Finite Group Databasebeta

← #16846150

Subgroups — #16846150

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
1C22×#92474C211yesmaximal, characteristic, complemented
2C2×#11758420C212yesmaximal, complemented
3#14520909C211yesmaximal, 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—
14C2×C4⋊Dic31C2212yes—
15C2×#92474—22no—
16C2×#92474—24no—
17C22×C31⋊C8C2212yes—
18#11758420—24no—
19C31⋊#95—21no—
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—42no—
40C4⋊Dic31—22no—
41C4⋊Dic31—22no—
42#92474—28no—
43C2×C31⋊C8—22no—
44C2×C31⋊C8—22no—
45C2×C31⋊C8D414yescomplemented
46C23×C31—22no—
47C23×C31—21no—
48C23×C31—22no—
49C23×C31—21no—
50C23×C31—22no—
51C23×C31—42no—
52C23×C31—42no—
53C23×C31—41no—
54C23×C31—41no—
55C23×C31C22⋊C412yes—
56C23×C31C2×D411yescharacteristic
57D4×C31—24no—
58D4×C31—48no—
59D4×C31—41no—
60D4×C31—41no—
61C2×C4×C31—22no—
62C2×C4×C31—24no—
63C2×C4×C31—22no—
64C2×C4×C31—22no—
65C2×C4×C31—22no—
66C2×C4×C31—42no—
67C2×C4×C31C22⋊C412yes—
68C2×C4×C31C22×C411yescharacteristic
69C2×C4×C31C2×D412yes—
70C2×C4×C31C2×D411yescharacteristic
71C2×C4×C31#4112yes—
72C2×Dic31—42no—
73C2×Dic31—42no—
74C2×Dic31—42no—
75C31⋊C8—24no—
76#1895—311nomaximal, Sylow
77C22×C31—22no—
78C22×C31—22no—
79C22×C31—22no—
80C22×C31—42no—
81C22×C31—42no—
82C22×C31—42no—
83C22×C31—42no—
84C22×C31—42no—
85C22×C31—82no—
86C22×C31—82no—
87C22×C31C2×C22⋊C411yescharacteristic
88C22×C31#12112yes—
89C22×C31AGL(1,ℤ/8)12yes—
90C22×C31AGL(1,ℤ/8)11yescharacteristic
91C22×C31#13711yescharacteristic
92C4×C31—22no—
93C4×C31—42no—
94C4×C31C4×D412yes—
95C4×C31#12011yescharacteristic
96C4×C31#12311yescharacteristic
97Dic31—82no—
98C22×M16—311no—
99C2×#121D3111yescharacteristic
100C2×#102—312no—
101#380—311no—
102#340—312no—
103C2×C31—42no—
104C2×C31—82no—
105C2×C31#38611yescharacteristic
106C2×C31#41711yescharacteristic
107C2×C31#41811yescharacteristic
108C2×C31#46812yes—
109C2×C31#46912yes—
110C22×D4—21no—
111C22×D4C2×D3111yescharacteristic
112C23×C4C2×D3111yescharacteristic
113C2×M16—624no—
114C2×M16—622no—
115C22×C8—312no—
116#121—22no—
117#121Dic3114yescomplemented
118C2×C4⋊C4—312no—
119C2×C4⋊C4C2×D3111yescharacteristic
120C2×C22⋊C4—21no—
121C2×C22⋊C4—621no—
122#102—624no—
123#95—621no—
124C31#189511yescharacteristic, complemented, Sylow
125C24—21no—
126C24C22⋊D3111yescharacteristic
127C2×D4—24no—
128C2×D4—22no—
129C2×D4—22no—
130C2×D4—21no—
131C2×D4—44no—
132C2×D4C2×Dic3112yes—
133C22×C4—22no—
134C22×C4—22no—
135C22×C4—21no—
136C22×C4—622no—
137C22×C4C2×Dic3112yes—
138C22×C4C22⋊D3111yescharacteristic
139C22×C4C22⋊D3112yes—
140C22×C4C22×D3111yescharacteristic
141M16—628no—
142C2×C8—314no—
143C2×C8—622no—
144C2×C8—622no—
145C4⋊C4—21no—
146C4⋊C4—622no—
147C4⋊C4—622no—
148C4⋊C4C2×Dic3112yes—
149C22⋊C4—24no—
150C22⋊C4—1242no—
151C23—22no—
152C23—22no—
153C23—21no—
154C23—21no—
155C23—22no—
156C23—42no—
157C23—42no—
158C23—41no—
159C23—41no—
160C23C22⋊Dic3112yes—
161C23C2×C22⋊D3111yescharacteristic
162D4—24no—
163D4—48no—
164D4—41no—
165D4—41no—
166C2×C4—22no—
167C2×C4—24no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—42no—
172C2×C4—1242no—
173C2×C4—1242no—
174C2×C4—1242no—
175C2×C4C22⋊Dic3112yes—
176C2×C4D4×D3112yes—
177C2×C4#9249712yes—
178C2×C4C22×Dic3111yescharacteristic
179C2×C4C2×C22⋊D3111yescharacteristic
180C8—624no—
181C22—22no—
182C22—22no—
183C22—22no—
184C22—42no—
185C22—42no—
186C22—42no—
187C22—42no—
188C22—42no—
189C22—82no—
190C22—82no—
191C22#1175850912yes—
192C22#1175851612yes—
193C22#1175852611yescharacteristic
194C22#1175852811yescharacteristic
195C22C2×C22⋊Dic3111yescharacteristic
196C4—22no—
197C4—42no—
198C4—2482no—
199C4D4×Dic3112yes—
200C4#1175851211yescharacteristic
201C4#1175851411yescharacteristic
202C2—42no—
203C2—82no—
204C2#1452092911yescharacteristic
205C2#1452105011yescharacteristic
206C2#1452105411yescharacteristic
207C2#1452129312yes—
208C2#1452130012yes—
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#1895
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. C22×#92474C2semidirect
2. C2×#11758420C2semidirect
3. #14520909C2semidirect
4. #14520811C2semidirect
10. C31×#121C4semidirect
45. C2×C31⋊C8D4semidirect
117. #121Dic31semidirect
124. C31#1895semidirect

Maximal subgroups

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

subgroupindex
C22×#924742
C2×#117584202
#145209092
#145208112
C2×C31×#1212
#189531