Finite Group Databasebeta

← #10720228

Subgroups — #10720228

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×#4984C211yesmaximal, characteristic, complemented
5C2×#4951C212yesmaximal, complemented
6C2×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
7#71563C211yesmaximal, characteristic, complemented
8#71548C212yesmaximal, complemented
9#71546C212yesmaximal, 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⋊Dic3C2212yes—
23C22×C4⋊Dic3C2211yescharacteristic
24C22×C4⋊Dic3C2211yescharacteristic
25C22×C4×Dic3C2211yescharacteristic
26C22×C4×Dic3C2211yescharacteristic
27C22×C4×Dic3C2212yes—
28C3×#390C418yescomplemented
29#5221—24no—
30#5221—24no—
31C2×C3⋊#95C2211yescharacteristic
32C2×C3⋊#95C2211yescharacteristic
33C2×C3⋊#95C2211yescharacteristic
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2211yescharacteristic
39#4984—24no—
40#4951—28no—
41C4×C4⋊Dic3—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×C4C2311yescharacteristic
62C23×C3×C4C2312yes—
63C23×C3×C4C2311yescharacteristic
64C23×C3×C4C2311yescharacteristic
65C23×Dic3C2311yescharacteristic
66C23×Dic3C2312yes—
67C23×Dic3C2312yes—
68C23×Dic3C2311yescharacteristic
69C23×Dic3C2311yescharacteristic
70C23×Dic3C2311yescharacteristic
71C2×C3×C4⋊C4—22no—
72C2×C3×C4⋊C4—22no—
73C2×C3×C4⋊C4C2×C414yes—
74C2×C3×C22⋊C4—24no—
75C2×C3×C22⋊C4—24no—
76C2×C3×C22⋊C4—42no—
77C2×C3×C22⋊C4—42no—
78C2×C3×C22⋊C4C2×C418yes—
79C2×C3×C22⋊C4C2×C418yes—
80C2×C3×C42—22no—
81C2×C3×C42—22no—
82C2×C3×C42C2×C414yes—
83C2×#217—24no—
84C2×#217—24no—
85C2×#217—24no—
86C2×#217—24no—
87C2×#217—24no—
88C2×#217—24no—
89C2×#217—24no—
90C2×#217—24no—
91C2×#217—42no—
92C2×#217—42no—
93C2×#217—42no—
94C2×#217—42no—
95C2×C4⋊Dic3—22no—
96C2×C4⋊Dic3—22no—
97C2×C4⋊Dic3—22no—
98C2×C4⋊Dic3—22no—
99C2×C4⋊Dic3—24no—
100C2×C4⋊Dic3—24no—
101C2×C4⋊Dic3—42no—
102C2×C4⋊Dic3D414yes—
103C2×C4⋊Dic3D414yes—
104C2×C4×Dic3—24no—
105C2×C4×Dic3—22no—
106C2×C4×Dic3—22no—
107C2×C4×Dic3—22no—
108C2×C4×Dic3—22no—
109C2×C4×Dic3—22no—
110C2×C4×Dic3—22no—
111C2×C4×Dic3—24no—
112C2×C4×Dic3—42no—
113C3⋊#95—22no—
114C3⋊#95—24no—
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—64no—
137#390—64no—
138#390Dic318yescomplemented
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—21no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—22no—
179C22×C3×C4—22no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
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×C4C22×C412yes—
190C22×C3×C4C22×C414yes—
191C22×C3×C4C22×C412yes—
192C22×C3×C4C22×C412yes—
193C22×C3×C4C2×D412yes—
194C22×C3×C4C2×D412yes—
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—22no—
203C22×Dic3—22no—
204C22×Dic3—21no—
205C22×Dic3—22no—
206C22×Dic3—21no—
207C22×Dic3—21no—
208C22×Dic3—21no—
209C22×Dic3—21no—
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—22no—
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—21no—
230C22×Dic3—22no—
231C22×Dic3—21no—
232C22×Dic3—21no—
233C22×Dic3—21no—
234C22×Dic3—21no—
235C22×Dic3—21no—
236C22×Dic3—21no—
237C22×Dic3C2×D412yes—
238C22×Dic3C2×D414yes—
239C22×Dic3C2×D414yes—
240C22×Dic3C2×D412yes—
241C22×Dic3#4112yes—
242C22×Dic3#4112yes—
243C3×C4⋊C4—28no—
244C3×C22⋊C4—216no—
245C3×C22⋊C4—48no—
246C3×C42—28no—
247#217—48no—
248#217—48no—
249#217—48no—
250#217—48no—
251C4⋊Dic3—28no—
252C4⋊Dic3—28no—
253C4⋊Dic3—48no—
254C4×Dic3—48no—
255C4×Dic3—44no—
256C4×Dic3—44no—
257C25C22×D312yes—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—22no—
262C22×D4—22no—
263C22×D4—22no—
264C22×D4C2×Dic314yes—
265C23×C4—31no—
266C23×C4—32no—
267C23×C4—32no—
268C23×C4—31no—
269C23×C4—31no—
270C23×C4—31no—
271C23×C4C22×D312yes—
272C23×C4C22×D311yescharacteristic
273C23×C4C22×D311yescharacteristic
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⋊C4C2×Dic314yes—
287C2×C22⋊C4—24no—
288C2×C22⋊C4—24no—
289C2×C22⋊C4—42no—
290C2×C22⋊C4—42no—
291C2×C22⋊C4—64no—
292C2×C22⋊C4—64no—
293C2×C22⋊C4—64no—
294C2×C22⋊C4—64no—
295C2×C22⋊C4—64no—
296C2×C22⋊C4—64no—
297C2×C22⋊C4—64no—
298C2×C22⋊C4—64no—
299C2×C22⋊C4—122no—
300C2×C22⋊C4—122no—
301C2×C22⋊C4—122no—
302C2×C22⋊C4—122no—
303C2×C22⋊C4C2×Dic318yes—
304C2×C22⋊C4C2×Dic318yes—
305C2×C42—22no—
306C2×C42—22no—
307C2×C42—64no—
308C2×C42—62no—
309C2×C42—62no—
310C2×C42—64no—
311C2×C42—62no—
312C2×C42—62no—
313C2×C42—62no—
314C2×C42—62no—
315C2×C42—122no—
316C2×C42C2×Dic314yes—
317#95—34no—
318#95—62no—
319#95—62no—
320#95—64no—
321#95—64no—
322#95—64no—
323#95—62no—
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—22no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—24no—
384C2×C3×C4—24no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—24no—
388C2×C3×C4—42no—
389C2×C3×C4—41no—
390C2×C3×C4—42no—
391C2×C3×C4—42no—
392C2×C3×C4—41no—
393C2×C3×C4—41no—
394C2×C3×C4—41no—
395C2×C3×C4—42no—
396C2×C3×C4#11714yes—
397C2×C3×C4C4×D414yes—
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—24no—
405C2×Dic3—24no—
406C2×Dic3—22no—
407C2×Dic3—22no—
408C2×Dic3—22no—
409C2×Dic3—22no—
410C2×Dic3—24no—
411C2×Dic3—22no—
412C2×Dic3—24no—
413C2×Dic3—22no—
414C2×Dic3—22no—
415C2×Dic3—22no—
416C2×Dic3—22no—
417C2×Dic3—24no—
418C2×Dic3—24no—
419C2×Dic3—22no—
420C2×Dic3—22no—
421C2×Dic3—22no—
422C2×Dic3—41no—
423C2×Dic3—41no—
424C2×Dic3—41no—
425C2×Dic3—41no—
426C2×Dic3—42no—
427C2×Dic3—42no—
428C2×Dic3—41no—
429C2×Dic3—42no—
430C2×Dic3—42no—
431C2×Dic3—41no—
432C2×Dic3—41no—
433C2×Dic3—41no—
434C2×Dic3—42no—
435C2×Dic3—41no—
436C2×Dic3—41no—
437C2×Dic3—41no—
438C2×Dic3—41no—
439C2×Dic3—42no—
440C2×Dic3—41no—
441C2×Dic3—42no—
442C2×Dic3—41no—
443C2×Dic3—41no—
444C2×Dic3—41no—
445C2×Dic3—42no—
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—
460C24C22×Dic314yes—
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—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—32no—
486C22×C4—32no—
487C22×C4—34no—
488C22×C4—34no—
489C22×C4—32no—
490C22×C4—32no—
491C22×C4—61no—
492C22×C4—61no—
493C22×C4—61no—
494C22×C4—61no—
495C22×C4—62no—
496C22×C4—62no—
497C22×C4—61no—
498C22×C4—62no—
499C22×C4—62no—
500C22×C4—61no—
501C22×C4—61no—
502C22×C4—61no—
503C22×C4—61no—
504C22×C4—62no—
505C22×C4—61no—
506C22×C4—61no—
507C22×C4—61no—
508C22×C4—61no—
509C22×C4—61no—
510C22×C4—62no—
511C22×C4—61no—
512C22×C4—62no—
513C22×C4—61no—
514C22×C4—61no—
515C22×C4—62no—
516C22×C4—61no—
517C22×C4—61no—
518C22×C4—61no—
519C22×C4—62no—
520C22×C4—62no—
521C22×C4—62no—
522C22×C4—62no—
523C22×C4—61no—
524C22×C4—61no—
525C22×C4—61no—
526C22×C4—61no—
527C22×C4#23512yes—
528C22×C4#23512yes—
529C22×C4D3×D412yes—
530C22×C4D3×D412yes—
531C22×C4D3×D412yes—
532C22×C4#23712yes—
533C22×C4#23712yes—
534C22×C4#23712yes—
535C22×C4C22×Dic312yes—
536C22×C4C22×Dic314yes—
537C22×C4C22×Dic312yes—
538C22×C4C22×Dic312yes—
539C4⋊C4—28no—
540C4⋊C4—68no—
541C4⋊C4—68no—
542C4⋊C4—128no—
543C22⋊C4—216no—
544C22⋊C4—48no—
545C22⋊C4—128no—
546C22⋊C4—128no—
547C22⋊C4—128no—
548C22⋊C4—128no—
549C42—28no—
550C42—128no—
551C42—124no—
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—24no—
604C3×C4—42no—
605C3×C4—44no—
606C3×C4#38818yescomplemented
607Dic3—42no—
608Dic3—44no—
609Dic3—42no—
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—
648C23C2×#23511yescharacteristic
649C23C2×#23511yescharacteristic
650C23C2×D3×D411yescharacteristic
651C23C2×D3×D411yescharacteristic
652C23C2×D3×D411yescharacteristic
653C23C2×#23711yescharacteristic
654C23C2×#23711yescharacteristic
655C23C2×#23711yescharacteristic
656C23#100411yescharacteristic
657C23#100411yescharacteristic
658C23D3×#4111yescharacteristic
659C23D3×#4111yescharacteristic
660C23#100911yescharacteristic
661C23#101011yescharacteristic
662C23C23×Dic311yescharacteristic
663D4—416no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—62no—
685C2×C4—64no—
686C2×C4—62no—
687C2×C4—62no—
688C2×C4—64no—
689C2×C4—62no—
690C2×C4—64no—
691C2×C4—64no—
692C2×C4—62no—
693C2×C4—62no—
694C2×C4—62no—
695C2×C4—62no—
696C2×C4—64no—
697C2×C4—62no—
698C2×C4—62no—
699C2×C4—62no—
700C2×C4—64no—
701C2×C4—62no—
702C2×C4—121no—
703C2×C4—121no—
704C2×C4—122no—
705C2×C4—122no—
706C2×C4—121no—
707C2×C4—121no—
708C2×C4—121no—
709C2×C4—121no—
710C2×C4—121no—
711C2×C4—121no—
712C2×C4—122no—
713C2×C4—122no—
714C2×C4—121no—
715C2×C4—121no—
716C2×C4—122no—
717C2×C4—121no—
718C2×C4—122no—
719C2×C4—121no—
720C2×C4—121no—
721C2×C4—122no—
722C2×C4—121no—
723C2×C4—122no—
724C2×C4—121no—
725C2×C4—121no—
726C2×C4#87914yes—
727C2×C4#88314yes—
728C2×C4#88414yes—
729C2×C4#88514yes—
730C2×C4#92614yes—
731C2×C4D4×Dic314yes—
732C2×C4D4×Dic314yes—
733C2×C4D4×Dic314yes—
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×#87911yescharacteristic
766C22C2×#88311yescharacteristic
767C22C2×#88411yescharacteristic
768C22C2×#88511yescharacteristic
769C22#554811yescharacteristic
770C22#554811yescharacteristic
771C22#555711yescharacteristic
772C22#555711yescharacteristic
773C22#556111yescharacteristic
774C22#556111yescharacteristic
775C22#556211yescharacteristic
776C22#556211yescharacteristic
777C22#559811yescharacteristic
778C22#559911yescharacteristic
779C22#560911yescharacteristic
780C22#561111yescharacteristic
781C22#561211yescharacteristic
782C22#561411yescharacteristic
783C22#561611yescharacteristic
784C22#561811yescharacteristic
785C22#567111yescharacteristic
786C22#567611yescharacteristic
787C22#567711yescharacteristic
788C22#568111yescharacteristic
789C22#571311yescharacteristic
790C22#571711yescharacteristic
791C22#571811yescharacteristic
792C22#571811yescharacteristic
793C22C2×#92611yescharacteristic
794C22C2×D4×Dic311yescharacteristic
795C22C2×D4×Dic311yescharacteristic
796C22C2×D4×Dic311yescharacteristic
797C22#579811yescharacteristic
798C22Dic3×#4111yescharacteristic
799C22#582711yescharacteristic
800C4—24no—
801C4—42no—
802C4—44no—
803C4—124no—
804C4—122no—
805C4—124no—
806C4—122no—
807C4—122no—
808C4—122no—
809C4#495118yescomplemented
810C3#1414111yescharacteristic, complemented, Sylow
811C2—84no—
812C2#7631611yescharacteristic
813C2#7632011yescharacteristic
814C2#7633811yescharacteristic
815C2#7634111yescharacteristic
816C2#7644311yescharacteristic
817C2#7644411yescharacteristic
818C2#7644911yescharacteristic
819C2#7645111yescharacteristic
820C2C2×#495111yescharacteristic
821C2#8231911yescharacteristic
822C2#8232511yescharacteristic
823C2#8263611yescharacteristic
824C2#8263711yescharacteristic
825C2#8295511yescharacteristic
826C2#8317311yescharacteristic
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×#4984C2semidirect
5. C2×#4951C2semidirect
6. C2×C4×C4⋊Dic3C2semidirect
7. #71563C2semidirect
8. #71548C2semidirect
9. #71546C2semidirect
10. #71545C2semidirect
11. C4×C3⋊#95C2semidirect
28. C3×#390C4semidirect
120. C3⋊#95D4semidirect
138. #390Dic3semidirect
606. C3×C4#388semidirect
809. C4#4951semidirect
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×#49842
C2×#49512
C2×C4×C4⋊Dic32
#715632
#715482
#715462
#715452
C4×C3⋊#952
#141413