Finite Group Databasebeta

← C43×#19174 #24939191

Subgroups — C43×#19174 #24939191

Order 11008.

680 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3138C211yesmaximal, characteristic
2C43×#3104C211yesmaximal, characteristic, complemented
3C2×C43×#460C211yesmaximal, characteristic
4Q8×M16×C43C211yesmaximal, characteristic, complemented
5C43×#1702C212yesmaximal, complemented
6C43×#1698C212yesmaximal, complemented
7C43×#1682C212yesmaximal, complemented
8C43×#1678C212yesmaximal, complemented
9C43×#1565C211yesmaximal, characteristic, complemented
10C43×#1550C211yesmaximal, characteristic, complemented
11C43×#1545C211yesmaximal, characteristic
12C22×SD16×C43—21no—
13C43×#533C2211yescharacteristic
14C2×#127×C43C2211yescharacteristic
15C2×C4×Q8×C43C2211yescharacteristic
16C43×#490—22no—
17C43×#486C2212yes—
18C43×#486C2212yes—
19C43×#484—21no—
20C43×#477C2211yescharacteristic, complemented
21C43×#477C2211yescharacteristic, complemented
22C43×#462C2211yescharacteristic, complemented
23C43×#462C2211yescharacteristic, complemented
24C43×#460—21no—
25C43×#460—21no—
26C43×#460C2212yes—
27C43×#460C2212yes—
28C43×#451—21no—
29C43×#446—22no—
30C43×#446C2212yescomplemented
31C8×Q8×C43C2212yescomplemented
32C4×Q16×C43—21no—
33C4×Q16×C43—21no—
34C43×#431C2211yescharacteristic
35C43×#423—21no—
36C43×#423C2211yescharacteristic
37C2×C4⋊C8×C43C2211yescharacteristic
38C43×#418—21no—
39C43×#418—21no—
40C2×#102×C43—21no—
41C4×M16×C43—21no—
42C4×M16×C43C2211yescharacteristic
43C43×#335C2212yescomplemented
44C43×#334C2212yescomplemented
45C43×#333C2212yescomplemented
46C43×#332C2212yescomplemented
47C43×#331C2212yes—
48C43×#331C2212yes—
49C22×Q8×C43D411yescharacteristic
50C22×D4×C43—21no—
51C22×D4×C43—21no—
52C22×D4×C43—21no—
53C2×Q16×C43—21no—
54C2×Q16×C43—21no—
55C2×SD16×C43—22no—
56C2×SD16×C43—22no—
57C2×SD16×C43—44no—
58C2×M16×C43—21no—
59C2×M16×C43D411yescharacteristic
60C2×M16×C43D411yescharacteristic
61C22×C8×C43—21no—
62C4⋊Q8×C43C2311yescharacteristic
63C4⋊Q8×C43C2311yescharacteristic
64#127×C43—21no—
65#127×C43—21no—
66#127×C43—21no—
67#127×C43C2312yes—
68#125×C43—21no—
69C22⋊Q8×C43—21no—
70C22⋊Q8×C43—21no—
71C4×Q8×C43—21no—
72C4×Q8×C43—21no—
73C4×Q8×C43—21no—
74C4×Q8×C43—21no—
75C4×Q8×C43D411yescharacteristic
76C4×Q8×C43D411yescharacteristic
77C4×Q8×C43C2311yescharacteristic
78C4×Q8×C43C2311yescharacteristic
79#117×C43—21no—
80C2×C4⋊C4×C43—21no—
81C2×C4⋊C4×C43D411yescharacteristic
82C2×C42×C43—21no—
83C2×C42×C43C2311yescharacteristic
84#107×C43—21no—
85#107×C43—21no—
86C4⋊C8×C43—22no—
87C4⋊C8×C43—22no—
88C4⋊C8×C43—21no—
89C4⋊C8×C43—21no—
90C4⋊C8×C43C2312yes—
91C4⋊C8×C43C2311yescharacteristic
92C4⋊C8×C43C2311yescharacteristic
93C4⋊C8×C43C2312yes—
94#103×C43—21no—
95#103×C43—21no—
96#103×C43—21no—
97#103×C43—21no—
98#102×C43—22no—
99#102×C43—22no—
100#102×C43—22no—
101#102×C43—22no—
102#102×C43—22no—
103#102×C43—22no—
104C22⋊C8×C43—21no—
105#97×C43—22no—
106#97×C43D412yes—
107C4×C8×C43—22no—
108C4×C8×C43—21no—
109C4×C8×C43C2312yes—
110C24×C43—41no—
111C2×Q8×C43—21no—
112C2×Q8×C43—22no—
113C2×Q8×C43—21no—
114C2×Q8×C43—21no—
115C2×Q8×C43—41no—
116C2×Q8×C43C2×D411yescharacteristic
117C2×Q8×C43C2×D411yescharacteristic
118C2×D4×C43—22no—
119C2×D4×C43—22no—
120C2×D4×C43—22no—
121C2×D4×C43—41no—
122C2×D4×C43—41no—
123C2×D4×C43—41no—
124C2×D4×C43—42no—
125C2×D4×C43—42no—
126C2×D4×C43—42no—
127C2×D4×C43—42no—
128C2×D4×C43—82no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43#4111yescharacteristic
134Q16×C43—42no—
135Q16×C43—42no—
136SD16×C43—44no—
137SD16×C43—44no—
138M16×C43—22no—
139M16×C43—22no—
140M16×C43—42no—
141C2×C8×C43—22no—
142C2×C8×C43—21no—
143C2×C8×C43—21no—
144C2×C8×C43—22no—
145C2×C8×C43—42no—
146C2×C8×C43C2×D412yes—
147C2×C8×C43C2×D412yes—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—21no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—41no—
158C4⋊C4×C43—41no—
159C4⋊C4×C43C2×D411yescharacteristic
160C4⋊C4×C43C2×D411yescharacteristic
161C22⋊C4×C43—41no—
162C42×C43—21no—
163C42×C43—21no—
164C42×C43—21no—
165C42×C43—21no—
166C42×C43—41no—
167C42×C43C2×D411yescharacteristic
168C42×C43C2×D411yescharacteristic
169C42×C43#4111yescharacteristic
170C42×C43C2411yescharacteristic
171C23×C43—42no—
172C23×C43—82no—
173C23×C43—82no—
174C23×C43—82no—
175C23×C43#12111yescharacteristic
176Q8×C43—21no—
177Q8×C43—21no—
178Q8×C43—21no—
179Q8×C43—42no—
180Q8×C43—41no—
181Q8×C43—41no—
182Q8×C43—81no—
183Q8×C43AGL(1,ℤ/8)12yes—
184D4×C43—42no—
185D4×C43—42no—
186D4×C43—42no—
187D4×C43—42no—
188D4×C43—82no—
189D4×C43—82no—
190D4×C43—82no—
191D4×C43—82no—
192C2×C4×C43—21no—
193C2×C4×C43—21no—
194C2×C4×C43—21no—
195C2×C4×C43—21no—
196C2×C4×C43—21no—
197C2×C4×C43—21no—
198C2×C4×C43—41no—
199C2×C4×C43—42no—
200C2×C4×C43—41no—
201C2×C4×C43—41no—
202C2×C4×C43—81no—
203C2×C4×C43#12111yescharacteristic
204C2×C4×C43#12111yescharacteristic
205C2×C4×C43#12111yescharacteristic
206C2×C4×C43#13512yes—
207C2×C4×C43#13712yes—
208C2×C4×C43C22×D411yescharacteristic
209C2×C4×C43C22×D411yescharacteristic
210C2×C4×C43C2×#4111yescharacteristic
211C8×C43—22no—
212C8×C43—22no—
213C8×C43—42no—
214C8×C43—42no—
215C8×C43—41no—
216C8×C43—41no—
217#19174C4311yesmaximal, characteristic, direct product factor, Sylow
218C22×C43—21no—
219C22×C43—21no—
220C22×C43—82no—
221C22×C43—82no—
222C22×C43—82no—
223C22×C43—164no—
224C22×C43#46412yes—
225C22×C43C2×#12111yescharacteristic
226C4×C43—21no—
227C4×C43—22no—
228C4×C43—21no—
229C4×C43—21no—
230C4×C43—41no—
231C4×C43—41no—
232C4×C43—41no—
233C4×C43—81no—
234C4×C43—81no—
235C4×C43#46412yes—
236C4×C43C2×#13511yescharacteristic
237C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
238C4×C43C2×#13711yescharacteristic
239C4×C43#57511yescharacteristic
240#3138C2×C4311yescharacteristic
241#3104C2×C4311yescharacteristic, complemented
242C2×#460C2×C4311yescharacteristic
243Q8×M16C2×C4311yescharacteristic, complemented
244#1702C2×C4312yescomplemented
245#1698C2×C4312yescomplemented
246#1682C2×C4312yescomplemented
247#1678C2×C4312yescomplemented
248#1565C2×C4311yescharacteristic, complemented
249#1550C2×C4311yescharacteristic, complemented
250#1545C2×C4311yescharacteristic
251C2×C43—22no—
252C2×C43—162no—
253C2×C43C2×#46411yescharacteristic
254C2×C43#305511yescharacteristic
255C2×C43#306811yescharacteristic
256C22×SD16—21no—
257#533C22×C4311yescharacteristic
258C2×#127C22×C4311yescharacteristic
259C2×C4×Q8C22×C4311yescharacteristic
260#490—22no—
261#486C22×C4312yes—
262#486C22×C4312yes—
263#484—21no—
264#477C22×C4311yescharacteristic, complemented
265#477C22×C4311yescharacteristic, complemented
266#462C22×C4311yescharacteristic, complemented
267#462C22×C4311yescharacteristic, complemented
268#460—21no—
269#460—21no—
270#460C22×C4312yes—
271#460C22×C4312yes—
272#451—21no—
273#446—22no—
274#446C22×C4312yescomplemented
275C8×Q8C22×C4312yescomplemented
276C4×Q16—21no—
277C4×Q16—21no—
278#431C22×C4311yescharacteristic
279#423—21no—
280#423C22×C4311yescharacteristic
281C2×C4⋊C8C22×C4311yescharacteristic
282#418—21no—
283#418—21no—
284C2×#102—21no—
285C4×M16—21no—
286C4×M16C22×C4311yescharacteristic
287#335C22×C4312yescomplemented
288#334C22×C4312yescomplemented
289#333C22×C4312yescomplemented
290#332C22×C4312yescomplemented
291#331C22×C4312yes—
292#331C22×C4312yes—
293C43#1917411yescharacteristic, direct product factor, Sylow
294C22×Q8D4×C4311yescharacteristic
295C22×D4—21no—
296C22×D4—21no—
297C22×D4—21no—
298C2×Q16—21no—
299C2×Q16—21no—
300C2×SD16—22no—
301C2×SD16—22no—
302C2×SD16—44no—
303C2×M16—21no—
304C2×M16D4×C4311yescharacteristic
305C2×M16D4×C4311yescharacteristic
306C22×C8—21no—
307C4⋊Q8C23×C4311yescharacteristic
308C4⋊Q8C23×C4311yescharacteristic
309#127—21no—
310#127—21no—
311#127—21no—
312#127C23×C4312yes—
313#125—21no—
314C22⋊Q8—21no—
315C22⋊Q8—21no—
316C4×Q8—21no—
317C4×Q8—21no—
318C4×Q8—21no—
319C4×Q8—21no—
320C4×Q8D4×C4311yescharacteristic
321C4×Q8D4×C4311yescharacteristic
322C4×Q8C23×C4311yescharacteristic
323C4×Q8C23×C4311yescharacteristic
324#117—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4D4×C4311yescharacteristic
327C2×C42—21no—
328C2×C42C23×C4311yescharacteristic
329#107—21no—
330#107—21no—
331C4⋊C8—22no—
332C4⋊C8—22no—
333C4⋊C8—21no—
334C4⋊C8—21no—
335C4⋊C8C23×C4312yes—
336C4⋊C8C23×C4311yescharacteristic
337C4⋊C8C23×C4311yescharacteristic
338C4⋊C8C23×C4312yes—
339#103—21no—
340#103—21no—
341#103—21no—
342#103—21no—
343#102—22no—
344#102—22no—
345#102—22no—
346#102—22no—
347#102—22no—
348#102—22no—
349C22⋊C8—21no—
350#97—22no—
351#97D4×C4312yes—
352C4×C8—22no—
353C4×C8—21no—
354C4×C8C23×C4312yes—
355C24—41no—
356C2×Q8—21no—
357C2×Q8—22no—
358C2×Q8—21no—
359C2×Q8—21no—
360C2×Q8—41no—
361C2×Q8C2×D4×C4311yescharacteristic
362C2×Q8C2×D4×C4311yescharacteristic
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—42no—
367C2×D4—42no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—42no—
372C2×D4—42no—
373C2×D4—82no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4C2×D4×C4311yescharacteristic
377C22×C4C2×D4×C4311yescharacteristic
378C22×C4#41×C4311yescharacteristic
379Q16—42no—
380Q16—42no—
381SD16—44no—
382SD16—44no—
383M16—22no—
384M16—22no—
385M16—42no—
386C2×C8—22no—
387C2×C8—21no—
388C2×C8—21no—
389C2×C8—22no—
390C2×C8—42no—
391C2×C8C2×D4×C4312yes—
392C2×C8C2×D4×C4312yes—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—41no—
403C4⋊C4—41no—
404C4⋊C4C2×D4×C4311yescharacteristic
405C4⋊C4C2×D4×C4311yescharacteristic
406C22⋊C4—41no—
407C42—21no—
408C42—21no—
409C42—21no—
410C42—21no—
411C42—41no—
412C42C2×D4×C4311yescharacteristic
413C42C2×D4×C4311yescharacteristic
414C42#41×C4311yescharacteristic
415C42C24×C4311yescharacteristic
416C23—42no—
417C23—82no—
418C23—82no—
419C23—82no—
420C23#121×C4311yescharacteristic
421Q8—21no—
422Q8—21no—
423Q8—21no—
424Q8—42no—
425Q8—41no—
426Q8—41no—
427Q8—81no—
428Q8AGL(1,ℤ/8)×C4312yes—
429D4—42no—
430D4—42no—
431D4—42no—
432D4—42no—
433D4—82no—
434D4—82no—
435D4—82no—
436D4—82no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—81no—
448C2×C4#121×C4311yescharacteristic
449C2×C4#121×C4311yescharacteristic
450C2×C4#121×C4311yescharacteristic
451C2×C4#135×C4312yes—
452C2×C4#137×C4312yes—
453C2×C4C22×D4×C4311yescharacteristic
454C2×C4C22×D4×C4311yescharacteristic
455C2×C4C2×#41×C4311yescharacteristic
456C8—22no—
457C8—22no—
458C8—42no—
459C8—42no—
460C8—41no—
461C8—41no—
462C22—21no—
463C22—21no—
464C22—82no—
465C22—82no—
466C22—82no—
467C22—164no—
468C22C43×#46412yes—
469C22C2×#121×C4311yescharacteristic
470C4—21no—
471C4—22no—
472C4—21no—
473C4—21no—
474C4—41no—
475C4—41no—
476C4—41no—
477C4—81no—
478C4—81no—
479C4C43×#46412yes—
480C4C2×#135×C4311yescharacteristic
481C4C2×AGL(1,ℤ/8)×C4311yescharacteristic
482C4C2×#137×C4311yescharacteristic
483C4C43×#57511yescharacteristic
484C2—22no—
485C2—162no—
486C2C2×C43×#46411yescharacteristic
487C2C43×#305511yescharacteristic
488C2C43×#306811yescharacteristic
subgroupG/H
center, socleC22×C43C2×#121
commutator, Frattini, cosocleC42C24×C43
prime radicalC2×#127×C43C22
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
2. C43×#3104C2semidirect
4. Q8×M16×C43C2semidirect
5. C43×#1702C2semidirect
6. C43×#1698C2semidirect
7. C43×#1682C2semidirect
8. C43×#1678C2semidirect
9. C43×#1565C2semidirect
10. C43×#1550C2semidirect
20. C43×#477C22semidirect
21. C43×#477C22semidirect
22. C43×#462C22semidirect
23. C43×#462C22semidirect
30. C43×#446C22semidirect
31. C8×Q8×C43C22semidirect
43. C43×#335C22semidirect
44. C43×#334C22semidirect
45. C43×#333C22semidirect
46. C43×#332C22semidirect
217. #19174C43direct (N × H)
241. #3104C2×C43semidirect
243. Q8×M16C2×C43semidirect
244. #1702C2×C43semidirect
245. #1698C2×C43semidirect
246. #1682C2×C43semidirect
247. #1678C2×C43semidirect
248. #1565C2×C43semidirect
249. #1550C2×C43semidirect
264. #477C22×C43semidirect
265. #477C22×C43semidirect
266. #462C22×C43semidirect
267. #462C22×C43semidirect
274. #446C22×C43semidirect
275. C8×Q8C22×C43semidirect
287. #335C22×C43semidirect
288. #334C22×C43semidirect
289. #333C22×C43semidirect
290. #332C22×C43semidirect
293. C43#19174direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#31382
C43×#31042
C2×C43×#4602
Q8×M16×C432
C43×#17022
C43×#16982
C43×#16822
C43×#16782
C43×#15652
C43×#15502
C43×#15452
#1917443