Finite Group Databasebeta

← #26224055

Subgroups — #26224055

Order 12032.

876 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689412C211yesmaximal, characteristic
2#20246135C211yesmaximal, characteristic, complemented
3#20245748C211yesmaximal, characteristic
4#20244338C211yesmaximal, characteristic, complemented
5#20244159C211yesmaximal, characteristic, complemented
6#20243973C211yesmaximal, characteristic, complemented
7#20243648C211yesmaximal, characteristic
8#20243638C211yesmaximal, characteristic
9#20243397C211yesmaximal, characteristic
10#20243288C211yesmaximal, characteristic, complemented
11#20243276C211yesmaximal, characteristic, complemented
12#20243244C211yesmaximal, characteristic, complemented
13#20243212C211yesmaximal, characteristic
14#20243202C211yesmaximal, characteristic
15C47×#1919C211yesmaximal, characteristic, complemented
16C2×#13094023C2211yescharacteristic
17C2×C4×D188C2211yescharacteristic
18C2×#13093986C2211yescharacteristic
19C2×#13093986C2211yescharacteristic
20#15689412C418yescomplemented
21C2×#13093958C2211yescharacteristic
22C2×#13093955C2211yescharacteristic
23C2×#13093955C2211yescharacteristic
24C2×Dic47⋊C8C2211yescharacteristic
25C2×Dic47⋊C8C2211yescharacteristic
26C2×#13093946C2211yescharacteristic
27C2×#13093946C2211yescharacteristic
28C2×#13093944C2211yescharacteristic
29C2×#13093944C2211yescharacteristic
30C2×#13093934C2211yescharacteristic
31C2×C8×Dic47C2211yescharacteristic
32#15689028—21no—
33#15689027—21no—
34#15689021C2211yescharacteristic
35#15689005—21no—
36#15689004—21no—
37#15688988C2211yescharacteristic
38C4⋊C4×Dic47C2211yescharacteristic
39C4⋊C4×Dic47C2211yescharacteristic
40C4⋊C4×Dic47C2211yescharacteristic
41C4⋊C4×Dic47C2211yescharacteristic
42C4×(C2×D47)⋊C4—21no—
43C4×(C2×D47)⋊C4—21no—
44#15688970—21no—
45#15688969C2211yescharacteristic
46#95×D47—21no—
47#15688886C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688885C2211yescharacteristic
51#15688885C2211yescharacteristic
52#15688878C2211yescharacteristic
53C2×#106×C47C2211yescharacteristic
54C47×#389C2211yescharacteristic
55C4×C4⋊C4×C47C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#336C2211yescharacteristic
60C22×Dic94—21no—
61C22×D188C2311yescharacteristic
62C22×C4×D47—21no—
63C22×C4×D47—21no—
64C22×C4×D47—21no—
65C22×C47⋊C8C2311yescharacteristic
66C22×C47⋊C8C2311yescharacteristic
67#13094023—22no—
68#13094023C2×C414yescomplemented
69C4×D188—22no—
70C4×D188—22no—
71#13093986—22no—
72#13093986—22no—
73#13093986C2×C414yes—
74#13093986Q814yescomplemented
75C2×C4⋊Dic47C2311yescharacteristic
76C2×C4⋊Dic47C2311yescharacteristic
77C2×C4⋊Dic47C2311yescharacteristic
78C2×Dic47⋊C4—21no—
79C2×Dic47⋊C4—21no—
80C2×(C2×D47)⋊C4—21no—
81C2×(C2×D47)⋊C4—21no—
82C2×(C2×D47)⋊C4—21no—
83C2×C4×Dic47—21no—
84C2×C4×Dic47—21no—
85C2×C4×Dic47—21no—
86C2×C4×Dic47—21no—
87C2×C4×Dic47C2311yescharacteristic
88C2×C4×Dic47C2311yescharacteristic
89#13093958—22no—
90#13093955—22no—
91#13093955C2×C414yescomplemented
92Dic47⋊C8—22no—
93Dic47⋊C8C2×C414yescomplemented
94#13093946—22no—
95#13093946C2×C414yes—
96#13093944—22no—
97#13093944C2×C414yes—
98#13093934—22no—
99C8×Dic47—22no—
100C47⋊#95—21no—
101C47⋊#95—21no—
102C47⋊#95—21no—
103C47⋊#95—21no—
104C47⋊#95—21no—
105C47⋊#95—21no—
106C47⋊#95—21no—
107C47⋊#95D411yescharacteristic
108C47⋊#95D411yescharacteristic
109C47⋊#95D411yescharacteristic
110C47⋊#95D411yescharacteristic
111C22×C8×C47C2311yescharacteristic
112C22×C8×C47C2311yescharacteristic
113C2×C4⋊C4×C47—21no—
114C2×C4⋊C4×C47C2311yescharacteristic
115C2×C4⋊C4×C47C2311yescharacteristic
116C2×C4⋊C4×C47C2311yescharacteristic
117C2×C4⋊C4×C47C2311yescharacteristic
118C2×C42×C47—21no—
119C2×C42×C47C2311yescharacteristic
120#106×C47C2×C414yescomplemented
121#95×C47—21no—
122#95×C47—21no—
123C23×D47—21no—
124C22×C4×C47—21no—
125C22×C4×C47—21no—
126C22×C4×C47—21no—
127C22×C4×C47—21no—
128C22×C4×C47C2×D411yescharacteristic
129C22×C4×C47C2×D411yescharacteristic
130C22×C4×C47C2411yescharacteristic
131C22×Dic47—21no—
132C22×Dic47—21no—
133C22×Dic47—21no—
134C22×Dic47C2×D411yescharacteristic
135C22×Dic47C2×D411yescharacteristic
136C22×Dic47C2×D411yescharacteristic
137C22×Dic47C2×D411yescharacteristic
138C2×D188—21no—
139C2×D188—21no—
140C2×D188—21no—
141C2×D188C22×C412yes—
142C2×D188C2×Q812yes—
143C2×D188#4112yes—
144C2×C4×D47—24no—
145C2×C4×D47—24no—
146C2×C4×D47—24no—
147C2×C4×D47—81no—
148C2×C4×D47—81no—
149C2×C4×D47—81no—
150C2×C4×D47—81no—
151C2×C4×D47—81no—
152C2×C4×D47—81no—
153C2×Dic94—24no—
154C2×Dic94—81no—
155C2×Dic94—81no—
156C2×C8×C47—21no—
157C2×C8×C47—21no—
158C2×C8×C47—21no—
159C2×C8×C47—21no—
160C2×C8×C47—21no—
161C2×C8×C47C22×C412yes—
162C4⋊C4×C47—21no—
163C4⋊C4×C47—21no—
164C4⋊C4×C47—21no—
165C4⋊C4×C47—21no—
166C4⋊C4×C47—21no—
167C4⋊C4×C47—81no—
168C4⋊C4×C47C22×C412yes—
169C4⋊C4×C47C22×C412yes—
170C4⋊C4×C47C2×Q812yes—
171C42×C47—21no—
172C42×C47—21no—
173C42×C47—81no—
174(C2×D47)⋊C4—24no—
175(C2×D47)⋊C4—24no—
176(C2×D47)⋊C4—24no—
177C4⋊Dic47—21no—
178C4⋊Dic47—21no—
179C4⋊Dic47—21no—
180C4⋊Dic47—21no—
181C4⋊Dic47C22×C412yes—
182C4⋊Dic47#4112yes—
183Dic47⋊C4—24no—
184Dic47⋊C4—81no—
185C4×Dic47—81no—
186C4×Dic47—81no—
187C4×Dic47—81no—
188C4×Dic47—81no—
189C4×Dic47C22×C412yes—
190C4×Dic47C2×Q812yes—
191C4×Dic47#4112yes—
192C4×Dic47#4112yes—
193C2×C47⋊C8—21no—
194C2×C47⋊C8—21no—
195C2×C47⋊C8—21no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8C22×C412yes—
199C23×C47C22×D411yescharacteristic
200C22×D47—22no—
201C22×D47—22no—
202C22×D47—22no—
203C22×D47—41no—
204C22×D47—41no—
205C22×D47—41no—
206C22×D47—41no—
207C2×C4×C47—22no—
208C2×C4×C47—22no—
209C2×C4×C47—22no—
210C2×C4×C47—21no—
211C2×C4×C47—21no—
212C2×C4×C47—21no—
213C2×C4×C47—21no—
214C2×C4×C47—21no—
215C2×C4×C47—21no—
216C2×C4×C47—41no—
217C2×C4×C47—41no—
218C2×C4×C47—41no—
219C2×C4×C47—41no—
220C2×C4×C47—41no—
221C2×C4×C47—41no—
222C2×C4×C47—41no—
223C2×C4×C47—41no—
224C2×C4×C47—41no—
225C2×C4×C47C23×C411yescharacteristic
226C2×C4×C47C22×Q811yescharacteristic
227C2×C4×C47C2×#4111yescharacteristic
228C2×C4×C47C2×#4111yescharacteristic
229C2×C4×C47C2×#4111yescharacteristic
230C2×C4×C47C2×#4111yescharacteristic
231C2×Dic47—21no—
232C2×Dic47—21no—
233C2×Dic47—21no—
234C2×Dic47—21no—
235C2×Dic47—21no—
236C2×Dic47—21no—
237C2×Dic47—21no—
238C2×Dic47—21no—
239C2×Dic47—22no—
240C2×Dic47—22no—
241C2×Dic47—41no—
242C2×Dic47—41no—
243C2×Dic47—41no—
244C2×Dic47—41no—
245C2×Dic47—41no—
246C2×Dic47—41no—
247C2×Dic47—41no—
248C2×Dic47C4×D412yes—
249C2×Dic47C4×D412yes—
250C2×Dic47C22⋊Q812yes—
251C2×Dic47C22⋊Q812yes—
252D188—22no—
253D188—22no—
254D188—22no—
255D188C4×Q814yes—
256C4×D47—84no—
257C4×D47—84no—
258C4×D47—84no—
259Dic94—84no—
260C8×C47—22no—
261C8×C47—41no—
262C47⋊C8—22no—
263C47⋊C8—41no—
264#21623—471nomaximal, Sylow
265C22×C47C2×C4×D411yescharacteristic
266C22×C47C2×C22⋊Q811yescharacteristic
267C22×C47#52511yescharacteristic
268C22×C47#57611yescharacteristic
269C22×C47#57711yescharacteristic
270C22×C47#57711yescharacteristic
271C22×C47#57711yescharacteristic
272C2×D47—24no—
273C2×D47—42no—
274C2×D47—42no—
275C2×D47—42no—
276C2×D47—42no—
277C2×D47—42no—
278C2×D47—42no—
279C4×C47—42no—
280C4×C47—41no—
281C4×C47—41no—
282C4×C47—42no—
283C4×C47—42no—
284C4×C47—81no—
285C4×C47C2×C4×Q811yescharacteristic
286C4×C47C4×#4111yescharacteristic
287C4×C47#52911yescharacteristic
288C4×C47#53311yescharacteristic
289Dic47—22no—
290Dic47—22no—
291Dic47—22no—
292Dic47—22no—
293Dic47—42no—
294Dic47—42no—
295Dic47—81no—
296C2×#476—471no—
297#2331—471no—
298#2275—471no—
299#1988—471no—
300#1949—471no—
301#1920—471no—
302#1919D4711yescharacteristic, complemented
303#1864—471no—
304#1862—471no—
305#1804—471no—
306#1776—471no—
307C4×#106—471no—
308#1768—471no—
309#1762—471no—
310C4×#102—471no—
311C2×C47C4×C22⋊Q811yescharacteristic
312C2×C47#294611yescharacteristic
313C2×C47#294911yescharacteristic
314C2×C47#308111yescharacteristic
315C2×C47#308411yescharacteristic
316C2×C47#311811yescharacteristic
317C2×C47#312511yescharacteristic
318D47—44no—
319C2×C4⋊Q8—471no—
320C2×C4×D4—471no—
321C2×C4×D4—471no—
322C2×C4×D4—471no—
323#476—478no—
324C2×#107—471no—
325C2×#106—471no—
326C2×#106—471no—
327C2×#106C2×D4711yescharacteristic
328C2×C4⋊C8—471no—
329C2×C4⋊C8—471no—
330C2×#102—471no—
331C2×#102—471no—
332C2×#102—471no—
333C2×#102—471no—
334C2×#97—471no—
335C2×C4×C8—471no—
336#391—941no—
337#391—941no—
338#389—471no—
339#389C2×D4711yescharacteristic
340#387—941no—
341#387—941no—
342#382—471no—
343C4×C4⋊C4—471no—
344C4×C4⋊C4—471no—
345C4×C4⋊C4—471no—
346C4×C4⋊C4—471no—
347C4×C4⋊C4C2×D4711yescharacteristic
348C4×C22⋊C4—941no—
349C4×C22⋊C4—941no—
350C4×C22⋊C4—941no—
351#376—471no—
352C2×#95—941no—
353#340—471no—
354#340—471no—
355#340—471no—
356#340—471no—
357#340—471no—
358#340C2×D4711yescharacteristic
359#340C2×D4711yescharacteristic
360#340C2×D4711yescharacteristic
361#336—471no—
362#336C2×D4711yescharacteristic
363C47#2162311yescharacteristic, complemented, Sylow
364C22×Q8—941no—
365C22×D4—471no—
366C23×C4—941no—
367C23×C4—941no—
368C23×C4—941no—
369C22×C8—471no—
370C22×C8—471no—
371C22×C8C22×D4711yescharacteristic
372C22×C8C22×D4711yescharacteristic
373C4⋊Q8—474no—
374C4⋊Q8—942no—
375C4×D4—474no—
376C4×D4—474no—
377C4×D4—942no—
378C4×D4—942no—
379C4×D4—942no—
380C4×D4—942no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—471no—
383C2×C4⋊C4—471no—
384C2×C4⋊C4—471no—
385C2×C4⋊C4—941no—
386C2×C4⋊C4—941no—
387C2×C4⋊C4C22×D4711yescharacteristic
388C2×C4⋊C4C22×D4711yescharacteristic
389C2×C4⋊C4C22×D4711yescharacteristic
390C2×C4⋊C4C22×D4711yescharacteristic
391C2×C22⋊C4—941no—
392C2×C22⋊C4—941no—
393C2×C22⋊C4—941no—
394C2×C42—21no—
395C2×C42—471no—
396C2×C42—471no—
397C2×C42—941no—
398C2×C42—941no—
399C2×C42—941no—
400C2×C42—941no—
401C2×C42C22×D4711yescharacteristic
402#107—942no—
403#106—474no—
404#106—942no—
405#106C4×D4714yescomplemented
406C4⋊C8—474no—
407C4⋊C8—942no—
408#102—474no—
409#102—474no—
410#102—942no—
411#102—942no—
412#97—942no—
413C4×C8—942no—
414#95—21no—
415#95—21no—
416#95—471no—
417#95—471no—
418#95—471no—
419#95—471no—
420#95—941no—
421#95—941no—
422#95—941no—
423#95—941no—
424#95—941no—
425#95—941no—
426#95—941no—
427C24—941no—
428C2×Q8—944no—
429C2×Q8—3761no—
430C2×Q8—3761no—
431C2×D4—472no—
432C2×D4—472no—
433C2×D4—472no—
434C2×D4—941no—
435C2×D4—941no—
436C2×D4—941no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—471no—
442C22×C4—471no—
443C22×C4—471no—
444C22×C4—471no—
445C22×C4—944no—
446C22×C4—944no—
447C22×C4—944no—
448C22×C4—941no—
449C22×C4—941no—
450C22×C4—941no—
451C22×C4—3761no—
452C22×C4—3761no—
453C22×C4—3761no—
454C22×C4—3761no—
455C22×C4—3761no—
456C22×C4—3761no—
457C22×C4D4×D4711yescharacteristic
458C22×C4D4×D4711yescharacteristic
459C22×C4C23×D4711yescharacteristic
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—472no—
466C2×C8—941no—
467C2×C8—941no—
468C2×C8—941no—
469C2×C8—941no—
470C2×C8—941no—
471C2×C8C2×C4×D4712yes—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—81no—
478C4⋊C4—472no—
479C4⋊C4—472no—
480C4⋊C4—944no—
481C4⋊C4—941no—
482C4⋊C4—941no—
483C4⋊C4—941no—
484C4⋊C4—941no—
485C4⋊C4—3761no—
486C4⋊C4C2×C4×D4712yes—
487C4⋊C4C2×C4×D4712yes—
488C4⋊C4Q8×D4712yes—
489C22⋊C4—944no—
490C22⋊C4—944no—
491C22⋊C4—944no—
492C42—21no—
493C42—21no—
494C42—81no—
495C42—472no—
496C42—472no—
497C42—472no—
498C42—472no—
499C42—3761no—
500C42—3761no—
501C42—3761no—
502C42—3761no—
503C23—942no—
504C23—942no—
505C23—942no—
506C23—1881no—
507C23—1881no—
508C23—1881no—
509C23—1881no—
510C23C2×D4×D4711yescharacteristic
511Q8—3764no—
512D4—474no—
513D4—942no—
514D4—942no—
515D4—942no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—472no—
535C2×C4—472no—
536C2×C4—472no—
537C2×C4—472no—
538C2×C4—941no—
539C2×C4—941no—
540C2×C4—941no—
541C2×C4—941no—
542C2×C4—941no—
543C2×C4—941no—
544C2×C4—941no—
545C2×C4—941no—
546C2×C4—942no—
547C2×C4—942no—
548C2×C4—3764no—
549C2×C4—3764no—
550C2×C4—3764no—
551C2×C4—1881no—
552C2×C4—1881no—
553C2×C4—1881no—
554C2×C4—1881no—
555C2×C4—1881no—
556C2×C4—1881no—
557C2×C4—1881no—
558C2×C4C22×C4×D4711yescharacteristic
559C2×C4C2×Q8×D4711yescharacteristic
560C2×C4#41×D4711yescharacteristic
561C2×C4#41×D4711yescharacteristic
562C2×C4#41×D4711yescharacteristic
563C2×C4#41×D4711yescharacteristic
564C8—22no—
565C8—41no—
566C8—942no—
567C8—1881no—
568C22—944no—
569C22—1882no—
570C22—1882no—
571C22—1882no—
572C22—1882no—
573C22—1882no—
574C22—1882no—
575C22C4×D4×D4711yescharacteristic
576C22C22⋊Q8×D4711yescharacteristic
577C22#1568963111yescharacteristic
578C22#1568992511yescharacteristic
579C22#1568992911yescharacteristic
580C22#1568993211yescharacteristic
581C22#1568993311yescharacteristic
582C4—42no—
583C4—42no—
584C4—42no—
585C4—41no—
586C4—41no—
587C4—81no—
588C4—942no—
589C4—942no—
590C4—942no—
591C4—942no—
592C4—3761no—
593C4—1882no—
594C4—1882no—
595C4C4×Q8×D4711yescharacteristic
596C4#1568959111yescharacteristic
597C4#1568965611yescharacteristic
598C4#1568967911yescharacteristic
599C2—1884no—
600C2#2024592211yescharacteristic
601C2#2025221511yescharacteristic
602C2#2025224411yescharacteristic
603C2#2025321611yescharacteristic
604C2#2025324711yescharacteristic
605C2#2025357511yescharacteristic
606C2#2025366811yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1919C2
socleC23×C47C22×D4
prime radicalC22×D188C23
cosocleC22×C4×C47C24
hypercenter#1919D47
hypocenterC47#21623
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1919

Complements

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

NH ≅ G/Ntype
2. #20246135C2semidirect
4. #20244338C2semidirect
5. #20244159C2semidirect
6. #20243973C2semidirect
10. #20243288C2semidirect
11. #20243276C2semidirect
12. #20243244C2semidirect
15. C47×#1919C2semidirect
20. #15689412C4semidirect
68. #13094023C2×C4semidirect
74. #13093986Q8semidirect
91. #13093955C2×C4semidirect
93. Dic47⋊C8C2×C4semidirect
120. #106×C47C2×C4semidirect
302. #1919D47semidirect
363. C47#21623semidirect
405. #106C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156894122
#202461352
#202457482
#202443382
#202441592
#202439732
#202436482
#202436382
#202433972
#202432882
#202432762
#202432442
#202432122
#202432022
C47×#19192
#2162347