Finite Group Databasebeta

← #16844287

Subgroups — #16844287

Order 3968.

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

normal subgroups only

This group has 218 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#14521099C211yesmaximal, characteristic, complemented
3#14520916C211yesmaximal, 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×C4×Dic31C2211yescharacteristic
13#11758475—21no—
14#11758470C411yescharacteristic, complemented
15#11758469—21no—
16#11758467C411yescharacteristic, complemented
17#11758463—21no—
18(C22⋊D31)⋊C4—21no—
19C31×C22⋊C8C2211yescharacteristic
20C31×#95C2211yescharacteristic
21C31⋊#95—21no—
22C31⋊#95—21no—
23C31⋊#95C2211yescharacteristic
24C22⋊(C31⋊C8)C2211yescharacteristic
25Dic31⋊C8—21no—
26C8×Dic31—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—
48C4×Dic31—21no—
49C4×Dic31C2×C411yescharacteristic
50C4×Dic31C2×C411yescharacteristic
51C4×Dic31D411yescharacteristic
52C4×Dic31D411yescharacteristic
53C2×C31⋊C8—21no—
54C23×C31C2×D411yescharacteristic
55C22×D31—21no—
56Q8×C31—41no—
57C2×C4×C31—21no—
58C2×C4×C31—21no—
59C2×C4×C31—41no—
60C2×C4×C31—41no—
61C2×C4×C31—41no—
62C2×C4×C31—41no—
63C2×C4×C31C22×C411yescharacteristic
64C2×C4×C31C2×D411yescharacteristic
65C22⋊D31—41no—
66C22⋊D31—41no—
67C2×Dic31—21no—
68C2×Dic31—21no—
69C2×Dic31—21no—
70C2×Dic31—41no—
71C2×Dic31—41no—
72C2×Dic31—41no—
73C2×Dic31—41no—
74C2×Dic31C22⋊C411yescharacteristic
75C2×Dic31C22⋊C411yescharacteristic
76C2×Dic31C22⋊C411yescharacteristic
77C2×Dic31C22⋊C411yescharacteristic
78D124—41no—
79C4×D31—42no—
80C8×C31—41no—
81C31⋊C8—41no—
82#1521—311nomaximal, Sylow
83C22×C31—21no—
84C22×C31—21no—
85C22×C31C2×C22⋊C411yescharacteristic
86C22×C31#13511yescharacteristic
87C22×C31#13511yescharacteristic
88C2×D31—41no—
89C2×D31—41no—
90C2×D31—41no—
91C4×C31—21no—
92C4×C31—21no—
93C4×C31—41no—
94C4×C31—41no—
95C4×C31—81no—
96Dic31—21no—
97Dic31—21no—
98Dic31—21no—
99Dic31—21no—
100Dic31—41no—
101Dic31—81no—
102#529—311no—
103#431—311no—
104#383—311no—
105#328—311no—
106#328D3111yescharacteristic, complemented
107#327—311no—
108#327—311no—
109C2×C31—21no—
110C2×C31—21no—
111C2×C31#41011yescharacteristic
112C2×C31#41611yescharacteristic
113C2×C31#42111yescharacteristic
114D31—81no—
115#126—621no—
116#125—311no—
117#124—311no—
118#123—621no—
119C22⋊Q8C2×D3111yescharacteristic
120#121—311no—
121C4×Q8—311no—
122C4×D4—311no—
123C4×D4—621no—
124#117—621no—
125C2×C42—311no—
126C4⋊C8—621no—
127C22⋊C8—311no—
128C22⋊C8C2×D3111yescharacteristic
129C4×C8—621no—
130#95—311no—
131#95—621no—
132#95—621no—
133#95C2×D3111yescharacteristic
134C31#152111yescharacteristic, complemented, Sylow
135C2×Q8C4×D3111yescharacteristic
136C2×D4—311no—
137C2×D4—621no—
138C22×C4—21no—
139C22×C4—311no—
140C22×C4—311no—
141C22×C4—621no—
142C22×C4—621no—
143C22×C4C22×D3111yescharacteristic
144C2×C8—21no—
145C2×C8—621no—
146C4⋊C4—21no—
147C4⋊C4—311no—
148C4⋊C4—621no—
149C4⋊C4—621no—
150C4⋊C4—621no—
151C4⋊C4C4×D3111yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—621no—
154C22⋊C4—621no—
155C22⋊C4—621no—
156C22⋊C4—621no—
157C42—311no—
158C42—311no—
159C42—311no—
160C42—311no—
161C42—621no—
162C23—621no—
163C23D4×D3111yescharacteristic
164Q8—41no—
165D4—1241no—
166D4—1241no—
167D4—1241no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—311no—
175C2×C4—311no—
176C2×C4—311no—
177C2×C4—311no—
178C2×C4—621no—
179C2×C4—621no—
180C2×C4—621no—
181C2×C4—1242no—
182C2×C4—1241no—
183C2×C4—1241no—
184C2×C4—1241no—
185C2×C4—1241no—
186C2×C4C2×C4×D3111yescharacteristic
187C2×C4D4×D3111yescharacteristic
188C8—41no—
189C8—1241no—
190C22—21no—
191C22—21no—
192C22—1241no—
193C22—1241no—
194C22—1241no—
195C22C22⋊C4×D3111yescharacteristic
196C22#1175849311yescharacteristic
197C22#1175849611yescharacteristic
198C4—21no—
199C4—21no—
200C4—41no—
201C4—41no—
202C4—81no—
203C4—621no—
204C4—621no—
205C4—621no—
206C4—621no—
207C4—1241no—
208C4—2481no—
209C2—21no—
210C2—21no—
211C2—2481no—
212C2#1452102111yescharacteristic
213C2#1452104411yescharacteristic
214C2#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#1521
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. #14521099C2semidirect
3. #14520916C2semidirect
4. #14520786C2semidirect
7. C31×#328C2semidirect
9. #11758524C4semidirect
10. Q8×Dic31C4semidirect
14. #11758470C4semidirect
16. #11758467C4semidirect
106. #328D31semidirect
134. C31#1521semidirect

Maximal subgroups

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

subgroupindex
#145215852
#145210992
#145209162
#145207862
#145207842
#145207822
C31×#3282
#152131