Finite Group Databasebeta

← #20248587

Subgroups — #20248587

Order 6016.

548 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 153 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×#13094015C211yesmaximal, characteristic, complemented
2C2×#13093986C211yesmaximal, characteristic
3#15689047C214yesmaximal, complemented
4#15689025C211yesmaximal, characteristic
5#15689024C211yesmaximal, characteristic
6#15688997C214yesmaximal, complemented
7#15688992C211yesmaximal, characteristic, complemented
8C4×Dic47⋊C4C211yesmaximal, characteristic, complemented
9C47×#382C211yesmaximal, characteristic, complemented
10C22×D188C2211yescharacteristic
11C22×C4×D47C2212yes—
12#13094015—24no—
13#13093986—24no—
14C2×C4⋊Dic47C2211yescharacteristic
15C2×C4⋊Dic47C2212yes—
16C2×Dic47⋊C4C2212yes—
17C2×Dic47⋊C4C2212yes—
18C2×Dic47⋊C4C2214yes—
19C2×(C2×D47)⋊C4C2214yes—
20C2×(C2×D47)⋊C4C2212yes—
21C2×(C2×D47)⋊C4C2214yes—
22C2×C4×Dic47C2211yescharacteristic
23C2×C4×Dic47C2211yescharacteristic
24C47⋊#95C2212yes—
25C2×C4⋊C4×C47C2211yescharacteristic
26C2×C4⋊C4×C47C2211yescharacteristic
27C2×C42×C47C2211yescharacteristic
28#95×C47C2214yes—
29C23×D47C2312yes—
30C22×C4×C47C2312yes—
31C22×C4×C47C2312yes—
32C22×C4×C47C2312yes—
33C22×C4×C47C2311yescharacteristic
34C22×Dic47C2312yes—
35C22×Dic47C2311yescharacteristic
36C22×Dic47C2311yescharacteristic
37C22×Dic47C2312yes—
38C2×D188—22no—
39C2×D188—22no—
40C2×D188Q814yes—
41C2×C4×D47—24no—
42C2×C4×D47—44no—
43C4⋊C4×C47—22no—
44C4⋊C4×C47—22no—
45C42×C47—22no—
46(C2×D47)⋊C4—24no—
47(C2×D47)⋊C4—28no—
48(C2×D47)⋊C4—44no—
49C4⋊Dic47—22no—
50C4⋊Dic47—24no—
51Dic47⋊C4—24no—
52Dic47⋊C4—24no—
53Dic47⋊C4—44no—
54C4×Dic47—22no—
55C4×Dic47D414yes—
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—24no—
66C2×C4×C47—22no—
67C2×C4×C47—24no—
68C2×C4×C47—22no—
69C2×C4×C47C2×D412yes—
70C2×C4×C47C2×Q812yes—
71C2×C4×C47#4112yes—
72C2×Dic47—22no—
73C2×Dic47—22no—
74C2×Dic47—22no—
75C2×Dic47—22no—
76C2×Dic47—22no—
77C2×Dic47—24no—
78C2×Dic47C2×D412yes—
79C2×Dic47C2×D412yes—
80C2×Dic47#4114yes—
81D188—28no—
82C4×D47—48no—
83C22×C47C22×D411yescharacteristic
84C22×C47C22×Q811yescharacteristic
85C22×C47C2×#4112yes—
86C22×C47C2×#4111yescharacteristic
87C22×C47H(5,𝔽2)12yes—
88C2×D47—24no—
89C2×D47—28no—
90C2×D47—42no—
91C2×D47—42no—
92C2×D47—44no—
93C4×C47—42no—
94C4×C47—42no—
95C4×C47—42no—
96C4×C47C22⋊Q814yes—
97Dic47—22no—
98Dic47—22no—
99Dic47—24no—
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#382D4711yescharacteristic, complemented
116C4×C4⋊C4—471no—
117C47#256611yescharacteristic, complemented, Sylow
118C22×D4—471no—
119C23×C4—472no—
120#125—944no—
121C4×D4—944no—
122C2×C4⋊C4—472no—
123C2×C4⋊C4—471no—
124C2×C4⋊C4—472no—
125C2×C4⋊C4—472no—
126C2×C4⋊C4—474no—
127C2×C4⋊C4C2×D4711yescharacteristic
128C2×C4⋊C4C2×D4711yescharacteristic
129C2×C22⋊C4—472no—
130C2×C22⋊C4—474no—
131C2×C22⋊C4—474no—
132C2×C42—471no—
133C2×C42—471no—
134C2×C42C2×D4711yescharacteristic
135#95—472no—
136#95C2×D4714yes—
137C24—472no—
138C2×D4—474no—
139C2×D4—942no—
140C2×D4—942no—
141C22×C4—471no—
142C22×C4—472no—
143C22×C4—471no—
144C22×C4—472no—
145C22×C4—944no—
146C22×C4—1884no—
147C22×C4C22×D4712yes—
148C22×C4C22×D4712yes—
149C22×C4C22×D4712yes—
150C22×C4C22×D4711yescharacteristic
151C4⋊C4—22no—
152C4⋊C4—22no—
153C4⋊C4—944no—
154C4⋊C4—944no—
155C4⋊C4—944no—
156C4⋊C4—942no—
157C4⋊C4—1884no—
158C22⋊C4—948no—
159C22⋊C4—944no—
160C22⋊C4—1884no—
161C42—22no—
162C42—474no—
163C42—942no—
164C23—474no—
165C23—942no—
166C23—944no—
167C23—942no—
168C23—944no—
169C23C23×D4711yescharacteristic
170D4—948no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—24no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—24no—
178C2×C4—472no—
179C2×C4—472no—
180C2×C4—474no—
181C2×C4—942no—
182C2×C4—942no—
183C2×C4—942no—
184C2×C4—942no—
185C2×C4—942no—
186C2×C4—944no—
187C2×C4—1888no—
188C2×C4#1062535012yes—
189C2×C4D4×D4712yes—
190C2×C4Q8×D4712yes—
191C22—948no—
192C22—944no—
193C22—1884no—
194C22—1882no—
195C22—1882no—
196C22C2×D4×D4711yescharacteristic
197C22C2×Q8×D4711yescharacteristic
198C22#41×D4712yes—
199C22C2×#1062535011yescharacteristic
200C22#1309407012yes—
201C4—42no—
202C4—42no—
203C4—42no—
204C4—944no—
205C4—942no—
206C4—942no—
207C4—1882no—
208C4#1309400214yes—
209C2—1884no—
210C2C2×#1309400211yescharacteristic
211C2#1568967211yescharacteristic
212C2#1568969111yescharacteristic
213C2#1568981712yes—
214C2#1568982912yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#382C2
hypercenter#382D47
hypocenterC47#2566
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
1. C2×#13094015C2semidirect
3. #15689047C2semidirect
6. #15688997C2semidirect
7. #15688992C2semidirect
8. C4×Dic47⋊C4C2semidirect
9. C47×#382C2semidirect
115. #382D47semidirect
117. C47#2566semidirect