Finite Group Databasebeta

← C43×#19167 #24939184

Subgroups — C43×#19167 #24939184

Order 11008.

674 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3139C211yesmaximal, characteristic, complemented
2C43×#3101C211yesmaximal, characteristic
3C2×C43×#474C211yesmaximal, characteristic
4D4×M16×C43C211yesmaximal, characteristic
5C43×#1703C212yesmaximal, complemented
6C43×#1699C212yesmaximal, complemented
7C43×#1683C212yesmaximal, complemented
8C43×#1679C212yesmaximal, complemented
9C43×#1565C211yesmaximal, characteristic, complemented
10C43×#1550C211yesmaximal, characteristic, complemented
11C43×#1546C211yesmaximal, characteristic, complemented
12C22×M16×C43—21no—
13C43×#533C2211yescharacteristic
14C2×C4⋊Q8×C43C2211yescharacteristic
15C2×C4×D4×C43C2211yescharacteristic
16C43×#491—22no—
17C43×#487C2212yescomplemented
18C43×#487C2212yescomplemented
19C43×#483—21no—
20C43×#476C2211yescharacteristic
21C43×#476C2211yescharacteristic
22C43×#474—21no—
23C43×#474—21no—
24C43×#474C2212yes—
25C43×#474C2212yes—
26C43×#461C2211yescharacteristic
27C43×#461C2211yescharacteristic
28C43×#450—21no—
29C4×SD16×C43—21no—
30C4×SD16×C43—21no—
31C43×#436C2212yes—
32C43×#435—22no—
33C8×D4×C43C2212yes—
34C43×#431C2211yescharacteristic
35C2×#107×C43—21no—
36C43×#423C2211yescharacteristic
37C2×C4⋊C8×C43C2211yescharacteristic
38C43×#419—21no—
39C43×#419—21no—
40C2×#102×C43—21no—
41C43×#407—21no—
42C4×M16×C43C2211yescharacteristic
43C43×#335C2212yescomplemented
44C43×#334C2212yescomplemented
45C43×#333C2212yescomplemented
46C43×#332C2212yescomplemented
47C43×#332C2212yescomplemented
48C43×#332C2212yescomplemented
49C22×Q8×C43—21no—
50C22×D4×C43D411yescharacteristic
51C23×C4×C43—21no—
52C2×SD16×C43—21no—
53C2×SD16×C43—21no—
54C2×M16×C43—21no—
55C2×M16×C43—22no—
56C2×M16×C43—44no—
57C2×M16×C43D411yescharacteristic
58C2×M16×C43D411yescharacteristic
59C22×C8×C43—21no—
60C22×C8×C43—22no—
61C4⋊Q8×C43—21no—
62C4⋊Q8×C43—21no—
63C4⋊Q8×C43—21no—
64C4⋊Q8×C43C2312yes—
65C4⋊Q8×C43C2311yescharacteristic
66C4⋊Q8×C43C2311yescharacteristic
67#125×C43—21no—
68C22⋊Q8×C43—21no—
69C22⋊Q8×C43—21no—
70C4×Q8×C43—21no—
71C4×Q8×C43—21no—
72C4×D4×C43—21no—
73C4×D4×C43—21no—
74C4×D4×C43D411yescharacteristic
75C4×D4×C43D411yescharacteristic
76C4×D4×C43C2311yescharacteristic
77C4×D4×C43C2311yescharacteristic
78#117×C43—21no—
79C2×C4⋊C4×C43—21no—
80C2×C4⋊C4×C43—21no—
81C2×C4⋊C4×C43D411yescharacteristic
82C2×C22⋊C4×C43—21no—
83C2×C42×C43C2311yescharacteristic
84#107×C43—22no—
85#107×C43—22no—
86#106×C43—21no—
87#106×C43—21no—
88C4⋊C8×C43—21no—
89C4⋊C8×C43—21no—
90C4⋊C8×C43C2312yes—
91C4⋊C8×C43C2311yescharacteristic
92C4⋊C8×C43C2311yescharacteristic
93C4⋊C8×C43C2312yes—
94#103×C43—22no—
95#103×C43—22no—
96#103×C43—22no—
97#103×C43—22no—
98#103×C43—21no—
99#103×C43—21no—
100#102×C43—22no—
101#102×C43—22no—
102#102×C43—21no—
103#102×C43—21no—
104C22⋊C8×C43—21no—
105C22⋊C8×C43—22no—
106C22⋊C8×C43—22no—
107#97×C43D412yes—
108C4×C8×C43—21no—
109C4×C8×C43C2312yes—
110C24×C43—21no—
111C2×Q8×C43—22no—
112C2×Q8×C43—21no—
113C2×Q8×C43—21no—
114C2×Q8×C43—41no—
115C2×Q8×C43—42no—
116C2×Q8×C43—42no—
117C2×D4×C43—21no—
118C2×D4×C43—22no—
119C2×D4×C43—41no—
120C2×D4×C43C2×D411yescharacteristic
121C2×D4×C43C2×D411yescharacteristic
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—42no—
128C22×C4×C43—42no—
129C22×C4×C43—41no—
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43#4111yescharacteristic
133SD16×C43—42no—
134SD16×C43—42no—
135M16×C43—22no—
136M16×C43—22no—
137M16×C43—44no—
138M16×C43—42no—
139C2×C8×C43—21no—
140C2×C8×C43—21no—
141C2×C8×C43—22no—
142C2×C8×C43—22no—
143C2×C8×C43—44no—
144C2×C8×C43—42no—
145C2×C8×C43C2×D412yes—
146C2×C8×C43C2×D412yes—
147C4⋊C4×C43—21no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—22no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—22no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—41no—
155C4⋊C4×C43—41no—
156C4⋊C4×C43—41no—
157C4⋊C4×C43—41no—
158C4⋊C4×C43C2×D411yescharacteristic
159C4⋊C4×C43C2×D411yescharacteristic
160C22⋊C4×C43—21no—
161C22⋊C4×C43—21no—
162C22⋊C4×C43—21no—
163C22⋊C4×C43—21no—
164C22⋊C4×C43—41no—
165C42×C43—41no—
166C42×C43C2×D411yescharacteristic
167C42×C43C2×D411yescharacteristic
168C42×C43#4111yescharacteristic
169C42×C43C2411yescharacteristic
170C23×C43—21no—
171C23×C43—21no—
172C23×C43—42no—
173C23×C43—42no—
174C23×C43—81no—
175C23×C43#12111yescharacteristic
176Q8×C43—42no—
177Q8×C43—42no—
178Q8×C43—41no—
179Q8×C43—41no—
180Q8×C43—81no—
181Q8×C43—82no—
182D4×C43—21no—
183D4×C43—21no—
184D4×C43—21no—
185D4×C43—42no—
186D4×C43#13712yes—
187C2×C4×C43—21no—
188C2×C4×C43—21no—
189C2×C4×C43—21no—
190C2×C4×C43—21no—
191C2×C4×C43—41no—
192C2×C4×C43—42no—
193C2×C4×C43—41no—
194C2×C4×C43—41no—
195C2×C4×C43—41no—
196C2×C4×C43—41no—
197C2×C4×C43—42no—
198C2×C4×C43—42no—
199C2×C4×C43—41no—
200C2×C4×C43—41no—
201C2×C4×C43—42no—
202C2×C4×C43—82no—
203C2×C4×C43#12111yescharacteristic
204C2×C4×C43#12111yescharacteristic
205C2×C4×C43#12111yescharacteristic
206C2×C4×C43#13512yes—
207C2×C4×C43AGL(1,ℤ/8)12yes—
208C2×C4×C43C22×D411yescharacteristic
209C2×C4×C43C22×D411yescharacteristic
210C2×C4×C43C2×#4111yescharacteristic
211C8×C43—22no—
212C8×C43—22no—
213C8×C43—42no—
214C8×C43—41no—
215C8×C43—42no—
216C8×C43—41no—
217#19167C4311yesmaximal, characteristic, direct product factor, Sylow
218C22×C43—21no—
219C22×C43—21no—
220C22×C43—22no—
221C22×C43—41no—
222C22×C43—41no—
223C22×C43—41no—
224C22×C43—41no—
225C22×C43—41no—
226C22×C43—84no—
227C22×C43#46312yes—
228C22×C43C2×#12111yescharacteristic
229C4×C43—21no—
230C4×C43—21no—
231C4×C43—21no—
232C4×C43—41no—
233C4×C43—41no—
234C4×C43—82no—
235C4×C43—81no—
236C4×C43—81no—
237C4×C43#46312yes—
238C4×C43C2×#13511yescharacteristic
239C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
240C4×C43C2×#13711yescharacteristic
241C4×C43#57511yescharacteristic
242#3139C2×C4311yescharacteristic, complemented
243#3101C2×C4311yescharacteristic
244C2×#474C2×C4311yescharacteristic
245D4×M16C2×C4311yescharacteristic
246#1703C2×C4312yescomplemented
247#1699C2×C4312yescomplemented
248#1683C2×C4312yescomplemented
249#1679C2×C4312yescomplemented
250#1565C2×C4311yescharacteristic, complemented
251#1550C2×C4311yescharacteristic, complemented
252#1546C2×C4311yescharacteristic, complemented
253C2×C43—22no—
254C2×C43—42no—
255C2×C43—81no—
256C2×C43C2×#46311yescharacteristic
257C2×C43#305611yescharacteristic
258C2×C43#306911yescharacteristic
259C22×M16—21no—
260#533C22×C4311yescharacteristic
261C2×C4⋊Q8C22×C4311yescharacteristic
262C2×C4×D4C22×C4311yescharacteristic
263#491—22no—
264#487C22×C4312yescomplemented
265#487C22×C4312yescomplemented
266#483—21no—
267#476C22×C4311yescharacteristic
268#476C22×C4311yescharacteristic
269#474—21no—
270#474—21no—
271#474C22×C4312yes—
272#474C22×C4312yes—
273#461C22×C4311yescharacteristic
274#461C22×C4311yescharacteristic
275#450—21no—
276C4×SD16—21no—
277C4×SD16—21no—
278#436C22×C4312yes—
279#435—22no—
280C8×D4C22×C4312yes—
281#431C22×C4311yescharacteristic
282C2×#107—21no—
283#423C22×C4311yescharacteristic
284C2×C4⋊C8C22×C4311yescharacteristic
285#419—21no—
286#419—21no—
287C2×#102—21no—
288#407—21no—
289C4×M16C22×C4311yescharacteristic
290#335C22×C4312yescomplemented
291#334C22×C4312yescomplemented
292#333C22×C4312yescomplemented
293#332C22×C4312yescomplemented
294#332C22×C4312yescomplemented
295#332C22×C4312yescomplemented
296C43#1916711yescharacteristic, direct product factor, Sylow
297C22×Q8—21no—
298C22×D4D4×C4311yescharacteristic
299C23×C4—21no—
300C2×SD16—21no—
301C2×SD16—21no—
302C2×M16—21no—
303C2×M16—22no—
304C2×M16—44no—
305C2×M16D4×C4311yescharacteristic
306C2×M16D4×C4311yescharacteristic
307C22×C8—21no—
308C22×C8—22no—
309C4⋊Q8—21no—
310C4⋊Q8—21no—
311C4⋊Q8—21no—
312C4⋊Q8C23×C4312yes—
313C4⋊Q8C23×C4311yescharacteristic
314C4⋊Q8C23×C4311yescharacteristic
315#125—21no—
316C22⋊Q8—21no—
317C22⋊Q8—21no—
318C4×Q8—21no—
319C4×Q8—21no—
320C4×D4—21no—
321C4×D4—21no—
322C4×D4D4×C4311yescharacteristic
323C4×D4D4×C4311yescharacteristic
324C4×D4C23×C4311yescharacteristic
325C4×D4C23×C4311yescharacteristic
326#117—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4D4×C4311yescharacteristic
330C2×C22⋊C4—21no—
331C2×C42C23×C4311yescharacteristic
332#107—22no—
333#107—22no—
334#106—21no—
335#106—21no—
336C4⋊C8—21no—
337C4⋊C8—21no—
338C4⋊C8C23×C4312yes—
339C4⋊C8C23×C4311yescharacteristic
340C4⋊C8C23×C4311yescharacteristic
341C4⋊C8C23×C4312yes—
342#103—22no—
343#103—22no—
344#103—22no—
345#103—22no—
346#103—21no—
347#103—21no—
348#102—22no—
349#102—22no—
350#102—21no—
351#102—21no—
352C22⋊C8—21no—
353C22⋊C8—22no—
354C22⋊C8—22no—
355#97D4×C4312yes—
356C4×C8—21no—
357C4×C8C23×C4312yes—
358C24—21no—
359C2×Q8—22no—
360C2×Q8—21no—
361C2×Q8—21no—
362C2×Q8—41no—
363C2×Q8—42no—
364C2×Q8—42no—
365C2×D4—22no—
366C2×D4—21no—
367C2×D4—41no—
368C2×D4C2×D4×C4311yescharacteristic
369C2×D4C2×D4×C4311yescharacteristic
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—42no—
376C22×C4—42no—
377C22×C4—41no—
378C22×C4C2×D4×C4311yescharacteristic
379C22×C4C2×D4×C4311yescharacteristic
380C22×C4#41×C4311yescharacteristic
381SD16—42no—
382SD16—42no—
383M16—22no—
384M16—22no—
385M16—44no—
386M16—42no—
387C2×C8—21no—
388C2×C8—21no—
389C2×C8—22no—
390C2×C8—22no—
391C2×C8—44no—
392C2×C8—42no—
393C2×C8C2×D4×C4312yes—
394C2×C8C2×D4×C4312yes—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—22no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—22no—
401C4⋊C4—21no—
402C4⋊C4—41no—
403C4⋊C4—41no—
404C4⋊C4—41no—
405C4⋊C4—41no—
406C4⋊C4C2×D4×C4311yescharacteristic
407C4⋊C4C2×D4×C4311yescharacteristic
408C22⋊C4—21no—
409C22⋊C4—21no—
410C22⋊C4—21no—
411C22⋊C4—21no—
412C22⋊C4—41no—
413C42—41no—
414C42C2×D4×C4311yescharacteristic
415C42C2×D4×C4311yescharacteristic
416C42#41×C4311yescharacteristic
417C42C24×C4311yescharacteristic
418C23—21no—
419C23—21no—
420C23—42no—
421C23—42no—
422C23—81no—
423C23#121×C4311yescharacteristic
424Q8—42no—
425Q8—42no—
426Q8—41no—
427Q8—41no—
428Q8—81no—
429Q8—82no—
430D4—21no—
431D4—21no—
432D4—21no—
433D4—42no—
434D4#137×C4312yes—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—41no—
440C2×C4—42no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—42no—
450C2×C4—82no—
451C2×C4#121×C4311yescharacteristic
452C2×C4#121×C4311yescharacteristic
453C2×C4#121×C4311yescharacteristic
454C2×C4#135×C4312yes—
455C2×C4AGL(1,ℤ/8)×C4312yes—
456C2×C4C22×D4×C4311yescharacteristic
457C2×C4C22×D4×C4311yescharacteristic
458C2×C4C2×#41×C4311yescharacteristic
459C8—22no—
460C8—22no—
461C8—42no—
462C8—41no—
463C8—42no—
464C8—41no—
465C22—21no—
466C22—21no—
467C22—22no—
468C22—41no—
469C22—41no—
470C22—41no—
471C22—41no—
472C22—41no—
473C22—84no—
474C22C43×#46312yes—
475C22C2×#121×C4311yescharacteristic
476C4—21no—
477C4—21no—
478C4—21no—
479C4—41no—
480C4—41no—
481C4—82no—
482C4—81no—
483C4—81no—
484C4C43×#46312yes—
485C4C2×#135×C4311yescharacteristic
486C4C2×AGL(1,ℤ/8)×C4311yescharacteristic
487C4C2×#137×C4311yescharacteristic
488C4C43×#57511yescharacteristic
489C2—22no—
490C2—42no—
491C2—81no—
492C2C2×C43×#46311yescharacteristic
493C2C43×#305611yescharacteristic
494C2C43×#306911yescharacteristic
subgroupG/H
center, socleC22×C43C2×#121
commutator, Frattini, cosocleC42C24×C43
prime radicalC22×D4×C43D4
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
1. C43×#3139C2semidirect
5. C43×#1703C2semidirect
6. C43×#1699C2semidirect
7. C43×#1683C2semidirect
8. C43×#1679C2semidirect
9. C43×#1565C2semidirect
10. C43×#1550C2semidirect
11. C43×#1546C2semidirect
17. C43×#487C22semidirect
18. C43×#487C22semidirect
43. C43×#335C22semidirect
44. C43×#334C22semidirect
45. C43×#333C22semidirect
46. C43×#332C22semidirect
47. C43×#332C22semidirect
48. C43×#332C22semidirect
217. #19167C43direct (N × H)
242. #3139C2×C43semidirect
246. #1703C2×C43semidirect
247. #1699C2×C43semidirect
248. #1683C2×C43semidirect
249. #1679C2×C43semidirect
250. #1565C2×C43semidirect
251. #1550C2×C43semidirect
252. #1546C2×C43semidirect
264. #487C22×C43semidirect
265. #487C22×C43semidirect
290. #335C22×C43semidirect
291. #334C22×C43semidirect
292. #333C22×C43semidirect
293. #332C22×C43semidirect
294. #332C22×C43semidirect
295. #332C22×C43semidirect
296. C43#19167direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#31392
C43×#31012
C2×C43×#4742
D4×M16×C432
C43×#17032
C43×#16992
C43×#16832
C43×#16792
C43×#15652
C43×#15502
C43×#15462
#1916743