Finite Group Databasebeta

← C43×#25397 #24945414

Subgroups — C43×#25397 #24945414

Order 11008.

1118 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#468C211yesmaximal, characteristic, complemented
2C2×C43×#466C211yesmaximal, characteristic, complemented
3C2×C43×#463C211yesmaximal, characteristic, complemented
4C2×C43×#435C211yesmaximal, characteristic, complemented
5C43×#2540C211yesmaximal, characteristic, complemented
6C43×#2537C211yesmaximal, characteristic, complemented
7C43×#2036C211yesmaximal, characteristic, complemented
8C43×#2033C211yesmaximal, characteristic, complemented
9C43×#2000C211yesmaximal, characteristic, complemented
10C43×#1999C211yesmaximal, characteristic, complemented
11C43×#1959C211yesmaximal, characteristic, complemented
12C43×#1947C211yesmaximal, characteristic, complemented
13C43×#1895C211yesmaximal, characteristic, complemented
14C43×#1892C211yesmaximal, characteristic, complemented
15C43×#1762C211yesmaximal, characteristic, complemented
16C22×SD16×C43C2211yescharacteristic
17C22×D8×C43C2211yescharacteristic
18C22×M16×C43C2211yescharacteristic
19C23×C8×C43C2211yescharacteristic
20C2×#124×C43C2211yescharacteristic
21C2×C22⋊Q8×C43C2211yescharacteristic
22C2×C22⋊Q8×C43C2211yescharacteristic
23C2×#121×C43—21no—
24C2×#121×C43C2211yescharacteristic
25C2×#121×C43C2211yescharacteristic
26C2×#121×C43C2211yescharacteristic
27C2×#121×C43C2211yescharacteristic
28C2×C4×D4×C43C2211yescharacteristic
29C2×C4×D4×C43C2211yescharacteristic
30C43×#468—24no—
31C43×#466—24no—
32C43×#463—24no—
33C43×#435—24no—
34C2×#107×C43C2211yescharacteristic
35C2×#107×C43C2211yescharacteristic
36C2×C4⋊C8×C43C2211yescharacteristic
37C2×#103×C43C2211yescharacteristic
38C2×#103×C43C2211yescharacteristic
39C2×#103×C43C2211yescharacteristic
40C2×#102×C43C2211yescharacteristic
41C2×#102×C43C2211yescharacteristic
42C2×#102×C43C2211yescharacteristic
43C2×#102×C43C2211yescharacteristic
44C2×#102×C43C2211yescharacteristic
45C2×C22⋊C8×C43C2211yescharacteristic
46C2×C22⋊C8×C43C2211yescharacteristic
47C2×#97×C43C2211yescharacteristic
48C43×#399—21no—
49C43×#394—21no—
50C43×#394—21no—
51C43×#392—21no—
52C43×#390—21no—
53C43×#390—21no—
54C43×#384C2211yescharacteristic
55C43×#380—21no—
56C43×#380C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C4×C4⋊C4×C43C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C22×Q8×C43C2311yescharacteristic
64C22×D4×C43—21no—
65C22×D4×C43—21no—
66C22×D4×C43—21no—
67C22×D4×C43—21no—
68C22×D4×C43D411yescharacteristic
69C22×D4×C43C2311yescharacteristic
70C22×D4×C43C2311yescharacteristic
71C23×C4×C43—21no—
72C23×C4×C43C2311yescharacteristic
73C23×C4×C43C2311yescharacteristic
74C2×SD16×C43—22no—
75C2×SD16×C43—22no—
76C2×SD16×C43—41no—
77C2×D8×C43—22no—
78C2×D8×C43—22no—
79C2×D8×C43—41no—
80C2×M16×C43—22no—
81C2×M16×C43—22no—
82C2×M16×C43—41no—
83C22×C8×C43—22no—
84C22×C8×C43—22no—
85C22×C8×C43—41no—
86C22×C8×C43C2311yescharacteristic
87C22×C8×C43C2311yescharacteristic
88C22×C8×C43C2311yescharacteristic
89C22×C8×C43C2311yescharacteristic
90#124×C43—22no—
91#124×C43—22no—
92C22⋊Q8×C43—22no—
93C22⋊Q8×C43—22no—
94C22⋊Q8×C43—41no—
95C22⋊Q8×C43—41no—
96#121×C43—22no—
97#121×C43—22no—
98#121×C43—22no—
99#121×C43—22no—
100#121×C43—41no—
101#121×C43—41no—
102#121×C43—41no—
103#121×C43—41no—
104#121×C43—44no—
105C4×D4×C43—22no—
106C4×D4×C43—22no—
107C4×D4×C43—22no—
108C4×D4×C43—22no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43D411yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C22⋊C4×C43—21no—
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122C2×C22⋊C4×C43—21no—
123C2×C22⋊C4×C43—21no—
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43D411yescharacteristic
131C2×C22⋊C4×C43D411yescharacteristic
132C2×C42×C43—21no—
133C2×C42×C43C2311yescharacteristic
134#107×C43—22no—
135#107×C43—22no—
136C4⋊C8×C43D414yescomplemented
137#103×C43—22no—
138#103×C43—22no—
139#103×C43—41no—
140#102×C43—22no—
141#102×C43—22no—
142#102×C43—22no—
143#102×C43—41no—
144#102×C43D414yescomplemented
145C22⋊C8×C43—22no—
146C22⋊C8×C43—22no—
147#97×C43—22no—
148#95×C43—21no—
149#95×C43—21no—
150#95×C43—21no—
151C24×C43—21no—
152C24×C43—21no—
153C24×C43C2×D411yescharacteristic
154C24×C43C2×D411yescharacteristic
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×D4×C43—22no—
162C2×D4×C43—21no—
163C2×D4×C43—22no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43—21no—
174C2×D4×C43—41no—
175C2×D4×C43—42no—
176C2×D4×C43—42no—
177C2×D4×C43—42no—
178C2×D4×C43—42no—
179C2×D4×C43—42no—
180C2×D4×C43—42no—
181C2×D4×C43—42no—
182C2×D4×C43—42no—
183C2×D4×C43—81no—
184C2×D4×C43—81no—
185C2×D4×C43—81no—
186C2×D4×C43—81no—
187C2×D4×C43C2×D412yes—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—42no—
207C22×C4×C43—42no—
208C22×C4×C43—42no—
209C22×C4×C43C2×D411yescharacteristic
210C22×C4×C43C2×D411yescharacteristic
211C22×C4×C43C2×D411yescharacteristic
212C22×C4×C43C2×D411yescharacteristic
213C22×C4×C43C2411yescharacteristic
214SD16×C43—44no—
215D8×C43—44no—
216M16×C43—44no—
217C2×C8×C43—21no—
218C2×C8×C43—21no—
219C2×C8×C43—21no—
220C2×C8×C43—21no—
221C2×C8×C43—21no—
222C2×C8×C43—21no—
223C2×C8×C43—21no—
224C2×C8×C43—21no—
225C2×C8×C43—21no—
226C2×C8×C43—44no—
227C2×C8×C43C2×D412yes—
228C2×C8×C43C2×D412yes—
229C2×C8×C43C2×D412yes—
230C4⋊C4×C43—22no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43—21no—
238C4⋊C4×C43—21no—
239C4⋊C4×C43—42no—
240C4⋊C4×C43—42no—
241C4⋊C4×C43—42no—
242C4⋊C4×C43—81no—
243C4⋊C4×C43C2×D412yes—
244C4⋊C4×C43#4112yes—
245C22⋊C4×C43—22no—
246C22⋊C4×C43—22no—
247C22⋊C4×C43—42no—
248C22⋊C4×C43—42no—
249C22⋊C4×C43—42no—
250C22⋊C4×C43—42no—
251C22⋊C4×C43—42no—
252C22⋊C4×C43—42no—
253C22⋊C4×C43—42no—
254C22⋊C4×C43—42no—
255C22⋊C4×C43—42no—
256C22⋊C4×C43—42no—
257C22⋊C4×C43—42no—
258C42×C43—81no—
259C42×C43C2×D412yes—
260C42×C43#4112yes—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43—21no—
266C23×C43—21no—
267C23×C43—21no—
268C23×C43—21no—
269C23×C43—22no—
270C23×C43—21no—
271C23×C43—21no—
272C23×C43—21no—
273C23×C43—21no—
274C23×C43—21no—
275C23×C43—41no—
276C23×C43—41no—
277C23×C43—41no—
278C23×C43—41no—
279C23×C43—41no—
280C23×C43—41no—
281C23×C43—41no—
282C23×C43—41no—
283C23×C43—41no—
284C23×C43—41no—
285C23×C43—41no—
286C23×C43—41no—
287C23×C43—41no—
288C23×C43AGL(1,ℤ/8)12yes—
289C23×C43C22×D411yescharacteristic
290Q8×C43—41no—
291Q8×C43—41no—
292Q8×C43—41no—
293Q8×C43—41no—
294D4×C43—22no—
295D4×C43—22no—
296D4×C43—44no—
297D4×C43—41no—
298D4×C43—41no—
299D4×C43—41no—
300D4×C43—41no—
301D4×C43—41no—
302D4×C43—41no—
303D4×C43—84no—
304D4×C43—84no—
305D4×C43—84no—
306D4×C43—84no—
307C2×C4×C43—21no—
308C2×C4×C43—21no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—21no—
313C2×C4×C43—21no—
314C2×C4×C43—22no—
315C2×C4×C43—21no—
316C2×C4×C43—22no—
317C2×C4×C43—21no—
318C2×C4×C43—21no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43—41no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43—41no—
327C2×C4×C43—41no—
328C2×C4×C43—41no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43—41no—
340C2×C4×C43—41no—
341C2×C4×C43—41no—
342C2×C4×C43—41no—
343C2×C4×C43—84no—
344C2×C4×C43#12112yes—
345C2×C4×C43#12112yes—
346C2×C4×C43C22×D411yescharacteristic
347C2×C4×C43C22×D411yescharacteristic
348C2×C4×C43C2×#4111yescharacteristic
349C2×C4×C43C2×#4111yescharacteristic
350C2×C4×C43H(5,𝔽2)11yescharacteristic
351C2×C4×C43H(5,𝔽2)11yescharacteristic
352C8×C43—22no—
353C8×C43—22no—
354C8×C43—22no—
355C8×C43—41no—
356#25397C4311yesmaximal, characteristic, direct product factor, Sylow
357C22×C43—22no—
358C22×C43—22no—
359C22×C43—22no—
360C22×C43—41no—
361C22×C43—41no—
362C22×C43—41no—
363C22×C43—41no—
364C22×C43—41no—
365C22×C43—42no—
366C22×C43—41no—
367C22×C43—42no—
368C22×C43—41no—
369C22×C43—42no—
370C22×C43—41no—
371C22×C43—41no—
372C22×C43—41no—
373C22×C43—41no—
374C22×C43—81no—
375C22×C43—81no—
376C22×C43—81no—
377C22×C43—81no—
378C22×C43—81no—
379C22×C43—81no—
380C22×C43—81no—
381C22×C43—81no—
382C22×C43—81no—
383C22×C43—81no—
384C22×C43—81no—
385C22×C43C2×#12111yescharacteristic
386C22×C43D4211yescharacteristic
387C22×C43#54611yescharacteristic
388C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
389C22×C43#57511yescharacteristic
390C22×C43#57611yescharacteristic
391C22×C43#57811yescharacteristic
392C4×C43—22no—
393C4×C43—22no—
394C4×C43—41no—
395C4×C43—41no—
396C4×C43—42no—
397C4×C43—42no—
398C4×C43—81no—
399C4×C43—81no—
400C4×C43—81no—
401C4×C43—81no—
402C4×C43#53211yescharacteristic
403C4×C43#54011yescharacteristic
404C4×C43D4211yescharacteristic
405C4×C43#55011yescharacteristic
406C2×#468C2×C4311yescharacteristic, complemented
407C2×#466C2×C4311yescharacteristic, complemented
408C2×#463C2×C4311yescharacteristic, complemented
409C2×#435C2×C4311yescharacteristic, complemented
410#2540C2×C4311yescharacteristic, complemented
411#2537C2×C4311yescharacteristic, complemented
412#2036C2×C4311yescharacteristic, complemented
413#2033C2×C4311yescharacteristic, complemented
414#2000C2×C4311yescharacteristic, complemented
415#1999C2×C4311yescharacteristic, complemented
416#1959C2×C4311yescharacteristic, complemented
417#1947C2×C4311yescharacteristic, complemented
418#1895C2×C4311yescharacteristic, complemented
419#1892C2×C4311yescharacteristic, complemented
420#1762C2×C4311yescharacteristic, complemented
421C2×C43—42no—
422C2×C43—81no—
423C2×C43—82no—
424C2×C43—161no—
425C2×C43#242811yescharacteristic
426C2×C43#305511yescharacteristic
427C2×C43#306111yescharacteristic
428C2×C43#326411yescharacteristic
429C2×C43#326911yescharacteristic
430C2×C43#330811yescharacteristic
431C2×C43#331911yescharacteristic
432C22×SD16C22×C4311yescharacteristic
433C22×D8C22×C4311yescharacteristic
434C22×M16C22×C4311yescharacteristic
435C23×C8C22×C4311yescharacteristic
436C2×#124C22×C4311yescharacteristic
437C2×C22⋊Q8C22×C4311yescharacteristic
438C2×C22⋊Q8C22×C4311yescharacteristic
439C2×#121—21no—
440C2×#121C22×C4311yescharacteristic
441C2×#121C22×C4311yescharacteristic
442C2×#121C22×C4311yescharacteristic
443C2×#121C22×C4311yescharacteristic
444C2×C4×D4C22×C4311yescharacteristic
445C2×C4×D4C22×C4311yescharacteristic
446#468—24no—
447#466—24no—
448#463—24no—
449#435—24no—
450C2×#107C22×C4311yescharacteristic
451C2×#107C22×C4311yescharacteristic
452C2×C4⋊C8C22×C4311yescharacteristic
453C2×#103C22×C4311yescharacteristic
454C2×#103C22×C4311yescharacteristic
455C2×#103C22×C4311yescharacteristic
456C2×#102C22×C4311yescharacteristic
457C2×#102C22×C4311yescharacteristic
458C2×#102C22×C4311yescharacteristic
459C2×#102C22×C4311yescharacteristic
460C2×#102C22×C4311yescharacteristic
461C2×C22⋊C8C22×C4311yescharacteristic
462C2×C22⋊C8C22×C4311yescharacteristic
463C2×#97C22×C4311yescharacteristic
464#399—21no—
465#394—21no—
466#394—21no—
467#392—21no—
468#390—21no—
469#390—21no—
470#384C22×C4311yescharacteristic
471#380—21no—
472#380C22×C4311yescharacteristic
473#380C22×C4311yescharacteristic
474C4×C4⋊C4C22×C4311yescharacteristic
475#340C22×C4311yescharacteristic
476#340C22×C4311yescharacteristic
477#340C22×C4311yescharacteristic
478#340C22×C4311yescharacteristic
479C43#2539711yescharacteristic, direct product factor, Sylow
480C22×Q8C23×C4311yescharacteristic
481C22×D4—21no—
482C22×D4—21no—
483C22×D4—21no—
484C22×D4—21no—
485C22×D4D4×C4311yescharacteristic
486C22×D4C23×C4311yescharacteristic
487C22×D4C23×C4311yescharacteristic
488C23×C4—21no—
489C23×C4C23×C4311yescharacteristic
490C23×C4C23×C4311yescharacteristic
491C2×SD16—22no—
492C2×SD16—22no—
493C2×SD16—41no—
494C2×D8—22no—
495C2×D8—22no—
496C2×D8—41no—
497C2×M16—22no—
498C2×M16—22no—
499C2×M16—41no—
500C22×C8—22no—
501C22×C8—22no—
502C22×C8—41no—
503C22×C8C23×C4311yescharacteristic
504C22×C8C23×C4311yescharacteristic
505C22×C8C23×C4311yescharacteristic
506C22×C8C23×C4311yescharacteristic
507#124—22no—
508#124—22no—
509C22⋊Q8—22no—
510C22⋊Q8—22no—
511C22⋊Q8—41no—
512C22⋊Q8—41no—
513#121—22no—
514#121—22no—
515#121—22no—
516#121—22no—
517#121—41no—
518#121—41no—
519#121—41no—
520#121—41no—
521#121—44no—
522C4×D4—22no—
523C4×D4—22no—
524C4×D4—22no—
525C4×D4—22no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4D4×C4311yescharacteristic
531C2×C4⋊C4C23×C4311yescharacteristic
532C2×C4⋊C4C23×C4311yescharacteristic
533C2×C4⋊C4C23×C4311yescharacteristic
534C2×C4⋊C4C23×C4311yescharacteristic
535C2×C4⋊C4C23×C4311yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4D4×C4311yescharacteristic
548C2×C22⋊C4D4×C4311yescharacteristic
549C2×C42—21no—
550C2×C42C23×C4311yescharacteristic
551#107—22no—
552#107—22no—
553C4⋊C8D4×C4314yescomplemented
554#103—22no—
555#103—22no—
556#103—41no—
557#102—22no—
558#102—22no—
559#102—22no—
560#102—41no—
561#102D4×C4314yescomplemented
562C22⋊C8—22no—
563C22⋊C8—22no—
564#97—22no—
565#95—21no—
566#95—21no—
567#95—21no—
568C24—21no—
569C24—21no—
570C24C2×D4×C4311yescharacteristic
571C24C2×D4×C4311yescharacteristic
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—41no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—81no—
601C2×D4—81no—
602C2×D4—81no—
603C2×D4—81no—
604C2×D4C2×D4×C4312yes—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4C2×D4×C4311yescharacteristic
627C22×C4C2×D4×C4311yescharacteristic
628C22×C4C2×D4×C4311yescharacteristic
629C22×C4C2×D4×C4311yescharacteristic
630C22×C4C24×C4311yescharacteristic
631SD16—44no—
632D8—44no—
633M16—44no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—44no—
644C2×C8C2×D4×C4312yes—
645C2×C8C2×D4×C4312yes—
646C2×C8C2×D4×C4312yes—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—42no—
657C4⋊C4—42no—
658C4⋊C4—42no—
659C4⋊C4—81no—
660C4⋊C4C2×D4×C4312yes—
661C4⋊C4#41×C4312yes—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C42—81no—
676C42C2×D4×C4312yes—
677C42#41×C4312yes—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—22no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23AGL(1,ℤ/8)×C4312yes—
706C23C22×D4×C4311yescharacteristic
707Q8—41no—
708Q8—41no—
709Q8—41no—
710Q8—41no—
711D4—22no—
712D4—22no—
713D4—44no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—84no—
721D4—84no—
722D4—84no—
723D4—84no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—84no—
761C2×C4#121×C4312yes—
762C2×C4#121×C4312yes—
763C2×C4C22×D4×C4311yescharacteristic
764C2×C4C22×D4×C4311yescharacteristic
765C2×C4C2×#41×C4311yescharacteristic
766C2×C4C2×#41×C4311yescharacteristic
767C2×C4H(5,𝔽2)×C4311yescharacteristic
768C2×C4H(5,𝔽2)×C4311yescharacteristic
769C8—22no—
770C8—22no—
771C8—22no—
772C8—41no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—42no—
782C22—41no—
783C22—42no—
784C22—41no—
785C22—42no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22C2×#121×C4311yescharacteristic
802C22D42×C4311yescharacteristic
803C22C43×#54611yescharacteristic
804C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
805C22C43×#57511yescharacteristic
806C22C43×#57611yescharacteristic
807C22C43×#57811yescharacteristic
808C4—22no—
809C4—22no—
810C4—41no—
811C4—41no—
812C4—42no—
813C4—42no—
814C4—81no—
815C4—81no—
816C4—81no—
817C4—81no—
818C4C43×#53211yescharacteristic
819C4C43×#54011yescharacteristic
820C4D42×C4311yescharacteristic
821C4C43×#55011yescharacteristic
822C2—42no—
823C2—81no—
824C2—82no—
825C2—161no—
826C2C43×#242811yescharacteristic
827C2C43×#305511yescharacteristic
828C2C43×#306111yescharacteristic
829C2C43×#326411yescharacteristic
830C2C43×#326911yescharacteristic
831C2C43×#330811yescharacteristic
832C2C43×#331911yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C2×C4×D4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#468C2semidirect
2. C2×C43×#466C2semidirect
3. C2×C43×#463C2semidirect
4. C2×C43×#435C2semidirect
5. C43×#2540C2semidirect
6. C43×#2537C2semidirect
7. C43×#2036C2semidirect
8. C43×#2033C2semidirect
9. C43×#2000C2semidirect
10. C43×#1999C2semidirect
11. C43×#1959C2semidirect
12. C43×#1947C2semidirect
13. C43×#1895C2semidirect
14. C43×#1892C2semidirect
15. C43×#1762C2semidirect
136. C4⋊C8×C43D4semidirect
144. #102×C43D4semidirect
356. #25397C43direct (N × H)
406. C2×#468C2×C43semidirect
407. C2×#466C2×C43semidirect
408. C2×#463C2×C43semidirect
409. C2×#435C2×C43semidirect
410. #2540C2×C43semidirect
411. #2537C2×C43semidirect
412. #2036C2×C43semidirect
413. #2033C2×C43semidirect
414. #2000C2×C43semidirect
415. #1999C2×C43semidirect
416. #1959C2×C43semidirect
417. #1947C2×C43semidirect
418. #1895C2×C43semidirect
419. #1892C2×C43semidirect
420. #1762C2×C43semidirect
479. C43#25397direct (N × H)
553. C4⋊C8D4×C43semidirect
561. #102D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4682
C2×C43×#4662
C2×C43×#4632
C2×C43×#4352
C43×#25402
C43×#25372
C43×#20362
C43×#20332
C43×#20002
C43×#19992
C43×#19592
C43×#19472
C43×#18952
C43×#18922
C43×#17622
#2539743