Finite Group Databasebeta

← #10726661

Subgroups — #10726661

Order 768.

4034 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C22⋊C4C211yesmaximal, characteristic, complemented
2C22×#953C211yesmaximal, characteristic
3C2×#5247C211yesmaximal, characteristic, complemented
4C2×#5213C211yesmaximal, characteristic, complemented
5C2×#5213C211yesmaximal, characteristic, complemented
6C2×#5212C211yesmaximal, characteristic, complemented
7C2×#4961C212yesmaximal, complemented
8#72127C211yesmaximal, characteristic, complemented
9#71550C212yesmaximal, complemented
10#71549C212yesmaximal, complemented
11#71546C212yesmaximal, complemented
12#14725—31nomaximal, Sylow
13C26×C3C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C24×C3×C4C2211yescharacteristic
16C23×#67C2211yescharacteristic
17C23×#67C2212yes—
18C22×C3×C22⋊C4—24no—
19C22×C3×C22⋊C4—28no—
20C22×C3×C22⋊C4C2212yes—
21C22×C3×C22⋊C4C2212yes—
22C2×#953—24no—
23C2×#953—24no—
24C2×#953—24no—
25C22×#217C2212yes—
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2212yes—
29C22×#217C2211yescharacteristic
30C22×#217C2212yes—
31C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
32C22×(C2×D3)⋊C4C2212yescomplemented
33C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
34C22×C4⋊Dic3C2212yescomplemented
35#5247—24no—
36#5213—24no—
37#5213—24no—
38#5212—24no—
39C2×C3⋊#95C2212yescomplemented
40C2×C3⋊#95C2211yescharacteristic, complemented
41C2×C3⋊#95C2212yescomplemented
42C2×C3⋊#95C2211yescharacteristic, complemented
43C2×C3⋊#95C2212yescomplemented
44C2×C3⋊#95C2212yescomplemented
45#4961—28no—
46C22×#120—31no—
47C23×C22⋊C4D311yescharacteristic, complemented
48C2×#394—32no—
49C2×#386—31no—
50C2×#386—31no—
51C2×#380—31no—
52C2×#379—31no—
53#1440—32no—
54#1439—32no—
55#1438—32no—
56C22⋊#95—31no—
57C25×C3—24no—
58C25×C3—22no—
59C25×C3—24no—
60C25×C3—22no—
61C25×C3—22no—
62C25×C3—22no—
63C25×C3—22no—
64C25×C3—22no—
65C25×C3—42no—
66C25×C3—42no—
67C25×C3D414yes—
68C25×C3C2312yes—
69C25×C3C2311yescharacteristic
70C24×D3C2311yescharacteristic
71C23×C3×C4—22no—
72C23×C3×C4—22no—
73C23×C3×C4—22no—
74C23×C3×C4—24no—
75C23×C3×C4—24no—
76C23×C3×C4—22no—
77C23×C3×C4—22no—
78C23×C3×C4—42no—
79C23×C3×C4—42no—
80C23×C3×C4D414yescomplemented
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2312yes—
83C23×C3×C4C2311yescharacteristic
84C22×#67—22no—
85C22×#67—24no—
86C22×#67—22no—
87C22×#67—22no—
88C22×#67—22no—
89C22×#67—22no—
90C22×#67—22no—
91C22×#67—24no—
92C22×#67—24no—
93C22×#67—24no—
94C22×#67—24no—
95C22×#67—42no—
96C22×#67—42no—
97C22×#67D414yes—
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2312yes—
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2312yes—
103C2×C3×C22⋊C4—232no—
104C2×C3×C22⋊C4—24no—
105C2×C3×C22⋊C4—24no—
106C2×C3×C22⋊C4—24no—
107C2×C3×C22⋊C4—24no—
108C2×C3×C22⋊C4—24no—
109C2×C3×C22⋊C4D418yescomplemented
110#953—232no—
111C2×#217—24no—
112C2×#217—22no—
113C2×#217—22no—
114C2×#217—24no—
115C2×#217—24no—
116C2×#217—22no—
117C2×#217—22no—
118C2×#217—22no—
119C2×#217—24no—
120C2×#217—24no—
121C2×#217—22no—
122C2×#217—24no—
123C2×#217—22no—
124C2×#217—24no—
125C2×#217—22no—
126C2×#217—42no—
127C2×#217—42no—
128C2×#217D414yes—
129C2×(C2×D3)⋊C4—24no—
130C2×(C2×D3)⋊C4—22no—
131C2×(C2×D3)⋊C4—22no—
132C2×(C2×D3)⋊C4—24no—
133C2×(C2×D3)⋊C4—24no—
134C2×(C2×D3)⋊C4—42no—
135C2×(C2×D3)⋊C4—42no—
136C2×C4⋊Dic3—24no—
137C2×C4⋊Dic3—24no—
138C2×C4⋊Dic3—42no—
139C3⋊#95—22no—
140C3⋊#95—22no—
141C3⋊#95—24no—
142C3⋊#95—24no—
143C3⋊#95—24no—
144C3⋊#95—42no—
145C26C2×D311yescharacteristic
146C23×D4—31no—
147C23×D4—32no—
148C24×C4C2×D311yescharacteristic
149C24×C4C2×D311yescharacteristic
150C2×#120—64no—
151C2×#120—64no—
152C2×#120—64no—
153C22×C4⋊C4—32no—
154C22×C22⋊C4—24no—
155C22×C22⋊C4—28no—
156C22×C22⋊C4—31no—
157C22×C22⋊C4—32no—
158C22×C22⋊C4—32no—
159C22×C22⋊C4—31no—
160C22×C22⋊C4—31no—
161C22×C22⋊C4—31no—
162C22×C22⋊C4—32no—
163C22×C22⋊C4—32no—
164C22×C22⋊C4—31no—
165C22×C22⋊C4C2×D312yes—
166C22×C22⋊C4C2×D312yes—
167#394—68no—
168#386—64no—
169#386—64no—
170#380—64no—
171#379—64no—
172C2×#95—32no—
173C2×#95—32no—
174C2×#95—31no—
175C2×#95—32no—
176C2×#95—31no—
177C2×#95—32no—
178C24×C3—22no—
179C24×C3—22no—
180C24×C3—22no—
181C24×C3—22no—
182C24×C3—28no—
183C24×C3—216no—
184C24×C3—28no—
185C24×C3—216no—
186C24×C3—28no—
187C24×C3—22no—
188C24×C3—22no—
189C24×C3—22no—
190C24×C3—22no—
191C24×C3—22no—
192C24×C3—22no—
193C24×C3—22no—
194C24×C3—22no—
195C24×C3—22no—
196C24×C3—22no—
197C24×C3—22no—
198C24×C3—22no—
199C24×C3—28no—
200C24×C3—28no—
201C24×C3—48no—
202C24×C3—48no—
203C24×C3—48no—
204C24×C3—48no—
205C24×C3—48no—
206C24×C3—48no—
207C24×C3—48no—
208C24×C3—48no—
209C24×C3—48no—
210C24×C3—44no—
211C24×C3—44no—
212C24×C3—48no—
213C24×C3—44no—
214C24×C3—44no—
215C24×C3—44no—
216C24×C3—44no—
217C24×C3C2×D414yes—
218C24×C3C2×D412yes—
219C24×C3C2×D412yes—
220C24×C3C2×D412yes—
221C24×C3C2×D414yes—
222C24×C3C2×D412yes—
223C24×C3#4114yes—
224C24×C3#4112yes—
225C24×C3#4112yes—
226C24×C3#4112yes—
227C24×C3C2411yescharacteristic
228C23×D3—21no—
229C23×D3—22no—
230C23×D3—21no—
231C23×D3—21no—
232C23×D3—21no—
233C23×D3—22no—
234C23×D3—21no—
235C23×D3—21no—
236C23×D3—22no—
237C23×D3—22no—
238C23×D3C2×D412yes—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—22no—
242C22×C3×C4—28no—
243C22×C3×C4—28no—
244C22×C3×C4—21no—
245C22×C3×C4—22no—
246C22×C3×C4—22no—
247C22×C3×C4—22no—
248C22×C3×C4—22no—
249C22×C3×C4—21no—
250C22×C3×C4—22no—
251C22×C3×C4—22no—
252C22×C3×C4—22no—
253C22×C3×C4—22no—
254C22×C3×C4—28no—
255C22×C3×C4—44no—
256C22×C3×C4—48no—
257C22×C3×C4—48no—
258C22×C3×C4—48no—
259C22×C3×C4—48no—
260C22×C3×C4—44no—
261C22×C3×C4—44no—
262C22×C3×C4C2×D412yes—
263C22×C3×C4C2×D414yes—
264C22×C3×C4C2×D412yes—
265C22×C3×C4C2×D414yes—
266C2×#67—216no—
267C2×#67—28no—
268C2×#67—28no—
269C2×#67—28no—
270C2×#67—48no—
271C2×#67—48no—
272C2×#67—48no—
273C2×#67—48no—
274C2×#67—48no—
275C2×#67—48no—
276C2×#67—44no—
277C2×#67—44no—
278C2×#67—44no—
279C2×#67—44no—
280C22×Dic3—21no—
281C22×Dic3—22no—
282C22×Dic3—21no—
283C22×Dic3—22no—
284C22×Dic3—21no—
285C22×Dic3—22no—
286C22×Dic3—21no—
287C22×Dic3—22no—
288C22×Dic3—21no—
289C22×Dic3—21no—
290C22×Dic3—22no—
291C22×Dic3—22no—
292C22×Dic3—22no—
293C22×Dic3—22no—
294C22×Dic3—21no—
295C22×Dic3—22no—
296C22×Dic3—21no—
297C22×Dic3—22no—
298C22×Dic3—22no—
299C22×Dic3—21no—
300C22×Dic3—21no—
301C22×Dic3—21no—
302C22×Dic3—22no—
303C22×Dic3—21no—
304C22×Dic3—22no—
305C22×Dic3—22no—
306C22×Dic3—22no—
307C22×Dic3—22no—
308C22×Dic3—22no—
309C22×Dic3C2×D412yes—
310C22×Dic3C2×D414yes—
311C3×C22⋊C4—216no—
312C3×C22⋊C4—216no—
313#217—216no—
314#217—28no—
315#217—48no—
316#217—44no—
317#217—48no—
318#217—44no—
319(C2×D3)⋊C4—48no—
320(C2×D3)⋊C4—44no—
321(C2×D3)⋊C4—44no—
322C4⋊Dic3—48no—
323C25—24no—
324C25—22no—
325C25—24no—
326C25—22no—
327C25—22no—
328C25—22no—
329C25—22no—
330C25—22no—
331C25—31no—
332C25—42no—
333C25—42no—
334C25D1214yes—
335C25C22×D312yes—
336C25C22×D311yescharacteristic
337C22×D4—34no—
338C22×D4—64no—
339C22×D4—64no—
340C22×D4—64no—
341C22×D4—62no—
342C22×D4—62no—
343C22×D4—62no—
344C22×D4—62no—
345C22×D4—62no—
346C22×D4—62no—
347C22×D4—64no—
348C22×D4—64no—
349C22×D4—122no—
350C22×D4—122no—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—24no—
355C23×C4—24no—
356C23×C4—22no—
357C23×C4—22no—
358C23×C4—32no—
359C23×C4—31no—
360C23×C4—32no—
361C23×C4—31no—
362C23×C4—31no—
363C23×C4—42no—
364C23×C4—42no—
365C23×C4#6714yescomplemented
366C23×C4C22×D311yescharacteristic
367C23×C4C22×D312yes—
368C23×C4C22×D311yescharacteristic
369#120—632no—
370C2×C4⋊C4—64no—
371C2×C4⋊C4—64no—
372C2×C4⋊C4—122no—
373C2×C22⋊C4—232no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—34no—
380C2×C22⋊C4—64no—
381C2×C22⋊C4—64no—
382C2×C22⋊C4—64no—
383C2×C22⋊C4—62no—
384C2×C22⋊C4—62no—
385C2×C22⋊C4—64no—
386C2×C22⋊C4—64no—
387C2×C22⋊C4—62no—
388C2×C22⋊C4—64no—
389C2×C22⋊C4—62no—
390C2×C22⋊C4—64no—
391C2×C22⋊C4—62no—
392C2×C22⋊C4—62no—
393C2×C22⋊C4—62no—
394C2×C22⋊C4—62no—
395C2×C22⋊C4—64no—
396C2×C22⋊C4—62no—
397C2×C22⋊C4—62no—
398C2×C22⋊C4—64no—
399C2×C22⋊C4—64no—
400C2×C22⋊C4—122no—
401C2×C22⋊C4—122no—
402C2×C22⋊C4—122no—
403C2×C22⋊C4—122no—
404C2×C22⋊C4#6718yescomplemented
405#95—64no—
406#95—64no—
407#95—62no—
408#95—62no—
409#95—64no—
410#95—122no—
411C23×C3—22no—
412C23×C3—24no—
413C23×C3—22no—
414C23×C3—24no—
415C23×C3—22no—
416C23×C3—24no—
417C23×C3—22no—
418C23×C3—24no—
419C23×C3—24no—
420C23×C3—24no—
421C23×C3—24no—
422C23×C3—24no—
423C23×C3—24no—
424C23×C3—24no—
425C23×C3—24no—
426C23×C3—24no—
427C23×C3—232no—
428C23×C3—24no—
429C23×C3—24no—
430C23×C3—24no—
431C23×C3—24no—
432C23×C3—24no—
433C23×C3—24no—
434C23×C3—24no—
435C23×C3—24no—
436C23×C3—24no—
437C23×C3—24no—
438C23×C3—24no—
439C23×C3—24no—
440C23×C3—24no—
441C23×C3—24no—
442C23×C3—24no—
443C23×C3—24no—
444C23×C3—24no—
445C23×C3—24no—
446C23×C3—432no—
447C23×C3—432no—
448C23×C3—416no—
449C23×C3—416no—
450C23×C3—416no—
451C23×C3—416no—
452C23×C3—432no—
453C23×C3—432no—
454C23×C3—416no—
455C23×C3—42no—
456C23×C3—42no—
457C23×C3—42no—
458C23×C3—42no—
459C23×C3—42no—
460C23×C3—42no—
461C23×C3—42no—
462C23×C3—42no—
463C23×C3—42no—
464C23×C3—42no—
465C23×C3—42no—
466C23×C3—42no—
467C23×C3—42no—
468C23×C3—42no—
469C23×C3—42no—
470C23×C3—42no—
471C23×C3—416no—
472C23×C3#12014yes—
473C23×C3#12118yes—
474C23×C3#12114yes—
475C23×C3#12114yes—
476C23×C3#12114yes—
477C23×C3#12314yes—
478C23×C3#12314yes—
479C23×C3#12414yes—
480C23×C3C22×D411yescharacteristic
481C23×C3C22×D411yescharacteristic
482C23×C3C22×D411yescharacteristic
483C23×C3C22×D411yescharacteristic
484C23×C3C22×D412yes—
485C23×C3C2×#4111yescharacteristic
486C23×C3C2×#4112yes—
487C23×C3C2×#4111yescharacteristic
488C23×C3C2×#4111yescharacteristic
489C23×C3H(5,𝔽2)12yes—
490C23×C3H(5,𝔽2)12yes—
491C22×D3—22no—
492C22×D3—22no—
493C22×D3—22no—
494C22×D3—24no—
495C22×D3—24no—
496C22×D3—41no—
497C22×D3—41no—
498C22×D3—42no—
499C22×D3—41no—
500C22×D3—41no—
501C22×D3—42no—
502C22×D3—41no—
503C22×D3—41no—
504C22×D3—41no—
505C22×D3—42no—
506C22×D3—41no—
507C22×D3—42no—
508C22×D3—42no—
509C22×D3—42no—
510C22×D3—42no—
511C22×D3—42no—
512C22×D3—42no—
513C22×D3—42no—
514C2×C3×C4—22no—
515C2×C3×C4—22no—
516C2×C3×C4—24no—
517C2×C3×C4—24no—
518C2×C3×C4—24no—
519C2×C3×C4—22no—
520C2×C3×C4—22no—
521C2×C3×C4—22no—
522C2×C3×C4—24no—
523C2×C3×C4—24no—
524C2×C3×C4—416no—
525C2×C3×C4—416no—
526C2×C3×C4—42no—
527C2×C3×C4—42no—
528C2×C3×C4—42no—
529C2×C3×C4—42no—
530C2×C3×C4—42no—
531C2×C3×C4—42no—
532C2×C3×C4#12014yescomplemented
533#67—432no—
534#67—416no—
535C2×Dic3—22no—
536C2×Dic3—24no—
537C2×Dic3—22no—
538C2×Dic3—22no—
539C2×Dic3—24no—
540C2×Dic3—24no—
541C2×Dic3—41no—
542C2×Dic3—42no—
543C2×Dic3—41no—
544C2×Dic3—41no—
545C2×Dic3—41no—
546C2×Dic3—42no—
547C2×Dic3—42no—
548C2×Dic3—42no—
549C2×Dic3—41no—
550C2×Dic3—42no—
551C2×Dic3—41no—
552C2×Dic3—42no—
553C2×Dic3—41no—
554C2×Dic3—42no—
555C2×Dic3—41no—
556C2×Dic3—42no—
557C2×Dic3—41no—
558C2×Dic3—42no—
559C2×Dic3—42no—
560C2×Dic3—41no—
561C2×Dic3—42no—
562C2×Dic3—42no—
563C2×Dic3—42no—
564C2×Dic3—42no—
565C2×Dic3—42no—
566C24—22no—
567C24—22no—
568C24—22no—
569C24—22no—
570C24—28no—
571C24—216no—
572C24—28no—
573C24—216no—
574C24—28no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—28no—
588C24—28no—
589C24—32no—
590C24—48no—
591C24—48no—
592C24—48no—
593C24—48no—
594C24—48no—
595C24—48no—
596C24—48no—
597C24—48no—
598C24—48no—
599C24—48no—
600C24—44no—
601C24—44no—
602C24—44no—
603C24—44no—
604C24—44no—
605C24—44no—
606C24—61no—
607C24—61no—
608C24—62no—
609C24—61no—
610C24—61no—
611C24—61no—
612C24—62no—
613C24—62no—
614C24—61no—
615C24—62no—
616C24C2×D1214yes—
617C24C2×D1212yes—
618C24#23514yes—
619C24#23512yes—
620C24D3×D412yes—
621C24D3×D412yes—
622C24#23712yes—
623C24#23712yes—
624C24C2×#6714yes—
625C24C2×#6712yes—
626C24C23×D311yescharacteristic
627C2×D4—616no—
628C2×D4—68no—
629C2×D4—68no—
630C2×D4—68no—
631C2×D4—128no—
632C2×D4—128no—
633C2×D4—128no—
634C2×D4—128no—
635C2×D4—128no—
636C2×D4—124no—
637C2×D4—124no—
638C2×D4—128no—
639C2×D4—124no—
640C2×D4—124no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—22no—
644C22×C4—28no—
645C22×C4—28no—
646C22×C4—21no—
647C22×C4—22no—
648C22×C4—21no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—28no—
657C22×C4—32no—
658C22×C4—34no—
659C22×C4—44no—
660C22×C4—48no—
661C22×C4—48no—
662C22×C4—48no—
663C22×C4—48no—
664C22×C4—44no—
665C22×C4—44no—
666C22×C4—61no—
667C22×C4—62no—
668C22×C4—61no—
669C22×C4—62no—
670C22×C4—62no—
671C22×C4—61no—
672C22×C4—61no—
673C22×C4—61no—
674C22×C4—62no—
675C22×C4—62no—
676C22×C4—61no—
677C22×C4—62no—
678C22×C4—62no—
679C22×C4—61no—
680C22×C4—61no—
681C22×C4—62no—
682C22×C4—61no—
683C22×C4—61no—
684C22×C4—62no—
685C22×C4—62no—
686C22×C4—62no—
687C22×C4—62no—
688C22×C4—62no—
689C22×C4—62no—
690C22×C4—62no—
691C22×C4—61no—
692C22×C4—62no—
693C22×C4—61no—
694C22×C4—62no—
695C22×C4C2×#6712yes—
696C22×C4C2×#6714yes—
697C22×C4C2×#6712yes—
698C22×C4C2×#6714yes—
699C4⋊C4—128no—
700C22⋊C4—216no—
701C22⋊C4—216no—
702C22⋊C4—616no—
703C22⋊C4—68no—
704C22⋊C4—128no—
705C22⋊C4—124no—
706C22⋊C4—128no—
707C22⋊C4—124no—
708C22⋊C4—128no—
709C22⋊C4—124no—
710C22⋊C4—124no—
711C22×C3—24no—
712C22×C3—24no—
713C22×C3—24no—
714C22×C3—24no—
715C22×C3—28no—
716C22×C3—24no—
717C22×C3—28no—
718C22×C3—28no—
719C22×C3—28no—
720C22×C3—24no—
721C22×C3—28no—
722C22×C3—28no—
723C22×C3—28no—
724C22×C3—464no—
725C22×C3—44no—
726C22×C3—44no—
727C22×C3—44no—
728C22×C3—44no—
729C22×C3—44no—
730C22×C3—44no—
731C22×C3—44no—
732C22×C3—44no—
733C22×C3—44no—
734C22×C3—44no—
735C22×C3—44no—
736C22×C3—44no—
737C22×C3#39418yescomplemented
738C22×C3C2×#12011yescharacteristic
739C22×C3C2×#12011yescharacteristic
740C22×C3C2×#12111yescharacteristic
741C22×C3C2×#12112yes—
742C22×C3C2×#12111yescharacteristic
743C22×C3C2×#12111yescharacteristic
744C22×C3C2×#12311yescharacteristic
745C22×C3C2×#12311yescharacteristic
746C22×C3#52511yescharacteristic
747C22×C3#52512yes—
748C22×C3C2×#12411yescharacteristic
749C22×C3#53412yes—
750C22×C3#53411yescharacteristic
751C22×C3#53511yescharacteristic
752C22×C3#53812yes—
753C22×C3D4212yes—
754C22×C3D4212yes—
755C22×C3#54612yes—
756C22×C3#54612yes—
757C22×C3#54612yes—
758C22×C3#54612yes—
759C22×C3#55112yes—
760C22×C3#55112yes—
761C2×D3—42no—
762C2×D3—42no—
763C2×D3—44no—
764C2×D3—44no—
765C2×D3—42no—
766C2×D3—81no—
767C2×D3—81no—
768C2×D3—81no—
769C2×D3—81no—
770C2×D3—82no—
771C2×D3—82no—
772C3×C4—24no—
773C3×C4—44no—
774C3×C4—42no—
775Dic3—42no—
776Dic3—44no—
777Dic3—81no—
778Dic3—81no—
779Dic3—82no—
780C23—24no—
781C23—24no—
782C23—24no—
783C23—24no—
784C23—24no—
785C23—24no—
786C23—24no—
787C23—24no—
788C23—22no—
789C23—24no—
790C23—24no—
791C23—22no—
792C23—22no—
793C23—24no—
794C23—24no—
795C23—22no—
796C23—232no—
797C23—24no—
798C23—24no—
799C23—24no—
800C23—24no—
801C23—24no—
802C23—24no—
803C23—24no—
804C23—24no—
805C23—24no—
806C23—24no—
807C23—24no—
808C23—24no—
809C23—24no—
810C23—24no—
811C23—24no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—432no—
816C23—432no—
817C23—416no—
818C23—416no—
819C23—416no—
820C23—432no—
821C23—432no—
822C23—416no—
823C23—416no—
824C23—416no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23—42no—
829C23—42no—
830C23—42no—
831C23—42no—
832C23—42no—
833C23—42no—
834C23—42no—
835C23—42no—
836C23—42no—
837C23—42no—
838C23—42no—
839C23—42no—
840C23—42no—
841C23—62no—
842C23—62no—
843C23—64no—
844C23—62no—
845C23—64no—
846C23—122no—
847C23—121no—
848C23—121no—
849C23—122no—
850C23—122no—
851C23—122no—
852C23—122no—
853C23—121no—
854C23—122no—
855C23—122no—
856C23—121no—
857C23—122no—
858C23—121no—
859C23—121no—
860C23—121no—
861C23—122no—
862C23—122no—
863C23—121no—
864C23#88214yes—
865C23#88314yes—
866C23#88514yes—
867C23#88614yes—
868C23#93018yes—
869C23#93014yes—
870C23#93814yes—
871C23#93914yes—
872C23C22×D1211yescharacteristic
873C23C2×#23511yescharacteristic
874C23C2×#23512yes—
875C23C2×D3×D411yescharacteristic
876C23C2×D3×D411yescharacteristic
877C23C2×#23711yescharacteristic
878C23C2×#23711yescharacteristic
879C23#100412yes—
880C23#100412yes—
881C23C22×#6711yescharacteristic
882C23C22×#6712yes—
883D4—1232no—
884D4—1216no—
885C2×C4—24no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—24no—
889C2×C4—24no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—24no—
893C2×C4—22no—
894C2×C4—24no—
895C2×C4—416no—
896C2×C4—416no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4—42no—
901C2×C4—42no—
902C2×C4—42no—
903C2×C4—62no—
904C2×C4—64no—
905C2×C4—62no—
906C2×C4—64no—
907C2×C4—62no—
908C2×C4—64no—
909C2×C4—122no—
910C2×C4—121no—
911C2×C4—121no—
912C2×C4—122no—
913C2×C4—121no—
914C2×C4—122no—
915C2×C4—122no—
916C2×C4—121no—
917C2×C4—122no—
918C2×C4—122no—
919C2×C4—122no—
920C2×C4—122no—
921C2×C4—122no—
922C2×C4—122no—
923C2×C4—121no—
924C2×C4—122no—
925C2×C4—122no—
926C2×C4—121no—
927C2×C4—121no—
928C2×C4—122no—
929C2×C4—122no—
930C2×C4—122no—
931C2×C4—121no—
932C2×C4—121no—
933C2×C4—121no—
934C2×C4#95314yescomplemented
935C2×C3—28no—
936C2×C3—48no—
937C2×C3C2×#39411yescharacteristic
938C2×C3#240811yescharacteristic
939C2×C3#241011yescharacteristic
940C2×C3#241012yes—
941C2×C3#241111yescharacteristic
942C2×C3#241212yes—
943C2×C3#241812yes—
944C2×C3#247212yes—
945C2×C3#253411yescharacteristic
946C2×C3#261711yescharacteristic
947C2×C3#284711yescharacteristic
948D3—82no—
949C22—24no—
950C22—24no—
951C22—24no—
952C22—24no—
953C22—28no—
954C22—28no—
955C22—28no—
956C22—28no—
957C22—24no—
958C22—24no—
959C22—28no—
960C22—28no—
961C22—28no—
962C22—464no—
963C22—44no—
964C22—44no—
965C22—44no—
966C22—44no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—44no—
974C22—44no—
975C22—122no—
976C22—122no—
977C22—124no—
978C22—124no—
979C22—122no—
980C22—241no—
981C22—241no—
982C22—241no—
983C22—242no—
984C22—242no—
985C22—241no—
986C22#496118yescomplemented
987C22C2×#88211yescharacteristic
988C22C2×#88311yescharacteristic
989C22#549012yes—
990C22#549012yes—
991C22C2×#88511yescharacteristic
992C22C2×#88611yescharacteristic
993C22#549312yes—
994C22#549412yes—
995C22#549512yes—
996C22#549512yes—
997C22C2×#93011yescharacteristic
998C22C2×#93012yes—
999C22#579111yescharacteristic
1000C22#579112yes—
1001C22C2×#93811yescharacteristic
1002C22D4×#6712yes—
1003C22D4×#6712yes—
1004C22C2×#93911yescharacteristic
1005C22#580411yescharacteristic
1006C22#580511yescharacteristic
1007C22#580612yes—
1008C22#580612yes—
1009C22C2×#95311yescharacteristic
1010C4—24no—
1011C4—42no—
1012C4—44no—
1013C4—122no—
1014C4—124no—
1015C4—241no—
1016C4—242no—
1017C4—241no—
1018C3#1472511yescharacteristic, complemented, Sylow
1019C2—28no—
1020C2—48no—
1021C2—242no—
1022C2C2×#496111yescharacteristic
1023C2#8210611yescharacteristic
1024C2#8210812yes—
1025C2#8211112yes—
1026C2#8212712yes—
1027C2#8212812yes—
1028C2#8212911yescharacteristic
1029C2#8213011yescharacteristic
1030C2#8403211yescharacteristic
1031C2#8404811yescharacteristic
1032C2#8405311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC23×C3×C22⋊C4C2
prime radicalC22×#953C2
hypercenterC23×C22⋊C4D3
hypocenterC3#14725
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C23×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×C3×C22⋊C4C2semidirect
3. C2×#5247C2semidirect
4. C2×#5213C2semidirect
5. C2×#5213C2semidirect
6. C2×#5212C2semidirect
7. C2×#4961C2semidirect
8. #72127C2semidirect
9. #71550C2semidirect
10. #71549C2semidirect
11. #71546C2semidirect
31. C22×(C2×D3)⋊C4C22semidirect
32. C22×(C2×D3)⋊C4C22semidirect
33. C22×(C2×D3)⋊C4C22semidirect
34. C22×C4⋊Dic3C22semidirect
39. C2×C3⋊#95C22semidirect
40. C2×C3⋊#95C22semidirect
41. C2×C3⋊#95C22semidirect
42. C2×C3⋊#95C22semidirect
43. C2×C3⋊#95C22semidirect
44. C2×C3⋊#95C22semidirect
47. C23×C22⋊C4D3semidirect
80. C23×C3×C4D4semidirect
109. C2×C3×C22⋊C4D4semidirect
365. C23×C4#67semidirect
404. C2×C22⋊C4#67semidirect
532. C2×C3×C4#120semidirect
737. C22×C3#394semidirect
934. C2×C4#953semidirect
986. C22#4961semidirect
1018. C3#14725semidirect

Maximal subgroups

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

subgroupindex
C23×C3×C22⋊C42
C22×#9532
C2×#52472
C2×#52132
C2×#52122
C2×#49612
#721272
#715502
#715492
#715462
#147253