Finite Group Databasebeta

← #14684739

Subgroups — #14684739

Order 2816.

1810 conjugacy classes of subgroups; only the 319 normal subgroups are shown.

normal subgroups only

This group has 1810 conjugacy classes of subgroups — too many to draw. Only its 319 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#13066878C212yesmaximal, complemented
2#13066865C213yesmaximal, complemented
3#13066857C216yesmaximal, complemented
4#13066853C213yesmaximal, complemented
5C2×C11×#392C211yesmaximal, characteristic
6C23×D4×C11C2213yes—
7C22×C11×C22⋊C4C2213yes—
8C22×C22⋊Dic11C2216yes—
9C22×C22⋊Dic11C2213yes—
10C22×C22⋊Dic11C2213yes—
11C22×C4×Dic11C2211yescharacteristic
12C11×#392C418yescomplemented
13C2×C11×#95C2211yescharacteristic
14C2×C11⋊#95C2216yes—
15C2×C11⋊#95C2213yes—
16C2×C11⋊#95C2216yes—
17C25×C11C2313yes—
18C22×D4×C11—46no—
19C22×D4×C11—46no—
20C22×D4×C11—43no—
21C22×D4×C11—43no—
22C22×D4×C11C2×C4112yes—
23C23×C4×C11C2311yescharacteristic
24C23×C4×C11C2313yes—
25C23×Dic11C2316yes—
26C23×Dic11C2312yes—
27C2×C11×C22⋊C4—43no—
28C2×C11×C22⋊C4—43no—
29C2×C11×C22⋊C4C2×C4112yes—
30C2×C22⋊Dic11—212no—
31C2×C22⋊Dic11—46no—
32C2×C22⋊Dic11—46no—
33C2×C22⋊Dic11—46no—
34C2×C22⋊Dic11—46no—
35C2×C22⋊Dic11—43no—
36C2×C22⋊Dic11—43no—
37C2×C4×Dic11—43no—
38C11×#95C2×C414yes—
39C11⋊#95—46no—
40C11⋊#95—46no—
41C11⋊#95—43no—
42#14651—111nomaximal, Sylow
43C24×C11—26no—
44C24×C11—23no—
45C24×C11—23no—
46C24×C11—26no—
47C24×C11—26no—
48C24×C11—26no—
49C24×C11—26no—
50C24×C11—26no—
51C24×C11C22×C416yes—
52C24×C11C2411yescharacteristic
53C2×D4×C11—412no—
54C2×D4×C11—424no—
55C2×D4×C11—424no—
56C2×D4×C11—412no—
57C2×D4×C11—412no—
58C22×C4×C11—23no—
59C22×C4×C11—26no—
60C22×C4×C11—26no—
61C22×C4×C11—23no—
62C22×C4×C11—23no—
63C22×C4×C11—23no—
64C22×C4×C11C22×C416yes—
65C22×C4×C11C22×C412yes—
66C22×Dic11—26no—
67C22×Dic11—26no—
68C22×Dic11—26no—
69C22×Dic11—26no—
70C22×Dic11—26no—
71C22×Dic11—26no—
72C22×Dic11—26no—
73C22×Dic11—26no—
74C22×Dic11—26no—
75C22×Dic11#4114yes—
76C11×C22⋊C4—412no—
77C22⋊Dic11—424no—
78C22⋊Dic11—412no—
79C22⋊Dic11—412no—
80C4×Dic11—44no—
81C2×#392D1111yescharacteristic
82#1443—112no—
83#1440—113no—
84#1438—116no—
85#1437—113no—
86C23×C11—26no—
87C23×C11—26no—
88C23×C11—26no—
89C23×C11—212no—
90C23×C11—212no—
91C23×C11—46no—
92C23×C11—46no—
93C23×C11—46no—
94C23×C11—46no—
95C23×C11—46no—
96C23×C11—46no—
97C23×C11—43no—
98C23×C11—46no—
99C23×C11—46no—
100C23×C11—46no—
101C23×C11—43no—
102C23×C11—46no—
103C23×C11—46no—
104C23×C11—43no—
105C23×C11—43no—
106C23×C11—46no—
107C23×C11C23×C411yescharacteristic
108C23×C11C2×#4112yes—
109C23×C11H(5,𝔽2)13yes—
110C23×C11H(5,𝔽2)16yes—
111C23×C11H(5,𝔽2)13yes—
112D4×C11—448no—
113C2×C4×C11—26no—
114C2×C4×C11—26no—
115C2×C4×C11—212no—
116C2×C4×C11—41no—
117C2×C4×C11—43no—
118C2×C4×C11—46no—
119C2×C4×C11—43no—
120C2×C4×C11—43no—
121C2×Dic11—212no—
122C2×Dic11—42no—
123C2×Dic11—46no—
124C2×Dic11—46no—
125C2×Dic11—46no—
126C2×Dic11—46no—
127C2×Dic11—46no—
128C2×Dic11—46no—
129C2×Dic11—46no—
130C2×Dic11—46no—
131C23×D4C2×D1113yes—
132C22×C22⋊C4—116no—
133C22×C22⋊C4—113no—
134C22×C22⋊C4—113no—
135C22×C22⋊C4C2×D1113yes—
136C22×C42—111no—
137#392Dic1118yescomplemented
138C2×#95—116no—
139C2×#95—113no—
140C2×#95—116no—
141C2×#95C2×D1111yescharacteristic
142C22×C11—46no—
143C22×C11—412no—
144C22×C11—412no—
145C22×C11—46no—
146C22×C11—46no—
147C22×C11—86no—
148C22×C11—86no—
149C22×C11—86no—
150C22×C11—86no—
151C22×C11C4×#4111yescharacteristic
152C22×C11#51813yes—
153C22×C11#51813yes—
154C22×C11#53816yes—
155C22×C11#54016yes—
156C22×C11#56011yescharacteristic
157C22×C11#56013yes—
158C22×C11#56016yes—
159C22×C11#56013yes—
160C22×C11H(3,𝔽4)13yes—
161C4×C11—46no—
162C4×C11—42no—
163Dic11—44no—
164Dic11—86no—
165C25C22×D1113yes—
166C22×D4—46no—
167C22×D4—46no—
168C22×D4—43no—
169C22×D4—43no—
170C22×D4C2×Dic11112yes—
171C23×C4—112no—
172C23×C4—116no—
173C23×C4C22×D1111yescharacteristic
174C23×C4C22×D1113yes—
175C2×C22⋊C4—43no—
176C2×C22⋊C4—43no—
177C2×C22⋊C4—2212no—
178C2×C22⋊C4—446no—
179C2×C22⋊C4—446no—
180C2×C22⋊C4—446no—
181C2×C22⋊C4—446no—
182C2×C22⋊C4—443no—
183C2×C22⋊C4—443no—
184C2×C22⋊C4C2×Dic11112yes—
185C2×C42—443no—
186#95—443no—
187#95—446no—
188#95—446no—
189#95C2×Dic1114yes—
190C2×C11—86no—
191C2×C11#233313yes—
192C2×C11#237513yes—
193C2×C11#238011yescharacteristic
194C2×C11#282512yes—
195C2×C11#282816yes—
196C24—23no—
197C24—23no—
198C24—26no—
199C24—26no—
200C24—26no—
201C24—26no—
202C24—26no—
203C24—26no—
204C24C22×Dic1116yes—
205C24C23×D1111yescharacteristic
206C2×D4—412no—
207C2×D4—424no—
208C2×D4—412no—
209C2×D4—424no—
210C2×D4—412no—
211C22×C4—23no—
212C22×C4—26no—
213C22×C4—26no—
214C22×C4—23no—
215C22×C4—23no—
216C22×C4—23no—
217C22×C4—114no—
218C22×C4—226no—
219C22×C4—226no—
220C22×C4—226no—
221C22×C4—226no—
222C22×C4—226no—
223C22×C4—226no—
224C22×C4—226no—
225C22×C4—226no—
226C22×C4—226no—
227C22×C4C22×Dic1116yes—
228C22×C4C22×Dic1112yes—
229C22⋊C4—412no—
230C22⋊C4—4424no—
231C22⋊C4—4412no—
232C22⋊C4—4412no—
233C42—444no—
234C11#1465111yescharacteristic, complemented, Sylow
235C23—26no—
236C23—26no—
237C23—212no—
238C23—212no—
239C23—26no—
240C23—43no—
241C23—43no—
242C23—46no—
243C23—43no—
244C23—46no—
245C23—46no—
246C23—46no—
247C23—46no—
248C23—46no—
249C23—43no—
250C23—46no—
251C23—46no—
252C23—46no—
253C23—46no—
254C23—46no—
255C23—46no—
256C23#6703713yes—
257C23#6703713yes—
258C23#6703716yes—
259C23#41×D1112yes—
260C23C23×Dic1111yescharacteristic
261D4—448no—
262C2×C4—26no—
263C2×C4—26no—
264C2×C4—212no—
265C2×C4—41no—
266C2×C4—43no—
267C2×C4—43no—
268C2×C4—46no—
269C2×C4—43no—
270C2×C4—2212no—
271C2×C4—442no—
272C2×C4—446no—
273C2×C4—446no—
274C2×C4—446no—
275C2×C4—446no—
276C2×C4—446no—
277C2×C4—446no—
278C2×C4—446no—
279C2×C4—446no—
280C22—46no—
281C22—412no—
282C22—412no—
283C22—46no—
284C22—46no—
285C22—86no—
286C22—86no—
287C22—86no—
288C22—86no—
289C22#1062312513yes—
290C22#1062312616yes—
291C22#1062312613yes—
292C22#1062314416yes—
293C22#1062314616yes—
294C22#1062325111yescharacteristic
295C22#1062325113yes—
296C22#1062332913yes—
297C22#1062332913yes—
298C22#41×Dic1111yescharacteristic
299C4—46no—
300C4—42no—
301C4—444no—
302C4—886no—
303C2—86no—
304C2#1307138313yes—
305C2#1307175713yes—
306C2#1307179311yescharacteristic
307C2#1307670512yes—
308C2#1307673416yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
Fitting, prime radicalC2×C11×#392C2
socle, cosocleC24×C11C24
hypercenterC2×#392D11
hypocenterC11#14651
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. #13066878C2semidirect
2. #13066865C2semidirect
3. #13066857C2semidirect
4. #13066853C2semidirect
12. C11×#392C4semidirect
137. #392Dic11semidirect
234. C11#14651semidirect

Maximal subgroups

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

subgroupindex
#130668782
#130668652
#130668572
#130668532
C2×C11×#3922
#1465111