Finite Group Databasebeta

← #14913824

Subgroups — #14913824

Order 2816.

2446 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66979C211yesmaximal, characteristic
2#13071478C218yesmaximal, complemented
3#13071472C218yesmaximal, complemented
4#13071228C212yesmaximal
5#13071217C214yesmaximal, complemented
6#13071007C214yesmaximal, complemented
7C2×#10622824C211yesmaximal, characteristic
8#13070969C212yesmaximal
9C2×C11×#381C211yesmaximal, characteristic
10C24×C4×C11C2211yescharacteristic
11C22×C11×C22⋊C4C2212yes—
12C22×C22⋊Dic11C2212yes—
13C22×C22⋊Dic11C2211yescharacteristic
14C22×C22⋊Dic11C2211yescharacteristic
15C2×#66979C4116yescomplemented
16C2×#66979C2214yes—
17C2×#66979C2214yes—
18C22×C4⋊Dic11C2212yes—
19C22×C4×Dic11C2212yes—
20C11×#381C2212yes—
21C11×#381C2214yes—
22C11×#381C2212yes—
23C2×C11×#95C2214yes—
24#10622824C2214yes—
25#10622824C2212yes—
26#10622824C2212yes—
27#10622823C2218yes—
28C4×C22⋊Dic11C2218yes—
29C2×C11⋊#95C2214yes—
30#10622559C2218yes—
31#10622555C2218yes—
32C22⋊C4×Dic11C2218yes—
33C22⋊C4×Dic11C2218yes—
34#10622267C22116yescomplemented
35#10622266C22116yescomplemented
36#10622264C2218yescomplemented
37#10622263C2218yescomplemented
38#10622262C2218yescomplemented
39#10622261C2218yescomplemented
40C25×C11C2311yescharacteristic
41C23×C4×C11—28no—
42C23×C4×C11C2×C418yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2312yes—
46C23×C4×C11C2312yes—
47C23×C4×C11C2314yes—
48C23×Dic11C2314yes—
49C23×Dic11C2312yes—
50C23×Dic11C2312yes—
51C2×C11×C22⋊C4—28no—
52C2×C11×C22⋊C4C2314yes—
53C2×C11×C22⋊C4C2314yes—
54C2×C22⋊Dic11—28no—
55C2×C22⋊Dic11C2×C418yes—
56C2×C22⋊Dic11C2×C418yes—
57C2×C22⋊Dic11C2314yes—
58C2×C22⋊Dic11C2314yes—
59C2×C22⋊Dic11C2312yes—
60C2×C22⋊Dic11C2312yes—
61C2×C22⋊Dic11C2312yes—
62C2×C22⋊Dic11C2312yes—
63#66979C2×C4132yescomplemented
64#66979C2×C4132yescomplemented
65C2×C4⋊Dic11C2×C4116yescomplemented
66C2×C4⋊Dic11C2314yes—
67C2×C4⋊Dic11C2314yes—
68C2×Dic11⋊C4C23116yes—
69C2×C4×Dic11C2×C4116yescomplemented
70C2×C4×Dic11C23116yes—
71C2×C4×Dic11C2314yes—
72C2×C4×Dic11C2314yes—
73C11×#95C2318yes—
74C11×#95C2318yes—
75C11⋊#95C2318yes—
76C11⋊#95C23116yes—
77C11⋊#95C23116yes—
78C11⋊#95C2318yes—
79#34177—111nomaximal, Sylow
80C24×C11—44no—
81C24×C11C22×C414yes—
82C24×C11#4118yes—
83C24×C11C2411yescharacteristic
84C24×C11C2411yescharacteristic
85C24×C11C2411yescharacteristic
86C22×C4×C11—232no—
87C22×C4×C11—24no—
88C22×C4×C11—24no—
89C22×C4×C11—28no—
90C22×C4×C11—28no—
91C22×C4×C11—28no—
92C22×C4×C11—48no—
93C22×C4×C11C22×C414yes—
94C22×C4×C11C22×C414yes—
95C22×C4×C11C22×C418yes—
96C22×C4×C11C22×C418yes—
97C22×C4×C11C2418yes—
98C22×C4×C11C2412yes—
99C22×C4×C11C2412yes—
100C22×Dic11—28no—
101C22×Dic11—44no—
102C22×Dic11—44no—
103C22×Dic11—48no—
104C22×Dic11C22×C418yes—
105C22×Dic11C22×C418yes—
106C22×Dic11C2418yes—
107C22×Dic11C2414yes—
108C22×Dic11C2414yes—
109C11×C22⋊C4—28no—
110C11×C22⋊C4—28no—
111C22⋊Dic11—28no—
112C22⋊Dic11—28no—
113C22⋊Dic11C22×C418yes—
114C22⋊Dic11C22×C418yes—
115C22⋊Dic11C22×C418yes—
116C22⋊Dic11C22×C418yes—
117C4⋊Dic11C22×C4116yes—
118C4⋊Dic11C22×C4116yes—
119Dic11⋊C4—416no—
120C4×Dic11—416no—
121C4×Dic11C22×C4116yes—
122C4×Dic11C22×C4116yes—
123C22×#117—111no—
124#2343—118no—
125#2343—118no—
126#2315—112no—
127#2313—114no—
128#2283—114no—
129C2×#381—111no—
130C2×#381D1111yescharacteristic
131#2273—112no—
132C23×C11—24no—
133C23×C11—24no—
134C23×C11—24no—
135C23×C11—48no—
136C23×C11—416no—
137C23×C11#117116yes—
138C23×C11C23×C412yes—
139C23×C11C23×C412yes—
140C23×C11C23×C412yes—
141C23×C11C2×#4114yes—
142C23×C11C2×#4114yes—
143C23×C11C2×#4114yes—
144C23×C11C2511yescharacteristic
145C2×C4×C11—28no—
146C2×C4×C11—28no—
147C2×C4×C11—216no—
148C2×C4×C11—216no—
149C2×C4×C11—24no—
150C2×C4×C11—24no—
151C2×C4×C11—28no—
152C2×C4×C11—216no—
153C2×C4×C11—88no—
154C2×C4×C11C23×C414yes—
155C2×C4×C11C23×C414yes—
156C2×Dic11—28no—
157C2×Dic11—28no—
158C2×Dic11—28no—
159C2×Dic11—216no—
160C2×Dic11—48no—
161C2×Dic11—48no—
162C2×Dic11—88no—
163C2×Dic11C23×C418yes—
164C2×Dic11C23×C418yes—
165C24×C4C2×D1111yescharacteristic
166C2×#117—114no—
167C2×#117—114no—
168C2×#117—1116no—
169C22×C4⋊C4—112no—
170C22×C22⋊C4—111no—
171C22×C22⋊C4—111no—
172C22×C22⋊C4—112no—
173C22×C22⋊C4C2×D1112yes—
174C22×C42—112no—
175#387—1116no—
176#387—1116no—
177#385—118no—
178#385—118no—
179#383—118no—
180#382—118no—
181#381—112no—
182#381—114no—
183#381—112no—
184#381C2×D1112yes—
185#381C2×D1114yes—
186#381C2×D1112yes—
187#380—118no—
188C4×C4⋊C4—118no—
189C4×C22⋊C4—118no—
190C4×C22⋊C4—118no—
191C4×C22⋊C4—118no—
192#376—118no—
193C2×#95—114no—
194C2×#95C2×D1114yes—
195C22×C11—24no—
196C22×C11—24no—
197C22×C11—24no—
198C22×C11—28no—
199C22×C11—28no—
200C22×C11—28no—
201C22×C11—416no—
202C22×C11C2×#11714yes—
203C22×C11C2×#11714yes—
204C22×C11C2×#11714yes—
205C22×C11C24×C411yescharacteristic
206C22×C11C22×#4112yes—
207C22×C11#58514yes—
208C4×C11—24no—
209C4×C11—24no—
210C4×C11—48no—
211Dic11—28no—
212Dic11—28no—
213Dic11—48no—
214C25C22×D1111yescharacteristic
215C23×C4—28no—
216C23×C4—112no—
217C23×C4—112no—
218C23×C4—114no—
219C23×C4C4×D1118yes—
220C23×C4C22×D1111yescharacteristic
221C23×C4C22×D1112yes—
222C23×C4C22×D1112yes—
223C23×C4C22×D1111yescharacteristic
224C23×C4C22×D1114yes—
225#117—1132no—
226#117—1132no—
227C2×C4⋊C4—1116no—
228C2×C4⋊C4—114no—
229C2×C4⋊C4—114no—
230C2×C4⋊C4—1116no—
231C2×C22⋊C4—28no—
232C2×C22⋊C4—118no—
233C2×C22⋊C4—118no—
234C2×C22⋊C4—112no—
235C2×C22⋊C4—112no—
236C2×C22⋊C4—112no—
237C2×C22⋊C4—112no—
238C2×C22⋊C4—114no—
239C2×C22⋊C4—114no—
240C2×C22⋊C4—228no—
241C2×C22⋊C4C22×D1114yes—
242C2×C22⋊C4C22×D1114yes—
243C2×C42—1116no—
244C2×C42—114no—
245C2×C42—114no—
246C2×C42—1116no—
247#95—118no—
248#95—118no—
249#95—1116no—
250#95—1116no—
251#95C22×D1118yes—
252#95C22×D1118yes—
253C2×C11—24no—
254C2×C11—24no—
255C2×C11—24no—
256C2×C11C22×#11711yescharacteristic
257C2×C11#342812yes—
258C2×C11#349114yes—
259C24—44no—
260C24C2×C4×D1114yes—
261C24#434118yes—
262C24C23×D1111yescharacteristic
263C24C23×D1111yescharacteristic
264C24C23×D1111yescharacteristic
265C22×C4—232no—
266C22×C4—24no—
267C22×C4—24no—
268C22×C4—28no—
269C22×C4—28no—
270C22×C4—28no—
271C22×C4—48no—
272C22×C4—114no—
273C22×C4—114no—
274C22×C4—118no—
275C22×C4—118no—
276C22×C4—118no—
277C22×C4—228no—
278C22×C4—444no—
279C22×C4—444no—
280C22×C4—448no—
281C22×C4C2×C4×D1114yes—
282C22×C4C2×C4×D1114yes—
283C22×C4C2×C4×D1118yes—
284C22×C4C2×C4×D1118yes—
285C22×C4C23×D1118yes—
286C22×C4C23×D1112yes—
287C22×C4C23×D1112yes—
288C4⋊C4—1116no—
289C4⋊C4—1116no—
290C4⋊C4—4416no—
291C22⋊C4—28no—
292C22⋊C4—28no—
293C22⋊C4—118no—
294C22⋊C4—118no—
295C22⋊C4—118no—
296C22⋊C4—118no—
297C22⋊C4—228no—
298C22⋊C4—228no—
299C42—1116no—
300C42—1116no—
301C42—4416no—
302C11#3417711yescharacteristic, complemented, Sylow
303C23—24no—
304C23—24no—
305C23—24no—
306C23—48no—
307C23—416no—
308C23#66930116yes—
309C23C22×C4×D1112yes—
310C23C22×C4×D1112yes—
311C23C22×C4×D1112yes—
312C23C2×#434114yes—
313C23C2×#434114yes—
314C23C2×#434114yes—
315C23C24×D1111yescharacteristic
316C2×C4—28no—
317C2×C4—28no—
318C2×C4—216no—
319C2×C4—216no—
320C2×C4—24no—
321C2×C4—24no—
322C2×C4—28no—
323C2×C4—216no—
324C2×C4—88no—
325C2×C4—118no—
326C2×C4—118no—
327C2×C4—228no—
328C2×C4—228no—
329C2×C4—228no—
330C2×C4—2216no—
331C2×C4—448no—
332C2×C4—448no—
333C2×C4—888no—
334C2×C4C22×C4×D1114yes—
335C2×C4C22×C4×D1114yes—
336C22—28no—
337C22—28no—
338C22—28no—
339C22—24no—
340C22—24no—
341C22—24no—
342C22—416no—
343C22C2×#6693014yes—
344C22C2×#6693014yes—
345C22C2×#6693014yes—
346C22C23×C4×D1111yescharacteristic
347C22C22×#434112yes—
348C22#1062345314yes—
349C4—24no—
350C4—24no—
351C4—48no—
352C4—228no—
353C4—228no—
354C4—448no—
355C2—24no—
356C2—24no—
357C2—24no—
358C2C22×#6693011yescharacteristic
359C2#1308181712yes—
360C2#1308231214yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC2×C11×#381C2
socle, cosocleC23×C11C25
prime radicalC25×C11C23
hypercenterC2×#381D11
hypocenterC11#34177
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
2. #13071478C2semidirect
3. #13071472C2semidirect
5. #13071217C2semidirect
6. #13071007C2semidirect
15. C2×#66979C4semidirect
34. #10622267C22semidirect
35. #10622266C22semidirect
36. #10622264C22semidirect
37. #10622263C22semidirect
38. #10622262C22semidirect
39. #10622261C22semidirect
63. #66979C2×C4semidirect
64. #66979C2×C4semidirect
65. C2×C4⋊Dic11C2×C4semidirect
69. C2×C4×Dic11C2×C4semidirect
302. C11#34177semidirect

Maximal subgroups

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

subgroupindex
C22×#669792
#130714782
#130714722
#130712282
#130712172
#130710072
C2×#106228242
#130709692
C2×C11×#3812
#3417711