Finite Group Databasebeta

← #14656769

Subgroups — #14656769

Order 2816.

640 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 640 conjugacy classes of subgroups — too many to draw. Only its 105 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#13074586C211yesmaximal, characteristic
2#13068552C212yesmaximal
3#13066886C211yesmaximal, characteristic
4#13066496C212yesmaximal
5C11×#1280C211yesmaximal, characteristic
6C23×Dic22C2211yescharacteristic
7C2×C11×C22⋊C8C2212yes—
8C2×C11×#95C2211yescharacteristic
9#10622825C2212yes—
10#10622823—22no—
11C2×C11⋊#95—22no—
12C2×C11⋊#95C2211yescharacteristic
13C2×#66880—22no—
14C2×#66880—22no—
15#10622273—22no—
16#10622270—22no—
17C23×C4×C11D412yes—
18C23×C4×C11C2311yescharacteristic
19C23×Dic11—21no—
20C23×Dic11—21no—
21C22×Dic22—22no—
22C22×Dic22—22no—
23C22×Dic22—21no—
24C22×Dic22—44no—
25C22×Dic22Q812yes—
26C22×C8×C11—22no—
27C2×C22⋊Dic11—22no—
28C2×C4⋊Dic11D412yes—
29C2×C4⋊Dic11D412yes—
30C2×Dic11⋊C4—22no—
31C2×Dic11⋊C4—22no—
32C11×C22⋊C8—22no—
33C11×C22⋊C8—22no—
34C11×#95—22no—
35C11⋊#95—22no—
36C11⋊#95—22no—
37C11⋊#95—22no—
38C11⋊#95—22no—
39C11⋊#95—44no—
40#66880—44no—
41#66880—44no—
42#10345—111nomaximal, Sylow
43C24×C11C2×D411yescharacteristic
44C22×C4×C11—22no—
45C22×C4×C11—22no—
46C22×C4×C11—22no—
47C22×C4×C11—42no—
48C22×C4×C11—42no—
49C22×C4×C11—42no—
50C22×C4×C11C2×D412yes—
51C22×C4×C11C2×Q811yescharacteristic
52C22×C4×C11#4112yes—
53C22×C4×C11#4111yescharacteristic
54C22×Dic11—24no—
55C22×Dic11—22no—
56C22×Dic11—22no—
57C22×Dic11—22no—
58C22×Dic11—22no—
59C22×Dic11—42no—
60C22×Dic11—42no—
61C22×Dic11—41no—
62C22×Dic11—41no—
63C22×Dic11—41no—
64C22×Dic11—41no—
65C22×Dic11—42no—
66C2×Dic22—24no—
67C2×Dic22—24no—
68C2×Dic22—24no—
69C2×Dic22—42no—
70C2×Dic22—42no—
71C2×Dic22—44no—
72C2×Dic22—48no—
73C2×Dic22—44no—
74C2×Dic22—42no—
75C2×C8×C11—42no—
76C2×C8×C11—42no—
77C2×C8×C11—42no—
78C22⋊Dic11—42no—
79C22⋊Dic11—42no—
80C4⋊Dic11—42no—
81C4⋊Dic11—42no—
82Dic11⋊C4—82no—
83Dic11⋊C4—82no—
84#2646—111no—
85#1787—112no—
86#1446—111no—
87#1294—112no—
88#1280D1111yescharacteristic
89C23×C11—21no—
90C23×C11—21no—
91C23×C11—22no—
92C23×C11#12011yescharacteristic
93C23×C11C22⋊Q811yescharacteristic
94C23×C11#12411yescharacteristic
95C23×C11#13512yes—
96C23×C11#13712yes—
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—41no—
100C2×C4×C11—42no—
101C2×C4×C11—41no—
102C2×C4×C11—44no—
103C2×C4×C11—42no—
104C2×C4×C11—42no—
105C2×C4×C11—42no—
106C2×C4×C11—82no—
107C2×C4×C11C22⋊Q812yes—
108C2×C4×C11#12412yes—
109C2×Dic11—24no—
110C2×Dic11—42no—
111C2×Dic11—44no—
112C2×Dic11—42no—
113C2×Dic11—44no—
114C2×Dic11—44no—
115C2×Dic11—42no—
116C2×Dic11—42no—
117C2×Dic11—42no—
118C2×Dic11—42no—
119C2×Dic11—42no—
120C2×Dic11—42no—
121C2×Dic11—42no—
122C2×Dic11—82no—
123C2×Dic11—81no—
124C2×Dic11—81no—
125Dic22—28no—
126Dic22—44no—
127Dic22—44no—
128Dic22—44no—
129C8×C11—82no—
130C23×Q8—111no—
131C2×#103—222no—
132C2×#103—222no—
133C2×C22⋊C8C2×D1112yes—
134#400—222no—
135#398—222no—
136#385—222no—
137#380—112no—
138C2×#95—111no—
139C2×#95—222no—
140C2×#95C2×D1111yescharacteristic
141C22×C11—22no—
142C22×C11—22no—
143C22×C11—22no—
144C22×C11—22no—
145C22×C11—21no—
146C22×C11—21no—
147C22×C11—21no—
148C22×C11—21no—
149C22×C11#39311yescharacteristic
150C22×C11#45212yes—
151C22×C11#45511yescharacteristic
152C22×C11#45611yescharacteristic
153C22×C11B(4,𝔽2)12yes—
154C22×C11#47912yes—
155C22×C11#48811yescharacteristic
156C22×C11#49111yescharacteristic
157C4×C11—22no—
158C4×C11—22no—
159C4×C11—82no—
160Dic11—44no—
161Dic11—82no—
162Dic11—82no—
163Dic11—82no—
164C22×Q8—112no—
165C22×Q8—221no—
166C22×Q8—222no—
167C22×Q8—222no—
168C22×Q8—444no—
169C23×C4—221no—
170C23×C4—221no—
171C23×C4D4412yes—
172C23×C4C22×D1111yescharacteristic
173C22×C8—22no—
174C2×C4⋊C4—112no—
175C2×C4⋊C4—112no—
176C2×C4⋊C4—222no—
177C2×C4⋊C4—222no—
178C2×C22⋊C4—222no—
179#103—444no—
180#103—444no—
181C22⋊C8—22no—
182C22⋊C8—22no—
183#95—22no—
184#95—222no—
185#95—222no—
186#95—222no—
187#95—222no—
188#95—444no—
189C2×C11—21no—
190C2×C11—22no—
191C2×C11—21no—
192C2×C11#160312yes—
193C2×C11#160612yes—
194C2×C11#202611yescharacteristic
195C2×C11#202811yescharacteristic
196C2×C11#202911yescharacteristic
197C24C2×D4411yescharacteristic
198C2×Q8—224no—
199C2×Q8—224no—
200C2×Q8—224no—
201C2×Q8—442no—
202C2×Q8—442no—
203C2×Q8—444no—
204C2×Q8—444no—
205C2×Q8—448no—
206C2×Q8—442no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—42no—
211C22×C4—42no—
212C22×C4—42no—
213C22×C4—224no—
214C22×C4—222no—
215C22×C4—222no—
216C22×C4—222no—
217C22×C4—222no—
218C22×C4—442no—
219C22×C4—441no—
220C22×C4—441no—
221C22×C4—442no—
222C22×C4—441no—
223C22×C4—441no—
224C22×C4—442no—
225C22×C4#433912yes—
226C22×C4D4×D1112yes—
227C22×C4#434111yescharacteristic
228C22×C4Q8×D1111yescharacteristic
229C2×C8—42no—
230C2×C8—42no—
231C2×C8—42no—
232C4⋊C4—442no—
233C4⋊C4—442no—
234C4⋊C4—882no—
235C4⋊C4—882no—
236C22⋊C4—442no—
237C22⋊C4—442no—
238C11#1034511yescharacteristic, complemented, Sylow
239C23—22no—
240C23—21no—
241C23—21no—
242C23#6692811yescharacteristic
243C23#6693511yescharacteristic
244C23#6695011yescharacteristic
245C23#6695712yes—
246C23#6696212yes—
247Q8—228no—
248Q8—444no—
249Q8—444no—
250Q8—444no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—42no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—44no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—82no—
261C2×C4—224no—
262C2×C4—442no—
263C2×C4—444no—
264C2×C4—442no—
265C2×C4—444no—
266C2×C4—444no—
267C2×C4—442no—
268C2×C4—442no—
269C2×C4—442no—
270C2×C4—442no—
271C2×C4—442no—
272C2×C4—442no—
273C2×C4—442no—
274C2×C4—882no—
275C2×C4—881no—
276C2×C4—881no—
277C2×C4#6693812yes—
278C2×C4#6694912yes—
279C8—82no—
280C22—22no—
281C22—22no—
282C22—22no—
283C22—22no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22#1062228611yescharacteristic
289C22#1062231011yescharacteristic
290C22#1062231611yescharacteristic
291C22#1062234612yes—
292C22#1062235412yes—
293C22#1062235911yescharacteristic
294C22#1062236511yescharacteristic
295C22#1062244212yes—
296C4—22no—
297C4—22no—
298C4—82no—
299C4—444no—
300C4—882no—
301C4—882no—
302C4—882no—
303C2—21no—
304C2—21no—
305C2—22no—
306C2#1306758112yes—
307C2#1306759812yes—
308C2#1306976811yescharacteristic
309C2#1306977811yescharacteristic
310C2#1306978111yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1280C2
socleC23×C11#120
prime radicalC24×C11C2×D4
hypercenter#1280D11
hypocenterC11#10345
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
238. C11#10345semidirect

Maximal subgroups

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

subgroupindex
#130745862
#130685522
#130668862
#130664962
C11×#12802
#1034511