Finite Group Databasebeta

← #11858511

Subgroups — #11858511

Order 1152.

1043 conjugacy classes of subgroups.

The subgroup lattice has 621 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#892C211yesmaximal, characteristic
2D3×#926C211yesmaximal, characteristic
3C2×D3×#208C211yesmaximal, characteristic
4#10592663C211yesmaximal, characteristic, complemented
5C3×#4964C211yesmaximal, characteristic, complemented
6#10591139C211yesmaximal, characteristic, complemented
7#10591130C211yesmaximal, characteristic, complemented
8#10590572C212yesmaximal, complemented
9#10590571C212yesmaximal, complemented
10#10590437C212yesmaximal, complemented
11#10590436C212yesmaximal, complemented
12#82207—31nomaximal
13#79208—31nomaximal
14C22×C3×C4×D3C2211yescharacteristic
15C2×C32×C4⋊C4C2211yescharacteristic
16#64135C2211yescharacteristic
17C2×#3748C2211yescharacteristic
18C2×C3×(C2×D3)⋊C4—21no—
19C3×#926C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4×Dic3—21no—
22C2×C3×#208C2211yescharacteristic
23C3×#892—21no—
24C3×#892—21no—
25C3×#892C2212yes—
26C3×#892C2212yes—
27D3×#217—21no—
28#63955—21no—
29D3×C4⋊Dic3C2211yescharacteristic
30D3×C4⋊Dic3C2211yescharacteristic
31C4×D3×Dic3—21no—
32#63855—21no—
33#63841C2211yescharacteristic
34#63841C2211yescharacteristic
35C2×#3711C2212yes—
36D3×#208C418yescomplemented
37C2×D3×C3⋊C8C2212yes—
38#63635C2212yescomplemented
39#63634C2212yescomplemented
40C3×#808C2212yescomplemented
41C3×#807C2212yescomplemented
42#63576C2212yescomplemented
43#63575C2212yescomplemented
44#63574C2212yescomplemented
45#63573C2212yescomplemented
46C2×C3×#117—31no—
47C2×#926—31no—
48C22×#208—31no—
49C2×D3×M16—31no—
50D3×#117—31no—
51C2×#892D311yescharacteristic
52C3×#428—31no—
53#5121—31no—
54#4998—32no—
55#4998—32no—
56#4995—31no—
57#4995—32no—
58#4995—32no—
59#4964—31no—
60#4964—31no—
61#4964—31no—
62#4964—31no—
63#4964—61no—
64#4964D311yescharacteristic, complemented
65#4881—32no—
66#4880—32no—
67#4861—32no—
68#4860—32no—
69C23×C3×D3D411yescharacteristic
70C22×C32×C4—21no—
71C22×C32×C4C2311yescharacteristic
72C22×C3×Dic3—21no—
73C22×C3×Dic3D411yescharacteristic
74C2×C3×C4×D3C2×C414yes—
75C2×C3×C4×D3D411yescharacteristic
76C2×C3×C4×D3D411yescharacteristic
77C2×C3×C4×D3Q814yes—
78C2×C3×C4×D3C2311yescharacteristic
79C2×C3×C4×D3C2311yescharacteristic
80C2×D3×Dic3—21no—
81C2×D3×Dic3—21no—
82C32×C4⋊C4—21no—
83C32×C4⋊C4C2312yes—
84#3757—21no—
85C4⋊(C3⋊Dic3)C2311yescharacteristic
86C4⋊(C3⋊Dic3)C2311yescharacteristic
87C4×C3⋊Dic3—21no—
88#3748C2×C414yescomplemented
89C2×C3⋊(C3⋊C8)C2312yes—
90C3×#217—21no—
91C3×(C2×D3)⋊C4—22no—
92C3×(C2×D3)⋊C4—22no—
93C3×C4⋊Dic3—21no—
94C3×C4⋊Dic3C2312yes—
95C3×C4⋊Dic3C2311yescharacteristic
96C3×C4⋊Dic3C2311yescharacteristic
97C3×C4×Dic3—21no—
98C3×C4×Dic3—22no—
99C3×C4×Dic3—22no—
100C3×#208C2×C414yescomplemented
101C2×C3×C3⋊C8C2312yes—
102Dic3⋊Dic3—21no—
103Dic3⋊Dic3—21no—
104(C2×D3)⋊Dic3—21no—
105(C2×D3)⋊Dic3—21no—
106Dic32—21no—
107Dic32—21no—
108#3711C2×C418yescomplemented
109D3×C3⋊C8C2×C418yescomplemented
110#2911—91noSylow
111C23×C3×C4—31no—
112C22×C4×D3C2×D311yescharacteristic
113C2×C3×M16—31no—
114C3×#117—31no—
115C3×#117—32no—
116C3×#117—32no—
117C3×#117—61no—
118C3×#117—61no—
119C2×C3×C4⋊C4—21no—
120C2×C3×C4⋊C4—31no—
121C2×C3×C4⋊C4C2×D311yescharacteristic
122C2×C3×C4⋊C4C2×D311yescharacteristic
123C2×C3×C22⋊C4—61no—
124C2×C3×C42—61no—
125C2×#217—61no—
126C2×(C2×D3)⋊C4—21no—
127#926—31no—
128#926—31no—
129#926—31no—
130#926—31no—
131#926—61no—
132#926—61no—
133#926—61no—
134#926C2×D311yescharacteristic
135C2×C4⋊Dic3—31no—
136C2×C4⋊Dic3—31no—
137C2×C4⋊Dic3C2×D311yescharacteristic
138C2×C4×Dic3—21no—
139C2×C4×Dic3—61no—
140C2×#208—31no—
141C2×#208—31no—
142C2×#208—38no—
143C2×#208—32no—
144C2×#208—61no—
145C2×#208C2×D311yescharacteristic
146C22×C3⋊C8—32no—
147D3×M16—38no—
148C2×ΓL(1,𝔽25)—32no—
149C2×D3×C8—32no—
150#892—21no—
151#892—21no—
152#892—31no—
153#892—31no—
154#892C2×D312yes—
155#892C2×D312yes—
156D3×C4⋊C4—31no—
157D3×C4⋊C4—31no—
158D3×C22⋊C4—61no—
159#877—61no—
160#872—61no—
161C42×D3—61no—
162C3×#107—32no—
163C3×#106—32no—
164#818—32no—
165#817—32no—
166#808—32no—
167#808—32no—
168#808—32no—
169#808—32no—
170#808—32no—
171#808—62no—
172#808C2×D312yescomplemented
173#807—32no—
174#807—32no—
175#807—32no—
176#807—32no—
177#807—32no—
178#807—62no—
179#807C2×D312yescomplemented
180C23×C32C2×D411yescharacteristic
181C22×C3×D3—41no—
182C22×C3×D3—41no—
183C22×C3×D3C4⋊C414yes—
184C22×C3×D3C2×D411yescharacteristic
185C22×C3×D3C2×D411yescharacteristic
186C2×C32×C4—22no—
187C2×C32×C4—42no—
188C2×C32×C4C22×C412yes—
189C2×C32×C4C2×D411yescharacteristic
190C2×C32×C4C2×Q812yes—
191C2×C32×C4C2411yescharacteristic
192C2×C3⋊Dic3—21no—
193C2×C3⋊Dic3—21no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—21no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—42no—
198C2×C3×Dic3C4⋊C414yes—
199C2×C3×Dic3C2×D411yescharacteristic
200C2×C3×Dic3C2×D411yescharacteristic
201C3×C4×D3C4⋊C414yes—
202C3×C4×D3C4⋊C414yes—
203C3×C4×D3C22×C412yes—
204C3×C4×D3C22×C412yes—
205C3×C4×D3C2×Q812yes—
206C3×C4×D3C2×Q812yes—
207D3×Dic3—42no—
208D3×Dic3—42no—
209C3⋊(C3⋊C8)C22×C414yes—
210C3×C3⋊C8C22×C414yes—
211C22×M16—91no—
212C2×#117—31no—
213C2×#117—91no—
214#428—31no—
215#428—92no—
216#428—92no—
217#428—91no—
218#428—91no—
219#428—91no—
220#427—92no—
221#427—92no—
222C24×C3—31no—
223C23×D3#6711yescharacteristic
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—31no—
228C22×C3×C4—34no—
229C22×C3×C4—31no—
230C22×C3×C4—31no—
231C22×C3×C4—34no—
232C22×C3×C4—31no—
233C22×C3×C4—31no—
234C22×C3×C4—41no—
235C22×C3×C4—61no—
236C22×C3×C4C22×D311yescharacteristic
237C22×C3×C4C22×D311yescharacteristic
238C22×Dic3—21no—
239C22×Dic3—61no—
240C22×Dic3—61no—
241C22×Dic3#6711yescharacteristic
242C2×C4×D3—61no—
243C2×C4×D3—61no—
244C2×C4×D3Dic614yes—
245C2×C4×D3C4×D314yes—
246C2×C4×D3#6711yescharacteristic
247C2×C4×D3#6711yescharacteristic
248C2×C4×D3C22×D311yescharacteristic
249C2×C4×D3C22×D311yescharacteristic
250C3×M16—34no—
251C2×C3×C8—32no—
252C3×C4⋊C4—21no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—22no—
255C3×C4⋊C4—32no—
256C3×C4⋊C4—31no—
257C3×C4⋊C4—31no—
258C3×C4⋊C4—41no—
259C3×C4⋊C4—61no—
260C3×C4⋊C4C22×D312yes—
261C3×C4⋊C4C22×D312yes—
262C3×C22⋊C4—62no—
263C3×C22⋊C4—62no—
264C3×C22⋊C4—61no—
265C3×C42—62no—
266C3×C42—62no—
267C3×C42—61no—
268#217—21no—
269#217—61no—
270#217—61no—
271#217—61no—
272#217—61no—
273#217—121no—
274(C2×D3)⋊C4—22no—
275(C2×D3)⋊C4—22no—
276(C2×D3)⋊C4—61no—
277(C2×D3)⋊C4—61no—
278C4⋊Dic3—21no—
279C4⋊Dic3—31no—
280C4⋊Dic3—31no—
281C4⋊Dic3—31no—
282C4⋊Dic3—31no—
283C4⋊Dic3—61no—
284C4⋊Dic3—61no—
285C4⋊Dic3—61no—
286C4⋊Dic3—61no—
287C4⋊Dic3C22×D311yescharacteristic
288C4⋊Dic3C22×D312yes—
289C4⋊Dic3C22×D311yescharacteristic
290Dic3⋊C4—61no—
291Dic3⋊C4—61no—
292C4×Dic3—21no—
293C4×Dic3—22no—
294C4×Dic3—22no—
295C4×Dic3—61no—
296C4×Dic3—61no—
297C4×Dic3—61no—
298C4×Dic3—61no—
299C4×Dic3—61no—
300C4×Dic3—61no—
301C4×Dic3—121no—
302#208—34no—
303#208—34no—
304#208—38no—
305#208—64no—
306#208C4×D314yescomplemented
307C2×C3⋊C8—32no—
308C2×C3⋊C8—32no—
309C2×C3⋊C8—38no—
310C2×C3⋊C8—62no—
311C2×C3⋊C8C22×D312yes—
312ΓL(1,𝔽25)—38no—
313D3×C8—38no—
314C22×C32—21no—
315C22×C32—21no—
316C22×C32C2×C4⋊C412yes—
317C22×C32C22×D411yescharacteristic
318C2×C3×D3—21no—
319C2×C3×D3—21no—
320C2×C3×D3—21no—
321C2×C3×D3—21no—
322C2×C3×D3—44no—
323C2×C3×D3C2×C4⋊C412yes—
324C2×C3×D3C2×C4⋊C412yes—
325C32×C4—42no—
326C32×C4C2×C4⋊C412yes—
327C32×C4C23×C411yescharacteristic
328C32×C4C22×Q811yescharacteristic
329C3⋊Dic3—41no—
330C3⋊Dic3—41no—
331C3×Dic3—41no—
332C3×Dic3—41no—
333C3×Dic3—42no—
334C3×Dic3C2×C4⋊C412yes—
335C3×Dic3C2×C4⋊C412yes—
336C23×C4—31no—
337C2×M16—31no—
338C2×M16—92no—
339C2×M16—98no—
340C2×M16—91no—
341C22×C8—92no—
342#117—31no—
343#117—32no—
344#117—32no—
345#117—61no—
346#117—61no—
347#117—91no—
348#117—91no—
349#117—91no—
350#117—181no—
351#117—181no—
352C2×C4⋊C4—31no—
353C2×C4⋊C4—91no—
354C2×C4⋊C4—91no—
355C2×C4⋊C4D3211yescharacteristic
356C2×C22⋊C4—61no—
357C2×C22⋊C4—181no—
358C2×C42—61no—
359C2×C42—181no—
360#107—32no—
361#107—92no—
362#107—92no—
363#107—92no—
364#106—32no—
365#106—92no—
366#106—92no—
367#106—92no—
368C23×C3—21no—
369C23×C3—31no—
370C23×C3—31no—
371C23×C3—34no—
372C23×C3—121no—
373C23×C3—121no—
374C23×C3D3×D411yescharacteristic
375C23×C3C2×#6711yescharacteristic
376C22×D3—41no—
377C22×D3—41no—
378C22×D3Dic3⋊C414yes—
379C22×D3C2×#6711yescharacteristic
380C22×D3C2×#6711yescharacteristic
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—21no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—21no—
387C2×C3×C4—34no—
388C2×C3×C4—31no—
389C2×C3×C4—31no—
390C2×C3×C4—34no—
391C2×C3×C4—34no—
392C2×C3×C4—32no—
393C2×C3×C4—32no—
394C2×C3×C4—32no—
395C2×C3×C4—32no—
396C2×C3×C4—42no—
397C2×C3×C4—42no—
398C2×C3×C4—42no—
399C2×C3×C4—62no—
400C2×C3×C4—61no—
401C2×C3×C4—61no—
402C2×C3×C4—82no—
403C2×C3×C4—122no—
404C2×C3×C4C2×Dic612yes—
405C2×C3×C4C2×C4×D312yes—
406C2×C3×C4C2×C4×D312yes—
407C2×C3×C4D3×D411yescharacteristic
408C2×C3×C4D3×Q812yes—
409C2×C3×C4C2×#6711yescharacteristic
410C2×C3×C4C23×D311yescharacteristic
411C2×C3×C4C23×D311yescharacteristic
412C2×Dic3—21no—
413C2×Dic3—21no—
414C2×Dic3—22no—
415C2×Dic3—42no—
416C2×Dic3—61no—
417C2×Dic3—61no—
418C2×Dic3—61no—
419C2×Dic3—61no—
420C2×Dic3—121no—
421C2×Dic3—121no—
422C2×Dic3—122no—
423C2×Dic3—122no—
424C2×Dic3Dic3⋊C414yes—
425C2×Dic3C2×#6711yescharacteristic
426C2×Dic3C2×#6711yescharacteristic
427C4×D3—122no—
428C4×D3—122no—
429C4×D3Dic3⋊C414yes—
430C4×D3Dic3⋊C414yes—
431C4×D3C2×Dic612yes—
432C4×D3C2×Dic612yes—
433C4×D3C2×C4×D312yes—
434C4×D3C2×C4×D312yes—
435C3×C8—34no—
436C3⋊C8—34no—
437C3⋊C8—34no—
438C3⋊C8—64no—
439C3⋊C8C2×C4×D314yes—
440C2×C32—22no—
441C2×C32C22×C4⋊C411yescharacteristic
442C2×C32#57511yescharacteristic
443C2×C32#57511yescharacteristic
444C3×D3—22no—
445C3×D3—22no—
446C24—31no—
447C22×C4—21no—
448C22×C4—31no—
449C22×C4—31no—
450C22×C4—31no—
451C22×C4—34no—
452C22×C4—34no—
453C22×C4—31no—
454C22×C4—31no—
455C22×C4—61no—
456C22×C4—181no—
457C22×C4—181no—
458C22×C4C2×D3211yescharacteristic
459M16—34no—
460M16—98no—
461M16—94no—
462C2×C8—32no—
463C2×C8—98no—
464C2×C8—92no—
465C4⋊C4—21no—
466C4⋊C4—31no—
467C4⋊C4—31no—
468C4⋊C4—32no—
469C4⋊C4—61no—
470C4⋊C4—91no—
471C4⋊C4—91no—
472C4⋊C4—181no—
473C4⋊C4—181no—
474C4⋊C4C2×D3212yes—
475C22⋊C4—62no—
476C22⋊C4—62no—
477C22⋊C4—61no—
478C22⋊C4—181no—
479C22⋊C4—181no—
480C22⋊C4—181no—
481C42—62no—
482C42—62no—
483C42—61no—
484C42—181no—
485C42—181no—
486C42—181no—
487C22×C3—21no—
488C22×C3—21no—
489C22×C3—21no—
490C22×C3—21no—
491C22×C3—21no—
492C22×C3—22no—
493C22×C3—32no—
494C22×C3—32no—
495C22×C3—41no—
496C22×C3—41no—
497C22×C3—61no—
498C22×C3—61no—
499C22×C3—61no—
500C22×C3—61no—
501C22×C3—124no—
502C22×C3D3×C4⋊C412yes—
503C22×C3C2×Dic3⋊C412yes—
504C22×C3C2×D3×D411yescharacteristic
505C22×C3C22×#6711yescharacteristic
506C2×D3—21no—
507C2×D3—21no—
508C2×D3—21no—
509C2×D3—21no—
510C2×D3—44no—
511C2×D3C2×Dic3⋊C412yes—
512C2×D3C2×Dic3⋊C412yes—
513C3×C4—21no—
514C3×C4—21no—
515C3×C4—22no—
516C3×C4—32no—
517C3×C4—32no—
518C3×C4—42no—
519C3×C4—42no—
520C3×C4—82no—
521C3×C4—122no—
522C3×C4—121no—
523C3×C4—121no—
524C3×C4D3×C4⋊C412yes—
525C3×C4C2×Dic3⋊C412yes—
526C3×C4C22×Dic611yescharacteristic
527C3×C4C22×C4×D311yescharacteristic
528C3×C4C22×C4×D311yescharacteristic
529C3×C4C2×D3×Q811yescharacteristic
530Dic3—41no—
531Dic3—41no—
532Dic3—42no—
533Dic3—121no—
534Dic3—121no—
535Dic3—121no—
536Dic3—121no—
537Dic3—241no—
538Dic3—241no—
539Dic3C2×Dic3⋊C412yes—
540Dic3C2×Dic3⋊C412yes—
541C32#291111yescharacteristic, complemented, Sylow
542C23—31no—
543C23—31no—
544C23—34no—
545C23—121no—
546C23—121no—
547C23D3×#6711yescharacteristic
548C2×C4—22no—
549C2×C4—31no—
550C2×C4—31no—
551C2×C4—34no—
552C2×C4—32no—
553C2×C4—32no—
554C2×C4—32no—
555C2×C4—32no—
556C2×C4—34no—
557C2×C4—34no—
558C2×C4—42no—
559C2×C4—62no—
560C2×C4—61no—
561C2×C4—61no—
562C2×C4—122no—
563C2×C4—181no—
564C2×C4—181no—
565C2×C4—362no—
566C2×C4—362no—
567C2×C4D3×Dic612yes—
568C2×C4C4×D3212yes—
569C2×C4D3×#6711yescharacteristic
570C2×C4C22×D3211yescharacteristic
571C8—34no—
572C8—94no—
573C2×C3—22no—
574C2×C3—22no—
575C2×C3—21no—
576C2×C3—21no—
577C2×C3—21no—
578C2×C3—42no—
579C2×C3—62no—
580C2×C3—62no—
581C2×C3C2×D3×C4⋊C411yescharacteristic
582C2×C3#577311yescharacteristic
583C2×C3#577711yescharacteristic
584C2×C3C22×Dic3⋊C411yescharacteristic
585C2×C3#582211yescharacteristic
586C2×C3#582211yescharacteristic
587D3—22no—
588D3—22no—
589C22—21no—
590C22—21no—
591C22—32no—
592C22—32no—
593C22—61no—
594C22—61no—
595C22—61no—
596C22—61no—
597C22—124no—
598C22D3×Dic3⋊C412yes—
599C22C2×D3×#6711yescharacteristic
600C4—32no—
601C4—32no—
602C4—42no—
603C4—121no—
604C4—122no—
605C4—121no—
606C4—361no—
607C4—361no—
608C4D3×Dic3⋊C412yes—
609C4C2×D3×Dic611yescharacteristic
610C4C2×C4×D3211yescharacteristic
611C3—21no—
612C3#7920811yescharacteristic, complemented
613C3#8220711yescharacteristic, complemented
614C2—22no—
615C2—62no—
616C2—62no—
617C2C2×D3×Dic3⋊C411yescharacteristic
618C2#1059509511yescharacteristic
619C2#1059531711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radicalC23×C3×D3D4
cosocleC2×C32×C4C24
hypercenterC2×C4⋊C4D32
hypocenterC32#2911
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
4. #10592663C2semidirect
5. C3×#4964C2semidirect
6. #10591139C2semidirect
7. #10591130C2semidirect
8. #10590572C2semidirect
9. #10590571C2semidirect
10. #10590437C2semidirect
11. #10590436C2semidirect
36. D3×#208C4semidirect
38. #63635C22semidirect
39. #63634C22semidirect
40. C3×#808C22semidirect
41. C3×#807C22semidirect
42. #63576C22semidirect
43. #63575C22semidirect
44. #63574C22semidirect
45. #63573C22semidirect
64. #4964D3semidirect
88. #3748C2×C4semidirect
100. C3×#208C2×C4semidirect
108. #3711C2×C4semidirect
109. D3×C3⋊C8C2×C4semidirect
172. #808C2×D3semidirect
179. #807C2×D3semidirect
306. #208C4×D3semidirect
541. C32#2911semidirect
612. C3#79208semidirect
613. C3#82207semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8922
D3×#9262
C2×D3×#2082
#105926632
C3×#49642
#105911392
#105911302
#105905722
#105905712
#105904372
#105904362
#822073
#792083