Finite Group Databasebeta

← C43×#33470 #24953487

Subgroups — C43×#33470 #24953487

Order 11008.

632 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#510C211yesmaximal, characteristic
2C43×#2957C211yesmaximal, characteristic
3C43×#2950C211yesmaximal, characteristic, complemented
4C43×#2180C218yesmaximal, complemented
5C43×#2155C211yesmaximal, characteristic, complemented
6C2×C43×#362C211yesmaximal, characteristic, complemented
7C43×#2145C211yesmaximal, characteristic
8C43×#2110C211yesmaximal, characteristic, complemented
9C2×#135×C43C2211yescharacteristic
10C22×Q16×C43C2211yescharacteristic
11C43×#568—21no—
12C43×#519—21no—
13C43×#510C414yescomplemented
14C43×#510C2214yes—
15C2×Q32×C43C412yescomplemented
16C2×SD32×C43C412yescomplemented
17C2×M32×C43C2211yescharacteristic
18C2×M32×C43C2211yescharacteristic
19C43×#444C2214yes—
20C43×#443—22no—
21C43×#441C2214yescomplemented
22C4×Q16×C43—22no—
23C2×#108×C43C2211yescharacteristic
24C43×#427C2211yescharacteristic
25C43×#421—21no—
26C43×#419—21no—
27C43×#405C2211yescharacteristic
28C43×#365C2214yescomplemented
29C43×#362C2214yescomplemented
30C43×#360C2214yes—
31C43×#347C2214yescomplemented
32C2×#41×C43—21no—
33C22×Q8×C43—21no—
34#135×C43—21no—
35#135×C43—21no—
36#135×C43C2×C412yes—
37#135×C43C2312yes—
38C2×Q16×C43—21no—
39C2×Q16×C43—21no—
40C2×Q16×C43—21no—
41C2×Q16×C43C2×C412yes—
42C2×Q16×C43C2×C411yescharacteristic
43C2×Q16×C43C2×C412yes—
44C2×Q16×C43C2312yes—
45C2×SD16×C43—21no—
46C2×D8×C43C2×C411yescharacteristic
47#131×C43—24no—
48#131×C43—42no—
49C2×M16×C43—21no—
50C2×M16×C43—42no—
51C2×M16×C43D411yescharacteristic
52C22×C8×C43C2311yescharacteristic
53C4×Q8×C43—24no—
54C4×Q8×C43—42no—
55#117×C43—21no—
56#117×C43—42no—
57#117×C43D411yescharacteristic
58Q32×C43C2×C418yes—
59SD32×C43C2×C418yes—
60M32×C43—21no—
61M32×C43C2×C412yes—
62M32×C43C2312yes—
63M32×C43C2312yes—
64C2×C16×C43—21no—
65C2×C16×C43C2×C412yes—
66#108×C43—21no—
67#108×C43C2312yes—
68#107×C43—21no—
69#106×C43C2312yes—
70#104×C43—24no—
71#103×C43—24no—
72#97×C43C2312yes—
73C4×C8×C43D412yes—
74#41×C43—22no—
75#41×C43—22no—
76#41×C43—41no—
77#41×C43—41no—
78C2×Q8×C43—21no—
79C2×Q8×C43—22no—
80C2×Q8×C43—22no—
81C2×Q8×C43—22no—
82C2×Q8×C43—41no—
83C2×Q8×C43—41no—
84C2×Q8×C43—41no—
85C2×D4×C43—21no—
86C2×D4×C43—41no—
87C22×C4×C43—41no—
88C22×C4×C43—41no—
89C22×C4×C43C2×D411yescharacteristic
90Q16×C43—22no—
91Q16×C43—22no—
92Q16×C43—21no—
93Q16×C43—22no—
94Q16×C43C22×C414yes—
95Q16×C43C22×C412yes—
96SD16×C43—22no—
97SD16×C43—22no—
98D8×C43—21no—
99D8×C43C22×C412yes—
100M16×C43—21no—
101M16×C43—21no—
102M16×C43—22no—
103M16×C43—44no—
104M16×C43—41no—
105C2×C8×C43—44no—
106C2×C8×C43—41no—
107C2×C8×C43C22×C411yescharacteristic
108C2×C8×C43C22×C411yescharacteristic
109C2×C8×C43C2×D412yes—
110C2×C8×C43C2×D411yescharacteristic
111C2×C8×C43#4111yescharacteristic
112C2×C8×C43#4111yescharacteristic
113C2×C8×C43C2411yescharacteristic
114C4⋊C4×C43—21no—
115C4⋊C4×C43—22no—
116C4⋊C4×C43—44no—
117C22⋊C4×C43—21no—
118C22⋊C4×C43—41no—
119C42×C43—44no—
120C42×C43—41no—
121C42×C43C2×D412yes—
122C16×C43—22no—
123C16×C43C22×C414yes—
124C23×C43—41no—
125C23×C43AGL(1,ℤ/8)11yescharacteristic
126Q8×C43—22no—
127Q8×C43—24no—
128Q8×C43—42no—
129Q8×C43—42no—
130Q8×C43—42no—
131Q8×C43—41no—
132D4×C43—22no—
133D4×C43—42no—
134D4×C43—42no—
135D4×C43—41no—
136C2×C4×C43—22no—
137C2×C4×C43—42no—
138C2×C4×C43—41no—
139C2×C4×C43—42no—
140C2×C4×C43—42no—
141C2×C4×C43—42no—
142C2×C4×C43—42no—
143C2×C4×C43—42no—
144C2×C4×C43C4×D411yescharacteristic
145C2×C4×C43C4×D411yescharacteristic
146C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C43C22×D411yescharacteristic
150C8×C43—22no—
151C8×C43—42no—
152C8×C43C4×D411yescharacteristic
153C8×C43C4×D411yescharacteristic
154C8×C43C23×C411yescharacteristic
155C8×C43C2×#4111yescharacteristic
156#33470C4311yesmaximal, characteristic, direct product factor, Sylow
157C22×C43—41no—
158C22×C43—42no—
159C22×C43—161no—
160C22×C43#44211yescharacteristic
161C22×C43#44211yescharacteristic
162C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
163C4×C43—42no—
164C4×C43—42no—
165C4×C43—44no—
166C4×C43—82no—
167C4×C43#44211yescharacteristic
168C4×C43#44211yescharacteristic
169C4×C43C2×C4×D411yescharacteristic
170C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
171C2×#510C2×C4311yescharacteristic
172#2957C2×C4311yescharacteristic
173#2950C2×C4311yescharacteristic, complemented
174#2180C2×C4318yescomplemented
175#2155C2×C4311yescharacteristic, complemented
176C2×#362C2×C4311yescharacteristic, complemented
177#2145C2×C4311yescharacteristic
178#2110C2×C4311yescharacteristic, complemented
179C2×C43—21no—
180C2×C43—21no—
181C2×C43—21no—
182C2×C43—82no—
183C2×C43C2×#44211yescharacteristic
184C2×#135C22×C4311yescharacteristic
185C22×Q16C22×C4311yescharacteristic
186#568—21no—
187#519—21no—
188#510C4×C4314yescomplemented
189#510C22×C4314yes—
190C2×Q32C4×C4312yescomplemented
191C2×SD32C4×C4312yescomplemented
192C2×M32C22×C4311yescharacteristic
193C2×M32C22×C4311yescharacteristic
194#444C22×C4314yes—
195#443—22no—
196#441C22×C4314yescomplemented
197C4×Q16—22no—
198C2×#108C22×C4311yescharacteristic
199#427C22×C4311yescharacteristic
200#421—21no—
201#419—21no—
202#405C22×C4311yescharacteristic
203#365C22×C4314yescomplemented
204#362C22×C4314yescomplemented
205#360C22×C4314yes—
206#347C22×C4314yescomplemented
207C43#3347011yescharacteristic, direct product factor, Sylow
208C2×#41—21no—
209C22×Q8—21no—
210#135—21no—
211#135—21no—
212#135C2×C4×C4312yes—
213#135C23×C4312yes—
214C2×Q16—21no—
215C2×Q16—21no—
216C2×Q16—21no—
217C2×Q16C2×C4×C4312yes—
218C2×Q16C2×C4×C4312yes—
219C2×Q16C2×C4×C4311yescharacteristic
220C2×Q16C23×C4312yes—
221C2×SD16—21no—
222C2×D8C2×C4×C4311yescharacteristic
223#131—24no—
224#131—42no—
225C2×M16—21no—
226C2×M16—42no—
227C2×M16D4×C4311yescharacteristic
228C22×C8C23×C4311yescharacteristic
229C4×Q8—24no—
230C4×Q8—42no—
231#117—21no—
232#117—42no—
233#117D4×C4311yescharacteristic
234Q32C2×C4×C4318yes—
235SD32C2×C4×C4318yes—
236M32—21no—
237M32C2×C4×C4312yes—
238M32C23×C4312yes—
239M32C23×C4312yes—
240C2×C16—21no—
241C2×C16C2×C4×C4312yes—
242#108—21no—
243#108C23×C4312yes—
244#107—21no—
245#106C23×C4312yes—
246#104—24no—
247#103—24no—
248#97C23×C4312yes—
249C4×C8D4×C4312yes—
250#41—22no—
251#41—22no—
252#41—41no—
253#41—41no—
254C2×Q8—21no—
255C2×Q8—22no—
256C2×Q8—22no—
257C2×Q8—22no—
258C2×Q8—41no—
259C2×Q8—41no—
260C2×Q8—41no—
261C2×D4—21no—
262C2×D4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4C2×D4×C4311yescharacteristic
266Q16—22no—
267Q16—22no—
268Q16—21no—
269Q16—22no—
270Q16C22×C4×C4314yes—
271Q16C22×C4×C4312yes—
272SD16—22no—
273SD16—22no—
274D8—21no—
275D8C22×C4×C4312yes—
276M16—21no—
277M16—21no—
278M16—22no—
279M16—44no—
280M16—41no—
281C2×C8—44no—
282C2×C8—41no—
283C2×C8C22×C4×C4311yescharacteristic
284C2×C8C22×C4×C4311yescharacteristic
285C2×C8C2×D4×C4312yes—
286C2×C8C2×D4×C4311yescharacteristic
287C2×C8#41×C4311yescharacteristic
288C2×C8#41×C4311yescharacteristic
289C2×C8C24×C4311yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—22no—
292C4⋊C4—44no—
293C22⋊C4—21no—
294C22⋊C4—41no—
295C42—44no—
296C42—41no—
297C42C2×D4×C4312yes—
298C16—22no—
299C16C22×C4×C4314yes—
300C23—41no—
301C23AGL(1,ℤ/8)×C4311yescharacteristic
302Q8—22no—
303Q8—24no—
304Q8—42no—
305Q8—42no—
306Q8—42no—
307Q8—41no—
308D4—22no—
309D4—42no—
310D4—42no—
311D4—41no—
312C2×C4—22no—
313C2×C4—42no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4C4×D4×C4311yescharacteristic
321C2×C4C4×D4×C4311yescharacteristic
322C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
323C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
324C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
325C2×C4C22×D4×C4311yescharacteristic
326C8—22no—
327C8—42no—
328C8C4×D4×C4311yescharacteristic
329C8C4×D4×C4311yescharacteristic
330C8C23×C4×C4311yescharacteristic
331C8C2×#41×C4311yescharacteristic
332C22—41no—
333C22—42no—
334C22—161no—
335C22C43×#44211yescharacteristic
336C22C43×#44211yescharacteristic
337C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
338C4—42no—
339C4—42no—
340C4—44no—
341C4—82no—
342C4C43×#44211yescharacteristic
343C4C43×#44211yescharacteristic
344C4C2×C4×D4×C4311yescharacteristic
345C4C2×AGL(1,ℤ/8)×C4311yescharacteristic
346C2—21no—
347C2—21no—
348C2—21no—
349C2—82no—
350C2C2×C43×#44211yescharacteristic
subgroupG/H
center, socleC2×C43C2×#442
commutatorC8C23×C4×C43
Frattini, cosocleC2×C8C24×C43
prime radicalC2×#135×C43C22
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C43 ◁ C22×C4×C43 ◁ C43×#405 ◁ G

Complements

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

NH ≅ G/Ntype
3. C43×#2950C2semidirect
4. C43×#2180C2semidirect
5. C43×#2155C2semidirect
6. C2×C43×#362C2semidirect
8. C43×#2110C2semidirect
13. C43×#510C4semidirect
15. C2×Q32×C43C4semidirect
16. C2×SD32×C43C4semidirect
21. C43×#441C22semidirect
28. C43×#365C22semidirect
29. C43×#362C22semidirect
31. C43×#347C22semidirect
156. #33470C43direct (N × H)
173. #2950C2×C43semidirect
174. #2180C2×C43semidirect
175. #2155C2×C43semidirect
176. C2×#362C2×C43semidirect
178. #2110C2×C43semidirect
188. #510C4×C43semidirect
190. C2×Q32C4×C43semidirect
191. C2×SD32C4×C43semidirect
196. #441C22×C43semidirect
203. #365C22×C43semidirect
204. #362C22×C43semidirect
206. #347C22×C43semidirect
207. C43#33470direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#5102
C43×#29572
C43×#29502
C43×#21802
C43×#21552
C2×C43×#3622
C43×#21452
C43×#21102
#3347043