Finite Group Databasebeta

← #14647271

Subgroups — #14647271

Order 2816.

814 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 814 conjugacy classes of subgroups — too many to draw. Only its 87 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#13071192C211yesmaximal, characteristic
2#13068530C212yesmaximal
3C11⋊#1304C211yesmaximal, characteristic, complemented
4C11⋊#1304C212yesmaximal, complemented
5C11×#1304C211yesmaximal, characteristic, complemented
6C23×C22⋊D11C2211yescharacteristic
7C2×C22⋊C4×D11C412yescomplemented
8C11×#379C2212yes—
9C11×#379C2211yescharacteristic
10#10622860C2212yes—
11#10622860C2211yescharacteristic
12#10622569—24no—
13C2×#66870—24no—
14#10622556C412yescomplemented
15C25×C11C2311yescharacteristic
16C24×D11C2×C411yescharacteristic
17C22×C22⋊D11—22no—
18C22×C22⋊D11—21no—
19C22×C22⋊D11—21no—
20C22×C22⋊D11—44no—
21C22×C22⋊D11D414yes—
22C23×Dic11C2×C411yescharacteristic
23C22×C4×D11—22no—
24C2×C11×C22⋊C4—22no—
25C2×C11×C22⋊C4—22no—
26C2×C11×C22⋊C4—22no—
27C2×C11×C22⋊C4—22no—
28C2×C11×C22⋊C4C2×C412yes—
29C2×C22⋊Dic11—22no—
30C2×C22⋊Dic11—22no—
31C2×C22⋊Dic11—22no—
32C2×C22⋊Dic11—22no—
33C2×C22⋊Dic11C2×C412yes—
34C2×(C2×D11)⋊C4—22no—
35C22⋊C4×D11—44no—
36C11⋊#95—24no—
37#66870—48no—
38#8746—111nomaximal, Sylow
39C24×C11—42no—
40C24×C11—82no—
41C24×C11C22×C411yescharacteristic
42C24×C11C2×D412yes—
43C24×C11#4112yes—
44C24×C11#4111yescharacteristic
45C24×C11#4111yescharacteristic
46C23×D11—21no—
47C23×D11—21no—
48C23×D11—24no—
49C23×D11—82no—
50C23×D11C22⋊C412yes—
51C22×C4×C11—22no—
52C22×C4×C11—42no—
53C2×C22⋊D11—24no—
54C2×C22⋊D11—24no—
55C2×C22⋊D11—28no—
56C2×C22⋊D11—44no—
57C2×C22⋊D11—48no—
58C2×C22⋊D11—44no—
59C2×C22⋊D11—44no—
60C22×Dic11—22no—
61C22×Dic11—21no—
62C22×Dic11—21no—
63C22×Dic11—42no—
64C22×Dic11—42no—
65C22×Dic11C22⋊C412yes—
66C2×C4×D11—44no—
67C2×C4×D11—84no—
68C11×C22⋊C4—42no—
69C11×C22⋊C4—44no—
70C11×C22⋊C4—82no—
71C11×C22⋊C4—82no—
72C11×C22⋊C4—82no—
73C22⋊Dic11—42no—
74C22⋊Dic11—44no—
75C22⋊Dic11—82no—
76C22⋊Dic11—82no—
77C22⋊Dic11—82no—
78(C2×D11)⋊C4—44no—
79#2308—111no—
80#1781—112no—
81#1304—112no—
82#1304—111no—
83#1304D1111yescharacteristic, complemented
84C23×C11—22no—
85C23×C11—24no—
86C23×C11—42no—
87C23×C11—42no—
88C23×C11—42no—
89C23×C11—42no—
90C23×C11—42no—
91C23×C11—42no—
92C23×C11—42no—
93C23×C11—42no—
94C23×C11—41no—
95C23×C11—41no—
96C23×C11—88no—
97C23×C11C2×C22⋊C411yescharacteristic
98C23×C11#11711yescharacteristic
99C23×C11#11711yescharacteristic
100C23×C11#12312yes—
101C23×C11#12312yes—
102C22×D11—22no—
103C22×D11—22no—
104C22×D11—24no—
105C22×D11—24no—
106C22×D11—44no—
107C22×D11—82no—
108C22×D11—82no—
109C22×D11—88no—
110C22×D11#9914yes—
111C2×C4×C11—44no—
112C2×C4×C11—42no—
113C2×C4×C11—82no—
114C2×C4×C11—82no—
115C2×C4×C11—82no—
116C22⋊D11—48no—
117C22⋊D11—48no—
118C2×Dic11—22no—
119C2×Dic11—24no—
120C2×Dic11—42no—
121C2×Dic11—42no—
122C2×Dic11—44no—
123C2×Dic11—42no—
124C2×Dic11—82no—
125C2×Dic11—82no—
126C2×Dic11—82no—
127C4×D11—88no—
128C23×D4—111no—
129C22×C22⋊C4—112no—
130C2×#99—224no—
131#386—224no—
132#381—112no—
133#379—111no—
134#379—112no—
135#379C2×D1112yes—
136#379C2×D1111yescharacteristic
137C22×C11—22no—
138C22×C11—22no—
139C22×C11—21no—
140C22×C11—21no—
141C22×C11—22no—
142C22×C11—22no—
143C22×C11—22no—
144C22×C11—22no—
145C22×C11—22no—
146C22×C11—22no—
147C22×C11—22no—
148C22×C11—44no—
149C22×C11—84no—
150C22×C11—82no—
151C22×C11—84no—
152C22×C11—82no—
153C22×C11#38111yescharacteristic
154C22×C11C2×#9912yes—
155C2×D11—24no—
156C2×D11—44no—
157C2×D11—44no—
158C2×D11—44no—
159C2×D11—84no—
160C2×D11—84no—
161C4×C11—82no—
162C4×C11—162no—
163Dic11—42no—
164Dic11—82no—
165Dic11—162no—
166C25—111no—
167C25C22×D1111yescharacteristic
168C22×D4—114no—
169C22×D4—222no—
170C22×D4—221no—
171C22×D4—221no—
172C22×D4—444no—
173C23×C4—111no—
174C23×C4—222no—
175C2×C22⋊C4—22no—
176C2×C22⋊C4—22no—
177C2×C22⋊C4—22no—
178C2×C22⋊C4—22no—
179C2×C22⋊C4—112no—
180C2×C22⋊C4—222no—
181C2×C22⋊C4—222no—
182C2×C22⋊C4—222no—
183C2×C22⋊C4—222no—
184C2×C22⋊C4—222no—
185C2×C22⋊C4—444no—
186C2×C22⋊C4C4×D1112yes—
187#99—448no—
188#95—224no—
189C2×C11—22no—
190C2×C11—42no—
191C2×C11—42no—
192C2×C11—41no—
193C2×C11—41no—
194C2×C11#181911yescharacteristic
195C2×C11#182812yes—
196D11—44no—
197C24—42no—
198C24—82no—
199C24—112no—
200C24—224no—
201C24—221no—
202C24—221no—
203C24—882no—
204C24C2×C4×D1111yescharacteristic
205C24#433912yes—
206C24D4×D1112yes—
207C24#434111yescharacteristic
208C24#434311yescharacteristic
209C2×D4—228no—
210C2×D4—224no—
211C2×D4—224no—
212C2×D4—444no—
213C2×D4—448no—
214C2×D4—444no—
215C2×D4—444no—
216C22×C4—22no—
217C22×C4—42no—
218C22×C4—112no—
219C22×C4—221no—
220C22×C4—221no—
221C22×C4—222no—
222C22×C4—444no—
223C22×C4—442no—
224C22×C4—442no—
225C22×C4—884no—
226C22⋊C4—42no—
227C22⋊C4—44no—
228C22⋊C4—82no—
229C22⋊C4—82no—
230C22⋊C4—82no—
231C22⋊C4—444no—
232C22⋊C4—442no—
233C22⋊C4—444no—
234C22⋊C4—882no—
235C22⋊C4—882no—
236C22⋊C4—882no—
237C11#874611yescharacteristic, complemented, Sylow
238C23—22no—
239C23—24no—
240C23—42no—
241C23—42no—
242C23—42no—
243C23—42no—
244C23—42no—
245C23—42no—
246C23—42no—
247C23—42no—
248C23—41no—
249C23—41no—
250C23—88no—
251C23—114no—
252C23—224no—
253C23—224no—
254C23—222no—
255C23—222no—
256C23—444no—
257C23—882no—
258C23—882no—
259C23—888no—
260C23#6692511yescharacteristic
261C23C22⋊C4×D1111yescharacteristic
262C23#6693612yes—
263C23#6694511yescharacteristic
264C23#6694712yes—
265D4—448no—
266D4—448no—
267C2×C4—44no—
268C2×C4—42no—
269C2×C4—82no—
270C2×C4—82no—
271C2×C4—82no—
272C2×C4—222no—
273C2×C4—224no—
274C2×C4—442no—
275C2×C4—442no—
276C2×C4—444no—
277C2×C4—442no—
278C2×C4—888no—
279C2×C4—882no—
280C2×C4—882no—
281C2×C4—882no—
282C22—22no—
283C22—22no—
284C22—21no—
285C22—21no—
286C22—22no—
287C22—22no—
288C22—22no—
289C22—22no—
290C22—22no—
291C22—22no—
292C22—22no—
293C22—44no—
294C22—84no—
295C22—82no—
296C22—84no—
297C22—82no—
298C22—224no—
299C22—444no—
300C22—444no—
301C22—444no—
302C22—884no—
303C22—884no—
304C22#1062227711yescharacteristic
305C22D11×#9912yes—
306C4—82no—
307C4—162no—
308C4—442no—
309C4—882no—
310C4—1762no—
311C2—22no—
312C2—42no—
313C2—42no—
314C2—41no—
315C2—41no—
316C2—444no—
317C2#1306868911yescharacteristic
318C2#1306872312yes—
subgroupG/H
centerC22#10622277
commutatorC24×C11C22×C4
FrattiniC25C22×D11
FittingC11×#1304C2
socleC22×C11#381
prime radicalC23×C22⋊D11C22
cosocleC25×C11C23
hypercenter#1304D11
hypocenterC11#8746
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C25 ◁ #1304

Complements

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

NH ≅ G/Ntype
3. C11⋊#1304C2semidirect
4. C11⋊#1304C2semidirect
5. C11×#1304C2semidirect
7. C2×C22⋊C4×D11C4semidirect
14. #10622556C4semidirect
83. #1304D11semidirect
237. C11#8746semidirect

Maximal subgroups

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

subgroupindex
#130711922
#130685302
C11⋊#13042
C11×#13042
#874611