Finite Group Databasebeta

← C43×#24031 #24944048

Subgroups — C43×#24031 #24944048

Order 11008.

1334 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3488C211yesmaximal, characteristic
2C43×#3093C211yesmaximal, characteristic, complemented
3C43×#2896C211yesmaximal, characteristic, complemented
4C43×#2500C211yesmaximal, characteristic, complemented
5C43×#2040C211yesmaximal, characteristic, complemented
6C43×#2039C211yesmaximal, characteristic, complemented
7C43×#2037C211yesmaximal, characteristic, complemented
8C43×#2037C211yesmaximal, characteristic, complemented
9C43×#1900C211yesmaximal, characteristic, complemented
10C43×#1871C211yesmaximal, characteristic, complemented
11C43×#1860C211yesmaximal, characteristic, complemented
12C43×#1859C211yesmaximal, characteristic, complemented
13C43×#1792C211yesmaximal, characteristic, complemented
14C43×#1792C211yesmaximal, characteristic, complemented
15C43×#1789C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C43C2211yescharacteristic
17C22×#41×C43C2211yescharacteristic
18C22×M16×C43C2211yescharacteristic, complemented
19C43×#550—21no—
20C43×#548—21no—
21C43×#546—21no—
22C43×#546—22no—
23D42×C43—22no—
24D42×C43—21no—
25C43×#537—21no—
26C43×#537C2211yescharacteristic
27C43×#535—21no—
28C43×#535C2211yescharacteristic
29C43×#525—21no—
30C43×#525C2211yescharacteristic
31C2×#121×C43—21no—
32C2×#121×C43C2211yescharacteristic
33C43×#520C2211yescharacteristic
34C2×#117×C43C2211yescharacteristic, complemented
35C43×#485—21no—
36C43×#485—21no—
37C43×#482—21no—
38C43×#482—21no—
39C43×#428C2211yescharacteristic, complemented
40C43×#428C2211yescharacteristic, complemented
41C2×#104×C43C2211yescharacteristic
42C2×#104×C43C2211yescharacteristic
43C2×#104×C43C2211yescharacteristic, complemented
44C2×#104×C43C2211yescharacteristic, complemented
45C2×#104×C43C2211yescharacteristic, complemented
46C2×#104×C43C2211yescharacteristic, complemented
47C43×#419—21no—
48C43×#418—21no—
49C43×#417C2211yescharacteristic
50C43×#417C2211yescharacteristic
51C43×#417C2211yescharacteristic, complemented
52C43×#417C2211yescharacteristic, complemented
53C43×#417C2211yescharacteristic, complemented
54C43×#417C2211yescharacteristic, complemented
55C43×#416—21no—
56C43×#416—21no—
57C2×#100×C43C2211yescharacteristic, complemented
58C2×#100×C43C2211yescharacteristic, complemented
59C43×#407C2211yescharacteristic, complemented
60C43×#394—22no—
61C43×#390C2211yescharacteristic, complemented
62C43×#390C2211yescharacteristic, complemented
63C43×#388—22no—
64C43×#384C2211yescharacteristic, complemented
65C43×#382C2211yescharacteristic, complemented
66C4×C22⋊C4×C43C2211yescharacteristic, complemented
67C43×#343C2211yescharacteristic, complemented
68C43×#343C2211yescharacteristic, complemented
69C43×#339C2211yescharacteristic, complemented
70C43×#339C2211yescharacteristic, complemented
71H(5,𝔽2)×C43—22no—
72H(5,𝔽2)×C43—22no—
73H(5,𝔽2)×C43—41no—
74H(5,𝔽2)×C43—41no—
75C2×#41×C43—21no—
76C2×#41×C43—21no—
77C2×#41×C43—21no—
78C2×#41×C43—21no—
79C2×#41×C43—22no—
80C2×#41×C43—22no—
81C2×#41×C43—41no—
82C2×#41×C43—41no—
83C2×#41×C43D411yescharacteristic
84C2×#41×C43D411yescharacteristic
85C2×#41×C43C2311yescharacteristic
86C2×#41×C43C2311yescharacteristic
87C2×#41×C43C2311yescharacteristic
88C22×Q8×C43D411yescharacteristic
89C22×D4×C43—21no—
90C22×D4×C43—22no—
91C22×D4×C43—22no—
92C22×D4×C43—21no—
93C22×D4×C43—21no—
94C22×D4×C43D411yescharacteristic
95C22×D4×C43D412yes—
96C22×D4×C43C2311yescharacteristic
97C23×C4×C43—21no—
98C23×C4×C43C2311yescharacteristic
99C2×M16×C43—21no—
100C2×M16×C43—41no—
101C2×M16×C43—41no—
102C2×M16×C43C2311yescharacteristic
103C2×M16×C43C2311yescharacteristic
104C2×M16×C43C2311yescharacteristic
105C2×M16×C43C2311yescharacteristic
106C22×C8×C43—21no—
107#127×C43—22no—
108#127×C43—21no—
109#124×C43—22no—
110#124×C43—21no—
111#123×C43—22no—
112#123×C43—21no—
113C22⋊Q8×C43—22no—
114C22⋊Q8×C43—21no—
115C22⋊Q8×C43—21no—
116C22⋊Q8×C43D411yescharacteristic
117C22⋊Q8×C43D411yescharacteristic
118#121×C43—22no—
119#121×C43—22no—
120#121×C43—22no—
121#121×C43—22no—
122#121×C43—22no—
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—22no—
130#121×C43—21no—
131#121×C43—21no—
132#121×C43D411yescharacteristic
133#121×C43D411yescharacteristic
134#120×C43—22no—
135#120×C43—22no—
136#120×C43—22no—
137#120×C43—21no—
138#120×C43—22no—
139C4×Q8×C43—21no—
140C4×D4×C43—22no—
141C4×D4×C43—22no—
142C4×D4×C43—21no—
143C4×D4×C43—22no—
144C4×D4×C43—21no—
145C4×D4×C43—21no—
146#117×C43—21no—
147#117×C43—21no—
148#117×C43—21no—
149#117×C43—21no—
150#117×C43—21no—
151#117×C43C2311yescharacteristic
152C2×C4⋊C4×C43—21no—
153C2×C4⋊C4×C43—22no—
154C2×C4⋊C4×C43C2311yescharacteristic
155C2×C4⋊C4×C43C2311yescharacteristic
156C2×C4⋊C4×C43C2311yescharacteristic
157C2×C22⋊C4×C43—22no—
158C2×C22⋊C4×C43—21no—
159C2×C22⋊C4×C43—21no—
160C2×C22⋊C4×C43—22no—
161C2×C22⋊C4×C43—22no—
162C2×C22⋊C4×C43D412yes—
163C2×C42×C43—21no—
164C2×C42×C43C2311yescharacteristic
165C2×C42×C43C2311yescharacteristic
166#107×C43—21no—
167#107×C43—21no—
168#106×C43—21no—
169#106×C43—21no—
170#104×C43—22no—
171#104×C43—22no—
172#104×C43—41no—
173#104×C43—41no—
174#104×C43—41no—
175#104×C43—41no—
176#103×C43—21no—
177#103×C43—21no—
178#103×C43—21no—
179#103×C43—21no—
180#103×C43—21no—
181#103×C43—21no—
182#102×C43—21no—
183#102×C43—21no—
184#102×C43—21no—
185#102×C43—21no—
186#102×C43—21no—
187#102×C43—21no—
188#100×C43—41no—
189#100×C43—41no—
190C22⋊C8×C43—21no—
191C22⋊C8×C43—21no—
192#95×C43—21no—
193#95×C43—22no—
194C24×C43—22no—
195C24×C43—21no—
196C24×C43C2×D412yes—
197C24×C43C2×D411yescharacteristic
198#41×C43—21no—
199#41×C43—21no—
200#41×C43—22no—
201#41×C43—22no—
202#41×C43—21no—
203#41×C43—21no—
204#41×C43—21no—
205#41×C43—21no—
206#41×C43—21no—
207#41×C43—21no—
208#41×C43—21no—
209#41×C43—21no—
210#41×C43—42no—
211#41×C43—42no—
212#41×C43—41no—
213#41×C43—41no—
214#41×C43—42no—
215#41×C43—42no—
216#41×C43—42no—
217#41×C43—42no—
218#41×C43—42no—
219#41×C43—42no—
220#41×C43#4112yes—
221#41×C43#4112yes—
222C2×Q8×C43—21no—
223C2×Q8×C43—22no—
224C2×Q8×C43—41no—
225C2×Q8×C43C2×D411yescharacteristic
226C2×Q8×C43C2×D411yescharacteristic
227C2×Q8×C43C2×D411yescharacteristic
228C2×D4×C43—22no—
229C2×D4×C43—22no—
230C2×D4×C43—22no—
231C2×D4×C43—22no—
232C2×D4×C43—22no—
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—22no—
241C2×D4×C43—21no—
242C2×D4×C43—21no—
243C2×D4×C43—21no—
244C2×D4×C43—21no—
245C2×D4×C43—22no—
246C2×D4×C43—21no—
247C2×D4×C43—21no—
248C2×D4×C43—21no—
249C2×D4×C43—22no—
250C2×D4×C43—42no—
251C2×D4×C43—42no—
252C2×D4×C43—44no—
253C2×D4×C43—44no—
254C2×D4×C43—41no—
255C2×D4×C43—42no—
256C2×D4×C43—42no—
257C2×D4×C43—42no—
258C2×D4×C43—42no—
259C2×D4×C43—82no—
260C2×D4×C43—84no—
261C2×D4×C43C2×D411yescharacteristic
262C2×D4×C43C2×D411yescharacteristic
263C2×D4×C43C2×D411yescharacteristic
264C22×C4×C43—21no—
265C22×C4×C43—21no—
266C22×C4×C43—21no—
267C22×C4×C43—21no—
268C22×C4×C43—21no—
269C22×C4×C43—22no—
270C22×C4×C43—22no—
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—21no—
279C22×C4×C43—21no—
280C22×C4×C43—42no—
281C22×C4×C43—42no—
282C22×C4×C43C2×D411yescharacteristic
283C22×C4×C43C2×D411yescharacteristic
284C22×C4×C43C2×D411yescharacteristic
285C22×C4×C43C2×D411yescharacteristic
286C22×C4×C43C2×D411yescharacteristic
287C22×C4×C43C2×D412yes—
288C22×C4×C43C2411yescharacteristic
289M16×C43—21no—
290M16×C43—21no—
291M16×C43—21no—
292M16×C43—21no—
293M16×C43—21no—
294M16×C43—21no—
295M16×C43—21no—
296M16×C43—21no—
297M16×C43—42no—
298C2×C8×C43—21no—
299C2×C8×C43—21no—
300C2×C8×C43—21no—
301C2×C8×C43—21no—
302C2×C8×C43—42no—
303C4⋊C4×C43—22no—
304C4⋊C4×C43—22no—
305C4⋊C4×C43—21no—
306C4⋊C4×C43—21no—
307C4⋊C4×C43—21no—
308C4⋊C4×C43—21no—
309C4⋊C4×C43—21no—
310C4⋊C4×C43—21no—
311C4⋊C4×C43—21no—
312C4⋊C4×C43—21no—
313C4⋊C4×C43—82no—
314C4⋊C4×C43C2×D411yescharacteristic
315C4⋊C4×C43C2×D411yescharacteristic
316C22⋊C4×C43—22no—
317C22⋊C4×C43—22no—
318C22⋊C4×C43—22no—
319C22⋊C4×C43—22no—
320C22⋊C4×C43—22no—
321C22⋊C4×C43—21no—
322C22⋊C4×C43—22no—
323C22⋊C4×C43—22no—
324C22⋊C4×C43—21no—
325C22⋊C4×C43—21no—
326C22⋊C4×C43—21no—
327C22⋊C4×C43—21no—
328C22⋊C4×C43—42no—
329C22⋊C4×C43—44no—
330C22⋊C4×C43—41no—
331C22⋊C4×C43—41no—
332C22⋊C4×C43—82no—
333C42×C43—22no—
334C42×C43—21no—
335C42×C43—21no—
336C42×C43—21no—
337C42×C43—21no—
338C42×C43—21no—
339C42×C43—41no—
340C42×C43—41no—
341C23×C43—21no—
342C23×C43—21no—
343C23×C43—21no—
344C23×C43—22no—
345C23×C43—21no—
346C23×C43—21no—
347C23×C43—22no—
348C23×C43—22no—
349C23×C43—41no—
350C23×C43—41no—
351C23×C43—42no—
352C23×C43—42no—
353C23×C43—44no—
354C23×C43—42no—
355C23×C43—42no—
356C23×C43—81no—
357C23×C43—82no—
358C23×C43—82no—
359C23×C43#12011yescharacteristic
360C23×C43#12011yescharacteristic
361C23×C43C22×D411yescharacteristic
362Q8×C43—21no—
363Q8×C43—21no—
364Q8×C43—21no—
365Q8×C43—21no—
366Q8×C43—21no—
367Q8×C43—42no—
368Q8×C43#12312yes—
369D4×C43—22no—
370D4×C43—22no—
371D4×C43—21no—
372D4×C43—21no—
373D4×C43—21no—
374D4×C43—21no—
375D4×C43—21no—
376D4×C43—42no—
377D4×C43—42no—
378D4×C43—44no—
379D4×C43—42no—
380D4×C43—44no—
381D4×C43—44no—
382D4×C43—42no—
383D4×C43—41no—
384D4×C43—41no—
385D4×C43—41no—
386D4×C43—41no—
387D4×C43—41no—
388D4×C43—41no—
389D4×C43—41no—
390D4×C43—41no—
391D4×C43—81no—
392D4×C43—82no—
393D4×C43—82no—
394D4×C43—82no—
395D4×C43—82no—
396D4×C43#12312yes—
397C2×C4×C43—21no—
398C2×C4×C43—21no—
399C2×C4×C43—21no—
400C2×C4×C43—21no—
401C2×C4×C43—21no—
402C2×C4×C43—21no—
403C2×C4×C43—21no—
404C2×C4×C43—21no—
405C2×C4×C43—21no—
406C2×C4×C43—21no—
407C2×C4×C43—21no—
408C2×C4×C43—22no—
409C2×C4×C43—22no—
410C2×C4×C43—22no—
411C2×C4×C43—21no—
412C2×C4×C43—22no—
413C2×C4×C43—21no—
414C2×C4×C43—21no—
415C2×C4×C43—21no—
416C2×C4×C43—42no—
417C2×C4×C43—42no—
418C2×C4×C43—42no—
419C2×C4×C43—44no—
420C2×C4×C43—41no—
421C2×C4×C43—41no—
422C2×C4×C43—41no—
423C2×C4×C43—41no—
424C2×C4×C43—41no—
425C2×C4×C43—41no—
426C2×C4×C43—42no—
427C2×C4×C43—41no—
428C2×C4×C43—42no—
429C2×C4×C43—41no—
430C2×C4×C43—42no—
431C2×C4×C43—41no—
432C2×C4×C43—41no—
433C2×C4×C43—41no—
434C2×C4×C43—82no—
435C2×C4×C43#12011yescharacteristic
436C2×C4×C43#12011yescharacteristic
437C2×C4×C43C22×D411yescharacteristic
438C2×C4×C43C22×D411yescharacteristic
439C2×C4×C43C2×#4111yescharacteristic
440C2×C4×C43C2×#4111yescharacteristic
441C2×C4×C43H(5,𝔽2)11yescharacteristic
442C2×C4×C43H(5,𝔽2)11yescharacteristic
443C8×C43—41no—
444C8×C43—41no—
445C8×C43—41no—
446C8×C43—41no—
447#24031C4311yesmaximal, characteristic, direct product factor, Sylow
448C22×C43—21no—
449C22×C43—21no—
450C22×C43—21no—
451C22×C43—21no—
452C22×C43—22no—
453C22×C43—21no—
454C22×C43—21no—
455C22×C43—21no—
456C22×C43—21no—
457C22×C43—41no—
458C22×C43—41no—
459C22×C43—42no—
460C22×C43—41no—
461C22×C43—41no—
462C22×C43—42no—
463C22×C43—41no—
464C22×C43—41no—
465C22×C43—41no—
466C22×C43—42no—
467C22×C43—41no—
468C22×C43—81no—
469C22×C43—81no—
470C22×C43—82no—
471C22×C43—82no—
472C22×C43—84no—
473C22×C43—164no—
474C22×C43C2×#12011yescharacteristic
475C22×C43#54611yescharacteristic
476C22×C43#54611yescharacteristic
477C4×C43—21no—
478C4×C43—21no—
479C4×C43—22no—
480C4×C43—42no—
481C4×C43—41no—
482C4×C43—41no—
483C4×C43—41no—
484C4×C43—42no—
485C4×C43—41no—
486C4×C43—81no—
487C4×C43—81no—
488C4×C43—81no—
489C4×C43C2×#12311yescharacteristic
490C4×C43#53411yescharacteristic
491C4×C43#54611yescharacteristic
492C4×C43#54611yescharacteristic
493#3488C2×C4311yescharacteristic
494#3093C2×C4311yescharacteristic, complemented
495#2896C2×C4311yescharacteristic, complemented
496#2500C2×C4311yescharacteristic, complemented
497#2040C2×C4311yescharacteristic, complemented
498#2039C2×C4311yescharacteristic, complemented
499#2037C2×C4311yescharacteristic, complemented
500#2037C2×C4311yescharacteristic, complemented
501#1900C2×C4311yescharacteristic, complemented
502#1871C2×C4311yescharacteristic, complemented
503#1860C2×C4311yescharacteristic, complemented
504#1859C2×C4311yescharacteristic, complemented
505#1792C2×C4311yescharacteristic, complemented
506#1792C2×C4311yescharacteristic, complemented
507#1789C2×C4311yescharacteristic, complemented
508C2×C43—21no—
509C2×C43—21no—
510C2×C43—41no—
511C2×C43—41no—
512C2×C43—42no—
513C2×C43—81no—
514C2×C43—82no—
515C2×C43—81no—
516C2×C43#240511yescharacteristic
517C2×C43#301811yescharacteristic
518C2×C43#301911yescharacteristic
519C2×H(5,𝔽2)C22×C4311yescharacteristic
520C22×#41C22×C4311yescharacteristic
521C22×M16C22×C4311yescharacteristic, complemented
522#550—21no—
523#548—21no—
524#546—21no—
525#546—22no—
526D42—22no—
527D42—21no—
528#537—21no—
529#537C22×C4311yescharacteristic
530#535—21no—
531#535C22×C4311yescharacteristic
532#525—21no—
533#525C22×C4311yescharacteristic
534C2×#121—21no—
535C2×#121C22×C4311yescharacteristic
536#520C22×C4311yescharacteristic
537C2×#117C22×C4311yescharacteristic, complemented
538#485—21no—
539#485—21no—
540#482—21no—
541#482—21no—
542#428C22×C4311yescharacteristic, complemented
543#428C22×C4311yescharacteristic, complemented
544C2×#104C22×C4311yescharacteristic
545C2×#104C22×C4311yescharacteristic
546C2×#104C22×C4311yescharacteristic, complemented
547C2×#104C22×C4311yescharacteristic, complemented
548C2×#104C22×C4311yescharacteristic, complemented
549C2×#104C22×C4311yescharacteristic, complemented
550#419—21no—
551#418—21no—
552#417C22×C4311yescharacteristic
553#417C22×C4311yescharacteristic
554#417C22×C4311yescharacteristic, complemented
555#417C22×C4311yescharacteristic, complemented
556#417C22×C4311yescharacteristic, complemented
557#417C22×C4311yescharacteristic, complemented
558#416—21no—
559#416—21no—
560C2×#100C22×C4311yescharacteristic, complemented
561C2×#100C22×C4311yescharacteristic, complemented
562#407C22×C4311yescharacteristic, complemented
563#394—22no—
564#390C22×C4311yescharacteristic, complemented
565#390C22×C4311yescharacteristic, complemented
566#388—22no—
567#384C22×C4311yescharacteristic, complemented
568#382C22×C4311yescharacteristic, complemented
569C4×C22⋊C4C22×C4311yescharacteristic, complemented
570#343C22×C4311yescharacteristic, complemented
571#343C22×C4311yescharacteristic, complemented
572#339C22×C4311yescharacteristic, complemented
573#339C22×C4311yescharacteristic, complemented
574C43#2403111yescharacteristic, direct product factor, Sylow
575H(5,𝔽2)—22no—
576H(5,𝔽2)—22no—
577H(5,𝔽2)—41no—
578H(5,𝔽2)—41no—
579C2×#41—21no—
580C2×#41—21no—
581C2×#41—21no—
582C2×#41—21no—
583C2×#41—22no—
584C2×#41—22no—
585C2×#41—41no—
586C2×#41—41no—
587C2×#41D4×C4311yescharacteristic
588C2×#41D4×C4311yescharacteristic
589C2×#41C23×C4311yescharacteristic
590C2×#41C23×C4311yescharacteristic
591C2×#41C23×C4311yescharacteristic
592C22×Q8D4×C4311yescharacteristic
593C22×D4—21no—
594C22×D4—22no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4D4×C4311yescharacteristic
599C22×D4D4×C4312yes—
600C22×D4C23×C4311yescharacteristic
601C23×C4—21no—
602C23×C4C23×C4311yescharacteristic
603C2×M16—21no—
604C2×M16—41no—
605C2×M16—41no—
606C2×M16C23×C4311yescharacteristic
607C2×M16C23×C4311yescharacteristic
608C2×M16C23×C4311yescharacteristic
609C2×M16C23×C4311yescharacteristic
610C22×C8—21no—
611#127—22no—
612#127—21no—
613#124—22no—
614#124—21no—
615#123—22no—
616#123—21no—
617C22⋊Q8—22no—
618C22⋊Q8—21no—
619C22⋊Q8—21no—
620C22⋊Q8D4×C4311yescharacteristic
621C22⋊Q8D4×C4311yescharacteristic
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—22no—
627#121—21no—
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—22no—
634#121—21no—
635#121—21no—
636#121D4×C4311yescharacteristic
637#121D4×C4311yescharacteristic
638#120—22no—
639#120—22no—
640#120—22no—
641#120—21no—
642#120—22no—
643C4×Q8—21no—
644C4×D4—22no—
645C4×D4—22no—
646C4×D4—21no—
647C4×D4—22no—
648C4×D4—21no—
649C4×D4—21no—
650#117—21no—
651#117—21no—
652#117—21no—
653#117—21no—
654#117—21no—
655#117C23×C4311yescharacteristic
656C2×C4⋊C4—21no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4C23×C4311yescharacteristic
659C2×C4⋊C4C23×C4311yescharacteristic
660C2×C4⋊C4C23×C4311yescharacteristic
661C2×C22⋊C4—22no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—22no—
666C2×C22⋊C4D4×C4312yes—
667C2×C42—21no—
668C2×C42C23×C4311yescharacteristic
669C2×C42C23×C4311yescharacteristic
670#107—21no—
671#107—21no—
672#106—21no—
673#106—21no—
674#104—22no—
675#104—22no—
676#104—41no—
677#104—41no—
678#104—41no—
679#104—41no—
680#103—21no—
681#103—21no—
682#103—21no—
683#103—21no—
684#103—21no—
685#103—21no—
686#102—21no—
687#102—21no—
688#102—21no—
689#102—21no—
690#102—21no—
691#102—21no—
692#100—41no—
693#100—41no—
694C22⋊C8—21no—
695C22⋊C8—21no—
696#95—21no—
697#95—22no—
698C24—22no—
699C24—21no—
700C24C2×D4×C4312yes—
701C24C2×D4×C4311yescharacteristic
702#41—21no—
703#41—21no—
704#41—22no—
705#41—22no—
706#41—21no—
707#41—21no—
708#41—21no—
709#41—21no—
710#41—21no—
711#41—21no—
712#41—21no—
713#41—21no—
714#41—42no—
715#41—42no—
716#41—41no—
717#41—41no—
718#41—42no—
719#41—42no—
720#41—42no—
721#41—42no—
722#41—42no—
723#41—42no—
724#41#41×C4312yes—
725#41#41×C4312yes—
726C2×Q8—21no—
727C2×Q8—22no—
728C2×Q8—41no—
729C2×Q8C2×D4×C4311yescharacteristic
730C2×Q8C2×D4×C4311yescharacteristic
731C2×Q8C2×D4×C4311yescharacteristic
732C2×D4—21no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—21no—
741C2×D4—21no—
742C2×D4—22no—
743C2×D4—22no—
744C2×D4—22no—
745C2×D4—21no—
746C2×D4—22no—
747C2×D4—21no—
748C2×D4—21no—
749C2×D4—21no—
750C2×D4—21no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—41no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—42no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—42no—
762C2×D4—42no—
763C2×D4—82no—
764C2×D4—84no—
765C2×D4C2×D4×C4311yescharacteristic
766C2×D4C2×D4×C4311yescharacteristic
767C2×D4C2×D4×C4311yescharacteristic
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—22no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4C2×D4×C4311yescharacteristic
787C22×C4C2×D4×C4311yescharacteristic
788C22×C4C2×D4×C4311yescharacteristic
789C22×C4C2×D4×C4311yescharacteristic
790C22×C4C2×D4×C4311yescharacteristic
791C22×C4C2×D4×C4312yes—
792C22×C4C24×C4311yescharacteristic
793M16—21no—
794M16—21no—
795M16—21no—
796M16—21no—
797M16—21no—
798M16—21no—
799M16—21no—
800M16—21no—
801M16—42no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—42no—
807C4⋊C4—22no—
808C4⋊C4—22no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—82no—
818C4⋊C4C2×D4×C4311yescharacteristic
819C4⋊C4C2×D4×C4311yescharacteristic
820C22⋊C4—22no—
821C22⋊C4—22no—
822C22⋊C4—22no—
823C22⋊C4—22no—
824C22⋊C4—22no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—22no—
830C22⋊C4—22no—
831C22⋊C4—21no—
832C22⋊C4—42no—
833C22⋊C4—44no—
834C22⋊C4—41no—
835C22⋊C4—41no—
836C22⋊C4—82no—
837C42—22no—
838C42—21no—
839C42—21no—
840C42—21no—
841C42—21no—
842C42—21no—
843C42—41no—
844C42—41no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—21no—
850C23—21no—
851C23—22no—
852C23—22no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—42no—
857C23—44no—
858C23—42no—
859C23—42no—
860C23—81no—
861C23—82no—
862C23—82no—
863C23#120×C4311yescharacteristic
864C23#120×C4311yescharacteristic
865C23C22×D4×C4311yescharacteristic
866Q8—21no—
867Q8—21no—
868Q8—21no—
869Q8—21no—
870Q8—21no—
871Q8—42no—
872Q8#123×C4312yes—
873D4—22no—
874D4—22no—
875D4—21no—
876D4—21no—
877D4—21no—
878D4—21no—
879D4—21no—
880D4—42no—
881D4—42no—
882D4—44no—
883D4—42no—
884D4—44no—
885D4—44no—
886D4—42no—
887D4—41no—
888D4—41no—
889D4—41no—
890D4—41no—
891D4—41no—
892D4—41no—
893D4—41no—
894D4—41no—
895D4—82no—
896D4—81no—
897D4—82no—
898D4—82no—
899D4—82no—
900D4#123×C4312yes—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—21no—
916C2×C4—22no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—44no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—42no—
931C2×C4—41no—
932C2×C4—42no—
933C2×C4—41no—
934C2×C4—42no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—82no—
939C2×C4#120×C4311yescharacteristic
940C2×C4#120×C4311yescharacteristic
941C2×C4C22×D4×C4311yescharacteristic
942C2×C4C22×D4×C4311yescharacteristic
943C2×C4C2×#41×C4311yescharacteristic
944C2×C4C2×#41×C4311yescharacteristic
945C2×C4H(5,𝔽2)×C4311yescharacteristic
946C2×C4H(5,𝔽2)×C4311yescharacteristic
947C8—41no—
948C8—41no—
949C8—41no—
950C8—41no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—22no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—42no—
965C22—41no—
966C22—42no—
967C22—41no—
968C22—42no—
969C22—41no—
970C22—41no—
971C22—81no—
972C22—81no—
973C22—82no—
974C22—82no—
975C22—84no—
976C22—164no—
977C22C2×#120×C4311yescharacteristic
978C22C43×#54611yescharacteristic
979C22C43×#54611yescharacteristic
980C4—21no—
981C4—21no—
982C4—22no—
983C4—42no—
984C4—41no—
985C4—41no—
986C4—41no—
987C4—42no—
988C4—41no—
989C4—81no—
990C4—81no—
991C4—81no—
992C4C2×#123×C4311yescharacteristic
993C4C43×#53411yescharacteristic
994C4C43×#54611yescharacteristic
995C4C43×#54611yescharacteristic
996C2—21no—
997C2—21no—
998C2—41no—
999C2—41no—
1000C2—42no—
1001C2—81no—
1002C2—82no—
1003C2—81no—
1004C2C43×#240511yescharacteristic
1005C2C43×#301811yescharacteristic
1006C2C43×#301911yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC43×#3488C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C23×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#3093C2semidirect
3. C43×#2896C2semidirect
4. C43×#2500C2semidirect
5. C43×#2040C2semidirect
6. C43×#2039C2semidirect
7. C43×#2037C2semidirect
8. C43×#2037C2semidirect
9. C43×#1900C2semidirect
10. C43×#1871C2semidirect
11. C43×#1860C2semidirect
12. C43×#1859C2semidirect
13. C43×#1792C2semidirect
14. C43×#1792C2semidirect
15. C43×#1789C2semidirect
18. C22×M16×C43C22semidirect
34. C2×#117×C43C22semidirect
39. C43×#428C22semidirect
40. C43×#428C22semidirect
43. C2×#104×C43C22semidirect
44. C2×#104×C43C22semidirect
45. C2×#104×C43C22semidirect
46. C2×#104×C43C22semidirect
51. C43×#417C22semidirect
52. C43×#417C22semidirect
53. C43×#417C22semidirect
54. C43×#417C22semidirect
57. C2×#100×C43C22semidirect
58. C2×#100×C43C22semidirect
59. C43×#407C22semidirect
61. C43×#390C22semidirect
62. C43×#390C22semidirect
64. C43×#384C22semidirect
65. C43×#382C22semidirect
66. C4×C22⋊C4×C43C22semidirect
67. C43×#343C22semidirect
68. C43×#343C22semidirect
69. C43×#339C22semidirect
70. C43×#339C22semidirect
447. #24031C43direct (N × H)
494. #3093C2×C43semidirect
495. #2896C2×C43semidirect
496. #2500C2×C43semidirect
497. #2040C2×C43semidirect
498. #2039C2×C43semidirect
499. #2037C2×C43semidirect
500. #2037C2×C43semidirect
501. #1900C2×C43semidirect
502. #1871C2×C43semidirect
503. #1860C2×C43semidirect
504. #1859C2×C43semidirect
505. #1792C2×C43semidirect
506. #1792C2×C43semidirect
507. #1789C2×C43semidirect
521. C22×M16C22×C43semidirect
537. C2×#117C22×C43semidirect
542. #428C22×C43semidirect
543. #428C22×C43semidirect
546. C2×#104C22×C43semidirect
547. C2×#104C22×C43semidirect
548. C2×#104C22×C43semidirect
549. C2×#104C22×C43semidirect
554. #417C22×C43semidirect
555. #417C22×C43semidirect
556. #417C22×C43semidirect
557. #417C22×C43semidirect
560. C2×#100C22×C43semidirect
561. C2×#100C22×C43semidirect
562. #407C22×C43semidirect
564. #390C22×C43semidirect
565. #390C22×C43semidirect
567. #384C22×C43semidirect
568. #382C22×C43semidirect
569. C4×C22⋊C4C22×C43semidirect
570. #343C22×C43semidirect
571. #343C22×C43semidirect
572. #339C22×C43semidirect
573. #339C22×C43semidirect
574. C43#24031direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#34882
C43×#30932
C43×#28962
C43×#25002
C43×#20402
C43×#20392
C43×#20372
C43×#19002
C43×#18712
C43×#18602
C43×#18592
C43×#17922
C43×#17892
#2403143