Finite Group Databasebeta

← #16844142

Subgroups — #16844142

Order 3968.

246 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 71 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
1C4×#92497C211yesmaximal, characteristic
2#14521105C211yesmaximal, 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
8C2×#92497C411yescharacteristic
9C4×D4×C31C2211yescharacteristic
10D4×Dic31C411yescharacteristic
11C4×C22⋊D31—21no—
12C2×C4×Dic31—21no—
13#11758469C411yescharacteristic
14#11758464C411yescharacteristic
15(C22⋊D31)⋊C4—21no—
16#11758454—21no—
17C42×D31C2211yescharacteristic
18C4×Dic62C2211yescharacteristic
19C31×C4⋊C8C2211yescharacteristic
20C4×C8×C31C2211yescharacteristic
21(C2×D31)⋊C8—21no—
22(C2×D31)⋊C8—21no—
23#11758403—21no—
24Dic31⋊C8—21no—
25C4⋊(C31⋊C8)C2211yescharacteristic
26C4×C31⋊C8C2211yescharacteristic
27C2×D4×C31C2×C411yescharacteristic
28C22×C4×C31—21no—
29C2×C22⋊D31—21no—
30C22×Dic31—21no—
31C22×Dic31—21no—
32#92497—22no—
33#92497—22no—
34C2×C4×D31C2×C411yescharacteristic
35C2×C4×D31D411yescharacteristic
36C2×C4×D31D411yescharacteristic
37C2×Dic62C2×C411yescharacteristic
38C2×C8×C31—21no—
39C2×C8×C31—21no—
40C4⋊C4×C31C2×C411yescharacteristic
41C22⋊C4×C31—21no—
42C42×C31C2311yescharacteristic
43C22⋊Dic31—21no—
44(C2×D31)⋊C4—21no—
45C4⋊Dic31C2×C411yescharacteristic
46Dic31⋊C4—21no—
47Dic31⋊C4—21no—
48C4×Dic31—21no—
49C4×Dic31—21no—
50C4×Dic31—21no—
51C4×Dic31C2×C411yescharacteristic
52C4×Dic31D411yescharacteristic
53C4×Dic31D411yescharacteristic
54C2×C31⋊C8—21no—
55C2×C31⋊C8—21no—
56C23×C31—21no—
57C22×D31C22⋊C411yescharacteristic
58D4×C31—21no—
59D4×C31M1612yes—
60C2×C4×C31—21no—
61C2×C4×C31—41no—
62C2×C4×C31—41no—
63C2×C4×C31C22×C411yescharacteristic
64C2×C4×C31C2×D411yescharacteristic
65C2×C4×C31C2×D411yescharacteristic
66C22⋊D31—24no—
67C2×Dic31—24no—
68C2×Dic31—21no—
69C2×Dic31—21no—
70C2×Dic31—42no—
71C2×Dic31C22⋊C411yescharacteristic
72C2×Dic31C22⋊C411yescharacteristic
73C2×Dic31C22⋊C411yescharacteristic
74C4×D31—21no—
75C4×D31—21no—
76C4×D31—21no—
77C4×D31—21no—
78C4×D31—41no—
79Dic62—21no—
80Dic62M1612yes—
81C8×C31—41no—
82C8×C31—41no—
83C31⋊C8—41no—
84C31⋊C8—41no—
85#1488—311nomaximal, Sylow
86C22×C31—22no—
87C22×C31—41no—
88C22×C31—41no—
89C22×C31C2×C22⋊C411yescharacteristic
90C2×D31—21no—
91C2×D31—21no—
92C2×D31—21no—
93C4×C31—21no—
94C4×C31—41no—
95C4×C31C2×M1611yescharacteristic
96C4×C31C2×M1611yescharacteristic
97C4×C31#13511yescharacteristic
98C4×C31#13511yescharacteristic
99Dic31—22no—
100Dic31—21no—
101Dic31—21no—
102Dic31—21no—
103Dic31—41no—
104C4×#41—311no—
105#432—311no—
106#431—311no—
107Q8⋊C8—311no—
108Q8⋊C8—311no—
109D4⋊C8—311no—
110D4⋊C8D3111yescharacteristic, complemented
111C2×C31—42no—
112C2×C31#40711yescharacteristic
113C2×C31#41611yescharacteristic
114C2×C31#42111yescharacteristic
115D31—41no—
116C2×#41—311no—
117C4×Q8—311no—
118C4×Q8—311no—
119C4×D4—311no—
120C4×D4—621no—
121C4×D4—621no—
122C4×D4C2×D3111yescharacteristic
123#117—311no—
124#117—621no—
125C2×C42—311no—
126C2×C42—621no—
127C4⋊C8—311no—
128C4⋊C8—621no—
129C4⋊C8C2×D3111yescharacteristic
130C22⋊C8—621no—
131C22⋊C8—621no—
132#97—621no—
133C4×C8—311no—
134C4×C8C2×D3111yescharacteristic
135C31#148811yescharacteristic, complemented, Sylow
136#41—622no—
137#41—622no—
138C2×Q8—311no—
139C2×D4—621no—
140C2×D4C4×D3111yescharacteristic
141C22×C4—21no—
142C22×C4—311no—
143C22×C4—311no—
144C22×C4—311no—
145C22×C4—621no—
146C22×C4—621no—
147C2×C8—21no—
148C2×C8—21no—
149C2×C8—621no—
150C2×C8—621no—
151C4⋊C4—311no—
152C4⋊C4—621no—
153C4⋊C4—621no—
154C4⋊C4C4×D3111yescharacteristic
155C22⋊C4—21no—
156C22⋊C4—621no—
157C22⋊C4—621no—
158C42—311no—
159C42—311no—
160C42—311no—
161C42—621no—
162C42—621no—
163C42—621no—
164C42C22×D3111yescharacteristic
165C23—21no—
166C23—311no—
167Q8—312no—
168Q8—621no—
169D4—21no—
170D4—624no—
171D4#9246912yes—
172C2×C4—21no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—311no—
176C2×C4—311no—
177C2×C4—311no—
178C2×C4—624no—
179C2×C4—621no—
180C2×C4—621no—
181C2×C4—621no—
182C2×C4—621no—
183C2×C4—621no—
184C2×C4—621no—
185C2×C4—1241no—
186C2×C4—1242no—
187C2×C4C2×C4×D3111yescharacteristic
188C2×C4D4×D3111yescharacteristic
189C2×C4D4×D3111yescharacteristic
190C8—41no—
191C8—41no—
192C8—1241no—
193C8—1241no—
194C22—22no—
195C22—41no—
196C22—41no—
197C22—621no—
198C22—621no—
199C22—621no—
200C22C22⋊C4×D3111yescharacteristic
201C4—21no—
202C4—41no—
203C4—621no—
204C4—622no—
205C4—621no—
206C4—621no—
207C4—1241no—
208C4C2×#9246911yescharacteristic
209C4M16×D3111yescharacteristic
210C4#1175848911yescharacteristic
211C4#1175849311yescharacteristic
212C2—42no—
213C2—1241no—
214C2#1452101111yescharacteristic
215C2#1452104211yescharacteristic
216C2#1452106411yescharacteristic
subgroupG/H
centerC2×C4D4×D31
commutatorC2×C4×C31C22×C4
FrattiniC42C22×D31
FittingC31×D4⋊C8C2
socleC22×C31C2×C22⋊C4
prime radicalC2×#92497C4
cosocleC42×C31C23
hypercenterD4⋊C8D31
hypocenterC31#1488
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. #14521105C2semidirect
3. #14521100C2semidirect
4. #14520781C2semidirect
5. #14520779C2semidirect
6. D4⋊(C31⋊C8)C2semidirect
7. C31×D4⋊C8C2semidirect
110. D4⋊C8D31semidirect
135. C31#1488semidirect

Maximal subgroups

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

subgroupindex
C4×#924972
#145211052
#145211002
#145207812
#145207792
D4⋊(C31⋊C8)2
C31×D4⋊C82
#148831