Finite Group Databasebeta

← #14676431

Subgroups — #14676431

Order 2816.

1342 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622550C211yesmaximal, characteristic
2C2×#10622545C211yesmaximal, characteristic
3#13066879C212yesmaximal
4#13066875C212yesmaximal
5#13066849C214yesmaximal
6Dic11⋊#95C212yesmaximal
7#13066842C212yesmaximal
8C2×C4×C11×C4⋊C4C211yesmaximal, characteristic
9C22×C11×C4⋊C4C2212yes—
10C22×C42×C11C2212yes—
11C22×C42×C11C2211yescharacteristic
12C22×Dic11⋊C4C2214yes—
13C22×C4×Dic11C2212yes—
14C4×C11×C4⋊C4—24no—
15C2×C11×#95C2212yes—
16C2×C11⋊#95C2211yescharacteristic
17C2×C11⋊#95C2214yes—
18C2×C11⋊#95C2214yes—
19C2×C11⋊#95C2211yescharacteristic
20C2×C11⋊#95C2212yes—
21C2×C11⋊#95C2212yes—
22C2×C11⋊#95C2214yes—
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2211yescharacteristic
25C2×C11⋊#95C2211yescharacteristic
26#10622550—24no—
27#10622545C418yescomplemented
28C23×C4×C11C2314yes—
29C23×C4×C11C2311yescharacteristic
30C23×C4×C11C2311yescharacteristic
31C23×C4×C11C2311yescharacteristic
32C23×Dic11C2312yes—
33C23×Dic11C2312yes—
34C23×Dic11C2312yes—
35C23×Dic11C2312yes—
36C2×C11×C4⋊C4—24no—
37C2×C11×C4⋊C4—28no—
38C2×C42×C11—24no—
39C2×C42×C11—42no—
40C2×C42×C11—42no—
41C2×C42×C11C2×C414yes—
42C2×C42×C11D414yes—
43C2×C42×C11Q814yes—
44C2×Dic11⋊C4—28no—
45C2×Dic11⋊C4—28no—
46C2×Dic11⋊C4—44no—
47C2×C4×Dic11—28no—
48C2×C4×Dic11C2×C418yes—
49C11×#95—24no—
50C11⋊#95—22no—
51C11⋊#95—22no—
52C11⋊#95—24no—
53C11⋊#95—24no—
54C11⋊#95—28no—
55C11⋊#95—28no—
56C11⋊#95—44no—
57C11⋊#95C2×C414yes—
58C11⋊#95C2×C418yes—
59C11⋊#95C2×C414yes—
60#13952—111nomaximal, Sylow
61C24×C11C2411yescharacteristic
62C22×C4×C11—24no—
63C22×C4×C11—24no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—24no—
69C22×C4×C11—24no—
70C22×C4×C11—24no—
71C22×C4×C11—24no—
72C22×C4×C11—24no—
73C22×C4×C11—24no—
74C22×C4×C11C22×C412yes—
75C22×C4×C11C22×C412yes—
76C22×C4×C11C22×C412yes—
77C22×C4×C11C2×D412yes—
78C22×C4×C11C2×D412yes—
79C22×C4×C11C2×D412yes—
80C22×C4×C11C2×Q812yes—
81C22×C4×C11C2×Q812yes—
82C22×C4×C11C2×Q812yes—
83C22×C4×C11#4118yes—
84C22×Dic11—22no—
85C22×Dic11—22no—
86C22×Dic11—24no—
87C22×Dic11—24no—
88C22×Dic11—24no—
89C22×Dic11—24no—
90C22×Dic11—24no—
91C22×Dic11—24no—
92C22×Dic11—24no—
93C22×Dic11—22no—
94C22×Dic11—22no—
95C22×Dic11—22no—
96C22×Dic11—22no—
97C22×Dic11—22no—
98C22×Dic11—22no—
99C22×Dic11—22no—
100C22×Dic11—22no—
101C22×Dic11C22×C414yes—
102C22×Dic11C22×C414yes—
103C22×Dic11#4118yes—
104C11×C4⋊C4—216no—
105C42×C11—48no—
106C42×C11C4⋊C4116yescomplemented
107Dic11⋊C4—416no—
108C4×Dic11—216no—
109C2×#383—111no—
110C2×C4×C4⋊C4D1111yescharacteristic
111C2×#376—111no—
112#1444—112no—
113#1442—112no—
114#1436—114no—
115C4⋊#95—112no—
116#1434—112no—
117C23×C11C23×C411yescharacteristic
118C23×C11C22×D411yescharacteristic
119C23×C11C22×Q811yescharacteristic
120C23×C11C2×#4114yes—
121C23×C11C2×#4114yes—
122C23×C11H(5,𝔽2)11yescharacteristic
123C23×C11H(5,𝔽2)11yescharacteristic
124C23×C112−1+411yescharacteristic
125C23×C112−1+411yescharacteristic
126C2×C4×C11—24no—
127C2×C4×C11—24no—
128C2×C4×C11—22no—
129C2×C4×C11—22no—
130C2×C4×C11—24no—
131C2×C4×C11—24no—
132C2×C4×C11—24no—
133C2×C4×C11—24no—
134C2×C4×C11—22no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—28no—
139C2×C4×C11—28no—
140C2×C4×C11—28no—
141C2×C4×C11—44no—
142C2×C4×C11—44no—
143C2×C4×C11—44no—
144C2×C4×C11—44no—
145C2×C4×C11C2×C4⋊C414yes—
146C2×C4×C11C2×C4⋊C414yes—
147C2×C4×C11C2×C4⋊C414yes—
148C2×Dic11—24no—
149C2×Dic11—24no—
150C2×Dic11—28no—
151C2×Dic11—28no—
152C2×Dic11—24no—
153C2×Dic11—24no—
154C2×Dic11—24no—
155C2×Dic11—44no—
156C2×Dic11—44no—
157C2×Dic11—42no—
158C2×Dic11—42no—
159C2×Dic11—42no—
160C2×Dic11—42no—
161C2×Dic11—42no—
162C2×Dic11—42no—
163C2×Dic11—44no—
164C2×Dic11—44no—
165C2×Dic11—44no—
166C2×Dic11—44no—
167C2×Dic11#11718yes—
168C22×C4⋊C4—114no—
169C22×C4⋊C4C2×D1112yes—
170C22×C42—112no—
171C22×C42C2×D1112yes—
172C22×C42C2×D1111yescharacteristic
173#383—224no—
174C4×C4⋊C4—24no—
175#376—118no—
176C2×#95—112no—
177C2×#95—111no—
178C2×#95—111no—
179C2×#95—111no—
180C2×#95—114no—
181C2×#95—114no—
182C2×#95—111no—
183C2×#95—112no—
184C2×#95—112no—
185C2×#95—114no—
186C2×#95C2×D1112yes—
187C22×C11C22×C4⋊C411yescharacteristic
188C22×C11C2×#11712yes—
189C22×C11C4×#4112yes—
190C22×C11#52011yescharacteristic
191C22×C11#52011yescharacteristic
192C22×C11#52512yes—
193C22×C11#53212yes—
194C22×C11#53312yes—
195C22×C11#53312yes—
196C22×C11#53511yescharacteristic
197C22×C11#53611yescharacteristic
198C22×C11#54411yescharacteristic
199C22×C11#54411yescharacteristic
200C22×C11#55114yes—
201C22×C11#55214yes—
202C22×C11#55314yes—
203C22×C11#55614yes—
204C4×C11—24no—
205C4×C11—24no—
206C4×C11—24no—
207C4×C11—48no—
208Dic11—28no—
209Dic11—44no—
210Dic11—82no—
211Dic11—82no—
212C23×C4—112no—
213C23×C4—112no—
214C23×C4—112no—
215C23×C4—112no—
216C23×C4C22×D1114yes—
217C23×C4C22×D1111yescharacteristic
218C23×C4C22×D1111yescharacteristic
219C23×C4C22×D1111yescharacteristic
220C2×C4⋊C4—28no—
221C2×C4⋊C4—24no—
222C2×C4⋊C4—228no—
223C2×C4⋊C4—228no—
224C2×C4⋊C4—444no—
225C2×C42—24no—
226C2×C42—42no—
227C2×C42—42no—
228C2×C42—118no—
229C2×C42—228no—
230C2×C42Dic2214yes—
231C2×C42C4×D1114yes—
232C2×C42C22⋊D1114yes—
233#95—24no—
234#95—114no—
235#95—118no—
236#95—114no—
237#95—228no—
238#95—228no—
239#95—222no—
240#95—222no—
241#95—224no—
242#95—224no—
243#95—444no—
244C2×C11#228511yescharacteristic
245C2×C11#229611yescharacteristic
246C2×C11#231711yescharacteristic
247C2×C11#234312yes—
248C2×C11#234712yes—
249C2×C11#260312yes—
250C2×C11#260412yes—
251C2×C11#260512yes—
252C2×C11#260612yes—
253C24C23×D1111yescharacteristic
254C22×C4—24no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—24no—
260C22×C4—24no—
261C22×C4—24no—
262C22×C4—24no—
263C22×C4—24no—
264C22×C4—24no—
265C22×C4—24no—
266C22×C4—114no—
267C22×C4—118no—
268C22×C4—114no—
269C22×C4—224no—
270C22×C4—222no—
271C22×C4—222no—
272C22×C4—224no—
273C22×C4—222no—
274C22×C4—222no—
275C22×C4—224no—
276C22×C4—224no—
277C22×C4—224no—
278C22×C4—222no—
279C22×C4—222no—
280C22×C4—222no—
281C22×C4—222no—
282C22×C4—224no—
283C22×C4—224no—
284C22×C4—222no—
285C22×C4—222no—
286C22×C4C2×Dic2212yes—
287C22×C4C2×Dic2212yes—
288C22×C4C2×Dic2212yes—
289C22×C4C2×C4×D1112yes—
290C22×C4C2×C4×D1112yes—
291C22×C4C2×C4×D1112yes—
292C22×C4#433918yes—
293C22×C4C2×C22⋊D1112yes—
294C22×C4C2×C22⋊D1112yes—
295C22×C4C2×C22⋊D1112yes—
296C4⋊C4—216no—
297C4⋊C4—4416no—
298C42—48no—
299C42—2216no—
300C42Dic11⋊C4116yescomplemented
301C11#1395211yescharacteristic, complemented, Sylow
302C23C22×Dic2211yescharacteristic
303C23C22×C4×D1111yescharacteristic
304C23C2×#433914yes—
305C23#6703711yescharacteristic
306C23#6703711yescharacteristic
307C23#6704011yescharacteristic
308C23#6704011yescharacteristic
309C23#41×D1114yes—
310C23C22×C22⋊D1111yescharacteristic
311C2×C4—24no—
312C2×C4—24no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—24no—
318C2×C4—24no—
319C2×C4—24no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—24no—
323C2×C4—28no—
324C2×C4—28no—
325C2×C4—28no—
326C2×C4—44no—
327C2×C4—44no—
328C2×C4—44no—
329C2×C4—44no—
330C2×C4—118no—
331C2×C4—224no—
332C2×C4—224no—
333C2×C4—228no—
334C2×C4—228no—
335C2×C4—224no—
336C2×C4—224no—
337C2×C4—224no—
338C2×C4—444no—
339C2×C4—444no—
340C2×C4—442no—
341C2×C4—442no—
342C2×C4—444no—
343C2×C4—442no—
344C2×C4—444no—
345C2×C4—442no—
346C2×C4—444no—
347C2×C4—442no—
348C2×C4—442no—
349C2×C4—444no—
350C2×C4C2×Dic11⋊C414yes—
351C2×C4C2×Dic11⋊C414yes—
352C2×C4C2×Dic11⋊C414yes—
353C22#1062300112yes—
354C22C4×#433912yes—
355C22#1062303111yescharacteristic
356C22#1062303111yescharacteristic
357C22#1062303511yescharacteristic
358C22#1062303511yescharacteristic
359C22#1062304812yes—
360C22D11×#11712yes—
361C22#1062307114yes—
362C22#1062308714yes—
363C22#1062309914yes—
364C22#1062311214yes—
365C22C22×Dic11⋊C411yescharacteristic
366C22#1062332212yes—
367C22#1062333611yescharacteristic
368C22#1062334711yescharacteristic
369C22#1062336312yes—
370C4—24no—
371C4—24no—
372C4—24no—
373C4—48no—
374C4—228no—
375C4—444no—
376C4—882no—
377C4—882no—
378C2#1307101911yescharacteristic
379C2#1307109911yescharacteristic
380C2#1307124011yescharacteristic
381C2#1307147912yes—
382C2#1307151012yes—
383C2#1307423712yes—
384C2#1307424812yes—
385C2#1307425912yes—
386C2#1307426812yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C4×C11×C4⋊C4C2
socle, prime radical, cosocleC24×C11C24
hypercenterC2×C4×C4⋊C4D11
hypocenterC11#13952
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
27. #10622545C4semidirect
106. C42×C11C4⋊C4semidirect
300. C42Dic11⋊C4semidirect
301. C11#13952semidirect

Maximal subgroups

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

subgroupindex
C2×#106225502
C2×#106225452
#130668792
#130668752
#130668492
Dic11⋊#952
#130668422
C2×C4×C11×C4⋊C42
#1395211