Finite Group Databasebeta

← #10732580

Subgroups — #10732580

Order 768.

1686 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#389C211yesmaximal, characteristic, complemented
2C2×#4987C211yesmaximal, characteristic
3C2×#4987C211yesmaximal, characteristic
4C2×#4977C211yesmaximal, characteristic, complemented
5C2×#4928C211yesmaximal, characteristic, complemented
6C2×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
7#71570C212yesmaximal
8#71569C212yesmaximal, complemented
9#71563C211yesmaximal, characteristic, complemented
10#69428C212yesmaximal
11#69421C212yesmaximal, complemented
12#15223—31nomaximal, Sylow
13C23×C4×D3C2211yescharacteristic
14C22×C3×C4⋊C4C2211yescharacteristic
15C22×C3×C4⋊C4C2212yes—
16C22×C3×C4⋊C4C2211yescharacteristic
17C22×C3×C42C2211yescharacteristic
18C22×(C2×D3)⋊C4C2211yescharacteristic
19C22×(C2×D3)⋊C4C2211yescharacteristic
20C22×(C2×D3)⋊C4C2212yes—
21C22×(C2×D3)⋊C4C2212yes—
22C22×C4⋊Dic3C2211yescharacteristic
23C22×C4⋊Dic3C2211yescharacteristic
24C22×Dic3⋊C4C2212yes—
25C22×C4×Dic3C2211yescharacteristic
26C3×#389—24no—
27C2×C3×#95C2212yes—
28C2×C3⋊#95C2212yes—
29C2×C3⋊#95C2212yes—
30C2×C3⋊#95C2211yescharacteristic
31C2×C3⋊#95C2212yes—
32C2×C3⋊#95C2212yes—
33C2×C3⋊#95C2211yescharacteristic
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2212yes—
37#4987—24no—
38#4987—24no—
39#4977—24no—
40C4×(C2×D3)⋊C4—24no—
41#4928—24no—
42C2×#389—31no—
43C2×#389D311yescharacteristic, complemented
44C2×#382—31no—
45C2×#380—31no—
46C2×#380—31no—
47C2×C4×C22⋊C4—31no—
48#1445—32no—
49#1445—32no—
50#1439—32no—
51#1439—32no—
52C4⋊#95—31no—
53C24×D3C2311yescharacteristic
54C23×C3×C4C2312yes—
55C23×C3×C4C2312yes—
56C23×C3×C4C2311yescharacteristic
57C23×C3×C4C2311yescharacteristic
58C23×C3×C4C2311yescharacteristic
59C23×Dic3C2312yes—
60C23×Dic3C2311yescharacteristic
61C23×Dic3C2311yescharacteristic
62C23×Dic3C2312yes—
63C23×Dic3C2311yescharacteristic
64C22×C4×D3—22no—
65C22×C4×D3—22no—
66C22×C4×D3—22no—
67C22×C4×D3—22no—
68C22×C4×D3—22no—
69C22×C4×D3—22no—
70C22×C4×D3Q814yes—
71C2×C3×C4⋊C4—22no—
72C2×C3×C4⋊C4—22no—
73C2×C3×C4⋊C4—22no—
74C2×C3×C4⋊C4—22no—
75C2×C3×C4⋊C4—24no—
76C2×C3×C4⋊C4—22no—
77C2×C3×C4⋊C4—24no—
78C2×C3×C4⋊C4—42no—
79C2×C3×C4⋊C4D414yes—
80C2×C3×C42—22no—
81C2×C3×C42—22no—
82C2×C3×C42—22no—
83C2×(C2×D3)⋊C4—22no—
84C2×(C2×D3)⋊C4—22no—
85C2×(C2×D3)⋊C4—22no—
86C2×(C2×D3)⋊C4—22no—
87C2×(C2×D3)⋊C4—22no—
88C2×(C2×D3)⋊C4—22no—
89C2×(C2×D3)⋊C4—24no—
90C2×(C2×D3)⋊C4—24no—
91C2×(C2×D3)⋊C4—24no—
92C2×(C2×D3)⋊C4—24no—
93C2×(C2×D3)⋊C4—42no—
94C2×(C2×D3)⋊C4—42no—
95C2×C4⋊Dic3—22no—
96C2×C4⋊Dic3—22no—
97C2×C4⋊Dic3—22no—
98C2×C4⋊Dic3—22no—
99C2×C4⋊Dic3—22no—
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×Dic3D414yes—
107C3×#95—24no—
108C3⋊#95—24no—
109C3⋊#95—24no—
110C3⋊#95—22no—
111C3⋊#95—22no—
112C3⋊#95—24no—
113C3⋊#95—24no—
114C3⋊#95—24no—
115C3⋊#95—42no—
116C3⋊#95—42no—
117C24×C4—31no—
118C22×C4⋊C4—31no—
119C22×C4⋊C4—31no—
120C22×C4⋊C4—32no—
121C22×C4⋊C4C2×D311yescharacteristic
122C22×C4⋊C4C2×D312yes—
123C22×C4⋊C4C2×D311yescharacteristic
124C22×C22⋊C4—31no—
125C22×C22⋊C4—31no—
126C22×C22⋊C4—32no—
127C22×C22⋊C4—32no—
128C22×C42—31no—
129C22×C42C2×D311yescharacteristic
130#389—24no—
131#389—64no—
132#382—64no—
133#380—64no—
134#380—64no—
135C4×C22⋊C4—64no—
136C2×#95—32no—
137C2×#95—32no—
138C2×#95—32no—
139C2×#95—31no—
140C2×#95—31no—
141C2×#95—32no—
142C2×#95—32no—
143C2×#95—32no—
144C2×#95—32no—
145C2×#95C2×D312yes—
146C24×C3C2411yescharacteristic
147C23×D3—21no—
148C23×D3—21no—
149C23×D3—21no—
150C23×D3—21no—
151C23×D3—21no—
152C23×D3—21no—
153C23×D3—21no—
154C23×D3—21no—
155C23×D3—21no—
156C23×D3—21no—
157C23×D3—21no—
158C23×D3—21no—
159C23×D3C2×Q812yes—
160C23×D3#4112yes—
161C23×D3#4112yes—
162C22×C3×C4—21no—
163C22×C3×C4—21no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—21no—
167C22×C3×C4—21no—
168C22×C3×C4—21no—
169C22×C3×C4—21no—
170C22×C3×C4—22no—
171C22×C3×C4—22no—
172C22×C3×C4—22no—
173C22×C3×C4—22no—
174C22×C3×C4—22no—
175C22×C3×C4—22no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—22no—
181C22×C3×C4—22no—
182C22×C3×C4—22no—
183C22×C3×C4—22no—
184C22×C3×C4—22no—
185C22×C3×C4—22no—
186C22×C3×C4—22no—
187C22×C3×C4C2×D412yes—
188C22×C3×C4C2×D412yes—
189C22×C3×C4C2×D414yes—
190C22×C3×C4C2×D412yes—
191C22×C3×C4C2×Q812yes—
192C22×C3×C4#4112yes—
193C22×C3×C4#4112yes—
194C22×C3×C4#4112yes—
195C22×C3×C4#4112yes—
196C22×C3×C4#4112yes—
197C22×Dic3—21no—
198C22×Dic3—21no—
199C22×Dic3—21no—
200C22×Dic3—21no—
201C22×Dic3—21no—
202C22×Dic3—21no—
203C22×Dic3—21no—
204C22×Dic3—22no—
205C22×Dic3—22no—
206C22×Dic3—22no—
207C22×Dic3—21no—
208C22×Dic3—21no—
209C22×Dic3—21no—
210C22×Dic3—21no—
211C22×Dic3—22no—
212C22×Dic3—21no—
213C22×Dic3—21no—
214C22×Dic3—21no—
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—22no—
224C22×Dic3—22no—
225C22×Dic3—22no—
226C22×Dic3—22no—
227C22×Dic3—22no—
228C22×Dic3C2×D412yes—
229C22×Dic3C2×D412yes—
230C22×Dic3C2×D414yes—
231C22×Dic3C2×Q812yes—
232C2×C4×D3—28no—
233C2×C4×D3—28no—
234C2×C4×D3—28no—
235C2×C4×D3—44no—
236C2×C4×D3—44no—
237C2×C4×D3—44no—
238C2×C4×D3—44no—
239C3×C4⋊C4—28no—
240C3×C4⋊C4—48no—
241C3×C4⋊C4—44no—
242C3×C42—44no—
243(C2×D3)⋊C4—28no—
244(C2×D3)⋊C4—28no—
245(C2×D3)⋊C4—48no—
246(C2×D3)⋊C4—48no—
247C4⋊Dic3—28no—
248C4⋊Dic3—44no—
249Dic3⋊C4—48no—
250C4×Dic3—28no—
251C25—31no—
252C23×C4—32no—
253C23×C4—31no—
254C23×C4—31no—
255C23×C4—31no—
256C23×C4—34no—
257C23×C4—32no—
258C23×C4—62no—
259C23×C4—62no—
260C23×C4—62no—
261C23×C4—62no—
262C23×C4—62no—
263C23×C4—62no—
264C23×C4C22×D312yes—
265C23×C4C22×D311yescharacteristic
266C23×C4C22×D311yescharacteristic
267C23×C4C22×D312yes—
268C23×C4C22×D311yescharacteristic
269C2×C4⋊C4—22no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—34no—
277C2×C4⋊C4—42no—
278C2×C4⋊C4—62no—
279C2×C4⋊C4—62no—
280C2×C4⋊C4—64no—
281C2×C4⋊C4—62no—
282C2×C4⋊C4—62no—
283C2×C4⋊C4—64no—
284C2×C4⋊C4—62no—
285C2×C4⋊C4—122no—
286C2×C4⋊C4#6714yes—
287C2×C22⋊C4—62no—
288C2×C22⋊C4—62no—
289C2×C22⋊C4—62no—
290C2×C22⋊C4—62no—
291C2×C22⋊C4—62no—
292C2×C22⋊C4—62no—
293C2×C22⋊C4—64no—
294C2×C22⋊C4—64no—
295C2×C22⋊C4—64no—
296C2×C22⋊C4—64no—
297C2×C22⋊C4—122no—
298C2×C22⋊C4—122no—
299C2×C42—22no—
300C2×C42—22no—
301C2×C42—22no—
302C2×C42—34no—
303C2×C42—62no—
304C2×C42—62no—
305#95—24no—
306#95—62no—
307#95—62no—
308#95—64no—
309#95—64no—
310#95—64no—
311#95—64no—
312#95—64no—
313#95—122no—
314#95—122no—
315C23×C3C22×D411yescharacteristic
316C23×C3C22×D411yescharacteristic
317C23×C3C22×D411yescharacteristic
318C23×C3C22×Q811yescharacteristic
319C23×C3C2×#4111yescharacteristic
320C23×C3C2×#4111yescharacteristic
321C23×C3C2×#4111yescharacteristic
322C23×C3C2×#4111yescharacteristic
323C23×C3C2×#4111yescharacteristic
324C23×C3C2×#4111yescharacteristic
325C23×C3C2×#4111yescharacteristic
326C23×C3H(5,𝔽2)11yescharacteristic
327C23×C3H(5,𝔽2)11yescharacteristic
328C23×C32−1+411yescharacteristic
329C23×C32−1+411yescharacteristic
330C22×D3—22no—
331C22×D3—22no—
332C22×D3—22no—
333C22×D3—22no—
334C22×D3—22no—
335C22×D3—22no—
336C22×D3—22no—
337C22×D3—22no—
338C22×D3—22no—
339C22×D3—22no—
340C22×D3—22no—
341C22×D3—22no—
342C22×D3—22no—
343C22×D3—22no—
344C22×D3—22no—
345C22×D3—22no—
346C22×D3—22no—
347C22×D3—22no—
348C22×D3—41no—
349C22×D3—41no—
350C22×D3—41no—
351C22×D3—41no—
352C22×D3—41no—
353C22×D3—41no—
354C22×D3—41no—
355C22×D3—41no—
356C22×D3—41no—
357C22×D3—41no—
358C22×D3—41no—
359C22×D3—41no—
360C22×D3—41no—
361C22×D3—41no—
362C22×D3—41no—
363C22×D3—41no—
364C22×D3#12514yes—
365C2×C3×C4—24no—
366C2×C3×C4—22no—
367C2×C3×C4—22no—
368C2×C3×C4—22no—
369C2×C3×C4—24no—
370C2×C3×C4—22no—
371C2×C3×C4—24no—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4—42no—
375C2×C3×C4—41no—
376C2×C3×C4—41no—
377C2×C3×C4—41no—
378C2×C3×C4—41no—
379C2×C3×C4—42no—
380C2×C3×C4—41no—
381C2×C3×C4—41no—
382C2×C3×C4—41no—
383C2×C3×C4—41no—
384C2×C3×C4—42no—
385C2×C3×C4—42no—
386C2×C3×C4—42no—
387C2×C3×C4—42no—
388C2×C3×C4—42no—
389C2×C3×C4—42no—
390C2×C3×C4—42no—
391C2×C3×C4—42no—
392C2×C3×C4—42no—
393C2×C3×C4C22⋊Q814yes—
394C2×C3×C4C22⋊Q814yes—
395C2×C3×C4C22⋊Q814yes—
396C2×C3×C4#12314yes—
397C2×C3×C4#12314yes—
398C2×C3×C4#12314yes—
399C2×C3×C4#12714yes—
400C2×Dic3—22no—
401C2×Dic3—22no—
402C2×Dic3—22no—
403C2×Dic3—22no—
404C2×Dic3—22no—
405C2×Dic3—24no—
406C2×Dic3—22no—
407C2×Dic3—22no—
408C2×Dic3—22no—
409C2×Dic3—22no—
410C2×Dic3—24no—
411C2×Dic3—24no—
412C2×Dic3—41no—
413C2×Dic3—41no—
414C2×Dic3—41no—
415C2×Dic3—42no—
416C2×Dic3—41no—
417C2×Dic3—42no—
418C2×Dic3—41no—
419C2×Dic3—41no—
420C2×Dic3—42no—
421C2×Dic3—41no—
422C2×Dic3—41no—
423C2×Dic3—42no—
424C2×Dic3—41no—
425C2×Dic3—41no—
426C2×Dic3—41no—
427C2×Dic3—41no—
428C2×Dic3—42no—
429C2×Dic3—42no—
430C2×Dic3—42no—
431C2×Dic3—42no—
432C2×Dic3—42no—
433C2×Dic3—42no—
434C2×Dic3—42no—
435C4×D3—416no—
436C24—32no—
437C24—32no—
438C24—32no—
439C24—61no—
440C24—61no—
441C24—61no—
442C24—61no—
443C24—61no—
444C24—61no—
445C24—61no—
446C24—61no—
447C24—61no—
448C24—61no—
449C24—61no—
450C24—61no—
451C24C23×D311yescharacteristic
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—32no—
478C22×C4—32no—
479C22×C4—34no—
480C22×C4—32no—
481C22×C4—61no—
482C22×C4—61no—
483C22×C4—62no—
484C22×C4—61no—
485C22×C4—61no—
486C22×C4—61no—
487C22×C4—61no—
488C22×C4—61no—
489C22×C4—61no—
490C22×C4—62no—
491C22×C4—61no—
492C22×C4—61no—
493C22×C4—61no—
494C22×C4—62no—
495C22×C4—62no—
496C22×C4—61no—
497C22×C4—61no—
498C22×C4—61no—
499C22×C4—62no—
500C22×C4—61no—
501C22×C4—61no—
502C22×C4—62no—
503C22×C4—61no—
504C22×C4—61no—
505C22×C4—68no—
506C22×C4—68no—
507C22×C4—68no—
508C22×C4—62no—
509C22×C4—62no—
510C22×C4—62no—
511C22×C4—62no—
512C22×C4—62no—
513C22×C4—62no—
514C22×C4—62no—
515C22×C4—124no—
516C22×C4—124no—
517C22×C4—124no—
518C22×C4—124no—
519C22×C4#23512yes—
520C22×C4#23512yes—
521C22×C4D3×D412yes—
522C22×C4D3×D412yes—
523C22×C4#23712yes—
524C22×C4D3×Q812yes—
525C22×C4#23912yes—
526C22×C4#23912yes—
527C22×C4C2×#6714yes—
528C22×C4C2×#6712yes—
529C4⋊C4—28no—
530C4⋊C4—48no—
531C4⋊C4—44no—
532C4⋊C4—68no—
533C4⋊C4—128no—
534C4⋊C4—124no—
535C22⋊C4—68no—
536C22⋊C4—68no—
537C22⋊C4—128no—
538C22⋊C4—128no—
539C42—44no—
540C42—68no—
541C22×C3C2×C22⋊Q811yescharacteristic
542C22×C3C2×C22⋊Q811yescharacteristic
543C22×C3C2×C22⋊Q811yescharacteristic
544C22×C3C2×#12311yescharacteristic
545C22×C3C2×#12311yescharacteristic
546C22×C3C2×#12311yescharacteristic
547C22×C3#52511yescharacteristic
548C22×C3#52511yescharacteristic
549C22×C3C2×#12511yescharacteristic
550C22×C3#52911yescharacteristic
551C22×C3#52911yescharacteristic
552C22×C3C2×#12711yescharacteristic
553C22×C3#53311yescharacteristic
554C22×C3#53711yescharacteristic
555C22×C3#53711yescharacteristic
556C22×C3#54011yescharacteristic
557C22×C3#54111yescharacteristic
558C22×C3#54411yescharacteristic
559C22×C3#54411yescharacteristic
560C22×C3#54611yescharacteristic
561C22×C3#54611yescharacteristic
562C22×C3#54611yescharacteristic
563C22×C3#54611yescharacteristic
564C22×C3#54811yescharacteristic
565C22×C3#54811yescharacteristic
566C22×C3#54811yescharacteristic
567C22×C3#54811yescharacteristic
568C22×C3#55211yescharacteristic
569C22×C3#55211yescharacteristic
570C22×C3#55311yescharacteristic
571C22×C3#55311yescharacteristic
572C22×C3#55511yescharacteristic
573C22×C3#55511yescharacteristic
574C22×C3#55611yescharacteristic
575C22×C3#55611yescharacteristic
576C2×D3—24no—
577C2×D3—24no—
578C2×D3—24no—
579C2×D3—42no—
580C2×D3—42no—
581C2×D3—42no—
582C2×D3—42no—
583C2×D3—42no—
584C2×D3—42no—
585C2×D3—42no—
586C2×D3—42no—
587C2×D3—42no—
588C2×D3—42no—
589C2×D3—42no—
590C2×D3—42no—
591C3×C4—44no—
592C3×C4—42no—
593C3×C4—42no—
594C3×C4—82no—
595C3×C4#39918yes—
596Dic3—42no—
597Dic3—44no—
598Dic3—42no—
599Dic3—42no—
600Dic3—82no—
601C23—34no—
602C23—62no—
603C23—62no—
604C23—62no—
605C23—62no—
606C23—62no—
607C23—62no—
608C23—62no—
609C23—62no—
610C23—62no—
611C23—62no—
612C23—62no—
613C23—62no—
614C23—62no—
615C23—62no—
616C23—62no—
617C23—62no—
618C23—62no—
619C23—62no—
620C23—121no—
621C23—121no—
622C23—121no—
623C23—121no—
624C23—121no—
625C23—121no—
626C23—121no—
627C23—121no—
628C23—121no—
629C23—121no—
630C23—121no—
631C23—121no—
632C23—121no—
633C23—121no—
634C23—121no—
635C23—121no—
636C23C2×#23511yescharacteristic
637C23C2×#23511yescharacteristic
638C23C2×D3×D411yescharacteristic
639C23C2×D3×D411yescharacteristic
640C23C2×#23711yescharacteristic
641C23#100411yescharacteristic
642C23C2×D3×Q811yescharacteristic
643C23C2×#23911yescharacteristic
644C23C2×#23911yescharacteristic
645C23#100711yescharacteristic
646C23D3×#4111yescharacteristic
647C23D3×#4111yescharacteristic
648C23#100911yescharacteristic
649C23#101011yescharacteristic
650C23C22×#6711yescharacteristic
651C2×C4—24no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—62no—
680C2×C4—62no—
681C2×C4—64no—
682C2×C4—62no—
683C2×C4—62no—
684C2×C4—62no—
685C2×C4—62no—
686C2×C4—62no—
687C2×C4—64no—
688C2×C4—62no—
689C2×C4—62no—
690C2×C4—64no—
691C2×C4—121no—
692C2×C4—122no—
693C2×C4—121no—
694C2×C4—121no—
695C2×C4—122no—
696C2×C4—121no—
697C2×C4—121no—
698C2×C4—121no—
699C2×C4—121no—
700C2×C4—121no—
701C2×C4—121no—
702C2×C4—122no—
703C2×C4—121no—
704C2×C4—122no—
705C2×C4—121no—
706C2×C4—121no—
707C2×C4—1216no—
708C2×C4—122no—
709C2×C4—122no—
710C2×C4—122no—
711C2×C4—122no—
712C2×C4—122no—
713C2×C4—122no—
714C2×C4—122no—
715C2×C4#89414yes—
716C2×C4#89414yes—
717C2×C4#89614yes—
718C2×C4#89614yes—
719C2×C4#92914yes—
720C2×C4#94014yes—
721C2×C4#94614yes—
722C2×C3C2×#39911yescharacteristic
723C2×C3#242011yescharacteristic
724C2×C3#242011yescharacteristic
725C2×C3#242111yescharacteristic
726C2×C3#242111yescharacteristic
727C2×C3#243911yescharacteristic
728C2×C3#243911yescharacteristic
729C2×C3#244211yescharacteristic
730C2×C3#244211yescharacteristic
731C2×C3#248511yescharacteristic
732C2×C3#248511yescharacteristic
733C2×C3#254011yescharacteristic
734C2×C3#254011yescharacteristic
735C2×C3#262911yescharacteristic
736C2×C3#285111yescharacteristic
737D3—44no—
738C22—64no—
739C22—64no—
740C22—64no—
741C22—122no—
742C22—122no—
743C22—122no—
744C22—122no—
745C22—122no—
746C22—122no—
747C22—122no—
748C22—122no—
749C22—122no—
750C22—122no—
751C22—122no—
752C22—122no—
753C22C2×#89411yescharacteristic
754C22C2×#89411yescharacteristic
755C22C2×#89611yescharacteristic
756C22C2×#89611yescharacteristic
757C22#555711yescharacteristic
758C22#555811yescharacteristic
759C22#556211yescharacteristic
760C22#556311yescharacteristic
761C22#558011yescharacteristic
762C22#558111yescharacteristic
763C22#558311yescharacteristic
764C22#558411yescharacteristic
765C22#559811yescharacteristic
766C22#560611yescharacteristic
767C22#560811yescharacteristic
768C22#561211yescharacteristic
769C22#562711yescharacteristic
770C22#562911yescharacteristic
771C22#563011yescharacteristic
772C22#563311yescharacteristic
773C22D3×#12511yescharacteristic
774C22#568911yescharacteristic
775C22#569411yescharacteristic
776C22#569511yescharacteristic
777C22#572811yescharacteristic
778C22#572911yescharacteristic
779C22#573211yescharacteristic
780C22#573411yescharacteristic
781C22C2×#92911yescharacteristic
782C22C2×#94011yescharacteristic
783C22#580611yescharacteristic
784C22C2×#94611yescharacteristic
785C22#581711yescharacteristic
786C22#582911yescharacteristic
787C22#583111yescharacteristic
788C4—42no—
789C4—44no—
790C4—42no—
791C4—82no—
792C4—122no—
793C4—124no—
794C4—122no—
795C4—122no—
796C4—242no—
797C4#499318yes—
798C3#1522311yescharacteristic, complemented, Sylow
799C2—124no—
800C2#7600211yescharacteristic
801C2#7621311yescharacteristic
802C2#7621411yescharacteristic
803C2#7622311yescharacteristic
804C2#7622911yescharacteristic
805C2#7623011yescharacteristic
806C2#7625111yescharacteristic
807C2#7628511yescharacteristic
808C2C2×#499311yescharacteristic
809C2#8240511yescharacteristic
810C2#8249311yescharacteristic
811C2#8266811yescharacteristic
812C2#8277911yescharacteristic
813C2#8302811yescharacteristic
814C2#8325611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#389C2
prime radicalC24×D3C23
hypercenterC2×#389D3
hypocenterC3#15223
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C2×C3×#389C2semidirect
4. C2×#4977C2semidirect
5. C2×#4928C2semidirect
8. #71569C2semidirect
9. #71563C2semidirect
11. #69421C2semidirect
43. C2×#389D3semidirect
798. C3#15223semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3892
C2×#49872
C2×#49772
C2×#49282
C2×C4×(C2×D3)⋊C42
#715702
#715692
#715632
#694282
#694212
#152233