Finite Group Databasebeta

← #14913797

Subgroups — #14913797

Order 2816.

5126 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Q8×D11C211yesmaximal, characteristic
2C2×#10623047C212yesmaximal, complemented
3#13071450C2116yesmaximal, complemented
4#13071202C211yesmaximal, characteristic, complemented
5#13071201C214yesmaximal, complemented
6#13070996C214yesmaximal
7#13070995C212yesmaximal
8C11×#2310C211yesmaximal, characteristic, complemented
9C23×Q8×C11C2211yescharacteristic
10C22×Q8×D11—216no—
11C22×Q8×D11C4116yescomplemented
12C22×Q8×D11C2218yes—
13C23×C4×D11C2211yescharacteristic
14C23×C4×D11C2212yes—
15C23×Dic22C2212yes—
16C23×Dic22C2211yescharacteristic
17C2×C11×#117C2212yes—
18C2×#66979C2212yes—
19#10623047—216no—
20C2×#66940C2218yescomplemented
21C2×#66930C2218yes—
22C2×C4×Dic22C2218yescomplemented
23C11×#391C2218yescomplemented
24C11×#381C2214yes—
25#10622843C2218yescomplemented
26#10622824C2214yes—
27#10622600C2218yes—
28#10622568C2214yes—
29#10622556C2214yes—
30C4×(C2×D11)⋊C4C2218yes—
31#10622280C22116yes—
32#10622279C22116yes—
33#10622259C22132yescomplemented
34C24×D11C2311yescharacteristic
35C22×Q8×C11—28no—
36C22×Q8×C11C2×C418yes—
37C22×Q8×C11C2314yes—
38C23×C4×C11C2312yes—
39C23×C4×C11C2311yescharacteristic
40C23×Dic11C2311yescharacteristic
41C23×Dic11C2312yes—
42C2×Q8×D11—2128no—
43C2×Q8×D11—232no—
44C2×Q8×D11—232no—
45C2×Q8×D11C2×C4164yes—
46C22×C4×D11—28no—
47C22×C4×D11—216no—
48C22×C4×D11C2×C4116yes—
49C22×C4×D11C2×C418yes—
50C22×C4×D11C2318yes—
51C22×C4×D11C2314yes—
52C22×Dic22—216no—
53C22×Dic22C2×C4116yes—
54C22×Dic22C2×C418yes—
55C22×Dic22D4116yes—
56C22×Dic22C2318yes—
57C22×Dic22C2314yes—
58C11×#117—28no—
59C2×C11×C4⋊C4C2314yes—
60C2×C11×C22⋊C4C2314yes—
61C2×C42×C11C2314yes—
62C2×C22⋊Dic11C2314yes—
63C2×(C2×D11)⋊C4C23116yes—
64#66979—28no—
65C2×C4⋊Dic11C2314yes—
66C2×Dic11⋊C4C23116yes—
67C2×C4×Dic11C23116yes—
68C2×C4×Dic11C2314yes—
69#66940—232no—
70#66930—232no—
71C4×Dic22—232no—
72C11×#95C23116yes—
73C11⋊#95C23116yes—
74C11⋊#95C23116yes—
75#34173—111nomaximal, Sylow
76C24×C11C2411yescharacteristic
77C23×D11—24no—
78C23×D11—28no—
79C23×D11C22×C414yes—
80C23×D11C2412yes—
81C2×Q8×C11—232no—
82C2×Q8×C11—28no—
83C2×Q8×C11—28no—
84C2×Q8×C11C22×C4116yes—
85C22×C4×C11—28no—
86C22×C4×C11C22×C418yes—
87C22×C4×C11C22×C414yes—
88C22×C4×C11C2×D418yes—
89C22×C4×C11C2418yes—
90C22×C4×C11C2414yes—
91C22×C4×C11C2412yes—
92C22×Dic11—24no—
93C22×Dic11C22×C414yes—
94C22×Dic11C22×C418yes—
95C22×Dic11C2×D4116yes—
96C22×Dic11C2418yes—
97C22×Dic11C2412yes—
98C22×Dic11C2414yes—
99Q8×D11—2256no—
100C2×C4×D11—264no—
101C2×C4×D11—232no—
102C2×C4×D11—232no—
103C2×C4×D11—28no—
104C2×C4×D11—28no—
105C2×C4×D11C22×C4132yes—
106C2×C4×D11C22×C4116yes—
107C2×Dic22—264no—
108C2×Dic22—232no—
109C2×Dic22C22⋊C4164yescomplemented
110C2×Dic22C22×C4132yes—
111C2×Dic22C22×C4116yes—
112C2×Dic22C2×D4116yes—
113C2×Dic22C2×D4116yes—
114C11×C4⋊C4—28no—
115C11×C22⋊C4—28no—
116C42×C11—28no—
117C22⋊Dic11—28no—
118(C2×D11)⋊C4—232no—
119C4⋊Dic11—28no—
120Dic11⋊C4—232no—
121C4×Dic11—232no—
122C4×Dic11—28no—
123C24×Q8—111no—
124C2×#519—112no—
125Q8×C22⋊C4—1116no—
126#2310—114no—
127#2310—111no—
128#2310D1111yescharacteristic, complemented
129#2280—114no—
130#2280—112no—
131C23×C11—24no—
132C23×C11C23×C412yes—
133C23×C11C22×D414yes—
134C23×C11C2511yescharacteristic
135C22×D11—232no—
136C22×D11—28no—
137C22×D11—24no—
138C22×D11—24no—
139C22×D11—216no—
140C22×D11C23×C414yes—
141C22×D112−1+418yes—
142Q8×C11—232no—
143C2×C4×C11—216no—
144C2×C4×C11—28no—
145C2×C4×C11—28no—
146C2×C4×C11—216no—
147C2×C4×C11C2×C22⋊C4116yes—
148C2×C4×C11C23×C418yes—
149C2×C4×C11C23×C414yes—
150C2×C4×C11C22×D414yes—
151C2×C4×C11C22×D414yes—
152C2×Dic11—28no—
153C2×Dic11—24no—
154C2×Dic11—28no—
155C2×Dic11—216no—
156C2×Dic11C2×C22⋊C4132yes—
157C2×Dic11C23×C414yes—
158C2×Dic11C23×C418yes—
159C2×Dic11C22×D4116yes—
160C4×D11—232no—
161C4×D11—264no—
162Dic22—264no—
163Dic22C2×C22⋊C4164yes—
164C23×Q8—118no—
165C23×Q8—1116no—
166C23×Q8—111no—
167C23×Q8—112no—
168C23×Q8—2216no—
169C23×Q8C2×D1111yescharacteristic
170C24×C4—112no—
171C24×C4—111no—
172#519—2216no—
173C2×C4×Q8—118no—
174C2×C4×Q8—118no—
175C2×#117—112no—
176C2×#117—118no—
177C2×#117C2×D1112yes—
178#391—118no—
179#391—1132no—
180#391C2×D1118yescomplemented
181#381—114no—
182#381—114no—
183#381C2×D1114yes—
184#380—118no—
185#380—1116no—
186#379—114no—
187C4×C22⋊C4—118no—
188C4×C22⋊C4—1116no—
189C22×C11—24no—
190C22×C11—28no—
191C22×C11C22×C22⋊C414yes—
192C22×C11C24×C411yescharacteristic
193C22×C11C23×D412yes—
194C22×C11C2×2−1+414yes—
195C2×D11—232no—
196C2×D11—24no—
197C2×D11—24no—
198C2×D11—216no—
199C2×D11#51918yescomplemented
200C4×C11—28no—
201C4×C11—48no—
202C4×C11C22×C22⋊C418yes—
203Dic11—24no—
204Dic11—48no—
205Dic11C22×C22⋊C4116yes—
206C25—111no—
207C22×Q8—28no—
208C22×Q8—1164no—
209C22×Q8—118no—
210C22×Q8—1116no—
211C22×Q8—1116no—
212C22×Q8—114no—
213C22×Q8—118no—
214C22×Q8—2216no—
215C22×Q8—22128no—
216C22×Q8—2232no—
217C22×Q8—2232no—
218C22×Q8C4×D1118yes—
219C22×Q8C22×D1114yes—
220C23×C4—112no—
221C23×C4—111no—
222C23×C4—1116no—
223C23×C4—118no—
224C23×C4—118no—
225C23×C4—114no—
226C23×C4—2216no—
227C23×C4—228no—
228C23×C4C22×D1112yes—
229C23×C4C22×D1111yescharacteristic
230C4×Q8—2232no—
231C4×Q8—2232no—
232#117—28no—
233#117—2232no—
234#117—228no—
235C2×C4⋊C4—1116no—
236C2×C4⋊C4—114no—
237C2×C4⋊C4C22×D1114yes—
238C2×C22⋊C4—114no—
239C2×C22⋊C4—1116no—
240C2×C22⋊C4C22×D1114yes—
241C2×C42—1116no—
242C2×C42—114no—
243C2×C42C22×D1114yes—
244#95—1116no—
245#95—1116no—
246#95C22×D11116yes—
247C2×C11—24no—
248C2×C11C23×C22⋊C411yescharacteristic
249C2×C11C2×#51912yes—
250C2×C11#348614yes—
251D11—28no—
252C24—112no—
253C24—114no—
254C24—228no—
255C24—224no—
256C24C23×D1111yescharacteristic
257C2×Q8—232no—
258C2×Q8—28no—
259C2×Q8—28no—
260C2×Q8—1164no—
261C2×Q8—1116no—
262C2×Q8—1132no—
263C2×Q8—1116no—
264C2×Q8—1116no—
265C2×Q8—2264no—
266C2×Q8—2232no—
267C2×Q8—22256no—
268C2×Q8C2×C4×D11116yes—
269C22×C4—28no—
270C22×C4—118no—
271C22×C4—1116no—
272C22×C4—114no—
273C22×C4—114no—
274C22×C4—112no—
275C22×C4—1132no—
276C22×C4—1116no—
277C22×C4—118no—
278C22×C4—2264no—
279C22×C4—2232no—
280C22×C4—224no—
281C22×C4—2232no—
282C22×C4—228no—
283C22×C4—228no—
284C22×C4C2×C4×D1118yes—
285C22×C4C2×C4×D1114yes—
286C22×C4D4×D1118yes—
287C22×C4C23×D1118yes—
288C22×C4C23×D1114yes—
289C22×C4C23×D1112yes—
290C4⋊C4—28no—
291C4⋊C4—2232no—
292C4⋊C4—228no—
293C22⋊C4—28no—
294C22⋊C4—2232no—
295C22⋊C4—228no—
296C42—28no—
297C42—2232no—
298C42—228no—
299C11#3417311yescharacteristic, complemented, Sylow
300C23—24no—
301C23—114no—
302C23—118no—
303C23—2216no—
304C23—2232no—
305C23—228no—
306C23—224no—
307C23—224no—
308C23C22×C4×D1112yes—
309C23C2×D4×D1114yes—
310C23C24×D1111yescharacteristic
311Q8—232no—
312Q8—1164no—
313Q8—2264no—
314C2×C4—216no—
315C2×C4—28no—
316C2×C4—28no—
317C2×C4—216no—
318C2×C4—1132no—
319C2×C4—118no—
320C2×C4—1116no—
321C2×C4—114no—
322C2×C4—2264no—
323C2×C4—228no—
324C2×C4—224no—
325C2×C4—2232no—
326C2×C4—228no—
327C2×C4—2216no—
328C2×C4C22⋊C4×D11116yes—
329C2×C4C22×C4×D1118yes—
330C2×C4C22×C4×D1114yes—
331C2×C4C2×D4×D1114yes—
332C2×C4C2×D4×D1114yes—
333C22—28no—
334C22—24no—
335C22—118no—
336C22—2232no—
337C22—2216no—
338C22—224no—
339C22—224no—
340C22C2×C22⋊C4×D1114yes—
341C22C23×C4×D1111yescharacteristic
342C22C22×D4×D1112yes—
343C22D11×2−1+414yes—
344C4—28no—
345C4—48no—
346C4—1116no—
347C4—224no—
348C4—448no—
349C4C2×C22⋊C4×D1118yes—
350C2—24no—
351C2—228no—
352C2C22×C22⋊C4×D1111yescharacteristic
353C2D11×#51912yes—
354C2#1308226514yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2310C2
socle, cosocleC23×C11C25
prime radicalC24×D11C23
hypercenter#2310D11
hypocenterC11#34173
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2310

Complements

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

NH ≅ G/Ntype
2. C2×#10623047C2semidirect
3. #13071450C2semidirect
4. #13071202C2semidirect
5. #13071201C2semidirect
8. C11×#2310C2semidirect
11. C22×Q8×D11C4semidirect
20. C2×#66940C22semidirect
22. C2×C4×Dic22C22semidirect
23. C11×#391C22semidirect
25. #10622843C22semidirect
33. #10622259C22semidirect
109. C2×Dic22C22⋊C4semidirect
128. #2310D11semidirect
180. #391C2×D11semidirect
199. C2×D11#519semidirect
299. C11#34173semidirect

Maximal subgroups

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

subgroupindex
C23×Q8×D112
C2×#106230472
#130714502
#130712022
#130712012
#130709962
#130709952
C11×#23102
#3417311