Finite Group Databasebeta

← #26275325

Subgroups — #26275325

Order 12032.

678 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20248622C211yesmaximal, characteristic, complemented
2#20246359C211yesmaximal, characteristic
3#20244915C211yesmaximal, characteristic
4#20244908C211yesmaximal, characteristic
5#20244761C211yesmaximal, characteristic
6#20244761C211yesmaximal, characteristic
7#20244158C211yesmaximal, characteristic, complemented
8#20244158C211yesmaximal, characteristic, complemented
9#20244152C211yesmaximal, characteristic, complemented
10#20243981C211yesmaximal, characteristic, complemented
11#20243960C211yesmaximal, characteristic, complemented
12#20243552C211yesmaximal, characteristic, complemented
13#20243399C211yesmaximal, characteristic
14C4×#13093946C211yesmaximal, characteristic
15C47×#1939C211yesmaximal, characteristic, complemented
16C2×C4×D188C2211yescharacteristic
17C2×#13093958C2211yescharacteristic
18C2×#13093958C2211yescharacteristic
19C2×#13093958C2211yescharacteristic
20C2×#13093956C2211yescharacteristic
21C2×#13093956C2211yescharacteristic
22C2×#13093956C2211yescharacteristic
23C2×#13093946C2211yescharacteristic
24C2×#13093946C2211yescharacteristic
25C2×#13093946C2211yescharacteristic
26C2×#13093946C2211yescharacteristic
27#15689062—21no—
28#15689056—21no—
29#15689025C2211yescharacteristic
30#15689025C2211yescharacteristic
31#15689021C2211yescharacteristic
32#15689021C2211yescharacteristic
33#15689013—21no—
34#15689013—21no—
35#15689010—21no—
36#15689006—21no—
37#15688993C2211yescharacteristic
38#15688989C2211yescharacteristic
39#15688989C2211yescharacteristic
40#15688989C2211yescharacteristic
41#15688985—21no—
42C4×C4⋊Dic47C2211yescharacteristic
43C4×C4⋊Dic47C2211yescharacteristic
44C4×C4⋊Dic47C2211yescharacteristic
45#15688970—21no—
46#15688886C2211yescharacteristic
47#15688886C2211yescharacteristic
48#15688886C2211yescharacteristic
49#15688886C2211yescharacteristic
50#15688886C2211yescharacteristic
51#15688886C2211yescharacteristic
52C2×C4⋊C8×C47C2211yescharacteristic
53C2×C4⋊C8×C47C2211yescharacteristic
54C2×C4⋊C8×C47C2211yescharacteristic
55C2×C4×C8×C47C2211yescharacteristic
56C4×C4⋊C4×C47C2211yescharacteristic
57C47×#336C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C22×D188C2311yescharacteristic
60C22×C4×D47—21no—
61C4×D188—22no—
62C4×D188Q814yes—
63C2×C4⋊Dic47—21no—
64C2×C4⋊Dic47—21no—
65C2×C4⋊Dic47C2311yescharacteristic
66C2×C4⋊Dic47C2311yescharacteristic
67C2×C4⋊Dic47C2311yescharacteristic
68C2×C4⋊Dic47C2311yescharacteristic
69C2×C4⋊Dic47C2311yescharacteristic
70C2×C4⋊Dic47C2311yescharacteristic
71C2×C4⋊Dic47C2311yescharacteristic
72C2×Dic47⋊C4—21no—
73C2×Dic47⋊C4—21no—
74C2×(C2×D47)⋊C4—21no—
75C2×(C2×D47)⋊C4—21no—
76C2×(C2×D47)⋊C4—21no—
77C2×(C2×D47)⋊C4—21no—
78C2×(C2×D47)⋊C4—21no—
79C2×C4×Dic47—21no—
80C2×C4×Dic47—21no—
81C2×C4×Dic47—21no—
82#13093958—22no—
83#13093958—22no—
84#13093958—41no—
85#13093956—41no—
86#13093956—41no—
87#13093956—41no—
88#13093946—22no—
89#13093946—22no—
90#13093946—41no—
91#13093946—41no—
92C47⋊#95—21no—
93C47⋊#95—21no—
94C47⋊#95—21no—
95C47⋊#95—21no—
96C47⋊#95—21no—
97C47⋊#95—21no—
98C47⋊#95—21no—
99C47⋊#95—21no—
100C47⋊#95—21no—
101C47⋊#95—21no—
102C47⋊#95—21no—
103C22×C8×C47C2311yescharacteristic
104C22×C8×C47C2311yescharacteristic
105C22×C8×C47C2311yescharacteristic
106C22×C8×C47C2311yescharacteristic
107C2×C4⋊C4×C47D411yescharacteristic
108C2×C4⋊C4×C47D411yescharacteristic
109C2×C42×C47C2311yescharacteristic
110C2×C42×C47C2311yescharacteristic
111C2×C42×C47C2311yescharacteristic
112C4⋊C8×C47—22no—
113C4⋊C8×C47—22no—
114C4⋊C8×C47—22no—
115C4×C8×C47—22no—
116#95×C47D411yescharacteristic
117#95×C47D411yescharacteristic
118C23×D47—21no—
119C22×C4×C47C2×D411yescharacteristic
120C22×C4×C47C2×D411yescharacteristic
121C22×C4×C47C2×D411yescharacteristic
122C22×C4×C47C2×D411yescharacteristic
123C22×C4×C47C2×D411yescharacteristic
124C22×C4×C47C2×D411yescharacteristic
125C22×C4×C47C2411yescharacteristic
126C22×Dic47—21no—
127C22×Dic47—21no—
128C22×Dic47—21no—
129C22×Dic47—21no—
130C22×Dic47—21no—
131C22×Dic47—21no—
132C22×Dic47—21no—
133C2×D188—21no—
134C2×D188—21no—
135C2×D188—21no—
136C2×D188—21no—
137C2×D188—21no—
138C2×D188C2×Q812yes—
139C2×C4×D47—24no—
140C2×C4×D47—81no—
141C2×C4×D47—81no—
142C2×C8×C47—21no—
143C2×C8×C47—21no—
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#4112yes—
153C2×C8×C47#4112yes—
154C4⋊C4×C47—22no—
155C4⋊C4×C47—41no—
156C42×C47—21no—
157C42×C47—21no—
158C42×C47—21no—
159C42×C47—21no—
160C42×C47C2×Q812yes—
161C42×C47#4112yes—
162(C2×D47)⋊C4—24no—
163(C2×D47)⋊C4—42no—
164(C2×D47)⋊C4—42no—
165(C2×D47)⋊C4—81no—
166(C2×D47)⋊C4—81no—
167C4⋊Dic47—21no—
168C4⋊Dic47—21no—
169C4⋊Dic47—21no—
170C4⋊Dic47—21no—
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—42no—
181C4⋊Dic47—81no—
182C4⋊Dic47C2×Q812yes—
183Dic47⋊C4—42no—
184Dic47⋊C4—81no—
185C4×Dic47—81no—
186C4×Dic47—81no—
187C4×Dic47—81no—
188C23×C47C22×D411yescharacteristic
189C22×D47—22no—
190C22×D47—41no—
191C22×D47—41no—
192C22×D47—41no—
193C22×D47—41no—
194C22×D47—41no—
195C22×D47—41no—
196C2×C4×C47—21no—
197C2×C4×C47—21no—
198C2×C4×C47—21no—
199C2×C4×C47—21no—
200C2×C4×C47—21no—
201C2×C4×C47—21no—
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×C47C22⋊Q812yes—
212C2×C4×C47C22⋊Q812yes—
213C2×C4×C47#13512yes—
214C2×C4×C47C22×Q811yescharacteristic
215C2×C4×C47C2×#4111yescharacteristic
216C2×C4×C47C2×#4111yescharacteristic
217C2×C4×C47C2×#4111yescharacteristic
218C2×C4×C47H(5,𝔽2)11yescharacteristic
219C2×C4×C472−1+411yescharacteristic
220C2×Dic47—22no—
221C2×Dic47—41no—
222C2×Dic47—41no—
223C2×Dic47—41no—
224C2×Dic47—41no—
225C2×Dic47—41no—
226C2×Dic47—41no—
227C2×Dic47—41no—
228C2×Dic47—41no—
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—
241D188—22no—
242D188—22no—
243D188—41no—
244D188—41no—
245C4×D47—84no—
246C8×C47—22no—
247C8×C47—22no—
248C8×C47—41no—
249C8×C47—41no—
250#26094—471nomaximal, Sylow
251C22×C47C2×C22⋊Q811yescharacteristic
252C22×C47#54711yescharacteristic
253C22×C47#55011yescharacteristic
254C22×C47C2×#13511yescharacteristic
255C22×C47#57511yescharacteristic
256C22×C47#57611yescharacteristic
257C22×C47#57711yescharacteristic
258C2×D47—42no—
259C2×D47—42no—
260C2×D47—42no—
261C2×D47—81no—
262C2×D47—81no—
263C2×D47—81no—
264C2×D47—81no—
265C4×C47—22no—
266C4×C47—22no—
267C4×C47—22no—
268C4×C47—41no—
269C4×C47—41no—
270C4×C47—41no—
271C4×C47#53311yescharacteristic
272C4×C47#54411yescharacteristic
273C4×C47#55211yescharacteristic
274C4×C47#55311yescharacteristic
275Dic47—42no—
276Dic47—81no—
277Dic47—81no—
278Dic47—81no—
279Dic47—81no—
280Dic47—81no—
281Dic47—81no—
282#2570—471no—
283#2357—471no—
284#2093—471no—
285#2092—471no—
286#2065—471no—
287#2065—471no—
288#1949—471no—
289#1949—471no—
290#1948—471no—
291#1939D4711yescharacteristic, complemented
292#1921—471no—
293#1918—471no—
294#1846—471no—
295#1804—471no—
296C4×#102—471no—
297C2×C47#244111yescharacteristic
298C2×C47#307611yescharacteristic
299C2×C47#308111yescharacteristic
300C2×C47#333711yescharacteristic
301C2×C47#335511yescharacteristic
302C2×C47#339611yescharacteristic
303C2×C47#340111yescharacteristic
304D47—82no—
305C2×C4×D4—471no—
306C2×#107—471no—
307C2×#107—471no—
308C2×#107—471no—
309C2×#106—471no—
310C2×#106—471no—
311C2×#106—471no—
312C2×C4⋊C8C2×D4711yescharacteristic
313C2×C4⋊C8C2×D4711yescharacteristic
314C2×C4⋊C8C2×D4711yescharacteristic
315C2×#102—471no—
316C2×#102—471no—
317C2×#102—471no—
318C2×#102—471no—
319C2×C4×C8C2×D4711yescharacteristic
320#400—941no—
321#398—941no—
322#390—471no—
323#390—471no—
324#389—471no—
325#389—471no—
326#388—941no—
327#388—941no—
328#387—941no—
329#387—941no—
330#384—471no—
331#382—471no—
332#382—471no—
333#382—471no—
334#381—941no—
335C4×C4⋊C4—471no—
336C4×C4⋊C4—471no—
337C4×C4⋊C4—471no—
338C4×C4⋊C4C2×D4711yescharacteristic
339C4×C22⋊C4—941no—
340#340—471no—
341#340—471no—
342#340—471no—
343#340—471no—
344#340—471no—
345#340—471no—
346#336C2×D4711yescharacteristic
347#336C2×D4711yescharacteristic
348C47#2609411yescharacteristic, complemented, Sylow
349C22×D4—471no—
350C23×C4—941no—
351C22×C8C22×D4711yescharacteristic
352C22×C8C22×D4711yescharacteristic
353C22×C8C22×D4711yescharacteristic
354C22×C8C22×D4711yescharacteristic
355C4×D4—474no—
356C4×D4—942no—
357C2×C4⋊C4—471no—
358C2×C4⋊C4—471no—
359C2×C4⋊C4—471no—
360C2×C4⋊C4—471no—
361C2×C4⋊C4—471no—
362C2×C4⋊C4—471no—
363C2×C4⋊C4—471no—
364C2×C4⋊C4—941no—
365C2×C4⋊C4—941no—
366C2×C4⋊C4—941no—
367C2×C4⋊C4—941no—
368C2×C4⋊C4D18811yescharacteristic
369C2×C4⋊C4D18811yescharacteristic
370C2×C22⋊C4—941no—
371C2×C22⋊C4—941no—
372C2×C22⋊C4—941no—
373C2×C22⋊C4—941no—
374C2×C22⋊C4—941no—
375C2×C42—941no—
376C2×C42—941no—
377C2×C42—941no—
378C2×C42C22×D4711yescharacteristic
379C2×C42C22×D4711yescharacteristic
380C2×C42C22×D4711yescharacteristic
381#107—942no—
382#107—942no—
383#107—1881no—
384#106—1881no—
385#106—1881no—
386#106—1881no—
387C4⋊C8—22no—
388C4⋊C8—22no—
389C4⋊C8—22no—
390#102—942no—
391#102—942no—
392#102—1881no—
393#102—1881no—
394C4×C8—22no—
395#95—941no—
396#95—941no—
397#95—941no—
398#95—941no—
399#95—941no—
400#95—941no—
401#95—941no—
402#95—941no—
403#95—941no—
404#95—941no—
405#95—941no—
406#95D18811yescharacteristic
407#95D18811yescharacteristic
408C24—941no—
409C2×D4—472no—
410C2×D4—941no—
411C2×D4—941no—
412C2×D4—941no—
413C2×D4—941no—
414C2×D4—941no—
415C22×C4—941no—
416C22×C4—944no—
417C22×C4—941no—
418C22×C4—941no—
419C22×C4—941no—
420C22×C4—941no—
421C22×C4—941no—
422C22×C4—941no—
423C22×C4—3761no—
424C22×C4—3761no—
425C22×C4C2×D18811yescharacteristic
426C22×C4C2×D18811yescharacteristic
427C22×C4C2×D18811yescharacteristic
428C22×C4C2×D18811yescharacteristic
429C22×C4C2×D18811yescharacteristic
430C22×C4C2×D18811yescharacteristic
431C22×C4C23×D4711yescharacteristic
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8#1062535212yes—
443C2×C8#1062535412yes—
444C4⋊C4—22no—
445C4⋊C4—41no—
446C4⋊C4—472no—
447C4⋊C4—941no—
448C4⋊C4—941no—
449C4⋊C4—941no—
450C4⋊C4—941no—
451C4⋊C4—941no—
452C4⋊C4—941no—
453C4⋊C4—941no—
454C4⋊C4—941no—
455C4⋊C4—941no—
456C4⋊C4—941no—
457C4⋊C4—941no—
458C4⋊C4—941no—
459C4⋊C4—941no—
460C4⋊C4—3761no—
461C4⋊C4—3761no—
462C4⋊C4—1882no—
463C4⋊C4—1882no—
464C22⋊C4—944no—
465C22⋊C4—3761no—
466C22⋊C4—3761no—
467C22⋊C4—1882no—
468C22⋊C4—1882no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—21no—
473C42—3761no—
474C42—3761no—
475C42—3761no—
476C42#1062535212yes—
477C42Q8×D4712yes—
478C23—942no—
479C23—1881no—
480C23—1881no—
481C23—1881no—
482C23—1881no—
483C23—1881no—
484C23—1881no—
485C23C22×D18811yescharacteristic
486D4—942no—
487D4—942no—
488D4—1881no—
489D4—1881no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—942no—
506C2×C4—3764no—
507C2×C4—1881no—
508C2×C4—1881no—
509C2×C4—1881no—
510C2×C4—1881no—
511C2×C4—1881no—
512C2×C4—1881no—
513C2×C4—1881no—
514C2×C4—1881no—
515C2×C4—1881no—
516C2×C4—1881no—
517C2×C4—1881no—
518C2×C4—1881no—
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#1309400412yes—
528C2×C4#1309400412yes—
529C2×C4#1309404612yes—
530C2×C4C2×Q8×D4711yescharacteristic
531C2×C4C2×#1062535211yescharacteristic
532C2×C4C2×#1062535211yescharacteristic
533C2×C4C2×#1062535411yescharacteristic
534C2×C4#1309407011yescharacteristic
535C2×C4#1309407111yescharacteristic
536C8—22no—
537C8—22no—
538C8—41no—
539C8—41no—
540C22—3761no—
541C22—3761no—
542C22—3761no—
543C22—3761no—
544C22—1882no—
545C22—1882no—
546C22—1882no—
547C22C2×#1309400411yescharacteristic
548C22#1568977711yescharacteristic
549C22#1568979511yescharacteristic
550C22C2×#1309404611yescharacteristic
551C22#1568992311yescharacteristic
552C22#1568992811yescharacteristic
553C22#1568993511yescharacteristic
554C4—22no—
555C4—22no—
556C4—22no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—3761no—
561C4—3761no—
562C4—3761no—
563C4—3761no—
564C4—3761no—
565C4—3761no—
566C4—1882no—
567C4#1568967811yescharacteristic
568C4#1568975311yescharacteristic
569C4#1568981511yescharacteristic
570C4#1568982511yescharacteristic
571C2—3762no—
572C2#2024709911yescharacteristic
573C2#2025317811yescharacteristic
574C2#2025322011yescharacteristic
575C2#2025576911yescharacteristic
576C2#2025599311yescharacteristic
577C2#2025640111yescharacteristic
578C2#2025645611yescharacteristic
subgroupG/H
centerC23C22×D188
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#1939C2
socleC23×C47C22×D4
prime radicalC22×D188C23
hypercenter#1939D47
hypocenterC47#26094
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1939

Complements

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

NH ≅ G/Ntype
1. #20248622C2semidirect
7. #20244158C2semidirect
8. #20244158C2semidirect
9. #20244152C2semidirect
10. #20243981C2semidirect
11. #20243960C2semidirect
12. #20243552C2semidirect
15. C47×#1939C2semidirect
291. #1939D47semidirect
348. C47#26094semidirect

Maximal subgroups

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

subgroupindex
#202486222
#202463592
#202449152
#202449082
#202447612
#202441582
#202441522
#202439812
#202439602
#202435522
#202433992
C4×#130939462
C47×#19392
#2609447