Finite Group Databasebeta

← #14751745

Subgroups — #14751745

Order 2816.

1110 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622731C211yesmaximal, characteristic
2C2×#10622735C211yesmaximal, characteristic
3C2×#10622610C211yesmaximal, characteristic
4C22×#66879C211yesmaximal, characteristic
5#13071019C211yesmaximal, characteristic
6#13068489C214yesmaximal, complemented
7#13068487C214yesmaximal, complemented
8#13068312C211yesmaximal, characteristic
9C11×#1729C211yesmaximal, characteristic
10C22×C11×M16C2211yescharacteristic
11C23×C8×C11C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C22×C4×Dic11C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16C23×C11⋊C8C2211yescharacteristic
17#10622735—24no—
18#10622731C418yescomplemented
19C2×#66879C418yescomplemented
20C2×#66879C2212yes—
21C2×#66879C2212yes—
22C2×#66879C2212yes—
23C2×Dic11⋊C8C2214yes—
24C2×C8×Dic11C2212yes—
25#10622610—24no—
26#10622590C412yes—
27#10622589C412yes—
28#10622555C414yes—
29C4×Dic11⋊C4C2214yes—
30C2×#66867C2212yes—
31C2×C4×C11⋊C8C2212yes—
32C11×#336C2214yes—
33#10622188C2214yes—
34C23×C4×C11C2311yescharacteristic
35C23×Dic11C2×C412yes—
36C2×C11×M16—22no—
37C2×C11×M16—22no—
38C2×C11×M16C2×C414yes—
39C22×C8×C11—22no—
40C22×C8×C11—22no—
41C22×C8×C11C2×C414yes—
42C22×C8×C11C2312yes—
43C22×C8×C11C2312yes—
44C11×#117—22no—
45C11×#117—22no—
46C2×C11×C4⋊C4C2×C412yes—
47C2×C11×C22⋊C4C2×C412yes—
48C2×C42×C11C2312yes—
49C2×C22⋊Dic11C2×C412yes—
50#66979—22no—
51#66979—22no—
52C2×C4⋊Dic11C2×C412yes—
53C2×Dic11⋊C4C2×C418yes—
54C2×C4×Dic11C2×C411yescharacteristic
55C2×C4×Dic11C2×C411yescharacteristic
56C2×C4×Dic11C2×C414yes—
57C2×C4×Dic11C2×C414yes—
58C2×C4×Dic11C2312yes—
59C2×C4×Dic11C2312yes—
60C2×#4318—22no—
61C2×#4318—22no—
62C2×#4318C2×C414yes—
63C22×C11⋊C8C2×C414yes—
64C22×C11⋊C8D414yes—
65C22×C11⋊C8Q814yes—
66C22×C11⋊C8C2312yes—
67C22×C11⋊C8C2311yescharacteristic
68C22×C11⋊C8C2311yescharacteristic
69C11⋊#95C2×C418yes—
70#66879—24no—
71#66879C2×C418yes—
72#66879C2×C418yes—
73Dic11⋊C8C2×C4116yes—
74C8×Dic11—24no—
75#66867—24no—
76C4×C11⋊C8—24no—
77#20438—111nomaximal, Sylow
78C24×C11C22×C411yescharacteristic
79C22×C4×C11C22×C414yes—
80C22×C4×C11C22×C411yescharacteristic
81C22×C4×C11C22×C412yes—
82C22×C4×C11C22×C412yes—
83C22×C4×C11C2×D412yes—
84C22×C4×C11C2×Q812yes—
85C22×C4×C11#4112yes—
86C22×C4×C11#4112yes—
87C22×C4×C11C2411yescharacteristic
88C22×Dic11—44no—
89C22×Dic11C4218yes—
90C22×Dic11C22×C414yes—
91C22×Dic11C22×C412yes—
92C22×Dic11C22×C412yes—
93C11×M16—28no—
94C2×C8×C11—28no—
95C2×C8×C11—22no—
96C2×C8×C11—22no—
97C2×C8×C11—22no—
98C2×C8×C11—22no—
99C2×C8×C11C22×C414yes—
100C2×C8×C11C22×C414yes—
101C11×C4⋊C4—24no—
102C11×C22⋊C4—24no—
103C42×C11—22no—
104C42×C11—22no—
105C22⋊Dic11—24no—
106C4⋊Dic11—24no—
107Dic11⋊C4—48no—
108C4×Dic11—22no—
109C4×Dic11—22no—
110C4×Dic11C4214yes—
111C4×Dic11C4214yes—
112C4×Dic11C22×C414yes—
113C4×Dic11C22×C414yes—
114#4318—28no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—22no—
117C2×C11⋊C8C4⋊C4116yescomplemented
118C2×C11⋊C8C22×C414yes—
119C2×C11⋊C8C22×C412yes—
120C2×C11⋊C8C22×C412yes—
121C2×C11⋊C8C2×D412yes—
122C2×C11⋊C8C2×D412yes—
123C2×C11⋊C8C2×Q812yes—
124C2×C11⋊C8C2×Q812yes—
125C2×#423—111no—
126C2×#405—111no—
127C2×#405—111no—
128C22×#97—111no—
129#2285—111no—
130#1771—114no—
131#1771—114no—
132#1729—111no—
133#1729D1111yescharacteristic
134C23×C11—24no—
135C23×C11C2×C4212yes—
136C23×C11C4×D412yes—
137C23×C11C4×Q812yes—
138C23×C11C23×C411yescharacteristic
139C2×C4×C11—24no—
140C2×C4×C11—28no—
141C2×C4×C11C2×C4212yes—
142C2×C4×C11C2×C4⋊C414yes—
143C2×C4×C11#11714yes—
144C2×C4×C11C4×D414yes—
145C2×C4×C11C4×D412yes—
146C2×C4×C11C4×Q814yes—
147C2×C4×C11C4×Q812yes—
148C2×C4×C11C23×C411yescharacteristic
149C2×C4×C11C23×C411yescharacteristic
150C2×C4×C11C22×D411yescharacteristic
151C2×C4×C11C22×Q811yescharacteristic
152C2×C4×C11C2×#4111yescharacteristic
153C2×C4×C11C2×#4111yescharacteristic
154C2×Dic11—24no—
155C2×Dic11—24no—
156C2×Dic11—24no—
157C2×Dic11—28no—
158C2×Dic11—48no—
159C2×Dic11C2×C4214yes—
160C2×Dic11C2×C4214yes—
161C8×C11—24no—
162C8×C11—24no—
163C11⋊C8—24no—
164C11⋊C8C2×C4⋊C414yes—
165C11⋊C8C2×C4⋊C414yes—
166C22×M16—111no—
167C22×M16C2×D1111yescharacteristic
168C23×C8—111no—
169C23×C8C2×D1111yescharacteristic
170C2×#117—111no—
171C2×#117C2×D1111yescharacteristic
172C22×C42—111no—
173#423—118no—
174C2×C4⋊C8—114no—
175#405—224no—
176#405—224no—
177C2×#97—112no—
178C2×#97—112no—
179C2×#97—118no—
180C2×#97—112no—
181C2×#97—112no—
182C2×C4×C8—112no—
183C2×C4×C8—112no—
184#384—112no—
185#382—112no—
186#380—114no—
187C4×C4⋊C4—114no—
188#336—114no—
189#336C2×D1114yes—
190C22×C11—24no—
191C22×C11—24no—
192C22×C11—24no—
193C22×C11C4×C4⋊C414yes—
194C22×C11C22×C4211yescharacteristic
195C22×C11C2×C4×D411yescharacteristic
196C22×C11C2×C4×Q811yescharacteristic
197C22×C11#56814yes—
198C4×C11—44no—
199C4×C11C4×C4⋊C414yes—
200C4×C11C22×C4⋊C411yescharacteristic
201C4×C11C2×#11711yescharacteristic
202C4×C11C2×C4×D411yescharacteristic
203C4×C11C2×C4×Q811yescharacteristic
204Dic11—24no—
205Dic11—24no—
206Dic11—44no—
207C23×C4—112no—
208C23×C4C22×D1111yescharacteristic
209C2×M16—22no—
210C2×M16—22no—
211C2×M16—114no—
212C2×M16—222no—
213C2×M16—222no—
214C2×M16C4×D1114yes—
215C22×C8—22no—
216C22×C8—22no—
217C22×C8—114no—
218C22×C8—114no—
219C22×C8—114no—
220C22×C8—111no—
221C22×C8—111no—
222C22×C8—112no—
223C22×C8C4×D1114yes—
224C22×C8C22×D1112yes—
225C22×C8C22×D1112yes—
226#117—22no—
227#117—22no—
228#117—222no—
229#117—222no—
230C2×C4⋊C4—112no—
231C2×C4⋊C4—118no—
232C2×C4⋊C4C4×D1112yes—
233C2×C22⋊C4—112no—
234C2×C22⋊C4C4×D1112yes—
235C2×C42—111no—
236C2×C42—111no—
237C2×C42—114no—
238C2×C42—114no—
239C2×C42—112no—
240C2×C42—112no—
241C2×C42C22×D1112yes—
242C4⋊C8—1116no—
243#97—118no—
244#97—118no—
245#97—224no—
246#97—224no—
247C4×C8—224no—
248C4×C8—224no—
249#95—118no—
250C2×C11—24no—
251C2×C11C2×C4×C4⋊C411yescharacteristic
252C2×C11#287312yes—
253C2×C11#293212yes—
254C2×C11#296112yes—
255C24C2×C4×D1111yescharacteristic
256C22×C4—112no—
257C22×C4—112no—
258C22×C4—118no—
259C22×C4—114no—
260C22×C4—444no—
261C22×C4C2×C4×D1114yes—
262C22×C4C2×C4×D1111yescharacteristic
263C22×C4C2×C4×D1112yes—
264C22×C4C2×C4×D1112yes—
265C22×C4D4×D1112yes—
266C22×C4#434112yes—
267C22×C4#434112yes—
268C22×C4Q8×D1112yes—
269C22×C4C23×D1111yescharacteristic
270M16—28no—
271M16—228no—
272C2×C8—28no—
273C2×C8—22no—
274C2×C8—22no—
275C2×C8—22no—
276C2×C8—22no—
277C2×C8—1116no—
278C2×C8—112no—
279C2×C8—112no—
280C2×C8—112no—
281C2×C8—112no—
282C2×C8—112no—
283C2×C8—112no—
284C2×C8—114no—
285C2×C8—222no—
286C2×C8—222no—
287C2×C8C2×C4×D1114yes—
288C2×C8C2×C4×D1114yes—
289C4⋊C4—24no—
290C4⋊C4—224no—
291C4⋊C4—448no—
292C22⋊C4—24no—
293C22⋊C4—224no—
294C42—22no—
295C42—22no—
296C42—114no—
297C42—114no—
298C42—114no—
299C42—114no—
300C42—222no—
301C42—222no—
302C11#2043811yescharacteristic, complemented, Sylow
303C23—24no—
304C23C42×D1112yes—
305C23(C22⋊D11)⋊C412yes—
306C23#6694012yes—
307C23C22×C4×D1111yescharacteristic
308C2×C4—24no—
309C2×C4—28no—
310C2×C4—114no—
311C2×C4—114no—
312C2×C4—224no—
313C2×C4—224no—
314C2×C4—224no—
315C2×C4—228no—
316C2×C4—448no—
317C2×C4C42×D1112yes—
318C2×C4#6693014yes—
319C2×C4(C22⋊D11)⋊C414yes—
320C2×C4(C22⋊D11)⋊C412yes—
321C2×C4#6694014yes—
322C2×C4#6694012yes—
323C2×C4C4⋊C4×D1114yes—
324C2×C4C22×C4×D1111yescharacteristic
325C2×C4C22×C4×D1111yescharacteristic
326C2×C4C2×D4×D1111yescharacteristic
327C2×C4C2×#434111yescharacteristic
328C2×C4C2×#434111yescharacteristic
329C2×C4C2×Q8×D1111yescharacteristic
330C8—24no—
331C8—24no—
332C8—114no—
333C8—114no—
334C8—224no—
335C22—24no—
336C22—24no—
337C22—24no—
338C22#1062226214yes—
339C22C2×C42×D1111yescharacteristic
340C22C2×(C22⋊D11)⋊C411yescharacteristic
341C22C2×#6694011yescharacteristic
342C22#1062328114yes—
343C4—44no—
344C4—224no—
345C4—224no—
346C4—444no—
347C4#1062226214yes—
348C4C2×#6693011yescharacteristic
349C4C2×(C22⋊D11)⋊C411yescharacteristic
350C4C2×#6694011yescharacteristic
351C4C2×C4⋊C4×D1111yescharacteristic
352C2—24no—
353C2C2×#1062226211yescharacteristic
354C2#1307703212yes—
355C2#1307733112yes—
356C2#1307755512yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C22×C42
FittingC11×#1729C2
socleC23×C11C23×C4
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenter#1729D11
hypocenterC11#20438
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1729

Complements

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

NH ≅ G/Ntype
6. #13068489C2semidirect
7. #13068487C2semidirect
18. #10622731C4semidirect
19. C2×#66879C4semidirect
117. C2×C11⋊C8C4⋊C4semidirect
302. C11#20438semidirect

Maximal subgroups

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

subgroupindex
C2×#106227312
C2×#106227352
C2×#106226102
C22×#668792
#130710192
#130684892
#130684872
#130683122
C11×#17292
#2043811