Finite Group Databasebeta

← C43×#9324 #24929341

Subgroups — C43×#9324 #24929341

Order 11008.

536 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3113C211yesmaximal, characteristic
2C43×#2276C211yesmaximal, characteristic
3C43×#1986C211yesmaximal, characteristic
4C43×#1506C211yesmaximal, characteristic
5C43×#1491C211yesmaximal, characteristic
6C43×#1300C211yesmaximal, characteristic
7C43×#1285C211yesmaximal, characteristic
8C43×#533C2211yescharacteristic
9C2×C4×Q8×C43—21no—
10C2×C4×Q8×C43C2211yescharacteristic
11C43×#483—21no—
12C43×#475C412yescomplemented
13C43×#462C412yescomplemented
14C43×#451—21no—
15C43×#441—22no—
16C43×#432C2211yescharacteristic
17C43×#432C2211yescharacteristic
18C4×M16×C43C2211yescharacteristic
19C4×C4⋊C4×C43—21no—
20C4×C4⋊C4×C43—22no—
21C4×C4⋊C4×C43—21no—
22C4×C4⋊C4×C43C2211yescharacteristic
23C43×#376—21no—
24C43×#376C2211yescharacteristic
25C43×#339—22no—
26C43×#328—21no—
27C43×#328—21no—
28C43×Q8⋊C8—22no—
29C22×Q8×C43D411yescharacteristic
30C2×Q16×C43—22no—
31C2×M16×C43—21no—
32C4⋊Q8×C43C2×C411yescharacteristic
33C4⋊Q8×C43C2×C411yescharacteristic
34#125×C43—21no—
35C22⋊Q8×C43—21no—
36C22⋊Q8×C43—21no—
37C4×Q8×C43—28no—
38C4×Q8×C43—21no—
39C4×Q8×C43—21no—
40C4×Q8×C43—21no—
41C4×Q8×C43—21no—
42C4×Q8×C43C2×C412yes—
43C4×Q8×C43D412yes—
44#117×C43—21no—
45C2×C4⋊C4×C43—22no—
46C2×C4⋊C4×C43—21no—
47C2×C4⋊C4×C43—21no—
48C2×C4⋊C4×C43D411yescharacteristic
49C2×C42×C43—22no—
50C2×C42×C43—21no—
51C2×C42×C43—21no—
52C2×C42×C43—22no—
53C2×C42×C43D412yes—
54C2×C42×C43C2311yescharacteristic
55#106×C43—22no—
56C4⋊C8×C43—21no—
57C4⋊C8×C43C2×C412yes—
58#103×C43—22no—
59#103×C43—22no—
60C22⋊C8×C43—21no—
61C22⋊C8×C43—21no—
62#97×C43—21no—
63#97×C43—21no—
64#97×C43—21no—
65C4×C8×C43—21no—
66#95×C43—22no—
67#95×C43—21no—
68#95×C43—21no—
69#95×C43D411yescharacteristic
70#95×C43D411yescharacteristic
71C2×Q8×C43—24no—
72C2×Q8×C43—21no—
73C2×Q8×C43—21no—
74C2×Q8×C43—21no—
75C2×Q8×C43C22⋊C412yes—
76C22×C4×C43—21no—
77C22×C4×C43—21no—
78C22×C4×C43—21no—
79C22×C4×C43—22no—
80C22×C4×C43—21no—
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43C2×D411yescharacteristic
83C22×C4×C43C2×D411yescharacteristic
84Q16×C43—44no—
85M16×C43—22no—
86M16×C43—41no—
87C2×C8×C43—22no—
88C2×C8×C43—41no—
89C2×C8×C43—41no—
90C4⋊C4×C43—28no—
91C4⋊C4×C43—24no—
92C4⋊C4×C43—22no—
93C4⋊C4×C43—22no—
94C4⋊C4×C43—21no—
95C4⋊C4×C43—21no—
96C4⋊C4×C43—21no—
97C4⋊C4×C43—21no—
98C4⋊C4×C43—21no—
99C4⋊C4×C43—41no—
100C4⋊C4×C43—41no—
101C4⋊C4×C43C22⋊C412yes—
102C22⋊C4×C43—41no—
103C42×C43—28no—
104C42×C43—24no—
105C42×C43—22no—
106C42×C43—22no—
107C42×C43—42no—
108C42×C43—41no—
109C42×C43—82no—
110C42×C43C22×C411yescharacteristic
111C42×C43C2×D411yescharacteristic
112C42×C43#4111yescharacteristic
113C42×C43#4111yescharacteristic
114C23×C43#12011yescharacteristic
115Q8×C43—24no—
116Q8×C43—22no—
117Q8×C43—42no—
118Q8×C43—81no—
119Q8×C43#10414yes—
120C2×C4×C43—24no—
121C2×C4×C43—22no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—22no—
125C2×C4×C43—22no—
126C2×C4×C43—24no—
127C2×C4×C43—22no—
128C2×C4×C43—22no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—42no—
132C2×C4×C43—41no—
133C2×C4×C43—42no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43C2×C22⋊C411yescharacteristic
141C2×C4×C43C4×D411yescharacteristic
142C2×C4×C43C4×D411yescharacteristic
143C2×C4×C43#12111yescharacteristic
144C2×C4×C43#12111yescharacteristic
145C2×C4×C43#12311yescharacteristic
146C8×C43—42no—
147C8×C43—42no—
148C8×C43—81no—
149#9324C4311yesmaximal, characteristic, direct product factor, Sylow
150C22×C43—21no—
151C22×C43—21no—
152C22×C43#38611yescharacteristic
153C22×C43#45511yescharacteristic
154C22×C43#45611yescharacteristic
155C4×C43—21no—
156C4×C43—21no—
157C4×C43—24no—
158C4×C43—21no—
159C4×C43—21no—
160C4×C43—21no—
161C4×C43—44no—
162C4×C43—42no—
163C4×C43—42no—
164C4×C43—42no—
165C4×C43—81no—
166C4×C43—81no—
167C4×C43C2×#10412yes—
168#3113C2×C4311yescharacteristic
169#2276C2×C4311yescharacteristic
170#1986C2×C4311yescharacteristic
171#1506C2×C4311yescharacteristic
172#1491C2×C4311yescharacteristic
173#1300C2×C4311yescharacteristic
174#1285C2×C4311yescharacteristic
175C2×C43—21no—
176C2×C43—21no—
177C2×C43#188211yescharacteristic
178C2×C43#189611yescharacteristic
179C2×C43#190511yescharacteristic
180#533C22×C4311yescharacteristic
181C2×C4×Q8—21no—
182C2×C4×Q8C22×C4311yescharacteristic
183#483—21no—
184#475C4×C4312yescomplemented
185#462C4×C4312yescomplemented
186#451—21no—
187#441—22no—
188#432C22×C4311yescharacteristic
189#432C22×C4311yescharacteristic
190C4×M16C22×C4311yescharacteristic
191C4×C4⋊C4—21no—
192C4×C4⋊C4—22no—
193C4×C4⋊C4—21no—
194C4×C4⋊C4C22×C4311yescharacteristic
195#376—21no—
196#376C22×C4311yescharacteristic
197#339—22no—
198#328—21no—
199#328—21no—
200Q8⋊C8—22no—
201C43#932411yescharacteristic, direct product factor, Sylow
202C22×Q8D4×C4311yescharacteristic
203C2×Q16—22no—
204C2×M16—21no—
205C4⋊Q8C2×C4×C4311yescharacteristic
206C4⋊Q8C2×C4×C4311yescharacteristic
207#125—21no—
208C22⋊Q8—21no—
209C22⋊Q8—21no—
210C4×Q8—28no—
211C4×Q8—21no—
212C4×Q8—21no—
213C4×Q8—21no—
214C4×Q8—21no—
215C4×Q8C2×C4×C4312yes—
216C4×Q8D4×C4312yes—
217#117—21no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4D4×C4311yescharacteristic
222C2×C42—22no—
223C2×C42—21no—
224C2×C42—21no—
225C2×C42—22no—
226C2×C42D4×C4312yes—
227C2×C42C23×C4311yescharacteristic
228#106—22no—
229C4⋊C8—21no—
230C4⋊C8C2×C4×C4312yes—
231#103—22no—
232#103—22no—
233C22⋊C8—21no—
234C22⋊C8—21no—
235#97—21no—
236#97—21no—
237#97—21no—
238C4×C8—21no—
239#95—22no—
240#95—21no—
241#95—21no—
242#95D4×C4311yescharacteristic
243#95D4×C4311yescharacteristic
244C2×Q8—24no—
245C2×Q8—21no—
246C2×Q8—21no—
247C2×Q8—21no—
248C2×Q8C22⋊C4×C4312yes—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—22no—
253C22×C4—21no—
254C22×C4C2×D4×C4311yescharacteristic
255C22×C4C2×D4×C4311yescharacteristic
256C22×C4C2×D4×C4311yescharacteristic
257Q16—44no—
258M16—22no—
259M16—41no—
260C2×C8—22no—
261C2×C8—41no—
262C2×C8—41no—
263C4⋊C4—28no—
264C4⋊C4—24no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4C22⋊C4×C4312yes—
275C22⋊C4—41no—
276C42—28no—
277C42—24no—
278C42—22no—
279C42—22no—
280C42—42no—
281C42—41no—
282C42—82no—
283C42C22×C4×C4311yescharacteristic
284C42C2×D4×C4311yescharacteristic
285C42#41×C4311yescharacteristic
286C42#41×C4311yescharacteristic
287C23#120×C4311yescharacteristic
288Q8—24no—
289Q8—22no—
290Q8—42no—
291Q8—81no—
292Q8#104×C4314yes—
293C2×C4—24no—
294C2×C4—22no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—24no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—41no—
306C2×C4—42no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4C2×C22⋊C4×C4311yescharacteristic
314C2×C4C4×D4×C4311yescharacteristic
315C2×C4C4×D4×C4311yescharacteristic
316C2×C4#121×C4311yescharacteristic
317C2×C4#121×C4311yescharacteristic
318C2×C4#123×C4311yescharacteristic
319C8—42no—
320C8—42no—
321C8—81no—
322C22—21no—
323C22—21no—
324C22C43×#38611yescharacteristic
325C22C43×#45511yescharacteristic
326C22C43×#45611yescharacteristic
327C4—21no—
328C4—21no—
329C4—24no—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—44no—
334C4—42no—
335C4—42no—
336C4—42no—
337C4—81no—
338C4—81no—
339C4C2×#104×C4312yes—
340C2—21no—
341C2—21no—
342C2C43×#188211yescharacteristic
343C2C43×#189611yescharacteristic
344C2C43×#190511yescharacteristic
subgroupG/H
center, socleC22×C43#386
commutatorC42C22×C4×C43
Frattini, cosocleC2×C42C23×C43
prime radicalC23×C43#120
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
12. C43×#475C4semidirect
13. C43×#462C4semidirect
149. #9324C43direct (N × H)
184. #475C4×C43semidirect
185. #462C4×C43semidirect
201. C43#9324direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#31132
C43×#22762
C43×#19862
C43×#15062
C43×#14912
C43×#13002
C43×#12852
#932443