Finite Group Databasebeta

← #10729029

Subgroups — #10729029

Order 768.

2314 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#935C211yesmaximal, characteristic
2C2×C3×#386C211yesmaximal, characteristic
3C2×#5220C211yesmaximal, characteristic
4C22×C3⋊#95C211yesmaximal, characteristic, complemented
5C2×#4950C211yesmaximal, characteristic, complemented
6C2×#4943C211yesmaximal, characteristic, complemented
7#72127C211yesmaximal, characteristic, complemented
8#71549C212yesmaximal, complemented
9#71546C212yesmaximal, complemented
10#69413C212yesmaximal, complemented
11#69411C212yesmaximal, complemented
12#14912—31nomaximal, Sylow
13C23×C3×D4C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C24×Dic3C2211yescharacteristic
16C24×Dic3C2211yescharacteristic
17C22×C3×C22⋊C4C2212yes—
18C22×C3×C22⋊C4C2211yescharacteristic
19C22×#217C2211yescharacteristic
20C22×#217C2211yescharacteristic
21C22×#217C2211yescharacteristic
22C22×#217C2212yes—
23C22×#217C2211yescharacteristic
24C2×#935—24no—
25C2×#935—24no—
26C2×#935—24no—
27C22×C4⋊Dic3C2212yes—
28C22×Dic3⋊C4C2211yescharacteristic
29C22×Dic3⋊C4C2211yescharacteristic
30C3×#386—24no—
31C2×C3×#95C2212yes—
32#5220—24no—
33C2×C3⋊#95—24no—
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2212yes—
40C2×C3⋊#95C2212yes—
41C2×C3⋊#95C2212yes—
42#4950—24no—
43#4943—24no—
44C22×#123—31no—
45C2×#386—31no—
46C2×#386D311yescharacteristic
47C2×#385—31no—
48C2×#381—31no—
49C22×#95—31no—
50#1442—32no—
51#1441—32no—
52#1440—32no—
53#1439—32no—
54C22⋊#95—31no—
55C25×C3C2311yescharacteristic
56C25×C3C2311yescharacteristic
57C22×C3×D4—22no—
58C22×C3×D4—22no—
59C22×C3×D4—22no—
60C22×C3×D4—22no—
61C22×C3×D4—22no—
62C22×C3×D4—22no—
63C22×C3×D4D414yes—
64C23×C3×C4—22no—
65C23×C3×C4—24no—
66C23×C3×C4—22no—
67C23×C3×C4—22no—
68C23×C3×C4—42no—
69C23×C3×C4C2311yescharacteristic
70C23×C3×C4C2312yes—
71C23×C3×C4C2312yes—
72C23×Dic3—22no—
73C23×Dic3—22no—
74C23×Dic3—22no—
75C23×Dic3—22no—
76C23×Dic3—22no—
77C23×Dic3—22no—
78C23×Dic3—22no—
79C23×Dic3—24no—
80C23×Dic3—22no—
81C23×Dic3—22no—
82C23×Dic3—42no—
83C23×Dic3D414yes—
84C23×Dic3C2312yes—
85C23×Dic3C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C23×Dic3C2311yescharacteristic
88C23×Dic3C2311yescharacteristic
89C23×Dic3C2312yes—
90C2×C3×C22⋊C4—22no—
91C2×C3×C22⋊C4—22no—
92C2×C3×C22⋊C4—24no—
93C2×C3×C22⋊C4—24no—
94C2×C3×C22⋊C4—42no—
95C2×C3×C22⋊C4D414yes—
96C2×#217—22no—
97C2×#217—22no—
98C2×#217—22no—
99C2×#217—22no—
100C2×#217—22no—
101C2×#217—22no—
102C2×#217—22no—
103C2×#217—22no—
104C2×#217—22no—
105C2×#217—24no—
106C2×#217—22no—
107C2×#217—22no—
108C2×#217—24no—
109C2×#217—42no—
110C2×#217D414yes—
111#935—232no—
112C2×C4⋊Dic3—24no—
113C2×C4⋊Dic3—24no—
114C2×C4⋊Dic3—42no—
115C2×Dic3⋊C4—22no—
116C2×Dic3⋊C4—22no—
117C2×Dic3⋊C4—22no—
118C2×Dic3⋊C4—22no—
119C2×Dic3⋊C4—22no—
120C2×Dic3⋊C4—22no—
121C3×#95—24no—
122C3⋊#95—24no—
123C3⋊#95—24no—
124C3⋊#95—24no—
125C3⋊#95—24no—
126C3⋊#95—24no—
127C3⋊#95—24no—
128C3⋊#95—24no—
129C3⋊#95—42no—
130C23×D4C2×D311yescharacteristic
131C24×C4—31no—
132C24×C4—31no—
133C24×C4C2×D311yescharacteristic
134C2×#123—64no—
135C2×#123—64no—
136C2×#123—64no—
137C22×C4⋊C4—31no—
138C22×C4⋊C4—31no—
139C22×C4⋊C4—32no—
140C22×C22⋊C4—31no—
141C22×C22⋊C4—31no—
142C22×C22⋊C4—31no—
143C22×C22⋊C4—31no—
144C22×C22⋊C4—32no—
145C22×C22⋊C4C2×D312yes—
146C22×C22⋊C4C2×D311yescharacteristic
147#386—24no—
148#386—64no—
149#385—64no—
150#381—64no—
151C2×#95—32no—
152C2×#95—32no—
153C2×#95—32no—
154C2×#95—32no—
155C2×#95—32no—
156C2×#95—32no—
157C2×#95—32no—
158C2×#95—32no—
159C2×#95—64no—
160C2×#95C2×D312yes—
161C24×C3—22no—
162C24×C3—22no—
163C24×C3—22no—
164C24×C3—22no—
165C24×C3—21no—
166C24×C3—21no—
167C24×C3—21no—
168C24×C3—22no—
169C24×C3—22no—
170C24×C3—21no—
171C24×C3—21no—
172C24×C3—21no—
173C24×C3—22no—
174C24×C3—22no—
175C24×C3C2×D412yes—
176C24×C3C2×D412yes—
177C24×C3C2×D412yes—
178C24×C3C2×D412yes—
179C24×C3C2×D412yes—
180C24×C3#4112yes—
181C24×C3#4112yes—
182C24×C3#4112yes—
183C24×C3C2411yescharacteristic
184C2×C3×D4—28no—
185C2×C3×D4—28no—
186C2×C3×D4—28no—
187C2×C3×D4—44no—
188C2×C3×D4—44no—
189C2×C3×D4—44no—
190C2×C3×D4—44no—
191C22×C3×C4—28no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—21no—
195C22×C3×C4—22no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—22no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—22no—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4—22no—
210C22×C3×C4—48no—
211C22×C3×C4—48no—
212C22×C3×C4—44no—
213C22×C3×C4—44no—
214C22×C3×C4C2×D412yes—
215C22×C3×C4C2×D414yes—
216C22×C3×C4#4114yes—
217C22×Dic3—28no—
218C22×Dic3—28no—
219C22×Dic3—28no—
220C22×Dic3—28no—
221C22×Dic3—22no—
222C22×Dic3—21no—
223C22×Dic3—21no—
224C22×Dic3—22no—
225C22×Dic3—22no—
226C22×Dic3—21no—
227C22×Dic3—21no—
228C22×Dic3—21no—
229C22×Dic3—21no—
230C22×Dic3—21no—
231C22×Dic3—21no—
232C22×Dic3—21no—
233C22×Dic3—21no—
234C22×Dic3—22no—
235C22×Dic3—22no—
236C22×Dic3—21no—
237C22×Dic3—21no—
238C22×Dic3—21no—
239C22×Dic3—21no—
240C22×Dic3—21no—
241C22×Dic3—21no—
242C22×Dic3—22no—
243C22×Dic3—22no—
244C22×Dic3—22no—
245C22×Dic3—22no—
246C22×Dic3—22no—
247C22×Dic3—22no—
248C22×Dic3—22no—
249C22×Dic3—22no—
250C22×Dic3—22no—
251C22×Dic3—22no—
252C22×Dic3—22no—
253C22×Dic3—22no—
254C22×Dic3—48no—
255C22×Dic3—48no—
256C22×Dic3—44no—
257C22×Dic3—44no—
258C22×Dic3—44no—
259C22×Dic3—44no—
260C22×Dic3—44no—
261C22×Dic3—44no—
262C22×Dic3C2×D412yes—
263C22×Dic3C2×D412yes—
264C22×Dic3C2×D412yes—
265C22×Dic3C2×D412yes—
266C22×Dic3#4114yes—
267C3×C22⋊C4—28no—
268C3×C22⋊C4—48no—
269#217—28no—
270#217—28no—
271#217—28no—
272#217—48no—
273#217—44no—
274C4⋊Dic3—48no—
275Dic3⋊C4—28no—
276Dic3⋊C4—28no—
277C25C22×D311yescharacteristic
278C25C22×D311yescharacteristic
279C22×D4—22no—
280C22×D4—22no—
281C22×D4—22no—
282C22×D4—22no—
283C22×D4—22no—
284C22×D4—22no—
285C22×D4D1214yes—
286C23×C4—22no—
287C23×C4—24no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—34no—
291C23×C4—31no—
292C23×C4—31no—
293C23×C4—31no—
294C23×C4—31no—
295C23×C4—32no—
296C23×C4—32no—
297C23×C4—42no—
298C23×C4—64no—
299C23×C4—62no—
300C23×C4—62no—
301C23×C4—62no—
302C23×C4—62no—
303C23×C4—62no—
304C23×C4—62no—
305C23×C4—62no—
306C23×C4—62no—
307C23×C4—62no—
308C23×C4—122no—
309C23×C4C22×D311yescharacteristic
310C23×C4C22×D312yes—
311C23×C4C22×D312yes—
312#123—632no—
313C2×C4⋊C4—62no—
314C2×C4⋊C4—62no—
315C2×C4⋊C4—62no—
316C2×C4⋊C4—62no—
317C2×C4⋊C4—62no—
318C2×C4⋊C4—62no—
319C2×C4⋊C4—64no—
320C2×C4⋊C4—64no—
321C2×C4⋊C4—122no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—34no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—62no—
329C2×C22⋊C4—62no—
330C2×C22⋊C4—62no—
331C2×C22⋊C4—62no—
332C2×C22⋊C4—62no—
333C2×C22⋊C4—62no—
334C2×C22⋊C4—62no—
335C2×C22⋊C4—62no—
336C2×C22⋊C4—64no—
337C2×C22⋊C4—64no—
338C2×C22⋊C4—62no—
339C2×C22⋊C4—62no—
340C2×C22⋊C4—62no—
341C2×C22⋊C4—122no—
342C2×C22⋊C4#6714yes—
343#95—24no—
344#95—64no—
345#95—64no—
346#95—64no—
347#95—64no—
348#95—64no—
349#95—64no—
350#95—64no—
351#95—122no—
352C23×C3—22no—
353C23×C3—22no—
354C23×C3—24no—
355C23×C3—24no—
356C23×C3—22no—
357C23×C3—22no—
358C23×C3—24no—
359C23×C3—24no—
360C23×C3—24no—
361C23×C3—24no—
362C23×C3—24no—
363C23×C3—24no—
364C23×C3—24no—
365C23×C3—24no—
366C23×C3—24no—
367C23×C3—24no—
368C23×C3—22no—
369C23×C3—22no—
370C23×C3—22no—
371C23×C3—24no—
372C23×C3—24no—
373C23×C3—41no—
374C23×C3—41no—
375C23×C3—41no—
376C23×C3—41no—
377C23×C3—41no—
378C23×C3—41no—
379C23×C3—42no—
380C23×C3—42no—
381C23×C3—41no—
382C23×C3—41no—
383C23×C3—42no—
384C23×C3—42no—
385C23×C3—42no—
386C23×C3—42no—
387C23×C3—42no—
388C23×C3—42no—
389C23×C3—42no—
390C23×C3—42no—
391C23×C3#12014yes—
392C23×C3#12114yes—
393C23×C3#12114yes—
394C23×C3#12114yes—
395C23×C3#12314yes—
396C23×C3#12314yes—
397C23×C3#12414yes—
398C23×C3C22×D411yescharacteristic
399C23×C3C22×D411yescharacteristic
400C23×C3C22×D411yescharacteristic
401C23×C3C22×D411yescharacteristic
402C23×C3C2×#4111yescharacteristic
403C23×C3C2×#4111yescharacteristic
404C23×C3C2×#4111yescharacteristic
405C23×C3C2×#4112yes—
406C23×C3C2×#4112yes—
407C23×C3H(5,𝔽2)12yes—
408C23×C32−1+412yes—
409C3×D4—416no—
410C2×C3×C4—22no—
411C2×C3×C4—24no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—24no—
415C2×C3×C4—24no—
416C2×C3×C4—24no—
417C2×C3×C4—24no—
418C2×C3×C4—24no—
419C2×C3×C4—416no—
420C2×C3×C4—42no—
421C2×C3×C4—41no—
422C2×C3×C4—41no—
423C2×C3×C4—41no—
424C2×C3×C4—41no—
425C2×C3×C4—42no—
426C2×C3×C4—42no—
427C2×C3×C4—42no—
428C2×C3×C4—42no—
429C2×C3×C4—42no—
430C2×C3×C4—42no—
431C2×C3×C4—42no—
432C2×Dic3—22no—
433C2×Dic3—22no—
434C2×Dic3—22no—
435C2×Dic3—22no—
436C2×Dic3—22no—
437C2×Dic3—22no—
438C2×Dic3—22no—
439C2×Dic3—22no—
440C2×Dic3—24no—
441C2×Dic3—24no—
442C2×Dic3—24no—
443C2×Dic3—24no—
444C2×Dic3—24no—
445C2×Dic3—416no—
446C2×Dic3—42no—
447C2×Dic3—41no—
448C2×Dic3—41no—
449C2×Dic3—41no—
450C2×Dic3—41no—
451C2×Dic3—41no—
452C2×Dic3—41no—
453C2×Dic3—41no—
454C2×Dic3—41no—
455C2×Dic3—41no—
456C2×Dic3—41no—
457C2×Dic3—41no—
458C2×Dic3—42no—
459C2×Dic3—41no—
460C2×Dic3—42no—
461C2×Dic3—42no—
462C2×Dic3—42no—
463C2×Dic3—42no—
464C2×Dic3—416no—
465C2×Dic3—42no—
466C2×Dic3—42no—
467C2×Dic3—42no—
468C2×Dic3—42no—
469C2×Dic3—42no—
470C2×Dic3—42no—
471C2×Dic3—42no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—21no—
477C24—21no—
478C24—21no—
479C24—22no—
480C24—21no—
481C24—21no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—21no—
486C24C2×D1212yes—
487C24C2×D1212yes—
488C24#23512yes—
489C24D3×D412yes—
490C24D3×D412yes—
491C24#23712yes—
492C24#23712yes—
493C24C2×#6712yes—
494C24C23×D311yescharacteristic
495C2×D4—28no—
496C2×D4—28no—
497C2×D4—28no—
498C2×D4—44no—
499C2×D4—44no—
500C2×D4—44no—
501C2×D4—44no—
502C22×C4—28no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—32no—
522C22×C4—32no—
523C22×C4—32no—
524C22×C4—32no—
525C22×C4—34no—
526C22×C4—48no—
527C22×C4—48no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—68no—
531C22×C4—68no—
532C22×C4—68no—
533C22×C4—68no—
534C22×C4—62no—
535C22×C4—61no—
536C22×C4—61no—
537C22×C4—61no—
538C22×C4—61no—
539C22×C4—61no—
540C22×C4—61no—
541C22×C4—62no—
542C22×C4—62no—
543C22×C4—61no—
544C22×C4—61no—
545C22×C4—61no—
546C22×C4—61no—
547C22×C4—62no—
548C22×C4—61no—
549C22×C4—61no—
550C22×C4—61no—
551C22×C4—61no—
552C22×C4—62no—
553C22×C4—62no—
554C22×C4—62no—
555C22×C4—62no—
556C22×C4—62no—
557C22×C4—62no—
558C22×C4—61no—
559C22×C4—61no—
560C22×C4—62no—
561C22×C4—62no—
562C22×C4—62no—
563C22×C4—62no—
564C22×C4—62no—
565C22×C4—62no—
566C22×C4—62no—
567C22×C4—128no—
568C22×C4—128no—
569C22×C4—124no—
570C22×C4—124no—
571C22×C4—124no—
572C22×C4—124no—
573C22×C4—124no—
574C22×C4—124no—
575C22×C4C2×D1212yes—
576C22×C4#23714yes—
577C22×C4C2×#6714yes—
578C4⋊C4—68no—
579C4⋊C4—68no—
580C4⋊C4—128no—
581C22⋊C4—28no—
582C22⋊C4—48no—
583C22⋊C4—68no—
584C22⋊C4—68no—
585C22⋊C4—68no—
586C22⋊C4—128no—
587C22⋊C4—124no—
588C22×C3—24no—
589C22×C3—24no—
590C22×C3—24no—
591C22×C3—24no—
592C22×C3—24no—
593C22×C3—24no—
594C22×C3—28no—
595C22×C3—28no—
596C22×C3—28no—
597C22×C3—28no—
598C22×C3—42no—
599C22×C3—42no—
600C22×C3—42no—
601C22×C3—44no—
602C22×C3—44no—
603C22×C3—81no—
604C22×C3—81no—
605C22×C3—81no—
606C22×C3—81no—
607C22×C3—82no—
608C22×C3—82no—
609C22×C3#39418yes—
610C22×C3C2×#12011yescharacteristic
611C22×C3C2×#12111yescharacteristic
612C22×C3C2×#12111yescharacteristic
613C22×C3C2×#12111yescharacteristic
614C22×C3C2×#12311yescharacteristic
615C22×C3C2×#12311yescharacteristic
616C22×C3#52511yescharacteristic
617C22×C3#52511yescharacteristic
618C22×C3C2×#12411yescharacteristic
619C22×C3#52912yes—
620C22×C3#52912yes—
621C22×C3#53511yescharacteristic
622C22×C3#53611yescharacteristic
623C22×C3#53912yes—
624C22×C3#53912yes—
625C22×C3#54612yes—
626C22×C3#54612yes—
627C22×C3#54612yes—
628C22×C3#54712yes—
629C22×C3#54712yes—
630C22×C3#54712yes—
631C22×C3#55112yes—
632C22×C3#55212yes—
633C3×C4—42no—
634C3×C4—44no—
635C3×C4—44no—
636Dic3—42no—
637Dic3—42no—
638Dic3—42no—
639Dic3—44no—
640Dic3—42no—
641Dic3—82no—
642C23—22no—
643C23—24no—
644C23—22no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—22no—
652C23—24no—
653C23—22no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—24no—
662C23—24no—
663C23—41no—
664C23—42no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—42no—
669C23—41no—
670C23—41no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—41no—
675C23—42no—
676C23—41no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23#88214yes—
682C23#88314yes—
683C23#88514yes—
684C23#88614yes—
685C23#93014yes—
686C23#93814yes—
687C23#93914yes—
688C23C22×D1211yescharacteristic
689C23C2×#23511yescharacteristic
690C23C2×D3×D411yescharacteristic
691C23C2×D3×D411yescharacteristic
692C23C2×#23711yescharacteristic
693C23C2×#23711yescharacteristic
694C23C2×#23712yes—
695C23#100412yes—
696C23D3×#4112yes—
697C23#101012yes—
698C23C22×#6711yescharacteristic
699D4—416no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—416no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—64no—
723C2×C4—62no—
724C2×C4—62no—
725C2×C4—62no—
726C2×C4—62no—
727C2×C4—62no—
728C2×C4—62no—
729C2×C4—62no—
730C2×C4—62no—
731C2×C4—64no—
732C2×C4—64no—
733C2×C4—64no—
734C2×C4—64no—
735C2×C4—1216no—
736C2×C4—121no—
737C2×C4—121no—
738C2×C4—1216no—
739C2×C4—122no—
740C2×C4—121no—
741C2×C4—121no—
742C2×C4—121no—
743C2×C4—121no—
744C2×C4—121no—
745C2×C4—121no—
746C2×C4—121no—
747C2×C4—121no—
748C2×C4—122no—
749C2×C4—122no—
750C2×C4—122no—
751C2×C4—121no—
752C2×C4—122no—
753C2×C4—121no—
754C2×C4—122no—
755C2×C4—122no—
756C2×C4—122no—
757C2×C4—122no—
758C2×C4—122no—
759C2×C4—122no—
760C2×C4—122no—
761C2×C4—122no—
762C2×C3—28no—
763C2×C3—82no—
764C2×C3C2×#39411yescharacteristic
765C2×C3#240411yescharacteristic
766C2×C3#240611yescharacteristic
767C2×C3#241111yescharacteristic
768C2×C3#241311yescharacteristic
769C2×C3#241912yes—
770C2×C3#242512yes—
771C2×C3#242512yes—
772C2×C3#248812yes—
773C2×C3#262311yescharacteristic
774C2×C3#285311yescharacteristic
775C22—24no—
776C22—24no—
777C22—24no—
778C22—24no—
779C22—24no—
780C22—28no—
781C22—24no—
782C22—28no—
783C22—28no—
784C22—28no—
785C22—42no—
786C22—44no—
787C22—42no—
788C22—42no—
789C22—44no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—82no—
795C22—82no—
796C22#496118yes—
797C22C2×#88211yescharacteristic
798C22C2×#88311yescharacteristic
799C22C2×#88511yescharacteristic
800C22C2×#88611yescharacteristic
801C22#553812yes—
802C22#555412yes—
803C22#555512yes—
804C22#556412yes—
805C22#558611yescharacteristic
806C22#558712yes—
807C22#559211yescharacteristic
808C22#560012yes—
809C22#560212yes—
810C22#561012yes—
811C22#561112yes—
812C22#564811yescharacteristic
813C22#565012yes—
814C22#565611yescharacteristic
815C22C2×#93011yescharacteristic
816C22C2×#93811yescharacteristic
817C22C2×#93911yescharacteristic
818C22#580612yes—
819C22#582412yes—
820C4—44no—
821C4—42no—
822C4—44no—
823C4—124no—
824C4—122no—
825C4—122no—
826C4—122no—
827C4—122no—
828C4—242no—
829C3#1491211yescharacteristic, complemented, Sylow
830C2—28no—
831C2—82no—
832C2#7468711yescharacteristic
833C2#7469412yes—
834C2#7473912yes—
835C2#7478211yescharacteristic
836C2#7487111yescharacteristic
837C2#7488511yescharacteristic
838C2C2×#496111yescharacteristic
839C2#8235512yes—
840C2#8258311yescharacteristic
841C2#8264512yes—
842C2#8284211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#386C2
prime radicalC23×C3×D4C22
hypercenterC2×#386D3
hypocenterC3#14912
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
4. C22×C3⋊#95C2semidirect
5. C2×#4950C2semidirect
6. C2×#4943C2semidirect
7. #72127C2semidirect
8. #71549C2semidirect
9. #71546C2semidirect
10. #69413C2semidirect
11. #69411C2semidirect
829. C3#14912semidirect

Maximal subgroups

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

subgroupindex
C22×#9352
C2×C3×#3862
C2×#52202
C22×C3⋊#952
C2×#49502
C2×#49432
#721272
#715492
#715462
#694132
#694112
#149123