Finite Group Databasebeta

← C43×#23889 #24943906

Subgroups — C43×#23889 #24943906

Order 11008.

1648 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#578C211yesmaximal, characteristic, complemented
2C2×C43×#577C211yesmaximal, characteristic, complemented
3C2×C43×#454C211yesmaximal, characteristic, complemented
4C2×C43×#455C211yesmaximal, characteristic, complemented
5C43×#3013C211yesmaximal, characteristic, complemented
6C43×#3012C211yesmaximal, characteristic, complemented
7C43×#2020C211yesmaximal, characteristic, complemented
8C43×#2019C211yesmaximal, characteristic, complemented
9C43×#2015C211yesmaximal, characteristic, complemented
10C43×#2007C211yesmaximal, characteristic, complemented
11C43×#1908C211yesmaximal, characteristic, complemented
12C43×#1907C211yesmaximal, characteristic, complemented
13C43×#1876C211yesmaximal, characteristic, complemented
14C43×#1876C211yesmaximal, characteristic, complemented
15C43×#1793C211yesmaximal, characteristic, complemented
16C2×2−1+4×C43C2211yescharacteristic
17C2×2−1+4×C43C2211yescharacteristic, complemented
18C2×H(5,𝔽2)×C43C2211yescharacteristic
19C43×#578—24no—
20C43×#578—24no—
21C43×#577—24no—
22C43×#577—24no—
23C2×#137×C43—21no—
24C2×#137×C43—21no—
25C2×#137×C43—21no—
26C2×#137×C43C2211yescharacteristic
27C2×#137×C43C2211yescharacteristic
28C2×#137×C43C2211yescharacteristic
29C2×#137×C43C2211yescharacteristic, complemented
30C2×AGL(1,ℤ/8)×C43—21no—
31C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
32C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
33C2×#135×C43—21no—
34C2×#135×C43—21no—
35C2×#135×C43C2211yescharacteristic
36C2×#135×C43C2211yescharacteristic
37C22×Q16×C43—21no—
38C22×Q16×C43C2211yescharacteristic, complemented
39C22×SD16×C43—21no—
40C22×SD16×C43C2211yescharacteristic
41C2×#131×C43C2211yescharacteristic
42C2×#131×C43C2211yescharacteristic, complemented
43C43×#537C2211yescharacteristic
44C2×#124×C43C2211yescharacteristic
45C43×#455—24no—
46C43×#454—24no—
47C43×#452—21no—
48C43×#452—21no—
49C43×#451—21no—
50C43×#450—21no—
51C43×#449—21no—
52C43×#449—21no—
53C43×#448—21no—
54C43×#447—21no—
55C2×#104×C43C2211yescharacteristic
56C2×#104×C43C2211yescharacteristic
57C2×#104×C43C2211yescharacteristic, complemented
58C2×#104×C43C2211yescharacteristic, complemented
59C43×#417C2211yescharacteristic
60C43×#417C2211yescharacteristic, complemented
61C2×#103×C43C2211yescharacteristic, complemented
62C2×#102×C43C2211yescharacteristic
63C2×#101×C43C2211yescharacteristic, complemented
64C2×#101×C43C2211yescharacteristic, complemented
65C2×#100×C43C2211yescharacteristic
66C43×#408C2211yescharacteristic
67C43×#408C2211yescharacteristic, complemented
68C43×#391C2211yescharacteristic, complemented
69C43×#343C2211yescharacteristic, complemented
70C43×#341C2211yescharacteristic, complemented
71C43×#341C2211yescharacteristic, complemented
72C43×#336C2211yescharacteristic, complemented
732−1+4×C43—22no—
742−1+4×C43—22no—
752−1+4×C43—22no—
762−1+4×C43—22no—
772−1+4×C43—22no—
782−1+4×C43—41no—
792−1+4×C43—41no—
802−1+4×C43D414yescomplemented
81H(5,𝔽2)×C43—22no—
82H(5,𝔽2)×C43—22no—
83H(5,𝔽2)×C43—22no—
84H(5,𝔽2)×C43—41no—
85C2×#41×C43—21no—
86C2×#41×C43—21no—
87C2×#41×C43—21no—
88C2×#41×C43—21no—
89C2×#41×C43—21no—
90C2×#41×C43—21no—
91C2×#41×C43—41no—
92C2×#41×C43—41no—
93C2×#41×C43C2311yescharacteristic
94C2×#41×C43C2311yescharacteristic
95C2×#41×C43C2311yescharacteristic
96C2×#41×C43C2311yescharacteristic
97C22×Q8×C43—21no—
98C22×Q8×C43—21no—
99C22×Q8×C43—21no—
100C22×Q8×C43—21no—
101C22×Q8×C43C2311yescharacteristic
102C22×Q8×C43C2311yescharacteristic
103C22×D4×C43—21no—
104C22×D4×C43—21no—
105C22×D4×C43—41no—
106C22×D4×C43C2311yescharacteristic
107#137×C43—28no—
108#137×C43—28no—
109#137×C43—28no—
110#137×C43—22no—
111#137×C43—22no—
112#137×C43—22no—
113#137×C43—22no—
114#137×C43—22no—
115#137×C43—22no—
116#137×C43—41no—
117#137×C43D414yescomplemented
118AGL(1,ℤ/8)×C43—28no—
119AGL(1,ℤ/8)×C43—22no—
120AGL(1,ℤ/8)×C43—22no—
121AGL(1,ℤ/8)×C43—41no—
122AGL(1,ℤ/8)×C43D414yescomplemented
123#135×C43—28no—
124#135×C43—28no—
125#135×C43—22no—
126#135×C43—22no—
127#135×C43—22no—
128#135×C43—22no—
129C2×Q16×C43—28no—
130C2×Q16×C43—21no—
131C2×Q16×C43—21no—
132C2×Q16×C43—22no—
133C2×Q16×C43—22no—
134C2×Q16×C43—21no—
135C2×Q16×C43—21no—
136C2×Q16×C43—21no—
137C2×Q16×C43—21no—
138C2×Q16×C43D411yescharacteristic
139C2×Q16×C43D411yescharacteristic
140C2×SD16×C43—28no—
141C2×SD16×C43—21no—
142C2×SD16×C43—22no—
143C2×SD16×C43—21no—
144C2×SD16×C43—22no—
145C2×SD16×C43—21no—
146C2×SD16×C43—21no—
147C2×SD16×C43—21no—
148C2×SD16×C43—21no—
149C2×SD16×C43—21no—
150C2×SD16×C43—21no—
151C2×SD16×C43D411yescharacteristic
152C2×SD16×C43D411yescharacteristic
153C2×SD16×C43D411yescharacteristic
154C2×SD16×C43D411yescharacteristic
155C2×D8×C43—21no—
156C2×D8×C43—21no—
157C2×D8×C43D411yescharacteristic
158C2×D8×C43D411yescharacteristic
159#131×C43—22no—
160#131×C43—22no—
161#131×C43—22no—
162#131×C43—22no—
163C2×M16×C43—21no—
164C2×M16×C43—21no—
165C2×M16×C43C2311yescharacteristic
166C2×M16×C43C2311yescharacteristic
167C2×M16×C43C2311yescharacteristic
168C2×M16×C43C2311yescharacteristic
169C22×C8×C43—21no—
170C22×C8×C43—21no—
171C22×C8×C43C2311yescharacteristic
172C22×C8×C43C2311yescharacteristic
173#124×C43—22no—
174#124×C43—22no—
175C22⋊Q8×C43—21no—
176C22⋊Q8×C43—21no—
177#121×C43—21no—
178#121×C43—21no—
179#121×C43—41no—
180C2×C4⋊C4×C43C2311yescharacteristic
181C2×C22⋊C4×C43—41no—
182C2×C42×C43C2311yescharacteristic
183#104×C43—22no—
184#104×C43—22no—
185#104×C43—22no—
186#104×C43—22no—
187#103×C43—21no—
188#103×C43—21no—
189#103×C43—21no—
190#103×C43—21no—
191#102×C43—21no—
192#102×C43—21no—
193#102×C43—21no—
194#102×C43—21no—
195#101×C43—22no—
196#101×C43—41no—
197#100×C43—22no—
198C22⋊C8×C43—21no—
199C22⋊C8×C43—21no—
200C22⋊C8×C43—21no—
201C22⋊C8×C43—21no—
202#95×C43—41no—
203C24×C43—21no—
204C24×C43—41no—
205#41×C43—21no—
206#41×C43—21no—
207#41×C43—21no—
208#41×C43—21no—
209#41×C43—24no—
210#41×C43—24no—
211#41×C43—24no—
212#41×C43—24no—
213#41×C43—21no—
214#41×C43—21no—
215#41×C43—21no—
216#41×C43—21no—
217#41×C43—21no—
218#41×C43—21no—
219#41×C43—21no—
220#41×C43—21no—
221#41×C43—44no—
222#41×C43—42no—
223#41×C43—42no—
224#41×C43—42no—
225#41×C43—44no—
226#41×C43—42no—
227#41×C43—44no—
228#41×C43—42no—
229#41×C43—42no—
230#41×C43—44no—
231#41×C43—42no—
232#41×C43—42no—
233#41×C43C2×D412yes—
234#41×C43C2×D412yes—
235#41×C43C2×D412yes—
236#41×C43C2×D412yes—
237C2×Q8×C43—21no—
238C2×Q8×C43—21no—
239C2×Q8×C43—24no—
240C2×Q8×C43—24no—
241C2×Q8×C43—24no—
242C2×Q8×C43—21no—
243C2×Q8×C43—21no—
244C2×Q8×C43—21no—
245C2×Q8×C43—21no—
246C2×Q8×C43—21no—
247C2×Q8×C43—21no—
248C2×Q8×C43—21no—
249C2×Q8×C43—21no—
250C2×Q8×C43—41no—
251C2×Q8×C43—41no—
252C2×Q8×C43—42no—
253C2×Q8×C43—42no—
254C2×Q8×C43—42no—
255C2×Q8×C43—42no—
256C2×Q8×C43—42no—
257C2×Q8×C43C2×D411yescharacteristic
258C2×Q8×C43C2×D411yescharacteristic
259C2×Q8×C43C2×D412yes—
260C2×Q8×C43C2×D412yes—
261C2×Q8×C43C2×D411yescharacteristic
262C2×Q8×C43C2×D411yescharacteristic
263C2×D4×C43—21no—
264C2×D4×C43—21no—
265C2×D4×C43—21no—
266C2×D4×C43—21no—
267C2×D4×C43—21no—
268C2×D4×C43—24no—
269C2×D4×C43—21no—
270C2×D4×C43—21no—
271C2×D4×C43—21no—
272C2×D4×C43—21no—
273C2×D4×C43—41no—
274C2×D4×C43—41no—
275C2×D4×C43—41no—
276C2×D4×C43—41no—
277C2×D4×C43—41no—
278C2×D4×C43—44no—
279C2×D4×C43—42no—
280C2×D4×C43—42no—
281C2×D4×C43—44no—
282C2×D4×C43—42no—
283C2×D4×C43C2×D411yescharacteristic
284C2×D4×C43C2×D411yescharacteristic
285C2×D4×C43C2×D412yes—
286C2×D4×C43C2×D411yescharacteristic
287C2×D4×C43C2×D411yescharacteristic
288C22×C4×C43—21no—
289C22×C4×C43—21no—
290C22×C4×C43—21no—
291C22×C4×C43—21no—
292C22×C4×C43—21no—
293C22×C4×C43—21no—
294C22×C4×C43—21no—
295C22×C4×C43—21no—
296C22×C4×C43—41no—
297C22×C4×C43—41no—
298C22×C4×C43—41no—
299C22×C4×C43—41no—
300C22×C4×C43—41no—
301C22×C4×C43C2411yescharacteristic
302Q16×C43—24no—
303Q16×C43—24no—
304Q16×C43—24no—
305Q16×C43—24no—
306Q16×C43—22no—
307Q16×C43—24no—
308Q16×C43—22no—
309Q16×C43—42no—
310SD16×C43—24no—
311SD16×C43—24no—
312SD16×C43—24no—
313SD16×C43—24no—
314SD16×C43—22no—
315SD16×C43—24no—
316SD16×C43—22no—
317SD16×C43—24no—
318SD16×C43—22no—
319SD16×C43—22no—
320SD16×C43—42no—
321SD16×C43—42no—
322D8×C43—24no—
323D8×C43—22no—
324D8×C43—22no—
325D8×C43—42no—
326M16×C43—24no—
327M16×C43—24no—
328M16×C43—21no—
329M16×C43—21no—
330M16×C43—21no—
331M16×C43—21no—
332M16×C43—21no—
333M16×C43—21no—
334M16×C43C2×D412yes—
335M16×C43C2×D412yes—
336C2×C8×C43—24no—
337C2×C8×C43—24no—
338C2×C8×C43—21no—
339C2×C8×C43—21no—
340C2×C8×C43—21no—
341C2×C8×C43—21no—
342C2×C8×C43—21no—
343C2×C8×C43—21no—
344C2×C8×C43—21no—
345C2×C8×C43—21no—
346C2×C8×C43C2×D411yescharacteristic
347C2×C8×C43C2×D411yescharacteristic
348C2×C8×C43C2×D411yescharacteristic
349C2×C8×C43C2×D411yescharacteristic
350C4⋊C4×C43—21no—
351C4⋊C4×C43—21no—
352C4⋊C4×C43—41no—
353C22⋊C4×C43—44no—
354C22⋊C4×C43—41no—
355C22⋊C4×C43—41no—
356C42×C43—21no—
357C42×C43—21no—
358C23×C43—21no—
359C23×C43—21no—
360C23×C43—21no—
361C23×C43—21no—
362C23×C43—22no—
363C23×C43—44no—
364C23×C43—41no—
365C23×C43—41no—
366C23×C43—81no—
367C23×C43—81no—
368C23×C43—161no—
369C23×C43—161no—
370C23×C43H(5,𝔽2)11yescharacteristic
371Q8×C43—21no—
372Q8×C43—21no—
373Q8×C43—22no—
374Q8×C43—22no—
375Q8×C43—22no—
376Q8×C43—21no—
377Q8×C43—21no—
378Q8×C43—21no—
379Q8×C43—22no—
380Q8×C43—21no—
381Q8×C43—44no—
382Q8×C43—44no—
383Q8×C43—41no—
384Q8×C43—41no—
385Q8×C43—41no—
386Q8×C43—41no—
387Q8×C43#12012yes—
388Q8×C43#12012yes—
389D4×C43—22no—
390D4×C43—22no—
391D4×C43—22no—
392D4×C43—22no—
393D4×C43—22no—
394D4×C43—21no—
395D4×C43—21no—
396D4×C43—21no—
397D4×C43—21no—
398D4×C43—21no—
399D4×C43—22no—
400D4×C43—21no—
401D4×C43—44no—
402D4×C43—44no—
403D4×C43—44no—
404D4×C43—44no—
405D4×C43—41no—
406D4×C43—41no—
407D4×C43—41no—
408D4×C43—41no—
409D4×C43—41no—
410D4×C43—41no—
411D4×C43—161no—
412D4×C43#12012yes—
413D4×C43#12012yes—
414C2×C4×C43—21no—
415C2×C4×C43—21no—
416C2×C4×C43—22no—
417C2×C4×C43—22no—
418C2×C4×C43—22no—
419C2×C4×C43—22no—
420C2×C4×C43—22no—
421C2×C4×C43—22no—
422C2×C4×C43—21no—
423C2×C4×C43—21no—
424C2×C4×C43—44no—
425C2×C4×C43—44no—
426C2×C4×C43—44no—
427C2×C4×C43—44no—
428C2×C4×C43—44no—
429C2×C4×C43—41no—
430C2×C4×C43—41no—
431C2×C4×C43—41no—
432C2×C4×C43—41no—
433C2×C4×C43—41no—
434C2×C4×C43—41no—
435C2×C4×C43—41no—
436C2×C4×C43—41no—
437C2×C4×C43—41no—
438C2×C4×C43—41no—
439C2×C4×C43—41no—
440C2×C4×C43—41no—
441C2×C4×C43—81no—
442C2×C4×C43C22×D411yescharacteristic
443C2×C4×C43C22×D411yescharacteristic
444C2×C4×C43C22×D411yescharacteristic
445C2×C4×C43C22×D411yescharacteristic
446C2×C4×C43C22×D411yescharacteristic
447C2×C4×C43H(5,𝔽2)11yescharacteristic
448C8×C43—21no—
449C8×C43—21no—
450C8×C43—22no—
451C8×C43—22no—
452C8×C43—21no—
453C8×C43—21no—
454C8×C43—41no—
455C8×C43—41no—
456#23889C4311yesmaximal, characteristic, direct product factor, Sylow
457C22×C43—21no—
458C22×C43—21no—
459C22×C43—22no—
460C22×C43—22no—
461C22×C43—41no—
462C22×C43—41no—
463C22×C43—41no—
464C22×C43—41no—
465C22×C43—41no—
466C22×C43—42no—
467C22×C43—41no—
468C22×C43—41no—
469C22×C43—41no—
470C22×C43—41no—
471C22×C43—41no—
472C22×C43—82no—
473C22×C43—81no—
474C22×C43—81no—
475C22×C43—161no—
476C22×C43—164no—
477C22×C43#53411yescharacteristic
478C22×C43D4211yescharacteristic
479C22×C43D4211yescharacteristic
480C4×C43—22no—
481C4×C43—22no—
482C4×C43—41no—
483C4×C43—42no—
484C4×C43—42no—
485C4×C43—41no—
486C4×C43—81no—
487C4×C43—81no—
488C4×C43C2×#12011yescharacteristic
489C4×C43C2×#12011yescharacteristic
490C4×C43D4211yescharacteristic
491C4×C43D4211yescharacteristic
492C2×#578C2×C4311yescharacteristic, complemented
493C2×#577C2×C4311yescharacteristic, complemented
494C2×#454C2×C4311yescharacteristic, complemented
495C2×#455C2×C4311yescharacteristic, complemented
496#3013C2×C4311yescharacteristic, complemented
497#3012C2×C4311yescharacteristic, complemented
498#2020C2×C4311yescharacteristic, complemented
499#2019C2×C4311yescharacteristic, complemented
500#2015C2×C4311yescharacteristic, complemented
501#2007C2×C4311yescharacteristic, complemented
502#1908C2×C4311yescharacteristic, complemented
503#1907C2×C4311yescharacteristic, complemented
504#1876C2×C4311yescharacteristic, complemented
505#1876C2×C4311yescharacteristic, complemented
506#1793C2×C4311yescharacteristic, complemented
507C2×C43—21no—
508C2×C43—21no—
509C2×C43—42no—
510C2×C43—42no—
511C2×C43—81no—
512C2×C43—81no—
513C2×C43—82no—
514C2×C43#240311yescharacteristic
515C2×C43#328911yescharacteristic
516C2×C43#329011yescharacteristic
517C2×2−1+4C22×C4311yescharacteristic
518C2×2−1+4C22×C4311yescharacteristic, complemented
519C2×H(5,𝔽2)C22×C4311yescharacteristic
520#578—24no—
521#578—24no—
522#577—24no—
523#577—24no—
524C2×#137—21no—
525C2×#137—21no—
526C2×#137—21no—
527C2×#137C22×C4311yescharacteristic
528C2×#137C22×C4311yescharacteristic
529C2×#137C22×C4311yescharacteristic
530C2×#137C22×C4311yescharacteristic, complemented
531C2×AGL(1,ℤ/8)—21no—
532C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
533C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
534C2×#135—21no—
535C2×#135—21no—
536C2×#135C22×C4311yescharacteristic
537C2×#135C22×C4311yescharacteristic
538C22×Q16—21no—
539C22×Q16C22×C4311yescharacteristic, complemented
540C22×SD16—21no—
541C22×SD16C22×C4311yescharacteristic
542C2×#131C22×C4311yescharacteristic
543C2×#131C22×C4311yescharacteristic, complemented
544#537C22×C4311yescharacteristic
545C2×#124C22×C4311yescharacteristic
546#455—24no—
547#454—24no—
548#452—21no—
549#452—21no—
550#451—21no—
551#450—21no—
552#449—21no—
553#449—21no—
554#448—21no—
555#447—21no—
556C2×#104C22×C4311yescharacteristic
557C2×#104C22×C4311yescharacteristic
558C2×#104C22×C4311yescharacteristic, complemented
559C2×#104C22×C4311yescharacteristic, complemented
560#417C22×C4311yescharacteristic
561#417C22×C4311yescharacteristic, complemented
562C2×#103C22×C4311yescharacteristic, complemented
563C2×#102C22×C4311yescharacteristic
564C2×#101C22×C4311yescharacteristic, complemented
565C2×#101C22×C4311yescharacteristic, complemented
566C2×#100C22×C4311yescharacteristic
567#408C22×C4311yescharacteristic
568#408C22×C4311yescharacteristic, complemented
569#391C22×C4311yescharacteristic, complemented
570#343C22×C4311yescharacteristic, complemented
571#341C22×C4311yescharacteristic, complemented
572#341C22×C4311yescharacteristic, complemented
573#336C22×C4311yescharacteristic, complemented
574C43#2388911yescharacteristic, direct product factor, Sylow
5752−1+4—22no—
5762−1+4—22no—
5772−1+4—22no—
5782−1+4—22no—
5792−1+4—22no—
5802−1+4—41no—
5812−1+4—41no—
5822−1+4D4×C4314yescomplemented
583H(5,𝔽2)—22no—
584H(5,𝔽2)—22no—
585H(5,𝔽2)—22no—
586H(5,𝔽2)—41no—
587C2×#41—21no—
588C2×#41—21no—
589C2×#41—21no—
590C2×#41—21no—
591C2×#41—21no—
592C2×#41—21no—
593C2×#41—41no—
594C2×#41—41no—
595C2×#41C23×C4311yescharacteristic
596C2×#41C23×C4311yescharacteristic
597C2×#41C23×C4311yescharacteristic
598C2×#41C23×C4311yescharacteristic
599C22×Q8—21no—
600C22×Q8—21no—
601C22×Q8—21no—
602C22×Q8—21no—
603C22×Q8C23×C4311yescharacteristic
604C22×Q8C23×C4311yescharacteristic
605C22×D4—21no—
606C22×D4—21no—
607C22×D4—41no—
608C22×D4C23×C4311yescharacteristic
609#137—28no—
610#137—28no—
611#137—28no—
612#137—22no—
613#137—22no—
614#137—22no—
615#137—22no—
616#137—22no—
617#137—22no—
618#137—41no—
619#137D4×C4314yescomplemented
620AGL(1,ℤ/8)—28no—
621AGL(1,ℤ/8)—22no—
622AGL(1,ℤ/8)—22no—
623AGL(1,ℤ/8)—41no—
624AGL(1,ℤ/8)D4×C4314yescomplemented
625#135—28no—
626#135—28no—
627#135—22no—
628#135—22no—
629#135—22no—
630#135—22no—
631C2×Q16—28no—
632C2×Q16—21no—
633C2×Q16—21no—
634C2×Q16—22no—
635C2×Q16—22no—
636C2×Q16—21no—
637C2×Q16—21no—
638C2×Q16—21no—
639C2×Q16—21no—
640C2×Q16D4×C4311yescharacteristic
641C2×Q16D4×C4311yescharacteristic
642C2×SD16—28no—
643C2×SD16—21no—
644C2×SD16—22no—
645C2×SD16—21no—
646C2×SD16—22no—
647C2×SD16—21no—
648C2×SD16—21no—
649C2×SD16—21no—
650C2×SD16—21no—
651C2×SD16—21no—
652C2×SD16—21no—
653C2×SD16D4×C4311yescharacteristic
654C2×SD16D4×C4311yescharacteristic
655C2×SD16D4×C4311yescharacteristic
656C2×SD16D4×C4311yescharacteristic
657C2×D8—21no—
658C2×D8—21no—
659C2×D8D4×C4311yescharacteristic
660C2×D8D4×C4311yescharacteristic
661#131—22no—
662#131—22no—
663#131—22no—
664#131—22no—
665C2×M16—21no—
666C2×M16—21no—
667C2×M16C23×C4311yescharacteristic
668C2×M16C23×C4311yescharacteristic
669C2×M16C23×C4311yescharacteristic
670C2×M16C23×C4311yescharacteristic
671C22×C8—21no—
672C22×C8—21no—
673C22×C8C23×C4311yescharacteristic
674C22×C8C23×C4311yescharacteristic
675#124—22no—
676#124—22no—
677C22⋊Q8—21no—
678C22⋊Q8—21no—
679#121—21no—
680#121—21no—
681#121—41no—
682C2×C4⋊C4C23×C4311yescharacteristic
683C2×C22⋊C4—41no—
684C2×C42C23×C4311yescharacteristic
685#104—22no—
686#104—22no—
687#104—22no—
688#104—22no—
689#103—21no—
690#103—21no—
691#103—21no—
692#103—21no—
693#102—21no—
694#102—21no—
695#102—21no—
696#102—21no—
697#101—22no—
698#101—41no—
699#100—22no—
700C22⋊C8—21no—
701C22⋊C8—21no—
702C22⋊C8—21no—
703C22⋊C8—21no—
704#95—41no—
705C24—21no—
706C24—41no—
707#41—21no—
708#41—21no—
709#41—21no—
710#41—21no—
711#41—24no—
712#41—24no—
713#41—24no—
714#41—24no—
715#41—21no—
716#41—21no—
717#41—21no—
718#41—21no—
719#41—21no—
720#41—21no—
721#41—21no—
722#41—21no—
723#41—44no—
724#41—42no—
725#41—42no—
726#41—42no—
727#41—44no—
728#41—42no—
729#41—44no—
730#41—42no—
731#41—42no—
732#41—44no—
733#41—42no—
734#41—42no—
735#41C2×D4×C4312yes—
736#41C2×D4×C4312yes—
737#41C2×D4×C4312yes—
738#41C2×D4×C4312yes—
739C2×Q8—21no—
740C2×Q8—21no—
741C2×Q8—24no—
742C2×Q8—24no—
743C2×Q8—24no—
744C2×Q8—21no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—21no—
748C2×Q8—21no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—41no—
753C2×Q8—41no—
754C2×Q8—42no—
755C2×Q8—42no—
756C2×Q8—42no—
757C2×Q8—42no—
758C2×Q8—42no—
759C2×Q8C2×D4×C4311yescharacteristic
760C2×Q8C2×D4×C4311yescharacteristic
761C2×Q8C2×D4×C4312yes—
762C2×Q8C2×D4×C4312yes—
763C2×Q8C2×D4×C4311yescharacteristic
764C2×Q8C2×D4×C4311yescharacteristic
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—24no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—42no—
776C2×D4—41no—
777C2×D4—41no—
778C2×D4—42no—
779C2×D4—44no—
780C2×D4—44no—
781C2×D4—41no—
782C2×D4—41no—
783C2×D4—42no—
784C2×D4—41no—
785C2×D4C2×D4×C4311yescharacteristic
786C2×D4C2×D4×C4311yescharacteristic
787C2×D4C2×D4×C4312yes—
788C2×D4C2×D4×C4311yescharacteristic
789C2×D4C2×D4×C4311yescharacteristic
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—41no—
799C22×C4—41no—
800C22×C4—41no—
801C22×C4—41no—
802C22×C4—41no—
803C22×C4C24×C4311yescharacteristic
804Q16—24no—
805Q16—24no—
806Q16—24no—
807Q16—24no—
808Q16—22no—
809Q16—24no—
810Q16—22no—
811Q16—42no—
812SD16—24no—
813SD16—24no—
814SD16—24no—
815SD16—24no—
816SD16—22no—
817SD16—24no—
818SD16—22no—
819SD16—24no—
820SD16—22no—
821SD16—22no—
822SD16—42no—
823SD16—42no—
824D8—24no—
825D8—22no—
826D8—22no—
827D8—42no—
828M16—24no—
829M16—24no—
830M16—21no—
831M16—21no—
832M16—21no—
833M16—21no—
834M16—21no—
835M16—21no—
836M16C2×D4×C4312yes—
837M16C2×D4×C4312yes—
838C2×C8—24no—
839C2×C8—24no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8C2×D4×C4311yescharacteristic
849C2×C8C2×D4×C4311yescharacteristic
850C2×C8C2×D4×C4311yescharacteristic
851C2×C8C2×D4×C4311yescharacteristic
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—41no—
855C22⋊C4—44no—
856C22⋊C4—41no—
857C22⋊C4—41no—
858C42—21no—
859C42—21no—
860C23—21no—
861C23—21no—
862C23—21no—
863C23—21no—
864C23—22no—
865C23—44no—
866C23—41no—
867C23—41no—
868C23—81no—
869C23—81no—
870C23—161no—
871C23—161no—
872C23H(5,𝔽2)×C4311yescharacteristic
873Q8—21no—
874Q8—21no—
875Q8—22no—
876Q8—22no—
877Q8—22no—
878Q8—21no—
879Q8—21no—
880Q8—21no—
881Q8—22no—
882Q8—21no—
883Q8—44no—
884Q8—44no—
885Q8—41no—
886Q8—41no—
887Q8—41no—
888Q8—41no—
889Q8#120×C4312yes—
890Q8#120×C4312yes—
891D4—22no—
892D4—22no—
893D4—22no—
894D4—22no—
895D4—22no—
896D4—21no—
897D4—21no—
898D4—21no—
899D4—21no—
900D4—21no—
901D4—22no—
902D4—21no—
903D4—44no—
904D4—44no—
905D4—44no—
906D4—44no—
907D4—41no—
908D4—41no—
909D4—41no—
910D4—41no—
911D4—41no—
912D4—41no—
913D4—161no—
914D4#120×C4312yes—
915D4#120×C4312yes—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—44no—
927C2×C4—44no—
928C2×C4—44no—
929C2×C4—44no—
930C2×C4—44no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—81no—
944C2×C4C22×D4×C4311yescharacteristic
945C2×C4C22×D4×C4311yescharacteristic
946C2×C4C22×D4×C4311yescharacteristic
947C2×C4C22×D4×C4311yescharacteristic
948C2×C4C22×D4×C4311yescharacteristic
949C2×C4H(5,𝔽2)×C4311yescharacteristic
950C8—21no—
951C8—21no—
952C8—22no—
953C8—22no—
954C8—21no—
955C8—21no—
956C8—41no—
957C8—41no—
958C22—21no—
959C22—21no—
960C22—22no—
961C22—22no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—42no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—41no—
973C22—82no—
974C22—81no—
975C22—81no—
976C22—161no—
977C22—164no—
978C22C43×#53411yescharacteristic
979C22D42×C4311yescharacteristic
980C22D42×C4311yescharacteristic
981C4—22no—
982C4—22no—
983C4—41no—
984C4—42no—
985C4—42no—
986C4—41no—
987C4—81no—
988C4—81no—
989C4C2×#120×C4311yescharacteristic
990C4C2×#120×C4311yescharacteristic
991C4D42×C4311yescharacteristic
992C4D42×C4311yescharacteristic
993C2—21no—
994C2—21no—
995C2—42no—
996C2—42no—
997C2—81no—
998C2—81no—
999C2—82no—
1000C2C43×#240311yescharacteristic
1001C2C43×#328911yescharacteristic
1002C2C43×#329011yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC22×C4C24×C43
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C22×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#578C2semidirect
2. C2×C43×#577C2semidirect
3. C2×C43×#454C2semidirect
4. C2×C43×#455C2semidirect
5. C43×#3013C2semidirect
6. C43×#3012C2semidirect
7. C43×#2020C2semidirect
8. C43×#2019C2semidirect
9. C43×#2015C2semidirect
10. C43×#2007C2semidirect
11. C43×#1908C2semidirect
12. C43×#1907C2semidirect
13. C43×#1876C2semidirect
14. C43×#1876C2semidirect
15. C43×#1793C2semidirect
17. C2×2−1+4×C43C22semidirect
29. C2×#137×C43C22semidirect
38. C22×Q16×C43C22semidirect
42. C2×#131×C43C22semidirect
57. C2×#104×C43C22semidirect
58. C2×#104×C43C22semidirect
60. C43×#417C22semidirect
61. C2×#103×C43C22semidirect
63. C2×#101×C43C22semidirect
64. C2×#101×C43C22semidirect
67. C43×#408C22semidirect
68. C43×#391C22semidirect
69. C43×#343C22semidirect
70. C43×#341C22semidirect
71. C43×#341C22semidirect
72. C43×#336C22semidirect
80. 2−1+4×C43D4semidirect
117. #137×C43D4semidirect
122. AGL(1,ℤ/8)×C43D4semidirect
456. #23889C43direct (N × H)
492. C2×#578C2×C43semidirect
493. C2×#577C2×C43semidirect
494. C2×#454C2×C43semidirect
495. C2×#455C2×C43semidirect
496. #3013C2×C43semidirect
497. #3012C2×C43semidirect
498. #2020C2×C43semidirect
499. #2019C2×C43semidirect
500. #2015C2×C43semidirect
501. #2007C2×C43semidirect
502. #1908C2×C43semidirect
503. #1907C2×C43semidirect
504. #1876C2×C43semidirect
505. #1876C2×C43semidirect
506. #1793C2×C43semidirect
518. C2×2−1+4C22×C43semidirect
530. C2×#137C22×C43semidirect
539. C22×Q16C22×C43semidirect
543. C2×#131C22×C43semidirect
558. C2×#104C22×C43semidirect
559. C2×#104C22×C43semidirect
561. #417C22×C43semidirect
562. C2×#103C22×C43semidirect
564. C2×#101C22×C43semidirect
565. C2×#101C22×C43semidirect
568. #408C22×C43semidirect
569. #391C22×C43semidirect
570. #343C22×C43semidirect
571. #341C22×C43semidirect
572. #341C22×C43semidirect
573. #336C22×C43semidirect
574. C43#23889direct (N × H)
582. 2−1+4D4×C43semidirect
619. #137D4×C43semidirect
624. AGL(1,ℤ/8)D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#5782
C2×C43×#5772
C2×C43×#4542
C2×C43×#4552
C43×#30132
C43×#30122
C43×#20202
C43×#20192
C43×#20152
C43×#20072
C43×#19082
C43×#19072
C43×#18762
C43×#17932
#2388943