Finite Group Databasebeta

← #11871269

Subgroups — #11871269

Order 1152.

1031 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594929C211yesmaximal, characteristic, complemented
2C2×#63898C211yesmaximal, characteristic, complemented
3#10592418C211yesmaximal, characteristic, complemented
4C3×#4735C211yesmaximal, characteristic, complemented
5C3×#4732C211yesmaximal, characteristic, complemented
6#10591160C211yesmaximal, characteristic, complemented
7#10591091C211yesmaximal, characteristic, complemented
8#10590781C212yesmaximal, complemented
9#10590776C212yesmaximal, complemented
10#10590749C212yesmaximal, complemented
11#10590741C212yesmaximal, complemented
12#81310—31nomaximal
13#79990—31nomaximal
14C22×C3×D12C2211yescharacteristic
15C2×#3805—21no—
16C22×D3×Dic3—21no—
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C3×#930C2211yescharacteristic
19C3×#930C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×D24C2212yes—
22#63980—21no—
23C2×(C2×D3)⋊Dic3—21no—
24#63919C2211yescharacteristic, complemented
25#63915—21no—
26#63914C2211yescharacteristic, complemented
27#63902—21no—
28#63898—21no—
29#63898—21no—
30#63898C2212yes—
31#63898C2212yes—
32#63898C2211yescharacteristic, complemented
33#63898C2211yescharacteristic, complemented
34C2×#3713C2212yes—
35C32×C22⋊C8C2211yescharacteristic
36#63657C2211yescharacteristic
37#63642C2212yescomplemented
38#63641C2212yescomplemented
39C3×#821C2212yes—
40C3×#821C2212yescomplemented
41C3×#817C2212yescomplemented
42#63574C2212yescomplemented
43#63562C2212yes—
44#63562C2212yescomplemented
45C2×D4×Dic3—31no—
46#5596—31no—
47#5596—31no—
48C2×#893—31no—
49C3×#481—31no—
50C3×#447—31no—
51#5217—31no—
52#5152—32no—
53#5150—32no—
54#5036—31no—
55#5034—31no—
56#4968—31no—
57#4870—32no—
58#4869—32no—
59#4786—32no—
60#4785—32no—
61#4785—32no—
62#4761—32no—
63#4735D311yescharacteristic, complemented
64#4732D311yescharacteristic, complemented
65#4719—31no—
66#4719—31no—
67#4719—61no—
68C23×C3×D3—21no—
69C22×C32×C4C2311yescharacteristic
70C22×C3⋊Dic3D411yescharacteristic
71C22×C3⋊Dic3D411yescharacteristic
72C2×C3×#67—21no—
73C2×C3×#67—21no—
74C22×C3×Dic3—21no—
75C2×C3×D12—21no—
76C2×C3×D12—24no—
77C2×C3×D12C2311yescharacteristic
78C2×C3×D12C2311yescharacteristic
79C2×C3×D12C2312yes—
80C2×#627—21no—
81C2×#625—21no—
82C2×#625—21no—
83#3805—44no—
84C2×D3×Dic3—22no—
85C2×D3×Dic3—22no—
86C2×D3×Dic3—21no—
87C2×D3×Dic3—21no—
88C2×D3×Dic3—44no—
89C2×C32×C8C2312yes—
90C4×C3⋊Dic3D411yescharacteristic
91C4×C3⋊Dic3D411yescharacteristic
92C4×C3⋊Dic3C2311yescharacteristic
93C4×C3⋊Dic3C2311yescharacteristic
94C2×C3⋊(C3⋊C8)C2312yes—
95C3×(C2×D3)⋊C4—21no—
96C3×(C2×D3)⋊C4—21no—
97C3×C4⋊Dic3—21no—
98C3×C4⋊Dic3C2312yes—
99C3×C4⋊Dic3C2311yescharacteristic
100C3×C4⋊Dic3C2311yescharacteristic
101C3×D24—24no—
102#3724—21no—
103(C2×D3)⋊Dic3—22no—
104(C2×D3)⋊Dic3—22no—
105(C2×D3)⋊Dic3—21no—
106(C2×D3)⋊Dic3—21no—
107#3713—24no—
108#3109—91noSylow
109C22×C3×D4—31no—
110C23×Dic3—61no—
111C2×#237—61no—
112C2×#237—61no—
113C22×D12C2×D311yescharacteristic
114C22×C4×D3—61no—
115C2×C3×D8—32no—
116C3×#121—31no—
117C3×#121—31no—
118C2×C3×C4⋊C4—31no—
119C2×#217—61no—
120#940—31no—
121#940—31no—
122#939—61no—
123#939—61no—
124D4×Dic3—32no—
125D4×Dic3—31no—
126D4×Dic3—32no—
127D4×Dic3—31no—
128D4×Dic3—61no—
129D4×Dic3—61no—
130C2×#213—32no—
131C2×#213—32no—
132#930C2×D311yescharacteristic
133#930C2×D311yescharacteristic
134C2×(C2×D3)⋊C4—61no—
135C2×C4⋊Dic3C2×D311yescharacteristic
136C2×C4×Dic3—31no—
137C2×C4×Dic3—31no—
138C2×C4×Dic3—61no—
139C2×D24C2×D312yes—
140#893—31no—
141#893—32no—
142#893—32no—
143#893—31no—
144#893—61no—
145#893—61no—
146#888—31no—
147#888—31no—
148#885—61no—
149#885—61no—
150#67⋊C4—61no—
151#67⋊C4—61no—
152C3×#106—32no—
153C3×#102—32no—
154C3×#102—32no—
155C3×C22⋊C8—21no—
156C3×C22⋊C8C2×D311yescharacteristic
157C3×C22⋊C8C2×D311yescharacteristic
158#832—32no—
159#832—32no—
160#830—31no—
161#830—31no—
162#830—61no—
163#821C2×D312yes—
164#821C2×D312yescomplemented
165#817C2×D312yescomplemented
166#815—32no—
167#815—32no—
168#815—62no—
169Dic3⋊C8—32no—
170Dic3⋊C8—32no—
171Dic3⋊C8—62no—
172#809—32no—
173#809—32no—
174#808—32no—
175#808—32no—
176C23×C32C2×D411yescharacteristic
177C22×C3×D3—24no—
178C22×C3×D3—22no—
179C22×C3×D3—21no—
180C22×C3×D3—21no—
181C22×C3×D3—42no—
182C22×C3×D3—42no—
183C2×C32×C4—22no—
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2411yescharacteristic
186C2×C3⋊Dic3—22no—
187C2×C3⋊Dic3—22no—
188C2×C3⋊Dic3C2×D411yescharacteristic
189C2×C3⋊Dic3C2×D411yescharacteristic
190C2×C3⋊Dic3C2×D411yescharacteristic
191C2×C3⋊Dic3C2×D411yescharacteristic
192C3×#67—42no—
193C3×#67—42no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—21no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—42no—
198C3×D12—24no—
199C3×D12—22no—
200C3×D12—22no—
201C3×D12—22no—
202C3×D12#4114yescomplemented
203#627—42no—
204#625—42no—
205#625—42no—
206D3×Dic3—44no—
207D3×Dic3—42no—
208D3×Dic3—42no—
209D3×Dic3—44no—
210C32×C8—22no—
211C3⋊(C3⋊C8)—22no—
212#532—91no—
213C2×C4×D4—91no—
214#481—31no—
215#481—91no—
216#476—92no—
217#459—92no—
218#447—31no—
219#447—91no—
220#442—92no—
221#442—92no—
222#432—91no—
223C24×C3—61no—
224C23×D3—21no—
225C2×C3×D4—32no—
226C2×C3×D4—31no—
227C2×C3×D4—31no—
228C2×C3×D4—64no—
229C2×C3×D4—61no—
230C2×C3×D4—61no—
231C2×C3×D4—61no—
232C22×C3×C4—21no—
233C22×C3×C4—61no—
234C22×C3×C4C22×D311yescharacteristic
235C22×C3×C4C22×D311yescharacteristic
236C2×#67—21no—
237C2×#67—21no—
238C2×#67—61no—
239C2×#67—61no—
240C2×#67—61no—
241C2×#67—61no—
242C22×Dic3—21no—
243C22×Dic3—31no—
244C22×Dic3—31no—
245C22×Dic3—31no—
246C22×Dic3—31no—
247C22×Dic3—61no—
248C22×Dic3—61no—
249C22×Dic3—61no—
250C22×Dic3—61no—
251C22×Dic3—62no—
252C22×Dic3—62no—
253C22×Dic3—124no—
254#237—124no—
255#237—124no—
256C2×D12—21no—
257C2×D12—24no—
258C2×D12C22×D311yescharacteristic
259C2×D12C22×D311yescharacteristic
260C2×D12C22×D312yes—
261C2×C4×D3—61no—
262C2×C4×D3—61no—
263C2×C4×D3—62no—
264C2×C4×D3—62no—
265C2×C4×D3—124no—
266C2×Dic6—61no—
267C2×Dic6—61no—
268C3×D8—64no—
269C2×C3×C8—22no—
270C2×C3×C8C22×D312yes—
271C2×C3×C8C22×D312yes—
272C3×C4⋊C4—31no—
273C3×C4⋊C4—32no—
274C3×C4⋊C4—31no—
275C3×C4⋊C4—61no—
276C3×C22⋊C4—61no—
277C3×C22⋊C4—61no—
278#217—61no—
279#217—61no—
280#217—62no—
281#217—62no—
282#213—64no—
283#213—64no—
284(C2×D3)⋊C4—21no—
285(C2×D3)⋊C4—21no—
286(C2×D3)⋊C4—61no—
287(C2×D3)⋊C4—61no—
288(C2×D3)⋊C4—62no—
289(C2×D3)⋊C4—62no—
290C4⋊Dic3—21no—
291C4⋊Dic3C22×D311yescharacteristic
292C4⋊Dic3C22×D312yes—
293C4⋊Dic3C22×D311yescharacteristic
294Dic3⋊C4—61no—
295Dic3⋊C4—61no—
296C4×Dic3—31no—
297C4×Dic3—31no—
298C4×Dic3—31no—
299C4×Dic3—31no—
300C4×Dic3—31no—
301C4×Dic3—31no—
302C4×Dic3—31no—
303C4×Dic3—31no—
304C4×Dic3—61no—
305C4×Dic3—61no—
306C4×Dic3—61no—
307C4×Dic3—61no—
308C2×C3⋊C8—32no—
309C2×C3⋊C8—32no—
310C2×C3⋊C8—62no—
311D24—24no—
312C22×C32—21no—
313C22×C32—21no—
314C22×C32AGL(1,ℤ/8)12yes—
315C22×C32C22×D411yescharacteristic
316C2×C3×D3—24no—
317C2×C3×D3—48no—
318C2×C3×D3—42no—
319C2×C3×D3—42no—
320C2×C3×D3—41no—
321C2×C3×D3—41no—
322C2×C3×D3—41no—
323C2×C3×D3—41no—
324C2×C3×D3—41no—
325C2×C3×D3—41no—
326C32×C4—21no—
327C32×C4C2×#4112yes—
328C3⋊Dic3—21no—
329C3⋊Dic3—21no—
330C3⋊Dic3—21no—
331C3⋊Dic3AGL(1,ℤ/8)12yes—
332C3×Dic3—42no—
333C3×Dic3—41no—
334C3×Dic3—41no—
335C2×#41—181no—
336C22×D4—31no—
337C23×C4—181no—
338C2×D8—32no—
339C2×D8—92no—
340C4⋊Q8—91no—
341#127—91no—
342#124—181no—
343#121—31no—
344#121—31no—
345#121—181no—
346C4×D4—92no—
347C4×D4—92no—
348C4×D4—91no—
349C4×D4—91no—
350C4×D4—181no—
351C4×D4—181no—
352C4×D4—181no—
353C2×C4⋊C4—31no—
354C2×C22⋊C4—181no—
355C2×C42—91no—
356#106—32no—
357#106—92no—
358C4⋊C8—92no—
359#102—32no—
360#102—32no—
361#102—92no—
362#102—92no—
363C22⋊C8—91no—
364C22⋊C8D3211yescharacteristic
365#97—92no—
366C23×C3—21no—
367C23×C3—64no—
368C23×C3—62no—
369C23×C3—61no—
370C23×C3—61no—
371C23×C3—122no—
372C23×C3—122no—
373C23×C3D3×D411yescharacteristic
374C23×C3D3×D411yescharacteristic
375C22×D3—24no—
376C22×D3—22no—
377C22×D3—21no—
378C22×D3—21no—
379C22×D3—42no—
380C22×D3—42no—
381C3×D4—34no—
382C3×D4—64no—
383C3×D4—62no—
384C3×D4—62no—
385C3×D4—62no—
386C3×D4—122no—
387C3×D4—122no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—42no—
393C2×C3×C4—61no—
394C2×C3×C4—61no—
395C2×C3×C4—62no—
396C2×C3×C4—122no—
397C2×C3×C4D3×D411yescharacteristic
398C2×C3×C4D3×D411yescharacteristic
399C2×C3×C4C23×D311yescharacteristic
400C2×C3×C4C23×D311yescharacteristic
401#67—42no—
402#67—42no—
403#67—122no—
404#67—122no—
405#67—122no—
406#67—122no—
407C2×Dic3—21no—
408C2×Dic3—21no—
409C2×Dic3—22no—
410C2×Dic3—31no—
411C2×Dic3—31no—
412C2×Dic3—31no—
413C2×Dic3—31no—
414C2×Dic3—31no—
415C2×Dic3—31no—
416C2×Dic3—31no—
417C2×Dic3—31no—
418C2×Dic3—42no—
419C2×Dic3—61no—
420C2×Dic3—61no—
421C2×Dic3—61no—
422C2×Dic3—61no—
423C2×Dic3—62no—
424C2×Dic3—62no—
425C2×Dic3—62no—
426C2×Dic3—62no—
427C2×Dic3—122no—
428C2×Dic3—122no—
429C2×Dic3—124no—
430C2×Dic3—122no—
431C2×Dic3—122no—
432C2×Dic3—124no—
433D12—24no—
434D12—22no—
435D12—22no—
436D12—22no—
437D12#23714yescomplemented
438C4×D3—124no—
439C4×D3—124no—
440C4×D3—122no—
441C4×D3—122no—
442Dic6—122no—
443Dic6—122no—
444C3×C8—22no—
445C3×C8—22no—
446C3×C8—42no—
447C3⋊C8—62no—
448C3⋊C8—62no—
449C3⋊C8—122no—
450C2×C32—22no—
451C2×C32#52511yescharacteristic
452C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
453C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
454C3×D3—44no—
455C3×D3—81no—
456C3×D3—81no—
457C24—61no—
458#41—364no—
459C2×Q8—181no—
460C2×D4—32no—
461C2×D4—31no—
462C2×D4—31no—
463C2×D4—64no—
464C2×D4—61no—
465C2×D4—61no—
466C2×D4—61no—
467C2×D4—181no—
468C2×D4—181no—
469C22×C4—61no—
470C22×C4—91no—
471C22×C4—91no—
472C22×C4—182no—
473C22×C4—182no—
474C22×C4—181no—
475C22×C4—181no—
476C22×C4—364no—
477C22×C4C2×D3211yescharacteristic
478D8—64no—
479D8—184no—
480C2×C8—92no—
481C2×C8C2×D3212yes—
482C4⋊C4—31no—
483C4⋊C4—32no—
484C4⋊C4—31no—
485C4⋊C4—61no—
486C4⋊C4—181no—
487C22⋊C4—61no—
488C22⋊C4—61no—
489C22⋊C4—182no—
490C22⋊C4—182no—
491C22⋊C4—181no—
492C22⋊C4—181no—
493C42—91no—
494C42—91no—
495C42—91no—
496C42—91no—
497C22×C3—21no—
498C22×C3—21no—
499C22×C3—21no—
500C22×C3—21no—
501C22×C3—21no—
502C22×C3—22no—
503C22×C3—41no—
504C22×C3—41no—
505C22×C3—64no—
506C22×C3—128no—
507C22×C3—122no—
508C22×C3—122no—
509C22×C3—121no—
510C22×C3—121no—
511C22×C3—121no—
512C22×C3—121no—
513C22×C3—121no—
514C22×C3—121no—
515C22×C3#91112yes—
516C22×C3#91412yes—
517C22×C3C2×D3×D411yescharacteristic
518C22×C3C2×D3×D411yescharacteristic
519C2×D3—24no—
520C2×D3—48no—
521C2×D3—42no—
522C2×D3—42no—
523C2×D3—41no—
524C2×D3—41no—
525C2×D3—41no—
526C2×D3—41no—
527C2×D3—41no—
528C2×D3—41no—
529C3×C4—21no—
530C3×C4—21no—
531C3×C4—22no—
532C3×C4—41no—
533C3×C4—121no—
534C3×C4—121no—
535C3×C4—122no—
536C3×C4C2×#23712yes—
537C3×C4D3×#4112yes—
538Dic3—32no—
539Dic3—32no—
540Dic3—41no—
541Dic3—41no—
542Dic3—42no—
543Dic3—62no—
544Dic3—61no—
545Dic3—61no—
546Dic3—61no—
547Dic3—61no—
548Dic3—61no—
549Dic3—61no—
550Dic3—121no—
551Dic3—121no—
552Dic3—121no—
553C32#310911yescharacteristic, complemented, Sylow
554C23—64no—
555C23—62no—
556C23—61no—
557C23—61no—
558C23—122no—
559C23—122no—
560C23#380211yescharacteristic
561Q8—362no—
562D4—34no—
563D4—64no—
564D4—62no—
565D4—62no—
566D4—62no—
567D4—122no—
568D4—122no—
569D4—362no—
570D4—362no—
571C2×C4—22no—
572C2×C4—61no—
573C2×C4—61no—
574C2×C4—62no—
575C2×C4—91no—
576C2×C4—91no—
577C2×C4—91no—
578C2×C4—91no—
579C2×C4—122no—
580C2×C4—182no—
581C2×C4—182no—
582C2×C4—364no—
583C2×C4—364no—
584C2×C4—362no—
585C2×C4—362no—
586C2×C4#380211yescharacteristic
587C2×C4C22×D3211yescharacteristic
588C8—22no—
589C8—182no—
590C2×C3—22no—
591C2×C3—22no—
592C2×C3—21no—
593C2×C3—21no—
594C2×C3—21no—
595C2×C3—42no—
596C2×C3—124no—
597C2×C3—241no—
598C2×C3—241no—
599C2×C3#558611yescharacteristic
600C2×C3#565611yescharacteristic
601C2×C3C2×#91111yescharacteristic
602C2×C3C2×#91411yescharacteristic
603C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
604C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
605D3—44no—
606D3—81no—
607D3—81no—
608C22—21no—
609C22—21no—
610C22—64no—
611C22—128no—
612C22—122no—
613C22—122no—
614C22—121no—
615C22—121no—
616C22—121no—
617C22—121no—
618C22—121no—
619C22—121no—
620C22#6379812yes—
621C22C2×#380211yescharacteristic
622C4—21no—
623C4—92no—
624C4—121no—
625C4—121no—
626C4—122no—
627C4—181no—
628C4—181no—
629C4—181no—
630C4D3×#23712yes—
631C3—21no—
632C3#7999011yescharacteristic, complemented
633C3#8131011yescharacteristic, complemented
634C2—22no—
635C2—124no—
636C2—241no—
637C2—241no—
638C2#1059408211yescharacteristic
639C2C2×#6379811yescharacteristic
640C2#1059471611yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
hypercenterC22⋊C8D32
hypocenterC32#3109
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #10594929C2semidirect
2. C2×#63898C2semidirect
3. #10592418C2semidirect
4. C3×#4735C2semidirect
5. C3×#4732C2semidirect
6. #10591160C2semidirect
7. #10591091C2semidirect
8. #10590781C2semidirect
9. #10590776C2semidirect
10. #10590749C2semidirect
11. #10590741C2semidirect
24. #63919C22semidirect
26. #63914C22semidirect
32. #63898C22semidirect
33. #63898C22semidirect
37. #63642C22semidirect
38. #63641C22semidirect
40. C3×#821C22semidirect
41. C3×#817C22semidirect
42. #63574C22semidirect
44. #63562C22semidirect
63. #4735D3semidirect
64. #4732D3semidirect
164. #821C2×D3semidirect
165. #817C2×D3semidirect
202. C3×D12#41semidirect
437. D12#237semidirect
553. C32#3109semidirect
632. C3#79990semidirect
633. C3#81310semidirect

Maximal subgroups

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

subgroupindex
#105949292
C2×#638982
#105924182
C3×#47352
C3×#47322
#105911602
#105910912
#105907812
#105907762
#105907492
#105907412
#813103
#799903