Finite Group Databasebeta

← #26235715

Subgroups — #26235715

Order 12032.

866 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689223C211yesmaximal, characteristic
2#20246308C211yesmaximal, characteristic, complemented
3#20244088C211yesmaximal, characteristic
4#20244074C211yesmaximal, characteristic
5#20243980C211yesmaximal, characteristic, complemented
6#20243959C211yesmaximal, characteristic, complemented
7#20243746C211yesmaximal, characteristic
8#20243746C211yesmaximal, characteristic
9#20243523C211yesmaximal, characteristic, complemented
10#20243398C211yesmaximal, characteristic
11#20243390C211yesmaximal, characteristic, complemented
12#20243263C211yesmaximal, characteristic, complemented
13#20243221C211yesmaximal, characteristic, complemented
14C4×#13093947C211yesmaximal, characteristic, complemented
15C47×#2354C211yesmaximal, characteristic
16C22×#10625335C2211yescharacteristic
17C2×C4×Dic94C2211yescharacteristic
18C2×C4×Dic94C2211yescharacteristic
19C2×C4×Dic94C2211yescharacteristic
20#15689223C418yescomplemented
21C2×#13093957C2211yescharacteristic
22C2×C4⋊(C47⋊C8)C2211yescharacteristic
23C2×#13093947C2211yescharacteristic
24C2×#13093947C2211yescharacteristic
25C2×#13093947C2211yescharacteristic
26C2×#13093945C2211yescharacteristic
27C2×#13093945C2211yescharacteristic
28C2×#13093945C2211yescharacteristic
29C2×#13093935C2211yescharacteristic
30C2×#13093935C2211yescharacteristic
31C2×C4×C47⋊C8C2211yescharacteristic
32#15689021C2211yescharacteristic
33#15689021C2211yescharacteristic
34#15689018—21no—
35#15689018—21no—
36#15688989C2211yescharacteristic
37#15688987—21no—
38#15688974—21no—
39#15688885C2211yescharacteristic
40#15688885C2211yescharacteristic
41#15688885C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688878C2211yescharacteristic
48#15688878C2211yescharacteristic
49C2×C4×D4×C47C2211yescharacteristic
50C2×#117×C47—21no—
51C47×#390C2211yescharacteristic
52C47×#390C2211yescharacteristic
53C47×#388—21no—
54C47×#388—21no—
55C47×#384C2211yescharacteristic
56C47×#380—21no—
57C4×C4⋊C4×C47C2211yescharacteristic
58C4×C4⋊C4×C47C2211yescharacteristic
59C4×C4⋊C4×C47C2211yescharacteristic
60C22×Dic94C2311yescharacteristic
61C2×#10625335—22no—
62C2×#10625335—22no—
63C2×#10625335C2×C414yes—
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66C22×C47⋊C8C2311yescharacteristic
67C22×C47⋊C8C2311yescharacteristic
68C4×Dic94—22no—
69C4×Dic94—22no—
70C4×Dic94—22no—
71C4×Dic94—41no—
72C4×Dic94—41no—
73C4×Dic94C2×C414yes—
74C2×C4⋊Dic47C2311yescharacteristic
75C2×C4⋊Dic47C2311yescharacteristic
76C2×C4⋊Dic47C2311yescharacteristic
77C2×Dic47⋊C4—21no—
78C2×Dic47⋊C4—21no—
79C2×Dic47⋊C4—21no—
80C2×Dic47⋊C4—21no—
81C2×Dic47⋊C4—21no—
82C2×C4×Dic47—21no—
83C2×C4×Dic47—21no—
84C2×C4×Dic47—21no—
85#13093957C2×C414yes—
86C4⋊(C47⋊C8)—22no—
87#13093947—22no—
88#13093947—22no—
89#13093947C2×C414yes—
90#13093945—41no—
91#13093945—41no—
92#13093945C2×C414yes—
93#13093935—41no—
94#13093935C2×C414yes—
95C4×C47⋊C8—41no—
96C47⋊#95—21no—
97C47⋊#95—21no—
98C47⋊#95—21no—
99C47⋊#95—21no—
100C22×D4×C47C2311yescharacteristic
101C23×C4×C47—21no—
102C4×D4×C47—22no—
103C4×D4×C47C2×C414yes—
104#117×C47—44no—
105C2×C4⋊C4×C47—21no—
106C2×C4⋊C4×C47—21no—
107C2×C4⋊C4×C47D411yescharacteristic
108C2×C4⋊C4×C47D411yescharacteristic
109C2×C4⋊C4×C47C2311yescharacteristic
110C2×C4⋊C4×C47C2311yescharacteristic
111C2×C4⋊C4×C47C2311yescharacteristic
112C2×C22⋊C4×C47—21no—
113C2×C22⋊C4×C47—21no—
114C2×C22⋊C4×C47—21no—
115C2×C22⋊C4×C47—21no—
116C2×C22⋊C4×C47—21no—
117C2×C42×C47—21no—
118C2×C42×C47—21no—
119C2×C42×C47C2311yescharacteristic
120C2×C42×C47C2311yescharacteristic
121C2×C42×C47C2311yescharacteristic
122#95×C47—21no—
123#95×C47—21no—
124#95×C47D411yescharacteristic
125#95×C47D411yescharacteristic
126C24×C47—21no—
127C2×D4×C47—21no—
128C2×D4×C47—21no—
129C2×D4×C47—21no—
130C2×D4×C47—21no—
131C2×D4×C47—21no—
132C2×D4×C47C22×C412yes—
133C22×C4×C47—21no—
134C22×C4×C47—24no—
135C22×C4×C47—21no—
136C22×C4×C47—21no—
137C22×C4×C47—42no—
138C22×C4×C47—42no—
139C22×C4×C47C2×D411yescharacteristic
140C22×C4×C47C2×D411yescharacteristic
141C22×C4×C47C2×D411yescharacteristic
142C22×C4×C47C2×D411yescharacteristic
143C22×C4×C47C2×D411yescharacteristic
144C22×C4×C47C2×D411yescharacteristic
145C22×C4×C47C2411yescharacteristic
146C22×Dic47—21no—
147C22×Dic47—21no—
148C22×Dic47—21no—
149C22×Dic47—21no—
150C2×Dic94—21no—
151C2×Dic94—21no—
152C2×Dic94—21no—
153C2×Dic94C22×C412yes—
154C2×Dic94#4112yes—
155C2×Dic94#4112yes—
156C4⋊C4×C47—22no—
157C4⋊C4×C47—21no—
158C4⋊C4×C47—21no—
159C4⋊C4×C47—21no—
160C4⋊C4×C47—21no—
161C4⋊C4×C47—21no—
162C4⋊C4×C47—41no—
163C4⋊C4×C47—42no—
164C4⋊C4×C47—81no—
165C4⋊C4×C47C22×C412yes—
166C22⋊C4×C47—24no—
167C22⋊C4×C47—42no—
168C22⋊C4×C47—42no—
169C22⋊C4×C47—81no—
170C22⋊C4×C47—81no—
171C42×C47—21no—
172C42×C47—21no—
173C42×C47—21no—
174C42×C47—21no—
175C42×C47—42no—
176C42×C47—42no—
177C42×C47C22×C412yes—
178C42×C47#4112yes—
179#10625335—28no—
180C4⋊Dic47—21no—
181C4⋊Dic47—21no—
182C4⋊Dic47—21no—
183C4⋊Dic47—21no—
184C4⋊Dic47—21no—
185C4⋊Dic47C22×C412yes—
186Dic47⋊C4—24no—
187Dic47⋊C4—42no—
188Dic47⋊C4—42no—
189Dic47⋊C4—42no—
190Dic47⋊C4—42no—
191C4×Dic47—24no—
192C4×Dic47—42no—
193C4×Dic47—42no—
194C2×C47⋊C8—21no—
195C2×C47⋊C8—21no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8—21no—
199C2×C47⋊C8—21no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8—21no—
202C2×C47⋊C8—21no—
203C2×C47⋊C8—21no—
204C2×C47⋊C8C22×C412yes—
205C2×C47⋊C8C22×C412yes—
206C23×C47—22no—
207C23×C47—41no—
208C23×C47—41no—
209C23×C47—41no—
210C23×C47—41no—
211C23×C47—41no—
212C23×C47—41no—
213C23×C47C22×D411yescharacteristic
214D4×C47—22no—
215D4×C47—22no—
216D4×C47—41no—
217D4×C47—41no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—22no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—21no—
228C2×C4×C47—21no—
229C2×C4×C47—21no—
230C2×C4×C47—21no—
231C2×C4×C47—21no—
232C2×C4×C47—21no—
233C2×C4×C47—21no—
234C2×C4×C47—48no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47—41no—
238C2×C4×C47—41no—
239C2×C4×C47—41no—
240C2×C4×C47—41no—
241C2×C4×C47—41no—
242C2×C4×C47—41no—
243C2×C4×C47C4×D412yes—
244C2×C4×C47C4×D412yes—
245C2×C4×C47AGL(1,ℤ/8)12yes—
246C2×C4×C47C23×C411yescharacteristic
247C2×C4×C47C2×#4111yescharacteristic
248C2×C4×C47C2×#4111yescharacteristic
249C2×C4×C47C2×#4111yescharacteristic
250C2×C4×C47H(5,𝔽2)11yescharacteristic
251C2×C4×C472−1+411yescharacteristic
252C2×Dic47—22no—
253C2×Dic47—22no—
254C2×Dic47—22no—
255C2×Dic47—22no—
256C2×Dic47—41no—
257C2×Dic47—41no—
258C2×Dic47—41no—
259C2×Dic47—41no—
260C2×Dic47—41no—
261C2×Dic47—41no—
262C2×Dic47—41no—
263C2×Dic47—41no—
264Dic94—22no—
265Dic94—22no—
266Dic94—22no—
267Dic94#11714yescomplemented
268C47⋊C8—22no—
269C47⋊C8—22no—
270C47⋊C8—41no—
271C47⋊C8—41no—
272#22781—471nomaximal, Sylow
273C22×C47—42no—
274C22×C47—42no—
275C22×C47—42no—
276C22×C47—81no—
277C22×C47—81no—
278C22×C47—81no—
279C22×C47—81no—
280C22×C47C2×C4×D411yescharacteristic
281C22×C47#54611yescharacteristic
282C22×C47#54811yescharacteristic
283C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
284C22×C47#57511yescharacteristic
285C22×C47#57711yescharacteristic
286C22×C47#57811yescharacteristic
287C4×C47—22no—
288C4×C47—22no—
289C4×C47—22no—
290C4×C47—42no—
291C4×C47—41no—
292C4×C47—41no—
293C4×C47—41no—
294C4×C47—81no—
295C4×C47—81no—
296C4×C47C2×#11711yescharacteristic
297C4×C47#52011yescharacteristic
298C4×C47#55211yescharacteristic
299C4×C47#55311yescharacteristic
300Dic47—24no—
301Dic47—42no—
302Dic47—81no—
303Dic47—81no—
304C2×#440—471no—
305#2354D4711yescharacteristic
306#2351—471no—
307#1936—471no—
308#1934—471no—
309#1921—471no—
310#1918—471no—
311#1880—471no—
312#1880—471no—
313#1836—471no—
314#1804—471no—
315#1803—471no—
316#1771—471no—
317#1763—471no—
318C4×#103—471no—
319C2×C47—82no—
320C2×C47#235211yescharacteristic
321C2×C47C4×AGL(1,ℤ/8)11yescharacteristic
322C2×C47#294711yescharacteristic
323C2×C47#330811yescharacteristic
324C2×C47#332111yescharacteristic
325C2×C47#336811yescharacteristic
326C2×C47#337711yescharacteristic
327C22×SD16—471no—
328C2×C4×Q8—471no—
329C2×C4×Q8—471no—
330C2×C4×Q8—471no—
331C2×C4×D4C2×D4711yescharacteristic
332C2×#117—21no—
333#440—478no—
334C2×#107—471no—
335C2×C4⋊C8—471no—
336C2×#103—471no—
337C2×#103—471no—
338C2×#103—471no—
339C2×#102—471no—
340C2×#102—471no—
341C2×#102—471no—
342C2×#97—471no—
343C2×#97—471no—
344C2×C4×C8—471no—
345#390C2×D4711yescharacteristic
346#390C2×D4711yescharacteristic
347#389—471no—
348#389—471no—
349#389—941no—
350#389—941no—
351#388—21no—
352#388—21no—
353#384C2×D4711yescharacteristic
354#382—471no—
355#382—941no—
356#380—21no—
357C4×C4⋊C4—941no—
358C4×C4⋊C4C2×D4711yescharacteristic
359C4×C4⋊C4C2×D4711yescharacteristic
360C4×C4⋊C4C2×D4711yescharacteristic
361#340—471no—
362#340—471no—
363#340—471no—
364#340—471no—
365#340—471no—
366#340—471no—
367#340—471no—
368#340—471no—
369#336—471no—
370#336—471no—
371C47#2278111yescharacteristic, complemented, Sylow
372C22×Q8—471no—
373C22×D4C22×D4711yescharacteristic
374C23×C4—21no—
375C2×SD16—474no—
376C2×SD16—942no—
377C2×SD16—942no—
378C22×C8—471no—
379C22×C8—471no—
380C22×C8—471no—
381C22×C8—471no—
382C4×Q8—474no—
383C4×Q8—942no—
384C4×Q8—942no—
385C4×Q8—942no—
386C4×Q8—1881no—
387C4×Q8—1881no—
388C4×D4—22no—
389C4×D4C4×D4714yes—
390#117—44no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—471no—
394C2×C4⋊C4—471no—
395C2×C4⋊C4—471no—
396C2×C4⋊C4—941no—
397C2×C4⋊C4—941no—
398C2×C4⋊C4—941no—
399C2×C4⋊C4—941no—
400C2×C4⋊C4—941no—
401C2×C4⋊C4C22⋊D4711yescharacteristic
402C2×C4⋊C4C22⋊D4711yescharacteristic
403C2×C4⋊C4C22×D4711yescharacteristic
404C2×C4⋊C4C22×D4711yescharacteristic
405C2×C4⋊C4C22×D4711yescharacteristic
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C42—21no—
412C2×C42—21no—
413C2×C42—941no—
414C2×C42—941no—
415C2×C42—941no—
416C2×C42C22×D4711yescharacteristic
417C2×C42C22×D4711yescharacteristic
418C2×C42C22×D4711yescharacteristic
419#107—474no—
420C4⋊C8—942no—
421#103—474no—
422#103—942no—
423#103—942no—
424#102—474no—
425#102—1881no—
426#102—1881no—
427#97—474no—
428#97—1881no—
429C4×C8—1881no—
430#95—21no—
431#95—21no—
432#95—941no—
433#95—941no—
434#95—941no—
435#95—941no—
436#95C22⋊D4711yescharacteristic
437#95C22⋊D4711yescharacteristic
438C24—21no—
439C2×Q8—472no—
440C2×Q8—472no—
441C2×Q8—472no—
442C2×Q8—941no—
443C2×Q8—941no—
444C2×Q8—941no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4C2×C4×D4712yes—
451C22×C4—21no—
452C22×C4—24no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—941no—
458C22×C4—941no—
459C22×C4—941no—
460C22×C4—941no—
461C22×C4C2×C22⋊D4711yescharacteristic
462C22×C4C2×C22⋊D4711yescharacteristic
463C22×C4C2×C22⋊D4711yescharacteristic
464C22×C4C2×C22⋊D4711yescharacteristic
465C22×C4C2×C22⋊D4711yescharacteristic
466C22×C4C2×C22⋊D4711yescharacteristic
467C22×C4C23×D4711yescharacteristic
468SD16—948no—
469C2×C8—472no—
470C2×C8—472no—
471C2×C8—941no—
472C2×C8—941no—
473C2×C8—941no—
474C2×C8—941no—
475C2×C8—941no—
476C2×C8—941no—
477C2×C8—941no—
478C2×C8—941no—
479C2×C8—941no—
480C2×C8—941no—
481C4⋊C4—22no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—41no—
488C4⋊C4—42no—
489C4⋊C4—81no—
490C4⋊C4—472no—
491C4⋊C4—944no—
492C4⋊C4—941no—
493C4⋊C4—941no—
494C4⋊C4—941no—
495C4⋊C4—941no—
496C4⋊C4—941no—
497C4⋊C4—1882no—
498C4⋊C4—1882no—
499C4⋊C4—1882no—
500C4⋊C4—1882no—
501C4⋊C4C2×C4×D4712yes—
502C22⋊C4—24no—
503C22⋊C4—42no—
504C22⋊C4—42no—
505C22⋊C4—81no—
506C22⋊C4—81no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—42no—
512C42—42no—
513C42—944no—
514C42—1882no—
515C42—1882no—
516C42C2×C4×D4712yes—
517C42#1062535012yes—
518C23—22no—
519C23—41no—
520C23—41no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23C22×C22⋊D4711yescharacteristic
526Q8—474no—
527Q8—942no—
528Q8—942no—
529Q8—942no—
530D4—22no—
531D4—22no—
532D4—41no—
533D4—41no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—22no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—48no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—942no—
560C2×C4—942no—
561C2×C4—942no—
562C2×C4—942no—
563C2×C4—1881no—
564C2×C4—1881no—
565C2×C4—1881no—
566C2×C4—1881no—
567C2×C4—1881no—
568C2×C4—1881no—
569C2×C4—1881no—
570C2×C4—1881no—
571C2×C4C4×C22⋊D4712yes—
572C2×C4C4×C22⋊D4712yes—
573C2×C4#1309405012yes—
574C2×C4C22×C4×D4711yescharacteristic
575C2×C4#41×D4711yescharacteristic
576C2×C4#41×D4711yescharacteristic
577C2×C4C2×#1062535011yescharacteristic
578C2×C4#1309407011yescharacteristic
579C2×C4#1309407111yescharacteristic
580C8—942no—
581C8—942no—
582C8—1881no—
583C8—1881no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22C2×C4×C22⋊D4711yescharacteristic
592C22#1568976111yescharacteristic
593C22#1568978011yescharacteristic
594C22C2×#1309405011yescharacteristic
595C22#1568992111yescharacteristic
596C22#1568993411yescharacteristic
597C22#1568993811yescharacteristic
598C4—22no—
599C4—22no—
600C4—22no—
601C4—42no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—81no—
606C4—81no—
607C4—944no—
608C4—3761no—
609C4—3761no—
610C4—1882no—
611C4#117×D4711yescharacteristic
612C4#1568960311yescharacteristic
613C4#1568981211yescharacteristic
614C4#1568981711yescharacteristic
615C2—82no—
616C2#2024631811yescharacteristic
617C2C4×#1309405011yescharacteristic
618C2#2025222711yescharacteristic
619C2#2025537311yescharacteristic
620C2#2025556811yescharacteristic
621C2#2025611311yescharacteristic
622C2#2025622411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2354C2
socleC23×C47C22×D4
prime radicalC22×D4×C47C23
cosocleC22×C4×C47C24
hypercenter#2354D47
hypocenterC47#22781
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2354

Complements

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

NH ≅ G/Ntype
2. #20246308C2semidirect
5. #20243980C2semidirect
6. #20243959C2semidirect
9. #20243523C2semidirect
11. #20243390C2semidirect
12. #20243263C2semidirect
13. #20243221C2semidirect
14. C4×#13093947C2semidirect
20. #15689223C4semidirect
267. Dic94#117semidirect
371. C47#22781semidirect

Maximal subgroups

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

subgroupindex
C2×#156892232
#202463082
#202440882
#202440742
#202439802
#202439592
#202437462
#202435232
#202433982
#202433902
#202432632
#202432212
C4×#130939472
C47×#23542
#2278147