Finite Group Databasebeta

← C43×#25457 #24945474

Subgroups — C43×#25457 #24945474

Order 11008.

754 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#499C211yesmaximal, characteristic, complemented
2C2×C43×#478C211yesmaximal, characteristic
3C43×#2566C211yesmaximal, characteristic
4C43×#2370C211yesmaximal, characteristic, complemented
5C43×#2085C211yesmaximal, characteristic, complemented
6C43×#2084C211yesmaximal, characteristic, complemented
7C43×#2067C211yesmaximal, characteristic
8C43×#2067C211yesmaximal, characteristic
9C43×#1989C211yesmaximal, characteristic, complemented
10C43×#1949C211yesmaximal, characteristic, complemented
11C43×#1947C211yesmaximal, characteristic, complemented
12C43×#1939C211yesmaximal, characteristic, complemented
13C43×#1926C211yesmaximal, characteristic
14C43×#1926C211yesmaximal, characteristic
15C4×#102×C43C211yesmaximal, characteristic
16C2×#125×C43C2211yescharacteristic
17C2×#125×C43C2211yescharacteristic
18C2×C4×D4×C43C2211yescharacteristic
19C43×#499—24no—
20C43×#478—24no—
21C2×#107×C43C2211yescharacteristic
22C2×#107×C43C2211yescharacteristic
23C2×#107×C43C2211yescharacteristic
24C2×#106×C43C2211yescharacteristic
25C2×#106×C43C2211yescharacteristic
26C2×#106×C43C2211yescharacteristic
27C2×C4⋊C8×C43C2211yescharacteristic
28C2×C4⋊C8×C43C2211yescharacteristic
29C2×C4⋊C8×C43C2211yescharacteristic
30C2×#102×C43C2211yescharacteristic
31C2×#102×C43C2211yescharacteristic
32C2×#102×C43C2211yescharacteristic
33C2×#102×C43C2211yescharacteristic
34C2×C4×C8×C43C2211yescharacteristic
35C43×#396—21no—
36C43×#396—21no—
37C43×#390C2211yescharacteristic
38C43×#390C2211yescharacteristic
39C43×#389—21no—
40C43×#389C2211yescharacteristic
41C43×#389C2211yescharacteristic
42C43×#387—21no—
43C43×#387—21no—
44C43×#385—21no—
45C43×#385—21no—
46C43×#384C2211yescharacteristic
47C43×#382C2211yescharacteristic
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×D4×C43C2311yescharacteristic
62C23×C4×C43—21no—
63C22×C8×C43C2311yescharacteristic
64C22×C8×C43C2311yescharacteristic
65C22×C8×C43C2311yescharacteristic
66C22×C8×C43C2311yescharacteristic
67#125×C43—22no—
68#125×C43—22no—
69#125×C43—22no—
70#125×C43D414yes—
71C4×D4×C43—22no—
72C4×D4×C43—22no—
73C2×C4⋊C4×C43—21no—
74C2×C4⋊C4×C43—21no—
75C2×C4⋊C4×C43—21no—
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×C43D411yescharacteristic
82C2×C4⋊C4×C43D411yescharacteristic
83C2×C4⋊C4×C43C2311yescharacteristic
84C2×C4⋊C4×C43C2311yescharacteristic
85C2×C4⋊C4×C43C2311yescharacteristic
86C2×C4⋊C4×C43C2311yescharacteristic
87C2×C4⋊C4×C43C2311yescharacteristic
88C2×C4⋊C4×C43C2311yescharacteristic
89C2×C4⋊C4×C43C2311yescharacteristic
90C2×C22⋊C4×C43—21no—
91C2×C22⋊C4×C43—21no—
92C2×C22⋊C4×C43—21no—
93C2×C22⋊C4×C43—21no—
94C2×C22⋊C4×C43—21no—
95C2×C42×C43—21no—
96C2×C42×C43—21no—
97C2×C42×C43—21no—
98C2×C42×C43C2311yescharacteristic
99C2×C42×C43C2311yescharacteristic
100C2×C42×C43C2311yescharacteristic
101#107×C43—22no—
102#107×C43—22no—
103#107×C43—22no—
104#106×C43—22no—
105#106×C43—22no—
106#106×C43—22no—
107C4⋊C8×C43—22no—
108C4⋊C8×C43—22no—
109C4⋊C8×C43—22no—
110#102×C43—22no—
111#102×C43—22no—
112#102×C43—22no—
113#102×C43Q814yes—
114C4×C8×C43—22no—
115#95×C43—21no—
116#95×C43—21no—
117#95×C43—21no—
118#95×C43—21no—
119#95×C43—21no—
120#95×C43—21no—
121#95×C43—21no—
122#95×C43D411yescharacteristic
123#95×C43D411yescharacteristic
124C24×C43—21no—
125C2×D4×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43C2×Q812yes—
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—21no—
138C22×C4×C43—42no—
139C22×C4×C43—81no—
140C22×C4×C43—81no—
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2411yescharacteristic
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×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43C2×Q812yes—
159C2×C8×C43#4112yes—
160C4⋊C4×C43—24no—
161C4⋊C4×C43—24no—
162C4⋊C4×C43—22no—
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—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—41no—
175C4⋊C4×C43—42no—
176C4⋊C4×C43—42no—
177C4⋊C4×C43—42no—
178C4⋊C4×C43—81no—
179C4⋊C4×C43—81no—
180C4⋊C4×C43—81no—
181C4⋊C4×C43C2×D412yes—
182C4⋊C4×C43C2×D412yes—
183C4⋊C4×C43C2×Q812yes—
184C22⋊C4×C43—42no—
185C22⋊C4×C43—42no—
186C22⋊C4×C43—42no—
187C22⋊C4×C43—81no—
188C22⋊C4×C43—81no—
189C42×C43—21no—
190C42×C43—21no—
191C42×C43—21no—
192C42×C43—21no—
193C42×C43—42no—
194C42×C43—81no—
195C42×C43—81no—
196C42×C43C2×D412yes—
197C42×C43#4112yes—
198C23×C43—22no—
199C23×C43—41no—
200C23×C43—41no—
201C23×C43—41no—
202C23×C43—41no—
203C23×C43—41no—
204C23×C43—41no—
205C23×C43C22×D411yescharacteristic
206D4×C43—22no—
207D4×C43—22no—
208D4×C43—41no—
209D4×C43—41no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—22no—
217C2×C4×C43—22no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—22no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
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—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—84no—
247C2×C4×C43#12112yes—
248C2×C4×C43#12112yes—
249C2×C4×C43#13512yes—
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43C22×Q811yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C432−1+411yescharacteristic
255C2×C4×C432−1+411yescharacteristic
256C8×C43—22no—
257C8×C43—22no—
258C8×C43—41no—
259C8×C43—41no—
260#25457C4311yesmaximal, characteristic, direct product factor, Sylow
261C22×C43—42no—
262C22×C43—42no—
263C22×C43—42no—
264C22×C43—81no—
265C22×C43—81no—
266C22×C43—81no—
267C22×C43—81no—
268C22×C43C2×#12111yescharacteristic
269C22×C43#54711yescharacteristic
270C22×C43D4×Q811yescharacteristic
271C22×C43C2×#13511yescharacteristic
272C22×C43#57511yescharacteristic
273C22×C43#57611yescharacteristic
274C22×C43#57711yescharacteristic
275C4×C43—22no—
276C4×C43—22no—
277C4×C43—22no—
278C4×C43—41no—
279C4×C43—41no—
280C4×C43—41no—
281C4×C43—42no—
282C4×C43—42no—
283C4×C43—42no—
284C4×C43—81no—
285C4×C43—81no—
286C4×C43—81no—
287C4×C43—81no—
288C4×C43#53311yescharacteristic
289C4×C43#54111yescharacteristic
290C4×C43#54811yescharacteristic
291C4×C43D4×Q811yescharacteristic
292C2×#499C2×C4311yescharacteristic, complemented
293C2×#478C2×C4311yescharacteristic
294#2566C2×C4311yescharacteristic
295#2370C2×C4311yescharacteristic, complemented
296#2085C2×C4311yescharacteristic, complemented
297#2084C2×C4311yescharacteristic, complemented
298#2067C2×C4311yescharacteristic
299#2067C2×C4311yescharacteristic
300#1989C2×C4311yescharacteristic, complemented
301#1949C2×C4311yescharacteristic, complemented
302#1947C2×C4311yescharacteristic, complemented
303#1939C2×C4311yescharacteristic, complemented
304#1926C2×C4311yescharacteristic
305#1926C2×C4311yescharacteristic
306C4×#102C2×C4311yescharacteristic
307C2×C43—82no—
308C2×C43#242911yescharacteristic
309C2×C43#303511yescharacteristic
310C2×C43#304511yescharacteristic
311C2×C43#333911yescharacteristic
312C2×C43#335111yescharacteristic
313C2×C43#338111yescharacteristic
314C2×C43#338911yescharacteristic
315C2×#125C22×C4311yescharacteristic
316C2×#125C22×C4311yescharacteristic
317C2×C4×D4C22×C4311yescharacteristic
318#499—24no—
319#478—24no—
320C2×#107C22×C4311yescharacteristic
321C2×#107C22×C4311yescharacteristic
322C2×#107C22×C4311yescharacteristic
323C2×#106C22×C4311yescharacteristic
324C2×#106C22×C4311yescharacteristic
325C2×#106C22×C4311yescharacteristic
326C2×C4⋊C8C22×C4311yescharacteristic
327C2×C4⋊C8C22×C4311yescharacteristic
328C2×C4⋊C8C22×C4311yescharacteristic
329C2×#102C22×C4311yescharacteristic
330C2×#102C22×C4311yescharacteristic
331C2×#102C22×C4311yescharacteristic
332C2×#102C22×C4311yescharacteristic
333C2×C4×C8C22×C4311yescharacteristic
334#396—21no—
335#396—21no—
336#390C22×C4311yescharacteristic
337#390C22×C4311yescharacteristic
338#389—21no—
339#389C22×C4311yescharacteristic
340#389C22×C4311yescharacteristic
341#387—21no—
342#387—21no—
343#385—21no—
344#385—21no—
345#384C22×C4311yescharacteristic
346#382C22×C4311yescharacteristic
347C4×C4⋊C4—21no—
348C4×C4⋊C4C22×C4311yescharacteristic
349C4×C4⋊C4C22×C4311yescharacteristic
350C4×C4⋊C4C22×C4311yescharacteristic
351C4×C4⋊C4C22×C4311yescharacteristic
352#340C22×C4311yescharacteristic
353#340C22×C4311yescharacteristic
354#340C22×C4311yescharacteristic
355#340C22×C4311yescharacteristic
356#340C22×C4311yescharacteristic
357#340C22×C4311yescharacteristic
358#336C22×C4311yescharacteristic
359#336C22×C4311yescharacteristic
360C43#2545711yescharacteristic, direct product factor, Sylow
361C22×D4C23×C4311yescharacteristic
362C23×C4—21no—
363C22×C8C23×C4311yescharacteristic
364C22×C8C23×C4311yescharacteristic
365C22×C8C23×C4311yescharacteristic
366C22×C8C23×C4311yescharacteristic
367#125—22no—
368#125—22no—
369#125—22no—
370#125D4×C4314yes—
371C4×D4—22no—
372C4×D4—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4D4×C4311yescharacteristic
382C2×C4⋊C4D4×C4311yescharacteristic
383C2×C4⋊C4C23×C4311yescharacteristic
384C2×C4⋊C4C23×C4311yescharacteristic
385C2×C4⋊C4C23×C4311yescharacteristic
386C2×C4⋊C4C23×C4311yescharacteristic
387C2×C4⋊C4C23×C4311yescharacteristic
388C2×C4⋊C4C23×C4311yescharacteristic
389C2×C4⋊C4C23×C4311yescharacteristic
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42C23×C4311yescharacteristic
399C2×C42C23×C4311yescharacteristic
400C2×C42C23×C4311yescharacteristic
401#107—22no—
402#107—22no—
403#107—22no—
404#106—22no—
405#106—22no—
406#106—22no—
407C4⋊C8—22no—
408C4⋊C8—22no—
409C4⋊C8—22no—
410#102—22no—
411#102—22no—
412#102—22no—
413#102Q8×C4314yes—
414C4×C8—22no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95D4×C4311yescharacteristic
423#95D4×C4311yescharacteristic
424C24—21no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4C2×Q8×C4312yes—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—42no—
439C22×C4—81no—
440C22×C4—81no—
441C22×C4C2×D4×C4311yescharacteristic
442C22×C4C2×D4×C4311yescharacteristic
443C22×C4C2×D4×C4311yescharacteristic
444C22×C4C2×D4×C4311yescharacteristic
445C22×C4C2×D4×C4311yescharacteristic
446C22×C4C2×D4×C4311yescharacteristic
447C22×C4C24×C4311yescharacteristic
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8C2×Q8×C4312yes—
459C2×C8#41×C4312yes—
460C4⋊C4—24no—
461C4⋊C4—24no—
462C4⋊C4—22no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—41no—
475C4⋊C4—42no—
476C4⋊C4—42no—
477C4⋊C4—42no—
478C4⋊C4—81no—
479C4⋊C4—81no—
480C4⋊C4—81no—
481C4⋊C4C2×D4×C4312yes—
482C4⋊C4C2×D4×C4312yes—
483C4⋊C4C2×Q8×C4312yes—
484C22⋊C4—42no—
485C22⋊C4—42no—
486C22⋊C4—42no—
487C22⋊C4—81no—
488C22⋊C4—81no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—42no—
494C42—81no—
495C42—81no—
496C42C2×D4×C4312yes—
497C42#41×C4312yes—
498C23—22no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23C22×D4×C4311yescharacteristic
506D4—22no—
507D4—22no—
508D4—41no—
509D4—41no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—84no—
547C2×C4#121×C4312yes—
548C2×C4#121×C4312yes—
549C2×C4#135×C4312yes—
550C2×C4C22×D4×C4311yescharacteristic
551C2×C4C22×Q8×C4311yescharacteristic
552C2×C4C2×#41×C4311yescharacteristic
553C2×C4C2×#41×C4311yescharacteristic
554C2×C42−1+4×C4311yescharacteristic
555C2×C42−1+4×C4311yescharacteristic
556C8—22no—
557C8—22no—
558C8—41no—
559C8—41no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22C2×#121×C4311yescharacteristic
568C22C43×#54711yescharacteristic
569C22D4×Q8×C4311yescharacteristic
570C22C2×#135×C4311yescharacteristic
571C22C43×#57511yescharacteristic
572C22C43×#57611yescharacteristic
573C22C43×#57711yescharacteristic
574C4—22no—
575C4—22no—
576C4—22no—
577C4—41no—
578C4—41no—
579C4—42no—
580C4—42no—
581C4—42no—
582C4—41no—
583C4—81no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4C43×#53311yescharacteristic
588C4C43×#54111yescharacteristic
589C4C43×#54811yescharacteristic
590C4D4×Q8×C4311yescharacteristic
591C2—82no—
592C2C43×#242911yescharacteristic
593C2C43×#303511yescharacteristic
594C2C43×#304511yescharacteristic
595C2C43×#333911yescharacteristic
596C2C43×#335111yescharacteristic
597C2C43×#338111yescharacteristic
598C2C43×#338911yescharacteristic
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×#499C2semidirect
4. C43×#2370C2semidirect
5. C43×#2085C2semidirect
6. C43×#2084C2semidirect
9. C43×#1989C2semidirect
10. C43×#1949C2semidirect
11. C43×#1947C2semidirect
12. C43×#1939C2semidirect
260. #25457C43direct (N × H)
292. C2×#499C2×C43semidirect
295. #2370C2×C43semidirect
296. #2085C2×C43semidirect
297. #2084C2×C43semidirect
300. #1989C2×C43semidirect
301. #1949C2×C43semidirect
302. #1947C2×C43semidirect
303. #1939C2×C43semidirect
360. C43#25457direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#4992
C2×C43×#4782
C43×#25662
C43×#23702
C43×#20852
C43×#20842
C43×#20672
C43×#19892
C43×#19492
C43×#19472
C43×#19392
C43×#19262
C4×#102×C432
#2545743