Finite Group Databasebeta

← #14680788

Subgroups — #14680788

Order 2816.

1590 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622598C213yesmaximal, complemented
2C2×#10622564C213yesmaximal
3#13066884C213yesmaximal, complemented
4#13066881C211yesmaximal, characteristic, complemented
5#13066861C213yesmaximal
6#95×Dic11C211yesmaximal, characteristic, complemented
7C2×C11×#399C211yesmaximal, characteristic
8C22×C11×C4⋊C4C2213yes—
9C22×C11×C22⋊C4C2213yes—
10C22×C22⋊Dic11C2211yescharacteristic
11C22×C22⋊Dic11C2213yes—
12C22×C4⋊Dic11C2213yes—
13C22×C4⋊Dic11C2213yes—
14C22×C4×Dic11C2213yes—
15C11×#399C418yescomplemented
16C2×C11×#95C2211yescharacteristic
17C2×C11⋊#95C2213yes—
18C2×C11⋊#95C2216yes—
19C2×C11⋊#95C2213yes—
20C2×C11⋊#95C2213yes—
21#10622598—212no—
22#10622564—212no—
23C25×C11C2311yescharacteristic
24C23×C4×C11C2313yes—
25C23×C4×C11C2313yes—
26C23×Dic11C2313yes—
27C23×Dic11C2311yescharacteristic
28C23×Dic11C2313yes—
29C23×Dic11C2311yescharacteristic
30C2×C11×C4⋊C4—26no—
31C2×C11×C4⋊C4—26no—
32C2×C11×C4⋊C4C2×C4112yes—
33C2×C11×C22⋊C4—26no—
34C2×C11×C22⋊C4—26no—
35C2×C11×C22⋊C4C2×C4112yes—
36C2×C22⋊Dic11—26no—
37C2×C22⋊Dic11—26no—
38C2×C22⋊Dic11—46no—
39C2×C4⋊Dic11—26no—
40C2×C4⋊Dic11—26no—
41C2×C4⋊Dic11—212no—
42C2×C4⋊Dic11—46no—
43C2×C4×Dic11—46no—
44C2×C4×Dic11D4112yes—
45C11×#95C2×C414yes—
46C11⋊#95—26no—
47C11⋊#95—26no—
48C11⋊#95—26no—
49C11⋊#95—212no—
50#14322—111nomaximal, Sylow
51C24×C11—23no—
52C24×C11—23no—
53C24×C11—23no—
54C24×C11—21no—
55C24×C11—21no—
56C24×C11—23no—
57C24×C11C22×C412yes—
58C24×C11C2411yescharacteristic
59C22×C4×C11—26no—
60C22×C4×C11—26no—
61C22×C4×C11—23no—
62C22×C4×C11—26no—
63C22×C4×C11—23no—
64C22×C4×C11—26no—
65C22×C4×C11C22×C416yes—
66C22×C4×C11C22×C416yes—
67C22×C4×C11C2×D416yes—
68C22×C4×C11#4116yes—
69C22×Dic11—23no—
70C22×Dic11—26no—
71C22×Dic11—23no—
72C22×Dic11—26no—
73C22×Dic11—23no—
74C22×Dic11—26no—
75C22×Dic11—23no—
76C22×Dic11—26no—
77C22×Dic11—21no—
78C22×Dic11—23no—
79C22×Dic11—23no—
80C22×Dic11—21no—
81C22×Dic11—23no—
82C22×Dic11—23no—
83C22×Dic11C2×D416yes—
84C22×Dic11C2×D416yes—
85C11×C4⋊C4—224no—
86C11×C22⋊C4—224no—
87C22⋊Dic11—412no—
88C22⋊Dic11—44no—
89C4⋊Dic11—412no—
90C4⋊Dic11—412no—
91C4×Dic11—412no—
92C2×#399D1111yescharacteristic
93C2×#389—113no—
94C2×#388—113no—
95#1445—113no—
96#1444—111no—
97#1439—113no—
98C4×#95—111no—
99C23×C11—26no—
100C23×C11—22no—
101C23×C11—26no—
102C23×C11—41no—
103C23×C11—43no—
104C23×C11—43no—
105C23×C11—43no—
106C23×C11—43no—
107C23×C11—43no—
108C23×C11—46no—
109C23×C11—43no—
110C23×C11—43no—
111C23×C11C23×C411yescharacteristic
112C23×C11C22×D413yes—
113C23×C11C2×#4113yes—
114C23×C11H(5,𝔽2)13yes—
115C23×C112−1+411yescharacteristic
116C23×C112−1+411yescharacteristic
117C23×C112−1+413yes—
118C2×C4×C11—212no—
119C2×C4×C11—26no—
120C2×C4×C11—26no—
121C2×C4×C11—212no—
122C2×C4×C11—26no—
123C2×C4×C11—212no—
124C2×C4×C11—43no—
125C2×C4×C11—43no—
126C2×C4×C11—46no—
127C2×C4×C11C4×D4112yes—
128C2×Dic11—26no—
129C2×Dic11—26no—
130C2×Dic11—26no—
131C2×Dic11—26no—
132C2×Dic11—26no—
133C2×Dic11—46no—
134C2×Dic11—46no—
135C2×Dic11—43no—
136C2×Dic11—41no—
137C2×Dic11—46no—
138C2×Dic11—43no—
139C2×Dic11—43no—
140C2×Dic11—43no—
141C2×Dic11—46no—
142C2×Dic11—43no—
143C2×Dic11#12714yes—
144C22×C4⋊C4—113no—
145C22×C4⋊C4—113no—
146C22×C4⋊C4C2×D1113yes—
147C22×C22⋊C4—111no—
148C22×C22⋊C4—113no—
149C22×C22⋊C4C2×D1113yes—
150C22×C42—113no—
151#399Dic1118yescomplemented
152#389—2212no—
153#388—2212no—
154C2×#95—113no—
155C2×#95—116no—
156C2×#95—113no—
157C2×#95—113no—
158C2×#95C2×D1111yescharacteristic
159C22×C11—42no—
160C22×C11—46no—
161C22×C11—46no—
162C22×C11—81no—
163C22×C11—81no—
164C22×C11—83no—
165C22×C11—83no—
166C22×C11C2×C4×D413yes—
167C22×C11#51911yescharacteristic
168C22×C11#52013yes—
169C22×C11C2×#12711yescharacteristic
170C22×C11#53213yes—
171C22×C11#53413yes—
172C22×C11#53613yes—
173C22×C11#53613yes—
174C22×C11#53713yes—
175C22×C11#53916yes—
176C22×C11#54113yes—
177C22×C11#54213yes—
178C4×C11—212no—
179C4×C11—46no—
180Dic11—24no—
181Dic11—46no—
182Dic11—83no—
183Dic11—81no—
184C25C22×D1111yescharacteristic
185C23×C4—111no—
186C23×C4—113no—
187C23×C4—113no—
188C23×C4—111no—
189C23×C4C22×D1113yes—
190C23×C4C22×D1113yes—
191C2×C4⋊C4—26no—
192C2×C4⋊C4—26no—
193C2×C4⋊C4—226no—
194C2×C4⋊C4—2212no—
195C2×C4⋊C4—226no—
196C2×C4⋊C4—446no—
197C2×C4⋊C4C2×Dic11112yes—
198C2×C22⋊C4—26no—
199C2×C22⋊C4—26no—
200C2×C22⋊C4—226no—
201C2×C22⋊C4—226no—
202C2×C22⋊C4—446no—
203C2×C22⋊C4C2×Dic11112yes—
204C2×C42—1112no—
205C2×C42—446no—
206#95—226no—
207#95—2212no—
208#95—226no—
209#95—226no—
210#95C2×Dic1114yes—
211C2×C11—82no—
212C2×C11C4×#12711yescharacteristic
213C2×C11#232213yes—
214C2×C11#232313yes—
215C2×C11#265611yescharacteristic
216C2×C11#265811yescharacteristic
217C2×C11#266313yes—
218C2×C11#266413yes—
219C24—23no—
220C24—23no—
221C24—21no—
222C24—21no—
223C24—23no—
224C24—23no—
225C24C22×Dic1112yes—
226C24C23×D1111yescharacteristic
227C22×C4—26no—
228C22×C4—26no—
229C22×C4—23no—
230C22×C4—26no—
231C22×C4—23no—
232C22×C4—26no—
233C22×C4—116no—
234C22×C4—116no—
235C22×C4—221no—
236C22×C4—223no—
237C22×C4—226no—
238C22×C4—223no—
239C22×C4—226no—
240C22×C4—223no—
241C22×C4—223no—
242C22×C4—223no—
243C22×C4—226no—
244C22×C4—221no—
245C22×C4—223no—
246C22×C4—226no—
247C22×C4—223no—
248C22×C4—223no—
249C22×C4D4×D1116yes—
250C22×C4#434116yes—
251C22×C4C22×Dic1116yes—
252C22×C4C22×Dic1116yes—
253C4⋊C4—224no—
254C4⋊C4—4412no—
255C4⋊C4—4412no—
256C22⋊C4—224no—
257C22⋊C4—444no—
258C22⋊C4—4412no—
259C42—4412no—
260C11#1432211yescharacteristic, complemented, Sylow
261C23—26no—
262C23—22no—
263C23—26no—
264C23—41no—
265C23—43no—
266C23—43no—
267C23—43no—
268C23—43no—
269C23—43no—
270C23—43no—
271C23—43no—
272C23—46no—
273C23C2×D4×D1113yes—
274C23C2×#434113yes—
275C23#6704011yescharacteristic
276C23#6704011yescharacteristic
277C23#6704213yes—
278C23#6704313yes—
279C23C23×Dic1111yescharacteristic
280C2×C4—212no—
281C2×C4—26no—
282C2×C4—26no—
283C2×C4—212no—
284C2×C4—26no—
285C2×C4—212no—
286C2×C4—43no—
287C2×C4—43no—
288C2×C4—46no—
289C2×C4—114no—
290C2×C4—226no—
291C2×C4—226no—
292C2×C4—226no—
293C2×C4—226no—
294C2×C4—226no—
295C2×C4—446no—
296C2×C4—446no—
297C2×C4—441no—
298C2×C4—443no—
299C2×C4—443no—
300C2×C4—443no—
301C2×C4—446no—
302C2×C4—443no—
303C2×C4—443no—
304C2×C4—446no—
305C2×C4D4×Dic11112yes—
306C22—42no—
307C22—46no—
308C22—46no—
309C22—81no—
310C22—81no—
311C22—83no—
312C22—83no—
313C22#1062315613yes—
314C22#1062315913yes—
315C22#1062316013yes—
316C22#1062317413yes—
317C22#1062317913yes—
318C22#1062318413yes—
319C22#1062319616yes—
320C22D11×#12711yescharacteristic
321C22#1062324713yes—
322C22C2×D4×Dic1113yes—
323C22#1062334311yescharacteristic
324C22#1062335813yes—
325C4—212no—
326C4—46no—
327C4—224no—
328C4—446no—
329C4—883no—
330C4—881no—
331C2—82no—
332C2#127×Dic1111yescharacteristic
333C2#1307128813yes—
334C2#1307130013yes—
335C2#1307471911yescharacteristic
336C2#1307472511yescharacteristic
337C2#1307476913yes—
338C2#1307478013yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#399C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#399D11
hypocenterC11#14322
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
1. C2×#10622598C2semidirect
3. #13066884C2semidirect
4. #13066881C2semidirect
6. #95×Dic11C2semidirect
15. C11×#399C4semidirect
151. #399Dic11semidirect
260. C11#14322semidirect

Maximal subgroups

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

subgroupindex
C2×#106225982
C2×#106225642
#130668842
#130668812
#130668612
#95×Dic112
C2×C11×#3992
#1432211