Finite Group Databasebeta

← #14684576

Subgroups — #14684576

Order 2816.

1378 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622289C211yesmaximal, characteristic
2#13066882C213yesmaximal, complemented
3#13066881C211yesmaximal, characteristic, complemented
4#13066870C213yesmaximal, complemented
5#13066862C213yesmaximal
6(C2×D11)⋊#95C213yesmaximal
7C11×#1443C211yesmaximal, characteristic, complemented
8C23×C4×D11C2211yescharacteristic
9C22×(C2×D11)⋊C4C2213yes—
10C22×(C2×D11)⋊C4C2213yes—
11C22×C4⋊Dic11C2213yes—
12C22×Dic11⋊C4C2213yes—
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×C11C2313yes—
25C23×C4×C11C2311yescharacteristic
26C23×Dic11C2313yes—
27C23×Dic11C2313yes—
28C23×Dic11C2311yescharacteristic
29C22×C4×D11—43no—
30C22×C4×D11—43no—
31C22×C4×D11Q814yes—
32C2×(C2×D11)⋊C4—26no—
33C2×(C2×D11)⋊C4—43no—
34C2×(C2×D11)⋊C4—43no—
35C2×(C2×D11)⋊C4—43no—
36C2×(C2×D11)⋊C4—43no—
37C2×(C2×D11)⋊C4C2×C4112yes—
38C2×C4⋊Dic11—43no—
39C2×C4⋊Dic11—43no—
40C2×C4⋊Dic11—43no—
41C2×Dic11⋊C4—43no—
42C2×Dic11⋊C4—43no—
43C2×Dic11⋊C4C2×C4112yescomplemented
44C11×#95—43no—
45C11×#95—43no—
46C11×#95C2×C414yescomplemented
47C11⋊#95—43no—
48C11⋊#95—43no—
49C11⋊#95—43no—
50C11⋊#95—43no—
51C11⋊#95—43no—
52#14637—111nomaximal, Sylow
53C24×C11C2411yescharacteristic
54C23×D11—23no—
55C23×D11—23no—
56C23×D11—23no—
57C23×D11—23no—
58C23×D11C22×C412yes—
59C23×D11C2×Q812yes—
60C23×D11#4112yes—
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—23no—
75C22×C4×C11—23no—
76C22×C4×C11C22×C416yes—
77C22×C4×C11C2×Q812yes—
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—23no—
89C22×Dic11—23no—
90C22×Dic11—23no—
91C22×Dic11—23no—
92C22×Dic11—23no—
93C22×Dic11C22×C416yes—
94C22×Dic11C2×Q812yes—
95C2×C4×D11—412no—
96C2×C4×D11—44no—
97C2×C4×D11—412no—
98(C2×D11)⋊C4—412no—
99(C2×D11)⋊C4—412no—
100C4⋊Dic11—412no—
101Dic11⋊C4—412no—
102C2×#396—111no—
103#1445—113no—
104#1444—111no—
105#1443D1111yescharacteristic, complemented
106#1441—113no—
107#1439—113no—
108C22⋊#95—113no—
109C23×C11C23×C411yescharacteristic
110C23×C11C22×Q811yescharacteristic
111C23×C11C2×#4111yescharacteristic
112C23×C11H(5,𝔽2)13yes—
113C23×C11H(5,𝔽2)13yes—
114C23×C11H(5,𝔽2)13yes—
115C23×C112−1+413yes—
116C22×D11—26no—
117C22×D11—26no—
118C22×D11—26no—
119C22×D11—26no—
120C22×D11—26no—
121C22×D11—26no—
122C22×D11—41no—
123C22×D11—43no—
124C22×D11—43no—
125C22×D11—43no—
126C22×D11—43no—
127C22×D11—43no—
128C22×D11C4×Q814yes—
129C2×C4×C11—26no—
130C2×C4×C11—26no—
131C2×C4×C11—26no—
132C2×C4×C11—26no—
133C2×C4×C11—43no—
134C2×C4×C11—41no—
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×C4×C11—43no—
143C2×C4×C11—43no—
144C2×C4×C11—43no—
145C2×C4×C11—43no—
146C2×Dic11—26no—
147C2×Dic11—26no—
148C2×Dic11—26no—
149C2×Dic11—26no—
150C2×Dic11—41no—
151C2×Dic11—43no—
152C2×Dic11—43no—
153C2×Dic11—43no—
154C2×Dic11—43no—
155C2×Dic11—43no—
156C2×Dic11—43no—
157C2×Dic11—43no—
158C2×Dic11—43no—
159C2×Dic11—43no—
160C2×Dic11—43no—
161C2×Dic11—43no—
162C2×Dic11—43no—
163C4×D11—416no—
164C24×C4—111no—
165C22×C4⋊C4—113no—
166C22×C4⋊C4—113no—
167C22×C22⋊C4—113no—
168C22×C22⋊C4—113no—
169#396—118no—
170C2×#95—113no—
171C2×#95—113no—
172C2×#95—113no—
173C2×#95—113no—
174C2×#95—113no—
175C2×#95C2×D1113yes—
176C2×#95C2×D1113yes—
177C2×#95C2×D1111yescharacteristic
178C22×C11C2×C4×Q811yescharacteristic
179C22×C11#51813yes—
180C22×C11#52013yes—
181C22×C11#53813yes—
182C22×C11#53913yes—
183C22×C11#54313yes—
184C22×C11#54413yes—
185C22×C11#56013yes—
186C22×C11#56011yescharacteristic
187C22×C11#56013yes—
188C22×C11#56213yes—
189C22×C11#56213yes—
190C22×C11#56313yes—
191C2×D11—212no—
192C2×D11—42no—
193C2×D11—46no—
194C2×D11—46no—
195C2×D11—42no—
196C2×D11—46no—
197C2×D11—42no—
198C4×C11—42no—
199C4×C11—46no—
200C4×C11—83no—
201Dic11—42no—
202Dic11—46no—
203Dic11—83no—
204C25—111no—
205C23×C4—113no—
206C23×C4—111no—
207C23×C4—114no—
208C23×C4—113no—
209C23×C4—443no—
210C23×C4—443no—
211C23×C4C22×D1113yes—
212C23×C4C22×D1113yes—
213C23×C4C22×D1111yescharacteristic
214C2×C4⋊C4—1112no—
215C2×C4⋊C4—443no—
216C2×C4⋊C4—443no—
217C2×C4⋊C4—443no—
218C2×C4⋊C4—443no—
219C2×C4⋊C4—443no—
220C2×C22⋊C4—1112no—
221C2×C22⋊C4—226no—
222C2×C22⋊C4—443no—
223C2×C22⋊C4—443no—
224C2×C22⋊C4—443no—
225C2×C22⋊C4—443no—
226#95—43no—
227#95—43no—
228#95—443no—
229#95—443no—
230#95—443no—
231#95—443no—
232#95—443no—
233#95C4×D1114yescomplemented
234C2×C11#232913yes—
235C2×C11#237713yes—
236C2×C11#238311yescharacteristic
237C2×C11#282511yescharacteristic
238C2×C11#282713yes—
239C2×C11#284113yes—
240C2×C11#284211yescharacteristic
241D11—44no—
242C24—112no—
243C24—112no—
244C24—112no—
245C24—223no—
246C24—223no—
247C24—223no—
248C24—223no—
249C24C23×D1111yescharacteristic
250C22×C4—23no—
251C22×C4—23no—
252C22×C4—23no—
253C22×C4—23no—
254C22×C4—23no—
255C22×C4—23no—
256C22×C4—23no—
257C22×C4—23no—
258C22×C4—23no—
259C22×C4—23no—
260C22×C4—23no—
261C22×C4—23no—
262C22×C4—23no—
263C22×C4—23no—
264C22×C4—23no—
265C22×C4—116no—
266C22×C4—112no—
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×C4—223no—
277C22×C4—223no—
278C22×C4—223no—
279C22×C4—223no—
280C22×C4—223no—
281C22×C4—223no—
282C22×C4—4412no—
283C22×C4—444no—
284C22×C4—4412no—
285C22×C4C2×C4×D1116yes—
286C22×C4Q8×D1112yes—
287C4⋊C4—4412no—
288C4⋊C4—4412no—
289C22⋊C4—4412no—
290C22⋊C4—4412no—
291C11#1463711yescharacteristic, complemented, Sylow
292C23—114no—
293C23—226no—
294C23—226no—
295C23—226no—
296C23—226no—
297C23—226no—
298C23—226no—
299C23—441no—
300C23—443no—
301C23—443no—
302C23—443no—
303C23—443no—
304C23—443no—
305C23C22×C4×D1111yescharacteristic
306C23#6703713yes—
307C23C2×Q8×D1111yescharacteristic
308C23#41×D1111yescharacteristic
309C23#6704213yes—
310C23#6704213yes—
311C23#6704313yes—
312C2×C4—26no—
313C2×C4—26no—
314C2×C4—26no—
315C2×C4—26no—
316C2×C4—43no—
317C2×C4—41no—
318C2×C4—43no—
319C2×C4—43no—
320C2×C4—43no—
321C2×C4—43no—
322C2×C4—43no—
323C2×C4—43no—
324C2×C4—43no—
325C2×C4—43no—
326C2×C4—43no—
327C2×C4—43no—
328C2×C4—43no—
329C2×C4—226no—
330C2×C4—226no—
331C2×C4—226no—
332C2×C4—226no—
333C2×C4—4416no—
334C2×C4—441no—
335C2×C4—443no—
336C2×C4—443no—
337C2×C4—443no—
338C2×C4—443no—
339C2×C4—443no—
340C2×C4—443no—
341C2×C4—443no—
342C2×C4—443no—
343C2×C4—443no—
344C2×C4—443no—
345C2×C4—443no—
346C2×C4—443no—
347C22—2212no—
348C22—446no—
349C22—442no—
350C22—446no—
351C22—442no—
352C22—442no—
353C22—446no—
354C22#1062305413yes—
355C22#1062307613yes—
356C22C4×Q8×D1111yescharacteristic
357C22#1062315113yes—
358C22#1062316513yes—
359C22#1062319113yes—
360C22#1062319813yes—
361C22#1062321513yes—
362C22#1062322013yes—
363C22#1062323513yes—
364C22#1062324213yes—
365C22#1062324211yescharacteristic
366C22#1062324313yes—
367C4—42no—
368C4—46no—
369C4—83no—
370C4—442no—
371C4—446no—
372C4—883no—
373C2—444no—
374C2#1307134313yes—
375C2#1307176913yes—
376C2#1307180511yescharacteristic
377C2#1307670311yescharacteristic
378C2#1307672913yes—
379C2#1307687513yes—
380C2#1307687911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1443C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1443D11
hypocenterC11#14637
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1443

Complements

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

NH ≅ G/Ntype
2. #13066882C2semidirect
3. #13066881C2semidirect
4. #13066870C2semidirect
7. C11×#1443C2semidirect
21. #10622289C4semidirect
43. C2×Dic11⋊C4C2×C4semidirect
46. C11×#95C2×C4semidirect
105. #1443D11semidirect
233. #95C4×D11semidirect
291. C11#14637semidirect

Maximal subgroups

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

subgroupindex
C2×#106222892
#130668822
#130668812
#130668702
#130668622
(C2×D11)⋊#952
C11×#14432
#1463711