Finite Group Databasebeta

← #10746870

Subgroups — #10746870

Order 768.

2246 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#894C211yesmaximal, characteristic
2C22×#897C211yesmaximal, characteristic, complemented
3C2×#4979C211yesmaximal, characteristic, complemented
4C2×#4673C211yesmaximal, characteristic, complemented
5C2×#4672C212yesmaximal
6C3×#1441C211yesmaximal, characteristic, complemented
7#71570C211yesmaximal, characteristic, complemented
8#69429C212yesmaximal, complemented
9#69427C212yesmaximal, complemented
10(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
11#69420C212yesmaximal, complemented
12#16251—31nomaximal, Sylow
13C23×D12C2211yescharacteristic
14C23×C4×D3C2211yescharacteristic
15C23×Dic6C2211yescharacteristic
16C22×C3×C4⋊C4C2211yescharacteristic
17C22×C3×C4⋊C4C2211yescharacteristic
18C22×(C2×D3)⋊C4C2211yescharacteristic
19C22×(C2×D3)⋊C4C2211yescharacteristic
20C22×(C2×D3)⋊C4C2212yes—
21C22×(C2×D3)⋊C4C2212yes—
22C22×(C2×D3)⋊C4C2212yes—
23C22×(C2×D3)⋊C4C2212yes—
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×C4⋊Dic3C2212yes—
26C22×Dic3⋊C4C2211yescharacteristic
27C22×Dic3⋊C4C2212yes—
28C2×#897—24no—
29C2×#897—28no—
30C2×#894—24no—
31C2×#894—24no—
32C2×#894—24no—
33C2×C3×#95C2212yes—
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2212yes—
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2211yescharacteristic
39C2×C3⋊#95C2212yes—
40C2×C3⋊#95C2212yes—
41#4979—24no—
42#4673—24no—
43#4672—28no—
44C22×#123—31no—
45C22×C22⋊Q8—31no—
46C2×#395—31no—
47C2×#394—32no—
48C2×#393—31no—
49#1444—32no—
50#1441D311yescharacteristic, complemented
51#1440—32no—
52#1439—32no—
53#1439—31no—
54C22⋊#95—31no—
55C24×D3C2311yescharacteristic
56C24×D3C2311yescharacteristic
57C23×C3×C4C2312yes—
58C23×C3×C4C2311yescharacteristic
59C23×C3×C4C2311yescharacteristic
60C23×C3×C4C2312yes—
61C23×C3×C4C2311yescharacteristic
62C23×Dic3C2312yes—
63C23×Dic3C2311yescharacteristic
64C23×Dic3C2311yescharacteristic
65C23×Dic3C2312yes—
66C22×D12—22no—
67C22×D12—22no—
68C22×D12—22no—
69C22×D12—24no—
70C22×D12—42no—
71C22×C4×D3—24no—
72C22×C4×D3—22no—
73C22×C4×D3—22no—
74C22×C4×D3—42no—
75C22×C4×D3D414yes—
76C22×Dic6—22no—
77C22×Dic6—24no—
78C22×Dic6—22no—
79C22×Dic6—22no—
80C22×Dic6—42no—
81C2×C3×C4⋊C4—22no—
82C2×C3×C4⋊C4—22no—
83C2×C3×C4⋊C4—24no—
84C2×C3×C4⋊C4—22no—
85C2×C3×C4⋊C4D414yes—
86C2×(C2×D3)⋊C4—22no—
87C2×(C2×D3)⋊C4—22no—
88C2×(C2×D3)⋊C4—24no—
89C2×(C2×D3)⋊C4—24no—
90C2×(C2×D3)⋊C4—22no—
91C2×(C2×D3)⋊C4—22no—
92C2×(C2×D3)⋊C4—22no—
93C2×(C2×D3)⋊C4—22no—
94C2×(C2×D3)⋊C4—22no—
95C2×(C2×D3)⋊C4—22no—
96C2×(C2×D3)⋊C4—24no—
97C2×(C2×D3)⋊C4—24no—
98C2×(C2×D3)⋊C4—24no—
99C2×(C2×D3)⋊C4—24no—
100C2×(C2×D3)⋊C4—24no—
101C2×(C2×D3)⋊C4—24no—
102C2×(C2×D3)⋊C4—42no—
103C2×(C2×D3)⋊C4—42no—
104C2×(C2×D3)⋊C4—42no—
105C2×(C2×D3)⋊C4D418yes—
106C2×(C2×D3)⋊C4D414yes—
107C2×C4⋊Dic3—24no—
108C2×C4⋊Dic3—24no—
109C2×C4⋊Dic3—24no—
110C2×Dic3⋊C4—22no—
111C2×Dic3⋊C4—22no—
112C2×Dic3⋊C4—22no—
113C2×Dic3⋊C4—24no—
114C2×Dic3⋊C4—24no—
115C2×Dic3⋊C4—42no—
116#897—232no—
117#894—232no—
118C3×#95—24no—
119C3×#95—22no—
120C3×#95—42no—
121C3⋊#95—22no—
122C3⋊#95—24no—
123C3⋊#95—24no—
124C3⋊#95—24no—
125C3⋊#95—42no—
126C23×Q8—31no—
127C23×D4—31no—
128C24×C4—31no—
129C2×#123—64no—
130C2×#123—64no—
131C2×#123—64no—
132C2×C22⋊Q8—68no—
133C2×C22⋊Q8—64no—
134C22×C4⋊C4—32no—
135C22×C4⋊C4—31no—
136C22×C4⋊C4—32no—
137C22×C4⋊C4C2×D311yescharacteristic
138C22×C4⋊C4C2×D311yescharacteristic
139C22×C22⋊C4—31no—
140C22×C22⋊C4—32no—
141C22×C22⋊C4—31no—
142C22×C22⋊C4—31no—
143C22×C22⋊C4—32no—
144C22×C22⋊C4—32no—
145C22×C22⋊C4—32no—
146#395—64no—
147#394—68no—
148#393—64no—
149C2×#95—32no—
150C2×#95—31no—
151C2×#95—32no—
152C2×#95—32no—
153C2×#95—32no—
154C2×#95C2×D311yescharacteristic
155C2×#95C2×D312yes—
156C2×#95C2×D312yes—
157C24×C3C2411yescharacteristic
158C23×D3—21no—
159C23×D3—21no—
160C23×D3—22no—
161C23×D3—21no—
162C23×D3—22no—
163C23×D3—21no—
164C23×D3—22no—
165C23×D3—21no—
166C23×D3—21no—
167C23×D3—21no—
168C23×D3—21no—
169C23×D3—22no—
170C23×D3—22no—
171C23×D3—21no—
172C23×D3—22no—
173C23×D3—21no—
174C23×D3—22no—
175C23×D3—21no—
176C23×D3—21no—
177C23×D3C2×D412yes—
178C23×D3C2×D412yes—
179C23×D3C2×D414yes—
180C22×C3×C4—22no—
181C22×C3×C4—22no—
182C22×C3×C4—22no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—22no—
186C22×C3×C4—22no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—22no—
190C22×C3×C4—22no—
191C22×C3×C4—21no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—22no—
203C22×C3×C4—22no—
204C22×C3×C4—22no—
205C22×C3×C4C2×D412yes—
206C22×C3×C4C2×D412yes—
207C22×C3×C4C2×D412yes—
208C22×C3×C4C2×D414yes—
209C22×C3×C4C2×D412yes—
210C22×C3×C4C2×D412yes—
211C22×Dic3—22no—
212C22×Dic3—22no—
213C22×Dic3—22no—
214C22×Dic3—21no—
215C22×Dic3—21no—
216C22×Dic3—22no—
217C22×Dic3—21no—
218C22×Dic3—21no—
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×Dic3C2×D412yes—
232C22×Dic3C2×D412yes—
233C22×Dic3C2×D414yes—
234C22×Dic3#4114yes—
235C2×D12—28no—
236C2×D12—48no—
237C2×D12—48no—
238C2×D12—44no—
239C2×D12—44no—
240C2×C4×D3—28no—
241C2×C4×D3—28no—
242C2×C4×D3—44no—
243C2×C4×D3—48no—
244C2×C4×D3—48no—
245C2×Dic6—28no—
246C2×Dic6—48no—
247C2×Dic6—48no—
248C2×Dic6—44no—
249C2×Dic6—44no—
250C3×C4⋊C4—28no—
251C3×C4⋊C4—28no—
252(C2×D3)⋊C4—28no—
253(C2×D3)⋊C4—28no—
254(C2×D3)⋊C4—216no—
255(C2×D3)⋊C4—28no—
256(C2×D3)⋊C4—48no—
257(C2×D3)⋊C4—48no—
258(C2×D3)⋊C4—48no—
259C4⋊Dic3—216no—
260Dic3⋊C4—28no—
261Dic3⋊C4—48no—
262C25—31no—
263C25—31no—
264C22×Q8—64no—
265C22×Q8—62no—
266C22×Q8—62no—
267C22×Q8—62no—
268C22×Q8—122no—
269C22×D4—62no—
270C22×D4—62no—
271C22×D4—64no—
272C22×D4—62no—
273C22×D4—122no—
274C23×C4—32no—
275C23×C4—31no—
276C23×C4—32no—
277C23×C4—31no—
278C23×C4—34no—
279C23×C4—64no—
280C23×C4—62no—
281C23×C4—62no—
282C23×C4—122no—
283C23×C4C22×D312yes—
284C23×C4C22×D311yescharacteristic
285C23×C4C22×D311yescharacteristic
286C23×C4C22×D312yes—
287C23×C4C22×D311yescharacteristic
288#123—632no—
289C22⋊Q8—632no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—64no—
295C2×C4⋊C4—64no—
296C2×C4⋊C4—62no—
297C2×C4⋊C4—62no—
298C2×C4⋊C4—62no—
299C2×C4⋊C4—64no—
300C2×C4⋊C4—64no—
301C2×C4⋊C4—64no—
302C2×C4⋊C4—122no—
303C2×C4⋊C4D1214yes—
304C2×C22⋊C4—38no—
305C2×C22⋊C4—34no—
306C2×C22⋊C4—62no—
307C2×C22⋊C4—62no—
308C2×C22⋊C4—64no—
309C2×C22⋊C4—64no—
310C2×C22⋊C4—62no—
311C2×C22⋊C4—62no—
312C2×C22⋊C4—62no—
313C2×C22⋊C4—62no—
314C2×C22⋊C4—62no—
315C2×C22⋊C4—62no—
316C2×C22⋊C4—64no—
317C2×C22⋊C4—64no—
318C2×C22⋊C4—64no—
319C2×C22⋊C4—64no—
320C2×C22⋊C4—64no—
321C2×C22⋊C4—64no—
322C2×C22⋊C4—122no—
323C2×C22⋊C4—122no—
324C2×C22⋊C4—122no—
325#95—22no—
326#95—24no—
327#95—42no—
328#95—64no—
329#95—64no—
330#95—62no—
331#95—64no—
332#95—122no—
333C23×C3C22×D411yescharacteristic
334C23×C3C22×D411yescharacteristic
335C23×C3C22×D412yes—
336C23×C3C22×D411yescharacteristic
337C23×C3C2×#4112yes—
338C23×C3H(5,𝔽2)11yescharacteristic
339C23×C3H(5,𝔽2)12yes—
340C23×C32−1+411yescharacteristic
341C23×C32−1+412yes—
342C23×C32−1+411yescharacteristic
343C23×C32−1+411yescharacteristic
344C22×D3—22no—
345C22×D3—22no—
346C22×D3—22no—
347C22×D3—24no—
348C22×D3—22no—
349C22×D3—22no—
350C22×D3—24no—
351C22×D3—22no—
352C22×D3—24no—
353C22×D3—24no—
354C22×D3—24no—
355C22×D3—24no—
356C22×D3—22no—
357C22×D3—22no—
358C22×D3—22no—
359C22×D3—24no—
360C22×D3—24no—
361C22×D3—41no—
362C22×D3—41no—
363C22×D3—41no—
364C22×D3—41no—
365C22×D3—42no—
366C22×D3—42no—
367C22×D3—42no—
368C22×D3—42no—
369C22×D3—42no—
370C22×D3—42no—
371C22×D3—41no—
372C22×D3—41no—
373C22×D3—41no—
374C22×D3—42no—
375C22×D3—41no—
376C22×D3—41no—
377C22×D3—41no—
378C22×D3—42no—
379C22×D3—41no—
380C22×D3—41no—
381C22×D3—42no—
382C22×D3—42no—
383C22×D3—42no—
384C22×D3—42no—
385C22×D3—42no—
386C22×D3—42no—
387C22×D3—42no—
388C22×D3—42no—
389C22×D3#12014yes—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—24no—
393C2×C3×C4—24no—
394C2×C3×C4—22no—
395C2×C3×C4—24no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—24no—
400C2×C3×C4—24no—
401C2×C3×C4—24no—
402C2×C3×C4—41no—
403C2×C3×C4—42no—
404C2×C3×C4—41no—
405C2×C3×C4—41no—
406C2×C3×C4—41no—
407C2×C3×C4—41no—
408C2×C3×C4—41no—
409C2×C3×C4—42no—
410C2×C3×C4—42no—
411C2×C3×C4—42no—
412C2×C3×C4—42no—
413C2×C3×C4—42no—
414C2×C3×C4—42no—
415C2×C3×C4—42no—
416C2×C3×C4—42no—
417C2×C3×C4—42no—
418C2×C3×C4—42no—
419C2×C3×C4—42no—
420C2×C3×C4#12014yes—
421C2×Dic3—22no—
422C2×Dic3—22no—
423C2×Dic3—22no—
424C2×Dic3—24no—
425C2×Dic3—22no—
426C2×Dic3—24no—
427C2×Dic3—24no—
428C2×Dic3—24no—
429C2×Dic3—24no—
430C2×Dic3—24no—
431C2×Dic3—24no—
432C2×Dic3—42no—
433C2×Dic3—41no—
434C2×Dic3—42no—
435C2×Dic3—42no—
436C2×Dic3—41no—
437C2×Dic3—42no—
438C2×Dic3—42no—
439C2×Dic3—42no—
440C2×Dic3—42no—
441C2×Dic3—42no—
442C2×Dic3—42no—
443C2×Dic3—42no—
444C2×Dic3—42no—
445D12—416no—
446C4×D3—416no—
447Dic6—416no—
448C24—34no—
449C24—32no—
450C24—32no—
451C24—61no—
452C24—61no—
453C24—61no—
454C24—62no—
455C24—61no—
456C24—62no—
457C24—62no—
458C24—61no—
459C24—61no—
460C24—61no—
461C24—61no—
462C24—62no—
463C24—61no—
464C24—61no—
465C24—62no—
466C24—62no—
467C24—62no—
468C24—61no—
469C24—61no—
470C24C23×D311yescharacteristic
471C2×Q8—68no—
472C2×Q8—128no—
473C2×Q8—128no—
474C2×Q8—124no—
475C2×Q8—124no—
476C2×D4—68no—
477C2×D4—128no—
478C2×D4—124no—
479C2×D4—128no—
480C2×D4—124no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—32no—
507C22×C4—34no—
508C22×C4—32no—
509C22×C4—34no—
510C22×C4—68no—
511C22×C4—62no—
512C22×C4—62no—
513C22×C4—61no—
514C22×C4—61no—
515C22×C4—62no—
516C22×C4—61no—
517C22×C4—62no—
518C22×C4—61no—
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×C4—62no—
529C22×C4—62no—
530C22×C4—62no—
531C22×C4—68no—
532C22×C4—124no—
533C22×C4—128no—
534C22×C4—128no—
535C22×C4C2×D1212yes—
536C22×C4C2×D1212yes—
537C22×C4C2×D1212yes—
538C22×C4D3×D414yes—
539C22×C4D3×D412yes—
540C22×C4D3×D412yes—
541C4⋊C4—28no—
542C4⋊C4—28no—
543C4⋊C4—616no—
544C4⋊C4—68no—
545C4⋊C4—128no—
546C22⋊C4—616no—
547C22⋊C4—68no—
548C22⋊C4—68no—
549C22⋊C4—68no—
550C22⋊C4—128no—
551C22⋊C4—128no—
552C22⋊C4—128no—
553C22×C3C2×#12011yescharacteristic
554C22×C3C2×#12011yescharacteristic
555C22×C3#53211yescharacteristic
556C22×C3#53411yescharacteristic
557C22×C3#53612yes—
558C22×C3#53611yescharacteristic
559C22×C3#53611yescharacteristic
560C22×C3#53611yescharacteristic
561C22×C3#53612yes—
562C22×C3#53611yescharacteristic
563C22×C3#53711yescharacteristic
564C22×C3#53711yescharacteristic
565C22×C3#53711yescharacteristic
566C22×C3#53912yes—
567C22×C3#54212yes—
568C22×C3D4212yes—
569C22×C3D4212yes—
570C22×C3#54612yes—
571C22×C3#54712yes—
572C22×C3#54712yes—
573C22×C3#54812yes—
574C22×C3#56212yes—
575C22×C3#56312yes—
576C2×D3—24no—
577C2×D3—24no—
578C2×D3—24no—
579C2×D3—42no—
580C2×D3—42no—
581C2×D3—44no—
582C2×D3—44no—
583C2×D3—44no—
584C2×D3—44no—
585C2×D3—42no—
586C2×D3—42no—
587C2×D3—42no—
588C2×D3—42no—
589C2×D3—44no—
590C2×D3—44no—
591C2×D3—42no—
592C2×D3—81no—
593C2×D3—81no—
594C2×D3—82no—
595C2×D3—82no—
596C2×D3—81no—
597C2×D3—81no—
598C3×C4—24no—
599C3×C4—42no—
600C3×C4—42no—
601C3×C4—44no—
602C3×C4—82no—
603Dic3—44no—
604Dic3—42no—
605Dic3—44no—
606Dic3—42no—
607C23—34no—
608C23—62no—
609C23—64no—
610C23—62no—
611C23—64no—
612C23—62no—
613C23—62no—
614C23—64no—
615C23—62no—
616C23—64no—
617C23—64no—
618C23—64no—
619C23—62no—
620C23—62no—
621C23—62no—
622C23—64no—
623C23—62no—
624C23—64no—
625C23—122no—
626C23—122no—
627C23—122no—
628C23—122no—
629C23—121no—
630C23—121no—
631C23—122no—
632C23—121no—
633C23—121no—
634C23—122no—
635C23—122no—
636C23—121no—
637C23—122no—
638C23—121no—
639C23—122no—
640C23—122no—
641C23—122no—
642C23—122no—
643C23—121no—
644C23—121no—
645C23—121no—
646C23—122no—
647C23—122no—
648C23—121no—
649C23—121no—
650C23—122no—
651C23—122no—
652C23—121no—
653C23C22×D1211yescharacteristic
654C23C2×D3×D411yescharacteristic
655C23C2×D3×D412yes—
656C23C2×D3×D411yescharacteristic
657C23#100411yescharacteristic
658C23#100712yes—
659C23#100711yescharacteristic
660C23D3×#4112yes—
661C23#100912yes—
662C23#101011yescharacteristic
663C23#101011yescharacteristic
664Q8—1216no—
665D4—1216no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—41no—
682C2×C4—42no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—62no—
697C2×C4—64no—
698C2×C4—62no—
699C2×C4—62no—
700C2×C4—64no—
701C2×C4—64no—
702C2×C4—64no—
703C2×C4—62no—
704C2×C4—64no—
705C2×C4—64no—
706C2×C4—64no—
707C2×C4—1216no—
708C2×C4—122no—
709C2×C4—122no—
710C2×C4—121no—
711C2×C4—121no—
712C2×C4—122no—
713C2×C4—122no—
714C2×C4—122no—
715C2×C4—122no—
716C2×C4—122no—
717C2×C4—122no—
718C2×C4—122no—
719C2×C4—122no—
720C2×C4—122no—
721C2×C4#88214yes—
722C2×C3#240311yescharacteristic
723C2×C3#243011yescharacteristic
724C2×C3#243211yescharacteristic
725C2×C3#261411yescharacteristic
726C2×C3#261611yescharacteristic
727C2×C3#266311yescharacteristic
728C2×C3#267212yes—
729C2×C3#267412yes—
730C2×C3#268012yes—
731C2×C3#268112yes—
732C2×C3#281411yescharacteristic
733D3—44no—
734D3—82no—
735C22—64no—
736C22—64no—
737C22—64no—
738C22—124no—
739C22—124no—
740C22—124no—
741C22—122no—
742C22—122no—
743C22—122no—
744C22—122no—
745C22—124no—
746C22—124no—
747C22—122no—
748C22—124no—
749C22—122no—
750C22—122no—
751C22—241no—
752C22—242no—
753C22—241no—
754C22—241no—
755C22—241no—
756C22—242no—
757C22C2×#88211yescharacteristic
758C22#551011yescharacteristic
759C22#552611yescharacteristic
760C22D4×D1212yes—
761C22#557612yes—
762C22D3×#12011yescharacteristic
763C22#560811yescharacteristic
764C22#560811yescharacteristic
765C22#560912yes—
766C22#561012yes—
767C22#562812yes—
768C22#562811yescharacteristic
769C22#562811yescharacteristic
770C22#563112yes—
771C22#564712yes—
772C22#565311yescharacteristic
773C22#565512yes—
774C22#566811yescharacteristic
775C22#569212yes—
776C22#569912yes—
777C22#571012yes—
778C22#572412yes—
779C22#572411yescharacteristic
780C4—24no—
781C4—44no—
782C4—42no—
783C4—42no—
784C4—82no—
785C4—122no—
786C4—124no—
787C4—122no—
788C4—124no—
789C3#1625111yescharacteristic, complemented, Sylow
790C2—124no—
791C2—242no—
792C2#7395011yescharacteristic
793C2#7488411yescharacteristic
794C2#7538812yes—
795C2#7625912yes—
796C2#7649811yescharacteristic
797C2#7711611yescharacteristic
798C2#7725611yescharacteristic
799C2#7742612yes—
800C2#7796912yes—
801C2#7800611yescharacteristic
802C2#7823211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1441C2
prime radicalC23×D12C22
hypercenter#1441D3
hypocenterC3#16251
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
2. C22×#897C2semidirect
3. C2×#4979C2semidirect
4. C2×#4673C2semidirect
6. C3×#1441C2semidirect
7. #71570C2semidirect
8. #69429C2semidirect
9. #69427C2semidirect
10. (C2×D3)⋊#95C2semidirect
11. #69420C2semidirect
50. #1441D3semidirect
789. C3#16251semidirect

Maximal subgroups

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

subgroupindex
C22×#8942
C22×#8972
C2×#49792
C2×#46732
C2×#46722
C3×#14412
#715702
#694292
#694272
(C2×D3)⋊#952
#694202
#162513