Finite Group Databasebeta

← #14680950

Subgroups — #14680950

Order 2816.

2142 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Dic11⋊C4C211yesmaximal, characteristic
2C2×#10622556C212yesmaximal
3C2×#10622555C212yesmaximal
4#13066867C218yesmaximal, complemented
5#13066839C211yesmaximal, characteristic
6C11×C22⋊#95C211yesmaximal, characteristic
7C24×C4×C11C2211yescharacteristic
8C24×Dic11C2211yescharacteristic
9C24×Dic11C2211yescharacteristic
10C22×C11×C22⋊C4C2212yes—
11C22×C22⋊Dic11C2212yes—
12C22×Dic11⋊C4—28no—
13C22×Dic11⋊C4C418yescomplemented
14C22×Dic11⋊C4C2214yes—
15C22×Dic11⋊C4C2214yes—
16C2×C11×#95C2214yes—
17C2×C11⋊#95C2214yes—
18C2×C11⋊#95C2218yes—
19C2×C11⋊#95C2214yes—
20#10622556—28no—
21#10622555—28no—
22C25×C11C2311yescharacteristic
23C23×C4×C11—24no—
24C23×C4×C11—44no—
25C23×C4×C11C2×C414yes—
26C23×C4×C11C2314yes—
27C23×C4×C11C2312yes—
28C23×Dic11—24no—
29C23×Dic11—24no—
30C23×Dic11—44no—
31C23×Dic11C2×C414yes—
32C23×Dic11C2×C414yes—
33C23×Dic11D414yes—
34C23×Dic11D418yes—
35C23×Dic11Q814yes—
36C23×Dic11C2314yes—
37C23×Dic11C2312yes—
38C23×Dic11C2312yes—
39C2×C11×C22⋊C4—24no—
40C2×C11×C22⋊C4—24no—
41C2×C11×C22⋊C4—24no—
42C2×C22⋊Dic11—24no—
43C2×C22⋊Dic11—24no—
44C2×C22⋊Dic11—24no—
45C2×Dic11⋊C4—232no—
46C2×Dic11⋊C4—28no—
47C2×Dic11⋊C4—28no—
48C2×Dic11⋊C4—28no—
49C2×Dic11⋊C4—48no—
50C2×Dic11⋊C4C2×C4116yes—
51C11×#95—44no—
52C11⋊#95—28no—
53C11⋊#95—216no—
54C11⋊#95—44no—
55#14339—111nomaximal, Sylow
56C24×C11—24no—
57C24×C11—24no—
58C24×C11C22×C412yes—
59C24×C11C2×D414yes—
60C24×C11C2×D412yes—
61C24×C11C2×Q812yes—
62C24×C11#4114yes—
63C24×C11C2411yescharacteristic
64C22×C4×C11—28no—
65C22×C4×C11—24no—
66C22×C4×C11—24no—
67C22×C4×C11—24no—
68C22×C4×C11—24no—
69C22×C4×C11—24no—
70C22×C4×C11—24no—
71C22×C4×C11—28no—
72C22×C4×C11—28no—
73C22×C4×C11—48no—
74C22×C4×C11—416no—
75C22×C4×C11C22×C414yes—
76C22×Dic11—28no—
77C22×Dic11—28no—
78C22×Dic11—216no—
79C22×Dic11—216no—
80C22×Dic11—24no—
81C22×Dic11—24no—
82C22×Dic11—24no—
83C22×Dic11—24no—
84C22×Dic11—24no—
85C22×Dic11—28no—
86C22×Dic11—28no—
87C22×Dic11—28no—
88C22×Dic11—48no—
89C22×Dic11—416no—
90C22×Dic11C22⋊C4116yes—
91C22×Dic11C4⋊C4116yescomplemented
92C22×Dic11C22×C414yes—
93C22×Dic11C22×C414yes—
94C22×Dic11C2×D414yes—
95C22×Dic11C2×D414yes—
96C22×Dic11C2×D414yes—
97C22×Dic11C2×Q814yes—
98C11×C22⋊C4—48no—
99C22⋊Dic11—48no—
100Dic11⋊C4—232no—
101Dic11⋊C4—416no—
102C23×C4⋊C4—111no—
103C2×#381—112no—
104C2×#380—112no—
105#1441—118no—
106C22⋊#95—111no—
107C22⋊#95D1111yescharacteristic
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—24no—
130C2×C4×C11—416no—
131C2×C4×C11—48no—
132C2×C4×C11—44no—
133C2×C4×C11—44no—
134C2×C4×C11—44no—
135C2×C4×C11—48no—
136C2×C4×C11—48no—
137C2×Dic11—24no—
138C2×Dic11—24no—
139C2×Dic11—28no—
140C2×Dic11—28no—
141C2×Dic11—28no—
142C2×Dic11—28no—
143C2×Dic11—28no—
144C2×Dic11—232no—
145C2×Dic11—416no—
146C2×Dic11—44no—
147C2×Dic11—44no—
148C2×Dic11—44no—
149C2×Dic11—48no—
150C2×Dic11—48no—
151C2×Dic11C2×C22⋊C418yes—
152C2×Dic11C2×C4⋊C418yes—
153C24×C4—111no—
154C24×C4—111no—
155C24×C4C2×D1111yescharacteristic
156C22×C4⋊C4—114no—
157C22×C4⋊C4—118no—
158C22×C4⋊C4—114no—
159C22×C4⋊C4—228no—
160C22×C22⋊C4—112no—
161C22×C22⋊C4C2×D1112yes—
162#381—228no—
163#380—228no—
164C2×#95—114no—
165C2×#95—118no—
166C2×#95—114no—
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—44no—
188C4×C11—84no—
189Dic11—28no—
190Dic11—28no—
191Dic11—84no—
192C25C22×D1111yescharacteristic
193C23×C4—24no—
194C23×C4—44no—
195C23×C4—114no—
196C23×C4—114no—
197C23×C4—114no—
198C23×C4—112no—
199C23×C4—112no—
200C23×C4—114no—
201C23×C4—118no—
202C23×C4—114no—
203C23×C4—224no—
204C23×C4—224no—
205C23×C4—444no—
206C23×C4C4×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—44no—
222#95—228no—
223#95—2216no—
224#95—444no—
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×C4×D1112yes—
236C24#433914yes—
237C24D4×D1114yes—
238C24D4×D1112yes—
239C24Q8×D1112yes—
240C24C23×D1111yescharacteristic
241C22×C4—28no—
242C22×C4—24no—
243C22×C4—24no—
244C22×C4—24no—
245C22×C4—24no—
246C22×C4—24no—
247C22×C4—24no—
248C22×C4—28no—
249C22×C4—28no—
250C22×C4—48no—
251C22×C4—416no—
252C22×C4—1116no—
253C22×C4—114no—
254C22×C4—114no—
255C22×C4—114no—
256C22×C4—114no—
257C22×C4—114no—
258C22×C4—114no—
259C22×C4—1116no—
260C22×C4—228no—
261C22×C4—228no—
262C22×C4—2216no—
263C22×C4—2216no—
264C22×C4—224no—
265C22×C4—224no—
266C22×C4—228no—
267C22×C4—224no—
268C22×C4—224no—
269C22×C4—224no—
270C22×C4—228no—
271C22×C4—228no—
272C22×C4—448no—
273C22×C4—4416no—
274C22×C4C2×C4×D1114yes—
275C4⋊C4—2232no—
276C4⋊C4—4416no—
277C22⋊C4—48no—
278C22⋊C4—448no—
279C11#1433911yescharacteristic, complemented, Sylow
280C23—24no—
281C23—24no—
282C23—216no—
283C23—28no—
284C23—28no—
285C23—28no—
286C23—28no—
287C23#6692514yes—
288C23C22⋊C4×D1114yes—
289C23#6693718yes—
290C23C4⋊C4×D1114yes—
291C23#6694918yes—
292C23C22×C4×D1111yescharacteristic
293C23C2×#433912yes—
294C23C2×D4×D1112yes—
295C23C2×D4×D1111yescharacteristic
296C23#6703714yes—
297C23C2×Q8×D1111yescharacteristic
298C23#6704314yes—
299C2×C4—24no—
300C2×C4—24no—
301C2×C4—24no—
302C2×C4—416no—
303C2×C4—48no—
304C2×C4—44no—
305C2×C4—48no—
306C2×C4—44no—
307C2×C4—48no—
308C2×C4—44no—
309C2×C4—118no—
310C2×C4—118no—
311C2×C4—224no—
312C2×C4—224no—
313C2×C4—228no—
314C2×C4—228no—
315C2×C4—228no—
316C2×C4—2232no—
317C2×C4—228no—
318C2×C4—228no—
319C2×C4—4416no—
320C2×C4—444no—
321C2×C4—448no—
322C2×C4—444no—
323C2×C4—448no—
324C2×C4—444no—
325C22—216no—
326C22—24no—
327C22—24no—
328C22—28no—
329C22—28no—
330C22—216no—
331C22#1062228018yes—
332C22C2×#6692511yescharacteristic
333C22C2×C22⋊C4×D1111yescharacteristic
334C22#1062301712yes—
335C22C2×#6693712yes—
336C22C2×C4⋊C4×D1111yescharacteristic
337C22C2×#6694912yes—
338C22#1062304712yes—
339C22#1062309518yes—
340C22#1062312014yes—
341C22#1062312814yes—
342C22#1062315414yes—
343C22#1062317914yes—
344C4—44no—
345C4—84no—
346C4—228no—
347C4—228no—
348C4—884no—
349C2—28no—
350C2C2×#1062228011yescharacteristic
351C2#1307119211yescharacteristic
352C2#1307120111yescharacteristic
353C2#1307121612yes—
354C2#1307123312yes—
355C2#1307436414yes—
356C2#1307443514yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC22⋊#95D11
hypocenterC11#14339
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
4. #13066867C2semidirect
13. C22×Dic11⋊C4C4semidirect
91. C22×Dic11C4⋊C4semidirect
279. C11#14339semidirect

Maximal subgroups

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

subgroupindex
C23×Dic11⋊C42
C2×#106225562
C2×#106225552
#130668672
#130668392
C11×C22⋊#952
#1433911