Finite Group Databasebeta

← C43×#25465 #24945482

Subgroups — C43×#25465 #24945482

Order 11008.

812 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#501C211yesmaximal, characteristic, complemented
2C2×C43×#478C211yesmaximal, characteristic
3C43×#2542C211yesmaximal, characteristic
4C43×#2370C211yesmaximal, characteristic, complemented
5C43×#2084C211yesmaximal, characteristic, complemented
6C43×#2083C211yesmaximal, characteristic, complemented
7C43×#2067C211yesmaximal, characteristic
8C43×#2065C211yesmaximal, characteristic
9C43×#1987C211yesmaximal, characteristic, complemented
10C43×#1948C211yesmaximal, characteristic, complemented
11C43×#1947C211yesmaximal, characteristic, complemented
12C43×#1940C211yesmaximal, characteristic, complemented
13C43×#1926C211yesmaximal, characteristic
14C43×#1925C211yesmaximal, characteristic
15C43×#1762C211yesmaximal, characteristic
16C2×C4⋊Q8×C43C2211yescharacteristic
17C2×#125×C43C2211yescharacteristic
18C2×C22⋊Q8×C43—21no—
19C2×C22⋊Q8×C43—21no—
20C2×C4×D4×C43C2211yescharacteristic
21C43×#501—24no—
22C43×#478—24no—
23C2×#107×C43C2211yescharacteristic
24C2×#107×C43C2211yescharacteristic
25C2×#107×C43C2211yescharacteristic
26C2×#106×C43C2211yescharacteristic
27C2×#106×C43C2211yescharacteristic
28C2×#106×C43C2211yescharacteristic
29C2×C4⋊C8×C43C2211yescharacteristic
30C2×C4⋊C8×C43C2211yescharacteristic
31C2×C4⋊C8×C43C2211yescharacteristic
32C2×#102×C43C2211yescharacteristic
33C2×#102×C43C2211yescharacteristic
34C2×#102×C43C2211yescharacteristic
35C2×#102×C43C2211yescharacteristic
36C2×#97×C43C2211yescharacteristic
37C43×#399—21no—
38C43×#399—21no—
39C43×#390C2211yescharacteristic
40C43×#390C2211yescharacteristic
41C43×#389—21no—
42C43×#389C2211yescharacteristic
43C43×#389C2211yescharacteristic
44C43×#387—21no—
45C43×#387—21no—
46C43×#384C2211yescharacteristic
47C43×#384C2211yescharacteristic
48C4×C4⋊C4×C43—21no—
49C4×C4⋊C4×C43C2211yescharacteristic
50C4×C4⋊C4×C43C2211yescharacteristic
51C4×C4⋊C4×C43C2211yescharacteristic
52C4×C4⋊C4×C43C2211yescharacteristic
53C43×#340C2211yescharacteristic
54C43×#340C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×Q8×C43—21no—
62C22×D4×C43C2311yescharacteristic
63C23×C4×C43—21no—
64C22×C8×C43C2311yescharacteristic
65C22×C8×C43C2311yescharacteristic
66C22×C8×C43C2311yescharacteristic
67C22×C8×C43C2311yescharacteristic
68C4⋊Q8×C43—22no—
69C4⋊Q8×C43—22no—
70#125×C43—22no—
71#125×C43D414yes—
72C22⋊Q8×C43—44no—
73C22⋊Q8×C43—44no—
74C4×D4×C43—22no—
75C4×D4×C43—22no—
76C2×C4⋊C4×C43—21no—
77C2×C4⋊C4×C43—21no—
78C2×C4⋊C4×C43—21no—
79C2×C4⋊C4×C43—21no—
80C2×C4⋊C4×C43—21no—
81C2×C4⋊C4×C43—21no—
82C2×C4⋊C4×C43—21no—
83C2×C4⋊C4×C43—21no—
84C2×C4⋊C4×C43—21no—
85C2×C4⋊C4×C43D411yescharacteristic
86C2×C4⋊C4×C43D411yescharacteristic
87C2×C4⋊C4×C43C2311yescharacteristic
88C2×C4⋊C4×C43C2311yescharacteristic
89C2×C4⋊C4×C43C2311yescharacteristic
90C2×C4⋊C4×C43C2311yescharacteristic
91C2×C4⋊C4×C43C2311yescharacteristic
92C2×C4⋊C4×C43C2311yescharacteristic
93C2×C4⋊C4×C43C2311yescharacteristic
94C2×C22⋊C4×C43—21no—
95C2×C22⋊C4×C43—21no—
96C2×C22⋊C4×C43—21no—
97C2×C22⋊C4×C43—21no—
98C2×C22⋊C4×C43—21no—
99C2×C42×C43—21no—
100C2×C42×C43—21no—
101C2×C42×C43—21no—
102C2×C42×C43C2311yescharacteristic
103C2×C42×C43C2311yescharacteristic
104C2×C42×C43C2311yescharacteristic
105#107×C43—22no—
106#107×C43—22no—
107#107×C43—22no—
108#106×C43—22no—
109#106×C43—22no—
110#106×C43—22no—
111C4⋊C8×C43—22no—
112C4⋊C8×C43—22no—
113C4⋊C8×C43—22no—
114#102×C43—22no—
115#102×C43—22no—
116#102×C43—22no—
117#102×C43Q814yescomplemented
118#97×C43—22no—
119#95×C43—21no—
120#95×C43—21no—
121#95×C43—21no—
122#95×C43—21no—
123#95×C43—21no—
124#95×C43D411yescharacteristic
125#95×C43D411yescharacteristic
126C24×C43—21no—
127C2×Q8×C43—42no—
128C2×Q8×C43—42no—
129C2×Q8×C43—42no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43C2×Q812yes—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—42no—
144C22×C4×C43—42no—
145C22×C4×C43—42no—
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2411yescharacteristic
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43C2×Q812yes—
164C2×C8×C43#4112yes—
165C4⋊C4×C43—24no—
166C4⋊C4×C43—24no—
167C4⋊C4×C43—22no—
168C4⋊C4×C43—22no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—42no—
181C4⋊C4×C43—42no—
182C4⋊C4×C43—42no—
183C4⋊C4×C43—42no—
184C4⋊C4×C43—42no—
185C4⋊C4×C43—42no—
186C4⋊C4×C43—81no—
187C4⋊C4×C43C2×D412yes—
188C4⋊C4×C43C2×D412yes—
189C4⋊C4×C43C2×Q812yes—
190C22⋊C4×C43—42no—
191C22⋊C4×C43—42no—
192C22⋊C4×C43—42no—
193C22⋊C4×C43—42no—
194C22⋊C4×C43—42no—
195C42×C43—21no—
196C42×C43—21no—
197C42×C43—21no—
198C42×C43—21no—
199C42×C43—42no—
200C42×C43—81no—
201C42×C43—81no—
202C42×C43C2×D412yes—
203C42×C43#4112yes—
204C23×C43—22no—
205C23×C43—41no—
206C23×C43—41no—
207C23×C43—41no—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43C22×D411yescharacteristic
212Q8×C43—84no—
213D4×C43—22no—
214D4×C43—22no—
215D4×C43—41no—
216D4×C43—41no—
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—21no—
224C2×C4×C43—21no—
225C2×C4×C43—22no—
226C2×C4×C43—22no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—22no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
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—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—84no—
253C2×C4×C43#12112yes—
254C2×C4×C43#12112yes—
255C2×C4×C43AGL(1,ℤ/8)12yes—
256C2×C4×C43AGL(1,ℤ/8)12yes—
257C2×C4×C43C22×D411yescharacteristic
258C2×C4×C43C22×Q811yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C432−1+411yescharacteristic
262C2×C4×C432−1+411yescharacteristic
263C8×C43—22no—
264C8×C43—22no—
265C8×C43—41no—
266C8×C43—41no—
267#25465C4311yesmaximal, characteristic, direct product factor, Sylow
268C22×C43—42no—
269C22×C43—42no—
270C22×C43—42no—
271C22×C43—81no—
272C22×C43—81no—
273C22×C43—81no—
274C22×C43—81no—
275C22×C43C2×#12111yescharacteristic
276C22×C43#54711yescharacteristic
277C22×C43D4×Q811yescharacteristic
278C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
279C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
280C22×C43#57711yescharacteristic
281C22×C43#57811yescharacteristic
282C4×C43—22no—
283C4×C43—22no—
284C4×C43—22no—
285C4×C43—22no—
286C4×C43—41no—
287C4×C43—41no—
288C4×C43—42no—
289C4×C43—42no—
290C4×C43—42no—
291C4×C43—81no—
292C4×C43—81no—
293C4×C43—81no—
294C4×C43—81no—
295C4×C43#53311yescharacteristic
296C4×C43#54111yescharacteristic
297C4×C43#54811yescharacteristic
298C4×C43D4×Q811yescharacteristic
299C2×#501C2×C4311yescharacteristic, complemented
300C2×#478C2×C4311yescharacteristic
301#2542C2×C4311yescharacteristic
302#2370C2×C4311yescharacteristic, complemented
303#2084C2×C4311yescharacteristic, complemented
304#2083C2×C4311yescharacteristic, complemented
305#2067C2×C4311yescharacteristic
306#2065C2×C4311yescharacteristic
307#1987C2×C4311yescharacteristic, complemented
308#1948C2×C4311yescharacteristic, complemented
309#1947C2×C4311yescharacteristic, complemented
310#1940C2×C4311yescharacteristic, complemented
311#1926C2×C4311yescharacteristic
312#1925C2×C4311yescharacteristic
313#1762C2×C4311yescharacteristic
314C2×C43—82no—
315C2×C43#242911yescharacteristic
316C2×C43#303811yescharacteristic
317C2×C43#304611yescharacteristic
318C2×C43#334311yescharacteristic
319C2×C43#334511yescharacteristic
320C2×C43#338411yescharacteristic
321C2×C43#338611yescharacteristic
322C2×C4⋊Q8C22×C4311yescharacteristic
323C2×#125C22×C4311yescharacteristic
324C2×C22⋊Q8—21no—
325C2×C22⋊Q8—21no—
326C2×C4×D4C22×C4311yescharacteristic
327#501—24no—
328#478—24no—
329C2×#107C22×C4311yescharacteristic
330C2×#107C22×C4311yescharacteristic
331C2×#107C22×C4311yescharacteristic
332C2×#106C22×C4311yescharacteristic
333C2×#106C22×C4311yescharacteristic
334C2×#106C22×C4311yescharacteristic
335C2×C4⋊C8C22×C4311yescharacteristic
336C2×C4⋊C8C22×C4311yescharacteristic
337C2×C4⋊C8C22×C4311yescharacteristic
338C2×#102C22×C4311yescharacteristic
339C2×#102C22×C4311yescharacteristic
340C2×#102C22×C4311yescharacteristic
341C2×#102C22×C4311yescharacteristic
342C2×#97C22×C4311yescharacteristic
343#399—21no—
344#399—21no—
345#390C22×C4311yescharacteristic
346#390C22×C4311yescharacteristic
347#389—21no—
348#389C22×C4311yescharacteristic
349#389C22×C4311yescharacteristic
350#387—21no—
351#387—21no—
352#384C22×C4311yescharacteristic
353#384C22×C4311yescharacteristic
354C4×C4⋊C4—21no—
355C4×C4⋊C4C22×C4311yescharacteristic
356C4×C4⋊C4C22×C4311yescharacteristic
357C4×C4⋊C4C22×C4311yescharacteristic
358C4×C4⋊C4C22×C4311yescharacteristic
359#340C22×C4311yescharacteristic
360#340C22×C4311yescharacteristic
361#340C22×C4311yescharacteristic
362#340C22×C4311yescharacteristic
363#340C22×C4311yescharacteristic
364#340C22×C4311yescharacteristic
365#336C22×C4311yescharacteristic
366#336C22×C4311yescharacteristic
367C43#2546511yescharacteristic, direct product factor, Sylow
368C22×Q8—21no—
369C22×D4C23×C4311yescharacteristic
370C23×C4—21no—
371C22×C8C23×C4311yescharacteristic
372C22×C8C23×C4311yescharacteristic
373C22×C8C23×C4311yescharacteristic
374C22×C8C23×C4311yescharacteristic
375C4⋊Q8—22no—
376C4⋊Q8—22no—
377#125—22no—
378#125D4×C4314yes—
379C22⋊Q8—44no—
380C22⋊Q8—44no—
381C4×D4—22no—
382C4×D4—22no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4D4×C4311yescharacteristic
393C2×C4⋊C4D4×C4311yescharacteristic
394C2×C4⋊C4C23×C4311yescharacteristic
395C2×C4⋊C4C23×C4311yescharacteristic
396C2×C4⋊C4C23×C4311yescharacteristic
397C2×C4⋊C4C23×C4311yescharacteristic
398C2×C4⋊C4C23×C4311yescharacteristic
399C2×C4⋊C4C23×C4311yescharacteristic
400C2×C4⋊C4C23×C4311yescharacteristic
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C42—21no—
407C2×C42—21no—
408C2×C42—21no—
409C2×C42C23×C4311yescharacteristic
410C2×C42C23×C4311yescharacteristic
411C2×C42C23×C4311yescharacteristic
412#107—22no—
413#107—22no—
414#107—22no—
415#106—22no—
416#106—22no—
417#106—22no—
418C4⋊C8—22no—
419C4⋊C8—22no—
420C4⋊C8—22no—
421#102—22no—
422#102—22no—
423#102—22no—
424#102Q8×C4314yescomplemented
425#97—22no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95D4×C4311yescharacteristic
432#95D4×C4311yescharacteristic
433C24—21no—
434C2×Q8—42no—
435C2×Q8—42no—
436C2×Q8—42no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4C2×Q8×C4312yes—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4C2×D4×C4311yescharacteristic
454C22×C4C2×D4×C4311yescharacteristic
455C22×C4C2×D4×C4311yescharacteristic
456C22×C4C2×D4×C4311yescharacteristic
457C22×C4C2×D4×C4311yescharacteristic
458C22×C4C2×D4×C4311yescharacteristic
459C22×C4C24×C4311yescharacteristic
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8C2×Q8×C4312yes—
471C2×C8#41×C4312yes—
472C4⋊C4—24no—
473C4⋊C4—24no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—42no—
488C4⋊C4—42no—
489C4⋊C4—42no—
490C4⋊C4—42no—
491C4⋊C4—42no—
492C4⋊C4—42no—
493C4⋊C4—81no—
494C4⋊C4C2×D4×C4312yes—
495C4⋊C4C2×D4×C4312yes—
496C4⋊C4C2×Q8×C4312yes—
497C22⋊C4—42no—
498C22⋊C4—42no—
499C22⋊C4—42no—
500C22⋊C4—42no—
501C22⋊C4—42no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—42no—
507C42—81no—
508C42—81no—
509C42C2×D4×C4312yes—
510C42#41×C4312yes—
511C23—22no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23C22×D4×C4311yescharacteristic
519Q8—84no—
520D4—22no—
521D4—22no—
522D4—41no—
523D4—41no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—84no—
560C2×C4#121×C4312yes—
561C2×C4#121×C4312yes—
562C2×C4AGL(1,ℤ/8)×C4312yes—
563C2×C4AGL(1,ℤ/8)×C4312yes—
564C2×C4C22×D4×C4311yescharacteristic
565C2×C4C22×Q8×C4311yescharacteristic
566C2×C4C2×#41×C4311yescharacteristic
567C2×C4C2×#41×C4311yescharacteristic
568C2×C42−1+4×C4311yescharacteristic
569C2×C42−1+4×C4311yescharacteristic
570C8—22no—
571C8—22no—
572C8—41no—
573C8—41no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22C2×#121×C4311yescharacteristic
582C22C43×#54711yescharacteristic
583C22D4×Q8×C4311yescharacteristic
584C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
585C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
586C22C43×#57711yescharacteristic
587C22C43×#57811yescharacteristic
588C4—22no—
589C4—22no—
590C4—22no—
591C4—22no—
592C4—41no—
593C4—41no—
594C4—42no—
595C4—42no—
596C4—42no—
597C4—81no—
598C4—81no—
599C4—81no—
600C4—81no—
601C4C43×#53311yescharacteristic
602C4C43×#54111yescharacteristic
603C4C43×#54811yescharacteristic
604C4D4×Q8×C4311yescharacteristic
605C2—82no—
606C2C43×#242911yescharacteristic
607C2C43×#303811yescharacteristic
608C2C43×#304611yescharacteristic
609C2C43×#334311yescharacteristic
610C2C43×#334511yescharacteristic
611C2C43×#338411yescharacteristic
612C2C43×#338611yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC22×D4×C43C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C4×C4⋊C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#501C2semidirect
4. C43×#2370C2semidirect
5. C43×#2084C2semidirect
6. C43×#2083C2semidirect
9. C43×#1987C2semidirect
10. C43×#1948C2semidirect
11. C43×#1947C2semidirect
12. C43×#1940C2semidirect
117. #102×C43Q8semidirect
267. #25465C43direct (N × H)
299. C2×#501C2×C43semidirect
302. #2370C2×C43semidirect
303. #2084C2×C43semidirect
304. #2083C2×C43semidirect
307. #1987C2×C43semidirect
308. #1948C2×C43semidirect
309. #1947C2×C43semidirect
310. #1940C2×C43semidirect
367. C43#25465direct (N × H)
424. #102Q8×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#5012
C2×C43×#4782
C43×#25422
C43×#23702
C43×#20842
C43×#20832
C43×#20672
C43×#20652
C43×#19872
C43×#19482
C43×#19472
C43×#19402
C43×#19262
C43×#19252
C43×#17622
#2546543