Finite Group Databasebeta

← #14680892

Subgroups — #14680892

Order 2816.

1290 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622289C211yesmaximal, characteristic
2#13066882C213yesmaximal, complemented
3#13066864C213yesmaximal
4#13066852C213yesmaximal
5#13066851C213yesmaximal, complemented
6#95×Dic11C211yesmaximal, characteristic, complemented
7C11×#1443C211yesmaximal, characteristic, complemented
8C22×(C2×D11)⋊C4C2211yescharacteristic
9C22×(C2×D11)⋊C4C2213yes—
10C22×(C2×D11)⋊C4C2213yes—
11C22×Dic11⋊C4C2213yes—
12C22×C4×Dic11C2213yes—
13C2×C11×#95C2213yes—
14C2×C11×#95C2213yes—
15C2×C11×#95C2211yescharacteristic
16C2×C11⋊#95C2213yes—
17C2×C11⋊#95C2213yes—
18C2×C11⋊#95C2213yes—
19C2×C11⋊#95C2213yes—
20C2×C11⋊#95C2213yes—
21#10622289C418yescomplemented
22C24×D11C2311yescharacteristic
23C23×C4×C11C2313yes—
24C23×C4×C11C2311yescharacteristic
25C23×C4×C11C2313yes—
26C23×Dic11C2313yes—
27C23×Dic11C2313yes—
28C23×Dic11C2311yescharacteristic
29C2×(C2×D11)⋊C4—26no—
30C2×(C2×D11)⋊C4—26no—
31C2×(C2×D11)⋊C4—43no—
32C2×(C2×D11)⋊C4—43no—
33C2×(C2×D11)⋊C4—43no—
34C2×(C2×D11)⋊C4—43no—
35C2×(C2×D11)⋊C4C2×C4112yes—
36C2×Dic11⋊C4—43no—
37C2×Dic11⋊C4—43no—
38C2×Dic11⋊C4C2×C4112yes—
39C2×C4×Dic11—26no—
40C2×C4×Dic11—43no—
41C2×C4×Dic11—43no—
42C11×#95—43no—
43C11×#95—43no—
44C11×#95C2×C414yes—
45C11⋊#95—26no—
46C11⋊#95—26no—
47C11⋊#95—26no—
48C11⋊#95—43no—
49C11⋊#95—43no—
50#14331—111nomaximal, Sylow
51C24×C11C2411yescharacteristic
52C23×D11—23no—
53C23×D11—23no—
54C23×D11—23no—
55C23×D11—23no—
56C23×D11—21no—
57C23×D11—21no—
58C23×D11C22×C412yes—
59C22×C4×C11—23no—
60C22×C4×C11—23no—
61C22×C4×C11—23no—
62C22×C4×C11—23no—
63C22×C4×C11—23no—
64C22×C4×C11—23no—
65C22×C4×C11—23no—
66C22×C4×C11—23no—
67C22×C4×C11—23no—
68C22×C4×C11—23no—
69C22×C4×C11—23no—
70C22×C4×C11—23no—
71C22×C4×C11—23no—
72C22×C4×C11—23no—
73C22×C4×C11—23no—
74C22×C4×C11—21no—
75C22×C4×C11C22×C416yes—
76C22×Dic11—23no—
77C22×Dic11—23no—
78C22×Dic11—23no—
79C22×Dic11—23no—
80C22×Dic11—23no—
81C22×Dic11—23no—
82C22×Dic11—23no—
83C22×Dic11—23no—
84C22×Dic11—23no—
85C22×Dic11—23no—
86C22×Dic11—23no—
87C22×Dic11—23no—
88C22×Dic11—21no—
89C22×Dic11—23no—
90C22×Dic11C22×C416yes—
91C22×Dic11#4116yes—
92C22×Dic11#4116yes—
93(C2×D11)⋊C4—412no—
94(C2×D11)⋊C4—412no—
95(C2×D11)⋊C4—44no—
96Dic11⋊C4—412no—
97C4×Dic11—412no—
98C2×#396—111no—
99#1445—113no—
100#1443D1111yescharacteristic, complemented
101#1440—113no—
102#1437—113no—
103#1436—113no—
104C4×#95—111no—
105C23×C11C23×C411yescharacteristic
106C23×C11C2×#4113yes—
107C23×C11C2×#4113yes—
108C23×C11H(5,𝔽2)13yes—
109C23×C11H(5,𝔽2)13yes—
110C23×C112−1+411yescharacteristic
111C23×C112−1+411yescharacteristic
112C22×D11—26no—
113C22×D11—26no—
114C22×D11—22no—
115C22×D11—41no—
116C22×D11—43no—
117C22×D11—43no—
118C22×D11—43no—
119C22×D11—43no—
120C22×D11—43no—
121C22×D11—43no—
122C22×D11—43no—
123C22×D11—43no—
124C22×D11—43no—
125C2×C4×C11—26no—
126C2×C4×C11—26no—
127C2×C4×C11—26no—
128C2×C4×C11—43no—
129C2×C4×C11—43no—
130C2×C4×C11—43no—
131C2×C4×C11—43no—
132C2×C4×C11—41no—
133C2×C4×C11—43no—
134C2×C4×C11—43no—
135C2×C4×C11—43no—
136C2×C4×C11—43no—
137C2×C4×C11—43no—
138C2×C4×C11—43no—
139C2×C4×C11—43no—
140C2×C4×C11—43no—
141C2×C4×C11—43no—
142C2×Dic11—26no—
143C2×Dic11—26no—
144C2×Dic11—26no—
145C2×Dic11—26no—
146C2×Dic11—26no—
147C2×Dic11—26no—
148C2×Dic11—26no—
149C2×Dic11—26no—
150C2×Dic11—43no—
151C2×Dic11—43no—
152C2×Dic11—43no—
153C2×Dic11—43no—
154C2×Dic11—43no—
155C2×Dic11—43no—
156C2×Dic11—43no—
157C2×Dic11—43no—
158C2×Dic11#12614yes—
159C22×C4⋊C4—113no—
160C22×C22⋊C4—113no—
161C22×C22⋊C4—111no—
162C22×C22⋊C4—113no—
163C22×C42—113no—
164#396—118no—
165C2×#95—113no—
166C2×#95—113no—
167C2×#95—113no—
168C2×#95—113no—
169C2×#95—113no—
170C2×#95C2×D1113yes—
171C2×#95C2×D1113yes—
172C2×#95C2×D1111yescharacteristic
173C22×C11C4×#4113yes—
174C22×C11#51813yes—
175C22×C11#51911yescharacteristic
176C22×C11C2×#12611yescharacteristic
177C22×C11#52913yes—
178C22×C11#53813yes—
179C22×C11#53813yes—
180C22×C11#53913yes—
181C22×C11#53913yes—
182C22×C11#54013yes—
183C22×C11#54013yes—
184C22×C11#54213yes—
185C22×C11#54213yes—
186C2×D11—42no—
187C2×D11—46no—
188C2×D11—46no—
189C2×D11—81no—
190C2×D11—81no—
191C2×D11—83no—
192C2×D11—83no—
193C4×C11—46no—
194C4×C11—81no—
195C4×C11—83no—
196Dic11—24no—
197Dic11—46no—
198Dic11—46no—
199C25—111no—
200C23×C4—111no—
201C23×C4—113no—
202C23×C4—113no—
203C23×C4C22×D1113yes—
204C23×C4C22×D1111yescharacteristic
205C23×C4C22×D1113yes—
206C2×C4⋊C4—1112no—
207C2×C4⋊C4—443no—
208C2×C4⋊C4—443no—
209C2×C22⋊C4—1112no—
210C2×C22⋊C4—226no—
211C2×C22⋊C4—226no—
212C2×C22⋊C4—443no—
213C2×C22⋊C4—443no—
214C2×C22⋊C4—443no—
215C2×C22⋊C4—443no—
216C2×C42—226no—
217C2×C42—443no—
218C2×C42—443no—
219#95—43no—
220#95—43no—
221#95—226no—
222#95—226no—
223#95—226no—
224#95—443no—
225#95—443no—
226#95C4×D1114yes—
227C2×C11C4×#12611yescharacteristic
228C2×C11#233213yes—
229C2×C11#233313yes—
230C2×C11#264311yescharacteristic
231C2×C11#264411yescharacteristic
232C2×C11#264913yes—
233C2×C11#265113yes—
234D11—82no—
235C24—112no—
236C24—223no—
237C24—221no—
238C24—223no—
239C24—223no—
240C24—223no—
241C24—221no—
242C24C23×D1111yescharacteristic
243C22×C4—23no—
244C22×C4—23no—
245C22×C4—23no—
246C22×C4—23no—
247C22×C4—23no—
248C22×C4—23no—
249C22×C4—23no—
250C22×C4—23no—
251C22×C4—23no—
252C22×C4—21no—
253C22×C4—23no—
254C22×C4—23no—
255C22×C4—23no—
256C22×C4—23no—
257C22×C4—23no—
258C22×C4—23no—
259C22×C4—116no—
260C22×C4—116no—
261C22×C4—116no—
262C22×C4—223no—
263C22×C4—221no—
264C22×C4—223no—
265C22×C4—223no—
266C22×C4—223no—
267C22×C4—223no—
268C22×C4—223no—
269C22×C4—223no—
270C22×C4—223no—
271C22×C4—223no—
272C22×C4—223no—
273C22×C4—223no—
274C22×C4—223no—
275C22×C4—223no—
276C22×C4C2×C4×D1116yes—
277C4⋊C4—4412no—
278C22⋊C4—4412no—
279C22⋊C4—444no—
280C22⋊C4—4412no—
281C42—4412no—
282C11#1433111yescharacteristic, complemented, Sylow
283C23—226no—
284C23—226no—
285C23—222no—
286C23—441no—
287C23—443no—
288C23—443no—
289C23—443no—
290C23—443no—
291C23—443no—
292C23—443no—
293C23—443no—
294C23—443no—
295C23—443no—
296C23C22×C4×D1111yescharacteristic
297C23#6703713yes—
298C23#6704011yescharacteristic
299C23#41×D1113yes—
300C23#41×D1113yes—
301C23#6704213yes—
302C23#6704311yescharacteristic
303C2×C4—26no—
304C2×C4—26no—
305C2×C4—26no—
306C2×C4—43no—
307C2×C4—43no—
308C2×C4—43no—
309C2×C4—43no—
310C2×C4—41no—
311C2×C4—43no—
312C2×C4—43no—
313C2×C4—43no—
314C2×C4—43no—
315C2×C4—43no—
316C2×C4—43no—
317C2×C4—43no—
318C2×C4—43no—
319C2×C4—43no—
320C2×C4—114no—
321C2×C4—226no—
322C2×C4—226no—
323C2×C4—226no—
324C2×C4—226no—
325C2×C4—226no—
326C2×C4—226no—
327C2×C4—226no—
328C2×C4—226no—
329C2×C4—443no—
330C2×C4—443no—
331C2×C4—443no—
332C2×C4—443no—
333C2×C4—443no—
334C2×C4—443no—
335C2×C4—443no—
336C2×C4—443no—
337C22—446no—
338C22—446no—
339C22—442no—
340C22—881no—
341C22—881no—
342C22—883no—
343C22—883no—
344C22#1062305313yes—
345C22#1062307613yes—
346C22#1062310311yescharacteristic
347C22#1062314613yes—
348C22#1062317113yes—
349C22#1062319313yes—
350C22#1062319413yes—
351C22#1062320913yes—
352C22#1062322313yes—
353C22D11×#12611yescharacteristic
354C22#1062323513yes—
355C22#1062323713yes—
356C22#1062323813yes—
357C4—46no—
358C4—81no—
359C4—83no—
360C4—224no—
361C4—446no—
362C4—446no—
363C2—882no—
364C2#1307116411yescharacteristic
365C2#1307137013yes—
366C2#1307137913yes—
367C2#1307457411yescharacteristic
368C2#1307457811yescharacteristic
369C2#1307462613yes—
370C2#1307465413yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1443C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1443D11
hypocenterC11#14331
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1443

Complements

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

NH ≅ G/Ntype
2. #13066882C2semidirect
5. #13066851C2semidirect
6. #95×Dic11C2semidirect
7. C11×#1443C2semidirect
21. #10622289C4semidirect
100. #1443D11semidirect
282. C11#14331semidirect

Maximal subgroups

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

subgroupindex
C2×#106222892
#130668822
#130668642
#130668522
#130668512
#95×Dic112
C11×#14432
#1433111