Finite Group Databasebeta

← #26109346

Subgroups — #26109346

Order 12032.

438 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689247C211yesmaximal, characteristic
2#20243515C211yesmaximal, characteristic
3#20243394C211yesmaximal, characteristic
4#20243390C211yesmaximal, characteristic
5C2×#15688873C211yesmaximal, characteristic
6#20241272C211yesmaximal, characteristic
7C47×#1296C211yesmaximal, characteristic
8C2×C4×Dic94C2211yescharacteristic
9#15689247—22no—
10#15689247C414yescomplemented
11C2×C4⋊(C47⋊C8)C2211yescharacteristic
12C2×Dic47⋊C8—21no—
13C2×#13093949—21no—
14C2×#13093947—21no—
15C2×C4×C47⋊C8C2211yescharacteristic
16C2×C8×Dic47—21no—
17#15688993C2211yescharacteristic
18#15688886—21no—
19#15688885—21no—
20#15688885—21no—
21#15688885—21no—
22#15688873—22no—
23C2×C4⋊C8×C47C2211yescharacteristic
24C2×C4⋊C8×C47C2211yescharacteristic
25C47×#384C2211yescharacteristic
26C22×Dic94D411yescharacteristic
27C22×C47⋊C8—21no—
28C22×C47⋊C8D411yescharacteristic
29C22×C47⋊C8D411yescharacteristic
30C4×Dic94—21no—
31C4×Dic94—21no—
32C4×Dic94C2×C412yes—
33C4×Dic94Q812yes—
34C2×C4⋊Dic47—21no—
35C2×C4⋊Dic47—21no—
36C2×C4⋊Dic47—21no—
37C2×C4⋊Dic47D411yescharacteristic
38C2×Dic47⋊C4—21no—
39C2×C4×Dic47—21no—
40C4⋊(C47⋊C8)—21no—
41C4⋊(C47⋊C8)—21no—
42Dic47⋊C8—24no—
43#13093949—42no—
44#13093947—42no—
45C4×C47⋊C8C2×C412yes—
46C4×C47⋊C8D412yes—
47C8×Dic47—24no—
48C22×C8×C47—21no—
49C22×C8×C47—21no—
50C2×C4⋊C4×C47—21no—
51C2×C4⋊C4×C47—21no—
52C2×C4⋊C4×C47—21no—
53C2×C42×C47C2311yescharacteristic
54C4⋊C8×C47—21no—
55C4⋊C8×C47—21no—
56C4⋊C8×C47—21no—
57C4⋊C8×C47C2×C412yes—
58C22×C4×C47—41no—
59C22×C4×C47C2×D411yescharacteristic
60C22×C4×C47C2×D411yescharacteristic
61C22×C4×C47#4111yescharacteristic
62C22×Dic47—21no—
63C22×Dic47—21no—
64C22×Dic47—41no—
65C2×Dic94—21no—
66C2×Dic94—21no—
67C2×Dic94—21no—
68C2×Dic94C4⋊C412yes—
69C2×Dic94SD1612yes—
70C2×Dic94SD1612yes—
71C2×C8×C47—22no—
72C2×C8×C47—41no—
73C2×C8×C47—41no—
74C2×C8×C47—41no—
75C2×C8×C47—41no—
76C2×C8×C47—41no—
77C4⋊C4×C47—41no—
78C4⋊C4×C47—41no—
79C4⋊C4×C47—41no—
80C4⋊C4×C47—41no—
81C4⋊C4×C47—81no—
82C42×C47C22×C411yescharacteristic
83C42×C47C2×D411yescharacteristic
84C42×C47C2×Q811yescharacteristic
85C42×C47#4111yescharacteristic
86C4⋊Dic47—21no—
87C4⋊Dic47—41no—
88C4⋊Dic47—41no—
89C4⋊Dic47—41no—
90C4⋊Dic47—41no—
91C4⋊Dic47—81no—
92C4⋊Dic47C4⋊C412yes—
93Dic47⋊C4—22no—
94Dic47⋊C4—22no—
95C4×Dic47—22no—
96C4×Dic47—22no—
97C2×C47⋊C8—21no—
98C2×C47⋊C8—21no—
99C2×C47⋊C8—21no—
100C2×C47⋊C8—21no—
101C2×C47⋊C8—41no—
102C2×C47⋊C8—41no—
103C2×C47⋊C8—41no—
104C2×C47⋊C8C22⋊C412yes—
105C2×C47⋊C8C22⋊C412yes—
106C23×C47#12111yescharacteristic
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—81no—
110C2×C4×C47—81no—
111C2×C4×C47—81no—
112C2×C4×C47C2×C22⋊C411yescharacteristic
113C2×C4×C47C2×C4⋊C411yescharacteristic
114C2×C4×C47#11711yescharacteristic
115C2×C4×C47#12111yescharacteristic
116C2×C4×C47C22⋊Q811yescharacteristic
117C2×C4×C47C22⋊Q811yescharacteristic
118C2×C4×C47C2×SD1611yescharacteristic
119C2×C4×C47C2×SD1611yescharacteristic
120C2×C4×C47#13511yescharacteristic
121C2×C4×C47#13511yescharacteristic
122C2×C4×C47#13511yescharacteristic
123C2×C4×C47#13511yescharacteristic
124C2×C4×C47#13711yescharacteristic
125C2×C4×C47#13711yescharacteristic
126C2×Dic47—22no—
127C2×Dic47—22no—
128C2×Dic47—22no—
129C2×Dic47—22no—
130C2×Dic47—41no—
131C2×Dic47—41no—
132C2×Dic47—81no—
133C2×Dic47—81no—
134C2×Dic47—81no—
135Dic94—22no—
136Dic94—22no—
137Dic94—22no—
138Dic94#10614yes—
139C8×C47—42no—
140C8×C47—81no—
141C47⋊C8—22no—
142C47⋊C8—22no—
143C47⋊C8—81no—
144#8647—471nomaximal, Sylow
145C22×C47#38011yescharacteristic
146C22×C47#46411yescharacteristic
147C22×C47#46411yescharacteristic
148C22×C47#46511yescharacteristic
149C22×C47#46511yescharacteristic
150C22×C47#47211yescharacteristic
151C22×C47#47311yescharacteristic
152C4×C47—21no—
153C4×C47—21no—
154C4×C47—161no—
155C4×C47#41611yescharacteristic
156C4×C47#41911yescharacteristic
157C4×C47C2×#10611yescharacteristic
158C4×C47#42711yescharacteristic
159C4×C47#46511yescharacteristic
160C4×C47#46511yescharacteristic
161C4×C47#47911yescharacteristic
162C4×C47#47911yescharacteristic
163Dic47—24no—
164Dic47—42no—
165Dic47—161no—
166C2×C8×Q8—471no—
167#1834—471no—
168#1803—471no—
169#1803—471no—
170C2×#334—471no—
171#1296—471no—
172#1296D4711yescharacteristic
173C2×C47#167811yescharacteristic
174C2×C47#167811yescharacteristic
175C2×C47#168011yescharacteristic
176C2×C47#168011yescharacteristic
177C2×C47#180511yescharacteristic
178C2×C47#180711yescharacteristic
179C2×C47#181611yescharacteristic
180C2×C4×Q8—471no—
181C8×Q8—474no—
182C8×Q8—942no—
183C2×C4⋊C8—471no—
184C2×C4⋊C8—941no—
185C2×C4⋊C8C2×D4711yescharacteristic
186C2×C4⋊C8C2×D4711yescharacteristic
187C2×#103—941no—
188C2×#103—941no—
189C2×C4×C8—471no—
190C2×C4×C8—941no—
191#384—471no—
192#384C2×D4711yescharacteristic
193#340—941no—
194#340—941no—
195#340—941no—
196#340—941no—
197#334—942no—
198C47#864711yescharacteristic, complemented, Sylow
199C22×Q8—471no—
200C22×C8—21no—
201C22×C8—21no—
202C22×C8—471no—
203C22×C8—471no—
204C22×C8—941no—
205C4×Q8—472no—
206C4×Q8—472no—
207C4×Q8—941no—
208C4×Q8—941no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—471no—
213C2×C4⋊C4—941no—
214C2×C4⋊C4—941no—
215C2×C4⋊C4—941no—
216C2×C4⋊C4—941no—
217C2×C42—941no—
218C2×C42C22×D4711yescharacteristic
219C4⋊C8—21no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—944no—
223C4⋊C8—941no—
224C4⋊C8—941no—
225C4⋊C8C4×D4712yes—
226#103—1882no—
227#103—1882no—
228C4×C8—472no—
229C4×C8—472no—
230C4×C8—944no—
231C2×Q8—472no—
232C2×Q8—472no—
233C2×Q8—472no—
234C2×Q8—941no—
235C2×Q8—941no—
236C2×Q8—941no—
237C22×C4—41no—
238C22×C4—941no—
239C22×C4—941no—
240C22×C4—1881no—
241C22×C4#1062535011yescharacteristic
242C22×C4D4×D4711yescharacteristic
243C22×C4D4×D4711yescharacteristic
244C2×C8—22no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—41no—
250C2×C8—472no—
251C2×C8—472no—
252C2×C8—941no—
253C2×C8—941no—
254C2×C8—941no—
255C2×C8—941no—
256C2×C8—1881no—
257C2×C8—1881no—
258C2×C8—1881no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—81no—
264C4⋊C4—472no—
265C4⋊C4—942no—
266C4⋊C4—941no—
267C4⋊C4—942no—
268C4⋊C4—3761no—
269C4⋊C4—1881no—
270C4⋊C4—1881no—
271C4⋊C4—1881no—
272C4⋊C4—1881no—
273C42—942no—
274C42—942no—
275C42C2×C4×D4711yescharacteristic
276C42#1062535011yescharacteristic
277C42D4×D4711yescharacteristic
278C42Q8×D4711yescharacteristic
279C23#1309399711yescharacteristic
280Q8—474no—
281Q8—942no—
282Q8—942no—
283Q8—942no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—942no—
290C2×C4—942no—
291C2×C4—942no—
292C2×C4—942no—
293C2×C4—3761no—
294C2×C4—3761no—
295C2×C4—3761no—
296C2×C4—1881no—
297C2×C4—1881no—
298C2×C4C22⋊C4×D4711yescharacteristic
299C2×C4C4⋊C4×D4711yescharacteristic
300C2×C4#1309398111yescharacteristic
301C2×C4#1309399711yescharacteristic
302C2×C4#1309400211yescharacteristic
303C2×C4#1309400211yescharacteristic
304C2×C4SD16×D4711yescharacteristic
305C2×C4SD16×D4711yescharacteristic
306C2×C4#1309404311yescharacteristic
307C2×C4#1309404311yescharacteristic
308C2×C4#1309404511yescharacteristic
309C2×C4#1309404711yescharacteristic
310C2×C4#1309405311yescharacteristic
311C2×C4#1309405611yescharacteristic
312C8—42no—
313C8—81no—
314C8—942no—
315C8—942no—
316C8—3761no—
317C22#1568898211yescharacteristic
318C22#1568934411yescharacteristic
319C22#1568934811yescharacteristic
320C22#1568935111yescharacteristic
321C22#1568935511yescharacteristic
322C22#1568939211yescharacteristic
323C22#1568939711yescharacteristic
324C4—21no—
325C4—21no—
326C4—161no—
327C4—944no—
328C4—1882no—
329C4—7521no—
330C4#1568911611yescharacteristic
331C4#1568913011yescharacteristic
332C4#106×D4711yescharacteristic
333C4#1568916011yescharacteristic
334C4#1568935111yescharacteristic
335C4#1568935511yescharacteristic
336C4#1568942911yescharacteristic
337C4#1568943311yescharacteristic
338C2#2024280311yescharacteristic
339C2#2024280711yescharacteristic
340C2#2024281711yescharacteristic
341C2#2024282111yescharacteristic
342C2#2024340211yescharacteristic
343C2#2024341211yescharacteristic
344C2#2024345111yescharacteristic
subgroupG/H
centerC23#13093997
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1296C2
socle, prime radicalC23×C47#121
cosocleC2×C42×C47C23
hypercenter#1296D47
hypocenterC47#8647
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
10. #15689247C4semidirect
198. C47#8647semidirect

Maximal subgroups

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

subgroupindex
C2×#156892472
#202435152
#202433942
#202433902
C2×#156888732
#202412722
C47×#12962
#864747