Finite Group Databasebeta

← C43×#7583 #24927600

Subgroups — C43×#7583 #24927600

Order 11008.

522 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C22⋊Q8×C43C211yesmaximal, characteristic
2C43×#1817C211yesmaximal, characteristic
3C4×C22⋊C8×C43C211yesmaximal, characteristic
4C43×#1272C212yesmaximal, complemented
5C43×#1271C212yesmaximal, complemented
6C2×C22⋊Q8×C43C411yescharacteristic
7C2×C4×Q8×C43C411yescharacteristic
8C22×C42×C43C2211yescharacteristic
9C2×C22⋊C8×C43—21no—
10C2×C22⋊C8×C43—21no—
11C2×C4×C8×C43—21no—
12C43×#391C2211yescharacteristic
13C43×#389C2211yescharacteristic
14C43×#387—21no—
15C43×#385—21no—
16C43×#380C411yescharacteristic
17C4×C4⋊C4×C43—21no—
18C4×C4⋊C4×C43C411yescharacteristic
19C4×C22⋊C4×C43—21no—
20C43×#336—21no—
21C43×#336C2212yes—
22C43×#336C2212yes—
23C22×Q8×C43C2×C411yescharacteristic
24C23×C4×C43C2×C411yescharacteristic
25C23×C4×C43D411yescharacteristic
26C23×C4×C43D411yescharacteristic
27C22×C8×C43—22no—
28C22×C8×C43—22no—
29C22⋊Q8×C43—22no—
30C22⋊Q8×C43C814yescomplemented
31C4×Q8×C43—42no—
32C2×C4⋊C4×C43—21no—
33C2×C4⋊C4×C43—21no—
34C2×C4⋊C4×C43—21no—
35C2×C4⋊C4×C43C2×C411yescharacteristic
36C2×C4⋊C4×C43C2×C411yescharacteristic
37C2×C4⋊C4×C43C2×C411yescharacteristic
38C2×C22⋊C4×C43—21no—
39C2×C22⋊C4×C43—21no—
40C2×C42×C43—21no—
41C2×C42×C43—21no—
42C2×C42×C43—42no—
43C2×C42×C43C2×C411yescharacteristic
44C2×C42×C43D411yescharacteristic
45C2×C42×C43D411yescharacteristic
46C2×C42×C43C2311yescharacteristic
47C22⋊C8×C43—24no—
48C22⋊C8×C43—42no—
49C4×C8×C43—42no—
50#95×C43—21no—
51#95×C43—21no—
52#95×C43—21no—
53#95×C43—21no—
54#95×C43—21no—
55C24×C43C22⋊C411yescharacteristic
56C2×Q8×C43—21no—
57C2×Q8×C43—41no—
58C2×Q8×C43—41no—
59C2×Q8×C43C2×C812yes—
60C22×C4×C43—22no—
61C22×C4×C43—22no—
62C22×C4×C43—22no—
63C22×C4×C43—22no—
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43—21no—
68C22×C4×C43—41no—
69C22×C4×C43—41no—
70C22×C4×C43—41no—
71C22×C4×C43—41no—
72C22×C4×C43C22⋊C411yescharacteristic
73C22×C4×C43C22⋊C411yescharacteristic
74C22×C4×C43C22⋊C411yescharacteristic
75C22×C4×C43C2×C812yes—
76C22×C4×C43M1612yes—
77C22×C4×C43C22×C411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43C2×D411yescharacteristic
80C2×C8×C43—24no—
81C2×C8×C43—42no—
82C2×C8×C43—42no—
83C2×C8×C43—42no—
84C2×C8×C43—42no—
85C2×C8×C43—42no—
86C4⋊C4×C43—24no—
87C4⋊C4×C43—21no—
88C4⋊C4×C43—41no—
89C4⋊C4×C43—41no—
90C4⋊C4×C43—42no—
91C4⋊C4×C43—42no—
92C4⋊C4×C43C2×C812yes—
93C22⋊C4×C43—24no—
94C22⋊C4×C43—42no—
95C42×C43—22no—
96C42×C43—22no—
97C42×C43—41no—
98C42×C43—41no—
99C42×C43—42no—
100C42×C43—42no—
101C23×C43—21no—
102C23×C43—21no—
103C23×C43—21no—
104C23×C43—21no—
105C23×C43—21no—
106C23×C43—21no—
107C23×C43C22⋊C812yes—
108C23×C43C2×C22⋊C411yescharacteristic
109Q8×C43—42no—
110Q8×C43—42no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—22no—
124C2×C4×C43—22no—
125C2×C4×C43—42no—
126C2×C4×C43—42no—
127C2×C4×C43—44no—
128C2×C4×C43—44no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43C22⋊C812yes—
140C2×C4×C43#9912yes—
141C2×C4×C43#10412yes—
142C2×C4×C43C22×C811yescharacteristic
143C2×C4×C43C2×M1611yescharacteristic
144C2×C4×C43#13512yes—
145C2×C4×C43#13712yes—
146C8×C43—44no—
147C8×C43—82no—
148#7583C4311yesmaximal, characteristic, direct product factor, Sylow
149C22×C43—22no—
150C22×C43—22no—
151C22×C43—22no—
152C22×C43—41no—
153C22×C43—41no—
154C22×C43—41no—
155C22×C43—41no—
156C22×C43C2×C22⋊C811yescharacteristic
157C22×C43C2×#9911yescharacteristic
158C22×C43#41311yescharacteristic
159C22×C43#41611yescharacteristic
160C22×C43#41911yescharacteristic
161C22×C43C2×#10411yescharacteristic
162C22×C43#42111yescharacteristic
163C4×C43—22no—
164C4×C43—21no—
165C4×C43—21no—
166C4×C43—22no—
167C4×C43—22no—
168C4×C43—22no—
169C4×C43—22no—
170C4×C43—42no—
171C4×C43—42no—
172C4×C43—81no—
173C4×C43—81no—
174C4×C22⋊Q8C2×C4311yescharacteristic
175#1817C2×C4311yescharacteristic
176C4×C22⋊C8C2×C4311yescharacteristic
177#1272C2×C4312yescomplemented
178#1271C2×C4312yescomplemented
179C2×C43—42no—
180C2×C43#145911yescharacteristic
181C2×C43#147611yescharacteristic
182C2×C43#147911yescharacteristic
183C2×C43#150811yescharacteristic
184C2×C43#151611yescharacteristic
185C2×C43#152911yescharacteristic
186C2×C43#155411yescharacteristic
187C2×C22⋊Q8C4×C4311yescharacteristic
188C2×C4×Q8C4×C4311yescharacteristic
189C22×C42C22×C4311yescharacteristic
190C2×C22⋊C8—21no—
191C2×C22⋊C8—21no—
192C2×C4×C8—21no—
193#391C22×C4311yescharacteristic
194#389C22×C4311yescharacteristic
195#387—21no—
196#385—21no—
197#380C4×C4311yescharacteristic
198C4×C4⋊C4—21no—
199C4×C4⋊C4C4×C4311yescharacteristic
200C4×C22⋊C4—21no—
201#336—21no—
202#336C22×C4312yes—
203#336C22×C4312yes—
204C43#758311yescharacteristic, direct product factor, Sylow
205C22×Q8C2×C4×C4311yescharacteristic
206C23×C4C2×C4×C4311yescharacteristic
207C23×C4D4×C4311yescharacteristic
208C23×C4D4×C4311yescharacteristic
209C22×C8—22no—
210C22×C8—22no—
211C22⋊Q8—22no—
212C22⋊Q8C8×C4314yescomplemented
213C4×Q8—42no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4C2×C4×C4311yescharacteristic
218C2×C4⋊C4C2×C4×C4311yescharacteristic
219C2×C4⋊C4C2×C4×C4311yescharacteristic
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C42—21no—
223C2×C42—21no—
224C2×C42—42no—
225C2×C42C2×C4×C4311yescharacteristic
226C2×C42D4×C4311yescharacteristic
227C2×C42D4×C4311yescharacteristic
228C2×C42C23×C4311yescharacteristic
229C22⋊C8—24no—
230C22⋊C8—42no—
231C4×C8—42no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95—21no—
237C24C22⋊C4×C4311yescharacteristic
238C2×Q8—21no—
239C2×Q8—41no—
240C2×Q8—41no—
241C2×Q8C2×C8×C4312yes—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4C22⋊C4×C4311yescharacteristic
255C22×C4C22⋊C4×C4311yescharacteristic
256C22×C4C22⋊C4×C4311yescharacteristic
257C22×C4C2×C8×C4312yes—
258C22×C4M16×C4312yes—
259C22×C4C22×C4×C4311yescharacteristic
260C22×C4C2×D4×C4311yescharacteristic
261C22×C4C2×D4×C4311yescharacteristic
262C2×C8—24no—
263C2×C8—42no—
264C2×C8—42no—
265C2×C8—42no—
266C2×C8—42no—
267C2×C8—42no—
268C4⋊C4—24no—
269C4⋊C4—21no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—42no—
273C4⋊C4—42no—
274C4⋊C4C2×C8×C4312yes—
275C22⋊C4—24no—
276C22⋊C4—42no—
277C42—22no—
278C42—22no—
279C42—41no—
280C42—41no—
281C42—42no—
282C42—42no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23C22⋊C8×C4312yes—
290C23C2×C22⋊C4×C4311yescharacteristic
291Q8—42no—
292Q8—42no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—44no—
310C2×C4—44no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4C22⋊C8×C4312yes—
322C2×C4#99×C4312yes—
323C2×C4#104×C4312yes—
324C2×C4C22×C8×C4311yescharacteristic
325C2×C4C2×M16×C4311yescharacteristic
326C2×C4#135×C4312yes—
327C2×C4#137×C4312yes—
328C8—44no—
329C8—82no—
330C22—22no—
331C22—22no—
332C22—22no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22C2×C22⋊C8×C4311yescharacteristic
338C22C2×#99×C4311yescharacteristic
339C22C43×#41311yescharacteristic
340C22C43×#41611yescharacteristic
341C22C43×#41911yescharacteristic
342C22C2×#104×C4311yescharacteristic
343C22C43×#42111yescharacteristic
344C4—22no—
345C4—21no—
346C4—21no—
347C4—22no—
348C4—22no—
349C4—22no—
350C4—22no—
351C4—42no—
352C4—42no—
353C4—81no—
354C4—81no—
355C2—42no—
356C2C43×#145911yescharacteristic
357C2C43×#147611yescharacteristic
358C2C43×#147911yescharacteristic
359C2C43×#150811yescharacteristic
360C2C43×#151611yescharacteristic
361C2C43×#152911yescharacteristic
362C2C43×#155411yescharacteristic
subgroupG/H
center, socleC23×C43C2×C22⋊C4
commutatorC2×C4C22×C8×C43
Frattini, cosocleC2×C42C23×C43
prime radicalC24×C43C22⋊C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C43 ◁ C22×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
4. C43×#1272C2semidirect
5. C43×#1271C2semidirect
30. C22⋊Q8×C43C8semidirect
148. #7583C43direct (N × H)
177. #1272C2×C43semidirect
178. #1271C2×C43semidirect
204. C43#7583direct (N × H)
212. C22⋊Q8C8×C43semidirect

Maximal subgroups

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

subgroupindex
C4×C22⋊Q8×C432
C43×#18172
C4×C22⋊C8×C432
C43×#12722
C43×#12712
#758343