Finite Group Databasebeta

← #11785735

Subgroups — #11785735

Order 1152.

408 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 102 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
1C2×#63454C211yesmaximal, characteristic
2#10588808C212yesmaximal
3C9×#343C211yesmaximal, characteristic, complemented
4#10588234C212yesmaximal, complemented
5#10588207C211yesmaximal, characteristic, complemented
6#68991—31nomaximal
7C22×C4×D9C2211yescharacteristic
8C2×C9×M16C2212yes—
9C2×C9×C4⋊C4C2211yescharacteristic
10C2×(C2×D9)⋊C4C412yes—
11C2×C4⋊Dic9C2211yescharacteristic
12C2×C4×Dic9C412yes—
13C2×#3667C2212yes—
14#63454—24no—
15(C2×D9)⋊C8—24no—
16C2×#892—31no—
17#5126—32no—
18C3×#343D311yescharacteristic
19#4554—32no—
20#4530—31no—
21C23×D9C2×C411yescharacteristic
22C22×C4×C9C2×C412yes—
23C22×C4×C9C2311yescharacteristic
24C22×Dic9C2×C411yescharacteristic
25C22×Dic9C2×C412yes—
26C2×C4×D9—22no—
27C2×C4×D9—21no—
28C2×C4×D9—21no—
29C2×C4×D9D414yes—
30C9×M16—22no—
31C9×M16—22no—
32C2×C8×C9—22no—
33C9×C4⋊C4—22no—
34(C2×D9)⋊C4—24no—
35C4⋊Dic9—22no—
36C4×Dic9—24no—
37#3667—22no—
38#3667—22no—
39C2×C9⋊C8—22no—
40#1822—91noSylow
41C22×C4×D3—31no—
42C2×C3×M16C2×D312yes—
43C2×C3×C4⋊C4C2×D311yescharacteristic
44C2×(C2×D3)⋊C4—32no—
45C2×C4⋊Dic3—31no—
46C2×C4×Dic3—32no—
47C2×#208—32no—
48#892—64no—
49(C2×D3)⋊C8—64no—
50C23×C9C22×C411yescharacteristic
51C22×D9—21no—
52C22×D9—21no—
53C22×D9—41no—
54C22×D9—41no—
55C22×D9C22⋊C412yes—
56C2×C4×C9—22no—
57C2×C4×C9—42no—
58C2×C4×C9C2×D412yes—
59C2×C4×C9#4112yes—
60C2×C4×C9#4111yescharacteristic
61C2×C4×C9#4111yescharacteristic
62C2×Dic9—21no—
63C2×Dic9—21no—
64C2×Dic9—22no—
65C2×Dic9—42no—
66C2×Dic9C22⋊C412yes—
67C4×D9—24no—
68C4×D9—24no—
69C8×C9—42no—
70C9⋊C8—42no—
71C2×#117—91no—
72#407—92no—
73#343—92no—
74#343—91no—
75#343D911yescharacteristic, complemented
76C23×D3—31no—
77C22×C3×C4C4×D312yes—
78C22×C3×C4C22×D311yescharacteristic
79C22×Dic3—31no—
80C22×Dic3—32no—
81C2×C4×D3—34no—
82C2×C4×D3—62no—
83C2×C4×D3—61no—
84C2×C4×D3—61no—
85C3×M16—22no—
86C3×M16—22no—
87C2×C3×C8—22no—
88C3×C4⋊C4—22no—
89(C2×D3)⋊C4—64no—
90C4⋊Dic3—62no—
91C4×Dic3—64no—
92#208—62no—
93#208—62no—
94C2×C3⋊C8—62no—
95C22×C9—21no—
96C22×C9—21no—
97C22×C9C2×C22⋊C411yescharacteristic
98C22×C9#11711yescharacteristic
99C22×C9#11711yescharacteristic
100C2×D9—22no—
101C2×D9—22no—
102C2×D9—22no—
103C2×D9—42no—
104C2×D9—42no—
105C4×C9—42no—
106C4×C9#12312yes—
107C4×C9#12312yes—
108Dic9—22no—
109Dic9—42no—
110C23×C4—91no—
111C2×M16—92no—
112C2×M16C2×D912yes—
113#117—184no—
114C2×C4⋊C4—91no—
115C2×C4⋊C4C2×D911yescharacteristic
116C2×C22⋊C4—92no—
117C2×C42—92no—
118C22⋊C8—184no—
119C23×C3C2×C4×D311yescharacteristic
120C22×D3—32no—
121C22×D3—61no—
122C22×D3—61no—
123C22×D3—121no—
124C22×D3—121no—
125C2×C3×C4—22no—
126C2×C3×C4—42no—
127C2×C3×C4#23512yes—
128C2×C3×C4D3×D412yes—
129C2×C3×C4#23711yescharacteristic
130C2×C3×C4#23911yescharacteristic
131C2×Dic3—32no—
132C2×Dic3—61no—
133C2×Dic3—61no—
134C2×Dic3—62no—
135C2×Dic3—122no—
136C4×D3—64no—
137C4×D3—64no—
138C3×C8—42no—
139C3⋊C8—122no—
140C2×C9—21no—
141C2×C9—21no—
142C2×C9#38111yescharacteristic
143C2×C9#41311yescharacteristic
144C2×C9#41311yescharacteristic
145D9—42no—
146C24—91no—
147C22×C4—91no—
148C22×C4—94no—
149C22×C4—92no—
150C22×C4—182no—
151C22×C4—181no—
152C22×C4—181no—
153C22×C4C4×D912yes—
154C22×C4C22×D911yescharacteristic
155M16—22no—
156M16—22no—
157M16—182no—
158M16—182no—
159C2×C8—22no—
160C2×C8—182no—
161C4⋊C4—22no—
162C4⋊C4—182no—
163C22⋊C4—184no—
164C42—184no—
165C22×C3—21no—
166C22×C3—21no—
167C22×C3#87211yescharacteristic
168C22×C3D3×C22⋊C411yescharacteristic
169C22×C3#89211yescharacteristic
170C2×D3—62no—
171C2×D3—62no—
172C2×D3—62no—
173C2×D3—122no—
174C2×D3—122no—
175C3×C4—42no—
176C3×C4#88312yes—
177C3×C4#89412yes—
178Dic3—62no—
179Dic3—122no—
180C9#182211yescharacteristic, complemented, Sylow
181C23—92no—
182C23—181no—
183C23—181no—
184C23—361no—
185C23—361no—
186C23C2×C4×D911yescharacteristic
187C2×C4—22no—
188C2×C4—42no—
189C2×C4—92no—
190C2×C4—181no—
191C2×C4—181no—
192C2×C4—184no—
193C2×C4—184no—
194C2×C4—182no—
195C2×C4—362no—
196C2×C4#369712yes—
197C2×C4D4×D912yes—
198C2×C4#369911yescharacteristic
199C2×C4#370111yescharacteristic
200C8—42no—
201C8—362no—
202C2×C3—21no—
203C2×C3—21no—
204C2×C3#466411yescharacteristic
205C2×C3#474511yescharacteristic
206C2×C3#475111yescharacteristic
207D3—122no—
208C22—21no—
209C22—21no—
210C22—182no—
211C22—182no—
212C22—182no—
213C22—362no—
214C22—362no—
215C22#6343411yescharacteristic
216C22C22⋊C4×D911yescharacteristic
217C22#6345411yescharacteristic
218C4—42no—
219C4—182no—
220C4—362no—
221C4#6344512yes—
222C4#6345612yes—
223C3#6899111yescharacteristic
224C2—21no—
225C2—21no—
226C2—362no—
227C2#1058834411yescharacteristic
228C2#1058842511yescharacteristic
229C2#1058843111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D9
commutatorC23×C9C22×C4
FrattiniC22×C3×C4C22×D3
FittingC9×#343C2
socleC22×C3D3×C22⋊C4
prime radicalC23×D9C2×C4
cosocleC22×C4×C9C23
hypercenter#343D9
hypocenterC9#1822
LCSG ▷ C23×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
3. C9×#343C2semidirect
4. #10588234C2semidirect
5. #10588207C2semidirect
75. #343D9semidirect
180. C9#1822semidirect

Maximal subgroups

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

subgroupindex
C2×#634542
#105888082
C9×#3432
#105882342
#105882072
#689913