Finite Group Databasebeta

← #16846034

Subgroups — #16846034

Order 3968.

412 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 113 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×#11758503C211yesmaximal, characteristic, complemented
2C2×#11758420C212yesmaximal, complemented
3C2×C22⋊(C31⋊C8)C211yesmaximal, characteristic, complemented
4#14520811C212yesmaximal, complemented
5C2×C31×#121C211yesmaximal, characteristic
6C22×D4×C31—21no—
7C22×D4×C31C2211yescharacteristic
8C23×C4×C31C2211yescharacteristic
9C31×#121—22no—
10C31×#121C414yescomplemented
11C2×C4⋊C4×C31C2211yescharacteristic
12C2×C22⋊C4×C31—21no—
13C2×C22⋊Dic31—21no—
14#11758503—24no—
15C2×C4⋊Dic31C2212yes—
16C2×C4×Dic31—21no—
17C22×C31⋊C8C2212yes—
18#11758420—24no—
19C22⋊(C31⋊C8)—22no—
20C24×C31—21no—
21C24×C31D411yescharacteristic
22C2×D4×C31—24no—
23C2×D4×C31—22no—
24C2×D4×C31—21no—
25C2×D4×C31—22no—
26C2×D4×C31—44no—
27C2×D4×C31C2×C412yes—
28C22×C4×C31—22no—
29C22×C4×C31—22no—
30C22×C4×C31—21no—
31C22×C4×C31C2×C412yes—
32C22×C4×C31D411yescharacteristic
33C22×C4×C31D412yes—
34C22×C4×C31C2311yescharacteristic
35C22×Dic31—22no—
36C4⋊C4×C31—21no—
37C4⋊C4×C31C2×C412yes—
38C22⋊C4×C31—24no—
39C22⋊Dic31—24no—
40C4⋊Dic31—22no—
41C4⋊Dic31D414yescomplemented
42C4×Dic31—24no—
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×C31—22no—
51C23×C31—41no—
52C23×C31—41no—
53C23×C31—42no—
54C23×C31—42no—
55C23×C31C22⋊C412yes—
56C23×C31C2×D411yescharacteristic
57D4×C31—24no—
58D4×C31—48no—
59D4×C31—42no—
60C2×C4×C31—21no—
61C2×C4×C31—21no—
62C2×C4×C31—24no—
63C2×C4×C31—24no—
64C2×C4×C31—22no—
65C2×C4×C31—42no—
66C2×C4×C31C22⋊C412yes—
67C2×C4×C31C22×C411yescharacteristic
68C2×C4×C31C2×D412yes—
69C2×C4×C31C2×D411yescharacteristic
70C2×C4×C31#4112yes—
71C2×Dic31—24no—
72C2×Dic31—42no—
73C2×Dic31—42no—
74C31⋊C8—42no—
75#1875—311nomaximal, Sylow
76C22×C31—22no—
77C22×C31—22no—
78C22×C31—22no—
79C22×C31—42no—
80C22×C31—42no—
81C22×C31—42no—
82C22×C31—42no—
83C22×C31—42no—
84C22×C31—82no—
85C22×C31—82no—
86C22×C31C2×C22⋊C411yescharacteristic
87C22×C31#12011yescharacteristic
88C22×C31#12311yescharacteristic
89C22×C31#13512yes—
90C22×C31AGL(1,ℤ/8)12yes—
91C4×C31—22no—
92C4×C31—42no—
93C4×C31C4×D412yes—
94C4×C31#12112yes—
95Dic31—44no—
96C2×#121D3111yescharacteristic
97C2×#117—311no—
98C2×#102—312no—
99C2×C22⋊C8—311no—
100#340—312no—
101C2×C31—42no—
102C2×C31—82no—
103C2×C31#38611yescharacteristic
104C2×C31#41611yescharacteristic
105C2×C31#41811yescharacteristic
106C2×C31#44912yes—
107C2×C31#48212yes—
108C22×D4—21no—
109C22×D4C2×D3111yescharacteristic
110C23×C4C2×D3111yescharacteristic
111C22×C8—312no—
112#121—22no—
113#121Dic3114yescomplemented
114#117—624no—
115C2×C4⋊C4—312no—
116C2×C4⋊C4C2×D3111yescharacteristic
117C2×C22⋊C4—21no—
118C2×C22⋊C4—621no—
119C2×C42—621no—
120#102—624no—
121C22⋊C8—622no—
122C31#187511yescharacteristic, complemented, Sylow
123C24—21no—
124C24C22⋊D3111yescharacteristic
125C2×D4—24no—
126C2×D4—22no—
127C2×D4—22no—
128C2×D4—21no—
129C2×D4—44no—
130C2×D4C2×Dic3112yes—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—21no—
134C22×C4—622no—
135C22×C4C2×Dic3112yes—
136C22×C4C22⋊D3111yescharacteristic
137C22×C4C22⋊D3112yes—
138C22×C4C22×D3111yescharacteristic
139C2×C8—622no—
140C2×C8—622no—
141C2×C8—622no—
142C4⋊C4—21no—
143C4⋊C4—314no—
144C4⋊C4—622no—
145C4⋊C4C2×Dic3112yes—
146C22⋊C4—24no—
147C22⋊C4—624no—
148C42—624no—
149C23—22no—
150C23—21no—
151C23—21no—
152C23—22no—
153C23—22no—
154C23—42no—
155C23—41no—
156C23—41no—
157C23—42no—
158C23C22⋊Dic3112yes—
159C23C2×C22⋊D3111yescharacteristic
160D4—24no—
161D4—48no—
162D4—42no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—24no—
166C2×C4—24no—
167C2×C4—22no—
168C2×C4—42no—
169C2×C4—624no—
170C2×C4—1242no—
171C2×C4—1242no—
172C2×C4C22⋊Dic3112yes—
173C2×C4D4×D3112yes—
174C2×C4#9249712yes—
175C2×C4C22×Dic3111yescharacteristic
176C2×C4C2×C22⋊D3111yescharacteristic
177C8—1242no—
178C22—22no—
179C22—22no—
180C22—22no—
181C22—42no—
182C22—42no—
183C22—42no—
184C22—42no—
185C22—42no—
186C22—82no—
187C22—82no—
188C22#1175850912yes—
189C22#1175851211yescharacteristic
190C22#1175851411yescharacteristic
191C22#1175852712yes—
192C22C2×C22⋊Dic3111yescharacteristic
193C4—22no—
194C4—42no—
195C4—1244no—
196C4D4×Dic3112yes—
197C4#1175851612yes—
198C2—42no—
199C2—82no—
200C2#1452092911yescharacteristic
201C2#1452104511yescharacteristic
202C2#1452105411yescharacteristic
203C2#1452119212yes—
204C2#1452137012yes—
subgroupG/H
centerC23C2×C22⋊D31
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
Fitting, prime radicalC2×C31×#121C2
socleC23×C31C2×D4
cosocleC22×C4×C31C23
hypercenterC2×#121D31
hypocenterC31#1875
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#11758503C2semidirect
2. C2×#11758420C2semidirect
3. C2×C22⋊(C31⋊C8)C2semidirect
4. #14520811C2semidirect
10. C31×#121C4semidirect
41. C4⋊Dic31D4semidirect
113. #121Dic31semidirect
122. C31#1875semidirect

Maximal subgroups

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

subgroupindex
C2×#117585032
C2×#117584202
C2×C22⋊(C31⋊C8)2
#145208112
C2×C31×#1212
#187531