Finite Group Databasebeta

← #16846033

Subgroups — #16846033

Order 3968.

412 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 109 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×#11758507C211yesmaximal, characteristic
2C2×#11758397C212yesmaximal, complemented
3C2×C22⋊(C31⋊C8)C211yesmaximal, characteristic, complemented
4#14520811C212yesmaximal, complemented
5C2×C31×#117C211yesmaximal, characteristic, complemented
6C23×C4×C31C2211yescharacteristic
7C22×C22⋊D31—21no—
8C22×D124C2211yescharacteristic
9C31×#117—24no—
10C2×C4⋊C4×C31C2212yes—
11C2×C22⋊C4×C31—21no—
12C2×C42×C31—21no—
13#11758507—22no—
14#11758507C414yescomplemented
15C2×(C2×D31)⋊C4—21no—
16C2×C4⋊Dic31C2211yescharacteristic
17C22×C31⋊C8C2212yes—
18C22⋊(C31⋊C8)—22no—
19#11758397—24no—
20C24×C31D411yescharacteristic
21C23×D31—21no—
22C22×C4×C31—22no—
23C22×C4×C31—22no—
24C22×C4×C31—22no—
25C22×C4×C31C2×C412yes—
26C22×C4×C31D411yescharacteristic
27C22×C4×C31D412yes—
28C22×C4×C31C2311yescharacteristic
29C2×C22⋊D31—24no—
30C2×C22⋊D31—44no—
31C22×Dic31—21no—
32C2×D124—22no—
33C2×D124—22no—
34C2×D124—21no—
35C2×D124C2×C412yes—
36C4⋊C4×C31—22no—
37C4⋊C4×C31D414yescomplemented
38C22⋊C4×C31—24no—
39C42×C31—24no—
40(C2×D31)⋊C4—24no—
41C4⋊Dic31—21no—
42C4⋊Dic31C2×C412yes—
43C2×C31⋊C8—22no—
44C2×C31⋊C8—22no—
45C2×C31⋊C8—22no—
46C23×C31—21no—
47C23×C31—21no—
48C23×C31—22no—
49C23×C31—22no—
50C23×C31C22⋊C412yes—
51C23×C31C2×D411yescharacteristic
52C22×D31—22no—
53C22×D31—41no—
54C22×D31—41no—
55C22×D31—42no—
56C22×D31—42no—
57C2×C4×C31—21no—
58C2×C4×C31—21no—
59C2×C4×C31—24no—
60C2×C4×C31—24no—
61C2×C4×C31—24no—
62C2×C4×C31—42no—
63C2×C4×C31—42no—
64C2×C4×C31C22⋊C412yes—
65C2×C4×C31C22×C411yescharacteristic
66C2×C4×C31C2×D411yescharacteristic
67C2×C4×C31C2×D412yes—
68C2×C4×C31#4112yes—
69C22⋊D31—48no—
70C2×Dic31—22no—
71C2×Dic31—42no—
72D124—24no—
73D124—42no—
74C31⋊C8—42no—
75#1875—311nomaximal, Sylow
76C22×C31—22no—
77C22×C31—22no—
78C22×C31—22no—
79C22×C31—42no—
80C22×C31—42no—
81C22×C31C2×C22⋊C411yescharacteristic
82C22×C31#12011yescharacteristic
83C22×C31#12311yescharacteristic
84C22×C31#13512yes—
85C22×C31AGL(1,ℤ/8)12yes—
86C2×D31—42no—
87C2×D31—42no—
88C2×D31—42no—
89C2×D31—82no—
90C2×D31—82no—
91C4×C31—22no—
92C4×C31—44no—
93C4×C31C4×D412yes—
94C4×C31#12112yes—
95Dic31—42no—
96C2×#121—311no—
97C2×#117D3111yescharacteristic, complemented
98C2×#102—312no—
99C2×C22⋊C8—311no—
100#340—312no—
101C2×C31—42no—
102C2×C31#38611yescharacteristic
103C2×C31#41611yescharacteristic
104C2×C31#41811yescharacteristic
105C2×C31#44912yes—
106C2×C31#48212yes—
107D31—82no—
108C22×D4—311no—
109C22×D4—621no—
110C23×C4C2×D3111yescharacteristic
111C22×C8—312no—
112#121—314no—
113#121—622no—
114#117—24no—
115C2×C4⋊C4—311no—
116C2×C4⋊C4C2×D3112yes—
117C2×C22⋊C4—21no—
118C2×C22⋊C4—621no—
119C2×C42—21no—
120#102—624no—
121C22⋊C8—622no—
122C31#187511yescharacteristic, complemented, Sylow
123C24—621no—
124C24C22⋊D3111yescharacteristic
125C2×D4—312no—
126C2×D4—624no—
127C2×D4—621no—
128C2×D4—622no—
129C2×D4—622no—
130C2×D4—1244no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—621no—
135C22×C4C4×D3112yes—
136C22×C4D12412yes—
137C22×C4C22⋊D3111yescharacteristic
138C22×C4C22×D3111yescharacteristic
139C2×C8—622no—
140C2×C8—622no—
141C2×C8—622no—
142C4⋊C4—22no—
143C4⋊C4—312no—
144C4⋊C4—621no—
145C4⋊C4C22⋊D3114yescomplemented
146C22⋊C4—24no—
147C22⋊C4—624no—
148C42—24no—
149C23—21no—
150C23—22no—
151C23—22no—
152C23—21no—
153C23—622no—
154C23—1241no—
155C23—1242no—
156C23—1242no—
157C23—1241no—
158C23(C2×D31)⋊C412yes—
159C23C2×C22⋊D3111yescharacteristic
160D4—624no—
161D4—1248no—
162D4—1242no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—24no—
166C2×C4—24no—
167C2×C4—24no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—622no—
171C2×C4—1242no—
172C2×C4(C2×D31)⋊C412yes—
173C2×C4C2×C4×D3111yescharacteristic
174C2×C4C2×D12411yescharacteristic
175C2×C4#9249512yes—
176C2×C4C2×C22⋊D3112yes—
177C8—1242no—
178C22—22no—
179C22—22no—
180C22—22no—
181C22—42no—
182C22—42no—
183C22—1242no—
184C22—1242no—
185C22—1242no—
186C22—2482no—
187C22—2482no—
188C22C2×(C2×D31)⋊C411yescharacteristic
189C22#1175850611yescharacteristic
190C22#1175852612yes—
191C22#1175852712yes—
192C22#1175853011yescharacteristic
193C4—22no—
194C4—44no—
195C4—1242no—
196C4C4×C22⋊D3112yes—
197C4#1175850712yes—
198C2—42no—
199C2—2482no—
200C2#1452092811yescharacteristic
201C2#1452104311yescharacteristic
202C2#1452105311yescharacteristic
203C2#1452119412yes—
204C2#1452137312yes—
subgroupG/H
centerC23C2×C22⋊D31
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC2×C31×#117C2
socleC23×C31C2×D4
prime radicalC2×#11758507C2
cosocleC22×C4×C31C23
hypercenterC2×#117D31
hypocenterC31#1875
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. C2×#11758397C2semidirect
3. C2×C22⋊(C31⋊C8)C2semidirect
4. #14520811C2semidirect
5. C2×C31×#117C2semidirect
14. #11758507C4semidirect
37. C4⋊C4×C31D4semidirect
97. C2×#117D31semidirect
122. C31#1875semidirect
145. C4⋊C4C22⋊D31semidirect

Maximal subgroups

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

subgroupindex
C2×#117585072
C2×#117583972
C2×C22⋊(C31⋊C8)2
#145208112
C2×C31×#1172
#187531