Finite Group Databasebeta

← #26117725

Subgroups — #26117725

Order 12032.

458 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 85 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#20254594C211yesmaximal, characteristic
2#20253930C211yesmaximal, characteristic
3#20242105C211yesmaximal, characteristic
4#20241990C211yesmaximal, characteristic
5#20241899C211yesmaximal, characteristic
6#20241281C211yesmaximal, characteristic
7C47×#2642C211yesmaximal, characteristic
8#15689680C2211yescharacteristic
9#15689533—21no—
10#15689529—22no—
11#15689526—21no—
12#15689519—21no—
13#15689493—21no—
14#15689458—21no—
15#15689453—21no—
16#15689427—22no—
17#15689180C2211yescharacteristic
18#15689180C2211yescharacteristic
19#15689163—22no—
20C4×#10625329C2211yescharacteristic
21#15688869—22no—
22#15688865—22no—
23#15688859—22no—
24C2×C4⋊Q8×C47C2211yescharacteristic
25C2×#125×C47C2211yescharacteristic
26C47×#400—22no—
27C47×#400—22no—
28C47×#391—21no—
29C47×#391—21no—
30C47×#376C2211yescharacteristic
31C2×#10625329—21no—
32#13094024D411yescharacteristic
33#13094024D411yescharacteristic
34#13094016—21no—
35#13094003—21no—
36#13094003—21no—
37C4×Dic94—21no—
38C4×Dic94—21no—
39#13093983—21no—
40#13093957—24no—
41#13093957—22no—
42#13093955—24no—
43#13093955—22no—
44C4⋊(C47⋊C8)—21no—
45C4⋊(C47⋊C8)D412yes—
46#13093947—22no—
47#13093947—22no—
48C22⋊(C47⋊C8)—21no—
49C22⋊(C47⋊C8)—21no—
50#13093935—21no—
51#13093935—21no—
52#13093935D412yes—
53C4×C47⋊C8—21no—
54C22×Q8×C47—21no—
55C4⋊Q8×C47—21no—
56C4⋊Q8×C47—21no—
57C4⋊Q8×C47—21no—
58C4⋊Q8×C47—21no—
59#125×C47—21no—
60#125×C47—21no—
61#125×C47—21no—
62#125×C47—21no—
63C2×C4⋊C4×C47—21no—
64C2×C4⋊C4×C47—21no—
65C2×C4⋊C4×C47—21no—
66C2×C4⋊C4×C47D411yescharacteristic
67C2×C4⋊C4×C47D411yescharacteristic
68C2×C4⋊C4×C47D412yes—
69C2×C42×C47—21no—
70C2×C42×C47C2311yescharacteristic
71#95×C47—24no—
72#95×C47—24no—
73#95×C47—21no—
74#95×C47D412yes—
75C2×Q8×C47—44no—
76C2×Q8×C47—41no—
77C2×Q8×C47—41no—
78C22×C4×C47—22no—
79C22×C4×C47—21no—
80C22×C4×C47—21no—
81C22×C4×C47—22no—
82C22×C4×C47C2×D411yescharacteristic
83C22×C4×C47C2×D411yescharacteristic
84C22×C4×C47C2×D411yescharacteristic
85C2×Dic94—21no—
86C2×Dic94—21no—
87C4⋊C4×C47—21no—
88C4⋊C4×C47—21no—
89C4⋊C4×C47—22no—
90C4⋊C4×C47—21no—
91C4⋊C4×C47—21no—
92C4⋊C4×C47—22no—
93C4⋊C4×C47—41no—
94C4⋊C4×C47—41no—
95C4⋊C4×C47—41no—
96C4⋊C4×C47—41no—
97C4⋊C4×C47—41no—
98C4⋊C4×C47—41no—
99C42×C47—42no—
100C42×C47C2×D411yescharacteristic
101C42×C47C2×D411yescharacteristic
102C42×C47C2×D411yescharacteristic
103C42×C47#4111yescharacteristic
104C22⋊Dic47—41no—
105C4⋊Dic47—21no—
106C4⋊Dic47—21no—
107C4⋊Dic47—21no—
108C4⋊Dic47—21no—
109Dic47⋊C4—41no—
110Dic47⋊C4—41no—
111C4×Dic47—41no—
112#10625329—24no—
113C2×C47⋊C8—22no—
114C2×C47⋊C8—22no—
115C2×C47⋊C8—41no—
116C23×C47#12011yescharacteristic
117Q8×C47—82no—
118Q8×C47—82no—
119C2×C4×C47—22no—
120C2×C4×C47—22no—
121C2×C4×C47—41no—
122C2×C4×C47—42no—
123C2×C4×C47—42no—
124C2×C4×C47—42no—
125C2×C4×C47—44no—
126C2×C4×C47—41no—
127C2×C4×C47—41no—
128C2×C4×C47—42no—
129C2×C4×C47—42no—
130C2×C4×C47—42no—
131C2×C4×C47#12011yescharacteristic
132C2×C4×C47#12011yescharacteristic
133C2×C4×C47#12111yescharacteristic
134C2×C4×C47#12111yescharacteristic
135C2×C4×C47#12111yescharacteristic
136C2×C4×C47#12711yescharacteristic
137C2×Dic47—41no—
138C2×Dic47—41no—
139Dic94—42no—
140Dic94—81no—
141C47⋊C8—24no—
142C47⋊C8—42no—
143C47⋊C8—81no—
144#10103—471nomaximal, Sylow
145C22×C47—21no—
146C22×C47—21no—
147C22×C47#39211yescharacteristic
148C22×C47#45612yes—
149C4×C47—21no—
150C4×C47—21no—
151C4×C47—21no—
152C4×C47—21no—
153C4×C47—21no—
154C4×C47—82no—
155C4×C47—82no—
156C4×C47—81no—
157C4×C47—81no—
158C4×C47#45412yes—
159Dic47—81no—
160Dic47—81no—
161#3236—471no—
162#3165—471no—
163#2642D4711yescharacteristic
164#1556—471no—
165#1528—471no—
166#1506—471no—
167#1300—471no—
168C2×C47—22no—
169C2×C47#200311yescharacteristic
170C2×C47#200511yescharacteristic
171C2×C47#200911yescharacteristic
172#533—471no—
173C2×C4⋊Q8C2×D4711yescharacteristic
174C2×#125C2×D4711yescharacteristic
175#501—942no—
176#501—941no—
177#500—941no—
178#498—941no—
179#491—941no—
180#484—941no—
181#483—941no—
182#479—942no—
183#432—471no—
184#432—471no—
185#428—942no—
186C4×M16—471no—
187#400—22no—
188#400—22no—
189#391—21no—
190#391—21no—
191#376C2×D4711yescharacteristic
192#332—942no—
193#330—942no—
194#328—942no—
195C47#1010311yescharacteristic, complemented, Sylow
196C22×Q8—21no—
197C2×M16—941no—
198C4⋊Q8—21no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—471no—
203C4⋊Q8—471no—
204#125—21no—
205#125—21no—
206#125—21no—
207#125—21no—
208#125—941no—
209C22⋊Q8—941no—
210C22⋊Q8—941no—
211C4×Q8—941no—
212C4×Q8—941no—
213#117—941no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4C22⋊D4711yescharacteristic
218C2×C4⋊C4C22⋊D4711yescharacteristic
219C2×C4⋊C4C22⋊D4712yes—
220C2×C42—21no—
221C2×C42C22×D4711yescharacteristic
222#107—944no—
223#107—942no—
224#106—944no—
225#106—942no—
226C4⋊C8—472no—
227C4⋊C8—941no—
228#103—942no—
229#103—942no—
230C22⋊C8—941no—
231C22⋊C8—941no—
232#97—472no—
233#97—941no—
234#97—941no—
235C4×C8—941no—
236#95—24no—
237#95—24no—
238#95—21no—
239#95C22⋊D4712yes—
240C2×Q8—44no—
241C2×Q8—41no—
242C2×Q8—41no—
243C2×Q8—941no—
244C2×Q8—941no—
245C22×C4—22no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—22no—
249C22×C4C2×C22⋊D4711yescharacteristic
250C22×C4C2×C22⋊D4711yescharacteristic
251C22×C4C2×C22⋊D4711yescharacteristic
252M16—944no—
253C2×C8—942no—
254C2×C8—942no—
255C2×C8—1881no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—22no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—22no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—941no—
269C4⋊C4—941no—
270C4⋊C4—941no—
271C4⋊C4—941no—
272C4⋊C4—1881no—
273C4⋊C4—1881no—
274C22⋊C4—1881no—
275C42—42no—
276C42—1881no—
277C42D4×D4711yescharacteristic
278C42D4×D4711yescharacteristic
279C42D4×D4711yescharacteristic
280C42#1062535211yescharacteristic
281C23#1309399311yescharacteristic
282Q8—82no—
283Q8—82no—
284Q8—3761no—
285Q8—1882no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—44no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—1881no—
299C2×C4—1881no—
300C2×C4#1309399211yescharacteristic
301C2×C4#1309399211yescharacteristic
302C2×C4#1309399511yescharacteristic
303C2×C4#1309399611yescharacteristic
304C2×C4#1309399611yescharacteristic
305C2×C4#1309402011yescharacteristic
306C8—944no—
307C8—3761no—
308C8—1882no—
309C22—21no—
310C22—21no—
311C22#1568903111yescharacteristic
312C22#1568930612yes—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—82no—
319C4—82no—
320C4—81no—
321C4—81no—
322C4—3761no—
323C4—3761no—
324C4#1568929512yes—
325C2—22no—
326C2#2024441011yescharacteristic
327C2#2024442211yescharacteristic
328C2#2024444811yescharacteristic
subgroupG/H
centerC22#15689031
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#2642C2
socleC22×C47#392
prime radicalC23×C47#120
hypercenter#2642D47
hypocenterC47#10103
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2642

Complements

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

NH ≅ G/Ntype
195. C47#10103semidirect

Maximal subgroups

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

subgroupindex
#202545942
#202539302
#202421052
#202419902
#202418992
#202412812
C47×#26422
#1010347