Finite Group Databasebeta

← C43×#25007 #24945024

Subgroups — C43×#25007 #24945024

Order 11008.

700 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
1C43×#2538C211yesmaximal, characteristic
2C43×#2355C211yesmaximal, characteristic, complemented
3C43×#2101C211yesmaximal, characteristic, complemented
4C43×#2100C211yesmaximal, characteristic, complemented
5C43×#2073C211yesmaximal, characteristic
6C43×#2071C211yesmaximal, characteristic
7C43×#1985C211yesmaximal, characteristic, complemented
8C43×#1947C211yesmaximal, characteristic, complemented
9C43×#1925C211yesmaximal, characteristic
10C43×#1925C211yesmaximal, characteristic
11C43×#1921C211yesmaximal, characteristic, complemented
12C43×#1918C211yesmaximal, characteristic, complemented
13C43×#1836C211yesmaximal, characteristic, complemented
14C43×#1804C211yesmaximal, characteristic
15C43×#1762C211yesmaximal, characteristic
16C2×C22⋊Q8×C43—21no—
17C2×C4×Q8×C43C2211yescharacteristic
18C2×C4×D4×C43C2211yescharacteristic
19C2×#107×C43C2211yescharacteristic
20C2×#107×C43C2211yescharacteristic
21C2×C4⋊C8×C43C2211yescharacteristic
22C2×#102×C43C2211yescharacteristic
23C2×#102×C43C2211yescharacteristic
24C2×#102×C43C2211yescharacteristic
25C2×#102×C43C2211yescharacteristic
26C2×#97×C43C2211yescharacteristic
27C43×#396—21no—
28C43×#396—21no—
29C43×#391—21no—
30C43×#390C2211yescharacteristic
31C43×#390C2211yescharacteristic
32C43×#389C2211yescharacteristic
33C43×#389C2211yescharacteristic
34C43×#387—21no—
35C43×#387—21no—
36C43×#384C2211yescharacteristic
37C43×#384C2211yescharacteristic
38C43×#382C2211yescharacteristic
39C43×#382C2211yescharacteristic
40C43×#380—21no—
41C4×C4⋊C4×C43—21no—
42C4×C4⋊C4×C43C2211yescharacteristic
43C4×C4⋊C4×C43C2211yescharacteristic
44C4×C4⋊C4×C43C2211yescharacteristic
45C43×#340C2211yescharacteristic
46C43×#340C2211yescharacteristic
47C43×#340C2211yescharacteristic
48C43×#340C2211yescharacteristic
49C43×#340C2211yescharacteristic
50C43×#340C2211yescharacteristic
51C43×#340C2211yescharacteristic
52C43×#340C2211yescharacteristic
53C43×#340C2211yescharacteristic
54C43×#340C2211yescharacteristic
55C43×#336C2211yescharacteristic
56C43×#336C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Q8×C43D411yescharacteristic
60C22×D4×C43C2311yescharacteristic
61C23×C4×C43—21no—
62C22×C8×C43C2311yescharacteristic
63C22×C8×C43C2311yescharacteristic
64C22×C8×C43C2311yescharacteristic
65C22×C8×C43C2311yescharacteristic
66C22⋊Q8×C43—44no—
67C4×Q8×C43—22no—
68C4×Q8×C43—22no—
69C4×D4×C43—22no—
70C4×D4×C43—22no—
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×C43—21no—
77C2×C4⋊C4×C43D411yescharacteristic
78C2×C4⋊C4×C43D411yescharacteristic
79C2×C4⋊C4×C43D411yescharacteristic
80C2×C4⋊C4×C43C2311yescharacteristic
81C2×C4⋊C4×C43C2311yescharacteristic
82C2×C4⋊C4×C43C2311yescharacteristic
83C2×C4⋊C4×C43C2311yescharacteristic
84C2×C4⋊C4×C43C2311yescharacteristic
85C2×C4⋊C4×C43C2311yescharacteristic
86C2×C4⋊C4×C43C2311yescharacteristic
87C2×C22⋊C4×C43—21no—
88C2×C22⋊C4×C43—21no—
89C2×C22⋊C4×C43—21no—
90C2×C22⋊C4×C43—21no—
91C2×C22⋊C4×C43—21no—
92C2×C42×C43—21no—
93C2×C42×C43—21no—
94C2×C42×C43—21no—
95C2×C42×C43C2311yescharacteristic
96C2×C42×C43C2311yescharacteristic
97C2×C42×C43C2311yescharacteristic
98#107×C43—22no—
99#107×C43—22no—
100C4⋊C8×C43—22no—
101#102×C43—22no—
102#102×C43—22no—
103#102×C43—22no—
104#102×C43—22no—
105#97×C43—22no—
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—
115C24×C43—21no—
116C2×Q8×C43—22no—
117C2×Q8×C43—22no—
118C2×Q8×C43—41no—
119C2×D4×C43—21no—
120C2×D4×C43—21no—
121C2×D4×C43—21no—
122C2×D4×C43—21no—
123C2×D4×C43—21no—
124C2×D4×C43#4112yes—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—42no—
133C22×C4×C43—42no—
134C22×C4×C43—42no—
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2411yescharacteristic
142C2×C8×C43—21no—
143C2×C8×C43—21no—
144C2×C8×C43—21no—
145C2×C8×C43—21no—
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—
154C4⋊C4×C43—22no—
155C4⋊C4×C43—22no—
156C4⋊C4×C43—22no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
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—42no—
171C4⋊C4×C43—42no—
172C4⋊C4×C43—42no—
173C4⋊C4×C43—42no—
174C4⋊C4×C43—81no—
175C4⋊C4×C43—81no—
176C4⋊C4×C43#4112yes—
177C22⋊C4×C43—42no—
178C22⋊C4×C43—42no—
179C22⋊C4×C43—42no—
180C22⋊C4×C43—81no—
181C22⋊C4×C43—81no—
182C42×C43—21no—
183C42×C43—21no—
184C42×C43—21no—
185C42×C43—21no—
186C42×C43—42no—
187C42×C43—81no—
188C42×C43—81no—
189C42×C43#4112yes—
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—44no—
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—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—22no—
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—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
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—84no—
241C2×C4×C43#12312yes—
242C2×C4×C43#12312yes—
243C2×C4×C43AGL(1,ℤ/8)12yes—
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C432−1+411yescharacteristic
249C2×C4×C432−1+411yescharacteristic
250C8×C43—41no—
251C8×C43—41no—
252C8×C43—41no—
253C8×C43—41no—
254#25007C4311yesmaximal, 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×#12311yescharacteristic
263C22×C43#54811yescharacteristic
264C22×C43#54811yescharacteristic
265C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
266C22×C43#57511yescharacteristic
267C22×C43#57611yescharacteristic
268C22×C43#57811yescharacteristic
269C4×C43—22no—
270C4×C43—22no—
271C4×C43—22no—
272C4×C43—41no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43—42no—
276C4×C43—81no—
277C4×C43—81no—
278C4×C43—81no—
279C4×C43—81no—
280C4×C43—81no—
281C4×C43—81no—
282C4×C43#52911yescharacteristic
283C4×C43#54111yescharacteristic
284C4×C43#55211yescharacteristic
285C4×C43#55611yescharacteristic
286#2538C2×C4311yescharacteristic
287#2355C2×C4311yescharacteristic, complemented
288#2101C2×C4311yescharacteristic, complemented
289#2100C2×C4311yescharacteristic, complemented
290#2073C2×C4311yescharacteristic
291#2071C2×C4311yescharacteristic
292#1985C2×C4311yescharacteristic, complemented
293#1947C2×C4311yescharacteristic, complemented
294#1925C2×C4311yescharacteristic
295#1925C2×C4311yescharacteristic
296#1921C2×C4311yescharacteristic, complemented
297#1918C2×C4311yescharacteristic, complemented
298#1836C2×C4311yescharacteristic, complemented
299#1804C2×C4311yescharacteristic
300#1762C2×C4311yescharacteristic
301C2×C43—82no—
302C2×C43#242111yescharacteristic
303C2×C43#309411yescharacteristic
304C2×C43#309811yescharacteristic
305C2×C43#336611yescharacteristic
306C2×C43#336711yescharacteristic
307C2×C43#337011yescharacteristic
308C2×C43#337711yescharacteristic
309C2×C22⋊Q8—21no—
310C2×C4×Q8C22×C4311yescharacteristic
311C2×C4×D4C22×C4311yescharacteristic
312C2×#107C22×C4311yescharacteristic
313C2×#107C22×C4311yescharacteristic
314C2×C4⋊C8C22×C4311yescharacteristic
315C2×#102C22×C4311yescharacteristic
316C2×#102C22×C4311yescharacteristic
317C2×#102C22×C4311yescharacteristic
318C2×#102C22×C4311yescharacteristic
319C2×#97C22×C4311yescharacteristic
320#396—21no—
321#396—21no—
322#391—21no—
323#390C22×C4311yescharacteristic
324#390C22×C4311yescharacteristic
325#389C22×C4311yescharacteristic
326#389C22×C4311yescharacteristic
327#387—21no—
328#387—21no—
329#384C22×C4311yescharacteristic
330#384C22×C4311yescharacteristic
331#382C22×C4311yescharacteristic
332#382C22×C4311yescharacteristic
333#380—21no—
334C4×C4⋊C4—21no—
335C4×C4⋊C4C22×C4311yescharacteristic
336C4×C4⋊C4C22×C4311yescharacteristic
337C4×C4⋊C4C22×C4311yescharacteristic
338#340C22×C4311yescharacteristic
339#340C22×C4311yescharacteristic
340#340C22×C4311yescharacteristic
341#340C22×C4311yescharacteristic
342#340C22×C4311yescharacteristic
343#340C22×C4311yescharacteristic
344#340C22×C4311yescharacteristic
345#340C22×C4311yescharacteristic
346#340C22×C4311yescharacteristic
347#340C22×C4311yescharacteristic
348#336C22×C4311yescharacteristic
349#336C22×C4311yescharacteristic
350#336C22×C4311yescharacteristic
351#336C22×C4311yescharacteristic
352C43#2500711yescharacteristic, direct product factor, Sylow
353C22×Q8D4×C4311yescharacteristic
354C22×D4C23×C4311yescharacteristic
355C23×C4—21no—
356C22×C8C23×C4311yescharacteristic
357C22×C8C23×C4311yescharacteristic
358C22×C8C23×C4311yescharacteristic
359C22×C8C23×C4311yescharacteristic
360C22⋊Q8—44no—
361C4×Q8—22no—
362C4×Q8—22no—
363C4×D4—22no—
364C4×D4—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4D4×C4311yescharacteristic
372C2×C4⋊C4D4×C4311yescharacteristic
373C2×C4⋊C4D4×C4311yescharacteristic
374C2×C4⋊C4C23×C4311yescharacteristic
375C2×C4⋊C4C23×C4311yescharacteristic
376C2×C4⋊C4C23×C4311yescharacteristic
377C2×C4⋊C4C23×C4311yescharacteristic
378C2×C4⋊C4C23×C4311yescharacteristic
379C2×C4⋊C4C23×C4311yescharacteristic
380C2×C4⋊C4C23×C4311yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42C23×C4311yescharacteristic
390C2×C42C23×C4311yescharacteristic
391C2×C42C23×C4311yescharacteristic
392#107—22no—
393#107—22no—
394C4⋊C8—22no—
395#102—22no—
396#102—22no—
397#102—22no—
398#102—22no—
399#97—22no—
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—
409C24—21no—
410C2×Q8—22no—
411C2×Q8—22no—
412C2×Q8—41no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4#41×C4312yes—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4C2×D4×C4311yescharacteristic
430C22×C4C2×D4×C4311yescharacteristic
431C22×C4C2×D4×C4311yescharacteristic
432C22×C4C2×D4×C4311yescharacteristic
433C22×C4C2×D4×C4311yescharacteristic
434C22×C4C2×D4×C4311yescharacteristic
435C22×C4C24×C4311yescharacteristic
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—21no—
452C4⋊C4—21no—
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—42no—
465C4⋊C4—42no—
466C4⋊C4—42no—
467C4⋊C4—42no—
468C4⋊C4—81no—
469C4⋊C4—81no—
470C4⋊C4#41×C4312yes—
471C22⋊C4—42no—
472C22⋊C4—42no—
473C22⋊C4—42no—
474C22⋊C4—81no—
475C22⋊C4—81no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—42no—
481C42—81no—
482C42—81no—
483C42#41×C4312yes—
484C42#41×C4312yes—
485C23—22no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23C22×D4×C4311yescharacteristic
493Q8—44no—
494D4—22no—
495D4—22no—
496D4—41no—
497D4—41no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
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—84no—
535C2×C4#123×C4312yes—
536C2×C4#123×C4312yes—
537C2×C4AGL(1,ℤ/8)×C4312yes—
538C2×C4C2×#41×C4311yescharacteristic
539C2×C4C2×#41×C4311yescharacteristic
540C2×C4C2×#41×C4311yescharacteristic
541C2×C4C2×#41×C4311yescharacteristic
542C2×C42−1+4×C4311yescharacteristic
543C2×C42−1+4×C4311yescharacteristic
544C8—41no—
545C8—41no—
546C8—41no—
547C8—41no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22C2×#123×C4311yescharacteristic
556C22C43×#54811yescharacteristic
557C22C43×#54811yescharacteristic
558C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
559C22C43×#57511yescharacteristic
560C22C43×#57611yescharacteristic
561C22C43×#57811yescharacteristic
562C4—22no—
563C4—22no—
564C4—22no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—42no—
569C4—81no—
570C4—81no—
571C4—81no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4C43×#52911yescharacteristic
576C4C43×#54111yescharacteristic
577C4C43×#55211yescharacteristic
578C4C43×#55611yescharacteristic
579C2—82no—
580C2C43×#242111yescharacteristic
581C2C43×#309411yescharacteristic
582C2C43×#309811yescharacteristic
583C2C43×#336611yescharacteristic
584C2C43×#336711yescharacteristic
585C2C43×#337011yescharacteristic
586C2C43×#337711yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC22×D4×C43C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C2×C4×Q8×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2355C2semidirect
3. C43×#2101C2semidirect
4. C43×#2100C2semidirect
7. C43×#1985C2semidirect
8. C43×#1947C2semidirect
11. C43×#1921C2semidirect
12. C43×#1918C2semidirect
13. C43×#1836C2semidirect
254. #25007C43direct (N × H)
287. #2355C2×C43semidirect
288. #2101C2×C43semidirect
289. #2100C2×C43semidirect
292. #1985C2×C43semidirect
293. #1947C2×C43semidirect
296. #1921C2×C43semidirect
297. #1918C2×C43semidirect
298. #1836C2×C43semidirect
352. C43#25007direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#25382
C43×#23552
C43×#21012
C43×#21002
C43×#20732
C43×#20712
C43×#19852
C43×#19472
C43×#19252
C43×#19212
C43×#19182
C43×#18362
C43×#18042
C43×#17622
#2500743