Finite Group Databasebeta

← #26126169

Subgroups — #26126169

Order 12032.

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

normal subgroups only

This group has 312 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#20252362C211yesmaximal, characteristic
2#20245189C211yesmaximal, characteristic, complemented
3C4⋊C16×D47C211yesmaximal, characteristic, complemented
4#20241370C211yesmaximal, characteristic, complemented
5#20241347C211yesmaximal, characteristic, complemented
6#20241345C211yesmaximal, characteristic, complemented
7C47×#1338C211yesmaximal, characteristic, complemented
8#15689660C411yescharacteristic
9C2×C16×D47—21no—
10Q8×C47⋊C8C411yescharacteristic
11#15689202C2211yescharacteristic
12#15689196—21no—
13#15689188—21no—
14#15689188C411yescharacteristic
15#15689183—21no—
16#15689179C411yescharacteristic
17#15689080—21no—
18C4×C8×D47C2211yescharacteristic
19C4⋊(C47⋊C16)C2211yescharacteristic
20Dic47⋊C16—21no—
21Dic47⋊C16—21no—
22(C2×D47)⋊C16—21no—
23#15688899C2211yescharacteristic
24C47×#446C2211yescharacteristic
25C47×C4⋊C16C2211yescharacteristic
26C47×#346C2211yescharacteristic
27C2×#10625324—21no—
28C2×C8×D47—21no—
29C2×C8×D47D411yescharacteristic
30C2×C8×D47D411yescharacteristic
31#13094019—21no—
32#13094015C811yescharacteristic
33#13094013C811yescharacteristic
34#13094009—21no—
35#13094000C811yescharacteristic
36#13093999C811yescharacteristic
37C4×D188—21no—
38C4×D188C2×C411yescharacteristic
39#13093981—21no—
40C42×D47C2×C411yescharacteristic
41C2×C47⋊C16—21no—
42C2×C47⋊C16—21no—
43C16×D47—42no—
44C4⋊(C47⋊C8)—21no—
45C4⋊(C47⋊C8)C2×C411yescharacteristic
46(C2×D47)⋊C8—21no—
47(C2×D47)⋊C8—21no—
48(C2×D47)⋊C8—21no—
49#13093934—21no—
50C4×C47⋊C8—21no—
51C4×C47⋊C8C2×C411yescharacteristic
52C8×Dic47D411yescharacteristic
53C8×Dic47D411yescharacteristic
54C4×Q8×C47C2×C411yescharacteristic
55C2×C16×C47—21no—
56C2×C16×C47—21no—
57C4⋊C8×C47—21no—
58C4⋊C8×C47C2×C411yescharacteristic
59#97×C47—21no—
60C4×C8×C47C2311yescharacteristic
61C2×Q8×C47C2×C811yescharacteristic
62C2×D188—21no—
63C2×D188C2×C811yescharacteristic
64C2×C4×D47—21no—
65C2×C4×D47C22⋊C411yescharacteristic
66C2×C4×D47C2×C811yescharacteristic
67C2×C4×D47M1611yescharacteristic
68C2×C8×C47—21no—
69C2×C8×C47C2×D411yescharacteristic
70C2×C8×C47C2×D411yescharacteristic
71C4⋊C4×C47—21no—
72C4⋊C4×C47C2×C811yescharacteristic
73C42×C47—21no—
74C42×C47C22×C411yescharacteristic
75(C2×D47)⋊C4—21no—
76(C2×D47)⋊C4—21no—
77(C2×D47)⋊C4—21no—
78(C2×D47)⋊C4—21no—
79(C2×D47)⋊C4—21no—
80C4⋊Dic47—21no—
81C4⋊Dic47C2×C811yescharacteristic
82Dic47⋊C4—21no—
83Dic47⋊C4—21no—
84C4×Dic47C22⋊C411yescharacteristic
85C4×Dic47C2×C811yescharacteristic
86C4×Dic47M1611yescharacteristic
87C2×C47⋊C8—21no—
88C2×C47⋊C8C22⋊C411yescharacteristic
89C2×C47⋊C8C22⋊C411yescharacteristic
90#10625324—41no—
91#10625324—41no—
92C8×D47—21no—
93C8×D47—21no—
94C8×D47—41no—
95C8×D47—42no—
96C16×C47—41no—
97C16×C47—41no—
98C47⋊C16—41no—
99C47⋊C16—41no—
100C22×D47—21no—
101C22×D47C22⋊C811yescharacteristic
102Q8×C47—41no—
103C2×C4×C47—21no—
104C2×C4×C47—21no—
105C2×C4×C47C2×C22⋊C411yescharacteristic
106C2×C4×C47C22×C811yescharacteristic
107C2×C4×C47C2×M1611yescharacteristic
108C2×Dic47—21no—
109C2×Dic47C22⋊C811yescharacteristic
110C2×Dic47C22⋊C811yescharacteristic
111C2×Dic47C22⋊C811yescharacteristic
112D188—41no—
113D188—42no—
114C4×D47—22no—
115C4×D47—21no—
116C4×D47—21no—
117C4×D47—41no—
118C4×D47—41no—
119C4×D47—41no—
120C8×C47—21no—
121C8×C47—41no—
122C8×C47AGL(1,ℤ/8)11yescharacteristic
123C8×C47#13711yescharacteristic
124C47⋊C8—21no—
125C47⋊C8—21no—
126C47⋊C8—41no—
127#11625—471nomaximal, Sylow
128C22×C47C2×C22⋊C811yescharacteristic
129C2×D47—21no—
130C2×D47—21no—
131C2×D47—41no—
132C2×D47—41no—
133C2×D47—41no—
134C2×D47#35012yes—
135C4×C47—21no—
136C4×C47—21no—
137C4×C47—41no—
138C4×C47—41no—
139C4×C47#41711yescharacteristic
140C4×C47#42111yescharacteristic
141Dic47—21no—
142Dic47—21no—
143Dic47—21no—
144Dic47—41no—
145#2966—471no—
146#2163—471no—
147C2×C4⋊C16—471no—
148#1338—471no—
149#1338D4711yescharacteristic, complemented
150#1330—471no—
151#1330—471no—
152C2×C47#147711yescharacteristic
153C2×C47#211511yescharacteristic
154C2×C47C2×#35011yescharacteristic
155D47—22no—
156D47—81no—
157#529—471no—
158C22×C16—941no—
159#446C2×D4711yescharacteristic
160C8×Q8—471no—
161#436—471no—
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⋊C16—941no—
171C4⋊C16—941no—
172C4⋊C16C2×D4711yescharacteristic
173C22⋊C16—941no—
174#346—471no—
175#346C2×D4711yescharacteristic
176C47#1162511yescharacteristic, complemented, Sylow
177C2×M16—941no—
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×Q8C4×D4711yescharacteristic
188C4×D4—471no—
189C4×D4—941no—
190#117—941no—
191C2×C42—471no—
192C2×C16—21no—
193C2×C16—21no—
194C2×C16—941no—
195C2×C16—941no—
196C2×C16—1882no—
197C4⋊C8—21no—
198C4⋊C8—471no—
199C4⋊C8—941no—
200C4⋊C8C4×D4711yescharacteristic
201C22⋊C8—941no—
202C22⋊C8—941no—
203C22⋊C8—941no—
204#97—21no—
205#97—941no—
206C4×C8—471no—
207C4×C8—471no—
208C4×C8—471no—
209C4×C8—941no—
210C4×C8C22×D4711yescharacteristic
211C2×Q8C8×D4711yescharacteristic
212C2×D4—471no—
213C2×D4—941no—
214C22×C4—471no—
215C22×C4—471no—
216C22×C4—471no—
217C22×C4—941no—
218M16—1881no—
219M16—1881no—
220C2×C8—21no—
221C2×C8—471no—
222C2×C8—471no—
223C2×C8—941no—
224C2×C8—941no—
225C2×C8—941no—
226C2×C8—1881no—
227C2×C8—1882no—
228C2×C8D4×D4711yescharacteristic
229C2×C8D4×D4711yescharacteristic
230C4⋊C4—21no—
231C4⋊C4—471no—
232C4⋊C4—941no—
233C4⋊C4—941no—
234C4⋊C4—941no—
235C4⋊C4C8×D4711yescharacteristic
236C22⋊C4—941no—
237C22⋊C4—941no—
238C22⋊C4—941no—
239C22⋊C4—941no—
240C22⋊C4—941no—
241C42—21no—
242C42—471no—
243C42—471no—
244C42—471no—
245C42C2×C4×D4711yescharacteristic
246C16—41no—
247C16—41no—
248C16—1881no—
249C16—1881no—
250C23—471no—
251C23—941no—
252Q8—41no—
253D4—1881no—
254D4—1882no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—471no—
258C2×C4—471no—
259C2×C4—471no—
260C2×C4—942no—
261C2×C4—941no—
262C2×C4—941no—
263C2×C4—941no—
264C2×C4—1881no—
265C2×C4—1881no—
266C2×C4—1881no—
267C2×C4C22⋊C4×D4711yescharacteristic
268C2×C4C2×C8×D4711yescharacteristic
269C2×C4M16×D4711yescharacteristic
270C8—21no—
271C8—41no—
272C8—941no—
273C8—941no—
274C8—1881no—
275C8#1309405111yescharacteristic
276C8#1309405611yescharacteristic
277C22—472no—
278C22—941no—
279C22—941no—
280C22—1881no—
281C22—1881no—
282C22—1881no—
283C22C22⋊C8×D4711yescharacteristic
284C4—21no—
285C4—21no—
286C4—41no—
287C4—41no—
288C4—941no—
289C4—941no—
290C4—941no—
291C4—1881no—
292C4#1568912311yescharacteristic
293C4#1568913811yescharacteristic
294C2—942no—
295C2—3761no—
296C2#2024177411yescharacteristic
297C2#2024500711yescharacteristic
298C2#350×D4711yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D47
commutatorC2×C4×C47C22×C8
FrattiniC4×C8C22×D47
FittingC47×#1338C2
socleC22×C47C2×C22⋊C8
prime radical#13093999C8
cosocleC4×C8×C47C23
hypercenter#1338D47
hypocenterC47#11625
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1338

Complements

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

NH ≅ G/Ntype
2. #20245189C2semidirect
3. C4⋊C16×D47C2semidirect
4. #20241370C2semidirect
5. #20241347C2semidirect
6. #20241345C2semidirect
7. C47×#1338C2semidirect
149. #1338D47semidirect
176. C47#11625semidirect

Maximal subgroups

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

subgroupindex
#202523622
#202451892
C4⋊C16×D472
#202413702
#202413472
#202413452
C47×#13382
#1162547