Finite Group Databasebeta

← C2×#20255150 #27092455

Subgroups — C2×#20255150 #27092455

Order 12032.

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×#15689931C211yesmaximal, characteristic, complemented
2C2×#15689926C211yesmaximal, characteristic, complemented
3C2×#15689925C211yesmaximal, characteristic, complemented
4#20255150C2116yesmaximal, direct product factor
5C2×#15689509C211yesmaximal, characteristic, complemented
6C2×#15689393C211yesmaximal, characteristic, complemented
7C2×#15689391C211yesmaximal, characteristic, complemented
8C2×#15689388C211yesmaximal, characteristic, complemented
9C2×#15689383C211yesmaximal, characteristic, complemented
10C2×#15689296C211yesmaximal, characteristic, complemented
11C2×#15689299C211yesmaximal, characteristic, complemented
12C2×#15689291C211yesmaximal, characteristic, complemented
13C2×#15689289C211yesmaximal, characteristic, complemented
14C2×#15689245C211yesmaximal, characteristic, complemented
15C2×#15689243C211yesmaximal, characteristic, complemented
16C2×C47×#577C211yesmaximal, characteristic, complemented
17C2×#13094070C2211yescharacteristic
18C2×#13094070C2211yescharacteristic, complemented
19#15689931—24no—
20#15689931C2218yescomplemented
21#15689926—24no—
22#15689926C2218yescomplemented
23#15689925—24no—
24#15689925C2218yescomplemented
25C2×#13094055—21no—
26C2×#13094055C2211yescharacteristic, complemented
27C2×#13094051—21no—
28C2×#13094051—21no—
29C2×#13094050—21no—
30C2×#13094050C2211yescharacteristic
31C2×#13094049—21no—
32C2×#13094049—21no—
33C2×#13094049C2211yescharacteristic
34C2×#13094049C2211yescharacteristic, complemented
35C2×#13094049C2211yescharacteristic, complemented
36C2×#13094049C2211yescharacteristic, complemented
37C2×#13094047—21no—
38C2×#13094044—21no—
39C2×#13094044—21no—
40C2×#13094044C2211yescharacteristic
41C22×#10625336—21no—
42C22×#10625336C2211yescharacteristic, complemented
43C22×D376C2211yescharacteristic, complemented
44C22×#10625334—21no—
45C22×#10625334C2211yescharacteristic, complemented
46C2×D8×D47—21no—
47C2×#13094031C2211yescharacteristic, complemented
48C2×#13094031C2211yescharacteristic, complemented
49C2×#13094030C2211yescharacteristic, complemented
50C2×#13094020C2211yescharacteristic, complemented
51C2×#13094013C2211yescharacteristic, complemented
52#15689509C2218yescomplemented
53#15689393C2218yescomplemented
54#15689391C2218yescomplemented
55#15689388C2218yescomplemented
56#15689383C2218yescomplemented
57#15689299C2218yescomplemented
58#15689296C2218yescomplemented
59#15689291C2218yescomplemented
60#15689289C2218yescomplemented
61#15689245C2218yescomplemented
62#15689243C2218yescomplemented
63C2×#13093960C2211yescharacteristic, complemented
64C2×#13093959C2211yescharacteristic, complemented
65C2×#13093951C2211yescharacteristic, complemented
66C2×#13093951C2211yescharacteristic, complemented
67C2×#13093951C2211yescharacteristic, complemented
68C2×#13093950C2211yescharacteristic, complemented
69C2×#13093943C2211yescharacteristic, complemented
70C2×#13093941C2211yescharacteristic, complemented
71C2×#13093940C2211yescharacteristic, complemented
72C2×#13093940C2211yescharacteristic, complemented
73C2×#13093934C2211yescharacteristic, complemented
74C2×2−1+4×C47C2211yescharacteristic, complemented
75C2×H(5,𝔽2)×C47C2211yescharacteristic, complemented
76C47×#577—24no—
77C47×#577C2218yescomplemented
78C2×#137×C47—21no—
79C2×#137×C47C2211yescharacteristic, complemented
80C2×AGL(1,ℤ/8)×C47—21no—
81C2×AGL(1,ℤ/8)×C47C2211yescharacteristic, complemented
82C2×#135×C47—21no—
83C2×#135×C47C2211yescharacteristic
84C22×SD16×C47—21no—
85C22×SD16×C47C2211yescharacteristic, complemented
86C2×#131×C47C2211yescharacteristic, complemented
87#13094070—22no—
88#13094070—22no—
89#13094070—22no—
90#13094070—22no—
91#13094070—41no—
92#13094070—41no—
93#13094070C2314yes—
94#13094070C2314yescomplemented
95C2×#10625354—21no—
96C2×#10625354—21no—
97C2×#10625350—21no—
98C2×#10625350—21no—
99C2×#10625350C2311yescharacteristic
100C22×D188—21no—
101C22×D188—21no—
102C22×D188C2311yescharacteristic
103C22×D188C2311yescharacteristic
104C22×C22⋊D47—41no—
105C2×D4×D47—21no—
106C2×D4×D47—21no—
107C2×D4×D47—41no—
108C2×D4×D47—41no—
109#13094055—22no—
110#13094055—28no—
111#13094055C2314yescomplemented
112#13094051—28no—
113#13094051—28no—
114#13094050—22no—
115#13094050—28no—
116#13094050C2314yes—
117#13094049—22no—
118#13094049—22no—
119#13094049—22no—
120#13094049—22no—
121#13094049—28no—
122#13094049—28no—
123#13094049C2314yes—
124#13094049C2314yescomplemented
125#13094049C2314yescomplemented
126#13094049C2314yescomplemented
127#13094047—28no—
128#13094044—28no—
129#13094044—28no—
130#13094044D414yescomplemented
131#13094044C2314yes—
132C2×#10625337—21no—
133C2×#10625337D411yescharacteristic, complemented
134C2×#10625335—21no—
135C2×#10625335D411yescharacteristic, complemented
136C2×#10625336—21no—
137C2×#10625336—21no—
138C2×#10625336—21no—
139C2×#10625336—21no—
140C2×#10625336—21no—
141C2×#10625336—28no—
142C2×#10625336—21no—
143C2×#10625336—21no—
144C2×#10625336—22no—
145C2×#10625336D411yescharacteristic, complemented
146C2×#10625336C2314yescomplemented
147C2×D376—21no—
148C2×D376—21no—
149C2×D376—22no—
150C2×D376C2314yescomplemented
151C2×#10625334—21no—
152C2×#10625334—21no—
153C2×#10625334—21no—
154C2×#10625334—21no—
155C2×#10625334—21no—
156C2×#10625334—28no—
157C2×#10625334—21no—
158C2×#10625334—21no—
159C2×#10625334—22no—
160C2×#10625334D411yescharacteristic, complemented
161C2×#10625334C2314yescomplemented
162D8×D47—28no—
163#13094031—22no—
164#13094031—22no—
165#13094031C2314yescomplemented
166#13094031C2314yescomplemented
167#13094030—22no—
168#13094030C2314yescomplemented
169C2×#10625329—21no—
170C2×#10625329—21no—
171C2×#10625329C2311yescharacteristic
172C2×#10625329C2311yescharacteristic
173C2×#10625329C2311yescharacteristic
174C2×#10625324—21no—
175C22×C47⋊C8—21no—
176C22×C47⋊C8—21no—
177C22×C47⋊C8C2311yescharacteristic
178C2×C8×D47—21no—
179#13094020—41no—
180#13094020C2314yescomplemented
181#13094013—41no—
182#13094013C2314yescomplemented
183C2×(C2×D47)⋊C4—41no—
184C2×C4×Dic47C2311yescharacteristic
185#13093960C2314yescomplemented
186#13093959C2314yescomplemented
187#13093951C2314yescomplemented
188#13093951C2314yescomplemented
189#13093951C2314yescomplemented
190#13093950C2314yescomplemented
191#13093943C2314yescomplemented
192#13093941C2314yescomplemented
193#13093940C2314yescomplemented
194#13093940C2314yescomplemented
195#13093934C2314yescomplemented
1962−1+4×C47—22no—
1972−1+4×C47—22no—
1982−1+4×C47—41no—
1992−1+4×C47C2314yescomplemented
200H(5,𝔽2)×C47—22no—
201H(5,𝔽2)×C47—22no—
202H(5,𝔽2)×C47—41no—
203H(5,𝔽2)×C47C2314yescomplemented
204C2×#41×C47—21no—
205C2×#41×C47—21no—
206C2×#41×C47—21no—
207C2×#41×C47—21no—
208C2×#41×C47—41no—
209C2×#41×C47C2311yescharacteristic
210C2×#41×C47C2311yescharacteristic
211C2×#41×C47C2311yescharacteristic
212C22×Q8×C47—21no—
213C22×Q8×C47—21no—
214C22×Q8×C47C2311yescharacteristic
215C22×D4×C47—21no—
216C22×D4×C47—21no—
217C22×D4×C47—41no—
218C22×D4×C47C2311yescharacteristic
219#137×C47—22no—
220#137×C47—28no—
221#137×C47C2314yescomplemented
222AGL(1,ℤ/8)×C47—22no—
223AGL(1,ℤ/8)×C47—28no—
224AGL(1,ℤ/8)×C47C2314yescomplemented
225#135×C47—28no—
226#135×C47D414yescomplemented
227#135×C47C2314yes—
228C2×Q16×C47—21no—
229C2×Q16×C47D411yescharacteristic, complemented
230C2×SD16×C47—21no—
231C2×SD16×C47—21no—
232C2×SD16×C47—28no—
233C2×SD16×C47—21no—
234C2×SD16×C47—21no—
235C2×SD16×C47—22no—
236C2×SD16×C47D411yescharacteristic, complemented
237C2×SD16×C47D411yescharacteristic, complemented
238C2×SD16×C47C2314yescomplemented
239C2×D8×C47—21no—
240C2×D8×C47D411yescharacteristic, complemented
241#131×C47—22no—
242#131×C47C2314yescomplemented
243C2×M16×C47—21no—
244C2×M16×C47C2311yescharacteristic
245C22×C8×C47—21no—
246C22×C8×C47C2311yescharacteristic
247C24×C47—21no—
248C24×C47—41no—
249C23×D47—21no—
250C23×D47—21no—
251C23×D47—41no—
252C23×D47—41no—
253#41×C47—21no—
254#41×C47—21no—
255#41×C47—21no—
256#41×C47—21no—
257#41×C47—21no—
258#41×C47—21no—
259#41×C47—24no—
260#41×C47—24no—
261#41×C47—24no—
262#41×C47—24no—
263#41×C47—44no—
264#41×C47—42no—
265#41×C47—42no—
266#41×C47—42no—
267#41×C47—42no—
268#41×C47—44no—
269#41×C47C2×D412yes—
270#41×C47C2×D412yes—
271#41×C47C2×D412yes—
272#41×C47C2412yes—
273#41×C47C2412yes—
274#41×C47C2412yes—
275C2×Q8×C47—21no—
276C2×Q8×C47—24no—
277C2×Q8×C47—24no—
278C2×Q8×C47—21no—
279C2×Q8×C47—21no—
280C2×Q8×C47—21no—
281C2×Q8×C47—21no—
282C2×Q8×C47—41no—
283C2×Q8×C47—42no—
284C2×Q8×C47—42no—
285C2×Q8×C47C2×D411yescharacteristic
286C2×Q8×C47C2×D411yescharacteristic
287C2×Q8×C47C2×D411yescharacteristic
288C2×Q8×C47C2412yes—
289C2×D4×C47—21no—
290C2×D4×C47—21no—
291C2×D4×C47—21no—
292C2×D4×C47—24no—
293C2×D4×C47—24no—
294C2×D4×C47—21no—
295C2×D4×C47—21no—
296C2×D4×C47—21no—
297C2×D4×C47—21no—
298C2×D4×C47—21no—
299C2×D4×C47—42no—
300C2×D4×C47—42no—
301C2×D4×C47—41no—
302C2×D4×C47—41no—
303C2×D4×C47—44no—
304C2×D4×C47—44no—
305C2×D4×C47—41no—
306C2×D4×C47C2×D411yescharacteristic
307C2×D4×C47C2×D411yescharacteristic
308C2×D4×C47C2×D411yescharacteristic
309C2×D4×C47C2412yes—
310C22×C4×C47—21no—
311C22×C4×C47—21no—
312C22×C4×C47—21no—
313C22×C4×C47—21no—
314C22×C4×C47—41no—
315C22×C4×C47—41no—
316C22×C4×C47—41no—
317C22×C4×C47C2411yescharacteristic
318C2×C22⋊D47—21no—
319C2×C22⋊D47—41no—
320C2×C22⋊D47—41no—
321C2×C22⋊D47—44no—
322C2×C22⋊D47—84no—
323C22×Dic47—21no—
324#10625354—24no—
325#10625354—24no—
326#10625354—42no—
327#10625354—42no—
328D4×D47—24no—
329D4×D47—24no—
330D4×D47—42no—
331D4×D47—42no—
332D4×D47—44no—
333D4×D47—44no—
334D4×D47—44no—
335D4×D47—44no—
336#10625350—21no—
337#10625350—21no—
338#10625350—24no—
339#10625350—24no—
340#10625350—42no—
341#10625350—42no—
342#10625350C2×D412yes—
343#10625350C2412yes—
344C2×D188—21no—
345C2×D188—21no—
346C2×D188—21no—
347C2×D188—21no—
348C2×D188—21no—
349C2×D188—21no—
350C2×D188—21no—
351C2×D188—21no—
352C2×D188—24no—
353C2×D188—24no—
354C2×D188—21no—
355C2×D188—21no—
356C2×D188—42no—
357C2×D188—42no—
358C2×D188—41no—
359C2×D188—41no—
360C2×D188C2×D411yescharacteristic
361C2×D188C2412yes—
362C2×D188C2412yes—
363C2×C4×D47—21no—
364C2×C4×D47—41no—
365C2×C4×D47—41no—
366C2×Dic94C2×D411yescharacteristic
367Q16×C47—24no—
368Q16×C47C2×D414yescomplemented
369SD16×C47—24no—
370SD16×C47—24no—
371SD16×C47—24no—
372SD16×C47—24no—
373SD16×C47C2×D414yescomplemented
374SD16×C47C2×D414yescomplemented
375D8×C47—24no—
376D8×C47C2×D414yescomplemented
377M16×C47—21no—
378M16×C47—24no—
379M16×C47C2412yes—
380C2×C8×C47—21no—
381C2×C8×C47—24no—
382C2×C8×C47C2×D411yescharacteristic
383C2×C8×C47C2×D411yescharacteristic
384C2×C8×C47C2×D412yes—
385C2×C8×C47C2412yes—
386#10625337—24no—
387#10625337C2×D414yescomplemented
388#10625336—24no—
389#10625336—24no—
390#10625336—24no—
391#10625336—24no—
392#10625336—24no—
393#10625336—24no—
394#10625336—24no—
395#10625336C2×D414yescomplemented
396#10625335—24no—
397#10625335C2×D414yescomplemented
398#10625334—24no—
399#10625334—24no—
400#10625334—24no—
401#10625334—24no—
402#10625334—24no—
403#10625334—24no—
404#10625334—24no—
405#10625334C2×D414yescomplemented
406(C2×D47)⋊C4—44no—
407C4×Dic47—21no—
408C4×Dic47C2412yes—
409#10625329—21no—
410#10625329—21no—
411#10625329—21no—
412#10625329—24no—
413#10625329—24no—
414#10625329C2412yes—
415#10625329C2412yes—
416#10625329C2412yes—
417C2×C47⋊C8—21no—
418C2×C47⋊C8—21no—
419C2×C47⋊C8—21no—
420C2×C47⋊C8—24no—
421C2×C47⋊C8—24no—
422C2×C47⋊C8C2×D411yescharacteristic
423C2×C47⋊C8C2×D411yescharacteristic
424C2×C47⋊C8C2×D412yes—
425C2×C47⋊C8C2412yes—
426D376—24no—
427D376—24no—
428#10625324—24no—
429C8×D47—24no—
430C23×C47—21no—
431C23×C47—21no—
432C23×C47—21no—
433C23×C47—22no—
434C23×C47—44no—
435C23×C47—41no—
436C23×C47—41no—
437C23×C47—82no—
438C23×C47—162no—
439C23×C47H(5,𝔽2)11yescharacteristic
440C22×D47—21no—
441C22×D47—22no—
442C22×D47—22no—
443C22×D47—44no—
444C22×D47—44no—
445C22×D47—41no—
446C22×D47—41no—
447C22×D47—41no—
448C22×D47—41no—
449C22×D47—82no—
450C22×D47—82no—
451C22×D47—162no—
452C22×D47—162no—
453Q8×C47—21no—
454Q8×C47—21no—
455Q8×C47—21no—
456Q8×C47—22no—
457Q8×C47—22no—
458Q8×C47—44no—
459Q8×C47—41no—
460Q8×C47—41no—
461Q8×C47C22×D412yes—
462Q8×C47C22×D412yes—
463Q8×C47C22×D412yes—
464D4×C47—22no—
465D4×C47—22no—
466D4×C47—22no—
467D4×C47—22no—
468D4×C47—22no—
469D4×C47—22no—
470D4×C47—21no—
471D4×C47—21no—
472D4×C47—21no—
473D4×C47—22no—
474D4×C47—22no—
475D4×C47—44no—
476D4×C47—44no—
477D4×C47—44no—
478D4×C47—41no—
479D4×C47—41no—
480D4×C47C22×D412yes—
481D4×C47C22×D412yes—
482D4×C47C22×D412yes—
483C2×C4×C47—21no—
484C2×C4×C47—21no—
485C2×C4×C47—21no—
486C2×C4×C47—22no—
487C2×C4×C47—22no—
488C2×C4×C47—22no—
489C2×C4×C47—22no—
490C2×C4×C47—22no—
491C2×C4×C47—22no—
492C2×C4×C47—22no—
493C2×C4×C47—44no—
494C2×C4×C47—44no—
495C2×C4×C47—44no—
496C2×C4×C47—41no—
497C2×C4×C47—41no—
498C2×C4×C47C22×D411yescharacteristic
499C2×C4×C47C22×D411yescharacteristic
500C2×C4×C47C22×D411yescharacteristic
501C2×C4×C47C22×D411yescharacteristic
502C2×C4×C47H(5,𝔽2)11yescharacteristic
503C2×C4×C47C2511yescharacteristic
504C22⋊D47—22no—
505C22⋊D47—22no—
506C22⋊D47—44no—
507C22⋊D47—44no—
508C22⋊D47—88no—
509C2×Dic47—21no—
510C2×Dic47—22no—
511C2×Dic47—42no—
512D188—21no—
513D188—22no—
514D188—22no—
515D188—22no—
516D188—22no—
517D188—44no—
518D188—44no—
519D188—41no—
520D188—41no—
521D188—41no—
522D188—41no—
523D188C22×D412yes—
524C4×D47—22no—
525C4×D47—22no—
526C4×D47—44no—
527C4×D47—44no—
528Dic94—21no—
529Dic94C22×D412yes—
530C8×C47—22no—
531C8×C47C22×D412yes—
532C8×C47C22×D412yes—
533C47⋊C8—22no—
534C47⋊C8—22no—
535C47⋊C8—22no—
536C47⋊C8C22×D412yes—
537C47⋊C8C22×D412yes—
538C2×#3288—471nomaximal, Sylow
539C22×C47—22no—
540C22×C47—22no—
541C22×C47—22no—
542C22×C47—22no—
543C22×C47—42no—
544C22×C47—42no—
545C22×C47—42no—
546C22×C47—42no—
547C22×C47—82no—
548C22×C47—82no—
549C22×C47—161no—
550C22×C47—164no—
551C22×C47D4211yescharacteristic
552C22×C47D4211yescharacteristic
553C22×C47C2×H(5,𝔽2)11yescharacteristic
554C2×D47—22no—
555C2×D47—42no—
556C2×D47—42no—
557C2×D47—42no—
558C2×D47—82no—
559C2×D47—82no—
560C2×D47—82no—
561C2×D47—82no—
562C2×D47—164no—
563C2×D47—164no—
564C2×D47—161no—
565C2×D47—161no—
566C4×C47—22no—
567C4×C47—22no—
568C4×C47—22no—
569C4×C47—42no—
570C4×C47D4211yescharacteristic
571C4×C47D4211yescharacteristic
572C4×C47C23×D411yescharacteristic
573C4×C47C23×D411yescharacteristic
574Dic47—22no—
575Dic47—42no—
576C2×#577—471no—
577C2×#577D4711yescharacteristic, complemented
578C2×#576—471no—
579C2×#576—471no—
580#3288—4716no—
581C2×#496—471no—
582C2×#472—471no—
583C2×#472—471no—
584C2×#471—471no—
585C2×#471—471no—
586C2×#454—471no—
587C2×#455—471no—
588C2×#453—471no—
589C2×#453—471no—
590C2×#444—471no—
591C2×#444—471no—
592C2×C47—21no—
593C2×C47—21no—
594C2×C47—42no—
595C2×C47—42no—
596C2×C47—42no—
597C2×C47—82no—
598C2×C47#328812yescomplemented
599C2×C47C2×D4211yescharacteristic
600D47—42no—
601D47—82no—
602D47—82no—
603C2×2−1+4C2×D4711yescharacteristic, complemented
604C2×H(5,𝔽2)—471no—
605C2×H(5,𝔽2)—471no—
606C2×H(5,𝔽2)C2×D4711yescharacteristic, complemented
607#577—24no—
608#577—478no—
609#577—944no—
610#577C2×D4718yescomplemented
611#576—478no—
612#576—478no—
613#576—944no—
614#576—944no—
615C2×#137—21no—
616C2×#137—471no—
617C2×#137—941no—
618C2×#137C2×D4711yescharacteristic, complemented
619C2×AGL(1,ℤ/8)—21no—
620C2×AGL(1,ℤ/8)—471no—
621C2×AGL(1,ℤ/8)—471no—
622C2×AGL(1,ℤ/8)—471no—
623C2×AGL(1,ℤ/8)—471no—
624C2×AGL(1,ℤ/8)—471no—
625C2×AGL(1,ℤ/8)—941no—
626C2×AGL(1,ℤ/8)—941no—
627C2×AGL(1,ℤ/8)—941no—
628C2×AGL(1,ℤ/8)—941no—
629C2×AGL(1,ℤ/8)—941no—
630C2×AGL(1,ℤ/8)C2×D4711yescharacteristic, complemented
631C2×#135—21no—
632C2×#135—471no—
633C2×#135—941no—
634C2×#135—941no—
635C2×#135—941no—
636C2×#135C2×D4711yescharacteristic
637C22×SD16—21no—
638C22×SD16—471no—
639C22×SD16—941no—
640C22×SD16C2×D4711yescharacteristic, complemented
641C22×D8—471no—
642C22×D8—471no—
643C22×D8—941no—
644C22×D8—941no—
645C2×#131—471no—
646C2×#131—471no—
647C2×#131—471no—
648C2×#131C2×D4711yescharacteristic, complemented
649C2×#127—471no—
650C2×#124—471no—
651#496—478no—
652#472—478no—
653#472—478no—
654#471—478no—
655#471—478no—
656#455—478no—
657#454—478no—
658#453—478no—
659#453—478no—
660#444—478no—
661#444—478no—
662C2×#108—471no—
663C2×#108—471no—
664C2×#104—471no—
665C2×#104—471no—
666C2×#104—471no—
667C2×#104—471no—
668C2×#101—471no—
669C2×#100—471no—
670C2×#100—471no—
671C2×#100—471no—
672C2×#97—471no—
673C47C2×#328811yescharacteristic, complemented, Sylow
6742−1+4—22no—
6752−1+4—22no—
6762−1+4—41no—
6772−1+4C22×D4714yescomplemented
678H(5,𝔽2)—22no—
679H(5,𝔽2)—22no—
680H(5,𝔽2)—41no—
681H(5,𝔽2)—474no—
682H(5,𝔽2)—474no—
683H(5,𝔽2)—942no—
684H(5,𝔽2)—942no—
685H(5,𝔽2)—942no—
686H(5,𝔽2)—942no—
687H(5,𝔽2)—1881no—
688H(5,𝔽2)—1881no—
689H(5,𝔽2)C22×D4714yescomplemented
690C2×#41—21no—
691C2×#41—21no—
692C2×#41—21no—
693C2×#41—21no—
694C2×#41—41no—
695C2×#41—471no—
696C2×#41—941no—
697C2×#41—941no—
698C2×#41—941no—
699C2×#41—941no—
700C2×#41C22×D4711yescharacteristic
701C2×#41C22×D4711yescharacteristic
702C2×#41C22×D4711yescharacteristic
703C22×Q8—21no—
704C22×Q8—21no—
705C22×Q8C22×D4711yescharacteristic
706C22×D4—21no—
707C22×D4—21no—
708C22×D4—41no—
709C22×D4—471no—
710C22×D4—471no—
711C22×D4—941no—
712C22×D4—941no—
713C22×D4—941no—
714C22×D4—941no—
715C22×D4—1881no—
716C22×D4—1881no—
717C22×D4—1881no—
718C22×D4C22×D4711yescharacteristic
719#137—22no—
720#137—28no—
721#137—474no—
722#137—948no—
723#137—942no—
724#137C22×D4714yescomplemented
725AGL(1,ℤ/8)—22no—
726AGL(1,ℤ/8)—28no—
727AGL(1,ℤ/8)—474no—
728AGL(1,ℤ/8)—474no—
729AGL(1,ℤ/8)—474no—
730AGL(1,ℤ/8)—474no—
731AGL(1,ℤ/8)—474no—
732AGL(1,ℤ/8)—948no—
733AGL(1,ℤ/8)—948no—
734AGL(1,ℤ/8)—948no—
735AGL(1,ℤ/8)—942no—
736AGL(1,ℤ/8)—942no—
737AGL(1,ℤ/8)—942no—
738AGL(1,ℤ/8)—942no—
739AGL(1,ℤ/8)—942no—
740AGL(1,ℤ/8)—948no—
741AGL(1,ℤ/8)—948no—
742AGL(1,ℤ/8)C22×D4714yescomplemented
743#135—28no—
744#135—474no—
745#135—474no—
746#135—948no—
747#135—948no—
748#135—948no—
749#135C22⋊D4714yescomplemented
750#135C22×D4714yes—
751C2×Q16—21no—
752C2×Q16—471no—
753C2×Q16—941no—
754C2×Q16C22⋊D4711yescharacteristic, complemented
755C2×SD16—21no—
756C2×SD16—21no—
757C2×SD16—28no—
758C2×SD16—21no—
759C2×SD16—21no—
760C2×SD16—22no—
761C2×SD16—471no—
762C2×SD16—471no—
763C2×SD16—474no—
764C2×SD16—941no—
765C2×SD16—941no—
766C2×SD16—942no—
767C2×SD16—948no—
768C2×SD16—941no—
769C2×SD16—941no—
770C2×SD16—941no—
771C2×SD16—941no—
772C2×SD16—941no—
773C2×SD16—941no—
774C2×SD16C22⋊D4711yescharacteristic, complemented
775C2×SD16C22⋊D4711yescharacteristic, complemented
776C2×SD16C22×D4714yescomplemented
777C2×D8—21no—
778C2×D8—471no—
779C2×D8—474no—
780C2×D8—474no—
781C2×D8—941no—
782C2×D8—941no—
783C2×D8—942no—
784C2×D8—948no—
785C2×D8—941no—
786C2×D8—941no—
787C2×D8—941no—
788C2×D8—941no—
789C2×D8—941no—
790C2×D8—948no—
791C2×D8—941no—
792C2×D8—941no—
793C2×D8—942no—
794C2×D8C22⋊D4711yescharacteristic, complemented
795#131—22no—
796#131—474no—
797#131—474no—
798#131—474no—
799#131—942no—
800#131—942no—
801#131—942no—
802#131C22×D4714yescomplemented
803C2×M16—21no—
804C2×M16—471no—
805C2×M16—471no—
806C2×M16—471no—
807C2×M16—941no—
808C2×M16—941no—
809C2×M16—941no—
810C2×M16C22×D4711yescharacteristic
811C22×C8—21no—
812C22×C8—471no—
813C22×C8—941no—
814C22×C8—941no—
815C22×C8—941no—
816C22×C8C22×D4711yescharacteristic
817#127—474no—
818#127—1881no—
819#124—474no—
820#124—1881no—
821C2×C22⋊C4—1881no—
822C2×C42—471no—
823#108—474no—
824#108—474no—
825#104—474no—
826#104—474no—
827#104—474no—
828#104—474no—
829#101—474no—
830#100—474no—
831#100—474no—
832#100—474no—
833#97—474no—
834C24—21no—
835C24—41no—
836C24—941no—
837C24—941no—
838C24—1881no—
839C24—1881no—
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—472no—
857#41—472no—
858#41—944no—
859#41—944no—
860#41—941no—
861#41—941no—
862#41—944no—
863#41—944no—
864#41—1882no—
865#41—1882no—
866#41—1882no—
867#41—1882no—
868#41D4×D4712yes—
869#41C2×C22⋊D4712yes—
870#41C2×C22⋊D4712yes—
871#41C23×D4712yes—
872#41C23×D4712yes—
873#41C23×D4712yes—
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—471no—
885C2×Q8D4×D4711yescharacteristic
886C2×Q8C2×C22⋊D4711yescharacteristic
887C2×Q8C2×C22⋊D4711yescharacteristic
888C2×Q8C23×D4712yes—
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—471no—
907C2×D4—472no—
908C2×D4—472no—
909C2×D4—944no—
910C2×D4—944no—
911C2×D4—941no—
912C2×D4—944no—
913C2×D4—944no—
914C2×D4—941no—
915C2×D4—941no—
916C2×D4—941no—
917C2×D4—941no—
918C2×D4—941no—
919C2×D4—941no—
920C2×D4—941no—
921C2×D4—941no—
922C2×D4—941no—
923C2×D4—941no—
924C2×D4—3764no—
925C2×D4—1882no—
926C2×D4—1882no—
927C2×D4—1881no—
928C2×D4—1881no—
929C2×D4—1882no—
930C2×D4—1882no—
931C2×D4—1884no—
932C2×D4—1881no—
933C2×D4—1881no—
934C2×D4—1884no—
935C2×D4—1884no—
936C2×D4—1884no—
937C2×D4—1884no—
938C2×D4D4×D4711yescharacteristic
939C2×D4C2×C22⋊D4711yescharacteristic
940C2×D4C2×C22⋊D4711yescharacteristic
941C2×D4C23×D4712yes—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—41no—
947C22×C4—41no—
948C22×C4—41no—
949C22×C4—941no—
950C22×C4—941no—
951C22×C4—1881no—
952C22×C4—1881no—
953C22×C4C23×D4711yescharacteristic
954Q16—24no—
955Q16—474no—
956Q16—944no—
957Q16C2×C22⋊D4714yescomplemented
958SD16—24no—
959SD16—24no—
960SD16—24no—
961SD16—24no—
962SD16—474no—
963SD16—474no—
964SD16—944no—
965SD16—944no—
966SD16—944no—
967SD16—944no—
968SD16—944no—
969SD16—944no—
970SD16—944no—
971SD16—944no—
972SD16C2×C22⋊D4714yescomplemented
973SD16C2×C22⋊D4714yescomplemented
974D8—24no—
975D8—474no—
976D8—944no—
977D8—944no—
978D8—944no—
979D8—944no—
980D8—944no—
981D8—944no—
982D8—944no—
983D8—944no—
984D8—944no—
985D8C2×C22⋊D4714yescomplemented
986M16—21no—
987M16—24no—
988M16—472no—
989M16—472no—
990M16—472no—
991M16—944no—
992M16—944no—
993M16—941no—
994M16—941no—
995M16—941no—
996M16—944no—
997M16C23×D4712yes—
998C2×C8—21no—
999C2×C8—24no—
1000C2×C8—471no—
1001C2×C8—471no—
1002C2×C8—472no—
1003C2×C8—472no—
1004C2×C8—944no—
1005C2×C8—944no—
1006C2×C8—941no—
1007C2×C8—941no—
1008C2×C8—941no—
1009C2×C8—944no—
1010C2×C8C2×C22⋊D4711yescharacteristic
1011C2×C8C2×C22⋊D4711yescharacteristic
1012C2×C8C2×C22⋊D4712yes—
1013C2×C8C23×D4712yes—
1014C22⋊C4—1884no—
1015C42—472no—
1016C42—941no—
1017C23—21no—
1018C23—21no—
1019C23—21no—
1020C23—22no—
1021C23—44no—
1022C23—41no—
1023C23—41no—
1024C23—82no—
1025C23—162no—
1026C23—941no—
1027C23—942no—
1028C23—942no—
1029C23—3762no—
1030C23—3762no—
1031C23—1884no—
1032C23—1884no—
1033C23—1881no—
1034C23—1881no—
1035C23—1881no—
1036C23—1881no—
1037C23—7522no—
1038C23—7522no—
1039C23#1309406911yescharacteristic
1040Q8—21no—
1041Q8—21no—
1042Q8—21no—
1043Q8—22no—
1044Q8—22no—
1045Q8—44no—
1046Q8—41no—
1047Q8—41no—
1048Q8—472no—
1049Q8—941no—
1050Q8C2×D4×D4712yes—
1051Q8C22×C22⋊D4712yes—
1052Q8C22×C22⋊D4712yes—
1053D4—22no—
1054D4—22no—
1055D4—22no—
1056D4—22no—
1057D4—22no—
1058D4—22no—
1059D4—21no—
1060D4—21no—
1061D4—21no—
1062D4—22no—
1063D4—22no—
1064D4—44no—
1065D4—44no—
1066D4—44no—
1067D4—41no—
1068D4—41no—
1069D4—472no—
1070D4—942no—
1071D4—942no—
1072D4—941no—
1073D4—942no—
1074D4—942no—
1075D4—942no—
1076D4—942no—
1077D4—3768no—
1078D4—1884no—
1079D4—1884no—
1080D4—1884no—
1081D4—1884no—
1082D4—1881no—
1083D4—1881no—
1084D4—1881no—
1085D4—1881no—
1086D4C2×D4×D4712yes—
1087D4C22×C22⋊D4712yes—
1088D4C22×C22⋊D4712yes—
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—941no—
1105C2×C4—942no—
1106C2×C4—942no—
1107C2×C4—942no—
1108C2×C4—1884no—
1109C2×C4—1884no—
1110C2×C4—1882no—
1111C2×C4C2×D4×D4711yescharacteristic
1112C2×C4C2×D4×D4711yescharacteristic
1113C2×C4C22×C22⋊D4711yescharacteristic
1114C2×C4C22×C22⋊D4711yescharacteristic
1115C2×C4#1309406911yescharacteristic
1116C2×C4C24×D4711yescharacteristic
1117C8—22no—
1118C8—472no—
1119C8—472no—
1120C8—942no—
1121C8—942no—
1122C8—942no—
1123C8C22×C22⋊D4712yes—
1124C8C22×C22⋊D4712yes—
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—942no—
1138C22—3762no—
1139C22—3762no—
1140C22—3762no—
1141C22—3762no—
1142C22—1882no—
1143C22—1882no—
1144C22—1882no—
1145C22—7521no—
1146C22—7521no—
1147C22—7524no—
1148C22—7524no—
1149C22D4×C22⋊D4711yescharacteristic
1150C22D4×C22⋊D4711yescharacteristic
1151C22C2×#1309406911yescharacteristic
1152C4—22no—
1153C4—22no—
1154C4—22no—
1155C4—42no—
1156C4—942no—
1157C4—1882no—
1158C4D4×C22⋊D4711yescharacteristic
1159C4D4×C22⋊D4711yescharacteristic
1160C4C22×D4×D4711yescharacteristic
1161C4C23×C22⋊D4711yescharacteristic
1162C2—21no—
1163C2—21no—
1164C2—42no—
1165C2—42no—
1166C2—42no—
1167C2—82no—
1168C2—3762no—
1169C2—3762no—
1170C2—1882no—
1171C2#2025515012yesdirect product factor
1172C2C2×D4×C22⋊D4711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#577C2
socleC22×C47D42
hypercenterC2×#577D47
hypocenterC47C2×#3288
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#577

Complements

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

NH ≅ G/Ntype
1. C2×#15689931C2semidirect
2. C2×#15689926C2semidirect
3. C2×#15689925C2semidirect
4. #20255150C2direct (N × H)
5. C2×#15689509C2semidirect
6. C2×#15689393C2semidirect
7. C2×#15689391C2semidirect
8. C2×#15689388C2semidirect
9. C2×#15689383C2semidirect
10. C2×#15689296C2semidirect
11. C2×#15689299C2semidirect
12. C2×#15689291C2semidirect
13. C2×#15689289C2semidirect
14. C2×#15689245C2semidirect
15. C2×#15689243C2semidirect
16. C2×C47×#577C2semidirect
18. C2×#13094070C22semidirect
20. #15689931C22semidirect
22. #15689926C22semidirect
24. #15689925C22semidirect
26. C2×#13094055C22semidirect
34. C2×#13094049C22semidirect
35. C2×#13094049C22semidirect
36. C2×#13094049C22semidirect
42. C22×#10625336C22semidirect
43. C22×D376C22semidirect
45. C22×#10625334C22semidirect
47. C2×#13094031C22semidirect
48. C2×#13094031C22semidirect
49. C2×#13094030C22semidirect
50. C2×#13094020C22semidirect
51. C2×#13094013C22semidirect
52. #15689509C22semidirect
53. #15689393C22semidirect
54. #15689391C22semidirect
55. #15689388C22semidirect
56. #15689383C22semidirect
57. #15689299C22semidirect
58. #15689296C22semidirect
59. #15689291C22semidirect
60. #15689289C22semidirect
61. #15689245C22semidirect
62. #15689243C22semidirect
63. C2×#13093960C22semidirect
64. C2×#13093959C22semidirect
65. C2×#13093951C22semidirect
66. C2×#13093951C22semidirect
67. C2×#13093951C22semidirect
68. C2×#13093950C22semidirect
69. C2×#13093943C22semidirect
70. C2×#13093941C22semidirect
71. C2×#13093940C22semidirect
72. C2×#13093940C22semidirect
73. C2×#13093934C22semidirect
74. C2×2−1+4×C47C22semidirect
75. C2×H(5,𝔽2)×C47C22semidirect
77. C47×#577C22semidirect
79. C2×#137×C47C22semidirect
81. C2×AGL(1,ℤ/8)×C47C22semidirect
85. C22×SD16×C47C22semidirect
86. C2×#131×C47C22semidirect
94. #13094070C23semidirect
111. #13094055C23semidirect
124. #13094049C23semidirect
125. #13094049C23semidirect
126. #13094049C23semidirect
130. #13094044D4semidirect
133. C2×#10625337D4semidirect
135. C2×#10625335D4semidirect
145. C2×#10625336D4semidirect
146. C2×#10625336C23semidirect
150. C2×D376C23semidirect
160. C2×#10625334D4semidirect
161. C2×#10625334C23semidirect
165. #13094031C23semidirect
166. #13094031C23semidirect
168. #13094030C23semidirect
180. #13094020C23semidirect
182. #13094013C23semidirect
185. #13093960C23semidirect
186. #13093959C23semidirect
187. #13093951C23semidirect
188. #13093951C23semidirect
189. #13093951C23semidirect
190. #13093950C23semidirect
191. #13093943C23semidirect
192. #13093941C23semidirect
193. #13093940C23semidirect
194. #13093940C23semidirect
195. #13093934C23semidirect
199. 2−1+4×C47C23semidirect
203. H(5,𝔽2)×C47C23semidirect
221. #137×C47C23semidirect
224. AGL(1,ℤ/8)×C47C23semidirect
226. #135×C47D4semidirect
229. C2×Q16×C47D4semidirect
236. C2×SD16×C47D4semidirect
237. C2×SD16×C47D4semidirect
238. C2×SD16×C47C23semidirect
240. C2×D8×C47D4semidirect
242. #131×C47C23semidirect
368. Q16×C47C2×D4semidirect
373. SD16×C47C2×D4semidirect
374. SD16×C47C2×D4semidirect
376. D8×C47C2×D4semidirect
387. #10625337C2×D4semidirect
395. #10625336C2×D4semidirect
397. #10625335C2×D4semidirect
405. #10625334C2×D4semidirect
577. C2×#577D47semidirect
598. C2×C47#3288semidirect
603. C2×2−1+4C2×D47semidirect
606. C2×H(5,𝔽2)C2×D47semidirect
610. #577C2×D47semidirect
618. C2×#137C2×D47semidirect
630. C2×AGL(1,ℤ/8)C2×D47semidirect
640. C22×SD16C2×D47semidirect
648. C2×#131C2×D47semidirect
673. C47C2×#3288semidirect
677. 2−1+4C22×D47semidirect
689. H(5,𝔽2)C22×D47semidirect
724. #137C22×D47semidirect
742. AGL(1,ℤ/8)C22×D47semidirect
749. #135C22⋊D47semidirect
754. C2×Q16C22⋊D47semidirect
774. C2×SD16C22⋊D47semidirect
775. C2×SD16C22⋊D47semidirect
776. C2×SD16C22×D47semidirect
794. C2×D8C22⋊D47semidirect
802. #131C22×D47semidirect
957. Q16C2×C22⋊D47semidirect
972. SD16C2×C22⋊D47semidirect
973. SD16C2×C22⋊D47semidirect
985. D8C2×C22⋊D47semidirect
1171. C2#20255150direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156899312
C2×#156899262
C2×#156899252
#202551502
C2×#156895092
C2×#156893932
C2×#156893912
C2×#156893882
C2×#156893832
C2×#156892962
C2×#156892992
C2×#156892912
C2×#156892892
C2×#156892452
C2×#156892432
C2×C47×#5772
C2×#328847