Finite Group Databasebeta

← #14663067

Subgroups — #14663067

Order 2816.

460 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 119 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#13066934C212yesmaximal
2#13066562C212yesmaximal, complemented
3#13066550C212yesmaximal, complemented
4C11×#2326C211yesmaximal, characteristic
5C2×C11×#124C411yescharacteristic
6C2×C4×Q8×C11C411yescharacteristic
7C2×C4×D4×C11C2211yescharacteristic
8C11×#391C2211yescharacteristic
9C11×#390C411yescharacteristic
10C11×#388—22no—
11C11×#385—22no—
12C11×#384C2211yescharacteristic
13C11×#376C411yescharacteristic
14C2×C22⋊(C11⋊C8)—22no—
15#10622166C2214yes—
16#10622163—22no—
17C22×Q8×C11C2×C411yescharacteristic
18C22×D4×C11C2×C411yescharacteristic
19C23×C4×C11D412yes—
20C11×#124—22no—
21C11×#124C814yescomplemented
22C4×Q8×C11—42no—
23C4×D4×C11—42no—
24C2×C11×C4⋊C4—21no—
25C2×C11×C4⋊C4—22no—
26C2×C11×C4⋊C4C2×C411yescharacteristic
27C2×C11×C4⋊C4C2311yescharacteristic
28C2×C11×C22⋊C4—22no—
29C2×C11×C22⋊C4—22no—
30C2×C11×C22⋊C4D412yes—
31C2×C42×C11—21no—
32C2×C42×C11C2×C411yescharacteristic
33C2×C42×C11C2×C411yescharacteristic
34C2×C42×C11C2×C411yescharacteristic
35C22×C11⋊C8—42no—
36C11×#95—21no—
37C11×#95—21no—
38C11×#95—22no—
39C22⋊(C11⋊C8)—24no—
40C22⋊(C11⋊C8)—42no—
41#11481—111nomaximal, Sylow
42C24×C11C22⋊C412yes—
43C2×Q8×C11—21no—
44C2×Q8×C11—41no—
45C2×Q8×C11—41no—
46C2×Q8×C11C2×C812yescomplemented
47C2×D4×C11—41no—
48C2×D4×C11—41no—
49C2×D4×C11C2×C812yes—
50C2×D4×C11M1612yes—
51C22×C4×C11—21no—
52C22×C4×C11—21no—
53C22×C4×C11—22no—
54C22×C4×C11—22no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—82no—
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C22×C411yescharacteristic
61C22×C4×C11C2×D412yes—
62C11×C4⋊C4—41no—
63C11×C4⋊C4—41no—
64C11×C4⋊C4—42no—
65C11×C4⋊C4—82no—
66C11×C22⋊C4—28no—
67C11×C22⋊C4—42no—
68C11×C22⋊C4—82no—
69C42×C11—22no—
70C42×C11—21no—
71C42×C11—42no—
72C42×C11—41no—
73C42×C11C2×C812yescomplemented
74C2×C11⋊C8—44no—
75C2×C11⋊C8—84no—
76#2326D1111yescharacteristic
77#1459—112no—
78#1325—112no—
79#1319—112no—
80C23×C11—22no—
81C23×C11—22no—
82C23×C11—42no—
83C23×C11—42no—
84C23×C11C22⋊C814yes—
85C23×C11C2×C22⋊C411yescharacteristic
86Q8×C11—42no—
87Q8×C11—42no—
88D4×C11—42no—
89D4×C11—42no—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11—22no—
95C2×C4×C11—21no—
96C2×C4×C11—41no—
97C2×C4×C11—44no—
98C2×C4×C11—41no—
99C2×C4×C11—41no—
100C2×C4×C11—41no—
101C2×C4×C11—41no—
102C2×C4×C11—42no—
103C2×C4×C11—41no—
104C2×C4×C11—41no—
105C2×C4×C11—42no—
106C2×C4×C11—41no—
107C2×C4×C11—41no—
108C2×C4×C11—41no—
109C2×C4×C11—82no—
110C2×C4×C11#9912yes—
111C2×C4×C11C22×C811yescharacteristic
112C2×C4×C11C2×M1611yescharacteristic
113C11⋊C8—84no—
114C2×#124Dic1111yescharacteristic
115C2×C4×Q8Dic1111yescharacteristic
116C2×C4×D4C2×D1111yescharacteristic
117C2×C22⋊C8—222no—
118#391C2×D1111yescharacteristic
119#390Dic1111yescharacteristic
120#388—22no—
121#385—22no—
122#384C2×D1111yescharacteristic
123#376Dic1111yescharacteristic
124#324—114no—
125#323—222no—
126C22×C11—21no—
127C22×C11—21no—
128C22×C11—24no—
129C22×C11—44no—
130C22×C11—42no—
131C22×C11—42no—
132C22×C11—82no—
133C22×C11C2×C22⋊C811yescharacteristic
134C22×C11C2×#9911yescharacteristic
135C22×C11#41311yescharacteristic
136C4×C11—22no—
137C4×C11—21no—
138C4×C11—21no—
139C4×C11—42no—
140C4×C11—42no—
141C4×C11—41no—
142C4×C11—42no—
143C4×C11—81no—
144C4×C11—81no—
145C22×Q8C2×Dic1111yescharacteristic
146C22×D4C2×Dic1111yescharacteristic
147C23×C4C22⋊D1112yes—
148C22×C8—442no—
149#124—22no—
150#124C11⋊C814yescomplemented
151C4×Q8—42no—
152C4×D4—42no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4C2×Dic1111yescharacteristic
156C2×C4⋊C4C22×D1111yescharacteristic
157C2×C22⋊C4—22no—
158C2×C22⋊C4—22no—
159C2×C22⋊C4C22⋊D1112yes—
160C2×C42—21no—
161C2×C42C2×Dic1111yescharacteristic
162C2×C42C2×Dic1111yescharacteristic
163C2×C42C2×Dic1111yescharacteristic
164C22⋊C8—224no—
165C22⋊C8—442no—
166#95—21no—
167#95—21no—
168#95—22no—
169C2×C11—21no—
170C2×C11—21no—
171C2×C11—44no—
172C2×C11#145911yescharacteristic
173C2×C11#212711yescharacteristic
174C2×C11#213511yescharacteristic
175C24C22⋊Dic1112yes—
176C2×Q8—21no—
177C2×Q8—41no—
178C2×Q8—41no—
179C2×Q8C2×C11⋊C812yescomplemented
180C2×D4—41no—
181C2×D4—41no—
182C2×D4C2×C11⋊C812yes—
183C2×D4#431812yes—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—22no—
187C22×C4—22no—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—82no—
191C22×C4C22⋊Dic1111yescharacteristic
192C22×C4C22⋊Dic1111yescharacteristic
193C22×C4C22×Dic1111yescharacteristic
194C22×C4C2×C22⋊D1112yes—
195C2×C8—444no—
196C2×C8—884no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—42no—
200C4⋊C4—82no—
201C22⋊C4—28no—
202C22⋊C4—42no—
203C22⋊C4—82no—
204C42—22no—
205C42—21no—
206C42—41no—
207C42—42no—
208C42C2×C11⋊C812yescomplemented
209C11#1148111yescharacteristic, complemented, Sylow
210C23—22no—
211C23—22no—
212C23—42no—
213C23—42no—
214C23C22⋊(C11⋊C8)14yes—
215C23C2×C22⋊Dic1111yescharacteristic
216Q8—42no—
217Q8—42no—
218D4—42no—
219D4—42no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—41no—
227C2×C4—44no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—42no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—82no—
240C2×C4#6689812yes—
241C2×C4C22×C11⋊C811yescharacteristic
242C2×C4C2×#431811yescharacteristic
243C8—884no—
244C22—21no—
245C22—21no—
246C22—24no—
247C22—44no—
248C22—42no—
249C22—42no—
250C22—82no—
251C22C2×C22⋊(C11⋊C8)11yescharacteristic
252C22C2×#6689811yescharacteristic
253C22#1062285011yescharacteristic
254C4—21no—
255C4—21no—
256C4—22no—
257C4—42no—
258C4—42no—
259C4—42no—
260C4—41no—
261C4—81no—
262C4—81no—
263C2—21no—
264C2—21no—
265C2—44no—
266C2#1306693411yescharacteristic
267C2#1307028511yescharacteristic
268C2#1307031111yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC2×C4×C11C22×C8
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2326C2
socleC22×C11C2×#99
prime radicalC22×D4×C11C2×C4
cosocleC2×C11×C4⋊C4C23
hypercenter#2326D11
hypocenterC11#11481
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2326

Complements

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

NH ≅ G/Ntype
2. #13066562C2semidirect
3. #13066550C2semidirect
21. C11×#124C8semidirect
46. C2×Q8×C11C2×C8semidirect
73. C42×C11C2×C8semidirect
150. #124C11⋊C8semidirect
179. C2×Q8C2×C11⋊C8semidirect
208. C42C2×C11⋊C8semidirect
209. C11#11481semidirect

Maximal subgroups

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

subgroupindex
#130669342
#130665622
#130665502
C11×#23262
#1148111