Finite Group Databasebeta

← #26109745

Subgroups — #26109745

Order 12032.

418 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 99 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#20245988C211yesmaximal, characteristic
2C2×#15688848C211yesmaximal, characteristic
3C2×#15688848C211yesmaximal, characteristic
4#20241236C211yesmaximal, characteristic
5#20241235C211yesmaximal, characteristic
6#20241234C211yesmaximal, characteristic
7C47×#1282C211yesmaximal, characteristic
8C22×Dic47⋊C4C2211yescharacteristic
9C2×C22⋊(C47⋊C8)C2211yescharacteristic
10C2×C22⋊(C47⋊C8)C2211yescharacteristic
11#15689007—22no—
12#15689005—22no—
13#15688984C412yes—
14#15688981C412yes—
15C4×C22⋊Dic47C2211yescharacteristic
16#15688848—22no—
17#15688848—22no—
18C2×C22⋊C8×C47C2211yescharacteristic
19C2×C22⋊C8×C47C2211yescharacteristic
20C4×C22⋊C4×C47C2211yescharacteristic
21C23×Dic47C2×C411yescharacteristic
22C23×Dic47C2×C411yescharacteristic
23C22×C47⋊C8—21no—
24C22×C47⋊C8—21no—
25C2×Dic47⋊C4—21no—
26C2×Dic47⋊C4—21no—
27C2×Dic47⋊C4—21no—
28C2×Dic47⋊C4—21no—
29C2×Dic47⋊C4—22no—
30C2×Dic47⋊C4D412yes—
31C2×Dic47⋊C4D412yes—
32C2×C22⋊Dic47C2×C412yes—
33C2×C4×Dic47—21no—
34C22⋊(C47⋊C8)—21no—
35C22⋊(C47⋊C8)—21no—
36C22⋊(C47⋊C8)—21no—
37C22⋊(C47⋊C8)—21no—
38C47⋊#95—21no—
39C47⋊#95—22no—
40C47⋊#95—24no—
41C23×C4×C47C2311yescharacteristic
42C22×C8×C47—21no—
43C22×C8×C47—21no—
44C2×C22⋊C4×C47C2×C412yes—
45C2×C42×C47—21no—
46C22⋊C8×C47—21no—
47C22⋊C8×C47—21no—
48C22⋊C8×C47—21no—
49C22⋊C8×C47—21no—
50#95×C47—21no—
51C24×C47C22×C411yescharacteristic
52C22×C4×C47—22no—
53C22×C4×C47—81no—
54C22×C4×C47C2×D411yescharacteristic
55C22×C4×C47C2×D411yescharacteristic
56C22×C4×C47#4111yescharacteristic
57C22×C4×C47#4111yescharacteristic
58C22×C4×C47#4111yescharacteristic
59C22×C4×C47#4111yescharacteristic
60C22×Dic47—21no—
61C22×Dic47—21no—
62C22×Dic47—22no—
63C22×Dic47—22no—
64C22×Dic47—21no—
65C22×Dic47—21no—
66C22×Dic47—22no—
67C22×Dic47—81no—
68C22×Dic47C22⋊C412yes—
69C22×Dic47C22⋊C412yes—
70C2×C8×C47—41no—
71C2×C8×C47—41no—
72C2×C8×C47—81no—
73C2×C8×C47—81no—
74C22⋊C4×C47—22no—
75C22⋊C4×C47—22no—
76C42×C47—81no—
77C22⋊Dic47—22no—
78C22⋊Dic47—22no—
79Dic47⋊C4—22no—
80Dic47⋊C4—22no—
81Dic47⋊C4—22no—
82Dic47⋊C4—22no—
83Dic47⋊C4—82no—
84C4×Dic47—81no—
85C2×C47⋊C8—41no—
86C2×C47⋊C8—41no—
87C2×C47⋊C8—81no—
88C2×C47⋊C8—81no—
89C23×C47—41no—
90C23×C47—41no—
91C23×C47C2×C22⋊C411yescharacteristic
92C23×C47#11711yescharacteristic
93C23×C47#11711yescharacteristic
94C23×C47#13112yes—
95C23×C47#13112yes—
96C2×C4×C47—41no—
97C2×C4×C47—41no—
98C2×C4×C47—41no—
99C2×C4×C47—41no—
100C2×C4×C47—41no—
101C2×C4×C47—41no—
102C2×C4×C47—42no—
103C2×C4×C47—42no—
104C2×C4×C47—42no—
105C2×C4×C47#12311yescharacteristic
106C2×C4×C47#12311yescharacteristic
107C2×C4×C47#12311yescharacteristic
108C2×C4×C47#12311yescharacteristic
109C2×Dic47—22no—
110C2×Dic47—22no—
111C2×Dic47—24no—
112C2×Dic47—41no—
113C2×Dic47—42no—
114C2×Dic47—41no—
115C2×Dic47—42no—
116C2×Dic47—42no—
117C2×Dic47—42no—
118C2×Dic47—42no—
119C2×Dic47—81no—
120C2×Dic47—81no—
121C8×C47—81no—
122C8×C47—81no—
123C47⋊C8—81no—
124C47⋊C8—81no—
125#8737—471nomaximal, Sylow
126C22×C47—21no—
127C22×C47—21no—
128C22×C47—21no—
129C22×C47—21no—
130C22×C47—21no—
131C22×C47—21no—
132C22×C47—42no—
133C22×C47—42no—
134C22×C47#38111yescharacteristic
135C22×C47#40812yes—
136C22×C47#43311yescharacteristic
137C22×C47#43312yes—
138C22×C47#43311yescharacteristic
139C4×C47—21no—
140C4×C47—21no—
141C4×C47—21no—
142C4×C47—21no—
143C4×C47—82no—
144Dic47—42no—
145Dic47—42no—
146Dic47—82no—
147#2313—471no—
148C2×#324—471no—
149C2×#324—471no—
150#1282—471no—
151#1282—471no—
152#1282—471no—
153#1282D4711yescharacteristic
154C2×C47—22no—
155C2×C47—21no—
156C2×C47—22no—
157C2×C47—21no—
158C2×C47#181811yescharacteristic
159C2×C47#182811yescharacteristic
160C2×C47#183011yescharacteristic
161C22×C4⋊C4—471no—
162C2×C22⋊C8—471no—
163C2×C22⋊C8—471no—
164C2×C22⋊C8C2×D4711yescharacteristic
165C2×C22⋊C8C2×D4711yescharacteristic
166#387—942no—
167#387—942no—
168#381—472no—
169#380—472no—
170C4×C22⋊C4—471no—
171C4×C22⋊C4C2×D4711yescharacteristic
172#324—942no—
173#324—942no—
174C47#873711yescharacteristic, complemented, Sylow
175C23×C4—471no—
176C23×C4—471no—
177C23×C4C22×D4711yescharacteristic
178C22×C8—21no—
179C22×C8—21no—
180C22×C8—941no—
181C22×C8—941no—
182C2×C4⋊C4—472no—
183C2×C4⋊C4—472no—
184C2×C4⋊C4—941no—
185C2×C4⋊C4—941no—
186C2×C4⋊C4—941no—
187C2×C4⋊C4—941no—
188C2×C4⋊C4—942no—
189C2×C22⋊C4—472no—
190C2×C22⋊C4C4×D4712yes—
191C2×C42—21no—
192C2×C42—941no—
193C22⋊C8—21no—
194C22⋊C8—21no—
195C22⋊C8—21no—
196C22⋊C8—21no—
197C22⋊C8—941no—
198C22⋊C8—941no—
199C22⋊C8—941no—
200C22⋊C8—941no—
201#95—21no—
202#95—942no—
203#95—944no—
204#95—941no—
205C24C2×C4×D4711yescharacteristic
206C22×C4—22no—
207C22×C4—81no—
208C22×C4—472no—
209C22×C4—472no—
210C22×C4—941no—
211C22×C4—941no—
212C22×C4—941no—
213C22×C4—941no—
214C22×C4—942no—
215C22×C4—942no—
216C22×C4—942no—
217C22×C4—3761no—
218C22×C4#1062535011yescharacteristic
219C22×C4#1062535011yescharacteristic
220C22×C4D4×D4711yescharacteristic
221C22×C4D4×D4711yescharacteristic
222C22×C4#1062535211yescharacteristic
223C22×C4#1062535411yescharacteristic
224C2×C8—41no—
225C2×C8—41no—
226C2×C8—81no—
227C2×C8—81no—
228C2×C8—3761no—
229C2×C8—3761no—
230C2×C8—1881no—
231C2×C8—1881no—
232C4⋊C4—942no—
233C4⋊C4—942no—
234C4⋊C4—942no—
235C4⋊C4—942no—
236C4⋊C4—3762no—
237C22⋊C4—22no—
238C22⋊C4—22no—
239C22⋊C4—942no—
240C22⋊C4—942no—
241C42—81no—
242C42—3761no—
243C23—41no—
244C23—41no—
245C23C22⋊C4×D4711yescharacteristic
246C23#1309398111yescharacteristic
247C23#1309398211yescharacteristic
248C23#1309403012yes—
249C23#1309403212yes—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—942no—
260C2×C4—942no—
261C2×C4—944no—
262C2×C4—3761no—
263C2×C4—3761no—
264C2×C4—1882no—
265C2×C4—1882no—
266C2×C4—1882no—
267C2×C4—1881no—
268C2×C4—1882no—
269C2×C4—1881no—
270C2×C4—1882no—
271C2×C4#1309400611yescharacteristic
272C2×C4#1309400611yescharacteristic
273C2×C4#1309400911yescharacteristic
274C2×C4#1309400911yescharacteristic
275C8—81no—
276C8—81no—
277C8—3761no—
278C8—3761no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—42no—
286C22—42no—
287C22#1568898511yescharacteristic
288C22#1568908812yes—
289C22#1568918211yescharacteristic
290C22#1568918312yes—
291C22#1568918511yescharacteristic
292C4—21no—
293C4—21no—
294C4—21no—
295C4—21no—
296C4—82no—
297C4—3762no—
298C4—1882no—
299C4—1882no—
300C2—22no—
301C2—21no—
302C2—22no—
303C2—21no—
304C2#2024345811yescharacteristic
305C2#2024349511yescharacteristic
306C2#2024350111yescharacteristic
subgroupG/H
centerC22#15688985
commutator, prime radicalC24×C47C22×C4
FrattiniC23×C4C22×D47
FittingC47×#1282C2
socleC22×C47#381
cosocleC23×C4×C47C23
hypercenter#1282D47
hypocenterC47#8737
LCSG ▷ C24×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1282

Complements

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

NH ≅ G/Ntype
174. C47#8737semidirect

Maximal subgroups

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

subgroupindex
#202459882
C2×#156888482
#202412362
#202412352
#202412342
C47×#12822
#873747