Finite Group Databasebeta

← #20249254

Subgroups — #20249254

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×#13094013C211yesmaximal, characteristic
2C2×#13093989C211yesmaximal, characteristic, complemented
3#15689058C212yesmaximal, complemented
4#15689042C211yesmaximal, characteristic, complemented
5#15689041C211yesmaximal, characteristic
6#15689040C211yesmaximal, characteristic
7#15689036C212yesmaximal, complemented
8#15689013C212yesmaximal, complemented
9#15689012C212yesmaximal, complemented
10#15688990C211yesmaximal, characteristic, complemented
11C47×#395C211yesmaximal, characteristic, complemented
12C22×Dic94C2211yescharacteristic
13C22×D188C2211yescharacteristic
14#13094013—24no—
15#13093989—24no—
16C2×Dic47⋊C4C2211yescharacteristic
17C2×Dic47⋊C4C2211yescharacteristic
18C2×Dic47⋊C4C2212yes—
19C2×(C2×D47)⋊C4C2212yes—
20C2×(C2×D47)⋊C4C2212yes—
21C2×(C2×D47)⋊C4C2212yes—
22C2×(C2×D47)⋊C4C2212yes—
23C2×(C2×D47)⋊C4C2212yes—
24C2×(C2×D47)⋊C4C2212yes—
25C2×C4×Dic47C2211yescharacteristic
26C2×C4×Dic47C2211yescharacteristic
27C2×C4×Dic47C2211yescharacteristic
28C47⋊#95C2212yes—
29C47⋊#95C2212yes—
30C47⋊#95C2211yescharacteristic
31C47⋊#95C2212yes—
32C22×Q8×C47C2211yescharacteristic
33C2×C4⋊C4×C47C2211yescharacteristic
34C2×C4⋊C4×C47C2212yes—
35#95×C47C2211yescharacteristic
36#95×C47C2212yes—
37C23×D47C2312yes—
38C2×Q8×C47—22no—
39C2×Q8×C47—42no—
40C22×C4×C47C2311yescharacteristic
41C22×C4×C47C2312yes—
42C22×C4×C47C2312yes—
43C22×C4×C47C2311yescharacteristic
44C22×C4×C47C2311yescharacteristic
45C22×Dic47C2312yes—
46C22×Dic47C2311yescharacteristic
47C22×Dic47C2311yescharacteristic
48C22×Dic47C2311yescharacteristic
49C22×Dic47C2311yescharacteristic
50C2×D188—22no—
51C2×D188—42no—
52C2×Dic94—22no—
53C2×Dic94—22no—
54C2×Dic94—22no—
55C4⋊C4×C47—22no—
56C4⋊C4×C47—42no—
57(C2×D47)⋊C4—24no—
58(C2×D47)⋊C4—24no—
59(C2×D47)⋊C4—24no—
60(C2×D47)⋊C4—24no—
61(C2×D47)⋊C4—42no—
62(C2×D47)⋊C4—42no—
63Dic47⋊C4—22no—
64Dic47⋊C4—22no—
65Dic47⋊C4—42no—
66C4×Dic47—22no—
67C4×Dic47—22no—
68C4×Dic47D414yes—
69C23×C47C2411yescharacteristic
70C22×D47—22no—
71C22×D47—22no—
72C22×D47—22no—
73C22×D47—22no—
74C22×D47—22no—
75C22×D47—22no—
76C22×D47—22no—
77Q8×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×C47—22no—
87C2×C4×C47—22no—
88C2×C4×C47—22no—
89C2×C4×C47C2×D412yes—
90C2×C4×C47#4112yes—
91C2×Dic47—21no—
92C2×Dic47—21no—
93C2×Dic47—21no—
94C2×Dic47—21no—
95C2×Dic47—22no—
96C2×Dic47—21no—
97C2×Dic47—22no—
98C2×Dic47—22no—
99C2×Dic47—22no—
100C2×Dic47—22no—
101C2×Dic47C2×D412yes—
102C2×Dic47C2×D412yes—
103C2×Dic47#4112yes—
104D188—44no—
105Dic94—28no—
106C22×C47C22×D411yescharacteristic
107C22×C47C2×#4111yescharacteristic
108C22×C47C2×#4111yescharacteristic
109C22×C47H(5,𝔽2)12yes—
110C22×C472−1+412yes—
111C2×D47—42no—
112C2×D47—42no—
113C2×D47—42no—
114C2×D47—42no—
115C2×D47—42no—
116C2×D47—42no—
117C2×D47—42no—
118C4×C47—22no—
119C4×C47—22no—
120C4×C47—41no—
121C4×C47—42no—
122C4×C47—42no—
123Dic47—22no—
124Dic47—22no—
125Dic47—22no—
126Dic47—41no—
127Dic47—42no—
128#2632—471nomaximal, Sylow
129C2×C47#52511yescharacteristic
130C2×C47#53511yescharacteristic
131C2×C47#53611yescharacteristic
132C2×C47#54212yes—
133C2×C47#54212yes—
134D47—82no—
135C2×#124—471no—
136C2×C4×Q8—471no—
137#399—472no—
138#395—471no—
139#395D4711yescharacteristic, complemented
140#394—471no—
141#394—471no—
142#393—472no—
143#388—472no—
144#388—472no—
145#383—471no—
146C47#263211yescharacteristic, complemented, Sylow
147C22×Q8—471no—
148C22×Q8C2×D4711yescharacteristic
149C22×D4—471no—
150#124—944no—
151C4×Q8—944no—
152C2×C4⋊C4—471no—
153C2×C4⋊C4—471no—
154C2×C4⋊C4—472no—
155C2×C4⋊C4C2×D4711yescharacteristic
156C2×C4⋊C4C2×D4712yes—
157C2×C22⋊C4—472no—
158C2×C22⋊C4—472no—
159C2×C22⋊C4—472no—
160C2×C22⋊C4—472no—
161C2×C22⋊C4—472no—
162C2×C22⋊C4—472no—
163C2×C42—471no—
164C2×C42—471no—
165C2×C42—471no—
166#95—472no—
167#95—472no—
168#95—471no—
169#95—472no—
170#95C2×D4711yescharacteristic
171#95C2×D4712yes—
172C24—472no—
173C2×Q8—22no—
174C2×Q8—42no—
175C2×Q8—942no—
176C2×Q8—942no—
177C2×Q8—942no—
178C2×D4—942no—
179C2×D4—1882no—
180C22×C4—471no—
181C22×C4—471no—
182C22×C4—471no—
183C22×C4—472no—
184C22×C4—471no—
185C22×C4C22×D4712yes—
186C22×C4C22×D4712yes—
187C22×C4C22×D4711yescharacteristic
188C22×C4C22×D4711yescharacteristic
189C22×C4C22×D4711yescharacteristic
190C4⋊C4—22no—
191C4⋊C4—42no—
192C4⋊C4—942no—
193C4⋊C4—942no—
194C4⋊C4—1882no—
195C22⋊C4—944no—
196C22⋊C4—944no—
197C22⋊C4—944no—
198C22⋊C4—944no—
199C22⋊C4—1882no—
200C22⋊C4—1882no—
201C42—474no—
202C42—942no—
203C42—942no—
204C23—942no—
205C23—942no—
206C23—942no—
207C23—942no—
208C23—942no—
209C23—942no—
210C23—942no—
211C23C23×D4711yescharacteristic
212Q8—44no—
213Q8—948no—
214D4—1884no—
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—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—472no—
227C2×C4—472no—
228C2×C4—472no—
229C2×C4—941no—
230C2×C4—941no—
231C2×C4—941no—
232C2×C4—941no—
233C2×C4—942no—
234C2×C4—941no—
235C2×C4—942no—
236C2×C4—942no—
237C2×C4—942no—
238C2×C4—942no—
239C2×C4D4×D4712yes—
240C2×C4#1062535412yes—
241C22—1882no—
242C22—1882no—
243C22—1882no—
244C22—1882no—
245C22—1882no—
246C22—1882no—
247C22—1882no—
248C22C2×D4×D4711yescharacteristic
249C22#41×D4711yescharacteristic
250C22C2×#1062535411yescharacteristic
251C22#1309406912yes—
252C22#1309407212yes—
253C4—22no—
254C4—22no—
255C4—42no—
256C4—42no—
257C4—41no—
258C4—942no—
259C4—942no—
260C4—942no—
261C4—1882no—
262C4—1881no—
263C2—3762no—
264C2#1568963611yescharacteristic
265C2#1568968811yescharacteristic
266C2#1568969811yescharacteristic
267C2#1568974312yes—
268C2#1568974712yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#395C2
hypercenter#395D47
hypocenterC47#2632
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
2. C2×#13093989C2semidirect
3. #15689058C2semidirect
4. #15689042C2semidirect
7. #15689036C2semidirect
8. #15689013C2semidirect
9. #15689012C2semidirect
10. #15688990C2semidirect
11. C47×#395C2semidirect
139. #395D47semidirect
146. C47#2632semidirect