Finite Group Databasebeta

← #14680949

Subgroups — #14680949

Order 2816.

2142 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4⋊Dic11C211yesmaximal, characteristic
2C2×#10622824C211yesmaximal, characteristic
3C2×#10622555C212yesmaximal
4#13066868C218yesmaximal, complemented
5#13066838C212yesmaximal
6C2×C11×#381C211yesmaximal, characteristic
7C24×C4×C11C2211yescharacteristic
8C24×Dic11C2211yescharacteristic
9C24×Dic11C2211yescharacteristic
10C22×C11×C22⋊C4C2212yes—
11C22×C22⋊Dic11C2212yes—
12C22×C4⋊Dic11—28no—
13C22×C4⋊Dic11C418yescomplemented
14C22×C4⋊Dic11C2214yes—
15C22×Dic11⋊C4C2214yes—
16C11×#381—24no—
17C2×C11×#95C2214yes—
18#10622824—24no—
19C2×C11⋊#95C2214yes—
20C2×C11⋊#95C2214yes—
21C2×C11⋊#95C2218yes—
22#10622555—28no—
23C25×C11C2311yescharacteristic
24C23×C4×C11—24no—
25C23×C4×C11—24no—
26C23×C4×C11C2×C414yes—
27C23×C4×C11D414yes—
28C23×C4×C11Q814yes—
29C23×C4×C11C2314yes—
30C23×C4×C11C2312yes—
31C23×Dic11—24no—
32C23×Dic11—44no—
33C23×Dic11—44no—
34C23×Dic11C2×C414yes—
35C23×Dic11C2×C414yes—
36C23×Dic11D418yes—
37C23×Dic11C2314yes—
38C23×Dic11C2312yes—
39C23×Dic11C2312yes—
40C2×C11×C22⋊C4—24no—
41C2×C11×C22⋊C4—24no—
42C2×C11×C22⋊C4—24no—
43C2×C22⋊Dic11—24no—
44C2×C22⋊Dic11—24no—
45C2×C22⋊Dic11—24no—
46C2×C4⋊Dic11—232no—
47C2×C4⋊Dic11—28no—
48C2×C4⋊Dic11—28no—
49C2×C4⋊Dic11C2×C4116yes—
50C2×Dic11⋊C4—28no—
51C2×Dic11⋊C4—48no—
52C11×#95—28no—
53C11⋊#95—28no—
54C11⋊#95—28no—
55C11⋊#95—48no—
56#14339—111nomaximal, Sylow
57C24×C11—24no—
58C24×C11—24no—
59C24×C11C22×C412yes—
60C24×C11C2×D414yes—
61C24×C11C2×D412yes—
62C24×C11C2×Q812yes—
63C24×C11#4114yes—
64C24×C11C2411yescharacteristic
65C22×C4×C11—28no—
66C22×C4×C11—28no—
67C22×C4×C11—216no—
68C22×C4×C11—216no—
69C22×C4×C11—24no—
70C22×C4×C11—24no—
71C22×C4×C11—24no—
72C22×C4×C11—24no—
73C22×C4×C11—24no—
74C22×C4×C11—28no—
75C22×C4×C11—28no—
76C22×C4×C11C4⋊C4116yescomplemented
77C22×C4×C11C22×C414yes—
78C22×C4×C11C2×D414yes—
79C22×C4×C11C2×Q814yes—
80C22×Dic11—28no—
81C22×Dic11—24no—
82C22×Dic11—24no—
83C22×Dic11—24no—
84C22×Dic11—24no—
85C22×Dic11—28no—
86C22×Dic11—28no—
87C22×Dic11—28no—
88C22×Dic11—28no—
89C22×Dic11—48no—
90C22×Dic11—48no—
91C22×Dic11—416no—
92C22×Dic11—416no—
93C22×Dic11C22⋊C4116yes—
94C22×Dic11C22×C414yes—
95C22×Dic11C22×C414yes—
96C22×Dic11C2×D414yes—
97C22×Dic11C2×D414yes—
98C11×C22⋊C4—48no—
99C22⋊Dic11—48no—
100C4⋊Dic11—232no—
101Dic11⋊C4—416no—
102C23×C4⋊C4—111no—
103C2×#381—111no—
104C2×#381D1111yescharacteristic
105C2×#380—112no—
106#1441—118no—
107C22⋊#95—112no—
108C23×C11—24no—
109C23×C11—24no—
110C23×C11—28no—
111C23×C11—28no—
112C23×C11—28no—
113C23×C11—216no—
114C23×C11—28no—
115C23×C11C2×C22⋊C414yes—
116C23×C11C2×C4⋊C414yes—
117C23×C11#11714yes—
118C23×C11#12118yes—
119C23×C11C22⋊Q818yes—
120C23×C11C23×C411yescharacteristic
121C23×C11C22×D412yes—
122C23×C11C22×D411yescharacteristic
123C23×C11C22×Q811yescharacteristic
124C23×C11C2×#4112yes—
125C23×C11H(5,𝔽2)14yes—
126C23×C112−1+414yes—
127C2×C4×C11—24no—
128C2×C4×C11—24no—
129C2×C4×C11—28no—
130C2×C4×C11—28no—
131C2×C4×C11—232no—
132C2×C4×C11—44no—
133C2×C4×C11—44no—
134C2×C4×C11—44no—
135C2×C4×C11—48no—
136C2×C4×C11—48no—
137C2×C4×C11C2×C4⋊C418yes—
138C2×Dic11—28no—
139C2×Dic11—28no—
140C2×Dic11—28no—
141C2×Dic11—24no—
142C2×Dic11—28no—
143C2×Dic11—416no—
144C2×Dic11—416no—
145C2×Dic11—48no—
146C2×Dic11—44no—
147C2×Dic11—44no—
148C2×Dic11—44no—
149C2×Dic11—48no—
150C2×Dic11—48no—
151C2×Dic11C2×C22⋊C418yes—
152C24×C4—111no—
153C24×C4—111no—
154C24×C4C2×D1111yescharacteristic
155C22×C4⋊C4—114no—
156C22×C4⋊C4—118no—
157C22×C4⋊C4—114no—
158C22×C4⋊C4—228no—
159C22×C22⋊C4—112no—
160C22×C22⋊C4C2×D1112yes—
161#381—24no—
162#381—224no—
163#380—228no—
164C2×#95—114no—
165C2×#95—114no—
166C2×#95—118no—
167C2×#95C2×D1114yes—
168C22×C11—24no—
169C22×C11—24no—
170C22×C11—28no—
171C22×C11—28no—
172C22×C11—216no—
173C22×C11—216no—
174C22×C11#38018yes—
175C22×C11C22×C22⋊C411yescharacteristic
176C22×C11C22×C4⋊C411yescharacteristic
177C22×C11C2×#11711yescharacteristic
178C22×C11#51812yes—
179C22×C11#51912yes—
180C22×C11C2×#12112yes—
181C22×C11C2×C22⋊Q812yes—
182C22×C11#53414yes—
183C22×C11#53614yes—
184C22×C11#53714yes—
185C22×C11#53918yes—
186C22×C11#54414yes—
187C4×C11—28no—
188C4×C11—84no—
189Dic11—28no—
190Dic11—44no—
191Dic11—84no—
192C25C22×D1111yescharacteristic
193C23×C4—24no—
194C23×C4—24no—
195C23×C4—112no—
196C23×C4—114no—
197C23×C4—118no—
198C23×C4—112no—
199C23×C4—114no—
200C23×C4—114no—
201C23×C4—224no—
202C23×C4—444no—
203C23×C4—444no—
204C23×C4Dic2214yes—
205C23×C4C4×D1114yes—
206C23×C4C22⋊D1114yes—
207C23×C4C22×D1114yes—
208C23×C4C22×D1112yes—
209C2×C4⋊C4—1116no—
210C2×C4⋊C4—2232no—
211C2×C4⋊C4—228no—
212C2×C4⋊C4—228no—
213C2×C4⋊C4—228no—
214C2×C4⋊C4—448no—
215C2×C22⋊C4—24no—
216C2×C22⋊C4—24no—
217C2×C22⋊C4—24no—
218C2×C22⋊C4—224no—
219C2×C22⋊C4—224no—
220C2×C22⋊C4—224no—
221#95—28no—
222#95—228no—
223#95—228no—
224#95—448no—
225C2×C11—28no—
226C2×C11C2×#38011yescharacteristic
227C2×C11#230811yescharacteristic
228C2×C11#231011yescharacteristic
229C2×C11#231312yes—
230C2×C11#231612yes—
231C2×C11#261814yes—
232C2×C11#262714yes—
233C24—24no—
234C24—24no—
235C24C2×Dic2212yes—
236C24C2×C4×D1112yes—
237C24D4×D1114yes—
238C24#434114yes—
239C24C2×C22⋊D1112yes—
240C24C23×D1111yescharacteristic
241C22×C4—28no—
242C22×C4—216no—
243C22×C4—28no—
244C22×C4—216no—
245C22×C4—24no—
246C22×C4—24no—
247C22×C4—24no—
248C22×C4—24no—
249C22×C4—28no—
250C22×C4—28no—
251C22×C4—24no—
252C22×C4—114no—
253C22×C4—114no—
254C22×C4—114no—
255C22×C4—1116no—
256C22×C4—114no—
257C22×C4—228no—
258C22×C4—228no—
259C22×C4—224no—
260C22×C4—228no—
261C22×C4—224no—
262C22×C4—224no—
263C22×C4—228no—
264C22×C4—228no—
265C22×C4—224no—
266C22×C4—448no—
267C22×C4—4416no—
268C22×C4—448no—
269C22×C4—4416no—
270C22×C4Dic11⋊C4116yescomplemented
271C22×C4C2×Dic2214yes—
272C22×C4C2×C4×D1114yes—
273C22×C4C2×C22⋊D1114yes—
274C4⋊C4—2232no—
275C4⋊C4—4416no—
276C22⋊C4—48no—
277C22⋊C4—448no—
278C11#1433911yescharacteristic, complemented, Sylow
279C23—24no—
280C23—28no—
281C23—24no—
282C23—28no—
283C23—28no—
284C23—28no—
285C23—216no—
286C23#6693014yes—
287C23#6693118yes—
288C23C22⋊C4×D1114yes—
289C23C2×Dic11⋊C414yes—
290C23#6699218yes—
291C23C22×Dic2211yescharacteristic
292C23C22×C4×D1111yescharacteristic
293C23C2×D4×D1112yes—
294C23C2×#434112yes—
295C23#6704214yes—
296C23#6704314yes—
297C23C22×C22⋊D1111yescharacteristic
298C2×C4—24no—
299C2×C4—28no—
300C2×C4—24no—
301C2×C4—232no—
302C2×C4—28no—
303C2×C4—44no—
304C2×C4—48no—
305C2×C4—44no—
306C2×C4—44no—
307C2×C4—48no—
308C2×C4—118no—
309C2×C4—228no—
310C2×C4—228no—
311C2×C4—228no—
312C2×C4—224no—
313C2×C4—228no—
314C2×C4—4416no—
315C2×C4—4416no—
316C2×C4—448no—
317C2×C4—444no—
318C2×C4—448no—
319C2×C4—444no—
320C2×C4—444no—
321C2×C4—448no—
322C2×C4C2×Dic11⋊C418yes—
323C22—216no—
324C22—24no—
325C22—24no—
326C22—28no—
327C22—28no—
328C22—216no—
329C22#1062255518yes—
330C22C2×#6693011yescharacteristic
331C22C2×#6693112yes—
332C22C2×C22⋊C4×D1111yescharacteristic
333C22#1062304712yes—
334C22#1062305014yes—
335C22#1062305212yes—
336C22#1062317914yes—
337C22#1062318414yes—
338C22#1062319618yes—
339C22C22×Dic11⋊C411yescharacteristic
340C22C2×#6699212yes—
341C22#1062336414yes—
342C4—28no—
343C4—84no—
344C4—228no—
345C4—444no—
346C4—884no—
347C2—28no—
348C2C2×#1062255511yescharacteristic
349C2#1307119311yescharacteristic
350C2#1307120111yescharacteristic
351C2#1307121712yes—
352C2#1307123212yes—
353C2#1307436214yes—
354C2#1307443314yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#381C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#381D11
hypocenterC11#14339
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
4. #13066868C2semidirect
13. C22×C4⋊Dic11C4semidirect
76. C22×C4×C11C4⋊C4semidirect
270. C22×C4Dic11⋊C4semidirect
278. C11#14339semidirect

Maximal subgroups

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

subgroupindex
C23×C4⋊Dic112
C2×#106228242
C2×#106225552
#130668682
#130668382
C2×C11×#3812
#1433911