Finite Group Databasebeta

← #11878672

Subgroups — #11878672

Order 1152.

1163 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#940C211yesmaximal, characteristic, complemented
2#10594910C211yesmaximal, characteristic, complemented
3#10592916C211yesmaximal, characteristic, complemented
4C3×#5217C211yesmaximal, characteristic, complemented
5#10591487C212yesmaximal, complemented
6#10591482C212yesmaximal, complemented
7#10591429C212yesmaximal, complemented
8#10591428C212yesmaximal, complemented
9#10591162C211yesmaximal, characteristic, complemented
10#10591160C211yesmaximal, characteristic, complemented
11#10591053C211yesmaximal, characteristic, complemented
12#83166—31nomaximal
13#79994—31nomaximal
14C22×C32×D4C2211yescharacteristic
15C22×C3×#67—21no—
16C22×C3×#67—21no—
17C22×C3×D12C2211yescharacteristic
18C2×#3804—21no—
19C2×#3753C2212yescomplemented
20#64139C2211yescharacteristic
21C3×#940—21no—
22C3×#940—21no—
23C3×#940C2212yes—
24C3×#940C2212yes—
25C2×C3×#213C2212yescomplemented
26C3×#930C2211yescharacteristic
27C2×C3×C4×Dic3C2211yescharacteristic
28#63978—21no—
29#63918C2211yescharacteristic, complemented
30#63911C2211yescharacteristic, complemented
31#63894C2211yescharacteristic, complemented
32Dic3×D12C2211yescharacteristic, complemented
33#63880—21no—
34#63852—21no—
35C2×#3714C2212yescomplemented
36C2×#3713C2212yescomplemented
37#63659C2212yescomplemented
38#63657C2211yescharacteristic
39C3×#832C2212yescomplemented
40C3×#830C2211yescharacteristic
41Dic3⋊(C3⋊C8)C2212yescomplemented
42#63563C2212yescomplemented
43#63562C2212yescomplemented
44Dic3×C3⋊C8C2212yescomplemented
45C2×C3×#127—31no—
46C2×#940D311yescharacteristic, complemented
47#5596—31no—
48#5477—31no—
49C3×#447—31no—
50#5217—31no—
51#5217—31no—
52#5217—31no—
53#5217—31no—
54#5217—61no—
55#5217D311yescharacteristic, complemented
56#5151—32no—
57#5150—32no—
58#5073—32no—
59#5072—32no—
60#5072—32no—
61#5070—32no—
62#5036—31no—
63#4925—31no—
64#4786—32no—
65#4760—32no—
66#4732—31no—
67#4718—31no—
68C24×C32—21no—
69C23×C3×D3—21no—
70C2×C32×D4—21no—
71C2×C32×D4—42no—
72C2×C32×D4C2312yes—
73C22×C32×C4C2311yescharacteristic
74C2×#638—21no—
75C2×C4⋊(C3⋊D3)C2311yescharacteristic
76C2×C3×#67—21no—
77C2×C3×#67—22no—
78C2×C3×#67—22no—
79C2×C3×#67—22no—
80C2×C3×#67—22no—
81C2×C3×#67—44no—
82C2×C3×#67—44no—
83C22×C3×Dic3D411yescharacteristic
84C22×C3×Dic3D411yescharacteristic
85C2×C3×D12—21no—
86C2×C3×D12—42no—
87C2×C3×D12C2311yescharacteristic
88C2×C3×D12C2312yes—
89C2×#627—21no—
90C2×#626—21no—
91C2×#626—21no—
92C2×#624—21no—
93#3804—44no—
94C2×D3×Dic3—21no—
95#3753—42no—
96#3752—21no—
97C4⋊(C3⋊Dic3)C2311yescharacteristic
98C2×C3⋊(C3⋊C8)C2312yes—
99C3×#213—42no—
100C3×(C2×D3)⋊C4—21no—
101C3×C4⋊Dic3C2311yescharacteristic
102C3×C4×Dic3D411yescharacteristic
103C3×C4×Dic3D411yescharacteristic
104C3×C4×Dic3C2311yescharacteristic
105C3×C4×Dic3C2311yescharacteristic
106C2×C3×C3⋊C8C2312yes—
107Dic3⋊Dic3—21no—
108#3722—21no—
109(C2×D3)⋊Dic3—21no—
110#3714—42no—
111#3713—42no—
112#3205—91noSylow
113C22×C3×D4—21no—
114C22×C3×D4—31no—
115C22×C3×D4—61no—
116C22×C3×D4—61no—
117C22×C3×D4C2×D311yescharacteristic
118C22×C3×D4C2×D311yescharacteristic
119C22×#67—21no—
120C22×#67—21no—
121C2×#237—61no—
122C2×#235—61no—
123C22×D12C2×D311yescharacteristic
124C2×C3×D8—32no—
125C3×#127—32no—
126C3×#127—32no—
127C3×#127—61no—
128C3×#127—61no—
129C3×#121—31no—
130C2×C3×C42—31no—
131#940—21no—
132#940—21no—
133#940—31no—
134#940C2×D312yes—
135#940C2×D312yes—
136#939—61no—
137D4×Dic3—31no—
138C2×#213—32no—
139C2×#213—32no—
140C2×#213—32no—
141C2×#213—32no—
142C2×#213—32no—
143C2×#213—62no—
144C2×#213C2×D312yescomplemented
145#930—31no—
146#930—31no—
147#930—61no—
148#930—61no—
149#930C2×D311yescharacteristic
150C2×C4×Dic3C2×D311yescharacteristic
151C2×D24—32no—
152#893—31no—
153#888—31no—
154#885—61no—
155#67⋊C4—61no—
156#875—61no—
157#874—31no—
158C4×D12—31no—
159C4×D12—31no—
160C4×D12—61no—
161#869—31no—
162C3×#102—32no—
163C3×C22⋊C8—31no—
164#832—32no—
165#832—32no—
166#832—32no—
167#832—32no—
168#832—62no—
169#832C2×D312yescomplemented
170#830—31no—
171#830—31no—
172#830—61no—
173#830C2×D311yescharacteristic
174#821—32no—
175Dic3⋊C8—32no—
176C8×Dic3—32no—
177#809—32no—
178C4⋊(C3⋊C8)—32no—
179C4×C3⋊C8—32no—
180C23×C32—22no—
181C23×C32—42no—
182C23×C32—42no—
183C23×C32—42no—
184C23×C32C2×D411yescharacteristic
185C22×C3⋊D3—21no—
186C22×C3×D3—22no—
187C22×C3×D3—21no—
188C22×C3×D3—42no—
189C22×C3×D3—42no—
190C22×C3×D3—42no—
191C32×D4—22no—
192C32×D4—22no—
193C32×D4—42no—
194C2×C32×C4—22no—
195C2×C32×C4C2×D411yescharacteristic
196C2×C32×C4C2411yescharacteristic
197#638—42no—
198C2×C3⋊Dic3—21no—
199C4⋊(C3⋊D3)—22no—
200C3×#67—44no—
201C3×#67—42no—
202C3×#67—44no—
203C3×#67—44no—
204C3×#67—44no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3—21no—
207C2×C3×Dic3D814yescomplemented
208C2×C3×Dic3C2×D411yescharacteristic
209C2×C3×Dic3C2×D411yescharacteristic
210C2×C3×Dic3C2×D411yescharacteristic
211C2×C3×Dic3C2×D411yescharacteristic
212C3×D12—22no—
213C3×D12—22no—
214C3×D12—22no—
215C3×D12—42no—
216#627—42no—
217#626—42no—
218#626—42no—
219#624—42no—
220D3×Dic3—42no—
221C3⋊(C3⋊C8)—22no—
222C3×C3⋊C8—22no—
223#532—91no—
224C2×#127—31no—
225#493—92no—
226#486—92no—
227#459—92no—
228#459—92no—
229#447—31no—
230#447—91no—
231#447—91no—
232#447—91no—
233#431—91no—
234C24×C3—21no—
235C24×C3—21no—
236C24×C3—41no—
237C24×C3—61no—
238C23×D3—21no—
239C2×C3×D4—21no—
240C2×C3×D4—21no—
241C2×C3×D4—22no—
242C2×C3×D4—32no—
243C2×C3×D4—31no—
244C2×C3×D4—41no—
245C2×C3×D4—42no—
246C2×C3×D4—42no—
247C2×C3×D4—44no—
248C2×C3×D4—62no—
249C2×C3×D4—62no—
250C2×C3×D4—62no—
251C2×C3×D4—62no—
252C2×C3×D4—61no—
253C2×C3×D4—61no—
254C2×C3×D4—122no—
255C2×C3×D4—124no—
256C2×C3×D4—124no—
257C2×C3×D4C22×D312yes—
258C2×C3×D4C22×D312yes—
259C22×C3×C4—21no—
260C22×C3×C4—31no—
261C22×C3×C4—31no—
262C22×C3×C4C22×D311yescharacteristic
263C22×C3×C4C22×D311yescharacteristic
264C2×#67—21no—
265C2×#67—22no—
266C2×#67—22no—
267C2×#67—22no—
268C2×#67—22no—
269C2×#67—44no—
270C2×#67—44no—
271C2×#67—61no—
272C2×#67—61no—
273C2×#67—61no—
274C2×#67—61no—
275C2×#67—121no—
276C22×Dic3—61no—
277C22×Dic3#6711yescharacteristic
278C22×Dic3#6711yescharacteristic
279#237—124no—
280#235—124no—
281C2×D12—21no—
282C2×D12—31no—
283C2×D12—31no—
284C2×D12—42no—
285C2×D12—61no—
286C2×D12—61no—
287C2×D12—61no—
288C2×D12C22×D312yes—
289C2×D12C22×D311yescharacteristic
290C2×C4×D3—61no—
291C2×C4×D3—61no—
292C2×C4×D3—61no—
293C2×Dic6—61no—
294C2×Dic6—61no—
295C3×D8—122no—
296C2×C3×C8—32no—
297C3×C4⋊C4—31no—
298C3×C22⋊C4—61no—
299C3×C42—31no—
300C3×C42—31no—
301C3×C42—31no—
302C3×C42—31no—
303#217—61no—
304#213—42no—
305#213—122no—
306#213—122no—
307#213—122no—
308#213—122no—
309#213—122no—
310#213—124no—
311(C2×D3)⋊C4—21no—
312(C2×D3)⋊C4—61no—
313(C2×D3)⋊C4—61no—
314(C2×D3)⋊C4—61no—
315(C2×D3)⋊C4—61no—
316(C2×D3)⋊C4—61no—
317(C2×D3)⋊C4—121no—
318C4⋊Dic3—31no—
319C4⋊Dic3—31no—
320C4⋊Dic3—61no—
321C4⋊Dic3—61no—
322C4⋊Dic3C22×D311yescharacteristic
323Dic3⋊C4—61no—
324C4×Dic3#6711yescharacteristic
325C4×Dic3#6711yescharacteristic
326C4×Dic3C22×D311yescharacteristic
327C4×Dic3C22×D311yescharacteristic
328C2×C3⋊C8—32no—
329C2×C3⋊C8—32no—
330C2×C3⋊C8—62no—
331C2×C3⋊C8C22×D312yes—
332D24—122no—
333C22×C32—21no—
334C22×C32—21no—
335C22×C32—42no—
336C22×C32—42no—
337C22×C32—42no—
338C22×C32—84no—
339C22×C32C2×D812yes—
340C22×C32C22×D411yescharacteristic
341C2×C3⋊D3—41no—
342C2×C3⋊D3—41no—
343C2×C3⋊D3—41no—
344C2×C3×D3—42no—
345C2×C3×D3—41no—
346C2×C3×D3—41no—
347C2×C3×D3—42no—
348C2×C3×D3—41no—
349C2×C3×D3—42no—
350C2×C3×D3—84no—
351C32×C4—21no—
352C32×C4H(5,𝔽2)12yes—
353C3⋊Dic3—41no—
354C3×Dic3—21no—
355C3×Dic3—41no—
356C3×Dic3C2×D812yes—
357C3×Dic3C2×D812yes—
358C3×Dic3AGL(1,ℤ/8)12yes—
359C2×#41—181no—
360C22×D4—31no—
361C22×D4—61no—
362C22×D4—61no—
363C22×D4D3211yescharacteristic
364C2×D8—32no—
365C2×D8—92no—
366C2×D8—92no—
367C2×D8—92no—
368C4⋊Q8—91no—
369#127—32no—
370#127—32no—
371#127—61no—
372#127—61no—
373#127—91no—
374#124—181no—
375#121—31no—
376#121—91no—
377#121—181no—
378C4×D4—91no—
379C4×D4—91no—
380C4×D4—181no—
381C2×C42—31no—
382C4⋊C8—92no—
383#102—32no—
384#102—92no—
385#102—92no—
386#102—92no—
387C22⋊C8—31no—
388C22⋊C8—91no—
389C4×C8—92no—
390C23×C3—22no—
391C23×C3—22no—
392C23×C3—21no—
393C23×C3—42no—
394C23×C3—42no—
395C23×C3—42no—
396C23×C3—42no—
397C23×C3—42no—
398C23×C3—44no—
399C23×C3—42no—
400C23×C3—42no—
401C23×C3—62no—
402C23×C3—61no—
403C23×C3—82no—
404C23×C3—82no—
405C23×C3—122no—
406C23×C3—122no—
407C23×C3—122no—
408C23×C3D3×D411yescharacteristic
409C23×C3C2×#6711yescharacteristic
410C22×D3—21no—
411C22×D3—22no—
412C22×D3—42no—
413C22×D3—42no—
414C22×D3—42no—
415C22×D3—61no—
416C22×D3—61no—
417C22×D3—121no—
418C3×D4—24no—
419C3×D4—22no—
420C3×D4—22no—
421C3×D4—22no—
422C3×D4—22no—
423C3×D4—42no—
424C3×D4—42no—
425C3×D4—42no—
426C3×D4—44no—
427C3×D4—62no—
428C3×D4—62no—
429C3×D4—62no—
430C3×D4—122no—
431C3×D4—124no—
432C3×D4—124no—
433C3×D4—124no—
434C3×D4—124no—
435C3×D4—122no—
436C2×C3×C4—22no—
437C2×C3×C4—22no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—34no—
441C2×C3×C4—31no—
442C2×C3×C4—31no—
443C2×C3×C4—31no—
444C2×C3×C4—31no—
445C2×C3×C4—42no—
446C2×C3×C4—62no—
447C2×C3×C4—61no—
448C2×C3×C4D3×D411yescharacteristic
449C2×C3×C4C2×#6711yescharacteristic
450C2×C3×C4C23×D311yescharacteristic
451C2×C3×C4C23×D311yescharacteristic
452#67—44no—
453#67—42no—
454#67—44no—
455#67—44no—
456#67—44no—
457#67—122no—
458#67—122no—
459#67—122no—
460#67—122no—
461#67—242no—
462C2×Dic3—22no—
463C2×Dic3—21no—
464C2×Dic3—61no—
465C2×Dic3—61no—
466C2×Dic3—121no—
467C2×Dic3—122no—
468C2×Dic3#21314yescomplemented
469C2×Dic3C2×#6711yescharacteristic
470C2×Dic3C2×#6711yescharacteristic
471C2×Dic3C2×#6711yescharacteristic
472C2×Dic3C2×#6711yescharacteristic
473D12—22no—
474D12—22no—
475D12—22no—
476D12—42no—
477D12—62no—
478D12—62no—
479D12—122no—
480D12—122no—
481D12—122no—
482C4×D3—122no—
483C4×D3—122no—
484C4×D3—122no—
485Dic6—122no—
486Dic6—122no—
487C3×C8—62no—
488C3⋊C8—22no—
489C3⋊C8—62no—
490C3⋊C8—62no—
491C3⋊C8—122no—
492C2×C32—22no—
493C2×C32—82no—
494C2×C32#53511yescharacteristic
495C2×C32C22×D811yescharacteristic
496C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
497C3⋊D3—81no—
498C3×D3—81no—
499C3×D3—82no—
500C24—21no—
501C24—61no—
502#41—364no—
503C2×Q8—181no—
504C2×D4—21no—
505C2×D4—32no—
506C2×D4—31no—
507C2×D4—42no—
508C2×D4—62no—
509C2×D4—62no—
510C2×D4—62no—
511C2×D4—62no—
512C2×D4—61no—
513C2×D4—61no—
514C2×D4—91no—
515C2×D4—122no—
516C2×D4—124no—
517C2×D4—124no—
518C2×D4—181no—
519C2×D4—181no—
520C2×D4—181no—
521C2×D4C2×D3212yes—
522C22×C4—31no—
523C22×C4—31no—
524C22×C4—181no—
525C22×C4—181no—
526C22×C4C2×D3211yescharacteristic
527D8—122no—
528D8—362no—
529D8—362no—
530D8—362no—
531C2×C8—32no—
532C2×C8—92no—
533C4⋊C4—31no—
534C4⋊C4—91no—
535C4⋊C4—181no—
536C22⋊C4—61no—
537C22⋊C4—181no—
538C22⋊C4—181no—
539C22⋊C4—181no—
540C42—31no—
541C42—31no—
542C42—31no—
543C42—31no—
544C22×C3—21no—
545C22×C3—21no—
546C22×C3—21no—
547C22×C3—21no—
548C22×C3—21no—
549C22×C3—22no—
550C22×C3—41no—
551C22×C3—41no—
552C22×C3—44no—
553C22×C3—42no—
554C22×C3—42no—
555C22×C3—42no—
556C22×C3—42no—
557C22×C3—42no—
558C22×C3—42no—
559C22×C3—82no—
560C22×C3—82no—
561C22×C3—84no—
562C22×C3—84no—
563C22×C3—88no—
564C22×C3—122no—
565C22×C3—122no—
566C22×C3—121no—
567C22×C3—121no—
568C22×C3—121no—
569C22×C3—122no—
570C22×C3—244no—
571C22×C3D3×D812yes—
572C22×C3C2×#21312yes—
573C22×C3C2×D3×D411yescharacteristic
574C22×C3C22×#6711yescharacteristic
575C2×D3—41no—
576C2×D3—41no—
577C2×D3—42no—
578C2×D3—42no—
579C2×D3—42no—
580C2×D3—41no—
581C2×D3—84no—
582C2×D3—121no—
583C2×D3—121no—
584C2×D3—121no—
585C2×D3—121no—
586C2×D3—121no—
587C2×D3—121no—
588C2×D3—241no—
589C2×D3—241no—
590C2×D3—241no—
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—22no—
594C3×C4—32no—
595C3×C4—32no—
596C3×C4—32no—
597C3×C4—41no—
598C3×C4—61no—
599C3×C4—121no—
600C3×C4#100412yes—
601C3×C4#100412yes—
602Dic3—21no—
603Dic3—41no—
604Dic3—121no—
605Dic3—121no—
606Dic3—241no—
607Dic3C2×#21312yes—
608Dic3C2×#21312yes—
609Dic3#93212yes—
610C32#320511yescharacteristic, complemented, Sylow
611C23—22no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—61no—
616C23—62no—
617C23—122no—
618C23—122no—
619C23—122no—
620C23—181no—
621C23D3×#6711yescharacteristic
622Q8—362no—
623D4—22no—
624D4—22no—
625D4—42no—
626D4—62no—
627D4—62no—
628D4—62no—
629D4—122no—
630D4—124no—
631D4—124no—
632D4—124no—
633D4—124no—
634D4—122no—
635D4—182no—
636D4—362no—
637D4—362no—
638D4—362no—
639C2×C4—22no—
640C2×C4—31no—
641C2×C4—31no—
642C2×C4—31no—
643C2×C4—34no—
644C2×C4—31no—
645C2×C4—62no—
646C2×C4—61no—
647C2×C4—181no—
648C2×C4—362no—
649C2×C4—362no—
650C2×C4D3×#6711yescharacteristic
651C2×C4C22×D3211yescharacteristic
652C8—62no—
653C8—182no—
654C2×C3—22no—
655C2×C3—22no—
656C2×C3—21no—
657C2×C3—21no—
658C2×C3—21no—
659C2×C3—42no—
660C2×C3—84no—
661C2×C3—82no—
662C2×C3—82no—
663C2×C3—242no—
664C2×C3—241no—
665C2×C3#559211yescharacteristic
666C2×C3C2×D3×D811yescharacteristic
667C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
668C2×C3C22×#21311yescharacteristic
669C2×C3C2×#93211yescharacteristic
670C2×C3#580511yescharacteristic
671D3—81no—
672D3—82no—
673D3—241no—
674D3—241no—
675D3—481no—
676C22—21no—
677C22—21no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—84no—
682C22—121no—
683C22—122no—
684C22—122no—
685C22—121no—
686C22—122no—
687C22—121no—
688C22—244no—
689C22—361no—
690C22—361no—
691C22—361no—
692C22D3×#21312yes—
693C22C2×D3×#6711yescharacteristic
694C4—21no—
695C4—32no—
696C4—32no—
697C4—32no—
698C4—61no—
699C4—121no—
700C4—361no—
701C4#6433012yes—
702C3—21no—
703C3#7999411yescharacteristic, complemented
704C3#8316611yescharacteristic, complemented
705C2—22no—
706C2—82no—
707C2—242no—
708C2—241no—
709C2—721no—
710C2C2×D3×#21311yescharacteristic
711C2D3×#93211yescharacteristic
712C2#1059551311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32#3205
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#940C2semidirect
2. #10594910C2semidirect
3. #10592916C2semidirect
4. C3×#5217C2semidirect
5. #10591487C2semidirect
6. #10591482C2semidirect
7. #10591429C2semidirect
8. #10591428C2semidirect
9. #10591162C2semidirect
10. #10591160C2semidirect
11. #10591053C2semidirect
19. C2×#3753C22semidirect
25. C2×C3×#213C22semidirect
29. #63918C22semidirect
30. #63911C22semidirect
31. #63894C22semidirect
32. Dic3×D12C22semidirect
35. C2×#3714C22semidirect
36. C2×#3713C22semidirect
37. #63659C22semidirect
39. C3×#832C22semidirect
41. Dic3⋊(C3⋊C8)C22semidirect
42. #63563C22semidirect
43. #63562C22semidirect
44. Dic3×C3⋊C8C22semidirect
46. C2×#940D3semidirect
55. #5217D3semidirect
144. C2×#213C2×D3semidirect
169. #832C2×D3semidirect
207. C2×C3×Dic3D8semidirect
468. C2×Dic3#213semidirect
610. C32#3205semidirect
703. C3#79994semidirect
704. C3#83166semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9402
#105949102
#105929162
C3×#52172
#105914872
#105914822
#105914292
#105914282
#105911622
#105911602
#105910532
#831663
#799943