Finite Group Databasebeta

← C43×#21122 #24941139

Subgroups — C43×#21122 #24941139

Order 11008.

1042 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#442C211yesmaximal, characteristic
2C43×#2293C211yesmaximal, characteristic, complemented
3C42×D4×C43C211yesmaximal, characteristic, complemented
4C43×#1926C211yesmaximal, characteristic, complemented
5C43×#1925C211yesmaximal, characteristic, complemented
6C43×#1920C211yesmaximal, characteristic, complemented
7C43×#1919C211yesmaximal, characteristic, complemented
8C43×#1879C211yesmaximal, characteristic
9C43×#1879C211yesmaximal, characteristic
10C43×#1864C211yesmaximal, characteristic, complemented
11C43×#1862C211yesmaximal, characteristic, complemented
12C43×#1776C211yesmaximal, characteristic, complemented
13C43×#1762C211yesmaximal, characteristic, complemented
14C43×#1762C211yesmaximal, characteristic, complemented
15C43×#1745C211yesmaximal, characteristic, complemented
16C22×D8×C43C2211yescharacteristic
17C2×C4×D4×C43C2211yescharacteristic
18C2×C4×D4×C43C2211yescharacteristic
19C2×C4×D4×C43C2211yescharacteristic
20C2×C4×D4×C43C2211yescharacteristic
21C2×#117×C43—21no—
22C22×C42×C43—21no—
23C43×#442C418yescomplemented
24C2×#107×C43C2211yescharacteristic
25C2×#106×C43C2211yescharacteristic
26C2×#106×C43C2211yescharacteristic
27C2×#102×C43C2211yescharacteristic
28C2×#102×C43C2211yescharacteristic
29C2×#102×C43C2211yescharacteristic
30C2×#102×C43C2211yescharacteristic
31C2×#102×C43C2211yescharacteristic
32C2×#102×C43C2211yescharacteristic
33C2×#97×C43C2211yescharacteristic
34C2×#97×C43C2211yescharacteristic
35C43×#390C2211yescharacteristic
36C43×#390C2211yescharacteristic
37C43×#389C2211yescharacteristic
38C43×#389C2211yescharacteristic
39C43×#388—21no—
40C43×#388—21no—
41C4×C4⋊C4×C43C2211yescharacteristic
42C4×C4⋊C4×C43C2211yescharacteristic
43C4×C4⋊C4×C43C2211yescharacteristic
44C4×C4⋊C4×C43C2211yescharacteristic
45C4×C22⋊C4×C43—21no—
46C4×C22⋊C4×C43—21no—
47C4×C22⋊C4×C43—21no—
48C4×C22⋊C4×C43—21no—
49C43×C43C2211yescharacteristic
50C43×#340C2211yescharacteristic
51C43×#340C2211yescharacteristic
52C43×#340C2211yescharacteristic
53C43×#340C2211yescharacteristic
54C43×#340C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#336C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C22×D4×C43C2311yescharacteristic
61C22×D4×C43C2311yescharacteristic
62C23×C4×C43—21no—
63C23×C4×C43—21no—
64C23×C4×C43—21no—
65C23×C4×C43—21no—
66C2×D8×C43—22no—
67C2×D8×C43—22no—
68C2×D8×C43C2×C414yes—
69C22×C8×C43C2311yescharacteristic
70C22×C8×C43C2311yescharacteristic
71C22×C8×C43C2311yescharacteristic
72C22×C8×C43C2311yescharacteristic
73C4×D4×C43—22no—
74C4×D4×C43—22no—
75C4×D4×C43—22no—
76C4×D4×C43—22no—
77C4×D4×C43—22no—
78C4×D4×C43—22no—
79C4×D4×C43C2×C414yes—
80C4×D4×C43C2×C414yescomplemented
81#117×C43—44no—
82C2×C4⋊C4×C43—21no—
83C2×C4⋊C4×C43—21no—
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×C22⋊C4×C43—21no—
96C2×C22⋊C4×C43—21no—
97C2×C22⋊C4×C43—21no—
98C2×C42×C43—21no—
99C2×C42×C43—21no—
100C2×C42×C43—21no—
101C2×C42×C43—21no—
102C2×C42×C43—44no—
103C2×C42×C43D411yescharacteristic
104C2×C42×C43D411yescharacteristic
105C2×C42×C43D411yescharacteristic
106C2×C42×C43D411yescharacteristic
107C2×C42×C43C2311yescharacteristic
108C2×C42×C43C2311yescharacteristic
109C2×C42×C43C2311yescharacteristic
110#107×C43—22no—
111#106×C43—22no—
112#106×C43C2×C414yescomplemented
113#102×C43—22no—
114#102×C43—22no—
115#102×C43—22no—
116#102×C43—22no—
117#102×C43C2×C414yes—
118#102×C43C2×C414yescomplemented
119#97×C43—22no—
120#97×C43C2×C414yescomplemented
121#95×C43—21no—
122#95×C43—21no—
123#95×C43—21no—
124#95×C43—21no—
125#95×C43—21no—
126#95×C43—21no—
127C24×C43—21no—
128C24×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43C22×C412yes—
138C2×D4×C43C22×C412yes—
139C2×D4×C43#4112yes—
140C2×D4×C43#4112yes—
141C22×C4×C43—24no—
142C22×C4×C43—24no—
143C22×C4×C43—24no—
144C22×C4×C43—24no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—42no—
152C22×C4×C43—42no—
153C22×C4×C43—42no—
154C22×C4×C43—42no—
155C22×C4×C43—42no—
156C22×C4×C43—42no—
157C22×C4×C43—42no—
158C22×C4×C43—42no—
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43C2411yescharacteristic
166D8×C43—28no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43C22×C412yes—
178C2×C8×C43C22×C412yes—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—42no—
188C4⋊C4×C43—42no—
189C4⋊C4×C43C22×C412yes—
190C4⋊C4×C43C22×C412yes—
191C4⋊C4×C43#4112yes—
192C4⋊C4×C43#4112yes—
193C22⋊C4×C43—24no—
194C22⋊C4×C43—24no—
195C22⋊C4×C43—24no—
196C22⋊C4×C43—24no—
197C22⋊C4×C43—42no—
198C22⋊C4×C43—42no—
199C22⋊C4×C43—42no—
200C22⋊C4×C43—42no—
201C42×C43—22no—
202C42×C43—22no—
203C42×C43—21no—
204C42×C43—21no—
205C42×C43—21no—
206C42×C43—21no—
207C42×C43—41no—
208C42×C43—41no—
209C42×C43—42no—
210C42×C43—42no—
211C42×C43—42no—
212C42×C43—42no—
213C42×C43C22×C412yes—
214C42×C43#4112yes—
215C23×C43—22no—
216C23×C43—22no—
217C23×C43—22no—
218C23×C43—22no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43—41no—
229C23×C43C22×D411yescharacteristic
230D4×C43—22no—
231D4×C43—22no—
232D4×C43—22no—
233D4×C43—22no—
234D4×C43—22no—
235D4×C43—41no—
236D4×C43—41no—
237D4×C43#11714yescomplemented
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—22no—
247C2×C4×C43—22no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—22no—
251C2×C4×C43—22no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—48no—
257C2×C4×C43—48no—
258C2×C4×C43—48no—
259C2×C4×C43—48no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43—41no—
268C2×C4×C43—41no—
269C2×C4×C43—41no—
270C2×C4×C43—41no—
271C2×C4×C43—41no—
272C2×C4×C43—41no—
273C2×C4×C43—41no—
274C2×C4×C43C4×D412yes—
275C2×C4×C43C4×D412yes—
276C2×C4×C43AGL(1,ℤ/8)12yes—
277C2×C4×C43AGL(1,ℤ/8)12yes—
278C2×C4×C43C23×C411yescharacteristic
279C2×C4×C43C2×#4111yescharacteristic
280C2×C4×C43C2×#4111yescharacteristic
281C2×C4×C43C2×#4111yescharacteristic
282C2×C4×C43C2×#4111yescharacteristic
283C2×C4×C43C2×#4111yescharacteristic
284C8×C43—22no—
285C8×C43—22no—
286C8×C43—41no—
287C8×C43—41no—
288#21122C4311yesmaximal, characteristic, direct product factor, Sylow
289C22×C43—24no—
290C22×C43—42no—
291C22×C43—42no—
292C22×C43—42no—
293C22×C43—42no—
294C22×C43—42no—
295C22×C43—42no—
296C22×C43—42no—
297C22×C43—42no—
298C22×C43—42no—
299C22×C43—81no—
300C22×C43—81no—
301C22×C43—81no—
302C22×C43—81no—
303C22×C43C2×C4×D411yescharacteristic
304C22×C43#52511yescharacteristic
305C22×C43#52511yescharacteristic
306C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
307C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
308C22×C43#57511yescharacteristic
309C22×C43#57511yescharacteristic
310C4×C43—22no—
311C4×C43—22no—
312C4×C43—22no—
313C4×C43—22no—
314C4×C43—42no—
315C4×C43—41no—
316C4×C43—42no—
317C4×C43—41no—
318C4×C43—42no—
319C4×C43—42no—
320C4×C43—81no—
321C4×C43—81no—
322C4×C43C2×#11711yescharacteristic
323C4×C43C4×#4111yescharacteristic
324C4×C43#52911yescharacteristic
325C4×C43#52911yescharacteristic
326C2×#442C2×C4311yescharacteristic
327#2293C2×C4311yescharacteristic, complemented
328C42×D4C2×C4311yescharacteristic, complemented
329#1926C2×C4311yescharacteristic, complemented
330#1925C2×C4311yescharacteristic, complemented
331#1920C2×C4311yescharacteristic, complemented
332#1919C2×C4311yescharacteristic, complemented
333#1879C2×C4311yescharacteristic
334#1879C2×C4311yescharacteristic
335#1864C2×C4311yescharacteristic, complemented
336#1862C2×C4311yescharacteristic, complemented
337#1776C2×C4311yescharacteristic, complemented
338#1762C2×C4311yescharacteristic, complemented
339#1762C2×C4311yescharacteristic, complemented
340#1745C2×C4311yescharacteristic, complemented
341C2×C43—44no—
342C2×C43—82no—
343C2×C43#229011yescharacteristic
344C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
345C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
346C2×C43#310911yescharacteristic
347C2×C43#311111yescharacteristic
348C2×C43#311411yescharacteristic
349C2×C43#311511yescharacteristic
350C22×D8C22×C4311yescharacteristic
351C2×C4×D4C22×C4311yescharacteristic
352C2×C4×D4C22×C4311yescharacteristic
353C2×C4×D4C22×C4311yescharacteristic
354C2×C4×D4C22×C4311yescharacteristic
355C2×#117—21no—
356C22×C42—21no—
357#442C4×C4318yescomplemented
358C2×#107C22×C4311yescharacteristic
359C2×#106C22×C4311yescharacteristic
360C2×#106C22×C4311yescharacteristic
361C2×#102C22×C4311yescharacteristic
362C2×#102C22×C4311yescharacteristic
363C2×#102C22×C4311yescharacteristic
364C2×#102C22×C4311yescharacteristic
365C2×#102C22×C4311yescharacteristic
366C2×#102C22×C4311yescharacteristic
367C2×#97C22×C4311yescharacteristic
368C2×#97C22×C4311yescharacteristic
369#390C22×C4311yescharacteristic
370#390C22×C4311yescharacteristic
371#389C22×C4311yescharacteristic
372#389C22×C4311yescharacteristic
373#388—21no—
374#388—21no—
375C4×C4⋊C4C22×C4311yescharacteristic
376C4×C4⋊C4C22×C4311yescharacteristic
377C4×C4⋊C4C22×C4311yescharacteristic
378C4×C4⋊C4C22×C4311yescharacteristic
379C4×C22⋊C4—21no—
380C4×C22⋊C4—21no—
381C4×C22⋊C4—21no—
382C4×C22⋊C4—21no—
383C43C22×C4311yescharacteristic
384#340C22×C4311yescharacteristic
385#340C22×C4311yescharacteristic
386#340C22×C4311yescharacteristic
387#340C22×C4311yescharacteristic
388#340C22×C4311yescharacteristic
389#340C22×C4311yescharacteristic
390#336C22×C4311yescharacteristic
391#336C22×C4311yescharacteristic
392#336C22×C4311yescharacteristic
393#336C22×C4311yescharacteristic
394C43#2112211yescharacteristic, direct product factor, Sylow
395C22×D4C23×C4311yescharacteristic
396C22×D4C23×C4311yescharacteristic
397C23×C4—21no—
398C23×C4—21no—
399C23×C4—21no—
400C23×C4—21no—
401C2×D8—22no—
402C2×D8—22no—
403C2×D8C2×C4×C4314yes—
404C22×C8C23×C4311yescharacteristic
405C22×C8C23×C4311yescharacteristic
406C22×C8C23×C4311yescharacteristic
407C22×C8C23×C4311yescharacteristic
408C4×D4—22no—
409C4×D4—22no—
410C4×D4—22no—
411C4×D4—22no—
412C4×D4—22no—
413C4×D4—22no—
414C4×D4C2×C4×C4314yes—
415C4×D4C2×C4×C4314yescomplemented
416#117—44no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4C23×C4311yescharacteristic
420C2×C4⋊C4C23×C4311yescharacteristic
421C2×C4⋊C4C23×C4311yescharacteristic
422C2×C4⋊C4C23×C4311yescharacteristic
423C2×C4⋊C4C23×C4311yescharacteristic
424C2×C4⋊C4C23×C4311yescharacteristic
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C42—21no—
434C2×C42—21no—
435C2×C42—21no—
436C2×C42—21no—
437C2×C42—44no—
438C2×C42D4×C4311yescharacteristic
439C2×C42D4×C4311yescharacteristic
440C2×C42D4×C4311yescharacteristic
441C2×C42D4×C4311yescharacteristic
442C2×C42C23×C4311yescharacteristic
443C2×C42C23×C4311yescharacteristic
444C2×C42C23×C4311yescharacteristic
445#107—22no—
446#106—22no—
447#106C2×C4×C4314yescomplemented
448#102—22no—
449#102—22no—
450#102—22no—
451#102—22no—
452#102C2×C4×C4314yes—
453#102C2×C4×C4314yescomplemented
454#97—22no—
455#97C2×C4×C4314yescomplemented
456#95—21no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462C24—21no—
463C24—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4C22×C4×C4312yes—
473C2×D4C22×C4×C4312yes—
474C2×D4#41×C4312yes—
475C2×D4#41×C4312yes—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4C2×D4×C4311yescharacteristic
495C22×C4C2×D4×C4311yescharacteristic
496C22×C4C2×D4×C4311yescharacteristic
497C22×C4C2×D4×C4311yescharacteristic
498C22×C4C2×D4×C4311yescharacteristic
499C22×C4C2×D4×C4311yescharacteristic
500C22×C4C24×C4311yescharacteristic
501D8—28no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8C22×C4×C4312yes—
513C2×C8C22×C4×C4312yes—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—42no—
523C4⋊C4—42no—
524C4⋊C4C22×C4×C4312yes—
525C4⋊C4C22×C4×C4312yes—
526C4⋊C4#41×C4312yes—
527C4⋊C4#41×C4312yes—
528C22⋊C4—24no—
529C22⋊C4—24no—
530C22⋊C4—24no—
531C22⋊C4—24no—
532C22⋊C4—42no—
533C22⋊C4—42no—
534C22⋊C4—42no—
535C22⋊C4—42no—
536C42—22no—
537C42—22no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—41no—
543C42—41no—
544C42—42no—
545C42—42no—
546C42—42no—
547C42—42no—
548C42C22×C4×C4312yes—
549C42#41×C4312yes—
550C23—22no—
551C23—22no—
552C23—22no—
553C23—22no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23C22×D4×C4311yescharacteristic
565D4—22no—
566D4—22no—
567D4—22no—
568D4—22no—
569D4—22no—
570D4—41no—
571D4—41no—
572D4#117×C4314yescomplemented
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—48no—
592C2×C4—48no—
593C2×C4—48no—
594C2×C4—48no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4C4×D4×C4312yes—
610C2×C4C4×D4×C4312yes—
611C2×C4AGL(1,ℤ/8)×C4312yes—
612C2×C4AGL(1,ℤ/8)×C4312yes—
613C2×C4C23×C4×C4311yescharacteristic
614C2×C4C2×#41×C4311yescharacteristic
615C2×C4C2×#41×C4311yescharacteristic
616C2×C4C2×#41×C4311yescharacteristic
617C2×C4C2×#41×C4311yescharacteristic
618C2×C4C2×#41×C4311yescharacteristic
619C8—22no—
620C8—22no—
621C8—41no—
622C8—41no—
623C22—24no—
624C22—42no—
625C22—42no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—42no—
633C22—81no—
634C22—81no—
635C22—81no—
636C22—81no—
637C22C2×C4×D4×C4311yescharacteristic
638C22C43×#52511yescharacteristic
639C22C43×#52511yescharacteristic
640C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
641C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
642C22C43×#57511yescharacteristic
643C22C43×#57511yescharacteristic
644C4—22no—
645C4—22no—
646C4—22no—
647C4—22no—
648C4—42no—
649C4—41no—
650C4—42no—
651C4—41no—
652C4—42no—
653C4—42no—
654C4—81no—
655C4—81no—
656C4C2×#117×C4311yescharacteristic
657C4C4×#41×C4311yescharacteristic
658C4C43×#52911yescharacteristic
659C4C43×#52911yescharacteristic
660C2—44no—
661C2—82no—
662C2C43×#229011yescharacteristic
663C2C4×AGL(1,ℤ/8)×C4311yescharacteristic
664C2C4×AGL(1,ℤ/8)×C4311yescharacteristic
665C2C43×#310911yescharacteristic
666C2C43×#311111yescharacteristic
667C2C43×#311411yescharacteristic
668C2C43×#311511yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutatorC2×C4C23×C4×C43
Frattini, cosocleC22×C4C24×C43
prime radicalC22×D8×C43C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C43×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2293C2semidirect
3. C42×D4×C43C2semidirect
4. C43×#1926C2semidirect
5. C43×#1925C2semidirect
6. C43×#1920C2semidirect
7. C43×#1919C2semidirect
10. C43×#1864C2semidirect
11. C43×#1862C2semidirect
12. C43×#1776C2semidirect
13. C43×#1762C2semidirect
14. C43×#1762C2semidirect
15. C43×#1745C2semidirect
23. C43×#442C4semidirect
80. C4×D4×C43C2×C4semidirect
112. #106×C43C2×C4semidirect
118. #102×C43C2×C4semidirect
120. #97×C43C2×C4semidirect
237. D4×C43#117semidirect
288. #21122C43direct (N × H)
327. #2293C2×C43semidirect
328. C42×D4C2×C43semidirect
329. #1926C2×C43semidirect
330. #1925C2×C43semidirect
331. #1920C2×C43semidirect
332. #1919C2×C43semidirect
335. #1864C2×C43semidirect
336. #1862C2×C43semidirect
337. #1776C2×C43semidirect
338. #1762C2×C43semidirect
339. #1762C2×C43semidirect
340. #1745C2×C43semidirect
357. #442C4×C43semidirect
394. C43#21122direct (N × H)
415. C4×D4C2×C4×C43semidirect
447. #106C2×C4×C43semidirect
453. #102C2×C4×C43semidirect
455. #97C2×C4×C43semidirect
572. D4#117×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4422
C43×#22932
C42×D4×C432
C43×#19262
C43×#19252
C43×#19202
C43×#19192
C43×#18792
C43×#18642
C43×#18622
C43×#17762
C43×#17622
C43×#17452
#2112243