Finite Group Databasebeta

← C43×#22127 #24942144

Subgroups — C43×#22127 #24942144

Order 11008.

740 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#474C211yesmaximal, characteristic
2C43×#2331C211yesmaximal, characteristic, complemented
3C43×#2319C211yesmaximal, characteristic
4C43×#1987C211yesmaximal, characteristic, complemented
5C43×#1949C211yesmaximal, characteristic, complemented
6C43×#1943C211yesmaximal, characteristic, complemented
7C43×#1942C211yesmaximal, characteristic, complemented
8C43×#1936C211yesmaximal, characteristic
9C43×#1934C211yesmaximal, characteristic
10C43×#1926C211yesmaximal, characteristic
11C43×#1925C211yesmaximal, characteristic
12C43×#1921C211yesmaximal, characteristic, complemented
13C43×#1918C211yesmaximal, characteristic, complemented
14C43×#1804C211yesmaximal, characteristic
15C43×#1768C211yesmaximal, characteristic, complemented
16C2×C4⋊Q8×C43C2211yescharacteristic
17C2×C4×D4×C43C2211yescharacteristic
18C43×#474C418yescomplemented
19C2×#107×C43C2211yescharacteristic
20C2×#107×C43C2211yescharacteristic
21C2×#107×C43C2211yescharacteristic
22C2×#106×C43C2211yescharacteristic
23C2×C4⋊C8×C43C2211yescharacteristic
24C2×C4⋊C8×C43C2211yescharacteristic
25C2×#102×C43C2211yescharacteristic
26C2×#102×C43C2211yescharacteristic
27C2×#102×C43C2211yescharacteristic
28C2×#102×C43C2211yescharacteristic
29C2×#97×C43C2211yescharacteristic
30C2×C4×C8×C43C2211yescharacteristic
31C43×#391—21no—
32C43×#391—21no—
33C43×#390C2211yescharacteristic
34C43×#390C2211yescharacteristic
35C43×#389C2211yescharacteristic
36C43×#389C2211yescharacteristic
37C43×#389C2211yescharacteristic
38C43×#389C2211yescharacteristic
39C43×#388—21no—
40C43×#388—21no—
41C43×#387—21no—
42C43×#387—21no—
43C43×#382C2211yescharacteristic
44C43×#381—21no—
45C43×#380—21no—
46C4×C4⋊C4×C43C2211yescharacteristic
47C4×C4⋊C4×C43C2211yescharacteristic
48C4×C4⋊C4×C43C2211yescharacteristic
49C43×#376C2211yescharacteristic
50C43×#340C2211yescharacteristic
51C43×#340C2211yescharacteristic
52C43×#340C2211yescharacteristic
53C43×#340C2211yescharacteristic
54C43×#340C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C22×Q8×C43—21no—
61C22×D4×C43C2311yescharacteristic
62C23×C4×C43—21no—
63C22×C8×C43C2311yescharacteristic
64C22×C8×C43C2311yescharacteristic
65C22×C8×C43C2311yescharacteristic
66C22×C8×C43C2311yescharacteristic
67C4⋊Q8×C43—22no—
68C4⋊Q8×C43C2×C414yes—
69C4×D4×C43—22no—
70C4×D4×C43C2×C414yes—
71C2×C4⋊C4×C43—21no—
72C2×C4⋊C4×C43—21no—
73C2×C4⋊C4×C43—21no—
74C2×C4⋊C4×C43—21no—
75C2×C4⋊C4×C43—21no—
76C2×C4⋊C4×C43C2311yescharacteristic
77C2×C4⋊C4×C43C2311yescharacteristic
78C2×C4⋊C4×C43C2311yescharacteristic
79C2×C4⋊C4×C43C2311yescharacteristic
80C2×C4⋊C4×C43C2311yescharacteristic
81C2×C4⋊C4×C43C2311yescharacteristic
82C2×C4⋊C4×C43C2311yescharacteristic
83C2×C22⋊C4×C43—21no—
84C2×C22⋊C4×C43—21no—
85C2×C22⋊C4×C43—21no—
86C2×C22⋊C4×C43—21no—
87C2×C22⋊C4×C43—21no—
88C2×C42×C43—21no—
89C2×C42×C43—21no—
90C2×C42×C43—21no—
91C2×C42×C43C2311yescharacteristic
92C2×C42×C43C2311yescharacteristic
93C2×C42×C43C2311yescharacteristic
94#107×C43—41no—
95#107×C43C2×C414yes—
96#107×C43C2×C414yes—
97#106×C43—41no—
98C4⋊C8×C43—22no—
99C4⋊C8×C43C2×C414yes—
100#102×C43—41no—
101#102×C43—41no—
102#102×C43C2×C414yes—
103#102×C43C2×C414yes—
104#97×C43—41no—
105C4×C8×C43—41no—
106#95×C43—21no—
107#95×C43—21no—
108#95×C43—21no—
109#95×C43—21no—
110#95×C43—21no—
111#95×C43—21no—
112#95×C43—21no—
113#95×C43—21no—
114#95×C43—21no—
115#95×C43D411yescharacteristic
116#95×C43D411yescharacteristic
117#95×C43D411yescharacteristic
118#95×C43D411yescharacteristic
119C24×C43—21no—
120C2×Q8×C43—24no—
121C2×Q8×C43—81no—
122C2×Q8×C43—81no—
123C2×D4×C43—21no—
124C2×D4×C43—21no—
125C2×D4×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43C22×C412yes—
129C22×C4×C43—24no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—81no—
138C22×C4×C43—81no—
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2411yescharacteristic
146C2×C8×C43—21no—
147C2×C8×C43—21no—
148C2×C8×C43—21no—
149C2×C8×C43—21no—
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43C22×C412yes—
157C2×C8×C43C22×C412yes—
158C4⋊C4×C43—24no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—81no—
171C4⋊C4×C43—81no—
172C4⋊C4×C43—81no—
173C4⋊C4×C43—81no—
174C4⋊C4×C43C22×C412yes—
175C4⋊C4×C43C22×C412yes—
176C4⋊C4×C43C22×C412yes—
177C22⋊C4×C43—24no—
178C22⋊C4×C43—81no—
179C22⋊C4×C43—81no—
180C22⋊C4×C43—81no—
181C22⋊C4×C43—81no—
182C42×C43—21no—
183C42×C43—21no—
184C42×C43—21no—
185C42×C43—21no—
186C42×C43—81no—
187C42×C43—81no—
188C42×C43—81no—
189C42×C43C22×C412yes—
190C42×C43#4112yes—
191C23×C43—22no—
192C23×C43—41no—
193C23×C43—41no—
194C23×C43—41no—
195C23×C43—41no—
196C23×C43—41no—
197C23×C43—41no—
198C23×C43C22×D411yescharacteristic
199Q8×C43—84no—
200D4×C43—22no—
201D4×C43—22no—
202D4×C43—41no—
203D4×C43—41no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—22no—
209C2×C4×C43—22no—
210C2×C4×C43—22no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—84no—
242C2×C4×C43C4×D412yes—
243C2×C4×C43C4×D412yes—
244C2×C4×C43C23×C411yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43H(5,𝔽2)11yescharacteristic
247C2×C4×C432−1+411yescharacteristic
248C2×C4×C432−1+411yescharacteristic
249C2×C4×C432−1+411yescharacteristic
250C8×C43—22no—
251C8×C43—22no—
252C8×C43—41no—
253C8×C43—41no—
254#22127C4311yesmaximal, characteristic, direct product factor, Sylow
255C22×C43—42no—
256C22×C43—42no—
257C22×C43—42no—
258C22×C43—81no—
259C22×C43—81no—
260C22×C43—81no—
261C22×C43—81no—
262C22×C43C2×C4×D411yescharacteristic
263C22×C43#53611yescharacteristic
264C22×C43#53711yescharacteristic
265C22×C43#57611yescharacteristic
266C22×C43#57611yescharacteristic
267C22×C43#57711yescharacteristic
268C22×C43#57811yescharacteristic
269C4×C43—22no—
270C4×C43—22no—
271C4×C43—42no—
272C4×C43—42no—
273C4×C43—42no—
274C4×C43—41no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43—81no—
279C4×C43—81no—
280C4×C43—81no—
281C4×C43—81no—
282C4×C43#51911yescharacteristic
283C4×C43#52011yescharacteristic
284C4×C43#54111yescharacteristic
285C4×C43#54211yescharacteristic
286C2×#474C2×C4311yescharacteristic
287#2331C2×C4311yescharacteristic, complemented
288#2319C2×C4311yescharacteristic
289#1987C2×C4311yescharacteristic, complemented
290#1949C2×C4311yescharacteristic, complemented
291#1943C2×C4311yescharacteristic, complemented
292#1942C2×C4311yescharacteristic, complemented
293#1936C2×C4311yescharacteristic
294#1934C2×C4311yescharacteristic
295#1926C2×C4311yescharacteristic
296#1925C2×C4311yescharacteristic
297#1921C2×C4311yescharacteristic, complemented
298#1918C2×C4311yescharacteristic, complemented
299#1804C2×C4311yescharacteristic
300#1768C2×C4311yescharacteristic, complemented
301C2×C43—82no—
302C2×C43#232311yescharacteristic
303C2×C43#294711yescharacteristic
304C2×C43#294811yescharacteristic
305C2×C43#324111yescharacteristic
306C2×C43#324311yescharacteristic
307C2×C43#325711yescharacteristic
308C2×C43#326211yescharacteristic
309C2×C4⋊Q8C22×C4311yescharacteristic
310C2×C4×D4C22×C4311yescharacteristic
311#474C4×C4318yescomplemented
312C2×#107C22×C4311yescharacteristic
313C2×#107C22×C4311yescharacteristic
314C2×#107C22×C4311yescharacteristic
315C2×#106C22×C4311yescharacteristic
316C2×C4⋊C8C22×C4311yescharacteristic
317C2×C4⋊C8C22×C4311yescharacteristic
318C2×#102C22×C4311yescharacteristic
319C2×#102C22×C4311yescharacteristic
320C2×#102C22×C4311yescharacteristic
321C2×#102C22×C4311yescharacteristic
322C2×#97C22×C4311yescharacteristic
323C2×C4×C8C22×C4311yescharacteristic
324#391—21no—
325#391—21no—
326#390C22×C4311yescharacteristic
327#390C22×C4311yescharacteristic
328#389C22×C4311yescharacteristic
329#389C22×C4311yescharacteristic
330#389C22×C4311yescharacteristic
331#389C22×C4311yescharacteristic
332#388—21no—
333#388—21no—
334#387—21no—
335#387—21no—
336#382C22×C4311yescharacteristic
337#381—21no—
338#380—21no—
339C4×C4⋊C4C22×C4311yescharacteristic
340C4×C4⋊C4C22×C4311yescharacteristic
341C4×C4⋊C4C22×C4311yescharacteristic
342#376C22×C4311yescharacteristic
343#340C22×C4311yescharacteristic
344#340C22×C4311yescharacteristic
345#340C22×C4311yescharacteristic
346#340C22×C4311yescharacteristic
347#340C22×C4311yescharacteristic
348#340C22×C4311yescharacteristic
349#340C22×C4311yescharacteristic
350#340C22×C4311yescharacteristic
351#336C22×C4311yescharacteristic
352#336C22×C4311yescharacteristic
353C43#2212711yescharacteristic, direct product factor, Sylow
354C22×Q8—21no—
355C22×D4C23×C4311yescharacteristic
356C23×C4—21no—
357C22×C8C23×C4311yescharacteristic
358C22×C8C23×C4311yescharacteristic
359C22×C8C23×C4311yescharacteristic
360C22×C8C23×C4311yescharacteristic
361C4⋊Q8—22no—
362C4⋊Q8C2×C4×C4314yes—
363C4×D4—22no—
364C4×D4C2×C4×C4314yes—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4C23×C4311yescharacteristic
371C2×C4⋊C4C23×C4311yescharacteristic
372C2×C4⋊C4C23×C4311yescharacteristic
373C2×C4⋊C4C23×C4311yescharacteristic
374C2×C4⋊C4C23×C4311yescharacteristic
375C2×C4⋊C4C23×C4311yescharacteristic
376C2×C4⋊C4C23×C4311yescharacteristic
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C42—21no—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42C23×C4311yescharacteristic
386C2×C42C23×C4311yescharacteristic
387C2×C42C23×C4311yescharacteristic
388#107—41no—
389#107C2×C4×C4314yes—
390#107C2×C4×C4314yes—
391#106—41no—
392C4⋊C8—22no—
393C4⋊C8C2×C4×C4314yes—
394#102—41no—
395#102—41no—
396#102C2×C4×C4314yes—
397#102C2×C4×C4314yes—
398#97—41no—
399C4×C8—41no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95D4×C4311yescharacteristic
410#95D4×C4311yescharacteristic
411#95D4×C4311yescharacteristic
412#95D4×C4311yescharacteristic
413C24—21no—
414C2×Q8—24no—
415C2×Q8—81no—
416C2×Q8—81no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4C22×C4×C4312yes—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—24no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—81no—
432C22×C4—81no—
433C22×C4C2×D4×C4311yescharacteristic
434C22×C4C2×D4×C4311yescharacteristic
435C22×C4C2×D4×C4311yescharacteristic
436C22×C4C2×D4×C4311yescharacteristic
437C22×C4C2×D4×C4311yescharacteristic
438C22×C4C2×D4×C4311yescharacteristic
439C22×C4C24×C4311yescharacteristic
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8C22×C4×C4312yes—
451C2×C8C22×C4×C4312yes—
452C4⋊C4—24no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—81no—
465C4⋊C4—81no—
466C4⋊C4—81no—
467C4⋊C4—81no—
468C4⋊C4C22×C4×C4312yes—
469C4⋊C4C22×C4×C4312yes—
470C4⋊C4C22×C4×C4312yes—
471C22⋊C4—24no—
472C22⋊C4—81no—
473C22⋊C4—81no—
474C22⋊C4—81no—
475C22⋊C4—81no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—81no—
481C42—81no—
482C42—81no—
483C42C22×C4×C4312yes—
484C42#41×C4312yes—
485C23—22no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23C22×D4×C4311yescharacteristic
493Q8—84no—
494D4—22no—
495D4—22no—
496D4—41no—
497D4—41no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—84no—
536C2×C4C4×D4×C4312yes—
537C2×C4C4×D4×C4312yes—
538C2×C4C23×C4×C4311yescharacteristic
539C2×C4C2×#41×C4311yescharacteristic
540C2×C4H(5,𝔽2)×C4311yescharacteristic
541C2×C42−1+4×C4311yescharacteristic
542C2×C42−1+4×C4311yescharacteristic
543C2×C42−1+4×C4311yescharacteristic
544C8—22no—
545C8—22no—
546C8—41no—
547C8—41no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22C2×C4×D4×C4311yescharacteristic
556C22C43×#53611yescharacteristic
557C22C43×#53711yescharacteristic
558C22C43×#57611yescharacteristic
559C22C43×#57611yescharacteristic
560C22C43×#57711yescharacteristic
561C22C43×#57811yescharacteristic
562C4—22no—
563C4—22no—
564C4—42no—
565C4—42no—
566C4—42no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—81no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4C43×#51911yescharacteristic
576C4C43×#52011yescharacteristic
577C4C43×#54111yescharacteristic
578C4C43×#54211yescharacteristic
579C2—82no—
580C2C43×#232311yescharacteristic
581C2C43×#294711yescharacteristic
582C2C43×#294811yescharacteristic
583C2C43×#324111yescharacteristic
584C2C43×#324311yescharacteristic
585C2C43×#325711yescharacteristic
586C2C43×#326211yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutatorC2×C4C23×C4×C43
Frattini, cosocleC22×C4C24×C43
prime radicalC22×D4×C43C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C43×#376 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2331C2semidirect
4. C43×#1987C2semidirect
5. C43×#1949C2semidirect
6. C43×#1943C2semidirect
7. C43×#1942C2semidirect
12. C43×#1921C2semidirect
13. C43×#1918C2semidirect
15. C43×#1768C2semidirect
18. C43×#474C4semidirect
254. #22127C43direct (N × H)
287. #2331C2×C43semidirect
289. #1987C2×C43semidirect
290. #1949C2×C43semidirect
291. #1943C2×C43semidirect
292. #1942C2×C43semidirect
297. #1921C2×C43semidirect
298. #1918C2×C43semidirect
300. #1768C2×C43semidirect
311. #474C4×C43semidirect
353. C43#22127direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#4742
C43×#23312
C43×#23192
C43×#19872
C43×#19492
C43×#19432
C43×#19422
C43×#19362
C43×#19342
C43×#19262
C43×#19252
C43×#19212
C43×#19182
C43×#18042
C43×#17682
#2212743