Finite Group Databasebeta

← #15623414

Subgroups — #15623414

Order 2816.

1770 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082021C212yesmaximal
2#13079154C218yesmaximal, complemented
3#13079146C218yesmaximal, complemented
4#13079139C214yesmaximal, complemented
5#13079128C214yesmaximal, complemented
6#13077206C211yesmaximal, characteristic
7C2×#10622611C212yesmaximal
8C2×#10622735C211yesmaximal, characteristic
9C11×#2911C211yesmaximal, characteristic
10C22×C11×M16C2211yescharacteristic
11C2×C11×#117C2212yes—
12C2×#66979C2212yes—
13C2×#66979C2211yescharacteristic
14C23×C11⋊C8C2211yescharacteristic
15#10623050—24no—
16#10623050C2218yes—
17#10623048—24no—
18#10623048C2218yes—
19#10623031C2218yes—
20#10623014—24no—
21#10623001—24no—
22C11×#428C2218yes—
23C11×#427C2214yes—
24#10622735C2214yes—
25#10622735C2214yes—
26#10622734C2218yes—
27#10622719C2214yes—
28C2×#66879C2212yes—
29C2×C8×Dic11C2212yes—
30#10622611C2214yes—
31#10622611C2214yes—
32#10622611C2214yes—
33#10622611C2214yes—
34C2×#66872C2214yes—
35C2×#66871C2214yes—
36#10622491C2218yescomplemented
37#10622489C22116yescomplemented
38#10622487C2218yescomplemented
39#10622471C2218yescomplemented
40#10622469C22116yescomplemented
41#10622468C2218yescomplemented
42C23×C4×C11C2311yescharacteristic
43C2×C11×M16Q818yescomplemented
44C2×C11×M16C2314yes—
45C22×C8×C11C2312yes—
46C11×#117—22no—
47C11×#117—22no—
48C11×#117C2314yes—
49C11×#117C2314yes—
50C2×C11×C4⋊C4C2314yes—
51C2×C11×C22⋊C4—22no—
52C2×C42×C11—22no—
53C2×C22⋊Dic11—22no—
54C2×C22⋊Dic11D412yes—
55#66979—22no—
56#66979—22no—
57#66979D414yes—
58#66979C2314yes—
59#66979C2314yes—
60#66979C2314yes—
61C2×C4⋊Dic11D412yes—
62C2×C4⋊Dic11C2314yes—
63#66977—216no—
64C2×C4×Dic11—22no—
65C2×C4×Dic11C2312yes—
66C22×C11⋊C8Q818yescomplemented
67C22×C11⋊C8C2312yes—
68C22×C11⋊C8C2312yes—
69C22×C11⋊C8C2311yescharacteristic
70C22×C11⋊C8C2311yescharacteristic
71#66943—28no—
72#66943C23116yes—
73#66941—28no—
74#66941C23116yes—
75#66931—216no—
76#66931—216no—
77#66923—28no—
78#66922—28no—
79C4×Dic22—216no—
80C11×#107C2318yes—
81C11×#106C2318yes—
82#66882C2318yes—
83#66881C2318yes—
84#66879C2318yes—
85C8×Dic11C2314yes—
86C8×Dic11C2314yes—
87#66872C2318yes—
88#66872C2318yes—
89#66871C2318yes—
90#66871C2318yes—
91#60660—111nomaximal, Sylow
92C24×C11C2×D411yescharacteristic
93C22×C4×C11—24no—
94C22×C4×C11C2×D412yes—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×Q814yes—
97C22×C4×C11C2×Q814yes—
98C22×C4×C11C2411yescharacteristic
99C22×C4×C11C2412yes—
100C22×Dic11—24no—
101C22×Dic11C2×D414yes—
102C2×Dic22—216no—
103C11×M16C2×Q8116yes—
104C2×C8×C11C2×Q818yes—
105C2×C8×C11C2414yes—
106C11×C4⋊C4—24no—
107C11×C4⋊C4C2418yes—
108C11×C22⋊C4—24no—
109C11×C22⋊C4—24no—
110C42×C11—24no—
111C42×C11—24no—
112C22⋊Dic11—24no—
113C22⋊Dic11—24no—
114C22⋊Dic11C2×D418yes—
115C4⋊Dic11—216no—
116C4⋊Dic11—24no—
117C4⋊Dic11C2×D418yes—
118C4⋊Dic11C2418yes—
119Dic11⋊C4—216no—
120Dic11⋊C4—216no—
121C4×Dic11—24no—
122C4×Dic11—24no—
123C4×Dic11C2×D414yes—
124C4×Dic11C2414yes—
125C2×C11⋊C8C2×Q818yes—
126C2×C11⋊C8C2×Q818yes—
127C2×C11⋊C8C2×Q814yes—
128C2×C11⋊C8C2×Q814yes—
129C2×C11⋊C8C2411yescharacteristic
130C2×C11⋊C8C2412yes—
131C2×C11⋊C8C2411yescharacteristic
132#3458—112no—
133#3164—118no—
134#3163—118no—
135#3162—114no—
136#3160—114no—
137#2911—111no—
138#2911D1111yescharacteristic
139C2×#427—112no—
140C2×#405—111no—
141C23×C11—42no—
142C23×C11C4⋊Q814yes—
143C23×C11C22×D411yescharacteristic
144C23×C11C22×D412yes—
145C2×C4×C11—28no—
146C2×C4×C11—84no—
147C2×C4×C11C4⋊Q818yes—
148C2×C4×C11C4⋊Q814yes—
149C2×C4×C11C22×D412yes—
150C2×C4×C11C22×D411yescharacteristic
151C2×C4×C11C22×Q812yes—
152C2×C4×C11C22×Q814yes—
153C2×C4×C11C22×Q812yes—
154C2×C4×C11C22×Q814yes—
155C2×C4×C11C2511yescharacteristic
156C2×Dic11—28no—
157C2×Dic11—44no—
158C2×Dic11—84no—
159C2×Dic11C22×D418yes—
160Dic22—816no—
161C8×C11C22×Q818yes—
162C11⋊C8C22×Q812yes—
163C11⋊C8C22×Q814yes—
164C11⋊C8C22×Q812yes—
165C22×M16C2×D1111yescharacteristic
166C23×C8—111no—
167#544—118no—
168#544—118no—
169#544—224no—
170#543—224no—
171#533—118no—
172#533—224no—
173#533—224no—
174C2×#117—111no—
175C2×#117—112no—
176C2×#117C2×D1112yes—
177#501—1116no—
178#501—1116no—
179#500—118no—
180#499—118no—
181#499—118no—
182#498—118no—
183#428—118no—
184#428C2×D1118yes—
185#427—114no—
186#427—114no—
187#427—114no—
188#427—114no—
189#427—114no—
190#427C2×D1114yes—
191C2×#107—114no—
192C2×#106—114no—
193#405—114no—
194#405—114no—
195C2×#97—112no—
196C2×C4×C8—112no—
197C22×C11—24no—
198C22×C11—22no—
199C22×C11—44no—
200C22×C11C2×C4⋊Q812yes—
201C22×C11C2×C4⋊Q814yes—
202C22×C11C23×D411yescharacteristic
203C4×C11—48no—
204C4×C11C2×C4⋊Q814yes—
205C4×C11C2×C4⋊Q812yes—
206C4×C11C23×Q811yescharacteristic
207C4×C11C23×Q811yescharacteristic
208Dic11—28no—
209Dic11—48no—
210C23×C4C22×D1111yescharacteristic
211C2×M16Dic2218yescomplemented
212C2×M16C22×D1114yes—
213C22×C8—118no—
214C22×C8—111no—
215C22×C8—111no—
216C22×C8—112no—
217C22×C8—112no—
218C22×C8C22×D1112yes—
219C4⋊Q8—1116no—
220C4⋊Q8—228no—
221C4⋊Q8—228no—
222#125—1116no—
223#125—228no—
224#125—228no—
225C22⋊Q8—2216no—
226C22⋊Q8—2216no—
227C22⋊Q8—2216no—
228C4×Q8—2216no—
229#117—22no—
230#117—22no—
231#117—114no—
232#117—114no—
233#117—114no—
234#117—114no—
235#117—222no—
236#117—222no—
237#117C22×D1114yes—
238#117C22×D1114yes—
239C2×C4⋊C4—112no—
240C2×C4⋊C4—114no—
241C2×C4⋊C4C22×D1114yes—
242C2×C22⋊C4—22no—
243C2×C22⋊C4—112no—
244C2×C22⋊C4—222no—
245C2×C42—22no—
246C2×C42—112no—
247C2×C42—222no—
248#107—118no—
249#107—118no—
250#107—118no—
251#107C22×D1118yes—
252#106—118no—
253#106—118no—
254#106—118no—
255#106C22×D1118yes—
256#97—118no—
257C4×C8—114no—
258C4×C8—114no—
259C2×C11—24no—
260C2×C11—22no—
261C2×C11C22×C4⋊Q811yescharacteristic
262C2×C11#358412yes—
263C24D4×D1111yescharacteristic
264C2×Q8—2216no—
265C22×C4—24no—
266C22×C4—114no—
267C22×C4—224no—
268C22×C4C2×Dic2214yes—
269C22×C4D4×D1111yescharacteristic
270C22×C4D4×D1112yes—
271C22×C4Q8×D1114yes—
272C22×C4C23×D1112yes—
273C22×C4C23×D1111yescharacteristic
274M16C2×Dic22116yes—
275C2×C8—114no—
276C2×C8—114no—
277C2×C8—118no—
278C2×C8—118no—
279C2×C8—111no—
280C2×C8—111no—
281C2×C8—112no—
282C2×C8C2×Dic2218yes—
283C2×C8C23×D1114yes—
284C4⋊C4—24no—
285C4⋊C4—118no—
286C4⋊C4—118no—
287C4⋊C4—2216no—
288C4⋊C4—2216no—
289C4⋊C4—2216no—
290C4⋊C4—224no—
291C4⋊C4C23×D1118yes—
292C22⋊C4—24no—
293C22⋊C4—24no—
294C22⋊C4—118no—
295C22⋊C4—224no—
296C22⋊C4—224no—
297C42—24no—
298C42—24no—
299C42—114no—
300C42—114no—
301C42—224no—
302C42—224no—
303C11#6066011yescharacteristic, complemented, Sylow
304C23—42no—
305C23#6694114yes—
306C23C2×D4×D1111yescharacteristic
307C23C2×D4×D1112yes—
308Q8—8816no—
309C2×C4—28no—
310C2×C4—84no—
311C2×C4—118no—
312C2×C4—228no—
313C2×C4—444no—
314C2×C4—884no—
315C2×C4#6694114yes—
316C2×C4#6694118yes—
317C2×C4C22×Dic2212yes—
318C2×C4C22×Dic2214yes—
319C2×C4C2×D4×D1112yes—
320C2×C4C2×D4×D1111yescharacteristic
321C2×C4C2×Q8×D1114yes—
322C2×C4C2×Q8×D1112yes—
323C2×C4C24×D1111yescharacteristic
324C8—112no—
325C8—112no—
326C8—114no—
327C8C22×Dic2218yes—
328C22—24no—
329C22—22no—
330C22—44no—
331C22C2×#6694112yes—
332C22C2×#6694114yes—
333C22C22×D4×D1111yescharacteristic
334C4—48no—
335C4—228no—
336C4—448no—
337C4C2×#6694114yes—
338C4C2×#6694112yes—
339C4C23×Dic2211yescharacteristic
340C4C22×Q8×D1111yescharacteristic
341C2—24no—
342C2—22no—
343C2C22×#6694111yescharacteristic
344C2#1308338912yes—
subgroupG/H
centerC2×C4C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#2911C2
socleC22×C11C23×D4
prime radicalC24×C11C2×D4
hypercenter#2911D11
hypocenterC11#60660
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2911

Complements

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

NH ≅ G/Ntype
2. #13079154C2semidirect
3. #13079146C2semidirect
4. #13079139C2semidirect
5. #13079128C2semidirect
36. #10622491C22semidirect
37. #10622489C22semidirect
38. #10622487C22semidirect
39. #10622471C22semidirect
40. #10622469C22semidirect
41. #10622468C22semidirect
43. C2×C11×M16Q8semidirect
66. C22×C11⋊C8Q8semidirect
211. C2×M16Dic22semidirect
303. C11#60660semidirect

Maximal subgroups

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

subgroupindex
#130820212
#130791542
#130791462
#130791392
#130791282
#130772062
C2×#106226112
C2×#106227352
C11×#29112
#6066011