Finite Group Databasebeta

← #11773870

Subgroups — #11773870

Order 1152.

468 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 134 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
1C22×C9×C4⋊C4C211yesmaximal, characteristic
2#10588887C212yesmaximal
3#10588205C214yesmaximal, complemented
4#71552—31nomaximal
5C23×C4×C9C411yescharacteristic
6C23×C4×C9C411yescharacteristic
7C23×C4×C9C2211yescharacteristic
8C2×C9×C4⋊C4—22no—
9C2×C9×C4⋊C4—22no—
10C2×C9×C4⋊C4C412yes—
11C2×C9×C4⋊C4C2212yes—
12C2×#3667—22no—
13#63389—22no—
14#63389C2214yes—
15C22×C3×C4⋊C4D311yescharacteristic
16#5207—32no—
17#4528—34no—
18C24×C9C2×C411yescharacteristic
19C22×C4×C9—21no—
20C22×C4×C9—21no—
21C22×C4×C9—24no—
22C22×C4×C9—21no—
23C22×C4×C9—21no—
24C22×C4×C9—42no—
25C22×C4×C9—42no—
26C22×C4×C9C2×C412yes—
27C22×C4×C9C2×C412yes—
28C22×C4×C9C2×C411yescharacteristic
29C22×C4×C9D412yes—
30C22×C4×C9D412yes—
31C22×C4×C9C2311yescharacteristic
32C9×C4⋊C4—24no—
33C9×C4⋊C4—24no—
34#3667—44no—
35C2×C9⋊C8—24no—
36#1463—91noSylow
37C23×C3×C4Dic311yescharacteristic
38C23×C3×C4Dic311yescharacteristic
39C23×C3×C4C2×D311yescharacteristic
40C2×C3×C4⋊C4—22no—
41C2×C3×C4⋊C4—22no—
42C2×C3×C4⋊C4Dic312yes—
43C2×C3×C4⋊C4C2×D312yes—
44C2×#208—62no—
45#830—34no—
46#830—62no—
47C23×C9—22no—
48C23×C9—22no—
49C23×C9—22no—
50C23×C9C22⋊C411yescharacteristic
51C23×C9C22⋊C411yescharacteristic
52C23×C9C22×C411yescharacteristic
53C2×C4×C9—24no—
54C2×C4×C9—24no—
55C2×C4×C9—24no—
56C2×C4×C9—22no—
57C2×C4×C9—22no—
58C2×C4×C9—22no—
59C2×C4×C9—41no—
60C2×C4×C9—42no—
61C2×C4×C9—41no—
62C2×C4×C9—42no—
63C2×C4×C9—42no—
64C2×C4×C9—42no—
65C2×C4×C9C22⋊C412yes—
66C2×C4×C9M1614yescomplemented
67C2×C4×C9C2×D412yes—
68C9⋊C8—44no—
69C22×C4⋊C4D911yescharacteristic
70#407—92no—
71#324—94no—
72C24×C3C2×Dic311yescharacteristic
73C22×C3×C4—21no—
74C22×C3×C4—21no—
75C22×C3×C4—24no—
76C22×C3×C4—21no—
77C22×C3×C4—21no—
78C22×C3×C4—42no—
79C22×C3×C4—42no—
80C22×C3×C4C2×Dic312yes—
81C22×C3×C4C2×Dic312yes—
82C22×C3×C4C2×Dic311yescharacteristic
83C22×C3×C4#6712yes—
84C22×C3×C4#6712yes—
85C22×C3×C4C22×D311yescharacteristic
86C3×C4⋊C4—24no—
87C3×C4⋊C4—24no—
88#208—124no—
89C2×C3⋊C8—64no—
90C22×C9—28no—
91C22×C9—21no—
92C22×C9—21no—
93C22×C9—21no—
94C22×C9—21no—
95C22×C9—21no—
96C22×C9—21no—
97C22×C9#9912yes—
98C22×C9#10112yes—
99C22×C9C2×C22⋊C411yescharacteristic
100C22×C9C2×M1612yes—
101C4×C9—24no—
102C4×C9—22no—
103C4×C9—22no—
104C4×C9—42no—
105C23×C4Dic911yescharacteristic
106C23×C4Dic911yescharacteristic
107C23×C4C2×D911yescharacteristic
108C2×M16—182no—
109C2×C4⋊C4—22no—
110C2×C4⋊C4—22no—
111C2×C4⋊C4Dic912yes—
112C2×C4⋊C4C2×D912yes—
113C22⋊C8—94no—
114C22⋊C8—182no—
115C23×C3—22no—
116C23×C3—22no—
117C23×C3—22no—
118C23×C3#21711yescharacteristic
119C23×C3#21711yescharacteristic
120C23×C3C22×Dic311yescharacteristic
121C2×C3×C4—24no—
122C2×C3×C4—24no—
123C2×C3×C4—24no—
124C2×C3×C4—22no—
125C2×C3×C4—22no—
126C2×C3×C4—22no—
127C2×C3×C4—41no—
128C2×C3×C4—42no—
129C2×C3×C4—41no—
130C2×C3×C4—42no—
131C2×C3×C4—42no—
132C2×C3×C4—42no—
133C2×C3×C4#20814yes—
134C2×C3×C4#21712yes—
135C2×C3×C4C2×#6712yes—
136C3⋊C8—124no—
137C2×C9—22no—
138C2×C9—22no—
139C2×C9—22no—
140C2×C9#40711yescharacteristic
141C2×C9C2×#9911yescharacteristic
142C2×C9C2×#10111yescharacteristic
143C24C2×Dic911yescharacteristic
144C22×C4—21no—
145C22×C4—21no—
146C22×C4—24no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—42no—
150C22×C4—42no—
151C22×C4C2×Dic912yes—
152C22×C4C2×Dic912yes—
153C22×C4C2×Dic911yescharacteristic
154C22×C4#61112yes—
155C22×C4#61112yes—
156C22×C4C22×D911yescharacteristic
157M16—364no—
158C2×C8—184no—
159C4⋊C4—24no—
160C4⋊C4—24no—
161C22×C3—28no—
162C22×C3—21no—
163C22×C3—21no—
164C22×C3—21no—
165C22×C3—21no—
166C22×C3—21no—
167C22×C3—21no—
168C22×C3#83412yes—
169C22×C3#83612yes—
170C22×C3C2×#20812yes—
171C22×C3C2×#21711yescharacteristic
172C3×C4—24no—
173C3×C4—22no—
174C3×C4—22no—
175C3×C4—42no—
176C9#146311yescharacteristic, complemented, Sylow
177C23—22no—
178C23—22no—
179C23—22no—
180C23#367611yescharacteristic
181C23#367611yescharacteristic
182C23C22×Dic911yescharacteristic
183C2×C4—24no—
184C2×C4—24no—
185C2×C4—22no—
186C2×C4—24no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—41no—
190C2×C4—42no—
191C2×C4—41no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4#366714yescomplemented
196C2×C4#367612yes—
197C2×C4C2×#61112yes—
198C8—364no—
199C2×C3—22no—
200C2×C3—22no—
201C2×C3—22no—
202C2×C3#520711yescharacteristic
203C2×C3C2×#83411yescharacteristic
204C2×C3C2×#83611yescharacteristic
205C22—28no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22#6339312yes—
213C22#6339412yes—
214C22C2×#366712yes—
215C22C2×#367611yescharacteristic
216C4—24no—
217C4—22no—
218C4—22no—
219C4—42no—
220C3#7155211yescharacteristic
221C2—22no—
222C2—22no—
223C2—22no—
224C2#1058888711yescharacteristic
225C2C2×#6339311yescharacteristic
226C2C2×#6339411yescharacteristic
subgroupG/H
centerC22C2×#3676
commutatorC23×C9C22×C4
FrattiniC22×C3×C4C22×D3
FittingC22×C9×C4⋊C4C2
socleC22×C3C2×#217
prime radicalC24×C3C2×Dic3
cosocleC22×C4×C9C23
hypercenterC22×C4⋊C4D9
hypocenterC9#1463
LCSG ▷ C23×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #10588205C2semidirect
66. C2×C4×C9M16semidirect
176. C9#1463semidirect
195. C2×C4#3667semidirect

Maximal subgroups

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

subgroupindex
C22×C9×C4⋊C42
#105888872
#105882052
#715523