Finite Group Databasebeta

← #10729208

Subgroups — #10729208

Order 768.

2314 conjugacy classes of subgroups.

The subgroup lattice has 818 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
4C2×#5212C211yesmaximal, characteristic, complemented
5C22×C3⋊#95C211yesmaximal, characteristic, complemented
6C2×#4943C211yesmaximal, characteristic, complemented
7#71549C212yesmaximal, complemented
8#71546C212yesmaximal, complemented
9#71544C211yesmaximal, characteristic, complemented
10#69413C212yesmaximal, complemented
11#69411C212yesmaximal, complemented
12#14927—31nomaximal, Sylow
13C23×C3×D4C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C24×Dic3C2211yescharacteristic
16C24×Dic3C2211yescharacteristic
17C22×C3×C22⋊C4C2211yescharacteristic
18C22×C3×C22⋊C4C2211yescharacteristic
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×#217C2211yescharacteristic
21C22×#217C2212yes—
22C22×#217C2212yes—
23C22×#217C2211yescharacteristic
24C2×#935—24no—
25C2×#935—24no—
26C2×#935—24no—
27C22×C4⋊Dic3C2212yes—
28C22×Dic3⋊C4C2212yes—
29C3×#386—24no—
30C2×C3×#95C2211yescharacteristic
31C2×C3×#95C2211yescharacteristic
32#5220—24no—
33#5212—24no—
34C2×C3⋊#95—24no—
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2212yes—
40C2×C3⋊#95C2212yes—
41C2×C3⋊#95C2212yes—
42C2×C3⋊#95C2212yes—
43#4943—24no—
44C22×#123—31no—
45C2×#386—31no—
46C2×#386D311yescharacteristic
47C2×#381—31no—
48C2×#380—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—22no—
66C23×C3×C4—24no—
67C23×C3×C4—42no—
68C23×C3×C4D414yes—
69C23×C3×C4C2311yescharacteristic
70C23×C3×C4C2311yescharacteristic
71C23×C3×C4C2311yescharacteristic
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×Dic3—22no—
75C23×Dic3—22no—
76C23×Dic3—22no—
77C23×Dic3—22no—
78C23×Dic3—22no—
79C23×Dic3—22no—
80C23×Dic3—22no—
81C23×Dic3—24no—
82C23×Dic3—22no—
83C23×Dic3—22no—
84C23×Dic3—42no—
85C23×Dic3D414yes—
86C23×Dic3C2312yes—
87C23×Dic3C2312yes—
88C23×Dic3C2312yes—
89C23×Dic3C2312yes—
90C2×C3×C22⋊C4—22no—
91C2×C3×C22⋊C4—22no—
92C2×C3×C22⋊C4—22no—
93C2×C3×C22⋊C4—22no—
94C2×C3×C22⋊C4—22no—
95C2×C3×C22⋊C4—24no—
96C2×C3×C22⋊C4—42no—
97C2×#217—24no—
98C2×#217—22no—
99C2×#217—22no—
100C2×#217—24no—
101C2×#217—24no—
102C2×#217—22no—
103C2×#217—22no—
104C2×#217—24no—
105C2×#217—22no—
106C2×#217—24no—
107C2×#217—42no—
108C2×#217D414yes—
109#935—232no—
110C2×C4⋊Dic3—24no—
111C2×C4⋊Dic3—24no—
112C2×C4⋊Dic3—42no—
113C2×Dic3⋊C4—24no—
114C2×Dic3⋊C4—24no—
115C2×Dic3⋊C4—24no—
116C3×#95—22no—
117C3×#95—22no—
118C3⋊#95—24no—
119C3⋊#95—24no—
120C3⋊#95—24no—
121C3⋊#95—24no—
122C3⋊#95—24no—
123C3⋊#95—24no—
124C3⋊#95—24no—
125C3⋊#95—42no—
126C23×D4C2×D311yescharacteristic
127C24×C4—31no—
128C24×C4—31no—
129C24×C4C2×D311yescharacteristic
130C2×#123—64no—
131C2×#123—64no—
132C2×#123—64no—
133C22×C4⋊C4—32no—
134C22×C4⋊C4—32no—
135C22×C22⋊C4—31no—
136C22×C22⋊C4—32no—
137C22×C22⋊C4—31no—
138C22×C22⋊C4—32no—
139C22×C22⋊C4C2×D311yescharacteristic
140C22×C22⋊C4C2×D311yescharacteristic
141C22×C22⋊C4C2×D311yescharacteristic
142#386—24no—
143#386—64no—
144#381—64no—
145#380—64no—
146C2×#95—32no—
147C2×#95—32no—
148C2×#95—32no—
149C2×#95—32no—
150C2×#95—32no—
151C2×#95—32no—
152C2×#95—32no—
153C2×#95—32no—
154C2×#95—64no—
155C2×#95C2×D311yescharacteristic
156C2×#95C2×D311yescharacteristic
157C24×C3—22no—
158C24×C3—22no—
159C24×C3—22no—
160C24×C3—22no—
161C24×C3—21no—
162C24×C3—21no—
163C24×C3—21no—
164C24×C3—22no—
165C24×C3—22no—
166C24×C3—21no—
167C24×C3—21no—
168C24×C3—21no—
169C24×C3—22no—
170C24×C3—22no—
171C24×C3C2×D412yes—
172C24×C3C2×D412yes—
173C24×C3C2×D412yes—
174C24×C3C2×D412yes—
175C24×C3C2×D412yes—
176C24×C3#4112yes—
177C24×C3#4112yes—
178C24×C3#4112yes—
179C24×C3C2411yescharacteristic
180C2×C3×D4—28no—
181C2×C3×D4—28no—
182C2×C3×D4—28no—
183C2×C3×D4—44no—
184C2×C3×D4—44no—
185C2×C3×D4—44no—
186C2×C3×D4—44no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—22no—
190C22×C3×C4—28no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—22no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—22no—
201C22×C3×C4—28no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—22no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—22no—
210C22×C3×C4—22no—
211C22×C3×C4—22no—
212C22×C3×C4—44no—
213C22×C3×C4—48no—
214C22×C3×C4—48no—
215C22×C3×C4C2×D412yes—
216C22×C3×C4C2×D412yes—
217C22×C3×C4C2×D412yes—
218C22×C3×C4#4114yes—
219C22×Dic3—28no—
220C22×Dic3—28no—
221C22×Dic3—28no—
222C22×Dic3—28no—
223C22×Dic3—22no—
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×Dic3—22no—
239C22×Dic3—22no—
240C22×Dic3—22no—
241C22×Dic3—22no—
242C22×Dic3—22no—
243C22×Dic3—22no—
244C22×Dic3—22no—
245C22×Dic3—22no—
246C22×Dic3—22no—
247C22×Dic3—22no—
248C22×Dic3—48no—
249C22×Dic3—48no—
250C22×Dic3—44no—
251C22×Dic3—44no—
252C22×Dic3—44no—
253C22×Dic3—44no—
254C22×Dic3—44no—
255C22×Dic3—44no—
256C22×Dic3C2×D414yes—
257C22×Dic3C2×D414yes—
258C22×Dic3#4114yes—
259C3×C22⋊C4—44no—
260C3×C22⋊C4—44no—
261C3×C22⋊C4—44no—
262#217—216no—
263#217—28no—
264#217—48no—
265#217—44no—
266C4⋊Dic3—48no—
267Dic3⋊C4—216no—
268C25C22×D311yescharacteristic
269C25C22×D311yescharacteristic
270C22×D4—22no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—22no—
274C22×D4—22no—
275C22×D4—22no—
276C22×D4D1214yes—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—24no—
280C23×C4—34no—
281C23×C4—32no—
282C23×C4—32no—
283C23×C4—32no—
284C23×C4—32no—
285C23×C4—42no—
286C23×C4—64no—
287C23×C4—62no—
288C23×C4—62no—
289C23×C4—62no—
290C23×C4—62no—
291C23×C4—62no—
292C23×C4—62no—
293C23×C4—62no—
294C23×C4—62no—
295C23×C4—62no—
296C23×C4—122no—
297C23×C4#6714yes—
298C23×C4C22×D311yescharacteristic
299C23×C4C22×D311yescharacteristic
300C23×C4C22×D311yescharacteristic
301C23×C4C22×D311yescharacteristic
302C23×C4C22×D311yescharacteristic
303#123—632no—
304C2×C4⋊C4—64no—
305C2×C4⋊C4—64no—
306C2×C4⋊C4—64no—
307C2×C4⋊C4—64no—
308C2×C4⋊C4—64no—
309C2×C4⋊C4—122no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—34no—
317C2×C22⋊C4—42no—
318C2×C22⋊C4—64no—
319C2×C22⋊C4—64no—
320C2×C22⋊C4—64no—
321C2×C22⋊C4—62no—
322C2×C22⋊C4—62no—
323C2×C22⋊C4—64no—
324C2×C22⋊C4—64no—
325C2×C22⋊C4—62no—
326C2×C22⋊C4—62no—
327C2×C22⋊C4—62no—
328C2×C22⋊C4—122no—
329#95—22no—
330#95—22no—
331#95—64no—
332#95—64no—
333#95—64no—
334#95—64no—
335#95—64no—
336#95—64no—
337#95—64no—
338#95—122no—
339C23×C3—22no—
340C23×C3—22no—
341C23×C3—24no—
342C23×C3—24no—
343C23×C3—22no—
344C23×C3—22no—
345C23×C3—24no—
346C23×C3—24no—
347C23×C3—24no—
348C23×C3—24no—
349C23×C3—24no—
350C23×C3—24no—
351C23×C3—24no—
352C23×C3—24no—
353C23×C3—24no—
354C23×C3—24no—
355C23×C3—22no—
356C23×C3—22no—
357C23×C3—22no—
358C23×C3—24no—
359C23×C3—24no—
360C23×C3—41no—
361C23×C3—41no—
362C23×C3—41no—
363C23×C3—41no—
364C23×C3—41no—
365C23×C3—41no—
366C23×C3—42no—
367C23×C3—42no—
368C23×C3—41no—
369C23×C3—41no—
370C23×C3—42no—
371C23×C3—42no—
372C23×C3—42no—
373C23×C3—42no—
374C23×C3—42no—
375C23×C3—42no—
376C23×C3—42no—
377C23×C3—42no—
378C23×C3#12014yes—
379C23×C3#12114yes—
380C23×C3#12114yes—
381C23×C3#12114yes—
382C23×C3#12314yes—
383C23×C3#12314yes—
384C23×C3#12414yes—
385C23×C3C22×D411yescharacteristic
386C23×C3C22×D411yescharacteristic
387C23×C3C22×D411yescharacteristic
388C23×C3C22×D411yescharacteristic
389C23×C3C2×#4111yescharacteristic
390C23×C3C2×#4111yescharacteristic
391C23×C3C2×#4111yescharacteristic
392C23×C3C2×#4112yes—
393C23×C3C2×#4112yes—
394C23×C3H(5,𝔽2)12yes—
395C23×C32−1+412yes—
396C3×D4—416no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—24no—
400C2×C3×C4—24no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—416no—
408C2×C3×C4—41no—
409C2×C3×C4—41no—
410C2×C3×C4—41no—
411C2×C3×C4—41no—
412C2×C3×C4—42no—
413C2×C3×C4—42no—
414C2×C3×C4—41no—
415C2×C3×C4—41no—
416C2×C3×C4—41no—
417C2×C3×C4—41no—
418C2×C3×C4—42no—
419C2×C3×C4—42no—
420C2×C3×C4—41no—
421C2×C3×C4—41no—
422C2×C3×C4—42no—
423C2×C3×C4—42no—
424C2×C3×C4#12314yescomplemented
425C2×Dic3—24no—
426C2×Dic3—24no—
427C2×Dic3—24no—
428C2×Dic3—24no—
429C2×Dic3—24no—
430C2×Dic3—24no—
431C2×Dic3—24no—
432C2×Dic3—24no—
433C2×Dic3—24no—
434C2×Dic3—416no—
435C2×Dic3—42no—
436C2×Dic3—42no—
437C2×Dic3—42no—
438C2×Dic3—42no—
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—416no—
448C2×Dic3—42no—
449C2×Dic3—42no—
450C2×Dic3—42no—
451C2×Dic3—42no—
452C2×Dic3—42no—
453C2×Dic3—42no—
454C2×Dic3—42no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—21no—
460C24—21no—
461C24—21no—
462C24—22no—
463C24—21no—
464C24—21no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—21no—
469C24C2×D1212yes—
470C24C2×D1212yes—
471C24#23512yes—
472C24D3×D412yes—
473C24D3×D412yes—
474C24#23712yes—
475C24#23712yes—
476C24C2×#6712yes—
477C24C23×D311yescharacteristic
478C2×D4—28no—
479C2×D4—28no—
480C2×D4—28no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—44no—
484C2×D4—44no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—28no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—28no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—34no—
511C22×C4—34no—
512C22×C4—34no—
513C22×C4—44no—
514C22×C4—48no—
515C22×C4—48no—
516C22×C4—68no—
517C22×C4—68no—
518C22×C4—68no—
519C22×C4—68no—
520C22×C4—62no—
521C22×C4—62no—
522C22×C4—62no—
523C22×C4—62no—
524C22×C4—62no—
525C22×C4—62no—
526C22×C4—62no—
527C22×C4—62no—
528C22×C4—62no—
529C22×C4—62no—
530C22×C4—62no—
531C22×C4—62no—
532C22×C4—62no—
533C22×C4—62no—
534C22×C4—62no—
535C22×C4—62no—
536C22×C4—62no—
537C22×C4—62no—
538C22×C4—62no—
539C22×C4—62no—
540C22×C4—62no—
541C22×C4—62no—
542C22×C4—62no—
543C22×C4—62no—
544C22×C4—62no—
545C22×C4—128no—
546C22×C4—128no—
547C22×C4—124no—
548C22×C4—124no—
549C22×C4—124no—
550C22×C4—124no—
551C22×C4—124no—
552C22×C4—124no—
553C22×C4C2×D1212yes—
554C22×C4#23714yes—
555C22×C4C2×#6712yes—
556C22×C4C2×#6712yes—
557C4⋊C4—616no—
558C4⋊C4—128no—
559C22⋊C4—44no—
560C22⋊C4—44no—
561C22⋊C4—44no—
562C22⋊C4—616no—
563C22⋊C4—68no—
564C22⋊C4—128no—
565C22⋊C4—124no—
566C22×C3—24no—
567C22×C3—24no—
568C22×C3—24no—
569C22×C3—24no—
570C22×C3—28no—
571C22×C3—28no—
572C22×C3—24no—
573C22×C3—28no—
574C22×C3—28no—
575C22×C3—24no—
576C22×C3—42no—
577C22×C3—44no—
578C22×C3—44no—
579C22×C3—42no—
580C22×C3—42no—
581C22×C3—81no—
582C22×C3—81no—
583C22×C3—81no—
584C22×C3—81no—
585C22×C3—82no—
586C22×C3—82no—
587C22×C3#39418yes—
588C22×C3C2×#12011yescharacteristic
589C22×C3C2×#12111yescharacteristic
590C22×C3C2×#12111yescharacteristic
591C22×C3C2×#12111yescharacteristic
592C22×C3C2×#12311yescharacteristic
593C22×C3C2×#12311yescharacteristic
594C22×C3C2×#12311yescharacteristic
595C22×C3#52511yescharacteristic
596C22×C3C2×#12411yescharacteristic
597C22×C3#52912yes—
598C22×C3#53212yes—
599C22×C3#53411yescharacteristic
600C22×C3#53611yescharacteristic
601C22×C3#53712yes—
602C22×C3#53912yes—
603C22×C3#54612yes—
604C22×C3#54612yes—
605C22×C3#54712yes—
606C22×C3#54712yes—
607C22×C3#55112yes—
608C22×C3#55112yes—
609C22×C3#55212yes—
610C22×C3#55212yes—
611C3×C4—24no—
612C3×C4—42no—
613C3×C4—42no—
614C3×C4—81no—
615C3×C4—81no—
616Dic3—44no—
617Dic3—44no—
618Dic3—44no—
619Dic3—82no—
620C23—24no—
621C23—24no—
622C23—22no—
623C23—24no—
624C23—22no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—22no—
629C23—22no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—24no—
640C23—24no—
641C23—42no—
642C23—42no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—42no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—42no—
651C23—41no—
652C23—41no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23#88214yes—
660C23#88314yes—
661C23#88514yes—
662C23#88614yes—
663C23#93014yes—
664C23#93814yes—
665C23#93914yes—
666C23C22×D1211yescharacteristic
667C23C2×#23511yescharacteristic
668C23C2×D3×D411yescharacteristic
669C23C2×D3×D411yescharacteristic
670C23C2×#23711yescharacteristic
671C23C2×#23711yescharacteristic
672C23C2×#23712yes—
673C23#100412yes—
674C23D3×#4112yes—
675C23#101012yes—
676C23C22×#6711yescharacteristic
677D4—416no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—416no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—64no—
706C2×C4—64no—
707C2×C4—64no—
708C2×C4—64no—
709C2×C4—64no—
710C2×C4—64no—
711C2×C4—64no—
712C2×C4—64no—
713C2×C4—64no—
714C2×C4—1216no—
715C2×C4—1216no—
716C2×C4—122no—
717C2×C4—122no—
718C2×C4—122no—
719C2×C4—122no—
720C2×C4—122no—
721C2×C4—122no—
722C2×C4—122no—
723C2×C4—122no—
724C2×C4—122no—
725C2×C4—122no—
726C2×C4—122no—
727C2×C4—122no—
728C2×C4—122no—
729C2×C4—122no—
730C2×C4—122no—
731C2×C4—122no—
732C2×C4—122no—
733C2×C4—122no—
734C2×C4—122no—
735C2×C4#93514yescomplemented
736C2×C3—28no—
737C2×C3—82no—
738C2×C3C2×#39411yescharacteristic
739C2×C3#241211yescharacteristic
740C2×C3#241311yescharacteristic
741C2×C3#241912yes—
742C2×C3#243012yes—
743C2×C3#248611yescharacteristic
744C2×C3#248812yes—
745C2×C3#249812yes—
746C2×C3#253411yescharacteristic
747C2×C3#261811yescharacteristic
748C2×C3#285411yescharacteristic
749C22—24no—
750C22—24no—
751C22—24no—
752C22—24no—
753C22—28no—
754C22—28no—
755C22—24no—
756C22—24no—
757C22—28no—
758C22—28no—
759C22—42no—
760C22—42no—
761C22—44no—
762C22—44no—
763C22—42no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—82no—
769C22—82no—
770C22#496118yes—
771C22C2×#88211yescharacteristic
772C22C2×#88311yescharacteristic
773C22C2×#88511yescharacteristic
774C22C2×#88611yescharacteristic
775C22#554112yes—
776C22#555412yes—
777C22#555512yes—
778C22#555612yes—
779C22#558712yes—
780C22#559112yes—
781C22#559612yes—
782C22#559712yes—
783C22#560012yes—
784C22#560212yes—
785C22#565012yes—
786C22#565512yes—
787C22C2×#93011yescharacteristic
788C22C2×#93511yescharacteristic
789C22C2×#93811yescharacteristic
790C22C2×#93911yescharacteristic
791C22#580411yescharacteristic
792C22#582511yescharacteristic
793C22#582811yescharacteristic
794C4—24no—
795C4—42no—
796C4—42no—
797C4—81no—
798C4—81no—
799C4—124no—
800C4—124no—
801C4—124no—
802C4—242no—
803C3#1492711yescharacteristic, complemented, Sylow
804C2—28no—
805C2—82no—
806C2#7469412yes—
807C2#7469912yes—
808C2#7474012yes—
809C2#7474112yes—
810C2C2×#496111yescharacteristic
811C2#8237311yescharacteristic
812C2#8241411yescharacteristic
813C2#8258411yescharacteristic
814C2#8267511yescharacteristic
815C2#8269911yescharacteristic
816C2#8284311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#386C2
prime radicalC23×C3×D4C22
hypercenterC2×#386D3
hypocenterC3#14927
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
4. C2×#5212C2semidirect
5. C22×C3⋊#95C2semidirect
6. C2×#4943C2semidirect
7. #71549C2semidirect
8. #71546C2semidirect
9. #71544C2semidirect
10. #69413C2semidirect
11. #69411C2semidirect
424. C2×C3×C4#123semidirect
735. C2×C4#935semidirect
803. C3#14927semidirect

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
C2×#52122
C22×C3⋊#952
C2×#49432
#715492
#715462
#715442
#694132
#694112
#149273