Finite Group Databasebeta

← #16844065

Subgroups — #16844065

Order 3968.

204 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 63 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
1C2×#11758466C211yesmaximal, characteristic
2#14521103C211yesmaximal, characteristic
3#14521099C211yesmaximal, characteristic
4#14520775C211yesmaximal, characteristic
5#14520774C211yesmaximal, characteristic
6#14520774C211yesmaximal, characteristic
7C31×#324C211yesmaximal, characteristic
8C2×C4⋊C4×C31C2211yescharacteristic
9C2×C4⋊Dic31C411yescharacteristic
10C2×Dic31⋊C4C411yescharacteristic
11C2×Dic31⋊C4C411yescharacteristic
12C2×Dic31⋊C4C411yescharacteristic
13C2×Dic31⋊C4C2211yescharacteristic
14C2×C4×Dic31C2211yescharacteristic
15#11758466—21no—
16#11758466—21no—
17#11758466—21no—
18#11758466—21no—
19C31×C22⋊C8C2211yescharacteristic
20C31×C22⋊C8C2211yescharacteristic
21C22⋊(C31⋊C8)C2211yescharacteristic
22C22⋊(C31⋊C8)C2211yescharacteristic
23#11758403—21no—
24Dic31⋊C8—21no—
25Dic31⋊C8—21no—
26C8×Dic31—21no—
27C22×C4×C31C2×C411yescharacteristic
28C22×C4×C31C2×C411yescharacteristic
29C22×C4×C31C2311yescharacteristic
30C22×Dic31C2×C411yescharacteristic
31C22×Dic31C2×C411yescharacteristic
32C22×Dic31C2×C411yescharacteristic
33C22×Dic31C2×C411yescharacteristic
34C2×C8×C31—21no—
35C2×C8×C31—21no—
36C4⋊C4×C31—21no—
37C4⋊C4×C31—21no—
38C4⋊Dic31—21no—
39C4⋊Dic31—21no—
40Dic31⋊C4—21no—
41Dic31⋊C4—21no—
42Dic31⋊C4—21no—
43Dic31⋊C4—21no—
44Dic31⋊C4—21no—
45Dic31⋊C4—21no—
46Dic31⋊C4—21no—
47Dic31⋊C4—21no—
48C4×Dic31D411yescharacteristic
49C4×Dic31D411yescharacteristic
50C4×Dic31D411yescharacteristic
51C4×Dic31D411yescharacteristic
52C2×C31⋊C8—21no—
53C2×C31⋊C8—21no—
54C23×C31C22×C411yescharacteristic
55C2×C4×C31—21no—
56C2×C4×C31—21no—
57C2×C4×C31—21no—
58C2×C4×C31—21no—
59C2×C4×C31—41no—
60C2×C4×C31—41no—
61C2×C4×C31C2×D411yescharacteristic
62C2×C4×C31C2×D411yescharacteristic
63C2×Dic31—21no—
64C2×Dic31—21no—
65C2×Dic31—22no—
66C2×Dic31—21no—
67C2×Dic31—21no—
68C2×Dic31—21no—
69C2×Dic31—21no—
70C2×Dic31—41no—
71C2×Dic31C22⋊C411yescharacteristic
72C2×Dic31C22⋊C411yescharacteristic
73C2×Dic31C22⋊C411yescharacteristic
74C2×Dic31C22⋊C411yescharacteristic
75C8×C31—41no—
76C8×C31—41no—
77C31⋊C8—41no—
78C31⋊C8—41no—
79#1470—311nomaximal, Sylow
80C22×C31—21no—
81C22×C31—21no—
82C22×C31C2×C22⋊C411yescharacteristic
83C22×C31#13111yescharacteristic
84C22×C31#13111yescharacteristic
85C4×C31—21no—
86C4×C31—21no—
87C4×C31—41no—
88C4×C31—41no—
89Dic31—21no—
90Dic31—21no—
91Dic31—21no—
92Dic31—41no—
93Dic31—41no—
94Dic31#10112yes—
95C2×#125—311no—
96#432—311no—
97#431—311no—
98#324—311no—
99#324—311no—
100#324—311no—
101#324D3111yescharacteristic
102C2×C31—21no—
103C2×C31—21no—
104C2×C31#40811yescharacteristic
105C2×C31#41011yescharacteristic
106C2×C31C2×#10111yescharacteristic
107#125—621no—
108#125—621no—
109#125—621no—
110#125—621no—
111C2×C4⋊C4—311no—
112C2×C4⋊C4—311no—
113C2×C4⋊C4—311no—
114C2×C4⋊C4—311no—
115C2×C4⋊C4—311no—
116C2×C4⋊C4C2×D3111yescharacteristic
117C2×C42—311no—
118C4⋊C8—621no—
119C4⋊C8—621no—
120C22⋊C8—311no—
121C22⋊C8—311no—
122C22⋊C8C2×D3111yescharacteristic
123C22⋊C8C2×D3111yescharacteristic
124#97—621no—
125C4×C8—621no—
126C31#147011yescharacteristic, complemented, Sylow
127C22×C4—311no—
128C22×C4—311no—
129C22×C4—311no—
130C22×C4—311no—
131C22×C4C4×D3111yescharacteristic
132C22×C4C4×D3111yescharacteristic
133C22×C4C22×D3111yescharacteristic
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⋊C4—621no—
143C4⋊C4—621no—
144C4⋊C4—621no—
145C4⋊C4—621no—
146C4⋊C4—621no—
147C4⋊C4—621no—
148C4⋊C4—621no—
149C4⋊C4—621no—
150C42—311no—
151C42—311no—
152C42—311no—
153C42—311no—
154C23C2×C4×D3111yescharacteristic
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—311no—
162C2×C4—311no—
163C2×C4—311no—
164C2×C4—311no—
165C2×C4—622no—
166C2×C4—621no—
167C2×C4—621no—
168C2×C4—621no—
169C2×C4—621no—
170C2×C4—621no—
171C2×C4—621no—
172C2×C4—1241no—
173C2×C4D4×D3111yescharacteristic
174C2×C4D4×D3111yescharacteristic
175C8—41no—
176C8—41no—
177C8—1241no—
178C8—1241no—
179C22—21no—
180C22—21no—
181C22C22⋊C4×D3111yescharacteristic
182C22#1175847811yescharacteristic
183C22#1175848411yescharacteristic
184C4—21no—
185C4—21no—
186C4—41no—
187C4—41no—
188C4—312no—
189C4—621no—
190C4—621no—
191C4—621no—
192C4—1241no—
193C4—1241no—
194C2—21no—
195C2—21no—
196C2#1452101411yescharacteristic
197C2#1452102111yescharacteristic
198C2#101×D3111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D31
commutator, prime radicalC23×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#324C2
socleC22×C31C2×C22⋊C4
cosocleC22×C4×C31C23
hypercenter#324D31
hypocenterC31#1470
LCSG ▷ C23×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
126. C31#1470semidirect

Maximal subgroups

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

subgroupindex
C2×#117584662
#145211032
#145210992
#145207752
#145207742
C31×#3242
#147031