Finite Group Databasebeta

← #14651025

Subgroups — #14651025

Order 2816.

368 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 99 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#13079830C211yesmaximal, characteristic
2#13067316C211yesmaximal, characteristic
3#13067253C211yesmaximal, characteristic
4#13067020C211yesmaximal, characteristic
5#13066485C211yesmaximal, characteristic
6#13066478C211yesmaximal, characteristic
7C11×#2985C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9#10623001C2211yescharacteristic
10C11×#446—22no—
11C11×#446—21no—
12C8×Q8×C11—21no—
13C11×#433—22no—
14C11×#432C2211yescharacteristic
15C11×#431C2211yescharacteristic
16#10622707—21no—
17#10622704—21no—
18#10622682C412yes—
19#10622678C412yes—
20#10622609—22no—
21#10622539C2211yescharacteristic
22#10622539C2211yescharacteristic
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24#10622185—21no—
25#10622185—21no—
26#10622103—22no—
27#10622094—21no—
28#10622094—21no—
29C11×C4⋊Q8D411yescharacteristic
30C11×C4⋊Q8D411yescharacteristic
31C11×#125C2×C412yes—
32C11×C22⋊Q8—21no—
33C11×C22⋊Q8—21no—
34C4×Q8×C11—21no—
35C4×Q8×C11—21no—
36C11×#117D412yes—
37C2×C42×C11C2311yescharacteristic
38#66979—21no—
39#66977—21no—
40#66977—21no—
41C22×C11⋊C8—21no—
42#66923—21no—
43#66922C2×C411yescharacteristic
44#66922C2×C411yescharacteristic
45C4×Dic22—21no—
46C4×Dic22—21no—
47C11×C4⋊C8—22no—
48C11×C4⋊C8—22no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8—21no—
51C11×C22⋊C8—21no—
52C11×C22⋊C8—21no—
53C11×#97—22no—
54C11×#97D412yes—
55C4×C8×C11—22no—
56C4×C8×C11D411yescharacteristic
57C4×C8×C11D411yescharacteristic
58C22⋊(C11⋊C8)—21no—
59C22⋊(C11⋊C8)—21no—
60#66874—22no—
61#66874—22no—
62#66872—22no—
63#66871—22no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)—21no—
68#66867—21no—
69#66867C2×C412yes—
70#9374—111nomaximal, Sylow
71C2×Q8×C11—21no—
72C2×Q8×C11—21no—
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11#4111yescharacteristic
75C22×C4×C11#4111yescharacteristic
76C2×Dic22—21no—
77C2×Dic22—21no—
78C2×C8×C11—21no—
79C2×C8×C11—22no—
80C2×C8×C11—21no—
81C11×C4⋊C4—22no—
82C11×C4⋊C4—22no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4C22⋊C412yes—
86C11×C4⋊C4C22⋊C412yes—
87C11×C22⋊C4—22no—
88C42×C11—22no—
89C42×C11C22×C411yescharacteristic
90C42×C11C2×D411yescharacteristic
91C42×C11C2×D411yescharacteristic
92C42×C11C2×D411yescharacteristic
93C22⋊Dic11—41no—
94C4⋊Dic11—21no—
95C4⋊Dic11—21no—
96C4⋊Dic11—21no—
97C4⋊Dic11—21no—
98Dic11⋊C4—41no—
99Dic11⋊C4—41no—
100C4×Dic11—41no—
101C2×C11⋊C8—22no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—81no—
105#3237—111no—
106#2985D1111yescharacteristic
107#1552—111no—
108#1537—111no—
109#1481—111no—
110#1290—111no—
111#1287—111no—
112C23×C11#12311yescharacteristic
113Q8×C11—41no—
114Q8×C11—41no—
115Q8×C11—81no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—22no—
119C2×C4×C11—22no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11C2×C22⋊C411yescharacteristic
123C2×C4×C11C4×D411yescharacteristic
124C2×C4×C11C4×D411yescharacteristic
125C2×C4×C11#12011yescharacteristic
126C2×C4×C11#12111yescharacteristic
127C2×C4×C11#12111yescharacteristic
128C2×Dic11—41no—
129C2×Dic11—41no—
130Dic22—42no—
131Dic22—42no—
132C8×C11—41no—
133C8×C11—42no—
134C8×C11—41no—
135C11⋊C8—42no—
136C11⋊C8—81no—
137C11⋊C8—81no—
138#533—111no—
139#533C2×D1111yescharacteristic
140#501—112no—
141#491—112no—
142#485—222no—
143#477—221no—
144#475—221no—
145#446—22no—
146#446—21no—
147C8×Q8—21no—
148#433—22no—
149#432—111no—
150#432—111no—
151#432C2×D1111yescharacteristic
152#431C2×D1111yescharacteristic
153C2×C4⋊C8—111no—
154#332—221no—
155#332—221no—
156#330—222no—
157Q8⋊C8—221no—
158Q8⋊C8—221no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11#38611yescharacteristic
163C4×C11—21no—
164C4×C11—21no—
165C4×C11—21no—
166C4×C11—21no—
167C4×C11—21no—
168C4×C11—42no—
169C4×C11—42no—
170C4×C11#47111yescharacteristic
171C4×C11#47311yescharacteristic
172Dic11—81no—
173Dic11—81no—
174C22×C8—221no—
175C4⋊Q8—111no—
176C4⋊Q8—111no—
177C4⋊Q8D4411yescharacteristic
178C4⋊Q8D4411yescharacteristic
179#125—221no—
180#125C4×D1112yes—
181C22⋊Q8—21no—
182C22⋊Q8—21no—
183C22⋊Q8—221no—
184C22⋊Q8—221no—
185C4×Q8—21no—
186C4×Q8—21no—
187C4×Q8—221no—
188C4×Q8—221no—
189#117—221no—
190#117C22⋊D1112yes—
191C2×C42C22×D1111yescharacteristic
192#107—222no—
193#106—222no—
194C4⋊C8—22no—
195C4⋊C8—22no—
196C4⋊C8—21no—
197C4⋊C8—21no—
198C4⋊C8—221no—
199C4⋊C8—221no—
200C4⋊C8—221no—
201C4⋊C8—221no—
202#103—222no—
203#103—222no—
204C22⋊C8—21no—
205C22⋊C8—21no—
206C22⋊C8—221no—
207C22⋊C8—221no—
208#97—22no—
209#97—112no—
210#97—221no—
211#97C22⋊D1112yes—
212C4×C8—22no—
213C4×C8C22⋊D1111yescharacteristic
214C4×C8C22⋊D1111yescharacteristic
215C2×C11—41no—
216C2×C11#188111yescharacteristic
217C2×C11#190811yescharacteristic
218C2×C11#191211yescharacteristic
219C2×Q8—21no—
220C2×Q8—21no—
221C2×Q8—221no—
222C2×Q8—221no—
223C22×C4#433911yescharacteristic
224C22×C4#433911yescharacteristic
225C22×C4C2×C22⋊D1111yescharacteristic
226C2×C8—21no—
227C2×C8—22no—
228C2×C8—21no—
229C2×C8—222no—
230C2×C8—441no—
231C2×C8—441no—
232C2×C8—881no—
233C4⋊C4—22no—
234C4⋊C4—22no—
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—221no—
238C4⋊C4—221no—
239C4⋊C4—221no—
240C4⋊C4—221no—
241C4⋊C4—441no—
242C4⋊C4—441no—
243C4⋊C4(C2×D11)⋊C412yes—
244C4⋊C4(C2×D11)⋊C412yes—
245C22⋊C4—22no—
246C22⋊C4—441no—
247C42—22no—
248C42—441no—
249C42C2×C4×D1111yescharacteristic
250C42C2×D4411yescharacteristic
251C42C2×C22⋊D1111yescharacteristic
252C42C2×C22⋊D1111yescharacteristic
253C11#937411yescharacteristic, complemented, Sylow
254C23#6698211yescharacteristic
255Q8—41no—
256Q8—41no—
257Q8—81no—
258Q8—442no—
259Q8—442no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—441no—
267C2×C4—441no—
268C2×C4C2×(C2×D11)⋊C411yescharacteristic
269C2×C4C4×C22⋊D1111yescharacteristic
270C2×C4C4×C22⋊D1111yescharacteristic
271C2×C4#6698311yescharacteristic
272C2×C4#6698311yescharacteristic
273C2×C4#6700611yescharacteristic
274C8—41no—
275C8—42no—
276C8—41no—
277C8—442no—
278C8—881no—
279C8—881no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22#1062282611yescharacteristic
284C4—21no—
285C4—21no—
286C4—21no—
287C4—21no—
288C4—21no—
289C4—42no—
290C4—42no—
291C4—881no—
292C4—881no—
293C4#1062275411yescharacteristic
294C4#1062275611yescharacteristic
295C2—41no—
296C2#1306897811yescharacteristic
297C2#1306913111yescharacteristic
298C2#1306915311yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2985C2
socleC22×C11#386
prime radicalC23×C11#123
cosocleC2×C42×C11C23
hypercenter#2985D11
hypocenterC11#9374
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2985

Complements

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

NH ≅ G/Ntype
253. C11#9374semidirect

Maximal subgroups

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

subgroupindex
#130798302
#130673162
#130672532
#130670202
#130664852
#130664782
C11×#29852
#937411