Finite Group Databasebeta

← #20255668

Subgroups — #20255668

Order 6016.

374 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 117 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#15689847C211yesmaximal, characteristic
2Q8×D188C211yesmaximal, characteristic
3#15689475C211yesmaximal, characteristic, complemented
4#15689467C212yesmaximal, complemented
5#15689382C212yesmaximal, complemented
6#15689334C211yesmaximal, characteristic, complemented
7#15689280C212yesmaximal, complemented
8C4×#10625337C211yesmaximal, characteristic, complemented
9#15689200C211yesmaximal, characteristic
10#15689130C212yesmaximal, complemented
11C47×#475C211yesmaximal, characteristic, complemented
12C2×Q8×D47C2212yes—
13C2×Dic188C2212yes—
14C2×#10625337C2211yescharacteristic
15C2×#10625324C2212yes—
16#13094024—21no—
17#13094024C2211yescharacteristic
18#13094019—22no—
19#13094013—21no—
20#13094004—22no—
21#13094004C2212yes—
22#13094004C2212yes—
23Q8×Dic47—21no—
24C4×Dic94C2211yescharacteristic
25C4×D188—21no—
26C4×D188C2211yescharacteristic
27#13093982C2212yes—
28#13093957C2211yescharacteristic
29#13093949C2212yes—
30#13093948C2211yescharacteristic
31#13093947C2211yescharacteristic
32#13093947C2212yes—
33#13093947C2212yes—
34(C2×D47)⋊C8C2212yes—
35C4×C47⋊C8C2211yescharacteristic
36C4⋊Q8×C47C2211yescharacteristic
37C4×Q8×C47C2211yescharacteristic
38#106×C47C2212yes—
39C4⋊C8×C47C2211yescharacteristic
40#103×C47C2212yes—
41C2×Q8×C47—21no—
42C2×Q8×C47C2311yescharacteristic
43Q8×D47—24no—
44Q8×D47—42no—
45C2×D188D411yescharacteristic
46C2×C4×D47—22no—
47C2×C4×D47C2312yes—
48C2×Dic94—22no—
49C2×Dic94C2312yes—
50C2×Dic94C2311yescharacteristic
51C2×C8×C47C2312yes—
52C4⋊C4×C47—21no—
53C4⋊C4×C47—21no—
54C4⋊C4×C47C2312yes—
55C4⋊C4×C47C2311yescharacteristic
56C42×C47—21no—
57C42×C47C2311yescharacteristic
58#10625337—22no—
59(C2×D47)⋊C4—22no—
60(C2×D47)⋊C4—22no—
61(C2×D47)⋊C4—22no—
62(C2×D47)⋊C4D412yes—
63C4⋊Dic47—21no—
64C4⋊Dic47—21no—
65C4⋊Dic47—22no—
66C4⋊Dic47—22no—
67C4⋊Dic47D411yescharacteristic
68C4⋊Dic47C2311yescharacteristic
69Dic47⋊C4—21no—
70C4×Dic47—21no—
71C4×Dic47—22no—
72C2×C47⋊C8C2311yescharacteristic
73C2×C47⋊C8C2311yescharacteristic
74Dic188—42no—
75#10625324—42no—
76C22×D47C2×D412yes—
77Q8×C47—21no—
78Q8×C47—42no—
79Q8×C47#4112yes—
80C2×C4×C47—21no—
81C2×C4×C47—22no—
82C2×C4×C47—21no—
83C2×C4×C47C2×D411yescharacteristic
84C2×C4×C47C2×D411yescharacteristic
85C2×C4×C47C2411yescharacteristic
86C2×Dic47—21no—
87C2×Dic47—21no—
88C2×Dic47—22no—
89C2×Dic47C2×D412yes—
90D188—22no—
91C4×D47—22no—
92C4×D47—22no—
93C4×D47—44no—
94Dic94—21no—
95Dic94—22no—
96Dic94—21no—
97Dic94—22no—
98Dic94—44no—
99C8×C47—22no—
100C47⋊C8—21no—
101C47⋊C8—21no—
102C22×C47C22×D411yescharacteristic
103C2×D47—22no—
104C2×D47—22no—
105C2×D47—22no—
106C4×C47—22no—
107C4×C47—21no—
108C4×C47—42no—
109C4×C47—41no—
110C4×C47#13712yes—
111C4×C47C2×#4111yescharacteristic
112C4×C47H(5,𝔽2)11yescharacteristic
113Dic47—22no—
114Dic47—42no—
115Dic47—41no—
116Dic47—41no—
117#3328—471nomaximal, Sylow
118C2×C47#54611yescharacteristic
119C2×C47C2×#13711yescharacteristic
120C2×C47#57811yescharacteristic
121D47—42no—
122#556—471no—
123D4×Q8—471no—
124#487—471no—
125#485—472no—
126#475D4711yescharacteristic, complemented
127#470—472no—
128#462—471no—
129#451—472no—
130C4×Q16—471no—
131#436—471no—
132#419—472no—
133C47#332811yescharacteristic, complemented, Sylow
134C22×Q8—472no—
135C2×Q16—471no—
136C2×Q16—472no—
137C2×M16—472no—
138C4⋊Q8—471no—
139C4⋊Q8—941no—
140C4⋊Q8C2×D4711yescharacteristic
141#126—942no—
142#124—941no—
143C22⋊Q8—472no—
144C22⋊Q8—472no—
145C22⋊Q8—942no—
146C4×Q8—471no—
147C4×Q8—941no—
148C4×Q8C2×D4711yescharacteristic
149C4×D4—471no—
150C4×D4—941no—
151#117—472no—
152#107—471no—
153#106C2×D4712yes—
154C4⋊C8C2×D4711yescharacteristic
155#103—471no—
156#103—472no—
157#103—472no—
158#103—471no—
159#103—472no—
160#103C2×D4712yes—
161C22⋊C8—472no—
162C4×C8—471no—
163C2×Q8—21no—
164C2×Q8—472no—
165C2×Q8—471no—
166C2×Q8—942no—
167C2×Q8—944no—
168C2×Q8—1882no—
169C2×Q8C22×D4711yescharacteristic
170C2×D4—471no—
171C22×C4—472no—
172C22×C4—942no—
173Q16—942no—
174Q16—1882no—
175M16—1882no—
176C2×C8—471no—
177C2×C8—471no—
178C2×C8C22×D4712yes—
179C4⋊C4—21no—
180C4⋊C4—21no—
181C4⋊C4—471no—
182C4⋊C4—471no—
183C4⋊C4—942no—
184C4⋊C4—942no—
185C4⋊C4—941no—
186C4⋊C4—941no—
187C4⋊C4—941no—
188C4⋊C4C22×D4712yes—
189C4⋊C4C22×D4711yescharacteristic
190C22⋊C4—472no—
191C22⋊C4—942no—
192C22⋊C4—942no—
193C22⋊C4—942no—
194C42—21no—
195C42—942no—
196C42—941no—
197C42C22×D4711yescharacteristic
198C23—472no—
199Q8—21no—
200Q8—42no—
201Q8—941no—
202Q8—942no—
203Q8—941no—
204Q8—942no—
205Q8—1884no—
206Q8#1062535412yes—
207D4—942no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—472no—
212C2×C4—942no—
213C2×C4—942no—
214C2×C4—941no—
215C2×C4—941no—
216C2×C4—942no—
217C2×C4—1884no—
218C2×C4D4×D4711yescharacteristic
219C2×C4D4×D4711yescharacteristic
220C2×C4C23×D4711yescharacteristic
221C8—22no—
222C8—941no—
223C8—941no—
224C22—942no—
225C22—942no—
226C22—942no—
227C22C2×D4×D4711yescharacteristic
228C4—22no—
229C4—21no—
230C4—42no—
231C4—41no—
232C4—942no—
233C4—1882no—
234C4—1881no—
235C4—1881no—
236C4#1309405312yes—
237C4C2×#1062535411yescharacteristic
238C4#1309407011yescharacteristic
239C2—1882no—
240C2#1568976411yescharacteristic
241C2C2×#1309405311yescharacteristic
242C2#1568993911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#475C2
socleC22×C47C22×D4
hypercenter#475D47
hypocenterC47#3328
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
3. #15689475C2semidirect
4. #15689467C2semidirect
5. #15689382C2semidirect
6. #15689334C2semidirect
7. #15689280C2semidirect
8. C4×#10625337C2semidirect
10. #15689130C2semidirect
11. C47×#475C2semidirect
126. #475D47semidirect
133. C47#3328semidirect