Finite Group Databasebeta

← C43×#25396 #24945413

Subgroups — C43×#25396 #24945413

Order 11008.

1184 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#469C211yesmaximal, characteristic, complemented
2C2×C43×#466C211yesmaximal, characteristic, complemented
3C2×C43×#459C211yesmaximal, characteristic, complemented
4C2×C43×#435C211yesmaximal, characteristic, complemented
5C43×#2541C211yesmaximal, characteristic, complemented
6C43×#2535C211yesmaximal, characteristic, complemented
7C43×#2034C211yesmaximal, characteristic, complemented
8C43×#2033C211yesmaximal, characteristic, complemented
9C43×#1999C211yesmaximal, characteristic, complemented
10C43×#1999C211yesmaximal, characteristic, complemented
11C43×#1961C211yesmaximal, characteristic, complemented
12C43×#1949C211yesmaximal, characteristic, complemented
13C43×#1895C211yesmaximal, characteristic, complemented
14C43×#1893C211yesmaximal, characteristic, complemented
15C43×#1762C211yesmaximal, characteristic, complemented
16C22×D8×C43C2211yescharacteristic
17C22×D8×C43C2211yescharacteristic
18C22×M16×C43C2211yescharacteristic
19C23×C8×C43C2211yescharacteristic
20C2×#127×C43—21no—
21C2×#127×C43C2211yescharacteristic
22C2×#121×C43C2211yescharacteristic
23C2×#121×C43C2211yescharacteristic
24C2×#121×C43C2211yescharacteristic
25C2×#121×C43C2211yescharacteristic
26C2×#121×C43C2211yescharacteristic
27C2×#121×C43C2211yescharacteristic
28C2×C4×D4×C43C2211yescharacteristic
29C2×C4×D4×C43C2211yescharacteristic
30C43×#469—24no—
31C43×#466—24no—
32C43×#459—24no—
33C43×#435—24no—
34C2×#107×C43C2211yescharacteristic
35C2×#106×C43C2211yescharacteristic
36C2×C4⋊C8×C43C2211yescharacteristic
37C2×#102×C43C2211yescharacteristic
38C2×#102×C43C2211yescharacteristic
39C2×#102×C43C2211yescharacteristic
40C2×#102×C43C2211yescharacteristic
41C2×#102×C43C2211yescharacteristic
42C2×#102×C43C2211yescharacteristic
43C2×#102×C43C2211yescharacteristic
44C2×#102×C43C2211yescharacteristic
45C2×C22⋊C8×C43C2211yescharacteristic
46C2×C22⋊C8×C43C2211yescharacteristic
47C2×#97×C43C2211yescharacteristic
48C43×#397—21no—
49C43×#392—21no—
50C43×#392—21no—
51C43×#392—21no—
52C43×#390—21no—
53C43×#386—21no—
54C43×#386—21no—
55C43×#382C2211yescharacteristic
56C43×#380C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C4×C4⋊C4×C43C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C22×D4×C43—21no—
64C22×D4×C43—21no—
65C22×D4×C43—21no—
66C22×D4×C43—21no—
67C22×D4×C43—21no—
68C22×D4×C43—21no—
69C22×D4×C43—21no—
70C22×D4×C43—21no—
71C22×D4×C43D411yescharacteristic
72C22×D4×C43C2311yescharacteristic
73C22×D4×C43C2311yescharacteristic
74C22×D4×C43C2311yescharacteristic
75C23×C4×C43—21no—
76C23×C4×C43C2311yescharacteristic
77C23×C4×C43C2311yescharacteristic
78C2×D8×C43—22no—
79C2×D8×C43—22no—
80C2×D8×C43—22no—
81C2×D8×C43—22no—
82C2×D8×C43—41no—
83C2×D8×C43—41no—
84C2×M16×C43—22no—
85C2×M16×C43—22no—
86C2×M16×C43—41no—
87C22×C8×C43—22no—
88C22×C8×C43—22no—
89C22×C8×C43—41no—
90C22×C8×C43C2311yescharacteristic
91C22×C8×C43C2311yescharacteristic
92C22×C8×C43C2311yescharacteristic
93C22×C8×C43C2311yescharacteristic
94#127×C43—22no—
95#127×C43—22no—
96#127×C43—44no—
97#121×C43—22no—
98#121×C43—22no—
99#121×C43—22no—
100#121×C43—22no—
101#121×C43—22no—
102#121×C43—22no—
103#121×C43—41no—
104#121×C43—41no—
105#121×C43—41no—
106#121×C43—41no—
107#121×C43—41no—
108#121×C43—41no—
109C4×D4×C43—22no—
110C4×D4×C43—22no—
111C4×D4×C43—22no—
112C4×D4×C43—22no—
113C2×C4⋊C4×C43D411yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C22⋊C4×C43—21no—
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122C2×C22⋊C4×C43—21no—
123C2×C22⋊C4×C43—21no—
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43D411yescharacteristic
129C2×C22⋊C4×C43D411yescharacteristic
130C2×C42×C43—21no—
131C2×C42×C43C2311yescharacteristic
132#107×C43—22no—
133#106×C43—22no—
134C4⋊C8×C43D414yescomplemented
135#102×C43—22no—
136#102×C43—22no—
137#102×C43—22no—
138#102×C43—22no—
139#102×C43—22no—
140#102×C43—41no—
141#102×C43—41no—
142#102×C43D414yescomplemented
143C22⋊C8×C43—22no—
144C22⋊C8×C43—22no—
145#97×C43—22no—
146#95×C43—21no—
147#95×C43—21no—
148#95×C43—21no—
149#95×C43—21no—
150#95×C43—21no—
151C24×C43—21no—
152C24×C43—21no—
153C24×C43—21no—
154C24×C43C2×D411yescharacteristic
155C24×C43C2×D411yescharacteristic
156C2×D4×C43—22no—
157C2×D4×C43—21no—
158C2×D4×C43—22no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43—21no—
174C2×D4×C43—21no—
175C2×D4×C43—41no—
176C2×D4×C43—42no—
177C2×D4×C43—42no—
178C2×D4×C43—42no—
179C2×D4×C43—42no—
180C2×D4×C43—42no—
181C2×D4×C43—42no—
182C2×D4×C43—42no—
183C2×D4×C43—42no—
184C2×D4×C43—42no—
185C2×D4×C43—42no—
186C2×D4×C43—42no—
187C2×D4×C43—42no—
188C2×D4×C43—42no—
189C2×D4×C43—42no—
190C2×D4×C43—42no—
191C2×D4×C43—42no—
192C2×D4×C43—81no—
193C2×D4×C43—81no—
194C2×D4×C43—81no—
195C2×D4×C43—81no—
196C2×D4×C43—81no—
197C2×D4×C43—81no—
198C2×D4×C43—81no—
199C2×D4×C43—81no—
200C2×D4×C43C2×D412yes—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
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×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—42no—
219C22×C4×C43—81no—
220C22×C4×C43—81no—
221C22×C4×C43C2×D411yescharacteristic
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2411yescharacteristic
226D8×C43—44no—
227D8×C43—44no—
228M16×C43—44no—
229C2×C8×C43—21no—
230C2×C8×C43—21no—
231C2×C8×C43—21no—
232C2×C8×C43—21no—
233C2×C8×C43—21no—
234C2×C8×C43—21no—
235C2×C8×C43—21no—
236C2×C8×C43—21no—
237C2×C8×C43—21no—
238C2×C8×C43—44no—
239C2×C8×C43C2×D412yes—
240C2×C8×C43C2×D412yes—
241C2×C8×C43C2×D412yes—
242C4⋊C4×C43—22no—
243C4⋊C4×C43—21no—
244C4⋊C4×C43—21no—
245C4⋊C4×C43—21no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43—21no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43—21no—
251C4⋊C4×C43C2×D412yes—
252C4⋊C4×C43#4112yes—
253C22⋊C4×C43—22no—
254C22⋊C4×C43—22no—
255C22⋊C4×C43—42no—
256C22⋊C4×C43—42no—
257C22⋊C4×C43—42no—
258C22⋊C4×C43—42no—
259C22⋊C4×C43—42no—
260C22⋊C4×C43—42no—
261C22⋊C4×C43—42no—
262C22⋊C4×C43—81no—
263C22⋊C4×C43—81no—
264C42×C43—42no—
265C42×C43C2×D412yes—
266C42×C43#4112yes—
267C23×C43—21no—
268C23×C43—21no—
269C23×C43—21no—
270C23×C43—21no—
271C23×C43—21no—
272C23×C43—21no—
273C23×C43—21no—
274C23×C43—22no—
275C23×C43—21no—
276C23×C43—21no—
277C23×C43—21no—
278C23×C43—21no—
279C23×C43—21no—
280C23×C43—21no—
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—41no—
290C23×C43—41no—
291C23×C43—41no—
292C23×C43—41no—
293C23×C43—41no—
294C23×C43—41no—
295C23×C43—41no—
296C23×C43—41no—
297C23×C43—41no—
298C23×C43—41no—
299C23×C43—41no—
300C23×C43—41no—
301C23×C43AGL(1,ℤ/8)12yes—
302C23×C43C22×D411yescharacteristic
303D4×C43—22no—
304D4×C43—22no—
305D4×C43—44no—
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—84no—
317D4×C43—84no—
318D4×C43—84no—
319D4×C43—84no—
320D4×C43—84no—
321D4×C43—84no—
322D4×C43—84no—
323D4×C43—84no—
324C2×C4×C43—21no—
325C2×C4×C43—21no—
326C2×C4×C43—21no—
327C2×C4×C43—21no—
328C2×C4×C43—21no—
329C2×C4×C43—21no—
330C2×C4×C43—21no—
331C2×C4×C43—21no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—21no—
335C2×C4×C43—21no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43—41no—
340C2×C4×C43—41no—
341C2×C4×C43—41no—
342C2×C4×C43—41no—
343C2×C4×C43—41no—
344C2×C4×C43—41no—
345C2×C4×C43—41no—
346C2×C4×C43—41no—
347C2×C4×C43—41no—
348C2×C4×C43—41no—
349C2×C4×C43—41no—
350C2×C4×C43—41no—
351C2×C4×C43—41no—
352C2×C4×C43—41no—
353C2×C4×C43—41no—
354C2×C4×C43—41no—
355C2×C4×C43—41no—
356C2×C4×C43—41no—
357C2×C4×C43—84no—
358C2×C4×C43#12112yes—
359C2×C4×C43#12112yes—
360C2×C4×C43C22×D411yescharacteristic
361C2×C4×C43C22×D411yescharacteristic
362C2×C4×C43C2×#4111yescharacteristic
363C2×C4×C43C2×#4111yescharacteristic
364C2×C4×C43H(5,𝔽2)11yescharacteristic
365C2×C4×C43H(5,𝔽2)11yescharacteristic
366C8×C43—22no—
367C8×C43—22no—
368C8×C43—22no—
369C8×C43—41no—
370#25396C4311yesmaximal, characteristic, direct product factor, Sylow
371C22×C43—22no—
372C22×C43—22no—
373C22×C43—22no—
374C22×C43—41no—
375C22×C43—41no—
376C22×C43—41no—
377C22×C43—41no—
378C22×C43—41no—
379C22×C43—42no—
380C22×C43—41no—
381C22×C43—42no—
382C22×C43—41no—
383C22×C43—42no—
384C22×C43—41no—
385C22×C43—41no—
386C22×C43—41no—
387C22×C43—41no—
388C22×C43—81no—
389C22×C43—81no—
390C22×C43—81no—
391C22×C43—81no—
392C22×C43—81no—
393C22×C43—81no—
394C22×C43—81no—
395C22×C43—81no—
396C22×C43—81no—
397C22×C43—81no—
398C22×C43—81no—
399C22×C43—81no—
400C22×C43—81no—
401C22×C43—81no—
402C22×C43—81no—
403C22×C43—81no—
404C22×C43—81no—
405C22×C43—81no—
406C22×C43C2×#12111yescharacteristic
407C22×C43D4211yescharacteristic
408C22×C43#54611yescharacteristic
409C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
410C22×C43#57511yescharacteristic
411C22×C43#57611yescharacteristic
412C22×C43#57611yescharacteristic
413C4×C43—22no—
414C4×C43—22no—
415C4×C43—41no—
416C4×C43—41no—
417C4×C43—42no—
418C4×C43—42no—
419C4×C43—81no—
420C4×C43—81no—
421C4×C43—81no—
422C4×C43#53211yescharacteristic
423C4×C43#54011yescharacteristic
424C4×C43D4211yescharacteristic
425C4×C43#55011yescharacteristic
426C2×#469C2×C4311yescharacteristic, complemented
427C2×#466C2×C4311yescharacteristic, complemented
428C2×#459C2×C4311yescharacteristic, complemented
429C2×#435C2×C4311yescharacteristic, complemented
430#2541C2×C4311yescharacteristic, complemented
431#2535C2×C4311yescharacteristic, complemented
432#2034C2×C4311yescharacteristic, complemented
433#2033C2×C4311yescharacteristic, complemented
434#1999C2×C4311yescharacteristic, complemented
435#1999C2×C4311yescharacteristic, complemented
436#1961C2×C4311yescharacteristic, complemented
437#1949C2×C4311yescharacteristic, complemented
438#1895C2×C4311yescharacteristic, complemented
439#1893C2×C4311yescharacteristic, complemented
440#1762C2×C4311yescharacteristic, complemented
441C2×C43—42no—
442C2×C43—81no—
443C2×C43—82no—
444C2×C43—161no—
445C2×C43—161no—
446C2×C43#242811yescharacteristic
447C2×C43#305511yescharacteristic
448C2×C43#305811yescharacteristic
449C2×C43#326411yescharacteristic
450C2×C43#326811yescharacteristic
451C2×C43#330911yescharacteristic
452C2×C43#331811yescharacteristic
453C22×D8C22×C4311yescharacteristic
454C22×D8C22×C4311yescharacteristic
455C22×M16C22×C4311yescharacteristic
456C23×C8C22×C4311yescharacteristic
457C2×#127—21no—
458C2×#127C22×C4311yescharacteristic
459C2×#121C22×C4311yescharacteristic
460C2×#121C22×C4311yescharacteristic
461C2×#121C22×C4311yescharacteristic
462C2×#121C22×C4311yescharacteristic
463C2×#121C22×C4311yescharacteristic
464C2×#121C22×C4311yescharacteristic
465C2×C4×D4C22×C4311yescharacteristic
466C2×C4×D4C22×C4311yescharacteristic
467#469—24no—
468#466—24no—
469#459—24no—
470#435—24no—
471C2×#107C22×C4311yescharacteristic
472C2×#106C22×C4311yescharacteristic
473C2×C4⋊C8C22×C4311yescharacteristic
474C2×#102C22×C4311yescharacteristic
475C2×#102C22×C4311yescharacteristic
476C2×#102C22×C4311yescharacteristic
477C2×#102C22×C4311yescharacteristic
478C2×#102C22×C4311yescharacteristic
479C2×#102C22×C4311yescharacteristic
480C2×#102C22×C4311yescharacteristic
481C2×#102C22×C4311yescharacteristic
482C2×C22⋊C8C22×C4311yescharacteristic
483C2×C22⋊C8C22×C4311yescharacteristic
484C2×#97C22×C4311yescharacteristic
485#397—21no—
486#392—21no—
487#392—21no—
488#392—21no—
489#390—21no—
490#386—21no—
491#386—21no—
492#382C22×C4311yescharacteristic
493#380C22×C4311yescharacteristic
494#380C22×C4311yescharacteristic
495C4×C4⋊C4C22×C4311yescharacteristic
496#340C22×C4311yescharacteristic
497#340C22×C4311yescharacteristic
498#340C22×C4311yescharacteristic
499#340C22×C4311yescharacteristic
500C43#2539611yescharacteristic, direct product factor, Sylow
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4D4×C4311yescharacteristic
510C22×D4C23×C4311yescharacteristic
511C22×D4C23×C4311yescharacteristic
512C22×D4C23×C4311yescharacteristic
513C23×C4—21no—
514C23×C4C23×C4311yescharacteristic
515C23×C4C23×C4311yescharacteristic
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—22no—
519C2×D8—22no—
520C2×D8—41no—
521C2×D8—41no—
522C2×M16—22no—
523C2×M16—22no—
524C2×M16—41no—
525C22×C8—22no—
526C22×C8—22no—
527C22×C8—41no—
528C22×C8C23×C4311yescharacteristic
529C22×C8C23×C4311yescharacteristic
530C22×C8C23×C4311yescharacteristic
531C22×C8C23×C4311yescharacteristic
532#127—22no—
533#127—22no—
534#127—44no—
535#121—22no—
536#121—22no—
537#121—22no—
538#121—22no—
539#121—22no—
540#121—22no—
541#121—41no—
542#121—41no—
543#121—41no—
544#121—41no—
545#121—41no—
546#121—41no—
547C4×D4—22no—
548C4×D4—22no—
549C4×D4—22no—
550C4×D4—22no—
551C2×C4⋊C4D4×C4311yescharacteristic
552C2×C4⋊C4C23×C4311yescharacteristic
553C2×C4⋊C4C23×C4311yescharacteristic
554C2×C4⋊C4C23×C4311yescharacteristic
555C2×C4⋊C4C23×C4311yescharacteristic
556C2×C4⋊C4C23×C4311yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4D4×C4311yescharacteristic
567C2×C22⋊C4D4×C4311yescharacteristic
568C2×C42—21no—
569C2×C42C23×C4311yescharacteristic
570#107—22no—
571#106—22no—
572C4⋊C8D4×C4314yescomplemented
573#102—22no—
574#102—22no—
575#102—22no—
576#102—22no—
577#102—22no—
578#102—41no—
579#102—41no—
580#102D4×C4314yescomplemented
581C22⋊C8—22no—
582C22⋊C8—22no—
583#97—22no—
584#95—21no—
585#95—21no—
586#95—21no—
587#95—21no—
588#95—21no—
589C24—21no—
590C24—21no—
591C24—21no—
592C24C2×D4×C4311yescharacteristic
593C24C2×D4×C4311yescharacteristic
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—41no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—42no—
620C2×D4—42no—
621C2×D4—42no—
622C2×D4—42no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4—81no—
634C2×D4—81no—
635C2×D4—81no—
636C2×D4—81no—
637C2×D4—81no—
638C2×D4C2×D4×C4312yes—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—42no—
657C22×C4—81no—
658C22×C4—81no—
659C22×C4C2×D4×C4311yescharacteristic
660C22×C4C2×D4×C4311yescharacteristic
661C22×C4C2×D4×C4311yescharacteristic
662C22×C4C2×D4×C4311yescharacteristic
663C22×C4C24×C4311yescharacteristic
664D8—44no—
665D8—44no—
666M16—44no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—44no—
677C2×C8C2×D4×C4312yes—
678C2×C8C2×D4×C4312yes—
679C2×C8C2×D4×C4312yes—
680C4⋊C4—22no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4C2×D4×C4312yes—
690C4⋊C4#41×C4312yes—
691C22⋊C4—22no—
692C22⋊C4—22no—
693C22⋊C4—42no—
694C22⋊C4—42no—
695C22⋊C4—42no—
696C22⋊C4—42no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4—81no—
701C22⋊C4—81no—
702C42—42no—
703C42C2×D4×C4312yes—
704C42#41×C4312yes—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23AGL(1,ℤ/8)×C4312yes—
740C23C22×D4×C4311yescharacteristic
741D4—22no—
742D4—22no—
743D4—44no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—84no—
755D4—84no—
756D4—84no—
757D4—84no—
758D4—84no—
759D4—84no—
760D4—84no—
761D4—84no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—84no—
796C2×C4#121×C4312yes—
797C2×C4#121×C4312yes—
798C2×C4C22×D4×C4311yescharacteristic
799C2×C4C22×D4×C4311yescharacteristic
800C2×C4C2×#41×C4311yescharacteristic
801C2×C4C2×#41×C4311yescharacteristic
802C2×C4H(5,𝔽2)×C4311yescharacteristic
803C2×C4H(5,𝔽2)×C4311yescharacteristic
804C8—22no—
805C8—22no—
806C8—22no—
807C8—41no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—42no—
817C22—41no—
818C22—42no—
819C22—41no—
820C22—42no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22C2×#121×C4311yescharacteristic
844C22D42×C4311yescharacteristic
845C22C43×#54611yescharacteristic
846C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
847C22C43×#57511yescharacteristic
848C22C43×#57611yescharacteristic
849C22C43×#57611yescharacteristic
850C4—22no—
851C4—22no—
852C4—41no—
853C4—41no—
854C4—42no—
855C4—42no—
856C4—81no—
857C4—81no—
858C4—81no—
859C4C43×#53211yescharacteristic
860C4C43×#54011yescharacteristic
861C4D42×C4311yescharacteristic
862C4C43×#55011yescharacteristic
863C2—42no—
864C2—81no—
865C2—82no—
866C2—161no—
867C2—161no—
868C2C43×#242811yescharacteristic
869C2C43×#305511yescharacteristic
870C2C43×#305811yescharacteristic
871C2C43×#326411yescharacteristic
872C2C43×#326811yescharacteristic
873C2C43×#330911yescharacteristic
874C2C43×#331811yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C2×C4×D4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#469C2semidirect
2. C2×C43×#466C2semidirect
3. C2×C43×#459C2semidirect
4. C2×C43×#435C2semidirect
5. C43×#2541C2semidirect
6. C43×#2535C2semidirect
7. C43×#2034C2semidirect
8. C43×#2033C2semidirect
9. C43×#1999C2semidirect
10. C43×#1999C2semidirect
11. C43×#1961C2semidirect
12. C43×#1949C2semidirect
13. C43×#1895C2semidirect
14. C43×#1893C2semidirect
15. C43×#1762C2semidirect
134. C4⋊C8×C43D4semidirect
142. #102×C43D4semidirect
370. #25396C43direct (N × H)
426. C2×#469C2×C43semidirect
427. C2×#466C2×C43semidirect
428. C2×#459C2×C43semidirect
429. C2×#435C2×C43semidirect
430. #2541C2×C43semidirect
431. #2535C2×C43semidirect
432. #2034C2×C43semidirect
433. #2033C2×C43semidirect
434. #1999C2×C43semidirect
435. #1999C2×C43semidirect
436. #1961C2×C43semidirect
437. #1949C2×C43semidirect
438. #1895C2×C43semidirect
439. #1893C2×C43semidirect
440. #1762C2×C43semidirect
500. C43#25396direct (N × H)
572. C4⋊C8D4×C43semidirect
580. #102D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4692
C2×C43×#4662
C2×C43×#4592
C2×C43×#4352
C43×#25412
C43×#25352
C43×#20342
C43×#20332
C43×#19992
C43×#19612
C43×#19492
C43×#18952
C43×#18932
C43×#17622
#2539643