Finite Group Databasebeta

← #15623436

Subgroups — #15623436

Order 2816.

1890 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#533C212yesmaximal
2#13079167C218yesmaximal, complemented
3#13079161C218yesmaximal, complemented
4#13079140C211yesmaximal, characteristic, complemented
5#13079138C212yesmaximal, complemented
6#13079128C214yesmaximal, complemented
7#13077204C214yesmaximal
8C2×#10622320C211yesmaximal, characteristic
9C11×#3162C211yesmaximal, characteristic, complemented
10C11×#533C2212yes—
11C22×#4313C2212yes—
12#10623259C2214yes—
13D11×C4⋊Q8C2214yes—
14#10623219C2214yes—
15D11×#125C2214yes—
16D11×C22⋊Q8—24no—
17#10623153—24no—
18#10623109—24no—
19C4×Q8×D11—24no—
20D11×#117C2214yes—
21#10623048C2214yes—
22C2×C42×D11C2211yescharacteristic
23#10623001C2212yes—
24C11×#501C2218yescomplemented
25C11×#427C2214yes—
26C2×C11×#97C2211yescharacteristic
27#10622719C2214yes—
28C2×C8×Dic11C2212yes—
29#10622693C2218yescomplemented
30#10622678C2218yescomplemented
31#10622611C2218yes—
32C2×#66867C2211yescharacteristic
33#10622494C22116yes—
34#10622491C2218yescomplemented
35#10622487C2218yescomplemented
36#10622474C22116yes—
37#10622471C2218yescomplemented
38#10622468C2218yescomplemented
39#10622320C2214yes—
40#10622320C2214yes—
41#10622315C2218yescomplemented
42C2×Q8×D11—24no—
43C22×C4×D11D412yes—
44C22×C4×D11C2311yescharacteristic
45C22×C8×C11C2312yes—
46C11×C4⋊Q8C2314yes—
47C11×#125C2314yes—
48C11×C22⋊Q8—24no—
49C4×Q8×C11—24no—
50C11×#117C2314yes—
51C2×C42×C11C2311yescharacteristic
52#66999—24no—
53Q8×Dic11—24no—
54#66997—24no—
55#66979C2314yes—
56#66977—24no—
57C2×C4×Dic11D412yes—
58C2×C4×Dic11C2311yescharacteristic
59C22×C11⋊C8C2312yes—
60C2×#4313Q8116yescomplemented
61C2×#4313C2318yes—
62#66950—24no—
63#66949—28no—
64#66945C2318yes—
65C4⋊C4×D11—24no—
66C4⋊C4×D11—28no—
67C4⋊C4×D11C2318yes—
68#66943C2318yes—
69#66942—28no—
70#66941—24no—
71#66941C2318yes—
72#66940—24no—
73#66940—28no—
74C22⋊C4×D11—24no—
75#66931—28no—
76#66930—24no—
77#66925—24no—
78C42×D11—24no—
79C42×D11D414yes—
80C42×D11C2312yes—
81C42×D11C2312yes—
82#66923C2314yes—
83#66922C2314yes—
84C4×Dic22—24no—
85C4×Dic22—28no—
86C11×#107C2318yes—
87C11×#106C2318yes—
88C11×#97C2314yes—
89#66882C2318yes—
90#66881C2318yes—
91C8×Dic11C2314yes—
92C8×Dic11C2314yes—
93#66872C23116yes—
94#66871C23116yes—
95#66867C2314yes—
96#60663—111nomaximal, Sylow
97C23×D11C2×D411yescharacteristic
98C2×Q8×C11—24no—
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2411yescharacteristic
101C22×Dic11C2×D412yes—
102C22×Dic11C2×D411yescharacteristic
103Q8×D11—416no—
104C2×C4×D11—28no—
105C2×C4×D11—44no—
106C2×C4×D11C2×D414yes—
107C2×C4×D11C2×D414yes—
108C2×C4×D11C2×D412yes—
109C2×C4×D11C2×Q818yes—
110C2×C4×D11C2412yes—
111C2×Dic22—28no—
112C2×Dic22—24no—
113C2×C8×C11C2×Q818yescomplemented
114C2×C8×C11C2414yes—
115C11×C4⋊C4—24no—
116C11×C4⋊C4—28no—
117C11×C4⋊C4C2418yes—
118C11×C22⋊C4—24no—
119C42×C11—24no—
120C42×C11C2×D412yes—
121C42×C11C2412yes—
122C22⋊Dic11—24no—
123(C2×D11)⋊C4—28no—
124C4⋊Dic11—28no—
125C4⋊Dic11—24no—
126C4⋊Dic11C2418yes—
127Dic11⋊C4—28no—
128Dic11⋊C4—28no—
129Dic11⋊C4—28no—
130Dic11⋊C4—28no—
131C4×Dic11—28no—
132C4×Dic11—24no—
133C4×Dic11C2×D412yes—
134C4×Dic11C2×D414yes—
135C4×Dic11C2×D414yes—
136C4×Dic11C2411yescharacteristic
137C4×Dic11C2411yescharacteristic
138C2×C11⋊C8C2×Q818yescomplemented
139C2×C11⋊C8C2414yes—
140#4313C2×Q8132yescomplemented
141C2×#533—112no—
142#3166—118no—
143#3165—118no—
144#3162—111no—
145#3162—112no—
146#3162D1111yescharacteristic, complemented
147#3160—114no—
148#2911—114no—
149C2×C4×M16—111no—
150C23×C11C22×D411yescharacteristic
151C22×D11—42no—
152C22×D11C4⋊Q814yes—
153C22×D11C22×D412yes—
154Q8×C11—48no—
155C2×C4×C11—28no—
156C2×C4×C11—42no—
157C2×C4×C11C22×D414yes—
158C2×C4×C11C22×D411yescharacteristic
159C2×C4×C11C22×Q814yes—
160C2×C4×C11C2511yescharacteristic
161C2×Dic11—24no—
162C2×Dic11—28no—
163C2×Dic11C4⋊Q814yes—
164C2×Dic11C22×D412yes—
165C2×Dic11C22×D412yes—
166C2×Dic11C22×D412yes—
167C4×D11—28no—
168C4×D11—44no—
169C4×D11—416no—
170C4×D11C4⋊Q818yes—
171C4×D11C22×Q818yes—
172Dic22—48no—
173Dic22—416no—
174C8×C11C22×Q818yes—
175C11⋊C8C22×Q818yes—
176C22×M16—112no—
177#533—114no—
178#533—114no—
179#533—114no—
180#533—112no—
181#533—224no—
182#533—224no—
183#533C2×D1112yes—
184C2×C4⋊Q8—114no—
185C2×#125—114no—
186C2×C22⋊Q8—224no—
187C2×C4×Q8—224no—
188C2×#117—114no—
189C22×C42—111no—
190#501—118no—
191#501—118no—
192#501—118no—
193#501C2×D1118yescomplemented
194#500—118no—
195#499—118no—
196#499—118no—
197#498—118no—
198#428—1116no—
199#428—1116no—
200#427—114no—
201#427—118no—
202#427C2×D1114yes—
203C4×M16—114no—
204C4×M16—114no—
205C2×#97—111no—
206C2×#97C2×D1111yescharacteristic
207C2×C4×C8—112no—
208C22×C11—22no—
209C22×C11C2×C4⋊Q812yes—
210C22×C11C23×D411yescharacteristic
211C2×D11—24no—
212C2×D11—44no—
213C2×D11C2×C4⋊Q814yes—
214C4×C11—24no—
215C4×C11—48no—
216C4×C11C2×C4⋊Q812yes—
217C4×C11C23×Q812yes—
218Dic11—22no—
219Dic11—48no—
220Dic11C2×C4⋊Q814yes—
221Dic11#57514yes—
222C22×Q8—224no—
223C23×C4—111no—
224C23×C4—112no—
225C2×M16—1116no—
226C2×M16—118no—
227C22×C8—112no—
228C22×C8C22×D1112yes—
229C4⋊Q8—118no—
230C4⋊Q8—114no—
231C4⋊Q8—224no—
232C4⋊Q8—224no—
233C4⋊Q8C22×D1114yes—
234#125—118no—
235#125—114no—
236#125—228no—
237#125C22×D1114yes—
238C22⋊Q8—24no—
239C22⋊Q8—228no—
240C22⋊Q8—228no—
241C22⋊Q8—224no—
242C22⋊Q8—224no—
243C22⋊Q8—224no—
244C4×Q8—24no—
245C4×Q8—228no—
246C4×Q8—224no—
247C4×Q8—228no—
248C4×Q8—224no—
249C4×Q8—224no—
250#117—114no—
251#117—118no—
252#117—224no—
253#117—224no—
254#117C22×D1114yes—
255C2×C4⋊C4—118no—
256C2×C4⋊C4—228no—
257C2×C4⋊C4—224no—
258C2×C22⋊C4—224no—
259C2×C42—112no—
260C2×C42—111no—
261C2×C42—114no—
262C2×C42—112no—
263C2×C42—112no—
264C2×C42—224no—
265C2×C42C22×D1111yescharacteristic
266#107—118no—
267#107—1116no—
268#107C22×D1118yes—
269#106—118no—
270#106—1116no—
271#106C22×D1118yes—
272#97—114no—
273#97C22×D1114yes—
274C4×C8—114no—
275C4×C8—114no—
276C2×C11—22no—
277C2×C11C22×C4⋊Q811yescharacteristic
278C2×C11C2×#57512yes—
279D11—24no—
280C24—111no—
281C2×Q8—24no—
282C2×Q8—228no—
283C2×Q8—224no—
284C2×Q8—4416no—
285C22×C4—111no—
286C22×C4—112no—
287C22×C4—118no—
288C22×C4—112no—
289C22×C4—112no—
290C22×C4—114no—
291C22×C4—114no—
292C22×C4—228no—
293C22×C4—444no—
294C22×C4D4×D1112yes—
295C22×C4C23×D1111yescharacteristic
296M16—1132no—
297C2×C8—118no—
298C2×C8—114no—
299C2×C8Q8×D1118yescomplemented
300C2×C8C23×D1114yes—
301C4⋊C4—28no—
302C4⋊C4—24no—
303C4⋊C4—118no—
304C4⋊C4—228no—
305C4⋊C4—228no—
306C4⋊C4—228no—
307C4⋊C4—228no—
308C4⋊C4—228no—
309C4⋊C4—224no—
310C4⋊C4C23×D1118yes—
311C22⋊C4—24no—
312C22⋊C4—228no—
313C22⋊C4—224no—
314C42—24no—
315C42—114no—
316C42—114no—
317C42—112no—
318C42—111no—
319C42—111no—
320C42—228no—
321C42—224no—
322C42D4×D1112yes—
323C42C23×D1112yes—
324C11#6066311yescharacteristic, complemented, Sylow
325C23—112no—
326C23—114no—
327C23—442no—
328C23C2×D4×D1111yescharacteristic
329Q8—48no—
330Q8—448no—
331Q8—4416no—
332C2×C4—28no—
333C2×C4—42no—
334C2×C4—114no—
335C2×C4—112no—
336C2×C4—112no—
337C2×C4—118no—
338C2×C4—118no—
339C2×C4—112no—
340C2×C4—228no—
341C2×C4—224no—
342C2×C4—228no—
343C2×C4—444no—
344C2×C4—4416no—
345C2×C4C2×D4×D1114yes—
346C2×C4C2×D4×D1111yescharacteristic
347C2×C4C2×Q8×D1114yes—
348C2×C4C24×D1111yescharacteristic
349C8—118no—
350C8C2×Q8×D1118yes—
351C22—22no—
352C22—114no—
353C22—224no—
354C22—444no—
355C22D11×C4⋊Q812yes—
356C22C22×D4×D1111yescharacteristic
357C4—24no—
358C4—48no—
359C4—114no—
360C4—114no—
361C4—222no—
362C4—448no—
363C4D11×C4⋊Q812yes—
364C4C22×Q8×D1112yes—
365C2—22no—
366C2—224no—
367C2C2×D11×C4⋊Q811yescharacteristic
368C2D11×#57512yes—
subgroupG/H
centerC2×C4C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3162C2
socleC22×C11C23×D4
prime radicalC23×D11C2×D4
hypercenter#3162D11
hypocenterC11#60663
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3162

Complements

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

NH ≅ G/Ntype
2. #13079167C2semidirect
3. #13079161C2semidirect
4. #13079140C2semidirect
5. #13079138C2semidirect
6. #13079128C2semidirect
9. C11×#3162C2semidirect
24. C11×#501C22semidirect
29. #10622693C22semidirect
30. #10622678C22semidirect
34. #10622491C22semidirect
35. #10622487C22semidirect
37. #10622471C22semidirect
38. #10622468C22semidirect
41. #10622315C22semidirect
60. C2×#4313Q8semidirect
113. C2×C8×C11C2×Q8semidirect
138. C2×C11⋊C8C2×Q8semidirect
140. #4313C2×Q8semidirect
146. #3162D11semidirect
193. #501C2×D11semidirect
299. C2×C8Q8×D11semidirect
324. C11#60663semidirect

Maximal subgroups

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

subgroupindex
D11×#5332
#130791672
#130791612
#130791402
#130791382
#130791282
#130772042
C2×#106223202
C11×#31622
#6066311