Finite Group Databasebeta

← #20249762

Subgroups — #20249762

Order 6016.

592 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13094002C212yesmaximal, complemented
2C2×#13094000C212yesmaximal, complemented
3#15689047C212yesmaximal, complemented
4#15689045C212yesmaximal, complemented
5#15689043C211yesmaximal, characteristic, complemented
6#15689024C211yesmaximal, characteristic
7#15689020C212yesmaximal, complemented
8#15689001C212yesmaximal
9C47×#395C211yesmaximal, characteristic, complemented
10C22×Dic94C2211yescharacteristic
11C22×D188C2211yescharacteristic
12C22×C4×D47C2212yes—
13#13094002—28no—
14#13094000—28no—
15C2×C4⋊Dic47C2212yes—
16C2×Dic47⋊C4C2212yes—
17C2×Dic47⋊C4C2212yes—
18C2×Dic47⋊C4C2212yes—
19C2×Dic47⋊C4C2212yes—
20C2×(C2×D47)⋊C4C2212yes—
21C2×(C2×D47)⋊C4C2212yes—
22C2×(C2×D47)⋊C4C2212yes—
23C2×(C2×D47)⋊C4C2212yes—
24C2×(C2×D47)⋊C4C2212yes—
25C2×C4×Dic47C2211yescharacteristic
26C47⋊#95C2212yes—
27C47⋊#95C2211yescharacteristic
28C22×Q8×C47C2211yescharacteristic
29C2×C4⋊C4×C47C2212yes—
30C2×C4⋊C4×C47C2211yescharacteristic
31#95×C47C2212yes—
32#95×C47C2211yescharacteristic
33C23×D47C2312yes—
34C2×Q8×C47—24no—
35C2×Q8×C47—41no—
36C22×C4×C47C2311yescharacteristic
37C22×C4×C47C2311yescharacteristic
38C22×C4×C47C2312yes—
39C22×C4×C47C2312yes—
40C22×C4×C47C2311yescharacteristic
41C22×Dic47C2312yes—
42C22×Dic47C2312yes—
43C22×Dic47C2312yes—
44C2×D188—41no—
45C2×D188—41no—
46C2×D188Q814yescomplemented
47C2×C4×D47—24no—
48C2×C4×D47—24no—
49C2×C4×D47—42no—
50C2×Dic94—24no—
51C2×Dic94—41no—
52C4⋊C4×C47—24no—
53C4⋊C4×C47—41no—
54(C2×D47)⋊C4—24no—
55(C2×D47)⋊C4—24no—
56(C2×D47)⋊C4—24no—
57(C2×D47)⋊C4—24no—
58(C2×D47)⋊C4—42no—
59C4⋊Dic47—24no—
60Dic47⋊C4—24no—
61Dic47⋊C4—24no—
62Dic47⋊C4—42no—
63Dic47⋊C4D418yescomplemented
64C4×Dic47—41no—
65C23×C47C2411yescharacteristic
66C22×D47—22no—
67C22×D47—22no—
68C22×D47—22no—
69C22×D47—22no—
70C22×D47—22no—
71C22×D47—22no—
72C22×D47C2×Q814yes—
73Q8×C47—44no—
74C2×C4×C47—22no—
75C2×C4×C47—21no—
76C2×C4×C47—21no—
77C2×C4×C47—22no—
78C2×C4×C47—22no—
79C2×C4×C47—22no—
80C2×C4×C47—22no—
81C2×C4×C47—22no—
82C2×C4×C47—21no—
83C2×C4×C47—21no—
84C2×C4×C47—22no—
85C2×C4×C47C2×D414yes—
86C2×C4×C47C2×Q812yes—
87C2×Dic47—22no—
88C2×Dic47—22no—
89C2×Dic47—22no—
90C2×Dic47—22no—
91C2×Dic47—22no—
92C2×Dic47—22no—
93C2×Dic47—22no—
94C2×Dic47C2×D414yes—
95C2×Dic47C2×D414yes—
96D188—44no—
97C4×D47—48no—
98Dic94—44no—
99C22×C47C22×D412yes—
100C22×C47C22×Q811yescharacteristic
101C22×C47H(5,𝔽2)11yescharacteristic
102C22×C47H(5,𝔽2)11yescharacteristic
103C22×C472−1+412yes—
104C2×D47—24no—
105C2×D47—24no—
106C2×D47—24no—
107C2×D47—42no—
108C2×D47—42no—
109C2×D47—42no—
110C2×D47—42no—
111C4×C47—22no—
112C4×C47—24no—
113C4×C47—42no—
114C4×C47—41no—
115C4×C47—41no—
116Dic47—24no—
117Dic47—24no—
118Dic47—42no—
119#2683—471nomaximal, Sylow
120C2×C47#53712yes—
121C2×C47#54311yescharacteristic
122C2×C47D4211yescharacteristic
123C2×C47D4×Q812yes—
124C2×C47#56311yescharacteristic
125D47—44no—
126C2×C22⋊Q8—472no—
127C2×C22⋊Q8—472no—
128#396—472no—
129#396—472no—
130#395—471no—
131#395D4711yescharacteristic, complemented
132#390—471no—
133#389—472no—
134#386—472no—
135C47#268311yescharacteristic, complemented, Sylow
136C22×Q8—471no—
137C22×Q8C2×D4711yescharacteristic
138C22×D4—471no—
139C23×C4—472no—
140C22⋊Q8—948no—
141C22⋊Q8—948no—
142C2×C4⋊C4—472no—
143C2×C4⋊C4—472no—
144C2×C4⋊C4—472no—
145C2×C4⋊C4—472no—
146C2×C4⋊C4—472no—
147C2×C4⋊C4C2×D4712yes—
148C2×C4⋊C4C2×D4711yescharacteristic
149C2×C22⋊C4—472no—
150C2×C22⋊C4—472no—
151C2×C22⋊C4—472no—
152C2×C22⋊C4—472no—
153C2×C22⋊C4—472no—
154C2×C42—471no—
155#95—472no—
156#95—471no—
157#95C2×D4712yes—
158#95C2×D4711yescharacteristic
159C24—472no—
160C2×Q8—24no—
161C2×Q8—41no—
162C2×Q8—944no—
163C2×Q8—1881no—
164C2×D4—474no—
165C2×D4—1881no—
166C2×D4—1881no—
167C22×C4—472no—
168C22×C4—472no—
169C22×C4—472no—
170C22×C4—944no—
171C22×C4—944no—
172C22×C4—1882no—
173C22×C4C22×D4711yescharacteristic
174C22×C4C22×D4712yes—
175C22×C4C22×D4711yescharacteristic
176C22×C4C22×D4712yes—
177C22×C4C22×D4711yescharacteristic
178C4⋊C4—24no—
179C4⋊C4—41no—
180C4⋊C4—478no—
181C4⋊C4—944no—
182C4⋊C4—944no—
183C4⋊C4—944no—
184C4⋊C4—1882no—
185C22⋊C4—944no—
186C22⋊C4—944no—
187C22⋊C4—944no—
188C22⋊C4—944no—
189C22⋊C4—1882no—
190C42—1881no—
191C23—474no—
192C23—942no—
193C23—942no—
194C23—942no—
195C23—942no—
196C23—942no—
197C23—942no—
198C23C23×D4711yescharacteristic
199Q8—44no—
200Q8—1884no—
201D4—1884no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—474no—
214C2×C4—474no—
215C2×C4—942no—
216C2×C4—942no—
217C2×C4—942no—
218C2×C4—942no—
219C2×C4—942no—
220C2×C4—942no—
221C2×C4—942no—
222C2×C4—1888no—
223C2×C4D4×D4714yes—
224C2×C4Q8×D4712yes—
225C22—944no—
226C22—944no—
227C22—944no—
228C22—1882no—
229C22—1882no—
230C22—1882no—
231C22—1882no—
232C22C2×D4×D4712yes—
233C22C2×Q8×D4711yescharacteristic
234C22#1309406911yescharacteristic
235C22#1309407011yescharacteristic
236C22#1309407212yes—
237C4—22no—
238C4—24no—
239C4—41no—
240C4—41no—
241C4—42no—
242C4—944no—
243C4—944no—
244C4—1882no—
245C2—1884no—
246C2#1568970312yes—
247C2#1568974811yescharacteristic
248C2#1568975511yescharacteristic
249C2#1568978812yes—
250C2#1568987211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#395C2
hypercenter#395D47
hypocenterC47#2683
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. C2×#13094002C2semidirect
2. C2×#13094000C2semidirect
3. #15689047C2semidirect
4. #15689045C2semidirect
5. #15689043C2semidirect
7. #15689020C2semidirect
9. C47×#395C2semidirect
46. C2×D188Q8semidirect
63. Dic47⋊C4D4semidirect
131. #395D47semidirect
135. C47#2683semidirect