Finite Group Databasebeta

← #26120805

Subgroups — #26120805

Order 12032.

370 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20244350C211yesmaximal, characteristic
2#20244337C211yesmaximal, characteristic
3#20244147C211yesmaximal, characteristic
4#20244104C211yesmaximal, characteristic
5C2×#15688873C211yesmaximal, characteristic
6#20241272C211yesmaximal, characteristic
7C2×C47×#333C211yesmaximal, characteristic
8C2×#13093958—21no—
9C2×C4⋊(C47⋊C8)C2211yescharacteristic
10C2×Dic47⋊C8—21no—
11C2×C4×C47⋊C8C2211yescharacteristic
12#15688993C2211yescharacteristic
13C4×C4⋊Dic47C2211yescharacteristic
14#15688886—21no—
15#15688885—21no—
16#15688885—21no—
17#15688885—21no—
18#15688885—21no—
19#15688877—21no—
20#15688873—22no—
21C2×C4⋊Q8×C47C2211yescharacteristic
22C2×C4⋊C8×C47C2211yescharacteristic
23C2×C4⋊C8×C47C2211yescharacteristic
24C47×#333—22no—
25C22×C47⋊C8—21no—
26C22×C47⋊C8D411yescharacteristic
27C22×C47⋊C8D411yescharacteristic
28C2×C4⋊Dic47—21no—
29C2×C4⋊Dic47—21no—
30C2×C4⋊Dic47—21no—
31C2×C4⋊Dic47D411yescharacteristic
32C2×C4⋊Dic47D411yescharacteristic
33C2×C4×Dic47—21no—
34#13093958—42no—
35C4⋊(C47⋊C8)—21no—
36C4⋊(C47⋊C8)—21no—
37Dic47⋊C8—42no—
38C4×C47⋊C8—21no—
39C4×C47⋊C8—21no—
40C47⋊#95—21no—
41C22×Q8×C47—21no—
42C22×C8×C47—21no—
43C22×C8×C47—21no—
44C4⋊Q8×C47—21no—
45C4⋊Q8×C47—21no—
46C4⋊Q8×C47—21no—
47C4⋊Q8×C47Q812yes—
48C2×C4⋊C4×C47—21no—
49C2×C4⋊C4×C47—21no—
50C2×C42×C47C2311yescharacteristic
51C4⋊C8×C47—21no—
52C4⋊C8×C47—21no—
53C4⋊C8×C47—21no—
54C4⋊C8×C47D412yes—
55C2×Q8×C47—22no—
56C2×Q8×C47—41no—
57C2×Q8×C47—81no—
58C2×Q8×C47—81no—
59C22×C4×C47—41no—
60C22×C4×C47C2×D411yescharacteristic
61C22×C4×C47C2×D411yescharacteristic
62C22×C4×C47#4111yescharacteristic
63C22×Dic47—21no—
64C22×Dic47—21no—
65C22×Dic47—41no—
66C2×C8×C47—22no—
67C2×C8×C47—41no—
68C2×C8×C47—41no—
69C2×C8×C47—41no—
70C2×C8×C47—41no—
71C2×C8×C47—41no—
72C4⋊C4×C47—22no—
73C4⋊C4×C47—22no—
74C4⋊C4×C47—41no—
75C4⋊C4×C47—41no—
76C42×C47C2×D411yescharacteristic
77C42×C47C2×Q811yescharacteristic
78C42×C47#4111yescharacteristic
79C42×C47#4111yescharacteristic
80C4⋊Dic47—21no—
81C4⋊Dic47—21no—
82C4⋊Dic47—21no—
83C4⋊Dic47—41no—
84C4⋊Dic47—41no—
85C4⋊Dic47—41no—
86C4⋊Dic47—41no—
87C4⋊Dic47—81no—
88C4⋊Dic47SD1612yes—
89C4×Dic47—41no—
90C4×Dic47—41no—
91C2×C47⋊C8—21no—
92C2×C47⋊C8—21no—
93C2×C47⋊C8—21no—
94C2×C47⋊C8—21no—
95C2×C47⋊C8—21no—
96C2×C47⋊C8—41no—
97C2×C47⋊C8—41no—
98C2×C47⋊C8—41no—
99C2×C47⋊C8Q1612yes—
100C23×C47#12111yescharacteristic
101Q8×C47—82no—
102Q8×C47—82no—
103C2×C4×C47—21no—
104C2×C4×C47—21no—
105C2×C4×C47—42no—
106C2×C4×C47—81no—
107C2×C4×C47—81no—
108C2×C4×C47#12111yescharacteristic
109C2×C4×C47#12111yescharacteristic
110C2×C4×C47C22⋊Q811yescharacteristic
111C2×C4×C47C22⋊Q811yescharacteristic
112C2×C4×C47C22⋊Q811yescharacteristic
113C2×C4×C47#12611yescharacteristic
114C2×C4×C47C2×SD1611yescharacteristic
115C2×C4×C47C2×Q1611yescharacteristic
116C2×C4×C47#13511yescharacteristic
117C2×C4×C47#13511yescharacteristic
118C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C47#13711yescharacteristic
120C2×C4×C47#13711yescharacteristic
121C2×C4×C47#13711yescharacteristic
122C2×Dic47—22no—
123C2×Dic47—41no—
124C2×Dic47—41no—
125C2×Dic47—41no—
126C2×Dic47—41no—
127C2×Dic47—41no—
128C2×Dic47—81no—
129C2×Dic47—81no—
130C2×Dic47—81no—
131C8×C47—42no—
132C8×C47—81no—
133C47⋊C8—22no—
134C47⋊C8—41no—
135C47⋊C8—81no—
136#10589—471nomaximal, Sylow
137C22×C47#39611yescharacteristic
138C22×C47#46211yescharacteristic
139C22×C47#46311yescharacteristic
140C22×C47#46511yescharacteristic
141C22×C47#47011yescharacteristic
142C22×C47#47111yescharacteristic
143C22×C47#47211yescharacteristic
144C4×C47—21no—
145C4×C47—21no—
146C4×C47—82no—
147C4×C47#46111yescharacteristic
148C4×C47#46411yescharacteristic
149C4×C47#46711yescharacteristic
150C4×C47#46811yescharacteristic
151C4×C47#47511yescharacteristic
152C4×C47#47711yescharacteristic
153C4×C47#47911yescharacteristic
154C4×C47#47911yescharacteristic
155Dic47—42no—
156Dic47—81no—
157Dic47—161no—
158#1990—471no—
159#1987—471no—
160#1947—471no—
161#1939—471no—
162C2×#334—471no—
163C2×#333D4711yescharacteristic
164#1296—471no—
165C2×C47#167211yescharacteristic
166C2×C47#167711yescharacteristic
167C2×C47#169611yescharacteristic
168C2×C47#170311yescharacteristic
169C2×C47#206311yescharacteristic
170C2×C47#206611yescharacteristic
171C2×C47#206811yescharacteristic
172C2×C4⋊Q8C2×D4711yescharacteristic
173C2×#107—941no—
174C2×C4⋊C8—471no—
175C2×C4⋊C8—941no—
176C2×C4⋊C8C2×D4711yescharacteristic
177C2×C4⋊C8C2×D4711yescharacteristic
178C2×C4×C8—471no—
179#384—471no—
180C4×C4⋊C4—471no—
181#340—941no—
182#340—941no—
183#340—941no—
184#340—941no—
185#340—941no—
186#336—941no—
187#334—942no—
188#333—22no—
189C47#1058911yescharacteristic, complemented, Sylow
190C22×Q8—21no—
191C22×C8—21no—
192C22×C8—21no—
193C22×C8—471no—
194C22×C8—471no—
195C22×C8—941no—
196C4⋊Q8—21no—
197C4⋊Q8—21no—
198C4⋊Q8—21no—
199C4⋊Q8Dic9412yes—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—471no—
203C2×C4⋊C4—471no—
204C2×C4⋊C4—941no—
205C2×C4⋊C4—941no—
206C2×C4⋊C4—941no—
207C2×C42—941no—
208C2×C42C22×D4711yescharacteristic
209#107—1882no—
210C4⋊C8—21no—
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—941no—
214C4⋊C8—941no—
215C4⋊C8—1882no—
216C4⋊C8C22⋊D4712yes—
217C4×C8—941no—
218C4×C8—941no—
219#95—941no—
220C2×Q8—22no—
221C2×Q8—41no—
222C2×Q8—81no—
223C2×Q8—81no—
224C22×C4—41no—
225C22×C4—941no—
226C22×C4—941no—
227C22×C4—1881no—
228C22×C4#1062535011yescharacteristic
229C22×C4D4×D4711yescharacteristic
230C22×C4D4×D4711yescharacteristic
231C2×C8—22no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—472no—
238C2×C8—941no—
239C2×C8—941no—
240C2×C8—941no—
241C2×C8—941no—
242C2×C8—941no—
243C2×C8—1881no—
244C2×C8—1881no—
245C2×C8—1881no—
246C4⋊C4—22no—
247C4⋊C4—22no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—472no—
251C4⋊C4—941no—
252C4⋊C4—941no—
253C4⋊C4—941no—
254C4⋊C4—3761no—
255C4⋊C4—1881no—
256C4⋊C4—1881no—
257C4⋊C4—1881no—
258C4⋊C4—1881no—
259C42—1881no—
260C42—1881no—
261C42C2×Dic9411yescharacteristic
262C42#1062535211yescharacteristic
263C42#1062535211yescharacteristic
264C42C2×C22⋊D4711yescharacteristic
265C23#1309399711yescharacteristic
266Q8—82no—
267Q8—82no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—42no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—942no—
274C2×C4—3761no—
275C2×C4—3761no—
276C2×C4—3761no—
277C2×C4—1881no—
278C2×C4—1881no—
279C2×C4—1881no—
280C2×C4—1881no—
281C2×C4—1881no—
282C2×C4#1309399511yescharacteristic
283C2×C4#1309399611yescharacteristic
284C2×C4#1309400111yescharacteristic
285C2×C4#1309400111yescharacteristic
286C2×C4#1309400311yescharacteristic
287C2×C4#1309401711yescharacteristic
288C2×C4SD16×D4711yescharacteristic
289C2×C4Q16×D4711yescharacteristic
290C2×C4#1309404711yescharacteristic
291C2×C4#1309404711yescharacteristic
292C2×C4#1309405111yescharacteristic
293C2×C4#1309405311yescharacteristic
294C2×C4#1309405311yescharacteristic
295C2×C4#1309405611yescharacteristic
296C8—42no—
297C8—81no—
298C8—942no—
299C8—3761no—
300C8—1881no—
301C22#1568904611yescharacteristic
302C22#1568933211yescharacteristic
303C22#1568934111yescharacteristic
304C22#1568935511yescharacteristic
305C22#1568938011yescharacteristic
306C22#1568938511yescharacteristic
307C22#1568939211yescharacteristic
308C4—21no—
309C4—21no—
310C4—82no—
311C4—3761no—
312C4—1882no—
313C4—7521no—
314C4#1568932611yescharacteristic
315C4#1568934711yescharacteristic
316C4#1568936111yescharacteristic
317C4#1568936611yescharacteristic
318C4#1568940611yescharacteristic
319C4#1568941611yescharacteristic
320C4#1568943211yescharacteristic
321C4#1568943211yescharacteristic
322C2#2024277311yescharacteristic
323C2#2024280011yescharacteristic
324C2#2024291511yescharacteristic
325C2#2024296611yescharacteristic
326C2#2024474411yescharacteristic
327C2#2024476511yescharacteristic
328C2#2024478111yescharacteristic
subgroupG/H
centerC23#13093997
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC2×C47×#333C2
socle, prime radicalC23×C47#121
hypercenterC2×#333D47
hypocenterC47#10589
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
189. C47#10589semidirect

Maximal subgroups

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

subgroupindex
#202443502
#202443372
#202441472
#202441042
C2×#156888732
#202412722
C2×C47×#3332
#1058947