Finite Group Databasebeta

← #11793984

Subgroups — #11793984

Order 1152.

792 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 792 conjugacy classes of subgroups — too many to draw. Only its 155 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#10596219C211yesmaximal, characteristic
2#10592818C211yesmaximal, characteristic, complemented
3#10592705C212yesmaximal, complemented
4#10592701C212yesmaximal, complemented
5C32×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
6#68698—34nomaximal
7C2×#3828C2212yes—
8C2×C32×M16C2211yescharacteristic
9C32×#117C2212yes—
10#64135C2211yescharacteristic
11C22×C3⋊(C3⋊C8)C2211yescharacteristic
12#64118—22no—
13#64117—22no—
14#64113—22no—
15#63641—22no—
16#63637—22no—
17#63636—22no—
18#63633—24no—
19#5748—34no—
20#5119—34no—
21#5006—38no—
22#5002—38no—
23C3×H(3,ℤ/4)D314yescomplemented
24C22×C32×C4C2311yescharacteristic
25C2×#638—22no—
26#3828—22no—
27#3828—22no—
28#3828—22no—
29#3828—22no—
30C2×C4⋊(C3⋊D3)D412yes—
31C2×C4×C3⋊D3—22no—
32C2×#634D412yes—
33C32×M16—22no—
34C2×C32×C8D412yes—
35C32×C4⋊C4—22no—
36C32×C22⋊C4—22no—
37C32×C42—22no—
38#3757D412yes—
39C4⋊(C3⋊Dic3)—21no—
40C4×C3⋊Dic3—21no—
41C2×C3⋊(C3⋊C8)—22no—
42C2×C3⋊(C3⋊C8)—21no—
43#3746—22no—
44#3745—22no—
45#3744—24no—
46#2053—91noSylow
47C2×#235—38no—
48C2×C3×M16C2×D314yes—
49C3×#117C2×D318yes—
50#926—34no—
51C22×C3⋊C8—34no—
52#909—68no—
53#908—68no—
54#904—68no—
55Dic3⋊C8—68no—
56#810—68no—
57#809—68no—
58#806—616no—
59C23×C32C2×D411yescharacteristic
60C22×C3⋊D3—22no—
61C2×C32×C4—42no—
62C2×C32×C4C2×D411yescharacteristic
63C2×C32×C4C2×D412yes—
64C2×C32×C4#4112yes—
65C2×C32×C4#4111yescharacteristic
66#638—42no—
67#638—42no—
68C2×C3⋊Dic3—22no—
69C2×C3⋊Dic3—22no—
70C4⋊(C3⋊D3)—22no—
71C4⋊(C3⋊D3)—22no—
72C4×C3⋊D3—42no—
73C4×C3⋊D3—42no—
74#634—22no—
75#634—22no—
76C32×C8—22no—
77C3⋊(C3⋊C8)—41no—
78#575—91no—
79#424—91no—
80#416—92no—
81#410—92no—
82H(3,ℤ/4)C3⋊D311yescharacteristic, complemented
83C22×C3×C4C22×D314yes—
84C2×#67—68no—
85#235—68no—
86#235—68no—
87#235—68no—
88#235—68no—
89C2×D12—38no—
90C2×C4×D3—68no—
91C2×Dic6—38no—
92C3×M16—28no—
93C2×C3×C8D1218yes—
94C3×C4⋊C4—28no—
95C3×C22⋊C4—28no—
96C3×C42—28no—
97#217—38no—
98C4⋊Dic3—64no—
99C4×Dic3—64no—
100C2×C3⋊C8—64no—
101C2×C3⋊C8—68no—
102Dic12—68no—
103D24—68no—
104#204—616no—
105C22×C32—41no—
106C22×C32#12112yes—
107C22×C32#12111yescharacteristic
108C2×C3⋊D3—42no—
109C2×C3⋊D3—82no—
110C32×C4—82no—
111C32×C4#12011yescharacteristic
112C32×C4#12312yes—
113C32×C4#12411yescharacteristic
114C3⋊Dic3—42no—
115C3⋊Dic3—42no—
116C2×#41—92no—
117#137—182no—
118AGL(1,ℤ/8)—182no—
119#135—182no—
120C2×M16C2×C3⋊D311yescharacteristic
121C22×C8—91no—
122#117—91no—
123#117C2×C3⋊D312yes—
124C4⋊C8—182no—
125#103—182no—
126#102—182no—
127#99—184no—
128C23×C3D3×D414yes—
129C22×D3—68no—
130C2×C3×C4—48no—
131C2×C3×C4C2×D1214yes—
132C2×C3×C4#23518yes—
133C2×C3×C4D3×D418yes—
134C2×C3×C4#23914yes—
135#67—128no—
136#67—128no—
137C2×Dic3—68no—
138C2×Dic3—68no—
139D12—68no—
140D12—68no—
141C4×D3—128no—
142C4×D3—128no—
143Dic6—68no—
144Dic6—68no—
145C3×C8—28no—
146C3⋊C8—124no—
147C2×C32—21no—
148C2×C32—22no—
149C2×C32#39411yescharacteristic
150C3⋊D3—82no—
151#41—182no—
152#41—182no—
153#41—182no—
154#41—182no—
155C2×Q8—92no—
156C2×D4—92no—
157C2×D4—182no—
158C22×C4—182no—
159C22×C4C22×C3⋊D311yescharacteristic
160Q16—182no—
161SD16—184no—
162D8—182no—
163M16—22no—
164C2×C8—181no—
165C2×C8—182no—
166C2×C8C4⋊(C3⋊D3)12yes—
167C4⋊C4—22no—
168C4⋊C4—181no—
169C22⋊C4—22no—
170C22⋊C4—92no—
171C42—22no—
172C42—181no—
173C22×C3—44no—
174C22×C3#88418yes—
175C22×C3#89514yes—
176C2×D3—128no—
177C2×D3—248no—
178C3×C4—88no—
179C3×C4#87514yes—
180C3×C4#88214yes—
181C3×C4#89418yes—
182Dic3—128no—
183Dic3—128no—
184C32#205311yescharacteristic, complemented, Sylow
185C23—182no—
186C23D4×C3⋊D311yescharacteristic
187Q8—182no—
188Q8—182no—
189D4—182no—
190D4—182no—
191D4—362no—
192D4—362no—
193C2×C4—42no—
194C2×C4—182no—
195C2×C4—182no—
196C2×C4—362no—
197C2×C4—362no—
198C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
199C2×C4#382812yes—
200C2×C4D4×C3⋊D312yes—
201C2×C4#383211yescharacteristic
202C8—22no—
203C8—361no—
204C2×C3—24no—
205C2×C3—28no—
206C2×C3#467214yes—
207D3—248no—
208C22—41no—
209C22—362no—
210C22—722no—
211C22#6409312yes—
212C22#6410411yescharacteristic
213C4—82no—
214C4—362no—
215C4—362no—
216C4#6408411yescharacteristic
217C4#6409111yescharacteristic
218C4#6410312yes—
219C3#6869814yescomplemented
220C2—22no—
221C2—21no—
222C2—722no—
223C2#1059237111yescharacteristic
subgroupG/H
centerC4#64084
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×H(3,ℤ/4)C2
socleC2×C32#394
prime radical#10596219C2
hypercenterH(3,ℤ/4)C3⋊D3
hypocenterC32#2053
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
2. #10592818C2semidirect
3. #10592705C2semidirect
4. #10592701C2semidirect
5. C32×H(3,ℤ/4)C2semidirect
23. C3×H(3,ℤ/4)D3semidirect
82. H(3,ℤ/4)C3⋊D3semidirect
184. C32#2053semidirect
219. C3#68698semidirect

Maximal subgroups

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

subgroupindex
#105962192
#105928182
#105927052
#105927012
C32×H(3,ℤ/4)2
#686983