Finite Group Databasebeta

← C43×#25106 #24945123

Subgroups — C43×#25106 #24945123

Order 11008.

1230 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#469C211yesmaximal, characteristic, complemented
2C2×C43×#463C211yesmaximal, characteristic, complemented
3C2×C43×#449C211yesmaximal, characteristic, complemented
4C2×C43×#417C211yesmaximal, characteristic, complemented
5C43×#2431C211yesmaximal, characteristic, complemented
6C43×#2361C211yesmaximal, characteristic, complemented
7C43×#2065C211yesmaximal, characteristic, complemented
8C43×#2055C211yesmaximal, characteristic, complemented
9C43×#2042C211yesmaximal, characteristic, complemented
10C43×#2011C211yesmaximal, characteristic, complemented
11C43×#1982C211yesmaximal, characteristic, complemented
12C43×#1927C211yesmaximal, characteristic, complemented
13C43×#1879C211yesmaximal, characteristic, complemented
14C43×#1874C211yesmaximal, characteristic, complemented
15C43×#1851C211yesmaximal, characteristic, complemented
16C22×#41×C43C2211yescharacteristic
17C22×SD16×C43C2211yescharacteristic
18C22×D8×C43C2211yescharacteristic
19C22×D8×C43C2211yescharacteristic
20C22×M16×C43C2211yescharacteristic
21C2×#127×C43C2211yescharacteristic
22C2×#124×C43C2211yescharacteristic
23C2×#121×C43C2211yescharacteristic
24C2×#121×C43C2211yescharacteristic
25C2×C4×D4×C43—21no—
26C2×C4×D4×C43C2211yescharacteristic
27C22×C4⋊C4×C43C2211yescharacteristic
28C43×#469—24no—
29C43×#463—24no—
30C43×#449—24no—
31C2×#106×C43C2211yescharacteristic
32C2×C4⋊C8×C43C2211yescharacteristic
33C2×C4⋊C8×C43C2211yescharacteristic
34C43×#417—24no—
35C2×#103×C43C2211yescharacteristic
36C2×#103×C43C2211yescharacteristic
37C2×#103×C43C2211yescharacteristic
38C2×#102×C43C2211yescharacteristic
39C2×#102×C43C2211yescharacteristic
40C2×#102×C43C2211yescharacteristic
41C2×#102×C43C2211yescharacteristic
42C2×#102×C43C2211yescharacteristic
43C2×#102×C43C2211yescharacteristic
44C2×#102×C43C2211yescharacteristic
45C2×C22⋊C8×C43C2211yescharacteristic
46C43×#392—21no—
47C43×#392—21no—
48C43×#391C2211yescharacteristic
49C43×#390C2211yescharacteristic
50C43×#390C2211yescharacteristic
51C43×#389C2211yescharacteristic
52C43×#388—21no—
53C43×#386—21no—
54C43×#386—21no—
55C43×#386—21no—
56C43×#385—21no—
57C4×C4⋊C4×C43C2211yescharacteristic
58C4×C22⋊C4×C43C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C2×#41×C43—22no—
64C2×#41×C43—22no—
65C2×#41×C43—22no—
66C2×#41×C43—22no—
67C2×#41×C43—41no—
68C2×#41×C43—41no—
69C22×Q8×C43C2311yescharacteristic
70C22×D4×C43—21no—
71C22×D4×C43—21no—
72C22×D4×C43—21no—
73C22×D4×C43—21no—
74C22×D4×C43—21no—
75C22×D4×C43C2311yescharacteristic
76C22×D4×C43C2311yescharacteristic
77C22×D4×C43C2311yescharacteristic
78C23×C4×C43—21no—
79C23×C4×C43—21no—
80C23×C4×C43—21no—
81C23×C4×C43C2311yescharacteristic
82C2×SD16×C43—22no—
83C2×SD16×C43—22no—
84C2×SD16×C43—41no—
85C2×D8×C43—22no—
86C2×D8×C43—22no—
87C2×D8×C43—22no—
88C2×D8×C43—22no—
89C2×D8×C43—41no—
90C2×D8×C43—41no—
91C2×M16×C43—22no—
92C2×M16×C43—22no—
93C2×M16×C43—41no—
94C22×C8×C43C2311yescharacteristic
95C22×C8×C43C2311yescharacteristic
96C22×C8×C43C2311yescharacteristic
97C22×C8×C43C2311yescharacteristic
98#127×C43—22no—
99#127×C43—41no—
100#124×C43—22no—
101#124×C43—41no—
102#121×C43—22no—
103#121×C43—22no—
104#121×C43—22no—
105#121×C43D414yescomplemented
106C4×D4×C43—22no—
107C4×D4×C43—41no—
108C4×D4×C43—44no—
109C2×C4⋊C4×C43—22no—
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43—41no—
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C22⋊C4×C43—21no—
118C2×C22⋊C4×C43—21no—
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×C43D411yescharacteristic
127C2×C22⋊C4×C43D411yescharacteristic
128C2×C42×C43—21no—
129C2×C42×C43C2311yescharacteristic
130C2×C42×C43C2311yescharacteristic
131#106×C43—22no—
132C4⋊C8×C43—22no—
133C4⋊C8×C43—41no—
134#103×C43—22no—
135#103×C43—22no—
136#103×C43D414yescomplemented
137#102×C43—22no—
138#102×C43—22no—
139#102×C43—22no—
140#102×C43—22no—
141#102×C43—22no—
142#102×C43—22no—
143#102×C43—41no—
144C22⋊C8×C43—22no—
145#95×C43—21no—
146#95×C43—21no—
147#95×C43—21no—
148#95×C43—21no—
149#95×C43D411yescharacteristic
150#95×C43D411yescharacteristic
151C24×C43—21no—
152C24×C43—21no—
153C24×C43—21no—
154C24×C43C2×D411yescharacteristic
155#41×C43—28no—
156#41×C43—44no—
157#41×C43—44no—
158#41×C43—44no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43C2×D412yes—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—24no—
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—21no—
175C2×D4×C43—21no—
176C2×D4×C43—21no—
177C2×D4×C43—21no—
178C2×D4×C43—21no—
179C2×D4×C43—21no—
180C2×D4×C43—21no—
181C2×D4×C43—21no—
182C2×D4×C43—42no—
183C2×D4×C43—42no—
184C2×D4×C43—42no—
185C2×D4×C43—42no—
186C2×D4×C43—42no—
187C2×D4×C43—42no—
188C2×D4×C43—42no—
189C2×D4×C43—42no—
190C2×D4×C43—42no—
191C2×D4×C43—42no—
192C2×D4×C43—81no—
193C2×D4×C43—81no—
194C2×D4×C43—81no—
195C2×D4×C43—81no—
196C2×D4×C43C2×D412yes—
197C2×D4×C43#4112yes—
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—21no—
207C22×C4×C43—42no—
208C22×C4×C43—42no—
209C22×C4×C43—42no—
210C22×C4×C43—42no—
211C22×C4×C43—42no—
212C22×C4×C43—42no—
213C22×C4×C43—42no—
214C22×C4×C43—81no—
215C22×C4×C43—81no—
216C22×C4×C43C2×D412yes—
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2×D411yescharacteristic
219C22×C4×C43C2×D411yescharacteristic
220C22×C4×C43C2×D411yescharacteristic
221C22×C4×C43C2×D411yescharacteristic
222C22×C4×C43#4112yes—
223C22×C4×C43C2411yescharacteristic
224SD16×C43—44no—
225D8×C43—44no—
226D8×C43—44no—
227M16×C43—44no—
228C2×C8×C43—21no—
229C2×C8×C43—21no—
230C2×C8×C43—21no—
231C2×C8×C43—21no—
232C2×C8×C43—21no—
233C2×C8×C43—21no—
234C2×C8×C43—21no—
235C2×C8×C43—21no—
236C2×C8×C43—21no—
237C2×C8×C43—21no—
238C2×C8×C43—21no—
239C2×C8×C43C2×D412yes—
240C4⋊C4×C43—21no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43—21no—
243C4⋊C4×C43—21no—
244C4⋊C4×C43—21no—
245C4⋊C4×C43—21no—
246C4⋊C4×C43—42no—
247C4⋊C4×C43—42no—
248C4⋊C4×C43C2×D412yes—
249C4⋊C4×C43C2×D412yes—
250C22⋊C4×C43—24no—
251C22⋊C4×C43—22no—
252C22⋊C4×C43—41no—
253C22⋊C4×C43—42no—
254C22⋊C4×C43—42no—
255C22⋊C4×C43—42no—
256C22⋊C4×C43—42no—
257C22⋊C4×C43—42no—
258C22⋊C4×C43—81no—
259C22⋊C4×C43—81no—
260C22⋊C4×C43—81no—
261C42×C43—21no—
262C42×C43—21no—
263C42×C43—21no—
264C42×C43—21no—
265C42×C43—42no—
266C23×C43—21no—
267C23×C43—21no—
268C23×C43—21no—
269C23×C43—21no—
270C23×C43—21no—
271C23×C43—21no—
272C23×C43—22no—
273C23×C43—22no—
274C23×C43—41no—
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×C43—41no—
289C23×C43—41no—
290C23×C43—41no—
291C23×C43—41no—
292C23×C43—41no—
293C23×C43#12112yes—
294C23×C43C22×D411yescharacteristic
295Q8×C43—22no—
296Q8×C43—22no—
297Q8×C43—41no—
298Q8×C43—41no—
299D4×C43—22no—
300D4×C43—22no—
301D4×C43—22no—
302D4×C43—22no—
303D4×C43—48no—
304D4×C43—48no—
305D4×C43—41no—
306D4×C43—41no—
307D4×C43—41no—
308D4×C43—41no—
309D4×C43—41no—
310D4×C43—41no—
311D4×C43—41no—
312D4×C43—41no—
313D4×C43—84no—
314D4×C43—84no—
315D4×C43—84no—
316C2×C4×C43—21no—
317C2×C4×C43—21no—
318C2×C4×C43—21no—
319C2×C4×C43—21no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—21no—
326C2×C4×C43—21no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—21no—
330C2×C4×C43—21no—
331C2×C4×C43—21no—
332C2×C4×C43—21no—
333C2×C4×C43—21no—
334C2×C4×C43—21no—
335C2×C4×C43—21no—
336C2×C4×C43—48no—
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—41no—
344C2×C4×C43—41no—
345C2×C4×C43—41no—
346C2×C4×C43—41no—
347C2×C4×C43—41no—
348C2×C4×C43—41no—
349C2×C4×C43—84no—
350C2×C4×C43—84no—
351C2×C4×C43#12112yes—
352C2×C4×C43AGL(1,ℤ/8)12yes—
353C2×C4×C43C22×D411yescharacteristic
354C2×C4×C43C22×D411yescharacteristic
355C2×C4×C43C2×#4111yescharacteristic
356C2×C4×C43C2×#4111yescharacteristic
357C2×C4×C43H(5,𝔽2)11yescharacteristic
358C2×C4×C43H(5,𝔽2)11yescharacteristic
359C8×C43—22no—
360C8×C43—41no—
361C8×C43—41no—
362C8×C43—41no—
363#25106C4311yesmaximal, characteristic, direct product factor, Sylow
364C22×C43—22no—
365C22×C43—22no—
366C22×C43—22no—
367C22×C43—41no—
368C22×C43—41no—
369C22×C43—41no—
370C22×C43—41no—
371C22×C43—42no—
372C22×C43—42no—
373C22×C43—42no—
374C22×C43—42no—
375C22×C43—42no—
376C22×C43—42no—
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×C43—81no—
386C22×C43—81no—
387C22×C43—81no—
388C22×C43—81no—
389C22×C43—81no—
390C22×C43—81no—
391C22×C43—81no—
392C22×C43C2×#12111yescharacteristic
393C22×C43D4211yescharacteristic
394C22×C43#54611yescharacteristic
395C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
396C22×C43#57511yescharacteristic
397C22×C43#57611yescharacteristic
398C22×C43#57711yescharacteristic
399C4×C43—22no—
400C4×C43—22no—
401C4×C43—42no—
402C4×C43—41no—
403C4×C43—41no—
404C4×C43—42no—
405C4×C43—42no—
406C4×C43—41no—
407C4×C43—81no—
408C4×C43—81no—
409C4×C43#52511yescharacteristic
410C4×C43#53811yescharacteristic
411C4×C43D4211yescharacteristic
412C4×C43#54611yescharacteristic
413C2×#469C2×C4311yescharacteristic, complemented
414C2×#463C2×C4311yescharacteristic, complemented
415C2×#449C2×C4311yescharacteristic, complemented
416C2×#417C2×C4311yescharacteristic, complemented
417#2431C2×C4311yescharacteristic, complemented
418#2361C2×C4311yescharacteristic, complemented
419#2065C2×C4311yescharacteristic, complemented
420#2055C2×C4311yescharacteristic, complemented
421#2042C2×C4311yescharacteristic, complemented
422#2011C2×C4311yescharacteristic, complemented
423#1982C2×C4311yescharacteristic, complemented
424#1927C2×C4311yescharacteristic, complemented
425#1879C2×C4311yescharacteristic, complemented
426#1874C2×C4311yescharacteristic, complemented
427#1851C2×C4311yescharacteristic, complemented
428C2×C43—42no—
429C2×C43—82no—
430C2×C43—82no—
431C2×C43—161no—
432C2×C43#242411yescharacteristic
433C2×C43#303611yescharacteristic
434C2×C43#304511yescharacteristic
435C2×C43#327111yescharacteristic
436C2×C43#327411yescharacteristic
437C2×C43#330611yescharacteristic
438C2×C43#332211yescharacteristic
439C22×#41C22×C4311yescharacteristic
440C22×SD16C22×C4311yescharacteristic
441C22×D8C22×C4311yescharacteristic
442C22×D8C22×C4311yescharacteristic
443C22×M16C22×C4311yescharacteristic
444C2×#127C22×C4311yescharacteristic
445C2×#124C22×C4311yescharacteristic
446C2×#121C22×C4311yescharacteristic
447C2×#121C22×C4311yescharacteristic
448C2×C4×D4—21no—
449C2×C4×D4C22×C4311yescharacteristic
450C22×C4⋊C4C22×C4311yescharacteristic
451#469—24no—
452#463—24no—
453#449—24no—
454C2×#106C22×C4311yescharacteristic
455C2×C4⋊C8C22×C4311yescharacteristic
456C2×C4⋊C8C22×C4311yescharacteristic
457#417—24no—
458C2×#103C22×C4311yescharacteristic
459C2×#103C22×C4311yescharacteristic
460C2×#103C22×C4311yescharacteristic
461C2×#102C22×C4311yescharacteristic
462C2×#102C22×C4311yescharacteristic
463C2×#102C22×C4311yescharacteristic
464C2×#102C22×C4311yescharacteristic
465C2×#102C22×C4311yescharacteristic
466C2×#102C22×C4311yescharacteristic
467C2×#102C22×C4311yescharacteristic
468C2×C22⋊C8C22×C4311yescharacteristic
469#392—21no—
470#392—21no—
471#391C22×C4311yescharacteristic
472#390C22×C4311yescharacteristic
473#390C22×C4311yescharacteristic
474#389C22×C4311yescharacteristic
475#388—21no—
476#386—21no—
477#386—21no—
478#386—21no—
479#385—21no—
480C4×C4⋊C4C22×C4311yescharacteristic
481C4×C22⋊C4C22×C4311yescharacteristic
482#340C22×C4311yescharacteristic
483#340C22×C4311yescharacteristic
484#336C22×C4311yescharacteristic
485#336C22×C4311yescharacteristic
486C43#2510611yescharacteristic, direct product factor, Sylow
487C2×#41—22no—
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—22no—
491C2×#41—41no—
492C2×#41—41no—
493C22×Q8C23×C4311yescharacteristic
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4C23×C4311yescharacteristic
500C22×D4C23×C4311yescharacteristic
501C22×D4C23×C4311yescharacteristic
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4C23×C4311yescharacteristic
506C2×SD16—22no—
507C2×SD16—22no—
508C2×SD16—41no—
509C2×D8—22no—
510C2×D8—22no—
511C2×D8—22no—
512C2×D8—22no—
513C2×D8—41no—
514C2×D8—41no—
515C2×M16—22no—
516C2×M16—22no—
517C2×M16—41no—
518C22×C8C23×C4311yescharacteristic
519C22×C8C23×C4311yescharacteristic
520C22×C8C23×C4311yescharacteristic
521C22×C8C23×C4311yescharacteristic
522#127—22no—
523#127—41no—
524#124—22no—
525#124—41no—
526#121—22no—
527#121—22no—
528#121—22no—
529#121D4×C4314yescomplemented
530C4×D4—22no—
531C4×D4—41no—
532C4×D4—44no—
533C2×C4⋊C4—22no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—41no—
537C2×C4⋊C4C23×C4311yescharacteristic
538C2×C4⋊C4C23×C4311yescharacteristic
539C2×C4⋊C4C23×C4311yescharacteristic
540C2×C4⋊C4C23×C4311yescharacteristic
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⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4D4×C4311yescharacteristic
551C2×C22⋊C4D4×C4311yescharacteristic
552C2×C42—21no—
553C2×C42C23×C4311yescharacteristic
554C2×C42C23×C4311yescharacteristic
555#106—22no—
556C4⋊C8—22no—
557C4⋊C8—41no—
558#103—22no—
559#103—22no—
560#103D4×C4314yescomplemented
561#102—22no—
562#102—22no—
563#102—22no—
564#102—22no—
565#102—22no—
566#102—22no—
567#102—41no—
568C22⋊C8—22no—
569#95—21no—
570#95—21no—
571#95—21no—
572#95—21no—
573#95D4×C4311yescharacteristic
574#95D4×C4311yescharacteristic
575C24—21no—
576C24—21no—
577C24—21no—
578C24C2×D4×C4311yescharacteristic
579#41—28no—
580#41—44no—
581#41—44no—
582#41—44no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8C2×D4×C4312yes—
589C2×D4—24no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—81no—
617C2×D4—81no—
618C2×D4—81no—
619C2×D4—81no—
620C2×D4C2×D4×C4312yes—
621C2×D4#41×C4312yes—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—81no—
639C22×C4—81no—
640C22×C4C2×D4×C4311yescharacteristic
641C22×C4C2×D4×C4311yescharacteristic
642C22×C4C2×D4×C4311yescharacteristic
643C22×C4C2×D4×C4311yescharacteristic
644C22×C4C2×D4×C4312yes—
645C22×C4C2×D4×C4311yescharacteristic
646C22×C4#41×C4312yes—
647C22×C4C24×C4311yescharacteristic
648SD16—44no—
649D8—44no—
650D8—44no—
651M16—44no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8C2×D4×C4312yes—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4C2×D4×C4312yes—
673C4⋊C4C2×D4×C4312yes—
674C22⋊C4—24no—
675C22⋊C4—22no—
676C22⋊C4—41no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—81no—
683C22⋊C4—81no—
684C22⋊C4—81no—
685C42—21no—
686C42—21no—
687C42—21no—
688C42—21no—
689C42—42no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—22no—
697C23—22no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23#121×C4312yes—
718C23C22×D4×C4311yescharacteristic
719Q8—22no—
720Q8—22no—
721Q8—41no—
722Q8—41no—
723D4—22no—
724D4—22no—
725D4—22no—
726D4—22no—
727D4—48no—
728D4—48no—
729D4—41no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—41no—
734D4—41no—
735D4—41no—
736D4—41no—
737D4—84no—
738D4—84no—
739D4—84no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—48no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—84no—
774C2×C4—84no—
775C2×C4#121×C4312yes—
776C2×C4AGL(1,ℤ/8)×C4312yes—
777C2×C4C22×D4×C4311yescharacteristic
778C2×C4C22×D4×C4311yescharacteristic
779C2×C4C2×#41×C4311yescharacteristic
780C2×C4C2×#41×C4311yescharacteristic
781C2×C4H(5,𝔽2)×C4311yescharacteristic
782C2×C4H(5,𝔽2)×C4311yescharacteristic
783C8—22no—
784C8—41no—
785C8—41no—
786C8—41no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22C2×#121×C4311yescharacteristic
816C22D42×C4311yescharacteristic
817C22C43×#54611yescharacteristic
818C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
819C22C43×#57511yescharacteristic
820C22C43×#57611yescharacteristic
821C22C43×#57711yescharacteristic
822C4—22no—
823C4—22no—
824C4—42no—
825C4—41no—
826C4—41no—
827C4—42no—
828C4—42no—
829C4—41no—
830C4—81no—
831C4—81no—
832C4C43×#52511yescharacteristic
833C4C43×#53811yescharacteristic
834C4D42×C4311yescharacteristic
835C4C43×#54611yescharacteristic
836C2—42no—
837C2—82no—
838C2—82no—
839C2—161no—
840C2C43×#242411yescharacteristic
841C2C43×#303611yescharacteristic
842C2C43×#304511yescharacteristic
843C2C43×#327111yescharacteristic
844C2C43×#327411yescharacteristic
845C2C43×#330611yescharacteristic
846C2C43×#332211yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C4×C22⋊C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#469C2semidirect
2. C2×C43×#463C2semidirect
3. C2×C43×#449C2semidirect
4. C2×C43×#417C2semidirect
5. C43×#2431C2semidirect
6. C43×#2361C2semidirect
7. C43×#2065C2semidirect
8. C43×#2055C2semidirect
9. C43×#2042C2semidirect
10. C43×#2011C2semidirect
11. C43×#1982C2semidirect
12. C43×#1927C2semidirect
13. C43×#1879C2semidirect
14. C43×#1874C2semidirect
15. C43×#1851C2semidirect
105. #121×C43D4semidirect
136. #103×C43D4semidirect
363. #25106C43direct (N × H)
413. C2×#469C2×C43semidirect
414. C2×#463C2×C43semidirect
415. C2×#449C2×C43semidirect
416. C2×#417C2×C43semidirect
417. #2431C2×C43semidirect
418. #2361C2×C43semidirect
419. #2065C2×C43semidirect
420. #2055C2×C43semidirect
421. #2042C2×C43semidirect
422. #2011C2×C43semidirect
423. #1982C2×C43semidirect
424. #1927C2×C43semidirect
425. #1879C2×C43semidirect
426. #1874C2×C43semidirect
427. #1851C2×C43semidirect
486. C43#25106direct (N × H)
529. #121D4×C43semidirect
560. #103D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4692
C2×C43×#4632
C2×C43×#4492
C2×C43×#4172
C43×#24312
C43×#23612
C43×#20652
C43×#20552
C43×#20422
C43×#20112
C43×#19822
C43×#19272
C43×#18792
C43×#18742
C43×#18512
#2510643