Finite Group Databasebeta

← C43×#29600 #24949617

Subgroups — C43×#29600 #24949617

Order 11008.

1540 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#525C211yesmaximal, characteristic, complemented
2C2×C43×#482C211yesmaximal, characteristic, complemented
3C2×C43×#449C211yesmaximal, characteristic, complemented
4C43×#2847C211yesmaximal, characteristic, complemented
5C43×#2036C211yesmaximal, characteristic, complemented
6C43×#2035C211yesmaximal, characteristic, complemented
7C43×#2034C211yesmaximal, characteristic, complemented
8C43×#2033C211yesmaximal, characteristic, complemented
9C43×#2000C211yesmaximal, characteristic, complemented
10C43×#2000C211yesmaximal, characteristic, complemented
11C43×#1999C211yesmaximal, characteristic, complemented
12C43×#1999C211yesmaximal, characteristic, complemented
13C43×#1825C211yesmaximal, characteristic, complemented
14C43×#1788C211yesmaximal, characteristic, complemented
15C43×#1779C211yesmaximal, characteristic, complemented
16C22×#41×C43C2211yescharacteristic
17C24×C4×C43C2211yescharacteristic
18C22×SD16×C43C2211yescharacteristic, complemented
19C22×D8×C43C2211yescharacteristic, complemented
20C43×#525—24no—
21C43×#525—24no—
22C2×#123×C43—21no—
23C2×C22⋊Q8×C43C2211yescharacteristic
24C2×C22⋊Q8×C43C2211yescharacteristic
25C2×#121×C43C2211yescharacteristic
26C2×#121×C43C2211yescharacteristic
27C2×#121×C43C2211yescharacteristic
28C2×#121×C43C2211yescharacteristic
29C2×#121×C43C2211yescharacteristic
30C2×#120×C43—21no—
31C2×#120×C43—21no—
32C2×C4×D4×C43—21no—
33C2×C4×D4×C43—21no—
34C2×#117×C43C2211yescharacteristic
35C43×#482—24no—
36C43×#449—24no—
37C2×#107×C43C2211yescharacteristic, complemented
38C2×#106×C43C2211yescharacteristic, complemented
39C2×#103×C43C2211yescharacteristic, complemented
40C2×#103×C43C2211yescharacteristic, complemented
41C2×#103×C43C2211yescharacteristic, complemented
42C2×#102×C43C2211yescharacteristic, complemented
43C2×#102×C43C2211yescharacteristic, complemented
44C2×#102×C43C2211yescharacteristic, complemented
45C2×#102×C43C2211yescharacteristic, complemented
46C2×#102×C43C2211yescharacteristic, complemented
47C2×C22⋊C8×C43C2211yescharacteristic
48C2×C22⋊C8×C43C2211yescharacteristic
49C2×C22⋊C8×C43C2211yescharacteristic
50C2×C22⋊C8×C43C2211yescharacteristic
51C2×C22⋊C8×C43C2211yescharacteristic
52C2×C22⋊C8×C43C2211yescharacteristic
53C43×#386—21no—
54C43×#386—21no—
55C43×#386—21no—
56C43×#380C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#380C2211yescharacteristic
59C43×#340C2211yescharacteristic, complemented
60C43×#340C2211yescharacteristic, complemented
61C43×#340C2211yescharacteristic, complemented
62C43×#340C2211yescharacteristic, complemented
63C25×C43D411yescharacteristic
64C2×#41×C43—22no—
65C2×#41×C43—41no—
66C2×#41×C43—41no—
67C2×#41×C43—41no—
68C2×#41×C43—41no—
69C2×#41×C43D414yescomplemented
70C22×Q8×C43C2311yescharacteristic
71C22×D4×C43—21no—
72C22×D4×C43—21no—
73C22×D4×C43—21no—
74C22×D4×C43—21no—
75C22×D4×C43—21no—
76C22×D4×C43—21no—
77C22×D4×C43C2311yescharacteristic
78C22×D4×C43C2311yescharacteristic
79C23×C4×C43—21no—
80C23×C4×C43—22no—
81C23×C4×C43—22no—
82C23×C4×C43—41no—
83C23×C4×C43—41no—
84C23×C4×C43—41no—
85C23×C4×C43—41no—
86C23×C4×C43D411yescharacteristic
87C23×C4×C43D411yescharacteristic
88C23×C4×C43D411yescharacteristic
89C23×C4×C43C2311yescharacteristic
90C23×C4×C43C2311yescharacteristic
91C23×C4×C43C2311yescharacteristic
92C2×SD16×C43—22no—
93C2×SD16×C43—41no—
94C2×SD16×C43—41no—
95C2×D8×C43—22no—
96C2×D8×C43—41no—
97C2×D8×C43—41no—
98C22×C8×C43C2311yescharacteristic
99C22×C8×C43C2311yescharacteristic
100C22×C8×C43C2311yescharacteristic
101C22×C8×C43C2311yescharacteristic
102#123×C43—28no—
103C22⋊Q8×C43—22no—
104C22⋊Q8×C43—22no—
105C22⋊Q8×C43—22no—
106C22⋊Q8×C43—22no—
107#121×C43—22no—
108#121×C43—22no—
109#121×C43—22no—
110#121×C43—22no—
111#121×C43—22no—
112#121×C43—22no—
113#121×C43—41no—
114#121×C43—41no—
115#121×C43—41no—
116#121×C43—41no—
117#120×C43—28no—
118#120×C43—44no—
119C4×D4×C43—28no—
120C4×D4×C43—28no—
121#117×C43—22no—
122#117×C43D414yescomplemented
123C2×C4⋊C4×C43—21no—
124C2×C4⋊C4×C43—21no—
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43—21no—
132C2×C22⋊C4×C43—21no—
133C2×C22⋊C4×C43—21no—
134C2×C22⋊C4×C43—21no—
135C2×C22⋊C4×C43—21no—
136C2×C22⋊C4×C43—21no—
137C2×C22⋊C4×C43—21no—
138C2×C22⋊C4×C43—21no—
139C2×C22⋊C4×C43—21no—
140C2×C22⋊C4×C43—21no—
141C2×C42×C43—21no—
142#107×C43—22no—
143#106×C43—22no—
144#103×C43—22no—
145#103×C43—41no—
146#103×C43—41no—
147#102×C43—22no—
148#102×C43—22no—
149#102×C43—22no—
150#102×C43—41no—
151#102×C43—41no—
152C22⋊C8×C43—22no—
153C22⋊C8×C43—22no—
154C22⋊C8×C43—41no—
155C22⋊C8×C43—41no—
156C22⋊C8×C43—41no—
157C22⋊C8×C43—41no—
158#95×C43—21no—
159#95×C43—21no—
160#95×C43—21no—
161C24×C43—22no—
162C24×C43—22no—
163C24×C43—22no—
164C24×C43—21no—
165C24×C43—21no—
166C24×C43—41no—
167C24×C43—41no—
168C24×C43—41no—
169C24×C43—41no—
170C24×C43C2×D411yescharacteristic
171C24×C43C2×D411yescharacteristic
172C24×C43C2×D411yescharacteristic
173#41×C43—44no—
174#41×C43—44no—
175#41×C43—44no—
176#41×C43—44no—
177C2×Q8×C43—21no—
178C2×Q8×C43—21no—
179C2×Q8×C43—21no—
180C2×Q8×C43—21no—
181C2×Q8×C43—21no—
182C2×Q8×C43C2×D412yes—
183C2×D4×C43—24no—
184C2×D4×C43—24no—
185C2×D4×C43—21no—
186C2×D4×C43—24no—
187C2×D4×C43—21no—
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—42no—
198C2×D4×C43—42no—
199C2×D4×C43—42no—
200C2×D4×C43—42no—
201C2×D4×C43—42no—
202C2×D4×C43—42no—
203C2×D4×C43—42no—
204C2×D4×C43—42no—
205C2×D4×C43—42no—
206C2×D4×C43—42no—
207C2×D4×C43—42no—
208C2×D4×C43—42no—
209C2×D4×C43—42no—
210C2×D4×C43—42no—
211C2×D4×C43—42no—
212C2×D4×C43C2×D412yes—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—22no—
218C22×C4×C43—22no—
219C22×C4×C43—24no—
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43—21no—
228C22×C4×C43—21no—
229C22×C4×C43—21no—
230C22×C4×C43—21no—
231C22×C4×C43—21no—
232C22×C4×C43—22no—
233C22×C4×C43—21no—
234C22×C4×C43—21no—
235C22×C4×C43—21no—
236C22×C4×C43—21no—
237C22×C4×C43—21no—
238C22×C4×C43—21no—
239C22×C4×C43—41no—
240C22×C4×C43—41no—
241C22×C4×C43—41no—
242C22×C4×C43—41no—
243C22×C4×C43—41no—
244C22×C4×C43—41no—
245C22×C4×C43—44no—
246C22×C4×C43—44no—
247C22×C4×C43—44no—
248C22×C4×C43—44no—
249C22×C4×C43—42no—
250C22×C4×C43—42no—
251C22×C4×C43C2×D412yes—
252C22×C4×C43C2×D412yes—
253C22×C4×C43C2×D411yescharacteristic
254C22×C4×C43C2×D411yescharacteristic
255C22×C4×C43C2×D411yescharacteristic
256C22×C4×C43C2411yescharacteristic
257SD16×C43—44no—
258D8×C43—44no—
259C2×C8×C43—21no—
260C2×C8×C43—21no—
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—
271C4⋊C4×C43—24no—
272C4⋊C4×C43—24no—
273C4⋊C4×C43—21no—
274C4⋊C4×C43—21no—
275C4⋊C4×C43—21no—
276C4⋊C4×C43—21no—
277C4⋊C4×C43—21no—
278C4⋊C4×C43—21no—
279C4⋊C4×C43—21no—
280C4⋊C4×C43—21no—
281C4⋊C4×C43C2×D412yes—
282C4⋊C4×C43C2×D412yes—
283C22⋊C4×C43—24no—
284C22⋊C4×C43—24no—
285C22⋊C4×C43—24no—
286C22⋊C4×C43—24no—
287C22⋊C4×C43—24no—
288C22⋊C4×C43—42no—
289C22⋊C4×C43—42no—
290C22⋊C4×C43—42no—
291C22⋊C4×C43—42no—
292C22⋊C4×C43—42no—
293C22⋊C4×C43—42no—
294C42×C43—24no—
295C23×C43—21no—
296C23×C43—21no—
297C23×C43—21no—
298C23×C43—21no—
299C23×C43—21no—
300C23×C43—21no—
301C23×C43—21no—
302C23×C43—21no—
303C23×C43—21no—
304C23×C43—21no—
305C23×C43—21no—
306C23×C43—21no—
307C23×C43—21no—
308C23×C43—21no—
309C23×C43—21no—
310C23×C43—21no—
311C23×C43—21no—
312C23×C43—21no—
313C23×C43—22no—
314C23×C43—44no—
315C23×C43—44no—
316C23×C43—44no—
317C23×C43—44no—
318C23×C43—44no—
319C23×C43—44no—
320C23×C43—44no—
321C23×C43—41no—
322C23×C43—41no—
323C23×C43—41no—
324C23×C43—41no—
325C23×C43—41no—
326C23×C43—41no—
327C23×C43—41no—
328C23×C43—41no—
329C23×C43—41no—
330C23×C43—41no—
331C23×C43—41no—
332C23×C43—41no—
333C23×C43—41no—
334C23×C43#12012yes—
335C23×C43#13512yes—
336C23×C43AGL(1,ℤ/8)12yes—
337C23×C43C22×D411yescharacteristic
338Q8×C43—22no—
339Q8×C43—22no—
340Q8×C43—41no—
341Q8×C43—41no—
342D4×C43—22no—
343D4×C43—22no—
344D4×C43—48no—
345D4×C43—48no—
346D4×C43—48no—
347D4×C43—41no—
348D4×C43—41no—
349D4×C43—41no—
350D4×C43—41no—
351D4×C43—41no—
352D4×C43—41no—
353D4×C43—84no—
354D4×C43—84no—
355D4×C43—84no—
356C2×C4×C43—21no—
357C2×C4×C43—21no—
358C2×C4×C43—22no—
359C2×C4×C43—22no—
360C2×C4×C43—22no—
361C2×C4×C43—22no—
362C2×C4×C43—22no—
363C2×C4×C43—22no—
364C2×C4×C43—21no—
365C2×C4×C43—21no—
366C2×C4×C43—22no—
367C2×C4×C43—21no—
368C2×C4×C43—21no—
369C2×C4×C43—21no—
370C2×C4×C43—21no—
371C2×C4×C43—44no—
372C2×C4×C43—44no—
373C2×C4×C43—48no—
374C2×C4×C43—44no—
375C2×C4×C43—41no—
376C2×C4×C43—41no—
377C2×C4×C43—41no—
378C2×C4×C43—41no—
379C2×C4×C43—41no—
380C2×C4×C43—41no—
381C2×C4×C43—41no—
382C2×C4×C43—41no—
383C2×C4×C43—41no—
384C2×C4×C43—41no—
385C2×C4×C43—41no—
386C2×C4×C43—41no—
387C2×C4×C43—41no—
388C2×C4×C43—41no—
389C2×C4×C43—41no—
390C2×C4×C43—41no—
391C2×C4×C43—41no—
392C2×C4×C43—41no—
393C2×C4×C43—41no—
394C2×C4×C43—41no—
395C2×C4×C43—41no—
396C2×C4×C43—41no—
397C2×C4×C43—41no—
398C2×C4×C43#12012yes—
399C2×C4×C43C22×D411yescharacteristic
400C2×C4×C43C22×D411yescharacteristic
401C2×C4×C43H(5,𝔽2)11yescharacteristic
402C2×C4×C43H(5,𝔽2)11yescharacteristic
403C2×C4×C43H(5,𝔽2)11yescharacteristic
404C2×C4×C43H(5,𝔽2)11yescharacteristic
405C8×C43—41no—
406C8×C43—41no—
407C8×C43—41no—
408C8×C43—41no—
409#29600C4311yesmaximal, characteristic, direct product factor, Sylow
410C22×C43—22no—
411C22×C43—22no—
412C22×C43—22no—
413C22×C43—22no—
414C22×C43—22no—
415C22×C43—22no—
416C22×C43—22no—
417C22×C43—22no—
418C22×C43—22no—
419C22×C43—416no—
420C22×C43—41no—
421C22×C43—41no—
422C22×C43—41no—
423C22×C43—41no—
424C22×C43—41no—
425C22×C43—41no—
426C22×C43—41no—
427C22×C43—41no—
428C22×C43—41no—
429C22×C43—41no—
430C22×C43—41no—
431C22×C43—41no—
432C22×C43—42no—
433C22×C43—42no—
434C22×C43—42no—
435C22×C43—81no—
436C22×C43—81no—
437C22×C43—81no—
438C22×C43—81no—
439C22×C43—81no—
440C22×C43—81no—
441C22×C43—81no—
442C22×C43—81no—
443C22×C43—81no—
444C22×C43—81no—
445C22×C43—81no—
446C22×C43C2×#12011yescharacteristic
447C22×C43#53411yescharacteristic
448C22×C43#53411yescharacteristic
449C22×C43C2×#13511yescharacteristic
450C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
451C22×C43#57511yescharacteristic
452C22×C43#57511yescharacteristic
453C4×C43—22no—
454C4×C43—41no—
455C4×C43—41no—
456C4×C43—42no—
457C4×C43—42no—
458C4×C43—42no—
459C4×C43—81no—
460C4×C43—81no—
461C4×C43—81no—
462C4×C43#53411yescharacteristic
463C4×C43#53411yescharacteristic
464C4×C43#53511yescharacteristic
465C4×C43#53511yescharacteristic
466C2×#525C2×C4311yescharacteristic, complemented
467C2×#482C2×C4311yescharacteristic, complemented
468C2×#449C2×C4311yescharacteristic, complemented
469#2847C2×C4311yescharacteristic, complemented
470#2036C2×C4311yescharacteristic, complemented
471#2035C2×C4311yescharacteristic, complemented
472#2034C2×C4311yescharacteristic, complemented
473#2033C2×C4311yescharacteristic, complemented
474#2000C2×C4311yescharacteristic, complemented
475#2000C2×C4311yescharacteristic, complemented
476#1999C2×C4311yescharacteristic, complemented
477#1999C2×C4311yescharacteristic, complemented
478#1825C2×C4311yescharacteristic, complemented
479#1788C2×C4311yescharacteristic, complemented
480#1779C2×C4311yescharacteristic, complemented
481C2×C43—42no—
482C2×C43—42no—
483C2×C43—42no—
484C2×C43—82no—
485C2×C43—161no—
486C2×C43#261311yescharacteristic
487C2×C43#300211yescharacteristic
488C2×C43#300611yescharacteristic
489C2×C43#318811yescharacteristic
490C2×C43#319111yescharacteristic
491C2×C43#319411yescharacteristic
492C2×C43#319711yescharacteristic
493C22×#41C22×C4311yescharacteristic
494C24×C4C22×C4311yescharacteristic
495C22×SD16C22×C4311yescharacteristic, complemented
496C22×D8C22×C4311yescharacteristic, complemented
497#525—24no—
498#525—24no—
499C2×#123—21no—
500C2×C22⋊Q8C22×C4311yescharacteristic
501C2×C22⋊Q8C22×C4311yescharacteristic
502C2×#121C22×C4311yescharacteristic
503C2×#121C22×C4311yescharacteristic
504C2×#121C22×C4311yescharacteristic
505C2×#121C22×C4311yescharacteristic
506C2×#121C22×C4311yescharacteristic
507C2×#120—21no—
508C2×#120—21no—
509C2×C4×D4—21no—
510C2×C4×D4—21no—
511C2×#117C22×C4311yescharacteristic
512#482—24no—
513#449—24no—
514C2×#107C22×C4311yescharacteristic, complemented
515C2×#106C22×C4311yescharacteristic, complemented
516C2×#103C22×C4311yescharacteristic, complemented
517C2×#103C22×C4311yescharacteristic, complemented
518C2×#103C22×C4311yescharacteristic, complemented
519C2×#102C22×C4311yescharacteristic, complemented
520C2×#102C22×C4311yescharacteristic, complemented
521C2×#102C22×C4311yescharacteristic, complemented
522C2×#102C22×C4311yescharacteristic, complemented
523C2×#102C22×C4311yescharacteristic, complemented
524C2×C22⋊C8C22×C4311yescharacteristic
525C2×C22⋊C8C22×C4311yescharacteristic
526C2×C22⋊C8C22×C4311yescharacteristic
527C2×C22⋊C8C22×C4311yescharacteristic
528C2×C22⋊C8C22×C4311yescharacteristic
529C2×C22⋊C8C22×C4311yescharacteristic
530#386—21no—
531#386—21no—
532#386—21no—
533#380C22×C4311yescharacteristic
534#380C22×C4311yescharacteristic
535#380C22×C4311yescharacteristic
536#340C22×C4311yescharacteristic, complemented
537#340C22×C4311yescharacteristic, complemented
538#340C22×C4311yescharacteristic, complemented
539#340C22×C4311yescharacteristic, complemented
540C43#2960011yescharacteristic, direct product factor, Sylow
541C25D4×C4311yescharacteristic
542C2×#41—22no—
543C2×#41—41no—
544C2×#41—41no—
545C2×#41—41no—
546C2×#41—41no—
547C2×#41D4×C4314yescomplemented
548C22×Q8C23×C4311yescharacteristic
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—21no—
554C22×D4—21no—
555C22×D4C23×C4311yescharacteristic
556C22×D4C23×C4311yescharacteristic
557C23×C4—21no—
558C23×C4—22no—
559C23×C4—22no—
560C23×C4—41no—
561C23×C4—41no—
562C23×C4—41no—
563C23×C4—41no—
564C23×C4D4×C4311yescharacteristic
565C23×C4D4×C4311yescharacteristic
566C23×C4D4×C4311yescharacteristic
567C23×C4C23×C4311yescharacteristic
568C23×C4C23×C4311yescharacteristic
569C23×C4C23×C4311yescharacteristic
570C2×SD16—22no—
571C2×SD16—41no—
572C2×SD16—41no—
573C2×D8—22no—
574C2×D8—41no—
575C2×D8—41no—
576C22×C8C23×C4311yescharacteristic
577C22×C8C23×C4311yescharacteristic
578C22×C8C23×C4311yescharacteristic
579C22×C8C23×C4311yescharacteristic
580#123—28no—
581C22⋊Q8—22no—
582C22⋊Q8—22no—
583C22⋊Q8—22no—
584C22⋊Q8—22no—
585#121—22no—
586#121—22no—
587#121—22no—
588#121—22no—
589#121—22no—
590#121—22no—
591#121—41no—
592#121—41no—
593#121—41no—
594#121—41no—
595#120—28no—
596#120—44no—
597C4×D4—28no—
598C4×D4—28no—
599#117—22no—
600#117D4×C4314yescomplemented
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4C23×C4311yescharacteristic
604C2×C4⋊C4C23×C4311yescharacteristic
605C2×C4⋊C4C23×C4311yescharacteristic
606C2×C4⋊C4C23×C4311yescharacteristic
607C2×C4⋊C4C23×C4311yescharacteristic
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C42—21no—
620#107—22no—
621#106—22no—
622#103—22no—
623#103—41no—
624#103—41no—
625#102—22no—
626#102—22no—
627#102—22no—
628#102—41no—
629#102—41no—
630C22⋊C8—22no—
631C22⋊C8—22no—
632C22⋊C8—41no—
633C22⋊C8—41no—
634C22⋊C8—41no—
635C22⋊C8—41no—
636#95—21no—
637#95—21no—
638#95—21no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—21no—
643C24—21no—
644C24—41no—
645C24—41no—
646C24—41no—
647C24—41no—
648C24C2×D4×C4311yescharacteristic
649C24C2×D4×C4311yescharacteristic
650C24C2×D4×C4311yescharacteristic
651#41—44no—
652#41—44no—
653#41—44no—
654#41—44no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8C2×D4×C4312yes—
661C2×D4—24no—
662C2×D4—24no—
663C2×D4—24no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—42no—
676C2×D4—42no—
677C2×D4—42no—
678C2×D4—42no—
679C2×D4—42no—
680C2×D4—42no—
681C2×D4—42no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—42no—
685C2×D4—42no—
686C2×D4—42no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4C2×D4×C4312yes—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—22no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—24no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—41no—
718C22×C4—41no—
719C22×C4—41no—
720C22×C4—41no—
721C22×C4—41no—
722C22×C4—41no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4—44no—
726C22×C4—44no—
727C22×C4—42no—
728C22×C4—42no—
729C22×C4C2×D4×C4311yescharacteristic
730C22×C4C2×D4×C4311yescharacteristic
731C22×C4C2×D4×C4311yescharacteristic
732C22×C4C2×D4×C4312yes—
733C22×C4C2×D4×C4312yes—
734C22×C4C24×C4311yescharacteristic
735SD16—44no—
736D8—44no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C4⋊C4—24no—
750C4⋊C4—24no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4C2×D4×C4312yes—
760C4⋊C4C2×D4×C4312yes—
761C22⋊C4—24no—
762C22⋊C4—24no—
763C22⋊C4—24no—
764C22⋊C4—24no—
765C22⋊C4—24no—
766C22⋊C4—42no—
767C22⋊C4—42no—
768C22⋊C4—42no—
769C22⋊C4—42no—
770C22⋊C4—42no—
771C22⋊C4—42no—
772C42—24no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—22no—
792C23—44no—
793C23—44no—
794C23—44no—
795C23—44no—
796C23—44no—
797C23—44no—
798C23—44no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23#120×C4312yes—
813C23#135×C4312yes—
814C23AGL(1,ℤ/8)×C4312yes—
815C23C22×D4×C4311yescharacteristic
816Q8—22no—
817Q8—22no—
818Q8—41no—
819Q8—41no—
820D4—22no—
821D4—22no—
822D4—48no—
823D4—48no—
824D4—48no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—41no—
831D4—84no—
832D4—84no—
833D4—84no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—22no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—44no—
850C2×C4—44no—
851C2×C4—48no—
852C2×C4—44no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4#120×C4312yes—
877C2×C4C22×D4×C4311yescharacteristic
878C2×C4C22×D4×C4311yescharacteristic
879C2×C4H(5,𝔽2)×C4311yescharacteristic
880C2×C4H(5,𝔽2)×C4311yescharacteristic
881C2×C4H(5,𝔽2)×C4311yescharacteristic
882C2×C4H(5,𝔽2)×C4311yescharacteristic
883C8—41no—
884C8—41no—
885C8—41no—
886C8—41no—
887C22—22no—
888C22—22no—
889C22—22no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—416no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22C2×#120×C4311yescharacteristic
924C22C43×#53411yescharacteristic
925C22C43×#53411yescharacteristic
926C22C2×#135×C4311yescharacteristic
927C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
928C22C43×#57511yescharacteristic
929C22C43×#57511yescharacteristic
930C4—22no—
931C4—41no—
932C4—41no—
933C4—42no—
934C4—42no—
935C4—42no—
936C4—81no—
937C4—81no—
938C4—81no—
939C4C43×#53411yescharacteristic
940C4C43×#53411yescharacteristic
941C4C43×#53511yescharacteristic
942C4C43×#53511yescharacteristic
943C2—42no—
944C2—42no—
945C2—42no—
946C2—82no—
947C2—161no—
948C2C43×#261311yescharacteristic
949C2C43×#300211yescharacteristic
950C2C43×#300611yescharacteristic
951C2C43×#318811yescharacteristic
952C2C43×#319111yescharacteristic
953C2C43×#319411yescharacteristic
954C2C43×#319711yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C24×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#525C2semidirect
2. C2×C43×#482C2semidirect
3. C2×C43×#449C2semidirect
4. C43×#2847C2semidirect
5. C43×#2036C2semidirect
6. C43×#2035C2semidirect
7. C43×#2034C2semidirect
8. C43×#2033C2semidirect
9. C43×#2000C2semidirect
10. C43×#2000C2semidirect
11. C43×#1999C2semidirect
12. C43×#1999C2semidirect
13. C43×#1825C2semidirect
14. C43×#1788C2semidirect
15. C43×#1779C2semidirect
18. C22×SD16×C43C22semidirect
19. C22×D8×C43C22semidirect
37. C2×#107×C43C22semidirect
38. C2×#106×C43C22semidirect
39. C2×#103×C43C22semidirect
40. C2×#103×C43C22semidirect
41. C2×#103×C43C22semidirect
42. C2×#102×C43C22semidirect
43. C2×#102×C43C22semidirect
44. C2×#102×C43C22semidirect
45. C2×#102×C43C22semidirect
46. C2×#102×C43C22semidirect
59. C43×#340C22semidirect
60. C43×#340C22semidirect
61. C43×#340C22semidirect
62. C43×#340C22semidirect
69. C2×#41×C43D4semidirect
122. #117×C43D4semidirect
409. #29600C43direct (N × H)
466. C2×#525C2×C43semidirect
467. C2×#482C2×C43semidirect
468. C2×#449C2×C43semidirect
469. #2847C2×C43semidirect
470. #2036C2×C43semidirect
471. #2035C2×C43semidirect
472. #2034C2×C43semidirect
473. #2033C2×C43semidirect
474. #2000C2×C43semidirect
475. #2000C2×C43semidirect
476. #1999C2×C43semidirect
477. #1999C2×C43semidirect
478. #1825C2×C43semidirect
479. #1788C2×C43semidirect
480. #1779C2×C43semidirect
495. C22×SD16C22×C43semidirect
496. C22×D8C22×C43semidirect
514. C2×#107C22×C43semidirect
515. C2×#106C22×C43semidirect
516. C2×#103C22×C43semidirect
517. C2×#103C22×C43semidirect
518. C2×#103C22×C43semidirect
519. C2×#102C22×C43semidirect
520. C2×#102C22×C43semidirect
521. C2×#102C22×C43semidirect
522. C2×#102C22×C43semidirect
523. C2×#102C22×C43semidirect
536. #340C22×C43semidirect
537. #340C22×C43semidirect
538. #340C22×C43semidirect
539. #340C22×C43semidirect
540. C43#29600direct (N × H)
547. C2×#41D4×C43semidirect
600. #117D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#5252
C2×C43×#4822
C2×C43×#4492
C43×#28472
C43×#20362
C43×#20352
C43×#20342
C43×#20332
C43×#20002
C43×#19992
C43×#18252
C43×#17882
C43×#17792
#2960043