Finite Group Databasebeta

← C43×#25380 #24945397

Subgroups — C43×#25380 #24945397

Order 11008.

1184 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#496C211yesmaximal, characteristic, complemented
2C2×C43×#460C211yesmaximal, characteristic, complemented
3C2×C43×#463C211yesmaximal, characteristic, complemented
4C2×C43×#459C211yesmaximal, characteristic, complemented
5C43×#2541C211yesmaximal, characteristic, complemented
6C43×#2367C211yesmaximal, characteristic, complemented
7C43×#2055C211yesmaximal, characteristic, complemented
8C43×#2054C211yesmaximal, characteristic, complemented
9C43×#2014C211yesmaximal, characteristic, complemented
10C43×#2011C211yesmaximal, characteristic, complemented
11C43×#1982C211yesmaximal, characteristic, complemented
12C43×#1940C211yesmaximal, characteristic, complemented
13C43×#1880C211yesmaximal, characteristic, complemented
14C43×#1879C211yesmaximal, characteristic, complemented
15C43×#1762C211yesmaximal, characteristic, complemented
16C22×SD16×C43C2211yescharacteristic
17C22×SD16×C43C2211yescharacteristic
18C22×SD16×C43C2211yescharacteristic
19C22×D8×C43C2211yescharacteristic
20C22×D8×C43C2211yescharacteristic
21C22×D8×C43C2211yescharacteristic
22C2×#127×C43C2211yescharacteristic
23C2×#127×C43C2211yescharacteristic
24C2×#127×C43C2211yescharacteristic
25C2×#124×C43C2211yescharacteristic
26C2×#121×C43—21no—
27C2×#121×C43—21no—
28C2×C4×Q8×C43C2211yescharacteristic
29C2×C4×D4×C43C2211yescharacteristic
30C2×C4×D4×C43C2211yescharacteristic
31C43×#496—24no—
32C43×#463—24no—
33C43×#460—24no—
34C43×#459—24no—
35C2×C4⋊C8×C43C2211yescharacteristic
36C2×C4⋊C8×C43C2211yescharacteristic
37C2×C4⋊C8×C43C2211yescharacteristic
38C2×#103×C43C2211yescharacteristic
39C2×#102×C43C2211yescharacteristic
40C2×#102×C43C2211yescharacteristic
41C2×#102×C43C2211yescharacteristic
42C2×#102×C43C2211yescharacteristic
43C2×#102×C43C2211yescharacteristic
44C2×#102×C43C2211yescharacteristic
45C2×#102×C43C2211yescharacteristic
46C2×#97×C43C2211yescharacteristic
47C43×#392—21no—
48C43×#392—21no—
49C43×#391C2211yescharacteristic
50C43×#390C2211yescharacteristic
51C43×#390C2211yescharacteristic
52C43×#390C2211yescharacteristic
53C43×#388—21no—
54C43×#388—21no—
55C43×#385—21no—
56C4×C4⋊C4×C43C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C4×C22⋊C4×C43—21no—
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×Q8×C43C2311yescharacteristic
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×C43C2311yescharacteristic
71C22×D4×C43C2311yescharacteristic
72C22×D4×C43C2311yescharacteristic
73C22×D4×C43C2311yescharacteristic
74C23×C4×C43—21no—
75C23×C4×C43—21no—
76C2×SD16×C43—22no—
77C2×SD16×C43—22no—
78C2×SD16×C43—22no—
79C2×SD16×C43—22no—
80C2×SD16×C43—22no—
81C2×SD16×C43—22no—
82C2×SD16×C43—41no—
83C2×SD16×C43—41no—
84C2×SD16×C43—41no—
85C2×D8×C43—22no—
86C2×D8×C43—22no—
87C2×D8×C43—22no—
88C2×D8×C43—22no—
89C2×D8×C43—22no—
90C2×D8×C43—22no—
91C2×D8×C43—41no—
92C2×D8×C43—41no—
93C2×D8×C43—41no—
94C22×C8×C43C2311yescharacteristic
95C22×C8×C43C2311yescharacteristic
96C22×C8×C43C2311yescharacteristic
97C22×C8×C43C2311yescharacteristic
98#127×C43—22no—
99#127×C43—22no—
100#127×C43—22no—
101#127×C43—22no—
102#127×C43—41no—
103#127×C43—41no—
104#124×C43—22no—
105#124×C43D414yescomplemented
106#121×C43—44no—
107#121×C43—44no—
108C4×Q8×C43—22no—
109C4×Q8×C43—41no—
110C4×D4×C43—22no—
111C4×D4×C43—22no—
112C4×D4×C43—22no—
113C4×D4×C43—41no—
114C2×C4⋊C4×C43—21no—
115C2×C4⋊C4×C43D411yescharacteristic
116C2×C4⋊C4×C43D411yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
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×C43—21no—
129C2×C22⋊C4×C43—21no—
130C2×C42×C43—21no—
131C2×C42×C43—21no—
132C2×C42×C43C2311yescharacteristic
133C2×C42×C43C2311yescharacteristic
134C2×C42×C43C2311yescharacteristic
135C4⋊C8×C43—22no—
136C4⋊C8×C43—22no—
137C4⋊C8×C43—22no—
138#103×C43—22no—
139#102×C43—22no—
140#102×C43—22no—
141#102×C43—22no—
142#102×C43—22no—
143#102×C43—41no—
144#102×C43—41no—
145#102×C43D414yescomplemented
146#97×C43—22no—
147#95×C43—21no—
148#95×C43—21no—
149#95×C43—21no—
150#95×C43D411yescharacteristic
151#95×C43D411yescharacteristic
152C24×C43—21no—
153C24×C43—21no—
154C24×C43—21no—
155C24×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43C2×D412yes—
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—21no—
176C2×D4×C43—21no—
177C2×D4×C43—21no—
178C2×D4×C43—21no—
179C2×D4×C43—21no—
180C2×D4×C43—21no—
181C2×D4×C43—21no—
182C2×D4×C43—21no—
183C2×D4×C43—21no—
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—42no—
193C2×D4×C43—42no—
194C2×D4×C43—42no—
195C2×D4×C43—42no—
196C2×D4×C43—81no—
197C2×D4×C43—81no—
198C2×D4×C43—81no—
199C2×D4×C43—81no—
200C2×D4×C43—81no—
201C2×D4×C43—81no—
202C2×D4×C43C2×D412yes—
203C2×D4×C43C2×D412yes—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—42no—
209C22×C4×C43—42no—
210C22×C4×C43—42no—
211C22×C4×C43—42no—
212C22×C4×C43—42no—
213C22×C4×C43—81no—
214C22×C4×C43C2×D411yescharacteristic
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2×D411yescharacteristic
219C22×C4×C43C2×D411yescharacteristic
220C22×C4×C43C2411yescharacteristic
221SD16×C43—44no—
222SD16×C43—44no—
223SD16×C43—44no—
224D8×C43—44no—
225D8×C43—44no—
226D8×C43—44no—
227C2×C8×C43—21no—
228C2×C8×C43—21no—
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×C43C2×D412yes—
238C2×C8×C43#4112yes—
239C4⋊C4×C43—22no—
240C4⋊C4×C43—22no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43—21no—
243C4⋊C4×C43—21no—
244C4⋊C4×C43—21no—
245C4⋊C4×C43—21no—
246C4⋊C4×C43—42no—
247C4⋊C4×C43C2×D412yes—
248C22⋊C4×C43—24no—
249C22⋊C4×C43—24no—
250C22⋊C4×C43—42no—
251C22⋊C4×C43—42no—
252C22⋊C4×C43—42no—
253C22⋊C4×C43—42no—
254C22⋊C4×C43—42no—
255C22⋊C4×C43—42no—
256C22⋊C4×C43—42no—
257C22⋊C4×C43—81no—
258C42×C43—21no—
259C42×C43—21no—
260C42×C43—21no—
261C42×C43—21no—
262C42×C43—42no—
263C42×C43—81no—
264C42×C43C2×D412yes—
265C42×C43#4112yes—
266C23×C43—22no—
267C23×C43—22no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43—41no—
274C23×C43—41no—
275C23×C43—41no—
276C23×C43—41no—
277C23×C43—41no—
278C23×C43—41no—
279C23×C43—41no—
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—41no—
290C23×C43—41no—
291C23×C43—41no—
292C23×C43—41no—
293C23×C43—41no—
294C23×C43C22×D411yescharacteristic
295Q8×C43—22no—
296Q8×C43—22no—
297Q8×C43—41no—
298Q8×C43—41no—
299D4×C43—22no—
300D4×C43—22no—
301D4×C43—22no—
302D4×C43—22no—
303D4×C43—41no—
304D4×C43—41no—
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—84no—
316D4×C43—84no—
317D4×C43—84no—
318D4×C43—84no—
319D4×C43—84no—
320D4×C43—84no—
321C2×C4×C43—21no—
322C2×C4×C43—21no—
323C2×C4×C43—21no—
324C2×C4×C43—21no—
325C2×C4×C43—21no—
326C2×C4×C43—21no—
327C2×C4×C43—21no—
328C2×C4×C43—21no—
329C2×C4×C43—22no—
330C2×C4×C43—21no—
331C2×C4×C43—21no—
332C2×C4×C43—22no—
333C2×C4×C43—21no—
334C2×C4×C43—21no—
335C2×C4×C43—21no—
336C2×C4×C43—21no—
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—84no—
348C2×C4×C43—84no—
349C2×C4×C43#12112yes—
350C2×C4×C43#12112yes—
351C2×C4×C43AGL(1,ℤ/8)12yes—
352C2×C4×C43AGL(1,ℤ/8)12yes—
353C2×C4×C43C22×D411yescharacteristic
354C2×C4×C43C22×D411yescharacteristic
355C2×C4×C43C2×#4111yescharacteristic
356C2×C4×C43C2×#4111yescharacteristic
357C2×C4×C43H(5,𝔽2)11yescharacteristic
358C2×C4×C43H(5,𝔽2)11yescharacteristic
359C8×C43—22no—
360C8×C43—22no—
361C8×C43—41no—
362C8×C43—41no—
363#25380C4311yesmaximal, characteristic, direct product factor, Sylow
364C22×C43—42no—
365C22×C43—42no—
366C22×C43—42no—
367C22×C43—42no—
368C22×C43—42no—
369C22×C43—42no—
370C22×C43—81no—
371C22×C43—81no—
372C22×C43—81no—
373C22×C43—81no—
374C22×C43—81no—
375C22×C43—81no—
376C22×C43—81no—
377C22×C43—81no—
378C22×C43—81no—
379C22×C43—81no—
380C22×C43—81no—
381C22×C43—81no—
382C22×C43—81no—
383C22×C43—81no—
384C22×C43—81no—
385C22×C43—81no—
386C22×C43—81no—
387C22×C43—81no—
388C22×C43—81no—
389C22×C43—81no—
390C22×C43—81no—
391C22×C43—81no—
392C22×C43C2×#12111yescharacteristic
393C22×C43D4211yescharacteristic
394C22×C43#55011yescharacteristic
395C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
396C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
397C22×C43#57611yescharacteristic
398C22×C43#57711yescharacteristic
399C4×C43—22no—
400C4×C43—22no—
401C4×C43—22no—
402C4×C43—22no—
403C4×C43—42no—
404C4×C43—41no—
405C4×C43—42no—
406C4×C43—41no—
407C4×C43—81no—
408C4×C43—81no—
409C4×C43#53211yescharacteristic
410C4×C43#54011yescharacteristic
411C4×C43D4211yescharacteristic
412C4×C43#54611yescharacteristic
413C2×#496C2×C4311yescharacteristic, complemented
414C2×#460C2×C4311yescharacteristic, complemented
415C2×#463C2×C4311yescharacteristic, complemented
416C2×#459C2×C4311yescharacteristic, complemented
417#2541C2×C4311yescharacteristic, complemented
418#2367C2×C4311yescharacteristic, complemented
419#2055C2×C4311yescharacteristic, complemented
420#2054C2×C4311yescharacteristic, complemented
421#2014C2×C4311yescharacteristic, complemented
422#2011C2×C4311yescharacteristic, complemented
423#1982C2×C4311yescharacteristic, complemented
424#1940C2×C4311yescharacteristic, complemented
425#1880C2×C4311yescharacteristic, complemented
426#1879C2×C4311yescharacteristic, complemented
427#1762C2×C4311yescharacteristic, complemented
428C2×C43—82no—
429C2×C43—82no—
430C2×C43—161no—
431C2×C43—161no—
432C2×C43#242811yescharacteristic
433C2×C43#303811yescharacteristic
434C2×C43#304511yescharacteristic
435C2×C43#326411yescharacteristic
436C2×C43#326511yescharacteristic
437C2×C43#339711yescharacteristic
438C2×C43#339911yescharacteristic
439C22×SD16C22×C4311yescharacteristic
440C22×SD16C22×C4311yescharacteristic
441C22×SD16C22×C4311yescharacteristic
442C22×D8C22×C4311yescharacteristic
443C22×D8C22×C4311yescharacteristic
444C22×D8C22×C4311yescharacteristic
445C2×#127C22×C4311yescharacteristic
446C2×#127C22×C4311yescharacteristic
447C2×#127C22×C4311yescharacteristic
448C2×#124C22×C4311yescharacteristic
449C2×#121—21no—
450C2×#121—21no—
451C2×C4×Q8C22×C4311yescharacteristic
452C2×C4×D4C22×C4311yescharacteristic
453C2×C4×D4C22×C4311yescharacteristic
454#496—24no—
455#463—24no—
456#460—24no—
457#459—24no—
458C2×C4⋊C8C22×C4311yescharacteristic
459C2×C4⋊C8C22×C4311yescharacteristic
460C2×C4⋊C8C22×C4311yescharacteristic
461C2×#103C22×C4311yescharacteristic
462C2×#102C22×C4311yescharacteristic
463C2×#102C22×C4311yescharacteristic
464C2×#102C22×C4311yescharacteristic
465C2×#102C22×C4311yescharacteristic
466C2×#102C22×C4311yescharacteristic
467C2×#102C22×C4311yescharacteristic
468C2×#102C22×C4311yescharacteristic
469C2×#97C22×C4311yescharacteristic
470#392—21no—
471#392—21no—
472#391C22×C4311yescharacteristic
473#390C22×C4311yescharacteristic
474#390C22×C4311yescharacteristic
475#390C22×C4311yescharacteristic
476#388—21no—
477#388—21no—
478#385—21no—
479C4×C4⋊C4C22×C4311yescharacteristic
480C4×C4⋊C4C22×C4311yescharacteristic
481C4×C22⋊C4—21no—
482#340C22×C4311yescharacteristic
483#340C22×C4311yescharacteristic
484#336C22×C4311yescharacteristic
485#336C22×C4311yescharacteristic
486C43#2538011yescharacteristic, direct product factor, Sylow
487C22×Q8C23×C4311yescharacteristic
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4C23×C4311yescharacteristic
495C22×D4C23×C4311yescharacteristic
496C22×D4C23×C4311yescharacteristic
497C22×D4C23×C4311yescharacteristic
498C23×C4—21no—
499C23×C4—21no—
500C2×SD16—22no—
501C2×SD16—22no—
502C2×SD16—22no—
503C2×SD16—22no—
504C2×SD16—22no—
505C2×SD16—22no—
506C2×SD16—41no—
507C2×SD16—41no—
508C2×SD16—41no—
509C2×D8—22no—
510C2×D8—22no—
511C2×D8—22no—
512C2×D8—22no—
513C2×D8—22no—
514C2×D8—22no—
515C2×D8—41no—
516C2×D8—41no—
517C2×D8—41no—
518C22×C8C23×C4311yescharacteristic
519C22×C8C23×C4311yescharacteristic
520C22×C8C23×C4311yescharacteristic
521C22×C8C23×C4311yescharacteristic
522#127—22no—
523#127—22no—
524#127—22no—
525#127—22no—
526#127—41no—
527#127—41no—
528#124—22no—
529#124D4×C4314yescomplemented
530#121—44no—
531#121—44no—
532C4×Q8—22no—
533C4×Q8—41no—
534C4×D4—22no—
535C4×D4—22no—
536C4×D4—22no—
537C4×D4—41no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4D4×C4311yescharacteristic
540C2×C4⋊C4D4×C4311yescharacteristic
541C2×C4⋊C4C23×C4311yescharacteristic
542C2×C4⋊C4C23×C4311yescharacteristic
543C2×C4⋊C4C23×C4311yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C42—21no—
555C2×C42—21no—
556C2×C42C23×C4311yescharacteristic
557C2×C42C23×C4311yescharacteristic
558C2×C42C23×C4311yescharacteristic
559C4⋊C8—22no—
560C4⋊C8—22no—
561C4⋊C8—22no—
562#103—22no—
563#102—22no—
564#102—22no—
565#102—22no—
566#102—22no—
567#102—41no—
568#102—41no—
569#102D4×C4314yescomplemented
570#97—22no—
571#95—21no—
572#95—21no—
573#95—21no—
574#95D4×C4311yescharacteristic
575#95D4×C4311yescharacteristic
576C24—21no—
577C24—21no—
578C24—21no—
579C24—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8C2×D4×C4312yes—
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—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—42no—
620C2×D4—81no—
621C2×D4—81no—
622C2×D4—81no—
623C2×D4—81no—
624C2×D4—81no—
625C2×D4—81no—
626C2×D4C2×D4×C4312yes—
627C2×D4C2×D4×C4312yes—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—81no—
638C22×C4C2×D4×C4311yescharacteristic
639C22×C4C2×D4×C4311yescharacteristic
640C22×C4C2×D4×C4311yescharacteristic
641C22×C4C2×D4×C4311yescharacteristic
642C22×C4C2×D4×C4311yescharacteristic
643C22×C4C2×D4×C4311yescharacteristic
644C22×C4C24×C4311yescharacteristic
645SD16—44no—
646SD16—44no—
647SD16—44no—
648D8—44no—
649D8—44no—
650D8—44no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8C2×D4×C4312yes—
662C2×C8#41×C4312yes—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—42no—
671C4⋊C4C2×D4×C4312yes—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—42no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—81no—
682C42—21no—
683C42—21no—
684C42—21no—
685C42—21no—
686C42—42no—
687C42—81no—
688C42C2×D4×C4312yes—
689C42#41×C4312yes—
690C23—22no—
691C23—22no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23C22×D4×C4311yescharacteristic
719Q8—22no—
720Q8—22no—
721Q8—41no—
722Q8—41no—
723D4—22no—
724D4—22no—
725D4—22no—
726D4—22no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—41no—
734D4—41no—
735D4—41no—
736D4—41no—
737D4—41no—
738D4—41no—
739D4—84no—
740D4—84no—
741D4—84no—
742D4—84no—
743D4—84no—
744D4—84no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—84no—
772C2×C4—84no—
773C2×C4#121×C4312yes—
774C2×C4#121×C4312yes—
775C2×C4AGL(1,ℤ/8)×C4312yes—
776C2×C4AGL(1,ℤ/8)×C4312yes—
777C2×C4C22×D4×C4311yescharacteristic
778C2×C4C22×D4×C4311yescharacteristic
779C2×C4C2×#41×C4311yescharacteristic
780C2×C4C2×#41×C4311yescharacteristic
781C2×C4H(5,𝔽2)×C4311yescharacteristic
782C2×C4H(5,𝔽2)×C4311yescharacteristic
783C8—22no—
784C8—22no—
785C8—41no—
786C8—41no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22C2×#121×C4311yescharacteristic
816C22D42×C4311yescharacteristic
817C22C43×#55011yescharacteristic
818C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
819C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
820C22C43×#57611yescharacteristic
821C22C43×#57711yescharacteristic
822C4—22no—
823C4—22no—
824C4—22no—
825C4—22no—
826C4—42no—
827C4—41no—
828C4—42no—
829C4—41no—
830C4—81no—
831C4—81no—
832C4C43×#53211yescharacteristic
833C4C43×#54011yescharacteristic
834C4D42×C4311yescharacteristic
835C4C43×#54611yescharacteristic
836C2—82no—
837C2—82no—
838C2—161no—
839C2—161no—
840C2C43×#242811yescharacteristic
841C2C43×#303811yescharacteristic
842C2C43×#304511yescharacteristic
843C2C43×#326411yescharacteristic
844C2C43×#326511yescharacteristic
845C2C43×#339711yescharacteristic
846C2C43×#339911yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C4×C4⋊C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#496C2semidirect
2. C2×C43×#460C2semidirect
3. C2×C43×#463C2semidirect
4. C2×C43×#459C2semidirect
5. C43×#2541C2semidirect
6. C43×#2367C2semidirect
7. C43×#2055C2semidirect
8. C43×#2054C2semidirect
9. C43×#2014C2semidirect
10. C43×#2011C2semidirect
11. C43×#1982C2semidirect
12. C43×#1940C2semidirect
13. C43×#1880C2semidirect
14. C43×#1879C2semidirect
15. C43×#1762C2semidirect
105. #124×C43D4semidirect
145. #102×C43D4semidirect
363. #25380C43direct (N × H)
413. C2×#496C2×C43semidirect
414. C2×#460C2×C43semidirect
415. C2×#463C2×C43semidirect
416. C2×#459C2×C43semidirect
417. #2541C2×C43semidirect
418. #2367C2×C43semidirect
419. #2055C2×C43semidirect
420. #2054C2×C43semidirect
421. #2014C2×C43semidirect
422. #2011C2×C43semidirect
423. #1982C2×C43semidirect
424. #1940C2×C43semidirect
425. #1880C2×C43semidirect
426. #1879C2×C43semidirect
427. #1762C2×C43semidirect
486. C43#25380direct (N × H)
529. #124D4×C43semidirect
569. #102D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4962
C2×C43×#4602
C2×C43×#4632
C2×C43×#4592
C43×#25412
C43×#23672
C43×#20552
C43×#20542
C43×#20142
C43×#20112
C43×#19822
C43×#19402
C43×#18802
C43×#18792
C43×#17622
#2538043