Finite Group Databasebeta

← #11793851

Subgroups — #11793851

Order 1152.

399 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 399 conjugacy classes of subgroups — too many to draw. Only its 90 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#10589850C211yesmaximal, characteristic
2C9×#423C211yesmaximal, characteristic, complemented
3#10588814C212yesmaximal, complemented
4C2×#63364C212yesmaximal, complemented
5C9⋊#338C211yesmaximal, characteristic, complemented
6#70531—31nomaximal
7C2×#3697C2212yes—
8C2×C9×M16C2211yescharacteristic
9C2×C9×M16C2211yescharacteristic
10C2×C42×C9C2211yescharacteristic
11C2×#3667C2212yes—
12#63471—22no—
13#63470—22no—
14#63467—22no—
15C9×C4⋊C8—22no—
16#63383—22no—
17#63382—22no—
18#63364—22no—
19#63364—22no—
20#5748—31no—
21C3×#423D311yescharacteristic
22#5132—32no—
23C2×#805—32no—
24C3⋊#338—31no—
25C22×C4×C9—21no—
26C22×C4×C9C2311yescharacteristic
27C2×#611—22no—
28#3697—22no—
29#3697—22no—
30#3697—22no—
31#3697—22no—
32C2×D36D412yes—
33C2×C4×D9—22no—
34C2×Dic18D412yes—
35C9×M16—22no—
36C9×M16—22no—
37C2×C8×C9—21no—
38C2×C8×C9D412yes—
39C42×C9—21no—
40C42×C9D411yescharacteristic
41C42×C9D411yescharacteristic
42#3667—22no—
43#3667—22no—
44C2×C9⋊C8—22no—
45D72—22no—
46#3664—24no—
47Dic36—22no—
48#2050—91noSylow
49C2×#235—32no—
50C2×C3×M16C2×D311yescharacteristic
51C2×C3×M16C2×D311yescharacteristic
52C2×C3×C42C2×D311yescharacteristic
53C2×#208—32no—
54#909—62no—
55#908—62no—
56#904—62no—
57C3×C4⋊C8—22no—
58#824—62no—
59#823—62no—
60#805—62no—
61#805—62no—
62C23×C9#4111yescharacteristic
63C22×D9—22no—
64C2×C4×C9—21no—
65C2×C4×C9—21no—
66C2×C4×C9—42no—
67C2×C4×C9C2×D411yescharacteristic
68C2×C4×C9C2×D412yes—
69C2×C4×C9C2×D411yescharacteristic
70C2×C4×C9#4112yes—
71#611—42no—
72#611—42no—
73C2×Dic9—22no—
74D36—22no—
75D36—22no—
76C4×D9—42no—
77C4×D9—42no—
78Dic18—22no—
79Dic18—22no—
80C8×C9—22no—
81C8×C9—41no—
82C9⋊C8—42no—
83#575—91no—
84#423D911yescharacteristic, complemented
85C2×#104—92no—
86#413—92no—
87#338—91no—
88C22×C3×C4—21no—
89C22×C3×C4C22×D311yescharacteristic
90C2×#67—62no—
91#235—62no—
92#235—62no—
93#235—62no—
94#235—62no—
95C2×D12—32no—
96C2×C4×D3—62no—
97C2×Dic6—32no—
98C3×M16—22no—
99C3×M16—22no—
100C2×C3×C8—21no—
101C2×C3×C8#6712yes—
102C3×C42—21no—
103C3×C42D1211yescharacteristic
104C3×C42D1211yescharacteristic
105#208—62no—
106#208—62no—
107C2×C3⋊C8—62no—
108Dic12—62no—
109D24—62no—
110#204—64no—
111C22×C9—41no—
112C22×C9#12111yescharacteristic
113C22×C9#12312yes—
114C2×D9—42no—
115C2×D9—82no—
116C4×C9—22no—
117C4×C9—41no—
118C4×C9#12011yescharacteristic
119C4×C9#12112yes—
120C4×C9#12411yescharacteristic
121Dic9—42no—
122C2×#41—92no—
123#137—182no—
124AGL(1,ℤ/8)—182no—
125#135—182no—
126C2×M16—92no—
127C2×M16C2×D911yescharacteristic
128C2×M16C2×D911yescharacteristic
129C2×C42C2×D911yescharacteristic
130C4⋊C8—22no—
131#104—182no—
132#104—182no—
133#101—182no—
134#100—182no—
135C23×C3#23511yescharacteristic
136C22×D3—62no—
137C2×C3×C4—21no—
138C2×C3×C4—21no—
139C2×C3×C4—42no—
140C2×C3×C4C2×D1211yescharacteristic
141C2×C3×C4D3×D412yes—
142C2×C3×C4#23912yes—
143C2×C3×C4C2×#6711yescharacteristic
144#67—122no—
145#67—122no—
146C2×Dic3—62no—
147D12—62no—
148D12—62no—
149C4×D3—122no—
150C4×D3—122no—
151Dic6—62no—
152Dic6—62no—
153C3×C8—22no—
154C3×C8—41no—
155C3⋊C8—122no—
156C2×C9—21no—
157C2×C9—22no—
158C2×C9#39411yescharacteristic
159D9—82no—
160#41—182no—
161#41—182no—
162#41—182no—
163#41—182no—
164C2×Q8—92no—
165C2×D4—92no—
166C2×D4—182no—
167C22×C4—21no—
168C22×C4—182no—
169C22×C4C22×D911yescharacteristic
170Q16—182no—
171SD16—184no—
172D8—182no—
173M16—22no—
174M16—22no—
175M16—182no—
176M16—182no—
177C2×C8—21no—
178C2×C8—182no—
179C2×C8#61112yes—
180C42—21no—
181C42D3611yescharacteristic
182C42D3611yescharacteristic
183C22×C3—41no—
184C22×C3#89412yes—
185C22×C3#93011yescharacteristic
186C2×D3—122no—
187C2×D3—242no—
188C3×C4—22no—
189C3×C4—41no—
190C3×C4#89512yes—
191C3×C4#93711yescharacteristic
192C3×C4#94711yescharacteristic
193Dic3—122no—
194C9#205011yescharacteristic, complemented, Sylow
195C23—182no—
196C23#369711yescharacteristic
197Q8—182no—
198Q8—182no—
199D4—182no—
200D4—182no—
201D4—362no—
202D4—362no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—42no—
206C2×C4—182no—
207C2×C4—362no—
208C2×C4—362no—
209C2×C4C2×D3611yescharacteristic
210C2×C4D4×D912yes—
211C2×C4#370112yes—
212C2×C4C2×#61111yescharacteristic
213C8—22no—
214C8—41no—
215C8—362no—
216C2×C3—21no—
217C2×C3—22no—
218C2×C3#499111yescharacteristic
219D3—242no—
220C22—41no—
221C22—362no—
222C22—722no—
223C22#6345612yes—
224C22#6349211yescharacteristic
225C4—22no—
226C4—41no—
227C4—362no—
228C4#6345712yes—
229C4#6349911yescharacteristic
230C4#6350911yescharacteristic
231C3#7053111yescharacteristic
232C2—21no—
233C2—22no—
234C2—722no—
235C2#1058867111yescharacteristic
subgroupG/H
centerC4#63509
commutator, cosocleC22×C4×C9C23
FrattiniC22×C3×C4C22×D3
FittingC9×#423C2
socleC2×C3#4991
prime radical#10589850C2
hypercenter#423D9
hypocenterC9#2050
LCSG ▷ C22×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C4 ◁ C22×C4 ◁ #423

Complements

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

NH ≅ G/Ntype
2. C9×#423C2semidirect
3. #10588814C2semidirect
4. C2×#63364C2semidirect
5. C9⋊#338C2semidirect
84. #423D9semidirect
194. C9#2050semidirect

Maximal subgroups

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

subgroupindex
#105898502
C9×#4232
#105888142
C2×#633642
C9⋊#3382
#705313