Finite Group Databasebeta

← #20243407

Subgroups — #20243407

Order 6016.

312 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 87 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#15689591C211yesmaximal, characteristic
2#15689146C211yesmaximal, characteristic, complemented
3C2×#13093952C211yesmaximal, characteristic
4C2×#13093950C211yesmaximal, characteristic
5C4×Dic47⋊C4C211yesmaximal, characteristic, complemented
6#15688882C211yesmaximal, characteristic, complemented
7C47×#339C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9C2×#10625329C2211yescharacteristic
10#13093989C411yescharacteristic, complemented
11#13093989C411yescharacteristic, complemented
12#13093986C411yescharacteristic, complemented
13#13093986C411yescharacteristic, complemented
14(C22⋊D47)⋊C4—21no—
15(C22⋊D47)⋊C4—21no—
16#13093981—21no—
17C2×Dic47⋊C4—21no—
18C2×C4×Dic47C2211yescharacteristic
19C2×C4×Dic47C2211yescharacteristic
20C42×D47—21no—
21Dic47⋊C8—21no—
22Dic47⋊C8—21no—
23#13093952—22no—
24#13093950—22no—
25C47⋊#95—21no—
26C2×M16×C47C2211yescharacteristic
27#117×C47C2211yescharacteristic
28C2×C42×C47C2211yescharacteristic
29C22×C4×C47—21no—
30C22×C4×C47C2311yescharacteristic
31C2×C22⋊D47—21no—
32C22×Dic47—21no—
33C22×Dic47D411yescharacteristic
34C22×Dic47D411yescharacteristic
35#10625350—21no—
36#10625350—21no—
37#10625350D412yes—
38#10625350Q812yes—
39C2×D188C2×C411yescharacteristic
40C2×C4×D47—21no—
41C2×C4×D47—21no—
42C2×C4×D47—21no—
43C2×Dic94C2×C411yescharacteristic
44M16×C47—21no—
45M16×C47—21no—
46C2×C8×C47—21no—
47C4⋊C4×C47C2×C411yescharacteristic
48C4⋊C4×C47C2×C411yescharacteristic
49C22⋊C4×C47—21no—
50C42×C47—21no—
51C42×C47—21no—
52C42×C47—21no—
53(C2×D47)⋊C4—21no—
54(C2×D47)⋊C4—21no—
55Dic47⋊C4—24no—
56Dic47⋊C4—21no—
57Dic47⋊C4—21no—
58C4×Dic47—21no—
59C4×Dic47—21no—
60C4×Dic47—21no—
61C4×Dic47—21no—
62C4×Dic47C2×C411yescharacteristic
63C4×Dic47C2×C411yescharacteristic
64C4×Dic47D411yescharacteristic
65C4×Dic47D411yescharacteristic
66#10625329—21no—
67#10625329—21no—
68C2×C47⋊C8—21no—
69C23×C47C2×D411yescharacteristic
70C22×D47—21no—
71C2×C4×C47—22no—
72C2×C4×C47—21no—
73C2×C4×C47—21no—
74C2×C4×C47—41no—
75C2×C4×C47—41no—
76C2×C4×C47C22×C411yescharacteristic
77C2×C4×C47C2×D411yescharacteristic
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2×Q811yescharacteristic
80C2×C4×C47#4111yescharacteristic
81C2×C4×C47#4111yescharacteristic
82C22⋊D47—22no—
83C22⋊D47—22no—
84C2×Dic47—21no—
85C2×Dic47—22no—
86C2×Dic47—22no—
87C2×Dic47—41no—
88C2×Dic47—41no—
89C2×Dic47—41no—
90C2×Dic47C22⋊C411yescharacteristic
91C2×Dic47C22⋊C411yescharacteristic
92C2×Dic47C22⋊C411yescharacteristic
93C2×Dic47C22⋊C411yescharacteristic
94D188—21no—
95D188C4⋊C412yescomplemented
96C4×D47—22no—
97C4×D47—22no—
98C4×D47—42no—
99C4×D47—42no—
100Dic94—21no—
101Dic94C4⋊C412yescomplemented
102C8×C47—41no—
103C47⋊C8—41no—
104C22×C47—21no—
105C22×C47—21no—
106C22×C47C2×C22⋊C411yescharacteristic
107C22×C47#12111yescharacteristic
108C22×C47C22⋊Q811yescharacteristic
109C2×D47—22no—
110C2×D47—41no—
111C2×D47—41no—
112C4×C47—42no—
113C4×C47—41no—
114C4×C47—41no—
115C4×C47C2×C4⋊C411yescharacteristic
116C4×C47#11711yescharacteristic
117C4×C47#12111yescharacteristic
118C4×C47C22⋊Q811yescharacteristic
119Dic47—22no—
120Dic47—21no—
121Dic47—21no—
122Dic47—21no—
123Dic47—42no—
124Dic47#10412yescomplemented
125#1806—471nomaximal, Sylow
126C2×C47—21no—
127C2×C47—21no—
128C2×C47#38011yescharacteristic
129C2×C47C2×#10411yescharacteristic
130C2×C47#42111yescharacteristic
131D47—42no—
132C4×#41—471no—
133#423—471no—
134C2×#104—471no—
135C2×#104—471no—
136C4×C4⋊C4—471no—
137#339—471no—
138#339D4711yescharacteristic, complemented
139C47#180611yescharacteristic, complemented, Sylow
140C2×#41—471no—
141C2×M16—471no—
142C2×M16C2×D4711yescharacteristic
143C4×Q8—471no—
144C4×Q8—471no—
145C4×D4—471no—
146C4×D4—471no—
147C4×D4—941no—
148C4×D4—941no—
149#117—941no—
150#117C2×D4711yescharacteristic
151C2×C4⋊C4—941no—
152C2×C42—471no—
153C2×C42—471no—
154C2×C42—941no—
155C2×C42C2×D4711yescharacteristic
156C4⋊C8—941no—
157C4⋊C8—941no—
158#104—942no—
159#104—942no—
160#95—941no—
161#41—472no—
162#41—472no—
163#41—941no—
164#41—941no—
165C2×Q8—471no—
166C2×D4—471no—
167C2×D4—941no—
168C22×C4—21no—
169C22×C4—471no—
170C22×C4—471no—
171C22×C4—941no—
172C22×C4—941no—
173C22×C4—941no—
174C22×C4—941no—
175C22×C4C22×D4711yescharacteristic
176M16—21no—
177M16—21no—
178M16—941no—
179M16—941no—
180C2×C8—21no—
181C2×C8—941no—
182C4⋊C4—941no—
183C4⋊C4—941no—
184C4⋊C4—944no—
185C4⋊C4C4×D4711yescharacteristic
186C4⋊C4C4×D4711yescharacteristic
187C22⋊C4—21no—
188C22⋊C4—941no—
189C22⋊C4—941no—
190C42—21no—
191C42—21no—
192C42—21no—
193C42—471no—
194C42—471no—
195C42—471no—
196C42—471no—
197C42—941no—
198C42—941no—
199C42—941no—
200C42—941no—
201C23—941no—
202C23D4×D4711yescharacteristic
203Q8—472no—
204Q8—941no—
205D4—472no—
206D4—942no—
207D4—942no—
208D4—941no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—471no—
215C2×C4—471no—
216C2×C4—471no—
217C2×C4—471no—
218C2×C4—942no—
219C2×C4—941no—
220C2×C4—942no—
221C2×C4—942no—
222C2×C4—942no—
223C2×C4—1882no—
224C2×C4—1882no—
225C2×C4—1881no—
226C2×C4—1881no—
227C2×C4—1881no—
228C2×C4C2×C4×D4711yescharacteristic
229C2×C4#1062535011yescharacteristic
230C2×C4#1062535011yescharacteristic
231C2×C4D4×D4711yescharacteristic
232C2×C4D4×D4711yescharacteristic
233C2×C4Q8×D4711yescharacteristic
234C8—41no—
235C8—1881no—
236C22—21no—
237C22—21no—
238C22—942no—
239C22—1881no—
240C22—1881no—
241C22C22⋊C4×D4711yescharacteristic
242C22#1309399711yescharacteristic
243C22#1309400211yescharacteristic
244C4—42no—
245C4—41no—
246C4—41no—
247C4—472no—
248C4—942no—
249C4—941no—
250C4—941no—
251C4—941no—
252C4—1882no—
253C4C4⋊C4×D4711yescharacteristic
254C4#1309398111yescharacteristic
255C4#1309399711yescharacteristic
256C4#1309400211yescharacteristic
257C2—21no—
258C2—21no—
259C2—1882no—
260C2#1568898211yescharacteristic
261C2#104×D4711yescharacteristic
262C2#1568913811yescharacteristic
subgroupG/H
centerC2×C4D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#339C2
socleC22×C47C2×C22⋊C4
hypercenter#339D47
hypocenterC47#1806
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #15689146C2semidirect
5. C4×Dic47⋊C4C2semidirect
6. #15688882C2semidirect
7. C47×#339C2semidirect
10. #13093989C4semidirect
11. #13093989C4semidirect
12. #13093986C4semidirect
13. #13093986C4semidirect
95. D188C4⋊C4semidirect
101. Dic94C4⋊C4semidirect
124. Dic47#104semidirect
138. #339D47semidirect
139. C47#1806semidirect