Finite Group Databasebeta

← #13068913

Subgroups — #13068913

Order 1408.

408 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 113 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×C11×M16C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊D11C211yesmaximal, characteristic
3C2×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
4C2×(C2×D11)⋊C8C212yesmaximal, complemented
5#10622188C212yesmaximal, complemented
6C23×C4×C11C2211yescharacteristic
7C22×C22⋊D11C411yescharacteristic
8C22×C4×D11C2211yescharacteristic
9C2×C11×M16—22no—
10C2×C11×M16—24no—
11C22×C8×C11C2212yes—
12C2×C22⋊Dic11C411yescharacteristic
13C4×C22⋊D11—22no—
14C4×C22⋊D11—22no—
15C2×(C2×D11)⋊C4C411yescharacteristic
16C2×Dic11⋊C4C411yescharacteristic
17C2×C4×Dic11C2211yescharacteristic
18C22×C11⋊C8C2212yes—
19C22⋊(C11⋊C8)—22no—
20(C2×D11)⋊C8—24no—
21C24×C11C2×C411yescharacteristic
22C23×D11C2×C411yescharacteristic
23C22×C4×C11—22no—
24C22×C4×C11—22no—
25C22×C4×C11C2×C411yescharacteristic
26C22×C4×C11D412yes—
27C22×C4×C11D412yes—
28C22×C4×C11C2311yescharacteristic
29C2×C22⋊D11—22no—
30C2×C22⋊D11—22no—
31C2×C22⋊D11—22no—
32C22×Dic11C2×C411yescharacteristic
33C22×Dic11C2×C411yescharacteristic
34C22×Dic11C2×C411yescharacteristic
35C2×C4×D11—22no—
36C2×C4×D11—21no—
37C2×C4×D11—21no—
38C2×C4×D11—22no—
39C11×M16—28no—
40C2×C8×C11—22no—
41C2×C8×C11—22no—
42C2×C8×C11D414yescomplemented
43C22⋊Dic11—22no—
44(C2×D11)⋊C4—22no—
45Dic11⋊C4—22no—
46C4×Dic11—21no—
47C4×Dic11—21no—
48C2×C11⋊C8—22no—
49C2×C11⋊C8—22no—
50C2×C11⋊C8—22no—
51#1870—111nomaximal, Sylow
52C23×C11—22no—
53C23×C11—21no—
54C23×C11—21no—
55C23×C11—22no—
56C23×C11C22⋊C412yes—
57C23×C11C22×C411yescharacteristic
58C22×D11—21no—
59C22×D11—22no—
60C22×D11—21no—
61C22×D11—22no—
62C22×D11M1612yescomplemented
63C2×C4×C11—22no—
64C2×C4×C11—22no—
65C2×C4×C11—24no—
66C2×C4×C11—22no—
67C2×C4×C11C22⋊C412yes—
68C2×C4×C11C2×D411yescharacteristic
69C2×C4×C11C2×D412yes—
70C2×C4×C11C2×D411yescharacteristic
71C2×C4×C11#4112yes—
72C22⋊D11—28no—
73C2×Dic11—21no—
74C2×Dic11—21no—
75C2×Dic11—21no—
76C2×Dic11—21no—
77C2×Dic11—22no—
78C2×Dic11—22no—
79C2×Dic11M1612yescomplemented
80C4×D11—41no—
81C4×D11—42no—
82C4×D11—41no—
83C8×C11—24no—
84C11⋊C8—42no—
85C22×M16D1111yescharacteristic, complemented
86C2×C4×D4—111no—
87C2×C22⋊C8—111no—
88C2×C22⋊C8—112no—
89#336—112no—
90C22×C11—22no—
91C22×C11—22no—
92C22×C11—22no—
93C22×C11—42no—
94C22×C11—42no—
95C22×C11C2×C22⋊C411yescharacteristic
96C22×C11C4×D412yes—
97C22×C11C2×M1611yescharacteristic
98C22×C11C2×M1611yescharacteristic
99C22×C11#13112yes—
100C2×D11—22no—
101C2×D11—24no—
102C2×D11—41no—
103C2×D11—41no—
104C2×D11—42no—
105C4×C11—22no—
106C4×C11#12011yescharacteristic
107C4×C11#12112yes—
108C4×C11#12311yescharacteristic
109Dic11—22no—
110Dic11—41no—
111Dic11—41no—
112C22×D4—111no—
113C23×C4—111no—
114C23×C4C2×D1111yescharacteristic
115C2×M16—22no—
116C2×M16—24no—
117C22×C8—112no—
118C22×C8C2×D1112yes—
119C4×D4—222no—
120C4×D4—222no—
121C2×C4⋊C4—111no—
122C2×C22⋊C4—111no—
123C2×C22⋊C4—111no—
124C2×C42—111no—
125C22⋊C8—222no—
126C22⋊C8—224no—
127C2×C11—42no—
128C2×C11#38611yescharacteristic
129C2×C11#40711yescharacteristic
130C2×C11#40811yescharacteristic
131C2×C11#43512yes—
132C2×C11#43612yes—
133D11—42no—
134C24—111no—
135C24C4×D1111yescharacteristic
136C2×D4—222no—
137C2×D4—222no—
138C2×D4—222no—
139C22×C4—22no—
140C22×C4—22no—
141C22×C4—111no—
142C22×C4—111no—
143C22×C4—111no—
144C22×C4—221no—
145C22×C4—222no—
146C22×C4—222no—
147C22×C4—221no—
148C22×C4C4×D1111yescharacteristic
149C22×C4D4412yes—
150C22×C4C22⋊D1112yes—
151C22×C4C22×D1111yescharacteristic
152M16—28no—
153C2×C8—22no—
154C2×C8—22no—
155C2×C8—222no—
156C2×C8—222no—
157C2×C8—222no—
158C2×C8C22⋊D1114yescomplemented
159C4⋊C4—222no—
160C22⋊C4—222no—
161C22⋊C4—222no—
162C42—221no—
163C42—221no—
164C11#187011yescharacteristic, complemented, Sylow
165C23—21no—
166C23—21no—
167C23—22no—
168C23—22no—
169C23—112no—
170C23—221no—
171C23—222no—
172C23—221no—
173C23—222no—
174C23(C2×D11)⋊C412yes—
175C23C2×C4×D1111yescharacteristic
176D4—228no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—24no—
180C2×C4—22no—
181C2×C4—112no—
182C2×C4—221no—
183C2×C4—221no—
184C2×C4—222no—
185C2×C4—221no—
186C2×C4—221no—
187C2×C4—222no—
188C2×C4—441no—
189C2×C4—442no—
190C2×C4—441no—
191C2×C4(C2×D11)⋊C412yes—
192C2×C4C2×D4411yescharacteristic
193C2×C4#433912yes—
194C2×C4C2×C22⋊D1111yescharacteristic
195C2×C4C2×C22⋊D1112yes—
196C8—24no—
197C8—442no—
198C22—22no—
199C22—22no—
200C22—22no—
201C22—42no—
202C22—42no—
203C22—222no—
204C22—224no—
205C22—442no—
206C22—441no—
207C22—441no—
208C22M16×D1111yescharacteristic
209C22M16×D1111yescharacteristic
210C22#6696012yes—
211C22C2×(C2×D11)⋊C411yescharacteristic
212C22C4×C22⋊D1112yes—
213C4—22no—
214C4—222no—
215C4—441no—
216C4—441no—
217C4#6698211yescharacteristic
218C4#6698312yes—
219C4#6700611yescharacteristic
220C2—42no—
221C2—442no—
222C2#1062273911yescharacteristic
223C2#1062274012yes—
224C2#1062274112yes—
225C2#1062274211yescharacteristic
226C2#1062282611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C22×D11
commutator, socleC23×C11C22×C4
FittingC22×C11×M16C2
prime radicalC22×C22⋊D11C4
cosocleC22×C4×C11C23
hypercenterC22×M16D11
hypocenterC11#1870
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
1. C22×C11×M16C2semidirect
3. C2×C22⋊(C11⋊C8)C2semidirect
4. C2×(C2×D11)⋊C8C2semidirect
5. #10622188C2semidirect
42. C2×C8×C11D4semidirect
62. C22×D11M16semidirect
79. C2×Dic11M16semidirect
85. C22×M16D11semidirect
158. C2×C8C22⋊D11semidirect
164. C11#1870semidirect

Maximal subgroups

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

subgroupindex
C22×C11×M162
C2×C4×C22⋊D112
C2×C22⋊(C11⋊C8)2
C2×(C2×D11)⋊C82
#106221882
#187011