Finite Group Databasebeta

← #16844317

Subgroups — #16844317

Order 3968.

216 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 59 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#14521584C211yesmaximal, characteristic
2#14521104C211yesmaximal, characteristic, complemented
3#14521001C211yesmaximal, characteristic, complemented
4#14520791C211yesmaximal, characteristic, complemented
5#14520788C211yesmaximal, characteristic, complemented
6#14520788C211yesmaximal, characteristic, complemented
7C31×#330C211yesmaximal, characteristic, complemented
8C31×#125C2211yescharacteristic
9C2×#92469—21no—
10#11758475—21no—
11#11758474C411yescharacteristic
12#11758472C411yescharacteristic
13#11758471—21no—
14#11758470—21no—
15#11758470C411yescharacteristic
16#11758469—21no—
17#11758464C411yescharacteristic
18#11758452C2211yescharacteristic
19C42×D31C2211yescharacteristic
20C31×#97C2211yescharacteristic
21C31×#97C2211yescharacteristic
22(C2×D31)⋊C8—21no—
23Dic31⋊C8—21no—
24C8×Dic31—21no—
25#11758391C2211yescharacteristic
26#11758391C2211yescharacteristic
27C2×D124—21no—
28C2×D124C2×C411yescharacteristic
29C2×C4×D31—21no—
30C2×C4×D31C2×C411yescharacteristic
31C2×C4×D31D411yescharacteristic
32C2×C4×D31D411yescharacteristic
33C2×Dic62C2×C411yescharacteristic
34C2×C8×C31—21no—
35C2×C8×C31—21no—
36C4⋊C4×C31—21no—
37C4⋊C4×C31—21no—
38C4⋊C4×C31C2×C411yescharacteristic
39C4⋊C4×C31C2×C411yescharacteristic
40C42×C31C2311yescharacteristic
41(C2×D31)⋊C4—21no—
42(C2×D31)⋊C4—21no—
43(C2×D31)⋊C4—21no—
44(C2×D31)⋊C4—21no—
45(C2×D31)⋊C4—21no—
46C4⋊Dic31—21no—
47Dic31⋊C4—21no—
48C4×Dic31—21no—
49C4×Dic31C2×C411yescharacteristic
50C4×Dic31D411yescharacteristic
51C4×Dic31D411yescharacteristic
52C2×C31⋊C8—21no—
53C2×C31⋊C8—21no—
54#92469—24no—
55C22×D31—21no—
56C22×D31C22⋊C411yescharacteristic
57C2×C4×C31—21no—
58C2×C4×C31—21no—
59C2×C4×C31C22×C411yescharacteristic
60C2×C4×C31C2×D411yescharacteristic
61C2×C4×C31C2×D411yescharacteristic
62C2×Dic31—21no—
63C2×Dic31C22⋊C411yescharacteristic
64C2×Dic31C22⋊C411yescharacteristic
65C2×Dic31C22⋊C411yescharacteristic
66D124—41no—
67D124—42no—
68C4×D31—22no—
69C4×D31—41no—
70C4×D31—41no—
71C4×D31—42no—
72Dic62—41no—
73C8×C31—22no—
74C8×C31—41no—
75C31⋊C8—22no—
76C31⋊C8—41no—
77#1529—311nomaximal, Sylow
78C22×C31C2×C22⋊C411yescharacteristic
79C2×D31—21no—
80C2×D31—21no—
81C2×D31—21no—
82C2×D31—41no—
83C2×D31—41no—
84C2×D31—41no—
85C4×C31—21no—
86C4×C31—21no—
87C4×C31—21no—
88C4×C31—41no—
89C4×C31—41no—
90Dic31—21no—
91Dic31—21no—
92Dic31—41no—
93Dic31#10412yes—
94#529—311no—
95#432—311no—
96C4×M16—311no—
97#330—311no—
98#330D3111yescharacteristic, complemented
99#329—311no—
100#329—311no—
101C2×C31#41311yescharacteristic
102C2×C31C2×#10411yescharacteristic
103C2×C31#42111yescharacteristic
104D31—41no—
105D31—81no—
106C2×M16—621no—
107#126—621no—
108#125C2×D3111yescharacteristic
109#124—311no—
110#123—621no—
111C22⋊Q8—311no—
112#121—311no—
113C4×Q8—311no—
114C4×D4—311no—
115C4×D4—621no—
116#117—621no—
117C2×C42—311no—
118C4⋊C8—621no—
119C22⋊C8—621no—
120#97—311no—
121#97—311no—
122#97C2×D3111yescharacteristic
123#97C2×D3111yescharacteristic
124C4×C8—621no—
125C31#152911yescharacteristic, complemented, Sylow
126C2×Q8—311no—
127C2×D4—311no—
128C2×D4—621no—
129C22×C4—311no—
130C22×C4—311no—
131C22×C4—311no—
132C22×C4—621no—
133M16—624no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—621no—
137C2×C8—621no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—621no—
141C4⋊C4—621no—
142C4⋊C4C4×D3111yescharacteristic
143C4⋊C4C4×D3111yescharacteristic
144C22⋊C4—621no—
145C22⋊C4—621no—
146C22⋊C4—621no—
147C22⋊C4—621no—
148C22⋊C4—621no—
149C42—311no—
150C42—311no—
151C42—311no—
152C42—621no—
153C42C22×D3111yescharacteristic
154C23—311no—
155C23—621no—
156Q8—1241no—
157D4—1241no—
158D4—1242no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—311no—
162C2×C4—311no—
163C2×C4—311no—
164C2×C4—622no—
165C2×C4—621no—
166C2×C4—1241no—
167C2×C4—1241no—
168C2×C4—1242no—
169C2×C4C2×C4×D3111yescharacteristic
170C2×C4D4×D3111yescharacteristic
171C2×C4D4×D3111yescharacteristic
172C8—22no—
173C8—41no—
174C8—622no—
175C8—1241no—
176C22—621no—
177C22—621no—
178C22—621no—
179C22—1241no—
180C22—1241no—
181C22—1241no—
182C22C22⋊C4×D3111yescharacteristic
183C4—21no—
184C4—21no—
185C4—21no—
186C4—41no—
187C4—41no—
188C4—312no—
189C4—621no—
190C4—621no—
191C4—1241no—
192C2—1241no—
193C2—2481no—
194C2#1452103211yescharacteristic
195C2#104×D3111yescharacteristic
196C2#1452106411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D31
commutatorC2×C4×C31C22×C4
FrattiniC42C22×D31
FittingC31×#330C2
socleC22×C31C2×C22⋊C4
prime radical#11758472C4
cosocleC42×C31C23
hypercenter#330D31
hypocenterC31#1529
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #14521104C2semidirect
3. #14521001C2semidirect
4. #14520791C2semidirect
5. #14520788C2semidirect
6. #14520788C2semidirect
7. C31×#330C2semidirect
98. #330D31semidirect
125. C31#1529semidirect

Maximal subgroups

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

subgroupindex
#145215842
#145211042
#145210012
#145207912
#145207882
C31×#3302
#152931