Finite Group Databasebeta

← #14912005

Subgroups — #14912005

Order 2816.

4186 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623052C212yesmaximal
2C22×#66946C211yesmaximal, characteristic
3#13070976C218yesmaximal, complemented
4#13070973C211yesmaximal, characteristic, complemented
5#13070968C214yesmaximal, complemented
6C4×#66946C218yesmaximal, complemented
7#117×Dic11C212yesmaximal, complemented
8C4×C22⋊C4×D11C214yesmaximal, complemented
9C11×#2274C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C23×C4×D11C2212yes—
12C2×C11×#117C2212yes—
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×(C2×D11)⋊C4C2212yes—
15C2×#66979C2212yes—
16C22×C4×Dic11C2211yescharacteristic
17#10623052C4132yescomplemented
18C2×#66946C4116yescomplemented
19C2×#66946C2214yes—
20C2×#66946C2218yes—
21C2×#66946C2214yes—
22C2×C22⋊C4×D11C2218yes—
23C2×C4×D44C2218yes—
24C2×C42×D11C2218yescomplemented
25C4×C11×C4⋊C4C2218yescomplemented
26C4×C11×C22⋊C4C2214yes—
27C4×C22⋊Dic11C2214yes—
28C4⋊C4×Dic11C2214yescomplemented
29C4⋊C4×Dic11C2214yescomplemented
30C4⋊C4×Dic11C2218yescomplemented
31C22⋊C4×Dic11C2214yes—
32C22⋊C4×Dic11C2214yes—
33C4×(C2×D11)⋊C4C2218yescomplemented
34C4×(C2×D11)⋊C4C22116yescomplemented
35#10622545C2214yescomplemented
36C42×Dic11C2214yescomplemented
37#10622279C2218yescomplemented
38#10622279C22116yescomplemented
39D11×#95C2218yescomplemented
40C24×D11C2312yes—
41C23×C4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C23×Dic11C2311yescharacteristic
44C23×Dic11C2311yescharacteristic
45C22×D44C2×C418yes—
46C22×D44C2×C4116yes—
47C22×D44C2314yes—
48C22×C4×D11—48no—
49C22×C4×D11C2×C4116yescomplemented
50C22×C4×D11C2314yes—
51C22×C4×D11C2314yes—
52C22×C4×D11C23116yes—
53C11×#117C2×C4116yescomplemented
54C2×C11×C4⋊C4C2×C418yescomplemented
55C2×C11×C4⋊C4C2314yes—
56C2×C11×C4⋊C4C2314yes—
57C2×C11×C22⋊C4C2314yes—
58C2×C42×C11C2318yes—
59C2×C42×C11C2314yes—
60C2×C22⋊Dic11C2314yes—
61C2×(C2×D11)⋊C4C2×C4116yescomplemented
62C2×(C2×D11)⋊C4C2318yes—
63C2×(C2×D11)⋊C4C23116yes—
64#66979C2×C4116yescomplemented
65C2×C4⋊Dic11C2314yes—
66C2×C4×Dic11C2×C418yescomplemented
67C2×C4×Dic11C2318yes—
68C2×C4×Dic11C2318yes—
69C2×C4×Dic11C2318yes—
70C2×C4×Dic11C2312yes—
71C2×C4×Dic11C2312yes—
72C2×C4×Dic11C2314yes—
73#66946C2×C4132yescomplemented
74#66946C2×C4132yescomplemented
75#66946C2×C4164yescomplemented
76C22⋊C4×D11C2×C4164yescomplemented
77C4×D44C2×C4164yescomplemented
78C42×D11—416no—
79C11×#95C2318yes—
80C11⋊#95C2318yes—
81C11⋊#95C2318yes—
82C11⋊#95C2318yes—
83C4×#518—111nomaximal, Sylow
84C24×C11C2411yescharacteristic
85C23×D11—44no—
86C23×D11—44no—
87C23×D11C22×C4116yes—
88C23×D11C22×C418yes—
89C23×D11C2414yes—
90C22×C4×C11—44no—
91C22×C4×C11C22×C418yes—
92C22×C4×C11C22×C414yes—
93C22×C4×C11C22×C418yes—
94C22×C4×C11C2418yes—
95C22×C4×C11C2414yes—
96C22×C4×C11C2412yes—
97C22×Dic11—24no—
98C22×Dic11—42no—
99C22×Dic11C22×C414yes—
100C22×Dic11C22×C414yes—
101C22×Dic11C2411yescharacteristic
102C22×Dic11C2412yes—
103C22×Dic11C2418yes—
104C22×Dic11C2411yescharacteristic
105C2×D44C42164yescomplemented
106C2×D44C22×C4116yes—
107C2×D44C22×C4116yes—
108C2×D44C22×C4116yes—
109C2×C4×D11—216no—
110C2×C4×D11—416no—
111C2×C4×D11—48no—
112C2×C4×D11—416no—
113C2×C4×D11—432no—
114C2×C4×D11C22×C4116yes—
115C2×C4×D11C22×C4116yes—
116C2×C4×D11C22×C4164yescomplemented
117C11×C4⋊C4C22×C4116yes—
118C11×C4⋊C4C22×C4116yescomplemented
119C11×C22⋊C4C22×C4116yes—
120C42×C11—48no—
121C42×C11C22×C4116yescomplemented
122C22⋊Dic11C22×C4116yes—
123(C2×D11)⋊C4C22×C4132yes—
124(C2×D11)⋊C4C22×C4164yescomplemented
125C4⋊Dic11C22×C4116yescomplemented
126C4×Dic11—216no—
127C4×Dic11—48no—
128C4×Dic11—48no—
129C4×Dic11C22×C418yes—
130C4×Dic11C22×C418yes—
131C4×Dic11C22×C4116yescomplemented
132C2×#518—112no—
133C22×C4×D4—111no—
134#2275—118no—
135#2274—111no—
136#2274D1111yescharacteristic, complemented
137#2273—114no—
138C42×D4—118no—
139C4×#117—112no—
140C2×C4×C22⋊C4—114no—
141C23×C11—22no—
142C23×C11—22no—
143C23×C11C23×C414yes—
144C23×C11C23×C412yes—
145C23×C11C2511yescharacteristic
146C22×D11—28no—
147C22×D11—28no—
148C22×D11—48no—
149C22×D11—48no—
150C22×D11—432no—
151C22×D11C2×C42132yescomplemented
152C22×D11C23×C418yes—
153C22×D11C23×C4116yes—
154C2×C4×C11—28no—
155C2×C4×C11—28no—
156C2×C4×C11—28no—
157C2×C4×C11—48no—
158C2×C4×C11C2×C42116yescomplemented
159C2×C4×C11C23×C418yes—
160C2×C4×C11C23×C4116yes—
161C2×C4×C11C23×C414yes—
162C2×C4×C11C23×C414yes—
163C2×C4×C11C23×C414yes—
164C2×Dic11—28no—
165C2×Dic11—22no—
166C2×Dic11—24no—
167C2×Dic11—28no—
168C2×Dic11—28no—
169C2×Dic11—44no—
170C2×Dic11C23×C414yes—
171C2×Dic11C23×C412yes—
172C2×Dic11C23×C4116yes—
173C2×Dic11C23×C412yes—
174C2×Dic11H(5,𝔽2)14yes—
175D44C2×C42164yescomplemented
176C4×D11—232no—
177C4×D11—416no—
178C4×D11—464no—
179C23×D4—111no—
180C24×C4—112no—
181#518—1132no—
182C2×C4×D4—114no—
183C2×C4×D4—114no—
184C2×C4×D4—118no—
185C2×C4×D4—1116no—
186C2×C4×D4—118no—
187C2×#117—112no—
188C2×#117C2×D1112yes—
189C22×C4⋊C4C2×D1111yescharacteristic
190C22×C22⋊C4—112no—
191C22×C22⋊C4—118no—
192C22×C42—111no—
193C22×C42—118no—
194C4×C4⋊C4—114no—
195C4×C4⋊C4—114no—
196C4×C4⋊C4—118no—
197C4×C4⋊C4C2×D1118yescomplemented
198C4×C22⋊C4—114no—
199C4×C22⋊C4—114no—
200C4×C22⋊C4—114no—
201C4×C22⋊C4—118no—
202C4×C22⋊C4—1116no—
203C4×C22⋊C4—118no—
204C4×C22⋊C4—1116no—
205C4×C22⋊C4C2×D1114yes—
206#376—114no—
207C2×#95—118no—
208C43—114no—
209C22×C11—22no—
210C22×C11—22no—
211C22×C11—28no—
212C22×C11C22×C4214yes—
213C22×C11C24×C411yescharacteristic
214C22×C11C24×C412yes—
215C22×C11C2×H(5,𝔽2)12yes—
216C22×C11#58512yes—
217C2×D11—28no—
218C2×D11—28no—
219C2×D11—232no—
220C2×D11—432no—
221C2×D11C22×C42116yes—
222C4×C11—28no—
223C4×C11—216no—
224C4×C11C22×C4218yes—
225Dic11—22no—
226Dic11—24no—
227Dic11—216no—
228Dic11#51814yescomplemented
229C25—112no—
230C22×D4—118no—
231C22×D4—1116no—
232C22×D4—114no—
233C23×C4—111no—
234C23×C4—111no—
235C23×C4—114no—
236C23×C4—1116no—
237C23×C4—1116no—
238C23×C4—114no—
239C23×C4—448no—
240C23×C4C22×D1112yes—
241C23×C4C22×D1111yescharacteristic
242C4×D4—1132no—
243C4×D4—1132no—
244C4×D4—1164no—
245C4×D4—1164no—
246#117—1116no—
247#117C4×D11116yescomplemented
248C2×C4⋊C4—114no—
249C2×C4⋊C4C4×D1118yescomplemented
250C2×C4⋊C4C22×D1114yes—
251C2×C4⋊C4C22×D1114yes—
252C2×C22⋊C4—114no—
253C2×C22⋊C4—1116no—
254C2×C22⋊C4—118no—
255C2×C22⋊C4—1116no—
256C2×C22⋊C4—1164no—
257C2×C22⋊C4C22×D1114yes—
258C2×C42—118no—
259C2×C42—114no—
260C2×C42—112no—
261C2×C42—112no—
262C2×C42—118no—
263C2×C42—118no—
264C2×C42—118no—
265C2×C42—4416no—
266C2×C42C22×D1118yes—
267C2×C42C22×D1114yes—
268#95—118no—
269#95—118no—
270#95—118no—
271#95C22×D1118yes—
272C2×C11—24no—
273C2×C11C23×C4211yescharacteristic
274C2×C11C2×#51811yescharacteristic
275C2×C11#342811yescharacteristic
276C2×C11C4×H(5,𝔽2)14yes—
277D11—216no—
278C24—114no—
279C24—1116no—
280C24—118no—
281C24—444no—
282C24—444no—
283C24C23×D1111yescharacteristic
284C2×D4—1164no—
285C2×D4—1116no—
286C2×D4—1116no—
287C2×D4—1116no—
288C22×C4—44no—
289C22×C4—111no—
290C22×C4—114no—
291C22×C4—111no—
292C22×C4—112no—
293C22×C4—118no—
294C22×C4—114no—
295C22×C4—1116no—
296C22×C4—1164no—
297C22×C4—1116no—
298C22×C4—2216no—
299C22×C4—224no—
300C22×C4—4416no—
301C22×C4—448no—
302C22×C4—4416no—
303C22×C4—4432no—
304C22×C4—442no—
305C22×C4C2×C4×D1118yes—
306C22×C4C2×C4×D1114yes—
307C22×C4C2×C4×D1118yes—
308C22×C4C23×D1118yes—
309C22×C4C23×D1114yes—
310C22×C4C23×D1112yes—
311C4⋊C4—1116no—
312C4⋊C4C2×C4×D11116yes—
313C4⋊C4C2×C4×D11116yescomplemented
314C22⋊C4—1116no—
315C22⋊C4—1132no—
316C22⋊C4—1164no—
317C22⋊C4C2×C4×D11116yes—
318C42—48no—
319C42—118no—
320C42—118no—
321C42—1116no—
322C42—2216no—
323C42—448no—
324C42—448no—
325C42C2×C4×D11116yescomplemented
326C11C4×#51811yescharacteristic, complemented, Sylow
327C23—22no—
328C23—22no—
329C23—118no—
330C23—1116no—
331C23—1132no—
332C23—228no—
333C23—228no—
334C23—448no—
335C23—448no—
336C23—4432no—
337C23C22×C4×D1114yes—
338C23C22×C4×D1112yes—
339C23C24×D1111yescharacteristic
340D4—1164no—
341C2×C4—28no—
342C2×C4—28no—
343C2×C4—28no—
344C2×C4—48no—
345C2×C4—112no—
346C2×C4—114no—
347C2×C4—114no—
348C2×C4—112no—
349C2×C4—1116no—
350C2×C4—2232no—
351C2×C4—228no—
352C2×C4—228no—
353C2×C4—222no—
354C2×C4—224no—
355C2×C4—228no—
356C2×C4—4416no—
357C2×C4—4464no—
358C2×C4—444no—
359C2×C4C42×D11116yescomplemented
360C2×C4C22×C4×D11116yes—
361C2×C4C22×C4×D1118yes—
362C2×C4C22×C4×D1114yes—
363C2×C4C22×C4×D1114yes—
364C2×C4C22×C4×D1114yes—
365C22—22no—
366C22—22no—
367C22—28no—
368C22—1116no—
369C22—228no—
370C22—228no—
371C22—2232no—
372C22—4432no—
373C22C2×C42×D1114yes—
374C22C23×C4×D1111yescharacteristic
375C22C23×C4×D1112yes—
376C22D11×H(5,𝔽2)12yes—
377C22#1062345712yes—
378C4—28no—
379C4—216no—
380C4—114no—
381C4—222no—
382C4—224no—
383C4—2216no—
384C4C2×C42×D1118yes—
385C2—24no—
386C2—2216no—
387C2C22×C42×D1111yescharacteristic
388C2D11×#51811yescharacteristic
389C2#1308181811yescharacteristic
390C2#1308182214yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC2×C11C23×C42
FittingC11×#2274C2
socle, cosocleC23×C11C25
prime radicalC23×D44C22
hypercenter#2274D11
hypocenterC11C4×#518
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2274

Complements

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

NH ≅ G/Ntype
3. #13070976C2semidirect
4. #13070973C2semidirect
5. #13070968C2semidirect
6. C4×#66946C2semidirect
7. #117×Dic11C2semidirect
8. C4×C22⋊C4×D11C2semidirect
9. C11×#2274C2semidirect
17. #10623052C4semidirect
18. C2×#66946C4semidirect
24. C2×C42×D11C22semidirect
25. C4×C11×C4⋊C4C22semidirect
28. C4⋊C4×Dic11C22semidirect
29. C4⋊C4×Dic11C22semidirect
30. C4⋊C4×Dic11C22semidirect
33. C4×(C2×D11)⋊C4C22semidirect
34. C4×(C2×D11)⋊C4C22semidirect
35. #10622545C22semidirect
36. C42×Dic11C22semidirect
37. #10622279C22semidirect
38. #10622279C22semidirect
39. D11×#95C22semidirect
49. C22×C4×D11C2×C4semidirect
53. C11×#117C2×C4semidirect
54. C2×C11×C4⋊C4C2×C4semidirect
61. C2×(C2×D11)⋊C4C2×C4semidirect
64. #66979C2×C4semidirect
66. C2×C4×Dic11C2×C4semidirect
73. #66946C2×C4semidirect
74. #66946C2×C4semidirect
75. #66946C2×C4semidirect
76. C22⋊C4×D11C2×C4semidirect
77. C4×D44C2×C4semidirect
105. C2×D44C42semidirect
116. C2×C4×D11C22×C4semidirect
118. C11×C4⋊C4C22×C4semidirect
121. C42×C11C22×C4semidirect
124. (C2×D11)⋊C4C22×C4semidirect
125. C4⋊Dic11C22×C4semidirect
131. C4×Dic11C22×C4semidirect
136. #2274D11semidirect
151. C22×D11C2×C42semidirect
158. C2×C4×C11C2×C42semidirect
175. D44C2×C42semidirect
197. C4×C4⋊C4C2×D11semidirect
228. Dic11#518semidirect
247. #117C4×D11semidirect
249. C2×C4⋊C4C4×D11semidirect
313. C4⋊C4C2×C4×D11semidirect
325. C42C2×C4×D11semidirect
326. C11C4×#518semidirect
359. C2×C4C42×D11semidirect

Maximal subgroups

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

subgroupindex
C2×#106230522
C22×#669462
#130709762
#130709732
#130709682
C4×#669462
#117×Dic112
C4×C22⋊C4×D112
C11×#22742
C4×#51811