Finite Group Databasebeta

← C43×#18338 #24938355

Subgroups — C43×#18338 #24938355

Order 11008.

928 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3461C211yesmaximal, characteristic
2C43×#3218C212yesmaximal, complemented
3C43×#2567C211yesmaximal, characteristic, complemented
4C43×#1605C212yesmaximal, complemented
5C43×#1604C212yesmaximal
6C43×#1603C214yesmaximal, complemented
7C43×#1509C212yesmaximal, complemented
8C43×#1467C211yesmaximal, characteristic, complemented
9C43×#544C2211yescharacteristic
10C43×#542—22no—
11C43×#541—22no—
12C43×#539—21no—
13C43×#539C2212yes—
14C43×#537C2211yescharacteristic
15C43×#536—21no—
16C43×#533—22no—
17C2×C4⋊Q8×C43C2211yescharacteristic
18C43×#529—22no—
19C43×#529—21no—
20C43×#529C2212yes—
21C4×#41×C43—21no—
22C2×C4×Q8×C43C2211yescharacteristic
23C43×#497—22no—
24C43×#491—22no—
25C43×#462—22no—
26C43×#461—22no—
27C43×#451C2214yes—
28C43×#448C2214yes—
29C43×#432C2212yes—
30C43×#395C2212yes—
31C43×#395C2212yes—
32C43×#391—21no—
33C43×#389—21no—
34C43×#389—21no—
35C43×#384—21no—
36C4×C4⋊C4×C43C2211yescharacteristic
37C43×#328C2214yes—
38C43×#327C2214yes—
39C43×#324C2212yes—
40C43×#324C2212yes—
41C2×#41×C43—21no—
42C22×Q8×C43D411yescharacteristic
43C22×Q8×C43C2312yes—
44C2×Q16×C43—24no—
45C2×SD16×C43—24no—
46C4⋊Q8×C43—22no—
47C4⋊Q8×C43—22no—
48C4⋊Q8×C43—22no—
49C4⋊Q8×C43—22no—
50#126×C43—22no—
51#126×C43—22no—
52#126×C43—22no—
53#126×C43—22no—
54#125×C43—21no—
55#125×C43—22no—
56#125×C43—22no—
57#125×C43—22no—
58#125×C43D412yes—
59#124×C43—22no—
60#124×C43—21no—
61#124×C43D412yes—
62#123×C43—22no—
63#123×C43—22no—
64#123×C43—22no—
65#123×C43—22no—
66C22⋊Q8×C43—22no—
67C22⋊Q8×C43—22no—
68C22⋊Q8×C43—22no—
69C22⋊Q8×C43—22no—
70C22⋊Q8×C43—21no—
71C22⋊Q8×C43—22no—
72C22⋊Q8×C43C2312yes—
73#121×C43—22no—
74#121×C43—21no—
75#121×C43C2312yes—
76C4×Q8×C43—21no—
77C4×Q8×C43—21no—
78C4×Q8×C43—21no—
79C4×Q8×C43—22no—
80C4×Q8×C43—22no—
81C4×Q8×C43D412yes—
82C4×D4×C43—21no—
83C4×D4×C43—21no—
84C4×D4×C43—21no—
85C4×D4×C43—22no—
86C4×D4×C43—22no—
87C4×D4×C43D412yes—
88#117×C43—22no—
89#117×C43—22no—
90#117×C43—21no—
91#117×C43—22no—
92C2×C4⋊C4×C43—21no—
93C2×C4⋊C4×C43—21no—
94C2×C4⋊C4×C43—21no—
95C2×C4⋊C4×C43—22no—
96C2×C4⋊C4×C43—22no—
97C2×C4⋊C4×C43D411yescharacteristic
98C2×C4⋊C4×C43C2311yescharacteristic
99C2×C4⋊C4×C43C2311yescharacteristic
100C2×C42×C43—22no—
101C2×C42×C43—21no—
102C2×C42×C43D411yescharacteristic
103C2×C42×C43D411yescharacteristic
104C2×C42×C43C2311yescharacteristic
105C4⋊C8×C43—22no—
106#103×C43—24no—
107#103×C43—24no—
108C22⋊C8×C43C2314yes—
109#97×C43—22no—
110#95×C43—22no—
111#95×C43—22no—
112#95×C43C2312yes—
113#41×C43—42no—
114#41×C43—42no—
115C2×Q8×C43—21no—
116C2×Q8×C43—21no—
117C2×Q8×C43—22no—
118C2×Q8×C43—22no—
119C2×Q8×C43—24no—
120C2×Q8×C43—41no—
121C2×Q8×C43—82no—
122C2×Q8×C43C2×D412yes—
123C2×D4×C43—21no—
124C2×D4×C43—21no—
125C2×D4×C43—22no—
126C2×D4×C43C2×D412yes—
127C22×C4×C43—22no—
128C22×C4×C43—22no—
129C22×C4×C43—22no—
130C22×C4×C43—22no—
131C22×C4×C43—22no—
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2411yescharacteristic
139Q16×C43—84no—
140SD16×C43—84no—
141C2×C8×C43—24no—
142C4⋊C4×C43—24no—
143C4⋊C4×C43—21no—
144C4⋊C4×C43—22no—
145C4⋊C4×C43—21no—
146C4⋊C4×C43—22no—
147C4⋊C4×C43—22no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—21no—
150C4⋊C4×C43—22no—
151C4⋊C4×C43—22no—
152C4⋊C4×C43—22no—
153C4⋊C4×C43—22no—
154C4⋊C4×C43—22no—
155C4⋊C4×C43—22no—
156C4⋊C4×C43—22no—
157C4⋊C4×C43—22no—
158C4⋊C4×C43—41no—
159C4⋊C4×C43—42no—
160C4⋊C4×C43—41no—
161C4⋊C4×C43—82no—
162C4⋊C4×C43—82no—
163C4⋊C4×C43C2×D412yes—
164C4⋊C4×C43C2×D412yes—
165C22⋊C4×C43—22no—
166C22⋊C4×C43—22no—
167C22⋊C4×C43—22no—
168C22⋊C4×C43—22no—
169C22⋊C4×C43—22no—
170C22⋊C4×C43—22no—
171C22⋊C4×C43—22no—
172C22⋊C4×C43—22no—
173C22⋊C4×C43—22no—
174C42×C43—22no—
175C42×C43—22no—
176C42×C43—21no—
177C42×C43—22no—
178C42×C43—21no—
179C42×C43—21no—
180C42×C43—21no—
181C42×C43—42no—
182C42×C43C2×D412yes—
183C42×C43C2×D412yes—
184C23×C43—22no—
185C23×C43C22×D411yescharacteristic
186Q8×C43—44no—
187Q8×C43—42no—
188Q8×C43—42no—
189Q8×C43—44no—
190Q8×C43—44no—
191Q8×C43—81no—
192D4×C43—42no—
193D4×C43—42no—
194D4×C43—42no—
195D4×C43—42no—
196D4×C43—81no—
197C2×C4×C43—21no—
198C2×C4×C43—21no—
199C2×C4×C43—21no—
200C2×C4×C43—21no—
201C2×C4×C43—22no—
202C2×C4×C43—24no—
203C2×C4×C43—21no—
204C2×C4×C43—22no—
205C2×C4×C43—22no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—22no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—41no—
212C2×C4×C43—44no—
213C2×C4×C43—42no—
214C2×C4×C43—42no—
215C2×C4×C43—44no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—42no—
219C2×C4×C43—42no—
220C2×C4×C43—42no—
221C2×C4×C43—82no—
222C2×C4×C43#12011yescharacteristic
223C2×C4×C43#12012yes—
224C2×C4×C43#12011yescharacteristic
225C2×C4×C43#13712yes—
226C2×C4×C43C22×D412yes—
227C8×C43—44no—
228#18338C4311yesmaximal, characteristic, direct product factor, Sylow
229C22×C43—21no—
230C22×C43—21no—
231C22×C43—42no—
232C22×C43—42no—
233C22×C43—42no—
234C22×C43C2×#12011yescharacteristic
235C22×C43C2×#13711yescharacteristic
236C22×C43#57511yescharacteristic
237C4×C43—22no—
238C4×C43—22no—
239C4×C43—21no—
240C4×C43—22no—
241C4×C43—44no—
242C4×C43—41no—
243C4×C43—42no—
244C4×C43—42no—
245C4×C43—41no—
246C4×C43—41no—
247C4×C43—42no—
248C4×C43—82no—
249C4×C43#45612yes—
250#3461C2×C4311yescharacteristic
251#3218C2×C4312yescomplemented
252#2567C2×C4311yescharacteristic, complemented
253#1605C2×C4312yescomplemented
254#1604C2×C4312yes—
255#1603C2×C4314yescomplemented
256#1509C2×C4312yescomplemented
257#1467C2×C4311yescharacteristic, complemented
258C2×C43—21no—
259C2×C43—21no—
260C2×C43—82no—
261C2×C43#300711yescharacteristic
262C2×C43C2×#45611yescharacteristic
263C2×C43#302711yescharacteristic
264#544C22×C4311yescharacteristic
265#542—22no—
266#541—22no—
267#539—21no—
268#539C22×C4312yes—
269#537C22×C4311yescharacteristic
270#536—21no—
271#533—22no—
272C2×C4⋊Q8C22×C4311yescharacteristic
273#529—22no—
274#529—21no—
275#529C22×C4312yes—
276C4×#41—21no—
277C2×C4×Q8C22×C4311yescharacteristic
278#497—22no—
279#491—22no—
280#462—22no—
281#461—22no—
282#451C22×C4314yes—
283#448C22×C4314yes—
284#432C22×C4312yes—
285#395C22×C4312yes—
286#395C22×C4312yes—
287#391—21no—
288#389—21no—
289#389—21no—
290#384—21no—
291C4×C4⋊C4C22×C4311yescharacteristic
292#328C22×C4314yes—
293#327C22×C4314yes—
294#324C22×C4312yes—
295#324C22×C4312yes—
296C43#1833811yescharacteristic, direct product factor, Sylow
297C2×#41—21no—
298C22×Q8D4×C4311yescharacteristic
299C22×Q8C23×C4312yes—
300C2×Q16—24no—
301C2×SD16—24no—
302C4⋊Q8—22no—
303C4⋊Q8—22no—
304C4⋊Q8—22no—
305C4⋊Q8—22no—
306#126—22no—
307#126—22no—
308#126—22no—
309#126—22no—
310#125—21no—
311#125—22no—
312#125—22no—
313#125—22no—
314#125D4×C4312yes—
315#124—22no—
316#124—21no—
317#124D4×C4312yes—
318#123—22no—
319#123—22no—
320#123—22no—
321#123—22no—
322C22⋊Q8—22no—
323C22⋊Q8—22no—
324C22⋊Q8—22no—
325C22⋊Q8—22no—
326C22⋊Q8—21no—
327C22⋊Q8—22no—
328C22⋊Q8C23×C4312yes—
329#121—22no—
330#121—21no—
331#121C23×C4312yes—
332C4×Q8—21no—
333C4×Q8—21no—
334C4×Q8—21no—
335C4×Q8—22no—
336C4×Q8—22no—
337C4×Q8D4×C4312yes—
338C4×D4—21no—
339C4×D4—21no—
340C4×D4—21no—
341C4×D4—22no—
342C4×D4—22no—
343C4×D4D4×C4312yes—
344#117—22no—
345#117—22no—
346#117—21no—
347#117—22no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4D4×C4311yescharacteristic
354C2×C4⋊C4C23×C4311yescharacteristic
355C2×C4⋊C4C23×C4311yescharacteristic
356C2×C42—22no—
357C2×C42—21no—
358C2×C42D4×C4311yescharacteristic
359C2×C42D4×C4311yescharacteristic
360C2×C42C23×C4311yescharacteristic
361C4⋊C8—22no—
362#103—24no—
363#103—24no—
364C22⋊C8C23×C4314yes—
365#97—22no—
366#95—22no—
367#95—22no—
368#95C23×C4312yes—
369#41—42no—
370#41—42no—
371C2×Q8—21no—
372C2×Q8—21no—
373C2×Q8—22no—
374C2×Q8—22no—
375C2×Q8—24no—
376C2×Q8—41no—
377C2×Q8—82no—
378C2×Q8C2×D4×C4312yes—
379C2×D4—21no—
380C2×D4—22no—
381C2×D4—21no—
382C2×D4C2×D4×C4312yes—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4C2×D4×C4311yescharacteristic
389C22×C4C2×D4×C4311yescharacteristic
390C22×C4C2×D4×C4311yescharacteristic
391C22×C4C2×D4×C4311yescharacteristic
392C22×C4C2×D4×C4311yescharacteristic
393C22×C4C2×D4×C4311yescharacteristic
394C22×C4C24×C4311yescharacteristic
395Q16—84no—
396SD16—84no—
397C2×C8—24no—
398C4⋊C4—24no—
399C4⋊C4—21no—
400C4⋊C4—22no—
401C4⋊C4—21no—
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—41no—
415C4⋊C4—42no—
416C4⋊C4—41no—
417C4⋊C4—82no—
418C4⋊C4—82no—
419C4⋊C4C2×D4×C4312yes—
420C4⋊C4C2×D4×C4312yes—
421C22⋊C4—22no—
422C22⋊C4—22no—
423C22⋊C4—22no—
424C22⋊C4—22no—
425C22⋊C4—22no—
426C22⋊C4—22no—
427C22⋊C4—22no—
428C22⋊C4—22no—
429C22⋊C4—22no—
430C42—22no—
431C42—22no—
432C42—21no—
433C42—22no—
434C42—21no—
435C42—21no—
436C42—21no—
437C42—42no—
438C42C2×D4×C4312yes—
439C42C2×D4×C4312yes—
440C23—22no—
441C23C22×D4×C4311yescharacteristic
442Q8—44no—
443Q8—42no—
444Q8—42no—
445Q8—44no—
446Q8—44no—
447Q8—81no—
448D4—42no—
449D4—42no—
450D4—42no—
451D4—42no—
452D4—81no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—22no—
458C2×C4—24no—
459C2×C4—21no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—22no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—41no—
468C2×C4—44no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—44no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—82no—
478C2×C4#120×C4311yescharacteristic
479C2×C4#120×C4312yes—
480C2×C4#120×C4311yescharacteristic
481C2×C4#137×C4312yes—
482C2×C4C22×D4×C4312yes—
483C8—44no—
484C22—21no—
485C22—21no—
486C22—42no—
487C22—42no—
488C22—42no—
489C22C2×#120×C4311yescharacteristic
490C22C2×#137×C4311yescharacteristic
491C22C43×#57511yescharacteristic
492C4—22no—
493C4—22no—
494C4—21no—
495C4—22no—
496C4—44no—
497C4—41no—
498C4—42no—
499C4—42no—
500C4—41no—
501C4—41no—
502C4—42no—
503C4—82no—
504C4C43×#45612yes—
505C2—21no—
506C2—21no—
507C2—82no—
508C2C43×#300711yescharacteristic
509C2C2×C43×#45611yescharacteristic
510C2C43×#302711yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC43×#537C22
LCSG ▷ C22×C4 ▷ 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×#3218C2semidirect
3. C43×#2567C2semidirect
4. C43×#1605C2semidirect
6. C43×#1603C2semidirect
7. C43×#1509C2semidirect
8. C43×#1467C2semidirect
228. #18338C43direct (N × H)
251. #3218C2×C43semidirect
252. #2567C2×C43semidirect
253. #1605C2×C43semidirect
255. #1603C2×C43semidirect
256. #1509C2×C43semidirect
257. #1467C2×C43semidirect
296. C43#18338direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#34612
C43×#32182
C43×#25672
C43×#16052
C43×#16042
C43×#16032
C43×#15092
C43×#14672
#1833843