Finite Group Databasebeta

← C43×#18262 #24938279

Subgroups — C43×#18262 #24938279

Order 11008.

1012 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3534C211yesmaximal, characteristic
2C43×#3094C211yesmaximal, characteristic, complemented
3C43×#3091C211yesmaximal, characteristic, complemented
4C43×#2498C211yesmaximal, characteristic, complemented
5C43×#1618C211yesmaximal, characteristic, complemented
6C43×#1616C211yesmaximal, characteristic, complemented
7C43×#1615C211yesmaximal, characteristic, complemented
8C43×#1613C211yesmaximal, characteristic, complemented
9C43×#1612C211yesmaximal, characteristic, complemented
10C43×#1610C211yesmaximal, characteristic, complemented
11C43×#1609C211yesmaximal, characteristic, complemented
12C43×#1607C211yesmaximal, characteristic, complemented
13C43×#1504C211yesmaximal, characteristic, complemented
14C2×C43×#327C211yesmaximal, characteristic, complemented
15C43×#1468C211yesmaximal, characteristic, complemented
16C43×#562—21no—
17C43×#560—21no—
18C43×#553—21no—
19C43×#551—21no—
20C43×#546—21no—
21C43×#546—21no—
22C43×#546—21no—
23D42×C43—21no—
24C43×#540—21no—
25C43×#539—21no—
26C43×#539C2211yescharacteristic
27C43×#538—21no—
28C43×#538C2211yescharacteristic
29C43×#537C2211yescharacteristic
30C43×#534—21no—
31C43×#534C2211yescharacteristic
32C43×#525C2211yescharacteristic
33C2×#123×C43C2211yescharacteristic
34C2×#121×C43C2211yescharacteristic
35C2×#117×C43C2211yescharacteristic, complemented
36C43×#485—21no—
37C43×#484C2211yescharacteristic, complemented
38C43×#483C2211yescharacteristic, complemented
39C43×#482—21no—
40C43×#482—21no—
41C43×#482—21no—
42C43×#481C2211yescharacteristic
43C43×#481C2211yescharacteristic, complemented
44C43×#481C2211yescharacteristic, complemented
45C43×#480C2211yescharacteristic
46C43×#480C2211yescharacteristic, complemented
47C43×#480C2211yescharacteristic, complemented
48C43×#428—21no—
49C43×#427—21no—
50C43×#418—21no—
51C43×#416—21no—
52C43×#407C2211yescharacteristic, complemented
53C2×C22⋊C8×C43C2211yescharacteristic, complemented
54C43×#400C2211yescharacteristic, complemented
55C43×#399C2211yescharacteristic, complemented
56C43×#398C2211yescharacteristic, complemented
57C43×#397C2211yescharacteristic, complemented
58C43×#388—21no—
59C43×#387—21no—
60C43×#386—21no—
61C43×#380—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×C43D411yescharacteristic
77C22×D4×C43—21no—
78C22×D4×C43—21no—
79C22×D4×C43—21no—
80C22×D4×C43D411yescharacteristic
81C22×D4×C43D411yescharacteristic
82C23×C4×C43—21no—
83C23×C4×C43C2311yescharacteristic
84C2×M16×C43—21no—
85C22×C8×C43—21no—
86#127×C43—21no—
87#126×C43—21no—
88#126×C43—21no—
89#126×C43—21no—
90#126×C43—21no—
91#125×C43—21no—
92#125×C43—21no—
93#124×C43—21no—
94#124×C43—21no—
95#124×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—
108#123×C43—21no—
109#123×C43—21no—
110C22⋊Q8×C43—21no—
111C22⋊Q8×C43—21no—
112C22⋊Q8×C43—21no—
113C22⋊Q8×C43—21no—
114C22⋊Q8×C43—21no—
115C22⋊Q8×C43D411yescharacteristic
116C22⋊Q8×C43C2311yescharacteristic
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×C43—21no—
131#121×C43—21no—
132#121×C43D411yescharacteristic
133#121×C43D411yescharacteristic
134#121×C43D411yescharacteristic
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—
143#120×C43—21no—
144#120×C43—21no—
145#120×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—
153C4×D4×C43—21no—
154#117×C43—21no—
155#117×C43—21no—
156#117×C43—21no—
157#117×C43—21no—
158#117×C43—21no—
159#117×C43D411yescharacteristic
160C2×C4⋊C4×C43—21no—
161C2×C4⋊C4×C43—21no—
162C2×C4⋊C4×C43D411yescharacteristic
163C2×C4⋊C4×C43D411yescharacteristic
164C2×C4⋊C4×C43C2311yescharacteristic
165C2×C4⋊C4×C43C2311yescharacteristic
166C2×C4⋊C4×C43C2311yescharacteristic
167C2×C22⋊C4×C43—21no—
168C2×C22⋊C4×C43—21no—
169C2×C22⋊C4×C43—21no—
170C2×C22⋊C4×C43—21no—
171C2×C22⋊C4×C43—21no—
172C2×C22⋊C4×C43—21no—
173C2×C22⋊C4×C43D411yescharacteristic
174C2×C22⋊C4×C43D411yescharacteristic
175C2×C22⋊C4×C43C2311yescharacteristic
176C2×C42×C43—21no—
177#107×C43—21no—
178#107×C43—21no—
179#107×C43—21no—
180#107×C43—21no—
181#106×C43—21no—
182#106×C43—21no—
183#106×C43—21no—
184#106×C43—21no—
185#103×C43—21no—
186#103×C43—21no—
187#102×C43—21no—
188#102×C43—21no—
189#102×C43—21no—
190#102×C43—21no—
191#102×C43—21no—
192#102×C43—21no—
193C22⋊C8×C43—21no—
194C22⋊C8×C43—21no—
195C22⋊C8×C43C2311yescharacteristic
196C22⋊C8×C43C2311yescharacteristic
197C22⋊C8×C43C2311yescharacteristic
198C22⋊C8×C43C2311yescharacteristic
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×C43—21no—
208C24×C43C2×D411yescharacteristic
209C24×C43C2×D411yescharacteristic
210#41×C43—42no—
211#41×C43—81no—
212#41×C43—81no—
213C2×Q8×C43—21no—
214C2×Q8×C43C2×D411yescharacteristic
215C2×D4×C43—21no—
216C2×D4×C43—21no—
217C2×D4×C43—21no—
218C2×D4×C43—21no—
219C2×D4×C43—21no—
220C2×D4×C43—21no—
221C2×D4×C43—21no—
222C2×D4×C43—21no—
223C2×D4×C43—21no—
224C2×D4×C43—21no—
225C2×D4×C43—21no—
226C2×D4×C43—21no—
227C2×D4×C43—21no—
228C2×D4×C43—21no—
229C2×D4×C43—21no—
230C2×D4×C43—21no—
231C2×D4×C43—21no—
232C2×D4×C43—42no—
233C2×D4×C43—42no—
234C2×D4×C43—81no—
235C2×D4×C43—81no—
236C2×D4×C43—81no—
237C2×D4×C43—81no—
238C2×D4×C43—82no—
239C2×D4×C43C2×D411yescharacteristic
240C2×D4×C43C2×D411yescharacteristic
241C2×D4×C43C2×D411yescharacteristic
242C22×C4×C43—21no—
243C22×C4×C43—21no—
244C22×C4×C43—21no—
245C22×C4×C43—21no—
246C22×C4×C43—21no—
247C22×C4×C43—21no—
248C22×C4×C43—21no—
249C22×C4×C43—21no—
250C22×C4×C43—21no—
251C22×C4×C43—21no—
252C22×C4×C43—21no—
253C22×C4×C43—42no—
254C22×C4×C43—42no—
255C22×C4×C43—42no—
256C22×C4×C43—81no—
257C22×C4×C43C2×D411yescharacteristic
258C22×C4×C43C2×D411yescharacteristic
259C22×C4×C43C2×D411yescharacteristic
260C22×C4×C43C2×D411yescharacteristic
261C22×C4×C43C2×D411yescharacteristic
262C22×C4×C43C2×D411yescharacteristic
263C22×C4×C43C2×D411yescharacteristic
264C22×C4×C43C2×D411yescharacteristic
265C22×C4×C43C2411yescharacteristic
266M16×C43—42no—
267C2×C8×C43—21no—
268C2×C8×C43—21no—
269C2×C8×C43—21no—
270C2×C8×C43—21no—
271C2×C8×C43—42no—
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—21no—
281C4⋊C4×C43—21no—
282C4⋊C4×C43—21no—
283C4⋊C4×C43—21no—
284C4⋊C4×C43—21no—
285C4⋊C4×C43—21no—
286C4⋊C4×C43—21no—
287C4⋊C4×C43—21no—
288C4⋊C4×C43—21no—
289C4⋊C4×C43—42no—
290C4⋊C4×C43—81no—
291C4⋊C4×C43C2×D411yescharacteristic
292C4⋊C4×C43C2×D411yescharacteristic
293C4⋊C4×C43C2×D411yescharacteristic
294C4⋊C4×C43C2×D411yescharacteristic
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—21no—
315C22⋊C4×C43—21no—
316C22⋊C4×C43—21no—
317C22⋊C4×C43—21no—
318C22⋊C4×C43—21no—
319C22⋊C4×C43—21no—
320C22⋊C4×C43—42no—
321C22⋊C4×C43—41no—
322C22⋊C4×C43—41no—
323C22⋊C4×C43—81no—
324C42×C43—21no—
325C42×C43—21no—
326C42×C43—21no—
327C42×C43—41no—
328C42×C43—41no—
329C23×C43—21no—
330C23×C43—21no—
331C23×C43—22no—
332C23×C43—21no—
333C23×C43—21no—
334C23×C43—21no—
335C23×C43—21no—
336C23×C43—21no—
337C23×C43—21no—
338C23×C43—41no—
339C23×C43—41no—
340C23×C43—41no—
341C23×C43—42no—
342C23×C43—81no—
343C23×C43—81no—
344C23×C43—81no—
345C23×C43—81no—
346C23×C43—81no—
347C23×C43#12011yescharacteristic
348C23×C43#12011yescharacteristic
349C23×C43C22×D411yescharacteristic
350Q8×C43—41no—
351Q8×C43—81no—
352D4×C43—41no—
353D4×C43—41no—
354D4×C43—41no—
355D4×C43—41no—
356D4×C43—41no—
357D4×C43—41no—
358D4×C43—41no—
359D4×C43—41no—
360D4×C43—41no—
361D4×C43—42no—
362D4×C43—42no—
363D4×C43—81no—
364D4×C43—81no—
365D4×C43—81no—
366D4×C43—81no—
367D4×C43—81no—
368D4×C43—81no—
369D4×C43—81no—
370D4×C43—81no—
371D4×C43—81no—
372D4×C43—81no—
373D4×C43—81no—
374D4×C43—81no—
375C2×C4×C43—22no—
376C2×C4×C43—22no—
377C2×C4×C43—22no—
378C2×C4×C43—21no—
379C2×C4×C43—21no—
380C2×C4×C43—21no—
381C2×C4×C43—21no—
382C2×C4×C43—21no—
383C2×C4×C43—21no—
384C2×C4×C43—21no—
385C2×C4×C43—21no—
386C2×C4×C43—21no—
387C2×C4×C43—21no—
388C2×C4×C43—41no—
389C2×C4×C43—41no—
390C2×C4×C43—41no—
391C2×C4×C43—41no—
392C2×C4×C43—41no—
393C2×C4×C43—41no—
394C2×C4×C43—41no—
395C2×C4×C43—41no—
396C2×C4×C43—41no—
397C2×C4×C43—41no—
398C2×C4×C43—41no—
399C2×C4×C43—41no—
400C2×C4×C43—41no—
401C2×C4×C43—41no—
402C2×C4×C43—41no—
403C2×C4×C43—41no—
404C2×C4×C43—41no—
405C2×C4×C43—81no—
406C2×C4×C43—81no—
407C2×C4×C43—81no—
408C2×C4×C43—81no—
409C2×C4×C43—81no—
410C2×C4×C43—81no—
411C2×C4×C43—81no—
412C2×C4×C43—84no—
413C2×C4×C43#12011yescharacteristic
414C2×C4×C43#12011yescharacteristic
415C2×C4×C43C22×D411yescharacteristic
416C2×C4×C43C22×D411yescharacteristic
417C8×C43—41no—
418C8×C43—41no—
419C8×C43—41no—
420C8×C43—41no—
421#18262C4311yesmaximal, characteristic, direct product factor, Sylow
422C22×C43—21no—
423C22×C43—21no—
424C22×C43—21no—
425C22×C43—21no—
426C22×C43—21no—
427C22×C43—21no—
428C22×C43—21no—
429C22×C43—42no—
430C22×C43—42no—
431C22×C43—41no—
432C22×C43—41no—
433C22×C43—41no—
434C22×C43—41no—
435C22×C43—41no—
436C22×C43—41no—
437C22×C43—41no—
438C22×C43—41no—
439C22×C43—41no—
440C22×C43—41no—
441C22×C43—41no—
442C22×C43—41no—
443C22×C43—81no—
444C22×C43—81no—
445C22×C43—162no—
446C22×C43—162no—
447C22×C43#45812yes—
448C22×C43C2×#12011yescharacteristic
449C22×C43#57611yescharacteristic
450C22×C43#57711yescharacteristic
451C4×C43—21no—
452C4×C43—21no—
453C4×C43—21no—
454C4×C43—21no—
455C4×C43—42no—
456C4×C43—41no—
457C4×C43—41no—
458C4×C43—41no—
459C4×C43—41no—
460C4×C43—41no—
461C4×C43—41no—
462C4×C43—41no—
463C4×C43—41no—
464C4×C43—81no—
465C4×C43—81no—
466C4×C43—81no—
467#3534C2×C4311yescharacteristic
468#3094C2×C4311yescharacteristic, complemented
469#3091C2×C4311yescharacteristic, complemented
470#2498C2×C4311yescharacteristic, complemented
471#1618C2×C4311yescharacteristic, complemented
472#1616C2×C4311yescharacteristic, complemented
473#1615C2×C4311yescharacteristic, complemented
474#1613C2×C4311yescharacteristic, complemented
475#1612C2×C4311yescharacteristic, complemented
476#1610C2×C4311yescharacteristic, complemented
477#1609C2×C4311yescharacteristic, complemented
478#1607C2×C4311yescharacteristic, complemented
479#1504C2×C4311yescharacteristic, complemented
480C2×#327C2×C4311yescharacteristic, complemented
481#1468C2×C4311yescharacteristic, complemented
482C2×C43—21no—
483C2×C43—21no—
484C2×C43—22no—
485C2×C43—41no—
486C2×C43—81no—
487C2×C43—81no—
488C2×C43—81no—
489C2×C43—81no—
490C2×C43#301211yescharacteristic
491C2×C43#301811yescharacteristic
492C2×C43C2×#45811yescharacteristic
493#562—21no—
494#560—21no—
495#553—21no—
496#551—21no—
497#546—21no—
498#546—21no—
499#546—21no—
500D42—21no—
501#540—21no—
502#539—21no—
503#539C22×C4311yescharacteristic
504#538—21no—
505#538C22×C4311yescharacteristic
506#537C22×C4311yescharacteristic
507#534—21no—
508#534C22×C4311yescharacteristic
509#525C22×C4311yescharacteristic
510C2×#123C22×C4311yescharacteristic
511C2×#121C22×C4311yescharacteristic
512C2×#117C22×C4311yescharacteristic, complemented
513#485—21no—
514#484C22×C4311yescharacteristic, complemented
515#483C22×C4311yescharacteristic, complemented
516#482—21no—
517#482—21no—
518#482—21no—
519#481C22×C4311yescharacteristic
520#481C22×C4311yescharacteristic, complemented
521#481C22×C4311yescharacteristic, complemented
522#480C22×C4311yescharacteristic
523#480C22×C4311yescharacteristic, complemented
524#480C22×C4311yescharacteristic, complemented
525#428—21no—
526#427—21no—
527#418—21no—
528#416—21no—
529#407C22×C4311yescharacteristic, complemented
530C2×C22⋊C8C22×C4311yescharacteristic, complemented
531#400C22×C4311yescharacteristic, complemented
532#399C22×C4311yescharacteristic, complemented
533#398C22×C4311yescharacteristic, complemented
534#397C22×C4311yescharacteristic, complemented
535#388—21no—
536#387—21no—
537#386—21no—
538#380—21no—
539C2×#95C22×C4311yescharacteristic, complemented
540#328C22×C4311yescharacteristic, complemented
541#328C22×C4311yescharacteristic, complemented
542#327C22×C4311yescharacteristic
543#327C22×C4311yescharacteristic
544#327C22×C4311yescharacteristic, complemented
545#327C22×C4311yescharacteristic, complemented
546#327C22×C4311yescharacteristic, complemented
547#327C22×C4311yescharacteristic, complemented
548#324C22×C4311yescharacteristic, complemented
549#324C22×C4311yescharacteristic, complemented
550#323C22×C4311yescharacteristic, complemented
551#323C22×C4311yescharacteristic, complemented
552C43#1826211yescharacteristic, direct product factor, Sylow
553C2×#41—21no—
554C2×#41D4×C4311yescharacteristic
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—21no—
558C22×D4D4×C4311yescharacteristic
559C22×D4D4×C4311yescharacteristic
560C23×C4—21no—
561C23×C4C23×C4311yescharacteristic
562C2×M16—21no—
563C22×C8—21no—
564#127—21no—
565#126—21no—
566#126—21no—
567#126—21no—
568#126—21no—
569#125—21no—
570#125—21no—
571#124—21no—
572#124—21no—
573#124—21no—
574#123—21no—
575#123—21no—
576#123—21no—
577#123—21no—
578#123—21no—
579#123—21no—
580#123—21no—
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588C22⋊Q8—21no—
589C22⋊Q8—21no—
590C22⋊Q8—21no—
591C22⋊Q8—21no—
592C22⋊Q8—21no—
593C22⋊Q8D4×C4311yescharacteristic
594C22⋊Q8C23×C4311yescharacteristic
595#121—21no—
596#121—21no—
597#121—21no—
598#121—21no—
599#121—21no—
600#121—21no—
601#121—21no—
602#121—21no—
603#121—21no—
604#121—21no—
605#121—21no—
606#121—21no—
607#121—21no—
608#121—21no—
609#121—21no—
610#121D4×C4311yescharacteristic
611#121D4×C4311yescharacteristic
612#121D4×C4311yescharacteristic
613#121C23×C4311yescharacteristic
614#121C23×C4311yescharacteristic
615#121C23×C4311yescharacteristic
616#120—21no—
617#120—21no—
618#120—21no—
619#120—21no—
620#120—21no—
621#120—21no—
622#120—21no—
623#120—21no—
624C4×D4—21no—
625C4×D4—21no—
626C4×D4—21no—
627C4×D4—21no—
628C4×D4—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632#117—21no—
633#117—21no—
634#117—21no—
635#117—21no—
636#117—21no—
637#117D4×C4311yescharacteristic
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4D4×C4311yescharacteristic
641C2×C4⋊C4D4×C4311yescharacteristic
642C2×C4⋊C4C23×C4311yescharacteristic
643C2×C4⋊C4C23×C4311yescharacteristic
644C2×C4⋊C4C23×C4311yescharacteristic
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4D4×C4311yescharacteristic
652C2×C22⋊C4D4×C4311yescharacteristic
653C2×C22⋊C4C23×C4311yescharacteristic
654C2×C42—21no—
655#107—21no—
656#107—21no—
657#107—21no—
658#107—21no—
659#106—21no—
660#106—21no—
661#106—21no—
662#106—21no—
663#103—21no—
664#103—21no—
665#102—21no—
666#102—21no—
667#102—21no—
668#102—21no—
669#102—21no—
670#102—21no—
671C22⋊C8—21no—
672C22⋊C8—21no—
673C22⋊C8C23×C4311yescharacteristic
674C22⋊C8C23×C4311yescharacteristic
675C22⋊C8C23×C4311yescharacteristic
676C22⋊C8C23×C4311yescharacteristic
677#95—21no—
678#95—21no—
679#95—21no—
680#95—21no—
681#95—21no—
682#95C23×C4311yescharacteristic
683#95C23×C4311yescharacteristic
684C24—21no—
685C24—21no—
686C24C2×D4×C4311yescharacteristic
687C24C2×D4×C4311yescharacteristic
688#41—42no—
689#41—81no—
690#41—81no—
691C2×Q8—21no—
692C2×Q8C2×D4×C4311yescharacteristic
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—42no—
711C2×D4—42no—
712C2×D4—81no—
713C2×D4—81no—
714C2×D4—81no—
715C2×D4—81no—
716C2×D4—82no—
717C2×D4C2×D4×C4311yescharacteristic
718C2×D4C2×D4×C4311yescharacteristic
719C2×D4C2×D4×C4311yescharacteristic
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—81no—
735C22×C4C2×D4×C4311yescharacteristic
736C22×C4C2×D4×C4311yescharacteristic
737C22×C4C2×D4×C4311yescharacteristic
738C22×C4C2×D4×C4311yescharacteristic
739C22×C4C2×D4×C4311yescharacteristic
740C22×C4C2×D4×C4311yescharacteristic
741C22×C4C2×D4×C4311yescharacteristic
742C22×C4C2×D4×C4311yescharacteristic
743C22×C4C24×C4311yescharacteristic
744M16—42no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—42no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—42no—
768C4⋊C4—81no—
769C4⋊C4C2×D4×C4311yescharacteristic
770C4⋊C4C2×D4×C4311yescharacteristic
771C4⋊C4C2×D4×C4311yescharacteristic
772C4⋊C4C2×D4×C4311yescharacteristic
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—42no—
799C22⋊C4—41no—
800C22⋊C4—41no—
801C22⋊C4—81no—
802C42—21no—
803C42—21no—
804C42—21no—
805C42—41no—
806C42—41no—
807C23—21no—
808C23—21no—
809C23—22no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—42no—
820C23—81no—
821C23—81no—
822C23—81no—
823C23—81no—
824C23—81no—
825C23#120×C4311yescharacteristic
826C23#120×C4311yescharacteristic
827C23C22×D4×C4311yescharacteristic
828Q8—41no—
829Q8—81no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—41no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—42no—
840D4—42no—
841D4—81no—
842D4—81no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—81no—
848D4—81no—
849D4—81no—
850D4—81no—
851D4—81no—
852D4—81no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4—81no—
887C2×C4—81no—
888C2×C4—81no—
889C2×C4—81no—
890C2×C4—84no—
891C2×C4#120×C4311yescharacteristic
892C2×C4#120×C4311yescharacteristic
893C2×C4C22×D4×C4311yescharacteristic
894C2×C4C22×D4×C4311yescharacteristic
895C8—41no—
896C8—41no—
897C8—41no—
898C8—41no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—42no—
907C22—42no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—81no—
921C22—81no—
922C22—162no—
923C22—162no—
924C22C43×#45812yes—
925C22C2×#120×C4311yescharacteristic
926C22C43×#57611yescharacteristic
927C22C43×#57711yescharacteristic
928C4—21no—
929C4—21no—
930C4—21no—
931C4—21no—
932C4—42no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—41no—
938C4—41no—
939C4—41no—
940C4—41no—
941C4—81no—
942C4—81no—
943C4—81no—
944C2—21no—
945C2—21no—
946C2—22no—
947C2—41no—
948C2—81no—
949C2—81no—
950C2—81no—
951C2—81no—
952C2C43×#301211yescharacteristic
953C2C43×#301811yescharacteristic
954C2C2×C43×#45811yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC43×#3534C2
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
2. C43×#3094C2semidirect
3. C43×#3091C2semidirect
4. C43×#2498C2semidirect
5. C43×#1618C2semidirect
6. C43×#1616C2semidirect
7. C43×#1615C2semidirect
8. C43×#1613C2semidirect
9. C43×#1612C2semidirect
10. C43×#1610C2semidirect
11. C43×#1609C2semidirect
12. C43×#1607C2semidirect
13. C43×#1504C2semidirect
14. C2×C43×#327C2semidirect
15. C43×#1468C2semidirect
35. C2×#117×C43C22semidirect
37. C43×#484C22semidirect
38. C43×#483C22semidirect
43. C43×#481C22semidirect
44. C43×#481C22semidirect
46. C43×#480C22semidirect
47. C43×#480C22semidirect
52. C43×#407C22semidirect
53. C2×C22⋊C8×C43C22semidirect
54. C43×#400C22semidirect
55. C43×#399C22semidirect
56. C43×#398C22semidirect
57. C43×#397C22semidirect
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
421. #18262C43direct (N × H)
468. #3094C2×C43semidirect
469. #3091C2×C43semidirect
470. #2498C2×C43semidirect
471. #1618C2×C43semidirect
472. #1616C2×C43semidirect
473. #1615C2×C43semidirect
474. #1613C2×C43semidirect
475. #1612C2×C43semidirect
476. #1610C2×C43semidirect
477. #1609C2×C43semidirect
478. #1607C2×C43semidirect
479. #1504C2×C43semidirect
480. C2×#327C2×C43semidirect
481. #1468C2×C43semidirect
512. C2×#117C22×C43semidirect
514. #484C22×C43semidirect
515. #483C22×C43semidirect
520. #481C22×C43semidirect
521. #481C22×C43semidirect
523. #480C22×C43semidirect
524. #480C22×C43semidirect
529. #407C22×C43semidirect
530. C2×C22⋊C8C22×C43semidirect
531. #400C22×C43semidirect
532. #399C22×C43semidirect
533. #398C22×C43semidirect
534. #397C22×C43semidirect
539. C2×#95C22×C43semidirect
540. #328C22×C43semidirect
541. #328C22×C43semidirect
544. #327C22×C43semidirect
545. #327C22×C43semidirect
546. #327C22×C43semidirect
547. #327C22×C43semidirect
548. #324C22×C43semidirect
549. #324C22×C43semidirect
550. #323C22×C43semidirect
551. #323C22×C43semidirect
552. C43#18262direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#35342
C43×#30942
C43×#30912
C43×#24982
C43×#16182
C43×#16162
C43×#16152
C43×#16132
C43×#16122
C43×#16102
C43×#16092
C43×#16072
C43×#15042
C2×C43×#3272
C43×#14682
#1826243