Finite Group Databasebeta

← #10727989

Subgroups — #10727989

Order 768.

2198 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4×D4C211yesmaximal, characteristic
2C2×#5212C211yesmaximal, characteristic, complemented
3C2×#4986C211yesmaximal, characteristic, complemented
4C2×#4949C211yesmaximal, characteristic, complemented
5#72131C212yesmaximal
6#72127C212yesmaximal, complemented
7#72127C211yesmaximal, characteristic, complemented
8#71565C211yesmaximal, characteristic, complemented
9#71547C212yesmaximal, complemented
10#71546C211yesmaximal, characteristic, complemented
11#71536C212yesmaximal, complemented
12#14825—31nomaximal, Sylow
13C23×C3×D4C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C24×C3×C4C2211yescharacteristic
16C2×C3×C4×D4—24no—
17C2×C3×C4×D4—24no—
18C2×C3×C4×D4—24no—
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C42C2211yescharacteristic
23C22×#217C2212yes—
24C22×#217C2212yes—
25C22×#217C2212yes—
26C22×#217C2212yes—
27C22×C4⋊Dic3C2211yescharacteristic
28C22×C4⋊Dic3C2211yescharacteristic
29C22×Dic3⋊C4C2212yes—
30#5212—24no—
31C2×C3⋊#95C2212yes—
32C2×C3⋊#95C2212yes—
33C2×C3⋊#95C2212yes—
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2211yescharacteristic
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2211yescharacteristic
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2212yes—
40#4986—24no—
41#4949—24no—
42C22×C4×D4D311yescharacteristic
43C2×#400—31no—
44C2×#399—31no—
45C2×#380—31no—
46#1441—31no—
47#1439—31no—
48#1439—32no—
49#1438—32no—
50#1436—32no—
51C22⋊#95—32no—
52C22⋊#95—31no—
53C25×C3C2311yescharacteristic
54C25×C3C2311yescharacteristic
55C22×C3×D4—22no—
56C22×C3×D4—22no—
57C22×C3×D4—22no—
58C22×C3×D4—22no—
59C22×C3×D4—22no—
60C22×C3×D4—22no—
61C22×C3×D4Q814yes—
62C23×C3×C4—22no—
63C23×C3×C4—22no—
64C23×C3×C4—22no—
65C23×C3×C4—22no—
66C23×C3×C4—22no—
67C23×C3×C4—24no—
68C23×C3×C4—24no—
69C23×C3×C4—42no—
70C23×C3×C4—42no—
71C23×C3×C4D414yes—
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×Dic3C2312yes—
78C23×Dic3C2312yes—
79C23×Dic3C2312yes—
80C23×Dic3C2312yes—
81C3×C4×D4—232no—
82C2×C3×C4⋊C4—22no—
83C2×C3×C4⋊C4—22no—
84C2×C3×C4⋊C4D414yes—
85C2×C3×C22⋊C4—22no—
86C2×C3×C22⋊C4—22no—
87C2×C3×C22⋊C4—22no—
88C2×C3×C22⋊C4—22no—
89C2×C3×C22⋊C4—22no—
90C2×C3×C22⋊C4D414yes—
91C2×C3×C42—22no—
92C2×C3×C42—22no—
93C2×C3×C42—22no—
94C2×#217—24no—
95C2×#217—24no—
96C2×#217—24no—
97C2×#217—24no—
98C2×#217—24no—
99C2×#217—24no—
100C2×#217—42no—
101C2×#217—42no—
102C2×#217—42no—
103C2×#217—42no—
104C2×#217—42no—
105C2×#217—42no—
106C2×C4⋊Dic3—22no—
107C2×C4⋊Dic3—22no—
108C2×C4⋊Dic3—22no—
109C2×C4⋊Dic3—22no—
110C2×C4⋊Dic3—42no—
111C2×Dic3⋊C4—24no—
112C2×Dic3⋊C4—24no—
113C2×Dic3⋊C4—42no—
114C3⋊#95—22no—
115C3⋊#95—24no—
116C3⋊#95—22no—
117C3⋊#95—24no—
118C3⋊#95—24no—
119C3⋊#95—24no—
120C3⋊#95—24no—
121C3⋊#95—42no—
122C3⋊#95—42no—
123C23×D4C2×D311yescharacteristic
124C24×C4C2×D311yescharacteristic
125C24×C4C2×D311yescharacteristic
126C2×C4×D4—24no—
127C2×C4×D4—24no—
128C2×C4×D4—24no—
129C22×C4⋊C4—31no—
130C22×C4⋊C4—32no—
131C22×C4⋊C4—31no—
132C22×C4⋊C4C2×D311yescharacteristic
133C22×C22⋊C4—32no—
134C22×C22⋊C4—32no—
135C22×C22⋊C4—32no—
136C22×C22⋊C4—32no—
137C22×C22⋊C4C2×D311yescharacteristic
138C22×C22⋊C4C2×D311yescharacteristic
139C22×C42C2×D311yescharacteristic
140#400—64no—
141#399—64no—
142#380—64no—
143C2×#95—31no—
144C2×#95—32no—
145C2×#95—31no—
146C2×#95—32no—
147C2×#95—32no—
148C2×#95—32no—
149C2×#95—32no—
150C2×#95—32no—
151C2×#95—32no—
152C24×C3—21no—
153C24×C3—21no—
154C24×C3—21no—
155C24×C3—21no—
156C24×C3—22no—
157C24×C3—22no—
158C24×C3—22no—
159C24×C3—22no—
160C24×C3—21no—
161C24×C3—21no—
162C24×C3—21no—
163C24×C3—21no—
164C24×C3—22no—
165C24×C3—22no—
166C24×C3—22no—
167C24×C3—22no—
168C24×C3C2×D412yes—
169C24×C3C2×D412yes—
170C24×C3C2×Q812yes—
171C24×C3C2×Q812yes—
172C24×C3#4112yes—
173C24×C3#4112yes—
174C24×C3C2411yescharacteristic
175C2×C3×D4—28no—
176C2×C3×D4—28no—
177C2×C3×D4—28no—
178C2×C3×D4—28no—
179C2×C3×D4—28no—
180C2×C3×D4—28no—
181C2×C3×D4—28no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—22no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—22no—
190C22×C3×C4—22no—
191C22×C3×C4—28no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—28no—
201C22×C3×C4—28no—
202C22×C3×C4—44no—
203C22×C3×C4—48no—
204C22×C3×C4—48no—
205C22×C3×C4—48no—
206C22×C3×C4—48no—
207C22×C3×C4—44no—
208C22×C3×C4—44no—
209C22×C3×C4C2×D412yes—
210C22×C3×C4C2×D412yes—
211C22×C3×C4C2×D412yes—
212C22×C3×C4C2×D412yes—
213C22×C3×C4C2×D412yes—
214C22×C3×C4C2×D412yes—
215C22×C3×C4C2×D412yes—
216C22×C3×C4C2×Q812yes—
217C22×C3×C4#4112yes—
218C22×C3×C4#4114yes—
219C22×Dic3—22no—
220C22×Dic3—22no—
221C22×Dic3—22no—
222C22×Dic3—22no—
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#4114yes—
247C3×C4⋊C4—28no—
248C3×C22⋊C4—28no—
249C3×C22⋊C4—28no—
250C3×C42—28no—
251#217—48no—
252#217—48no—
253#217—48no—
254#217—48no—
255C4⋊Dic3—44no—
256C4⋊Dic3—44no—
257Dic3⋊C4—48no—
258C25C22×D311yescharacteristic
259C25C22×D311yescharacteristic
260C22×D4—22no—
261C22×D4—22no—
262C22×D4—22no—
263C22×D4—22no—
264C22×D4—22no—
265C22×D4—22no—
266C22×D4Dic614yes—
267C23×C4—22no—
268C23×C4—24no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—24no—
274C23×C4—32no—
275C23×C4—32no—
276C23×C4—32no—
277C23×C4—32no—
278C23×C4—42no—
279C23×C4—42no—
280C23×C4#6714yes—
281C23×C4C22×D311yescharacteristic
282C23×C4C22×D311yescharacteristic
283C23×C4C22×D311yescharacteristic
284C23×C4C22×D311yescharacteristic
285C23×C4C22×D311yescharacteristic
286C4×D4—232no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—64no—
290C2×C4⋊C4—62no—
291C2×C4⋊C4—62no—
292C2×C4⋊C4—64no—
293C2×C4⋊C4—62no—
294C2×C4⋊C4—62no—
295C2×C4⋊C4—122no—
296C2×C4⋊C4—122no—
297C2×C4⋊C4#6714yes—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—22no—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—64no—
304C2×C22⋊C4—64no—
305C2×C22⋊C4—64no—
306C2×C22⋊C4—64no—
307C2×C22⋊C4—64no—
308C2×C22⋊C4—64no—
309C2×C22⋊C4—122no—
310C2×C22⋊C4—122no—
311C2×C22⋊C4—122no—
312C2×C22⋊C4—122no—
313C2×C22⋊C4—122no—
314C2×C22⋊C4—122no—
315C2×C22⋊C4#6714yes—
316C2×C42—22no—
317C2×C42—22no—
318C2×C42—22no—
319#95—64no—
320#95—64no—
321#95—64no—
322#95—62no—
323#95—62no—
324#95—64no—
325#95—64no—
326#95—122no—
327#95—122no—
328C23×C3—22no—
329C23×C3—22no—
330C23×C3—22no—
331C23×C3—22no—
332C23×C3—22no—
333C23×C3—22no—
334C23×C3—22no—
335C23×C3—22no—
336C23×C3—22no—
337C23×C3—22no—
338C23×C3—22no—
339C23×C3—22no—
340C23×C3—22no—
341C23×C3—24no—
342C23×C3—22no—
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—41no—
355C23×C3—42no—
356C23×C3—42no—
357C23×C3—42no—
358C23×C3—41no—
359C23×C3—41no—
360C23×C3—41no—
361C23×C3—42no—
362C23×C3—42no—
363C23×C3—42no—
364C23×C3—42no—
365C23×C3—42no—
366C23×C3—42no—
367C23×C3—42no—
368C23×C3—42no—
369C23×C3—42no—
370C23×C3—42no—
371C23×C3—42no—
372C23×C3C22⋊Q814yes—
373C23×C3C22⋊Q814yes—
374C23×C3C22×D411yescharacteristic
375C23×C3C22×D411yescharacteristic
376C23×C3C22×D411yescharacteristic
377C23×C3C22×Q811yescharacteristic
378C23×C3C2×#4111yescharacteristic
379C23×C3C2×#4111yescharacteristic
380C23×C3C2×#4111yescharacteristic
381C23×C3C2×#4112yes—
382C23×C3C2×#4112yes—
383C23×C3H(5,𝔽2)12yes—
384C23×C3H(5,𝔽2)12yes—
385C3×D4—232no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—24no—
397C2×C3×C4—24no—
398C2×C3×C4—24no—
399C2×C3×C4—24no—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—24no—
403C2×C3×C4—24no—
404C2×C3×C4—416no—
405C2×C3×C4—416no—
406C2×C3×C4—41no—
407C2×C3×C4—41no—
408C2×C3×C4—41no—
409C2×C3×C4—41no—
410C2×C3×C4—42no—
411C2×C3×C4—42no—
412C2×C3×C4#12014yes—
413C2×C3×C4C22⋊Q814yes—
414C2×C3×C4#12314yes—
415C2×Dic3—24no—
416C2×Dic3—24no—
417C2×Dic3—24no—
418C2×Dic3—42no—
419C2×Dic3—42no—
420C2×Dic3—42no—
421C2×Dic3—42no—
422C2×Dic3—42no—
423C2×Dic3—42no—
424C2×Dic3—42no—
425C2×Dic3—42no—
426C2×Dic3—42no—
427C2×Dic3—42no—
428C2×Dic3—42no—
429C2×Dic3—42no—
430C2×Dic3—42no—
431C2×Dic3—42no—
432C2×Dic3—42no—
433C2×Dic3—42no—
434C2×Dic3—42no—
435C2×Dic3—42no—
436C2×Dic3—42no—
437C2×Dic3—42no—
438C2×Dic3—42no—
439C2×Dic3—42no—
440C2×Dic3—42no—
441C2×Dic3—42no—
442C2×Dic3—42no—
443C24—21no—
444C24—21no—
445C24—21no—
446C24—21no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—21no—
456C24—21no—
457C24—21no—
458C24—21no—
459C24C2×Dic612yes—
460C24C2×Dic612yes—
461C24#23512yes—
462C24#23512yes—
463C24C2×#6712yes—
464C24C2×#6712yes—
465C24C23×D311yescharacteristic
466C2×D4—28no—
467C2×D4—28no—
468C2×D4—28no—
469C2×D4—28no—
470C2×D4—28no—
471C2×D4—28no—
472C2×D4—28no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—28no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—28no—
492C22×C4—28no—
493C22×C4—34no—
494C22×C4—44no—
495C22×C4—48no—
496C22×C4—48no—
497C22×C4—48no—
498C22×C4—48no—
499C22×C4—44no—
500C22×C4—44no—
501C22×C4—62no—
502C22×C4—62no—
503C22×C4—62no—
504C22×C4—62no—
505C22×C4—62no—
506C22×C4—62no—
507C22×C4—62no—
508C22×C4—62no—
509C22×C4—62no—
510C22×C4—62no—
511C22×C4—62no—
512C22×C4—62no—
513C22×C4—62no—
514C22×C4—62no—
515C22×C4—62no—
516C22×C4—62no—
517C22×C4—62no—
518C22×C4—62no—
519C22×C4—62no—
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×C4C2×Dic612yes—
529C22×C4#23512yes—
530C22×C4#23714yes—
531C22×C4C2×#6712yes—
532C22×C4C2×#6712yes—
533C22×C4C2×#6712yes—
534C22×C4C2×#6712yes—
535C22×C4C2×#6712yes—
536C22×C4C2×#6712yes—
537C22×C4C2×#6712yes—
538C4⋊C4—28no—
539C4⋊C4—128no—
540C4⋊C4—124no—
541C4⋊C4—124no—
542C22⋊C4—28no—
543C22⋊C4—28no—
544C22⋊C4—128no—
545C22⋊C4—128no—
546C22⋊C4—128no—
547C22⋊C4—128no—
548C42—28no—
549C22×C3—24no—
550C22×C3—24no—
551C22×C3—24no—
552C22×C3—28no—
553C22×C3—24no—
554C22×C3—42no—
555C22×C3—42no—
556C22×C3—42no—
557C22×C3—42no—
558C22×C3—42no—
559C22×C3—42no—
560C22×C3—42no—
561C22×C3—42no—
562C22×C3—42no—
563C22×C3—44no—
564C22×C3—44no—
565C22×C3—44no—
566C22×C3—44no—
567C22×C3—44no—
568C22×C3—44no—
569C22×C3—44no—
570C22×C3—42no—
571C22×C3C2×#12011yescharacteristic
572C22×C3C2×C22⋊Q811yescharacteristic
573C22×C3C2×C22⋊Q811yescharacteristic
574C22×C3C2×C22⋊Q811yescharacteristic
575C22×C3C2×#12311yescharacteristic
576C22×C3#52511yescharacteristic
577C22×C3#52511yescharacteristic
578C22×C3#52511yescharacteristic
579C22×C3#52912yes—
580C22×C3#52912yes—
581C22×C3#53211yescharacteristic
582C22×C3#53411yescharacteristic
583C22×C3#53511yescharacteristic
584C22×C3#53812yes—
585C22×C3#54012yes—
586C22×C3#54612yes—
587C22×C3#54612yes—
588C22×C3#54612yes—
589C22×C3#55012yes—
590C22×C3#55112yes—
591C22×C3#55312yes—
592C22×C3#55412yes—
593C22×C3#55412yes—
594C3×C4—24no—
595C3×C4—24no—
596C3×C4—24no—
597C3×C4—42no—
598C3×C4—42no—
599Dic3—44no—
600Dic3—82no—
601Dic3—82no—
602Dic3—82no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—22no—
617C23—24no—
618C23—24no—
619C23—22no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—42no—
630C23—41no—
631C23—41no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—41no—
644C23—41no—
645C23—42no—
646C23—42no—
647C23#92414yes—
648C23#92414yes—
649C23C22×Dic611yescharacteristic
650C23C2×#23511yescharacteristic
651C23C2×#23511yescharacteristic
652C23C2×#23511yescharacteristic
653C23C2×#23712yes—
654C23#100412yes—
655C23D3×#4112yes—
656C23#100912yes—
657C23C22×#6711yescharacteristic
658C23C22×#6711yescharacteristic
659C23C22×#6711yescharacteristic
660D4—232no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—416no—
680C2×C4—416no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—42no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—64no—
688C2×C4—64no—
689C2×C4—64no—
690C2×C4—122no—
691C2×C4—122no—
692C2×C4—122no—
693C2×C4—122no—
694C2×C4—122no—
695C2×C4—122no—
696C2×C4—122no—
697C2×C4—122no—
698C2×C4—122no—
699C2×C4—122no—
700C2×C4—122no—
701C2×C4—122no—
702C2×C4—122no—
703C2×C4—122no—
704C2×C4—122no—
705C2×C4—122no—
706C2×C4—122no—
707C2×C4—122no—
708C2×C4—122no—
709C2×C4—122no—
710C2×C4—122no—
711C2×C4—122no—
712C2×C4—122no—
713C2×C4—122no—
714C2×C4—122no—
715C2×C4#92414yes—
716C2×C4#93514yes—
717C2×C4#95314yes—
718C2×C3—44no—
719C2×C3—44no—
720C2×C3#239511yescharacteristic
721C2×C3#240511yescharacteristic
722C2×C3#243111yescharacteristic
723C2×C3#245012yes—
724C2×C3#245412yes—
725C2×C3#245712yes—
726C2×C3#246712yes—
727C2×C3#248711yescharacteristic
728C2×C3#256411yescharacteristic
729C2×C3#263511yescharacteristic
730C2×C3#284811yescharacteristic
731C22—24no—
732C22—24no—
733C22—28no—
734C22—24no—
735C22—24no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—44no—
743C22—44no—
744C22—44no—
745C22—44no—
746C22—44no—
747C22—42no—
748C22—42no—
749C22—44no—
750C22—44no—
751C22—42no—
752C22—42no—
753C22#553812yes—
754C22#553912yes—
755C22#554312yes—
756C22#555612yes—
757C22#555712yes—
758C22#556012yes—
759C22#556212yes—
760C22#556512yes—
761C22C2×#92411yescharacteristic
762C22C2×#92411yescharacteristic
763C22C2×#92411yescharacteristic
764C22#579111yescharacteristic
765C22#579111yescharacteristic
766C22#579111yescharacteristic
767C22C2×#93511yescharacteristic
768C22#580411yescharacteristic
769C22#580612yes—
770C22#580612yes—
771C22#582912yes—
772C22#583011yescharacteristic
773C22#583211yescharacteristic
774C22#583412yes—
775C22C2×#95311yescharacteristic
776C4—24no—
777C4—24no—
778C4—24no—
779C4—42no—
780C4—42no—
781C4—124no—
782C4—242no—
783C4—242no—
784C4—242no—
785C3#1482511yescharacteristic, complemented, Sylow
786C2—44no—
787C2—44no—
788C2#8234611yescharacteristic
789C2#8236112yes—
790C2#8236312yes—
791C2#8237012yes—
792C2#8237411yescharacteristic
793C2#8238511yescharacteristic
794C2#8241212yes—
795C2#8242211yescharacteristic
796C2#8403111yescharacteristic
797C2#8404711yescharacteristic
798C2#8409211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC22×C3×C4×D4C2
prime radicalC23×C3×D4C22
hypercenterC22×C4×D4D3
hypocenterC3#14825
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×#5212C2semidirect
3. C2×#4986C2semidirect
4. C2×#4949C2semidirect
6. #72127C2semidirect
7. #72127C2semidirect
8. #71565C2semidirect
9. #71547C2semidirect
10. #71546C2semidirect
11. #71536C2semidirect
785. C3#14825semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4×D42
C2×#52122
C2×#49862
C2×#49492
#721312
#721272
#715652
#715472
#715462
#715362
#148253