Finite Group Databasebeta

← #11885771

Subgroups — #11885771

Order 1152.

1321 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×D8C211yesmaximal, characteristic, complemented
2#10595288C212yesmaximal, complemented
3C2×D3×D24C211yesmaximal, characteristic, complemented
4#10592850C211yesmaximal, characteristic, complemented
5C3×#5157C211yesmaximal, characteristic, complemented
6#10591515C212yesmaximal, complemented
7#10591448C212yesmaximal, complemented
8#10591433C212yesmaximal, complemented
9#10590832C211yesmaximal, characteristic, complemented
10#10590777C211yesmaximal, characteristic, complemented
11C8×#625C211yesmaximal, characteristic, complemented
12D8×#67—31nomaximal
13#80729—31nomaximal
14C2×C3×D3×D4C2212yescomplemented
15C2×D3×#67—22no—
16C2×D3×D12C2212yescomplemented
17C2×C32×D8C2211yescharacteristic, complemented
18#64149C2212yescomplemented
19C2×#3753C2212yescomplemented
20C2×#3745C2211yescharacteristic, complemented
21C3×#938C2212yescomplemented
22C2×C3×#213C2212yescomplemented
23C3×D3×D8—24no—
24C2×C3×D24C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic, complemented
26C2×C3×D3×C8C2211yescharacteristic, complemented
27#63983—22no—
28#63977—22no—
29#63971—22no—
30#63909C2212yescomplemented
31C4×#625C2211yescharacteristic
32#63898C2212yescomplemented
33C2×#3714C2212yescomplemented
34D3×D24—24no—
35C8×C3⋊Dic3C2211yescharacteristic, complemented
36C3×#832C2212yescomplemented
37C3×#818C2211yescharacteristic, complemented
38#63572C2211yescharacteristic, complemented
39#63564C2212yescomplemented
40#63562C2212yescomplemented
41(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
42(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
43C22×C3×D8—31no—
44D4×#67—32no—
45C2×D3×D8—31no—
46C2×D3×D8D311yescharacteristic, complemented
47C22×D24—31no—
48#5609—32no—
49C3×#466—31no—
50#5217—32no—
51#5157D311yescharacteristic, complemented
52#5156—32no—
53#5151—31no—
54#5151—31no—
55#5151—61no—
56#5150—32no—
57Dic3×D8—31no—
58#5115—31no—
59C8×#67—31no—
60C8×#67—31no—
61#5036—32no—
62#4883—31no—
63#4872—31no—
64#4786—32no—
65#4773—32no—
66C23×C3×D3—22no—
67C22×D32—22no—
68C2×C32×D4C2312yes—
69C2×#638—22no—
70C2×#638—22no—
71C2×C4⋊(C3⋊D3)C2312yes—
72C2×C3×#67—22no—
73C2×C3×#67—22no—
74C3×D3×D4—24no—
75C3×D3×D4—42no—
76C2×C3×D12C2312yes—
77C2×C3×C4×D3C2311yescharacteristic
78C2×C3×C4×D3C2311yescharacteristic
79D3×#67—48no—
80C2×#626—22no—
81C2×#626—22no—
82C2×#625D411yescharacteristic
83C2×D3×Dic3—22no—
84D3×D12—24no—
85D3×D12—42no—
86C32×D8—22no—
87C2×C32×C8C2311yescharacteristic
88#3753—42no—
89C4×C3⋊Dic3C2311yescharacteristic
90C2×C3⋊(C3⋊C8)C2311yescharacteristic
91#3745—22no—
92C3×#217—22no—
93C3×#213—24no—
94C3×C4⋊Dic3C2312yes—
95C2×C3×C3⋊C8C2311yescharacteristic
96C2×C3×C3⋊C8C2311yescharacteristic
97C3×D24D414yescomplemented
98C3×D3×C8—22no—
99C3×D3×C8—22no—
100#3724D411yescharacteristic
101#3722—22no—
102(C2×D3)⋊Dic3—22no—
103(C2×D3)⋊Dic3D411yescharacteristic
104(C2×D3)⋊Dic3D411yescharacteristic
105#3714—24no—
106D4×D8—91noSylow
107C22×C3×D4—32no—
108C22×#67—62no—
109C2×D3×D4—32no—
110C2×D3×D4—62no—
111C2×D3×D4C2×D312yescomplemented
112C22×D12—32no—
113C2×C3×D8—21no—
114C2×C3×D8—32no—
115C2×C3×D8—31no—
116C2×C3×D8—64no—
117C2×C3×D8C2×D311yescharacteristic, complemented
118C2×C3×D8C2×D311yescharacteristic, complemented
119C22×C3×C8—31no—
120C22×C3×C8—31no—
121C3×#121—32no—
122#953—62no—
123#940—32no—
124#940—32no—
125#940—62no—
126#939—62no—
127#938C2×D312yescomplemented
128#937—62no—
129#937—62no—
130D4×Dic3—32no—
131C2×#213—32no—
132C2×#213—32no—
133C2×#213—32no—
134C2×#213—62no—
135C2×#213C2×D312yescomplemented
136#930—32no—
137C4×#67—31no—
138C4×#67—31no—
139D3×D8—24no—
140D3×D8—64no—
141C2×D24—32no—
142C2×D24—31no—
143C2×D24—31no—
144C2×D24—61no—
145C2×D24—64no—
146C2×D24C2×D311yescharacteristic
147C2×D3×C8C2×D311yescharacteristic, complemented
148C2×D3×C8C2×D311yescharacteristic, complemented
149#895—32no—
150#893—32no—
151#884—62no—
152#882—62no—
153C3×#107—31no—
154C3×#102—32no—
155#832—32no—
156#832C2×D312yescomplemented
157#830—31no—
158#830—31no—
159#821—32no—
160(C2×D3)⋊C8—31no—
161(C2×D3)⋊C8—31no—
162#818C2×D311yescharacteristic, complemented
163Dic3⋊C8—31no—
164Dic3⋊C8—31no—
165C8×Dic3—31no—
166C8×Dic3—31no—
167C8×Dic3—61no—
168#809—32no—
169#809—32no—
170C23×C32—22no—
171C22×C3⋊D3—22no—
172C22×C3×D3—22no—
173C22×C3×D3—44no—
174C22×C3×D3—44no—
175C22×C3×D3—82no—
176C22×C3×D3C2×D411yescharacteristic
177C22×C3×D3C2×D411yescharacteristic
178C2×D32—44no—
179C2×D32—44no—
180C2×D32—82no—
181C32×D4—22no—
182C32×D4—22no—
183C2×C32×C4C2411yescharacteristic
184#638—44no—
185#638—82no—
186C2×C3⋊Dic3C2×D411yescharacteristic
187C2×C3⋊Dic3C2×D411yescharacteristic
188C4⋊(C3⋊D3)—22no—
189C4⋊(C3⋊D3)—22no—
190C3×#67—44no—
191C3×#67—44no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3C2×D411yescharacteristic
194C2×C3×Dic3C2×D411yescharacteristic
195C3×D12—22no—
196C3×D12C2×D414yescomplemented
197C3×C4×D3—21no—
198C3×C4×D3—21no—
199C3×C4×D3—21no—
200C3×C4×D3—21no—
201#626—44no—
202#626—44no—
203#625D814yescomplemented
204D3×Dic3—44no—
205C32×C8C2×D412yescomplemented
206C3⋊(C3⋊C8)—21no—
207C3×C3⋊C8—21no—
208C3×C3⋊C8—21no—
209C22×D8—31no—
210C22×D8—91no—
211D42—92no—
212#493—91no—
213#466—31no—
214#466—91no—
215#459—92no—
216#447—92no—
217#447—92no—
218C4×D8—91no—
219C8×D4—91no—
220C24×C3—62no—
221C23×D3—22no—
222C23×D3—62no—
223C23×D3—62no—
224C2×C3×D4—22no—
225C2×C3×D4—32no—
226C2×C3×D4—62no—
227C2×C3×D4—64no—
228C2×C3×D4—62no—
229C2×C3×D4—122no—
230C2×C3×D4C22×D312yes—
231C2×C3×D4C22×D312yes—
232C22×C3×C4—31no—
233C22×C3×C4—31no—
234C2×#67—22no—
235C2×#67—22no—
236C2×#67—31no—
237C2×#67—31no—
238C2×#67—62no—
239C2×#67—62no—
240C2×#67—62no—
241C2×#67—62no—
242C2×#67—62no—
243C2×#67—62no—
244C2×#67—122no—
245C2×#67—122no—
246C2×#67—128no—
247C22×Dic3—62no—
248D3×D4—24no—
249D3×D4—42no—
250D3×D4—64no—
251D3×D4—122no—
252D3×D4—128no—
253C2×D12—32no—
254C2×D12—32no—
255C2×D12—62no—
256C2×D12—64no—
257C2×D12—62no—
258C2×D12—62no—
259C2×D12—122no—
260C2×D12C22×D312yes—
261C2×C4×D3—62no—
262C2×C4×D3C22×D311yescharacteristic
263C2×C4×D3C22×D311yescharacteristic
264C3×D8—22no—
265C3×D8—22no—
266C3×D8—34no—
267C3×D8—42no—
268C3×D8—64no—
269C2×C3×C8—21no—
270C2×C3×C8—31no—
271C2×C3×C8—31no—
272C2×C3×C8—62no—
273C2×C3×C8—62no—
274C2×C3×C8C22×D311yescharacteristic
275C2×C3×C8C22×D311yescharacteristic
276C3×C4⋊C4—32no—
277C3×C22⋊C4—62no—
278#217—22no—
279#217—31no—
280#217—31no—
281#217—62no—
282#213—24no—
283#213—64no—
284#213—122no—
285#213—122no—
286#213—124no—
287(C2×D3)⋊C4—31no—
288(C2×D3)⋊C4—31no—
289(C2×D3)⋊C4—62no—
290(C2×D3)⋊C4—62no—
291(C2×D3)⋊C4—62no—
292C4⋊Dic3C22×D312yes—
293Dic3⋊C4—31no—
294Dic3⋊C4—31no—
295C4×Dic3—31no—
296C4×Dic3—31no—
297C4×Dic3—61no—
298C2×C3⋊C8—31no—
299C2×C3⋊C8—31no—
300C2×C3⋊C8—61no—
301C2×C3⋊C8C22×D311yescharacteristic
302C2×C3⋊C8C22×D311yescharacteristic
303D24—64no—
304D24—62no—
305D24—62no—
306D24—122no—
307D24#6714yescomplemented
308D3×C8—22no—
309D3×C8—22no—
310C22×C32—42no—
311C22×C32—42no—
312C22×C32—42no—
313C22×C32C22×D411yescharacteristic
314C2×C3⋊D3—42no—
315C2×C3⋊D3—42no—
316C2×C3⋊D3—42no—
317C2×C3×D3—21no—
318C2×C3×D3—21no—
319C2×C3×D3—21no—
320C2×C3×D3—21no—
321C2×C3×D3—24no—
322C2×C3×D3—42no—
323C2×C3×D3—42no—
324C2×C3×D3—88no—
325C2×C3×D3C2×D812yescomplemented
326C2×C3×D3C2×D812yescomplemented
327D32—88no—
328C32×C4C22×D411yescharacteristic
329C32×C4H(5,𝔽2)11yescharacteristic
330C3⋊Dic3—21no—
331C3⋊Dic3C2×D812yescomplemented
332C3×Dic3—21no—
333C3×Dic3—21no—
334C3×Dic3—42no—
335C22×D4—32no—
336C22×D4—92no—
337C22×D4—182no—
338C2×D8—32no—
339C2×D8—31no—
340C2×D8—64no—
341C2×D8—92no—
342C2×D8—92no—
343C2×D8—91no—
344C2×D8—184no—
345C2×D8D3211yescharacteristic, complemented
346C22×C8—31no—
347C22×C8—31no—
348#127—92no—
349#121—32no—
350#121—92no—
351#121—182no—
352#120—182no—
353#120—182no—
354C4×D4—91no—
355C4×D4—92no—
356#107—31no—
357C4⋊C8—91no—
358#102—32no—
359#102—92no—
360#102—92no—
361C22⋊C8—91no—
362C22⋊C8—91no—
363C4×C8—91no—
364C23×C3—22no—
365C23×C3—22no—
366C23×C3—31no—
367C23×C3—31no—
368C23×C3—42no—
369C23×C3—62no—
370C23×C3—124no—
371C23×C3—124no—
372C23×C3—242no—
373C22×D3—22no—
374C22×D3—44no—
375C22×D3—44no—
376C22×D3—62no—
377C22×D3—62no—
378C22×D3—82no—
379C22×D3—122no—
380C22×D3—124no—
381C22×D3—124no—
382C22×D3—124no—
383C22×D3—124no—
384C22×D3—242no—
385C22×D3—242no—
386C22×D3D3×D411yescharacteristic
387C22×D3D3×D411yescharacteristic
388C3×D4—22no—
389C3×D4—22no—
390C3×D4—22no—
391C3×D4—22no—
392C3×D4—34no—
393C3×D4—42no—
394C3×D4—42no—
395C3×D4—62no—
396C3×D4—124no—
397C3×D4—124no—
398C2×C3×C4—21no—
399C2×C3×C4—31no—
400C2×C3×C4—31no—
401C2×C3×C4—61no—
402C2×C3×C4—61no—
403C2×C3×C4—61no—
404C2×C3×C4—61no—
405C2×C3×C4—62no—
406C2×C3×C4C23×D311yescharacteristic
407C2×C3×C4C23×D311yescharacteristic
408#67—34no—
409#67—34no—
410#67—44no—
411#67—44no—
412#67—124no—
413#67—124no—
414#67—124no—
415#67—124no—
416#67—244no—
417#67—242no—
418#67—242no—
419#67—244no—
420C2×Dic3—22no—
421C2×Dic3—31no—
422C2×Dic3—31no—
423C2×Dic3—31no—
424C2×Dic3—31no—
425C2×Dic3—61no—
426C2×Dic3—61no—
427C2×Dic3—124no—
428C2×Dic3D3×D411yescharacteristic
429C2×Dic3D3×D411yescharacteristic
430D12—22no—
431D12—62no—
432D12—62no—
433D12—62no—
434D12—62no—
435D12—122no—
436D12—122no—
437D12—124no—
438D12—124no—
439D12C2×#6714yescomplemented
440C4×D3—21no—
441C4×D3—21no—
442C4×D3—21no—
443C4×D3—21no—
444C4×D3—124no—
445C3×C8—22no—
446C3×C8—61no—
447C3×C8—61no—
448C3×C8D3×D412yescomplemented
449C3×C8C2×#6712yescomplemented
450C3⋊C8—21no—
451C3⋊C8—21no—
452C3⋊C8—62no—
453C3⋊C8—61no—
454C3⋊C8—61no—
455C2×C32—82no—
456C2×C32D4211yescharacteristic
457C2×C32C22×D811yescharacteristic
458C2×C32#57611yescharacteristic
459C3⋊D3—82no—
460C3×D3—22no—
461C3×D3—22no—
462C3×D3—44no—
463C24—62no—
464C24—182no—
465C2×D4—32no—
466C2×D4—62no—
467C2×D4—64no—
468C2×D4—62no—
469C2×D4—91no—
470C2×D4—92no—
471C2×D4—122no—
472C2×D4—182no—
473C2×D4—184no—
474C2×D4—182no—
475C2×D4—182no—
476C2×D4—182no—
477C2×D4—362no—
478C2×D4—368no—
479C2×D4C2×D3212yes—
480C22×C4—31no—
481C22×C4—31no—
482C22×C4—182no—
483D8—22no—
484D8—34no—
485D8—64no—
486D8—184no—
487D8—182no—
488D8—362no—
489C2×C8—31no—
490C2×C8—31no—
491C2×C8—62no—
492C2×C8—62no—
493C2×C8—91no—
494C2×C8C2×D3211yescharacteristic
495C4⋊C4—32no—
496C4⋊C4—91no—
497C22⋊C4—62no—
498C22⋊C4—91no—
499C22⋊C4—91no—
500C22⋊C4—182no—
501C22⋊C4—182no—
502C42—91no—
503C22×C3—21no—
504C22×C3—32no—
505C22×C3—32no—
506C22×C3—42no—
507C22×C3—42no—
508C22×C3—42no—
509C22×C3—42no—
510C22×C3—42no—
511C22×C3—42no—
512C22×C3—61no—
513C22×C3—61no—
514C22×C3—61no—
515C22×C3—61no—
516C22×C3—64no—
517C22×C3—82no—
518C22×C3—82no—
519C22×C3—82no—
520C22×C3—122no—
521C22×C3—122no—
522C22×C3—248no—
523C22×C3C2×D3×D411yescharacteristic
524C22×C3C2×D3×D411yescharacteristic
525C2×D3—21no—
526C2×D3—21no—
527C2×D3—21no—
528C2×D3—21no—
529C2×D3—24no—
530C2×D3—42no—
531C2×D3—42no—
532C2×D3—88no—
533C2×D3—122no—
534C2×D3—122no—
535C2×D3—122no—
536C2×D3—122no—
537C2×D3—122no—
538C2×D3—122no—
539C2×D3—242no—
540C2×D3—242no—
541C2×D3—242no—
542C2×D3—248no—
543C2×D3—248no—
544C2×D3D3×D812yescomplemented
545C2×D3D3×D812yescomplemented
546C3×C4—21no—
547C3×C4—21no—
548C3×C4—61no—
549C3×C4—61no—
550C3×C4—122no—
551C3×C4C2×D3×D411yescharacteristic
552C3×C4#100411yescharacteristic
553C3×C4#100911yescharacteristic
554C3×C4C22×#6711yescharacteristic
555Dic3—21no—
556Dic3—21no—
557Dic3—32no—
558Dic3—32no—
559Dic3—42no—
560Dic3—62no—
561Dic3—62no—
562Dic3—61no—
563Dic3—61no—
564C32D4×D811yescharacteristic, complemented, Sylow
565C23—22no—
566C23—31no—
567C23—31no—
568C23—62no—
569C23—124no—
570C23—124no—
571C23—182no—
572C23—242no—
573C23—364no—
574C23—364no—
575C23—722no—
576D4—22no—
577D4—22no—
578D4—34no—
579D4—62no—
580D4—94no—
581D4—124no—
582D4—124no—
583D4—182no—
584D4—182no—
585D4—364no—
586D4—364no—
587D4—364no—
588D4—722no—
589C2×C4—31no—
590C2×C4—31no—
591C2×C4—61no—
592C2×C4—61no—
593C2×C4—61no—
594C2×C4—61no—
595C2×C4—62no—
596C2×C4—91no—
597C2×C4—91no—
598C2×C4—364no—
599C2×C4C22×D3211yescharacteristic
600C8—61no—
601C8—61no—
602C8—181no—
603C8D3×#6712yescomplemented
604C2×C3—21no—
605C2×C3—21no—
606C2×C3—21no—
607C2×C3—62no—
608C2×C3—62no—
609C2×C3—82no—
610C2×C3—82no—
611C2×C3—124no—
612C2×C3—162no—
613C2×C3#560911yescharacteristic
614C2×C3C2×D3×D811yescharacteristic
615C2×C3C2×D3×D811yescharacteristic
616C2×C3#575711yescharacteristic
617C2×C3#576911yescharacteristic
618C2×C3D4×#6711yescharacteristic
619D3—22no—
620D3—22no—
621D3—44no—
622D3—242no—
623D3—242no—
624D3—482no—
625C22—32no—
626C22—32no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—61no—
631C22—61no—
632C22—61no—
633C22—61no—
634C22—64no—
635C22—122no—
636C22—122no—
637C22—248no—
638C22—362no—
639C22—362no—
640C22—362no—
641C22—728no—
642C22D32×D411yescharacteristic
643C4—61no—
644C4—61no—
645C4—92no—
646C4—122no—
647C4—181no—
648C4#6431411yescharacteristic
649C4C2×D3×#6711yescharacteristic
650C3—21no—
651C3#8072911yescharacteristic, complemented
652C3D8×#6711yescharacteristic, complemented
653C2—62no—
654C2—62no—
655C2—82no—
656C2—124no—
657C2—722no—
658C2D32×D811yescharacteristic
659C2#1059473411yescharacteristic
660C2#1059528811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32D4×D8
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×D8C2semidirect
2. #10595288C2semidirect
3. C2×D3×D24C2semidirect
4. #10592850C2semidirect
5. C3×#5157C2semidirect
6. #10591515C2semidirect
7. #10591448C2semidirect
8. #10591433C2semidirect
9. #10590832C2semidirect
10. #10590777C2semidirect
11. C8×#625C2semidirect
14. C2×C3×D3×D4C22semidirect
16. C2×D3×D12C22semidirect
17. C2×C32×D8C22semidirect
18. #64149C22semidirect
19. C2×#3753C22semidirect
20. C2×#3745C22semidirect
21. C3×#938C22semidirect
22. C2×C3×#213C22semidirect
25. C2×C3×D3×C8C22semidirect
26. C2×C3×D3×C8C22semidirect
30. #63909C22semidirect
32. #63898C22semidirect
33. C2×#3714C22semidirect
35. C8×C3⋊Dic3C22semidirect
36. C3×#832C22semidirect
37. C3×#818C22semidirect
38. #63572C22semidirect
39. #63564C22semidirect
40. #63562C22semidirect
41. (C2×D3)⋊(C3⋊C8)C22semidirect
42. (C2×D3)⋊(C3⋊C8)C22semidirect
46. C2×D3×D8D3semidirect
51. #5157D3semidirect
97. C3×D24D4semidirect
111. C2×D3×D4C2×D3semidirect
117. C2×C3×D8C2×D3semidirect
118. C2×C3×D8C2×D3semidirect
127. #938C2×D3semidirect
135. C2×#213C2×D3semidirect
147. C2×D3×C8C2×D3semidirect
148. C2×D3×C8C2×D3semidirect
156. #832C2×D3semidirect
162. #818C2×D3semidirect
196. C3×D12C2×D4semidirect
203. #625D8semidirect
205. C32×C8C2×D4semidirect
307. D24#67semidirect
325. C2×C3×D3C2×D8semidirect
326. C2×C3×D3C2×D8semidirect
331. C3⋊Dic3C2×D8semidirect
345. C2×D8D32semidirect
439. D12C2×#67semidirect
448. C3×C8D3×D4semidirect
449. C3×C8C2×#67semidirect
544. C2×D3D3×D8semidirect
545. C2×D3D3×D8semidirect
564. C32D4×D8semidirect
603. C8D3×#67semidirect
651. C3#80729semidirect
652. C3D8×#67semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×D82
#105952882
C2×D3×D242
#105928502
C3×#51572
#105915152
#105914482
#105914332
#105908322
#105907772
C8×#6252
D8×#673
#807293