Finite Group Databasebeta

← #16848102

Subgroups — #16848102

Order 3968.

568 conjugacy classes of subgroups; only the 205 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 205 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×C4×Dic31C211yesmaximal, characteristic
2#14520916C212yesmaximal, complemented
3#14520913C212yesmaximal, complemented
4#14520912C211yesmaximal, characteristic
5#14520907C212yesmaximal
6#14520900C212yesmaximal, complemented
7C22⋊C4×Dic31C212yesmaximal
8#14520894C212yesmaximal, complemented
9C31×#381C211yesmaximal, characteristic
10C23×C4×C31C2211yescharacteristic
11C23×Dic31C2211yescharacteristic
12C23×Dic31C2211yescharacteristic
13C2×C22⋊C4×C31C2212yes—
14C2×C22⋊Dic31C2212yes—
15C2×Dic31⋊C4C2214yes—
16C2×C4×Dic31C418yescomplemented
17C2×C4×Dic31C2214yes—
18C2×C4×Dic31C2211yescharacteristic
19C2×C4×Dic31C2211yescharacteristic
20C2×C4×Dic31C2211yescharacteristic
21C2×C4×Dic31C2211yescharacteristic
22C31×#95C2212yes—
23C31×#95C2212yes—
24C31⋊#95C2214yes—
25C31⋊#95C2212yes—
26C31⋊#95C2214yes—
27C31⋊#95C2212yes—
28C24×C31C2311yescharacteristic
29C22×C4×C31—24no—
30C22×C4×C31C2×C414yes—
31C22×C4×C31C2314yes—
32C22×C4×C31C2311yescharacteristic
33C22×C4×C31C2311yescharacteristic
34C22×Dic31—24no—
35C22×Dic31—24no—
36C22×Dic31C2×C414yes—
37C22×Dic31C2×C414yes—
38C22×Dic31C2314yes—
39C22×Dic31C2311yescharacteristic
40C22×Dic31C2311yescharacteristic
41C22×Dic31C2311yescharacteristic
42C22×Dic31C2311yescharacteristic
43C22⋊C4×C31—24no—
44C22⋊Dic31—24no—
45Dic31⋊C4—28no—
46C4×Dic31—28no—
47C4×Dic31C2×C414yes—
48C4×Dic31C2×C414yes—
49C4×Dic31C2×C414yes—
50C4×Dic31C2×C414yes—
51C23×C31—22no—
52C23×C31—22no—
53C23×C31C22×C412yes—
54C23×C31#4114yes—
55C23×C31C2411yescharacteristic
56C2×C4×C31—28no—
57C2×C4×C31—22no—
58C2×C4×C31—22no—
59C2×C4×C31—24no—
60C2×C4×C31—24no—
61C2×C4×C31—24no—
62C2×C4×C31C22×C412yes—
63C2×C4×C31C22×C412yes—
64C2×Dic31—22no—
65C2×Dic31—22no—
66C2×Dic31—28no—
67C2×Dic31—28no—
68C2×Dic31—24no—
69C2×Dic31—24no—
70C2×Dic31—24no—
71C2×Dic31C22×C412yes—
72C2×Dic31C22×C412yes—
73C2×Dic31C22×C412yes—
74C2×Dic31C22×C412yes—
75C2×Dic31#4114yes—
76C2×Dic31#4114yes—
77#2283—311nomaximal, Sylow
78C22×C31—22no—
79C22×C31—22no—
80C22×C31—28no—
81C22×C31#11714yes—
82C22×C31C23×C411yescharacteristic
83C22×C31C2×#4112yes—
84C22×C31C2×#4112yes—
85C22×C31C2×#4112yes—
86C4×C31—22no—
87C4×C31—22no—
88C4×C31—44no—
89Dic31—22no—
90Dic31—22no—
91Dic31—44no—
92Dic31#11714yes—
93Dic31#11714yes—
94C22×C42—311no—
95#383—312no—
96#382—312no—
97#381—311no—
98#381D3111yescharacteristic
99#380—312no—
100C4×C4⋊C4—312no—
101C4×C22⋊C4—312no—
102#376—312no—
103C2×C31—24no—
104C2×C31C2×#11711yescharacteristic
105C2×C31C2×#11711yescharacteristic
106C2×C31C2×#11711yescharacteristic
107C2×C31#52914yes—
108C23×C4—311no—
109C23×C4—311no—
110C23×C4C2×D3111yescharacteristic
111C2×C4⋊C4—314no—
112C2×C22⋊C4—312no—
113C2×C22⋊C4C2×D3112yes—
114C2×C42—318no—
115C2×C42—311no—
116C2×C42—311no—
117C2×C42—311no—
118C2×C42—311no—
119C2×C42—314no—
120#95—314no—
121#95—312no—
122#95—314no—
123#95—312no—
124#95C2×D3112yes—
125#95C2×D3112yes—
126C31#228311yescharacteristic, complemented, Sylow
127C24C22×D3111yescharacteristic
128C22×C4—24no—
129C22×C4—311no—
130C22×C4—311no—
131C22×C4—314no—
132C22×C4—314no—
133C22×C4—311no—
134C22×C4—311no—
135C22×C4—314no—
136C22×C4—624no—
137C22×C4—624no—
138C22×C4C4×D3114yes—
139C22×C4C22×D3114yes—
140C22×C4C22×D3111yescharacteristic
141C22×C4C22×D3111yescharacteristic
142C4⋊C4—628no—
143C22⋊C4—24no—
144C22⋊C4—624no—
145C42—314no—
146C42—314no—
147C42—314no—
148C42—314no—
149C42—628no—
150C23—22no—
151C23—22no—
152C23C2×C4×D3112yes—
153C23#9249714yes—
154C23C23×D3111yescharacteristic
155C2×C4—28no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—24no—
159C2×C4—24no—
160C2×C4—24no—
161C2×C4—312no—
162C2×C4—312no—
163C2×C4—314no—
164C2×C4—314no—
165C2×C4—312no—
166C2×C4—312no—
167C2×C4—628no—
168C2×C4—628no—
169C2×C4—622no—
170C2×C4—622no—
171C2×C4—624no—
172C2×C4—624no—
173C2×C4—624no—
174C2×C4C2×C4×D3112yes—
175C2×C4C2×C4×D3112yes—
176C22—22no—
177C22—22no—
178C22—28no—
179C22#1175845414yes—
180C22C22×C4×D3111yescharacteristic
181C22C2×#9249712yes—
182C22#41×D3112yes—
183C22#41×D3112yes—
184C4—22no—
185C4—22no—
186C4—44no—
187C4—314no—
188C4—314no—
189C4—622no—
190C4—622no—
191C4—1244no—
192C2—24no—
193C2#117×D3111yescharacteristic
194C2#117×D3111yescharacteristic
195C2C2×#1175845411yescharacteristic
196C2#1452157614yes—
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC31×#381C2
socle, cosocleC23×C31C24
prime radicalC24×C31C23
hypercenter#381D31
hypocenterC31#2283
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. #14520916C2semidirect
3. #14520913C2semidirect
6. #14520900C2semidirect
8. #14520894C2semidirect
16. C2×C4×Dic31C4semidirect
126. C31#2283semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic312
#145209162
#145209132
#145209122
#145209072
#145209002
C22⋊C4×Dic312
#145208942
C31×#3812
#228331