Finite Group Databasebeta

← #14657028

Subgroups — #14657028

Order 2816.

746 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 746 conjugacy classes of subgroups — too many to draw. Only its 77 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#13068530C212yesmaximal
2#13068530C211yesmaximal, characteristic
3C11⋊#1304C211yesmaximal, characteristic, complemented
4C11⋊#1304C212yesmaximal, complemented
5C11×#2842C211yesmaximal, characteristic, complemented
6C23×C22⋊D11C2211yescharacteristic
7C11×#399—22no—
8C11×#396—24no—
9C11×#379C2211yescharacteristic
10C11×#379C2212yes—
11#10622860C2212yes—
12#10622860C2211yescharacteristic
13C2×#66870—24no—
14C2×#66870—22no—
15C25×C11C2311yescharacteristic
16C24×D11Q811yescharacteristic
17C22×C22⋊D11—22no—
18C22×C22⋊D11—21no—
19C22×C22⋊D11—22no—
20C22×C22⋊D11—21no—
21C22×C22⋊D11—44no—
22C23×Dic11Q811yescharacteristic
23C2×C11×C4⋊C4—24no—
24C2×C11×C4⋊C4—22no—
25C2×C11×C22⋊C4—22no—
26C2×C11×C22⋊C4—22no—
27C2×C11×C22⋊C4—22no—
28C2×C11×C22⋊C4D414yes—
29C2×C11×C22⋊C4D412yes—
30C2×C22⋊Dic11—22no—
31C2×C22⋊Dic11—21no—
32C2×C22⋊Dic11—22no—
33C2×C22⋊Dic11—22no—
34C2×C22⋊Dic11—22no—
35C11×#95—22no—
36#66870—48no—
37#66870—44no—
38#10392—111nomaximal, Sylow
39C24×C11—42no—
40C24×C11—82no—
41C24×C11C2×D412yes—
42C24×C11C2×D411yescharacteristic
43C24×C11C2×Q811yescharacteristic
44C24×C11#4112yes—
45C24×C11#4111yescharacteristic
46C23×D11—22no—
47C23×D11—21no—
48C23×D11—42no—
49C23×D11—82no—
50C22×C4×C11—22no—
51C22×C4×C11—24no—
52C2×C22⋊D11—28no—
53C2×C22⋊D11—24no—
54C2×C22⋊D11—44no—
55C2×C22⋊D11—42no—
56C2×C22⋊D11—44no—
57C2×C22⋊D11—42no—
58C2×C22⋊D11—44no—
59C2×C22⋊D11—42no—
60C2×C22⋊D11—41no—
61C2×C22⋊D11—42no—
62C2×C22⋊D11—41no—
63C22×Dic11—22no—
64C22×Dic11—21no—
65C22×Dic11—42no—
66C22×Dic11—42no—
67C22×Dic11—41no—
68C11×C4⋊C4—84no—
69C11×C4⋊C4—82no—
70C11×C22⋊C4—44no—
71C11×C22⋊C4—42no—
72C11×C22⋊C4—82no—
73C11×C22⋊C4—82no—
74C11×C22⋊C4—82no—
75C22⋊Dic11—44no—
76C22⋊Dic11—42no—
77C22⋊Dic11—82no—
78C22⋊Dic11—82no—
79C22⋊Dic11—82no—
80#2842D1111yescharacteristic, complemented
81#1781—111no—
82#1781—112no—
83#1304—111no—
84#1304—112no—
85C23×C11—24no—
86C23×C11—22no—
87C23×C11—41no—
88C23×C11—42no—
89C23×C11—42no—
90C23×C11—42no—
91C23×C11—42no—
92C23×C11—42no—
93C23×C11—42no—
94C23×C11—42no—
95C23×C11—42no—
96C23×C11—41no—
97C23×C11—88no—
98C23×C11#12011yescharacteristic
99C23×C11C22⋊Q812yes—
100C23×C11C22⋊Q811yescharacteristic
101C23×C11#12412yes—
102C23×C11#12411yescharacteristic
103C22×D11—24no—
104C22×D11—22no—
105C22×D11—42no—
106C22×D11—41no—
107C22×D11—41no—
108C22×D11—88no—
109C22×D11—82no—
110C22×D11—82no—
111C22×D11—82no—
112C2×C4×C11—44no—
113C2×C4×C11—44no—
114C2×C4×C11—44no—
115C2×C4×C11—44no—
116C2×C4×C11—42no—
117C22⋊D11—48no—
118C22⋊D11—44no—
119C22⋊D11—44no—
120C2×Dic11—24no—
121C2×Dic11—22no—
122C2×Dic11—42no—
123C2×Dic11—41no—
124C2×Dic11—41no—
125C2×Dic11—82no—
126C2×Dic11—81no—
127C2×Dic11—82no—
128C2×Dic11—82no—
129C2×Dic11—82no—
130C23×D4—111no—
131C2×#99—224no—
132C2×#99—222no—
133#399—22no—
134#396—24no—
135#379—112no—
136#379—111no—
137#379C2×D1111yescharacteristic
138#379C2×D1112yes—
139C22×C11—22no—
140C22×C11—22no—
141C22×C11—21no—
142C22×C11—22no—
143C22×C11—21no—
144C22×C11—22no—
145C22×C11—22no—
146C22×C11—22no—
147C22×C11—22no—
148C22×C11—22no—
149C22×C11—22no—
150C22×C11—44no—
151C22×C11—84no—
152C22×C11—82no—
153C22×C11—82no—
154C22×C11—84no—
155C22×C11#39311yescharacteristic
156C22×C11B(4,𝔽2)12yes—
157C2×D11—42no—
158C2×D11—84no—
159C2×D11—82no—
160C2×D11—82no—
161C2×D11—84no—
162C2×D11—82no—
163C4×C11—82no—
164C4×C11—84no—
165Dic11—42no—
166Dic11—162no—
167Dic11—161no—
168C25—111no—
169C25C22×D1111yescharacteristic
170C22×D4—222no—
171C22×D4—221no—
172C22×D4—222no—
173C22×D4—221no—
174C22×D4—444no—
175C23×C4—111no—
176C2×C4⋊C4—24no—
177C2×C4⋊C4—22no—
178C2×C22⋊C4—22no—
179C2×C22⋊C4—22no—
180C2×C22⋊C4—22no—
181C2×C22⋊C4—222no—
182C2×C22⋊C4—221no—
183C2×C22⋊C4—222no—
184C2×C22⋊C4—222no—
185C2×C22⋊C4—222no—
186C2×C22⋊C4C22⋊D1114yes—
187C2×C22⋊C4C22⋊D1112yes—
188#99—448no—
189#99—444no—
190#95—22no—
191C2×C11—22no—
192C2×C11—42no—
193C2×C11—41no—
194C2×C11—42no—
195C2×C11—41no—
196C2×C11#202911yescharacteristic
197C2×C11#203212yes—
198D11—82no—
199C24—42no—
200C24—82no—
201C24—222no—
202C24—221no—
203C24—442no—
204C24—882no—
205C24Q8×D1111yescharacteristic
206C24#434312yes—
207C24#434311yescharacteristic
208C24C2×C22⋊D1112yes—
209C24C2×C22⋊D1111yescharacteristic
210C2×D4—228no—
211C2×D4—224no—
212C2×D4—444no—
213C2×D4—442no—
214C2×D4—444no—
215C2×D4—442no—
216C2×D4—444no—
217C2×D4—442no—
218C2×D4—442no—
219C2×D4—441no—
220C2×D4—441no—
221C22×C4—22no—
222C22×C4—24no—
223C22×C4—222no—
224C22×C4—221no—
225C22×C4—442no—
226C22×C4—442no—
227C22×C4—441no—
228C4⋊C4—84no—
229C4⋊C4—82no—
230C22⋊C4—44no—
231C22⋊C4—42no—
232C22⋊C4—82no—
233C22⋊C4—82no—
234C22⋊C4—82no—
235C22⋊C4—444no—
236C22⋊C4—442no—
237C22⋊C4—882no—
238C22⋊C4—882no—
239C22⋊C4—882no—
240C11#1039211yescharacteristic, complemented, Sylow
241C23—24no—
242C23—22no—
243C23—41no—
244C23—42no—
245C23—42no—
246C23—42no—
247C23—42no—
248C23—42no—
249C23—42no—
250C23—42no—
251C23—42no—
252C23—41no—
253C23—88no—
254C23—224no—
255C23—222no—
256C23—442no—
257C23—441no—
258C23—441no—
259C23—882no—
260C23—882no—
261C23—882no—
262C23—888no—
263C23#6699912yes—
264C23#6699911yescharacteristic
265C23#6700012yes—
266C23#6700011yescharacteristic
267C23#6700611yescharacteristic
268D4—448no—
269D4—444no—
270D4—444no—
271C2×C4—44no—
272C2×C4—44no—
273C2×C4—44no—
274C2×C4—44no—
275C2×C4—42no—
276C2×C4—224no—
277C2×C4—222no—
278C2×C4—442no—
279C2×C4—441no—
280C2×C4—441no—
281C2×C4—882no—
282C2×C4—881no—
283C2×C4—882no—
284C2×C4—882no—
285C2×C4—882no—
286C22—22no—
287C22—22no—
288C22—21no—
289C22—22no—
290C22—21no—
291C22—22no—
292C22—22no—
293C22—22no—
294C22—22no—
295C22—22no—
296C22—22no—
297C22—44no—
298C22—84no—
299C22—82no—
300C22—82no—
301C22—84no—
302C22—442no—
303C22—884no—
304C22—882no—
305C22—884no—
306C22—882no—
307C22—882no—
308C22#1062284411yescharacteristic
309C22#1062285712yes—
310C4—82no—
311C4—84no—
312C4—442no—
313C4—1762no—
314C4—1761no—
315C2—22no—
316C2—42no—
317C2—41no—
318C2—42no—
319C2—41no—
320C2—882no—
321C2#1306977911yescharacteristic
322C2#1306979212yes—
subgroupG/H
centerC22#10622844
commutator, cosocleC25×C11C23
FrattiniC25C22×D11
FittingC11×#2842C2
socleC22×C11#393
prime radicalC23×C22⋊D11C22
hypercenter#2842D11
hypocenterC11#10392
LCSG ▷ C25×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C25 ◁ #2842

Complements

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

NH ≅ G/Ntype
3. C11⋊#1304C2semidirect
4. C11⋊#1304C2semidirect
5. C11×#2842C2semidirect
80. #2842D11semidirect
240. C11#10392semidirect

Maximal subgroups

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

subgroupindex
#130685302
C11⋊#13042
C11×#28422
#1039211