Finite Group Databasebeta

← #16844154

Subgroups — #16844154

Order 3968.

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

normal subgroups only

This group has 316 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
1#14521106C211yesmaximal, characteristic, complemented
2C4×#92474C211yesmaximal, characteristic, complemented
3D4⋊(C31⋊C8)C214yesmaximal, complemented
4C2×C4×D4×C31C211yesmaximal, characteristic
5C22×D4×C31C411yescharacteristic
6C23×C4×C31—21no—
7C4×D4×C31—21no—
8C4×D4×C31—21no—
9C4×D4×C31C412yes—
10C4×D4×C31C2212yes—
11C2×C4⋊C4×C31C411yescharacteristic
12C2×C22⋊C4×C31—21no—
13C2×C42×C31C2211yescharacteristic
14C2×#92474—21no—
15C22⋊(C31⋊C8)—21no—
16C4⋊(C31⋊C8)C2212yescomplemented
17#11758391—21no—
18#11758391—21no—
19C4×C31⋊C8C2212yescomplemented
20C24×C31—21no—
21C2×D4×C31—24no—
22C2×D4×C31—21no—
23C2×D4×C31C2×C412yes—
24C22×C4×C31—21no—
25C22×C4×C31—22no—
26C22×C4×C31—22no—
27C22×C4×C31—44no—
28C22×C4×C31C2×C411yescharacteristic
29C22×C4×C31D411yescharacteristic
30C22×C4×C31D411yescharacteristic
31C4⋊C4×C31—21no—
32C4⋊C4×C31C2×C412yes—
33C22⋊C4×C31—22no—
34C22⋊C4×C31—22no—
35C42×C31C2×C411yescharacteristic
36C42×C31D411yescharacteristic
37C42×C31D411yescharacteristic
38C42×C31C2311yescharacteristic
39#92474—24no—
40C2×C31⋊C8—22no—
41C2×C31⋊C8—22no—
42C23×C31—24no—
43C23×C31—22no—
44C23×C31—42no—
45C23×C31—42no—
46C23×C31C22⋊C411yescharacteristic
47D4×C31—24no—
48D4×C31—22no—
49D4×C31M1614yescomplemented
50C2×C4×C31—22no—
51C2×C4×C31—22no—
52C2×C4×C31—22no—
53C2×C4×C31—22no—
54C2×C4×C31—44no—
55C2×C4×C31—42no—
56C2×C4×C31—44no—
57C2×C4×C31C22⋊C411yescharacteristic
58C2×C4×C31C22⋊C411yescharacteristic
59C2×C4×C31C22⋊C411yescharacteristic
60C2×C4×C31C22×C411yescharacteristic
61C2×C4×C31C2×D411yescharacteristic
62C2×C4×C31C2×D411yescharacteristic
63C31⋊C8—24no—
64C31⋊C8—42no—
65#1490—311nomaximal, Sylow
66C22×C31—21no—
67C22×C31—21no—
68C22×C31—24no—
69C22×C31—48no—
70C22×C31—42no—
71C22×C31—42no—
72C22×C31#10412yes—
73C22×C31C2×C22⋊C411yescharacteristic
74C4×C31—21no—
75C4×C31—21no—
76C4×C31—21no—
77C4×C31—21no—
78C4×C31—42no—
79C4×C31C2×M1612yes—
80C4×C31AGL(1,ℤ/8)12yes—
81C2×C4×D4D3111yescharacteristic
82#432—311no—
83C4×M16—311no—
84D4⋊C8—314no—
85C2×C31—22no—
86C2×C31—44no—
87C2×C31#40711yescharacteristic
88C2×C31#41811yescharacteristic
89C2×C31C2×#10411yescharacteristic
90C22×D4Dic3111yescharacteristic
91C23×C4—21no—
92C2×M16—621no—
93C4×D4—21no—
94C4×D4—21no—
95C4×D4Dic3112yes—
96C4×D4C2×D3112yes—
97C2×C4⋊C4Dic3111yescharacteristic
98C2×C22⋊C4—21no—
99C2×C42C2×D3111yescharacteristic
100C4⋊C8—312no—
101C22⋊C8—621no—
102#97—621no—
103#97—621no—
104C4×C8—312no—
105C31#149011yescharacteristic, complemented, Sylow
106C24—21no—
107C2×D4—24no—
108C2×D4—21no—
109C2×D4C2×Dic3112yes—
110C22×C4—21no—
111C22×C4—22no—
112C22×C4—22no—
113C22×C4—44no—
114C22×C4C2×Dic3111yescharacteristic
115C22×C4C22⋊D3111yescharacteristic
116C22×C4C22⋊D3111yescharacteristic
117M16—624no—
118C2×C8—622no—
119C2×C8—622no—
120C4⋊C4—21no—
121C4⋊C4C2×Dic3112yes—
122C22⋊C4—22no—
123C22⋊C4—22no—
124C42C2×Dic3111yescharacteristic
125C42C22⋊D3111yescharacteristic
126C42C22⋊D3111yescharacteristic
127C42C22×D3111yescharacteristic
128C23—24no—
129C23—22no—
130C23—42no—
131C23—42no—
132C23C22⋊Dic3111yescharacteristic
133D4—24no—
134D4—22no—
135D4#9247414yescomplemented
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—44no—
141C2×C4—42no—
142C2×C4—44no—
143C2×C4C22⋊Dic3111yescharacteristic
144C2×C4C22⋊Dic3111yescharacteristic
145C2×C4C22⋊Dic3111yescharacteristic
146C2×C4C22×Dic3111yescharacteristic
147C2×C4C2×C22⋊D3111yescharacteristic
148C2×C4C2×C22⋊D3111yescharacteristic
149C8—624no—
150C8—1242no—
151C22—21no—
152C22—21no—
153C22—24no—
154C22—48no—
155C22—42no—
156C22—42no—
157C22#1175842512yes—
158C22C2×C22⋊Dic3111yescharacteristic
159C4—21no—
160C4—21no—
161C4—21no—
162C4—21no—
163C4—42no—
164C4C2×#9247412yes—
165C4#1175850912yes—
166C2—22no—
167C2—44no—
168C2#1452101311yescharacteristic
169C2#1452105411yescharacteristic
170C2C2×#1175842511yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D31
commutatorC2×C4×C31C22×C4
FrattiniC42C22×D31
FittingC2×C4×D4×C31C2
socleC22×C31C2×C22⋊C4
prime radicalC22×D4×C31C4
cosocleC42×C31C23
hypercenterC2×C4×D4D31
hypocenterC31#1490
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #14521106C2semidirect
2. C4×#92474C2semidirect
3. D4⋊(C31⋊C8)C2semidirect
16. C4⋊(C31⋊C8)C22semidirect
19. C4×C31⋊C8C22semidirect
49. D4×C31M16semidirect
105. C31#1490semidirect
135. D4#92474semidirect

Maximal subgroups

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

subgroupindex
#145211062
C4×#924742
D4⋊(C31⋊C8)2
C2×C4×D4×C312
#149031