Finite Group Databasebeta

← #16845024

Subgroups — #16845024

Order 3968.

196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 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#14521803C211yesmaximal, characteristic
2#14521459C211yesmaximal, characteristic, complemented
3#14521458C211yesmaximal, characteristic, complemented
4#14521443C211yesmaximal, characteristic
5#14520790C211yesmaximal, characteristic, complemented
6#14520788C211yesmaximal, characteristic
7C31×#330C211yesmaximal, characteristic, complemented
8C31×#125C2211yescharacteristic
9C2×Dic124—21no—
10C2×#92470—21no—
11#11758475—21no—
12#11758475—21no—
13#11758474—21no—
14#11758473—21no—
15#11758471—21no—
16#11758465—21no—
17#11758452C2211yescharacteristic
18#11758447C2211yescharacteristic
19#11758446C2211yescharacteristic
20C31×#97C2211yescharacteristic
21C31×#97C2211yescharacteristic
22#11758406—21no—
23#11758405—21no—
24#11758396—21no—
25#11758395—21no—
26#11758391C2211yescharacteristic
27C2×D124D411yescharacteristic
28C2×C4×D31—21no—
29C2×Dic62—21no—
30C2×Dic62—21no—
31C2×Dic62D411yescharacteristic
32C2×C8×C31—21no—
33C2×C8×C31—21no—
34C4⋊C4×C31—21no—
35C4⋊C4×C31—21no—
36C4⋊C4×C31D411yescharacteristic
37C4⋊C4×C31D411yescharacteristic
38C42×C31C2311yescharacteristic
39(C2×D31)⋊C4—21no—
40(C2×D31)⋊C4—21no—
41(C2×D31)⋊C4—21no—
42(C2×D31)⋊C4—21no—
43(C2×D31)⋊C4—21no—
44C4⋊Dic31—21no—
45C4⋊Dic31—21no—
46C4⋊Dic31—21no—
47C4⋊Dic31D411yescharacteristic
48C4⋊Dic31D411yescharacteristic
49Dic31⋊C4—21no—
50Dic31⋊C4—21no—
51Dic31⋊C4—21no—
52C4×Dic31—21no—
53C2×C31⋊C8—21no—
54Dic124—42no—
55#92470—42no—
56C22×D31—21no—
57C2×C4×C31—21no—
58C2×C4×C31—21no—
59C2×C4×C31C2×D411yescharacteristic
60C2×C4×C31C2×D411yescharacteristic
61C2×C4×C31C2×D411yescharacteristic
62C2×Dic31—21no—
63C2×Dic31—21no—
64C2×Dic31—21no—
65C2×Dic31—41no—
66D124—41no—
67C4×D31—81no—
68Dic62—41no—
69Dic62—41no—
70Dic62—41no—
71Dic62—81no—
72C8×C31—22no—
73C8×C31—22no—
74C31⋊C8—22no—
75#1660—311nomaximal, Sylow
76C22×C31#12011yescharacteristic
77C2×D31—41no—
78C2×D31—41no—
79C2×D31—41no—
80C4×C31—21no—
81C4×C31—21no—
82C4×C31—21no—
83C4×C31—41no—
84C4×C31—41no—
85Dic31—41no—
86Dic31—41no—
87Dic31—41no—
88Dic31—81no—
89#563—311no—
90#501—311no—
91#501—311no—
92#497—311no—
93#330—311no—
94#330D3111yescharacteristic, complemented
95#329—311no—
96C2×C31#45311yescharacteristic
97C2×C31#45611yescharacteristic
98C2×C31#45611yescharacteristic
99D31—81no—
100C2×Q16—621no—
101C2×SD16—621no—
102C4⋊Q8—311no—
103C4⋊Q8—621no—
104#126—621no—
105#126—621no—
106#125—311no—
107#125C2×D3111yescharacteristic
108#124—311no—
109#123—621no—
110C22⋊Q8—621no—
111C22⋊Q8—621no—
112#107—621no—
113#107—621no—
114#106—621no—
115#106—621no—
116#97—311no—
117#97C2×D3111yescharacteristic
118#97C2×D3111yescharacteristic
119C31#166011yescharacteristic, complemented, Sylow
120C2×Q8—311no—
121C2×Q8—621no—
122C2×Q8—621no—
123C2×D4—311no—
124C22×C4—621no—
125Q16—1242no—
126SD16—1242no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—621no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—311no—
133C4⋊C4—311no—
134C4⋊C4—621no—
135C4⋊C4—621no—
136C4⋊C4—621no—
137C4⋊C4—621no—
138C4⋊C4—621no—
139C4⋊C4—621no—
140C4⋊C4D12411yescharacteristic
141C4⋊C4D12411yescharacteristic
142C22⋊C4—621no—
143C22⋊C4—621no—
144C22⋊C4—621no—
145C22⋊C4—621no—
146C22⋊C4—621no—
147C42—621no—
148C42C22×D3111yescharacteristic
149C23—621no—
150Q8—1241no—
151Q8—1241no—
152Q8—1241no—
153Q8—2481no—
154D4—1241no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—621no—
158C2×C4—621no—
159C2×C4—621no—
160C2×C4—1241no—
161C2×C4—2481no—
162C2×C4C2×D12411yescharacteristic
163C2×C4D4×D3111yescharacteristic
164C2×C4D4×D3111yescharacteristic
165C8—22no—
166C8—22no—
167C8—622no—
168C22—1241no—
169C22—1241no—
170C22—1241no—
171C22#1175845911yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—1241no—
178C4—1241no—
179C4—1241no—
180C4—2481no—
181C2—2481no—
182C2#1452121811yescharacteristic
183C2#1452123311yescharacteristic
184C2#1452123411yescharacteristic
subgroupG/H
centerC22#11758459
commutator, cosocleC42×C31C23
FrattiniC42C22×D31
FittingC31×#330C2
socleC22×C31#120
prime radicalC2×D124D4
hypercenter#330D31
hypocenterC31#1660
LCSG ▷ C42×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #14521459C2semidirect
3. #14521458C2semidirect
5. #14520790C2semidirect
7. C31×#330C2semidirect
94. #330D31semidirect
119. C31#1660semidirect

Maximal subgroups

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

subgroupindex
#145218032
#145214592
#145214582
#145214432
#145207902
#145207882
C31×#3302
#166031