Finite Group Databasebeta

← #14960200

Subgroups — #14960200

Order 2816.

1778 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076880C212yesmaximal
2#13076878C214yesmaximal, complemented
3#13076877C218yesmaximal, complemented
4#13076869C211yesmaximal, characteristic
5#13071891C218yesmaximal, complemented
6#13071885C214yesmaximal, complemented
7#13070994C211yesmaximal, characteristic
8#13070994C212yesmaximal
9C11×#2842C211yesmaximal, characteristic
10C24×Dic11C2211yescharacteristic
11C2×#66940C2214yescomplemented
12C2×#66930C2212yes—
13C2×#66930C2214yes—
14C11×#399C2214yes—
15C11×#396C2218yes—
16C11×#379C2211yescharacteristic
17C11×#379C2212yes—
18#10622860C2212yes—
19#10622860C2211yescharacteristic
20#10622597C2218yescomplemented
21#10622596C2218yescomplemented
22#10622595C2214yescomplemented
23#10622593C2218yescomplemented
24#10622592C2218yescomplemented
25C4⋊C4×Dic11C2218yescomplemented
26#10622562C2218yes—
27#10622561C2218yes—
28#10622561C2218yes—
29#10622560C2214yes—
30#10622560C2218yes—
31#10622556C2214yes—
32#10622556C2212yes—
33#10622555C2214yes—
34#10622555C2214yes—
35#10622555C2214yes—
36C22⋊C4×Dic11C2214yes—
37C22⋊C4×Dic11C2214yes—
38C22⋊C4×Dic11C2214yes—
39#10622271C2218yescomplemented
40#10622269C2214yescomplemented
41#10622262C2214yescomplemented
42C25×C11C2311yescharacteristic
43C23×Dic11—44no—
44C23×Dic11Q818yescomplemented
45C23×Dic11C2311yescharacteristic
46C23×Dic11C2312yes—
47C23×Dic11C2312yes—
48C23×Dic11C2311yescharacteristic
49C22×Dic22C2314yes—
50C2×C11×C4⋊C4C2314yes—
51C2×C11×C4⋊C4C2318yes—
52C2×C11×C22⋊C4C2312yes—
53C2×C11×C22⋊C4C2314yes—
54C2×C11×C22⋊C4C2314yes—
55C2×C11×C22⋊C4C2314yes—
56C2×C11×C22⋊C4C2314yes—
57C2×C22⋊Dic11C2314yes—
58C2×C22⋊Dic11C2312yes—
59C2×C22⋊Dic11C2314yes—
60C2×C22⋊Dic11C2314yes—
61C2×C22⋊Dic11C2314yes—
62C2×C4⋊Dic11C2318yes—
63C2×Dic11⋊C4C2314yes—
64C2×Dic11⋊C4C2318yes—
65C2×Dic11⋊C4C2318yes—
66C2×Dic11⋊C4C2318yes—
67C2×C4×Dic11C2318yes—
68C2×C4×Dic11C2314yes—
69#66940—48no—
70#66930—44no—
71#66930—48no—
72C11×#95C2314yes—
73C11⋊#95C2314yes—
74C11⋊#95C2318yes—
75C11⋊#95C2318yes—
76C11⋊#95C2318yes—
77C11⋊#95C2318yes—
78C11⋊#95C2318yes—
79#36674—111nomaximal, Sylow
80C24×C11—42no—
81C24×C11—44no—
82C24×C11C2×Q814yes—
83C24×C11C2412yes—
84C24×C11C2411yescharacteristic
85C22×C4×C11C2414yes—
86C22×C4×C11C2418yes—
87C22×Dic11—24no—
88C22×Dic11—28no—
89C22×Dic11—44no—
90C22×Dic11—42no—
91C22×Dic11—416no—
92C22×Dic11C2×Q814yes—
93C22×Dic11C2×Q818yes—
94C22×Dic11C2×Q818yes—
95C22×Dic11C2×Q814yes—
96C22×Dic11C2418yes—
97C22×Dic11C2414yes—
98C22×Dic11C2411yescharacteristic
99C22×Dic11C2412yes—
100C22×Dic11C2411yescharacteristic
101C2×Dic22—44no—
102C2×Dic22—48no—
103C11×C4⋊C4—44no—
104C11×C4⋊C4—48no—
105C11×C22⋊C4—44no—
106C11×C22⋊C4—42no—
107C11×C22⋊C4—44no—
108C11×C22⋊C4—44no—
109C11×C22⋊C4—44no—
110C22⋊Dic11—42no—
111C22⋊Dic11—44no—
112C22⋊Dic11—44no—
113C22⋊Dic11—44no—
114C22⋊Dic11—44no—
115C4⋊Dic11—48no—
116Dic11⋊C4—48no—
117Dic11⋊C4—44no—
118Dic11⋊C4—48no—
119Dic11⋊C4—48no—
120C4×Dic11—216no—
121C4×Dic11—28no—
122#2842—112no—
123#2842D1111yescharacteristic
124#2841—114no—
125#2841—118no—
126#2840—111no—
127#2396—114no—
128#2396—118no—
129#2280—112no—
130#2280—111no—
131C23×C11—22no—
132C23×C11—24no—
133C23×C11—24no—
134C23×C11—24no—
135C23×C11—24no—
136C23×C11—44no—
137C23×C11—48no—
138C23×C11—416no—
139C23×C11C22×Q814yes—
140C23×C11C22×Q812yes—
141C23×C11C2511yescharacteristic
142C2×C4×C11—28no—
143C2×C4×C11—24no—
144C2×C4×C11—28no—
145C2×C4×C11—28no—
146C2×C4×C11—28no—
147C2×Dic11—24no—
148C2×Dic11—22no—
149C2×Dic11—28no—
150C2×Dic11—216no—
151C2×Dic11—24no—
152C2×Dic11—28no—
153C2×Dic11—28no—
154C2×Dic11—28no—
155C2×Dic11—28no—
156C2×Dic11—48no—
157C2×Dic11—44no—
158C2×Dic11C22×Q812yes—
159C2×Dic11C22×Q814yes—
160C2×Dic11C22×Q812yes—
161C2×Dic11H(5,𝔽2)14yes—
162Dic22—416no—
163C24×C4—111no—
164C2×C4×Q8—114no—
165C2×#117—114no—
166C2×#117—112no—
167#400—114no—
168#400—118no—
169#399—118no—
170#399C2×D1114yes—
171#398—118no—
172#398—118no—
173#398—118no—
174#396—118no—
175#396—118no—
176#396C2×D1118yes—
177#395—118no—
178#395—114no—
179#393—118no—
180#393—114no—
181#381—114no—
182#381—112no—
183#380—114no—
184#380—114no—
185#380—114no—
186#379—112no—
187#379—111no—
188#379C2×D1111yescharacteristic
189#379C2×D1112yes—
190C4×C4⋊C4—118no—
191C4×C4⋊C4—114no—
192C4×C22⋊C4—114no—
193C4×C22⋊C4—114no—
194C4×C22⋊C4—114no—
195C22×C11—22no—
196C22×C11—24no—
197C22×C11—24no—
198C22×C11—24no—
199C22×C11—24no—
200C22×C11—416no—
201C22×C11—44no—
202C22×C11—48no—
203C22×C11C23×Q811yescharacteristic
204C22×C11C2×H(5,𝔽2)12yes—
205C22×C11#58514yes—
206C4×C11—48no—
207C4×C11—44no—
208Dic11—24no—
209Dic11—22no—
210Dic11—48no—
211Dic11—44no—
212Dic11#54314yes—
213C25C22×D1111yescharacteristic
214C22×Q8—114no—
215C23×C4—112no—
216C23×C4—111no—
217C23×C4—118no—
218C23×C4—112no—
219C23×C4—111no—
220C23×C4—444no—
221C4×Q8—448no—
222#117—448no—
223#117—444no—
224C2×C4⋊C4—118no—
225C2×C4⋊C4—114no—
226C2×C4⋊C4—118no—
227C2×C4⋊C4—118no—
228C2×C4⋊C4—118no—
229C2×C4⋊C4C22×D1114yes—
230C2×C4⋊C4C22×D1118yes—
231C2×C22⋊C4—114no—
232C2×C22⋊C4—112no—
233C2×C22⋊C4—114no—
234C2×C22⋊C4—114no—
235C2×C22⋊C4—114no—
236C2×C22⋊C4C22×D1112yes—
237C2×C22⋊C4C22×D1114yes—
238C2×C22⋊C4C22×D1114yes—
239C2×C22⋊C4C22×D1114yes—
240C2×C22⋊C4C22×D1114yes—
241C2×C42—118no—
242C2×C42—114no—
243#95—118no—
244#95—118no—
245#95—118no—
246#95—114no—
247#95—118no—
248#95—118no—
249#95C22×D1114yes—
250C2×C11—42no—
251C2×C11—44no—
252C2×C11C2×#54311yescharacteristic
253C2×C11#345812yes—
254C2×C11#352914yes—
255C24—42no—
256C24—44no—
257C24Q8×D1114yes—
258C24C23×D1112yes—
259C24C23×D1111yescharacteristic
260C2×Q8—444no—
261C2×Q8—448no—
262C22×C4—111no—
263C22×C4—118no—
264C22×C4—114no—
265C22×C4—111no—
266C22×C4—112no—
267C22×C4—118no—
268C22×C4—114no—
269C22×C4—118no—
270C22×C4—114no—
271C22×C4—228no—
272C22×C4—224no—
273C22×C4—4416no—
274C22×C4—442no—
275C22×C4—444no—
276C22×C4C23×D1114yes—
277C22×C4C23×D1118yes—
278C4⋊C4—44no—
279C4⋊C4—48no—
280C4⋊C4—448no—
281C4⋊C4—444no—
282C4⋊C4—448no—
283C4⋊C4—448no—
284C4⋊C4—448no—
285C22⋊C4—44no—
286C22⋊C4—42no—
287C22⋊C4—44no—
288C22⋊C4—44no—
289C22⋊C4—44no—
290C22⋊C4—442no—
291C22⋊C4—444no—
292C22⋊C4—444no—
293C22⋊C4—444no—
294C22⋊C4—444no—
295C42—2216no—
296C42—228no—
297C11#3667411yescharacteristic, complemented, Sylow
298C23—24no—
299C23—22no—
300C23—24no—
301C23—24no—
302C23—24no—
303C23—44no—
304C23—48no—
305C23—416no—
306C23C2×Q8×D1114yes—
307C23C2×Q8×D1112yes—
308C23C24×D1111yescharacteristic
309Q8—4416no—
310C2×C4—28no—
311C2×C4—24no—
312C2×C4—28no—
313C2×C4—28no—
314C2×C4—28no—
315C2×C4—112no—
316C2×C4—114no—
317C2×C4—112no—
318C2×C4—114no—
319C2×C4—2216no—
320C2×C4—228no—
321C2×C4—224no—
322C2×C4—222no—
323C2×C4—224no—
324C2×C4—228no—
325C2×C4—228no—
326C2×C4—228no—
327C2×C4—228no—
328C2×C4—444no—
329C2×C4—448no—
330C22—24no—
331C22—22no—
332C22—24no—
333C22—24no—
334C22—24no—
335C22—416no—
336C22—48no—
337C22—44no—
338C22C22×Q8×D1111yescharacteristic
339C22D11×H(5,𝔽2)12yes—
340C22#1062345514yes—
341C4—44no—
342C4—48no—
343C4—114no—
344C4—224no—
345C4—222no—
346C4—448no—
347C4—444no—
348C2—44no—
349C2—42no—
350C2D11×#54311yescharacteristic
351C2#1308201812yes—
352C2#1308275114yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2842C2
prime radicalC25×C11C23
hypercenter#2842D11
hypocenterC11#36674
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2842

Complements

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

NH ≅ G/Ntype
2. #13076878C2semidirect
3. #13076877C2semidirect
5. #13071891C2semidirect
6. #13071885C2semidirect
11. C2×#66940C22semidirect
20. #10622597C22semidirect
21. #10622596C22semidirect
22. #10622595C22semidirect
23. #10622593C22semidirect
24. #10622592C22semidirect
25. C4⋊C4×Dic11C22semidirect
39. #10622271C22semidirect
40. #10622269C22semidirect
41. #10622262C22semidirect
44. C23×Dic11Q8semidirect
297. C11#36674semidirect

Maximal subgroups

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

subgroupindex
#130768802
#130768782
#130768772
#130768692
#130718912
#130718852
#130709942
C11×#28422
#3667411