Finite Group Databasebeta

← C43×#8669 #24928686

Subgroups — C43×#8669 #24928686

Order 11008.

432 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2965C211yesmaximal, characteristic
2C43×#1806C212yesmaximal
3C4×#106×C43C211yesmaximal, characteristic, complemented
4C43×#1567C211yesmaximal, characteristic, complemented
5C43×#1303C212yesmaximal, complemented
6C4×#41×C43C2211yescharacteristic
7C43×#446C411yescharacteristic, complemented
8C43×#446C411yescharacteristic, complemented
9C43×#436C411yescharacteristic, complemented
10C43×#436C411yescharacteristic, complemented
11C43×#435—21no—
12C43×#435—21no—
13C43×#431—21no—
14C43×#431C2211yescharacteristic
15C2×#106×C43—21no—
16C43×#423C2212yes—
17C2×#104×C43—22no—
18C4×M16×C43—21no—
19C2×C4×C8×C43C2211yescharacteristic
20C4×C4⋊C4×C43C2212yes—
21C43×#340—21no—
22C43×#339—22no—
23C43×#335—21no—
24C43×#335—21no—
25C2×#41×C43D411yescharacteristic
26C2×M16×C43—21no—
27C2×M16×C43—21no—
28C2×M16×C43—22no—
29C22×C8×C43D411yescharacteristic
30C22×C8×C43D411yescharacteristic
31C4×Q8×C43C2×C411yescharacteristic
32C4×Q8×C43Q811yescharacteristic
33C4×D4×C43—21no—
34C4×D4×C43—21no—
35C4×D4×C43C2×C411yescharacteristic
36C4×D4×C43Q811yescharacteristic
37#117×C43—21no—
38#117×C43D411yescharacteristic
39C2×C4⋊C4×C43—22no—
40C2×C42×C43—21no—
41C2×C42×C43—22no—
42C2×C42×C43C2311yescharacteristic
43#106×C43—24no—
44C4⋊C8×C43—21no—
45C4⋊C8×C43—21no—
46C4⋊C8×C43—22no—
47C4⋊C8×C43—22no—
48C4⋊C8×C43C2×C411yescharacteristic
49C4⋊C8×C43C2×C411yescharacteristic
50#104×C43—44no—
51C22⋊C8×C43—21no—
52C22⋊C8×C43—21no—
53C22⋊C8×C43—21no—
54#97×C43—21no—
55#97×C43—21no—
56C4×C8×C43—21no—
57C4×C8×C43C2×C411yescharacteristic
58C4×C8×C43C2×C411yescharacteristic
59C4×C8×C43D411yescharacteristic
60C4×C8×C43D411yescharacteristic
61#95×C43—22no—
62#41×C43—22no—
63#41×C43—22no—
64C2×Q8×C43C4⋊C411yescharacteristic
65C2×D4×C43—21no—
66C2×D4×C43C4⋊C411yescharacteristic
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43—21no—
70C22×C4×C43—42no—
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×C4×C43#4111yescharacteristic
74M16×C43—42no—
75M16×C43—42no—
76M16×C43—42no—
77M16×C43—42no—
78C2×C8×C43—22no—
79C2×C8×C43—21no—
80C2×C8×C43—21no—
81C2×C8×C43—41no—
82C2×C8×C43—42no—
83C2×C8×C43C22⋊C411yescharacteristic
84C2×C8×C43C22⋊C411yescharacteristic
85C2×C8×C43C22⋊C411yescharacteristic
86C2×C8×C43C22⋊C411yescharacteristic
87C4⋊C4×C43—21no—
88C4⋊C4×C43—21no—
89C4⋊C4×C43—24no—
90C4⋊C4×C43—42no—
91C4⋊C4×C43C4⋊C411yescharacteristic
92C4⋊C4×C43C4⋊C411yescharacteristic
93C22⋊C4×C43—21no—
94C22⋊C4×C43—21no—
95C22⋊C4×C43—21no—
96C42×C43—21no—
97C42×C43—21no—
98C42×C43—21no—
99C42×C43—42no—
100C42×C43—42no—
101C42×C43C22×C411yescharacteristic
102C42×C43C2×D411yescharacteristic
103C42×C43C2×Q811yescharacteristic
104C42×C43#4111yescharacteristic
105C23×C43—21no—
106C23×C43#12111yescharacteristic
107Q8×C43—22no—
108D4×C43—22no—
109D4×C43—42no—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—41no—
116C2×C4×C43—42no—
117C2×C4×C43—41no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
121C2×C4×C43—44no—
122C2×C4×C43—82no—
123C2×C4×C43—82no—
124C2×C4×C43C2×C22⋊C411yescharacteristic
125C2×C4×C43C2×C4⋊C411yescharacteristic
126C2×C4×C43#11711yescharacteristic
127C2×C4×C43#12111yescharacteristic
128C2×C4×C43C22⋊Q811yescharacteristic
129C2×C4×C43C22⋊Q811yescharacteristic
130C2×C4×C43AGL(1,ℤ/8)12yes—
131C2×C4×C43#13712yes—
132C8×C43—21no—
133C8×C43—21no—
134C8×C43—21no—
135C8×C43—41no—
136C8×C43—41no—
137C8×C43—82no—
138C8×C43#10412yescomplemented
139#8669C4311yesmaximal, characteristic, direct product factor, Sylow
140C22×C43—21no—
141C22×C43—21no—
142C22×C43—41no—
143C22×C43—41no—
144C22×C43—41no—
145C22×C43#38011yescharacteristic
146C22×C43#46812yes—
147C4×C43—21no—
148C4×C43—21no—
149C4×C43—21no—
150C4×C43—41no—
151C4×C43—41no—
152C4×C43—41no—
153C4×C43—84no—
154C4×C43C2×#10411yescharacteristic
155C4×C43#42111yescharacteristic
156C4×C43#42812yes—
157C4×C43#46911yescharacteristic
158C4×C43#47011yescharacteristic
159#2965C2×C4311yescharacteristic
160#1806C2×C4312yes—
161C4×#106C2×C4311yescharacteristic, complemented
162#1567C2×C4311yescharacteristic, complemented
163#1303C2×C4312yescomplemented
164C2×C43—22no—
165C2×C43—81no—
166C2×C43#180611yescharacteristic
167C2×C43#180911yescharacteristic
168C2×C43#181411yescharacteristic
169C4×#41C22×C4311yescharacteristic
170#446C4×C4311yescharacteristic, complemented
171#446C4×C4311yescharacteristic, complemented
172#436C4×C4311yescharacteristic, complemented
173#436C4×C4311yescharacteristic, complemented
174#435—21no—
175#435—21no—
176#431—21no—
177#431C22×C4311yescharacteristic
178C2×#106—21no—
179#423C22×C4312yes—
180C2×#104—22no—
181C4×M16—21no—
182C2×C4×C8C22×C4311yescharacteristic
183C4×C4⋊C4C22×C4312yes—
184#340—21no—
185#339—22no—
186#335—21no—
187#335—21no—
188C43#866911yescharacteristic, direct product factor, Sylow
189C2×#41D4×C4311yescharacteristic
190C2×M16—21no—
191C2×M16—21no—
192C2×M16—22no—
193C22×C8D4×C4311yescharacteristic
194C22×C8D4×C4311yescharacteristic
195C4×Q8C2×C4×C4311yescharacteristic
196C4×Q8Q8×C4311yescharacteristic
197C4×D4—21no—
198C4×D4—21no—
199C4×D4C2×C4×C4311yescharacteristic
200C4×D4Q8×C4311yescharacteristic
201#117—21no—
202#117D4×C4311yescharacteristic
203C2×C4⋊C4—22no—
204C2×C42—21no—
205C2×C42—22no—
206C2×C42C23×C4311yescharacteristic
207#106—24no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—22no—
211C4⋊C8—22no—
212C4⋊C8C2×C4×C4311yescharacteristic
213C4⋊C8C2×C4×C4311yescharacteristic
214#104—44no—
215C22⋊C8—21no—
216C22⋊C8—21no—
217C22⋊C8—21no—
218#97—21no—
219#97—21no—
220C4×C8—21no—
221C4×C8C2×C4×C4311yescharacteristic
222C4×C8C2×C4×C4311yescharacteristic
223C4×C8D4×C4311yescharacteristic
224C4×C8D4×C4311yescharacteristic
225#95—22no—
226#41—22no—
227#41—22no—
228C2×Q8C4⋊C4×C4311yescharacteristic
229C2×D4—21no—
230C2×D4C4⋊C4×C4311yescharacteristic
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—42no—
235C22×C4C2×D4×C4311yescharacteristic
236C22×C4C2×D4×C4311yescharacteristic
237C22×C4#41×C4311yescharacteristic
238M16—42no—
239M16—42no—
240M16—42no—
241M16—42no—
242C2×C8—22no—
243C2×C8—21no—
244C2×C8—21no—
245C2×C8—41no—
246C2×C8—42no—
247C2×C8C22⋊C4×C4311yescharacteristic
248C2×C8C22⋊C4×C4311yescharacteristic
249C2×C8C22⋊C4×C4311yescharacteristic
250C2×C8C22⋊C4×C4311yescharacteristic
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—24no—
254C4⋊C4—42no—
255C4⋊C4C4⋊C4×C4311yescharacteristic
256C4⋊C4C4⋊C4×C4311yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—21no—
259C22⋊C4—21no—
260C42—21no—
261C42—21no—
262C42—21no—
263C42—42no—
264C42—42no—
265C42C22×C4×C4311yescharacteristic
266C42C2×D4×C4311yescharacteristic
267C42C2×Q8×C4311yescharacteristic
268C42#41×C4311yescharacteristic
269C23—21no—
270C23#121×C4311yescharacteristic
271Q8—22no—
272D4—22no—
273D4—42no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—41no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—44no—
286C2×C4—82no—
287C2×C4—82no—
288C2×C4C2×C22⋊C4×C4311yescharacteristic
289C2×C4C2×C4⋊C4×C4311yescharacteristic
290C2×C4#117×C4311yescharacteristic
291C2×C4#121×C4311yescharacteristic
292C2×C4C22⋊Q8×C4311yescharacteristic
293C2×C4C22⋊Q8×C4311yescharacteristic
294C2×C4AGL(1,ℤ/8)×C4312yes—
295C2×C4#137×C4312yes—
296C8—21no—
297C8—21no—
298C8—21no—
299C8—41no—
300C8—41no—
301C8—82no—
302C8#104×C4312yescomplemented
303C22—21no—
304C22—21no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22C43×#38011yescharacteristic
309C22C43×#46812yes—
310C4—21no—
311C4—21no—
312C4—21no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—84no—
317C4C2×#104×C4311yescharacteristic
318C4C43×#42111yescharacteristic
319C4C43×#42812yes—
320C4C43×#46911yescharacteristic
321C4C43×#47011yescharacteristic
322C2—22no—
323C2—81no—
324C2C43×#180611yescharacteristic
325C2C43×#180911yescharacteristic
326C2C43×#181411yescharacteristic
subgroupG/H
centerC2×C4×C43#121
commutatorC42C22×C4×C43
Frattini, cosocleC2×C42C23×C43
socleC22×C43#380
prime radicalC2×#41×C43D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
3. C4×#106×C43C2semidirect
4. C43×#1567C2semidirect
5. C43×#1303C2semidirect
7. C43×#446C4semidirect
8. C43×#446C4semidirect
9. C43×#436C4semidirect
10. C43×#436C4semidirect
138. C8×C43#104semidirect
139. #8669C43direct (N × H)
161. C4×#106C2×C43semidirect
162. #1567C2×C43semidirect
163. #1303C2×C43semidirect
170. #446C4×C43semidirect
171. #446C4×C43semidirect
172. #436C4×C43semidirect
173. #436C4×C43semidirect
188. C43#8669direct (N × H)
302. C8#104×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#29652
C43×#18062
C4×#106×C432
C43×#15672
C43×#13032
#866943