Finite Group Databasebeta

← #10726602

Subgroups — #10726602

Order 768.

2494 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#946C211yesmaximal, characteristic
2C22×D3×C4⋊C4C211yesmaximal, characteristic
3C2×C3×#395C211yesmaximal, characteristic, complemented
4C2×#5230C211yesmaximal, characteristic, complemented
5C2×#4989C212yesmaximal
6#71568C212yesmaximal, complemented
7#71565C211yesmaximal, characteristic, complemented
8(C2×D3)⋊#95C212yesmaximal
9(C2×D3)⋊#95C211yesmaximal, characteristic
10#69420C212yesmaximal, complemented
11#69410C211yesmaximal, characteristic, complemented
12#14720—31nomaximal, Sylow
13C23×C3×Q8C2211yescharacteristic
14C23×C4×D3C2211yescharacteristic
15C23×C4×D3C2211yescharacteristic
16C23×C4×D3C2211yescharacteristic
17C22×C3×C4⋊C4C2212yes—
18C22×C3×C4⋊C4C2211yescharacteristic
19C2×#946—24no—
20C2×#946—28no—
21C22×(C2×D3)⋊C4C2212yes—
22C22×(C2×D3)⋊C4C2212yes—
23C22×C4⋊Dic3C2211yescharacteristic
24C22×C4⋊Dic3C2211yescharacteristic
25C22×Dic3⋊C4C2212yes—
26C22×Dic3⋊C4C2211yescharacteristic
27C22×Dic3⋊C4C2212yes—
28C22×Dic3⋊C4C2211yescharacteristic
29C2×D3×C4⋊C4—24no—
30C2×D3×C4⋊C4—24no—
31C2×D3×C4⋊C4—24no—
32C3×#395—24no—
33C2×C3×#95C2211yescharacteristic
34C2×C3×#95C2212yes—
35#5230—24no—
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2212yes—
40C2×C3⋊#95C2211yescharacteristic
41C2×C3⋊#95C2212yes—
42C2×C3⋊#95C2212yes—
43#4989—28no—
44C22×C22⋊Q8—31no—
45C23×C4⋊C4—31no—
46C2×#395—31no—
47C2×#395D311yescharacteristic, complemented
48C2×#385—32no—
49#1444—32no—
50#1444—32no—
51#1441—31no—
52#1441—31no—
53C22⋊#95—32no—
54C22⋊#95—31no—
55C24×D3C2311yescharacteristic
56C22×C3×Q8—24no—
57C22×C3×Q8—22no—
58C22×C3×Q8—22no—
59C22×C3×Q8—22no—
60C22×C3×Q8—42no—
61C23×C3×C4C2311yescharacteristic
62C23×C3×C4C2312yes—
63C23×C3×C4C2312yes—
64C23×C3×C4C2311yescharacteristic
65C23×C3×C4C2311yescharacteristic
66C23×Dic3C2311yescharacteristic
67C23×Dic3C2311yescharacteristic
68C23×Dic3C2312yes—
69C23×Dic3C2312yes—
70C23×Dic3C2311yescharacteristic
71C22×C4×D3—22no—
72C22×C4×D3—22no—
73C22×C4×D3—22no—
74C22×C4×D3—22no—
75C22×C4×D3—22no—
76C22×C4×D3—22no—
77C22×C4×D3—22no—
78C22×C4×D3—24no—
79C22×C4×D3—22no—
80C22×C4×D3—22no—
81C22×C4×D3—22no—
82C22×C4×D3—22no—
83C22×C4×D3—24no—
84C22×C4×D3—42no—
85C22×C4×D3—42no—
86C22×C4×D3D414yes—
87C22×C4×D3Q814yescomplemented
88C2×C3×C4⋊C4—22no—
89C2×C3×C4⋊C4—22no—
90C2×C3×C4⋊C4—24no—
91C2×C3×C4⋊C4—24no—
92C2×C3×C4⋊C4—42no—
93C2×C3×C4⋊C4D414yes—
94#946—232no—
95C2×(C2×D3)⋊C4—24no—
96C2×(C2×D3)⋊C4—24no—
97C2×(C2×D3)⋊C4—24no—
98C2×(C2×D3)⋊C4—24no—
99C2×(C2×D3)⋊C4D418yes—
100C2×(C2×D3)⋊C4Q818yescomplemented
101C2×C4⋊Dic3—22no—
102C2×C4⋊Dic3—22no—
103C2×C4⋊Dic3—22no—
104C2×C4⋊Dic3—22no—
105C2×C4⋊Dic3—24no—
106C2×Dic3⋊C4—22no—
107C2×Dic3⋊C4—22no—
108C2×Dic3⋊C4—22no—
109C2×Dic3⋊C4—24no—
110C2×Dic3⋊C4—22no—
111C2×Dic3⋊C4—22no—
112C2×Dic3⋊C4—24no—
113C2×Dic3⋊C4—24no—
114C2×Dic3⋊C4—24no—
115C2×Dic3⋊C4—24no—
116C2×Dic3⋊C4—42no—
117C2×Dic3⋊C4D414yes—
118D3×C4⋊C4—232no—
119C3×#95—22no—
120C3×#95—24no—
121C3⋊#95—22no—
122C3⋊#95—24no—
123C3⋊#95—24no—
124C3⋊#95—24no—
125C3⋊#95—24no—
126C3⋊#95—24no—
127C3⋊#95—42no—
128C23×Q8C2×D311yescharacteristic
129C24×C4—31no—
130C24×C4—31no—
131C24×C4—31no—
132C2×C22⋊Q8—68no—
133C2×C22⋊Q8—64no—
134C22×C4⋊C4—31no—
135C22×C4⋊C4—31no—
136C22×C4⋊C4—31no—
137C22×C4⋊C4—32no—
138C22×C4⋊C4—31no—
139C22×C4⋊C4—32no—
140C22×C4⋊C4—64no—
141C22×C4⋊C4—64no—
142C22×C4⋊C4—64no—
143C22×C4⋊C4C2×D312yes—
144C22×C4⋊C4C2×D311yescharacteristic
145C22×C22⋊C4—32no—
146C22×C22⋊C4—32no—
147#395—24no—
148#395—64no—
149#385—68no—
150C2×#95—31no—
151C2×#95—32no—
152C2×#95—32no—
153C2×#95—32no—
154C2×#95—32no—
155C2×#95—32no—
156C2×#95—32no—
157C2×#95C2×D311yescharacteristic
158C2×#95C2×D312yes—
159C24×C3C2411yescharacteristic
160C23×D3—21no—
161C23×D3—21no—
162C23×D3—21no—
163C23×D3—21no—
164C23×D3—22no—
165C23×D3—22no—
166C23×D3C2×D414yes—
167C23×D3C2×D412yes—
168C23×D3C2×Q814yes—
169C23×D3C2×Q812yes—
170C23×D3#4112yes—
171C2×C3×Q8—28no—
172C2×C3×Q8—48no—
173C2×C3×Q8—48no—
174C2×C3×Q8—44no—
175C2×C3×Q8—44no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—22no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—22no—
182C22×C3×C4—22no—
183C22×C3×C4—22no—
184C22×C3×C4—22no—
185C22×C3×C4—22no—
186C22×C3×C4—22no—
187C22×C3×C4—22no—
188C22×C3×C4—22no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4C2×D414yes—
199C22×C3×C4C2×D412yes—
200C22×C3×C4C2×D412yes—
201C22×C3×C4C2×D412yes—
202C22×C3×C4C2×D412yes—
203C22×C3×C4C2×D412yes—
204C22×C3×C4C2×Q814yes—
205C22×C3×C4C2×Q812yes—
206C22×C3×C4#4112yes—
207C22×Dic3—21no—
208C22×Dic3—21no—
209C22×Dic3—21no—
210C22×Dic3—21no—
211C22×Dic3—22no—
212C22×Dic3—22no—
213C22×Dic3—22no—
214C22×Dic3—22no—
215C22×Dic3—22no—
216C22×Dic3—22no—
217C22×Dic3—21no—
218C22×Dic3—21no—
219C22×Dic3—21no—
220C22×Dic3—21no—
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×Dic3C2×D414yes—
232C22×Dic3C2×D412yes—
233C22×Dic3C2×D412yes—
234C22×Dic3C2×D412yes—
235C22×Dic3C2×Q814yes—
236C22×Dic3C2×Q812yes—
237C22×Dic3#4112yes—
238C2×C4×D3—28no—
239C2×C4×D3—28no—
240C2×C4×D3—28no—
241C2×C4×D3—28no—
242C2×C4×D3—28no—
243C2×C4×D3—28no—
244C2×C4×D3—28no—
245C2×C4×D3—28no—
246C2×C4×D3—28no—
247C2×C4×D3—28no—
248C2×C4×D3—44no—
249C2×C4×D3—48no—
250C2×C4×D3—48no—
251C2×C4×D3—48no—
252C2×C4×D3—48no—
253C2×C4×D3—44no—
254C2×C4×D3—44no—
255C3×C4⋊C4—28no—
256C3×C4⋊C4—48no—
257(C2×D3)⋊C4—216no—
258(C2×D3)⋊C4—216no—
259C4⋊Dic3—28no—
260C4⋊Dic3—28no—
261Dic3⋊C4—28no—
262Dic3⋊C4—216no—
263Dic3⋊C4—28no—
264Dic3⋊C4—48no—
265C25—31no—
266C22×Q8—24no—
267C22×Q8—22no—
268C22×Q8—22no—
269C22×Q8—22no—
270C22×Q8—42no—
271C23×C4—31no—
272C23×C4—32no—
273C23×C4—32no—
274C23×C4—31no—
275C23×C4—31no—
276C23×C4—34no—
277C23×C4—34no—
278C23×C4—62no—
279C23×C4—62no—
280C23×C4—62no—
281C23×C4—62no—
282C23×C4—62no—
283C23×C4—62no—
284C23×C4—64no—
285C23×C4—64no—
286C23×C4—62no—
287C23×C4—62no—
288C23×C4—62no—
289C23×C4—62no—
290C23×C4—62no—
291C23×C4—122no—
292C23×C4—122no—
293C23×C4C22×D312yes—
294C23×C4C22×D312yes—
295C23×C4C22×D311yescharacteristic
296C23×C4C22×D311yescharacteristic
297C23×C4C22×D311yescharacteristic
298C22⋊Q8—632no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—34no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—632no—
306C2×C4⋊C4—62no—
307C2×C4⋊C4—62no—
308C2×C4⋊C4—62no—
309C2×C4⋊C4—62no—
310C2×C4⋊C4—64no—
311C2×C4⋊C4—64no—
312C2×C4⋊C4—64no—
313C2×C4⋊C4—62no—
314C2×C4⋊C4—64no—
315C2×C4⋊C4—62no—
316C2×C4⋊C4—62no—
317C2×C4⋊C4—62no—
318C2×C4⋊C4—62no—
319C2×C4⋊C4—64no—
320C2×C4⋊C4—64no—
321C2×C4⋊C4—122no—
322C2×C4⋊C4#6714yes—
323C2×C22⋊C4—38no—
324C2×C22⋊C4—38no—
325C2×C22⋊C4—64no—
326C2×C22⋊C4—64no—
327C2×C22⋊C4—64no—
328C2×C22⋊C4—64no—
329#95—22no—
330#95—24no—
331#95—64no—
332#95—64no—
333#95—64no—
334#95—64no—
335#95—62no—
336#95—64no—
337#95—122no—
338C23×C3C22×D411yescharacteristic
339C23×C3C22×D411yescharacteristic
340C23×C3C22×D412yes—
341C23×C3C22×D411yescharacteristic
342C23×C3C22×Q811yescharacteristic
343C23×C3C22×Q812yes—
344C23×C3C2×#4111yescharacteristic
345C23×C3C2×#4111yescharacteristic
346C23×C3C2×#4111yescharacteristic
347C23×C3H(5,𝔽2)12yes—
348C23×C32−1+412yes—
349C22×D3—22no—
350C22×D3—22no—
351C22×D3—22no—
352C22×D3—22no—
353C22×D3—22no—
354C22×D3—22no—
355C22×D3—22no—
356C22×D3—22no—
357C22×D3—24no—
358C22×D3—24no—
359C22×D3—24no—
360C22×D3—24no—
361C22×D3—24no—
362C22×D3—24no—
363C22×D3—24no—
364C22×D3—24no—
365C22×D3—24no—
366C22×D3—24no—
367C22×D3#12014yes—
368C22×D3C22⋊Q818yes—
369C22×D3C22⋊Q814yes—
370C22×D3C4⋊Q814yes—
371C22×D3C4⋊Q818yes—
372C3×Q8—416no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—24no—
382C2×C3×C4—24no—
383C2×C3×C4—24no—
384C2×C3×C4—22no—
385C2×C3×C4—24no—
386C2×C3×C4—24no—
387C2×C3×C4—24no—
388C2×C3×C4—24no—
389C2×C3×C4—24no—
390C2×C3×C4—24no—
391C2×C3×C4—41no—
392C2×C3×C4—42no—
393C2×C3×C4—42no—
394C2×C3×C4—41no—
395C2×C3×C4—42no—
396C2×C3×C4—42no—
397C2×C3×C4—42no—
398C2×C3×C4—42no—
399C2×C3×C4—42no—
400C2×C3×C4—42no—
401C2×C3×C4—42no—
402C2×C3×C4#12014yes—
403C2×C3×C4C22⋊Q814yescomplemented
404C2×Dic3—22no—
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—22no—
408C2×Dic3—22no—
409C2×Dic3—22no—
410C2×Dic3—22no—
411C2×Dic3—24no—
412C2×Dic3—22no—
413C2×Dic3—22no—
414C2×Dic3—24no—
415C2×Dic3—22no—
416C2×Dic3—24no—
417C2×Dic3—24no—
418C2×Dic3—24no—
419C2×Dic3—24no—
420C2×Dic3—24no—
421C2×Dic3—41no—
422C2×Dic3—42no—
423C2×Dic3—42no—
424C2×Dic3—41no—
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×Dic3C22⋊Q814yescomplemented
435C4×D3—232no—
436C4×D3—416no—
437C4×D3—416no—
438C24—34no—
439C24—32no—
440C24—34no—
441C24—32no—
442C24—32no—
443C24—61no—
444C24—62no—
445C24—61no—
446C24—62no—
447C24—61no—
448C24—61no—
449C24C23×D311yescharacteristic
450C2×Q8—28no—
451C2×Q8—48no—
452C2×Q8—48no—
453C2×Q8—44no—
454C2×Q8—44no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—32no—
478C22×C4—32no—
479C22×C4—32no—
480C22×C4—34no—
481C22×C4—32no—
482C22×C4—32no—
483C22×C4—34no—
484C22×C4—68no—
485C22×C4—68no—
486C22×C4—68no—
487C22×C4—68no—
488C22×C4—68no—
489C22×C4—68no—
490C22×C4—68no—
491C22×C4—68no—
492C22×C4—61no—
493C22×C4—61no—
494C22×C4—61no—
495C22×C4—61no—
496C22×C4—68no—
497C22×C4—62no—
498C22×C4—62no—
499C22×C4—62no—
500C22×C4—62no—
501C22×C4—62no—
502C22×C4—61no—
503C22×C4—61no—
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—61no—
516C22×C4—61no—
517C22×C4—68no—
518C22×C4—124no—
519C22×C4—128no—
520C22×C4—128no—
521C22×C4—128no—
522C22×C4—128no—
523C22×C4—124no—
524C22×C4—124no—
525C22×C4D3×D414yes—
526C22×C4D3×D412yes—
527C22×C4D3×D412yes—
528C22×C4D3×Q814yes—
529C22×C4D3×Q812yes—
530C22×C4#23912yes—
531C22×C4C2×#6712yes—
532C22×C4C2×#6712yes—
533C22×C4C2×#6712yes—
534C4⋊C4—28no—
535C4⋊C4—48no—
536C4⋊C4—68no—
537C4⋊C4—68no—
538C4⋊C4—616no—
539C4⋊C4—68no—
540C4⋊C4—68no—
541C4⋊C4—128no—
542C22⋊C4—616no—
543C22⋊C4—616no—
544C22×C3C2×#12011yescharacteristic
545C22×C3C2×#12011yescharacteristic
546C22×C3C2×C22⋊Q811yescharacteristic
547C22×C3C2×C22⋊Q811yescharacteristic
548C22×C3C2×C22⋊Q811yescharacteristic
549C22×C3C2×C22⋊Q812yes—
550C22×C3#52511yescharacteristic
551C22×C3#52511yescharacteristic
552C22×C3#52511yescharacteristic
553C22×C3C2×C4⋊Q811yescharacteristic
554C22×C3C2×C4⋊Q812yes—
555C22×C3#53411yescharacteristic
556C22×C3#53611yescharacteristic
557C22×C3#53912yes—
558C22×C3#54412yes—
559C22×C3D4212yes—
560C22×C3D4212yes—
561C22×C3#54712yes—
562C22×C3#54712yes—
563C22×C3D4×Q812yes—
564C22×C3D4×Q812yes—
565C22×C3#55412yes—
566C22×C3#55412yes—
567C2×D3—24no—
568C2×D3—24no—
569C2×D3—24no—
570C2×D3—24no—
571C2×D3—24no—
572C2×D3—24no—
573C2×D3—28no—
574C2×D3—28no—
575C2×D3—28no—
576C2×D3—28no—
577C2×D3#39518yescomplemented
578C3×C4—24no—
579C3×C4—24no—
580C3×C4—42no—
581C3×C4—44no—
582C3×C4—44no—
583Dic3—24no—
584Dic3—42no—
585Dic3—42no—
586Dic3—44no—
587Dic3—44no—
588C23—34no—
589C23—38no—
590C23—34no—
591C23—38no—
592C23—34no—
593C23—64no—
594C23—64no—
595C23—62no—
596C23—64no—
597C23—64no—
598C23—64no—
599C23—64no—
600C23—62no—
601C23—64no—
602C23—62no—
603C23—64no—
604C23—62no—
605C23—62no—
606C23—64no—
607C23—62no—
608C23—62no—
609C23—62no—
610C23—64no—
611C23C2×D3×D411yescharacteristic
612C23C2×D3×D412yes—
613C23C2×D3×D411yescharacteristic
614C23#100412yes—
615C23C2×D3×Q812yes—
616C23C2×D3×Q811yescharacteristic
617C23C2×#23911yescharacteristic
618C23#100712yes—
619C23D3×#4111yescharacteristic
620C23D3×#4111yescharacteristic
621C23C22×#6711yescharacteristic
622Q8—416no—
623C2×C4—22no—
624C2×C4—24no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—24no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—24no—
634C2×C4—22no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—34no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—632no—
654C2×C4—62no—
655C2×C4—62no—
656C2×C4—62no—
657C2×C4—62no—
658C2×C4—62no—
659C2×C4—62no—
660C2×C4—64no—
661C2×C4—64no—
662C2×C4—64no—
663C2×C4—62no—
664C2×C4—62no—
665C2×C4—64no—
666C2×C4—62no—
667C2×C4—62no—
668C2×C4—64no—
669C2×C4—64no—
670C2×C4—64no—
671C2×C4—1216no—
672C2×C4—1216no—
673C2×C4—122no—
674C2×C4—122no—
675C2×C4—122no—
676C2×C4—122no—
677C2×C4—122no—
678C2×C4—122no—
679C2×C4—121no—
680C2×C4—121no—
681C2×C4—122no—
682C2×C4—122no—
683C2×C4—122no—
684C2×C4—122no—
685C2×C4—122no—
686C2×C4#93714yes—
687C2×C4#94614yescomplemented
688C2×C3C2×#39511yescharacteristic
689C2×C3#240311yescharacteristic
690C2×C3#240611yescharacteristic
691C2×C3#243411yescharacteristic
692C2×C3#244012yes—
693C2×C3#244012yes—
694C2×C3#244912yes—
695C2×C3#244912yes—
696C2×C3#258311yescharacteristic
697C2×C3#262711yescharacteristic
698C2×C3#284811yescharacteristic
699D3—28no—
700C22—38no—
701C22—64no—
702C22—68no—
703C22—68no—
704C22—68no—
705C22—64no—
706C22—64no—
707C22—64no—
708C22—68no—
709C22—64no—
710C22—64no—
711C22D3×#12011yescharacteristic
712C22#558911yescharacteristic
713C22#559012yes—
714C22D3×C22⋊Q811yescharacteristic
715C22D3×C22⋊Q812yes—
716C22D3×C22⋊Q811yescharacteristic
717C22#562711yescharacteristic
718C22#562711yescharacteristic
719C22#563112yes—
720C22#563612yes—
721C22#563812yes—
722C22D3×C4⋊Q811yescharacteristic
723C22D3×C4⋊Q812yes—
724C22#572411yescharacteristic
725C22#572612yes—
726C22#572712yes—
727C22#572912yes—
728C22#573012yes—
729C22C2×#93711yescharacteristic
730C22D4×#6712yes—
731C22C2×#94611yescharacteristic
732C22Q8×#6712yes—
733C22#582811yescharacteristic
734C4—24no—
735C4—24no—
736C4—44no—
737C4—42no—
738C4—44no—
739C4—64no—
740C4—122no—
741C4—122no—
742C4—124no—
743C4—124no—
744C3#1472011yescharacteristic, complemented, Sylow
745C2—68no—
746C2#7717412yes—
747C2D3×#39511yescharacteristic
748C2#7724911yescharacteristic
749C2#7725212yes—
750C2#7725511yescharacteristic
751C2#7725711yescharacteristic
752C2#8260411yescharacteristic
753C2#8281712yes—
754C2#8283411yescharacteristic
755C2#8323211yescharacteristic
756C2#8323312yes—
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#395C2
prime radicalC24×D3C23
hypercenterC2×#395D3
hypocenterC3#14720
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
3. C2×C3×#395C2semidirect
4. C2×#5230C2semidirect
6. #71568C2semidirect
7. #71565C2semidirect
10. #69420C2semidirect
11. #69410C2semidirect
47. C2×#395D3semidirect
87. C22×C4×D3Q8semidirect
100. C2×(C2×D3)⋊C4Q8semidirect
403. C2×C3×C4C22⋊Q8semidirect
434. C2×Dic3C22⋊Q8semidirect
577. C2×D3#395semidirect
687. C2×C4#946semidirect
744. C3#14720semidirect

Maximal subgroups

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

subgroupindex
C22×#9462
C22×D3×C4⋊C42
C2×C3×#3952
C2×#52302
C2×#49892
#715682
#715652
(C2×D3)⋊#952
#694202
#694102
#147203