Finite Group Databasebeta

← #11787945

Subgroups — #11787945

Order 1152.

1409 conjugacy classes of subgroups.

The subgroup lattice has 731 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#953C211yesmaximal, characteristic
2#10595506C211yesmaximal, characteristic, complemented
3#10592946C211yesmaximal, characteristic, complemented
4C3×#5247C211yesmaximal, characteristic, complemented
5C2×#63580C211yesmaximal, characteristic, complemented
6#10589187C211yesmaximal, characteristic, complemented
7#10589186C211yesmaximal, characteristic, complemented
8#71669—31nomaximal
9#69499—31nomaximal
10C25×C32C2211yescharacteristic
11C22×C3×#67—21no—
12C22×C3×#67C2211yescharacteristic
13C2×#3757—22no—
14C2×#3757C2211yescharacteristic
15C2×#3757C2211yescharacteristic
16C3×#953—22no—
17C3×#953C414yescomplemented
18C2×C3×#217—21no—
19C2×C3×#217—22no—
20C2×C3×#217C2211yescharacteristic
21C2×C3×#217C2211yescharacteristic
22C2×C3×#217C2211yescharacteristic
23#67⋊Dic3—22no—
24Dic3×#67—22no—
25D3×#217—21no—
26#63955—21no—
27#63580—22no—
28C2×C3×#120—31no—
29C2×#953D311yescharacteristic
30#5798—31no—
31#5486—31no—
32C3×#379—31no—
33#5247—31no—
34#5247—31no—
35#5247—61no—
36#5247D311yescharacteristic, complemented
37C2×#834—31no—
38C2×#806—31no—
39#4527—31no—
40#4527—31no—
41#4527—31no—
42#4526—31no—
43C24×C32—21no—
44C24×C32—21no—
45C24×C32—21no—
46C24×C32—21no—
47C24×C32—21no—
48C24×C32—21no—
49C24×C32—44no—
50C24×C32C2×C412yescomplemented
51C24×C32C2311yescharacteristic
52C23×C3×D3D411yescharacteristic
53C22×C3⋊Dic3—21no—
54C22×C3⋊Dic3D412yescomplemented
55C2×C3×#67—21no—
56C2×C3×#67—21no—
57C2×C3×#67—21no—
58C2×C3×#67—21no—
59C2×C3×#67—24no—
60C2×C3×#67—44no—
61C2×C3×#67C2×C412yes—
62C2×C3×#67D412yes—
63C22×C3×Dic3—21no—
64C22×C3×Dic3—21no—
65C22×C3×Dic3D411yescharacteristic
66C22×C3×Dic3D412yescomplemented
67C2×D3×Dic3—22no—
68#3757—21no—
69#3757—21no—
70#3757—21no—
71#3757—21no—
72#3757—44no—
73C3×#217—21no—
74C3×#217—21no—
75C3×#217—21no—
76C3×#217—24no—
77C3×#217—21no—
78C3×#217—21no—
79C3×#217—44no—
80C3×#217C2×C412yescomplemented
81Dic3⋊Dic3—22no—
82(C2×D3)⋊Dic3—22no—
83Dic32—22no—
84#1889—91noSylow
85C25×C3—21no—
86C25×C3C2×D311yescharacteristic
87C25×C3C2×D311yescharacteristic
88C22×C3×D4—31no—
89C22×C3×D4—61no—
90C22×#67—21no—
91C22×#67C2×D311yescharacteristic
92C3×#120—34no—
93C3×#120—62no—
94C2×C3×C22⋊C4—31no—
95C2×C3×C22⋊C4—31no—
96C2×C3×C22⋊C4—31no—
97C2×C3×C22⋊C4—61no—
98C2×C3×C22⋊C4—62no—
99#953—22no—
100#953Dic314yescomplemented
101C2×#217—21no—
102C2×#217—22no—
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×#217—62no—
112C2×#217—64no—
113C2×#217C2×D311yescharacteristic
114C2×#217C2×D311yescharacteristic
115C2×#217C2×D311yescharacteristic
116D4×Dic3—62no—
117D4×Dic3—62no—
118C4×#67—62no—
119#926—61no—
120#67⋊C4—62no—
121D3×C22⋊C4—61no—
122#877—61no—
123#834—62no—
124#806—62no—
125C23×C32—24no—
126C23×C32—22no—
127C23×C32—24no—
128C23×C32—24no—
129C23×C32—22no—
130C23×C32—22no—
131C23×C32—44no—
132C23×C32—42no—
133C23×C32—42no—
134C23×C32—44no—
135C23×C32—42no—
136C23×C32—42no—
137C23×C32—44no—
138C23×C32—44no—
139C23×C32—41no—
140C23×C32—41no—
141C23×C32—41no—
142C23×C32—41no—
143C23×C32C22×C411yescharacteristic
144C23×C32C2×D411yescharacteristic
145C23×C32C2×D411yescharacteristic
146C23×C32C2×D411yescharacteristic
147C23×C32C2×D411yescharacteristic
148C23×C32#4111yescharacteristic
149C23×C32#4111yescharacteristic
150C22×C3×D3—21no—
151C22×C3×D3—21no—
152C22×C3×D3—42no—
153C22×C3×D3C22⋊C412yescomplemented
154C2×C3⋊Dic3—22no—
155C2×C3⋊Dic3—42no—
156C2×C3⋊Dic3—42no—
157C2×C3⋊Dic3—41no—
158C3×#67—22no—
159C3×#67—22no—
160C3×#67—22no—
161C3×#67—22no—
162C3×#67—48no—
163C2×C3×Dic3—21no—
164C2×C3×Dic3—21no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—42no—
168C2×C3×Dic3—42no—
169C2×C3×Dic3—42no—
170C2×C3×Dic3—41no—
171C2×C3×Dic3C22⋊C412yescomplemented
172D3×Dic3—82no—
173C2×#120—31no—
174#518—91no—
175C2×#99—91no—
176#379—31no—
177#379—91no—
178#342—91no—
179#342—91no—
180C24×C3—22no—
181C24×C3—21no—
182C24×C3—21no—
183C24×C3—21no—
184C24×C3—21no—
185C24×C3—21no—
186C24×C3—21no—
187C24×C3—22no—
188C24×C3—21no—
189C24×C3—21no—
190C24×C3—21no—
191C24×C3—21no—
192C24×C3—21no—
193C24×C3—21no—
194C24×C3—22no—
195C24×C3—21no—
196C24×C3—31no—
197C24×C3—41no—
198C24×C3—41no—
199C24×C3—41no—
200C24×C3—41no—
201C24×C3—44no—
202C24×C3—44no—
203C24×C3—48no—
204C24×C3C4×D312yescomplemented
205C24×C3C2×Dic312yescomplemented
206C24×C3C22×D311yescharacteristic
207C24×C3C22×D311yescharacteristic
208C23×D3#6711yescharacteristic
209C2×C3×D4—32no—
210C2×C3×D4—32no—
211C2×C3×D4—61no—
212C2×C3×D4—61no—
213C2×C3×D4—61no—
214C2×C3×D4—61no—
215C2×C3×D4—64no—
216C2×C3×D4—124no—
217C22×C3×C4—31no—
218C22×C3×C4—32no—
219C22×C3×C4—61no—
220C22×C3×C4—61no—
221C2×#67—21no—
222C2×#67—21no—
223C2×#67—21no—
224C2×#67—21no—
225C2×#67—24no—
226C2×#67—44no—
227C2×#67C2×Dic312yes—
228C2×#67#6712yes—
229C22×Dic3—21no—
230C22×Dic3—21no—
231C22×Dic3—32no—
232C22×Dic3—32no—
233C22×Dic3—62no—
234C22×Dic3—62no—
235C22×Dic3—62no—
236C22×Dic3—61no—
237C22×Dic3—61no—
238C22×Dic3#6711yescharacteristic
239C22×Dic3#6712yescomplemented
240C2×C4×D3—62no—
241C3×C22⋊C4—32no—
242C3×C22⋊C4—64no—
243C3×C22⋊C4—61no—
244C3×C22⋊C4—61no—
245C3×C22⋊C4—61no—
246C3×C22⋊C4—61no—
247C3×C22⋊C4—61no—
248C3×C22⋊C4—124no—
249#217—21no—
250#217—21no—
251#217—21no—
252#217—24no—
253#217—21no—
254#217—21no—
255#217—44no—
256#217—62no—
257#217—61no—
258#217—61no—
259#217—61no—
260#217—61no—
261#217—61no—
262#217—61no—
263#217—61no—
264#217—61no—
265#217—121no—
266#217—121no—
267#217—121no—
268#217—121no—
269#217—124no—
270#217—124no—
271#217—128no—
272#217C2×Dic312yescomplemented
273(C2×D3)⋊C4—62no—
274C4⋊Dic3—62no—
275Dic3⋊C4—62no—
276C4×Dic3—62no—
277C4×Dic3—62no—
278C22×C32—22no—
279C22×C32—24no—
280C22×C32—22no—
281C22×C32—22no—
282C22×C32—24no—
283C22×C32—24no—
284C22×C32—41no—
285C22×C32—41no—
286C22×C32—41no—
287C22×C32—41no—
288C22×C32—44no—
289C22×C32—42no—
290C22×C32—42no—
291C22×C32—44no—
292C22×C32—44no—
293C22×C32—42no—
294C22×C32—42no—
295C22×C32—44no—
296C22×C32C2×C22⋊C411yescharacteristic
297C22×C32C4×D411yescharacteristic
298C22×C32C4×D411yescharacteristic
299C22×C32#12011yescharacteristic
300C22×C32#12111yescharacteristic
301C22×C32#12111yescharacteristic
302C22×C32#12311yescharacteristic
303C2×C3×D3—22no—
304C2×C3×D3—42no—
305C2×C3×D3—42no—
306C2×C3×D3—81no—
307C3⋊Dic3—42no—
308C3⋊Dic3—81no—
309C3×Dic3—22no—
310C3×Dic3—42no—
311C3×Dic3—42no—
312C3×Dic3—81no—
313C25D3211yescharacteristic
314C22×D4—31no—
315C22×D4—61no—
316#120—34no—
317#120—62no—
318C4×D4—182no—
319C4×D4—182no—
320#117—181no—
321C2×C22⋊C4—31no—
322C2×C22⋊C4—31no—
323C2×C22⋊C4—31no—
324C2×C22⋊C4—61no—
325C2×C22⋊C4—62no—
326C2×C22⋊C4—91no—
327C2×C22⋊C4—91no—
328C2×C22⋊C4—181no—
329C2×C22⋊C4—182no—
330#99—182no—
331C23×C3—24no—
332C23×C3—28no—
333C23×C3—24no—
334C23×C3—24no—
335C23×C3—24no—
336C23×C3—24no—
337C23×C3—24no—
338C23×C3—24no—
339C23×C3—22no—
340C23×C3—22no—
341C23×C3—22no—
342C23×C3—22no—
343C23×C3—22no—
344C23×C3—22no—
345C23×C3—21no—
346C23×C3—21no—
347C23×C3—21no—
348C23×C3—21no—
349C23×C3—21no—
350C23×C3—21no—
351C23×C3—21no—
352C23×C3—32no—
353C23×C3—42no—
354C23×C3—42no—
355C23×C3—44no—
356C23×C3—44no—
357C23×C3—44no—
358C23×C3—44no—
359C23×C3—42no—
360C23×C3—42no—
361C23×C3—48no—
362C23×C3—44no—
363C23×C3—44no—
364C23×C3—42no—
365C23×C3—42no—
366C23×C3—42no—
367C23×C3—42no—
368C23×C3—42no—
369C23×C3—42no—
370C23×C3—44no—
371C23×C3—44no—
372C23×C3—44no—
373C23×C3—44no—
374C23×C3—44no—
375C23×C3—44no—
376C23×C3—48no—
377C23×C3—42no—
378C23×C3—42no—
379C23×C3—42no—
380C23×C3—42no—
381C23×C3—44no—
382C23×C3—44no—
383C23×C3—48no—
384C23×C3—48no—
385C23×C3—41no—
386C23×C3—41no—
387C23×C3—41no—
388C23×C3—41no—
389C23×C3—41no—
390C23×C3—41no—
391C23×C3—41no—
392C23×C3—41no—
393C23×C3—61no—
394C23×C3—61no—
395C23×C3—122no—
396C23×C3C2×C4×D311yescharacteristic
397C23×C3#23511yescharacteristic
398C23×C3D3×D411yescharacteristic
399C23×C3D3×D411yescharacteristic
400C23×C3D3×D411yescharacteristic
401C23×C3D3×D411yescharacteristic
402C23×C3D3×D411yescharacteristic
403C23×C3#23711yescharacteristic
404C23×C3#23711yescharacteristic
405C23×C3#23711yescharacteristic
406C23×C3C22×Dic311yescharacteristic
407C23×C3C2×#6711yescharacteristic
408C23×C3C2×#6711yescharacteristic
409C23×C3C2×#6711yescharacteristic
410C22×D3—21no—
411C22×D3—21no—
412C22×D3—42no—
413C22×D3#21712yescomplemented
414C3×D4—62no—
415C3×D4—62no—
416C3×D4—62no—
417C3×D4—62no—
418C3×D4—128no—
419C2×C3×C4—32no—
420C2×C3×C4—61no—
421C2×C3×C4—61no—
422C2×C3×C4—62no—
423C2×C3×C4—62no—
424C2×C3×C4—122no—
425C2×C3×C4—122no—
426C2×C3×C4—122no—
427C2×C3×C4—121no—
428#67—22no—
429#67—22no—
430#67—22no—
431#67—22no—
432#67—48no—
433C2×Dic3—21no—
434C2×Dic3—21no—
435C2×Dic3—22no—
436C2×Dic3—22no—
437C2×Dic3—42no—
438C2×Dic3—42no—
439C2×Dic3—42no—
440C2×Dic3—41no—
441C2×Dic3—62no—
442C2×Dic3—62no—
443C2×Dic3—122no—
444C2×Dic3—122no—
445C2×Dic3—122no—
446C2×Dic3—124no—
447C2×Dic3—124no—
448C2×Dic3—122no—
449C2×Dic3—122no—
450C2×Dic3—122no—
451C2×Dic3—121no—
452C2×Dic3—121no—
453C2×Dic3—242no—
454C2×Dic3#21712yescomplemented
455C4×D3—242no—
456C2×C32—21no—
457C2×C32—21no—
458C2×C32—21no—
459C2×C32—21no—
460C2×C32—21no—
461C2×C32—21no—
462C2×C32—44no—
463C2×C32#38611yescharacteristic
464C2×C32B(4,𝔽2)12yes—
465C3×D3—42no—
466C24—21no—
467C24—21no—
468C24—21no—
469C24—21no—
470C24—21no—
471C24—21no—
472C24—31no—
473C24—44no—
474C24D3×Dic312yescomplemented
475C24C2×D3211yescharacteristic
476C2×D4—32no—
477C2×D4—32no—
478C2×D4—61no—
479C2×D4—61no—
480C2×D4—61no—
481C2×D4—61no—
482C2×D4—64no—
483C2×D4—124no—
484C22×C4—31no—
485C22×C4—32no—
486C22×C4—61no—
487C22×C4—61no—
488C22×C4—92no—
489C22×C4—182no—
490C22×C4—181no—
491C4⋊C4—182no—
492C22⋊C4—32no—
493C22⋊C4—64no—
494C22⋊C4—61no—
495C22⋊C4—61no—
496C22⋊C4—61no—
497C22⋊C4—61no—
498C22⋊C4—61no—
499C22⋊C4—124no—
500C22⋊C4—182no—
501C22⋊C4—181no—
502C22⋊C4—181no—
503C22⋊C4—181no—
504C22⋊C4—181no—
505C22⋊C4—364no—
506C42—182no—
507C22×C3—24no—
508C22×C3—22no—
509C22×C3—22no—
510C22×C3—22no—
511C22×C3—22no—
512C22×C3—22no—
513C22×C3—22no—
514C22×C3—24no—
515C22×C3—24no—
516C22×C3—28no—
517C22×C3—24no—
518C22×C3—24no—
519C22×C3—24no—
520C22×C3—24no—
521C22×C3—21no—
522C22×C3—21no—
523C22×C3—21no—
524C22×C3—21no—
525C22×C3—21no—
526C22×C3—21no—
527C22×C3—21no—
528C22×C3—42no—
529C22×C3—42no—
530C22×C3—44no—
531C22×C3—44no—
532C22×C3—41no—
533C22×C3—41no—
534C22×C3—41no—
535C22×C3—41no—
536C22×C3—41no—
537C22×C3—41no—
538C22×C3—41no—
539C22×C3—41no—
540C22×C3—42no—
541C22×C3—42no—
542C22×C3—42no—
543C22×C3—42no—
544C22×C3—48no—
545C22×C3—44no—
546C22×C3—44no—
547C22×C3—44no—
548C22×C3—42no—
549C22×C3—42no—
550C22×C3—42no—
551C22×C3—44no—
552C22×C3—42no—
553C22×C3—44no—
554C22×C3—44no—
555C22×C3—44no—
556C22×C3—42no—
557C22×C3—42no—
558C22×C3—44no—
559C22×C3—48no—
560C22×C3—44no—
561C22×C3—44no—
562C22×C3—48no—
563C22×C3—48no—
564C22×C3—42no—
565C22×C3—42no—
566C22×C3—44no—
567C22×C3—44no—
568C22×C3—62no—
569C22×C3—122no—
570C22×C3—122no—
571C22×C3—241no—
572C22×C3D3×C22⋊C411yescharacteristic
573C22×C3#67⋊C411yescharacteristic
574C22×C3#88311yescharacteristic
575C22×C3#88411yescharacteristic
576C22×C3C4×#6711yescharacteristic
577C22×C3D4×Dic311yescharacteristic
578C22×C3D4×Dic311yescharacteristic
579C22×C3#93511yescharacteristic
580C22×C3#93711yescharacteristic
581C22×C3#93711yescharacteristic
582C22×C3#93811yescharacteristic
583C22×C3#93911yescharacteristic
584C22×C3#93911yescharacteristic
585C22×C3C2×#21711yescharacteristic
586C2×D3—22no—
587C2×D3—42no—
588C2×D3—42no—
589C2×D3—81no—
590C3×C4—62no—
591C3×C4—122no—
592C3×C4—122no—
593C3×C4—241no—
594Dic3—22no—
595Dic3—42no—
596Dic3—42no—
597Dic3—81no—
598Dic3—122no—
599Dic3—122no—
600Dic3—242no—
601Dic3—242no—
602Dic3—241no—
603Dic3—241no—
604C32#188911yescharacteristic, complemented, Sylow
605C23—24no—
606C23—24no—
607C23—24no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—32no—
612C23—44no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—44no—
618C23—44no—
619C23—44no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—61no—
625C23—61no—
626C23—122no—
627C23C2×D3×Dic311yescharacteristic
628C23#380411yescharacteristic
629C23#380511yescharacteristic
630C23D3×#6711yescharacteristic
631C23D3×#6711yescharacteristic
632C23D3×#6711yescharacteristic
633C23#381111yescharacteristic
634D4—62no—
635D4—62no—
636D4—62no—
637D4—62no—
638D4—128no—
639C2×C4—32no—
640C2×C4—61no—
641C2×C4—61no—
642C2×C4—62no—
643C2×C4—62no—
644C2×C4—122no—
645C2×C4—122no—
646C2×C4—122no—
647C2×C4—121no—
648C2×C4—182no—
649C2×C4—362no—
650C2×C4—362no—
651C2×C4—361no—
652C2×C4—722no—
653C2×C3—22no—
654C2×C3—22no—
655C2×C3—21no—
656C2×C3—21no—
657C2×C3—21no—
658C2×C3—21no—
659C2×C3—21no—
660C2×C3—21no—
661C2×C3—21no—
662C2×C3—21no—
663C2×C3—21no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—21no—
667C2×C3—21no—
668C2×C3—22no—
669C2×C3—41no—
670C2×C3—41no—
671C2×C3—41no—
672C2×C3—41no—
673C2×C3—48no—
674C2×C3—44no—
675C2×C3—44no—
676C2×C3—122no—
677C2×C3#495611yescharacteristic
678C2×C3#503212yes—
679C2×C3#503212yes—
680C2×C3#522011yescharacteristic
681D3—42no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—24no—
686C22—24no—
687C22—24no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—42no—
693C22—44no—
694C22—44no—
695C22—42no—
696C22—42no—
697C22—44no—
698C22—42no—
699C22—44no—
700C22—62no—
701C22—122no—
702C22—122no—
703C22—241no—
704C22D3×#21711yescharacteristic
705C22#6396911yescharacteristic
706C22#6397011yescharacteristic
707C22#6397111yescharacteristic
708C22Dic3×#6711yescharacteristic
709C22#67⋊Dic311yescharacteristic
710C22#6398311yescharacteristic
711C4—62no—
712C4—122no—
713C4—122no—
714C4—241no—
715C4—362no—
716C4—721no—
717C3—21no—
718C3#6949911yescharacteristic, complemented
719C3#7166911yescharacteristic, complemented
720C2—21no—
721C2—21no—
722C2—21no—
723C2—21no—
724C2—21no—
725C2—21no—
726C2—44no—
727C2—122no—
728C2#1059172111yescharacteristic
729C2#1059172512yes—
subgroupG/H
centerC22#63983
commutatorC23×C32C22×C4
FrattiniC24C2×D32
FittingC25×C32C22
socleC22×C32#120
prime radicalC2×C3×#953C2
cosocleC24×C32C23
hypercenterC25D32
hypocenterC32#1889
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C25

Complements

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

NH ≅ G/Ntype
2. #10595506C2semidirect
3. #10592946C2semidirect
4. C3×#5247C2semidirect
5. C2×#63580C2semidirect
6. #10589187C2semidirect
7. #10589186C2semidirect
17. C3×#953C4semidirect
36. #5247D3semidirect
50. C24×C32C2×C4semidirect
54. C22×C3⋊Dic3D4semidirect
66. C22×C3×Dic3D4semidirect
80. C3×#217C2×C4semidirect
100. #953Dic3semidirect
153. C22×C3×D3C22⋊C4semidirect
171. C2×C3×Dic3C22⋊C4semidirect
204. C24×C3C4×D3semidirect
205. C24×C3C2×Dic3semidirect
239. C22×Dic3#67semidirect
272. #217C2×Dic3semidirect
413. C22×D3#217semidirect
454. C2×Dic3#217semidirect
474. C24D3×Dic3semidirect
604. C32#1889semidirect
718. C3#69499semidirect
719. C3#71669semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9532
#105955062
#105929462
C3×#52472
C2×#635802
#105891872
#105891862
#716693
#694993