Finite Group Databasebeta

← #16844982

Subgroups — #16844982

Order 3968.

200 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 53 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#14521773C211yesmaximal, characteristic
2#14521445C211yesmaximal, characteristic, complemented
3#14521330C211yesmaximal, characteristic
4#14521260C211yesmaximal, characteristic, complemented
5#14520779C211yesmaximal, characteristic, complemented
6#14520776C211yesmaximal, characteristic
7C31×#332C211yesmaximal, characteristic, complemented
8C31×C4⋊Q8C2211yescharacteristic
9#11758524—21no—
10Q8×Dic31—21no—
11C2×Dic124—21no—
12#11758475—22no—
13#11758474—21no—
14#11758469—21no—
15C4×D124C2211yescharacteristic
16#11758446C2211yescharacteristic
17C4×Dic62C2211yescharacteristic
18C31×C4⋊C8C2211yescharacteristic
19C31×C4⋊C8C2211yescharacteristic
20#11758409—21no—
21#11758406—21no—
22#11758404—21no—
23#11758396—22no—
24C4×C31⋊C8C2211yescharacteristic
25C2×Q8×C31—21no—
26C2×D124D411yescharacteristic
27C2×C4×D31—21no—
28C2×Dic62—21no—
29C2×Dic62D411yescharacteristic
30C2×C8×C31—21no—
31C2×C8×C31—21no—
32C4⋊C4×C31—21no—
33C4⋊C4×C31D412yes—
34C42×C31C2311yescharacteristic
35(C2×D31)⋊C4—22no—
36(C2×D31)⋊C4—22no—
37(C2×D31)⋊C4—21no—
38C4⋊Dic31—22no—
39C4⋊Dic31—21no—
40C4⋊Dic31—21no—
41C4⋊Dic31D411yescharacteristic
42C4⋊Dic31D411yescharacteristic
43Dic31⋊C4—21no—
44C4×Dic31—22no—
45C4×Dic31—21no—
46C2×C31⋊C8—21no—
47Dic124—42no—
48C22×D31—21no—
49Q8×C31—41no—
50Q8×C31—41no—
51C2×C4×C31—22no—
52C2×C4×C31C2×D411yescharacteristic
53C2×C4×C31C2×D411yescharacteristic
54C2×C4×C31C2×D411yescharacteristic
55C2×Dic31—21no—
56C2×Dic31—21no—
57C2×Dic31—21no—
58C2×Dic31—41no—
59D124—21no—
60D124—21no—
61C4×D31—41no—
62C4×D31—41no—
63Dic62—21no—
64Dic62—21no—
65Dic62—41no—
66Dic62—41no—
67C8×C31—41no—
68C8×C31—41no—
69C31⋊C8—22no—
70#1652—311nomaximal, Sylow
71C22×C31#12011yescharacteristic
72C2×D31—41no—
73C2×D31—41no—
74C2×D31—41no—
75C4×C31—21no—
76C4×C31—42no—
77C4×C31#13511yescharacteristic
78C4×C31#13511yescharacteristic
79C4×C31AGL(1,ℤ/8)11yescharacteristic
80C4×C31#13711yescharacteristic
81Dic31—41no—
82Dic31—41no—
83Dic31—41no—
84Dic31—81no—
85#556—311no—
86#498—311no—
87#474—311no—
88#462—311no—
89#332D3111yescharacteristic, complemented
90Q8⋊C8—311no—
91D4⋊C8—311no—
92C2×C31#44911yescharacteristic
93C2×C31#45211yescharacteristic
94C2×C31#45611yescharacteristic
95D31—81no—
96C2×Q16—621no—
97C4⋊Q8—311no—
98C4⋊Q8C2×D3111yescharacteristic
99#126—622no—
100#124—621no—
101C22⋊Q8—621no—
102C4×Q8—311no—
103C4×Q8—621no—
104C4×D4—311no—
105#117—621no—
106#107—621no—
107#106—622no—
108C4⋊C8C2×D3111yescharacteristic
109C4⋊C8C2×D3111yescharacteristic
110#103—621no—
111#102—621no—
112C4×C8—311no—
113C31#165211yescharacteristic, complemented, Sylow
114C2×Q8—21no—
115C2×Q8—311no—
116C2×Q8—621no—
117C2×D4—311no—
118C22×C4—621no—
119Q16—1242no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—621no—
123C4⋊C4—21no—
124C4⋊C4—311no—
125C4⋊C4—311no—
126C4⋊C4—622no—
127C4⋊C4—621no—
128C4⋊C4—621no—
129C4⋊C4—621no—
130C4⋊C4D12412yes—
131C22⋊C4—622no—
132C22⋊C4—622no—
133C22⋊C4—621no—
134C42—622no—
135C42—621no—
136C42C22×D3111yescharacteristic
137C23—621no—
138Q8—41no—
139Q8—41no—
140Q8—621no—
141Q8—621no—
142Q8—1241no—
143Q8—1241no—
144D4—621no—
145D4—621no—
146C2×C4—22no—
147C2×C4—621no—
148C2×C4—621no—
149C2×C4—621no—
150C2×C4—1241no—
151C2×C4—1241no—
152C2×C4—1241no—
153C2×C4C2×D12411yescharacteristic
154C2×C4D4×D3111yescharacteristic
155C2×C4D4×D3111yescharacteristic
156C8—41no—
157C8—41no—
158C8—622no—
159C22—1241no—
160C22—1241no—
161C22—1241no—
162C22#1175845911yescharacteristic
163C4—21no—
164C4—42no—
165C4—1241no—
166C4—1241no—
167C4—1241no—
168C4—2481no—
169C4#1175848911yescharacteristic
170C4#1175849111yescharacteristic
171C4#1175849211yescharacteristic
172C4#1175849611yescharacteristic
173C2—2481no—
174C2#1452119711yescharacteristic
175C2#1452121211yescharacteristic
176C2#1452123411yescharacteristic
subgroupG/H
centerC22#11758459
commutator, cosocleC42×C31C23
FrattiniC42C22×D31
FittingC31×#332C2
socleC22×C31#120
prime radicalC2×D124D4
hypercenter#332D31
hypocenterC31#1652
LCSG ▷ C42×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #14521445C2semidirect
4. #14521260C2semidirect
5. #14520779C2semidirect
7. C31×#332C2semidirect
89. #332D31semidirect
113. C31#1652semidirect

Maximal subgroups

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

subgroupindex
#145217732
#145214452
#145213302
#145212602
#145207792
#145207762
C31×#3322
#165231