Finite Group Databasebeta

← #11776227

Subgroups — #11776227

Order 1152.

647 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 647 conjugacy classes of subgroups — too many to draw. Only its 132 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#10595948C211yesmaximal, characteristic
2C3×#4925C212yesmaximal, complemented
3#10589096C212yesmaximal, complemented
4#10589091C212yesmaximal, complemented
5#70773—32nomaximal
6C2×#3828C412yes—
7C2×C32×C42C2211yescharacteristic
8#64139—22no—
9#64084C412yes—
10#64083C2211yescharacteristic
11C4×C4⋊(C3⋊D3)—22no—
12#64078C2211yescharacteristic
13C3×#830—22no—
14C3×C4⋊(C3⋊C8)C2214yes—
15C3×C4×C3⋊C8—22no—
16#5477—32no—
17#5477—61no—
18C3×#431—32no—
19#4925D312yescomplemented
20#4485—34no—
21#4481—34no—
22C22×C32×C4C2×C411yescharacteristic
23C22×C32×C4D412yes—
24C2×#638—22no—
25#3828—44no—
26C2×C4⋊(C3⋊D3)—22no—
27C2×C4⋊(C3⋊D3)C2×C412yes—
28C2×C4×C3⋊D3—22no—
29C2×#634C2×C412yes—
30C32×C42C2×C411yescharacteristic
31C32×C42D412yes—
32C32×C42C2311yescharacteristic
33#3752—24no—
34C4⋊(C3⋊Dic3)—22no—
35C2×C3×C3⋊C8—24no—
36#1543—91noSylow
37C2×#235—34no—
38C2×#235—62no—
39C2×C3×C42—21no—
40C2×C3×C42C2×D312yes—
41#930—64no—
42#930—62no—
43#930—62no—
44#875—34no—
45#875—62no—
46#874—32no—
47#874—61no—
48C4×D12—64no—
49C4×D12—62no—
50C4×D12—62no—
51#869—32no—
52#869—61no—
53C3×C4⋊C8—34no—
54C3×C22⋊C8—62no—
55C3×C4×C8—62no—
56#830—22no—
57C4⋊(C3⋊C8)C2×D314yes—
58C4×C3⋊C8—22no—
59C23×C32C22⋊C411yescharacteristic
60C22×C3⋊D3—22no—
61C2×C32×C4—22no—
62C2×C32×C4—24no—
63C2×C32×C4C22⋊C412yes—
64C2×C32×C4C22⋊C411yescharacteristic
65C2×C32×C4C22×C411yescharacteristic
66C2×C32×C4C2×D412yes—
67#638—44no—
68C2×C3⋊Dic3—22no—
69C4⋊(C3⋊D3)—42no—
70C4⋊(C3⋊D3)—44no—
71C4×C3⋊D3—44no—
72#634—42no—
73C3×C3⋊C8—44no—
74#532—91no—
75#431—32no—
76#333—92no—
77#331—92no—
78C22×C3×C4—21no—
79C22×C3×C4—22no—
80C22×C3×C4C4×D312yes—
81C22×C3×C4D1212yes—
82C22×C3×C4#6712yes—
83C2×#67—64no—
84C2×#67—64no—
85#235—128no—
86#235—128no—
87C2×D12—34no—
88C2×D12—62no—
89C2×D12—64no—
90C2×D12—62no—
91C2×D12—62no—
92C2×C4×D3—64no—
93C2×C4×D3—64no—
94C2×Dic6—34no—
95C2×Dic6—62no—
96C2×C3×C8—64no—
97C3×C42—21no—
98C3×C42—22no—
99C3×C42—21no—
100C3×C42C4×D312yes—
101C3×C42D1212yes—
102C3×C42#6712yes—
103C3×C42C22×D312yes—
104(C2×D3)⋊C4—68no—
105(C2×D3)⋊C4—64no—
106(C2×D3)⋊C4—64no—
107C4⋊Dic3—64no—
108C4⋊Dic3—62no—
109C4⋊Dic3—62no—
110C2×C3⋊C8—24no—
111C22×C32—21no—
112C22×C32—22no—
113C22×C32C2×C22⋊C411yescharacteristic
114C2×C3⋊D3—42no—
115C2×C3⋊D3—44no—
116C32×C4—21no—
117C32×C4—22no—
118C32×C4#10012yes—
119C32×C4#13514yes—
120C3⋊Dic3—42no—
121C2×#41—92no—
122C4⋊Q8—91no—
123#127—91no—
124#124—92no—
125#121—182no—
126C4×D4—182no—
127C2×C42D3211yescharacteristic
128C4⋊C8—34no—
129C22⋊C8—62no—
130C4×C8—62no—
131C23×C3—21no—
132C23×C3(C2×D3)⋊C412yes—
133C22×D3—64no—
134C22×D3—64no—
135C2×C3×C4—24no—
136C2×C3×C4—24no—
137C2×C3×C4—24no—
138C2×C3×C4—24no—
139C2×C3×C4—22no—
140C2×C3×C4—21no—
141C2×C3×C4—21no—
142C2×C3×C4—22no—
143C2×C3×C4—44no—
144C2×C3×C4(C2×D3)⋊C412yes—
145C2×C3×C4(C2×D3)⋊C412yes—
146C2×C3×C4(C2×D3)⋊C412yes—
147C2×C3×C4C2×C4×D312yes—
148C2×C3×C4C2×D1212yes—
149C2×C3×C4C2×#6712yes—
150#67—128no—
151#67—128no—
152C2×Dic3—64no—
153C2×Dic3—64no—
154D12—124no—
155D12—128no—
156D12—124no—
157D12—124no—
158D12—124no—
159C4×D3—128no—
160C4×D3—128no—
161Dic6—124no—
162Dic6—124no—
163C3×C8—124no—
164C3⋊C8—44no—
165C2×C32—41no—
166C2×C32C2×#10011yescharacteristic
167C2×C32#41612yes—
168C3⋊D3—82no—
169#41—364no—
170C2×Q8—92no—
171C2×D4—92no—
172C2×D4—182no—
173C2×D4—182no—
174C22×C4—182no—
175C22×C4#62411yescharacteristic
176C22×C4#62612yes—
177C2×C8—64no—
178C4⋊C4—182no—
179C22⋊C4—184no—
180C42#62411yescharacteristic
181C42#62612yes—
182C42C2×D3211yescharacteristic
183C22×C3—22no—
184C22×C3—22no—
185C22×C3—22no—
186C22×C3—22no—
187C22×C3—21no—
188C22×C3—42no—
189C22×C3C2×(C2×D3)⋊C412yes—
190C2×D3—124no—
191C2×D3—128no—
192C2×D3—124no—
193C2×D3—124no—
194C2×D3—124no—
195C3×C4—22no—
196C3×C4—22no—
197C3×C4—22no—
198C3×C4—22no—
199C3×C4—22no—
200C3×C4—24no—
201C3×C4—42no—
202C3×C4#82314yes—
203C3×C4#90414yes—
204C3×C4#95014yes—
205Dic3—124no—
206Dic3—124no—
207C32#154311yescharacteristic, complemented, Sylow
208C23—182no—
209C23#372211yescharacteristic
210Q8—362no—
211D4—362no—
212D4—364no—
213D4—364no—
214C2×C4—22no—
215C2×C4—24no—
216C2×C4—182no—
217C2×C4—364no—
218C2×C4#372212yes—
219C2×C4#372211yescharacteristic
220C2×C4C2×#62411yescharacteristic
221C2×C4C2×#62612yes—
222C8—124no—
223C2×C3—21no—
224C2×C3—22no—
225C2×C3—42no—
226C2×C3—42no—
227C2×C3#500212yes—
228C2×C3#511312yes—
229C2×C3C2×#82312yes—
230D3—244no—
231D3—244no—
232C22—21no—
233C22—22no—
234C22—362no—
235C22—364no—
236C22C2×#372211yescharacteristic
237C4—21no—
238C4—22no—
239C4—362no—
240C4#6355912yes—
241C4#6382914yes—
242C3—21no—
243C3#7077312yescomplemented
244C2—41no—
245C2—722no—
246C2C2×#6355911yescharacteristic
247C2#1059110512yes—
subgroupG/H
centerC2×C4#3722
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radical#10595948C2
cosocleC32×C42C23
hypercenterC2×C42D32
hypocenterC32#1543
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×#4925C2semidirect
3. #10589096C2semidirect
4. #10589091C2semidirect
19. #4925D3semidirect
207. C32#1543semidirect
243. C3#70773semidirect

Maximal subgroups

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

subgroupindex
#105959482
C3×#49252
#105890962
#105890912
#707733