Finite Group Databasebeta

← C43×#18315 #24938332

Subgroups — C43×#18315 #24938332

Order 11008.

868 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3461C211yesmaximal, characteristic
2C43×#3232C212yesmaximal, complemented
3C43×#2634C211yesmaximal, characteristic, complemented
4C43×#1617C211yesmaximal, characteristic, complemented
5C43×#1616C211yesmaximal, characteristic
6C43×#1615C212yesmaximal, complemented
7C43×#1611C211yesmaximal, characteristic, complemented
8C43×#1610C211yesmaximal, characteristic
9C43×#1609C212yesmaximal, complemented
10C43×#1521C212yesmaximal, complemented
11C43×#1461C211yesmaximal, characteristic, complemented
12C43×#544C2211yescharacteristic
13C43×#542—22no—
14C43×#541—22no—
15C43×#539—21no—
16C43×#539C2212yes—
17C43×#537C2211yescharacteristic
18C43×#536—21no—
19C43×#533—22no—
20C43×#529—22no—
21C43×#529—21no—
22C43×#529C2212yes—
23C2×#125×C43C2211yescharacteristic
24C4×#41×C43—21no—
25C2×C4×Q8×C43C2211yescharacteristic
26C43×#499—22no—
27C43×#488—22no—
28C43×#484C2212yes—
29C43×#483C2212yes—
30C43×#481C2212yes—
31C43×#480C2212yes—
32C43×#479—22no—
33C43×#478—22no—
34C43×#431C2212yes—
35C43×#400—21no—
36C43×#400C2211yescharacteristic
37C43×#400C2211yescharacteristic
38C43×#398C2211yescharacteristic
39C43×#398C2211yescharacteristic
40C43×#395—21no—
41C43×#387—21no—
42C43×#387—21no—
43C43×#383C2211yescharacteristic
44C43×#328C2212yes—
45C43×#328C2212yes—
46C43×#327C2212yes—
47C43×#327C2212yes—
48C43×#324C2212yes—
49C43×#324C2211yescharacteristic
50C43×#324C2211yescharacteristic
51C2×#41×C43—21no—
52C22×Q8×C43D411yescharacteristic
53C4⋊Q8×C43—22no—
54C4⋊Q8×C43—22no—
55#126×C43—22no—
56#126×C43—22no—
57#126×C43—22no—
58#126×C43—22no—
59#125×C43—21no—
60#125×C43—22no—
61#125×C43—22no—
62#125×C43—22no—
63#125×C43—22no—
64#125×C43—22no—
65#125×C43D412yes—
66#124×C43—22no—
67#124×C43—21no—
68#124×C43D412yes—
69#123×C43—22no—
70#123×C43—22no—
71#123×C43—22no—
72#123×C43—22no—
73C22⋊Q8×C43—22no—
74C22⋊Q8×C43—22no—
75C22⋊Q8×C43—22no—
76C22⋊Q8×C43—22no—
77C22⋊Q8×C43—21no—
78C22⋊Q8×C43—22no—
79C22⋊Q8×C43C2312yes—
80#121×C43—22no—
81#121×C43—21no—
82#121×C43C2312yes—
83C4×Q8×C43—21no—
84C4×Q8×C43—21no—
85C4×Q8×C43—21no—
86C4×Q8×C43—22no—
87C4×Q8×C43—22no—
88C4×Q8×C43D412yes—
89C4×D4×C43—21no—
90C4×D4×C43—21no—
91C4×D4×C43—21no—
92C4×D4×C43—22no—
93C4×D4×C43—22no—
94C4×D4×C43D412yes—
95#117×C43—22no—
96#117×C43—22no—
97#117×C43—21no—
98#117×C43—22no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43D411yescharacteristic
104C2×C4⋊C4×C43C2311yescharacteristic
105C2×C4⋊C4×C43C2311yescharacteristic
106C2×C4⋊C4×C43C2311yescharacteristic
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C42×C43—22no—
109C2×C42×C43D411yescharacteristic
110C2×C42×C43D411yescharacteristic
111C2×C42×C43C2311yescharacteristic
112#107×C43—22no—
113#107×C43—22no—
114#106×C43—22no—
115#106×C43—22no—
116C4⋊C8×C43—22no—
117#103×C43—22no—
118#103×C43—22no—
119#102×C43—22no—
120#102×C43—22no—
121C22⋊C8×C43C2312yes—
122C22⋊C8×C43C2312yes—
123C4×C8×C43—22no—
124#95×C43—21no—
125#95×C43—21no—
126#95×C43—21no—
127#95×C43—21no—
128#95×C43—21no—
129#95×C43—21no—
130#95×C43—21no—
131#95×C43—21no—
132#95×C43C2311yescharacteristic
133#95×C43C2311yescharacteristic
134#41×C43—42no—
135#41×C43—42no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43—22no—
139C2×Q8×C43—22no—
140C2×Q8×C43—41no—
141C2×Q8×C43C2×D412yes—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—22no—
145C2×D4×C43C2×D412yes—
146C22×C4×C43—22no—
147C22×C4×C43—22no—
148C22×C4×C43—22no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2411yescharacteristic
160C2×C8×C43—22no—
161C2×C8×C43—22no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—22no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—22no—
166C4⋊C4×C43—22no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—22no—
170C4⋊C4×C43—22no—
171C4⋊C4×C43—22no—
172C4⋊C4×C43—22no—
173C4⋊C4×C43—22no—
174C4⋊C4×C43—22no—
175C4⋊C4×C43—22no—
176C4⋊C4×C43—22no—
177C4⋊C4×C43—22no—
178C4⋊C4×C43—22no—
179C4⋊C4×C43—42no—
180C4⋊C4×C43—41no—
181C4⋊C4×C43—41no—
182C4⋊C4×C43—42no—
183C4⋊C4×C43—42no—
184C4⋊C4×C43C2×D412yes—
185C4⋊C4×C43C2×D412yes—
186C22⋊C4×C43—22no—
187C22⋊C4×C43—22no—
188C22⋊C4×C43—22no—
189C22⋊C4×C43—22no—
190C22⋊C4×C43—22no—
191C22⋊C4×C43—22no—
192C22⋊C4×C43—22no—
193C22⋊C4×C43—22no—
194C22⋊C4×C43—22no—
195C42×C43—22no—
196C42×C43—22no—
197C42×C43—21no—
198C42×C43—22no—
199C42×C43—21no—
200C42×C43—21no—
201C42×C43—21no—
202C42×C43C2×D412yes—
203C42×C43C2×D412yes—
204C23×C43—22no—
205C23×C43C22×D411yescharacteristic
206Q8×C43—44no—
207Q8×C43—42no—
208Q8×C43—42no—
209Q8×C43—81no—
210D4×C43—42no—
211D4×C43—42no—
212D4×C43—42no—
213D4×C43—42no—
214D4×C43—81no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—22no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—44no—
230C2×C4×C43—44no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—42no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—82no—
245C2×C4×C43#12011yescharacteristic
246C2×C4×C43#12011yescharacteristic
247C2×C4×C43#12012yes—
248C2×C4×C43#13512yes—
249C2×C4×C43C22×D412yes—
250C8×C43—42no—
251C8×C43—42no—
252#18315C4311yesmaximal, characteristic, direct product factor, Sylow
253C22×C43—21no—
254C22×C43—21no—
255C22×C43—42no—
256C22×C43—42no—
257C22×C43—42no—
258C22×C43C2×#12011yescharacteristic
259C22×C43C2×#13511yescharacteristic
260C22×C43#57511yescharacteristic
261C4×C43—22no—
262C4×C43—22no—
263C4×C43—21no—
264C4×C43—21no—
265C4×C43—22no—
266C4×C43—41no—
267C4×C43—42no—
268C4×C43—42no—
269C4×C43—41no—
270C4×C43—41no—
271C4×C43—42no—
272C4×C43—81no—
273C4×C43—81no—
274C4×C43—81no—
275C4×C43—81no—
276#3461C2×C4311yescharacteristic
277#3232C2×C4312yescomplemented
278#2634C2×C4311yescharacteristic, complemented
279#1617C2×C4311yescharacteristic, complemented
280#1616C2×C4311yescharacteristic
281#1615C2×C4312yescomplemented
282#1611C2×C4311yescharacteristic, complemented
283#1610C2×C4311yescharacteristic
284#1609C2×C4312yescomplemented
285#1521C2×C4312yescomplemented
286#1461C2×C4311yescharacteristic, complemented
287C2×C43—21no—
288C2×C43—21no—
289C2×C43—82no—
290C2×C43#300211yescharacteristic
291C2×C43#302011yescharacteristic
292C2×C43#302811yescharacteristic
293#544C22×C4311yescharacteristic
294#542—22no—
295#541—22no—
296#539—21no—
297#539C22×C4312yes—
298#537C22×C4311yescharacteristic
299#536—21no—
300#533—22no—
301#529—22no—
302#529—21no—
303#529C22×C4312yes—
304C2×#125C22×C4311yescharacteristic
305C4×#41—21no—
306C2×C4×Q8C22×C4311yescharacteristic
307#499—22no—
308#488—22no—
309#484C22×C4312yes—
310#483C22×C4312yes—
311#481C22×C4312yes—
312#480C22×C4312yes—
313#479—22no—
314#478—22no—
315#431C22×C4312yes—
316#400—21no—
317#400C22×C4311yescharacteristic
318#400C22×C4311yescharacteristic
319#398C22×C4311yescharacteristic
320#398C22×C4311yescharacteristic
321#395—21no—
322#387—21no—
323#387—21no—
324#383C22×C4311yescharacteristic
325#328C22×C4312yes—
326#328C22×C4312yes—
327#327C22×C4312yes—
328#327C22×C4312yes—
329#324C22×C4312yes—
330#324C22×C4311yescharacteristic
331#324C22×C4311yescharacteristic
332C43#1831511yescharacteristic, direct product factor, Sylow
333C2×#41—21no—
334C22×Q8D4×C4311yescharacteristic
335C4⋊Q8—22no—
336C4⋊Q8—22no—
337#126—22no—
338#126—22no—
339#126—22no—
340#126—22no—
341#125—21no—
342#125—22no—
343#125—22no—
344#125—22no—
345#125—22no—
346#125—22no—
347#125D4×C4312yes—
348#124—22no—
349#124—21no—
350#124D4×C4312yes—
351#123—22no—
352#123—22no—
353#123—22no—
354#123—22no—
355C22⋊Q8—22no—
356C22⋊Q8—22no—
357C22⋊Q8—22no—
358C22⋊Q8—22no—
359C22⋊Q8—21no—
360C22⋊Q8—22no—
361C22⋊Q8C23×C4312yes—
362#121—22no—
363#121—21no—
364#121C23×C4312yes—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8—22no—
369C4×Q8—22no—
370C4×Q8D4×C4312yes—
371C4×D4—21no—
372C4×D4—21no—
373C4×D4—21no—
374C4×D4—22no—
375C4×D4—22no—
376C4×D4D4×C4312yes—
377#117—22no—
378#117—22no—
379#117—21no—
380#117—22no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4D4×C4311yescharacteristic
386C2×C4⋊C4C23×C4311yescharacteristic
387C2×C4⋊C4C23×C4311yescharacteristic
388C2×C4⋊C4C23×C4311yescharacteristic
389C2×C4⋊C4C23×C4311yescharacteristic
390C2×C42—22no—
391C2×C42D4×C4311yescharacteristic
392C2×C42D4×C4311yescharacteristic
393C2×C42C23×C4311yescharacteristic
394#107—22no—
395#107—22no—
396#106—22no—
397#106—22no—
398C4⋊C8—22no—
399#103—22no—
400#103—22no—
401#102—22no—
402#102—22no—
403C22⋊C8C23×C4312yes—
404C22⋊C8C23×C4312yes—
405C4×C8—22no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95C23×C4311yescharacteristic
415#95C23×C4311yescharacteristic
416#41—42no—
417#41—42no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—22no—
421C2×Q8—22no—
422C2×Q8—41no—
423C2×Q8C2×D4×C4312yes—
424C2×D4—21no—
425C2×D4—22no—
426C2×D4—21no—
427C2×D4C2×D4×C4312yes—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4C2×D4×C4311yescharacteristic
436C22×C4C2×D4×C4311yescharacteristic
437C22×C4C2×D4×C4311yescharacteristic
438C22×C4C2×D4×C4311yescharacteristic
439C22×C4C2×D4×C4311yescharacteristic
440C22×C4C2×D4×C4311yescharacteristic
441C22×C4C24×C4311yescharacteristic
442C2×C8—22no—
443C2×C8—22no—
444C4⋊C4—21no—
445C4⋊C4—22no—
446C4⋊C4—21no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—22no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—42no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—42no—
465C4⋊C4—42no—
466C4⋊C4C2×D4×C4312yes—
467C4⋊C4C2×D4×C4312yes—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C22⋊C4—22no—
471C22⋊C4—22no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—22no—
477C42—22no—
478C42—22no—
479C42—21no—
480C42—22no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42C2×D4×C4312yes—
485C42C2×D4×C4312yes—
486C23—22no—
487C23C22×D4×C4311yescharacteristic
488Q8—44no—
489Q8—42no—
490Q8—42no—
491Q8—81no—
492D4—42no—
493D4—42no—
494D4—42no—
495D4—42no—
496D4—81no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—44no—
512C2×C4—44no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—42no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—82no—
527C2×C4#120×C4311yescharacteristic
528C2×C4#120×C4311yescharacteristic
529C2×C4#120×C4312yes—
530C2×C4#135×C4312yes—
531C2×C4C22×D4×C4312yes—
532C8—42no—
533C8—42no—
534C22—21no—
535C22—21no—
536C22—42no—
537C22—42no—
538C22—42no—
539C22C2×#120×C4311yescharacteristic
540C22C2×#135×C4311yescharacteristic
541C22C43×#57511yescharacteristic
542C4—22no—
543C4—22no—
544C4—21no—
545C4—21no—
546C4—22no—
547C4—41no—
548C4—42no—
549C4—42no—
550C4—41no—
551C4—41no—
552C4—42no—
553C4—81no—
554C4—81no—
555C4—81no—
556C4—81no—
557C2—21no—
558C2—21no—
559C2—82no—
560C2C43×#300211yescharacteristic
561C2C43×#302011yescharacteristic
562C2C43×#302811yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC43×#537C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#3232C2semidirect
3. C43×#2634C2semidirect
4. C43×#1617C2semidirect
6. C43×#1615C2semidirect
7. C43×#1611C2semidirect
9. C43×#1609C2semidirect
10. C43×#1521C2semidirect
11. C43×#1461C2semidirect
252. #18315C43direct (N × H)
277. #3232C2×C43semidirect
278. #2634C2×C43semidirect
279. #1617C2×C43semidirect
281. #1615C2×C43semidirect
282. #1611C2×C43semidirect
284. #1609C2×C43semidirect
285. #1521C2×C43semidirect
286. #1461C2×C43semidirect
332. C43#18315direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#34612
C43×#32322
C43×#26342
C43×#16172
C43×#16162
C43×#16152
C43×#16112
C43×#16102
C43×#16092
C43×#15212
C43×#14612
#1831543