Finite Group Databasebeta

← #20243847

Subgroups — #20243847

Order 6016.

378 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 97 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×#13093983C211yesmaximal, characteristic, complemented
2C2×#13093939C212yesmaximal
3#15688986C211yesmaximal, characteristic, complemented
4#15688890C212yesmaximal, complemented
5C2×#123×C47C211yesmaximal, characteristic
6#13093983—24no—
7C2×C4⋊Dic47—21no—
8C2×C22⋊Dic47C2212yes—
9C2×C22⋊Dic47C2212yes—
10C2×C4×Dic47—21no—
11#13093939—24no—
12C47⋊#95—22no—
13C22×D4×C47C2211yescharacteristic
14C23×C4×C47C2211yescharacteristic
15#123×C47—22no—
16#123×C47—21no—
17#123×C47—21no—
18C2×C4⋊C4×C47C412yescomplemented
19C2×C22⋊C4×C47C412yescomplemented
20C2×C22⋊C4×C47C2211yescharacteristic
21C24×C47C2×C411yescharacteristic
22C24×C47C2311yescharacteristic
23C2×D4×C47—21no—
24C2×D4×C47—21no—
25C2×D4×C47—22no—
26C2×D4×C47—22no—
27C22×C4×C47—22no—
28C22×C4×C47—22no—
29C22×C4×C47C2×C411yescharacteristic
30C22×C4×C47C2×C412yes—
31C22×C4×C47C2×C412yes—
32C22×C4×C47D412yes—
33C22×C4×C47D411yescharacteristic
34C22×C4×C47D411yescharacteristic
35C22×Dic47—22no—
36C22×Dic47—22no—
37C4⋊C4×C47—22no—
38C4⋊C4×C47—22no—
39C22⋊C4×C47—21no—
40C22⋊C4×C47—21no—
41C22⋊C4×C47—22no—
42C22⋊C4×C47—22no—
43C22⋊Dic47—22no—
44C22⋊Dic47—22no—
45C22⋊Dic47—22no—
46C22⋊Dic47D414yes—
47C4⋊Dic47—24no—
48C4×Dic47—24no—
49C23×C47—21no—
50C23×C47—22no—
51C23×C47—42no—
52C23×C47—42no—
53C23×C47C22×C411yescharacteristic
54C23×C47C2×D412yes—
55C23×C47C2×D411yescharacteristic
56C23×C47C2×D411yescharacteristic
57C23×C47#4112yes—
58D4×C47—41no—
59D4×C47—42no—
60D4×C47—41no—
61C2×C4×C47—24no—
62C2×C4×C47—21no—
63C2×C4×C47—21no—
64C2×C4×C47—24no—
65C2×C4×C47—21no—
66C2×C4×C47—21no—
67C2×C4×C47—22no—
68C2×C4×C47—21no—
69C2×C4×C47—22no—
70C2×C4×C47—42no—
71C2×C4×C47C22⋊C412yes—
72C2×C4×C47C22⋊C412yes—
73C2×Dic47—24no—
74C2×Dic47—44no—
75C2×Dic47—44no—
76C2×Dic47—42no—
77C22×C47—22no—
78C22×C47—22no—
79C22×C47—22no—
80C22×C47—42no—
81C22×C47—42no—
82C22×C47—41no—
83C22×C47—42no—
84C22×C47—82no—
85C22×C47C2×C22⋊C411yescharacteristic
86C22×C47C4×D412yes—
87C22×C47#12011yescharacteristic
88C22×C47#12112yes—
89C22×C47#12311yescharacteristic
90C4×C47—22no—
91C4×C47—22no—
92C4×C47—41no—
93C4×C47—42no—
94Dic47—44no—
95Dic47—82no—
96#1899—471nomaximal, Sylow
97C2×C47—21no—
98C2×C47—22no—
99C2×C47—22no—
100C2×C47—21no—
101C2×C47—81no—
102C2×C47#38611yescharacteristic
103C2×C47#41012yes—
104C2×#123D4711yescharacteristic
105C2×#117—471no—
106C2×#99—472no—
107#381—471no—
108#342—472no—
109C47#189911yescharacteristic, complemented, Sylow
110C22×D4C2×D4711yescharacteristic
111C23×C4C2×D4711yescharacteristic
112#123—22no—
113#123—21no—
114#123—21no—
115#117—944no—
116C2×C4⋊C4—941no—
117C2×C4⋊C4Dic4712yescomplemented
118C2×C22⋊C4—472no—
119C2×C22⋊C4—472no—
120C2×C22⋊C4Dic4712yescomplemented
121C2×C22⋊C4C2×D4711yescharacteristic
122C2×C42—941no—
123#99—944no—
124#95—942no—
125C24C2×Dic4711yescharacteristic
126C24C22×D4711yescharacteristic
127C2×D4—22no—
128C2×D4—22no—
129C2×D4—21no—
130C2×D4—21no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—942no—
134C22×C4—942no—
135C22×C4C2×Dic4711yescharacteristic
136C22×C4C2×Dic4712yes—
137C22×C4C2×Dic4712yes—
138C22×C4C22⋊D4712yes—
139C22×C4C22⋊D4711yescharacteristic
140C22×C4C22⋊D4711yescharacteristic
141C4⋊C4—22no—
142C4⋊C4—22no—
143C4⋊C4—944no—
144C22⋊C4—21no—
145C22⋊C4—21no—
146C22⋊C4—22no—
147C22⋊C4—22no—
148C22⋊C4—474no—
149C22⋊C4—942no—
150C22⋊C4—942no—
151C22⋊C4—942no—
152C42—944no—
153C23—21no—
154C23—22no—
155C23—42no—
156C23—42no—
157C23D4×D4712yes—
158C23#1062535212yes—
159C23C22×Dic4711yescharacteristic
160C23C2×C22⋊D4711yescharacteristic
161C23C2×C22⋊D4711yescharacteristic
162D4—41no—
163D4—42no—
164D4—41no—
165C2×C4—24no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—24no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—42no—
175C2×C4—944no—
176C2×C4—1884no—
177C2×C4—1882no—
178C2×C4—1884no—
179C2×C4C22⋊Dic4712yes—
180C2×C4C22⋊Dic4712yes—
181C22—22no—
182C22—22no—
183C22—22no—
184C22—42no—
185C22—42no—
186C22—41no—
187C22—42no—
188C22—82no—
189C22C2×C22⋊Dic4711yescharacteristic
190C22D4×Dic4712yes—
191C22#1309399211yescharacteristic
192C22#1309399612yes—
193C22#1309400511yescharacteristic
194C4—22no—
195C4—22no—
196C4—41no—
197C4—42no—
198C4—3762no—
199C4—1884no—
200C2—22no—
201C2—21no—
202C2—22no—
203C2—21no—
204C2—81no—
205C2#1568900311yescharacteristic
206C2#1568909712yes—
subgroupG/H
centerC22C2×C22⋊Dic47
commutatorC23×C47C22×C4
FrattiniC24C22×D47
FittingC2×#123×C47C2
socleC22×C47C2×C22⋊C4
hypercenterC2×#123D47
hypocenterC47#1899
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×#13093983C2semidirect
3. #15688986C2semidirect
4. #15688890C2semidirect
18. C2×C4⋊C4×C47C4semidirect
19. C2×C22⋊C4×C47C4semidirect
109. C47#1899semidirect
117. C2×C4⋊C4Dic47semidirect
120. C2×C22⋊C4Dic47semidirect