Finite Group Databasebeta

← #20249759

Subgroups — #20249759

Order 6016.

592 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 157 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×#13094004C212yesmaximal, complemented
2C2×#13094002C212yesmaximal, complemented
3#15689045C212yesmaximal, complemented
4#15689045C212yesmaximal, complemented
5#15689044C212yesmaximal, complemented
6#15689025C211yesmaximal, characteristic
7#15689021C211yesmaximal, characteristic, complemented
8#15689001C212yesmaximal
9C47×#389C211yesmaximal, characteristic, complemented
10C22×Dic94C2212yes—
11C22×D188C2211yescharacteristic
12C22×C4×D47C2212yes—
13#13094004—28no—
14#13094002—28no—
15C2×C4⋊Dic47C2212yes—
16C2×C4⋊Dic47C2211yescharacteristic
17C2×C4⋊Dic47C2211yescharacteristic
18C2×C4⋊Dic47C2211yescharacteristic
19C2×Dic47⋊C4C2212yes—
20C2×Dic47⋊C4C2212yes—
21C2×(C2×D47)⋊C4C2212yes—
22C2×(C2×D47)⋊C4C2212yes—
23C2×(C2×D47)⋊C4C2212yes—
24C2×(C2×D47)⋊C4C2212yes—
25C2×(C2×D47)⋊C4C2212yes—
26C47⋊#95C2212yes—
27C47⋊#95C2212yes—
28C2×C4⋊C4×C47C2212yes—
29C2×C4⋊C4×C47C2211yescharacteristic
30C2×C4⋊C4×C47C2211yescharacteristic
31C2×C42×C47C2211yescharacteristic
32#95×C47C2212yes—
33C23×D47C2312yes—
34C22×C4×C47C2312yes—
35C22×C4×C47C2311yescharacteristic
36C22×C4×C47C2311yescharacteristic
37C22×C4×C47C2312yes—
38C22×C4×C47C2311yescharacteristic
39C22×Dic47C2312yes—
40C22×Dic47C2312yes—
41C22×Dic47C2312yes—
42C2×D188—41no—
43C2×D188—41no—
44C2×D188Q814yescomplemented
45C2×C4×D47—24no—
46C2×C4×D47—24no—
47C2×C4×D47—42no—
48C2×Dic94—24no—
49C2×Dic94—24no—
50C2×Dic94—42no—
51C4⋊C4×C47—24no—
52C4⋊C4×C47—41no—
53C4⋊C4×C47D414yescomplemented
54C42×C47—41no—
55(C2×D47)⋊C4—24no—
56(C2×D47)⋊C4—24no—
57(C2×D47)⋊C4—24no—
58(C2×D47)⋊C4—24no—
59(C2×D47)⋊C4—42no—
60C4⋊Dic47—24no—
61C4⋊Dic47—41no—
62C4⋊Dic47—41no—
63C4⋊Dic47D414yescomplemented
64Dic47⋊C4—24no—
65Dic47⋊C4—24no—
66C23×C47C2411yescharacteristic
67C22×D47—22no—
68C22×D47—22no—
69C22×D47—22no—
70C22×D47—22no—
71C22×D47—22no—
72C22×D47—22no—
73C22×D47C2×Q814yes—
74C2×C4×C47—22no—
75C2×C4×C47—21no—
76C2×C4×C47—21no—
77C2×C4×C47—21no—
78C2×C4×C47—21no—
79C2×C4×C47—22no—
80C2×C4×C47—21no—
81C2×C4×C47—21no—
82C2×C4×C47—22no—
83C2×C4×C47—22no—
84C2×C4×C47—22no—
85C2×C4×C47C2×D412yes—
86C2×C4×C47C2×D414yes—
87C2×C4×C47C2×D412yes—
88C2×C4×C47C2×Q812yes—
89C2×Dic47—22no—
90C2×Dic47—22no—
91C2×Dic47—22no—
92C2×Dic47—22no—
93C2×Dic47—22no—
94C2×Dic47—22no—
95C2×Dic47—22no—
96C2×Dic47—22no—
97C2×Dic47C2×D414yes—
98D188—44no—
99C4×D47—48no—
100Dic94—48no—
101C22×C47C22×D411yescharacteristic
102C22×C47C22×D411yescharacteristic
103C22×C47C22×Q811yescharacteristic
104C22×C47H(5,𝔽2)11yescharacteristic
105C22×C47H(5,𝔽2)11yescharacteristic
106C22×C472−1+411yescharacteristic
107C22×C472−1+411yescharacteristic
108C2×D47—24no—
109C2×D47—24no—
110C2×D47—24no—
111C2×D47—42no—
112C2×D47—42no—
113C2×D47—42no—
114C2×D47—42no—
115C4×C47—22no—
116C4×C47—22no—
117C4×C47—22no—
118C4×C47—24no—
119C4×C47—42no—
120Dic47—24no—
121Dic47—42no—
122Dic47—42no—
123#2683—471nomaximal, Sylow
124C2×C47#53711yescharacteristic
125C2×C47#53711yescharacteristic
126C2×C47#54311yescharacteristic
127C2×C47D4211yescharacteristic
128C2×C47D4×Q811yescharacteristic
129C2×C47D4×Q811yescharacteristic
130C2×C47#56311yescharacteristic
131D47—44no—
132C2×C22⋊Q8—472no—
133C2×C22⋊Q8—472no—
134#396—472no—
135#396—472no—
136#395—472no—
137#390—471no—
138#389—471no—
139#389D4711yescharacteristic, complemented
140#386—472no—
141C47#268311yescharacteristic, complemented, Sylow
142C22×Q8—472no—
143C22×D4—471no—
144C23×C4—472no—
145C22⋊Q8—948no—
146C22⋊Q8—948no—
147C2×C4⋊C4—471no—
148C2×C4⋊C4—472no—
149C2×C4⋊C4—472no—
150C2×C4⋊C4—472no—
151C2×C4⋊C4—471no—
152C2×C4⋊C4—471no—
153C2×C4⋊C4C2×D4712yes—
154C2×C4⋊C4C2×D4711yescharacteristic
155C2×C4⋊C4C2×D4711yescharacteristic
156C2×C22⋊C4—472no—
157C2×C22⋊C4—472no—
158C2×C22⋊C4—472no—
159C2×C22⋊C4—472no—
160C2×C22⋊C4—472no—
161C2×C42C2×D4711yescharacteristic
162#95—472no—
163#95—472no—
164#95C2×D4712yes—
165C24—472no—
166C2×Q8—944no—
167C2×Q8—944no—
168C2×Q8—1882no—
169C2×D4—474no—
170C2×D4—1881no—
171C2×D4—1881no—
172C22×C4—472no—
173C22×C4—472no—
174C22×C4—472no—
175C22×C4—944no—
176C22×C4—944no—
177C22×C4—1882no—
178C22×C4C22×D4712yes—
179C22×C4C22×D4712yes—
180C22×C4C22×D4711yescharacteristic
181C22×C4C22×D4711yescharacteristic
182C22×C4C22×D4711yescharacteristic
183C4⋊C4—24no—
184C4⋊C4—41no—
185C4⋊C4—474no—
186C4⋊C4—944no—
187C4⋊C4—944no—
188C4⋊C4—944no—
189C4⋊C4—1881no—
190C4⋊C4—1881no—
191C4⋊C4D18814yescomplemented
192C22⋊C4—944no—
193C22⋊C4—944no—
194C22⋊C4—944no—
195C22⋊C4—944no—
196C22⋊C4—1882no—
197C42—41no—
198C23—474no—
199C23—942no—
200C23—942no—
201C23—942no—
202C23—942no—
203C23—942no—
204C23—942no—
205C23C23×D4711yescharacteristic
206Q8—1888no—
207D4—1884no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—474no—
220C2×C4—942no—
221C2×C4—942no—
222C2×C4—942no—
223C2×C4—942no—
224C2×C4—942no—
225C2×C4—942no—
226C2×C4—942no—
227C2×C4—942no—
228C2×C4—1888no—
229C2×C4C2×D18812yes—
230C2×C4C2×D18814yes—
231C2×C4D4×D4712yes—
232C2×C4Q8×D4712yes—
233C22—944no—
234C22—944no—
235C22—944no—
236C22—1882no—
237C22—1882no—
238C22—1882no—
239C22—1882no—
240C22C2×D4×D4711yescharacteristic
241C22C22×D18811yescharacteristic
242C22C2×Q8×D4711yescharacteristic
243C22#1309406911yescharacteristic
244C22#1309407011yescharacteristic
245C22#1309407111yescharacteristic
246C22#1309407211yescharacteristic
247C4—22no—
248C4—24no—
249C4—22no—
250C4—22no—
251C4—42no—
252C4—944no—
253C4—1882no—
254C4—1882no—
255C2—1884no—
256C2#1568970011yescharacteristic
257C2#1568970411yescharacteristic
258C2#1568974811yescharacteristic
259C2D4×D18811yescharacteristic
260C2#1568978811yescharacteristic
261C2Q8×D18811yescharacteristic
262C2#1568987711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#389C2
hypercenter#389D47
hypocenterC47#2683
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
1. C2×#13094004C2semidirect
2. C2×#13094002C2semidirect
3. #15689045C2semidirect
4. #15689045C2semidirect
5. #15689044C2semidirect
7. #15689021C2semidirect
9. C47×#389C2semidirect
44. C2×D188Q8semidirect
53. C4⋊C4×C47D4semidirect
63. C4⋊Dic47D4semidirect
139. #389D47semidirect
141. C47#2683semidirect
191. C4⋊C4D188semidirect