Finite Group Databasebeta

← #26119306

Subgroups — #26119306

Order 12032.

500 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20248627C211yesmaximal, characteristic, complemented
2#20244315C211yesmaximal, characteristic
3#20244314C211yesmaximal, characteristic
4#20244194C211yesmaximal, characteristic
5#20241272C211yesmaximal, characteristic, complemented
6#20241228C211yesmaximal, characteristic, complemented
7C47×#1279C211yesmaximal, characteristic, complemented
8C2×#13094021C2211yescharacteristic
9C2×C4⋊(C47⋊C8)C2211yescharacteristic
10C2×#13093946—21no—
11C2×#13093946—21no—
12C2×#13093946—22no—
13C2×#13093944—21no—
14C2×#13093944—21no—
15#15689065—22no—
16#15689021—21no—
17#15689019—21no—
18#15688993C2211yescharacteristic
19#15688989—21no—
20#15688988—21no—
21C4×C4⋊Dic47C2211yescharacteristic
22C2×C4⋊C8×C47C2211yescharacteristic
23C2×C4×C8×C47C2211yescharacteristic
24C4×C4⋊C4×C47C2211yescharacteristic
25C22×D188—21no—
26C22×D188—21no—
27C22×D188—21no—
28C22×C47⋊C8—21no—
29#13094021—21no—
30#13094021—21no—
31#13094021—21no—
32#13094021Q812yes—
33C2×C4⋊Dic47—21no—
34C2×C4⋊Dic47—21no—
35C2×C4⋊Dic47D411yescharacteristic
36C2×C4⋊Dic47D411yescharacteristic
37C2×C4⋊Dic47D412yes—
38C2×Dic47⋊C4—22no—
39C2×C4×Dic47—21no—
40C4⋊(C47⋊C8)—21no—
41C4⋊(C47⋊C8)—21no—
42#13093946—42no—
43#13093946—42no—
44#13093946—44no—
45#13093944—42no—
46#13093944—42no—
47C47⋊#95—22no—
48C47⋊#95—22no—
49C47⋊#95—22no—
50C47⋊#95—21no—
51C22×C8×C47—21no—
52C22×C8×C47—21no—
53C2×C4⋊C4×C47D411yescharacteristic
54C2×C4⋊C4×C47D411yescharacteristic
55C2×C42×C47—21no—
56C2×C42×C47C2311yescharacteristic
57C4⋊C8×C47—21no—
58C4⋊C8×C47—21no—
59C4×C8×C47—21no—
60C4×C8×C47—21no—
61#95×C47—21no—
62C23×D47—41no—
63C22×C4×C47—21no—
64C22×C4×C47—21no—
65C22×C4×C47C2×D411yescharacteristic
66C22×C4×C47C2×D411yescharacteristic
67C22×C4×C47C2×D411yescharacteristic
68C22×Dic47—21no—
69C22×Dic47—21no—
70C22×Dic47—22no—
71C2×D188—22no—
72C2×D188—22no—
73C2×D188—22no—
74C2×D188—42no—
75C2×D188—42no—
76C2×D188—41no—
77C2×D188—41no—
78C2×D188—41no—
79C2×D188—41no—
80C2×D188—41no—
81C2×D188—41no—
82C2×D188—41no—
83C2×D188—41no—
84C2×D188—41no—
85C2×D188—41no—
86C2×D188—41no—
87C2×C8×C47—22no—
88C2×C8×C47—41no—
89C2×C8×C47—41no—
90C2×C8×C47—41no—
91C2×C8×C47—41no—
92C2×C8×C47—41no—
93C4⋊C4×C47—21no—
94C4⋊C4×C47—21no—
95C4⋊C4×C47—21no—
96C4⋊C4×C47—21no—
97C42×C47—41no—
98C42×C47—41no—
99C42×C47C2×Q811yescharacteristic
100C42×C47#4111yescharacteristic
101C42×C47#4111yescharacteristic
102C42×C47#4111yescharacteristic
103C4⋊Dic47—21no—
104C4⋊Dic47—21no—
105C4⋊Dic47—21no—
106C4⋊Dic47—21no—
107C4⋊Dic47—41no—
108C4⋊Dic47—41no—
109C4⋊Dic47—41no—
110C4⋊Dic47—41no—
111C4⋊Dic47—42no—
112Dic47⋊C4—82no—
113C4×Dic47—41no—
114C4×Dic47—41no—
115C2×C47⋊C8—41no—
116C2×C47⋊C8—41no—
117C2×C47⋊C8—41no—
118C23×C47#12011yescharacteristic
119C22×D47—42no—
120C22×D47—81no—
121C22×D47—81no—
122C22×D47—81no—
123C22×D47—81no—
124C22×D47—81no—
125C22×D47—81no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—41no—
129C2×C4×C47—41no—
130C2×C4×C47—41no—
131C2×C4×C47—41no—
132C2×C4×C47—41no—
133C2×C4×C47—41no—
134C2×C4×C47C22⋊Q811yescharacteristic
135C2×C4×C47C22⋊Q811yescharacteristic
136C2×C4×C47C22⋊Q811yescharacteristic
137C2×C4×C47#12411yescharacteristic
138C2×C4×C47#12411yescharacteristic
139C2×C4×C47#12411yescharacteristic
140C2×C4×C47#13511yescharacteristic
141C2×C4×C47#13511yescharacteristic
142C2×C4×C47#13511yescharacteristic
143C2×C4×C47#13511yescharacteristic
144C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
148C2×Dic47—41no—
149C2×Dic47—41no—
150C2×Dic47—41no—
151C2×Dic47—41no—
152C2×Dic47—42no—
153C2×Dic47—42no—
154C2×Dic47—41no—
155C2×Dic47—42no—
156C2×Dic47—41no—
157D188—44no—
158D188—42no—
159D188—42no—
160D188—42no—
161D188—42no—
162D188—82no—
163D188—81no—
164D188—81no—
165D188—81no—
166D188—81no—
167C8×C47—42no—
168C8×C47—81no—
169C47⋊C8—81no—
170#10351—471nomaximal, Sylow
171C22×C47#39311yescharacteristic
172C22×C47#44911yescharacteristic
173C22×C47#44911yescharacteristic
174C22×C47#44911yescharacteristic
175C22×C47#44911yescharacteristic
176C22×C47#45311yescharacteristic
177C22×C47#45411yescharacteristic
178C2×D47—82no—
179C2×D47—82no—
180C2×D47—82no—
181C2×D47—161no—
182C2×D47—161no—
183C2×D47—161no—
184C2×D47—161no—
185C4×C47—21no—
186C4×C47—21no—
187C4×C47—81no—
188C4×C47—81no—
189C4×C47#47811yescharacteristic
190C4×C47#47811yescharacteristic
191C4×C47#47811yescharacteristic
192C4×C47#47811yescharacteristic
193C4×C47#48811yescharacteristic
194C4×C47#48811yescharacteristic
195C4×C47#49011yescharacteristic
196C4×C47#49011yescharacteristic
197Dic47—82no—
198Dic47—81no—
199Dic47—81no—
200#2571—471no—
201#1982—471no—
202#1982—471no—
203#1957—471no—
204#1296—471no—
205#1279—471no—
206#1279D4711yescharacteristic, complemented
207C2×C47#162011yescharacteristic
208C2×C47#162411yescharacteristic
209C2×C47#162811yescharacteristic
210C2×C47#162811yescharacteristic
211C2×C47#202511yescharacteristic
212C2×C47#202511yescharacteristic
213C2×C47#202711yescharacteristic
214D47—162no—
215C2×#127—471no—
216C2×C4⋊C8—471no—
217C2×C4⋊C8C2×D4711yescharacteristic
218C2×#102—942no—
219C2×#102—941no—
220C2×#102—941no—
221C2×#102—941no—
222C2×#102—941no—
223C2×C4×C8C2×D4711yescharacteristic
224#400—942no—
225#389—941no—
226#389—941no—
227#384—471no—
228#382—941no—
229#382—941no—
230C4×C4⋊C4—471no—
231C4×C4⋊C4C2×D4711yescharacteristic
232C47#1035111yescharacteristic, complemented, Sylow
233C22×D4—941no—
234C22×D4—941no—
235C22×D4—941no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—941no—
239#127—472no—
240#127—941no—
241#127—941no—
242#127—941no—
243C2×C4⋊C4—471no—
244C2×C4⋊C4—471no—
245C2×C4⋊C4—472no—
246C2×C4⋊C4—942no—
247C2×C4⋊C4—941no—
248C2×C4⋊C4—941no—
249C2×C4⋊C4D18811yescharacteristic
250C2×C4⋊C4D18811yescharacteristic
251C2×C42—21no—
252C2×C42—941no—
253C2×C42C22×D4711yescharacteristic
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8—941no—
257C4⋊C8—941no—
258#102—1882no—
259#102—1882no—
260#102—1882no—
261#102—1882no—
262#102—1884no—
263C4×C8—21no—
264C4×C8—21no—
265#95—21no—
266#95—942no—
267#95—942no—
268#95—942no—
269#95—941no—
270C24—1881no—
271C2×D4—942no—
272C2×D4—942no—
273C2×D4—942no—
274C2×D4—1882no—
275C2×D4—1882no—
276C2×D4—1881no—
277C2×D4—1881no—
278C2×D4—1881no—
279C2×D4—1881no—
280C2×D4—1881no—
281C2×D4—1881no—
282C2×D4—1881no—
283C2×D4—1881no—
284C2×D4—1881no—
285C2×D4—1881no—
286C2×D4—1881no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—941no—
290C22×C4—941no—
291C22×C4—942no—
292C22×C4C2×D18811yescharacteristic
293C22×C4D4×D4711yescharacteristic
294C22×C4D4×D4711yescharacteristic
295C2×C8—22no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—1881no—
302C2×C8—1881no—
303C2×C8—1881no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—941no—
309C4⋊C4—941no—
310C4⋊C4—941no—
311C4⋊C4—941no—
312C4⋊C4—3762no—
313C4⋊C4—1882no—
314C4⋊C4—1881no—
315C4⋊C4—1881no—
316C4⋊C4—1881no—
317C4⋊C4—1881no—
318C42—41no—
319C42—41no—
320C42—1881no—
321C42—1881no—
322C42#1062535011yescharacteristic
323C42#1062535011yescharacteristic
324C42#1062535211yescharacteristic
325C42Q8×D4711yescharacteristic
326C23—3761no—
327C23—3761no—
328C23—3761no—
329C23—3761no—
330C23—3761no—
331C23—3761no—
332C23—1882no—
333C23#1309399411yescharacteristic
334D4—3762no—
335D4—3761no—
336D4—3761no—
337D4—3761no—
338D4—3761no—
339D4—1884no—
340D4—1882no—
341D4—1882no—
342D4—1882no—
343D4—1882no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—1881no—
353C2×C4—1881no—
354C2×C4—1881no—
355C2×C4—1882no—
356C2×C4—1881no—
357C2×C4—1882no—
358C2×C4—1881no—
359C2×C4—1882no—
360C2×C4—1881no—
361C2×C4#1309400211yescharacteristic
362C2×C4#1309400211yescharacteristic
363C2×C4#1309400411yescharacteristic
364C2×C4#1309401011yescharacteristic
365C2×C4#1309401011yescharacteristic
366C2×C4#1309401211yescharacteristic
367C2×C4#1309404511yescharacteristic
368C2×C4#1309404611yescharacteristic
369C2×C4#1309404611yescharacteristic
370C2×C4#1309404711yescharacteristic
371C2×C4#1309404811yescharacteristic
372C2×C4#1309405111yescharacteristic
373C2×C4#1309405211yescharacteristic
374C2×C4#1309405211yescharacteristic
375C8—42no—
376C8—81no—
377C8—3761no—
378C22—3762no—
379C22—3762no—
380C22—3762no—
381C22—7521no—
382C22—7521no—
383C22—7521no—
384C22—7521no—
385C22#1568903611yescharacteristic
386C22#1568926911yescharacteristic
387C22#1568927011yescharacteristic
388C22#1568927011yescharacteristic
389C22#1568927111yescharacteristic
390C22#1568929211yescharacteristic
391C22#1568929711yescharacteristic
392C4—21no—
393C4—21no—
394C4—81no—
395C4—81no—
396C4—3762no—
397C4—3761no—
398C4—3761no—
399C4#1568942211yescharacteristic
400C4#1568942411yescharacteristic
401C4#1568942411yescharacteristic
402C4#1568942611yescharacteristic
403C4#1568947811yescharacteristic
404C4#1568947911yescharacteristic
405C4#1568948611yescharacteristic
406C4#1568948811yescharacteristic
407C2—7522no—
408C2#2024244911yescharacteristic
409C2#2024247311yescharacteristic
410C2#2024250011yescharacteristic
411C2#2024250111yescharacteristic
412C2#2024453311yescharacteristic
413C2#2024453511yescharacteristic
414C2#2024454311yescharacteristic
subgroupG/H
centerC23#13093994
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1279C2
socleC23×C47#120
prime radicalC2×#13094021C22
hypercenter#1279D47
hypocenterC47#10351
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
1. #20248627C2semidirect
5. #20241272C2semidirect
6. #20241228C2semidirect
7. C47×#1279C2semidirect
206. #1279D47semidirect
232. C47#10351semidirect

Maximal subgroups

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

subgroupindex
#202486272
#202443152
#202443142
#202441942
#202412722
#202412282
C47×#12792
#1035147