Finite Group Databasebeta

← #14651129

Subgroups — #14651129

Order 2816.

538 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 139 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#13077640C211yesmaximal, characteristic
2#13068608C211yesmaximal, characteristic
3#13067297C212yesmaximal, complemented
4#13066519C212yesmaximal, complemented
5C11×#2563C211yesmaximal, characteristic
6C2×C11×C4⋊Q8C2211yescharacteristic
7C2×C4×D4×C11C2211yescharacteristic
8C11×#393C414yes—
9C11×#390—21no—
10C11×#382—21no—
11C11×#380—22no—
12C4×C11×C4⋊C4C2211yescharacteristic
13C2×#66897—21no—
14C2×C22⋊(C11⋊C8)—22no—
15D4×C11⋊C8—24no—
16#10622538C2212yes—
17#10622537C2212yes—
18#10622184—24no—
19#10622168—21no—
20C22×Q8×C11C2×C412yes—
21C22×D4×C11D411yescharacteristic
22C23×C4×C11D412yes—
23C11×C4⋊Q8—22no—
24C11×C4⋊Q8—22no—
25C4×D4×C11—22no—
26C4×D4×C11—22no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C22⋊C4—24no—
32C2×C11×C22⋊C4C2×C412yes—
33C2×C42×C11—21no—
34C2×C42×C11C2311yescharacteristic
35C2×#4318—22no—
36C22×C11⋊C8—24no—
37C11×#95—24no—
38C11×#95C2×C412yes—
39#66897—42no—
40C22⋊(C11⋊C8)—24no—
41C22⋊(C11⋊C8)—22no—
42C4⋊(C11⋊C8)—22no—
43C4⋊(C11⋊C8)—22no—
44C4⋊(C11⋊C8)D414yes—
45C4×C11⋊C8—22no—
46#9391—111nomaximal, Sylow
47C24×C11C22⋊C412yes—
48C2×Q8×C11—24no—
49C2×Q8×C11—82no—
50C2×D4×C11—22no—
51C2×D4×C11—22no—
52C2×D4×C11SD1612yes—
53C2×D4×C11Q1612yes—
54C22×C4×C11—22no—
55C22×C4×C11—22no—
56C22×C4×C11—22no—
57C22×C4×C11—22no—
58C22×C4×C11—44no—
59C22×C4×C11C22⋊C412yes—
60C22×C4×C11C22×C411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C11×C4⋊C4—22no—
64C11×C4⋊C4—42no—
65C11×C4⋊C4—41no—
66C11×C4⋊C4—42no—
67C11×C4⋊C4—41no—
68C11×C22⋊C4—24no—
69C11×C22⋊C4—84no—
70C42×C11—42no—
71C42×C11C2×D412yes—
72C42×C11#4112yes—
73#4318—42no—
74#4318—42no—
75C2×C11⋊C8—24no—
76C2×C11⋊C8—42no—
77C2×C11⋊C8—84no—
78#2972—111no—
79#2563D1111yescharacteristic
80#1800—111no—
81#1548—112no—
82#1303—112no—
83C23×C11—22no—
84C23×C11—22no—
85C23×C11—42no—
86C23×C11—42no—
87C23×C11#10314yes—
88C23×C11C2×C22⋊C411yescharacteristic
89Q8×C11—84no—
90D4×C11—24no—
91D4×C11—24no—
92C2×C4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11—41no—
95C2×C4×C11—44no—
96C2×C4×C11—42no—
97C2×C4×C11—42no—
98C2×C4×C11—44no—
99C2×C4×C11—42no—
100C2×C4×C11—42no—
101C2×C4×C11—42no—
102C2×C4×C11—82no—
103C2×C4×C11C4×D412yes—
104C2×C4×C11#12011yescharacteristic
105C2×C4×C11#12112yes—
106C2×C4×C11#12311yescharacteristic
107C2×C4×C11C2×SD1611yescharacteristic
108C2×C4×C11C2×Q1611yescharacteristic
109C2×C4×C11#13512yes—
110C11⋊C8—44no—
111C11⋊C8—82no—
112C2×C4⋊Q8C2×D1111yescharacteristic
113C2×C4×D4C2×D1111yescharacteristic
114C8×D4—224no—
115#431—112no—
116#423—112no—
117C2×#100—221no—
118C2×C22⋊C8—222no—
119#393Dic1114yes—
120#390—21no—
121#382—21no—
122#380—22no—
123C4×C4⋊C4C2×D1111yescharacteristic
124#343—221no—
125#333—224no—
126C22×C11—21no—
127C22×C11—21no—
128C22×C11—24no—
129C22×C11—44no—
130C22×C11—42no—
131C22×C11—42no—
132C22×C11—82no—
133C22×C11#38611yescharacteristic
134C22×C11C2×#10311yescharacteristic
135C22×C11#41611yescharacteristic
136C4×C11—21no—
137C4×C11—22no—
138C4×C11—42no—
139C4×C11—82no—
140C4×C11—82no—
141C4×C11#45512yes—
142C4×C11#46512yes—
143C4×C11#46712yes—
144C22×Q8C2×Dic1112yes—
145C22×D4C22⋊D1111yescharacteristic
146C23×C4C22⋊D1112yes—
147C2×M16—222no—
148C22×C8—224no—
149C4⋊Q8—22no—
150C4⋊Q8—22no—
151C4×D4—22no—
152C4×D4—22no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4C22⋊D1111yescharacteristic
157C2×C22⋊C4—24no—
158C2×C22⋊C4C2×Dic1112yes—
159C2×C42—21no—
160C2×C42C22×D1111yescharacteristic
161C4⋊C8—114no—
162C4⋊C8—222no—
163C4⋊C8—222no—
164#100—442no—
165C22⋊C8—224no—
166C22⋊C8—222no—
167C4×C8—222no—
168#95—24no—
169#95C2×Dic1112yes—
170C2×C11—21no—
171C2×C11—21no—
172C2×C11—44no—
173C2×C11#188511yescharacteristic
174C2×C11#189211yescharacteristic
175C2×C11#191411yescharacteristic
176C24C22⋊Dic1112yes—
177C2×Q8—24no—
178C2×Q8—82no—
179C2×D4—22no—
180C2×D4—22no—
181C2×D4#432512yes—
182C2×D4#432612yes—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—44no—
188C22×C4C22⋊Dic1112yes—
189C22×C4C22×Dic1111yescharacteristic
190C22×C4C2×C22⋊D1111yescharacteristic
191C22×C4C2×C22⋊D1111yescharacteristic
192M16—442no—
193M16—442no—
194C2×C8—224no—
195C2×C8—442no—
196C2×C8—884no—
197C4⋊C4—22no—
198C4⋊C4—42no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—42no—
202C22⋊C4—24no—
203C22⋊C4—84no—
204C42—42no—
205C42D4×D1112yes—
206C42#434112yes—
207C11#939111yescharacteristic, complemented, Sylow
208C23—22no—
209C23—22no—
210C23—42no—
211C23—42no—
212C23#6689914yes—
213C23C2×C22⋊Dic1111yescharacteristic
214Q8—84no—
215D4—24no—
216D4—24no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—41no—
220C2×C4—44no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—44no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—82no—
228C2×C4D4×Dic1112yes—
229C2×C4#6698811yescharacteristic
230C2×C4#6699011yescharacteristic
231C2×C4#6699212yes—
232C2×C4C2×#432511yescharacteristic
233C2×C4C2×#432611yescharacteristic
234C2×C4#6700312yes—
235C8—444no—
236C8—882no—
237C22—21no—
238C22—21no—
239C22—24no—
240C22—44no—
241C22—42no—
242C22—42no—
243C22—82no—
244C22#1062283311yescharacteristic
245C22C2×#6689911yescharacteristic
246C22#1062284611yescharacteristic
247C4—22no—
248C4—21no—
249C4—42no—
250C4—82no—
251C4—82no—
252C4#1062266112yes—
253C4#1062266412yes—
254C4#1062267412yes—
255C2—21no—
256C2—21no—
257C2—44no—
258C2#1306900511yescharacteristic
259C2#1306904011yescharacteristic
260C2#1306916411yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2563C2
socleC22×C11#386
prime radicalC22×D4×C11D4
cosocleC2×C42×C11C23
hypercenter#2563D11
hypocenterC11#9391
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2563

Complements

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

NH ≅ G/Ntype
3. #13067297C2semidirect
4. #13066519C2semidirect
207. C11#9391semidirect

Maximal subgroups

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

subgroupindex
#130776402
#130686082
#130672972
#130665192
C11×#25632
#939111