Finite Group Databasebeta

← #20249253

Subgroups — #20249253

Order 6016.

500 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 131 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×#13094011C211yesmaximal, characteristic
2C2×#13093989C211yesmaximal, characteristic, complemented
3#15689059C212yesmaximal, complemented
4#15689044C211yesmaximal, characteristic, complemented
5#15689043C211yesmaximal, characteristic, complemented
6#15689037C211yesmaximal, characteristic
7#15689035C212yesmaximal, complemented
8#15689017C212yesmaximal, complemented
9#15689016C212yesmaximal, complemented
10#15688990C211yesmaximal, characteristic, complemented
11C47×#394C211yesmaximal, characteristic
12C22×Dic94C2211yescharacteristic
13C22×Dic94C2211yescharacteristic
14#13094011—24no—
15#13093989—24no—
16C2×C4⋊Dic47C2212yes—
17C2×Dic47⋊C4C2211yescharacteristic
18C2×Dic47⋊C4C2211yescharacteristic
19C2×Dic47⋊C4C2212yes—
20C2×C22⋊Dic47C2212yes—
21C2×C22⋊Dic47C2212yes—
22C2×C22⋊Dic47C2212yes—
23C2×C22⋊Dic47C2212yes—
24C2×C4×Dic47C2211yescharacteristic
25C2×C4×Dic47C2211yescharacteristic
26C2×C4×Dic47C2211yescharacteristic
27C47⋊#95C2212yes—
28C47⋊#95C2212yes—
29C47⋊#95C2211yescharacteristic
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C22×D4×C47C2211yescharacteristic
33C2×C4⋊C4×C47C2211yescharacteristic
34C2×C22⋊C4×C47C2212yes—
35C2×C22⋊C4×C47C2212yes—
36#95×C47C2211yescharacteristic
37C24×C47C2312yes—
38C2×D4×C47—22no—
39C2×D4×C47—42no—
40C22×C4×C47C2311yescharacteristic
41C22×C4×C47C2312yes—
42C22×C4×C47C2311yescharacteristic
43C22×C4×C47C2311yescharacteristic
44C22×Dic47C2312yes—
45C22×Dic47C2312yes—
46C22×Dic47C2311yescharacteristic
47C22×Dic47C2311yescharacteristic
48C22×Dic47C2311yescharacteristic
49C22×Dic47C2311yescharacteristic
50C2×Dic94—22no—
51C2×Dic94—22no—
52C2×Dic94—22no—
53C2×Dic94—22no—
54C2×Dic94—42no—
55C4⋊C4×C47—22no—
56C22⋊C4×C47—24no—
57C22⋊C4×C47—42no—
58C22⋊Dic47—24no—
59C22⋊Dic47—24no—
60C22⋊Dic47—24no—
61C22⋊Dic47—42no—
62C4⋊Dic47—42no—
63Dic47⋊C4—22no—
64Dic47⋊C4—22no—
65Dic47⋊C4—42no—
66C4×Dic47—22no—
67C4×Dic47—22no—
68C4×Dic47D414yes—
69C23×C47—22no—
70C23×C47—22no—
71C23×C47—22no—
72C23×C47—22no—
73C23×C47—22no—
74C23×C47—22no—
75C23×C47—22no—
76C23×C47C2411yescharacteristic
77D4×C47—44no—
78C2×C4×C47—21no—
79C2×C4×C47—21no—
80C2×C4×C47—22no—
81C2×C4×C47—21no—
82C2×C4×C47—22no—
83C2×C4×C47—22no—
84C2×C4×C47—22no—
85C2×C4×C47—22no—
86C2×C4×C47C2×D412yes—
87C2×C4×C47#4112yes—
88C2×Dic47—21no—
89C2×Dic47—21no—
90C2×Dic47—21no—
91C2×Dic47—21no—
92C2×Dic47—22no—
93C2×Dic47—21no—
94C2×Dic47—22no—
95C2×Dic47—22no—
96C2×Dic47—22no—
97C2×Dic47—22no—
98C2×Dic47—22no—
99C2×Dic47—22no—
100C2×Dic47—22no—
101C2×Dic47C2×D412yes—
102C2×Dic47C2×D412yes—
103C2×Dic47#4112yes—
104Dic94—28no—
105Dic94—44no—
106C22×C47—42no—
107C22×C47—42no—
108C22×C47—42no—
109C22×C47—42no—
110C22×C47—42no—
111C22×C47—42no—
112C22×C47—42no—
113C22×C47C22×D411yescharacteristic
114C22×C47C2×#4111yescharacteristic
115C22×C47C2×#4111yescharacteristic
116C22×C47H(5,𝔽2)12yes—
117C22×C472−1+412yes—
118C4×C47—22no—
119C4×C47—22no—
120C4×C47—41no—
121C4×C47—42no—
122Dic47—22no—
123Dic47—22no—
124Dic47—22no—
125Dic47—42no—
126Dic47—41no—
127Dic47—42no—
128#2632—471nomaximal, Sylow
129C2×C47—82no—
130C2×C47#52511yescharacteristic
131C2×C47#53511yescharacteristic
132C2×C47#53611yescharacteristic
133C2×C47#54212yes—
134C2×C47#54212yes—
135C2×#124—471no—
136C2×C4×Q8—471no—
137#399—472no—
138#395—471no—
139#395—471no—
140#394—471no—
141#394D4711yescharacteristic
142#393—472no—
143#388—472no—
144#388—472no—
145#383—471no—
146C47#263211yescharacteristic, complemented, Sylow
147C22×Q8—471no—
148C22×Q8—471no—
149C22×D4C2×D4711yescharacteristic
150#124—944no—
151C4×Q8—944no—
152C2×C4⋊C4—471no—
153C2×C4⋊C4—471no—
154C2×C4⋊C4—472no—
155C2×C4⋊C4—472no—
156C2×C4⋊C4C2×D4711yescharacteristic
157C2×C22⋊C4—472no—
158C2×C22⋊C4—472no—
159C2×C22⋊C4—472no—
160C2×C22⋊C4—472no—
161C2×C22⋊C4C2×D4712yes—
162C2×C22⋊C4C2×D4712yes—
163C2×C42—471no—
164C2×C42—471no—
165C2×C42—471no—
166#95—472no—
167#95—472no—
168#95—471no—
169#95—472no—
170#95—472no—
171#95C2×D4711yescharacteristic
172C24C22×D4712yes—
173C2×Q8—942no—
174C2×Q8—942no—
175C2×Q8—942no—
176C2×Q8—942no—
177C2×Q8—1882no—
178C2×D4—22no—
179C2×D4—42no—
180C22×C4—471no—
181C22×C4—471no—
182C22×C4—471no—
183C22×C4—472no—
184C22×C4—472no—
185C22×C4—471no—
186C22×C4C22×D4712yes—
187C22×C4C22×D4711yescharacteristic
188C22×C4C22×D4711yescharacteristic
189C22×C4C22×D4711yescharacteristic
190C4⋊C4—22no—
191C4⋊C4—942no—
192C4⋊C4—942no—
193C4⋊C4—1882no—
194C4⋊C4—1882no—
195C22⋊C4—24no—
196C22⋊C4—42no—
197C22⋊C4—944no—
198C22⋊C4—944no—
199C22⋊C4—944no—
200C22⋊C4—1882no—
201C42—474no—
202C42—942no—
203C42—942no—
204C23—22no—
205C23—22no—
206C23—22no—
207C23—22no—
208C23—22no—
209C23—22no—
210C23—22no—
211C23C23×D4711yescharacteristic
212Q8—948no—
213Q8—1884no—
214D4—44no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—472no—
224C2×C4—472no—
225C2×C4—472no—
226C2×C4—941no—
227C2×C4—941no—
228C2×C4—941no—
229C2×C4—941no—
230C2×C4—942no—
231C2×C4—941no—
232C2×C4—942no—
233C2×C4—942no—
234C2×C4—942no—
235C2×C4—942no—
236C2×C4—942no—
237C2×C4—942no—
238C2×C4—942no—
239C2×C4D4×D4712yes—
240C2×C4#1062535212yes—
241C22—42no—
242C22—42no—
243C22—42no—
244C22—42no—
245C22—42no—
246C22—42no—
247C22—42no—
248C22C2×D4×D4711yescharacteristic
249C22#41×D4711yescharacteristic
250C22C2×#1062535211yescharacteristic
251C22#1309406912yes—
252C22#1309407112yes—
253C4—22no—
254C4—22no—
255C4—42no—
256C4—41no—
257C4—942no—
258C4—942no—
259C4—942no—
260C4—1882no—
261C4—1882no—
262C4—1881no—
263C2—82no—
264C2#1568963311yescharacteristic
265C2#1568968811yescharacteristic
266C2#1568969311yescharacteristic
267C2#1568974012yes—
268C2#1568974112yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#394C2
hypercenter#394D47
hypocenterC47#2632
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#13093989C2semidirect
3. #15689059C2semidirect
4. #15689044C2semidirect
5. #15689043C2semidirect
7. #15689035C2semidirect
8. #15689017C2semidirect
9. #15689016C2semidirect
10. #15688990C2semidirect
146. C47#2632semidirect