Finite Group Databasebeta

← #26275321

Subgroups — #26275321

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#20244916C211yesmaximal, characteristic
3#20244909C211yesmaximal, characteristic
4#20244762C211yesmaximal, characteristic
5#20244762C211yesmaximal, characteristic
6#20244156C211yesmaximal, characteristic, complemented
7#20244154C211yesmaximal, characteristic, complemented
8#20244151C211yesmaximal, characteristic, complemented
9#20244107C211yesmaximal, characteristic, complemented
10#20243980C211yesmaximal, characteristic, complemented
11#20243959C211yesmaximal, characteristic, complemented
12#20243550C211yesmaximal, characteristic, complemented
13#20243398C211yesmaximal, characteristic
14C4×#13093945C211yesmaximal, characteristic
15C47×#2357C211yesmaximal, characteristic
16C2×#13093957C2211yescharacteristic
17C2×#13093957C2211yescharacteristic
18C2×#13093957C2211yescharacteristic
19C2×#13093955C2211yescharacteristic
20C2×#13093955C2211yescharacteristic
21C2×#13093955C2211yescharacteristic
22C2×C4⋊(C47⋊C8)C2211yescharacteristic
23C2×C4⋊(C47⋊C8)C2211yescharacteristic
24C2×C4⋊(C47⋊C8)C2211yescharacteristic
25C2×#13093945C2211yescharacteristic
26C2×#13093945C2211yescharacteristic
27C2×#13093945C2211yescharacteristic
28C2×#13093945C2211yescharacteristic
29C2×C4×C47⋊C8C2211yescharacteristic
30#15689062—21no—
31#15689056—21no—
32#15689021C2211yescharacteristic
33#15689021C2211yescharacteristic
34#15689010—21no—
35#15689006—21no—
36#15688993C2211yescharacteristic
37#15688989C2211yescharacteristic
38#15688989C2211yescharacteristic
39C4×C4⋊Dic47C2211yescharacteristic
40#15688885C2211yescharacteristic
41#15688885C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688878C2211yescharacteristic
47#15688878C2211yescharacteristic
48C2×C4×D4×C47C2211yescharacteristic
49C47×#390C2211yescharacteristic
50C47×#390C2211yescharacteristic
51C47×#388—21no—
52C47×#388—21no—
53C47×#382C2211yescharacteristic
54C47×#381—21no—
55C4×C4⋊C4×C47C2211yescharacteristic
56C4×C4⋊C4×C47C2211yescharacteristic
57C4×C4⋊C4×C47C2211yescharacteristic
58C4×C22⋊C4×C47—21no—
59C22×C47⋊C8C2311yescharacteristic
60C22×C47⋊C8C2311yescharacteristic
61C22×C47⋊C8C2311yescharacteristic
62C22×C47⋊C8C2311yescharacteristic
63C2×C4⋊Dic47—21no—
64C2×C4⋊Dic47—21no—
65C2×C4⋊Dic47C2311yescharacteristic
66C2×C4⋊Dic47C2311yescharacteristic
67C2×C4⋊Dic47C2311yescharacteristic
68C2×C4⋊Dic47C2311yescharacteristic
69C2×Dic47⋊C4—21no—
70C2×Dic47⋊C4—21no—
71C2×C4×Dic47—21no—
72#13093957—22no—
73#13093957—22no—
74#13093957—41no—
75#13093955—41no—
76#13093955—41no—
77#13093955—41no—
78C4⋊(C47⋊C8)—22no—
79C4⋊(C47⋊C8)—22no—
80C4⋊(C47⋊C8)—22no—
81#13093945—22no—
82#13093945—22no—
83#13093945—41no—
84#13093945—41no—
85C4×C47⋊C8—22no—
86C47⋊#95—21no—
87C47⋊#95—21no—
88C47⋊#95—21no—
89C47⋊#95—21no—
90C47⋊#95—21no—
91C47⋊#95—21no—
92C47⋊#95—21no—
93C22×D4×C47C2311yescharacteristic
94C23×C4×C47—21no—
95C4×D4×C47—22no—
96C4×D4×C47Q814yes—
97C2×C4⋊C4×C47D411yescharacteristic
98C2×C4⋊C4×C47D411yescharacteristic
99C2×C4⋊C4×C47C2311yescharacteristic
100C2×C4⋊C4×C47C2311yescharacteristic
101C2×C4⋊C4×C47C2311yescharacteristic
102C2×C22⋊C4×C47—21no—
103C2×C22⋊C4×C47—21no—
104C2×C22⋊C4×C47—21no—
105C2×C22⋊C4×C47—21no—
106C2×C22⋊C4×C47—21no—
107C2×C42×C47—21no—
108C2×C42×C47—21no—
109C2×C42×C47C2311yescharacteristic
110C2×C42×C47C2311yescharacteristic
111C2×C42×C47C2311yescharacteristic
112#95×C47—21no—
113#95×C47—21no—
114#95×C47—21no—
115#95×C47—21no—
116#95×C47D411yescharacteristic
117#95×C47D411yescharacteristic
118C24×C47—21no—
119C2×D4×C47—21no—
120C2×D4×C47—21no—
121C2×D4×C47—21no—
122C2×D4×C47—21no—
123C2×D4×C47—21no—
124C2×D4×C47C2×Q812yes—
125C22×C4×C47—21no—
126C22×C4×C47—24no—
127C22×C4×C47—21no—
128C22×C4×C47—21no—
129C22×C4×C47—81no—
130C22×C4×C47—81no—
131C22×C4×C47C2×D411yescharacteristic
132C22×C4×C47C2×D411yescharacteristic
133C22×C4×C47C2×D411yescharacteristic
134C22×C4×C47C2×D411yescharacteristic
135C22×C4×C47C2×D411yescharacteristic
136C22×C4×C47C2×D411yescharacteristic
137C22×C4×C47C2411yescharacteristic
138C22×Dic47—21no—
139C22×Dic47—21no—
140C22×Dic47—21no—
141C22×Dic47—21no—
142C4⋊C4×C47—22no—
143C4⋊C4×C47—21no—
144C4⋊C4×C47—21no—
145C4⋊C4×C47—21no—
146C4⋊C4×C47—21no—
147C4⋊C4×C47—21no—
148C4⋊C4×C47—41no—
149C4⋊C4×C47C2×Q812yes—
150C22⋊C4×C47—24no—
151C22⋊C4×C47—42no—
152C22⋊C4×C47—42no—
153C22⋊C4×C47—81no—
154C22⋊C4×C47—81no—
155C42×C47—21no—
156C42×C47—21no—
157C42×C47—21no—
158C42×C47—21no—
159C42×C47—81no—
160C42×C47—81no—
161C42×C47C2×Q812yes—
162C42×C47#4112yes—
163C4⋊Dic47—21no—
164C4⋊Dic47—21no—
165C4⋊Dic47—21no—
166C4⋊Dic47—21no—
167C4⋊Dic47—21no—
168C4⋊Dic47—21no—
169C4⋊Dic47—21no—
170C4⋊Dic47—21no—
171C4⋊Dic47—42no—
172C4⋊Dic47—81no—
173Dic47⋊C4—42no—
174Dic47⋊C4—81no—
175C4×Dic47—81no—
176C2×C47⋊C8—21no—
177C2×C47⋊C8—21no—
178C2×C47⋊C8—21no—
179C2×C47⋊C8—21no—
180C2×C47⋊C8—21no—
181C2×C47⋊C8—21no—
182C2×C47⋊C8—21no—
183C2×C47⋊C8—21no—
184C2×C47⋊C8—21no—
185C2×C47⋊C8—21no—
186C2×C47⋊C8#4112yes—
187C2×C47⋊C8#4112yes—
188C23×C47—22no—
189C23×C47—41no—
190C23×C47—41no—
191C23×C47—41no—
192C23×C47—41no—
193C23×C47—41no—
194C23×C47—41no—
195C23×C47C22×D411yescharacteristic
196D4×C47—22no—
197D4×C47—22no—
198D4×C47—41no—
199D4×C47—41no—
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—22no—
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×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—84no—
225C2×C4×C47C22⋊Q812yes—
226C2×C4×C47C22⋊Q812yes—
227C2×C4×C47#13512yes—
228C2×C4×C47C22×Q811yescharacteristic
229C2×C4×C47C2×#4111yescharacteristic
230C2×C4×C47C2×#4111yescharacteristic
231C2×C4×C47C2×#4111yescharacteristic
232C2×C4×C47H(5,𝔽2)11yescharacteristic
233C2×C4×C472−1+411yescharacteristic
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—
246C47⋊C8—22no—
247C47⋊C8—22no—
248C47⋊C8—41no—
249C47⋊C8—41no—
250#26094—471nomaximal, Sylow
251C22×C47—42no—
252C22×C47—42no—
253C22×C47—42no—
254C22×C47—81no—
255C22×C47—81no—
256C22×C47—81no—
257C22×C47—81no—
258C22×C47C2×C22⋊Q811yescharacteristic
259C22×C47#54711yescharacteristic
260C22×C47#55011yescharacteristic
261C22×C47C2×#13511yescharacteristic
262C22×C47#57511yescharacteristic
263C22×C47#57611yescharacteristic
264C22×C47#57711yescharacteristic
265C4×C47—22no—
266C4×C47—22no—
267C4×C47—22no—
268C4×C47—42no—
269C4×C47—41no—
270C4×C47—41no—
271C4×C47—41no—
272C4×C47—81no—
273C4×C47—81no—
274C4×C47#53311yescharacteristic
275C4×C47#54411yescharacteristic
276C4×C47#55211yescharacteristic
277C4×C47#55311yescharacteristic
278Dic47—81no—
279Dic47—81no—
280Dic47—81no—
281Dic47—81no—
282#2570—471no—
283#2357D4711yescharacteristic
284#2093—471no—
285#2092—471no—
286#2065—471no—
287#2065—471no—
288#1949—471no—
289#1949—471no—
290#1948—471no—
291#1939—471no—
292#1921—471no—
293#1918—471no—
294#1846—471no—
295#1804—471no—
296C4×#102—471no—
297C2×C47—82no—
298C2×C47#244111yescharacteristic
299C2×C47#307611yescharacteristic
300C2×C47#308111yescharacteristic
301C2×C47#333711yescharacteristic
302C2×C47#335511yescharacteristic
303C2×C47#339611yescharacteristic
304C2×C47#340111yescharacteristic
305C2×C4×D4C2×D4711yescharacteristic
306C2×#107—471no—
307C2×#107—471no—
308C2×#107—471no—
309C2×#106—471no—
310C2×#106—471no—
311C2×#106—471no—
312C2×C4⋊C8—471no—
313C2×C4⋊C8—471no—
314C2×C4⋊C8—471no—
315C2×#102—471no—
316C2×#102—471no—
317C2×#102—471no—
318C2×#102—471no—
319C2×C4×C8—471no—
320#400—941no—
321#398—941no—
322#390C2×D4711yescharacteristic
323#390C2×D4711yescharacteristic
324#389—471no—
325#389—471no—
326#388—21no—
327#388—21no—
328#387—941no—
329#387—941no—
330#384—471no—
331#382—471no—
332#382—471no—
333#382C2×D4711yescharacteristic
334#381—21no—
335C4×C4⋊C4—471no—
336C4×C4⋊C4C2×D4711yescharacteristic
337C4×C4⋊C4C2×D4711yescharacteristic
338C4×C4⋊C4C2×D4711yescharacteristic
339C4×C22⋊C4—21no—
340#340—471no—
341#340—471no—
342#340—471no—
343#340—471no—
344#340—471no—
345#340—471no—
346#336—471no—
347#336—471no—
348C47#2609411yescharacteristic, complemented, Sylow
349C22×D4C22×D4711yescharacteristic
350C23×C4—21no—
351C22×C8—471no—
352C22×C8—471no—
353C22×C8—471no—
354C22×C8—471no—
355C4×D4—22no—
356C4×D4Dic9414yes—
357C2×C4⋊C4—471no—
358C2×C4⋊C4—471no—
359C2×C4⋊C4—471no—
360C2×C4⋊C4—471no—
361C2×C4⋊C4—941no—
362C2×C4⋊C4—941no—
363C2×C4⋊C4—941no—
364C2×C4⋊C4—941no—
365C2×C4⋊C4C22⋊D4711yescharacteristic
366C2×C4⋊C4C22⋊D4711yescharacteristic
367C2×C4⋊C4C22×D4711yescharacteristic
368C2×C4⋊C4C22×D4711yescharacteristic
369C2×C4⋊C4C22×D4711yescharacteristic
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C42—21no—
376C2×C42—21no—
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—942no—
388C4⋊C8—942no—
389C4⋊C8—942no—
390#102—942no—
391#102—942no—
392#102—1881no—
393#102—1881no—
394C4×C8—942no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—941no—
400#95—941no—
401#95—941no—
402#95—941no—
403#95—941no—
404#95—941no—
405#95—941no—
406#95C22⋊D4711yescharacteristic
407#95C22⋊D4711yescharacteristic
408C24—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4C2×Dic9412yes—
415C22×C4—21no—
416C22×C4—24no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—81no—
420C22×C4—81no—
421C22×C4—941no—
422C22×C4—941no—
423C22×C4—941no—
424C22×C4—941no—
425C22×C4C2×C22⋊D4711yescharacteristic
426C22×C4C2×C22⋊D4711yescharacteristic
427C22×C4C2×C22⋊D4711yescharacteristic
428C22×C4C2×C22⋊D4711yescharacteristic
429C22×C4C2×C22⋊D4711yescharacteristic
430C22×C4C2×C22⋊D4711yescharacteristic
431C22×C4C23×D4711yescharacteristic
432C2×C8—472no—
433C2×C8—472no—
434C2×C8—941no—
435C2×C8—941no—
436C2×C8—941no—
437C2×C8—941no—
438C2×C8—941no—
439C2×C8—941no—
440C2×C8—941no—
441C2×C8—941no—
442C2×C8—941no—
443C2×C8—941no—
444C4⋊C4—22no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—41no—
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—3761no—
460C4⋊C4—3761no—
461C4⋊C4—1882no—
462C4⋊C4—1882no—
463C4⋊C4C2×Dic9412yes—
464C22⋊C4—24no—
465C22⋊C4—42no—
466C22⋊C4—42no—
467C22⋊C4—81no—
468C22⋊C4—81no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—21no—
473C42—81no—
474C42—81no—
475C42—3761no—
476C42C2×Dic9412yes—
477C42#1062535012yes—
478C23—22no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23C22×C22⋊D4711yescharacteristic
486D4—22no—
487D4—22no—
488D4—41no—
489D4—41no—
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—22no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—84no—
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#1309400312yes—
528C2×C4#1309400312yes—
529C2×C4#1309404412yes—
530C2×C4C22×Dic9411yescharacteristic
531C2×C4#41×D4711yescharacteristic
532C2×C4#41×D4711yescharacteristic
533C2×C4C2×#1062535011yescharacteristic
534C2×C4#1309407011yescharacteristic
535C2×C4#1309407111yescharacteristic
536C8—942no—
537C8—942no—
538C8—1881no—
539C8—1881no—
540C22—42no—
541C22—42no—
542C22—42no—
543C22—81no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22C2×#1309400311yescharacteristic
548C22#1568977211yescharacteristic
549C22#1568979211yescharacteristic
550C22C2×#1309404411yescharacteristic
551C22#1568992111yescharacteristic
552C22#1568992611yescharacteristic
553C22#1568993411yescharacteristic
554C4—22no—
555C4—22no—
556C4—22no—
557C4—41no—
558C4—42no—
559C4—41no—
560C4—41no—
561C4—81no—
562C4—81no—
563C4—3761no—
564C4—3761no—
565C4—3761no—
566C4—3761no—
567C4#1568967611yescharacteristic
568C4#1568975111yescharacteristic
569C4#1568981211yescharacteristic
570C4#1568981711yescharacteristic
571C2—82no—
572C2#2024709511yescharacteristic
573C2#2025317611yescharacteristic
574C2#2025321911yescharacteristic
575C2#2025576111yescharacteristic
576C2#2025598811yescharacteristic
577C2#2025639611yescharacteristic
578C2#2025644811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2357C2
socleC23×C47C22×D4
prime radicalC22×D4×C47C23
hypercenter#2357D47
hypocenterC47#26094
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2357

Complements

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

NH ≅ G/Ntype
1. #20248622C2semidirect
6. #20244156C2semidirect
7. #20244154C2semidirect
8. #20244151C2semidirect
9. #20244107C2semidirect
10. #20243980C2semidirect
11. #20243959C2semidirect
12. #20243550C2semidirect
348. C47#26094semidirect

Maximal subgroups

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

subgroupindex
#202486222
#202449162
#202449092
#202447622
#202441562
#202441542
#202441512
#202441072
#202439802
#202439592
#202435502
#202433982
C4×#130939452
C47×#23572
#2609447