Finite Group Databasebeta

← #11866155

Subgroups — #11866155

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×#64120C211yesmaximal, characteristic, complemented
2C2×D8×C3⋊D3C211yesmaximal, characteristic, complemented
3#10596186C211yesmaximal, characteristic, complemented
4#10596016C211yesmaximal, characteristic, complemented
5C32×#459C211yesmaximal, characteristic, complemented
6#10592852C211yesmaximal, characteristic, complemented
7#10592849C211yesmaximal, characteristic, complemented
8#10592771C211yesmaximal, characteristic, complemented
9#10592715C211yesmaximal, characteristic, complemented
10#10592543C211yesmaximal, characteristic, complemented
11#10592538C211yesmaximal, characteristic, complemented
12#10592486C211yesmaximal, characteristic, complemented
13#10592485C211yesmaximal, characteristic, complemented
14#10592471C211yesmaximal, characteristic, complemented
15#10592469C211yesmaximal, characteristic, complemented
16#80334—34nomaximal
17C2×#3830C2211yescharacteristic
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×D4×C3⋊D3C2211yescharacteristic
20C2×C32×D8C2211yescharacteristic
21C2×C32×D8C2211yescharacteristic, complemented
22C32×#127C2211yescharacteristic, complemented
23C32×C4×D4C2211yescharacteristic, complemented
24#64149C2211yescharacteristic, complemented
25#64148—21no—
26#64148—21no—
27#64146—21no—
28#64146—21no—
29#64145C2211yescharacteristic, complemented
30D4×C3⋊Dic3C2211yescharacteristic, complemented
31C2×#3754C2211yescharacteristic, complemented
32C2×#3753C2211yescharacteristic
33C2×#3753C2211yescharacteristic
34C2×#3753C2211yescharacteristic, complemented
35C4×#638—21no—
36C2×#3752—21no—
37#64120—24no—
38D8×C3⋊D3—24no—
39C2×#3745C2211yescharacteristic
40C2×#3744C2211yescharacteristic, complemented
41C2×#3743C2211yescharacteristic
42C2×C8×C3⋊D3C2211yescharacteristic
43#64102C2211yescharacteristic, complemented
44#64101C2211yescharacteristic
45#64090—21no—
46C22⋊C4×C3⋊D3—21no—
47#64084C2211yescharacteristic, complemented
48C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
49#64081C2211yescharacteristic
50C32×C4⋊C8C2211yescharacteristic, complemented
51C32×#102C2211yescharacteristic, complemented
52C32×#102C2211yescharacteristic, complemented
53#63659C2211yescharacteristic, complemented
54#63659C2211yescharacteristic, complemented
55#63648C2211yescharacteristic, complemented
56#63643C2211yescharacteristic, complemented
57#63641C2211yescharacteristic, complemented
58#63641C2211yescharacteristic, complemented
59#63637C2211yescharacteristic, complemented
60#63636C2211yescharacteristic, complemented
61C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
62C2×#911—34no—
63C2×D3×D8—34no—
64#5715—34no—
65#5545—34no—
66C3×#459D314yescomplemented
67#5153—34no—
68#5150—34no—
69#5072—34no—
70#5016—34no—
71#4844—34no—
72#4839—34no—
73#4787—34no—
74#4786—34no—
75#4772—34no—
76#4770—34no—
77C23×C3⋊D3—21no—
78C23×C3⋊D3—21no—
79C2×C32×D4—21no—
80C2×C32×D4—21no—
81C2×C32×D4C2311yescharacteristic
82C2×C32×D4C2311yescharacteristic
83C2×C32×D4C2311yescharacteristic
84C22×C32×C4—21no—
85C2×#638—21no—
86C2×#638—21no—
87C2×#638—21no—
88C2×#638—21no—
89C2×#638—21no—
90C22×C3⋊Dic3—21no—
91C22×C3⋊Dic3—21no—
92#3830—22no—
93#3830—22no—
94D4×C3⋊D3—22no—
95D4×C3⋊D3—22no—
96D4×C3⋊D3—22no—
97D4×C3⋊D3D414yescomplemented
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3—21no—
101C2×C4×C3⋊D3—21no—
102C2×C4×C3⋊D3C2311yescharacteristic
103C2×#634C2311yescharacteristic
104C32×D8—22no—
105C32×D8—22no—
106C2×C32×C8C2311yescharacteristic
107C2×C32×C8C2311yescharacteristic
108C32×C4⋊C4C2311yescharacteristic
109C32×C22⋊C4—21no—
110C32×C42C2311yescharacteristic
111#3757—21no—
112#3757—21no—
113#3757—21no—
114#3754—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#3744—22no—
134#3743—22no—
135C8×C3⋊D3—22no—
136#3041—91noSylow
137C2×#237—34no—
138C2×D3×D4—34no—
139C2×D3×D4—34no—
140C2×C3×D8C2×D314yes—
141C2×C3×D8C2×D314yescomplemented
142C3×#127C2×D314yescomplemented
143C3×C4×D4C2×D314yescomplemented
144#940—34no—
145#939—64no—
146#939—64no—
147#937—64no—
148#937—64no—
149#936—34no—
150D4×Dic3—34no—
151C2×#214—34no—
152C2×#213—34no—
153C2×#213—34no—
154C2×#213—34no—
155C4×#67—64no—
156C2×(C2×D3)⋊C4—64no—
157#911—616no—
158D3×D8—616no—
159C2×D24—34no—
160C2×#204—34no—
161C2×ΓL(1,𝔽25)—34no—
162C2×D3×C8—34no—
163#893—34no—
164#892—34no—
165#67⋊C4—64no—
166D3×C22⋊C4—64no—
167#875—34no—
168C4×D12—34no—
169#872—34no—
170C3×C4⋊C8C2×D314yescomplemented
171C3×#102C2×D314yescomplemented
172C3×#102C2×D314yescomplemented
173#832—34no—
174#832—34no—
175#821—34no—
176#816—34no—
177Dic3⋊C8—34no—
178Dic3⋊C8—34no—
179#810—34no—
180#809—34no—
181C4⋊(C3⋊C8)—34no—
182C23×C32—21no—
183C23×C32—21no—
184C23×C32—21no—
185C22×C3⋊D3—21no—
186C22×C3⋊D3—24no—
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×D4—21no—
195C32×D4—21no—
196C32×D4—21no—
197C32×D4—21no—
198C32×D4—21no—
199C32×D4—81no—
200C32×D4—81no—
201C32×D4C2×D412yes—
202C2×C32×C4—21no—
203C2×C32×C4—81no—
204C2×C32×C4C2×D411yescharacteristic
205C2×C32×C4C2×D411yescharacteristic
206C2×C32×C4C2411yescharacteristic
207#638—24no—
208#638—42no—
209#638—42no—
210#638—81no—
211#638—81no—
212C2×C3⋊Dic3—21no—
213C2×C3⋊Dic3—21no—
214C2×C3⋊Dic3—42no—
215C2×C3⋊Dic3—81no—
216C2×C3⋊Dic3C2×D411yescharacteristic
217C2×C3⋊Dic3C2×D411yescharacteristic
218C2×C3⋊Dic3C2×D411yescharacteristic
219C4⋊(C3⋊D3)—21no—
220C4⋊(C3⋊D3)—21no—
221C4⋊(C3⋊D3)—21no—
222C4⋊(C3⋊D3)C2×D412yes—
223C4×C3⋊D3—81no—
224C4×C3⋊D3—81no—
225C4×C3⋊D3C2×D412yes—
226C4×C3⋊D3#4112yes—
227#634—21no—
228#634—21no—
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#463—91no—
241#459—91no—
242#459—91no—
243#459—91no—
244#459C3⋊D311yescharacteristic, complemented
245#424—91no—
246#418—91no—
247#416—91no—
248C23×D3—64no—
249C23×D3—64no—
250C2×C3×D4—24no—
251C2×C3×D4—24no—
252C2×C3×D4C22×D314yes—
253C2×C3×D4C22×D314yes—
254C2×C3×D4C22×D314yes—
255C22×C3×C4—24no—
256C2×#67—64no—
257C2×#67—64no—
258C2×#67—64no—
259C2×#67—64no—
260C2×#67—64no—
261C22×Dic3—64no—
262C22×Dic3—64no—
263#237—68no—
264#237—68no—
265D3×D4—316no—
266D3×D4—68no—
267D3×D4—68no—
268D3×D4—68no—
269C2×D12—34no—
270C2×D12—34no—
271C2×C4×D3—34no—
272C2×C4×D3—64no—
273C2×C4×D3—64no—
274C2×Dic6—34no—
275C3×D8—28no—
276C3×D8—28no—
277C2×C3×C8C22×D314yes—
278C2×C3×C8C22×D314yes—
279C3×C4⋊C4C22×D314yes—
280C3×C22⋊C4—24no—
281C3×C42C22×D314yes—
282#217—64no—
283#217—64no—
284#217—64no—
285#214—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—
304#204—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×C32—41no—
314C22×C32—41no—
315C22×C32—41no—
316C22×C32C22×D411yescharacteristic
317C2×C3⋊D3—21no—
318C2×C3⋊D3—21no—
319C2×C3⋊D3—22no—
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×C4C22×D411yescharacteristic
332C32×C4C2×#4111yescharacteristic
333C3⋊Dic3—21no—
334C3⋊Dic3—21no—
335C3⋊Dic3—41no—
336C3⋊Dic3—41no—
337C3⋊Dic3#12112yes—
338C2×#41—91no—
339C22×D4—91no—
340C22×D4—91no—
341AGL(1,ℤ/8)—184no—
342C2×SD16—91no—
343C2×SD16—91no—
344C2×D8—91no—
345C2×D8—91no—
346C2×D8—91no—
347C2×D8—91no—
348C2×D8—184no—
349C2×D8C2×C3⋊D311yescharacteristic
350C2×D8C2×C3⋊D311yescharacteristic, complemented
351C2×M16—91no—
352C22×C8—91no—
353#127—91no—
354#127C2×C3⋊D311yescharacteristic, complemented
355#124—91no—
356#124—91no—
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#103—91no—
377#102—91no—
378#102—91no—
379#102—91no—
380#102—91no—
381#102C2×C3⋊D311yescharacteristic, complemented
382#102C2×C3⋊D311yescharacteristic, complemented
383C23×C3—24no—
384C23×C3—24no—
385C23×C3—24no—
386C22×D3—34no—
387C22×D3—616no—
388C22×D3—64no—
389C22×D3—64no—
390C22×D3—128no—
391C22×D3—244no—
392C22×D3—244no—
393C22×D3—244no—
394C22×D3—244no—
395C3×D4—24no—
396C3×D4—24no—
397C3×D4—24no—
398C3×D4—24no—
399C3×D4—24no—
400C3×D4—84no—
401C3×D4—84no—
402C3×D4D3×D418yes—
403C2×C3×C4—24no—
404C2×C3×C4—84no—
405C2×C3×C4D3×D414yes—
406C2×C3×C4D3×D414yes—
407C2×C3×C4C23×D314yes—
408#67—616no—
409#67—128no—
410#67—128no—
411#67—244no—
412#67—244no—
413C2×Dic3—34no—
414C2×Dic3—34no—
415C2×Dic3—34no—
416C2×Dic3—64no—
417C2×Dic3—64no—
418C2×Dic3—128no—
419C2×Dic3—244no—
420D12—38no—
421D12—64no—
422D12—64no—
423D12—64no—
424C4×D3—38no—
425C4×D3—38no—
426C4×D3—244no—
427C4×D3—244no—
428Dic6—64no—
429Dic6—64no—
430C3×C8—24no—
431C3×C8—24no—
432C3⋊C8—64no—
433C3⋊C8—64no—
434C2×C32—42no—
435C2×C32—81no—
436C2×C32—81no—
437C2×C32C2×#12111yescharacteristic
438C2×C32#57611yescharacteristic
439C2×C32#57611yescharacteristic
440C3⋊D3—22no—
441C3⋊D3—42no—
442C3⋊D3—81no—
443C24—181no—
444C24—181no—
445#41—182no—
446#41—182no—
447C2×Q8—91no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—94no—
451C2×D4—91no—
452C2×D4—91no—
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×D4C22×C3⋊D311yescharacteristic
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—182no—
471SD16—182no—
472D8—22no—
473D8—22no—
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—91no—
490C22⋊C4—91no—
491C22⋊C4—181no—
492C22⋊C4—181no—
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×C3—44no—
509C22×C3—44no—
510C22×C3—44no—
511C22×C3C2×D3×D414yes—
512C2×D3—38no—
513C2×D3—64no—
514C2×D3—64no—
515C2×D3—68no—
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×C4C2×D3×D414yes—
527C3×C4D3×#4114yes—
528Dic3—38no—
529Dic3—64no—
530Dic3—64no—
531Dic3—124no—
532Dic3—124no—
533C32#304111yescharacteristic, complemented, Sylow
534C23—21no—
535C23—21no—
536C23—21no—
537C23—91no—
538C23—184no—
539C23—181no—
540C23—181no—
541C23—362no—
542C23—721no—
543C23—721no—
544C23—721no—
545C23—721no—
546Q8—181no—
547Q8—181no—
548D4—21no—
549D4—21no—
550D4—21no—
551D4—21no—
552D4—21no—
553D4—81no—
554D4—81no—
555D4—92no—
556D4—184no—
557D4—181no—
558D4—181no—
559D4—181no—
560D4—362no—
561D4—362no—
562D4—721no—
563D4—721no—
564D4D4×C3⋊D312yes—
565C2×C4—21no—
566C2×C4—81no—
567C2×C4—91no—
568C2×C4—92no—
569C2×C4—92no—
570C2×C4—91no—
571C2×C4—91no—
572C2×C4—181no—
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×C3—84no—
588C2×C3D3×#12114yes—
589C2×C3#575714yes—
590C2×C3#577414yes—
591D3—68no—
592D3—128no—
593D3—244no—
594C22—22no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—92no—
604C22—181no—
605C22—181no—
606C22—182no—
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—92no—
619C4—181no—
620C4—181no—
621C4—361no—
622C4—361no—
623C4C2×D4×C3⋊D311yescharacteristic
624C4#41×C3⋊D311yescharacteristic
625C3#8033414yescomplemented
626C2—42no—
627C2—81no—
628C2—81no—
629C2—182no—
630C2—362no—
631C2—721no—
632C2C3⋊D3×#12111yescharacteristic
633C2#1059622811yescharacteristic
634C2#1059624511yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#459C2
socleC22×C32C22×D4
hypercenter#459C3⋊D3
hypocenterC32#3041
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#64120C2semidirect
2. C2×D8×C3⋊D3C2semidirect
3. #10596186C2semidirect
4. #10596016C2semidirect
5. C32×#459C2semidirect
6. #10592852C2semidirect
7. #10592849C2semidirect
8. #10592771C2semidirect
9. #10592715C2semidirect
10. #10592543C2semidirect
11. #10592538C2semidirect
12. #10592486C2semidirect
13. #10592485C2semidirect
14. #10592471C2semidirect
15. #10592469C2semidirect
21. C2×C32×D8C22semidirect
22. C32×#127C22semidirect
23. C32×C4×D4C22semidirect
24. #64149C22semidirect
29. #64145C22semidirect
30. D4×C3⋊Dic3C22semidirect
31. C2×#3754C22semidirect
34. C2×#3753C22semidirect
40. C2×#3744C22semidirect
43. #64102C22semidirect
47. #64084C22semidirect
48. C4×C4⋊(C3⋊D3)C22semidirect
50. C32×C4⋊C8C22semidirect
51. C32×#102C22semidirect
52. C32×#102C22semidirect
53. #63659C22semidirect
54. #63659C22semidirect
55. #63648C22semidirect
56. #63643C22semidirect
57. #63641C22semidirect
58. #63641C22semidirect
59. #63637C22semidirect
60. #63636C22semidirect
61. C4⋊(C3⋊(C3⋊C8))C22semidirect
66. C3×#459D3semidirect
97. D4×C3⋊D3D4semidirect
141. C2×C3×D8C2×D3semidirect
142. C3×#127C2×D3semidirect
143. C3×C4×D4C2×D3semidirect
170. C3×C4⋊C8C2×D3semidirect
171. C3×#102C2×D3semidirect
172. C3×#102C2×D3semidirect
244. #459C3⋊D3semidirect
350. C2×D8C2×C3⋊D3semidirect
354. #127C2×C3⋊D3semidirect
366. C4×D4C2×C3⋊D3semidirect
374. C4⋊C8C2×C3⋊D3semidirect
381. #102C2×C3⋊D3semidirect
382. #102C2×C3⋊D3semidirect
533. C32#3041semidirect
625. C3#80334semidirect

Maximal subgroups

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

subgroupindex
C2×#641202
C2×D8×C3⋊D32
#105961862
#105960162
C32×#4592
#105928522
#105928492
#105927712
#105927152
#105925432
#105925382
#105924862
#105924852
#105924712
#105924692
#803343