Finite Group Databasebeta

← #14913929

Subgroups — #14913929

Order 2816.

2342 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071589C214yesmaximal, complemented
2#13071581C214yesmaximal, complemented
3#13071556C218yesmaximal, complemented
4#13071225C214yesmaximal, complemented
5#13071208C212yesmaximal
6#13071023C211yesmaximal, characteristic, complemented
7#13071014C214yesmaximal, complemented
8C2×#10622549C211yesmaximal, characteristic, complemented
9#13070972C212yesmaximal, 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#10622825C2214yes—
27#10622824C2218yes—
28C4×C22⋊Dic11C2218yes—
29C2×C11⋊#95C2214yes—
30#10622594C22116yes—
31C4⋊C4×Dic11C2218yes—
32#10622564C22116yes—
33C22⋊C4×Dic11C2218yes—
34#10622550C2218yes—
35#10622549C2212yes—
36#10622549C2212yes—
37#10622549C2214yes—
38#10622549C2212yes—
39#10622548C2212yes—
40C4×C4⋊Dic11C2218yes—
41C4×C4⋊Dic11C2214yes—
42#10622545C2218yes—
43C2×C11×#41—24no—
44C2×C11×#41—24no—
45C2×C11×#41C2×C418yes—
46C22×Q8×C11C2311yescharacteristic
47C22×D4×C11C2312yes—
48C22×D4×C11C2311yescharacteristic
49C23×C4×C11C2312yes—
50C23×C4×C11C2312yes—
51C23×C4×C11C2314yes—
52C23×C4×C11C2311yescharacteristic
53C23×Dic11C2314yes—
54C4×Q8×C11C2×C4116yescomplemented
55C4×D4×C11C2×C4132yes—
56C4×D4×C11C2×C4116yescomplemented
57C11×#117C2×C418yes—
58C11×#117C2×C4116yescomplemented
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C4⋊C4C2314yes—
61C2×C11×C22⋊C4C2312yes—
62C2×C11×C22⋊C4C2314yes—
63C2×C42×C11C2×C418yes—
64C2×C42×C11C2×C4116yescomplemented
65C2×C42×C11C2314yes—
66C2×C42×C11C2312yes—
67C2×C42×C11C2312yes—
68C2×C42×C11C2311yescharacteristic
69C2×C42×C11C2311yescharacteristic
70C2×C22⋊Dic11C2314yes—
71C2×C22⋊Dic11C23116yes—
72#66979—28no—
73C2×C4⋊Dic11—28no—
74C2×C4⋊Dic11C2314yes—
75C2×C4⋊Dic11C2314yes—
76C2×C4⋊Dic11C2314yes—
77C2×C4⋊Dic11C2318yes—
78C2×C4×Dic11C2314yes—
79C2×C4×Dic11C23116yes—
80C11⋊#95C2314yes—
81C11⋊#95C2318yes—
82C11⋊#95C23116yes—
83C11⋊#95C2314yes—
84C11⋊#95C23116yes—
85C11⋊#95C2318yes—
86#34189—111nomaximal, Sylow
87C24×C11C2412yes—
88C24×C11C2411yescharacteristic
89C11×#41—232no—
90C2×Q8×C11—22no—
91C2×Q8×C11—22no—
92C2×Q8×C11C22×C414yes—
93C2×D4×C11—24no—
94C2×D4×C11—24no—
95C2×D4×C11—22no—
96C2×D4×C11—22no—
97C2×D4×C11C22×C418yes—
98C2×D4×C11C22×C414yes—
99C22×C4×C11—24no—
100C22×C4×C11—24no—
101C22×C4×C11—48no—
102C22×C4×C11—44no—
103C22×C4×C11C22×C418yes—
104C22×C4×C11C22×C418yes—
105C22×C4×C11C22×C4116yes—
106C22×C4×C11C22×C414yes—
107C22×C4×C11#4114yes—
108C22×C4×C11#4114yes—
109C22×C4×C11C2412yes—
110C22×C4×C11C2412yes—
111C22×C4×C11C2414yes—
112C22×C4×C11C2412yes—
113C22×C4×C11C2411yescharacteristic
114C22×C4×C11C2411yescharacteristic
115C22×Dic11—28no—
116C22×Dic11—48no—
117C22×Dic11C2418yes—
118C22×Dic11C2418yes—
119C11×C4⋊C4C22×C418yes—
120C11×C4⋊C4C22×C4116yes—
121C11×C22⋊C4C22×C418yes—
122C11×C22⋊C4C22×C4116yes—
123C42×C11C22×C414yes—
124C42×C11C22×C414yes—
125C42×C11C22×C418yes—
126C42×C11C22×C418yes—
127C42×C11C22×C4116yes—
128C22⋊Dic11—28no—
129C22⋊Dic11—416no—
130C4⋊Dic11—28no—
131C4⋊Dic11—28no—
132C4⋊Dic11—28no—
133C4⋊Dic11—48no—
134C4×Dic11—28no—
135C4×Dic11—416no—
136C2×C4×#41D1111yescharacteristic
137#2357—114no—
138#2356—114no—
139#2353—118no—
140#2314—114no—
141#2311—112no—
142#2285—111no—
143#2283—114no—
144C2×#382—111no—
145#2274—112no—
146C23×C11—24no—
147C23×C11—22no—
148C23×C11—22no—
149C23×C11—28no—
150C23×C11C23×C414yes—
151C23×C11C23×C412yes—
152C23×C11C2×#4112yes—
153C23×C11C2×#4112yes—
154C23×C11C2511yescharacteristic
155Q8×C11—28no—
156D4×C11—216no—
157D4×C11—28no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—28no—
161C2×C4×C11—24no—
162C2×C4×C11—24no—
163C2×C4×C11—216no—
164C2×C4×C11—48no—
165C2×C4×C11—416no—
166C2×C4×C11#117116yes—
167C2×C4×C11C23×C414yes—
168C2×C4×C11C23×C414yes—
169C2×C4×C11C23×C418yes—
170C2×C4×C11C23×C414yes—
171C2×C4×C11C23×C412yes—
172C2×C4×C11C23×C412yes—
173C2×C4×C11C2×#4112yes—
174C2×C4×C11C2×#4112yes—
175C2×C4×C11C2×#4112yes—
176C2×C4×C11C2×#4112yes—
177C2×Dic11—28no—
178C2×Dic11—28no—
179C2×Dic11—28no—
180C2×Dic11—216no—
181C2×Dic11—28no—
182C2×Dic11—88no—
183C22×#41C2×D1111yescharacteristic
184C4×#41Dic11116yescomplemented
185C2×C4×Q8C2×D1112yes—
186C2×C4×D4C2×D1114yes—
187C2×C4×D4C2×D1112yes—
188C2×#117—112no—
189C2×#117C2×D1111yescharacteristic
190C2×#117C2×D1112yes—
191C22×C4⋊C4—112no—
192C22×C42C2×D1111yescharacteristic
193C22×C42C2×D1112yes—
194#391—114no—
195#390—114no—
196#388—1116no—
197#387—1116no—
198#386—118no—
199#384—112no—
200#383—118no—
201#382—112no—
202#382—114no—
203#382—112no—
204#382—112no—
205#381—118no—
206#380—118no—
207#380—114no—
208C4×C4⋊C4—118no—
209C4×C4⋊C4—118no—
210C4×C4⋊C4—114no—
211C4×C22⋊C4—118no—
212C4×C22⋊C4—118no—
213#376—118no—
214C2×#95—114no—
215C22×C11—24no—
216C22×C11—24no—
217C22×C11—24no—
218C22×C11—24no—
219C22×C11—28no—
220C22×C11—44no—
221C22×C11—44no—
222C22×C11C2×#11714yes—
223C22×C11C24×C411yescharacteristic
224C22×C11C22×#4111yescharacteristic
225C22×C11C22×#4111yescharacteristic
226C22×C11#58514yes—
227C4×C11—24no—
228C4×C11—24no—
229C4×C11—28no—
230C4×C11—24no—
231C4×C11C2×#11714yes—
232C4×C11C2×#11714yes—
233Dic11—48no—
234Dic11—48no—
235C2×#41—24no—
236C2×#41—24no—
237C2×#41C2×Dic1118yes—
238C22×Q8C22×D1111yescharacteristic
239C22×D4C22×D1112yes—
240C22×D4C22×D1111yescharacteristic
241C23×C4—114no—
242C23×C4C22×D1112yes—
243C23×C4C22×D1112yes—
244C23×C4C22×D1114yes—
245C23×C4C22×D1111yescharacteristic
246C4×Q8C2×Dic11116yescomplemented
247C4×D4C2×Dic11132yes—
248C4×D4C2×Dic11116yescomplemented
249#117—228no—
250#117C2×Dic1118yes—
251#117C2×Dic11116yescomplemented
252C2×C4⋊C4—114no—
253C2×C4⋊C4—114no—
254C2×C4⋊C4—114no—
255C2×C4⋊C4—118no—
256C2×C4⋊C4—228no—
257C2×C4⋊C4C22×D1112yes—
258C2×C4⋊C4C22×D1114yes—
259C2×C22⋊C4—114no—
260C2×C22⋊C4—1116no—
261C2×C22⋊C4C22×D1112yes—
262C2×C22⋊C4C22×D1114yes—
263C2×C42—114no—
264C2×C42—1116no—
265C2×C42C2×Dic1118yes—
266C2×C42C2×Dic11116yescomplemented
267C2×C42C22×D1112yes—
268C2×C42C22×D1111yescharacteristic
269C2×C42C22×D1114yes—
270C2×C42C22×D1112yes—
271C2×C42C22×D1111yescharacteristic
272#95—118no—
273#95—118no—
274#95—114no—
275#95—1116no—
276#95—114no—
277#95—1116no—
278C2×C11—24no—
279C2×C11—44no—
280C2×C11C22×#11711yescharacteristic
281C2×C11#342812yes—
282C2×C11#351012yes—
283C2×C11#351212yes—
284C24C23×D1112yes—
285C24C23×D1111yescharacteristic
286#41—232no—
287C2×Q8—22no—
288C2×Q8—22no—
289C2×Q8C22×Dic1114yes—
290C2×D4—24no—
291C2×D4—24no—
292C2×D4—22no—
293C2×D4—22no—
294C2×D4C22×Dic1118yes—
295C2×D4C22×Dic1114yes—
296C22×C4—24no—
297C22×C4—24no—
298C22×C4—48no—
299C22×C4—44no—
300C22×C4—118no—
301C22×C4—118no—
302C22×C4—228no—
303C22×C4—448no—
304C22×C4#433914yes—
305C22×C4#433914yes—
306C22×C4C22×Dic1118yes—
307C22×C4C22×Dic1118yes—
308C22×C4C22×Dic11116yes—
309C22×C4C22×Dic1114yes—
310C22×C4C23×D1112yes—
311C22×C4C23×D1112yes—
312C22×C4C23×D1114yes—
313C22×C4C23×D1112yes—
314C22×C4C23×D1111yescharacteristic
315C22×C4C23×D1111yescharacteristic
316C4⋊C4—228no—
317C4⋊C4—228no—
318C4⋊C4—228no—
319C4⋊C4—448no—
320C4⋊C4C22×Dic1118yes—
321C4⋊C4C22×Dic11116yes—
322C22⋊C4—228no—
323C22⋊C4—4416no—
324C22⋊C4C22×Dic1118yes—
325C22⋊C4C22×Dic11116yes—
326C42—228no—
327C42—4416no—
328C42C22×Dic1114yes—
329C42C22×Dic1114yes—
330C42C22×Dic1118yes—
331C42C22×Dic1118yes—
332C42C22×Dic11116yes—
333C11#3418911yescharacteristic, complemented, Sylow
334C23—24no—
335C23—22no—
336C23—22no—
337C23—28no—
338C23C2×#433912yes—
339C23C2×#433912yes—
340C23C23×Dic1114yes—
341C23C23×Dic1112yes—
342C23C24×D1111yescharacteristic
343Q8—28no—
344D4—216no—
345D4—28no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—28no—
349C2×C4—24no—
350C2×C4—24no—
351C2×C4—216no—
352C2×C4—48no—
353C2×C4—416no—
354C2×C4—228no—
355C2×C4—228no—
356C2×C4—228no—
357C2×C4—2216no—
358C2×C4—228no—
359C2×C4—888no—
360C2×C4#66979116yes—
361C2×C4C2×#433912yes—
362C2×C4C2×#433912yes—
363C2×C4C2×#433912yes—
364C2×C4C2×#433912yes—
365C2×C4C23×Dic1114yes—
366C2×C4C23×Dic1114yes—
367C2×C4C23×Dic1118yes—
368C2×C4C23×Dic1114yes—
369C2×C4C23×Dic1112yes—
370C2×C4C23×Dic1112yes—
371C22—24no—
372C22—24no—
373C22—24no—
374C22—24no—
375C22—28no—
376C22—44no—
377C22—44no—
378C22C2×#6697914yes—
379C22C22×#433911yescharacteristic
380C22C22×#433911yescharacteristic
381C22#1062345314yes—
382C22C24×Dic1111yescharacteristic
383C4—24no—
384C4—24no—
385C4—28no—
386C4—24no—
387C4—448no—
388C4—448no—
389C4C2×#6697914yes—
390C4C2×#6697914yes—
391C2—24no—
392C2—44no—
393C2C22×#6697911yescharacteristic
394C2#1308181912yes—
395C2#1308251212yes—
396C2#1308253812yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC2×C4×C11×#41C2
socle, cosocleC23×C11C25
prime radicalC22×C11×#41C22
hypercenterC2×C4×#41D11
hypocenterC11#34189
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #13071589C2semidirect
2. #13071581C2semidirect
3. #13071556C2semidirect
4. #13071225C2semidirect
6. #13071023C2semidirect
7. #13071014C2semidirect
8. C2×#10622549C2semidirect
9. #13070972C2semidirect
12. C4×C11×#41C4semidirect
54. C4×Q8×C11C2×C4semidirect
56. C4×D4×C11C2×C4semidirect
58. C11×#117C2×C4semidirect
64. C2×C42×C11C2×C4semidirect
184. C4×#41Dic11semidirect
246. C4×Q8C2×Dic11semidirect
248. C4×D4C2×Dic11semidirect
251. #117C2×Dic11semidirect
266. C2×C42C2×Dic11semidirect
333. C11#34189semidirect

Maximal subgroups

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

subgroupindex
#130715892
#130715812
#130715562
#130712252
#130712082
#130710232
#130710142
C2×#106225492
#130709722
C2×C4×C11×#412
#3418911