Finite Group Databasebeta

← #26318985

Subgroups — #26318985

Order 12032.

664 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20246129C211yesmaximal, characteristic, complemented
2#20244859C211yesmaximal, characteristic, complemented
3#20244791C211yesmaximal, characteristic
4#20244726C211yesmaximal, characteristic, complemented
5#20244534C211yesmaximal, characteristic
6#20244012C211yesmaximal, characteristic
7#20244005C211yesmaximal, characteristic
8#20243980C211yesmaximal, characteristic, complemented
9#20243977C211yesmaximal, characteristic, complemented
10#20243973C211yesmaximal, characteristic, complemented
11#20243956C211yesmaximal, characteristic, complemented
12#20243635C211yesmaximal, characteristic
13#20243635C211yesmaximal, characteristic
14#20243533C211yesmaximal, characteristic, complemented
15C47×#2319C211yesmaximal, characteristic
16C2×#13094016C2211yescharacteristic
17C2×#13093957C2211yescharacteristic
18C2×#13093957C2211yescharacteristic
19C2×#13093957C2211yescharacteristic
20C2×#13093955C2211yescharacteristic
21C2×#13093945C2211yescharacteristic
22C2×#13093945C2211yescharacteristic
23C2×#13093945C2211yescharacteristic
24C2×#13093945C2211yescharacteristic
25#15689021C2211yescharacteristic
26#15689021C2211yescharacteristic
27#15689020—21no—
28#15689020—21no—
29#15689010—21no—
30#15689010—21no—
31#15688993C2211yescharacteristic
32C4×C4⋊Dic47C2211yescharacteristic
33C4×C4⋊Dic47C2211yescharacteristic
34#15688885C2211yescharacteristic
35#15688885C2211yescharacteristic
36#15688885C2211yescharacteristic
37#15688885C2211yescharacteristic
38#15688885C2211yescharacteristic
39#15688885C2211yescharacteristic
40#15688885C2211yescharacteristic
41#15688885C2211yescharacteristic
42#15688878C2211yescharacteristic
43#15688878C2211yescharacteristic
44#15688878C2211yescharacteristic
45#15688878C2211yescharacteristic
46#15688878C2211yescharacteristic
47#15688878C2211yescharacteristic
48C2×C4×D4×C47C2211yescharacteristic
49C47×#390C2211yescharacteristic
50C47×#390C2211yescharacteristic
51C47×#389C2211yescharacteristic
52C47×#389C2211yescharacteristic
53C47×#388—21no—
54C47×#388—21no—
55C47×#381—21no—
56C47×#380—21no—
57C4×C4⋊C4×C47C2211yescharacteristic
58C47×#376C2211yescharacteristic
59C22×C47⋊C8C2311yescharacteristic
60C22×C47⋊C8C2311yescharacteristic
61C22×C47⋊C8C2311yescharacteristic
62C22×C47⋊C8C2311yescharacteristic
63#13094016—22no—
64#13094016—22no—
65C2×C4⋊Dic47—21no—
66C2×C4⋊Dic47—21no—
67C2×C4⋊Dic47C2311yescharacteristic
68C2×C4⋊Dic47C2311yescharacteristic
69C2×C4⋊Dic47C2311yescharacteristic
70C2×C4⋊Dic47C2311yescharacteristic
71C2×Dic47⋊C4—21no—
72C2×Dic47⋊C4—21no—
73C2×Dic47⋊C4—21no—
74C2×Dic47⋊C4—21no—
75C2×C4×Dic47—21no—
76C2×C4×Dic47—21no—
77#13093957—22no—
78#13093957—22no—
79#13093957—22no—
80#13093955—22no—
81#13093945—22no—
82#13093945—22no—
83#13093945—22no—
84#13093945—22no—
85C47⋊#95—21no—
86C47⋊#95—21no—
87C47⋊#95—21no—
88C47⋊#95—21no—
89C22×D4×C47C2311yescharacteristic
90C23×C4×C47—21no—
91C4×D4×C47—22no—
92C4×D4×C47—22no—
93C2×C4⋊C4×C47—21no—
94C2×C4⋊C4×C47—21no—
95C2×C4⋊C4×C47C2311yescharacteristic
96C2×C4⋊C4×C47C2311yescharacteristic
97C2×C4⋊C4×C47C2311yescharacteristic
98C2×C22⋊C4×C47—21no—
99C2×C22⋊C4×C47—21no—
100C2×C22⋊C4×C47—21no—
101C2×C22⋊C4×C47—21no—
102C2×C22⋊C4×C47—21no—
103C2×C42×C47—21no—
104C2×C42×C47C2311yescharacteristic
105C2×C42×C47C2311yescharacteristic
106C2×C42×C47C2311yescharacteristic
107#95×C47—21no—
108#95×C47—21no—
109#95×C47—21no—
110#95×C47D411yescharacteristic
111#95×C47D411yescharacteristic
112#95×C47D411yescharacteristic
113#95×C47D411yescharacteristic
114C24×C47—21no—
115C2×D4×C47—21no—
116C2×D4×C47—21no—
117C2×D4×C47—21no—
118C2×D4×C47—21no—
119C2×D4×C47—21no—
120C2×D4×C47#4112yes—
121C22×C4×C47—21no—
122C22×C4×C47—24no—
123C22×C4×C47—21no—
124C22×C4×C47—21no—
125C22×C4×C47—81no—
126C22×C4×C47—81no—
127C22×C4×C47C2×D411yescharacteristic
128C22×C4×C47C2×D411yescharacteristic
129C22×C4×C47C2×D411yescharacteristic
130C22×C4×C47C2×D411yescharacteristic
131C22×C4×C47C2×D411yescharacteristic
132C22×C4×C47C2×D411yescharacteristic
133C22×C4×C47C2411yescharacteristic
134C22×Dic47—21no—
135C22×Dic47—21no—
136C22×Dic47—21no—
137C22×Dic47—21no—
138C4⋊C4×C47—21no—
139C4⋊C4×C47—21no—
140C4⋊C4×C47—21no—
141C4⋊C4×C47—21no—
142C4⋊C4×C47—21no—
143C4⋊C4×C47—81no—
144C4⋊C4×C47—81no—
145C4⋊C4×C47#4112yes—
146C22⋊C4×C47—24no—
147C22⋊C4×C47—81no—
148C22⋊C4×C47—81no—
149C22⋊C4×C47—81no—
150C22⋊C4×C47—81no—
151C42×C47—21no—
152C42×C47—21no—
153C42×C47—21no—
154C42×C47—21no—
155C42×C47—21no—
156C42×C47—21no—
157C42×C47—81no—
158C4⋊Dic47—21no—
159C4⋊Dic47—21no—
160C4⋊Dic47—21no—
161C4⋊Dic47—21no—
162C4⋊Dic47—21no—
163C4⋊Dic47—21no—
164C4⋊Dic47—81no—
165C4⋊Dic47—81no—
166C4⋊Dic47#4112yes—
167C4⋊Dic47#4112yes—
168Dic47⋊C4—24no—
169Dic47⋊C4—24no—
170Dic47⋊C4—81no—
171Dic47⋊C4—81no—
172C4×Dic47—81no—
173C4×Dic47—81no—
174C2×C47⋊C8—21no—
175C2×C47⋊C8—21no—
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—
186C23×C47—22no—
187C23×C47—41no—
188C23×C47—41no—
189C23×C47—41no—
190C23×C47—41no—
191C23×C47—41no—
192C23×C47—41no—
193C23×C47C22×D411yescharacteristic
194D4×C47—22no—
195D4×C47—22no—
196D4×C47—41no—
197D4×C47—41no—
198C2×C4×C47—21no—
199C2×C4×C47—21no—
200C2×C4×C47—21no—
201C2×C4×C47—21no—
202C2×C4×C47—22no—
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×C47—21no—
216C2×C4×C47—21no—
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×C47—84no—
226C2×C4×C47C2×#4111yescharacteristic
227C2×C4×C47C2×#4111yescharacteristic
228C2×C4×C47C2×#4111yescharacteristic
229C2×C4×C47C2×#4111yescharacteristic
230C2×C4×C472−1+411yescharacteristic
231C2×C4×C472−1+411yescharacteristic
232C2×Dic47—22no—
233C2×Dic47—22no—
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—
244C47⋊C8—41no—
245C47⋊C8—41no—
246C47⋊C8—41no—
247C47⋊C8—41no—
248#29404—471nomaximal, Sylow
249C22×C47—42no—
250C22×C47—42no—
251C22×C47—42no—
252C22×C47—81no—
253C22×C47—81no—
254C22×C47—81no—
255C22×C47—81no—
256C22×C47#52511yescharacteristic
257C22×C47#52511yescharacteristic
258C22×C47#53611yescharacteristic
259C22×C47#57611yescharacteristic
260C22×C47#57611yescharacteristic
261C22×C47#57711yescharacteristic
262C22×C47#57811yescharacteristic
263C4×C47—41no—
264C4×C47—41no—
265C4×C47—41no—
266C4×C47—42no—
267C4×C47—41no—
268C4×C47—41no—
269C4×C47—41no—
270C4×C47—81no—
271C4×C47—81no—
272C4×C47#55211yescharacteristic
273C4×C47#55211yescharacteristic
274C4×C47#55611yescharacteristic
275C4×C47#55611yescharacteristic
276Dic47—42no—
277Dic47—42no—
278Dic47—81no—
279Dic47—81no—
280#2330—471no—
281#2319D4711yescharacteristic
282#2083—471no—
283#2071—471no—
284#2059—471no—
285#2025—471no—
286#1926—471no—
287#1925—471no—
288#1921—471no—
289#1921—471no—
290#1920—471no—
291#1918—471no—
292#1862—471no—
293#1862—471no—
294#1840—471no—
295C2×C47—82no—
296C2×C47#259911yescharacteristic
297C2×C47#311911yescharacteristic
298C2×C47#312011yescharacteristic
299C2×C47#312211yescharacteristic
300C2×C47#312411yescharacteristic
301C2×C47#324111yescharacteristic
302C2×C47#324311yescharacteristic
303C2×#125—471no—
304C2×C4×D4C2×D4711yescharacteristic
305C2×#107—471no—
306C2×#107—471no—
307C2×#107—471no—
308C2×#106—471no—
309C2×#102—471no—
310C2×#102—471no—
311C2×#102—471no—
312C2×#102—471no—
313#390C2×D4711yescharacteristic
314#390C2×D4711yescharacteristic
315#389—471no—
316#389—471no—
317#389—941no—
318#389—941no—
319#389C2×D4711yescharacteristic
320#389C2×D4711yescharacteristic
321#388—21no—
322#388—21no—
323#387—941no—
324#387—941no—
325#384—471no—
326#381—21no—
327#380—21no—
328C4×C4⋊C4—471no—
329C4×C4⋊C4—471no—
330C4×C4⋊C4C2×D4711yescharacteristic
331#376C2×D4711yescharacteristic
332#340—471no—
333#340—471no—
334#340—471no—
335#340—471no—
336#340—471no—
337#340—471no—
338#340—471no—
339#340—471no—
340#336—471no—
341#336—471no—
342#336—471no—
343#336—471no—
344#336—471no—
345#336—471no—
346C47#2940411yescharacteristic, complemented, Sylow
347C22×D4C22×D4711yescharacteristic
348C23×C4—21no—
349C22×C8—471no—
350C22×C8—471no—
351C22×C8—471no—
352C22×C8—471no—
353#125—942no—
354#125—942no—
355C4×D4—22no—
356C4×D4—22no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—471no—
360C2×C4⋊C4—471no—
361C2×C4⋊C4—471no—
362C2×C4⋊C4—471no—
363C2×C4⋊C4—941no—
364C2×C4⋊C4—941no—
365C2×C4⋊C4—941no—
366C2×C4⋊C4—941no—
367C2×C4⋊C4—941no—
368C2×C4⋊C4—941no—
369C2×C4⋊C4C22×D4711yescharacteristic
370C2×C4⋊C4C22×D4711yescharacteristic
371C2×C4⋊C4C22×D4711yescharacteristic
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C42—21no—
378C2×C42—941no—
379C2×C42—941no—
380C2×C42C22×D4711yescharacteristic
381C2×C42C22×D4711yescharacteristic
382C2×C42C22×D4711yescharacteristic
383#107—942no—
384#107—942no—
385#107—942no—
386#106—942no—
387#102—942no—
388#102—942no—
389#102—942no—
390#102—942no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—941no—
395#95—941no—
396#95—941no—
397#95—941no—
398#95C22⋊D4711yescharacteristic
399#95C22⋊D4711yescharacteristic
400#95C22⋊D4711yescharacteristic
401#95C22⋊D4711yescharacteristic
402C24—21no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4#1062535012yes—
409C22×C4—21no—
410C22×C4—24no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—81no—
414C22×C4—81no—
415C22×C4—941no—
416C22×C4—941no—
417C22×C4—941no—
418C22×C4—941no—
419C22×C4C2×C22⋊D4711yescharacteristic
420C22×C4C2×C22⋊D4711yescharacteristic
421C22×C4C2×C22⋊D4711yescharacteristic
422C22×C4C2×C22⋊D4711yescharacteristic
423C22×C4C2×C22⋊D4711yescharacteristic
424C22×C4C2×C22⋊D4711yescharacteristic
425C22×C4C23×D4711yescharacteristic
426C2×C8—941no—
427C2×C8—941no—
428C2×C8—941no—
429C2×C8—941no—
430C2×C8—941no—
431C2×C8—941no—
432C2×C8—941no—
433C2×C8—941no—
434C2×C8—941no—
435C2×C8—941no—
436C2×C8—941no—
437C2×C8—941no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—81no—
444C4⋊C4—81no—
445C4⋊C4—472no—
446C4⋊C4—472no—
447C4⋊C4—944no—
448C4⋊C4—944no—
449C4⋊C4—941no—
450C4⋊C4—941no—
451C4⋊C4—941no—
452C4⋊C4—941no—
453C4⋊C4—941no—
454C4⋊C4—941no—
455C4⋊C4—3761no—
456C4⋊C4—3761no—
457C4⋊C4—3761no—
458C4⋊C4—3761no—
459C4⋊C4#1062535012yes—
460C22⋊C4—24no—
461C22⋊C4—81no—
462C22⋊C4—81no—
463C22⋊C4—81no—
464C22⋊C4—81no—
465C42—21no—
466C42—21no—
467C42—21no—
468C42—21no—
469C42—21no—
470C42—21no—
471C42—81no—
472C42—3761no—
473C42—3761no—
474C23—22no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23—41no—
481C23C22×C22⋊D4711yescharacteristic
482D4—22no—
483D4—22no—
484D4—41no—
485D4—41no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—22no—
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—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—84no—
514C2×C4—942no—
515C2×C4—942no—
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#41×D4711yescharacteristic
527C2×C4#41×D4711yescharacteristic
528C2×C4C2×#1062535011yescharacteristic
529C2×C4C2×#1062535011yescharacteristic
530C2×C4#1309407111yescharacteristic
531C2×C4#1309407111yescharacteristic
532C8—1881no—
533C8—1881no—
534C8—1881no—
535C8—1881no—
536C22—42no—
537C22—42no—
538C22—42no—
539C22—81no—
540C22—81no—
541C22—81no—
542C22—81no—
543C22#1568963011yescharacteristic
544C22#1568963411yescharacteristic
545C22#1568969411yescharacteristic
546C22#1568992611yescharacteristic
547C22#1568992611yescharacteristic
548C22#1568993411yescharacteristic
549C22#1568993811yescharacteristic
550C4—41no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—42no—
555C4—41no—
556C4—41no—
557C4—81no—
558C4—81no—
559C4—3761no—
560C4—3761no—
561C4—1882no—
562C4—1882no—
563C4#1568980611yescharacteristic
564C4#1568980611yescharacteristic
565C4#1568984111yescharacteristic
566C4#1568984111yescharacteristic
567C2—82no—
568C2#2024896511yescharacteristic
569C2#2025358111yescharacteristic
570C2#2025360211yescharacteristic
571C2#2025363111yescharacteristic
572C2#2025364411yescharacteristic
573C2#2025463511yescharacteristic
574C2#2025466511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2319C2
socleC23×C47C22×D4
prime radicalC22×D4×C47C23
hypercenter#2319D47
hypocenterC47#29404
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ #376 ◁ #2319

Complements

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

NH ≅ G/Ntype
1. #20246129C2semidirect
2. #20244859C2semidirect
4. #20244726C2semidirect
8. #20243980C2semidirect
9. #20243977C2semidirect
10. #20243973C2semidirect
11. #20243956C2semidirect
14. #20243533C2semidirect
346. C47#29404semidirect

Maximal subgroups

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

subgroupindex
#202461292
#202448592
#202447912
#202447262
#202445342
#202440122
#202440052
#202439802
#202439772
#202439732
#202439562
#202436352
#202435332
C47×#23192
#2940447