Finite Group Databasebeta

← #16846018

Subgroups — #16846018

Order 3968.

404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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×#11758501C211yesmaximal, characteristic
2C2×#11758398C212yesmaximal, complemented
3C2×C22⋊(C31⋊C8)C211yesmaximal, characteristic
4#14520811C212yesmaximal, complemented
5C22×C4⋊C4×C31C211yesmaximal, characteristic
6C23×C4×C31—21no—
7C23×C4×C31C2211yescharacteristic
8C22×Dic62C2211yescharacteristic
9C2×C4⋊C4×C31—21no—
10C2×C4⋊C4×C31—24no—
11C2×C4⋊C4×C31C2212yes—
12C2×C22⋊Dic31—21no—
13C2×C4⋊Dic31C2211yescharacteristic
14#11758501—22no—
15#11758501C414yescomplemented
16C2×Dic31⋊C4—21no—
17C22×C31⋊C8C2212yes—
18C22⋊(C31⋊C8)—22no—
19#11758398—24no—
20C24×C31D411yescharacteristic
21C22×C4×C31—22no—
22C22×C4×C31—22no—
23C22×C4×C31—24no—
24C22×C4×C31—22no—
25C22×C4×C31—42no—
26C22×C4×C31—42no—
27C22×C4×C31C2×C412yes—
28C22×C4×C31D411yescharacteristic
29C22×C4×C31D412yes—
30C22×C4×C31C2311yescharacteristic
31C22×Dic31—21no—
32C22×Dic31—21no—
33C2×Dic62—22no—
34C2×Dic62—22no—
35C2×Dic62—21no—
36C2×Dic62C2×C412yescomplemented
37C4⋊C4×C31—24no—
38C4⋊C4×C31—22no—
39C4⋊C4×C31D414yes—
40C22⋊Dic31—24no—
41C4⋊Dic31—21no—
42C4⋊Dic31C2×C412yescomplemented
43Dic31⋊C4—24no—
44C2×C31⋊C8—22no—
45C2×C31⋊C8—22no—
46C2×C31⋊C8—22no—
47C23×C31—21no—
48C23×C31—21no—
49C23×C31—21no—
50C23×C31—21no—
51C23×C31C22⋊C412yes—
52C23×C31SD1612yes—
53C23×C31Q1612yes—
54C23×C31C2×D411yescharacteristic
55C2×C4×C31—21no—
56C2×C4×C31—21no—
57C2×C4×C31—24no—
58C2×C4×C31—24no—
59C2×C4×C31—24no—
60C2×C4×C31—48no—
61C2×C4×C31—42no—
62C2×C4×C31—42no—
63C2×C4×C31C22⋊C412yes—
64C2×C4×C31C22×C411yescharacteristic
65C2×C4×C31C2×D411yescharacteristic
66C2×C4×C31C2×D412yes—
67C2×C4×C31#4112yes—
68C2×Dic31—22no—
69C2×Dic31—22no—
70C2×Dic31—41no—
71C2×Dic31—41no—
72C2×Dic31—41no—
73C2×Dic31—41no—
74Dic62—24no—
75Dic62—42no—
76C31⋊C8—42no—
77#1872—311nomaximal, Sylow
78C22×C31—22no—
79C22×C31—22no—
80C22×C31—22no—
81C22×C31—22no—
82C22×C31—22no—
83C22×C31—22no—
84C22×C31#10314yescomplemented
85C22×C31C2×C22⋊C411yescharacteristic
86C22×C31#12011yescharacteristic
87C22×C31#12311yescharacteristic
88C22×C31C2×SD1611yescharacteristic
89C22×C31C2×Q1611yescharacteristic
90C22×C31AGL(1,ℤ/8)11yescharacteristic
91C22×C31#13711yescharacteristic
92C4×C31—22no—
93C4×C31—44no—
94C4×C31C4×D412yes—
95C4×C31#12112yes—
96Dic31—42no—
97Dic31—42no—
98C2×C22⋊Q8—311no—
99C22×C4⋊C4D3111yescharacteristic
100C2×#103—312no—
101C2×C22⋊C8—311no—
102#340—312no—
103C2×C31—24no—
104C2×C31#38611yescharacteristic
105C2×C31C2×#10311yescharacteristic
106C2×C31#41711yescharacteristic
107C2×C31#45011yescharacteristic
108C2×C31#45111yescharacteristic
109C2×C31#48311yescharacteristic
110C2×C31#48411yescharacteristic
111C22×Q8—311no—
112C23×C4—21no—
113C23×C4C2×D3111yescharacteristic
114C22×C8—312no—
115C22⋊Q8—314no—
116C22⋊Q8—622no—
117C2×C4⋊C4—21no—
118C2×C4⋊C4—24no—
119C2×C4⋊C4—311no—
120C2×C4⋊C4—621no—
121C2×C4⋊C4C2×D3112yes—
122C2×C22⋊C4—621no—
123#103—624no—
124C22⋊C8—622no—
125C31#187211yescharacteristic, complemented, Sylow
126C24C22⋊D3111yescharacteristic
127C2×Q8—312no—
128C2×Q8—621no—
129C2×Q8—622no—
130C2×Q8—622no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—24no—
134C22×C4—22no—
135C22×C4—42no—
136C22×C4—42no—
137C22×C4—621no—
138C22×C4—621no—
139C22×C4C4×D3112yes—
140C22×C4D12412yes—
141C22×C4C22⋊D3111yescharacteristic
142C22×C4C22×D3111yescharacteristic
143C2×C8—622no—
144C2×C8—622no—
145C2×C8—622no—
146C4⋊C4—24no—
147C4⋊C4—22no—
148C4⋊C4—312no—
149C4⋊C4—624no—
150C4⋊C4—621no—
151C4⋊C4C22⋊D3114yes—
152C22⋊C4—624no—
153C23—21no—
154C23—21no—
155C23—21no—
156C23—21no—
157C23(C2×D31)⋊C412yes—
158C23#9248012yes—
159C23#9248212yes—
160C23C2×C22⋊D3111yescharacteristic
161Q8—624no—
162Q8—1242no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—24no—
166C2×C4—24no—
167C2×C4—24no—
168C2×C4—48no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—622no—
172C2×C4—622no—
173C2×C4—1241no—
174C2×C4—1241no—
175C2×C4—1241no—
176C2×C4—1241no—
177C2×C4(C2×D31)⋊C412yes—
178C2×C4C2×C4×D3111yescharacteristic
179C2×C4C2×D12411yescharacteristic
180C2×C4#9249512yes—
181C2×C4C2×C22⋊D3112yes—
182C8—1242no—
183C22—22no—
184C22—22no—
185C22—22no—
186C22—22no—
187C22—22no—
188C22—22no—
189C22#1175839814yescomplemented
190C22C2×(C2×D31)⋊C411yescharacteristic
191C22#1175850611yescharacteristic
192C22#1175850911yescharacteristic
193C22C2×#9248011yescharacteristic
194C22#1175851911yescharacteristic
195C22C2×#9248211yescharacteristic
196C22#1175853011yescharacteristic
197C4—22no—
198C4—44no—
199C4—1242no—
200C4—1242no—
201C4C4×C22⋊D3112yes—
202C4#1175850712yes—
203C2—24no—
204C2#1452092811yescharacteristic
205C2C2×#1175839811yescharacteristic
206C2#1452104811yescharacteristic
207C2#1452120011yescharacteristic
208C2#1452120511yescharacteristic
209C2#1452137911yescharacteristic
210C2#1452138411yescharacteristic
subgroupG/H
centerC23C2×C22⋊D31
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC22×C4⋊C4×C31C2
socleC23×C31C2×D4
prime radicalC24×C31D4
cosocleC22×C4×C31C23
hypercenterC22×C4⋊C4D31
hypocenterC31#1872
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#11758398C2semidirect
4. #14520811C2semidirect
15. #11758501C4semidirect
36. C2×Dic62C2×C4semidirect
42. C4⋊Dic31C2×C4semidirect
84. C22×C31#103semidirect
125. C31#1872semidirect
189. C22#11758398semidirect

Maximal subgroups

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

subgroupindex
C2×#117585012
C2×#117583982
C2×C22⋊(C31⋊C8)2
#145208112
C22×C4⋊C4×C312
#187231