Finite Group Databasebeta

← C43×#9235 #24929252

Subgroups — C43×#9235 #24929252

Order 11008.

550 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3101C211yesmaximal, characteristic
2C43×#2293C211yesmaximal, characteristic
3C43×#1994C211yesmaximal, characteristic, complemented
4C43×#1503C211yesmaximal, characteristic, complemented
5C43×#1486C211yesmaximal, characteristic
6C43×#1303C211yesmaximal, characteristic, complemented
7C43×#1276C211yesmaximal, characteristic, complemented
8C43×#533C2211yescharacteristic
9C2×C4×D4×C43C2211yescharacteristic
10C2×#117×C43—21no—
11C43×#483—21no—
12C43×#476C412yescomplemented
13C43×#461C412yescomplemented
14C43×#450—21no—
15C4×SD16×C43—22no—
16C43×#431C2211yescharacteristic
17C43×#431C2211yescharacteristic
18C43×#423C2211yescharacteristic
19C43×#390—21no—
20C43×#389—21no—
21C43×#388—22no—
22C4×C4⋊C4×C43C2211yescharacteristic
23C4×C22⋊C4×C43—21no—
24C43×C43C2211yescharacteristic
25C43×#339—21no—
26C43×#339—21no—
27C43×#328—22no—
28C43×D4⋊C8—22no—
29C22×D4×C43D411yescharacteristic
30C23×C4×C43—21no—
31C2×SD16×C43—22no—
32C2×M16×C43—21no—
33C4⋊Q8×C43C2×C411yescharacteristic
34C4⋊Q8×C43C2×C411yescharacteristic
35#125×C43—21no—
36C22⋊Q8×C43—21no—
37C22⋊Q8×C43—21no—
38C4×Q8×C43—21no—
39C4×Q8×C43—21no—
40C4×D4×C43—21no—
41C4×D4×C43—21no—
42C4×D4×C43C2×C412yes—
43C4×D4×C43D412yes—
44#117×C43—21no—
45#117×C43—42no—
46#117×C43—42no—
47C2×C4⋊C4×C43—22no—
48C2×C4⋊C4×C43—21no—
49C2×C4⋊C4×C43D411yescharacteristic
50C2×C22⋊C4×C43—21no—
51C2×C22⋊C4×C43—22no—
52C2×C22⋊C4×C43—22no—
53C2×C42×C43—21no—
54C2×C42×C43—21no—
55C2×C42×C43—21no—
56C2×C42×C43D411yescharacteristic
57C2×C42×C43D411yescharacteristic
58C2×C42×C43C2311yescharacteristic
59#106×C43—22no—
60C4⋊C8×C43—21no—
61C4⋊C8×C43—21no—
62C4⋊C8×C43—21no—
63C4⋊C8×C43C2×C412yes—
64#103×C43—22no—
65#102×C43—22no—
66C22⋊C8×C43—21no—
67C22⋊C8×C43—21no—
68C4×C8×C43—21no—
69C4×C8×C43—21no—
70#95×C43—22no—
71#95×C43D412yes—
72C24×C43—21no—
73C2×Q8×C43—21no—
74C2×Q8×C43—21no—
75C2×D4×C43—21no—
76C2×D4×C43—42no—
77C2×D4×C43C22⋊C412yes—
78C22×C4×C43—22no—
79C22×C4×C43—22no—
80C22×C4×C43—21no—
81C22×C4×C43—21no—
82C22×C4×C43—21no—
83C22×C4×C43—22no—
84C22×C4×C43—41no—
85C22×C4×C43—41no—
86C22×C4×C43—41no—
87C22×C4×C43—41no—
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91SD16×C43—44no—
92M16×C43—41no—
93M16×C43—41no—
94C2×C8×C43—22no—
95C2×C8×C43—41no—
96C2×C8×C43—41no—
97C4⋊C4×C43—21no—
98C4⋊C4×C43—21no—
99C4⋊C4×C43—21no—
100C4⋊C4×C43—21no—
101C4⋊C4×C43—21no—
102C4⋊C4×C43—42no—
103C4⋊C4×C43—44no—
104C4⋊C4×C43—41no—
105C4⋊C4×C43—41no—
106C4⋊C4×C43C22⋊C412yes—
107C22⋊C4×C43—22no—
108C22⋊C4×C43—22no—
109C22⋊C4×C43—44no—
110C22⋊C4×C43—44no—
111C22⋊C4×C43—41no—
112C42×C43—21no—
113C42×C43—21no—
114C42×C43—21no—
115C42×C43—42no—
116C42×C43—42no—
117C42×C43—41no—
118C42×C43—41no—
119C42×C43—41no—
120C42×C43SD1612yescomplemented
121C42×C43C22×C411yescharacteristic
122C42×C43C2×D411yescharacteristic
123C42×C43#4111yescharacteristic
124C42×C43#4111yescharacteristic
125C23×C43—22no—
126C23×C43—42no—
127C23×C43—42no—
128C23×C43—41no—
129C23×C43—41no—
130C23×C43#12011yescharacteristic
131Q8×C43—42no—
132Q8×C43—81no—
133D4×C43—22no—
134D4×C43—22no—
135D4×C43—42no—
136C2×C4×C43—22no—
137C2×C4×C43—22no—
138C2×C4×C43—22no—
139C2×C4×C43—22no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—42no—
148C2×C4×C43—42no—
149C2×C4×C43—42no—
150C2×C4×C43—42no—
151C2×C4×C43—42no—
152C2×C4×C43—42no—
153C2×C4×C43—41no—
154C2×C4×C43—41no—
155C2×C4×C43—42no—
156C2×C4×C43C2×C22⋊C411yescharacteristic
157C2×C4×C43C4×D411yescharacteristic
158C2×C4×C43C4×D411yescharacteristic
159C2×C4×C43#12111yescharacteristic
160C2×C4×C43#12111yescharacteristic
161C2×C4×C43#12311yescharacteristic
162C2×C4×C43C2×SD1611yescharacteristic
163C2×C4×C43#13511yescharacteristic
164C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C43#13711yescharacteristic
166C8×C43—42no—
167C8×C43—81no—
168C8×C43—81no—
169#9235C4311yesmaximal, characteristic, direct product factor, Sylow
170C22×C43—21no—
171C22×C43—21no—
172C22×C43—42no—
173C22×C43—42no—
174C22×C43—42no—
175C22×C43—82no—
176C22×C43—82no—
177C22×C43#38611yescharacteristic
178C22×C43#45011yescharacteristic
179C22×C43#45211yescharacteristic
180C4×C43—21no—
181C4×C43—21no—
182C4×C43—21no—
183C4×C43—42no—
184C4×C43—42no—
185C4×C43—42no—
186C4×C43—82no—
187C4×C43—81no—
188C4×C43—81no—
189C4×C43#42112yes—
190C4×C43C4×SD1611yescharacteristic
191C4×C43#44011yescharacteristic
192C4×C43#46111yescharacteristic
193C4×C43#46311yescharacteristic
194#3101C2×C4311yescharacteristic
195#2293C2×C4311yescharacteristic
196#1994C2×C4311yescharacteristic, complemented
197#1503C2×C4311yescharacteristic, complemented
198#1486C2×C4311yescharacteristic
199#1303C2×C4311yescharacteristic, complemented
200#1276C2×C4311yescharacteristic, complemented
201C2×C43—21no—
202C2×C43—21no—
203C2×C43—82no—
204C2×C43#187711yescharacteristic
205C2×C43#189711yescharacteristic
206C2×C43#190611yescharacteristic
207#533C22×C4311yescharacteristic
208C2×C4×D4C22×C4311yescharacteristic
209C2×#117—21no—
210#483—21no—
211#476C4×C4312yescomplemented
212#461C4×C4312yescomplemented
213#450—21no—
214C4×SD16—22no—
215#431C22×C4311yescharacteristic
216#431C22×C4311yescharacteristic
217#423C22×C4311yescharacteristic
218#390—21no—
219#389—21no—
220#388—22no—
221C4×C4⋊C4C22×C4311yescharacteristic
222C4×C22⋊C4—21no—
223C43C22×C4311yescharacteristic
224#339—21no—
225#339—21no—
226#328—22no—
227D4⋊C8—22no—
228C43#923511yescharacteristic, direct product factor, Sylow
229C22×D4D4×C4311yescharacteristic
230C23×C4—21no—
231C2×SD16—22no—
232C2×M16—21no—
233C4⋊Q8C2×C4×C4311yescharacteristic
234C4⋊Q8C2×C4×C4311yescharacteristic
235#125—21no—
236C22⋊Q8—21no—
237C22⋊Q8—21no—
238C4×Q8—21no—
239C4×Q8—21no—
240C4×D4—21no—
241C4×D4—21no—
242C4×D4C2×C4×C4312yes—
243C4×D4D4×C4312yes—
244#117—21no—
245#117—42no—
246#117—42no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4D4×C4311yescharacteristic
250C2×C22⋊C4—21no—
251C2×C22⋊C4—22no—
252C2×C22⋊C4—22no—
253C2×C42—21no—
254C2×C42—21no—
255C2×C42—21no—
256C2×C42D4×C4311yescharacteristic
257C2×C42D4×C4311yescharacteristic
258C2×C42C23×C4311yescharacteristic
259#106—22no—
260C4⋊C8—21no—
261C4⋊C8—21no—
262C4⋊C8—21no—
263C4⋊C8C2×C4×C4312yes—
264#103—22no—
265#102—22no—
266C22⋊C8—21no—
267C22⋊C8—21no—
268C4×C8—21no—
269C4×C8—21no—
270#95—22no—
271#95D4×C4312yes—
272C24—21no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×D4—21no—
276C2×D4—42no—
277C2×D4C22⋊C4×C4312yes—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4C2×D4×C4311yescharacteristic
289C22×C4C2×D4×C4311yescharacteristic
290C22×C4C2×D4×C4311yescharacteristic
291SD16—44no—
292M16—41no—
293M16—41no—
294C2×C8—22no—
295C2×C8—41no—
296C2×C8—41no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—44no—
303C4⋊C4—42no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4C22⋊C4×C4312yes—
307C22⋊C4—22no—
308C22⋊C4—22no—
309C22⋊C4—44no—
310C22⋊C4—44no—
311C22⋊C4—41no—
312C42—21no—
313C42—21no—
314C42—21no—
315C42—42no—
316C42—42no—
317C42—41no—
318C42—41no—
319C42—41no—
320C42SD16×C4312yescomplemented
321C42C22×C4×C4311yescharacteristic
322C42C2×D4×C4311yescharacteristic
323C42#41×C4311yescharacteristic
324C42#41×C4311yescharacteristic
325C23—22no—
326C23—42no—
327C23—42no—
328C23—41no—
329C23—41no—
330C23#120×C4311yescharacteristic
331Q8—42no—
332Q8—81no—
333D4—22no—
334D4—22no—
335D4—42no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—42no—
356C2×C4C2×C22⋊C4×C4311yescharacteristic
357C2×C4C4×D4×C4311yescharacteristic
358C2×C4C4×D4×C4311yescharacteristic
359C2×C4#121×C4311yescharacteristic
360C2×C4#121×C4311yescharacteristic
361C2×C4#123×C4311yescharacteristic
362C2×C4C2×SD16×C4311yescharacteristic
363C2×C4#135×C4311yescharacteristic
364C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
365C2×C4#137×C4311yescharacteristic
366C8—42no—
367C8—81no—
368C8—81no—
369C22—21no—
370C22—21no—
371C22—42no—
372C22—42no—
373C22—42no—
374C22—82no—
375C22—82no—
376C22C43×#38611yescharacteristic
377C22C43×#45011yescharacteristic
378C22C43×#45211yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—42no—
383C4—42no—
384C4—42no—
385C4—82no—
386C4—81no—
387C4—81no—
388C4C43×#42112yes—
389C4C4×SD16×C4311yescharacteristic
390C4C43×#44011yescharacteristic
391C4C43×#46111yescharacteristic
392C4C43×#46311yescharacteristic
393C2—21no—
394C2—21no—
395C2—82no—
396C2C43×#187711yescharacteristic
397C2C43×#189711yescharacteristic
398C2C43×#190611yescharacteristic
subgroupG/H
centerC2×C4×C43#121
commutatorC42C22×C4×C43
Frattini, cosocleC2×C42C23×C43
socleC22×C43#386
prime radicalC22×D4×C43D4
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
3. C43×#1994C2semidirect
4. C43×#1503C2semidirect
6. C43×#1303C2semidirect
7. C43×#1276C2semidirect
12. C43×#476C4semidirect
13. C43×#461C4semidirect
120. C42×C43SD16semidirect
169. #9235C43direct (N × H)
196. #1994C2×C43semidirect
197. #1503C2×C43semidirect
199. #1303C2×C43semidirect
200. #1276C2×C43semidirect
211. #476C4×C43semidirect
212. #461C4×C43semidirect
228. C43#9235direct (N × H)
320. C42SD16×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#31012
C43×#22932
C43×#19942
C43×#15032
C43×#14862
C43×#13032
C43×#12762
#923543