Finite Group Databasebeta

← #11860321

Subgroups — #11860321

Order 1152.

1177 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#893C211yesmaximal, characteristic, complemented
2#10594954C211yesmaximal, characteristic, complemented
3C2×#63830C211yesmaximal, characteristic
4#10592665C211yesmaximal, characteristic, complemented
5C3×#4964C211yesmaximal, characteristic, complemented
6#10591085C211yesmaximal, characteristic, complemented
7Dic3×#208C211yesmaximal, characteristic, complemented
8#10590590C212yesmaximal, complemented
9#10590589C212yesmaximal, complemented
10#10590479C212yesmaximal, complemented
11#10590456C212yesmaximal, complemented
12C4×#932—31nomaximal
13#79199—31nomaximal
14C2×#3828C2211yescharacteristic
15C22×C3×D12C2211yescharacteristic
16C22×C3×C4×D3—21no—
17C2×C32×C4⋊C4C2211yescharacteristic
18C2×#3748C2211yescharacteristic
19C2×C3×(C2×D3)⋊C4—21no—
20C3×#926C2211yescharacteristic
21C2×C3×C4×Dic3C2211yescharacteristic
22C2×C3×#208C2211yescharacteristic
23C3×#893—21no—
24C3×#893—21no—
25C3×#893C2212yes—
26C3×#893C2212yes—
27#63952—21no—
28#63952—21no—
29#63894C2211yescharacteristic, complemented
30#63894C2211yescharacteristic, complemented
31C4×#624—21no—
32#63874—21no—
33#63844C2211yescharacteristic, complemented
34#63844C2211yescharacteristic, complemented
35#63830C418yescomplemented
36C2×#3716C2212yes—
37C2×#3714C2212yes—
38#63637C2212yescomplemented
39#63636C2212yescomplemented
40C3×#808C2212yescomplemented
41C3×#807C2212yescomplemented
42#63562C2212yes—
43#63562C2212yes—
44#63554C2212yescomplemented
45Dic3×C3⋊C8C2212yescomplemented
46C2×C3×C4×D4—31no—
47C2×#932—31no—
48C2×#908—31no—
49#5522—31no—
50C2×#893D311yescharacteristic, complemented
51C4×#235—31no—
52C3×#428—31no—
53#5215—31no—
54Dic3×M16—31no—
55#5018—32no—
56C4×#214—32no—
57#5014—32no—
58C4×#213—32no—
59#5001—31no—
60#4966—31no—
61#4966—31no—
62#4966—61no—
63#4964D311yescharacteristic, complemented
64C4×#208—31no—
65#4889—32no—
66#4872—32no—
67#4869—32no—
68#4852—32no—
69C23×C3×D3—21no—
70C22×C32×C4—21no—
71C22×C32×C4C2311yescharacteristic
72C2×#638—21no—
73#3828—22no—
74#3828C2×C414yescomplemented
75C2×C4⋊(C3⋊D3)C2311yescharacteristic
76C2×C4×C3⋊D3—21no—
77C2×#634C2311yescharacteristic
78C22×C3×Dic3D411yescharacteristic
79C22×C3×Dic3D411yescharacteristic
80C2×C3×D12—21no—
81C2×C3×D12—22no—
82C2×C3×D12C2×C414yescomplemented
83C2×C3×D12C2312yes—
84C2×C3×C4×D3—22no—
85C2×C3×C4×D3—22no—
86C2×C3×C4×D3—44no—
87C2×#624—21no—
88C2×#624—21no—
89C32×C4⋊C4—21no—
90C32×C4⋊C4C2312yes—
91#3748—22no—
92C2×C3⋊(C3⋊C8)C2312yes—
93C3×#217—21no—
94C3×(C2×D3)⋊C4—22no—
95C3×(C2×D3)⋊C4—22no—
96C3×C4⋊Dic3C2311yescharacteristic
97C3×C4⋊Dic3C2311yescharacteristic
98C3×C4×Dic3—21no—
99C3×C4×Dic3D411yescharacteristic
100C3×C4×Dic3D411yescharacteristic
101C3×C4×Dic3C2311yescharacteristic
102C3×C4×Dic3C2311yescharacteristic
103C3×#208C2×C414yescomplemented
104C2×C3×C3⋊C8C2312yes—
105#3724—21no—
106#3724—21no—
107#3722—21no—
108#3722—21no—
109Dic32—21no—
110Dic32—21no—
111#3716C2×C418yescomplemented
112#3714C2×C418yescomplemented
113C4×AGL(1,ℤ/8)—91noSylow
114C22×C3×D4—31no—
115C23×C3×C4—61no—
116C2×#235—31no—
117C2×#235—31no—
118C2×#235—61no—
119C22×D12C2×D311yescharacteristic
120C22×C4×D3—21no—
121C2×C3×M16—31no—
122C3×C4×D4—32no—
123C3×C4×D4—32no—
124C3×C4×D4—61no—
125C3×C4×D4—61no—
126C3×#117—31no—
127C2×C3×C4⋊C4—21no—
128C2×C3×C4⋊C4C2×D311yescharacteristic
129C2×C3×C4⋊C4C2×D311yescharacteristic
130C2×C3×C22⋊C4—61no—
131C2×C3×C42—31no—
132C2×#214—32no—
133#932—38no—
134C2×#213—32no—
135C4×#67—61no—
136C4×#67—61no—
137C2×(C2×D3)⋊C4—21no—
138#926C2×D311yescharacteristic
139C2×C4×Dic3C2×D311yescharacteristic
140C2×#208—31no—
141C2×#208—31no—
142C2×#208—61no—
143C2×#208C2×D311yescharacteristic
144#908—38no—
145C2×D24—32no—
146C2×#204—32no—
147#893—21no—
148#893—21no—
149#893—31no—
150#893—31no—
151#893C2×D312yes—
152#893C2×D312yes—
153#887—31no—
154#887—31no—
155#67⋊C4—61no—
156#67⋊C4—61no—
157C4×D12—31no—
158C4×D12—31no—
159#872—61no—
160#872—61no—
161C42×D3—61no—
162C42×D3—61no—
163C4×Dic6—31no—
164C4×Dic6—31no—
165C3×#107—32no—
166C3×#106—32no—
167#832—32no—
168#832—32no—
169#815—32no—
170C8×Dic3—32no—
171#810—32no—
172#810—32no—
173#810—62no—
174#809—32no—
175#809—32no—
176#809—32no—
177#809—32no—
178#809—62no—
179#808C2×D312yescomplemented
180#807C2×D312yescomplemented
181#803—32no—
182C4×C3⋊C8—32no—
183C23×C32C2×D411yescharacteristic
184C22×C3⋊D3—21no—
185C22×C3×D3—24no—
186C22×C3×D3—22no—
187C22×C3×D3—42no—
188C22×C3×D3—42no—
189C2×C32×C4—22no—
190C2×C32×C4—42no—
191C2×C32×C4C22×C412yes—
192C2×C32×C4C2×D411yescharacteristic
193C2×C32×C4#4112yes—
194C2×C32×C4C2411yescharacteristic
195#638—24no—
196C2×C3⋊Dic3—21no—
197C4⋊(C3⋊D3)—21no—
198C4⋊(C3⋊D3)C22×C412yescomplemented
199C4×C3⋊D3—24no—
200#634—21no—
201#634C22×C412yescomplemented
202C2×C3×Dic3—22no—
203C2×C3×Dic3—21no—
204C2×C3×Dic3—21no—
205C2×C3×Dic3—41no—
206C2×C3×Dic3C2×D411yescharacteristic
207C2×C3×Dic3C2×D411yescharacteristic
208C2×C3×Dic3C2×D411yescharacteristic
209C2×C3×Dic3C2×D411yescharacteristic
210C3×D12—24no—
211C3×D12—22no—
212C3×D12C22×C414yes—
213C3×C4×D3—44no—
214C3×C4×D3—44no—
215#624—42no—
216#624—42no—
217C3⋊(C3⋊C8)—22no—
218C3×C3⋊C8C22×C414yescomplemented
219C2×AGL(1,ℤ/8)—91no—
220C4×#41—91no—
221C2×C4×D4—31no—
222#442—92no—
223#440—92no—
224C4×SD16—92no—
225C4×D8—92no—
226#428—31no—
227#418—91no—
228#417—91no—
229C4×M16—91no—
230C24×C3—61no—
231C23×D3—21no—
232C2×C3×D4—34no—
233C2×C3×D4—32no—
234C2×C3×D4—61no—
235C2×C3×D4—62no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—31no—
240C22×C3×C4—31no—
241C22×C3×C4—41no—
242C22×C3×C4—62no—
243C22×C3×C4—62no—
244C22×C3×C4—124no—
245C22×C3×C4C22×D311yescharacteristic
246C22×C3×C4C22×D311yescharacteristic
247C2×#67—61no—
248C2×#67—61no—
249C2×#67—121no—
250C22×Dic3#6711yescharacteristic
251C22×Dic3#6711yescharacteristic
252#235—34no—
253#235—34no—
254#235—64no—
255#235—62no—
256#235—62no—
257#235—122no—
258C2×D12—22no—
259C2×D12—21no—
260C2×D12—31no—
261C2×D12—31no—
262C2×D12—61no—
263C2×D12C4×D314yescomplemented
264C2×D12C22×D312yes—
265C2×C4×D3—22no—
266C2×C4×D3—22no—
267C2×C4×D3—44no—
268C2×C4×D3—61no—
269C2×C4×D3—61no—
270C2×C4×D3—61no—
271C2×C4×D3—61no—
272C2×C4×D3—61no—
273C2×C4×D3—61no—
274C2×C4×D3—121no—
275C2×Dic6—31no—
276C2×Dic6—31no—
277C2×Dic6—61no—
278C3×M16—34no—
279C2×C3×C8—32no—
280C3×C4⋊C4—21no—
281C3×C4⋊C4—21no—
282C3×C4⋊C4—22no—
283C3×C4⋊C4—31no—
284C3×C4⋊C4—31no—
285C3×C4⋊C4—41no—
286C3×C4⋊C4C22×D312yes—
287C3×C4⋊C4C22×D312yes—
288C3×C22⋊C4—62no—
289C3×C22⋊C4—62no—
290C3×C22⋊C4—61no—
291C3×C42—31no—
292C3×C42—31no—
293C3×C42—31no—
294C3×C42—31no—
295C3×C42—61no—
296#217—21no—
297#214—38no—
298#213—38no—
299(C2×D3)⋊C4—22no—
300(C2×D3)⋊C4—22no—
301(C2×D3)⋊C4—61no—
302(C2×D3)⋊C4—61no—
303(C2×D3)⋊C4—61no—
304(C2×D3)⋊C4—61no—
305C4⋊Dic3C22×D311yescharacteristic
306C4⋊Dic3C22×D311yescharacteristic
307Dic3⋊C4—61no—
308Dic3⋊C4—61no—
309Dic3⋊C4—61no—
310Dic3⋊C4—61no—
311C4×Dic3—21no—
312C4×Dic3—61no—
313C4×Dic3—61no—
314C4×Dic3—61no—
315C4×Dic3—61no—
316C4×Dic3#6711yescharacteristic
317C4×Dic3#6711yescharacteristic
318C4×Dic3C22×D311yescharacteristic
319C4×Dic3C22×D311yescharacteristic
320#208—62no—
321#208—62no—
322#208—122no—
323#208C4×D314yescomplemented
324C2×C3⋊C8—32no—
325C2×C3⋊C8—32no—
326C2×C3⋊C8—62no—
327C2×C3⋊C8C22×D312yes—
328D24—38no—
329#204—38no—
330C22×C32—21no—
331C22×C32—21no—
332C22×C32C4×D412yes—
333C22×C32C22×D411yescharacteristic
334C2×C3⋊D3—22no—
335C2×C3⋊D3—41no—
336C2×C3⋊D3—41no—
337C2×C3×D3—24no—
338C2×C3×D3—48no—
339C2×C3×D3—42no—
340C2×C3×D3—42no—
341C32×C4—42no—
342C32×C4C4×D412yes—
343C32×C4C23×C411yescharacteristic
344C32×C4C2×#4111yescharacteristic
345C3⋊Dic3—22no—
346C3×Dic3—21no—
347C3×Dic3—21no—
348C3×Dic3—21no—
349C3×Dic3—41no—
350C3×Dic3—41no—
351C3×Dic3AGL(1,ℤ/8)12yescomplemented
352C2×#41—91no—
353C22×D4—31no—
354C23×C4—61no—
355AGL(1,ℤ/8)—98no—
356C2×SD16—92no—
357C2×D8—92no—
358C2×M16—31no—
359C2×M16—91no—
360C4×Q8—91no—
361C4×Q8—91no—
362C4×D4—32no—
363C4×D4—32no—
364C4×D4—61no—
365C4×D4—61no—
366C4×D4—91no—
367C4×D4—91no—
368C4×D4—181no—
369C4×D4—181no—
370#117—31no—
371#117—181no—
372C2×C4⋊C4D3211yescharacteristic
373C2×C22⋊C4—61no—
374C2×C42—31no—
375C2×C42—181no—
376#107—32no—
377#106—32no—
378#103—92no—
379#102—92no—
380#102—92no—
381#102—92no—
382#97—92no—
383C4×C8—92no—
384C23×C3—21no—
385C23×C3—64no—
386C23×C3—62no—
387C23×C3—122no—
388C23×C3—122no—
389C23×C3D3×D411yescharacteristic
390C23×C3C2×#6711yescharacteristic
391C22×D3—24no—
392C22×D3—22no—
393C22×D3—42no—
394C22×D3—42no—
395C22×D3—61no—
396C22×D3—61no—
397C22×D3—121no—
398C3×D4—34no—
399C3×D4—64no—
400C3×D4—62no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—21no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—21no—
407C2×C3×C4—31no—
408C2×C3×C4—31no—
409C2×C3×C4—31no—
410C2×C3×C4—31no—
411C2×C3×C4—42no—
412C2×C3×C4—42no—
413C2×C3×C4—42no—
414C2×C3×C4—62no—
415C2×C3×C4—61no—
416C2×C3×C4—61no—
417C2×C3×C4—82no—
418C2×C3×C4—124no—
419C2×C3×C4—124no—
420C2×C3×C4—121no—
421C2×C3×C4C2×C4×D312yes—
422C2×C3×C4C2×C4×D312yes—
423C2×C3×C4#23512yes—
424C2×C3×C4D3×D411yescharacteristic
425C2×C3×C4#23912yes—
426C2×C3×C4C2×#6711yescharacteristic
427C2×C3×C4C23×D311yescharacteristic
428C2×C3×C4C23×D311yescharacteristic
429#67—64no—
430#67—64no—
431#67—124no—
432C2×Dic3—22no—
433C2×Dic3—21no—
434C2×Dic3—21no—
435C2×Dic3—41no—
436C2×Dic3—61no—
437C2×Dic3—61no—
438C2×Dic3—121no—
439C2×Dic3C2×#6711yescharacteristic
440C2×Dic3C2×#6711yescharacteristic
441C2×Dic3C2×#6711yescharacteristic
442C2×Dic3C2×#6711yescharacteristic
443D12—24no—
444D12—22no—
445D12—32no—
446D12—32no—
447D12—62no—
448D12—61no—
449D12—61no—
450D12—121no—
451D12C2×C4×D314yes—
452C4×D3—44no—
453C4×D3—44no—
454C4×D3—64no—
455C4×D3—64no—
456C4×D3—124no—
457C4×D3—122no—
458C4×D3—122no—
459C4×D3—122no—
460C4×D3—122no—
461Dic6—32no—
462Dic6—32no—
463Dic6—62no—
464Dic6—61no—
465Dic6—61no—
466Dic6—121no—
467C3×C8—34no—
468C3⋊C8—62no—
469C3⋊C8—62no—
470C3⋊C8—122no—
471C3⋊C8C2×C4×D314yescomplemented
472C2×C32—22no—
473C2×C32C2×C4×D411yescharacteristic
474C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
475C2×C32#57511yescharacteristic
476C3⋊D3—42no—
477C3×D3—44no—
478C24—61no—
479#41—94no—
480#41—182no—
481C2×Q8—91no—
482C2×D4—32no—
483C2×D4—34no—
484C2×D4—62no—
485C2×D4—61no—
486C2×D4—91no—
487C2×D4—181no—
488C22×C4—21no—
489C22×C4—31no—
490C22×C4—31no—
491C22×C4—62no—
492C22×C4—62no—
493C22×C4—124no—
494C22×C4—181no—
495C22×C4—181no—
496C22×C4—181no—
497C22×C4C2×D3211yescharacteristic
498SD16—98no—
499D8—98no—
500M16—34no—
501M16—182no—
502C2×C8—32no—
503C2×C8—92no—
504C4⋊C4—21no—
505C4⋊C4—31no—
506C4⋊C4—31no—
507C4⋊C4—181no—
508C4⋊C4—181no—
509C4⋊C4C2×D3212yes—
510C22⋊C4—62no—
511C22⋊C4—62no—
512C22⋊C4—61no—
513C22⋊C4—181no—
514C22⋊C4—181no—
515C42—31no—
516C42—31no—
517C42—31no—
518C42—31no—
519C42—61no—
520C42—181no—
521C42—181no—
522C22×C3—21no—
523C22×C3—21no—
524C22×C3—21no—
525C22×C3—21no—
526C22×C3—21no—
527C22×C3—22no—
528C22×C3—41no—
529C22×C3—41no—
530C22×C3—64no—
531C22×C3—128no—
532C22×C3—122no—
533C22×C3—122no—
534C22×C3#89312yes—
535C22×C3C4×#6712yes—
536C22×C3C2×D3×D411yescharacteristic
537C22×C3C22×#6711yescharacteristic
538C2×D3—24no—
539C2×D3—48no—
540C2×D3—42no—
541C2×D3—42no—
542C2×D3—62no—
543C2×D3—62no—
544C2×D3—122no—
545C2×D3—121no—
546C2×D3—121no—
547C2×D3—121no—
548C2×D3—121no—
549C2×D3—241no—
550C2×D3—241no—
551C3×C4—21no—
552C3×C4—21no—
553C3×C4—22no—
554C3×C4—32no—
555C3×C4—42no—
556C3×C4—42no—
557C3×C4—61no—
558C3×C4—61no—
559C3×C4—61no—
560C3×C4—82no—
561C3×C4—121no—
562C3×C4—121no—
563C3×C4#89312yes—
564C3×C4C4×#6712yes—
565C3×C4C22×C4×D311yescharacteristic
566C3×C4C22×C4×D311yescharacteristic
567C3×C4C2×#23511yescharacteristic
568C3×C4C2×#23911yescharacteristic
569Dic3—21no—
570Dic3—21no—
571Dic3—21no—
572Dic3—41no—
573Dic3—41no—
574Dic3—62no—
575Dic3—62no—
576Dic3—122no—
577Dic3#93212yescomplemented
578C32C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
579C23—62no—
580C23—64no—
581C23—122no—
582C23—122no—
583C23—181no—
584C23D3×#6711yescharacteristic
585Q8—92no—
586Q8—181no—
587D4—34no—
588D4—62no—
589D4—64no—
590D4—92no—
591D4—184no—
592D4—181no—
593C2×C4—22no—
594C2×C4—31no—
595C2×C4—31no—
596C2×C4—31no—
597C2×C4—31no—
598C2×C4—42no—
599C2×C4—62no—
600C2×C4—61no—
601C2×C4—61no—
602C2×C4—124no—
603C2×C4—124no—
604C2×C4—121no—
605C2×C4—181no—
606C2×C4—184no—
607C2×C4—362no—
608C2×C4—362no—
609C2×C4#379912yes—
610C2×C4C4×D3212yes—
611C2×C4D3×#6711yescharacteristic
612C2×C4C22×D3211yescharacteristic
613C8—34no—
614C8—182no—
615C2×C3—22no—
616C2×C3—22no—
617C2×C3—21no—
618C2×C3—21no—
619C2×C3—21no—
620C2×C3—42no—
621C2×C3—124no—
622C2×C3C2×#89311yescharacteristic
623C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
624C2×C3#577711yescharacteristic
625C2×C3C2×C4×#6711yescharacteristic
626C2×C3C2×#93211yescharacteristic
627C2×C3#582211yescharacteristic
628D3—44no—
629D3—122no—
630D3—122no—
631D3—242no—
632C22—21no—
633C22—21no—
634C22—64no—
635C22—128no—
636C22—122no—
637C22—122no—
638C22—182no—
639C22—361no—
640C22—361no—
641C22#6390412yes—
642C22C2×D3×#6711yescharacteristic
643C4—32no—
644C4—42no—
645C4—61no—
646C4—61no—
647C4—61no—
648C4—121no—
649C4—121no—
650C4—182no—
651C4#6390412yes—
652C4C2×#379911yescharacteristic
653C4C2×C4×D3211yescharacteristic
654C3—21no—
655C3#7919911yescharacteristic, complemented
656C3C4×#93211yescharacteristic, complemented
657C2—22no—
658C2—124no—
659C2—362no—
660C2C2×#6390411yescharacteristic
661C2D3×#93211yescharacteristic
662C2#1059531711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radicalC2×#63830C2
cosocleC2×C32×C4C24
hypercenterC2×C4⋊C4D32
hypocenterC32C4×AGL(1,ℤ/8)
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#893C2semidirect
2. #10594954C2semidirect
4. #10592665C2semidirect
5. C3×#4964C2semidirect
6. #10591085C2semidirect
7. Dic3×#208C2semidirect
8. #10590590C2semidirect
9. #10590589C2semidirect
10. #10590479C2semidirect
11. #10590456C2semidirect
29. #63894C22semidirect
30. #63894C22semidirect
33. #63844C22semidirect
34. #63844C22semidirect
35. #63830C4semidirect
38. #63637C22semidirect
39. #63636C22semidirect
40. C3×#808C22semidirect
41. C3×#807C22semidirect
44. #63554C22semidirect
45. Dic3×C3⋊C8C22semidirect
50. C2×#893D3semidirect
63. #4964D3semidirect
74. #3828C2×C4semidirect
82. C2×C3×D12C2×C4semidirect
103. C3×#208C2×C4semidirect
111. #3716C2×C4semidirect
112. #3714C2×C4semidirect
179. #808C2×D3semidirect
180. #807C2×D3semidirect
198. C4⋊(C3⋊D3)C22×C4semidirect
201. #634C22×C4semidirect
218. C3×C3⋊C8C22×C4semidirect
263. C2×D12C4×D3semidirect
323. #208C4×D3semidirect
351. C3×Dic3AGL(1,ℤ/8)semidirect
471. C3⋊C8C2×C4×D3semidirect
577. Dic3#932semidirect
578. C32C4×AGL(1,ℤ/8)semidirect
655. C3#79199semidirect
656. C3C4×#932semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8932
#105949542
C2×#638302
#105926652
C3×#49642
#105910852
Dic3×#2082
#105905902
#105905892
#105904792
#105904562
C4×#9323
#791993