Finite Group Databasebeta

← C43×#10539 #24930556

Subgroups — C43×#10539 #24930556

Order 11008.

490 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#486C211yesmaximal, characteristic
2C43×#1987C211yesmaximal, characteristic, complemented
3C43×#1982C211yesmaximal, characteristic
4C43×#1939C211yesmaximal, characteristic, complemented
5C2×C43×#333C211yesmaximal, characteristic, complemented
6C2×C43×#331C211yesmaximal, characteristic
7C43×#1277C211yesmaximal, characteristic, complemented
8C2×C4⋊Q8×C43C2211yescharacteristic
9C2×#127×C43C2211yescharacteristic
10C43×#486—22no—
11C43×#486—22no—
12C2×C4⋊C8×C43—21no—
13C2×C4⋊C8×C43C2211yescharacteristic
14C2×C4⋊C8×C43C2211yescharacteristic
15C2×C4⋊C8×C43C2211yescharacteristic
16C2×#102×C43—21no—
17C2×#102×C43—21no—
18C2×#102×C43—21no—
19C2×#102×C43—21no—
20C2×C4×C8×C43C2211yescharacteristic
21C4×C4⋊C4×C43C2211yescharacteristic
22C43×#340—21no—
23C43×#340—21no—
24C43×#336—21no—
25C43×#333—22no—
26C43×#331—22no—
27C22×Q8×C43—21no—
28C22×D4×C43—21no—
29C22×D4×C43—21no—
30C22×D4×C43—21no—
31C22×C8×C43—21no—
32C22×C8×C43—21no—
33C22×C8×C43—21no—
34C22×C8×C43D411yescharacteristic
35C22×C8×C43D411yescharacteristic
36C4⋊Q8×C43—21no—
37C4⋊Q8×C43—21no—
38C4⋊Q8×C43—21no—
39C4⋊Q8×C43D412yes—
40#127×C43—21no—
41#127×C43—21no—
42#127×C43—21no—
43#127×C43D412yes—
44C2×C4⋊C4×C43—21no—
45C2×C4⋊C4×C43—21no—
46C2×C4⋊C4×C43D411yescharacteristic
47C2×C4⋊C4×C43D411yescharacteristic
48C2×C42×C43—21no—
49C2×C42×C43C2311yescharacteristic
50C4⋊C8×C43—21no—
51C4⋊C8×C43—21no—
52C4⋊C8×C43—21no—
53C4⋊C8×C43—21no—
54C4⋊C8×C43—21no—
55C4⋊C8×C43—21no—
56C4⋊C8×C43—42no—
57#102×C43—24no—
58#102×C43—24no—
59#102×C43—42no—
60#102×C43—42no—
61C4×C8×C43—21no—
62C4×C8×C43—21no—
63#95×C43—21no—
64C24×C43—41no—
65C2×Q8×C43—22no—
66C2×Q8×C43—41no—
67C2×Q8×C43—81no—
68C2×Q8×C43—81no—
69C2×D4×C43—22no—
70C2×D4×C43—22no—
71C2×D4×C43—22no—
72C2×D4×C43—41no—
73C2×D4×C43—41no—
74C2×D4×C43—41no—
75C2×D4×C43—41no—
76C2×D4×C43—41no—
77C2×D4×C43—41no—
78C2×D4×C43—41no—
79C2×D4×C43—41no—
80C2×D4×C43—41no—
81C2×D4×C43—41no—
82C2×D4×C43—41no—
83C2×D4×C43—81no—
84C2×D4×C43—81no—
85C22×C4×C43—21no—
86C22×C4×C43—21no—
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—21no—
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×C43—41no—
106C4⋊C4×C43—21no—
107C4⋊C4×C43—22no—
108C4⋊C4×C43—22no—
109C4⋊C4×C43—21no—
110C4⋊C4×C43—21no—
111C4⋊C4×C43—41no—
112C4⋊C4×C43—41no—
113C4⋊C4×C43SD1612yes—
114C42×C43—41no—
115C42×C43—41no—
116C42×C43C2×D411yescharacteristic
117C42×C43C2×D411yescharacteristic
118C42×C43#4111yescharacteristic
119C42×C43#4111yescharacteristic
120C23×C43—42no—
121C23×C43—81no—
122C23×C43—81no—
123C23×C43—81no—
124C23×C43—81no—
125C23×C43—81no—
126C23×C43—81no—
127C23×C43#12111yescharacteristic
128Q8×C43—82no—
129Q8×C43—82no—
130D4×C43—42no—
131D4×C43—42no—
132D4×C43—42no—
133D4×C43—42no—
134D4×C43—82no—
135D4×C43—82no—
136D4×C43—81no—
137D4×C43—81no—
138D4×C43—81no—
139D4×C43—81no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—22no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—42no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—81no—
150C2×C4×C43—81no—
151C2×C4×C43#12011yescharacteristic
152C2×C4×C43#12111yescharacteristic
153C2×C4×C43#12111yescharacteristic
154C2×C4×C43#12311yescharacteristic
155C2×C4×C43#12311yescharacteristic
156C2×C4×C43#12411yescharacteristic
157C2×C4×C43C2×SD1611yescharacteristic
158C2×C4×C43#13511yescharacteristic
159C2×C4×C43#13511yescharacteristic
160C2×C4×C43#13511yescharacteristic
161C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C43#13711yescharacteristic
164C2×C4×C43#13711yescharacteristic
165C8×C43—41no—
166C8×C43—41no—
167C8×C43—81no—
168C8×C43—81no—
169C8×C43—81no—
170#10539C4311yesmaximal, characteristic, direct product factor, Sylow
171C22×C43—82no—
172C22×C43—82no—
173C22×C43—82no—
174C22×C43—161no—
175C22×C43—161no—
176C22×C43—161no—
177C22×C43—161no—
178C22×C43#39411yescharacteristic
179C22×C43#46311yescharacteristic
180C22×C43#46411yescharacteristic
181C22×C43#46511yescharacteristic
182C22×C43#46811yescharacteristic
183C22×C43#47211yescharacteristic
184C22×C43#47211yescharacteristic
185C4×C43—21no—
186C4×C43—21no—
187C4×C43—42no—
188C4×C43—81no—
189C4×C43—82no—
190C4×C43#44911yescharacteristic
191C4×C43#45211yescharacteristic
192C4×C43#46011yescharacteristic
193C4×C43#46111yescharacteristic
194C4×C43#46311yescharacteristic
195C4×C43#46411yescharacteristic
196C4×C43#48811yescharacteristic
197C4×C43#48911yescharacteristic
198C2×#486C2×C4311yescharacteristic
199#1987C2×C4311yescharacteristic, complemented
200#1982C2×C4311yescharacteristic
201#1939C2×C4311yescharacteristic, complemented
202C2×#333C2×C4311yescharacteristic, complemented
203C2×#331C2×C4311yescharacteristic
204#1277C2×C4311yescharacteristic, complemented
205C2×C43—162no—
206C2×C43#167711yescharacteristic
207C2×C43#167811yescharacteristic
208C2×C43#169711yescharacteristic
209C2×C43#169811yescharacteristic
210C2×C43#204211yescharacteristic
211C2×C43#204511yescharacteristic
212C2×C43#205511yescharacteristic
213C2×C4⋊Q8C22×C4311yescharacteristic
214C2×#127C22×C4311yescharacteristic
215#486—22no—
216#486—22no—
217C2×C4⋊C8—21no—
218C2×C4⋊C8C22×C4311yescharacteristic
219C2×C4⋊C8C22×C4311yescharacteristic
220C2×C4⋊C8C22×C4311yescharacteristic
221C2×#102—21no—
222C2×#102—21no—
223C2×#102—21no—
224C2×#102—21no—
225C2×C4×C8C22×C4311yescharacteristic
226C4×C4⋊C4C22×C4311yescharacteristic
227#340—21no—
228#340—21no—
229#336—21no—
230#333—22no—
231#331—22no—
232C43#1053911yescharacteristic, direct product factor, Sylow
233C22×Q8—21no—
234C22×D4—21no—
235C22×D4—21no—
236C22×D4—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8D4×C4311yescharacteristic
241C22×C8D4×C4311yescharacteristic
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8D4×C4312yes—
246#127—21no—
247#127—21no—
248#127—21no—
249#127D4×C4312yes—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4D4×C4311yescharacteristic
253C2×C4⋊C4D4×C4311yescharacteristic
254C2×C42—21no—
255C2×C42C23×C4311yescharacteristic
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8—21no—
260C4⋊C8—21no—
261C4⋊C8—21no—
262C4⋊C8—42no—
263#102—24no—
264#102—24no—
265#102—42no—
266#102—42no—
267C4×C8—21no—
268C4×C8—21no—
269#95—21no—
270C24—41no—
271C2×Q8—22no—
272C2×Q8—41no—
273C2×Q8—81no—
274C2×Q8—81no—
275C2×D4—22no—
276C2×D4—22no—
277C2×D4—22no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—41no—
282C2×D4—41no—
283C2×D4—41no—
284C2×D4—41no—
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4—81no—
290C2×D4—81no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—41no—
294C22×C4C2×D4×C4311yescharacteristic
295C22×C4C2×D4×C4311yescharacteristic
296C22×C4#41×C4311yescharacteristic
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—21no—
300C2×C8—21no—
301C2×C8—21no—
302C2×C8—21no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C4⋊C4—21no—
313C4⋊C4—22no—
314C4⋊C4—22no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4SD16×C4312yes—
320C42—41no—
321C42—41no—
322C42C2×D4×C4311yescharacteristic
323C42C2×D4×C4311yescharacteristic
324C42#41×C4311yescharacteristic
325C42#41×C4311yescharacteristic
326C23—42no—
327C23—81no—
328C23—81no—
329C23—81no—
330C23—81no—
331C23—81no—
332C23—81no—
333C23#121×C4311yescharacteristic
334Q8—82no—
335Q8—82no—
336D4—42no—
337D4—42no—
338D4—42no—
339D4—42no—
340D4—82no—
341D4—82no—
342D4—81no—
343D4—81no—
344D4—81no—
345D4—81no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—22no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4#120×C4311yescharacteristic
358C2×C4#121×C4311yescharacteristic
359C2×C4#121×C4311yescharacteristic
360C2×C4#123×C4311yescharacteristic
361C2×C4#123×C4311yescharacteristic
362C2×C4#124×C4311yescharacteristic
363C2×C4C2×SD16×C4311yescharacteristic
364C2×C4#135×C4311yescharacteristic
365C2×C4#135×C4311yescharacteristic
366C2×C4#135×C4311yescharacteristic
367C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
368C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
369C2×C4#137×C4311yescharacteristic
370C2×C4#137×C4311yescharacteristic
371C8—41no—
372C8—41no—
373C8—81no—
374C8—81no—
375C8—81no—
376C22—82no—
377C22—82no—
378C22—82no—
379C22—161no—
380C22—161no—
381C22—161no—
382C22—161no—
383C22C43×#39411yescharacteristic
384C22C43×#46311yescharacteristic
385C22C43×#46411yescharacteristic
386C22C43×#46511yescharacteristic
387C22C43×#46811yescharacteristic
388C22C43×#47211yescharacteristic
389C22C43×#47211yescharacteristic
390C4—21no—
391C4—21no—
392C4—42no—
393C4—81no—
394C4—82no—
395C4C43×#44911yescharacteristic
396C4C43×#45211yescharacteristic
397C4C43×#46011yescharacteristic
398C4C43×#46111yescharacteristic
399C4C43×#46311yescharacteristic
400C4C43×#46411yescharacteristic
401C4C43×#48811yescharacteristic
402C4C43×#48911yescharacteristic
403C2—162no—
404C2C43×#167711yescharacteristic
405C2C43×#167811yescharacteristic
406C2C43×#169711yescharacteristic
407C2C43×#169811yescharacteristic
408C2C43×#204211yescharacteristic
409C2C43×#204511yescharacteristic
410C2C43×#205511yescharacteristic
subgroupG/H
center, socleC23×C43#121
commutator, Frattini, cosocleC2×C42C23×C43
prime radicalC2×#127×C43C22
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×#1987C2semidirect
4. C43×#1939C2semidirect
5. C2×C43×#333C2semidirect
7. C43×#1277C2semidirect
170. #10539C43direct (N × H)
199. #1987C2×C43semidirect
201. #1939C2×C43semidirect
202. C2×#333C2×C43semidirect
204. #1277C2×C43semidirect
232. C43#10539direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#4862
C43×#19872
C43×#19822
C43×#19392
C2×C43×#3332
C2×C43×#3312
C43×#12772
#1053943