Finite Group Databasebeta

← C43×#9215 #24929232

Subgroups — C43×#9215 #24929232

Order 11008.

578 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#476C211yesmaximal, characteristic
2C2×C8×D4×C43C211yesmaximal, characteristic
3C43×#1990C211yesmaximal, characteristic, complemented
4C43×#1802C211yesmaximal, characteristic
5C2×C43×#333C211yesmaximal, characteristic, complemented
6C43×#1296C211yesmaximal, characteristic, complemented
7C43×#1277C211yesmaximal, characteristic, complemented
8C23×C8×C43—21no—
9C2×C4⋊Q8×C43C2211yescharacteristic
10C2×C4×D4×C43C2211yescharacteristic
11C43×#476—22no—
12C43×#476C414yescomplemented
13C8×D4×C43—22no—
14C8×D4×C43—22no—
15C2×#106×C43—21no—
16C2×C4⋊C8×C43C2211yescharacteristic
17C2×C4⋊C8×C43C2211yescharacteristic
18C2×C4⋊C8×C43C2211yescharacteristic
19C2×#102×C43—21no—
20C2×#102×C43—21no—
21C2×C22⋊C8×C43—21no—
22C2×C4×C8×C43C2211yescharacteristic
23C43×#384C2211yescharacteristic
24C43×#340—21no—
25C43×#340—21no—
26C43×#340—21no—
27C43×#333—22no—
28C22×Q8×C43—21no—
29C22×D4×C43D411yescharacteristic
30C23×C4×C43—21no—
31C22×C8×C43—24no—
32C22×C8×C43—21no—
33C22×C8×C43—21no—
34C22×C8×C43—21no—
35C22×C8×C43—42no—
36C22×C8×C43—42no—
37C22×C8×C43D411yescharacteristic
38C22×C8×C43D411yescharacteristic
39C4⋊Q8×C43—21no—
40C4⋊Q8×C43—21no—
41C4⋊Q8×C43—21no—
42C4⋊Q8×C43C2×C412yes—
43C4×D4×C43—21no—
44C4×D4×C43—21no—
45C4×D4×C43C2×C412yes—
46C4×D4×C43D412yes—
47C2×C4⋊C4×C43—21no—
48C2×C4⋊C4×C43—21no—
49C2×C4⋊C4×C43—21no—
50C2×C4⋊C4×C43—21no—
51C2×C4⋊C4×C43—21no—
52C2×C4⋊C4×C43D411yescharacteristic
53C2×C22⋊C4×C43—21no—
54C2×C42×C43C2311yescharacteristic
55#106×C43—24no—
56C4⋊C8×C43—21no—
57C4⋊C8×C43—21no—
58C4⋊C8×C43—21no—
59C4⋊C8×C43—21no—
60C4⋊C8×C43C2×C412yes—
61C4⋊C8×C43D412yes—
62#102×C43—24no—
63#102×C43—42no—
64C22⋊C8×C43—24no—
65C4×C8×C43—21no—
66C4×C8×C43—21no—
67C24×C43—21no—
68C2×Q8×C43—22no—
69C2×Q8×C43—41no—
70C2×Q8×C43—81no—
71C2×Q8×C43—81no—
72C2×D4×C43—21no—
73C2×D4×C43—21no—
74C2×D4×C43—21no—
75C2×D4×C43C22⋊C412yes—
76C2×D4×C43SD1612yes—
77C2×D4×C43Q1612yes—
78C22×C4×C43—22no—
79C22×C4×C43—22no—
80C22×C4×C43—21no—
81C22×C4×C43—41no—
82C22×C4×C43—41no—
83C22×C4×C43—41no—
84C22×C4×C43—41no—
85C22×C4×C43—41no—
86C22×C4×C43—41no—
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43#4111yescharacteristic
90C2×C8×C43—21no—
91C2×C8×C43—21no—
92C2×C8×C43—22no—
93C2×C8×C43—21no—
94C2×C8×C43—22no—
95C2×C8×C43—21no—
96C2×C8×C43—21no—
97C2×C8×C43—48no—
98C2×C8×C43—41no—
99C2×C8×C43—41no—
100C2×C8×C43—41no—
101C2×C8×C43—41no—
102C2×C8×C43—41no—
103C2×C8×C43—41no—
104C2×C8×C43—41no—
105C2×C8×C43SD1612yes—
106C4⋊C4×C43—21no—
107C4⋊C4×C43—22no—
108C4⋊C4×C43—22no—
109C4⋊C4×C43—41no—
110C4⋊C4×C43—41no—
111C4⋊C4×C43—41no—
112C4⋊C4×C43—41no—
113C4⋊C4×C43—41no—
114C4⋊C4×C43—41no—
115C4⋊C4×C43—81no—
116C4⋊C4×C43C22⋊C412yes—
117C22⋊C4×C43—22no—
118C22⋊C4×C43—22no—
119C42×C43C22×C411yescharacteristic
120C42×C43C2×D411yescharacteristic
121C42×C43C2×D411yescharacteristic
122C42×C43#4111yescharacteristic
123C23×C43—22no—
124C23×C43—22no—
125C23×C43—22no—
126C23×C43—41no—
127C23×C43—41no—
128C23×C43—41no—
129C23×C43—41no—
130C23×C43#12111yescharacteristic
131Q8×C43—82no—
132Q8×C43—82no—
133D4×C43—22no—
134D4×C43—22no—
135D4×C43—22no—
136D4×C43#10314yes—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—22no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—42no—
143C2×C4×C43—42no—
144C2×C4×C43—42no—
145C2×C4×C43—42no—
146C2×C4×C43—42no—
147C2×C4×C43—81no—
148C2×C4×C43—81no—
149C2×C4×C43—81no—
150C2×C4×C43—81no—
151C2×C4×C43—81no—
152C2×C4×C43C2×C22⋊C411yescharacteristic
153C2×C4×C43C4×D411yescharacteristic
154C2×C4×C43C4×D411yescharacteristic
155C2×C4×C43#12011yescharacteristic
156C2×C4×C43#12111yescharacteristic
157C2×C4×C43#12311yescharacteristic
158C2×C4×C43C2×SD1611yescharacteristic
159C2×C4×C43C2×SD1611yescharacteristic
160C2×C4×C43C2×Q1611yescharacteristic
161C2×C4×C43#13511yescharacteristic
162C2×C4×C43#13511yescharacteristic
163C2×C4×C43#13511yescharacteristic
164C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C43#13711yescharacteristic
166C8×C43—22no—
167C8×C43—42no—
168C8×C43—42no—
169C8×C43—41no—
170C8×C43—81no—
171#9215C4311yesmaximal, characteristic, direct product factor, Sylow
172C22×C43—24no—
173C22×C43—42no—
174C22×C43—42no—
175C22×C43—42no—
176C22×C43—42no—
177C22×C43—42no—
178C22×C43—42no—
179C22×C43#38611yescharacteristic
180C22×C43#46111yescharacteristic
181C22×C43#46311yescharacteristic
182C22×C43#46511yescharacteristic
183C22×C43#46711yescharacteristic
184C22×C43#47111yescharacteristic
185C22×C43#47211yescharacteristic
186C4×C43—21no—
187C4×C43—21no—
188C4×C43—42no—
189C4×C43—82no—
190C4×C43—161no—
191C4×C43C2×#10311yescharacteristic
192C4×C43#41611yescharacteristic
193C4×C43C4×SD1611yescharacteristic
194C4×C43#44011yescharacteristic
195C4×C43#45011yescharacteristic
196C4×C43#45211yescharacteristic
197C4×C43#46511yescharacteristic
198C4×C43#46711yescharacteristic
199C2×#476C2×C4311yescharacteristic
200C2×C8×D4C2×C4311yescharacteristic
201#1990C2×C4311yescharacteristic, complemented
202#1802C2×C4311yescharacteristic
203C2×#333C2×C4311yescharacteristic, complemented
204#1296C2×C4311yescharacteristic, complemented
205#1277C2×C4311yescharacteristic, complemented
206C2×C43—44no—
207C2×C43#167111yescharacteristic
208C2×C43#167511yescharacteristic
209C2×C43#167711yescharacteristic
210C2×C43#168311yescharacteristic
211C2×C43#187711yescharacteristic
212C2×C43#189211yescharacteristic
213C2×C43#190711yescharacteristic
214C23×C8—21no—
215C2×C4⋊Q8C22×C4311yescharacteristic
216C2×C4×D4C22×C4311yescharacteristic
217#476—22no—
218#476C4×C4314yescomplemented
219C8×D4—22no—
220C8×D4—22no—
221C2×#106—21no—
222C2×C4⋊C8C22×C4311yescharacteristic
223C2×C4⋊C8C22×C4311yescharacteristic
224C2×C4⋊C8C22×C4311yescharacteristic
225C2×#102—21no—
226C2×#102—21no—
227C2×C22⋊C8—21no—
228C2×C4×C8C22×C4311yescharacteristic
229#384C22×C4311yescharacteristic
230#340—21no—
231#340—21no—
232#340—21no—
233#333—22no—
234C43#921511yescharacteristic, direct product factor, Sylow
235C22×Q8—21no—
236C22×D4D4×C4311yescharacteristic
237C23×C4—21no—
238C22×C8—24no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—42no—
243C22×C8—42no—
244C22×C8D4×C4311yescharacteristic
245C22×C8D4×C4311yescharacteristic
246C4⋊Q8—21no—
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8C2×C4×C4312yes—
250C4×D4—21no—
251C4×D4—21no—
252C4×D4C2×C4×C4312yes—
253C4×D4D4×C4312yes—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4D4×C4311yescharacteristic
260C2×C22⋊C4—21no—
261C2×C42C23×C4311yescharacteristic
262#106—24no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8C2×C4×C4312yes—
268C4⋊C8D4×C4312yes—
269#102—24no—
270#102—42no—
271C22⋊C8—24no—
272C4×C8—21no—
273C4×C8—21no—
274C24—21no—
275C2×Q8—22no—
276C2×Q8—41no—
277C2×Q8—81no—
278C2×Q8—81no—
279C2×D4—21no—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4C22⋊C4×C4312yes—
283C2×D4SD16×C4312yes—
284C2×D4Q16×C4312yes—
285C22×C4—21no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4C2×D4×C4311yescharacteristic
295C22×C4C2×D4×C4311yescharacteristic
296C22×C4#41×C4311yescharacteristic
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—22no—
300C2×C8—21no—
301C2×C8—22no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—48no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8SD16×C4312yes—
313C4⋊C4—21no—
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—81no—
323C4⋊C4C22⋊C4×C4312yes—
324C22⋊C4—22no—
325C22⋊C4—22no—
326C42C22×C4×C4311yescharacteristic
327C42C2×D4×C4311yescharacteristic
328C42C2×D4×C4311yescharacteristic
329C42#41×C4311yescharacteristic
330C23—22no—
331C23—22no—
332C23—22no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23#121×C4311yescharacteristic
338Q8—82no—
339Q8—82no—
340D4—22no—
341D4—22no—
342D4—22no—
343D4#103×C4314yes—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—22no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4C2×C22⋊C4×C4311yescharacteristic
360C2×C4C4×D4×C4311yescharacteristic
361C2×C4C4×D4×C4311yescharacteristic
362C2×C4#120×C4311yescharacteristic
363C2×C4#121×C4311yescharacteristic
364C2×C4#123×C4311yescharacteristic
365C2×C4C2×SD16×C4311yescharacteristic
366C2×C4C2×SD16×C4311yescharacteristic
367C2×C4C2×Q16×C4311yescharacteristic
368C2×C4#135×C4311yescharacteristic
369C2×C4#135×C4311yescharacteristic
370C2×C4#135×C4311yescharacteristic
371C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
372C2×C4#137×C4311yescharacteristic
373C8—22no—
374C8—42no—
375C8—42no—
376C8—41no—
377C8—81no—
378C22—24no—
379C22—42no—
380C22—42no—
381C22—42no—
382C22—42no—
383C22—42no—
384C22—42no—
385C22C43×#38611yescharacteristic
386C22C43×#46111yescharacteristic
387C22C43×#46311yescharacteristic
388C22C43×#46511yescharacteristic
389C22C43×#46711yescharacteristic
390C22C43×#47111yescharacteristic
391C22C43×#47211yescharacteristic
392C4—21no—
393C4—21no—
394C4—42no—
395C4—82no—
396C4—161no—
397C4C2×#103×C4311yescharacteristic
398C4C43×#41611yescharacteristic
399C4C4×SD16×C4311yescharacteristic
400C4C43×#44011yescharacteristic
401C4C43×#45011yescharacteristic
402C4C43×#45211yescharacteristic
403C4C43×#46511yescharacteristic
404C4C43×#46711yescharacteristic
405C2—44no—
406C2C43×#167111yescharacteristic
407C2C43×#167511yescharacteristic
408C2C43×#167711yescharacteristic
409C2C43×#168311yescharacteristic
410C2C43×#187711yescharacteristic
411C2C43×#189211yescharacteristic
412C2C43×#190711yescharacteristic
subgroupG/H
center, socleC23×C43#121
commutatorC42C22×C4×C43
Frattini, cosocleC2×C42C23×C43
prime radicalC22×D4×C43D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
3. C43×#1990C2semidirect
5. C2×C43×#333C2semidirect
6. C43×#1296C2semidirect
7. C43×#1277C2semidirect
12. C43×#476C4semidirect
171. #9215C43direct (N × H)
201. #1990C2×C43semidirect
203. C2×#333C2×C43semidirect
204. #1296C2×C43semidirect
205. #1277C2×C43semidirect
218. #476C4×C43semidirect
234. C43#9215direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#4762
C2×C8×D4×C432
C43×#19902
C43×#18022
C2×C43×#3332
C43×#12962
C43×#12772
#921543