Finite Group Databasebeta

← #10732582

Subgroups — #10732582

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×#380C211yesmaximal, characteristic
2C2×#5212C211yesmaximal, characteristic
3C2×C4×#217C211yesmaximal, characteristic
4C2×#4984C211yesmaximal, characteristic, complemented
5C2×#4972C211yesmaximal, characteristic, complemented
6C2×#4977C211yesmaximal, characteristic, complemented
7#71563C211yesmaximal, characteristic, complemented
8#71547C212yesmaximal
9#71546C212yesmaximal
10#69423C212yesmaximal, complemented
11#69421C212yesmaximal, complemented
12#15223—31nomaximal, Sylow
13C24×C3×C4C2211yescharacteristic
14C22×C3×C4⋊C4C2211yescharacteristic
15C22×C3×C4⋊C4C2211yescharacteristic
16C22×C3×C22⋊C4C2212yes—
17C22×#217C2211yescharacteristic
18C22×#217C2211yescharacteristic
19C22×#217C2212yes—
20C22×C4⋊Dic3C2211yescharacteristic
21C22×C4⋊Dic3C2212yes—
22C22×C4⋊Dic3C2211yescharacteristic
23C22×Dic3⋊C4C2212yes—
24C22×C4×Dic3C2211yescharacteristic
25C22×C4×Dic3C2211yescharacteristic
26C3×#380—24no—
27C2×C3×#95C2212yes—
28#5212—24no—
29C4×#217—24no—
30C2×C3⋊#95C2211yescharacteristic
31C2×C3⋊#95C2212yes—
32C2×C3⋊#95C2212yes—
33C2×C3⋊#95C2212yes—
34C2×C3⋊#95C2211yescharacteristic
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39#4984—24no—
40#4977—24no—
41#4972—24no—
42C2×#389—31no—
43C2×#389—31no—
44C2×#382—31no—
45C2×#380—31no—
46C2×#380D311yescharacteristic
47C2×C4×C22⋊C4—31no—
48#1445—32no—
49#1445—32no—
50#1439—32no—
51#1439—32no—
52C4⋊#95—31no—
53C25×C3C2311yescharacteristic
54C23×C3×C4—22no—
55C23×C3×C4—22no—
56C23×C3×C4—22no—
57C23×C3×C4—22no—
58C23×C3×C4—22no—
59C23×C3×C4—22no—
60C23×C3×C4Q814yes—
61C23×C3×C4C2312yes—
62C23×C3×C4C2312yes—
63C23×C3×C4C2311yescharacteristic
64C23×C3×C4C2311yescharacteristic
65C23×Dic3C2312yes—
66C23×Dic3C2311yescharacteristic
67C23×Dic3C2311yescharacteristic
68C23×Dic3C2312yes—
69C23×Dic3C2311yescharacteristic
70C23×Dic3C2311yescharacteristic
71C2×C3×C4⋊C4—22no—
72C2×C3×C4⋊C4—22no—
73C2×C3×C4⋊C4—22no—
74C2×C3×C4⋊C4—22no—
75C2×C3×C4⋊C4—22no—
76C2×C3×C4⋊C4D414yes—
77C2×C3×C22⋊C4—24no—
78C2×C3×C22⋊C4—24no—
79C2×C3×C22⋊C4—42no—
80C2×#217—22no—
81C2×#217—22no—
82C2×#217—22no—
83C2×#217—22no—
84C2×#217—22no—
85C2×#217—22no—
86C2×#217—24no—
87C2×#217—24no—
88C2×#217—42no—
89C2×C4⋊Dic3—22no—
90C2×C4⋊Dic3—22no—
91C2×C4⋊Dic3—22no—
92C2×C4⋊Dic3—22no—
93C2×C4⋊Dic3—24no—
94C2×C4⋊Dic3—22no—
95C2×C4⋊Dic3—24no—
96C2×C4⋊Dic3—42no—
97C2×C4⋊Dic3D414yes—
98C2×Dic3⋊C4—24no—
99C2×Dic3⋊C4—24no—
100C2×Dic3⋊C4—42no—
101C2×C4×Dic3—22no—
102C2×C4×Dic3—22no—
103C2×C4×Dic3—22no—
104C2×C4×Dic3—22no—
105C2×C4×Dic3—22no—
106C2×C4×Dic3D414yes—
107C3×#95—24no—
108C3⋊#95—24no—
109C3⋊#95—22no—
110C3⋊#95—22no—
111C3⋊#95—24no—
112C3⋊#95—24no—
113C3⋊#95—24no—
114C3⋊#95—24no—
115C3⋊#95—42no—
116C3⋊#95—42no—
117C24×C4C2×D311yescharacteristic
118C22×C4⋊C4—31no—
119C22×C4⋊C4—31no—
120C22×C4⋊C4—32no—
121C22×C4⋊C4—32no—
122C22×C4⋊C4C2×D311yescharacteristic
123C22×C4⋊C4C2×D311yescharacteristic
124C22×C22⋊C4—31no—
125C22×C22⋊C4—31no—
126C22×C22⋊C4—32no—
127C22×C22⋊C4C2×D312yes—
128C22×C42—31no—
129C22×C42—31no—
130#389—64no—
131#389—64no—
132#382—64no—
133#380—24no—
134#380—64no—
135C4×C22⋊C4—64no—
136C2×#95—32no—
137C2×#95—32no—
138C2×#95—32no—
139C2×#95—32no—
140C2×#95—31no—
141C2×#95—31no—
142C2×#95—32no—
143C2×#95—32no—
144C2×#95—32no—
145C2×#95C2×D312yes—
146C24×C3—21no—
147C24×C3—21no—
148C24×C3—21no—
149C24×C3—21no—
150C24×C3—21no—
151C24×C3—21no—
152C24×C3—21no—
153C24×C3—21no—
154C24×C3—21no—
155C24×C3—21no—
156C24×C3—21no—
157C24×C3—21no—
158C24×C3C2×Q812yes—
159C24×C3#4112yes—
160C24×C3#4112yes—
161C24×C3C2411yescharacteristic
162C22×C3×C4—21no—
163C22×C3×C4—21no—
164C22×C3×C4—21no—
165C22×C3×C4—22no—
166C22×C3×C4—22no—
167C22×C3×C4—22no—
168C22×C3×C4—22no—
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4—21no—
172C22×C3×C4—22no—
173C22×C3×C4—22no—
174C22×C3×C4—28no—
175C22×C3×C4—28no—
176C22×C3×C4—28no—
177C22×C3×C4—22no—
178C22×C3×C4—22no—
179C22×C3×C4—22no—
180C22×C3×C4—22no—
181C22×C3×C4—22no—
182C22×C3×C4—22no—
183C22×C3×C4—22no—
184C22×C3×C4—44no—
185C22×C3×C4—44no—
186C22×C3×C4—44no—
187C22×C3×C4—44no—
188C22×C3×C4C2×D412yes—
189C22×C3×C4C2×D412yes—
190C22×C3×C4C2×D414yes—
191C22×C3×C4C2×D412yes—
192C22×C3×C4C2×Q812yes—
193C22×C3×C4C2×Q812yes—
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—21no—
205C22×Dic3—21no—
206C22×Dic3—21no—
207C22×Dic3—22no—
208C22×Dic3—22no—
209C22×Dic3—22no—
210C22×Dic3—21no—
211C22×Dic3—21no—
212C22×Dic3—21no—
213C22×Dic3—21no—
214C22×Dic3—22no—
215C22×Dic3—21no—
216C22×Dic3—21no—
217C22×Dic3—21no—
218C22×Dic3—21no—
219C22×Dic3—22no—
220C22×Dic3—22no—
221C22×Dic3—21no—
222C22×Dic3—21no—
223C22×Dic3—21no—
224C22×Dic3—21no—
225C22×Dic3—21no—
226C22×Dic3—21no—
227C22×Dic3—22no—
228C22×Dic3—22no—
229C22×Dic3—22no—
230C22×Dic3—22no—
231C22×Dic3—22no—
232C22×Dic3—22no—
233C22×Dic3—22no—
234C22×Dic3C2×D412yes—
235C22×Dic3C2×D412yes—
236C22×Dic3C2×D414yes—
237C22×Dic3#4112yes—
238C22×Dic3#4112yes—
239C3×C4⋊C4—28no—
240C3×C4⋊C4—44no—
241C3×C22⋊C4—48no—
242#217—28no—
243#217—28no—
244#217—48no—
245C4⋊Dic3—28no—
246C4⋊Dic3—48no—
247C4⋊Dic3—44no—
248Dic3⋊C4—48no—
249C4×Dic3—28no—
250C4×Dic3—44no—
251C25C22×D311yescharacteristic
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—32no—
259C23×C4—31no—
260C23×C4—31no—
261C23×C4—31no—
262C23×C4—31no—
263C23×C4—32no—
264C23×C4Dic614yes—
265C23×C4C22×D312yes—
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—22no—
274C2×C4⋊C4—34no—
275C2×C4⋊C4—62no—
276C2×C4⋊C4—62no—
277C2×C4⋊C4—64no—
278C2×C4⋊C4—64no—
279C2×C4⋊C4—64no—
280C2×C4⋊C4—62no—
281C2×C4⋊C4—62no—
282C2×C4⋊C4—64no—
283C2×C4⋊C4—62no—
284C2×C4⋊C4—122no—
285C2×C4⋊C4—122no—
286C2×C4⋊C4#6714yes—
287C2×C22⋊C4—24no—
288C2×C22⋊C4—24no—
289C2×C22⋊C4—42no—
290C2×C22⋊C4—62no—
291C2×C22⋊C4—62no—
292C2×C22⋊C4—62no—
293C2×C22⋊C4—62no—
294C2×C22⋊C4—62no—
295C2×C22⋊C4—62no—
296C2×C22⋊C4—64no—
297C2×C22⋊C4—64no—
298C2×C22⋊C4—122no—
299C2×C42—34no—
300C2×C42—62no—
301C2×C42—62no—
302C2×C42—62no—
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×C3—22no—
316C23×C3—22no—
317C23×C3—22no—
318C23×C3—22no—
319C23×C3—22no—
320C23×C3—22no—
321C23×C3—22no—
322C23×C3—22no—
323C23×C3—22no—
324C23×C3—22no—
325C23×C3—22no—
326C23×C3—22no—
327C23×C3—22no—
328C23×C3—22no—
329C23×C3—22no—
330C23×C3—22no—
331C23×C3—22no—
332C23×C3—22no—
333C23×C3—41no—
334C23×C3—41no—
335C23×C3—41no—
336C23×C3—41no—
337C23×C3—41no—
338C23×C3—41no—
339C23×C3—41no—
340C23×C3—41no—
341C23×C3—41no—
342C23×C3—41no—
343C23×C3—41no—
344C23×C3—41no—
345C23×C3—41no—
346C23×C3—41no—
347C23×C3—41no—
348C23×C3—41no—
349C23×C3#12514yes—
350C23×C3C22×D411yescharacteristic
351C23×C3C22×D411yescharacteristic
352C23×C3C22×D411yescharacteristic
353C23×C3C22×Q811yescharacteristic
354C23×C3C2×#4111yescharacteristic
355C23×C3C2×#4111yescharacteristic
356C23×C3C2×#4111yescharacteristic
357C23×C3C2×#4111yescharacteristic
358C23×C3C2×#4111yescharacteristic
359C23×C3C2×#4111yescharacteristic
360C23×C3C2×#4111yescharacteristic
361C23×C3H(5,𝔽2)11yescharacteristic
362C23×C3H(5,𝔽2)11yescharacteristic
363C23×C32−1+411yescharacteristic
364C23×C32−1+411yescharacteristic
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—22no—
368C2×C3×C4—24no—
369C2×C3×C4—24no—
370C2×C3×C4—24no—
371C2×C3×C4—41no—
372C2×C3×C4—41no—
373C2×C3×C4—41no—
374C2×C3×C4—42no—
375C2×C3×C4—41no—
376C2×C3×C4—42no—
377C2×C3×C4—42no—
378C2×C3×C4—42no—
379C2×C3×C4—416no—
380C2×C3×C4—42no—
381C2×C3×C4—42no—
382C2×C3×C4—42no—
383C2×C3×C4—42no—
384C2×C3×C4—42no—
385C2×C3×C4—42no—
386C2×C3×C4—42no—
387C2×C3×C4C22⋊Q814yes—
388C2×C3×C4C22⋊Q814yes—
389C2×C3×C4C22⋊Q814yes—
390C2×C3×C4#12314yes—
391C2×C3×C4#12314yes—
392C2×C3×C4#12314yes—
393C2×C3×C4#12714yes—
394C2×Dic3—22no—
395C2×Dic3—22no—
396C2×Dic3—24no—
397C2×Dic3—22no—
398C2×Dic3—22no—
399C2×Dic3—22no—
400C2×Dic3—22no—
401C2×Dic3—22no—
402C2×Dic3—22no—
403C2×Dic3—22no—
404C2×Dic3—24no—
405C2×Dic3—22no—
406C2×Dic3—24no—
407C2×Dic3—22no—
408C2×Dic3—22no—
409C2×Dic3—42no—
410C2×Dic3—41no—
411C2×Dic3—41no—
412C2×Dic3—41no—
413C2×Dic3—41no—
414C2×Dic3—42no—
415C2×Dic3—41no—
416C2×Dic3—41no—
417C2×Dic3—41no—
418C2×Dic3—41no—
419C2×Dic3—41no—
420C2×Dic3—41no—
421C2×Dic3—42no—
422C2×Dic3—41no—
423C2×Dic3—41no—
424C2×Dic3—42no—
425C2×Dic3—41no—
426C2×Dic3—41no—
427C2×Dic3—41no—
428C2×Dic3—41no—
429C2×Dic3—42no—
430C2×Dic3—42no—
431C2×Dic3—42no—
432C2×Dic3—42no—
433C2×Dic3—42no—
434C2×Dic3—42no—
435C2×Dic3—42no—
436C24—21no—
437C24—21no—
438C24—21no—
439C24—21no—
440C24—21no—
441C24—21no—
442C24—21no—
443C24—21no—
444C24—21no—
445C24—21no—
446C24—21no—
447C24—21no—
448C24C2×Dic612yes—
449C24#23712yes—
450C24#23912yes—
451C24C23×D311yescharacteristic
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—28no—
465C22×C4—28no—
466C22×C4—28no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—32no—
475C22×C4—32no—
476C22×C4—34no—
477C22×C4—32no—
478C22×C4—32no—
479C22×C4—44no—
480C22×C4—44no—
481C22×C4—44no—
482C22×C4—44no—
483C22×C4—61no—
484C22×C4—61no—
485C22×C4—62no—
486C22×C4—61no—
487C22×C4—61no—
488C22×C4—61no—
489C22×C4—61no—
490C22×C4—61no—
491C22×C4—61no—
492C22×C4—61no—
493C22×C4—61no—
494C22×C4—62no—
495C22×C4—61no—
496C22×C4—62no—
497C22×C4—61no—
498C22×C4—61no—
499C22×C4—61no—
500C22×C4—62no—
501C22×C4—61no—
502C22×C4—61no—
503C22×C4—61no—
504C22×C4—61no—
505C22×C4—62no—
506C22×C4—61no—
507C22×C4—62no—
508C22×C4—61no—
509C22×C4—61no—
510C22×C4—61no—
511C22×C4—61no—
512C22×C4—61no—
513C22×C4—62no—
514C22×C4—62no—
515C22×C4—62no—
516C22×C4—62no—
517C22×C4—62no—
518C22×C4—62no—
519C22×C4—62no—
520C22×C4C2×Dic612yes—
521C22×C4C2×Dic612yes—
522C22×C4#23512yes—
523C22×C4D3×D412yes—
524C22×C4D3×D412yes—
525C22×C4#23712yes—
526C22×C4#23712yes—
527C22×C4C2×#6714yes—
528C22×C4C2×#6712yes—
529C4⋊C4—28no—
530C4⋊C4—44no—
531C4⋊C4—68no—
532C4⋊C4—128no—
533C4⋊C4—128no—
534C4⋊C4—124no—
535C22⋊C4—48no—
536C22⋊C4—68no—
537C22⋊C4—68no—
538C22⋊C4—128no—
539C42—68no—
540C42—124no—
541C22×C3—24no—
542C22×C3—24no—
543C22×C3—24no—
544C22×C3—42no—
545C22×C3—42no—
546C22×C3—42no—
547C22×C3—42no—
548C22×C3—42no—
549C22×C3—42no—
550C22×C3—42no—
551C22×C3—42no—
552C22×C3—42no—
553C22×C3—42no—
554C22×C3—42no—
555C22×C3—42no—
556C22×C3C2×C22⋊Q811yescharacteristic
557C22×C3C2×C22⋊Q811yescharacteristic
558C22×C3C2×C22⋊Q811yescharacteristic
559C22×C3C2×#12311yescharacteristic
560C22×C3C2×#12311yescharacteristic
561C22×C3C2×#12311yescharacteristic
562C22×C3#52511yescharacteristic
563C22×C3#52511yescharacteristic
564C22×C3C2×#12511yescharacteristic
565C22×C3#52911yescharacteristic
566C22×C3#52911yescharacteristic
567C22×C3C2×#12711yescharacteristic
568C22×C3#53311yescharacteristic
569C22×C3#53711yescharacteristic
570C22×C3#53711yescharacteristic
571C22×C3#54011yescharacteristic
572C22×C3#54111yescharacteristic
573C22×C3#54411yescharacteristic
574C22×C3#54411yescharacteristic
575C22×C3#54611yescharacteristic
576C22×C3#54611yescharacteristic
577C22×C3#54611yescharacteristic
578C22×C3#54611yescharacteristic
579C22×C3#54811yescharacteristic
580C22×C3#54811yescharacteristic
581C22×C3#54811yescharacteristic
582C22×C3#54811yescharacteristic
583C22×C3#55211yescharacteristic
584C22×C3#55211yescharacteristic
585C22×C3#55311yescharacteristic
586C22×C3#55311yescharacteristic
587C22×C3#55511yescharacteristic
588C22×C3#55511yescharacteristic
589C22×C3#55611yescharacteristic
590C22×C3#55611yescharacteristic
591C3×C4—42no—
592C3×C4—44no—
593C3×C4—82no—
594C3×C4#39918yes—
595Dic3—44no—
596Dic3—42no—
597Dic3—42no—
598Dic3—42no—
599Dic3—42no—
600Dic3—82no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23#89014yes—
636C23C22×Dic611yescharacteristic
637C23C2×#23511yescharacteristic
638C23C2×D3×D411yescharacteristic
639C23C2×D3×D411yescharacteristic
640C23C2×#23711yescharacteristic
641C23C2×#23711yescharacteristic
642C23C2×#23711yescharacteristic
643C23#100411yescharacteristic
644C23C2×#23911yescharacteristic
645C23#100711yescharacteristic
646C23D3×#4111yescharacteristic
647C23D3×#4111yescharacteristic
648C23#100911yescharacteristic
649C23#101011yescharacteristic
650C23C22×#6711yescharacteristic
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—416no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—62no—
674C2×C4—62no—
675C2×C4—62no—
676C2×C4—64no—
677C2×C4—62no—
678C2×C4—62no—
679C2×C4—62no—
680C2×C4—62no—
681C2×C4—62no—
682C2×C4—62no—
683C2×C4—64no—
684C2×C4—62no—
685C2×C4—62no—
686C2×C4—62no—
687C2×C4—64no—
688C2×C4—121no—
689C2×C4—121no—
690C2×C4—121no—
691C2×C4—121no—
692C2×C4—122no—
693C2×C4—121no—
694C2×C4—122no—
695C2×C4—121no—
696C2×C4—121no—
697C2×C4—121no—
698C2×C4—121no—
699C2×C4—121no—
700C2×C4—121no—
701C2×C4—121no—
702C2×C4—121no—
703C2×C4—121no—
704C2×C4—122no—
705C2×C4—122no—
706C2×C4—121no—
707C2×C4—121no—
708C2×C4—122no—
709C2×C4—122no—
710C2×C4—122no—
711C2×C4—122no—
712C2×C4—122no—
713C2×C4—122no—
714C2×C4—122no—
715C2×C4#87814yes—
716C2×C4#87814yes—
717C2×C4#88314yes—
718C2×C4#88314yes—
719C2×C4#92414yes—
720C2×C4#93514yes—
721C2×C4#94014yes—
722C2×C3—44no—
723C2×C3C2×#39911yescharacteristic
724C2×C3#242011yescharacteristic
725C2×C3#242011yescharacteristic
726C2×C3#242111yescharacteristic
727C2×C3#242111yescharacteristic
728C2×C3#243911yescharacteristic
729C2×C3#243911yescharacteristic
730C2×C3#244211yescharacteristic
731C2×C3#244211yescharacteristic
732C2×C3#248511yescharacteristic
733C2×C3#248511yescharacteristic
734C2×C3#254011yescharacteristic
735C2×C3#254011yescharacteristic
736C2×C3#262911yescharacteristic
737C2×C3#285111yescharacteristic
738C22—24no—
739C22—24no—
740C22—24no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22C2×#87811yescharacteristic
754C22C2×#87811yescharacteristic
755C22C2×#88311yescharacteristic
756C22C2×#88311yescharacteristic
757C22C2×#89011yescharacteristic
758C22#550011yescharacteristic
759C22#551311yescharacteristic
760C22#551411yescharacteristic
761C22#551711yescharacteristic
762C22#551911yescharacteristic
763C22#553211yescharacteristic
764C22#553311yescharacteristic
765C22#559811yescharacteristic
766C22#560011yescharacteristic
767C22#560611yescharacteristic
768C22#560811yescharacteristic
769C22#561211yescharacteristic
770C22#561611yescharacteristic
771C22#561811yescharacteristic
772C22#561911yescharacteristic
773C22#562411yescharacteristic
774C22#562511yescharacteristic
775C22#562711yescharacteristic
776C22#562911yescharacteristic
777C22#563011yescharacteristic
778C22#563311yescharacteristic
779C22#564111yescharacteristic
780C22#564211yescharacteristic
781C22C2×#92411yescharacteristic
782C22C2×#93511yescharacteristic
783C22C2×#94011yescharacteristic
784C22#580611yescharacteristic
785C22#581711yescharacteristic
786C22#582911yescharacteristic
787C22#583111yescharacteristic
788C4—42no—
789C4—44no—
790C4—82no—
791C4—122no—
792C4—122no—
793C4—122no—
794C4—124no—
795C4—122no—
796C4—242no—
797C4#494918yes—
798C3#1522311yescharacteristic, complemented, Sylow
799C2—44no—
800C2#7389111yescharacteristic
801C2#7389211yescharacteristic
802C2#7389811yescharacteristic
803C2#7390111yescharacteristic
804C2#7395511yescharacteristic
805C2#7399811yescharacteristic
806C2#7402411yescharacteristic
807C2#7402511yescharacteristic
808C2C2×#494911yescharacteristic
809C2#8217211yescharacteristic
810C2#8224811yescharacteristic
811C2#8264311yescharacteristic
812C2#8266811yescharacteristic
813C2#8275311yescharacteristic
814C2#8277911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#380C2
prime radicalC25×C3C23
hypercenterC2×#380D3
hypocenterC3#15223
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
4. C2×#4984C2semidirect
5. C2×#4972C2semidirect
6. C2×#4977C2semidirect
7. #71563C2semidirect
10. #69423C2semidirect
11. #69421C2semidirect
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×#3802
C2×#52122
C2×C4×#2172
C2×#49842
C2×#49722
C2×#49772
#715632
#715472
#715462
#694232
#694212
#152233