Finite Group Databasebeta

← #10727875

Subgroups — #10727875

Order 768.

2278 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5223C211yesmaximal, characteristic
2C2×#5221C211yesmaximal, characteristic, complemented
3C2×#4959C212yesmaximal, complemented
4C2×#4948C212yesmaximal, complemented
5C2×#4957C212yesmaximal, complemented
6C2×#4670C211yesmaximal, characteristic, complemented
7C2×#4649C211yesmaximal, characteristic, complemented
8C3×#1438C211yesmaximal, characteristic, complemented
9#71545C212yesmaximal, complemented
10#69427C211yesmaximal, characteristic, complemented
11#69420C211yesmaximal, characteristic, complemented
12#14815—31nomaximal, Sylow
13C23×C3×D4C2211yescharacteristic
14C23×#67C2212yes—
15C22×C3×C22⋊C4C2212yes—
16C22×C3×C22⋊C4C2212yes—
17C22×#217C2212yes—
18C22×#217C2212yes—
19C22×#217C2212yes—
20C22×(C2×D3)⋊C4C2211yescharacteristic
21C22×(C2×D3)⋊C4C2211yescharacteristic
22C22×(C2×D3)⋊C4C2212yes—
23C22×(C2×D3)⋊C4C2211yescharacteristic
24C22×C4⋊Dic3C2211yescharacteristic
25C22×C4⋊Dic3C2211yescharacteristic
26C22×Dic3⋊C4C2212yes—
27C22×Dic3⋊C4C2212yes—
28C22×C4×Dic3C2212yes—
29C22×C4×Dic3C2211yescharacteristic
30C2×C3×#95C2211yescharacteristic
31C2×C3×#95C2211yescharacteristic
32#5223—24no—
33#5221—24no—
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2211yescharacteristic
37C2×C3⋊#95C2211yescharacteristic
38#4959—28no—
39#4957—28no—
40#4948—28no—
41#4670—24no—
42#4649—24no—
43C2×#396—32no—
44C2×#394—32no—
45C2×#392—31no—
46C2×#390—31no—
47C2×#390—32no—
48C2×#388—31no—
49C2×C4×C4⋊C4—31no—
50#1444—31no—
51#1439—31no—
52#1438D311yescharacteristic, complemented
53#1437—32no—
54C25×C3C2312yes—
55C24×D3C2311yescharacteristic
56C22×C3×D4—24no—
57C22×C3×D4—22no—
58C22×C3×D4—22no—
59C22×C3×D4—22no—
60C22×C3×D4—42no—
61C23×C3×C4C2311yescharacteristic
62C23×C3×C4C2312yes—
63C23×C3×C4C2311yescharacteristic
64C23×C3×C4C2311yescharacteristic
65C22×#67—24no—
66C22×#67—24no—
67C22×#67—24no—
68C22×#67—24no—
69C22×#67—24no—
70C22×#67—42no—
71C22×#67—42no—
72C23×Dic3C2311yescharacteristic
73C23×Dic3C2312yes—
74C23×Dic3C2311yescharacteristic
75C23×Dic3C2312yes—
76C23×Dic3C2311yescharacteristic
77C2×C3×C22⋊C4—24no—
78C2×C3×C22⋊C4—24no—
79C2×C3×C22⋊C4—24no—
80C2×C3×C22⋊C4—24no—
81C2×C3×C22⋊C4—42no—
82C2×C3×C22⋊C4—42no—
83C2×#217—24no—
84C2×#217—24no—
85C2×#217—24no—
86C2×#217—24no—
87C2×#217—24no—
88C2×#217—24no—
89C2×#217—24no—
90C2×#217—24no—
91C2×#217—24no—
92C2×(C2×D3)⋊C4—22no—
93C2×(C2×D3)⋊C4—22no—
94C2×(C2×D3)⋊C4—24no—
95C2×(C2×D3)⋊C4—22no—
96C2×(C2×D3)⋊C4—24no—
97C2×(C2×D3)⋊C4—22no—
98C2×(C2×D3)⋊C4—22no—
99C2×(C2×D3)⋊C4—22no—
100C2×(C2×D3)⋊C4—24no—
101C2×(C2×D3)⋊C4—42no—
102C2×(C2×D3)⋊C4D414yescomplemented
103C2×C4⋊Dic3—22no—
104C2×C4⋊Dic3—22no—
105C2×C4⋊Dic3—24no—
106C2×C4⋊Dic3—42no—
107C2×Dic3⋊C4—24no—
108C2×Dic3⋊C4—24no—
109C2×Dic3⋊C4—24no—
110C2×Dic3⋊C4—24no—
111C2×Dic3⋊C4—42no—
112C2×Dic3⋊C4D418yescomplemented
113C2×C4×Dic3—22no—
114C2×C4×Dic3—22no—
115C2×C4×Dic3—24no—
116C2×C4×Dic3—24no—
117C2×C4×Dic3—42no—
118C2×C4×Dic3D414yescomplemented
119C3×#95—22no—
120C3×#95—22no—
121C3⋊#95—24no—
122C3⋊#95—22no—
123C3⋊#95—24no—
124C3⋊#95D414yes—
125C23×D4—32no—
126C23×D4C2×D311yescharacteristic
127C22×C4⋊C4—32no—
128C22×C4⋊C4—31no—
129C22×C4⋊C4—32no—
130C22×C4⋊C4—31no—
131C22×C22⋊C4—31no—
132C22×C22⋊C4—32no—
133C22×C22⋊C4—32no—
134C22×C22⋊C4—32no—
135C22×C22⋊C4—31no—
136C22×C22⋊C4—31no—
137C22×C22⋊C4—32no—
138C22×C22⋊C4C2×D312yes—
139C22×C22⋊C4C2×D312yes—
140C22×C42—31no—
141C22×C42—32no—
142#396—68no—
143#394—68no—
144#392—64no—
145#390—64no—
146#390—68no—
147#388—64no—
148C4×C4⋊C4—64no—
149C2×#95—31no—
150C2×#95—32no—
151C2×#95—32no—
152C2×#95—31no—
153C2×#95C2×D311yescharacteristic
154C2×#95C2×D311yescharacteristic
155C24×C3—22no—
156C24×C3—22no—
157C24×C3—22no—
158C24×C3—22no—
159C24×C3—22no—
160C24×C3—22no—
161C24×C3—22no—
162C24×C3—22no—
163C24×C3—22no—
164C24×C3—22no—
165C24×C3—22no—
166C24×C3—22no—
167C24×C3—22no—
168C24×C3—22no—
169C24×C3#4114yes—
170C24×C3C2411yescharacteristic
171C23×D3—21no—
172C23×D3—22no—
173C23×D3—21no—
174C23×D3—21no—
175C23×D3—21no—
176C23×D3—22no—
177C23×D3—22no—
178C23×D3—22no—
179C23×D3—21no—
180C23×D3—21no—
181C23×D3C2×D412yes—
182C2×C3×D4—28no—
183C2×C3×D4—48no—
184C2×C3×D4—48no—
185C2×C3×D4—44no—
186C2×C3×D4—44no—
187C22×C3×C4—22no—
188C22×C3×C4—22no—
189C22×C3×C4—22no—
190C22×C3×C4—21no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—21no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—21no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4C2×D414yes—
205C22×C3×C4C2×D412yes—
206C22×C3×C4C2×D412yes—
207C22×C3×C4C2×D412yes—
208C22×C3×C4#4112yes—
209C2×#67—216no—
210C2×#67—48no—
211C2×#67—48no—
212C2×#67—48no—
213C2×#67—48no—
214C2×#67—48no—
215C2×#67—48no—
216C22×Dic3—21no—
217C22×Dic3—21no—
218C22×Dic3—22no—
219C22×Dic3—21no—
220C22×Dic3—21no—
221C22×Dic3—22no—
222C22×Dic3—22no—
223C22×Dic3—21no—
224C22×Dic3—22no—
225C22×Dic3—22no—
226C22×Dic3—21no—
227C22×Dic3—22no—
228C22×Dic3—21no—
229C22×Dic3—22no—
230C22×Dic3—22no—
231C22×Dic3—22no—
232C22×Dic3—22no—
233C22×Dic3—21no—
234C22×Dic3—21no—
235C22×Dic3—22no—
236C22×Dic3—22no—
237C22×Dic3—22no—
238C22×Dic3—22no—
239C22×Dic3C2×D412yes—
240C22×Dic3C2×D414yes—
241C22×Dic3C2×D414yes—
242C22×Dic3C2×D412yes—
243C22×Dic3C2×D412yes—
244C22×Dic3C2×D414yes—
245C22×Dic3#4114yes—
246C22×Dic3#4112yes—
247C3×C22⋊C4—48no—
248C3×C22⋊C4—48no—
249#217—48no—
250#217—48no—
251#217—48no—
252(C2×D3)⋊C4—28no—
253(C2×D3)⋊C4—48no—
254(C2×D3)⋊C4—44no—
255(C2×D3)⋊C4—44no—
256C4⋊Dic3—44no—
257C4⋊Dic3—44no—
258Dic3⋊C4—216no—
259Dic3⋊C4—48no—
260C4×Dic3—28no—
261C4×Dic3—48no—
262C25—31no—
263C25C22×D312yes—
264C22×D4—24no—
265C22×D4—22no—
266C22×D4—22no—
267C22×D4—22no—
268C22×D4—42no—
269C22×D4—64no—
270C22×D4—64no—
271C22×D4—64no—
272C22×D4—64no—
273C22×D4—64no—
274C22×D4—122no—
275C22×D4—122no—
276C23×C4—31no—
277C23×C4—31no—
278C23×C4—32no—
279C23×C4—32no—
280C23×C4—31no—
281C23×C4C22×D311yescharacteristic
282C23×C4C22×D311yescharacteristic
283C23×C4C22×D312yes—
284C23×C4C22×D311yescharacteristic
285C2×C4⋊C4—38no—
286C2×C4⋊C4—64no—
287C2×C4⋊C4—64no—
288C2×C4⋊C4—62no—
289C2×C4⋊C4—64no—
290C2×C4⋊C4—64no—
291C2×C4⋊C4—64no—
292C2×C4⋊C4—62no—
293C2×C4⋊C4—122no—
294C2×C4⋊C4—122no—
295C2×C22⋊C4—24no—
296C2×C22⋊C4—24no—
297C2×C22⋊C4—24no—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—34no—
300C2×C22⋊C4—42no—
301C2×C22⋊C4—42no—
302C2×C22⋊C4—62no—
303C2×C22⋊C4—62no—
304C2×C22⋊C4—62no—
305C2×C22⋊C4—64no—
306C2×C22⋊C4—64no—
307C2×C22⋊C4—64no—
308C2×C22⋊C4—64no—
309C2×C22⋊C4—64no—
310C2×C22⋊C4—64no—
311C2×C22⋊C4—64no—
312C2×C22⋊C4—64no—
313C2×C22⋊C4—64no—
314C2×C22⋊C4—64no—
315C2×C22⋊C4—64no—
316C2×C22⋊C4—62no—
317C2×C22⋊C4—62no—
318C2×C22⋊C4—62no—
319C2×C22⋊C4—64no—
320C2×C22⋊C4—122no—
321C2×C42—34no—
322C2×C42—62no—
323C2×C42—62no—
324C2×C42—64no—
325C2×C42—64no—
326C2×C42—122no—
327#95—22no—
328#95—22no—
329#95—34no—
330#95—62no—
331#95—64no—
332#95—64no—
333C23×C3—24no—
334C23×C3—24no—
335C23×C3—24no—
336C23×C3—24no—
337C23×C3—24no—
338C23×C3—24no—
339C23×C3—24no—
340C23×C3—42no—
341C23×C3—42no—
342C23×C3—42no—
343C23×C3—42no—
344C23×C3—42no—
345C23×C3—42no—
346C23×C3—42no—
347C23×C3—42no—
348C23×C3—42no—
349C23×C3—42no—
350C23×C3—42no—
351C23×C3—42no—
352C23×C3—42no—
353C23×C3—42no—
354C23×C3—42no—
355C23×C3—42no—
356C23×C3—42no—
357C23×C3—42no—
358C23×C3—42no—
359C23×C3—42no—
360C23×C3—42no—
361C23×C3—42no—
362C23×C3—42no—
363C23×C3—42no—
364C23×C3—42no—
365C23×C3—42no—
366C23×C3—42no—
367C23×C3—42no—
368C23×C3C22×D411yescharacteristic
369C23×C3C22×D411yescharacteristic
370C23×C3C22×D411yescharacteristic
371C23×C3C22×D412yes—
372C23×C3C2×#4111yescharacteristic
373C23×C3C2×#4112yes—
374C23×C3C2×#4112yes—
375C23×C3C2×#4111yescharacteristic
376C23×C3H(5,𝔽2)12yes—
377C23×C3H(5,𝔽2)11yescharacteristic
378C23×C32−1+411yescharacteristic
379C22×D3—22no—
380C22×D3—24no—
381C22×D3—24no—
382C22×D3—22no—
383C22×D3—22no—
384C22×D3—41no—
385C22×D3—42no—
386C22×D3—41no—
387C22×D3—42no—
388C22×D3—41no—
389C22×D3—41no—
390C22×D3—42no—
391C22×D3—41no—
392C22×D3—41no—
393C22×D3—42no—
394C22×D3—42no—
395C22×D3—42no—
396C22×D3—42no—
397C22×D3—41no—
398C22×D3—42no—
399C22×D3—42no—
400C22×D3—42no—
401C22×D3—41no—
402C3×D4—416no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—24no—
406C2×C3×C4—24no—
407C2×C3×C4—24no—
408C2×C3×C4—22no—
409C2×C3×C4—24no—
410C2×C3×C4—24no—
411C2×C3×C4—24no—
412C2×C3×C4—42no—
413C2×C3×C4—41no—
414C2×C3×C4—41no—
415C2×C3×C4—42no—
416C2×C3×C4—42no—
417C2×C3×C4—42no—
418C2×C3×C4—42no—
419C2×C3×C4—41no—
420C2×C3×C4—41no—
421C2×C3×C4—41no—
422C2×C3×C4—42no—
423C2×C3×C4—42no—
424C2×C3×C4#12114yes—
425#67—432no—
426C2×Dic3—22no—
427C2×Dic3—22no—
428C2×Dic3—24no—
429C2×Dic3—24no—
430C2×Dic3—22no—
431C2×Dic3—24no—
432C2×Dic3—22no—
433C2×Dic3—24no—
434C2×Dic3—22no—
435C2×Dic3—24no—
436C2×Dic3—24no—
437C2×Dic3—24no—
438C2×Dic3—24no—
439C2×Dic3—22no—
440C2×Dic3—22no—
441C2×Dic3—22no—
442C2×Dic3—41no—
443C2×Dic3—42no—
444C2×Dic3—42no—
445C2×Dic3—41no—
446C2×Dic3—42no—
447C2×Dic3—41no—
448C2×Dic3—42no—
449C2×Dic3—42no—
450C2×Dic3—42no—
451C2×Dic3—42no—
452C2×Dic3—42no—
453C2×Dic3—42no—
454C2×Dic3#12118yes—
455C2×Dic3#12114yes—
456C2×Dic3#12714yes—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—32no—
472C24—61no—
473C24—61no—
474C24—62no—
475C24—61no—
476C24—62no—
477C24—62no—
478C24—61no—
479C24—61no—
480C24—62no—
481C24—61no—
482C24#23714yes—
483C24C23×D311yescharacteristic
484C2×D4—28no—
485C2×D4—48no—
486C2×D4—48no—
487C2×D4—44no—
488C2×D4—44no—
489C2×D4—616no—
490C2×D4—128no—
491C2×D4—128no—
492C2×D4—128no—
493C2×D4—128no—
494C2×D4—128no—
495C2×D4—128no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—34no—
514C22×C4—32no—
515C22×C4—34no—
516C22×C4—32no—
517C22×C4—32no—
518C22×C4—34no—
519C22×C4—32no—
520C22×C4—34no—
521C22×C4—61no—
522C22×C4—61no—
523C22×C4—61no—
524C22×C4—61no—
525C22×C4—62no—
526C22×C4—62no—
527C22×C4—61no—
528C22×C4—62no—
529C22×C4—62no—
530C22×C4—62no—
531C22×C4—61no—
532C22×C4—61no—
533C22×C4—62no—
534C22×C4—61no—
535C22×C4—62no—
536C22×C4—62no—
537C22×C4—61no—
538C22×C4—62no—
539C22×C4—62no—
540C22×C4—62no—
541C22×C4—62no—
542C22×C4—62no—
543C22×C4—62no—
544C22×C4#23512yes—
545C22×C4D3×D414yes—
546C22×C4D3×D412yes—
547C22×C4D3×D412yes—
548C22×C4D3×D412yes—
549C4⋊C4—616no—
550C4⋊C4—128no—
551C4⋊C4—124no—
552C4⋊C4—124no—
553C22⋊C4—48no—
554C22⋊C4—48no—
555C22⋊C4—68no—
556C22⋊C4—128no—
557C22⋊C4—124no—
558C22⋊C4—128no—
559C22⋊C4—128no—
560C22⋊C4—128no—
561C22⋊C4—124no—
562C42—68no—
563C42—128no—
564C22×C3—44no—
565C22×C3—44no—
566C22×C3—44no—
567C22×C3—44no—
568C22×C3—44no—
569C22×C3—44no—
570C22×C3—44no—
571C22×C3—82no—
572C22×C3—82no—
573C22×C3—82no—
574C22×C3—82no—
575C22×C3—82no—
576C22×C3—82no—
577C22×C3—82no—
578C22×C3—82no—
579C22×C3C2×#12111yescharacteristic
580C22×C3C2×#12112yes—
581C22×C3C2×#12111yescharacteristic
582C22×C3#52511yescharacteristic
583C22×C3#52512yes—
584C22×C3#52912yes—
585C22×C3C2×#12711yescharacteristic
586C22×C3#53211yescharacteristic
587C22×C3#53212yes—
588C22×C3#53511yescharacteristic
589C22×C3#53711yescharacteristic
590C22×C3#53812yes—
591C22×C3#54212yes—
592C22×C3D4211yescharacteristic
593C22×C3D4212yes—
594C22×C3#54612yes—
595C22×C3#54612yes—
596C22×C3#54711yescharacteristic
597C22×C3#54811yescharacteristic
598C22×C3#54812yes—
599C22×C3#55012yes—
600C22×C3#55112yes—
601C22×C3#55311yescharacteristic
602C2×D3—42no—
603C2×D3—42no—
604C2×D3—44no—
605C2×D3—44no—
606C2×D3—42no—
607C2×D3—81no—
608C2×D3—81no—
609C2×D3—81no—
610C2×D3—82no—
611C2×D3—81no—
612C2×D3—82no—
613C3×C4—24no—
614C3×C4—44no—
615C3×C4—42no—
616C3×C4—81no—
617Dic3—24no—
618Dic3—24no—
619Dic3—28no—
620Dic3—81no—
621Dic3—82no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—62no—
658C23—62no—
659C23—64no—
660C23—62no—
661C23—64no—
662C23—122no—
663C23—122no—
664C23—121no—
665C23—121no—
666C23—121no—
667C23—121no—
668C23—122no—
669C23—122no—
670C23—121no—
671C23—121no—
672C23—122no—
673C23—122no—
674C23—121no—
675C23—122no—
676C23—122no—
677C23—122no—
678C23—121no—
679C23—122no—
680C23C2×#23511yescharacteristic
681C23C2×D3×D411yescharacteristic
682C23C2×D3×D411yescharacteristic
683C23C2×D3×D412yes—
684C23C2×D3×D411yescharacteristic
685C23C2×#23712yes—
686C23#100412yes—
687C23#100411yescharacteristic
688C23D3×#4111yescharacteristic
689C23D3×#4112yes—
690C23#101011yescharacteristic
691D4—416no—
692D4—1232no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—34no—
703C2×C4—34no—
704C2×C4—38no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—41no—
717C2×C4—62no—
718C2×C4—62no—
719C2×C4—62no—
720C2×C4—64no—
721C2×C4—62no—
722C2×C4—62no—
723C2×C4—64no—
724C2×C4—62no—
725C2×C4—62no—
726C2×C4—64no—
727C2×C4—64no—
728C2×C4—64no—
729C2×C4—64no—
730C2×C4—64no—
731C2×C4—62no—
732C2×C4—64no—
733C2×C4—121no—
734C2×C4—122no—
735C2×C4—121no—
736C2×C4—121no—
737C2×C4—122no—
738C2×C4—122no—
739C2×C4—122no—
740C2×C4—122no—
741C2×C4—122no—
742C2×C4—122no—
743C2×C4—122no—
744C2×C4—122no—
745C2×C4#88414yes—
746C2×C3—84no—
747C2×C3#239211yescharacteristic
748C2×C3#241111yescharacteristic
749C2×C3#241611yescharacteristic
750C2×C3#242412yes—
751C2×C3#242612yes—
752C2×C3#246112yes—
753C2×C3#254011yescharacteristic
754C2×C3#254111yescharacteristic
755C2×C3#255412yes—
756C2×C3#266211yescharacteristic
757C2×C3#285611yescharacteristic
758D3—82no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—44no—
765C22—44no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—122no—
775C22—122no—
776C22—122no—
777C22—124no—
778C22—124no—
779C22—242no—
780C22—241no—
781C22—242no—
782C22—241no—
783C22—241no—
784C22—241no—
785C22C2×#88411yescharacteristic
786C22#549512yes—
787C22#554812yes—
788C22#555111yescharacteristic
789C22#555811yescharacteristic
790C22#558611yescharacteristic
791C22#559012yes—
792C22#559112yes—
793C22#559112yes—
794C22#559211yescharacteristic
795C22#559812yes—
796C22#559912yes—
797C22D3×#12111yescharacteristic
798C22D3×#12112yes—
799C22#560612yes—
800C22#560811yescharacteristic
801C22#561312yes—
802C22#564912yes—
803C22#566212yes—
804C22#566811yescharacteristic
805C22#567711yescharacteristic
806C22D3×#12711yescharacteristic
807C22#571711yescharacteristic
808C4—24no—
809C4—42no—
810C4—44no—
811C4—64no—
812C4—64no—
813C4—68no—
814C4—81no—
815C4—242no—
816C4—241no—
817C3#1481511yescharacteristic, complemented, Sylow
818C2—84no—
819C2—242no—
820C2#7382511yescharacteristic
821C2#7471812yes—
822C2#7475512yes—
823C2#7643911yescharacteristic
824C2#7647611yescharacteristic
825C2#7668711yescharacteristic
826C2#7668811yescharacteristic
827C2#7675612yes—
828C2#7689111yescharacteristic
829C2#7690112yes—
830C2#7699711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1438C2
prime radicalC2×#5223C2
hypercenter#1438D3
hypocenterC3#14815
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. C2×#5221C2semidirect
3. C2×#4959C2semidirect
4. C2×#4948C2semidirect
5. C2×#4957C2semidirect
6. C2×#4670C2semidirect
7. C2×#4649C2semidirect
8. C3×#1438C2semidirect
9. #71545C2semidirect
10. #69427C2semidirect
11. #69420C2semidirect
52. #1438D3semidirect
102. C2×(C2×D3)⋊C4D4semidirect
112. C2×Dic3⋊C4D4semidirect
118. C2×C4×Dic3D4semidirect
817. C3#14815semidirect

Maximal subgroups

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

subgroupindex
C2×#52232
C2×#52212
C2×#49592
C2×#49482
C2×#49572
C2×#46702
C2×#46492
C3×#14382
#715452
#694272
#694202
#148153