Finite Group Databasebeta

← C43×#9417 #24929434

Subgroups — C43×#9417 #24929434

Order 11008.

442 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3184C211yesmaximal, characteristic
2C43×#2980C211yesmaximal, characteristic, complemented
3C43×#1536C211yesmaximal, characteristic, complemented
4C43×#1514C211yesmaximal, characteristic, complemented
5C43×#1514C211yesmaximal, characteristic, complemented
6C43×#1291C211yesmaximal, characteristic, complemented
7C43×#1288C211yesmaximal, characteristic, complemented
8C43×#532C2211yescharacteristic
9C43×#532C2211yescharacteristic
10C43×#498C411yescharacteristic, complemented
11C43×#493C411yescharacteristic, complemented
12C43×#486C411yescharacteristic, complemented
13C43×#486C411yescharacteristic, complemented
14C43×#469—22no—
15C43×#442—22no—
16C43×#435—22no—
17C43×#435—22no—
18C43×#432C2211yescharacteristic
19C43×#432C2211yescharacteristic
20C43×#432C2211yescharacteristic
21C43×#408—22no—
22C4×M16×C43C2211yescharacteristic
23C43×#383C2211yescharacteristic
24C43×#329—22no—
25C43×#327—22no—
26C43×#327—22no—
27C2×#41×C43—21no—
28C2×#41×C43—21no—
29C2×D8×C43—22no—
30C2×M16×C43—21no—
31C2×M16×C43—22no—
32C22×C8×C43—22no—
33C4⋊Q8×C43C2×C411yescharacteristic
34C4⋊Q8×C43C2×C411yescharacteristic
35#127×C43C2×C411yescharacteristic
36#127×C43C2×C411yescharacteristic
37#124×C43—21no—
38#124×C43—21no—
39#121×C43—21no—
40#121×C43—21no—
41#121×C43—21no—
42#121×C43D412yes—
43C4×D4×C43—21no—
44C4×D4×C43—21no—
45C4×D4×C43—21no—
46C4×D4×C43D412yes—
47C2×C42×C43C2311yescharacteristic
48#106×C43—22no—
49C4⋊C8×C43—21no—
50C4⋊C8×C43—21no—
51C4⋊C8×C43—21no—
52#102×C43—22no—
53#102×C43—22no—
54C22⋊C8×C43—24no—
55C22⋊C8×C43—21no—
56C22⋊C8×C43—21no—
57C22⋊C8×C43D412yes—
58#97×C43—21no—
59#97×C43—21no—
60#97×C43—21no—
61#97×C43D412yes—
62C4×C8×C43C2×C411yescharacteristic
63C4×C8×C43C2×C411yescharacteristic
64#95×C43—21no—
65#95×C43—21no—
66#95×C43—21no—
67#41×C43—81no—
68#41×C43—81no—
69#41×C43—82no—
70C2×Q8×C43—21no—
71C2×Q8×C43—21no—
72C2×D4×C43—21no—
73C2×D4×C43—21no—
74C2×D4×C43—22no—
75C2×D4×C43—21no—
76C2×D4×C43—21no—
77C2×D4×C43—21no—
78C2×D4×C43—41no—
79C2×D4×C43C22⋊C412yes—
80C22×C4×C43—22no—
81C22×C4×C43—41no—
82C22×C4×C43—41no—
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43#4111yescharacteristic
86D8×C43—44no—
87M16×C43—42no—
88M16×C43—82no—
89C2×C8×C43—21no—
90C2×C8×C43—21no—
91C2×C8×C43—22no—
92C2×C8×C43—22no—
93C2×C8×C43—41no—
94C2×C8×C43—82no—
95C4⋊C4×C43—21no—
96C4⋊C4×C43—21no—
97C4⋊C4×C43—21no—
98C4⋊C4×C43C22⋊C412yes—
99C22⋊C4×C43—22no—
100C22⋊C4×C43—22no—
101C22⋊C4×C43—41no—
102C22⋊C4×C43—41no—
103C42×C43C22×C411yescharacteristic
104C42×C43C2×D411yescharacteristic
105C42×C43C2×D411yescharacteristic
106C42×C43#4111yescharacteristic
107C23×C43—22no—
108C23×C43—41no—
109C23×C43#12111yescharacteristic
110Q8×C43—81no—
111Q8×C43—81no—
112D4×C43—42no—
113D4×C43—42no—
114D4×C43—81no—
115D4×C43—81no—
116D4×C43—81no—
117D4×C43—81no—
118D4×C43—82no—
119D4×C43—82no—
120C2×C4×C43—22no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—42no—
125C2×C4×C43—42no—
126C2×C4×C43—41no—
127C2×C4×C43—82no—
128C2×C4×C43—81no—
129C2×C4×C43—81no—
130C2×C4×C43—81no—
131C2×C4×C43C2×C22⋊C411yescharacteristic
132C2×C4×C43C4×D411yescharacteristic
133C2×C4×C43C4×D411yescharacteristic
134C2×C4×C43#12011yescharacteristic
135C2×C4×C43#12111yescharacteristic
136C2×C4×C43#12311yescharacteristic
137C8×C43—22no—
138C8×C43—42no—
139C8×C43—42no—
140C8×C43—41no—
141C8×C43—81no—
142#9417C4311yesmaximal, characteristic, direct product factor, Sylow
143C22×C43—21no—
144C22×C43—21no—
145C22×C43—21no—
146C22×C43—42no—
147C22×C43—42no—
148C22×C43—42no—
149C22×C43—81no—
150C22×C43—81no—
151C22×C43—81no—
152C22×C43#38611yescharacteristic
153C4×C43—21no—
154C4×C43—21no—
155C4×C43—21no—
156C4×C43—21no—
157C4×C43—21no—
158C4×C43—21no—
159C4×C43—42no—
160C4×C43—81no—
161C4×C43—161no—
162#3184C2×C4311yescharacteristic
163#2980C2×C4311yescharacteristic, complemented
164#1536C2×C4311yescharacteristic, complemented
165#1514C2×C4311yescharacteristic, complemented
166#1514C2×C4311yescharacteristic, complemented
167#1291C2×C4311yescharacteristic, complemented
168#1288C2×C4311yescharacteristic, complemented
169C2×C43—41no—
170C2×C43—82no—
171C2×C43—161no—
172C2×C43#188411yescharacteristic
173C2×C43#190311yescharacteristic
174C2×C43#190411yescharacteristic
175#532C22×C4311yescharacteristic
176#532C22×C4311yescharacteristic
177#498C4×C4311yescharacteristic, complemented
178#493C4×C4311yescharacteristic, complemented
179#486C4×C4311yescharacteristic, complemented
180#486C4×C4311yescharacteristic, complemented
181#469—22no—
182#442—22no—
183#435—22no—
184#435—22no—
185#432C22×C4311yescharacteristic
186#432C22×C4311yescharacteristic
187#432C22×C4311yescharacteristic
188#408—22no—
189C4×M16C22×C4311yescharacteristic
190#383C22×C4311yescharacteristic
191#329—22no—
192#327—22no—
193#327—22no—
194C43#941711yescharacteristic, direct product factor, Sylow
195C2×#41—21no—
196C2×#41—21no—
197C2×D8—22no—
198C2×M16—21no—
199C2×M16—22no—
200C22×C8—22no—
201C4⋊Q8C2×C4×C4311yescharacteristic
202C4⋊Q8C2×C4×C4311yescharacteristic
203#127C2×C4×C4311yescharacteristic
204#127C2×C4×C4311yescharacteristic
205#124—21no—
206#124—21no—
207#121—21no—
208#121—21no—
209#121—21no—
210#121D4×C4312yes—
211C4×D4—21no—
212C4×D4—21no—
213C4×D4—21no—
214C4×D4D4×C4312yes—
215C2×C42C23×C4311yescharacteristic
216#106—22no—
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—21no—
220#102—22no—
221#102—22no—
222C22⋊C8—24no—
223C22⋊C8—21no—
224C22⋊C8—21no—
225C22⋊C8D4×C4312yes—
226#97—21no—
227#97—21no—
228#97—21no—
229#97D4×C4312yes—
230C4×C8C2×C4×C4311yescharacteristic
231C4×C8C2×C4×C4311yescharacteristic
232#95—21no—
233#95—21no—
234#95—21no—
235#41—81no—
236#41—81no—
237#41—82no—
238C2×Q8—21no—
239C2×Q8—21no—
240C2×D4—22no—
241C2×D4—21no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—41no—
247C2×D4C22⋊C4×C4312yes—
248C22×C4—22no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4C2×D4×C4311yescharacteristic
252C22×C4C2×D4×C4311yescharacteristic
253C22×C4#41×C4311yescharacteristic
254D8—44no—
255M16—42no—
256M16—82no—
257C2×C8—21no—
258C2×C8—21no—
259C2×C8—22no—
260C2×C8—22no—
261C2×C8—41no—
262C2×C8—82no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4C22⋊C4×C4312yes—
267C22⋊C4—22no—
268C22⋊C4—22no—
269C22⋊C4—41no—
270C22⋊C4—41no—
271C42C22×C4×C4311yescharacteristic
272C42C2×D4×C4311yescharacteristic
273C42C2×D4×C4311yescharacteristic
274C42#41×C4311yescharacteristic
275C23—22no—
276C23—41no—
277C23#121×C4311yescharacteristic
278Q8—81no—
279Q8—81no—
280D4—42no—
281D4—42no—
282D4—81no—
283D4—81no—
284D4—81no—
285D4—81no—
286D4—82no—
287D4—82no—
288C2×C4—22no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—41no—
295C2×C4—82no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4C2×C22⋊C4×C4311yescharacteristic
300C2×C4C4×D4×C4311yescharacteristic
301C2×C4C4×D4×C4311yescharacteristic
302C2×C4#120×C4311yescharacteristic
303C2×C4#121×C4311yescharacteristic
304C2×C4#123×C4311yescharacteristic
305C8—22no—
306C8—42no—
307C8—42no—
308C8—41no—
309C8—81no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—42no—
314C22—42no—
315C22—42no—
316C22—81no—
317C22—81no—
318C22—81no—
319C22C43×#38611yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—42no—
327C4—81no—
328C4—161no—
329C2—41no—
330C2—82no—
331C2—161no—
332C2C43×#188411yescharacteristic
333C2C43×#190311yescharacteristic
334C2C43×#190411yescharacteristic
subgroupG/H
center, socleC22×C43#386
commutatorC42C22×C4×C43
Frattini, cosocleC2×C42C23×C43
prime radicalC43×#3184C2
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. C43×#2980C2semidirect
3. C43×#1536C2semidirect
4. C43×#1514C2semidirect
5. C43×#1514C2semidirect
6. C43×#1291C2semidirect
7. C43×#1288C2semidirect
10. C43×#498C4semidirect
11. C43×#493C4semidirect
12. C43×#486C4semidirect
13. C43×#486C4semidirect
142. #9417C43direct (N × H)
163. #2980C2×C43semidirect
164. #1536C2×C43semidirect
165. #1514C2×C43semidirect
166. #1514C2×C43semidirect
167. #1291C2×C43semidirect
168. #1288C2×C43semidirect
177. #498C4×C43semidirect
178. #493C4×C43semidirect
179. #486C4×C43semidirect
180. #486C4×C43semidirect
194. C43#9417direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#31842
C43×#29802
C43×#15362
C43×#15142
C43×#12912
C43×#12882
#941743