Finite Group Databasebeta

← #16846154

Subgroups — #16846154

Order 3968.

442 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 101 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
1#14521560C211yesmaximal, characteristic
2C2×#11758393C212yesmaximal, complemented
3#14521013C211yesmaximal, characteristic, complemented
4#14520809C212yesmaximal, complemented
5C22×C42×C31C211yesmaximal, characteristic, complemented
6C23×C4×C31—21no—
7C23×C4×C31C2211yescharacteristic
8C2×#92495C2211yescharacteristic
9C2×C42×C31—21no—
10C2×C42×C31—24no—
11C2×C42×C31C2212yes—
12#11758530—21no—
13#11758507C412yescomplemented
14#11758506—21no—
15C4×C22⋊D31—22no—
16#11758503C2211yescharacteristic
17#11758501C412yescomplemented
18C2×#92474C2212yes—
19C22⋊(C31⋊C8)—22no—
20#11758393—24no—
21C24×C31D411yescharacteristic
22C22×C4×C31—24no—
23C22×C4×C31—28no—
24C22×C4×C31—22no—
25C22×C4×C31—22no—
26C22×C4×C31—22no—
27C22×C4×C31C2×C412yes—
28C22×C4×C31D411yescharacteristic
29C22×C4×C31D412yes—
30C22×C4×C31C2311yescharacteristic
31C2×C22⋊D31—22no—
32C2×C22⋊D31—21no—
33#92495—22no—
34#92495—22no—
35C2×D124C2×C411yescharacteristic, complemented
36C2×C4×D31—21no—
37C2×Dic62C2×C411yescharacteristic, complemented
38C42×C31—24no—
39C42×C31—22no—
40C42×C31D414yescomplemented
41C22⋊Dic31—22no—
42C22⋊Dic31—21no—
43(C2×D31)⋊C4—22no—
44C4⋊Dic31C2×C412yescomplemented
45Dic31⋊C4—22no—
46C4×Dic31—21no—
47#92474—22no—
48#92474—22no—
49C2×C31⋊C8—22no—
50C23×C31—24no—
51C23×C31—21no—
52C23×C31—21no—
53C23×C31C22⋊C412yes—
54C23×C31C2×D411yescharacteristic
55C22×D31—21no—
56C2×C4×C31—216no—
57C2×C4×C31—28no—
58C2×C4×C31—21no—
59C2×C4×C31—24no—
60C2×C4×C31—21no—
61C2×C4×C31—24no—
62C2×C4×C31—24no—
63C2×C4×C31C22⋊C412yes—
64C2×C4×C31C22×C411yescharacteristic
65C2×C4×C31C2×D411yescharacteristic
66C2×C4×C31C2×D412yes—
67C2×C4×C31#4112yes—
68C22⋊D31—44no—
69C22⋊D31—41no—
70C22⋊D31—41no—
71C2×Dic31—22no—
72C2×Dic31—21no—
73D124—22no—
74C4×D31—42no—
75Dic62—22no—
76C31⋊C8—42no—
77#1896—311nomaximal, Sylow
78C22×C31—24no—
79C22×C31—24no—
80C22×C31—22no—
81C22×C31—22no—
82C22×C31—22no—
83C22×C31#10414yescomplemented
84C22×C31C2×C22⋊C411yescharacteristic
85C22×C31#12011yescharacteristic
86C22×C31#12311yescharacteristic
87C2×D31—41no—
88C2×D31—42no—
89C4×C31—28no—
90C4×C31—22no—
91C4×C31C4×D412yes—
92C4×C31#12112yes—
93Dic31—41no—
94Dic31—42no—
95#525—311no—
96C22×C42D3111yescharacteristic, complemented
97C2×#104—312no—
98#407—311no—
99#339—312no—
100C2×C31—21no—
101C2×C31—24no—
102C2×C31—21no—
103C2×C31#38611yescharacteristic
104C2×C31C2×#10412yes—
105D31—81no—
106C2×#41—311no—
107C23×C4—21no—
108C23×C4C2×D3111yescharacteristic
109C2×M16—312no—
110#123—621no—
111C22⋊Q8—312no—
112#121—312no—
113#120—621no—
114C4×D4—622no—
115#117—311no—
116C2×C42—21no—
117C2×C42—24no—
118C2×C42C2×D3112yes—
119#104—624no—
120C22⋊C8—622no—
121C31#189611yescharacteristic, complemented, Sylow
122C24C22⋊D3111yescharacteristic
123#41—622no—
124#41—622no—
125C2×Q8—311no—
126C2×D4—311no—
127C2×D4—622no—
128C2×D4—621no—
129C22×C4—24no—
130C22×C4—28no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—621no—
135C22×C4C4×D3112yes—
136C22×C4D12412yes—
137C22×C4C22⋊D3111yescharacteristic
138C22×C4C22×D3111yescharacteristic
139M16—622no—
140M16—622no—
141C2×C8—622no—
142C4⋊C4—312no—
143C4⋊C4—622no—
144C22⋊C4—622no—
145C22⋊C4—621no—
146C22⋊C4—622no—
147C42—24no—
148C42—22no—
149C42—621no—
150C42C22⋊D3114yescomplemented
151C23—24no—
152C23—21no—
153C23—21no—
154C23—621no—
155C23(C2×D31)⋊C412yes—
156C23C2×C22⋊D3111yescharacteristic
157Q8—622no—
158D4—622no—
159D4—1244no—
160D4—1241no—
161D4—1241no—
162C2×C4—216no—
163C2×C4—28no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—24no—
167C2×C4—24no—
168C2×C4—24no—
169C2×C4—622no—
170C2×C4—621no—
171C2×C4—1242no—
172C2×C4(C2×D31)⋊C412yes—
173C2×C4C2×C4×D3111yescharacteristic
174C2×C4C2×D12411yescharacteristic
175C2×C4#9249512yes—
176C2×C4C2×C22⋊D3112yes—
177C8—1242no—
178C22—24no—
179C22—24no—
180C22—22no—
181C22—22no—
182C22—22no—
183C22—1241no—
184C22—1242no—
185C22#1175839314yescomplemented
186C22C2×(C2×D31)⋊C411yescharacteristic
187C22#1175850611yescharacteristic
188C22#1175853011yescharacteristic
189C4—28no—
190C4—22no—
191C4—1241no—
192C4—1242no—
193C4C4×C22⋊D3112yes—
194C4#1175850712yes—
195C2—21no—
196C2—24no—
197C2—21no—
198C2—2481no—
199C2#1452092811yescharacteristic
200C2C2×#1175839312yes—
subgroupG/H
centerC2×C4C2×D124
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC22×C42×C31C2
socleC22×C31C2×C22⋊C4
prime radical#14521560C2
cosocleC22×C4×C31C23
hypercenterC22×C42D31
hypocenterC31#1896
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
2. C2×#11758393C2semidirect
3. #14521013C2semidirect
4. #14520809C2semidirect
5. C22×C42×C31C2semidirect
13. #11758507C4semidirect
17. #11758501C4semidirect
35. C2×D124C2×C4semidirect
37. C2×Dic62C2×C4semidirect
40. C42×C31D4semidirect
44. C4⋊Dic31C2×C4semidirect
83. C22×C31#104semidirect
96. C22×C42D31semidirect
121. C31#1896semidirect
150. C42C22⋊D31semidirect
185. C22#11758393semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145215602
C2×#117583932
#145210132
#145208092
C22×C42×C312
#189631