Finite Group Databasebeta

← C43×#9683 #24929700

Subgroups — C43×#9683 #24929700

Order 11008.

630 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2857C211yesmaximal, characteristic
2C43×#1749C211yesmaximal, characteristic
3C2×C43×#328C214yesmaximal
4C43×#1434C211yesmaximal, characteristic
5C2×C4⋊Q8×C43C411yescharacteristic, complemented
6C2×C22⋊Q8×C43C2212yes—
7C22×C42×C43C2211yescharacteristic
8C2×C22⋊C8×C43C2212yes—
9C2×#97×C43—21no—
10C43×#391C412yescomplemented
11C43×#389—21no—
12C43×#389—21no—
13C43×#384C411yescharacteristic, complemented
14C43×#380—21no—
15C43×#380—21no—
16C2×#95×C43—21no—
17C2×#95×C43—21no—
18C2×#95×C43C2212yes—
19C43×#336—21no—
20C43×#328—28no—
21C22×Q8×C43C2×C412yes—
22C23×C4×C43—22no—
23C23×C4×C43D411yescharacteristic
24C23×C4×C43D411yescharacteristic
25C23×C4×C43C2311yescharacteristic
26C22×C8×C43—22no—
27C4⋊Q8×C43—42no—
28C22⋊Q8×C43—24no—
29C22⋊Q8×C43—24no—
30C2×C4⋊C4×C43—21no—
31C2×C4⋊C4×C43—21no—
32C2×C4⋊C4×C43—21no—
33C2×C4⋊C4×C43—21no—
34C2×C4⋊C4×C43—22no—
35C2×C4⋊C4×C43C2×C412yes—
36C2×C22⋊C4×C43—22no—
37C2×C42×C43—42no—
38C2×C42×C43C2×C411yescharacteristic
39C2×C42×C43C2×C411yescharacteristic
40C2×C42×C43D411yescharacteristic
41C2×C42×C43D411yescharacteristic
42C22⋊C8×C43—22no—
43C22⋊C8×C43D414yes—
44#97×C43—42no—
45#95×C43—24no—
46#95×C43—22no—
47#95×C43—22no—
48#95×C43—24no—
49#95×C43—42no—
50C24×C43C2×D411yescharacteristic
51C2×Q8×C43—24no—
52C2×Q8×C43—42no—
53C2×Q8×C43—42no—
54C22×C4×C43—22no—
55C22×C4×C43—22no—
56C22×C4×C43—24no—
57C22×C4×C43—22no—
58C22×C4×C43—22no—
59C22×C4×C43—22no—
60C22×C4×C43—22no—
61C22×C4×C43—41no—
62C22×C4×C43—41no—
63C22×C4×C43—41no—
64C22×C4×C43—41no—
65C22×C4×C43—42no—
66C22×C4×C43—42no—
67C22×C4×C43—42no—
68C22×C4×C43—42no—
69C22×C4×C43—42no—
70C22×C4×C43—42no—
71C22×C4×C43C22⋊C411yescharacteristic
72C22×C4×C43C22⋊C411yescharacteristic
73C22×C4×C43C22⋊C411yescharacteristic
74C22×C4×C43C22⋊C411yescharacteristic
75C22×C4×C43C22×C411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×D412yes—
78C22×C4×C43#4112yes—
79C2×C8×C43—24no—
80C2×C8×C43—42no—
81C2×C8×C43—42no—
82C4⋊C4×C43—24no—
83C4⋊C4×C43—42no—
84C4⋊C4×C43—42no—
85C4⋊C4×C43—42no—
86C4⋊C4×C43—42no—
87C4⋊C4×C43—44no—
88C22⋊C4×C43—42no—
89C22⋊C4×C43—42no—
90C42×C43—22no—
91C42×C43—22no—
92C42×C43—41no—
93C42×C43—41no—
94C23×C43—21no—
95C23×C43—21no—
96C23×C43—21no—
97C23×C43—21no—
98C23×C43C2×C22⋊C411yescharacteristic
99C23×C43#12411yescharacteristic
100C23×C43#12711yescharacteristic
101C23×C43#13712yes—
102C23×C43#13712yes—
103Q8×C43—84no—
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
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—42no—
119C2×C4×C43—42no—
120C2×C4×C43—44no—
121C2×C4×C43—44no—
122C2×C4×C43—44no—
123C2×C4×C43—44no—
124C2×C4×C43—44no—
125C2×C4×C43—42no—
126C2×C4×C43—42no—
127C2×C4×C43—42no—
128C2×C4×C43—42no—
129C2×C4×C43—42no—
130C2×C4×C43—42no—
131C2×C4×C43—82no—
132C2×C4×C43—82no—
133C2×C4×C43—82no—
134C2×C4×C43—82no—
135C2×C4×C43#9912yes—
136C2×C4×C43#10412yes—
137C2×C4×C43C4×D412yes—
138C2×C4×C43#12112yes—
139C8×C43—44no—
140#9683C4311yesmaximal, characteristic, direct product factor, Sylow
141C22×C43—21no—
142C22×C43—21no—
143C22×C43—21no—
144C22×C43—21no—
145C22×C43—22no—
146C22×C43—22no—
147C22×C43—22no—
148C22×C43—22no—
149C22×C43#39011yescharacteristic
150C22×C43C2×#9911yescharacteristic
151C22×C43#41011yescharacteristic
152C22×C43#41911yescharacteristic
153C22×C43#41911yescharacteristic
154C22×C43C2×#10411yescharacteristic
155C22×C43#42111yescharacteristic
156C22×C43#49112yes—
157C22×C43#49712yes—
158C4×C43—22no—
159C4×C43—22no—
160C4×C43—22no—
161C4×C43—22no—
162C4×C43—41no—
163C4×C43—41no—
164C4×C43—84no—
165C4×C43—82no—
166C4×C43—82no—
167#2857C2×C4311yescharacteristic
168#1749C2×C4311yescharacteristic
169C2×#328C2×C4314yes—
170#1434C2×C4311yescharacteristic
171C2×C43—22no—
172C2×C43—22no—
173C2×C43#150611yescharacteristic
174C2×C43#150811yescharacteristic
175C2×C43#151111yescharacteristic
176C2×C43#151511yescharacteristic
177C2×C43#196011yescharacteristic
178C2×C43#196411yescharacteristic
179C2×C43#198011yescharacteristic
180C2×C4⋊Q8C4×C4311yescharacteristic, complemented
181C2×C22⋊Q8C22×C4312yes—
182C22×C42C22×C4311yescharacteristic
183C2×C22⋊C8C22×C4312yes—
184C2×#97—21no—
185#391C4×C4312yescomplemented
186#389—21no—
187#389—21no—
188#384C4×C4311yescharacteristic, complemented
189#380—21no—
190#380—21no—
191C2×#95—21no—
192C2×#95—21no—
193C2×#95C22×C4312yes—
194#336—21no—
195#328—28no—
196C43#968311yescharacteristic, direct product factor, Sylow
197C22×Q8C2×C4×C4312yes—
198C23×C4—22no—
199C23×C4D4×C4311yescharacteristic
200C23×C4D4×C4311yescharacteristic
201C23×C4C23×C4311yescharacteristic
202C22×C8—22no—
203C4⋊Q8—42no—
204C22⋊Q8—24no—
205C22⋊Q8—24no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—22no—
211C2×C4⋊C4C2×C4×C4312yes—
212C2×C22⋊C4—22no—
213C2×C42—42no—
214C2×C42C2×C4×C4311yescharacteristic
215C2×C42C2×C4×C4311yescharacteristic
216C2×C42D4×C4311yescharacteristic
217C2×C42D4×C4311yescharacteristic
218C22⋊C8—22no—
219C22⋊C8D4×C4314yes—
220#97—42no—
221#95—24no—
222#95—22no—
223#95—22no—
224#95—24no—
225#95—42no—
226C24C2×D4×C4311yescharacteristic
227C2×Q8—24no—
228C2×Q8—42no—
229C2×Q8—42no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—24no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4C22⋊C4×C4311yescharacteristic
248C22×C4C22⋊C4×C4311yescharacteristic
249C22×C4C22⋊C4×C4311yescharacteristic
250C22×C4C22⋊C4×C4311yescharacteristic
251C22×C4C22×C4×C4311yescharacteristic
252C22×C4C2×D4×C4311yescharacteristic
253C22×C4C2×D4×C4312yes—
254C22×C4#41×C4312yes—
255C2×C8—24no—
256C2×C8—42no—
257C2×C8—42no—
258C4⋊C4—24no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C4⋊C4—42no—
262C4⋊C4—42no—
263C4⋊C4—44no—
264C22⋊C4—42no—
265C22⋊C4—42no—
266C42—22no—
267C42—22no—
268C42—41no—
269C42—41no—
270C23—21no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23C2×C22⋊C4×C4311yescharacteristic
275C23#124×C4311yescharacteristic
276C23#127×C4311yescharacteristic
277C23#137×C4312yes—
278C23#137×C4312yes—
279Q8—84no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—44no—
297C2×C4—44no—
298C2×C4—44no—
299C2×C4—44no—
300C2×C4—44no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—82no—
308C2×C4—82no—
309C2×C4—82no—
310C2×C4—82no—
311C2×C4#99×C4312yes—
312C2×C4#104×C4312yes—
313C2×C4C4×D4×C4312yes—
314C2×C4#121×C4312yes—
315C8—44no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—22no—
321C22—22no—
322C22—22no—
323C22—22no—
324C22C43×#39011yescharacteristic
325C22C2×#99×C4311yescharacteristic
326C22C43×#41011yescharacteristic
327C22C43×#41911yescharacteristic
328C22C43×#41911yescharacteristic
329C22C2×#104×C4311yescharacteristic
330C22C43×#42111yescharacteristic
331C22C43×#49112yes—
332C22C43×#49712yes—
333C4—22no—
334C4—22no—
335C4—22no—
336C4—22no—
337C4—41no—
338C4—41no—
339C4—84no—
340C4—82no—
341C4—82no—
342C2—22no—
343C2—22no—
344C2C43×#150611yescharacteristic
345C2C43×#150811yescharacteristic
346C2C43×#151111yescharacteristic
347C2C43×#151511yescharacteristic
348C2C43×#196011yescharacteristic
349C2C43×#196411yescharacteristic
350C2C43×#198011yescharacteristic
subgroupG/H
center, socleC23×C43C2×C22⋊C4
commutatorC22×C4C22×C4×C43
Frattini, cosocleC23×C4C23×C43
prime radicalC24×C43C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C43 ◁ C22×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
5. C2×C4⋊Q8×C43C4semidirect
10. C43×#391C4semidirect
13. C43×#384C4semidirect
140. #9683C43direct (N × H)
180. C2×C4⋊Q8C4×C43semidirect
185. #391C4×C43semidirect
188. #384C4×C43semidirect
196. C43#9683direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#28572
C43×#17492
C2×C43×#3282
C43×#14342
#968343