Finite Group Databasebeta

← #14675390

Subgroups — #14675390

Order 2816.

2878 conjugacy classes of subgroups; only the 427 normal subgroups are shown.

normal subgroups only

This group has 2878 conjugacy classes of subgroups — too many to draw. Only its 427 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
1C2×#10622568C213yesmaximal
2#13066854C212yesmaximal, complemented
3#13066853C213yesmaximal, complemented
4#13066852C216yesmaximal, complemented
5C11×#1437C211yesmaximal, characteristic, complemented
6C25×D11C2211yescharacteristic
7C22×C11×C22⋊C4C2213yes—
8C22×C42×C11C2211yescharacteristic, complemented
9C22×C22⋊Dic11C2213yes—
10C22×(C2×D11)⋊C4C2216yes—
11C22×(C2×D11)⋊C4C2216yes—
12C22×C4×Dic11C2213yescomplemented
13C2×C11×#95C2213yescomplemented
14C2×C11⋊#95C2213yescomplemented
15C2×C11⋊#95C2216yescomplemented
16#10622568C4124yescomplemented
17C25×C11C2311yescharacteristic
18C24×D11—46no—
19C24×D11—43no—
20C24×D11—43no—
21C24×D11C2×C4112yes—
22C24×D11C2312yes—
23C23×C4×C11C2313yes—
24C23×C4×C11C2313yes—
25C23×Dic11C2316yes—
26C2×C11×C22⋊C4—43no—
27C2×C11×C22⋊C4—43no—
28C2×C11×C22⋊C4C2×C4112yes—
29C2×C42×C11—43no—
30C2×C22⋊Dic11—46no—
31C2×C22⋊Dic11C2×C4112yes—
32C2×(C2×D11)⋊C4—46no—
33C2×(C2×D11)⋊C4—46no—
34C2×(C2×D11)⋊C4—46no—
35C2×(C2×D11)⋊C4—46no—
36C2×(C2×D11)⋊C4C2×C4124yes—
37C2×(C2×D11)⋊C4C2×C4124yes—
38C2×C4×Dic11—43no—
39C2×C4×Dic11—46no—
40C11×#95—43no—
41C11⋊#95—43no—
42C11⋊#95—46no—
43#13827—111nomaximal, Sylow
44C24×C11—26no—
45C24×C11—23no—
46C24×C11—23no—
47C24×C11C22×C416yes—
48C24×C11C2411yescharacteristic
49C23×D11—26no—
50C23×D11—26no—
51C23×D11—26no—
52C23×D11—26no—
53C23×D11—424no—
54C23×D11—424no—
55C23×D11—412no—
56C23×D11—412no—
57C23×D11—48no—
58C23×D11—44no—
59C23×D11—424no—
60C23×D11—412no—
61C23×D11—44no—
62C23×D11—412no—
63C23×D11C42116yescomplemented
64C23×D11C22×C4112yes—
65C22×C4×C11—26no—
66C22×C4×C11—23no—
67C22×C4×C11—26no—
68C22×C4×C11—23no—
69C22×C4×C11—26no—
70C22×C4×C11—23no—
71C22×C4×C11—26no—
72C22×C4×C11—23no—
73C22×C4×C11C22×C416yes—
74C22×C4×C11C22×C416yes—
75C22×Dic11—26no—
76C22×Dic11—26no—
77C22×Dic11—26no—
78C22×Dic11—26no—
79C22×Dic11—26no—
80C22×Dic11—26no—
81C22×Dic11C22×C4112yes—
82C11×C22⋊C4—412no—
83C42×C11—44no—
84C22⋊Dic11—412no—
85(C2×D11)⋊C4—424no—
86(C2×D11)⋊C4—424no—
87C4×Dic11—412no—
88C2×#379—113no—
89#1437—112no—
90#1437—116no—
91#1437—113no—
92#1437D1111yescharacteristic, complemented
93C23×C11—26no—
94C23×C11—26no—
95C23×C11—212no—
96C23×C11—212no—
97C23×C11—42no—
98C23×C11—41no—
99C23×C11—46no—
100C23×C11—43no—
101C23×C11—41no—
102C23×C11—43no—
103C23×C11C2×C4214yes—
104C23×C11C23×C413yes—
105C23×C11H(5,𝔽2)13yes—
106C23×C11H(5,𝔽2)13yes—
107C23×C11H(5,𝔽2)16yes—
108C22×D11—212no—
109C22×D11—212no—
110C22×D11—212no—
111C22×D11—212no—
112C22×D11—212no—
113C22×D11—212no—
114C22×D11—448no—
115C22×D11—448no—
116C22×D11—448no—
117C22×D11—496no—
118C22×D11—42no—
119C22×D11—42no—
120C22×D11—42no—
121C22×D11—46no—
122C22×D11—46no—
123C22×D11—46no—
124C22×D11—42no—
125C22×D11—46no—
126C22×D11C2×C4218yes—
127C2×C4×C11—212no—
128C2×C4×C11—212no—
129C2×C4×C11—26no—
130C2×C4×C11—26no—
131C2×C4×C11—43no—
132C2×C4×C11—46no—
133C2×C4×C11—46no—
134C2×C4×C11—43no—
135C2×C4×C11—43no—
136C2×C4×C11—43no—
137C2×Dic11—212no—
138C2×Dic11—212no—
139C2×Dic11—212no—
140C2×Dic11—46no—
141C2×Dic11—46no—
142C2×Dic11—46no—
143C2×Dic11—46no—
144C26—111no—
145C22×C22⋊C4—113no—
146C22×C22⋊C4—116no—
147C22×C22⋊C4—116no—
148C22×C22⋊C4C2×D1113yes—
149C22×C42—113no—
150C22×C42C2×D1111yescharacteristic, complemented
151#379—1124no—
152C2×#95—116no—
153C2×#95—113no—
154C2×#95C2×D1113yescomplemented
155C22×C11—212no—
156C22×C11—46no—
157C22×C11—46no—
158C22×C11—412no—
159C22×C11C22×C4211yescharacteristic
160C22×C11#51813yes—
161C22×C11#51813yes—
162C22×C11#51816yes—
163C22×C11#51816yes—
164C22×C11#56012yes—
165C22×C11#56011yescharacteristic
166C22×C11#56016yes—
167C22×C11#56013yes—
168C22×C11H(3,𝔽4)11yescharacteristic
169C22×C11H(3,𝔽4)13yes—
170C2×D11—224no—
171C2×D11—464no—
172C2×D11—412no—
173C2×D11—412no—
174C2×D11—412no—
175C2×D11—412no—
176C4×C11—46no—
177C4×C11—46no—
178Dic11—412no—
179C25—112no—
180C25—1112no—
181C25—443no—
182C25—443no—
183C25—446no—
184C25C22×D1111yescharacteristic
185C23×C4—116no—
186C23×C4C22×D1113yes—
187C23×C4C22×D1113yes—
188C2×C22⋊C4—43no—
189C2×C22⋊C4—43no—
190C2×C22⋊C4—1112no—
191C2×C22⋊C4—1124no—
192C2×C22⋊C4—1124no—
193C2×C22⋊C4—446no—
194C2×C22⋊C4—446no—
195C2×C22⋊C4—446no—
196C2×C22⋊C4—446no—
197C2×C22⋊C4—446no—
198C2×C22⋊C4C4×D11112yes—
199C2×C42—43no—
200C2×C42—443no—
201C2×C42—446no—
202#95—43no—
203#95—443no—
204#95—446no—
205C2×C11—44no—
206C2×C11#227313yes—
207C2×C11#237513yes—
208C2×C11#237513yes—
209C2×C11#237516yes—
210D11—48no—
211C24—23no—
212C24—23no—
213C24—26no—
214C24—1112no—
215C24—1116no—
216C24—226no—
217C24—226no—
218C24—226no—
219C24—226no—
220C24—4412no—
221C24—4412no—
222C24—4424no—
223C24—4424no—
224C24—448no—
225C24—444no—
226C24—444no—
227C24—4424no—
228C24—4412no—
229C24—4412no—
230C24C2×C4×D1116yes—
231C24C23×D1111yescharacteristic
232C22×C4—23no—
233C22×C4—26no—
234C22×C4—23no—
235C22×C4—23no—
236C22×C4—26no—
237C22×C4—23no—
238C22×C4—26no—
239C22×C4—26no—
240C22×C4—1112no—
241C22×C4—226no—
242C22×C4—226no—
243C22×C4—226no—
244C22×C4—226no—
245C22×C4—226no—
246C22×C4—226no—
247C22×C4C2×C4×D1116yes—
248C22×C4C2×C4×D1116yes—
249C22⋊C4—412no—
250C22⋊C4—4424no—
251C22⋊C4—4424no—
252C22⋊C4—4412no—
253C42—44no—
254C42—4412no—
255C11#1382711yescharacteristic, complemented, Sylow
256C23—26no—
257C23—26no—
258C23—212no—
259C23—212no—
260C23—42no—
261C23—41no—
262C23—41no—
263C23—46no—
264C23—43no—
265C23—43no—
266C23—118no—
267C23—2212no—
268C23—2212no—
269C23—2212no—
270C23—2212no—
271C23—2212no—
272C23—2212no—
273C23—4448no—
274C23—4448no—
275C23—4448no—
276C23—4496no—
277C23—442no—
278C23—442no—
279C23—442no—
280C23—442no—
281C23—446no—
282C23—446no—
283C23—446no—
284C23—446no—
285C23C42×D1114yes—
286C23C22×C4×D1113yes—
287C23#6703713yes—
288C23#6703713yes—
289C23#6704216yes—
290C2×C4—26no—
291C2×C4—26no—
292C2×C4—212no—
293C2×C4—212no—
294C2×C4—43no—
295C2×C4—43no—
296C2×C4—46no—
297C2×C4—46no—
298C2×C4—43no—
299C2×C4—43no—
300C2×C4—2212no—
301C2×C4—2212no—
302C2×C4—2212no—
303C2×C4—446no—
304C2×C4—446no—
305C2×C4—446no—
306C2×C4—446no—
307C22—212no—
308C22—46no—
309C22—46no—
310C22—412no—
311C22—2224no—
312C22—4464no—
313C22—4412no—
314C22—4412no—
315C22—4412no—
316C22—4412no—
317C22C2×C42×D1111yescharacteristic
318C22#1062301713yes—
319C22#1062305213yes—
320C22#1062307616yes—
321C22#1062307616yes—
322C22#1062312511yescharacteristic
323C22#1062315116yes—
324C22#1062319713yes—
325C22#1062321413yes—
326C22#1062324212yes—
327C22#1062325111yescharacteristic
328C4—46no—
329C4—46no—
330C4—4412no—
331C2—44no—
332C2—448no—
333C2#1307096813yes—
334C2#1307175313yes—
335C2#1307175413yes—
336C2#1307175616yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC11×#1437C2
socle, cosocleC24×C11C24
prime radicalC25×D11C22
hypercenter#1437D11
hypocenterC11#13827
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. #13066854C2semidirect
3. #13066853C2semidirect
4. #13066852C2semidirect
5. C11×#1437C2semidirect
8. C22×C42×C11C22semidirect
12. C22×C4×Dic11C22semidirect
13. C2×C11×#95C22semidirect
14. C2×C11⋊#95C22semidirect
15. C2×C11⋊#95C22semidirect
16. #10622568C4semidirect
63. C23×D11C42semidirect
92. #1437D11semidirect
150. C22×C42C2×D11semidirect
154. C2×#95C2×D11semidirect
255. C11#13827semidirect

Maximal subgroups

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

subgroupindex
C2×#106225682
#130668542
#130668532
#130668522
C11×#14372
#1382711