Finite Group Databasebeta

← C43×#8469 #24928486

Subgroups — C43×#8469 #24928486

Order 11008.

1092 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3498C211yesmaximal, characteristic
2C43×#1965C212yesmaximal, complemented
3C43×#1560C211yesmaximal, characteristic, complemented
4C43×#1525C211yesmaximal, characteristic, complemented
5C43×#1489C212yesmaximal, complemented
6C2×H(5,𝔽2)×C43C412yes—
7C43×#550—22no—
8D42×C43—24no—
9D42×C43—22no—
10C43×#535—22no—
11C43×#535C412yes—
12C43×#532—21no—
13C43×#532C2211yescharacteristic
14C2×#127×C43—21no—
15C2×#127×C43C2211yescharacteristic
16C4×#41×C43C2211yescharacteristic
17C43×#423C2212yescomplemented
18C2×#100×C43—24no—
19C4×M16×C43C2212yescomplemented
20C43×#333—21no—
21C43×#331—21no—
22C43×#329—22no—
23C43×Q8⋊C8—22no—
24C43×D4⋊C8—22no—
25H(5,𝔽2)×C43—44no—
26H(5,𝔽2)×C43—44no—
27C2×#41×C43—22no—
28C2×#41×C43—22no—
29C2×#41×C43C2×C411yescharacteristic
30C2×#41×C43C2×C412yes—
31C22×D4×C43—24no—
32C22×D4×C43—24no—
33C22×D4×C43—22no—
34C22×D4×C43—22no—
35C22×D4×C43C2×C412yes—
36C22×D4×C43D414yes—
37C2×M16×C43—22no—
38C2×M16×C43—22no—
39C4⋊Q8×C43D411yescharacteristic
40#127×C43—24no—
41#127×C43—22no—
42#127×C43—21no—
43#127×C43—21no—
44#127×C43—22no—
45#127×C43D411yescharacteristic
46#124×C43—22no—
47#124×C43D412yes—
48#121×C43—24no—
49#121×C43—28no—
50#121×C43—22no—
51#121×C43—24no—
52#120×C43—28no—
53#120×C43—24no—
54C4×Q8×C43D412yes—
55C4×D4×C43—24no—
56C4×D4×C43—22no—
57C4×D4×C43—22no—
58C4×D4×C43D412yes—
59#117×C43—21no—
60#117×C43C2×C411yescharacteristic
61C2×C42×C43—21no—
62C2×C42×C43C2311yescharacteristic
63C4⋊C8×C43—22no—
64C4⋊C8×C43—22no—
65#100×C43—48no—
66#97×C43—22no—
67C4×C8×C43—22no—
68C24×C43—24no—
69C24×C43C22⋊C414yes—
70#41×C43—22no—
71#41×C43—22no—
72#41×C43—48no—
73#41×C43—42no—
74#41×C43—42no—
75#41×C43—44no—
76#41×C43—44no—
77C2×Q8×C43C22⋊C411yescharacteristic
78C2×Q8×C43C22⋊C412yes—
79C2×D4×C43—24no—
80C2×D4×C43—24no—
81C2×D4×C43—28no—
82C2×D4×C43—22no—
83C2×D4×C43—22no—
84C2×D4×C43—24no—
85C2×D4×C43—22no—
86C2×D4×C43—24no—
87C2×D4×C43—21no—
88C2×D4×C43—22no—
89C2×D4×C43—42no—
90C2×D4×C43—42no—
91C2×D4×C43—48no—
92C2×D4×C43—44no—
93C2×D4×C43—44no—
94C2×D4×C43—44no—
95C2×D4×C43—416no—
96C2×D4×C43—44no—
97C2×D4×C43—84no—
98C2×D4×C43—84no—
99C2×D4×C43C22⋊C411yescharacteristic
100C2×D4×C43C22⋊C412yes—
101C22×C4×C43—21no—
102C22×C4×C43—24no—
103C22×C4×C43—22no—
104C22×C4×C43—22no—
105C22×C4×C43C22×C411yescharacteristic
106C22×C4×C43C2×D412yes—
107M16×C43—24no—
108M16×C43—42no—
109M16×C43—44no—
110C2×C8×C43—42no—
111C2×C8×C43—42no—
112C4⋊C4×C43—22no—
113C4⋊C4×C43—22no—
114C4⋊C4×C43C22⋊C412yes—
115C22⋊C4×C43—28no—
116C22⋊C4×C43—22no—
117C22⋊C4×C43—24no—
118C22⋊C4×C43—21no—
119C42×C43—21no—
120C42×C43—22no—
121C42×C43C2×D412yes—
122C42×C43C2×D411yescharacteristic
123C42×C43C2×D411yescharacteristic
124C23×C43—21no—
125C23×C43—24no—
126C23×C43—22no—
127C23×C43—48no—
128C23×C43—44no—
129C23×C43—48no—
130C23×C43—88no—
131C23×C43C2×C22⋊C411yescharacteristic
132Q8×C43—21no—
133Q8×C43—42no—
134Q8×C43#10012yescomplemented
135D4×C43—24no—
136D4×C43—21no—
137D4×C43—42no—
138D4×C43—44no—
139D4×C43—48no—
140D4×C43—48no—
141D4×C43—44no—
142D4×C43—42no—
143D4×C43—42no—
144D4×C43—44no—
145D4×C43—42no—
146D4×C43—44no—
147D4×C43—42no—
148D4×C43—84no—
149D4×C43—88no—
150D4×C43#10012yescomplemented
151C2×C4×C43—24no—
152C2×C4×C43—21no—
153C2×C4×C43—21no—
154C2×C4×C43—21no—
155C2×C4×C43—22no—
156C2×C4×C43—22no—
157C2×C4×C43—22no—
158C2×C4×C43—22no—
159C2×C4×C43—48no—
160C2×C4×C43—42no—
161C2×C4×C43—42no—
162C2×C4×C43—42no—
163C2×C4×C43—42no—
164C2×C4×C43C2×C22⋊C411yescharacteristic
165C2×C4×C43C2×C22⋊C411yescharacteristic
166C2×C4×C43#12012yes—
167C2×C4×C43#12012yes—
168C8×C43—44no—
169C8×C43—82no—
170#8469C4311yesmaximal, characteristic, direct product factor, Sylow
171C22×C43—22no—
172C22×C43—22no—
173C22×C43—21no—
174C22×C43—42no—
175C22×C43—48no—
176C22×C43—44no—
177C22×C43—42no—
178C22×C43—44no—
179C22×C43—164no—
180C22×C43—168no—
181C22×C43#37911yescharacteristic
182C4×C43—22no—
183C4×C43—21no—
184C4×C43—22no—
185C4×C43—42no—
186C4×C43—42no—
187C4×C43C2×#10011yescharacteristic
188C4×C43C2×#10011yescharacteristic
189C4×C43#45312yes—
190C4×C43#45512yes—
191#3498C2×C4311yescharacteristic
192#1965C2×C4312yescomplemented
193#1560C2×C4311yescharacteristic, complemented
194#1525C2×C4311yescharacteristic, complemented
195#1489C2×C4312yescomplemented
196C2×C43—41no—
197C2×C43—42no—
198C2×C43—84no—
199C2×C43—82no—
200C2×C43#178311yescharacteristic
201C2×C43#179212yes—
202C2×H(5,𝔽2)C4×C4312yes—
203#550—22no—
204D42—24no—
205D42—22no—
206#535—22no—
207#535C4×C4312yes—
208#532—21no—
209#532C22×C4311yescharacteristic
210C2×#127—21no—
211C2×#127C22×C4311yescharacteristic
212C4×#41C22×C4311yescharacteristic
213#423C22×C4312yescomplemented
214C2×#100—24no—
215C4×M16C22×C4312yescomplemented
216#333—21no—
217#331—21no—
218#329—22no—
219Q8⋊C8—22no—
220D4⋊C8—22no—
221C43#846911yescharacteristic, direct product factor, Sylow
222H(5,𝔽2)—44no—
223H(5,𝔽2)—44no—
224C2×#41—22no—
225C2×#41—22no—
226C2×#41C2×C4×C4311yescharacteristic
227C2×#41C2×C4×C4312yes—
228C22×D4—24no—
229C22×D4—24no—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4C2×C4×C4312yes—
233C22×D4D4×C4314yes—
234C2×M16—22no—
235C2×M16—22no—
236C4⋊Q8D4×C4311yescharacteristic
237#127—24no—
238#127—22no—
239#127—21no—
240#127—21no—
241#127—22no—
242#127D4×C4311yescharacteristic
243#124—22no—
244#124D4×C4312yes—
245#121—24no—
246#121—28no—
247#121—22no—
248#121—24no—
249#120—28no—
250#120—24no—
251C4×Q8D4×C4312yes—
252C4×D4—24no—
253C4×D4—22no—
254C4×D4—22no—
255C4×D4D4×C4312yes—
256#117—21no—
257#117C2×C4×C4311yescharacteristic
258C2×C42—21no—
259C2×C42C23×C4311yescharacteristic
260C4⋊C8—22no—
261C4⋊C8—22no—
262#100—48no—
263#97—22no—
264C4×C8—22no—
265C24—24no—
266C24C22⋊C4×C4314yes—
267#41—22no—
268#41—22no—
269#41—48no—
270#41—42no—
271#41—42no—
272#41—44no—
273#41—44no—
274C2×Q8C22⋊C4×C4311yescharacteristic
275C2×Q8C22⋊C4×C4312yes—
276C2×D4—21no—
277C2×D4—24no—
278C2×D4—24no—
279C2×D4—22no—
280C2×D4—28no—
281C2×D4—22no—
282C2×D4—22no—
283C2×D4—24no—
284C2×D4—22no—
285C2×D4—24no—
286C2×D4—48no—
287C2×D4—42no—
288C2×D4—42no—
289C2×D4—44no—
290C2×D4—44no—
291C2×D4—416no—
292C2×D4—44no—
293C2×D4—44no—
294C2×D4—84no—
295C2×D4—84no—
296C2×D4C22⋊C4×C4311yescharacteristic
297C2×D4C22⋊C4×C4312yes—
298C22×C4—21no—
299C22×C4—24no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4C22×C4×C4311yescharacteristic
303C22×C4C2×D4×C4312yes—
304M16—24no—
305M16—42no—
306M16—44no—
307C2×C8—42no—
308C2×C8—42no—
309C4⋊C4—22no—
310C4⋊C4—22no—
311C4⋊C4C22⋊C4×C4312yes—
312C22⋊C4—28no—
313C22⋊C4—21no—
314C22⋊C4—22no—
315C22⋊C4—24no—
316C42—21no—
317C42—22no—
318C42C2×D4×C4312yes—
319C42C2×D4×C4311yescharacteristic
320C42C2×D4×C4311yescharacteristic
321C23—21no—
322C23—24no—
323C23—22no—
324C23—48no—
325C23—44no—
326C23—48no—
327C23—88no—
328C23C2×C22⋊C4×C4311yescharacteristic
329Q8—21no—
330Q8—42no—
331Q8#100×C4312yescomplemented
332D4—24no—
333D4—21no—
334D4—42no—
335D4—44no—
336D4—48no—
337D4—44no—
338D4—48no—
339D4—42no—
340D4—42no—
341D4—44no—
342D4—42no—
343D4—44no—
344D4—42no—
345D4—84no—
346D4—88no—
347D4#100×C4312yescomplemented
348C2×C4—24no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—48no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4C2×C22⋊C4×C4311yescharacteristic
362C2×C4C2×C22⋊C4×C4311yescharacteristic
363C2×C4#120×C4312yes—
364C2×C4#120×C4312yes—
365C8—44no—
366C8—82no—
367C22—21no—
368C22—22no—
369C22—22no—
370C22—42no—
371C22—44no—
372C22—42no—
373C22—48no—
374C22—44no—
375C22—164no—
376C22—168no—
377C22C43×#37911yescharacteristic
378C4—21no—
379C4—22no—
380C4—22no—
381C4—42no—
382C4—42no—
383C4C2×#100×C4311yescharacteristic
384C4C2×#100×C4311yescharacteristic
385C4C43×#45312yes—
386C4C43×#45512yes—
387C2—41no—
388C2—42no—
389C2—82no—
390C2—84no—
391C2C43×#178311yescharacteristic
392C2C43×#179212yes—
subgroupG/H
center, socleC22×C43#379
commutatorC22×C4C22×C4×C43
Frattini, cosocleC2×C42C23×C43
prime radicalC43×#3498C2
LCSG ▷ C22×C4 ▷ 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×#1965C2semidirect
3. C43×#1560C2semidirect
4. C43×#1525C2semidirect
5. C43×#1489C2semidirect
17. C43×#423C22semidirect
19. C4×M16×C43C22semidirect
134. Q8×C43#100semidirect
150. D4×C43#100semidirect
170. #8469C43direct (N × H)
192. #1965C2×C43semidirect
193. #1560C2×C43semidirect
194. #1525C2×C43semidirect
195. #1489C2×C43semidirect
213. #423C22×C43semidirect
215. C4×M16C22×C43semidirect
221. C43#8469direct (N × H)
331. Q8#100×C43semidirect
347. D4#100×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#34982
C43×#19652
C43×#15602
C43×#15252
C43×#14892
#846943