Finite Group Databasebeta

← #16846122

Subgroups — #16846122

Order 3968.

386 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 89 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×#11758512C211yesmaximal, characteristic
2#14521524C211yesmaximal, characteristic
3#14520910C212yesmaximal, complemented
4#14520815C212yesmaximal, complemented
5C2×C31×#99C211yesmaximal, characteristic
6C22×D4×C31C2211yescharacteristic
7C23×Dic31C2211yescharacteristic
8C2×C22⋊C4×C31C2212yes—
9C2×C22⋊Dic31—21no—
10C2×C22⋊Dic31—21no—
11C2×C22⋊Dic31C2212yes—
12C2×C22⋊Dic31C2211yescharacteristic
13#11758512—22no—
14#11758512C414yescomplemented
15D4×Dic31—24no—
16#11758503—21no—
17C2×Dic31⋊C4—21no—
18C31×#99—22no—
19C31⋊#95—24no—
20C24×C31D411yescharacteristic
21C24×C31C2311yescharacteristic
22C2×D4×C31—22no—
23C2×D4×C31—22no—
24C2×D4×C31C2×C412yes—
25C2×D4×C31D412yes—
26C22×C4×C31—22no—
27C22×C4×C31D411yescharacteristic
28C22×Dic31—22no—
29C22×Dic31—21no—
30C22×Dic31—21no—
31C22×Dic31—21no—
32C22×Dic31—22no—
33C22×Dic31—22no—
34C22×Dic31C2×C412yescomplemented
35C22×Dic31D414yes—
36C22⋊C4×C31—22no—
37C22⋊C4×C31—22no—
38C22⋊Dic31—22no—
39C22⋊Dic31—24no—
40C22⋊Dic31—22no—
41C22⋊Dic31—22no—
42C22⋊Dic31—21no—
43C22⋊Dic31C2×C412yescomplemented
44C4⋊Dic31—22no—
45Dic31⋊C4—24no—
46C4×Dic31—22no—
47C23×C31—21no—
48C23×C31—21no—
49C23×C31—42no—
50C23×C31—42no—
51C23×C31C22⋊C412yes—
52C23×C31C22×C411yescharacteristic
53C23×C31C2×D411yescharacteristic
54C23×C31C2×D412yes—
55C23×C31C2×D411yescharacteristic
56C23×C31#4112yes—
57D4×C31—24no—
58D4×C31—24no—
59C2×C4×C31—21no—
60C2×C4×C31—21no—
61C2×C4×C31—44no—
62C2×C4×C31—42no—
63C2×C4×C31C22⋊C412yes—
64C2×Dic31—22no—
65C2×Dic31—22no—
66C2×Dic31—24no—
67C2×Dic31—24no—
68C2×Dic31—42no—
69C2×Dic31—41no—
70C2×Dic31—42no—
71C2×Dic31—41no—
72C2×Dic31—44no—
73C2×Dic31—82no—
74#1890—311nomaximal, Sylow
75C22×C31—24no—
76C22×C31—22no—
77C22×C31—22no—
78C22×C31—41no—
79C22×C31—41no—
80C22×C31—42no—
81C22×C31—42no—
82C22×C31—42no—
83C22×C31—81no—
84C22×C31C2×C22⋊C411yescharacteristic
85C22×C31C4×D412yes—
86C22×C31#12011yescharacteristic
87C22×C31#12112yes—
88C22×C31#12311yescharacteristic
89C4×C31—22no—
90C4×C31—82no—
91Dic31—42no—
92Dic31—42no—
93Dic31—44no—
94C2×#123—311no—
95#518—311no—
96C2×#99D3111yescharacteristic
97#381—312no—
98#342—312no—
99C2×C31—21no—
100C2×C31—22no—
101C2×C31—21no—
102C2×C31—22no—
103C2×C31—42no—
104C2×C31#38611yescharacteristic
105C2×C31#45812yes—
106C22×D4C2×D3111yescharacteristic
107C23×C4—311no—
108#123—314no—
109#123—622no—
110C4×D4—624no—
111#117—621no—
112C2×C4⋊C4—621no—
113C2×C22⋊C4—311no—
114C2×C22⋊C4—312no—
115C2×C22⋊C4—621no—
116C2×C22⋊C4—621no—
117C2×C22⋊C4C2×D3112yes—
118#99—22no—
119#95—624no—
120C31#189011yescharacteristic, complemented, Sylow
121C24D12411yescharacteristic
122C24C22×D3111yescharacteristic
123C2×D4—22no—
124C2×D4—22no—
125C2×D4C4×D3112yes—
126C2×D4C22⋊D3112yes—
127C22×C4—22no—
128C22×C4—312no—
129C22×C4—314no—
130C22×C4—621no—
131C22×C4—621no—
132C22×C4—622no—
133C22×C4—622no—
134C22×C4—621no—
135C22×C4—622no—
136C22×C4D12411yescharacteristic
137C4⋊C4—622no—
138C4⋊C4—624no—
139C22⋊C4—22no—
140C22⋊C4—22no—
141C22⋊C4—312no—
142C22⋊C4—622no—
143C22⋊C4—624no—
144C22⋊C4—622no—
145C22⋊C4—622no—
146C22⋊C4—621no—
147C42—622no—
148C23—21no—
149C23—21no—
150C23—42no—
151C23—42no—
152C23(C2×D31)⋊C412yes—
153C23C2×C4×D3111yescharacteristic
154C23C2×D12411yescharacteristic
155C23D4×D3112yes—
156C23#9249712yes—
157C23C2×C22⋊D3111yescharacteristic
158D4—24no—
159D4—24no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—44no—
163C2×C4—42no—
164C2×C4—624no—
165C2×C4—624no—
166C2×C4—622no—
167C2×C4—622no—
168C2×C4—1242no—
169C2×C4—1241no—
170C2×C4—1241no—
171C2×C4—1242no—
172C2×C4—1244no—
173C2×C4—2482no—
174C2×C4(C2×D31)⋊C412yes—
175C22—24no—
176C22—22no—
177C22—22no—
178C22—41no—
179C22—42no—
180C22—41no—
181C22—42no—
182C22—42no—
183C22—81no—
184C22(C22⋊D31)⋊C412yes—
185C22#1175845911yescharacteristic
186C22#1175846311yescharacteristic
187C22C2×(C2×D31)⋊C411yescharacteristic
188C22#1175851612yes—
189C4—22no—
190C4—82no—
191C4—1242no—
192C4—1242no—
193C4—1244no—
194C2—22no—
195C2—21no—
196C2—21no—
197C2—22no—
198C2—42no—
199C2#1452092611yescharacteristic
200C2#1452124012yes—
subgroupG/H
centerC22#11758459
commutatorC23×C31C22×C4
FrattiniC24C22×D31
FittingC2×C31×#99C2
socleC22×C31#120
prime radicalC22×D4×C31C22
cosocleC24×C31C23
hypercenterC2×#99D31
hypocenterC31#1890
LCSG ▷ C23×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
3. #14520910C2semidirect
4. #14520815C2semidirect
14. #11758512C4semidirect
34. C22×Dic31C2×C4semidirect
43. C22⋊Dic31C2×C4semidirect
120. C31#1890semidirect

Maximal subgroups

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

subgroupindex
C2×#117585122
#145215242
#145209102
#145208152
C2×C31×#992
#189031