Finite Group Databasebeta

← D43×#3586 #26010440

Subgroups — D43×#3586 #26010440

Order 11008.

10794 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#585×D43C211yesmaximal, characteristic, complemented
2C2×2−1+4×D43C211yesmaximal, characteristic, complemented
3#19149383C211yesmaximal, characteristic, complemented
4#19149382C211yesmaximal, characteristic, complemented
5#19149381C211yesmaximal, characteristic, complemented
6#19149380C218yesmaximal, complemented
7#19149379C216yesmaximal, complemented
8#19149378C216yesmaximal, complemented
9#19149377C218yesmaximal, complemented
10#578×D43C218yesmaximal, complemented
11#577×D43C218yesmaximal, complemented
12#575×D43C216yesmaximal, complemented
13C2×#137×D43C216yesmaximal, complemented
14#568×D43C211yesmaximal, characteristic, complemented
15C43×#3586C211yesmaximal, characteristic, complemented
16#14583736—21no—
17#14583736C2214yescomplemented
18#14583735—24no—
19#14583735C2211yescharacteristic, complemented
20#14583735C2216yescomplemented
21#14583734—23no—
22#14583734C2214yescomplemented
23C2×#13063373—21no—
24C2×#13063373C2213yescomplemented
25C2×#13063372—23no—
26C2×#13063372C2211yescharacteristic, complemented
27C2×#13063372C2213yescomplemented
282−1+4×D43—24no—
292−1+4×D43—24no—
302−1+4×D43—21no—
312−1+4×D43C2218yescomplemented
322−1+4×D43C2214yescomplemented
332−1+4×D43C2218yescomplemented
34H(5,𝔽2)×D43—23no—
35H(5,𝔽2)×D43C2214yescomplemented
36C2×#41×D43—24no—
37C2×#41×D43—23no—
38C2×#41×D43C2216yes—
39C2×#41×D43C2211yescharacteristic
40C2×#41×D43C2213yescomplemented
41C22×Q8×D43—21no—
42C22×Q8×D43C2213yescomplemented
43#14583716C2218yescomplemented
44#14583715C22124yescomplemented
45#14583715C22124yescomplemented
46#14583714C2218yescomplemented
47#14583714C2218yescomplemented
48#14583713C22124yescomplemented
49#14583712C22124yescomplemented
50#14583711C2218yescomplemented
51#14583710C2218yescomplemented
52#14583709C22124yescomplemented
53#14583708C22124yescomplemented
54#14583707C2218yescomplemented
55#14583706C22124yescomplemented
56#14583705C22124yescomplemented
57#14583699C2216yescomplemented
58#14583698C22112yescomplemented
59#14583698C22112yescomplemented
60#14583697C2216yescomplemented
61#14583697C2216yescomplemented
62#14583696C22124yescomplemented
63#14583695C22112yescomplemented
64#14583695C22112yescomplemented
65C2×#13063358C2216yescomplemented
66C2×#13063357C22112yescomplemented
67C2×#13063356C2216yescomplemented
68C2×#13063355C2216yescomplemented
69C2×#13063354C22112yescomplemented
70#137×D43C22112yescomplemented
71#137×D43C22124yescomplemented
72#137×D43C22112yescomplemented
73#137×D43C22124yescomplemented
74#137×D43C22124yescomplemented
75AGL(1,ℤ/8)×D43C2214yescomplemented
76AGL(1,ℤ/8)×D43C22112yescomplemented
77#135×D43C22124yescomplemented
78C2×Q16×D43C22112yescomplemented
79C2×SD16×D43C22112yescomplemented
80#14583666C2211yescharacteristic, complemented
81#14583665C2216yescomplemented
82#14583664C2218yescomplemented
83#131×D43C2218yescomplemented
84C2×M16×D43C2216yescomplemented
85C43×#585C2211yescharacteristic, complemented
86C2×2−1+4×C43C2211yescharacteristic, complemented
87C43×#578C2218yescomplemented
88C43×#577C2218yescomplemented
89C43×#575C2216yescomplemented
90C2×#137×C43C2216yescomplemented
91C43×#568C2211yescharacteristic, complemented
92#13063373—21no—
93#13063373—28no—
94#13063373—28no—
95#13063373—24no—
96#13063373—24no—
97#13063373—212no—
98#13063373C23124yescomplemented
99#13063373C23112yescomplemented
100#13063372—24no—
101#13063372—24no—
102#13063372—224no—
103#13063372—224no—
104#13063372—212no—
105#13063372—212no—
106#13063372—26no—
107#13063372C23124yescomplemented
108#13063372C23112yescomplemented
109#13063372C2318yescomplemented
110#13063372C2314yescomplemented
111#13063371—24no—
112#13063371—212no—
113#13063371—26no—
114#13063371C23112yescomplemented
115#13063371C2314yescomplemented
116#13063370—23no—
117#13063370—212no—
118#13063370—212no—
119#13063370—212no—
120#13063370C23112yescomplemented
121C2×#10621902—24no—
122C2×#10621902—23no—
123C2×#10621902D411yescharacteristic
124C2×#10621902C2316yes—
125C2×#10621902C2313yescomplemented
126C2×#10621898—26no—
127C2×#10621898—212no—
128C2×#10621898—23no—
129C2×#10621898—26no—
130C2×#10621898—23no—
131C2×#10621898C2313yes—
132C2×#10621898C2316yes—
133C2×#10621898C2313yescomplemented
134C2×#10621900—23no—
135C2×#10621900—26no—
136C2×#10621900—26no—
137C2×#10621900—23no—
138C2×#10621900—212no—
139C2×#10621900D413yes—
140C2×#10621900C2316yes—
141C2×#10621900C2313yescomplemented
142#41×D43—24no—
143#41×D43—24no—
144#41×D43—24no—
145#41×D43—212no—
146#41×D43—212no—
147#41×D43—224no—
148#41×D43—224no—
149#41×D43—212no—
150#41×D43—26no—
151#41×D43—26no—
152#41×D43—26no—
153#41×D43—26no—
154#41×D43—26no—
155#41×D43—26no—
156#41×D43D414yes—
157#41×D43D414yes—
158#41×D43C23112yes—
159#41×D43C23112yes—
160#41×D43C2314yes—
161#41×D43C23112yes—
162#41×D43C23112yes—
163#41×D43C2314yes—
164#41×D43C2314yes—
165#41×D43C23112yescomplemented
166C22×Dic86—23no—
167C22×Dic86—23no—
168C22×Dic86C2313yescomplemented
169C2×Q8×D43—21no—
170C2×Q8×D43—28no—
171C2×Q8×D43—28no—
172C2×Q8×D43—24no—
173C2×Q8×D43—23no—
174C2×Q8×D43—26no—
175C2×Q8×D43—26no—
176C2×Q8×D43—23no—
177C2×Q8×D43—23no—
178C2×Q8×D43D411yescharacteristic
179C2×Q8×D43C23112yes—
180C2×Q8×D43C2316yes—
181C2×Q8×D43C2313yes—
182C2×Q8×D43C2316yescomplemented
183C2×Q8×D43C23112yescomplemented
184C2×D4×D43—23no—
185C2×D4×D43—26no—
186C2×D4×D43—212no—
187C2×D4×D43D413yes—
188C2×D4×D43C2316yes—
189C2×D4×D43C2311yescharacteristic
190C22×C4×D43—23no—
191C22×C4×D43—23no—
192C22×C4×D43—26no—
193C22×C4×D43C2313yes—
194#13063358C23112yescomplemented
195#13063358C23124yescomplemented
196#13063358C23112yescomplemented
197#13063357C23124yescomplemented
198#13063357C23148yescomplemented
199#13063357C23124yescomplemented
200#13063356C23112yescomplemented
201#13063356C23124yescomplemented
202#13063356C23112yescomplemented
203#13063355C23112yescomplemented
204#13063355C23124yescomplemented
205#13063355C23112yescomplemented
206#13063354C23124yescomplemented
207#13063354C23148yescomplemented
208#13063354C23124yescomplemented
209#13063353C2314yescomplemented
210#13063353C23112yescomplemented
211#13063352C2318yescomplemented
212#13063352C23124yescomplemented
213#13063351C2314yescomplemented
214#13063351C23112yescomplemented
215#13063350C2314yescomplemented
216#13063350C23112yescomplemented
217#13063349C2318yescomplemented
218#13063349C23124yescomplemented
219#13063348C23124yescomplemented
220#13063347C23124yescomplemented
221#13063346C23124yescomplemented
222#13063346C23124yescomplemented
223#13063345C23124yescomplemented
224#13063345C23124yescomplemented
225#13063344C23124yescomplemented
226C2×Dic172C23112yescomplemented
227C2×#10621885C23112yescomplemented
228C2×#10621885C23112yescomplemented
229Q16×D43C23124yes—
230Q16×D43C23148yescomplemented
231C2×#10621873C23112yescomplemented
232C2×#10621883C23112yescomplemented
233C2×#10621884C23112yescomplemented
234SD16×D43C23124yes—
235SD16×D43C2318yes—
236SD16×D43C23148yescomplemented
237D8×D43C2318yes—
238#13063333C23124yescomplemented
239#13063332C2318yescomplemented
240#13063331C23124yescomplemented
241C2×#10621877C2316yescomplemented
242C2×#10621872C23112yescomplemented
243M16×D43C2314yes—
244M16×D43C23112yes—
245M16×D43C23112yescomplemented
246M16×D43C23112yescomplemented
247C2×C8×D43C23112yes—
2482−1+4×C43—24no—
2492−1+4×C43—21no—
2502−1+4×C43C2318yescomplemented
2512−1+4×C43C2314yescomplemented
252H(5,𝔽2)×C43—23no—
253H(5,𝔽2)×C43C2314yescomplemented
254C2×#41×C43—24no—
255C2×#41×C43—23no—
256C2×#41×C43C2316yes—
257C2×#41×C43C2311yescharacteristic
258C2×#41×C43C2313yescomplemented
259C22×Q8×C43—21no—
260C22×Q8×C43C2313yescomplemented
261#137×C43C23112yescomplemented
262#137×C43C23124yescomplemented
263#137×C43C23112yescomplemented
264AGL(1,ℤ/8)×C43C2314yescomplemented
265AGL(1,ℤ/8)×C43C23112yescomplemented
266#135×C43C23124yescomplemented
267C2×Q16×C43C23112yescomplemented
268C2×SD16×C43C23112yescomplemented
269#131×C43C2318yescomplemented
270C2×M16×C43C2316yescomplemented
271C23×D43—21no—
272C23×D43—26no—
273C23×D43C2×D413yes—
274#41×C43—24no—
275#41×C43—212no—
276#41×C43—224no—
277#41×C43—26no—
278#41×C43—26no—
279#41×C43—26no—
280#41×C43C2×D414yes—
281#41×C43C24112yes—
282#41×C43C24112yes—
283#41×C43C2414yes—
284#41×C43C2414yes—
285C2×Q8×C43—28no—
286C2×Q8×C43—24no—
287C2×Q8×C43—23no—
288C2×Q8×C43—26no—
289C2×Q8×C43C2×D411yescharacteristic
290C2×Q8×C43C24112yes—
291C2×Q8×C43C2416yes—
292C2×Q8×C43C2413yes—
293C2×D4×C43—212no—
294C2×D4×C43—23no—
295C2×D4×C43—26no—
296C2×D4×C43C2×D413yes—
297C2×D4×C43C2416yes—
298C2×D4×C43C2411yescharacteristic
299C22×C4×C43—23no—
300C22×C4×C43—26no—
301C22×C4×C43—23no—
302C22×C4×C43C2413yes—
303C2×C22⋊D43—224no—
304C2×C22⋊D43—21no—
305C2×C22⋊D43—26no—
306C2×C22⋊D43—23no—
307C2×C22⋊D43—26no—
308C2×C22⋊D43—23no—
309C2×C22⋊D43—26no—
310C2×C22⋊D43C2×D416yes—
311C22×Dic43—23no—
312C22×Dic43—26no—
313C22×Dic43—23no—
314C22×Dic43C2×D413yes—
315#10621902—24no—
316#10621902—212no—
317#10621902—224no—
318#10621902—26no—
319#10621902—26no—
320#10621902—26no—
321#10621902C2×D414yes—
322#10621902C2×D414yes—
323#10621902C24112yes—
324#10621902C24112yes—
325#10621902C2414yes—
326Q8×D43—28no—
327Q8×D43—24no—
328Q8×D43—23no—
329Q8×D43—212no—
330Q8×D43—23no—
331Q8×D43—212no—
332Q8×D43—26no—
333Q8×D43—212no—
334Q8×D43—212no—
335Q8×D43—212no—
336Q8×D43—26no—
337Q8×D43—224no—
338Q8×D43—212no—
339Q8×D43C2×D414yes—
340Q8×D43C2×D414yes—
341Q8×D43C2416yes—
342Q8×D43C2414yes—
343Q8×D43C24124yes—
344Q8×D43C24112yes—
345Q8×D43C2416yes—
346#10621900—212no—
347#10621900—224no—
348#10621900—224no—
349#10621900—248no—
350#10621900—24no—
351#10621900—212no—
352#10621900—212no—
353#10621900—212no—
354#10621900—212no—
355#10621900—212no—
356#10621900—26no—
357#10621900—26no—
358#10621900—26no—
359#10621900—212no—
360#10621900C2×D4112yes—
361#10621900C2×D4112yes—
362#10621900C24112yes—
363#10621900C24112yes—
364#10621900C2414yes—
365D4×D43—212no—
366D4×D43—224no—
367D4×D43—212no—
368D4×D43—26no—
369D4×D43—21no—
370D4×D43—21no—
371D4×D43—26no—
372D4×D43—24no—
373D4×D43—212no—
374D4×D43—212no—
375D4×D43—212no—
376D4×D43—212no—
377D4×D43—212no—
378D4×D43C2×D4112yes—
379D4×D43C2×D4112yes—
380D4×D43C2412yes—
381D4×D43C2414yes—
382D4×D43C24112yes—
383D4×D43C2412yes—
384#10621898—26no—
385#10621898—26no—
386#10621898—26no—
387#10621898—224no—
388#10621898—248no—
389#10621898—212no—
390#10621898—224no—
391#10621898—212no—
392#10621898—24no—
393#10621898—212no—
394#10621898—212no—
395#10621898—212no—
396#10621898—212no—
397#10621898—212no—
398#10621898C2×D4112yes—
399#10621898C24112yes—
400#10621898C24112yes—
401#10621898C24112yes—
402#10621898C2414yes—
403C2×D172—212no—
404C2×D172—23no—
405C2×D172—26no—
406C2×D172C2×D413yes—
407C2×D172C2416yes—
408C2×D172C2411yescharacteristic
409C2×C4×D43—23no—
410C2×C4×D43—26no—
411C2×C4×D43—23no—
412C2×C4×D43—26no—
413C2×C4×D43—24no—
414C2×C4×D43—212no—
415C2×C4×D43—212no—
416C2×C4×D43—212no—
417C2×C4×D43—212no—
418C2×C4×D43—212no—
419C2×C4×D43—23no—
420C2×C4×D43—26no—
421C2×C4×D43—212no—
422C2×C4×D43—212no—
423C2×C4×D43—26no—
424C2×C4×D43C2×D413yes—
425C2×C4×D43C2×D416yes—
426C2×C4×D43C2×D416yes—
427C2×C4×D43C2×D413yes—
428C2×C4×D43C2416yes—
429C2×C4×D43C2411yescharacteristic
430C2×C4×D43C2413yes—
431C2×C4×D43C2416yes—
432C2×Dic86—23no—
433C2×Dic86—26no—
434C2×Dic86—23no—
435C2×Dic86—26no—
436C2×Dic86—212no—
437C2×Dic86—212no—
438C2×Dic86—26no—
439C2×Dic86—224no—
440C2×Dic86—212no—
441C2×Dic86C2×D413yes—
442C2×Dic86C24112yes—
443C2×Dic86C2416yes—
444C2×Dic86C2413yes—
445Q16×C43C24124yes—
446SD16×C43C24124yes—
447SD16×C43C2418yes—
448D8×C43C2418yes—
449M16×C43C2414yes—
450M16×C43C24112yes—
451C2×C8×C43C24112yes—
452#10621885C24124yes—
453#10621885C24124yes—
454#10621884C24124yes—
455#10621884C2418yes—
456#10621883C24124yes—
457#10621883C2418yes—
458#10621882C2418yes—
459#10621882C2418yes—
460#10621877C2414yes—
461#10621877C24112yes—
462C2×C43⋊C8C24112yes—
463Dic172C24124yes—
464D344C2418yes—
465#10621873C24124yes—
466#10621873C2418yes—
467#10621872C2418yes—
468#10621872C24124yes—
469C8×D43C2418yes—
470C8×D43C24124yes—
471C23×C43—21no—
472C23×C43—26no—
473C23×C43C22×D413yes—
474C22×D43—21no—
475C22×D43—26no—
476C22×D43—22no—
477C22×D43—22no—
478C22×D43—24no—
479C22×D43—212no—
480C22×D43—46no—
481C22×D43—44no—
482C22×D43—812no—
483C22×D43C22×D411yescharacteristic
484C22×D43C22×D416yes—
485C22×D43C22×D413yes—
486C22×D43C22×D416yes—
487Q8×C43—212no—
488Q8×C43—23no—
489Q8×C43—26no—
490Q8×C43C22×D414yes—
491Q8×C43C2516yes—
492Q8×C43C2514yes—
493D4×C43—24no—
494D4×C43—212no—
495D4×C43—212no—
496D4×C43—26no—
497D4×C43—21no—
498D4×C43C22×D4112yes—
499D4×C43C2512yes—
500D4×C43C2514yes—
501C2×C4×C43—23no—
502C2×C4×C43—212no—
503C2×C4×C43—26no—
504C2×C4×C43—212no—
505C2×C4×C43—212no—
506C2×C4×C43—24no—
507C2×C4×C43C22×D413yes—
508C2×C4×C43C22×D416yes—
509C2×C4×C43C2516yes—
510C2×C4×C43C2511yescharacteristic
511C22⋊D43—212no—
512C22⋊D43—24no—
513C22⋊D43—212no—
514C22⋊D43—212no—
515C22⋊D43—24no—
516C22⋊D43—212no—
517C22⋊D43—22no—
518C22⋊D43—22no—
519C22⋊D43—24no—
520C22⋊D43—212no—
521C22⋊D43C22×D4124yes—
522C2×Dic43—23no—
523C2×Dic43—212no—
524C2×Dic43—26no—
525C2×Dic43—212no—
526C2×Dic43—212no—
527C2×Dic43—24no—
528C2×Dic43C22×D411yescharacteristic
529C2×Dic43C22×D416yes—
530C2×Dic43C22×D413yes—
531C2×Dic43C22×D416yes—
532D172—24no—
533D172—212no—
534D172—212no—
535D172—26no—
536D172—21no—
537D172C22×D4112yes—
538D172C2514yes—
539D172C2512yes—
540C4×D43—24no—
541C4×D43—26no—
542C4×D43—26no—
543C4×D43—212no—
544C4×D43—224no—
545C4×D43—24no—
546C4×D43—212no—
547C4×D43—212no—
548C4×D43—24no—
549C4×D43—212no—
550C4×D43—212no—
551C4×D43C22×D411yescharacteristic
552C4×D43C22×D416yes—
553C4×D43C22×D416yes—
554C4×D43C22×D416yes—
555C4×D43C22×D416yes—
556C4×D43C22×D411yescharacteristic
557C4×D43C22×D416yes—
558C4×D43C2511yescharacteristic
559C4×D43C2516yes—
560C4×D43C2511yescharacteristic
561Dic86—212no—
562Dic86—23no—
563Dic86—26no—
564Dic86—26no—
565Dic86—224no—
566Dic86—26no—
567Dic86—24no—
568Dic86—212no—
569Dic86C22×D4112yes—
570Dic86C2516yes—
571Dic86C2514yes—
572C8×C43C2518yes—
573C43⋊C8C2518yes—
574C2×#3586—431nomaximal, Sylow
575C22×C43—24no—
576C22×C43—22no—
577C22×C43—43no—
578C22×C43—42no—
579C22×C43—86no—
580C22×C43C23×D411yescharacteristic
581C22×C43C23×D416yes—
582C2×D43—22no—
583C2×D43—212no—
584C2×D43—24no—
585C2×D43—22no—
586C2×D43—46no—
587C2×D43—43no—
588C2×D43—44no—
589C2×D43—42no—
590C2×D43—44no—
591C2×D43—48no—
592C2×D43—812no—
593C2×D43—86no—
594C2×D43C23×D411yescharacteristic
595C2×D43C23×D416yes—
596C2×D43C23×D411yescharacteristic
597C4×C43—26no—
598C4×C43—24no—
599C4×C43C23×D416yes—
600C4×C43C23×D411yescharacteristic
601C4×C43C2611yescharacteristic
602Dic43—26no—
603Dic43—24no—
604Dic43C23×D411yescharacteristic
605Dic43C23×D416yes—
606Dic43C23×D411yescharacteristic
607C2×#585—431no—
608C22×2−1+4—431no—
609#3586—431no—
610#3586—431no—
611#3586—438no—
612#3586—438no—
613#3586—436no—
614#3586—436no—
615#3586—431no—
616#3586D4311yescharacteristic, direct product factor
617C2×#578—438no—
618C2×#577—438no—
619C2×#575—436no—
620C22×#137—436no—
621C2×#568—431no—
622C2×C43—21no—
623C2×C43—26no—
624C2×C43—42no—
625C2×C43—44no—
626C2×C43C24×D411yescharacteristic
627D43—21no—
628D43—26no—
629D43—42no—
630D43—44no—
631D43#358612yesdirect product factor
632#585—434no—
633#585—434no—
634#585—436no—
635#585—431no—
636#585—864no—
637#585—863no—
638#585—861no—
639#585C2×D4311yescharacteristic, complemented
640C2×2−1+4—438no—
641C2×2−1+4—438no—
642C2×2−1+4—434no—
643C2×2−1+4—431no—
644C2×2−1+4—433no—
645C2×2−1+4—433no—
646C2×2−1+4—861no—
647C2×2−1+4—861no—
648C2×2−1+4—863no—
649C2×2−1+4—864no—
650C2×2−1+4—864no—
651C2×2−1+4C2×D4311yescharacteristic, complemented
652C2×H(5,𝔽2)—434no—
653C2×H(5,𝔽2)—863no—
654C22×#41—431no—
655C22×#41—436no—
656C22×#41—433no—
657C22×#41—863no—
658C22×#41—864no—
659C23×Q8—433no—
660C23×Q8—861no—
661#578—438no—
662#578—438no—
663#578—4324no—
664#578—4324no—
665#578—4324no—
666#578—4324no—
667#578—438no—
668#578C2×D4318yescomplemented
669#577—438no—
670#577—438no—
671#577—4324no—
672#577—4324no—
673#577—4324no—
674#577—4324no—
675#577—438no—
676#577C2×D4318yescomplemented
677#575—436no—
678#575—436no—
679#575—4312no—
680#575—4312no—
681#575—4312no—
682#575—4312no—
683#575—4324no—
684#575—436no—
685#575C2×D4316yescomplemented
686C2×#137—436no—
687C2×#137—436no—
688C2×#137—4324no—
689C2×#137—4324no—
690C2×#137—4312no—
691C2×#137—4324no—
692C2×#137—4312no—
693C2×#137—4312no—
694C2×#137—4312no—
695C2×#137—436no—
696C2×#137C2×D4316yescomplemented
697C2×AGL(1,ℤ/8)—434no—
698C2×AGL(1,ℤ/8)—4312no—
699C2×#135—4324no—
700C22×Q16—4312no—
701C22×SD16—4312no—
702#568—431no—
703#568—438no—
704#568—436no—
705#568C2×D4311yescharacteristic, complemented
706C2×#131—438no—
707C22×M16—436no—
708C43C2×#358611yescharacteristic, complemented, Sylow
7092−1+4—24no—
7102−1+4—21no—
7112−1+4—4324no—
7122−1+4—438no—
7132−1+4—4312no—
7142−1+4—434no—
7152−1+4—4324no—
7162−1+4—4312no—
7172−1+4—864no—
7182−1+4—868no—
7192−1+4—868no—
7202−1+4—8612no—
7212−1+4—864no—
7222−1+4—864no—
7232−1+4—866no—
7242−1+4—8624no—
7252−1+4—8624no—
7262−1+4—8612no—
7272−1+4—8612no—
7282−1+4—864no—
7292−1+4—861no—
7302−1+4C22×D4318yescomplemented
7312−1+4C22×D4314yescomplemented
732H(5,𝔽2)—23no—
733H(5,𝔽2)—4312no—
734H(5,𝔽2)—434no—
735H(5,𝔽2)—4312no—
736H(5,𝔽2)—8612no—
737H(5,𝔽2)—8612no—
738H(5,𝔽2)—8612no—
739H(5,𝔽2)—8612no—
740H(5,𝔽2)—866no—
741H(5,𝔽2)—864no—
742H(5,𝔽2)—863no—
743H(5,𝔽2)C22×D4314yescomplemented
744C2×#41—24no—
745C2×#41—23no—
746C2×#41—434no—
747C2×#41—434no—
748C2×#41—434no—
749C2×#41—434no—
750C2×#41—431no—
751C2×#41—433no—
752C2×#41—433no—
753C2×#41—4312no—
754C2×#41—4312no—
755C2×#41—434no—
756C2×#41—4312no—
757C2×#41—4312no—
758C2×#41—4312no—
759C2×#41—436no—
760C2×#41—433no—
761C2×#41—436no—
762C2×#41—433no—
763C2×#41—436no—
764C2×#41—433no—
765C2×#41—863no—
766C2×#41—866no—
767C2×#41—866no—
768C2×#41—863no—
769C2×#41—8612no—
770C2×#41—863no—
771C2×#41—866no—
772C2×#41—866no—
773C2×#41—866no—
774C2×#41—866no—
775C2×#41—866no—
776C2×#41—866no—
777C2×#41—866no—
778C2×#41—866no—
779C2×#41—8612no—
780C2×#41—863no—
781C2×#41—8612no—
782C2×#41—8624no—
783C2×#41—8624no—
784C2×#41—864no—
785C2×#41—864no—
786C2×#41—864no—
787C2×#41—8612no—
788C2×#41—8612no—
789C2×#41—864no—
790C2×#41—863no—
791C2×#41C22×D4316yes—
792C2×#41C22×D4311yescharacteristic
793C2×#41C22×D4313yescomplemented
794C22×Q8—21no—
795C22×Q8—431no—
796C22×Q8—4312no—
797C22×Q8—436no—
798C22×Q8—433no—
799C22×Q8—436no—
800C22×Q8—4312no—
801C22×Q8—433no—
802C22×Q8—863no—
803C22×Q8—863no—
804C22×Q8—863no—
805C22×Q8—866no—
806C22×Q8—863no—
807C22×Q8—866no—
808C22×Q8—868no—
809C22×Q8—868no—
810C22×Q8—863no—
811C22×Q8—864no—
812C22×Q8—861no—
813C22×Q8C22×D4313yescomplemented
814C22×D4—433no—
815C22×D4—436no—
816C22×D4—431no—
817C22×D4—8612no—
818C22×D4—863no—
819C22×D4—866no—
820C23×C4—433no—
821C23×C4—863no—
822C23×C4—866no—
823C23×C4—863no—
824#137—4312no—
825#137—4324no—
826#137—4312no—
827#137—4312no—
828#137—4324no—
829#137—4312no—
830#137—4324no—
831#137—4348no—
832#137—4324no—
833#137—4324no—
834#137—4348no—
835#137—4324no—
836#137—4312no—
837#137—4324no—
838#137—4312no—
839#137C22×D43112yescomplemented
840#137C22×D43124yescomplemented
841#137C22×D43112yescomplemented
842AGL(1,ℤ/8)—434no—
843AGL(1,ℤ/8)—4312no—
844AGL(1,ℤ/8)—434no—
845AGL(1,ℤ/8)—4312no—
846AGL(1,ℤ/8)—438no—
847AGL(1,ℤ/8)—4324no—
848AGL(1,ℤ/8)—438no—
849AGL(1,ℤ/8)—4324no—
850AGL(1,ℤ/8)—434no—
851AGL(1,ℤ/8)—4312no—
852AGL(1,ℤ/8)C22×D4314yescomplemented
853AGL(1,ℤ/8)C22×D43112yescomplemented
854#135—4324no—
855#135—4324no—
856#135—4324no—
857#135—4324no—
858#135—4324no—
859#135—4324no—
860#135—4324no—
861#135C22×D43124yescomplemented
862C2×Q16—4312no—
863C2×Q16—4312no—
864C2×Q16—4324no—
865C2×Q16—4348no—
866C2×Q16—4312no—
867C2×Q16C22×D43112yescomplemented
868C2×SD16—4312no—
869C2×SD16—4312no—
870C2×SD16—4324no—
871C2×SD16—4348no—
872C2×SD16—438no—
873C2×SD16—4312no—
874C2×SD16C22×D43112yescomplemented
875C2×D8—438no—
876#131—438no—
877#131—4324no—
878#131—4324no—
879#131C22×D4318yescomplemented
880C2×M16—436no—
881C2×M16—434no—
882C2×M16—4312no—
883C2×M16—4312no—
884C2×M16—4312no—
885C2×M16—4312no—
886C2×M16C22×D4316yescomplemented
887C22×C8—4312no—
888C24—433no—
889C24—866no—
890C24—861no—
891#41—24no—
892#41—212no—
893#41—224no—
894#41—26no—
895#41—26no—
896#41—26no—
897#41—434no—
898#41—434no—
899#41—4312no—
900#41—4312no—
901#41—4312no—
902#41—4312no—
903#41—4312no—
904#41—4312no—
905#41—434no—
906#41—4312no—
907#41—4312no—
908#41—434no—
909#41—4312no—
910#41—4312no—
911#41—434no—
912#41—864no—
913#41—8612no—
914#41—8612no—
915#41—8612no—
916#41—8612no—
917#41—8612no—
918#41—8624no—
919#41—8612no—
920#41—8648no—
921#41—8624no—
922#41—8612no—
923#41—864no—
924#41—8612no—
925#41—866no—
926#41—8612no—
927#41—8612no—
928#41—866no—
929#41—8612no—
930#41—8612no—
931#41—866no—
932#41—866no—
933#41—866no—
934#41—866no—
935#41—8624no—
936#41—8648no—
937#41—8612no—
938#41—8612no—
939#41—8624no—
940#41—864no—
941#41—8612no—
942#41—8624no—
943#41—866no—
944#41—866no—
945#41—866no—
946#41D4×D4314yes—
947#41C23×D43112yes—
948#41C23×D43112yes—
949#41C23×D4314yes—
950#41C23×D4314yes—
951C2×Q8—28no—
952C2×Q8—24no—
953C2×Q8—23no—
954C2×Q8—26no—
955C2×Q8—434no—
956C2×Q8—434no—
957C2×Q8—433no—
958C2×Q8—436no—
959C2×Q8—434no—
960C2×Q8—4324no—
961C2×Q8—4312no—
962C2×Q8—436no—
963C2×Q8—4312no—
964C2×Q8—436no—
965C2×Q8—433no—
966C2×Q8—863no—
967C2×Q8—866no—
968C2×Q8—8612no—
969C2×Q8—8612no—
970C2×Q8—866no—
971C2×Q8—8624no—
972C2×Q8—8612no—
973C2×Q8—863no—
974C2×Q8—863no—
975C2×Q8—8612no—
976C2×Q8—8612no—
977C2×Q8—866no—
978C2×Q8—8612no—
979C2×Q8—8612no—
980C2×Q8—8612no—
981C2×Q8—866no—
982C2×Q8—8624no—
983C2×Q8—8612no—
984C2×Q8—868no—
985C2×Q8—864no—
986C2×Q8—863no—
987C2×Q8—866no—
988C2×Q8D4×D4311yescharacteristic
989C2×Q8C23×D43112yes—
990C2×Q8C23×D4316yes—
991C2×Q8C23×D4313yes—
992C2×D4—23no—
993C2×D4—26no—
994C2×D4—212no—
995C2×D4—436no—
996C2×D4—4312no—
997C2×D4—4312no—
998C2×D4—432no—
999C2×D4—434no—
1000C2×D4—4312no—
1001C2×D4—432no—
1002C2×D4—433no—
1003C2×D4—436no—
1004C2×D4—431no—
1005C2×D4—8612no—
1006C2×D4—863no—
1007C2×D4—866no—
1008C2×D4—866no—
1009C2×D4—861no—
1010C2×D4—861no—
1011C2×D4—866no—
1012C2×D4—861no—
1013C2×D4—866no—
1014C2×D4—8624no—
1015C2×D4—8612no—
1016C2×D4—864no—
1017C2×D4—8612no—
1018C2×D4—8612no—
1019C2×D4—8612no—
1020C2×D4—8612no—
1021C2×D4—8612no—
1022C2×D4—8624no—
1023C2×D4—863no—
1024C2×D4—866no—
1025C2×D4—863no—
1026C2×D4—866no—
1027C2×D4—8612no—
1028C2×D4D4×D4313yes—
1029C2×D4C23×D4316yes—
1030C2×D4C23×D4311yescharacteristic
1031C22×C4—23no—
1032C22×C4—23no—
1033C22×C4—26no—
1034C22×C4—433no—
1035C22×C4—433no—
1036C22×C4—436no—
1037C22×C4—433no—
1038C22×C4—436no—
1039C22×C4—436no—
1040C22×C4—431no—
1041C22×C4—433no—
1042C22×C4—436no—
1043C22×C4—864no—
1044C22×C4—8612no—
1045C22×C4—863no—
1046C22×C4—8612no—
1047C22×C4—8612no—
1048C22×C4—866no—
1049C22×C4—8612no—
1050C22×C4—8612no—
1051C22×C4—863no—
1052C22×C4—866no—
1053C22×C4—866no—
1054C22×C4—8612no—
1055C22×C4—8612no—
1056C22×C4—863no—
1057C22×C4—866no—
1058C22×C4—863no—
1059C22×C4—863no—
1060C22×C4—866no—
1061C22×C4C23×D4313yes—
1062Q16—4324no—
1063Q16—4324no—
1064Q16—4324no—
1065Q16C23×D43124yes—
1066SD16—4324no—
1067SD16—438no—
1068SD16—4324no—
1069SD16—438no—
1070SD16—4324no—
1071SD16—438no—
1072SD16C23×D43124yes—
1073SD16C23×D4318yes—
1074D8—438no—
1075D8—438no—
1076D8—438no—
1077D8C23×D4318yes—
1078M16—434no—
1079M16—4312no—
1080M16—438no—
1081M16—4324no—
1082M16C23×D4314yes—
1083M16C23×D43112yes—
1084C2×C8—4312no—
1085C2×C8—438no—
1086C2×C8—4324no—
1087C2×C8C23×D43112yes—
1088C23—21no—
1089C23—26no—
1090C23—431no—
1091C23—436no—
1092C23—436no—
1093C23—433no—
1094C23—8612no—
1095C23—862no—
1096C23—862no—
1097C23—864no—
1098C23—866no—
1099C23—861no—
1100C23—34412no—
1101C23—1726no—
1102C23—1724no—
1103C23C2×D4×D4313yes—
1104Q8—23no—
1105Q8—212no—
1106Q8—26no—
1107Q8—4312no—
1108Q8—436no—
1109Q8—434no—
1110Q8—866no—
1111Q8—866no—
1112Q8—8624no—
1113Q8—864no—
1114Q8—8612no—
1115Q8—863no—
1116Q8—8612no—
1117Q8—866no—
1118Q8C2×D4×D4314yes—
1119Q8C24×D4316yes—
1120Q8C24×D4314yes—
1121D4—24no—
1122D4—212no—
1123D4—212no—
1124D4—26no—
1125D4—21no—
1126D4—4324no—
1127D4—4312no—
1128D4—432no—
1129D4—434no—
1130D4—864no—
1131D4—8612no—
1132D4—8612no—
1133D4—864no—
1134D4—8612no—
1135D4—862no—
1136D4—862no—
1137D4—864no—
1138D4—8612no—
1139D4—8612no—
1140D4—864no—
1141D4—8612no—
1142D4—8612no—
1143D4—866no—
1144D4—861no—
1145D4C2×D4×D43112yes—
1146D4C24×D4312yes—
1147D4C24×D4314yes—
1148C2×C4—23no—
1149C2×C4—26no—
1150C2×C4—212no—
1151C2×C4—24no—
1152C2×C4—212no—
1153C2×C4—212no—
1154C2×C4—431no—
1155C2×C4—433no—
1156C2×C4—436no—
1157C2×C4—436no—
1158C2×C4—431no—
1159C2×C4—431no—
1160C2×C4—436no—
1161C2×C4—436no—
1162C2×C4—436no—
1163C2×C4—436no—
1164C2×C4—436no—
1165C2×C4—431no—
1166C2×C4—436no—
1167C2×C4—431no—
1168C2×C4—864no—
1169C2×C4—8612no—
1170C2×C4—8612no—
1171C2×C4—864no—
1172C2×C4—866no—
1173C2×C4—866no—
1174C2×C4—8612no—
1175C2×C4—8624no—
1176C2×C4—864no—
1177C2×C4—8612no—
1178C2×C4—8612no—
1179C2×C4—863no—
1180C2×C4—866no—
1181C2×C4—8612no—
1182C2×C4—864no—
1183C2×C4—8612no—
1184C2×C4—8612no—
1185C2×C4C2×D4×D4313yes—
1186C2×C4C2×D4×D4316yes—
1187C2×C4C24×D4316yes—
1188C2×C4C24×D4311yescharacteristic
1189C8—438no—
1190C8C24×D4318yes—
1191C22—22no—
1192C22—24no—
1193C22—43no—
1194C22—42no—
1195C22—86no—
1196C22—431no—
1197C22—431no—
1198C22—436no—
1199C22—8612no—
1200C22—862no—
1201C22—862no—
1202C22—864no—
1203C22—3446no—
1204C22—34412no—
1205C22—1723no—
1206C22—1726no—
1207C22—1722no—
1208C22—1728no—
1209C22—1724no—
1210C22—1724no—
1211C22C22×D4×D4311yescharacteristic
1212C22C22×D4×D4316yes—
1213C4—24no—
1214C4—26no—
1215C4—431no—
1216C4—431no—
1217C4—436no—
1218C4—864no—
1219C4—866no—
1220C4C22×D4×D4311yescharacteristic
1221C4C22×D4×D4316yes—
1222C4C25×D4311yescharacteristic
1223C2—21no—
1224C2—26no—
1225C2—42no—
1226C2—44no—
1227C2—432no—
1228C2—866no—
1229C2—861no—
1230C2—1724no—
1231C2—1722no—
1232C2C23×D4×D4311yescharacteristic
subgroupG/H
centerC2C23×D4×D43
commutator, cosocleC4×C43C26
FrattiniC4C25×D43
FittingC43×#3586C2
socleC2×C43C24×D4
hypercenter#3586D43
hypocenterC43C2×#3586
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×#41 ◁ #3586

Complements

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

NH ≅ G/Ntype
1. #585×D43C2semidirect
2. C2×2−1+4×D43C2semidirect
3. #19149383C2semidirect
4. #19149382C2semidirect
5. #19149381C2semidirect
6. #19149380C2semidirect
7. #19149379C2semidirect
8. #19149378C2semidirect
9. #19149377C2semidirect
10. #578×D43C2semidirect
11. #577×D43C2semidirect
12. #575×D43C2semidirect
13. C2×#137×D43C2semidirect
14. #568×D43C2semidirect
15. C43×#3586C2semidirect
17. #14583736C22semidirect
19. #14583735C22semidirect
20. #14583735C22semidirect
22. #14583734C22semidirect
24. C2×#13063373C22semidirect
26. C2×#13063372C22semidirect
27. C2×#13063372C22semidirect
31. 2−1+4×D43C22semidirect
32. 2−1+4×D43C22semidirect
33. 2−1+4×D43C22semidirect
35. H(5,𝔽2)×D43C22semidirect
40. C2×#41×D43C22semidirect
42. C22×Q8×D43C22semidirect
43. #14583716C22semidirect
44. #14583715C22semidirect
45. #14583715C22semidirect
46. #14583714C22semidirect
47. #14583714C22semidirect
48. #14583713C22semidirect
49. #14583712C22semidirect
50. #14583711C22semidirect
51. #14583710C22semidirect
52. #14583709C22semidirect
53. #14583708C22semidirect
54. #14583707C22semidirect
55. #14583706C22semidirect
56. #14583705C22semidirect
57. #14583699C22semidirect
58. #14583698C22semidirect
59. #14583698C22semidirect
60. #14583697C22semidirect
61. #14583697C22semidirect
62. #14583696C22semidirect
63. #14583695C22semidirect
64. #14583695C22semidirect
65. C2×#13063358C22semidirect
66. C2×#13063357C22semidirect
67. C2×#13063356C22semidirect
68. C2×#13063355C22semidirect
69. C2×#13063354C22semidirect
70. #137×D43C22semidirect
71. #137×D43C22semidirect
72. #137×D43C22semidirect
73. #137×D43C22semidirect
74. #137×D43C22semidirect
75. AGL(1,ℤ/8)×D43C22semidirect
76. AGL(1,ℤ/8)×D43C22semidirect
77. #135×D43C22semidirect
78. C2×Q16×D43C22semidirect
79. C2×SD16×D43C22semidirect
80. #14583666C22semidirect
81. #14583665C22semidirect
82. #14583664C22semidirect
83. #131×D43C22semidirect
84. C2×M16×D43C22semidirect
85. C43×#585C22semidirect
86. C2×2−1+4×C43C22semidirect
87. C43×#578C22semidirect
88. C43×#577C22semidirect
89. C43×#575C22semidirect
90. C2×#137×C43C22semidirect
91. C43×#568C22semidirect
98. #13063373C23semidirect
99. #13063373C23semidirect
107. #13063372C23semidirect
108. #13063372C23semidirect
109. #13063372C23semidirect
110. #13063372C23semidirect
114. #13063371C23semidirect
115. #13063371C23semidirect
120. #13063370C23semidirect
125. C2×#10621902C23semidirect
133. C2×#10621898C23semidirect
141. C2×#10621900C23semidirect
165. #41×D43C23semidirect
168. C22×Dic86C23semidirect
182. C2×Q8×D43C23semidirect
183. C2×Q8×D43C23semidirect
194. #13063358C23semidirect
195. #13063358C23semidirect
196. #13063358C23semidirect
197. #13063357C23semidirect
198. #13063357C23semidirect
199. #13063357C23semidirect
200. #13063356C23semidirect
201. #13063356C23semidirect
202. #13063356C23semidirect
203. #13063355C23semidirect
204. #13063355C23semidirect
205. #13063355C23semidirect
206. #13063354C23semidirect
207. #13063354C23semidirect
208. #13063354C23semidirect
209. #13063353C23semidirect
210. #13063353C23semidirect
211. #13063352C23semidirect
212. #13063352C23semidirect
213. #13063351C23semidirect
214. #13063351C23semidirect
215. #13063350C23semidirect
216. #13063350C23semidirect
217. #13063349C23semidirect
218. #13063349C23semidirect
219. #13063348C23semidirect
220. #13063347C23semidirect
221. #13063346C23semidirect
222. #13063346C23semidirect
223. #13063345C23semidirect
224. #13063345C23semidirect
225. #13063344C23semidirect
226. C2×Dic172C23semidirect
227. C2×#10621885C23semidirect
228. C2×#10621885C23semidirect
230. Q16×D43C23semidirect
231. C2×#10621873C23semidirect
232. C2×#10621883C23semidirect
233. C2×#10621884C23semidirect
236. SD16×D43C23semidirect
238. #13063333C23semidirect
239. #13063332C23semidirect
240. #13063331C23semidirect
241. C2×#10621877C23semidirect
242. C2×#10621872C23semidirect
245. M16×D43C23semidirect
246. M16×D43C23semidirect
250. 2−1+4×C43C23semidirect
251. 2−1+4×C43C23semidirect
253. H(5,𝔽2)×C43C23semidirect
258. C2×#41×C43C23semidirect
260. C22×Q8×C43C23semidirect
261. #137×C43C23semidirect
262. #137×C43C23semidirect
263. #137×C43C23semidirect
264. AGL(1,ℤ/8)×C43C23semidirect
265. AGL(1,ℤ/8)×C43C23semidirect
266. #135×C43C23semidirect
267. C2×Q16×C43C23semidirect
268. C2×SD16×C43C23semidirect
269. #131×C43C23semidirect
270. C2×M16×C43C23semidirect
616. #3586D43direct (N × H)
631. D43#3586direct (N × H)
639. #585C2×D43semidirect
651. C2×2−1+4C2×D43semidirect
668. #578C2×D43semidirect
676. #577C2×D43semidirect
685. #575C2×D43semidirect
696. C2×#137C2×D43semidirect
705. #568C2×D43semidirect
708. C43C2×#3586semidirect
730. 2−1+4C22×D43semidirect
731. 2−1+4C22×D43semidirect
743. H(5,𝔽2)C22×D43semidirect
793. C2×#41C22×D43semidirect
813. C22×Q8C22×D43semidirect
839. #137C22×D43semidirect
840. #137C22×D43semidirect
841. #137C22×D43semidirect
852. AGL(1,ℤ/8)C22×D43semidirect
853. AGL(1,ℤ/8)C22×D43semidirect
861. #135C22×D43semidirect
867. C2×Q16C22×D43semidirect
874. C2×SD16C22×D43semidirect
879. #131C22×D43semidirect
886. C2×M16C22×D43semidirect

Maximal subgroups

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

subgroupindex
#585×D432
C2×2−1+4×D432
#191493832
#191493822
#191493812
#191493802
#191493792
#191493782
#191493772
#578×D432
#577×D432
#575×D432
C2×#137×D432
#568×D432
C43×#35862
C2×#358643