Finite Group Databasebeta

← #20248588

Subgroups — #20248588

Order 6016.

548 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 165 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×#13094016C211yesmaximal, characteristic, complemented
2C2×C4×D188C211yesmaximal, characteristic
3#15689045C214yesmaximal, complemented
4#15689025C211yesmaximal, characteristic
5#15689025C211yesmaximal, characteristic
6#15688997C214yesmaximal, complemented
7#15688993C211yesmaximal, characteristic, complemented
8#15688989C211yesmaximal, characteristic, complemented
9C4×C4⋊C4×C47C211yesmaximal, characteristic, complemented
10C22×D188C2211yescharacteristic
11C22×C4×D47C2212yes—
12#13094016—24no—
13C4×D188—24no—
14C2×C4⋊Dic47C2211yescharacteristic
15C2×C4⋊Dic47C2211yescharacteristic
16C2×C4⋊Dic47C2211yescharacteristic
17C2×C4⋊Dic47C2214yes—
18C2×Dic47⋊C4C2212yes—
19C2×Dic47⋊C4C2212yes—
20C2×(C2×D47)⋊C4C2214yes—
21C2×(C2×D47)⋊C4C2212yes—
22C2×(C2×D47)⋊C4C2214yes—
23C47⋊#95C2214yes—
24C2×C4⋊C4×C47C2212yes—
25C2×C42×C47C2211yescharacteristic
26C2×C42×C47C2211yescharacteristic
27C2×C42×C47C2211yescharacteristic
28#95×C47C2212yes—
29C23×D47C2312yes—
30C22×C4×C47C2312yes—
31C22×C4×C47C2311yescharacteristic
32C22×C4×C47C2311yescharacteristic
33C22×C4×C47C2312yes—
34C22×C4×C47C2311yescharacteristic
35C22×Dic47C2312yes—
36C22×Dic47C2312yes—
37C22×Dic47C2312yes—
38C2×D188—22no—
39C2×D188—22no—
40C2×D188Q814yes—
41C2×C4×D47—24no—
42C2×C4×D47—44no—
43C4⋊C4×C47—24no—
44C42×C47—22no—
45C42×C47—22no—
46C42×C47D414yes—
47(C2×D47)⋊C4—24no—
48(C2×D47)⋊C4—28no—
49(C2×D47)⋊C4—44no—
50C4⋊Dic47—22no—
51C4⋊Dic47—22no—
52C4⋊Dic47—22no—
53C4⋊Dic47—44no—
54Dic47⋊C4—24no—
55Dic47⋊C4—24no—
56C23×C47C2411yescharacteristic
57C22×D47—22no—
58C22×D47—24no—
59C22×D47—22no—
60C22×D47—24no—
61C22×D47C2×Q814yes—
62C2×C4×C47—22no—
63C2×C4×C47—22no—
64C2×C4×C47—22no—
65C2×C4×C47—22no—
66C2×C4×C47—22no—
67C2×C4×C47—22no—
68C2×C4×C47—22no—
69C2×C4×C47C2×D412yes—
70C2×C4×C47C2×D412yes—
71C2×C4×C47C2×D412yes—
72C2×C4×C47C2×Q812yes—
73C2×C4×C47#4114yes—
74C2×C4×C47#4112yes—
75C2×Dic47—22no—
76C2×Dic47—22no—
77C2×Dic47—22no—
78C2×Dic47—24no—
79C2×Dic47—24no—
80C2×Dic47—24no—
81D188—28no—
82C4×D47—48no—
83C22×C47C22×D411yescharacteristic
84C22×C47C22×Q811yescharacteristic
85C22×C47C2×#4111yescharacteristic
86C22×C47C2×#4112yes—
87C22×C47H(5,𝔽2)12yes—
88C2×D47—24no—
89C2×D47—28no—
90C2×D47—42no—
91C2×D47—42no—
92C2×D47—44no—
93C4×C47—22no—
94C4×C47—22no—
95C4×C47—24no—
96C4×C47—42no—
97C4×C47C22⋊Q814yes—
98Dic47—42no—
99Dic47—42no—
100Dic47—42no—
101#2566—471nomaximal, Sylow
102C2×C47C2×C22⋊Q811yescharacteristic
103C2×C47#53211yescharacteristic
104C2×C47#53511yescharacteristic
105C2×C47#55312yes—
106C2×C47#55412yes—
107D47—44no—
108C2×#125—471no—
109C2×C4×D4—471no—
110#396—474no—
111#390—471no—
112#390—471no—
113#385—474no—
114#384—471no—
115#382—471no—
116C4×C4⋊C4D4711yescharacteristic, complemented
117C47#256611yescharacteristic, complemented, Sylow
118C22×D4—471no—
119C23×C4—472no—
120#125—944no—
121C4×D4—944no—
122C2×C4⋊C4—471no—
123C2×C4⋊C4—472no—
124C2×C4⋊C4—472no—
125C2×C4⋊C4—471no—
126C2×C4⋊C4—471no—
127C2×C4⋊C4—474no—
128C2×C4⋊C4C2×D4712yes—
129C2×C22⋊C4—472no—
130C2×C22⋊C4—474no—
131C2×C22⋊C4—474no—
132C2×C42C2×D4711yescharacteristic
133C2×C42C2×D4711yescharacteristic
134C2×C42C2×D4711yescharacteristic
135#95—474no—
136#95C2×D4712yes—
137C24—472no—
138C2×D4—474no—
139C2×D4—942no—
140C2×D4—942no—
141C22×C4—472no—
142C22×C4—472no—
143C22×C4—472no—
144C22×C4—944no—
145C22×C4—1884no—
146C22×C4C22×D4712yes—
147C22×C4C22×D4711yescharacteristic
148C22×C4C22×D4711yescharacteristic
149C22×C4C22×D4712yes—
150C22×C4C22×D4711yescharacteristic
151C4⋊C4—24no—
152C4⋊C4—944no—
153C4⋊C4—944no—
154C4⋊C4—942no—
155C4⋊C4—942no—
156C4⋊C4—942no—
157C4⋊C4—1884no—
158C22⋊C4—944no—
159C22⋊C4—948no—
160C22⋊C4—1884no—
161C42—22no—
162C42—22no—
163C42D18814yes—
164C23—474no—
165C23—942no—
166C23—942no—
167C23—944no—
168C23—944no—
169C23C23×D4711yescharacteristic
170D4—948no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—942no—
179C2×C4—942no—
180C2×C4—942no—
181C2×C4—944no—
182C2×C4—944no—
183C2×C4—944no—
184C2×C4—1888no—
185C2×C4C2×D18812yes—
186C2×C4C2×D18812yes—
187C2×C4C2×D18812yes—
188C2×C4#1062535014yes—
189C2×C4#1062535212yes—
190C2×C4Q8×D4712yes—
191C22—948no—
192C22—944no—
193C22—1884no—
194C22—1882no—
195C22—1882no—
196C22C22×D18811yescharacteristic
197C22C2×Q8×D4711yescharacteristic
198C22C2×#1062535211yescharacteristic
199C22C2×#1062535012yes—
200C22#1309407012yes—
201C4—24no—
202C4—22no—
203C4—22no—
204C4—42no—
205C4—1882no—
206C4—1882no—
207C4—1882no—
208C4#1309400414yes—
209C2—1884no—
210C2C2×#1309400411yescharacteristic
211C2#1568967311yescharacteristic
212C2#1568969211yescharacteristic
213C2#1568981912yes—
214C2#1568983312yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC4×C4⋊C4×C47C2
hypercenterC4×C4⋊C4D47
hypocenterC47#2566
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#13094016C2semidirect
3. #15689045C2semidirect
6. #15688997C2semidirect
7. #15688993C2semidirect
8. #15688989C2semidirect
9. C4×C4⋊C4×C47C2semidirect
116. C4×C4⋊C4D47semidirect
117. C47#2566semidirect