Finite Group Databasebeta

← #26220711

Subgroups — #26220711

Order 12032.

738 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252184C211yesmaximal, characteristic
2#20252038C211yesmaximal, characteristic, complemented
3#20252035C211yesmaximal, characteristic, complemented
4#20244280C211yesmaximal, characteristic
5#20244273C211yesmaximal, characteristic
6#20244138C211yesmaximal, characteristic, complemented
7#20244135C211yesmaximal, characteristic, complemented
8#20244101C211yesmaximal, characteristic, complemented
9#20244097C211yesmaximal, characteristic, complemented
10#20244092C211yesmaximal, characteristic, complemented
11#20243293C211yesmaximal, characteristic, complemented
12#104×Dic47C211yesmaximal, characteristic, complemented
13#20243192C211yesmaximal, characteristic, complemented
14C4×#13093934C211yesmaximal, characteristic, complemented
15C47×#1937C211yesmaximal, characteristic, complemented
16C2×#13094044C2211yescharacteristic
17#41×Dic47C2211yescharacteristic
18#15689591C2211yescharacteristic
19#15689232C412yescomplemented
20#15689227C412yescomplemented
21#15689226C412yescomplemented
22#15689220C412yescomplemented
23#15689183—22no—
24#15689181—22no—
25#15689179—22no—
26#15689177—22no—
27C2×#13093959C2211yescharacteristic
28C2×#13093959C2211yescharacteristic
29#15689159C2211yescharacteristic
30#15689151C2211yescharacteristic
31#15689150C2211yescharacteristic
32#15689149C2211yescharacteristic
33C2×#13093952C2211yescharacteristic
34C2×#13093951C2211yescharacteristic
35C2×#13093950C2211yescharacteristic
36#15689120C2211yescharacteristic
37#15689091C2211yescharacteristic
38#15689090C2211yescharacteristic
39#15689089C2211yescharacteristic
40M16×Dic47C2211yescharacteristic
41M16×Dic47C2211yescharacteristic
42C2×#13093934C2211yescharacteristic
43C2×#13093934C2211yescharacteristic
44C2×#13093934C2211yescharacteristic
45C2×#13093934C2211yescharacteristic
46C2×C4×C47⋊C8C2211yescharacteristic
47C42×Dic47C2211yescharacteristic
48#15688888C2211yescharacteristic
49#15688884C2211yescharacteristic
50#15688883C2211yescharacteristic
51#15688882C2211yescharacteristic
52C47×#424C2211yescharacteristic
53C2×#104×C47C2211yescharacteristic
54C47×#416C2211yescharacteristic
55C47×#408C2211yescharacteristic
56C2×C4×C8×C47C2211yescharacteristic
57C47×#341C2211yescharacteristic
58C47×#339C2211yescharacteristic
59C2×#10625350C2311yescharacteristic
60#13094044—22no—
61#13094044—22no—
62C2×#10625337C2×C411yescharacteristic
63C2×#10625335C2×C411yescharacteristic
64C2×#10625336C2×C411yescharacteristic
65C2×#10625334C2×C411yescharacteristic
66C2×#10625329C2311yescharacteristic
67C2×#10625329C2311yescharacteristic
68C22×C47⋊C8C2311yescharacteristic
69C22×C47⋊C8C2311yescharacteristic
70Q8×Dic47C2×C412yes—
71#13093989C2×C412yes—
72D4×Dic47—22no—
73D4×Dic47C2×C412yes—
74#13093986C2×C412yes—
75(C22⋊D47)⋊C4—22no—
76#13093983—21no—
77#13093983C2311yescharacteristic
78#13093981—21no—
79C2×C4×Dic47—21no—
80C2×C4×Dic47—22no—
81C2×C4×Dic47C2311yescharacteristic
82C2×C4×Dic47C2311yescharacteristic
83C42×D47—21no—
84#13093959—22no—
85#13093959—22no—
86#13093957C2×C412yes—
87#13093955C2×C412yes—
88C4⋊(C47⋊C8)—22no—
89Dic47⋊C8—22no—
90Dic47⋊C8—22no—
91#13093952—22no—
92#13093951—22no—
93#13093950—22no—
94#13093949C2×C412yes—
95#13093946C2×C412yes—
96C22⋊(C47⋊C8)—22no—
97(C2×D47)⋊C8—22no—
98(C2×D47)⋊C8—22no—
99#13093934—21no—
100#13093934—21no—
101#13093934—22no—
102#13093934—22no—
103#13093934C2×C412yes—
104#13093934C2×C412yes—
105#13093934D412yes—
106#13093934D412yes—
107C4×C47⋊C8—22no—
108C8×Dic47—21no—
109C8×Dic47—21no—
110C2×#41×C47C2311yescharacteristic
111C2×M16×C47C2311yescharacteristic
112C2×M16×C47C2311yescharacteristic
113C22×C8×C47C2311yescharacteristic
114C22×C8×C47C2311yescharacteristic
115#117×C47C2311yescharacteristic
116C2×C42×C47C2311yescharacteristic
117C4⋊C8×C47—22no—
118#104×C47—22no—
119#103×C47C2×C412yes—
120#102×C47C2×C412yes—
121C22⋊C8×C47—22no—
122C4×C8×C47—22no—
123#41×C47—21no—
124#41×C47—21no—
125#41×C47—21no—
126#41×C47—21no—
127C2×Q8×C47C22×C411yescharacteristic
128C2×D4×C47—21no—
129C2×D4×C47C22×C411yescharacteristic
130C22×C4×C47—21no—
131C22×C4×C47—21no—
132C22×C4×C47C2411yescharacteristic
133C2×C22⋊D47—21no—
134C22×Dic47—21no—
135C22×Dic47—22no—
136C22×Dic47#4112yes—
137#10625350—21no—
138#10625350—21no—
139#10625350—21no—
140#10625350—21no—
141C2×D188C22×C411yescharacteristic
142C2×C4×D47—21no—
143C2×C4×D47—22no—
144C2×Dic94C22×C411yescharacteristic
145M16×C47—21no—
146M16×C47—21no—
147M16×C47—21no—
148M16×C47—21no—
149C2×C8×C47—21no—
150C2×C8×C47—21no—
151C2×C8×C47—21no—
152C2×C8×C47—21no—
153C2×C8×C47—21no—
154C2×C8×C47—21no—
155C2×C8×C47C22×C412yes—
156C2×C8×C47C2×D412yes—
157C4⋊C4×C47C22×C412yes—
158C22⋊C4×C47—21no—
159C42×C47—21no—
160C42×C47—21no—
161C42×C47#4112yes—
162C22⋊Dic47—21no—
163C22⋊Dic47—22no—
164#10625337—22no—
165#10625336—22no—
166#10625335—22no—
167#10625334—22no—
168(C2×D47)⋊C4—22no—
169C4⋊Dic47—22no—
170C4⋊Dic47C22×C412yes—
171Dic47⋊C4—22no—
172C4×Dic47—21no—
173C4×Dic47—21no—
174C4×Dic47—22no—
175C4×Dic47—22no—
176C4×Dic47—44no—
177C4×Dic47C22×C412yes—
178C4×Dic47C2×D411yescharacteristic
179C4×Dic47C2×D411yescharacteristic
180C4×Dic47#4112yes—
181#10625329—21no—
182#10625329—21no—
183#10625329—21no—
184#10625329—21no—
185C2×C47⋊C8—21no—
186C2×C47⋊C8—21no—
187C2×C47⋊C8—21no—
188C2×C47⋊C8—21no—
189C2×C47⋊C8C22×C411yescharacteristic
190C2×C47⋊C8C22×C411yescharacteristic
191C2×C47⋊C8C2×D412yes—
192C2×C47⋊C8#4112yes—
193C2×C47⋊C8#4112yes—
194C23×C47—21no—
195C23×C47C2×#4111yescharacteristic
196C22×D47—21no—
197Q8×C47—21no—
198Q8×C47—21no—
199D4×C47—21no—
200D4×C47—21no—
201D4×C47—41no—
202D4×C47—41no—
203C2×C4×C47—24no—
204C2×C4×C47—22no—
205C2×C4×C47—21no—
206C2×C4×C47—22no—
207C2×C4×C47—41no—
208C2×C4×C47—41no—
209C2×C4×C47C23×C411yescharacteristic
210C2×C4×C47C22×D411yescharacteristic
211C2×C4×C47C2×#4111yescharacteristic
212C2×C4×C47C2×#4111yescharacteristic
213C2×C4×C47C2×#4111yescharacteristic
214C2×C4×C47C2×#4111yescharacteristic
215C22⋊D47—41no—
216C22⋊D47—41no—
217C2×Dic47—21no—
218C2×Dic47—22no—
219C2×Dic47—22no—
220C2×Dic47—42no—
221C2×Dic47—42no—
222C2×Dic47—82no—
223C2×Dic47C4×D412yes—
224C2×Dic47C4×D412yes—
225D188—21no—
226D188—21no—
227C4×D47—41no—
228C4×D47—41no—
229C4×D47—82no—
230Dic94—21no—
231Dic94—21no—
232C8×C47—22no—
233C8×C47—22no—
234C8×C47—41no—
235C8×C47—41no—
236C47⋊C8—22no—
237C47⋊C8—41no—
238C47⋊C8—41no—
239C47⋊C8#11712yes—
240C47⋊C8#11712yes—
241#21297—471nomaximal, Sylow
242C22×C47—22no—
243C22×C47—42no—
244C22×C47—41no—
245C22×C47C2×C4×D411yescharacteristic
246C22×C47#52911yescharacteristic
247C22×C47#52911yescharacteristic
248C2×D47—42no—
249C2×D47—41no—
250C4×C47—24no—
251C4×C47—42no—
252C4×C47—41no—
253C4×C47C2×#11711yescharacteristic
254C4×C47C4×#4111yescharacteristic
255C4×C47#53211yescharacteristic
256C4×C47#53211yescharacteristic
257Dic47—22no—
258Dic47—22no—
259Dic47—42no—
260Dic47—42no—
261Dic47—41no—
262#2943—471no—
263#2923—471no—
264#2923—471no—
265#1975—471no—
266#1974—471no—
267#1946—471no—
268#1945—471no—
269#1938—471no—
270#1938—471no—
271#1937—471no—
272#1937D4711yescharacteristic, complemented
273#1778—471no—
274C4×#104—471no—
275C4×#104—471no—
276C4×#97—471no—
277C2×C47—21no—
278C2×C47—21no—
279C2×C47—81no—
280C2×C47#229311yescharacteristic
281C2×C47#295612yes—
282D47—81no—
283C2×#135—471no—
284C4×#41—471no—
285C4×#41—471no—
286#442—472no—
287#441—472no—
288#440—472no—
289#440—472no—
290#433—942no—
291#433—942no—
292#432—942no—
293#432—942no—
294C2×#108—471no—
295C2×#108—471no—
296#427—471no—
297#424—471no—
298#424—471no—
299#424—471no—
300#424C2×D4711yescharacteristic
301C2×#104—471no—
302C2×#104—471no—
303C2×#104—471no—
304C2×#104C2×D4711yescharacteristic
305#416—471no—
306#416C2×D4711yescharacteristic
307#408—471no—
308#408—471no—
309#408—471no—
310#408C2×D4711yescharacteristic
311C4×M16—471no—
312C4×M16—471no—
313C2×#97—471no—
314C2×#97—471no—
315C2×#97—471no—
316C2×#97—471no—
317C2×C4×C8—471no—
318C2×C4×C8C2×D4711yescharacteristic
319C43—471no—
320#341—471no—
321#341C2×D4711yescharacteristic
322#339—471no—
323#339—471no—
324#339—471no—
325#339C2×D4711yescharacteristic
326C47#2129711yescharacteristic, complemented, Sylow
327C2×#41—471no—
328C2×#41C22×D4711yescharacteristic
329#135—942no—
330#135—942no—
331C2×Q16—471no—
332C2×SD16—471no—
333C2×SD16—471no—
334C2×D8—471no—
335C2×M16—471no—
336C2×M16—471no—
337C2×M16C22×D4711yescharacteristic
338C2×M16C22×D4711yescharacteristic
339C22×C8—471no—
340C22×C8—471no—
341C22×C8C22×D4711yescharacteristic
342C22×C8C22×D4711yescharacteristic
343C4×Q8—472no—
344C4×Q8—472no—
345C4×D4—472no—
346C4×D4—472no—
347C4×D4—942no—
348C4×D4—942no—
349#117—471no—
350#117—941no—
351#117—941no—
352#117C22×D4711yescharacteristic
353C2×C42—471no—
354C2×C42—471no—
355C2×C42—941no—
356C2×C42—941no—
357C2×C42—942no—
358C2×C42C22×D4711yescharacteristic
359#108—942no—
360#108—942no—
361#107—472no—
362#106—472no—
363C4⋊C8—22no—
364C4⋊C8—942no—
365C4⋊C8—942no—
366C4⋊C8—942no—
367#104—22no—
368#104—942no—
369#104—942no—
370#104—942no—
371#103—472no—
372#103C4×D4712yes—
373#102—472no—
374#102C4×D4712yes—
375C22⋊C8—22no—
376C22⋊C8—942no—
377C22⋊C8—942no—
378C22⋊C8—942no—
379#97—472no—
380#97—472no—
381#97—472no—
382#97—472no—
383#97—942no—
384#97—941no—
385#97—941no—
386#97—942no—
387C4×C8—22no—
388C4×C8—942no—
389C4×C8—941no—
390C4×C8—941no—
391#41—21no—
392#41—21no—
393#41—21no—
394#41—21no—
395#41—941no—
396#41—941no—
397#41—941no—
398#41—941no—
399C2×Q8—471no—
400C2×Q8C2×C4×D4711yescharacteristic
401C2×D4—21no—
402C2×D4—471no—
403C2×D4—941no—
404C2×D4C2×C4×D4711yescharacteristic
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—472no—
408C22×C4—942no—
409C22×C4—942no—
410C22×C4—941no—
411C22×C4—941no—
412C22×C4C23×D4711yescharacteristic
413Q16—942no—
414SD16—942no—
415SD16—942no—
416D8—942no—
417M16—21no—
418M16—21no—
419M16—21no—
420M16—21no—
421M16—941no—
422M16—941no—
423M16—941no—
424M16—941no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—471no—
432C2×C8—471no—
433C2×C8—472no—
434C2×C8—472no—
435C2×C8—472no—
436C2×C8—941no—
437C2×C8—941no—
438C2×C8—941no—
439C2×C8—941no—
440C2×C8C2×C4×D4712yes—
441C2×C8D4×D4712yes—
442C4⋊C4—472no—
443C4⋊C4—942no—
444C4⋊C4—942no—
445C4⋊C4C2×C4×D4712yes—
446C22⋊C4—21no—
447C22⋊C4—942no—
448C22⋊C4—942no—
449C22⋊C4—941no—
450C42—21no—
451C42—21no—
452C42—472no—
453C42—471no—
454C42—471no—
455C42—472no—
456C42—942no—
457C42—942no—
458C42—941no—
459C42—941no—
460C42—1884no—
461C42#1062535212yes—
462C23—21no—
463C23—941no—
464C23#41×D4711yescharacteristic
465Q8—21no—
466Q8—21no—
467Q8—941no—
468Q8—941no—
469D4—21no—
470D4—21no—
471D4—41no—
472D4—41no—
473D4—941no—
474D4—941no—
475D4—1881no—
476D4—1881no—
477C2×C4—24no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—21no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—472no—
484C2×C4—472no—
485C2×C4—942no—
486C2×C4—941no—
487C2×C4—942no—
488C2×C4—3762no—
489C2×C4—3762no—
490C2×C4—1882no—
491C2×C4—1882no—
492C2×C4—1881no—
493C2×C4—1881no—
494C2×C4C22×C4×D4711yescharacteristic
495C2×C4C2×D4×D4711yescharacteristic
496C2×C4#41×D4711yescharacteristic
497C2×C4#41×D4711yescharacteristic
498C2×C4#41×D4711yescharacteristic
499C2×C4C2×#1062535211yescharacteristic
500C8—22no—
501C8—22no—
502C8—41no—
503C8—41no—
504C8—472no—
505C8—472no—
506C8—942no—
507C8—1881no—
508C8—1881no—
509C22—22no—
510C22—41no—
511C22—42no—
512C22—1881no—
513C22—1882no—
514C22C4×D4×D4711yescharacteristic
515C22#1568965011yescharacteristic
516C22#1568965611yescharacteristic
517C4—24no—
518C4—41no—
519C4—42no—
520C4—942no—
521C4—942no—
522C4—1882no—
523C4—1881no—
524C4—1882no—
525C4#117×D4711yescharacteristic
526C4C4×#1062535211yescharacteristic
527C4#1568966811yescharacteristic
528C4#1568967211yescharacteristic
529C2—21no—
530C2—21no—
531C2—81no—
532C2—3761no—
533C2#2024584811yescharacteristic
534C2#2025229312yes—
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1937C2
socleC22×C47C2×C4×D4
prime radicalC2×#13094044C22
cosocleC22×C4×C47C24
hypercenter#1937D47
hypocenterC47#21297
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1937

Complements

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

NH ≅ G/Ntype
2. #20252038C2semidirect
3. #20252035C2semidirect
6. #20244138C2semidirect
7. #20244135C2semidirect
8. #20244101C2semidirect
9. #20244097C2semidirect
10. #20244092C2semidirect
11. #20243293C2semidirect
12. #104×Dic47C2semidirect
13. #20243192C2semidirect
14. C4×#13093934C2semidirect
15. C47×#1937C2semidirect
19. #15689232C4semidirect
20. #15689227C4semidirect
21. #15689226C4semidirect
22. #15689220C4semidirect
272. #1937D47semidirect
326. C47#21297semidirect

Maximal subgroups

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

subgroupindex
#202521842
#202520382
#202520352
#202442802
#202442732
#202441382
#202441352
#202441012
#202440972
#202440922
#202432932
#104×Dic472
#202431922
C4×#130939342
C47×#19372
#2129747