Finite Group Databasebeta

← C43×#9238 #24929255

Subgroups — C43×#9238 #24929255

Order 11008.

512 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3103C211yesmaximal, characteristic
2C43×#2295C211yesmaximal, characteristic, complemented
3C43×#1962C211yesmaximal, characteristic
4C43×#1502C211yesmaximal, characteristic
5C43×#1487C211yesmaximal, characteristic, complemented
6C43×#1303C211yesmaximal, characteristic, complemented
7C43×#1276C211yesmaximal, characteristic, complemented
8C43×#532C2211yescharacteristic
9C2×C4×Q8×C43C2211yescharacteristic
10C43×#481—21no—
11C43×#475C412yescomplemented
12C43×#460C412yescomplemented
13C43×#448—21no—
14C4×SD16×C43—22no—
15C43×#431C2211yescharacteristic
16C43×#431C2211yescharacteristic
17C43×#423C2211yescharacteristic
18C2×#104×C43—21no—
19C2×#104×C43—21no—
20C43×#391—21no—
21C43×#389—21no—
22C43×#387—22no—
23C4×C4⋊C4×C43—21no—
24C4×C4⋊C4×C43C2211yescharacteristic
25C43×#376—21no—
26C43×C43C2211yescharacteristic
27C43×#327—22no—
28C43×Q8⋊C8—22no—
29C2×#41×C43—21no—
30C22×Q8×C43D411yescharacteristic
31C2×SD16×C43—22no—
32C2×M16×C43—21no—
33C4⋊Q8×C43C2×C411yescharacteristic
34#127×C43C2×C411yescharacteristic
35#124×C43—21no—
36#121×C43—21no—
37#121×C43—21no—
38C4×Q8×C43—21no—
39C4×Q8×C43—21no—
40C4×Q8×C43C2×C412yes—
41C4×Q8×C43D412yes—
42C4×D4×C43—21no—
43C4×D4×C43—21no—
44C2×C4⋊C4×C43—21no—
45C2×C4⋊C4×C43—22no—
46C2×C4⋊C4×C43—21no—
47C2×C4⋊C4×C43D411yescharacteristic
48C2×C42×C43—21no—
49C2×C42×C43—21no—
50C2×C42×C43—21no—
51C2×C42×C43—21no—
52C2×C42×C43D411yescharacteristic
53C2×C42×C43D411yescharacteristic
54C2×C42×C43C2311yescharacteristic
55#106×C43—22no—
56C4⋊C8×C43—21no—
57C4⋊C8×C43—21no—
58C4⋊C8×C43—21no—
59C4⋊C8×C43C2×C412yes—
60#104×C43—42no—
61#104×C43—42no—
62#103×C43—22no—
63#102×C43—22no—
64C22⋊C8×C43—21no—
65C22⋊C8×C43—21no—
66C4×C8×C43—21no—
67C4×C8×C43—21no—
68#95×C43—22no—
69#95×C43—22no—
70#95×C43—22no—
71#95×C43D412yes—
72#41×C43—41no—
73#41×C43—41no—
74#41×C43—41no—
75#41×C43—41no—
76C2×Q8×C43—21no—
77C2×Q8×C43—21no—
78C2×Q8×C43—42no—
79C2×Q8×C43C22⋊C412yes—
80C2×D4×C43—21no—
81C2×D4×C43—21no—
82C2×D4×C43—21no—
83C2×D4×C43—41no—
84C22×C4×C43—21no—
85C22×C4×C43—21no—
86C22×C4×C43—21no—
87C22×C4×C43—21no—
88C22×C4×C43—22no—
89C22×C4×C43—41no—
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93SD16×C43—44no—
94M16×C43—41no—
95M16×C43—41no—
96C2×C8×C43—22no—
97C2×C8×C43—41no—
98C2×C8×C43—41no—
99C4⋊C4×C43—22no—
100C4⋊C4×C43—22no—
101C4⋊C4×C43—21no—
102C4⋊C4×C43—21no—
103C4⋊C4×C43—21no—
104C4⋊C4×C43—42no—
105C4⋊C4×C43—44no—
106C4⋊C4×C43C22⋊C412yes—
107C22⋊C4×C43—41no—
108C22⋊C4×C43—41no—
109C42×C43—22no—
110C42×C43—22no—
111C42×C43—21no—
112C42×C43—21no—
113C42×C43—21no—
114C42×C43—42no—
115C42×C43—42no—
116C42×C43—41no—
117C42×C43—41no—
118C42×C43SD1612yescomplemented
119C42×C43C22×C411yescharacteristic
120C42×C43C2×D411yescharacteristic
121C42×C43#4111yescharacteristic
122C42×C43#4111yescharacteristic
123C23×C43—41no—
124C23×C43#12011yescharacteristic
125Q8×C43—22no—
126Q8×C43—22no—
127Q8×C43—42no—
128Q8×C43—41no—
129Q8×C43—41no—
130D4×C43—42no—
131D4×C43—41no—
132D4×C43—41no—
133D4×C43—81no—
134D4×C43—81no—
135D4×C43—81no—
136C2×C4×C43—22no—
137C2×C4×C43—22no—
138C2×C4×C43—22no—
139C2×C4×C43—22no—
140C2×C4×C43—22no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—42no—
146C2×C4×C43—42no—
147C2×C4×C43—41no—
148C2×C4×C43—42no—
149C2×C4×C43—42no—
150C2×C4×C43—41no—
151C2×C4×C43—42no—
152C2×C4×C43—81no—
153C2×C4×C43—81no—
154C2×C4×C43C2×C22⋊C411yescharacteristic
155C2×C4×C43C4×D411yescharacteristic
156C2×C4×C43C4×D411yescharacteristic
157C2×C4×C43#12111yescharacteristic
158C2×C4×C43#12111yescharacteristic
159C2×C4×C43#12311yescharacteristic
160C2×C4×C43C2×SD1611yescharacteristic
161C2×C4×C43#13511yescharacteristic
162C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C43#13711yescharacteristic
164C8×C43—42no—
165C8×C43—81no—
166C8×C43—81no—
167#9238C4311yesmaximal, characteristic, direct product factor, Sylow
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—81no—
171C22×C43—81no—
172C22×C43—81no—
173C22×C43#38611yescharacteristic
174C22×C43#44811yescharacteristic
175C22×C43#44911yescharacteristic
176C4×C43—21no—
177C4×C43—21no—
178C4×C43—21no—
179C4×C43—42no—
180C4×C43—42no—
181C4×C43—42no—
182C4×C43—42no—
183C4×C43—82no—
184C4×C43—81no—
185C4×C43#42112yes—
186C4×C43C4×SD1611yescharacteristic
187C4×C43#44011yescharacteristic
188C4×C43#46011yescharacteristic
189C4×C43#46411yescharacteristic
190#3103C2×C4311yescharacteristic
191#2295C2×C4311yescharacteristic, complemented
192#1962C2×C4311yescharacteristic
193#1502C2×C4311yescharacteristic
194#1487C2×C4311yescharacteristic, complemented
195#1303C2×C4311yescharacteristic, complemented
196#1276C2×C4311yescharacteristic, complemented
197C2×C43—21no—
198C2×C43—21no—
199C2×C43—161no—
200C2×C43#188011yescharacteristic
201C2×C43#189711yescharacteristic
202C2×C43#190611yescharacteristic
203#532C22×C4311yescharacteristic
204C2×C4×Q8C22×C4311yescharacteristic
205#481—21no—
206#475C4×C4312yescomplemented
207#460C4×C4312yescomplemented
208#448—21no—
209C4×SD16—22no—
210#431C22×C4311yescharacteristic
211#431C22×C4311yescharacteristic
212#423C22×C4311yescharacteristic
213C2×#104—21no—
214C2×#104—21no—
215#391—21no—
216#389—21no—
217#387—22no—
218C4×C4⋊C4—21no—
219C4×C4⋊C4C22×C4311yescharacteristic
220#376—21no—
221C43C22×C4311yescharacteristic
222#327—22no—
223Q8⋊C8—22no—
224C43#923811yescharacteristic, direct product factor, Sylow
225C2×#41—21no—
226C22×Q8D4×C4311yescharacteristic
227C2×SD16—22no—
228C2×M16—21no—
229C4⋊Q8C2×C4×C4311yescharacteristic
230#127C2×C4×C4311yescharacteristic
231#124—21no—
232#121—21no—
233#121—21no—
234C4×Q8—21no—
235C4×Q8—21no—
236C4×Q8C2×C4×C4312yes—
237C4×Q8D4×C4312yes—
238C4×D4—21no—
239C4×D4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4D4×C4311yescharacteristic
244C2×C42—21no—
245C2×C42—21no—
246C2×C42—21no—
247C2×C42—21no—
248C2×C42D4×C4311yescharacteristic
249C2×C42D4×C4311yescharacteristic
250C2×C42C23×C4311yescharacteristic
251#106—22no—
252C4⋊C8—21no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8C2×C4×C4312yes—
256#104—42no—
257#104—42no—
258#103—22no—
259#102—22no—
260C22⋊C8—21no—
261C22⋊C8—21no—
262C4×C8—21no—
263C4×C8—21no—
264#95—22no—
265#95—22no—
266#95—22no—
267#95D4×C4312yes—
268#41—41no—
269#41—41no—
270#41—41no—
271#41—41no—
272C2×Q8—21no—
273C2×Q8—21no—
274C2×Q8—42no—
275C2×Q8C22⋊C4×C4312yes—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—41no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—22no—
285C22×C4—41no—
286C22×C4C2×D4×C4311yescharacteristic
287C22×C4C2×D4×C4311yescharacteristic
288C22×C4C2×D4×C4311yescharacteristic
289SD16—44no—
290M16—41no—
291M16—41no—
292C2×C8—22no—
293C2×C8—41no—
294C2×C8—41no—
295C4⋊C4—22no—
296C4⋊C4—22no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—42no—
301C4⋊C4—44no—
302C4⋊C4C22⋊C4×C4312yes—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C42—22no—
306C42—22no—
307C42—21no—
308C42—21no—
309C42—21no—
310C42—42no—
311C42—42no—
312C42—41no—
313C42—41no—
314C42SD16×C4312yescomplemented
315C42C22×C4×C4311yescharacteristic
316C42C2×D4×C4311yescharacteristic
317C42#41×C4311yescharacteristic
318C42#41×C4311yescharacteristic
319C23—41no—
320C23#120×C4311yescharacteristic
321Q8—22no—
322Q8—22no—
323Q8—42no—
324Q8—41no—
325Q8—41no—
326D4—42no—
327D4—41no—
328D4—41no—
329D4—81no—
330D4—81no—
331D4—81no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4C2×C22⋊C4×C4311yescharacteristic
351C2×C4C4×D4×C4311yescharacteristic
352C2×C4C4×D4×C4311yescharacteristic
353C2×C4#121×C4311yescharacteristic
354C2×C4#121×C4311yescharacteristic
355C2×C4#123×C4311yescharacteristic
356C2×C4C2×SD16×C4311yescharacteristic
357C2×C4#135×C4311yescharacteristic
358C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
359C2×C4#137×C4311yescharacteristic
360C8—42no—
361C8—81no—
362C8—81no—
363C22—21no—
364C22—21no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22C43×#38611yescharacteristic
369C22C43×#44811yescharacteristic
370C22C43×#44911yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—42no—
375C4—42no—
376C4—42no—
377C4—42no—
378C4—82no—
379C4—81no—
380C4C43×#42112yes—
381C4C4×SD16×C4311yescharacteristic
382C4C43×#44011yescharacteristic
383C4C43×#46011yescharacteristic
384C4C43×#46411yescharacteristic
385C2—21no—
386C2—21no—
387C2—161no—
388C2C43×#188011yescharacteristic
389C2C43×#189711yescharacteristic
390C2C43×#190611yescharacteristic
subgroupG/H
centerC2×C4×C43#121
commutatorC42C22×C4×C43
Frattini, cosocleC2×C42C23×C43
socleC22×C43#386
prime radicalC43×#532C22
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×#2295C2semidirect
5. C43×#1487C2semidirect
6. C43×#1303C2semidirect
7. C43×#1276C2semidirect
11. C43×#475C4semidirect
12. C43×#460C4semidirect
118. C42×C43SD16semidirect
167. #9238C43direct (N × H)
191. #2295C2×C43semidirect
194. #1487C2×C43semidirect
195. #1303C2×C43semidirect
196. #1276C2×C43semidirect
206. #475C4×C43semidirect
207. #460C4×C43semidirect
224. C43#9238direct (N × H)
314. C42SD16×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#31032
C43×#22952
C43×#19622
C43×#15022
C43×#14872
C43×#13032
C43×#12762
#923843