Finite Group Databasebeta

← #16844408

Subgroups — #16844408

Order 3968.

208 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 67 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#14521604C211yesmaximal, characteristic
2#14521105C211yesmaximal, characteristic
3C4⋊C8×D31C211yesmaximal, characteristic
4#14520796C211yesmaximal, characteristic, complemented
5#14520795C211yesmaximal, characteristic, complemented
6#14520794C211yesmaximal, characteristic, complemented
7C31×#332C211yesmaximal, characteristic, complemented
8C31×C4⋊Q8C2211yescharacteristic
9#11758523—21no—
10Q8×Dic31—21no—
11C2×C8×D31—21no—
12#11758474—21no—
13#11758469C412yes—
14#11758467C412yes—
15#11758464—21no—
16C42×D31C2211yescharacteristic
17#11758446C2211yescharacteristic
18C31×C4⋊C8C2211yescharacteristic
19C31×C4⋊C8C2211yescharacteristic
20(C2×D31)⋊C8—21no—
21#11758403—21no—
22Dic31⋊C8—21no—
23C4⋊(C31⋊C8)C2211yescharacteristic
24C4⋊(C31⋊C8)C2211yescharacteristic
25C2×Q8×C31—21no—
26C2×C4×D31C2×C411yescharacteristic
27C2×C4×D31D411yescharacteristic
28C2×C4×D31D411yescharacteristic
29C2×Dic62—21no—
30C2×C8×C31—21no—
31C2×C8×C31—21no—
32C4⋊C4×C31—21no—
33C4⋊C4×C31C2×C412yes—
34C42×C31C2311yescharacteristic
35(C2×D31)⋊C4—22no—
36C4⋊Dic31—21no—
37C4⋊Dic31—22no—
38C4⋊Dic31C2×C412yes—
39Dic31⋊C4—22no—
40C4×Dic31—22no—
41C4×Dic31C2×C411yescharacteristic
42C4×Dic31D411yescharacteristic
43C4×Dic31D411yescharacteristic
44C2×C31⋊C8—21no—
45C2×C31⋊C8—21no—
46C8×D31—42no—
47C22×D31C22⋊C411yescharacteristic
48Q8×C31—41no—
49Q8×C31—41no—
50C2×C4×C31—22no—
51C2×C4×C31C22×C411yescharacteristic
52C2×C4×C31C2×D411yescharacteristic
53C2×C4×C31C2×D411yescharacteristic
54C2×Dic31—22no—
55C2×Dic31C22⋊C411yescharacteristic
56C2×Dic31C22⋊C411yescharacteristic
57C2×Dic31C22⋊C411yescharacteristic
58C4×D31—22no—
59C4×D31—21no—
60C4×D31—21no—
61C4×D31—21no—
62C4×D31—21no—
63Dic62—41no—
64Dic62—41no—
65C8×C31—41no—
66C8×C31—41no—
67C31⋊C8—41no—
68C31⋊C8—41no—
69#1552—311nomaximal, Sylow
70C22×C31C2×C22⋊C411yescharacteristic
71C2×D31—21no—
72C2×D31—21no—
73C2×D31#10112yes—
74C4×C31—21no—
75C4×C31—42no—
76C4×C31#13511yescharacteristic
77C4×C31#13511yescharacteristic
78C4×C31AGL(1,ℤ/8)11yescharacteristic
79C4×C31#13711yescharacteristic
80Dic31—21no—
81Dic31—21no—
82Dic31—21no—
83Dic31—42no—
84#533—311no—
85#432—311no—
86C2×C4⋊C8—311no—
87#332—311no—
88#332—311no—
89#332—311no—
90#332D3111yescharacteristic, complemented
91C2×C31C2×#10111yescharacteristic
92C2×C31#41611yescharacteristic
93C2×C31#41711yescharacteristic
94D31—22no—
95C22×C8—621no—
96C4⋊Q8—311no—
97C4⋊Q8C2×D3111yescharacteristic
98#125—312no—
99C22⋊Q8—621no—
100C22⋊Q8—621no—
101C4×Q8—621no—
102C4×Q8—621no—
103#117—312no—
104C2×C42—311no—
105C4⋊C8—311no—
106C4⋊C8—311no—
107C4⋊C8—621no—
108C4⋊C8C2×D3111yescharacteristic
109C4⋊C8C2×D3111yescharacteristic
110C22⋊C8—621no—
111#97—621no—
112C31#155211yescharacteristic, complemented, Sylow
113C2×Q8—21no—
114C2×Q8—621no—
115C22×C4—311no—
116C22×C4—311no—
117C22×C4—311no—
118C2×C8—21no—
119C2×C8—21no—
120C2×C8—621no—
121C2×C8—621no—
122C2×C8—1242no—
123C4⋊C4—21no—
124C4⋊C4—312no—
125C4⋊C4—622no—
126C4⋊C4—622no—
127C4⋊C4—621no—
128C4⋊C4C4×D3112yes—
129C22⋊C4—622no—
130C42—311no—
131C42—311no—
132C42—311no—
133C42—622no—
134C42C22×D3111yescharacteristic
135C23—311no—
136Q8—41no—
137Q8—41no—
138Q8—1241no—
139Q8—1241no—
140C2×C4—22no—
141C2×C4—311no—
142C2×C4—311no—
143C2×C4—311no—
144C2×C4—622no—
145C2×C4—621no—
146C2×C4—621no—
147C2×C4—621no—
148C2×C4—621no—
149C2×C4—622no—
150C2×C4C2×C4×D3111yescharacteristic
151C2×C4D4×D3111yescharacteristic
152C2×C4D4×D3111yescharacteristic
153C8—41no—
154C8—41no—
155C8—1241no—
156C8—1241no—
157C22—312no—
158C22—621no—
159C22—621no—
160C22C22⋊C4×D3111yescharacteristic
161C4—21no—
162C4—42no—
163C4—621no—
164C4—621no—
165C4—621no—
166C4—1242no—
167C4#1175848911yescharacteristic
168C4#1175849111yescharacteristic
169C4#1175849311yescharacteristic
170C4#1175849511yescharacteristic
171C2—622no—
172C2#101×D3111yescharacteristic
173C2#1452104211yescharacteristic
174C2#1452104911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D31
commutatorC2×C4×C31C22×C4
FrattiniC42C22×D31
FittingC31×#332C2
socleC22×C31C2×C22⋊C4
prime radicalC22×D31C22⋊C4
cosocleC42×C31C23
hypercenter#332D31
hypocenterC31#1552
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
4. #14520796C2semidirect
5. #14520795C2semidirect
6. #14520794C2semidirect
7. C31×#332C2semidirect
90. #332D31semidirect
112. C31#1552semidirect

Maximal subgroups

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

subgroupindex
#145216042
#145211052
C4⋊C8×D312
#145207962
#145207952
#145207942
C31×#3322
#155231