Finite Group Databasebeta

← C22×#14582895 #25960115

Subgroups — C22×#14582895 #25960115

Order 11008.

5326 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C43⋊C8C211yesmaximal, characteristic, complemented
2C22×#13063284C211yesmaximal, characteristic, complemented
3C2×#14582895C2124yesmaximal, direct product factor
4C22×#13063249C212yesmaximal, complemented
5C22×#13063246C212yesmaximal, complemented
6C23×#41×C43C211yesmaximal, characteristic
7C23×C43⋊C8—28no—
8C23×C43⋊C8C2212yes—
9C23×C43⋊C8C22112yescomplemented
10C2×#13063284—26no—
11C2×#13063284C22112yescomplemented
12C22×C4⋊Dic43C2212yes—
13C22×C22⋊Dic43—21no—
14C22×C4×Dic43—21no—
15#14582895C22164yesdirect product factor
16C2×#13063249C22124yescomplemented
17C2×#13063246C22124yescomplemented
18C22×#41×C43—28no—
19C22×#41×C43—26no—
20C22×#41×C43C4116yescomplemented
21C22×#41×C43C22112yes—
22C23×Q8×C43C2211yescharacteristic
23C23×D4×C43—21no—
24C23×D4×C43C2211yescharacteristic
25C24×C4×C43—21no—
26C24×C4×C43C2211yescharacteristic
27C23×Dic43—22no—
28C22×C43⋊C8—28no—
29C22×C43⋊C8—248no—
30C22×C43⋊C8C23112yes—
31C22×C43⋊C8C23116yescomplemented
32#13063284—224no—
33#13063284C23116yescomplemented
34C2×C4⋊Dic43—26no—
35C2×C4⋊Dic43C23112yes—
36C2×C22⋊Dic43—212no—
37C2×C4×Dic43—212no—
38#13063249C23132yescomplemented
39#13063246C23132yescomplemented
40C25×C43—21no—
41C25×C43D411yescharacteristic
42C2×#41×C43—296no—
43C2×#41×C43—248no—
44C2×#41×C43—224no—
45C2×#41×C43C2×C4196yescomplemented
46C2×#41×C43C23116yes—
47C22×Q8×C43—24no—
48C22×Q8×C43—23no—
49C22×Q8×C43C2×C418yes—
50C22×Q8×C43C2316yes—
51C22×D4×C43—216no—
52C22×D4×C43—212no—
53C22×D4×C43—24no—
54C22×D4×C43—23no—
55C22×D4×C43C2×C418yes—
56C22×D4×C43C2316yes—
57C23×C4×C43—21no—
58C23×C4×C43—216no—
59C23×C4×C43—212no—
60C23×C4×C43C2×C418yes—
61C23×C4×C43D416yes—
62C23×C4×C43D418yes—
63C23×C4×C43D411yescharacteristic
64C23×C4×C43C2311yescharacteristic
65C23×C4×C43C2316yes—
66C24×C43—28no—
67C24×C43—28no—
68C24×C43—26no—
69C24×C43—48no—
70C24×C43C22⋊C418yes—
71C24×C43C2×D416yes—
72C24×C43C2×D411yescharacteristic
73#41×C43—2192no—
74#41×C43—232no—
75#41×C43C22×C4164yescomplemented
76C2×Q8×C43—224no—
77C2×Q8×C43—212no—
78C2×Q8×C43—26no—
79C2×Q8×C43C22×C4124yes—
80C2×Q8×C43C2414yes—
81C2×D4×C43—224no—
82C2×D4×C43—212no—
83C2×D4×C43—26no—
84C2×D4×C43—296no—
85C2×D4×C43—216no—
86C2×D4×C43C22×C4124yes—
87C2×D4×C43C2414yes—
88C22×C4×C43—296no—
89C22×C4×C43—216no—
90C22×C4×C43—28no—
91C22×C4×C43—26no—
92C22×C4×C43C22⋊C418yes—
93C22×C4×C43C22⋊C4148yes—
94C22×C4×C43C22×C414yes—
95C22×C4×C43C22×C4124yes—
96C22×C4×C43C2×D414yes—
97C22×C4×C43C2×D4124yes—
98C22×C4×C43C2×D416yes—
99C22×C4×C43C2×D413yes—
100C22×C4×C43C2×D4112yes—
101C22×C4×C43C2413yes—
102C22×C4×C43C2414yes—
103C22×Dic43—212no—
104C22×Dic43—48no—
105C22⋊Dic43—216no—
106C4⋊Dic43—212no—
107C4⋊Dic43C2418yes—
108C4×Dic43—216no—
109C2×C43⋊C8—224no—
110C2×C43⋊C8—232no—
111C2×C43⋊C8C2418yes—
112C23×C43—224no—
113C23×C43—232no—
114C23×C43—224no—
115C23×C43—24no—
116C23×C43—424no—
117C23×C43—432no—
118C23×C43C2×C22⋊C4124yes—
119C23×C43C2×C22⋊C414yes—
120C23×C43#13518yes—
121C23×C43C22×D414yes—
122C23×C43C22×D413yes—
123Q8×C43—224no—
124Q8×C43—24no—
125Q8×C43C23×C418yes—
126D4×C43—264no—
127D4×C43—224no—
128D4×C43—24no—
129D4×C43C23×C418yes—
130C2×C4×C43—224no—
131C2×C4×C43—24no—
132C2×C4×C43—264no—
133C2×C4×C43C2×C22⋊C4124yes—
134C2×C4×C43C2×C22⋊C4112yes—
135C2×C4×C43C2×C22⋊C4148yes—
136C2×C4×C43C23×C416yes—
137C2×C4×C43C23×C418yes—
138C2×C4×C43C22×D414yes—
139C2×C4×C43C22×D413yes—
140C2×C4×C43C22×D416yes—
141C2×C4×C43C22×D418yes—
142C2×C4×C43C2511yescharacteristic
143C2×Dic43—28no—
144C2×Dic43—424no—
145C43⋊C8—28no—
146C22×#416—431nomaximal, Sylow
147C22×C43—248no—
148C22×C43—28no—
149C22×C43—28no—
150C22×C43—448no—
151C22×C43—48no—
152C22×C43#416116yescomplemented
153C22×C43C22×C22⋊C418yes—
154C22×C43C22×C22⋊C416yes—
155C22×C43C2×#135112yes—
156C22×C43C23×D411yescharacteristic
157C4×C43—28no—
158C4×C43C22×C22⋊C418yes—
159C4×C43C22×C22⋊C416yes—
160C4×C43C24×C411yescharacteristic
161C4×C43C23×D411yescharacteristic
162Dic43—48no—
163C23×#41D4311yescharacteristic
164C24×C8—431no—
165C22×#117—431no—
166C2×#416—4324no—
167C22×#103—432no—
168C22×#102—432no—
169C2×C43—28no—
170C2×C43—48no—
171C2×C43C2×#416112yescomplemented
172C2×C43C23×C22⋊C411yescharacteristic
173C2×C43C22×#13512yes—
174C22×#41—28no—
175C22×#41—26no—
176C22×#41Dic43116yescomplemented
177C22×#41C2×D43112yes—
178C23×Q8C2×D4311yescharacteristic
179C23×D4—21no—
180C23×D4C2×D4311yescharacteristic
181C24×C4—21no—
182C24×C4C2×D4311yescharacteristic
183C23×C8—432no—
184C23×C8—4312no—
185C23×C8—868no—
186C2×#117—4312no—
187C2×#117—866no—
188C22×C4⋊C4—432no—
189C22×C22⋊C4—861no—
190C22×C42—861no—
191#416—4364no—
192C2×#103—4324no—
193C2×#102—4324no—
194C43C22×#41611yescharacteristic, complemented, Sylow
195C25—21no—
196C25C22⋊D4311yescharacteristic
197C2×#41—296no—
198C2×#41—248no—
199C2×#41—224no—
200C2×#41C2×Dic43196yescomplemented
201C2×#41C22×D43116yes—
202C22×Q8—24no—
203C22×Q8—23no—
204C22×Q8C2×Dic4318yes—
205C22×Q8C22×D4316yes—
206C22×D4—216no—
207C22×D4—212no—
208C22×D4—23no—
209C22×D4—24no—
210C22×D4C2×Dic4318yes—
211C22×D4C22×D4316yes—
212C23×C4—21no—
213C23×C4—216no—
214C23×C4—212no—
215C23×C4—862no—
216C23×C4C2×Dic4318yes—
217C23×C4C22⋊D4316yes—
218C23×C4C22⋊D4318yes—
219C23×C4C22⋊D4311yescharacteristic
220C23×C4C22×D4311yescharacteristic
221C23×C4C22×D4316yes—
222C22×C8—4312no—
223C22×C8—4316no—
224C22×C8—868no—
225C22×C8—8648no—
226#117—4316no—
227#117—8624no—
228C2×C4⋊C4—4312no—
229C2×C4⋊C4—866no—
230C2×C22⋊C4—8612no—
231C2×C42—8612no—
232#103—4332no—
233#102—4332no—
234C24—28no—
235C24—28no—
236C24—26no—
237C24—48no—
238C24C22⋊Dic4318yes—
239C24C2×C22⋊D4316yes—
240C24C2×C22⋊D4311yescharacteristic
241#41—2192no—
242#41—232no—
243#41C22×Dic43164yescomplemented
244C2×Q8—224no—
245C2×Q8—212no—
246C2×Q8—26no—
247C2×Q8C22×Dic43124yes—
248C2×Q8C23×D4314yes—
249C2×D4—296no—
250C2×D4—216no—
251C2×D4—224no—
252C2×D4—26no—
253C2×D4—212no—
254C2×D4C22×Dic43124yes—
255C2×D4C23×D4314yes—
256C22×C4—28no—
257C22×C4—26no—
258C22×C4—296no—
259C22×C4—216no—
260C22×C4—8612no—
261C22×C4—1728no—
262C22×C4C22⋊Dic4318yes—
263C22×C4C22⋊Dic43148yes—
264C22×C4C22×Dic4314yes—
265C22×C4C22×Dic43124yes—
266C22×C4C2×C22⋊D4316yes—
267C22×C4C2×C22⋊D4313yes—
268C22×C4C2×C22⋊D43112yes—
269C22×C4C2×C22⋊D4314yes—
270C22×C4C2×C22⋊D43124yes—
271C22×C4C23×D4313yes—
272C22×C4C23×D4314yes—
273C2×C8—438no—
274C2×C8—8624no—
275C2×C8—8632no—
276C4⋊C4—438no—
277C4⋊C4—8612no—
278C22⋊C4—8616no—
279C42—8616no—
280C23—232no—
281C23—224no—
282C23—224no—
283C23—24no—
284C23—432no—
285C23—424no—
286C23C2×C22⋊Dic43124yes—
287C23C2×C22⋊Dic4314yes—
288C23#1306334518yes—
289C23C22×C22⋊D4314yes—
290C23C22×C22⋊D4313yes—
291Q8—224no—
292Q8—24no—
293Q8C23×Dic4318yes—
294D4—264no—
295D4—224no—
296D4—24no—
297D4C23×Dic4318yes—
298C2×C4—224no—
299C2×C4—24no—
300C2×C4—264no—
301C2×C4—868no—
302C2×C4—17224no—
303C2×C4C2×C22⋊Dic43124yes—
304C2×C4C2×C22⋊Dic43112yes—
305C2×C4C2×C22⋊Dic43148yes—
306C2×C4C23×Dic4316yes—
307C2×C4C23×Dic4318yes—
308C2×C4C22×C22⋊D4314yes—
309C2×C4C22×C22⋊D4313yes—
310C2×C4C22×C22⋊D4316yes—
311C2×C4C22×C22⋊D4318yes—
312C2×C4C24×D4311yescharacteristic
313C8—868no—
314C22—28no—
315C22—248no—
316C22—28no—
317C22—48no—
318C22—448no—
319C22#14582895116yesdirect product factor
320C22C22×C22⋊Dic4318yes—
321C22C22×C22⋊Dic4316yes—
322C22C2×#13063345112yes—
323C22C23×C22⋊D4311yescharacteristic
324C4—28no—
325C4—1728no—
326C4C22×C22⋊Dic4318yes—
327C4C22×C22⋊Dic4316yes—
328C4C24×Dic4311yescharacteristic
329C4C23×C22⋊D4311yescharacteristic
330C2—28no—
331C2—48no—
332C2C2×#14582895112yesdirect product factor
333C2C23×C22⋊Dic4311yescharacteristic
334C2C22×#1306334512yes—
subgroupG/H
centerC23×C4C22⋊D43
commutatorC4×C43C24×C4
FrattiniC2×C4C24×D43
Fitting, prime radicalC23×#41×C43C2
socleC24×C43C2×D4
cosocleC2×C4×C43C25
hypercenterC23×#41D43
hypocenterC43C22×#416
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C24×C4 ◁ C23×#41

Complements

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

NH ≅ G/Ntype
1. C24×C43⋊C8C2semidirect
2. C22×#13063284C2semidirect
3. C2×#14582895C2direct (N × H)
4. C22×#13063249C2semidirect
5. C22×#13063246C2semidirect
9. C23×C43⋊C8C22semidirect
11. C2×#13063284C22semidirect
15. #14582895C22direct (N × H)
16. C2×#13063249C22semidirect
17. C2×#13063246C22semidirect
20. C22×#41×C43C4semidirect
31. C22×C43⋊C8C23semidirect
33. #13063284C23semidirect
38. #13063249C23semidirect
39. #13063246C23semidirect
45. C2×#41×C43C2×C4semidirect
75. #41×C43C22×C4semidirect
152. C22×C43#416semidirect
171. C2×C43C2×#416semidirect
176. C22×#41Dic43semidirect
194. C43C22×#416semidirect
200. C2×#41C2×Dic43semidirect
243. #41C22×Dic43semidirect
319. C22#14582895direct (N × H)
332. C2C2×#14582895direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C43⋊C82
C22×#130632842
C2×#145828952
C22×#130632492
C22×#130632462
C23×#41×C432
C22×#41643