Finite Group Databasebeta

← #11793980

Subgroups — #11793980

Order 1152.

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

normal subgroups only

This group has 396 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×#424C211yesmaximal, characteristic, complemented
3#10588794C212yesmaximal, complemented
4#10588686C212yesmaximal, complemented
5#10588237C211yesmaximal, characteristic, complemented
6#70547—31nomaximal
7C2×#3697C2212yes—
8C2×C9×M16C2211yescharacteristic
9C22×C8×C9C2211yescharacteristic
10C9×#117C2211yescharacteristic
11#63488C2212yes—
12#63471—22no—
13#63470—22no—
14#63467—22no—
15C9×C4⋊C8—22no—
16#63380—22no—
17#63376—22no—
18#63365—24no—
19#5748—31no—
20C3×#424D311yescharacteristic
21#5113—32no—
22#5006—32no—
23#4557—31no—
24C22×C4×C9C2311yescharacteristic
25C2×#611—22no—
26#3697—22no—
27#3697—22no—
28#3697—22no—
29#3697—22no—
30C2×D36D412yes—
31C2×C4×D9—22no—
32C2×Dic18D412yes—
33C9×M16—22no—
34C2×C8×C9—22no—
35C2×C8×C9—21no—
36C2×C8×C9D412yes—
37C9×C4⋊C4—21no—
38C9×C22⋊C4D412yes—
39C42×C9—21no—
40#3676—22no—
41C4⋊Dic9—22no—
42C4×Dic9—22no—
43D72—22no—
44#3664—24no—
45Dic36—22no—
46#2053—91noSylow
47C2×#235—32no—
48C2×C3×M16C2×D311yescharacteristic
49C22×C3×C8C2×D311yescharacteristic
50C3×#117C2×D311yescharacteristic
51#926—32no—
52#909—62no—
53#908—62no—
54#904—62no—
55C3×C4⋊C8—22no—
56#821—62no—
57#816—62no—
58#806—64no—
59C23×C9C2×D411yescharacteristic
60C22×D9—22no—
61C2×C4×C9—22no—
62C2×C4×C9C2×D412yes—
63C2×C4×C9C2×D411yescharacteristic
64C2×C4×C9#4111yescharacteristic
65C2×C4×C9#4112yes—
66#611—42no—
67#611—42no—
68C2×Dic9—22no—
69C2×Dic9—42no—
70D36—22no—
71D36—22no—
72C4×D9—42no—
73C4×D9—42no—
74Dic18—22no—
75Dic18—22no—
76C8×C9—22no—
77C8×C9—41no—
78#575—91no—
79#424D911yescharacteristic, complemented
80#416—92no—
81#410—92no—
82H(3,ℤ/4)—91no—
83C22×C3×C4C22×D311yescharacteristic
84C2×#67—62no—
85#235—62no—
86#235—62no—
87#235—62no—
88#235—62no—
89C2×D12—32no—
90C2×C4×D3—62no—
91C2×Dic6—32no—
92C3×M16—22no—
93C2×C3×C8—22no—
94C2×C3×C8—21no—
95C2×C3×C8#6712yes—
96C3×C4⋊C4—21no—
97C3×C22⋊C4D1212yes—
98C3×C42—21no—
99#217—62no—
100C4⋊Dic3—62no—
101C4×Dic3—62no—
102Dic12—62no—
103D24—62no—
104#204—64no—
105C22×C9—41no—
106C22×C9#12112yes—
107C22×C9#12111yescharacteristic
108C2×D9—42no—
109C2×D9—82no—
110C4×C9—42no—
111C4×C9#12011yescharacteristic
112C4×C9#12312yes—
113C4×C9#12411yescharacteristic
114Dic9—42no—
115Dic9—82no—
116C2×#41—92no—
117#137—182no—
118AGL(1,ℤ/8)—182no—
119#135—182no—
120C2×M16C2×D911yescharacteristic
121C22×C8C2×D911yescharacteristic
122#117—92no—
123#117C2×D911yescharacteristic
124C4⋊C8—22no—
125#103—182no—
126#102—182no—
127#99—184no—
128C23×C3C2×D1211yescharacteristic
129C22×D3—62no—
130C2×C3×C4—22no—
131C2×C3×C4#23511yescharacteristic
132C2×C3×C4D3×D412yes—
133C2×C3×C4#23912yes—
134C2×C3×C4C2×#6711yescharacteristic
135#67—122no—
136#67—122no—
137C2×Dic3—62no—
138C2×Dic3—122no—
139D12—62no—
140D12—62no—
141C4×D3—122no—
142C4×D3—122no—
143Dic6—62no—
144Dic6—62no—
145C3×C8—22no—
146C3×C8—41no—
147C2×C9—22no—
148C2×C9—21no—
149C2×C9#39411yescharacteristic
150D9—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×D911yescharacteristic
160Q16—182no—
161SD16—184no—
162D8—182no—
163M16—22no—
164C2×C8—22no—
165C2×C8—21no—
166C2×C8#61112yes—
167C4⋊C4—21no—
168C4⋊C4—182no—
169C22⋊C4—182no—
170C22⋊C4D3612yes—
171C42—21no—
172C42—182no—
173C22×C3—41no—
174C22×C3#89512yes—
175C22×C3#93011yescharacteristic
176C2×D3—122no—
177C2×D3—242no—
178C3×C4—42no—
179C3×C4#89412yes—
180C3×C4#93711yescharacteristic
181C3×C4#94711yescharacteristic
182Dic3—122no—
183Dic3—242no—
184C9#205311yescharacteristic, complemented, Sylow
185C23—182no—
186C23C2×D3611yescharacteristic
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#369711yescharacteristic
199C2×C4D4×D912yes—
200C2×C4#370112yes—
201C2×C4C2×#61111yescharacteristic
202C8—22no—
203C8—41no—
204C2×C3—22no—
205C2×C3—21no—
206C2×C3#499111yescharacteristic
207D3—242no—
208C22—41no—
209C22—362no—
210C22—722no—
211C22#6345712yes—
212C22#6349211yescharacteristic
213C4—42no—
214C4—362no—
215C4—722no—
216C4#6345612yes—
217C4#6349911yescharacteristic
218C4#6350911yescharacteristic
219C3#7054711yescharacteristic
220C2—21no—
221C2—22no—
222C2—722no—
223C2#1058867111yescharacteristic
subgroupG/H
centerC4#63509
commutator, cosocleC22×C4×C9C23
FrattiniC22×C3×C4C22×D3
FittingC9×#424C2
socleC2×C3#4991
prime radical#10589850C2
hypercenter#424D9
hypocenterC9#2053
LCSG ▷ C22×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C4 ◁ C22×C4 ◁ #424

Complements

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

NH ≅ G/Ntype
2. C9×#424C2semidirect
3. #10588794C2semidirect
4. #10588686C2semidirect
5. #10588237C2semidirect
79. #424D9semidirect
184. C9#2053semidirect

Maximal subgroups

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

subgroupindex
#105898502
C9×#4242
#105887942
#105886862
#105882372
#705473