Finite Group Databasebeta

← C43×#25136 #24945153

Subgroups — C43×#25136 #24945153

Order 11008.

1264 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#468C211yesmaximal, characteristic, complemented
2C2×C43×#450C211yesmaximal, characteristic, complemented
3C2×C43×#436C211yesmaximal, characteristic, complemented
4C2×C43×#418C211yesmaximal, characteristic, complemented
5C43×#2415C211yesmaximal, characteristic, complemented
6C43×#2408C211yesmaximal, characteristic
7C43×#2067C211yesmaximal, characteristic, complemented
8C43×#2055C211yesmaximal, characteristic, complemented
9C43×#2034C211yesmaximal, characteristic, complemented
10C43×#2000C211yesmaximal, characteristic, complemented
11C43×#1968C211yesmaximal, characteristic, complemented
12C43×#1934C211yesmaximal, characteristic, complemented
13C43×#1895C211yesmaximal, characteristic, complemented
14C43×#1894C211yesmaximal, characteristic, complemented
15C43×#1854C211yesmaximal, characteristic, complemented
16C23×D4×C43C2211yescharacteristic
17C22×SD16×C43C2211yescharacteristic
18C22×SD16×C43C2211yescharacteristic
19C22×M16×C43C2211yescharacteristic
20C22×M16×C43C2211yescharacteristic, complemented
21C2×C22⋊Q8×C43C2211yescharacteristic
22C2×C22⋊Q8×C43C2211yescharacteristic, complemented
23C2×#121×C43C2211yescharacteristic
24C2×#121×C43C2211yescharacteristic
25C2×#120×C43—21no—
26C2×C4×D4×C43C2211yescharacteristic
27C2×#117×C43C2211yescharacteristic
28C43×#468—24no—
29C43×#450—24no—
30C43×#436—24no—
31C2×#107×C43C2211yescharacteristic, complemented
32C2×#106×C43C2211yescharacteristic, complemented
33C2×C4⋊C8×C43C2211yescharacteristic, complemented
34C43×#418—24no—
35C2×#103×C43C2211yescharacteristic, complemented
36C2×#103×C43C2211yescharacteristic, complemented
37C2×#102×C43C2211yescharacteristic
38C2×#102×C43C2211yescharacteristic
39C2×#102×C43C2211yescharacteristic
40C2×#102×C43C2211yescharacteristic
41C2×#102×C43C2211yescharacteristic
42C2×#102×C43C2211yescharacteristic
43C2×C22⋊C8×C43C2211yescharacteristic
44C2×C22⋊C8×C43C2211yescharacteristic, complemented
45C2×C4×C8×C43C2211yescharacteristic, complemented
46C43×#397—21no—
47C43×#394—21no—
48C43×#394—21no—
49C43×#392—21no—
50C43×#391C2211yescharacteristic, complemented
51C43×#390C2211yescharacteristic
52C43×#390C2211yescharacteristic
53C43×#389—21no—
54C43×#389C2211yescharacteristic, complemented
55C43×#388—21no—
56C43×#380C2211yescharacteristic
57C43×#380C2211yescharacteristic, complemented
58C43×#379—21no—
59C43×#340C2211yescharacteristic, complemented
60C43×#340C2211yescharacteristic, complemented
61C43×#340C2211yescharacteristic, complemented
62C43×#340C2211yescharacteristic, complemented
63C25×C43—21no—
64C22×Q8×C43C2311yescharacteristic
65C22×D4×C43—22no—
66C22×D4×C43—22no—
67C22×D4×C43—21no—
68C22×D4×C43—21no—
69C22×D4×C43—22no—
70C22×D4×C43—21no—
71C22×D4×C43—22no—
72C22×D4×C43—41no—
73C22×D4×C43—41no—
74C22×D4×C43D411yescharacteristic
75C22×D4×C43C2311yescharacteristic
76C22×D4×C43C2311yescharacteristic
77C23×C4×C43C2311yescharacteristic
78C23×C4×C43C2311yescharacteristic
79C2×SD16×C43—22no—
80C2×SD16×C43—22no—
81C2×SD16×C43—22no—
82C2×SD16×C43—22no—
83C2×SD16×C43—41no—
84C2×SD16×C43—41no—
85C2×M16×C43—22no—
86C2×M16×C43—22no—
87C2×M16×C43—22no—
88C2×M16×C43—22no—
89C2×M16×C43—41no—
90C2×M16×C43—41no—
91C22×C8×C43C2311yescharacteristic
92C22×C8×C43C2311yescharacteristic
93C22×C8×C43C2311yescharacteristic
94C22×C8×C43C2311yescharacteristic
95C22⋊Q8×C43—22no—
96C22⋊Q8×C43—22no—
97C22⋊Q8×C43—22no—
98C22⋊Q8×C43—41no—
99#121×C43—22no—
100#121×C43—22no—
101#121×C43—41no—
102#121×C43—41no—
103#120×C43—44no—
104C4×D4×C43—22no—
105C4×D4×C43—22no—
106#117×C43—22no—
107#117×C43—41no—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43D411yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C22⋊C4×C43—21no—
118C2×C22⋊C4×C43—21no—
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—41no—
134C4⋊C8×C43—22no—
135#103×C43—22no—
136#103×C43—41no—
137#102×C43—22no—
138#102×C43—22no—
139#102×C43—22no—
140#102×C43—22no—
141#102×C43—22no—
142#102×C43D414yescomplemented
143C22⋊C8×C43—22no—
144C22⋊C8×C43D414yescomplemented
145C4×C8×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—42no—
154C24×C43—42no—
155C24×C43—42no—
156C24×C43—42no—
157C24×C43—42no—
158C24×C43—81no—
159C24×C43—81no—
160C24×C43C2×D411yescharacteristic
161C24×C43C2×D411yescharacteristic
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×Q8×C43—21no—
166C2×Q8×C43—21no—
167C2×Q8×C43—21no—
168C2×D4×C43—22no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—22no—
172C2×D4×C43—28no—
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—41no—
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—44no—
189C2×D4×C43—44no—
190C2×D4×C43—44no—
191C2×D4×C43—42no—
192C2×D4×C43—81no—
193C2×D4×C43—81no—
194C2×D4×C43C2×D412yes—
195C2×D4×C43#4112yes—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
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×C43C2×D412yes—
213C22×C4×C43C2×D411yescharacteristic
214C22×C4×C43C2×D411yescharacteristic
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43#4112yes—
218C22×C4×C43C2411yescharacteristic
219SD16×C43—44no—
220SD16×C43—44no—
221M16×C43—44no—
222M16×C43—44no—
223C2×C8×C43—21no—
224C2×C8×C43—21no—
225C2×C8×C43—21no—
226C2×C8×C43—21no—
227C2×C8×C43—21no—
228C2×C8×C43—21no—
229C2×C8×C43—21no—
230C2×C8×C43—21no—
231C2×C8×C43—21no—
232C2×C8×C43C2×D412yes—
233C2×C8×C43C2×D412yes—
234C2×C8×C43C2×D412yes—
235C4⋊C4×C43—22no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43—21no—
238C4⋊C4×C43—21no—
239C4⋊C4×C43—21no—
240C4⋊C4×C43—21no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43—21no—
243C4⋊C4×C43—21no—
244C4⋊C4×C43—21no—
245C4⋊C4×C43—42no—
246C4⋊C4×C43—42no—
247C4⋊C4×C43—42no—
248C4⋊C4×C43C2×D412yes—
249C22⋊C4×C43—22no—
250C22⋊C4×C43—22no—
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—42no—
258C22⋊C4×C43—42no—
259C22⋊C4×C43—42no—
260C22⋊C4×C43—81no—
261C22⋊C4×C43—81no—
262C42×C43—21no—
263C42×C43—21no—
264C42×C43—42no—
265C23×C43—21no—
266C23×C43—21no—
267C23×C43—21no—
268C23×C43—21no—
269C23×C43—21no—
270C23×C43—21no—
271C23×C43—21no—
272C23×C43—21no—
273C23×C43—22no—
274C23×C43—22no—
275C23×C43—21no—
276C23×C43—21no—
277C23×C43—21no—
278C23×C43—21no—
279C23×C43—21no—
280C23×C43—48no—
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—84no—
294C23×C43—84no—
295C23×C43—84no—
296C23×C43—84no—
297C23×C43—84no—
298C23×C43—84no—
299C23×C43#12112yes—
300C23×C43C22×D411yescharacteristic
301Q8×C43—41no—
302Q8×C43—41no—
303Q8×C43—41no—
304Q8×C43—41no—
305D4×C43—22no—
306D4×C43—22no—
307D4×C43—22no—
308D4×C43—22no—
309D4×C43—44no—
310D4×C43—48no—
311D4×C43—41no—
312D4×C43—41no—
313D4×C43—41no—
314D4×C43—41no—
315D4×C43—84no—
316D4×C43—84no—
317C2×C4×C43—21no—
318C2×C4×C43—21no—
319C2×C4×C43—21no—
320C2×C4×C43—21no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—21no—
326C2×C4×C43—21no—
327C2×C4×C43—22no—
328C2×C4×C43—21no—
329C2×C4×C43—21no—
330C2×C4×C43—21no—
331C2×C4×C43—21no—
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—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#12112yes—
354C2×C4×C43AGL(1,ℤ/8)12yes—
355C2×C4×C43C22×D411yescharacteristic
356C2×C4×C43C22×D411yescharacteristic
357C2×C4×C43C2×#4111yescharacteristic
358C2×C4×C43C2×#4111yescharacteristic
359C2×C4×C43H(5,𝔽2)11yescharacteristic
360C2×C4×C43H(5,𝔽2)11yescharacteristic
361C8×C43—22no—
362C8×C43—22no—
363C8×C43—22no—
364C8×C43—41no—
365#25136C4311yesmaximal, characteristic, direct product factor, Sylow
366C22×C43—22no—
367C22×C43—22no—
368C22×C43—22no—
369C22×C43—41no—
370C22×C43—41no—
371C22×C43—41no—
372C22×C43—41no—
373C22×C43—41no—
374C22×C43—42no—
375C22×C43—42no—
376C22×C43—41no—
377C22×C43—42no—
378C22×C43—41no—
379C22×C43—42no—
380C22×C43—41no—
381C22×C43—41no—
382C22×C43—41no—
383C22×C43—42no—
384C22×C43—41no—
385C22×C43—42no—
386C22×C43—816no—
387C22×C43—81no—
388C22×C43—81no—
389C22×C43—81no—
390C22×C43—81no—
391C22×C43—81no—
392C22×C43—81no—
393C22×C43—81no—
394C22×C43—81no—
395C22×C43C2×#12111yescharacteristic
396C22×C43D4211yescharacteristic
397C22×C43#54611yescharacteristic
398C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
399C22×C43#57511yescharacteristic
400C22×C43#57711yescharacteristic
401C22×C43#57711yescharacteristic
402C4×C43—22no—
403C4×C43—22no—
404C4×C43—41no—
405C4×C43—42no—
406C4×C43—41no—
407C4×C43—81no—
408C4×C43—81no—
409C4×C43—81no—
410C4×C43—81no—
411C4×C43—81no—
412C4×C43#52511yescharacteristic
413C4×C43#53811yescharacteristic
414C4×C43D4211yescharacteristic
415C4×C43#54611yescharacteristic
416C2×#468C2×C4311yescharacteristic, complemented
417C2×#450C2×C4311yescharacteristic, complemented
418C2×#436C2×C4311yescharacteristic, complemented
419C2×#418C2×C4311yescharacteristic, complemented
420#2415C2×C4311yescharacteristic, complemented
421#2408C2×C4311yescharacteristic
422#2067C2×C4311yescharacteristic, complemented
423#2055C2×C4311yescharacteristic, complemented
424#2034C2×C4311yescharacteristic, complemented
425#2000C2×C4311yescharacteristic, complemented
426#1968C2×C4311yescharacteristic, complemented
427#1934C2×C4311yescharacteristic, complemented
428#1895C2×C4311yescharacteristic, complemented
429#1894C2×C4311yescharacteristic, complemented
430#1854C2×C4311yescharacteristic, complemented
431C2×C43—42no—
432C2×C43—81no—
433C2×C43—82no—
434C2×C43—82no—
435C2×C43#242411yescharacteristic
436C2×C43#305511yescharacteristic
437C2×C43#305711yescharacteristic
438C2×C43#327211yescharacteristic
439C2×C43#327511yescharacteristic
440C2×C43#332311yescharacteristic
441C2×C43#332411yescharacteristic
442C23×D4C22×C4311yescharacteristic
443C22×SD16C22×C4311yescharacteristic
444C22×SD16C22×C4311yescharacteristic
445C22×M16C22×C4311yescharacteristic
446C22×M16C22×C4311yescharacteristic, complemented
447C2×C22⋊Q8C22×C4311yescharacteristic
448C2×C22⋊Q8C22×C4311yescharacteristic, complemented
449C2×#121C22×C4311yescharacteristic
450C2×#121C22×C4311yescharacteristic
451C2×#120—21no—
452C2×C4×D4C22×C4311yescharacteristic
453C2×#117C22×C4311yescharacteristic
454#468—24no—
455#450—24no—
456#436—24no—
457C2×#107C22×C4311yescharacteristic, complemented
458C2×#106C22×C4311yescharacteristic, complemented
459C2×C4⋊C8C22×C4311yescharacteristic, complemented
460#418—24no—
461C2×#103C22×C4311yescharacteristic, complemented
462C2×#103C22×C4311yescharacteristic, complemented
463C2×#102C22×C4311yescharacteristic
464C2×#102C22×C4311yescharacteristic
465C2×#102C22×C4311yescharacteristic
466C2×#102C22×C4311yescharacteristic
467C2×#102C22×C4311yescharacteristic
468C2×#102C22×C4311yescharacteristic
469C2×C22⋊C8C22×C4311yescharacteristic
470C2×C22⋊C8C22×C4311yescharacteristic, complemented
471C2×C4×C8C22×C4311yescharacteristic, complemented
472#397—21no—
473#394—21no—
474#394—21no—
475#392—21no—
476#391C22×C4311yescharacteristic, complemented
477#390C22×C4311yescharacteristic
478#390C22×C4311yescharacteristic
479#389—21no—
480#389C22×C4311yescharacteristic, complemented
481#388—21no—
482#380C22×C4311yescharacteristic
483#380C22×C4311yescharacteristic, complemented
484#379—21no—
485#340C22×C4311yescharacteristic, complemented
486#340C22×C4311yescharacteristic, complemented
487#340C22×C4311yescharacteristic, complemented
488#340C22×C4311yescharacteristic, complemented
489C43#2513611yescharacteristic, direct product factor, Sylow
490C25—21no—
491C22×Q8C23×C4311yescharacteristic
492C22×D4—22no—
493C22×D4—22no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—22no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4D4×C4311yescharacteristic
502C22×D4C23×C4311yescharacteristic
503C22×D4C23×C4311yescharacteristic
504C23×C4C23×C4311yescharacteristic
505C23×C4C23×C4311yescharacteristic
506C2×SD16—22no—
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—41no—
511C2×SD16—41no—
512C2×M16—22no—
513C2×M16—22no—
514C2×M16—22no—
515C2×M16—22no—
516C2×M16—41no—
517C2×M16—41no—
518C22×C8C23×C4311yescharacteristic
519C22×C8C23×C4311yescharacteristic
520C22×C8C23×C4311yescharacteristic
521C22×C8C23×C4311yescharacteristic
522C22⋊Q8—22no—
523C22⋊Q8—22no—
524C22⋊Q8—22no—
525C22⋊Q8—41no—
526#121—22no—
527#121—22no—
528#121—41no—
529#121—41no—
530#120—44no—
531C4×D4—22no—
532C4×D4—22no—
533#117—22no—
534#117—41no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4D4×C4311yescharacteristic
539C2×C4⋊C4C23×C4311yescharacteristic
540C2×C4⋊C4C23×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×C22⋊C4—21no—
555C2×C22⋊C4D4×C4311yescharacteristic
556C2×C22⋊C4D4×C4311yescharacteristic
557C2×C42—21no—
558C2×C42C23×C4311yescharacteristic
559#107—22no—
560#106—41no—
561C4⋊C8—22no—
562#103—22no—
563#103—41no—
564#102—22no—
565#102—22no—
566#102—22no—
567#102—22no—
568#102—22no—
569#102D4×C4314yescomplemented
570C22⋊C8—22no—
571C22⋊C8D4×C4314yescomplemented
572C4×C8—22no—
573#95—21no—
574#95—21no—
575#95—21no—
576#95—21no—
577#95—21no—
578C24—21no—
579C24—21no—
580C24—42no—
581C24—42no—
582C24—42no—
583C24—42no—
584C24—42no—
585C24—81no—
586C24—81no—
587C24C2×D4×C4311yescharacteristic
588C24C2×D4×C4311yescharacteristic
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×D4—28no—
596C2×D4—22no—
597C2×D4—22no—
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—44no—
609C2×D4—44no—
610C2×D4—41no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—44no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4—81no—
621C2×D4C2×D4×C4312yes—
622C2×D4#41×C4312yes—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4C2×D4×C4311yescharacteristic
640C22×C4C2×D4×C4311yescharacteristic
641C22×C4C2×D4×C4311yescharacteristic
642C22×C4C2×D4×C4312yes—
643C22×C4C2×D4×C4311yescharacteristic
644C22×C4#41×C4312yes—
645C22×C4C24×C4311yescharacteristic
646SD16—44no—
647SD16—44no—
648M16—44no—
649M16—44no—
650C2×C8—21no—
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×C8C2×D4×C4312yes—
660C2×C8C2×D4×C4312yes—
661C2×C8C2×D4×C4312yes—
662C4⋊C4—22no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4C2×D4×C4312yes—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—81no—
688C22⋊C4—81no—
689C42—21no—
690C42—21no—
691C42—42no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—22no—
701C23—22no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—48no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—84no—
721C23—84no—
722C23—84no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23#121×C4312yes—
727C23C22×D4×C4311yescharacteristic
728Q8—41no—
729Q8—41no—
730Q8—41no—
731Q8—41no—
732D4—22no—
733D4—22no—
734D4—22no—
735D4—22no—
736D4—44no—
737D4—48no—
738D4—41no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—84no—
743D4—84no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—41no—
760C2×C4—41no—
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—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4#121×C4312yes—
781C2×C4AGL(1,ℤ/8)×C4312yes—
782C2×C4C22×D4×C4311yescharacteristic
783C2×C4C22×D4×C4311yescharacteristic
784C2×C4C2×#41×C4311yescharacteristic
785C2×C4C2×#41×C4311yescharacteristic
786C2×C4H(5,𝔽2)×C4311yescharacteristic
787C2×C4H(5,𝔽2)×C4311yescharacteristic
788C8—22no—
789C8—22no—
790C8—22no—
791C8—41no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—42no—
801C22—42no—
802C22—41no—
803C22—42no—
804C22—41no—
805C22—42no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—42no—
810C22—41no—
811C22—42no—
812C22—816no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22C2×#121×C4311yescharacteristic
822C22D42×C4311yescharacteristic
823C22C43×#54611yescharacteristic
824C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
825C22C43×#57511yescharacteristic
826C22C43×#57711yescharacteristic
827C22C43×#57711yescharacteristic
828C4—22no—
829C4—22no—
830C4—41no—
831C4—42no—
832C4—41no—
833C4—81no—
834C4—81no—
835C4—81no—
836C4—81no—
837C4—81no—
838C4C43×#52511yescharacteristic
839C4C43×#53811yescharacteristic
840C4D42×C4311yescharacteristic
841C4C43×#54611yescharacteristic
842C2—42no—
843C2—81no—
844C2—82no—
845C2—82no—
846C2C43×#242411yescharacteristic
847C2C43×#305511yescharacteristic
848C2C43×#305711yescharacteristic
849C2C43×#327211yescharacteristic
850C2C43×#327511yescharacteristic
851C2C43×#332311yescharacteristic
852C2C43×#332411yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC43×#2408C2
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×#468C2semidirect
2. C2×C43×#450C2semidirect
3. C2×C43×#436C2semidirect
4. C2×C43×#418C2semidirect
5. C43×#2415C2semidirect
7. C43×#2067C2semidirect
8. C43×#2055C2semidirect
9. C43×#2034C2semidirect
10. C43×#2000C2semidirect
11. C43×#1968C2semidirect
12. C43×#1934C2semidirect
13. C43×#1895C2semidirect
14. C43×#1894C2semidirect
15. C43×#1854C2semidirect
20. C22×M16×C43C22semidirect
22. C2×C22⋊Q8×C43C22semidirect
31. C2×#107×C43C22semidirect
32. C2×#106×C43C22semidirect
33. C2×C4⋊C8×C43C22semidirect
35. C2×#103×C43C22semidirect
36. C2×#103×C43C22semidirect
44. C2×C22⋊C8×C43C22semidirect
45. C2×C4×C8×C43C22semidirect
50. C43×#391C22semidirect
54. C43×#389C22semidirect
57. C43×#380C22semidirect
59. C43×#340C22semidirect
60. C43×#340C22semidirect
61. C43×#340C22semidirect
62. C43×#340C22semidirect
142. #102×C43D4semidirect
144. C22⋊C8×C43D4semidirect
365. #25136C43direct (N × H)
416. C2×#468C2×C43semidirect
417. C2×#450C2×C43semidirect
418. C2×#436C2×C43semidirect
419. C2×#418C2×C43semidirect
420. #2415C2×C43semidirect
422. #2067C2×C43semidirect
423. #2055C2×C43semidirect
424. #2034C2×C43semidirect
425. #2000C2×C43semidirect
426. #1968C2×C43semidirect
427. #1934C2×C43semidirect
428. #1895C2×C43semidirect
429. #1894C2×C43semidirect
430. #1854C2×C43semidirect
446. C22×M16C22×C43semidirect
448. C2×C22⋊Q8C22×C43semidirect
457. C2×#107C22×C43semidirect
458. C2×#106C22×C43semidirect
459. C2×C4⋊C8C22×C43semidirect
461. C2×#103C22×C43semidirect
462. C2×#103C22×C43semidirect
470. C2×C22⋊C8C22×C43semidirect
471. C2×C4×C8C22×C43semidirect
476. #391C22×C43semidirect
480. #389C22×C43semidirect
483. #380C22×C43semidirect
485. #340C22×C43semidirect
486. #340C22×C43semidirect
487. #340C22×C43semidirect
488. #340C22×C43semidirect
489. C43#25136direct (N × H)
569. #102D4×C43semidirect
571. C22⋊C8D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4682
C2×C43×#4502
C2×C43×#4362
C2×C43×#4182
C43×#24152
C43×#24082
C43×#20672
C43×#20552
C43×#20342
C43×#20002
C43×#19682
C43×#19342
C43×#18952
C43×#18942
C43×#18542
#2513643