Finite Group Databasebeta

← C43×#18249 #24938266

Subgroups — C43×#18249 #24938266

Order 11008.

936 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3560C211yesmaximal, characteristic
2C43×#3112C211yesmaximal, characteristic, complemented
3C43×#3108C211yesmaximal, characteristic, complemented
4C43×#2637C211yesmaximal, characteristic, complemented
5C43×#1612C211yesmaximal, characteristic, complemented
6C43×#1610C211yesmaximal, characteristic, complemented
7C43×#1609C211yesmaximal, characteristic, complemented
8C43×#1607C211yesmaximal, characteristic, complemented
9C43×#1606C211yesmaximal, characteristic, complemented
10C43×#1604C211yesmaximal, characteristic, complemented
11C43×#1603C211yesmaximal, characteristic, complemented
12C43×#1601C211yesmaximal, characteristic, complemented
13C43×#1517C211yesmaximal, characteristic, complemented
14C43×#1512C211yesmaximal, characteristic, complemented
15C43×#1473C211yesmaximal, characteristic, complemented
16C43×#563—21no—
17C43×#560—21no—
18C43×#553—21no—
19C43×#553—21no—
20C43×#551—21no—
21C43×#547—21no—
22C43×#546—21no—
23C43×#546—21no—
24C43×#542—21no—
25C43×#539—21no—
26C43×#539C2211yescharacteristic
27C43×#538—21no—
28C43×#538—21no—
29C43×#538C2211yescharacteristic
30C43×#537C2211yescharacteristic
31C43×#534C2211yescharacteristic
32C43×#532C2211yescharacteristic
33C43×#529C2211yescharacteristic
34C2×#126×C43C2211yescharacteristic
35C2×C4×Q8×C43C2211yescharacteristic, complemented
36C43×#483C2211yescharacteristic, complemented
37C43×#480C2211yescharacteristic
38C43×#480C2211yescharacteristic
39C43×#480C2211yescharacteristic, complemented
40C43×#479—21no—
41C43×#477—21no—
42C43×#464—21no—
43C43×#460—21no—
44C43×#451C2211yescharacteristic, complemented
45C43×#448C2211yescharacteristic
46C43×#448C2211yescharacteristic
47C43×#448C2211yescharacteristic, complemented
48C43×#440—21no—
49C43×#440—21no—
50C4×Q16×C43—21no—
51C4×SD16×C43—21no—
52C43×#432C2211yescharacteristic, complemented
53C43×#431C2211yescharacteristic, complemented
54C43×#398—21no—
55C43×#398C2211yescharacteristic, complemented
56C43×#397C2211yescharacteristic
57C43×#396—21no—
58C43×#395C2211yescharacteristic, complemented
59C43×#393C2211yescharacteristic
60C43×#388—21no—
61C43×#387—21no—
62C43×#382C2211yescharacteristic, complemented
63C43×#328C2211yescharacteristic, complemented
64C43×#328C2211yescharacteristic, complemented
65C43×#327C2211yescharacteristic
66C43×#327C2211yescharacteristic
67C43×#327C2211yescharacteristic
68C43×#327C2211yescharacteristic
69C43×#327C2211yescharacteristic, complemented
70C43×#327C2211yescharacteristic, complemented
71C43×#324C2211yescharacteristic, complemented
72C43×#324C2211yescharacteristic, complemented
73C43×#323C2211yescharacteristic
74C43×#323C2211yescharacteristic
75C2×#41×C43—21no—
76C2×#41×C43—21no—
77C22×Q8×C43C2311yescharacteristic
78C22×D4×C43—21no—
79C2×Q16×C43—21no—
80C2×SD16×C43—21no—
81C2×SD16×C43—21no—
82C2×SD16×C43—21no—
83C4⋊Q8×C43—21no—
84C4⋊Q8×C43D411yescharacteristic
85#127×C43D411yescharacteristic
86#126×C43—21no—
87#126×C43—21no—
88#126×C43—21no—
89#126×C43—21no—
90#126×C43—21no—
91#126×C43—21no—
92#126×C43—21no—
93#126×C43—21no—
94#126×C43—21no—
95#125×C43—21no—
96#125×C43—21no—
97#125×C43D411yescharacteristic
98#124×C43—21no—
99#124×C43—21no—
100#124×C43—21no—
101#124×C43—21no—
102#124×C43D411yescharacteristic
103#123×C43—21no—
104#123×C43—21no—
105#123×C43—21no—
106#123×C43—21no—
107#123×C43—21no—
108#123×C43—21no—
109#123×C43—21no—
110#123×C43—21no—
111#123×C43—21no—
112#123×C43—21no—
113#123×C43—21no—
114#123×C43—21no—
115C22⋊Q8×C43—21no—
116C22⋊Q8×C43—21no—
117C22⋊Q8×C43—21no—
118C22⋊Q8×C43—21no—
119C22⋊Q8×C43—21no—
120C22⋊Q8×C43—21no—
121C22⋊Q8×C43—21no—
122C22⋊Q8×C43C2311yescharacteristic
123#121×C43—21no—
124#121×C43—21no—
125#121×C43—21no—
126#121×C43—21no—
127#121×C43—21no—
128#121×C43—21no—
129#121×C43—21no—
130#121×C43—21no—
131#121×C43—21no—
132#121×C43—21no—
133#121×C43—21no—
134#121×C43—21no—
135#121×C43C2311yescharacteristic
136#121×C43C2311yescharacteristic
137#121×C43C2311yescharacteristic
138#120×C43—21no—
139#120×C43—21no—
140#120×C43—21no—
141#120×C43—21no—
142#120×C43—21no—
143C4×Q8×C43—21no—
144C4×Q8×C43—21no—
145C4×Q8×C43—21no—
146C4×Q8×C43—21no—
147C4×Q8×C43D411yescharacteristic
148C4×D4×C43—21no—
149C4×D4×C43—21no—
150C4×D4×C43—21no—
151C4×D4×C43—21no—
152C4×D4×C43—21no—
153C4×D4×C43—21no—
154C4×D4×C43—21no—
155C4×D4×C43—21no—
156C4×D4×C43D411yescharacteristic
157C4×D4×C43D411yescharacteristic
158C4×D4×C43D411yescharacteristic
159#117×C43—21no—
160#117×C43—21no—
161C2×C4⋊C4×C43—21no—
162C2×C4⋊C4×C43—21no—
163C2×C4⋊C4×C43—21no—
164C2×C4⋊C4×C43—21no—
165C2×C4⋊C4×C43—21no—
166C2×C4⋊C4×C43D411yescharacteristic
167C2×C4⋊C4×C43D411yescharacteristic
168C2×C4⋊C4×C43C2311yescharacteristic
169C2×C4⋊C4×C43C2311yescharacteristic
170C2×C22⋊C4×C43—21no—
171C2×C22⋊C4×C43—21no—
172C2×C22⋊C4×C43—21no—
173C2×C22⋊C4×C43—21no—
174C2×C22⋊C4×C43D411yescharacteristic
175C2×C22⋊C4×C43D411yescharacteristic
176C2×C22⋊C4×C43C2311yescharacteristic
177C2×C42×C43—21no—
178C2×C42×C43C2311yescharacteristic
179#107×C43—21no—
180#107×C43—21no—
181#107×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#102×C43—21no—
191#102×C43—21no—
192#102×C43—21no—
193C22⋊C8×C43C2311yescharacteristic
194C22⋊C8×C43C2311yescharacteristic
195C22⋊C8×C43C2311yescharacteristic
196C22⋊C8×C43C2311yescharacteristic
197#97×C43—21no—
198C4×C8×C43—21no—
199#95×C43—21no—
200#95×C43—21no—
201#95×C43—21no—
202#95×C43—21no—
203#95×C43—21no—
204#95×C43C2311yescharacteristic
205#95×C43C2311yescharacteristic
206C24×C43—21no—
207C24×C43C2×D411yescharacteristic
208#41×C43—81no—
209#41×C43—81no—
210#41×C43—81no—
211#41×C43—81no—
212C2×Q8×C43—21no—
213C2×Q8×C43—21no—
214C2×Q8×C43—21no—
215C2×Q8×C43—21no—
216C2×Q8×C43—42no—
217C2×Q8×C43C2×D411yescharacteristic
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×C43—81no—
231C2×D4×C43—81no—
232C2×D4×C43C2×D411yescharacteristic
233C2×D4×C43C2×D411yescharacteristic
234C2×D4×C43C2×D411yescharacteristic
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—21no—
244C22×C4×C43—21no—
245C22×C4×C43—21no—
246C22×C4×C43—21no—
247C22×C4×C43C2×D411yescharacteristic
248C22×C4×C43C2×D411yescharacteristic
249C22×C4×C43C2×D411yescharacteristic
250C22×C4×C43C2×D411yescharacteristic
251C22×C4×C43C2×D411yescharacteristic
252C22×C4×C43C2411yescharacteristic
253Q16×C43—42no—
254SD16×C43—42no—
255SD16×C43—42no—
256SD16×C43—42no—
257C2×C8×C43—21no—
258C2×C8×C43—21no—
259C2×C8×C43—21no—
260C2×C8×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—42no—
281C4⋊C4×C43—41no—
282C4⋊C4×C43—41no—
283C4⋊C4×C43—81no—
284C4⋊C4×C43—81no—
285C4⋊C4×C43C2×D411yescharacteristic
286C4⋊C4×C43C2×D411yescharacteristic
287C4⋊C4×C43C2×D411yescharacteristic
288C4⋊C4×C43C2×D411yescharacteristic
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—21no—
311C22⋊C4×C43—21no—
312C22⋊C4×C43—21no—
313C22⋊C4×C43—21no—
314C22⋊C4×C43—42no—
315C22⋊C4×C43—81no—
316C42×C43—21no—
317C42×C43—21no—
318C42×C43—21no—
319C42×C43—41no—
320C42×C43—41no—
321C42×C43C2×D411yescharacteristic
322C42×C43C2×D411yescharacteristic
323C42×C43C2×D411yescharacteristic
324C42×C43C2×D411yescharacteristic
325C23×C43—21no—
326C23×C43—21no—
327C23×C43—21no—
328C23×C43—21no—
329C23×C43—21no—
330C23×C43—21no—
331C23×C43—41no—
332C23×C43—41no—
333C23×C43—81no—
334C23×C43—81no—
335C23×C43—81no—
336C23×C43C22×D411yescharacteristic
337Q8×C43—22no—
338Q8×C43—22no—
339Q8×C43—41no—
340Q8×C43—41no—
341Q8×C43—41no—
342Q8×C43—81no—
343Q8×C43—81no—
344D4×C43—41no—
345D4×C43—41no—
346D4×C43—41no—
347D4×C43—41no—
348D4×C43—41no—
349D4×C43—41no—
350D4×C43—41no—
351D4×C43—41no—
352D4×C43—41no—
353D4×C43—81no—
354D4×C43—81no—
355D4×C43—81no—
356D4×C43—81no—
357D4×C43—81no—
358D4×C43—81no—
359D4×C43—81no—
360D4×C43—81no—
361D4×C43—81no—
362C2×C4×C43—21no—
363C2×C4×C43—21no—
364C2×C4×C43—22no—
365C2×C4×C43—21no—
366C2×C4×C43—21no—
367C2×C4×C43—21no—
368C2×C4×C43—21no—
369C2×C4×C43—21no—
370C2×C4×C43—21no—
371C2×C4×C43—21no—
372C2×C4×C43—21no—
373C2×C4×C43—21no—
374C2×C4×C43—21no—
375C2×C4×C43—41no—
376C2×C4×C43—41no—
377C2×C4×C43—41no—
378C2×C4×C43—41no—
379C2×C4×C43—41no—
380C2×C4×C43—41no—
381C2×C4×C43—41no—
382C2×C4×C43—41no—
383C2×C4×C43—41no—
384C2×C4×C43—41no—
385C2×C4×C43—41no—
386C2×C4×C43—41no—
387C2×C4×C43—41no—
388C2×C4×C43—41no—
389C2×C4×C43—41no—
390C2×C4×C43—81no—
391C2×C4×C43—81no—
392C2×C4×C43—81no—
393C2×C4×C43—81no—
394C2×C4×C43—81no—
395C2×C4×C43—81no—
396C2×C4×C43—81no—
397C2×C4×C43—81no—
398C2×C4×C43#12011yescharacteristic
399C2×C4×C43#12011yescharacteristic
400C2×C4×C43#12011yescharacteristic
401C2×C4×C43#12011yescharacteristic
402C2×C4×C43C22×D411yescharacteristic
403C2×C4×C43C22×D411yescharacteristic
404C8×C43—41no—
405C8×C43—41no—
406C8×C43—41no—
407C8×C43—41no—
408#18249C4311yesmaximal, characteristic, direct product factor, Sylow
409C22×C43—21no—
410C22×C43—21no—
411C22×C43—41no—
412C22×C43—41no—
413C22×C43—41no—
414C22×C43—41no—
415C22×C43—41no—
416C22×C43—41no—
417C22×C43—41no—
418C22×C43—41no—
419C22×C43—41no—
420C22×C43—41no—
421C22×C43—41no—
422C22×C43—41no—
423C22×C43—81no—
424C22×C43—81no—
425C22×C43—162no—
426C22×C43C2×#12011yescharacteristic
427C22×C43#57611yescharacteristic
428C22×C43#57711yescharacteristic
429C4×C43—21no—
430C4×C43—21no—
431C4×C43—21no—
432C4×C43—21no—
433C4×C43—21no—
434C4×C43—21no—
435C4×C43—41no—
436C4×C43—41no—
437C4×C43—41no—
438C4×C43—41no—
439C4×C43—41no—
440C4×C43—41no—
441C4×C43—42no—
442C4×C43—41no—
443C4×C43—41no—
444C4×C43—81no—
445C4×C43—81no—
446C4×C43—81no—
447#3560C2×C4311yescharacteristic
448#3112C2×C4311yescharacteristic, complemented
449#3108C2×C4311yescharacteristic, complemented
450#2637C2×C4311yescharacteristic, complemented
451#1612C2×C4311yescharacteristic, complemented
452#1610C2×C4311yescharacteristic, complemented
453#1609C2×C4311yescharacteristic, complemented
454#1607C2×C4311yescharacteristic, complemented
455#1606C2×C4311yescharacteristic, complemented
456#1604C2×C4311yescharacteristic, complemented
457#1603C2×C4311yescharacteristic, complemented
458#1601C2×C4311yescharacteristic, complemented
459#1517C2×C4311yescharacteristic, complemented
460#1512C2×C4311yescharacteristic, complemented
461#1473C2×C4311yescharacteristic, complemented
462C2×C43—21no—
463C2×C43—21no—
464C2×C43—81no—
465C2×C43—81no—
466C2×C43—81no—
467C2×C43—81no—
468C2×C43#301211yescharacteristic
469C2×C43#302211yescharacteristic
470C2×C43#302511yescharacteristic
471#563—21no—
472#560—21no—
473#553—21no—
474#553—21no—
475#551—21no—
476#547—21no—
477#546—21no—
478#546—21no—
479#542—21no—
480#539—21no—
481#539C22×C4311yescharacteristic
482#538—21no—
483#538—21no—
484#538C22×C4311yescharacteristic
485#537C22×C4311yescharacteristic
486#534C22×C4311yescharacteristic
487#532C22×C4311yescharacteristic
488#529C22×C4311yescharacteristic
489C2×#126C22×C4311yescharacteristic
490C2×C4×Q8C22×C4311yescharacteristic, complemented
491#483C22×C4311yescharacteristic, complemented
492#480C22×C4311yescharacteristic
493#480C22×C4311yescharacteristic
494#480C22×C4311yescharacteristic, complemented
495#479—21no—
496#477—21no—
497#464—21no—
498#460—21no—
499#451C22×C4311yescharacteristic, complemented
500#448C22×C4311yescharacteristic
501#448C22×C4311yescharacteristic
502#448C22×C4311yescharacteristic, complemented
503#440—21no—
504#440—21no—
505C4×Q16—21no—
506C4×SD16—21no—
507#432C22×C4311yescharacteristic, complemented
508#431C22×C4311yescharacteristic, complemented
509#398—21no—
510#398C22×C4311yescharacteristic, complemented
511#397C22×C4311yescharacteristic
512#396—21no—
513#395C22×C4311yescharacteristic, complemented
514#393C22×C4311yescharacteristic
515#388—21no—
516#387—21no—
517#382C22×C4311yescharacteristic, complemented
518#328C22×C4311yescharacteristic, complemented
519#328C22×C4311yescharacteristic, complemented
520#327C22×C4311yescharacteristic
521#327C22×C4311yescharacteristic
522#327C22×C4311yescharacteristic
523#327C22×C4311yescharacteristic
524#327C22×C4311yescharacteristic, complemented
525#327C22×C4311yescharacteristic, complemented
526#324C22×C4311yescharacteristic, complemented
527#324C22×C4311yescharacteristic, complemented
528#323C22×C4311yescharacteristic
529#323C22×C4311yescharacteristic
530C43#1824911yescharacteristic, direct product factor, Sylow
531C2×#41—21no—
532C2×#41—21no—
533C22×Q8C23×C4311yescharacteristic
534C22×D4—21no—
535C2×Q16—21no—
536C2×SD16—21no—
537C2×SD16—21no—
538C2×SD16—21no—
539C4⋊Q8—21no—
540C4⋊Q8D4×C4311yescharacteristic
541#127D4×C4311yescharacteristic
542#126—21no—
543#126—21no—
544#126—21no—
545#126—21no—
546#126—21no—
547#126—21no—
548#126—21no—
549#126—21no—
550#126—21no—
551#125—21no—
552#125—21no—
553#125D4×C4311yescharacteristic
554#124—21no—
555#124—21no—
556#124—21no—
557#124—21no—
558#124D4×C4311yescharacteristic
559#123—21no—
560#123—21no—
561#123—21no—
562#123—21no—
563#123—21no—
564#123—21no—
565#123—21no—
566#123—21no—
567#123—21no—
568#123—21no—
569#123—21no—
570#123—21no—
571C22⋊Q8—21no—
572C22⋊Q8—21no—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8—21no—
576C22⋊Q8—21no—
577C22⋊Q8—21no—
578C22⋊Q8C23×C4311yescharacteristic
579#121—21no—
580#121—21no—
581#121—21no—
582#121—21no—
583#121—21no—
584#121—21no—
585#121—21no—
586#121—21no—
587#121—21no—
588#121—21no—
589#121—21no—
590#121—21no—
591#121C23×C4311yescharacteristic
592#121C23×C4311yescharacteristic
593#121C23×C4311yescharacteristic
594#120—21no—
595#120—21no—
596#120—21no—
597#120—21no—
598#120—21no—
599C4×Q8—21no—
600C4×Q8—21no—
601C4×Q8—21no—
602C4×Q8—21no—
603C4×Q8D4×C4311yescharacteristic
604C4×D4—21no—
605C4×D4—21no—
606C4×D4—21no—
607C4×D4—21no—
608C4×D4—21no—
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4D4×C4311yescharacteristic
613C4×D4D4×C4311yescharacteristic
614C4×D4D4×C4311yescharacteristic
615#117—21no—
616#117—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4D4×C4311yescharacteristic
623C2×C4⋊C4D4×C4311yescharacteristic
624C2×C4⋊C4C23×C4311yescharacteristic
625C2×C4⋊C4C23×C4311yescharacteristic
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4D4×C4311yescharacteristic
631C2×C22⋊C4D4×C4311yescharacteristic
632C2×C22⋊C4C23×C4311yescharacteristic
633C2×C42—21no—
634C2×C42C23×C4311yescharacteristic
635#107—21no—
636#107—21no—
637#107—21no—
638#106—21no—
639C4⋊C8—21no—
640C4⋊C8—21no—
641#103—21no—
642#103—21no—
643#103—21no—
644#103—21no—
645#103—21no—
646#102—21no—
647#102—21no—
648#102—21no—
649C22⋊C8C23×C4311yescharacteristic
650C22⋊C8C23×C4311yescharacteristic
651C22⋊C8C23×C4311yescharacteristic
652C22⋊C8C23×C4311yescharacteristic
653#97—21no—
654C4×C8—21no—
655#95—21no—
656#95—21no—
657#95—21no—
658#95—21no—
659#95—21no—
660#95C23×C4311yescharacteristic
661#95C23×C4311yescharacteristic
662C24—21no—
663C24C2×D4×C4311yescharacteristic
664#41—81no—
665#41—81no—
666#41—81no—
667#41—81no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8—42no—
673C2×Q8C2×D4×C4311yescharacteristic
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—81no—
687C2×D4—81no—
688C2×D4C2×D4×C4311yescharacteristic
689C2×D4C2×D4×C4311yescharacteristic
690C2×D4C2×D4×C4311yescharacteristic
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4C2×D4×C4311yescharacteristic
704C22×C4C2×D4×C4311yescharacteristic
705C22×C4C2×D4×C4311yescharacteristic
706C22×C4C2×D4×C4311yescharacteristic
707C22×C4C2×D4×C4311yescharacteristic
708C22×C4C24×C4311yescharacteristic
709Q16—42no—
710SD16—42no—
711SD16—42no—
712SD16—42no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—42no—
737C4⋊C4—41no—
738C4⋊C4—41no—
739C4⋊C4—81no—
740C4⋊C4—81no—
741C4⋊C4C2×D4×C4311yescharacteristic
742C4⋊C4C2×D4×C4311yescharacteristic
743C4⋊C4C2×D4×C4311yescharacteristic
744C4⋊C4C2×D4×C4311yescharacteristic
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—21no—
761C22⋊C4—21no—
762C22⋊C4—21no—
763C22⋊C4—21no—
764C22⋊C4—21no—
765C22⋊C4—21no—
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—42no—
771C22⋊C4—81no—
772C42—21no—
773C42—21no—
774C42—21no—
775C42—41no—
776C42—41no—
777C42C2×D4×C4311yescharacteristic
778C42C2×D4×C4311yescharacteristic
779C42C2×D4×C4311yescharacteristic
780C42C2×D4×C4311yescharacteristic
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—41no—
788C23—41no—
789C23—81no—
790C23—81no—
791C23—81no—
792C23C22×D4×C4311yescharacteristic
793Q8—22no—
794Q8—22no—
795Q8—41no—
796Q8—41no—
797Q8—41no—
798Q8—81no—
799Q8—81no—
800D4—41no—
801D4—41no—
802D4—41no—
803D4—41no—
804D4—41no—
805D4—41no—
806D4—41no—
807D4—41no—
808D4—41no—
809D4—81no—
810D4—81no—
811D4—81no—
812D4—81no—
813D4—81no—
814D4—81no—
815D4—81no—
816D4—81no—
817D4—81no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—22no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—81no—
847C2×C4—81no—
848C2×C4—81no—
849C2×C4—81no—
850C2×C4—81no—
851C2×C4—81no—
852C2×C4—81no—
853C2×C4—81no—
854C2×C4#120×C4311yescharacteristic
855C2×C4#120×C4311yescharacteristic
856C2×C4#120×C4311yescharacteristic
857C2×C4#120×C4311yescharacteristic
858C2×C4C22×D4×C4311yescharacteristic
859C2×C4C22×D4×C4311yescharacteristic
860C8—41no—
861C8—41no—
862C8—41no—
863C8—41no—
864C22—21no—
865C22—21no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—81no—
879C22—81no—
880C22—162no—
881C22C2×#120×C4311yescharacteristic
882C22C43×#57611yescharacteristic
883C22C43×#57711yescharacteristic
884C4—21no—
885C4—21no—
886C4—21no—
887C4—21no—
888C4—21no—
889C4—21no—
890C4—41no—
891C4—41no—
892C4—41no—
893C4—41no—
894C4—41no—
895C4—41no—
896C4—42no—
897C4—41no—
898C4—41no—
899C4—81no—
900C4—81no—
901C4—81no—
902C2—21no—
903C2—21no—
904C2—81no—
905C2—81no—
906C2—81no—
907C2—81no—
908C2C43×#301211yescharacteristic
909C2C43×#302211yescharacteristic
910C2C43×#302511yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC43×#3560C2
LCSG ▷ C22×C4 ▷ 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×#3112C2semidirect
3. C43×#3108C2semidirect
4. C43×#2637C2semidirect
5. C43×#1612C2semidirect
6. C43×#1610C2semidirect
7. C43×#1609C2semidirect
8. C43×#1607C2semidirect
9. C43×#1606C2semidirect
10. C43×#1604C2semidirect
11. C43×#1603C2semidirect
12. C43×#1601C2semidirect
13. C43×#1517C2semidirect
14. C43×#1512C2semidirect
15. C43×#1473C2semidirect
35. C2×C4×Q8×C43C22semidirect
36. C43×#483C22semidirect
39. C43×#480C22semidirect
44. C43×#451C22semidirect
47. C43×#448C22semidirect
52. C43×#432C22semidirect
53. C43×#431C22semidirect
55. C43×#398C22semidirect
58. C43×#395C22semidirect
62. C43×#382C22semidirect
63. C43×#328C22semidirect
64. C43×#328C22semidirect
69. C43×#327C22semidirect
70. C43×#327C22semidirect
71. C43×#324C22semidirect
72. C43×#324C22semidirect
408. #18249C43direct (N × H)
448. #3112C2×C43semidirect
449. #3108C2×C43semidirect
450. #2637C2×C43semidirect
451. #1612C2×C43semidirect
452. #1610C2×C43semidirect
453. #1609C2×C43semidirect
454. #1607C2×C43semidirect
455. #1606C2×C43semidirect
456. #1604C2×C43semidirect
457. #1603C2×C43semidirect
458. #1601C2×C43semidirect
459. #1517C2×C43semidirect
460. #1512C2×C43semidirect
461. #1473C2×C43semidirect
490. C2×C4×Q8C22×C43semidirect
491. #483C22×C43semidirect
494. #480C22×C43semidirect
499. #451C22×C43semidirect
502. #448C22×C43semidirect
507. #432C22×C43semidirect
508. #431C22×C43semidirect
510. #398C22×C43semidirect
513. #395C22×C43semidirect
517. #382C22×C43semidirect
518. #328C22×C43semidirect
519. #328C22×C43semidirect
524. #327C22×C43semidirect
525. #327C22×C43semidirect
526. #324C22×C43semidirect
527. #324C22×C43semidirect
530. C43#18249direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#35602
C43×#31122
C43×#31082
C43×#26372
C43×#16122
C43×#16102
C43×#16092
C43×#16072
C43×#16062
C43×#16042
C43×#16032
C43×#16012
C43×#15172
C43×#15122
C43×#14732
#1824943