Finite Group Databasebeta

← #10732020

Subgroups — #10732020

Order 768.

2294 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#390C211yesmaximal, characteristic, complemented
2C2×#5223C211yesmaximal, characteristic
3C2×#4992C211yesmaximal, characteristic, complemented
4C2×#4956C212yesmaximal, complemented
5C2×#4961C212yesmaximal, complemented
6C2×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
7#72131C211yesmaximal, characteristic, complemented
8#71569C211yesmaximal, characteristic, complemented
9#71546C212yesmaximal, complemented
10#71545C212yesmaximal, complemented
11#71535C211yesmaximal, characteristic, complemented
12#15160—31nomaximal, Sylow
13C23×C3×D4C2211yescharacteristic
14C23×#67C2212yes—
15C23×C4×D3C2211yescharacteristic
16C22×C3×C4⋊C4C2211yescharacteristic
17C22×C3×C22⋊C4C2212yes—
18C22×C3×C22⋊C4C2212yes—
19C22×C3×C42C2211yescharacteristic
20C22×#217C2212yes—
21C22×#217C2212yes—
22C22×#217C2212yes—
23C22×(C2×D3)⋊C4C2212yes—
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×C4⋊Dic3C2212yes—
27C22×C4×Dic3C2211yescharacteristic
28C3×#390—24no—
29#5223—24no—
30C2×C3⋊#95C2211yescharacteristic
31C2×C3⋊#95C2212yes—
32C2×C3⋊#95C2211yescharacteristic
33C2×C3⋊#95C2212yes—
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2211yescharacteristic
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2211yescharacteristic
38#4992—24no—
39#4961—28no—
40#4956—28no—
41C4×(C2×D3)⋊C4—24no—
42C2×#397—31no—
43C2×#394—32no—
44C2×#392—31no—
45C2×#390D311yescharacteristic, complemented
46C2×#386—32no—
47C2×C4×C22⋊C4—31no—
48#1445—31no—
49#1439—32no—
50#1438—31no—
51#1437—32no—
52C4⋊#95—31no—
53C25×C3C2312yes—
54C24×D3C2311yescharacteristic
55C22×C3×D4—24no—
56C22×C3×D4—22no—
57C22×C3×D4—22no—
58C22×C3×D4—22no—
59C22×C3×D4—42no—
60C23×C3×C4C2312yes—
61C23×C3×C4C2311yescharacteristic
62C23×C3×C4C2311yescharacteristic
63C23×C3×C4C2311yescharacteristic
64C22×#67—24no—
65C22×#67—24no—
66C22×#67—24no—
67C22×#67—24no—
68C22×#67—24no—
69C22×#67—42no—
70C22×#67—42no—
71C23×Dic3C2312yes—
72C23×Dic3C2311yescharacteristic
73C23×Dic3C2311yescharacteristic
74C23×Dic3C2311yescharacteristic
75C23×Dic3C2312yes—
76C22×C4×D3—22no—
77C22×C4×D3—22no—
78C22×C4×D3—42no—
79C22×C4×D3—42no—
80C22×C4×D3D414yescomplemented
81C2×C3×C4⋊C4—22no—
82C2×C3×C4⋊C4—22no—
83C2×C3×C4⋊C4—22no—
84C2×C3×C22⋊C4—24no—
85C2×C3×C22⋊C4—24no—
86C2×C3×C22⋊C4—24no—
87C2×C3×C22⋊C4—24no—
88C2×C3×C22⋊C4—24no—
89C2×C3×C22⋊C4—24no—
90C2×C3×C42—42no—
91C2×C3×C42D414yescomplemented
92C2×#217—24no—
93C2×#217—24no—
94C2×#217—24no—
95C2×#217—24no—
96C2×#217—24no—
97C2×#217—42no—
98C2×#217—42no—
99C2×#217—42no—
100C2×#217—42no—
101C2×(C2×D3)⋊C4—22no—
102C2×(C2×D3)⋊C4—22no—
103C2×(C2×D3)⋊C4—22no—
104C2×(C2×D3)⋊C4—22no—
105C2×(C2×D3)⋊C4—24no—
106C2×(C2×D3)⋊C4—24no—
107C2×(C2×D3)⋊C4—24no—
108C2×(C2×D3)⋊C4D414yes—
109C2×(C2×D3)⋊C4D414yescomplemented
110C2×C4⋊Dic3—24no—
111C2×C4⋊Dic3—24no—
112C2×C4⋊Dic3—42no—
113C2×C4×Dic3—22no—
114C2×C4×Dic3—42no—
115C3⋊#95—22no—
116C3⋊#95—22no—
117C3⋊#95—24no—
118C3⋊#95—22no—
119C3⋊#95—22no—
120C3⋊#95—24no—
121C3⋊#95—24no—
122C3⋊#95—24no—
123C23×D4—32no—
124C23×D4C2×D311yescharacteristic
125C24×C4—31no—
126C22×C4⋊C4—32no—
127C22×C4⋊C4C2×D311yescharacteristic
128C22×C22⋊C4—31no—
129C22×C22⋊C4—31no—
130C22×C22⋊C4—32no—
131C22×C22⋊C4—32no—
132C22×C22⋊C4—32no—
133C22×C22⋊C4—32no—
134C22×C22⋊C4C2×D312yes—
135C22×C22⋊C4C2×D312yes—
136C22×C42—31no—
137C22×C42C2×D311yescharacteristic
138#397—64no—
139#394—68no—
140#392—64no—
141#390—24no—
142#386—68no—
143C4×C22⋊C4—64no—
144C2×#95—31no—
145C2×#95—32no—
146C2×#95—31no—
147C2×#95—32no—
148C2×#95—32no—
149C2×#95—31no—
150C2×#95—31no—
151C2×#95—32no—
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×C3—22no—
165C24×C3—22no—
166C24×C3#4114yes—
167C24×C3C2411yescharacteristic
168C23×D3—21no—
169C23×D3—21no—
170C23×D3—21no—
171C23×D3—21no—
172C23×D3—22no—
173C23×D3—22no—
174C23×D3—22no—
175C23×D3—22no—
176C23×D3C2×D412yes—
177C23×D3C2×D412yes—
178C23×D3C2×D412yes—
179C2×C3×D4—28no—
180C2×C3×D4—48no—
181C2×C3×D4—48no—
182C2×C3×D4—44no—
183C2×C3×D4—44no—
184C22×C3×C4—22no—
185C22×C3×C4—22no—
186C22×C3×C4—22no—
187C22×C3×C4—22no—
188C22×C3×C4—22no—
189C22×C3×C4—22no—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4C2×D412yes—
198C22×C3×C4C2×D412yes—
199C22×C3×C4C2×D412yes—
200C22×C3×C4C2×D412yes—
201C22×C3×C4C2×D412yes—
202C22×C3×C4C2×D412yes—
203C22×C3×C4#4112yes—
204C22×C3×C4#4112yes—
205C22×C3×C4#4112yes—
206C2×#67—216no—
207C2×#67—48no—
208C2×#67—48no—
209C2×#67—48no—
210C2×#67—48no—
211C2×#67—48no—
212C2×#67—48no—
213C22×Dic3—21no—
214C22×Dic3—22no—
215C22×Dic3—21no—
216C22×Dic3—21no—
217C22×Dic3—22no—
218C22×Dic3—22no—
219C22×Dic3—21no—
220C22×Dic3—21no—
221C22×Dic3—22no—
222C22×Dic3—22no—
223C22×Dic3—21no—
224C22×Dic3—22no—
225C22×Dic3—22no—
226C22×Dic3—22no—
227C22×Dic3—22no—
228C22×Dic3—22no—
229C22×Dic3—22no—
230C22×Dic3—22no—
231C22×Dic3—22no—
232C22×Dic3—22no—
233C22×Dic3—22no—
234C22×Dic3—22no—
235C22×Dic3—22no—
236C22×Dic3—22no—
237C22×Dic3—22no—
238C22×Dic3C2×D412yes—
239C22×Dic3C2×D412yes—
240C22×Dic3C2×D412yes—
241C22×Dic3#4114yes—
242C2×C4×D3—28no—
243C2×C4×D3—48no—
244C2×C4×D3—44no—
245C2×C4×D3—44no—
246C2×C4×D3—48no—
247C3×C4⋊C4—44no—
248C3×C22⋊C4—48no—
249C3×C22⋊C4—48no—
250C3×C42—44no—
251#217—48no—
252#217—48no—
253#217—48no—
254(C2×D3)⋊C4—28no—
255(C2×D3)⋊C4—28no—
256(C2×D3)⋊C4—48no—
257C4⋊Dic3—48no—
258C4×Dic3—44no—
259C25—31no—
260C25C22×D312yes—
261C22×D4—24no—
262C22×D4—22no—
263C22×D4—22no—
264C22×D4—22no—
265C22×D4—42no—
266C22×D4—64no—
267C22×D4—64no—
268C22×D4—64no—
269C22×D4—64no—
270C22×D4—64no—
271C22×D4—122no—
272C22×D4—122no—
273C23×C4—31no—
274C23×C4—31no—
275C23×C4—31no—
276C23×C4—32no—
277C23×C4—34no—
278C23×C4—32no—
279C23×C4—62no—
280C23×C4—62no—
281C23×C4—122no—
282C23×C4—122no—
283C23×C4C22×D312yes—
284C23×C4C22×D311yescharacteristic
285C23×C4C22×D311yescharacteristic
286C23×C4C22×D311yescharacteristic
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—64no—
291C2×C4⋊C4—64no—
292C2×C4⋊C4—122no—
293C2×C22⋊C4—24no—
294C2×C22⋊C4—24no—
295C2×C22⋊C4—24no—
296C2×C22⋊C4—24no—
297C2×C22⋊C4—24no—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—34no—
300C2×C22⋊C4—34no—
301C2×C22⋊C4—62no—
302C2×C22⋊C4—62no—
303C2×C22⋊C4—62no—
304C2×C22⋊C4—62no—
305C2×C22⋊C4—64no—
306C2×C22⋊C4—64no—
307C2×C22⋊C4—64no—
308C2×C22⋊C4—64no—
309C2×C22⋊C4—64no—
310C2×C22⋊C4—64no—
311C2×C22⋊C4—64no—
312C2×C22⋊C4—64no—
313C2×C22⋊C4—122no—
314C2×C22⋊C4—122no—
315C2×C22⋊C4—122no—
316C2×C22⋊C4—122no—
317C2×C42—42no—
318C2×C42—62no—
319C2×C42—122no—
320C2×C42#6714yescomplemented
321#95—64no—
322#95—64no—
323#95—64no—
324#95—64no—
325#95—62no—
326#95—62no—
327#95—62no—
328#95—62no—
329C23×C3—24no—
330C23×C3—24no—
331C23×C3—24no—
332C23×C3—24no—
333C23×C3—24no—
334C23×C3—24no—
335C23×C3—24no—
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×C3—42no—
361C23×C3—42no—
362C23×C3—42no—
363C23×C3—42no—
364C23×C3C22×D411yescharacteristic
365C23×C3C22×D411yescharacteristic
366C23×C3C22×D411yescharacteristic
367C23×C3C22×D411yescharacteristic
368C23×C3C2×#4112yes—
369C23×C3C2×#4111yescharacteristic
370C23×C3C2×#4111yescharacteristic
371C23×C3C2×#4111yescharacteristic
372C23×C3C2×#4112yes—
373C23×C3H(5,𝔽2)12yes—
374C23×C3H(5,𝔽2)12yes—
375C22×D3—22no—
376C22×D3—22no—
377C22×D3—22no—
378C22×D3—24no—
379C22×D3—22no—
380C22×D3—22no—
381C22×D3—22no—
382C22×D3—24no—
383C22×D3—24no—
384C22×D3—24no—
385C22×D3—24no—
386C22×D3—24no—
387C22×D3—41no—
388C22×D3—42no—
389C22×D3—41no—
390C22×D3—41no—
391C22×D3—41no—
392C22×D3—42no—
393C22×D3—42no—
394C22×D3—42no—
395C22×D3—42no—
396C22×D3—42no—
397C22×D3#12714yes—
398C3×D4—416no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—24no—
405C2×C3×C4—22no—
406C2×C3×C4—24no—
407C2×C3×C4—24no—
408C2×C3×C4—24no—
409C2×C3×C4—24no—
410C2×C3×C4—24no—
411C2×C3×C4—42no—
412C2×C3×C4—42no—
413C2×C3×C4—42no—
414C2×C3×C4—42no—
415C2×C3×C4—42no—
416C2×C3×C4—42no—
417C2×C3×C4—42no—
418C2×C3×C4#12114yes—
419C2×C3×C4#12114yes—
420C2×C3×C4#12114yes—
421#67—432no—
422C2×Dic3—22no—
423C2×Dic3—22no—
424C2×Dic3—22no—
425C2×Dic3—24no—
426C2×Dic3—24no—
427C2×Dic3—24no—
428C2×Dic3—24no—
429C2×Dic3—24no—
430C2×Dic3—24no—
431C2×Dic3—41no—
432C2×Dic3—42no—
433C2×Dic3—41no—
434C2×Dic3—41no—
435C2×Dic3—42no—
436C2×Dic3—41no—
437C2×Dic3—41no—
438C2×Dic3—41no—
439C2×Dic3—42no—
440C2×Dic3—42no—
441C2×Dic3—42no—
442C2×Dic3—42no—
443C2×Dic3—42no—
444C2×Dic3—42no—
445C2×Dic3—42no—
446C2×Dic3—42no—
447C2×Dic3—42no—
448C2×Dic3—42no—
449C2×Dic3—42no—
450C2×Dic3—42no—
451C4×D3—416no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—32no—
467C24—32no—
468C24—32no—
469C24—62no—
470C24—61no—
471C24—61no—
472C24—61no—
473C24—62no—
474C24—62no—
475C24—62no—
476C24—61no—
477C24#23514yes—
478C24C23×D311yescharacteristic
479C2×D4—28no—
480C2×D4—48no—
481C2×D4—48no—
482C2×D4—44no—
483C2×D4—44no—
484C2×D4—616no—
485C2×D4—128no—
486C2×D4—128no—
487C2×D4—128no—
488C2×D4—128no—
489C2×D4—128no—
490C2×D4—128no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—32no—
505C22×C4—32no—
506C22×C4—32no—
507C22×C4—34no—
508C22×C4—62no—
509C22×C4—62no—
510C22×C4—62no—
511C22×C4—62no—
512C22×C4—62no—
513C22×C4—61no—
514C22×C4—61no—
515C22×C4—61no—
516C22×C4—62no—
517C22×C4—62no—
518C22×C4—62no—
519C22×C4—62no—
520C22×C4—62no—
521C22×C4—62no—
522C22×C4—62no—
523C22×C4—61no—
524C22×C4—61no—
525C22×C4—61no—
526C22×C4—68no—
527C22×C4—62no—
528C22×C4—62no—
529C22×C4—62no—
530C22×C4—62no—
531C22×C4—62no—
532C22×C4—62no—
533C22×C4—62no—
534C22×C4—128no—
535C22×C4—124no—
536C22×C4—124no—
537C22×C4—128no—
538C22×C4D3×D412yes—
539C22×C4D3×D412yes—
540C22×C4D3×D412yes—
541C22×C4#23712yes—
542C22×C4#23712yes—
543C22×C4#23712yes—
544C22×C4C2×#6712yes—
545C22×C4C2×#6712yes—
546C22×C4C2×#6712yes—
547C4⋊C4—44no—
548C4⋊C4—128no—
549C22⋊C4—48no—
550C22⋊C4—48no—
551C22⋊C4—68no—
552C22⋊C4—68no—
553C22⋊C4—128no—
554C22⋊C4—128no—
555C22⋊C4—128no—
556C22⋊C4—128no—
557C42—44no—
558C42—124no—
559C22×C3—44no—
560C22×C3—44no—
561C22×C3—44no—
562C22×C3—44no—
563C22×C3—44no—
564C22×C3—44no—
565C22×C3—44no—
566C22×C3—82no—
567C22×C3—82no—
568C22×C3—82no—
569C22×C3—82no—
570C22×C3—82no—
571C22×C3—82no—
572C22×C3—82no—
573C22×C3—82no—
574C22×C3C2×#12111yescharacteristic
575C22×C3C2×#12111yescharacteristic
576C22×C3C2×#12111yescharacteristic
577C22×C3#52511yescharacteristic
578C22×C3#52512yes—
579C22×C3#52912yes—
580C22×C3C2×#12711yescharacteristic
581C22×C3#53211yescharacteristic
582C22×C3#53211yescharacteristic
583C22×C3#53211yescharacteristic
584C22×C3#53211yescharacteristic
585C22×C3#53411yescharacteristic
586C22×C3#53412yes—
587C22×C3#53511yescharacteristic
588C22×C3#53812yes—
589C22×C3#54612yes—
590C22×C3#54612yes—
591C22×C3#54612yes—
592C22×C3#54612yes—
593C22×C3#55112yes—
594C22×C3#55312yes—
595C22×C3#55312yes—
596C22×C3#55912yes—
597C2×D3—24no—
598C2×D3—28no—
599C2×D3—44no—
600C2×D3—42no—
601C2×D3—42no—
602C2×D3—42no—
603C2×D3—42no—
604C2×D3—42no—
605C2×D3—42no—
606C2×D3—44no—
607C2×D3—44no—
608C3×C4—24no—
609C3×C4—24no—
610C3×C4—24no—
611C3×C4—82no—
612Dic3—42no—
613Dic3—42no—
614Dic3—44no—
615Dic3—42no—
616Dic3—82no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—34no—
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—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—64no—
654C23—62no—
655C23—62no—
656C23—62no—
657C23—64no—
658C23—62no—
659C23—62no—
660C23—62no—
661C23—64no—
662C23—64no—
663C23—64no—
664C23—64no—
665C23—122no—
666C23—122no—
667C23—121no—
668C23—122no—
669C23—121no—
670C23—122no—
671C23—121no—
672C23—121no—
673C23—122no—
674C23—122no—
675C23C2×#23512yes—
676C23C2×D3×D411yescharacteristic
677C23C2×D3×D411yescharacteristic
678C23C2×D3×D411yescharacteristic
679C23C2×#23711yescharacteristic
680C23C2×#23711yescharacteristic
681C23C2×#23711yescharacteristic
682C23#100412yes—
683C23D3×#4112yes—
684C23#100912yes—
685C23C22×#6711yescharacteristic
686D4—416no—
687D4—1232no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—64no—
708C2×C4—64no—
709C2×C4—62no—
710C2×C4—62no—
711C2×C4—62no—
712C2×C4—64no—
713C2×C4—64no—
714C2×C4—64no—
715C2×C4—64no—
716C2×C4—1216no—
717C2×C4—122no—
718C2×C4—122no—
719C2×C4—122no—
720C2×C4—121no—
721C2×C4—121no—
722C2×C4—122no—
723C2×C4—122no—
724C2×C4—121no—
725C2×C4—121no—
726C2×C4—121no—
727C2×C4—121no—
728C2×C4—122no—
729C2×C4—122no—
730C2×C4—122no—
731C2×C4—122no—
732C2×C4—122no—
733C2×C4—122no—
734C2×C4—122no—
735C2×C4—122no—
736C2×C4—122no—
737C2×C4#93814yes—
738C2×C4#93814yes—
739C2×C4#93814yes—
740C2×C3—84no—
741C2×C3#239211yescharacteristic
742C2×C3#253411yescharacteristic
743C2×C3#253511yescharacteristic
744C2×C3#253912yes—
745C2×C3#254311yescharacteristic
746C2×C3#254411yescharacteristic
747C2×C3#255712yes—
748C2×C3#255912yes—
749C2×C3#260212yes—
750C2×C3#261711yescharacteristic
751C2×C3#285611yescharacteristic
752D3—44no—
753C22—44no—
754C22—44no—
755C22—44no—
756C22—44no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—68no—
761C22—64no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—122no—
771C22—122no—
772C22—124no—
773C22—124no—
774C22—124no—
775C22—122no—
776C22—122no—
777C22—122no—
778C22—122no—
779C22#549012yes—
780C22#549512yes—
781C22#553812yes—
782C22#554712yes—
783C22#555012yes—
784C22#556512yes—
785C22#560112yes—
786C22#560512yes—
787C22#561012yes—
788C22#561712yes—
789C22#567612yes—
790C22#568112yes—
791C22D3×#12711yescharacteristic
792C22#571611yescharacteristic
793C22#571611yescharacteristic
794C22#571611yescharacteristic
795C22#579111yescharacteristic
796C22C2×#93811yescharacteristic
797C22C2×#93811yescharacteristic
798C22C2×#93811yescharacteristic
799C22#580411yescharacteristic
800C22#583011yescharacteristic
801C22#583211yescharacteristic
802C4—24no—
803C4—24no—
804C4—24no—
805C4—82no—
806C4—122no—
807C4—122no—
808C4—124no—
809C4—122no—
810C4—242no—
811C3#1516011yescharacteristic, complemented, Sylow
812C2—84no—
813C2—124no—
814C2#7635712yes—
815C2#7635912yes—
816C2#7637012yes—
817C2#7645412yes—
818C2#8212911yescharacteristic
819C2#8240111yescharacteristic
820C2#8241511yescharacteristic
821C2#8267111yescharacteristic
822C2#8271011yescharacteristic
823C2#8296911yescharacteristic
824C2#8319211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#390C2
prime radicalC2×#5223C2
hypercenterC2×#390D3
hypocenterC3#15160
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C2×C3×#390C2semidirect
3. C2×#4992C2semidirect
4. C2×#4956C2semidirect
5. C2×#4961C2semidirect
6. C2×C4×(C2×D3)⋊C4C2semidirect
7. #72131C2semidirect
8. #71569C2semidirect
9. #71546C2semidirect
10. #71545C2semidirect
11. #71535C2semidirect
45. C2×#390D3semidirect
80. C22×C4×D3D4semidirect
91. C2×C3×C42D4semidirect
109. C2×(C2×D3)⋊C4D4semidirect
320. C2×C42#67semidirect
811. C3#15160semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3902
C2×#52232
C2×#49922
C2×#49562
C2×#49612
C2×C4×(C2×D3)⋊C42
#721312
#715692
#715462
#715452
#715352
#151603