Finite Group Databasebeta

← C22×#14582938 #25960249

Subgroups — C22×#14582938 #25960249

Order 11008.

3182 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×#10621872C211yesmaximal, characteristic
2C22×#13063283C211yesmaximal, characteristic
3C22×C4⋊C4×D43C211yesmaximal, characteristic
4C2×#14582938C2124yesmaximal, direct product factor
5C22×#13063259C211yesmaximal, characteristic, complemented
6C22×#13063258C211yesmaximal, characteristic, complemented
7C22×#13063256C211yesmaximal, characteristic, complemented
8C22×#106×C43C211yesmaximal, characteristic, complemented
9C23×C4×D43—21no—
10C23×C4×D43C2211yescharacteristic
11C22×#10621872C4116yescomplemented
12C22×#10621872C22112yes—
13C23×C43⋊C8C2211yescharacteristic
14C2×#13063283—26no—
15C2×#13063283C22112yes—
16C22×C4⋊Dic43C2211yescharacteristic
17C22×C4⋊Dic43C2211yescharacteristic
18C22×Dic43⋊C4—21no—
19C2×C4⋊C4×D43—26no—
20C2×C4⋊C4×D43C22112yes—
21C22×(C2×D43)⋊C4—21no—
22C22×C4×Dic43—21no—
23#14582938C22164yesdirect product factor
24C2×#13063259C22112yescomplemented
25C2×#13063258C22112yescomplemented
26C2×#13063256C22112yescomplemented
27C23×C8×C43C2211yescharacteristic
28C22×C4⋊C4×C43C2211yescharacteristic
29C22×C4⋊C4×C43C2211yescharacteristic
30C2×#106×C43C22112yescomplemented
31C24×D43D411yescharacteristic
32C23×Dic43—21no—
33C23×Dic43—21no—
34C23×Dic43D411yescharacteristic
35C22×C4×D43—212no—
36C22×C4×D43—48no—
37C22×C4×D43C2×C418yes—
38C22×C4×D43D416yes—
39C22×C4×D43Q818yes—
40C22×C4×D43C2316yes—
41C2×#10621872C2×C4196yescomplemented
42C2×#10621872C23116yes—
43C22×C43⋊C8C2×C418yescomplemented
44C22×C43⋊C8C2316yes—
45#13063283—224no—
46#13063283C23116yes—
47C2×C4⋊Dic43—23no—
48C2×C4⋊Dic43—23no—
49C2×C4⋊Dic43C2316yes—
50C2×C4⋊Dic43C2316yes—
51C2×Dic43⋊C4—212no—
52C4⋊C4×D43—224no—
53C4⋊C4×D43C23116yes—
54C2×(C2×D43)⋊C4—212no—
55C2×C4×Dic43—212no—
56#13063259C23116yescomplemented
57#13063258C23116yescomplemented
58#13063256C23116yescomplemented
59C23×C4×C43—21no—
60C23×C4×C43—21no—
61C23×C4×C43C2311yescharacteristic
62C22×C8×C43C2×C418yescomplemented
63C22×C8×C43C2316yes—
64C2×C4⋊C4×C43—23no—
65C2×C4⋊C4×C43—23no—
66C2×C4⋊C4×C43C2316yes—
67C2×C4⋊C4×C43C2316yes—
68#106×C43C23116yescomplemented
69C24×C43C2×D411yescharacteristic
70C23×D43—24no—
71C23×D43—24no—
72C23×D43C4⋊C418yes—
73C23×D43C2×D416yes—
74C22×C4×C43—26no—
75C22×C4×C43—26no—
76C22×C4×C43—44no—
77C22×C4×C43—44no—
78C22×C4×C43C22×C414yes—
79C22×C4×C43C2×D413yes—
80C22×C4×C43C2×Q814yes—
81C22×C4×C43C2413yes—
82C22×Dic43—26no—
83C22×Dic43—26no—
84C22×Dic43—44no—
85C22×Dic43—44no—
86C22×Dic43C4⋊C418yes—
87C22×Dic43C2×D416yes—
88C2×C4×D43—216no—
89C2×C4×D43—448no—
90C2×C4×D43C4⋊C4148yes—
91C2×C4×D43C22×C4124yes—
92C2×C4×D43C2×D4112yes—
93C2×C4×D43C2×Q8124yes—
94C2×C4×D43C2414yes—
95C2×C8×C43C22×C4124yescomplemented
96C2×C8×C43C2414yes—
97C4⋊C4×C43—26no—
98C4⋊C4×C43—26no—
99C4⋊C4×C43C2414yes—
100C4⋊C4×C43C2414yes—
101(C2×D43)⋊C4—216no—
102C4⋊Dic43—26no—
103C4⋊Dic43—26no—
104C4⋊Dic43C2414yes—
105C4⋊Dic43C2414yes—
106Dic43⋊C4—216no—
107C4×Dic43—216no—
108C2×C43⋊C8C22×C4124yescomplemented
109C2×C43⋊C8C2414yes—
110#10621872C22×C4164yescomplemented
111C23×C43C2×C4⋊C414yes—
112C23×C43AGL(1,ℤ/8)14yes—
113C23×C43#13714yes—
114C23×C43C22×D413yes—
115C22×D43—212no—
116C22×D43—212no—
117C22×D43—232no—
118C22×D43C2×C4⋊C4124yes—
119C22×D43C22×D414yes—
120C2×C4×C43—24no—
121C2×C4×C43—24no—
122C2×C4×C43—412no—
123C2×C4×C43—412no—
124C2×C4×C43C2×C4⋊C4112yes—
125C2×C4×C43C23×C416yes—
126C2×C4×C43C22×D413yes—
127C2×C4×C43C22×Q816yes—
128C2×C4×C43C2511yescharacteristic
129C2×Dic43—24no—
130C2×Dic43—24no—
131C2×Dic43—412no—
132C2×Dic43—412no—
133C2×Dic43C2×C4⋊C4124yes—
134C2×Dic43C22×D414yes—
135C4×D43—432no—
136C4×D43C2×C4⋊C4148yes—
137C4×D43C23×C418yes—
138C4×D43C22×Q818yes—
139C8×C43C23×C418yescomplemented
140C43⋊C8C23×C418yescomplemented
141C22×#428—431nomaximal, Sylow
142C22×C43#428116yescomplemented
143C22×C43C22×C4⋊C416yes—
144C22×C43C2×AGL(1,ℤ/8)16yes—
145C22×C43C2×#13716yes—
146C22×C43C23×D411yescharacteristic
147C2×D43—248no—
148C2×D43—24no—
149C2×D43—24no—
150C2×D43C22×C4⋊C418yes—
151C4×C43—44no—
152C4×C43—44no—
153C4×C43C22×C4⋊C416yes—
154C4×C43C24×C411yescharacteristic
155C4×C43C23×Q811yescharacteristic
156Dic43—44no—
157Dic43—44no—
158Dic43C22×C4⋊C418yes—
159C23×M16—431no—
160C22×#117—431no—
161C23×C4⋊C4—431no—
162C2×#428—4324no—
163C22×#107—431no—
164C22×#107—431no—
165C22×#106—431no—
166C22×#106D4311yescharacteristic, complemented
167C2×C43C2×#428112yescomplemented
168C2×C43C23×C4⋊C411yescharacteristic
169C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
170C2×C43C22×#13711yescharacteristic
171D43—28no—
172C24×C4—431no—
173C24×C4—861no—
174C22×M16—4312no—
175C22×M16—4316no—
176C23×C8—431no—
177C23×C8C2×D4311yescharacteristic
178C2×#117—4312no—
179C2×#117—866no—
180C22×C4⋊C4—431no—
181C22×C4⋊C4—431no—
182C22×C4⋊C4—4312no—
183C22×C4⋊C4—866no—
184C22×C4⋊C4—861no—
185C22×C4⋊C4C2×D4311yescharacteristic
186C22×C4⋊C4C2×D4311yescharacteristic
187C22×C22⋊C4—861no—
188C22×C42—861no—
189#428—4364no—
190C2×#107—4312no—
191C2×#107—4312no—
192C2×#106—4312no—
193C2×#106C2×D43112yescomplemented
194C43C22×#42811yescharacteristic, complemented, Sylow
195C25—431no—
196C23×C4—21no—
197C23×C4—21no—
198C23×C4—431no—
199C23×C4—438no—
200C23×C4—436no—
201C23×C4—438no—
202C23×C4—436no—
203C23×C4—8612no—
204C23×C4—861no—
205C23×C4—861no—
206C23×C4—1728no—
207C23×C4C22×D4311yescharacteristic
208C2×M16—4396no—
209C2×M16—4316no—
210C22×C8—438no—
211C22×C8—436no—
212C22×C8C4×D4318yescomplemented
213C22×C8C22×D4316yes—
214#117—4316no—
215#117—8624no—
216C2×C4⋊C4—23no—
217C2×C4⋊C4—23no—
218C2×C4⋊C4—436no—
219C2×C4⋊C4—436no—
220C2×C4⋊C4—4316no—
221C2×C4⋊C4—8624no—
222C2×C4⋊C4—8612no—
223C2×C4⋊C4—863no—
224C2×C4⋊C4—863no—
225C2×C4⋊C4C22×D4316yes—
226C2×C4⋊C4C22×D4316yes—
227C2×C22⋊C4—8612no—
228C2×C42—8612no—
229#107—4316no—
230#107—4316no—
231#106—4316no—
232#106C22×D43116yescomplemented
233C24—438no—
234C24—436no—
235C24—864no—
236C24—864no—
237C24D4×D4311yescharacteristic
238C22×C4—26no—
239C22×C4—26no—
240C22×C4—44no—
241C22×C4—44no—
242C22×C4—438no—
243C22×C4—436no—
244C22×C4—4348no—
245C22×C4—4324no—
246C22×C4—4312no—
247C22×C4—4324no—
248C22×C4—434no—
249C22×C4—8616no—
250C22×C4—866no—
251C22×C4—866no—
252C22×C4—17248no—
253C22×C4—1724no—
254C22×C4—1724no—
255C22×C4C2×C4×D4314yes—
256C22×C4D4×D4313yes—
257C22×C4Q8×D4314yes—
258C22×C4C23×D4313yes—
259M16—4364no—
260C2×C8—4324no—
261C2×C8—434no—
262C2×C8C2×C4×D43124yescomplemented
263C2×C8C23×D4314yes—
264C4⋊C4—26no—
265C4⋊C4—26no—
266C4⋊C4—434no—
267C4⋊C4—434no—
268C4⋊C4—8616no—
269C4⋊C4—866no—
270C4⋊C4—866no—
271C4⋊C4C23×D4314yes—
272C4⋊C4C23×D4314yes—
273C22⋊C4—8616no—
274C42—8616no—
275C23—4324no—
276C23—434no—
277C23—8612no—
278C23—8612no—
279C23—8632no—
280C23C4⋊C4×D4314yes—
281C23#1306335214yes—
282C23#1306335414yes—
283C23C2×D4×D4313yes—
284C2×C4—24no—
285C2×C4—24no—
286C2×C4—412no—
287C2×C4—412no—
288C2×C4—4324no—
289C2×C4—434no—
290C2×C4—4348no—
291C2×C4—438no—
292C2×C4—438no—
293C2×C4—864no—
294C2×C4—864no—
295C2×C4—17232no—
296C2×C4—17212no—
297C2×C4—17212no—
298C2×C4C4⋊C4×D43112yes—
299C2×C4C22×C4×D4316yes—
300C2×C4C2×D4×D4313yes—
301C2×C4C2×Q8×D4316yes—
302C2×C4C24×D4311yescharacteristic
303C8—438no—
304C8C22×C4×D4318yescomplemented
305C22—438no—
306C22—8648no—
307C22—864no—
308C22—864no—
309C22#14582938116yesdirect product factor
310C22C2×C4⋊C4×D4316yes—
311C22C2×#1306335216yes—
312C22C2×#1306335416yes—
313C22C22×D4×D4311yescharacteristic
314C4—44no—
315C4—44no—
316C4—438no—
317C4—1724no—
318C4—1724no—
319C4C2×C4⋊C4×D4316yes—
320C4C23×C4×D4311yescharacteristic
321C4C22×Q8×D4311yescharacteristic
322C2—868no—
323C2C2×#14582938112yesdirect product factor
324C2C22×C4⋊C4×D4311yescharacteristic
325C2C22×#1306335211yescharacteristic
326C2C22×#1306335411yescharacteristic
subgroupG/H
centerC24D4×D43
commutatorC4×C43C24×C4
FrattiniC2×C4C24×D43
FittingC22×#106×C43C2
socleC24×C43C2×D4
prime radicalC24×D43D4
cosocleC2×C4×C43C25
hypercenterC22×#106D43
hypocenterC43C22×#428
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#106

Complements

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

NH ≅ G/Ntype
4. C2×#14582938C2direct (N × H)
5. C22×#13063259C2semidirect
6. C22×#13063258C2semidirect
7. C22×#13063256C2semidirect
8. C22×#106×C43C2semidirect
11. C22×#10621872C4semidirect
23. #14582938C22direct (N × H)
24. C2×#13063259C22semidirect
25. C2×#13063258C22semidirect
26. C2×#13063256C22semidirect
30. C2×#106×C43C22semidirect
41. C2×#10621872C2×C4semidirect
43. C22×C43⋊C8C2×C4semidirect
56. #13063259C23semidirect
57. #13063258C23semidirect
58. #13063256C23semidirect
62. C22×C8×C43C2×C4semidirect
68. #106×C43C23semidirect
95. C2×C8×C43C22×C4semidirect
108. C2×C43⋊C8C22×C4semidirect
110. #10621872C22×C4semidirect
139. C8×C43C23×C4semidirect
140. C43⋊C8C23×C4semidirect
142. C22×C43#428semidirect
166. C22×#106D43semidirect
167. C2×C43C2×#428semidirect
193. C2×#106C2×D43semidirect
194. C43C22×#428semidirect
212. C22×C8C4×D43semidirect
232. #106C22×D43semidirect
262. C2×C8C2×C4×D43semidirect
304. C8C22×C4×D43semidirect
309. C22#14582938direct (N × H)
323. C2C2×#14582938direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#106218722
C22×#130632832
C22×C4⋊C4×D432
C2×#145829382
C22×#130632592
C22×#130632582
C22×#130632562
C22×#106×C432
C22×#42843