Finite Group Databasebeta

← #16845620

Subgroups — #16845620

Order 3968.

852 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 852 conjugacy classes of subgroups — too many to draw. Only its 153 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
1C23×C4×D31C211yesmaximal, characteristic
2C2×C22⋊(C31⋊C8)C211yesmaximal, characteristic, complemented
3C2×(C2×D31)⋊C8C214yesmaximal, complemented
4C2×C31×C22⋊C8C211yesmaximal, characteristic, complemented
5C24×D31C411yescharacteristic
6C23×C4×C31C2211yescharacteristic
7C23×Dic31C411yescharacteristic
8C22×C4×D31—22no—
9C22×C4×D31—22no—
10C22×C4×D31—28no—
11C22×C4×D31C412yes—
12C22×C4×D31C2212yes—
13C22×C8×C31C2212yescomplemented
14C22×C31⋊C8C2212yescomplemented
15C31×C22⋊C8—22no—
16C22⋊(C31⋊C8)—22no—
17(C2×D31)⋊C8—28no—
18C24×C31C2×C411yescharacteristic
19C23×D31—22no—
20C23×D31—22no—
21C23×D31—24no—
22C23×D31—24no—
23C23×D31C814yescomplemented
24C23×D31C2×C412yes—
25C22×C4×C31—24no—
26C22×C4×C31C2×C411yescharacteristic
27C22×C4×C31D412yes—
28C22×C4×C31D412yes—
29C22×C4×C31C2311yescharacteristic
30C22×Dic31—22no—
31C22×Dic31—24no—
32C22×Dic31C2×C412yes—
33C2×C4×D31—216no—
34C2×C4×D31—216no—
35C2×C4×D31—24no—
36C2×C4×D31—24no—
37C2×C4×D31—22no—
38C2×C4×D31—24no—
39C2×C4×D31—22no—
40C2×C4×D31—24no—
41C2×C4×D31D418yes—
42C2×C8×C31—24no—
43C2×C8×C31—22no—
44C2×C31⋊C8—24no—
45C2×C31⋊C8—22no—
46C23×C31—22no—
47C23×C31—22no—
48C23×C31C22⋊C412yes—
49C23×C31C2×C812yes—
50C23×C31M1612yes—
51C23×C31C22×C411yescharacteristic
52C22×D31—28no—
53C22×D31—216no—
54C22×D31—28no—
55C22×D31—28no—
56C22×D31—22no—
57C22×D31—22no—
58C22×D31—22no—
59C22×D31—22no—
60C22×D31—216no—
61C22×D31C22⋊C414yes—
62C22×D31C2×C814yes—
63C22×D31M1614yes—
64C2×C4×C31—22no—
65C2×C4×C31—24no—
66C2×C4×C31—24no—
67C2×C4×C31C22⋊C412yes—
68C2×C4×C31C2×D411yescharacteristic
69C2×C4×C31C2×D414yes—
70C2×C4×C31C2×D411yescharacteristic
71C2×Dic31—28no—
72C2×Dic31—22no—
73C2×Dic31—22no—
74C2×Dic31C22⋊C414yes—
75C4×D31—216no—
76C4×D31—28no—
77C4×D31—28no—
78C8×C31—42no—
79C31⋊C8—42no—
80#1779—311nomaximal, Sylow
81C22×C31—22no—
82C22×C31—24no—
83C22×C31—22no—
84C22×C31—24no—
85C22×C31C22⋊C814yescomplemented
86C22×C31C2×C22⋊C412yes—
87C22×C31C2×C22⋊C411yescharacteristic
88C22×C31C22×C811yescharacteristic
89C22×C31C2×M1611yescharacteristic
90C22×C31C2×M1612yes—
91C2×D31—232no—
92C2×D31—24no—
93C2×D31—24no—
94C2×D31—24no—
95C2×D31—24no—
96C2×D31—24no—
97C2×D31—24no—
98C2×D31C22⋊C818yescomplemented
99C4×C31—22no—
100C4×C31#12012yes—
101C4×C31#12012yes—
102Dic31—24no—
103C24×C4—311no—
104C2×C22⋊C8—311no—
105C2×C22⋊C8—314no—
106C2×C22⋊C8D3111yescharacteristic, complemented
107C2×C31—24no—
108C2×C31#37911yescharacteristic
109C2×C31C2×C22⋊C812yes—
110C2×C31C2×C22⋊C811yescharacteristic
111C2×C31#40712yes—
112C2×C31#40711yescharacteristic
113D31—28no—
114C25—311no—
115C23×C4—312no—
116C23×C4—311no—
117C23×C4—312no—
118C23×C4—628no—
119C23×C4—622no—
120C23×C4—622no—
121C23×C4C2×D3111yescharacteristic
122C22×C8—312no—
123C22×C8C2×D3112yescomplemented
124C22⋊C8—22no—
125C22⋊C8—628no—
126C22⋊C8—622no—
127C31#177911yescharacteristic, complemented, Sylow
128C24—312no—
129C24—314no—
130C24—624no—
131C24—624no—
132C24—622no—
133C24—622no—
134C24C4×D3111yescharacteristic
135C22×C4—24no—
136C22×C4—312no—
137C22×C4—318no—
138C22×C4—624no—
139C22×C4—624no—
140C22×C4—6216no—
141C22×C4—6216no—
142C22×C4—624no—
143C22×C4—622no—
144C22×C4—624no—
145C22×C4—622no—
146C22×C4—624no—
147C22×C4—622no—
148C22×C4C4×D3111yescharacteristic
149C22×C4D12412yes—
150C22×C4C22⋊D3112yes—
151C22×C4C22×D3111yescharacteristic
152C2×C8—24no—
153C2×C8—22no—
154C2×C8—622no—
155C2×C8—624no—
156C23—22no—
157C23—22no—
158C23—314no—
159C23—314no—
160C23—314no—
161C23—6216no—
162C23—628no—
163C23—6216no—
164C23—628no—
165C23—628no—
166C23—622no—
167C23—622no—
168C23—622no—
169C23—622no—
170C23C8×D3112yes—
171C23#9246912yes—
172C23(C2×D31)⋊C412yes—
173C23C2×C4×D3111yescharacteristic
174C2×C4—22no—
175C2×C4—24no—
176C2×C4—24no—
177C2×C4—314no—
178C2×C4—6216no—
179C2×C4—628no—
180C2×C4—622no—
181C2×C4—622no—
182C2×C4—628no—
183C2×C4—628no—
184C2×C4(C2×D31)⋊C412yes—
185C2×C4C2×D12411yescharacteristic
186C2×C4D4×D3114yes—
187C2×C4C2×C22⋊D3111yescharacteristic
188C8—42no—
189C8—1242no—
190C22—22no—
191C22—24no—
192C22—24no—
193C22—22no—
194C22—318no—
195C22—6232no—
196C22—624no—
197C22—624no—
198C22—624no—
199C22—624no—
200C22—624no—
201C22—624no—
202C22(C2×D31)⋊C814yescomplemented
203C22C22⋊C4×D3112yes—
204C22C2×C8×D3111yescharacteristic
205C22C2×#9246911yescharacteristic
206C22M16×D3112yes—
207C22C2×(C2×D31)⋊C411yescharacteristic
208C4—22no—
209C4—624no—
210C4#1175845912yes—
211C4#1175851412yes—
212C2—24no—
213C2—628no—
214C2#1452090411yescharacteristic
215C2C22⋊C8×D3112yes—
216C2C2×(C2×D31)⋊C811yescharacteristic
217C2#1452101112yes—
218C2#1452101211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C22×D31
commutatorC22×C31C22×C8
FittingC2×C31×C22⋊C8C2
socleC23×C31C22×C4
prime radicalC24×D31C4
cosocleC22×C4×C31C23
hypercenterC2×C22⋊C8D31
hypocenterC31#1779
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C22×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊(C31⋊C8)C2semidirect
3. C2×(C2×D31)⋊C8C2semidirect
4. C2×C31×C22⋊C8C2semidirect
13. C22×C8×C31C22semidirect
14. C22×C31⋊C8C22semidirect
23. C23×D31C8semidirect
85. C22×C31C22⋊C8semidirect
98. C2×D31C22⋊C8semidirect
106. C2×C22⋊C8D31semidirect
123. C22×C8C2×D31semidirect
127. C31#1779semidirect
202. C22(C2×D31)⋊C8semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D312
C2×C22⋊(C31⋊C8)2
C2×(C2×D31)⋊C82
C2×C31×C22⋊C82
#177931