Finite Group Databasebeta

← C43×#28507 #24948524

Subgroups — C43×#28507 #24948524

Order 11008.

1074 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3155C211yesmaximal, characteristic, complemented
2C43×#3154C211yesmaximal, characteristic, complemented
3C2×C43×#496C211yesmaximal, characteristic, complemented
4C2×C43×#472C211yesmaximal, characteristic, complemented
5C2×C43×#471C211yesmaximal, characteristic, complemented
6C43×#3058C211yesmaximal, characteristic, complemented
7C43×#3057C211yesmaximal, characteristic, complemented
8C2×C43×#444C211yesmaximal, characteristic, complemented
9C43×#2004C211yesmaximal, characteristic, complemented
10C43×#2003C211yesmaximal, characteristic, complemented
11C43×#2002C211yesmaximal, characteristic, complemented
12C43×#2002C211yesmaximal, characteristic, complemented
13C43×#1978C211yesmaximal, characteristic, complemented
14C43×#1977C211yesmaximal, characteristic, complemented
15C43×#1773C211yesmaximal, characteristic, complemented
16C2×#137×C43C2211yescharacteristic
17C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
20C2×#135×C43C2211yescharacteristic
21C22×SD16×C43C2211yescharacteristic
22C22×SD16×C43C2211yescharacteristic
23C22×D8×C43C2211yescharacteristic
24C22×D8×C43C2211yescharacteristic
25C2×#131×C43C2211yescharacteristic
26C2×#131×C43C2211yescharacteristic
27C43×#536C2211yescharacteristic
28C43×#535C2211yescharacteristic
29C43×#535C2211yescharacteristic
30C43×#535C2211yescharacteristic
31C2×#127×C43C2211yescharacteristic
32C2×#124×C43C2211yescharacteristic
33C43×#497—21no—
34C43×#496—21no—
35C43×#496—21no—
36C43×#496—21no—
37C43×#496—24no—
38C43×#495—21no—
39C43×#495—21no—
40C43×#493—21no—
41C43×#492—21no—
42C43×#472—24no—
43C43×#471—24no—
44C43×#469—22no—
45C43×#468—22no—
46C43×#466—22no—
47C43×#465—22no—
48C43×#444—24no—
49C2×#108×C43C2211yescharacteristic
50C2×#108×C43C2211yescharacteristic
51C43×#427C2211yescharacteristic
52C2×#104×C43C2211yescharacteristic
53C2×#104×C43C2211yescharacteristic
54C43×#419C2211yescharacteristic
55C43×#418C2211yescharacteristic
56C43×#418C2211yescharacteristic
57C43×#418C2211yescharacteristic
58C2×#101×C43C2211yescharacteristic
59C2×#100×C43C2211yescharacteristic
60C2×#100×C43C2211yescharacteristic
61C2×#100×C43C2211yescharacteristic
62C43×#405C2211yescharacteristic
63C43×#405C2211yescharacteristic
64C2×#97×C43C2211yescharacteristic
65C43×#339C2211yescharacteristic
66C43×#339C2211yescharacteristic
67C2×#41×C43C2311yescharacteristic
68C2×#41×C43C2311yescharacteristic
69C22×Q8×C43C2311yescharacteristic
70C22×D4×C43—41no—
71C22×D4×C43C2311yescharacteristic
72C22×D4×C43C2311yescharacteristic
73C22×D4×C43C2311yescharacteristic
74#137×C43—22no—
75#137×C43—41no—
76AGL(1,ℤ/8)×C43—22no—
77AGL(1,ℤ/8)×C43—22no—
78AGL(1,ℤ/8)×C43—22no—
79AGL(1,ℤ/8)×C43—41no—
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×C43D411yescharacteristic, complemented
86C2×SD16×C43—21no—
87C2×SD16×C43—21no—
88C2×SD16×C43—21no—
89C2×SD16×C43—21no—
90C2×SD16×C43—21no—
91C2×SD16×C43—21no—
92C2×SD16×C43—21no—
93C2×SD16×C43—22no—
94C2×SD16×C43—21no—
95C2×SD16×C43—22no—
96C2×SD16×C43—22no—
97C2×SD16×C43—22no—
98C2×SD16×C43D411yescharacteristic, complemented
99C2×SD16×C43D411yescharacteristic, complemented
100C2×D8×C43—21no—
101C2×D8×C43—21no—
102C2×D8×C43—21no—
103C2×D8×C43—21no—
104C2×D8×C43—21no—
105C2×D8×C43—22no—
106C2×D8×C43—21no—
107C2×D8×C43—21no—
108C2×D8×C43—22no—
109C2×D8×C43—22no—
110C2×D8×C43—22no—
111C2×D8×C43D411yescharacteristic, complemented
112#131×C43—22no—
113#131×C43—22no—
114#131×C43—22no—
115#131×C43—22no—
116C2×M16×C43—21no—
117C2×M16×C43—21no—
118C2×M16×C43C2311yescharacteristic
119C2×M16×C43C2311yescharacteristic
120C2×M16×C43C2311yescharacteristic
121C2×M16×C43C2311yescharacteristic
122C22×C8×C43—21no—
123C22×C8×C43—21no—
124C22×C8×C43C2311yescharacteristic
125C22×C8×C43C2311yescharacteristic
126C4⋊Q8×C43—21no—
127#127×C43—21no—
128#127×C43—21no—
129#127×C43—21no—
130#127×C43—22no—
131#127×C43—41no—
132#124×C43—21no—
133#124×C43—21no—
134#124×C43—21no—
135#124×C43—21no—
136#124×C43—22no—
137#124×C43—41no—
138#123×C43—41no—
139C22⋊Q8×C43—22no—
140#121×C43—22no—
141#121×C43—22no—
142#121×C43—22no—
143#120×C43—41no—
144#120×C43—41no—
145#120×C43—41no—
146#117×C43C2311yescharacteristic
147#117×C43C2311yescharacteristic
148C2×C22⋊C4×C43—41no—
149C2×C42×C43C2311yescharacteristic
150#108×C43—22no—
151#108×C43D414yescomplemented
152#107×C43D412yescomplemented
153#106×C43D412yescomplemented
154#104×C43—22no—
155#104×C43—22no—
156#103×C43—22no—
157#102×C43—22no—
158#102×C43—22no—
159#102×C43—22no—
160#101×C43—22no—
161#100×C43—22no—
162#100×C43—22no—
163#100×C43—22no—
164#97×C43—21no—
165#97×C43—21no—
166#97×C43D414yescomplemented
167C4×C8×C43—21no—
168C4×C8×C43—21no—
169C24×C43—21no—
170C24×C43—21no—
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—
180C2×Q8×C43—21no—
181C2×Q8×C43—21no—
182C2×Q8×C43—21no—
183C2×Q8×C43—21no—
184C2×Q8×C43—21no—
185C2×Q8×C43—21no—
186C2×Q8×C43C2×D411yescharacteristic
187C2×Q8×C43C2×D411yescharacteristic
188C2×D4×C43—21no—
189C2×D4×C43—21no—
190C2×D4×C43—21no—
191C2×D4×C43—21no—
192C2×D4×C43—21no—
193C2×D4×C43—21no—
194C2×D4×C43—21no—
195C2×D4×C43—21no—
196C2×D4×C43—21no—
197C2×D4×C43—21no—
198C2×D4×C43—21no—
199C2×D4×C43—21no—
200C2×D4×C43—21no—
201C2×D4×C43—21no—
202C2×D4×C43—21no—
203C2×D4×C43—21no—
204C2×D4×C43—21no—
205C2×D4×C43—21no—
206C2×D4×C43—21no—
207C2×D4×C43—21no—
208C2×D4×C43—42no—
209C2×D4×C43—42no—
210C2×D4×C43—42no—
211C2×D4×C43—44no—
212C2×D4×C43—84no—
213C2×D4×C43C2×D411yescharacteristic
214C2×D4×C43C2×D411yescharacteristic
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43C2411yescharacteristic
220Q16×C43—22no—
221Q16×C43—42no—
222SD16×C43—22no—
223SD16×C43—22no—
224SD16×C43—42no—
225SD16×C43—42no—
226SD16×C43—42no—
227SD16×C43—42no—
228SD16×C43—42no—
229SD16×C43—42no—
230SD16×C43—42no—
231SD16×C43—42no—
232D8×C43—22no—
233D8×C43—42no—
234D8×C43—42no—
235D8×C43—42no—
236D8×C43—42no—
237D8×C43—42no—
238D8×C43—42no—
239D8×C43—42no—
240M16×C43—21no—
241M16×C43—21no—
242M16×C43—21no—
243M16×C43—21no—
244M16×C43—21no—
245M16×C43—21no—
246M16×C43—42no—
247M16×C43—42no—
248M16×C43C2×D412yes—
249M16×C43C2×D412yes—
250C2×C8×C43—21no—
251C2×C8×C43—21no—
252C2×C8×C43—21no—
253C2×C8×C43—21no—
254C2×C8×C43—42no—
255C2×C8×C43—42no—
256C2×C8×C43C2×D411yescharacteristic
257C2×C8×C43C2×D411yescharacteristic
258C2×C8×C43C2×D412yes—
259C2×C8×C43C2×D412yes—
260C2×C8×C43C2×D411yescharacteristic
261C2×C8×C43C2×D411yescharacteristic
262C2×C8×C43C2×D412yes—
263C2×C8×C43#4112yes—
264C4⋊C4×C43—42no—
265C4⋊C4×C43C2×D412yes—
266C4⋊C4×C43C2×D412yes—
267C22⋊C4×C43—21no—
268C22⋊C4×C43—21no—
269C22⋊C4×C43—42no—
270C22⋊C4×C43—42no—
271C22⋊C4×C43—42no—
272C22⋊C4×C43—42no—
273C22⋊C4×C43—44no—
274C42×C43—21no—
275C42×C43—21no—
276C42×C43—21no—
277C42×C43C2×D412yes—
278C23×C43—21no—
279C23×C43—21no—
280C23×C43—41no—
281C23×C43—41no—
282C23×C43—41no—
283C23×C43—41no—
284C23×C43—41no—
285C23×C43—41no—
286C23×C43—41no—
287C23×C43—41no—
288C23×C43—41no—
289C23×C43—82no—
290C23×C43—82no—
291C23×C43—82no—
292C23×C43H(5,𝔽2)11yescharacteristic
293Q8×C43—21no—
294Q8×C43—21no—
295Q8×C43—21no—
296Q8×C43—21no—
297Q8×C43—41no—
298Q8×C43—41no—
299Q8×C43—41no—
300Q8×C43—41no—
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—41no—
316D4×C43—41no—
317D4×C43—41no—
318D4×C43—41no—
319D4×C43—41no—
320D4×C43—41no—
321D4×C43—88no—
322D4×C43—162no—
323D4×C43—162no—
324D4×C43—162no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—21no—
329C2×C4×C43—21no—
330C2×C4×C43—42no—
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×C43C22×D411yescharacteristic
339C2×C4×C43C22×D411yescharacteristic
340C2×C4×C43C22×D411yescharacteristic
341C2×C4×C43C22×D411yescharacteristic
342C2×C4×C43C2×#4111yescharacteristic
343C2×C4×C43H(5,𝔽2)11yescharacteristic
344C8×C43—22no—
345C8×C43—22no—
346C8×C43—41no—
347C8×C43—41no—
348C8×C43#12112yes—
349C8×C43#12112yes—
350C8×C43#12712yes—
351C8×C43#12712yes—
352#28507C4311yesmaximal, characteristic, direct product factor, Sylow
353C22×C43—22no—
354C22×C43—42no—
355C22×C43—42no—
356C22×C43—41no—
357C22×C43—41no—
358C22×C43—82no—
359C22×C43—82no—
360C22×C43—82no—
361C22×C43—82no—
362C22×C43—82no—
363C22×C43—82no—
364C22×C43—81no—
365C22×C43—81no—
366C22×C43—81no—
367C22×C43—161no—
368C22×C43—161no—
369C22×C43—161no—
370C22×C43#53511yescharacteristic
371C22×C43D4211yescharacteristic
372C22×C43#55011yescharacteristic
373C4×C43—42no—
374C4×C43—42no—
375C4×C43—42no—
376C4×C43—41no—
377C4×C43—41no—
378C4×C43—81no—
379C4×C43C2×#12111yescharacteristic
380C4×C43C2×#12711yescharacteristic
381C4×C43D4211yescharacteristic
382C4×C43#55011yescharacteristic
383#3155C2×C4311yescharacteristic, complemented
384#3154C2×C4311yescharacteristic, complemented
385C2×#496C2×C4311yescharacteristic, complemented
386C2×#472C2×C4311yescharacteristic, complemented
387C2×#471C2×C4311yescharacteristic, complemented
388#3058C2×C4311yescharacteristic, complemented
389#3057C2×C4311yescharacteristic, complemented
390C2×#444C2×C4311yescharacteristic, complemented
391#2004C2×C4311yescharacteristic, complemented
392#2003C2×C4311yescharacteristic, complemented
393#2002C2×C4311yescharacteristic, complemented
394#2002C2×C4311yescharacteristic, complemented
395#1978C2×C4311yescharacteristic, complemented
396#1977C2×C4311yescharacteristic, complemented
397#1773C2×C4311yescharacteristic, complemented
398C2×C43—21no—
399C2×C43—21no—
400C2×C43—81no—
401C2×C43—81no—
402C2×C43—161no—
403C2×C43—161no—
404C2×C43—161no—
405C2×C43#254111yescharacteristic
406C2×C43#328812yes—
407C2×#137C22×C4311yescharacteristic
408C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
409C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
410C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
411C2×#135C22×C4311yescharacteristic
412C22×SD16C22×C4311yescharacteristic
413C22×SD16C22×C4311yescharacteristic
414C22×D8C22×C4311yescharacteristic
415C22×D8C22×C4311yescharacteristic
416C2×#131C22×C4311yescharacteristic
417C2×#131C22×C4311yescharacteristic
418#536C22×C4311yescharacteristic
419#535C22×C4311yescharacteristic
420#535C22×C4311yescharacteristic
421#535C22×C4311yescharacteristic
422C2×#127C22×C4311yescharacteristic
423C2×#124C22×C4311yescharacteristic
424#497—21no—
425#496—21no—
426#496—21no—
427#496—21no—
428#496—24no—
429#495—21no—
430#495—21no—
431#493—21no—
432#492—21no—
433#472—24no—
434#471—24no—
435#469—22no—
436#468—22no—
437#466—22no—
438#465—22no—
439#444—24no—
440C2×#108C22×C4311yescharacteristic
441C2×#108C22×C4311yescharacteristic
442#427C22×C4311yescharacteristic
443C2×#104C22×C4311yescharacteristic
444C2×#104C22×C4311yescharacteristic
445#419C22×C4311yescharacteristic
446#418C22×C4311yescharacteristic
447#418C22×C4311yescharacteristic
448#418C22×C4311yescharacteristic
449C2×#101C22×C4311yescharacteristic
450C2×#100C22×C4311yescharacteristic
451C2×#100C22×C4311yescharacteristic
452C2×#100C22×C4311yescharacteristic
453#405C22×C4311yescharacteristic
454#405C22×C4311yescharacteristic
455C2×#97C22×C4311yescharacteristic
456#339C22×C4311yescharacteristic
457#339C22×C4311yescharacteristic
458C43#2850711yescharacteristic, direct product factor, Sylow
459C2×#41C23×C4311yescharacteristic
460C2×#41C23×C4311yescharacteristic
461C22×Q8C23×C4311yescharacteristic
462C22×D4—41no—
463C22×D4C23×C4311yescharacteristic
464C22×D4C23×C4311yescharacteristic
465C22×D4C23×C4311yescharacteristic
466#137—22no—
467#137—41no—
468AGL(1,ℤ/8)—22no—
469AGL(1,ℤ/8)—22no—
470AGL(1,ℤ/8)—22no—
471AGL(1,ℤ/8)—41no—
472AGL(1,ℤ/8)—41no—
473AGL(1,ℤ/8)—41no—
474#135—22no—
475#135—22no—
476C2×Q16—21no—
477C2×Q16D4×C4311yescharacteristic, complemented
478C2×SD16—21no—
479C2×SD16—21no—
480C2×SD16—21no—
481C2×SD16—21no—
482C2×SD16—21no—
483C2×SD16—21no—
484C2×SD16—22no—
485C2×SD16—21no—
486C2×SD16—22no—
487C2×SD16—22no—
488C2×SD16—21no—
489C2×SD16—22no—
490C2×SD16D4×C4311yescharacteristic, complemented
491C2×SD16D4×C4311yescharacteristic, complemented
492C2×D8—21no—
493C2×D8—21no—
494C2×D8—21no—
495C2×D8—21no—
496C2×D8—21no—
497C2×D8—22no—
498C2×D8—21no—
499C2×D8—21no—
500C2×D8—22no—
501C2×D8—22no—
502C2×D8—22no—
503C2×D8D4×C4311yescharacteristic, complemented
504#131—22no—
505#131—22no—
506#131—22no—
507#131—22no—
508C2×M16—21no—
509C2×M16—21no—
510C2×M16C23×C4311yescharacteristic
511C2×M16C23×C4311yescharacteristic
512C2×M16C23×C4311yescharacteristic
513C2×M16C23×C4311yescharacteristic
514C22×C8—21no—
515C22×C8—21no—
516C22×C8C23×C4311yescharacteristic
517C22×C8C23×C4311yescharacteristic
518C4⋊Q8—21no—
519#127—21no—
520#127—21no—
521#127—21no—
522#127—22no—
523#127—41no—
524#124—21no—
525#124—21no—
526#124—21no—
527#124—21no—
528#124—22no—
529#124—41no—
530#123—41no—
531C22⋊Q8—22no—
532#121—22no—
533#121—22no—
534#121—22no—
535#120—41no—
536#120—41no—
537#120—41no—
538#117C23×C4311yescharacteristic
539#117C23×C4311yescharacteristic
540C2×C22⋊C4—41no—
541C2×C42C23×C4311yescharacteristic
542#108—22no—
543#108D4×C4314yescomplemented
544#107D4×C4312yescomplemented
545#106D4×C4312yescomplemented
546#104—22no—
547#104—22no—
548#103—22no—
549#102—22no—
550#102—22no—
551#102—22no—
552#101—22no—
553#100—22no—
554#100—22no—
555#100—22no—
556#97—21no—
557#97—21no—
558#97D4×C4314yescomplemented
559C4×C8—21no—
560C4×C8—21no—
561C24—21no—
562C24—21no—
563C24—21no—
564#41—21no—
565#41—21no—
566#41—21no—
567#41—21no—
568#41—21no—
569#41—21no—
570#41—21no—
571#41—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8C2×D4×C4311yescharacteristic
579C2×Q8C2×D4×C4311yescharacteristic
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
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—21no—
599C2×D4—21no—
600C2×D4—44no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—84no—
605C2×D4C2×D4×C4311yescharacteristic
606C2×D4C2×D4×C4311yescharacteristic
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4C24×C4311yescharacteristic
612Q16—22no—
613Q16—42no—
614SD16—22no—
615SD16—22no—
616SD16—42no—
617SD16—42no—
618SD16—42no—
619SD16—42no—
620SD16—42no—
621SD16—42no—
622SD16—42no—
623SD16—42no—
624D8—22no—
625D8—42no—
626D8—42no—
627D8—42no—
628D8—42no—
629D8—42no—
630D8—42no—
631D8—42no—
632M16—21no—
633M16—21no—
634M16—21no—
635M16—21no—
636M16—21no—
637M16—21no—
638M16—42no—
639M16—42no—
640M16C2×D4×C4312yes—
641M16C2×D4×C4312yes—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—42no—
647C2×C8—42no—
648C2×C8C2×D4×C4311yescharacteristic
649C2×C8C2×D4×C4311yescharacteristic
650C2×C8C2×D4×C4312yes—
651C2×C8C2×D4×C4312yes—
652C2×C8C2×D4×C4311yescharacteristic
653C2×C8C2×D4×C4311yescharacteristic
654C2×C8C2×D4×C4312yes—
655C2×C8#41×C4312yes—
656C4⋊C4—42no—
657C4⋊C4C2×D4×C4312yes—
658C4⋊C4C2×D4×C4312yes—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—44no—
666C42—21no—
667C42—21no—
668C42—21no—
669C42C2×D4×C4312yes—
670C23—21no—
671C23—21no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—82no—
682C23—82no—
683C23—82no—
684C23H(5,𝔽2)×C4311yescharacteristic
685Q8—21no—
686Q8—21no—
687Q8—21no—
688Q8—21no—
689Q8—41no—
690Q8—41no—
691Q8—41no—
692Q8—41no—
693D4—21no—
694D4—21no—
695D4—21no—
696D4—21no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—88no—
714D4—162no—
715D4—162no—
716D4—162no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—42no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4C22×D4×C4311yescharacteristic
731C2×C4C22×D4×C4311yescharacteristic
732C2×C4C22×D4×C4311yescharacteristic
733C2×C4C22×D4×C4311yescharacteristic
734C2×C4C2×#41×C4311yescharacteristic
735C2×C4H(5,𝔽2)×C4311yescharacteristic
736C8—22no—
737C8—22no—
738C8—41no—
739C8—41no—
740C8#121×C4312yes—
741C8#121×C4312yes—
742C8#127×C4312yes—
743C8#127×C4312yes—
744C22—22no—
745C22—42no—
746C22—42no—
747C22—41no—
748C22—41no—
749C22—82no—
750C22—82no—
751C22—82no—
752C22—82no—
753C22—82no—
754C22—82no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—161no—
759C22—161no—
760C22—161no—
761C22C43×#53511yescharacteristic
762C22D42×C4311yescharacteristic
763C22C43×#55011yescharacteristic
764C4—42no—
765C4—42no—
766C4—42no—
767C4—41no—
768C4—41no—
769C4—81no—
770C4C2×#121×C4311yescharacteristic
771C4C2×#127×C4311yescharacteristic
772C4D42×C4311yescharacteristic
773C4C43×#55011yescharacteristic
774C2—21no—
775C2—21no—
776C2—81no—
777C2—81no—
778C2—161no—
779C2—161no—
780C2—161no—
781C2C43×#254111yescharacteristic
782C2C43×#328812yes—
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×#3155C2semidirect
2. C43×#3154C2semidirect
3. C2×C43×#496C2semidirect
4. C2×C43×#472C2semidirect
5. C2×C43×#471C2semidirect
6. C43×#3058C2semidirect
7. C43×#3057C2semidirect
8. C2×C43×#444C2semidirect
9. C43×#2004C2semidirect
10. C43×#2003C2semidirect
11. C43×#2002C2semidirect
12. C43×#2002C2semidirect
13. C43×#1978C2semidirect
14. C43×#1977C2semidirect
15. C43×#1773C2semidirect
85. C2×Q16×C43D4semidirect
98. C2×SD16×C43D4semidirect
99. C2×SD16×C43D4semidirect
111. C2×D8×C43D4semidirect
151. #108×C43D4semidirect
152. #107×C43D4semidirect
153. #106×C43D4semidirect
166. #97×C43D4semidirect
352. #28507C43direct (N × H)
383. #3155C2×C43semidirect
384. #3154C2×C43semidirect
385. C2×#496C2×C43semidirect
386. C2×#472C2×C43semidirect
387. C2×#471C2×C43semidirect
388. #3058C2×C43semidirect
389. #3057C2×C43semidirect
390. C2×#444C2×C43semidirect
391. #2004C2×C43semidirect
392. #2003C2×C43semidirect
393. #2002C2×C43semidirect
394. #2002C2×C43semidirect
395. #1978C2×C43semidirect
396. #1977C2×C43semidirect
397. #1773C2×C43semidirect
458. C43#28507direct (N × H)
477. C2×Q16D4×C43semidirect
490. C2×SD16D4×C43semidirect
491. C2×SD16D4×C43semidirect
503. C2×D8D4×C43semidirect
543. #108D4×C43semidirect
544. #107D4×C43semidirect
545. #106D4×C43semidirect
558. #97D4×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#31552
C43×#31542
C2×C43×#4962
C2×C43×#4722
C2×C43×#4712
C43×#30582
C43×#30572
C2×C43×#4442
C43×#20042
C43×#20032
C43×#20022
C43×#19782
C43×#19772
C43×#17732
#2850743