Finite Group Databasebeta

← C43×#13885 #24933902

Subgroups — C43×#13885 #24933902

Order 11008.

1342 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#382C211yesmaximal, characteristic
2C2×C4×C4⋊C4×C43C211yesmaximal, characteristic
3C2×C4×C4⋊C4×C43C211yesmaximal, characteristic
4C43×#1445C212yesmaximal
5C43×#1443C212yesmaximal
6C43×#1436C212yesmaximal
7C43×C4⋊#95C211yesmaximal, characteristic
8C43×C4⋊#95C211yesmaximal, characteristic
9C43×C4⋊#95C211yesmaximal, characteristic
10C43×C4⋊#95C211yesmaximal, characteristic
11C43×#1434C212yesmaximal
12C22×C4⋊C4×C43C2211yescharacteristic
13C22×C4⋊C4×C43C2211yescharacteristic
14C22×C4⋊C4×C43C2211yescharacteristic
15C22×C4⋊C4×C43C2211yescharacteristic
16C22×C4⋊C4×C43C2211yescharacteristic
17C22×C4⋊C4×C43C2211yescharacteristic
18C22×C42×C43C2212yes—
19C22×C42×C43C2211yescharacteristic
20C22×C42×C43C2211yescharacteristic
21C22×C42×C43C2211yescharacteristic
22C43×#382—24no—
23C4×C4⋊C4×C43—24no—
24C4×C4⋊C4×C43C418yescomplemented
25C2×#95×C43C2212yes—
26C2×#95×C43C2212yes—
27C2×#95×C43C2212yes—
28C2×#95×C43C2212yes—
29C2×#95×C43C2212yes—
30C2×#95×C43C2212yes—
31C2×#95×C43C2212yes—
32C2×#95×C43C2212yes—
33C2×#95×C43C2212yes—
34C2×#95×C43C2212yes—
35C2×#95×C43C2212yes—
36C2×#95×C43C2211yescharacteristic
37C2×#95×C43C2211yescharacteristic
38C23×C4×C43C2312yes—
39C23×C4×C43C2312yes—
40C23×C4×C43C2311yescharacteristic
41C23×C4×C43C2311yescharacteristic
42C23×C4×C43C2311yescharacteristic
43C23×C4×C43C2311yescharacteristic
44C23×C4×C43C2312yes—
45C23×C4×C43C2312yes—
46C23×C4×C43C2311yescharacteristic
47C23×C4×C43C2311yescharacteristic
48C23×C4×C43C2311yescharacteristic
49C2×C4⋊C4×C43—22no—
50C2×C4⋊C4×C43—22no—
51C2×C4⋊C4×C43—22no—
52C2×C4⋊C4×C43—22no—
53C2×C4⋊C4×C43—22no—
54C2×C4⋊C4×C43—22no—
55C2×C4⋊C4×C43—22no—
56C2×C4⋊C4×C43—22no—
57C2×C4⋊C4×C43—22no—
58C2×C4⋊C4×C43—22no—
59C2×C4⋊C4×C43—22no—
60C2×C4⋊C4×C43—22no—
61C2×C4⋊C4×C43—22no—
62C2×C4⋊C4×C43—22no—
63C2×C4⋊C4×C43C2×C414yes—
64C2×C4⋊C4×C43C2×C414yes—
65C2×C4⋊C4×C43D414yes—
66C2×C4⋊C4×C43Q814yes—
67C2×C42×C43—22no—
68C2×C42×C43—22no—
69C2×C42×C43—22no—
70C2×C42×C43—22no—
71C2×C42×C43—22no—
72C2×C42×C43—22no—
73C2×C42×C43—24no—
74C2×C42×C43—24no—
75C2×C42×C43—42no—
76C2×C42×C43C2×C414yes—
77C2×C42×C43C2×C414yes—
78C2×C42×C43C2×C414yes—
79#95×C43—24no—
80#95×C43—24no—
81#95×C43—24no—
82#95×C43—24no—
83#95×C43—24no—
84#95×C43—24no—
85#95×C43—42no—
86#95×C43—42no—
87#95×C43—42no—
88#95×C43—42no—
89#95×C43—42no—
90#95×C43C2×C414yes—
91#95×C43C2×C414yes—
92C24×C43C2411yescharacteristic
93C22×C4×C43—21no—
94C22×C4×C43—21no—
95C22×C4×C43—21no—
96C22×C4×C43—21no—
97C22×C4×C43—22no—
98C22×C4×C43—22no—
99C22×C4×C43—21no—
100C22×C4×C43—21no—
101C22×C4×C43—21no—
102C22×C4×C43—21no—
103C22×C4×C43—21no—
104C22×C4×C43—22no—
105C22×C4×C43—22no—
106C22×C4×C43—21no—
107C22×C4×C43—21no—
108C22×C4×C43—22no—
109C22×C4×C43—22no—
110C22×C4×C43—21no—
111C22×C4×C43—21no—
112C22×C4×C43—21no—
113C22×C4×C43—22no—
114C22×C4×C43—22no—
115C22×C4×C43—21no—
116C22×C4×C43—21no—
117C22×C4×C43—21no—
118C22×C4×C43—21no—
119C22×C4×C43—21no—
120C22×C4×C43—21no—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—22no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43—22no—
128C22×C4×C43—22no—
129C22×C4×C43—22no—
130C22×C4×C43—22no—
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—22no—
138C22×C4×C43—22no—
139C22×C4×C43—22no—
140C22×C4×C43—22no—
141C22×C4×C43—22no—
142C22×C4×C43—22no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—22no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—22no—
151C22×C4×C43C22×C412yes—
152C22×C4×C43C22×C412yes—
153C22×C4×C43C22×C412yes—
154C22×C4×C43C22×C412yes—
155C22×C4×C43C22×C412yes—
156C22×C4×C43C22×C412yes—
157C22×C4×C43C22×C412yes—
158C22×C4×C43C2×D414yes—
159C22×C4×C43C2×D412yes—
160C22×C4×C43C2×Q814yes—
161C22×C4×C43C2×Q812yes—
162C22×C4×C43#4112yes—
163C22×C4×C43#4112yes—
164C22×C4×C43#4112yes—
165C22×C4×C43#4112yes—
166C22×C4×C43#4112yes—
167C22×C4×C43#4112yes—
168C22×C4×C43#4112yes—
169C22×C4×C43#4112yes—
170C4⋊C4×C43—28no—
171C4⋊C4×C43—28no—
172C4⋊C4×C43—28no—
173C4⋊C4×C43—28no—
174C4⋊C4×C43—44no—
175C4⋊C4×C43—44no—
176C42×C43—28no—
177C42×C43—28no—
178C42×C43—28no—
179C42×C43—48no—
180C23×C43C23×C411yescharacteristic
181C23×C43C22×D411yescharacteristic
182C23×C43C22×Q811yescharacteristic
183C23×C43C2×#4111yescharacteristic
184C23×C43C2×#4111yescharacteristic
185C23×C43C2×#4111yescharacteristic
186C23×C43C2×#4111yescharacteristic
187C23×C43C2×#4111yescharacteristic
188C23×C43C2×#4111yescharacteristic
189C23×C43C2×#4111yescharacteristic
190C23×C43C2×#4111yescharacteristic
191C23×C43H(5,𝔽2)11yescharacteristic
192C23×C43H(5,𝔽2)11yescharacteristic
193C23×C432−1+411yescharacteristic
194C23×C432−1+411yescharacteristic
195C2×C4×C43—22no—
196C2×C4×C43—22no—
197C2×C4×C43—22no—
198C2×C4×C43—22no—
199C2×C4×C43—22no—
200C2×C4×C43—22no—
201C2×C4×C43—22no—
202C2×C4×C43—22no—
203C2×C4×C43—22no—
204C2×C4×C43—22no—
205C2×C4×C43—22no—
206C2×C4×C43—22no—
207C2×C4×C43—22no—
208C2×C4×C43—22no—
209C2×C4×C43—22no—
210C2×C4×C43—22no—
211C2×C4×C43—22no—
212C2×C4×C43—22no—
213C2×C4×C43—22no—
214C2×C4×C43—22no—
215C2×C4×C43—22no—
216C2×C4×C43—22no—
217C2×C4×C43—22no—
218C2×C4×C43—22no—
219C2×C4×C43—24no—
220C2×C4×C43—24no—
221C2×C4×C43—24no—
222C2×C4×C43—24no—
223C2×C4×C43—24no—
224C2×C4×C43—24no—
225C2×C4×C43—42no—
226C2×C4×C43—42no—
227C2×C4×C43—41no—
228C2×C4×C43—42no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—42no—
233C2×C4×C43—42no—
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—42no—
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—42no—
248C2×C4×C43—42no—
249C2×C4×C43—42no—
250C2×C4×C43—42no—
251C2×C4×C43—42no—
252C2×C4×C43—42no—
253C2×C4×C43—42no—
254C2×C4×C43—42no—
255C2×C4×C43—42no—
256C2×C4×C43—42no—
257C2×C4×C43—42no—
258C2×C4×C43—42no—
259C2×C4×C43—42no—
260C2×C4×C43—42no—
261C2×C4×C43—42no—
262C2×C4×C43—42no—
263C2×C4×C43#11714yes—
264C2×C4×C43#11714yes—
265C2×C4×C43#11714yes—
266C2×C4×C43C4×D414yes—
267C2×C4×C43C4×Q814yes—
268C2×C4×C43C22⋊Q814yes—
269C2×C4×C43#12314yes—
270C2×C4×C43#12514yes—
271C2×C4×C43#12614yes—
272#13885C4311yesmaximal, characteristic, direct product factor, Sylow
273C22×C43C2×#11711yescharacteristic
274C22×C43C2×#11711yescharacteristic
275C22×C43C2×#11711yescharacteristic
276C22×C43C2×C4×D411yescharacteristic
277C22×C43C2×C4×Q811yescharacteristic
278C22×C43#52011yescharacteristic
279C22×C43#52011yescharacteristic
280C22×C43C2×C22⋊Q811yescharacteristic
281C22×C43C2×#12311yescharacteristic
282C22×C43C2×#12511yescharacteristic
283C22×C43C2×#12611yescharacteristic
284C22×C43#52911yescharacteristic
285C22×C43#52911yescharacteristic
286C22×C43#52911yescharacteristic
287C22×C43#52911yescharacteristic
288C22×C43#54011yescharacteristic
289C22×C43#54111yescharacteristic
290C22×C43#54211yescharacteristic
291C22×C43#54211yescharacteristic
292C22×C43#54611yescharacteristic
293C22×C43#54711yescharacteristic
294C22×C43#54811yescharacteristic
295C22×C43#55011yescharacteristic
296C22×C43#55211yescharacteristic
297C22×C43#55311yescharacteristic
298C22×C43#55411yescharacteristic
299C22×C43#55411yescharacteristic
300C22×C43#55511yescharacteristic
301C22×C43#55611yescharacteristic
302C22×C43#55611yescharacteristic
303C22×C43#55611yescharacteristic
304C22×C43#55711yescharacteristic
305C22×C43#55711yescharacteristic
306C22×C43#55911yescharacteristic
307C22×C43#55911yescharacteristic
308C4×C43—24no—
309C4×C43—24no—
310C4×C43—42no—
311C4×C43—42no—
312C4×C43—42no—
313C4×C43—42no—
314C4×C43—44no—
315C4×C43—44no—
316C4×C43—82no—
317C4×C43—82no—
318C4×C43#38718yes—
319C2×#382C2×C4311yescharacteristic
320C2×C4×C4⋊C4C2×C4311yescharacteristic
321C2×C4×C4⋊C4C2×C4311yescharacteristic
322#1445C2×C4312yes—
323#1443C2×C4312yes—
324#1436C2×C4312yes—
325C4⋊#95C2×C4311yescharacteristic
326C4⋊#95C2×C4311yescharacteristic
327C4⋊#95C2×C4311yescharacteristic
328C4⋊#95C2×C4311yescharacteristic
329#1434C2×C4312yes—
330C2×C43#228311yescharacteristic
331C2×C43C2×#38711yescharacteristic
332C2×C43#231411yescharacteristic
333C2×C43#235211yescharacteristic
334C2×C43#235411yescharacteristic
335C2×C43#235511yescharacteristic
336C2×C43#235511yescharacteristic
337C2×C43#244711yescharacteristic
338C2×C43#244811yescharacteristic
339C2×C43#245311yescharacteristic
340C2×C43#245411yescharacteristic
341C2×C43#250811yescharacteristic
342C2×C43#250911yescharacteristic
343C2×C43#251311yescharacteristic
344C2×C43#251411yescharacteristic
345C22×C4⋊C4C22×C4311yescharacteristic
346C22×C4⋊C4C22×C4311yescharacteristic
347C22×C4⋊C4C22×C4311yescharacteristic
348C22×C4⋊C4C22×C4311yescharacteristic
349C22×C4⋊C4C22×C4311yescharacteristic
350C22×C4⋊C4C22×C4311yescharacteristic
351C22×C42C22×C4312yes—
352C22×C42C22×C4311yescharacteristic
353C22×C42C22×C4311yescharacteristic
354C22×C42C22×C4311yescharacteristic
355#382—24no—
356C4×C4⋊C4—24no—
357C4×C4⋊C4C4×C4318yescomplemented
358C2×#95C22×C4312yes—
359C2×#95C22×C4312yes—
360C2×#95C22×C4312yes—
361C2×#95C22×C4312yes—
362C2×#95C22×C4312yes—
363C2×#95C22×C4312yes—
364C2×#95C22×C4312yes—
365C2×#95C22×C4312yes—
366C2×#95C22×C4312yes—
367C2×#95C22×C4312yes—
368C2×#95C22×C4312yes—
369C2×#95C22×C4311yescharacteristic
370C2×#95C22×C4311yescharacteristic
371C43#1388511yescharacteristic, direct product factor, Sylow
372C23×C4C23×C4312yes—
373C23×C4C23×C4312yes—
374C23×C4C23×C4311yescharacteristic
375C23×C4C23×C4311yescharacteristic
376C23×C4C23×C4311yescharacteristic
377C23×C4C23×C4311yescharacteristic
378C23×C4C23×C4312yes—
379C23×C4C23×C4312yes—
380C23×C4C23×C4311yescharacteristic
381C23×C4C23×C4311yescharacteristic
382C23×C4C23×C4311yescharacteristic
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4C2×C4×C4314yes—
398C2×C4⋊C4C2×C4×C4314yes—
399C2×C4⋊C4D4×C4314yes—
400C2×C4⋊C4Q8×C4314yes—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—24no—
408C2×C42—24no—
409C2×C42—42no—
410C2×C42C2×C4×C4314yes—
411C2×C42C2×C4×C4314yes—
412C2×C42C2×C4×C4314yes—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—42no—
420#95—42no—
421#95—42no—
422#95—42no—
423#95—42no—
424#95C2×C4×C4314yes—
425#95C2×C4×C4314yes—
426C24C24×C4311yescharacteristic
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4C22×C4×C4312yes—
486C22×C4C22×C4×C4312yes—
487C22×C4C22×C4×C4312yes—
488C22×C4C22×C4×C4312yes—
489C22×C4C22×C4×C4312yes—
490C22×C4C22×C4×C4312yes—
491C22×C4C22×C4×C4312yes—
492C22×C4C2×D4×C4314yes—
493C22×C4C2×D4×C4312yes—
494C22×C4C2×Q8×C4314yes—
495C22×C4C2×Q8×C4312yes—
496C22×C4#41×C4312yes—
497C22×C4#41×C4312yes—
498C22×C4#41×C4312yes—
499C22×C4#41×C4312yes—
500C22×C4#41×C4312yes—
501C22×C4#41×C4312yes—
502C22×C4#41×C4312yes—
503C22×C4#41×C4312yes—
504C4⋊C4—28no—
505C4⋊C4—28no—
506C4⋊C4—28no—
507C4⋊C4—28no—
508C4⋊C4—44no—
509C4⋊C4—44no—
510C42—28no—
511C42—28no—
512C42—28no—
513C42—48no—
514C23C23×C4×C4311yescharacteristic
515C23C22×D4×C4311yescharacteristic
516C23C22×Q8×C4311yescharacteristic
517C23C2×#41×C4311yescharacteristic
518C23C2×#41×C4311yescharacteristic
519C23C2×#41×C4311yescharacteristic
520C23C2×#41×C4311yescharacteristic
521C23C2×#41×C4311yescharacteristic
522C23C2×#41×C4311yescharacteristic
523C23C2×#41×C4311yescharacteristic
524C23C2×#41×C4311yescharacteristic
525C23H(5,𝔽2)×C4311yescharacteristic
526C23H(5,𝔽2)×C4311yescharacteristic
527C232−1+4×C4311yescharacteristic
528C232−1+4×C4311yescharacteristic
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4#117×C4314yes—
598C2×C4#117×C4314yes—
599C2×C4#117×C4314yes—
600C2×C4C4×D4×C4314yes—
601C2×C4C4×Q8×C4314yes—
602C2×C4C22⋊Q8×C4314yes—
603C2×C4#123×C4314yes—
604C2×C4#125×C4314yes—
605C2×C4#126×C4314yes—
606C22C2×#117×C4311yescharacteristic
607C22C2×#117×C4311yescharacteristic
608C22C2×#117×C4311yescharacteristic
609C22C2×C4×D4×C4311yescharacteristic
610C22C2×C4×Q8×C4311yescharacteristic
611C22C43×#52011yescharacteristic
612C22C43×#52011yescharacteristic
613C22C2×C22⋊Q8×C4311yescharacteristic
614C22C2×#123×C4311yescharacteristic
615C22C2×#125×C4311yescharacteristic
616C22C2×#126×C4311yescharacteristic
617C22C43×#52911yescharacteristic
618C22C43×#52911yescharacteristic
619C22C43×#52911yescharacteristic
620C22C43×#52911yescharacteristic
621C22C43×#54011yescharacteristic
622C22C43×#54111yescharacteristic
623C22C43×#54211yescharacteristic
624C22C43×#54211yescharacteristic
625C22C43×#54611yescharacteristic
626C22C43×#54711yescharacteristic
627C22C43×#54811yescharacteristic
628C22C43×#55011yescharacteristic
629C22C43×#55211yescharacteristic
630C22C43×#55311yescharacteristic
631C22C43×#55411yescharacteristic
632C22C43×#55411yescharacteristic
633C22C43×#55511yescharacteristic
634C22C43×#55611yescharacteristic
635C22C43×#55611yescharacteristic
636C22C43×#55611yescharacteristic
637C22C43×#55711yescharacteristic
638C22C43×#55711yescharacteristic
639C22C43×#55911yescharacteristic
640C22C43×#55911yescharacteristic
641C4—24no—
642C4—24no—
643C4—42no—
644C4—42no—
645C4—42no—
646C4—44no—
647C4—44no—
648C4—42no—
649C4—82no—
650C4—82no—
651C4C43×#38718yes—
652C2C43×#228311yescharacteristic
653C2C2×C43×#38711yescharacteristic
654C2C43×#231411yescharacteristic
655C2C43×#235211yescharacteristic
656C2C43×#235411yescharacteristic
657C2C43×#235511yescharacteristic
658C2C43×#235511yescharacteristic
659C2C43×#244711yescharacteristic
660C2C43×#244811yescharacteristic
661C2C43×#245311yescharacteristic
662C2C43×#245411yescharacteristic
663C2C43×#250811yescharacteristic
664C2C43×#250911yescharacteristic
665C2C43×#251311yescharacteristic
666C2C43×#251411yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C43C24
commutatorC23C23×C4×C43
Frattini, cosocleC24C24×C43
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C43 ◁ G

Complements

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

NH ≅ G/Ntype
24. C4×C4⋊C4×C43C4semidirect
272. #13885C43direct (N × H)
357. C4×C4⋊C4C4×C43semidirect
371. C43#13885direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#3822
C2×C4×C4⋊C4×C432
C43×#14452
C43×#14432
C43×#14362
C43×C4⋊#952
C43×#14342
#1388543