Finite Group Databasebeta

← C43×#25713 #24945730

Subgroups — C43×#25713 #24945730

Order 11008.

1102 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#553C211yesmaximal, characteristic
2C2×C43×#501C211yesmaximal, characteristic, complemented
3C2×C43×#474C211yesmaximal, characteristic, complemented
4C43×#2563C211yesmaximal, characteristic, complemented
5C43×#2034C212yesmaximal, complemented
6C43×#2033C212yesmaximal, complemented
7C43×#1989C211yesmaximal, characteristic, complemented
8C43×#1955C211yesmaximal, characteristic, complemented
9C43×#1854C212yesmaximal, complemented
10C43×#1852C212yesmaximal, complemented
11C43×#1762C211yesmaximal, characteristic, complemented
12C43×#553—24no—
13C43×#553—24no—
14C2×C4⋊Q8×C43C2211yescharacteristic
15C2×#126×C43—21no—
16C2×#125×C43C2211yescharacteristic
17C2×#123×C43—21no—
18C2×#121×C43—21no—
19C2×#121×C43C2211yescharacteristic
20C2×#121×C43C2211yescharacteristic
21C2×C4×D4×C43—21no—
22C2×C4×D4×C43C2211yescharacteristic
23C2×C4×D4×C43C2211yescharacteristic
24C2×#117×C43C2211yescharacteristic
25C22×C4⋊C4×C43C2211yescharacteristic
26C43×#501—24no—
27C43×#474—24no—
28C2×#107×C43C2212yes—
29C2×#107×C43C2212yes—
30C2×#106×C43C2212yes—
31C2×C4⋊C8×C43C2211yescharacteristic
32C2×#102×C43C2212yes—
33C2×#102×C43C2212yes—
34C2×C22⋊C8×C43C2212yes—
35C2×C22⋊C8×C43C2212yes—
36C2×#97×C43C2211yescharacteristic
37C43×#393—21no—
38C43×#393—21no—
39C43×#390—21no—
40C43×#382—21no—
41C43×#380C2212yes—
42C43×#380C2212yes—
43C4×C4⋊C4×C43C2211yescharacteristic
44C43×#340C2212yes—
45C43×#340C2212yes—
46C43×#340C2212yes—
47C22×Q8×C43—21no—
48C22×D4×C43—21no—
49C22×D4×C43—21no—
50C22×D4×C43D411yescharacteristic
51C22×D4×C43C2311yescharacteristic
52C23×C4×C43—21no—
53C23×C4×C43—21no—
54C23×C4×C43C2311yescharacteristic
55C23×C4×C43C2311yescharacteristic
56C22×C8×C43C2312yes—
57C22×C8×C43C2312yes—
58C4⋊Q8×C43—22no—
59C4⋊Q8×C43—22no—
60#126×C43—28no—
61#125×C43—22no—
62#125×C43D414yes—
63#123×C43—28no—
64#121×C43—28no—
65#121×C43—22no—
66#121×C43—22no—
67#121×C43—22no—
68#121×C43—22no—
69C4×D4×C43—28no—
70C4×D4×C43—22no—
71C4×D4×C43—22no—
72C4×D4×C43—22no—
73C4×D4×C43D414yes—
74#117×C43—22no—
75#117×C43—22no—
76C2×C4⋊C4×C43—21no—
77C2×C4⋊C4×C43—21no—
78C2×C4⋊C4×C43—21no—
79C2×C4⋊C4×C43—22no—
80C2×C4⋊C4×C43—22no—
81C2×C4⋊C4×C43—21no—
82C2×C4⋊C4×C43D411yescharacteristic
83C2×C4⋊C4×C43C2312yes—
84C2×C4⋊C4×C43C2312yes—
85C2×C4⋊C4×C43C2311yescharacteristic
86C2×C4⋊C4×C43C2311yescharacteristic
87C2×C4⋊C4×C43C2311yescharacteristic
88C2×C22⋊C4×C43—21no—
89C2×C22⋊C4×C43—21no—
90C2×C22⋊C4×C43—21no—
91C2×C22⋊C4×C43—21no—
92C2×C22⋊C4×C43—22no—
93C2×C22⋊C4×C43—22no—
94C2×C22⋊C4×C43D411yescharacteristic
95C2×C22⋊C4×C43D411yescharacteristic
96C2×C42×C43—21no—
97C2×C42×C43—21no—
98C2×C42×C43C2311yescharacteristic
99#107×C43—24no—
100#107×C43—24no—
101#106×C43—24no—
102C4⋊C8×C43—22no—
103#102×C43—24no—
104#102×C43—24no—
105C22⋊C8×C43—24no—
106C22⋊C8×C43—24no—
107#97×C43—22no—
108#95×C43—21no—
109#95×C43—22no—
110#95×C43—22no—
111C24×C43—21no—
112C24×C43C2×D411yescharacteristic
113C24×C43C2×D411yescharacteristic
114C2×Q8×C43—42no—
115C2×Q8×C43—82no—
116C2×D4×C43—24no—
117C2×D4×C43—24no—
118C2×D4×C43—22no—
119C2×D4×C43—21no—
120C2×D4×C43—22no—
121C2×D4×C43—22no—
122C2×D4×C43—22no—
123C2×D4×C43—41no—
124C2×D4×C43—42no—
125C2×D4×C43—42no—
126C2×D4×C43—82no—
127C2×D4×C43C2×D412yes—
128C22×C4×C43—24no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—22no—
134C22×C4×C43—22no—
135C22×C4×C43—22no—
136C22×C4×C43—22no—
137C22×C4×C43—24no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—22no—
142C22×C4×C43—22no—
143C22×C4×C43—82no—
144C22×C4×C43—82no—
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2411yescharacteristic
150C2×C8×C43—22no—
151C2×C8×C43—22no—
152C2×C8×C43—22no—
153C2×C8×C43—22no—
154C2×C8×C43—22no—
155C2×C8×C43#4114yes—
156C4⋊C4×C43—24no—
157C4⋊C4×C43—24no—
158C4⋊C4×C43—24no—
159C4⋊C4×C43—22no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—22no—
164C4⋊C4×C43—22no—
165C4⋊C4×C43—22no—
166C4⋊C4×C43—22no—
167C4⋊C4×C43—42no—
168C4⋊C4×C43C2×D412yes—
169C4⋊C4×C43C2×D412yes—
170C4⋊C4×C43C2×D412yes—
171C22⋊C4×C43—24no—
172C22⋊C4×C43—24no—
173C22⋊C4×C43—24no—
174C22⋊C4×C43—24no—
175C22⋊C4×C43—22no—
176C22⋊C4×C43—22no—
177C22⋊C4×C43—82no—
178C22⋊C4×C43—82no—
179C42×C43—24no—
180C42×C43—42no—
181C42×C43C2×D412yes—
182C42×C43C2×D412yes—
183C23×C43—21no—
184C23×C43—22no—
185C23×C43—21no—
186C23×C43—22no—
187C23×C43—21no—
188C23×C43—22no—
189C23×C43—22no—
190C23×C43—21no—
191C23×C43—21no—
192C23×C43—22no—
193C23×C43—42no—
194C23×C43—41no—
195C23×C43—41no—
196C23×C43—42no—
197C23×C43#13712yes—
198C23×C43C22×D411yescharacteristic
199Q8×C43—84no—
200D4×C43—22no—
201D4×C43—22no—
202D4×C43—44no—
203D4×C43—48no—
204D4×C43—42no—
205D4×C43—84no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—22no—
209C2×C4×C43—21no—
210C2×C4×C43—22no—
211C2×C4×C43—22no—
212C2×C4×C43—21no—
213C2×C4×C43—22no—
214C2×C4×C43—22no—
215C2×C4×C43—22no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—42no—
219C2×C4×C43—42no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—42no—
225C2×C4×C43—42no—
226C2×C4×C43—42no—
227C2×C4×C43—42no—
228C2×C4×C43—42no—
229C2×C4×C43—42no—
230C2×C4×C43—42no—
231C2×C4×C43—42no—
232C2×C4×C43—84no—
233C2×C4×C43—84no—
234C2×C4×C43#12012yes—
235C2×C4×C43#12012yes—
236C2×C4×C43C22×D411yescharacteristic
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C43C2×#4112yes—
239C2×C4×C432−1+412yes—
240C8×C43—24no—
241C8×C43—42no—
242#25713C4311yesmaximal, characteristic, direct product factor, Sylow
243C22×C43—24no—
244C22×C43—22no—
245C22×C43—42no—
246C22×C43—41no—
247C22×C43—41no—
248C22×C43—42no—
249C22×C43—42no—
250C22×C43—41no—
251C22×C43—42no—
252C22×C43—41no—
253C22×C43—42no—
254C22×C43—41no—
255C22×C43—42no—
256C22×C43—82no—
257C22×C43—82no—
258C22×C43C2×#12011yescharacteristic
259C22×C43#54712yes—
260C22×C43C2×#13711yescharacteristic
261C22×C43#57511yescharacteristic
262C22×C43#57612yes—
263C4×C43—22no—
264C4×C43—22no—
265C4×C43—41no—
266C4×C43—41no—
267C4×C43—42no—
268C4×C43—42no—
269C4×C43—42no—
270C4×C43—82no—
271C4×C43—82no—
272C4×C43#53211yescharacteristic
273C4×C43#53611yescharacteristic
274C4×C43#54812yes—
275C2×#553C2×C4311yescharacteristic
276C2×#501C2×C4311yescharacteristic, complemented
277C2×#474C2×C4311yescharacteristic, complemented
278#2563C2×C4311yescharacteristic, complemented
279#2034C2×C4312yescomplemented
280#2033C2×C4312yescomplemented
281#1989C2×C4311yescharacteristic, complemented
282#1955C2×C4311yescharacteristic, complemented
283#1854C2×C4312yescomplemented
284#1852C2×C4312yescomplemented
285#1762C2×C4311yescharacteristic, complemented
286C2×C43—42no—
287C2×C43—81no—
288C2×C43—82no—
289C2×C43#243211yescharacteristic
290C2×C43#300711yescharacteristic
291C2×C43#300811yescharacteristic
292C2×C43#334612yes—
293C2×C43#334712yes—
294#553—24no—
295#553—24no—
296C2×C4⋊Q8C22×C4311yescharacteristic
297C2×#126—21no—
298C2×#125C22×C4311yescharacteristic
299C2×#123—21no—
300C2×#121—21no—
301C2×#121C22×C4311yescharacteristic
302C2×#121C22×C4311yescharacteristic
303C2×C4×D4—21no—
304C2×C4×D4C22×C4311yescharacteristic
305C2×C4×D4C22×C4311yescharacteristic
306C2×#117C22×C4311yescharacteristic
307C22×C4⋊C4C22×C4311yescharacteristic
308#501—24no—
309#474—24no—
310C2×#107C22×C4312yes—
311C2×#107C22×C4312yes—
312C2×#106C22×C4312yes—
313C2×C4⋊C8C22×C4311yescharacteristic
314C2×#102C22×C4312yes—
315C2×#102C22×C4312yes—
316C2×C22⋊C8C22×C4312yes—
317C2×C22⋊C8C22×C4312yes—
318C2×#97C22×C4311yescharacteristic
319#393—21no—
320#393—21no—
321#390—21no—
322#382—21no—
323#380C22×C4312yes—
324#380C22×C4312yes—
325C4×C4⋊C4C22×C4311yescharacteristic
326#340C22×C4312yes—
327#340C22×C4312yes—
328#340C22×C4312yes—
329C43#2571311yescharacteristic, direct product factor, Sylow
330C22×Q8—21no—
331C22×D4—21no—
332C22×D4—21no—
333C22×D4D4×C4311yescharacteristic
334C22×D4C23×C4311yescharacteristic
335C23×C4—21no—
336C23×C4—21no—
337C23×C4C23×C4311yescharacteristic
338C23×C4C23×C4311yescharacteristic
339C22×C8C23×C4312yes—
340C22×C8C23×C4312yes—
341C4⋊Q8—22no—
342C4⋊Q8—22no—
343#126—28no—
344#125—22no—
345#125D4×C4314yes—
346#123—28no—
347#121—28no—
348#121—22no—
349#121—22no—
350#121—22no—
351#121—22no—
352C4×D4—28no—
353C4×D4—22no—
354C4×D4—22no—
355C4×D4—22no—
356C4×D4D4×C4314yes—
357#117—22no—
358#117—22no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4D4×C4311yescharacteristic
366C2×C4⋊C4C23×C4312yes—
367C2×C4⋊C4C23×C4312yes—
368C2×C4⋊C4C23×C4311yescharacteristic
369C2×C4⋊C4C23×C4311yescharacteristic
370C2×C4⋊C4C23×C4311yescharacteristic
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4D4×C4311yescharacteristic
378C2×C22⋊C4D4×C4311yescharacteristic
379C2×C42—21no—
380C2×C42—21no—
381C2×C42C23×C4311yescharacteristic
382#107—24no—
383#107—24no—
384#106—24no—
385C4⋊C8—22no—
386#102—24no—
387#102—24no—
388C22⋊C8—24no—
389C22⋊C8—24no—
390#97—22no—
391#95—21no—
392#95—22no—
393#95—22no—
394C24—21no—
395C24C2×D4×C4311yescharacteristic
396C24C2×D4×C4311yescharacteristic
397C2×Q8—42no—
398C2×Q8—82no—
399C2×D4—24no—
400C2×D4—22no—
401C2×D4—24no—
402C2×D4—22no—
403C2×D4—21no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—41no—
407C2×D4—42no—
408C2×D4—42no—
409C2×D4—82no—
410C2×D4C2×D4×C4312yes—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—24no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—24no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—82no—
427C22×C4—82no—
428C22×C4C2×D4×C4311yescharacteristic
429C22×C4C2×D4×C4311yescharacteristic
430C22×C4C2×D4×C4311yescharacteristic
431C22×C4C2×D4×C4311yescharacteristic
432C22×C4C24×C4311yescharacteristic
433C2×C8—22no—
434C2×C8—22no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8#41×C4314yes—
439C4⋊C4—24no—
440C4⋊C4—24no—
441C4⋊C4—24no—
442C4⋊C4—22no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—42no—
451C4⋊C4C2×D4×C4312yes—
452C4⋊C4C2×D4×C4312yes—
453C4⋊C4C2×D4×C4312yes—
454C22⋊C4—24no—
455C22⋊C4—24no—
456C22⋊C4—24no—
457C22⋊C4—24no—
458C22⋊C4—22no—
459C22⋊C4—22no—
460C22⋊C4—82no—
461C22⋊C4—82no—
462C42—24no—
463C42—42no—
464C42C2×D4×C4312yes—
465C42C2×D4×C4312yes—
466C23—21no—
467C23—22no—
468C23—21no—
469C23—22no—
470C23—21no—
471C23—22no—
472C23—22no—
473C23—21no—
474C23—21no—
475C23—22no—
476C23—42no—
477C23—41no—
478C23—41no—
479C23—42no—
480C23#137×C4312yes—
481C23C22×D4×C4311yescharacteristic
482Q8—84no—
483D4—22no—
484D4—22no—
485D4—44no—
486D4—48no—
487D4—42no—
488D4—84no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—22no—
492C2×C4—21no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—84no—
516C2×C4—84no—
517C2×C4#120×C4312yes—
518C2×C4#120×C4312yes—
519C2×C4C22×D4×C4311yescharacteristic
520C2×C4C22×D4×C4311yescharacteristic
521C2×C4C2×#41×C4312yes—
522C2×C42−1+4×C4312yes—
523C8—24no—
524C8—42no—
525C22—24no—
526C22—22no—
527C22—42no—
528C22—41no—
529C22—41no—
530C22—42no—
531C22—42no—
532C22—41no—
533C22—42no—
534C22—41no—
535C22—42no—
536C22—42no—
537C22—41no—
538C22—82no—
539C22—82no—
540C22C2×#120×C4311yescharacteristic
541C22C43×#54712yes—
542C22C2×#137×C4311yescharacteristic
543C22C43×#57511yescharacteristic
544C22C43×#57612yes—
545C4—22no—
546C4—22no—
547C4—41no—
548C4—41no—
549C4—42no—
550C4—42no—
551C4—42no—
552C4—82no—
553C4—82no—
554C4C43×#53211yescharacteristic
555C4C43×#53611yescharacteristic
556C4C43×#54812yes—
557C2—42no—
558C2—81no—
559C2—82no—
560C2C43×#243211yescharacteristic
561C2C43×#300711yescharacteristic
562C2C43×#300811yescharacteristic
563C2C43×#334612yes—
564C2C43×#334712yes—
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC2×C43×#553C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C2×C4×D4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C43×#501C2semidirect
3. C2×C43×#474C2semidirect
4. C43×#2563C2semidirect
5. C43×#2034C2semidirect
6. C43×#2033C2semidirect
7. C43×#1989C2semidirect
8. C43×#1955C2semidirect
9. C43×#1854C2semidirect
10. C43×#1852C2semidirect
11. C43×#1762C2semidirect
242. #25713C43direct (N × H)
276. C2×#501C2×C43semidirect
277. C2×#474C2×C43semidirect
278. #2563C2×C43semidirect
279. #2034C2×C43semidirect
280. #2033C2×C43semidirect
281. #1989C2×C43semidirect
282. #1955C2×C43semidirect
283. #1854C2×C43semidirect
284. #1852C2×C43semidirect
285. #1762C2×C43semidirect
329. C43#25713direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#5532
C2×C43×#5012
C2×C43×#4742
C43×#25632
C43×#20342
C43×#20332
C43×#19892
C43×#19552
C43×#18542
C43×#18522
C43×#17622
#2571343