Finite Group Databasebeta

← #10732014

Subgroups — #10732014

Order 768.

2578 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic3C211yesmaximal, characteristic, complemented
2C2×C3×#394C211yesmaximal, characteristic, complemented
3C2×#5223C211yesmaximal, characteristic
4C2×#4990C211yesmaximal, characteristic, complemented
5C2×#4958C212yesmaximal, complemented
6#71565C211yesmaximal, characteristic, complemented
7#71550C212yesmaximal, complemented
8#71548C212yesmaximal, complemented
9#71544C212yesmaximal, complemented
10#69427C211yesmaximal, characteristic, complemented
11#69403C211yesmaximal, characteristic, complemented
12#15159—31nomaximal, Sylow
13C23×C3×D4C2211yescharacteristic
14C23×#67C2212yes—
15C24×Dic3C2212yes—
16C22×C3×C4⋊C4C2211yescharacteristic
17C22×C3×C22⋊C4C2212yes—
18C22×C3×C22⋊C4C2212yes—
19C22×#217C2212yes—
20C22×#217C2212yes—
21C2×D4×Dic3—28no—
22C2×D4×Dic3—24no—
23C22×(C2×D3)⋊C4C2211yescharacteristic
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×(C2×D3)⋊C4C2212yes—
27C22×C4⋊Dic3C2211yescharacteristic
28C22×C4×Dic3C2211yescharacteristic
29C3×#394—24no—
30C2×C3×#95C2211yescharacteristic
31#5223—24no—
32C2×C3⋊#95C2211yescharacteristic
33C2×C3⋊#95C2212yes—
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2211yescharacteristic
36C2×C3⋊#95C2211yescharacteristic
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2212yes—
40#4990—24no—
41#4958—28no—
42C22×C4×D4—31no—
43C2×#394D311yescharacteristic, complemented
44C2×#392—31no—
45C2×#388—31no—
46C2×#386—32no—
47#1441—31no—
48#1440—32no—
49#1439—31no—
50#1438—32no—
51#1434—31no—
52C22⋊#95—32no—
53C25×C3C2312yes—
54C24×D3C2311yescharacteristic
55C22×C3×D4—24no—
56C22×C3×D4—24no—
57C22×C3×D4—22no—
58C22×C3×D4—22no—
59C22×C3×D4D414yes—
60C23×C3×C4C2312yes—
61C23×C3×C4C2311yescharacteristic
62C23×C3×C4C2311yescharacteristic
63C23×C3×C4C2311yescharacteristic
64C22×#67—24no—
65C22×#67—24no—
66C22×#67—24no—
67C22×#67—24no—
68C22×#67—24no—
69C22×#67—42no—
70C22×#67—42no—
71C23×Dic3—24no—
72C23×Dic3—24no—
73C23×Dic3—42no—
74C23×Dic3—42no—
75C23×Dic3—42no—
76C23×Dic3—42no—
77C23×Dic3D418yescomplemented
78C23×Dic3C2311yescharacteristic
79C23×Dic3C2312yes—
80C23×Dic3C2311yescharacteristic
81C23×Dic3C2312yes—
82C23×Dic3C2311yescharacteristic
83C2×C3×C4⋊C4—22no—
84C2×C3×C4⋊C4—22no—
85C2×C3×C4⋊C4—22no—
86C2×C3×C22⋊C4—24no—
87C2×C3×C22⋊C4—24no—
88C2×C3×C22⋊C4—24no—
89C2×C3×C22⋊C4—24no—
90C2×C3×C22⋊C4—24no—
91C2×C3×C22⋊C4—42no—
92C2×#217—24no—
93C2×#217—24no—
94C2×#217—24no—
95C2×#217—24no—
96C2×#217—24no—
97C2×#217—42no—
98D4×Dic3—232no—
99C2×(C2×D3)⋊C4—22no—
100C2×(C2×D3)⋊C4—22no—
101C2×(C2×D3)⋊C4—22no—
102C2×(C2×D3)⋊C4—22no—
103C2×(C2×D3)⋊C4—22no—
104C2×(C2×D3)⋊C4—22no—
105C2×(C2×D3)⋊C4—24no—
106C2×(C2×D3)⋊C4—24no—
107C2×(C2×D3)⋊C4—22no—
108C2×(C2×D3)⋊C4—42no—
109C2×(C2×D3)⋊C4—42no—
110C2×C4⋊Dic3—22no—
111C2×C4⋊Dic3—24no—
112C2×C4×Dic3—24no—
113C2×C4×Dic3D414yescomplemented
114C3×#95—22no—
115C3⋊#95—22no—
116C3⋊#95—24no—
117C3⋊#95—24no—
118C3⋊#95—22no—
119C3⋊#95—22no—
120C3⋊#95—24no—
121C3⋊#95—42no—
122C3⋊#95—42no—
123C23×D4—32no—
124C23×D4C2×D311yescharacteristic
125C24×C4—32no—
126C2×C4×D4—64no—
127C2×C4×D4—68no—
128C22×C4⋊C4—31no—
129C22×C4⋊C4C2×D311yescharacteristic
130C22×C22⋊C4—32no—
131C22×C22⋊C4—31no—
132C22×C22⋊C4—31no—
133C22×C22⋊C4—31no—
134C22×C22⋊C4—32no—
135C22×C22⋊C4—32no—
136C22×C22⋊C4C2×D312yes—
137C22×C22⋊C4C2×D312yes—
138C22×C42—31no—
139#394—24no—
140#392—64no—
141#388—64no—
142#386—68no—
143C2×#95—31no—
144C2×#95—31no—
145C2×#95—32no—
146C2×#95—32no—
147C2×#95—31no—
148C2×#95—32no—
149C2×#95—32no—
150C2×#95—32no—
151C2×#95C2×D311yescharacteristic
152C24×C3—22no—
153C24×C3—22no—
154C24×C3—22no—
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×C3C2×D414yes—
165C24×C3C2×D414yes—
166C24×C3#4114yes—
167C24×C3C2411yescharacteristic
168C23×D3—21no—
169C23×D3—22no—
170C23×D3—21no—
171C23×D3—21no—
172C23×D3—21no—
173C23×D3—22no—
174C23×D3—22no—
175C23×D3—21no—
176C23×D3—22no—
177C23×D3—21no—
178C23×D3#4112yes—
179C2×C3×D4—28no—
180C2×C3×D4—28no—
181C2×C3×D4—216no—
182C2×C3×D4—216no—
183C2×C3×D4—28no—
184C22×C3×C4—22no—
185C22×C3×C4—22no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—21no—
195C22×C3×C4—22no—
196C22×C3×C4—21no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—21no—
202C22×C3×C4—22no—
203C22×C3×C4—22no—
204C22×C3×C4C2×D412yes—
205C22×C3×C4C2×D412yes—
206C22×C3×C4#4112yes—
207C22×C3×C4#4112yes—
208C2×#67—216no—
209C2×#67—48no—
210C2×#67—48no—
211C2×#67—48no—
212C2×#67—48no—
213C2×#67—48no—
214C2×#67—48no—
215C22×Dic3—21no—
216C22×Dic3—21no—
217C22×Dic3—22no—
218C22×Dic3—22no—
219C22×Dic3—22no—
220C22×Dic3—22no—
221C22×Dic3—22no—
222C22×Dic3—22no—
223C22×Dic3—22no—
224C22×Dic3—21no—
225C22×Dic3—21no—
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—216no—
235C22×Dic3—21no—
236C22×Dic3—21no—
237C22×Dic3—21no—
238C22×Dic3—22no—
239C22×Dic3—22no—
240C22×Dic3—48no—
241C22×Dic3—48no—
242C22×Dic3—48no—
243C22×Dic3—48no—
244C22×Dic3—48no—
245C22×Dic3—48no—
246C22×Dic3C2×D412yes—
247C22×Dic3C2×D414yes—
248C22×Dic3C2×D414yes—
249C22×Dic3C2×D412yes—
250C22×Dic3#4114yes—
251C3×C4⋊C4—44no—
252C3×C22⋊C4—48no—
253C3×C22⋊C4—48no—
254#217—216no—
255#217—48no—
256(C2×D3)⋊C4—28no—
257(C2×D3)⋊C4—48no—
258(C2×D3)⋊C4—44no—
259(C2×D3)⋊C4—44no—
260C4⋊Dic3—28no—
261C4×Dic3—28no—
262C25—31no—
263C25C22×D312yes—
264C22×D4—24no—
265C22×D4—24no—
266C22×D4—22no—
267C22×D4—22no—
268C22×D4—64no—
269C22×D4—64no—
270C22×D4—64no—
271C22×D4—64no—
272C22×D4—64no—
273C22×D4—122no—
274C22×D4—122no—
275C22×D4#6714yes—
276C23×C4—31no—
277C23×C4—31no—
278C23×C4—32no—
279C23×C4—32no—
280C23×C4—38no—
281C23×C4—31no—
282C23×C4—64no—
283C23×C4—64no—
284C23×C4—122no—
285C23×C4—122no—
286C23×C4—122no—
287C23×C4—122no—
288C23×C4C22×D311yescharacteristic
289C23×C4C22×D312yes—
290C23×C4C22×D311yescharacteristic
291C23×C4C22×D311yescharacteristic
292C4×D4—632no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—64no—
297C2×C4⋊C4—62no—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—42no—
304C2×C22⋊C4—62no—
305C2×C22⋊C4—62no—
306C2×C22⋊C4—64no—
307C2×C22⋊C4—64no—
308C2×C22⋊C4—64no—
309C2×C22⋊C4—62no—
310C2×C22⋊C4—64no—
311C2×C22⋊C4—64no—
312C2×C22⋊C4—62no—
313C2×C22⋊C4—64no—
314C2×C22⋊C4—64no—
315C2×C22⋊C4—62no—
316C2×C22⋊C4—62no—
317C2×C22⋊C4—62no—
318C2×C22⋊C4—122no—
319C2×C22⋊C4—122no—
320C2×C22⋊C4—122no—
321C2×C42—34no—
322C2×C42—64no—
323#95—22no—
324#95—64no—
325#95—64no—
326#95—64no—
327#95—62no—
328#95—62no—
329#95—62no—
330#95—122no—
331#95—122no—
332C23×C3—24no—
333C23×C3—24no—
334C23×C3—24no—
335C23×C3—24no—
336C23×C3—24no—
337C23×C3—24no—
338C23×C3—24no—
339C23×C3—24no—
340C23×C3—24no—
341C23×C3—24no—
342C23×C3—24no—
343C23×C3—24no—
344C23×C3—24no—
345C23×C3—24no—
346C23×C3—24no—
347C23×C3—24no—
348C23×C3—24no—
349C23×C3—24no—
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#12118yes—
367C23×C3C22×D412yes—
368C23×C3C22×D411yescharacteristic
369C23×C3C22×D411yescharacteristic
370C23×C3C2×#4112yes—
371C23×C3C2×#4111yescharacteristic
372C23×C3C2×#4111yescharacteristic
373C23×C3C2×#4111yescharacteristic
374C23×C3C2×#4112yes—
375C23×C3H(5,𝔽2)11yescharacteristic
376C23×C3H(5,𝔽2)11yescharacteristic
377C23×C3H(5,𝔽2)12yes—
378C22×D3—22no—
379C22×D3—24no—
380C22×D3—22no—
381C22×D3—24no—
382C22×D3—22no—
383C22×D3—41no—
384C22×D3—41no—
385C22×D3—42no—
386C22×D3—41no—
387C22×D3—42no—
388C22×D3—41no—
389C22×D3—42no—
390C22×D3—42no—
391C22×D3—42no—
392C22×D3—41no—
393C22×D3—41no—
394C22×D3—42no—
395C22×D3—41no—
396C22×D3—42no—
397C22×D3—42no—
398C22×D3—42no—
399C22×D3—41no—
400C22×D3—42no—
401C3×D4—232no—
402C2×C3×C4—22no—
403C2×C3×C4—24no—
404C2×C3×C4—22no—
405C2×C3×C4—24no—
406C2×C3×C4—22no—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—41no—
410C2×C3×C4—41no—
411C2×C3×C4—41no—
412C2×C3×C4—41no—
413C2×C3×C4—41no—
414C2×C3×C4—42no—
415C2×C3×C4—42no—
416C2×C3×C4—41no—
417C2×C3×C4—41no—
418C2×C3×C4—42no—
419C2×C3×C4—42no—
420C2×C3×C4—42no—
421C2×C3×C4—42no—
422C2×C3×C4—42no—
423C2×C3×C4—42no—
424C2×C3×C4—42no—
425C2×C3×C4#12114yes—
426#67—432no—
427C2×Dic3—24no—
428C2×Dic3—24no—
429C2×Dic3—22no—
430C2×Dic3—22no—
431C2×Dic3—22no—
432C2×Dic3—24no—
433C2×Dic3—22no—
434C2×Dic3—24no—
435C2×Dic3—22no—
436C2×Dic3—24no—
437C2×Dic3—24no—
438C2×Dic3—24no—
439C2×Dic3—24no—
440C2×Dic3—432no—
441C2×Dic3—42no—
442C2×Dic3—42no—
443C2×Dic3—42no—
444C2×Dic3—42no—
445C2×Dic3—42no—
446C2×Dic3—42no—
447C2×Dic3—42no—
448C2×Dic3—42no—
449C2×Dic3—42no—
450C2×Dic3—42no—
451C2×Dic3—41no—
452C2×Dic3—41no—
453C2×Dic3—41no—
454C2×Dic3—42no—
455C2×Dic3—42no—
456C2×Dic3#12014yes—
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—32no—
470C24—61no—
471C24—62no—
472C24—61no—
473C24—61no—
474C24—62no—
475C24—61no—
476C24—62no—
477C24—62no—
478C24—61no—
479C24—61no—
480C24D3×D414yes—
481C24#23714yes—
482C24C2×#6714yes—
483C24C23×D311yescharacteristic
484C2×D4—28no—
485C2×D4—28no—
486C2×D4—216no—
487C2×D4—216no—
488C2×D4—28no—
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—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—32no—
517C22×C4—34no—
518C22×C4—32no—
519C22×C4—34no—
520C22×C4—34no—
521C22×C4—616no—
522C22×C4—61no—
523C22×C4—61no—
524C22×C4—62no—
525C22×C4—62no—
526C22×C4—62no—
527C22×C4—62no—
528C22×C4—62no—
529C22×C4—61no—
530C22×C4—62no—
531C22×C4—62no—
532C22×C4—62no—
533C22×C4—61no—
534C22×C4—62no—
535C22×C4—62no—
536C22×C4—62no—
537C22×C4—62no—
538C22×C4—62no—
539C22×C4—62no—
540C22×C4—62no—
541C22×C4—61no—
542C22×C4—61no—
543C22×C4—62no—
544C22×C4—62no—
545C22×C4—61no—
546C22×C4—128no—
547C22×C4—128no—
548C22×C4—128no—
549C22×C4—128no—
550C22×C4—128no—
551C22×C4—128no—
552C22×C4D3×D412yes—
553C22×C4#23712yes—
554C22×C4#23712yes—
555C22×C4C2×#6712yes—
556C4⋊C4—44no—
557C4⋊C4—68no—
558C22⋊C4—48no—
559C22⋊C4—48no—
560C22⋊C4—68no—
561C22⋊C4—616no—
562C22⋊C4—124no—
563C22⋊C4—128no—
564C22⋊C4—128no—
565C22⋊C4—124no—
566C42—68no—
567C22×C3—28no—
568C22×C3—28no—
569C22×C3—28no—
570C22×C3—44no—
571C22×C3—44no—
572C22×C3—44no—
573C22×C3—44no—
574C22×C3—44no—
575C22×C3—44no—
576C22×C3—44no—
577C22×C3—44no—
578C22×C3—44no—
579C22×C3—44no—
580C22×C3—44no—
581C22×C3—44no—
582C22×C3C2×#12011yescharacteristic
583C22×C3C2×#12112yes—
584C22×C3C2×#12111yescharacteristic
585C22×C3#52512yes—
586C22×C3#52511yescharacteristic
587C22×C3#52512yes—
588C22×C3#52511yescharacteristic
589C22×C3#53211yescharacteristic
590C22×C3#53212yes—
591C22×C3#53412yes—
592C22×C3#53412yes—
593C22×C3#53511yescharacteristic
594C22×C3#53511yescharacteristic
595C22×C3#54611yescharacteristic
596C22×C3#54611yescharacteristic
597C22×C3#54612yes—
598C22×C3#55112yes—
599C22×C3#55112yes—
600C22×C3#55312yes—
601C22×C3#55311yescharacteristic
602C22×C3#55312yes—
603C22×C3#55311yescharacteristic
604C22×C3#55912yes—
605C2×D3—42no—
606C2×D3—44no—
607C2×D3—42no—
608C2×D3—44no—
609C2×D3—42no—
610C2×D3—81no—
611C2×D3—82no—
612C2×D3—81no—
613C2×D3—81no—
614C2×D3—82no—
615C2×D3—81no—
616C3×C4—24no—
617C3×C4—42no—
618C3×C4—81no—
619C3×C4—82no—
620Dic3—24no—
621Dic3—44no—
622Dic3—42no—
623Dic3—44no—
624Dic3—81no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
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—42no—
658C23—42no—
659C23—64no—
660C23—64no—
661C23—62no—
662C23—62no—
663C23—62no—
664C23—122no—
665C23—122no—
666C23—121no—
667C23—121no—
668C23—122no—
669C23—121no—
670C23—122no—
671C23—121no—
672C23—122no—
673C23—121no—
674C23—122no—
675C23—121no—
676C23—122no—
677C23—122no—
678C23—122no—
679C23—121no—
680C23—122no—
681C23—121no—
682C23#93918yes—
683C23C2×D3×D412yes—
684C23C2×D3×D411yescharacteristic
685C23C2×#23712yes—
686C23C2×#23711yescharacteristic
687C23C2×#23711yescharacteristic
688C23#100411yescharacteristic
689C23D3×#4111yescharacteristic
690C23D3×#4112yes—
691C23#100911yescharacteristic
692C23#100912yes—
693C23C22×#6711yescharacteristic
694D4—232no—
695D4—1232no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—34no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—64no—
721C2×C4—62no—
722C2×C4—64no—
723C2×C4—62no—
724C2×C4—64no—
725C2×C4—64no—
726C2×C4—64no—
727C2×C4—62no—
728C2×C4—64no—
729C2×C4—62no—
730C2×C4—64no—
731C2×C4—64no—
732C2×C4—62no—
733C2×C4—1232no—
734C2×C4—122no—
735C2×C4—122no—
736C2×C4—122no—
737C2×C4—122no—
738C2×C4—122no—
739C2×C4—122no—
740C2×C4—122no—
741C2×C4—122no—
742C2×C4—122no—
743C2×C4—122no—
744C2×C4—121no—
745C2×C4—121no—
746C2×C4—122no—
747C2×C4—121no—
748C2×C4—122no—
749C2×C4#93914yes—
750C2×C3—48no—
751C2×C3#238811yescharacteristic
752C2×C3#253412yes—
753C2×C3#253511yescharacteristic
754C2×C3#254312yes—
755C2×C3#254411yescharacteristic
756C2×C3#259811yescharacteristic
757C2×C3#260012yes—
758C2×C3#260212yes—
759C2×C3#260311yescharacteristic
760C2×C3#261311yescharacteristic
761C2×C3#284711yescharacteristic
762D3—82no—
763C22—28no—
764C22—28no—
765C22—28no—
766C22—44no—
767C22—44no—
768C22—44no—
769C22—44no—
770C22—44no—
771C22—44no—
772C22—44no—
773C22—44no—
774C22—44no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22—122no—
779C22—122no—
780C22—124no—
781C22—124no—
782C22—122no—
783C22—241no—
784C22—241no—
785C22—242no—
786C22—241no—
787C22—241no—
788C22—242no—
789C22#558611yescharacteristic
790C22#558612yes—
791C22D3×#12011yescharacteristic
792C22#559612yes—
793C22#560112yes—
794C22#560512yes—
795C22#560611yescharacteristic
796C22#560711yescharacteristic
797C22#561411yescharacteristic
798C22#561812yes—
799C22#561811yescharacteristic
800C22#565312yes—
801C22#565612yes—
802C22#565812yes—
803C22#565812yes—
804C22#566811yescharacteristic
805C22#567411yescharacteristic
806C22#568112yes—
807C22C2×#93911yescharacteristic
808C22C2×#93912yes—
809C22#580611yescharacteristic
810C22#582912yes—
811C22#582911yescharacteristic
812C4—24no—
813C4—42no—
814C4—64no—
815C4—81no—
816C4—82no—
817C4—124no—
818C4—122no—
819C4—124no—
820C4—241no—
821C3#1515911yescharacteristic, complemented, Sylow
822C2—48no—
823C2—242no—
824C2#7688911yescharacteristic
825C2#7696211yescharacteristic
826C2#7696312yes—
827C2#7696512yes—
828C2#7696711yescharacteristic
829C2#7712211yescharacteristic
830C2#8260111yescharacteristic
831C2#8266611yescharacteristic
832C2#8267012yes—
833C2#8290012yes—
834C2#8297011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#394C2
prime radicalC2×#5223C2
hypercenterC2×#394D3
hypocenterC3#15159
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×D4×Dic3C2semidirect
2. C2×C3×#394C2semidirect
4. C2×#4990C2semidirect
5. C2×#4958C2semidirect
6. #71565C2semidirect
7. #71550C2semidirect
8. #71548C2semidirect
9. #71544C2semidirect
10. #69427C2semidirect
11. #69403C2semidirect
43. C2×#394D3semidirect
77. C23×Dic3D4semidirect
113. C2×C4×Dic3D4semidirect
821. C3#15159semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic32
C2×C3×#3942
C2×#52232
C2×#49902
C2×#49582
#715652
#715502
#715482
#715442
#694272
#694032
#151593