Finite Group Databasebeta

← #26105342

Subgroups — #26105342

Order 12032.

374 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 91 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#20244859C211yesmaximal, characteristic
4#20241211C211yesmaximal, characteristic
5#20241211C211yesmaximal, characteristic
6#20241211C211yesmaximal, characteristic
7C47×#2726C211yesmaximal, characteristic
8C2×#13093957—21no—
9C2×#13093957—21no—
10#15688993C2211yescharacteristic
11#15688885—21no—
12#15688885—21no—
13#15688885—21no—
14#15688885—21no—
15#15688878C2211yescharacteristic
16#15688878C2211yescharacteristic
17#15688878C2211yescharacteristic
18C2×#125×C47—21no—
19C47×#398—21no—
20C47×#398—21no—
21C47×#398—21no—
22C47×#389—21no—
23C47×#389C2211yescharacteristic
24C47×#389C2211yescharacteristic
25C47×#389C2211yescharacteristic
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#13093957—42no—
35#125×C47—42no—
36#125×C47—42no—
37C2×C4⋊C4×C47—21no—
38C2×C4⋊C4×C47—21no—
39C2×C4⋊C4×C47—21no—
40C2×C4⋊C4×C47—21no—
41C2×C4⋊C4×C47—21no—
42C2×C4⋊C4×C47—21no—
43C2×C4⋊C4×C47—21no—
44C2×C4⋊C4×C47D411yescharacteristic
45C2×C4⋊C4×C47D411yescharacteristic
46C2×C4⋊C4×C47D411yescharacteristic
47C2×C4⋊C4×C47D411yescharacteristic
48C2×C4⋊C4×C47D411yescharacteristic
49C2×C4⋊C4×C47D411yescharacteristic
50C2×C42×C47—21no—
51C2×C42×C47C2311yescharacteristic
52#95×C47—21no—
53#95×C47—21no—
54#95×C47—21no—
55#95×C47—21no—
56#95×C47—21no—
57#95×C47—21no—
58C22×C4×C47—21no—
59C22×C4×C47—21no—
60C22×C4×C47—21no—
61C22×C4×C47—21no—
62C22×C4×C47—21no—
63C22×C4×C47—21no—
64C22×C4×C47C2×D411yescharacteristic
65C22×C4×C47C2×D411yescharacteristic
66C22×C4×C47C2×D411yescharacteristic
67C22×Dic47—41no—
68C4⋊C4×C47—21no—
69C4⋊C4×C47—21no—
70C4⋊C4×C47—21no—
71C4⋊C4×C47—21no—
72C4⋊C4×C47—42no—
73C4⋊C4×C47—42no—
74C4⋊C4×C47—42no—
75C4⋊C4×C47—41no—
76C4⋊C4×C47—41no—
77C4⋊C4×C47—41no—
78C4⋊C4×C47—41no—
79C4⋊C4×C47—41no—
80C4⋊C4×C47—41no—
81C4⋊C4×C47—41no—
82C4⋊C4×C47—41no—
83C4⋊C4×C47—41no—
84C4⋊C4×C47—81no—
85C4⋊C4×C47D812yes—
86C4⋊C4×C47Q1612yes—
87C42×C47—41no—
88C42×C47—42no—
89C4⋊Dic47—42no—
90C4⋊Dic47—41no—
91C4⋊Dic47—41no—
92C4⋊Dic47—41no—
93C4⋊Dic47—41no—
94C2×C47⋊C8—22no—
95C2×C47⋊C8—22no—
96C2×C47⋊C8—41no—
97C2×C47⋊C8—41no—
98C2×C47⋊C8—41no—
99C2×C47⋊C8—41no—
100C2×C47⋊C8—41no—
101C2×C47⋊C8—41no—
102C2×C47⋊C8—41no—
103C23×C47#12011yescharacteristic
104C2×C4×C47—21no—
105C2×C4×C47—21no—
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—22no—
111C2×C4×C47—22no—
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×C47—41no—
127C2×C4×C47—41no—
128C2×C4×C47C2×D811yescharacteristic
129C2×C4×C47C2×Q1611yescharacteristic
130C2×C4×C47#13511yescharacteristic
131C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C47#13711yescharacteristic
134C2×Dic47—81no—
135C2×Dic47—81no—
136C2×Dic47—81no—
137C47⋊C8—42no—
138C47⋊C8—42no—
139C47⋊C8—81no—
140#7792—471nomaximal, Sylow
141C22×C47#44711yescharacteristic
142C22×C47#44911yescharacteristic
143C22×C47#45111yescharacteristic
144C22×C47#45411yescharacteristic
145C22×C47#45611yescharacteristic
146C22×C47#45611yescharacteristic
147C22×C47#45811yescharacteristic
148C4×C47—21no—
149C4×C47—21no—
150C4×C47—21no—
151C4×C47—21no—
152C4×C47—21no—
153C4×C47—21no—
154C4×C47—42no—
155C4×C47—42no—
156C4×C47—81no—
157C4×C47—81no—
158C4×C47—81no—
159C4×C47—81no—
160Dic47—161no—
161#2726D4711yescharacteristic
162#2099—471no—
163#2083—471no—
164#2083—471no—
165#1271—471no—
166#1271—471no—
167#1271—471no—
168C2×C47#160911yescharacteristic
169C2×C47#161011yescharacteristic
170C2×C47#161711yescharacteristic
171C2×C47#162511yescharacteristic
172C2×C47#164811yescharacteristic
173C2×C47#164911yescharacteristic
174C2×C47#166311yescharacteristic
175C2×#125—21no—
176C2×#107—941no—
177C2×#107—941no—
178#398—21no—
179#398—21no—
180#398—21no—
181#389—21no—
182#389C2×D4711yescharacteristic
183#389C2×D4711yescharacteristic
184#389C2×D4711yescharacteristic
185#387—21no—
186#384—471no—
187#340—941no—
188#340—941no—
189#340—941no—
190#340—941no—
191#336—471no—
192#336—471no—
193#336—471no—
194C47#779211yescharacteristic, complemented, Sylow
195C22×C8—941no—
196C22×C8—941no—
197C22×C8—941no—
198#125—42no—
199#125—42no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—941no—
208C2×C4⋊C4—941no—
209C2×C4⋊C4—941no—
210C2×C4⋊C4C22⋊D4711yescharacteristic
211C2×C4⋊C4C22⋊D4711yescharacteristic
212C2×C4⋊C4C22⋊D4711yescharacteristic
213C2×C4⋊C4C22⋊D4711yescharacteristic
214C2×C4⋊C4C22⋊D4711yescharacteristic
215C2×C4⋊C4C22⋊D4711yescharacteristic
216C2×C42—21no—
217C2×C42C22×D4711yescharacteristic
218#107—1882no—
219#107—1882no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95—21no—
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—942no—
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—21no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—81no—
262C4⋊C4—1882no—
263C4⋊C4—1881no—
264C4⋊C4—1881no—
265C4⋊C4—1881no—
266C4⋊C4—1881no—
267C4⋊C4#1062533412yes—
268C4⋊C4#1062533712yes—
269C42—41no—
270C42—42no—
271C23#1309399311yescharacteristic
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—22no—
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—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—3761no—
297C2×C4—3761no—
298C2×C4—3761no—
299C2×C4C2×#1062533411yescharacteristic
300C2×C4C2×#1062533711yescharacteristic
301C2×C4#1309404411yescharacteristic
302C2×C4#1309404911yescharacteristic
303C2×C4#1309405011yescharacteristic
304C2×C4#1309405511yescharacteristic
305C8—3761no—
306C8—1882no—
307C8—1882no—
308C22#1568925711yescharacteristic
309C22#1568926811yescharacteristic
310C22#1568927911yescharacteristic
311C22#1568929611yescharacteristic
312C22#1568930611yescharacteristic
313C22#1568930611yescharacteristic
314C22#1568931311yescharacteristic
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—42no—
322C4—42no—
323C4—81no—
324C4—81no—
325C4—81no—
326C4—81no—
327C4—7521no—
328C2#2024238511yescharacteristic
329C2#2024239111yescharacteristic
330C2#2024243011yescharacteristic
331C2#2024247711yescharacteristic
332C2#2024263011yescharacteristic
333C2#2024263711yescharacteristic
334C2#2024271611yescharacteristic
subgroupG/H
centerC23#13093993
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#2726C2
socle, prime radicalC23×C47#120
hypercenter#2726D47
hypocenterC47#7792
LCSG ▷ C2×C42×C47 ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2726

Complements

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

NH ≅ G/Ntype
194. C47#7792semidirect

Maximal subgroups

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

subgroupindex
#202449462
#202448592
#202412112
C47×#27262
#779247