Finite Group Databasebeta

← #26228363

Subgroups — #26228363

Order 12032.

796 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689424C211yesmaximal, characteristic
2C4×#13094016C211yesmaximal, characteristic, complemented
3#20245852C211yesmaximal, characteristic
4#20244343C211yesmaximal, characteristic, complemented
5#20244158C211yesmaximal, characteristic, complemented
6#20244121C211yesmaximal, characteristic, complemented
7#20244116C211yesmaximal, characteristic, complemented
8#20244071C211yesmaximal, characteristic
9#20244071C211yesmaximal, characteristic
10#20244016C211yesmaximal, characteristic
11#20244009C211yesmaximal, characteristic
12#20243981C211yesmaximal, characteristic, complemented
13#20243974C211yesmaximal, characteristic, complemented
14#20243399C211yesmaximal, characteristic
15C4×C4⋊C8×C47C211yesmaximal, characteristic, complemented
16C2×#13094016C2211yescharacteristic
17C2×C4×D188C2211yescharacteristic
18C2×#13093981—21no—
19#15689424C418yescomplemented
20C2×#13093958C2211yescharacteristic
21C2×#13093958C2211yescharacteristic
22C2×#13093956C2211yescharacteristic
23C2×#13093956C2211yescharacteristic
24C2×#13093946C2211yescharacteristic
25C2×#13093946C2211yescharacteristic
26C2×#13093946C2211yescharacteristic
27C2×#13093946C2211yescharacteristic
28#15689025C2211yescharacteristic
29#15689025C2211yescharacteristic
30#15689021C2211yescharacteristic
31#15689021C2211yescharacteristic
32#15689021C2211yescharacteristic
33#15689021C2211yescharacteristic
34#15689014—21no—
35#15689014—21no—
36#15689007—21no—
37#15689007—21no—
38#15688989C2211yescharacteristic
39C4×Dic47⋊C4—21no—
40C4×Dic47⋊C4—21no—
41C4×C4⋊Dic47C2211yescharacteristic
42C4×C4⋊Dic47C2211yescharacteristic
43C4×C4⋊Dic47C2211yescharacteristic
44C4×(C2×D47)⋊C4—21no—
45#15688886C2211yescharacteristic
46#15688886C2211yescharacteristic
47#15688886C2211yescharacteristic
48#15688886C2211yescharacteristic
49#15688886C2211yescharacteristic
50#15688886C2211yescharacteristic
51#15688886C2211yescharacteristic
52#15688886C2211yescharacteristic
53C2×C4⋊C8×C47C2211yescharacteristic
54C2×C4⋊C8×C47C2211yescharacteristic
55C2×C4×C8×C47C2211yescharacteristic
56C2×C4×C8×C47C2211yescharacteristic
57C43×C47C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C47×#336C2211yescharacteristic
60C22×D188C2311yescharacteristic
61C22×C4×D47—21no—
62#13094016—22no—
63#13094016C2×C414yes—
64C4×D188—22no—
65C4×D188C2×C414yes—
66#13093981—44no—
67C2×C4⋊Dic47C2311yescharacteristic
68C2×C4⋊Dic47C2311yescharacteristic
69C2×C4⋊Dic47C2311yescharacteristic
70C2×C4⋊Dic47C2311yescharacteristic
71C2×C4⋊Dic47C2311yescharacteristic
72C2×C4⋊Dic47C2311yescharacteristic
73C2×C4⋊Dic47C2311yescharacteristic
74C2×Dic47⋊C4—21no—
75C2×Dic47⋊C4—21no—
76C2×Dic47⋊C4—21no—
77C2×Dic47⋊C4—21no—
78C2×Dic47⋊C4—21no—
79C2×Dic47⋊C4—21no—
80C2×(C2×D47)⋊C4—21no—
81C2×(C2×D47)⋊C4—21no—
82C2×(C2×D47)⋊C4—21no—
83C2×(C2×D47)⋊C4—21no—
84C2×(C2×D47)⋊C4—21no—
85C2×C4×Dic47—21no—
86C2×C4×Dic47—21no—
87C2×C4×Dic47—21no—
88#13093958—41no—
89#13093958C2×C414yes—
90#13093956—41no—
91#13093956C2×C414yes—
92#13093946—41no—
93#13093946—41no—
94#13093946C2×C414yes—
95#13093946C2×C414yes—
96C47⋊#95—21no—
97C47⋊#95—21no—
98C47⋊#95—21no—
99C47⋊#95—21no—
100C47⋊#95—21no—
101C47⋊#95—21no—
102C47⋊#95—21no—
103C47⋊#95—21no—
104C47⋊#95—21no—
105C22×C8×C47C2311yescharacteristic
106C22×C8×C47C2311yescharacteristic
107C22×C8×C47C2311yescharacteristic
108C22×C8×C47C2311yescharacteristic
109C2×C42×C47D411yescharacteristic
110C2×C42×C47D411yescharacteristic
111C2×C42×C47D411yescharacteristic
112C2×C42×C47D411yescharacteristic
113C2×C42×C47C2311yescharacteristic
114C2×C42×C47C2311yescharacteristic
115C2×C42×C47C2311yescharacteristic
116C4⋊C8×C47—22no—
117C4⋊C8×C47C2×C414yes—
118C4×C8×C47—41no—
119C4×C8×C47—41no—
120C23×D47—21no—
121C22×C4×C47C2×D411yescharacteristic
122C22×C4×C47C2×D411yescharacteristic
123C22×C4×C47C2×D411yescharacteristic
124C22×C4×C47C2×D411yescharacteristic
125C22×C4×C47C2×D411yescharacteristic
126C22×C4×C47C2×D411yescharacteristic
127C22×C4×C47C2411yescharacteristic
128C22×Dic47—21no—
129C22×Dic47—21no—
130C22×Dic47—21no—
131C22×Dic47—21no—
132C22×Dic47—21no—
133C22×Dic47—21no—
134C22×Dic47—21no—
135C2×D188—21no—
136C2×D188—21no—
137C2×D188—21no—
138C2×D188—21no—
139C2×D188—21no—
140C2×D188C22×C412yes—
141C2×C4×D47—24no—
142C2×C4×D47—42no—
143C2×C4×D47—42no—
144C2×C8×C47—21no—
145C2×C8×C47—21no—
146C2×C8×C47—21no—
147C2×C8×C47—21no—
148C2×C8×C47—21no—
149C2×C8×C47—21no—
150C2×C8×C47—21no—
151C2×C8×C47—21no—
152C2×C8×C47—21no—
153C2×C8×C47—21no—
154C2×C8×C47C22×C412yes—
155C2×C8×C47C22×C412yes—
156C42×C47—22no—
157C42×C47—22no—
158C42×C47—22no—
159C42×C47—21no—
160C42×C47—21no—
161C42×C47—21no—
162C42×C47—21no—
163C42×C47—41no—
164C42×C47C22×C412yes—
165C42×C47#4112yes—
166(C2×D47)⋊C4—24no—
167(C2×D47)⋊C4—42no—
168(C2×D47)⋊C4—42no—
169(C2×D47)⋊C4—42no—
170(C2×D47)⋊C4—42no—
171C4⋊Dic47—21no—
172C4⋊Dic47—21no—
173C4⋊Dic47—21no—
174C4⋊Dic47—21no—
175C4⋊Dic47—21no—
176C4⋊Dic47—21no—
177C4⋊Dic47—21no—
178C4⋊Dic47—21no—
179C4⋊Dic47—21no—
180C4⋊Dic47—21no—
181C4⋊Dic47—21no—
182C4⋊Dic47C22×C412yes—
183C4⋊Dic47C22×C412yes—
184C4⋊Dic47C22×C412yes—
185Dic47⋊C4—24no—
186Dic47⋊C4—24no—
187Dic47⋊C4—42no—
188Dic47⋊C4—42no—
189Dic47⋊C4—42no—
190Dic47⋊C4—42no—
191C4×Dic47—42no—
192C4×Dic47—42no—
193C4×Dic47—42no—
194C23×C47C22×D411yescharacteristic
195C22×D47—22no—
196C22×D47—41no—
197C22×D47—41no—
198C22×D47—41no—
199C22×D47—41no—
200C22×D47—41no—
201C22×D47—41no—
202C2×C4×C47—21no—
203C2×C4×C47—21no—
204C2×C4×C47—21no—
205C2×C4×C47—21no—
206C2×C4×C47—21no—
207C2×C4×C47—21no—
208C2×C4×C47—21no—
209C2×C4×C47—21no—
210C2×C4×C47—21no—
211C2×C4×C47—21no—
212C2×C4×C47—21no—
213C2×C4×C47—21no—
214C2×C4×C47—21no—
215C2×C4×C47C4×D412yes—
216C2×C4×C47C4×D412yes—
217C2×C4×C47#13512yes—
218C2×C4×C47#13512yes—
219C2×C4×C47AGL(1,ℤ/8)12yes—
220C2×C4×C47C23×C411yescharacteristic
221C2×C4×C47C2×#4111yescharacteristic
222C2×C4×C47H(5,𝔽2)11yescharacteristic
223C2×C4×C472−1+411yescharacteristic
224C2×C4×C472−1+411yescharacteristic
225C2×C4×C472−1+411yescharacteristic
226C2×Dic47—22no—
227C2×Dic47—22no—
228C2×Dic47—22no—
229C2×Dic47—41no—
230C2×Dic47—41no—
231C2×Dic47—41no—
232C2×Dic47—41no—
233C2×Dic47—41no—
234C2×Dic47—41no—
235C2×Dic47—41no—
236C2×Dic47—41no—
237C2×Dic47—41no—
238C2×Dic47—41no—
239C2×Dic47—41no—
240C2×Dic47—41no—
241C2×Dic47—41no—
242C2×Dic47—41no—
243C2×Dic47—41no—
244C2×Dic47—41no—
245C2×Dic47—41no—
246C2×Dic47—41no—
247D188—22no—
248D188—22no—
249D188—41no—
250D188—41no—
251C4×D47—48no—
252C8×C47—22no—
253C8×C47—22no—
254C8×C47—41no—
255C8×C47—41no—
256#22114—471nomaximal, Sylow
257C22×C47C2×C4×D411yescharacteristic
258C22×C47#53611yescharacteristic
259C22×C47#53711yescharacteristic
260C22×C47C2×#13511yescharacteristic
261C22×C47C2×#13511yescharacteristic
262C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
263C22×C47#57511yescharacteristic
264C2×D47—42no—
265C2×D47—42no—
266C2×D47—42no—
267C2×D47—81no—
268C2×D47—81no—
269C2×D47—81no—
270C2×D47—81no—
271C4×C47—22no—
272C4×C47—22no—
273C4×C47—22no—
274C4×C47—22no—
275C4×C47—22no—
276C4×C47—41no—
277C4×C47#51911yescharacteristic
278C4×C47#52011yescharacteristic
279C4×C47#54111yescharacteristic
280C4×C47#54211yescharacteristic
281Dic47—42no—
282Dic47—42no—
283Dic47—42no—
284Dic47—81no—
285Dic47—81no—
286Dic47—81no—
287Dic47—81no—
288C2×#478—471no—
289C4×#125—471no—
290#2293—471no—
291#1989—471no—
292#1949—471no—
293#1942—471no—
294#1941—471no—
295#1934—471no—
296#1934—471no—
297#1926—471no—
298#1925—471no—
299#1921—471no—
300#1920—471no—
301#1804—471no—
302C4×C4⋊C8D4711yescharacteristic, complemented
303C2×C47#232311yescharacteristic
304C2×C47C4×#13511yescharacteristic
305C2×C47C4×AGL(1,ℤ/8)11yescharacteristic
306C2×C47#322811yescharacteristic
307C2×C47#323211yescharacteristic
308C2×C47#324711yescharacteristic
309C2×C47#325011yescharacteristic
310D47—82no—
311C2×#125—471no—
312C2×C4×D4—471no—
313C2×#117—941no—
314#478—478no—
315C2×#107—471no—
316C2×#107—471no—
317C2×#106—471no—
318C2×#106—471no—
319C2×C4⋊C8C2×D4711yescharacteristic
320C2×C4⋊C8C2×D4711yescharacteristic
321C2×#102—471no—
322C2×#102—471no—
323C2×#102—471no—
324C2×#102—471no—
325C2×C4×C8C2×D4711yescharacteristic
326C2×C4×C8C2×D4711yescharacteristic
327#390—471no—
328#390—471no—
329#389—471no—
330#389—471no—
331#389—471no—
332#389—471no—
333#388—941no—
334#388—941no—
335#387—941no—
336#387—941no—
337#382—471no—
338C4×C4⋊C4—471no—
339C4×C4⋊C4—471no—
340C4×C4⋊C4—471no—
341C4×C4⋊C4—941no—
342C4×C4⋊C4—941no—
343C4×C22⋊C4—941no—
344C43C2×D4711yescharacteristic
345#340—471no—
346#340—471no—
347#340—471no—
348#340—471no—
349#340—471no—
350#340—471no—
351#340—471no—
352#340—471no—
353#336C2×D4711yescharacteristic
354#336C2×D4711yescharacteristic
355C47#2211411yescharacteristic, complemented, Sylow
356C22×D4—471no—
357C23×C4—941no—
358C22×C8C22×D4711yescharacteristic
359C22×C8C22×D4711yescharacteristic
360C22×C8C22×D4711yescharacteristic
361C22×C8C22×D4711yescharacteristic
362#125—474no—
363#125—942no—
364C4×D4—474no—
365C4×D4—942no—
366#117—1884no—
367C2×C4⋊C4—471no—
368C2×C4⋊C4—471no—
369C2×C4⋊C4—471no—
370C2×C4⋊C4—471no—
371C2×C4⋊C4—471no—
372C2×C4⋊C4—471no—
373C2×C4⋊C4—471no—
374C2×C4⋊C4—941no—
375C2×C4⋊C4—941no—
376C2×C4⋊C4—941no—
377C2×C4⋊C4—941no—
378C2×C4⋊C4—941no—
379C2×C4⋊C4—941no—
380C2×C22⋊C4—941no—
381C2×C22⋊C4—941no—
382C2×C22⋊C4—941no—
383C2×C22⋊C4—941no—
384C2×C22⋊C4—941no—
385C2×C42—941no—
386C2×C42—941no—
387C2×C42—941no—
388C2×C42D18811yescharacteristic
389C2×C42D18811yescharacteristic
390C2×C42D18811yescharacteristic
391C2×C42D18811yescharacteristic
392C2×C42C22×D4711yescharacteristic
393C2×C42C22×D4711yescharacteristic
394C2×C42C22×D4711yescharacteristic
395#107—474no—
396#107—1881no—
397#106—474no—
398#106—1881no—
399C4⋊C8—22no—
400C4⋊C8C4×D4714yes—
401#102—474no—
402#102—474no—
403#102—1881no—
404#102—1881no—
405C4×C8—41no—
406C4×C8—41no—
407#95—941no—
408#95—941no—
409#95—941no—
410#95—941no—
411#95—941no—
412#95—941no—
413#95—941no—
414#95—941no—
415#95—941no—
416C24—941no—
417C2×D4—472no—
418C2×D4—941no—
419C2×D4—941no—
420C2×D4—941no—
421C2×D4—941no—
422C2×D4—941no—
423C22×C4—941no—
424C22×C4—941no—
425C22×C4—941no—
426C22×C4—944no—
427C22×C4—941no—
428C22×C4—941no—
429C22×C4—941no—
430C22×C4—941no—
431C22×C4—1882no—
432C22×C4—1882no—
433C22×C4C2×D18811yescharacteristic
434C22×C4C2×D18811yescharacteristic
435C22×C4C2×D18811yescharacteristic
436C22×C4C2×D18811yescharacteristic
437C22×C4C2×D18811yescharacteristic
438C22×C4C2×D18811yescharacteristic
439C22×C4C23×D4711yescharacteristic
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8C2×C4×D4712yes—
451C2×C8C2×C4×D4712yes—
452C4⋊C4—472no—
453C4⋊C4—472no—
454C4⋊C4—472no—
455C4⋊C4—944no—
456C4⋊C4—944no—
457C4⋊C4—941no—
458C4⋊C4—941no—
459C4⋊C4—941no—
460C4⋊C4—941no—
461C4⋊C4—941no—
462C4⋊C4—941no—
463C4⋊C4—941no—
464C4⋊C4—941no—
465C4⋊C4—941no—
466C4⋊C4—941no—
467C4⋊C4—941no—
468C4⋊C4—1882no—
469C4⋊C4—1882no—
470C4⋊C4—1882no—
471C4⋊C4—1882no—
472C22⋊C4—944no—
473C22⋊C4—1882no—
474C22⋊C4—1882no—
475C22⋊C4—1882no—
476C22⋊C4—1882no—
477C42—22no—
478C42—22no—
479C42—22no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—41no—
485C42—1882no—
486C42—1882no—
487C42—1882no—
488C42C2×C4×D4712yes—
489C42#1062535012yes—
490C23—942no—
491C23—1881no—
492C23—1881no—
493C23—1881no—
494C23—1881no—
495C23—1881no—
496C23—1881no—
497C23C22×D18811yescharacteristic
498D4—942no—
499D4—942no—
500D4—1881no—
501D4—1881no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—942no—
516C2×C4—942no—
517C2×C4—942no—
518C2×C4—1888no—
519C2×C4—1881no—
520C2×C4—1881no—
521C2×C4—1881no—
522C2×C4—1881no—
523C2×C4—1881no—
524C2×C4—1881no—
525C2×C4—1881no—
526C2×C4—1881no—
527C2×C4—1881no—
528C2×C4—1881no—
529C2×C4—1881no—
530C2×C4—1881no—
531C2×C4—1881no—
532C2×C4—1881no—
533C2×C4—1881no—
534C2×C4—1881no—
535C2×C4—1881no—
536C2×C4—1881no—
537C2×C4C4×D18812yes—
538C2×C4C4×D18812yes—
539C2×C4#1309404612yes—
540C2×C4#1309404612yes—
541C2×C4#1309405212yes—
542C2×C4C22×C4×D4711yescharacteristic
543C2×C4C2×#1062535011yescharacteristic
544C2×C4#1309406911yescharacteristic
545C2×C4#1309407111yescharacteristic
546C2×C4#1309407111yescharacteristic
547C2×C4#1309407211yescharacteristic
548C8—22no—
549C8—22no—
550C8—41no—
551C8—41no—
552C22—3761no—
553C22—3761no—
554C22—3761no—
555C22—3761no—
556C22—1882no—
557C22—1882no—
558C22—1882no—
559C22C2×C4×D18811yescharacteristic
560C22#1568969911yescharacteristic
561C22#1568970411yescharacteristic
562C22C2×#1309404611yescharacteristic
563C22C2×#1309404611yescharacteristic
564C22C2×#1309405211yescharacteristic
565C22#1568992311yescharacteristic
566C4—22no—
567C4—22no—
568C4—22no—
569C4—22no—
570C4—22no—
571C4—41no—
572C4—3761no—
573C4—3761no—
574C4—3761no—
575C4—3761no—
576C4—1882no—
577C4—1882no—
578C4—1882no—
579C4#1568959911yescharacteristic
580C4#1568960211yescharacteristic
581C4#1568973111yescharacteristic
582C4#1568973811yescharacteristic
583C2—3762no—
584C2#2024607111yescharacteristic
585C2C4×#1309404611yescharacteristic
586C2C4×#1309405211yescharacteristic
587C2#2025452611yescharacteristic
588C2#2025455811yescharacteristic
589C2#2025471511yescharacteristic
590C2#2025474011yescharacteristic
subgroupG/H
centerC23C22×D188
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC4×C4⋊C8×C47C2
socleC23×C47C22×D4
prime radicalC22×D188C23
cosocleC22×C4×C47C24
hypercenterC4×C4⋊C8D47
hypocenterC47#22114
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C43 ◁ C4×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C4×#13094016C2semidirect
4. #20244343C2semidirect
5. #20244158C2semidirect
6. #20244121C2semidirect
7. #20244116C2semidirect
12. #20243981C2semidirect
13. #20243974C2semidirect
15. C4×C4⋊C8×C47C2semidirect
19. #15689424C4semidirect
302. C4×C4⋊C8D47semidirect
355. C47#22114semidirect

Maximal subgroups

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

subgroupindex
C2×#156894242
C4×#130940162
#202458522
#202443432
#202441582
#202441212
#202441162
#202440712
#202440162
#202440092
#202439812
#202439742
#202433992
C4×C4⋊C8×C472
#2211447