Finite Group Databasebeta

← #14647286

Subgroups — #14647286

Order 2816.

538 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 91 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#13071214C211yesmaximal, characteristic
2#13068690C211yesmaximal, characteristic
3C11⋊#1304C212yesmaximal
4C11⋊#1304C212yesmaximal
5C11×#1819C211yesmaximal, characteristic
6C22×C11×C22⋊C4C2211yescharacteristic
7C11×#379C2212yes—
8#10622860C2212yes—
9#10622860C2211yescharacteristic
10#10622860C2211yescharacteristic
11#10622825C412yescomplemented
12C4×C22⋊Dic11C412yescomplemented
13#10622564—22no—
14#10622564—22no—
15C11×#342—22no—
16#10622164—22no—
17C25×C11C2311yescharacteristic
18C23×C4×C11C2×C411yescharacteristic
19C23×C4×C11C2×C411yescharacteristic
20C2×C11×C22⋊C4—22no—
21C2×C11×C22⋊C4—22no—
22C2×C11×C22⋊C4—22no—
23C2×C11×C22⋊C4—22no—
24C2×C11×C22⋊C4—22no—
25C2×C11×C22⋊C4D412yes—
26C2×C11×C22⋊C4D412yes—
27C2×C22⋊Dic11—22no—
28C2×C22⋊Dic11—21no—
29C2×C22⋊Dic11—21no—
30C2×C22⋊Dic11—21no—
31C2×C22⋊Dic11—21no—
32C2×C22⋊Dic11—22no—
33C2×C22⋊Dic11—22no—
34C2×C22⋊Dic11C2×C412yes—
35C2×C22⋊Dic11C2×C412yes—
36C2×C4⋊Dic11—22no—
37C2×C4×Dic11—22no—
38C11⋊#95—22no—
39C11⋊#95—22no—
40#8750—111nomaximal, Sylow
41C24×C11—42no—
42C24×C11—81no—
43C24×C11—81no—
44C24×C11C22×C411yescharacteristic
45C24×C11C2×D411yescharacteristic
46C24×C11C2×D411yescharacteristic
47C24×C11#4112yes—
48C24×C11#4112yes—
49C22×C4×C11—21no—
50C22×C4×C11—21no—
51C22×C4×C11—21no—
52C22×C4×C11—21no—
53C22×C4×C11—42no—
54C22×C4×C11—81no—
55C22×C4×C11—81no—
56C22×C4×C11C22⋊C412yes—
57C22×C4×C11C22⋊C412yes—
58C22×Dic11—22no—
59C22×Dic11—22no—
60C22×Dic11—42no—
61C11×C22⋊C4—24no—
62C11×C22⋊C4—24no—
63C11×C22⋊C4—44no—
64C11×C22⋊C4—82no—
65C11×C22⋊C4—82no—
66C22⋊Dic11—42no—
67C22⋊Dic11—42no—
68C22⋊Dic11—44no—
69C22⋊Dic11—81no—
70C22⋊Dic11—81no—
71C22⋊Dic11—81no—
72C22⋊Dic11—81no—
73C22⋊Dic11—82no—
74C22⋊Dic11—82no—
75C4⋊Dic11—82no—
76C4×Dic11—82no—
77#2312—111no—
78#1819—111no—
79#1819D1111yescharacteristic
80#1304—112no—
81#1304—112no—
82C23×C11—22no—
83C23×C11—22no—
84C23×C11—22no—
85C23×C11—41no—
86C23×C11—41no—
87C23×C11—41no—
88C23×C11—41no—
89C23×C11—41no—
90C23×C11—41no—
91C23×C11—42no—
92C23×C11—42no—
93C23×C11—42no—
94C23×C11—42no—
95C23×C11—42no—
96C23×C11—42no—
97C23×C11—88no—
98C23×C11C2×C22⋊C411yescharacteristic
99C23×C11#11711yescharacteristic
100C23×C11#11711yescharacteristic
101C23×C11#12312yes—
102C23×C11#12312yes—
103C2×C4×C11—22no—
104C2×C4×C11—22no—
105C2×C4×C11—42no—
106C2×C4×C11—42no—
107C2×C4×C11—81no—
108C2×C4×C11—81no—
109C2×C4×C11—81no—
110C2×C4×C11—81no—
111C2×C4×C11—82no—
112C2×C4×C11—82no—
113C2×C4×C11—82no—
114C2×Dic11—42no—
115C2×Dic11—42no—
116C2×Dic11—42no—
117C2×Dic11—42no—
118C2×Dic11—42no—
119C2×Dic11—42no—
120C2×Dic11—82no—
121C2×Dic11—82no—
122C2×Dic11—82no—
123C22×C22⋊C4C2×D1111yescharacteristic
124#388—222no—
125#388—222no—
126#380—112no—
127#379—111no—
128#379—111no—
129#379—112no—
130#379C2×D1112yes—
131C4×C22⋊C4—112no—
132#342—22no—
133#342—222no—
134C22×C11—21no—
135C22×C11—21no—
136C22×C11—22no—
137C22×C11—21no—
138C22×C11—21no—
139C22×C11—22no—
140C22×C11—21no—
141C22×C11—21no—
142C22×C11—21no—
143C22×C11—21no—
144C22×C11—22no—
145C22×C11—22no—
146C22×C11—22no—
147C22×C11—22no—
148C22×C11—44no—
149C22×C11—82no—
150C22×C11—82no—
151C22×C11—84no—
152C22×C11—84no—
153C22×C11#38111yescharacteristic
154C22×C11#41012yes—
155C4×C11—42no—
156C4×C11—42no—
157C4×C11—162no—
158Dic11—82no—
159Dic11—82no—
160Dic11—162no—
161C25C22×D1111yescharacteristic
162C23×C4C4×D1111yescharacteristic
163C23×C4C4×D1111yescharacteristic
164C2×C4⋊C4—222no—
165C2×C22⋊C4—22no—
166C2×C22⋊C4—22no—
167C2×C22⋊C4—22no—
168C2×C22⋊C4—22no—
169C2×C22⋊C4—22no—
170C2×C22⋊C4—112no—
171C2×C22⋊C4—112no—
172C2×C22⋊C4—222no—
173C2×C22⋊C4—221no—
174C2×C22⋊C4—221no—
175C2×C22⋊C4—221no—
176C2×C22⋊C4—221no—
177C2×C22⋊C4—222no—
178C2×C22⋊C4—222no—
179C2×C22⋊C4D4412yes—
180C2×C22⋊C4C22⋊D1112yes—
181C2×C42—222no—
182#95—222no—
183#95—222no—
184C2×C11—22no—
185C2×C11—42no—
186C2×C11—42no—
187C2×C11—41no—
188C2×C11—41no—
189C2×C11#182011yescharacteristic
190C2×C11#182811yescharacteristic
191C2×C11#182811yescharacteristic
192C24—42no—
193C24—81no—
194C24—81no—
195C24C2×C4×D1111yescharacteristic
196C24C2×D4411yescharacteristic
197C24#434112yes—
198C24#434112yes—
199C24C2×C22⋊D1111yescharacteristic
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—42no—
205C22×C4—81no—
206C22×C4—81no—
207C22×C4—222no—
208C22×C4—222no—
209C22×C4—442no—
210C22×C4(C2×D11)⋊C412yes—
211C22×C4(C2×D11)⋊C412yes—
212C4⋊C4—882no—
213C22⋊C4—24no—
214C22⋊C4—24no—
215C22⋊C4—44no—
216C22⋊C4—82no—
217C22⋊C4—82no—
218C22⋊C4—442no—
219C22⋊C4—442no—
220C22⋊C4—444no—
221C22⋊C4—881no—
222C22⋊C4—881no—
223C22⋊C4—881no—
224C22⋊C4—881no—
225C22⋊C4—882no—
226C22⋊C4—882no—
227C42—882no—
228C11#875011yescharacteristic, complemented, Sylow
229C23—22no—
230C23—22no—
231C23—22no—
232C23—41no—
233C23—41no—
234C23—42no—
235C23—42no—
236C23—41no—
237C23—41no—
238C23—42no—
239C23—42no—
240C23—41no—
241C23—41no—
242C23—42no—
243C23—42no—
244C23—88no—
245C23#6693011yescharacteristic
246C23#6693011yescharacteristic
247C23#6693912yes—
248C23C2×(C2×D11)⋊C411yescharacteristic
249C23#6698812yes—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—81no—
255C2×C4—81no—
256C2×C4—81no—
257C2×C4—81no—
258C2×C4—82no—
259C2×C4—82no—
260C2×C4—82no—
261C2×C4—442no—
262C2×C4—442no—
263C2×C4—442no—
264C2×C4—442no—
265C2×C4—442no—
266C2×C4—442no—
267C2×C4—882no—
268C2×C4—882no—
269C2×C4—882no—
270C22—21no—
271C22—21no—
272C22—22no—
273C22—22no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—22no—
281C22—22no—
282C22—22no—
283C22—22no—
284C22—44no—
285C22—82no—
286C22—82no—
287C22—84no—
288C22—84no—
289C22#1062255611yescharacteristic
290C22#1062261912yes—
291C4—42no—
292C4—42no—
293C4—162no—
294C4—882no—
295C4—882no—
296C4—1762no—
297C2—22no—
298C2—42no—
299C2—42no—
300C2—41no—
301C2—41no—
302C2#1306869111yescharacteristic
303C2#1306872211yescharacteristic
304C2#1306872211yescharacteristic
subgroupG/H
centerC22#10622556
commutatorC24×C11C22×C4
FrattiniC25C22×D11
FittingC11×#1819C2
socleC22×C11#381
prime radical, cosocleC25×C11C23
hypercenter#1819D11
hypocenterC11#8750
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C25 ◁ #1819

Complements

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

NH ≅ G/Ntype
11. #10622825C4semidirect
12. C4×C22⋊Dic11C4semidirect
228. C11#8750semidirect

Maximal subgroups

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

subgroupindex
#130712142
#130686902
C11⋊#13042
C11×#18192
#875011