Finite Group Databasebeta

← C43×#18252 #24938269

Subgroups — C43×#18252 #24938269

Order 11008.

1260 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3534C211yesmaximal, characteristic, complemented
2C43×#3006C211yesmaximal, characteristic, complemented
3C43×#3002C211yesmaximal, characteristic, complemented
4C43×#2430C211yesmaximal, characteristic, complemented
5C43×#1606C211yesmaximal, characteristic, complemented
6C43×#1604C211yesmaximal, characteristic, complemented
7C43×#1603C211yesmaximal, characteristic, complemented
8C43×#1601C211yesmaximal, characteristic, complemented
9C43×#1600C211yesmaximal, characteristic, complemented
10C43×#1598C211yesmaximal, characteristic, complemented
11C43×#1597C211yesmaximal, characteristic, complemented
12C43×#1595C211yesmaximal, characteristic, complemented
13C43×#1504C211yesmaximal, characteristic, complemented
14C2×C43×#327C211yesmaximal, characteristic, complemented
15C43×#1468C211yesmaximal, characteristic, complemented
16C22×#41×C43C2211yescharacteristic, complemented
17C2×AGL(1,ℤ/8)×C43—21no—
18C2×#135×C43—21no—
19C43×#562—21no—
20C43×#560—21no—
21C43×#553—21no—
22C43×#551—21no—
23C43×#546—21no—
24C43×#546—21no—
25C43×#546—21no—
26D42×C43—21no—
27C43×#540—21no—
28C43×#539—21no—
29C43×#539C2211yescharacteristic
30C43×#538—21no—
31C43×#538C2211yescharacteristic
32C43×#537C2211yescharacteristic
33C43×#534—21no—
34C43×#534C2211yescharacteristic
35C43×#525C2211yescharacteristic
36C2×#123×C43C2211yescharacteristic
37C2×#121×C43—21no—
38C2×#121×C43C2211yescharacteristic
39C43×#452—21no—
40C43×#451C2211yescharacteristic, complemented
41C43×#450C2211yescharacteristic, complemented
42C43×#449—21no—
43C43×#449—21no—
44C43×#449—21no—
45C43×#448C2211yescharacteristic
46C43×#448C2211yescharacteristic, complemented
47C43×#448C2211yescharacteristic, complemented
48C43×#447C2211yescharacteristic
49C43×#447C2211yescharacteristic, complemented
50C43×#447C2211yescharacteristic, complemented
51C43×#417—21no—
52C43×#416—21no—
53C43×#407C2211yescharacteristic, complemented
54C2×C22⋊C8×C43C2211yescharacteristic, complemented
55C43×#395C2211yescharacteristic, complemented
56C43×#394C2211yescharacteristic, complemented
57C43×#393C2211yescharacteristic, complemented
58C43×#392C2211yescharacteristic, complemented
59C43×#386—21no—
60C43×#386—21no—
61C43×#385—21no—
62C2×#95×C43C2211yescharacteristic, complemented
63C43×#328C2211yescharacteristic, complemented
64C43×#328C2211yescharacteristic, complemented
65C43×#327C2211yescharacteristic
66C43×#327C2211yescharacteristic
67C43×#327C2211yescharacteristic, complemented
68C43×#327C2211yescharacteristic, complemented
69C43×#327C2211yescharacteristic, complemented
70C43×#327C2211yescharacteristic, complemented
71C43×#324C2211yescharacteristic, complemented
72C43×#324C2211yescharacteristic, complemented
73C43×#323C2211yescharacteristic, complemented
74C43×#323C2211yescharacteristic, complemented
75C2×#41×C43—21no—
76C2×#41×C43—21no—
77C2×#41×C43—21no—
78C2×#41×C43—21no—
79C2×#41×C43—21no—
80C2×#41×C43—44no—
81C2×#41×C43D411yescharacteristic, complemented
82C22×Q8×C43C2311yescharacteristic
83C22×D4×C43—21no—
84C22×D4×C43—21no—
85C22×D4×C43—21no—
86C22×D4×C43—21no—
87C22×D4×C43—21no—
88C22×D4×C43D411yescharacteristic
89C22×D4×C43D411yescharacteristic, complemented
90C22×D4×C43C2311yescharacteristic
91C23×C4×C43—21no—
92C23×C4×C43—21no—
93C23×C4×C43C2311yescharacteristic
94AGL(1,ℤ/8)×C43—44no—
95#135×C43—44no—
96C2×Q16×C43—21no—
97C2×SD16×C43—21no—
98C2×SD16×C43—21no—
99C2×SD16×C43—21no—
100C2×SD16×C43—21no—
101C2×D8×C43—21no—
102C2×D8×C43—21no—
103C2×D8×C43—21no—
104C2×M16×C43—21no—
105C22×C8×C43—21no—
106#127×C43—21no—
107#126×C43—21no—
108#126×C43—21no—
109#126×C43—21no—
110#126×C43—21no—
111#125×C43—21no—
112#125×C43—21no—
113#124×C43—21no—
114#124×C43—21no—
115#124×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—
123#123×C43—21no—
124#123×C43—21no—
125#123×C43—21no—
126#123×C43—21no—
127#123×C43—21no—
128#123×C43—21no—
129#123×C43—21no—
130C22⋊Q8×C43—21no—
131C22⋊Q8×C43—21no—
132C22⋊Q8×C43—21no—
133C22⋊Q8×C43—21no—
134C22⋊Q8×C43—21no—
135C22⋊Q8×C43D411yescharacteristic, complemented
136C22⋊Q8×C43C2311yescharacteristic
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×C43—21no—
150#121×C43—21no—
151#121×C43—21no—
152#121×C43—44no—
153#121×C43D411yescharacteristic, complemented
154#121×C43D411yescharacteristic, complemented
155#121×C43D411yescharacteristic, complemented
156#121×C43C2311yescharacteristic
157#121×C43C2311yescharacteristic
158#121×C43C2311yescharacteristic
159#120×C43—21no—
160#120×C43—21no—
161#120×C43—21no—
162#120×C43—21no—
163#120×C43—21no—
164#120×C43—21no—
165#120×C43—21no—
166#120×C43—21no—
167C4×D4×C43—21no—
168C4×D4×C43—21no—
169C4×D4×C43—21no—
170C4×D4×C43—21no—
171C4×D4×C43—21no—
172C4×D4×C43—21no—
173C4×D4×C43—21no—
174C4×D4×C43—21no—
175#117×C43—21no—
176#117×C43D411yescharacteristic, complemented
177C2×C4⋊C4×C43—21no—
178C2×C4⋊C4×C43D411yescharacteristic
179C2×C4⋊C4×C43D411yescharacteristic, complemented
180C2×C4⋊C4×C43C2311yescharacteristic
181C2×C22⋊C4×C43—21no—
182C2×C22⋊C4×C43—21no—
183C2×C22⋊C4×C43—21no—
184C2×C22⋊C4×C43—21no—
185C2×C22⋊C4×C43—21no—
186C2×C22⋊C4×C43—21no—
187C2×C22⋊C4×C43—21no—
188C2×C22⋊C4×C43D411yescharacteristic
189C2×C22⋊C4×C43D411yescharacteristic
190C2×C22⋊C4×C43C2311yescharacteristic
191#103×C43—21no—
192#103×C43—21no—
193#103×C43—21no—
194#103×C43—21no—
195#102×C43—21no—
196#102×C43—21no—
197#102×C43—21no—
198#102×C43—21no—
199C22⋊C8×C43—21no—
200C22⋊C8×C43—21no—
201C22⋊C8×C43C2311yescharacteristic
202C22⋊C8×C43C2311yescharacteristic
203C22⋊C8×C43C2311yescharacteristic
204C22⋊C8×C43C2311yescharacteristic
205#95×C43—21no—
206#95×C43—21no—
207#95×C43—21no—
208#95×C43C2311yescharacteristic
209#95×C43C2311yescharacteristic
210C24×C43—21no—
211C24×C43—21no—
212C24×C43—21no—
213C24×C43C2×D411yescharacteristic
214C24×C43C2×D411yescharacteristic
215#41×C43—24no—
216#41×C43—24no—
217#41×C43—42no—
218#41×C43—42no—
219#41×C43—42no—
220#41×C43—42no—
221#41×C43—42no—
222#41×C43—42no—
223#41×C43—42no—
224#41×C43—81no—
225#41×C43—81no—
226C2×Q8×C43—21no—
227C2×Q8×C43—21no—
228C2×Q8×C43—21no—
229C2×Q8×C43—42no—
230C2×Q8×C43C2×D411yescharacteristic
231C2×D4×C43—24no—
232C2×D4×C43—21no—
233C2×D4×C43—21no—
234C2×D4×C43—21no—
235C2×D4×C43—21no—
236C2×D4×C43—21no—
237C2×D4×C43—21no—
238C2×D4×C43—21no—
239C2×D4×C43—21no—
240C2×D4×C43—21no—
241C2×D4×C43—21no—
242C2×D4×C43—21no—
243C2×D4×C43—21no—
244C2×D4×C43—21no—
245C2×D4×C43—21no—
246C2×D4×C43—21no—
247C2×D4×C43—21no—
248C2×D4×C43—21no—
249C2×D4×C43—21no—
250C2×D4×C43—21no—
251C2×D4×C43—42no—
252C2×D4×C43—42no—
253C2×D4×C43—42no—
254C2×D4×C43—42no—
255C2×D4×C43—42no—
256C2×D4×C43—41no—
257C2×D4×C43—41no—
258C2×D4×C43—42no—
259C2×D4×C43—81no—
260C2×D4×C43—81no—
261C2×D4×C43—81no—
262C2×D4×C43—81no—
263C2×D4×C43—81no—
264C2×D4×C43—82no—
265C2×D4×C43C2×D411yescharacteristic
266C2×D4×C43C2×D411yescharacteristic
267C2×D4×C43C2×D411yescharacteristic
268C22×C4×C43—21no—
269C22×C4×C43—21no—
270C22×C4×C43—21no—
271C22×C4×C43—21no—
272C22×C4×C43—21no—
273C22×C4×C43—21no—
274C22×C4×C43—21no—
275C22×C4×C43—21no—
276C22×C4×C43—21no—
277C22×C4×C43—21no—
278C22×C4×C43—42no—
279C22×C4×C43—42no—
280C22×C4×C43—42no—
281C22×C4×C43—42no—
282C22×C4×C43—42no—
283C22×C4×C43—41no—
284C22×C4×C43—41no—
285C22×C4×C43—81no—
286C22×C4×C43C2×D411yescharacteristic
287C22×C4×C43C2×D411yescharacteristic
288C22×C4×C43C2×D411yescharacteristic
289C22×C4×C43C2×D411yescharacteristic
290C22×C4×C43C2×D411yescharacteristic
291C22×C4×C43C2×D411yescharacteristic
292C22×C4×C43C2×D411yescharacteristic
293C22×C4×C43C2×D411yescharacteristic
294C22×C4×C43C2411yescharacteristic
295Q16×C43—42no—
296SD16×C43—42no—
297SD16×C43—42no—
298SD16×C43—42no—
299SD16×C43—42no—
300D8×C43—42no—
301D8×C43—42no—
302D8×C43—42no—
303M16×C43—42no—
304C2×C8×C43—21no—
305C2×C8×C43—21no—
306C2×C8×C43—21no—
307C2×C8×C43—21no—
308C2×C8×C43—42no—
309C4⋊C4×C43—21no—
310C4⋊C4×C43—21no—
311C4⋊C4×C43—21no—
312C4⋊C4×C43—21no—
313C4⋊C4×C43—21no—
314C4⋊C4×C43—21no—
315C4⋊C4×C43—21no—
316C4⋊C4×C43—21no—
317C4⋊C4×C43—21no—
318C4⋊C4×C43—21no—
319C4⋊C4×C43—21no—
320C4⋊C4×C43—21no—
321C4⋊C4×C43—21no—
322C4⋊C4×C43—42no—
323C4⋊C4×C43C2×D411yescharacteristic
324C4⋊C4×C43C2×D411yescharacteristic
325C4⋊C4×C43C2×D411yescharacteristic
326C4⋊C4×C43C2×D411yescharacteristic
327C22⋊C4×C43—21no—
328C22⋊C4×C43—21no—
329C22⋊C4×C43—21no—
330C22⋊C4×C43—21no—
331C22⋊C4×C43—21no—
332C22⋊C4×C43—21no—
333C22⋊C4×C43—21no—
334C22⋊C4×C43—21no—
335C22⋊C4×C43—21no—
336C22⋊C4×C43—21no—
337C22⋊C4×C43—21no—
338C22⋊C4×C43—21no—
339C22⋊C4×C43—21no—
340C22⋊C4×C43—21no—
341C22⋊C4×C43—21no—
342C22⋊C4×C43—21no—
343C22⋊C4×C43—21no—
344C22⋊C4×C43—21no—
345C22⋊C4×C43—21no—
346C22⋊C4×C43—21no—
347C22⋊C4×C43—21no—
348C22⋊C4×C43—21no—
349C22⋊C4×C43—21no—
350C22⋊C4×C43—21no—
351C22⋊C4×C43—21no—
352C22⋊C4×C43—42no—
353C22⋊C4×C43—42no—
354C22⋊C4×C43—42no—
355C22⋊C4×C43—81no—
356C42×C43—21no—
357C42×C43—21no—
358C42×C43—21no—
359C23×C43—21no—
360C23×C43—21no—
361C23×C43—22no—
362C23×C43—22no—
363C23×C43—21no—
364C23×C43—21no—
365C23×C43—21no—
366C23×C43—21no—
367C23×C43—21no—
368C23×C43—21no—
369C23×C43—41no—
370C23×C43—41no—
371C23×C43—41no—
372C23×C43—41no—
373C23×C43—41no—
374C23×C43—41no—
375C23×C43—41no—
376C23×C43—41no—
377C23×C43—41no—
378C23×C43—42no—
379C23×C43—81no—
380C23×C43—81no—
381C23×C43—81no—
382C23×C43—81no—
383C23×C43—81no—
384C23×C43#12011yescharacteristic
385C23×C43#12011yescharacteristic
386C23×C43C22×D411yescharacteristic
387Q8×C43—22no—
388Q8×C43—22no—
389Q8×C43—41no—
390Q8×C43—41no—
391Q8×C43—41no—
392Q8×C43—81no—
393D4×C43—22no—
394D4×C43—22no—
395D4×C43—41no—
396D4×C43—41no—
397D4×C43—41no—
398D4×C43—41no—
399D4×C43—41no—
400D4×C43—44no—
401D4×C43—41no—
402D4×C43—41no—
403D4×C43—41no—
404D4×C43—41no—
405D4×C43—41no—
406D4×C43—41no—
407D4×C43—44no—
408D4×C43—42no—
409D4×C43—42no—
410D4×C43—81no—
411D4×C43—81no—
412D4×C43—81no—
413D4×C43—81no—
414D4×C43—81no—
415D4×C43—81no—
416D4×C43—81no—
417D4×C43—81no—
418D4×C43—81no—
419D4×C43—81no—
420D4×C43—81no—
421D4×C43—81no—
422D4×C43—84no—
423C2×C4×C43—22no—
424C2×C4×C43—22no—
425C2×C4×C43—22no—
426C2×C4×C43—22no—
427C2×C4×C43—21no—
428C2×C4×C43—21no—
429C2×C4×C43—21no—
430C2×C4×C43—21no—
431C2×C4×C43—21no—
432C2×C4×C43—21no—
433C2×C4×C43—21no—
434C2×C4×C43—21no—
435C2×C4×C43—21no—
436C2×C4×C43—21no—
437C2×C4×C43—41no—
438C2×C4×C43—41no—
439C2×C4×C43—41no—
440C2×C4×C43—41no—
441C2×C4×C43—44no—
442C2×C4×C43—44no—
443C2×C4×C43—41no—
444C2×C4×C43—41no—
445C2×C4×C43—41no—
446C2×C4×C43—41no—
447C2×C4×C43—41no—
448C2×C4×C43—41no—
449C2×C4×C43—41no—
450C2×C4×C43—41no—
451C2×C4×C43—41no—
452C2×C4×C43—81no—
453C2×C4×C43—81no—
454C2×C4×C43—81no—
455C2×C4×C43—81no—
456C2×C4×C43—81no—
457C2×C4×C43—81no—
458C2×C4×C43—81no—
459C2×C4×C43—84no—
460C2×C4×C43#12011yescharacteristic
461C2×C4×C43#12011yescharacteristic
462C2×C4×C43C22×D411yescharacteristic
463C2×C4×C43C22×D411yescharacteristic
464C8×C43—41no—
465C8×C43—41no—
466C8×C43—41no—
467C8×C43—41no—
468#18252C4311yesmaximal, characteristic, direct product factor, Sylow
469C22×C43—21no—
470C22×C43—21no—
471C22×C43—21no—
472C22×C43—21no—
473C22×C43—21no—
474C22×C43—21no—
475C22×C43—21no—
476C22×C43—42no—
477C22×C43—42no—
478C22×C43—42no—
479C22×C43—42no—
480C22×C43—41no—
481C22×C43—41no—
482C22×C43—41no—
483C22×C43—41no—
484C22×C43—41no—
485C22×C43—41no—
486C22×C43—41no—
487C22×C43—41no—
488C22×C43—41no—
489C22×C43—42no—
490C22×C43—41no—
491C22×C43—41no—
492C22×C43—41no—
493C22×C43—81no—
494C22×C43—81no—
495C22×C43—81no—
496C22×C43—81no—
497C22×C43—81no—
498C22×C43—81no—
499C22×C43—162no—
500C22×C43—162no—
501C22×C43B(4,𝔽2)12yes—
502C22×C43C2×#12011yescharacteristic
503C22×C43#57611yescharacteristic
504C22×C43#57711yescharacteristic
505C4×C43—21no—
506C4×C43—21no—
507C4×C43—21no—
508C4×C43—21no—
509C4×C43—42no—
510C4×C43—41no—
511C4×C43—41no—
512C4×C43—41no—
513C4×C43—41no—
514C4×C43—41no—
515C4×C43—41no—
516C4×C43—42no—
517C4×C43—41no—
518C4×C43—41no—
519C4×C43—81no—
520#3534C2×C4311yescharacteristic, complemented
521#3006C2×C4311yescharacteristic, complemented
522#3002C2×C4311yescharacteristic, complemented
523#2430C2×C4311yescharacteristic, complemented
524#1606C2×C4311yescharacteristic, complemented
525#1604C2×C4311yescharacteristic, complemented
526#1603C2×C4311yescharacteristic, complemented
527#1601C2×C4311yescharacteristic, complemented
528#1600C2×C4311yescharacteristic, complemented
529#1598C2×C4311yescharacteristic, complemented
530#1597C2×C4311yescharacteristic, complemented
531#1595C2×C4311yescharacteristic, complemented
532#1504C2×C4311yescharacteristic, complemented
533C2×#327C2×C4311yescharacteristic, complemented
534#1468C2×C4311yescharacteristic, complemented
535C2×C43—21no—
536C2×C43—21no—
537C2×C43—22no—
538C2×C43—41no—
539C2×C43—82no—
540C2×C43—81no—
541C2×C43—81no—
542C2×C43—81no—
543C2×C43—81no—
544C2×C43#301211yescharacteristic
545C2×C43#301811yescharacteristic
546C2×C43C2×B(4,𝔽2)11yescharacteristic
547C22×#41C22×C4311yescharacteristic, complemented
548C2×AGL(1,ℤ/8)—21no—
549C2×#135—21no—
550#562—21no—
551#560—21no—
552#553—21no—
553#551—21no—
554#546—21no—
555#546—21no—
556#546—21no—
557D42—21no—
558#540—21no—
559#539—21no—
560#539C22×C4311yescharacteristic
561#538—21no—
562#538C22×C4311yescharacteristic
563#537C22×C4311yescharacteristic
564#534—21no—
565#534C22×C4311yescharacteristic
566#525C22×C4311yescharacteristic
567C2×#123C22×C4311yescharacteristic
568C2×#121—21no—
569C2×#121C22×C4311yescharacteristic
570#452—21no—
571#451C22×C4311yescharacteristic, complemented
572#450C22×C4311yescharacteristic, complemented
573#449—21no—
574#449—21no—
575#449—21no—
576#448C22×C4311yescharacteristic
577#448C22×C4311yescharacteristic, complemented
578#448C22×C4311yescharacteristic, complemented
579#447C22×C4311yescharacteristic
580#447C22×C4311yescharacteristic, complemented
581#447C22×C4311yescharacteristic, complemented
582#417—21no—
583#416—21no—
584#407C22×C4311yescharacteristic, complemented
585C2×C22⋊C8C22×C4311yescharacteristic, complemented
586#395C22×C4311yescharacteristic, complemented
587#394C22×C4311yescharacteristic, complemented
588#393C22×C4311yescharacteristic, complemented
589#392C22×C4311yescharacteristic, complemented
590#386—21no—
591#386—21no—
592#385—21no—
593C2×#95C22×C4311yescharacteristic, complemented
594#328C22×C4311yescharacteristic, complemented
595#328C22×C4311yescharacteristic, complemented
596#327C22×C4311yescharacteristic
597#327C22×C4311yescharacteristic
598#327C22×C4311yescharacteristic, complemented
599#327C22×C4311yescharacteristic, complemented
600#327C22×C4311yescharacteristic, complemented
601#327C22×C4311yescharacteristic, complemented
602#324C22×C4311yescharacteristic, complemented
603#324C22×C4311yescharacteristic, complemented
604#323C22×C4311yescharacteristic, complemented
605#323C22×C4311yescharacteristic, complemented
606C43#1825211yescharacteristic, direct product factor, Sylow
607C2×#41—21no—
608C2×#41—21no—
609C2×#41—21no—
610C2×#41—21no—
611C2×#41—21no—
612C2×#41—44no—
613C2×#41D4×C4311yescharacteristic, complemented
614C22×Q8C23×C4311yescharacteristic
615C22×D4—21no—
616C22×D4—21no—
617C22×D4—21no—
618C22×D4—21no—
619C22×D4—21no—
620C22×D4D4×C4311yescharacteristic
621C22×D4D4×C4311yescharacteristic, complemented
622C22×D4C23×C4311yescharacteristic
623C23×C4—21no—
624C23×C4—21no—
625C23×C4C23×C4311yescharacteristic
626AGL(1,ℤ/8)—44no—
627#135—44no—
628C2×Q16—21no—
629C2×SD16—21no—
630C2×SD16—21no—
631C2×SD16—21no—
632C2×SD16—21no—
633C2×D8—21no—
634C2×D8—21no—
635C2×D8—21no—
636C2×M16—21no—
637C22×C8—21no—
638#127—21no—
639#126—21no—
640#126—21no—
641#126—21no—
642#126—21no—
643#125—21no—
644#125—21no—
645#124—21no—
646#124—21no—
647#124—21no—
648#123—21no—
649#123—21no—
650#123—21no—
651#123—21no—
652#123—21no—
653#123—21no—
654#123—21no—
655#123—21no—
656#123—21no—
657#123—21no—
658#123—21no—
659#123—21no—
660#123—21no—
661#123—21no—
662C22⋊Q8—21no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8D4×C4311yescharacteristic, complemented
668C22⋊Q8C23×C4311yescharacteristic
669#121—21no—
670#121—21no—
671#121—21no—
672#121—21no—
673#121—21no—
674#121—21no—
675#121—21no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—21no—
683#121—21no—
684#121—44no—
685#121D4×C4311yescharacteristic, complemented
686#121D4×C4311yescharacteristic, complemented
687#121D4×C4311yescharacteristic, complemented
688#121C23×C4311yescharacteristic
689#121C23×C4311yescharacteristic
690#121C23×C4311yescharacteristic
691#120—21no—
692#120—21no—
693#120—21no—
694#120—21no—
695#120—21no—
696#120—21no—
697#120—21no—
698#120—21no—
699C4×D4—21no—
700C4×D4—21no—
701C4×D4—21no—
702C4×D4—21no—
703C4×D4—21no—
704C4×D4—21no—
705C4×D4—21no—
706C4×D4—21no—
707#117—21no—
708#117D4×C4311yescharacteristic, complemented
709C2×C4⋊C4—21no—
710C2×C4⋊C4D4×C4311yescharacteristic
711C2×C4⋊C4D4×C4311yescharacteristic, complemented
712C2×C4⋊C4C23×C4311yescharacteristic
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4D4×C4311yescharacteristic
721C2×C22⋊C4D4×C4311yescharacteristic
722C2×C22⋊C4C23×C4311yescharacteristic
723#103—21no—
724#103—21no—
725#103—21no—
726#103—21no—
727#102—21no—
728#102—21no—
729#102—21no—
730#102—21no—
731C22⋊C8—21no—
732C22⋊C8—21no—
733C22⋊C8C23×C4311yescharacteristic
734C22⋊C8C23×C4311yescharacteristic
735C22⋊C8C23×C4311yescharacteristic
736C22⋊C8C23×C4311yescharacteristic
737#95—21no—
738#95—21no—
739#95—21no—
740#95C23×C4311yescharacteristic
741#95C23×C4311yescharacteristic
742C24—21no—
743C24—21no—
744C24—21no—
745C24C2×D4×C4311yescharacteristic
746C24C2×D4×C4311yescharacteristic
747#41—24no—
748#41—24no—
749#41—42no—
750#41—42no—
751#41—42no—
752#41—42no—
753#41—42no—
754#41—42no—
755#41—42no—
756#41—81no—
757#41—81no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—42no—
762C2×Q8C2×D4×C4311yescharacteristic
763C2×D4—24no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—42no—
784C2×D4—42no—
785C2×D4—42no—
786C2×D4—42no—
787C2×D4—41no—
788C2×D4—41no—
789C2×D4—42no—
790C2×D4—42no—
791C2×D4—81no—
792C2×D4—81no—
793C2×D4—81no—
794C2×D4—81no—
795C2×D4—81no—
796C2×D4—82no—
797C2×D4C2×D4×C4311yescharacteristic
798C2×D4C2×D4×C4311yescharacteristic
799C2×D4C2×D4×C4311yescharacteristic
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4—42no—
817C22×C4—81no—
818C22×C4C2×D4×C4311yescharacteristic
819C22×C4C2×D4×C4311yescharacteristic
820C22×C4C2×D4×C4311yescharacteristic
821C22×C4C2×D4×C4311yescharacteristic
822C22×C4C2×D4×C4311yescharacteristic
823C22×C4C2×D4×C4311yescharacteristic
824C22×C4C2×D4×C4311yescharacteristic
825C22×C4C2×D4×C4311yescharacteristic
826C22×C4C24×C4311yescharacteristic
827Q16—42no—
828SD16—42no—
829SD16—42no—
830SD16—42no—
831SD16—42no—
832D8—42no—
833D8—42no—
834D8—42no—
835M16—42no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—42no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—42no—
855C4⋊C4C2×D4×C4311yescharacteristic
856C4⋊C4C2×D4×C4311yescharacteristic
857C4⋊C4C2×D4×C4311yescharacteristic
858C4⋊C4C2×D4×C4311yescharacteristic
859C22⋊C4—21no—
860C22⋊C4—21no—
861C22⋊C4—21no—
862C22⋊C4—21no—
863C22⋊C4—21no—
864C22⋊C4—21no—
865C22⋊C4—21no—
866C22⋊C4—21no—
867C22⋊C4—21no—
868C22⋊C4—21no—
869C22⋊C4—21no—
870C22⋊C4—21no—
871C22⋊C4—21no—
872C22⋊C4—21no—
873C22⋊C4—21no—
874C22⋊C4—21no—
875C22⋊C4—21no—
876C22⋊C4—21no—
877C22⋊C4—21no—
878C22⋊C4—21no—
879C22⋊C4—21no—
880C22⋊C4—21no—
881C22⋊C4—21no—
882C22⋊C4—21no—
883C22⋊C4—21no—
884C22⋊C4—42no—
885C22⋊C4—42no—
886C22⋊C4—42no—
887C22⋊C4—81no—
888C42—21no—
889C42—21no—
890C42—21no—
891C23—21no—
892C23—21no—
893C23—22no—
894C23—22no—
895C23—21no—
896C23—21no—
897C23—21no—
898C23—21no—
899C23—21no—
900C23—21no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—42no—
911C23—81no—
912C23—81no—
913C23—81no—
914C23—81no—
915C23—81no—
916C23#120×C4311yescharacteristic
917C23#120×C4311yescharacteristic
918C23C22×D4×C4311yescharacteristic
919Q8—22no—
920Q8—22no—
921Q8—41no—
922Q8—41no—
923Q8—41no—
924Q8—81no—
925D4—22no—
926D4—22no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—41no—
932D4—44no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—41no—
938D4—41no—
939D4—44no—
940D4—42no—
941D4—42no—
942D4—81no—
943D4—81no—
944D4—81no—
945D4—81no—
946D4—81no—
947D4—81no—
948D4—81no—
949D4—81no—
950D4—81no—
951D4—81no—
952D4—81no—
953D4—81no—
954D4—84no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—44no—
974C2×C4—44no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—81no—
985C2×C4—81no—
986C2×C4—81no—
987C2×C4—81no—
988C2×C4—81no—
989C2×C4—81no—
990C2×C4—81no—
991C2×C4—84no—
992C2×C4#120×C4311yescharacteristic
993C2×C4#120×C4311yescharacteristic
994C2×C4C22×D4×C4311yescharacteristic
995C2×C4C22×D4×C4311yescharacteristic
996C8—41no—
997C8—41no—
998C8—41no—
999C8—41no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—42no—
1008C22—42no—
1009C22—42no—
1010C22—42no—
1011C22—41no—
1012C22—41no—
1013C22—41no—
1014C22—41no—
1015C22—41no—
1016C22—41no—
1017C22—41no—
1018C22—41no—
1019C22—42no—
1020C22—41no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—81no—
1025C22—81no—
1026C22—81no—
1027C22—81no—
1028C22—81no—
1029C22—81no—
1030C22—162no—
1031C22—162no—
1032C22C43×B(4,𝔽2)12yes—
1033C22C2×#120×C4311yescharacteristic
1034C22C43×#57611yescharacteristic
1035C22C43×#57711yescharacteristic
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—42no—
1041C4—41no—
1042C4—41no—
1043C4—41no—
1044C4—41no—
1045C4—41no—
1046C4—41no—
1047C4—42no—
1048C4—41no—
1049C4—41no—
1050C4—81no—
1051C2—21no—
1052C2—21no—
1053C2—22no—
1054C2—41no—
1055C2—82no—
1056C2—81no—
1057C2—81no—
1058C2—81no—
1059C2—81no—
1060C2C43×#301211yescharacteristic
1061C2C43×#301811yescharacteristic
1062C2C2×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×#3006C2semidirect
3. C43×#3002C2semidirect
4. C43×#2430C2semidirect
5. C43×#1606C2semidirect
6. C43×#1604C2semidirect
7. C43×#1603C2semidirect
8. C43×#1601C2semidirect
9. C43×#1600C2semidirect
10. C43×#1598C2semidirect
11. C43×#1597C2semidirect
12. C43×#1595C2semidirect
13. C43×#1504C2semidirect
14. C2×C43×#327C2semidirect
15. C43×#1468C2semidirect
16. C22×#41×C43C22semidirect
40. C43×#451C22semidirect
41. C43×#450C22semidirect
46. C43×#448C22semidirect
47. C43×#448C22semidirect
49. C43×#447C22semidirect
50. C43×#447C22semidirect
53. C43×#407C22semidirect
54. C2×C22⋊C8×C43C22semidirect
55. C43×#395C22semidirect
56. C43×#394C22semidirect
57. C43×#393C22semidirect
58. C43×#392C22semidirect
62. C2×#95×C43C22semidirect
63. C43×#328C22semidirect
64. C43×#328C22semidirect
67. C43×#327C22semidirect
68. C43×#327C22semidirect
69. C43×#327C22semidirect
70. C43×#327C22semidirect
71. C43×#324C22semidirect
72. C43×#324C22semidirect
73. C43×#323C22semidirect
74. C43×#323C22semidirect
81. C2×#41×C43D4semidirect
89. C22×D4×C43D4semidirect
135. C22⋊Q8×C43D4semidirect
153. #121×C43D4semidirect
154. #121×C43D4semidirect
155. #121×C43D4semidirect
176. #117×C43D4semidirect
179. C2×C4⋊C4×C43D4semidirect
468. #18252C43direct (N × H)
520. #3534C2×C43semidirect
521. #3006C2×C43semidirect
522. #3002C2×C43semidirect
523. #2430C2×C43semidirect
524. #1606C2×C43semidirect
525. #1604C2×C43semidirect
526. #1603C2×C43semidirect
527. #1601C2×C43semidirect
528. #1600C2×C43semidirect
529. #1598C2×C43semidirect
530. #1597C2×C43semidirect
531. #1595C2×C43semidirect
532. #1504C2×C43semidirect
533. C2×#327C2×C43semidirect
534. #1468C2×C43semidirect
547. C22×#41C22×C43semidirect
571. #451C22×C43semidirect
572. #450C22×C43semidirect
577. #448C22×C43semidirect
578. #448C22×C43semidirect
580. #447C22×C43semidirect
581. #447C22×C43semidirect
584. #407C22×C43semidirect
585. C2×C22⋊C8C22×C43semidirect
586. #395C22×C43semidirect
587. #394C22×C43semidirect
588. #393C22×C43semidirect
589. #392C22×C43semidirect
593. C2×#95C22×C43semidirect
594. #328C22×C43semidirect
595. #328C22×C43semidirect
598. #327C22×C43semidirect
599. #327C22×C43semidirect
600. #327C22×C43semidirect
601. #327C22×C43semidirect
602. #324C22×C43semidirect
603. #324C22×C43semidirect
604. #323C22×C43semidirect
605. #323C22×C43semidirect
606. C43#18252direct (N × H)
613. C2×#41D4×C43semidirect
621. C22×D4D4×C43semidirect
667. C22⋊Q8D4×C43semidirect
685. #121D4×C43semidirect
686. #121D4×C43semidirect
687. #121D4×C43semidirect
708. #117D4×C43semidirect
711. 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×#30062
C43×#30022
C43×#24302
C43×#16062
C43×#16042
C43×#16032
C43×#16012
C43×#16002
C43×#15982
C43×#15972
C43×#15952
C43×#15042
C2×C43×#3272
C43×#14682
#1825243