Finite Group Databasebeta

← #14684795

Subgroups — #14684795

Order 2816.

1898 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66939C211yesmaximal, characteristic
2C2×#10622555C212yesmaximal, complemented
3#13066868C214yesmaximal, complemented
4#13066865C211yesmaximal, characteristic, complemented
5#13066860C214yesmaximal, complemented
6#13066855C212yesmaximal
7C11×#1440C211yesmaximal, characteristic, complemented
8C23×C22⋊D11C2211yescharacteristic
9C24×Dic11C2211yescharacteristic
10C22×C11×C22⋊C4C2211yescharacteristic
11C22×C11×C22⋊C4C2212yes—
12C22×C22⋊Dic11C2212yes—
13C22×(C2×D11)⋊C4C2212yes—
14C22×(C2×D11)⋊C4C2214yes—
15C22×C4⋊Dic11C2212yes—
16C22×Dic11⋊C4C2214yes—
17C2×#66939—28no—
18C2×#66939C418yescomplemented
19C2×C11×#95C2214yes—
20C2×C11⋊#95C2214yes—
21C2×C11⋊#95C2214yes—
22C2×C11⋊#95C2214yes—
23#10622555—28no—
24C25×C11C2311yescharacteristic
25C24×D11C2311yescharacteristic
26C23×C4×C11C2314yes—
27C23×C4×C11C2312yes—
28C22×C22⋊D11—24no—
29C22×C22⋊D11—44no—
30C22×C22⋊D11C2×C414yes—
31C23×Dic11—44no—
32C23×Dic11C2×C414yes—
33C23×Dic11D418yes—
34C23×Dic11C2314yes—
35C23×Dic11C2311yescharacteristic
36C23×Dic11C2312yes—
37C2×C11×C22⋊C4—24no—
38C2×C11×C22⋊C4—24no—
39C2×C11×C22⋊C4—44no—
40C2×C11×C22⋊C4C2×C414yes—
41C2×C22⋊Dic11—24no—
42C2×C22⋊Dic11—44no—
43C2×(C2×D11)⋊C4—24no—
44C2×(C2×D11)⋊C4—24no—
45C2×(C2×D11)⋊C4—44no—
46C2×(C2×D11)⋊C4—44no—
47C2×(C2×D11)⋊C4—44no—
48C2×(C2×D11)⋊C4C2×C418yes—
49C2×C4⋊Dic11—24no—
50C2×C4⋊Dic11—24no—
51C2×C4⋊Dic11C2×C418yes—
52C2×Dic11⋊C4—28no—
53C2×Dic11⋊C4—44no—
54C2×Dic11⋊C4—44no—
55#66939—232no—
56C11×#95—44no—
57C11⋊#95—28no—
58C11⋊#95—44no—
59C11⋊#95—44no—
60#14658—111nomaximal, Sylow
61C24×C11—24no—
62C24×C11—24no—
63C24×C11—24no—
64C24×C11C22×C412yes—
65C24×C11C2×D414yes—
66C24×C11C2411yescharacteristic
67C23×D11—22no—
68C23×D11—24no—
69C23×D11—24no—
70C23×D11—24no—
71C23×D11C22×C412yes—
72C22×C4×C11—22no—
73C22×C4×C11—22no—
74C22×C4×C11—24no—
75C22×C4×C11—24no—
76C22×C4×C11—24no—
77C22×C4×C11—24no—
78C22×C4×C11—24no—
79C22×C4×C11—24no—
80C22×C4×C11—24no—
81C22×C4×C11—24no—
82C22×C4×C11—24no—
83C22×C4×C11C22×C414yes—
84C2×C22⋊D11—28no—
85C2×C22⋊D11—48no—
86C2×C22⋊D11—416no—
87C22×Dic11—22no—
88C22×Dic11—24no—
89C22×Dic11—24no—
90C22×Dic11—24no—
91C22×Dic11—24no—
92C22×Dic11—24no—
93C22×Dic11—24no—
94C22×Dic11—24no—
95C22×Dic11—24no—
96C22×Dic11—24no—
97C22×Dic11—24no—
98C22×Dic11—48no—
99C22×Dic11—416no—
100C22×Dic11C22⋊C4116yescomplemented
101C22×Dic11C22×C412yes—
102C22×Dic11C22×C414yes—
103C22×Dic11C2×D414yes—
104C22×Dic11C2×D414yes—
105C11×C22⋊C4—28no—
106C11×C22⋊C4—48no—
107C22⋊Dic11—48no—
108(C2×D11)⋊C4—216no—
109(C2×D11)⋊C4—416no—
110C4⋊Dic11—216no—
111Dic11⋊C4—416no—
112C22×#123—111no—
113C2×#380—112no—
114#1441—114no—
115#1440—111no—
116#1440D1111yescharacteristic, complemented
117#1439—114no—
118#1438—112no—
119C23×C11—24no—
120C23×C11—28no—
121C23×C11—28no—
122C23×C11—24no—
123C23×C11—24no—
124C23×C11—28no—
125C23×C11—44no—
126C23×C11—44no—
127C23×C11—44no—
128C23×C11—44no—
129C23×C11C2×C22⋊C414yes—
130C23×C11C23×C411yescharacteristic
131C23×C11C22×D412yes—
132C23×C11H(5,𝔽2)14yes—
133C23×C11H(5,𝔽2)14yes—
134C23×C112−1+414yes—
135C22×D11—22no—
136C22×D11—24no—
137C22×D11—28no—
138C22×D11—44no—
139C22×D11—42no—
140C22×D11—42no—
141C22×D11—44no—
142C22×D11—44no—
143C22×D11—44no—
144C22×D11—44no—
145C22×D11—44no—
146C2×C4×C11—24no—
147C2×C4×C11—28no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—44no—
151C2×C4×C11—44no—
152C2×C4×C11—44no—
153C2×C4×C11—44no—
154C2×C4×C11—44no—
155C2×C4×C11—44no—
156C2×C4×C11—44no—
157C2×C4×C11—44no—
158C22⋊D11—416no—
159C2×Dic11—24no—
160C2×Dic11—24no—
161C2×Dic11—28no—
162C2×Dic11—28no—
163C2×Dic11—22no—
164C2×Dic11—24no—
165C2×Dic11—416no—
166C2×Dic11—44no—
167C2×Dic11—44no—
168C2×Dic11—44no—
169C2×Dic11—44no—
170C2×Dic11—44no—
171C2×Dic11—44no—
172C2×Dic11—44no—
173C2×Dic11—44no—
174C2×Dic11C2×C22⋊C418yes—
175C23×D4—111no—
176C24×C4—111no—
177C2×#123—118no—
178C2×#123—228no—
179C22×C4⋊C4—112no—
180C22×C4⋊C4—114no—
181C22×C22⋊C4—112no—
182C22×C22⋊C4—112no—
183C22×C22⋊C4—114no—
184C22×C22⋊C4C2×D1111yescharacteristic
185C22×C22⋊C4C2×D1112yes—
186#380—228no—
187C2×#95—114no—
188C2×#95—114no—
189C2×#95—114no—
190C2×#95C2×D1114yes—
191C22×C11—24no—
192C22×C11—28no—
193C22×C11—48no—
194C22×C11—48no—
195C22×C11—48no—
196C22×C11C22×C22⋊C411yescharacteristic
197C22×C11#51812yes—
198C22×C11#52014yes—
199C22×C11#53414yes—
200C22×C11#53512yes—
201C22×C11#53612yes—
202C22×C11#53714yes—
203C22×C11#56014yes—
204C22×C11#56214yes—
205C22×C11#56214yes—
206C22×C11#56314yes—
207C2×D11—42no—
208C2×D11—44no—
209C2×D11—48no—
210C2×D11—84no—
211C2×D11—84no—
212C4×C11—44no—
213C4×C11—84no—
214Dic11—28no—
215Dic11—42no—
216Dic11—84no—
217C25—111no—
218C25C22×D1111yescharacteristic
219C22×D4—114no—
220C22×D4—224no—
221C22×D4—444no—
222C23×C4—112no—
223C23×C4—114no—
224C23×C4—118no—
225C23×C4—111no—
226C23×C4—114no—
227C23×C4—444no—
228C23×C4C22×D1114yes—
229C23×C4C22×D1112yes—
230#123—2232no—
231C2×C4⋊C4—118no—
232C2×C4⋊C4—224no—
233C2×C4⋊C4—224no—
234C2×C4⋊C4—228no—
235C2×C4⋊C4—444no—
236C2×C4⋊C4—444no—
237C2×C22⋊C4—24no—
238C2×C22⋊C4—24no—
239C2×C22⋊C4—44no—
240C2×C22⋊C4—118no—
241C2×C22⋊C4—224no—
242C2×C22⋊C4—224no—
243C2×C22⋊C4—224no—
244C2×C22⋊C4—444no—
245C2×C22⋊C4—444no—
246C2×C22⋊C4—444no—
247C2×C22⋊C4—444no—
248C2×C22⋊C4C4×D1114yes—
249#95—44no—
250#95—228no—
251#95—444no—
252#95—444no—
253C2×C11—44no—
254C2×C11#230811yescharacteristic
255C2×C11#231112yes—
256C2×C11#237614yes—
257C2×C11#281314yes—
258C2×C11#281414yes—
259D11—82no—
260C24—24no—
261C24—24no—
262C24—24no—
263C24—112no—
264C24—222no—
265C24—224no—
266C24—224no—
267C24—224no—
268C24C2×C4×D1112yes—
269C24D4×D1114yes—
270C24C23×D1111yescharacteristic
271C2×D4—228no—
272C2×D4—448no—
273C2×D4—4416no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—24no—
277C22×C4—24no—
278C22×C4—24no—
279C22×C4—24no—
280C22×C4—24no—
281C22×C4—24no—
282C22×C4—24no—
283C22×C4—24no—
284C22×C4—24no—
285C22×C4—114no—
286C22×C4—114no—
287C22×C4—114no—
288C22×C4—1116no—
289C22×C4—112no—
290C22×C4—224no—
291C22×C4—224no—
292C22×C4—222no—
293C22×C4—224no—
294C22×C4—224no—
295C22×C4—224no—
296C22×C4—224no—
297C22×C4—224no—
298C22×C4—224no—
299C22×C4—224no—
300C22×C4—224no—
301C22×C4—448no—
302C22×C4—4416no—
303C22×C4C2×C4×D1114yes—
304C4⋊C4—2216no—
305C4⋊C4—4416no—
306C22⋊C4—28no—
307C22⋊C4—48no—
308C22⋊C4—2216no—
309C22⋊C4—4416no—
310C22⋊C4—448no—
311C11#1465811yescharacteristic, complemented, Sylow
312C23—24no—
313C23—28no—
314C23—24no—
315C23—28no—
316C23—24no—
317C23—28no—
318C23—44no—
319C23—44no—
320C23—44no—
321C23—44no—
322C23—222no—
323C23—224no—
324C23—228no—
325C23—444no—
326C23—442no—
327C23—444no—
328C23—444no—
329C23—442no—
330C23—444no—
331C23—444no—
332C23—444no—
333C23C22⋊C4×D1114yes—
334C23C22×C4×D1111yescharacteristic
335C23C2×D4×D1112yes—
336C23#6703714yes—
337C23#6704214yes—
338C23#6704314yes—
339D4—4416no—
340C2×C4—24no—
341C2×C4—28no—
342C2×C4—42no—
343C2×C4—44no—
344C2×C4—42no—
345C2×C4—44no—
346C2×C4—44no—
347C2×C4—44no—
348C2×C4—44no—
349C2×C4—44no—
350C2×C4—44no—
351C2×C4—44no—
352C2×C4—118no—
353C2×C4—224no—
354C2×C4—224no—
355C2×C4—228no—
356C2×C4—228no—
357C2×C4—222no—
358C2×C4—224no—
359C2×C4—4416no—
360C2×C4—444no—
361C2×C4—444no—
362C2×C4—444no—
363C2×C4—444no—
364C2×C4—444no—
365C2×C4—444no—
366C2×C4—444no—
367C2×C4—444no—
368C22—24no—
369C22—28no—
370C22—48no—
371C22—48no—
372C22—48no—
373C22—442no—
374C22—444no—
375C22—448no—
376C22—884no—
377C22—884no—
378C22C2×C22⋊C4×D1111yescharacteristic
379C22#1062305212yes—
380C22#1062307714yes—
381C22#1062312312yes—
382C22#1062312814yes—
383C22#1062315114yes—
384C22#1062317912yes—
385C22#1062318414yes—
386C22#1062319814yes—
387C22#1062321514yes—
388C22#1062324314yes—
389C4—44no—
390C4—84no—
391C4—228no—
392C4—442no—
393C4—884no—
394C2—44no—
395C2—882no—
396C2#1307119311yescharacteristic
397C2#1307120312yes—
398C2#1307176214yes—
399C2#1307662414yes—
400C2#1307663514yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1440C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenter#1440D11
hypocenterC11#14658
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
2. C2×#10622555C2semidirect
3. #13066868C2semidirect
4. #13066865C2semidirect
5. #13066860C2semidirect
7. C11×#1440C2semidirect
18. C2×#66939C4semidirect
100. C22×Dic11C22⋊C4semidirect
116. #1440D11semidirect
311. C11#14658semidirect

Maximal subgroups

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

subgroupindex
C22×#669392
C2×#106225552
#130668682
#130668652
#130668602
#130668552
C11×#14402
#1465811