Finite Group Databasebeta

← #16848517

Subgroups — #16848517

Order 3968.

428 conjugacy classes of subgroups; only the 217 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 217 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#14520948C212yesmaximal
2#14520935C212yesmaximal
3#14520935C212yesmaximal
4#14520935C212yesmaximal
5#14520935C212yesmaximal
6#14520917C211yesmaximal, characteristic
7C4⋊C4×Dic31C212yesmaximal
8C4×C4⋊Dic31C211yesmaximal, characteristic
9C2×C31×#125C211yesmaximal, characteristic
10C31×#125C418yescomplemented
11C2×C4⋊C4×C31C2212yes—
12C2×C4⋊C4×C31C2211yescharacteristic
13C2×C4⋊C4×C31C2211yescharacteristic
14C2×C4⋊C4×C31C2212yes—
15C2×C42×C31C2211yescharacteristic
16C2×C4⋊Dic31C2212yes—
17C2×C4⋊Dic31C2212yes—
18C2×C4⋊Dic31C2212yes—
19C2×C4×Dic31C2212yes—
20C2×C4×Dic31C2211yescharacteristic
21C2×C4×Dic31C2211yescharacteristic
22C2×C4×Dic31C2212yes—
23C31⋊#95C2212yes—
24C31⋊#95C2212yes—
25C31⋊#95C2212yes—
26C31⋊#95C2211yescharacteristic
27C31⋊#95C2212yes—
28C31⋊#95C2211yescharacteristic
29C31⋊#95C2212yes—
30C31⋊#95C2212yes—
31C31⋊#95C2212yes—
32C22×C4×C31C2311yescharacteristic
33C22×C4×C31C2311yescharacteristic
34C22×C4×C31C2312yes—
35C22×C4×C31C2312yes—
36C22×C4×C31C2311yescharacteristic
37C22×Dic31C2312yes—
38C22×Dic31C2312yes—
39C22×Dic31C2312yes—
40C22×Dic31C2312yes—
41C4⋊C4×C31C2×C418yes—
42C4⋊C4×C31C2×C414yes—
43C4⋊C4×C31C2×C414yes—
44C4⋊C4×C31C2×C418yes—
45C42×C31C2×C414yes—
46C4⋊Dic31—24no—
47C4⋊Dic31—24no—
48C4⋊Dic31—42no—
49C4×Dic31—24no—
50C4×Dic31—41no—
51C4×Dic31—42no—
52C4×Dic31—41no—
53C23×C31C2411yescharacteristic
54C2×C4×C31—22no—
55C2×C4×C31—22no—
56C2×C4×C31—22no—
57C2×C4×C31—21no—
58C2×C4×C31—22no—
59C2×C4×C31—22no—
60C2×C4×C31—21no—
61C2×C4×C31—22no—
62C2×C4×C31C22×C412yes—
63C2×C4×C31C22×C412yes—
64C2×C4×C31C22×C412yes—
65C2×C4×C31C22×C414yes—
66C2×C4×C31C22×C414yes—
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×Dic31—22no—
77C2×Dic31—22no—
78C2×Dic31#4114yes—
79#2336—311nomaximal, Sylow
80C22×C31C23×C411yescharacteristic
81C22×C31C2×#4112yes—
82C22×C31H(5,𝔽2)11yescharacteristic
83C22×C312−1+412yes—
84C22×C312−1+411yescharacteristic
85C4×C31—24no—
86C4×C31—22no—
87C4×C31—22no—
88C4×C31—22no—
89C4×C31—24no—
90Dic31—24no—
91Dic31—42no—
92Dic31—42no—
93Dic31—42no—
94C2×#125D3111yescharacteristic
95#389—312no—
96#387—312no—
97#387—312no—
98#387—312no—
99#387—312no—
100#383—311no—
101C4×C4⋊C4—312no—
102C4×C4⋊C4—311no—
103C2×C31C4×#4111yescharacteristic
104C2×C31#51911yescharacteristic
105C2×C31#52011yescharacteristic
106C2×C31#53912yes—
107C2×C31#54112yes—
108#125Dic3118yescomplemented
109C2×C4⋊C4—312no—
110C2×C4⋊C4—312no—
111C2×C4⋊C4—312no—
112C2×C4⋊C4C2×D3112yes—
113C2×C4⋊C4C2×D3111yescharacteristic
114C2×C4⋊C4C2×D3111yescharacteristic
115C2×C4⋊C4C2×D3112yes—
116C2×C42—312no—
117C2×C42—311no—
118C2×C42—311no—
119C2×C42—312no—
120C2×C42C2×D3111yescharacteristic
121#95—312no—
122#95—312no—
123#95—312no—
124#95—311no—
125#95—312no—
126#95—311no—
127#95—312no—
128#95—312no—
129#95—312no—
130C31#233611yescharacteristic, complemented, Sylow
131C22×C4—312no—
132C22×C4—312no—
133C22×C4—312no—
134C22×C4—312no—
135C22×C4C22×D3111yescharacteristic
136C22×C4C22×D3111yescharacteristic
137C22×C4C22×D3112yes—
138C22×C4C22×D3112yes—
139C22×C4C22×D3111yescharacteristic
140C4⋊C4—624no—
141C4⋊C4—624no—
142C4⋊C4—1242no—
143C4⋊C4C2×Dic3118yes—
144C4⋊C4C2×Dic3114yes—
145C4⋊C4C2×Dic3114yes—
146C4⋊C4C2×Dic3118yes—
147C42—624no—
148C42—1241no—
149C42—1241no—
150C42—1242no—
151C42C2×Dic3114yes—
152C23C23×D3111yescharacteristic
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—314no—
162C2×C4—622no—
163C2×C4—622no—
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×C4C22×Dic3112yes—
174C2×C4C22×Dic3112yes—
175C2×C4C22×Dic3112yes—
176C2×C4C22×Dic3114yes—
177C2×C4C22×Dic3114yes—
178C22#1175856412yes—
179C22#41×D3112yes—
180C22#1175856611yescharacteristic
181C22#1175856711yescharacteristic
182C22C23×Dic3111yescharacteristic
183C4—24no—
184C4—22no—
185C4—22no—
186C4—22no—
187C4—24no—
188C4—624no—
189C4—1242no—
190C4—1242no—
191C4—1242no—
192C2#41×Dic3111yescharacteristic
193C2#1452152711yescharacteristic
194C2#1452153211yescharacteristic
195C2#1452164712yes—
196C2#1452165812yes—
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC2×C31×#125C2
socle, prime radical, cosocleC23×C31C24
hypercenterC2×#125D31
hypocenterC31#2336
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
10. C31×#125C4semidirect
108. #125Dic31semidirect
130. C31#2336semidirect

Maximal subgroups

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

subgroupindex
#145209482
#145209352
#145209172
C4⋊C4×Dic312
C4×C4⋊Dic312
C2×C31×#1252
#233631