Finite Group Databasebeta

← #11793981

Subgroups — #11793981

Order 1152.

792 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 792 conjugacy classes of subgroups — too many to draw. Only its 165 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
2C32×#424C211yesmaximal, characteristic, complemented
3#10592812C212yesmaximal, complemented
4#10592705C212yesmaximal, complemented
5#10589423C211yesmaximal, characteristic, complemented
6#70547—34nomaximal
7C2×#3828C2212yes—
8C2×C32×M16C2211yescharacteristic
9C22×C32×C8C2211yescharacteristic
10C32×#117C2211yescharacteristic
11#64135C2212yes—
12#64118—22no—
13#64117—22no—
14#64113—22no—
15C32×C4⋊C8—22no—
16#63648—22no—
17#63643—22no—
18#63633—24no—
19#5748—34no—
20C3×#424D314yescomplemented
21#5113—38no—
22#5006—38no—
23#4557—34no—
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×C8—22no—
35C2×C32×C8—21no—
36C2×C32×C8D412yes—
37C32×C4⋊C4—21no—
38C32×C22⋊C4D412yes—
39C32×C42—21no—
40#3757—22no—
41C4⋊(C3⋊Dic3)—22no—
42C4×C3⋊Dic3—22no—
43#3746—22no—
44#3745—22no—
45#3744—24no—
46#2053—91noSylow
47C2×#235—38no—
48C2×C3×M16C2×D314yes—
49C22×C3×C8C2×D314yes—
50C3×#117C2×D314yes—
51#926—38no—
52#909—68no—
53#908—68no—
54#904—68no—
55C3×C4⋊C8—28no—
56#821—68no—
57#816—68no—
58#806—616no—
59C23×C32C2×D411yescharacteristic
60C22×C3⋊D3—22no—
61C2×C32×C4—22no—
62C2×C32×C4C2×D412yes—
63C2×C32×C4C2×D411yescharacteristic
64C2×C32×C4#4111yescharacteristic
65C2×C32×C4#4112yes—
66#638—42no—
67#638—42no—
68C2×C3⋊Dic3—22no—
69C2×C3⋊Dic3—42no—
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—
77C32×C8—41no—
78#575—91no—
79#424C3⋊D311yescharacteristic, complemented
80#416—92no—
81#410—92no—
82H(3,ℤ/4)—91no—
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×C8—28no—
94C2×C3×C8—24no—
95C2×C3×C8#6718yes—
96C3×C4⋊C4—24no—
97C3×C22⋊C4D1218yes—
98C3×C42—24no—
99#217—68no—
100C4⋊Dic3—68no—
101C4×Dic3—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—42no—
111C32×C4#12011yescharacteristic
112C32×C4#12312yes—
113C32×C4#12411yescharacteristic
114C3⋊Dic3—42no—
115C3⋊Dic3—82no—
116C2×#41—92no—
117#137—182no—
118AGL(1,ℤ/8)—182no—
119#135—182no—
120C2×M16C2×C3⋊D311yescharacteristic
121C22×C8C2×C3⋊D311yescharacteristic
122#117—92no—
123#117C2×C3⋊D311yescharacteristic
124C4⋊C8—22no—
125#103—182no—
126#102—182no—
127#99—184no—
128C23×C3C2×D1214yes—
129C22×D3—68no—
130C2×C3×C4—28no—
131C2×C3×C4#23514yes—
132C2×C3×C4D3×D418yes—
133C2×C3×C4#23918yes—
134C2×C3×C4C2×#6714yes—
135#67—128no—
136#67—128no—
137C2×Dic3—68no—
138C2×Dic3—128no—
139D12—68no—
140D12—68no—
141C4×D3—128no—
142C4×D3—128no—
143Dic6—68no—
144Dic6—68no—
145C3×C8—28no—
146C3×C8—44no—
147C2×C32—22no—
148C2×C32—21no—
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—22no—
165C2×C8—21no—
166C2×C8#63812yes—
167C4⋊C4—21no—
168C4⋊C4—182no—
169C22⋊C4—182no—
170C22⋊C4C4⋊(C3⋊D3)12yes—
171C42—21no—
172C42—182no—
173C22×C3—44no—
174C22×C3#89518yes—
175C22×C3#93014yes—
176C2×D3—128no—
177C2×D3—248no—
178C3×C4—48no—
179C3×C4#89418yes—
180C3×C4#93714yes—
181C3×C4#94714yes—
182Dic3—128no—
183Dic3—248no—
184C32#205311yescharacteristic, complemented, Sylow
185C23—182no—
186C23C2×C4⋊(C3⋊D3)11yescharacteristic
187Q8—182no—
188Q8—182no—
189D4—182no—
190D4—182no—
191D4—362no—
192D4—362no—
193C2×C4—22no—
194C2×C4—182no—
195C2×C4—362no—
196C2×C4—362no—
197C2×C4—362no—
198C2×C4#382811yescharacteristic
199C2×C4D4×C3⋊D312yes—
200C2×C4#383212yes—
201C2×C4C2×#63811yescharacteristic
202C8—22no—
203C8—41no—
204C2×C3—28no—
205C2×C3—24no—
206C2×C3#499114yes—
207D3—248no—
208C22—41no—
209C22—362no—
210C22—722no—
211C22#6410412yes—
212C22#6413911yescharacteristic
213C4—42no—
214C4—362no—
215C4—722no—
216C4#6410312yes—
217C4#6414611yescharacteristic
218C4#6415611yescharacteristic
219C3#7054714yescomplemented
220C2—21no—
221C2—22no—
222C2—722no—
223C2#1059269011yescharacteristic
subgroupG/H
centerC4#64156
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#424C2
socleC2×C32#394
prime radical#10596219C2
hypercenter#424C3⋊D3
hypocenterC32#2053
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #424

Complements

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

NH ≅ G/Ntype
2. C32×#424C2semidirect
3. #10592812C2semidirect
4. #10592705C2semidirect
5. #10589423C2semidirect
20. C3×#424D3semidirect
79. #424C3⋊D3semidirect
184. C32#2053semidirect
219. C3#70547semidirect

Maximal subgroups

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

subgroupindex
#105962192
C32×#4242
#105928122
#105927052
#105894232
#705473