Finite Group Databasebeta

← #16846109

Subgroups — #16846109

Order 3968.

444 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 93 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×#11758517C211yesmaximal, characteristic
2#14521053C212yesmaximal, complemented
3C2×#11758421C211yesmaximal, characteristic, complemented
4#14520808C212yesmaximal, complemented
5C31×#518C211yesmaximal, characteristic, complemented
6C22×D4×C31C2211yescharacteristic
7C22×C22⋊D31—22no—
8C22×D124C2211yescharacteristic
9C4×D4×C31—24no—
10C31×#117C2212yes—
11C2×C22⋊C4×C31—22no—
12#11758517—22no—
13#11758517C414yescomplemented
14C2×C4×Dic31C2211yescharacteristic
15C2×#92474C2212yes—
16#11758421—22no—
17#11758397—24no—
18C24×C31D412yes—
19C23×D31—21no—
20C2×D4×C31—22no—
21C2×D4×C31—22no—
22C2×D4×C31C2×C412yes—
23C2×D4×C31D412yes—
24C22×C4×C31—24no—
25C22×C4×C31C2311yescharacteristic
26C2×C22⋊D31—28no—
27C2×C22⋊D31—48no—
28C22×Dic31—21no—
29C2×D124—22no—
30C2×D124—22no—
31C2×D124—21no—
32C2×D124C2×C412yescomplemented
33C4⋊C4×C31D414yescomplemented
34C22⋊C4×C31—24no—
35C22⋊C4×C31—22no—
36C42×C31—22no—
37C4×Dic31—21no—
38C4×Dic31C2×C412yescomplemented
39#92474—22no—
40#92474—22no—
41C2×C31⋊C8—22no—
42C23×C31—22no—
43C23×C31—22no—
44C23×C31—44no—
45C23×C31C22⋊C414yes—
46C23×C31C2×D411yescharacteristic
47C22×D31—22no—
48C22×D31—44no—
49C22×D31—41no—
50C22×D31—41no—
51D4×C31—24no—
52D4×C31—24no—
53C2×C4×C31—24no—
54C2×C4×C31—84no—
55C2×C4×C31C22×C411yescharacteristic
56C2×C4×C31C2×D411yescharacteristic
57C2×C4×C31C2×D412yes—
58C2×C4×C31#4112yes—
59C22⋊D31—416no—
60C2×Dic31—24no—
61C2×Dic31—22no—
62D124—24no—
63D124—42no—
64C31⋊C8—42no—
65#1887—311nomaximal, Sylow
66C22×C31—22no—
67C22×C31—24no—
68C22×C31—44no—
69C22×C31—44no—
70C22×C31—82no—
71C22×C31C2×C22⋊C411yescharacteristic
72C22×C31#12011yescharacteristic
73C22×C31#12311yescharacteristic
74C2×D31—44no—
75C2×D31—42no—
76C2×D31—82no—
77C2×D31—82no—
78C4×C31—44no—
79C4×C31C4×D412yes—
80C4×C31#12112yes—
81Dic31—24no—
82C2×#127—311no—
83#518D3111yescharacteristic, complemented
84#418—312no—
85C2×#100—311no—
86#339—312no—
87C2×C31—21no—
88C2×C31—21no—
89C2×C31—44no—
90C2×C31#38611yescharacteristic
91C2×C31#45312yes—
92D31—82no—
93C22×D4—311no—
94C22×D4—622no—
95C22×D4C2×D3111yescharacteristic
96C2×M16—312no—
97#127—314no—
98#127—622no—
99C4×D4—24no—
100#117C2×D3112yes—
101C2×C22⋊C4—22no—
102C2×C42—311no—
103#102—624no—
104#100—622no—
105C31#188711yescharacteristic, complemented, Sylow
106C24—621no—
107C24C22⋊D3112yes—
108C2×D4—22no—
109C2×D4—22no—
110C2×D4—312no—
111C2×D4—628no—
112C2×D4—621no—
113C2×D4—622no—
114C2×D4—622no—
115C2×D4—1248no—
116C2×D4C4×D3112yes—
117C2×D4D12412yes—
118C22×C4—24no—
119C22×C4—621no—
120C22×C4C22×D3111yescharacteristic
121M16—622no—
122M16—622no—
123C2×C8—622no—
124C4⋊C4C22⋊D3114yescomplemented
125C22⋊C4—24no—
126C22⋊C4—22no—
127C42—22no—
128C42—312no—
129C42—621no—
130C23—22no—
131C23—22no—
132C23—44no—
133C23—622no—
134C23—1244no—
135C23—1241no—
136C23—1241no—
137C23(C2×D31)⋊C414yes—
138C23C2×C22⋊D3111yescharacteristic
139D4—24no—
140D4—24no—
141D4—624no—
142D4—12416no—
143D4—1242no—
144C2×C4—24no—
145C2×C4—84no—
146C2×C4—624no—
147C2×C4—622no—
148C2×C4C2×C4×D3111yescharacteristic
149C2×C4C2×D12411yescharacteristic
150C2×C4#9249512yes—
151C2×C4C2×C22⋊D3112yes—
152C8—1242no—
153C22—22no—
154C22—24no—
155C22—44no—
156C22—44no—
157C22—82no—
158C22—1244no—
159C22—1242no—
160C22—2482no—
161C22—2482no—
162C22C2×(C2×D31)⋊C411yescharacteristic
163C22#1175850611yescharacteristic
164C22#1175853011yescharacteristic
165C4—44no—
166C4—624no—
167C4C4×C22⋊D3112yes—
168C4#1175850712yes—
169C2—21no—
170C2—21no—
171C2—44no—
172C2—2482no—
173C2#1452092811yescharacteristic
174C2#1452121712yes—
subgroupG/H
centerC22#11758530
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#518C2
socleC22×C31#120
prime radicalC2×#11758517C2
cosocleC22×C4×C31C23
hypercenter#518D31
hypocenterC31#1887
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #518

Complements

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

NH ≅ G/Ntype
2. #14521053C2semidirect
3. C2×#11758421C2semidirect
4. #14520808C2semidirect
5. C31×#518C2semidirect
13. #11758517C4semidirect
32. C2×D124C2×C4semidirect
33. C4⋊C4×C31D4semidirect
38. C4×Dic31C2×C4semidirect
83. #518D31semidirect
105. C31#1887semidirect
124. C4⋊C4C22⋊D31semidirect

Maximal subgroups

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

subgroupindex
C2×#117585172
#145210532
C2×#117584212
#145208082
C31×#5182
#188731