Finite Group Databasebeta

← C43×#10485 #24930502

Subgroups — C43×#10485 #24930502

Order 11008.

490 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#474C211yesmaximal, characteristic
2C43×#1956C211yesmaximal, characteristic, complemented
3C43×#1954C211yesmaximal, characteristic
4C43×#1802C211yesmaximal, characteristic
5C2×C43×#335C211yesmaximal, characteristic, complemented
6C2×C43×#332C211yesmaximal, characteristic, complemented
7C43×#1296C211yesmaximal, characteristic, complemented
8C2×C4⋊Q8×C43C2211yescharacteristic
9C2×C4×D4×C43C2211yescharacteristic
10C43×#474—22no—
11C43×#474—22no—
12C2×#107×C43—21no—
13C2×C4⋊C8×C43C2211yescharacteristic
14C2×C4⋊C8×C43C2211yescharacteristic
15C2×C4⋊C8×C43C2211yescharacteristic
16C2×#103×C43—21no—
17C2×#103×C43—21no—
18C2×#102×C43—21no—
19C2×#102×C43—21no—
20C2×C22⋊C8×C43—21no—
21C2×C22⋊C8×C43—21no—
22C2×C4×C8×C43C2211yescharacteristic
23C43×#384C2211yescharacteristic
24C43×#340—21no—
25C43×#335—22no—
26C43×#332—22no—
27C22×Q8×C43—21no—
28C22×D4×C43D411yescharacteristic
29C23×C4×C43—21no—
30C22×C8×C43—21no—
31C22×C8×C43—21no—
32C22×C8×C43—21no—
33C22×C8×C43D411yescharacteristic
34C22×C8×C43D411yescharacteristic
35C4⋊Q8×C43—21no—
36C4⋊Q8×C43—21no—
37C4⋊Q8×C43—21no—
38C4⋊Q8×C43D412yes—
39C4×D4×C43—21no—
40C4×D4×C43—21no—
41C4×D4×C43—21no—
42C4×D4×C43—21no—
43C2×C4⋊C4×C43—21no—
44C2×C4⋊C4×C43—21no—
45C2×C4⋊C4×C43—21no—
46C2×C4⋊C4×C43—21no—
47C2×C4⋊C4×C43—21no—
48C2×C4⋊C4×C43D411yescharacteristic
49C2×C22⋊C4×C43—21no—
50C2×C42×C43C2311yescharacteristic
51#107×C43—24no—
52C4⋊C8×C43—21no—
53C4⋊C8×C43—21no—
54C4⋊C8×C43—21no—
55C4⋊C8×C43—21no—
56C4⋊C8×C43—21no—
57C4⋊C8×C43D412yes—
58#103×C43—42no—
59#103×C43—42no—
60#102×C43—24no—
61#102×C43—42no—
62C22⋊C8×C43—42no—
63C22⋊C8×C43—42no—
64C4×C8×C43—21no—
65C4×C8×C43—21no—
66C24×C43—21no—
67C2×Q8×C43—22no—
68C2×Q8×C43—41no—
69C2×Q8×C43—41no—
70C2×Q8×C43—41no—
71C2×Q8×C43—41no—
72C2×Q8×C43—41no—
73C2×D4×C43—21no—
74C2×D4×C43—21no—
75C2×D4×C43—21no—
76C2×D4×C43—21no—
77C2×D4×C43—21no—
78C2×D4×C43Q1612yes—
79C22×C4×C43—21no—
80C22×C4×C43—41no—
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×C43—41no—
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43#4111yescharacteristic
91C2×C8×C43—21no—
92C2×C8×C43—21no—
93C2×C8×C43—22no—
94C2×C8×C43—21no—
95C2×C8×C43—21no—
96C2×C8×C43—21no—
97C2×C8×C43—41no—
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×C43D812yes—
106C4⋊C4×C43—22no—
107C4⋊C4×C43—21no—
108C4⋊C4×C43—22no—
109C4⋊C4×C43—21no—
110C4⋊C4×C43—41no—
111C4⋊C4×C43—41no—
112C4⋊C4×C43—41no—
113C4⋊C4×C43—41no—
114C4⋊C4×C43—41no—
115C4⋊C4×C43—41no—
116C4⋊C4×C43—81no—
117C22⋊C4×C43—41no—
118C22⋊C4×C43—41no—
119C42×C43C2×D411yescharacteristic
120C42×C43C2×D411yescharacteristic
121C42×C43#4111yescharacteristic
122C42×C43#4111yescharacteristic
123C23×C43—22no—
124C23×C43—41no—
125C23×C43—41no—
126C23×C43—41no—
127C23×C43—41no—
128C23×C43—41no—
129C23×C43—41no—
130C23×C43#12111yescharacteristic
131Q8×C43—42no—
132Q8×C43—42no—
133Q8×C43—81no—
134Q8×C43—81no—
135D4×C43—22no—
136D4×C43—22no—
137D4×C43—41no—
138D4×C43—41no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—41no—
142C2×C4×C43—42no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—81no—
146C2×C4×C43—81no—
147C2×C4×C43—81no—
148C2×C4×C43—81no—
149C2×C4×C43—81no—
150C2×C4×C43—81no—
151C2×C4×C43—81no—
152C2×C4×C43—81no—
153C2×C4×C43—81no—
154C2×C4×C43#12011yescharacteristic
155C2×C4×C43#12111yescharacteristic
156C2×C4×C43#12111yescharacteristic
157C2×C4×C43#12311yescharacteristic
158C2×C4×C43#12311yescharacteristic
159C2×C4×C43#12411yescharacteristic
160C2×C4×C43C2×D811yescharacteristic
161C2×C4×C43C2×Q1611yescharacteristic
162C2×C4×C43#13511yescharacteristic
163C2×C4×C43#13511yescharacteristic
164C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C43#13711yescharacteristic
168C8×C43—22no—
169C8×C43—42no—
170C8×C43—41no—
171C8×C43—81no—
172C8×C43—81no—
173#10485C4311yesmaximal, characteristic, direct product factor, Sylow
174C22×C43—42no—
175C22×C43—42no—
176C22×C43—42no—
177C22×C43—81no—
178C22×C43—81no—
179C22×C43—81no—
180C22×C43—81no—
181C22×C43#39411yescharacteristic
182C22×C43#45911yescharacteristic
183C22×C43#46311yescharacteristic
184C22×C43#46711yescharacteristic
185C22×C43#46811yescharacteristic
186C22×C43#47111yescharacteristic
187C22×C43#47311yescharacteristic
188C4×C43—21no—
189C4×C43—21no—
190C4×C43—81no—
191C4×C43—82no—
192C4×C43—161no—
193C4×C43#44911yescharacteristic
194C4×C43#45111yescharacteristic
195C4×C43#45911yescharacteristic
196C4×C43#46311yescharacteristic
197C4×C43#46611yescharacteristic
198C4×C43#46911yescharacteristic
199C4×C43#48411yescharacteristic
200C4×C43#48511yescharacteristic
201C2×#474C2×C4311yescharacteristic
202#1956C2×C4311yescharacteristic, complemented
203#1954C2×C4311yescharacteristic
204#1802C2×C4311yescharacteristic
205C2×#335C2×C4311yescharacteristic, complemented
206C2×#332C2×C4311yescharacteristic, complemented
207#1296C2×C4311yescharacteristic, complemented
208C2×C43—82no—
209C2×C43#166911yescharacteristic
210C2×C43#168311yescharacteristic
211C2×C43#168511yescharacteristic
212C2×C43#169911yescharacteristic
213C2×C43#203611yescharacteristic
214C2×C43#205211yescharacteristic
215C2×C43#205411yescharacteristic
216C2×C4⋊Q8C22×C4311yescharacteristic
217C2×C4×D4C22×C4311yescharacteristic
218#474—22no—
219#474—22no—
220C2×#107—21no—
221C2×C4⋊C8C22×C4311yescharacteristic
222C2×C4⋊C8C22×C4311yescharacteristic
223C2×C4⋊C8C22×C4311yescharacteristic
224C2×#103—21no—
225C2×#103—21no—
226C2×#102—21no—
227C2×#102—21no—
228C2×C22⋊C8—21no—
229C2×C22⋊C8—21no—
230C2×C4×C8C22×C4311yescharacteristic
231#384C22×C4311yescharacteristic
232#340—21no—
233#335—22no—
234#332—22no—
235C43#1048511yescharacteristic, direct product factor, Sylow
236C22×Q8—21no—
237C22×D4D4×C4311yescharacteristic
238C23×C4—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8D4×C4311yescharacteristic
243C22×C8D4×C4311yescharacteristic
244C4⋊Q8—21no—
245C4⋊Q8—21no—
246C4⋊Q8—21no—
247C4⋊Q8D4×C4312yes—
248C4×D4—21no—
249C4×D4—21no—
250C4×D4—21no—
251C4×D4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4D4×C4311yescharacteristic
258C2×C22⋊C4—21no—
259C2×C42C23×C4311yescharacteristic
260#107—24no—
261C4⋊C8—21no—
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8D4×C4312yes—
267#103—42no—
268#103—42no—
269#102—24no—
270#102—42no—
271C22⋊C8—42no—
272C22⋊C8—42no—
273C4×C8—21no—
274C4×C8—21no—
275C24—21no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4Q16×C4312yes—
288C22×C4—21no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4C2×D4×C4311yescharacteristic
298C22×C4C2×D4×C4311yescharacteristic
299C22×C4#41×C4311yescharacteristic
300C2×C8—21no—
301C2×C8—21no—
302C2×C8—22no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—21no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8D8×C4312yes—
315C4⋊C4—22no—
316C4⋊C4—21no—
317C4⋊C4—22no—
318C4⋊C4—21no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—81no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C42C2×D4×C4311yescharacteristic
329C42C2×D4×C4311yescharacteristic
330C42#41×C4311yescharacteristic
331C42#41×C4311yescharacteristic
332C23—22no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23#121×C4311yescharacteristic
340Q8—42no—
341Q8—42no—
342Q8—81no—
343Q8—81no—
344D4—22no—
345D4—22no—
346D4—41no—
347D4—41no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4#120×C4311yescharacteristic
364C2×C4#121×C4311yescharacteristic
365C2×C4#121×C4311yescharacteristic
366C2×C4#123×C4311yescharacteristic
367C2×C4#123×C4311yescharacteristic
368C2×C4#124×C4311yescharacteristic
369C2×C4C2×D8×C4311yescharacteristic
370C2×C4C2×Q16×C4311yescharacteristic
371C2×C4#135×C4311yescharacteristic
372C2×C4#135×C4311yescharacteristic
373C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
374C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
375C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
376C2×C4#137×C4311yescharacteristic
377C8—22no—
378C8—42no—
379C8—41no—
380C8—81no—
381C8—81no—
382C22—42no—
383C22—42no—
384C22—42no—
385C22—81no—
386C22—81no—
387C22—81no—
388C22—81no—
389C22C43×#39411yescharacteristic
390C22C43×#45911yescharacteristic
391C22C43×#46311yescharacteristic
392C22C43×#46711yescharacteristic
393C22C43×#46811yescharacteristic
394C22C43×#47111yescharacteristic
395C22C43×#47311yescharacteristic
396C4—21no—
397C4—21no—
398C4—81no—
399C4—82no—
400C4—161no—
401C4C43×#44911yescharacteristic
402C4C43×#45111yescharacteristic
403C4C43×#45911yescharacteristic
404C4C43×#46311yescharacteristic
405C4C43×#46611yescharacteristic
406C4C43×#46911yescharacteristic
407C4C43×#48411yescharacteristic
408C4C43×#48511yescharacteristic
409C2—82no—
410C2C43×#166911yescharacteristic
411C2C43×#168311yescharacteristic
412C2C43×#168511yescharacteristic
413C2C43×#169911yescharacteristic
414C2C43×#203611yescharacteristic
415C2C43×#205211yescharacteristic
416C2C43×#205411yescharacteristic
subgroupG/H
center, socleC23×C43#121
commutator, Frattini, cosocleC2×C42C23×C43
prime radicalC22×D4×C43D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#1956C2semidirect
5. C2×C43×#335C2semidirect
6. C2×C43×#332C2semidirect
7. C43×#1296C2semidirect
173. #10485C43direct (N × H)
202. #1956C2×C43semidirect
205. C2×#335C2×C43semidirect
206. C2×#332C2×C43semidirect
207. #1296C2×C43semidirect
235. C43#10485direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#4742
C43×#19562
C43×#19542
C43×#18022
C2×C43×#3352
C2×C43×#3322
C43×#12962
#1048543