Finite Group Databasebeta

← #16844248

Subgroups — #16844248

Order 3968.

222 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 61 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#14521585C211yesmaximal, characteristic
2#14521103C211yesmaximal, characteristic, complemented
3#14520913C211yesmaximal, characteristic, complemented
4#14520786C211yesmaximal, characteristic, complemented
5#14520784C211yesmaximal, characteristic
6#14520782C211yesmaximal, characteristic
7C31×#328C211yesmaximal, characteristic, complemented
8C31×C22⋊Q8C2211yescharacteristic
9#11758524C411yescharacteristic, complemented
10Q8×Dic31C411yescharacteristic, complemented
11#11758507C2211yescharacteristic
12C2×Dic31⋊C4—21no—
13C2×C4×Dic31C2211yescharacteristic
14#11758475—21no—
15#11758470C411yescharacteristic, complemented
16#11758469—21no—
17#11758467C411yescharacteristic, complemented
18#11758463—21no—
19(C22⋊D31)⋊C4—21no—
20C31×C22⋊C8C2211yescharacteristic
21C31×#95C2211yescharacteristic
22C31⋊#95—21no—
23C31⋊#95C2211yescharacteristic
24C22⋊(C31⋊C8)C2211yescharacteristic
25#11758403—21no—
26Dic31⋊C8—21no—
27C2×Q8×C31C2×C411yescharacteristic
28C22×C4×C31—21no—
29C22×C4×C31C2311yescharacteristic
30C2×C22⋊D31—21no—
31C22×Dic31—21no—
32C22×Dic31D411yescharacteristic
33C22×Dic31D411yescharacteristic
34C2×D124C2×C411yescharacteristic
35C2×C4×D31—21no—
36C2×C8×C31—21no—
37C4⋊C4×C31—21no—
38C4⋊C4×C31C2×C411yescharacteristic
39C22⋊C4×C31—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⋊Dic31C2×C411yescharacteristic
47Dic31⋊C4—21no—
48Dic31⋊C4—42no—
49C4×Dic31—21no—
50C4×Dic31C2×C411yescharacteristic
51C4×Dic31C2×C411yescharacteristic
52C4×Dic31D411yescharacteristic
53C4×Dic31D411yescharacteristic
54C2×C31⋊C8—21no—
55C23×C31C2×D411yescharacteristic
56C22×D31—21no—
57Q8×C31—41no—
58C2×C4×C31—21no—
59C2×C4×C31—21no—
60C2×C4×C31—41no—
61C2×C4×C31—41no—
62C2×C4×C31—41no—
63C2×C4×C31—41no—
64C2×C4×C31C22×C411yescharacteristic
65C2×C4×C31C2×D411yescharacteristic
66C22⋊D31—41no—
67C22⋊D31—41no—
68C2×Dic31—21no—
69C2×Dic31—21no—
70C2×Dic31—21no—
71C2×Dic31—41no—
72C2×Dic31—41no—
73C2×Dic31—41no—
74C2×Dic31—41no—
75C2×Dic31C22⋊C411yescharacteristic
76C2×Dic31C22⋊C411yescharacteristic
77C2×Dic31C22⋊C411yescharacteristic
78C2×Dic31C22⋊C411yescharacteristic
79D124—41no—
80C4×D31—42no—
81C8×C31—41no—
82C31⋊C8—41no—
83#1512—311nomaximal, Sylow
84C22×C31—21no—
85C22×C31—21no—
86C22×C31C2×C22⋊C411yescharacteristic
87C22×C31AGL(1,ℤ/8)11yescharacteristic
88C22×C31#13711yescharacteristic
89C2×D31—41no—
90C2×D31—41no—
91C2×D31—41no—
92C4×C31—21no—
93C4×C31—21no—
94C4×C31—41no—
95C4×C31—41no—
96C4×C31—81no—
97Dic31—21no—
98Dic31—21no—
99Dic31—21no—
100Dic31—21no—
101Dic31—41no—
102Dic31—81no—
103#529—311no—
104#432—311no—
105#382—311no—
106#328—311no—
107#328D3111yescharacteristic, complemented
108#327—311no—
109#327—311no—
110C2×C31—21no—
111C2×C31—21no—
112C2×C31#41011yescharacteristic
113C2×C31#41711yescharacteristic
114C2×C31#42111yescharacteristic
115D31—81no—
116#126—621no—
117#125—311no—
118#124—311no—
119#123—621no—
120C22⋊Q8C2×D3111yescharacteristic
121#121—311no—
122C4×Q8—311no—
123C4×D4—311no—
124C4×D4—621no—
125#117—621no—
126C2×C4⋊C4—621no—
127C2×C42—311no—
128C4⋊C8—621no—
129C22⋊C8—311no—
130C22⋊C8C2×D3111yescharacteristic
131#97—621no—
132#95—311no—
133#95—621no—
134#95C2×D3111yescharacteristic
135C31#151211yescharacteristic, complemented, Sylow
136C2×Q8C4×D3111yescharacteristic
137C2×D4—311no—
138C2×D4—621no—
139C22×C4—21no—
140C22×C4—311no—
141C22×C4—311no—
142C22×C4—621no—
143C22×C4—621no—
144C22×C4C22×D3111yescharacteristic
145C2×C8—21no—
146C2×C8—621no—
147C4⋊C4—21no—
148C4⋊C4—311no—
149C4⋊C4—621no—
150C4⋊C4—621no—
151C4⋊C4—621no—
152C4⋊C4—1242no—
153C4⋊C4C4×D3111yescharacteristic
154C22⋊C4—21no—
155C22⋊C4—621no—
156C22⋊C4—621no—
157C22⋊C4—621no—
158C22⋊C4—621no—
159C42—311no—
160C42—311no—
161C42—311no—
162C42—311no—
163C42—621no—
164C23—621no—
165C23D4×D3111yescharacteristic
166Q8—41no—
167D4—1241no—
168D4—1241no—
169D4—1241no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—311no—
177C2×C4—311no—
178C2×C4—311no—
179C2×C4—311no—
180C2×C4—621no—
181C2×C4—621no—
182C2×C4—621no—
183C2×C4—1242no—
184C2×C4—1241no—
185C2×C4—1241no—
186C2×C4—1241no—
187C2×C4—1241no—
188C2×C4C2×C4×D3111yescharacteristic
189C2×C4D4×D3111yescharacteristic
190C8—41no—
191C8—1241no—
192C22—21no—
193C22—21no—
194C22—1241no—
195C22—1241no—
196C22—1241no—
197C22C22⋊C4×D3111yescharacteristic
198C22#1175849111yescharacteristic
199C22#1175849511yescharacteristic
200C4—21no—
201C4—21no—
202C4—41no—
203C4—41no—
204C4—81no—
205C4—621no—
206C4—621no—
207C4—621no—
208C4—621no—
209C4—1241no—
210C4—2481no—
211C2—21no—
212C2—21no—
213C2—2481no—
214C2#1452102111yescharacteristic
215C2#1452104911yescharacteristic
216C2#1452106411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D31
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#328C2
socleC22×C31C2×C22⋊C4
prime radical#11758507C22
cosocleC22×C4×C31C23
hypercenter#328D31
hypocenterC31#1512
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #14521103C2semidirect
3. #14520913C2semidirect
4. #14520786C2semidirect
7. C31×#328C2semidirect
9. #11758524C4semidirect
10. Q8×Dic31C4semidirect
15. #11758470C4semidirect
17. #11758467C4semidirect
107. #328D31semidirect
135. C31#1512semidirect

Maximal subgroups

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

subgroupindex
#145215852
#145211032
#145209132
#145207862
#145207842
#145207822
C31×#3282
#151231