Finite Group Databasebeta

← C43×#25147 #24945164

Subgroups — C43×#25147 #24945164

Order 11008.

1022 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#471C211yesmaximal, characteristic, complemented
2C43×#3055C211yesmaximal, characteristic, complemented
3C43×#3005C211yesmaximal, characteristic, complemented
4C2×C43×#449C211yesmaximal, characteristic, complemented
5C43×#2933C211yesmaximal, characteristic, complemented
6C2×C43×#413C211yesmaximal, characteristic, complemented
7C43×#2063C211yesmaximal, characteristic, complemented
8C43×#2052C211yesmaximal, characteristic, complemented
9C43×#2046C211yesmaximal, characteristic, complemented
10C43×#2018C211yesmaximal, characteristic, complemented
11C43×#1978C211yesmaximal, characteristic, complemented
12C43×#1930C211yesmaximal, characteristic, complemented
13C43×#1907C211yesmaximal, characteristic, complemented
14C43×#1900C211yesmaximal, characteristic, complemented
15C43×#1855C211yesmaximal, characteristic, complemented
16C22×#41×C43C2211yescharacteristic
17C2×#137×C43C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
20C22×SD16×C43C2211yescharacteristic
21C22×D8×C43C2211yescharacteristic
22C2×#131×C43C2211yescharacteristic
23C22×M16×C43C2211yescharacteristic
24C22×M16×C43C2211yescharacteristic
25C43×#525C2211yescharacteristic
26C2×#121×C43C2211yescharacteristic
27C43×#471—24no—
28C43×#469—21no—
29C43×#468—21no—
30C43×#466—21no—
31C43×#465—21no—
32C43×#452—21no—
33C43×#452—21no—
34C43×#449—21no—
35C43×#449—21no—
36C43×#449—21no—
37C43×#449—21no—
38C43×#449—21no—
39C43×#449—21no—
40C43×#436—21no—
41C43×#435—21no—
42C43×#435—21no—
43C8×D4×C43—21no—
44C2×#108×C43C2211yescharacteristic
45C2×#108×C43C2211yescharacteristic
46C43×#428C2211yescharacteristic
47C43×#424C2211yescharacteristic
48C43×#419C2211yescharacteristic
49C43×#418C2211yescharacteristic
50C43×#418C2211yescharacteristic
51C43×#417C2211yescharacteristic
52C2×#103×C43C2211yescharacteristic
53C2×#102×C43C2211yescharacteristic
54C43×#413—24no—
55C2×#101×C43C2211yescharacteristic
56C2×#101×C43C2211yescharacteristic
57C2×#100×C43C2211yescharacteristic
58C2×#100×C43C2211yescharacteristic
59C2×#100×C43C2211yescharacteristic
60C2×#100×C43C2211yescharacteristic
61C43×#408C2211yescharacteristic
62C43×#407C2211yescharacteristic
63C2×C22⋊C8×C43C2211yescharacteristic
64C43×#405C2211yescharacteristic
65C43×#343C2211yescharacteristic
66C43×#343C2211yescharacteristic
67C43×#341C2211yescharacteristic
68C43×#341C2211yescharacteristic
69C2×#41×C43—22no—
70C2×#41×C43—22no—
71C2×#41×C43—21no—
72C2×#41×C43—21no—
73C2×#41×C43—21no—
74C2×#41×C43—21no—
75C2×#41×C43—41no—
76C2×#41×C43—41no—
77C2×#41×C43C2311yescharacteristic
78C22×Q8×C43C2311yescharacteristic
79C22×D4×C43—21no—
80C22×D4×C43—21no—
81C22×D4×C43C2311yescharacteristic
82C22×D4×C43C2311yescharacteristic
83C23×C4×C43—21no—
84C23×C4×C43C2311yescharacteristic
85#137×C43—22no—
86#137×C43—41no—
87AGL(1,ℤ/8)×C43—22no—
88AGL(1,ℤ/8)×C43—22no—
89AGL(1,ℤ/8)×C43—41no—
90AGL(1,ℤ/8)×C43—41no—
91C2×Q16×C43—21no—
92C2×SD16×C43—22no—
93C2×SD16×C43—21no—
94C2×SD16×C43—21no—
95C2×SD16×C43—21no—
96C2×SD16×C43—21no—
97C2×SD16×C43—21no—
98C2×SD16×C43—41no—
99C2×D8×C43—21no—
100C2×D8×C43—21no—
101C2×D8×C43—22no—
102C2×D8×C43—21no—
103C2×D8×C43—21no—
104C2×D8×C43—41no—
105#131×C43—22no—
106#131×C43—41no—
107C2×M16×C43—21no—
108C2×M16×C43—21no—
109C2×M16×C43—21no—
110C2×M16×C43—22no—
111C2×M16×C43—22no—
112C2×M16×C43—41no—
113C2×M16×C43—41no—
114C2×M16×C43C2311yescharacteristic
115C2×M16×C43C2311yescharacteristic
116C2×M16×C43C2311yescharacteristic
117C2×M16×C43C2311yescharacteristic
118C2×M16×C43C2311yescharacteristic
119C2×M16×C43C2311yescharacteristic
120C22×C8×C43—21no—
121C22×C8×C43—21no—
122C22×C8×C43—21no—
123C22×C8×C43C2311yescharacteristic
124C22×C8×C43C2311yescharacteristic
125#123×C43—21no—
126C22⋊Q8×C43D411yescharacteristic
127C22⋊Q8×C43D411yescharacteristic
128#121×C43—21no—
129#121×C43—21no—
130#121×C43—21no—
131#121×C43—21no—
132#121×C43D411yescharacteristic
133#121×C43D411yescharacteristic
134#120×C43—21no—
135C4×D4×C43—21no—
136C4×D4×C43—21no—
137#117×C43C2311yescharacteristic
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C22⋊C4×C43—21no—
140#108×C43—22no—
141#108×C43—41no—
142#107×C43—21no—
143#106×C43—21no—
144C4⋊C8×C43—21no—
145C4⋊C8×C43—21no—
146#103×C43—21no—
147#103×C43—21no—
148#103×C43—21no—
149#103×C43—21no—
150#103×C43—21no—
151#102×C43—21no—
152#102×C43—21no—
153#102×C43—21no—
154#102×C43—21no—
155#102×C43—21no—
156#102×C43—21no—
157#102×C43—21no—
158#101×C43—22no—
159#101×C43D414yescomplemented
160#100×C43—22no—
161#100×C43—22no—
162#100×C43—22no—
163#100×C43—41no—
164C22⋊C8×C43—21no—
165C22⋊C8×C43—21no—
166C22⋊C8×C43—21no—
167C22⋊C8×C43—21no—
168C22⋊C8×C43D411yescharacteristic
169C22⋊C8×C43D411yescharacteristic
170C22⋊C8×C43D411yescharacteristic
171C22⋊C8×C43D411yescharacteristic
172#97×C43—21no—
173C4×C8×C43—21no—
174C24×C43—21no—
175C24×C43—21no—
176C24×C43#4111yescharacteristic
177#41×C43—21no—
178#41×C43—21no—
179#41×C43—21no—
180#41×C43—21no—
181#41×C43—42no—
182#41×C43—42no—
183#41×C43—42no—
184#41×C43—42no—
185#41×C43—42no—
186#41×C43—42no—
187#41×C43—42no—
188#41×C43—42no—
189C2×Q8×C43—21no—
190C2×Q8×C43—21no—
191C2×Q8×C43—21no—
192C2×Q8×C43—21no—
193C2×Q8×C43—21no—
194C2×Q8×C43C2×D412yes—
195C2×Q8×C43C2×D411yescharacteristic
196C2×D4×C43—24no—
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—21no—
209C2×D4×C43—21no—
210C2×D4×C43—21no—
211C2×D4×C43—42no—
212C2×D4×C43—41no—
213C2×D4×C43—41no—
214C2×D4×C43—41no—
215C2×D4×C43—41no—
216C2×D4×C43—82no—
217C2×D4×C43C2×D411yescharacteristic
218C2×D4×C43#4112yes—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43—24no—
224C22×C4×C43—21no—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43—42no—
228C22×C4×C43—41no—
229C22×C4×C43—41no—
230C22×C4×C43C2×D411yescharacteristic
231C22×C4×C43C2×D411yescharacteristic
232C22×C4×C43C2×D411yescharacteristic
233C22×C4×C43C2×D411yescharacteristic
234C22×C4×C43#4111yescharacteristic
235C22×C4×C43C2411yescharacteristic
236Q16×C43—42no—
237SD16×C43—42no—
238SD16×C43—42no—
239SD16×C43—42no—
240SD16×C43—42no—
241SD16×C43—42no—
242D8×C43—42no—
243D8×C43—42no—
244D8×C43—42no—
245D8×C43—42no—
246M16×C43—21no—
247M16×C43—21no—
248M16×C43—21no—
249M16×C43—21no—
250M16×C43—21no—
251M16×C43—21no—
252M16×C43—21no—
253M16×C43—21no—
254M16×C43—21no—
255M16×C43—21no—
256M16×C43—42no—
257M16×C43—42no—
258M16×C43—42no—
259M16×C43C2×D412yes—
260M16×C43C2×D412yes—
261C2×C8×C43—21no—
262C2×C8×C43—21no—
263C2×C8×C43—21no—
264C2×C8×C43—21no—
265C2×C8×C43—21no—
266C2×C8×C43—21no—
267C2×C8×C43—21no—
268C2×C8×C43—21no—
269C2×C8×C43—21no—
270C2×C8×C43—21no—
271C2×C8×C43—42no—
272C2×C8×C43—42no—
273C2×C8×C43—42no—
274C2×C8×C43C2×D411yescharacteristic
275C2×C8×C43C2×D411yescharacteristic
276C2×C8×C43C2×D411yescharacteristic
277C2×C8×C43C2×D411yescharacteristic
278C4⋊C4×C43—21no—
279C4⋊C4×C43—21no—
280C4⋊C4×C43—21no—
281C4⋊C4×C43—21no—
282C4⋊C4×C43C2×D411yescharacteristic
283C4⋊C4×C43C2×D411yescharacteristic
284C22⋊C4×C43—21no—
285C22⋊C4×C43—21no—
286C22⋊C4×C43—21no—
287C22⋊C4×C43—21no—
288C22⋊C4×C43—21no—
289C22⋊C4×C43—41no—
290C22⋊C4×C43—41no—
291C42×C43—21no—
292C23×C43—21no—
293C23×C43—21no—
294C23×C43—21no—
295C23×C43—22no—
296C23×C43—41no—
297C23×C43—41no—
298C23×C43—41no—
299C23×C43—41no—
300C23×C43—41no—
301C23×C43—41no—
302C23×C43—41no—
303C23×C43—81no—
304C23×C43—81no—
305C23×C43—81no—
306C23×C43—81no—
307C23×C43#12111yescharacteristic
308C23×C43#12111yescharacteristic
309C23×C43C2×#4111yescharacteristic
310Q8×C43—21no—
311Q8×C43—22no—
312Q8×C43—22no—
313Q8×C43—21no—
314Q8×C43—41no—
315Q8×C43—41no—
316D4×C43—21no—
317D4×C43—22no—
318D4×C43—21no—
319D4×C43—22no—
320D4×C43—42no—
321D4×C43—44no—
322D4×C43—44no—
323D4×C43—41no—
324D4×C43—41no—
325D4×C43—41no—
326D4×C43—41no—
327D4×C43—41no—
328D4×C43—41no—
329D4×C43—41no—
330D4×C43—41no—
331D4×C43—81no—
332D4×C43—82no—
333D4×C43—82no—
334C2×C4×C43—21no—
335C2×C4×C43—21no—
336C2×C4×C43—21no—
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—21no—
341C2×C4×C43—21no—
342C2×C4×C43—21no—
343C2×C4×C43—21no—
344C2×C4×C43—21no—
345C2×C4×C43—21no—
346C2×C4×C43—21no—
347C2×C4×C43—22no—
348C2×C4×C43—44no—
349C2×C4×C43—44no—
350C2×C4×C43—41no—
351C2×C4×C43—41no—
352C2×C4×C43—41no—
353C2×C4×C43—41no—
354C2×C4×C43—41no—
355C2×C4×C43—81no—
356C2×C4×C43#12111yescharacteristic
357C2×C4×C43#12111yescharacteristic
358C2×C4×C43C22×D411yescharacteristic
359C2×C4×C43C22×D411yescharacteristic
360C2×C4×C43C22×D411yescharacteristic
361C2×C4×C43C2×#4111yescharacteristic
362C2×C4×C43H(5,𝔽2)11yescharacteristic
363C2×C4×C43H(5,𝔽2)11yescharacteristic
364C8×C43—21no—
365C8×C43—21no—
366C8×C43—22no—
367C8×C43—22no—
368C8×C43—21no—
369C8×C43—21no—
370C8×C43—41no—
371C8×C43—41no—
372C8×C43—41no—
373C8×C43—41no—
374#25147C4311yesmaximal, characteristic, direct product factor, Sylow
375C22×C43—21no—
376C22×C43—21no—
377C22×C43—21no—
378C22×C43—21no—
379C22×C43—21no—
380C22×C43—21no—
381C22×C43—21no—
382C22×C43—21no—
383C22×C43—42no—
384C22×C43—41no—
385C22×C43—41no—
386C22×C43—41no—
387C22×C43—81no—
388C22×C43—81no—
389C22×C43—82no—
390C22×C43—82no—
391C22×C43—81no—
392C22×C43—81no—
393C22×C43—81no—
394C22×C43—81no—
395C22×C43—81no—
396C22×C43—161no—
397C22×C43—161no—
398C22×C43C2×#12111yescharacteristic
399C22×C43#52511yescharacteristic
400C22×C43#53811yescharacteristic
401C4×C43—21no—
402C4×C43—21no—
403C4×C43—42no—
404C4×C43—41no—
405C4×C43—41no—
406C4×C43—41no—
407C4×C43—81no—
408C4×C43D4211yescharacteristic
409C4×C43D4211yescharacteristic
410C4×C43#54611yescharacteristic
411C4×C43#54611yescharacteristic
412C2×#471C2×C4311yescharacteristic, complemented
413#3055C2×C4311yescharacteristic, complemented
414#3005C2×C4311yescharacteristic, complemented
415C2×#449C2×C4311yescharacteristic, complemented
416#2933C2×C4311yescharacteristic, complemented
417C2×#413C2×C4311yescharacteristic, complemented
418#2063C2×C4311yescharacteristic, complemented
419#2052C2×C4311yescharacteristic, complemented
420#2046C2×C4311yescharacteristic, complemented
421#2018C2×C4311yescharacteristic, complemented
422#1978C2×C4311yescharacteristic, complemented
423#1930C2×C4311yescharacteristic, complemented
424#1907C2×C4311yescharacteristic, complemented
425#1900C2×C4311yescharacteristic, complemented
426#1855C2×C4311yescharacteristic, complemented
427C2×C43—21no—
428C2×C43—21no—
429C2×C43—41no—
430C2×C43—41no—
431C2×C43—81no—
432C2×C43—82no—
433C2×C43—161no—
434C2×C43#242411yescharacteristic
435C2×C43#306711yescharacteristic
436C2×C43#306811yescharacteristic
437C22×#41C22×C4311yescharacteristic
438C2×#137C22×C4311yescharacteristic
439C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
440C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
441C22×SD16C22×C4311yescharacteristic
442C22×D8C22×C4311yescharacteristic
443C2×#131C22×C4311yescharacteristic
444C22×M16C22×C4311yescharacteristic
445C22×M16C22×C4311yescharacteristic
446#525C22×C4311yescharacteristic
447C2×#121C22×C4311yescharacteristic
448#471—24no—
449#469—21no—
450#468—21no—
451#466—21no—
452#465—21no—
453#452—21no—
454#452—21no—
455#449—21no—
456#449—21no—
457#449—21no—
458#449—21no—
459#449—21no—
460#449—21no—
461#436—21no—
462#435—21no—
463#435—21no—
464C8×D4—21no—
465C2×#108C22×C4311yescharacteristic
466C2×#108C22×C4311yescharacteristic
467#428C22×C4311yescharacteristic
468#424C22×C4311yescharacteristic
469#419C22×C4311yescharacteristic
470#418C22×C4311yescharacteristic
471#418C22×C4311yescharacteristic
472#417C22×C4311yescharacteristic
473C2×#103C22×C4311yescharacteristic
474C2×#102C22×C4311yescharacteristic
475#413—24no—
476C2×#101C22×C4311yescharacteristic
477C2×#101C22×C4311yescharacteristic
478C2×#100C22×C4311yescharacteristic
479C2×#100C22×C4311yescharacteristic
480C2×#100C22×C4311yescharacteristic
481C2×#100C22×C4311yescharacteristic
482#408C22×C4311yescharacteristic
483#407C22×C4311yescharacteristic
484C2×C22⋊C8C22×C4311yescharacteristic
485#405C22×C4311yescharacteristic
486#343C22×C4311yescharacteristic
487#343C22×C4311yescharacteristic
488#341C22×C4311yescharacteristic
489#341C22×C4311yescharacteristic
490C43#2514711yescharacteristic, direct product factor, Sylow
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—21no—
494C2×#41—21no—
495C2×#41—21no—
496C2×#41—21no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41C23×C4311yescharacteristic
500C22×Q8C23×C4311yescharacteristic
501C22×D4—21no—
502C22×D4—21no—
503C22×D4C23×C4311yescharacteristic
504C22×D4C23×C4311yescharacteristic
505C23×C4—21no—
506C23×C4C23×C4311yescharacteristic
507#137—22no—
508#137—41no—
509AGL(1,ℤ/8)—22no—
510AGL(1,ℤ/8)—22no—
511AGL(1,ℤ/8)—41no—
512AGL(1,ℤ/8)—41no—
513C2×Q16—21no—
514C2×SD16—22no—
515C2×SD16—21no—
516C2×SD16—21no—
517C2×SD16—21no—
518C2×SD16—21no—
519C2×SD16—21no—
520C2×SD16—41no—
521C2×D8—21no—
522C2×D8—21no—
523C2×D8—22no—
524C2×D8—21no—
525C2×D8—21no—
526C2×D8—41no—
527#131—22no—
528#131—41no—
529C2×M16—21no—
530C2×M16—21no—
531C2×M16—21no—
532C2×M16—22no—
533C2×M16—22no—
534C2×M16—41no—
535C2×M16—41no—
536C2×M16C23×C4311yescharacteristic
537C2×M16C23×C4311yescharacteristic
538C2×M16C23×C4311yescharacteristic
539C2×M16C23×C4311yescharacteristic
540C2×M16C23×C4311yescharacteristic
541C2×M16C23×C4311yescharacteristic
542C22×C8—21no—
543C22×C8—21no—
544C22×C8—21no—
545C22×C8C23×C4311yescharacteristic
546C22×C8C23×C4311yescharacteristic
547#123—21no—
548C22⋊Q8D4×C4311yescharacteristic
549C22⋊Q8D4×C4311yescharacteristic
550#121—21no—
551#121—21no—
552#121—21no—
553#121—21no—
554#121D4×C4311yescharacteristic
555#121D4×C4311yescharacteristic
556#120—21no—
557C4×D4—21no—
558C4×D4—21no—
559#117C23×C4311yescharacteristic
560C2×C4⋊C4C23×C4311yescharacteristic
561C2×C22⋊C4—21no—
562#108—22no—
563#108—41no—
564#107—21no—
565#106—21no—
566C4⋊C8—21no—
567C4⋊C8—21no—
568#103—21no—
569#103—21no—
570#103—21no—
571#103—21no—
572#103—21no—
573#102—21no—
574#102—21no—
575#102—21no—
576#102—21no—
577#102—21no—
578#102—21no—
579#102—21no—
580#101—22no—
581#101D4×C4314yescomplemented
582#100—22no—
583#100—22no—
584#100—22no—
585#100—41no—
586C22⋊C8—21no—
587C22⋊C8—21no—
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8D4×C4311yescharacteristic
591C22⋊C8D4×C4311yescharacteristic
592C22⋊C8D4×C4311yescharacteristic
593C22⋊C8D4×C4311yescharacteristic
594#97—21no—
595C4×C8—21no—
596C24—21no—
597C24—21no—
598C24#41×C4311yescharacteristic
599#41—21no—
600#41—21no—
601#41—21no—
602#41—21no—
603#41—42no—
604#41—42no—
605#41—42no—
606#41—42no—
607#41—42no—
608#41—42no—
609#41—42no—
610#41—42no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8C2×D4×C4312yes—
617C2×Q8C2×D4×C4311yescharacteristic
618C2×D4—24no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—42no—
634C2×D4—41no—
635C2×D4—41no—
636C2×D4—41no—
637C2×D4—41no—
638C2×D4—82no—
639C2×D4C2×D4×C4311yescharacteristic
640C2×D4#41×C4312yes—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—24no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—42no—
650C22×C4—41no—
651C22×C4—41no—
652C22×C4C2×D4×C4311yescharacteristic
653C22×C4C2×D4×C4311yescharacteristic
654C22×C4C2×D4×C4311yescharacteristic
655C22×C4C2×D4×C4311yescharacteristic
656C22×C4#41×C4311yescharacteristic
657C22×C4C24×C4311yescharacteristic
658Q16—42no—
659SD16—42no—
660SD16—42no—
661SD16—42no—
662SD16—42no—
663SD16—42no—
664D8—42no—
665D8—42no—
666D8—42no—
667D8—42no—
668M16—21no—
669M16—21no—
670M16—21no—
671M16—21no—
672M16—21no—
673M16—21no—
674M16—21no—
675M16—21no—
676M16—21no—
677M16—21no—
678M16—42no—
679M16—42no—
680M16—42no—
681M16C2×D4×C4312yes—
682M16C2×D4×C4312yes—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—42no—
694C2×C8—42no—
695C2×C8—42no—
696C2×C8C2×D4×C4311yescharacteristic
697C2×C8C2×D4×C4311yescharacteristic
698C2×C8C2×D4×C4311yescharacteristic
699C2×C8C2×D4×C4311yescharacteristic
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4C2×D4×C4311yescharacteristic
705C4⋊C4C2×D4×C4311yescharacteristic
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—21no—
709C22⋊C4—21no—
710C22⋊C4—21no—
711C22⋊C4—41no—
712C22⋊C4—41no—
713C42—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—22no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—81no—
726C23—81no—
727C23—81no—
728C23—81no—
729C23#121×C4311yescharacteristic
730C23#121×C4311yescharacteristic
731C23C2×#41×C4311yescharacteristic
732Q8—21no—
733Q8—22no—
734Q8—22no—
735Q8—21no—
736Q8—41no—
737Q8—41no—
738D4—21no—
739D4—22no—
740D4—21no—
741D4—22no—
742D4—44no—
743D4—44no—
744D4—42no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—81no—
754D4—82no—
755D4—82no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—81no—
778C2×C4#121×C4311yescharacteristic
779C2×C4#121×C4311yescharacteristic
780C2×C4C22×D4×C4311yescharacteristic
781C2×C4C22×D4×C4311yescharacteristic
782C2×C4C22×D4×C4311yescharacteristic
783C2×C4C2×#41×C4311yescharacteristic
784C2×C4H(5,𝔽2)×C4311yescharacteristic
785C2×C4H(5,𝔽2)×C4311yescharacteristic
786C8—21no—
787C8—21no—
788C8—22no—
789C8—22no—
790C8—21no—
791C8—21no—
792C8—41no—
793C8—41no—
794C8—41no—
795C8—41no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—42no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—81no—
809C22—81no—
810C22—82no—
811C22—82no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—161no—
818C22—161no—
819C22C2×#121×C4311yescharacteristic
820C22C43×#52511yescharacteristic
821C22C43×#53811yescharacteristic
822C4—21no—
823C4—21no—
824C4—42no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—81no—
829C4D42×C4311yescharacteristic
830C4D42×C4311yescharacteristic
831C4C43×#54611yescharacteristic
832C4C43×#54611yescharacteristic
833C2—21no—
834C2—21no—
835C2—41no—
836C2—41no—
837C2—81no—
838C2—82no—
839C2—161no—
840C2C43×#242411yescharacteristic
841C2C43×#306711yescharacteristic
842C2C43×#306811yescharacteristic
subgroupG/H
center, socleC22×C43C2×#121
commutator, Frattini, cosocleC22×C4C24×C43
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
1. C2×C43×#471C2semidirect
2. C43×#3055C2semidirect
3. C43×#3005C2semidirect
4. C2×C43×#449C2semidirect
5. C43×#2933C2semidirect
6. C2×C43×#413C2semidirect
7. C43×#2063C2semidirect
8. C43×#2052C2semidirect
9. C43×#2046C2semidirect
10. C43×#2018C2semidirect
11. C43×#1978C2semidirect
12. C43×#1930C2semidirect
13. C43×#1907C2semidirect
14. C43×#1900C2semidirect
15. C43×#1855C2semidirect
159. #101×C43D4semidirect
374. #25147C43direct (N × H)
412. C2×#471C2×C43semidirect
413. #3055C2×C43semidirect
414. #3005C2×C43semidirect
415. C2×#449C2×C43semidirect
416. #2933C2×C43semidirect
417. C2×#413C2×C43semidirect
418. #2063C2×C43semidirect
419. #2052C2×C43semidirect
420. #2046C2×C43semidirect
421. #2018C2×C43semidirect
422. #1978C2×C43semidirect
423. #1930C2×C43semidirect
424. #1907C2×C43semidirect
425. #1900C2×C43semidirect
426. #1855C2×C43semidirect
490. C43#25147direct (N × H)
581. #101D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4712
C43×#30552
C43×#30052
C2×C43×#4492
C43×#29332
C2×C43×#4132
C43×#20632
C43×#20522
C43×#20462
C43×#20182
C43×#19782
C43×#19302
C43×#19072
C43×#19002
C43×#18552
#2514743