Finite Group Databasebeta

← C43×#8696 #24928713

Subgroups — C43×#8696 #24928713

Order 11008.

384 conjugacy classes of subgroups.

The subgroup lattice has 306 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2966C211yesmaximal, characteristic
2C4×#106×C43C211yesmaximal, characteristic, complemented
3C43×#1568C211yesmaximal, characteristic, complemented
4C43×#1509C212yesmaximal
5C43×#1285C212yesmaximal, complemented
6C43×#529C2211yescharacteristic
7C43×#446C411yescharacteristic, complemented
8C8×Q8×C43C411yescharacteristic, complemented
9C43×#436C411yescharacteristic, complemented
10C43×#435—21no—
11C8×D4×C43—21no—
12C8×D4×C43C411yescharacteristic, complemented
13C43×#433—21no—
14C43×#432C2212yes—
15C43×#432C2211yescharacteristic
16C2×#106×C43—21no—
17C43×#405—21no—
18C2×C4×C8×C43C2211yescharacteristic
19C4×C4⋊C4×C43C2212yes—
20C43×#340—21no—
21C43×#335—21no—
22C43×#334—21no—
23C43×#328—22no—
24C43×#327—22no—
25C2×M16×C43—21no—
26C22×C8×C43—21no—
27C22×C8×C43D411yescharacteristic
28C22×C8×C43D411yescharacteristic
29#126×C43—21no—
30#125×C43Q811yescharacteristic
31#124×C43Q811yescharacteristic
32#123×C43—21no—
33C22⋊Q8×C43D411yescharacteristic
34#121×C43D411yescharacteristic
35C4×Q8×C43C2×C411yescharacteristic
36C4×D4×C43—21no—
37C4×D4×C43C2×C411yescharacteristic
38#117×C43—21no—
39C2×C4⋊C4×C43—22no—
40C2×C42×C43—22no—
41C2×C42×C43C2311yescharacteristic
42#106×C43—24no—
43C4⋊C8×C43—21no—
44C4⋊C8×C43—21no—
45C4⋊C8×C43—22no—
46C4⋊C8×C43C2×C411yescharacteristic
47C4⋊C8×C43C2×C411yescharacteristic
48C22⋊C8×C43—21no—
49C22⋊C8×C43—21no—
50C22⋊C8×C43—21no—
51C22⋊C8×C43—22no—
52#97×C43—21no—
53#97×C43—21no—
54#97×C43—22no—
55C4×C8×C43—21no—
56C4×C8×C43C2×C411yescharacteristic
57C4×C8×C43C2×C411yescharacteristic
58C4×C8×C43D411yescharacteristic
59C4×C8×C43D411yescharacteristic
60#95×C43—22no—
61C2×Q8×C43C4⋊C411yescharacteristic
62C2×D4×C43—21no—
63C2×D4×C43C4⋊C411yescharacteristic
64C22×C4×C43—21no—
65C22×C4×C43—42no—
66C22×C4×C43C2×D411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×C4×C43#4111yescharacteristic
69M16×C43—42no—
70C2×C8×C43—22no—
71C2×C8×C43—21no—
72C2×C8×C43—21no—
73C2×C8×C43—41no—
74C2×C8×C43—42no—
75C2×C8×C43—42no—
76C2×C8×C43C22⋊C411yescharacteristic
77C2×C8×C43C22⋊C411yescharacteristic
78C2×C8×C43C22⋊C411yescharacteristic
79C2×C8×C43C22⋊C411yescharacteristic
80C4⋊C4×C43—21no—
81C4⋊C4×C43—21no—
82C4⋊C4×C43—21no—
83C4⋊C4×C43—21no—
84C4⋊C4×C43—24no—
85C4⋊C4×C43—42no—
86C4⋊C4×C43C4⋊C411yescharacteristic
87C4⋊C4×C43C4⋊C411yescharacteristic
88C22⋊C4×C43—21no—
89C22⋊C4×C43—21no—
90C22⋊C4×C43—21no—
91C22⋊C4×C43—21no—
92C22⋊C4×C43—21no—
93C42×C43—21no—
94C42×C43—82no—
95C42×C43C22×C411yescharacteristic
96C42×C43C2×D411yescharacteristic
97C42×C43C2×Q811yescharacteristic
98C42×C43#4111yescharacteristic
99C23×C43—21no—
100C23×C43#12111yescharacteristic
101Q8×C43—41no—
102D4×C43—41no—
103D4×C43—42no—
104C2×C4×C43—22no—
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—41no—
111C2×C4×C43—41no—
112C2×C4×C43—41no—
113C2×C4×C43—44no—
114C2×C4×C43—82no—
115C2×C4×C43—82no—
116C2×C4×C43C2×C22⋊C411yescharacteristic
117C2×C4×C43C2×C4⋊C411yescharacteristic
118C2×C4×C43#11711yescharacteristic
119C2×C4×C43#12111yescharacteristic
120C2×C4×C43C22⋊Q811yescharacteristic
121C2×C4×C43C22⋊Q811yescharacteristic
122C8×C43—21no—
123C8×C43—21no—
124C8×C43—21no—
125C8×C43—41no—
126C8×C43—41no—
127C8×C43—82no—
128C8×C43#10412yes—
129#8696C4311yesmaximal, characteristic, direct product factor, Sylow
130C22×C43—21no—
131C22×C43—21no—
132C22×C43—41no—
133C22×C43—41no—
134C22×C43—41no—
135C22×C43#38011yescharacteristic
136C22×C43#47112yes—
137C4×C43—21no—
138C4×C43—21no—
139C4×C43—21no—
140C4×C43—21no—
141C4×C43—21no—
142C4×C43—41no—
143C4×C43—41no—
144C4×C43—41no—
145C4×C43—84no—
146C4×C43C2×#10411yescharacteristic
147C4×C43#42111yescharacteristic
148#2966C2×C4311yescharacteristic
149C4×#106C2×C4311yescharacteristic, complemented
150#1568C2×C4311yescharacteristic, complemented
151#1509C2×C4312yes—
152#1285C2×C4312yescomplemented
153C2×C43—22no—
154C2×C43—81no—
155C2×C43#180611yescharacteristic
156C2×C43#181211yescharacteristic
157C2×C43#181511yescharacteristic
158#529C22×C4311yescharacteristic
159#446C4×C4311yescharacteristic, complemented
160C8×Q8C4×C4311yescharacteristic, complemented
161#436C4×C4311yescharacteristic, complemented
162#435—21no—
163C8×D4—21no—
164C8×D4C4×C4311yescharacteristic, complemented
165#433—21no—
166#432C22×C4312yes—
167#432C22×C4311yescharacteristic
168C2×#106—21no—
169#405—21no—
170C2×C4×C8C22×C4311yescharacteristic
171C4×C4⋊C4C22×C4312yes—
172#340—21no—
173#335—21no—
174#334—21no—
175#328—22no—
176#327—22no—
177C43#869611yescharacteristic, direct product factor, Sylow
178C2×M16—21no—
179C22×C8—21no—
180C22×C8D4×C4311yescharacteristic
181C22×C8D4×C4311yescharacteristic
182#126—21no—
183#125Q8×C4311yescharacteristic
184#124Q8×C4311yescharacteristic
185#123—21no—
186C22⋊Q8D4×C4311yescharacteristic
187#121D4×C4311yescharacteristic
188C4×Q8C2×C4×C4311yescharacteristic
189C4×D4—21no—
190C4×D4C2×C4×C4311yescharacteristic
191#117—21no—
192C2×C4⋊C4—22no—
193C2×C42—22no—
194C2×C42C23×C4311yescharacteristic
195#106—24no—
196C4⋊C8—21no—
197C4⋊C8—21no—
198C4⋊C8—22no—
199C4⋊C8C2×C4×C4311yescharacteristic
200C4⋊C8C2×C4×C4311yescharacteristic
201C22⋊C8—21no—
202C22⋊C8—21no—
203C22⋊C8—21no—
204C22⋊C8—22no—
205#97—21no—
206#97—21no—
207#97—22no—
208C4×C8—21no—
209C4×C8C2×C4×C4311yescharacteristic
210C4×C8C2×C4×C4311yescharacteristic
211C4×C8D4×C4311yescharacteristic
212C4×C8D4×C4311yescharacteristic
213#95—22no—
214C2×Q8C4⋊C4×C4311yescharacteristic
215C2×D4—21no—
216C2×D4C4⋊C4×C4311yescharacteristic
217C22×C4—21no—
218C22×C4—42no—
219C22×C4C2×D4×C4311yescharacteristic
220C22×C4C2×D4×C4311yescharacteristic
221C22×C4#41×C4311yescharacteristic
222M16—42no—
223C2×C8—22no—
224C2×C8—21no—
225C2×C8—21no—
226C2×C8—41no—
227C2×C8—42no—
228C2×C8—42no—
229C2×C8C22⋊C4×C4311yescharacteristic
230C2×C8C22⋊C4×C4311yescharacteristic
231C2×C8C22⋊C4×C4311yescharacteristic
232C2×C8C22⋊C4×C4311yescharacteristic
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—24no—
238C4⋊C4—42no—
239C4⋊C4C4⋊C4×C4311yescharacteristic
240C4⋊C4C4⋊C4×C4311yescharacteristic
241C22⋊C4—21no—
242C22⋊C4—21no—
243C22⋊C4—21no—
244C22⋊C4—21no—
245C22⋊C4—21no—
246C42—21no—
247C42—82no—
248C42C22×C4×C4311yescharacteristic
249C42C2×D4×C4311yescharacteristic
250C42C2×Q8×C4311yescharacteristic
251C42#41×C4311yescharacteristic
252C23—21no—
253C23#121×C4311yescharacteristic
254Q8—41no—
255D4—41no—
256D4—42no—
257C2×C4—22no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—44no—
267C2×C4—82no—
268C2×C4—82no—
269C2×C4C2×C22⋊C4×C4311yescharacteristic
270C2×C4C2×C4⋊C4×C4311yescharacteristic
271C2×C4#117×C4311yescharacteristic
272C2×C4#121×C4311yescharacteristic
273C2×C4C22⋊Q8×C4311yescharacteristic
274C2×C4C22⋊Q8×C4311yescharacteristic
275C8—21no—
276C8—21no—
277C8—21no—
278C8—41no—
279C8—41no—
280C8—82no—
281C8#104×C4312yes—
282C22—21no—
283C22—21no—
284C22—41no—
285C22—41no—
286C22—41no—
287C22C43×#38011yescharacteristic
288C22C43×#47112yes—
289C4—21no—
290C4—21no—
291C4—21no—
292C4—21no—
293C4—21no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—84no—
298C4C2×#104×C4311yescharacteristic
299C4C43×#42111yescharacteristic
300C2—22no—
301C2—81no—
302C2C43×#180611yescharacteristic
303C2C43×#181211yescharacteristic
304C2C43×#181511yescharacteristic
subgroupG/H
center, socleC22×C43#380
commutatorC42C22×C4×C43
Frattini, cosocleC2×C42C23×C43
prime radical#121×C43D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×#106×C43C2semidirect
3. C43×#1568C2semidirect
5. C43×#1285C2semidirect
7. C43×#446C4semidirect
8. C8×Q8×C43C4semidirect
9. C43×#436C4semidirect
12. C8×D4×C43C4semidirect
129. #8696C43direct (N × H)
149. C4×#106C2×C43semidirect
150. #1568C2×C43semidirect
152. #1285C2×C43semidirect
159. #446C4×C43semidirect
160. C8×Q8C4×C43semidirect
161. #436C4×C43semidirect
164. C8×D4C4×C43semidirect
177. C43#8696direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#29662
C4×#106×C432
C43×#15682
C43×#15092
C43×#12852
#869643