Finite Group Databasebeta

← #20244192

Subgroups — #20244192

Order 6016.

436 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 115 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×#13093946C211yesmaximal, characteristic, complemented
3C2×#13093945C211yesmaximal, characteristic, complemented
4C2×#13093944C211yesmaximal, characteristic, complemented
5C2×C8×Dic47C211yesmaximal, characteristic, complemented
6#15688992C211yesmaximal, characteristic, complemented
7C2×#102×C47C211yesmaximal, characteristic, complemented
8C22×D188C2211yescharacteristic
9C22×C22⋊D47—22no—
10C22×C47⋊C8C2211yescharacteristic
11#13094020—22no—
12#13094020C414yescomplemented
13C2×C4⋊Dic47C2211yescharacteristic
14C2×Dic47⋊C4—22no—
15C2×C4×Dic47C2211yescharacteristic
16#13093946—22no—
17#13093945—22no—
18#13093944—22no—
19C8×Dic47—22no—
20C22×D4×C47C2211yescharacteristic
21C22×C8×C47C2211yescharacteristic
22C2×C4⋊C4×C47C2211yescharacteristic
23#102×C47—22no—
24C24×C47—21no—
25C23×D47—21no—
26C2×D4×C47—21no—
27C2×D4×C47—21no—
28C2×D4×C47—21no—
29C2×D4×C47—21no—
30C2×D4×C47—21no—
31C2×D4×C47C2×C412yes—
32C22×C4×C47—21no—
33C22×C4×C47C2311yescharacteristic
34C2×C22⋊D47—28no—
35C2×C22⋊D47—44no—
36C2×C22⋊D47—44no—
37C22×Dic47—21no—
38C22×Dic47D412yes—
39C2×D188—21no—
40C2×D188—21no—
41C2×D188—21no—
42C2×D188—21no—
43C2×D188—21no—
44C2×D188C2×C412yes—
45C2×C8×C47—21no—
46C2×C8×C47—21no—
47C2×C8×C47D412yescomplemented
48C4⋊C4×C47—21no—
49C4⋊C4×C47—21no—
50C4⋊Dic47—21no—
51C4⋊Dic47—21no—
52Dic47⋊C4—44no—
53C4×Dic47C2×C412yes—
54C4×Dic47D412yes—
55C2×C47⋊C8—21no—
56C2×C47⋊C8—21no—
57C2×C47⋊C8D412yescomplemented
58C23×C47—22no—
59C23×C47—41no—
60C23×C47—41no—
61C23×C47—42no—
62C23×C47—42no—
63C23×C47C2×D411yescharacteristic
64C22×D47—22no—
65C22×D47—41no—
66C22×D47—41no—
67C22×D47—42no—
68C22×D47—42no—
69D4×C47—22no—
70D4×C47—22no—
71D4×C47—41no—
72D4×C47—41no—
73C2×C4×C47—41no—
74C2×C4×C47—42no—
75C2×C4×C47C22×C411yescharacteristic
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47C2×D411yescharacteristic
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47#4111yescharacteristic
80C2×C4×C47#4111yescharacteristic
81C22⋊D47—416no—
82C2×Dic47—41no—
83C2×Dic47—42no—
84C2×Dic47C22⋊C414yes—
85C2×Dic47D814yes—
86C2×Dic47SD1614yes—
87D188—22no—
88D188—22no—
89D188—41no—
90D188—41no—
91C8×C47—22no—
92C47⋊C8—22no—
93C22×C47—42no—
94C22×C47—44no—
95C22×C47—82no—
96C22×C47—81no—
97C22×C47—81no—
98C22×C47C2×C22⋊C411yescharacteristic
99C22×C47#12411yescharacteristic
100C22×C47#12711yescharacteristic
101C22×C47C2×D812yes—
102C22×C47C2×SD1612yes—
103C2×D47—42no—
104C2×D47—44no—
105C2×D47—82no—
106C2×D47—81no—
107C2×D47—81no—
108C4×C47—81no—
109C4×C47C4×D411yescharacteristic
110C4×C47C4×D411yescharacteristic
111C4×C47#12111yescharacteristic
112C4×C47#12111yescharacteristic
113Dic47—81no—
114Dic47#10218yescomplemented
115#1957—471nomaximal, Sylow
116C2×C47—82no—
117C2×C47#39011yescharacteristic
118C2×C47C2×#10212yes—
119C2×C47#48612yes—
120C2×C47#49211yescharacteristic
121C2×C47#49311yescharacteristic
122D47—82no—
123C2×#127—471no—
124C2×#102—471no—
125C2×#102—471no—
126C2×#102—471no—
127C2×#102D4711yescharacteristic, complemented
128C2×C4×C8—471no—
129#384—471no—
130C47#195711yescharacteristic, complemented, Sylow
131C22×D4—471no—
132C22×D4—942no—
133C22×D4C2×D4711yescharacteristic
134C22×C8—471no—
135C22×C8C2×D4711yescharacteristic
136#127—474no—
137#127—942no—
138C2×C4⋊C4—471no—
139C2×C4⋊C4—942no—
140C2×C4⋊C4C2×D4711yescharacteristic
141C2×C42—471no—
142#102—22no—
143#102—942no—
144#102—942no—
145#102—942no—
146C4×C8—942no—
147C24—21no—
148C24—941no—
149C2×D4—21no—
150C2×D4—21no—
151C2×D4—21no—
152C2×D4—21no—
153C2×D4—21no—
154C2×D4—472no—
155C2×D4—948no—
156C2×D4—941no—
157C2×D4—941no—
158C2×D4—941no—
159C2×D4—941no—
160C2×D4—941no—
161C2×D4—1884no—
162C2×D4—1884no—
163C2×D4C4×D4712yes—
164C22×C4—21no—
165C22×C4—472no—
166C22×C4—941no—
167C22×C4C22×D4711yescharacteristic
168C2×C8—21no—
169C2×C8—21no—
170C2×C8—472no—
171C2×C8—941no—
172C2×C8—941no—
173C2×C8C22⋊D4712yescomplemented
174C4⋊C4—21no—
175C4⋊C4—21no—
176C4⋊C4—941no—
177C4⋊C4—941no—
178C4⋊C4—1884no—
179C42—472no—
180C42—472no—
181C23—22no—
182C23—41no—
183C23—41no—
184C23—42no—
185C23—42no—
186C23—942no—
187C23—1881no—
188C23—1881no—
189C23—1882no—
190C23—1882no—
191C23D4×D4711yescharacteristic
192D4—22no—
193D4—22no—
194D4—41no—
195D4—41no—
196D4—942no—
197D4—942no—
198D4—18816no—
199D4—1881no—
200D4—1881no—
201C2×C4—41no—
202C2×C4—42no—
203C2×C4—474no—
204C2×C4—474no—
205C2×C4—474no—
206C2×C4—1881no—
207C2×C4—1882no—
208C2×C4C2×C4×D4711yescharacteristic
209C2×C4#1062535011yescharacteristic
210C2×C4D4×D4711yescharacteristic
211C2×C4D4×D4711yescharacteristic
212C2×C4#1062535211yescharacteristic
213C2×C4C2×C22⋊D4711yescharacteristic
214C8—22no—
215C8—942no—
216C22—42no—
217C22—44no—
218C22—81no—
219C22—81no—
220C22—82no—
221C22—3761no—
222C22—3761no—
223C22—3762no—
224C22—1882no—
225C22—1884no—
226C22C22⋊C4×D4711yescharacteristic
227C22#1309401011yescharacteristic
228C22#1309402011yescharacteristic
229C22D8×D4712yes—
230C22SD16×D4712yes—
231C4—81no—
232C4—478no—
233C4—3761no—
234C4(C22⋊D47)⋊C411yescharacteristic
235C4C4×C22⋊D4711yescharacteristic
236C4#1309399611yescharacteristic
237C4#1309399711yescharacteristic
238C2—82no—
239C2—3762no—
240C2#1568902311yescharacteristic
241C2#102×D4712yes—
242C2#1568946812yes—
243C2#1568949411yescharacteristic
244C2#1568949811yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#102×C47C2
socleC23×C47C2×D4
hypercenterC2×#102D47
hypocenterC47#1957
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×#13093946C2semidirect
3. C2×#13093945C2semidirect
4. C2×#13093944C2semidirect
5. C2×C8×Dic47C2semidirect
6. #15688992C2semidirect
7. C2×#102×C47C2semidirect
12. #13094020C4semidirect
47. C2×C8×C47D4semidirect
57. C2×C47⋊C8D4semidirect
114. Dic47#102semidirect
127. C2×#102D47semidirect
130. C47#1957semidirect
173. C2×C8C22⋊D47semidirect