Finite Group Databasebeta

← #14913841

Subgroups — #14913841

Order 2816.

2390 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66945C211yesmaximal, characteristic
2#13071508C218yesmaximal, complemented
3#13071500C218yesmaximal, complemented
4#13071234C211yesmaximal, characteristic, complemented
5#13071213C214yesmaximal
6#13071011C214yesmaximal, complemented
7#13070995C212yesmaximal
8#13070972C212yesmaximal, complemented
9C11×#2316C211yesmaximal, characteristic, complemented
10C23×C4×D11C2211yescharacteristic
11C2×C11×#117C2212yes—
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×(C2×D11)⋊C4C2212yes—
14C2×#66979C2212yes—
15C22×C4⋊Dic11C2211yescharacteristic
16C22×C4×Dic11C2212yes—
17C2×#66945C4116yescomplemented
18C2×#66945C2214yes—
19C2×#66945C2214yes—
20C11×#389C2218yescomplemented
21C11×#380C2214yes—
22#10622825C2214yes—
23#10622603C22116yes—
24#10622600C2214yes—
25#10622600C2214yes—
26#10622598C2218yescomplemented
27#10622590C2218yescomplemented
28C4⋊C4×Dic11C2218yescomplemented
29C4⋊C4×Dic11C2218yescomplemented
30#10622568C2214yes—
31#10622556C2214yes—
32C22⋊C4×Dic11C2218yes—
33C4×(C2×D11)⋊C4C2214yes—
34C4×(C2×D11)⋊C4C2214yes—
35C4×C4⋊Dic11C2218yescomplemented
36#10622283C22116yes—
37#10622264C2218yescomplemented
38#10622261C2218yescomplemented
39C24×D11C2311yescharacteristic
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C23×Dic11C2311yescharacteristic
43C23×Dic11C2312yes—
44C22×C4×D11—24no—
45C22×C4×D11—24no—
46C22×C4×D11C2×C418yes—
47C22×C4×D11C2312yes—
48C22×C4×D11C2312yes—
49C11×#117—28no—
50C2×C11×C4⋊C4C2×C418yes—
51C2×C11×C4⋊C4C2314yes—
52C2×C11×C4⋊C4C2318yes—
53C2×C11×C4⋊C4C2314yes—
54C2×C11×C22⋊C4C2314yes—
55C2×C42×C11C2314yes—
56C2×C22⋊Dic11C2314yes—
57C2×(C2×D11)⋊C4C2×C4116yes—
58C2×(C2×D11)⋊C4C2318yes—
59C2×(C2×D11)⋊C4C2318yes—
60C2×(C2×D11)⋊C4C2318yes—
61#66979—28no—
62C2×C4⋊Dic11C2×C418yes—
63C2×C4⋊Dic11C2314yes—
64C2×C4⋊Dic11C2318yes—
65C2×C4⋊Dic11C2314yes—
66C2×C4×Dic11C2×C4116yes—
67C2×C4×Dic11C2314yes—
68C2×C4×Dic11C23116yes—
69C2×C4×Dic11C2314yes—
70C2×C4×Dic11C2314yes—
71#66945C2×C4132yes—
72#66945C2×C4132yes—
73C11×#95C2318yes—
74C11⋊#95C2318yes—
75C11⋊#95C2318yes—
76C11⋊#95C2318yes—
77C11⋊#95C23116yes—
78#34179—111nomaximal, Sylow
79C24×C11C2411yescharacteristic
80C23×D11—22no—
81C23×D11—22no—
82C23×D11—42no—
83C23×D11—42no—
84C23×D11C22×C414yes—
85C23×D11C2412yes—
86C22×C4×C11—44no—
87C22×C4×C11C22×C418yes—
88C22×C4×C11C22×C414yes—
89C22×C4×C11#4114yes—
90C22×C4×C11#4114yes—
91C22×C4×C11C2418yes—
92C22×C4×C11C2414yes—
93C22×C4×C11C2412yes—
94C22×Dic11—22no—
95C22×Dic11—22no—
96C22×Dic11—44no—
97C22×Dic11C22×C414yes—
98C22×Dic11C22×C418yes—
99C22×Dic11C2418yes—
100C22×Dic11C2411yescharacteristic
101C22×Dic11C2411yescharacteristic
102C22×Dic11C2414yes—
103C2×C4×D11—232no—
104C2×C4×D11—24no—
105C2×C4×D11—24no—
106C2×C4×D11—24no—
107C2×C4×D11—24no—
108C2×C4×D11C22×C418yes—
109C2×C4×D11C22×C418yes—
110C11×C4⋊C4—28no—
111C11×C4⋊C4—48no—
112C11×C4⋊C4C22×C4116yes—
113C11×C22⋊C4—28no—
114C42×C11—28no—
115C22⋊Dic11—28no—
116(C2×D11)⋊C4—48no—
117(C2×D11)⋊C4—48no—
118(C2×D11)⋊C4C22×C4132yes—
119C4⋊Dic11—28no—
120C4⋊Dic11—48no—
121C4⋊Dic11C22×C4116yes—
122C4×Dic11—28no—
123C4×Dic11—416no—
124C4×Dic11C22×C4116yes—
125C4×Dic11C22×C4116yes—
126C22×#117—111no—
127#2347—118no—
128#2346—118no—
129#2316—111no—
130#2316D1111yescharacteristic, complemented
131#2312—114no—
132#2283—114no—
133#2280—112no—
134#2274—112no—
135C23×C11—22no—
136C23×C11—22no—
137C23×C11C23×C412yes—
138C23×C11C2×#4112yes—
139C23×C11C2×#4112yes—
140C23×C11C2511yescharacteristic
141C22×D11—28no—
142C22×D11—22no—
143C22×D11—22no—
144C22×D11—24no—
145C22×D11—24no—
146C22×D11—44no—
147C22×D11—44no—
148C22×D11—48no—
149C22×D11—48no—
150C22×D11C23×C414yes—
151C2×C4×C11—28no—
152C2×C4×C11—28no—
153C2×C4×C11—28no—
154C2×C4×C11—28no—
155C2×C4×C11—48no—
156C2×C4×C11#117116yes—
157C2×C4×C11C23×C418yes—
158C2×C4×C11C23×C414yes—
159C2×C4×C11C2×#4114yes—
160C2×C4×C11C2×#4114yes—
161C2×Dic11—28no—
162C2×Dic11—21no—
163C2×Dic11—21no—
164C2×Dic11—21no—
165C2×Dic11—21no—
166C2×Dic11—28no—
167C2×Dic11—28no—
168C2×Dic11—28no—
169C2×Dic11—28no—
170C2×Dic11—48no—
171C2×Dic11C23×C412yes—
172C2×Dic11C23×C412yes—
173C2×Dic11C23×C418yes—
174C4×D11—216no—
175C4×D11—216no—
176C24×C4—111no—
177C2×#117—112no—
178C2×#117—114no—
179C2×#117—114no—
180C2×#117—1116no—
181C2×#117C2×D1112yes—
182C22×C4⋊C4—111no—
183C22×C4⋊C4C2×D1111yescharacteristic
184C22×C22⋊C4—112no—
185C22×C42—112no—
186#389—118no—
187#389C2×D1118yescomplemented
188#388—1116no—
189#388—1116no—
190#383—118no—
191#382—118no—
192#381—114no—
193#380—114no—
194#380—114no—
195#380—114no—
196#380C2×D1114yes—
197#379—114no—
198C4×C4⋊C4—118no—
199C4×C4⋊C4—118no—
200C4×C4⋊C4—118no—
201C4×C22⋊C4—118no—
202C4×C22⋊C4—114no—
203C4×C22⋊C4—114no—
204#376—118no—
205C22×C11—22no—
206C22×C11—22no—
207C22×C11—24no—
208C22×C11—24no—
209C22×C11C2×#11714yes—
210C22×C11C24×C411yescharacteristic
211C22×C11C22×#4111yescharacteristic
212C22×C11C22×#4111yescharacteristic
213C22×C11#58512yes—
214C22×C11#58512yes—
215C2×D11—24no—
216C2×D11—24no—
217C2×D11—24no—
218C2×D11—416no—
219C2×D11—44no—
220C2×D11—44no—
221C4×C11—28no—
222C4×C11—48no—
223C4×C11C2×#11718yes—
224Dic11—22no—
225Dic11—22no—
226Dic11—28no—
227Dic11—48no—
228C25—111no—
229C23×C4—111no—
230C23×C4—112no—
231C23×C4—118no—
232C23×C4—112no—
233C23×C4—112no—
234C23×C4—224no—
235C23×C4—224no—
236C23×C4C22×D1112yes—
237C23×C4C22×D1111yescharacteristic
238#117—28no—
239#117—1132no—
240#117—1132no—
241#117—228no—
242C2×C4⋊C4—118no—
243C2×C4⋊C4—114no—
244C2×C4⋊C4—114no—
245C2×C4⋊C4—118no—
246C2×C4⋊C4C4×D1118yes—
247C2×C4⋊C4C22×D1114yes—
248C2×C4⋊C4C22×D1118yes—
249C2×C4⋊C4C22×D1114yes—
250C2×C22⋊C4—1116no—
251C2×C22⋊C4—118no—
252C2×C22⋊C4—114no—
253C2×C22⋊C4—118no—
254C2×C22⋊C4—118no—
255C2×C22⋊C4C22×D1114yes—
256C2×C42—1116no—
257C2×C42—114no—
258C2×C42—114no—
259C2×C42—114no—
260C2×C42—1116no—
261C2×C42C22×D1114yes—
262#95—118no—
263#95—118no—
264#95—118no—
265#95—1116no—
266#95C22×D1118yes—
267C2×C11—24no—
268C2×C11C22×#11711yescharacteristic
269C2×C11#342811yescharacteristic
270C2×C11#342811yescharacteristic
271C2×C11#349312yes—
272C2×C11#349312yes—
273D11—44no—
274C24—112no—
275C24—114no—
276C24—222no—
277C24—222no—
278C24—442no—
279C24—442no—
280C24C23×D1111yescharacteristic
281C22×C4—44no—
282C22×C4—114no—
283C22×C4—111no—
284C22×C4—111no—
285C22×C4—114no—
286C22×C4—118no—
287C22×C4—118no—
288C22×C4—118no—
289C22×C4—118no—
290C22×C4—222no—
291C22×C4—222no—
292C22×C4—2232no—
293C22×C4—224no—
294C22×C4—224no—
295C22×C4—224no—
296C22×C4—224no—
297C22×C4—444no—
298C22×C4C2×C4×D1118yes—
299C22×C4C2×C4×D1114yes—
300C22×C4#434114yes—
301C22×C4#434314yes—
302C22×C4C23×D1118yes—
303C22×C4C23×D1114yes—
304C22×C4C23×D1112yes—
305C4⋊C4—28no—
306C4⋊C4—48no—
307C4⋊C4—1116no—
308C4⋊C4—228no—
309C4⋊C4—448no—
310C4⋊C4C2×C4×D11116yes—
311C22⋊C4—28no—
312C22⋊C4—1132no—
313C22⋊C4—228no—
314C22⋊C4—448no—
315C22⋊C4—448no—
316C42—28no—
317C42—1116no—
318C42—1116no—
319C42—228no—
320C42—4416no—
321C11#3417911yescharacteristic, complemented, Sylow
322C23—22no—
323C23—22no—
324C23—114no—
325C23—228no—
326C23—222no—
327C23—222no—
328C23—224no—
329C23—224no—
330C23—444no—
331C23—444no—
332C23—448no—
333C23—448no—
334C23C22×C4×D1112yes—
335C23C2×#434112yes—
336C23C2×#434312yes—
337C23C24×D1111yescharacteristic
338C2×C4—28no—
339C2×C4—28no—
340C2×C4—28no—
341C2×C4—28no—
342C2×C4—48no—
343C2×C4—112no—
344C2×C4—112no—
345C2×C4—118no—
346C2×C4—228no—
347C2×C4—221no—
348C2×C4—221no—
349C2×C4—221no—
350C2×C4—221no—
351C2×C4—228no—
352C2×C4—2216no—
353C2×C4—2216no—
354C2×C4—228no—
355C2×C4—228no—
356C2×C4—228no—
357C2×C4—448no—
358C2×C4#66945116yes—
359C2×C4C22×C4×D1118yes—
360C2×C4C22×C4×D1114yes—
361C2×C4C2×#434114yes—
362C2×C4C2×#434314yes—
363C22—22no—
364C22—22no—
365C22—24no—
366C22—24no—
367C22—224no—
368C22—224no—
369C22—224no—
370C22—4416no—
371C22—444no—
372C22—444no—
373C22C2×#6694514yes—
374C22C23×C4×D1111yescharacteristic
375C22C22×#434111yescharacteristic
376C22C22×#434311yescharacteristic
377C22#1062345512yes—
378C22#1062345712yes—
379C4—28no—
380C4—48no—
381C4—222no—
382C4—222no—
383C4—228no—
384C4—448no—
385C4C2×#6694518yes—
386C2—24no—
387C2—444no—
388C2C22×#6694511yescharacteristic
389C2#1308181411yescharacteristic
390C2#1308181811yescharacteristic
391C2#1308233512yes—
392C2#1308233712yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2316C2
socle, cosocleC23×C11C25
prime radicalC24×D11C23
hypercenter#2316D11
hypocenterC11#34179
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2316

Complements

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

NH ≅ G/Ntype
2. #13071508C2semidirect
3. #13071500C2semidirect
4. #13071234C2semidirect
6. #13071011C2semidirect
8. #13070972C2semidirect
9. C11×#2316C2semidirect
17. C2×#66945C4semidirect
20. C11×#389C22semidirect
26. #10622598C22semidirect
27. #10622590C22semidirect
28. C4⋊C4×Dic11C22semidirect
29. C4⋊C4×Dic11C22semidirect
35. C4×C4⋊Dic11C22semidirect
37. #10622264C22semidirect
38. #10622261C22semidirect
130. #2316D11semidirect
187. #389C2×D11semidirect
321. C11#34179semidirect

Maximal subgroups

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

subgroupindex
C22×#669452
#130715082
#130715002
#130712342
#130712132
#130710112
#130709952
#130709722
C11×#23162
#3417911