Finite Group Databasebeta

← #16844420

Subgroups — #16844420

Order 3968.

198 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 65 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
3#14521101C211yesmaximal, characteristic
4#14520798C211yesmaximal, characteristic, complemented
5#14520796C211yesmaximal, characteristic, complemented
6#14520794C211yesmaximal, characteristic, complemented
7C31×#333C211yesmaximal, characteristic, complemented
8C31×C4⋊Q8C2211yescharacteristic
9#11758523C412yes—
10Q8×Dic31C412yes—
11#11758474—21no—
12#11758469—21no—
13#11758467—21no—
14#11758464—21no—
15C42×D31C2211yescharacteristic
16#11758446C2211yescharacteristic
17C31×C4⋊C8C2211yescharacteristic
18C31×C4⋊C8C2211yescharacteristic
19(C2×D31)⋊C8—21no—
20(C2×D31)⋊C8—21no—
21#11758403—21no—
22C8×Dic31—21no—
23C4⋊(C31⋊C8)C2211yescharacteristic
24C4⋊(C31⋊C8)C2211yescharacteristic
25C2×Q8×C31C2×C412yes—
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×C31—21no—
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—
46C22×D31C22⋊C411yescharacteristic
47Q8×C31—42no—
48C2×C4×C31—22no—
49C2×C4×C31C22×C411yescharacteristic
50C2×C4×C31C2×D411yescharacteristic
51C2×C4×C31C2×D411yescharacteristic
52C2×Dic31—22no—
53C2×Dic31C22⋊C411yescharacteristic
54C2×Dic31C22⋊C411yescharacteristic
55C2×Dic31C22⋊C411yescharacteristic
56C4×D31—21no—
57C4×D31—21no—
58C4×D31—21no—
59C4×D31—21no—
60C4×D31—41no—
61Dic62—41no—
62Dic62—41no—
63C8×C31—41no—
64C8×C31—41no—
65C31⋊C8—41no—
66C31⋊C8—41no—
67#1554—311nomaximal, Sylow
68C22×C31C2×C22⋊C411yescharacteristic
69C2×D31—21no—
70C2×D31—21no—
71C2×D31—21no—
72C4×C31—21no—
73C4×C31—42no—
74C4×C31#13511yescharacteristic
75C4×C31#13511yescharacteristic
76C4×C31#13711yescharacteristic
77C4×C31#13711yescharacteristic
78Dic31—21no—
79Dic31—21no—
80Dic31—21no—
81Dic31—42no—
82#533—311no—
83#432—311no—
84#431—311no—
85#333—311no—
86#333D3111yescharacteristic, complemented
87#332—311no—
88#332—311no—
89C2×C31#41311yescharacteristic
90C2×C31#41611yescharacteristic
91C2×C31#41911yescharacteristic
92D31—41no—
93C4⋊Q8—311no—
94C4⋊Q8C2×D3111yescharacteristic
95#125—621no—
96C22⋊Q8—312no—
97C22⋊Q8—621no—
98C4×Q8—312no—
99C4×Q8—621no—
100#117—621no—
101C2×C42—311no—
102C4⋊C8—311no—
103C4⋊C8—311no—
104C4⋊C8C2×D3111yescharacteristic
105C4⋊C8C2×D3111yescharacteristic
106C22⋊C8—621no—
107C22⋊C8—621no—
108#97—621no—
109C4×C8—621no—
110C31#155411yescharacteristic, complemented, Sylow
111C2×Q8—621no—
112C2×Q8C4×D3112yes—
113C22×C4—311no—
114C22×C4—311no—
115C22×C4—311no—
116C2×C8—21no—
117C2×C8—21no—
118C2×C8—621no—
119C2×C8—621no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—312no—
123C4⋊C4—622no—
124C4⋊C4—622no—
125C4⋊C4—621no—
126C22⋊C4—622no—
127C42—311no—
128C42—311no—
129C42—311no—
130C42—622no—
131C42C22×D3111yescharacteristic
132C23—311no—
133Q8—42no—
134Q8—1241no—
135Q8—1241no—
136C2×C4—22no—
137C2×C4—311no—
138C2×C4—311no—
139C2×C4—311no—
140C2×C4—621no—
141C2×C4—621no—
142C2×C4—621no—
143C2×C4—621no—
144C2×C4—622no—
145C2×C4—1241no—
146C2×C4C2×C4×D3111yescharacteristic
147C2×C4D4×D3111yescharacteristic
148C2×C4D4×D3111yescharacteristic
149C8—41no—
150C8—41no—
151C8—1241no—
152C8—1241no—
153C22—621no—
154C22—621no—
155C22—621no—
156C22C22⋊C4×D3111yescharacteristic
157C4—21no—
158C4—42no—
159C4—621no—
160C4—621no—
161C4—621no—
162C4—1242no—
163C4#1175849211yescharacteristic
164C4#1175849311yescharacteristic
165C4#1175849511yescharacteristic
166C4#1175849611yescharacteristic
167C2—1241no—
168C2#1452103011yescharacteristic
169C2#1452104411yescharacteristic
170C2#1452105611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D31
commutatorC2×C4×C31C22×C4
FrattiniC42C22×D31
FittingC31×#333C2
socleC22×C31C2×C22⋊C4
prime radicalC22×D31C22⋊C4
cosocleC42×C31C23
hypercenter#333D31
hypocenterC31#1554
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
4. #14520798C2semidirect
5. #14520796C2semidirect
6. #14520794C2semidirect
7. C31×#333C2semidirect
86. #333D31semidirect
110. C31#1554semidirect

Maximal subgroups

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

subgroupindex
#145216042
#145211052
#145211012
#145207982
#145207962
#145207942
C31×#3332
#155431