Finite Group Databasebeta

← #11787941

Subgroups — #11787941

Order 1152.

1227 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5486C211yesmaximal, characteristic, complemented
2C2×#63976C211yesmaximal, characteristic
3C3×#4955C211yesmaximal, characteristic, complemented
4#10591706C211yesmaximal, characteristic, complemented
5C2×#63580C211yesmaximal, characteristic, complemented
6#10589392C211yesmaximal, characteristic, complemented
7#10589186C211yesmaximal, characteristic, complemented
8#71654—31nomaximal
9#69499—31nomaximal
10C24×C3×D3C2211yescharacteristic
11C22×C3×#67C2211yescharacteristic
12C22×#625—21no—
13C2×C32×C22⋊C4C2211yescharacteristic
14C2×#3757C2211yescharacteristic
15C2×#3757C2211yescharacteristic
16C2×C3×#217C2211yescharacteristic
17C2×C3×#217C2211yescharacteristic
18C3×C4×#67—22no—
19C2×C3×(C2×D3)⋊C4—22no—
20C3×#67⋊C4—22no—
21C3×D3×C22⋊C4—21no—
22C3×#877—21no—
23#63976—22no—
24#63976C414yescomplemented
25C2×(C2×D3)⋊Dic3—21no—
26C2×(C2×D3)⋊Dic3—22no—
27#63580—22no—
28C3×#518—31no—
29C2×#953—31no—
30C2×#937—31no—
31#5486D311yescharacteristic, complemented
32C3×#379—31no—
33#5247—31no—
34C2×#834—31no—
35#4955—31no—
36#4955D311yescharacteristic, complemented
37C2×#806—31no—
38#4527—31no—
39#4526—31no—
40#4526—31no—
41#4526—31no—
42#4526—61no—
43C24×C32C2311yescharacteristic
44C23×C3×D3—21no—
45C23×C3×D3—21no—
46C23×C3×D3—21no—
47C23×C3×D3—21no—
48C23×C3×D3—21no—
49C23×C3×D3—21no—
50C23×C3×D3—44no—
51C23×C3×D3C2×C412yescomplemented
52C23×C3×D3D411yescharacteristic
53C22×C32×C4D412yescomplemented
54C22×C3⋊Dic3—21no—
55C22×C3⋊Dic3—21no—
56C2×C3×#67—21no—
57C2×C3×#67—21no—
58C2×C3×#67—21no—
59C2×C3×#67—21no—
60C2×C3×#67C2×C412yes—
61C2×C3×#67D412yes—
62C22×C3×Dic3—21no—
63C22×C3×Dic3D411yescharacteristic
64C22×C3×Dic3D412yescomplemented
65C2×C3×C4×D3—22no—
66C2×#625—24no—
67C2×#625—44no—
68C32×C22⋊C4—21no—
69C32×C22⋊C4—21no—
70#3757—21no—
71#3757—21no—
72#3757—21no—
73#3757C2×C412yescomplemented
74C3×#217—21no—
75C3×#217—21no—
76C3×#217—21no—
77C3×#217—21no—
78C3×(C2×D3)⋊C4—22no—
79C3×(C2×D3)⋊C4—44no—
80C3×Dic3⋊C4—22no—
81C3×C4×Dic3—22no—
82(C2×D3)⋊Dic3—24no—
83(C2×D3)⋊Dic3—44no—
84#1889—91noSylow
85C25×C3—31no—
86C24×D3C2×D311yescharacteristic
87C22×C3×D4—31no—
88C22×#67—61no—
89C22×#67—61no—
90C22×#67C2×D311yescharacteristic
91C3×C4×D4—62no—
92C3×C4×D4—62no—
93C3×#117—61no—
94C2×C3×C22⋊C4—21no—
95C2×C3×C22⋊C4—31no—
96C2×C3×C22⋊C4—31no—
97C2×C3×C22⋊C4—61no—
98C2×C3×C22⋊C4—62no—
99C2×C3×C22⋊C4C2×D311yescharacteristic
100C2×C3×C22⋊C4C2×D311yescharacteristic
101#953—34no—
102#953—62no—
103C2×#217—31no—
104C2×#217—31no—
105C2×#217—31no—
106C2×#217—31no—
107C2×#217—61no—
108C2×#217—61no—
109C2×#217—61no—
110C2×#217—62no—
111C2×#217C2×D311yescharacteristic
112C2×#217C2×D311yescharacteristic
113#937—34no—
114#937—62no—
115C4×#67—22no—
116C2×(C2×D3)⋊C4—22no—
117C2×(C2×D3)⋊C4—61no—
118C2×(C2×D3)⋊C4—62no—
119#67⋊C4—22no—
120D3×C22⋊C4—21no—
121#877—21no—
122#834—62no—
123#806—62no—
124C23×C32—42no—
125C23×C32C22×C411yescharacteristic
126C23×C32C2×D411yescharacteristic
127C23×C32C2×D411yescharacteristic
128C23×C32C2×D411yescharacteristic
129C23×C32C2×D411yescharacteristic
130C23×C32#4111yescharacteristic
131C23×C32#4111yescharacteristic
132C22×C3×D3—24no—
133C22×C3×D3—24no—
134C22×C3×D3—24no—
135C22×C3×D3—22no—
136C22×C3×D3—22no—
137C22×C3×D3—22no—
138C22×C3×D3—21no—
139C22×C3×D3—21no—
140C22×C3×D3—44no—
141C22×C3×D3—44no—
142C22×C3×D3—44no—
143C22×C3×D3—44no—
144C22×C3×D3—42no—
145C22×C3×D3—42no—
146C22×C3×D3—42no—
147C22×C3×D3—41no—
148C22×C3×D3—41no—
149C22×C3×D3—41no—
150C22×C3×D3—41no—
151C22×C3×D3—42no—
152C22×C3×D3C22⋊C412yescomplemented
153C2×C32×C4—22no—
154C2×C32×C4—42no—
155C2×C3⋊Dic3—22no—
156C2×C3⋊Dic3—41no—
157C2×C3⋊Dic3—42no—
158C2×C3⋊Dic3—42no—
159C3×#67—22no—
160C3×#67—22no—
161C3×#67—22no—
162C3×#67—22no—
163C2×C3×Dic3—21no—
164C2×C3×Dic3—21no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—42no—
167C2×C3×Dic3—42no—
168C2×C3×Dic3—41no—
169C2×C3×Dic3C22⋊C412yescomplemented
170C3×C4×D3—82no—
171#625—48no—
172C2×#120—91no—
173#518—31no—
174C2×#99—91no—
175#379—31no—
176#379—91no—
177#342—91no—
178#342—91no—
179C24×C3—21no—
180C24×C3—31no—
181C24×C3—32no—
182C24×C3—61no—
183C24×C3—61no—
184C24×C3—61no—
185C24×C3—61no—
186C24×C3—61no—
187C24×C3—61no—
188C24×C3—124no—
189C24×C3C22×D311yescharacteristic
190C24×C3C22×D311yescharacteristic
191C23×D3—21no—
192C23×D3—21no—
193C23×D3—21no—
194C23×D3—21no—
195C23×D3—21no—
196C23×D3—21no—
197C23×D3—44no—
198C23×D3C4×D312yescomplemented
199C23×D3#6711yescharacteristic
200C2×C3×D4—32no—
201C2×C3×D4—32no—
202C2×C3×D4—61no—
203C2×C3×D4—61no—
204C2×C3×D4—61no—
205C2×C3×D4—61no—
206C22×C3×C4—22no—
207C22×C3×C4—31no—
208C22×C3×C4—32no—
209C22×C3×C4—62no—
210C22×C3×C4—61no—
211C22×C3×C4#6712yescomplemented
212C22×C3×C4#6712yescomplemented
213C2×#67—21no—
214C2×#67—21no—
215C2×#67—21no—
216C2×#67—21no—
217C2×#67—64no—
218C2×#67—64no—
219C2×#67—124no—
220C2×#67—124no—
221C2×#67C4×D312yes—
222C2×#67D1212yes—
223C22×Dic3—21no—
224C22×Dic3—61no—
225C22×Dic3—61no—
226C22×Dic3—61no—
227C22×Dic3—61no—
228C22×Dic3—121no—
229C22×Dic3—121no—
230C22×Dic3#6711yescharacteristic
231C22×Dic3#6712yescomplemented
232C2×C4×D3—22no—
233C3×C4⋊C4—62no—
234C3×C22⋊C4—21no—
235C3×C22⋊C4—21no—
236C3×C22⋊C4—21no—
237C3×C22⋊C4—21no—
238C3×C22⋊C4—41no—
239C3×C22⋊C4—41no—
240C3×C22⋊C4—62no—
241C3×C22⋊C4—61no—
242C3×C22⋊C4—61no—
243C3×C22⋊C4—61no—
244C3×C22⋊C4—61no—
245C3×C22⋊C4—124no—
246C3×C42—62no—
247#217—21no—
248#217—21no—
249#217—21no—
250#217—21no—
251#217—32no—
252#217—32no—
253#217—62no—
254#217—61no—
255#217—61no—
256#217—64no—
257#217—62no—
258#217—61no—
259#217—61no—
260#217—61no—
261#217—61no—
262#217—121no—
263#217—121no—
264#217—124no—
265(C2×D3)⋊C4—22no—
266(C2×D3)⋊C4—44no—
267(C2×D3)⋊C4—64no—
268(C2×D3)⋊C4—124no—
269Dic3⋊C4—22no—
270C4×Dic3—22no—
271C22×C32—22no—
272C22×C32—22no—
273C22×C32—22no—
274C22×C32—41no—
275C22×C32—41no—
276C22×C32—41no—
277C22×C32—41no—
278C22×C32C2×C22⋊C411yescharacteristic
279C22×C32C4×D411yescharacteristic
280C22×C32C4×D411yescharacteristic
281C22×C32#12011yescharacteristic
282C22×C32#12111yescharacteristic
283C22×C32#12111yescharacteristic
284C22×C32#12311yescharacteristic
285C2×C3×D3—24no—
286C2×C3×D3—24no—
287C2×C3×D3—24no—
288C2×C3×D3—22no—
289C2×C3×D3—44no—
290C2×C3×D3—42no—
291C2×C3×D3—44no—
292C2×C3×D3—42no—
293C2×C3×D3—42no—
294C2×C3×D3—44no—
295C2×C3×D3—42no—
296C2×C3×D3—42no—
297C2×C3×D3—44no—
298C2×C3×D3—42no—
299C2×C3×D3—81no—
300C32×C4—42no—
301C3⋊Dic3—42no—
302C3⋊Dic3—81no—
303C3×Dic3—22no—
304C3×Dic3—42no—
305C3×Dic3—81no—
306C25—31no—
307C22×D4—31no—
308C22×D4—181no—
309#120—94no—
310#120—182no—
311C4×D4—62no—
312C4×D4—62no—
313#117—61no—
314C2×C22⋊C4—31no—
315C2×C22⋊C4—31no—
316C2×C22⋊C4—61no—
317C2×C22⋊C4—62no—
318C2×C22⋊C4—91no—
319C2×C22⋊C4—91no—
320C2×C22⋊C4—181no—
321C2×C22⋊C4—182no—
322C2×C22⋊C4D3211yescharacteristic
323#99—182no—
324C23×C3—21no—
325C23×C3—21no—
326C23×C3—21no—
327C23×C3—21no—
328C23×C3—21no—
329C23×C3—21no—
330C23×C3—21no—
331C23×C3—32no—
332C23×C3—42no—
333C23×C3—42no—
334C23×C3—64no—
335C23×C3—64no—
336C23×C3—64no—
337C23×C3—62no—
338C23×C3—62no—
339C23×C3—62no—
340C23×C3—61no—
341C23×C3—61no—
342C23×C3—82no—
343C23×C3—122no—
344C23×C3—122no—
345C23×C3—122no—
346C23×C3—122no—
347C23×C3—124no—
348C23×C3—124no—
349C23×C3—124no—
350C23×C3—124no—
351C23×C3—121no—
352C23×C3—121no—
353C23×C3—121no—
354C23×C3—121no—
355C23×C3C2×C4×D311yescharacteristic
356C23×C3C2×C4×D311yescharacteristic
357C23×C3C2×D1211yescharacteristic
358C23×C3#23511yescharacteristic
359C23×C3#23511yescharacteristic
360C23×C3#23511yescharacteristic
361C23×C3D3×D411yescharacteristic
362C23×C3D3×D411yescharacteristic
363C23×C3D3×D411yescharacteristic
364C23×C3#23711yescharacteristic
365C23×C3C2×#6711yescharacteristic
366C23×C3C2×#6711yescharacteristic
367C23×C3C2×#6711yescharacteristic
368C23×C3C2×#6711yescharacteristic
369C22×D3—24no—
370C22×D3—24no—
371C22×D3—24no—
372C22×D3—22no—
373C22×D3—22no—
374C22×D3—22no—
375C22×D3—21no—
376C22×D3—21no—
377C22×D3—44no—
378C22×D3—44no—
379C22×D3—44no—
380C22×D3—44no—
381C22×D3—42no—
382C22×D3—42no—
383C22×D3—42no—
384C22×D3—41no—
385C22×D3—41no—
386C22×D3—41no—
387C22×D3—41no—
388C22×D3—42no—
389C22×D3(C2×D3)⋊C412yescomplemented
390C3×D4—62no—
391C3×D4—62no—
392C3×D4—62no—
393C3×D4—62no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—32no—
397C2×C3×C4—42no—
398C2×C3×C4—42no—
399C2×C3×C4—42no—
400C2×C3×C4—61no—
401C2×C3×C4—61no—
402C2×C3×C4—62no—
403C2×C3×C4—82no—
404C2×C3×C4—122no—
405C2×C3×C4—122no—
406C2×C3×C4—121no—
407C2×C3×C4—242no—
408#67—22no—
409#67—22no—
410#67—22no—
411#67—22no—
412#67—128no—
413#67—128no—
414C2×Dic3—21no—
415C2×Dic3—21no—
416C2×Dic3—22no—
417C2×Dic3—42no—
418C2×Dic3—42no—
419C2×Dic3—41no—
420C2×Dic3—62no—
421C2×Dic3—62no—
422C2×Dic3—122no—
423C2×Dic3—122no—
424C2×Dic3—122no—
425C2×Dic3—122no—
426C2×Dic3—122no—
427C2×Dic3—122no—
428C2×Dic3—121no—
429C2×Dic3—121no—
430C2×Dic3—242no—
431C2×Dic3—242no—
432C2×Dic3(C2×D3)⋊C412yescomplemented
433C4×D3—82no—
434C2×C32—21no—
435C2×C32—21no—
436C2×C32—21no—
437C2×C32—21no—
438C2×C32—21no—
439C2×C32—21no—
440C2×C32#38611yescharacteristic
441C2×C32B(4,𝔽2)12yes—
442C3×D3—44no—
443C3×D3—42no—
444C24—31no—
445C24—32no—
446C24—61no—
447C24—61no—
448C24—61no—
449C24—61no—
450C24—61no—
451C24—61no—
452C24—124no—
453C24C2×D3211yescharacteristic
454C2×D4—32no—
455C2×D4—32no—
456C2×D4—61no—
457C2×D4—61no—
458C2×D4—61no—
459C2×D4—61no—
460C2×D4—184no—
461C2×D4—364no—
462C22×C4—31no—
463C22×C4—32no—
464C22×C4—62no—
465C22×C4—61no—
466C22×C4—181no—
467C22×C4—181no—
468C22×C4#62512yescomplemented
469C4⋊C4—62no—
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—62no—
473C22⋊C4—61no—
474C22⋊C4—61no—
475C22⋊C4—61no—
476C22⋊C4—61no—
477C22⋊C4—92no—
478C22⋊C4—124no—
479C22⋊C4—184no—
480C22⋊C4—181no—
481C22⋊C4—181no—
482C22⋊C4—181no—
483C22⋊C4—364no—
484C42—62no—
485C22×C3—22no—
486C22×C3—22no—
487C22×C3—22no—
488C22×C3—22no—
489C22×C3—22no—
490C22×C3—22no—
491C22×C3—21no—
492C22×C3—21no—
493C22×C3—21no—
494C22×C3—21no—
495C22×C3—21no—
496C22×C3—21no—
497C22×C3—21no—
498C22×C3—42no—
499C22×C3—42no—
500C22×C3—42no—
501C22×C3—41no—
502C22×C3—41no—
503C22×C3—41no—
504C22×C3—41no—
505C22×C3—41no—
506C22×C3—41no—
507C22×C3—41no—
508C22×C3—41no—
509C22×C3—64no—
510C22×C3—64no—
511C22×C3—64no—
512C22×C3—62no—
513C22×C3—81no—
514C22×C3—81no—
515C22×C3—81no—
516C22×C3—81no—
517C22×C3—122no—
518C22×C3—122no—
519C22×C3—124no—
520C22×C3—124no—
521C22×C3—124no—
522C22×C3—122no—
523C22×C3—122no—
524C22×C3—122no—
525C22×C3—124no—
526C22×C3—122no—
527C22×C3—241no—
528C22×C3D3×C22⋊C411yescharacteristic
529C22×C3#67⋊C411yescharacteristic
530C22×C3#88311yescharacteristic
531C22×C3#88411yescharacteristic
532C22×C3C2×(C2×D3)⋊C411yescharacteristic
533C22×C3C4×#6711yescharacteristic
534C22×C3C4×#6711yescharacteristic
535C22×C3C4×#6711yescharacteristic
536C22×C3#92911yescharacteristic
537C22×C3#93011yescharacteristic
538C22×C3#93011yescharacteristic
539C22×C3#93711yescharacteristic
540C22×C3#93811yescharacteristic
541C22×C3#95311yescharacteristic
542C2×D3—24no—
543C2×D3—24no—
544C2×D3—24no—
545C2×D3—22no—
546C2×D3—44no—
547C2×D3—42no—
548C2×D3—44no—
549C2×D3—42no—
550C2×D3—42no—
551C2×D3—44no—
552C2×D3—42no—
553C2×D3—42no—
554C2×D3—44no—
555C2×D3—42no—
556C2×D3—81no—
557C3×C4—42no—
558C3×C4—42no—
559C3×C4—62no—
560C3×C4—82no—
561C3×C4—122no—
562C3×C4—241no—
563Dic3—22no—
564Dic3—42no—
565Dic3—81no—
566Dic3—122no—
567Dic3—122no—
568Dic3—242no—
569Dic3—241no—
570Dic3—241no—
571Dic3—242no—
572C32#188911yescharacteristic, complemented, Sylow
573C23—32no—
574C23—42no—
575C23—64no—
576C23—64no—
577C23—64no—
578C23—62no—
579C23—62no—
580C23—62no—
581C23—61no—
582C23—61no—
583C23—122no—
584C23—122no—
585C23—122no—
586C23—122no—
587C23—124no—
588C23—124no—
589C23—124no—
590C23—124no—
591C23—121no—
592C23—121no—
593C23—121no—
594C23—121no—
595C23#379511yescharacteristic
596C23#379811yescharacteristic
597C23C4×D3211yescharacteristic
598C23D3×D1211yescharacteristic
599C23C2×#62511yescharacteristic
600C23D3×#6711yescharacteristic
601C23D3×#6711yescharacteristic
602D4—62no—
603D4—62no—
604D4—62no—
605D4—62no—
606D4—368no—
607C2×C4—22no—
608C2×C4—32no—
609C2×C4—42no—
610C2×C4—61no—
611C2×C4—61no—
612C2×C4—62no—
613C2×C4—122no—
614C2×C4—122no—
615C2×C4—121no—
616C2×C4—182no—
617C2×C4—242no—
618C2×C4—362no—
619C2×C4—362no—
620C2×C4—361no—
621C2×C3—21no—
622C2×C3—21no—
623C2×C3—21no—
624C2×C3—21no—
625C2×C3—21no—
626C2×C3—21no—
627C2×C3—21no—
628C2×C3—21no—
629C2×C3—21no—
630C2×C3—21no—
631C2×C3—21no—
632C2×C3—21no—
633C2×C3—22no—
634C2×C3—21no—
635C2×C3—41no—
636C2×C3—41no—
637C2×C3—41no—
638C2×C3—41no—
639C2×C3—41no—
640C2×C3—41no—
641C2×C3—122no—
642C2×C3—124no—
643C2×C3#495611yescharacteristic
644C2×C3#503212yes—
645C2×C3#521311yescharacteristic
646C2×C3#524412yes—
647D3—44no—
648D3—42no—
649C22—22no—
650C22—22no—
651C22—22no—
652C22—41no—
653C22—41no—
654C22—41no—
655C22—41no—
656C22—64no—
657C22—64no—
658C22—64no—
659C22—62no—
660C22—122no—
661C22—124no—
662C22—122no—
663C22—124no—
664C22—122no—
665C22—122no—
666C22—124no—
667C22—122no—
668C22—124no—
669C22—122no—
670C22—241no—
671C22#6387911yescharacteristic
672C22C4×#62511yescharacteristic
673C22#6390511yescharacteristic
674C22#6390611yescharacteristic
675C22#6390811yescharacteristic
676C22D3×(C2×D3)⋊C411yescharacteristic
677C22#6397611yescharacteristic
678C4—42no—
679C4—62no—
680C4—122no—
681C4—241no—
682C4—362no—
683C4—721no—
684C3—21no—
685C3#6949911yescharacteristic, complemented
686C3#7165411yescharacteristic, complemented
687C2—21no—
688C2—21no—
689C2—21no—
690C2—21no—
691C2—21no—
692C2—21no—
693C2—124no—
694C2—122no—
695C2#1059138111yescharacteristic
696C2#1059153012yes—
subgroupG/H
centerC22#63976
commutatorC23×C32C22×C4
FrattiniC24C2×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32#120
prime radicalC2×#63976C2
cosocleC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#1889
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#5486C2semidirect
3. C3×#4955C2semidirect
4. #10591706C2semidirect
5. C2×#63580C2semidirect
6. #10589392C2semidirect
7. #10589186C2semidirect
24. #63976C4semidirect
31. #5486D3semidirect
36. #4955D3semidirect
51. C23×C3×D3C2×C4semidirect
53. C22×C32×C4D4semidirect
64. C22×C3×Dic3D4semidirect
73. #3757C2×C4semidirect
152. C22×C3×D3C22⋊C4semidirect
169. C2×C3×Dic3C22⋊C4semidirect
198. C23×D3C4×D3semidirect
211. C22×C3×C4#67semidirect
212. C22×C3×C4#67semidirect
231. C22×Dic3#67semidirect
389. C22×D3(C2×D3)⋊C4semidirect
432. C2×Dic3(C2×D3)⋊C4semidirect
468. C22×C4#625semidirect
572. C32#1889semidirect
685. C3#69499semidirect
686. C3#71654semidirect

Maximal subgroups

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

subgroupindex
C3×#54862
C2×#639762
C3×#49552
#105917062
C2×#635802
#105893922
#105891862
#716543
#694993