Finite Group Databasebeta

← #26233876

Subgroups — #26233876

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#20252048C211yesmaximal, characteristic
2#20252046C211yesmaximal, characteristic
3C2×#15689159C211yesmaximal, characteristic
4#20244140C212yesmaximal, complemented
5#20243990C212yesmaximal, complemented
6#20243985C212yesmaximal, complemented
7#20243488C211yesmaximal, characteristic
8#20243424C211yesmaximal, characteristic
9#20243271C212yesmaximal, complemented
10#20243166C211yesmaximal, characteristic
11C47×#1826C211yesmaximal, characteristic
12C23×C47⋊C8C2211yescharacteristic
13C2×#13093983C2211yescharacteristic
14#15689184—22no—
15#15689181—22no—
16#15689180—21no—
17#15689177—21no—
18#15689176—21no—
19#15689173—21no—
20C2×#13093959C2212yes—
21#15689159C411yescharacteristic, complemented
22#15689159C411yescharacteristic, complemented
23#15689159C411yescharacteristic, complemented
24#15689159C411yescharacteristic, complemented
25#15689159C2211yescharacteristic
26#15689159C2211yescharacteristic
27#15689159C2211yescharacteristic
28#15689159C2211yescharacteristic
29C2×#13093957C411yescharacteristic, complemented
30C2×#13093957C411yescharacteristic, complemented
31C2×#13093955C411yescharacteristic, complemented
32C2×#13093955C411yescharacteristic, complemented
33#15689151C2212yes—
34#15689150C2212yes—
35#15689087C2211yescharacteristic
36C2×C22⋊(C47⋊C8)C2211yescharacteristic
37#15689081C2212yes—
38#15689079C2212yes—
39C2×#13093935C2212yes—
40#15688887C2212yes—
41#15688883C2212yes—
42#15688883C2212yes—
43#15688878C2212yes—
44C2×#117×C47C2211yescharacteristic
45C47×#407C2211yescharacteristic
46C4×C22⋊C4×C47C2211yescharacteristic
47C47×#339C2212yes—
48C47×#339C2212yes—
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⋊C8C2312yes—
57C22×C47⋊C8C2311yescharacteristic
58#13093983—21no—
59#13093983—21no—
60#13093983C2×C411yescharacteristic
61#13093983C2×C411yescharacteristic
62#13093983C2311yescharacteristic
63#13093983C2311yescharacteristic
64C2×C4⋊Dic47C2×C411yescharacteristic
65C2×C4⋊Dic47C2×C411yescharacteristic
66C2×C22⋊Dic47—21no—
67C2×C4×Dic47—21no—
68#13093959—24no—
69#13093957C2×C411yescharacteristic
70#13093957C2×C411yescharacteristic
71#13093957C2×C411yescharacteristic
72#13093957C2×C411yescharacteristic
73#13093957C2×C411yescharacteristic
74#13093957C2×C411yescharacteristic
75#13093957C2×C411yescharacteristic
76#13093957C2×C411yescharacteristic
77#13093955C2×C411yescharacteristic
78#13093955C2×C411yescharacteristic
79#13093955C2×C411yescharacteristic
80#13093955C2×C411yescharacteristic
81#13093955C2×C411yescharacteristic
82#13093955C2×C411yescharacteristic
83#13093955C2×C411yescharacteristic
84#13093955C2×C411yescharacteristic
85C4⋊(C47⋊C8)—22no—
86C4⋊(C47⋊C8)—22no—
87Dic47⋊C8—22no—
88Dic47⋊C8—22no—
89C22⋊(C47⋊C8)—21no—
90C22⋊(C47⋊C8)—21no—
91C22⋊(C47⋊C8)D411yescharacteristic
92C22⋊(C47⋊C8)D411yescharacteristic
93C22⋊(C47⋊C8)D412yes—
94#13093935—22no—
95#13093935—24no—
96#13093934—22no—
97C4×C47⋊C8—22no—
98C8×Dic47—22no—
99C23×C4×C47C2311yescharacteristic
100C2×M16×C47C2312yes—
101#117×C47—21no—
102#117×C47—21no—
103#117×C47C2×C411yescharacteristic
104#117×C47C2×C411yescharacteristic
105#117×C47C2311yescharacteristic
106#117×C47C2311yescharacteristic
107C2×C4⋊C4×C47C2×C411yescharacteristic
108C2×C4⋊C4×C47C2×C411yescharacteristic
109C2×C22⋊C4×C47—21no—
110C2×C22⋊C4×C47—21no—
111C2×C42×C47—21no—
112C2×C42×C47C2312yes—
113C22⋊C8×C47—21no—
114C22⋊C8×C47—21no—
115#95×C47—21no—
116C24×C47#4111yescharacteristic
117C22×C4×C47—22no—
118C22×C4×C47—22no—
119C22×C4×C47—21no—
120C22×C4×C47—21no—
121C22×C4×C47—22no—
122C22×C4×C47C22×C411yescharacteristic
123C22×C4×C47C22×C411yescharacteristic
124C22×C4×C47C2×D411yescharacteristic
125C22×C4×C47C2×D411yescharacteristic
126C22×C4×C47#4111yescharacteristic
127C22×C4×C47C2411yescharacteristic
128C22×Dic47—21no—
129C22×Dic47—21no—
130M16×C47—22no—
131M16×C47—22no—
132C2×C8×C47—22no—
133C4⋊C4×C47—21no—
134C4⋊C4×C47—21no—
135C4⋊C4×C47C22×C411yescharacteristic
136C4⋊C4×C47C22×C411yescharacteristic
137C4⋊C4×C47C22×C411yescharacteristic
138C4⋊C4×C47C22×C411yescharacteristic
139C22⋊C4×C47—21no—
140C22⋊C4×C47—21no—
141C22⋊C4×C47—21no—
142C22⋊C4×C47—21no—
143C22⋊C4×C47—42no—
144C42×C47—21no—
145C42×C47—21no—
146C42×C47—21no—
147C42×C47—21no—
148C42×C47—22no—
149C42×C47—22no—
150C22⋊Dic47—21no—
151C22⋊Dic47—21no—
152C22⋊Dic47—21no—
153C22⋊Dic47—21no—
154C4⋊Dic47—21no—
155C4⋊Dic47—21no—
156C4⋊Dic47C22×C411yescharacteristic
157C4⋊Dic47C22×C411yescharacteristic
158C4⋊Dic47C22×C411yescharacteristic
159C4⋊Dic47C22×C411yescharacteristic
160C4×Dic47—21no—
161C4×Dic47—21no—
162C4×Dic47—21no—
163C4×Dic47—21no—
164#10625329—22no—
165#10625329—22no—
166C2×C47⋊C8—22no—
167C2×C47⋊C8—22no—
168C2×C47⋊C8—22no—
169C2×C47⋊C8—22no—
170C2×C47⋊C8—22no—
171C2×C47⋊C8—22no—
172C2×C47⋊C8—22no—
173C2×C47⋊C8—22no—
174C2×C47⋊C8C22×C411yescharacteristic
175C2×C47⋊C8C22×C411yescharacteristic
176C2×C47⋊C8C22×C411yescharacteristic
177C2×C47⋊C8C22×C411yescharacteristic
178C2×C47⋊C8C2×D412yes—
179C2×C47⋊C8C2×D412yes—
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—42no—
200C2×C4×C47—42no—
201C2×C4×C47—42no—
202C2×C4×C47—81no—
203C2×C4×C47C4×D411yescharacteristic
204C2×C4×C47C4×D411yescharacteristic
205C2×C4×C47C23×C411yescharacteristic
206C2×C4×C47C22×D411yescharacteristic
207C2×C4×C47C2×#4112yes—
208C2×C4×C472−1+412yes—
209C2×Dic47—21no—
210C2×Dic47—21no—
211C2×Dic47—21no—
212C2×Dic47—21no—
213C2×Dic47—42no—
214C2×Dic47—81no—
215C8×C47—42no—
216C47⋊C8—21no—
217C47⋊C8—21no—
218C47⋊C8—22no—
219C47⋊C8—22no—
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×C47—82no—
242C4×C47C2×#11711yescharacteristic
243C4×C47#51911yescharacteristic
244C4×C47#54712yes—
245Dic47—41no—
246Dic47—41no—
247Dic47—41no—
248Dic47—41no—
249#2924—471no—
250#2924—471no—
251C2×#427—471no—
252#1946—472no—
253#1922—472no—
254#1922—472no—
255#1826—471no—
256#1826D4711yescharacteristic
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—942no—
270#433—942no—
271#432—941no—
272#432—941no—
273#431—941no—
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#424—472no—
290#407—471no—
291#407C2×D4711yescharacteristic
292C2×C22⋊C8—471no—
293#405—472no—
294#405—472no—
295C2×#97—472no—
296C4×C22⋊C4C2×D4711yescharacteristic
297#341—472no—
298#339—472no—
299#339—472no—
300#339C2×D4712yes—
301#339C2×D4712yes—
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—472no—
314C22×C8—944no—
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—21no—
333C2×C22⋊C4—941no—
334C2×C42—21no—
335C2×C42—941no—
336C2×C42C22×D4712yes—
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—942no—
355C4⋊C8—942no—
356C4⋊C8—942no—
357C4⋊C8—942no—
358C22⋊C8—21no—
359C22⋊C8—21no—
360C22⋊C8—471no—
361C22⋊C8—471no—
362C22⋊C8—472no—
363C22⋊C8—941no—
364C22⋊C8—941no—
365#97—944no—
366#97—942no—
367#97—942no—
368C4×C8—942no—
369C4×C8—942no—
370#95—21no—
371C24#1062535211yescharacteristic
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—941no—
378C22×C4—941no—
379C22×C4C2×C4×D4711yescharacteristic
380C22×C4C2×C4×D4711yescharacteristic
381C22×C4D4×D4711yescharacteristic
382C22×C4D4×D4711yescharacteristic
383C22×C4#1062535211yescharacteristic
384C22×C4C23×D4711yescharacteristic
385M16—22no—
386M16—22no—
387M16—942no—
388M16—942no—
389C2×C8—22no—
390C2×C8—471no—
391C2×C8—471no—
392C2×C8—474no—
393C2×C8—471no—
394C2×C8—471no—
395C2×C8—472no—
396C2×C8—472no—
397C2×C8—942no—
398C2×C8—942no—
399C2×C8—942no—
400C2×C8—942no—
401C2×C8—942no—
402C2×C8—942no—
403C2×C8—942no—
404C2×C8—942no—
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—42no—
422C22⋊C4—941no—
423C22⋊C4—941no—
424C22⋊C4—941no—
425C22⋊C4—941no—
426C42—21no—
427C42—21no—
428C42—21no—
429C42—21no—
430C42—22no—
431C42—22no—
432C42—941no—
433C42—941no—
434C42—941no—
435C42—941no—
436C23—22no—
437C23—22no—
438C23—41no—
439C23(C22⋊D47)⋊C411yescharacteristic
440C23(C22⋊D47)⋊C411yescharacteristic
441C23C2×#1062535211yescharacteristic
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—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—81no—
458C2×C4—941no—
459C2×C4—941no—
460C2×C4—941no—
461C2×C4—941no—
462C2×C4—3761no—
463C2×C4—1882no—
464C2×C4(C22⋊D47)⋊C411yescharacteristic
465C2×C4(C22⋊D47)⋊C411yescharacteristic
466C2×C4C22×C4×D4711yescharacteristic
467C2×C4C2×D4×D4711yescharacteristic
468C2×C4#41×D4712yes—
469C2×C4#1309407112yes—
470C8—42no—
471C8—472no—
472C8—472no—
473C8—942no—
474C8—942no—
475C8—941no—
476C8—941no—
477C8—1882no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—21no—
485C22—44no—
486C22#1568924212yes—
487C22C2×(C22⋊D47)⋊C411yescharacteristic
488C22#1568981012yes—
489C4—21no—
490C4—21no—
491C4—41no—
492C4—41no—
493C4—41no—
494C4—41no—
495C4—82no—
496C4—1881no—
497C4—1881no—
498C4—1881no—
499C4—1881no—
500C4#117×D4711yescharacteristic
501C4#1568960011yescharacteristic
502C4#1568977112yes—
503C2—22no—
504C2—22no—
505C2—41no—
506C2#2024625211yescharacteristic
507C2C2×#1568924211yescharacteristic
508C2#2025230111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1826C2
socleC22×C47C2×C4×D4
prime radicalC24×C47#41
cosocleC22×C4×C47C24
hypercenter#1826D47
hypocenterC47#22607
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
4. #20244140C2semidirect
5. #20243990C2semidirect
6. #20243985C2semidirect
9. #20243271C2semidirect
21. #15689159C4semidirect
22. #15689159C4semidirect
23. #15689159C4semidirect
24. #15689159C4semidirect
29. C2×#13093957C4semidirect
30. C2×#13093957C4semidirect
31. C2×#13093955C4semidirect
32. 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
#202520482
#202520462
C2×#156891592
#202441402
#202439902
#202439852
#202434882
#202434242
#202432712
#202431662
C47×#18262
#2260747