Finite Group Databasebeta

← #10732650

Subgroups — #10732650

Order 768.

1166 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#382C211yesmaximal, characteristic
2C2×#4984C211yesmaximal, characteristic
3#71563C211yesmaximal, characteristic
4#71563C211yesmaximal, characteristic
5#71563C211yesmaximal, characteristic
6#71535C211yesmaximal, characteristic
7C4×C3⋊#95C211yesmaximal, characteristic
8#69423C212yesmaximal
9#69417C212yesmaximal
10#69417C212yesmaximal
11#69415C212yesmaximal
12#15232—31nomaximal, Sylow
13C22×C3×C4⋊C4C2211yescharacteristic
14C22×C3×C4⋊C4C2211yescharacteristic
15C22×C3×C42C2211yescharacteristic
16C22×C4⋊Dic3C2211yescharacteristic
17C22×C4⋊Dic3C2211yescharacteristic
18C22×C4⋊Dic3C2212yes—
19C22×C4×Dic3C2211yescharacteristic
20C22×C4×Dic3C2211yescharacteristic
21C3×#382—24no—
22C2×C3×#95C2212yes—
23C2×C3×#95C2212yes—
24C2×C3⋊#95C2211yescharacteristic
25C2×C3⋊#95C2212yes—
26C2×C3⋊#95C2211yescharacteristic
27C2×C3⋊#95C2211yescharacteristic
28C2×C3⋊#95C2212yes—
29C2×C3⋊#95C2212yes—
30C2×C3⋊#95C2212yes—
31C2×C3⋊#95C2211yescharacteristic
32C2×C3⋊#95C2212yes—
33C2×C3⋊#95C2212yes—
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2212yes—
37#4984—24no—
38C2×#389—31no—
39C2×#382D311yescharacteristic
40#1445—32no—
41#1443—32no—
42#1443—32no—
43#1442—32no—
44C4⋊#95—31no—
45C4⋊#95—31no—
46C4⋊#95—31no—
47C4⋊#95—31no—
48C4×#95—31no—
49C23×C3×C4C2312yes—
50C23×C3×C4C2312yes—
51C23×C3×C4C2311yescharacteristic
52C23×C3×C4C2311yescharacteristic
53C23×C3×C4C2311yescharacteristic
54C23×Dic3C2312yes—
55C23×Dic3C2312yes—
56C23×Dic3C2311yescharacteristic
57C23×Dic3C2311yescharacteristic
58C23×Dic3C2311yescharacteristic
59C23×Dic3C2311yescharacteristic
60C2×C3×C4⋊C4—22no—
61C2×C3×C4⋊C4—22no—
62C2×C3×C4⋊C4—22no—
63C2×C3×C4⋊C4—22no—
64C2×C3×C4⋊C4—22no—
65C2×C3×C4⋊C4D414yes—
66C2×C3×C42—22no—
67C2×C3×C42—22no—
68C2×C3×C42Q814yes—
69C2×C4⋊Dic3—24no—
70C2×C4⋊Dic3—22no—
71C2×C4⋊Dic3—22no—
72C2×C4⋊Dic3—22no—
73C2×C4⋊Dic3—22no—
74C2×C4⋊Dic3—22no—
75C2×C4⋊Dic3—22no—
76C2×C4⋊Dic3—24no—
77C2×C4⋊Dic3—42no—
78C2×C4×Dic3—22no—
79C2×C4×Dic3—22no—
80C2×C4×Dic3—22no—
81C2×C4×Dic3—22no—
82C2×C4×Dic3—22no—
83C2×C4×Dic3—22no—
84C3×#95—24no—
85C3×#95—24no—
86C3⋊#95—24no—
87C3⋊#95—22no—
88C3⋊#95—22no—
89C3⋊#95—22no—
90C3⋊#95—22no—
91C3⋊#95—24no—
92C3⋊#95—24no—
93C3⋊#95—24no—
94C3⋊#95—42no—
95C3⋊#95—42no—
96C3⋊#95—42no—
97C3⋊#95—42no—
98C3⋊#95—42no—
99C22×C4⋊C4—31no—
100C22×C4⋊C4—31no—
101C22×C4⋊C4—32no—
102C22×C4⋊C4C2×D311yescharacteristic
103C22×C4⋊C4C2×D311yescharacteristic
104C22×C42—31no—
105C22×C42—31no—
106C22×C42C2×D311yescharacteristic
107#389—64no—
108#382—24no—
109C2×#95—31no—
110C2×#95—31no—
111C2×#95—31no—
112C2×#95—31no—
113C2×#95—32no—
114C2×#95—32no—
115C2×#95—32no—
116C2×#95—32no—
117C2×#95—32no—
118C2×#95—32no—
119C2×#95—32no—
120C2×#95—32no—
121C2×#95—32no—
122C2×#95C2×D312yes—
123C2×#95C2×D312yes—
124C24×C3C2411yescharacteristic
125C22×C3×C4—21no—
126C22×C3×C4—21no—
127C22×C3×C4—21no—
128C22×C3×C4—21no—
129C22×C3×C4—21no—
130C22×C3×C4—21no—
131C22×C3×C4—22no—
132C22×C3×C4—22no—
133C22×C3×C4—21no—
134C22×C3×C4—21no—
135C22×C3×C4—22no—
136C22×C3×C4—22no—
137C22×C3×C4—21no—
138C22×C3×C4—21no—
139C22×C3×C4—22no—
140C22×C3×C4—21no—
141C22×C3×C4—21no—
142C22×C3×C4—22no—
143C22×C3×C4—22no—
144C22×C3×C4—22no—
145C22×C3×C4—22no—
146C22×C3×C4—22no—
147C22×C3×C4—22no—
148C22×C3×C4—22no—
149C22×C3×C4—22no—
150C22×C3×C4C2×D414yes—
151C22×C3×C4C2×D412yes—
152C22×C3×C4C2×Q812yes—
153C22×C3×C4C2×Q812yes—
154C22×C3×C4C2×Q812yes—
155C22×C3×C4#4112yes—
156C22×C3×C4#4112yes—
157C22×C3×C4#4112yes—
158C22×C3×C4#4112yes—
159C22×C3×C4#4112yes—
160C22×Dic3—21no—
161C22×Dic3—21no—
162C22×Dic3—21no—
163C22×Dic3—21no—
164C22×Dic3—21no—
165C22×Dic3—21no—
166C22×Dic3—21no—
167C22×Dic3—21no—
168C22×Dic3—21no—
169C22×Dic3—21no—
170C22×Dic3—21no—
171C22×Dic3—21no—
172C22×Dic3—21no—
173C22×Dic3—21no—
174C22×Dic3—21no—
175C22×Dic3—21no—
176C22×Dic3—21no—
177C22×Dic3—21no—
178C22×Dic3—21no—
179C22×Dic3—21no—
180C22×Dic3—21no—
181C22×Dic3—21no—
182C22×Dic3—21no—
183C22×Dic3—21no—
184C22×Dic3—22no—
185C22×Dic3—22no—
186C22×Dic3—22no—
187C22×Dic3—22no—
188C22×Dic3—22no—
189C22×Dic3—22no—
190C22×Dic3—22no—
191C22×Dic3—22no—
192C22×Dic3—22no—
193C22×Dic3—22no—
194C22×Dic3—22no—
195C22×Dic3—22no—
196C22×Dic3—22no—
197C22×Dic3—22no—
198C22×Dic3#4112yes—
199C22×Dic3#4112yes—
200C22×Dic3#4112yes—
201C22×Dic3#4112yes—
202C3×C4⋊C4—28no—
203C3×C4⋊C4—44no—
204C3×C42—28no—
205C4⋊Dic3—48no—
206C4⋊Dic3—44no—
207C4⋊Dic3—44no—
208C4×Dic3—44no—
209C4×Dic3—44no—
210C23×C4—31no—
211C23×C4—31no—
212C23×C4—31no—
213C23×C4—31no—
214C23×C4—32no—
215C23×C4—32no—
216C23×C4C22×D312yes—
217C23×C4C22×D311yescharacteristic
218C23×C4C22×D311yescharacteristic
219C23×C4C22×D312yes—
220C23×C4C22×D311yescharacteristic
221C2×C4⋊C4—22no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4—64no—
227C2×C4⋊C4—62no—
228C2×C4⋊C4—62no—
229C2×C4⋊C4—62no—
230C2×C4⋊C4—62no—
231C2×C4⋊C4—62no—
232C2×C4⋊C4—64no—
233C2×C4⋊C4—62no—
234C2×C4⋊C4—122no—
235C2×C4⋊C4#6714yes—
236C2×C42—22no—
237C2×C42—22no—
238C2×C42—62no—
239C2×C42—62no—
240C2×C42—62no—
241C2×C42—62no—
242C2×C42—62no—
243C2×C42—62no—
244C2×C42Dic614yes—
245#95—24no—
246#95—24no—
247#95—62no—
248#95—62no—
249#95—62no—
250#95—64no—
251#95—62no—
252#95—64no—
253#95—64no—
254#95—64no—
255#95—122no—
256#95—122no—
257#95—122no—
258#95—122no—
259#95—122no—
260C23×C3C22×D411yescharacteristic
261C23×C3C22×Q811yescharacteristic
262C23×C3C2×#4111yescharacteristic
263C23×C3C2×#4111yescharacteristic
264C23×C3C2×#4111yescharacteristic
265C23×C3C2×#4111yescharacteristic
266C23×C3C2×#4111yescharacteristic
267C23×C3C2×#4111yescharacteristic
268C23×C3C2×#4111yescharacteristic
269C23×C3C2×#4111yescharacteristic
270C23×C3C2×#4111yescharacteristic
271C23×C3H(5,𝔽2)11yescharacteristic
272C23×C3H(5,𝔽2)11yescharacteristic
273C23×C32−1+411yescharacteristic
274C23×C32−1+411yescharacteristic
275C2×C3×C4—22no—
276C2×C3×C4—22no—
277C2×C3×C4—24no—
278C2×C3×C4—22no—
279C2×C3×C4—22no—
280C2×C3×C4—22no—
281C2×C3×C4—22no—
282C2×C3×C4—24no—
283C2×C3×C4—24no—
284C2×C3×C4—42no—
285C2×C3×C4—42no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—41no—
289C2×C3×C4—41no—
290C2×C3×C4—41no—
291C2×C3×C4—41no—
292C2×C3×C4—41no—
293C2×C3×C4—42no—
294C2×C3×C4—41no—
295C2×C3×C4—42no—
296C2×C3×C4—42no—
297C2×C3×C4—42no—
298C2×C3×C4—42no—
299C2×C3×C4—42no—
300C2×C3×C4—42no—
301C2×C3×C4—42no—
302C2×C3×C4—42no—
303C2×C3×C4C22⋊Q814yes—
304C2×C3×C4#12314yes—
305C2×C3×C4#12414yes—
306C2×C3×C4#12514yes—
307C2×C3×C4#12514yes—
308C2×C3×C4#12614yes—
309C2×C3×C4#12614yes—
310C2×Dic3—22no—
311C2×Dic3—22no—
312C2×Dic3—22no—
313C2×Dic3—22no—
314C2×Dic3—22no—
315C2×Dic3—22no—
316C2×Dic3—22no—
317C2×Dic3—22no—
318C2×Dic3—22no—
319C2×Dic3—22no—
320C2×Dic3—22no—
321C2×Dic3—22no—
322C2×Dic3—41no—
323C2×Dic3—41no—
324C2×Dic3—41no—
325C2×Dic3—41no—
326C2×Dic3—41no—
327C2×Dic3—41no—
328C2×Dic3—41no—
329C2×Dic3—41no—
330C2×Dic3—41no—
331C2×Dic3—41no—
332C2×Dic3—41no—
333C2×Dic3—41no—
334C2×Dic3—41no—
335C2×Dic3—41no—
336C2×Dic3—41no—
337C2×Dic3—41no—
338C2×Dic3—42no—
339C2×Dic3—42no—
340C2×Dic3—42no—
341C2×Dic3—42no—
342C2×Dic3—42no—
343C2×Dic3—42no—
344C2×Dic3—42no—
345C2×Dic3—42no—
346C2×Dic3—42no—
347C2×Dic3—42no—
348C2×Dic3—42no—
349C2×Dic3—42no—
350C2×Dic3—42no—
351C2×Dic3—42no—
352C24C23×D311yescharacteristic
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—22no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—22no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—32no—
379C22×C4—32no—
380C22×C4—32no—
381C22×C4—32no—
382C22×C4—61no—
383C22×C4—61no—
384C22×C4—61no—
385C22×C4—61no—
386C22×C4—61no—
387C22×C4—61no—
388C22×C4—61no—
389C22×C4—61no—
390C22×C4—61no—
391C22×C4—61no—
392C22×C4—61no—
393C22×C4—61no—
394C22×C4—61no—
395C22×C4—61no—
396C22×C4—61no—
397C22×C4—61no—
398C22×C4—61no—
399C22×C4—61no—
400C22×C4—61no—
401C22×C4—61no—
402C22×C4—61no—
403C22×C4—61no—
404C22×C4—61no—
405C22×C4—61no—
406C22×C4—62no—
407C22×C4—62no—
408C22×C4—62no—
409C22×C4—62no—
410C22×C4—62no—
411C22×C4—62no—
412C22×C4—62no—
413C22×C4—62no—
414C22×C4—62no—
415C22×C4—62no—
416C22×C4—62no—
417C22×C4—62no—
418C22×C4—62no—
419C22×C4—62no—
420C22×C4C2×Dic612yes—
421C22×C4C2×Dic612yes—
422C22×C4C2×Dic612yes—
423C22×C4#23512yes—
424C22×C4#23712yes—
425C22×C4#23712yes—
426C22×C4#23912yes—
427C22×C4#23912yes—
428C22×C4C2×#6714yes—
429C22×C4C2×#6712yes—
430C4⋊C4—28no—
431C4⋊C4—44no—
432C4⋊C4—128no—
433C4⋊C4—124no—
434C4⋊C4—124no—
435C42—28no—
436C42—124no—
437C42—124no—
438C22×C3C2×C22⋊Q811yescharacteristic
439C22×C3C2×#12311yescharacteristic
440C22×C3C2×#12411yescharacteristic
441C22×C3C2×#12511yescharacteristic
442C22×C3C2×#12511yescharacteristic
443C22×C3C2×#12611yescharacteristic
444C22×C3C2×#12611yescharacteristic
445C22×C3#52911yescharacteristic
446C22×C3#52911yescharacteristic
447C22×C3#52911yescharacteristic
448C22×C3#52911yescharacteristic
449C22×C3#53311yescharacteristic
450C22×C3#53311yescharacteristic
451C22×C3#54011yescharacteristic
452C22×C3#54111yescharacteristic
453C22×C3#54211yescharacteristic
454C22×C3#54211yescharacteristic
455C22×C3#54411yescharacteristic
456C22×C3#54411yescharacteristic
457C22×C3#54611yescharacteristic
458C22×C3#54711yescharacteristic
459C22×C3#54811yescharacteristic
460C22×C3#55011yescharacteristic
461C22×C3#55211yescharacteristic
462C22×C3#55211yescharacteristic
463C22×C3#55211yescharacteristic
464C22×C3#55311yescharacteristic
465C22×C3#55311yescharacteristic
466C22×C3#55311yescharacteristic
467C22×C3#55511yescharacteristic
468C22×C3#55611yescharacteristic
469C22×C3#55611yescharacteristic
470C22×C3#55611yescharacteristic
471C22×C3#55911yescharacteristic
472C22×C3#55911yescharacteristic
473C3×C4—42no—
474C3×C4—42no—
475C3×C4—44no—
476C3×C4—82no—
477C3×C4#40018yes—
478Dic3—42no—
479Dic3—42no—
480Dic3—42no—
481Dic3—42no—
482Dic3—82no—
483Dic3—82no—
484C23C22×Dic611yescharacteristic
485C23C2×#23511yescharacteristic
486C23C2×#23711yescharacteristic
487C23C2×#23711yescharacteristic
488C23C2×#23911yescharacteristic
489C23C2×#23911yescharacteristic
490C23D3×#4111yescharacteristic
491C23D3×#4111yescharacteristic
492C23D3×#4111yescharacteristic
493C23D3×#4111yescharacteristic
494C23#100911yescharacteristic
495C23#100911yescharacteristic
496C23#101011yescharacteristic
497C23#101011yescharacteristic
498C23C22×#6711yescharacteristic
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—62no—
528C2×C4—62no—
529C2×C4—62no—
530C2×C4—62no—
531C2×C4—62no—
532C2×C4—62no—
533C2×C4—62no—
534C2×C4—62no—
535C2×C4—62no—
536C2×C4—62no—
537C2×C4—62no—
538C2×C4—62no—
539C2×C4—121no—
540C2×C4—121no—
541C2×C4—121no—
542C2×C4—121no—
543C2×C4—121no—
544C2×C4—121no—
545C2×C4—121no—
546C2×C4—121no—
547C2×C4—121no—
548C2×C4—121no—
549C2×C4—121no—
550C2×C4—121no—
551C2×C4—121no—
552C2×C4—121no—
553C2×C4—121no—
554C2×C4—121no—
555C2×C4—122no—
556C2×C4—122no—
557C2×C4—122no—
558C2×C4—122no—
559C2×C4—122no—
560C2×C4—122no—
561C2×C4—122no—
562C2×C4—122no—
563C2×C4—122no—
564C2×C4—122no—
565C2×C4—122no—
566C2×C4—122no—
567C2×C4—122no—
568C2×C4—122no—
569C2×C4#89014yes—
570C2×C4#89014yes—
571C2×C4#89814yes—
572C2×C4#89814yes—
573C2×C4#92414yes—
574C2×C4#93514yes—
575C2×C4#94714yes—
576C2×C3C2×#40011yescharacteristic
577C2×C3#243911yescharacteristic
578C2×C3#244111yescharacteristic
579C2×C3#244711yescharacteristic
580C2×C3#244811yescharacteristic
581C2×C3#248911yescharacteristic
582C2×C3#249011yescharacteristic
583C2×C3#249411yescharacteristic
584C2×C3#249511yescharacteristic
585C2×C3#251311yescharacteristic
586C2×C3#251411yescharacteristic
587C2×C3#257011yescharacteristic
588C2×C3#257011yescharacteristic
589C2×C3#264711yescharacteristic
590C2×C3#286411yescharacteristic
591C22C2×#89011yescharacteristic
592C22C2×#89011yescharacteristic
593C22C2×#89811yescharacteristic
594C22C2×#89811yescharacteristic
595C22#551711yescharacteristic
596C22#551711yescharacteristic
597C22#551911yescharacteristic
598C22#551911yescharacteristic
599C22#552911yescharacteristic
600C22#553011yescharacteristic
601C22#553211yescharacteristic
602C22#553311yescharacteristic
603C22#567111yescharacteristic
604C22#567111yescharacteristic
605C22#568011yescharacteristic
606C22#568011yescharacteristic
607C22#568111yescharacteristic
608C22#568111yescharacteristic
609C22#568211yescharacteristic
610C22#568211yescharacteristic
611C22#569111yescharacteristic
612C22#569111yescharacteristic
613C22#569411yescharacteristic
614C22#569411yescharacteristic
615C22#569511yescharacteristic
616C22#569511yescharacteristic
617C22#569711yescharacteristic
618C22#569811yescharacteristic
619C22C2×#92411yescharacteristic
620C22C2×#93511yescharacteristic
621C22C2×#94711yescharacteristic
622C22#582411yescharacteristic
623C22#582911yescharacteristic
624C22#583111yescharacteristic
625C22#583411yescharacteristic
626C4—44no—
627C4—42no—
628C4—42no—
629C4—82no—
630C4—122no—
631C4—122no—
632C4—122no—
633C4—122no—
634C4—242no—
635C4—242no—
636C4#498618yes—
637C3#1523211yescharacteristic, complemented, Sylow
638C2#7417211yescharacteristic
639C2#7417311yescharacteristic
640C2#7418611yescharacteristic
641C2#7418611yescharacteristic
642C2#7419511yescharacteristic
643C2#7422211yescharacteristic
644C2#7423411yescharacteristic
645C2#7423511yescharacteristic
646C2C2×#498611yescharacteristic
647C2#8224811yescharacteristic
648C2#8224911yescharacteristic
649C2#8296211yescharacteristic
650C2#8296311yescharacteristic
651C2#8306011yescharacteristic
652C2#8306111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, prime radical, cosocleC24×C3C24
FittingC2×C3×#382C2
hypercenterC2×#382D3
hypocenterC3#15232
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
637. C3#15232semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3822
C2×#49842
#715632
#715352
C4×C3⋊#952
#694232
#694172
#694152
#152323