Finite Group Databasebeta

← #14651128

Subgroups — #14651128

Order 2816.

538 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 135 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#13073789C211yesmaximal, characteristic
2#13068608C211yesmaximal, characteristic
3#13067296C212yesmaximal, complemented
4#13066518C212yesmaximal, complemented
5C11×#2972C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66922C2211yescharacteristic
8C8×D4×C11—24no—
9C11×#431C2212yes—
10C2×C11×C22⋊C8—22no—
11#10622834—21no—
12C2×#66897—21no—
13#10622825—22no—
14#10622590—21no—
15#10622560C414yes—
16C4×C4⋊Dic11C2211yescharacteristic
17#10622537C2212yes—
18#10622168—21no—
19#10622119—24no—
20C22×D4×C11D411yescharacteristic
21C23×C4×C11D412yes—
22C22×Dic22C2×C412yes—
23C22×C8×C11—24no—
24C4×D4×C11—22no—
25C4×D4×C11—22no—
26C2×C11×C4⋊C4D411yescharacteristic
27C2×C11×C22⋊C4C2×C412yes—
28C2×C42×C11C2311yescharacteristic
29C2×C22⋊Dic11—24no—
30C2×C4⋊Dic11—21no—
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11—21no—
33C2×C4×Dic11—21no—
34C2×#4318—22no—
35#66922—22no—
36#66922—22no—
37C11×C4⋊C8D414yes—
38C11×C22⋊C8—24no—
39C11×C22⋊C8—22no—
40C4×C8×C11—22no—
41#66897—42no—
42C11⋊#95—24no—
43C11⋊#95C2×C412yes—
44C4⋊(C11⋊C8)—22no—
45C4⋊(C11⋊C8)—22no—
46#9391—111nomaximal, Sylow
47C24×C11C22⋊C412yes—
48C2×D4×C11—22no—
49C2×D4×C11—22no—
50C2×D4×C11SD1612yes—
51C2×D4×C11Q1612yes—
52C22×C4×C11—22no—
53C22×C4×C11—22no—
54C22×C4×C11—44no—
55C22×C4×C11C22⋊C412yes—
56C22×C4×C11C22×C411yescharacteristic
57C22×C4×C11C2×D411yescharacteristic
58C22×C4×C11C2×D411yescharacteristic
59C22×Dic11—22no—
60C22×Dic11—22no—
61C2×Dic22—24no—
62C2×Dic22—82no—
63C2×C8×C11—24no—
64C2×C8×C11—84no—
65C11×C4⋊C4—22no—
66C11×C22⋊C4—24no—
67C42×C11C2×D412yes—
68C42×C11#4112yes—
69C22⋊Dic11—84no—
70C4⋊Dic11—42no—
71C4⋊Dic11—41no—
72C4⋊Dic11—42no—
73C4⋊Dic11—41no—
74C4×Dic11—42no—
75#4318—42no—
76#4318—42no—
77C2×C11⋊C8—42no—
78#2972D1111yescharacteristic
79#2563—111no—
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
89D4×C11—24no—
90D4×C11—24no—
91C2×C4×C11—22no—
92C2×C4×C11—22no—
93C2×C4×C11—41no—
94C2×C4×C11—44no—
95C2×C4×C11—42no—
96C2×C4×C11—82no—
97C2×C4×C11C4×D412yes—
98C2×C4×C11#12011yescharacteristic
99C2×C4×C11#12112yes—
100C2×C4×C11#12311yescharacteristic
101C2×C4×C11C2×SD1611yescharacteristic
102C2×C4×C11C2×Q1611yescharacteristic
103C2×C4×C11#13512yes—
104C2×Dic11—42no—
105C2×Dic11—42no—
106C2×Dic11—44no—
107C2×Dic11—42no—
108C2×Dic11—42no—
109Dic22—84no—
110C8×C11—44no—
111C11⋊C8—82no—
112C2×C4⋊Q8—111no—
113C2×C4×D4C2×D1111yescharacteristic
114C8×D4—24no—
115#431C2×D1112yes—
116#423—112no—
117C2×#100—221no—
118C2×C22⋊C8—22no—
119#393—114no—
120#390—221no—
121#382—221no—
122#380—222no—
123C4×C4⋊C4—111no—
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#45512yes—
140C4×C11#46512yes—
141C4×C11#46712yes—
142Dic11—82no—
143Dic11—82no—
144C22×Q8—112no—
145C22×D4D4411yescharacteristic
146C23×C4C22⋊D1112yes—
147C2×M16—222no—
148C22×C8—24no—
149C4⋊Q8—222no—
150C4⋊Q8—222no—
151C4×D4—22no—
152C4×D4—22no—
153C2×C4⋊C4—221no—
154C2×C4⋊C4—221no—
155C2×C4⋊C4—221no—
156C2×C4⋊C4D4411yescharacteristic
157C2×C22⋊C4—224no—
158C2×C22⋊C4C4×D1112yes—
159C2×C42—221no—
160C2×C42C22×D1111yescharacteristic
161C4⋊C8—222no—
162C4⋊C8—222no—
163C4⋊C8C22⋊D1114yes—
164#100—442no—
165C22⋊C8—24no—
166C22⋊C8—22no—
167C4×C8—22no—
168#95—112no—
169#95—224no—
170C2×C11—21no—
171C2×C11—21no—
172C2×C11—44no—
173C2×C11#188511yescharacteristic
174C2×C11#189211yescharacteristic
175C2×C11#191411yescharacteristic
176C24(C2×D11)⋊C412yes—
177C2×Q8—224no—
178C2×Q8—882no—
179C2×D4—22no—
180C2×D4—22no—
181C2×D4#431412yes—
182C2×D4Dic4412yes—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—44no—
186C22×C4—222no—
187C22×C4—222no—
188C22×C4(C2×D11)⋊C412yes—
189C22×C4C2×C4×D1111yescharacteristic
190C22×C4C2×D4411yescharacteristic
191C22×C4C2×C22⋊D1111yescharacteristic
192M16—442no—
193M16—442no—
194C2×C8—24no—
195C2×C8—84no—
196C2×C8—442no—
197C4⋊C4—22no—
198C4⋊C4—442no—
199C4⋊C4—441no—
200C4⋊C4—442no—
201C4⋊C4—441no—
202C22⋊C4—24no—
203C22⋊C4—884no—
204C42—442no—
205C42#433912yes—
206C42C2×C22⋊D1112yes—
207C11#939111yescharacteristic, complemented, Sylow
208C23—22no—
209C23—22no—
210C23—42no—
211C23—42no—
212C23#6688014yes—
213C23C2×(C2×D11)⋊C411yescharacteristic
214Q8—884no—
215D4—24no—
216D4—24no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—41no—
220C2×C4—44no—
221C2×C4—42no—
222C2×C4—82no—
223C2×C4—442no—
224C2×C4—444no—
225C2×C4—442no—
226C2×C4—442no—
227C2×C4—442no—
228C2×C4C2×#431411yescharacteristic
229C2×C4#6695712yes—
230C2×C4C2×Dic4411yescharacteristic
231C2×C4C4×C22⋊D1112yes—
232C2×C4#6698211yescharacteristic
233C2×C4#6698312yes—
234C2×C4#6700611yescharacteristic
235C8—44no—
236C8—882no—
237C22—21no—
238C22—21no—
239C22—24no—
240C22—44no—
241C22—42no—
242C22—42no—
243C22—82no—
244C22C2×#6688011yescharacteristic
245C22#1062272611yescharacteristic
246C22#1062282611yescharacteristic
247C4—22no—
248C4—21no—
249C4—42no—
250C4—882no—
251C4—882no—
252C4#1062272712yes—
253C4#1062272912yes—
254C4#1062285512yes—
255C2—21no—
256C2—21no—
257C2—44no—
258C2#1306900411yescharacteristic
259C2#1306903911yescharacteristic
260C2#1306916311yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2972C2
socleC22×C11#386
prime radicalC22×D4×C11D4
cosocleC2×C42×C11C23
hypercenter#2972D11
hypocenterC11#9391
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2972

Complements

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

NH ≅ G/Ntype
3. #13067296C2semidirect
4. #13066518C2semidirect
207. C11#9391semidirect

Maximal subgroups

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

subgroupindex
#130737892
#130686082
#130672962
#130665182
C11×#29722
#939111