Finite Group Databasebeta

← #14916635

Subgroups — #14916635

Order 2816.

2410 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071797C212yesmaximal, complemented
2#13071793C212yesmaximal, complemented
3#13071728C214yesmaximal, complemented
4#13071545C218yesmaximal, complemented
5#13071383C218yesmaximal, complemented
6#13071208C214yesmaximal, complemented
7#13071014C212yesmaximal, complemented
8C2×C11×#532C211yesmaximal, characteristic
9C22×C11×#41C2212yes—
10C11×#532C4116yescomplemented
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C11×#127C2211yescharacteristic
13C2×C11×#124C2212yes—
14C2×C11×#121C2214yes—
15C2×C4×D4×C11C2214yes—
16C22×C42×C11C2211yescharacteristic
17C2×#66979C2214yes—
18C22×C4⋊Dic11C2214yes—
19#10622843C2218yes—
20#10622834C2218yes—
21#10622833C2218yes—
22#10622833C22116yes—
23#10622833C2218yes—
24#10622825C2214yes—
25#10622825C2218yes—
26#10622824C2214yes—
27C4×C22⋊Dic11C2214yes—
28#10622594C22116yes—
29#10622564C22116yes—
30C22⋊C4×Dic11C22116yes—
31#10622550C2214yes—
32#10622549C2214yes—
33C4×C4⋊Dic11C2214yes—
34#10622545C2214yes—
35C2×C11×#41—44no—
36C2×C11×#41—44no—
37C2×C11×#41C2×C4116yescomplemented
38C22×Q8×C11C2312yes—
39C22×D4×C11C2314yes—
40C22×D4×C11C2312yes—
41C22×D4×C11C2314yes—
42C23×C4×C11C2314yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2312yes—
45C23×Dic11C2318yes—
46C11×C4⋊Q8C2×C418yescomplemented
47C11×#127C2×C418yes—
48C11×#124C2×C4116yescomplemented
49C11×#121C2×C4132yescomplemented
50C4×D4×C11C2×C4132yescomplemented
51C2×C11×C4⋊C4C2314yes—
52C2×C11×C22⋊C4C2318yes—
53C2×C42×C11C2×C418yescomplemented
54C2×C42×C11C2311yescharacteristic
55C2×C42×C11C2312yes—
56C2×C42×C11C2311yescharacteristic
57C2×C22⋊Dic11C2318yes—
58C2×C22⋊Dic11C23116yes—
59C2×C22⋊Dic11C2318yes—
60#66979—48no—
61C2×C4⋊Dic11—48no—
62C2×C4⋊Dic11C2318yes—
63C2×C4⋊Dic11C2318yes—
64C2×C4×Dic11C2318yes—
65C2×C4×Dic11C2318yes—
66C11⋊#95C2318yes—
67C11⋊#95C2318yes—
68C11⋊#95C2318yes—
69C11⋊#95C2318yes—
70C11⋊#95C23116yes—
71#34369—111nomaximal, Sylow
72C24×C11C2411yescharacteristic
73C24×C11C2414yes—
74C11×#41—432no—
75C2×Q8×C11—42no—
76C2×Q8×C11—42no—
77C2×Q8×C11C22×C418yes—
78C2×D4×C11—44no—
79C2×D4×C11—44no—
80C2×D4×C11—44no—
81C2×D4×C11—44no—
82C2×D4×C11—42no—
83C2×D4×C11—42no—
84C2×D4×C11C22×C4116yes—
85C2×D4×C11C22×C4116yes—
86C2×D4×C11C22×C418yes—
87C22×C4×C11—28no—
88C22×C4×C11—28no—
89C22×C4×C11—24no—
90C22×C4×C11—44no—
91C22×C4×C11C22×C414yes—
92C22×C4×C11C22×C4116yes—
93C22×C4×C11C22×C418yes—
94C22×C4×C11C2412yes—
95C22×C4×C11C2411yescharacteristic
96C22×C4×C11C2412yes—
97C22×C4×C11C2414yes—
98C22×C4×C11C2411yescharacteristic
99C22×Dic11—48no—
100C22×Dic11—416no—
101C22×Dic11C24116yes—
102C11×C4⋊C4C22×C4116yes—
103C11×C22⋊C4C22×C4132yes—
104C42×C11C22×C418yes—
105C42×C11C22×C414yes—
106C42×C11C22×C414yes—
107C22⋊Dic11—48no—
108C22⋊Dic11—48no—
109C22⋊Dic11—416no—
110C4⋊Dic11—216no—
111C4⋊Dic11—48no—
112C4×Dic11—48no—
113C4×Dic11—48no—
114C2×#532D1111yescharacteristic
115#2381—112no—
116#2380—112no—
117#2372—114no—
118#2352—118no—
119#2333—118no—
120#2311—114no—
121#2283—112no—
122C23×C11—24no—
123C23×C11—24no—
124C23×C11—22no—
125C23×C11—24no—
126C23×C11—28no—
127C23×C11—28no—
128C23×C11C23×C418yes—
129C23×C11C23×C412yes—
130C23×C11C2511yescharacteristic
131Q8×C11—48no—
132D4×C11—416no—
133D4×C11—48no—
134D4×C11—416no—
135C2×C4×C11—24no—
136C2×C4×C11—24no—
137C2×C4×C11—22no—
138C2×C4×C11—24no—
139C2×C4×C11—24no—
140C2×C4×C11—232no—
141C2×C4×C11—28no—
142C2×C4×C11—48no—
143C2×C4×C11C23×C414yes—
144C2×C4×C11C23×C414yes—
145C2×C4×C11C23×C412yes—
146C2×C4×C11C23×C418yes—
147C2×C4×C11C23×C412yes—
148C2×C4×C11H(5,𝔽2)14yes—
149C2×Dic11—216no—
150C2×Dic11—216no—
151C2×Dic11—216no—
152C2×Dic11—816no—
153C22×#41C2×D1112yes—
154#532Dic11116yescomplemented
155C2×C4⋊Q8C2×D1111yescharacteristic
156C2×#127C2×D1111yescharacteristic
157C2×#124C2×D1112yes—
158C2×#121C2×D1114yes—
159C2×C4×D4C2×D1114yes—
160C2×#117—114no—
161C22×C4⋊C4—114no—
162C22×C42C2×D1111yescharacteristic
163#391—118no—
164#390—118no—
165#388—1116no—
166#387—1116no—
167#386—118no—
168#386—118no—
169#386—1116no—
170#383—114no—
171#382—114no—
172#381—114no—
173#380—114no—
174#380—118no—
175C4×C4⋊C4—114no—
176C4×C22⋊C4—114no—
177C4×C22⋊C4—1116no—
178#376—114no—
179C22×C11—22no—
180C22×C11—28no—
181C22×C11—24no—
182C22×C11—216no—
183C22×C11—48no—
184C22×C11—44no—
185C22×C11—44no—
186C22×C11—44no—
187C22×C11C24×C411yescharacteristic
188C22×C11C2×H(5,𝔽2)12yes—
189C22×C11#58514yes—
190C4×C11—22no—
191C4×C11—28no—
192C4×C11—24no—
193C4×C11—24no—
194C4×C11#51814yes—
195Dic11—416no—
196C2×#41—44no—
197C2×#41—44no—
198C2×#41C2×Dic11116yescomplemented
199C22×Q8C22×D1112yes—
200C22×D4C22×D1114yes—
201C22×D4C22×D1114yes—
202C22×D4C22×D1112yes—
203C23×C4—118no—
204C23×C4C22×D1114yes—
205C23×C4C22×D1111yescharacteristic
206C23×C4C22×D1112yes—
207C4⋊Q8C2×Dic1118yescomplemented
208#127C2×Dic1118yes—
209#124C2×Dic11116yescomplemented
210#121C2×Dic11132yescomplemented
211C4×D4C2×Dic11132yescomplemented
212#117—448no—
213C2×C4⋊C4—118no—
214C2×C4⋊C4—118no—
215C2×C4⋊C4—448no—
216C2×C4⋊C4C22×D1114yes—
217C2×C22⋊C4—118no—
218C2×C22⋊C4—118no—
219C2×C22⋊C4—1116no—
220C2×C22⋊C4C22×D1118yes—
221C2×C42—118no—
222C2×C42—118no—
223C2×C42C2×Dic1118yescomplemented
224C2×C42C22×D1112yes—
225C2×C42C22×D1111yescharacteristic
226C2×C42C22×D1111yescharacteristic
227#95—118no—
228#95—118no—
229#95—1116no—
230#95—118no—
231#95—118no—
232C2×C11—42no—
233C2×C11—48no—
234C2×C11C2×#51811yescharacteristic
235C2×C11#342812yes—
236C2×C11#355114yes—
237C24C23×D1111yescharacteristic
238C24C23×D1114yes—
239#41—432no—
240C2×Q8—42no—
241C2×Q8—42no—
242C2×Q8C22×Dic1118yes—
243C2×D4—44no—
244C2×D4—44no—
245C2×D4—42no—
246C2×D4—42no—
247C2×D4—44no—
248C2×D4—44no—
249C2×D4C22×Dic11116yes—
250C2×D4C22×Dic11116yes—
251C2×D4C22×Dic1118yes—
252C22×C4—28no—
253C22×C4—28no—
254C22×C4—24no—
255C22×C4—44no—
256C22×C4—1116no—
257C22×C4—448no—
258C22×C4—4416no—
259C22×C4C22×Dic1114yes—
260C22×C4C22×Dic11116yes—
261C22×C4C22×Dic1118yes—
262C22×C4C23×D1112yes—
263C22×C4C23×D1111yescharacteristic
264C22×C4C23×D1112yes—
265C22×C4C23×D1114yes—
266C22×C4C23×D1111yescharacteristic
267C4⋊C4—2216no—
268C4⋊C4—448no—
269C4⋊C4C22×Dic11116yes—
270C22⋊C4—448no—
271C22⋊C4—4416no—
272C22⋊C4—448no—
273C22⋊C4C22×Dic11132yes—
274C42—448no—
275C42—448no—
276C42C22×Dic1118yes—
277C42C22×Dic1114yes—
278C42C22×Dic1114yes—
279C11#3436911yescharacteristic, complemented, Sylow
280C23—24no—
281C23—24no—
282C23—22no—
283C23—24no—
284C23—28no—
285C23—28no—
286C23C23×Dic1118yes—
287C23C23×Dic1112yes—
288C23C24×D1111yescharacteristic
289Q8—48no—
290D4—416no—
291D4—48no—
292D4—416no—
293C2×C4—24no—
294C2×C4—24no—
295C2×C4—22no—
296C2×C4—24no—
297C2×C4—24no—
298C2×C4—232no—
299C2×C4—28no—
300C2×C4—48no—
301C2×C4—2216no—
302C2×C4—2216no—
303C2×C4—2216no—
304C2×C4—8816no—
305C2×C4#6703714yes—
306C2×C4C23×Dic1114yes—
307C2×C4C23×Dic1114yes—
308C2×C4C23×Dic1112yes—
309C2×C4C23×Dic1118yes—
310C2×C4C23×Dic1112yes—
311C22—22no—
312C22—28no—
313C22—24no—
314C22—216no—
315C22—44no—
316C22—48no—
317C22—44no—
318C22—44no—
319C22C2×#6703712yes—
320C22#1062345314yes—
321C22C24×Dic1111yescharacteristic
322C4—22no—
323C4—28no—
324C4—24no—
325C4—24no—
326C4—4416no—
327C4#1062332914yes—
328C2—42no—
329C2—48no—
330C2C2×#1062332911yescharacteristic
331C2#1308181912yes—
332C2#1308304314yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
Fitting, prime radicalC2×C11×#532C2
socle, cosocleC23×C11C25
hypercenterC2×#532D11
hypocenterC11#34369
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. #13071797C2semidirect
2. #13071793C2semidirect
3. #13071728C2semidirect
4. #13071545C2semidirect
5. #13071383C2semidirect
6. #13071208C2semidirect
7. #13071014C2semidirect
10. C11×#532C4semidirect
37. C2×C11×#41C2×C4semidirect
46. C11×C4⋊Q8C2×C4semidirect
48. C11×#124C2×C4semidirect
49. C11×#121C2×C4semidirect
50. C4×D4×C11C2×C4semidirect
53. C2×C42×C11C2×C4semidirect
154. #532Dic11semidirect
198. C2×#41C2×Dic11semidirect
207. C4⋊Q8C2×Dic11semidirect
209. #124C2×Dic11semidirect
210. #121C2×Dic11semidirect
211. C4×D4C2×Dic11semidirect
223. C2×C42C2×Dic11semidirect
279. C11#34369semidirect

Maximal subgroups

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

subgroupindex
#130717972
#130717932
#130717282
#130715452
#130713832
#130712082
#130710142
C2×C11×#5322
#3436911