Finite Group Databasebeta

← C43×#9912 #24929929

Subgroups — C43×#9912 #24929929

Order 11008.

592 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2857C211yesmaximal, characteristic
2C43×#1797C211yesmaximal, characteristic
3C43×#1434C211yesmaximal, characteristic
4C43×#1294C214yesmaximal
5C2×C4⋊Q8×C43C411yescharacteristic, complemented
6C2×C22⋊Q8×C43—21no—
7C22×C42×C43C2211yescharacteristic
8C2×C4⋊C8×C43—21no—
9C2×C22⋊C8×C43C2212yes—
10C43×#391—21no—
11C43×#389—21no—
12C43×#389C412yescomplemented
13C43×#384C411yescharacteristic, complemented
14C43×#380—21no—
15C43×#380C2212yes—
16C2×#95×C43—21no—
17C2×#95×C43—21no—
18C2×#95×C43C2212yes—
19C43×#336—21no—
20C22×Q8×C43—21no—
21C23×C4×C43—22no—
22C23×C4×C43D411yescharacteristic
23C23×C4×C43D411yescharacteristic
24C23×C4×C43C2311yescharacteristic
25C22×C8×C43—22no—
26C4⋊Q8×C43—42no—
27C22⋊Q8×C43—42no—
28C22⋊Q8×C43—42no—
29C2×C4⋊C4×C43—21no—
30C2×C4⋊C4×C43—22no—
31C2×C4⋊C4×C43—21no—
32C2×C4⋊C4×C43—21no—
33C2×C4⋊C4×C43C2×C412yes—
34C2×C4⋊C4×C43C2×C412yes—
35C2×C22⋊C4×C43—22no—
36C2×C42×C43—42no—
37C2×C42×C43C2×C411yescharacteristic
38C2×C42×C43C2×C411yescharacteristic
39C2×C42×C43D411yescharacteristic
40C2×C42×C43D411yescharacteristic
41C4⋊C8×C43—42no—
42C22⋊C8×C43—24no—
43#95×C43—22no—
44#95×C43—22no—
45#95×C43—22no—
46#95×C43—42no—
47#95×C43—42no—
48#95×C43Q814yescomplemented
49C24×C43C2×D411yescharacteristic
50C2×Q8×C43—42no—
51C2×Q8×C43—42no—
52C2×Q8×C43—42no—
53C22×C4×C43—22no—
54C22×C4×C43—22no—
55C22×C4×C43—22no—
56C22×C4×C43—24no—
57C22×C4×C43—22no—
58C22×C4×C43—41no—
59C22×C4×C43—41no—
60C22×C4×C43—41no—
61C22×C4×C43—41no—
62C22×C4×C43—41no—
63C22×C4×C43—42no—
64C22×C4×C43—42no—
65C22×C4×C43—42no—
66C22×C4×C43—42no—
67C22×C4×C43—42no—
68C22×C4×C43—42no—
69C22×C4×C43C22⋊C411yescharacteristic
70C22×C4×C43C22⋊C411yescharacteristic
71C22×C4×C43C22⋊C411yescharacteristic
72C22×C4×C43C22⋊C411yescharacteristic
73C22×C4×C43D812yes—
74C22×C4×C43SD1612yes—
75C22×C4×C43C22×C411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×Q812yes—
78C22×C4×C43#4112yes—
79C2×C8×C43—42no—
80C2×C8×C43—42no—
81C2×C8×C43—42no—
82C4⋊C4×C43—42no—
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×C43C22⋊Q812yes—
100C23×C43C2×D811yescharacteristic
101C23×C43C2×SD1611yescharacteristic
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—42no—
118C2×C4×C43—42no—
119C2×C4×C43—42no—
120C2×C4×C43—42no—
121C2×C4×C43—44no—
122C2×C4×C43—44no—
123C2×C4×C43—44no—
124C2×C4×C43—42no—
125C2×C4×C43—42no—
126C2×C4×C43—42no—
127C2×C4×C43—42no—
128C2×C4×C43—42no—
129C2×C4×C43—42no—
130C2×C4×C43—44no—
131C2×C4×C43—82no—
132C2×C4×C43—82no—
133C2×C4×C43—82no—
134C2×C4×C43—82no—
135C2×C4×C43#9912yes—
136C2×C4×C43#10212yes—
137C2×C4×C43#10212yes—
138C2×C4×C43C4×Q812yes—
139C2×C4×C43#12411yescharacteristic
140C2×C4×C43C4⋊Q811yescharacteristic
141C8×C43—82no—
142#9912C4311yesmaximal, characteristic, direct product factor, Sylow
143C22×C43—22no—
144C22×C43—22no—
145C22×C43—22no—
146C22×C43—22no—
147C22×C43—21no—
148C22×C43—21no—
149C22×C43—21no—
150C22×C43—21no—
151C22×C43#39111yescharacteristic
152C22×C43C2×#9911yescharacteristic
153C22×C43#41011yescharacteristic
154C22×C43C2×#10211yescharacteristic
155C22×C43#41911yescharacteristic
156C22×C43#42111yescharacteristic
157C22×C43#42111yescharacteristic
158C22×C43#47412yes—
159C22×C43#47512yes—
160C4×C43—21no—
161C4×C43—22no—
162C4×C43—21no—
163C4×C43—22no—
164C4×C43—22no—
165C4×C43—22no—
166C4×C43—41no—
167C4×C43—84no—
168C4×C43—82no—
169C4×C43—82no—
170#2857C2×C4311yescharacteristic
171#1797C2×C4311yescharacteristic
172#1434C2×C4311yescharacteristic
173#1294C2×C4314yes—
174C2×C43—22no—
175C2×C43—22no—
176C2×C43#151111yescharacteristic
177C2×C43#151511yescharacteristic
178C2×C43#151711yescharacteristic
179C2×C43#151911yescharacteristic
180C2×C43#198811yescharacteristic
181C2×C43#199511yescharacteristic
182C2×C43#199611yescharacteristic
183C2×C4⋊Q8C4×C4311yescharacteristic, complemented
184C2×C22⋊Q8—21no—
185C22×C42C22×C4311yescharacteristic
186C2×C4⋊C8—21no—
187C2×C22⋊C8C22×C4312yes—
188#391—21no—
189#389—21no—
190#389C4×C4312yescomplemented
191#384C4×C4311yescharacteristic, complemented
192#380—21no—
193#380C22×C4312yes—
194C2×#95—21no—
195C2×#95—21no—
196C2×#95C22×C4312yes—
197#336—21no—
198C43#991211yescharacteristic, direct product factor, Sylow
199C22×Q8—21no—
200C23×C4—22no—
201C23×C4D4×C4311yescharacteristic
202C23×C4D4×C4311yescharacteristic
203C23×C4C23×C4311yescharacteristic
204C22×C8—22no—
205C4⋊Q8—42no—
206C22⋊Q8—42no—
207C22⋊Q8—42no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—22no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4C2×C4×C4312yes—
213C2×C4⋊C4C2×C4×C4312yes—
214C2×C22⋊C4—22no—
215C2×C42—42no—
216C2×C42C2×C4×C4311yescharacteristic
217C2×C42C2×C4×C4311yescharacteristic
218C2×C42D4×C4311yescharacteristic
219C2×C42D4×C4311yescharacteristic
220C4⋊C8—42no—
221C22⋊C8—24no—
222#95—22no—
223#95—22no—
224#95—22no—
225#95—42no—
226#95—42no—
227#95Q8×C4314yescomplemented
228C24C2×D4×C4311yescharacteristic
229C2×Q8—42no—
230C2×Q8—42no—
231C2×Q8—42no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—24no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4C22⋊C4×C4311yescharacteristic
249C22×C4C22⋊C4×C4311yescharacteristic
250C22×C4C22⋊C4×C4311yescharacteristic
251C22×C4C22⋊C4×C4311yescharacteristic
252C22×C4D8×C4312yes—
253C22×C4SD16×C4312yes—
254C22×C4C22×C4×C4311yescharacteristic
255C22×C4C2×D4×C4311yescharacteristic
256C22×C4C2×Q8×C4312yes—
257C22×C4#41×C4312yes—
258C2×C8—42no—
259C2×C8—42no—
260C2×C8—42no—
261C4⋊C4—42no—
262C4⋊C4—42no—
263C4⋊C4—42no—
264C4⋊C4—42no—
265C4⋊C4—42no—
266C4⋊C4—44no—
267C22⋊C4—42no—
268C22⋊C4—42no—
269C42—22no—
270C42—22no—
271C42—41no—
272C42—41no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23C2×C22⋊C4×C4311yescharacteristic
278C23C22⋊Q8×C4312yes—
279C23C2×D8×C4311yescharacteristic
280C23C2×SD16×C4311yescharacteristic
281C23#137×C4312yes—
282Q8—84no—
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—21no—
295C2×C4—21no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—44no—
301C2×C4—44no—
302C2×C4—44no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—44no—
310C2×C4—82no—
311C2×C4—82no—
312C2×C4—82no—
313C2×C4—82no—
314C2×C4#99×C4312yes—
315C2×C4#102×C4312yes—
316C2×C4#102×C4312yes—
317C2×C4C4×Q8×C4312yes—
318C2×C4#124×C4311yescharacteristic
319C2×C4C4⋊Q8×C4311yescharacteristic
320C8—82no—
321C22—22no—
322C22—22no—
323C22—22no—
324C22—22no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22C43×#39111yescharacteristic
330C22C2×#99×C4311yescharacteristic
331C22C43×#41011yescharacteristic
332C22C2×#102×C4311yescharacteristic
333C22C43×#41911yescharacteristic
334C22C43×#42111yescharacteristic
335C22C43×#42111yescharacteristic
336C22C43×#47412yes—
337C22C43×#47512yes—
338C4—21no—
339C4—22no—
340C4—21no—
341C4—22no—
342C4—22no—
343C4—22no—
344C4—41no—
345C4—84no—
346C4—82no—
347C4—82no—
348C2—22no—
349C2—22no—
350C2C43×#151111yescharacteristic
351C2C43×#151511yescharacteristic
352C2C43×#151711yescharacteristic
353C2C43×#151911yescharacteristic
354C2C43×#198811yescharacteristic
355C2C43×#199511yescharacteristic
356C2C43×#199611yescharacteristic
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
12. C43×#389C4semidirect
13. C43×#384C4semidirect
48. #95×C43Q8semidirect
142. #9912C43direct (N × H)
183. C2×C4⋊Q8C4×C43semidirect
190. #389C4×C43semidirect
191. #384C4×C43semidirect
198. C43#9912direct (N × H)
227. #95Q8×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#28572
C43×#17972
C43×#14342
C43×#12942
#991243