Finite Group Databasebeta

← #14912441

Subgroups — #14912441

Order 2816.

2358 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071267C214yesmaximal, complemented
2#13071259C214yesmaximal, complemented
3#13071249C218yesmaximal, complemented
4#13071114C214yesmaximal, complemented
5#13071107C212yesmaximal
6#13071100C212yesmaximal, complemented
7#13071014C214yesmaximal, complemented
8C4×#66979C211yesmaximal, characteristic, complemented
9C2×#10622545C211yesmaximal, characteristic, complemented
10C2×C4×C11×#41C211yesmaximal, characteristic
11C22×C11×#41C2211yescharacteristic
12C4×C11×#41C4116yescomplemented
13C2×C4×Q8×C11C2212yes—
14C2×C4×D4×C11C2214yes—
15C2×C4×D4×C11C2212yes—
16C2×C11×#117C2211yescharacteristic
17C2×C11×#117C2212yes—
18C22×C42×C11C2211yescharacteristic
19C22×C42×C11C2212yes—
20C2×#66979C2212yes—
21C22×C4×Dic11C2212yes—
22#10622843C2214yes—
23#10622834C2214yes—
24#10622833C2218yes—
25#10622825C2218yes—
26#10622824C2218yes—
27C4×C22⋊Dic11C2218yes—
28C4×C22⋊Dic11C2214yes—
29C2×C11⋊#95C2214yes—
30#10622598C2218yes—
31#10622594C22116yes—
32#10622564C22116yes—
33#10622563C2218yes—
34#10622550C2218yes—
35#10622549C2218yes—
36C4×C4⋊Dic11C2218yes—
37C4×C4⋊Dic11C2214yes—
38#10622545C2212yes—
39#10622545C2214yes—
40#10622545C2212yes—
41#10622545C2212yes—
42C42×Dic11C2212yes—
43C2×C11×#41—28no—
44C2×C11×#41C2×C418yes—
45C22×Q8×C11C2311yescharacteristic
46C22×D4×C11C2312yes—
47C22×D4×C11C2311yescharacteristic
48C23×C4×C11C2312yes—
49C23×C4×C11C2312yes—
50C23×C4×C11C2314yes—
51C23×C4×C11C2311yescharacteristic
52C23×Dic11C2314yes—
53C4×Q8×C11C2×C4116yescomplemented
54C4×D4×C11C2×C4132yes—
55C4×D4×C11C2×C4116yescomplemented
56C11×#117C2×C418yes—
57C11×#117C2×C4116yescomplemented
58C2×C11×C4⋊C4C2314yes—
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C22⋊C4C2312yes—
61C2×C11×C22⋊C4C2314yes—
62C2×C42×C11C2×C418yes—
63C2×C42×C11C2×C4116yescomplemented
64C2×C42×C11C2311yescharacteristic
65C2×C42×C11C2311yescharacteristic
66C2×C42×C11C2312yes—
67C2×C42×C11C2312yes—
68C2×C42×C11C2314yes—
69C2×C22⋊Dic11C2314yes—
70C2×C22⋊Dic11C23116yes—
71#66979—28no—
72C2×C4⋊Dic11C2314yes—
73C2×C4⋊Dic11C23116yes—
74C2×C4×Dic11—28no—
75C2×C4×Dic11C2314yes—
76C2×C4×Dic11C2314yes—
77C2×C4×Dic11C2314yes—
78C2×C4×Dic11C2318yes—
79C11⋊#95C2314yes—
80C11⋊#95C2314yes—
81C11⋊#95C2318yes—
82C11⋊#95C2318yes—
83C11⋊#95C23116yes—
84C11⋊#95C23116yes—
85#34056—111nomaximal, Sylow
86C24×C11C2412yes—
87C24×C11C2411yescharacteristic
88C11×#41—232no—
89C2×Q8×C11—24no—
90C2×Q8×C11C22×C414yes—
91C2×D4×C11—28no—
92C2×D4×C11—24no—
93C2×D4×C11C22×C418yes—
94C2×D4×C11C22×C414yes—
95C22×C4×C11—28no—
96C22×C4×C11—44no—
97C22×C4×C11—48no—
98C22×C4×C11C22×C418yes—
99C22×C4×C11C22×C418yes—
100C22×C4×C11C22×C4116yes—
101C22×C4×C11C22×C414yes—
102C22×C4×C11#4118yes—
103C22×C4×C11C2412yes—
104C22×C4×C11C2412yes—
105C22×C4×C11C2412yes—
106C22×C4×C11C2414yes—
107C22×C4×C11C2411yescharacteristic
108C22×C4×C11C2411yescharacteristic
109C22×Dic11—28no—
110C22×Dic11—48no—
111C22×Dic11C2418yes—
112C22×Dic11C2418yes—
113C11×C4⋊C4C22×C418yes—
114C11×C4⋊C4C22×C4116yes—
115C11×C22⋊C4C22×C418yes—
116C11×C22⋊C4C22×C4116yes—
117C42×C11C22×C414yes—
118C42×C11C22×C414yes—
119C42×C11C22×C418yes—
120C42×C11C22×C418yes—
121C42×C11C22×C4116yes—
122C22⋊Dic11—28no—
123C22⋊Dic11—416no—
124C4⋊Dic11—28no—
125C4⋊Dic11—416no—
126C4×Dic11—28no—
127C4×Dic11—28no—
128C4×Dic11—28no—
129C4×Dic11—48no—
130C2×C4×#41D1111yescharacteristic
131#2320—114no—
132#2319—114no—
133#2318—118no—
134#2298—114no—
135#2297—112no—
136#2296—112no—
137#2283—114no—
138C4×#117—111no—
139C2×#376—111no—
140C23×C11—24no—
141C23×C11—24no—
142C23×C11—28no—
143C23×C11C23×C414yes—
144C23×C11C23×C412yes—
145C23×C11C2×#4114yes—
146C23×C11C2511yescharacteristic
147Q8×C11—28no—
148D4×C11—216no—
149D4×C11—28no—
150C2×C4×C11—24no—
151C2×C4×C11—24no—
152C2×C4×C11—28no—
153C2×C4×C11—24no—
154C2×C4×C11—216no—
155C2×C4×C11—48no—
156C2×C4×C11—416no—
157C2×C4×C11#117116yes—
158C2×C4×C11C23×C414yes—
159C2×C4×C11C23×C414yes—
160C2×C4×C11C23×C418yes—
161C2×C4×C11C23×C414yes—
162C2×C4×C11C23×C412yes—
163C2×C4×C11C23×C412yes—
164C2×C4×C11C2×#4114yes—
165C2×C4×C11C2×#4114yes—
166C2×Dic11—28no—
167C2×Dic11—28no—
168C2×Dic11—216no—
169C2×Dic11—28no—
170C2×Dic11—28no—
171C2×Dic11—416no—
172C22×#41C2×D1111yescharacteristic
173C4×#41Dic11116yescomplemented
174C2×C4×Q8C2×D1112yes—
175C2×C4×D4C2×D1114yes—
176C2×C4×D4C2×D1112yes—
177C2×#117—112no—
178C2×#117C2×D1111yescharacteristic
179C2×#117C2×D1112yes—
180C22×C42—112no—
181C22×C42C2×D1111yescharacteristic
182C22×C42C2×D1112yes—
183#391—114no—
184#390—114no—
185#389—118no—
186#388—1116no—
187#387—1116no—
188#386—118no—
189#385—118no—
190#383—118no—
191#382—118no—
192#381—118no—
193#380—118no—
194C4×C4⋊C4—114no—
195C4×C4⋊C4—118no—
196C4×C22⋊C4—114no—
197C4×C22⋊C4—118no—
198#376—114no—
199#376—112no—
200#376—112no—
201#376—112no—
202C2×#95—114no—
203C43—112no—
204C22×C11—24no—
205C22×C11—28no—
206C22×C11—24no—
207C22×C11—28no—
208C22×C11—48no—
209C22×C11C2×#11714yes—
210C22×C11C24×C411yescharacteristic
211C22×C11C22×#4112yes—
212C22×C11#58514yes—
213C4×C11—24no—
214C4×C11—24no—
215C4×C11—24no—
216C4×C11—28no—
217C4×C11C2×#11714yes—
218C4×C11C2×#11714yes—
219Dic11—48no—
220Dic11—48no—
221C2×#41—28no—
222C2×#41C2×Dic1118yes—
223C22×Q8C22×D1111yescharacteristic
224C22×D4C22×D1112yes—
225C22×D4C22×D1111yescharacteristic
226C23×C4—114no—
227C23×C4C22×D1112yes—
228C23×C4C22×D1112yes—
229C23×C4C22×D1114yes—
230C23×C4C22×D1111yescharacteristic
231C4×Q8C2×Dic11116yescomplemented
232C4×D4C2×Dic11132yes—
233C4×D4C2×Dic11116yescomplemented
234#117—228no—
235#117C2×Dic1118yes—
236#117C2×Dic11116yescomplemented
237C2×C4⋊C4—114no—
238C2×C4⋊C4—1116no—
239C2×C4⋊C4C22×D1114yes—
240C2×C4⋊C4C22×D1112yes—
241C2×C22⋊C4—114no—
242C2×C22⋊C4—1116no—
243C2×C22⋊C4C22×D1112yes—
244C2×C22⋊C4C22×D1114yes—
245C2×C42—114no—
246C2×C42—114no—
247C2×C42—114no—
248C2×C42—118no—
249C2×C42—228no—
250C2×C42C2×Dic1118yes—
251C2×C42C2×Dic11116yescomplemented
252C2×C42C22×D1112yes—
253C2×C42C22×D1114yes—
254C2×C42C22×D1111yescharacteristic
255C2×C42C22×D1112yes—
256C2×C42C22×D1111yescharacteristic
257#95—114no—
258#95—114no—
259#95—118no—
260#95—118no—
261#95—1116no—
262#95—1116no—
263C2×C11—24no—
264C2×C11—44no—
265C2×C11C22×#11711yescharacteristic
266C2×C11#342812yes—
267C2×C11#345514yes—
268C24C23×D1112yes—
269C24C23×D1111yescharacteristic
270#41—232no—
271C2×Q8—24no—
272C2×Q8C22×Dic1114yes—
273C2×D4—28no—
274C2×D4—24no—
275C2×D4C22×Dic1118yes—
276C2×D4C22×Dic1114yes—
277C22×C4—28no—
278C22×C4—44no—
279C22×C4—48no—
280C22×C4—118no—
281C22×C4—118no—
282C22×C4—228no—
283C22×C4—448no—
284C22×C4#433918yes—
285C22×C4C22×Dic1118yes—
286C22×C4C22×Dic1118yes—
287C22×C4C22×Dic11116yes—
288C22×C4C22×Dic1114yes—
289C22×C4C23×D1112yes—
290C22×C4C23×D1112yes—
291C22×C4C23×D1112yes—
292C22×C4C23×D1114yes—
293C22×C4C23×D1111yescharacteristic
294C22×C4C23×D1111yescharacteristic
295C4⋊C4—228no—
296C4⋊C4—4416no—
297C4⋊C4C22×Dic1118yes—
298C4⋊C4C22×Dic11116yes—
299C22⋊C4—228no—
300C22⋊C4—4416no—
301C22⋊C4C22×Dic1118yes—
302C22⋊C4C22×Dic11116yes—
303C42—228no—
304C42—228no—
305C42—228no—
306C42—448no—
307C42C22×Dic1114yes—
308C42C22×Dic1114yes—
309C42C22×Dic1118yes—
310C42C22×Dic1118yes—
311C42C22×Dic11116yes—
312C11#3405611yescharacteristic, complemented, Sylow
313C23—24no—
314C23—24no—
315C23—28no—
316C23C2×#433914yes—
317C23C23×Dic1114yes—
318C23C23×Dic1112yes—
319C23C24×D1111yescharacteristic
320Q8—28no—
321D4—216no—
322D4—28no—
323C2×C4—24no—
324C2×C4—24no—
325C2×C4—28no—
326C2×C4—24no—
327C2×C4—216no—
328C2×C4—48no—
329C2×C4—416no—
330C2×C4—228no—
331C2×C4—228no—
332C2×C4—2216no—
333C2×C4—228no—
334C2×C4—228no—
335C2×C4—4416no—
336C2×C4#66979116yes—
337C2×C4C2×#433914yes—
338C2×C4C2×#433914yes—
339C2×C4C23×Dic1114yes—
340C2×C4C23×Dic1114yes—
341C2×C4C23×Dic1118yes—
342C2×C4C23×Dic1114yes—
343C2×C4C23×Dic1112yes—
344C2×C4C23×Dic1112yes—
345C22—28no—
346C22—24no—
347C22—24no—
348C22—28no—
349C22—48no—
350C22C2×#6697914yes—
351C22C22×#433912yes—
352C22#1062345314yes—
353C22C24×Dic1111yescharacteristic
354C4—24no—
355C4—24no—
356C4—24no—
357C4—28no—
358C4—448no—
359C4—448no—
360C4C2×#6697914yes—
361C4C2×#6697914yes—
362C2—24no—
363C2—44no—
364C2C22×#6697911yescharacteristic
365C2#1308181912yes—
366C2#1308200114yes—
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C4×C11×#41C2
socle, cosocleC23×C11C25
prime radicalC22×C11×#41C22
hypercenterC2×C4×#41D11
hypocenterC11#34056
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #13071267C2semidirect
2. #13071259C2semidirect
3. #13071249C2semidirect
4. #13071114C2semidirect
6. #13071100C2semidirect
7. #13071014C2semidirect
8. C4×#66979C2semidirect
9. C2×#10622545C2semidirect
12. C4×C11×#41C4semidirect
53. C4×Q8×C11C2×C4semidirect
55. C4×D4×C11C2×C4semidirect
57. C11×#117C2×C4semidirect
63. C2×C42×C11C2×C4semidirect
173. C4×#41Dic11semidirect
231. C4×Q8C2×Dic11semidirect
233. C4×D4C2×Dic11semidirect
236. #117C2×Dic11semidirect
251. C2×C42C2×Dic11semidirect
312. C11#34056semidirect

Maximal subgroups

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

subgroupindex
#130712672
#130712592
#130712492
#130711142
#130711072
#130711002
#130710142
C4×#669792
C2×#106225452
C2×C4×C11×#412
#3405611