Finite Group Databasebeta

← #14959885

Subgroups — #14959885

Order 2816.

2502 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623219C212yesmaximal
2#13077013C212yesmaximal, complemented
3#13076992C212yesmaximal, complemented
4#13076979C211yesmaximal, characteristic, complemented
5#13076976C212yesmaximal, complemented
6#13076967C218yesmaximal
7#13071187C218yesmaximal, complemented
8#13071022C212yesmaximal
9#13071021C212yesmaximal
10C43×D11C211yesmaximal, characteristic
11C11×#2859C211yesmaximal, characteristic, complemented
12C2×C11×#125C2212yes—
13#10623219—216no—
14C2×#66949C2218yes—
15C2×#66945C2214yes—
16C2×#66941C2214yes—
17C2×#66941C2218yes—
18C2×#66940C2218yes—
19C2×C42×D11C2214yes—
20C2×C42×D11C2211yescharacteristic
21C2×C42×D11C2211yescharacteristic
22C2×C42×D11C2211yescharacteristic
23C2×#66923C2212yes—
24C11×#389C2218yes—
25C11×#384C2212yes—
26C11×#382C2212yes—
27C43×C11C2211yescharacteristic
28#10622600C2218yes—
29#10622590C2214yes—
30#10622589C2218yes—
31#10622589C2214yes—
32C4⋊C4×Dic11C2218yes—
33#10622585C22116yes—
34#10622549C2212yes—
35#10622548C2212yes—
36C42×Dic11C2211yescharacteristic
37C42×Dic11C2211yescharacteristic
38C42×Dic11C2214yes—
39C42×Dic11C2211yescharacteristic
40#10622541C2218yes—
41#10622280C2218yes—
42#10622262C2218yes—
43#10622259C22116yes—
44C22×C4×D11C2312yes—
45C22×C4×D11C2312yes—
46C22×C4×D11C2312yes—
47C22×C4×D11C2311yescharacteristic
48C22×Dic22C2318yes—
49C11×#125—28no—
50C2×C11×C4⋊C4C2318yes—
51C2×C11×C4⋊C4C2314yes—
52C2×C11×C4⋊C4C2318yes—
53C2×C42×C11C2314yes—
54C2×C42×C11C2311yescharacteristic
55C2×C42×C11C2311yescharacteristic
56C2×C42×C11C2311yescharacteristic
57C2×(C2×D11)⋊C4C2318yes—
58C2×C4⋊Dic11C2314yes—
59C2×C4⋊Dic11C2318yes—
60C2×Dic11⋊C4C2318yes—
61C2×Dic11⋊C4C2318yes—
62C2×Dic11⋊C4C23116yes—
63C2×C4×Dic11C2314yes—
64C2×C4×Dic11C2314yes—
65C2×C4×Dic11C2318yes—
66C2×C4×Dic11C2312yes—
67C2×C4×Dic11C2311yescharacteristic
68C2×C4×Dic11C2312yes—
69C2×C4×Dic11C2312yes—
70C2×C4×Dic11C2311yescharacteristic
71C2×C4×Dic11C2311yescharacteristic
72C2×C4×Dic11C2314yes—
73#66949—232no—
74#66945—216no—
75#66941—216no—
76#66941—232no—
77#66940—232no—
78C42×D11—216no—
79C42×D11D418yes—
80C42×D11Q818yescomplemented
81C42×D11Q818yescomplemented
82#66923—28no—
83C11×#95C2318yes—
84C11⋊#95C2318yes—
85C11⋊#95C23116yes—
86#36645—111nomaximal, Sylow
87C23×D11C2411yescharacteristic
88C22×C4×C11C2418yes—
89C22×C4×C11C2412yes—
90C22×C4×C11C2412yes—
91C22×C4×C11C2411yescharacteristic
92C22×C4×C11C2412yes—
93C22×Dic11C2418yes—
94C22×Dic11C2412yes—
95C22×Dic11C2411yescharacteristic
96C22×Dic11C2412yes—
97C22×Dic11C2412yes—
98C2×C4×D11—28no—
99C2×C4×D11—28no—
100C2×C4×D11—28no—
101C2×C4×D11C2×D418yes—
102C2×C4×D11C2×D414yes—
103C2×C4×D11C2×Q818yes—
104C2×C4×D11C2×Q818yes—
105C2×C4×D11C2×Q814yes—
106C2×C4×D11C2×Q814yes—
107C2×Dic22—216no—
108C2×Dic22—232no—
109C11×C4⋊C4—216no—
110C11×C4⋊C4—28no—
111C11×C4⋊C4—216no—
112C42×C11—28no—
113C42×C11C2×D414yes—
114C42×C11C2×Q814yes—
115C42×C11C2×Q814yes—
116(C2×D11)⋊C4—216no—
117C4⋊Dic11—28no—
118C4⋊Dic11—216no—
119Dic11⋊C4—216no—
120Dic11⋊C4—232no—
121Dic11⋊C4—216no—
122C4×Dic11—216no—
123C4×Dic11—28no—
124C4×Dic11—28no—
125C4×Dic11C2×D418yes—
126C4×Dic11C2×D414yes—
127C4×Dic11C2×Q818yes—
128C4×Dic11C2×Q814yes—
129C4×Dic11C2×Q814yes—
130C4×Dic11C2×Q818yes—
131C4×Dic11#41116yes—
132C2×#533—112no—
133#2868—112no—
134#2862—112no—
135#2859—111no—
136#2859—112no—
137#2859D1111yescharacteristic, complemented
138#2857—118no—
139C4×C4⋊Q8—118no—
140#2285—112no—
141#2285—112no—
142C2×C43—111no—
143C23×C11C2511yescharacteristic
144C22×D11—24no—
145C22×D11C22×D412yes—
146C22×D11C22×Q812yes—
147C22×D11C22×Q812yes—
148C2×C4×C11—24no—
149C2×C4×C11—24no—
150C2×C4×C11—28no—
151C2×C4×C11—216no—
152C2×C4×C11C22×D414yes—
153C2×C4×C11C22×D412yes—
154C2×C4×C11C22×Q814yes—
155C2×C4×C11C22×Q812yes—
156C2×C4×C11C22×Q812yes—
157C2×C4×C11C22×Q814yes—
158C2×C4×C11C2×#4118yes—
159C2×Dic11—24no—
160C2×Dic11—28no—
161C2×Dic11—216no—
162C2×Dic11C22×D412yes—
163C2×Dic11C22×D414yes—
164C2×Dic11C22×Q814yes—
165C2×Dic11C22×Q812yes—
166C2×Dic11C22×Q812yes—
167C2×Dic11C22×Q814yes—
168C2×Dic11C2×#4118yes—
169C2×Dic11C2×#4118yes—
170C4×D11—216no—
171C4×D11—216no—
172C4×D11—216no—
173C4×D11C4⋊Q8116yescomplemented
174Dic22—432no—
175#533—2216no—
176C2×C4⋊Q8—118no—
177C2×C4⋊Q8—114no—
178C2×#125—112no—
179C2×#125C2×D1112yes—
180C2×C22⋊Q8—118no—
181C2×C4×Q8—118no—
182C2×#117—114no—
183C22×C42—111no—
184C22×C42—111no—
185C22×C42—111no—
186C22×C42—114no—
187#391—1116no—
188#389—1116no—
189#389—118no—
190#389C2×D1118yes—
191#384—118no—
192#384—114no—
193#384—112no—
194#384C2×D1112yes—
195#382—114no—
196#382—112no—
197#382C2×D1112yes—
198#380—118no—
199#380—118no—
200C4×C4⋊C4—118no—
201C4×C4⋊C4—118no—
202C43—114no—
203C43—111no—
204C43—111no—
205C43—111no—
206C43C2×D1111yescharacteristic
207C22×C11C23×D411yescharacteristic
208C22×C11C23×Q811yescharacteristic
209C22×C11C23×Q811yescharacteristic
210C22×C11C22×#4114yes—
211C2×D11—24no—
212C2×D11—24no—
213C2×D11—24no—
214C2×D11C2×C4⋊Q814yes—
215C4×C11—24no—
216C4×C11—24no—
217C4×C11—48no—
218C4×C11C2×C4⋊Q814yes—
219C4×C11#53318yescomplemented
220Dic11—24no—
221Dic11—48no—
222Dic11C2×C4⋊Q814yes—
223Dic11#53218yes—
224Dic11#53318yescomplemented
225C22×Q8—118no—
226C23×C4—111no—
227C23×C4—112no—
228C23×C4—112no—
229C23×C4—112no—
230C4⋊Q8—2216no—
231C4⋊Q8—2232no—
232#125—28no—
233#125—228no—
234C22⋊Q8—2232no—
235C4×Q8—2232no—
236#117—2216no—
237C2×C4⋊C4—114no—
238C2×C4⋊C4—118no—
239C2×C4⋊C4—118no—
240C2×C4⋊C4—1116no—
241C2×C4⋊C4—118no—
242C2×C4⋊C4C22×D1114yes—
243C2×C4⋊C4C22×D1118yes—
244C2×C4⋊C4C22×D1118yes—
245C2×C22⋊C4—118no—
246C2×C42—112no—
247C2×C42—111no—
248C2×C42—114no—
249C2×C42—112no—
250C2×C42—112no—
251C2×C42—111no—
252C2×C42—111no—
253C2×C42—118no—
254C2×C42—118no—
255C2×C42—118no—
256C2×C42—118no—
257C2×C42—114no—
258C2×C42—114no—
259C2×C42—2216no—
260C2×C42C22×D1114yes—
261C2×C42C22×D1111yescharacteristic
262C2×C42C22×D1111yescharacteristic
263C2×C42C22×D1111yescharacteristic
264#95—1116no—
265#95—118no—
266#95C22×D1118yes—
267C2×C11C22×C4⋊Q811yescharacteristic
268C2×C11C2×#53212yes—
269C2×C11C2×#53312yes—
270C2×C11C2×#53312yes—
271D11—24no—
272C24—111no—
273C2×Q8—2216no—
274C2×Q8—2232no—
275C22×C4—111no—
276C22×C4—112no—
277C22×C4—112no—
278C22×C4—114no—
279C22×C4—114no—
280C22×C4—114no—
281C22×C4—112no—
282C22×C4—118no—
283C22×C4—118no—
284C22×C4—118no—
285C22×C4—118no—
286C22×C4—228no—
287C22×C4—228no—
288C22×C4—228no—
289C22×C4C23×D1118yes—
290C22×C4C23×D1112yes—
291C22×C4C23×D1112yes—
292C22×C4C23×D1111yescharacteristic
293C22×C4C23×D1112yes—
294C4⋊C4—28no—
295C4⋊C4—216no—
296C4⋊C4—216no—
297C4⋊C4—2216no—
298C4⋊C4—2232no—
299C4⋊C4—228no—
300C4⋊C4—2216no—
301C4⋊C4—2216no—
302C22⋊C4—2216no—
303C42—28no—
304C42—118no—
305C42—114no—
306C42—118no—
307C42—114no—
308C42—118no—
309C42—114no—
310C42—1116no—
311C42—228no—
312C42—228no—
313C42—2216no—
314C42D4×D1114yes—
315C42Q8×D1114yes—
316C42Q8×D1114yes—
317C11#3664511yescharacteristic, complemented, Sylow
318C23—112no—
319C23—112no—
320C23—112no—
321C23—224no—
322C23C24×D1111yescharacteristic
323Q8—4432no—
324C2×C4—24no—
325C2×C4—24no—
326C2×C4—28no—
327C2×C4—216no—
328C2×C4—112no—
329C2×C4—114no—
330C2×C4—112no—
331C2×C4—112no—
332C2×C4—114no—
333C2×C4—118no—
334C2×C4—118no—
335C2×C4—1116no—
336C2×C4—114no—
337C2×C4—2216no—
338C2×C4—2216no—
339C2×C4—224no—
340C2×C4—2216no—
341C2×C4—228no—
342C2×C4—2216no—
343C2×C4C2×D4×D1114yes—
344C2×C4C2×D4×D1112yes—
345C2×C4C2×Q8×D1114yes—
346C2×C4C2×Q8×D1112yes—
347C2×C4C2×Q8×D1112yes—
348C2×C4C2×Q8×D1114yes—
349C2×C4#41×D1118yes—
350C22—114no—
351C22—224no—
352C22—224no—
353C22—224no—
354C22C22×D4×D1111yescharacteristic
355C22C22×Q8×D1111yescharacteristic
356C22C22×Q8×D1111yescharacteristic
357C22C2×#41×D1114yes—
358C4—24no—
359C4—24no—
360C4—48no—
361C4—114no—
362C4—118no—
363C4—118no—
364C4—224no—
365C4—448no—
366C4#1062321918yescomplemented
367C4D11×C4⋊Q814yes—
368C2—224no—
369C2C2×D11×C4⋊Q811yescharacteristic
370C2D11×#53212yes—
371C2D11×#53312yes—
372C2C2×#1062321912yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2859C2
prime radicalC23×D11C24
hypercenter#2859D11
hypocenterC11#36645
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2859

Complements

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

NH ≅ G/Ntype
2. #13077013C2semidirect
3. #13076992C2semidirect
4. #13076979C2semidirect
5. #13076976C2semidirect
7. #13071187C2semidirect
11. C11×#2859C2semidirect
80. C42×D11Q8semidirect
81. C42×D11Q8semidirect
137. #2859D11semidirect
173. C4×D11C4⋊Q8semidirect
219. C4×C11#533semidirect
224. Dic11#533semidirect
317. C11#36645semidirect
366. C4#10623219semidirect

Maximal subgroups

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

subgroupindex
C2×#106232192
#130770132
#130769922
#130769792
#130769762
#130769672
#130711872
#130710222
#130710212
C43×D112
C11×#28592
#3664511