Finite Group Databasebeta

← #11885758

Subgroups — #11885758

Order 1152.

1307 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D24C211yesmaximal, characteristic, complemented
2#10595069C212yesmaximal, complemented
3C2×#63797C211yesmaximal, characteristic, complemented
4C8×#638C211yesmaximal, characteristic, complemented
5C3×#5115C211yesmaximal, characteristic, complemented
6#10591160C212yesmaximal, complemented
7#10590945C212yesmaximal, complemented
8#10590886C211yesmaximal, characteristic, complemented
9#10590844C211yesmaximal, characteristic, complemented
10#10590777C211yesmaximal, characteristic, complemented
11#10590749C212yesmaximal, complemented
12D8×#67—31nomaximal
13#80729—31nomaximal
14C22×C3×D12C2212yescomplemented
15C2×D3×#67—22no—
16C2×#3802C2212yescomplemented
17C22×C32×C8C2211yescharacteristic, complemented
18C4×#638C2211yescharacteristic
19C2×C8×C3⋊D3C2211yescharacteristic, complemented
20C3×#930C2212yescomplemented
21C2×C3×D24—24no—
22C2×C3×D24C2211yescharacteristic
23C2×C3×D24C2212yescomplemented
24C2×C3×D24C2211yescharacteristic, complemented
25C2×C3×D24C2211yescharacteristic, complemented
26#63976—22no—
27#63922—22no—
28#63916C2212yescomplemented
29#63914C2212yescomplemented
30#63898C2212yescomplemented
31#63885—22no—
32C2×#3713C2212yescomplemented
33C2×#3713C2212yescomplemented
34#63797—24no—
35#63657C2211yescharacteristic, complemented
36#63647C2211yescharacteristic, complemented
37#63641C2211yescharacteristic, complemented
38C8×C3⋊Dic3C2211yescharacteristic, complemented
39C3×#821C2212yescomplemented
40C3×#818C2211yescharacteristic, complemented
41#63562C2212yescomplemented
42#63562C2212yescomplemented
43C22×C3×D8—31no—
44D4×#67—32no—
45C2×D3×D8—31no—
46C2×D3×D8—31no—
47C22×D24D311yescharacteristic, complemented
48#5609—32no—
49C3×#466—31no—
50#5217—32no—
51#5157—31no—
52#5156—32no—
53#5151—31no—
54#5151—31no—
55#5150—32no—
56Dic3×D8—31no—
57#5115D311yescharacteristic, complemented
58C8×#67—31no—
59C8×#67—31no—
60C8×#67—61no—
61#5036—32no—
62#4883—31no—
63#4872—31no—
64#4786—32no—
65#4773—32no—
66C23×C3×D3—22no—
67C22×D32—22no—
68C22×C32×C4C2311yescharacteristic
69C2×#638D411yescharacteristic
70C2×C4×C3⋊D3C2311yescharacteristic
71C2×C3×#67—22no—
72C2×C3×D12—24no—
73C2×C3×D12—22no—
74C2×C3×D12—42no—
75C2×C3×D12C2312yes—
76C2×C3×D12C2312yes—
77C2×C3×D12C2312yes—
78D3×#67—48no—
79C2×#626—22no—
80C2×#625—22no—
81C2×#625—22no—
82C2×#625—22no—
83C2×D3×Dic3—22no—
84#3802—24no—
85#3802—42no—
86C2×C32×C8—22no—
87C2×C32×C8C2311yescharacteristic
88C2×C32×C8C2311yescharacteristic
89#3757D411yescharacteristic
90#3752D411yescharacteristic
91#3750D411yescharacteristic
92C4×C3⋊Dic3C2311yescharacteristic
93C2×C3⋊(C3⋊C8)C2311yescharacteristic
94C2×C3⋊(C3⋊C8)C2311yescharacteristic
95C8×C3⋊D3—22no—
96C3×(C2×D3)⋊C4—22no—
97C3×C4⋊Dic3C2312yes—
98C3×D24—24no—
99C3×D24—22no—
100C3×D24—22no—
101C3×D24D414yescomplemented
102(C2×D3)⋊Dic3—22no—
103(C2×D3)⋊Dic3—22no—
104#3713—24no—
105#3713—42no—
106D4×D8—91noSylow
107C22×C3×D4—32no—
108C22×#67—62no—
109C2×D3×D4—32no—
110C2×D3×D4—32no—
111C2×D3×D4—62no—
112C22×D12C2×D312yescomplemented
113C2×C3×D8—31no—
114C2×C3×D8—32no—
115C2×C3×D8—31no—
116C2×C3×D8—31no—
117C2×C3×D8—64no—
118C22×C3×C8—21no—
119C22×C3×C8C2×D311yescharacteristic, complemented
120C22×C3×C8C2×D311yescharacteristic, complemented
121C3×#121—32no—
122#953—62no—
123#940—32no—
124#940—32no—
125#939—62no—
126#938—32no—
127#937—62no—
128#937—62no—
129D4×Dic3—32no—
130C2×#213—32no—
131C2×#213—32no—
132C2×#213—32no—
133C2×#213—32no—
134#930C2×D312yescomplemented
135C4×#67—31no—
136C4×#67—31no—
137C4×#67—61no—
138D3×D8—64no—
139D3×D8—64no—
140C2×D24—24no—
141C2×D24C2×D311yescharacteristic
142C2×D24C2×D311yescharacteristic, complemented
143C2×D24C2×D311yescharacteristic, complemented
144C2×D24C2×D312yescomplemented
145C2×D3×C8—31no—
146C2×D3×C8—31no—
147C2×D3×C8—61no—
148#895—32no—
149#893—32no—
150#884—62no—
151#882—62no—
152C3×#107—31no—
153C3×#102—32no—
154#832—32no—
155#832—32no—
156#830—31no—
157#830—31no—
158#830—61no—
159#821C2×D312yescomplemented
160(C2×D3)⋊C8—31no—
161(C2×D3)⋊C8—31no—
162(C2×D3)⋊C8—61no—
163#818C2×D311yescharacteristic, complemented
164Dic3⋊C8—31no—
165Dic3⋊C8—31no—
166Dic3⋊C8—61no—
167C8×Dic3—31no—
168C8×Dic3—31no—
169C8×Dic3—61no—
170#809—32no—
171#809—32no—
172C23×C32C2×D411yescharacteristic
173C22×C3⋊D3C2×D411yescharacteristic
174C22×C3×D3—22no—
175C22×C3×D3—22no—
176C22×C3×D3—22no—
177C22×C3×D3—44no—
178C22×C3×D3—44no—
179C22×C3×D3—82no—
180C2×D32—44no—
181C2×D32—44no—
182C2×D32—82no—
183C2×C32×C4—21no—
184C2×C32×C4—21no—
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4C2411yescharacteristic
187#638D814yescomplemented
188C2×C3⋊Dic3C2×D411yescharacteristic
189C2×C3⋊Dic3C2×D411yescharacteristic
190C2×C3⋊Dic3C2×D411yescharacteristic
191C4×C3⋊D3—21no—
192C4×C3⋊D3—21no—
193C3×#67—44no—
194C2×C3×Dic3—22no—
195C3×D12—22no—
196C3×D12—22no—
197C3×D12—22no—
198C3×D12—22no—
199C3×D12—22no—
200C3×D12—44no—
201C3×D12C2×D414yescomplemented
202#626—44no—
203#625—44no—
204#625—44no—
205#625—82no—
206D3×Dic3—44no—
207C32×C8—21no—
208C32×C8C2×D412yescomplemented
209C3⋊(C3⋊C8)—21no—
210C3⋊(C3⋊C8)—21no—
211C22×D8—31no—
212C22×D8—91no—
213D42—92no—
214#493—91no—
215#466—31no—
216#466—91no—
217#459—92no—
218#447—92no—
219#447—92no—
220C4×D8—91no—
221C8×D4—91no—
222C24×C3—62no—
223C23×D3—22no—
224C23×D3—62no—
225C23×D3—62no—
226C2×C3×D4—32no—
227C2×C3×D4—32no—
228C2×C3×D4—32no—
229C2×C3×D4—64no—
230C2×C3×D4—62no—
231C2×C3×D4—62no—
232C2×C3×D4—122no—
233C22×C3×C4—21no—
234C22×C3×C4C22×D311yescharacteristic
235C22×C3×C4C22×D311yescharacteristic
236C2×#67—22no—
237C2×#67—31no—
238C2×#67—31no—
239C2×#67—61no—
240C2×#67—62no—
241C2×#67—62no—
242C2×#67—62no—
243C2×#67—62no—
244C2×#67—62no—
245C2×#67—62no—
246C2×#67—62no—
247C2×#67—128no—
248C22×Dic3—62no—
249D3×D4—64no—
250D3×D4—64no—
251D3×D4—122no—
252D3×D4—122no—
253D3×D4—128no—
254C2×D12—24no—
255C2×D12—22no—
256C2×D12—42no—
257C2×D12—62no—
258C2×D12C22×D312yes—
259C2×D12C22×D312yes—
260C2×D12C22×D312yes—
261C2×C4×D3—31no—
262C2×C4×D3—31no—
263C2×C4×D3—61no—
264C2×C4×D3—62no—
265C3×D8—34no—
266C3×D8—64no—
267C3×D8—62no—
268C3×D8—62no—
269C2×C3×C8—22no—
270C2×C3×C8—22no—
271C2×C3×C8—21no—
272C2×C3×C8—21no—
273C2×C3×C8—42no—
274C2×C3×C8C22×D311yescharacteristic
275C2×C3×C8C22×D311yescharacteristic
276C2×C3×C8C22×D311yescharacteristic
277C2×C3×C8C22×D311yescharacteristic
278C3×C4⋊C4—32no—
279C3×C22⋊C4—62no—
280#217—31no—
281#217—31no—
282#217—61no—
283#217—62no—
284#217—62no—
285#213—64no—
286#213—64no—
287#213—122no—
288#213—122no—
289(C2×D3)⋊C4—22no—
290(C2×D3)⋊C4—31no—
291(C2×D3)⋊C4—31no—
292(C2×D3)⋊C4—61no—
293(C2×D3)⋊C4—62no—
294(C2×D3)⋊C4—62no—
295C4⋊Dic3C22×D312yes—
296Dic3⋊C4—31no—
297Dic3⋊C4—31no—
298Dic3⋊C4—61no—
299C4×Dic3—31no—
300C4×Dic3—31no—
301C4×Dic3—61no—
302C2×C3⋊C8—31no—
303C2×C3⋊C8—31no—
304C2×C3⋊C8—31no—
305C2×C3⋊C8—31no—
306C2×C3⋊C8—61no—
307C2×C3⋊C8—61no—
308D24—24no—
309D24—22no—
310D24—22no—
311D24#6714yescomplemented
312D3×C8—62no—
313D3×C8—62no—
314D3×C8—122no—
315C22×C32—21no—
316C22×C32—21no—
317C22×C32C2×D812yescomplemented
318C22×C32C22×D411yescharacteristic
319C2×C3⋊D3—21no—
320C2×C3⋊D3—21no—
321C2×C3⋊D3C2×D812yescomplemented
322C2×C3×D3—24no—
323C2×C3×D3—42no—
324C2×C3×D3—42no—
325C2×C3×D3—42no—
326C2×C3×D3—42no—
327C2×C3×D3—42no—
328C2×C3×D3—42no—
329C2×C3×D3—42no—
330C2×C3×D3—42no—
331C2×C3×D3—88no—
332D32—88no—
333C32×C4—21no—
334C32×C4C22×D411yescharacteristic
335C32×C4H(5,𝔽2)11yescharacteristic
336C3⋊Dic3—21no—
337C3⋊Dic3—21no—
338C3⋊Dic3C2×D812yescomplemented
339C3×Dic3—42no—
340C22×D4—32no—
341C22×D4—92no—
342C22×D4—182no—
343C2×D8—31no—
344C2×D8—32no—
345C2×D8—31no—
346C2×D8—31no—
347C2×D8—64no—
348C2×D8—92no—
349C2×D8—92no—
350C2×D8—184no—
351C22×C8—91no—
352C22×C8D3211yescharacteristic, complemented
353#127—92no—
354#121—32no—
355#121—92no—
356#121—182no—
357#120—182no—
358#120—182no—
359C4×D4—91no—
360C4×D4—92no—
361#107—31no—
362C4⋊C8—91no—
363#102—32no—
364#102—92no—
365#102—92no—
366C22⋊C8—91no—
367C22⋊C8—91no—
368C4×C8—91no—
369C23×C3—21no—
370C23×C3—62no—
371C23×C3—62no—
372C23×C3—62no—
373C23×C3—124no—
374C23×C3—124no—
375C23×C3—242no—
376C23×C3D3×D411yescharacteristic
377C23×C3D3×D411yescharacteristic
378C22×D3—22no—
379C22×D3—22no—
380C22×D3—22no—
381C22×D3—31no—
382C22×D3—31no—
383C22×D3—44no—
384C22×D3—44no—
385C22×D3—61no—
386C22×D3—82no—
387C22×D3—124no—
388C22×D3—124no—
389C22×D3—124no—
390C22×D3—124no—
391C22×D3—242no—
392C22×D3—242no—
393C3×D4—34no—
394C3×D4—62no—
395C3×D4—62no—
396C3×D4—62no—
397C3×D4—62no—
398C3×D4—62no—
399C3×D4—124no—
400C3×D4—124no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—41no—
408C2×C3×C4—41no—
409C2×C3×C4—62no—
410C2×C3×C4D3×D411yescharacteristic
411C2×C3×C4D3×D411yescharacteristic
412C2×C3×C4C23×D311yescharacteristic
413C2×C3×C4C23×D311yescharacteristic
414#67—34no—
415#67—34no—
416#67—44no—
417#67—64no—
418#67—124no—
419#67—124no—
420#67—124no—
421#67—124no—
422#67—124no—
423#67—242no—
424#67—242no—
425C2×Dic3—22no—
426C2×Dic3—31no—
427C2×Dic3—31no—
428C2×Dic3—31no—
429C2×Dic3—31no—
430C2×Dic3—31no—
431C2×Dic3—31no—
432C2×Dic3—61no—
433C2×Dic3—61no—
434C2×Dic3—61no—
435C2×Dic3—124no—
436D12—22no—
437D12—22no—
438D12—22no—
439D12—22no—
440D12—22no—
441D12—44no—
442D12—124no—
443D12C2×#6714yescomplemented
444C4×D3—61no—
445C4×D3—61no—
446C4×D3—61no—
447C4×D3—61no—
448C4×D3—121no—
449C4×D3—121no—
450C4×D3—124no—
451C3×C8—21no—
452C3×C8—21no—
453C3×C8—22no—
454C3×C8—41no—
455C3×C8D3×D412yescomplemented
456C3×C8C2×#6712yescomplemented
457C3⋊C8—61no—
458C3⋊C8—61no—
459C3⋊C8—61no—
460C3⋊C8—61no—
461C3⋊C8—121no—
462C3⋊C8—121no—
463C2×C32—22no—
464C2×C32D4211yescharacteristic
465C2×C32C22×D811yescharacteristic
466C2×C32#57611yescharacteristic
467C3⋊D3—22no—
468C3×D3—44no—
469C3×D3—82no—
470C3×D3—82no—
471C24—62no—
472C24—182no—
473C2×D4—32no—
474C2×D4—32no—
475C2×D4—32no—
476C2×D4—64no—
477C2×D4—62no—
478C2×D4—62no—
479C2×D4—91no—
480C2×D4—122no—
481C2×D4—182no—
482C2×D4—182no—
483C2×D4—182no—
484C2×D4—182no—
485C2×D4—184no—
486C2×D4—362no—
487C2×D4—368no—
488C22×C4—91no—
489C22×C4—182no—
490C22×C4C2×D3211yescharacteristic
491D8—34no—
492D8—64no—
493D8—62no—
494D8—62no—
495D8—184no—
496D8—362no—
497C2×C8—22no—
498C2×C8—91no—
499C2×C8—91no—
500C2×C8—182no—
501C2×C8C2×D3211yescharacteristic
502C2×C8C2×D3211yescharacteristic
503C4⋊C4—32no—
504C4⋊C4—91no—
505C22⋊C4—62no—
506C22⋊C4—91no—
507C22⋊C4—91no—
508C22⋊C4—182no—
509C22⋊C4—182no—
510C42—91no—
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—21no—
514C22×C3—21no—
515C22×C3—21no—
516C22×C3—22no—
517C22×C3—41no—
518C22×C3—41no—
519C22×C3—64no—
520C22×C3—122no—
521C22×C3—122no—
522C22×C3—122no—
523C22×C3—122no—
524C22×C3—122no—
525C22×C3—122no—
526C22×C3—122no—
527C22×C3—122no—
528C22×C3—248no—
529C22×C3D3×D812yescomplemented
530C22×C3D3×D812yescomplemented
531C22×C3C2×D3×D411yescharacteristic
532C22×C3C2×D3×D411yescharacteristic
533C2×D3—24no—
534C2×D3—32no—
535C2×D3—32no—
536C2×D3—42no—
537C2×D3—42no—
538C2×D3—42no—
539C2×D3—42no—
540C2×D3—42no—
541C2×D3—42no—
542C2×D3—42no—
543C2×D3—42no—
544C2×D3—62no—
545C2×D3—61no—
546C2×D3—61no—
547C2×D3—61no—
548C2×D3—61no—
549C2×D3—88no—
550C2×D3—121no—
551C2×D3—121no—
552C2×D3—248no—
553C2×D3—248no—
554C3×C4—21no—
555C3×C4—21no—
556C3×C4—21no—
557C3×C4—21no—
558C3×C4—41no—
559C3×C4—122no—
560C3×C4C2×D3×D411yescharacteristic
561C3×C4#100411yescharacteristic
562C3×C4#100911yescharacteristic
563C3×C4C22×#6711yescharacteristic
564Dic3—32no—
565Dic3—32no—
566Dic3—42no—
567Dic3—62no—
568Dic3—61no—
569Dic3—61no—
570Dic3—61no—
571Dic3—61no—
572Dic3—121no—
573Dic3—121no—
574C32D4×D811yescharacteristic, complemented, Sylow
575C23—62no—
576C23—62no—
577C23—62no—
578C23—91no—
579C23—124no—
580C23—124no—
581C23—242no—
582C23—364no—
583C23—364no—
584C23—722no—
585C23#380211yescharacteristic
586D4—34no—
587D4—62no—
588D4—62no—
589D4—62no—
590D4—62no—
591D4—62no—
592D4—94no—
593D4—124no—
594D4—124no—
595D4—364no—
596D4—364no—
597D4—364no—
598D4—722no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—62no—
602C2×C4—91no—
603C2×C4—91no—
604C2×C4—91no—
605C2×C4—181no—
606C2×C4—181no—
607C2×C4—364no—
608C2×C4#380211yescharacteristic
609C2×C4C22×D3211yescharacteristic
610C8—21no—
611C8—181no—
612C8—181no—
613C8D3×#6712yescomplemented
614C2×C3—22no—
615C2×C3—22no—
616C2×C3—21no—
617C2×C3—21no—
618C2×C3—21no—
619C2×C3—42no—
620C2×C3—124no—
621C2×C3—242no—
622C2×C3—242no—
623C2×C3#560911yescharacteristic
624C2×C3C2×D3×D811yescharacteristic
625C2×C3C2×D3×D811yescharacteristic
626C2×C3#575711yescharacteristic
627C2×C3#576911yescharacteristic
628C2×C3D4×#6711yescharacteristic
629D3—44no—
630D3—62no—
631D3—62no—
632D3—82no—
633D3—82no—
634D3—122no—
635C22—21no—
636C22—21no—
637C22—64no—
638C22—92no—
639C22—122no—
640C22—122no—
641C22—122no—
642C22—122no—
643C22—122no—
644C22—122no—
645C22—122no—
646C22—122no—
647C22—181no—
648C22—181no—
649C22—248no—
650C22—728no—
651C22#6379712yescomplemented
652C22C2×#380211yescharacteristic
653C4—21no—
654C4—92no—
655C4—122no—
656C4—181no—
657C4—181no—
658C4#6430711yescharacteristic
659C4C2×D3×#6711yescharacteristic
660C3—21no—
661C3#8072911yescharacteristic, complemented
662C3D8×#6711yescharacteristic, complemented
663C2—22no—
664C2—124no—
665C2—182no—
666C2—242no—
667C2—242no—
668C2C2×#6379711yescharacteristic
669C2#1059468711yescharacteristic
670C2#1059506911yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
hypercenterC22×C8D32
hypocenterC32D4×D8
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×C3×D24C2semidirect
2. #10595069C2semidirect
3. C2×#63797C2semidirect
4. C8×#638C2semidirect
5. C3×#5115C2semidirect
6. #10591160C2semidirect
7. #10590945C2semidirect
8. #10590886C2semidirect
9. #10590844C2semidirect
10. #10590777C2semidirect
11. #10590749C2semidirect
14. C22×C3×D12C22semidirect
16. C2×#3802C22semidirect
17. C22×C32×C8C22semidirect
19. C2×C8×C3⋊D3C22semidirect
20. C3×#930C22semidirect
23. C2×C3×D24C22semidirect
24. C2×C3×D24C22semidirect
25. C2×C3×D24C22semidirect
28. #63916C22semidirect
29. #63914C22semidirect
30. #63898C22semidirect
32. C2×#3713C22semidirect
33. C2×#3713C22semidirect
35. #63657C22semidirect
36. #63647C22semidirect
37. #63641C22semidirect
38. C8×C3⋊Dic3C22semidirect
39. C3×#821C22semidirect
40. C3×#818C22semidirect
41. #63562C22semidirect
42. #63562C22semidirect
47. C22×D24D3semidirect
57. #5115D3semidirect
101. C3×D24D4semidirect
112. C22×D12C2×D3semidirect
119. C22×C3×C8C2×D3semidirect
120. C22×C3×C8C2×D3semidirect
134. #930C2×D3semidirect
142. C2×D24C2×D3semidirect
143. C2×D24C2×D3semidirect
144. C2×D24C2×D3semidirect
159. #821C2×D3semidirect
163. #818C2×D3semidirect
187. #638D8semidirect
201. C3×D12C2×D4semidirect
208. C32×C8C2×D4semidirect
311. D24#67semidirect
317. C22×C32C2×D8semidirect
321. C2×C3⋊D3C2×D8semidirect
338. C3⋊Dic3C2×D8semidirect
352. C22×C8D32semidirect
443. D12C2×#67semidirect
455. C3×C8D3×D4semidirect
456. C3×C8C2×#67semidirect
529. C22×C3D3×D8semidirect
530. C22×C3D3×D8semidirect
574. C32D4×D8semidirect
613. C8D3×#67semidirect
651. C22#63797semidirect
661. C3#80729semidirect
662. C3D8×#67semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D242
#105950692
C2×#637972
C8×#6382
C3×#51152
#105911602
#105909452
#105908862
#105908442
#105907772
#105907492
D8×#673
#807293