Finite Group Databasebeta

← #11870510

Subgroups — #11870510

Order 1152.

950 conjugacy classes of subgroups.

The subgroup lattice has 629 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×D3×D4C211yesmaximal, characteristic
2#10593859C211yesmaximal, characteristic, complemented
3#10592707C211yesmaximal, characteristic, complemented
4C3×#5019C211yesmaximal, characteristic, complemented
5#10591458C212yesmaximal
6Dic3×#214C212yesmaximal, complemented
7#10590516C212yesmaximal, complemented
8#10590475C212yesmaximal, complemented
9#10590363C211yesmaximal, characteristic, complemented
10#10590268C211yesmaximal, characteristic, complemented
11#10590248C211yesmaximal, characteristic, complemented
12#82314—31nomaximal
13#80408—31nomaximal
14C2×C3×D3×D4C2211yescharacteristic
15C22×C3×C4×D3—21no—
16C32×C4×D4C2211yescharacteristic
17#64078C2211yescharacteristic, complemented
18C3×D4×Dic3C2211yescharacteristic
19C2×C3×#214C2212yes—
20C3×C4×#67—21no—
21C3×#893C2211yescharacteristic
22C3×D3×C4⋊C4C2211yescharacteristic
23C3×#67⋊C4—21no—
24C3×D3×C22⋊C4—21no—
25C3×C4×D12C2211yescharacteristic
26C3×C42×D3C2211yescharacteristic
27C3×#869C2211yescharacteristic, complemented
28#63869—21no—
29#63857—21no—
30#63856C2212yes—
31#63844—21no—
32Dic3×Dic6C2212yescomplemented
33#63841—21no—
34C2×#3715C2212yes—
35#63659C2212yes—
36#63635C2212yescomplemented
37C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
38C3×#810C2212yescomplemented
39C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
40#63573C2212yescomplemented
41#63565C2212yescomplemented
42#63563C2212yes—
43(C2×D3)⋊(C3⋊C8)C2212yes—
44Dic3×C3⋊C8C2212yescomplemented
45C2×C3×C4×D4—31no—
46#5728—31no—
47C4×D3×D4D311yescharacteristic
48#5470—31no—
49C3×#461—31no—
50#5218—32no—
51#5169—32no—
52Dic3×SD16—32no—
53#5083—31no—
54#5019—31no—
55#5019D311yescharacteristic, complemented
56C4×#214—32no—
57C4×#214—32no—
58#5008—31no—
59#5008—31no—
60#5008—31no—
61#5008—61no—
62#4971—32no—
63#4925—31no—
64#4842—31no—
65#4833—31no—
66#4805—32no—
67#4788—32no—
68C23×C3×D3—21no—
69C2×C32×D4C2311yescharacteristic
70C22×C32×C4—21no—
71C2×#634—21no—
72C2×C3×#67—21no—
73C22×C3×Dic3—21no—
74C3×D3×D4—22no—
75C3×D3×D4—22no—
76C2×C3×D12C2311yescharacteristic
77C2×C3×C4×D3—21no—
78C2×C3×C4×D3—21no—
79C2×C3×C4×D3—21no—
80C2×C3×C4×D3—44no—
81C2×C3×C4×D3D411yescharacteristic
82C2×C3×C4×D3D411yescharacteristic
83C2×C3×C4×D3C2311yescharacteristic
84C2×C3×Dic6C2312yes—
85C32×C4⋊C4C2311yescharacteristic
86C32×C22⋊C4—21no—
87C32×C42C2311yescharacteristic
88C4⋊(C3⋊Dic3)—21no—
89C4⋊(C3⋊Dic3)C2312yes—
90C2×C3⋊(C3⋊C8)C2312yes—
91C3×#217—21no—
92C3×#214—24no—
93C3×(C2×D3)⋊C4—21no—
94C3×(C2×D3)⋊C4—21no—
95C3×C4⋊Dic3—21no—
96C3×C4⋊Dic3—21no—
97C3×C4⋊Dic3C2311yescharacteristic
98C3×Dic3⋊C4—21no—
99C3×C4×Dic3D411yescharacteristic
100C3×C4×Dic3D411yescharacteristic
101C3×C4×Dic3C2311yescharacteristic
102C2×C3×C3⋊C8C2312yes—
103#3724—22no—
104Dic3⋊Dic3—22no—
105(C2×D3)⋊Dic3—22no—
106Dic32—22no—
107#3715—24no—
108#3101—91noSylow
109C22×C3×D4—31no—
110C23×C3×C4—61no—
111C2×D3×D4C2×D311yescharacteristic
112C22×C4×D3—21no—
113C2×C3×SD16—32no—
114C3×C4⋊Q8—31no—
115C3×C4×D4—21no—
116C3×C4×D4—31no—
117C3×C4×D4—31no—
118C3×C4×D4—31no—
119C3×C4×D4—61no—
120C3×C4×D4—61no—
121C3×C4×D4C2×D311yescharacteristic
122C3×C4×D4C2×D311yescharacteristic
123C2×C3×C4⋊C4—31no—
124C2×C3×C22⋊C4—61no—
125C2×C3×C42—31no—
126#946—32no—
127Q8×Dic3—32no—
128C2×#215—32no—
129D4×Dic3C2×D311yescharacteristic
130C2×#214—32no—
131C2×#214C2×D312yes—
132C4×#67—21no—
133#926—61no—
134#924—32no—
135#924—61no—
136#897—61no—
137#893C2×D311yescharacteristic
138#892—61no—
139D3×C4⋊C4C2×D311yescharacteristic
140#890—61no—
141#887—61no—
142#67⋊C4—21no—
143D3×C22⋊C4—21no—
144C4×D12C2×D311yescharacteristic
145C42×D3C2×D311yescharacteristic
146#870—61no—
147#869—31no—
148#869—31no—
149#869—61no—
150#869C2×D311yescharacteristic, complemented
151C4×Dic6—32no—
152C4×Dic6—61no—
153C3×C4⋊C8—31no—
154C3×#103—32no—
155#835—32no—
156#832—32no—
157#832—32no—
158#832—32no—
159#832—62no—
160#830—32no—
161#821—32no—
162(C2×D3)⋊C8—32no—
163#817—32no—
164C8×Dic3—32no—
165#810—32no—
166#810C2×D312yescomplemented
167#808—32no—
168#808—32no—
169#808—32no—
170#808—62no—
171C4⋊(C3⋊C8)—31no—
172C4⋊(C3⋊C8)—31no—
173C4⋊(C3⋊C8)—61no—
174C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
175C4×C3⋊C8—32no—
176C23×C32—21no—
177C22×C3×D3—24no—
178C22×C3×D3—21no—
179C22×C3×D3—42no—
180C22×C3×D3—42no—
181C22×C3×D3C2×D411yescharacteristic
182C32×D4—21no—
183C32×D4#4112yes—
184C2×C32×C4—21no—
185C2×C32×C4—42no—
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2411yescharacteristic
189C2×C3⋊Dic3—22no—
190#634—42no—
191C3×#67—24no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3—42no—
195C2×C3×Dic3C2×D411yescharacteristic
196C2×C3×Dic3C2×D411yescharacteristic
197C2×C3×Dic3C2×D411yescharacteristic
198C3×D12—21no—
199C3×D12#4112yes—
200C3×C4×D3—21no—
201C3×C4×D3—21no—
202C3×C4×D3—41no—
203C3×C4×D3—42no—
204C3×C4×D3—42no—
205C3×C4×D3—42no—
206C3×C4×D3SD1614yescomplemented
207C3×Dic6—22no—
208C3×Dic6—22no—
209C3⋊(C3⋊C8)—22no—
210C3×C3⋊C8—22no—
211#533—91no—
212C2×C4×D4—31no—
213#483—92no—
214#476—91no—
215#476—91no—
216#461—31no—
217#461—91no—
218#450—92no—
219C4×SD16—92no—
220C4×SD16—92no—
221#431—91no—
222C24×C3—61no—
223C23×D3—21no—
224C2×C3×Q8—32no—
225C2×C3×D4—21no—
226C2×C3×D4—31no—
227C2×C3×D4—61no—
228C2×C3×D4—62no—
229C2×C3×D4—62no—
230C2×C3×D4C22×D311yescharacteristic
231C2×C3×D4C22×D311yescharacteristic
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—31no—
235C22×C3×C4—31no—
236C22×C3×C4—31no—
237C22×C3×C4—41no—
238C22×C3×C4—61no—
239C22×C3×C4—61no—
240C22×C3×C4—61no—
241C22×C3×C4—61no—
242C22×C3×C4—124no—
243C2×#67—21no—
244C22×Dic3—21no—
245D3×D4—22no—
246D3×D4—22no—
247C2×D12C22×D311yescharacteristic
248C2×C4×D3—21no—
249C2×C4×D3—21no—
250C2×C4×D3—21no—
251C2×C4×D3—44no—
252C2×C4×D3#6711yescharacteristic
253C2×C4×D3#6711yescharacteristic
254C2×C4×D3C22×D311yescharacteristic
255C2×Dic6—61no—
256C2×Dic6—61no—
257C2×Dic6—121no—
258C2×Dic6C22×D312yes—
259C3×SD16—64no—
260C2×C3×C8—32no—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—31no—
263C3×C4⋊C4—61no—
264C3×C4⋊C4—61no—
265C3×C4⋊C4—61no—
266C3×C4⋊C4C22×D311yescharacteristic
267C3×C4⋊C4C22×D311yescharacteristic
268C3×C22⋊C4—21no—
269C3×C22⋊C4—21no—
270C3×C22⋊C4—41no—
271C3×C22⋊C4—61no—
272C3×C22⋊C4—61no—
273C3×C22⋊C4—61no—
274C3×C42—21no—
275C3×C42—31no—
276C3×C42—31no—
277C3×C42—31no—
278C3×C42C22×D311yescharacteristic
279C3×C42C22×D311yescharacteristic
280#217—21no—
281#217—62no—
282#215—64no—
283#214—24no—
284#214—64no—
285(C2×D3)⋊C4—21no—
286(C2×D3)⋊C4—21no—
287(C2×D3)⋊C4—62no—
288C4⋊Dic3—21no—
289C4⋊Dic3—21no—
290C4⋊Dic3—32no—
291C4⋊Dic3—32no—
292C4⋊Dic3—62no—
293C4⋊Dic3—61no—
294C4⋊Dic3—61no—
295C4⋊Dic3—62no—
296C4⋊Dic3—121no—
297C4⋊Dic3C22×D311yescharacteristic
298Dic3⋊C4—21no—
299Dic3⋊C4—62no—
300Dic3⋊C4—62no—
301Dic3⋊C4—62no—
302C4×Dic3—62no—
303C4×Dic3—62no—
304C4×Dic3#6711yescharacteristic
305C4×Dic3#6711yescharacteristic
306C4×Dic3C22×D311yescharacteristic
307C2×C3⋊C8—32no—
308C2×C3⋊C8—32no—
309C2×C3⋊C8—62no—
310C2×C3⋊C8C22×D312yes—
311C22×C32—22no—
312C22×C32—41no—
313C22×C32—41no—
314C22×C32C22×D411yescharacteristic
315C2×C3×D3—21no—
316C2×C3×D3—21no—
317C2×C3×D3—22no—
318C2×C3×D3—48no—
319C2×C3×D3—41no—
320C2×C3×D3—41no—
321C2×C3×D3C2×SD1612yes—
322C32×C4—21no—
323C32×C4—41no—
324C32×C4C2×SD1612yes—
325C32×C4C2×#4111yescharacteristic
326C32×C4C2×#4111yescharacteristic
327C3⋊Dic3—42no—
328C3×Dic3—21no—
329C3×Dic3—21no—
330C3×Dic3—42no—
331C3×Dic3—41no—
332C3×Dic3C2×SD1612yes—
333C22×D4—31no—
334C23×C4—61no—
335C2×SD16—32no—
336C2×SD16—92no—
337C4⋊Q8—31no—
338C4⋊Q8—91no—
339#125—181no—
340C22⋊Q8—92no—
341C22⋊Q8—181no—
342C4×Q8—92no—
343C4×Q8—181no—
344C4×D4—31no—
345C4×D4—31no—
346C4×D4—31no—
347C4×D4—61no—
348C4×D4—61no—
349C4×D4D3211yescharacteristic
350#117—181no—
351C2×C4⋊C4—31no—
352C2×C22⋊C4—61no—
353C2×C42—31no—
354#106—92no—
355#106—92no—
356C4⋊C8—31no—
357C4⋊C8—91no—
358#103—32no—
359#103—92no—
360#102—92no—
361#102—92no—
362C22⋊C8—92no—
363C4×C8—92no—
364C23×C3—21no—
365C23×C3—21no—
366C23×C3—31no—
367C23×C3—41no—
368C23×C3—64no—
369C23×C3—61no—
370C23×C3—122no—
371C23×C3—122no—
372C22×D3—24no—
373C22×D3—21no—
374C22×D3—42no—
375C22×D3—42no—
376C22×D3C2×#6711yescharacteristic
377C3×Q8—62no—
378C3×Q8—62no—
379C3×D4—21no—
380C3×D4—21no—
381C3×D4—22no—
382C3×D4—32no—
383C3×D4—41no—
384C3×D4—64no—
385C3×D4—61no—
386C3×D4#23512yes—
387C3×D4#23712yes—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—31no—
394C2×C3×C4—34no—
395C2×C3×C4—31no—
396C2×C3×C4—31no—
397C2×C3×C4—41no—
398C2×C3×C4—42no—
399C2×C3×C4—42no—
400C2×C3×C4—61no—
401C2×C3×C4—61no—
402C2×C3×C4—61no—
403C2×C3×C4—62no—
404C2×C3×C4—82no—
405C2×C3×C4—121no—
406C2×C3×C4—122no—
407C2×C3×C4—122no—
408C2×C3×C4—122no—
409C2×C3×C4—122no—
410C2×C3×C4D3×D411yescharacteristic
411C2×C3×C4D3×D411yescharacteristic
412C2×C3×C4C2×#6711yescharacteristic
413C2×C3×C4C2×#6711yescharacteristic
414C2×C3×C4C23×D311yescharacteristic
415C2×C3×C4C23×D311yescharacteristic
416#67—24no—
417C2×Dic3—22no—
418C2×Dic3—21no—
419C2×Dic3—42no—
420C2×Dic3—62no—
421C2×Dic3—62no—
422C2×Dic3—122no—
423C2×Dic3C2×#6711yescharacteristic
424C2×Dic3C2×#6711yescharacteristic
425C2×Dic3C2×#6711yescharacteristic
426D12—21no—
427D12#23512yes—
428C4×D3—21no—
429C4×D3—21no—
430C4×D3—41no—
431C4×D3—42no—
432C4×D3—42no—
433C4×D3—42no—
434C4×D3#21414yescomplemented
435Dic6—22no—
436Dic6—22no—
437Dic6—122no—
438Dic6—122no—
439Dic6—242no—
440C3×C8—62no—
441C3⋊C8—22no—
442C3⋊C8—62no—
443C3⋊C8—62no—
444C3⋊C8—122no—
445C2×C32—42no—
446C2×C32#52511yescharacteristic
447C2×C32C22×SD1611yescharacteristic
448C2×C32#57511yescharacteristic
449C3×D3—22no—
450C3×D3—42no—
451C24—61no—
452C2×Q8—32no—
453C2×Q8—181no—
454C2×D4—31no—
455C2×D4—61no—
456C2×D4—62no—
457C2×D4—62no—
458C2×D4C2×D3211yescharacteristic
459C22×C4—21no—
460C22×C4—31no—
461C22×C4—31no—
462C22×C4—31no—
463C22×C4—61no—
464C22×C4—61no—
465C22×C4—61no—
466C22×C4—61no—
467C22×C4—124no—
468SD16—64no—
469SD16—184no—
470C2×C8—32no—
471C2×C8—92no—
472C4⋊C4—31no—
473C4⋊C4—61no—
474C4⋊C4—61no—
475C4⋊C4—61no—
476C4⋊C4—92no—
477C4⋊C4—182no—
478C4⋊C4—182no—
479C4⋊C4—181no—
480C4⋊C4C2×D3211yescharacteristic
481C22⋊C4—21no—
482C22⋊C4—61no—
483C22⋊C4—61no—
484C22⋊C4—61no—
485C22⋊C4—182no—
486C42—31no—
487C42—31no—
488C42—31no—
489C42—182no—
490C42C2×D3211yescharacteristic
491C22×C3—22no—
492C22×C3—22no—
493C22×C3—21no—
494C22×C3—32no—
495C22×C3—42no—
496C22×C3—41no—
497C22×C3—41no—
498C22×C3—41no—
499C22×C3—41no—
500C22×C3—61no—
501C22×C3—61no—
502C22×C3—62no—
503C22×C3—81no—
504C22×C3—81no—
505C22×C3—128no—
506C22×C3—121no—
507C22×C3—121no—
508C22×C3C2×D3×D411yescharacteristic
509C22×C3C22×#6711yescharacteristic
510C2×D3—21no—
511C2×D3—21no—
512C2×D3—22no—
513C2×D3—48no—
514C2×D3—41no—
515C2×D3—41no—
516C2×D3C2×#21412yes—
517C3×C4—21no—
518C3×C4—21no—
519C3×C4—21no—
520C3×C4—21no—
521C3×C4—22no—
522C3×C4—32no—
523C3×C4—41no—
524C3×C4—41no—
525C3×C4—41no—
526C3×C4—61no—
527C3×C4—61no—
528C3×C4—81no—
529C3×C4—121no—
530C3×C4—122no—
531C3×C4D3×SD1612yes—
532C3×C4C2×#21412yes—
533C3×C4C2×#23511yescharacteristic
534C3×C4C2×#23511yescharacteristic
535C3×C4C2×#23711yescharacteristic
536C3×C4D3×#4111yescharacteristic
537Dic3—21no—
538Dic3—21no—
539Dic3—41no—
540Dic3—42no—
541Dic3—122no—
542Dic3—122no—
543Dic3—242no—
544Dic3C2×#21412yes—
545C32#310111yescharacteristic, complemented, Sylow
546C23—21no—
547C23—31no—
548C23—64no—
549C23—61no—
550C23—122no—
551C23—122no—
552Q8—62no—
553Q8—62no—
554Q8—362no—
555D4—21no—
556D4—32no—
557D4—64no—
558D4—61no—
559D4#379512yes—
560C2×C4—21no—
561C2×C4—31no—
562C2×C4—34no—
563C2×C4—31no—
564C2×C4—31no—
565C2×C4—42no—
566C2×C4—61no—
567C2×C4—61no—
568C2×C4—62no—
569C2×C4—61no—
570C2×C4—121no—
571C2×C4—122no—
572C2×C4—122no—
573C2×C4—122no—
574C2×C4—122no—
575C2×C4—182no—
576C2×C4D3×#6711yescharacteristic
577C2×C4D3×#6711yescharacteristic
578C2×C4C22×D3211yescharacteristic
579C8—62no—
580C8—182no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—42no—
585C2×C3—42no—
586C2×C3—62no—
587C2×C3—82no—
588C2×C3—122no—
589C2×C3#560611yescharacteristic
590C2×C3C2×D3×SD1611yescharacteristic
591C2×C3#577711yescharacteristic
592C2×C3#579111yescharacteristic
593C2×C3C22×#21411yescharacteristic
594C2×C3#582211yescharacteristic
595D3—22no—
596D3—42no—
597C22—22no—
598C22—32no—
599C22—41no—
600C22—41no—
601C22—61no—
602C22—61no—
603C22—62no—
604C22—128no—
605C22—121no—
606C22—121no—
607C22C2×D3×#6711yescharacteristic
608C4—21no—
609C4—32no—
610C4—41no—
611C4—61no—
612C4—61no—
613C4—121no—
614C4—122no—
615C4—362no—
616C4D3×#21412yes—
617C4C2×#379511yescharacteristic
618C4D3×#23511yescharacteristic
619C3—21no—
620C3#8040811yescharacteristic, complemented
621C3#8231411yescharacteristic, complemented
622C2—42no—
623C2—62no—
624C2—122no—
625C2#1059489211yescharacteristic
626C2C2×D3×#21411yescharacteristic
627C2#1059547011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×C3×D3×D4C22
hypercenterC4×D4D32
hypocenterC32#3101
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #10593859C2semidirect
3. #10592707C2semidirect
4. C3×#5019C2semidirect
6. Dic3×#214C2semidirect
7. #10590516C2semidirect
8. #10590475C2semidirect
9. #10590363C2semidirect
10. #10590268C2semidirect
11. #10590248C2semidirect
17. #64078C22semidirect
27. C3×#869C22semidirect
32. Dic3×Dic6C22semidirect
36. #63635C22semidirect
37. C4⋊(C3⋊(C3⋊C8))C22semidirect
38. C3×#810C22semidirect
39. C3×C4⋊(C3⋊C8)C22semidirect
40. #63573C22semidirect
41. #63565C22semidirect
44. Dic3×C3⋊C8C22semidirect
55. #5019D3semidirect
150. #869C2×D3semidirect
166. #810C2×D3semidirect
174. C4⋊(C3⋊C8)C2×D3semidirect
206. C3×C4×D3SD16semidirect
434. C4×D3#214semidirect
545. C32#3101semidirect
620. C3#80408semidirect
621. C3#82314semidirect

Maximal subgroups

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

subgroupindex
C3×C4×D3×D42
#105938592
#105927072
C3×#50192
#105914582
Dic3×#2142
#105905162
#105904752
#105903632
#105902682
#105902482
#823143
#804083