Finite Group Databasebeta

← C43×#19011 #24939028

Subgroups — C43×#19011 #24939028

Order 11008.

886 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3529C211yesmaximal, characteristic
2C43×#3240C211yesmaximal, characteristic, complemented
3C43×#3216C211yesmaximal, characteristic, complemented
4C43×#3181C211yesmaximal, characteristic, complemented
5C43×#1664C211yesmaximal, characteristic, complemented
6C43×#1662C211yesmaximal, characteristic, complemented
7C43×#1661C211yesmaximal, characteristic, complemented
8C43×#1661C211yesmaximal, characteristic, complemented
9C43×#1661C211yesmaximal, characteristic, complemented
10C43×#1660C211yesmaximal, characteristic, complemented
11C43×#1659C211yesmaximal, characteristic, complemented
12C43×#1659C211yesmaximal, characteristic, complemented
13C43×#1535C211yesmaximal, characteristic, complemented
14C43×#1532C211yesmaximal, characteristic, complemented
15C43×#1530C211yesmaximal, characteristic, complemented
16C43×#563—21no—
17C43×#563C2211yescharacteristic
18C43×#562—21no—
19C43×#562—21no—
20C43×#562C2211yescharacteristic
21C43×#562C2211yescharacteristic
22C43×H(3,𝔽4)C2211yescharacteristic
23C43×#560—21no—
24C43×#560—21no—
25C43×#560—21no—
26C43×#533C2211yescharacteristic, complemented
27C43×#532—21no—
28C43×#532C2211yescharacteristic
29C43×#529—21no—
30C43×#529—21no—
31C43×#529C2211yescharacteristic
32C43×#529C2211yescharacteristic
33C43×#525—21no—
34C43×#525—21no—
35C43×#525—21no—
36C43×#501C2211yescharacteristic, complemented
37C43×#501C2211yescharacteristic, complemented
38C43×#501C2211yescharacteristic, complemented
39C43×#497C2211yescharacteristic
40C43×#497C2211yescharacteristic
41C43×#497C2211yescharacteristic, complemented
42C43×#491C2211yescharacteristic, complemented
43C43×#489C2211yescharacteristic
44C43×#489C2211yescharacteristic
45C43×#489C2211yescharacteristic
46C43×#489C2211yescharacteristic
47C43×#489C2211yescharacteristic, complemented
48C43×#485—21no—
49C43×#482—21no—
50C43×#479—21no—
51C43×#478—21no—
52C43×#467—21no—
53C43×#465—21no—
54C43×#462—21no—
55C43×#460—21no—
56C43×#452—21no—
57C43×#452—21no—
58C43×#441—21no—
59C43×#440—21no—
60C43×#432C2211yescharacteristic, complemented
61C43×#432C2211yescharacteristic, complemented
62C2×#97×C43C2211yescharacteristic, complemented
63C43×#330C2211yescharacteristic, complemented
64C43×#330C2211yescharacteristic, complemented
65C43×#330C2211yescharacteristic, complemented
66C43×#330C2211yescharacteristic, complemented
67C43×#329C2211yescharacteristic
68C43×#329C2211yescharacteristic
69C43×#329C2211yescharacteristic
70C43×#329C2211yescharacteristic
71C43×#329C2211yescharacteristic
72C43×#329C2211yescharacteristic
73C43×#329C2211yescharacteristic, complemented
74C43×#329C2211yescharacteristic, complemented
75C2×#41×C43—21no—
76C2×#41×C43D411yescharacteristic
77C2×#41×C43D411yescharacteristic
78C23×C4×C43—21no—
79C2×Q16×C43—21no—
80C2×Q16×C43—21no—
81C2×Q16×C43—21no—
82C2×SD16×C43—21no—
83C2×SD16×C43—21no—
84C2×SD16×C43—21no—
85C22×C8×C43—21no—
86C4⋊Q8×C43—21no—
87C4⋊Q8×C43D411yescharacteristic
88C4⋊Q8×C43C2311yescharacteristic
89C4⋊Q8×C43C2311yescharacteristic
90#127×C43—21no—
91#127×C43D411yescharacteristic
92#126×C43—21no—
93#126×C43—21no—
94#126×C43—21no—
95#126×C43—21no—
96#126×C43—21no—
97#126×C43—21no—
98#125×C43—21no—
99#125×C43—21no—
100#125×C43—21no—
101#125×C43C2311yescharacteristic
102#125×C43C2311yescharacteristic
103#124×C43—21no—
104#124×C43—21no—
105#124×C43—21no—
106#124×C43—21no—
107#124×C43C2311yescharacteristic
108#124×C43C2311yescharacteristic
109#124×C43C2311yescharacteristic
110#124×C43C2311yescharacteristic
111#123×C43—21no—
112#123×C43—21no—
113#123×C43—21no—
114#123×C43—21no—
115#123×C43—21no—
116#123×C43—21no—
117#123×C43—21no—
118#123×C43—21no—
119#123×C43—21no—
120#123×C43—21no—
121#123×C43—21no—
122#123×C43—21no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43—21no—
126C22⋊Q8×C43—21no—
127C22⋊Q8×C43—21no—
128C22⋊Q8×C43—21no—
129C22⋊Q8×C43—21no—
130C22⋊Q8×C43—21no—
131C22⋊Q8×C43—21no—
132C22⋊Q8×C43—21no—
133C22⋊Q8×C43D411yescharacteristic
134C22⋊Q8×C43D411yescharacteristic
135#121×C43—21no—
136#121×C43—21no—
137#121×C43—21no—
138#121×C43—21no—
139#121×C43—21no—
140#121×C43—21no—
141#121×C43—21no—
142#121×C43—21no—
143#121×C43—21no—
144#121×C43—21no—
145#121×C43—21no—
146#121×C43—21no—
147#121×C43—21no—
148#121×C43—21no—
149#121×C43D411yescharacteristic
150#121×C43D411yescharacteristic
151#120×C43—21no—
152#120×C43—21no—
153#120×C43—21no—
154#120×C43—21no—
155#120×C43—21no—
156#120×C43—21no—
157C4×Q8×C43—21no—
158C4×Q8×C43—21no—
159C4×Q8×C43D411yescharacteristic
160C4×Q8×C43D411yescharacteristic
161C4×D4×C43—21no—
162C4×D4×C43—21no—
163C4×D4×C43—21no—
164C4×D4×C43—21no—
165C4×D4×C43—21no—
166C4×D4×C43—21no—
167C4×D4×C43—21no—
168C4×D4×C43—21no—
169C4×D4×C43D411yescharacteristic
170C4×D4×C43D411yescharacteristic
171#117×C43—21no—
172#117×C43—21no—
173#117×C43—21no—
174#117×C43—21no—
175C2×C42×C43—21no—
176C2×C42×C43C2311yescharacteristic
177#107×C43—21no—
178#107×C43—21no—
179#107×C43—21no—
180#106×C43—21no—
181#106×C43—21no—
182#106×C43—21no—
183C4⋊C8×C43—21no—
184C4⋊C8×C43—21no—
185#103×C43—21no—
186#103×C43—21no—
187#103×C43—21no—
188#103×C43—21no—
189#103×C43—21no—
190#103×C43—21no—
191#103×C43—21no—
192#102×C43—21no—
193#102×C43—21no—
194#102×C43—21no—
195#102×C43—21no—
196#102×C43—21no—
197C22⋊C8×C43—21no—
198C22⋊C8×C43—21no—
199#97×C43—21no—
200#97×C43C2311yescharacteristic
201#97×C43C2311yescharacteristic
202#97×C43C2311yescharacteristic
203#97×C43C2311yescharacteristic
204#97×C43C2311yescharacteristic
205#97×C43C2311yescharacteristic
206C24×C43—21no—
207#41×C43—81no—
208#41×C43—81no—
209#41×C43—82no—
210C2×Q8×C43—21no—
211C2×Q8×C43—21no—
212C2×Q8×C43—21no—
213C2×Q8×C43C2×D411yescharacteristic
214C2×Q8×C43C2×D411yescharacteristic
215C2×Q8×C43C2×D411yescharacteristic
216C2×Q8×C43C2×D411yescharacteristic
217C2×D4×C43—21no—
218C2×D4×C43—21no—
219C2×D4×C43—21no—
220C2×D4×C43—21no—
221C2×D4×C43—21no—
222C2×D4×C43—21no—
223C2×D4×C43—21no—
224C2×D4×C43—21no—
225C2×D4×C43—21no—
226C2×D4×C43—21no—
227C2×D4×C43—21no—
228C2×D4×C43—21no—
229C2×D4×C43—21no—
230C2×D4×C43C2×D411yescharacteristic
231C2×D4×C43C2×D411yescharacteristic
232C2×D4×C43C2×D411yescharacteristic
233C2×D4×C43C2×D411yescharacteristic
234C22×C4×C43—21no—
235C22×C4×C43—21no—
236C22×C4×C43—21no—
237C22×C4×C43—21no—
238C22×C4×C43—21no—
239C22×C4×C43—21no—
240C22×C4×C43—21no—
241C22×C4×C43—21no—
242C22×C4×C43—21no—
243C22×C4×C43—82no—
244C22×C4×C43C2×D411yescharacteristic
245C22×C4×C43C2×D411yescharacteristic
246C22×C4×C43C2×D411yescharacteristic
247Q16×C43—42no—
248Q16×C43—81no—
249Q16×C43—81no—
250SD16×C43—42no—
251SD16×C43—81no—
252SD16×C43—81no—
253C2×C8×C43—21no—
254C2×C8×C43—21no—
255C2×C8×C43—21no—
256C2×C8×C43—21no—
257C2×C8×C43—21no—
258C2×C8×C43—21no—
259C2×C8×C43—42no—
260C4⋊C4×C43—21no—
261C4⋊C4×C43—21no—
262C4⋊C4×C43—21no—
263C4⋊C4×C43—21no—
264C4⋊C4×C43—21no—
265C4⋊C4×C43—21no—
266C4⋊C4×C43—21no—
267C4⋊C4×C43—21no—
268C4⋊C4×C43—21no—
269C4⋊C4×C43—21no—
270C4⋊C4×C43—21no—
271C4⋊C4×C43—21no—
272C4⋊C4×C43—21no—
273C4⋊C4×C43—21no—
274C4⋊C4×C43—21no—
275C4⋊C4×C43—21no—
276C4⋊C4×C43—21no—
277C4⋊C4×C43—21no—
278C4⋊C4×C43—21no—
279C4⋊C4×C43—21no—
280C4⋊C4×C43—41no—
281C4⋊C4×C43—41no—
282C4⋊C4×C43C2×D411yescharacteristic
283C4⋊C4×C43C2×D411yescharacteristic
284C4⋊C4×C43C2×D411yescharacteristic
285C4⋊C4×C43C2×D411yescharacteristic
286C22⋊C4×C43—21no—
287C22⋊C4×C43—21no—
288C22⋊C4×C43—21no—
289C22⋊C4×C43—21no—
290C22⋊C4×C43—21no—
291C22⋊C4×C43—21no—
292C22⋊C4×C43—21no—
293C22⋊C4×C43—21no—
294C22⋊C4×C43—21no—
295C22⋊C4×C43—21no—
296C22⋊C4×C43—21no—
297C22⋊C4×C43—21no—
298C22⋊C4×C43—21no—
299C22⋊C4×C43—21no—
300C22⋊C4×C43—21no—
301C22⋊C4×C43—21no—
302C22⋊C4×C43—21no—
303C22⋊C4×C43—21no—
304C22⋊C4×C43—21no—
305C22⋊C4×C43—21no—
306C22⋊C4×C43—21no—
307C22⋊C4×C43—21no—
308C22⋊C4×C43—21no—
309C22⋊C4×C43—21no—
310C22⋊C4×C43—41no—
311C42×C43—21no—
312C42×C43—21no—
313C42×C43—21no—
314C42×C43—21no—
315C42×C43—41no—
316C42×C43C2×D411yescharacteristic
317C42×C43C2×D411yescharacteristic
318C42×C43C2×D411yescharacteristic
319C42×C43C2411yescharacteristic
320C23×C43—21no—
321C23×C43—21no—
322C23×C43—21no—
323C23×C43—21no—
324C23×C43—81no—
325C23×C43—81no—
326C23×C43—81no—
327C23×C43#12011yescharacteristic
328Q8×C43—41no—
329Q8×C43—41no—
330Q8×C43—41no—
331Q8×C43—41no—
332Q8×C43—41no—
333Q8×C43—41no—
334Q8×C43—41no—
335Q8×C43—41no—
336Q8×C43—81no—
337D4×C43—41no—
338D4×C43—41no—
339D4×C43—41no—
340D4×C43—41no—
341D4×C43—81no—
342D4×C43—81no—
343D4×C43—81no—
344D4×C43—81no—
345D4×C43—81no—
346D4×C43—81no—
347D4×C43—81no—
348D4×C43—81no—
349D4×C43—81no—
350D4×C43—81no—
351D4×C43—81no—
352D4×C43—81no—
353D4×C43—81no—
354C2×C4×C43—21no—
355C2×C4×C43—21no—
356C2×C4×C43—21no—
357C2×C4×C43—21no—
358C2×C4×C43—21no—
359C2×C4×C43—21no—
360C2×C4×C43—21no—
361C2×C4×C43—21no—
362C2×C4×C43—41no—
363C2×C4×C43—41no—
364C2×C4×C43—41no—
365C2×C4×C43—42no—
366C2×C4×C43—42no—
367C2×C4×C43—42no—
368C2×C4×C43—42no—
369C2×C4×C43—41no—
370C2×C4×C43—41no—
371C2×C4×C43—81no—
372C2×C4×C43—81no—
373C2×C4×C43—81no—
374C2×C4×C43—81no—
375C2×C4×C43—81no—
376C2×C4×C43#12011yescharacteristic
377C2×C4×C43#12011yescharacteristic
378C2×C4×C43#12011yescharacteristic
379C2×C4×C43C22×D411yescharacteristic
380C2×C4×C43C22×D411yescharacteristic
381C2×C4×C43C22×D411yescharacteristic
382C8×C43—22no—
383C8×C43—41no—
384C8×C43—41no—
385C8×C43—41no—
386C8×C43—41no—
387C8×C43—41no—
388#19011C4311yesmaximal, characteristic, direct product factor, Sylow
389C22×C43—21no—
390C22×C43—21no—
391C22×C43—21no—
392C22×C43—41no—
393C22×C43—41no—
394C22×C43—41no—
395C22×C43—41no—
396C22×C43—41no—
397C22×C43—41no—
398C22×C43—41no—
399C22×C43—41no—
400C22×C43—41no—
401C22×C43—41no—
402C22×C43—41no—
403C22×C43—41no—
404C22×C43—84no—
405C22×C43C2×#12011yescharacteristic
406C4×C43—21no—
407C4×C43—21no—
408C4×C43—21no—
409C4×C43—21no—
410C4×C43—21no—
411C4×C43—21no—
412C4×C43—41no—
413C4×C43—41no—
414C4×C43—41no—
415C4×C43—41no—
416C4×C43—41no—
417C4×C43—41no—
418C4×C43—41no—
419C4×C43—41no—
420C4×C43—81no—
421C4×C43—81no—
422#3529C2×C4311yescharacteristic
423#3240C2×C4311yescharacteristic, complemented
424#3216C2×C4311yescharacteristic, complemented
425#3181C2×C4311yescharacteristic, complemented
426#1664C2×C4311yescharacteristic, complemented
427#1662C2×C4311yescharacteristic, complemented
428#1661C2×C4311yescharacteristic, complemented
429#1661C2×C4311yescharacteristic, complemented
430#1661C2×C4311yescharacteristic, complemented
431#1660C2×C4311yescharacteristic, complemented
432#1659C2×C4311yescharacteristic, complemented
433#1659C2×C4311yescharacteristic, complemented
434#1535C2×C4311yescharacteristic, complemented
435#1532C2×C4311yescharacteristic, complemented
436#1530C2×C4311yescharacteristic, complemented
437C2×C43—41no—
438C2×C43—81no—
439C2×C43—81no—
440C2×C43—81no—
441C2×C43—81no—
442C2×C43#301811yescharacteristic
443C2×C43#301911yescharacteristic
444C2×C43#302211yescharacteristic
445#563—21no—
446#563C22×C4311yescharacteristic
447#562—21no—
448#562—21no—
449#562C22×C4311yescharacteristic
450#562C22×C4311yescharacteristic
451H(3,𝔽4)C22×C4311yescharacteristic
452#560—21no—
453#560—21no—
454#560—21no—
455#533C22×C4311yescharacteristic, complemented
456#532—21no—
457#532C22×C4311yescharacteristic
458#529—21no—
459#529—21no—
460#529C22×C4311yescharacteristic
461#529C22×C4311yescharacteristic
462#525—21no—
463#525—21no—
464#525—21no—
465#501C22×C4311yescharacteristic, complemented
466#501C22×C4311yescharacteristic, complemented
467#501C22×C4311yescharacteristic, complemented
468#497C22×C4311yescharacteristic
469#497C22×C4311yescharacteristic
470#497C22×C4311yescharacteristic, complemented
471#491C22×C4311yescharacteristic, complemented
472#489C22×C4311yescharacteristic
473#489C22×C4311yescharacteristic
474#489C22×C4311yescharacteristic
475#489C22×C4311yescharacteristic
476#489C22×C4311yescharacteristic, complemented
477#485—21no—
478#482—21no—
479#479—21no—
480#478—21no—
481#467—21no—
482#465—21no—
483#462—21no—
484#460—21no—
485#452—21no—
486#452—21no—
487#441—21no—
488#440—21no—
489#432C22×C4311yescharacteristic, complemented
490#432C22×C4311yescharacteristic, complemented
491C2×#97C22×C4311yescharacteristic, complemented
492#330C22×C4311yescharacteristic, complemented
493#330C22×C4311yescharacteristic, complemented
494#330C22×C4311yescharacteristic, complemented
495#330C22×C4311yescharacteristic, complemented
496#329C22×C4311yescharacteristic
497#329C22×C4311yescharacteristic
498#329C22×C4311yescharacteristic
499#329C22×C4311yescharacteristic
500#329C22×C4311yescharacteristic
501#329C22×C4311yescharacteristic
502#329C22×C4311yescharacteristic, complemented
503#329C22×C4311yescharacteristic, complemented
504C43#1901111yescharacteristic, direct product factor, Sylow
505C2×#41—21no—
506C2×#41D4×C4311yescharacteristic
507C2×#41D4×C4311yescharacteristic
508C23×C4—21no—
509C2×Q16—21no—
510C2×Q16—21no—
511C2×Q16—21no—
512C2×SD16—21no—
513C2×SD16—21no—
514C2×SD16—21no—
515C22×C8—21no—
516C4⋊Q8—21no—
517C4⋊Q8D4×C4311yescharacteristic
518C4⋊Q8C23×C4311yescharacteristic
519C4⋊Q8C23×C4311yescharacteristic
520#127—21no—
521#127D4×C4311yescharacteristic
522#126—21no—
523#126—21no—
524#126—21no—
525#126—21no—
526#126—21no—
527#126—21no—
528#125—21no—
529#125—21no—
530#125—21no—
531#125C23×C4311yescharacteristic
532#125C23×C4311yescharacteristic
533#124—21no—
534#124—21no—
535#124—21no—
536#124—21no—
537#124C23×C4311yescharacteristic
538#124C23×C4311yescharacteristic
539#124C23×C4311yescharacteristic
540#124C23×C4311yescharacteristic
541#123—21no—
542#123—21no—
543#123—21no—
544#123—21no—
545#123—21no—
546#123—21no—
547#123—21no—
548#123—21no—
549#123—21no—
550#123—21no—
551#123—21no—
552#123—21no—
553C22⋊Q8—21no—
554C22⋊Q8—21no—
555C22⋊Q8—21no—
556C22⋊Q8—21no—
557C22⋊Q8—21no—
558C22⋊Q8—21no—
559C22⋊Q8—21no—
560C22⋊Q8—21no—
561C22⋊Q8—21no—
562C22⋊Q8—21no—
563C22⋊Q8D4×C4311yescharacteristic
564C22⋊Q8D4×C4311yescharacteristic
565#121—21no—
566#121—21no—
567#121—21no—
568#121—21no—
569#121—21no—
570#121—21no—
571#121—21no—
572#121—21no—
573#121—21no—
574#121—21no—
575#121—21no—
576#121—21no—
577#121—21no—
578#121—21no—
579#121D4×C4311yescharacteristic
580#121D4×C4311yescharacteristic
581#120—21no—
582#120—21no—
583#120—21no—
584#120—21no—
585#120—21no—
586#120—21no—
587C4×Q8—21no—
588C4×Q8—21no—
589C4×Q8D4×C4311yescharacteristic
590C4×Q8D4×C4311yescharacteristic
591C4×D4—21no—
592C4×D4—21no—
593C4×D4—21no—
594C4×D4—21no—
595C4×D4—21no—
596C4×D4—21no—
597C4×D4—21no—
598C4×D4—21no—
599C4×D4D4×C4311yescharacteristic
600C4×D4D4×C4311yescharacteristic
601#117—21no—
602#117—21no—
603#117—21no—
604#117—21no—
605C2×C42—21no—
606C2×C42C23×C4311yescharacteristic
607#107—21no—
608#107—21no—
609#107—21no—
610#106—21no—
611#106—21no—
612#106—21no—
613C4⋊C8—21no—
614C4⋊C8—21no—
615#103—21no—
616#103—21no—
617#103—21no—
618#103—21no—
619#103—21no—
620#103—21no—
621#103—21no—
622#102—21no—
623#102—21no—
624#102—21no—
625#102—21no—
626#102—21no—
627C22⋊C8—21no—
628C22⋊C8—21no—
629#97—21no—
630#97C23×C4311yescharacteristic
631#97C23×C4311yescharacteristic
632#97C23×C4311yescharacteristic
633#97C23×C4311yescharacteristic
634#97C23×C4311yescharacteristic
635#97C23×C4311yescharacteristic
636C24—21no—
637#41—81no—
638#41—81no—
639#41—82no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8C2×D4×C4311yescharacteristic
644C2×Q8C2×D4×C4311yescharacteristic
645C2×Q8C2×D4×C4311yescharacteristic
646C2×Q8C2×D4×C4311yescharacteristic
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4C2×D4×C4311yescharacteristic
661C2×D4C2×D4×C4311yescharacteristic
662C2×D4C2×D4×C4311yescharacteristic
663C2×D4C2×D4×C4311yescharacteristic
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—82no—
674C22×C4C2×D4×C4311yescharacteristic
675C22×C4C2×D4×C4311yescharacteristic
676C22×C4C2×D4×C4311yescharacteristic
677Q16—42no—
678Q16—81no—
679Q16—81no—
680SD16—42no—
681SD16—81no—
682SD16—81no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—42no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—41no—
711C4⋊C4—41no—
712C4⋊C4C2×D4×C4311yescharacteristic
713C4⋊C4C2×D4×C4311yescharacteristic
714C4⋊C4C2×D4×C4311yescharacteristic
715C4⋊C4C2×D4×C4311yescharacteristic
716C22⋊C4—21no—
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—21no—
727C22⋊C4—21no—
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—21no—
731C22⋊C4—21no—
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—41no—
741C42—21no—
742C42—21no—
743C42—21no—
744C42—21no—
745C42—41no—
746C42C2×D4×C4311yescharacteristic
747C42C2×D4×C4311yescharacteristic
748C42C2×D4×C4311yescharacteristic
749C42C24×C4311yescharacteristic
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—81no—
755C23—81no—
756C23—81no—
757C23#120×C4311yescharacteristic
758Q8—41no—
759Q8—41no—
760Q8—41no—
761Q8—41no—
762Q8—41no—
763Q8—41no—
764Q8—41no—
765Q8—41no—
766Q8—81no—
767D4—41no—
768D4—41no—
769D4—41no—
770D4—41no—
771D4—81no—
772D4—81no—
773D4—81no—
774D4—81no—
775D4—81no—
776D4—81no—
777D4—81no—
778D4—81no—
779D4—81no—
780D4—81no—
781D4—81no—
782D4—81no—
783D4—81no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4—81no—
804C2×C4—81no—
805C2×C4—81no—
806C2×C4#120×C4311yescharacteristic
807C2×C4#120×C4311yescharacteristic
808C2×C4#120×C4311yescharacteristic
809C2×C4C22×D4×C4311yescharacteristic
810C2×C4C22×D4×C4311yescharacteristic
811C2×C4C22×D4×C4311yescharacteristic
812C8—22no—
813C8—41no—
814C8—41no—
815C8—41no—
816C8—41no—
817C8—41no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—84no—
834C22C2×#120×C4311yescharacteristic
835C4—21no—
836C4—21no—
837C4—21no—
838C4—21no—
839C4—21no—
840C4—21no—
841C4—41no—
842C4—41no—
843C4—41no—
844C4—41no—
845C4—41no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—81no—
850C4—81no—
851C2—41no—
852C2—81no—
853C2—81no—
854C2—81no—
855C2—81no—
856C2C43×#301811yescharacteristic
857C2C43×#301911yescharacteristic
858C2C43×#302211yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#3529C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#3240C2semidirect
3. C43×#3216C2semidirect
4. C43×#3181C2semidirect
5. C43×#1664C2semidirect
6. C43×#1662C2semidirect
7. C43×#1661C2semidirect
8. C43×#1661C2semidirect
9. C43×#1661C2semidirect
10. C43×#1660C2semidirect
11. C43×#1659C2semidirect
12. C43×#1659C2semidirect
13. C43×#1535C2semidirect
14. C43×#1532C2semidirect
15. C43×#1530C2semidirect
26. C43×#533C22semidirect
36. C43×#501C22semidirect
37. C43×#501C22semidirect
38. C43×#501C22semidirect
41. C43×#497C22semidirect
42. C43×#491C22semidirect
47. C43×#489C22semidirect
60. C43×#432C22semidirect
61. C43×#432C22semidirect
62. C2×#97×C43C22semidirect
63. C43×#330C22semidirect
64. C43×#330C22semidirect
65. C43×#330C22semidirect
66. C43×#330C22semidirect
73. C43×#329C22semidirect
74. C43×#329C22semidirect
388. #19011C43direct (N × H)
423. #3240C2×C43semidirect
424. #3216C2×C43semidirect
425. #3181C2×C43semidirect
426. #1664C2×C43semidirect
427. #1662C2×C43semidirect
428. #1661C2×C43semidirect
429. #1661C2×C43semidirect
430. #1661C2×C43semidirect
431. #1660C2×C43semidirect
432. #1659C2×C43semidirect
433. #1659C2×C43semidirect
434. #1535C2×C43semidirect
435. #1532C2×C43semidirect
436. #1530C2×C43semidirect
455. #533C22×C43semidirect
465. #501C22×C43semidirect
466. #501C22×C43semidirect
467. #501C22×C43semidirect
470. #497C22×C43semidirect
471. #491C22×C43semidirect
476. #489C22×C43semidirect
489. #432C22×C43semidirect
490. #432C22×C43semidirect
491. C2×#97C22×C43semidirect
492. #330C22×C43semidirect
493. #330C22×C43semidirect
494. #330C22×C43semidirect
495. #330C22×C43semidirect
502. #329C22×C43semidirect
503. #329C22×C43semidirect
504. C43#19011direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#35292
C43×#32402
C43×#32162
C43×#31812
C43×#16642
C43×#16622
C43×#16612
C43×#16602
C43×#16592
C43×#15352
C43×#15322
C43×#15302
#1901143