Finite Group Databasebeta

← D43×#2237 #25251371

Subgroups — D43×#2237 #25251371

Order 11008.

586 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#467×D43C211yesmaximal, characteristic
2#427×D43C211yesmaximal, characteristic
3#19136806C211yesmaximal, characteristic, complemented
4#19136805C211yesmaximal, characteristic, complemented
5#19136804C211yesmaximal, characteristic, complemented
6#19136803C211yesmaximal, characteristic, complemented
7#19136802C211yesmaximal, characteristic, complemented
8#19136801C211yesmaximal, characteristic, complemented
9#19136800C211yesmaximal, characteristic, complemented
10#367×D43C211yesmaximal, characteristic, complemented
11#366×D43C211yesmaximal, characteristic, complemented
12#358×D43C211yesmaximal, characteristic, complemented
13#358×D43C211yesmaximal, characteristic, complemented
14C22⋊C16×D43C211yesmaximal, characteristic
15C43×#2237C211yesmaximal, characteristic, complemented
16C2×Q16×D43C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C22⋊Q8×D43—21no—
19#117×D43—21no—
20C2×C16×D43C2211yescharacteristic
21C2×C16×D43C2211yescharacteristic
22#14583141C2211yescharacteristic
23#14583140C2211yescharacteristic
24#14583139—21no—
25#14583138—21no—
26#14583137C2211yescharacteristic
27#14582937C2211yescharacteristic
28#14582936C2211yescharacteristic
29#14582936C2211yescharacteristic
30#14582935—21no—
31#14582934—21no—
32#107×D43C2211yescharacteristic
33#107×D43C2211yescharacteristic
34#107×D43C2211yescharacteristic
35#106×D43—21no—
36#103×D43—21no—
37#14582727C2211yescharacteristic, complemented
38#14582726C2211yescharacteristic, complemented
39#14582726C2211yescharacteristic, complemented
40#14582725C2211yescharacteristic, complemented
41#14582724C2211yescharacteristic, complemented
42#14582724C2211yescharacteristic, complemented
43#14582704C2211yescharacteristic, complemented
44#14582704C2211yescharacteristic, complemented
45#14582703C2211yescharacteristic, complemented
46#14582703C2211yescharacteristic, complemented
47#14582702C2211yescharacteristic, complemented
48#14582702C2211yescharacteristic, complemented
49C22⋊(C43⋊C16)C2211yescharacteristic
50(C2×D43)⋊C16C2211yescharacteristic
51(C2×D43)⋊C16C2211yescharacteristic
52C43×#467C2211yescharacteristic
53C43×#427C2211yescharacteristic
54C43×#367C2211yescharacteristic, complemented
55C43×#366C2211yescharacteristic, complemented
56C43×#358C2211yescharacteristic, complemented
57C43×#358C2211yescharacteristic, complemented
58C43×C22⋊C16C2211yescharacteristic
59C2×Q8×D43—21no—
60C22×C4×D43D411yescharacteristic
61C2×Dic172C2311yescharacteristic
62C2×#10621885—21no—
63Q16×D43—22no—
64Q16×D43—22no—
65C22×C43⋊C8D411yescharacteristic
66C2×C8×D43—22no—
67C2×C8×D43—22no—
68C2×C8×D43D411yescharacteristic
69C2×C8×D43D411yescharacteristic
70C2×C8×D43C2311yescharacteristic
71C2×C8×D43C2311yescharacteristic
72#13063305—21no—
73#13063304—21no—
74#13063303—41no—
75#13063302—41no—
76#13063301—21no—
77#13063284—21no—
78#13063283—21no—
79#13063283—21no—
80#13063282—41no—
81#13063281—41no—
82C4⋊C4×D43—21no—
83C4⋊C4×D43—21no—
84C4⋊C4×D43—21no—
85C4⋊C4×D43—41no—
86C22⋊C4×D43—41no—
87C22⋊C4×D43—41no—
88C42×D43—41no—
89C2×C43⋊C16C2311yescharacteristic
90C2×C43⋊C16C2311yescharacteristic
91C16×D43—22no—
92C16×D43—22no—
93#13063259C2311yescharacteristic
94#13063259C2311yescharacteristic
95#13063259C2311yescharacteristic
96#13063258—21no—
97#13063258—21no—
98#13063258—21no—
99#13063257—21no—
100#13063256—21no—
101#13063256—21no—
102#13063250—21no—
103#13063249—21no—
104#13063248—21no—
105C2×Q16×C43C2311yescharacteristic
106C22×C8×C43C2311yescharacteristic
107C22⋊Q8×C43—21no—
108#117×C43—21no—
109C2×C16×C43C2311yescharacteristic
110C2×C16×C43C2311yescharacteristic
111#107×C43C2311yescharacteristic
112#107×C43C2311yescharacteristic
113#107×C43C2311yescharacteristic
114#106×C43—21no—
115#103×C43—21no—
116C23×D43D811yescharacteristic
117C2×Q8×C43—21no—
118C22×C4×C43C2×D411yescharacteristic
119C22×Dic43D811yescharacteristic
120Q8×D43—42no—
121Q8×D43—42no—
122C2×C4×D43—22no—
123C2×C4×D43—22no—
124C2×C4×D43—41no—
125C2×C4×D43—41no—
126C2×C4×D43—41no—
127C2×C4×D43—41no—
128C2×C4×D43D811yescharacteristic
129C2×C4×D43D811yescharacteristic
130C2×C4×D43C2×D411yescharacteristic
131C2×C4×D43C2×D411yescharacteristic
132C2×Dic86—21no—
133C2×Dic86—41no—
134Q16×C43—21no—
135Q16×C43—21no—
136C2×C8×C43—21no—
137C2×C8×C43—21no—
138C2×C8×C43C2×D411yescharacteristic
139C2×C8×C43C2411yescharacteristic
140C4⋊C4×C43—21no—
141C4⋊C4×C43—21no—
142C4⋊C4×C43—21no—
143C4⋊C4×C43—41no—
144C22⋊C4×C43—41no—
145C22⋊C4×C43—41no—
146C42×C43—41no—
147C22⋊Dic43—41no—
148C22⋊Dic43—41no—
149#10621885—42no—
150(C2×D43)⋊C4—41no—
151(C2×D43)⋊C4—41no—
152(C2×D43)⋊C4—41no—
153(C2×D43)⋊C4—41no—
154C4⋊Dic43—21no—
155C4⋊Dic43—21no—
156C4⋊Dic43—21no—
157C4⋊Dic43—41no—
158Dic43⋊C4—41no—
159Dic43⋊C4—41no—
160Dic43⋊C4—41no—
161Dic43⋊C4—41no—
162Dic43⋊C4—41no—
163C4×Dic43—41no—
164C4×Dic43—41no—
165C4×Dic43—41no—
166C2×C43⋊C8—22no—
167C2×C43⋊C8C2×D411yescharacteristic
168C2×C43⋊C8C2×D411yescharacteristic
169Dic172—21no—
170Dic172—21no—
171C8×D43—22no—
172C8×D43—21no—
173C8×D43—21no—
174C8×D43—22no—
175C8×D43#4112yes—
176C8×D43#4112yes—
177C16×C43—21no—
178C16×C43—21no—
179C43⋊C16—21no—
180C43⋊C16—21no—
181C23×C43C2×D811yescharacteristic
182C22×D43—22no—
183C22×D43—22no—
184C22×D43—22no—
185C22×D43C2×D811yescharacteristic
186C22×D43C2×D811yescharacteristic
187Q8×C43—41no—
188Q8×C43—41no—
189C2×C4×C43—21no—
190C2×C4×C43—21no—
191C2×C4×C43—41no—
192C2×C4×C43—41no—
193C2×C4×C43—41no—
194C2×C4×C43—41no—
195C2×C4×C43C2×D811yescharacteristic
196C2×C4×C43C22×D411yescharacteristic
197C2×Dic43—22no—
198C2×Dic43—41no—
199C2×Dic43—41no—
200C2×Dic43—41no—
201C2×Dic43—41no—
202C2×Dic43C2×D811yescharacteristic
203C2×Dic43C2×D811yescharacteristic
204C4×D43—22no—
205C4×D43—21no—
206C4×D43—21no—
207C4×D43—22no—
208C4×D43—82no—
209C4×D43—82no—
210C4×D43—82no—
211C4×D43—82no—
212C4×D43#12312yes—
213C4×D43#13712yes—
214Dic86—41no—
215Dic86—41no—
216Dic86—82no—
217C8×C43—21no—
218C8×C43C2×#4111yescharacteristic
219C8×C43C2×#4111yescharacteristic
220C43⋊C8—21no—
221C43⋊C8#12312yes—
222C2×#2237—431nomaximal, Sylow
223C22×C43—21no—
224C22×C43—21no—
225C22×C43—21no—
226C22×C43C22×D811yescharacteristic
227C2×D43—21no—
228C2×D43—21no—
229C2×D43—21no—
230C2×D43—44no—
231C2×D43#48012yes—
232C2×D43#50812yes—
233C2×D43#51012yes—
234C4×C43—21no—
235C4×C43—81no—
236C4×C43—81no—
237C4×C43—81no—
238C4×C43—81no—
239C4×C43C2×#12311yescharacteristic
240C4×C43C2×#13711yescharacteristic
241Dic43—21no—
242Dic43—81no—
243Dic43—81no—
244Dic43—81no—
245Dic43—81no—
246Dic43#48012yes—
247C2×#467—431no—
248C2×#427—431no—
249#2237—431no—
250#2237—431no—
251#2237—431no—
252#2237—431no—
253#2237—431no—
254#2237—431no—
255#2237—431no—
256#2237D4311yescharacteristic, direct product factor
257C2×#367—431no—
258C2×#366—431no—
259C2×#358—431no—
260C2×#358—431no—
261C2×C22⋊C16—431no—
262C2×C43—41no—
263C2×C43C2×#48011yescharacteristic
264C2×C43C2×#50811yescharacteristic
265C2×C43C2×#51011yescharacteristic
266D43—41no—
267D43#223714yesdirect product factor
268C22×Q16—431no—
269C23×C8—431no—
270C2×C22⋊Q8—861no—
271C2×#117—861no—
272C22×C16—431no—
273C22×C16—431no—
274#467—431no—
275#467—431no—
276#467—431no—
277#467—861no—
278#467—861no—
279#467C2×D4311yescharacteristic
280#427—431no—
281#427—431no—
282#427—431no—
283#427—861no—
284#427—861no—
285#427C2×D4311yescharacteristic
286C2×#107—431no—
287C2×#107—431no—
288C2×#107—431no—
289C2×#106—861no—
290C2×#103—861no—
291#367—431no—
292#367—431no—
293#367—431no—
294#367C2×D4311yescharacteristic, complemented
295#366—431no—
296#366—431no—
297#366—431no—
298#366C2×D4311yescharacteristic, complemented
299#358—431no—
300#358—431no—
301#358—431no—
302#358—431no—
303#358—431no—
304#358—431no—
305#358C2×D4311yescharacteristic, complemented
306#358C2×D4311yescharacteristic, complemented
307C22⋊C16—431no—
308C22⋊C16—431no—
309C22⋊C16—431no—
310C22⋊C16C2×D4311yescharacteristic
311C43C2×#223711yescharacteristic, complemented, Sylow
312C22×Q8—861no—
313C23×C4—431no—
314C2×Q16—431no—
315C2×Q16—862no—
316C2×Q16—862no—
317C2×Q16—861no—
318C2×Q16C22×D4311yescharacteristic
319C22×C8—431no—
320C22×C8—431no—
321C22×C8—431no—
322C22×C8—431no—
323C22×C8—431no—
324C22×C8—862no—
325C22×C8—862no—
326C22×C8C22×D4311yescharacteristic
327C22⋊Q8—21no—
328C22⋊Q8—861no—
329C22⋊Q8—861no—
330C22⋊Q8—861no—
331C22⋊Q8—1721no—
332C22⋊Q8—1721no—
333#117—21no—
334#117—861no—
335#117—861no—
336#117—861no—
337#117—1721no—
338#117—1721no—
339C2×C4⋊C4—861no—
340C2×C4⋊C4—861no—
341C2×C4⋊C4—861no—
342C2×C4⋊C4—1721no—
343C2×C22⋊C4—1721no—
344C2×C22⋊C4—1721no—
345C2×C42—1721no—
346C2×C16—431no—
347C2×C16—431no—
348C2×C16—862no—
349C2×C16—862no—
350C2×C16C22×D4311yescharacteristic
351C2×C16C22×D4311yescharacteristic
352#107—431no—
353#107—431no—
354#107—431no—
355#107—861no—
356#107—861no—
357#107—861no—
358#107C22×D4311yescharacteristic
359#107C22×D4311yescharacteristic
360#107C22×D4311yescharacteristic
361#106—21no—
362#106—861no—
363#106—861no—
364#106—861no—
365#103—21no—
366#103—861no—
367#103—861no—
368#103—861no—
369C24—431no—
370C2×Q8—21no—
371C2×Q8—861no—
372C2×Q8—1721no—
373C2×Q8—1722no—
374C2×Q8—1722no—
375C22×C4—431no—
376C22×C4—431no—
377C22×C4—431no—
378C22×C4—431no—
379C22×C4—431no—
380C22×C4—862no—
381C22×C4—862no—
382C22×C4—1721no—
383C22×C4—1721no—
384C22×C4—1721no—
385C22×C4—1721no—
386C22×C4D4×D4311yescharacteristic
387Q16—21no—
388Q16—21no—
389Q16—861no—
390Q16—861no—
391Q16—1722no—
392C2×C8—21no—
393C2×C8—21no—
394C2×C8—431no—
395C2×C8—432no—
396C2×C8—432no—
397C2×C8—431no—
398C2×C8—862no—
399C2×C8—862no—
400C2×C8—862no—
401C2×C8—861no—
402C2×C8—861no—
403C2×C8D4×D4311yescharacteristic
404C2×C8C23×D4311yescharacteristic
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—41no—
409C4⋊C4—861no—
410C4⋊C4—861no—
411C4⋊C4—861no—
412C4⋊C4—1721no—
413C4⋊C4—1721no—
414C4⋊C4—1721no—
415C4⋊C4—1721no—
416C4⋊C4—1721no—
417C4⋊C4—1721no—
418C22⋊C4—41no—
419C22⋊C4—41no—
420C22⋊C4—1721no—
421C22⋊C4—1721no—
422C22⋊C4—1721no—
423C22⋊C4—1721no—
424C22⋊C4—1721no—
425C22⋊C4—1721no—
426C42—41no—
427C42—1721no—
428C42—1721no—
429C42—1721no—
430C16—21no—
431C16—21no—
432C16—861no—
433C16—861no—
434C23—431no—
435C23—431no—
436C23—862no—
437C23—862no—
438C23—862no—
439C23D8×D4311yescharacteristic
440Q8—41no—
441Q8—41no—
442Q8—3442no—
443Q8—1721no—
444Q8—1721no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—431no—
452C2×C4—432no—
453C2×C4—432no—
454C2×C4—431no—
455C2×C4—862no—
456C2×C4—862no—
457C2×C4—862no—
458C2×C4—861no—
459C2×C4—861no—
460C2×C4—3442no—
461C2×C4—3442no—
462C2×C4—3442no—
463C2×C4—3442no—
464C2×C4—1721no—
465C2×C4—1721no—
466C2×C4—1721no—
467C2×C4—1721no—
468C2×C4D8×D4311yescharacteristic
469C2×C4C2×D4×D4311yescharacteristic
470C8—21no—
471C8—432no—
472C8—861no—
473C8#41×D4311yescharacteristic
474C8#41×D4311yescharacteristic
475C22—21no—
476C22—21no—
477C22—21no—
478C22—432no—
479C22—432no—
480C22—432no—
481C22—861no—
482C22—861no—
483C22—861no—
484C22—1724no—
485C22C2×D8×D4311yescharacteristic
486C4—21no—
487C4—81no—
488C4—81no—
489C4—81no—
490C4—81no—
491C4—432no—
492C4—861no—
493C4—3441no—
494C4—3441no—
495C4—3441no—
496C4—3441no—
497C4#123×D4311yescharacteristic
498C4#137×D4311yescharacteristic
499C2—41no—
500C2—434no—
501C2—1721no—
502C2#480×D4311yescharacteristic
503C2#508×D4311yescharacteristic
504C2#510×D4311yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2237C2
socleC22×C43C22×D8
prime radicalC23×D43D8
hypercenter#2237D43
hypocenterC43C2×#2237
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2237

Complements

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

NH ≅ G/Ntype
3. #19136806C2semidirect
4. #19136805C2semidirect
5. #19136804C2semidirect
6. #19136803C2semidirect
7. #19136802C2semidirect
8. #19136801C2semidirect
9. #19136800C2semidirect
10. #367×D43C2semidirect
11. #366×D43C2semidirect
12. #358×D43C2semidirect
13. #358×D43C2semidirect
15. C43×#2237C2semidirect
37. #14582727C22semidirect
38. #14582726C22semidirect
39. #14582726C22semidirect
40. #14582725C22semidirect
41. #14582724C22semidirect
42. #14582724C22semidirect
43. #14582704C22semidirect
44. #14582704C22semidirect
45. #14582703C22semidirect
46. #14582703C22semidirect
47. #14582702C22semidirect
48. #14582702C22semidirect
54. C43×#367C22semidirect
55. C43×#366C22semidirect
56. C43×#358C22semidirect
57. C43×#358C22semidirect
256. #2237D43direct (N × H)
267. D43#2237direct (N × H)
294. #367C2×D43semidirect
298. #366C2×D43semidirect
305. #358C2×D43semidirect
306. #358C2×D43semidirect
311. C43C2×#2237semidirect

Maximal subgroups

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

subgroupindex
#467×D432
#427×D432
#191368062
#191368052
#191368042
#191368032
#191368022
#191368012
#191368002
#367×D432
#366×D432
#358×D432
C22⋊C16×D432
C43×#22372
C2×#223743