Finite Group Databasebeta

← C22×#14583139 #25963694

Subgroups — C22×#14583139 #25963694

Order 11008.

3006 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#10621885C211yesmaximal, characteristic, complemented
2C23×C8×D43C211yesmaximal, characteristic
3C22×#13063305C211yesmaximal, characteristic
4C22×#13063301C211yesmaximal, characteristic
5C2×#14583139C2124yesmaximal, direct product factor
6C22×#13063258C211yesmaximal, characteristic, complemented
7C22×#13063250C211yesmaximal, characteristic, complemented
8C22×#103×C43C211yesmaximal, characteristic, complemented
9C23×Dic86C2211yescharacteristic
10C23×C4×D43C2211yescharacteristic
11C22×#10621885—28no—
12C22×#10621885C22112yescomplemented
13C23×C43⋊C8C2211yescharacteristic
14C22×C8×D43—28no—
15C22×C8×D43C22112yes—
16C2×#13063305—26no—
17C2×#13063305C22112yes—
18C2×#13063301—26no—
19C2×#13063301C22112yes—
20C22×C4⋊Dic43—21no—
21C22×C4⋊Dic43C2211yescharacteristic
22C22×Dic43⋊C4—21no—
23C22×(C2×D43)⋊C4—21no—
24C22×(C2×D43)⋊C4—21no—
25#14583139C22164yesdirect product factor
26C2×#13063258C22112yescomplemented
27C2×#13063250C22112yescomplemented
28C23×Q8×C43C2211yescharacteristic
29C23×C8×C43C2211yescharacteristic
30C22×C4⋊C4×C43C2211yescharacteristic
31C2×#103×C43C22112yescomplemented
32C24×D43D411yescharacteristic
33C22×Dic86—24no—
34C22×Dic86—24no—
35C22×Dic86—23no—
36C22×Dic86C2316yes—
37C23×Dic43—21no—
38C23×Dic43—21no—
39C23×Dic43D411yescharacteristic
40C22×C4×D43—24no—
41C22×C4×D43—24no—
42C22×C4×D43D416yes—
43C22×C4×D43C2316yes—
44C2×#10621885—248no—
45C2×#10621885C23116yescomplemented
46C22×C43⋊C8D418yes—
47C22×C43⋊C8C2316yes—
48C2×C8×D43—248no—
49C2×C8×D43C23116yes—
50#13063305—224no—
51#13063305C23116yes—
52#13063301—224no—
53#13063301C23116yes—
54C2×C4⋊Dic43—23no—
55C2×C4⋊Dic43—212no—
56C2×C4⋊Dic43C2316yes—
57C2×Dic43⋊C4—212no—
58C2×(C2×D43)⋊C4—212no—
59C2×(C2×D43)⋊C4—212no—
60#13063258C23116yescomplemented
61#13063250C23116yescomplemented
62C22×Q8×C43—23no—
63C22×Q8×C43—24no—
64C22×Q8×C43—24no—
65C22×Q8×C43C2316yes—
66C23×C4×C43—21no—
67C23×C4×C43—21no—
68C23×C4×C43C2311yescharacteristic
69C22×C8×C43—24no—
70C22×C8×C43C2316yes—
71C2×C4⋊C4×C43—23no—
72C2×C4⋊C4×C43C2316yes—
73#103×C43C23116yescomplemented
74C24×C43C2×D411yescharacteristic
75C23×D43—24no—
76C23×D43—24no—
77C23×D43Q1618yescomplemented
78C23×D43C2×D416yes—
79C2×Q8×C43—26no—
80C2×Q8×C43—212no—
81C2×Q8×C43—212no—
82C2×Q8×C43—412no—
83C2×Q8×C43C2414yes—
84C22×C4×C43—26no—
85C22×C4×C43—26no—
86C22×C4×C43—44no—
87C22×C4×C43—44no—
88C22×C4×C43C2×D414yes—
89C22×C4×C43C2×D413yes—
90C22×C4×C43#4114yes—
91C22×C4×C43C2413yes—
92C22×Dic43—24no—
93C22×Dic43—26no—
94C22×Dic43—26no—
95C22×Dic43—44no—
96C22×Dic43—44no—
97C22×Dic43C2×D416yes—
98C2×C4×D43—224no—
99C2×C4×D43—212no—
100C2×C4×D43—212no—
101C2×C4×D43C2×D4112yes—
102C2×C4×D43C2414yes—
103C2×Dic86—212no—
104C2×Dic86—212no—
105C2×Dic86—26no—
106C2×Dic86—412no—
107C2×Dic86C2414yes—
108C2×C8×C43—212no—
109C2×C8×C43C2414yes—
110C4⋊C4×C43—26no—
111C4⋊C4×C43C2414yes—
112#10621885—232no—
113(C2×D43)⋊C4—216no—
114(C2×D43)⋊C4—216no—
115C4⋊Dic43—26no—
116C4⋊Dic43—216no—
117C4⋊Dic43C2414yes—
118Dic43⋊C4—216no—
119C2×C43⋊C8C2×D4124yes—
120C2×C43⋊C8C2414yes—
121C8×D43—232no—
122C23×C43#12114yes—
123C23×C43C2×Q1614yes—
124C23×C43#13514yes—
125C23×C43C22×D413yes—
126C22×D43—212no—
127C22×D43—212no—
128C22×D43—232no—
129C22×D43C2×Q16124yescomplemented
130C22×D43C22×D414yes—
131Q8×C43—24no—
132Q8×C43—24no—
133Q8×C43—412no—
134C2×C4×C43—24no—
135C2×C4×C43—24no—
136C2×C4×C43—412no—
137C2×C4×C43—412no—
138C2×C4×C43#121112yes—
139C2×C4×C43C22×D413yes—
140C2×C4×C43C22×D416yes—
141C2×C4×C43C2×#4116yes—
142C2×C4×C43C2511yescharacteristic
143C2×Dic43—212no—
144C2×Dic43—24no—
145C2×Dic43—24no—
146C2×Dic43—412no—
147C2×Dic43—412no—
148C2×Dic43C22×D414yes—
149C4×D43—224no—
150C4×D43—24no—
151C4×D43—24no—
152Dic86—24no—
153Dic86—24no—
154Dic86—412no—
155C8×C43—24no—
156C43⋊C8C22×D418yes—
157C22×#467—431nomaximal, Sylow
158C22×C43#467116yescomplemented
159C22×C43C2×#12116yes—
160C22×C43C22×Q1616yes—
161C22×C43C2×#13516yes—
162C22×C43C23×D411yescharacteristic
163C2×D43—24no—
164C2×D43—248no—
165C2×D43—24no—
166C2×D43C22×Q1618yescomplemented
167C4×C43—44no—
168C4×C43—44no—
169C4×C43C2×#12116yes—
170C4×C43C23×D411yescharacteristic
171C4×C43C22×#4111yescharacteristic
172Dic43—24no—
173Dic43—44no—
174Dic43—44no—
175C23×Q16—431no—
176C24×C8—431no—
177C22×C22⋊Q8—431no—
178C22×C22⋊Q8—431no—
179C2×#467—4324no—
180C22×#107—431no—
181C22×#103—431no—
182C22×#103D4311yescharacteristic, complemented
183C2×C43C2×#467112yescomplemented
184C2×C43C22×#12111yescharacteristic
185C2×C43C23×Q1611yescharacteristic
186C2×C43C22×#13511yescharacteristic
187D43—28no—
188C23×Q8—431no—
189C23×Q8C2×D4311yescharacteristic
190C24×C4—431no—
191C22×Q16—4312no—
192C22×Q16—868no—
193C23×C8—431no—
194C23×C8—4312no—
195C23×C8—868no—
196C23×C8C2×D4311yescharacteristic
197C2×C22⋊Q8—4312no—
198C2×C22⋊Q8—4312no—
199C2×C22⋊Q8—866no—
200C2×C22⋊Q8—866no—
201C22×C4⋊C4—431no—
202C22×C4⋊C4—861no—
203C22×C4⋊C4—861no—
204C22×C4⋊C4C2×D4311yescharacteristic
205C22×C22⋊C4—861no—
206C22×C22⋊C4—861no—
207#467—4364no—
208C2×#107—4312no—
209C2×#103—4312no—
210C2×#103C2×D43112yescomplemented
211C43C22×#46711yescharacteristic, complemented, Sylow
212C25—431no—
213C22×Q8—23no—
214C22×Q8—24no—
215C22×Q8—24no—
216C22×Q8—436no—
217C22×Q8—863no—
218C22×Q8—864no—
219C22×Q8—864no—
220C22×Q8C22×D4316yes—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—431no—
224C23×C4—436no—
225C23×C4—436no—
226C23×C4—864no—
227C23×C4—864no—
228C23×C4—861no—
229C23×C4—861no—
230C23×C4C22×D4311yescharacteristic
231C2×Q16—4316no—
232C2×Q16—8648no—
233C22×C8—24no—
234C22×C8—438no—
235C22×C8—436no—
236C22×C8—4316no—
237C22×C8—8648no—
238C22×C8C22×D4316yes—
239C22⋊Q8—4316no—
240C22⋊Q8—4316no—
241C22⋊Q8—8624no—
242C22⋊Q8—8624no—
243C2×C4⋊C4—23no—
244C2×C4⋊C4—436no—
245C2×C4⋊C4—8612no—
246C2×C4⋊C4—8612no—
247C2×C4⋊C4—863no—
248C2×C4⋊C4C22×D4316yes—
249C2×C22⋊C4—8612no—
250C2×C22⋊C4—8612no—
251#107—4316no—
252#103—4316no—
253#103C22×D43116yescomplemented
254C24—438no—
255C24—436no—
256C24—864no—
257C24—864no—
258C24D4×D4311yescharacteristic
259C2×Q8—26no—
260C2×Q8—212no—
261C2×Q8—212no—
262C2×Q8—412no—
263C2×Q8—434no—
264C2×Q8—866no—
265C2×Q8—8612no—
266C2×Q8—8612no—
267C2×Q8—17212no—
268C2×Q8C23×D4314yes—
269C22×C4—26no—
270C22×C4—26no—
271C22×C4—44no—
272C22×C4—44no—
273C22×C4—436no—
274C22×C4—4312no—
275C22×C4—434no—
276C22×C4—864no—
277C22×C4—8624no—
278C22×C4—8612no—
279C22×C4—8612no—
280C22×C4—866no—
281C22×C4—866no—
282C22×C4—1724no—
283C22×C4—1724no—
284C22×C4#1062189814yes—
285C22×C4D4×D4313yes—
286C22×C4D4×D4314yes—
287C22×C4C23×D4313yes—
288Q16—8632no—
289C2×C8—212no—
290C2×C8—4324no—
291C2×C8—434no—
292C2×C8—8632no—
293C2×C8C23×D4314yes—
294C4⋊C4—26no—
295C4⋊C4—434no—
296C4⋊C4—8616no—
297C4⋊C4—8616no—
298C4⋊C4—866no—
299C4⋊C4C23×D4314yes—
300C22⋊C4—8616no—
301C22⋊C4—8616no—
302C23—4324no—
303C23—434no—
304C23—8612no—
305C23—8632no—
306C23—8612no—
307C23#1306329814yes—
308C23Q16×D4314yes—
309C23#1306334614yes—
310C23C2×D4×D4313yes—
311Q8—24no—
312Q8—24no—
313Q8—412no—
314Q8—864no—
315Q8—864no—
316Q8—17212no—
317C2×C4—24no—
318C2×C4—24no—
319C2×C4—412no—
320C2×C4—412no—
321C2×C4—434no—
322C2×C4—8612no—
323C2×C4—8624no—
324C2×C4—864no—
325C2×C4—864no—
326C2×C4—864no—
327C2×C4—864no—
328C2×C4—17212no—
329C2×C4—17212no—
330C2×C4#13063298112yes—
331C2×C4C2×D4×D4313yes—
332C2×C4C2×D4×D4316yes—
333C2×C4C2×#1062189816yes—
334C2×C4C24×D4311yescharacteristic
335C8—24no—
336C8—438no—
337C22—438no—
338C22—864no—
339C22—864no—
340C22—8648no—
341C22#14583139116yesdirect product factor
342C22C2×#1306329816yes—
343C22C2×Q16×D4316yes—
344C22C2×#1306334616yes—
345C22C22×D4×D4311yescharacteristic
346C4—44no—
347C4—44no—
348C4—864no—
349C4—1724no—
350C4—1724no—
351C4C2×#1306329816yes—
352C4C22×D4×D4311yescharacteristic
353C4C22×#1062189811yescharacteristic
354C2—868no—
355C2C2×#14583139112yesdirect product factor
356C2C22×#1306329811yescharacteristic
357C2C22×Q16×D4311yescharacteristic
358C2C22×#1306334611yescharacteristic
subgroupG/H
centerC24D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC22×#103×C43C2
socleC24×C43C2×D4
prime radicalC24×D43D4
hypercenterC22×#103D43
hypocenterC43C22×#467
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
1. C23×#10621885C2semidirect
5. C2×#14583139C2direct (N × H)
6. C22×#13063258C2semidirect
7. C22×#13063250C2semidirect
8. C22×#103×C43C2semidirect
12. C22×#10621885C22semidirect
25. #14583139C22direct (N × H)
26. C2×#13063258C22semidirect
27. C2×#13063250C22semidirect
31. C2×#103×C43C22semidirect
45. C2×#10621885C23semidirect
60. #13063258C23semidirect
61. #13063250C23semidirect
73. #103×C43C23semidirect
77. C23×D43Q16semidirect
129. C22×D43C2×Q16semidirect
158. C22×C43#467semidirect
166. C2×D43C22×Q16semidirect
182. C22×#103D43semidirect
183. C2×C43C2×#467semidirect
210. C2×#103C2×D43semidirect
211. C43C22×#467semidirect
253. #103C22×D43semidirect
341. C22#14583139direct (N × H)
355. C2C2×#14583139direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#106218852
C23×C8×D432
C22×#130633052
C22×#130633012
C2×#145831392
C22×#130632582
C22×#130632502
C22×#103×C432
C22×#46743