Finite Group Databasebeta

← C2×#19149377 #26010441

Subgroups — C2×#19149377 #26010441

Order 11008.

10794 conjugacy classes of subgroups.

The subgroup lattice has 1104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583734C211yesmaximal, characteristic, complemented
2C2×2−1+4×D43C211yesmaximal, characteristic, complemented
3#19149377C2132yesmaximal, direct product factor
4C2×#14583716C211yesmaximal, characteristic, complemented
5C2×#14583715C213yesmaximal, complemented
6C2×#14583714C211yesmaximal, characteristic, complemented
7C2×#14583713C213yesmaximal, complemented
8C2×#14583710C211yesmaximal, characteristic, complemented
9C2×#14583709C213yesmaximal, complemented
10C2×#14583705C213yesmaximal, complemented
11C2×#14583696C213yesmaximal, complemented
12C2×#14583695C213yesmaximal, complemented
13C22×#13063354C213yesmaximal, complemented
14C2×#137×D43C213yesmaximal, complemented
15C2×#14583664C211yesmaximal, characteristic, complemented
16C2×C43×#577C211yesmaximal, characteristic, complemented
17#14583734—28no—
18#14583734C22116yescomplemented
19C2×#13063373—21no—
20C2×#13063373C2213yescomplemented
21C2×#13063372—23no—
22C2×#13063372—21no—
23C2×#13063372C2211yescharacteristic, complemented
24C2×#13063372C2211yescharacteristic, complemented
25C2×#13063372C2213yescomplemented
26C2×#13063372C2213yescomplemented
272−1+4×D43—28no—
282−1+4×D43C22116yescomplemented
29C2×#13063370—23no—
30C2×#13063370C2213yescomplemented
31C22×#10621900—23no—
32C22×#10621900C2213yes—
33C2×#41×D43—21no—
34C2×#41×D43—23no—
35C2×#41×D43C2213yes—
36C2×#41×D43C2211yescharacteristic
37C2×#41×D43C2213yescomplemented
38C22×Q8×D43—21no—
39C22×Q8×D43C2213yescomplemented
40#14583716C22116yescomplemented
41#14583715C22148yescomplemented
42#14583714C22116yescomplemented
43#14583713C22148yescomplemented
44#14583710C22116yescomplemented
45#14583709C22148yescomplemented
46#14583705C22148yescomplemented
47#14583696C22148yescomplemented
48#14583695C22148yescomplemented
49C2×#13063358C2213yescomplemented
50C2×#13063358C2213yescomplemented
51C2×#13063357C2213yescomplemented
52C2×#13063357C2213yescomplemented
53C2×#13063356C2213yescomplemented
54C2×#13063355C2213yescomplemented
55C2×#13063355C2213yescomplemented
56C2×#13063354C2216yescomplemented
57C2×#13063354C2213yescomplemented
58C2×#13063354C2216yescomplemented
59C2×#13063354C2216yescomplemented
60C2×#13063354C2213yescomplemented
61C2×#13063354C22148yescomplemented
62#137×D43C22148yescomplemented
63C2×#13063352C2211yescharacteristic, complemented
64C2×#13063352C2213yescomplemented
65C2×#13063351C2213yescomplemented
66C2×#13063349C2213yescomplemented
67C2×#13063349C2213yescomplemented
68C2×#13063347C2213yescomplemented
69C2×#13063346C2216yescomplemented
70C2×#13063345C2213yescomplemented
71C2×#13063345C2213yescomplemented
72C2×#13063344C2216yescomplemented
73C22×Dic172C2213yescomplemented
74C22×#10621885C2213yescomplemented
75C2×Q16×D43C2216yescomplemented
76C22×#10621883C2213yescomplemented
77C2×SD16×D43C2216yescomplemented
78#14583664C22116yescomplemented
79C2×#13063333C2213yescomplemented
80C2×#13063332C2211yescharacteristic, complemented
81C2×#13063331C2213yescomplemented
82C22×#10621872C2213yescomplemented
83C2×M16×D43C2213yescomplemented
84C2×2−1+4×C43C2211yescharacteristic, complemented
85C2×H(5,𝔽2)×C43C2211yescharacteristic, complemented
86C43×#577C22116yescomplemented
87C2×#137×C43C2213yescomplemented
88C2×AGL(1,ℤ/8)×C43C2213yescomplemented
89C2×#135×C43C2213yescomplemented
90C22×SD16×C43C2213yescomplemented
91C2×#131×C43C2211yescharacteristic, complemented
92#13063373—216no—
93#13063373—212no—
94#13063373C23124yescomplemented
95#13063372—24no—
96#13063372—24no—
97#13063372—216no—
98#13063372—248no—
99#13063372—212no—
100#13063372—212no—
101#13063372C23124yescomplemented
102#13063372C23124yescomplemented
103#13063372C2318yescomplemented
104#13063372C2318yescomplemented
105#13063370—248no—
106#13063370—212no—
107#13063370C23124yescomplemented
108C2×#10621902—23no—
109C2×#10621902D411yescharacteristic
110C2×#10621902C2313yes—
111C2×#10621902C2311yescharacteristic
112C2×#10621898—26no—
113C2×#10621898—23no—
114C2×#10621898—23no—
115C2×#10621898—23no—
116C2×#10621898—23no—
117C2×#10621898C2313yes—
118C2×#10621898C2313yes—
119C2×#10621898C2313yes—
120C2×#10621900—23no—
121C2×#10621900—23no—
122C2×#10621900—26no—
123C2×#10621900—26no—
124C2×#10621900—23no—
125C2×#10621900—23no—
126C2×#10621900—248no—
127C2×#10621900—23no—
128C2×#10621900—23no—
129C2×#10621900—212no—
130C2×#10621900—23no—
131C2×#10621900D413yes—
132C2×#10621900C2313yes—
133C2×#10621900C2316yes—
134C2×#10621900C2313yes—
135C2×#10621900C23124yes—
136#41×D43—216no—
137#41×D43—248no—
138#41×D43—212no—
139#41×D43—212no—
140#41×D43D418yes—
141#41×D43C23124yes—
142#41×D43C2318yes—
143#41×D43C23124yescomplemented
144C22×Dic86—23no—
145C22×Dic86—23no—
146C22×Dic86—23no—
147C22×Dic86C2313yes—
148C22×Dic86C2313yes—
149C2×Q8×D43—21no—
150C2×Q8×D43—21no—
151C2×Q8×D43—216no—
152C2×Q8×D43—23no—
153C2×Q8×D43—212no—
154C2×Q8×D43—23no—
155C2×Q8×D43—23no—
156C2×Q8×D43D411yescharacteristic
157C2×Q8×D43C2316yes—
158C2×Q8×D43C2313yes—
159C2×Q8×D43C2313yes—
160C2×Q8×D43C23124yescomplemented
161C22×C22⋊D43—23no—
162C22×C22⋊D43—26no—
163C2×D4×D43—23no—
164C2×D4×D43—23no—
165C2×D4×D43—23no—
166C2×D4×D43D413yes—
167C2×D4×D43C2313yes—
168C2×D4×D43C2311yescharacteristic
169C23×Dic43—23no—
170C22×C4×D43—23no—
171C22×C4×D43—23no—
172C22×C4×D43—23no—
173C22×C4×D43C2313yes—
174#13063358C23124yescomplemented
175#13063358C23124yescomplemented
176#13063357C23124yescomplemented
177#13063357C23124yescomplemented
178#13063356C23124yescomplemented
179#13063355C23124yescomplemented
180#13063355C23124yescomplemented
181#13063354C23148yescomplemented
182#13063354C23124yescomplemented
183#13063354C23148yescomplemented
184#13063354C23148yescomplemented
185#13063354C23124yescomplemented
186#13063352C2318yescomplemented
187#13063352C23124yescomplemented
188#13063351C23124yescomplemented
189#13063349C23124yescomplemented
190#13063349C23124yescomplemented
191#13063347C23124yescomplemented
192#13063346C23148yescomplemented
193#13063345C23124yescomplemented
194#13063345C23124yescomplemented
195#13063344C23148yescomplemented
196C2×Dic172C2316yes—
197C2×Dic172C2313yes—
198C2×Dic172C23124yescomplemented
199C2×#10621885C2313yes—
200C2×#10621885C2316yes—
201C2×#10621885C2313yes—
202C2×#10621885C23124yescomplemented
203Q16×D43C23148yescomplemented
204C2×#10621873C2313yes—
205C2×#10621873C2313yes—
206C2×#10621883C2316yes—
207C2×#10621883C2313yes—
208C2×#10621883C2313yes—
209C2×#10621883C23124yescomplemented
210C2×#10621884C2313yes—
211C2×#10621884C2311yescharacteristic
212SD16×D43C23148yescomplemented
213C2×D344C2311yescharacteristic
214C2×#10621882C2311yescharacteristic
215C2×#10621882C2313yes—
216#13063333C23124yescomplemented
217#13063332C2318yescomplemented
218#13063331C23124yescomplemented
219C2×#10621877C2313yes—
220C2×#10621872C2313yes—
221C2×#10621872C2311yescharacteristic
222C2×#10621872C2313yes—
223C2×#10621872C2313yes—
224C2×#10621872C23124yescomplemented
225M16×D43C23124yescomplemented
226C22×C43⋊C8C2313yes—
227C2×C8×D43C2316yes—
2282−1+4×C43—24no—
2292−1+4×C43C2318yescomplemented
230H(5,𝔽2)×C43—24no—
231H(5,𝔽2)×C43C2318yescomplemented
232C2×#41×C43—21no—
233C2×#41×C43—23no—
234C2×#41×C43C2313yes—
235C2×#41×C43C2313yes—
236C2×#41×C43C2311yescharacteristic
237C22×Q8×C43—21no—
238C22×Q8×C43C2313yes—
239C22×D4×C43—23no—
240C22×D4×C43C2313yes—
241#137×C43C23124yescomplemented
242AGL(1,ℤ/8)×C43C23124yescomplemented
243#135×C43C23124yescomplemented
244C2×Q16×C43C2313yes—
245C2×SD16×C43C2313yes—
246C2×SD16×C43C2316yes—
247C2×SD16×C43C2311yescharacteristic
248C2×SD16×C43C23124yescomplemented
249C2×D8×C43C2313yes—
250#131×C43C2318yescomplemented
251C2×M16×C43C2313yes—
252C22×C8×C43C2313yes—
253C24×C43—23no—
254C23×D43—21no—
255C23×D43—23no—
256C23×D43C2×D413yes—
257#41×C43—28no—
258#41×C43—224no—
259#41×C43—26no—
260#41×C43—26no—
261#41×C43C2×D414yes—
262#41×C43C24112yes—
263#41×C43C24112yes—
264#41×C43C2414yes—
265C2×Q8×C43—28no—
266C2×Q8×C43—23no—
267C2×Q8×C43—26no—
268C2×Q8×C43C2×D411yescharacteristic
269C2×Q8×C43C2413yes—
270C2×Q8×C43C2411yescharacteristic
271C2×Q8×C43C24112yes—
272C2×D4×C43—224no—
273C2×D4×C43—23no—
274C2×D4×C43—26no—
275C2×D4×C43—23no—
276C2×D4×C43—23no—
277C2×D4×C43C2×D413yes—
278C2×D4×C43C2411yescharacteristic
279C2×D4×C43C2413yes—
280C2×D4×C43C24112yes—
281C22×C4×C43—23no—
282C22×C4×C43—23no—
283C22×C4×C43—23no—
284C22×C4×C43C2413yes—
285C2×C22⋊D43—248no—
286C2×C22⋊D43—23no—
287C2×C22⋊D43—21no—
288C2×C22⋊D43—23no—
289C2×C22⋊D43—23no—
290C2×C22⋊D43—23no—
291C2×C22⋊D43—26no—
292C2×C22⋊D43—23no—
293C2×C22⋊D43—224no—
294C2×C22⋊D43C2×D416yes—
295C22×Dic43—23no—
296C22×Dic43—23no—
297C22×Dic43—26no—
298C22×Dic43—224no—
299C22×Dic43—23no—
300C22×Dic43—23no—
301C22×Dic43C2×D413yes—
302#10621902—224no—
303#10621902—22no—
304#10621902—26no—
305#10621902C2×D418yes—
306#10621902C24112yes—
307#10621902C2414yes—
308Q8×D43—28no—
309Q8×D43—28no—
310Q8×D43—26no—
311Q8×D43—224no—
312Q8×D43—212no—
313Q8×D43—224no—
314Q8×D43—26no—
315Q8×D43—224no—
316Q8×D43C2×D418yes—
317Q8×D43C24124yes—
318Q8×D43C24112yes—
319Q8×D43C24112yes—
320#10621900—224no—
321#10621900—224no—
322#10621900—248no—
323#10621900—248no—
324#10621900—224no—
325#10621900—224no—
326#10621900—224no—
327#10621900—26no—
328#10621900—26no—
329#10621900—224no—
330#10621900—212no—
331#10621900—224no—
332#10621900C2×D4124yes—
333#10621900C24112yes—
334#10621900C24124yes—
335#10621900C24112yes—
336D4×D43—224no—
337D4×D43—22no—
338D4×D43—26no—
339D4×D43—224no—
340D4×D43—224no—
341D4×D43C2×D4124yes—
342D4×D43C24112yes—
343D4×D43C2414yes—
344#10621898—26no—
345#10621898—26no—
346#10621898—248no—
347#10621898—224no—
348#10621898—224no—
349#10621898—224no—
350#10621898—224no—
351#10621898C2×D4112yes—
352#10621898C24112yes—
353#10621898C24112yes—
354#10621898C24112yes—
355C2×D172—21no—
356C2×D172—23no—
357C2×D172C2×D413yes—
358C2×D172C2411yescharacteristic
359C2×D172C2411yescharacteristic
360C2×C4×D43—23no—
361C2×C4×D43—23no—
362C2×C4×D43—21no—
363C2×C4×D43—23no—
364C2×C4×D43—224no—
365C2×C4×D43—224no—
366C2×C4×D43—23no—
367C2×C4×D43—23no—
368C2×C4×D43—26no—
369C2×C4×D43—224no—
370C2×C4×D43C2×D413yes—
371C2×C4×D43C2×D413yes—
372C2×C4×D43C2×D4112yes—
373C2×C4×D43C2413yes—
374C2×C4×D43C24112yes—
375C2×C4×D43C2411yescharacteristic
376C2×Dic86—23no—
377C2×Dic86—26no—
378C2×Dic86—23no—
379C2×Dic86—26no—
380C2×Dic86—26no—
381C2×Dic86—23no—
382C2×Dic86—224no—
383C2×Dic86—23no—
384C2×Dic86—224no—
385C2×Dic86—224no—
386C2×Dic86C2×D413yes—
387C2×Dic86C2413yes—
388C2×Dic86C2413yes—
389C2×Dic86C24112yes—
390C2×Dic86C24112yes—
391Q16×C43C24112yes—
392SD16×C43C24112yes—
393SD16×C43C24124yes—
394SD16×C43C2414yes—
395D8×C43C24112yes—
396M16×C43C24112yes—
397C2×C8×C43C2411yescharacteristic
398C2×C8×C43C2413yes—
399C2×C8×C43C24112yes—
400#10621885C24112yes—
401#10621885C24124yes—
402#10621885C24112yes—
403#10621884C24112yes—
404#10621884C2414yes—
405#10621883C24124yes—
406#10621883C24112yes—
407#10621883C24112yes—
408#10621882C2414yes—
409#10621882C24112yes—
410#10621877C24112yes—
411C2×C43⋊C8C2413yes—
412C2×C43⋊C8C2411yescharacteristic
413C2×C43⋊C8C24112yes—
414Dic172C24124yes—
415Dic172C24112yes—
416D344C2414yes—
417#10621873C24112yes—
418#10621873C24112yes—
419#10621872C24112yes—
420#10621872C2414yes—
421#10621872C24112yes—
422#10621872C24112yes—
423C8×D43C24124yes—
424C23×C43—21no—
425C23×C43—23no—
426C23×C43—212no—
427C23×C43—86no—
428C23×C43C22×D413yes—
429C22×D43—21no—
430C22×D43—21no—
431C22×D43—24no—
432C22×D43—212no—
433C22×D43—46no—
434C22×D43—44no—
435C22×D43—86no—
436C22×D43C22×D411yescharacteristic
437C22×D43C22×D413yes—
438C22×D43C22×D4112yes—
439Q8×C43—23no—
440Q8×C43—212no—
441Q8×C43—21no—
442Q8×C43C22×D414yes—
443Q8×C43C2516yes—
444Q8×C43C2512yes—
445D4×C43—212no—
446D4×C43—212no—
447D4×C43—23no—
448D4×C43—212no—
449D4×C43—21no—
450D4×C43C22×D4112yes—
451D4×C43C2512yes—
452D4×C43C2516yes—
453C2×C4×C43—21no—
454C2×C4×C43—23no—
455C2×C4×C43—212no—
456C2×C4×C43—212no—
457C2×C4×C43—212no—
458C2×C4×C43C22×D413yes—
459C2×C4×C43C22×D416yes—
460C2×C4×C43C2511yescharacteristic
461C2×C4×C43C2516yes—
462C22⋊D43—212no—
463C22⋊D43—212no—
464C22⋊D43—212no—
465C22⋊D43—212no—
466C22⋊D43—224no—
467C22⋊D43—24no—
468C22⋊D43—212no—
469C22⋊D43C22×D4124yes—
470C2×Dic43—23no—
471C2×Dic43—212no—
472C2×Dic43—23no—
473C2×Dic43—212no—
474C2×Dic43—212no—
475C2×Dic43—224no—
476C2×Dic43—212no—
477C2×Dic43C22×D413yes—
478C2×Dic43C22×D411yescharacteristic
479C2×Dic43C22×D4112yes—
480D172—24no—
481D172—212no—
482D172—21no—
483D172—21no—
484D172C22×D4112yes—
485D172C2512yes—
486D172C2512yes—
487C4×D43—212no—
488C4×D43—212no—
489C4×D43—224no—
490C4×D43—212no—
491C4×D43—212no—
492C4×D43—24no—
493C4×D43—212no—
494C4×D43C22×D4112yes—
495C4×D43C22×D4112yes—
496C4×D43C22×D412yes—
497C4×D43C22×D416yes—
498C4×D43C2516yes—
499C4×D43C2512yes—
500Dic86—23no—
501Dic86—212no—
502Dic86—23no—
503Dic86—212no—
504Dic86—212no—
505Dic86—224no—
506Dic86—212no—
507Dic86C22×D4112yes—
508Dic86C2516yes—
509Dic86C2516yes—
510C8×C43C2516yes—
511C8×C43C2512yes—
512C43⋊C8C2516yes—
513C43⋊C8C2512yes—
514C2×#3586—431nomaximal, Sylow
515C22×C43—26no—
516C22×C43—26no—
517C22×C43—22no—
518C22×C43—42no—
519C22×C43—46no—
520C22×C43—812no—
521C22×C43C23×D416yes—
522C22×C43C23×D411yescharacteristic
523C2×D43—22no—
524C2×D43—26no—
525C2×D43—22no—
526C2×D43—22no—
527C2×D43—412no—
528C2×D43—48no—
529C2×D43—42no—
530C2×D43—42no—
531C2×D43—812no—
532C2×D43C23×D412yes—
533C2×D43C23×D416yes—
534C4×C43—22no—
535C4×C43—26no—
536C4×C43C23×D411yescharacteristic
537C4×C43C23×D416yes—
538C4×C43C2611yescharacteristic
539Dic43—26no—
540Dic43—26no—
541Dic43C23×D416yes—
542Dic43C23×D412yes—
543C2×#585—431no—
544C22×2−1+4—431no—
545#3586—4332no—
546C2×#578—431no—
547C2×#578—433no—
548C2×#578—433no—
549C2×#578—431no—
550C2×#577—431no—
551C2×#577—433no—
552C2×#577—433no—
553C2×#577D4311yescharacteristic, complemented
554C2×#575—433no—
555C2×#575—433no—
556C22×#137—433no—
557C22×#137—433no—
558C2×#568—431no—
559C2×C43—26no—
560C2×C43—42no—
561C2×C43—46no—
562C2×C43#358612yescomplemented
563C2×C43C24×D411yescharacteristic
564D43—22no—
565D43—26no—
566D43—42no—
567D43—42no—
568#585—4316no—
569#585—868no—
570C2×2−1+4—4316no—
571C2×2−1+4—433no—
572C2×2−1+4—433no—
573C2×2−1+4—431no—
574C2×2−1+4—431no—
575C2×2−1+4—433no—
576C2×2−1+4—861no—
577C2×2−1+4—861no—
578C2×2−1+4—863no—
579C2×2−1+4—868no—
580C2×2−1+4C2×D4311yescharacteristic, complemented
581C2×H(5,𝔽2)—433no—
582C2×H(5,𝔽2)—863no—
583C2×H(5,𝔽2)C2×D4311yescharacteristic, complemented
584C22×#41—431no—
585C22×#41—433no—
586C22×#41—433no—
587C22×#41—433no—
588C22×#41—863no—
589C22×#41—863no—
590C22×#41—861no—
591C23×Q8—433no—
592C23×Q8—861no—
593#578—4316no—
594#578—4348no—
595#578—4348no—
596#578—4316no—
597#577—4316no—
598#577—4348no—
599#577—4348no—
600#577C2×D43116yescomplemented
601#575—4348no—
602#575—4348no—
603C2×#137—433no—
604C2×#137—433no—
605C2×#137—433no—
606C2×#137—4348no—
607C2×#137—433no—
608C2×#137—433no—
609C2×#137—436no—
610C2×#137—433no—
611C2×#137—436no—
612C2×#137—436no—
613C2×#137—433no—
614C2×#137—4348no—
615C2×#137—433no—
616C2×#137—433no—
617C2×#137C2×D4313yescomplemented
618C2×AGL(1,ℤ/8)—433no—
619C2×AGL(1,ℤ/8)—431no—
620C2×AGL(1,ℤ/8)—433no—
621C2×AGL(1,ℤ/8)—433no—
622C2×AGL(1,ℤ/8)—433no—
623C2×AGL(1,ℤ/8)C2×D4313yescomplemented
624C2×#135—433no—
625C2×#135—433no—
626C2×#135—436no—
627C2×#135—436no—
628C2×#135—433no—
629C2×#135C2×D4313yescomplemented
630C22×Q16—433no—
631C22×Q16—436no—
632C22×Q16—433no—
633C22×SD16—433no—
634C22×SD16—436no—
635C22×SD16C2×D4313yescomplemented
636#568—4316no—
637C2×#131—431no—
638C2×#131—433no—
639C2×#131—433no—
640C2×#131C2×D4311yescharacteristic, complemented
641C22×M16—433no—
642C22×M16—433no—
643C43C2×#358611yescharacteristic, complemented, Sylow
6442−1+4—24no—
6452−1+4—4324no—
6462−1+4—438no—
6472−1+4—4324no—
6482−1+4—438no—
6492−1+4—4324no—
6502−1+4—8616no—
6512−1+4—8612no—
6522−1+4—8616no—
6532−1+4—8648no—
6542−1+4—8612no—
6552−1+4—8612no—
6562−1+4—864no—
6572−1+4—864no—
6582−1+4C22×D4318yescomplemented
659H(5,𝔽2)—24no—
660H(5,𝔽2)—4324no—
661H(5,𝔽2)—8648no—
662H(5,𝔽2)—8612no—
663H(5,𝔽2)C22×D4318yescomplemented
664C2×#41—21no—
665C2×#41—23no—
666C2×#41—438no—
667C2×#41—438no—
668C2×#41—431no—
669C2×#41—433no—
670C2×#41—433no—
671C2×#41—4324no—
672C2×#41—4324no—
673C2×#41—433no—
674C2×#41—431no—
675C2×#41—433no—
676C2×#41—436no—
677C2×#41—433no—
678C2×#41—4324no—
679C2×#41—433no—
680C2×#41—433no—
681C2×#41—863no—
682C2×#41—863no—
683C2×#41—863no—
684C2×#41—866no—
685C2×#41—863no—
686C2×#41—863no—
687C2×#41—863no—
688C2×#41—863no—
689C2×#41—863no—
690C2×#41—8612no—
691C2×#41—8612no—
692C2×#41—8612no—
693C2×#41—866no—
694C2×#41—866no—
695C2×#41—863no—
696C2×#41—8648no—
697C2×#41—863no—
698C2×#41—8648no—
699C2×#41—8616no—
700C2×#41—863no—
701C2×#41—863no—
702C2×#41C22×D4313yes—
703C2×#41C22×D4313yes—
704C2×#41C22×D4311yescharacteristic
705C22×Q8—21no—
706C22×Q8—431no—
707C22×Q8—436no—
708C22×Q8—433no—
709C22×Q8—433no—
710C22×Q8—4324no—
711C22×Q8—433no—
712C22×Q8—433no—
713C22×Q8—863no—
714C22×Q8—863no—
715C22×Q8—863no—
716C22×Q8—863no—
717C22×Q8—863no—
718C22×Q8—8612no—
719C22×Q8—8616no—
720C22×Q8—863no—
721C22×Q8—861no—
722C22×Q8—861no—
723C22×Q8C22×D4313yes—
724C22×D4—23no—
725C22×D4—433no—
726C22×D4—433no—
727C22×D4—431no—
728C22×D4—863no—
729C22×D4—863no—
730C22×D4—863no—
731C22×D4—866no—
732C22×D4—863no—
733C22×D4C22×D4313yes—
734C23×C4—433no—
735C23×C4—863no—
736C23×C4—863no—
737C23×C4—863no—
738C23×C4—863no—
739#137—4324no—
740#137—4324no—
741#137—4324no—
742#137—4324no—
743#137—4324no—
744#137—4348no—
745#137—4324no—
746#137—4348no—
747#137—4348no—
748#137—4324no—
749#137—4324no—
750#137—4324no—
751#137C22×D43124yescomplemented
752AGL(1,ℤ/8)—4324no—
753AGL(1,ℤ/8)—438no—
754AGL(1,ℤ/8)—4324no—
755AGL(1,ℤ/8)—4324no—
756AGL(1,ℤ/8)—4324no—
757AGL(1,ℤ/8)C22×D43124yescomplemented
758#135—4324no—
759#135—4324no—
760#135—4348no—
761#135—4348no—
762#135—4324no—
763#135C22×D43124yescomplemented
764C2×Q16—433no—
765C2×Q16—433no—
766C2×Q16—436no—
767C2×Q16—4324no—
768C2×Q16—4348no—
769C2×Q16—436no—
770C2×Q16—433no—
771C2×Q16—4324no—
772C2×Q16C22×D4313yes—
773C2×SD16—433no—
774C2×SD16—431no—
775C2×SD16—433no—
776C2×SD16—436no—
777C2×SD16—4324no—
778C2×SD16—433no—
779C2×SD16—4348no—
780C2×SD16—433no—
781C2×SD16—433no—
782C2×SD16C22×D4316yes—
783C2×SD16C22×D4313yes—
784C2×SD16C22×D4311yescharacteristic
785C2×SD16C22×D43124yescomplemented
786C2×D8—433no—
787C2×D8—431no—
788C2×D8—431no—
789C2×D8C22×D4313yes—
790#131—438no—
791#131—4324no—
792#131—4324no—
793#131C22×D4318yescomplemented
794C2×M16—433no—
795C2×M16—4324no—
796C2×M16—433no—
797C2×M16—431no—
798C2×M16—433no—
799C2×M16—433no—
800C2×M16—4324no—
801C2×M16C22×D4313yes—
802C22×C8—433no—
803C22×C8—436no—
804C22×C8C22×D4313yes—
805C24—23no—
806C24—433no—
807C24—863no—
808C24—861no—
809#41—28no—
810#41—224no—
811#41—26no—
812#41—26no—
813#41—438no—
814#41—4324no—
815#41—4312no—
816#41—4312no—
817#41—4312no—
818#41—434no—
819#41—4312no—
820#41—4324no—
821#41—4312no—
822#41—4312no—
823#41—4312no—
824#41—8624no—
825#41—8624no—
826#41—8624no—
827#41—8648no—
828#41—8624no—
829#41—8624no—
830#41—866no—
831#41—8624no—
832#41—8624no—
833#41—8612no—
834#41—8624no—
835#41—866no—
836#41—862no—
837#41—866no—
838#41—8648no—
839#41—8648no—
840#41—8624no—
841#41—8624no—
842#41—8624no—
843#41—8624no—
844#41—866no—
845#41—866no—
846#41D4×D4314yes—
847#41C23×D43112yes—
848#41C23×D43112yes—
849#41C23×D4314yes—
850C2×Q8—28no—
851C2×Q8—23no—
852C2×Q8—26no—
853C2×Q8—438no—
854C2×Q8—433no—
855C2×Q8—4324no—
856C2×Q8—4312no—
857C2×Q8—4312no—
858C2×Q8—433no—
859C2×Q8—433no—
860C2×Q8—4312no—
861C2×Q8—4312no—
862C2×Q8—863no—
863C2×Q8—866no—
864C2×Q8—863no—
865C2×Q8—8624no—
866C2×Q8—8624no—
867C2×Q8—8624no—
868C2×Q8—866no—
869C2×Q8—8624no—
870C2×Q8—8624no—
871C2×Q8—8612no—
872C2×Q8—866no—
873C2×Q8—8624no—
874C2×Q8—868no—
875C2×Q8—868no—
876C2×Q8—863no—
877C2×Q8—863no—
878C2×Q8—866no—
879C2×Q8—866no—
880C2×Q8D4×D4311yescharacteristic
881C2×Q8C23×D4313yes—
882C2×Q8C23×D4311yescharacteristic
883C2×Q8C23×D43112yes—
884C2×D4—23no—
885C2×D4—23no—
886C2×D4—224no—
887C2×D4—23no—
888C2×D4—26no—
889C2×D4—436no—
890C2×D4—4324no—
891C2×D4—4312no—
892C2×D4—434no—
893C2×D4—433no—
894C2×D4—431no—
895C2×D4—431no—
896C2×D4—861no—
897C2×D4—863no—
898C2×D4—862no—
899C2×D4—866no—
900C2×D4—863no—
901C2×D4—861no—
902C2×D4—8624no—
903C2×D4—8624no—
904C2×D4—8624no—
905C2×D4—8648no—
906C2×D4—863no—
907C2×D4—866no—
908C2×D4—863no—
909C2×D4—8624no—
910C2×D4—863no—
911C2×D4—863no—
912C2×D4D4×D4313yes—
913C2×D4C23×D4311yescharacteristic
914C2×D4C23×D4313yes—
915C2×D4C23×D43112yes—
916C22×C4—23no—
917C22×C4—23no—
918C22×C4—23no—
919C22×C4—433no—
920C22×C4—433no—
921C22×C4—433no—
922C22×C4—4312no—
923C22×C4—433no—
924C22×C4—431no—
925C22×C4—4312no—
926C22×C4—861no—
927C22×C4—863no—
928C22×C4—8624no—
929C22×C4—8624no—
930C22×C4—863no—
931C22×C4—863no—
932C22×C4—8624no—
933C22×C4—866no—
934C22×C4—863no—
935C22×C4—866no—
936C22×C4—863no—
937C22×C4—8624no—
938C22×C4—863no—
939C22×C4—863no—
940C22×C4—863no—
941C22×C4—863no—
942C22×C4C23×D4313yes—
943Q16—4312no—
944Q16—4312no—
945Q16—4324no—
946Q16—4324no—
947Q16—4312no—
948Q16C23×D43112yes—
949SD16—4312no—
950SD16—434no—
951SD16—4312no—
952SD16—4324no—
953SD16—4312no—
954SD16—4312no—
955SD16—4312no—
956SD16C23×D43124yes—
957SD16C23×D43112yes—
958SD16C23×D4314yes—
959D8—4312no—
960D8—434no—
961D8—434no—
962D8C23×D43112yes—
963M16—4312no—
964M16—4312no—
965M16—434no—
966M16—4312no—
967M16—4312no—
968M16C23×D43112yes—
969C2×C8—431no—
970C2×C8—433no—
971C2×C8—4312no—
972C2×C8—4324no—
973C2×C8C23×D4313yes—
974C2×C8C23×D4311yescharacteristic
975C2×C8C23×D43112yes—
976C23—21no—
977C23—23no—
978C23—212no—
979C23—86no—
980C23—431no—
981C23—433no—
982C23—4312no—
983C23—8612no—
984C23—864no—
985C23—861no—
986C23—861no—
987C23—3446no—
988C23—1726no—
989C23—1724no—
990C23C2×D4×D4313yes—
991Q8—212no—
992Q8—23no—
993Q8—21no—
994Q8—4312no—
995Q8—436no—
996Q8—436no—
997Q8—8612no—
998Q8—8624no—
999Q8—8612no—
1000Q8—8612no—
1001Q8—863no—
1002Q8—8612no—
1003Q8—863no—
1004Q8C2×D4×D4314yes—
1005Q8C24×D4316yes—
1006Q8C24×D4312yes—
1007D4—212no—
1008D4—212no—
1009D4—212no—
1010D4—23no—
1011D4—21no—
1012D4—4324no—
1013D4—4312no—
1014D4—432no—
1015D4—432no—
1016D4—864no—
1017D4—8612no—
1018D4—8612no—
1019D4—864no—
1020D4—8612no—
1021D4—8624no—
1022D4—8612no—
1023D4—8612no—
1024D4—8612no—
1025D4—861no—
1026D4—861no—
1027D4C2×D4×D43112yes—
1028D4C24×D4312yes—
1029D4C24×D4316yes—
1030C2×C4—212no—
1031C2×C4—21no—
1032C2×C4—23no—
1033C2×C4—212no—
1034C2×C4—212no—
1035C2×C4—4312no—
1036C2×C4—431no—
1037C2×C4—433no—
1038C2×C4—432no—
1039C2×C4—4312no—
1040C2×C4—4312no—
1041C2×C4—436no—
1042C2×C4—436no—
1043C2×C4—432no—
1044C2×C4—864no—
1045C2×C4—8612no—
1046C2×C4—8612no—
1047C2×C4—8612no—
1048C2×C4—8624no—
1049C2×C4—8612no—
1050C2×C4—8624no—
1051C2×C4—8612no—
1052C2×C4—8612no—
1053C2×C4—8612no—
1054C2×C4—863no—
1055C2×C4—863no—
1056C2×C4—8612no—
1057C2×C4—8612no—
1058C2×C4C2×D4×D4316yes—
1059C2×C4C2×D4×D4313yes—
1060C2×C4C24×D4316yes—
1061C2×C4C24×D4311yescharacteristic
1062C8—432no—
1063C8—436no—
1064C8C24×D4316yes—
1065C8C24×D4312yes—
1066C22—26no—
1067C22—22no—
1068C22—26no—
1069C22—46no—
1070C22—42no—
1071C22—812no—
1072C22—432no—
1073C22—436no—
1074C22—866no—
1075C22—862no—
1076C22—862no—
1077C22—862no—
1078C22—34412no—
1079C22—17212no—
1080C22—1728no—
1081C22—1722no—
1082C22—1722no—
1083C22C22×D4×D4316yes—
1084C22C22×D4×D4311yescharacteristic
1085C4—22no—
1086C4—26no—
1087C4—432no—
1088C4—436no—
1089C4—866no—
1090C4—866no—
1091C4C22×D4×D4316yes—
1092C4C22×D4×D4311yescharacteristic
1093C4C25×D4311yescharacteristic
1094C2—26no—
1095C2—46no—
1096C2—42no—
1097C2—866no—
1098C2—862no—
1099C2—1722no—
1100C2—1722no—
1101C2#1914937712yesdirect product factor
1102C2C23×D4×D4311yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC4×C43C26
FrattiniC4C25×D43
FittingC2×C43×#577C2
socleC22×C43C23×D4
hypercenterC2×#577D43
hypocenterC43C2×#3586
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#577

Complements

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

NH ≅ G/Ntype
1. C2×#14583734C2semidirect
2. C2×2−1+4×D43C2semidirect
3. #19149377C2direct (N × H)
4. C2×#14583716C2semidirect
5. C2×#14583715C2semidirect
6. C2×#14583714C2semidirect
7. C2×#14583713C2semidirect
8. C2×#14583710C2semidirect
9. C2×#14583709C2semidirect
10. C2×#14583705C2semidirect
11. C2×#14583696C2semidirect
12. C2×#14583695C2semidirect
13. C22×#13063354C2semidirect
14. C2×#137×D43C2semidirect
15. C2×#14583664C2semidirect
16. C2×C43×#577C2semidirect
18. #14583734C22semidirect
20. C2×#13063373C22semidirect
23. C2×#13063372C22semidirect
24. C2×#13063372C22semidirect
25. C2×#13063372C22semidirect
26. C2×#13063372C22semidirect
28. 2−1+4×D43C22semidirect
30. C2×#13063370C22semidirect
37. C2×#41×D43C22semidirect
39. C22×Q8×D43C22semidirect
40. #14583716C22semidirect
41. #14583715C22semidirect
42. #14583714C22semidirect
43. #14583713C22semidirect
44. #14583710C22semidirect
45. #14583709C22semidirect
46. #14583705C22semidirect
47. #14583696C22semidirect
48. #14583695C22semidirect
49. C2×#13063358C22semidirect
50. C2×#13063358C22semidirect
51. C2×#13063357C22semidirect
52. C2×#13063357C22semidirect
53. C2×#13063356C22semidirect
54. C2×#13063355C22semidirect
55. C2×#13063355C22semidirect
56. C2×#13063354C22semidirect
57. C2×#13063354C22semidirect
58. C2×#13063354C22semidirect
59. C2×#13063354C22semidirect
60. C2×#13063354C22semidirect
61. C2×#13063354C22semidirect
62. #137×D43C22semidirect
63. C2×#13063352C22semidirect
64. C2×#13063352C22semidirect
65. C2×#13063351C22semidirect
66. C2×#13063349C22semidirect
67. C2×#13063349C22semidirect
68. C2×#13063347C22semidirect
69. C2×#13063346C22semidirect
70. C2×#13063345C22semidirect
71. C2×#13063345C22semidirect
72. C2×#13063344C22semidirect
73. C22×Dic172C22semidirect
74. C22×#10621885C22semidirect
75. C2×Q16×D43C22semidirect
76. C22×#10621883C22semidirect
77. C2×SD16×D43C22semidirect
78. #14583664C22semidirect
79. C2×#13063333C22semidirect
80. C2×#13063332C22semidirect
81. C2×#13063331C22semidirect
82. C22×#10621872C22semidirect
83. C2×M16×D43C22semidirect
84. C2×2−1+4×C43C22semidirect
85. C2×H(5,𝔽2)×C43C22semidirect
86. C43×#577C22semidirect
87. C2×#137×C43C22semidirect
88. C2×AGL(1,ℤ/8)×C43C22semidirect
89. C2×#135×C43C22semidirect
90. C22×SD16×C43C22semidirect
91. C2×#131×C43C22semidirect
94. #13063373C23semidirect
101. #13063372C23semidirect
102. #13063372C23semidirect
103. #13063372C23semidirect
104. #13063372C23semidirect
107. #13063370C23semidirect
143. #41×D43C23semidirect
160. C2×Q8×D43C23semidirect
174. #13063358C23semidirect
175. #13063358C23semidirect
176. #13063357C23semidirect
177. #13063357C23semidirect
178. #13063356C23semidirect
179. #13063355C23semidirect
180. #13063355C23semidirect
181. #13063354C23semidirect
182. #13063354C23semidirect
183. #13063354C23semidirect
184. #13063354C23semidirect
185. #13063354C23semidirect
186. #13063352C23semidirect
187. #13063352C23semidirect
188. #13063351C23semidirect
189. #13063349C23semidirect
190. #13063349C23semidirect
191. #13063347C23semidirect
192. #13063346C23semidirect
193. #13063345C23semidirect
194. #13063345C23semidirect
195. #13063344C23semidirect
198. C2×Dic172C23semidirect
202. C2×#10621885C23semidirect
203. Q16×D43C23semidirect
209. C2×#10621883C23semidirect
212. SD16×D43C23semidirect
216. #13063333C23semidirect
217. #13063332C23semidirect
218. #13063331C23semidirect
224. C2×#10621872C23semidirect
225. M16×D43C23semidirect
229. 2−1+4×C43C23semidirect
231. H(5,𝔽2)×C43C23semidirect
241. #137×C43C23semidirect
242. AGL(1,ℤ/8)×C43C23semidirect
243. #135×C43C23semidirect
248. C2×SD16×C43C23semidirect
250. #131×C43C23semidirect
553. C2×#577D43semidirect
562. C2×C43#3586semidirect
580. C2×2−1+4C2×D43semidirect
583. C2×H(5,𝔽2)C2×D43semidirect
600. #577C2×D43semidirect
617. C2×#137C2×D43semidirect
623. C2×AGL(1,ℤ/8)C2×D43semidirect
629. C2×#135C2×D43semidirect
635. C22×SD16C2×D43semidirect
640. C2×#131C2×D43semidirect
643. C43C2×#3586semidirect
658. 2−1+4C22×D43semidirect
663. H(5,𝔽2)C22×D43semidirect
751. #137C22×D43semidirect
757. AGL(1,ℤ/8)C22×D43semidirect
763. #135C22×D43semidirect
785. C2×SD16C22×D43semidirect
793. #131C22×D43semidirect
1101. C2#19149377direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145837342
C2×2−1+4×D432
#191493772
C2×#145837162
C2×#145837152
C2×#145837142
C2×#145837132
C2×#145837102
C2×#145837092
C2×#145837052
C2×#145836962
C2×#145836952
C22×#130633542
C2×#137×D432
C2×#145836642
C2×C43×#5772
C2×#358643