Finite Group Databasebeta

← #14652253

Subgroups — #14652253

Order 2816.

290 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 89 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#13067280C211yesmaximal, characteristic
2#13067070C211yesmaximal, characteristic
3#13067036C211yesmaximal, characteristic
4#13066900C211yesmaximal, characteristic
5#13066505C211yesmaximal, characteristic
6#13066452C211yesmaximal, characteristic
7C11×#1574C211yesmaximal, characteristic
8#10623001C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12#10622538C2211yescharacteristic
13C4×#4318C2211yescharacteristic
14C2×C4×C11⋊C8C2211yescharacteristic
15C11×#335—21no—
16C11×#334—21no—
17#10622124C411yescharacteristic
18#10622124C411yescharacteristic
19#10622122—21no—
20#10622122—21no—
21#10622122—21no—
22#10622122—21no—
23#10622120C411yescharacteristic
24#10622120C411yescharacteristic
25#10622092—21no—
26C8×C11⋊C8—21no—
27C2×C11×M16—21no—
28C2×C42×C11C2311yescharacteristic
29#66979—21no—
30#66977—21no—
31#66977—21no—
32C2×#4318—21no—
33C22×C11⋊C8—21no—
34#66923—21no—
35#66922C2×C411yescharacteristic
36#66922C2×C411yescharacteristic
37C4×Dic22—21no—
38C4×Dic22—21no—
39C11×C4⋊C8—21no—
40C11×C4⋊C8—21no—
41C11×C4⋊C8C2×C411yescharacteristic
42C11×C4⋊C8C2×C411yescharacteristic
43C11×C4⋊C8D411yescharacteristic
44C11×C4⋊C8D411yescharacteristic
45C11×C22⋊C8—21no—
46C11×C22⋊C8—21no—
47C4×C8×C11—21no—
48C4×C8×C11—21no—
49C22⋊(C11⋊C8)—21no—
50C4⋊(C11⋊C8)C2×C411yescharacteristic
51C4⋊(C11⋊C8)C2×C411yescharacteristic
52#66867—21no—
53C4×C11⋊C8—21no—
54C4×C11⋊C8—21no—
55C4×C11⋊C8—21no—
56C4×C11⋊C8D411yescharacteristic
57C4×C11⋊C8D411yescharacteristic
58#9585—111nomaximal, Sylow
59C22×C4×C11#4111yescharacteristic
60C22×C4×C11#4111yescharacteristic
61C22×C4×C11#4111yescharacteristic
62C2×Dic22—21no—
63C2×Dic22—21no—
64C11×M16—81no—
65C2×C8×C11—21no—
66C2×C8×C11—21no—
67C2×C8×C11—21no—
68C2×C8×C11—21no—
69C2×C8×C11—41no—
70C42×C11C22×C411yescharacteristic
71C42×C11C2×D411yescharacteristic
72C42×C11C2×D411yescharacteristic
73C42×C11#4111yescharacteristic
74C22⋊Dic11—41no—
75C4⋊Dic11—21no—
76C4⋊Dic11—21no—
77C4⋊Dic11—21no—
78C4⋊Dic11—21no—
79Dic11⋊C4—41no—
80Dic11⋊C4—41no—
81C4×Dic11—41no—
82#4318—22no—
83#4318—41no—
84C2×C11⋊C8—22no—
85C2×C11⋊C8—22no—
86C2×C11⋊C8—21no—
87C2×C11⋊C8—21no—
88C2×C11⋊C8—21no—
89C2×C11⋊C8—21no—
90C2×C11⋊C8—41no—
91#1574D1111yescharacteristic
92#1544—111no—
93#1493—111no—
94#1485—111no—
95#1450—111no—
96#1299—111no—
97#1278—111no—
98C23×C11#12611yescharacteristic
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11#11711yescharacteristic
106C2×C4×C11C4×D411yescharacteristic
107C2×C4×C11C4×D411yescharacteristic
108C2×C4×C11#12111yescharacteristic
109C2×C4×C11#12311yescharacteristic
110C2×C4×C11#12411yescharacteristic
111C2×Dic11—41no—
112C2×Dic11—41no—
113Dic22—41no—
114Dic22—41no—
115Dic22—41no—
116Dic22—41no—
117C8×C11—41no—
118C8×C11—41no—
119C8×C11—41no—
120C8×C11—41no—
121C8×C11—81no—
122C11⋊C8—22no—
123C11⋊C8—22no—
124C11⋊C8—42no—
125C11⋊C8—41no—
126C11⋊C8—41no—
127#533—111no—
128#431—111no—
129#431C2×D1111yescharacteristic
130#431C2×D1111yescharacteristic
131#423C2×D1111yescharacteristic
132C4×M16—111no—
133C2×C4×C8—111no—
134#335—21no—
135#334—21no—
136#332—111no—
137#332—111no—
138#332—111no—
139#332—111no—
140Q8⋊C8—221no—
141Q8⋊C8—221no—
142Q8⋊C8—221no—
143Q8⋊C8—221no—
144#322—221no—
145C82—221no—
146C22×C11—21no—
147C22×C11—21no—
148C22×C11—21no—
149C22×C11#38811yescharacteristic
150C4×C11—21no—
151C4×C11—21no—
152C4×C11—21no—
153C4×C11#44311yescharacteristic
154C4×C11#44311yescharacteristic
155C4×C11#44311yescharacteristic
156C4×C11#44411yescharacteristic
157C4×C11#47111yescharacteristic
158C4×C11#47311yescharacteristic
159Dic11—81no—
160Dic11—81no—
161C2×M16—21no—
162C2×M16—221no—
163C22×C8—221no—
164C4⋊Q8—111no—
165C4⋊Q8—111no—
166#125—221no—
167C22⋊Q8—221no—
168C22⋊Q8—221no—
169C4×Q8—221no—
170C4×Q8—221no—
171#117—221no—
172C2×C42C22×D1111yescharacteristic
173C4⋊C8—21no—
174C4⋊C8—21no—
175C4⋊C8—111no—
176C4⋊C8—111no—
177C4⋊C8C4×D1111yescharacteristic
178C4⋊C8C4×D1111yescharacteristic
179C4⋊C8C22⋊D1111yescharacteristic
180C4⋊C8C22⋊D1111yescharacteristic
181C22⋊C8—21no—
182C22⋊C8—21no—
183C22⋊C8—221no—
184#97—221no—
185C4×C8—21no—
186C4×C8—21no—
187C4×C8—111no—
188C4×C8—111no—
189C4×C8—221no—
190C4×C8—221no—
191C4×C8—221no—
192C2×C11—41no—
193C2×C11#192911yescharacteristic
194C2×C11#193011yescharacteristic
195C2×C11#193711yescharacteristic
196C2×Q8—221no—
197C2×Q8—221no—
198C22×C4#433911yescharacteristic
199C22×C4#434111yescharacteristic
200C22×C4#434311yescharacteristic
201M16—81no—
202M16—222no—
203M16—441no—
204C2×C8—21no—
205C2×C8—21no—
206C2×C8—21no—
207C2×C8—21no—
208C2×C8—41no—
209C2×C8—222no—
210C2×C8—222no—
211C2×C8—221no—
212C2×C8—221no—
213C2×C8—221no—
214C2×C8—221no—
215C2×C8—441no—
216C4⋊C4—221no—
217C4⋊C4—221no—
218C4⋊C4—221no—
219C4⋊C4—221no—
220C4⋊C4—441no—
221C4⋊C4—441no—
222C22⋊C4—441no—
223C42—441no—
224C42C2×C4×D1111yescharacteristic
225C42D4×D1111yescharacteristic
226C42#434311yescharacteristic
227C42C2×C22⋊D1111yescharacteristic
228C11#958511yescharacteristic, complemented, Sylow
229C23#6695111yescharacteristic
230Q8—441no—
231Q8—441no—
232Q8—441no—
233Q8—441no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—441no—
241C2×C4—441no—
242C2×C4#6694511yescharacteristic
243C2×C4#6694611yescharacteristic
244C2×C4#6694711yescharacteristic
245C2×C4C4×C22⋊D1111yescharacteristic
246C2×C4#6699211yescharacteristic
247C2×C4#6700011yescharacteristic
248C8—41no—
249C8—41no—
250C8—41no—
251C8—41no—
252C8—81no—
253C8—222no—
254C8—222no—
255C8—442no—
256C8—441no—
257C8—441no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22#1062260311yescharacteristic
262C4—21no—
263C4—21no—
264C4—21no—
265C4—881no—
266C4—881no—
267C4#1062250711yescharacteristic
268C4#1062250811yescharacteristic
269C4#1062275711yescharacteristic
270C4#1062275711yescharacteristic
271C4#1062281311yescharacteristic
272C4#1062281711yescharacteristic
273C2—41no—
274C2#1306926311yescharacteristic
275C2#1306927011yescharacteristic
276C2#1306931911yescharacteristic
subgroupG/H
centerC2×C4#66992
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1574C2
socleC22×C11#388
prime radicalC23×C11#126
cosocleC2×C42×C11C23
hypercenter#1574D11
hypocenterC11#9585
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1574

Complements

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

NH ≅ G/Ntype
228. C11#9585semidirect

Maximal subgroups

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

subgroupindex
#130672802
#130670702
#130670362
#130669002
#130665052
#130664522
C11×#15742
#958511