Finite Group Databasebeta

← #20244313

Subgroups — #20244313

Order 6016.

428 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 107 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
1C2×#13094020C211yesmaximal, characteristic
2C2×Dic47⋊C8C211yesmaximal, characteristic, complemented
3C2×#13093946C211yesmaximal, characteristic, complemented
4C2×#13093945C211yesmaximal, characteristic, complemented
5C2×#13093944C211yesmaximal, characteristic, complemented
6C4⋊C4×Dic47C211yesmaximal, characteristic, complemented
7C2×#102×C47C211yesmaximal, characteristic, complemented
8C22×D188C2211yescharacteristic
9C22×C22⋊D47—21no—
10C22×C22⋊D47—21no—
11C22×C47⋊C8C2211yescharacteristic
12#13094020—22no—
13#13094020C414yescomplemented
14C2×C4⋊Dic47C2211yescharacteristic
15C2×C4×Dic47—21no—
16C2×C4×Dic47C2211yescharacteristic
17Dic47⋊C8—22no—
18#13093946—22no—
19#13093945—22no—
20#13093944—22no—
21C47⋊#95—21no—
22C22×D4×C47C2211yescharacteristic
23C22×C8×C47C2211yescharacteristic
24C2×C4⋊C4×C47C2211yescharacteristic
25#102×C47—22no—
26C24×C47—21no—
27C23×D47—21no—
28C2×D4×C47—21no—
29C2×D4×C47—21no—
30C2×D4×C47—21no—
31C2×D4×C47—21no—
32C2×D4×C47—21no—
33C2×D4×C47C2×C412yes—
34C22×C4×C47—21no—
35C22×C4×C47C2311yescharacteristic
36C2×C22⋊D47—24no—
37C2×C22⋊D47—24no—
38C2×C22⋊D47—42no—
39C2×C22⋊D47—42no—
40C2×C22⋊D47—42no—
41C2×C22⋊D47—42no—
42C22×Dic47—21no—
43C22×Dic47D411yescharacteristic
44C22×Dic47D411yescharacteristic
45C2×D188—21no—
46C2×D188—21no—
47C2×D188—21no—
48C2×D188—21no—
49C2×D188—21no—
50C2×D188C2×C412yes—
51C2×C8×C47—21no—
52C2×C8×C47—21no—
53C2×C8×C47—21no—
54C4⋊C4×C47—21no—
55C4⋊C4×C47D412yescomplemented
56C4⋊Dic47—21no—
57C4⋊Dic47D412yescomplemented
58C4×Dic47—42no—
59C4×Dic47C2×C412yes—
60C4×Dic47D412yes—
61C2×C47⋊C8—21no—
62C2×C47⋊C8—21no—
63C2×C47⋊C8—21no—
64C23×C47—22no—
65C23×C47—41no—
66C23×C47—41no—
67C23×C47—41no—
68C23×C47—41no—
69C23×C47—41no—
70C23×C47—41no—
71C23×C47C2×D411yescharacteristic
72C22×D47—22no—
73C22×D47—41no—
74C22×D47—41no—
75C22×D47—41no—
76C22×D47—41no—
77C22×D47—41no—
78C22×D47—41no—
79D4×C47—22no—
80D4×C47—22no—
81D4×C47—41no—
82D4×C47—41no—
83C2×C4×C47—22no—
84C2×C4×C47—41no—
85C2×C4×C47—41no—
86C2×C4×C47C22×C411yescharacteristic
87C2×C4×C47C2×D411yescharacteristic
88C2×C4×C47C2×D411yescharacteristic
89C2×C4×C47C2×D411yescharacteristic
90C2×C4×C47#4111yescharacteristic
91C2×C4×C47#4111yescharacteristic
92C22⋊D47—48no—
93C22⋊D47—48no—
94C2×Dic47—21no—
95C2×Dic47—21no—
96C2×Dic47—22no—
97C2×Dic47—41no—
98C2×Dic47—41no—
99C2×Dic47C22⋊C412yes—
100C2×Dic47C22⋊C412yes—
101C2×Dic47D812yes—
102C2×Dic47SD1612yes—
103D188—22no—
104D188—22no—
105D188—41no—
106D188—41no—
107C8×C47—41no—
108C47⋊C8—41no—
109C22×C47—42no—
110C22×C47—42no—
111C22×C47—42no—
112C22×C47—81no—
113C22×C47—81no—
114C22×C47—81no—
115C22×C47—81no—
116C22×C47C2×C22⋊C411yescharacteristic
117C22×C47#12111yescharacteristic
118C22×C47#12111yescharacteristic
119C22×C47C2×D811yescharacteristic
120C22×C47C2×SD1611yescharacteristic
121C22×C47AGL(1,ℤ/8)11yescharacteristic
122C22×C47AGL(1,ℤ/8)11yescharacteristic
123C2×D47—42no—
124C2×D47—42no—
125C2×D47—42no—
126C2×D47—81no—
127C2×D47—81no—
128C2×D47—81no—
129C2×D47—81no—
130C4×C47—42no—
131C4×C47C4×D411yescharacteristic
132C4×C47C4×D411yescharacteristic
133C4×C47#12411yescharacteristic
134C4×C47#12711yescharacteristic
135Dic47—22no—
136Dic47—42no—
137Dic47#10214yescomplemented
138#1982—471nomaximal, Sylow
139C2×C47—82no—
140C2×C47#39011yescharacteristic
141C2×C47C2×#10211yescharacteristic
142C2×C47#41811yescharacteristic
143C2×C47#45911yescharacteristic
144C2×C47#45911yescharacteristic
145C2×C47#46011yescharacteristic
146C2×C47#46011yescharacteristic
147D47—82no—
148C2×#127—471no—
149C2×C4⋊C8—471no—
150C2×#102—471no—
151C2×#102—471no—
152C2×#102—471no—
153C2×#102D4711yescharacteristic, complemented
154C4×C4⋊C4—471no—
155C47#198211yescharacteristic, complemented, Sylow
156C22×D4—471no—
157C22×D4—941no—
158C22×D4—941no—
159C22×D4C2×D4711yescharacteristic
160C22×C8—471no—
161C22×C8C2×D4711yescharacteristic
162#127—474no—
163#127—942no—
164C2×C4⋊C4—471no—
165C2×C4⋊C4C2×D4711yescharacteristic
166C2×C42—471no—
167C2×C42—941no—
168C4⋊C8—942no—
169#102—22no—
170#102—942no—
171#102—942no—
172#102—942no—
173#95—941no—
174C24—21no—
175C24—941no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—21no—
180C2×D4—21no—
181C2×D4—472no—
182C2×D4—944no—
183C2×D4—944no—
184C2×D4—941no—
185C2×D4—941no—
186C2×D4—941no—
187C2×D4—941no—
188C2×D4—941no—
189C2×D4—1882no—
190C2×D4—1882no—
191C2×D4—1882no—
192C2×D4—1882no—
193C2×D4C4×D4712yes—
194C22×C4—21no—
195C22×C4—471no—
196C22×C4—471no—
197C22×C4—941no—
198C22×C4C22×D4711yescharacteristic
199C2×C8—21no—
200C2×C8—21no—
201C2×C8—21no—
202C2×C8—941no—
203C2×C8—941no—
204C2×C8—941no—
205C4⋊C4—21no—
206C4⋊C4—472no—
207C4⋊C4—941no—
208C4⋊C4C22⋊D4712yescomplemented
209C42—472no—
210C42—472no—
211C42—1882no—
212C23—22no—
213C23—41no—
214C23—41no—
215C23—41no—
216C23—41no—
217C23—41no—
218C23—41no—
219C23—942no—
220C23—1881no—
221C23—1881no—
222C23—1881no—
223C23—1881no—
224C23—1881no—
225C23—1881no—
226C23D4×D4711yescharacteristic
227D4—22no—
228D4—22no—
229D4—41no—
230D4—41no—
231D4—942no—
232D4—942no—
233D4—1888no—
234D4—1888no—
235D4—1881no—
236D4—1881no—
237C2×C4—22no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—472no—
241C2×C4—472no—
242C2×C4—472no—
243C2×C4—472no—
244C2×C4—941no—
245C2×C4—941no—
246C2×C4—942no—
247C2×C4—1881no—
248C2×C4—1881no—
249C2×C4C2×C4×D4711yescharacteristic
250C2×C4#1062535011yescharacteristic
251C2×C4D4×D4711yescharacteristic
252C2×C4D4×D4711yescharacteristic
253C2×C4#1062535211yescharacteristic
254C2×C4C2×C22⋊D4711yescharacteristic
255C8—41no—
256C8—1881no—
257C22—42no—
258C22—42no—
259C22—42no—
260C22—81no—
261C22—81no—
262C22—81no—
263C22—81no—
264C22—3761no—
265C22—3761no—
266C22—3761no—
267C22—3761no—
268C22—1882no—
269C22—1882no—
270C22—1882no—
271C22C22⋊C4×D4711yescharacteristic
272C22#1309399611yescharacteristic
273C22#1309399711yescharacteristic
274C22D8×D4711yescharacteristic
275C22SD16×D4711yescharacteristic
276C22#1309404811yescharacteristic
277C22#1309405111yescharacteristic
278C4—42no—
279C4—474no—
280C4—942no—
281C4—1882no—
282C4(C22⋊D47)⋊C411yescharacteristic
283C4C4×C22⋊D4711yescharacteristic
284C4#1309401011yescharacteristic
285C4#1309402011yescharacteristic
286C2—82no—
287C2—3762no—
288C2#1568902311yescharacteristic
289C2#102×D4711yescharacteristic
290C2#1568912611yescharacteristic
291C2#1568931611yescharacteristic
292C2#1568931711yescharacteristic
293C2#1568932111yescharacteristic
294C2#1568932211yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#102×C47C2
socleC23×C47C2×D4
hypercenterC2×#102D47
hypocenterC47#1982
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×Dic47⋊C8C2semidirect
3. C2×#13093946C2semidirect
4. C2×#13093945C2semidirect
5. C2×#13093944C2semidirect
6. C4⋊C4×Dic47C2semidirect
7. C2×#102×C47C2semidirect
13. #13094020C4semidirect
55. C4⋊C4×C47D4semidirect
57. C4⋊Dic47D4semidirect
137. Dic47#102semidirect
153. C2×#102D47semidirect
155. C47#1982semidirect
208. C4⋊C4C22⋊D47semidirect