Finite Group Databasebeta

← C43×#9467 #24929484

Subgroups — C43×#9467 #24929484

Order 11008.

738 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2972C211yesmaximal, characteristic
2C43×#2409C211yesmaximal, characteristic
3C43×#1799C211yesmaximal, characteristic
4C43×#1787C212yesmaximal, complemented
5C43×#1289C212yesmaximal, complemented
6C23×Q8×C43C2211yescharacteristic
7C2×C22⋊Q8×C43—21no—
8C2×C4×D4×C43C2211yescharacteristic
9C8×D4×C43—24no—
10C43×#431—21no—
11C2×#103×C43—24no—
12C2×#99×C43—21no—
13C2×C22⋊C8×C43—21no—
14C2×C22⋊C8×C43C2212yes—
15C43×#395C412yescomplemented
16C43×#393C412yescomplemented
17C43×#391—21no—
18C43×#386—21no—
19C43×#385—21no—
20C43×#380C2212yes—
21C43×#380C2211yescharacteristic
22C43×#342—21no—
23C22×Q8×C43—21no—
24C22×Q8×C43—22no—
25C22×Q8×C43—22no—
26C22×Q8×C43—44no—
27C22×Q8×C43C2×C412yes—
28C22×D4×C43D411yescharacteristic
29C23×C4×C43—21no—
30C23×C4×C43D411yescharacteristic
31C23×C4×C43C2311yescharacteristic
32C22×C8×C43—22no—
33C22×C8×C43D414yes—
34C22⋊Q8×C43—44no—
35C4×D4×C43—22no—
36C4×D4×C43—22no—
37C2×C4⋊C4×C43—22no—
38C2×C4⋊C4×C43—21no—
39C2×C4⋊C4×C43—22no—
40C2×C4⋊C4×C43C2×C411yescharacteristic
41C2×C22⋊C4×C43—22no—
42C2×C22⋊C4×C43—21no—
43C2×C22⋊C4×C43—22no—
44C2×C22⋊C4×C43C2×C411yescharacteristic
45C2×C22⋊C4×C43D411yescharacteristic
46C2×C42×C43D411yescharacteristic
47C4⋊C8×C43—22no—
48#103×C43—48no—
49#99×C43—42no—
50C22⋊C8×C43—22no—
51C22⋊C8×C43—22no—
52C22⋊C8×C43—22no—
53C4×C8×C43—22no—
54#95×C43—22no—
55#95×C43—22no—
56#95×C43—22no—
57#95×C43C2×C412yes—
58C24×C43C22⋊C411yescharacteristic
59C24×C43C2×D411yescharacteristic
60C2×Q8×C43—24no—
61C2×Q8×C43—28no—
62C2×Q8×C43—24no—
63C2×Q8×C43—44no—
64C2×Q8×C43—44no—
65C2×Q8×C43—42no—
66C2×Q8×C43—48no—
67C2×Q8×C43—41no—
68C2×Q8×C43—41no—
69C2×D4×C43—22no—
70C2×D4×C43—22no—
71C2×D4×C43SD1612yes—
72C2×D4×C43Q1612yes—
73C22×C4×C43—21no—
74C22×C4×C43—21no—
75C22×C4×C43—22no—
76C22×C4×C43—22no—
77C22×C4×C43—42no—
78C22×C4×C43—44no—
79C22×C4×C43—42no—
80C22×C4×C43—42no—
81C22×C4×C43—42no—
82C22×C4×C43C22⋊C411yescharacteristic
83C22×C4×C43C22⋊C411yescharacteristic
84C22×C4×C43C22⋊C411yescharacteristic
85C22×C4×C43C22×C411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D412yes—
88C22×C4×C43#4112yes—
89C2×C8×C43—24no—
90C2×C8×C43—44no—
91C2×C8×C43—82no—
92C4⋊C4×C43—22no—
93C4⋊C4×C43—42no—
94C4⋊C4×C43—44no—
95C4⋊C4×C43—44no—
96C22⋊C4×C43—22no—
97C22⋊C4×C43—22no—
98C22⋊C4×C43—44no—
99C22⋊C4×C43—42no—
100C22⋊C4×C43—42no—
101C22⋊C4×C43—42no—
102C42×C43—21no—
103C42×C43—21no—
104C23×C43—21no—
105C23×C43—21no—
106C23×C43—41no—
107C23×C43—41no—
108C23×C43—41no—
109C23×C43—41no—
110C23×C43#10312yescomplemented
111C23×C43C2×C22⋊C411yescharacteristic
112C23×C43#12112yes—
113C23×C43C2×SD1611yescharacteristic
114C23×C43C2×Q1611yescharacteristic
115C23×C43#13512yes—
116Q8×C43—28no—
117Q8×C43—44no—
118Q8×C43—44no—
119Q8×C43—44no—
120D4×C43—24no—
121D4×C43—24no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—24no—
125C2×C4×C43—22no—
126C2×C4×C43—24no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—41no—
130C2×C4×C43—42no—
131C2×C4×C43—42no—
132C2×C4×C43—48no—
133C2×C4×C43—42no—
134C2×C4×C43—42no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—42no—
138C2×C4×C43—42no—
139C2×C4×C43—42no—
140C2×C4×C43—81no—
141C2×C4×C43—82no—
142C2×C4×C43—82no—
143C2×C4×C43—82no—
144C2×C4×C43#10312yescomplemented
145C2×C4×C43C4×D412yes—
146C2×C4×C43#12011yescharacteristic
147C2×C4×C43#12311yescharacteristic
148C8×C43—44no—
149#9467C4311yesmaximal, characteristic, direct product factor, Sylow
150C22×C43—21no—
151C22×C43—22no—
152C22×C43—21no—
153C22×C43—22no—
154C22×C43—22no—
155C22×C43—41no—
156C22×C43—41no—
157C22×C43—42no—
158C22×C43—42no—
159C22×C43—41no—
160C22×C43—41no—
161C22×C43—81no—
162C22×C43#38611yescharacteristic
163C22×C43C2×#10311yescharacteristic
164C22×C43#41611yescharacteristic
165C22×C43#46512yes—
166C22×C43#46712yes—
167C4×C43—21no—
168C4×C43—22no—
169C4×C43—22no—
170C4×C43—44no—
171C4×C43—41no—
172C4×C43—41no—
173C4×C43—82no—
174C4×C43—162no—
175C4×C43B(4,𝔽2)12yes—
176#2972C2×C4311yescharacteristic
177#2409C2×C4311yescharacteristic
178#1799C2×C4311yescharacteristic
179#1787C2×C4312yescomplemented
180#1289C2×C4312yescomplemented
181C2×C43—21no—
182C2×C43—22no—
183C2×C43—21no—
184C2×C43—22no—
185C2×C43—42no—
186C2×C43#188911yescharacteristic
187C2×C43#189211yescharacteristic
188C2×C43#190911yescharacteristic
189C23×Q8C22×C4311yescharacteristic
190C2×C22⋊Q8—21no—
191C2×C4×D4C22×C4311yescharacteristic
192C8×D4—24no—
193#431—21no—
194C2×#103—24no—
195C2×#99—21no—
196C2×C22⋊C8—21no—
197C2×C22⋊C8C22×C4312yes—
198#395C4×C4312yescomplemented
199#393C4×C4312yescomplemented
200#391—21no—
201#386—21no—
202#385—21no—
203#380C22×C4312yes—
204#380C22×C4311yescharacteristic
205#342—21no—
206C43#946711yescharacteristic, direct product factor, Sylow
207C22×Q8—21no—
208C22×Q8—22no—
209C22×Q8—22no—
210C22×Q8—44no—
211C22×Q8C2×C4×C4312yes—
212C22×D4D4×C4311yescharacteristic
213C23×C4—21no—
214C23×C4D4×C4311yescharacteristic
215C23×C4C23×C4311yescharacteristic
216C22×C8—22no—
217C22×C8D4×C4314yes—
218C22⋊Q8—44no—
219C4×D4—22no—
220C4×D4—22no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4C2×C4×C4311yescharacteristic
225C2×C22⋊C4—22no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—22no—
228C2×C22⋊C4C2×C4×C4311yescharacteristic
229C2×C22⋊C4D4×C4311yescharacteristic
230C2×C42D4×C4311yescharacteristic
231C4⋊C8—22no—
232#103—48no—
233#99—42no—
234C22⋊C8—22no—
235C22⋊C8—22no—
236C22⋊C8—22no—
237C4×C8—22no—
238#95—22no—
239#95—22no—
240#95—22no—
241#95C2×C4×C4312yes—
242C24C22⋊C4×C4311yescharacteristic
243C24C2×D4×C4311yescharacteristic
244C2×Q8—24no—
245C2×Q8—28no—
246C2×Q8—24no—
247C2×Q8—44no—
248C2×Q8—44no—
249C2×Q8—42no—
250C2×Q8—48no—
251C2×Q8—41no—
252C2×Q8—41no—
253C2×D4—22no—
254C2×D4—22no—
255C2×D4SD16×C4312yes—
256C2×D4Q16×C4312yes—
257C22×C4—22no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—22no—
261C22×C4—42no—
262C22×C4—44no—
263C22×C4—42no—
264C22×C4—42no—
265C22×C4—42no—
266C22×C4C22⋊C4×C4311yescharacteristic
267C22×C4C22⋊C4×C4311yescharacteristic
268C22×C4C22⋊C4×C4311yescharacteristic
269C22×C4C22×C4×C4311yescharacteristic
270C22×C4C2×D4×C4312yes—
271C22×C4C2×D4×C4311yescharacteristic
272C22×C4#41×C4312yes—
273C2×C8—24no—
274C2×C8—44no—
275C2×C8—82no—
276C4⋊C4—22no—
277C4⋊C4—42no—
278C4⋊C4—44no—
279C4⋊C4—44no—
280C22⋊C4—22no—
281C22⋊C4—22no—
282C22⋊C4—44no—
283C22⋊C4—42no—
284C22⋊C4—42no—
285C22⋊C4—42no—
286C42—21no—
287C42—21no—
288C23—21no—
289C23—21no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23#103×C4312yescomplemented
295C23C2×C22⋊C4×C4311yescharacteristic
296C23#121×C4312yes—
297C23C2×SD16×C4311yescharacteristic
298C23C2×Q16×C4311yescharacteristic
299C23#135×C4312yes—
300Q8—28no—
301Q8—44no—
302Q8—44no—
303Q8—44no—
304D4—24no—
305D4—24no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—24no—
309C2×C4—22no—
310C2×C4—24no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—48no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—81no—
325C2×C4—82no—
326C2×C4—82no—
327C2×C4—82no—
328C2×C4#103×C4312yescomplemented
329C2×C4C4×D4×C4312yes—
330C2×C4#120×C4311yescharacteristic
331C2×C4#123×C4311yescharacteristic
332C8—44no—
333C22—21no—
334C22—22no—
335C22—21no—
336C22—22no—
337C22—22no—
338C22—41no—
339C22—41no—
340C22—42no—
341C22—42no—
342C22—41no—
343C22—41no—
344C22—81no—
345C22C43×#38611yescharacteristic
346C22C2×#103×C4311yescharacteristic
347C22C43×#41611yescharacteristic
348C22C43×#46512yes—
349C22C43×#46712yes—
350C4—21no—
351C4—22no—
352C4—22no—
353C4—44no—
354C4—41no—
355C4—41no—
356C4—82no—
357C4—162no—
358C4C43×B(4,𝔽2)12yes—
359C2—21no—
360C2—22no—
361C2—21no—
362C2—22no—
363C2—42no—
364C2C43×#188911yescharacteristic
365C2C43×#189211yescharacteristic
366C2C43×#190911yescharacteristic
subgroupG/H
center, socleC22×C43#386
commutatorC22×C4C22×C4×C43
Frattini, cosocleC23×C4C23×C43
prime radicalC22×D4×C43D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C23×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
4. C43×#1787C2semidirect
5. C43×#1289C2semidirect
15. C43×#395C4semidirect
16. C43×#393C4semidirect
110. C23×C43#103semidirect
144. C2×C4×C43#103semidirect
149. #9467C43direct (N × H)
179. #1787C2×C43semidirect
180. #1289C2×C43semidirect
198. #395C4×C43semidirect
199. #393C4×C43semidirect
206. C43#9467direct (N × H)
294. C23#103×C43semidirect
328. C2×C4#103×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#29722
C43×#24092
C43×#17992
C43×#17872
C43×#12892
#946743