Finite Group Databasebeta

← #26233882

Subgroups — #26233882

Order 12032.

692 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252042C211yesmaximal, characteristic
2C2×#15689159C211yesmaximal, characteristic
3#20244138C212yesmaximal, complemented
4#20243987C212yesmaximal, complemented
5#20243984C212yesmaximal, complemented
6#20243487C211yesmaximal, characteristic
7#20243485C211yesmaximal, characteristic
8#20243424C211yesmaximal, characteristic
9#20243273C212yesmaximal, complemented
10#20243167C211yesmaximal, characteristic
11C47×#2924C211yesmaximal, characteristic
12C23×C47⋊C8C2211yescharacteristic
13C2×#13093983C2211yescharacteristic
14#15689181—22no—
15#15689177—21no—
16#15689173—21no—
17C2×#13093959C2212yes—
18#15689159C411yescharacteristic, complemented
19#15689159C411yescharacteristic, complemented
20#15689159C411yescharacteristic, complemented
21#15689159C411yescharacteristic, complemented
22#15689159C2211yescharacteristic
23#15689159C2211yescharacteristic
24#15689159C2211yescharacteristic
25#15689159C2211yescharacteristic
26C2×#13093957C411yescharacteristic, complemented
27C2×#13093957C411yescharacteristic, complemented
28C2×#13093955C411yescharacteristic, complemented
29C2×#13093955C411yescharacteristic, complemented
30#15689149C2212yes—
31#15689087C2211yescharacteristic
32#15689078C2212yes—
33C2×#13093934C2212yes—
34C4×C22⋊Dic47C2211yescharacteristic
35#15688887C2212yes—
36#15688884C2212yes—
37#15688884C2212yes—
38#15688882C2212yes—
39#15688882C2212yes—
40#15688877C2212yes—
41C2×#117×C47C2211yescharacteristic
42C47×#433—22no—
43C47×#432—21no—
44C47×#431—21no—
45C47×#424C2212yes—
46C47×#407C2211yescharacteristic
47C2×C22⋊C8×C47C2211yescharacteristic
48C47×#405C2212yes—
49C2×#10625329C2312yes—
50C22×C47⋊C8—24no—
51C22×C47⋊C8C2×C411yescharacteristic
52C22×C47⋊C8C2×C411yescharacteristic
53C22×C47⋊C8C2×C411yescharacteristic
54C22×C47⋊C8C2×C411yescharacteristic
55C22×C47⋊C8C2311yescharacteristic
56C22×C47⋊C8C2311yescharacteristic
57#13093983—21no—
58#13093983—21no—
59#13093983C2×C411yescharacteristic
60#13093983C2×C411yescharacteristic
61#13093983C2311yescharacteristic
62#13093983C2311yescharacteristic
63C2×C4⋊Dic47C2×C411yescharacteristic
64C2×C4⋊Dic47C2×C411yescharacteristic
65C2×C22⋊Dic47—21no—
66C2×C22⋊Dic47—21no—
67C2×C4×Dic47—21no—
68C2×C4×Dic47C2312yes—
69#13093959—24no—
70#13093957C2×C411yescharacteristic
71#13093957C2×C411yescharacteristic
72#13093957C2×C411yescharacteristic
73#13093957C2×C411yescharacteristic
74#13093957C2×C411yescharacteristic
75#13093957C2×C411yescharacteristic
76#13093957C2×C411yescharacteristic
77#13093957C2×C411yescharacteristic
78#13093955C2×C411yescharacteristic
79#13093955C2×C411yescharacteristic
80#13093955C2×C411yescharacteristic
81#13093955C2×C411yescharacteristic
82#13093955C2×C411yescharacteristic
83#13093955C2×C411yescharacteristic
84#13093955C2×C411yescharacteristic
85#13093955C2×C411yescharacteristic
86Dic47⋊C8—22no—
87Dic47⋊C8—22no—
88C22⋊(C47⋊C8)—21no—
89C22⋊(C47⋊C8)—21no—
90#13093934—22no—
91#13093934—24no—
92C8×Dic47—22no—
93C47⋊#95—21no—
94C23×C4×C47C2311yescharacteristic
95C2×M16×C47C2312yes—
96C22×C8×C47C2312yes—
97#117×C47—21no—
98#117×C47—21no—
99#117×C47C2×C411yescharacteristic
100#117×C47C2×C411yescharacteristic
101#117×C47C2311yescharacteristic
102#117×C47C2311yescharacteristic
103C2×C4⋊C4×C47C2×C411yescharacteristic
104C2×C4⋊C4×C47C2×C411yescharacteristic
105C2×C22⋊C4×C47—21no—
106C2×C42×C47—21no—
107C4⋊C8×C47—22no—
108C4⋊C8×C47—22no—
109C22⋊C8×C47—21no—
110C22⋊C8×C47—21no—
111C22⋊C8×C47D411yescharacteristic
112C22⋊C8×C47D411yescharacteristic
113C22⋊C8×C47D412yes—
114#97×C47—22no—
115C4×C8×C47—22no—
116C24×C47#4111yescharacteristic
117C22×C4×C47—22no—
118C22×C4×C47—22no—
119C22×C4×C47—21no—
120C22×C4×C47—21no—
121C22×C4×C47C22×C411yescharacteristic
122C22×C4×C47C22×C411yescharacteristic
123C22×C4×C47C2×D411yescharacteristic
124C22×C4×C47C2×D411yescharacteristic
125C22×C4×C47#4111yescharacteristic
126C22×C4×C47C2411yescharacteristic
127C22×Dic47—21no—
128C22×Dic47—21no—
129C22×Dic47—22no—
130M16×C47—22no—
131M16×C47—22no—
132C2×C8×C47—22no—
133C2×C8×C47—22no—
134C2×C8×C47—22no—
135C2×C8×C47C2×D412yes—
136C2×C8×C47C2×D412yes—
137C4⋊C4×C47—21no—
138C4⋊C4×C47—21no—
139C4⋊C4×C47C22×C411yescharacteristic
140C4⋊C4×C47C22×C411yescharacteristic
141C4⋊C4×C47C22×C411yescharacteristic
142C4⋊C4×C47C22×C411yescharacteristic
143C22⋊C4×C47—21no—
144C22⋊C4×C47—21no—
145C22⋊C4×C47—21no—
146C22⋊C4×C47—21no—
147C42×C47—21no—
148C42×C47—21no—
149C42×C47—21no—
150C42×C47—21no—
151C22⋊Dic47—21no—
152C22⋊Dic47—21no—
153C22⋊Dic47—21no—
154C22⋊Dic47—21no—
155C22⋊Dic47—42no—
156C4⋊Dic47—21no—
157C4⋊Dic47—21no—
158C4⋊Dic47C22×C411yescharacteristic
159C4⋊Dic47C22×C411yescharacteristic
160C4⋊Dic47C22×C411yescharacteristic
161C4⋊Dic47C22×C411yescharacteristic
162C4×Dic47—21no—
163C4×Dic47—21no—
164C4×Dic47—21no—
165C4×Dic47—21no—
166C4×Dic47—22no—
167C4×Dic47—22no—
168#10625329—22no—
169#10625329—22no—
170C2×C47⋊C8—22no—
171C2×C47⋊C8—22no—
172C2×C47⋊C8—22no—
173C2×C47⋊C8—22no—
174C2×C47⋊C8—22no—
175C2×C47⋊C8—22no—
176C2×C47⋊C8C22×C411yescharacteristic
177C2×C47⋊C8C22×C411yescharacteristic
178C2×C47⋊C8C22×C411yescharacteristic
179C2×C47⋊C8C22×C411yescharacteristic
180C2×C47⋊C8#4114yes—
181C23×C47—22no—
182C23×C47—22no—
183C23×C47—41no—
184C23×C47C4×D411yescharacteristic
185C23×C47C4×D411yescharacteristic
186C23×C47C2×#4111yescharacteristic
187C2×C4×C47—22no—
188C2×C4×C47—21no—
189C2×C4×C47—21no—
190C2×C4×C47—21no—
191C2×C4×C47—21no—
192C2×C4×C47—22no—
193C2×C4×C47—22no—
194C2×C4×C47—21no—
195C2×C4×C47—21no—
196C2×C4×C47—21no—
197C2×C4×C47—21no—
198C2×C4×C47—42no—
199C2×C4×C47—81no—
200C2×C4×C47C4×D411yescharacteristic
201C2×C4×C47C4×D411yescharacteristic
202C2×C4×C47C23×C411yescharacteristic
203C2×C4×C47C22×D411yescharacteristic
204C2×C4×C47C2×#4112yes—
205C2×C4×C472−1+412yes—
206C2×Dic47—21no—
207C2×Dic47—21no—
208C2×Dic47—21no—
209C2×Dic47—21no—
210C2×Dic47—42no—
211C2×Dic47—42no—
212C2×Dic47—42no—
213C2×Dic47—42no—
214C2×Dic47—81no—
215C8×C47—22no—
216C8×C47—22no—
217C8×C47—42no—
218C47⋊C8—21no—
219C47⋊C8—21no—
220C47⋊C8—42no—
221C47⋊C8#11712yes—
222C47⋊C8#11712yes—
223#22607—471nomaximal, Sylow
224C22×C47—21no—
225C22×C47—21no—
226C22×C47—21no—
227C22×C47—21no—
228C22×C47—21no—
229C22×C47—21no—
230C22×C47—21no—
231C22×C47—44no—
232C22×C47#44412yes—
233C22×C47C2×C4×D411yescharacteristic
234C22×C47#55212yes—
235C4×C47—21no—
236C4×C47—21no—
237C4×C47—41no—
238C4×C47—41no—
239C4×C47—41no—
240C4×C47—41no—
241C4×C47C2×#11711yescharacteristic
242C4×C47#51911yescharacteristic
243C4×C47#54712yes—
244Dic47—41no—
245Dic47—41no—
246Dic47—41no—
247Dic47—41no—
248Dic47—82no—
249#2924—471no—
250#2924D4711yescharacteristic
251C2×#427—471no—
252#1946—472no—
253#1922—472no—
254#1922—472no—
255#1826—471no—
256#1826—471no—
257#1810—471no—
258#1773—472no—
259#1752—471no—
260C2×C47—22no—
261C2×C47—22no—
262C2×C47—41no—
263C2×C47#234411yescharacteristic
264C2×C47C2×#44411yescharacteristic
265C2×C47#295711yescharacteristic
266C23×C8—471no—
267C2×#117—471no—
268C2×#117C2×D4711yescharacteristic
269#433—22no—
270#433—942no—
271#432—21no—
272#432—941no—
273#431—21no—
274#431—941no—
275C2×#108—472no—
276#427—471no—
277#427—471no—
278#427—471no—
279#427—471no—
280#427—471no—
281#427—471no—
282#427—471no—
283#427—471no—
284C2×#107—471no—
285C2×#107—471no—
286C2×#106—471no—
287C2×#106—471no—
288#424—472no—
289#424C2×D4712yes—
290#407—471no—
291#407C2×D4711yescharacteristic
292C2×C22⋊C8C2×D4711yescharacteristic
293#405—472no—
294#405C2×D4712yes—
295C2×#97—472no—
296C4×C22⋊C4—471no—
297#341—472no—
298#339—472no—
299#339—472no—
300#339—472no—
301#339—472no—
302#336—472no—
303C47#2260711yescharacteristic, complemented, Sylow
304C23×C4C22×D4711yescharacteristic
305C2×M16—472no—
306C2×M16C22×D4712yes—
307C22×C8—471no—
308C22×C8—471no—
309C22×C8—471no—
310C22×C8—471no—
311C22×C8—471no—
312C22×C8—471no—
313C22×C8—944no—
314C22×C8C22×D4712yes—
315#117—21no—
316#117—21no—
317#117—471no—
318#117—471no—
319#117—471no—
320#117—471no—
321#117—941no—
322#117—941no—
323#117C4×D4711yescharacteristic
324#117C4×D4711yescharacteristic
325#117C22×D4711yescharacteristic
326#117C22×D4711yescharacteristic
327C2×C4⋊C4—471no—
328C2×C4⋊C4—471no—
329C2×C4⋊C4C4×D4711yescharacteristic
330C2×C4⋊C4C4×D4711yescharacteristic
331C2×C22⋊C4—21no—
332C2×C22⋊C4—941no—
333C2×C22⋊C4—941no—
334C2×C42—21no—
335C2×C42—472no—
336C2×C42—941no—
337#108—944no—
338#107—471no—
339#107—471no—
340#107—471no—
341#107—471no—
342#107—471no—
343#107—471no—
344#107—471no—
345#107—471no—
346#106—471no—
347#106—471no—
348#106—471no—
349#106—471no—
350#106—471no—
351#106—471no—
352#106—471no—
353#106—471no—
354C4⋊C8—22no—
355C4⋊C8—22no—
356C4⋊C8—942no—
357C4⋊C8—942no—
358C22⋊C8—21no—
359C22⋊C8—21no—
360C22⋊C8—941no—
361C22⋊C8—941no—
362C22⋊C8C22⋊D4711yescharacteristic
363C22⋊C8C22⋊D4711yescharacteristic
364C22⋊C8C22⋊D4712yes—
365#97—22no—
366#97—944no—
367#97—942no—
368C4×C8—22no—
369C4×C8—942no—
370#95—941no—
371C24#1062535011yescharacteristic
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—941no—
377C22×C4—941no—
378C22×C4—942no—
379C22×C4C2×C4×D4711yescharacteristic
380C22×C4C2×C4×D4711yescharacteristic
381C22×C4#1062535011yescharacteristic
382C22×C4C2×C22⋊D4711yescharacteristic
383C22×C4C2×C22⋊D4711yescharacteristic
384C22×C4C23×D4711yescharacteristic
385M16—22no—
386M16—22no—
387M16—942no—
388M16—942no—
389C2×C8—22no—
390C2×C8—22no—
391C2×C8—22no—
392C2×C8—471no—
393C2×C8—471no—
394C2×C8—474no—
395C2×C8—471no—
396C2×C8—471no—
397C2×C8—942no—
398C2×C8—942no—
399C2×C8—942no—
400C2×C8—942no—
401C2×C8—942no—
402C2×C8—942no—
403C2×C8C2×C22⋊D4712yes—
404C2×C8C2×C22⋊D4712yes—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—471no—
408C4⋊C4—471no—
409C4⋊C4—471no—
410C4⋊C4—471no—
411C4⋊C4—941no—
412C4⋊C4—941no—
413C4⋊C4C2×C4×D4711yescharacteristic
414C4⋊C4C2×C4×D4711yescharacteristic
415C4⋊C4C2×C4×D4711yescharacteristic
416C4⋊C4C2×C4×D4711yescharacteristic
417C22⋊C4—21no—
418C22⋊C4—21no—
419C22⋊C4—21no—
420C22⋊C4—21no—
421C22⋊C4—941no—
422C22⋊C4—941no—
423C22⋊C4—941no—
424C22⋊C4—941no—
425C22⋊C4—1882no—
426C42—21no—
427C42—21no—
428C42—21no—
429C42—21no—
430C42—941no—
431C42—941no—
432C42—941no—
433C42—941no—
434C42—942no—
435C42—942no—
436C23—22no—
437C23—22no—
438C23—41no—
439C23C4×C22⋊D4711yescharacteristic
440C23C4×C22⋊D4711yescharacteristic
441C23C2×#1062535011yescharacteristic
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—42no—
454C2×C4—81no—
455C2×C4—941no—
456C2×C4—941no—
457C2×C4—941no—
458C2×C4—941no—
459C2×C4—3761no—
460C2×C4—1882no—
461C2×C4—1882no—
462C2×C4—1882no—
463C2×C4—1882no—
464C2×C4C4×C22⋊D4711yescharacteristic
465C2×C4C4×C22⋊D4711yescharacteristic
466C2×C4C22×C4×D4711yescharacteristic
467C2×C4C22×C22⋊D4711yescharacteristic
468C2×C4#41×D4712yes—
469C2×C4#1309407112yes—
470C8—22no—
471C8—22no—
472C8—42no—
473C8—472no—
474C8—472no—
475C8—941no—
476C8—941no—
477C8—1882no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—21no—
485C22—44no—
486C22#1568924312yes—
487C22C2×C4×C22⋊D4711yescharacteristic
488C22#1568980612yes—
489C4—21no—
490C4—21no—
491C4—41no—
492C4—41no—
493C4—41no—
494C4—41no—
495C4—3762no—
496C4—1881no—
497C4—1881no—
498C4—1881no—
499C4—1881no—
500C4#117×D4711yescharacteristic
501C4#1568960011yescharacteristic
502C4#1568977212yes—
503C2—22no—
504C2—22no—
505C2—41no—
506C2#2024625811yescharacteristic
507C2C2×#1568924311yescharacteristic
508C2#2025230311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2924C2
socleC22×C47C2×C4×D4
prime radicalC24×C47#41
cosocleC22×C4×C47C24
hypercenter#2924D47
hypocenterC47#22607
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2924

Complements

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

NH ≅ G/Ntype
3. #20244138C2semidirect
4. #20243987C2semidirect
5. #20243984C2semidirect
9. #20243273C2semidirect
18. #15689159C4semidirect
19. #15689159C4semidirect
20. #15689159C4semidirect
21. #15689159C4semidirect
26. C2×#13093957C4semidirect
27. C2×#13093957C4semidirect
28. C2×#13093955C4semidirect
29. C2×#13093955C4semidirect
303. C47#22607semidirect

Maximal subgroups

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

subgroupindex
#202520422
C2×#156891592
#202441382
#202439872
#202439842
#202434872
#202434852
#202434242
#202432732
#202431672
C47×#29242
#2260747