Finite Group Databasebeta

← #20243798

Subgroups — #20243798

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×#13094007C211yesmaximal, characteristic
2#15689596C211yesmaximal, characteristic
3C2×#13093938C211yesmaximal, characteristic
4#15688986C211yesmaximal, characteristic, complemented
5#15688890C211yesmaximal, characteristic, complemented
6#15688889C211yesmaximal, characteristic, complemented
7C47×#381C211yesmaximal, characteristic, complemented
8C22×C22⋊D47C2211yescharacteristic
9#13094007—22no—
10#13094007C414yescomplemented
11C4×C22⋊D47—22no—
12(C22⋊D47)⋊C4—22no—
13#13093980—21no—
14C2×Dic47⋊C4—21no—
15C2×C22⋊Dic47C2211yescharacteristic
16C2×C22⋊Dic47C2211yescharacteristic
17C2×C22⋊Dic47C2211yescharacteristic
18C2×(C2×D47)⋊C4—21no—
19C22⋊C4×D47—21no—
20#13093938—22no—
21C47⋊#95—22no—
22C23×C4×C47C2211yescharacteristic
23C2×C22⋊C4×C47C2211yescharacteristic
24C2×C22⋊C4×C47C2211yescharacteristic
25#95×C47—22no—
26C24×C47C2311yescharacteristic
27C23×D47D411yescharacteristic
28C22×C4×C47—21no—
29C22×C4×C47—21no—
30C22×C4×C47—21no—
31C22×C4×C47—21no—
32C22×C4×C47—21no—
33C22×C4×C47—21no—
34C22×C4×C47—21no—
35C22×C4×C47C2×C412yescomplemented
36C22×C4×C47D412yes—
37C2×C22⋊D47—21no—
38C2×C22⋊D47—21no—
39C2×C22⋊D47—21no—
40C2×C22⋊D47—21no—
41C2×C22⋊D47C2×C412yes—
42C2×C22⋊D47D412yes—
43C22×Dic47—21no—
44C22×Dic47—21no—
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⋊Dic47—21no—
53C22⋊Dic47—21no—
54C22⋊Dic47—21no—
55C22⋊Dic47—21no—
56C22⋊Dic47—21no—
57C22⋊Dic47C2×C412yescomplemented
58(C2×D47)⋊C4—22no—
59(C2×D47)⋊C4—24no—
60Dic47⋊C4—22no—
61Dic47⋊C4—24no—
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—22no—
78C2×C4×C47—22no—
79C2×C4×C47—41no—
80C2×C4×C47—41no—
81C2×C4×C47—41no—
82C2×C4×C47—41no—
83C2×C4×C47—42no—
84C2×C4×C47—42no—
85C2×C4×C47—41no—
86C22⋊D47—22no—
87C22⋊D47—22no—
88C22⋊D47—22no—
89C22⋊D47—22no—
90C2×Dic47—21no—
91C2×Dic47—21no—
92C2×Dic47—22no—
93C2×Dic47—22no—
94C2×Dic47—42no—
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#381D4711yescharacteristic, complemented
140#342—471no—
141#342—471no—
142C47#189011yescharacteristic, complemented, Sylow
143C22×D4—471no—
144C23×C4C2×D4711yescharacteristic
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—471no—
154C2×C22⋊C4—941no—
155C2×C22⋊C4—941no—
156C2×C22⋊C4C2×D4711yescharacteristic
157C2×C22⋊C4C2×D4711yescharacteristic
158#99—942no—
159#95—22no—
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—21no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—471no—
177C22×C4—472no—
178C22×C4—942no—
179C22×C4—941no—
180C22×C4—941no—
181C22×C4C4×D4712yescomplemented
182C22×C4C22⋊D4712yes—
183C4⋊C4—944no—
184C4⋊C4—942no—
185C22⋊C4—21no—
186C22⋊C4—21no—
187C22⋊C4—21no—
188C22⋊C4—21no—
189C22⋊C4—472no—
190C22⋊C4—944no—
191C22⋊C4—942no—
192C22⋊C4—941no—
193C22⋊C4—941no—
194C22⋊C4—941no—
195C22⋊C4—941no—
196C22⋊C4—941no—
197C42—942no—
198C23—42no—
199C23—472no—
200C23—941no—
201C23—941no—
202C23—1882no—
203C23C2×C4×D4711yescharacteristic
204C23#1062535011yescharacteristic
205C23D4×D4711yescharacteristic
206C23D4×D4711yescharacteristic
207C23D4×D4711yescharacteristic
208C23#1062535211yescharacteristic
209C23C2×C22⋊D4711yescharacteristic
210D4—942no—
211D4—942no—
212D4—942no—
213D4—942no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—41no—
225C2×C4—472no—
226C2×C4—941no—
227C2×C4—941no—
228C2×C4—942no—
229C2×C4—942no—
230C2×C4—3762no—
231C2×C4—1882no—
232C2×C4—1881no—
233C2×C4—1882no—
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(C22⋊D47)⋊C411yescharacteristic
248C22C4×C22⋊D4711yescharacteristic
249C22#1309399211yescharacteristic
250C22#1309399511yescharacteristic
251C22#1309399711yescharacteristic
252C22#1309400611yescharacteristic
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#1568899911yescharacteristic
268C2#1568931212yes—
subgroupG/H
centerC22#13093992
commutatorC23×C47C22×C4
FrattiniC24C22×D47
FittingC47×#381C2
socleC22×C47#120
hypercenter#381D47
hypocenterC47#1890
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C24 ◁ #381

Complements

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

NH ≅ G/Ntype
4. #15688986C2semidirect
5. #15688890C2semidirect
6. #15688889C2semidirect
7. C47×#381C2semidirect
10. #13094007C4semidirect
35. C22×C4×C47C2×C4semidirect
57. C22⋊Dic47C2×C4semidirect
139. #381D47semidirect
142. C47#1890semidirect
181. C22×C4C4×D47semidirect