Finite Group Databasebeta

← C43×#25698 #24945715

Subgroups — C43×#25698 #24945715

Order 11008.

950 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3507C211yesmaximal, characteristic
2C43×#3166C211yesmaximal, characteristic, complemented
3C43×#3142C211yesmaximal, characteristic
4C43×#2565C211yesmaximal, characteristic, complemented
5C43×#2038C212yesmaximal, complemented
6C43×#2038C212yesmaximal, complemented
7C43×#1986C211yesmaximal, characteristic, complemented
8C43×#1980C211yesmaximal, characteristic
9C43×#1860C212yesmaximal, complemented
10C43×#1859C212yesmaximal, complemented
11C4×#101×C43C211yesmaximal, characteristic, complemented
12C43×#559—21no—
13C43×#557—21no—
14C43×#556—21no—
15C43×#556—22no—
16C43×#554—21no—
17C43×#552—22no—
18C43×#539—22no—
19C43×#536C2212yes—
20C43×#533C2211yescharacteristic
21C43×#532C2211yescharacteristic
22C43×#529—22no—
23C2×#125×C43C2211yescharacteristic
24C43×#520C2212yes—
25C2×C4×Q8×C43C2211yescharacteristic
26C43×#501—21no—
27C43×#501—21no—
28C43×#499—22no—
29C43×#491—21no—
30C43×#490—21no—
31C43×#488—22no—
32C43×#428C2212yes—
33C43×#428C2212yes—
34C2×#104×C43C2212yes—
35C2×#104×C43C2212yes—
36C43×#417C2212yes—
37C43×#417C2212yes—
38C2×#101×C43C2212yes—
39C4×M16×C43C2211yescharacteristic
40C4×M16×C43C2211yescharacteristic
41C43×#398—22no—
42C43×#391C2211yescharacteristic
43C43×#391C2211yescharacteristic
44C43×#387—22no—
45C43×#384C2211yescharacteristic
46C43×#382C2211yescharacteristic
47C4×C4⋊C4×C43C2211yescharacteristic
48C43×#343C2212yes—
49C43×#339C2212yes—
50C43×#339C2212yes—
51C2×#41×C43C2312yes—
52C22×Q8×C43C2311yescharacteristic
53C2×M16×C43C2312yes—
54C2×M16×C43C2312yes—
55C4⋊Q8×C43—22no—
56C4⋊Q8×C43D411yescharacteristic
57C4⋊Q8×C43D411yescharacteristic
58C4⋊Q8×C43D411yescharacteristic
59#127×C43D411yescharacteristic
60#126×C43—24no—
61#126×C43—24no—
62#125×C43—22no—
63#125×C43—24no—
64#125×C43—21no—
65#125×C43—21no—
66#125×C43—21no—
67#125×C43—21no—
68#125×C43D412yes—
69#124×C43—22no—
70#124×C43—22no—
71#124×C43D412yes—
72#123×C43—24no—
73#123×C43—24no—
74C22⋊Q8×C43—24no—
75C22⋊Q8×C43—21no—
76C22⋊Q8×C43—21no—
77C22⋊Q8×C43—22no—
78C22⋊Q8×C43—22no—
79#121×C43—21no—
80#121×C43—21no—
81C4×Q8×C43—22no—
82C4×Q8×C43—22no—
83C4×Q8×C43—21no—
84C4×Q8×C43—21no—
85C4×Q8×C43—21no—
86C4×Q8×C43—21no—
87C4×Q8×C43—21no—
88C4×Q8×C43—21no—
89C4×D4×C43—22no—
90C4×D4×C43—22no—
91C4×D4×C43—24no—
92C4×D4×C43—21no—
93C4×D4×C43—21no—
94#117×C43—24no—
95#117×C43—22no—
96#117×C43C2312yes—
97C2×C4⋊C4×C43—22no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—22no—
102C2×C4⋊C4×C43D412yes—
103C2×C4⋊C4×C43C2311yescharacteristic
104C2×C4⋊C4×C43C2311yescharacteristic
105C2×C4⋊C4×C43C2311yescharacteristic
106C2×C42×C43D412yes—
107C2×C42×C43C2311yescharacteristic
108C2×C42×C43C2311yescharacteristic
109C2×C42×C43C2311yescharacteristic
110#107×C43—22no—
111#107×C43—22no—
112#106×C43—22no—
113#106×C43—22no—
114#104×C43—24no—
115#104×C43—24no—
116#103×C43—22no—
117#103×C43—22no—
118#102×C43—22no—
119#102×C43—22no—
120#101×C43—24no—
121#97×C43—21no—
122#97×C43—21no—
123C4×C8×C43—21no—
124C4×C8×C43—21no—
125#95×C43—21no—
126#95×C43—22no—
127#95×C43—22no—
128#95×C43—22no—
129#41×C43—22no—
130#41×C43—22no—
131#41×C43—22no—
132#41×C43—22no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—22no—
138C2×Q8×C43—22no—
139C2×Q8×C43C2×D412yes—
140C2×D4×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—22no—
143C2×D4×C43C2×D412yes—
144C22×C4×C43—24no—
145C22×C4×C43—22no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43C2×D412yes—
151C22×C4×C43C2×D412yes—
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2411yescharacteristic
155M16×C43—22no—
156M16×C43—22no—
157M16×C43—22no—
158M16×C43#4114yes—
159C2×C8×C43—22no—
160C2×C8×C43—22no—
161C4⋊C4×C43—24no—
162C4⋊C4×C43—24no—
163C4⋊C4×C43—24no—
164C4⋊C4×C43—22no—
165C4⋊C4×C43—22no—
166C4⋊C4×C43—22no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—22no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—42no—
179C4⋊C4×C43—44no—
180C4⋊C4×C43—41no—
181C4⋊C4×C43—41no—
182C4⋊C4×C43—41no—
183C4⋊C4×C43—41no—
184C4⋊C4×C43C2×D412yes—
185C4⋊C4×C43C2×D412yes—
186C22⋊C4×C43—24no—
187C22⋊C4×C43—24no—
188C22⋊C4×C43—24no—
189C22⋊C4×C43—22no—
190C22⋊C4×C43—22no—
191C22⋊C4×C43—22no—
192C42×C43—24no—
193C42×C43—22no—
194C42×C43—22no—
195C42×C43—22no—
196C42×C43—22no—
197C42×C43—22no—
198C42×C43C2×D411yescharacteristic
199C42×C43C2×D411yescharacteristic
200C42×C43C2×D411yescharacteristic
201C42×C43C2×D411yescharacteristic
202C23×C43—22no—
203C23×C43C22×D411yescharacteristic
204Q8×C43—22no—
205Q8×C43—22no—
206Q8×C43—42no—
207Q8×C43—42no—
208Q8×C43—42no—
209Q8×C43—81no—
210D4×C43—22no—
211D4×C43—22no—
212D4×C43—42no—
213D4×C43—42no—
214D4×C43—42no—
215D4×C43—81no—
216C2×C4×C43—22no—
217C2×C4×C43—22no—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—42no—
229C2×C4×C43—42no—
230C2×C4×C43—42no—
231C2×C4×C43—41no—
232C2×C4×C43—42no—
233C2×C4×C43—41no—
234C2×C4×C43—42no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—84no—
239C2×C4×C43#12011yescharacteristic
240C2×C4×C43#12011yescharacteristic
241C2×C4×C43#12011yescharacteristic
242C2×C4×C43#12011yescharacteristic
243C2×C4×C43C22×D411yescharacteristic
244C2×C4×C43C22×D411yescharacteristic
245C2×C4×C43C2×#4112yes—
246C2×C4×C432−1+412yes—
247C8×C43—24no—
248C8×C43—42no—
249#25698C4311yesmaximal, characteristic, direct product factor, Sylow
250C22×C43—21no—
251C22×C43—21no—
252C22×C43—42no—
253C22×C43—42no—
254C22×C43—42no—
255C22×C43C2×#12011yescharacteristic
256C22×C43#53211yescharacteristic
257C22×C43#53611yescharacteristic
258C4×C43—21no—
259C4×C43—21no—
260C4×C43—21no—
261C4×C43—21no—
262C4×C43—42no—
263C4×C43—42no—
264C4×C43—42no—
265C4×C43—42no—
266C4×C43—42no—
267C4×C43—42no—
268C4×C43—81no—
269C4×C43—81no—
270C4×C43—81no—
271C4×C43#54712yes—
272C4×C43#54812yes—
273#3507C2×C4311yescharacteristic
274#3166C2×C4311yescharacteristic, complemented
275#3142C2×C4311yescharacteristic
276#2565C2×C4311yescharacteristic, complemented
277#2038C2×C4312yescomplemented
278#2038C2×C4312yescomplemented
279#1986C2×C4311yescharacteristic, complemented
280#1980C2×C4311yescharacteristic
281#1860C2×C4312yescomplemented
282#1859C2×C4312yescomplemented
283C4×#101C2×C4311yescharacteristic, complemented
284C2×C43—21no—
285C2×C43—21no—
286C2×C43—82no—
287C2×C43#243211yescharacteristic
288C2×C43#301811yescharacteristic
289C2×C43#302011yescharacteristic
290#559—21no—
291#557—21no—
292#556—21no—
293#556—22no—
294#554—21no—
295#552—22no—
296#539—22no—
297#536C22×C4312yes—
298#533C22×C4311yescharacteristic
299#532C22×C4311yescharacteristic
300#529—22no—
301C2×#125C22×C4311yescharacteristic
302#520C22×C4312yes—
303C2×C4×Q8C22×C4311yescharacteristic
304#501—21no—
305#501—21no—
306#499—22no—
307#491—21no—
308#490—21no—
309#488—22no—
310#428C22×C4312yes—
311#428C22×C4312yes—
312C2×#104C22×C4312yes—
313C2×#104C22×C4312yes—
314#417C22×C4312yes—
315#417C22×C4312yes—
316C2×#101C22×C4312yes—
317C4×M16C22×C4311yescharacteristic
318C4×M16C22×C4311yescharacteristic
319#398—22no—
320#391C22×C4311yescharacteristic
321#391C22×C4311yescharacteristic
322#387—22no—
323#384C22×C4311yescharacteristic
324#382C22×C4311yescharacteristic
325C4×C4⋊C4C22×C4311yescharacteristic
326#343C22×C4312yes—
327#339C22×C4312yes—
328#339C22×C4312yes—
329C43#2569811yescharacteristic, direct product factor, Sylow
330C2×#41C23×C4312yes—
331C22×Q8C23×C4311yescharacteristic
332C2×M16C23×C4312yes—
333C2×M16C23×C4312yes—
334C4⋊Q8—22no—
335C4⋊Q8D4×C4311yescharacteristic
336C4⋊Q8D4×C4311yescharacteristic
337C4⋊Q8D4×C4311yescharacteristic
338#127D4×C4311yescharacteristic
339#126—24no—
340#126—24no—
341#125—22no—
342#125—24no—
343#125—21no—
344#125—21no—
345#125—21no—
346#125—21no—
347#125D4×C4312yes—
348#124—22no—
349#124—22no—
350#124D4×C4312yes—
351#123—24no—
352#123—24no—
353C22⋊Q8—24no—
354C22⋊Q8—21no—
355C22⋊Q8—21no—
356C22⋊Q8—22no—
357C22⋊Q8—22no—
358#121—21no—
359#121—21no—
360C4×Q8—22no—
361C4×Q8—22no—
362C4×Q8—21no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×D4—22no—
369C4×D4—22no—
370C4×D4—24no—
371C4×D4—21no—
372C4×D4—21no—
373#117—24no—
374#117—22no—
375#117C23×C4312yes—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4D4×C4312yes—
382C2×C4⋊C4C23×C4311yescharacteristic
383C2×C4⋊C4C23×C4311yescharacteristic
384C2×C4⋊C4C23×C4311yescharacteristic
385C2×C42D4×C4312yes—
386C2×C42C23×C4311yescharacteristic
387C2×C42C23×C4311yescharacteristic
388C2×C42C23×C4311yescharacteristic
389#107—22no—
390#107—22no—
391#106—22no—
392#106—22no—
393#104—24no—
394#104—24no—
395#103—22no—
396#103—22no—
397#102—22no—
398#102—22no—
399#101—24no—
400#97—21no—
401#97—21no—
402C4×C8—21no—
403C4×C8—21no—
404#95—21no—
405#95—22no—
406#95—22no—
407#95—22no—
408#41—22no—
409#41—22no—
410#41—22no—
411#41—22no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—22no—
417C2×Q8—22no—
418C2×Q8C2×D4×C4312yes—
419C2×D4—22no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4C2×D4×C4312yes—
423C22×C4—21no—
424C22×C4—24no—
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4C2×D4×C4312yes—
430C22×C4C2×D4×C4312yes—
431C22×C4C2×D4×C4311yescharacteristic
432C22×C4C2×D4×C4311yescharacteristic
433C22×C4C24×C4311yescharacteristic
434M16—22no—
435M16—22no—
436M16—22no—
437M16#41×C4314yes—
438C2×C8—22no—
439C2×C8—22no—
440C4⋊C4—24no—
441C4⋊C4—24no—
442C4⋊C4—24no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—22no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—42no—
458C4⋊C4—44no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4C2×D4×C4312yes—
464C4⋊C4C2×D4×C4312yes—
465C22⋊C4—24no—
466C22⋊C4—24no—
467C22⋊C4—24no—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C22⋊C4—22no—
471C42—24no—
472C42—22no—
473C42—22no—
474C42—22no—
475C42—22no—
476C42—22no—
477C42C2×D4×C4311yescharacteristic
478C42C2×D4×C4311yescharacteristic
479C42C2×D4×C4311yescharacteristic
480C42C2×D4×C4311yescharacteristic
481C23—22no—
482C23C22×D4×C4311yescharacteristic
483Q8—22no—
484Q8—22no—
485Q8—42no—
486Q8—42no—
487Q8—42no—
488Q8—81no—
489D4—22no—
490D4—22no—
491D4—42no—
492D4—42no—
493D4—42no—
494D4—81no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—41no—
513C2×C4—42no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—84no—
518C2×C4#120×C4311yescharacteristic
519C2×C4#120×C4311yescharacteristic
520C2×C4#120×C4311yescharacteristic
521C2×C4#120×C4311yescharacteristic
522C2×C4C22×D4×C4311yescharacteristic
523C2×C4C22×D4×C4311yescharacteristic
524C2×C4C2×#41×C4312yes—
525C2×C42−1+4×C4312yes—
526C8—24no—
527C8—42no—
528C22—21no—
529C22—21no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22C2×#120×C4311yescharacteristic
534C22C43×#53211yescharacteristic
535C22C43×#53611yescharacteristic
536C4—21no—
537C4—21no—
538C4—21no—
539C4—21no—
540C4—42no—
541C4—42no—
542C4—42no—
543C4—42no—
544C4—42no—
545C4—42no—
546C4—81no—
547C4—81no—
548C4—81no—
549C4C43×#54712yes—
550C4C43×#54812yes—
551C2—21no—
552C2—21no—
553C2—82no—
554C2C43×#243211yescharacteristic
555C2C43×#301811yescharacteristic
556C2C43×#302011yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC43×#532C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#3166C2semidirect
4. C43×#2565C2semidirect
5. C43×#2038C2semidirect
6. C43×#2038C2semidirect
7. C43×#1986C2semidirect
9. C43×#1860C2semidirect
10. C43×#1859C2semidirect
11. C4×#101×C43C2semidirect
249. #25698C43direct (N × H)
274. #3166C2×C43semidirect
276. #2565C2×C43semidirect
277. #2038C2×C43semidirect
278. #2038C2×C43semidirect
279. #1986C2×C43semidirect
281. #1860C2×C43semidirect
282. #1859C2×C43semidirect
283. C4×#101C2×C43semidirect
329. C43#25698direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#35072
C43×#31662
C43×#31422
C43×#25652
C43×#20382
C43×#19862
C43×#19802
C43×#18602
C43×#18592
C4×#101×C432
#2569843