Finite Group Databasebeta

← C43×#24448 #24944465

Subgroups — C43×#24448 #24944465

Order 11008.

1888 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C43C211yesmaximal, characteristic
2C2×C43×#468C211yesmaximal, characteristic, complemented
3C2×C43×#450C211yesmaximal, characteristic, complemented
4C2×C43×#450C211yesmaximal, characteristic, complemented
5C2×C43×#418C211yesmaximal, characteristic, complemented
6C43×#2415C211yesmaximal, characteristic, complemented
7C43×#2041C211yesmaximal, characteristic, complemented
8C43×#2033C211yesmaximal, characteristic, complemented
9C43×#2014C211yesmaximal, characteristic, complemented
10C43×#2000C211yesmaximal, characteristic, complemented
11C43×#1877C211yesmaximal, characteristic, complemented
12C43×#1875C211yesmaximal, characteristic, complemented
13C43×#1870C211yesmaximal, characteristic, complemented
14C43×#1862C211yesmaximal, characteristic, complemented
15C43×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C43—21no—
17C23×D4×C43C2211yescharacteristic
18C23×D4×C43C2211yescharacteristic
19C22×SD16×C43C2211yescharacteristic
20C22×SD16×C43C2211yescharacteristic, complemented
21C22×SD16×C43C2211yescharacteristic, complemented
22C22×M16×C43C2211yescharacteristic, complemented
23D42×C43—24no—
24D42×C43—24no—
25C2×#127×C43C2211yescharacteristic
26C2×C22⋊Q8×C43C2211yescharacteristic, complemented
27C2×C22⋊Q8×C43C2211yescharacteristic, complemented
28C2×#121×C43—21no—
29C2×#121×C43C2211yescharacteristic
30C2×#121×C43C2211yescharacteristic
31C2×#120×C43—21no—
32C2×#120×C43—21no—
33C2×C4×D4×C43C2211yescharacteristic
34C2×C4×D4×C43C2211yescharacteristic
35C2×#117×C43C2211yescharacteristic, complemented
36C43×#468—24no—
37C43×#450—24no—
38C43×#450—24no—
39C2×#107×C43C2211yescharacteristic, complemented
40C43×#418—24no—
41C2×#103×C43C2211yescharacteristic, complemented
42C2×#102×C43C2211yescharacteristic
43C2×#102×C43C2211yescharacteristic
44C2×#102×C43C2211yescharacteristic
45C2×#102×C43C2211yescharacteristic, complemented
46C2×#102×C43C2211yescharacteristic, complemented
47C2×#102×C43C2211yescharacteristic, complemented
48C2×#102×C43C2211yescharacteristic, complemented
49C2×#102×C43C2211yescharacteristic, complemented
50C2×#102×C43C2211yescharacteristic, complemented
51C2×C22⋊C8×C43C2211yescharacteristic, complemented
52C2×C22⋊C8×C43C2211yescharacteristic, complemented
53C2×C22⋊C8×C43C2211yescharacteristic, complemented
54C43×#397—21no—
55C43×#394—21no—
56C43×#391C2211yescharacteristic, complemented
57C43×#389—21no—
58C43×#389C2211yescharacteristic, complemented
59C43×#388—21no—
60C43×#380C2211yescharacteristic, complemented
61C43×#340C2211yescharacteristic, complemented
62C43×#340C2211yescharacteristic, complemented
63C43×#336C2211yescharacteristic, complemented
64C43×#336C2211yescharacteristic, complemented
65C25×C43—21no—
66C25×C43—21no—
67C22×Q8×C43C2311yescharacteristic
68C22×D4×C43—22no—
69C22×D4×C43—22no—
70C22×D4×C43—28no—
71C22×D4×C43—21no—
72C22×D4×C43—21no—
73C22×D4×C43—22no—
74C22×D4×C43—22no—
75C22×D4×C43—22no—
76C22×D4×C43—22no—
77C22×D4×C43—21no—
78C22×D4×C43—21no—
79C22×D4×C43—21no—
80C22×D4×C43—22no—
81C22×D4×C43—21no—
82C22×D4×C43—41no—
83C22×D4×C43—41no—
84C22×D4×C43—41no—
85C22×D4×C43—41no—
86C22×D4×C43—44no—
87C22×D4×C43—44no—
88C22×D4×C43D411yescharacteristic
89C22×D4×C43D414yes—
90C22×D4×C43C2311yescharacteristic
91C22×D4×C43C2311yescharacteristic
92C22×D4×C43C2311yescharacteristic
93C23×C4×C43—21no—
94C23×C4×C43C2311yescharacteristic
95C23×C4×C43C2311yescharacteristic
96C2×SD16×C43—22no—
97C2×SD16×C43—22no—
98C2×SD16×C43—22no—
99C2×SD16×C43—22no—
100C2×SD16×C43—22no—
101C2×SD16×C43—22no—
102C2×SD16×C43—41no—
103C2×SD16×C43—41no—
104C2×SD16×C43—41no—
105C2×M16×C43—22no—
106C2×M16×C43—22no—
107C2×M16×C43—41no—
108C22×C8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C22×C8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112#127×C43—22no—
113#127×C43—22no—
114C22⋊Q8×C43—22no—
115C22⋊Q8×C43—22no—
116C22⋊Q8×C43—22no—
117C22⋊Q8×C43—41no—
118#121×C43—28no—
119#121×C43—22no—
120#121×C43—22no—
121#121×C43—22no—
122#121×C43D414yes—
123#120×C43—28no—
124#120×C43—28no—
125C4×D4×C43—22no—
126C4×D4×C43—22no—
127C4×D4×C43—22no—
128C4×D4×C43—22no—
129#117×C43—22no—
130#117×C43—41no—
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43D411yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C22⋊C4×C43—21no—
140C2×C22⋊C4×C43—21no—
141C2×C22⋊C4×C43—21no—
142C2×C22⋊C4×C43—21no—
143C2×C22⋊C4×C43—21no—
144C2×C22⋊C4×C43—21no—
145C2×C22⋊C4×C43—21no—
146C2×C22⋊C4×C43D411yescharacteristic
147C2×C22⋊C4×C43D411yescharacteristic
148C2×C42×C43—21no—
149C2×C42×C43C2311yescharacteristic
150#107×C43—22no—
151#103×C43—22no—
152#102×C43—22no—
153#102×C43—22no—
154#102×C43—22no—
155#102×C43—22no—
156#102×C43—22no—
157#102×C43—22no—
158#102×C43—22no—
159#102×C43—41no—
160#102×C43D414yescomplemented
161C22⋊C8×C43—22no—
162C22⋊C8×C43—22no—
163C22⋊C8×C43—41no—
164#95×C43—21no—
165#95×C43—21no—
166#95×C43—21no—
167#95×C43—21no—
168C24×C43—21no—
169C24×C43—24no—
170C24×C43—21no—
171C24×C43—21no—
172C24×C43—24no—
173C24×C43—42no—
174C24×C43—42no—
175C24×C43—42no—
176C24×C43—42no—
177C24×C43—42no—
178C24×C43—42no—
179C24×C43—42no—
180C24×C43—42no—
181C24×C43—81no—
182C24×C43—81no—
183C24×C43—81no—
184C24×C43—81no—
185C24×C43C2×D411yescharacteristic
186C24×C43C2×D411yescharacteristic
187C2×Q8×C43—21no—
188C2×Q8×C43—21no—
189C2×Q8×C43—21no—
190C2×Q8×C43—21no—
191C2×Q8×C43—21no—
192C2×Q8×C43—21no—
193C2×D4×C43—24no—
194C2×D4×C43—24no—
195C2×D4×C43—24no—
196C2×D4×C43—24no—
197C2×D4×C43—24no—
198C2×D4×C43—22no—
199C2×D4×C43—21no—
200C2×D4×C43—21no—
201C2×D4×C43—21no—
202C2×D4×C43—21no—
203C2×D4×C43—21no—
204C2×D4×C43—22no—
205C2×D4×C43—24no—
206C2×D4×C43—22no—
207C2×D4×C43—28no—
208C2×D4×C43—21no—
209C2×D4×C43—21no—
210C2×D4×C43—21no—
211C2×D4×C43—21no—
212C2×D4×C43—21no—
213C2×D4×C43—21no—
214C2×D4×C43—21no—
215C2×D4×C43—21no—
216C2×D4×C43—42no—
217C2×D4×C43—42no—
218C2×D4×C43—42no—
219C2×D4×C43—42no—
220C2×D4×C43—42no—
221C2×D4×C43—42no—
222C2×D4×C43—42no—
223C2×D4×C43—44no—
224C2×D4×C43—44no—
225C2×D4×C43—44no—
226C2×D4×C43—42no—
227C2×D4×C43—44no—
228C2×D4×C43—44no—
229C2×D4×C43—432no—
230C2×D4×C43—44no—
231C2×D4×C43—44no—
232C2×D4×C43—42no—
233C2×D4×C43—42no—
234C2×D4×C43—81no—
235C2×D4×C43—81no—
236C2×D4×C43C2×D412yes—
237C2×D4×C43C2×D412yes—
238C2×D4×C43C2×D412yes—
239C2×D4×C43C2×D412yes—
240C2×D4×C43#4112yes—
241C22×C4×C43—21no—
242C22×C4×C43—21no—
243C22×C4×C43—21no—
244C22×C4×C43—21no—
245C22×C4×C43—24no—
246C22×C4×C43—21no—
247C22×C4×C43—21no—
248C22×C4×C43—21no—
249C22×C4×C43—21no—
250C22×C4×C43—21no—
251C22×C4×C43—21no—
252C22×C4×C43—21no—
253C22×C4×C43—21no—
254C22×C4×C43—21no—
255C22×C4×C43—21no—
256C22×C4×C43—21no—
257C22×C4×C43—42no—
258C22×C4×C43—42no—
259C22×C4×C43C2×D412yes—
260C22×C4×C43C2×D412yes—
261C22×C4×C43C2×D411yescharacteristic
262C22×C4×C43C2×D411yescharacteristic
263C22×C4×C43C2×D411yescharacteristic
264C22×C4×C43C2×D411yescharacteristic
265C22×C4×C43C2411yescharacteristic
266SD16×C43—44no—
267SD16×C43—44no—
268SD16×C43—44no—
269M16×C43—44no—
270C2×C8×C43—21no—
271C2×C8×C43—21no—
272C2×C8×C43—21no—
273C2×C8×C43—21no—
274C2×C8×C43—21no—
275C2×C8×C43—21no—
276C2×C8×C43—21no—
277C2×C8×C43—21no—
278C2×C8×C43—21no—
279C2×C8×C43—21no—
280C2×C8×C43—21no—
281C2×C8×C43C2×D412yescomplemented
282C4⋊C4×C43—22no—
283C4⋊C4×C43—21no—
284C4⋊C4×C43—21no—
285C4⋊C4×C43—21no—
286C4⋊C4×C43—21no—
287C4⋊C4×C43—21no—
288C4⋊C4×C43—21no—
289C4⋊C4×C43—42no—
290C4⋊C4×C43—42no—
291C4⋊C4×C43—42no—
292C4⋊C4×C43C2×D412yes—
293C4⋊C4×C43C2×D412yescomplemented
294C22⋊C4×C43—24no—
295C22⋊C4×C43—24no—
296C22⋊C4×C43—24no—
297C22⋊C4×C43—22no—
298C22⋊C4×C43—22no—
299C22⋊C4×C43—42no—
300C22⋊C4×C43—42no—
301C22⋊C4×C43—42no—
302C22⋊C4×C43—42no—
303C42×C43—21no—
304C42×C43—21no—
305C42×C43—42no—
306C23×C43—21no—
307C23×C43—22no—
308C23×C43—21no—
309C23×C43—21no—
310C23×C43—22no—
311C23×C43—21no—
312C23×C43—21no—
313C23×C43—22no—
314C23×C43—21no—
315C23×C43—21no—
316C23×C43—21no—
317C23×C43—21no—
318C23×C43—21no—
319C23×C43—21no—
320C23×C43—21no—
321C23×C43—22no—
322C23×C43—22no—
323C23×C43—48no—
324C23×C43—48no—
325C23×C43—48no—
326C23×C43—48no—
327C23×C43—41no—
328C23×C43—41no—
329C23×C43—41no—
330C23×C43—41no—
331C23×C43—41no—
332C23×C43—41no—
333C23×C43—41no—
334C23×C43—41no—
335C23×C43—41no—
336C23×C43—41no—
337C23×C43—41no—
338C23×C43—41no—
339C23×C43—41no—
340C23×C43—41no—
341C23×C43—41no—
342C23×C43—41no—
343C23×C43—84no—
344C23×C43—84no—
345C23×C43—84no—
346C23×C43—84no—
347C23×C43—84no—
348C23×C43—84no—
349C23×C43—84no—
350C23×C43—84no—
351C23×C43—84no—
352C23×C43—84no—
353C23×C43#12012yes—
354C23×C43AGL(1,ℤ/8)12yes—
355C23×C43C22×D411yescharacteristic
356Q8×C43—41no—
357Q8×C43—41no—
358Q8×C43—41no—
359Q8×C43—41no—
360D4×C43—28no—
361D4×C43—22no—
362D4×C43—22no—
363D4×C43—22no—
364D4×C43—22no—
365D4×C43—22no—
366D4×C43—22no—
367D4×C43—22no—
368D4×C43—48no—
369D4×C43—48no—
370D4×C43—48no—
371D4×C43—48no—
372D4×C43—48no—
373D4×C43—41no—
374D4×C43—41no—
375D4×C43—41no—
376D4×C43—41no—
377D4×C43—84no—
378D4×C43#12114yes—
379C2×C4×C43—21no—
380C2×C4×C43—21no—
381C2×C4×C43—21no—
382C2×C4×C43—21no—
383C2×C4×C43—22no—
384C2×C4×C43—22no—
385C2×C4×C43—22no—
386C2×C4×C43—22no—
387C2×C4×C43—21no—
388C2×C4×C43—21no—
389C2×C4×C43—22no—
390C2×C4×C43—22no—
391C2×C4×C43—21no—
392C2×C4×C43—21no—
393C2×C4×C43—21no—
394C2×C4×C43—21no—
395C2×C4×C43—48no—
396C2×C4×C43—41no—
397C2×C4×C43—41no—
398C2×C4×C43—41no—
399C2×C4×C43—41no—
400C2×C4×C43—41no—
401C2×C4×C43—41no—
402C2×C4×C43—41no—
403C2×C4×C43—41no—
404C2×C4×C43—41no—
405C2×C4×C43—41no—
406C2×C4×C43—41no—
407C2×C4×C43—41no—
408C2×C4×C43—41no—
409C2×C4×C43—41no—
410C2×C4×C43—41no—
411C2×C4×C43—41no—
412C2×C4×C43—41no—
413C2×C4×C43#12012yes—
414C2×C4×C43AGL(1,ℤ/8)12yes—
415C2×C4×C43C22×D411yescharacteristic
416C2×C4×C43C22×D411yescharacteristic
417C2×C4×C43C22×D411yescharacteristic
418C2×C4×C43C2×#4111yescharacteristic
419C2×C4×C43H(5,𝔽2)11yescharacteristic
420C2×C4×C43H(5,𝔽2)11yescharacteristic
421C8×C43—22no—
422C8×C43—41no—
423C8×C43—41no—
424C8×C43—41no—
425#24448C4311yesmaximal, characteristic, direct product factor, Sylow
426C22×C43—24no—
427C22×C43—22no—
428C22×C43—22no—
429C22×C43—22no—
430C22×C43—22no—
431C22×C43—22no—
432C22×C43—22no—
433C22×C43—41no—
434C22×C43—42no—
435C22×C43—41no—
436C22×C43—42no—
437C22×C43—41no—
438C22×C43—42no—
439C22×C43—41no—
440C22×C43—41no—
441C22×C43—42no—
442C22×C43—41no—
443C22×C43—42no—
444C22×C43—41no—
445C22×C43—41no—
446C22×C43—42no—
447C22×C43—42no—
448C22×C43—42no—
449C22×C43—42no—
450C22×C43—42no—
451C22×C43—42no—
452C22×C43—42no—
453C22×C43—816no—
454C22×C43—816no—
455C22×C43—81no—
456C22×C43—81no—
457C22×C43—81no—
458C22×C43—81no—
459C22×C43—81no—
460C22×C43—81no—
461C22×C43—81no—
462C22×C43—81no—
463C22×C43C2×#12011yescharacteristic
464C22×C43D4211yescharacteristic
465C22×C43#54611yescharacteristic
466C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
467C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
468C22×C43#57711yescharacteristic
469C22×C43#57711yescharacteristic
470C4×C43—22no—
471C4×C43—22no—
472C4×C43—41no—
473C4×C43—42no—
474C4×C43—41no—
475C4×C43—42no—
476C4×C43—81no—
477C4×C43—81no—
478C4×C43—81no—
479C4×C43C2×#12111yescharacteristic
480C4×C43#53411yescharacteristic
481C4×C43D4211yescharacteristic
482C4×C43#54611yescharacteristic
483C2×D42C2×C4311yescharacteristic
484C2×#468C2×C4311yescharacteristic, complemented
485C2×#450C2×C4311yescharacteristic, complemented
486C2×#450C2×C4311yescharacteristic, complemented
487C2×#418C2×C4311yescharacteristic, complemented
488#2415C2×C4311yescharacteristic, complemented
489#2041C2×C4311yescharacteristic, complemented
490#2033C2×C4311yescharacteristic, complemented
491#2014C2×C4311yescharacteristic, complemented
492#2000C2×C4311yescharacteristic, complemented
493#1877C2×C4311yescharacteristic, complemented
494#1875C2×C4311yescharacteristic, complemented
495#1870C2×C4311yescharacteristic, complemented
496#1862C2×C4311yescharacteristic, complemented
497#1786C2×C4311yescharacteristic, complemented
498C2×C43—42no—
499C2×C43—42no—
500C2×C43—44no—
501C2×C43—82no—
502C2×C43—82no—
503C2×C43#241011yescharacteristic
504C2×C43#300311yescharacteristic
505C2×C43#300911yescharacteristic
506C2×C43#326511yescharacteristic
507C2×C43#327211yescharacteristic
508C2×C43#331011yescharacteristic
509C2×C43#332411yescharacteristic
510C23×D4—21no—
511C23×D4C22×C4311yescharacteristic
512C23×D4C22×C4311yescharacteristic
513C22×SD16C22×C4311yescharacteristic
514C22×SD16C22×C4311yescharacteristic, complemented
515C22×SD16C22×C4311yescharacteristic, complemented
516C22×M16C22×C4311yescharacteristic, complemented
517D42—24no—
518D42—24no—
519C2×#127C22×C4311yescharacteristic
520C2×C22⋊Q8C22×C4311yescharacteristic, complemented
521C2×C22⋊Q8C22×C4311yescharacteristic, complemented
522C2×#121—21no—
523C2×#121C22×C4311yescharacteristic
524C2×#121C22×C4311yescharacteristic
525C2×#120—21no—
526C2×#120—21no—
527C2×C4×D4C22×C4311yescharacteristic
528C2×C4×D4C22×C4311yescharacteristic
529C2×#117C22×C4311yescharacteristic, complemented
530#468—24no—
531#450—24no—
532#450—24no—
533C2×#107C22×C4311yescharacteristic, complemented
534#418—24no—
535C2×#103C22×C4311yescharacteristic, complemented
536C2×#102C22×C4311yescharacteristic
537C2×#102C22×C4311yescharacteristic
538C2×#102C22×C4311yescharacteristic
539C2×#102C22×C4311yescharacteristic, complemented
540C2×#102C22×C4311yescharacteristic, complemented
541C2×#102C22×C4311yescharacteristic, complemented
542C2×#102C22×C4311yescharacteristic, complemented
543C2×#102C22×C4311yescharacteristic, complemented
544C2×#102C22×C4311yescharacteristic, complemented
545C2×C22⋊C8C22×C4311yescharacteristic, complemented
546C2×C22⋊C8C22×C4311yescharacteristic, complemented
547C2×C22⋊C8C22×C4311yescharacteristic, complemented
548#397—21no—
549#394—21no—
550#391C22×C4311yescharacteristic, complemented
551#389—21no—
552#389C22×C4311yescharacteristic, complemented
553#388—21no—
554#380C22×C4311yescharacteristic, complemented
555#340C22×C4311yescharacteristic, complemented
556#340C22×C4311yescharacteristic, complemented
557#336C22×C4311yescharacteristic, complemented
558#336C22×C4311yescharacteristic, complemented
559C43#2444811yescharacteristic, direct product factor, Sylow
560C25—21no—
561C25—21no—
562C22×Q8C23×C4311yescharacteristic
563C22×D4—22no—
564C22×D4—22no—
565C22×D4—28no—
566C22×D4—21no—
567C22×D4—21no—
568C22×D4—22no—
569C22×D4—22no—
570C22×D4—22no—
571C22×D4—22no—
572C22×D4—21no—
573C22×D4—21no—
574C22×D4—21no—
575C22×D4—22no—
576C22×D4—21no—
577C22×D4—41no—
578C22×D4—41no—
579C22×D4—41no—
580C22×D4—41no—
581C22×D4—44no—
582C22×D4—44no—
583C22×D4D4×C4311yescharacteristic
584C22×D4D4×C4314yes—
585C22×D4C23×C4311yescharacteristic
586C22×D4C23×C4311yescharacteristic
587C22×D4C23×C4311yescharacteristic
588C23×C4—21no—
589C23×C4C23×C4311yescharacteristic
590C23×C4C23×C4311yescharacteristic
591C2×SD16—22no—
592C2×SD16—22no—
593C2×SD16—22no—
594C2×SD16—22no—
595C2×SD16—22no—
596C2×SD16—22no—
597C2×SD16—41no—
598C2×SD16—41no—
599C2×SD16—41no—
600C2×M16—22no—
601C2×M16—22no—
602C2×M16—41no—
603C22×C8C23×C4311yescharacteristic
604C22×C8C23×C4311yescharacteristic
605C22×C8C23×C4311yescharacteristic
606C22×C8C23×C4311yescharacteristic
607#127—22no—
608#127—22no—
609C22⋊Q8—22no—
610C22⋊Q8—22no—
611C22⋊Q8—22no—
612C22⋊Q8—41no—
613#121—28no—
614#121—22no—
615#121—22no—
616#121—22no—
617#121D4×C4314yes—
618#120—28no—
619#120—28no—
620C4×D4—22no—
621C4×D4—22no—
622C4×D4—22no—
623C4×D4—22no—
624#117—22no—
625#117—41no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4D4×C4311yescharacteristic
630C2×C4⋊C4C23×C4311yescharacteristic
631C2×C4⋊C4C23×C4311yescharacteristic
632C2×C4⋊C4C23×C4311yescharacteristic
633C2×C4⋊C4C23×C4311yescharacteristic
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4D4×C4311yescharacteristic
642C2×C22⋊C4D4×C4311yescharacteristic
643C2×C42—21no—
644C2×C42C23×C4311yescharacteristic
645#107—22no—
646#103—22no—
647#102—22no—
648#102—22no—
649#102—22no—
650#102—22no—
651#102—22no—
652#102—22no—
653#102—22no—
654#102—41no—
655#102D4×C4314yescomplemented
656C22⋊C8—22no—
657C22⋊C8—22no—
658C22⋊C8—41no—
659#95—21no—
660#95—21no—
661#95—21no—
662#95—21no—
663C24—21no—
664C24—24no—
665C24—21no—
666C24—21no—
667C24—24no—
668C24—42no—
669C24—42no—
670C24—42no—
671C24—42no—
672C24—42no—
673C24—42no—
674C24—42no—
675C24—42no—
676C24—81no—
677C24—81no—
678C24—81no—
679C24—81no—
680C24C2×D4×C4311yescharacteristic
681C24C2×D4×C4311yescharacteristic
682C2×Q8—21no—
683C2×Q8—21no—
684C2×Q8—21no—
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×D4—22no—
689C2×D4—22no—
690C2×D4—28no—
691C2×D4—24no—
692C2×D4—24no—
693C2×D4—24no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—22no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—44no—
712C2×D4—44no—
713C2×D4—44no—
714C2×D4—42no—
715C2×D4—42no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—44no—
720C2×D4—44no—
721C2×D4—432no—
722C2×D4—44no—
723C2×D4—42no—
724C2×D4—42no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—44no—
728C2×D4—42no—
729C2×D4—81no—
730C2×D4—81no—
731C2×D4C2×D4×C4312yes—
732C2×D4C2×D4×C4312yes—
733C2×D4C2×D4×C4312yes—
734C2×D4C2×D4×C4312yes—
735C2×D4#41×C4312yes—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—24no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—42no—
753C22×C4—42no—
754C22×C4C2×D4×C4311yescharacteristic
755C22×C4C2×D4×C4311yescharacteristic
756C22×C4C2×D4×C4311yescharacteristic
757C22×C4C2×D4×C4312yes—
758C22×C4C2×D4×C4312yes—
759C22×C4C2×D4×C4311yescharacteristic
760C22×C4C24×C4311yescharacteristic
761SD16—44no—
762SD16—44no—
763SD16—44no—
764M16—44no—
765C2×C8—21no—
766C2×C8—21no—
767C2×C8—21no—
768C2×C8—21no—
769C2×C8—21no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8C2×D4×C4312yescomplemented
777C4⋊C4—22no—
778C4⋊C4—21no—
779C4⋊C4—21no—
780C4⋊C4—21no—
781C4⋊C4—21no—
782C4⋊C4—21no—
783C4⋊C4—21no—
784C4⋊C4—42no—
785C4⋊C4—42no—
786C4⋊C4—42no—
787C4⋊C4C2×D4×C4312yes—
788C4⋊C4C2×D4×C4312yescomplemented
789C22⋊C4—24no—
790C22⋊C4—24no—
791C22⋊C4—22no—
792C22⋊C4—24no—
793C22⋊C4—22no—
794C22⋊C4—42no—
795C22⋊C4—42no—
796C22⋊C4—42no—
797C22⋊C4—42no—
798C42—21no—
799C42—21no—
800C42—42no—
801C23—21no—
802C23—22no—
803C23—21no—
804C23—21no—
805C23—22no—
806C23—21no—
807C23—21no—
808C23—22no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—22no—
817C23—22no—
818C23—48no—
819C23—48no—
820C23—48no—
821C23—48no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—84no—
839C23—84no—
840C23—84no—
841C23—84no—
842C23—84no—
843C23—84no—
844C23—84no—
845C23—84no—
846C23—84no—
847C23—84no—
848C23#120×C4312yes—
849C23AGL(1,ℤ/8)×C4312yes—
850C23C22×D4×C4311yescharacteristic
851Q8—41no—
852Q8—41no—
853Q8—41no—
854Q8—41no—
855D4—28no—
856D4—22no—
857D4—22no—
858D4—22no—
859D4—22no—
860D4—22no—
861D4—22no—
862D4—22no—
863D4—48no—
864D4—48no—
865D4—48no—
866D4—48no—
867D4—48no—
868D4—41no—
869D4—41no—
870D4—41no—
871D4—41no—
872D4—84no—
873D4#121×C4314yes—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—21no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—21no—
890C2×C4—48no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4#120×C4312yes—
909C2×C4AGL(1,ℤ/8)×C4312yes—
910C2×C4C22×D4×C4311yescharacteristic
911C2×C4C22×D4×C4311yescharacteristic
912C2×C4C22×D4×C4311yescharacteristic
913C2×C4C2×#41×C4311yescharacteristic
914C2×C4H(5,𝔽2)×C4311yescharacteristic
915C2×C4H(5,𝔽2)×C4311yescharacteristic
916C8—22no—
917C8—41no—
918C8—41no—
919C8—41no—
920C22—22no—
921C22—24no—
922C22—22no—
923C22—22no—
924C22—22no—
925C22—22no—
926C22—22no—
927C22—41no—
928C22—42no—
929C22—41no—
930C22—42no—
931C22—41no—
932C22—42no—
933C22—41no—
934C22—41no—
935C22—42no—
936C22—41no—
937C22—42no—
938C22—41no—
939C22—41no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—816no—
948C22—816no—
949C22—81no—
950C22—81no—
951C22—81no—
952C22—81no—
953C22—81no—
954C22—81no—
955C22—81no—
956C22—81no—
957C22C2×#120×C4311yescharacteristic
958C22D42×C4311yescharacteristic
959C22C43×#54611yescharacteristic
960C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
961C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
962C22C43×#57711yescharacteristic
963C22C43×#57711yescharacteristic
964C4—22no—
965C4—22no—
966C4—41no—
967C4—42no—
968C4—41no—
969C4—42no—
970C4—81no—
971C4—81no—
972C4—81no—
973C4C2×#121×C4311yescharacteristic
974C4C43×#53411yescharacteristic
975C4D42×C4311yescharacteristic
976C4C43×#54611yescharacteristic
977C2—42no—
978C2—42no—
979C2—44no—
980C2—82no—
981C2—82no—
982C2C43×#241011yescharacteristic
983C2C43×#300311yescharacteristic
984C2C43×#300911yescharacteristic
985C2C43×#326511yescharacteristic
986C2C43×#327211yescharacteristic
987C2C43×#331011yescharacteristic
988C2C43×#332411yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC2×D42×C43C2
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
2. C2×C43×#468C2semidirect
3. C2×C43×#450C2semidirect
4. C2×C43×#450C2semidirect
5. C2×C43×#418C2semidirect
6. C43×#2415C2semidirect
7. C43×#2041C2semidirect
8. C43×#2033C2semidirect
9. C43×#2014C2semidirect
10. C43×#2000C2semidirect
11. C43×#1877C2semidirect
12. C43×#1875C2semidirect
13. C43×#1870C2semidirect
14. C43×#1862C2semidirect
15. C43×#1786C2semidirect
20. C22×SD16×C43C22semidirect
21. C22×SD16×C43C22semidirect
22. C22×M16×C43C22semidirect
26. C2×C22⋊Q8×C43C22semidirect
27. C2×C22⋊Q8×C43C22semidirect
35. C2×#117×C43C22semidirect
39. C2×#107×C43C22semidirect
41. C2×#103×C43C22semidirect
45. C2×#102×C43C22semidirect
46. C2×#102×C43C22semidirect
47. C2×#102×C43C22semidirect
48. C2×#102×C43C22semidirect
49. C2×#102×C43C22semidirect
50. C2×#102×C43C22semidirect
51. C2×C22⋊C8×C43C22semidirect
52. C2×C22⋊C8×C43C22semidirect
53. C2×C22⋊C8×C43C22semidirect
56. C43×#391C22semidirect
58. C43×#389C22semidirect
60. C43×#380C22semidirect
61. C43×#340C22semidirect
62. C43×#340C22semidirect
63. C43×#336C22semidirect
64. C43×#336C22semidirect
160. #102×C43D4semidirect
281. C2×C8×C43C2×D4semidirect
293. C4⋊C4×C43C2×D4semidirect
425. #24448C43direct (N × H)
484. C2×#468C2×C43semidirect
485. C2×#450C2×C43semidirect
486. C2×#450C2×C43semidirect
487. C2×#418C2×C43semidirect
488. #2415C2×C43semidirect
489. #2041C2×C43semidirect
490. #2033C2×C43semidirect
491. #2014C2×C43semidirect
492. #2000C2×C43semidirect
493. #1877C2×C43semidirect
494. #1875C2×C43semidirect
495. #1870C2×C43semidirect
496. #1862C2×C43semidirect
497. #1786C2×C43semidirect
514. C22×SD16C22×C43semidirect
515. C22×SD16C22×C43semidirect
516. C22×M16C22×C43semidirect
520. C2×C22⋊Q8C22×C43semidirect
521. C2×C22⋊Q8C22×C43semidirect
529. C2×#117C22×C43semidirect
533. C2×#107C22×C43semidirect
535. C2×#103C22×C43semidirect
539. C2×#102C22×C43semidirect
540. C2×#102C22×C43semidirect
541. C2×#102C22×C43semidirect
542. C2×#102C22×C43semidirect
543. C2×#102C22×C43semidirect
544. C2×#102C22×C43semidirect
545. C2×C22⋊C8C22×C43semidirect
546. C2×C22⋊C8C22×C43semidirect
547. C2×C22⋊C8C22×C43semidirect
550. #391C22×C43semidirect
552. #389C22×C43semidirect
554. #380C22×C43semidirect
555. #340C22×C43semidirect
556. #340C22×C43semidirect
557. #336C22×C43semidirect
558. #336C22×C43semidirect
559. C43#24448direct (N × H)
655. #102D4×C43semidirect
776. C2×C8C2×D4×C43semidirect
788. C4⋊C4C2×D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×D42×C432
C2×C43×#4682
C2×C43×#4502
C2×C43×#4182
C43×#24152
C43×#20412
C43×#20332
C43×#20142
C43×#20002
C43×#18772
C43×#18752
C43×#18702
C43×#18622
C43×#17862
#2444843