Finite Group Databasebeta

← #14680184

Subgroups — #14680184

Order 2816.

3390 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622823C212yesmaximal, complemented
2C2×#10622860C211yesmaximal, characteristic
3C2×#10622860C211yesmaximal, characteristic
4#13066859C218yesmaximal, complemented
5#13066839C212yesmaximal, complemented
6C23×C11×C22⋊C4C211yesmaximal, characteristic
7C26×C11C2211yescharacteristic
8C24×C4×C11C2212yes—
9C22×C11×C22⋊C4—24no—
10C22×C11×C22⋊C4—28no—
11C22×C11×C22⋊C4C2214yes—
12C22×C22⋊Dic11C2211yescharacteristic
13C22×C22⋊Dic11C2211yescharacteristic
14C22×C22⋊Dic11C2212yes—
15C22×C22⋊Dic11C2214yes—
16C22×C22⋊Dic11C2214yes—
17C22×Dic11⋊C4C2214yescomplemented
18#10622860—24no—
19#10622860C418yescomplemented
20#10622823—28no—
21C2×C11⋊#95C2214yescomplemented
22C2×C11⋊#95C2218yescomplemented
23C25×C11—24no—
24C25×C11—24no—
25C25×C11—48no—
26C25×C11C2×C414yes—
27C25×C11D414yes—
28C25×C11Q814yes—
29C25×C11C2312yes—
30C25×C11C2311yescharacteristic
31C23×C4×C11—24no—
32C23×C4×C11—24no—
33C23×C4×C11—48no—
34C23×C4×C11D418yes—
35C23×C4×C11C2314yes—
36C23×Dic11C2312yes—
37C23×Dic11C2312yes—
38C23×Dic11C2314yes—
39C2×C11×C22⋊C4—232no—
40C2×C11×C22⋊C4—28no—
41C2×C11×C22⋊C4—216no—
42C2×C22⋊Dic11—24no—
43C2×C22⋊Dic11—24no—
44C2×C22⋊Dic11—24no—
45C2×C22⋊Dic11—28no—
46C2×C22⋊Dic11—22no—
47C2×C22⋊Dic11—22no—
48C2×C22⋊Dic11—24no—
49C2×C22⋊Dic11—48no—
50C2×C22⋊Dic11—48no—
51C2×C22⋊Dic11C2×C418yes—
52C2×C22⋊Dic11C2×C4116yescomplemented
53C2×Dic11⋊C4—28no—
54C2×Dic11⋊C4—48no—
55C11⋊#95—28no—
56C11⋊#95—48no—
57#14262—111nomaximal, Sylow
58C24×C11—28no—
59C24×C11—216no—
60C24×C11—28no—
61C24×C11—216no—
62C24×C11—28no—
63C24×C11—24no—
64C24×C11—24no—
65C24×C11—28no—
66C24×C11—28no—
67C24×C11—416no—
68C24×C11—416no—
69C24×C11—416no—
70C24×C11—416no—
71C24×C11—416no—
72C24×C11—432no—
73C24×C11C4⋊C4116yescomplemented
74C24×C11C22×C414yes—
75C24×C11C22×C412yes—
76C24×C11C2×D414yes—
77C24×C11C2×D412yes—
78C24×C11C2×D414yes—
79C24×C11C2×Q814yes—
80C24×C11C2×Q812yes—
81C24×C11#4114yes—
82C24×C11C2411yescharacteristic
83C22×C4×C11—216no—
84C22×C4×C11—24no—
85C22×C4×C11—24no—
86C22×C4×C11—28no—
87C22×C4×C11—28no—
88C22×C4×C11—416no—
89C22×C4×C11—416no—
90C22×C4×C11—416no—
91C22×C4×C11C2×D418yes—
92C22×Dic11—24no—
93C22×Dic11—22no—
94C22×Dic11—22no—
95C22×Dic11—22no—
96C22×Dic11—22no—
97C22×Dic11—24no—
98C22×Dic11—24no—
99C22×Dic11—28no—
100C22×Dic11—28no—
101C22×Dic11—28no—
102C22×Dic11—28no—
103C22×Dic11C22×C418yes—
104C11×C22⋊C4—232no—
105C22⋊Dic11—216no—
106C22⋊Dic11—416no—
107C22⋊Dic11—416no—
108C22⋊Dic11—44no—
109C22⋊Dic11—44no—
110Dic11⋊C4—416no—
111C23×C22⋊C4D1111yescharacteristic
112C2×#385—112no—
113C2×#379—111no—
114C2×#379—111no—
115#1439—118no—
116C22⋊#95—112no—
117C23×C11—28no—
118C23×C11—28no—
119C23×C11—28no—
120C23×C11—28no—
121C23×C11—216no—
122C23×C11—28no—
123C23×C11—28no—
124C23×C11—28no—
125C23×C11—28no—
126C23×C11—24no—
127C23×C11—28no—
128C23×C11—24no—
129C23×C11—28no—
130C23×C11—28no—
131C23×C11—28no—
132C23×C11—28no—
133C23×C11—232no—
134C23×C11—432no—
135C23×C11—464no—
136C23×C11—432no—
137C23×C11—432no—
138C23×C11—464no—
139C23×C11—48no—
140C23×C11—48no—
141C23×C11—416no—
142C23×C11C2×C4⋊C418yes—
143C23×C11C2×C4⋊C414yes—
144C23×C11C4×D418yes—
145C23×C11#12014yes—
146C23×C11C22⋊Q818yes—
147C23×C11#12314yes—
148C23×C11C23×C411yescharacteristic
149C23×C11C22×D411yescharacteristic
150C23×C11C22×D412yes—
151C23×C11C22×Q811yescharacteristic
152C23×C11C2×#4112yes—
153C23×C11H(5,𝔽2)18yes—
154C2×C4×C11—28no—
155C2×C4×C11—28no—
156C2×C4×C11—28no—
157C2×C4×C11—432no—
158C2×C4×C11—48no—
159C2×C4×C11—48no—
160C2×Dic11—28no—
161C2×Dic11—216no—
162C2×Dic11—44no—
163C2×Dic11—44no—
164C2×Dic11—48no—
165C2×Dic11—42no—
166C2×Dic11—42no—
167C2×Dic11—44no—
168C2×Dic11—44no—
169C2×Dic11—44no—
170C2×Dic11—44no—
171C2×Dic11—48no—
172C26C2×D1111yescharacteristic
173C24×C4C2×D1112yes—
174C22×C4⋊C4—114no—
175C22×C22⋊C4—24no—
176C22×C22⋊C4—28no—
177C22×C22⋊C4—112no—
178C22×C22⋊C4—114no—
179C22×C22⋊C4—111no—
180C22×C22⋊C4—111no—
181C22×C22⋊C4—114no—
182C22×C22⋊C4C2×D1114yes—
183#385—228no—
184#379—118no—
185#379—224no—
186C2×#95—114no—
187C2×#95—118no—
188C22×C11—28no—
189C22×C11—216no—
190C22×C11—28no—
191C22×C11—28no—
192C22×C11—216no—
193C22×C11—28no—
194C22×C11—28no—
195C22×C11—28no—
196C22×C11—464no—
197C22×C11—416no—
198C22×C11—48no—
199C22×C11—48no—
200C22×C11—416no—
201C22×C11#38518yes—
202C22×C11C22×C4⋊C411yescharacteristic
203C22×C11C2×C4×D412yes—
204C22×C11#51814yes—
205C22×C11C2×#12011yescharacteristic
206C22×C11C2×C22⋊Q812yes—
207C22×C11C2×#12311yescharacteristic
208C22×C11#53414yes—
209C22×C11#53414yes—
210C22×C11#53514yes—
211C22×C11#53818yes—
212C22×C11#54314yes—
213C4×C11—48no—
214Dic11—48no—
215Dic11—82no—
216Dic11—82no—
217C25—24no—
218C25—24no—
219C25—48no—
220C25Dic2214yes—
221C25C4×D1114yes—
222C25C22⋊D1114yes—
223C25C22×D1112yes—
224C25C22×D1111yescharacteristic
225C23×C4—24no—
226C23×C4—24no—
227C23×C4—48no—
228C23×C4—114no—
229C23×C4—112no—
230C23×C4—112no—
231C23×C4C22⋊D1118yes—
232C23×C4C22×D1114yes—
233C2×C4⋊C4—228no—
234C2×C4⋊C4—448no—
235C2×C22⋊C4—232no—
236C2×C22⋊C4—28no—
237C2×C22⋊C4—216no—
238C2×C22⋊C4—118no—
239C2×C22⋊C4—1116no—
240C2×C22⋊C4—224no—
241C2×C22⋊C4—224no—
242C2×C22⋊C4—224no—
243C2×C22⋊C4—228no—
244C2×C22⋊C4—222no—
245C2×C22⋊C4—222no—
246C2×C22⋊C4—224no—
247C2×C22⋊C4—448no—
248C2×C22⋊C4—448no—
249#95—228no—
250#95—448no—
251C2×C11—28no—
252C2×C11—48no—
253C2×C11C2×#38511yescharacteristic
254C2×C11#231512yes—
255C2×C11#232114yes—
256C2×C11#261312yes—
257C2×C11#262212yes—
258C2×C11#262614yes—
259C24—28no—
260C24—216no—
261C24—216no—
262C24—28no—
263C24—28no—
264C24—24no—
265C24—28no—
266C24—28no—
267C24—24no—
268C24—416no—
269C24—416no—
270C24—416no—
271C24—432no—
272C24—416no—
273C24—416no—
274C24Dic11⋊C4116yescomplemented
275C24C2×Dic2214yes—
276C24C2×Dic2212yes—
277C24C2×C4×D1114yes—
278C24C2×C4×D1112yes—
279C24#433914yes—
280C24C2×C22⋊D1114yes—
281C24C2×C22⋊D1112yes—
282C24C2×C22⋊D1114yes—
283C24C23×D1111yescharacteristic
284C22×C4—216no—
285C22×C4—28no—
286C22×C4—28no—
287C22×C4—24no—
288C22×C4—24no—
289C22×C4—416no—
290C22×C4—416no—
291C22×C4—416no—
292C22×C4—118no—
293C22×C4—224no—
294C22×C4—228no—
295C22×C4—228no—
296C22×C4—224no—
297C22×C4—224no—
298C22×C4—228no—
299C22×C4—228no—
300C22×C4—222no—
301C22×C4—222no—
302C22×C4—222no—
303C22×C4—222no—
304C22×C4C2×C22⋊D1118yes—
305C4⋊C4—4416no—
306C22⋊C4—232no—
307C22⋊C4—2216no—
308C22⋊C4—4416no—
309C22⋊C4—4416no—
310C22⋊C4—444no—
311C22⋊C4—444no—
312C11#1426211yescharacteristic, complemented, Sylow
313C23—28no—
314C23—28no—
315C23—216no—
316C23—28no—
317C23—28no—
318C23—28no—
319C23—28no—
320C23—28no—
321C23—28no—
322C23—28no—
323C23—28no—
324C23—28no—
325C23—24no—
326C23—232no—
327C23—28no—
328C23—28no—
329C23—24no—
330C23—432no—
331C23—432no—
332C23—464no—
333C23—432no—
334C23—464no—
335C23—416no—
336C23—48no—
337C23—48no—
338C23C2×Dic11⋊C418yes—
339C23C2×Dic11⋊C414yes—
340C23#6697718yes—
341C23C4×C22⋊D1118yes—
342C23#6698214yes—
343C23#6700614yes—
344C23C22×Dic2211yescharacteristic
345C23C22×C4×D1111yescharacteristic
346C23C2×#433912yes—
347C23#6703718yes—
348C23C22×C22⋊D1111yescharacteristic
349C23C22×C22⋊D1112yes—
350C2×C4—28no—
351C2×C4—28no—
352C2×C4—28no—
353C2×C4—432no—
354C2×C4—48no—
355C2×C4—48no—
356C2×C4—2216no—
357C2×C4—228no—
358C2×C4—448no—
359C2×C4—444no—
360C2×C4—444no—
361C2×C4—448no—
362C2×C4—442no—
363C2×C4—444no—
364C2×C4—444no—
365C2×C4—444no—
366C2×C4—444no—
367C2×C4—442no—
368C22—28no—
369C22—28no—
370C22—216no—
371C22—28no—
372C22—216no—
373C22—28no—
374C22—28no—
375C22—28no—
376C22—464no—
377C22—48no—
378C22—416no—
379C22—48no—
380C22—416no—
381C22#1062282318yes—
382C22#1062301414yes—
383C22#1062301714yes—
384C22#1062302518yes—
385C22C22×Dic11⋊C411yescharacteristic
386C22C2×#6697712yes—
387C22C2×C4×C22⋊D1112yes—
388C22C2×#6698211yescharacteristic
389C22#1062333514yes—
390C22#1062333514yes—
391C22#1062333614yes—
392C22C2×#6700611yescharacteristic
393C4—48no—
394C4—448no—
395C4—882no—
396C4—882no—
397C2—28no—
398C2—48no—
399C2C2×#1062282311yescharacteristic
400C2#1307122812yes—
401C2#1307127414yes—
402C2#1307432812yes—
403C2#1307438912yes—
404C2#1307442114yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC23×C11×C22⋊C4C2
socle, cosocleC24×C11C24
prime radicalC26×C11C22
hypercenterC23×C22⋊C4D11
hypocenterC11#14262
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10622823C2semidirect
4. #13066859C2semidirect
5. #13066839C2semidirect
17. C22×Dic11⋊C4C22semidirect
19. #10622860C4semidirect
21. C2×C11⋊#95C22semidirect
22. C2×C11⋊#95C22semidirect
52. C2×C22⋊Dic11C2×C4semidirect
73. C24×C11C4⋊C4semidirect
274. C24Dic11⋊C4semidirect
312. C11#14262semidirect

Maximal subgroups

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

subgroupindex
C2×#106228232
C2×#106228602
#130668592
#130668392
C23×C11×C22⋊C42
#1426211