Finite Group Databasebeta

← C43×#20297 #24940314

Subgroups — C43×#20297 #24940314

Order 11008.

572 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3398C211yesmaximal, characteristic
2C43×#3386C211yesmaximal, characteristic
3C43×#3374C211yesmaximal, characteristic, complemented
4C43×#3328C211yesmaximal, characteristic
5C43×#1707C211yesmaximal, characteristic, complemented
6C43×#1700C211yesmaximal, characteristic, complemented
7C43×#1699C211yesmaximal, characteristic
8C43×#1694C211yesmaximal, characteristic, complemented
9C43×#1690C211yesmaximal, characteristic, complemented
10C43×#1653C211yesmaximal, characteristic, complemented
11C43×#1653C211yesmaximal, characteristic, complemented
12C43×#1652C211yesmaximal, characteristic
13C43×#1651C211yesmaximal, characteristic
14C43×#1591C211yesmaximal, characteristic, complemented
15C43×#1590C211yesmaximal, characteristic
16C43×#557C2211yescharacteristic
17C43×#557C2211yescharacteristic
18C43×#556C2211yescharacteristic
19D4×Q8×C43C2211yescharacteristic
20C43×#501—21no—
21C43×#500C2211yescharacteristic
22C43×#498C2211yescharacteristic
23C43×#498C2211yescharacteristic
24C43×#497—21no—
25C43×#494C2211yescharacteristic
26C43×#491—21no—
27C43×#487C2211yescharacteristic
28C43×#487C2211yescharacteristic
29C43×#485—21no—
30C43×#479—21no—
31C43×#478—21no—
32C43×#477—21no—
33C43×#475C2211yescharacteristic
34C43×#475C2211yescharacteristic
35C43×#475C2211yescharacteristic
36C43×#474C2211yescharacteristic
37C43×#470—21no—
38C43×#464—21no—
39C43×#462—21no—
40C43×#462—21no—
41C43×#462C2211yescharacteristic
42C43×#462C2211yescharacteristic
43C43×#462C2211yescharacteristic
44C43×#461C2211yescharacteristic
45C43×#451—21no—
46C43×#446C2211yescharacteristic
47C43×#446C2211yescharacteristic
48C43×#446C2211yescharacteristic
49C43×#441—21no—
50C43×#441—21no—
51C43×#440—21no—
52C4×Q16×C43C2211yescharacteristic
53C4×SD16×C43C2211yescharacteristic
54C43×#436C2211yescharacteristic
55C43×#419—21no—
56C43×#335C2211yescharacteristic
57C43×#334C2211yescharacteristic
58C43×#332C2211yescharacteristic
59C43×#332C2211yescharacteristic
60C43×#332C2211yescharacteristic
61C43×#332C2211yescharacteristic
62C43×Q8⋊C8C2211yescharacteristic
63C43×Q8⋊C8C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C82×C43C2211yescharacteristic
67C22×Q8×C43—21no—
68C2×Q16×C43—21no—
69C2×Q16×C43—21no—
70C2×Q16×C43—21no—
71C2×Q16×C43—21no—
72C2×Q16×C43—21no—
73C2×Q16×C43D411yescharacteristic
74C2×SD16×C43—21no—
75C2×SD16×C43D411yescharacteristic
76C2×M16×C43—21no—
77C4⋊Q8×C43—21no—
78C4⋊Q8×C43—21no—
79C4⋊Q8×C43—21no—
80C4⋊Q8×C43C2311yescharacteristic
81C4⋊Q8×C43C2311yescharacteristic
82C4⋊Q8×C43C2311yescharacteristic
83C4⋊Q8×C43C2311yescharacteristic
84#126×C43—41no—
85#125×C43—21no—
86#125×C43—21no—
87#125×C43—41no—
88#125×C43—41no—
89#124×C43—21no—
90C22⋊Q8×C43—21no—
91C22⋊Q8×C43—21no—
92C22⋊Q8×C43—41no—
93C4×Q8×C43—21no—
94C4×Q8×C43—21no—
95C4×Q8×C43—21no—
96C4×Q8×C43—21no—
97C4×Q8×C43—21no—
98C4×Q8×C43C2311yescharacteristic
99C4×Q8×C43C2311yescharacteristic
100C4×Q8×C43C2311yescharacteristic
101C4×D4×C43—21no—
102C4×D4×C43C2311yescharacteristic
103#117×C43—21no—
104#107×C43—21no—
105#107×C43—21no—
106#107×C43—21no—
107#107×C43D411yescharacteristic
108#106×C43—21no—
109#106×C43—21no—
110#106×C43—21no—
111#106×C43—41no—
112#106×C43—41no—
113#106×C43D411yescharacteristic
114C4⋊C8×C43—21no—
115C4⋊C8×C43—21no—
116C4⋊C8×C43—21no—
117C4⋊C8×C43C2311yescharacteristic
118C4⋊C8×C43C2311yescharacteristic
119C4⋊C8×C43C2311yescharacteristic
120C4⋊C8×C43C2311yescharacteristic
121#103×C43—21no—
122#103×C43—21no—
123#103×C43—21no—
124#103×C43—21no—
125#103×C43—21no—
126#103×C43—21no—
127#103×C43—21no—
128#103×C43—21no—
129#103×C43—21no—
130#103×C43—21no—
131#103×C43—21no—
132#103×C43D411yescharacteristic
133#103×C43D411yescharacteristic
134#103×C43D411yescharacteristic
135#102×C43—21no—
136#102×C43D411yescharacteristic
137C22⋊C8×C43—21no—
138#97×C43—21no—
139#97×C43—21no—
140#97×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—41no—
149C2×Q8×C43—42no—
150C2×Q8×C43—81no—
151C2×Q8×C43C2×D411yescharacteristic
152C2×Q8×C43C2×D411yescharacteristic
153C2×Q8×C43C2×D411yescharacteristic
154C2×D4×C43C2×D411yescharacteristic
155C22×C4×C43—21no—
156C22×C4×C43—41no—
157Q16×C43—41no—
158Q16×C43—42no—
159Q16×C43—42no—
160Q16×C43—81no—
161Q16×C43—81no—
162Q16×C43—81no—
163SD16×C43—22no—
164SD16×C43—81no—
165M16×C43—81no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43C2×D411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C2×C8×C43C2×D411yescharacteristic
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—41no—
187C4⋊C4×C43—41no—
188C4⋊C4×C43—41no—
189C4⋊C4×C43—41no—
190C4⋊C4×C43—41no—
191C4⋊C4×C43—41no—
192C4⋊C4×C43—41no—
193C4⋊C4×C43—41no—
194C4⋊C4×C43C2×D411yescharacteristic
195C4⋊C4×C43C2×D411yescharacteristic
196C4⋊C4×C43C2×D411yescharacteristic
197C4⋊C4×C43C2×D411yescharacteristic
198C22⋊C4×C43—21no—
199C22⋊C4×C43—41no—
200C22⋊C4×C43—41no—
201C22⋊C4×C43—41no—
202C42×C43—21no—
203C42×C43—21no—
204C42×C43—21no—
205C42×C43—41no—
206C42×C43—41no—
207C42×C43—41no—
208C42×C43C2411yescharacteristic
209C23×C43—21no—
210Q8×C43—21no—
211Q8×C43—21no—
212Q8×C43—21no—
213Q8×C43—21no—
214Q8×C43—21no—
215Q8×C43—21no—
216Q8×C43—41no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—41no—
220Q8×C43—41no—
221Q8×C43—41no—
222Q8×C43—41no—
223Q8×C43—41no—
224Q8×C43—82no—
225D4×C43—21no—
226D4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—82no—
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43H(5,𝔽2)11yescharacteristic
244C8×C43—22no—
245C8×C43—21no—
246C8×C43—21no—
247C8×C43—21no—
248C8×C43—41no—
249C8×C43—41no—
250C8×C43—41no—
251C8×C43—41no—
252C8×C43#13712yes—
253#20297C4311yesmaximal, characteristic, direct product factor, Sylow
254C22×C43—41no—
255C22×C43—41no—
256C22×C43—41no—
257C22×C43D4211yescharacteristic
258C4×C43—21no—
259C4×C43—41no—
260C4×C43—41no—
261C4×C43—41no—
262C4×C43—41no—
263C4×C43—41no—
264C4×C43—41no—
265C4×C43—41no—
266C4×C43—81no—
267C4×C43—81no—
268C4×C43—81no—
269C4×C43—81no—
270C4×C43C2×#13711yescharacteristic
271C4×C43#57511yescharacteristic
272C4×C43#57711yescharacteristic
273C4×C43#57711yescharacteristic
274#3398C2×C4311yescharacteristic
275#3386C2×C4311yescharacteristic
276#3374C2×C4311yescharacteristic, complemented
277#3328C2×C4311yescharacteristic
278#1707C2×C4311yescharacteristic, complemented
279#1700C2×C4311yescharacteristic, complemented
280#1699C2×C4311yescharacteristic
281#1694C2×C4311yescharacteristic, complemented
282#1690C2×C4311yescharacteristic, complemented
283#1653C2×C4311yescharacteristic, complemented
284#1653C2×C4311yescharacteristic, complemented
285#1652C2×C4311yescharacteristic
286#1651C2×C4311yescharacteristic
287#1591C2×C4311yescharacteristic, complemented
288#1590C2×C4311yescharacteristic
289C2×C43—81no—
290C2×C43#327511yescharacteristic
291C2×C43#327811yescharacteristic
292C2×C43#329311yescharacteristic
293#557C22×C4311yescharacteristic
294#557C22×C4311yescharacteristic
295#556C22×C4311yescharacteristic
296D4×Q8C22×C4311yescharacteristic
297#501—21no—
298#500C22×C4311yescharacteristic
299#498C22×C4311yescharacteristic
300#498C22×C4311yescharacteristic
301#497—21no—
302#494C22×C4311yescharacteristic
303#491—21no—
304#487C22×C4311yescharacteristic
305#487C22×C4311yescharacteristic
306#485—21no—
307#479—21no—
308#478—21no—
309#477—21no—
310#475C22×C4311yescharacteristic
311#475C22×C4311yescharacteristic
312#475C22×C4311yescharacteristic
313#474C22×C4311yescharacteristic
314#470—21no—
315#464—21no—
316#462—21no—
317#462—21no—
318#462C22×C4311yescharacteristic
319#462C22×C4311yescharacteristic
320#462C22×C4311yescharacteristic
321#461C22×C4311yescharacteristic
322#451—21no—
323#446C22×C4311yescharacteristic
324#446C22×C4311yescharacteristic
325#446C22×C4311yescharacteristic
326#441—21no—
327#441—21no—
328#440—21no—
329C4×Q16C22×C4311yescharacteristic
330C4×SD16C22×C4311yescharacteristic
331#436C22×C4311yescharacteristic
332#419—21no—
333#335C22×C4311yescharacteristic
334#334C22×C4311yescharacteristic
335#332C22×C4311yescharacteristic
336#332C22×C4311yescharacteristic
337#332C22×C4311yescharacteristic
338#332C22×C4311yescharacteristic
339Q8⋊C8C22×C4311yescharacteristic
340Q8⋊C8C22×C4311yescharacteristic
341Q8⋊C8C22×C4311yescharacteristic
342D4⋊C8C22×C4311yescharacteristic
343C82C22×C4311yescharacteristic
344C43#2029711yescharacteristic, direct product factor, Sylow
345C22×Q8—21no—
346C2×Q16—21no—
347C2×Q16—21no—
348C2×Q16—21no—
349C2×Q16—21no—
350C2×Q16—21no—
351C2×Q16D4×C4311yescharacteristic
352C2×SD16—21no—
353C2×SD16D4×C4311yescharacteristic
354C2×M16—21no—
355C4⋊Q8—21no—
356C4⋊Q8—21no—
357C4⋊Q8—21no—
358C4⋊Q8C23×C4311yescharacteristic
359C4⋊Q8C23×C4311yescharacteristic
360C4⋊Q8C23×C4311yescharacteristic
361C4⋊Q8C23×C4311yescharacteristic
362#126—41no—
363#125—21no—
364#125—21no—
365#125—41no—
366#125—41no—
367#124—21no—
368C22⋊Q8—21no—
369C22⋊Q8—21no—
370C22⋊Q8—41no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×Q8—21no—
376C4×Q8C23×C4311yescharacteristic
377C4×Q8C23×C4311yescharacteristic
378C4×Q8C23×C4311yescharacteristic
379C4×D4—21no—
380C4×D4C23×C4311yescharacteristic
381#117—21no—
382#107—21no—
383#107—21no—
384#107—21no—
385#107D4×C4311yescharacteristic
386#106—21no—
387#106—21no—
388#106—21no—
389#106—41no—
390#106—41no—
391#106D4×C4311yescharacteristic
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8—21no—
395C4⋊C8C23×C4311yescharacteristic
396C4⋊C8C23×C4311yescharacteristic
397C4⋊C8C23×C4311yescharacteristic
398C4⋊C8C23×C4311yescharacteristic
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103D4×C4311yescharacteristic
411#103D4×C4311yescharacteristic
412#103D4×C4311yescharacteristic
413#102—21no—
414#102D4×C4311yescharacteristic
415C22⋊C8—21no—
416#97—21no—
417#97—21no—
418#97—21no—
419C4×C8C23×C4311yescharacteristic
420C4×C8C23×C4311yescharacteristic
421C4×C8C23×C4311yescharacteristic
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—41no—
427C2×Q8—42no—
428C2×Q8—81no—
429C2×Q8C2×D4×C4311yescharacteristic
430C2×Q8C2×D4×C4311yescharacteristic
431C2×Q8C2×D4×C4311yescharacteristic
432C2×D4C2×D4×C4311yescharacteristic
433C22×C4—21no—
434C22×C4—41no—
435Q16—41no—
436Q16—42no—
437Q16—42no—
438Q16—81no—
439Q16—81no—
440Q16—81no—
441SD16—22no—
442SD16—81no—
443M16—81no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8C2×D4×C4311yescharacteristic
450C2×C8C2×D4×C4311yescharacteristic
451C2×C8C2×D4×C4311yescharacteristic
452C2×C8C2×D4×C4311yescharacteristic
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4C2×D4×C4311yescharacteristic
473C4⋊C4C2×D4×C4311yescharacteristic
474C4⋊C4C2×D4×C4311yescharacteristic
475C4⋊C4C2×D4×C4311yescharacteristic
476C22⋊C4—21no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—41no—
484C42—41no—
485C42—41no—
486C42C24×C4311yescharacteristic
487C23—21no—
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—41no—
495Q8—41no—
496Q8—41no—
497Q8—41no—
498Q8—41no—
499Q8—41no—
500Q8—41no—
501Q8—41no—
502Q8—82no—
503D4—21no—
504D4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—82no—
519C2×C4C22×D4×C4311yescharacteristic
520C2×C4C22×D4×C4311yescharacteristic
521C2×C4H(5,𝔽2)×C4311yescharacteristic
522C8—22no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8#137×C4312yes—
531C22—41no—
532C22—41no—
533C22—41no—
534C22D42×C4311yescharacteristic
535C4—21no—
536C4—41no—
537C4—41no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—41no—
543C4—81no—
544C4—81no—
545C4—81no—
546C4—81no—
547C4C2×#137×C4311yescharacteristic
548C4C43×#57511yescharacteristic
549C4C43×#57711yescharacteristic
550C4C43×#57711yescharacteristic
551C2—81no—
552C2C43×#327511yescharacteristic
553C2C43×#327811yescharacteristic
554C2C43×#329311yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC42C24×C43
prime radicalC2×D4×C43C2×D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
3. C43×#3374C2semidirect
5. C43×#1707C2semidirect
6. C43×#1700C2semidirect
8. C43×#1694C2semidirect
9. C43×#1690C2semidirect
10. C43×#1653C2semidirect
11. C43×#1653C2semidirect
14. C43×#1591C2semidirect
253. #20297C43direct (N × H)
276. #3374C2×C43semidirect
278. #1707C2×C43semidirect
279. #1700C2×C43semidirect
281. #1694C2×C43semidirect
282. #1690C2×C43semidirect
283. #1653C2×C43semidirect
284. #1653C2×C43semidirect
287. #1591C2×C43semidirect
344. C43#20297direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#33982
C43×#33862
C43×#33742
C43×#33282
C43×#17072
C43×#17002
C43×#16992
C43×#16942
C43×#16902
C43×#16532
C43×#16522
C43×#16512
C43×#15912
C43×#15902
#2029743