Finite Group Databasebeta

← #20247786

Subgroups — #20247786

Order 6016.

412 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 137 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
1C47⋊#401C212yesmaximal, complemented
2#15689049C212yesmaximal
3#15689019C211yesmaximal, characteristic, complemented
4#15689012C212yesmaximal
5#15689004C212yesmaximal, complemented
6#15688989C211yesmaximal, characteristic, complemented
7#15688980C211yesmaximal, characteristic
8#15688980C211yesmaximal, characteristic
9C4⋊C4×Dic47C211yesmaximal, characteristic, complemented
10C4×(C2×D47)⋊C4C211yesmaximal, characteristic
11C47×#389C211yesmaximal, characteristic, complemented
12C22×C4×D47C2211yescharacteristic
13C2×C4⋊Dic47C2211yescharacteristic
14C2×C4⋊Dic47C2211yescharacteristic
15C2×Dic47⋊C4C2212yes—
16C2×(C2×D47)⋊C4C2211yescharacteristic
17C2×(C2×D47)⋊C4C2211yescharacteristic
18C2×(C2×D47)⋊C4C2212yes—
19C2×(C2×D47)⋊C4C2212yes—
20C2×C4×Dic47C2211yescharacteristic
21C2×C4×Dic47C2212yes—
22C47⋊#95C2211yescharacteristic
23C47⋊#95C2211yescharacteristic
24C47⋊#95C2212yes—
25C47⋊#95C2212yes—
26C47⋊#95C2212yes—
27C47⋊#95C2212yes—
28C47⋊#95C2212yes—
29C47⋊#95C2212yes—
30C2×C4⋊C4×C47C2211yescharacteristic
31C2×C4⋊C4×C47C2211yescharacteristic
32C2×C4⋊C4×C47C2212yes—
33C2×C42×C47C2211yescharacteristic
34#95×C47C2212yes—
35C23×D47C2311yescharacteristic
36C22×C4×C47C2311yescharacteristic
37C22×C4×C47C2311yescharacteristic
38C22×C4×C47C2312yes—
39C22×C4×C47C2312yes—
40C22×C4×C47C2311yescharacteristic
41C22×Dic47C2311yescharacteristic
42C22×Dic47C2311yescharacteristic
43C22×Dic47C2312yes—
44C22×Dic47C2312yes—
45C22×Dic47C2311yescharacteristic
46C2×C4×D47—22no—
47C2×C4×D47—22no—
48C2×C4×D47—22no—
49C4⋊C4×C47—22no—
50C4⋊C4×C47—22no—
51C4⋊C4×C47—42no—
52C42×C47—22no—
53(C2×D47)⋊C4—22no—
54(C2×D47)⋊C4—24no—
55(C2×D47)⋊C4—22no—
56(C2×D47)⋊C4—42no—
57C4⋊Dic47—22no—
58C4⋊Dic47—22no—
59Dic47⋊C4—24no—
60C4×Dic47—22no—
61C4×Dic47—42no—
62C23×C47C2411yescharacteristic
63C22×D47—21no—
64C22×D47—21no—
65C22×D47—21no—
66C22×D47—21no—
67C22×D47—21no—
68C22×D47—21no—
69C22×D47#4112yes—
70C2×C4×C47—22no—
71C2×C4×C47—21no—
72C2×C4×C47—22no—
73C2×C4×C47—21no—
74C2×C4×C47—21no—
75C2×C4×C47—21no—
76C2×C4×C47—22no—
77C2×C4×C47—22no—
78C2×C4×C47—22no—
79C2×C4×C47—22no—
80C2×C4×C47—21no—
81C2×C4×C47—21no—
82C2×C4×C47#4112yes—
83C2×C4×C47#4112yes—
84C2×C4×C47#4112yes—
85C2×Dic47—21no—
86C2×Dic47—21no—
87C2×Dic47—21no—
88C2×Dic47—22no—
89C2×Dic47—22no—
90C2×Dic47—22no—
91C2×Dic47—22no—
92C2×Dic47—21no—
93C2×Dic47—21no—
94C2×Dic47—21no—
95C2×Dic47—21no—
96C2×Dic47—22no—
97C2×Dic47—22no—
98C2×Dic47—21no—
99C2×Dic47#4112yes—
100C4×D47—44no—
101C22×C47C2×#4111yescharacteristic
102C22×C47C2×#4111yescharacteristic
103C22×C47C2×#4111yescharacteristic
104C22×C47C2×#4111yescharacteristic
105C22×C47C2×#4111yescharacteristic
106C22×C47H(5,𝔽2)11yescharacteristic
107C22×C472−1+411yescharacteristic
108C2×D47—22no—
109C2×D47—22no—
110C2×D47—22no—
111C2×D47—41no—
112C2×D47—41no—
113C2×D47—41no—
114C2×D47—41no—
115C4×C47—41no—
116C4×C47—42no—
117C4×C47—42no—
118C4×C47—41no—
119C4×C47#12614yes—
120Dic47—22no—
121Dic47—41no—
122Dic47—42no—
123Dic47—42no—
124Dic47—41no—
125#2494—471nomaximal, Sylow
126C2×C47C2×#12611yescharacteristic
127C2×C47#52911yescharacteristic
128C2×C47#54211yescharacteristic
129C2×C47#55211yescharacteristic
130C2×C47#55311yescharacteristic
131C2×C47#55311yescharacteristic
132C2×C47#55611yescharacteristic
133D47—42no—
134#401—472no—
135#397—472no—
136#389—471no—
137#389D4711yescharacteristic, complemented
138#388—472no—
139#387—472no—
140#382—471no—
141#380—471no—
142#380—471no—
143C4×C4⋊C4—471no—
144C4×C22⋊C4—471no—
145C47#249411yescharacteristic, complemented, Sylow
146C23×C4—471no—
147C2×C4⋊C4—472no—
148C2×C4⋊C4—471no—
149C2×C4⋊C4—471no—
150C2×C4⋊C4C2×D4711yescharacteristic
151C2×C4⋊C4C2×D4711yescharacteristic
152C2×C4⋊C4C2×D4712yes—
153C2×C22⋊C4—471no—
154C2×C22⋊C4—471no—
155C2×C22⋊C4—472no—
156C2×C22⋊C4—472no—
157C2×C42—471no—
158C2×C42—472no—
159C2×C42C2×D4711yescharacteristic
160#95—471no—
161#95—471no—
162#95—472no—
163#95—472no—
164#95—472no—
165#95—472no—
166#95—472no—
167#95—472no—
168#95C2×D4712yes—
169C24—471no—
170C22×C4—471no—
171C22×C4—471no—
172C22×C4—471no—
173C22×C4—472no—
174C22×C4—472no—
175C22×C4—942no—
176C22×C4—942no—
177C22×C4—942no—
178C22×C4C22×D4711yescharacteristic
179C22×C4C22×D4711yescharacteristic
180C22×C4C22×D4712yes—
181C22×C4C22×D4712yes—
182C22×C4C22×D4711yescharacteristic
183C4⋊C4—22no—
184C4⋊C4—22no—
185C4⋊C4—42no—
186C4⋊C4—944no—
187C4⋊C4—942no—
188C4⋊C4—942no—
189C22⋊C4—942no—
190C22⋊C4—942no—
191C22⋊C4—944no—
192C22⋊C4—1882no—
193C42—22no—
194C42—942no—
195C42—1882no—
196C23—472no—
197C23—941no—
198C23—941no—
199C23—941no—
200C23—941no—
201C23—941no—
202C23—941no—
203C23C23×D4711yescharacteristic
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—472no—
217C2×C4—941no—
218C2×C4—941no—
219C2×C4—941no—
220C2×C4—942no—
221C2×C4—942no—
222C2×C4—941no—
223C2×C4—941no—
224C2×C4—941no—
225C2×C4—942no—
226C2×C4—942no—
227C2×C4—941no—
228C2×C4—942no—
229C2×C4—942no—
230C2×C4—941no—
231C2×C4—1884no—
232C2×C4#1062535012yes—
233C2×C4#1062535212yes—
234C2×C4#1062535412yes—
235C22—942no—
236C22—942no—
237C22—942no—
238C22—1881no—
239C22—1881no—
240C22—1881no—
241C22—1881no—
242C22#41×D4711yescharacteristic
243C22#41×D4711yescharacteristic
244C22C2×#1062535211yescharacteristic
245C22C2×#1062535011yescharacteristic
246C22C2×#1062535411yescharacteristic
247C22#1309406911yescharacteristic
248C22#1309407211yescharacteristic
249C4—41no—
250C4—42no—
251C4—42no—
252C4—41no—
253C4—942no—
254C4—1882no—
255C4—1881no—
256C4—1881no—
257C4—1882no—
258C4#1309401914yes—
259C2—1882no—
260C2C2×#1309401911yescharacteristic
261C2#1568965811yescharacteristic
262C2#1568974711yescharacteristic
263C2#1568981411yescharacteristic
264C2#1568982011yescharacteristic
265C2#1568982311yescharacteristic
266C2#1568984411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#389C2
hypercenter#389D47
hypocenterC47#2494
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
1. C47⋊#401C2semidirect
3. #15689019C2semidirect
5. #15689004C2semidirect
6. #15688989C2semidirect
9. C4⋊C4×Dic47C2semidirect
11. C47×#389C2semidirect
137. #389D47semidirect
145. C47#2494semidirect