Finite Group Databasebeta

← C2×#19146357 #25972774

Subgroups — C2×#19146357 #25972774

Order 11008.

2704 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583707C211yesmaximal, characteristic, complemented
2C2×#14583702C211yesmaximal, characteristic, complemented
3C2×#14583701C211yesmaximal, characteristic, complemented
4#19146357C2116yesmaximal, direct product factor
5C2×#14583285C211yesmaximal, characteristic, complemented
6C2×#14583169C211yesmaximal, characteristic, complemented
7C2×#14583167C211yesmaximal, characteristic, complemented
8C2×#14583164C211yesmaximal, characteristic, complemented
9C2×#14583159C211yesmaximal, characteristic, complemented
10C2×#14583072C211yesmaximal, characteristic, complemented
11C2×#14583075C211yesmaximal, characteristic, complemented
12C2×#14583067C211yesmaximal, characteristic, complemented
13C2×#14583065C211yesmaximal, characteristic, complemented
14C2×#14583021C211yesmaximal, characteristic, complemented
15C2×#14583019C211yesmaximal, characteristic, complemented
16C2×C43×#577C211yesmaximal, characteristic, complemented
17C2×#13063371C2211yescharacteristic
18C2×#13063371C2211yescharacteristic, complemented
19#14583707—24no—
20#14583707C2218yescomplemented
21#14583702—24no—
22#14583702C2218yescomplemented
23#14583701—24no—
24#14583701C2218yescomplemented
25C2×#13063356—21no—
26C2×#13063356C2211yescharacteristic, complemented
27C2×#13063352—21no—
28C2×#13063352—21no—
29C2×#13063351—21no—
30C2×#13063351C2211yescharacteristic
31C2×#13063350—21no—
32C2×#13063350—21no—
33C2×#13063350C2211yescharacteristic
34C2×#13063350C2211yescharacteristic, complemented
35C2×#13063350C2211yescharacteristic, complemented
36C2×#13063350C2211yescharacteristic, complemented
37C2×#13063348—21no—
38C2×#13063345—21no—
39C2×#13063345—21no—
40C2×#13063345C2211yescharacteristic
41C22×#10621884—21no—
42C22×#10621884C2211yescharacteristic, complemented
43C22×D344C2211yescharacteristic, complemented
44C22×#10621882—21no—
45C22×#10621882C2211yescharacteristic, complemented
46C2×D8×D43—21no—
47C2×#13063332C2211yescharacteristic, complemented
48C2×#13063332C2211yescharacteristic, complemented
49C2×#13063331C2211yescharacteristic, complemented
50C2×#13063321C2211yescharacteristic, complemented
51C2×#13063314C2211yescharacteristic, complemented
52#14583285C2218yescomplemented
53#14583169C2218yescomplemented
54#14583167C2218yescomplemented
55#14583164C2218yescomplemented
56#14583159C2218yescomplemented
57#14583075C2218yescomplemented
58#14583072C2218yescomplemented
59#14583067C2218yescomplemented
60#14583065C2218yescomplemented
61#14583021C2218yescomplemented
62#14583019C2218yescomplemented
63C2×#13063261C2211yescharacteristic, complemented
64C2×#13063260C2211yescharacteristic, complemented
65C2×#13063252C2211yescharacteristic, complemented
66C2×#13063252C2211yescharacteristic, complemented
67C2×#13063252C2211yescharacteristic, complemented
68C2×#13063251C2211yescharacteristic, complemented
69C2×#13063244C2211yescharacteristic, complemented
70C2×#13063242C2211yescharacteristic, complemented
71C2×#13063241C2211yescharacteristic, complemented
72C2×#13063241C2211yescharacteristic, complemented
73C2×#13063235C2211yescharacteristic, complemented
74C2×2−1+4×C43C2211yescharacteristic, complemented
75C2×H(5,𝔽2)×C43C2211yescharacteristic, complemented
76C43×#577—24no—
77C43×#577C2218yescomplemented
78C2×#137×C43—21no—
79C2×#137×C43C2211yescharacteristic, complemented
80C2×AGL(1,ℤ/8)×C43—21no—
81C2×AGL(1,ℤ/8)×C43C2211yescharacteristic, complemented
82C2×#135×C43—21no—
83C2×#135×C43C2211yescharacteristic
84C22×SD16×C43—21no—
85C22×SD16×C43C2211yescharacteristic, complemented
86C2×#131×C43C2211yescharacteristic, complemented
87#13063371—22no—
88#13063371—22no—
89#13063371—22no—
90#13063371—22no—
91#13063371—41no—
92#13063371—41no—
93#13063371C2314yes—
94#13063371C2314yescomplemented
95C2×#10621902—21no—
96C2×#10621902—21no—
97C2×#10621898—21no—
98C2×#10621898—21no—
99C2×#10621898C2311yescharacteristic
100C22×D172—21no—
101C22×D172—21no—
102C22×D172C2311yescharacteristic
103C22×D172C2311yescharacteristic
104C22×C22⋊D43—41no—
105C2×D4×D43—21no—
106C2×D4×D43—21no—
107C2×D4×D43—41no—
108C2×D4×D43—41no—
109#13063356—22no—
110#13063356—28no—
111#13063356C2314yescomplemented
112#13063352—28no—
113#13063352—28no—
114#13063351—22no—
115#13063351—28no—
116#13063351C2314yes—
117#13063350—22no—
118#13063350—22no—
119#13063350—22no—
120#13063350—22no—
121#13063350—28no—
122#13063350—28no—
123#13063350C2314yes—
124#13063350C2314yescomplemented
125#13063350C2314yescomplemented
126#13063350C2314yescomplemented
127#13063348—28no—
128#13063345—28no—
129#13063345—28no—
130#13063345D414yescomplemented
131#13063345C2314yes—
132C2×#10621885—21no—
133C2×#10621885D411yescharacteristic, complemented
134C2×#10621883—21no—
135C2×#10621883D411yescharacteristic, complemented
136C2×#10621884—21no—
137C2×#10621884—21no—
138C2×#10621884—21no—
139C2×#10621884—21no—
140C2×#10621884—21no—
141C2×#10621884—28no—
142C2×#10621884—21no—
143C2×#10621884—21no—
144C2×#10621884—22no—
145C2×#10621884D411yescharacteristic, complemented
146C2×#10621884C2314yescomplemented
147C2×D344—21no—
148C2×D344—21no—
149C2×D344—22no—
150C2×D344C2314yescomplemented
151C2×#10621882—21no—
152C2×#10621882—21no—
153C2×#10621882—21no—
154C2×#10621882—21no—
155C2×#10621882—21no—
156C2×#10621882—28no—
157C2×#10621882—21no—
158C2×#10621882—21no—
159C2×#10621882—22no—
160C2×#10621882D411yescharacteristic, complemented
161C2×#10621882C2314yescomplemented
162D8×D43—28no—
163#13063332—22no—
164#13063332—22no—
165#13063332C2314yescomplemented
166#13063332C2314yescomplemented
167#13063331—22no—
168#13063331C2314yescomplemented
169C2×#10621877—21no—
170C2×#10621877—21no—
171C2×#10621877C2311yescharacteristic
172C2×#10621877C2311yescharacteristic
173C2×#10621877C2311yescharacteristic
174C2×#10621872—21no—
175C22×C43⋊C8—21no—
176C22×C43⋊C8—21no—
177C22×C43⋊C8C2311yescharacteristic
178C2×C8×D43—21no—
179#13063321—41no—
180#13063321C2314yescomplemented
181#13063314—41no—
182#13063314C2314yescomplemented
183C2×(C2×D43)⋊C4—41no—
184C2×C4×Dic43C2311yescharacteristic
185#13063261C2314yescomplemented
186#13063260C2314yescomplemented
187#13063252C2314yescomplemented
188#13063252C2314yescomplemented
189#13063252C2314yescomplemented
190#13063251C2314yescomplemented
191#13063244C2314yescomplemented
192#13063242C2314yescomplemented
193#13063241C2314yescomplemented
194#13063241C2314yescomplemented
195#13063235C2314yescomplemented
1962−1+4×C43—22no—
1972−1+4×C43—22no—
1982−1+4×C43—41no—
1992−1+4×C43C2314yescomplemented
200H(5,𝔽2)×C43—22no—
201H(5,𝔽2)×C43—22no—
202H(5,𝔽2)×C43—41no—
203H(5,𝔽2)×C43C2314yescomplemented
204C2×#41×C43—21no—
205C2×#41×C43—21no—
206C2×#41×C43—21no—
207C2×#41×C43—21no—
208C2×#41×C43—41no—
209C2×#41×C43C2311yescharacteristic
210C2×#41×C43C2311yescharacteristic
211C2×#41×C43C2311yescharacteristic
212C22×Q8×C43—21no—
213C22×Q8×C43—21no—
214C22×Q8×C43C2311yescharacteristic
215C22×D4×C43—21no—
216C22×D4×C43—21no—
217C22×D4×C43—41no—
218C22×D4×C43C2311yescharacteristic
219#137×C43—22no—
220#137×C43—28no—
221#137×C43C2314yescomplemented
222AGL(1,ℤ/8)×C43—22no—
223AGL(1,ℤ/8)×C43—28no—
224AGL(1,ℤ/8)×C43C2314yescomplemented
225#135×C43—28no—
226#135×C43D414yescomplemented
227#135×C43C2314yes—
228C2×Q16×C43—21no—
229C2×Q16×C43D411yescharacteristic, complemented
230C2×SD16×C43—21no—
231C2×SD16×C43—21no—
232C2×SD16×C43—28no—
233C2×SD16×C43—21no—
234C2×SD16×C43—21no—
235C2×SD16×C43—22no—
236C2×SD16×C43D411yescharacteristic, complemented
237C2×SD16×C43D411yescharacteristic, complemented
238C2×SD16×C43C2314yescomplemented
239C2×D8×C43—21no—
240C2×D8×C43D411yescharacteristic, complemented
241#131×C43—22no—
242#131×C43C2314yescomplemented
243C2×M16×C43—21no—
244C2×M16×C43C2311yescharacteristic
245C22×C8×C43—21no—
246C22×C8×C43C2311yescharacteristic
247C24×C43—21no—
248C24×C43—41no—
249C23×D43—21no—
250C23×D43—21no—
251C23×D43—41no—
252C23×D43—41no—
253#41×C43—21no—
254#41×C43—21no—
255#41×C43—21no—
256#41×C43—21no—
257#41×C43—21no—
258#41×C43—21no—
259#41×C43—24no—
260#41×C43—24no—
261#41×C43—24no—
262#41×C43—24no—
263#41×C43—44no—
264#41×C43—42no—
265#41×C43—42no—
266#41×C43—42no—
267#41×C43—42no—
268#41×C43—44no—
269#41×C43C2×D412yes—
270#41×C43C2×D412yes—
271#41×C43C2×D412yes—
272#41×C43C2412yes—
273#41×C43C2412yes—
274#41×C43C2412yes—
275C2×Q8×C43—21no—
276C2×Q8×C43—24no—
277C2×Q8×C43—24no—
278C2×Q8×C43—21no—
279C2×Q8×C43—21no—
280C2×Q8×C43—21no—
281C2×Q8×C43—21no—
282C2×Q8×C43—41no—
283C2×Q8×C43—42no—
284C2×Q8×C43—42no—
285C2×Q8×C43C2×D411yescharacteristic
286C2×Q8×C43C2×D411yescharacteristic
287C2×Q8×C43C2×D411yescharacteristic
288C2×Q8×C43C2412yes—
289C2×D4×C43—21no—
290C2×D4×C43—21no—
291C2×D4×C43—21no—
292C2×D4×C43—21no—
293C2×D4×C43—24no—
294C2×D4×C43—24no—
295C2×D4×C43—21no—
296C2×D4×C43—21no—
297C2×D4×C43—21no—
298C2×D4×C43—21no—
299C2×D4×C43—41no—
300C2×D4×C43—41no—
301C2×D4×C43—41no—
302C2×D4×C43—44no—
303C2×D4×C43—42no—
304C2×D4×C43—42no—
305C2×D4×C43—44no—
306C2×D4×C43C2×D411yescharacteristic
307C2×D4×C43C2×D411yescharacteristic
308C2×D4×C43C2×D411yescharacteristic
309C2×D4×C43C2412yes—
310C22×C4×C43—21no—
311C22×C4×C43—21no—
312C22×C4×C43—21no—
313C22×C4×C43—21no—
314C22×C4×C43—41no—
315C22×C4×C43—41no—
316C22×C4×C43—41no—
317C22×C4×C43C2411yescharacteristic
318C2×C22⋊D43—21no—
319C2×C22⋊D43—44no—
320C2×C22⋊D43—41no—
321C2×C22⋊D43—41no—
322C2×C22⋊D43—84no—
323C22×Dic43—21no—
324#10621902—24no—
325#10621902—24no—
326#10621902—42no—
327#10621902—42no—
328D4×D43—24no—
329D4×D43—24no—
330D4×D43—44no—
331D4×D43—44no—
332D4×D43—42no—
333D4×D43—42no—
334D4×D43—44no—
335D4×D43—44no—
336#10621898—21no—
337#10621898—21no—
338#10621898—24no—
339#10621898—24no—
340#10621898—42no—
341#10621898—42no—
342#10621898C2×D412yes—
343#10621898C2412yes—
344C2×D172—21no—
345C2×D172—21no—
346C2×D172—21no—
347C2×D172—21no—
348C2×D172—21no—
349C2×D172—21no—
350C2×D172—21no—
351C2×D172—21no—
352C2×D172—21no—
353C2×D172—21no—
354C2×D172—24no—
355C2×D172—24no—
356C2×D172—41no—
357C2×D172—41no—
358C2×D172—42no—
359C2×D172—42no—
360C2×D172C2×D411yescharacteristic
361C2×D172C2412yes—
362C2×D172C2412yes—
363C2×C4×D43—21no—
364C2×C4×D43—41no—
365C2×C4×D43—41no—
366C2×Dic86C2×D411yescharacteristic
367Q16×C43—24no—
368Q16×C43C2×D414yescomplemented
369SD16×C43—24no—
370SD16×C43—24no—
371SD16×C43—24no—
372SD16×C43—24no—
373SD16×C43C2×D414yescomplemented
374SD16×C43C2×D414yescomplemented
375D8×C43—24no—
376D8×C43C2×D414yescomplemented
377M16×C43—21no—
378M16×C43—24no—
379M16×C43C2412yes—
380C2×C8×C43—21no—
381C2×C8×C43—24no—
382C2×C8×C43C2×D411yescharacteristic
383C2×C8×C43C2×D411yescharacteristic
384C2×C8×C43C2×D412yes—
385C2×C8×C43C2412yes—
386#10621885—24no—
387#10621885C2×D414yescomplemented
388#10621884—24no—
389#10621884—24no—
390#10621884—24no—
391#10621884—24no—
392#10621884—24no—
393#10621884—24no—
394#10621884—24no—
395#10621884C2×D414yescomplemented
396#10621883—24no—
397#10621883C2×D414yescomplemented
398#10621882—24no—
399#10621882—24no—
400#10621882—24no—
401#10621882—24no—
402#10621882—24no—
403#10621882—24no—
404#10621882—24no—
405#10621882C2×D414yescomplemented
406(C2×D43)⋊C4—44no—
407C4×Dic43—21no—
408C4×Dic43C2412yes—
409#10621877—21no—
410#10621877—21no—
411#10621877—21no—
412#10621877—24no—
413#10621877—24no—
414#10621877C2412yes—
415#10621877C2412yes—
416#10621877C2412yes—
417C2×C43⋊C8—21no—
418C2×C43⋊C8—21no—
419C2×C43⋊C8—21no—
420C2×C43⋊C8—24no—
421C2×C43⋊C8—24no—
422C2×C43⋊C8C2×D411yescharacteristic
423C2×C43⋊C8C2×D411yescharacteristic
424C2×C43⋊C8C2×D412yes—
425C2×C43⋊C8C2412yes—
426D344—24no—
427D344—24no—
428#10621872—24no—
429C8×D43—24no—
430C23×C43—21no—
431C23×C43—21no—
432C23×C43—21no—
433C23×C43—22no—
434C23×C43—44no—
435C23×C43—41no—
436C23×C43—41no—
437C23×C43—82no—
438C23×C43—162no—
439C23×C43H(5,𝔽2)11yescharacteristic
440C22×D43—21no—
441C22×D43—22no—
442C22×D43—22no—
443C22×D43—44no—
444C22×D43—44no—
445C22×D43—41no—
446C22×D43—41no—
447C22×D43—41no—
448C22×D43—41no—
449C22×D43—82no—
450C22×D43—82no—
451C22×D43—162no—
452C22×D43—162no—
453Q8×C43—21no—
454Q8×C43—21no—
455Q8×C43—21no—
456Q8×C43—22no—
457Q8×C43—22no—
458Q8×C43—44no—
459Q8×C43—41no—
460Q8×C43—41no—
461Q8×C43C22×D412yes—
462Q8×C43C22×D412yes—
463Q8×C43C22×D412yes—
464D4×C43—22no—
465D4×C43—22no—
466D4×C43—22no—
467D4×C43—22no—
468D4×C43—22no—
469D4×C43—22no—
470D4×C43—21no—
471D4×C43—21no—
472D4×C43—21no—
473D4×C43—22no—
474D4×C43—22no—
475D4×C43—44no—
476D4×C43—44no—
477D4×C43—44no—
478D4×C43—41no—
479D4×C43—41no—
480D4×C43C22×D412yes—
481D4×C43C22×D412yes—
482D4×C43C22×D412yes—
483C2×C4×C43—21no—
484C2×C4×C43—21no—
485C2×C4×C43—21no—
486C2×C4×C43—22no—
487C2×C4×C43—22no—
488C2×C4×C43—22no—
489C2×C4×C43—22no—
490C2×C4×C43—22no—
491C2×C4×C43—22no—
492C2×C4×C43—22no—
493C2×C4×C43—44no—
494C2×C4×C43—44no—
495C2×C4×C43—44no—
496C2×C4×C43—41no—
497C2×C4×C43—41no—
498C2×C4×C43C22×D411yescharacteristic
499C2×C4×C43C22×D411yescharacteristic
500C2×C4×C43C22×D411yescharacteristic
501C2×C4×C43C22×D411yescharacteristic
502C2×C4×C43H(5,𝔽2)11yescharacteristic
503C2×C4×C43C2511yescharacteristic
504C22⋊D43—22no—
505C22⋊D43—22no—
506C22⋊D43—44no—
507C22⋊D43—44no—
508C22⋊D43—88no—
509C2×Dic43—21no—
510C2×Dic43—22no—
511C2×Dic43—42no—
512D172—21no—
513D172—22no—
514D172—22no—
515D172—22no—
516D172—22no—
517D172—44no—
518D172—44no—
519D172—41no—
520D172—41no—
521D172—41no—
522D172—41no—
523D172C22×D412yes—
524C4×D43—22no—
525C4×D43—22no—
526C4×D43—44no—
527C4×D43—44no—
528Dic86—21no—
529Dic86C22×D412yes—
530C8×C43—22no—
531C8×C43C22×D412yes—
532C8×C43C22×D412yes—
533C43⋊C8—22no—
534C43⋊C8—22no—
535C43⋊C8—22no—
536C43⋊C8C22×D412yes—
537C43⋊C8C22×D412yes—
538C2×#3288—431nomaximal, Sylow
539C22×C43—22no—
540C22×C43—22no—
541C22×C43—22no—
542C22×C43—22no—
543C22×C43—42no—
544C22×C43—42no—
545C22×C43—42no—
546C22×C43—42no—
547C22×C43—82no—
548C22×C43—82no—
549C22×C43—161no—
550C22×C43—164no—
551C22×C43D4211yescharacteristic
552C22×C43D4211yescharacteristic
553C22×C43C2×H(5,𝔽2)11yescharacteristic
554C2×D43—22no—
555C2×D43—42no—
556C2×D43—42no—
557C2×D43—42no—
558C2×D43—82no—
559C2×D43—82no—
560C2×D43—82no—
561C2×D43—82no—
562C2×D43—164no—
563C2×D43—164no—
564C2×D43—161no—
565C2×D43—161no—
566C4×C43—22no—
567C4×C43—22no—
568C4×C43—22no—
569C4×C43—42no—
570C4×C43D4211yescharacteristic
571C4×C43D4211yescharacteristic
572C4×C43C23×D411yescharacteristic
573C4×C43C23×D411yescharacteristic
574Dic43—22no—
575Dic43—42no—
576C2×#577—431no—
577C2×#577D4311yescharacteristic, complemented
578C2×#576—431no—
579C2×#576—431no—
580#3288—4316no—
581C2×#496—431no—
582C2×#472—431no—
583C2×#472—431no—
584C2×#471—431no—
585C2×#471—431no—
586C2×#454—431no—
587C2×#455—431no—
588C2×#453—431no—
589C2×#453—431no—
590C2×#444—431no—
591C2×#444—431no—
592C2×C43—21no—
593C2×C43—21no—
594C2×C43—42no—
595C2×C43—42no—
596C2×C43—42no—
597C2×C43—82no—
598C2×C43#328812yescomplemented
599C2×C43C2×D4211yescharacteristic
600D43—42no—
601D43—82no—
602D43—82no—
603C2×2−1+4C2×D4311yescharacteristic, complemented
604C2×H(5,𝔽2)—431no—
605C2×H(5,𝔽2)—431no—
606C2×H(5,𝔽2)C2×D4311yescharacteristic, complemented
607#577—24no—
608#577—438no—
609#577—864no—
610#577C2×D4318yescomplemented
611#576—438no—
612#576—438no—
613#576—864no—
614#576—864no—
615C2×#137—21no—
616C2×#137—431no—
617C2×#137—861no—
618C2×#137C2×D4311yescharacteristic, complemented
619C2×AGL(1,ℤ/8)—21no—
620C2×AGL(1,ℤ/8)—431no—
621C2×AGL(1,ℤ/8)—431no—
622C2×AGL(1,ℤ/8)—431no—
623C2×AGL(1,ℤ/8)—431no—
624C2×AGL(1,ℤ/8)—431no—
625C2×AGL(1,ℤ/8)—861no—
626C2×AGL(1,ℤ/8)—861no—
627C2×AGL(1,ℤ/8)—861no—
628C2×AGL(1,ℤ/8)—861no—
629C2×AGL(1,ℤ/8)—861no—
630C2×AGL(1,ℤ/8)C2×D4311yescharacteristic, complemented
631C2×#135—21no—
632C2×#135—431no—
633C2×#135—861no—
634C2×#135—861no—
635C2×#135—861no—
636C2×#135C2×D4311yescharacteristic
637C22×SD16—21no—
638C22×SD16—431no—
639C22×SD16—861no—
640C22×SD16C2×D4311yescharacteristic, complemented
641C22×D8—431no—
642C22×D8—431no—
643C22×D8—861no—
644C22×D8—861no—
645C2×#131—431no—
646C2×#131—431no—
647C2×#131—431no—
648C2×#131C2×D4311yescharacteristic, complemented
649C2×#127—431no—
650C2×#124—431no—
651#496—438no—
652#472—438no—
653#472—438no—
654#471—438no—
655#471—438no—
656#455—438no—
657#454—438no—
658#453—438no—
659#453—438no—
660#444—438no—
661#444—438no—
662C2×#108—431no—
663C2×#108—431no—
664C2×#104—431no—
665C2×#104—431no—
666C2×#104—431no—
667C2×#104—431no—
668C2×#101—431no—
669C2×#100—431no—
670C2×#100—431no—
671C2×#100—431no—
672C2×#97—431no—
673C43C2×#328811yescharacteristic, complemented, Sylow
6742−1+4—22no—
6752−1+4—22no—
6762−1+4—41no—
6772−1+4C22×D4314yescomplemented
678H(5,𝔽2)—22no—
679H(5,𝔽2)—22no—
680H(5,𝔽2)—41no—
681H(5,𝔽2)—434no—
682H(5,𝔽2)—434no—
683H(5,𝔽2)—862no—
684H(5,𝔽2)—862no—
685H(5,𝔽2)—862no—
686H(5,𝔽2)—862no—
687H(5,𝔽2)—1721no—
688H(5,𝔽2)—1721no—
689H(5,𝔽2)C22×D4314yescomplemented
690C2×#41—21no—
691C2×#41—21no—
692C2×#41—21no—
693C2×#41—21no—
694C2×#41—41no—
695C2×#41—431no—
696C2×#41—861no—
697C2×#41—861no—
698C2×#41—861no—
699C2×#41—861no—
700C2×#41C22×D4311yescharacteristic
701C2×#41C22×D4311yescharacteristic
702C2×#41C22×D4311yescharacteristic
703C22×Q8—21no—
704C22×Q8—21no—
705C22×Q8C22×D4311yescharacteristic
706C22×D4—21no—
707C22×D4—21no—
708C22×D4—41no—
709C22×D4—431no—
710C22×D4—431no—
711C22×D4—861no—
712C22×D4—861no—
713C22×D4—861no—
714C22×D4—861no—
715C22×D4—1721no—
716C22×D4—1721no—
717C22×D4—1721no—
718C22×D4C22×D4311yescharacteristic
719#137—22no—
720#137—28no—
721#137—434no—
722#137—868no—
723#137—862no—
724#137C22×D4314yescomplemented
725AGL(1,ℤ/8)—22no—
726AGL(1,ℤ/8)—28no—
727AGL(1,ℤ/8)—434no—
728AGL(1,ℤ/8)—434no—
729AGL(1,ℤ/8)—434no—
730AGL(1,ℤ/8)—434no—
731AGL(1,ℤ/8)—434no—
732AGL(1,ℤ/8)—868no—
733AGL(1,ℤ/8)—868no—
734AGL(1,ℤ/8)—868no—
735AGL(1,ℤ/8)—862no—
736AGL(1,ℤ/8)—862no—
737AGL(1,ℤ/8)—862no—
738AGL(1,ℤ/8)—862no—
739AGL(1,ℤ/8)—862no—
740AGL(1,ℤ/8)—868no—
741AGL(1,ℤ/8)—868no—
742AGL(1,ℤ/8)C22×D4314yescomplemented
743#135—28no—
744#135—434no—
745#135—434no—
746#135—868no—
747#135—868no—
748#135—868no—
749#135C22⋊D4314yescomplemented
750#135C22×D4314yes—
751C2×Q16—21no—
752C2×Q16—431no—
753C2×Q16—861no—
754C2×Q16C22⋊D4311yescharacteristic, complemented
755C2×SD16—21no—
756C2×SD16—21no—
757C2×SD16—28no—
758C2×SD16—21no—
759C2×SD16—21no—
760C2×SD16—22no—
761C2×SD16—431no—
762C2×SD16—431no—
763C2×SD16—434no—
764C2×SD16—861no—
765C2×SD16—861no—
766C2×SD16—862no—
767C2×SD16—868no—
768C2×SD16—861no—
769C2×SD16—861no—
770C2×SD16—861no—
771C2×SD16—861no—
772C2×SD16—861no—
773C2×SD16—861no—
774C2×SD16C22⋊D4311yescharacteristic, complemented
775C2×SD16C22⋊D4311yescharacteristic, complemented
776C2×SD16C22×D4314yescomplemented
777C2×D8—21no—
778C2×D8—431no—
779C2×D8—434no—
780C2×D8—434no—
781C2×D8—861no—
782C2×D8—861no—
783C2×D8—862no—
784C2×D8—868no—
785C2×D8—861no—
786C2×D8—861no—
787C2×D8—861no—
788C2×D8—861no—
789C2×D8—861no—
790C2×D8—868no—
791C2×D8—861no—
792C2×D8—861no—
793C2×D8—862no—
794C2×D8C22⋊D4311yescharacteristic, complemented
795#131—22no—
796#131—434no—
797#131—434no—
798#131—434no—
799#131—862no—
800#131—862no—
801#131—862no—
802#131C22×D4314yescomplemented
803C2×M16—21no—
804C2×M16—431no—
805C2×M16—431no—
806C2×M16—431no—
807C2×M16—861no—
808C2×M16—861no—
809C2×M16—861no—
810C2×M16C22×D4311yescharacteristic
811C22×C8—21no—
812C22×C8—431no—
813C22×C8—861no—
814C22×C8—861no—
815C22×C8—861no—
816C22×C8C22×D4311yescharacteristic
817#127—434no—
818#127—1721no—
819#124—434no—
820#124—1721no—
821C2×C22⋊C4—1721no—
822C2×C42—431no—
823#108—434no—
824#108—434no—
825#104—434no—
826#104—434no—
827#104—434no—
828#104—434no—
829#101—434no—
830#100—434no—
831#100—434no—
832#100—434no—
833#97—434no—
834C24—21no—
835C24—41no—
836C24—861no—
837C24—861no—
838C24—1721no—
839C24—1721no—
840#41—21no—
841#41—21no—
842#41—21no—
843#41—21no—
844#41—21no—
845#41—21no—
846#41—24no—
847#41—24no—
848#41—24no—
849#41—24no—
850#41—44no—
851#41—42no—
852#41—42no—
853#41—42no—
854#41—42no—
855#41—44no—
856#41—432no—
857#41—432no—
858#41—864no—
859#41—864no—
860#41—861no—
861#41—861no—
862#41—864no—
863#41—864no—
864#41—1722no—
865#41—1722no—
866#41—1722no—
867#41—1722no—
868#41D4×D4312yes—
869#41C2×C22⋊D4312yes—
870#41C2×C22⋊D4312yes—
871#41C23×D4312yes—
872#41C23×D4312yes—
873#41C23×D4312yes—
874C2×Q8—21no—
875C2×Q8—24no—
876C2×Q8—24no—
877C2×Q8—21no—
878C2×Q8—21no—
879C2×Q8—21no—
880C2×Q8—21no—
881C2×Q8—41no—
882C2×Q8—42no—
883C2×Q8—42no—
884C2×Q8—431no—
885C2×Q8D4×D4311yescharacteristic
886C2×Q8C2×C22⋊D4311yescharacteristic
887C2×Q8C2×C22⋊D4311yescharacteristic
888C2×Q8C23×D4312yes—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—24no—
893C2×D4—24no—
894C2×D4—21no—
895C2×D4—21no—
896C2×D4—21no—
897C2×D4—21no—
898C2×D4—21no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4—41no—
902C2×D4—41no—
903C2×D4—44no—
904C2×D4—44no—
905C2×D4—41no—
906C2×D4—431no—
907C2×D4—432no—
908C2×D4—432no—
909C2×D4—864no—
910C2×D4—864no—
911C2×D4—861no—
912C2×D4—864no—
913C2×D4—864no—
914C2×D4—861no—
915C2×D4—861no—
916C2×D4—861no—
917C2×D4—861no—
918C2×D4—861no—
919C2×D4—861no—
920C2×D4—861no—
921C2×D4—861no—
922C2×D4—861no—
923C2×D4—861no—
924C2×D4—3444no—
925C2×D4—1722no—
926C2×D4—1722no—
927C2×D4—1721no—
928C2×D4—1721no—
929C2×D4—1722no—
930C2×D4—1722no—
931C2×D4—1724no—
932C2×D4—1721no—
933C2×D4—1721no—
934C2×D4—1724no—
935C2×D4—1724no—
936C2×D4—1724no—
937C2×D4—1724no—
938C2×D4D4×D4311yescharacteristic
939C2×D4C2×C22⋊D4311yescharacteristic
940C2×D4C2×C22⋊D4311yescharacteristic
941C2×D4C23×D4312yes—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—41no—
947C22×C4—41no—
948C22×C4—41no—
949C22×C4—861no—
950C22×C4—861no—
951C22×C4—1721no—
952C22×C4—1721no—
953C22×C4C23×D4311yescharacteristic
954Q16—24no—
955Q16—434no—
956Q16—864no—
957Q16C2×C22⋊D4314yescomplemented
958SD16—24no—
959SD16—24no—
960SD16—24no—
961SD16—24no—
962SD16—434no—
963SD16—434no—
964SD16—864no—
965SD16—864no—
966SD16—864no—
967SD16—864no—
968SD16—864no—
969SD16—864no—
970SD16—864no—
971SD16—864no—
972SD16C2×C22⋊D4314yescomplemented
973SD16C2×C22⋊D4314yescomplemented
974D8—24no—
975D8—434no—
976D8—864no—
977D8—864no—
978D8—864no—
979D8—864no—
980D8—864no—
981D8—864no—
982D8—864no—
983D8—864no—
984D8—864no—
985D8C2×C22⋊D4314yescomplemented
986M16—21no—
987M16—24no—
988M16—432no—
989M16—432no—
990M16—432no—
991M16—864no—
992M16—864no—
993M16—861no—
994M16—861no—
995M16—861no—
996M16—864no—
997M16C23×D4312yes—
998C2×C8—21no—
999C2×C8—24no—
1000C2×C8—431no—
1001C2×C8—431no—
1002C2×C8—432no—
1003C2×C8—432no—
1004C2×C8—864no—
1005C2×C8—864no—
1006C2×C8—861no—
1007C2×C8—861no—
1008C2×C8—861no—
1009C2×C8—864no—
1010C2×C8C2×C22⋊D4311yescharacteristic
1011C2×C8C2×C22⋊D4311yescharacteristic
1012C2×C8C2×C22⋊D4312yes—
1013C2×C8C23×D4312yes—
1014C22⋊C4—1724no—
1015C42—432no—
1016C42—861no—
1017C23—21no—
1018C23—21no—
1019C23—21no—
1020C23—22no—
1021C23—44no—
1022C23—41no—
1023C23—41no—
1024C23—82no—
1025C23—162no—
1026C23—861no—
1027C23—862no—
1028C23—862no—
1029C23—3442no—
1030C23—3442no—
1031C23—1724no—
1032C23—1724no—
1033C23—1721no—
1034C23—1721no—
1035C23—1721no—
1036C23—1721no—
1037C23—6882no—
1038C23—6882no—
1039C23#1306337011yescharacteristic
1040Q8—21no—
1041Q8—21no—
1042Q8—21no—
1043Q8—22no—
1044Q8—22no—
1045Q8—44no—
1046Q8—41no—
1047Q8—41no—
1048Q8—432no—
1049Q8—861no—
1050Q8C2×D4×D4312yes—
1051Q8C22×C22⋊D4312yes—
1052Q8C22×C22⋊D4312yes—
1053D4—22no—
1054D4—22no—
1055D4—22no—
1056D4—22no—
1057D4—22no—
1058D4—22no—
1059D4—22no—
1060D4—22no—
1061D4—21no—
1062D4—21no—
1063D4—21no—
1064D4—44no—
1065D4—44no—
1066D4—44no—
1067D4—41no—
1068D4—41no—
1069D4—432no—
1070D4—862no—
1071D4—862no—
1072D4—862no—
1073D4—862no—
1074D4—862no—
1075D4—862no—
1076D4—861no—
1077D4—3448no—
1078D4—1724no—
1079D4—1724no—
1080D4—1724no—
1081D4—1724no—
1082D4—1721no—
1083D4—1721no—
1084D4—1721no—
1085D4—1721no—
1086D4C2×D4×D4312yes—
1087D4C22×C22⋊D4312yes—
1088D4C22×C22⋊D4312yes—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—44no—
1100C2×C4—44no—
1101C2×C4—44no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—861no—
1105C2×C4—862no—
1106C2×C4—862no—
1107C2×C4—862no—
1108C2×C4—1724no—
1109C2×C4—1724no—
1110C2×C4—1722no—
1111C2×C4C2×D4×D4311yescharacteristic
1112C2×C4C2×D4×D4311yescharacteristic
1113C2×C4C22×C22⋊D4311yescharacteristic
1114C2×C4C22×C22⋊D4311yescharacteristic
1115C2×C4#1306337011yescharacteristic
1116C2×C4C24×D4311yescharacteristic
1117C8—22no—
1118C8—432no—
1119C8—432no—
1120C8—862no—
1121C8—862no—
1122C8—862no—
1123C8C22×C22⋊D4312yes—
1124C8C22×C22⋊D4312yes—
1125C22—22no—
1126C22—22no—
1127C22—22no—
1128C22—22no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—82no—
1134C22—82no—
1135C22—161no—
1136C22—164no—
1137C22—862no—
1138C22—3442no—
1139C22—3442no—
1140C22—3442no—
1141C22—3442no—
1142C22—1722no—
1143C22—1722no—
1144C22—1722no—
1145C22—6881no—
1146C22—6881no—
1147C22—6884no—
1148C22—6884no—
1149C22D4×C22⋊D4311yescharacteristic
1150C22D4×C22⋊D4311yescharacteristic
1151C22C2×#1306337011yescharacteristic
1152C4—22no—
1153C4—22no—
1154C4—22no—
1155C4—42no—
1156C4—862no—
1157C4—1722no—
1158C4D4×C22⋊D4311yescharacteristic
1159C4D4×C22⋊D4311yescharacteristic
1160C4C22×D4×D4311yescharacteristic
1161C4C23×C22⋊D4311yescharacteristic
1162C2—21no—
1163C2—21no—
1164C2—42no—
1165C2—42no—
1166C2—42no—
1167C2—82no—
1168C2—3442no—
1169C2—3442no—
1170C2—1722no—
1171C2#1914635712yesdirect product factor
1172C2C2×D4×C22⋊D4311yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#577C2
socleC22×C43D42
hypercenterC2×#577D43
hypocenterC43C2×#3288
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#577

Complements

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

NH ≅ G/Ntype
1. C2×#14583707C2semidirect
2. C2×#14583702C2semidirect
3. C2×#14583701C2semidirect
4. #19146357C2direct (N × H)
5. C2×#14583285C2semidirect
6. C2×#14583169C2semidirect
7. C2×#14583167C2semidirect
8. C2×#14583164C2semidirect
9. C2×#14583159C2semidirect
10. C2×#14583072C2semidirect
11. C2×#14583075C2semidirect
12. C2×#14583067C2semidirect
13. C2×#14583065C2semidirect
14. C2×#14583021C2semidirect
15. C2×#14583019C2semidirect
16. C2×C43×#577C2semidirect
18. C2×#13063371C22semidirect
20. #14583707C22semidirect
22. #14583702C22semidirect
24. #14583701C22semidirect
26. C2×#13063356C22semidirect
34. C2×#13063350C22semidirect
35. C2×#13063350C22semidirect
36. C2×#13063350C22semidirect
42. C22×#10621884C22semidirect
43. C22×D344C22semidirect
45. C22×#10621882C22semidirect
47. C2×#13063332C22semidirect
48. C2×#13063332C22semidirect
49. C2×#13063331C22semidirect
50. C2×#13063321C22semidirect
51. C2×#13063314C22semidirect
52. #14583285C22semidirect
53. #14583169C22semidirect
54. #14583167C22semidirect
55. #14583164C22semidirect
56. #14583159C22semidirect
57. #14583075C22semidirect
58. #14583072C22semidirect
59. #14583067C22semidirect
60. #14583065C22semidirect
61. #14583021C22semidirect
62. #14583019C22semidirect
63. C2×#13063261C22semidirect
64. C2×#13063260C22semidirect
65. C2×#13063252C22semidirect
66. C2×#13063252C22semidirect
67. C2×#13063252C22semidirect
68. C2×#13063251C22semidirect
69. C2×#13063244C22semidirect
70. C2×#13063242C22semidirect
71. C2×#13063241C22semidirect
72. C2×#13063241C22semidirect
73. C2×#13063235C22semidirect
74. C2×2−1+4×C43C22semidirect
75. C2×H(5,𝔽2)×C43C22semidirect
77. C43×#577C22semidirect
79. C2×#137×C43C22semidirect
81. C2×AGL(1,ℤ/8)×C43C22semidirect
85. C22×SD16×C43C22semidirect
86. C2×#131×C43C22semidirect
94. #13063371C23semidirect
111. #13063356C23semidirect
124. #13063350C23semidirect
125. #13063350C23semidirect
126. #13063350C23semidirect
130. #13063345D4semidirect
133. C2×#10621885D4semidirect
135. C2×#10621883D4semidirect
145. C2×#10621884D4semidirect
146. C2×#10621884C23semidirect
150. C2×D344C23semidirect
160. C2×#10621882D4semidirect
161. C2×#10621882C23semidirect
165. #13063332C23semidirect
166. #13063332C23semidirect
168. #13063331C23semidirect
180. #13063321C23semidirect
182. #13063314C23semidirect
185. #13063261C23semidirect
186. #13063260C23semidirect
187. #13063252C23semidirect
188. #13063252C23semidirect
189. #13063252C23semidirect
190. #13063251C23semidirect
191. #13063244C23semidirect
192. #13063242C23semidirect
193. #13063241C23semidirect
194. #13063241C23semidirect
195. #13063235C23semidirect
199. 2−1+4×C43C23semidirect
203. H(5,𝔽2)×C43C23semidirect
221. #137×C43C23semidirect
224. AGL(1,ℤ/8)×C43C23semidirect
226. #135×C43D4semidirect
229. C2×Q16×C43D4semidirect
236. C2×SD16×C43D4semidirect
237. C2×SD16×C43D4semidirect
238. C2×SD16×C43C23semidirect
240. C2×D8×C43D4semidirect
242. #131×C43C23semidirect
368. Q16×C43C2×D4semidirect
373. SD16×C43C2×D4semidirect
374. SD16×C43C2×D4semidirect
376. D8×C43C2×D4semidirect
387. #10621885C2×D4semidirect
395. #10621884C2×D4semidirect
397. #10621883C2×D4semidirect
405. #10621882C2×D4semidirect
577. C2×#577D43semidirect
598. C2×C43#3288semidirect
603. C2×2−1+4C2×D43semidirect
606. C2×H(5,𝔽2)C2×D43semidirect
610. #577C2×D43semidirect
618. C2×#137C2×D43semidirect
630. C2×AGL(1,ℤ/8)C2×D43semidirect
640. C22×SD16C2×D43semidirect
648. C2×#131C2×D43semidirect
673. C43C2×#3288semidirect
677. 2−1+4C22×D43semidirect
689. H(5,𝔽2)C22×D43semidirect
724. #137C22×D43semidirect
742. AGL(1,ℤ/8)C22×D43semidirect
749. #135C22⋊D43semidirect
754. C2×Q16C22⋊D43semidirect
774. C2×SD16C22⋊D43semidirect
775. C2×SD16C22⋊D43semidirect
776. C2×SD16C22×D43semidirect
794. C2×D8C22⋊D43semidirect
802. #131C22×D43semidirect
957. Q16C2×C22⋊D43semidirect
972. SD16C2×C22⋊D43semidirect
973. SD16C2×C22⋊D43semidirect
985. D8C2×C22⋊D43semidirect
1171. C2#19146357direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145837072
C2×#145837022
C2×#145837012
#191463572
C2×#145832852
C2×#145831692
C2×#145831672
C2×#145831642
C2×#145831592
C2×#145830722
C2×#145830752
C2×#145830672
C2×#145830652
C2×#145830212
C2×#145830192
C2×C43×#5772
C2×#328843