Finite Group Databasebeta

← C43×#19574 #24939591

Subgroups — C43×#19574 #24939591

Order 11008.

534 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3249C211yesmaximal, characteristic
2C43×#3237C211yesmaximal, characteristic
3C43×#3231C211yesmaximal, characteristic
4C43×#2986C211yesmaximal, characteristic
5C43×#1704C211yesmaximal, characteristic, complemented
6C43×#1700C211yesmaximal, characteristic, complemented
7C43×#1696C211yesmaximal, characteristic, complemented
8C43×#1692C211yesmaximal, characteristic, complemented
9C43×#1684C211yesmaximal, characteristic, complemented
10C43×#1680C211yesmaximal, characteristic, complemented
11C43×#1676C211yesmaximal, characteristic, complemented
12C43×#1672C211yesmaximal, characteristic, complemented
13C43×#1573C211yesmaximal, characteristic
14C43×#1554C211yesmaximal, characteristic
15C43×#1542C211yesmaximal, characteristic
16C43×#533C2211yescharacteristic
17C43×#533C2211yescharacteristic
18C43×#533C2211yescharacteristic
19C43×#501—21no—
20C43×#500C2211yescharacteristic
21C43×#498C2211yescharacteristic
22C43×#491—21no—
23C43×#487C2211yescharacteristic
24C43×#487C2211yescharacteristic
25C43×#485—21no—
26C43×#485—21no—
27C43×#485—21no—
28C43×#485—21no—
29C43×#479—21no—
30C43×#479—21no—
31C43×#477—21no—
32C43×#477C2211yescharacteristic
33C43×#477C2211yescharacteristic
34C43×#477C2211yescharacteristic
35C43×#477C2211yescharacteristic
36C43×#475C2211yescharacteristic
37C43×#475C2211yescharacteristic
38C43×#467—21no—
39C43×#467—21no—
40C43×#462—21no—
41C43×#462C2211yescharacteristic
42C43×#462C2211yescharacteristic
43C43×#446—21no—
44C43×#446C2211yescharacteristic
45C43×#446C2211yescharacteristic
46C8×Q8×C43—21no—
47C8×Q8×C43C2211yescharacteristic
48C8×Q8×C43C2211yescharacteristic
49C43×#433—21no—
50C43×#433—21no—
51C43×#432C2211yescharacteristic
52C43×#431C2211yescharacteristic
53C43×#431C2211yescharacteristic
54C2×C4⋊C8×C43C2211yescharacteristic
55C43×#335C2211yescharacteristic
56C43×#335C2211yescharacteristic
57C43×#334C2211yescharacteristic
58C43×#334C2211yescharacteristic
59C43×#333C2211yescharacteristic
60C43×#333C2211yescharacteristic
61C43×#333C2211yescharacteristic
62C43×#333C2211yescharacteristic
63C43×#332C2211yescharacteristic
64C43×#332C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×Q16×C43—21no—
68C2×Q16×C43—21no—
69C22×C8×C43—21no—
70C4⋊Q8×C43D411yescharacteristic
71C4⋊Q8×C43D411yescharacteristic
72C4⋊Q8×C43C2311yescharacteristic
73C4⋊Q8×C43C2311yescharacteristic
74C4⋊Q8×C43C2311yescharacteristic
75C4⋊Q8×C43C2311yescharacteristic
76#125×C43—21no—
77#125×C43—21no—
78#125×C43—21no—
79C22⋊Q8×C43—21no—
80C22⋊Q8×C43—21no—
81C22⋊Q8×C43—21no—
82C22⋊Q8×C43—21no—
83C22⋊Q8×C43—21no—
84C22⋊Q8×C43D411yescharacteristic
85C22⋊Q8×C43D411yescharacteristic
86C4×Q8×C43—21no—
87C4×Q8×C43—21no—
88C4×Q8×C43—21no—
89C4×Q8×C43—21no—
90C4×Q8×C43—21no—
91C4×Q8×C43C2311yescharacteristic
92C4×Q8×C43C2311yescharacteristic
93#117×C43—21no—
94#117×C43—21no—
95#117×C43—21no—
96C2×C42×C43C2311yescharacteristic
97#107×C43—21no—
98#107×C43—21no—
99#107×C43—21no—
100#107×C43—21no—
101#107×C43—21no—
102#107×C43—21no—
103#106×C43—21no—
104#106×C43—21no—
105#106×C43—21no—
106#106×C43—21no—
107C4⋊C8×C43—21no—
108C4⋊C8×C43—21no—
109C4⋊C8×C43—21no—
110C4⋊C8×C43—21no—
111C4⋊C8×C43—21no—
112C4⋊C8×C43D411yescharacteristic
113C4⋊C8×C43D411yescharacteristic
114C4⋊C8×C43C2311yescharacteristic
115C4⋊C8×C43C2311yescharacteristic
116C4⋊C8×C43C2311yescharacteristic
117C4⋊C8×C43C2311yescharacteristic
118C4⋊C8×C43C2311yescharacteristic
119C4⋊C8×C43C2311yescharacteristic
120#103×C43—21no—
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—
132C22⋊C8×C43—21no—
133C22⋊C8×C43—21no—
134C22⋊C8×C43D411yescharacteristic
135C22⋊C8×C43D411yescharacteristic
136#97×C43—21no—
137#97×C43—21no—
138#97×C43—21no—
139C4×C8×C43—21no—
140C4×C8×C43—21no—
141C4×C8×C43—21no—
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—21no—
149C2×Q8×C43C2×D411yescharacteristic
150C2×Q8×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43#4111yescharacteristic
154Q16×C43—81no—
155Q16×C43—81no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—81no—
163C2×C8×C43C2×D411yescharacteristic
164C2×C8×C43C2×D411yescharacteristic
165C2×C8×C43C2×D411yescharacteristic
166C2×C8×C43C2×D411yescharacteristic
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
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—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—41no—
183C4⋊C4×C43—41no—
184C4⋊C4×C43—41no—
185C4⋊C4×C43—41no—
186C4⋊C4×C43C2×D411yescharacteristic
187C4⋊C4×C43C2×D411yescharacteristic
188C22⋊C4×C43—21no—
189C22⋊C4×C43—21no—
190C22⋊C4×C43—41no—
191C22⋊C4×C43—41no—
192C42×C43—21no—
193C42×C43—21no—
194C42×C43—41no—
195C42×C43—41no—
196C42×C43C2×D411yescharacteristic
197C42×C43C2×D411yescharacteristic
198C42×C43#4111yescharacteristic
199C42×C43C2411yescharacteristic
200C23×C43#12111yescharacteristic
201Q8×C43—21no—
202Q8×C43—21no—
203Q8×C43—21no—
204Q8×C43—21no—
205Q8×C43—42no—
206Q8×C43—41no—
207Q8×C43—41no—
208Q8×C43—41no—
209Q8×C43—41no—
210Q8×C43—81no—
211Q8×C43—81no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43#12111yescharacteristic
226C2×C4×C43#12111yescharacteristic
227C2×C4×C43#12111yescharacteristic
228C2×C4×C43C22×D411yescharacteristic
229C2×C4×C43C22×D411yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C8×C43—21no—
232C8×C43—21no—
233C8×C43—21no—
234C8×C43—21no—
235C8×C43—41no—
236C8×C43—41no—
237C8×C43—41no—
238C8×C43—41no—
239C8×C43—41no—
240C8×C43—41no—
241#19574C4311yesmaximal, characteristic, direct product factor, Sylow
242C22×C43—21no—
243C22×C43—21no—
244C22×C43—21no—
245C22×C43C2×#12111yescharacteristic
246C4×C43—21no—
247C4×C43—21no—
248C4×C43—21no—
249C4×C43—21no—
250C4×C43—41no—
251C4×C43—41no—
252C4×C43—41no—
253C4×C43—41no—
254C4×C43—81no—
255C4×C43—81no—
256C4×C43—81no—
257C4×C43—81no—
258C4×C43#57711yescharacteristic
259C4×C43#57811yescharacteristic
260C4×C43#57811yescharacteristic
261C4×C43#57811yescharacteristic
262#3249C2×C4311yescharacteristic
263#3237C2×C4311yescharacteristic
264#3231C2×C4311yescharacteristic
265#2986C2×C4311yescharacteristic
266#1704C2×C4311yescharacteristic, complemented
267#1700C2×C4311yescharacteristic, complemented
268#1696C2×C4311yescharacteristic, complemented
269#1692C2×C4311yescharacteristic, complemented
270#1684C2×C4311yescharacteristic, complemented
271#1680C2×C4311yescharacteristic, complemented
272#1676C2×C4311yescharacteristic, complemented
273#1672C2×C4311yescharacteristic, complemented
274#1573C2×C4311yescharacteristic
275#1554C2×C4311yescharacteristic
276#1542C2×C4311yescharacteristic
277C2×C43—41no—
278C2×C43#304411yescharacteristic
279C2×C43#306311yescharacteristic
280C2×C43#306711yescharacteristic
281#533C22×C4311yescharacteristic
282#533C22×C4311yescharacteristic
283#533C22×C4311yescharacteristic
284#501—21no—
285#500C22×C4311yescharacteristic
286#498C22×C4311yescharacteristic
287#491—21no—
288#487C22×C4311yescharacteristic
289#487C22×C4311yescharacteristic
290#485—21no—
291#485—21no—
292#485—21no—
293#485—21no—
294#479—21no—
295#479—21no—
296#477—21no—
297#477C22×C4311yescharacteristic
298#477C22×C4311yescharacteristic
299#477C22×C4311yescharacteristic
300#477C22×C4311yescharacteristic
301#475C22×C4311yescharacteristic
302#475C22×C4311yescharacteristic
303#467—21no—
304#467—21no—
305#462—21no—
306#462C22×C4311yescharacteristic
307#462C22×C4311yescharacteristic
308#446—21no—
309#446C22×C4311yescharacteristic
310#446C22×C4311yescharacteristic
311C8×Q8—21no—
312C8×Q8C22×C4311yescharacteristic
313C8×Q8C22×C4311yescharacteristic
314#433—21no—
315#433—21no—
316#432C22×C4311yescharacteristic
317#431C22×C4311yescharacteristic
318#431C22×C4311yescharacteristic
319C2×C4⋊C8C22×C4311yescharacteristic
320#335C22×C4311yescharacteristic
321#335C22×C4311yescharacteristic
322#334C22×C4311yescharacteristic
323#334C22×C4311yescharacteristic
324#333C22×C4311yescharacteristic
325#333C22×C4311yescharacteristic
326#333C22×C4311yescharacteristic
327#333C22×C4311yescharacteristic
328#332C22×C4311yescharacteristic
329#332C22×C4311yescharacteristic
330#332C22×C4311yescharacteristic
331#332C22×C4311yescharacteristic
332C43#1957411yescharacteristic, direct product factor, Sylow
333C2×Q16—21no—
334C2×Q16—21no—
335C22×C8—21no—
336C4⋊Q8D4×C4311yescharacteristic
337C4⋊Q8D4×C4311yescharacteristic
338C4⋊Q8C23×C4311yescharacteristic
339C4⋊Q8C23×C4311yescharacteristic
340C4⋊Q8C23×C4311yescharacteristic
341C4⋊Q8C23×C4311yescharacteristic
342#125—21no—
343#125—21no—
344#125—21no—
345C22⋊Q8—21no—
346C22⋊Q8—21no—
347C22⋊Q8—21no—
348C22⋊Q8—21no—
349C22⋊Q8—21no—
350C22⋊Q8D4×C4311yescharacteristic
351C22⋊Q8D4×C4311yescharacteristic
352C4×Q8—21no—
353C4×Q8—21no—
354C4×Q8—21no—
355C4×Q8—21no—
356C4×Q8—21no—
357C4×Q8C23×C4311yescharacteristic
358C4×Q8C23×C4311yescharacteristic
359#117—21no—
360#117—21no—
361#117—21no—
362C2×C42C23×C4311yescharacteristic
363#107—21no—
364#107—21no—
365#107—21no—
366#107—21no—
367#107—21no—
368#107—21no—
369#106—21no—
370#106—21no—
371#106—21no—
372#106—21no—
373C4⋊C8—21no—
374C4⋊C8—21no—
375C4⋊C8—21no—
376C4⋊C8—21no—
377C4⋊C8—21no—
378C4⋊C8D4×C4311yescharacteristic
379C4⋊C8D4×C4311yescharacteristic
380C4⋊C8C23×C4311yescharacteristic
381C4⋊C8C23×C4311yescharacteristic
382C4⋊C8C23×C4311yescharacteristic
383C4⋊C8C23×C4311yescharacteristic
384C4⋊C8C23×C4311yescharacteristic
385C4⋊C8C23×C4311yescharacteristic
386#103—21no—
387#103—21no—
388#103—21no—
389#103—21no—
390#103—21no—
391#103—21no—
392#103—21no—
393#103—21no—
394#103—21no—
395#103—21no—
396#103—21no—
397#103—21no—
398C22⋊C8—21no—
399C22⋊C8—21no—
400C22⋊C8D4×C4311yescharacteristic
401C22⋊C8D4×C4311yescharacteristic
402#97—21no—
403#97—21no—
404#97—21no—
405C4×C8—21no—
406C4×C8—21no—
407C4×C8—21no—
408C4×C8C23×C4311yescharacteristic
409C4×C8C23×C4311yescharacteristic
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8C2×D4×C4311yescharacteristic
416C2×Q8C2×D4×C4311yescharacteristic
417C22×C4C2×D4×C4311yescharacteristic
418C22×C4C2×D4×C4311yescharacteristic
419C22×C4#41×C4311yescharacteristic
420Q16—81no—
421Q16—81no—
422C2×C8—21no—
423C2×C8—21no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8—21no—
428C2×C8—81no—
429C2×C8C2×D4×C4311yescharacteristic
430C2×C8C2×D4×C4311yescharacteristic
431C2×C8C2×D4×C4311yescharacteristic
432C2×C8C2×D4×C4311yescharacteristic
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—41no—
449C4⋊C4—41no—
450C4⋊C4—41no—
451C4⋊C4—41no—
452C4⋊C4C2×D4×C4311yescharacteristic
453C4⋊C4C2×D4×C4311yescharacteristic
454C22⋊C4—21no—
455C22⋊C4—21no—
456C22⋊C4—41no—
457C22⋊C4—41no—
458C42—21no—
459C42—21no—
460C42—41no—
461C42—41no—
462C42C2×D4×C4311yescharacteristic
463C42C2×D4×C4311yescharacteristic
464C42#41×C4311yescharacteristic
465C42C24×C4311yescharacteristic
466C23#121×C4311yescharacteristic
467Q8—21no—
468Q8—21no—
469Q8—21no—
470Q8—21no—
471Q8—42no—
472Q8—41no—
473Q8—41no—
474Q8—41no—
475Q8—41no—
476Q8—81no—
477Q8—81no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4#121×C4311yescharacteristic
492C2×C4#121×C4311yescharacteristic
493C2×C4#121×C4311yescharacteristic
494C2×C4C22×D4×C4311yescharacteristic
495C2×C4C22×D4×C4311yescharacteristic
496C2×C4C2×#41×C4311yescharacteristic
497C8—21no—
498C8—21no—
499C8—21no—
500C8—21no—
501C8—41no—
502C8—41no—
503C8—41no—
504C8—41no—
505C8—41no—
506C8—41no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22C2×#121×C4311yescharacteristic
511C4—21no—
512C4—21no—
513C4—21no—
514C4—21no—
515C4—41no—
516C4—41no—
517C4—41no—
518C4—41no—
519C4—81no—
520C4—81no—
521C4—81no—
522C4—81no—
523C4C43×#57711yescharacteristic
524C4C43×#57811yescharacteristic
525C4C43×#57811yescharacteristic
526C4C43×#57811yescharacteristic
527C2—41no—
528C2C43×#304411yescharacteristic
529C2C43×#306311yescharacteristic
530C2C43×#306711yescharacteristic
subgroupG/H
center, socleC22×C43C2×#121
commutator, Frattini, cosocleC42C24×C43
prime radicalC23×C43#121
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
5. C43×#1704C2semidirect
6. C43×#1700C2semidirect
7. C43×#1696C2semidirect
8. C43×#1692C2semidirect
9. C43×#1684C2semidirect
10. C43×#1680C2semidirect
11. C43×#1676C2semidirect
12. C43×#1672C2semidirect
241. #19574C43direct (N × H)
266. #1704C2×C43semidirect
267. #1700C2×C43semidirect
268. #1696C2×C43semidirect
269. #1692C2×C43semidirect
270. #1684C2×C43semidirect
271. #1680C2×C43semidirect
272. #1676C2×C43semidirect
273. #1672C2×C43semidirect
332. C43#19574direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#32492
C43×#32372
C43×#32312
C43×#29862
C43×#17042
C43×#17002
C43×#16962
C43×#16922
C43×#16842
C43×#16802
C43×#16762
C43×#16722
C43×#15732
C43×#15542
C43×#15422
#1957443