Finite Group Databasebeta

← #11783770

Subgroups — #11783770

Order 1152.

1080 conjugacy classes of subgroups; only the 223 normal subgroups are shown.

normal subgroups only

This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 223 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×#64102C211yesmaximal, characteristic
2C2×#63650C212yesmaximal
3M16×C3⋊Dic3C212yesmaximal, complemented
4C32×#343C211yesmaximal, characteristic, complemented
5#10589396C211yesmaximal, characteristic, complemented
6#68972—34nomaximal
7C22×C4⋊(C3⋊D3)C2211yescharacteristic
8C22×C4×C3⋊D3C412yes—
9C2×C32×M16C2212yes—
10C2×C32×C4⋊C4C2211yescharacteristic
11C2×#3752C412yes—
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×#3748C2212yes—
14#64102—22no—
15#64102—22no—
16#63650C418yescomplemented
17#63642—22no—
18C8×C3⋊Dic3—22no—
19C2×#893—34no—
20C2×#823—38no—
21Dic3×M16—38no—
22C3×#343D314yescomplemented
23#4530—34no—
24C23×C3⋊D3C2×C412yes—
25C22×C32×C4C2×C412yes—
26C22×C32×C4C2311yescharacteristic
27C22×C3⋊Dic3C2×C411yescharacteristic
28C22×C3⋊Dic3C2×C411yescharacteristic
29C2×C4⋊(C3⋊D3)—22no—
30C2×C4⋊(C3⋊D3)—21no—
31C2×C4⋊(C3⋊D3)—21no—
32C2×C4⋊(C3⋊D3)C2×C414yes—
33C2×C4×C3⋊D3—22no—
34C2×C4×C3⋊D3—22no—
35C2×C4×C3⋊D3—44no—
36C32×M16—22no—
37C32×M16C2×C414yescomplemented
38C2×C32×C8—22no—
39C32×C4⋊C4—22no—
40#3752—24no—
41C4×C3⋊Dic3D412yes—
42C4×C3⋊Dic3D412yes—
43#3748—22no—
44#3748C2×C414yescomplemented
45C2×C3⋊(C3⋊C8)—22no—
46C4×#100—91noSylow
47C22×D12—34no—
48C22×C4×D3—38no—
49C2×C3×M16C2×D318yes—
50C2×C3×C4⋊C4C2×D314yes—
51C2×(C2×D3)⋊C4—38no—
52C2×C4×Dic3—34no—
53C2×#208—38no—
54#893—68no—
55#893—68no—
56#823—332no—
57#815—68no—
58C8×Dic3—68no—
59C23×C32C22×C411yescharacteristic
60C22×C3⋊D3—22no—
61C22×C3⋊D3—22no—
62C22×C3⋊D3—42no—
63C22×C3⋊D3—42no—
64C22×C3⋊D3C4214yes—
65C2×C32×C4—22no—
66C2×C32×C4—42no—
67C2×C32×C4C22×C412yes—
68C2×C32×C4C2×D412yes—
69C2×C32×C4#4111yescharacteristic
70C2×C32×C4#4111yescharacteristic
71C2×C3⋊Dic3—22no—
72C2×C3⋊Dic3—41no—
73C2×C3⋊Dic3C22⋊C412yes—
74C2×C3⋊Dic3C22⋊C411yescharacteristic
75C2×C3⋊Dic3C22⋊C411yescharacteristic
76C4⋊(C3⋊D3)—24no—
77C4⋊(C3⋊D3)—24no—
78C4×C3⋊D3—44no—
79C4×C3⋊D3—44no—
80C32×C8—24no—
81C3⋊(C3⋊C8)—24no—
82C2×C4×D4—91no—
83C2×#100—92no—
84C4×M16—92no—
85#343—91no—
86#343C3⋊D311yescharacteristic, complemented
87C23×D3—38no—
88C22×C3×C4C4×D318yes—
89C22×C3×C4C22×D314yes—
90C22×Dic3—34no—
91C22×Dic3—34no—
92C2×D12—316no—
93C2×D12—68no—
94C2×D12—64no—
95C2×D12—64no—
96C2×C4×D3—68no—
97C2×C4×D3—68no—
98C2×C4×D3—1216no—
99C3×M16—28no—
100C3×M16C4×D3116yescomplemented
101C2×C3×C8—28no—
102C3×C4⋊C4—28no—
103(C2×D3)⋊C4—616no—
104C4×Dic3—38no—
105C4×Dic3—38no—
106#208—316no—
107#208—68no—
108C2×C3⋊C8—68no—
109C22×C32—21no—
110C22×C32—21no—
111C22×C32C2×C4211yescharacteristic
112C22×C32C2×C22⋊C411yescharacteristic
113C22×C32#11711yescharacteristic
114C2×C3⋊D3—24no—
115C2×C3⋊D3—44no—
116C2×C3⋊D3—42no—
117C2×C3⋊D3—42no—
118C2×C3⋊D3—44no—
119C32×C4—42no—
120C32×C4C4×D412yes—
121C32×C4C4×D412yes—
122C3⋊Dic3—21no—
123C3⋊Dic3—22no—
124C3⋊Dic3#10012yescomplemented
125C22×D4—91no—
126C23×C4—92no—
127C2×M16—92no—
128C2×M16C2×C3⋊D312yes—
129C4×D4—182no—
130C4×D4—182no—
131C2×C4⋊C4C2×C3⋊D311yescharacteristic
132C2×C22⋊C4—92no—
133C2×C42—91no—
134#100—98no—
135#97—182no—
136C4×C8—182no—
137C23×C3C2×C4×D314yes—
138C22×D3—316no—
139C22×D3—68no—
140C22×D3—68no—
141C22×D3—128no—
142C22×D3—128no—
143C2×C3×C4—28no—
144C2×C3×C4—48no—
145C2×C3×C4C2×C4×D318yes—
146C2×C3×C4D3×D418yes—
147C2×C3×C4#23714yes—
148C2×C3×C4#23914yes—
149C2×Dic3—34no—
150C2×Dic3—38no—
151C2×Dic3—34no—
152C2×Dic3—68no—
153C2×Dic3—124no—
154D12—616no—
155D12—616no—
156C4×D3—1216no—
157C4×D3—1216no—
158C3×C8—216no—
159C3⋊C8—616no—
160C2×C32—21no—
161C2×C32—21no—
162C2×C32C4×C22⋊C411yescharacteristic
163C2×C32C2×#10011yescharacteristic
164C2×C32#41311yescharacteristic
165C3⋊D3—44no—
166C24—92no—
167C2×D4—94no—
168C2×D4—182no—
169C2×D4—181no—
170C2×D4—181no—
171C22×C4—91no—
172C22×C4—91no—
173C22×C4—182no—
174C22×C4—182no—
175C22×C4—364no—
176C22×C4C4×C3⋊D312yes—
177C22×C4C22×C3⋊D311yescharacteristic
178M16—22no—
179M16—94no—
180M16—182no—
181M16C4×C3⋊D314yescomplemented
182C2×C8—22no—
183C2×C8—182no—
184C4⋊C4—22no—
185C22⋊C4—184no—
186C42—92no—
187C42—92no—
188C22×C3—24no—
189C22×C3—24no—
190C22×C3C42×D314yes—
191C22×C3D3×C22⋊C414yes—
192C22×C3#89214yes—
193C2×D3—616no—
194C2×D3—1216no—
195C2×D3—128no—
196C2×D3—128no—
197C2×D3—1216no—
198C3×C4—48no—
199C3×C4#67⋊C418yes—
200C3×C4#89318yes—
201Dic3—38no—
202Dic3—64no—
203Dic3—68no—
204C32C4×#10011yescharacteristic, complemented, Sylow
205C23—94no—
206C23—182no—
207C23—182no—
208C23—362no—
209C23—362no—
210C23C2×C4×C3⋊D311yescharacteristic
211D4—184no—
212D4—184no—
213C2×C4—22no—
214C2×C4—42no—
215C2×C4—91no—
216C2×C4—92no—
217C2×C4—91no—
218C2×C4—182no—
219C2×C4—364no—
220C2×C4—364no—
221C2×C4—361no—
222C2×C4C2×C4×C3⋊D312yes—
223C2×C4D4×C3⋊D312yes—
224C2×C4#383011yescharacteristic
225C2×C4#383211yescharacteristic
226C8—24no—
227C8—184no—
228C2×C3—24no—
229C2×C3—24no—
230C2×C3#466614yes—
231C2×C3D3×#10014yes—
232C2×C3#475114yes—
233D3—1216no—
234C22—21no—
235C22—21no—
236C22—184no—
237C22—364no—
238C22—364no—
239C22—362no—
240C22—362no—
241C22C42×C3⋊D311yescharacteristic
242C22C22⋊C4×C3⋊D311yescharacteristic
243C22#6410111yescharacteristic
244C4—42no—
245C4—92no—
246C4—181no—
247C4—182no—
248C4#6409012yes—
249C4#6410212yes—
250C3#6897214yescomplemented
251C2—21no—
252C2—21no—
253C2—364no—
254C2#1059236511yescharacteristic
255C2C3⋊D3×#10011yescharacteristic
256C2#1059245011yescharacteristic
subgroupG/H
centerC22C22⋊C4×C3⋊D3
commutatorC22×C32C2×C42
FrattiniC22×C4C22×C3⋊D3
FittingC32×#343C2
socleC22×C32C2×C22⋊C4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenter#343C3⋊D3
hypocenterC32C4×#100
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
3. M16×C3⋊Dic3C2semidirect
4. C32×#343C2semidirect
5. #10589396C2semidirect
16. #63650C4semidirect
22. C3×#343D3semidirect
37. C32×M16C2×C4semidirect
44. #3748C2×C4semidirect
86. #343C3⋊D3semidirect
100. C3×M16C4×D3semidirect
124. C3⋊Dic3#100semidirect
181. M16C4×C3⋊D3semidirect
204. C32C4×#100semidirect
250. C3#68972semidirect

Maximal subgroups

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

subgroupindex
C2×#641022
C2×#636502
M16×C3⋊Dic32
C32×#3432
#105893962
#689723