Finite Group Databasebeta

← #11858515

Subgroups — #11858515

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
1C3×D3×#117C211yesmaximal, characteristic
2C2×#63841C211yesmaximal, characteristic
3C2×D3×#208C211yesmaximal, characteristic
4#10592694C211yesmaximal, characteristic, complemented
5C3×#4995C211yesmaximal, characteristic, complemented
6#10591139C211yesmaximal, characteristic, complemented
7#10591131C211yesmaximal, characteristic, complemented
8#10590581C212yesmaximal, complemented
9#10590580C212yesmaximal, complemented
10#10590572C212yesmaximal, complemented
11#10590571C212yesmaximal, complemented
12#82207—31nomaximal
13#79208—31nomaximal
14C22×C3×C4×D3C2211yescharacteristic
15C32×#117C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×#3748C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C3×#892C2211yescharacteristic
22C3×#892C2211yescharacteristic
23C3×D3×C4⋊C4C2211yescharacteristic
24C3×D3×C4⋊C4C2211yescharacteristic
25C3×D3×C22⋊C4—21no—
26C3×#877—21no—
27C3×#872—21no—
28C3×C42×D3—21no—
29C2×(C2×D3)⋊Dic3—21no—
30C2×Dic32—21no—
31#63841—21no—
32#63841—21no—
33#63841C2212yes—
34#63841C2212yes—
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×#117D311yescharacteristic
51C2×#892—31no—
52C3×#428—31no—
53#5121—31no—
54#4998—32no—
55#4998—32no—
56#4995—31no—
57#4995—31no—
58#4995—31no—
59#4995—31no—
60#4995—61no—
61#4995D311yescharacteristic, complemented
62#4964—31no—
63#4964—32no—
64#4964—32no—
65#4881—32no—
66#4880—32no—
67#4861—32no—
68#4860—32no—
69C23×C3×D3D411yescharacteristic
70C22×C32×C4C2311yescharacteristic
71C22×C3⋊Dic3—21no—
72C22×C3×Dic3—21no—
73C22×C3×Dic3D411yescharacteristic
74C2×C3×C4×D3—21no—
75C2×C3×C4×D3—21no—
76C2×C3×C4×D3C2×C414yes—
77C2×C3×C4×D3D411yescharacteristic
78C2×C3×C4×D3D411yescharacteristic
79C2×C3×C4×D3Q814yes—
80C2×C3×C4×D3C2311yescharacteristic
81C2×C3×C4×D3C2311yescharacteristic
82C32×C4⋊C4C2311yescharacteristic
83C32×C4⋊C4C2311yescharacteristic
84C32×C22⋊C4—21no—
85C32×C42—21no—
86C4⋊(C3⋊Dic3)—21no—
87C4⋊(C3⋊Dic3)C2312yes—
88#3748C2×C414yescomplemented
89C2×C3⋊(C3⋊C8)C2312yes—
90C3×#217—21no—
91C3×(C2×D3)⋊C4—21no—
92C3×(C2×D3)⋊C4—21no—
93C3×C4⋊Dic3—21no—
94C3×C4⋊Dic3C2311yescharacteristic
95C3×C4⋊Dic3C2311yescharacteristic
96C3×C4⋊Dic3C2312yes—
97C3×Dic3⋊C4—21no—
98C3×Dic3⋊C4—21no—
99C3×C4×Dic3—21no—
100C3×C4×Dic3—21no—
101C3×C4×Dic3—21no—
102C3×#208C2×C414yescomplemented
103C2×C3×C3⋊C8C2312yes—
104(C2×D3)⋊Dic3—22no—
105(C2×D3)⋊Dic3—22no—
106Dic32—22no—
107Dic32—22no—
108#3711C2×C418yescomplemented
109D3×C3⋊C8C2×C418yescomplemented
110#2911—91noSylow
111C23×C3×C4—31no—
112C22×C4×D3C2×D311yescharacteristic
113C2×C3×M16—31no—
114C3×#117—21no—
115C3×#117—31no—
116C3×#117—31no—
117C3×#117—31no—
118C3×#117—61no—
119C3×#117—61no—
120C3×#117C2×D311yescharacteristic
121C3×#117C2×D311yescharacteristic
122C2×C3×C4⋊C4—31no—
123C2×C3×C4⋊C4—31no—
124C2×C3×C4⋊C4—31no—
125C2×C3×C22⋊C4—61no—
126C2×C3×C42—61no—
127C2×#217—61no—
128C2×(C2×D3)⋊C4—61no—
129#926—32no—
130#926—32no—
131#926—61no—
132#926—61no—
133#926C2×D311yescharacteristic
134C2×C4⋊Dic3—31no—
135C2×C4⋊Dic3—31no—
136C2×C4⋊Dic3—61no—
137C2×C4⋊Dic3C2×D311yescharacteristic
138C2×C4×Dic3—61no—
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—32no—
151#892—32no—
152#892—61no—
153#892—61no—
154#892C2×D311yescharacteristic
155#892C2×D311yescharacteristic
156D3×C4⋊C4C2×D311yescharacteristic
157D3×C4⋊C4C2×D311yescharacteristic
158D3×C22⋊C4—21no—
159#877—21no—
160#872—21no—
161C42×D3—21no—
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—21no—
187C2×C32×C4—21no—
188C2×C32×C4C22×C412yes—
189C2×C32×C4C2×D411yescharacteristic
190C2×C32×C4C2×Q812yes—
191C2×C32×C4C2411yescharacteristic
192C2×C3⋊Dic3—22no—
193C2×C3⋊Dic3—42no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—21no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—42no—
198C2×C3×Dic3C4⋊C414yes—
199C2×C3×Dic3C2×D411yescharacteristic
200C2×C3×Dic3C2×D411yescharacteristic
201C3×C4×D3—42no—
202C3×C4×D3—42no—
203C3×C4×D3C4⋊C414yes—
204C3×C4×D3C4⋊C414yes—
205C3×C4×D3C22×C412yes—
206C3×C4×D3C22×C412yes—
207C3×C4×D3C2×Q812yes—
208C3×C4×D3C2×Q812yes—
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—31no—
226C22×C3×C4—34no—
227C22×C3×C4—31no—
228C22×C3×C4—31no—
229C22×C3×C4—34no—
230C22×C3×C4—31no—
231C22×C3×C4—31no—
232C22×C3×C4—61no—
233C22×C3×C4—61no—
234C22×C3×C4—61no—
235C22×C3×C4C22×D311yescharacteristic
236C22×C3×C4C22×D311yescharacteristic
237C22×Dic3—21no—
238C22×Dic3—61no—
239C22×Dic3—61no—
240C22×Dic3—121no—
241C22×Dic3#6711yescharacteristic
242C2×C4×D3—21no—
243C2×C4×D3—21no—
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—31no—
255C3×C4⋊C4—31no—
256C3×C4⋊C4—32no—
257C3×C4⋊C4—61no—
258C3×C4⋊C4—61no—
259C3×C4⋊C4—61no—
260C3×C4⋊C4C22×D311yescharacteristic
261C3×C4⋊C4C22×D311yescharacteristic
262C3×C4⋊C4C22×D311yescharacteristic
263C3×C4⋊C4C22×D311yescharacteristic
264C3×C22⋊C4—21no—
265C3×C22⋊C4—21no—
266C3×C22⋊C4—41no—
267C3×C22⋊C4—61no—
268C3×C22⋊C4—61no—
269C3×C22⋊C4—61no—
270C3×C42—21no—
271C3×C42—21no—
272C3×C42—41no—
273C3×C42—61no—
274C3×C42—61no—
275C3×C42—61no—
276#217—21no—
277#217—62no—
278#217—62no—
279(C2×D3)⋊C4—21no—
280(C2×D3)⋊C4—21no—
281(C2×D3)⋊C4—62no—
282(C2×D3)⋊C4—62no—
283C4⋊Dic3—21no—
284C4⋊Dic3—32no—
285C4⋊Dic3—32no—
286C4⋊Dic3—62no—
287C4⋊Dic3—61no—
288C4⋊Dic3—61no—
289C4⋊Dic3—121no—
290C4⋊Dic3C22×D311yescharacteristic
291C4⋊Dic3C22×D312yes—
292C4⋊Dic3C22×D311yescharacteristic
293Dic3⋊C4—21no—
294Dic3⋊C4—21no—
295C4×Dic3—21no—
296C4×Dic3—21no—
297C4×Dic3—21no—
298C4×Dic3—62no—
299C4×Dic3—62no—
300C4×Dic3—62no—
301C4×Dic3—62no—
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—41no—
326C32×C4—41no—
327C32×C4C2×C4⋊C412yes—
328C32×C4C23×C411yescharacteristic
329C32×C4C22×Q811yescharacteristic
330C3⋊Dic3—42no—
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—31no—
344#117—31no—
345#117—61no—
346#117—61no—
347#117—92no—
348#117—92no—
349#117—181no—
350#117—181no—
351#117D3211yescharacteristic
352C2×C4⋊C4—31no—
353C2×C4⋊C4—31no—
354C2×C4⋊C4—31no—
355C2×C4⋊C4—91no—
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—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—21no—
389C2×C3×C4—34no—
390C2×C3×C4—31no—
391C2×C3×C4—31no—
392C2×C3×C4—34no—
393C2×C3×C4—34no—
394C2×C3×C4—32no—
395C2×C3×C4—32no—
396C2×C3×C4—32no—
397C2×C3×C4—32no—
398C2×C3×C4—41no—
399C2×C3×C4—41no—
400C2×C3×C4—61no—
401C2×C3×C4—61no—
402C2×C3×C4—62no—
403C2×C3×C4—122no—
404C2×C3×C4—122no—
405C2×C3×C4—122no—
406C2×C3×C4C2×Dic612yes—
407C2×C3×C4C2×C4×D312yes—
408C2×C3×C4C2×C4×D312yes—
409C2×C3×C4D3×D411yescharacteristic
410C2×C3×C4D3×Q812yes—
411C2×C3×C4C2×#6711yescharacteristic
412C2×C3×C4C23×D311yescharacteristic
413C2×C3×C4C23×D311yescharacteristic
414C2×Dic3—22no—
415C2×Dic3—21no—
416C2×Dic3—21no—
417C2×Dic3—42no—
418C2×Dic3—62no—
419C2×Dic3—62no—
420C2×Dic3—122no—
421C2×Dic3—122no—
422C2×Dic3—122no—
423C2×Dic3—242no—
424C2×Dic3Dic3⋊C414yes—
425C2×Dic3C2×#6711yescharacteristic
426C2×Dic3C2×#6711yescharacteristic
427C4×D3—42no—
428C4×D3—42no—
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—31no—
448C22×C4—31no—
449C22×C4—31no—
450C22×C4—34no—
451C22×C4—34no—
452C22×C4—31no—
453C22×C4—31no—
454C22×C4—61no—
455C22×C4—61no—
456C22×C4—61no—
457C22×C4—181no—
458C22×C4C2×D3211yescharacteristic
459M16—34no—
460M16—98no—
461M16—94no—
462C2×C8—32no—
463C2×C8—98no—
464C2×C8—92no—
465C4⋊C4—32no—
466C4⋊C4—31no—
467C4⋊C4—31no—
468C4⋊C4—61no—
469C4⋊C4—61no—
470C4⋊C4—61no—
471C4⋊C4—92no—
472C4⋊C4—181no—
473C4⋊C4C2×D3211yescharacteristic
474C4⋊C4C2×D3211yescharacteristic
475C22⋊C4—21no—
476C22⋊C4—61no—
477C22⋊C4—61no—
478C22⋊C4—61no—
479C22⋊C4—182no—
480C22⋊C4—182no—
481C42—21no—
482C42—61no—
483C42—61no—
484C42—61no—
485C42—182no—
486C42—182no—
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—41no—
519C3×C4—41no—
520C3×C4—41no—
521C3×C4—41no—
522C3×C4—81no—
523C3×C4—81no—
524C3×C4—121no—
525C3×C4—121no—
526C3×C4—122no—
527C3×C4D3×C4⋊C412yes—
528C3×C4C2×Dic3⋊C412yes—
529C3×C4C22×Dic611yescharacteristic
530C3×C4C22×C4×D311yescharacteristic
531C3×C4C22×C4×D311yescharacteristic
532C3×C4C2×D3×Q811yescharacteristic
533Dic3—42no—
534Dic3—41no—
535Dic3—41no—
536Dic3—122no—
537Dic3—122no—
538Dic3—242no—
539Dic3C2×Dic3⋊C412yes—
540Dic3C2×Dic3⋊C412yes—
541C32#291111yescharacteristic, complemented, Sylow
542C23—31no—
543C23—31no—
544C23—34no—
545C23—121no—
546C23—121no—
547C23D3×#6711yescharacteristic
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—31no—
551C2×C4—31no—
552C2×C4—34no—
553C2×C4—32no—
554C2×C4—32no—
555C2×C4—32no—
556C2×C4—32no—
557C2×C4—34no—
558C2×C4—34no—
559C2×C4—61no—
560C2×C4—61no—
561C2×C4—62no—
562C2×C4—122no—
563C2×C4—122no—
564C2×C4—122no—
565C2×C4—182no—
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—41no—
603C4—41no—
604C4—121no—
605C4—122no—
606C4—121no—
607C4—362no—
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#1059546911yescharacteristic
619C2#1059547011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC23×C3×D3D4
cosocleC2×C32×C4C24
hypercenter#117D32
hypocenterC32#2911
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
4. #10592694C2semidirect
5. C3×#4995C2semidirect
6. #10591139C2semidirect
7. #10591131C2semidirect
8. #10590581C2semidirect
9. #10590580C2semidirect
10. #10590572C2semidirect
11. #10590571C2semidirect
36. D3×#208C4semidirect
38. #63635C22semidirect
39. #63634C22semidirect
40. C3×#808C22semidirect
41. C3×#807C22semidirect
42. #63576C22semidirect
43. #63575C22semidirect
44. #63574C22semidirect
45. #63573C22semidirect
61. #4995D3semidirect
88. #3748C2×C4semidirect
102. 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
C3×D3×#1172
C2×#638412
C2×D3×#2082
#105926942
C3×#49952
#105911392
#105911312
#105905812
#105905802
#105905722
#105905712
#822073
#792083