Finite Group Databasebeta

← #16844952

Subgroups — #16844952

Order 3968.

194 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 57 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#14521778C211yesmaximal, characteristic
2#14521452C211yesmaximal, characteristic
3#14521256C211yesmaximal, characteristic
4#14520794C211yesmaximal, characteristic
5Q8⋊(C31⋊C8)C211yesmaximal, characteristic
6#14520779C211yesmaximal, characteristic
7C31×#475C211yesmaximal, characteristic
8C31×C4⋊Q8C2211yescharacteristic
9C4×Q8×C31C2211yescharacteristic
10Q8×Dic31—21no—
11C2×#92482—21no—
12#11758467—21no—
13#11758467—22no—
14#11758446—21no—
15#11758446C2211yescharacteristic
16C4×Dic62—21no—
17C4×Dic62C2211yescharacteristic
18C31×#106—21no—
19C31×C4⋊C8C2211yescharacteristic
20C31×#103—21no—
21#11758423—21no—
22#11758395—22no—
23C4⋊(C31⋊C8)C2211yescharacteristic
24C4×C31⋊C8C2211yescharacteristic
25C2×Q8×C31—21no—
26C2×Q8×C31D411yescharacteristic
27C2×Dic62—21no—
28C2×Dic62D411yescharacteristic
29C2×C8×C31—21no—
30C4⋊C4×C31—21no—
31C4⋊C4×C31—21no—
32C4⋊C4×C31—21no—
33C4⋊C4×C31D411yescharacteristic
34C42×C31—21no—
35C42×C31C2311yescharacteristic
36#92482—42no—
37C4⋊Dic31—22no—
38C4⋊Dic31—22no—
39C4⋊Dic31—21no—
40C4⋊Dic31D412yes—
41C4⋊Dic31D411yescharacteristic
42Dic31⋊C4—22no—
43Dic31⋊C4—21no—
44C4×Dic31—22no—
45C4×Dic31—21no—
46C2×C31⋊C8—21no—
47C2×C31⋊C8—21no—
48Q8×C31—21no—
49Q8×C31—41no—
50Q8×C31—41no—
51Q8×C31Q1612yescomplemented
52C2×C4×C31—21no—
53C2×C4×C31—21no—
54C2×C4×C31—41no—
55C2×C4×C31C2×D411yescharacteristic
56C2×C4×C31C2×D411yescharacteristic
57C2×C4×C31C2×D411yescharacteristic
58C2×Dic31—21no—
59C2×Dic31—21no—
60C2×Dic31—22no—
61Dic62—21no—
62Dic62—21no—
63Dic62—41no—
64Dic62—41no—
65C8×C31—41no—
66C31⋊C8—22no—
67C31⋊C8—41no—
68#1648—311nomaximal, Sylow
69C22×C31#12011yescharacteristic
70C4×C31—22no—
71C4×C31—21no—
72C4×C31—41no—
73C4×C31—81no—
74C4×C31C2×Q1611yescharacteristic
75C4×C31#13511yescharacteristic
76C4×C31AGL(1,ℤ/8)11yescharacteristic
77C4×C31#13711yescharacteristic
78Dic31—41no—
79Dic31—42no—
80Dic31—41no—
81#557—311no—
82#500—311no—
83#475D3111yescharacteristic
84#462—311no—
85#332—311no—
86Q8⋊C8—311no—
87Q8⋊C8—311no—
88C2×C31#44911yescharacteristic
89C2×C31#45111yescharacteristic
90C2×C31#45611yescharacteristic
91C2×Q16—621no—
92C4⋊Q8—311no—
93C4⋊Q8—621no—
94C4⋊Q8C2×D3111yescharacteristic
95#125—622no—
96#125—621no—
97C4×Q8—311no—
98C4×Q8—621no—
99C4×Q8—621no—
100C4×Q8C2×D3111yescharacteristic
101#107—622no—
102#106—21no—
103C4⋊C8—311no—
104C4⋊C8C2×D3111yescharacteristic
105#103—21no—
106#103—621no—
107C4×C8—311no—
108C31#164811yescharacteristic, complemented, Sylow
109C2×Q8—21no—
110C2×Q8—311no—
111C2×Q8—621no—
112C2×Q8C22⋊D3111yescharacteristic
113Q16—1242no—
114C2×C8—21no—
115C2×C8—621no—
116C2×C8—621no—
117C4⋊C4—21no—
118C4⋊C4—21no—
119C4⋊C4—21no—
120C4⋊C4—311no—
121C4⋊C4—312no—
122C4⋊C4—622no—
123C4⋊C4—622no—
124C4⋊C4—622no—
125C4⋊C4—621no—
126C4⋊C4—621no—
127C4⋊C4C22⋊D3111yescharacteristic
128C42—21no—
129C42—622no—
130C42—621no—
131C42C22×D3111yescharacteristic
132Q8—21no—
133Q8—41no—
134Q8—41no—
135Q8—621no—
136Q8—621no—
137Q8—1241no—
138Q8—1241no—
139Q8#9248212yescomplemented
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—41no—
143C2×C4—621no—
144C2×C4—622no—
145C2×C4—621no—
146C2×C4D4×D3111yescharacteristic
147C2×C4D4×D3111yescharacteristic
148C2×C4C2×C22⋊D3111yescharacteristic
149C8—41no—
150C8—622no—
151C8—1241no—
152C22#1175851411yescharacteristic
153C4—22no—
154C4—21no—
155C4—41no—
156C4—81no—
157C4—1241no—
158C4—1242no—
159C4—1241no—
160C4#1175849111yescharacteristic
161C4#1175849311yescharacteristic
162C4C2×#9248211yescharacteristic
163C4#1175852811yescharacteristic
164C2#1452119311yescharacteristic
165C2#1452120411yescharacteristic
166C2#1452123011yescharacteristic
subgroupG/H
centerC22#11758514
commutator, cosocleC42×C31C23
FrattiniC42C22×D31
FittingC31×#475C2
socle, prime radicalC22×C31#120
hypercenter#475D31
hypocenterC31#1648
LCSG ▷ C42×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
51. Q8×C31Q16semidirect
108. C31#1648semidirect
139. Q8#92482semidirect

Maximal subgroups

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

subgroupindex
#145217782
#145214522
#145212562
#145207942
Q8⋊(C31⋊C8)2
#145207792
C31×#4752
#164831