22×C47—22no—
266C22×C47—41no—
267C22×C47—41no—
268C22×C47—42no—
269C22×C47—42no—
270C22×C47—42no—
271C22×C47—41no—
272C22×C47—41no—
273C22×C47C22×C22⋊C411yescharacteristic
274C22×C47C2×C4×D411yescharacteristic
275C22×C47#51811yescharacteristic
276C22×C47D4212yes—
277C22×C47#54612yes—
278C2×D47—42no—
279C2×D47—42no—
280C2×D47—42no—
281C2×D47—82no—
282C2×D47—82no—
283C4×C47—22no—
284C4×C47—21no—
285C4×C47—22no—
286C4×C47—44no—
287C4×C47—41no—
288C4×C47—41no—
289C4×C47—82no—
290C4×C47#41012yescomplemented
291Dic47—24no—
292Dic47—22no—
293Dic47—22no—
294Dic47—42no—
295Dic47—84no—
296C2×#547—471no—
297C2×#410—472no—
298#2344—472no—
299#1964—472no—
300#1899—474no—
301#1799—471no—
302#1782—472no—
303C4×#99D4711yescharacteristic, complemented
304C2×C47—22no—
305C2×C47—22no—
306C2×C47—21no—
307C2×C47—21no—
308C2×C47—42no—
309C2×C47D4×C22⋊C411yescharacteristic
310C2×C47C2×#41011yescharacteristic
311C2×C47#288411yescharacteristic
312D47—82no—
313C22×#41—472no—
314#547—942no—
315#547—944no—
316#547—942no—
317C2×C4⋊Q8—471no—
318C2×#123—472no—
319C2×#123—472no—
320C2×C22⋊Q8—472no—
321C2×#121—471no—
322C2×#121—471no—
323C2×C4×D4—471no—
324C2×C4×D4C2×D4711yescharacteristic
325C2×#117—474no—
326C22×C4⋊C4—471no—
327C22×C4⋊C4—471no—
328#410—948no—
329C2×#99—472no—
330C2×#99—474no—
331C2×#99—474no—
332C2×#99C2×D4711yescharacteristic
333C2×#99C2×D4711yescharacteristic
334#389—942no—
335#387—944no—
336#381—474no—
337#380—472no—
338C4×C4⋊C4—942no—
339C4×C22⋊C4C2×D4712yes—
340#342—472no—
341#342C2×D4712yes—
342C47#2240611yescharacteristic, complemented, Sylow
343C2×#41—944no—
344C2×#41—944no—
345C2×#41—944no—
346C2×#41—944no—
347C2×#41—1884no—
348C22×Q8—472no—
349C22×D4—472no—
350C22×D4—472no—
351C22×D4—471no—
352C22×D4C22×D4711yescharacteristic
353C23×C4—472no—
354C23×C4—472no—
355C23×C4—472no—
356C23×C4C4×D4711yescharacteristic
357C23×C4C22×D4711yescharacteristic
358C4⋊Q8—942no—
359C4⋊Q8—942no—
360#123—944no—
361#123—944no—
362#123—944no—
363#123—944no—
364C22⋊Q8—944no—
365C22⋊Q8—944no—
366#121—942no—
367#121—942no—
368#121—942no—
369#121—942no—
370C4×D4—22no—
371C4×D4—22no—
372C4×D4—942no—
373C4×D4—941no—
374C4×D4—941no—
375#117—948no—
376#117—1884no—
377C2×C4⋊C4—471no—
378C2×C4⋊C4—471no—
379C2×C4⋊C4—472no—
380C2×C4⋊C4—472no—
381C2×C4⋊C4—474no—
382C2×C4⋊C4—472no—
383C2×C4⋊C4—471no—
384C2×C4⋊C4—472no—
385C2×C4⋊C4—472no—
386C2×C4⋊C4—942no—
387C2×C4⋊C4—941no—
388C2×C4⋊C4—941no—
389C2×C4⋊C4—944no—
390C2×C4⋊C4—942no—
391C2×C4⋊C4C4×D4711yescharacteristic
392C2×C22⋊C4—472no—
393C2×C22⋊C4—472no—
394C2×C22⋊C4—472no—
395C2×C22⋊C4—474no—
396C2×C22⋊C4C4×D4711yescharacteristic
397C2×C22⋊C4C22×D4712yes—
398C2×C22⋊C4C22×D4711yescharacteristic
399C2×C22⋊C4C22×D4712yes—
400C2×C42—22no—
401C2×C42—944no—
402C2×C42C4×D4711yescharacteristic
403#99—22no—
404#99—944no—
405#99—948no—
406#99—1884no—
407#99D18814yescomplemented
408#95—22no—
409#95—944no—
410#95—944no—
411#95—942no—
412C24—472no—
413C24C2×C4×D4711yescharacteristic
414C24C23×D4711yescharacteristic
415#41—1888no—
416#41—1888no—
417#41—1888no—
418#41—1888no—
419C2×Q8—944no—
420C2×Q8—944no—
421C2×Q8—1882no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—944no—
425C2×D4—944no—
426C2×D4—944no—
427C2×D4—942no—
428C2×D4—942no—
429C2×D4—944no—
430C2×D4—941no—
431C2×D4—941no—
432C2×D4—1882no—
433C2×D4—1882no—
434C2×D4C2×D18812yes—
435C2×D4#1062535012yes—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—472no—
443C22×C4—472no—
444C22×C4—474no—
445C22×C4—474no—
446C22×C4—472no—
447C22×C4—942no—
448C22×C4—942no—
449C22×C4—942no—
450C22×C4—942no—
451C22×C4—942no—
452C22×C4—942no—
453C22×C4—944no—
454C22×C4—944no—
455C22×C4—944no—
456C22×C4—944no—
457C22×C4—1882no—
458C22×C4—1882no—
459C22×C4C2×C4×D4711yescharacteristic
460C22×C4C2×C4×D4711yescharacteristic
461C22×C4C2×C4×D4711yescharacteristic
462C22×C4C2×C4×D4711yescharacteristic
463C22×C4C2×C4×D4711yescharacteristic
464C22×C4D4×D4712yes—
465C22×C4D4×D4712yes—
466C4⋊C4—22no—
467C4⋊C4—472no—
468C4⋊C4—471no—
469C4⋊C4—471no—
470C4⋊C4—472no—
471C4⋊C4—472no—
472C4⋊C4—474no—
473C4⋊C4—474no—
474C4⋊C4—942no—
475C4⋊C4—942no—
476C4⋊C4—944no—
477C4⋊C4—941no—
478C4⋊C4—941no—
479C4⋊C4—1888no—
480C4⋊C4—1884no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—22no—
486C22⋊C4—942no—
487C22⋊C4—942no—
488C22⋊C4—944no—
489C22⋊C4—944no—
490C22⋊C4—944no—
491C22⋊C4—944no—
492C22⋊C4C2×D18814yes—
493C42—21no—
494C42—21no—
495C42—44no—
496C42—1888no—
497C23—21no—
498C23—21no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—942no—
504C23—942no—
505C23—942no—
506C23—1882no—
507C23—1882no—
508C23C4×D18812yes—
509C23C22×C4×D4711yescharacteristic
510C23C2×D4×D4712yes—
511C23C22×D18811yescharacteristic
512C23C2×#1062535011yescharacteristic
513C23#1309407012yes—
514Q8—1888no—
515D4—24no—
516D4—24no—
517D4—1882no—
518D4—1888no—
519D4—1884no—
520D4—1884no—
521D4—1882no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—24no—
525C2×C4—22no—
526C2×C4—24no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—472no—
541C2×C4—472no—
542C2×C4—474no—
543C2×C4—944no—
544C2×C4—944no—
545C2×C4—944no—
546C2×C4—944no—
547C2×C4—942no—
548C2×C4—942no—
549C2×C4—942no—
550C2×C4—942no—
551C2×C4—942no—
552C2×C4—942no—
553C2×C4—942no—
554C2×C4—1884no—
555C2×C4—1884no—
556C2×C4—1884no—
557C2×C4—1884no—
558C2×C4—1884no—
559C2×C4—1884no—
560C2×C4—1884no—
561C2×C4C22⋊C4×D4711yescharacteristic
562C2×C4C22⋊C4×D4712yes—
563C2×C4C22⋊C4×D4711yescharacteristic
564C2×C4C4×D18812yes—
565C22—22no—
566C22—21no—
567C22—22no—
568C22—21no—
569C22—22no—
570C22—41no—
571C22—41no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22—41no—
576C22—41no—
577C22—3762no—
578C22—3762no—
579C22—1882no—
580C22—1882no—
581C22—1882no—
582C22C2×C22⋊C4×D4711yescharacteristic
583C22C2×C4×D18811yescharacteristic
584C22#1568959711yescharacteristic
585C22D4×D18812yes—
586C22#1568976912yes—
587C4—21no—
588C4—22no—
589C4—22no—
590C4—44no—
591C4—41no—
592C4—41no—
593C4—82no—
594C4—942no—
595C4—942no—
596C4—944no—
597C4—3764no—
598C4—1882no—
599C4#1568909512yescomplemented
600C2—22no—
601C2—22no—
602C2—21no—
603C2—21no—
604C2—42no—
605C2—3762no—
606C2C22⋊C4×D18811yescharacteristic
607C2C2×#1568909511yescharacteristic
608C2#2025185011yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D47
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC4×#99×C47C2
socleC22×C47C22×C22⋊C4
prime radicalC2×#15689777C2
cosocleC24×C47C24
hypercenterC4×#99D47
hypocenterC47#22406
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. C2×#15689095C2semidirect
3. #20246255C2semidirect
4. #20244224C2semidirect
5. #20243845C2semidirect
6. #20243376C2semidirect
7. #20243304C2semidirect
8. C4×#99×C47C2semidirect
13. C2×#13094024C4semidirect
14. C2×#13094008C4semidirect
16. C2×#13094004C4semidirect
17. C2×#13093998C4semidirect
19. C2×C4×D188C4semidirect
21. C22×C4⋊Dic47C4semidirect
105. #99×C47D4semidirect
290. C4×C47#410semidirect
303. C4×#99D47semidirect
342. C47#22406semidirect
407. #99D188semidirect
599. C4#15689095semidirect

Maximal subgroups

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

subgroupindex
C2×#156897772
C2×#156890952
#202462552
#202442242
#202438452
#202433762
#202433042
C4×#99×C472
#2240647