Finite Group Databasebeta

← #16844050

Subgroups — #16844050

Order 3968.

300 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 69 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×(C22⋊D31)⋊C4C211yesmaximal, characteristic
2#14521103C212yesmaximal, complemented
3#14520773C211yesmaximal, characteristic, complemented
4#14520772C212yesmaximal, complemented
5C31×#323C211yesmaximal, characteristic, complemented
6C22×C22⋊D31C411yescharacteristic
7C23×Dic31C411yescharacteristic
8C22×C4×D31C411yescharacteristic
9C2×C22⋊C4×C31C2211yescharacteristic
10C2×(C2×D31)⋊C4C2211yescharacteristic
11C2×Dic31⋊C4C411yescharacteristic
12C2×C4×Dic31C2211yescharacteristic
13(C22⋊D31)⋊C4—22no—
14(C22⋊D31)⋊C4—22no—
15C31×C22⋊C8C2212yes—
16C22⋊(C31⋊C8)C2212yes—
17#11758403—22no—
18Dic31⋊C8—22no—
19C24×C31C2×C411yescharacteristic
20C23×D31C2×C411yescharacteristic
21C22×C4×C31C2×C411yescharacteristic
22C22×C4×C31C2311yescharacteristic
23C2×C22⋊D31—22no—
24C2×C22⋊D31—22no—
25C2×C22⋊D31—22no—
26C22×Dic31—21no—
27C22×Dic31—21no—
28C22×Dic31—42no—
29C22×Dic31C2×C411yescharacteristic
30C22×Dic31C2×C411yescharacteristic
31C22×Dic31C2×C411yescharacteristic
32C2×C4×D31—21no—
33C2×C4×D31—21no—
34C2×C4×D31—42no—
35C2×C8×C31—22no—
36C22⋊C4×C31—22no—
37(C2×D31)⋊C4—22no—
38Dic31⋊C4—22no—
39C4×Dic31D412yes—
40C4×Dic31D412yes—
41C2×C31⋊C8—22no—
42C23×C31—21no—
43C23×C31—21no—
44C23×C31—41no—
45C23×C31—41no—
46C23×C31M1612yes—
47C23×C31C22×C411yescharacteristic
48C22×D31—21no—
49C22×D31—21no—
50C22×D31—41no—
51C22×D31—41no—
52C22×D31M1612yes—
53C2×C4×C31—21no—
54C2×C4×C31—41no—
55C2×C4×C31—41no—
56C2×C4×C31C2×D412yes—
57C22⋊D31—28no—
58C2×Dic31—21no—
59C2×Dic31—21no—
60C2×Dic31—22no—
61C2×Dic31—21no—
62C2×Dic31—42no—
63C2×Dic31—42no—
64C2×Dic31—41no—
65C2×Dic31C22⋊C412yes—
66C2×Dic31C22⋊C411yescharacteristic
67C2×Dic31C22⋊C411yescharacteristic
68C4×D31—42no—
69C4×D31—42no—
70C8×C31—42no—
71C31⋊C8—42no—
72#1466—311nomaximal, Sylow
73C22×C31—21no—
74C22×C31—21no—
75C22×C31—22no—
76C22×C31—42no—
77C22×C31—42no—
78C22×C31—41no—
79C22×C31—41no—
80C22×C31C2×C22⋊C411yescharacteristic
81C22×C31C2×M1611yescharacteristic
82C22×C31C2×M1611yescharacteristic
83C2×D31—22no—
84C2×D31—42no—
85C2×D31—41no—
86C2×D31—41no—
87C2×D31—42no—
88C4×C31—22no—
89C4×C31—41no—
90Dic31—22no—
91Dic31—21no—
92Dic31—41no—
93Dic31#10012yes—
94C2×C4×D4—311no—
95#432—312no—
96#323—311no—
97#323—312no—
98#323D3111yescharacteristic, complemented
99C2×C31—21no—
100C2×C31—21no—
101C2×C31—42no—
102C2×C31#40711yescharacteristic
103C2×C31#41011yescharacteristic
104C2×C31C2×#10011yescharacteristic
105D31—42no—
106C22×D4—311no—
107C23×C4—311no—
108C23×C4—311no—
109C4×D4—622no—
110C4×D4—622no—
111C2×C4⋊C4—311no—
112C2×C22⋊C4—311no—
113C2×C22⋊C4C2×D3111yescharacteristic
114C2×C42—311no—
115C4⋊C8—622no—
116C22⋊C8—312no—
117C22⋊C8C2×D3112yes—
118#97—622no—
119C31#146611yescharacteristic, complemented, Sylow
120C24—311no—
121C24C4×D3111yescharacteristic
122C2×D4—622no—
123C2×D4—622no—
124C2×D4—622no—
125C22×C4—311no—
126C22×C4—311no—
127C22×C4—311no—
128C22×C4—621no—
129C22×C4—621no—
130C22×C4—621no—
131C22×C4—621no—
132C22×C4—1242no—
133C22×C4—1242no—
134C22×C4C4×D3111yescharacteristic
135C22×C4C22×D3111yescharacteristic
136C2×C8—22no—
137C2×C8—622no—
138C4⋊C4—622no—
139C22⋊C4—22no—
140C22⋊C4—622no—
141C42—312no—
142C42—312no—
143C23—21no—
144C23—21no—
145C23—41no—
146C23—41no—
147C23—312no—
148C23—621no—
149C23—621no—
150C23—1241no—
151C23—1241no—
152C23#9246912yes—
153C23C2×C4×D3111yescharacteristic
154D4—628no—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—311no—
159C2×C4—312no—
160C2×C4—311no—
161C2×C4—622no—
162C2×C4—621no—
163C2×C4—621no—
164C2×C4—621no—
165C2×C4—1242no—
166C2×C4—1242no—
167C2×C4—1242no—
168C2×C4—1242no—
169C2×C4—1241no—
170C2×C4D4×D3112yes—
171C8—42no—
172C8—1242no—
173C22—21no—
174C22—21no—
175C22—22no—
176C22—42no—
177C22—42no—
178C22—41no—
179C22—41no—
180C22—622no—
181C22—1242no—
182C22—1242no—
183C22—1241no—
184C22—1241no—
185C22C22⋊C4×D3111yescharacteristic
186C22C2×#9246911yescharacteristic
187C22M16×D3111yescharacteristic
188C4—22no—
189C4—41no—
190C4—312no—
191C4—622no—
192C4—621no—
193C4—1241no—
194C2—21no—
195C2—21no—
196C2—42no—
197C2—1242no—
198C2#1452101111yescharacteristic
199C2#1452102111yescharacteristic
200C2#100×D3111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D31
commutatorC23×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#323C2
socleC22×C31C2×C22⋊C4
prime radicalC22×C22⋊D31C4
cosocleC22×C4×C31C23
hypercenter#323D31
hypocenterC31#1466
LCSG ▷ C23×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #14521103C2semidirect
3. #14520773C2semidirect
4. #14520772C2semidirect
5. C31×#323C2semidirect
98. #323D31semidirect
119. C31#1466semidirect

Maximal subgroups

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

subgroupindex
C2×(C22⋊D31)⋊C42
#145211032
#145207732
#145207722
C31×#3232
#146631