Finite Group Databasebeta

← C43×#8504 #24928521

Subgroups — C43×#8504 #24928521

Order 11008.

728 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3529C211yesmaximal, characteristic
2C43×#1963C211yesmaximal, characteristic, complemented
3C43×#1543C211yesmaximal, characteristic, complemented
4C43×#1500C212yesmaximal, complemented
5C43×#1495C212yesmaximal, complemented
6C43×#563—21no—
7C43×#563C411yescharacteristic, complemented
8C43×#562—22no—
9C43×#562C412yescomplemented
10C43×H(3,𝔽4)C411yescharacteristic, complemented
11C43×#560—21no—
12C43×#560—22no—
13C43×#532—21no—
14C43×#532C2211yescharacteristic
15C43×#529—22no—
16C43×#529C2212yes—
17C43×#525—21no—
18C43×#525—22no—
19C43×#431C2212yescomplemented
20C43×#423C2211yescharacteristic, complemented
21C2×#104×C43—21no—
22C2×#104×C43—21no—
23C43×#376C2211yescharacteristic, complemented
24C43×#333—21no—
25C43×#331—21no—
26C43×#328—22no—
27C43×#327—22no—
28C43×Q8⋊C8—22no—
29C43×D4⋊C8—22no—
30C2×#41×C43—21no—
31C2×#41×C43D411yescharacteristic
32C2×#41×C43D411yescharacteristic
33C23×C4×C43—21no—
34C2×M16×C43—21no—
35C4⋊Q8×C43—21no—
36C4⋊Q8×C43D411yescharacteristic
37#127×C43—21no—
38#127×C43D411yescharacteristic
39#126×C43—22no—
40#126×C43—22no—
41#126×C43—22no—
42#125×C43—22no—
43#125×C43C2×C412yes—
44#124×C43—21no—
45#124×C43—22no—
46#124×C43—21no—
47#124×C43C2×C412yes—
48#124×C43C2×C411yescharacteristic
49#124×C43C2×C411yescharacteristic
50#123×C43—22no—
51#123×C43—21no—
52#123×C43—22no—
53#123×C43—21no—
54#123×C43—22no—
55#123×C43—22no—
56#123×C43—22no—
57C22⋊Q8×C43—22no—
58C22⋊Q8×C43—22no—
59C22⋊Q8×C43—22no—
60C22⋊Q8×C43—22no—
61C22⋊Q8×C43D412yes—
62#121×C43—22no—
63#121×C43—22no—
64#121×C43—22no—
65#121×C43—22no—
66#121×C43—22no—
67#121×C43—22no—
68#121×C43—22no—
69#121×C43D412yes—
70#120×C43—21no—
71#120×C43—22no—
72#120×C43—21no—
73#120×C43—22no—
74C4×Q8×C43D412yes—
75C4×D4×C43—22no—
76C4×D4×C43—22no—
77C4×D4×C43—22no—
78C4×D4×C43—22no—
79C4×D4×C43D412yes—
80#117×C43—21no—
81#117×C43—22no—
82C2×C42×C43—21no—
83C2×C42×C43—21no—
84C2×C42×C43C2311yescharacteristic
85C4⋊C8×C43—22no—
86C4⋊C8×C43—22no—
87#104×C43—42no—
88#104×C43—42no—
89C22⋊C8×C43—22no—
90C4×C8×C43—22no—
91#95×C43—22no—
92C24×C43—21no—
93#41×C43—41no—
94#41×C43—41no—
95#41×C43—41no—
96#41×C43—41no—
97#41×C43—81no—
98#41×C43—81no—
99C2×Q8×C43—21no—
100C2×Q8×C43C22⋊C412yes—
101C2×Q8×C43C22⋊C411yescharacteristic
102C2×Q8×C43C22⋊C411yescharacteristic
103C2×D4×C43—22no—
104C2×D4×C43—22no—
105C2×D4×C43—21no—
106C2×D4×C43—22no—
107C2×D4×C43—22no—
108C2×D4×C43—22no—
109C2×D4×C43—21no—
110C2×D4×C43—21no—
111C2×D4×C43C22⋊C412yes—
112C2×D4×C43C22⋊C411yescharacteristic
113C2×D4×C43C22⋊C411yescharacteristic
114C22×C4×C43—22no—
115C22×C4×C43—22no—
116C22×C4×C43—21no—
117C22×C4×C43—21no—
118C22×C4×C43—21no—
119C22×C4×C43—22no—
120C22×C4×C43—41no—
121C22×C4×C43—81no—
122C22×C4×C43—81no—
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D412yes—
125M16×C43—41no—
126M16×C43—41no—
127C2×C8×C43—42no—
128C2×C8×C43—41no—
129C4⋊C4×C43—22no—
130C4⋊C4×C43—22no—
131C4⋊C4×C43—22no—
132C4⋊C4×C43—22no—
133C4⋊C4×C43—22no—
134C4⋊C4×C43—22no—
135C4⋊C4×C43—22no—
136C4⋊C4×C43—22no—
137C4⋊C4×C43C22⋊C412yes—
138C4⋊C4×C43C22⋊C412yes—
139C22⋊C4×C43—21no—
140C22⋊C4×C43—21no—
141C22⋊C4×C43—22no—
142C22⋊C4×C43—22no—
143C22⋊C4×C43—22no—
144C22⋊C4×C43—22no—
145C22⋊C4×C43—22no—
146C22⋊C4×C43—22no—
147C22⋊C4×C43—22no—
148C22⋊C4×C43—22no—
149C22⋊C4×C43—22no—
150C22⋊C4×C43—22no—
151C22⋊C4×C43—22no—
152C42×C43—21no—
153C42×C43—21no—
154C42×C43—22no—
155C42×C43—22no—
156C42×C43—41no—
157C42×C43C22×C411yescharacteristic
158C42×C43C2×D411yescharacteristic
159C42×C43C2×D412yes—
160C23×C43—21no—
161C23×C43—22no—
162C23×C43—21no—
163C23×C43—81no—
164C23×C43—82no—
165C23×C43#12011yescharacteristic
166Q8×C43—42no—
167Q8×C43—41no—
168Q8×C43—41no—
169Q8×C43—81no—
170D4×C43—42no—
171D4×C43—41no—
172D4×C43—41no—
173D4×C43—82no—
174D4×C43—82no—
175D4×C43—81no—
176D4×C43—81no—
177D4×C43—82no—
178D4×C43—82no—
179D4×C43—82no—
180D4×C43—81no—
181C2×C4×C43—21no—
182C2×C4×C43—21no—
183C2×C4×C43—22no—
184C2×C4×C43—22no—
185C2×C4×C43—21no—
186C2×C4×C43—21no—
187C2×C4×C43—22no—
188C2×C4×C43—42no—
189C2×C4×C43—41no—
190C2×C4×C43—42no—
191C2×C4×C43—41no—
192C2×C4×C43—41no—
193C2×C4×C43—42no—
194C2×C4×C43—41no—
195C2×C4×C43—42no—
196C2×C4×C43—82no—
197C2×C4×C43—82no—
198C2×C4×C43—81no—
199C2×C4×C43—82no—
200C2×C4×C43C2×C22⋊C412yes—
201C2×C4×C43C2×C22⋊C411yescharacteristic
202C2×C4×C43#12012yes—
203C2×C4×C43#12011yescharacteristic
204C8×C43—82no—
205C8×C43—81no—
206#8504C4311yesmaximal, characteristic, direct product factor, Sylow
207C22×C43—21no—
208C22×C43—22no—
209C22×C43—41no—
210C22×C43—42no—
211C22×C43—41no—
212C22×C43—42no—
213C22×C43—42no—
214C22×C43—42no—
215C22×C43—42no—
216C22×C43—84no—
217C22×C43#37911yescharacteristic
218C4×C43—21no—
219C4×C43—22no—
220C4×C43—22no—
221C4×C43—41no—
222C4×C43—42no—
223C4×C43—41no—
224C4×C43—42no—
225C4×C43—42no—
226C4×C43—82no—
227C4×C43#45311yescharacteristic
228C4×C43#45511yescharacteristic
229#3529C2×C4311yescharacteristic
230#1963C2×C4311yescharacteristic, complemented
231#1543C2×C4311yescharacteristic, complemented
232#1500C2×C4312yescomplemented
233#1495C2×C4312yescomplemented
234C2×C43—41no—
235C2×C43—81no—
236C2×C43—81no—
237C2×C43—82no—
238C2×C43#179211yescharacteristic
239C2×C43#179412yes—
240#563—21no—
241#563C4×C4311yescharacteristic, complemented
242#562—22no—
243#562C4×C4312yescomplemented
244H(3,𝔽4)C4×C4311yescharacteristic, complemented
245#560—21no—
246#560—22no—
247#532—21no—
248#532C22×C4311yescharacteristic
249#529—22no—
250#529C22×C4312yes—
251#525—21no—
252#525—22no—
253#431C22×C4312yescomplemented
254#423C22×C4311yescharacteristic, complemented
255C2×#104—21no—
256C2×#104—21no—
257#376C22×C4311yescharacteristic, complemented
258#333—21no—
259#331—21no—
260#328—22no—
261#327—22no—
262Q8⋊C8—22no—
263D4⋊C8—22no—
264C43#850411yescharacteristic, direct product factor, Sylow
265C2×#41—21no—
266C2×#41D4×C4311yescharacteristic
267C2×#41D4×C4311yescharacteristic
268C23×C4—21no—
269C2×M16—21no—
270C4⋊Q8—21no—
271C4⋊Q8D4×C4311yescharacteristic
272#127—21no—
273#127D4×C4311yescharacteristic
274#126—22no—
275#126—22no—
276#126—22no—
277#125—22no—
278#125C2×C4×C4312yes—
279#124—21no—
280#124—22no—
281#124—21no—
282#124C2×C4×C4312yes—
283#124C2×C4×C4311yescharacteristic
284#124C2×C4×C4311yescharacteristic
285#123—22no—
286#123—21no—
287#123—22no—
288#123—21no—
289#123—22no—
290#123—22no—
291#123—22no—
292C22⋊Q8—22no—
293C22⋊Q8—22no—
294C22⋊Q8—22no—
295C22⋊Q8—22no—
296C22⋊Q8D4×C4312yes—
297#121—22no—
298#121—22no—
299#121—22no—
300#121—22no—
301#121—22no—
302#121—22no—
303#121—22no—
304#121D4×C4312yes—
305#120—21no—
306#120—22no—
307#120—21no—
308#120—22no—
309C4×Q8D4×C4312yes—
310C4×D4—22no—
311C4×D4—22no—
312C4×D4—22no—
313C4×D4—22no—
314C4×D4D4×C4312yes—
315#117—21no—
316#117—22no—
317C2×C42—21no—
318C2×C42—21no—
319C2×C42C23×C4311yescharacteristic
320C4⋊C8—22no—
321C4⋊C8—22no—
322#104—42no—
323#104—42no—
324C22⋊C8—22no—
325C4×C8—22no—
326#95—22no—
327C24—21no—
328#41—41no—
329#41—41no—
330#41—41no—
331#41—41no—
332#41—81no—
333#41—81no—
334C2×Q8—21no—
335C2×Q8C22⋊C4×C4312yes—
336C2×Q8C22⋊C4×C4311yescharacteristic
337C2×Q8C22⋊C4×C4311yescharacteristic
338C2×D4—22no—
339C2×D4—22no—
340C2×D4—21no—
341C2×D4—22no—
342C2×D4—22no—
343C2×D4—21no—
344C2×D4—21no—
345C2×D4—22no—
346C2×D4C22⋊C4×C4312yes—
347C2×D4C22⋊C4×C4311yescharacteristic
348C2×D4C22⋊C4×C4311yescharacteristic
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—22no—
355C22×C4—41no—
356C22×C4—81no—
357C22×C4—81no—
358C22×C4C2×D4×C4311yescharacteristic
359C22×C4C2×D4×C4312yes—
360M16—41no—
361M16—41no—
362C2×C8—42no—
363C2×C8—41no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4C22⋊C4×C4312yes—
373C4⋊C4C22⋊C4×C4312yes—
374C22⋊C4—21no—
375C22⋊C4—21no—
376C22⋊C4—22no—
377C22⋊C4—22no—
378C22⋊C4—22no—
379C22⋊C4—22no—
380C22⋊C4—22no—
381C22⋊C4—22no—
382C22⋊C4—22no—
383C22⋊C4—22no—
384C22⋊C4—22no—
385C22⋊C4—22no—
386C22⋊C4—22no—
387C42—21no—
388C42—21no—
389C42—22no—
390C42—22no—
391C42—41no—
392C42C22×C4×C4311yescharacteristic
393C42C2×D4×C4312yes—
394C42C2×D4×C4311yescharacteristic
395C23—21no—
396C23—22no—
397C23—21no—
398C23—81no—
399C23—82no—
400C23#120×C4311yescharacteristic
401Q8—41no—
402Q8—41no—
403Q8—42no—
404Q8—81no—
405D4—41no—
406D4—41no—
407D4—42no—
408D4—82no—
409D4—81no—
410D4—81no—
411D4—82no—
412D4—82no—
413D4—81no—
414D4—82no—
415D4—82no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—22no—
423C2×C4—42no—
424C2×C4—41no—
425C2×C4—42no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—82no—
432C2×C4—81no—
433C2×C4—82no—
434C2×C4—82no—
435C2×C4C2×C22⋊C4×C4312yes—
436C2×C4C2×C22⋊C4×C4311yescharacteristic
437C2×C4#120×C4312yes—
438C2×C4#120×C4311yescharacteristic
439C8—82no—
440C8—81no—
441C22—21no—
442C22—22no—
443C22—41no—
444C22—42no—
445C22—41no—
446C22—42no—
447C22—42no—
448C22—42no—
449C22—42no—
450C22—84no—
451C22C43×#37911yescharacteristic
452C4—21no—
453C4—22no—
454C4—22no—
455C4—41no—
456C4—42no—
457C4—41no—
458C4—42no—
459C4—42no—
460C4—82no—
461C4C43×#45311yescharacteristic
462C4C43×#45511yescharacteristic
463C2—41no—
464C2—81no—
465C2—82no—
466C2—81no—
467C2C43×#179211yescharacteristic
468C2C43×#179412yes—
subgroupG/H
centerC2×C4×C43#120
commutatorC42C22×C4×C43
Frattini, cosocleC2×C42C23×C43
socleC22×C43#379
prime radicalC43×#3529C2
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
2. C43×#1963C2semidirect
3. C43×#1543C2semidirect
4. C43×#1500C2semidirect
5. C43×#1495C2semidirect
7. C43×#563C4semidirect
9. C43×#562C4semidirect
10. C43×H(3,𝔽4)C4semidirect
19. C43×#431C22semidirect
20. C43×#423C22semidirect
23. C43×#376C22semidirect
206. #8504C43direct (N × H)
230. #1963C2×C43semidirect
231. #1543C2×C43semidirect
232. #1500C2×C43semidirect
233. #1495C2×C43semidirect
241. #563C4×C43semidirect
243. #562C4×C43semidirect
244. H(3,𝔽4)C4×C43semidirect
253. #431C22×C43semidirect
254. #423C22×C43semidirect
257. #376C22×C43semidirect
264. C43#8504direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#35292
C43×#19632
C43×#15432
C43×#15002
C43×#14952
#850443