Finite Group Databasebeta

← #10690739

Subgroups — #10690739

Order 768.

984 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#82834C211yesmaximal, characteristic
2C2×D3×C22⋊C8C211yesmaximal, characteristic
3C2×C3×#328C211yesmaximal, characteristic, complemented
4C2×#4538C211yesmaximal, characteristic, complemented
5(C2×D3)⋊#95C211yesmaximal, characteristic
6#67675C211yesmaximal, characteristic, complemented
7#67612C211yesmaximal, characteristic, complemented
8#9111—31nomaximal, Sylow
9C23×C4×D3C2211yescharacteristic
10C2×C3×C22⋊Q8C2211yescharacteristic
11C2×#946C411yescharacteristic, complemented
12C2×#946C411yescharacteristic, complemented
13C22×(C2×D3)⋊C4—21no—
14C22×D3×C8—21no—
15C2×C3×C22⋊C8C2211yescharacteristic
16C2×C3×#95C2211yescharacteristic
17#5212C2211yescharacteristic
18C2×C3⋊#95—21no—
19C2×C3⋊#95C2211yescharacteristic
20C2×#830C2211yescharacteristic
21C2×(C2×D3)⋊C8—21no—
22#4989—21no—
23#4989—21no—
24#4987C411yescharacteristic, complemented
25#4987C411yescharacteristic, complemented
26#4955—21no—
27#4946—21no—
28D3×C22⋊C8—22no—
29D3×C22⋊C8—22no—
30C3×#328—22no—
31#4538—22no—
32C22×C22⋊C8—31no—
33#2848—31no—
34C2×#328—31no—
35C2×#328D311yescharacteristic, complemented
36C22⋊#95—31no—
37#1294—31no—
38#1294—31no—
39C24×D3D411yescharacteristic
40C22×C3×Q8C2×C411yescharacteristic
41C23×C3×C4—21no—
42C23×C3×C4C2311yescharacteristic
43C23×Dic3—21no—
44C23×Dic3D411yescharacteristic
45C22×C4×D3—21no—
46C22×C4×D3—21no—
47C22×C4×D3—21no—
48C22×C4×D3—21no—
49C22×C4×D3—42no—
50C22×C4×D3—42no—
51C22×C4×D3C2×C411yescharacteristic
52C22×C4×D3C2×C411yescharacteristic
53C22×C4×D3D411yescharacteristic
54C22×C4×D3D411yescharacteristic
55C22×C3×C8—21no—
56C3×C22⋊Q8—21no—
57C3×C22⋊Q8—21no—
58C3×C22⋊Q8—21no—
59C3×C22⋊Q8—21no—
60C2×C3×C4⋊C4—21no—
61C2×C3×C4⋊C4C2×C411yescharacteristic
62C2×C3×C22⋊C4—21no—
63C2×#217—21no—
64#946—42no—
65#946—42no—
66C2×(C2×D3)⋊C4—24no—
67C2×(C2×D3)⋊C4—21no—
68C2×(C2×D3)⋊C4—21no—
69C2×(C2×D3)⋊C4—21no—
70C2×(C2×D3)⋊C4—21no—
71C2×(C2×D3)⋊C4—42no—
72C2×(C2×D3)⋊C4—42no—
73C2×C4⋊Dic3C2×C411yescharacteristic
74C2×C4⋊Dic3C2×C411yescharacteristic
75C2×Dic3⋊C4—21no—
76C2×Dic3⋊C4—21no—
77C22×C3⋊C8—21no—
78C2×D3×C8—24no—
79C2×D3×C8—42no—
80C2×D3×C8—42no—
81C3×C22⋊C8—21no—
82C3×C22⋊C8D412yes—
83C3×#95—21no—
84C3×#95—21no—
85C3⋊#95—21no—
86C3⋊#95—21no—
87C3⋊#95—21no—
88C3⋊#95—21no—
89C3⋊#95—21no—
90C3⋊#95—42no—
91#830—21no—
92#830D412yes—
93(C2×D3)⋊C8—24no—
94C24×C4—31no—
95C23×C8—61no—
96C2×C22⋊Q8—31no—
97C2×C22⋊Q8—31no—
98C2×C22⋊Q8C2×D311yescharacteristic
99C22×C22⋊C4—61no—
100C2×C22⋊C8—31no—
101C2×C22⋊C8—62no—
102C2×C22⋊C8—61no—
103C2×C22⋊C8—62no—
104C2×C22⋊C8C2×D311yescharacteristic
105#385—61no—
106#385—61no—
107#385—61no—
108#380—31no—
109#380—31no—
110#380—31no—
111#379—61no—
112C2×#95—31no—
113C2×#95—61no—
114C2×#95C2×D311yescharacteristic
115#328—22no—
116#328—62no—
117C24×C3C2×D411yescharacteristic
118C23×D3—21no—
119C23×D3—21no—
120C23×D3—21no—
121C23×D3—21no—
122C23×D3—22no—
123C23×D3—22no—
124C23×D3—41no—
125C23×D3—41no—
126C23×D3C22⋊C411yescharacteristic
127C23×D3C22⋊C411yescharacteristic
128C23×D3SD1612yes—
129C23×D3Q1612yes—
130C2×C3×Q8—21no—
131C2×C3×Q8—21no—
132C2×C3×Q8—41no—
133C2×C3×Q8—41no—
134C22×C3×C4—22no—
135C22×C3×C4—21no—
136C22×C3×C4—21no—
137C22×C3×C4—41no—
138C22×C3×C4—41no—
139C22×C3×C4—41no—
140C22×C3×C4—41no—
141C22×C3×C4—41no—
142C22×C3×C4—41no—
143C22×C3×C4—41no—
144C22×C3×C4—41no—
145C22×C3×C4C22×C411yescharacteristic
146C22×C3×C4C2×D411yescharacteristic
147C22×C3×C4C2×D411yescharacteristic
148C22×C3×C4C2×D411yescharacteristic
149C22×C3×C4#4111yescharacteristic
150C22×C3×C4#4111yescharacteristic
151C22×Dic3—21no—
152C22×Dic3—21no—
153C22×Dic3—22no—
154C22×Dic3—22no—
155C22×Dic3—21no—
156C22×Dic3—21no—
157C22×Dic3—41no—
158C22×Dic3—41no—
159C22×Dic3—41no—
160C22×Dic3—41no—
161C22×Dic3—41no—
162C22×Dic3—41no—
163C22×Dic3—41no—
164C22×Dic3C22⋊C411yescharacteristic
165C22×Dic3C22⋊C411yescharacteristic
166C2×C4×D3—22no—
167C2×C4×D3—21no—
168C2×C4×D3—21no—
169C2×C4×D3—22no—
170C2×C4×D3—22no—
171C2×C4×D3—21no—
172C2×C4×D3—21no—
173C2×C4×D3—21no—
174C2×C4×D3—21no—
175C2×C4×D3—21no—
176C2×C4×D3—21no—
177C2×C4×D3—22no—
178C2×C4×D3—44no—
179C2×C4×D3—44no—
180C2×C4×D3—44no—
181C2×C4×D3—44no—
182C2×C4×D3—41no—
183C2×C4×D3—41no—
184C2×C4×D3—41no—
185C2×C4×D3—41no—
186C2×C3×C8—22no—
187C2×C3×C8—41no—
188C2×C3×C8—41no—
189C3×C4⋊C4—21no—
190C3×C4⋊C4—21no—
191C3×C4⋊C4—41no—
192C3×C4⋊C4—41no—
193C3×C22⋊C4—41no—
194C3×C22⋊C4—41no—
195#217—41no—
196#217—41no—
197(C2×D3)⋊C4—42no—
198(C2×D3)⋊C4—48no—
199(C2×D3)⋊C4—42no—
200(C2×D3)⋊C4—42no—
201(C2×D3)⋊C4—42no—
202C4⋊Dic3—41no—
203C4⋊Dic3—41no—
204Dic3⋊C4—42no—
205Dic3⋊C4—42no—
206C2×C3⋊C8—22no—
207C2×C3⋊C8—41no—
208C2×C3⋊C8—41no—
209D3×C8—48no—
210C25—31no—
211C22×Q8C4×D311yescharacteristic
212C23×C4—21no—
213C23×C4—31no—
214C23×C4—31no—
215C23×C4—31no—
216C23×C4—31no—
217C23×C4—31no—
218C23×C4—61no—
219C23×C4—61no—
220C23×C4—61no—
221C23×C4—61no—
222C23×C4—61no—
223C23×C4—122no—
224C23×C4—122no—
225C23×C4C22×D311yescharacteristic
226C22×C8—21no—
227C22×C8—64no—
228C22×C8—61no—
229C22×C8—122no—
230C22×C8—122no—
231C22⋊Q8—21no—
232C22⋊Q8—21no—
233C22⋊Q8—21no—
234C22⋊Q8—21no—
235C22⋊Q8—122no—
236C22⋊Q8—122no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—31no—
239C2×C4⋊C4—31no—
240C2×C4⋊C4—61no—
241C2×C4⋊C4—61no—
242C2×C4⋊C4C4×D311yescharacteristic
243C2×C22⋊C4—21no—
244C2×C22⋊C4—61no—
245C2×C22⋊C4—61no—
246C2×C22⋊C4—61no—
247C2×C22⋊C4—61no—
248C2×C22⋊C4—64no—
249C2×C22⋊C4—61no—
250C2×C22⋊C4—122no—
251C2×C22⋊C4—122no—
252C22⋊C8—21no—
253C22⋊C8—32no—
254C22⋊C8—64no—
255C22⋊C8—61no—
256C22⋊C8#6712yes—
257#95—21no—
258#95—21no—
259#95—61no—
260#95—61no—
261#95—61no—
262#95—61no—
263#95—61no—
264#95—122no—
265C23×C3—21no—
266C23×C3—21no—
267C23×C3—21no—
268C23×C3—21no—
269C23×C3C2×C22⋊C411yescharacteristic
270C23×C3#12111yescharacteristic
271C23×C3#12111yescharacteristic
272C23×C3C2×SD1611yescharacteristic
273C23×C3C2×Q1611yescharacteristic
274C23×C3#13511yescharacteristic
275C23×C3#13511yescharacteristic
276C22×D3—21no—
277C22×D3—21no—
278C22×D3—21no—
279C22×D3—21no—
280C22×D3—21no—
281C22×D3—21no—
282C22×D3—21no—
283C22×D3—21no—
284C22×D3—21no—
285C22×D3—21no—
286C22×D3—22no—
287C22×D3—22no—
288C22×D3—22no—
289C22×D3—22no—
290C22×D3—24no—
291C22×D3—24no—
292C22×D3—42no—
293C22×D3—42no—
294C22×D3—42no—
295C22×D3—42no—
296C22×D3—42no—
297C22×D3—42no—
298C22×D3—42no—
299C22×D3—42no—
300C22×D3—42no—
301C22×D3—42no—
302C22×D3#9912yes—
303C22×D3#10312yes—
304C22×D3#10312yes—
305C22×D3#10412yes—
306C3×Q8—81no—
307C3×Q8—81no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—41no—
313C2×C3×C4—41no—
314C2×C3×C4—41no—
315C2×C3×C4—41no—
316C2×C3×C4—42no—
317C2×C3×C4—42no—
318C2×C3×C4—42no—
319C2×C3×C4—41no—
320C2×C3×C4—41no—
321C2×C3×C4—41no—
322C2×C3×C4—41no—
323C2×C3×C4—41no—
324C2×C3×C4—41no—
325C2×C3×C4—81no—
326C2×C3×C4—81no—
327C2×C3×C4—81no—
328C2×C3×C4—81no—
329C2×C3×C4C4×D411yescharacteristic
330C2×C3×C4C4×D411yescharacteristic
331C2×C3×C4#12011yescharacteristic
332C2×C3×C4#12311yescharacteristic
333C2×Dic3—21no—
334C2×Dic3—21no—
335C2×Dic3—21no—
336C2×Dic3—21no—
337C2×Dic3—21no—
338C2×Dic3—42no—
339C2×Dic3—42no—
340C2×Dic3—42no—
341C2×Dic3—42no—
342C2×Dic3—42no—
343C2×Dic3—41no—
344C2×Dic3—41no—
345C2×Dic3—41no—
346C2×Dic3—41no—
347C2×Dic3—41no—
348C2×Dic3—41no—
349C2×Dic3—81no—
350C2×Dic3—81no—
351C2×Dic3—81no—
352C2×Dic3—81no—
353C2×Dic3#9912yes—
354C4×D3—24no—
355C4×D3—24no—
356C4×D3—42no—
357C4×D3—42no—
358C4×D3—42no—
359C4×D3—42no—
360C4×D3—42no—
361C4×D3—42no—
362C3×C8—42no—
363C3⋊C8—42no—
364C24—31no—
365C24—31no—
366C24—32no—
367C24—32no—
368C24—62no—
369C24—62no—
370C24—61no—
371C24—61no—
372C24—61no—
373C24—61no—
374C24—121no—
375C24—121no—
376C24D3×D411yescharacteristic
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8—41no—
380C2×Q8—41no—
381C22×C4—22no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—31no—
385C22×C4—31no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—62no—
395C22×C4—62no—
396C22×C4—62no—
397C22×C4—62no—
398C22×C4—62no—
399C22×C4—61no—
400C22×C4—61no—
401C22×C4—61no—
402C22×C4—61no—
403C22×C4—61no—
404C22×C4—61no—
405C22×C4—61no—
406C22×C4—61no—
407C22×C4—61no—
408C22×C4—61no—
409C22×C4—62no—
410C22×C4—61no—
411C22×C4—61no—
412C22×C4—121no—
413C22×C4—121no—
414C22×C4—121no—
415C22×C4—121no—
416C22×C4—124no—
417C22×C4—124no—
418C22×C4—124no—
419C22×C4—124no—
420C22×C4—121no—
421C22×C4—121no—
422C22×C4—121no—
423C22×C4—121no—
424C22×C4—121no—
425C22×C4—121no—
426C22×C4—121no—
427C22×C4C2×C4×D311yescharacteristic
428C22×C4#23511yescharacteristic
429C22×C4D3×D411yescharacteristic
430C22×C4D3×D411yescharacteristic
431C22×C4#23711yescharacteristic
432C22×C4C2×#6711yescharacteristic
433C2×C8—22no—
434C2×C8—41no—
435C2×C8—41no—
436C2×C8—62no—
437C2×C8—128no—
438C2×C8—121no—
439C2×C8—121no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—41no—
443C4⋊C4—41no—
444C4⋊C4—121no—
445C4⋊C4—121no—
446C4⋊C4—122no—
447C4⋊C4—122no—
448C22⋊C4—41no—
449C22⋊C4—41no—
450C22⋊C4—122no—
451C22⋊C4—122no—
452C22⋊C4—128no—
453C22⋊C4—122no—
454C22⋊C4—122no—
455C22⋊C4—121no—
456C22⋊C4—121no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—21no—
466C22×C3—21no—
467C22×C3—21no—
468C22×C3—21no—
469C22×C3#38611yescharacteristic
470C22×C3C2×#9911yescharacteristic
471C22×C3C2×#9911yescharacteristic
472C22×C3C2×#10311yescharacteristic
473C22×C3#41611yescharacteristic
474C22×C3C2×#10411yescharacteristic
475C22×C3#42111yescharacteristic
476C22×C3#46511yescharacteristic
477C22×C3#46511yescharacteristic
478C22×C3#46711yescharacteristic
479C22×C3#46711yescharacteristic
480C2×D3—22no—
481C2×D3—22no—
482C2×D3—22no—
483C2×D3—22no—
484C2×D3—22no—
485C2×D3—22no—
486C2×D3—22no—
487C2×D3—22no—
488C2×D3—22no—
489C2×D3—44no—
490C2×D3—44no—
491C2×D3—44no—
492C2×D3—44no—
493C2×D3—41no—
494C2×D3—41no—
495C2×D3—41no—
496C2×D3—41no—
497C2×D3#32814yescomplemented
498C3×C4—21no—
499C3×C4—21no—
500C3×C4—21no—
501C3×C4—21no—
502C3×C4—82no—
503C3×C4—81no—
504C3×C4—81no—
505Dic3—22no—
506Dic3—41no—
507Dic3—82no—
508Dic3—81no—
509Dic3—81no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—32no—
515C23—32no—
516C23—32no—
517C23—32no—
518C23—64no—
519C23—64no—
520C23—61no—
521C23—61no—
522C23—61no—
523C23—61no—
524C23—62no—
525C23—62no—
526C23—61no—
527C23—61no—
528C23—61no—
529C23—61no—
530C23—62no—
531C23—62no—
532C23—61no—
533C23—61no—
534C23—122no—
535C23—122no—
536C23—122no—
537C23—122no—
538C23—122no—
539C23—122no—
540C23—122no—
541C23—122no—
542C23—122no—
543C23—122no—
544C23D3×C22⋊C411yescharacteristic
545C23#88411yescharacteristic
546C23D3×SD1611yescharacteristic
547C23#91611yescharacteristic
548C23D3×Q1611yescharacteristic
549C23#91911yescharacteristic
550C23#93811yescharacteristic
551Q8—81no—
552Q8—81no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—32no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—64no—
572C2×C4—64no—
573C2×C4—61no—
574C2×C4—61no—
575C2×C4—61no—
576C2×C4—61no—
577C2×C4—61no—
578C2×C4—81no—
579C2×C4—81no—
580C2×C4—81no—
581C2×C4—81no—
582C2×C4—122no—
583C2×C4—122no—
584C2×C4—122no—
585C2×C4—122no—
586C2×C4—122no—
587C2×C4—122no—
588C2×C4—122no—
589C2×C4—122no—
590C2×C4—122no—
591C2×C4—122no—
592C2×C4—122no—
593C2×C4—121no—
594C2×C4—121no—
595C2×C4—121no—
596C2×C4—121no—
597C2×C4—121no—
598C2×C4—121no—
599C2×C4—241no—
600C2×C4—241no—
601C2×C4—241no—
602C2×C4—241no—
603C2×C4#67⋊C411yescharacteristic
604C2×C4#88311yescharacteristic
605C2×C4C4×#6711yescharacteristic
606C2×C4#93711yescharacteristic
607C8—42no—
608C8—122no—
609C2×C3—21no—
610C2×C3—21no—
611C2×C3—21no—
612C2×C3—21no—
613C2×C3C2×#32811yescharacteristic
614C2×C3#150111yescharacteristic
615C2×C3#151611yescharacteristic
616C2×C3#152011yescharacteristic
617C2×C3#187111yescharacteristic
618C2×C3#189211yescharacteristic
619C2×C3#189811yescharacteristic
620D3—24no—
621D3—42no—
622C22—21no—
623C22—21no—
624C22—21no—
625C22—21no—
626C22—21no—
627C22—21no—
628C22—21no—
629C22—21no—
630C22—21no—
631C22—21no—
632C22—21no—
633C22—21no—
634C22—34no—
635C22—62no—
636C22—62no—
637C22—62no—
638C22—62no—
639C22—62no—
640C22—62no—
641C22—62no—
642C22—62no—
643C22—62no—
644C22—124no—
645C22—124no—
646C22—124no—
647C22—124no—
648C22—121no—
649C22—121no—
650C22—121no—
651C22—121no—
652C22D3×#9911yescharacteristic
653C22D3×#9911yescharacteristic
654C22D3×#10311yescharacteristic
655C22#480411yescharacteristic
656C22#480711yescharacteristic
657C22#481311yescharacteristic
658C22D3×#10411yescharacteristic
659C22#482111yescharacteristic
660C22#495611yescharacteristic
661C22#517111yescharacteristic
662C22#518811yescharacteristic
663C4—21no—
664C4—21no—
665C4—21no—
666C4—21no—
667C4—62no—
668C4—82no—
669C4—81no—
670C4—81no—
671C4—121no—
672C4—242no—
673C4—241no—
674C4—241no—
675C3#911111yescharacteristic, complemented, Sylow
676C2—21no—
677C2—21no—
678C2—21no—
679C2—21no—
680C2—64no—
681C2—122no—
682C2D3×#32811yescharacteristic
683C2#6833311yescharacteristic
684C2#6833811yescharacteristic
685C2#6833911yescharacteristic
686C2#7003611yescharacteristic
687C2#7027011yescharacteristic
688C2#7038111yescharacteristic
subgroupG/H
centerC23D3×C22⋊C4
commutatorC22×C3×C4C22×C4
FrattiniC23×C4C22×D3
FittingC2×C3×#328C2
socleC23×C3C2×C22⋊C4
prime radicalC24×D3D4
cosocleC23×C3×C4C23
hypercenterC2×#328D3
hypocenterC3#9111
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
3. C2×C3×#328C2semidirect
4. C2×#4538C2semidirect
6. #67675C2semidirect
7. #67612C2semidirect
11. C2×#946C4semidirect
12. C2×#946C4semidirect
24. #4987C4semidirect
25. #4987C4semidirect
35. C2×#328D3semidirect
497. C2×D3#328semidirect
675. C3#9111semidirect

Maximal subgroups

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

subgroupindex
#828342
C2×D3×C22⋊C82
C2×C3×#3282
C2×#45382
(C2×D3)⋊#952
#676752
#676122
#91113