Finite Group Databasebeta

← #16844040

Subgroups — #16844040

Order 3968.

312 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 81 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
1C22×Dic31⋊C4C211yesmaximal, characteristic
2#14521013C211yesmaximal, characteristic
3#14520774C214yesmaximal, complemented
4C31×#407C211yesmaximal, characteristic
5C23×C4×C31C2211yescharacteristic
6C23×Dic31C411yescharacteristic
7C23×Dic31C411yescharacteristic
8C2×M16×C31—21no—
9C2×Dic31⋊C4—21no—
10C2×Dic31⋊C4—21no—
11C2×Dic31⋊C4—21no—
12C2×Dic31⋊C4—21no—
13C2×Dic31⋊C4C412yes—
14C2×Dic31⋊C4C2212yes—
15C2×#92474—21no—
16C31×C22⋊C8—21no—
17C31×C22⋊C8C2212yes—
18C22⋊(C31⋊C8)—21no—
19C22⋊(C31⋊C8)C2212yes—
20C24×C31C2×C411yescharacteristic
21C22×C4×C31—42no—
22C22×C4×C31C2×C411yescharacteristic
23C22×C4×C31D411yescharacteristic
24C22×C4×C31D411yescharacteristic
25C22×C4×C31D411yescharacteristic
26C22×C4×C31D411yescharacteristic
27C22×C4×C31C2311yescharacteristic
28C22×Dic31—21no—
29C22×Dic31—21no—
30C22×Dic31—24no—
31C22×Dic31—21no—
32C22×Dic31—21no—
33C22×Dic31—42no—
34C22×Dic31C2×C412yes—
35C22×Dic31C2×C412yes—
36M16×C31—42no—
37C2×C8×C31—22no—
38Dic31⋊C4—22no—
39Dic31⋊C4—22no—
40Dic31⋊C4—22no—
41Dic31⋊C4—22no—
42#92474—42no—
43C2×C31⋊C8—22no—
44C23×C31—22no—
45C23×C31—22no—
46C23×C31—22no—
47C23×C31C22⋊C411yescharacteristic
48C23×C31C22⋊C411yescharacteristic
49C23×C31C22×C411yescharacteristic
50C2×C4×C31—22no—
51C2×C4×C31—22no—
52C2×C4×C31—41no—
53C2×C4×C31—41no—
54C2×C4×C31—41no—
55C2×C4×C31—41no—
56C2×C4×C31C22⋊C411yescharacteristic
57C2×C4×C31C22⋊C411yescharacteristic
58C2×C4×C31C2×D411yescharacteristic
59C2×C4×C31C2×D411yescharacteristic
60C2×Dic31—24no—
61C2×Dic31—24no—
62C2×Dic31—22no—
63C2×Dic31—22no—
64C2×Dic31—22no—
65C2×Dic31—42no—
66C2×Dic31—42no—
67C2×Dic31—42no—
68C2×Dic31M1614yescomplemented
69C8×C31—42no—
70C31⋊C8—42no—
71#1463—311nomaximal, Sylow
72C22×C31—28no—
73C22×C31—21no—
74C22×C31—21no—
75C22×C31—21no—
76C22×C31—21no—
77C22×C31—21no—
78C22×C31—21no—
79C22×C31#9912yes—
80C22×C31#10112yes—
81C22×C31C2×C22⋊C411yescharacteristic
82C22×C31C2×M1612yes—
83C4×C31—21no—
84C4×C31—21no—
85C4×C31—21no—
86C4×C31—21no—
87Dic31—24no—
88Dic31—42no—
89C22×C4⋊C4—311no—
90#407—311no—
91#407D3111yescharacteristic
92#324—314no—
93C2×C31—22no—
94C2×C31—22no—
95C2×C31—22no—
96C2×C31#40711yescharacteristic
97C2×C31C2×#9911yescharacteristic
98C2×C31C2×#10111yescharacteristic
99C23×C4—311no—
100C23×C4—311no—
101C23×C4C2×D3111yescharacteristic
102C2×M16—21no—
103C2×M16—621no—
104C2×C4⋊C4—312no—
105C2×C4⋊C4—312no—
106C2×C4⋊C4—621no—
107C2×C4⋊C4—621no—
108C2×C4⋊C4—621no—
109C2×C4⋊C4—621no—
110C22⋊C8—21no—
111C22⋊C8—312no—
112C22⋊C8—621no—
113C22⋊C8C2×D3112yes—
114C31#146311yescharacteristic, complemented, Sylow
115C24C4×D3111yescharacteristic
116C22×C4—42no—
117C22×C4—312no—
118C22×C4—312no—
119C22×C4—624no—
120C22×C4—621no—
121C22×C4—621no—
122C22×C4—621no—
123C22×C4—621no—
124C22×C4—1242no—
125C22×C4C4×D3111yescharacteristic
126C22×C4D12411yescharacteristic
127C22×C4D12411yescharacteristic
128C22×C4C22⋊D3111yescharacteristic
129C22×C4C22⋊D3111yescharacteristic
130C22×C4C22×D3111yescharacteristic
131M16—42no—
132M16—1242no—
133C2×C8—22no—
134C2×C8—622no—
135C4⋊C4—622no—
136C4⋊C4—622no—
137C4⋊C4—622no—
138C4⋊C4—622no—
139C23—22no—
140C23—22no—
141C23—22no—
142C23(C2×D31)⋊C411yescharacteristic
143C23(C2×D31)⋊C411yescharacteristic
144C23C2×C4×D3111yescharacteristic
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—314no—
152C2×C4—624no—
153C2×C4—624no—
154C2×C4—622no—
155C2×C4—622no—
156C2×C4—622no—
157C2×C4—1242no—
158C2×C4—1242no—
159C2×C4—1242no—
160C2×C4(C2×D31)⋊C411yescharacteristic
161C2×C4(C2×D31)⋊C411yescharacteristic
162C2×C4C2×D12411yescharacteristic
163C2×C4C2×C22⋊D3111yescharacteristic
164C8—42no—
165C8—1242no—
166C22—28no—
167C22—21no—
168C22—21no—
169C22—21no—
170C22—21no—
171C22—21no—
172C22—21no—
173C22#1175839412yes—
174C22#1175841212yes—
175C22M16×D3112yes—
176C22C2×(C2×D31)⋊C411yescharacteristic
177C4—21no—
178C4—21no—
179C4—21no—
180C4—21no—
181C4—624no—
182C4—1242no—
183C2—22no—
184C2—22no—
185C2—22no—
186C2#1452101211yescharacteristic
187C2C2×#1175839411yescharacteristic
188C2C2×#1175841211yescharacteristic
subgroupG/H
centerC22C2×(C2×D31)⋊C4
commutatorC23×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#407C2
socleC22×C31C2×C22⋊C4
prime radicalC24×C31C2×C4
cosocleC22×C4×C31C23
hypercenter#407D31
hypocenterC31#1463
LCSG ▷ C23×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
3. #14520774C2semidirect
68. C2×Dic31M16semidirect
114. C31#1463semidirect

Maximal subgroups

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

subgroupindex
C22×Dic31⋊C42
#145210132
#145207742
C31×#4072
#146331