Finite Group Databasebeta

← #20243800

Subgroups — #20243800

Order 6016.

386 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 83 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×#13094008C211yesmaximal, characteristic
2#15689596C211yesmaximal, characteristic
3C2×#13093938C211yesmaximal, characteristic
4#15688984C211yesmaximal, characteristic, complemented
5#15688984C211yesmaximal, characteristic, complemented
6#15688889C211yesmaximal, characteristic, complemented
7C47×#342C211yesmaximal, characteristic, complemented
8C22×C22⋊D47C2211yescharacteristic
9C23×Dic47C2211yescharacteristic
10#13094008—22no—
11#13094008C414yescomplemented
12C4×C22⋊D47—22no—
13(C22⋊D47)⋊C4—22no—
14#13093980—21no—
15C2×C4⋊Dic47—21no—
16C2×C22⋊Dic47C2211yescharacteristic
17C2×C22⋊Dic47C2211yescharacteristic
18C2×(C2×D47)⋊C4—21no—
19C22⋊C4×D47—21no—
20#13093938—22no—
21C47⋊#95—22no—
22C47⋊#95—22no—
23C2×C22⋊C4×C47C2211yescharacteristic
24C2×C22⋊C4×C47C2211yescharacteristic
25C2×C22⋊C4×C47C2211yescharacteristic
26C24×C47C2311yescharacteristic
27C23×D47D411yescharacteristic
28C22×C4×C47—21no—
29C22×C4×C47—21no—
30C22×C4×C47D412yes—
31C2×C22⋊D47—21no—
32C2×C22⋊D47—21no—
33C2×C22⋊D47—21no—
34C2×C22⋊D47—21no—
35C2×C22⋊D47C2×C412yes—
36C2×C22⋊D47D412yes—
37C22×Dic47—21no—
38C22×Dic47—21no—
39C22×Dic47—21no—
40C22×Dic47—21no—
41C22×Dic47—21no—
42C22×Dic47—21no—
43C22×Dic47—21no—
44C22×Dic47C2×C412yescomplemented
45C22×Dic47D411yescharacteristic
46C22×Dic47D412yes—
47C2×C4×D47—22no—
48C22⋊C4×C47—21no—
49C22⋊C4×C47—21no—
50C22⋊C4×C47—21no—
51C22⋊C4×C47—21no—
52C22⋊C4×C47—21no—
53C22⋊C4×C47C2×C412yescomplemented
54C22⋊Dic47—21no—
55C22⋊Dic47—21no—
56C22⋊Dic47—21no—
57C22⋊Dic47—21no—
58(C2×D47)⋊C4—22no—
59(C2×D47)⋊C4—24no—
60C4⋊Dic47—24no—
61Dic47⋊C4—22no—
62C4×Dic47—22no—
63C23×C47—42no—
64C23×C47C22×C411yescharacteristic
65C23×C47C2×D411yescharacteristic
66C23×C47C2×D411yescharacteristic
67C23×C47C2×D411yescharacteristic
68C23×C47C2×D411yescharacteristic
69C23×C47#4111yescharacteristic
70C23×C47#4111yescharacteristic
71C22×D47—21no—
72C22×D47—21no—
73C22×D47—42no—
74C22×D47C22⋊C412yes—
75C2×C4×C47—22no—
76C2×C4×C47—22no—
77C2×C4×C47—42no—
78C2×C4×C47—42no—
79C2×C4×C47—42no—
80C2×C4×C47—41no—
81C22⋊D47—22no—
82C22⋊D47—22no—
83C22⋊D47—22no—
84C22⋊D47—22no—
85C2×Dic47—21no—
86C2×Dic47—21no—
87C2×Dic47—22no—
88C2×Dic47—22no—
89C2×Dic47—22no—
90C2×Dic47—22no—
91C2×Dic47—41no—
92C2×Dic47—41no—
93C2×Dic47—41no—
94C2×Dic47—41no—
95C2×Dic47—42no—
96C2×Dic47—42no—
97C2×Dic47—41no—
98C2×Dic47C22⋊C412yes—
99C4×D47—82no—
100C22×C47—22no—
101C22×C47—22no—
102C22×C47—22no—
103C22×C47—41no—
104C22×C47—41no—
105C22×C47—41no—
106C22×C47—41no—
107C22×C47C2×C22⋊C411yescharacteristic
108C22×C47C4×D411yescharacteristic
109C22×C47C4×D411yescharacteristic
110C22×C47#12011yescharacteristic
111C22×C47#12111yescharacteristic
112C22×C47#12111yescharacteristic
113C22×C47#12311yescharacteristic
114C2×D47—22no—
115C2×D47—42no—
116C2×D47—42no—
117C2×D47—81no—
118C4×C47—42no—
119C4×C47—42no—
120C4×C47—81no—
121Dic47—22no—
122Dic47—42no—
123Dic47—42no—
124Dic47—81no—
125#1890—471nomaximal, Sylow
126C2×C47—21no—
127C2×C47—21no—
128C2×C47—21no—
129C2×C47—21no—
130C2×C47—21no—
131C2×C47—21no—
132C2×C47#38611yescharacteristic
133C2×C47#45812yes—
134D47—42no—
135C2×#123—471no—
136#518—471no—
137C2×#99—471no—
138#381—471no—
139#381—471no—
140#342—471no—
141#342D4711yescharacteristic, complemented
142C47#189011yescharacteristic, complemented, Sylow
143C22×D4—471no—
144C23×C4—471no—
145#123—474no—
146#123—942no—
147C4×D4—942no—
148C4×D4—942no—
149#117—941no—
150C2×C4⋊C4—941no—
151C2×C22⋊C4—471no—
152C2×C22⋊C4—471no—
153C2×C22⋊C4—941no—
154C2×C22⋊C4—941no—
155C2×C22⋊C4C2×D4711yescharacteristic
156C2×C22⋊C4C2×D4711yescharacteristic
157C2×C22⋊C4C2×D4711yescharacteristic
158#99—942no—
159#95—942no—
160#95—942no—
161C24—471no—
162C24C22×D4711yescharacteristic
163C2×D4—472no—
164C2×D4—472no—
165C2×D4—941no—
166C2×D4—941no—
167C2×D4—941no—
168C2×D4—941no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—471no—
172C22×C4—472no—
173C22×C4—472no—
174C22×C4—942no—
175C22×C4—941no—
176C22×C4—941no—
177C22×C4—941no—
178C22×C4—941no—
179C22×C4—941no—
180C22×C4—941no—
181C22×C4—941no—
182C22×C4D18812yes—
183C4⋊C4—944no—
184C4⋊C4—942no—
185C22⋊C4—21no—
186C22⋊C4—21no—
187C22⋊C4—21no—
188C22⋊C4—21no—
189C22⋊C4—21no—
190C22⋊C4—944no—
191C22⋊C4—942no—
192C22⋊C4—941no—
193C22⋊C4—941no—
194C22⋊C4—941no—
195C22⋊C4—941no—
196C22⋊C4C4×D4712yescomplemented
197C42—942no—
198C23—42no—
199C23—472no—
200C23—941no—
201C23—941no—
202C23—1882no—
203C23C2×C4×D4711yescharacteristic
204C23C2×D18811yescharacteristic
205C23#1062535011yescharacteristic
206C23D4×D4711yescharacteristic
207C23D4×D4711yescharacteristic
208C23D4×D4711yescharacteristic
209C23#1062535411yescharacteristic
210D4—942no—
211D4—942no—
212D4—942no—
213D4—942no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—41no—
220C2×C4—472no—
221C2×C4—941no—
222C2×C4—941no—
223C2×C4—942no—
224C2×C4—942no—
225C2×C4—942no—
226C2×C4—942no—
227C2×C4—3762no—
228C2×C4—1882no—
229C2×C4—1881no—
230C2×C4—1881no—
231C2×C4—1881no—
232C2×C4—1881no—
233C2×C4—1881no—
234C2×C4—1882no—
235C22—22no—
236C22—22no—
237C22—22no—
238C22—41no—
239C22—41no—
240C22—41no—
241C22—41no—
242C22—942no—
243C22—3761no—
244C22—1882no—
245C22—1882no—
246C22C22⋊C4×D4711yescharacteristic
247C22#1309398611yescharacteristic
248C22C4×D18811yescharacteristic
249C22#1309399411yescharacteristic
250C22#1309399711yescharacteristic
251C22#1309399911yescharacteristic
252C22#1309400911yescharacteristic
253C4—42no—
254C4—42no—
255C4—81no—
256C4—942no—
257C4—3761no—
258C4—1882no—
259C4—1882no—
260C2—21no—
261C2—21no—
262C2—21no—
263C2—21no—
264C2—21no—
265C2—21no—
266C2—1882no—
267C2#1568900111yescharacteristic
268C2#1568931412yes—
subgroupG/H
centerC22#13093994
commutatorC23×C47C22×C4
FrattiniC24C22×D47
FittingC47×#342C2
socleC22×C47#120
hypercenter#342D47
hypocenterC47#1890
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
4. #15688984C2semidirect
5. #15688984C2semidirect
6. #15688889C2semidirect
7. C47×#342C2semidirect
11. #13094008C4semidirect
44. C22×Dic47C2×C4semidirect
53. C22⋊C4×C47C2×C4semidirect
141. #342D47semidirect
142. C47#1890semidirect
196. C22⋊C4C4×D47semidirect