Finite Group Databasebeta

← #26105436

Subgroups — #26105436

Order 12032.

350 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20244946C211yesmaximal, characteristic
2#20244859C211yesmaximal, characteristic
3#20244796C211yesmaximal, characteristic
4#20241214C211yesmaximal, characteristic
5#20241211C211yesmaximal, characteristic
6#20241211C211yesmaximal, characteristic
7C47×#2805C211yesmaximal, characteristic
8C2×#13093957—21no—
9C2×#13093948—21no—
10#15688993C2211yescharacteristic
11#15688885—21no—
12#15688885—21no—
13#15688885—21no—
14#15688885—21no—
15#15688878C2211yescharacteristic
16#15688878C2211yescharacteristic
17#15688878C2211yescharacteristic
18C47×#400—21no—
19C47×#400—21no—
20C47×#395—21no—
21C47×#391C2211yescharacteristic
22C47×#389—21no—
23C47×#389C2211yescharacteristic
24C47×#389C2211yescharacteristic
25C47×#387—21no—
26C47×#387—21no—
27C22×C47⋊C8—21no—
28C22×C47⋊C8—21no—
29C22×C47⋊C8—21no—
30C2×C4⋊Dic47—21no—
31C2×C4⋊Dic47—21no—
32C2×C4⋊Dic47—21no—
33#13093957—42no—
34#13093948—42no—
35C22×Q8×C47D411yescharacteristic
36C2×C4⋊C4×C47—21no—
37C2×C4⋊C4×C47—21no—
38C2×C4⋊C4×C47—21no—
39C2×C4⋊C4×C47—21no—
40C2×C4⋊C4×C47D411yescharacteristic
41C2×C4⋊C4×C47D411yescharacteristic
42C2×C4⋊C4×C47D411yescharacteristic
43C2×C4⋊C4×C47D411yescharacteristic
44C2×C4⋊C4×C47D411yescharacteristic
45C2×C42×C47—21no—
46C2×C42×C47C2311yescharacteristic
47#95×C47—21no—
48#95×C47—21no—
49#95×C47—21no—
50#95×C47—21no—
51#95×C47—21no—
52#95×C47—21no—
53#95×C47—21no—
54#95×C47—21no—
55#95×C47—21no—
56C2×Q8×C47—21no—
57C2×Q8×C47—21no—
58C2×Q8×C47—41no—
59C2×Q8×C47—41no—
60C22×C4×C47—21no—
61C22×C4×C47—21no—
62C22×C4×C47—21no—
63C22×C4×C47—21no—
64C22×C4×C47—21no—
65C22×C4×C47—21no—
66C22×C4×C47C2×D411yescharacteristic
67C22×C4×C47C2×D411yescharacteristic
68C22×C4×C47C2×D411yescharacteristic
69C22×Dic47—41no—
70C4⋊C4×C47—21no—
71C4⋊C4×C47—21no—
72C4⋊C4×C47—21no—
73C4⋊C4×C47—41no—
74C4⋊C4×C47—41no—
75C4⋊C4×C47—41no—
76C4⋊C4×C47—41no—
77C4⋊C4×C47—41no—
78C4⋊C4×C47—41no—
79C4⋊C4×C47—41no—
80C4⋊C4×C47—81no—
81C4⋊C4×C47—81no—
82C4⋊C4×C47Q1612yes—
83C42×C47—41no—
84C42×C47—81no—
85C4⋊Dic47—42no—
86C4⋊Dic47—41no—
87C4⋊Dic47—41no—
88C4⋊Dic47—41no—
89C4⋊Dic47—41no—
90C2×C47⋊C8—22no—
91C2×C47⋊C8—41no—
92C2×C47⋊C8—41no—
93C2×C47⋊C8—41no—
94C2×C47⋊C8—41no—
95C2×C47⋊C8—41no—
96C2×C47⋊C8—41no—
97C2×C47⋊C8—41no—
98C2×C47⋊C8—41no—
99C23×C47#12011yescharacteristic
100Q8×C47—42no—
101Q8×C47—81no—
102C2×C4×C47—21no—
103C2×C4×C47—21no—
104C2×C4×C47—21no—
105C2×C4×C47—21no—
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—22no—
109C2×C4×C47—41no—
110C2×C4×C47—41no—
111C2×C4×C47—41no—
112C2×C4×C47—41no—
113C2×C4×C47—41no—
114C2×C4×C47—41no—
115C2×C4×C47—41no—
116C2×C4×C47—41no—
117C2×C4×C47—41no—
118C2×C4×C47—41no—
119C2×C4×C47—41no—
120C2×C4×C47—41no—
121C2×C4×C47—41no—
122C2×C4×C47—41no—
123C2×C4×C47—41no—
124C2×C4×C47—41no—
125C2×C4×C47—41no—
126C2×C4×C47C2×Q1611yescharacteristic
127C2×C4×C47#13511yescharacteristic
128C2×C4×C47#13511yescharacteristic
129C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C47#13711yescharacteristic
132C2×Dic47—81no—
133C2×Dic47—81no—
134C2×Dic47—81no—
135C47⋊C8—42no—
136C47⋊C8—81no—
137C47⋊C8—81no—
138#7806—471nomaximal, Sylow
139C22×C47#44911yescharacteristic
140C22×C47#44911yescharacteristic
141C22×C47#45111yescharacteristic
142C22×C47#45411yescharacteristic
143C22×C47#45511yescharacteristic
144C22×C47#45611yescharacteristic
145C22×C47#45811yescharacteristic
146C4×C47—21no—
147C4×C47—21no—
148C4×C47—21no—
149C4×C47—21no—
150C4×C47—21no—
151C4×C47—21no—
152C4×C47—42no—
153C4×C47—81no—
154C4×C47—81no—
155C4×C47—81no—
156C4×C47—81no—
157C4×C47—81no—
158Dic47—161no—
159#2805D4711yescharacteristic
160#2099—471no—
161#2083—471no—
162#2072—471no—
163#1272—471no—
164#1271—471no—
165#1271—471no—
166C2×C47#160911yescharacteristic
167C2×C47#161211yescharacteristic
168C2×C47#161711yescharacteristic
169C2×C47#162811yescharacteristic
170C2×C47#164411yescharacteristic
171C2×C47#164811yescharacteristic
172C2×C47#166411yescharacteristic
173C2×#107—941no—
174C2×#103—941no—
175#400—21no—
176#400—21no—
177#395—21no—
178#391C2×D4711yescharacteristic
179#389—21no—
180#389C2×D4711yescharacteristic
181#389C2×D4711yescharacteristic
182#387—21no—
183#387—21no—
184#384—471no—
185#340—941no—
186#340—941no—
187#340—941no—
188#340—941no—
189#336—471no—
190#336—471no—
191#336—471no—
192C47#780611yescharacteristic, complemented, Sylow
193C22×Q8C22⋊D4711yescharacteristic
194C22×C8—941no—
195C22×C8—941no—
196C22×C8—941no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—941no—
202C2×C4⋊C4—941no—
203C2×C4⋊C4—941no—
204C2×C4⋊C4C22⋊D4711yescharacteristic
205C2×C4⋊C4C22⋊D4711yescharacteristic
206C2×C4⋊C4C22⋊D4711yescharacteristic
207C2×C4⋊C4C22⋊D4711yescharacteristic
208C2×C4⋊C4C22⋊D4711yescharacteristic
209C2×C42—21no—
210C2×C42C22×D4711yescharacteristic
211#107—1882no—
212#103—1882no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95—21no—
222C2×Q8—21no—
223C2×Q8—21no—
224C2×Q8—41no—
225C2×Q8—41no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—1881no—
233C22×C4C2×C22⋊D4711yescharacteristic
234C22×C4C2×C22⋊D4711yescharacteristic
235C22×C4C2×C22⋊D4711yescharacteristic
236C2×C8—942no—
237C2×C8—1881no—
238C2×C8—1881no—
239C2×C8—1881no—
240C2×C8—1881no—
241C2×C8—1881no—
242C2×C8—1881no—
243C2×C8—1881no—
244C2×C8—1881no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—81no—
256C4⋊C4—81no—
257C4⋊C4—1882no—
258C4⋊C4—1881no—
259C4⋊C4—1881no—
260C4⋊C4—1881no—
261C4⋊C4—1881no—
262C4⋊C4#1062533712yes—
263C42—41no—
264C42—81no—
265C23#1309399311yescharacteristic
266Q8—42no—
267Q8—81no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—22no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—3761no—
293C2×C4—3761no—
294C2×C4—3761no—
295C2×C4C2×#1062533711yescharacteristic
296C2×C4#1309404411yescharacteristic
297C2×C4#1309404411yescharacteristic
298C2×C4#1309404911yescharacteristic
299C2×C4#1309404911yescharacteristic
300C2×C4#1309405511yescharacteristic
301C8—3761no—
302C8—3761no—
303C8—1882no—
304C22#1568926811yescharacteristic
305C22#1568926811yescharacteristic
306C22#1568927911yescharacteristic
307C22#1568929611yescharacteristic
308C22#1568930111yescharacteristic
309C22#1568930611yescharacteristic
310C22#1568931311yescharacteristic
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—42no—
318C4—81no—
319C4—81no—
320C4—81no—
321C4—81no—
322C4—81no—
323C4—7521no—
324C2#2024238511yescharacteristic
325C2#2024240211yescharacteristic
326C2#2024243011yescharacteristic
327C2#2024249811yescharacteristic
328C2#2024260211yescharacteristic
329C2#2024263011yescharacteristic
330C2#2024272211yescharacteristic
subgroupG/H
centerC23#13093993
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#2805C2
socle, prime radicalC23×C47#120
hypercenter#2805D47
hypocenterC47#7806
LCSG ▷ C2×C42×C47 ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2805

Complements

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

NH ≅ G/Ntype
192. C47#7806semidirect

Maximal subgroups

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

subgroupindex
#202449462
#202448592
#202447962
#202412142
#202412112
C47×#28052
#780647