Finite Group Databasebeta

← #16853981

Subgroups — #16853981

Order 3968.

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

normal subgroups only

This group has 348 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
1#14520990C212yesmaximal
2#14520983C212yesmaximal
3#14520981C212yesmaximal
4#14520979C212yesmaximal
5#14520970C212yesmaximal
6#14520969C211yesmaximal, characteristic
7#14520918C211yesmaximal, characteristic
8#14520916C212yesmaximal
9C31×#400C211yesmaximal, characteristic
10C22×Dic62C2211yescharacteristic
11C2×C4⋊C4×C31C2211yescharacteristic
12C2×C4⋊C4×C31C2211yescharacteristic
13C2×C4⋊Dic31C2211yescharacteristic
14C2×C4⋊Dic31C2212yes—
15C2×C4⋊Dic31C2212yes—
16C2×Dic31⋊C4C2212yes—
17C2×Dic31⋊C4C2212yes—
18C2×Dic31⋊C4C2212yes—
19C2×Dic31⋊C4C2212yes—
20C2×C4×Dic31C2211yescharacteristic
21C31×#95C2212yes—
22C31×#95C2212yes—
23C31×#95C2211yescharacteristic
24C31⋊#95C2212yes—
25C31⋊#95C2212yes—
26C31⋊#95C2212yes—
27C31⋊#95C2212yes—
28C31⋊#95C2212yes—
29C31⋊#95C2211yescharacteristic
30C31⋊#95C2212yes—
31C22×C4×C31C2312yes—
32C22×C4×C31C2312yes—
33C22×C4×C31C2311yescharacteristic
34C22×C4×C31C2311yescharacteristic
35C22×C4×C31C2311yescharacteristic
36C22×Dic31C2312yes—
37C22×Dic31C2312yes—
38C22×Dic31C2312yes—
39C22×Dic31C2312yes—
40C2×Dic62—42no—
41C2×Dic62—41no—
42C4⋊C4×C31—41no—
43C4⋊C4×C31—41no—
44C4⋊Dic31—42no—
45C4⋊Dic31—41no—
46C4⋊Dic31—42no—
47Dic31⋊C4—42no—
48Dic31⋊C4—42no—
49Dic31⋊C4—42no—
50Dic31⋊C4—42no—
51C4×Dic31Q814yescomplemented
52C23×C31C2411yescharacteristic
53C2×C4×C31—21no—
54C2×C4×C31—21no—
55C2×C4×C31—22no—
56C2×C4×C31—22no—
57C2×C4×C31—22no—
58C2×C4×C31—22no—
59C2×C4×C31—21no—
60C2×C4×C31—21no—
61C2×C4×C31—24no—
62C2×C4×C31—22no—
63C2×C4×C31—22no—
64C2×C4×C31C2×Q812yes—
65C2×Dic31—22no—
66C2×Dic31—22no—
67C2×Dic31—22no—
68C2×Dic31—22no—
69C2×Dic31—22no—
70C2×Dic31—22no—
71C2×Dic31—22no—
72C2×Dic31—22no—
73C2×Dic31—22no—
74C2×Dic31—22no—
75C2×Dic31—22no—
76C2×Dic31C2×Q814yes—
77Dic62—44no—
78#2843—311nomaximal, Sylow
79C22×C31C22×Q811yescharacteristic
80C22×C31H(5,𝔽2)11yescharacteristic
81C22×C31H(5,𝔽2)12yes—
82C22×C312−1+411yescharacteristic
83C22×C312−1+412yes—
84C4×C31—22no—
85C4×C31—41no—
86C4×C31—41no—
87C4×C31—42no—
88C4×C31—42no—
89Dic31—24no—
90Dic31—42no—
91Dic31—42no—
92Dic31—42no—
93#400—312no—
94#400D3111yescharacteristic
95#398—312no—
96#398—312no—
97#398—312no—
98#395—311no—
99#395—312no—
100#384—311no—
101#383—312no—
102C2×C31#54411yescharacteristic
103C2×C31#54412yes—
104C2×C31#56011yescharacteristic
105C2×C31#56311yescharacteristic
106C2×C31#56312yes—
107C22×Q8—311no—
108C2×C4⋊C4—312no—
109C2×C4⋊C4—312no—
110C2×C4⋊C4—311no—
111C2×C4⋊C4—312no—
112C2×C4⋊C4—312no—
113C2×C4⋊C4—312no—
114C2×C4⋊C4—312no—
115C2×C4⋊C4C2×D3111yescharacteristic
116C2×C4⋊C4C2×D3111yescharacteristic
117C2×C42—311no—
118#95—312no—
119#95—312no—
120#95—312no—
121#95—312no—
122#95—312no—
123#95—311no—
124#95—312no—
125#95C2×D3112yes—
126#95C2×D3112yes—
127#95C2×D3111yescharacteristic
128C31#284311yescharacteristic, complemented, Sylow
129C2×Q8—1241no—
130C2×Q8—1242no—
131C22×C4—312no—
132C22×C4—312no—
133C22×C4—312no—
134C22×C4—312no—
135C22×C4C22×D3112yes—
136C22×C4C22×D3112yes—
137C22×C4C22×D3111yescharacteristic
138C22×C4C22×D3111yescharacteristic
139C22×C4C22×D3111yescharacteristic
140C4⋊C4—41no—
141C4⋊C4—41no—
142C4⋊C4—1242no—
143C4⋊C4—1242no—
144C4⋊C4—1242no—
145C4⋊C4—1242no—
146C4⋊C4—1241no—
147C4⋊C4—1242no—
148C4⋊C4—1242no—
149C42—314no—
150C23C23×D3111yescharacteristic
151Q8—1244no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—24no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—314no—
164C2×C4—622no—
165C2×C4—622no—
166C2×C4—622no—
167C2×C4—622no—
168C2×C4—622no—
169C2×C4—622no—
170C2×C4—622no—
171C2×C4—622no—
172C2×C4—622no—
173C2×C4—622no—
174C2×C4—622no—
175C2×C4Q8×D3112yes—
176C22#1175856111yescharacteristic
177C22C2×Q8×D3111yescharacteristic
178C22#1175856612yes—
179C22#1175856711yescharacteristic
180C22#1175856712yes—
181C4—22no—
182C4—41no—
183C4—41no—
184C4—42no—
185C4—42no—
186C4—624no—
187C4—1242no—
188C4—1242no—
189C4—1242no—
190C2#1452167811yescharacteristic
191C2#1452167912yes—
192C2#1452178911yescharacteristic
193C2#1452179911yescharacteristic
194C2#1452180112yes—
subgroupG/H
center, FrattiniC23C23×D31
commutator, socle, prime radical, cosocleC23×C31C24
FittingC31×#400C2
hypercenter#400D31
hypocenterC31#2843
LCSG ▷ C23×C31 ▷ C31
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
51. C4×Dic31Q8semidirect
128. C31#2843semidirect

Maximal subgroups

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

subgroupindex
#145209902
#145209832
#145209812
#145209792
#145209702
#145209692
#145209182
#145209162
C31×#4002
#284331