Finite Group Databasebeta

← #26126142

Subgroups — #26126142

Order 12032.

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

normal subgroups only

This group has 318 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#20252366C211yesmaximal, characteristic
2#20245190C211yesmaximal, characteristic, complemented
3#20244981C211yesmaximal, characteristic, complemented
4#20241371C211yesmaximal, characteristic, complemented
5#20241369C211yesmaximal, characteristic, complemented
6#20241346C211yesmaximal, characteristic, complemented
7C47×#1330C211yesmaximal, characteristic, complemented
8#15689655C411yescharacteristic
9C2×#13093963—21no—
10#15689253C2211yescharacteristic
11#15689247C411yescharacteristic
12#15689192—21no—
13D4×C47⋊C8C411yescharacteristic
14(C22⋊D47)⋊C8—21no—
15#15689181—21no—
16#15689179C411yescharacteristic
17#15689081—21no—
18C4×C8×D47C2211yescharacteristic
19C4⋊(C47⋊C16)C2211yescharacteristic
20(C2×D47)⋊C16—21no—
21#15688899C2211yescharacteristic
22#15688898—21no—
23C16×Dic47—21no—
24C47×#436C2211yescharacteristic
25C47×C4⋊C16C2211yescharacteristic
26C47×#346C2211yescharacteristic
27C22×C47⋊C8—21no—
28C2×C8×D47D411yescharacteristic
29C2×C8×D47D411yescharacteristic
30#13094017—21no—
31#13094015C811yescharacteristic
32#13094011C811yescharacteristic
33#13094006—21no—
34#13094004C811yescharacteristic
35#13093995C811yescharacteristic
36C4×Dic94C2×C411yescharacteristic
37C4×C22⋊D47—21no—
38#13093983—21no—
39C42×D47C2×C411yescharacteristic
40#13093963—24no—
41C2×C47⋊C16—21no—
42C2×C47⋊C16—21no—
43C4⋊(C47⋊C8)C2×C411yescharacteristic
44Dic47⋊C8—21no—
45Dic47⋊C8—21no—
46C22⋊(C47⋊C8)—21no—
47(C2×D47)⋊C8—21no—
48#13093934—21no—
49#13093934—21no—
50C4×C47⋊C8C2×C411yescharacteristic
51C8×Dic47—21no—
52C8×Dic47D411yescharacteristic
53C8×Dic47D411yescharacteristic
54C2×M16×C47—21no—
55C4×D4×C47C2×C411yescharacteristic
56C2×C16×C47—21no—
57C2×C16×C47—21no—
58C4⋊C8×C47C2×C411yescharacteristic
59C22⋊C8×C47—21no—
60C4×C8×C47C2311yescharacteristic
61C2×D4×C47C2×C811yescharacteristic
62C22×C4×C47—21no—
63C2×C22⋊D47—21no—
64C2×C4×D47C22⋊C411yescharacteristic
65C2×C4×D47C2×C811yescharacteristic
66C2×C4×D47M1611yescharacteristic
67C2×Dic94C2×C811yescharacteristic
68M16×C47—41no—
69M16×C47—41no—
70C2×C8×C47—21no—
71C2×C8×C47C2×D411yescharacteristic
72C2×C8×C47C2×D411yescharacteristic
73C4⋊C4×C47C2×C811yescharacteristic
74C22⋊C4×C47—21no—
75C42×C47C22×C411yescharacteristic
76C22⋊Dic47—21no—
77C22⋊Dic47—21no—
78C22⋊Dic47—21no—
79(C2×D47)⋊C4—21no—
80C4⋊Dic47—21no—
81C4⋊Dic47—21no—
82C4⋊Dic47C2×C811yescharacteristic
83Dic47⋊C4—21no—
84Dic47⋊C4—21no—
85C4×Dic47—21no—
86C4×Dic47C22⋊C411yescharacteristic
87C4×Dic47C2×C811yescharacteristic
88C4×Dic47M1611yescharacteristic
89C2×C47⋊C8—21no—
90C2×C47⋊C8—42no—
91C2×C47⋊C8C22⋊C411yescharacteristic
92C2×C47⋊C8C22⋊C411yescharacteristic
93C8×D47—21no—
94C8×D47—21no—
95C8×D47—22no—
96C16×C47—22no—
97C16×C47—41no—
98C47⋊C16—22no—
99C47⋊C16—41no—
100C23×C47—21no—
101C22×D47C22⋊C811yescharacteristic
102D4×C47—41no—
103C2×C4×C47—21no—
104C2×C4×C47—41no—
105C2×C4×C47—41no—
106C2×C4×C47C2×C22⋊C411yescharacteristic
107C2×C4×C47C22×C811yescharacteristic
108C2×C4×C47C2×M1611yescharacteristic
109C22⋊D47—42no—
110C2×Dic47—21no—
111C2×Dic47—21no—
112C2×Dic47C22⋊C811yescharacteristic
113C2×Dic47C22⋊C811yescharacteristic
114C2×Dic47C22⋊C811yescharacteristic
115C4×D47—21no—
116C4×D47—21no—
117C4×D47—41no—
118C4×D47—41no—
119Dic94—41no—
120C8×C47—21no—
121C8×C47—41no—
122C8×C47#13511yescharacteristic
123C8×C47#13511yescharacteristic
124C47⋊C8—21no—
125C47⋊C8—41no—
126C47⋊C8#10412yes—
127#11620—471nomaximal, Sylow
128C22×C47—41no—
129C22×C47—41no—
130C22×C47—41no—
131C22×C47C2×C22⋊C811yescharacteristic
132C2×D47—21no—
133C2×D47—21no—
134C2×D47—21no—
135C4×C47—21no—
136C4×C47—21no—
137C4×C47—41no—
138C4×C47#41611yescharacteristic
139C4×C47C2×#10411yescharacteristic
140Dic47—21no—
141Dic47—21no—
142Dic47—21no—
143Dic47—41no—
144Dic47—41no—
145#2966—471no—
146#2163—471no—
147C4×M32—471no—
148#1338—471no—
149#1338—471no—
150#1330—471no—
151#1330D4711yescharacteristic, complemented
152C2×C47—81no—
153C2×C47#147611yescharacteristic
154C2×C47#211511yescharacteristic
155C2×C47#211711yescharacteristic
156D47—41no—
157#529—471no—
158C2×M32—941no—
159#446—471no—
160C8×Q8—471no—
161#436C2×D4711yescharacteristic
162#435—941no—
163C8×D4—471no—
164C8×D4—941no—
165#433—941no—
166#432—471no—
167#405—941no—
168C2×C4×C8—471no—
169C4⋊C16—471no—
170C4⋊C16C2×D4711yescharacteristic
171C22⋊C16—941no—
172#346—471no—
173#346—941no—
174#346C2×D4711yescharacteristic
175C4×C16—941no—
176C47#1162011yescharacteristic, complemented, Sylow
177C2×M16—21no—
178C22×C8—471no—
179C22×C8—471no—
180C22×C8—941no—
181#126—941no—
182#125—471no—
183#124—471no—
184#123—941no—
185C22⋊Q8—471no—
186#121—471no—
187C4×Q8—471no—
188C4×D4—941no—
189C4×D4C4×D4711yescharacteristic
190#117—941no—
191C2×C42—471no—
192M32—944no—
193C2×C16—21no—
194C2×C16—21no—
195C2×C16—941no—
196C2×C16—941no—
197C4⋊C8—471no—
198C4⋊C8—941no—
199C4⋊C8—941no—
200C4⋊C8C4×D4711yescharacteristic
201C22⋊C8—21no—
202C22⋊C8—941no—
203C22⋊C8—941no—
204#97—941no—
205#97—941no—
206C4×C8—471no—
207C4×C8—471no—
208C4×C8—471no—
209C4×C8—941no—
210C4×C8C22×D4711yescharacteristic
211C2×Q8—471no—
212C2×D4—941no—
213C2×D4C8×D4711yescharacteristic
214C22×C4—21no—
215C22×C4—471no—
216C22×C4—471no—
217C22×C4—471no—
218M16—41no—
219M16—41no—
220C2×C8—21no—
221C2×C8—471no—
222C2×C8—471no—
223C2×C8—942no—
224C2×C8—941no—
225C2×C8—941no—
226C2×C8—941no—
227C2×C8—1882no—
228C2×C8D4×D4711yescharacteristic
229C2×C8D4×D4711yescharacteristic
230C4⋊C4—471no—
231C4⋊C4—941no—
232C4⋊C4—941no—
233C4⋊C4—941no—
234C4⋊C4—941no—
235C4⋊C4C8×D4711yescharacteristic
236C22⋊C4—21no—
237C22⋊C4—941no—
238C22⋊C4—941no—
239C22⋊C4—941no—
240C22⋊C4—941no—
241C42—471no—
242C42—471no—
243C42—471no—
244C42—941no—
245C42C2×C4×D4711yescharacteristic
246C16—22no—
247C16—41no—
248C16—942no—
249C16—1881no—
250C23—21no—
251C23—471no—
252Q8—1881no—
253D4—41no—
254D4—1882no—
255C2×C4—21no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—471no—
259C2×C4—471no—
260C2×C4—471no—
261C2×C4—941no—
262C2×C4—941no—
263C2×C4—941no—
264C2×C4—941no—
265C2×C4—1881no—
266C2×C4—1881no—
267C2×C4C22⋊C4×D4711yescharacteristic
268C2×C4C2×C8×D4711yescharacteristic
269C2×C4M16×D4711yescharacteristic
270C8—21no—
271C8—41no—
272C8—472no—
273C8—941no—
274C8—1881no—
275C8#1309404311yescharacteristic
276C8#1309404511yescharacteristic
277C22—41no—
278C22—41no—
279C22—41no—
280C22—941no—
281C22—941no—
282C22—941no—
283C22C22⋊C8×D4711yescharacteristic
284C4—21no—
285C4—21no—
286C4—41no—
287C4—941no—
288C4—941no—
289C4—941no—
290C4—1881no—
291C4—1881no—
292C4#1568911611yescharacteristic
293C4#104×D4711yescharacteristic
294C2—81no—
295C2—1881no—
296C2#2024176711yescharacteristic
297C2#2024500711yescharacteristic
298C2#2024501411yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D47
commutatorC2×C4×C47C22×C8
FrattiniC4×C8C22×D47
FittingC47×#1330C2
socleC22×C47C2×C22⋊C8
prime radical#13093995C8
cosocleC4×C8×C47C23
hypercenter#1330D47
hypocenterC47#11620
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1330

Complements

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

NH ≅ G/Ntype
2. #20245190C2semidirect
3. #20244981C2semidirect
4. #20241371C2semidirect
5. #20241369C2semidirect
6. #20241346C2semidirect
7. C47×#1330C2semidirect
151. #1330D47semidirect
176. C47#11620semidirect

Maximal subgroups

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

subgroupindex
#202523662
#202451902
#202449812
#202413712
#202413692
#202413462
C47×#13302
#1162047