Finite Group Databasebeta

← #11904913

Subgroups — #11904913

Order 1152.

2777 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595954C211yesmaximal, characteristic, complemented
2C3×#5493C211yesmaximal, characteristic, complemented
3C2×C3×D3×C22⋊C4C211yesmaximal, characteristic, complemented
4C2×#63976C212yesmaximal, complemented
5#10595506C212yesmaximal, complemented
6#10594977C214yesmaximal, complemented
7#10594892C214yesmaximal, complemented
8#10594211C218yesmaximal, complemented
9#10594184C218yesmaximal, complemented
10#86309—31nomaximal
11#85697—31nomaximal
12C24×C3×D3C2211yescharacteristic
13C22×C3×#67C2212yes—
14C22×C3×C4×D3C2212yescomplemented
15C22×#625C2214yescomplemented
16C2×#3795C2214yescomplemented
17C2×C32×C22⋊C4C2211yescharacteristic
18C2×#3757C2212yes—
19#64133C2214yescomplemented
20#64087C2218yescomplemented
21C2×C3×#217C2211yescharacteristic
22C3×#930C2214yescomplemented
23C2×C3×(C2×D3)⋊C4C2212yescomplemented
24C3×#886C2214yescomplemented
25C3×#882C2214yescomplemented
26C3×D3×C22⋊C4C2218yescomplemented
27#63976C2218yes—
28#63976C2214yescomplemented
29#63976C2214yescomplemented
30#67⋊Dic3C2218yescomplemented
31Dic3×#67C2218yescomplemented
32D3×#217C2214yescomplemented
33C2×(C2×D3)⋊Dic3C2214yescomplemented
34#63955C2214yescomplemented
35#63913C2218yescomplemented
36#63908C2214yescomplemented
37#63905C2218yescomplemented
38#63891C2218yescomplemented
39#63885C2218yescomplemented
40#63879C2218yescomplemented
41#63858C2218yescomplemented
42#63857C2214yescomplemented
43#63841C2214yescomplemented
44C3×#534—31no—
45C22×C3×C22⋊C4—31no—
46C2×#953—32no—
47C2×#937—32no—
48#5798—32no—
49#5791—34no—
50#5658—38no—
51#5617—34no—
52#5606—34no—
53#5591—38no—
54#5495—38no—
55#5494—34no—
56#5493D311yescharacteristic, complemented
57#5490—38no—
58#5486—32no—
59C2×D3×C22⋊C4D311yescharacteristic, complemented
60#5483—31no—
61#5483—31no—
62#5483—61no—
63C24×C32C2311yescharacteristic
64C23×C3×D3—24no—
65C23×C3×D3—44no—
66C23×C3×D3C2311yescharacteristic
67C23×C3×D3C2314yes—
68C23×C3×D3C2312yes—
69C23×C3×D3C2311yescharacteristic
70C22×C32×C4C2312yes—
71C22×C3⋊Dic3C2314yes—
72C2×#634C2314yescomplemented
73C2×C3×#67—28no—
74C2×C3×#67C2314yes—
75C2×C3×#67C2314yes—
76C22×C3×Dic3C2312yes—
77C22×C3×Dic3C2312yes—
78C2×C3×D12C2314yescomplemented
79C2×C3×C4×D3—44no—
80C2×C3×C4×D3C2314yes—
81C2×C3×C4×D3C2314yes—
82C2×#625—48no—
83C2×#625C2318yes—
84C2×#625C2318yes—
85C2×D3×Dic3C2318yescomplemented
86#3795—48no—
87C32×C22⋊C4C2314yes—
88#3757C2314yes—
89#3757C2314yes—
90C4⋊(C3⋊Dic3)C2314yescomplemented
91#3750C2318yescomplemented
92C3×#217C2314yes—
93C3×(C2×D3)⋊C4C2318yes—
94C3×(C2×D3)⋊C4C2318yescomplemented
95C3×C4⋊Dic3C2314yescomplemented
96Dic3⋊Dic3C2318yescomplemented
97(C2×D3)⋊Dic3C2318yes—
98(C2×D3)⋊Dic3C2318yes—
99(C2×D3)⋊Dic3C2318yescomplemented
100Dic32C2318yescomplemented
101#3490—91noSylow
102C25×C3—31no—
103C24×D3C2×D311yescharacteristic
104C22×C3×D4—32no—
105C23×C3×C4—32no—
106C22×#67—34no—
107C22×#67—34no—
108C22×#67C2×D312yes—
109C2×#237—34no—
110C2×#235—34no—
111C22×C4×D3C2×D312yescomplemented
112C3×#123—34no—
113C3×#121—34no—
114C3×#120—34no—
115C2×C3×C22⋊C4—21no—
116C2×C3×C22⋊C4—31no—
117C2×C3×C22⋊C4—32no—
118C2×C3×C22⋊C4—38no—
119C2×C3×C22⋊C4C2×D311yescharacteristic
120C2×C3×C22⋊C4C2×D311yescharacteristic
121#953—38no—
122#953—34no—
123#953—34no—
124C2×#217—32no—
125C2×#217—32no—
126C2×#217—34no—
127C2×#217—34no—
128C2×#217—62no—
129C2×#217C2×D311yescharacteristic
130#939—38no—
131#938—34no—
132#937—38no—
133#937—34no—
134#937—34no—
135D4×Dic3—38no—
136D4×Dic3—38no—
137#930—34no—
138#930C2×D314yescomplemented
139#929—38no—
140C4×#67—38no—
141C4×#67—38no—
142C2×(C2×D3)⋊C4—34no—
143C2×(C2×D3)⋊C4C2×D312yescomplemented
144#926—34no—
145#926—34no—
146#924—34no—
147#924—34no—
148#924—34no—
149#924—64no—
150#898—38no—
151#897—34no—
152#892—34no—
153#886—38no—
154#886C2×D314yescomplemented
155#885—38no—
156#885—38no—
157#884—38no—
158#883—38no—
159#883—38no—
160#882C2×D314yescomplemented
161#67⋊C4—38no—
162#67⋊C4—38no—
163D3×C22⋊C4—34no—
164D3×C22⋊C4C2×D318yescomplemented
165#879—38no—
166#878—38no—
167#878—38no—
168#878—68no—
169#877—34no—
170C23×C32—42no—
171C23×C32#4114yescomplemented
172C23×C32C2412yes—
173C23×C32C2411yescharacteristic
174C22×C3×D3—22no—
175C22×C3×D3—24no—
176C22×C3×D3—28no—
177C22×C3×D3—22no—
178C22×C3×D3—24no—
179C22×C3×D3—28no—
180C22×C3×D3—44no—
181C22×C3×D3—42no—
182C22×C3×D3—44no—
183C22×C3×D3—416no—
184C22×C3×D3C2412yes—
185C22×C3×D3C2414yes—
186C22×C3×D3C2412yes—
187C2×C32×C4—42no—
188C2×C32×C4C2414yes—
189C2×C3⋊Dic3—44no—
190C2×C3⋊Dic3C2418yes—
191#634—44no—
192C3×#67—28no—
193C3×#67—28no—
194C2×C3×Dic3—24no—
195C2×C3×Dic3—42no—
196C2×C3×Dic3C2414yes—
197C2×C3×Dic3C2414yes—
198C3×D12—44no—
199C3×C4×D3—28no—
200C3×C4×D3—44no—
201#625—216no—
202#625—48no—
203D3×Dic3—48no—
204#551—98no—
205#546—98no—
206#543—91no—
207#538—94no—
208#534—31no—
209#525—94no—
210C2×#120—92no—
211#518—92no—
212C22×C22⋊C4—31no—
213C24×C3—21no—
214C24×C3—31no—
215C24×C3—34no—
216C24×C3—31no—
217C24×C3—32no—
218C24×C3—64no—
219C24×C3—124no—
220C24×C3C22×D311yescharacteristic
221C24×C3C22×D311yescharacteristic
222C23×D3—24no—
223C23×D3—44no—
224C23×D3C22×D311yescharacteristic
225C23×D3C22×D314yes—
226C23×D3C22×D312yes—
227C23×D3C22×D311yescharacteristic
228C2×C3×D4—34no—
229C2×C3×D4—34no—
230C2×C3×D4—34no—
231C2×C3×D4—68no—
232C22×C3×C4—22no—
233C22×C3×C4—32no—
234C22×C3×C4—32no—
235C22×C3×C4—34no—
236C22×C3×C4—34no—
237C22×C3×C4—124no—
238C22×C3×C4C22×D312yes—
239C22×C3×C4C22×D312yes—
240C2×#67—28no—
241C2×#67—38no—
242C2×#67—38no—
243C2×#67—38no—
244C2×#67—38no—
245C2×#67—128no—
246C2×#67—128no—
247C2×#67C22×D314yes—
248C2×#67C22×D314yes—
249C22×Dic3—34no—
250C22×Dic3—34no—
251C22×Dic3—38no—
252C22×Dic3—64no—
253C22×Dic3C22×D312yes—
254C22×Dic3C22×D312yes—
255#237—128no—
256#235—128no—
257C2×D12C22×D314yescomplemented
258C2×C4×D3—38no—
259C2×C4×D3—44no—
260C2×C4×D3C22×D314yes—
261C2×C4×D3C22×D314yes—
262C2×Dic6—34no—
263C2×Dic6—34no—
264C2×Dic6—64no—
265C3×C4⋊C4—34no—
266C3×C22⋊C4—24no—
267C3×C22⋊C4—34no—
268C3×C22⋊C4—38no—
269C3×C22⋊C4—38no—
270C3×C22⋊C4C22×D314yes—
271C3×C22⋊C4C22×D314yes—
272#217—34no—
273#217—34no—
274#217—34no—
275#217—34no—
276#217—38no—
277#217—38no—
278#217—38no—
279#217—64no—
280#217—64no—
281#217C22×D314yes—
282(C2×D3)⋊C4—38no—
283(C2×D3)⋊C4—38no—
284(C2×D3)⋊C4—38no—
285(C2×D3)⋊C4C22×D318yes—
286(C2×D3)⋊C4C22×D318yescomplemented
287C4⋊Dic3—34no—
288C4⋊Dic3—34no—
289C4⋊Dic3—38no—
290C4⋊Dic3—64no—
291C4⋊Dic3C22×D314yescomplemented
292Dic3⋊C4—38no—
293Dic3⋊C4—38no—
294Dic3⋊C4—38no—
295Dic3⋊C4—68no—
296C4×Dic3—38no—
297C4×Dic3—38no—
298C22×C32—22no—
299C22×C32—24no—
300C22×C32—44no—
301C22×C32C2×#4114yes—
302C22×C32C2×#4112yes—
303C22×C32C2511yescharacteristic
304C2×C3×D3—28no—
305C2×C3×D3—22no—
306C2×C3×D3—22no—
307C2×C3×D3—24no—
308C2×C3×D3—22no—
309C2×C3×D3—28no—
310C2×C3×D3—24no—
311C2×C3×D3—416no—
312C2×C3×D3—44no—
313C2×C3×D3—84no—
314C2×C3×D3H(5,𝔽2)14yes—
315C32×C4—24no—
316C3⋊Dic3—28no—
317C3×Dic3—24no—
318C3×Dic3—24no—
319C25—31no—
320C2×#41—94no—
321C22×D4—32no—
322C22×D4—94no—
323C23×C4—32no—
324#126—98no—
325#124—98no—
326#123—34no—
327#123—98no—
328#123—98no—
329C22⋊Q8—94no—
330C22⋊Q8—94no—
331C22⋊Q8—98no—
332#121—34no—
333#121—98no—
334#121—94no—
335#120—34no—
336#120—94no—
337#120—94no—
338#120—98no—
339C4×D4—98no—
340C4×D4—98no—
341C4×D4—98no—
342#117—94no—
343#117—94no—
344C2×C22⋊C4—31no—
345C2×C22⋊C4—32no—
346C2×C22⋊C4—38no—
347C2×C22⋊C4—94no—
348C2×C22⋊C4—94no—
349C2×C22⋊C4—92no—
350C2×C22⋊C4D3211yescharacteristic
351C23×C3—21no—
352C23×C3—22no—
353C23×C3—24no—
354C23×C3—32no—
355C23×C3—32no—
356C23×C3—34no—
357C23×C3—42no—
358C23×C3—42no—
359C23×C3—64no—
360C23×C3—68no—
361C23×C3—62no—
362C23×C3—68no—
363C23×C3—62no—
364C23×C3—64no—
365C23×C3—82no—
366C23×C3—124no—
367C23×C3—122no—
368C23×C3—124no—
369C23×C3—1216no—
370C23×C3#23514yescomplemented
371C23×C3#23714yescomplemented
372C23×C3C23×D311yescharacteristic
373C23×C3C23×D312yes—
374C23×C3C23×D311yescharacteristic
375C23×C3C23×D312yes—
376C22×D3—22no—
377C22×D3—24no—
378C22×D3—28no—
379C22×D3—22no—
380C22×D3—24no—
381C22×D3—28no—
382C22×D3—44no—
383C22×D3—42no—
384C22×D3—44no—
385C22×D3—416no—
386C22×D3C23×D312yes—
387C22×D3C23×D314yes—
388C22×D3C23×D312yes—
389C3×D4—68no—
390C3×D4—68no—
391C3×D4—124no—
392C2×C3×C4—24no—
393C2×C3×C4—34no—
394C2×C3×C4—34no—
395C2×C3×C4—42no—
396C2×C3×C4—42no—
397C2×C3×C4—68no—
398C2×C3×C4—64no—
399C2×C3×C4—82no—
400C2×C3×C4—124no—
401C2×C3×C4—122no—
402C2×C3×C4C23×D314yes—
403C2×C3×C4C23×D314yes—
404#67—28no—
405#67—28no—
406#67—616no—
407#67—616no—
408#67—128no—
409#67—128no—
410C2×Dic3—24no—
411C2×Dic3—38no—
412C2×Dic3—38no—
413C2×Dic3—42no—
414C2×Dic3—68no—
415C2×Dic3—128no—
416C2×Dic3—124no—
417C2×Dic3—124no—
418C2×Dic3—244no—
419C2×Dic3C23×D314yes—
420C2×Dic3C23×D314yes—
421D12—44no—
422C4×D3—28no—
423C4×D3—44no—
424C4×D3—128no—
425Dic6—124no—
426Dic6—124no—
427Dic6—244no—
428C2×C32—22no—
429C2×C32—24no—
430C2×C32C22×#4111yescharacteristic
431C2×C32C2×H(5,𝔽2)12yes—
432C3×D3—24no—
433C3×D3—42no—
434C3×D3—44no—
435C24—31no—
436C24—34no—
437C24—31no—
438C24—32no—
439C24—64no—
440C24—124no—
441C24C2×D3211yescharacteristic
442#41—368no—
443C2×Q8—94no—
444C2×D4—34no—
445C2×D4—34no—
446C2×D4—34no—
447C2×D4—68no—
448C2×D4—98no—
449C2×D4—98no—
450C2×D4—368no—
451C22×C4—32no—
452C22×C4—32no—
453C22×C4—34no—
454C22×C4—34no—
455C22×C4—98no—
456C22×C4—94no—
457C22×C4—124no—
458C22×C4C2×D3212yes—
459C4⋊C4—34no—
460C4⋊C4—98no—
461C4⋊C4—94no—
462C4⋊C4—98no—
463C22⋊C4—34no—
464C22⋊C4—38no—
465C22⋊C4—38no—
466C22⋊C4—98no—
467C22⋊C4—98no—
468C22⋊C4—98no—
469C22⋊C4—94no—
470C22⋊C4—94no—
471C22⋊C4C2×D3214yes—
472C42—98no—
473C22×C3—22no—
474C22×C3—24no—
475C22×C3—24no—
476C22×C3—22no—
477C22×C3—24no—
478C22×C3—22no—
479C22×C3—21no—
480C22×C3—34no—
481C22×C3—44no—
482C22×C3—42no—
483C22×C3—44no—
484C22×C3—44no—
485C22×C3—68no—
486C22×C3—62no—
487C22×C3—62no—
488C22×C3—64no—
489C22×C3—62no—
490C22×C3—68no—
491C22×C3—64no—
492C22×C3—84no—
493C22×C3—1216no—
494C22×C3—124no—
495C22×C3—244no—
496C22×C3C2×#23514yes—
497C22×C3C2×#23512yes—
498C22×C3C2×#23714yes—
499C22×C3C2×#23712yes—
500C22×C3C24×D311yescharacteristic
501C22×C3C24×D311yescharacteristic
502C2×D3—28no—
503C2×D3—22no—
504C2×D3—22no—
505C2×D3—22no—
506C2×D3—24no—
507C2×D3—24no—
508C2×D3—28no—
509C2×D3—416no—
510C2×D3—44no—
511C2×D3—84no—
512C2×D3#100414yes—
513C3×C4—24no—
514C3×C4—24no—
515C3×C4—44no—
516C3×C4—64no—
517C3×C4—64no—
518Dic3—24no—
519Dic3—24no—
520Dic3—68no—
521Dic3—68no—
522Dic3—128no—
523C32#349011yescharacteristic, complemented, Sylow
524C23—32no—
525C23—32no—
526C23—34no—
527C23—42no—
528C23—64no—
529C23—68no—
530C23—62no—
531C23—68no—
532C23—62no—
533C23—64no—
534C23—122no—
535C23—124no—
536C23—124no—
537C23—1216no—
538C23#379514yescomplemented
539C23C22×D3212yes—
540C23C22×D3211yescharacteristic
541Q8—364no—
542D4—68no—
543D4—68no—
544D4—124no—
545D4—1816no—
546D4—368no—
547C2×C4—34no—
548C2×C4—34no—
549C2×C4—42no—
550C2×C4—68no—
551C2×C4—64no—
552C2×C4—98no—
553C2×C4—124no—
554C2×C4—122no—
555C2×C4—368no—
556C2×C4—364no—
557C2×C4C22×D3214yes—
558C2×C3—24no—
559C2×C3—22no—
560C2×C3—22no—
561C2×C3—24no—
562C2×C3—21no—
563C2×C3—22no—
564C2×C3—42no—
565C2×C3—44no—
566C2×C3—64no—
567C2×C3—122no—
568C2×C3—124no—
569C2×C3C22×#23511yescharacteristic
570C2×C3C22×#23711yescharacteristic
571C2×C3C2×#100412yes—
572C2×C3D3×H(5,𝔽2)12yes—
573D3—24no—
574D3—44no—
575D3—42no—
576C22—22no—
577C22—24no—
578C22—34no—
579C22—44no—
580C22—68no—
581C22—62no—
582C22—62no—
583C22—64no—
584C22—62no—
585C22—68no—
586C22—64no—
587C22—1216no—
588C22—124no—
589C22—244no—
590C22C2×#379514yes—
591C22C2×#379512yes—
592C22C23×D3211yescharacteristic
593C4—24no—
594C4—64no—
595C4—64no—
596C4—188no—
597C3—21no—
598C3#8569711yescharacteristic, complemented
599C3#8630911yescharacteristic, complemented
600C2—22no—
601C2—24no—
602C2—64no—
603C2—122no—
604C2—124no—
605C2C22×#379511yescharacteristic
606C2D3×#100412yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C22⋊C4C22
hypercenterC2×C22⋊C4D32
hypocenterC32#3490
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #10595954C2semidirect
2. C3×#5493C2semidirect
3. C2×C3×D3×C22⋊C4C2semidirect
4. C2×#63976C2semidirect
5. #10595506C2semidirect
6. #10594977C2semidirect
7. #10594892C2semidirect
8. #10594211C2semidirect
9. #10594184C2semidirect
14. C22×C3×C4×D3C22semidirect
15. C22×#625C22semidirect
16. C2×#3795C22semidirect
19. #64133C22semidirect
20. #64087C22semidirect
22. C3×#930C22semidirect
23. C2×C3×(C2×D3)⋊C4C22semidirect
24. C3×#886C22semidirect
25. C3×#882C22semidirect
26. C3×D3×C22⋊C4C22semidirect
28. #63976C22semidirect
29. #63976C22semidirect
30. #67⋊Dic3C22semidirect
31. Dic3×#67C22semidirect
32. D3×#217C22semidirect
33. C2×(C2×D3)⋊Dic3C22semidirect
34. #63955C22semidirect
35. #63913C22semidirect
36. #63908C22semidirect
37. #63905C22semidirect
38. #63891C22semidirect
39. #63885C22semidirect
40. #63879C22semidirect
41. #63858C22semidirect
42. #63857C22semidirect
43. #63841C22semidirect
56. #5493D3semidirect
59. C2×D3×C22⋊C4D3semidirect
72. C2×#634C23semidirect
78. C2×C3×D12C23semidirect
85. C2×D3×Dic3C23semidirect
90. C4⋊(C3⋊Dic3)C23semidirect
91. #3750C23semidirect
94. C3×(C2×D3)⋊C4C23semidirect
95. C3×C4⋊Dic3C23semidirect
96. Dic3⋊Dic3C23semidirect
99. (C2×D3)⋊Dic3C23semidirect
100. Dic32C23semidirect
111. C22×C4×D3C2×D3semidirect
138. #930C2×D3semidirect
143. C2×(C2×D3)⋊C4C2×D3semidirect
154. #886C2×D3semidirect
160. #882C2×D3semidirect
164. D3×C22⋊C4C2×D3semidirect
171. C23×C32#41semidirect
257. C2×D12C22×D3semidirect
286. (C2×D3)⋊C4C22×D3semidirect
291. C4⋊Dic3C22×D3semidirect
370. C23×C3#235semidirect
371. C23×C3#237semidirect
523. C32#3490semidirect
538. C23#3795semidirect
598. C3#85697semidirect
599. C3#86309semidirect

Maximal subgroups

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

subgroupindex
#105959542
C3×#54932
C2×C3×D3×C22⋊C42
C2×#639762
#105955062
#105949772
#105948922
#105942112
#105941842
#863093
#856973