Finite Group Databasebeta

← C43×#19620 #24939637

Subgroups — C43×#19620 #24939637

Order 11008.

712 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3170C211yesmaximal, characteristic, complemented
2C43×#3170C211yesmaximal, characteristic, complemented
3C43×#3167C211yesmaximal, characteristic
4C43×#3167C211yesmaximal, characteristic
5C43×#3160C211yesmaximal, characteristic, complemented
6C43×#3131C211yesmaximal, characteristic
7C43×#1723C211yesmaximal, characteristic, complemented
8C43×#1722C211yesmaximal, characteristic, complemented
9C43×#1720C211yesmaximal, characteristic, complemented
10C43×#1719C211yesmaximal, characteristic, complemented
11C43×#1718C211yesmaximal, characteristic, complemented
12C43×#1718C211yesmaximal, characteristic, complemented
13C43×#1716C211yesmaximal, characteristic, complemented
14C43×#1714C211yesmaximal, characteristic, complemented
15C2×C43×#322C211yesmaximal, characteristic, complemented
16C43×#533C2211yescharacteristic
17C43×#533C2211yescharacteristic
18C43×#533C2211yescharacteristic
19C43×#532C2211yescharacteristic
20C43×#500C2211yescharacteristic
21C43×#500C2211yescharacteristic
22C43×#500C2211yescharacteristic
23C43×#500C2211yescharacteristic
24C43×#499—22no—
25C43×#498C2211yescharacteristic
26C43×#498C2211yescharacteristic
27C43×#498C2211yescharacteristic
28C43×#498C2211yescharacteristic
29C43×#494C2211yescharacteristic
30C43×#494C2211yescharacteristic
31C43×#492C2211yescharacteristic
32C43×#492C2211yescharacteristic
33C43×#488—22no—
34C43×#487C2211yescharacteristic
35C43×#487C2211yescharacteristic
36C43×#487C2211yescharacteristic
37C43×#487C2211yescharacteristic
38C43×#487C2211yescharacteristic
39C43×#487C2211yescharacteristic
40C43×#487C2211yescharacteristic
41C43×#487C2211yescharacteristic
42C43×#486C2211yescharacteristic
43C43×#486C2211yescharacteristic
44C43×#486C2211yescharacteristic
45C43×#486C2211yescharacteristic
46C43×#467—22no—
47C43×#467—22no—
48C43×#465—22no—
49C43×#465—22no—
50C4×Q16×C43—22no—
51C4×Q16×C43—22no—
52C4×SD16×C43—22no—
53C4×SD16×C43—22no—
54C43×#427—22no—
55C43×#416—22no—
56C2×C4×C8×C43C2211yescharacteristic
57C2×C4×C8×C43C2211yescharacteristic
58C2×C4×C8×C43C2211yescharacteristic
59C43×#322C2211yescharacteristic
60C43×#322C2211yescharacteristic
61C43×#322C2211yescharacteristic
62C43×#322C2211yescharacteristic
63C2×#41×C43—21no—
64C2×Q16×C43—22no—
65C2×Q16×C43—22no—
66C2×SD16×C43—22no—
67C2×SD16×C43—22no—
68C22×C8×C43D412yes—
69C22×C8×C43D412yes—
70C22×C8×C43D412yes—
71C4⋊Q8×C43C2311yescharacteristic
72C4⋊Q8×C43C2311yescharacteristic
73C4⋊Q8×C43C2311yescharacteristic
74C4⋊Q8×C43C2311yescharacteristic
75C4⋊Q8×C43C2311yescharacteristic
76C4⋊Q8×C43C2311yescharacteristic
77C4⋊Q8×C43C2311yescharacteristic
78#127×C43C2311yescharacteristic
79#125×C43—21no—
80#125×C43—21no—
81#125×C43—21no—
82#124×C43—21no—
83C22⋊Q8×C43—21no—
84C22⋊Q8×C43—21no—
85C22⋊Q8×C43—21no—
86C22⋊Q8×C43—21no—
87C22⋊Q8×C43—21no—
88C22⋊Q8×C43—21no—
89#121×C43—21no—
90#121×C43—21no—
91C4×Q8×C43—21no—
92C4×Q8×C43—21no—
93C4×Q8×C43—21no—
94C4×Q8×C43—21no—
95C4×Q8×C43—21no—
96C4×Q8×C43—21no—
97C4×D4×C43—21no—
98C4×D4×C43—21no—
99#117×C43—21no—
100#117×C43—21no—
101#117×C43—21no—
102C2×C42×C43C2311yescharacteristic
103#107×C43—22no—
104#107×C43—22no—
105#107×C43—22no—
106#107×C43—22no—
107#106×C43—22no—
108#106×C43—22no—
109#106×C43—22no—
110#106×C43—22no—
111#103×C43—22no—
112#103×C43—22no—
113#103×C43—22no—
114#103×C43—22no—
115#103×C43—22no—
116#103×C43—22no—
117#103×C43—22no—
118#103×C43—22no—
119#102×C43—22no—
120#102×C43—22no—
121#102×C43—22no—
122#102×C43—22no—
123C4×C8×C43D412yes—
124C4×C8×C43D412yes—
125C4×C8×C43D412yes—
126C4×C8×C43C2311yescharacteristic
127C4×C8×C43C2311yescharacteristic
128C4×C8×C43C2311yescharacteristic
129C4×C8×C43C2311yescharacteristic
130C4×C8×C43C2311yescharacteristic
131C4×C8×C43C2311yescharacteristic
132#41×C43—44no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43—21no—
140C2×D4×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—41no—
144C22×C4×C43—41no—
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148Q16×C43—44no—
149Q16×C43—44no—
150SD16×C43—44no—
151SD16×C43—44no—
152C2×C8×C43—24no—
153C2×C8×C43—24no—
154C2×C8×C43—42no—
155C2×C8×C43C2×D412yes—
156C2×C8×C43C2×D412yes—
157C2×C8×C43C2×D412yes—
158C2×C8×C43C2×D412yes—
159C2×C8×C43C2×D412yes—
160C2×C8×C43C2×D412yes—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
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—41no—
176C4⋊C4×C43—41no—
177C4⋊C4×C43—41no—
178C4⋊C4×C43—41no—
179C4⋊C4×C43—41no—
180C4⋊C4×C43—41no—
181C22⋊C4×C43—41no—
182C22⋊C4×C43—41no—
183C22⋊C4×C43—41no—
184C22⋊C4×C43—41no—
185C22⋊C4×C43—41no—
186C42×C43—41no—
187C42×C43—41no—
188C42×C43—41no—
189C42×C43C2×D411yescharacteristic
190C42×C43C2×D411yescharacteristic
191C42×C43C2×D411yescharacteristic
192C42×C43C2411yescharacteristic
193C23×C43—41no—
194C23×C43#12711yescharacteristic
195Q8×C43—42no—
196Q8×C43—42no—
197Q8×C43—42no—
198Q8×C43—42no—
199Q8×C43—42no—
200Q8×C43—42no—
201Q8×C43—42no—
202D4×C43—42no—
203D4×C43—42no—
204D4×C43—42no—
205D4×C43—82no—
206C2×C4×C43—22no—
207C2×C4×C43—22no—
208C2×C4×C43—41no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43—82no—
216C2×C4×C43#12711yescharacteristic
217C2×C4×C43#12711yescharacteristic
218C2×C4×C43#12711yescharacteristic
219C2×C4×C43#13714yes—
220C2×C4×C43C22×D411yescharacteristic
221C2×C4×C43C22×D411yescharacteristic
222C2×C4×C43C22×D411yescharacteristic
223C8×C43—22no—
224C8×C43—22no—
225C8×C43—22no—
226C8×C43—22no—
227C8×C43—22no—
228C8×C43#13514yes—
229#19620C4311yesmaximal, characteristic, direct product factor, Sylow
230C22×C43—21no—
231C22×C43—21no—
232C22×C43—81no—
233C22×C43—81no—
234C22×C43—81no—
235C22×C43#49712yes—
236C22×C43C2×#12711yescharacteristic
237C4×C43—21no—
238C4×C43—21no—
239C4×C43—81no—
240C4×C43—81no—
241C4×C43—81no—
242C4×C43—81no—
243C4×C43—81no—
244C4×C43—81no—
245C4×C43—81no—
246C4×C43#49712yes—
247C4×C43C2×#13512yes—
248C4×C43C2×#13712yes—
249C4×C43#57512yes—
250#3170C2×C4311yescharacteristic, complemented
251#3170C2×C4311yescharacteristic, complemented
252#3167C2×C4311yescharacteristic
253#3167C2×C4311yescharacteristic
254#3160C2×C4311yescharacteristic, complemented
255#3131C2×C4311yescharacteristic
256#1723C2×C4311yescharacteristic, complemented
257#1722C2×C4311yescharacteristic, complemented
258#1720C2×C4311yescharacteristic, complemented
259#1719C2×C4311yescharacteristic, complemented
260#1718C2×C4311yescharacteristic, complemented
261#1718C2×C4311yescharacteristic, complemented
262#1716C2×C4311yescharacteristic, complemented
263#1714C2×C4311yescharacteristic, complemented
264C2×#322C2×C4311yescharacteristic, complemented
265C2×C43—22no—
266C2×C43—161no—
267C2×C43#314711yescharacteristic
268C2×C43C2×#49711yescharacteristic
269C2×C43#315011yescharacteristic
270#533C22×C4311yescharacteristic
271#533C22×C4311yescharacteristic
272#533C22×C4311yescharacteristic
273#532C22×C4311yescharacteristic
274#500C22×C4311yescharacteristic
275#500C22×C4311yescharacteristic
276#500C22×C4311yescharacteristic
277#500C22×C4311yescharacteristic
278#499—22no—
279#498C22×C4311yescharacteristic
280#498C22×C4311yescharacteristic
281#498C22×C4311yescharacteristic
282#498C22×C4311yescharacteristic
283#494C22×C4311yescharacteristic
284#494C22×C4311yescharacteristic
285#492C22×C4311yescharacteristic
286#492C22×C4311yescharacteristic
287#488—22no—
288#487C22×C4311yescharacteristic
289#487C22×C4311yescharacteristic
290#487C22×C4311yescharacteristic
291#487C22×C4311yescharacteristic
292#487C22×C4311yescharacteristic
293#487C22×C4311yescharacteristic
294#487C22×C4311yescharacteristic
295#487C22×C4311yescharacteristic
296#486C22×C4311yescharacteristic
297#486C22×C4311yescharacteristic
298#486C22×C4311yescharacteristic
299#486C22×C4311yescharacteristic
300#467—22no—
301#467—22no—
302#465—22no—
303#465—22no—
304C4×Q16—22no—
305C4×Q16—22no—
306C4×SD16—22no—
307C4×SD16—22no—
308#427—22no—
309#416—22no—
310C2×C4×C8C22×C4311yescharacteristic
311C2×C4×C8C22×C4311yescharacteristic
312C2×C4×C8C22×C4311yescharacteristic
313#322C22×C4311yescharacteristic
314#322C22×C4311yescharacteristic
315#322C22×C4311yescharacteristic
316#322C22×C4311yescharacteristic
317C43#1962011yescharacteristic, direct product factor, Sylow
318C2×#41—21no—
319C2×Q16—22no—
320C2×Q16—22no—
321C2×SD16—22no—
322C2×SD16—22no—
323C22×C8D4×C4312yes—
324C22×C8D4×C4312yes—
325C22×C8D4×C4312yes—
326C4⋊Q8C23×C4311yescharacteristic
327C4⋊Q8C23×C4311yescharacteristic
328C4⋊Q8C23×C4311yescharacteristic
329C4⋊Q8C23×C4311yescharacteristic
330C4⋊Q8C23×C4311yescharacteristic
331C4⋊Q8C23×C4311yescharacteristic
332C4⋊Q8C23×C4311yescharacteristic
333#127C23×C4311yescharacteristic
334#125—21no—
335#125—21no—
336#125—21no—
337#124—21no—
338C22⋊Q8—21no—
339C22⋊Q8—21no—
340C22⋊Q8—21no—
341C22⋊Q8—21no—
342C22⋊Q8—21no—
343C22⋊Q8—21no—
344#121—21no—
345#121—21no—
346C4×Q8—21no—
347C4×Q8—21no—
348C4×Q8—21no—
349C4×Q8—21no—
350C4×Q8—21no—
351C4×Q8—21no—
352C4×D4—21no—
353C4×D4—21no—
354#117—21no—
355#117—21no—
356#117—21no—
357C2×C42C23×C4311yescharacteristic
358#107—22no—
359#107—22no—
360#107—22no—
361#107—22no—
362#106—22no—
363#106—22no—
364#106—22no—
365#106—22no—
366#103—22no—
367#103—22no—
368#103—22no—
369#103—22no—
370#103—22no—
371#103—22no—
372#103—22no—
373#103—22no—
374#102—22no—
375#102—22no—
376#102—22no—
377#102—22no—
378C4×C8D4×C4312yes—
379C4×C8D4×C4312yes—
380C4×C8D4×C4312yes—
381C4×C8C23×C4311yescharacteristic
382C4×C8C23×C4311yescharacteristic
383C4×C8C23×C4311yescharacteristic
384C4×C8C23×C4311yescharacteristic
385C4×C8C23×C4311yescharacteristic
386C4×C8C23×C4311yescharacteristic
387#41—44no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—21no—
393C2×Q8—21no—
394C2×Q8—21no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—21no—
398C2×D4—41no—
399C22×C4—41no—
400C22×C4C2×D4×C4311yescharacteristic
401C22×C4C2×D4×C4311yescharacteristic
402C22×C4C2×D4×C4311yescharacteristic
403Q16—44no—
404Q16—44no—
405SD16—44no—
406SD16—44no—
407C2×C8—24no—
408C2×C8—24no—
409C2×C8—42no—
410C2×C8C2×D4×C4312yes—
411C2×C8C2×D4×C4312yes—
412C2×C8C2×D4×C4312yes—
413C2×C8C2×D4×C4312yes—
414C2×C8C2×D4×C4312yes—
415C2×C8C2×D4×C4312yes—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—41no—
431C4⋊C4—41no—
432C4⋊C4—41no—
433C4⋊C4—41no—
434C4⋊C4—41no—
435C4⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—41no—
440C22⋊C4—41no—
441C42—41no—
442C42—41no—
443C42—41no—
444C42C2×D4×C4311yescharacteristic
445C42C2×D4×C4311yescharacteristic
446C42C2×D4×C4311yescharacteristic
447C42C24×C4311yescharacteristic
448C23—41no—
449C23#127×C4311yescharacteristic
450Q8—42no—
451Q8—42no—
452Q8—42no—
453Q8—42no—
454Q8—42no—
455Q8—42no—
456Q8—42no—
457D4—42no—
458D4—42no—
459D4—42no—
460D4—82no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—82no—
471C2×C4#127×C4311yescharacteristic
472C2×C4#127×C4311yescharacteristic
473C2×C4#127×C4311yescharacteristic
474C2×C4#137×C4314yes—
475C2×C4C22×D4×C4311yescharacteristic
476C2×C4C22×D4×C4311yescharacteristic
477C2×C4C22×D4×C4311yescharacteristic
478C8—22no—
479C8—22no—
480C8—22no—
481C8—22no—
482C8—22no—
483C8#135×C4314yes—
484C22—21no—
485C22—21no—
486C22—81no—
487C22—81no—
488C22—81no—
489C22C43×#49712yes—
490C22C2×#127×C4311yescharacteristic
491C4—21no—
492C4—21no—
493C4—81no—
494C4—81no—
495C4—81no—
496C4—81no—
497C4—81no—
498C4—81no—
499C4—81no—
500C4C43×#49712yes—
501C4C2×#135×C4312yes—
502C4C2×#137×C4312yes—
503C4C43×#57512yes—
504C2—22no—
505C2—161no—
506C2C43×#314711yescharacteristic
507C2C2×C43×#49711yescharacteristic
508C2C43×#315011yescharacteristic
subgroupG/H
centerC2×C4×C43#127
commutator, Frattini, cosocleC42C24×C43
socleC22×C43C2×#127
prime radicalC43×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3170C2semidirect
2. C43×#3170C2semidirect
5. C43×#3160C2semidirect
7. C43×#1723C2semidirect
8. C43×#1722C2semidirect
9. C43×#1720C2semidirect
10. C43×#1719C2semidirect
11. C43×#1718C2semidirect
12. C43×#1718C2semidirect
13. C43×#1716C2semidirect
14. C43×#1714C2semidirect
15. C2×C43×#322C2semidirect
229. #19620C43direct (N × H)
250. #3170C2×C43semidirect
251. #3170C2×C43semidirect
254. #3160C2×C43semidirect
256. #1723C2×C43semidirect
257. #1722C2×C43semidirect
258. #1720C2×C43semidirect
259. #1719C2×C43semidirect
260. #1718C2×C43semidirect
261. #1718C2×C43semidirect
262. #1716C2×C43semidirect
263. #1714C2×C43semidirect
264. C2×#322C2×C43semidirect
317. C43#19620direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#31702
C43×#31672
C43×#31602
C43×#31312
C43×#17232
C43×#17222
C43×#17202
C43×#17192
C43×#17182
C43×#17162
C43×#17142
C2×C43×#3222
#1962043