Finite Group Databasebeta

← #11866164

Subgroups — #11866164

Order 1152.

1578 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64123C211yesmaximal, characteristic, complemented
2C2×D8×C3⋊D3C211yesmaximal, characteristic, complemented
3#10596145C211yesmaximal, characteristic, complemented
4#10596016C211yesmaximal, characteristic, complemented
5C32×#463C211yesmaximal, characteristic, complemented
6#10592864C211yesmaximal, characteristic, complemented
7#10592849C211yesmaximal, characteristic, complemented
8#10592756C211yesmaximal, characteristic, complemented
9#10592714C211yesmaximal, characteristic, complemented
10#10592542C211yesmaximal, characteristic, complemented
11#10592538C211yesmaximal, characteristic, complemented
12#10592518C211yesmaximal, characteristic, complemented
13#10592503C211yesmaximal, characteristic, complemented
14#10592485C211yesmaximal, characteristic, complemented
15#10592469C211yesmaximal, characteristic, complemented
16#80536—34nomaximal
17C2×#3832C2211yescharacteristic
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×D4×C3⋊D3C2211yescharacteristic
20C2×C32×SD16C2211yescharacteristic, complemented
21C2×C32×D8C2211yescharacteristic
22C32×#124C2211yescharacteristic, complemented
23C32×C4×D4C2211yescharacteristic, complemented
24#64156C2211yescharacteristic, complemented
25C2×#3755C2211yescharacteristic, complemented
26#64149C2211yescharacteristic, complemented
27D4×C3⋊Dic3C2211yescharacteristic, complemented
28C2×#3753C2211yescharacteristic
29C2×#3753C2211yescharacteristic
30C2×#3753C2211yescharacteristic, complemented
31C4×#638—21no—
32C2×#3752—21no—
33#64123—24no—
34D8×C3⋊D3—24no—
35C2×#3745C2211yescharacteristic
36C2×#3745C2211yescharacteristic, complemented
37C2×#3743C2211yescharacteristic
38C2×C8×C3⋊D3C2211yescharacteristic
39#64102C2211yescharacteristic, complemented
40#64101C2211yescharacteristic
41#64093—21no—
42#64093—21no—
43#64091—21no—
44#64091—21no—
45#64090—21no—
46C22⋊C4×C3⋊D3—21no—
47#64083C2211yescharacteristic, complemented
48C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
49#64081C2211yescharacteristic
50C32×C4⋊C8C2211yescharacteristic, complemented
51C32×#103C2211yescharacteristic, complemented
52C32×#102C2211yescharacteristic, complemented
53#63662C2211yescharacteristic, complemented
54#63659C2211yescharacteristic, complemented
55#63648C2211yescharacteristic, complemented
56#63648C2211yescharacteristic, complemented
57#63641C2211yescharacteristic, complemented
58#63641C2211yescharacteristic, complemented
59#63636C2211yescharacteristic, complemented
60#63636C2211yescharacteristic, complemented
61C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
62C2×#914—34no—
63C2×D3×D8—34no—
64#5674—34no—
65#5545—34no—
66C3×#463D314yescomplemented
67#5165—34no—
68#5150—34no—
69#5057—34no—
70#5015—34no—
71#4843—34no—
72#4839—34no—
73#4819—34no—
74#4804—34no—
75#4786—34no—
76#4770—34no—
77C23×C3⋊D3—21no—
78C23×C3⋊D3—21no—
79C2×C32×Q8C2311yescharacteristic
80C2×C32×D4C2311yescharacteristic
81C2×C32×D4C2311yescharacteristic
82C22×C32×C4—21no—
83C2×#638—21no—
84C2×#638—21no—
85C2×#638—21no—
86C2×#638—21no—
87C22×C3⋊Dic3—21no—
88#3832—22no—
89#3832—22no—
90D4×C3⋊D3—22no—
91D4×C3⋊D3—22no—
92D4×C3⋊D3—22no—
93D4×C3⋊D3D414yescomplemented
94C2×C4⋊(C3⋊D3)—21no—
95C2×C4⋊(C3⋊D3)—21no—
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3—21no—
101C2×C4×C3⋊D3—21no—
102C2×C4×C3⋊D3—21no—
103C2×C4×C3⋊D3C2311yescharacteristic
104C32×SD16—22no—
105C32×D8—22no—
106C2×C32×C8C2311yescharacteristic
107C2×C32×C8C2311yescharacteristic
108C32×C4⋊C4C2311yescharacteristic
109C32×C22⋊C4—21no—
110C32×C22⋊C4—21no—
111C32×C22⋊C4—21no—
112C32×C42C2311yescharacteristic
113#3757—21no—
114#3755—22no—
115#3753—22no—
116#3753—22no—
117#3753—22no—
118#3752—21no—
119#3752—21no—
120#3752—21no—
121#3752—21no—
122#3752—21no—
123#3752D411yescharacteristic
124#3752D411yescharacteristic
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126#3750D411yescharacteristic
127#3750D411yescharacteristic
128C4×C3⋊Dic3—21no—
129C4×C3⋊Dic3C2311yescharacteristic
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132#3745—22no—
133#3745—22no—
134#3743—22no—
135C8×C3⋊D3—22no—
136#3041—91noSylow
137C2×#239—34no—
138C2×D3×D4—34no—
139C2×D3×D4—34no—
140C2×C3×SD16C2×D314yescomplemented
141C2×C3×D8C2×D314yes—
142C3×#124C2×D314yescomplemented
143C3×C4×D4C2×D314yescomplemented
144#947—34no—
145C2×#215—34no—
146#940—34no—
147D4×Dic3—34no—
148C2×#213—34no—
149C2×#213—34no—
150C2×#213—34no—
151C4×#67—64no—
152C2×(C2×D3)⋊C4—64no—
153#914—616no—
154D3×D8—616no—
155C2×D24—34no—
156C2×D24—34no—
157C2×ΓL(1,𝔽25)—34no—
158C2×D3×C8—34no—
159#893—34no—
160#892—34no—
161#884—64no—
162#884—64no—
163#882—64no—
164#882—64no—
165#67⋊C4—64no—
166D3×C22⋊C4—64no—
167#874—34no—
168C4×D12—34no—
169#872—34no—
170C3×C4⋊C8C2×D314yescomplemented
171C3×#103C2×D314yescomplemented
172C3×#102C2×D314yescomplemented
173#835—34no—
174#832—34no—
175#821—34no—
176#821—34no—
177Dic3⋊C8—34no—
178Dic3⋊C8—34no—
179#809—34no—
180#809—34no—
181C4⋊(C3⋊C8)—34no—
182C23×C32—21no—
183C23×C32—21no—
184C22×C3⋊D3—21no—
185C22×C3⋊D3—24no—
186C22×C3⋊D3—21no—
187C22×C3⋊D3—21no—
188C22×C3⋊D3—42no—
189C22×C3⋊D3—81no—
190C22×C3⋊D3—81no—
191C22×C3⋊D3—81no—
192C22×C3⋊D3—81no—
193C22×C3⋊D3C2×D411yescharacteristic
194C32×Q8—21no—
195C32×Q8—21no—
196C32×D4—21no—
197C32×D4—21no—
198C32×D4—21no—
199C32×D4C2×D412yes—
200C2×C32×C4—21no—
201C2×C32×C4—21no—
202C2×C32×C4—81no—
203C2×C32×C4C2×D411yescharacteristic
204C2×C32×C4C2×D411yescharacteristic
205C2×C32×C4C2411yescharacteristic
206#638—24no—
207#638—42no—
208#638—81no—
209#638—81no—
210C2×C3⋊Dic3—21no—
211C2×C3⋊Dic3—81no—
212C2×C3⋊Dic3C2×D411yescharacteristic
213C2×C3⋊Dic3C2×D411yescharacteristic
214C2×C3⋊Dic3C2×D411yescharacteristic
215C4⋊(C3⋊D3)—21no—
216C4⋊(C3⋊D3)—21no—
217C4⋊(C3⋊D3)—21no—
218C4⋊(C3⋊D3)—21no—
219C4⋊(C3⋊D3)—21no—
220C4⋊(C3⋊D3)—42no—
221C4⋊(C3⋊D3)—81no—
222C4⋊(C3⋊D3)—81no—
223C4⋊(C3⋊D3)C2×D412yes—
224C4×C3⋊D3—42no—
225C4×C3⋊D3—81no—
226C4×C3⋊D3—81no—
227C4×C3⋊D3C2×D412yes—
228C4×C3⋊D3#4112yes—
229C32×C8—21no—
230C32×C8—21no—
231C3⋊(C3⋊C8)—21no—
232C3⋊(C3⋊C8)—21no—
233C2×AGL(1,ℤ/8)—91no—
234C22×D8—91no—
235#535—91no—
236#518—91no—
237#463—91no—
238#463—91no—
239#463—91no—
240#463C3⋊D311yescharacteristic, complemented
241#459—91no—
242#459—91no—
243#459—91no—
244#459—91no—
245#424—91no—
246#418—91no—
247#416—91no—
248C23×D3—64no—
249C23×D3—64no—
250C2×C3×Q8C22×D314yes—
251C2×C3×D4C22×D314yes—
252C2×C3×D4C22×D314yes—
253C22×C3×C4—24no—
254C2×#67—64no—
255C2×#67—64no—
256C2×#67—64no—
257C2×#67—64no—
258C22×Dic3—64no—
259#239—68no—
260#239—68no—
261D3×D4—316no—
262D3×D4—68no—
263D3×D4—68no—
264D3×D4—68no—
265C2×D12—34no—
266C2×D12—34no—
267C2×D12—34no—
268C2×D12—64no—
269C2×D12—64no—
270C2×D12—64no—
271C2×C4×D3—34no—
272C2×C4×D3—64no—
273C2×C4×D3—64no—
274C2×C4×D3—64no—
275C3×SD16—28no—
276C3×D8—28no—
277C2×C3×C8C22×D314yes—
278C2×C3×C8C22×D314yes—
279C3×C4⋊C4C22×D314yes—
280C3×C22⋊C4—24no—
281C3×C22⋊C4—24no—
282C3×C22⋊C4—24no—
283C3×C42C22×D314yes—
284#217—64no—
285#215—68no—
286#213—68no—
287#213—68no—
288#213—68no—
289(C2×D3)⋊C4—34no—
290(C2×D3)⋊C4—34no—
291(C2×D3)⋊C4—64no—
292(C2×D3)⋊C4—64no—
293(C2×D3)⋊C4—64no—
294(C2×D3)⋊C4—64no—
295(C2×D3)⋊C4—64no—
296C4⋊Dic3—34no—
297Dic3⋊C4—34no—
298Dic3⋊C4—34no—
299C4×Dic3—34no—
300C4×Dic3—64no—
301C2×C3⋊C8—34no—
302C2×C3⋊C8—34no—
303D24—68no—
304D24—68no—
305ΓL(1,𝔽25)—68no—
306D3×C8—68no—
307C22×C32—22no—
308C22×C32—41no—
309C22×C32—41no—
310C22×C32—41no—
311C22×C32—41no—
312C22×C32—41no—
313C22×C32C22×D411yescharacteristic
314C2×C3⋊D3—21no—
315C2×C3⋊D3—21no—
316C2×C3⋊D3—22no—
317C2×C3⋊D3—41no—
318C2×C3⋊D3—41no—
319C2×C3⋊D3—41no—
320C2×C3⋊D3—41no—
321C2×C3⋊D3—41no—
322C2×C3⋊D3—41no—
323C2×C3⋊D3—41no—
324C2×C3⋊D3—41no—
325C2×C3⋊D3—84no—
326C2×C3⋊D3—84no—
327C2×C3⋊D3#12112yes—
328C32×C4—21no—
329C32×C4—21no—
330C32×C4—41no—
331C32×C4—41no—
332C32×C4C22×D411yescharacteristic
333C32×C4C2×#4111yescharacteristic
334C3⋊Dic3—21no—
335C3⋊Dic3—21no—
336C3⋊Dic3—41no—
337C3⋊Dic3#12112yes—
338C2×#41—91no—
339C22×D4—91no—
340C22×D4—91no—
341AGL(1,ℤ/8)—184no—
342C2×SD16—91no—
343C2×SD16C2×C3⋊D311yescharacteristic, complemented
344C2×D8—91no—
345C2×D8—91no—
346C2×D8—91no—
347C2×D8—91no—
348C2×D8—91no—
349C2×D8—184no—
350C2×D8C2×C3⋊D311yescharacteristic
351C2×M16—91no—
352C22×C8—91no—
353#127—91no—
354#127—91no—
355#124—91no—
356#124C2×C3⋊D311yescharacteristic, complemented
357#121—181no—
358#121—181no—
359#120—181no—
360#120—181no—
361C4×D4—91no—
362C4×D4—91no—
363C4×D4—91no—
364C4×D4—181no—
365C4×D4—181no—
366C4×D4C2×C3⋊D311yescharacteristic, complemented
367#117—91no—
368#117—91no—
369C2×C22⋊C4—181no—
370C2×C22⋊C4—181no—
371C4⋊C8—91no—
372C4⋊C8—91no—
373C4⋊C8—91no—
374C4⋊C8C2×C3⋊D311yescharacteristic, complemented
375#103—91no—
376#103C2×C3⋊D311yescharacteristic, complemented
377#102—91no—
378#102—91no—
379#102—91no—
380#102—91no—
381#102—91no—
382#102C2×C3⋊D311yescharacteristic, complemented
383C23×C3—24no—
384C23×C3—24no—
385C22×D3—34no—
386C22×D3—616no—
387C22×D3—64no—
388C22×D3—64no—
389C22×D3—64no—
390C22×D3—128no—
391C22×D3—244no—
392C22×D3—244no—
393C22×D3—244no—
394C22×D3—244no—
395C3×Q8—24no—
396C3×Q8—24no—
397C3×D4—24no—
398C3×D4—24no—
399C3×D4—24no—
400C3×D4D3×D418yes—
401C2×C3×C4—24no—
402C2×C3×C4—24no—
403C2×C3×C4—84no—
404C2×C3×C4D3×D414yes—
405C2×C3×C4D3×D414yes—
406C2×C3×C4C23×D314yes—
407#67—616no—
408#67—128no—
409#67—244no—
410#67—244no—
411C2×Dic3—34no—
412C2×Dic3—34no—
413C2×Dic3—34no—
414C2×Dic3—64no—
415C2×Dic3—244no—
416D12—38no—
417D12—64no—
418D12—64no—
419D12—64no—
420D12—64no—
421D12—64no—
422D12—128no—
423D12—244no—
424D12—244no—
425C4×D3—38no—
426C4×D3—38no—
427C4×D3—128no—
428C4×D3—244no—
429C4×D3—244no—
430C3×C8—24no—
431C3×C8—24no—
432C3⋊C8—64no—
433C3⋊C8—64no—
434C2×C32—42no—
435C2×C32—81no—
436C2×C32C2×#12111yescharacteristic
437C2×C32#57611yescharacteristic
438C2×C32#57611yescharacteristic
439C3⋊D3—22no—
440C3⋊D3—42no—
441C3⋊D3—81no—
442C3⋊D3—81no—
443C24—181no—
444C24—181no—
445#41—182no—
446#41—182no—
447C2×Q8C22×C3⋊D311yescharacteristic
448C2×D4—94no—
449C2×D4—91no—
450C2×D4—91no—
451C2×D4—91no—
452C2×D4—181no—
453C2×D4—182no—
454C2×D4—182no—
455C2×D4—182no—
456C2×D4—181no—
457C2×D4—181no—
458C2×D4—181no—
459C2×D4—181no—
460C2×D4—181no—
461C2×D4—181no—
462C2×D4C22×C3⋊D311yescharacteristic
463C2×D4C22×C3⋊D311yescharacteristic
464C22×C4—21no—
465C22×C4—91no—
466C22×C4—181no—
467C22×C4—181no—
468C22×C4—181no—
469C22×C4—181no—
470SD16—22no—
471SD16—182no—
472D8—22no—
473D8—182no—
474D8—182no—
475D8—182no—
476D8—182no—
477D8—182no—
478M16—182no—
479C2×C8—91no—
480C2×C8—91no—
481C2×C8—182no—
482C2×C8C22×C3⋊D311yescharacteristic
483C2×C8C22×C3⋊D311yescharacteristic
484C4⋊C4—91no—
485C4⋊C4—91no—
486C4⋊C4—91no—
487C4⋊C4C22×C3⋊D311yescharacteristic
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—21no—
491C22⋊C4—91no—
492C22⋊C4—91no—
493C22⋊C4—181no—
494C22⋊C4—181no—
495C22⋊C4—181no—
496C22⋊C4—181no—
497C22⋊C4—181no—
498C22⋊C4—181no—
499C42—91no—
500C42—181no—
501C42C22×C3⋊D311yescharacteristic
502C22×C3—28no—
503C22×C3—44no—
504C22×C3—44no—
505C22×C3—44no—
506C22×C3—44no—
507C22×C3—44no—
508C22×C3C2×D3×D414yes—
509C2×D3—38no—
510C2×D3—64no—
511C2×D3—64no—
512C2×D3—68no—
513C2×D3—124no—
514C2×D3—124no—
515C2×D3—124no—
516C2×D3—124no—
517C2×D3—124no—
518C2×D3—124no—
519C2×D3—124no—
520C2×D3—124no—
521C2×D3—2416no—
522C2×D3—2416no—
523C3×C4—24no—
524C3×C4—24no—
525C3×C4—44no—
526C3×C4—44no—
527C3×C4C2×D3×D414yes—
528C3×C4D3×#4114yes—
529Dic3—38no—
530Dic3—64no—
531Dic3—64no—
532Dic3—124no—
533C32#304111yescharacteristic, complemented, Sylow
534C23—21no—
535C23—21no—
536C23—91no—
537C23—184no—
538C23—181no—
539C23—181no—
540C23—181no—
541C23—362no—
542C23—721no—
543C23—721no—
544C23—721no—
545C23—721no—
546Q8—21no—
547Q8—21no—
548D4—21no—
549D4—21no—
550D4—21no—
551D4—92no—
552D4—184no—
553D4—181no—
554D4—181no—
555D4—181no—
556D4—181no—
557D4—181no—
558D4—362no—
559D4—362no—
560D4—721no—
561D4—721no—
562D4—721no—
563D4—721no—
564D4D4×C3⋊D312yes—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—81no—
568C2×C4—91no—
569C2×C4—92no—
570C2×C4—92no—
571C2×C4—91no—
572C2×C4—91no—
573C2×C4—181no—
574C2×C4—362no—
575C2×C4—721no—
576C2×C4—721no—
577C2×C4—721no—
578C2×C4D4×C3⋊D311yescharacteristic
579C2×C4D4×C3⋊D311yescharacteristic
580C2×C4C23×C3⋊D311yescharacteristic
581C8—21no—
582C8—21no—
583C8—181no—
584C8—181no—
585C2×C3—48no—
586C2×C3—84no—
587C2×C3D3×#12114yes—
588C2×C3#576914yes—
589C2×C3#577414yes—
590D3—68no—
591D3—128no—
592D3—244no—
593D3—244no—
594C22—22no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—92no—
601C22—181no—
602C22—181no—
603C22—182no—
604C22—361no—
605C22—361no—
606C22—361no—
607C22—361no—
608C22—361no—
609C22—361no—
610C22—361no—
611C22—361no—
612C22—724no—
613C22—724no—
614C22C2×D4×C3⋊D311yescharacteristic
615C4—21no—
616C4—21no—
617C4—41no—
618C4—41no—
619C4—92no—
620C4—181no—
621C4—181no—
622C4—361no—
623C4C2×D4×C3⋊D311yescharacteristic
624C4#41×C3⋊D311yescharacteristic
625C3#8053614yescomplemented
626C2—42no—
627C2—81no—
628C2—182no—
629C2—362no—
630C2—721no—
631C2—721no—
632C2C3⋊D3×#12111yescharacteristic
633C2#1059624011yescharacteristic
634C2#1059624511yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#463C2
socleC22×C32C22×D4
hypercenter#463C3⋊D3
hypocenterC32#3041
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#64123C2semidirect
2. C2×D8×C3⋊D3C2semidirect
3. #10596145C2semidirect
4. #10596016C2semidirect
5. C32×#463C2semidirect
6. #10592864C2semidirect
7. #10592849C2semidirect
8. #10592756C2semidirect
9. #10592714C2semidirect
10. #10592542C2semidirect
11. #10592538C2semidirect
12. #10592518C2semidirect
13. #10592503C2semidirect
14. #10592485C2semidirect
15. #10592469C2semidirect
20. C2×C32×SD16C22semidirect
22. C32×#124C22semidirect
23. C32×C4×D4C22semidirect
24. #64156C22semidirect
25. C2×#3755C22semidirect
26. #64149C22semidirect
27. D4×C3⋊Dic3C22semidirect
30. C2×#3753C22semidirect
36. C2×#3745C22semidirect
39. #64102C22semidirect
47. #64083C22semidirect
48. C4×C4⋊(C3⋊D3)C22semidirect
50. C32×C4⋊C8C22semidirect
51. C32×#103C22semidirect
52. C32×#102C22semidirect
53. #63662C22semidirect
54. #63659C22semidirect
55. #63648C22semidirect
56. #63648C22semidirect
57. #63641C22semidirect
58. #63641C22semidirect
59. #63636C22semidirect
60. #63636C22semidirect
61. C4⋊(C3⋊(C3⋊C8))C22semidirect
66. C3×#463D3semidirect
93. D4×C3⋊D3D4semidirect
140. C2×C3×SD16C2×D3semidirect
142. C3×#124C2×D3semidirect
143. C3×C4×D4C2×D3semidirect
170. C3×C4⋊C8C2×D3semidirect
171. C3×#103C2×D3semidirect
172. C3×#102C2×D3semidirect
240. #463C3⋊D3semidirect
343. C2×SD16C2×C3⋊D3semidirect
356. #124C2×C3⋊D3semidirect
366. C4×D4C2×C3⋊D3semidirect
374. C4⋊C8C2×C3⋊D3semidirect
376. #103C2×C3⋊D3semidirect
382. #102C2×C3⋊D3semidirect
533. C32#3041semidirect
625. C3#80536semidirect

Maximal subgroups

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

subgroupindex
C2×#641232
C2×D8×C3⋊D32
#105961452
#105960162
C32×#4632
#105928642
#105928492
#105927562
#105927142
#105925422
#105925382
#105925182
#105925032
#105924852
#105924692
#805363