Finite Group Databasebeta

← C22×#10622452 #15617387

Subgroups — C22×#10622452 #15617387

Order 2816.

3006 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4313C211yesmaximal, characteristic
2C23×C8×D11C211yesmaximal, characteristic
3C22×#66925C211yesmaximal, characteristic
4C2×#10622452C2124yesmaximal, direct product factor
5C22×C4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
6C22×Dic11⋊C8C211yesmaximal, characteristic, complemented
7C22×Dic11⋊C8C211yesmaximal, characteristic, complemented
8C22×C11×C4⋊C8C211yesmaximal, characteristic, complemented
9C23×C4×D11C2211yescharacteristic
10C23×C8×C11C2211yescharacteristic
11C23×C8×C11C2211yescharacteristic
12C22×C42×C11C2211yescharacteristic
13C22×(C2×D11)⋊C4C411yescharacteristic
14C22×(C2×D11)⋊C4C411yescharacteristic
15C22×Dic11⋊C4C411yescharacteristic
16C22×Dic11⋊C4C411yescharacteristic
17C22×C4×Dic11C2211yescharacteristic
18C23×C11⋊C8C2211yescharacteristic
19C23×C11⋊C8C2211yescharacteristic
20C22×#4313—28no—
21C22×#4313C22112yes—
22C22×C8×D11—28no—
23C22×C8×D11C22112yes—
24C2×#66925C4112yes—
25C2×#66925C22112yes—
26C2×C11×C4⋊C8C22112yescomplemented
27C2×Dic11⋊C8C22112yescomplemented
28C2×Dic11⋊C8C22112yescomplemented
29C2×C4⋊(C11⋊C8)C22112yescomplemented
30#10622452C22164yesdirect product factor
31C24×D11C2×C411yescharacteristic
32C23×C4×C11C2×C411yescharacteristic
33C23×C4×C11C2×C411yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C23×Dic11C2×C411yescharacteristic
36C23×Dic11C2×C411yescharacteristic
37C23×Dic11C2×C411yescharacteristic
38C22×C4×D11C2×C416yes—
39C22×C4×D11D418yes—
40C22×C4×D11Q818yes—
41C22×C4×D11C2316yes—
42C22×C8×C11—24no—
43C22×C8×C11—24no—
44C22×C8×C11C2316yes—
45C22×C8×C11C2316yes—
46C2×C42×C11C2×C416yes—
47C2×C42×C11C2316yes—
48C2×(C2×D11)⋊C4C2×C4112yes—
49C2×(C2×D11)⋊C4C2×C4112yes—
50C2×Dic11⋊C4C2×C4112yes—
51C2×Dic11⋊C4C2×C4112yes—
52C2×C4×Dic11C2×C416yes—
53C2×C4×Dic11C2316yes—
54C22×C11⋊C8—24no—
55C22×C11⋊C8—24no—
56C22×C11⋊C8C2316yes—
57C22×C11⋊C8C2316yes—
58C2×#4313—248no—
59C2×#4313C23116yes—
60C2×C8×D11—248no—
61C2×C8×D11C23116yes—
62#66925C2×C4148yes—
63#66925C23116yes—
64C11×C4⋊C8C23116yescomplemented
65Dic11⋊C8C23116yescomplemented
66Dic11⋊C8C23116yescomplemented
67C4⋊(C11⋊C8)C23116yescomplemented
68C22×#424—111nomaximal, Sylow
69C24×C11C22×C411yescharacteristic
70C23×D11—24no—
71C23×D11—24no—
72C23×D11C4⋊C418yes—
73C23×D11C22×C416yes—
74C22×C4×C11—24no—
75C22×C4×C11—24no—
76C22×C4×C11C22×C416yes—
77C22×C4×C11C22×C416yes—
78C22×C4×C11C22×C413yes—
79C22×C4×C11C2×D414yes—
80C22×C4×C11C2×Q814yes—
81C22×C4×C11C2413yes—
82C22×Dic11—24no—
83C22×Dic11—24no—
84C22×Dic11C4⋊C418yes—
85C22×Dic11C22×C416yes—
86C22×Dic11C22×C416yes—
87C22×Dic11C22×C416yes—
88C2×C4×D11C4⋊C4148yes—
89C2×C4×D11C22×C4112yes—
90C2×C4×D11C2×D4124yes—
91C2×C4×D11C2×Q8124yes—
92C2×C4×D11C2414yes—
93C2×C8×C11—212no—
94C2×C8×C11—212no—
95C2×C8×C11C2414yes—
96C2×C8×C11C2414yes—
97C42×C11C22×C4112yes—
98C42×C11C2414yes—
99(C2×D11)⋊C4C22×C4116yes—
100(C2×D11)⋊C4C22×C4116yes—
101Dic11⋊C4C22×C4116yes—
102Dic11⋊C4C22×C4116yes—
103C4×Dic11C22×C4112yes—
104C4×Dic11C2414yes—
105C2×C11⋊C8—212no—
106C2×C11⋊C8—212no—
107C2×C11⋊C8C2414yes—
108C2×C11⋊C8C2414yes—
109#4313—232no—
110C8×D11—232no—
111C23×M16—111no—
112C24×C8—111no—
113C22×#117—111no—
114C2×#424—1124no—
115C22×C4⋊C8—111no—
116C22×C4⋊C8—111no—
117C22×C4⋊C8—111no—
118C22×C4⋊C8D1111yescharacteristic, complemented
119C23×C11C2×C4⋊C414yes—
120C23×C11#13114yes—
121C23×C11#13114yes—
122C23×C11C23×C413yes—
123C22×D11—212no—
124C22×D11—212no—
125C22×D11—232no—
126C22×D11C2×C4⋊C4124yes—
127C22×D11C23×C414yes—
128C2×C4×C11—212no—
129C2×C4×C11—212no—
130C2×C4×C11C2×C4⋊C4112yes—
131C2×C4×C11C23×C414yes—
132C2×C4×C11C23×C414yes—
133C2×C4×C11C23×C413yes—
134C2×C4×C11C22×D416yes—
135C2×C4×C11C22×Q816yes—
136C2×C4×C11C2511yescharacteristic
137C2×Dic11—212no—
138C2×Dic11—212no—
139C2×Dic11C2×C4⋊C4124yes—
140C2×Dic11C23×C414yes—
141C2×Dic11C23×C414yes—
142C2×Dic11C23×C414yes—
143C4×D11C2×C4⋊C4148yes—
144C4×D11C22×D418yes—
145C4×D11C22×Q818yes—
146C8×C11—24no—
147C8×C11—24no—
148C11⋊C8—24no—
149C11⋊C8—24no—
150C24×C4—111no—
151C22×M16—1112no—
152C22×M16—228no—
153C23×C8—111no—
154C23×C8—111no—
155C23×C8—1112no—
156C23×C8—228no—
157C23×C8C2×D1111yescharacteristic
158C23×C8C2×D1111yescharacteristic
159C2×#117—1112no—
160C2×#117—1112no—
161C22×C4⋊C4—111no—
162C22×C4⋊C4—111no—
163C22×C22⋊C4—111no—
164C22×C22⋊C4—111no—
165C22×C42—111no—
166C22×C42C2×D1111yescharacteristic
167#424—1164no—
168C2×C4⋊C8—1112no—
169C2×C4⋊C8—1112no—
170C2×C4⋊C8—1112no—
171C2×C4⋊C8C2×D11112yescomplemented
172C22×C11#424116yescomplemented
173C22×C11C22×C4⋊C416yes—
174C22×C11C2×#13116yes—
175C22×C11C2×#13116yes—
176C22×C11C24×C411yescharacteristic
177C2×D11—248no—
178C2×D11—24no—
179C2×D11—24no—
180C2×D11C22×C4⋊C418yes—
181C4×C11—24no—
182C4×C11—24no—
183C4×C11C22×C4⋊C416yes—
184C4×C11C23×D411yescharacteristic
185C4×C11C23×Q811yescharacteristic
186Dic11—24no—
187Dic11—24no—
188Dic11C22×C4⋊C418yes—
189C25—111no—
190C23×C4—111no—
191C23×C4—116no—
192C23×C4—118no—
193C23×C4—118no—
194C23×C4—116no—
195C23×C4—111no—
196C23×C4—111no—
197C23×C4C4×D1111yescharacteristic
198C23×C4C4×D1111yescharacteristic
199C23×C4C22×D1111yescharacteristic
200C2×M16—1116no—
201C2×M16—2248no—
202C22×C8—24no—
203C22×C8—24no—
204C22×C8—116no—
205C22×C8—116no—
206C22×C8—1116no—
207C22×C8—2248no—
208C22×C8—224no—
209C22×C8—224no—
210C22×C8C22×D1116yes—
211C22×C8C22×D1116yes—
212#117—1148no—
213#117—1116no—
214C2×C4⋊C4—1112no—
215C2×C4⋊C4—1112no—
216C2×C22⋊C4—1112no—
217C2×C22⋊C4—1112no—
218C2×C42—116no—
219C2×C42—116no—
220C2×C42C4×D1116yes—
221C2×C42C22×D1116yes—
222C4⋊C8—1116no—
223C4⋊C8—1116no—
224C4⋊C8—1116no—
225C4⋊C8C22×D11116yescomplemented
226C2×C11C2×#424112yescomplemented
227C2×C11C23×C4⋊C411yescharacteristic
228C2×C11C22×#13111yescharacteristic
229C2×C11C22×#13111yescharacteristic
230D11—28no—
231C24—118no—
232C24—116no—
233C24—224no—
234C24—224no—
235C24C2×C4×D1111yescharacteristic
236C22×C4—24no—
237C22×C4—24no—
238C22×C4—118no—
239C22×C4—116no—
240C22×C4—1148no—
241C22×C4—1112no—
242C22×C4—1124no—
243C22×C4—1124no—
244C22×C4—114no—
245C22×C4—116no—
246C22×C4—116no—
247C22×C4—224no—
248C22×C4—224no—
249C22×C4C2×C4×D1116yes—
250C22×C4C2×C4×D1116yes—
251C22×C4C2×C4×D1113yes—
252C22×C4D4×D1114yes—
253C22×C4Q8×D1114yes—
254C22×C4C23×D1113yes—
255M16—2232no—
256C2×C8—212no—
257C2×C8—212no—
258C2×C8—114no—
259C2×C8—114no—
260C2×C8—2232no—
261C2×C8—2212no—
262C2×C8—2212no—
263C2×C8C23×D1114yes—
264C2×C8C23×D1114yes—
265C4⋊C4—1116no—
266C4⋊C4—1116no—
267C22⋊C4—1116no—
268C22⋊C4—1116no—
269C42—1112no—
270C42—114no—
271C42C2×C4×D11112yes—
272C42C23×D1114yes—
273C11C22×#42411yescharacteristic, complemented, Sylow
274C23—1124no—
275C23—114no—
276C23—2212no—
277C23—2212no—
278C23—2232no—
279C23C4⋊C4×D1114yes—
280C23#6695414yes—
281C23#6696014yes—
282C23C22×C4×D1113yes—
283C2×C4—212no—
284C2×C4—212no—
285C2×C4—1124no—
286C2×C4—114no—
287C2×C4—1148no—
288C2×C4—118no—
289C2×C4—118no—
290C2×C4—114no—
291C2×C4—114no—
292C2×C4—2212no—
293C2×C4—2212no—
294C2×C4C4⋊C4×D11112yes—
295C2×C4C22×C4×D1114yes—
296C2×C4C22×C4×D1114yes—
297C2×C4C22×C4×D1113yes—
298C2×C4C2×D4×D1116yes—
299C2×C4C2×Q8×D1116yes—
300C2×C4C24×D1111yescharacteristic
301C8—24no—
302C8—24no—
303C8—224no—
304C8—224no—
305C22—118no—
306C22—2248no—
307C22—224no—
308C22—224no—
309C22#10622452116yesdirect product factor
310C22C2×C4⋊C4×D1116yes—
311C22C2×#6695416yes—
312C22C2×#6696016yes—
313C22C23×C4×D1111yescharacteristic
314C4—24no—
315C4—24no—
316C4—118no—
317C4—224no—
318C4—224no—
319C4C2×C4⋊C4×D1116yes—
320C4C22×D4×D1111yescharacteristic
321C4C22×Q8×D1111yescharacteristic
322C2—228no—
323C2C2×#10622452112yesdirect product factor
324C2C22×C4⋊C4×D1111yescharacteristic
325C2C22×#6695411yescharacteristic
326C2C22×#6696011yescharacteristic
subgroupG/H
centerC23×C4C22×D11
commutatorC22×C11C24×C4
FrattiniC2×C4C24×D11
FittingC22×C11×C4⋊C8C2
socleC24×C11C22×C4
prime radicalC24×D11C2×C4
cosocleC2×C4×C11C25
hypercenterC22×C4⋊C8D11
hypocenterC11C22×#424
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23×C4 ◁ C22×C4⋊C8

Complements

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

NH ≅ G/Ntype
4. C2×#10622452C2direct (N × H)
5. C22×C4⋊(C11⋊C8)C2semidirect
6. C22×Dic11⋊C8C2semidirect
7. C22×Dic11⋊C8C2semidirect
8. C22×C11×C4⋊C8C2semidirect
26. C2×C11×C4⋊C8C22semidirect
27. C2×Dic11⋊C8C22semidirect
28. C2×Dic11⋊C8C22semidirect
29. C2×C4⋊(C11⋊C8)C22semidirect
30. #10622452C22direct (N × H)
64. C11×C4⋊C8C23semidirect
65. Dic11⋊C8C23semidirect
66. Dic11⋊C8C23semidirect
67. C4⋊(C11⋊C8)C23semidirect
118. C22×C4⋊C8D11semidirect
171. C2×C4⋊C8C2×D11semidirect
172. C22×C11#424semidirect
225. C4⋊C8C22×D11semidirect
226. C2×C11C2×#424semidirect
273. C11C22×#424semidirect
309. C22#10622452direct (N × H)
323. C2C2×#10622452direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43132
C23×C8×D112
C22×#669252
C2×#106224522
C22×C4⋊(C11⋊C8)2
C22×Dic11⋊C82
C22×C11×C4⋊C82
C22×#42411