Finite Group Databasebeta

← #26221632

Subgroups — #26221632

Order 12032.

1318 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689710C211yesmaximal, characteristic
2#20245985C211yesmaximal, characteristic, complemented
3#20245740C211yesmaximal, characteristic, complemented
4#20244373C211yesmaximal, characteristic, complemented
5#20244372C211yesmaximal, characteristic, complemented
6#20244225C211yesmaximal, characteristic, complemented
7#20243838C214yesmaximal, complemented
8#99×Dic47C214yesmaximal, complemented
9C47×#1964C211yesmaximal, characteristic, complemented
10#15689710—22no—
11#15689710—22no—
12#15689710—22no—
13#15689710—22no—
14C2×#13094019C412yescomplemented
15C2×#13094010C412yescomplemented
16C2×#13094008C412yescomplemented
17C2×#13094003C2211yescharacteristic
18C2×#13093996C412yescomplemented
19C2×#13093992C2212yes—
20C2×D4×Dic47C2212yes—
21C22×(C2×D47)⋊C4C2211yescharacteristic
22C2×C22⋊C4×D47C2212yes—
23C2×#13093939C2214yes—
24#15689015—22no—
25#15689013—22no—
26#15688983C2211yescharacteristic
27#15688978C2212yes—
28C22⋊C4×Dic47C2212yes—
29C22⋊C4×Dic47C2212yes—
30C4×(C2×D47)⋊C4—22no—
31C4×C22⋊Dic47C2211yescharacteristic
32#15688970—22no—
33#15688889C2214yes—
34#15688889C2214yes—
35C2×#121×C47C2211yescharacteristic
36C2×#99×C47C2214yes—
37C47×#380C2211yescharacteristic
38C4×C22⋊C4×C47C2211yescharacteristic
39C24×D47C2311yescharacteristic
40C22×Dic94C2×C411yescharacteristic, complemented
41C22×C22⋊D47C2×C412yes—
42C22×C22⋊D47C2×C412yes—
43C23×Dic47C2×C412yescomplemented
44C23×Dic47C2311yescharacteristic
45C22×C4×D47—22no—
46#13094019—24no—
47#13094019—24no—
48#13094010—24no—
49#13094010—24no—
50#13094008—24no—
51#13094008—24no—
52#13094003—21no—
53#13094003—21no—
54#13094003—21no—
55#13094003—21no—
56#13093996—24no—
57#13093996—24no—
58#13093992—24no—
59#13093992—24no—
60D4×Dic47—24no—
61D4×Dic47—24no—
62C2×C4⋊Dic47—21no—
63C2×C4⋊Dic47C2×C412yescomplemented
64C2×C4⋊Dic47C2×C411yescharacteristic, complemented
65C2×Dic47⋊C4C2×C412yescomplemented
66C2×C22⋊Dic47C2×C412yescomplemented
67C2×C22⋊Dic47C2312yes—
68C2×C22⋊Dic47C2312yes—
69C2×C22⋊Dic47C2312yes—
70C2×(C2×D47)⋊C4—22no—
71C2×(C2×D47)⋊C4—22no—
72C2×(C2×D47)⋊C4—22no—
73C2×(C2×D47)⋊C4C2×C412yes—
74C2×(C2×D47)⋊C4C2×C412yes—
75C2×(C2×D47)⋊C4C2×C412yes—
76C2×(C2×D47)⋊C4C2×C412yes—
77C2×(C2×D47)⋊C4D412yes—
78C2×(C2×D47)⋊C4D412yes—
79C2×(C2×D47)⋊C4D412yes—
80C2×(C2×D47)⋊C4D412yes—
81C22⋊C4×D47—24no—
82C22⋊C4×D47—24no—
83C2×C4×Dic47—21no—
84C2×C4×Dic47—22no—
85C2×C4×Dic47—22no—
86C2×C4×Dic47C2×C412yescomplemented
87#13093939—28no—
88C47⋊#95—21no—
89C47⋊#95—21no—
90C47⋊#95—22no—
91C47⋊#95—22no—
92C22×D4×C47C2×C411yescharacteristic, complemented
93C22×D4×C47C2312yes—
94C23×C4×C47C2311yescharacteristic
95#121×C47—21no—
96#121×C47—21no—
97#121×C47—21no—
98#121×C47—21no—
99C2×C4⋊C4×C47—21no—
100C2×C4⋊C4×C47C2×C411yescharacteristic, complemented
101C2×C22⋊C4×C47C2×C412yescomplemented
102C2×C22⋊C4×C47C2312yes—
103C2×C22⋊C4×C47C2312yes—
104C2×C42×C47—21no—
105#99×C47—28no—
106#95×C47—21no—
107#95×C47—21no—
108C24×C47C22×C412yes—
109C24×C47C2411yescharacteristic
110C23×D47—22no—
111C23×D47—22no—
112C23×D47—81no—
113C23×D47—81no—
114C23×D47C22×C412yes—
115C23×D47C2×D412yes—
116C23×D47C2×D412yes—
117C2×D4×C47—22no—
118C2×D4×C47—22no—
119C2×D4×C47—24no—
120C2×D4×C47—24no—
121C2×D4×C47—21no—
122C2×D4×C47—21no—
123C2×D4×C47—81no—
124C22×C4×C47—22no—
125C22×C4×C47—22no—
126C22×C4×C47—81no—
127C22×C4×C47C22×C412yes—
128C22×C4×C47C22×C411yescharacteristic
129C22×C4×C47C22×C411yescharacteristic
130C22×C4×C47C2×D411yescharacteristic
131C22×C4×C47C2×D411yescharacteristic
132C22×C4×C47C2×D411yescharacteristic
133C22×C4×C47C2×D411yescharacteristic
134C2×C22⋊D47—24no—
135C2×C22⋊D47—24no—
136C2×C22⋊D47—82no—
137C2×C22⋊D47—82no—
138C22×Dic47—22no—
139C22×Dic47—24no—
140C22×Dic47—22no—
141C22×Dic47—81no—
142C22×Dic47—82no—
143C22×Dic47C22×C412yes—
144C22×Dic47C22×C412yes—
145C22×Dic47C22×C412yes—
146C22×Dic47C2×D412yes—
147C22×Dic47C2×D412yes—
148C2×C4×D47—28no—
149C2×C4×D47—82no—
150C2×C4×D47—82no—
151C2×Dic94—21no—
152C2×Dic94—21no—
153C2×Dic94—81no—
154C4⋊C4×C47—21no—
155C4⋊C4×C47—21no—
156C4⋊C4×C47—81no—
157C22⋊C4×C47—22no—
158C22⋊C4×C47—22no—
159C22⋊C4×C47—22no—
160C22⋊C4×C47—24no—
161C22⋊C4×C47#4114yes—
162C42×C47—81no—
163C22⋊Dic47—22no—
164C22⋊Dic47—22no—
165C22⋊Dic47—22no—
166C22⋊Dic47—24no—
167C22⋊Dic47—24no—
168C22⋊Dic47#4114yes—
169(C2×D47)⋊C4—28no—
170(C2×D47)⋊C4—24no—
171(C2×D47)⋊C4—24no—
172(C2×D47)⋊C4—82no—
173(C2×D47)⋊C4—82no—
174(C2×D47)⋊C4C22⋊C414yes—
175(C2×D47)⋊C4C22⋊C414yes—
176(C2×D47)⋊C4C22⋊C414yes—
177(C2×D47)⋊C4C22⋊C414yes—
178C4⋊Dic47—21no—
179C4⋊Dic47—21no—
180C4⋊Dic47—24no—
181C4⋊Dic47—81no—
182Dic47⋊C4—22no—
183Dic47⋊C4—22no—
184C4×Dic47—24no—
185C4×Dic47—82no—
186C4×Dic47—82no—
187C4×Dic47—81no—
188C23×C47—22no—
189C23×C47—24no—
190C23×C47—41no—
191C23×C47—41no—
192C23×C47—42no—
193C23×C47—42no—
194C23×C47C23×C411yescharacteristic
195C23×C47C22×D411yescharacteristic
196C23×C47C22×D411yescharacteristic
197C23×C47C2×#4112yes—
198C23×C47C2×#4112yes—
199C22×D47—22no—
200C22×D47—22no—
201C22×D47—24no—
202C22×D47—22no—
203C22×D47—22no—
204C22×D47—42no—
205C22×D47—42no—
206C22×D47—42no—
207C22×D47—42no—
208C22×D47—42no—
209C22×D47—42no—
210C22×D47—84no—
211C22×D47—84no—
212C22×D47C2×C22⋊C414yes—
213D4×C47—44no—
214D4×C47—42no—
215D4×C47—42no—
216D4×C47—81no—
217D4×C47—81no—
218C2×C4×C47—22no—
219C2×C4×C47—24no—
220C2×C4×C47—24no—
221C2×C4×C47—41no—
222C2×C4×C47—41no—
223C2×C4×C47—41no—
224C2×C4×C47—41no—
225C2×C4×C47—41no—
226C2×C4×C47—41no—
227C2×C4×C47—42no—
228C2×C4×C47—42no—
229C2×C4×C47—42no—
230C2×C4×C47—42no—
231C2×C4×C47—42no—
232C2×C4×C47C2×C22⋊C411yescharacteristic
233C2×C4×C47C2×C22⋊C411yescharacteristic
234C2×C4×C47C2×C22⋊C411yescharacteristic
235C2×C4×C47C2×C22⋊C411yescharacteristic
236C22⋊D47—84no—
237C22⋊D47—84no—
238C2×Dic47—22no—
239C2×Dic47—22no—
240C2×Dic47—24no—
241C2×Dic47—42no—
242C2×Dic47—42no—
243C2×Dic47—42no—
244C2×Dic47—42no—
245C2×Dic47—42no—
246C2×Dic47—42no—
247C2×Dic47—42no—
248C2×Dic47—42no—
249C2×Dic47—42no—
250C2×Dic47—42no—
251C2×Dic47—84no—
252C2×Dic47C2×C22⋊C414yes—
253C4×D47—88no—
254Dic94—81no—
255Dic94—81no—
256#21422—471nomaximal, Sylow
257C22×C47—21no—
258C22×C47—21no—
259C22×C47—21no—
260C22×C47—21no—
261C22×C47—21no—
262C22×C47—21no—
263C22×C47—42no—
264C22×C47—42no—
265C22×C47—42no—
266C22×C47—42no—
267C22×C47—42no—
268C22×C47—84no—
269C22×C47C22×C22⋊C411yescharacteristic
270C22×C47C4×#4112yes—
271C22×C47#52512yes—
272C22×C47#53211yescharacteristic
273C22×C47#53211yescharacteristic
274C2×D47—24no—
275C2×D47—24no—
276C2×D47—24no—
277C2×D47—44no—
278C2×D47—44no—
279C2×D47—82no—
280C2×D47—82no—
281C2×D47—84no—
282C4×C47—21no—
283C4×C47—21no—
284C4×C47—21no—
285C4×C47—21no—
286C4×C47—44no—
287C4×C47—42no—
288C4×C47—82no—
289Dic47—24no—
290Dic47—44no—
291Dic47—42no—
292Dic47—42no—
293Dic47—82no—
294C2×#538—471no—
295#2312—471no—
296#2273—471no—
297#1996—471no—
298#1996—471no—
299#1964—471no—
300#1964D4711yescharacteristic, complemented
301#1898—474no—
302C4×#99—474no—
303C2×C47—22no—
304C2×C47—21no—
305C2×C47—21no—
306C2×C47—22no—
307C2×C47—82no—
308C2×C47#229711yescharacteristic
309C2×C47#288311yescharacteristic
310C2×C47#288311yescharacteristic
311D47—44no—
312#538—942no—
313#538—942no—
314#538—942no—
315#538—942no—
316C2×#126—472no—
317C2×#124—472no—
318C2×#123—472no—
319C2×C22⋊Q8—471no—
320C2×#121—472no—
321C2×#121C2×D4711yescharacteristic
322C2×#120—472no—
323C2×C4×D4—472no—
324C22×C22⋊C4—471no—
325C22×C22⋊C4—472no—
326C2×#99—474no—
327C2×#99C2×D4714yes—
328#388—942no—
329#388—942no—
330#380—471no—
331#380C2×D4711yescharacteristic
332#379—472no—
333C4×C22⋊C4—471no—
334C4×C22⋊C4—472no—
335C4×C22⋊C4—472no—
336C4×C22⋊C4—942no—
337C4×C22⋊C4—942no—
338C4×C22⋊C4C2×D4711yescharacteristic
339#342—474no—
340#342—474no—
341C47#2142211yescharacteristic, complemented, Sylow
342C25—471no—
343C22×Q8—471no—
344C22×D4—472no—
345C22×D4—472no—
346C22×D4C4×D4711yescharacteristic, complemented
347C22×D4C22×D4712yes—
348C23×C4—471no—
349C23×C4—472no—
350C23×C4—942no—
351C23×C4C22×D4711yescharacteristic
352#126—944no—
353#126—944no—
354#124—944no—
355#124—944no—
356#123—944no—
357#123—944no—
358C22⋊Q8—941no—
359C22⋊Q8—941no—
360C22⋊Q8—941no—
361C22⋊Q8—941no—
362#121—21no—
363#121—21no—
364#121—21no—
365#121—21no—
366#121—944no—
367#121—944no—
368#120—944no—
369#120—944no—
370C4×D4—944no—
371C4×D4—944no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—472no—
374C2×C4⋊C4—472no—
375C2×C4⋊C4—471no—
376C2×C4⋊C4—941no—
377C2×C4⋊C4C4×D4711yescharacteristic, complemented
378C2×C22⋊C4—472no—
379C2×C22⋊C4—472no—
380C2×C22⋊C4—472no—
381C2×C22⋊C4—472no—
382C2×C22⋊C4—472no—
383C2×C22⋊C4—472no—
384C2×C22⋊C4—472no—
385C2×C22⋊C4—472no—
386C2×C22⋊C4—472no—
387C2×C22⋊C4—472no—
388C2×C22⋊C4—472no—
389C2×C22⋊C4—472no—
390C2×C22⋊C4—944no—
391C2×C22⋊C4—942no—
392C2×C22⋊C4—944no—
393C2×C22⋊C4—942no—
394C2×C22⋊C4—942no—
395C2×C22⋊C4C4×D4712yescomplemented
396C2×C22⋊C4C22×D4712yes—
397C2×C22⋊C4C22×D4712yes—
398C2×C42—21no—
399C2×C42—472no—
400C2×C42—942no—
401C2×C42—942no—
402C2×C42—941no—
403#99—28no—
404#99—948no—
405#95—21no—
406#95—21no—
407#95—942no—
408#95—942no—
409#95—941no—
410#95—941no—
411C24—472no—
412C24—472no—
413C24—472no—
414C24—942no—
415C24—942no—
416C24—3761no—
417C24—3761no—
418C24C2×C4×D4712yes—
419C24C23×D4711yescharacteristic
420C2×Q8—941no—
421C2×Q8—941no—
422C2×Q8—3761no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—24no—
426C2×D4—24no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—81no—
430C2×D4—944no—
431C2×D4—944no—
432C2×D4—3762no—
433C2×D4—3762no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—81no—
437C22×C4—472no—
438C22×C4—472no—
439C22×C4—472no—
440C22×C4—472no—
441C22×C4—472no—
442C22×C4—948no—
443C22×C4—944no—
444C22×C4—942no—
445C22×C4—942no—
446C22×C4—3762no—
447C22×C4—3762no—
448C22×C4—3762no—
449C22×C4—3761no—
450C22×C4C2×C4×D4712yes—
451C22×C4C2×C4×D4711yescharacteristic
452C22×C4C2×C4×D4711yescharacteristic
453C22×C4D4×D4711yescharacteristic
454C22×C4D4×D4711yescharacteristic
455C22×C4D4×D4711yescharacteristic
456C22×C4D4×D4711yescharacteristic
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—81no—
460C4⋊C4—944no—
461C4⋊C4—942no—
462C4⋊C4—942no—
463C4⋊C4—941no—
464C4⋊C4—941no—
465C4⋊C4—3761no—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—24no—
470C22⋊C4—474no—
471C22⋊C4—474no—
472C22⋊C4—474no—
473C22⋊C4—474no—
474C22⋊C4—474no—
475C22⋊C4—944no—
476C22⋊C4—944no—
477C22⋊C4—948no—
478C22⋊C4—944no—
479C22⋊C4—942no—
480C22⋊C4—942no—
481C22⋊C4—942no—
482C22⋊C4—944no—
483C22⋊C4—3762no—
484C22⋊C4—3762no—
485C22⋊C4#1062535214yes—
486C42—81no—
487C42—944no—
488C42—3761no—
489C42—3762no—
490C42—3762no—
491C23—22no—
492C23—24no—
493C23—41no—
494C23—41no—
495C23—42no—
496C23—42no—
497C23—474no—
498C23—944no—
499C23—942no—
500C23—942no—
501C23—942no—
502C23—942no—
503C23—3764no—
504C23—3764no—
505C23—1882no—
506C23—1882no—
507C23—1882no—
508C23—1882no—
509C23—1882no—
510C23—1882no—
511C23C22×C4×D4711yescharacteristic
512C23C2×D4×D4711yescharacteristic
513C23C2×D4×D4711yescharacteristic
514C23#41×D4712yes—
515C23C2×#1062535212yes—
516Q8—3761no—
517Q8—3761no—
518D4—44no—
519D4—42no—
520D4—42no—
521D4—81no—
522D4—81no—
523D4—3764no—
524D4—3764no—
525C2×C4—22no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—474no—
540C2×C4—942no—
541C2×C4—942no—
542C2×C4—944no—
543C2×C4—3768no—
544C2×C4—3764no—
545C2×C4—1882no—
546C2×C4—1882no—
547C2×C4—1882no—
548C2×C4—1882no—
549C2×C4—1882no—
550C2×C4—1882no—
551C2×C4—1882no—
552C2×C4—1882no—
553C2×C4—1882no—
554C2×C4—1882no—
555C2×C4C22⋊C4×D4711yescharacteristic
556C2×C4C22⋊C4×D4711yescharacteristic
557C2×C4C22⋊C4×D4711yescharacteristic
558C2×C4C22⋊C4×D4711yescharacteristic
559C22—21no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—21no—
565C22—42no—
566C22—42no—
567C22—42no—
568C22—42no—
569C22—42no—
570C22—84no—
571C22—944no—
572C22—944no—
573C22—944no—
574C22—3762no—
575C22—3762no—
576C22—3764no—
577C22—1884no—
578C22—1884no—
579C22C2×C22⋊C4×D4711yescharacteristic
580C22C4×#1062535212yes—
581C22#1568963312yes—
582C22#1568967111yescharacteristic
583C22#1568967211yescharacteristic
584C4—21no—
585C4—21no—
586C4—21no—
587C4—21no—
588C4—44no—
589C4—42no—
590C4—82no—
591C4—944no—
592C4—3762no—
593C4—1884no—
594C4—1882no—
595C4—1882no—
596C2—22no—
597C2—21no—
598C2—21no—
599C2—22no—
600C2—82no—
601C2—1884no—
602C2#2024587511yescharacteristic
603C2#2025184611yescharacteristic
604C2#2025184711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D47
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC47×#1964C2
socleC22×C47C22×C22⋊C4
prime radicalC2×#15689710C2
cosocleC24×C47C24
hypercenter#1964D47
hypocenterC47#21422
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1964

Complements

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

NH ≅ G/Ntype
2. #20245985C2semidirect
3. #20245740C2semidirect
4. #20244373C2semidirect
5. #20244372C2semidirect
6. #20244225C2semidirect
7. #20243838C2semidirect
8. #99×Dic47C2semidirect
9. C47×#1964C2semidirect
14. C2×#13094019C4semidirect
15. C2×#13094010C4semidirect
16. C2×#13094008C4semidirect
18. C2×#13093996C4semidirect
40. C22×Dic94C2×C4semidirect
43. C23×Dic47C2×C4semidirect
63. C2×C4⋊Dic47C2×C4semidirect
64. C2×C4⋊Dic47C2×C4semidirect
65. C2×Dic47⋊C4C2×C4semidirect
66. C2×C22⋊Dic47C2×C4semidirect
86. C2×C4×Dic47C2×C4semidirect
92. C22×D4×C47C2×C4semidirect
100. C2×C4⋊C4×C47C2×C4semidirect
101. C2×C22⋊C4×C47C2×C4semidirect
300. #1964D47semidirect
341. C47#21422semidirect
346. C22×D4C4×D47semidirect
377. C2×C4⋊C4C4×D47semidirect
395. C2×C22⋊C4C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156897102
#202459852
#202457402
#202443732
#202443722
#202442252
#202438382
#99×Dic472
C47×#19642
#2142247