Finite Group Databasebeta

← D43×#2175 #25249882

Subgroups — D43×#2175 #25249882

Order 11008.

734 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD32×D43C211yesmaximal, characteristic
2C4×Q16×D43C211yesmaximal, characteristic, complemented
3C4×D8×D43C211yesmaximal, characteristic
4#19136462C211yesmaximal, characteristic, complemented
5#19136461C211yesmaximal, characteristic, complemented
6#19136460C211yesmaximal, characteristic, complemented
7#19136459C211yesmaximal, characteristic, complemented
8#19136458C211yesmaximal, characteristic, complemented
9#19136457C211yesmaximal, characteristic, complemented
10#19136456C211yesmaximal, characteristic, complemented
11#366×D43C211yesmaximal, characteristic, complemented
12#358×D43C211yesmaximal, characteristic, complemented
13#357×D43C211yesmaximal, characteristic
14#346×D43C211yesmaximal, characteristic, complemented
15C43×#2175C211yesmaximal, characteristic, complemented
16C2×Q16×D43C2211yescharacteristic
17C2×D8×D43C2211yescharacteristic
18C4×Q8×D43—21no—
19C4×D4×D43—21no—
20C2×#13063270C2211yescharacteristic
21C2×#13063269C2211yescharacteristic
22C2×#13063268C2211yescharacteristic
23SD32×D43C418yescomplemented
24C2×C16×D43C2211yescharacteristic
25C2×C16×D43C2211yescharacteristic
26C4×Dic172C2211yescharacteristic, complemented
27Q16×Dic43C2211yescharacteristic, complemented
28#14582993C2211yescharacteristic, complemented
29C4×#10621885—21no—
30#14582991—21no—
31C4×D344C2211yescharacteristic
32D8×Dic43C2211yescharacteristic
33#14582981C2211yescharacteristic
34C4×#10621882—21no—
35#14582979—21no—
36#107×D43C2211yescharacteristic
37#107×D43C2211yescharacteristic
38#103×D43—21no—
39#102×D43—21no—
40C4×C8×D43C2211yescharacteristic
41#14582725C2211yescharacteristic, complemented
42#14582724C2211yescharacteristic, complemented
43#14582724C2211yescharacteristic, complemented
44#14582704C2211yescharacteristic, complemented
45#14582703C2211yescharacteristic, complemented
46#14582702C2211yescharacteristic, complemented
47#14582701C2211yescharacteristic
48#14582700C2211yescharacteristic
49#14582699C2211yescharacteristic
50#14582675C2211yescharacteristic, complemented
51#14582674C2211yescharacteristic, complemented
52#14582674C2211yescharacteristic, complemented
53C2×SD32×C43C2211yescharacteristic
54C4×Q16×C43C2211yescharacteristic, complemented
55C4×D8×C43C2211yescharacteristic
56C43×#366C2211yescharacteristic, complemented
57C43×#358C2211yescharacteristic, complemented
58C43×#357C2211yescharacteristic
59C43×#346C2211yescharacteristic, complemented
60C2×Q8×D43—21no—
61C2×D4×D43—21no—
62C22×C4×D43—41no—
63C2×Dic172C2311yescharacteristic
64C2×#10621885—21no—
65Q16×D43—22no—
66Q16×D43C2×C414yescomplemented
67C2×D344C2311yescharacteristic
68C2×#10621882—21no—
69D8×D43—22no—
70D8×D43C2×C414yes—
71C2×C8×D43D411yescharacteristic
72C2×C8×D43C2311yescharacteristic
73Q8×Dic43—21no—
74C4×Dic86—21no—
75C4×Dic86—41no—
76#13063290—21no—
77#13063290—41no—
78C4×D172—21no—
79D4×Dic43—21no—
80#13063287—21no—
81C4×C22⋊D43—41no—
82(C22⋊D43)⋊C4—41no—
83C4⋊C4×D43—21no—
84C4⋊C4×D43—21no—
85C4⋊C4×D43—41no—
86C22⋊C4×D43—41no—
87C42×D43—41no—
88C42×D43D411yescharacteristic
89#13063270C2×C414yescomplemented
90#13063269C2×C414yescomplemented
91#13063268C2×C414yescomplemented
92C2×C43⋊C16C2311yescharacteristic
93C2×C43⋊C16C2311yescharacteristic
94C16×D43—22no—
95C16×D43C2×C414yescomplemented
96#13063259C2311yescharacteristic
97#13063259C2311yescharacteristic
98#13063258—21no—
99#13063258—21no—
100#13063250—21no—
101#13063249—21no—
102#13063248—21no—
103#13063247—21no—
104#13063246—21no—
105#13063245—21no—
106C4×C43⋊C8D411yescharacteristic
107C8×Dic43D411yescharacteristic
108C8×Dic43C2311yescharacteristic
109C2×Q16×C43C2311yescharacteristic
110C2×D8×C43C2311yescharacteristic
111C4×Q8×C43—21no—
112C4×D4×C43—21no—
113SD32×C43C2×C414yescomplemented
114C2×C16×C43C2311yescharacteristic
115C2×C16×C43C2311yescharacteristic
116#107×C43C2311yescharacteristic
117#107×C43C2311yescharacteristic
118#103×C43—21no—
119#102×C43—21no—
120C4×C8×C43C2311yescharacteristic
121C23×D43—41no—
122C2×Q8×C43—21no—
123C2×D4×C43—21no—
124C22×C4×C43—41no—
125C2×C22⋊D43—41no—
126C22×Dic43—41no—
127Q8×D43—24no—
128Q8×D43—42no—
129D4×D43—24no—
130D4×D43—42no—
131C2×D172—21no—
132C2×C4×D43—41no—
133C2×C4×D43—41no—
134C2×C4×D43—41no—
135C2×C4×D43—41no—
136C2×C4×D43—41no—
137C2×C4×D43—84no—
138C2×C4×D43D811yescharacteristic
139C2×C4×D43D811yescharacteristic
140C2×C4×D43C2×D411yescharacteristic
141C2×Dic86—21no—
142C2×Dic86—41no—
143Q16×C43—21no—
144Q16×C43C22×C412yescomplemented
145D8×C43—21no—
146D8×C43C22×C412yes—
147C2×C8×C43C2×D411yescharacteristic
148C2×C8×C43C2411yescharacteristic
149C4⋊C4×C43—21no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—41no—
152C22⋊C4×C43—41no—
153C42×C43—41no—
154C42×C43C2×D411yescharacteristic
155C22⋊Dic43—41no—
156#10621885—24no—
157#10621882—24no—
158(C2×D43)⋊C4—41no—
159(C2×D43)⋊C4—41no—
160C4⋊Dic43—21no—
161C4⋊Dic43—21no—
162C4⋊Dic43—41no—
163Dic43⋊C4—41no—
164Dic43⋊C4—41no—
165Dic43⋊C4—41no—
166Dic43⋊C4—41no—
167C4×Dic43—41no—
168C4×Dic43—41no—
169C4×Dic43—41no—
170C4×Dic43D811yescharacteristic
171C4×Dic43D811yescharacteristic
172C4×Dic43C2×D411yescharacteristic
173C2×C43⋊C8C2×D411yescharacteristic
174C2×C43⋊C8C2×D411yescharacteristic
175Dic172—21no—
176Dic172C22×C412yescomplemented
177D344—21no—
178D344C22×C412yes—
179C8×D43—22no—
180C8×D43C22×C412yes—
181C8×D43#4112yes—
182C16×C43—21no—
183C16×C43C22×C412yescomplemented
184C43⋊C16—21no—
185C43⋊C16C22×C412yescomplemented
186C23×C43—41no—
187C22×D43—41no—
188C22×D43—44no—
189C22×D43—82no—
190C22×D43—82no—
191C22×D43C2×D811yescharacteristic
192Q8×C43—22no—
193Q8×C43—41no—
194D4×C43—22no—
195D4×C43—41no—
196C2×C4×C43—41no—
197C2×C4×C43—41no—
198C2×C4×C43—41no—
199C2×C4×C43—82no—
200C2×C4×C43C2×D811yescharacteristic
201C2×C4×C43C2×D811yescharacteristic
202C2×C4×C43C22×D411yescharacteristic
203C22⋊D43—44no—
204C2×Dic43—41no—
205C2×Dic43—41no—
206C2×Dic43—41no—
207C2×Dic43—82no—
208C2×Dic43C2×D811yescharacteristic
209C2×Dic43C2×D811yescharacteristic
210C2×Dic43C2×D811yescharacteristic
211D172—22no—
212D172—41no—
213C4×D43—22no—
214C4×D43—22no—
215C4×D43—44no—
216C4×D43—82no—
217C4×D43—82no—
218C4×D43—82no—
219C4×D43—82no—
220C4×D43C4×D412yes—
221C4×D43#13512yes—
222Dic86—22no—
223Dic86—41no—
224Dic86—44no—
225C8×C43—21no—
226C8×C43C23×C411yescharacteristic
227C8×C43C2×#4111yescharacteristic
228C43⋊C8—21no—
229C43⋊C8C4×D412yes—
230C2×#2175—431nomaximal, Sylow
231C22×C43—42no—
232C22×C43—81no—
233C22×C43—81no—
234C22×C43C22×D811yescharacteristic
235C2×D43—42no—
236C2×D43—81no—
237C2×D43—81no—
238C2×D43—88no—
239C2×D43C4×D812yes—
240C2×D43#50912yes—
241C2×D43#51012yes—
242C4×C43—21no—
243C4×C43—21no—
244C4×C43—42no—
245C4×C43—81no—
246C4×C43—81no—
247C4×C43C2×C4×D411yescharacteristic
248C4×C43C2×#13511yescharacteristic
249Dic43—21no—
250Dic43—21no—
251Dic43—42no—
252Dic43—81no—
253Dic43—81no—
254Dic43C4×D812yes—
255C22×SD32—431no—
256C2×C4×Q16—431no—
257C2×C4×D8—431no—
258#2175—431no—
259#2175—431no—
260#2175—431no—
261#2175—431no—
262#2175—431no—
263#2175—431no—
264#2175—431no—
265#2175D4311yescharacteristic, direct product factor
266C2×#366—431no—
267C2×#358—431no—
268C2×#357—431no—
269C2×#346—431no—
270C2×C43—82no—
271C2×C43C2×C4×D811yescharacteristic
272C2×C43C2×#50911yescharacteristic
273C2×C43C2×#51011yescharacteristic
274D43—82no—
275D43#217514yesdirect product factor
276C22×Q16—431no—
277C22×D8—431no—
278C2×C4×Q8—861no—
279C2×C4×D4—861no—
280C2×SD32—431no—
281C2×SD32—431no—
282C2×SD32—438no—
283C2×SD32—431no—
284C2×SD32C2×D4311yescharacteristic
285C22×C16—431no—
286C22×C16—431no—
287C4×Q16—431no—
288C4×Q16—431no—
289C4×Q16—431no—
290C4×Q16—861no—
291C4×Q16—861no—
292C4×Q16C2×D4311yescharacteristic, complemented
293C4×D8—431no—
294C4×D8—431no—
295C4×D8—431no—
296C4×D8—861no—
297C4×D8—861no—
298C4×D8C2×D4311yescharacteristic
299C2×#107—431no—
300C2×#107—431no—
301C2×#103—861no—
302C2×#102—861no—
303C2×C4×C8—431no—
304#366—431no—
305#366—431no—
306#366—431no—
307#366C2×D4311yescharacteristic, complemented
308#358—431no—
309#358—431no—
310#358—431no—
311#358C2×D4311yescharacteristic, complemented
312#357—431no—
313#357—431no—
314#357—431no—
315#357C2×D4311yescharacteristic
316#346—431no—
317#346—431no—
318#346—431no—
319#346C2×D4311yescharacteristic, complemented
320C43C2×#217511yescharacteristic, complemented, Sylow
321C22×Q8—861no—
322C22×D4—861no—
323C23×C4—1721no—
324C2×Q16—434no—
325C2×Q16—431no—
326C2×Q16—862no—
327C2×Q16—861no—
328C2×Q16C22×D4311yescharacteristic
329C2×D8—434no—
330C2×D8—431no—
331C2×D8—862no—
332C2×D8—861no—
333C2×D8C22×D4311yescharacteristic
334C22×C8—431no—
335C22×C8—431no—
336C4×Q8—21no—
337C4×Q8—861no—
338C4×Q8—861no—
339C4×Q8—861no—
340C4×Q8—1721no—
341C4×Q8—1721no—
342C4×D4—21no—
343C4×D4—861no—
344C4×D4—861no—
345C4×D4—861no—
346C4×D4—1721no—
347C4×D4—1721no—
348C2×C4⋊C4—861no—
349C2×C4⋊C4—861no—
350C2×C4⋊C4—1721no—
351C2×C22⋊C4—1721no—
352C2×C42—431no—
353C2×C42—1721no—
354SD32—434no—
355SD32—434no—
356SD32—434no—
357SD32C4×D4314yescomplemented
358C2×C16—431no—
359C2×C16—434no—
360C2×C16—431no—
361C2×C16—862no—
362C2×C16C22×D4311yescharacteristic
363C2×C16C22×D4311yescharacteristic
364#107—431no—
365#107—431no—
366#107—861no—
367#107—861no—
368#107C22×D4311yescharacteristic
369#107C22×D4311yescharacteristic
370#103—21no—
371#103—861no—
372#103—861no—
373#103—861no—
374#102—21no—
375#102—861no—
376#102—861no—
377#102—861no—
378C4×C8—431no—
379C4×C8—431no—
380C4×C8—431no—
381C4×C8C22×D4311yescharacteristic
382C24—1721no—
383C2×Q8—21no—
384C2×Q8—864no—
385C2×Q8—861no—
386C2×Q8—1721no—
387C2×Q8—1722no—
388C2×D4—21no—
389C2×D4—864no—
390C2×D4—861no—
391C2×D4—1722no—
392C2×D4—1721no—
393C22×C4—41no—
394C22×C4—431no—
395C22×C4—431no—
396C22×C4—431no—
397C22×C4—3444no—
398C22×C4—1721no—
399C22×C4—1721no—
400C22×C4—1721no—
401C22×C4—1721no—
402C22×C4—1721no—
403C22×C4—1721no—
404Q16—21no—
405Q16—432no—
406Q16—864no—
407Q16—861no—
408Q16C2×C4×D4312yescomplemented
409D8—21no—
410D8—432no—
411D8—864no—
412D8—861no—
413D8C2×C4×D4312yes—
414C2×C8—431no—
415C2×C8—432no—
416C2×C8—432no—
417C2×C8—431no—
418C2×C8—862no—
419C2×C8D4×D4311yescharacteristic
420C2×C8C23×D4311yescharacteristic
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—41no—
424C4⋊C4—861no—
425C4⋊C4—861no—
426C4⋊C4—1721no—
427C4⋊C4—1721no—
428C4⋊C4—1721no—
429C4⋊C4—1721no—
430C4⋊C4—1721no—
431C22⋊C4—41no—
432C22⋊C4—1721no—
433C22⋊C4—1721no—
434C22⋊C4—1721no—
435C42—41no—
436C42—431no—
437C42—431no—
438C42—431no—
439C42—1721no—
440C42—1721no—
441C42—1721no—
442C42D4×D4311yescharacteristic
443C16—21no—
444C16—432no—
445C16—861no—
446C16C2×C4×D4312yescomplemented
447C23—41no—
448C23—431no—
449C23—3442no—
450C23—3442no—
451C23—1724no—
452C23—1721no—
453Q8—22no—
454Q8—41no—
455Q8—862no—
456Q8—1724no—
457Q8—1721no—
458D4—22no—
459D4—41no—
460D4—862no—
461D4—1724no—
462D4—1721no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—82no—
467C2×C4—431no—
468C2×C4—432no—
469C2×C4—432no—
470C2×C4—431no—
471C2×C4—431no—
472C2×C4—862no—
473C2×C4—862no—
474C2×C4—3442no—
475C2×C4—3442no—
476C2×C4—3442no—
477C2×C4—3442no—
478C2×C4—3442no—
479C2×C4—1724no—
480C2×C4—1721no—
481C2×C4—1721no—
482C2×C4—1721no—
483C2×C4D8×D4311yescharacteristic
484C2×C4D8×D4311yescharacteristic
485C2×C4C2×D4×D4311yescharacteristic
486C8—21no—
487C8—432no—
488C8—861no—
489C8C22×C4×D4311yescharacteristic
490C8#41×D4311yescharacteristic
491C22—42no—
492C22—81no—
493C22—81no—
494C22—432no—
495C22—432no—
496C22—432no—
497C22—3448no—
498C22—3441no—
499C22—3441no—
500C22—1722no—
501C22C2×D8×D4311yescharacteristic
502C4—21no—
503C4—21no—
504C4—42no—
505C4—81no—
506C4—81no—
507C4—432no—
508C4—861no—
509C4—861no—
510C4—3441no—
511C4—3441no—
512C4—1722no—
513C4C4×D4×D4311yescharacteristic
514C4#135×D4311yescharacteristic
515C2—82no—
516C2—434no—
517C2—3442no—
518C2C4×D8×D4311yescharacteristic
519C2#509×D4311yescharacteristic
520C2#510×D4311yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC43×#2175C2
socleC22×C43C22×D8
prime radicalC2×D8×D43C22
cosocleC2×C8×C43C24
hypercenter#2175D43
hypocenterC43C2×#2175
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2175

Complements

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

NH ≅ G/Ntype
2. C4×Q16×D43C2semidirect
4. #19136462C2semidirect
5. #19136461C2semidirect
6. #19136460C2semidirect
7. #19136459C2semidirect
8. #19136458C2semidirect
9. #19136457C2semidirect
10. #19136456C2semidirect
11. #366×D43C2semidirect
12. #358×D43C2semidirect
14. #346×D43C2semidirect
15. C43×#2175C2semidirect
23. SD32×D43C4semidirect
26. C4×Dic172C22semidirect
27. Q16×Dic43C22semidirect
28. #14582993C22semidirect
41. #14582725C22semidirect
42. #14582724C22semidirect
43. #14582724C22semidirect
44. #14582704C22semidirect
45. #14582703C22semidirect
46. #14582702C22semidirect
50. #14582675C22semidirect
51. #14582674C22semidirect
52. #14582674C22semidirect
54. C4×Q16×C43C22semidirect
56. C43×#366C22semidirect
57. C43×#358C22semidirect
59. C43×#346C22semidirect
66. Q16×D43C2×C4semidirect
89. #13063270C2×C4semidirect
90. #13063269C2×C4semidirect
91. #13063268C2×C4semidirect
95. C16×D43C2×C4semidirect
113. SD32×C43C2×C4semidirect
144. Q16×C43C22×C4semidirect
176. Dic172C22×C4semidirect
183. C16×C43C22×C4semidirect
185. C43⋊C16C22×C4semidirect
265. #2175D43direct (N × H)
275. D43#2175direct (N × H)
292. C4×Q16C2×D43semidirect
307. #366C2×D43semidirect
311. #358C2×D43semidirect
319. #346C2×D43semidirect
320. C43C2×#2175semidirect
357. SD32C4×D43semidirect
408. Q16C2×C4×D43semidirect
446. C16C2×C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×SD32×D432
C4×Q16×D432
C4×D8×D432
#191364622
#191364612
#191364602
#191364592
#191364582
#191364572
#191364562
#366×D432
#358×D432
#357×D432
#346×D432
C43×#21752
C2×#217543