Finite Group Databasebeta

← #16846243

Subgroups — #16846243

Order 3968.

362 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 89 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
1#14521616C211yesmaximal, characteristic
2#14521067C212yesmaximal, complemented
3C2×#11758421C211yesmaximal, characteristic, complemented
4#14520805C212yesmaximal, complemented
5C31×#518C211yesmaximal, characteristic, complemented
6C22×D4×C31C2211yescharacteristic
7C2×#92495C2211yescharacteristic
8C4×D4×C31—24no—
9C31×#117C2212yes—
10C2×C22⋊C4×C31—22no—
11#11758530—22no—
12#11758517C412yescomplemented
13#11758515—22no—
14#11758513C412yescomplemented
15#11758503C2211yescharacteristic
16C2×#92474C2212yes—
17#11758421—22no—
18#11758393—24no—
19C24×C31D412yes—
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—21no—
27C2×C22⋊D31—24no—
28#92495—22no—
29#92495—22no—
30C2×D124C2×C411yescharacteristic, complemented
31C2×C4×D31—21no—
32C2×Dic62C2×C411yescharacteristic, complemented
33C4⋊C4×C31—22no—
34C22⋊C4×C31—24no—
35C22⋊C4×C31—22no—
36C42×C31D414yescomplemented
37C22⋊Dic31—24no—
38C22⋊Dic31—21no—
39C4⋊Dic31—21no—
40C4×Dic31C2×C412yescomplemented
41#92474—22no—
42#92474—22no—
43C2×C31⋊C8—22no—
44C23×C31—22no—
45C23×C31—22no—
46C23×C31—82no—
47C23×C31C22⋊C414yes—
48C23×C31C2×D411yescharacteristic
49C22×D31—21no—
50D4×C31—24no—
51D4×C31—24no—
52C2×C4×C31—24no—
53C2×C4×C31—84no—
54C2×C4×C31C22×C411yescharacteristic
55C2×C4×C31C2×D411yescharacteristic
56C2×C4×C31C2×D412yes—
57C2×C4×C31#4112yes—
58C22⋊D31—41no—
59C22⋊D31—41no—
60C22⋊D31—84no—
61C2×Dic31—22no—
62C2×Dic31—21no—
63D124—22no—
64C4×D31—42no—
65Dic62—22no—
66C31⋊C8—42no—
67#1911—311nomaximal, Sylow
68C22×C31—24no—
69C22×C31—41no—
70C22×C31—44no—
71C22×C31—44no—
72C22×C31—82no—
73C22×C31C2×C22⋊C411yescharacteristic
74C22×C31#12011yescharacteristic
75C22×C31#12311yescharacteristic
76C2×D31—42no—
77C2×D31—41no—
78C4×C31—44no—
79C4×C31C4×D412yes—
80C4×C31#12112yes—
81Dic31—42no—
82Dic31—41no—
83#535—311no—
84#518D3111yescharacteristic, complemented
85#421—312no—
86C2×#100—311no—
87H(3,ℤ/4)—312no—
88C2×C31—21no—
89C2×C31—21no—
90C2×C31—21no—
91C2×C31—44no—
92C2×C31#38611yescharacteristic
93D31—81no—
94C2×#41—311no—
95C22×D4C2×D3111yescharacteristic
96C2×M16—312no—
97#127—312no—
98#124—312no—
99#121—622no—
100#120—622no—
101C4×D4—24no—
102#117—311no—
103#117C2×D3112yes—
104C2×C22⋊C4—22no—
105#104—624no—
106#100—622no—
107C31#191111yescharacteristic, complemented, Sylow
108C24C22⋊D3112yes—
109#41—622no—
110#41—622no—
111C2×Q8—311no—
112C2×D4—22no—
113C2×D4—22no—
114C2×D4—311no—
115C2×D4—621no—
116C2×D4—624no—
117C2×D4C4×D3112yes—
118C2×D4D12412yes—
119C22×C4—24no—
120C22×C4—621no—
121C22×C4C22×D3111yescharacteristic
122M16—622no—
123M16—622no—
124C2×C8—622no—
125C4⋊C4—22no—
126C4⋊C4—621no—
127C22⋊C4—24no—
128C22⋊C4—22no—
129C22⋊C4—624no—
130C22⋊C4—621no—
131C42—312no—
132C42C22⋊D3114yescomplemented
133C23—22no—
134C23—22no—
135C23—82no—
136C23—621no—
137C23(C2×D31)⋊C414yes—
138C23C2×C22⋊D3111yescharacteristic
139Q8—622no—
140D4—24no—
141D4—24no—
142D4—622no—
143D4—1241no—
144D4—1241no—
145D4—2484no—
146C2×C4—24no—
147C2×C4—84no—
148C2×C4—622no—
149C2×C4—621no—
150C2×C4—1242no—
151C2×C4C2×C4×D3111yescharacteristic
152C2×C4C2×D12411yescharacteristic
153C2×C4#9249512yes—
154C2×C4C2×C22⋊D3112yes—
155C8—1242no—
156C22—24no—
157C22—41no—
158C22—44no—
159C22—44no—
160C22—82no—
161C22—1242no—
162C22—1241no—
163C22C2×(C2×D31)⋊C411yescharacteristic
164C22#1175850611yescharacteristic
165C22#1175853011yescharacteristic
166C4—44no—
167C4—1242no—
168C4—1241no—
169C4C4×C22⋊D3112yes—
170C4#1175850712yes—
171C2—21no—
172C2—21no—
173C2—21no—
174C2—44no—
175C2—2481no—
176C2#1452092811yescharacteristic
subgroupG/H
centerC2#14520928
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#518C2
socleC2×C31#386
prime radical#14521616C2
cosocleC22×C4×C31C23
hypercenter#518D31
hypocenterC31#1911
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C22×C4 ◁ #518

Complements

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

NH ≅ G/Ntype
2. #14521067C2semidirect
3. C2×#11758421C2semidirect
4. #14520805C2semidirect
5. C31×#518C2semidirect
12. #11758517C4semidirect
14. #11758513C4semidirect
30. C2×D124C2×C4semidirect
32. C2×Dic62C2×C4semidirect
36. C42×C31D4semidirect
40. C4×Dic31C2×C4semidirect
84. #518D31semidirect
107. C31#1911semidirect
132. C42C22⋊D31semidirect

Maximal subgroups

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

subgroupindex
#145216162
#145210672
C2×#117584212
#145208052
C31×#5182
#191131