Finite Group Databasebeta

← C43×#25440 #24945457

Subgroups — C43×#25440 #24945457

Order 11008.

914 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3154C211yesmaximal, characteristic, complemented
2C2×C43×#471C211yesmaximal, characteristic, complemented
3C43×#3063C211yesmaximal, characteristic, complemented
4C43×#3062C211yesmaximal, characteristic, complemented
5C43×#3060C211yesmaximal, characteristic, complemented
6C2×C43×#443C211yesmaximal, characteristic, complemented
7C43×#2038C211yesmaximal, characteristic, complemented
8C43×#2037C211yesmaximal, characteristic, complemented
9C43×#2007C211yesmaximal, characteristic, complemented
10C43×#2006C211yesmaximal, characteristic, complemented
11C43×#1968C211yesmaximal, characteristic, complemented
12C43×#1951C211yesmaximal, characteristic, complemented
13C43×#1908C211yesmaximal, characteristic, complemented
14C43×#1907C211yesmaximal, characteristic, complemented
15C43×#1764C211yesmaximal, characteristic, complemented
16C2×#137×C43C2211yescharacteristic
17C2×#137×C43C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
20C2×#135×C43C2211yescharacteristic
21C22×SD16×C43C2211yescharacteristic
22C2×#131×C43C2211yescharacteristic
23C2×#131×C43C2211yescharacteristic
24C2×#131×C43C2211yescharacteristic
25C43×#537C2211yescharacteristic
26C43×#537C2211yescharacteristic
27C43×#536C2211yescharacteristic
28C43×#535C2211yescharacteristic
29C43×#497—21no—
30C43×#496—21no—
31C43×#495—21no—
32C43×#492—21no—
33C43×#471—24no—
34C43×#470—21no—
35C43×#470—21no—
36C43×#469—21no—
37C43×#469—21no—
38C43×#468—21no—
39C43×#468—21no—
40C43×#467—21no—
41C43×#466—21no—
42C43×#465—21no—
43C43×#465—21no—
44C43×#465—21no—
45C43×#465—21no—
46C43×#443—24no—
47C2×#108×C43C2211yescharacteristic
48C43×#428C2211yescharacteristic
49C43×#428C2211yescharacteristic
50C2×#106×C43C2211yescharacteristic
51C2×#104×C43C2211yescharacteristic
52C2×#104×C43C2211yescharacteristic
53C2×#104×C43C2211yescharacteristic
54C43×#417C2211yescharacteristic
55C43×#417C2211yescharacteristic
56C43×#416C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×#101×C43C2211yescharacteristic
60C2×#100×C43C2211yescharacteristic
61C43×#405C2211yescharacteristic
62C2×C4×C8×C43C2211yescharacteristic
63C43×#391C2211yescharacteristic
64C43×#390C2211yescharacteristic
65C43×#343C2211yescharacteristic
66C43×#343C2211yescharacteristic
67C43×#341C2211yescharacteristic
68C43×#339C2211yescharacteristic
69C2×#41×C43C2311yescharacteristic
70C2×#41×C43C2311yescharacteristic
71C2×#41×C43C2311yescharacteristic
72C22×Q8×C43C2311yescharacteristic
73C22×D4×C43C2311yescharacteristic
74#137×C43—22no—
75#137×C43—22no—
76#137×C43—41no—
77#137×C43—41no—
78AGL(1,ℤ/8)×C43—22no—
79AGL(1,ℤ/8)×C43—22no—
80AGL(1,ℤ/8)×C43—41no—
81AGL(1,ℤ/8)×C43—41no—
82#135×C43—22no—
83#135×C43—22no—
84C2×Q16×C43—21no—
85C2×Q16×C43—21no—
86C2×Q16×C43D411yescharacteristic
87C2×SD16×C43—21no—
88C2×SD16×C43—21no—
89C2×SD16×C43—21no—
90C2×SD16×C43—21no—
91C2×SD16×C43—21no—
92C2×SD16×C43—22no—
93C2×SD16×C43—21no—
94C2×SD16×C43—22no—
95C2×SD16×C43D411yescharacteristic
96C2×SD16×C43D411yescharacteristic
97C2×D8×C43—21no—
98C2×D8×C43—21no—
99C2×D8×C43D411yescharacteristic
100#131×C43—22no—
101#131×C43—22no—
102#131×C43—22no—
103#131×C43—22no—
104#131×C43—41no—
105#131×C43—41no—
106C2×M16×C43—21no—
107C2×M16×C43—21no—
108C2×M16×C43—21no—
109C2×M16×C43C2311yescharacteristic
110C2×M16×C43C2311yescharacteristic
111C2×M16×C43C2311yescharacteristic
112C2×M16×C43C2311yescharacteristic
113C22×C8×C43—21no—
114C22×C8×C43—21no—
115C22×C8×C43—21no—
116C22×C8×C43C2311yescharacteristic
117C22×C8×C43C2311yescharacteristic
118C4⋊Q8×C43—21no—
119#127×C43—21no—
120#124×C43—21no—
121#124×C43—21no—
122#123×C43—41no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43—21no—
126C22⋊Q8×C43—21no—
127C22⋊Q8×C43—21no—
128C22⋊Q8×C43—21no—
129#121×C43—21no—
130#121×C43—21no—
131#121×C43—21no—
132#121×C43—21no—
133#121×C43—21no—
134#121×C43—21no—
135#121×C43—41no—
136#121×C43—41no—
137#120×C43—41no—
138#117×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C22⋊C4×C43—41no—
142C2×C42×C43C2311yescharacteristic
143#108×C43D414yescomplemented
144#107×C43—21no—
145#107×C43—21no—
146#106×C43—21no—
147#106×C43—21no—
148#106×C43—21no—
149#106×C43—21no—
150#104×C43—22no—
151#104×C43—22no—
152#104×C43—22no—
153#103×C43—21no—
154#103×C43—21no—
155#103×C43—21no—
156#103×C43—21no—
157#103×C43D411yescharacteristic
158#103×C43D411yescharacteristic
159#102×C43—21no—
160#102×C43—21no—
161#102×C43—21no—
162#102×C43—21no—
163#102×C43D411yescharacteristic
164#102×C43D411yescharacteristic
165#101×C43—22no—
166#100×C43—22no—
167#97×C43—21no—
168C4×C8×C43—22no—
169C4×C8×C43—21no—
170#95×C43—41no—
171C24×C43—21no—
172#41×C43—21no—
173#41×C43—21no—
174#41×C43—21no—
175#41×C43—21no—
176#41×C43—21no—
177#41×C43—21no—
178#41×C43—21no—
179#41×C43—21no—
180#41×C43—21no—
181#41×C43—21no—
182#41×C43—21no—
183#41×C43—21no—
184C2×Q8×C43—21no—
185C2×Q8×C43—21no—
186C2×Q8×C43—21no—
187C2×Q8×C43—21no—
188C2×Q8×C43—21no—
189C2×Q8×C43—21no—
190C2×Q8×C43C2×D411yescharacteristic
191C2×Q8×C43C2×D411yescharacteristic
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—41no—
203C2×D4×C43—41no—
204C2×D4×C43—41no—
205C2×D4×C43—41no—
206C2×D4×C43C2×D411yescharacteristic
207C2×D4×C43C2×D411yescharacteristic
208C2×D4×C43C2×D411yescharacteristic
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43C2411yescharacteristic
217Q16×C43—22no—
218Q16×C43—42no—
219Q16×C43—42no—
220SD16×C43—22no—
221SD16×C43—22no—
222SD16×C43—42no—
223SD16×C43—42no—
224SD16×C43—42no—
225SD16×C43—42no—
226SD16×C43—42no—
227SD16×C43—42no—
228D8×C43—22no—
229D8×C43—42no—
230D8×C43—42no—
231M16×C43—21no—
232M16×C43—21no—
233M16×C43—21no—
234M16×C43—21no—
235M16×C43—21no—
236M16×C43—42no—
237M16×C43—42no—
238M16×C43—42no—
239M16×C43C2×D412yes—
240M16×C43C2×D412yes—
241M16×C43#4112yes—
242C2×C8×C43—21no—
243C2×C8×C43—21no—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C2×C8×C43—42no—
249C2×C8×C43—42no—
250C2×C8×C43—42no—
251C2×C8×C43C2×D411yescharacteristic
252C2×C8×C43C2×D411yescharacteristic
253C2×C8×C43C2×D411yescharacteristic
254C2×C8×C43C2×D412yes—
255C2×C8×C43C2×D411yescharacteristic
256C2×C8×C43#4112yes—
257C4⋊C4×C43—21no—
258C4⋊C4×C43—21no—
259C4⋊C4×C43—21no—
260C4⋊C4×C43—21no—
261C4⋊C4×C43—41no—
262C4⋊C4×C43—41no—
263C4⋊C4×C43—41no—
264C4⋊C4×C43—41no—
265C4⋊C4×C43C2×D411yescharacteristic
266C4⋊C4×C43C2×D411yescharacteristic
267C22⋊C4×C43—21no—
268C22⋊C4×C43—41no—
269C22⋊C4×C43—41no—
270C22⋊C4×C43—41no—
271C22⋊C4×C43—41no—
272C22⋊C4×C43—41no—
273C22⋊C4×C43—41no—
274C22⋊C4×C43—41no—
275C22⋊C4×C43—41no—
276C22⋊C4×C43—82no—
277C42×C43—21no—
278C42×C43—21no—
279C42×C43—21no—
280C23×C43—21no—
281C23×C43—21no—
282C23×C43—21no—
283C23×C43—41no—
284C23×C43—41no—
285C23×C43—41no—
286C23×C43—81no—
287C23×C43—81no—
288C23×C43H(5,𝔽2)11yescharacteristic
289Q8×C43—21no—
290Q8×C43—21no—
291Q8×C43—21no—
292Q8×C43—21no—
293Q8×C43—21no—
294Q8×C43—21no—
295Q8×C43—41no—
296Q8×C43—41no—
297Q8×C43—41no—
298Q8×C43—41no—
299D4×C43—21no—
300D4×C43—21no—
301D4×C43—21no—
302D4×C43—21no—
303D4×C43—21no—
304D4×C43—21no—
305D4×C43—41no—
306D4×C43—41no—
307D4×C43—41no—
308D4×C43—41no—
309D4×C43—41no—
310D4×C43—41no—
311D4×C43—41no—
312D4×C43—41no—
313D4×C43—41no—
314D4×C43—41no—
315D4×C43—161no—
316D4×C43—161no—
317D4×C43—161no—
318D4×C43—161no—
319C2×C4×C43—22no—
320C2×C4×C43—21no—
321C2×C4×C43—21no—
322C2×C4×C43—21no—
323C2×C4×C43—21no—
324C2×C4×C43—21no—
325C2×C4×C43—41no—
326C2×C4×C43—41no—
327C2×C4×C43—41no—
328C2×C4×C43—41no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—81no—
339C2×C4×C43—81no—
340C2×C4×C43C22×D411yescharacteristic
341C2×C4×C43C22×D411yescharacteristic
342C2×C4×C43C22×D411yescharacteristic
343C2×C4×C43C2×#4111yescharacteristic
344C2×C4×C43C2×#4111yescharacteristic
345C2×C4×C43H(5,𝔽2)11yescharacteristic
346C8×C43—21no—
347C8×C43—21no—
348C8×C43—22no—
349C8×C43—22no—
350C8×C43—22no—
351C8×C43—41no—
352C8×C43#12112yes—
353C8×C43#12112yes—
354#25440C4311yesmaximal, characteristic, direct product factor, Sylow
355C22×C43—21no—
356C22×C43—21no—
357C22×C43—41no—
358C22×C43—41no—
359C22×C43—41no—
360C22×C43—41no—
361C22×C43—41no—
362C22×C43—41no—
363C22×C43—41no—
364C22×C43—41no—
365C22×C43—41no—
366C22×C43—82no—
367C22×C43—81no—
368C22×C43—81no—
369C22×C43—81no—
370C22×C43—161no—
371C22×C43#54011yescharacteristic
372C22×C43D4211yescharacteristic
373C22×C43#55011yescharacteristic
374C4×C43—42no—
375C4×C43—41no—
376C4×C43—41no—
377C4×C43—41no—
378C4×C43—41no—
379C4×C43—41no—
380C4×C43—81no—
381C4×C43—81no—
382C4×C43—81no—
383C4×C43C2×#12111yescharacteristic
384C4×C43#53211yescharacteristic
385C4×C43D4211yescharacteristic
386C4×C43#54611yescharacteristic
387#3154C2×C4311yescharacteristic, complemented
388C2×#471C2×C4311yescharacteristic, complemented
389#3063C2×C4311yescharacteristic, complemented
390#3062C2×C4311yescharacteristic, complemented
391#3060C2×C4311yescharacteristic, complemented
392C2×#443C2×C4311yescharacteristic, complemented
393#2038C2×C4311yescharacteristic, complemented
394#2037C2×C4311yescharacteristic, complemented
395#2007C2×C4311yescharacteristic, complemented
396#2006C2×C4311yescharacteristic, complemented
397#1968C2×C4311yescharacteristic, complemented
398#1951C2×C4311yescharacteristic, complemented
399#1908C2×C4311yescharacteristic, complemented
400#1907C2×C4311yescharacteristic, complemented
401#1764C2×C4311yescharacteristic, complemented
402C2×C43—21no—
403C2×C43—21no—
404C2×C43—81no—
405C2×C43—81no—
406C2×C43—81no—
407C2×C43—161no—
408C2×C43#242811yescharacteristic
409C2×C43#329011yescharacteristic
410C2×C43#329111yescharacteristic
411C2×#137C22×C4311yescharacteristic
412C2×#137C22×C4311yescharacteristic
413C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
414C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
415C2×#135C22×C4311yescharacteristic
416C22×SD16C22×C4311yescharacteristic
417C2×#131C22×C4311yescharacteristic
418C2×#131C22×C4311yescharacteristic
419C2×#131C22×C4311yescharacteristic
420#537C22×C4311yescharacteristic
421#537C22×C4311yescharacteristic
422#536C22×C4311yescharacteristic
423#535C22×C4311yescharacteristic
424#497—21no—
425#496—21no—
426#495—21no—
427#492—21no—
428#471—24no—
429#470—21no—
430#470—21no—
431#469—21no—
432#469—21no—
433#468—21no—
434#468—21no—
435#467—21no—
436#466—21no—
437#465—21no—
438#465—21no—
439#465—21no—
440#465—21no—
441#443—24no—
442C2×#108C22×C4311yescharacteristic
443#428C22×C4311yescharacteristic
444#428C22×C4311yescharacteristic
445C2×#106C22×C4311yescharacteristic
446C2×#104C22×C4311yescharacteristic
447C2×#104C22×C4311yescharacteristic
448C2×#104C22×C4311yescharacteristic
449#417C22×C4311yescharacteristic
450#417C22×C4311yescharacteristic
451#416C22×C4311yescharacteristic
452C2×#103C22×C4311yescharacteristic
453C2×#102C22×C4311yescharacteristic
454C2×#101C22×C4311yescharacteristic
455C2×#100C22×C4311yescharacteristic
456#405C22×C4311yescharacteristic
457C2×C4×C8C22×C4311yescharacteristic
458#391C22×C4311yescharacteristic
459#390C22×C4311yescharacteristic
460#343C22×C4311yescharacteristic
461#343C22×C4311yescharacteristic
462#341C22×C4311yescharacteristic
463#339C22×C4311yescharacteristic
464C43#2544011yescharacteristic, direct product factor, Sylow
465C2×#41C23×C4311yescharacteristic
466C2×#41C23×C4311yescharacteristic
467C2×#41C23×C4311yescharacteristic
468C22×Q8C23×C4311yescharacteristic
469C22×D4C23×C4311yescharacteristic
470#137—22no—
471#137—22no—
472#137—41no—
473#137—41no—
474AGL(1,ℤ/8)—22no—
475AGL(1,ℤ/8)—22no—
476AGL(1,ℤ/8)—41no—
477AGL(1,ℤ/8)—41no—
478#135—22no—
479#135—22no—
480C2×Q16—21no—
481C2×Q16—21no—
482C2×Q16D4×C4311yescharacteristic
483C2×SD16—21no—
484C2×SD16—21no—
485C2×SD16—21no—
486C2×SD16—21no—
487C2×SD16—22no—
488C2×SD16—21no—
489C2×SD16—21no—
490C2×SD16—22no—
491C2×SD16D4×C4311yescharacteristic
492C2×SD16D4×C4311yescharacteristic
493C2×D8—21no—
494C2×D8—21no—
495C2×D8D4×C4311yescharacteristic
496#131—22no—
497#131—22no—
498#131—22no—
499#131—22no—
500#131—41no—
501#131—41no—
502C2×M16—21no—
503C2×M16—21no—
504C2×M16—21no—
505C2×M16C23×C4311yescharacteristic
506C2×M16C23×C4311yescharacteristic
507C2×M16C23×C4311yescharacteristic
508C2×M16C23×C4311yescharacteristic
509C22×C8—21no—
510C22×C8—21no—
511C22×C8—21no—
512C22×C8C23×C4311yescharacteristic
513C22×C8C23×C4311yescharacteristic
514C4⋊Q8—21no—
515#127—21no—
516#124—21no—
517#124—21no—
518#123—41no—
519C22⋊Q8—21no—
520C22⋊Q8—21no—
521C22⋊Q8—21no—
522C22⋊Q8—21no—
523C22⋊Q8—21no—
524C22⋊Q8—21no—
525#121—21no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—21no—
530#121—21no—
531#121—41no—
532#121—41no—
533#120—41no—
534#117C23×C4311yescharacteristic
535C2×C4⋊C4C23×C4311yescharacteristic
536C2×C4⋊C4C23×C4311yescharacteristic
537C2×C22⋊C4—41no—
538C2×C42C23×C4311yescharacteristic
539#108D4×C4314yescomplemented
540#107—21no—
541#107—21no—
542#106—21no—
543#106—21no—
544#106—21no—
545#106—21no—
546#104—22no—
547#104—22no—
548#104—22no—
549#103—21no—
550#103—21no—
551#103—21no—
552#103—21no—
553#103D4×C4311yescharacteristic
554#103D4×C4311yescharacteristic
555#102—21no—
556#102—21no—
557#102—21no—
558#102—21no—
559#102D4×C4311yescharacteristic
560#102D4×C4311yescharacteristic
561#101—22no—
562#100—22no—
563#97—21no—
564C4×C8—22no—
565C4×C8—21no—
566#95—41no—
567C24—21no—
568#41—21no—
569#41—21no—
570#41—21no—
571#41—21no—
572#41—21no—
573#41—21no—
574#41—21no—
575#41—21no—
576#41—21no—
577#41—21no—
578#41—21no—
579#41—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8C2×D4×C4311yescharacteristic
587C2×Q8C2×D4×C4311yescharacteristic
588C2×Q8C2×D4×C4311yescharacteristic
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—41no—
599C2×D4—41no—
600C2×D4—41no—
601C2×D4—41no—
602C2×D4C2×D4×C4311yescharacteristic
603C2×D4C2×D4×C4311yescharacteristic
604C2×D4C2×D4×C4311yescharacteristic
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4C24×C4311yescharacteristic
613Q16—22no—
614Q16—42no—
615Q16—42no—
616SD16—22no—
617SD16—22no—
618SD16—42no—
619SD16—42no—
620SD16—42no—
621SD16—42no—
622SD16—42no—
623SD16—42no—
624D8—22no—
625D8—42no—
626D8—42no—
627M16—21no—
628M16—21no—
629M16—21no—
630M16—21no—
631M16—21no—
632M16—42no—
633M16—42no—
634M16—42no—
635M16C2×D4×C4312yes—
636M16C2×D4×C4312yes—
637M16#41×C4312yes—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—42no—
645C2×C8—42no—
646C2×C8—42no—
647C2×C8C2×D4×C4311yescharacteristic
648C2×C8C2×D4×C4311yescharacteristic
649C2×C8C2×D4×C4311yescharacteristic
650C2×C8C2×D4×C4312yes—
651C2×C8C2×D4×C4311yescharacteristic
652C2×C8#41×C4312yes—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—41no—
658C4⋊C4—41no—
659C4⋊C4—41no—
660C4⋊C4—41no—
661C4⋊C4C2×D4×C4311yescharacteristic
662C4⋊C4C2×D4×C4311yescharacteristic
663C22⋊C4—21no—
664C22⋊C4—41no—
665C22⋊C4—41no—
666C22⋊C4—41no—
667C22⋊C4—41no—
668C22⋊C4—41no—
669C22⋊C4—41no—
670C22⋊C4—41no—
671C22⋊C4—41no—
672C22⋊C4—82no—
673C42—21no—
674C42—21no—
675C42—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—81no—
683C23—81no—
684C23H(5,𝔽2)×C4311yescharacteristic
685Q8—21no—
686Q8—21no—
687Q8—21no—
688Q8—21no—
689Q8—21no—
690Q8—21no—
691Q8—41no—
692Q8—41no—
693Q8—41no—
694Q8—41no—
695D4—21no—
696D4—21no—
697D4—21no—
698D4—21no—
699D4—21no—
700D4—21no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—41no—
711D4—161no—
712D4—161no—
713D4—161no—
714D4—161no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—81no—
735C2×C4—81no—
736C2×C4C22×D4×C4311yescharacteristic
737C2×C4C22×D4×C4311yescharacteristic
738C2×C4C22×D4×C4311yescharacteristic
739C2×C4C2×#41×C4311yescharacteristic
740C2×C4C2×#41×C4311yescharacteristic
741C2×C4H(5,𝔽2)×C4311yescharacteristic
742C8—21no—
743C8—21no—
744C8—22no—
745C8—22no—
746C8—22no—
747C8—41no—
748C8#121×C4312yes—
749C8#121×C4312yes—
750C22—21no—
751C22—21no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—82no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—161no—
766C22C43×#54011yescharacteristic
767C22D42×C4311yescharacteristic
768C22C43×#55011yescharacteristic
769C4—42no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—81no—
776C4—81no—
777C4—81no—
778C4C2×#121×C4311yescharacteristic
779C4C43×#53211yescharacteristic
780C4D42×C4311yescharacteristic
781C4C43×#54611yescharacteristic
782C2—21no—
783C2—21no—
784C2—81no—
785C2—81no—
786C2—81no—
787C2—161no—
788C2C43×#242811yescharacteristic
789C2C43×#329011yescharacteristic
790C2C43×#329111yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC22×C4C24×C43
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C22×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3154C2semidirect
2. C2×C43×#471C2semidirect
3. C43×#3063C2semidirect
4. C43×#3062C2semidirect
5. C43×#3060C2semidirect
6. C2×C43×#443C2semidirect
7. C43×#2038C2semidirect
8. C43×#2037C2semidirect
9. C43×#2007C2semidirect
10. C43×#2006C2semidirect
11. C43×#1968C2semidirect
12. C43×#1951C2semidirect
13. C43×#1908C2semidirect
14. C43×#1907C2semidirect
15. C43×#1764C2semidirect
143. #108×C43D4semidirect
354. #25440C43direct (N × H)
387. #3154C2×C43semidirect
388. C2×#471C2×C43semidirect
389. #3063C2×C43semidirect
390. #3062C2×C43semidirect
391. #3060C2×C43semidirect
392. C2×#443C2×C43semidirect
393. #2038C2×C43semidirect
394. #2037C2×C43semidirect
395. #2007C2×C43semidirect
396. #2006C2×C43semidirect
397. #1968C2×C43semidirect
398. #1951C2×C43semidirect
399. #1908C2×C43semidirect
400. #1907C2×C43semidirect
401. #1764C2×C43semidirect
464. C43#25440direct (N × H)
539. #108D4×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#31542
C2×C43×#4712
C43×#30632
C43×#30622
C43×#30602
C2×C43×#4432
C43×#20382
C43×#20372
C43×#20072
C43×#20062
C43×#19682
C43×#19512
C43×#19082
C43×#19072
C43×#17642
#2544043