Finite Group Databasebeta

← C43×#25533 #24945550

Subgroups — C43×#25533 #24945550

Order 11008.

1444 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#547C211yesmaximal, characteristic, complemented
2C2×C43×#480C211yesmaximal, characteristic, complemented
3C2×C43×#466C211yesmaximal, characteristic, complemented
4C43×#2416C211yesmaximal, characteristic, complemented
5C43×#2057C211yesmaximal, characteristic, complemented
6C43×#2033C211yesmaximal, characteristic, complemented
7C43×#2023C211yesmaximal, characteristic, complemented
8C43×#1999C211yesmaximal, characteristic, complemented
9C43×#1879C211yesmaximal, characteristic, complemented
10C43×#1874C211yesmaximal, characteristic, complemented
11C43×#1874C211yesmaximal, characteristic, complemented
12C43×#1869C211yesmaximal, characteristic, complemented
13C43×#1862C211yesmaximal, characteristic, complemented
14C43×#1852C211yesmaximal, characteristic, complemented
15C2×C43×#340C211yesmaximal, characteristic, complemented
16C22×#41×C43—21no—
17C22×D8×C43C2211yescharacteristic
18C23×C8×C43C2211yescharacteristic
19C43×#547—24no—
20C43×#547—24no—
21C2×C4⋊Q8×C43C2211yescharacteristic
22C2×#123×C43—21no—
23C2×#123×C43—21no—
24C2×C22⋊Q8×C43—21no—
25C2×#121×C43—21no—
26C2×#121×C43C2211yescharacteristic
27C2×#121×C43C2211yescharacteristic
28C2×#121×C43C2211yescharacteristic
29C2×#121×C43C2211yescharacteristic
30C2×C4×D4×C43C2211yescharacteristic
31C2×C4×D4×C43C2211yescharacteristic
32C22×C4⋊C4×C43C2211yescharacteristic
33C22×C4⋊C4×C43C2211yescharacteristic
34C22×C4⋊C4×C43C2211yescharacteristic
35C43×#480—24no—
36C43×#466—24no—
37C2×#107×C43C2211yescharacteristic
38C2×#107×C43C2211yescharacteristic
39C2×#107×C43C2211yescharacteristic
40C2×#102×C43C2211yescharacteristic
41C2×#102×C43C2211yescharacteristic
42C2×#102×C43C2211yescharacteristic
43C2×#102×C43C2211yescharacteristic
44C2×#102×C43C2211yescharacteristic
45C2×#102×C43C2211yescharacteristic
46C2×C22⋊C8×C43C2211yescharacteristic
47C2×C22⋊C8×C43C2211yescharacteristic
48C2×C22⋊C8×C43C2211yescharacteristic
49C43×#396—21no—
50C43×#394—21no—
51C43×#390C2211yescharacteristic
52C43×#389C2211yescharacteristic
53C43×#386—21no—
54C43×#380C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C2×#41×C43—28no—
64C2×#41×C43—44no—
65C2×#41×C43—44no—
66C22×Q8×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
74C23×C4×C43—21no—
75C23×C4×C43—21no—
76C23×C4×C43—21no—
77C23×C4×C43—21no—
78C23×C4×C43C2311yescharacteristic
79C23×C4×C43C2311yescharacteristic
80C2×D8×C43—22no—
81C2×D8×C43—22no—
82C2×D8×C43—41no—
83C22×C8×C43—22no—
84C22×C8×C43—22no—
85C22×C8×C43—41no—
86C22×C8×C43C2311yescharacteristic
87C22×C8×C43C2311yescharacteristic
88C22×C8×C43C2311yescharacteristic
89C22×C8×C43C2311yescharacteristic
90C4⋊Q8×C43—22no—
91C4⋊Q8×C43—22no—
92#123×C43—28no—
93#123×C43—28no—
94C22⋊Q8×C43—28no—
95#121×C43—22no—
96#121×C43—22no—
97#121×C43—22no—
98#121×C43—22no—
99#121×C43—22no—
100#121×C43—22no—
101#121×C43—41no—
102#121×C43—44no—
103#121×C43D414yescomplemented
104C4×D4×C43—22no—
105C4×D4×C43—22no—
106C4×D4×C43—22no—
107C4×D4×C43—22no—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43—22no—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43—22no—
113C2×C4⋊C4×C43—22no—
114C2×C4⋊C4×C43—22no—
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43—41no—
118C2×C4⋊C4×C43D411yescharacteristic
119C2×C4⋊C4×C43D414yescomplemented
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43—21no—
132C2×C22⋊C4×C43—21no—
133C2×C22⋊C4×C43—21no—
134C2×C22⋊C4×C43D411yescharacteristic
135C2×C22⋊C4×C43D411yescharacteristic
136C2×C42×C43C2311yescharacteristic
137#107×C43—22no—
138#107×C43—22no—
139#107×C43—22no—
140#102×C43—22no—
141#102×C43—22no—
142#102×C43—22no—
143#102×C43—22no—
144#102×C43—22no—
145#102×C43—41no—
146C22⋊C8×C43—22no—
147C22⋊C8×C43—22no—
148C22⋊C8×C43—41no—
149#95×C43—21no—
150#95×C43—21no—
151C24×C43—21no—
152C24×C43—21no—
153C24×C43C2×D411yescharacteristic
154C24×C43C2×D411yescharacteristic
155#41×C43—432no—
156C2×Q8×C43—24no—
157C2×Q8×C43—42no—
158C2×Q8×C43—42no—
159C2×D4×C43—24no—
160C2×D4×C43—21no—
161C2×D4×C43—22no—
162C2×D4×C43—24no—
163C2×D4×C43—22no—
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—42no—
175C2×D4×C43—42no—
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—81no—
184C2×D4×C43D814yescomplemented
185C2×D4×C43C2×D412yes—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—24no—
191C22×C4×C43—24no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—24no—
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—42no—
206C22×C4×C43—42no—
207C22×C4×C43—42no—
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×D412yes—
215C22×C4×C43C2×D412yes—
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2×D411yescharacteristic
219C22×C4×C43C2×D411yescharacteristic
220C22×C4×C43C2411yescharacteristic
221D8×C43—44no—
222C2×C8×C43—21no—
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×C43—21no—
233C2×C8×C43—44no—
234C2×C8×C43#4112yescomplemented
235C4⋊C4×C43—24no—
236C4⋊C4×C43—24no—
237C4⋊C4×C43—24no—
238C4⋊C4×C43—22no—
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—21no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43—42no—
248C4⋊C4×C43—42no—
249C4⋊C4×C43C2×D412yes—
250C4⋊C4×C43C2×D412yes—
251C4⋊C4×C43C2×D412yes—
252C4⋊C4×C43#4112yescomplemented
253C22⋊C4×C43—24no—
254C22⋊C4×C43—24no—
255C22⋊C4×C43—24no—
256C22⋊C4×C43—22no—
257C22⋊C4×C43—22no—
258C22⋊C4×C43—42no—
259C22⋊C4×C43—42no—
260C22⋊C4×C43—42no—
261C22⋊C4×C43—42no—
262C22⋊C4×C43—81no—
263C42×C43—21no—
264C42×C43—21no—
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—21no—
274C23×C43—21no—
275C23×C43—22no—
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#12012yes—
290C23×C43C2×D812yes—
291C23×C43C2×D812yes—
292C23×C43AGL(1,ℤ/8)12yes—
293C23×C43C22×D411yescharacteristic
294Q8×C43—48no—
295D4×C43—28no—
296D4×C43—22no—
297D4×C43—22no—
298D4×C43—48no—
299D4×C43—48no—
300D4×C43—41no—
301D4×C43—41no—
302D4×C43—41no—
303D4×C43—41no—
304D4×C43—41no—
305D4×C43—41no—
306D4×C43—84no—
307D4×C43—84no—
308C2×C4×C43—21no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—22no—
316C2×C4×C43—21no—
317C2×C4×C43—21no—
318C2×C4×C43—22no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—21no—
322C2×C4×C43—22no—
323C2×C4×C43—21no—
324C2×C4×C43—21no—
325C2×C4×C43—21no—
326C2×C4×C43—48no—
327C2×C4×C43—48no—
328C2×C4×C43—41no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—48no—
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#12012yes—
349C2×C4×C43C2×D812yes—
350C2×C4×C43C22×D411yescharacteristic
351C2×C4×C43C22×D411yescharacteristic
352C2×C4×C43C2×#4111yescharacteristic
353C2×C4×C43C2×#4111yescharacteristic
354C2×C4×C43H(5,𝔽2)11yescharacteristic
355C2×C4×C432−1+411yescharacteristic
356C8×C43—22no—
357C8×C43—41no—
358C8×C43—41no—
359C8×C43—41no—
360#25533C4311yesmaximal, characteristic, direct product factor, Sylow
361C22×C43—22no—
362C22×C43—22no—
363C22×C43—22no—
364C22×C43—22no—
365C22×C43—22no—
366C22×C43—22no—
367C22×C43—22no—
368C22×C43—22no—
369C22×C43—22no—
370C22×C43—41no—
371C22×C43—41no—
372C22×C43—41no—
373C22×C43—41no—
374C22×C43—42no—
375C22×C43—42no—
376C22×C43—42no—
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#44714yes—
389C22×C43C2×#12011yescharacteristic
390C22×C43#54611yescharacteristic
391C22×C43#54711yescharacteristic
392C22×C43C22×D811yescharacteristic
393C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
394C22×C43#57711yescharacteristic
395C22×C43#57811yescharacteristic
396C4×C43—22no—
397C4×C43—22no—
398C4×C43—41no—
399C4×C43—42no—
400C4×C43—42no—
401C4×C43—42no—
402C4×C43—41no—
403C4×C43—42no—
404C4×C43—81no—
405C4×C43—81no—
406C4×C43#53211yescharacteristic
407C4×C43#53711yescharacteristic
408C4×C43#54611yescharacteristic
409C4×C43#54711yescharacteristic
410C2×#547C2×C4311yescharacteristic, complemented
411C2×#480C2×C4311yescharacteristic, complemented
412C2×#466C2×C4311yescharacteristic, complemented
413#2416C2×C4311yescharacteristic, complemented
414#2057C2×C4311yescharacteristic, complemented
415#2033C2×C4311yescharacteristic, complemented
416#2023C2×C4311yescharacteristic, complemented
417#1999C2×C4311yescharacteristic, complemented
418#1879C2×C4311yescharacteristic, complemented
419#1874C2×C4311yescharacteristic, complemented
420#1874C2×C4311yescharacteristic, complemented
421#1869C2×C4311yescharacteristic, complemented
422#1862C2×C4311yescharacteristic, complemented
423#1852C2×C4311yescharacteristic, complemented
424C2×#340C2×C4311yescharacteristic, complemented
425C2×C43—24no—
426C2×C43—42no—
427C2×C43—82no—
428C2×C43—161no—
429C2×C43#243011yescharacteristic
430C2×C43C2×#44711yescharacteristic
431C2×C43#301311yescharacteristic
432C2×C43#329411yescharacteristic
433C2×C43#330811yescharacteristic
434C2×C43#333411yescharacteristic
435C2×C43#334511yescharacteristic
436C22×#41—21no—
437C22×D8C22×C4311yescharacteristic
438C23×C8C22×C4311yescharacteristic
439#547—24no—
440#547—24no—
441C2×C4⋊Q8C22×C4311yescharacteristic
442C2×#123—21no—
443C2×#123—21no—
444C2×C22⋊Q8—21no—
445C2×#121—21no—
446C2×#121C22×C4311yescharacteristic
447C2×#121C22×C4311yescharacteristic
448C2×#121C22×C4311yescharacteristic
449C2×#121C22×C4311yescharacteristic
450C2×C4×D4C22×C4311yescharacteristic
451C2×C4×D4C22×C4311yescharacteristic
452C22×C4⋊C4C22×C4311yescharacteristic
453C22×C4⋊C4C22×C4311yescharacteristic
454C22×C4⋊C4C22×C4311yescharacteristic
455#480—24no—
456#466—24no—
457C2×#107C22×C4311yescharacteristic
458C2×#107C22×C4311yescharacteristic
459C2×#107C22×C4311yescharacteristic
460C2×#102C22×C4311yescharacteristic
461C2×#102C22×C4311yescharacteristic
462C2×#102C22×C4311yescharacteristic
463C2×#102C22×C4311yescharacteristic
464C2×#102C22×C4311yescharacteristic
465C2×#102C22×C4311yescharacteristic
466C2×C22⋊C8C22×C4311yescharacteristic
467C2×C22⋊C8C22×C4311yescharacteristic
468C2×C22⋊C8C22×C4311yescharacteristic
469#396—21no—
470#394—21no—
471#390C22×C4311yescharacteristic
472#389C22×C4311yescharacteristic
473#386—21no—
474#380C22×C4311yescharacteristic
475#340C22×C4311yescharacteristic
476#340C22×C4311yescharacteristic
477#340C22×C4311yescharacteristic
478#340C22×C4311yescharacteristic
479#340C22×C4311yescharacteristic
480#340C22×C4311yescharacteristic
481#336C22×C4311yescharacteristic
482#336C22×C4311yescharacteristic
483C43#2553311yescharacteristic, direct product factor, Sylow
484C2×#41—28no—
485C2×#41—44no—
486C2×#41—44no—
487C22×Q8—21no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4D4×C4311yescharacteristic
493C22×D4C23×C4311yescharacteristic
494C22×D4C23×C4311yescharacteristic
495C23×C4—21no—
496C23×C4—21no—
497C23×C4—21no—
498C23×C4—21no—
499C23×C4C23×C4311yescharacteristic
500C23×C4C23×C4311yescharacteristic
501C2×D8—22no—
502C2×D8—22no—
503C2×D8—41no—
504C22×C8—22no—
505C22×C8—22no—
506C22×C8—41no—
507C22×C8C23×C4311yescharacteristic
508C22×C8C23×C4311yescharacteristic
509C22×C8C23×C4311yescharacteristic
510C22×C8C23×C4311yescharacteristic
511C4⋊Q8—22no—
512C4⋊Q8—22no—
513#123—28no—
514#123—28no—
515C22⋊Q8—28no—
516#121—22no—
517#121—22no—
518#121—22no—
519#121—22no—
520#121—22no—
521#121—22no—
522#121—41no—
523#121—44no—
524#121D4×C4314yescomplemented
525C4×D4—22no—
526C4×D4—22no—
527C4×D4—22no—
528C4×D4—22no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—22no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—22no—
534C2×C4⋊C4—22no—
535C2×C4⋊C4—22no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—41no—
539C2×C4⋊C4D4×C4311yescharacteristic
540C2×C4⋊C4D4×C4314yescomplemented
541C2×C4⋊C4C23×C4311yescharacteristic
542C2×C4⋊C4C23×C4311yescharacteristic
543C2×C4⋊C4C23×C4311yescharacteristic
544C2×C4⋊C4C23×C4311yescharacteristic
545C2×C4⋊C4C23×C4311yescharacteristic
546C2×C4⋊C4C23×C4311yescharacteristic
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×C42C23×C4311yescharacteristic
558#107—22no—
559#107—22no—
560#107—22no—
561#102—22no—
562#102—22no—
563#102—22no—
564#102—22no—
565#102—22no—
566#102—41no—
567C22⋊C8—22no—
568C22⋊C8—22no—
569C22⋊C8—41no—
570#95—21no—
571#95—21no—
572C24—21no—
573C24—21no—
574C24C2×D4×C4311yescharacteristic
575C24C2×D4×C4311yescharacteristic
576#41—432no—
577C2×Q8—24no—
578C2×Q8—42no—
579C2×Q8—42no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—24no—
583C2×D4—24no—
584C2×D4—21no—
585C2×D4—21no—
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—42no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—81no—
605C2×D4D8×C4314yescomplemented
606C2×D4C2×D4×C4312yes—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—24no—
612C22×C4—24no—
613C22×C4—24no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—81no—
635C22×C4C2×D4×C4311yescharacteristic
636C22×C4C2×D4×C4311yescharacteristic
637C22×C4C2×D4×C4311yescharacteristic
638C22×C4C2×D4×C4312yes—
639C22×C4C2×D4×C4312yes—
640C22×C4C2×D4×C4311yescharacteristic
641C22×C4C24×C4311yescharacteristic
642D8—44no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—44no—
655C2×C8#41×C4312yescomplemented
656C4⋊C4—24no—
657C4⋊C4—24no—
658C4⋊C4—24no—
659C4⋊C4—22no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4C2×D4×C4312yes—
671C4⋊C4C2×D4×C4312yes—
672C4⋊C4C2×D4×C4312yes—
673C4⋊C4#41×C4312yescomplemented
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—22no—
677C22⋊C4—24no—
678C22⋊C4—22no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—81no—
684C42—21no—
685C42—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—22no—
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#120×C4312yes—
711C23C2×D8×C4312yes—
712C23C2×D8×C4312yes—
713C23AGL(1,ℤ/8)×C4312yes—
714C23C22×D4×C4311yescharacteristic
715Q8—48no—
716D4—28no—
717D4—22no—
718D4—22no—
719D4—48no—
720D4—48no—
721D4—41no—
722D4—41no—
723D4—41no—
724D4—41no—
725D4—41no—
726D4—41no—
727D4—84no—
728D4—84no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—48no—
748C2×C4—48no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—48no—
758C2×C4—41no—
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—84no—
769C2×C4#120×C4312yes—
770C2×C4C2×D8×C4312yes—
771C2×C4C22×D4×C4311yescharacteristic
772C2×C4C22×D4×C4311yescharacteristic
773C2×C4C2×#41×C4311yescharacteristic
774C2×C4C2×#41×C4311yescharacteristic
775C2×C4H(5,𝔽2)×C4311yescharacteristic
776C2×C42−1+4×C4311yescharacteristic
777C8—22no—
778C8—41no—
779C8—41no—
780C8—41no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22C43×#44714yes—
809C22C2×#120×C4311yescharacteristic
810C22C43×#54611yescharacteristic
811C22C43×#54711yescharacteristic
812C22C22×D8×C4311yescharacteristic
813C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
814C22C43×#57711yescharacteristic
815C22C43×#57811yescharacteristic
816C4—22no—
817C4—22no—
818C4—41no—
819C4—42no—
820C4—42no—
821C4—42no—
822C4—41no—
823C4—42no—
824C4—81no—
825C4—81no—
826C4C43×#53211yescharacteristic
827C4C43×#53711yescharacteristic
828C4C43×#54611yescharacteristic
829C4C43×#54711yescharacteristic
830C2—24no—
831C2—42no—
832C2—82no—
833C2—161no—
834C2C43×#243011yescharacteristic
835C2C2×C43×#44711yescharacteristic
836C2C43×#301311yescharacteristic
837C2C43×#329411yescharacteristic
838C2C43×#330811yescharacteristic
839C2C43×#333411yescharacteristic
840C2C43×#334511yescharacteristic
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×#547C2semidirect
2. C2×C43×#480C2semidirect
3. C2×C43×#466C2semidirect
4. C43×#2416C2semidirect
5. C43×#2057C2semidirect
6. C43×#2033C2semidirect
7. C43×#2023C2semidirect
8. C43×#1999C2semidirect
9. C43×#1879C2semidirect
10. C43×#1874C2semidirect
11. C43×#1874C2semidirect
12. C43×#1869C2semidirect
13. C43×#1862C2semidirect
14. C43×#1852C2semidirect
15. C2×C43×#340C2semidirect
103. #121×C43D4semidirect
119. C2×C4⋊C4×C43D4semidirect
184. C2×D4×C43D8semidirect
234. C2×C8×C43#41semidirect
252. C4⋊C4×C43#41semidirect
360. #25533C43direct (N × H)
410. C2×#547C2×C43semidirect
411. C2×#480C2×C43semidirect
412. C2×#466C2×C43semidirect
413. #2416C2×C43semidirect
414. #2057C2×C43semidirect
415. #2033C2×C43semidirect
416. #2023C2×C43semidirect
417. #1999C2×C43semidirect
418. #1879C2×C43semidirect
419. #1874C2×C43semidirect
420. #1874C2×C43semidirect
421. #1869C2×C43semidirect
422. #1862C2×C43semidirect
423. #1852C2×C43semidirect
424. C2×#340C2×C43semidirect
483. C43#25533direct (N × H)
524. #121D4×C43semidirect
540. C2×C4⋊C4D4×C43semidirect
605. C2×D4D8×C43semidirect
655. C2×C8#41×C43semidirect
673. C4⋊C4#41×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#5472
C2×C43×#4802
C2×C43×#4662
C43×#24162
C43×#20572
C43×#20332
C43×#20232
C43×#19992
C43×#18792
C43×#18742
C43×#18692
C43×#18622
C43×#18522
C2×C43×#3402
#2553343