Finite Group Databasebeta

← C22×#14583118 #25963402

Subgroups — C22×#14583118 #25963402

Order 11008.

2918 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×#10621883C211yesmaximal, characteristic
3C22×C4×Dic86C211yesmaximal, characteristic, complemented
4C2×#14583118C2124yesmaximal, direct product factor
5C22×C4⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
6C22×#13063249C211yesmaximal, characteristic, complemented
7C22×#13063246C211yesmaximal, characteristic
8C22×#124×C43C211yesmaximal, characteristic
9C23×Dic86C2211yescharacteristic
10C22×#10621885—28no—
11C22×#10621885C22112yescomplemented
12C22×#10621883—28no—
13C22×#10621883C22112yes—
14C23×C43⋊C8C2211yescharacteristic
15C23×C43⋊C8C2211yescharacteristic
16C2×C4×Dic86—26no—
17C2×C4×Dic86C22112yescomplemented
18C22×C4⋊Dic43C2211yescharacteristic
19C22×Dic43⋊C4—21no—
20C22×C4×Dic43—21no—
21#14583118C22164yesdirect product factor
22C2×C4⋊(C43⋊C8)C22112yescomplemented
23C2×#13063249C22112yescomplemented
24C2×#13063246C22112yes—
25C23×Q8×C43C2211yescharacteristic
26C23×D4×C43C2211yescharacteristic
27C2×#124×C43—26no—
28C2×#124×C43C22112yes—
29C22×C22⋊C4×C43—21no—
30C22×C22⋊C4×C43—21no—
31C22×C42×C43C2211yescharacteristic
32C22×Dic86—23no—
33C22×Dic86—24no—
34C22×Dic86D418yes—
35C22×Dic86C2316yes—
36C23×Dic43—21no—
37C23×Dic43—21no—
38C2×#10621885—248no—
39C2×#10621885C23116yescomplemented
40C2×#10621883—248no—
41C2×#10621883C23116yes—
42C22×C43⋊C8—24no—
43C22×C43⋊C8—24no—
44C22×C43⋊C8C2316yes—
45C22×C43⋊C8C2316yes—
46C4×Dic86—224no—
47C4×Dic86C23116yescomplemented
48C2×C4⋊Dic43—23no—
49C2×C4⋊Dic43C2316yes—
50C2×Dic43⋊C4—212no—
51C2×C4×Dic43—212no—
52C4⋊(C43⋊C8)C23116yescomplemented
53#13063249C23116yescomplemented
54#13063246C23116yes—
55C25×C43—21no—
56C22×Q8×C43—23no—
57C22×Q8×C43—24no—
58C22×Q8×C43—24no—
59C22×Q8×C43C2316yes—
60C22×D4×C43—24no—
61C22×D4×C43—23no—
62C22×D4×C43—24no—
63C22×D4×C43C2316yes—
64C23×C4×C43—21no—
65C23×C4×C43D411yescharacteristic
66C23×C4×C43D411yescharacteristic
67C23×C4×C43C2311yescharacteristic
68#124×C43—224no—
69#124×C43C23116yes—
70C2×C22⋊C4×C43—212no—
71C2×C22⋊C4×C43—212no—
72C2×C42×C43D416yes—
73C2×C42×C43C2316yes—
74C24×C43—26no—
75C24×C43—44no—
76C24×C43—44no—
77C24×C43—44no—
78C24×C43C2×D411yescharacteristic
79C2×Q8×C43—26no—
80C2×Q8×C43—212no—
81C2×Q8×C43—212no—
82C2×Q8×C43—412no—
83C2×Q8×C43C2414yes—
84C2×D4×C43—26no—
85C2×D4×C43—212no—
86C2×D4×C43—212no—
87C2×D4×C43—412no—
88C2×D4×C43C2414yes—
89C22×C4×C43—24no—
90C22×C4×C43—24no—
91C22×C4×C43—26no—
92C22×C4×C43—44no—
93C22×C4×C43C2×D414yes—
94C22×C4×C43C2×D416yes—
95C22×C4×C43C2×D416yes—
96C22×C4×C43C2×D413yes—
97C22×C4×C43#4114yes—
98C22×C4×C43C2413yes—
99C22×Dic43—28no—
100C22×Dic43—26no—
101C22×Dic43—26no—
102C22×Dic43—44no—
103C2×Dic86—224no—
104C2×Dic86—26no—
105C2×Dic86—212no—
106C2×Dic86C2×D4124yes—
107C2×Dic86C2414yes—
108C22⋊C4×C43—216no—
109C22⋊C4×C43—216no—
110C42×C43C2×D4112yes—
111C42×C43C2414yes—
112#10621885—232no—
113#10621883—232no—
114C4⋊Dic43—26no—
115C4⋊Dic43C2414yes—
116Dic43⋊C4—216no—
117C4×Dic43—216no—
118C2×C43⋊C8—212no—
119C2×C43⋊C8—212no—
120C2×C43⋊C8C2414yes—
121C2×C43⋊C8C2414yes—
122C23×C43—24no—
123C23×C43—412no—
124C23×C43—412no—
125C23×C43—412no—
126C23×C43—816no—
127C23×C43#12114yes—
128C23×C43#13514yes—
129C23×C43#13714yes—
130C23×C43C22×D413yes—
131Q8×C43—24no—
132Q8×C43—24no—
133Q8×C43—412no—
134D4×C43—24no—
135D4×C43—24no—
136D4×C43—412no—
137C2×C4×C43—212no—
138C2×C4×C43—212no—
139C2×C4×C43—24no—
140C2×C4×C43—412no—
141C2×C4×C43#121112yes—
142C2×C4×C43C22×D416yes—
143C2×C4×C43C22×D414yes—
144C2×C4×C43C22×D414yes—
145C2×C4×C43C22×D413yes—
146C2×C4×C43C2×#4116yes—
147C2×C4×C43C2511yescharacteristic
148C2×Dic43—224no—
149C2×Dic43—24no—
150C2×Dic43—24no—
151C2×Dic43—412no—
152Dic86—224no—
153Dic86—24no—
154Dic86C22×D418yes—
155C43⋊C8—24no—
156C43⋊C8—24no—
157C22×#464—431nomaximal, Sylow
158C22×C43—44no—
159C22×C43—44no—
160C22×C43—44no—
161C22×C43—824no—
162C22×C43#464116yescomplemented
163C22×C43C2×#12116yes—
164C22×C43C2×#13516yes—
165C22×C43C2×#13716yes—
166C22×C43C23×D411yescharacteristic
167C4×C43—24no—
168C4×C43—24no—
169C4×C43—44no—
170C4×C43C2×#12116yes—
171C4×C43C23×D411yescharacteristic
172C4×C43C22×#4111yescharacteristic
173Dic43—28no—
174Dic43—44no—
175C23×Q16—431no—
176C23×SD16—431no—
177C22×#124D4311yescharacteristic
178C22×C4×Q8—431no—
179C2×#464—4324no—
180C22×C4⋊C8—431no—
181C22×#103—431no—
182C22×#102—431no—
183C2×C43—84no—
184C2×C43C2×#464112yescomplemented
185C2×C43C22×#12111yescharacteristic
186C2×C43C22×#13511yescharacteristic
187C2×C43C22×#13711yescharacteristic
188C23×Q8—431no—
189C23×Q8C2×D4311yescharacteristic
190C23×D4C2×D4311yescharacteristic
191C22×Q16—4312no—
192C22×Q16—868no—
193C22×SD16—4312no—
194C22×SD16—868no—
195C23×C8—431no—
196C23×C8—431no—
197C2×#124—26no—
198C2×#124C2×D43112yes—
199C2×C4×Q8—4312no—
200C2×C4×Q8—866no—
201C22×C4⋊C4—431no—
202C22×C4⋊C4—861no—
203C22×C22⋊C4—21no—
204C22×C22⋊C4—21no—
205C22×C42—861no—
206C22×C42C2×D4311yescharacteristic
207#464—4364no—
208C2×C4⋊C8—4312no—
209C2×#103—4312no—
210C2×#102—4312no—
211C43C22×#46411yescharacteristic, complemented, Sylow
212C25—21no—
213C22×Q8—23no—
214C22×Q8—24no—
215C22×Q8—24no—
216C22×Q8—438no—
217C22×Q8—436no—
218C22×Q8—864no—
219C22×Q8—863no—
220C22×Q8C22×D4316yes—
221C22×D4—24no—
222C22×D4—24no—
223C22×D4—23no—
224C22×D4C22×D4316yes—
225C23×C4—21no—
226C23×C4—861no—
227C23×C4—861no—
228C23×C4C22⋊D4311yescharacteristic
229C23×C4C22⋊D4311yescharacteristic
230C23×C4C22×D4311yescharacteristic
231C2×Q16—4316no—
232C2×Q16—8648no—
233C2×SD16—4316no—
234C2×SD16—8648no—
235C22×C8—436no—
236C22×C8—436no—
237C22×C8—864no—
238C22×C8—864no—
239#124—224no—
240#124C22×D43116yes—
241C4×Q8—4316no—
242C4×Q8—8624no—
243C2×C4⋊C4—436no—
244C2×C4⋊C4—863no—
245C2×C4⋊C4—8612no—
246C2×C22⋊C4—212no—
247C2×C22⋊C4—212no—
248C2×C42—8612no—
249C2×C42C22⋊D4316yes—
250C2×C42C22×D4316yes—
251C4⋊C8—4316no—
252#103—4316no—
253#102—4316no—
254C24—26no—
255C24—44no—
256C24—44no—
257C24—44no—
258C24C2×C22⋊D4311yescharacteristic
259C2×Q8—26no—
260C2×Q8—212no—
261C2×Q8—212no—
262C2×Q8—412no—
263C2×Q8—4324no—
264C2×Q8—434no—
265C2×Q8—8624no—
266C2×Q8—866no—
267C2×Q8—8612no—
268C2×Q8C23×D4314yes—
269C2×D4—212no—
270C2×D4—26no—
271C2×D4—212no—
272C2×D4—412no—
273C2×D4C23×D4314yes—
274C22×C4—24no—
275C22×C4—24no—
276C22×C4—26no—
277C22×C4—44no—
278C22×C4—868no—
279C22×C4—866no—
280C22×C4—866no—
281C22×C4—1724no—
282C22×C4D4×D4314yes—
283C22×C4#1062190014yes—
284C22×C4C2×C22⋊D4316yes—
285C22×C4C2×C22⋊D4316yes—
286C22×C4C2×C22⋊D4313yes—
287C22×C4C23×D4313yes—
288Q16—8632no—
289SD16—8632no—
290C2×C8—434no—
291C2×C8—434no—
292C2×C8—8612no—
293C2×C8—8612no—
294C4⋊C4—434no—
295C4⋊C4—866no—
296C4⋊C4—8616no—
297C22⋊C4—216no—
298C22⋊C4—216no—
299C42—8616no—
300C42C2×C22⋊D43112yes—
301C42C23×D4314yes—
302C23—24no—
303C23—412no—
304C23—412no—
305C23—412no—
306C23—816no—
307C23#1306329614yes—
308C23#1306334514yes—
309C23#1306335514yes—
310C23C22×C22⋊D4313yes—
311Q8—24no—
312Q8—24no—
313Q8—412no—
314Q8—438no—
315Q8—8624no—
316Q8—864no—
317D4—24no—
318D4—24no—
319D4—412no—
320C2×C4—212no—
321C2×C4—212no—
322C2×C4—24no—
323C2×C4—412no—
324C2×C4—8624no—
325C2×C4—864no—
326C2×C4—864no—
327C2×C4—17212no—
328C2×C4#13063296112yes—
329C2×C4C2×D4×D4316yes—
330C2×C4C22×C22⋊D4314yes—
331C2×C4C22×C22⋊D4314yes—
332C2×C4C22×C22⋊D4313yes—
333C2×C4C2×#1062190016yes—
334C2×C4C24×D4311yescharacteristic
335C8—864no—
336C8—864no—
337C22—44no—
338C22—44no—
339C22—44no—
340C22—824no—
341C22#14583118116yesdirect product factor
342C22C2×#1306329616yes—
343C22C2×#1306334516yes—
344C22C2×#1306335516yes—
345C22C23×C22⋊D4311yescharacteristic
346C4—24no—
347C4—24no—
348C4—44no—
349C4—868no—
350C4—1724no—
351C4C2×#1306329616yes—
352C4C22×D4×D4311yescharacteristic
353C4C22×#1062190011yescharacteristic
354C2—84no—
355C2C2×#14583118112yesdirect product factor
356C2C22×#1306329611yescharacteristic
357C2C22×#1306334511yescharacteristic
358C2C22×#1306335511yescharacteristic
subgroupG/H
centerC24C2×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC22×#124×C43C2
socleC24×C43C2×D4
prime radicalC23×D4×C43C22
hypercenterC22×#124D43
hypocenterC43C22×#464
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×#124

Complements

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

NH ≅ G/Ntype
1. C23×#10621885C2semidirect
3. C22×C4×Dic86C2semidirect
4. C2×#14583118C2direct (N × H)
5. C22×C4⋊(C43⋊C8)C2semidirect
6. C22×#13063249C2semidirect
11. C22×#10621885C22semidirect
17. C2×C4×Dic86C22semidirect
21. #14583118C22direct (N × H)
22. C2×C4⋊(C43⋊C8)C22semidirect
23. C2×#13063249C22semidirect
39. C2×#10621885C23semidirect
47. C4×Dic86C23semidirect
52. C4⋊(C43⋊C8)C23semidirect
53. #13063249C23semidirect
162. C22×C43#464semidirect
184. C2×C43C2×#464semidirect
211. C43C22×#464semidirect
341. C22#14583118direct (N × H)
355. C2C2×#14583118direct (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×#106218832
C22×C4×Dic862
C2×#145831182
C22×C4⋊(C43⋊C8)2
C22×#130632492
C22×#130632462
C22×#124×C432
C22×#46443