Finite Group Databasebeta

← #11785113

Subgroups — #11785113

Order 1152.

1008 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 187 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
3#10592817C212yesmaximal, complemented
4C32×#343C211yesmaximal, characteristic, complemented
5#10589396C211yesmaximal, characteristic, complemented
6#68994—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#63650—24no—
17#63641—22no—
18#63641—22no—
19C2×#893—34no—
20C2×#823—38no—
21#5118—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)—22no—
31C2×C4⋊(C3⋊D3)D412yes—
32C2×C4⋊(C3⋊D3)Q812yes—
33C2×C4×C3⋊D3—22no—
34C2×C4×C3⋊D3—22no—
35C2×C4×C3⋊D3—44no—
36C32×M16—22no—
37C32×M16—22no—
38C2×C32×C8—22no—
39C32×C4⋊C4—22no—
40#3752—24no—
41C4×C3⋊Dic3D412yes—
42C4×C3⋊Dic3D412yes—
43#3748—22no—
44#3748—22no—
45C2×C3⋊(C3⋊C8)—22no—
46#1800—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—616no—
57Dic3⋊C8—68no—
58Dic3⋊C8—68no—
59C23×C32C22×C411yescharacteristic
60C22×C3⋊D3—22no—
61C22×C3⋊D3—22no—
62C22×C3⋊D3—42no—
63C22×C3⋊D3—42no—
64C22×C3⋊D3C4⋊C414yes—
65C2×C32×C4—22no—
66C2×C32×C4—42no—
67C2×C32×C4C2×D411yescharacteristic
68C2×C32×C4C2×D412yes—
69C2×C32×C4C2×Q811yescharacteristic
70C2×C32×C4#4112yes—
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—42no—
81C3⋊(C3⋊C8)—42no—
82C2×C4×D4—91no—
83#423—92no—
84C2×#100—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—38no—
93C2×D12—38no—
94C2×D12—68no—
95C2×D12—68no—
96C2×C4×D3—68no—
97C2×C4×D3—68no—
98C2×C4×D3—1216no—
99C3×M16—28no—
100C3×M16—28no—
101C2×C3×C8—28no—
102C3×C4⋊C4—28no—
103(C2×D3)⋊C4—616no—
104C4×Dic3—38no—
105C4×Dic3—38no—
106#208—68no—
107#208—68no—
108C2×C3⋊C8—68no—
109C22×C32—21no—
110C22×C32—21no—
111C22×C32C2×C22⋊C411yescharacteristic
112C22×C32C2×C4⋊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×C4#12112yes—
121C32×C4C22⋊Q812yes—
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—
134C4⋊C8—182no—
135C4⋊C8—182no—
136#100—184no—
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×C4#23518yes—
146C2×C3×C4D3×D414yes—
147C2×C3×C4D3×D418yes—
148C2×C3×C4D3×Q814yes—
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—48no—
159C3⋊C8—128no—
160C2×C32—21no—
161C2×C32—21no—
162C2×C32#38011yescharacteristic
163C2×C32C2×#10011yescharacteristic
164C2×C32#41311yescharacteristic
165C3⋊D3—44no—
166C24—92no—
167C2×D4—92no—
168C2×D4—92no—
169C2×D4—182no—
170C2×D4—182no—
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—22no—
180M16—182no—
181M16—182no—
182C2×C8—22no—
183C2×C8—182no—
184C4⋊C4—22no—
185C22⋊C4—184no—
186C42—92no—
187C42—92no—
188C22×C3—24no—
189C22×C3—24no—
190C22×C3#87214yes—
191C22×C3D3×C22⋊C414yes—
192C22×C3D3×C4⋊C414yes—
193C2×D3—616no—
194C2×D3—1216no—
195C2×D3—128no—
196C2×D3—128no—
197C2×D3—1216no—
198C3×C4—48no—
199C3×C4#88418yes—
200C3×C4#89618yes—
201Dic3—38no—
202Dic3—64no—
203Dic3—68no—
204C32#180011yescharacteristic, 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×C4#382812yes—
223C2×C4D4×C3⋊D311yescharacteristic
224C2×C4D4×C3⋊D312yes—
225C2×C4Q8×C3⋊D311yescharacteristic
226C8—42no—
227C8—362no—
228C2×C3—24no—
229C2×C3—24no—
230C2×C3#466714yes—
231C2×C3D3×#10014yes—
232C2×C3#475114yes—
233D3—1216no—
234C22—21no—
235C22—21no—
236C22—184no—
237C22—364no—
238C22—364no—
239C22—362no—
240C22—362no—
241C22#6408111yescharacteristic
242C22C22⋊C4×C3⋊D311yescharacteristic
243C22C4⋊C4×C3⋊D311yescharacteristic
244C4—42no—
245C4—92no—
246C4—181no—
247C4—182no—
248C4#6409312yes—
249C4#6410512yes—
250C3#6899414yescomplemented
251C2—21no—
252C2—21no—
253C2—364no—
254C2#1059236611yescharacteristic
255C2C3⋊D3×#10011yescharacteristic
256C2#1059245011yescharacteristic
subgroupG/H
centerC22C22⋊C4×C3⋊D3
commutatorC23×C32C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#343C2
socleC22×C32C2×C22⋊C4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenter#343C3⋊D3
hypocenterC32#1800
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
3. #10592817C2semidirect
4. C32×#343C2semidirect
5. #10589396C2semidirect
22. C3×#343D3semidirect
86. #343C3⋊D3semidirect
124. C3⋊Dic3#100semidirect
204. C32#1800semidirect
250. C3#68994semidirect

Maximal subgroups

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

subgroupindex
C2×#641022
C2×#636502
#105928172
C32×#3432
#105893962
#689943