Finite Group Databasebeta

← C43×#19358 #24939375

Subgroups — C43×#19358 #24939375

Order 11008.

608 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3218C212yesmaximal
2C2×C43×#500C211yesmaximal, characteristic, complemented
3C43×#2966C211yesmaximal, characteristic
4C43×#1694C212yesmaximal, complemented
5C43×#1693C212yesmaximal, complemented
6C43×#1674C212yesmaximal, complemented
7C43×#1673C212yesmaximal, complemented
8C43×#1568C211yesmaximal, characteristic, complemented
9C43×#1556C212yesmaximal, complemented
10C2×C4⋊Q8×C43C2212yes—
11C43×#529C2211yescharacteristic
12C43×#500—21no—
13C43×#500—21no—
14C43×#500C2212yes—
15C43×#500C2212yes—
16C43×#497—22no—
17C43×#491—22no—
18C43×#462C2214yes—
19C43×#461C2214yes—
20C43×#451—22no—
21C43×#448—22no—
22C43×#446C2211yescharacteristic
23C8×Q8×C43C2211yescharacteristic
24C43×#436C2211yescharacteristic
25C43×#435—21no—
26C8×D4×C43—21no—
27C8×D4×C43C2211yescharacteristic
28C43×#433—21no—
29C43×#432C2211yescharacteristic
30C43×#432C2212yes—
31C2×#107×C43—21no—
32C2×#107×C43—21no—
33C43×#405—21no—
34C2×C4×C8×C43C2211yescharacteristic
35C43×#335C2212yes—
36C43×#334C2212yes—
37C43×#332C2214yes—
38C43×#332C2214yes—
39C22×Q8×C43—22no—
40C2×Q16×C43—24no—
41C2×SD16×C43—24no—
42C2×M16×C43—21no—
43C22×C8×C43—21no—
44C22×C8×C43D411yescharacteristic
45C22×C8×C43D411yescharacteristic
46C4⋊Q8×C43—22no—
47C4⋊Q8×C43—22no—
48C4⋊Q8×C43—22no—
49C4⋊Q8×C43C2314yes—
50#126×C43—21no—
51#125×C43D411yescharacteristic
52#124×C43D411yescharacteristic
53#123×C43—21no—
54C22⋊Q8×C43D411yescharacteristic
55#121×C43D411yescharacteristic
56C4×Q8×C43C2311yescharacteristic
57C4×D4×C43—21no—
58C4×D4×C43C2311yescharacteristic
59#117×C43—21no—
60C2×C4⋊C4×C43—22no—
61C2×C4⋊C4×C43—22no—
62C2×C42×C43C2311yescharacteristic
63#107×C43—22no—
64#107×C43—22no—
65#107×C43—22no—
66#107×C43—22no—
67C4⋊C8×C43—21no—
68C4⋊C8×C43—21no—
69C4⋊C8×C43C2311yescharacteristic
70C4⋊C8×C43C2311yescharacteristic
71C4⋊C8×C43C2314yes—
72#103×C43—24no—
73#103×C43—24no—
74C22⋊C8×C43—21no—
75C22⋊C8×C43—22no—
76C22⋊C8×C43—21no—
77C22⋊C8×C43—21no—
78#97×C43—21no—
79#97×C43—22no—
80#97×C43—21no—
81C4×C8×C43—21no—
82C4×C8×C43D411yescharacteristic
83C4×C8×C43D411yescharacteristic
84C4×C8×C43C2311yescharacteristic
85C4×C8×C43C2311yescharacteristic
86C2×Q8×C43—24no—
87C2×Q8×C43—42no—
88C2×Q8×C43—84no—
89C2×Q8×C43C2×D411yescharacteristic
90C2×D4×C43—21no—
91C2×D4×C43C2×D411yescharacteristic
92C22×C4×C43—21no—
93C22×C4×C43—42no—
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43#4111yescharacteristic
97Q16×C43—84no—
98SD16×C43—84no—
99M16×C43—42no—
100C2×C8×C43—22no—
101C2×C8×C43—22no—
102C2×C8×C43—21no—
103C2×C8×C43—21no—
104C2×C8×C43—24no—
105C2×C8×C43—42no—
106C2×C8×C43C2×D411yescharacteristic
107C2×C8×C43C2×D411yescharacteristic
108C2×C8×C43C2×D411yescharacteristic
109C2×C8×C43C2×D411yescharacteristic
110C4⋊C4×C43—21no—
111C4⋊C4×C43—21no—
112C4⋊C4×C43—21no—
113C4⋊C4×C43—21no—
114C4⋊C4×C43—24no—
115C4⋊C4×C43—24no—
116C4⋊C4×C43—42no—
117C4⋊C4×C43—42no—
118C4⋊C4×C43C2×D411yescharacteristic
119C4⋊C4×C43C2×D411yescharacteristic
120C22⋊C4×C43—21no—
121C22⋊C4×C43—21no—
122C22⋊C4×C43—21no—
123C22⋊C4×C43—21no—
124C22⋊C4×C43—21no—
125C42×C43—21no—
126C42×C43C2×D411yescharacteristic
127C42×C43C2×D411yescharacteristic
128C42×C43#4111yescharacteristic
129C42×C43C2411yescharacteristic
130C23×C43—21no—
131C23×C43#12111yescharacteristic
132Q8×C43—22no—
133Q8×C43—44no—
134Q8×C43—44no—
135Q8×C43—84no—
136D4×C43—22no—
137D4×C43—42no—
138C2×C4×C43—22no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—22no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—21no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—44no—
148C2×C4×C43—84no—
149C2×C4×C43#12111yescharacteristic
150C2×C4×C43#12111yescharacteristic
151C2×C4×C43#12111yescharacteristic
152C2×C4×C43C22×D411yescharacteristic
153C2×C4×C43C22×D411yescharacteristic
154C2×C4×C43C2×#4111yescharacteristic
155C8×C43—21no—
156C8×C43—21no—
157C8×C43—41no—
158C8×C43—41no—
159C8×C43—44no—
160C8×C43#13712yes—
161C8×C43#13712yes—
162#19358C4311yesmaximal, characteristic, direct product factor, Sylow
163C22×C43—21no—
164C22×C43—21no—
165C22×C43—41no—
166C22×C43—41no—
167C22×C43—41no—
168C22×C43#47312yes—
169C22×C43C2×#12111yescharacteristic
170C4×C43—21no—
171C4×C43—21no—
172C4×C43—21no—
173C4×C43—21no—
174C4×C43—41no—
175C4×C43—41no—
176C4×C43—41no—
177C4×C43—84no—
178C4×C43C2×#13711yescharacteristic
179C4×C43C2×#13711yescharacteristic
180C4×C43#57612yes—
181#3218C2×C4312yes—
182C2×#500C2×C4311yescharacteristic, complemented
183#2966C2×C4311yescharacteristic
184#1694C2×C4312yescomplemented
185#1693C2×C4312yescomplemented
186#1674C2×C4312yescomplemented
187#1673C2×C4312yescomplemented
188#1568C2×C4311yescharacteristic, complemented
189#1556C2×C4312yescomplemented
190C2×C43—22no—
191C2×C43—81no—
192C2×C43#303911yescharacteristic
193C2×C43#305811yescharacteristic
194C2×C43C2×#47311yescharacteristic
195C2×C4⋊Q8C22×C4312yes—
196#529C22×C4311yescharacteristic
197#500—21no—
198#500—21no—
199#500C22×C4312yes—
200#500C22×C4312yes—
201#497—22no—
202#491—22no—
203#462C22×C4314yes—
204#461C22×C4314yes—
205#451—22no—
206#448—22no—
207#446C22×C4311yescharacteristic
208C8×Q8C22×C4311yescharacteristic
209#436C22×C4311yescharacteristic
210#435—21no—
211C8×D4—21no—
212C8×D4C22×C4311yescharacteristic
213#433—21no—
214#432C22×C4311yescharacteristic
215#432C22×C4312yes—
216C2×#107—21no—
217C2×#107—21no—
218#405—21no—
219C2×C4×C8C22×C4311yescharacteristic
220#335C22×C4312yes—
221#334C22×C4312yes—
222#332C22×C4314yes—
223#332C22×C4314yes—
224C43#1935811yescharacteristic, direct product factor, Sylow
225C22×Q8—22no—
226C2×Q16—24no—
227C2×SD16—24no—
228C2×M16—21no—
229C22×C8—21no—
230C22×C8D4×C4311yescharacteristic
231C22×C8D4×C4311yescharacteristic
232C4⋊Q8—22no—
233C4⋊Q8—22no—
234C4⋊Q8—22no—
235C4⋊Q8C23×C4314yes—
236#126—21no—
237#125D4×C4311yescharacteristic
238#124D4×C4311yescharacteristic
239#123—21no—
240C22⋊Q8D4×C4311yescharacteristic
241#121D4×C4311yescharacteristic
242C4×Q8C23×C4311yescharacteristic
243C4×D4—21no—
244C4×D4C23×C4311yescharacteristic
245#117—21no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—22no—
248C2×C42C23×C4311yescharacteristic
249#107—22no—
250#107—22no—
251#107—22no—
252#107—22no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8C23×C4311yescharacteristic
256C4⋊C8C23×C4311yescharacteristic
257C4⋊C8C23×C4314yes—
258#103—24no—
259#103—24no—
260C22⋊C8—21no—
261C22⋊C8—22no—
262C22⋊C8—21no—
263C22⋊C8—21no—
264#97—21no—
265#97—21no—
266#97—22no—
267C4×C8—21no—
268C4×C8D4×C4311yescharacteristic
269C4×C8D4×C4311yescharacteristic
270C4×C8C23×C4311yescharacteristic
271C4×C8C23×C4311yescharacteristic
272C2×Q8—24no—
273C2×Q8—42no—
274C2×Q8—84no—
275C2×Q8C2×D4×C4311yescharacteristic
276C2×D4—21no—
277C2×D4C2×D4×C4311yescharacteristic
278C22×C4—21no—
279C22×C4—42no—
280C22×C4C2×D4×C4311yescharacteristic
281C22×C4C2×D4×C4311yescharacteristic
282C22×C4#41×C4311yescharacteristic
283Q16—84no—
284SD16—84no—
285M16—42no—
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—21no—
289C2×C8—21no—
290C2×C8—24no—
291C2×C8—42no—
292C2×C8C2×D4×C4311yescharacteristic
293C2×C8C2×D4×C4311yescharacteristic
294C2×C8C2×D4×C4311yescharacteristic
295C2×C8C2×D4×C4311yescharacteristic
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—24no—
301C4⋊C4—24no—
302C4⋊C4—42no—
303C4⋊C4—42no—
304C4⋊C4C2×D4×C4311yescharacteristic
305C4⋊C4C2×D4×C4311yescharacteristic
306C22⋊C4—21no—
307C22⋊C4—21no—
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—21no—
311C42—21no—
312C42C2×D4×C4311yescharacteristic
313C42C2×D4×C4311yescharacteristic
314C42#41×C4311yescharacteristic
315C42C24×C4311yescharacteristic
316C23—21no—
317C23#121×C4311yescharacteristic
318Q8—22no—
319Q8—44no—
320Q8—44no—
321Q8—84no—
322D4—22no—
323D4—42no—
324C2×C4—22no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—22no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—44no—
334C2×C4—84no—
335C2×C4#121×C4311yescharacteristic
336C2×C4#121×C4311yescharacteristic
337C2×C4#121×C4311yescharacteristic
338C2×C4C22×D4×C4311yescharacteristic
339C2×C4C22×D4×C4311yescharacteristic
340C2×C4C2×#41×C4311yescharacteristic
341C8—21no—
342C8—21no—
343C8—41no—
344C8—41no—
345C8—44no—
346C8#137×C4312yes—
347C8#137×C4312yes—
348C22—21no—
349C22—21no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22C43×#47312yes—
354C22C2×#121×C4311yescharacteristic
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—84no—
363C4C2×#137×C4311yescharacteristic
364C4C2×#137×C4311yescharacteristic
365C4C43×#57612yes—
366C2—22no—
367C2—81no—
368C2C43×#303911yescharacteristic
369C2C43×#305811yescharacteristic
370C2C2×C43×#47311yescharacteristic
subgroupG/H
center, socleC22×C43C2×#121
commutator, Frattini, cosocleC42C24×C43
prime radical#121×C43D4
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
2. C2×C43×#500C2semidirect
4. C43×#1694C2semidirect
5. C43×#1693C2semidirect
6. C43×#1674C2semidirect
7. C43×#1673C2semidirect
8. C43×#1568C2semidirect
9. C43×#1556C2semidirect
162. #19358C43direct (N × H)
182. C2×#500C2×C43semidirect
184. #1694C2×C43semidirect
185. #1693C2×C43semidirect
186. #1674C2×C43semidirect
187. #1673C2×C43semidirect
188. #1568C2×C43semidirect
189. #1556C2×C43semidirect
224. C43#19358direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#32182
C2×C43×#5002
C43×#29662
C43×#16942
C43×#16932
C43×#16742
C43×#16732
C43×#15682
C43×#15562
#1935843