Finite Group Databasebeta

← #16844116

Subgroups — #16844116

Order 3968.

212 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 65 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#14521581C211yesmaximal, characteristic
2#14521101C211yesmaximal, characteristic, complemented
3#14521100C211yesmaximal, characteristic, complemented
4#14520781C211yesmaximal, characteristic, complemented
5#14520779C211yesmaximal, characteristic, complemented
6D4⋊(C31⋊C8)C211yesmaximal, characteristic, complemented
7C31×D4⋊C8C211yesmaximal, characteristic, complemented
8C4×D4×C31C2211yescharacteristic
9#11758515C411yescharacteristic
10#11758513C411yescharacteristic
11C4×C22⋊D31—21no—
12#11758503—21no—
13#11758474C411yescharacteristic
14#11758467C411yescharacteristic
15#11758460—21no—
16#11758456—21no—
17C42×D31C2211yescharacteristic
18C4×Dic62C2211yescharacteristic
19C31×C4⋊C8C2211yescharacteristic
20C4×C8×C31C2211yescharacteristic
21(C2×D31)⋊C8—21no—
22(C2×D31)⋊C8—21no—
23Dic31⋊C8—21no—
24C8×Dic31—21no—
25C4⋊(C31⋊C8)C2211yescharacteristic
26C4×C31⋊C8C2211yescharacteristic
27C2×D4×C31C2×C411yescharacteristic
28C22×C4×C31—21no—
29C2×C22⋊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×C31C2×C411yescharacteristic
37C22⋊C4×C31—21no—
38C42×C31C2311yescharacteristic
39C22⋊Dic31—21no—
40C22⋊Dic31—21no—
41C22⋊Dic31—21no—
42(C2×D31)⋊C4—21no—
43C4⋊Dic31—21no—
44C4⋊Dic31—21no—
45C4⋊Dic31C2×C411yescharacteristic
46Dic31⋊C4—21no—
47Dic31⋊C4—21no—
48C4×Dic31—21no—
49C4×Dic31C2×C411yescharacteristic
50C4×Dic31D411yescharacteristic
51C4×Dic31D411yescharacteristic
52C2×C31⋊C8—21no—
53C2×C31⋊C8—21no—
54C23×C31—21no—
55C22×D31C22⋊C411yescharacteristic
56D4×C31—21no—
57D4×C31—21no—
58C2×C4×C31—21no—
59C2×C4×C31—41no—
60C2×C4×C31—41no—
61C2×C4×C31C22×C411yescharacteristic
62C2×C4×C31C2×D411yescharacteristic
63C2×C4×C31C2×D411yescharacteristic
64C22⋊D31—42no—
65C2×Dic31—21no—
66C2×Dic31—21no—
67C2×Dic31C22⋊C411yescharacteristic
68C2×Dic31C22⋊C411yescharacteristic
69C2×Dic31C22⋊C411yescharacteristic
70C4×D31—21no—
71C4×D31—21no—
72C4×D31—21no—
73C4×D31—21no—
74C4×D31—41no—
75Dic62—21no—
76Dic62—21no—
77C8×C31—41no—
78C8×C31—41no—
79C31⋊C8—41no—
80C31⋊C8—41no—
81#1482—311nomaximal, Sylow
82C22×C31—41no—
83C22×C31—41no—
84C22×C31—41no—
85C22×C31C2×C22⋊C411yescharacteristic
86C2×D31—21no—
87C2×D31—21no—
88C2×D31—21no—
89C4×C31—21no—
90C4×C31—41no—
91C4×C31#13111yescharacteristic
92C4×C31#13111yescharacteristic
93C4×C31#13511yescharacteristic
94C4×C31#13511yescharacteristic
95Dic31—21no—
96Dic31—21no—
97Dic31—21no—
98Dic31—41no—
99Dic31—41no—
100#529—311no—
101#431—311no—
102#431—311no—
103Q8⋊C8—311no—
104Q8⋊C8—311no—
105D4⋊C8—311no—
106D4⋊C8D3111yescharacteristic, complemented
107C2×C31—81no—
108C2×C31#40811yescharacteristic
109C2×C31#41611yescharacteristic
110C2×C31#42111yescharacteristic
111D31—41no—
112#126—621no—
113#125—311no—
114#124—311no—
115#123—621no—
116C22⋊Q8—311no—
117#121—311no—
118C4×Q8—311no—
119C4×D4—621no—
120C4×D4C2×D3111yescharacteristic
121#117—621no—
122C2×C42—311no—
123C4⋊C8—311no—
124C4⋊C8—621no—
125C4⋊C8C2×D3111yescharacteristic
126C22⋊C8—621no—
127C22⋊C8—621no—
128C4×C8—311no—
129C4×C8—621no—
130C4×C8C2×D3111yescharacteristic
131C31#148211yescharacteristic, complemented, Sylow
132C2×Q8—311no—
133C2×D4—621no—
134C2×D4C4×D3111yescharacteristic
135C22×C4—21no—
136C22×C4—311no—
137C22×C4—311no—
138C22×C4—311no—
139C2×C8—21no—
140C2×C8—21no—
141C2×C8—621no—
142C2×C8—621no—
143C4⋊C4—311no—
144C4⋊C4—621no—
145C4⋊C4—621no—
146C4⋊C4—621no—
147C4⋊C4—621no—
148C4⋊C4C4×D3111yescharacteristic
149C22⋊C4—21no—
150C22⋊C4—621no—
151C22⋊C4—621no—
152C22⋊C4—621no—
153C22⋊C4—621no—
154C42—311no—
155C42—311no—
156C42—311no—
157C42—621no—
158C42C22×D3111yescharacteristic
159C23—21no—
160C23—311no—
161Q8—621no—
162Q8—621no—
163D4—21no—
164D4—21no—
165D4—1242no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—311no—
170C2×C4—311no—
171C2×C4—311no—
172C2×C4—621no—
173C2×C4—621no—
174C2×C4—621no—
175C2×C4—621no—
176C2×C4—621no—
177C2×C4—621no—
178C2×C4—1241no—
179C2×C4C2×C4×D3111yescharacteristic
180C2×C4D4×D3111yescharacteristic
181C2×C4D4×D3111yescharacteristic
182C8—41no—
183C8—41no—
184C8—1241no—
185C8—1241no—
186C22—41no—
187C22—41no—
188C22—41no—
189C22—621no—
190C22—621no—
191C22—621no—
192C22C22⋊C4×D3111yescharacteristic
193C4—21no—
194C4—41no—
195C4—621no—
196C4—621no—
197C4—621no—
198C4—1241no—
199C4—1241no—
200C4#1175847811yescharacteristic
201C4#1175848411yescharacteristic
202C4#1175848911yescharacteristic
203C4#1175849311yescharacteristic
204C2—81no—
205C2—1241no—
206C2#1452101411yescharacteristic
207C2#1452104211yescharacteristic
208C2#1452106411yescharacteristic
subgroupG/H
centerC2×C4D4×D31
commutatorC2×C4×C31C22×C4
FrattiniC42C22×D31
FittingC31×D4⋊C8C2
socleC22×C31C2×C22⋊C4
prime radical#11758515C4
cosocleC42×C31C23
hypercenterD4⋊C8D31
hypocenterC31#1482
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #14521101C2semidirect
3. #14521100C2semidirect
4. #14520781C2semidirect
5. #14520779C2semidirect
6. D4⋊(C31⋊C8)C2semidirect
7. C31×D4⋊C8C2semidirect
106. D4⋊C8D31semidirect
131. C31#1482semidirect

Maximal subgroups

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

subgroupindex
#145215812
#145211012
#145211002
#145207812
#145207792
D4⋊(C31⋊C8)2
C31×D4⋊C82
#148231