Finite Group Databasebeta

← C43×#9107 #24929124

Subgroups — C43×#9107 #24929124

Order 11008.

674 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2972C211yesmaximal, characteristic, complemented
2C43×#2321C211yesmaximal, characteristic
3C43×#1459C211yesmaximal, characteristic, complemented
4C2×C43×#323C212yesmaximal, complemented
5C43×#1282C212yesmaximal, complemented
6C2×#120×C43C411yescharacteristic
7C2×C4×D4×C43C2211yescharacteristic
8C22×C22⋊C4×C43C2211yescharacteristic
9C8×D4×C43—24no—
10C43×#431—21no—
11C2×C22⋊C8×C43—21no—
12C2×C22⋊C8×C43C2212yes—
13C2×C22⋊C8×C43C2212yes—
14C43×#390—21no—
15C43×#388—21no—
16C43×#388—21no—
17C43×#386—21no—
18C43×#386C411yescharacteristic
19C43×#385C411yescharacteristic
20C43×#379C411yescharacteristic
21C4×C22⋊C4×C43C2211yescharacteristic
22C43×#324—21no—
23C43×#323—21no—
24C43×#323—24no—
25C25×C43C2×C411yescharacteristic
26C22×D4×C43—21no—
27C22×D4×C43C2×C411yescharacteristic
28C23×C4×C43C2×C411yescharacteristic
29C23×C4×C43D411yescharacteristic
30C23×C4×C43C2311yescharacteristic
31C22×C8×C43—22no—
32C22×C8×C43—22no—
33C22×C8×C43—22no—
34#120×C43—22no—
35#120×C43C814yescomplemented
36C4×D4×C43—22no—
37C4×D4×C43—22no—
38C2×C4⋊C4×C43—21no—
39C2×C4⋊C4×C43D411yescharacteristic
40C2×C22⋊C4×C43—21no—
41C2×C22⋊C4×C43—22no—
42C2×C22⋊C4×C43—21no—
43C2×C22⋊C4×C43—21no—
44C2×C22⋊C4×C43—22no—
45C2×C22⋊C4×C43—21no—
46C2×C22⋊C4×C43—21no—
47C2×C22⋊C4×C43—21no—
48C2×C22⋊C4×C43C2×C411yescharacteristic
49C2×C22⋊C4×C43C2×C411yescharacteristic
50C2×C22⋊C4×C43C2×C411yescharacteristic
51C2×C22⋊C4×C43D411yescharacteristic
52C2×C42×C43—21no—
53C2×C42×C43D411yescharacteristic
54C4⋊C8×C43—22no—
55C22⋊C8×C43—22no—
56C22⋊C8×C43—22no—
57C22⋊C8×C43—22no—
58C22⋊C8×C43—22no—
59C22⋊C8×C43D414yescomplemented
60C4×C8×C43—22no—
61#95×C43—21no—
62#95×C43—21no—
63#95×C43—21no—
64C24×C43—21no—
65C24×C43—22no—
66C24×C43—21no—
67C24×C43—22no—
68C24×C43—81no—
69C24×C43—81no—
70C24×C43C22⋊C411yescharacteristic
71C24×C43C2×C812yescomplemented
72C24×C43C22×C411yescharacteristic
73C2×D4×C43—24no—
74C2×D4×C43—22no—
75C2×D4×C43—22no—
76C2×D4×C43—81no—
77C2×D4×C43—81no—
78C2×D4×C43C2×C812yes—
79C2×D4×C43M1612yes—
80C22×C4×C43—21no—
81C22×C4×C43—21no—
82C22×C4×C43—21no—
83C22×C4×C43—21no—
84C22×C4×C43—21no—
85C22×C4×C43—22no—
86C22×C4×C43—81no—
87C22×C4×C43—81no—
88C22×C4×C43—81no—
89C22×C4×C43C22⋊C411yescharacteristic
90C22×C4×C43C22⋊C411yescharacteristic
91C22×C4×C43C22⋊C411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43C2×D411yescharacteristic
94C22×C4×C43C2×D412yes—
95C22×C4×C43#4112yes—
96C2×C8×C43—24no—
97C2×C8×C43—42no—
98C2×C8×C43—82no—
99C2×C8×C43—82no—
100C2×C8×C43—82no—
101C4⋊C4×C43—22no—
102C4⋊C4×C43—81no—
103C22⋊C4×C43—24no—
104C22⋊C4×C43—22no—
105C22⋊C4×C43—22no—
106C22⋊C4×C43—21no—
107C22⋊C4×C43—22no—
108C22⋊C4×C43—41no—
109C22⋊C4×C43—42no—
110C22⋊C4×C43—41no—
111C22⋊C4×C43—81no—
112C22⋊C4×C43—81no—
113C22⋊C4×C43—81no—
114C22⋊C4×C43C2×C812yescomplemented
115C42×C43—21no—
116C42×C43—21no—
117C42×C43—81no—
118C23×C43—21no—
119C23×C43—21no—
120C23×C43—22no—
121C23×C43—24no—
122C23×C43—41no—
123C23×C43—41no—
124C23×C43—41no—
125C23×C43—41no—
126C23×C43—41no—
127C23×C43—41no—
128C23×C43—41no—
129C23×C43—41no—
130C23×C43—41no—
131C23×C43—41no—
132C23×C43—42no—
133C23×C43—82no—
134C23×C43—82no—
135C23×C43—82no—
136C23×C43—82no—
137C23×C43—84no—
138C23×C43C22⋊C812yes—
139C23×C43C2×C22⋊C411yescharacteristic
140C23×C43C4×D412yes—
141C23×C43C22×C811yescharacteristic
142C23×C43C2×M1611yescharacteristic
143C23×C43#13112yes—
144D4×C43—24no—
145D4×C43—24no—
146D4×C43—84no—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—21no—
150C2×C4×C43—21no—
151C2×C4×C43—22no—
152C2×C4×C43—41no—
153C2×C4×C43—42no—
154C2×C4×C43—42no—
155C2×C4×C43—41no—
156C2×C4×C43—42no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43—41no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—41no—
164C2×C4×C43—41no—
165C2×C4×C43—41no—
166C2×C4×C43—41no—
167C2×C4×C43—81no—
168C2×C4×C43—82no—
169C2×C4×C43C22⋊C812yes—
170C2×C4×C43#12011yescharacteristic
171C2×C4×C43#12112yes—
172C2×C4×C43#12311yescharacteristic
173C8×C43—44no—
174C8×C43—82no—
175#9107C4311yesmaximal, characteristic, direct product factor, Sylow
176C22×C43—21no—
177C22×C43—22no—
178C22×C43—21no—
179C22×C43—22no—
180C22×C43—22no—
181C22×C43—41no—
182C22×C43—41no—
183C22×C43—42no—
184C22×C43—42no—
185C22×C43—42no—
186C22×C43—42no—
187C22×C43—41no—
188C22×C43—41no—
189C22×C43—42no—
190C22×C43—81no—
191C22×C43—84no—
192C22×C43—81no—
193C22×C43—81no—
194C22×C43—84no—
195C22×C43—81no—
196C22×C43—81no—
197C22×C43#38611yescharacteristic
198C22×C43C2×C22⋊C811yescharacteristic
199C22×C43#40811yescharacteristic
200C22×C43C8×D412yes—
201C22×C43#43512yes—
202C4×C43—22no—
203C4×C43—21no—
204C4×C43—22no—
205C4×C43—21no—
206C4×C43—42no—
207C4×C43—41no—
208C4×C43—41no—
209C4×C43—81no—
210C4×C43—81no—
211#2972C2×C4311yescharacteristic, complemented
212#2321C2×C4311yescharacteristic
213#1459C2×C4311yescharacteristic, complemented
214C2×#323C2×C4312yescomplemented
215#1282C2×C4312yescomplemented
216C2×C43—21no—
217C2×C43—21no—
218C2×C43—22no—
219C2×C43—22no—
220C2×C43—42no—
221C2×C43—82no—
222C2×C43#186911yescharacteristic
223C2×C43#191311yescharacteristic
224C2×C43#191411yescharacteristic
225C2×#120C4×C4311yescharacteristic
226C2×C4×D4C22×C4311yescharacteristic
227C22×C22⋊C4C22×C4311yescharacteristic
228C8×D4—24no—
229#431—21no—
230C2×C22⋊C8—21no—
231C2×C22⋊C8C22×C4312yes—
232C2×C22⋊C8C22×C4312yes—
233#390—21no—
234#388—21no—
235#388—21no—
236#386—21no—
237#386C4×C4311yescharacteristic
238#385C4×C4311yescharacteristic
239#379C4×C4311yescharacteristic
240C4×C22⋊C4C22×C4311yescharacteristic
241#324—21no—
242#323—21no—
243#323—24no—
244C43#910711yescharacteristic, direct product factor, Sylow
245C25C2×C4×C4311yescharacteristic
246C22×D4—21no—
247C22×D4C2×C4×C4311yescharacteristic
248C23×C4C2×C4×C4311yescharacteristic
249C23×C4D4×C4311yescharacteristic
250C23×C4C23×C4311yescharacteristic
251C22×C8—22no—
252C22×C8—22no—
253C22×C8—22no—
254#120—22no—
255#120C8×C4314yescomplemented
256C4×D4—22no—
257C4×D4—22no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4D4×C4311yescharacteristic
260C2×C22⋊C4—21no—
261C2×C22⋊C4—22no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—22no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4C2×C4×C4311yescharacteristic
269C2×C22⋊C4C2×C4×C4311yescharacteristic
270C2×C22⋊C4C2×C4×C4311yescharacteristic
271C2×C22⋊C4D4×C4311yescharacteristic
272C2×C42—21no—
273C2×C42D4×C4311yescharacteristic
274C4⋊C8—22no—
275C22⋊C8—22no—
276C22⋊C8—22no—
277C22⋊C8—22no—
278C22⋊C8—22no—
279C22⋊C8D4×C4314yescomplemented
280C4×C8—22no—
281#95—21no—
282#95—21no—
283#95—21no—
284C24—21no—
285C24—22no—
286C24—21no—
287C24—22no—
288C24—81no—
289C24—81no—
290C24C22⋊C4×C4311yescharacteristic
291C24C2×C8×C4312yescomplemented
292C24C22×C4×C4311yescharacteristic
293C2×D4—22no—
294C2×D4—22no—
295C2×D4—24no—
296C2×D4—81no—
297C2×D4—81no—
298C2×D4C2×C8×C4312yes—
299C2×D4M16×C4312yes—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—22no—
306C22×C4—81no—
307C22×C4—81no—
308C22×C4—81no—
309C22×C4C22⋊C4×C4311yescharacteristic
310C22×C4C22⋊C4×C4311yescharacteristic
311C22×C4C22⋊C4×C4311yescharacteristic
312C22×C4C2×D4×C4312yes—
313C22×C4C2×D4×C4311yescharacteristic
314C22×C4C2×D4×C4311yescharacteristic
315C22×C4#41×C4312yes—
316C2×C8—24no—
317C2×C8—42no—
318C2×C8—82no—
319C2×C8—82no—
320C2×C8—82no—
321C4⋊C4—22no—
322C4⋊C4—81no—
323C22⋊C4—22no—
324C22⋊C4—21no—
325C22⋊C4—24no—
326C22⋊C4—22no—
327C22⋊C4—22no—
328C22⋊C4—41no—
329C22⋊C4—42no—
330C22⋊C4—41no—
331C22⋊C4—81no—
332C22⋊C4—81no—
333C22⋊C4—81no—
334C22⋊C4C2×C8×C4312yescomplemented
335C42—21no—
336C42—21no—
337C42—81no—
338C23—21no—
339C23—21no—
340C23—22no—
341C23—24no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—42no—
353C23—82no—
354C23—82no—
355C23—82no—
356C23—82no—
357C23—84no—
358C23C22⋊C8×C4312yes—
359C23C2×C22⋊C4×C4311yescharacteristic
360C23C4×D4×C4312yes—
361C23C22×C8×C4311yescharacteristic
362C23C2×M16×C4311yescharacteristic
363C23#131×C4312yes—
364D4—24no—
365D4—24no—
366D4—84no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—22no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—81no—
388C2×C4—82no—
389C2×C4C22⋊C8×C4312yes—
390C2×C4#120×C4311yescharacteristic
391C2×C4#121×C4312yes—
392C2×C4#123×C4311yescharacteristic
393C8—44no—
394C8—82no—
395C22—21no—
396C22—22no—
397C22—21no—
398C22—22no—
399C22—22no—
400C22—41no—
401C22—41no—
402C22—42no—
403C22—42no—
404C22—42no—
405C22—42no—
406C22—41no—
407C22—41no—
408C22—42no—
409C22—81no—
410C22—84no—
411C22—81no—
412C22—81no—
413C22—84no—
414C22—81no—
415C22—81no—
416C22C43×#38611yescharacteristic
417C22C2×C22⋊C8×C4311yescharacteristic
418C22C43×#40811yescharacteristic
419C22C8×D4×C4312yes—
420C22C43×#43512yes—
421C4—22no—
422C4—21no—
423C4—22no—
424C4—21no—
425C4—42no—
426C4—41no—
427C4—41no—
428C4—81no—
429C4—81no—
430C2—21no—
431C2—21no—
432C2—22no—
433C2—22no—
434C2—42no—
435C2—82no—
436C2C43×#186911yescharacteristic
437C2C43×#191311yescharacteristic
438C2C43×#191411yescharacteristic
subgroupG/H
center, socleC22×C43#386
commutatorC23C22×C8×C43
Frattini, cosocleC23×C4C23×C43
prime radicalC2×#120×C43C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C23×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#2972C2semidirect
3. C43×#1459C2semidirect
4. C2×C43×#323C2semidirect
5. C43×#1282C2semidirect
35. #120×C43C8semidirect
59. C22⋊C8×C43D4semidirect
71. C24×C43C2×C8semidirect
114. C22⋊C4×C43C2×C8semidirect
175. #9107C43direct (N × H)
211. #2972C2×C43semidirect
213. #1459C2×C43semidirect
214. C2×#323C2×C43semidirect
215. #1282C2×C43semidirect
244. C43#9107direct (N × H)
255. #120C8×C43semidirect
279. C22⋊C8D4×C43semidirect
291. C24C2×C8×C43semidirect
334. C22⋊C4C2×C8×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#29722
C43×#23212
C43×#14592
C2×C43×#3232
C43×#12822
#910743