Finite Group Databasebeta

← #26191183

Subgroups — #26191183

Order 12032.

870 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 870 conjugacy classes of subgroups — too many to draw. Only its 191 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#20257198C211yesmaximal, characteristic
2#20254539C212yesmaximal
3#20242429C218yesmaximal
4#20241886C212yesmaximal
5#20241712C211yesmaximal, characteristic
6C47×#2568C211yesmaximal, characteristic
7Q8×Dic94—22no—
8#15689852—22no—
9#15689849—24no—
10#15689754—21no—
11#15689754C2214yes—
12#15689680—22no—
13#15689680C2212yes—
14#15689601—21no—
15#15689526—22no—
16#15689475—22no—
17#15689458C2218yes—
18#15689415—24no—
19#15689176C2212yes—
20#15688859C2218yes—
21#15688849C2214yes—
22C2×C4⋊Q8×C47C2211yescharacteristic
23C2×C4×Q8×C47C2211yescharacteristic
24C47×#400C2214yes—
25C47×#391—21no—
26C47×#391—22no—
27C47×#382—21no—
28C4×C4⋊C4×C47C2211yescharacteristic
29#13094024—22no—
30#13094024—22no—
31#13094024D412yes—
32#13094024D412yes—
33#13094023—24no—
34#13094023—28no—
35#13094016—24no—
36#13094016—22no—
37#13094015—24no—
38#13094015—28no—
39#13094003—24no—
40#13094003—22no—
41#13094003C2314yes—
42Q8×Dic47—24no—
43Q8×Dic47—24no—
44C4×Dic94—24no—
45C4×Dic94—24no—
46C4×Dic94—22no—
47C4×Dic94D414yes—
48#13093983—22no—
49#13093983—24no—
50#13093957—28no—
51C4⋊(C47⋊C8)—22no—
52#13093947—28no—
53C22⋊(C47⋊C8)C2314yes—
54C4×C47⋊C8—22no—
55C22×Q8×C47—21no—
56C22×Q8×C47D411yescharacteristic
57C4⋊Q8×C47—22no—
58C4⋊Q8×C47—22no—
59C4×Q8×C47—22no—
60C4×Q8×C47—22no—
61C2×C4⋊C4×C47—21no—
62C2×C4⋊C4×C47—21no—
63C2×C4⋊C4×C47D411yescharacteristic
64C2×C4⋊C4×C47C2312yes—
65C2×C4⋊C4×C47C2312yes—
66C2×C42×C47—21no—
67C2×C42×C47D412yes—
68C2×C42×C47C2311yescharacteristic
69#95×C47—24no—
70#95×C47—24no—
71#95×C47C2312yes—
72C2×Q8×C47—22no—
73C2×Q8×C47—22no—
74C2×Q8×C47—44no—
75C2×Q8×C47—41no—
76C2×Q8×C47—41no—
77C2×Q8×C47Q1614yes—
78C22×C4×C47—22no—
79C22×C4×C47—22no—
80C22×C4×C47C2×D411yescharacteristic
81C22×C4×C47C2×D412yes—
82C22×C4×C47C2×D412yes—
83C22×C4×C47C2×D411yescharacteristic
84C22×C4×C47C2411yescharacteristic
85C2×Dic94—22no—
86C2×Dic94—24no—
87C2×Dic94C2×D414yes—
88C4⋊C4×C47—22no—
89C4⋊C4×C47—24no—
90C4⋊C4×C47—24no—
91C4⋊C4×C47—42no—
92C4⋊C4×C47—42no—
93C42×C47—22no—
94C42×C47—22no—
95C42×C47—42no—
96C42×C47C2×D412yes—
97C42×C47C2×D412yes—
98C22⋊Dic47—24no—
99C4⋊Dic47—24no—
100C4⋊Dic47—24no—
101C4⋊Dic47—24no—
102C4⋊Dic47—22no—
103C4⋊Dic47—22no—
104C4⋊Dic47—22no—
105C4⋊Dic47C2×D414yes—
106Dic47⋊C4—28no—
107Dic47⋊C4—24no—
108Dic47⋊C4—24no—
109C4×Dic47—28no—
110C4×Dic47—24no—
111C2×C47⋊C8—24no—
112C23×C47C22×D411yescharacteristic
113Q8×C47—28no—
114Q8×C47—82no—
115Q8×C47—82no—
116C2×C4×C47—22no—
117C2×C4×C47—22no—
118C2×C4×C47—22no—
119C2×C4×C47—22no—
120C2×C4×C47—41no—
121C2×C4×C47—42no—
122C2×C4×C47—42no—
123C2×C4×C47—42no—
124C2×C4×C47—44no—
125C2×C4×C47—42no—
126C2×C4×C47—42no—
127C2×C4×C47#12011yescharacteristic
128C2×C4×C47#12012yes—
129C2×C4×C47#12011yescharacteristic
130C2×C4×C47C2×Q1614yes—
131C2×C4×C47C2×Q1612yes—
132C2×C4×C47#13712yes—
133C2×C4×C47C22×D412yes—
134C2×Dic47—24no—
135C2×Dic47—24no—
136Dic94—44no—
137Dic94—44no—
138Dic94—84no—
139C47⋊C8—44no—
140#18411—471nomaximal, Sylow
141C22×C47—21no—
142C22×C47—21no—
143C22×C47C2×#12011yescharacteristic
144C22×C47C22×Q1611yescharacteristic
145C22×C47C2×#13711yescharacteristic
146C4×C47—24no—
147C4×C47—21no—
148C4×C47—22no—
149C4×C47—42no—
150C4×C47—82no—
151C4×C47—82no—
152C4×C47#45114yes—
153C4×C47#45412yes—
154Dic47—44no—
155Dic47—44no—
156#3502—471no—
157#3230—472no—
158#2568D4711yescharacteristic
159#1617—478no—
160#1503—472no—
161#1461—471no—
162C2×C47—21no—
163C2×C47—21no—
164C2×C47C2×#45111yescharacteristic
165C2×C47C2×#45411yescharacteristic
166C2×C47#302811yescharacteristic
167Q82—942no—
168#557—944no—
169#557—942no—
170#544—474no—
171#544—941no—
172#533—472no—
173#533—942no—
174C2×C4⋊Q8C2×D4711yescharacteristic
175#519—941no—
176C2×C4×Q8C2×D4711yescharacteristic
177#500—942no—
178#487—942no—
179#484—478no—
180#477—944no—
181#431—472no—
182#400C2×D4714yes—
183#391—21no—
184#391—22no—
185#382—21no—
186C4×C4⋊C4C2×D4711yescharacteristic
187#328—478no—
188#324—474no—
189C47#1841111yescharacteristic, complemented, Sylow
190C22×Q8—21no—
191C22×Q8C22⋊D4711yescharacteristic
192C4⋊Q8—22no—
193C4⋊Q8—22no—
194C4⋊Q8—472no—
195C4⋊Q8—472no—
196C4⋊Q8—942no—
197C4⋊Q8—942no—
198C4⋊Q8—948no—
199C4⋊Q8—944no—
200#125—944no—
201#125—948no—
202#125—944no—
203#125—942no—
204C22⋊Q8—474no—
205C22⋊Q8—942no—
206C22⋊Q8—944no—
207C4×Q8—22no—
208C4×Q8—22no—
209C4×Q8—474no—
210C4×Q8—944no—
211C4×Q8—944no—
212C4×Q8—944no—
213C4×Q8—944no—
214C4×Q8—942no—
215#117—942no—
216#117—944no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4C22⋊D4711yescharacteristic
220C2×C4⋊C4C22×D4712yes—
221C2×C4⋊C4C22×D4712yes—
222C2×C42—21no—
223C2×C42C22⋊D4712yes—
224C2×C42C22×D4711yescharacteristic
225#107—948no—
226C4⋊C8—942no—
227#103—948no—
228C22⋊C8—474no—
229C4×C8—942no—
230#95—24no—
231#95—24no—
232#95C22×D4712yes—
233C2×Q8—22no—
234C2×Q8—22no—
235C2×Q8—44no—
236C2×Q8—41no—
237C2×Q8—41no—
238C2×Q8—474no—
239C2×Q8—944no—
240C2×Q8—942no—
241C2×Q8#1062533714yes—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4C2×C22⋊D4711yescharacteristic
245C22×C4C2×C22⋊D4712yes—
246C22×C4C2×C22⋊D4712yes—
247C22×C4C2×C22⋊D4711yescharacteristic
248C22×C4C23×D4711yescharacteristic
249C2×C8—944no—
250C4⋊C4—22no—
251C4⋊C4—24no—
252C4⋊C4—24no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4—474no—
256C4⋊C4—948no—
257C4⋊C4—944no—
258C4⋊C4—944no—
259C4⋊C4—944no—
260C4⋊C4—944no—
261C4⋊C4—942no—
262C4⋊C4—942no—
263C4⋊C4—942no—
264C4⋊C4—944no—
265C22⋊C4—944no—
266C42—22no—
267C42—22no—
268C42—42no—
269C42—948no—
270C42—944no—
271C42D4×D4712yes—
272C42D4×D4712yes—
273C23C22×C22⋊D4711yescharacteristic
274Q8—28no—
275Q8—82no—
276Q8—82no—
277Q8—3764no—
278Q8—1884no—
279Q8—1884no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—41no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—44no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—944no—
292C2×C4—944no—
293C2×C4#1309399211yescharacteristic
294C2×C4#1309399212yes—
295C2×C4#1309399211yescharacteristic
296C2×C4C2×#1062533714yes—
297C2×C4C2×#1062533712yes—
298C2×C4#1309405412yes—
299C2×C4C2×D4×D4712yes—
300C8—1884no—
301C22—21no—
302C22—21no—
303C22C2×#1309399211yescharacteristic
304C22C22×#1062533711yescharacteristic
305C22C2×#1309405411yescharacteristic
306C4—21no—
307C4—22no—
308C4—24no—
309C4—42no—
310C4—82no—
311C4—82no—
312C4—1884no—
313C4—1884no—
314C4#1568927814yes—
315C4#1568929512yes—
316C2—21no—
317C2—21no—
318C2C2×#1568927811yescharacteristic
319C2C2×#1568929511yescharacteristic
320C2#2025279311yescharacteristic
subgroupG/H
centerC22C2×#13093992
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2568C2
socleC22×C47C2×#120
prime radicalC23×C47C22×D4
hypercenter#2568D47
hypocenterC47#18411
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2568

Complements

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

NH ≅ G/Ntype
189. C47#18411semidirect

Maximal subgroups

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

subgroupindex
#202571982
#202545392
#202424292
#202418862
#202417122
C47×#25682
#1841147