Finite Group Databasebeta

← #26114273

Subgroups — #26114273

Order 12032.

478 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 103 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#20252026C211yesmaximal, characteristic
2#20243471C211yesmaximal, characteristic
3#20241718C212yesmaximal
4#20241296C212yesmaximal
5C47×#2484C211yesmaximal, characteristic
6#15689184—24no—
7#15689147—21no—
8#15689087C2212yes—
9#15689087C2212yes—
10C4×#10625329—21no—
11#15688892—21no—
12#15688892—21no—
13#15688849—24no—
14C2×#117×C47C2211yescharacteristic
15C22×C4⋊C4×C47C2211yescharacteristic
16C47×#400—21no—
17C47×#398—21no—
18C47×#387—21no—
19C47×#387—21no—
20C47×#385C411yescharacteristic
21C47×#385C411yescharacteristic
22C47×#381C411yescharacteristic
23C47×#381C411yescharacteristic
24C47×#381C2211yescharacteristic
25C2×#10625329—22no—
26C2×#10625329—22no—
27C4⋊(C47⋊C8)—24no—
28C22⋊(C47⋊C8)—22no—
29C22⋊(C47⋊C8)—22no—
30C22⋊(C47⋊C8)—22no—
31C22⋊(C47⋊C8)D414yes—
32#13093935—22no—
33C4×C47⋊C8—22no—
34C23×C4×C47C2×C411yescharacteristic
35C23×C4×C47C2×C411yescharacteristic
36C23×C4×C47C2311yescharacteristic
37#117×C47—22no—
38#117×C47—22no—
39C2×C4⋊C4×C47—21no—
40C2×C4⋊C4×C47—21no—
41C2×C4⋊C4×C47—22no—
42C2×C4⋊C4×C47—21no—
43C2×C4⋊C4×C47—21no—
44C2×C4⋊C4×C47—22no—
45C2×C4⋊C4×C47D411yescharacteristic
46C2×C4⋊C4×C47D411yescharacteristic
47C2×C22⋊C4×C47C2×C411yescharacteristic
48C2×C22⋊C4×C47C2×C411yescharacteristic
49C2×C22⋊C4×C47C2×C411yescharacteristic
50C2×C22⋊C4×C47C2×C411yescharacteristic
51C2×C42×C47D411yescharacteristic
52C2×C42×C47D411yescharacteristic
53#95×C47—21no—
54#95×C47—21no—
55#95×C47—21no—
56#95×C47—21no—
57#95×C47—21no—
58#95×C47—21no—
59#95×C47—21no—
60#95×C47—21no—
61C24×C47C22×C411yescharacteristic
62C22×C4×C47—21no—
63C22×C4×C47—22no—
64C22×C4×C47—21no—
65C22×C4×C47—21no—
66C22×C4×C47—21no—
67C22×C4×C47—22no—
68C22×C4×C47—42no—
69C22×C4×C47—41no—
70C22×C4×C47—41no—
71C22×C4×C47—41no—
72C22×C4×C47—41no—
73C22×C4×C47C22⋊C411yescharacteristic
74C22×C4×C47C22⋊C411yescharacteristic
75C22×C4×C47C22⋊C411yescharacteristic
76C22×C4×C47C22⋊C411yescharacteristic
77C22×C4×C47C2×D411yescharacteristic
78C22×C4×C47C2×D411yescharacteristic
79C22×C4×C47C2×D412yes—
80C22×C4×C47#4112yes—
81C4⋊C4×C47—22no—
82C4⋊C4×C47—22no—
83C4⋊C4×C47—42no—
84C4⋊C4×C47—42no—
85C4⋊C4×C47—41no—
86C4⋊C4×C47—42no—
87C4⋊C4×C47—41no—
88C22⋊C4×C47—22no—
89C22⋊C4×C47—22no—
90C22⋊C4×C47—41no—
91C22⋊C4×C47—41no—
92C42×C47—21no—
93C42×C47—21no—
94C42×C47—21no—
95C42×C47—21no—
96#10625329—42no—
97#10625329—42no—
98#10625329—42no—
99#10625329—42no—
100C2×C47⋊C8—24no—
101C2×C47⋊C8—42no—
102C23×C47—21no—
103C23×C47—21no—
104C23×C47—41no—
105C23×C47—41no—
106C23×C47C2×C22⋊C411yescharacteristic
107C23×C47C4×D412yes—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—22no—
113C2×C4×C47—24no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—42no—
119C2×C4×C47—42no—
120C2×C4×C47—41no—
121C2×C4×C47—42no—
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×C47—41no—
129C2×C4×C47—41no—
130C2×C4×C47—41no—
131C2×C4×C47—41no—
132C2×C4×C47—41no—
133C2×C4×C47—41no—
134C2×C4×C47—41no—
135C2×C4×C47—41no—
136C2×C4×C47—82no—
137C2×C4×C47#12011yescharacteristic
138C2×C4×C47#12112yes—
139C2×C4×C47#12311yescharacteristic
140C47⋊C8—44no—
141C47⋊C8—82no—
142#9514—471nomaximal, Sylow
143C22×C47—21no—
144C22×C47—21no—
145C22×C47—22no—
146C22×C47—22no—
147C22×C47—22no—
148C22×C47—42no—
149C22×C47—42no—
150C22×C47#38611yescharacteristic
151C22×C47#41011yescharacteristic
152C22×C47#41011yescharacteristic
153C4×C47—21no—
154C4×C47—22no—
155C4×C47—21no—
156C4×C47—42no—
157C4×C47—41no—
158C4×C47—41no—
159C4×C47—41no—
160C4×C47—41no—
161C4×C47—81no—
162C4×C47—81no—
163C4×C47—81no—
164#2921—471no—
165#2484D4711yescharacteristic
166#1822—471no—
167#1463—472no—
168#1306—472no—
169C2×C47—21no—
170C2×C47—21no—
171C2×C47—42no—
172C2×C47#189111yescharacteristic
173C2×C47#189911yescharacteristic
174C2×C47#191511yescharacteristic
175C2×#117C2×D4711yescharacteristic
176C22×C4⋊C4C2×D4711yescharacteristic
177#433—944no—
178#423—941no—
179#407—472no—
180#407—472no—
181C4×M16—941no—
182#400—21no—
183#398—21no—
184#387—21no—
185#387—21no—
186#385Dic4711yescharacteristic
187#385Dic4711yescharacteristic
188#381Dic4711yescharacteristic
189#381Dic4711yescharacteristic
190#381C2×D4711yescharacteristic
191#343—941no—
192#343—941no—
193#324—944no—
194C47#951411yescharacteristic, complemented, Sylow
195C23×C4C2×Dic4711yescharacteristic
196C23×C4C2×Dic4711yescharacteristic
197C23×C4C22×D4711yescharacteristic
198C2×M16—942no—
199C2×M16—942no—
200#117—22no—
201#117—22no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—22no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4C22⋊D4711yescharacteristic
209C2×C4⋊C4C22⋊D4711yescharacteristic
210C2×C22⋊C4C2×Dic4711yescharacteristic
211C2×C22⋊C4C2×Dic4711yescharacteristic
212C2×C22⋊C4C2×Dic4711yescharacteristic
213C2×C22⋊C4C2×Dic4711yescharacteristic
214C2×C42C22⋊D4711yescharacteristic
215C2×C42C22⋊D4711yescharacteristic
216C4⋊C8—944no—
217C22⋊C8—474no—
218C22⋊C8—942no—
219C22⋊C8—942no—
220C22⋊C8—942no—
221#97—942no—
222C4×C8—942no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231C24C22×Dic4711yescharacteristic
232C22×C4—21no—
233C22×C4—22no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—22no—
238C22×C4—42no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4C22⋊Dic4711yescharacteristic
244C22×C4C22⋊Dic4711yescharacteristic
245C22×C4C22⋊Dic4711yescharacteristic
246C22×C4C22⋊Dic4711yescharacteristic
247C22×C4D4×D4712yes—
248C22×C4#1062535212yes—
249C22×C4C2×C22⋊D4711yescharacteristic
250C22×C4C2×C22⋊D4711yescharacteristic
251M16—1882no—
252M16—1882no—
253M16—1882no—
254M16—1882no—
255C2×C8—944no—
256C2×C8—1882no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C4⋊C4—41no—
262C4⋊C4—42no—
263C4⋊C4—41no—
264C22⋊C4—22no—
265C22⋊C4—22no—
266C22⋊C4—41no—
267C22⋊C4—41no—
268C42—21no—
269C42—21no—
270C42—21no—
271C42—21no—
272C23—21no—
273C23—21no—
274C23—41no—
275C23—41no—
276C23C2×C22⋊Dic4711yescharacteristic
277C23D4×Dic4712yes—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—24no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—82no—
307C2×C4#1309399211yescharacteristic
308C2×C4#1309399612yes—
309C2×C4#1309400511yescharacteristic
310C8—3762no—
311C8—1884no—
312C22—21no—
313C22—21no—
314C22—22no—
315C22—22no—
316C22—22no—
317C22—42no—
318C22—42no—
319C22#1568900311yescharacteristic
320C22#1568909711yescharacteristic
321C22#1568909711yescharacteristic
322C4—22no—
323C4—21no—
324C4—21no—
325C4—42no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—81no—
331C4—81no—
332C4—81no—
333C2—21no—
334C2—21no—
335C2—42no—
336C2#2024380711yescharacteristic
337C2#2024384711yescharacteristic
338C2#2024394111yescharacteristic
subgroupG/H
centerC22#15689003
commutator, prime radicalC24×C47C22×C4
FrattiniC23×C4C22×D47
FittingC47×#2484C2
socleC22×C47#386
cosocleC23×C4×C47C23
hypercenter#2484D47
hypocenterC47#9514
LCSG ▷ C24×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2484

Complements

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

NH ≅ G/Ntype
194. C47#9514semidirect

Maximal subgroups

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

subgroupindex
#202520262
#202434712
#202417182
#202412962
C47×#24842
#951447