Finite Group Databasebeta

← #10720223

Subgroups — #10720223

Order 768.

1938 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#390C211yesmaximal, characteristic
2C2×#5221C211yesmaximal, characteristic
3C2×#5221C211yesmaximal, characteristic
4C2×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
5C2×#4944C212yesmaximal, complemented
6C2×#4928C211yesmaximal, characteristic, complemented
7#71563C211yesmaximal, characteristic, complemented
8#71549C212yesmaximal, complemented
9#71547C212yesmaximal, complemented
10#71545C212yesmaximal, complemented
11C4×C3⋊#95C211yesmaximal, characteristic, complemented
12#14141—31nomaximal, Sylow
13C23×C3×D4C2211yescharacteristic
14C22×C3×C4⋊C4C2211yescharacteristic
15C22×C3×C22⋊C4C2212yes—
16C22×C3×C22⋊C4C2212yes—
17C22×C3×C42C2211yescharacteristic
18C22×#217C2212yes—
19C22×#217C2212yes—
20C22×#217C2212yes—
21C22×#217C2212yes—
22C22×C4⋊Dic3C2211yescharacteristic
23C22×C4⋊Dic3C2211yescharacteristic
24C22×Dic3⋊C4C2212yes—
25C22×C4×Dic3C2211yescharacteristic
26C22×C4×Dic3C2212yes—
27C22×C4×Dic3C2211yescharacteristic
28C3×#390—24no—
29#5221—24no—
30#5221C418yescomplemented
31C2×C3⋊#95C2211yescharacteristic
32C2×C3⋊#95C2211yescharacteristic
33C2×C3⋊#95C2211yescharacteristic
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2211yescharacteristic
39Dic3×C4⋊C4—24no—
40#4944—28no—
41#4928—24no—
42C2×#390—31no—
43C2×#390—31no—
44C2×#390D311yescharacteristic
45C2×#389—31no—
46C2×#388—32no—
47C2×C4×C4⋊C4—31no—
48#1440—32no—
49#1439—32no—
50#1437—32no—
51C4⋊#95—31no—
52C4×#95—31no—
53C25×C3C2312yes—
54C22×C3×D4—22no—
55C22×C3×D4—22no—
56C22×C3×D4—22no—
57C22×C3×D4—22no—
58C22×C3×D4—22no—
59C22×C3×D4—22no—
60C22×C3×D4C2×C414yes—
61C23×C3×C4C2312yes—
62C23×C3×C4C2311yescharacteristic
63C23×C3×C4C2311yescharacteristic
64C23×C3×C4C2311yescharacteristic
65C23×Dic3C2311yescharacteristic
66C23×Dic3C2312yes—
67C23×Dic3C2311yescharacteristic
68C23×Dic3C2312yes—
69C23×Dic3C2311yescharacteristic
70C23×Dic3C2311yescharacteristic
71C2×C3×C4⋊C4—22no—
72C2×C3×C4⋊C4—22no—
73C2×C3×C4⋊C4D414yes—
74C2×C3×C22⋊C4—24no—
75C2×C3×C22⋊C4—24no—
76C2×C3×C22⋊C4—24no—
77C2×C3×C22⋊C4—24no—
78C2×C3×C22⋊C4—42no—
79C2×C3×C22⋊C4—42no—
80C2×C3×C42—22no—
81C2×C3×C42—22no—
82C2×C3×C42—22no—
83C2×#217—24no—
84C2×#217—24no—
85C2×#217—24no—
86C2×#217—24no—
87C2×#217—24no—
88C2×#217—24no—
89C2×#217—42no—
90C2×#217—42no—
91C2×#217—42no—
92C2×#217—42no—
93C2×#217C2×C418yes—
94C2×#217C2×C418yes—
95C2×C4⋊Dic3—22no—
96C2×C4⋊Dic3—22no—
97C2×C4⋊Dic3—22no—
98C2×C4⋊Dic3—22no—
99C2×C4⋊Dic3C2×C414yes—
100C2×C4⋊Dic3D414yes—
101C2×Dic3⋊C4—24no—
102C2×Dic3⋊C4—24no—
103C2×Dic3⋊C4—42no—
104C2×C4×Dic3—22no—
105C2×C4×Dic3—22no—
106C2×C4×Dic3—22no—
107C2×C4×Dic3—24no—
108C2×C4×Dic3—22no—
109C2×C4×Dic3—22no—
110C2×C4×Dic3—24no—
111C2×C4×Dic3—42no—
112C2×C4×Dic3C2×C414yes—
113C3⋊#95—24no—
114C3⋊#95—22no—
115C3⋊#95—24no—
116C3⋊#95—24no—
117C3⋊#95—22no—
118C3⋊#95—22no—
119C3⋊#95—42no—
120C3⋊#95D414yescomplemented
121C23×D4C2×D311yescharacteristic
122C22×C4⋊C4—31no—
123C22×C4⋊C4—31no—
124C22×C4⋊C4—32no—
125C22×C4⋊C4C2×D311yescharacteristic
126C22×C22⋊C4—32no—
127C22×C22⋊C4—32no—
128C22×C22⋊C4—32no—
129C22×C22⋊C4—32no—
130C22×C22⋊C4C2×D312yes—
131C22×C22⋊C4C2×D312yes—
132C22×C42—31no—
133C22×C42—31no—
134C22×C42—32no—
135C22×C42C2×D311yescharacteristic
136#390—24no—
137#390—38no—
138#390—64no—
139#389—64no—
140#388—68no—
141C4×C4⋊C4—64no—
142C2×#95—31no—
143C2×#95—31no—
144C2×#95—31no—
145C2×#95—31no—
146C2×#95—32no—
147C2×#95—32no—
148C2×#95—32no—
149C2×#95—32no—
150C24×C3—22no—
151C24×C3—22no—
152C24×C3—22no—
153C24×C3—22no—
154C24×C3—22no—
155C24×C3—22no—
156C24×C3—22no—
157C24×C3—22no—
158C24×C3—22no—
159C24×C3—22no—
160C24×C3—22no—
161C24×C3—22no—
162C24×C3—22no—
163C24×C3—22no—
164C24×C3C22×C414yes—
165C24×C3C2411yescharacteristic
166C2×C3×D4—28no—
167C2×C3×D4—28no—
168C2×C3×D4—28no—
169C2×C3×D4—44no—
170C2×C3×D4—44no—
171C2×C3×D4—44no—
172C2×C3×D4—44no—
173C22×C3×C4—21no—
174C22×C3×C4—22no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—22no—
183C22×C3×C4—22no—
184C22×C3×C4—22no—
185C22×C3×C4—22no—
186C22×C3×C4—22no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4C22×C412yes—
192C22×C3×C4C2×D412yes—
193C22×C3×C4C2×D412yes—
194C22×C3×C4C2×D414yes—
195C22×C3×C4C2×D412yes—
196C22×C3×C4#4112yes—
197C22×C3×C4#4112yes—
198C22×C3×C4#4112yes—
199C22×C3×C4#4112yes—
200C22×C3×C4#4112yes—
201C22×Dic3—21no—
202C22×Dic3—21no—
203C22×Dic3—21no—
204C22×Dic3—21no—
205C22×Dic3—21no—
206C22×Dic3—22no—
207C22×Dic3—22no—
208C22×Dic3—22no—
209C22×Dic3—22no—
210C22×Dic3—21no—
211C22×Dic3—21no—
212C22×Dic3—21no—
213C22×Dic3—21no—
214C22×Dic3—21no—
215C22×Dic3—21no—
216C22×Dic3—21no—
217C22×Dic3—21no—
218C22×Dic3—21no—
219C22×Dic3—21no—
220C22×Dic3—21no—
221C22×Dic3—22no—
222C22×Dic3—22no—
223C22×Dic3—22no—
224C22×Dic3—22no—
225C22×Dic3—21no—
226C22×Dic3—22no—
227C22×Dic3—22no—
228C22×Dic3—22no—
229C22×Dic3—22no—
230C22×Dic3—21no—
231C22×Dic3—21no—
232C22×Dic3—21no—
233C22×Dic3—21no—
234C22×Dic3—21no—
235C22×Dic3C22×C412yes—
236C22×Dic3C22×C414yes—
237C22×Dic3C22×C412yes—
238C22×Dic3C2×D412yes—
239C22×Dic3C2×D414yes—
240C22×Dic3C2×D412yes—
241C22×Dic3#4112yes—
242C22×Dic3#4112yes—
243C3×C4⋊C4—28no—
244C3×C22⋊C4—48no—
245C3×C22⋊C4—48no—
246C3×C42—44no—
247#217—216no—
248#217—48no—
249#217—48no—
250#217—48no—
251C4⋊Dic3—28no—
252C4⋊Dic3—28no—
253Dic3⋊C4—48no—
254C4×Dic3—28no—
255C4×Dic3—48no—
256C4×Dic3—44no—
257C25C22×D312yes—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—22no—
262C22×D4—22no—
263C22×D4—22no—
264C22×D4C4×D314yes—
265C23×C4—31no—
266C23×C4—32no—
267C23×C4—32no—
268C23×C4—31no—
269C23×C4—31no—
270C23×C4—31no—
271C23×C4C22×D311yescharacteristic
272C23×C4C22×D311yescharacteristic
273C23×C4C22×D312yes—
274C23×C4C22×D311yescharacteristic
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—34no—
278C2×C4⋊C4—34no—
279C2×C4⋊C4—62no—
280C2×C4⋊C4—62no—
281C2×C4⋊C4—62no—
282C2×C4⋊C4—62no—
283C2×C4⋊C4—64no—
284C2×C4⋊C4—64no—
285C2×C4⋊C4—122no—
286C2×C4⋊C4#6714yes—
287C2×C22⋊C4—24no—
288C2×C22⋊C4—24no—
289C2×C22⋊C4—24no—
290C2×C22⋊C4—24no—
291C2×C22⋊C4—38no—
292C2×C22⋊C4—38no—
293C2×C22⋊C4—42no—
294C2×C22⋊C4—42no—
295C2×C22⋊C4—64no—
296C2×C22⋊C4—64no—
297C2×C22⋊C4—64no—
298C2×C22⋊C4—64no—
299C2×C22⋊C4—64no—
300C2×C22⋊C4—64no—
301C2×C22⋊C4—122no—
302C2×C22⋊C4—122no—
303C2×C22⋊C4—122no—
304C2×C22⋊C4—122no—
305C2×C42—22no—
306C2×C42—22no—
307C2×C42—22no—
308C2×C42—34no—
309C2×C42—62no—
310C2×C42—62no—
311C2×C42—64no—
312C2×C42—62no—
313C2×C42—62no—
314C2×C42—62no—
315C2×C42—64no—
316C2×C42—122no—
317#95—34no—
318#95—62no—
319#95—62no—
320#95—64no—
321#95—64no—
322#95—62no—
323#95—64no—
324#95—122no—
325C23×C3—24no—
326C23×C3—24no—
327C23×C3—24no—
328C23×C3—24no—
329C23×C3—24no—
330C23×C3—24no—
331C23×C3—24no—
332C23×C3—42no—
333C23×C3—42no—
334C23×C3—42no—
335C23×C3—42no—
336C23×C3—42no—
337C23×C3—42no—
338C23×C3—42no—
339C23×C3—42no—
340C23×C3—42no—
341C23×C3—42no—
342C23×C3—42no—
343C23×C3—42no—
344C23×C3—42no—
345C23×C3—42no—
346C23×C3—42no—
347C23×C3—42no—
348C23×C3—42no—
349C23×C3—42no—
350C23×C3—42no—
351C23×C3—42no—
352C23×C3—42no—
353C23×C3—42no—
354C23×C3—42no—
355C23×C3—42no—
356C23×C3—42no—
357C23×C3—42no—
358C23×C3—42no—
359C23×C3—42no—
360C23×C3C23×C411yescharacteristic
361C23×C3C22×D411yescharacteristic
362C23×C3C22×D411yescharacteristic
363C23×C3C22×D411yescharacteristic
364C23×C3C2×#4111yescharacteristic
365C23×C3C2×#4111yescharacteristic
366C23×C3C2×#4111yescharacteristic
367C23×C3C2×#4111yescharacteristic
368C23×C3C2×#4111yescharacteristic
369C23×C3C2×#4111yescharacteristic
370C23×C3C2×#4111yescharacteristic
371C23×C3H(5,𝔽2)11yescharacteristic
372C23×C3H(5,𝔽2)11yescharacteristic
373C23×C3H(5,𝔽2)11yescharacteristic
374C23×C32−1+411yescharacteristic
375C3×D4—416no—
376C2×C3×C4—24no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—24no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—24no—
384C2×C3×C4—22no—
385C2×C3×C4—41no—
386C2×C3×C4—41no—
387C2×C3×C4—42no—
388C2×C3×C4—42no—
389C2×C3×C4—41no—
390C2×C3×C4—41no—
391C2×C3×C4—41no—
392C2×C3×C4—41no—
393C2×C3×C4—42no—
394C2×C3×C4—41no—
395C2×C3×C4—41no—
396C2×C3×C4—42no—
397C2×C3×C4#11714yes—
398C2×C3×C4C4×D414yes—
399C2×C3×C4C4×D414yes—
400C2×C3×C4#12114yes—
401C2×C3×C4#12314yes—
402C2×C3×C4#12414yes—
403C2×C3×C4#12614yes—
404C2×Dic3—22no—
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—22no—
408C2×Dic3—22no—
409C2×Dic3—22no—
410C2×Dic3—22no—
411C2×Dic3—24no—
412C2×Dic3—24no—
413C2×Dic3—22no—
414C2×Dic3—22no—
415C2×Dic3—24no—
416C2×Dic3—24no—
417C2×Dic3—22no—
418C2×Dic3—22no—
419C2×Dic3—24no—
420C2×Dic3—22no—
421C2×Dic3—22no—
422C2×Dic3—24no—
423C2×Dic3—22no—
424C2×Dic3—22no—
425C2×Dic3—41no—
426C2×Dic3—41no—
427C2×Dic3—42no—
428C2×Dic3—41no—
429C2×Dic3—42no—
430C2×Dic3—41no—
431C2×Dic3—42no—
432C2×Dic3—42no—
433C2×Dic3—41no—
434C2×Dic3—41no—
435C2×Dic3—42no—
436C2×Dic3—41no—
437C2×Dic3—42no—
438C2×Dic3—42no—
439C2×Dic3—41no—
440C2×Dic3—41no—
441C2×Dic3—41no—
442C2×Dic3—41no—
443C2×Dic3—41no—
444C2×Dic3—42no—
445C2×Dic3C4×D414yes—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24C2×C4×D314yes—
461C24C23×D311yescharacteristic
462C2×D4—28no—
463C2×D4—28no—
464C2×D4—28no—
465C2×D4—44no—
466C2×D4—44no—
467C2×D4—44no—
468C2×D4—44no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—32no—
488C22×C4—32no—
489C22×C4—32no—
490C22×C4—32no—
491C22×C4—34no—
492C22×C4—32no—
493C22×C4—34no—
494C22×C4—32no—
495C22×C4—61no—
496C22×C4—61no—
497C22×C4—61no—
498C22×C4—61no—
499C22×C4—61no—
500C22×C4—61no—
501C22×C4—61no—
502C22×C4—62no—
503C22×C4—62no—
504C22×C4—61no—
505C22×C4—61no—
506C22×C4—62no—
507C22×C4—61no—
508C22×C4—61no—
509C22×C4—61no—
510C22×C4—61no—
511C22×C4—62no—
512C22×C4—62no—
513C22×C4—61no—
514C22×C4—62no—
515C22×C4—62no—
516C22×C4—61no—
517C22×C4—61no—
518C22×C4—61no—
519C22×C4—61no—
520C22×C4—62no—
521C22×C4—62no—
522C22×C4—61no—
523C22×C4—61no—
524C22×C4—62no—
525C22×C4—62no—
526C22×C4—61no—
527C22×C4—61no—
528C22×C4—62no—
529C22×C4C2×C4×D312yes—
530C22×C4#23512yes—
531C22×C4D3×D412yes—
532C22×C4D3×D412yes—
533C22×C4#23712yes—
534C22×C4#23712yes—
535C22×C4#23712yes—
536C22×C4#23712yes—
537C22×C4C2×#6714yes—
538C22×C4C2×#6712yes—
539C4⋊C4—28no—
540C4⋊C4—68no—
541C4⋊C4—68no—
542C4⋊C4—128no—
543C22⋊C4—48no—
544C22⋊C4—48no—
545C22⋊C4—616no—
546C22⋊C4—128no—
547C22⋊C4—128no—
548C22⋊C4—128no—
549C42—44no—
550C42—68no—
551C42—128no—
552C42—124no—
553C22×C3—44no—
554C22×C3—44no—
555C22×C3—44no—
556C22×C3—44no—
557C22×C3—44no—
558C22×C3—44no—
559C22×C3—44no—
560C22×C3—82no—
561C22×C3—82no—
562C22×C3—82no—
563C22×C3—82no—
564C22×C3—82no—
565C22×C3—82no—
566C22×C3—82no—
567C22×C3—82no—
568C22×C3C2×#11711yescharacteristic
569C22×C3C2×C4×D411yescharacteristic
570C22×C3C2×C4×D411yescharacteristic
571C22×C3C2×C4×D411yescharacteristic
572C22×C3C4×#4111yescharacteristic
573C22×C3#51811yescharacteristic
574C22×C3#52011yescharacteristic
575C22×C3C2×#12111yescharacteristic
576C22×C3C2×#12311yescharacteristic
577C22×C3C2×#12411yescharacteristic
578C22×C3C2×#12611yescharacteristic
579C22×C3#52911yescharacteristic
580C22×C3#52911yescharacteristic
581C22×C3#53211yescharacteristic
582C22×C3#53211yescharacteristic
583C22×C3#54011yescharacteristic
584C22×C3#54011yescharacteristic
585C22×C3#54211yescharacteristic
586C22×C3#54211yescharacteristic
587C22×C3D4211yescharacteristic
588C22×C3D4211yescharacteristic
589C22×C3#54611yescharacteristic
590C22×C3#54611yescharacteristic
591C22×C3#54711yescharacteristic
592C22×C3#54811yescharacteristic
593C22×C3#54811yescharacteristic
594C22×C3#55011yescharacteristic
595C22×C3#55011yescharacteristic
596C22×C3#55011yescharacteristic
597C22×C3#55311yescharacteristic
598C22×C3#55311yescharacteristic
599C22×C3#55511yescharacteristic
600C22×C3#55611yescharacteristic
601C22×C3#55911yescharacteristic
602C22×C3#55911yescharacteristic
603C3×C4—42no—
604C3×C4—42no—
605C3×C4—44no—
606C3×C4#38818yescomplemented
607Dic3—24no—
608Dic3—42no—
609Dic3—44no—
610Dic3—44no—
611Dic3—42no—
612Dic3—42no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23C22×C4×D311yescharacteristic
649C23C2×#23511yescharacteristic
650C23C2×D3×D411yescharacteristic
651C23C2×D3×D411yescharacteristic
652C23C2×#23711yescharacteristic
653C23C2×#23711yescharacteristic
654C23C2×#23711yescharacteristic
655C23C2×#23711yescharacteristic
656C23#100411yescharacteristic
657C23#100411yescharacteristic
658C23D3×#4111yescharacteristic
659C23D3×#4111yescharacteristic
660C23#100911yescharacteristic
661C23#101011yescharacteristic
662C23C22×#6711yescharacteristic
663D4—416no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—34no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—62no—
687C2×C4—62no—
688C2×C4—62no—
689C2×C4—62no—
690C2×C4—62no—
691C2×C4—62no—
692C2×C4—62no—
693C2×C4—62no—
694C2×C4—64no—
695C2×C4—62no—
696C2×C4—62no—
697C2×C4—64no—
698C2×C4—64no—
699C2×C4—62no—
700C2×C4—64no—
701C2×C4—62no—
702C2×C4—62no—
703C2×C4—62no—
704C2×C4—64no—
705C2×C4—62no—
706C2×C4—64no—
707C2×C4—122no—
708C2×C4—121no—
709C2×C4—122no—
710C2×C4—121no—
711C2×C4—121no—
712C2×C4—121no—
713C2×C4—122no—
714C2×C4—121no—
715C2×C4—121no—
716C2×C4—121no—
717C2×C4—121no—
718C2×C4—121no—
719C2×C4—121no—
720C2×C4—122no—
721C2×C4—122no—
722C2×C4—121no—
723C2×C4—122no—
724C2×C4—121no—
725C2×C4—122no—
726C2×C4—122no—
727C2×C4#87714yes—
728C2×C4#87914yes—
729C2×C4#67⋊C414yes—
730C2×C4#88514yes—
731C2×C4C4×#6714yes—
732C2×C4#93514yes—
733C2×C4#93814yes—
734C2×C3—84no—
735C2×C3C2×#38811yescharacteristic
736C2×C3#229311yescharacteristic
737C2×C3#231911yescharacteristic
738C2×C3#236111yescharacteristic
739C2×C3#236311yescharacteristic
740C2×C3#236611yescharacteristic
741C2×C3#236711yescharacteristic
742C2×C3#242611yescharacteristic
743C2×C3#242811yescharacteristic
744C2×C3#244511yescharacteristic
745C2×C3#244811yescharacteristic
746C2×C3#249011yescharacteristic
747C2×C3#249111yescharacteristic
748C2×C3#251211yescharacteristic
749C2×C3#251311yescharacteristic
750C22—44no—
751C22—44no—
752C22—44no—
753C22—44no—
754C22—44no—
755C22—44no—
756C22—44no—
757C22—82no—
758C22—82no—
759C22—82no—
760C22—82no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22C2×#87711yescharacteristic
766C22C2×#87911yescharacteristic
767C22C2×#67⋊C411yescharacteristic
768C22C2×#88511yescharacteristic
769C22C4×#23711yescharacteristic
770C22C4×D3×D411yescharacteristic
771C22#554511yescharacteristic
772C22#554611yescharacteristic
773C22#555111yescharacteristic
774C22#555811yescharacteristic
775C22#555811yescharacteristic
776C22#556311yescharacteristic
777C22#559611yescharacteristic
778C22#559811yescharacteristic
779C22#559911yescharacteristic
780C22#560011yescharacteristic
781C22#560311yescharacteristic
782C22#560911yescharacteristic
783C22#561211yescharacteristic
784C22#561911yescharacteristic
785C22#567111yescharacteristic
786C22#568011yescharacteristic
787C22#568111yescharacteristic
788C22#568211yescharacteristic
789C22#571311yescharacteristic
790C22#571611yescharacteristic
791C22#571811yescharacteristic
792C22#571911yescharacteristic
793C22C2×C4×#6711yescharacteristic
794C22C2×#93511yescharacteristic
795C22C2×#93811yescharacteristic
796C22D4×#6711yescharacteristic
797C22#580611yescharacteristic
798C22#583111yescharacteristic
799C22#583411yescharacteristic
800C4—42no—
801C4—42no—
802C4—44no—
803C4—64no—
804C4—124no—
805C4—122no—
806C4—122no—
807C4—122no—
808C4—124no—
809C4#494418yescomplemented
810C3#1414111yescharacteristic, complemented, Sylow
811C2—84no—
812C2#7628911yescharacteristic
813C2#7629511yescharacteristic
814C2#7630611yescharacteristic
815C2#7630711yescharacteristic
816C2#7633911yescharacteristic
817C2#7634211yescharacteristic
818C2#7645011yescharacteristic
819C2#7645211yescharacteristic
820C2C2×#494411yescharacteristic
821C2#8234111yescharacteristic
822C2#8239911yescharacteristic
823C2#8264611yescharacteristic
824C2#8264811yescharacteristic
825C2#8296311yescharacteristic
826C2#8317611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC2×C3×#390C2
socle, cosocleC24×C3C24
prime radicalC23×C3×D4C22
hypercenterC2×#390D3
hypocenterC3#14141
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
4. C2×Dic3×C4⋊C4C2semidirect
5. C2×#4944C2semidirect
6. C2×#4928C2semidirect
7. #71563C2semidirect
8. #71549C2semidirect
9. #71547C2semidirect
10. #71545C2semidirect
11. C4×C3⋊#95C2semidirect
30. #5221C4semidirect
120. C3⋊#95D4semidirect
606. C3×C4#388semidirect
809. C4#4944semidirect
810. C3#14141semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3902
C2×#52212
C2×Dic3×C4⋊C42
C2×#49442
C2×#49282
#715632
#715492
#715472
#715452
C4×C3⋊#952
#141413