Finite Group Databasebeta

← #11793855

Subgroups — #11793855

Order 1152.

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

normal subgroups only

This group has 798 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
2C2×#63652C212yesmaximal, complemented
3#10592831C212yesmaximal, complemented
4#10592817C211yesmaximal, characteristic, complemented
5C32×#338C211yesmaximal, characteristic, complemented
6#68719—34nomaximal
7C2×#3828C2212yes—
8C2×C32×M16C2212yes—
9C2×C32×M16C2211yescharacteristic
10C2×C4×C3⋊Dic3C2211yescharacteristic
11C2×#3748C2211yescharacteristic
12#64118—22no—
13#64117—22no—
14#64113—22no—
15#63652—22no—
16#63652—22no—
17#63651—22no—
18#63650—22no—
19#63641—22no—
20#5748—34no—
21C2×#825—38no—
22#5132—38no—
23#5118—34no—
24C3×#338D314yescomplemented
25C22×C32×C4C2311yescharacteristic
26C2×#638—22no—
27C22×C3⋊Dic3—21no—
28#3828—22no—
29#3828—22no—
30#3828—22no—
31#3828—22no—
32C2×C4⋊(C3⋊D3)D412yes—
33C2×C4×C3⋊D3—22no—
34C2×#634D412yes—
35C32×M16—22no—
36C32×M16—22no—
37C32×M16—22no—
38C2×C32×C8—22no—
39C2×C32×C8D412yes—
40C4×C3⋊Dic3—21no—
41C4×C3⋊Dic3D411yescharacteristic
42C4×C3⋊Dic3D411yescharacteristic
43#3748—22no—
44C2×C3⋊(C3⋊C8)—21no—
45#3746—22no—
46#3745—22no—
47#3744—24no—
48#2050—91noSylow
49C2×#235—38no—
50C2×C3×M16C2×D318yes—
51C2×C3×M16C2×D314yes—
52C2×C4×Dic3—34no—
53C2×#208—34no—
54#909—68no—
55#908—68no—
56#904—68no—
57#825—68no—
58#825—68no—
59#824—68no—
60#823—68no—
61Dic3⋊C8—68no—
62C23×C32#4111yescharacteristic
63C22×C3⋊D3—22no—
64C2×C32×C4C2×D411yescharacteristic
65C2×C32×C4C2×D412yes—
66C2×C32×C4C2×D411yescharacteristic
67C2×C32×C4#4112yes—
68#638—42no—
69#638—42no—
70C2×C3⋊Dic3—21no—
71C2×C3⋊Dic3—21no—
72C2×C3⋊Dic3—22no—
73C2×C3⋊Dic3—42no—
74C4⋊(C3⋊D3)—22no—
75C4⋊(C3⋊D3)—22no—
76C4×C3⋊D3—42no—
77C4×C3⋊D3—42no—
78#634—22no—
79#634—22no—
80C32×C8—22no—
81C32×C8—42no—
82C3⋊(C3⋊C8)—41no—
83#575—91no—
84#423—91no—
85C2×#104—92no—
86#413—92no—
87#338C3⋊D311yescharacteristic, complemented
88C22×C3×C4C22×D314yes—
89C2×#67—68no—
90C22×Dic3—64no—
91#235—68no—
92#235—68no—
93#235—68no—
94#235—68no—
95C2×D12—38no—
96C2×C4×D3—68no—
97C2×Dic6—38no—
98C3×M16—28no—
99C3×M16—28no—
100C3×M16—28no—
101C2×C3×C8—28no—
102C2×C3×C8D1218yes—
103C4×Dic3—34no—
104C4×Dic3—34no—
105C4×Dic3—64no—
106#208—68no—
107C2×C3⋊C8—64no—
108Dic12—68no—
109D24—68no—
110#204—616no—
111C22×C32—41no—
112C22×C32#12111yescharacteristic
113C22×C32#12312yes—
114C2×C3⋊D3—42no—
115C2×C3⋊D3—82no—
116C32×C4#12011yescharacteristic
117C32×C4#12112yes—
118C32×C4#12411yescharacteristic
119C3⋊Dic3—22no—
120C3⋊Dic3—41no—
121C3⋊Dic3—42no—
122C2×#41—92no—
123#137—182no—
124AGL(1,ℤ/8)—182no—
125#135—182no—
126C2×M16—91no—
127C2×M16C2×C3⋊D312yes—
128C2×M16C2×C3⋊D311yescharacteristic
129C2×C42—91no—
130C4⋊C8—182no—
131#104—182no—
132#104—182no—
133#101—182no—
134#100—182no—
135C23×C3#23914yes—
136C22×D3—68no—
137C2×C3×C4C2×D1214yes—
138C2×C3×C4#23518yes—
139C2×C3×C4D3×D418yes—
140C2×C3×C4D3×D414yes—
141#67—128no—
142#67—128no—
143C2×Dic3—64no—
144C2×Dic3—68no—
145C2×Dic3—64no—
146C2×Dic3—128no—
147D12—68no—
148D12—68no—
149C4×D3—128no—
150C4×D3—128no—
151Dic6—68no—
152Dic6—68no—
153C3×C8—28no—
154C3×C8—48no—
155C3⋊C8—124no—
156C2×C32—21no—
157C2×C32—22no—
158C2×C32#39411yescharacteristic
159C3⋊D3—82no—
160#41—182no—
161#41—182no—
162#41—182no—
163#41—182no—
164C2×Q8—92no—
165C2×D4—92no—
166C2×D4—182no—
167C22×C4—181no—
168C22×C4—182no—
169C22×C4C22×C3⋊D311yescharacteristic
170Q16—182no—
171SD16—184no—
172D8—182no—
173M16—22no—
174M16—22no—
175M16—22no—
176M16—182no—
177C2×C8—22no—
178C2×C8—181no—
179C2×C8C4⋊(C3⋊D3)12yes—
180C42—91no—
181C42—91no—
182C42—181no—
183C22×C3—44no—
184C22×C3#89418yes—
185C22×C3#89514yes—
186C2×D3—128no—
187C2×D3—248no—
188C3×C4#87514yes—
189C3×C4#88214yes—
190C3×C4#88418yes—
191Dic3—68no—
192Dic3—124no—
193Dic3—128no—
194C32#205011yescharacteristic, complemented, Sylow
195C23—182no—
196C23#383211yescharacteristic
197Q8—182no—
198Q8—182no—
199D4—182no—
200D4—182no—
201D4—362no—
202D4—362no—
203C2×C4—181no—
204C2×C4—182no—
205C2×C4—181no—
206C2×C4—362no—
207C2×C4—362no—
208C2×C4—362no—
209C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
210C2×C4#382812yes—
211C2×C4D4×C3⋊D312yes—
212C2×C4D4×C3⋊D311yescharacteristic
213C8—22no—
214C8—42no—
215C8—361no—
216C2×C3—24no—
217C2×C3—28no—
218C2×C3#467214yes—
219D3—248no—
220C22—41no—
221C22—362no—
222C22—722no—
223C22#6410312yes—
224C22#6410411yescharacteristic
225C4—182no—
226C4—361no—
227C4—362no—
228C4#6408411yescharacteristic
229C4#6409111yescharacteristic
230C4#6409312yes—
231C3#6871914yescomplemented
232C2—21no—
233C2—22no—
234C2—722no—
235C2#1059237111yescharacteristic
subgroupG/H
centerC4#64084
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#338C2
socleC2×C32#394
prime radical#10596219C2
hypercenter#338C3⋊D3
hypocenterC32#2050
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #338

Complements

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

NH ≅ G/Ntype
2. C2×#63652C2semidirect
3. #10592831C2semidirect
4. #10592817C2semidirect
5. C32×#338C2semidirect
24. C3×#338D3semidirect
87. #338C3⋊D3semidirect
194. C32#2050semidirect
231. C3#68719semidirect

Maximal subgroups

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

subgroupindex
#105962192
C2×#636522
#105928312
#105928172
C32×#3382
#687193