Finite Group Databasebeta

← C22×#14582636 #25063679

Subgroups — C22×#14582636 #25063679

Order 11008.

1846 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊(C43⋊C8)C211yesmaximal, characteristic
2C22×C43⋊#95C211yesmaximal, characteristic
3C2×#14582636C2112yesmaximal, direct product factor
4C22×C22⋊Q8×C43C211yesmaximal, characteristic
5C24×Dic43—21no—
6C23×C43⋊C8—21no—
7C2×C22⋊(C43⋊C8)—23no—
8C2×C22⋊(C43⋊C8)C2216yes—
9C2×C43⋊#95—23no—
10C2×C43⋊#95C2216yes—
11#14582636C22116yesdirect product factor
12C23×Q8×C43C411yescharacteristic, complemented
13C24×C4×C43C2211yescharacteristic
14C2×C22⋊Q8×C43—23no—
15C2×C22⋊Q8×C43—23no—
16C2×C22⋊Q8×C43C416yescomplemented
17C2×C22⋊Q8×C43C2216yes—
18C22×C4⋊C4×C43—21no—
19C22×C4⋊C4×C43C411yescharacteristic, complemented
20C22×C22⋊C4×C43—21no—
21C23×Dic43—28no—
22C23×Dic43—26no—
23C23×Dic43—44no—
24C23×Dic43—44no—
25C22×C43⋊C8—26no—
26C22×C43⋊C8—44no—
27C22⋊(C43⋊C8)—26no—
28C22⋊(C43⋊C8)C2314yes—
29C43⋊#95—26no—
30C43⋊#95C2314yes—
31C25×C43D411yescharacteristic
32C22×Q8×C43—23no—
33C22×Q8×C43—44no—
34C22×Q8×C43C2×C416yescomplemented
35C23×C4×C43—21no—
36C23×C4×C43—21no—
37C23×C4×C43—44no—
38C23×C4×C43C2×C411yescharacteristic
39C23×C4×C43C2×C413yes—
40C23×C4×C43D411yescharacteristic
41C23×C4×C43D413yes—
42C23×C4×C43D413yes—
43C23×C4×C43C2313yes—
44C22⋊Q8×C43—212no—
45C22⋊Q8×C43—26no—
46C22⋊Q8×C43—26no—
47C22⋊Q8×C43C2×C4112yescomplemented
48C22⋊Q8×C43C2314yes—
49C2×C4⋊C4×C43—26no—
50C2×C4⋊C4×C43—23no—
51C2×C4⋊C4×C43—26no—
52C2×C4⋊C4×C43C2×C416yescomplemented
53C2×C22⋊C4×C43—26no—
54C2×C22⋊C4×C43—26no—
55C24×C43—24no—
56C24×C43—24no—
57C24×C43C22⋊C413yes—
58C24×C43C22⋊C411yescharacteristic
59C24×C43SD1614yes—
60C24×C43Q1614yes—
61C24×C43C2×D413yes—
62C2×Q8×C43—26no—
63C2×Q8×C43—412no—
64C2×Q8×C43—412no—
65C2×Q8×C43C22×C414yescomplemented
66C22×C4×C43—24no—
67C22×C4×C43—24no—
68C22×C4×C43—26no—
69C22×C4×C43—26no—
70C22×C4×C43—46no—
71C22×C4×C43—46no—
72C22×C4×C43—46no—
73C22×C4×C43—46no—
74C22×C4×C43—44no—
75C22×C4×C43—44no—
76C22×C4×C43C22⋊C413yes—
77C22×C4×C43C22⋊C413yes—
78C22×C4×C43C22⋊C416yes—
79C22×C4×C43C22×C413yes—
80C22×C4×C43C22×C413yes—
81C22×C4×C43C2×D413yes—
82C22×C4×C43C2×D413yes—
83C22×C4×C43C2×D413yes—
84C22×C4×C43C2411yescharacteristic
85C22×Dic43—224no—
86C22×Dic43—24no—
87C22×Dic43—432no—
88C22×Dic43—412no—
89C22×Dic43—412no—
90C4⋊C4×C43—212no—
91C4⋊C4×C43—26no—
92C4⋊C4×C43—24no—
93C4⋊C4×C43C22×C414yescomplemented
94C22⋊C4×C43—212no—
95C22⋊C4×C43—24no—
96C2×C43⋊C8—24no—
97C2×C43⋊C8—412no—
98C23×C43—216no—
99C23×C43—216no—
100C23×C43—26no—
101C23×C43—26no—
102C23×C43—26no—
103C23×C43—26no—
104C23×C43#9914yes—
105C23×C43#103112yes—
106C23×C43#10314yes—
107C23×C43#10414yes—
108C23×C43C2×C22⋊C413yes—
109C23×C43C2×C22⋊C413yes—
110C23×C43C2×SD1616yes—
111C23×C43C2×Q1616yes—
112C23×C43C22×D411yescharacteristic
113Q8×C43—44no—
114Q8×C43—412no—
115C2×C4×C43—26no—
116C2×C4×C43—26no—
117C2×C4×C43—26no—
118C2×C4×C43—26no—
119C2×C4×C43—24no—
120C2×C4×C43—24no—
121C2×C4×C43—46no—
122C2×C4×C43—43no—
123C2×C4×C43—43no—
124C2×C4×C43—43no—
125C2×C4×C43—41no—
126C2×C4×C43—412no—
127C2×C4×C43—412no—
128C2×C4×C43C2×C22⋊C413yes—
129C2×C4×C43C2×C22⋊C413yes—
130C2×C4×C43C23×C411yescharacteristic
131C2×C4×C43C22×D411yescharacteristic
132C2×Dic43—28no—
133C2×Dic43—44no—
134C2×Dic43—448no—
135C2×Dic43—44no—
136C43⋊C8—44no—
137C22×#328—431nomaximal, Sylow
138C22×C43—23no—
139C22×C43—21no—
140C22×C43—23no—
141C22×C43—21no—
142C22×C43—224no—
143C22×C43—212no—
144C22×C43—212no—
145C22×C43#328116yescomplemented
146C22×C43C2×#9916yes—
147C22×C43C2×#10316yes—
148C22×C43C2×#10316yes—
149C22×C43C2×#10416yes—
150C22×C43C22×C22⋊C411yescharacteristic
151C22×C43C22×SD1611yescharacteristic
152C22×C43C22×Q1611yescharacteristic
153C4×C43—21no—
154C4×C43—23no—
155C4×C43—23no—
156C4×C43—21no—
157C4×C43—44no—
158C4×C43—44no—
159Dic43—48no—
160C22×C22⋊Q8D4311yescharacteristic
161C22×C22⋊C8—431no—
162C22×#95—431no—
163C2×#328—4312no—
164C2×C43—21no—
165C2×C43—21no—
166C2×C43—26no—
167C2×C43C2×#328112yescomplemented
168C2×C43C22×#9911yescharacteristic
169C2×C43C22×#10311yescharacteristic
170C2×C43C22×#10411yescharacteristic
171C23×Q8Dic4311yescharacteristic, complemented
172C24×C4—861no—
173C24×C4C2×D4311yescharacteristic
174C23×C8—861no—
175C2×C22⋊Q8—23no—
176C2×C22⋊Q8—23no—
177C2×C22⋊Q8Dic4316yescomplemented
178C2×C22⋊Q8C2×D4316yes—
179C22×C4⋊C4—21no—
180C22×C4⋊C4Dic4311yescharacteristic, complemented
181C22×C22⋊C4—21no—
182C2×C22⋊C8—436no—
183C2×C22⋊C8—863no—
184C2×#95—436no—
185C2×#95—863no—
186#328—4316no—
187C43C22×#32811yescharacteristic, complemented, Sylow
188C25C22⋊D4311yescharacteristic
189C22×Q8—23no—
190C22×Q8—44no—
191C22×Q8C2×Dic4316yescomplemented
192C23×C4—21no—
193C23×C4—21no—
194C23×C4—44no—
195C23×C4—868no—
196C23×C4—866no—
197C23×C4—1724no—
198C23×C4—1724no—
199C23×C4C2×Dic4311yescharacteristic
200C23×C4C2×Dic4313yes—
201C23×C4C22⋊D4311yescharacteristic
202C23×C4C22⋊D4313yes—
203C23×C4C22⋊D4313yes—
204C23×C4C22×D4313yes—
205C22×C8—866no—
206C22×C8—1724no—
207C22⋊Q8—212no—
208C22⋊Q8—26no—
209C22⋊Q8—26no—
210C22⋊Q8C2×Dic43112yescomplemented
211C22⋊Q8C22×D4314yes—
212C2×C4⋊C4—26no—
213C2×C4⋊C4—23no—
214C2×C4⋊C4—26no—
215C2×C4⋊C4C2×Dic4316yescomplemented
216C2×C22⋊C4—26no—
217C2×C22⋊C4—26no—
218C22⋊C8—434no—
219C22⋊C8—866no—
220#95—434no—
221#95—866no—
222C24—24no—
223C24—24no—
224C24#1062188414yes—
225C24#1062188514yes—
226C24C22⋊Dic4313yes—
227C24C22⋊Dic4311yescharacteristic
228C24C2×C22⋊D4313yes—
229C2×Q8—26no—
230C2×Q8—412no—
231C2×Q8—412no—
232C2×Q8C22×Dic4314yescomplemented
233C22×C4—24no—
234C22×C4—24no—
235C22×C4—26no—
236C22×C4—26no—
237C22×C4—46no—
238C22×C4—46no—
239C22×C4—46no—
240C22×C4—46no—
241C22×C4—44no—
242C22×C4—44no—
243C22×C4—8624no—
244C22×C4—864no—
245C22×C4—17212no—
246C22×C4—17232no—
247C22×C4—17212no—
248C22×C4C22⋊Dic4313yes—
249C22×C4C22⋊Dic4313yes—
250C22×C4C22⋊Dic4316yes—
251C22×C4C22×Dic4313yes—
252C22×C4C22×Dic4313yes—
253C22×C4C2×C22⋊D4313yes—
254C22×C4C2×C22⋊D4313yes—
255C22×C4C2×C22⋊D4313yes—
256C22×C4C23×D4311yescharacteristic
257C2×C8—864no—
258C2×C8—17212no—
259C4⋊C4—212no—
260C4⋊C4—26no—
261C4⋊C4—24no—
262C4⋊C4C22×Dic4314yescomplemented
263C22⋊C4—212no—
264C22⋊C4—24no—
265C23—26no—
266C23—26no—
267C23—216no—
268C23—216no—
269C23—26no—
270C23—26no—
271C23#1306324014yes—
272C23#13063249112yes—
273C23#1306324914yes—
274C23#1306325214yes—
275C23C2×C22⋊Dic4313yes—
276C23C2×C22⋊Dic4313yes—
277C23C2×#1062188416yes—
278C23C2×#1062188516yes—
279C23C22×C22⋊D4311yescharacteristic
280Q8—44no—
281Q8—412no—
282C2×C4—26no—
283C2×C4—26no—
284C2×C4—26no—
285C2×C4—26no—
286C2×C4—24no—
287C2×C4—24no—
288C2×C4—46no—
289C2×C4—43no—
290C2×C4—43no—
291C2×C4—43no—
292C2×C4—41no—
293C2×C4—412no—
294C2×C4—412no—
295C2×C4—868no—
296C2×C4—1724no—
297C2×C4—17248no—
298C2×C4—1724no—
299C2×C4C2×C22⋊Dic4313yes—
300C2×C4C2×C22⋊Dic4313yes—
301C2×C4C23×Dic4311yescharacteristic
302C2×C4C22×C22⋊D4311yescharacteristic
303C8—1724no—
304C22—21no—
305C22—23no—
306C22—212no—
307C22—224no—
308C22—212no—
309C22—21no—
310C22—23no—
311C22#14582636116yesdirect product factor
312C22C2×#1306324016yes—
313C22C2×#1306324916yes—
314C22C2×#1306324916yes—
315C22C2×#1306325216yes—
316C22C22×C22⋊Dic4311yescharacteristic
317C22C22×#1062188411yescharacteristic
318C22C22×#1062188511yescharacteristic
319C4—21no—
320C4—23no—
321C4—23no—
322C4—21no—
323C4—44no—
324C4—44no—
325C4—1728no—
326C2—21no—
327C2—26no—
328C2—21no—
329C2C2×#14582636112yesdirect product factor
330C2C22×#1306324011yescharacteristic
331C2C22×#1306324911yescharacteristic
332C2C22×#1306325211yescharacteristic
subgroupG/H
centerC24C22⋊Dic43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC22×C22⋊Q8×C43C2
socleC24×C43C22⋊C4
prime radicalC25×C43D4
cosocleC22×C4×C43C24
hypercenterC22×C22⋊Q8D43
hypocenterC43C22×#328
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. C2×#14582636C2direct (N × H)
11. #14582636C22direct (N × H)
12. C23×Q8×C43C4semidirect
16. C2×C22⋊Q8×C43C4semidirect
19. C22×C4⋊C4×C43C4semidirect
34. C22×Q8×C43C2×C4semidirect
47. C22⋊Q8×C43C2×C4semidirect
52. C2×C4⋊C4×C43C2×C4semidirect
65. C2×Q8×C43C22×C4semidirect
93. C4⋊C4×C43C22×C4semidirect
145. C22×C43#328semidirect
167. C2×C43C2×#328semidirect
171. C23×Q8Dic43semidirect
177. C2×C22⋊Q8Dic43semidirect
180. C22×C4⋊C4Dic43semidirect
187. C43C22×#328semidirect
191. C22×Q8C2×Dic43semidirect
210. C22⋊Q8C2×Dic43semidirect
215. C2×C4⋊C4C2×Dic43semidirect
232. C2×Q8C22×Dic43semidirect
262. C4⋊C4C22×Dic43semidirect
311. C22#14582636direct (N × H)
329. C2C2×#14582636direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C22⋊(C43⋊C8)2
C22×C43⋊#952
C2×#145826362
C22×C22⋊Q8×C432
C22×#32843