Finite Group Databasebeta

← #14684955

Subgroups — #14684955

Order 2816.

2430 conjugacy classes of subgroups.

The subgroup lattice has 380 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
4Dic11⋊#95C214yesmaximal, complemented
5#13066842C214yesmaximal, complemented
6#13066838C212yesmaximal
7C2×C11×#381C211yesmaximal, characteristic
8C24×C4×C11C2211yescharacteristic
9C24×Dic11C2211yescharacteristic
10C24×Dic11C2211yescharacteristic
11C22×C11×C22⋊C4C2212yes—
12C22×C22⋊Dic11C2212yes—
13C22×Dic11⋊C4C2214yes—
14C22×C4×Dic11—28no—
15C22×C4×Dic11C418yescomplemented
16C22×C4×Dic11C2212yes—
17C22×C4×Dic11C2212yes—
18C11×#381—24no—
19C2×C11×#95C2214yes—
20#10622824—24no—
21C2×C11⋊#95C2218yes—
22C2×C11⋊#95C2214yes—
23C2×C11⋊#95C2214yes—
24#10622555—28no—
25C25×C11C2311yescharacteristic
26C23×C4×C11—24no—
27C23×C4×C11—24no—
28C23×C4×C11C2×C414yes—
29C23×C4×C11D414yes—
30C23×C4×C11Q814yes—
31C23×C4×C11C2314yes—
32C23×C4×C11C2312yes—
33C23×Dic11—24no—
34C23×Dic11—28no—
35C23×Dic11—28no—
36C23×Dic11C2×C414yes—
37C23×Dic11C2×C414yes—
38C23×Dic11D418yes—
39C23×Dic11C2314yes—
40C23×Dic11C2311yescharacteristic
41C23×Dic11C2312yes—
42C23×Dic11C2311yescharacteristic
43C2×C11×C22⋊C4—24no—
44C2×C11×C22⋊C4—24no—
45C2×C11×C22⋊C4—24no—
46C2×C22⋊Dic11—24no—
47C2×C22⋊Dic11—24no—
48C2×C22⋊Dic11—24no—
49C2×Dic11⋊C4—28no—
50C2×Dic11⋊C4—216no—
51C2×C4×Dic11—232no—
52C2×C4×Dic11—28no—
53C2×C4×Dic11—28no—
54C2×C4×Dic11C2×C418yes—
55C2×C4×Dic11C2×C418yes—
56C11×#95—28no—
57C11⋊#95—28no—
58C11⋊#95—28no—
59C11⋊#95—216no—
60#14685—111nomaximal, Sylow
61C24×C11—24no—
62C24×C11—24no—
63C24×C11C22×C412yes—
64C24×C11C2×D414yes—
65C24×C11C2×D412yes—
66C24×C11C2×Q812yes—
67C24×C11#4114yes—
68C24×C11C2411yescharacteristic
69C22×C4×C11—28no—
70C22×C4×C11—28no—
71C22×C4×C11—216no—
72C22×C4×C11—216no—
73C22×C4×C11—24no—
74C22×C4×C11—24no—
75C22×C4×C11—24no—
76C22×C4×C11—24no—
77C22×C4×C11—28no—
78C22×C4×C11—28no—
79C22×C4×C11—24no—
80C22×C4×C11C4⋊C4116yescomplemented
81C22×C4×C11C22×C414yes—
82C22×C4×C11C2×D414yes—
83C22×C4×C11C2×Q814yes—
84C22×Dic11—232no—
85C22×Dic11—216no—
86C22×Dic11—216no—
87C22×Dic11—232no—
88C22×Dic11—28no—
89C22×Dic11—24no—
90C22×Dic11—24no—
91C22×Dic11—24no—
92C22×Dic11—24no—
93C22×Dic11—24no—
94C22×Dic11—28no—
95C22×Dic11—28no—
96C22×Dic11—24no—
97C22×Dic11C22⋊C4116yes—
98C22×Dic11C22×C412yes—
99C22×Dic11C22×C414yes—
100C22×Dic11C22×C412yes—
101C22×Dic11C2×D414yes—
102C22×Dic11C2×D414yes—
103C22×Dic11#4118yes—
104C22×Dic11#4118yes—
105C11×C22⋊C4—48no—
106C22⋊Dic11—48no—
107Dic11⋊C4—416no—
108C4×Dic11—216no—
109C4×Dic11—216no—
110C23×C42—111no—
111C2×#381—111no—
112C2×#381D1111yescharacteristic
113C2×#380—112no—
114C4⋊#95—114no—
115#1434—114no—
116C22⋊#95—112no—
117C23×C11—24no—
118C23×C11—24no—
119C23×C11—28no—
120C23×C11—28no—
121C23×C11—216no—
122C23×C11—28no—
123C23×C11—28no—
124C23×C11C2×C22⋊C414yes—
125C23×C11C2×C4⋊C414yes—
126C23×C11#11714yes—
127C23×C11#12118yes—
128C23×C11C22⋊Q818yes—
129C23×C11C23×C411yescharacteristic
130C23×C11C22×D412yes—
131C23×C11C22×D411yescharacteristic
132C23×C11C22×Q811yescharacteristic
133C23×C11C2×#4112yes—
134C23×C11C2×#4114yes—
135C23×C11C2×#4114yes—
136C2×C4×C11—24no—
137C2×C4×C11—24no—
138C2×C4×C11—28no—
139C2×C4×C11—28no—
140C2×C4×C11—232no—
141C2×C4×C11—44no—
142C2×C4×C11—44no—
143C2×C4×C11—44no—
144C2×C4×C11—48no—
145C2×C4×C11—48no—
146C2×C4×C11C2×C4⋊C418yes—
147C2×Dic11—232no—
148C2×Dic11—24no—
149C2×Dic11—24no—
150C2×Dic11—24no—
151C2×Dic11—28no—
152C2×Dic11—216no—
153C2×Dic11—232no—
154C2×Dic11—44no—
155C2×Dic11—44no—
156C2×Dic11—44no—
157C2×Dic11—48no—
158C2×Dic11—48no—
159C2×Dic11C2×C22⋊C414yes—
160C2×Dic11C2×C22⋊C414yes—
161C2×Dic11#11718yes—
162C2×Dic11#11718yes—
163C2×Dic11#123116yes—
164C24×C4—111no—
165C24×C4—111no—
166C24×C4C2×D1111yescharacteristic
167C22×C4⋊C4—114no—
168C22×C22⋊C4—112no—
169C22×C22⋊C4C2×D1112yes—
170C22×C42—112no—
171C22×C42—112no—
172C22×C42—118no—
173C22×C42—228no—
174#381—24no—
175#381—224no—
176#380—228no—
177C2×#95—118no—
178C2×#95—114no—
179C2×#95—114no—
180C2×#95C2×D1114yes—
181C22×C11—216no—
182C22×C11—216no—
183C22×C11—24no—
184C22×C11—24no—
185C22×C11—28no—
186C22×C11—28no—
187C22×C11#38018yes—
188C22×C11C22×C22⋊C411yescharacteristic
189C22×C11C22×C4⋊C411yescharacteristic
190C22×C11C2×#11711yescharacteristic
191C22×C11C2×#11712yes—
192C22×C11C2×#11712yes—
193C22×C11C2×#12112yes—
194C22×C11C2×C22⋊Q812yes—
195C22×C11C2×#12314yes—
196C22×C11#52514yes—
197C22×C11#52918yes—
198C22×C11#53214yes—
199C22×C11#53314yes—
200C4×C11—28no—
201C4×C11—84no—
202Dic11—24no—
203Dic11—28no—
204Dic11—84no—
205Dic11#38118yescomplemented
206C25C22×D1111yescharacteristic
207C23×C4—24no—
208C23×C4—24no—
209C23×C4—111no—
210C23×C4—114no—
211C23×C4—118no—
212C23×C4—111no—
213C23×C4—112no—
214C23×C4—114no—
215C23×C4—114no—
216C23×C4—228no—
217C23×C4—228no—
218C23×C4—224no—
219C23×C4Dic2214yes—
220C23×C4C4×D1114yes—
221C23×C4C22⋊D1114yes—
222C23×C4C22×D1114yes—
223C23×C4C22×D1112yes—
224C2×C4⋊C4—228no—
225C2×C4⋊C4—2216no—
226C2×C22⋊C4—24no—
227C2×C22⋊C4—24no—
228C2×C22⋊C4—24no—
229C2×C22⋊C4—224no—
230C2×C22⋊C4—224no—
231C2×C22⋊C4—224no—
232C2×C42—118no—
233C2×C42—118no—
234C2×C42—2232no—
235C2×C42—228no—
236C2×C42—228no—
237#95—28no—
238#95—2216no—
239#95—228no—
240#95—228no—
241C2×C11—28no—
242C2×C11C2×#38011yescharacteristic
243C2×C11C2×#38111yescharacteristic
244C2×C11#228011yescharacteristic
245C2×C11#228312yes—
246C2×C11#228512yes—
247C2×C11#285414yes—
248C2×C11#285514yes—
249C24—24no—
250C24—24no—
251C24C2×Dic2212yes—
252C24C2×C4×D1112yes—
253C24D4×D1114yes—
254C24#434114yes—
255C24C2×C22⋊D1112yes—
256C24C23×D1111yescharacteristic
257C22×C4—28no—
258C22×C4—216no—
259C22×C4—28no—
260C22×C4—216no—
261C22×C4—24no—
262C22×C4—24no—
263C22×C4—24no—
264C22×C4—24no—
265C22×C4—28no—
266C22×C4—28no—
267C22×C4—24no—
268C22×C4—112no—
269C22×C4—114no—
270C22×C4—118no—
271C22×C4—1116no—
272C22×C4—112no—
273C22×C4—114no—
274C22×C4—114no—
275C22×C4—118no—
276C22×C4—2216no—
277C22×C4—2232no—
278C22×C4—2216no—
279C22×C4—2232no—
280C22×C4—228no—
281C22×C4—224no—
282C22×C4—224no—
283C22×C4—224no—
284C22×C4—224no—
285C22×C4—224no—
286C22×C4—228no—
287C22×C4—228no—
288C22×C4—224no—
289C22×C4Dic11⋊C4116yescomplemented
290C22×C4C2×Dic2214yes—
291C22×C4C2×C4×D1114yes—
292C22×C4C2×C22⋊D1114yes—
293C4⋊C4—4416no—
294C22⋊C4—48no—
295C22⋊C4—448no—
296C42—2216no—
297C42—2216no—
298C11#1468511yescharacteristic, complemented, Sylow
299C23—28no—
300C23—24no—
301C23—24no—
302C23—28no—
303C23—216no—
304C23—28no—
305C23—28no—
306C23#6693014yes—
307C23#6693118yes—
308C23C22⋊C4×D1114yes—
309C23C2×Dic11⋊C414yes—
310C23#6699218yes—
311C23C22×Dic2211yescharacteristic
312C23C22×C4×D1111yescharacteristic
313C23C2×D4×D1112yes—
314C23C2×#434112yes—
315C23#41×D1114yes—
316C23#41×D1114yes—
317C23C22×C22⋊D1111yescharacteristic
318C2×C4—24no—
319C2×C4—28no—
320C2×C4—24no—
321C2×C4—232no—
322C2×C4—28no—
323C2×C4—44no—
324C2×C4—48no—
325C2×C4—48no—
326C2×C4—44no—
327C2×C4—44no—
328C2×C4—114no—
329C2×C4—118no—
330C2×C4—1116no—
331C2×C4—114no—
332C2×C4—118no—
333C2×C4—2232no—
334C2×C4—2232no—
335C2×C4—224no—
336C2×C4—224no—
337C2×C4—224no—
338C2×C4—228no—
339C2×C4—2216no—
340C2×C4—444no—
341C2×C4—448no—
342C2×C4—448no—
343C2×C4—444no—
344C2×C4—444no—
345C2×C4C2×Dic11⋊C418yes—
346C22—24no—
347C22—24no—
348C22—28no—
349C22—28no—
350C22—216no—
351C22—216no—
352C22#1062255518yes—
353C22C2×#6693011yescharacteristic
354C22C2×#6693112yes—
355C22C2×C22⋊C4×D1111yescharacteristic
356C22#1062304814yes—
357C22D11×#11712yes—
358C22D11×#11712yes—
359C22#1062318018yes—
360C22D11×#12314yes—
361C22#1062318714yes—
362C22C22×Dic11⋊C411yescharacteristic
363C22C2×#6699212yes—
364C22#1062336314yes—
365C4—28no—
366C4—84no—
367C4—118no—
368C4—224no—
369C4—228no—
370C4—884no—
371C2—28no—
372C2C2×#1062255511yescharacteristic
373C2D11×#38111yescharacteristic
374C2#1307099611yescharacteristic
375C2#1307100712yes—
376C2#1307101912yes—
377C2#1307694514yes—
378C2#1307695314yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#381C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#381D11
hypocenterC11#14685
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
4. Dic11⋊#95C2semidirect
5. #13066842C2semidirect
15. C22×C4×Dic11C4semidirect
80. C22×C4×C11C4⋊C4semidirect
205. Dic11#381semidirect
289. C22×C4Dic11⋊C4semidirect
298. C11#14685semidirect

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
Dic11⋊#952
#130668422
#130668382
C2×C11×#3812
#1468511