Finite Group Databasebeta

← #26112461

Subgroups — #26112461

Order 12032.

678 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C47⋊C8C211yesmaximal, characteristic, complemented
2#20244195C211yesmaximal, characteristic, complemented
3#20243388C211yesmaximal, characteristic, complemented
4C2×#15688867C211yesmaximal, characteristic, complemented
5#20241272C211yesmaximal, characteristic, complemented
6#20241222C211yesmaximal, characteristic, complemented
7C2×C47×#459C211yesmaximal, characteristic
8C23×C47⋊C8—21no—
9D4×C47⋊C8—22no—
10D4×C47⋊C8—22no—
11C2×C4⋊(C47⋊C8)C2211yescharacteristic
12C2×C4⋊(C47⋊C8)C2211yescharacteristic
13C2×#13093945—21no—
14C2×#13093945—21no—
15C2×#13093945—21no—
16C2×C22⋊(C47⋊C8)—21no—
17C2×C4×C47⋊C8C2211yescharacteristic
18#15688993C2211yescharacteristic
19#15688885—21no—
20#15688867—22no—
21C22×D8×C47—21no—
22C2×#127×C47C2211yescharacteristic
23C2×C4×D4×C47C2211yescharacteristic
24C47×#459—22no—
25C47×#459C414yescomplemented
26C2×C4⋊C8×C47C2211yescharacteristic
27C2×#102×C47—21no—
28C22×C47⋊C8—24no—
29C22×C47⋊C8—21no—
30C22×C47⋊C8—21no—
31C22×C47⋊C8—42no—
32C22×C47⋊C8—42no—
33C22×C47⋊C8D411yescharacteristic
34C22×C47⋊C8D411yescharacteristic
35C2×C4⋊Dic47—21no—
36C2×C4⋊Dic47—21no—
37C2×C4⋊Dic47—21no—
38C4⋊(C47⋊C8)—21no—
39C4⋊(C47⋊C8)—21no—
40C4⋊(C47⋊C8)—21no—
41C4⋊(C47⋊C8)D412yes—
42#13093945—42no—
43#13093945—42no—
44#13093945—42no—
45C22⋊(C47⋊C8)—24no—
46C4×C47⋊C8—21no—
47C4×C47⋊C8—21no—
48C22×D4×C47—21no—
49C22×D4×C47—21no—
50C22×D4×C47—21no—
51C22×D4×C47D411yescharacteristic
52C23×C4×C47—21no—
53C2×D8×C47—24no—
54C2×D8×C47—42no—
55C2×D8×C47—42no—
56C22×C8×C47—21no—
57#127×C47—21no—
58#127×C47—21no—
59#127×C47—21no—
60#127×C47C2×C412yes—
61C4×D4×C47—21no—
62C4×D4×C47—21no—
63C4×D4×C47C2×C412yes—
64C4×D4×C47D412yes—
65C2×C4⋊C4×C47D411yescharacteristic
66C2×C22⋊C4×C47—21no—
67C2×C42×C47C2311yescharacteristic
68C4⋊C8×C47—21no—
69C4⋊C8×C47C2×C412yes—
70#102×C47—24no—
71C24×C47—21no—
72C24×C47—41no—
73C2×D4×C47—22no—
74C2×D4×C47—22no—
75C2×D4×C47—22no—
76C2×D4×C47—21no—
77C2×D4×C47—21no—
78C2×D4×C47—21no—
79C2×D4×C47—41no—
80C2×D4×C47—41no—
81C2×D4×C47—41no—
82C2×D4×C47—41no—
83C2×D4×C47—41no—
84C2×D4×C47—41no—
85C2×D4×C47—41no—
86C2×D4×C47—41no—
87C2×D4×C47—41no—
88C2×D4×C47—41no—
89C2×D4×C47—41no—
90C2×D4×C47—81no—
91C2×D4×C47—81no—
92C2×D4×C47C22⋊C412yes—
93C2×D4×C47D812yes—
94C2×D4×C47SD1612yes—
95C22×C4×C47—21no—
96C22×C4×C47—22no—
97C22×C4×C47—22no—
98C22×C4×C47—41no—
99C22×C4×C47—41no—
100C22×C4×C47—41no—
101C22×C4×C47—41no—
102C22×C4×C47C2×D411yescharacteristic
103C22×C4×C47C2×D411yescharacteristic
104C22×C4×C47#4111yescharacteristic
105C22×Dic47—41no—
106D8×C47—48no—
107C2×C8×C47—22no—
108C2×C8×C47—41no—
109C2×C8×C47—41no—
110C4⋊C4×C47—21no—
111C4⋊C4×C47C22⋊C412yes—
112C22⋊C4×C47—22no—
113C22⋊C4×C47—22no—
114C42×C47C22×C411yescharacteristic
115C42×C47C2×D411yescharacteristic
116C42×C47C2×D411yescharacteristic
117C42×C47#4111yescharacteristic
118C4⋊Dic47—41no—
119C4⋊Dic47—41no—
120C4⋊Dic47—41no—
121C4⋊Dic47—41no—
122C4⋊Dic47—81no—
123C2×C47⋊C8—21no—
124C2×C47⋊C8—21no—
125C2×C47⋊C8—21no—
126C2×C47⋊C8—22no—
127C2×C47⋊C8—21no—
128C2×C47⋊C8—21no—
129C2×C47⋊C8—48no—
130C2×C47⋊C8—41no—
131C2×C47⋊C8—41no—
132C2×C47⋊C8—41no—
133C2×C47⋊C8—41no—
134C2×C47⋊C8—41no—
135C2×C47⋊C8D812yescomplemented
136C23×C47—22no—
137C23×C47—22no—
138C23×C47—22no—
139C23×C47—41no—
140C23×C47—41no—
141C23×C47—41no—
142C23×C47—41no—
143C23×C47—42no—
144C23×C47—81no—
145C23×C47—81no—
146C23×C47—81no—
147C23×C47—81no—
148C23×C47—81no—
149C23×C47—81no—
150C23×C47#12111yescharacteristic
151D4×C47—22no—
152D4×C47—22no—
153D4×C47—22no—
154D4×C47—42no—
155D4×C47—42no—
156D4×C47—42no—
157D4×C47—42no—
158D4×C47—82no—
159D4×C47—82no—
160D4×C47—81no—
161D4×C47—81no—
162D4×C47—81no—
163D4×C47—81no—
164D4×C47#10214yescomplemented
165C2×C4×C47—21no—
166C2×C4×C47—21no—
167C2×C4×C47—22no—
168C2×C4×C47—41no—
169C2×C4×C47—41no—
170C2×C4×C47—42no—
171C2×C4×C47—42no—
172C2×C4×C47—42no—
173C2×C4×C47—42no—
174C2×C4×C47C2×C22⋊C411yescharacteristic
175C2×C4×C47C4×D411yescharacteristic
176C2×C4×C47C4×D411yescharacteristic
177C2×C4×C47#12011yescharacteristic
178C2×C4×C47#12111yescharacteristic
179C2×C4×C47#12311yescharacteristic
180C2×C4×C47C2×D811yescharacteristic
181C2×C4×C47C2×D811yescharacteristic
182C2×C4×C47C2×SD1611yescharacteristic
183C2×C4×C47#13511yescharacteristic
184C2×C4×C47#13511yescharacteristic
185C2×C4×C47#13511yescharacteristic
186C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
187C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
188C2×Dic47—81no—
189C2×Dic47—81no—
190C2×Dic47—81no—
191C8×C47—42no—
192C47⋊C8—22no—
193C47⋊C8—42no—
194C47⋊C8—41no—
195C47⋊C8—81no—
196#9221—471nomaximal, Sylow
197C22×C47—24no—
198C22×C47—42no—
199C22×C47—42no—
200C22×C47—42no—
201C22×C47—42no—
202C22×C47—42no—
203C22×C47—42no—
204C22×C47—82no—
205C22×C47—82no—
206C22×C47—82no—
207C22×C47—161no—
208C22×C47—161no—
209C22×C47—161no—
210C22×C47—161no—
211C22×C47#38611yescharacteristic
212C22×C47#45911yescharacteristic
213C22×C47#46311yescharacteristic
214C22×C47#46511yescharacteristic
215C22×C47#46611yescharacteristic
216C22×C47#47111yescharacteristic
217C22×C47#47211yescharacteristic
218C4×C47—21no—
219C4×C47—21no—
220C4×C47—42no—
221C4×C47C2×#10211yescharacteristic
222C4×C47#41611yescharacteristic
223C4×C47C4×D811yescharacteristic
224C4×C47#44211yescharacteristic
225C4×C47#44711yescharacteristic
226C4×C47#44911yescharacteristic
227C4×C47#46511yescharacteristic
228C4×C47#46611yescharacteristic
229Dic47—161no—
230C2×#459D4711yescharacteristic
231C2×C8×D4—471no—
232#1957—471no—
233#1802—471no—
234C2×#331—471no—
235#1296—471no—
236#1277—471no—
237C2×C47—44no—
238C2×C47—162no—
239C2×C47#166511yescharacteristic
240C2×C47#166711yescharacteristic
241C2×C47#167711yescharacteristic
242C2×C47#168111yescharacteristic
243C2×C47#187911yescharacteristic
244C2×C47#189311yescharacteristic
245C2×C47#190711yescharacteristic
246C22×D8—21no—
247C23×C8—941no—
248C2×#127C2×D4711yescharacteristic
249C2×C4×D4C2×D4711yescharacteristic
250#459—22no—
251#459Dic4714yescomplemented
252C8×D4—942no—
253C8×D4—942no—
254C2×C4⋊C8—471no—
255C2×C4⋊C8—471no—
256C2×C4⋊C8C2×D4711yescharacteristic
257C2×#102—21no—
258C2×#102—941no—
259C2×#102—941no—
260C2×#102—941no—
261C2×C22⋊C8—941no—
262C2×C4×C8—471no—
263#384—471no—
264#340—941no—
265#331—942no—
266C47#922111yescharacteristic, complemented, Sylow
267C22×D4—21no—
268C22×D4—21no—
269C22×D4—21no—
270C22×D4C22⋊D4711yescharacteristic
271C23×C4—21no—
272C2×D8—24no—
273C2×D8—42no—
274C2×D8—42no—
275C22×C8—21no—
276C22×C8—471no—
277C22×C8—471no—
278C22×C8—944no—
279C22×C8—941no—
280C22×C8—941no—
281C22×C8—1882no—
282C22×C8—1882no—
283#127—21no—
284#127—21no—
285#127—21no—
286#127C2×Dic4712yes—
287C4×D4—21no—
288C4×D4—21no—
289C4×D4C2×Dic4712yes—
290C4×D4C22⋊D4712yes—
291C2×C4⋊C4—941no—
292C2×C4⋊C4—941no—
293C2×C4⋊C4—941no—
294C2×C4⋊C4C22⋊D4711yescharacteristic
295C2×C22⋊C4—21no—
296C2×C42C22×D4711yescharacteristic
297C4⋊C8—21no—
298C4⋊C8—472no—
299C4⋊C8—941no—
300C4⋊C8—941no—
301C4⋊C8—941no—
302C4⋊C8C2×Dic4712yes—
303#102—24no—
304#102—1882no—
305#102—1882no—
306#102—1882no—
307C22⋊C8—944no—
308C4×C8—941no—
309C4×C8—941no—
310C24—21no—
311C24—41no—
312C2×D4—22no—
313C2×D4—22no—
314C2×D4—22no—
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—21no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4—41no—
326C2×D4—41no—
327C2×D4—41no—
328C2×D4—41no—
329C2×D4—81no—
330C2×D4—81no—
331C2×D4#1062533412yes—
332C2×D4#1062533512yes—
333C2×D4C22⋊Dic4712yes—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—1881no—
342C22×C4D4×D4711yescharacteristic
343C22×C4#1062535211yescharacteristic
344C22×C4C2×C22⋊D4711yescharacteristic
345D8—48no—
346C2×C8—22no—
347C2×C8—41no—
348C2×C8—41no—
349C2×C8—472no—
350C2×C8—941no—
351C2×C8—941no—
352C2×C8—941no—
353C2×C8—942no—
354C2×C8—941no—
355C2×C8—941no—
356C2×C8—1888no—
357C2×C8—1881no—
358C2×C8—1881no—
359C2×C8—1881no—
360C2×C8—1881no—
361C2×C8—1881no—
362C4⋊C4—21no—
363C4⋊C4—3761no—
364C4⋊C4—1881no—
365C4⋊C4—1881no—
366C4⋊C4—1881no—
367C4⋊C4—1881no—
368C4⋊C4C22⋊Dic4712yes—
369C22⋊C4—22no—
370C22⋊C4—22no—
371C42D4×D4711yescharacteristic
372C42#1062535211yescharacteristic
373C42C22×Dic4711yescharacteristic
374C42C2×C22⋊D4711yescharacteristic
375C23—22no—
376C23—22no—
377C23—22no—
378C23—41no—
379C23—41no—
380C23—41no—
381C23—41no—
382C23—42no—
383C23—81no—
384C23—81no—
385C23—81no—
386C23—81no—
387C23—81no—
388C23—81no—
389C23#1309399611yescharacteristic
390D4—22no—
391D4—22no—
392D4—22no—
393D4—42no—
394D4—42no—
395D4—42no—
396D4—42no—
397D4—82no—
398D4—82no—
399D4—81no—
400D4—81no—
401D4—81no—
402D4—81no—
403D4#1309394514yescomplemented
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—22no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—3761no—
414C2×C4—3761no—
415C2×C4—3761no—
416C2×C4C2×C22⋊Dic4711yescharacteristic
417C2×C4D4×Dic4711yescharacteristic
418C2×C4D4×Dic4711yescharacteristic
419C2×C4#1309399211yescharacteristic
420C2×C4#1309399611yescharacteristic
421C2×C4#1309400511yescharacteristic
422C2×C4D8×D4711yescharacteristic
423C2×C4C2×#1062533411yescharacteristic
424C2×C4C2×#1062533511yescharacteristic
425C2×C4#1309404311yescharacteristic
426C2×C4#1309404411yescharacteristic
427C2×C4#1309404411yescharacteristic
428C2×C4#1309404811yescharacteristic
429C2×C4#1309404811yescharacteristic
430C8—42no—
431C8—942no—
432C8—3761no—
433C8—1882no—
434C8—1881no—
435C22—24no—
436C22—42no—
437C22—42no—
438C22—42no—
439C22—42no—
440C22—42no—
441C22—42no—
442C22—82no—
443C22—82no—
444C22—82no—
445C22—161no—
446C22—161no—
447C22—161no—
448C22—161no—
449C22#1568900311yescharacteristic
450C22#1568931611yescharacteristic
451C22#1568933611yescharacteristic
452C22#1568935011yescharacteristic
453C22#1568935711yescharacteristic
454C22#1568938411yescharacteristic
455C22#1568939111yescharacteristic
456C4—21no—
457C4—21no—
458C4—42no—
459C4—7521no—
460C4C2×#1309394511yescharacteristic
461C4#1568911911yescharacteristic
462C4D8×Dic4711yescharacteristic
463C4#1568923511yescharacteristic
464C4#1568925511yescharacteristic
465C4#1568926511yescharacteristic
466C4#1568935011yescharacteristic
467C4#1568935711yescharacteristic
468C2—44no—
469C2—162no—
470C2#2024272711yescharacteristic
471C2#2024274111yescharacteristic
472C2#2024279511yescharacteristic
473C2#2024282311yescharacteristic
474C2#2024373811yescharacteristic
475C2#2024381711yescharacteristic
476C2#2024389811yescharacteristic
subgroupG/H
centerC23#13093996
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
Fitting, prime radicalC2×C47×#459C2
socleC23×C47#121
cosocleC2×C42×C47C23
hypercenterC2×#459D47
hypocenterC47#9221
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C2×D4×C47⋊C8C2semidirect
2. #20244195C2semidirect
3. #20243388C2semidirect
4. C2×#15688867C2semidirect
5. #20241272C2semidirect
6. #20241222C2semidirect
25. C47×#459C4semidirect
135. C2×C47⋊C8D8semidirect
164. D4×C47#102semidirect
251. #459Dic47semidirect
266. C47#9221semidirect
403. D4#13093945semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C47⋊C82
#202441952
#202433882
C2×#156888672
#202412722
#202412222
C2×C47×#4592
#922147