Finite Group Databasebeta

← #11885769

Subgroups — #11885769

Order 1152.

1307 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×D8C211yesmaximal, characteristic, complemented
2#10595293C212yesmaximal, complemented
3C2×#63797C211yesmaximal, characteristic, complemented
4#10592856C211yesmaximal, characteristic, complemented
5C3×#5151C211yesmaximal, characteristic, complemented
6#10591516C212yesmaximal, complemented
7#10591447C212yesmaximal, complemented
8#10591428C212yesmaximal, complemented
9#10590831C211yesmaximal, characteristic, complemented
10Dic3×D24C211yesmaximal, characteristic, complemented
11C8×#626C211yesmaximal, characteristic, complemented
12D8×#67—31nomaximal
13#81789—31nomaximal
14C2×C3×D3×D4C2212yescomplemented
15C2×D3×#67—22no—
16C2×#3802C2212yescomplemented
17C2×C32×D8C2211yescharacteristic, complemented
18#64147C2212yescomplemented
19C2×C8×C3⋊D3C2211yescharacteristic, complemented
20C3×#940C2212yescomplemented
21C2×C3×#213C2212yescomplemented
22C2×C3×#213C2212yescomplemented
23C3×D3×D8—24no—
24C2×C3×D24C2211yescharacteristic
25C2×C3×D24C2211yescharacteristic, complemented
26C2×C3×D3×C8C2211yescharacteristic, complemented
27#63983—22no—
28#63976—22no—
29#63970—22no—
30#63908C2212yescomplemented
31C4×#626C2211yescharacteristic
32Dic3×D12C2212yescomplemented
33C2×#3713C2212yescomplemented
34#63797—24no—
35#63659C2212yescomplemented
36#63645C2211yescharacteristic, complemented
37C3×C8×Dic3C2211yescharacteristic, complemented
38Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
39#63563C2212yescomplemented
40#63563C2212yescomplemented
41#63557C2211yescharacteristic, complemented
42(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
43C22×C3×D8—31no—
44D4×#67—32no—
45C2×D3×D8—31no—
46C2×D3×D8—31no—
47C2×D3×D8D311yescharacteristic, complemented
48#5717—32no—
49C3×#493—31no—
50#5217—32no—
51#5157—31no—
52#5157—31no—
53#5157—31no—
54#5157—61no—
55#5156—32no—
56#5156—32no—
57#5156—32no—
58#5151D311yescharacteristic, complemented
59#5150—32no—
60Dic3×D8—31no—
61#5115—31no—
62C8×#67—31no—
63#5072—32no—
64C4×D24—31no—
65C8×D12—31no—
66C23×C3×D3—22no—
67C22×D32—22no—
68C2×C32×D4C2312yes—
69C2×#638—22no—
70C2×C4×C3⋊D3C2311yescharacteristic
71C2×C3×#67—22no—
72C2×C3×#67—22no—
73C2×C3×#67—22no—
74C3×D3×D4—24no—
75C3×D3×D4—42no—
76C2×C3×D12C2312yes—
77C2×C3×D12C2312yes—
78C2×C3×C4×D3C2311yescharacteristic
79D3×#67—48no—
80C2×#626D411yescharacteristic
81C2×#625—22no—
82C2×#625—22no—
83C2×D3×Dic3—22no—
84#3802—24no—
85#3802—42no—
86C32×D8—22no—
87C2×C32×C8C2311yescharacteristic
88#3757—22no—
89C4⋊(C3⋊Dic3)C2312yes—
90C2×C3⋊(C3⋊C8)C2311yescharacteristic
91C8×C3⋊D3—22no—
92C3×#213—24no—
93C3×#213—42no—
94C3×C4×Dic3C2311yescharacteristic
95C2×C3×C3⋊C8C2311yescharacteristic
96C2×C3×C3⋊C8C2311yescharacteristic
97C3×D24—22no—
98C3×D24D414yescomplemented
99C3×D3×C8—22no—
100Dic3⋊Dic3D411yescharacteristic
101#3722D411yescharacteristic
102(C2×D3)⋊Dic3—22no—
103(C2×D3)⋊Dic3—22no—
104(C2×D3)⋊Dic3D411yescharacteristic
105#3713—24no—
106D4×D8—91noSylow
107C22×C3×D4—32no—
108C22×#67—62no—
109C2×D3×D4—32no—
110C2×D3×D4—32no—
111C2×D3×D4—62no—
112C2×D3×D4C2×D312yescomplemented
113C2×C3×D8—21no—
114C2×C3×D8—32no—
115C2×C3×D8—32no—
116C2×C3×D8—31no—
117C2×C3×D8—31no—
118C2×C3×D8—64no—
119C2×C3×D8C2×D311yescharacteristic, complemented
120C2×C3×D8C2×D311yescharacteristic, complemented
121C22×C3×C8—31no—
122C3×#127—32no—
123#953—62no—
124#940C2×D312yescomplemented
125#939—62no—
126#938—32no—
127#938—32no—
128#938—32no—
129#938—62no—
130#938—62no—
131#937—62no—
132#937—62no—
133#937—62no—
134D4×Dic3—32no—
135C2×#213—32no—
136C2×#213—32no—
137C2×#213C2×D312yescomplemented
138C2×#213C2×D312yescomplemented
139#930—32no—
140C4×#67—31no—
141D3×D8—24no—
142D3×D8—64no—
143D3×D8—64no—
144C2×D24C2×D311yescharacteristic
145C2×D24C2×D311yescharacteristic, complemented
146C2×D3×C8—31no—
147C2×D3×C8—31no—
148C2×D3×C8—61no—
149C2×D3×C8C2×D311yescharacteristic, complemented
150C4×D12—31no—
151C4×D12—32no—
152C3×C4×C8—31no—
153#832—32no—
154#832—32no—
155#832—32no—
156#832—32no—
157#832—62no—
158#830—31no—
159#821—32no—
160#821—32no—
161(C2×D3)⋊C8—31no—
162(C2×D3)⋊C8—31no—
163(C2×D3)⋊C8—31no—
164#818—31no—
165#818—31no—
166#818—61no—
167Dic3⋊C8—31no—
168C8×Dic3C2×D311yescharacteristic, complemented
169C4⋊(C3⋊C8)—31no—
170C23×C32—22no—
171C22×C3⋊D3C2×D411yescharacteristic
172C22×C3×D3—22no—
173C22×C3×D3—22no—
174C22×C3×D3—44no—
175C22×C3×D3—44no—
176C22×C3×D3—82no—
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—
185C2×C3⋊Dic3—22no—
186C2×C3⋊Dic3C2×D411yescharacteristic
187C4×C3⋊D3—21no—
188C4×C3⋊D3—21no—
189C3×#67—44no—
190C3×#67—44no—
191C3×#67—82no—
192C2×C3×Dic3C2×D411yescharacteristic
193C2×C3×Dic3C2×D411yescharacteristic
194C2×C3×Dic3C2×D411yescharacteristic
195C3×D12—22no—
196C3×D12—22no—
197C3×D12—22no—
198C3×D12C2×D414yescomplemented
199C3×C4×D3—21no—
200C3×C4×D3—21no—
201#626D814yescomplemented
202#625—44no—
203#625—44no—
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—31no—
213#466—91no—
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—32no—
227C2×C3×D4—62no—
228C2×C3×D4—62no—
229C2×C3×D4—62no—
230C2×C3×D4—64no—
231C2×C3×D4—122no—
232C2×C3×D4C22×D312yes—
233C2×C3×D4C22×D312yes—
234C22×C3×C4—31no—
235C2×#67—22no—
236C2×#67—22no—
237C2×#67—22no—
238C2×#67—31no—
239C2×#67—62no—
240C2×#67—62no—
241C2×#67—62no—
242C2×#67—62no—
243C2×#67—62no—
244C2×#67—62no—
245C2×#67—122no—
246C2×#67—128no—
247C22×Dic3—62no—
248D3×D4—24no—
249D3×D4—42no—
250D3×D4—64no—
251D3×D4—64no—
252D3×D4—122no—
253D3×D4—122no—
254D3×D4—128no—
255C2×D12—31no—
256C2×D12C22×D312yes—
257C2×D12C22×D312yes—
258C2×C4×D3—31no—
259C2×C4×D3—31no—
260C2×C4×D3—61no—
261C2×C4×D3—62no—
262C2×C4×D3C22×D311yescharacteristic
263C3×D8—22no—
264C3×D8—22no—
265C3×D8—34no—
266C3×D8—42no—
267C3×D8—64no—
268C3×D8—62no—
269C3×D8—122no—
270C2×C3×C8—21no—
271C2×C3×C8—31no—
272C2×C3×C8—31no—
273C2×C3×C8—62no—
274C2×C3×C8C22×D311yescharacteristic
275C2×C3×C8C22×D311yescharacteristic
276C3×C42—31no—
277#217—31no—
278#217—62no—
279#217—62no—
280#217—62no—
281#217—62no—
282#217—122no—
283#213—24no—
284#213—42no—
285#213—64no—
286#213—64no—
287(C2×D3)⋊C4—31no—
288(C2×D3)⋊C4—31no—
289(C2×D3)⋊C4—31no—
290(C2×D3)⋊C4—62no—
291(C2×D3)⋊C4—62no—
292C4⋊Dic3—31no—
293C4⋊Dic3—32no—
294C4⋊Dic3—32no—
295C4⋊Dic3—62no—
296Dic3⋊C4—31no—
297C4×Dic3C22×D311yescharacteristic
298C2×C3⋊C8—31no—
299C2×C3⋊C8—31no—
300C2×C3⋊C8—61no—
301C2×C3⋊C8C22×D311yescharacteristic
302C2×C3⋊C8C22×D311yescharacteristic
303D24—22no—
304D24#6714yescomplemented
305D3×C8—22no—
306D3×C8—62no—
307D3×C8—62no—
308D3×C8—122no—
309C22×C32—42no—
310C22×C32—42no—
311C22×C32—42no—
312C22×C32C22×D411yescharacteristic
313C2×C3⋊D3—21no—
314C2×C3⋊D3—21no—
315C2×C3⋊D3C2×D812yescomplemented
316C2×C3×D3—21no—
317C2×C3×D3—21no—
318C2×C3×D3—24no—
319C2×C3×D3—42no—
320C2×C3×D3—42no—
321C2×C3×D3—42no—
322C2×C3×D3—42no—
323C2×C3×D3—42no—
324C2×C3×D3—88no—
325C2×C3×D3C2×D812yescomplemented
326D32—88no—
327C32×C4C22×D411yescharacteristic
328C32×C4H(5,𝔽2)11yescharacteristic
329C3⋊Dic3—21no—
330C3⋊Dic3—42no—
331C3×Dic3—21no—
332C3×Dic3—21no—
333C3×Dic3C2×D812yescomplemented
334C22×D4—32no—
335C22×D4—92no—
336C22×D4—182no—
337C2×D8—32no—
338C2×D8—32no—
339C2×D8—31no—
340C2×D8—31no—
341C2×D8—64no—
342C2×D8—92no—
343C2×D8—184no—
344C2×D8D3211yescharacteristic, complemented
345C22×C8—31no—
346C22×C8—91no—
347#127—32no—
348#121—92no—
349#121—92no—
350#121—182no—
351#120—182no—
352#120—182no—
353C4×D4—91no—
354C4×D4—92no—
355#107—91no—
356C4⋊C8—91no—
357#102—92no—
358#102—92no—
359#102—92no—
360C22⋊C8—91no—
361C22⋊C8—91no—
362C4×C8—31no—
363C23×C3—22no—
364C23×C3—22no—
365C23×C3—31no—
366C23×C3—42no—
367C23×C3—62no—
368C23×C3—62no—
369C23×C3—124no—
370C23×C3—124no—
371C23×C3—242no—
372C22×D3—22no—
373C22×D3—22no—
374C22×D3—31no—
375C22×D3—31no—
376C22×D3—44no—
377C22×D3—44no—
378C22×D3—61no—
379C22×D3—82no—
380C22×D3—124no—
381C22×D3—124no—
382C22×D3—124no—
383C22×D3—124no—
384C22×D3—242no—
385C22×D3—242no—
386C22×D3D3×D411yescharacteristic
387C3×D4—22no—
388C3×D4—22no—
389C3×D4—22no—
390C3×D4—22no—
391C3×D4—34no—
392C3×D4—42no—
393C3×D4—42no—
394C3×D4—62no—
395C3×D4—62no—
396C3×D4—62no—
397C3×D4—124no—
398C3×D4—124no—
399C3×D4—242no—
400C2×C3×C4—21no—
401C2×C3×C4—31no—
402C2×C3×C4—31no—
403C2×C3×C4—31no—
404C2×C3×C4—61no—
405C2×C3×C4—61no—
406C2×C3×C4C23×D311yescharacteristic
407C2×C3×C4C23×D311yescharacteristic
408#67—34no—
409#67—44no—
410#67—44no—
411#67—82no—
412#67—124no—
413#67—124no—
414#67—124no—
415#67—124no—
416#67—124no—
417#67—124no—
418#67—244no—
419C2×Dic3—31no—
420C2×Dic3—31no—
421C2×Dic3—61no—
422C2×Dic3—62no—
423C2×Dic3—62no—
424C2×Dic3—122no—
425C2×Dic3—124no—
426C2×Dic3D3×D411yescharacteristic
427C2×Dic3D3×D411yescharacteristic
428C2×Dic3D3×D411yescharacteristic
429D12—22no—
430D12—22no—
431D12—22no—
432D12—34no—
433D12C2×#6714yescomplemented
434C4×D3—21no—
435C4×D3—21no—
436C4×D3—61no—
437C4×D3—61no—
438C4×D3—61no—
439C4×D3—61no—
440C4×D3—121no—
441C4×D3—121no—
442C4×D3—124no—
443C3×C8—22no—
444C3×C8—61no—
445C3×C8—61no—
446C3×C8D3×D412yescomplemented
447C3×C8C2×#6712yescomplemented
448C3⋊C8—21no—
449C3⋊C8—21no—
450C3⋊C8—61no—
451C3⋊C8—61no—
452C3⋊C8—121no—
453C2×C32—82no—
454C2×C32D4211yescharacteristic
455C2×C32C22×D811yescharacteristic
456C2×C32#57611yescharacteristic
457C3⋊D3—22no—
458C3×D3—22no—
459C3×D3—44no—
460C3×D3—82no—
461C24—62no—
462C24—182no—
463C2×D4—32no—
464C2×D4—32no—
465C2×D4—62no—
466C2×D4—62no—
467C2×D4—62no—
468C2×D4—64no—
469C2×D4—91no—
470C2×D4—122no—
471C2×D4—182no—
472C2×D4—184no—
473C2×D4—182no—
474C2×D4—182no—
475C2×D4—362no—
476C2×D4—368no—
477C2×D4C2×D3212yes—
478C22×C4—31no—
479C22×C4—91no—
480C22×C4—182no—
481D8—22no—
482D8—34no—
483D8—64no—
484D8—62no—
485D8—122no—
486D8—184no—
487C2×C8—31no—
488C2×C8—31no—
489C2×C8—62no—
490C2×C8—91no—
491C2×C8—182no—
492C2×C8C2×D3211yescharacteristic
493C4⋊C4—91no—
494C4⋊C4—92no—
495C22⋊C4—91no—
496C22⋊C4—91no—
497C22⋊C4—182no—
498C22⋊C4—182no—
499C22⋊C4—182no—
500C42—31no—
501C22×C3—21no—
502C22×C3—32no—
503C22×C3—42no—
504C22×C3—42no—
505C22×C3—42no—
506C22×C3—42no—
507C22×C3—42no—
508C22×C3—42no—
509C22×C3—61no—
510C22×C3—61no—
511C22×C3—64no—
512C22×C3—82no—
513C22×C3—82no—
514C22×C3—82no—
515C22×C3—122no—
516C22×C3—122no—
517C22×C3—122no—
518C22×C3—122no—
519C22×C3—122no—
520C22×C3—248no—
521C22×C3C2×D3×D411yescharacteristic
522C22×C3C2×D3×D411yescharacteristic
523C2×D3—21no—
524C2×D3—21no—
525C2×D3—24no—
526C2×D3—32no—
527C2×D3—32no—
528C2×D3—42no—
529C2×D3—42no—
530C2×D3—42no—
531C2×D3—42no—
532C2×D3—42no—
533C2×D3—62no—
534C2×D3—61no—
535C2×D3—61no—
536C2×D3—61no—
537C2×D3—61no—
538C2×D3—88no—
539C2×D3—121no—
540C2×D3—121no—
541C2×D3—248no—
542C2×D3—248no—
543C2×D3D3×D812yescomplemented
544C3×C4—21no—
545C3×C4—21no—
546C3×C4—32no—
547C3×C4—61no—
548C3×C4—61no—
549C3×C4C2×D3×D411yescharacteristic
550C3×C4#100411yescharacteristic
551C3×C4#100411yescharacteristic
552C3×C4C22×#6711yescharacteristic
553Dic3—21no—
554Dic3—21no—
555Dic3—61no—
556Dic3—61no—
557Dic3—121no—
558Dic3—122no—
559Dic3—122no—
560Dic3—242no—
561Dic3D3×D812yescomplemented
562C32D4×D811yescharacteristic, complemented, Sylow
563C23—22no—
564C23—31no—
565C23—62no—
566C23—62no—
567C23—91no—
568C23—124no—
569C23—124no—
570C23—242no—
571C23—364no—
572C23—364no—
573C23—722no—
574D4—22no—
575D4—22no—
576D4—34no—
577D4—62no—
578D4—62no—
579D4—62no—
580D4—94no—
581D4—124no—
582D4—124no—
583D4—242no—
584D4—364no—
585D4—364no—
586D4—364no—
587C2×C4—31no—
588C2×C4—31no—
589C2×C4—31no—
590C2×C4—61no—
591C2×C4—61no—
592C2×C4—91no—
593C2×C4—181no—
594C2×C4—181no—
595C2×C4—182no—
596C2×C4—364no—
597C2×C4C22×D3211yescharacteristic
598C8—61no—
599C8—61no—
600C8—181no—
601C8D3×#6712yescomplemented
602C2×C3—21no—
603C2×C3—21no—
604C2×C3—21no—
605C2×C3—62no—
606C2×C3—82no—
607C2×C3—82no—
608C2×C3—124no—
609C2×C3—162no—
610C2×C3—242no—
611C2×C3#571711yescharacteristic
612C2×C3C2×D3×D811yescharacteristic
613C2×C3C2×D3×D811yescharacteristic
614C2×C3#575711yescharacteristic
615C2×C3#575711yescharacteristic
616C2×C3D4×#6711yescharacteristic
617D3—22no—
618D3—44no—
619D3—62no—
620D3—62no—
621D3—82no—
622D3—122no—
623C22—32no—
624C22—42no—
625C22—42no—
626C22—42no—
627C22—61no—
628C22—61no—
629C22—64no—
630C22—92no—
631C22—122no—
632C22—122no—
633C22—122no—
634C22—122no—
635C22—122no—
636C22—181no—
637C22—181no—
638C22—248no—
639C22—728no—
640C22D32×D411yescharacteristic
641C4—32no—
642C4—61no—
643C4—61no—
644C4—181no—
645C4—362no—
646C4#6431311yescharacteristic
647C4C2×D3×#6711yescharacteristic
648C3—21no—
649C3#8178911yescharacteristic, complemented
650C3D8×#6711yescharacteristic, complemented
651C2—62no—
652C2—82no—
653C2—124no—
654C2—182no—
655C2—242no—
656C2D32×D811yescharacteristic
657C2#1059473111yescharacteristic
658C2#1059529311yescharacteristic
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. #10595293C2semidirect
3. C2×#63797C2semidirect
4. #10592856C2semidirect
5. C3×#5151C2semidirect
6. #10591516C2semidirect
7. #10591447C2semidirect
8. #10591428C2semidirect
9. #10590831C2semidirect
10. Dic3×D24C2semidirect
11. C8×#626C2semidirect
14. C2×C3×D3×D4C22semidirect
16. C2×#3802C22semidirect
17. C2×C32×D8C22semidirect
18. #64147C22semidirect
19. C2×C8×C3⋊D3C22semidirect
20. C3×#940C22semidirect
21. C2×C3×#213C22semidirect
22. C2×C3×#213C22semidirect
25. C2×C3×D24C22semidirect
26. C2×C3×D3×C8C22semidirect
30. #63908C22semidirect
32. Dic3×D12C22semidirect
33. C2×#3713C22semidirect
35. #63659C22semidirect
36. #63645C22semidirect
37. C3×C8×Dic3C22semidirect
38. Dic3⋊(C3⋊C8)C22semidirect
39. #63563C22semidirect
40. #63563C22semidirect
41. #63557C22semidirect
42. (C2×D3)⋊(C3⋊C8)C22semidirect
47. C2×D3×D8D3semidirect
58. #5151D3semidirect
98. C3×D24D4semidirect
112. C2×D3×D4C2×D3semidirect
119. C2×C3×D8C2×D3semidirect
120. C2×C3×D8C2×D3semidirect
124. #940C2×D3semidirect
137. C2×#213C2×D3semidirect
138. C2×#213C2×D3semidirect
145. C2×D24C2×D3semidirect
149. C2×D3×C8C2×D3semidirect
168. C8×Dic3C2×D3semidirect
198. C3×D12C2×D4semidirect
201. #626D8semidirect
205. C32×C8C2×D4semidirect
304. D24#67semidirect
315. C2×C3⋊D3C2×D8semidirect
325. C2×C3×D3C2×D8semidirect
333. C3×Dic3C2×D8semidirect
344. C2×D8D32semidirect
433. D12C2×#67semidirect
446. C3×C8D3×D4semidirect
447. C3×C8C2×#67semidirect
543. C2×D3D3×D8semidirect
561. Dic3D3×D8semidirect
562. C32D4×D8semidirect
601. C8D3×#67semidirect
649. C3#81789semidirect
650. 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
#105952932
C2×#637972
#105928562
C3×#51512
#105915162
#105914472
#105914282
#105908312
Dic3×D242
C8×#6262
D8×#673
#817893