Finite Group Databasebeta

← C43×#9332 #24929349

Subgroups — C43×#9332 #24929349

Order 11008.

464 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3194C211yesmaximal, characteristic
2C43×#2978C211yesmaximal, characteristic, complemented
3C43×#1516C211yesmaximal, characteristic, complemented
4C43×#1510C211yesmaximal, characteristic, complemented
5C43×#1471C211yesmaximal, characteristic, complemented
6C43×#1306C211yesmaximal, characteristic, complemented
7C43×#1293C211yesmaximal, characteristic, complemented
8C43×#525C2211yescharacteristic
9C2×#121×C43C2211yescharacteristic
10C43×#483C411yescharacteristic, complemented
11C43×#482—21no—
12C43×#480C411yescharacteristic, complemented
13C43×#469—21no—
14C43×#468—21no—
15C43×#450C411yescharacteristic, complemented
16C43×#449—21no—
17C43×#447C411yescharacteristic, complemented
18C43×#436—21no—
19C43×#436—21no—
20C43×#435—21no—
21C43×#435—21no—
22C43×#433—21no—
23C43×#408—21no—
24C43×#407C2211yescharacteristic
25C43×#407C2211yescharacteristic
26C43×#407C2211yescharacteristic
27C2×C22⋊C8×C43C2211yescharacteristic
28C43×#381C2211yescharacteristic
29C43×#328—21no—
30C43×#327—21no—
31C43×#327—21no—
32C43×#327—21no—
33C43×#323—21no—
34C43×#323—21no—
35C2×#41×C43D411yescharacteristic
36C22×D4×C43—21no—
37C22×D4×C43C2×C411yescharacteristic
38C23×C4×C43C2311yescharacteristic
39C2×SD16×C43—21no—
40C2×D8×C43—21no—
41C2×M16×C43—21no—
42C2×M16×C43—21no—
43C2×M16×C43—21no—
44C2×M16×C43—21no—
45C22×C8×C43—21no—
46C22×C8×C43—21no—
47#123×C43—21no—
48C22⋊Q8×C43C2×C411yescharacteristic
49C22⋊Q8×C43D411yescharacteristic
50#121×C43—21no—
51#121×C43—21no—
52#121×C43—21no—
53#121×C43—21no—
54#121×C43C2×C411yescharacteristic
55#121×C43D411yescharacteristic
56#120×C43—21no—
57C4×D4×C43—21no—
58C4×D4×C43—21no—
59#117×C43D411yescharacteristic
60C2×C4⋊C4×C43C2×C411yescharacteristic
61C2×C22⋊C4×C43—21no—
62C2×C22⋊C4×C43—21no—
63#107×C43—21no—
64#106×C43—21no—
65C4⋊C8×C43—21no—
66C4⋊C8×C43—21no—
67#103×C43—21no—
68#102×C43—21no—
69#102×C43—21no—
70#102×C43—21no—
71C22⋊C8×C43—21no—
72C22⋊C8×C43—21no—
73C22⋊C8×C43—21no—
74C22⋊C8×C43—21no—
75C22⋊C8×C43—21no—
76C22⋊C8×C43—21no—
77C22⋊C8×C43—21no—
78C22⋊C8×C43C2×C411yescharacteristic
79C22⋊C8×C43C2×C411yescharacteristic
80C22⋊C8×C43D411yescharacteristic
81C22⋊C8×C43D411yescharacteristic
82C22⋊C8×C43D411yescharacteristic
83C22⋊C8×C43D411yescharacteristic
84#97×C43—21no—
85C4×C8×C43—21no—
86#95×C43—21no—
87#95×C43—21no—
88C24×C43—21no—
89C24×C43#4111yescharacteristic
90#41×C43—81no—
91C2×Q8×C43C22⋊C411yescharacteristic
92C2×D4×C43—21no—
93C2×D4×C43—21no—
94C2×D4×C43—21no—
95C2×D4×C43—21no—
96C2×D4×C43—21no—
97C2×D4×C43—41no—
98C2×D4×C43—41no—
99C2×D4×C43—82no—
100C2×D4×C43—81no—
101C2×D4×C43C22⋊C411yescharacteristic
102C22×C4×C43—21no—
103C22×C4×C43—21no—
104C22×C4×C43—41no—
105C22×C4×C43—81no—
106C22×C4×C43C22×C411yescharacteristic
107C22×C4×C43C2×D411yescharacteristic
108C22×C4×C43C2×D411yescharacteristic
109C22×C4×C43C2×D411yescharacteristic
110C22×C4×C43C2×D411yescharacteristic
111C22×C4×C43#4111yescharacteristic
112SD16×C43—81no—
113D8×C43—81no—
114M16×C43—81no—
115M16×C43—81no—
116M16×C43—81no—
117M16×C43—81no—
118C2×C8×C43—21no—
119C2×C8×C43—21no—
120C2×C8×C43—21no—
121C2×C8×C43—21no—
122C2×C8×C43—21no—
123C2×C8×C43—21no—
124C2×C8×C43—41no—
125C2×C8×C43—81no—
126C2×C8×C43—81no—
127C4⋊C4×C43—21no—
128C4⋊C4×C43—21no—
129C4⋊C4×C43—21no—
130C4⋊C4×C43—21no—
131C4⋊C4×C43C22⋊C411yescharacteristic
132C4⋊C4×C43C22⋊C411yescharacteristic
133C22⋊C4×C43—21no—
134C22⋊C4×C43—21no—
135C22⋊C4×C43—21no—
136C22⋊C4×C43—21no—
137C22⋊C4×C43—21no—
138C22⋊C4×C43—41no—
139C22⋊C4×C43—41no—
140C22⋊C4×C43—81no—
141C42×C43—21no—
142C23×C43—21no—
143C23×C43—41no—
144C23×C43—41no—
145C23×C43—41no—
146C23×C43—42no—
147C23×C43—41no—
148C23×C43—81no—
149C23×C43—81no—
150C23×C43C4×D411yescharacteristic
151C23×C43#12111yescharacteristic
152C23×C43#12311yescharacteristic
153Q8×C43—41no—
154D4×C43—41no—
155D4×C43—41no—
156D4×C43—41no—
157D4×C43—81no—
158D4×C43—81no—
159D4×C43—81no—
160D4×C43—81no—
161D4×C43—82no—
162D4×C43—82no—
163C2×C4×C43—21no—
164C2×C4×C43—21no—
165C2×C4×C43—21no—
166C2×C4×C43—41no—
167C2×C4×C43—41no—
168C2×C4×C43—41no—
169C2×C4×C43—41no—
170C2×C4×C43—41no—
171C2×C4×C43—41no—
172C2×C4×C43—41no—
173C2×C4×C43—41no—
174C2×C4×C43—41no—
175C2×C4×C43—81no—
176C2×C4×C43—81no—
177C2×C4×C43—81no—
178C2×C4×C43—81no—
179C2×C4×C43C2×C22⋊C411yescharacteristic
180C2×C4×C43C4×D411yescharacteristic
181C2×C4×C43#12011yescharacteristic
182C2×C4×C43#12111yescharacteristic
183C8×C43—41no—
184C8×C43—41no—
185C8×C43—41no—
186C8×C43—41no—
187C8×C43—41no—
188C8×C43—41no—
189C8×C43—81no—
190#9332C4311yesmaximal, characteristic, direct product factor, Sylow
191C22×C43—21no—
192C22×C43—21no—
193C22×C43—21no—
194C22×C43—21no—
195C22×C43—21no—
196C22×C43—21no—
197C22×C43—21no—
198C22×C43—21no—
199C22×C43—21no—
200C22×C43—41no—
201C22×C43—41no—
202C22×C43—41no—
203C22×C43—82no—
204C22×C43—81no—
205C22×C43—81no—
206C22×C43—81no—
207C22×C43—162no—
208C22×C43#38611yescharacteristic
209C4×C43—21no—
210C4×C43—21no—
211C4×C43—21no—
212C4×C43—21no—
213C4×C43—41no—
214C4×C43—41no—
215C4×C43—41no—
216C4×C43—81no—
217C4×C43—161no—
218#3194C2×C4311yescharacteristic
219#2978C2×C4311yescharacteristic, complemented
220#1516C2×C4311yescharacteristic, complemented
221#1510C2×C4311yescharacteristic, complemented
222#1471C2×C4311yescharacteristic, complemented
223#1306C2×C4311yescharacteristic, complemented
224#1293C2×C4311yescharacteristic, complemented
225C2×C43—41no—
226C2×C43—41no—
227C2×C43—41no—
228C2×C43—81no—
229C2×C43—161no—
230C2×C43#188111yescharacteristic
231C2×C43#190311yescharacteristic
232C2×C43#191311yescharacteristic
233#525C22×C4311yescharacteristic
234C2×#121C22×C4311yescharacteristic
235#483C4×C4311yescharacteristic, complemented
236#482—21no—
237#480C4×C4311yescharacteristic, complemented
238#469—21no—
239#468—21no—
240#450C4×C4311yescharacteristic, complemented
241#449—21no—
242#447C4×C4311yescharacteristic, complemented
243#436—21no—
244#436—21no—
245#435—21no—
246#435—21no—
247#433—21no—
248#408—21no—
249#407C22×C4311yescharacteristic
250#407C22×C4311yescharacteristic
251#407C22×C4311yescharacteristic
252C2×C22⋊C8C22×C4311yescharacteristic
253#381C22×C4311yescharacteristic
254#328—21no—
255#327—21no—
256#327—21no—
257#327—21no—
258#323—21no—
259#323—21no—
260C43#933211yescharacteristic, direct product factor, Sylow
261C2×#41D4×C4311yescharacteristic
262C22×D4—21no—
263C22×D4C2×C4×C4311yescharacteristic
264C23×C4C23×C4311yescharacteristic
265C2×SD16—21no—
266C2×D8—21no—
267C2×M16—21no—
268C2×M16—21no—
269C2×M16—21no—
270C2×M16—21no—
271C22×C8—21no—
272C22×C8—21no—
273#123—21no—
274C22⋊Q8C2×C4×C4311yescharacteristic
275C22⋊Q8D4×C4311yescharacteristic
276#121—21no—
277#121—21no—
278#121—21no—
279#121—21no—
280#121C2×C4×C4311yescharacteristic
281#121D4×C4311yescharacteristic
282#120—21no—
283C4×D4—21no—
284C4×D4—21no—
285#117D4×C4311yescharacteristic
286C2×C4⋊C4C2×C4×C4311yescharacteristic
287C2×C22⋊C4—21no—
288C2×C22⋊C4—21no—
289#107—21no—
290#106—21no—
291C4⋊C8—21no—
292C4⋊C8—21no—
293#103—21no—
294#102—21no—
295#102—21no—
296#102—21no—
297C22⋊C8—21no—
298C22⋊C8—21no—
299C22⋊C8—21no—
300C22⋊C8—21no—
301C22⋊C8—21no—
302C22⋊C8—21no—
303C22⋊C8—21no—
304C22⋊C8C2×C4×C4311yescharacteristic
305C22⋊C8C2×C4×C4311yescharacteristic
306C22⋊C8D4×C4311yescharacteristic
307C22⋊C8D4×C4311yescharacteristic
308C22⋊C8D4×C4311yescharacteristic
309C22⋊C8D4×C4311yescharacteristic
310#97—21no—
311C4×C8—21no—
312#95—21no—
313#95—21no—
314C24—21no—
315C24#41×C4311yescharacteristic
316#41—81no—
317C2×Q8C22⋊C4×C4311yescharacteristic
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4—81no—
326C2×D4—82no—
327C2×D4C22⋊C4×C4311yescharacteristic
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—41no—
331C22×C4—81no—
332C22×C4C22×C4×C4311yescharacteristic
333C22×C4C2×D4×C4311yescharacteristic
334C22×C4C2×D4×C4311yescharacteristic
335C22×C4C2×D4×C4311yescharacteristic
336C22×C4C2×D4×C4311yescharacteristic
337C22×C4#41×C4311yescharacteristic
338SD16—81no—
339D8—81no—
340M16—81no—
341M16—81no—
342M16—81no—
343M16—81no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—21no—
347C2×C8—21no—
348C2×C8—21no—
349C2×C8—21no—
350C2×C8—41no—
351C2×C8—81no—
352C2×C8—81no—
353C4⋊C4—21no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4C22⋊C4×C4311yescharacteristic
358C4⋊C4C22⋊C4×C4311yescharacteristic
359C22⋊C4—21no—
360C22⋊C4—21no—
361C22⋊C4—21no—
362C22⋊C4—21no—
363C22⋊C4—21no—
364C22⋊C4—41no—
365C22⋊C4—41no—
366C22⋊C4—81no—
367C42—21no—
368C23—21no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—42no—
373C23—41no—
374C23—81no—
375C23—81no—
376C23C4×D4×C4311yescharacteristic
377C23#121×C4311yescharacteristic
378C23#123×C4311yescharacteristic
379Q8—41no—
380D4—41no—
381D4—41no—
382D4—41no—
383D4—81no—
384D4—81no—
385D4—81no—
386D4—81no—
387D4—82no—
388D4—82no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4C2×C22⋊C4×C4311yescharacteristic
406C2×C4C4×D4×C4311yescharacteristic
407C2×C4#120×C4311yescharacteristic
408C2×C4#121×C4311yescharacteristic
409C8—41no—
410C8—41no—
411C8—41no—
412C8—41no—
413C8—41no—
414C8—41no—
415C8—81no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—82no—
429C22—81no—
430C22—81no—
431C22—81no—
432C22—162no—
433C22C43×#38611yescharacteristic
434C4—21no—
435C4—21no—
436C4—21no—
437C4—21no—
438C4—41no—
439C4—41no—
440C4—41no—
441C4—81no—
442C4—161no—
443C2—41no—
444C2—41no—
445C2—41no—
446C2—81no—
447C2—161no—
448C2C43×#188111yescharacteristic
449C2C43×#190311yescharacteristic
450C2C43×#191311yescharacteristic
subgroupG/H
center, socleC22×C43#386
commutatorC22×C4C22×C4×C43
Frattini, cosocleC23×C4C23×C43
prime radicalC43×#3194C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C23×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2978C2semidirect
3. C43×#1516C2semidirect
4. C43×#1510C2semidirect
5. C43×#1471C2semidirect
6. C43×#1306C2semidirect
7. C43×#1293C2semidirect
10. C43×#483C4semidirect
12. C43×#480C4semidirect
15. C43×#450C4semidirect
17. C43×#447C4semidirect
190. #9332C43direct (N × H)
219. #2978C2×C43semidirect
220. #1516C2×C43semidirect
221. #1510C2×C43semidirect
222. #1471C2×C43semidirect
223. #1306C2×C43semidirect
224. #1293C2×C43semidirect
235. #483C4×C43semidirect
237. #480C4×C43semidirect
240. #450C4×C43semidirect
242. #447C4×C43semidirect
260. C43#9332direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#31942
C43×#29782
C43×#15162
C43×#15102
C43×#14712
C43×#13062
C43×#12932
#933243