Finite Group Databasebeta

← C22×#14583244 #25965780

Subgroups — C22×#14583244 #25965780

Order 11008.

3086 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063324C211yesmaximal, characteristic, complemented
2C22×#13063321C211yesmaximal, characteristic
3C2×#14583244C2124yesmaximal, direct product factor
4C22×#13063247C211yesmaximal, characteristic, complemented
5C22×#13063246C211yesmaximal, characteristic, complemented
6C22×#13063245C211yesmaximal, characteristic, complemented
7C22×C8×Dic43C211yesmaximal, characteristic, complemented
8C22×#102×C43C211yesmaximal, characteristic, complemented
9C23×Dic86—21no—
10C23×D172C2211yescharacteristic
11C23×C22⋊D43—21no—
12C23×C22⋊D43—21no—
13C23×C43⋊C8C2211yescharacteristic
14C2×#13063324—26no—
15C2×#13063324C22112yescomplemented
16C2×#13063321—26no—
17C2×#13063321C22112yes—
18C22×C4⋊Dic43C2211yescharacteristic
19C22×Dic43⋊C4—21no—
20C22×C4×Dic43C2211yescharacteristic
21#14583244C22164yesdirect product factor
22C2×#13063247C22112yescomplemented
23C2×#13063246C22112yescomplemented
24C2×#13063245C22112yescomplemented
25C2×C8×Dic43C22112yescomplemented
26C23×D4×C43C2211yescharacteristic
27C23×C8×C43C2211yescharacteristic
28C22×C4⋊C4×C43C2211yescharacteristic
29C2×#102×C43C22112yescomplemented
30C24×D43—21no—
31C22×Dic86—212no—
32C22×Dic86—48no—
33C22×D172—24no—
34C22×D172—24no—
35C22×D172—23no—
36C22×D172C2316yes—
37C22×C22⋊D43—212no—
38C22×C22⋊D43—212no—
39C22×C22⋊D43—48no—
40C22×C22⋊D43—48no—
41C23×Dic43—21no—
42C23×Dic43D411yescharacteristic
43C23×Dic43D411yescharacteristic
44C22×C43⋊C8—24no—
45C22×C43⋊C8C2316yes—
46#13063324—224no—
47#13063324C23116yescomplemented
48#13063321—224no—
49#13063321C23116yes—
50C2×C4⋊Dic43—23no—
51C2×C4⋊Dic43C2316yes—
52C2×Dic43⋊C4—212no—
53C2×C4×Dic43D416yes—
54C2×C4×Dic43C2316yes—
55#13063247C23116yescomplemented
56#13063246C23116yescomplemented
57#13063245C23116yescomplemented
58C8×Dic43C23116yescomplemented
59C25×C43—21no—
60C22×D4×C43—23no—
61C22×D4×C43—24no—
62C22×D4×C43—24no—
63C22×D4×C43C2316yes—
64C23×C4×C43—21no—
65C23×C4×C43C2311yescharacteristic
66C22×C8×C43—24no—
67C22×C8×C43C2316yes—
68C2×C4⋊C4×C43—23no—
69C2×C4⋊C4×C43C2316yes—
70#102×C43C23116yescomplemented
71C24×C43—26no—
72C24×C43—44no—
73C24×C43—44no—
74C24×C43—44no—
75C24×C43C2×D411yescharacteristic
76C23×D43—26no—
77C23×D43—44no—
78C23×D43—44no—
79C23×D43—44no—
80C2×D4×C43—26no—
81C2×D4×C43—212no—
82C2×D4×C43—212no—
83C2×D4×C43—412no—
84C2×D4×C43C2414yes—
85C22×C4×C43—26no—
86C22×C4×C43—44no—
87C22×C4×C43C2×D413yes—
88C22×C4×C43#4114yes—
89C22×C4×C43#4114yes—
90C22×C4×C43C2413yes—
91C2×C22⋊D43—216no—
92C2×C22⋊D43—216no—
93C2×C22⋊D43—448no—
94C2×C22⋊D43—448no—
95C22×Dic43—26no—
96C22×Dic43—44no—
97C22×Dic43D818yes—
98C22×Dic43SD1618yes—
99C22×Dic43C2×D416yes—
100C22×Dic43C2×D416yes—
101C2×D172—26no—
102C2×D172—212no—
103C2×D172—212no—
104C2×D172—412no—
105C2×D172C2414yes—
106C2×Dic86—216no—
107C2×Dic86—448no—
108C2×C8×C43—212no—
109C2×C8×C43C2414yes—
110C4⋊C4×C43—26no—
111C4⋊C4×C43C2414yes—
112C4⋊Dic43—26no—
113C4⋊Dic43C2414yes—
114Dic43⋊C4—216no—
115C4×Dic43C2×D4112yes—
116C4×Dic43C2414yes—
117C2×C43⋊C8—212no—
118C2×C43⋊C8C2414yes—
119C23×C43—24no—
120C23×C43—412no—
121C23×C43—412no—
122C23×C43—412no—
123C23×C43—816no—
124C23×C43#12414yes—
125C23×C43C2×D814yes—
126C23×C43C2×SD1614yes—
127C23×C43C22×D413yes—
128C22×D43—24no—
129C22×D43—412no—
130C22×D43—412no—
131C22×D43—412no—
132C22×D43—816no—
133D4×C43—24no—
134D4×C43—24no—
135D4×C43—412no—
136C2×C4×C43—24no—
137C2×C4×C43—412no—
138C2×C4×C43#124112yes—
139C2×C4×C43C22×D413yes—
140C2×C4×C43C2×#4116yes—
141C2×C4×C43C2×#4116yes—
142C2×C4×C43C2511yescharacteristic
143C22⋊D43—432no—
144C22⋊D43—432no—
145C2×Dic43—24no—
146C2×Dic43—412no—
147C2×Dic43C2×D8124yes—
148C2×Dic43C2×SD16124yes—
149C2×Dic43C22×D414yes—
150C2×Dic43C22×D414yes—
151D172—24no—
152D172—24no—
153D172—412no—
154Dic86—432no—
155C8×C43—24no—
156C43⋊C8—24no—
157C22×#486—431nomaximal, Sylow
158C22×C43—44no—
159C22×C43—44no—
160C22×C43—44no—
161C22×C43—824no—
162C22×C43#486116yescomplemented
163C22×C43C2×#12416yes—
164C22×C43C22×D816yes—
165C22×C43C22×SD1616yes—
166C22×C43C23×D411yescharacteristic
167C2×D43—44no—
168C2×D43—44no—
169C2×D43—44no—
170C2×D43—824no—
171C4×C43—44no—
172C4×C43C2×#12416yes—
173C4×C43C22×#4111yescharacteristic
174C4×C43C22×#4111yescharacteristic
175Dic43—44no—
176Dic43C22×D818yes—
177Dic43C22×SD1618yes—
178C22×C4⋊Q8—431no—
179C22×#127—431no—
180C2×#486—4324no—
181C22×#102—431no—
182C22×#102—431no—
183C22×#102—431no—
184C22×#102D4311yescharacteristic, complemented
185C22×C4×C8—431no—
186C2×C43—84no—
187C2×C43C2×#486112yescomplemented
188C2×C43C22×#12411yescharacteristic
189C2×C43C23×D811yescharacteristic
190C2×C43C23×SD1611yescharacteristic
191D43—84no—
192C23×Q8—861no—
193C23×D4—431no—
194C23×D4—861no—
195C23×D4—861no—
196C23×D4C2×D4311yescharacteristic
197C23×C8—431no—
198C23×C8C2×D4311yescharacteristic
199C2×C4⋊Q8—4312no—
200C2×C4⋊Q8—866no—
201C2×#127—4312no—
202C2×#127—866no—
203C22×C4⋊C4—431no—
204C22×C4⋊C4—861no—
205C22×C4⋊C4C2×D4311yescharacteristic
206C22×C42—431no—
207#486—4364no—
208C2×#102—4312no—
209C2×#102—4312no—
210C2×#102—4312no—
211C2×#102C2×D43112yescomplemented
212C2×C4×C8—4312no—
213C43C22×#48611yescharacteristic, complemented, Sylow
214C25—21no—
215C25—861no—
216C22×Q8—8612no—
217C22×Q8—1728no—
218C22×D4—24no—
219C22×D4—23no—
220C22×D4—24no—
221C22×D4—436no—
222C22×D4—8612no—
223C22×D4—8612no—
224C22×D4—864no—
225C22×D4—863no—
226C22×D4—864no—
227C22×D4—1728no—
228C22×D4—1728no—
229C22×D4C22×D4316yes—
230C23×C4—21no—
231C23×C4—431no—
232C23×C4—431no—
233C23×C4—861no—
234C23×C4C22×D4311yescharacteristic
235C22×C8—24no—
236C22×C8—436no—
237C22×C8—864no—
238C22×C8C22×D4316yes—
239C4⋊Q8—4316no—
240C4⋊Q8—8624no—
241#127—4316no—
242#127—8624no—
243C2×C4⋊C4—23no—
244C2×C4⋊C4—436no—
245C2×C4⋊C4—8612no—
246C2×C4⋊C4—863no—
247C2×C4⋊C4C22×D4316yes—
248C2×C42—436no—
249C2×C42—436no—
250#102—4316no—
251#102—4316no—
252#102—4316no—
253#102C22×D43116yescomplemented
254C4×C8—4316no—
255C24—26no—
256C24—44no—
257C24—44no—
258C24—44no—
259C24—866no—
260C24—1724no—
261C24—1724no—
262C24—1724no—
263C24D4×D4311yescharacteristic
264C2×Q8—8616no—
265C2×Q8—17248no—
266C2×D4—26no—
267C2×D4—212no—
268C2×D4—212no—
269C2×D4—412no—
270C2×D4—434no—
271C2×D4—8616no—
272C2×D4—8616no—
273C2×D4—866no—
274C2×D4—8612no—
275C2×D4—8612no—
276C2×D4—17248no—
277C2×D4—17248no—
278C2×D4—17212no—
279C2×D4C23×D4314yes—
280C22×C4—26no—
281C22×C4—44no—
282C22×C4—438no—
283C22×C4—438no—
284C22×C4—436no—
285C22×C4—436no—
286C22×C4—866no—
287C22×C4—1724no—
288C22×C4#1062189814yes—
289C22×C4D4×D4313yes—
290C22×C4#1062190014yes—
291C22×C4C23×D4313yes—
292C2×C8—212no—
293C2×C8—434no—
294C2×C8—8612no—
295C2×C8C23×D4314yes—
296C4⋊C4—26no—
297C4⋊C4—434no—
298C4⋊C4—8616no—
299C4⋊C4—866no—
300C4⋊C4C23×D4314yes—
301C42—4312no—
302C42—434no—
303C23—24no—
304C23—412no—
305C23—412no—
306C23—412no—
307C23—816no—
308C23—864no—
309C23—34416no—
310C23—17212no—
311C23—17212no—
312C23—17212no—
313C23#1306331114yes—
314C23D8×D4314yes—
315C23SD16×D4314yes—
316C23C2×D4×D4313yes—
317Q8—17232no—
318D4—24no—
319D4—24no—
320D4—412no—
321D4—864no—
322D4—864no—
323D4—17232no—
324D4—17232no—
325D4—17212no—
326C2×C4—24no—
327C2×C4—412no—
328C2×C4—4324no—
329C2×C4—4324no—
330C2×C4—434no—
331C2×C4—434no—
332C2×C4—864no—
333C2×C4—17212no—
334C2×C4#13063311112yes—
335C2×C4C2×D4×D4313yes—
336C2×C4C2×#1062190016yes—
337C2×C4C2×#1062189816yes—
338C2×C4C24×D4311yescharacteristic
339C8—24no—
340C8—864no—
341C22—44no—
342C22—44no—
343C22—44no—
344C22—824no—
345C22—34424no—
346C22—1724no—
347C22—1724no—
348C22—1724no—
349C22#14583244116yesdirect product factor
350C22C2×#1306331116yes—
351C22C2×D8×D4316yes—
352C22C2×SD16×D4316yes—
353C22C22×D4×D4311yescharacteristic
354C4—44no—
355C4—438no—
356C4—438no—
357C4—1724no—
358C4C2×#1306331116yes—
359C4C22×#1062190011yescharacteristic
360C4C22×#1062189811yescharacteristic
361C2—84no—
362C2—3444no—
363C2C2×#14583244112yesdirect product factor
364C2C22×#1306331111yescharacteristic
365C2C22×D8×D4311yescharacteristic
366C2C22×SD16×D4311yescharacteristic
subgroupG/H
centerC24D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC22×#102×C43C2
socleC24×C43C2×D4
prime radicalC22×#13063321C2
hypercenterC22×#102D43
hypocenterC43C22×#486
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
1. C22×#13063324C2semidirect
3. C2×#14583244C2direct (N × H)
4. C22×#13063247C2semidirect
5. C22×#13063246C2semidirect
6. C22×#13063245C2semidirect
7. C22×C8×Dic43C2semidirect
8. C22×#102×C43C2semidirect
15. C2×#13063324C22semidirect
21. #14583244C22direct (N × H)
22. C2×#13063247C22semidirect
23. C2×#13063246C22semidirect
24. C2×#13063245C22semidirect
25. C2×C8×Dic43C22semidirect
29. C2×#102×C43C22semidirect
47. #13063324C23semidirect
55. #13063247C23semidirect
56. #13063246C23semidirect
57. #13063245C23semidirect
58. C8×Dic43C23semidirect
70. #102×C43C23semidirect
162. C22×C43#486semidirect
184. C22×#102D43semidirect
187. C2×C43C2×#486semidirect
211. C2×#102C2×D43semidirect
213. C43C22×#486semidirect
253. #102C22×D43semidirect
349. C22#14583244direct (N × H)
363. C2C2×#14583244direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633242
C22×#130633212
C2×#145832442
C22×#130632472
C22×#130632462
C22×#130632452
C22×C8×Dic432
C22×#102×C432
C22×#48643