Finite Group Databasebeta

← C43×#9112 #24929129

Subgroups — C43×#9112 #24929129

Order 11008.

632 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#431C211yesmaximal, characteristic
2C43×#2855C211yesmaximal, characteristic
3C2×C43×#328C212yesmaximal
4C43×#1434C211yesmaximal, characteristic
5C43×#1294C212yesmaximal
6C2×C22⋊Q8×C43C2211yescharacteristic
7C22×C42×C43C2211yescharacteristic
8C43×#431—24no—
9C2×C4⋊C8×C43—21no—
10C2×C22⋊C8×C43C2212yes—
11C2×C4×C8×C43—21no—
12C43×#391C411yescharacteristic, complemented
13C43×#391C411yescharacteristic, complemented
14C43×#389C411yescharacteristic, complemented
15C43×#389C411yescharacteristic, complemented
16C43×#387—21no—
17C43×#387—21no—
18C43×#385—21no—
19C43×#381—21no—
20C43×#380C2211yescharacteristic
21C2×#95×C43—21no—
22C2×#95×C43—21no—
23C2×#95×C43C2212yes—
24C43×#328—24no—
25C22×Q8×C43C2×C411yescharacteristic
26C23×C4×C43—22no—
27C23×C4×C43D411yescharacteristic
28C23×C4×C43D411yescharacteristic
29C23×C4×C43C2311yescharacteristic
30C22×C8×C43—22no—
31C22⋊Q8×C43—22no—
32C22⋊Q8×C43—22no—
33C2×C4⋊C4×C43—21no—
34C2×C4⋊C4×C43—21no—
35C2×C4⋊C4×C43—21no—
36C2×C4⋊C4×C43C2×C411yescharacteristic
37C2×C4⋊C4×C43C2×C411yescharacteristic
38C2×C4⋊C4×C43C2×C411yescharacteristic
39C2×C22⋊C4×C43—21no—
40C2×C22⋊C4×C43—21no—
41C2×C42×C43—22no—
42C2×C42×C43—22no—
43C2×C42×C43C2×C411yescharacteristic
44C2×C42×C43C2×C411yescharacteristic
45C2×C42×C43D411yescharacteristic
46C2×C42×C43D411yescharacteristic
47C4⋊C8×C43—24no—
48C22⋊C8×C43—22no—
49C22⋊C8×C43D414yes—
50C4×C8×C43—24no—
51#95×C43—24no—
52#95×C43—21no—
53#95×C43—21no—
54#95×C43—21no—
55#95×C43—21no—
56#95×C43—21no—
57#95×C43—21no—
58#95×C43—21no—
59#95×C43—22no—
60#95×C43—22no—
61#95×C43—42no—
62C24×C43C2×D411yescharacteristic
63C2×Q8×C43—22no—
64C2×Q8×C43—41no—
65C2×Q8×C43—41no—
66C22×C4×C43—22no—
67C22×C4×C43—24no—
68C22×C4×C43—21no—
69C22×C4×C43—21no—
70C22×C4×C43—21no—
71C22×C4×C43—21no—
72C22×C4×C43—22no—
73C22×C4×C43—22no—
74C22×C4×C43—22no—
75C22×C4×C43—41no—
76C22×C4×C43—41no—
77C22×C4×C43—41no—
78C22×C4×C43—42no—
79C22×C4×C43—42no—
80C22×C4×C43—42no—
81C22×C4×C43—42no—
82C22×C4×C43—42no—
83C22×C4×C43—42no—
84C22×C4×C43C22⋊C411yescharacteristic
85C22×C4×C43C22⋊C411yescharacteristic
86C22×C4×C43C22⋊C411yescharacteristic
87C22×C4×C43C22⋊C411yescharacteristic
88C22×C4×C43SD1612yes—
89C22×C4×C43Q1612yes—
90C22×C4×C43C22×C411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43C2×D412yes—
93C22×C4×C43#4112yes—
94C2×C8×C43—24no—
95C2×C8×C43—42no—
96C2×C8×C43—42no—
97C4⋊C4×C43—22no—
98C4⋊C4×C43—41no—
99C4⋊C4×C43—41no—
100C4⋊C4×C43—42no—
101C4⋊C4×C43—42no—
102C4⋊C4×C43—41no—
103C4⋊C4×C43—41no—
104C22⋊C4×C43—42no—
105C22⋊C4×C43—42no—
106C42×C43—22no—
107C42×C43—22no—
108C42×C43—21no—
109C42×C43—21no—
110C42×C43—21no—
111C42×C43—21no—
112C23×C43—21no—
113C23×C43—21no—
114C23×C43—21no—
115C23×C43—21no—
116C23×C43C2×C22⋊C411yescharacteristic
117C23×C43#12112yes—
118C23×C43C2×SD1611yescharacteristic
119C23×C43C2×Q1611yescharacteristic
120C23×C43#13512yes—
121Q8×C43—82no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—24no—
133C2×C4×C43—24no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—42no—
138C2×C4×C43—42no—
139C2×C4×C43—44no—
140C2×C4×C43—44no—
141C2×C4×C43—44no—
142C2×C4×C43—44no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—41no—
154C2×C4×C43—41no—
155C2×C4×C43—82no—
156C2×C4×C43—82no—
157C2×C4×C43—82no—
158C2×C4×C43—82no—
159C2×C4×C43#10312yes—
160C2×C4×C43#10312yes—
161C2×C4×C43#10412yes—
162C2×C4×C43C4×D412yes—
163C2×C4×C43#12011yescharacteristic
164C2×C4×C43#12311yescharacteristic
165C8×C43—44no—
166#9112C4311yesmaximal, characteristic, direct product factor, Sylow
167C22×C43—22no—
168C22×C43—22no—
169C22×C43—22no—
170C22×C43—21no—
171C22×C43—21no—
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—22no—
175C22×C43#38611yescharacteristic
176C22×C43#41011yescharacteristic
177C22×C43#41011yescharacteristic
178C22×C43C2×#10311yescharacteristic
179C22×C43#41611yescharacteristic
180C22×C43C2×#10411yescharacteristic
181C22×C43#42111yescharacteristic
182C22×C43#46512yes—
183C22×C43#46712yes—
184C4×C43—22no—
185C4×C43—22no—
186C4×C43—22no—
187C4×C43—21no—
188C4×C43—22no—
189C4×C43—21no—
190C4×C43—41no—
191C4×C43—84no—
192C4×C43—81no—
193C4×C43—81no—
194C4×C43—81no—
195C4×C43—81no—
196C2×#431C2×C4311yescharacteristic
197#2855C2×C4311yescharacteristic
198C2×#328C2×C4312yes—
199#1434C2×C4311yescharacteristic
200#1294C2×C4312yes—
201C2×C43—22no—
202C2×C43—22no—
203C2×C43#150011yescharacteristic
204C2×C43#150311yescharacteristic
205C2×C43#151811yescharacteristic
206C2×C43#152111yescharacteristic
207C2×C43#187111yescharacteristic
208C2×C43#189211yescharacteristic
209C2×C43#189911yescharacteristic
210C2×C22⋊Q8C22×C4311yescharacteristic
211C22×C42C22×C4311yescharacteristic
212#431—24no—
213C2×C4⋊C8—21no—
214C2×C22⋊C8C22×C4312yes—
215C2×C4×C8—21no—
216#391C4×C4311yescharacteristic, complemented
217#391C4×C4311yescharacteristic, complemented
218#389C4×C4311yescharacteristic, complemented
219#389C4×C4311yescharacteristic, complemented
220#387—21no—
221#387—21no—
222#385—21no—
223#381—21no—
224#380C22×C4311yescharacteristic
225C2×#95—21no—
226C2×#95—21no—
227C2×#95C22×C4312yes—
228#328—24no—
229C43#911211yescharacteristic, direct product factor, Sylow
230C22×Q8C2×C4×C4311yescharacteristic
231C23×C4—22no—
232C23×C4D4×C4311yescharacteristic
233C23×C4D4×C4311yescharacteristic
234C23×C4C23×C4311yescharacteristic
235C22×C8—22no—
236C22⋊Q8—22no—
237C22⋊Q8—22no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4C2×C4×C4311yescharacteristic
242C2×C4⋊C4C2×C4×C4311yescharacteristic
243C2×C4⋊C4C2×C4×C4311yescharacteristic
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C42—22no—
247C2×C42—22no—
248C2×C42C2×C4×C4311yescharacteristic
249C2×C42C2×C4×C4311yescharacteristic
250C2×C42D4×C4311yescharacteristic
251C2×C42D4×C4311yescharacteristic
252C4⋊C8—24no—
253C22⋊C8—22no—
254C22⋊C8D4×C4314yes—
255C4×C8—24no—
256#95—24no—
257#95—21no—
258#95—21no—
259#95—21no—
260#95—21no—
261#95—21no—
262#95—21no—
263#95—21no—
264#95—22no—
265#95—22no—
266#95—42no—
267C24C2×D4×C4311yescharacteristic
268C2×Q8—22no—
269C2×Q8—41no—
270C2×Q8—41no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—24no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4C22⋊C4×C4311yescharacteristic
290C22×C4C22⋊C4×C4311yescharacteristic
291C22×C4C22⋊C4×C4311yescharacteristic
292C22×C4C22⋊C4×C4311yescharacteristic
293C22×C4SD16×C4312yes—
294C22×C4Q16×C4312yes—
295C22×C4C22×C4×C4311yescharacteristic
296C22×C4C2×D4×C4311yescharacteristic
297C22×C4C2×D4×C4312yes—
298C22×C4#41×C4312yes—
299C2×C8—24no—
300C2×C8—42no—
301C2×C8—42no—
302C4⋊C4—22no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—42no—
306C4⋊C4—42no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C22⋊C4—42no—
310C22⋊C4—42no—
311C42—22no—
312C42—22no—
313C42—21no—
314C42—21no—
315C42—21no—
316C42—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23C2×C22⋊C4×C4311yescharacteristic
322C23#121×C4312yes—
323C23C2×SD16×C4311yescharacteristic
324C23C2×Q16×C4311yescharacteristic
325C23#135×C4312yes—
326Q8—82no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—24no—
338C2×C4—24no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—44no—
345C2×C4—44no—
346C2×C4—44no—
347C2×C4—44no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—82no—
361C2×C4—82no—
362C2×C4—82no—
363C2×C4—82no—
364C2×C4#103×C4312yes—
365C2×C4#103×C4312yes—
366C2×C4#104×C4312yes—
367C2×C4C4×D4×C4312yes—
368C2×C4#120×C4311yescharacteristic
369C2×C4#123×C4311yescharacteristic
370C8—44no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—22no—
379C22C43×#38611yescharacteristic
380C22C43×#41011yescharacteristic
381C22C43×#41011yescharacteristic
382C22C2×#103×C4311yescharacteristic
383C22C43×#41611yescharacteristic
384C22C2×#104×C4311yescharacteristic
385C22C43×#42111yescharacteristic
386C22C43×#46512yes—
387C22C43×#46712yes—
388C4—22no—
389C4—22no—
390C4—22no—
391C4—21no—
392C4—22no—
393C4—21no—
394C4—41no—
395C4—84no—
396C4—81no—
397C4—81no—
398C4—81no—
399C4—81no—
400C2—22no—
401C2—22no—
402C2C43×#150011yescharacteristic
403C2C43×#150311yescharacteristic
404C2C43×#151811yescharacteristic
405C2C43×#152111yescharacteristic
406C2C43×#187111yescharacteristic
407C2C43×#189211yescharacteristic
408C2C43×#189911yescharacteristic
subgroupG/H
center, socleC23×C43C2×C22⋊C4
commutatorC22×C4C22×C4×C43
Frattini, cosocleC23×C4C23×C43
prime radicalC24×C43C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C43 ◁ C22×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
12. C43×#391C4semidirect
13. C43×#391C4semidirect
14. C43×#389C4semidirect
15. C43×#389C4semidirect
166. #9112C43direct (N × H)
216. #391C4×C43semidirect
217. #391C4×C43semidirect
218. #389C4×C43semidirect
219. #389C4×C43semidirect
229. C43#9112direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#4312
C43×#28552
C2×C43×#3282
C43×#14342
C43×#12942
#911243