Finite Group Databasebeta

← #26234045

Subgroups — #26234045

Order 12032.

782 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689166C211yesmaximal, characteristic
2#20246263C211yesmaximal, characteristic
3#20244128C211yesmaximal, characteristic, complemented
4#20244113C211yesmaximal, characteristic, complemented
5#20243980C211yesmaximal, characteristic, complemented
6#20243970C211yesmaximal, characteristic, complemented
7#20243963C211yesmaximal, characteristic, complemented
8#20243959C211yesmaximal, characteristic, complemented
9#20243483C211yesmaximal, characteristic
10#20243472C211yesmaximal, characteristic
11#20243419C211yesmaximal, characteristic
12#20243286C211yesmaximal, characteristic, complemented
13C4×#13093957C211yesmaximal, characteristic, complemented
14#20243172C211yesmaximal, characteristic
15C47×#2347C211yesmaximal, characteristic
16C22×#10625329C2211yescharacteristic
17C22×C4⋊Dic47C2211yescharacteristic
18#15689166C418yescomplemented
19C2×#13093957C2211yescharacteristic
20C2×#13093957C2211yescharacteristic
21C2×#13093957C2211yescharacteristic
22C2×#13093955C2211yescharacteristic
23C2×#13093955C2211yescharacteristic
24C2×#13093955C2211yescharacteristic
25C2×C22⋊(C47⋊C8)C2211yescharacteristic
26C2×#13093935C2211yescharacteristic
27C2×C4×C47⋊C8C2211yescharacteristic
28#15689021C2211yescharacteristic
29#15689021C2211yescharacteristic
30#15689006—21no—
31#15689006—21no—
32#15688983C2211yescharacteristic
33#15688981—21no—
34C4×C4⋊Dic47C2211yescharacteristic
35C4×C4⋊Dic47C2211yescharacteristic
36C22⋊C4×Dic47—21no—
37#15688885C2211yescharacteristic
38#15688885C2211yescharacteristic
39#15688885C2211yescharacteristic
40#15688885C2211yescharacteristic
41#15688885C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688878C2211yescharacteristic
48#15688878C2211yescharacteristic
49C2×#117×C47C2211yescharacteristic
50C47×#389C2211yescharacteristic
51C47×#389C2211yescharacteristic
52C47×#388—21no—
53C47×#388—21no—
54C47×#383—21no—
55C47×#380C2211yescharacteristic
56C4×C4⋊C4×C47—21no—
57C4×C4⋊C4×C47C2211yescharacteristic
58C4×C4⋊C4×C47C2211yescharacteristic
59C4×C22⋊C4×C47C2211yescharacteristic
60C23×Dic47—21no—
61C2×#10625329—22no—
62C2×#10625329—22no—
63C2×#10625329C2×C414yes—
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66C22×C47⋊C8C2311yescharacteristic
67C22×C47⋊C8C2311yescharacteristic
68C2×C4⋊Dic47—21no—
69C2×C4⋊Dic47—22no—
70C2×C4⋊Dic47C2×C414yes—
71C2×C4⋊Dic47C2311yescharacteristic
72C2×C4⋊Dic47C2311yescharacteristic
73C2×C4⋊Dic47C2311yescharacteristic
74C2×C4⋊Dic47C2311yescharacteristic
75C2×Dic47⋊C4—21no—
76C2×Dic47⋊C4—21no—
77C2×C22⋊Dic47—21no—
78C2×C4×Dic47—21no—
79C2×C4×Dic47—21no—
80#13093957—22no—
81#13093957C2×C414yes—
82#13093957C2×C414yes—
83#13093955—22no—
84#13093955C2×C414yes—
85#13093955C2×C414yes—
86C22⋊(C47⋊C8)—22no—
87#13093935—22no—
88C4×C47⋊C8—22no—
89C47⋊#95—21no—
90C47⋊#95—21no—
91C47⋊#95—21no—
92C47⋊#95—21no—
93C47⋊#95—21no—
94C23×C4×C47C2311yescharacteristic
95#117×C47—22no—
96#117×C47C2×C414yes—
97C2×C4⋊C4×C47—21no—
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47C2311yescharacteristic
100C2×C4⋊C4×C47C2311yescharacteristic
101C2×C4⋊C4×C47C2311yescharacteristic
102C2×C4⋊C4×C47C2311yescharacteristic
103C2×C22⋊C4×C47—21no—
104C2×C22⋊C4×C47—21no—
105C2×C22⋊C4×C47D411yescharacteristic
106C2×C22⋊C4×C47D411yescharacteristic
107C2×C42×C47—21no—
108C2×C42×C47—21no—
109C2×C42×C47—21no—
110C2×C42×C47C2311yescharacteristic
111C2×C42×C47C2311yescharacteristic
112#95×C47—21no—
113#95×C47—21no—
114#95×C47—21no—
115#95×C47—21no—
116#95×C47—21no—
117#95×C47D411yescharacteristic
118#95×C47D411yescharacteristic
119C24×C47C2×D411yescharacteristic
120C22×C4×C47—21no—
121C22×C4×C47—21no—
122C22×C4×C47—21no—
123C22×C4×C47—21no—
124C22×C4×C47—21no—
125C22×C4×C47—21no—
126C22×C4×C47—21no—
127C22×C4×C47—21no—
128C22×C4×C47C22×C412yes—
129C22×C4×C47C2×D411yescharacteristic
130C22×C4×C47C2×D411yescharacteristic
131C22×C4×C47C2×D411yescharacteristic
132C22×C4×C47C2×D411yescharacteristic
133C22×C4×C47C2×D411yescharacteristic
134C22×C4×C47#4112yes—
135C22×C4×C47C2411yescharacteristic
136C22×Dic47—21no—
137C22×Dic47—21no—
138C22×Dic47—24no—
139C22×Dic47—21no—
140C22×Dic47—21no—
141C22×Dic47—81no—
142C22×Dic47—81no—
143C4⋊C4×C47—21no—
144C4⋊C4×C47—21no—
145C4⋊C4×C47—21no—
146C4⋊C4×C47—21no—
147C4⋊C4×C47—21no—
148C4⋊C4×C47—21no—
149C4⋊C4×C47—42no—
150C4⋊C4×C47—42no—
151C4⋊C4×C47C22×C412yes—
152C4⋊C4×C47C22×C412yes—
153C22⋊C4×C47—24no—
154C22⋊C4×C47—22no—
155C22⋊C4×C47—41no—
156C22⋊C4×C47—81no—
157C42×C47—24no—
158C42×C47—21no—
159C42×C47—21no—
160C42×C47—21no—
161C42×C47—21no—
162C42×C47—81no—
163C42×C47—81no—
164C22⋊Dic47—42no—
165C4⋊Dic47—24no—
166C4⋊Dic47—21no—
167C4⋊Dic47—21no—
168C4⋊Dic47—21no—
169C4⋊Dic47—21no—
170C4⋊Dic47—21no—
171C4⋊Dic47—21no—
172C4⋊Dic47C22×C412yes—
173C4⋊Dic47C22×C412yes—
174Dic47⋊C4—81no—
175Dic47⋊C4—81no—
176C4×Dic47—81no—
177C4×Dic47—81no—
178#10625329—28no—
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—21no—
187C2×C47⋊C8C22×C412yes—
188C2×C47⋊C8C22×C412yes—
189C2×C47⋊C8#4112yes—
190C2×C47⋊C8#4112yes—
191C23×C47—21no—
192C23×C47—21no—
193C23×C47—21no—
194C23×C47—21no—
195C23×C47—21no—
196C23×C47—21no—
197C23×C47C4×D412yes—
198C23×C47C22×D411yescharacteristic
199C2×C4×C47—21no—
200C2×C4×C47—21no—
201C2×C4×C47—21no—
202C2×C4×C47—21no—
203C2×C4×C47—22no—
204C2×C4×C47—22no—
205C2×C4×C47—22no—
206C2×C4×C47—22no—
207C2×C4×C47—22no—
208C2×C4×C47—22no—
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—21no—
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—41no—
226C2×C4×C47—41no—
227C2×C4×C47—41no—
228C2×C4×C47C4×D412yes—
229C2×C4×C47#13712yes—
230C2×C4×C47C23×C411yescharacteristic
231C2×C4×C47C2×#4111yescharacteristic
232C2×C4×C47C2×#4111yescharacteristic
233C2×C4×C47C2×#4111yescharacteristic
234C2×C4×C472−1+411yescharacteristic
235C2×C4×C472−1+411yescharacteristic
236C2×Dic47—22no—
237C2×Dic47—22no—
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—
247C2×Dic47—41no—
248C2×Dic47—84no—
249C47⋊C8—22no—
250C47⋊C8—41no—
251C47⋊C8—41no—
252C47⋊C8#11714yes—
253#22623—471nomaximal, Sylow
254C22×C47—22no—
255C22×C47—22no—
256C22×C47—22no—
257C22×C47—41no—
258C22×C47—41no—
259C22×C47—41no—
260C22×C47—41no—
261C22×C47C2×C4×D411yescharacteristic
262C22×C47#54711yescharacteristic
263C22×C47#54711yescharacteristic
264C22×C47C2×#13711yescharacteristic
265C22×C47#57511yescharacteristic
266C22×C47#57611yescharacteristic
267C22×C47#57711yescharacteristic
268C4×C47—22no—
269C4×C47—22no—
270C4×C47—41no—
271C4×C47—41no—
272C4×C47—41no—
273C4×C47—42no—
274C4×C47—42no—
275C4×C47—81no—
276C4×C47—81no—
277C4×C47C2×#11711yescharacteristic
278C4×C47#51911yescharacteristic
279C4×C47#55211yescharacteristic
280C4×C47#55211yescharacteristic
281Dic47—42no—
282Dic47—42no—
283Dic47—81no—
284Dic47—81no—
285C2×#428—471no—
286#2347D4711yescharacteristic
287#2345—471no—
288#1944—471no—
289#1941—471no—
290#1921—471no—
291#1920—471no—
292#1919—471no—
293#1918—471no—
294#1825—471no—
295#1823—471no—
296#1809—471no—
297#1776—471no—
298C4×#107—471no—
299#1753—471no—
300C2×C47—42no—
301C2×C47#234411yescharacteristic
302C2×C47C4×#13711yescharacteristic
303C2×C47#294611yescharacteristic
304C2×C47#334611yescharacteristic
305C2×C47#335011yescharacteristic
306C2×C47#335511yescharacteristic
307C2×C47#335611yescharacteristic
308C22×M16—471no—
309C2×#117C2×D4711yescharacteristic
310C22×C4⋊C4—471no—
311#428—478no—
312C2×#107—471no—
313C2×#107—471no—
314C2×#107—471no—
315C2×#106—471no—
316C2×#106—471no—
317C2×#106—471no—
318C2×C22⋊C8—471no—
319C2×#97—471no—
320C2×C4×C8—471no—
321#389—471no—
322#389—471no—
323#389C2×D4711yescharacteristic
324#389C2×D4711yescharacteristic
325#388—21no—
326#388—21no—
327#387—941no—
328#387—941no—
329#383—21no—
330#380—471no—
331#380—941no—
332#380C2×D4711yescharacteristic
333C4×C4⋊C4—21no—
334C4×C4⋊C4—471no—
335C4×C4⋊C4—471no—
336C4×C4⋊C4C2×D4711yescharacteristic
337C4×C4⋊C4C2×D4711yescharacteristic
338C4×C22⋊C4—941no—
339C4×C22⋊C4C2×D4711yescharacteristic
340#340—471no—
341#340—471no—
342#340—471no—
343#340—471no—
344#340—471no—
345#340—471no—
346#340—471no—
347#340—471no—
348#340—471no—
349#340—471no—
350#336—471no—
351#336—471no—
352C47#2262311yescharacteristic, complemented, Sylow
353C23×C4—941no—
354C23×C4C22×D4711yescharacteristic
355C2×M16—474no—
356C2×M16—942no—
357C2×M16—942no—
358C22×C8—471no—
359C22×C8—471no—
360C22×C8—471no—
361C22×C8—471no—
362#117—22no—
363#117C4×D4714yes—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—474no—
367C2×C4⋊C4—471no—
368C2×C4⋊C4—471no—
369C2×C4⋊C4—471no—
370C2×C4⋊C4—471no—
371C2×C4⋊C4—942no—
372C2×C4⋊C4—941no—
373C2×C4⋊C4—941no—
374C2×C4⋊C4—941no—
375C2×C4⋊C4C22×D4711yescharacteristic
376C2×C4⋊C4C22×D4711yescharacteristic
377C2×C4⋊C4C22×D4711yescharacteristic
378C2×C4⋊C4C22×D4711yescharacteristic
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—941no—
382C2×C22⋊C4C22⋊D4711yescharacteristic
383C2×C22⋊C4C22⋊D4711yescharacteristic
384C2×C42—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—941no—
388C2×C42—941no—
389C2×C42C22×D4711yescharacteristic
390C2×C42C22×D4711yescharacteristic
391#107—474no—
392#107—474no—
393#107—942no—
394#106—474no—
395#106—474no—
396#106—942no—
397C22⋊C8—942no—
398#97—942no—
399C4×C8—942no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—941no—
406#95—941no—
407#95—941no—
408#95—941no—
409#95—941no—
410#95C22⋊D4711yescharacteristic
411#95C22⋊D4711yescharacteristic
412C24C2×C22⋊D4711yescharacteristic
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—944no—
422C22×C4—941no—
423C22×C4—941no—
424C22×C4—941no—
425C22×C4—941no—
426C22×C4—3761no—
427C22×C4—3761no—
428C22×C4C2×C4×D4712yes—
429C22×C4#1062535012yes—
430C22×C4C2×C22⋊D4711yescharacteristic
431C22×C4C2×C22⋊D4711yescharacteristic
432C22×C4C2×C22⋊D4711yescharacteristic
433C22×C4C2×C22⋊D4711yescharacteristic
434C22×C4C2×C22⋊D4711yescharacteristic
435C22×C4C23×D4711yescharacteristic
436M16—948no—
437C2×C8—472no—
438C2×C8—472no—
439C2×C8—472no—
440C2×C8—472no—
441C2×C8—941no—
442C2×C8—941no—
443C2×C8—941no—
444C2×C8—941no—
445C2×C8—941no—
446C2×C8—941no—
447C2×C8—941no—
448C2×C8—941no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—42no—
456C4⋊C4—42no—
457C4⋊C4—472no—
458C4⋊C4—472no—
459C4⋊C4—944no—
460C4⋊C4—941no—
461C4⋊C4—941no—
462C4⋊C4—941no—
463C4⋊C4—941no—
464C4⋊C4—941no—
465C4⋊C4—941no—
466C4⋊C4—3761no—
467C4⋊C4—3761no—
468C4⋊C4C2×C4×D4712yes—
469C4⋊C4C2×C4×D4712yes—
470C22⋊C4—24no—
471C22⋊C4—22no—
472C22⋊C4—41no—
473C22⋊C4—81no—
474C22⋊C4—1882no—
475C42—24no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—81no—
481C42—81no—
482C42—3761no—
483C42—3761no—
484C23—21no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23C4×C22⋊D4712yes—
491C23C22×C22⋊D4711yescharacteristic
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—942no—
522C2×C4—942no—
523C2×C4—3764no—
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×C4C4×C22⋊D4712yes—
535C2×C4#1309405412yes—
536C2×C4C22×C4×D4711yescharacteristic
537C2×C4#41×D4711yescharacteristic
538C2×C4#41×D4711yescharacteristic
539C2×C4C2×#1062535011yescharacteristic
540C2×C4#1309407111yescharacteristic
541C2×C4#1309407111yescharacteristic
542C8—474no—
543C8—942no—
544C8—1881no—
545C8—1881no—
546C22—22no—
547C22—22no—
548C22—22no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22C2×C4×C22⋊D4711yescharacteristic
554C22#1568977211yescharacteristic
555C22#1568977211yescharacteristic
556C22C2×#1309405411yescharacteristic
557C22#1568992111yescharacteristic
558C22#1568992611yescharacteristic
559C22#1568993111yescharacteristic
560C4—22no—
561C4—22no—
562C4—42no—
563C4—42no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—81no—
568C4—81no—
569C4—3761no—
570C4—3761no—
571C4—1882no—
572C4—1882no—
573C4#117×D4711yescharacteristic
574C4#1568960011yescharacteristic
575C4#1568980611yescharacteristic
576C4#1568980611yescharacteristic
577C2—42no—
578C2#2024625811yescharacteristic
579C2C4×#1309405411yescharacteristic
580C2#2025221611yescharacteristic
581C2#2025587311yescharacteristic
582C2#2025593311yescharacteristic
583C2#2025598811yescharacteristic
584C2#2025599711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2347C2
socleC23×C47C22×D4
prime radicalC24×C47C2×D4
cosocleC22×C4×C47C24
hypercenter#2347D47
hypocenterC47#22623
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2347

Complements

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

NH ≅ G/Ntype
3. #20244128C2semidirect
4. #20244113C2semidirect
5. #20243980C2semidirect
6. #20243970C2semidirect
7. #20243963C2semidirect
8. #20243959C2semidirect
12. #20243286C2semidirect
13. C4×#13093957C2semidirect
18. #15689166C4semidirect
352. C47#22623semidirect

Maximal subgroups

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

subgroupindex
C2×#156891662
#202462632
#202441282
#202441132
#202439802
#202439702
#202439632
#202439592
#202434832
#202434722
#202434192
#202432862
C4×#130939572
#202431722
C47×#23472
#2262347