Finite Group Databasebeta

← #20243856

Subgroups — #20243856

Order 6016.

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

normal subgroups only

This group has 338 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×#13094003C211yesmaximal, characteristic
2C2×#13093942C212yesmaximal, complemented
3#15689087C211yesmaximal, characteristic
4#15688891C212yesmaximal, complemented
5C22×M16×C47C211yesmaximal, characteristic
6C22×Dic94C2211yescharacteristic
7C2×#10625329C2212yes—
8#13094003—21no—
9#13094003—21no—
10#13094003—21no—
11#13094003—21no—
12C2×C4⋊Dic47C2211yescharacteristic
13C2×Dic47⋊C4C412yes—
14C2×C22⋊Dic47C412yes—
15#13093942—24no—
16C22⋊(C47⋊C8)—21no—
17C22⋊(C47⋊C8)—21no—
18C23×C4×C47C2211yescharacteristic
19C2×M16×C47—21no—
20C2×M16×C47—24no—
21C2×M16×C47C2212yes—
22C22×C8×C47—21no—
23C24×C47C2×C411yescharacteristic
24C22×C4×C47—22no—
25C22×C4×C47—22no—
26C22×C4×C47C2×C411yescharacteristic
27C22×C4×C47D411yescharacteristic
28C22×C4×C47D411yescharacteristic
29C22×C4×C47D411yescharacteristic
30C22×C4×C47D411yescharacteristic
31C22×C4×C47C2311yescharacteristic
32C22×Dic47C2×C412yes—
33C22×Dic47C2×C412yes—
34C2×Dic94—22no—
35C2×Dic94—21no—
36C2×Dic94—21no—
37C2×Dic94—22no—
38M16×C47—24no—
39M16×C47—22no—
40M16×C47D414yes—
41C2×C8×C47—24no—
42C2×C8×C47—22no—
43C22⋊Dic47—22no—
44C22⋊Dic47—22no—
45C4⋊Dic47—21no—
46C4⋊Dic47—21no—
47Dic47⋊C4—22no—
48Dic47⋊C4—22no—
49#10625329—22no—
50#10625329—22no—
51C2×C47⋊C8—22no—
52C23×C47—22no—
53C23×C47—22no—
54C23×C47—41no—
55C23×C47C22⋊C411yescharacteristic
56C23×C47C22⋊C411yescharacteristic
57C23×C47C22×C411yescharacteristic
58C2×C4×C47—22no—
59C2×C4×C47—21no—
60C2×C4×C47—21no—
61C2×C4×C47—22no—
62C2×C4×C47—22no—
63C2×C4×C47—21no—
64C2×C4×C47—21no—
65C2×C4×C47C22⋊C411yescharacteristic
66C2×C4×C47C22⋊C411yescharacteristic
67C2×C4×C47C2×D411yescharacteristic
68C2×C4×C47C2×D412yes—
69C2×C4×C47C2×D411yescharacteristic
70C2×C4×C47#4112yes—
71C2×Dic47—22no—
72C2×Dic47—22no—
73C2×Dic47—24no—
74C2×Dic47—42no—
75Dic94—41no—
76Dic94—42no—
77Dic94—41no—
78C8×C47—24no—
79C47⋊C8—42no—
80C22×C47—21no—
81C22×C47—21no—
82C22×C47—21no—
83C22×C47—21no—
84C22×C47—21no—
85C22×C47—21no—
86C22×C47—21no—
87C22×C47—44no—
88C22×C47#10112yescomplemented
89C22×C47C2×C22⋊C411yescharacteristic
90C22×C47C4×D412yes—
91C4×C47—21no—
92C4×C47—21no—
93C4×C47#12011yescharacteristic
94C4×C47#12112yes—
95C4×C47#12311yescharacteristic
96Dic47—42no—
97Dic47—42no—
98#1901—471nomaximal, Sylow
99C2×C47—22no—
100C2×C47—22no—
101C2×C47—41no—
102C2×C47#38611yescharacteristic
103C2×C47C2×#10111yescharacteristic
104C2×C47#41311yescharacteristic
105C22×M16D4711yescharacteristic
106C2×C22⋊Q8—471no—
107C2×#101—472no—
108#407—471no—
109#343—472no—
110C47#190111yescharacteristic, complemented, Sylow
111C22×Q8—471no—
112C23×C4C2×D4711yescharacteristic
113C2×M16—21no—
114C2×M16—24no—
115C2×M16—472no—
116C2×M16C2×D4712yes—
117C22×C8—21no—
118C22⋊Q8—941no—
119C22⋊Q8—941no—
120C22⋊Q8—941no—
121C22⋊Q8—941no—
122C2×C4⋊C4—472no—
123C2×C4⋊C4—471no—
124C2×C22⋊C4—472no—
125#101—944no—
126C22⋊C8—941no—
127C22⋊C8—941no—
128C24C4×D4711yescharacteristic
129C2×Q8—941no—
130C2×Q8—942no—
131C2×Q8—942no—
132C2×Q8—941no—
133C22×C4—22no—
134C22×C4—22no—
135C22×C4—472no—
136C22×C4—472no—
137C22×C4C4×D4711yescharacteristic
138C22×C4D18811yescharacteristic
139C22×C4D18811yescharacteristic
140C22×C4C22⋊D4711yescharacteristic
141C22×C4C22⋊D4711yescharacteristic
142C22×C4C22×D4711yescharacteristic
143M16—24no—
144M16—22no—
145M16—942no—
146M16—942no—
147M16C22⋊D4714yes—
148C2×C8—24no—
149C2×C8—22no—
150C2×C8—942no—
151C4⋊C4—942no—
152C4⋊C4—942no—
153C4⋊C4—941no—
154C4⋊C4—941no—
155C22⋊C4—942no—
156C22⋊C4—942no—
157C23—22no—
158C23—22no—
159C23—41no—
160C23(C2×D47)⋊C411yescharacteristic
161C23(C2×D47)⋊C411yescharacteristic
162C23C2×C4×D4711yescharacteristic
163Q8—1881no—
164Q8—1882no—
165Q8—1881no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—942no—
174C2×C4—942no—
175C2×C4—944no—
176C2×C4—1882no—
177C2×C4(C2×D47)⋊C411yescharacteristic
178C2×C4(C2×D47)⋊C411yescharacteristic
179C2×C4C2×D18811yescharacteristic
180C2×C4#1062535012yes—
181C2×C4C2×C22⋊D4712yes—
182C2×C4C2×C22⋊D4711yescharacteristic
183C8—24no—
184C8—1882no—
185C22—21no—
186C22—21no—
187C22—21no—
188C22—21no—
189C22—21no—
190C22—21no—
191C22—21no—
192C22—44no—
193C22#1309394212yescomplemented
194C22C2×(C2×D47)⋊C411yescharacteristic
195C22C4×C22⋊D4712yes—
196C4—21no—
197C4—21no—
198C4—1882no—
199C4—1882no—
200C4#1309399311yescharacteristic
201C4#1309399812yes—
202C4#1309400711yescharacteristic
203C2—22no—
204C2—22no—
205C2—41no—
206C2#1568900211yescharacteristic
207C2C2×#1309394211yescharacteristic
208C2#1568910511yescharacteristic
subgroupG/H
centerC22C2×(C2×D47)⋊C4
commutatorC23×C47C22×C4
FrattiniC22×C4C22×D47
FittingC22×M16×C47C2
socleC22×C47C2×C22⋊C4
hypercenterC22×M16D47
hypocenterC47#1901
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
2. C2×#13093942C2semidirect
4. #15688891C2semidirect
88. C22×C47#101semidirect
110. C47#1901semidirect
193. C22#13093942semidirect