Finite Group Databasebeta

← C43×#18224 #24938241

Subgroups — C43×#18224 #24938241

Order 11008.

1370 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3534C211yesmaximal, characteristic, complemented
2C43×#3003C211yesmaximal, characteristic, complemented
3C2×C43×#447C211yesmaximal, characteristic, complemented
4C43×#2613C211yesmaximal, characteristic, complemented
5C43×#1600C212yesmaximal, complemented
6C43×#1598C212yesmaximal, complemented
7C43×#1597C212yesmaximal, complemented
8C43×#1595C212yesmaximal, complemented
9C43×#1516C211yesmaximal, characteristic, complemented
10C43×#1510C211yesmaximal, characteristic, complemented
11C43×#1468C211yesmaximal, characteristic, complemented
12C23×D4×C43C2211yescharacteristic, complemented
13C2×AGL(1,ℤ/8)×C43—21no—
14C22×D8×C43—21no—
15C43×#562—21no—
16C43×#560—21no—
17C43×#553—21no—
18C43×#551—21no—
19C43×#546—21no—
20C43×#546—21no—
21C43×#546—21no—
22D42×C43—21no—
23C43×#540—21no—
24C43×#539—21no—
25C43×#539C2211yescharacteristic, complemented
26C43×#538—21no—
27C43×#538C2211yescharacteristic, complemented
28C43×#537C2211yescharacteristic, complemented
29C43×#534—21no—
30C43×#534C2211yescharacteristic, complemented
31C43×#525C2211yescharacteristic
32C2×#123×C43C2211yescharacteristic
33C2×#121×C43C2211yescharacteristic
34C2×#120×C43—21no—
35C43×#450—21no—
36C43×#450C2212yescomplemented
37C43×#447—21no—
38C43×#447—21no—
39C43×#447—21no—
40C43×#447C2212yes—
41C43×#447C2212yescomplemented
42C43×#447C2212yescomplemented
43C43×#418—21no—
44C2×#102×C43—21no—
45C43×#407C2211yescharacteristic, complemented
46C2×C22⋊C8×C43C2211yescharacteristic, complemented
47C43×#394—21no—
48C43×#394C2212yescomplemented
49C43×#392—21no—
50C43×#392C2212yescomplemented
51C43×#381C2211yescharacteristic, complemented
52C43×#379—21no—
53C43×#328C2212yescomplemented
54C43×#327C2212yescomplemented
55C43×#327C2212yescomplemented
56C43×#327C2212yescomplemented
57C43×#324C2212yescomplemented
58C43×#323C2212yescomplemented
59C25×C43—21no—
60C2×#41×C43—21no—
61C2×#41×C43D411yescharacteristic, complemented
62C22×D4×C43—21no—
63C22×D4×C43—21no—
64C22×D4×C43—21no—
65C22×D4×C43—22no—
66C22×D4×C43—21no—
67C22×D4×C43—21no—
68C22×D4×C43—21no—
69C22×D4×C43—21no—
70C22×D4×C43—21no—
71C22×D4×C43—44no—
72C22×D4×C43D411yescharacteristic
73C22×D4×C43D411yescharacteristic, complemented
74C22×D4×C43C2312yes—
75C23×C4×C43C2311yescharacteristic
76AGL(1,ℤ/8)×C43—44no—
77C2×SD16×C43—22no—
78C2×D8×C43—22no—
79C2×D8×C43—22no—
80C2×D8×C43—22no—
81C2×D8×C43—44no—
82C2×M16×C43—21no—
83C22×C8×C43—21no—
84#127×C43—21no—
85#126×C43—21no—
86#126×C43—21no—
87#126×C43—21no—
88#126×C43—21no—
89#125×C43—21no—
90#125×C43—21no—
91#124×C43—21no—
92#124×C43—21no—
93#124×C43—21no—
94#123×C43—21no—
95#123×C43—21no—
96#123×C43—21no—
97#123×C43—21no—
98#123×C43—21no—
99#123×C43—21no—
100#123×C43—21no—
101#123×C43—21no—
102#123×C43—21no—
103#123×C43—21no—
104#123×C43—21no—
105#123×C43—21no—
106#123×C43—21no—
107#123×C43—21no—
108C22⋊Q8×C43—21no—
109C22⋊Q8×C43—21no—
110C22⋊Q8×C43—21no—
111C22⋊Q8×C43—21no—
112C22⋊Q8×C43—21no—
113C22⋊Q8×C43D411yescharacteristic, complemented
114C22⋊Q8×C43C2311yescharacteristic
115#121×C43—21no—
116#121×C43—21no—
117#121×C43—21no—
118#121×C43—21no—
119#121×C43—21no—
120#121×C43—21no—
121#121×C43—21no—
122#121×C43—21no—
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×C43D411yescharacteristic, complemented
131#121×C43D411yescharacteristic, complemented
132#121×C43D411yescharacteristic, complemented
133#121×C43C2311yescharacteristic
134#121×C43C2311yescharacteristic
135#121×C43C2311yescharacteristic
136#120×C43—21no—
137#120×C43—21no—
138#120×C43—21no—
139#120×C43—21no—
140#120×C43—21no—
141#120×C43—21no—
142#120×C43—21no—
143#120×C43—21no—
144#120×C43—44no—
145C4×D4×C43—21no—
146C4×D4×C43—21no—
147C4×D4×C43—21no—
148C4×D4×C43—21no—
149C4×D4×C43—21no—
150C4×D4×C43—21no—
151C4×D4×C43—21no—
152C4×D4×C43—21no—
153#117×C43—21no—
154#117×C43D411yescharacteristic, complemented
155C2×C4⋊C4×C43D411yescharacteristic
156C2×C4⋊C4×C43D411yescharacteristic, complemented
157C2×C4⋊C4×C43C2311yescharacteristic
158C2×C22⋊C4×C43—21no—
159C2×C22⋊C4×C43—21no—
160C2×C22⋊C4×C43—21no—
161C2×C22⋊C4×C43—21no—
162C2×C22⋊C4×C43—22no—
163C2×C22⋊C4×C43—22no—
164C2×C22⋊C4×C43—22no—
165C2×C22⋊C4×C43D411yescharacteristic
166C2×C22⋊C4×C43D411yescharacteristic
167C2×C22⋊C4×C43C2311yescharacteristic
168#102×C43—22no—
169#102×C43—22no—
170#102×C43—22no—
171#102×C43—22no—
172C22⋊C8×C43—21no—
173C22⋊C8×C43—21no—
174C22⋊C8×C43C2312yes—
175C22⋊C8×C43C2312yes—
176#95×C43—21no—
177#95×C43C2312yes—
178C24×C43—24no—
179C24×C43—21no—
180C24×C43—22no—
181C24×C43—21no—
182C24×C43—42no—
183C24×C43—41no—
184C24×C43—41no—
185C24×C43—82no—
186C24×C43—82no—
187C24×C43C2×D411yescharacteristic
188C24×C43C2×D411yescharacteristic
189#41×C43—42no—
190#41×C43—82no—
191C2×Q8×C43—21no—
192C2×Q8×C43C2×D411yescharacteristic
193C2×D4×C43—21no—
194C2×D4×C43—21no—
195C2×D4×C43—21no—
196C2×D4×C43—21no—
197C2×D4×C43—21no—
198C2×D4×C43—21no—
199C2×D4×C43—21no—
200C2×D4×C43—21no—
201C2×D4×C43—21no—
202C2×D4×C43—21no—
203C2×D4×C43—21no—
204C2×D4×C43—21no—
205C2×D4×C43—21no—
206C2×D4×C43—21no—
207C2×D4×C43—21no—
208C2×D4×C43—21no—
209C2×D4×C43—21no—
210C2×D4×C43—24no—
211C2×D4×C43—24no—
212C2×D4×C43—22no—
213C2×D4×C43—22no—
214C2×D4×C43—44no—
215C2×D4×C43—44no—
216C2×D4×C43—42no—
217C2×D4×C43—44no—
218C2×D4×C43—42no—
219C2×D4×C43—42no—
220C2×D4×C43—44no—
221C2×D4×C43—44no—
222C2×D4×C43—41no—
223C2×D4×C43—41no—
224C2×D4×C43—42no—
225C2×D4×C43—82no—
226C2×D4×C43—82no—
227C2×D4×C43—82no—
228C2×D4×C43—82no—
229C2×D4×C43—82no—
230C2×D4×C43C2×D411yescharacteristic
231C2×D4×C43C2×D411yescharacteristic
232C2×D4×C43C2×D411yescharacteristic
233C22×C4×C43—21no—
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—22no—
241C22×C4×C43—42no—
242C22×C4×C43C2×D411yescharacteristic
243C22×C4×C43C2×D411yescharacteristic
244C22×C4×C43C2×D411yescharacteristic
245C22×C4×C43C2×D411yescharacteristic
246C22×C4×C43C2×D411yescharacteristic
247C22×C4×C43C2×D411yescharacteristic
248C22×C4×C43C2×D411yescharacteristic
249C22×C4×C43C2×D411yescharacteristic
250C22×C4×C43C2411yescharacteristic
251SD16×C43—44no—
252D8×C43—44no—
253D8×C43—44no—
254D8×C43—44no—
255M16×C43—42no—
256C2×C8×C43—22no—
257C2×C8×C43—22no—
258C2×C8×C43—42no—
259C4⋊C4×C43—21no—
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×C43C2×D411yescharacteristic
273C4⋊C4×C43C2×D411yescharacteristic
274C4⋊C4×C43C2×D411yescharacteristic
275C4⋊C4×C43C2×D411yescharacteristic
276C22⋊C4×C43—21no—
277C22⋊C4×C43—21no—
278C22⋊C4×C43—21no—
279C22⋊C4×C43—21no—
280C22⋊C4×C43—21no—
281C22⋊C4×C43—21no—
282C22⋊C4×C43—21no—
283C22⋊C4×C43—21no—
284C22⋊C4×C43—21no—
285C22⋊C4×C43—21no—
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—42no—
302C22⋊C4×C43—44no—
303C22⋊C4×C43—82no—
304C22⋊C4×C43—82no—
305C42×C43—21no—
306C42×C43—21no—
307C42×C43—21no—
308C23×C43—22no—
309C23×C43—22no—
310C23×C43—24no—
311C23×C43—21no—
312C23×C43—21no—
313C23×C43—21no—
314C23×C43—21no—
315C23×C43—22no—
316C23×C43—41no—
317C23×C43—42no—
318C23×C43—42no—
319C23×C43—44no—
320C23×C43—42no—
321C23×C43—41no—
322C23×C43—41no—
323C23×C43—42no—
324C23×C43—42no—
325C23×C43—42no—
326C23×C43—44no—
327C23×C43—42no—
328C23×C43—81no—
329C23×C43—81no—
330C23×C43—82no—
331C23×C43—82no—
332C23×C43—82no—
333C23×C43—82no—
334C23×C43—88no—
335C23×C43—81no—
336C23×C43—81no—
337C23×C43—81no—
338C23×C43—88no—
339C23×C43#12011yescharacteristic
340C23×C43#12011yescharacteristic
341C23×C43C22×D411yescharacteristic
342Q8×C43—41no—
343Q8×C43—81no—
344D4×C43—24no—
345D4×C43—24no—
346D4×C43—41no—
347D4×C43—41no—
348D4×C43—41no—
349D4×C43—42no—
350D4×C43—42no—
351D4×C43—44no—
352D4×C43—44no—
353D4×C43—42no—
354D4×C43—42no—
355D4×C43—42no—
356D4×C43—42no—
357D4×C43—42no—
358D4×C43—81no—
359D4×C43—81no—
360D4×C43—81no—
361D4×C43—81no—
362D4×C43—81no—
363D4×C43—81no—
364D4×C43—81no—
365D4×C43—81no—
366D4×C43—81no—
367D4×C43—81no—
368D4×C43—81no—
369D4×C43—81no—
370D4×C43—88no—
371C2×C4×C43—22no—
372C2×C4×C43—22no—
373C2×C4×C43—21no—
374C2×C4×C43—21no—
375C2×C4×C43—21no—
376C2×C4×C43—21no—
377C2×C4×C43—21no—
378C2×C4×C43—21no—
379C2×C4×C43—21no—
380C2×C4×C43—21no—
381C2×C4×C43—22no—
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—42no—
389C2×C4×C43—42no—
390C2×C4×C43—42no—
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×C43C22×D411yescharacteristic
401C2×C4×C43C22×D411yescharacteristic
402C8×C43—42no—
403C8×C43—42no—
404#18224C4311yesmaximal, characteristic, direct product factor, Sylow
405C22×C43—21no—
406C22×C43—21no—
407C22×C43—21no—
408C22×C43—21no—
409C22×C43—21no—
410C22×C43—21no—
411C22×C43—21no—
412C22×C43—44no—
413C22×C43—44no—
414C22×C43—44no—
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—44no—
424C22×C43—41no—
425C22×C43—41no—
426C22×C43—41no—
427C22×C43—41no—
428C22×C43—82no—
429C22×C43—82no—
430C22×C43—82no—
431C22×C43—88no—
432C22×C43—88no—
433C22×C43—82no—
434C22×C43—82no—
435C22×C43—162no—
436C22×C43—162no—
437C22×C43B(4,𝔽2)12yes—
438C22×C43C2×#12011yescharacteristic
439C22×C43#57612yes—
440C4×C43—21no—
441C4×C43—21no—
442C4×C43—21no—
443C4×C43—21no—
444C4×C43—41no—
445C4×C43—41no—
446C4×C43—41no—
447C4×C43—41no—
448C4×C43—41no—
449C4×C43—41no—
450C4×C43—41no—
451C4×C43—41no—
452C4×C43—82no—
453#3534C2×C4311yescharacteristic, complemented
454#3003C2×C4311yescharacteristic, complemented
455C2×#447C2×C4311yescharacteristic, complemented
456#2613C2×C4311yescharacteristic, complemented
457#1600C2×C4312yescomplemented
458#1598C2×C4312yescomplemented
459#1597C2×C4312yescomplemented
460#1595C2×C4312yescomplemented
461#1516C2×C4311yescharacteristic, complemented
462#1510C2×C4311yescharacteristic, complemented
463#1468C2×C4311yescharacteristic, complemented
464C2×C43—22no—
465C2×C43—22no—
466C2×C43—41no—
467C2×C43—84no—
468C2×C43—81no—
469C2×C43—81no—
470C2×C43—81no—
471C2×C43—81no—
472C2×C43#300811yescharacteristic
473C2×C43#302111yescharacteristic
474C2×C43C2×B(4,𝔽2)11yescharacteristic
475C23×D4C22×C4311yescharacteristic, complemented
476C2×AGL(1,ℤ/8)—21no—
477C22×D8—21no—
478#562—21no—
479#560—21no—
480#553—21no—
481#551—21no—
482#546—21no—
483#546—21no—
484#546—21no—
485D42—21no—
486#540—21no—
487#539—21no—
488#539C22×C4311yescharacteristic, complemented
489#538—21no—
490#538C22×C4311yescharacteristic, complemented
491#537C22×C4311yescharacteristic, complemented
492#534—21no—
493#534C22×C4311yescharacteristic, complemented
494#525C22×C4311yescharacteristic
495C2×#123C22×C4311yescharacteristic
496C2×#121C22×C4311yescharacteristic
497C2×#120—21no—
498#450—21no—
499#450C22×C4312yescomplemented
500#447—21no—
501#447—21no—
502#447—21no—
503#447C22×C4312yes—
504#447C22×C4312yescomplemented
505#447C22×C4312yescomplemented
506#418—21no—
507C2×#102—21no—
508#407C22×C4311yescharacteristic, complemented
509C2×C22⋊C8C22×C4311yescharacteristic, complemented
510#394—21no—
511#394C22×C4312yescomplemented
512#392—21no—
513#392C22×C4312yescomplemented
514#381C22×C4311yescharacteristic, complemented
515#379—21no—
516#328C22×C4312yescomplemented
517#327C22×C4312yescomplemented
518#327C22×C4312yescomplemented
519#327C22×C4312yescomplemented
520#324C22×C4312yescomplemented
521#323C22×C4312yescomplemented
522C43#1822411yescharacteristic, direct product factor, Sylow
523C25—21no—
524C2×#41—21no—
525C2×#41D4×C4311yescharacteristic, complemented
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—22no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—21no—
533C22×D4—21no—
534C22×D4—21no—
535C22×D4—44no—
536C22×D4D4×C4311yescharacteristic
537C22×D4D4×C4311yescharacteristic, complemented
538C22×D4C23×C4312yes—
539C23×C4C23×C4311yescharacteristic
540AGL(1,ℤ/8)—44no—
541C2×SD16—22no—
542C2×D8—22no—
543C2×D8—22no—
544C2×D8—22no—
545C2×D8—44no—
546C2×M16—21no—
547C22×C8—21no—
548#127—21no—
549#126—21no—
550#126—21no—
551#126—21no—
552#126—21no—
553#125—21no—
554#125—21no—
555#124—21no—
556#124—21no—
557#124—21no—
558#123—21no—
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—
571#123—21no—
572C22⋊Q8—21no—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8—21no—
576C22⋊Q8—21no—
577C22⋊Q8D4×C4311yescharacteristic, complemented
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#121—21no—
592#121—21no—
593#121—21no—
594#121D4×C4311yescharacteristic, complemented
595#121D4×C4311yescharacteristic, complemented
596#121D4×C4311yescharacteristic, complemented
597#121C23×C4311yescharacteristic
598#121C23×C4311yescharacteristic
599#121C23×C4311yescharacteristic
600#120—21no—
601#120—21no—
602#120—21no—
603#120—21no—
604#120—21no—
605#120—21no—
606#120—21no—
607#120—21no—
608#120—44no—
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—21no—
617#117—21no—
618#117D4×C4311yescharacteristic, complemented
619C2×C4⋊C4D4×C4311yescharacteristic
620C2×C4⋊C4D4×C4311yescharacteristic, complemented
621C2×C4⋊C4C23×C4311yescharacteristic
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4D4×C4311yescharacteristic
630C2×C22⋊C4D4×C4311yescharacteristic
631C2×C22⋊C4C23×C4311yescharacteristic
632#102—22no—
633#102—22no—
634#102—22no—
635#102—22no—
636C22⋊C8—21no—
637C22⋊C8—21no—
638C22⋊C8C23×C4312yes—
639C22⋊C8C23×C4312yes—
640#95—21no—
641#95C23×C4312yes—
642C24—24no—
643C24—21no—
644C24—22no—
645C24—21no—
646C24—42no—
647C24—41no—
648C24—41no—
649C24—82no—
650C24—82no—
651C24C2×D4×C4311yescharacteristic
652C24C2×D4×C4311yescharacteristic
653#41—42no—
654#41—82no—
655C2×Q8—21no—
656C2×Q8C2×D4×C4311yescharacteristic
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—42no—
679C2×D4—42no—
680C2×D4—42no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—42no—
686C2×D4—44no—
687C2×D4—41no—
688C2×D4—41no—
689C2×D4—82no—
690C2×D4—82no—
691C2×D4—82no—
692C2×D4—82no—
693C2×D4—82no—
694C2×D4C2×D4×C4311yescharacteristic
695C2×D4C2×D4×C4311yescharacteristic
696C2×D4C2×D4×C4311yescharacteristic
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—22no—
705C22×C4—42no—
706C22×C4C2×D4×C4311yescharacteristic
707C22×C4C2×D4×C4311yescharacteristic
708C22×C4C2×D4×C4311yescharacteristic
709C22×C4C2×D4×C4311yescharacteristic
710C22×C4C2×D4×C4311yescharacteristic
711C22×C4C2×D4×C4311yescharacteristic
712C22×C4C2×D4×C4311yescharacteristic
713C22×C4C2×D4×C4311yescharacteristic
714C22×C4C24×C4311yescharacteristic
715SD16—44no—
716D8—44no—
717D8—44no—
718D8—44no—
719M16—42no—
720C2×C8—22no—
721C2×C8—22no—
722C2×C8—42no—
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⋊C4C2×D4×C4311yescharacteristic
737C4⋊C4C2×D4×C4311yescharacteristic
738C4⋊C4C2×D4×C4311yescharacteristic
739C4⋊C4C2×D4×C4311yescharacteristic
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
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—44no—
766C22⋊C4—42no—
767C22⋊C4—82no—
768C22⋊C4—82no—
769C42—21no—
770C42—21no—
771C42—21no—
772C23—22no—
773C23—22no—
774C23—24no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—22no—
780C23—41no—
781C23—42no—
782C23—42no—
783C23—44no—
784C23—42no—
785C23—41no—
786C23—41no—
787C23—42no—
788C23—42no—
789C23—42no—
790C23—44no—
791C23—42no—
792C23—81no—
793C23—81no—
794C23—82no—
795C23—82no—
796C23—82no—
797C23—82no—
798C23—88no—
799C23—81no—
800C23—81no—
801C23—81no—
802C23—88no—
803C23#120×C4311yescharacteristic
804C23#120×C4311yescharacteristic
805C23C22×D4×C4311yescharacteristic
806Q8—41no—
807Q8—81no—
808D4—24no—
809D4—24no—
810D4—41no—
811D4—41no—
812D4—41no—
813D4—42no—
814D4—42no—
815D4—44no—
816D4—44no—
817D4—42no—
818D4—42no—
819D4—42no—
820D4—42no—
821D4—42no—
822D4—81no—
823D4—81no—
824D4—81no—
825D4—81no—
826D4—81no—
827D4—81no—
828D4—81no—
829D4—81no—
830D4—81no—
831D4—81no—
832D4—81no—
833D4—81no—
834D4—88no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—81no—
856C2×C4—81no—
857C2×C4—81no—
858C2×C4—81no—
859C2×C4—81no—
860C2×C4—81no—
861C2×C4—81no—
862C2×C4#120×C4311yescharacteristic
863C2×C4#120×C4311yescharacteristic
864C2×C4C22×D4×C4311yescharacteristic
865C2×C4C22×D4×C4311yescharacteristic
866C8—42no—
867C8—42no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—44no—
876C22—44no—
877C22—44no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—44no—
889C22—41no—
890C22—41no—
891C22—82no—
892C22—82no—
893C22—82no—
894C22—88no—
895C22—88no—
896C22—82no—
897C22—82no—
898C22—162no—
899C22—162no—
900C22C43×B(4,𝔽2)12yes—
901C22C2×#120×C4311yescharacteristic
902C22C43×#57612yes—
903C4—21no—
904C4—21no—
905C4—21no—
906C4—21no—
907C4—41no—
908C4—41no—
909C4—41no—
910C4—41no—
911C4—41no—
912C4—41no—
913C4—41no—
914C4—41no—
915C4—82no—
916C2—22no—
917C2—22no—
918C2—41no—
919C2—84no—
920C2—81no—
921C2—81no—
922C2—81no—
923C2—81no—
924C2C43×#300811yescharacteristic
925C2C43×#302111yescharacteristic
926C2C2×C43×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC22×C4C24×C43
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C23×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3534C2semidirect
2. C43×#3003C2semidirect
3. C2×C43×#447C2semidirect
4. C43×#2613C2semidirect
5. C43×#1600C2semidirect
6. C43×#1598C2semidirect
7. C43×#1597C2semidirect
8. C43×#1595C2semidirect
9. C43×#1516C2semidirect
10. C43×#1510C2semidirect
11. C43×#1468C2semidirect
12. C23×D4×C43C22semidirect
25. C43×#539C22semidirect
27. C43×#538C22semidirect
28. C43×#537C22semidirect
30. C43×#534C22semidirect
36. C43×#450C22semidirect
41. C43×#447C22semidirect
42. C43×#447C22semidirect
45. C43×#407C22semidirect
46. C2×C22⋊C8×C43C22semidirect
48. C43×#394C22semidirect
50. C43×#392C22semidirect
51. C43×#381C22semidirect
53. C43×#328C22semidirect
54. C43×#327C22semidirect
55. C43×#327C22semidirect
56. C43×#327C22semidirect
57. C43×#324C22semidirect
58. C43×#323C22semidirect
61. C2×#41×C43D4semidirect
73. C22×D4×C43D4semidirect
113. C22⋊Q8×C43D4semidirect
130. #121×C43D4semidirect
131. #121×C43D4semidirect
132. #121×C43D4semidirect
154. #117×C43D4semidirect
156. C2×C4⋊C4×C43D4semidirect
404. #18224C43direct (N × H)
453. #3534C2×C43semidirect
454. #3003C2×C43semidirect
455. C2×#447C2×C43semidirect
456. #2613C2×C43semidirect
457. #1600C2×C43semidirect
458. #1598C2×C43semidirect
459. #1597C2×C43semidirect
460. #1595C2×C43semidirect
461. #1516C2×C43semidirect
462. #1510C2×C43semidirect
463. #1468C2×C43semidirect
475. C23×D4C22×C43semidirect
488. #539C22×C43semidirect
490. #538C22×C43semidirect
491. #537C22×C43semidirect
493. #534C22×C43semidirect
499. #450C22×C43semidirect
504. #447C22×C43semidirect
505. #447C22×C43semidirect
508. #407C22×C43semidirect
509. C2×C22⋊C8C22×C43semidirect
511. #394C22×C43semidirect
513. #392C22×C43semidirect
514. #381C22×C43semidirect
516. #328C22×C43semidirect
517. #327C22×C43semidirect
518. #327C22×C43semidirect
519. #327C22×C43semidirect
520. #324C22×C43semidirect
521. #323C22×C43semidirect
522. C43#18224direct (N × H)
525. C2×#41D4×C43semidirect
537. C22×D4D4×C43semidirect
577. C22⋊Q8D4×C43semidirect
594. #121D4×C43semidirect
595. #121D4×C43semidirect
596. #121D4×C43semidirect
618. #117D4×C43semidirect
620. C2×C4⋊C4D4×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#35342
C43×#30032
C2×C43×#4472
C43×#26132
C43×#16002
C43×#15982
C43×#15972
C43×#15952
C43×#15162
C43×#15102
C43×#14682
#1822443