Finite Group Databasebeta

← #11775748

Subgroups — #11775748

Order 1152.

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

normal subgroups only

This group has 695 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×C4×#208C212yesmaximal, complemented
3#10589087C214yesmaximal, complemented
4#69859—32nomaximal
5C2×#3828C412yes—
6C2×C32×C42C2211yescharacteristic
7#64139—22no—
8#64084C2212yes—
9#64083C411yescharacteristic
10C4×C4⋊(C3⋊D3)—22no—
11#64078C411yescharacteristic
12C2×C3×#208—22no—
13C3×#803C2214yes—
14C3×C4×C3⋊C8—22no—
15#5477—32no—
16#5477—61no—
17C3×C4×M16—32no—
18C4×#208D312yescomplemented
19#4464—38no—
20C22×C32×C4C2×C411yescharacteristic
21C22×C32×C4D412yes—
22C2×#638—22no—
23#3828—44no—
24C2×C4⋊(C3⋊D3)—22no—
25C2×C4⋊(C3⋊D3)C2×C412yes—
26C2×C4×C3⋊D3—22no—
27C2×#634C2×C412yes—
28C32×C42C2×C411yescharacteristic
29C32×C42D412yes—
30C32×C42C2311yescharacteristic
31#3752—24no—
32C4⋊(C3⋊Dic3)—22no—
33C3×#208—28no—
34C2×C3×C3⋊C8—24no—
35#1525—91noSylow
36C2×#235—34no—
37C2×#235—62no—
38C2×C3×M16—62no—
39C2×C3×C42—21no—
40C2×C3×C42C2×D312yes—
41#930—64no—
42#930—62no—
43#930—62no—
44C2×#208—22no—
45#875—34no—
46#875—62no—
47#874—32no—
48#874—61no—
49C4×D12—64no—
50C4×D12—62no—
51C4×D12—62no—
52#869—32no—
53#869—61no—
54C3×#97—34no—
55C3×C4×C8—62no—
56#803C2×D314yes—
57C4×C3⋊C8—22no—
58C23×C32C22⋊C411yescharacteristic
59C22×C3⋊D3—22no—
60C2×C32×C4—22no—
61C2×C32×C4—24no—
62C2×C32×C4C22⋊C411yescharacteristic
63C2×C32×C4C22⋊C412yes—
64C2×C32×C4C22×C411yescharacteristic
65C2×C32×C4C2×D412yes—
66#638—44no—
67C2×C3⋊Dic3—22no—
68C4⋊(C3⋊D3)—42no—
69C4⋊(C3⋊D3)—44no—
70C4×C3⋊D3—44no—
71#634—42no—
72C3×C3⋊C8—28no—
73#532—91no—
74C4×M16—32no—
75#329—94no—
76C22×C3×C4—21no—
77C22×C3×C4—22no—
78C22×C3×C4C4×D312yes—
79C22×C3×C4D1212yes—
80C22×C3×C4#6712yes—
81C2×#67—64no—
82C2×#67—64no—
83#235—128no—
84#235—128no—
85C2×D12—34no—
86C2×D12—62no—
87C2×D12—64no—
88C2×D12—62no—
89C2×D12—62no—
90C2×C4×D3—64no—
91C2×C4×D3—64no—
92C2×Dic6—34no—
93C2×Dic6—62no—
94C3×M16—68no—
95C2×C3×C8—64no—
96C3×C42—21no—
97C3×C42—22no—
98C3×C42—21no—
99C3×C42C4×D312yes—
100C3×C42D1212yes—
101C3×C42#6712yes—
102C3×C42C22×D312yes—
103(C2×D3)⋊C4—68no—
104(C2×D3)⋊C4—64no—
105(C2×D3)⋊C4—64no—
106C4⋊Dic3—64no—
107C4⋊Dic3—62no—
108C4⋊Dic3—62no—
109#208—28no—
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#10414yes—
120C3⋊Dic3—42no—
121C2×#41—92no—
122C2×M16—62no—
123C4⋊Q8—91no—
124#127—91no—
125#124—92no—
126#121—182no—
127C4×D4—182no—
128C2×C42D3211yescharacteristic
129#97—34no—
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—68no—
164C3⋊C8—28no—
165C2×C32—41no—
166C2×C32C2×#10011yescharacteristic
167C2×C32C2×#10412yes—
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—
177M16—68no—
178C2×C8—64no—
179C4⋊C4—182no—
180C22⋊C4—184no—
181C42#62411yescharacteristic
182C42#62612yes—
183C42C2×D3211yescharacteristic
184C22×C3—22no—
185C22×C3—22no—
186C22×C3—22no—
187C22×C3—22no—
188C22×C3—21no—
189C22×C3—42no—
190C22×C3C2×(C2×D3)⋊C412yes—
191C2×D3—124no—
192C2×D3—128no—
193C2×D3—124no—
194C2×D3—124no—
195C2×D3—124no—
196C3×C4—22no—
197C3×C4—22no—
198C3×C4—22no—
199C3×C4—22no—
200C3×C4—22no—
201C3×C4—24no—
202C3×C4—42no—
203C3×C4#80514yes—
204C3×C4#82314yes—
205C3×C4#82514yes—
206Dic3—124no—
207Dic3—124no—
208C32#152511yescharacteristic, complemented, Sylow
209C23—182no—
210C23#372211yescharacteristic
211Q8—362no—
212D4—362no—
213D4—364no—
214D4—364no—
215C2×C4—22no—
216C2×C4—24no—
217C2×C4—182no—
218C2×C4—364no—
219C2×C4#372212yes—
220C2×C4#372211yescharacteristic
221C2×C4C2×#62411yescharacteristic
222C2×C4C2×#62612yes—
223C8—68no—
224C2×C3—21no—
225C2×C3—22no—
226C2×C3—42no—
227C2×C3—42no—
228C2×C3C2×#80512yes—
229C2×C3C2×#82312yes—
230C2×C3C2×#82512yes—
231D3—244no—
232D3—244no—
233C22—21no—
234C22—22no—
235C22—362no—
236C22—364no—
237C22C2×#372211yescharacteristic
238C4—21no—
239C4—22no—
240C4—362no—
241C4#6355912yes—
242C4#6357014yes—
243C3—21no—
244C3#6985912yescomplemented
245C2—41no—
246C2—722no—
247C2C2×#6355911yescharacteristic
248C2C2×#6357012yes—
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#1525
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×C4×#208C2semidirect
3. #10589087C2semidirect
18. C4×#208D3semidirect
208. C32#1525semidirect
244. C3#69859semidirect

Maximal subgroups

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

subgroupindex
#105959482
C3×C4×#2082
#105890872
#698593