Finite Group Databasebeta

← C22×#14582658 #25093978

Subgroups — C22×#14582658 #25093978

Order 11008.

2830 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#10621877C211yesmaximal, characteristic
2C23×C4×Dic43C211yesmaximal, characteristic
3C2×#14582658C2112yesmaximal, direct product factor
4C22×#117×C43C211yesmaximal, characteristic
5C24×Dic43—21no—
6C22×#10621877—24no—
7C22×#10621877—23no—
8C22×#10621877C418yescomplemented
9C22×#10621877C2216yes—
10C23×C43⋊C8—21no—
11C22×C4×Dic43—24no—
12C22×C4×Dic43—23no—
13C22×C4×Dic43C418yescomplemented
14C22×C4×Dic43C2216yes—
15#14582658C22116yesdirect product factor
16C24×C4×C43C2211yescharacteristic
17C2×#117×C43—23no—
18C2×#117×C43—23no—
19C2×#117×C43C416yescomplemented
20C2×#117×C43C2216yes—
21C22×C4⋊C4×C43C412yescomplemented
22C22×C22⋊C4×C43—21no—
23C22×C42×C43—21no—
24C23×Dic43—216no—
25C23×Dic43—28no—
26C23×Dic43—26no—
27C2×#10621877—224no—
28C2×#10621877—212no—
29C2×#10621877—26no—
30C2×#10621877C2×C4124yescomplemented
31C2×#10621877C2314yes—
32C22×C43⋊C8—28no—
33C22×C43⋊C8—26no—
34C2×C4×Dic43—224no—
35C2×C4×Dic43—212no—
36C2×C4×Dic43—26no—
37C2×C4×Dic43C2×C4124yescomplemented
38C2×C4×Dic43C2314yes—
39C25×C43D411yescharacteristic
40C23×C4×C43—22no—
41C23×C4×C43C2×C414yes—
42C23×C4×C43C2×C414yes—
43C23×C4×C43C2×C411yescharacteristic
44C23×C4×C43C2×C413yes—
45C23×C4×C43D414yes—
46C23×C4×C43D413yes—
47C23×C4×C43D413yes—
48C23×C4×C43D411yescharacteristic
49C23×C4×C43Q814yes—
50C23×C4×C43C2313yes—
51#117×C43—212no—
52#117×C43—26no—
53#117×C43—26no—
54#117×C43C2×C4112yescomplemented
55#117×C43C2314yes—
56C2×C4⋊C4×C43—26no—
57C2×C4⋊C4×C43C2×C4112yescomplemented
58C2×C22⋊C4×C43—26no—
59C2×C22⋊C4×C43—26no—
60C2×C42×C43—26no—
61C2×C42×C43—26no—
62C24×C43—28no—
63C24×C43C22⋊C414yes—
64C24×C43C22⋊C413yes—
65C24×C43C22⋊C411yescharacteristic
66C24×C43C4⋊C414yes—
67C24×C43C2×D413yes—
68C22×C4×C43—212no—
69C22×C4×C43—48no—
70C22×C4×C43C42112yes—
71C22×C4×C43C4214yes—
72C22×C4×C43C22⋊C414yes—
73C22×C4×C43C22⋊C4112yes—
74C22×C4×C43C22⋊C4112yes—
75C22×C4×C43C22⋊C413yes—
76C22×C4×C43C22⋊C413yes—
77C22×C4×C43C22⋊C416yes—
78C22×C4×C43C4⋊C4112yes—
79C22×C4×C43C4⋊C414yes—
80C22×C4×C43C4⋊C4112yes—
81C22×C4×C43C4⋊C414yes—
82C22×C4×C43C4⋊C4112yes—
83C22×C4×C43C22×C416yes—
84C22×C4×C43C22×C413yes—
85C22×C4×C43C22×C413yes—
86C22×C4×C43C22×C416yes—
87C22×C4×C43C2×D416yes—
88C22×C4×C43C2×D413yes—
89C22×C4×C43C2×D413yes—
90C22×C4×C43C2×D413yes—
91C22×C4×C43C2×Q816yes—
92C22×C4×C43C2411yescharacteristic
93C22×Dic43—264no—
94C22×Dic43—248no—
95C22×Dic43—224no—
96C22×Dic43—24no—
97C4⋊C4×C43—212no—
98C4⋊C4×C43C22×C418yescomplemented
99C22⋊C4×C43—212no—
100C22⋊C4×C43—24no—
101C42×C43—212no—
102C42×C43—24no—
103C4×Dic43—224no—
104C4×Dic43—24no—
105C4×Dic43C22×C418yescomplemented
106#10621877—224no—
107#10621877—24no—
108#10621877C22×C418yescomplemented
109C2×C43⋊C8—224no—
110C2×C43⋊C8—24no—
111C23×C43—216no—
112C23×C43—216no—
113C23×C43—212no—
114C23×C43—212no—
115C23×C43#95112yes—
116C23×C43#9514yes—
117C23×C43#10418yes—
118C23×C43C2×C22⋊C416yes—
119C23×C43C2×C22⋊C413yes—
120C23×C43C2×C22⋊C413yes—
121C23×C43C2×C4⋊C416yes—
122C23×C43C22×D411yescharacteristic
123C2×C4×C43—28no—
124C2×C4×C43—424no—
125C2×C4×C43#95124yes—
126C2×C4×C43#95112yes—
127C2×C4×C43#95112yes—
128C2×C4×C43C2×C4216yes—
129C2×C4×C43C2×C4216yes—
130C2×C4×C43C2×C22⋊C416yes—
131C2×C4×C43C2×C22⋊C416yes—
132C2×C4×C43C2×C22⋊C416yes—
133C2×C4×C43C2×C22⋊C413yes—
134C2×C4×C43C2×C22⋊C413yes—
135C2×C4×C43C2×C4⋊C416yes—
136C2×C4×C43C2×C4⋊C416yes—
137C2×C4×C43C2×C4⋊C416yes—
138C2×C4×C43C2×C4⋊C416yes—
139C2×C4×C43C2×C4⋊C416yes—
140C2×C4×C43C23×C411yescharacteristic
141C2×C4×C43C23×C411yescharacteristic
142C2×C4×C43C23×C411yescharacteristic
143C2×C4×C43C22×D411yescharacteristic
144C2×C4×C43C22×D411yescharacteristic
145C2×C4×C43C22×Q811yescharacteristic
146C2×Dic43—216no—
147C2×Dic43—296no—
148C2×Dic43—28no—
149C43⋊C8—28no—
150C22×#339—431nomaximal, Sylow
151C22×C43—26no—
152C22×C43—22no—
153C22×C43—224no—
154C22×C43—212no—
155C22×C43—212no—
156C22×C43#339116yescomplemented
157C22×C43C2×#9516yes—
158C22×C43C2×#9516yes—
159C22×C43C2×#104112yes—
160C22×C43C22×C22⋊C411yescharacteristic
161C22×C43C22×C22⋊C411yescharacteristic
162C22×C43C22×C4⋊C411yescharacteristic
163C4×C43—48no—
164C4×C43C2×#9516yes—
165C4×C43C2×#9516yes—
166C4×C43C22×C4211yescharacteristic
167C4×C43C22×C22⋊C411yescharacteristic
168C4×C43C22×C4⋊C411yescharacteristic
169C4×C43C22×C4⋊C411yescharacteristic
170Dic43—216no—
171C23×M16—431no—
172C22×#117D4311yescharacteristic
173C23×C42—431no—
174C2×#339—4312no—
175C2×C43—21no—
176C2×C43—21no—
177C2×C43—26no—
178C2×C43C2×#339112yescomplemented
179C2×C43C22×#9511yescharacteristic
180C2×C43C22×#10412yes—
181C24×C4—861no—
182C24×C4C2×D4311yescharacteristic
183C22×M16—436no—
184C22×M16—438no—
185C22×M16—864no—
186C22×M16—863no—
187C23×C8—861no—
188C2×#117—23no—
189C2×#117—23no—
190C2×#117Dic4316yescomplemented
191C2×#117C2×D4316yes—
192C22×C4⋊C4Dic4312yescomplemented
193C22×C22⋊C4—21no—
194C22×C42—21no—
195C22×C42—436no—
196C22×C42—438no—
197C22×C42—864no—
198C22×C42—863no—
199#339—4316no—
200C43C22×#33911yescharacteristic, complemented, Sylow
201C25C22⋊D4311yescharacteristic
202C23×C4—22no—
203C23×C4—8616no—
204C23×C4—868no—
205C23×C4—866no—
206C23×C4Dic8614yes—
207C23×C4C4×D4314yes—
208C23×C4C4×D4314yes—
209C23×C4D17214yes—
210C23×C4C2×Dic4311yescharacteristic
211C23×C4C2×Dic4313yes—
212C23×C4C22⋊D4313yes—
213C23×C4C22⋊D4313yes—
214C23×C4C22⋊D4311yescharacteristic
215C23×C4C22×D4313yes—
216C2×M16—4324no—
217C2×M16—434no—
218C2×M16—8624no—
219C2×M16—8612no—
220C2×M16—866no—
221C22×C8—868no—
222C22×C8—866no—
223#117—212no—
224#117—26no—
225#117—26no—
226#117C2×Dic43112yescomplemented
227#117C22×D4314yes—
228C2×C4⋊C4—26no—
229C2×C4⋊C4C2×Dic43112yescomplemented
230C2×C22⋊C4—26no—
231C2×C22⋊C4—26no—
232C2×C42—26no—
233C2×C42—26no—
234C2×C42—4324no—
235C2×C42—434no—
236C2×C42—8624no—
237C2×C42—8612no—
238C2×C42—866no—
239C24—28no—
240C24Dic43⋊C414yes—
241C24(C2×D43)⋊C414yes—
242C24C22⋊Dic4313yes—
243C24C22⋊Dic4311yescharacteristic
244C24C2×C22⋊D4313yes—
245C22×C4—212no—
246C22×C4—48no—
247C22×C4—8648no—
248C22×C4—8664no—
249C22×C4—8624no—
250C22×C4—864no—
251C22×C4C4×Dic43112yes—
252C22×C4C4×Dic4314yes—
253C22×C4Dic43⋊C4112yes—
254C22×C4Dic43⋊C4112yes—
255C22×C4Dic43⋊C414yes—
256C22×C4C4⋊Dic43112yes—
257C22×C4C4⋊Dic4314yes—
258C22×C4(C2×D43)⋊C4112yes—
259C22×C4(C2×D43)⋊C414yes—
260C22×C4(C2×D43)⋊C4112yes—
261C22×C4C22⋊Dic4313yes—
262C22×C4C22⋊Dic4313yes—
263C22×C4C22⋊Dic4316yes—
264C22×C4C2×Dic8616yes—
265C22×C4C2×C4×D4316yes—
266C22×C4C2×C4×D4316yes—
267C22×C4C2×D17216yes—
268C22×C4C22×Dic4313yes—
269C22×C4C22×Dic4313yes—
270C22×C4C2×C22⋊D4313yes—
271C22×C4C2×C22⋊D4313yes—
272C22×C4C2×C22⋊D4313yes—
273C22×C4C23×D4311yescharacteristic
274M16—438no—
275M16—8624no—
276M16—864no—
277C2×C8—8624no—
278C2×C8—864no—
279C4⋊C4—212no—
280C4⋊C4C22×Dic4318yescomplemented
281C22⋊C4—212no—
282C22⋊C4—24no—
283C42—212no—
284C42—24no—
285C42—438no—
286C42—8624no—
287C42—864no—
288C23—212no—
289C23—212no—
290C23—216no—
291C23—216no—
292C23C43⋊#95112yes—
293C23C43⋊#9514yes—
294C23#1306325218yes—
295C23C2×(C2×D43)⋊C416yes—
296C23C2×C22⋊Dic4313yes—
297C23C2×C22⋊Dic4313yes—
298C23C2×Dic43⋊C416yes—
299C23C22×C22⋊D4311yescharacteristic
300C2×C4—28no—
301C2×C4—424no—
302C2×C4—8696no—
303C2×C4—8616no—
304C2×C4—868no—
305C2×C4C43⋊#95124yes—
306C2×C4C43⋊#95112yes—
307C2×C4C43⋊#95112yes—
308C2×C4C2×C4×Dic4316yes—
309C2×C4C2×C4×Dic4316yes—
310C2×C4C2×(C2×D43)⋊C416yes—
311C2×C4C2×(C2×D43)⋊C416yes—
312C2×C4C2×(C2×D43)⋊C416yes—
313C2×C4C2×C22⋊Dic4313yes—
314C2×C4C2×C22⋊Dic4313yes—
315C2×C4C2×Dic43⋊C416yes—
316C2×C4C2×Dic43⋊C416yes—
317C2×C4C2×Dic43⋊C416yes—
318C2×C4C2×C4⋊Dic4316yes—
319C2×C4C2×C4⋊Dic4316yes—
320C2×C4C22×C4×D4311yescharacteristic
321C2×C4C22×C4×D4311yescharacteristic
322C2×C4C23×Dic4311yescharacteristic
323C2×C4C22×C22⋊D4311yescharacteristic
324C2×C4C22×D17211yescharacteristic
325C2×C4C22×Dic8611yescharacteristic
326C8—868no—
327C22—212no—
328C22—224no—
329C22—212no—
330C22—22no—
331C22—26no—
332C22#14582658116yesdirect product factor
333C22C2×C43⋊#9516yes—
334C22C2×C43⋊#9516yes—
335C22C2×#13063252112yes—
336C22C22×(C2×D43)⋊C411yescharacteristic
337C22C22×C22⋊Dic4311yescharacteristic
338C22C22×Dic43⋊C411yescharacteristic
339C4—48no—
340C4—8616no—
341C4C2×C43⋊#9516yes—
342C4C2×C43⋊#9516yes—
343C4C22×C4×Dic4311yescharacteristic
344C4C22×(C2×D43)⋊C411yescharacteristic
345C4C22×Dic43⋊C411yescharacteristic
346C4C22×C4⋊Dic4311yescharacteristic
347C2—21no—
348C2—21no—
349C2—26no—
350C2C2×#14582658112yesdirect product factor
351C2C22×C43⋊#9511yescharacteristic
352C2C22×#1306325212yes—
subgroupG/H
centerC23×C4C22⋊D43
commutatorC4×C43C22×C42
FrattiniC22×C4C23×D43
FittingC22×#117×C43C2
socleC24×C43C22⋊C4
prime radicalC25×C43D4
cosocleC22×C4×C43C24
hypercenterC22×#117D43
hypocenterC43C22×#339
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C24×C4 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
3. C2×#14582658C2direct (N × H)
8. C22×#10621877C4semidirect
13. C22×C4×Dic43C4semidirect
15. #14582658C22direct (N × H)
19. C2×#117×C43C4semidirect
21. C22×C4⋊C4×C43C4semidirect
30. C2×#10621877C2×C4semidirect
37. C2×C4×Dic43C2×C4semidirect
54. #117×C43C2×C4semidirect
57. C2×C4⋊C4×C43C2×C4semidirect
98. C4⋊C4×C43C22×C4semidirect
105. C4×Dic43C22×C4semidirect
108. #10621877C22×C4semidirect
156. C22×C43#339semidirect
178. C2×C43C2×#339semidirect
190. C2×#117Dic43semidirect
192. C22×C4⋊C4Dic43semidirect
200. C43C22×#339semidirect
226. #117C2×Dic43semidirect
229. C2×C4⋊C4C2×Dic43semidirect
280. C4⋊C4C22×Dic43semidirect
332. C22#14582658direct (N × H)
350. C2C2×#14582658direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#106218772
C23×C4×Dic432
C2×#145826582
C22×#117×C432
C22×#33943