Finite Group Databasebeta

← #11870427

Subgroups — #11870427

Order 1152.

1041 conjugacy classes of subgroups.

The subgroup lattice has 643 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5596C211yesmaximal, characteristic, complemented
2C2×Dic3×D12C211yesmaximal, characteristic, complemented
3#10592732C211yesmaximal, characteristic, complemented
4C3×#5036C211yesmaximal, characteristic, complemented
5#10591428C212yesmaximal, complemented
6Dic3×#213C212yesmaximal, complemented
7#10591160C211yesmaximal, characteristic, complemented
8#10591094C211yesmaximal, characteristic, complemented
9#10591053C211yesmaximal, characteristic, complemented
10#10590463C212yesmaximal, complemented
11#10590452C212yesmaximal, complemented
12#83298—31nomaximal
13#79988—31nomaximal
14C2×C3×#237—21no—
15C22×C3×D12C2211yescharacteristic
16C22×D3×Dic3—21no—
17C32×#121C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C3×#940C2211yescharacteristic, complemented
20C3×#939—21no—
21C3×D4×Dic3C2211yescharacteristic, complemented
22C2×C3×#213C2212yes—
23C3×#930C2211yescharacteristic
24C2×C3×C4×Dic3C2211yescharacteristic
25C3×#893C2211yescharacteristic, complemented
26C3×#888C2211yescharacteristic, complemented
27C3×#885—21no—
28C3×#67⋊C4—21no—
29C2×(C2×D3)⋊Dic3—21no—
30Dic3×D12—21no—
31Dic3×D12—21no—
32Dic3×D12C2212yes—
33Dic3×D12C2212yes—
34C2×#3713C2212yes—
35#63659C2212yescomplemented
36#63657C2211yescharacteristic
37#63634C2212yescomplemented
38C3×#830C2211yescharacteristic
39C3×#809C2212yes—
40#63575C2212yescomplemented
41Dic3⋊(C3⋊C8)C2212yescomplemented
42#63563C2212yescomplemented
43#63562C2212yes—
44Dic3×C3⋊C8C2212yescomplemented
45C3×#532—31no—
46C2×D4×Dic3—31no—
47#5596D311yescharacteristic, complemented
48C2×C4×D12—31no—
49C3×#447—31no—
50#5217—31no—
51#5150—32no—
52Dic3×D8—32no—
53#5087—32no—
54#5072—32no—
55#5036—31no—
56#5036D311yescharacteristic, complemented
57#5033—31no—
58#5033—31no—
59#5033—31no—
60#5033—61no—
61C4×#213—32no—
62C4×#213—32no—
63#4925—31no—
64#4759—32no—
65#4756—32no—
66#4736—31no—
67#4718—31no—
68C23×C3×D3—21no—
69C2×C32×D4—21no—
70C2×C32×D4C2311yescharacteristic
71C22×C32×C4C2311yescharacteristic
72C22×C3⋊Dic3—21no—
73C2×C3×#67—21no—
74C2×C3×#67—21no—
75C2×C3×#67—21no—
76C22×C3×Dic3—21no—
77C22×C3×Dic3D411yescharacteristic
78C22×C3×Dic3D411yescharacteristic
79C3×#237—44no—
80C2×C3×D12—21no—
81C2×C3×D12—24no—
82C2×C3×D12C2311yescharacteristic
83C2×C3×D12C2312yes—
84C2×C3×C4×D3—21no—
85C2×C3×Dic6—21no—
86C2×D3×Dic3—22no—
87C2×D3×Dic3—22no—
88C2×D3×Dic3—44no—
89C32×C4⋊C4C2311yescharacteristic
90C32×C22⋊C4—21no—
91C4⋊(C3⋊Dic3)—21no—
92C4⋊(C3⋊Dic3)C2312yes—
93C2×C3⋊(C3⋊C8)C2312yes—
94C3×#217—21no—
95C3×#213—24no—
96C3×(C2×D3)⋊C4—21no—
97C3×(C2×D3)⋊C4—21no—
98C3×C4⋊Dic3C2311yescharacteristic
99C3×Dic3⋊C4—21no—
100C3×C4×Dic3D411yescharacteristic
101C3×C4×Dic3D411yescharacteristic
102C3×C4×Dic3C2311yescharacteristic
103C3×C4×Dic3C2311yescharacteristic
104C2×C3×C3⋊C8C2312yes—
105(C2×D3)⋊Dic3—22no—
106(C2×D3)⋊Dic3—22no—
107#3713—24no—
108#3100—91noSylow
109C2×C3×#41—61no—
110C22×C3×D4—31no—
111C23×Dic3—61no—
112C2×#237—21no—
113C22×D12C2×D311yescharacteristic
114C22×C4×D3—61no—
115C2×C3×D8—32no—
116C3×C4⋊Q8—31no—
117C3×#127—31no—
118C3×#124—61no—
119C3×#121—21no—
120C3×#121—31no—
121C3×#121—61no—
122C3×#121C2×D311yescharacteristic
123C3×#121C2×D311yescharacteristic
124C3×C4×D4—31no—
125C3×C4×D4—31no—
126C3×C4×D4—61no—
127C2×C3×C42—31no—
128C2×#217—61no—
129#940C2×D311yescharacteristic, complemented
130#939—21no—
131D4×Dic3—32no—
132D4×Dic3—32no—
133D4×Dic3—61no—
134D4×Dic3—61no—
135D4×Dic3C2×D311yescharacteristic, complemented
136C2×#213—32no—
137C2×#213—32no—
138C2×#213C2×D312yes—
139#930C2×D311yescharacteristic
140C2×(C2×D3)⋊C4—61no—
141C2×C4⋊Dic3—31no—
142C2×C4⋊Dic3—31no—
143C2×C4⋊Dic3—61no—
144C2×C4×Dic3C2×D311yescharacteristic
145#893C2×D311yescharacteristic, complemented
146#888C2×D311yescharacteristic, complemented
147#885—21no—
148#67⋊C4—21no—
149C4×D12—32no—
150C4×D12—32no—
151C4×D12—61no—
152C4×D12—61no—
153C3×#102—32no—
154C3×C22⋊C8—31no—
155#832—32no—
156#832—32no—
157#832—32no—
158#832—32no—
159#832—62no—
160#830—31no—
161#830—31no—
162#830—61no—
163#830C2×D311yescharacteristic
164#821—32no—
165#818—32no—
166Dic3⋊C8—32no—
167C8×Dic3—32no—
168#809—32no—
169#809C2×D312yes—
170#807—32no—
171#807—32no—
172#807—32no—
173#807—62no—
174C4⋊(C3⋊C8)—32no—
175C4×C3⋊C8—32no—
176C23×C32—21no—
177C23×C32C2×D411yescharacteristic
178C22×C3×D3—24no—
179C22×C3×D3—22no—
180C22×C3×D3—21no—
181C22×C3×D3—42no—
182C22×C3×D3—42no—
183C32×D4—22no—
184C32×D4—42no—
185C2×C32×C4—22no—
186C2×C32×C4—21no—
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2411yescharacteristic
189C2×C3⋊Dic3—22no—
190C2×C3⋊Dic3—42no—
191C3×#67—42no—
192C3×#67—42no—
193C3×#67—42no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—41no—
196C2×C3×Dic3—42no—
197C2×C3×Dic3D814yescomplemented
198C2×C3×Dic3C2×D411yescharacteristic
199C2×C3×Dic3C2×D411yescharacteristic
200C2×C3×Dic3C2×D411yescharacteristic
201C2×C3×Dic3C2×D411yescharacteristic
202C3×D12—24no—
203C3×D12—22no—
204C3×D12—22no—
205C3×D12#4114yescomplemented
206C3×C4×D3—42no—
207C3×Dic6—42no—
208D3×Dic3—44no—
209D3×Dic3—44no—
210C3⋊(C3⋊C8)—22no—
211C3×C3⋊C8—22no—
212#532—31no—
213C2×C4×D4—91no—
214#480—91no—
215#480—91no—
216#474—92no—
217#459—92no—
218#447—31no—
219#447—91no—
220C4×D8—92no—
221C4×D8—92no—
222#431—91no—
223C24×C3—61no—
224C23×D3—21no—
225C3×#41—124no—
226C2×C3×Q8—61no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—32no—
231C2×C3×D4—31no—
232C2×C3×D4—41no—
233C2×C3×D4—64no—
234C2×C3×D4—61no—
235C2×C3×D4—61no—
236C2×C3×D4—61no—
237C2×C3×D4—61no—
238C2×C3×D4C22×D311yescharacteristic
239C2×C3×D4C22×D311yescharacteristic
240C22×C3×C4—21no—
241C22×C3×C4—31no—
242C22×C3×C4—31no—
243C22×C3×C4—61no—
244C22×C3×C4—61no—
245C22×C3×C4C22×D311yescharacteristic
246C22×C3×C4C22×D311yescharacteristic
247C2×#67—21no—
248C2×#67—21no—
249C2×#67—21no—
250C22×Dic3—21no—
251C22×Dic3—61no—
252C22×Dic3—61no—
253C22×Dic3—62no—
254C22×Dic3—62no—
255C22×Dic3—121no—
256C22×Dic3—124no—
257C22×Dic3#6711yescharacteristic
258C22×Dic3#6711yescharacteristic
259#237—44no—
260C2×D12—21no—
261C2×D12—24no—
262C2×D12C22×D311yescharacteristic
263C2×D12C22×D312yes—
264C2×C4×D3—21no—
265C2×C4×D3—62no—
266C2×C4×D3—62no—
267C2×C4×D3—124no—
268C2×Dic6—21no—
269C3×D8—64no—
270C2×C3×C8—32no—
271C3×C4⋊C4—21no—
272C3×C4⋊C4—31no—
273C3×C4⋊C4—61no—
274C3×C4⋊C4C22×D311yescharacteristic
275C3×C4⋊C4C22×D311yescharacteristic
276C3×C22⋊C4—21no—
277C3×C22⋊C4—21no—
278C3×C22⋊C4—41no—
279C3×C22⋊C4—61no—
280C3×C22⋊C4—61no—
281C3×C22⋊C4—61no—
282C3×C42—31no—
283C3×C42—31no—
284C3×C42—31no—
285C3×C42—31no—
286#217—21no—
287#217—62no—
288#217—62no—
289#213—24no—
290#213—64no—
291#213—64no—
292(C2×D3)⋊C4—21no—
293(C2×D3)⋊C4—21no—
294(C2×D3)⋊C4—62no—
295(C2×D3)⋊C4—62no—
296C4⋊Dic3—32no—
297C4⋊Dic3—32no—
298C4⋊Dic3—62no—
299C4⋊Dic3—61no—
300C4⋊Dic3—61no—
301C4⋊Dic3—121no—
302C4⋊Dic3C22×D311yescharacteristic
303Dic3⋊C4—21no—
304C4×Dic3#6711yescharacteristic
305C4×Dic3#6711yescharacteristic
306C4×Dic3C22×D311yescharacteristic
307C4×Dic3C22×D311yescharacteristic
308C2×C3⋊C8—32no—
309C2×C3⋊C8—32no—
310C2×C3⋊C8—62no—
311C2×C3⋊C8C22×D312yes—
312C22×C32—21no—
313C22×C32—21no—
314C22×C32—41no—
315C22×C32—41no—
316C22×C32—41no—
317C22×C32C2×D812yes—
318C22×C32C22×D411yescharacteristic
319C2×C3×D3—24no—
320C2×C3×D3—48no—
321C2×C3×D3—42no—
322C2×C3×D3—42no—
323C2×C3×D3—41no—
324C2×C3×D3—41no—
325C2×C3×D3—41no—
326C32×C4—21no—
327C32×C4—41no—
328C32×C4C2×#4112yes—
329C3⋊Dic3—42no—
330C3×Dic3—21no—
331C3×Dic3—21no—
332C3×Dic3—41no—
333C3×Dic3C2×D812yes—
334C3×Dic3C2×D812yes—
335C2×#41—61no—
336C22×D4—31no—
337C23×C4—181no—
338C2×D8—32no—
339C2×D8—92no—
340C4⋊Q8—31no—
341#127—31no—
342#124—61no—
343#121—31no—
344#121—61no—
345#121D3211yescharacteristic
346C4×D4—31no—
347C4×D4—31no—
348C4×D4—61no—
349C4×D4—92no—
350C4×D4—92no—
351C4×D4—181no—
352C4×D4—181no—
353C2×C4⋊C4—91no—
354C2×C22⋊C4—181no—
355C2×C42—31no—
356#107—92no—
357#107—92no—
358C4⋊C8—92no—
359#102—32no—
360#102—92no—
361#102—92no—
362#102—92no—
363C22⋊C8—31no—
364C22⋊C8—91no—
365C4×C8—92no—
366C23×C3—21no—
367C23×C3—21no—
368C23×C3—21no—
369C23×C3—41no—
370C23×C3—64no—
371C23×C3—62no—
372C23×C3—61no—
373C23×C3—122no—
374C23×C3—122no—
375C23×C3D3×D411yescharacteristic
376C23×C3C2×#6711yescharacteristic
377C22×D3—24no—
378C22×D3—22no—
379C22×D3—21no—
380C22×D3—42no—
381C22×D3—42no—
382C3×Q8—122no—
383C3×D4—22no—
384C3×D4—22no—
385C3×D4—34no—
386C3×D4—42no—
387C3×D4—42no—
388C3×D4—42no—
389C3×D4—64no—
390C3×D4—62no—
391C3×D4—62no—
392C3×D4—82no—
393C3×D4—122no—
394C3×D4—122no—
395C3×D4—122no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—34no—
403C2×C3×C4—31no—
404C2×C3×C4—31no—
405C2×C3×C4—31no—
406C2×C3×C4—31no—
407C2×C3×C4—42no—
408C2×C3×C4—41no—
409C2×C3×C4—61no—
410C2×C3×C4—122no—
411C2×C3×C4—122no—
412C2×C3×C4—121no—
413C2×C3×C4D3×D411yescharacteristic
414C2×C3×C4C2×#6711yescharacteristic
415C2×C3×C4C23×D311yescharacteristic
416C2×C3×C4C23×D311yescharacteristic
417#67—42no—
418#67—42no—
419#67—42no—
420C2×Dic3—21no—
421C2×Dic3—41no—
422C2×Dic3—42no—
423C2×Dic3—62no—
424C2×Dic3—62no—
425C2×Dic3—122no—
426C2×Dic3—122no—
427C2×Dic3—122no—
428C2×Dic3—124no—
429C2×Dic3—124no—
430C2×Dic3—242no—
431C2×Dic3#21314yescomplemented
432C2×Dic3C2×#6711yescharacteristic
433C2×Dic3C2×#6711yescharacteristic
434C2×Dic3C2×#6711yescharacteristic
435C2×Dic3C2×#6711yescharacteristic
436D12—24no—
437D12—22no—
438D12—22no—
439D12#23714yescomplemented
440C4×D3—42no—
441C4×D3—124no—
442C4×D3—124no—
443Dic6—42no—
444C3×C8—62no—
445C3⋊C8—22no—
446C3⋊C8—62no—
447C3⋊C8—62no—
448C3⋊C8—122no—
449C2×C32—22no—
450C2×C32—81no—
451C2×C32#52511yescharacteristic
452C2×C32C22×D811yescharacteristic
453C2×C32#57511yescharacteristic
454C3×D3—44no—
455C3×D3—81no—
456C24—61no—
457#41—124no—
458C2×Q8—61no—
459C2×D4—21no—
460C2×D4—32no—
461C2×D4—31no—
462C2×D4—64no—
463C2×D4—61no—
464C2×D4—61no—
465C2×D4—61no—
466C2×D4—61no—
467C2×D4C2×D3211yescharacteristic
468C22×C4—31no—
469C22×C4—31no—
470C22×C4—61no—
471C22×C4—61no—
472C22×C4—182no—
473C22×C4—182no—
474C22×C4—181no—
475C22×C4—364no—
476C22×C4C2×D3211yescharacteristic
477D8—64no—
478D8—184no—
479C2×C8—32no—
480C2×C8—92no—
481C4⋊C4—31no—
482C4⋊C4—61no—
483C4⋊C4—92no—
484C4⋊C4—181no—
485C4⋊C4C2×D3211yescharacteristic
486C22⋊C4—21no—
487C22⋊C4—61no—
488C22⋊C4—61no—
489C22⋊C4—61no—
490C22⋊C4—182no—
491C22⋊C4—182no—
492C42—31no—
493C42—31no—
494C42—31no—
495C42—31no—
496C22×C3—21no—
497C22×C3—21no—
498C22×C3—21no—
499C22×C3—21no—
500C22×C3—21no—
501C22×C3—22no—
502C22×C3—41no—
503C22×C3—41no—
504C22×C3—41no—
505C22×C3—41no—
506C22×C3—41no—
507C22×C3—41no—
508C22×C3—41no—
509C22×C3—41no—
510C22×C3—64no—
511C22×C3—81no—
512C22×C3—81no—
513C22×C3—81no—
514C22×C3—128no—
515C22×C3—122no—
516C22×C3—122no—
517C22×C3—121no—
518C22×C3—121no—
519C22×C3—121no—
520C22×C3D3×D812yes—
521C22×C3C2×#21312yes—
522C22×C3C2×D3×D411yescharacteristic
523C22×C3C22×#6711yescharacteristic
524C2×D3—24no—
525C2×D3—48no—
526C2×D3—42no—
527C2×D3—42no—
528C2×D3—41no—
529C2×D3—41no—
530C2×D3—41no—
531C3×C4—21no—
532C3×C4—21no—
533C3×C4—22no—
534C3×C4—32no—
535C3×C4—32no—
536C3×C4—41no—
537C3×C4—41no—
538C3×C4—41no—
539C3×C4—61no—
540C3×C4—61no—
541C3×C4—81no—
542C3×C4—121no—
543C3×C4C2×#23712yes—
544C3×C4D3×#4112yes—
545Dic3—21no—
546Dic3—21no—
547Dic3—41no—
548Dic3—122no—
549Dic3—122no—
550Dic3—242no—
551Dic3C2×#21312yes—
552Dic3C2×#21312yes—
553C32#310011yescharacteristic, complemented, Sylow
554C23—21no—
555C23—64no—
556C23—62no—
557C23—61no—
558C23—122no—
559C23—122no—
560C23D3×#6711yescharacteristic
561Q8—122no—
562D4—22no—
563D4—34no—
564D4—42no—
565D4—64no—
566D4—62no—
567D4—62no—
568D4—122no—
569D4—122no—
570D4—122no—
571C2×C4—22no—
572C2×C4—21no—
573C2×C4—31no—
574C2×C4—31no—
575C2×C4—34no—
576C2×C4—31no—
577C2×C4—31no—
578C2×C4—61no—
579C2×C4—122no—
580C2×C4—122no—
581C2×C4—121no—
582C2×C4—182no—
583C2×C4—364no—
584C2×C4—364no—
585C2×C4—362no—
586C2×C4D3×#6711yescharacteristic
587C2×C4C22×D3211yescharacteristic
588C8—62no—
589C8—182no—
590C2×C3—22no—
591C2×C3—22no—
592C2×C3—21no—
593C2×C3—21no—
594C2×C3—21no—
595C2×C3—42no—
596C2×C3—81no—
597C2×C3—81no—
598C2×C3—124no—
599C2×C3—161no—
600C2×C3—241no—
601C2×C3#558611yescharacteristic
602C2×C3C2×D3×D811yescharacteristic
603C2×C3#577311yescharacteristic
604C2×C3C22×#21311yescharacteristic
605C2×C3#582211yescharacteristic
606C2×C3#582811yescharacteristic
607D3—44no—
608D3—81no—
609C22—21no—
610C22—21no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—64no—
615C22—128no—
616C22—122no—
617C22—122no—
618C22—121no—
619C22—121no—
620C22—121no—
621C22D3×#21312yes—
622C22C2×D3×#6711yescharacteristic
623C4—21no—
624C4—32no—
625C4—32no—
626C4—41no—
627C4—61no—
628C4—61no—
629C4—121no—
630C4—362no—
631C4D3×#23712yes—
632C3—21no—
633C3#7998811yescharacteristic, complemented
634C3#8329811yescharacteristic, complemented
635C2—22no—
636C2—81no—
637C2—124no—
638C2—241no—
639C2C2×D3×#21311yescharacteristic
640C2#1059515411yescharacteristic
641C2#1059546911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3100
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C3×#5596C2semidirect
2. C2×Dic3×D12C2semidirect
3. #10592732C2semidirect
4. C3×#5036C2semidirect
5. #10591428C2semidirect
6. Dic3×#213C2semidirect
7. #10591160C2semidirect
8. #10591094C2semidirect
9. #10591053C2semidirect
10. #10590463C2semidirect
11. #10590452C2semidirect
19. C3×#940C22semidirect
21. C3×D4×Dic3C22semidirect
25. C3×#893C22semidirect
26. C3×#888C22semidirect
35. #63659C22semidirect
37. #63634C22semidirect
40. #63575C22semidirect
41. Dic3⋊(C3⋊C8)C22semidirect
42. #63563C22semidirect
44. Dic3×C3⋊C8C22semidirect
47. #5596D3semidirect
56. #5036D3semidirect
129. #940C2×D3semidirect
135. D4×Dic3C2×D3semidirect
145. #893C2×D3semidirect
146. #888C2×D3semidirect
197. C2×C3×Dic3D8semidirect
205. C3×D12#41semidirect
431. C2×Dic3#213semidirect
439. D12#237semidirect
553. C32#3100semidirect
633. C3#79988semidirect
634. C3#83298semidirect

Maximal subgroups

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

subgroupindex
C3×#55962
C2×Dic3×D122
#105927322
C3×#50362
#105914282
Dic3×#2132
#105911602
#105910942
#105910532
#105904632
#105904522
#832983
#799883