Finite Group Databasebeta

← #10727990

Subgroups — #10727990

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×#67⋊C4C211yesmaximal, characteristic
2C2×#4987C211yesmaximal, characteristic, complemented
3C2×#4949C211yesmaximal, characteristic, complemented
4C2×#4659C211yesmaximal, characteristic, complemented
5C3×#1439C211yesmaximal, characteristic, complemented
6#71566C211yesmaximal, characteristic, complemented
7#71550C212yesmaximal
8#71544C212yesmaximal, complemented
9#69428C212yesmaximal, complemented
10(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
11#69405C212yesmaximal, complemented
12#14825—31nomaximal, Sylow
13C23×#67C2211yescharacteristic
14C24×Dic3C2211yescharacteristic
15C23×C4×D3C2211yescharacteristic
16C22×C3×C4⋊C4C2211yescharacteristic
17C22×C3×C22⋊C4C2211yescharacteristic
18C22×C3×C22⋊C4C2212yes—
19C22×#217C2212yes—
20C22×(C2×D3)⋊C4C2211yescharacteristic
21C22×(C2×D3)⋊C4C2212yes—
22C22×(C2×D3)⋊C4C2212yes—
23C22×C4⋊Dic3C2211yescharacteristic
24C22×Dic3⋊C4C2212yes—
25C22×Dic3⋊C4C2211yescharacteristic
26C22×C4×Dic3C2211yescharacteristic
27C2×#67⋊C4—24no—
28C2×#67⋊C4—24no—
29C2×#67⋊C4—24no—
30C2×C3×#95C2211yescharacteristic
31C2×C3×#95C2212yes—
32C2×C3⋊#95C2212yes—
33C2×C3⋊#95C2212yes—
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2211yescharacteristic
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39#4987—24no—
40#4949—24no—
41#4659—24no—
42C22×C4×D4—31no—
43C2×#400—31no—
44C2×#399—31no—
45C2×#380—31no—
46#1441—31no—
47#1439—32no—
48#1439D311yescharacteristic, complemented
49#1438—32no—
50#1436—32no—
51C22⋊#95—31no—
52C22⋊#95—32no—
53C25×C3C2311yescharacteristic
54C24×D3C2311yescharacteristic
55C23×C3×C4C2312yes—
56C23×C3×C4C2312yes—
57C23×C3×C4C2311yescharacteristic
58C23×C3×C4C2311yescharacteristic
59C22×#67—22no—
60C22×#67—22no—
61C22×#67—22no—
62C22×#67—22no—
63C22×#67—22no—
64C22×#67—22no—
65C22×#67Q814yes—
66C23×Dic3—22no—
67C23×Dic3—22no—
68C23×Dic3—22no—
69C23×Dic3—24no—
70C23×Dic3—42no—
71C23×Dic3C2312yes—
72C23×Dic3C2311yescharacteristic
73C23×Dic3C2312yes—
74C23×Dic3C2311yescharacteristic
75C23×Dic3C2311yescharacteristic
76C22×C4×D3—22no—
77C22×C4×D3—22no—
78C22×C4×D3—24no—
79C22×C4×D3—42no—
80C22×C4×D3D414yes—
81C2×C3×C4⋊C4—22no—
82C2×C3×C4⋊C4—42no—
83C2×C3×C22⋊C4—22no—
84C2×C3×C22⋊C4—22no—
85C2×C3×C22⋊C4—24no—
86C2×C3×C22⋊C4—42no—
87C2×C3×C22⋊C4—42no—
88C2×C3×C22⋊C4D414yes—
89C2×#217—24no—
90C2×#217—24no—
91C2×#217—42no—
92C2×(C2×D3)⋊C4—22no—
93C2×(C2×D3)⋊C4—22no—
94C2×(C2×D3)⋊C4—22no—
95C2×(C2×D3)⋊C4—24no—
96C2×(C2×D3)⋊C4—24no—
97C2×(C2×D3)⋊C4—24no—
98C2×(C2×D3)⋊C4—42no—
99C2×(C2×D3)⋊C4—42no—
100C2×(C2×D3)⋊C4—42no—
101C2×C4⋊Dic3—22no—
102C2×C4⋊Dic3—22no—
103C2×C4⋊Dic3—22no—
104C2×Dic3⋊C4—22no—
105C2×Dic3⋊C4—22no—
106C2×Dic3⋊C4—24no—
107C2×Dic3⋊C4—24no—
108C2×Dic3⋊C4—42no—
109C2×Dic3⋊C4D414yes—
110C2×C4×Dic3—22no—
111C2×C4×Dic3—22no—
112C2×C4×Dic3—22no—
113#67⋊C4—232no—
114C3×#95—22no—
115C3×#95—42no—
116C3⋊#95—22no—
117C3⋊#95—24no—
118C3⋊#95—24no—
119C3⋊#95—24no—
120C3⋊#95—24no—
121C3⋊#95—24no—
122C3⋊#95—42no—
123C23×D4—31no—
124C24×C4—31no—
125C24×C4—31no—
126C2×C4×D4—64no—
127C2×C4×D4—64no—
128C2×C4×D4—64no—
129C22×C4⋊C4—31no—
130C22×C4⋊C4—31no—
131C22×C4⋊C4—32no—
132C22×C4⋊C4C2×D311yescharacteristic
133C22×C22⋊C4—31no—
134C22×C22⋊C4—32no—
135C22×C22⋊C4—32no—
136C22×C22⋊C4—32no—
137C22×C22⋊C4C2×D311yescharacteristic
138C22×C22⋊C4C2×D312yes—
139C22×C42—31no—
140#400—64no—
141#399—64no—
142#380—64no—
143C2×#95—31no—
144C2×#95—32no—
145C2×#95—32no—
146C2×#95—32no—
147C2×#95—32no—
148C2×#95—32no—
149C2×#95—32no—
150C2×#95C2×D311yescharacteristic
151C2×#95C2×D312yes—
152C24×C3—21no—
153C24×C3—21no—
154C24×C3—22no—
155C24×C3—22no—
156C24×C3—21no—
157C24×C3—21no—
158C24×C3—22no—
159C24×C3—22no—
160C24×C3C2×D412yes—
161C24×C3C2×Q812yes—
162C24×C3#4112yes—
163C24×C3C2411yescharacteristic
164C23×D3—21no—
165C23×D3—21no—
166C23×D3—22no—
167C23×D3—22no—
168C23×D3—21no—
169C23×D3—21no—
170C23×D3—22no—
171C23×D3—22no—
172C23×D3C2×D412yes—
173C23×D3C2×Q812yes—
174C23×D3#4112yes—
175C22×C3×C4—22no—
176C22×C3×C4—22no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—22no—
180C22×C3×C4—22no—
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—22no—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—22no—
195C22×C3×C4C2×D412yes—
196C22×C3×C4C2×D412yes—
197C22×C3×C4C2×D412yes—
198C22×C3×C4C2×D412yes—
199C2×#67—28no—
200C2×#67—28no—
201C2×#67—28no—
202C2×#67—28no—
203C2×#67—28no—
204C2×#67—28no—
205C2×#67—28no—
206C22×Dic3—21no—
207C22×Dic3—21no—
208C22×Dic3—21no—
209C22×Dic3—21no—
210C22×Dic3—21no—
211C22×Dic3—21no—
212C22×Dic3—22no—
213C22×Dic3—28no—
214C22×Dic3—22no—
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—22no—
225C22×Dic3—22no—
226C22×Dic3—22no—
227C22×Dic3—22no—
228C22×Dic3—22no—
229C22×Dic3—22no—
230C22×Dic3—22no—
231C22×Dic3—48no—
232C22×Dic3—48no—
233C22×Dic3—44no—
234C22×Dic3—44no—
235C22×Dic3C2×D412yes—
236C22×Dic3C2×D412yes—
237C22×Dic3C2×D412yes—
238C22×Dic3C2×Q812yes—
239C22×Dic3#4114yes—
240C22×Dic3#4112yes—
241C22×Dic3#4114yes—
242C2×C4×D3—28no—
243C2×C4×D3—28no—
244C2×C4×D3—44no—
245C2×C4×D3—48no—
246C2×C4×D3—48no—
247C3×C4⋊C4—44no—
248C3×C22⋊C4—28no—
249C3×C22⋊C4—48no—
250#217—48no—
251(C2×D3)⋊C4—28no—
252(C2×D3)⋊C4—48no—
253(C2×D3)⋊C4—48no—
254C4⋊Dic3—44no—
255Dic3⋊C4—28no—
256Dic3⋊C4—48no—
257C4×Dic3—28no—
258C25—31no—
259C25C22×D311yescharacteristic
260C22×D4—34no—
261C22×D4—62no—
262C22×D4—62no—
263C22×D4—62no—
264C22×D4—62no—
265C22×D4—62no—
266C22×D4—62no—
267C23×C4—31no—
268C23×C4—31no—
269C23×C4—32no—
270C23×C4—31no—
271C23×C4—34no—
272C23×C4—32no—
273C23×C4—64no—
274C23×C4—62no—
275C23×C4—62no—
276C23×C4—64no—
277C23×C4—62no—
278C23×C4—62no—
279C23×C4—62no—
280C23×C4—122no—
281C23×C4—122no—
282C23×C4C22×D312yes—
283C23×C4C22×D312yes—
284C23×C4C22×D311yescharacteristic
285C23×C4C22×D311yescharacteristic
286C4×D4—632no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—34no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—62no—
291C2×C4⋊C4—62no—
292C2×C4⋊C4—64no—
293C2×C4⋊C4—64no—
294C2×C4⋊C4—62no—
295C2×C4⋊C4—62no—
296C2×C4⋊C4—62no—
297C2×C4⋊C4—122no—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—42no—
302C2×C22⋊C4—42no—
303C2×C22⋊C4—62no—
304C2×C22⋊C4—62no—
305C2×C22⋊C4—62no—
306C2×C22⋊C4—64no—
307C2×C22⋊C4—64no—
308C2×C22⋊C4—64no—
309C2×C22⋊C4—64no—
310C2×C22⋊C4—64no—
311C2×C22⋊C4—122no—
312C2×C22⋊C4—122no—
313C2×C22⋊C4—122no—
314C2×C22⋊C4—122no—
315C2×C22⋊C4D1214yes—
316C2×C42—62no—
317C2×C42—62no—
318C2×C42—62no—
319#95—22no—
320#95—42no—
321#95—64no—
322#95—64no—
323#95—64no—
324#95—64no—
325#95—64no—
326#95—62no—
327#95—122no—
328C23×C3—22no—
329C23×C3—22no—
330C23×C3—22no—
331C23×C3—22no—
332C23×C3—22no—
333C23×C3—22no—
334C23×C3—24no—
335C23×C3—24no—
336C23×C3—24no—
337C23×C3—24no—
338C23×C3—24no—
339C23×C3—24no—
340C23×C3—41no—
341C23×C3—42no—
342C23×C3—41no—
343C23×C3—41no—
344C23×C3—41no—
345C23×C3—42no—
346C23×C3—42no—
347C23×C3—42no—
348C23×C3—42no—
349C23×C3—42no—
350C23×C3C22⋊Q814yes—
351C23×C3C22×D411yescharacteristic
352C23×C3C22×D411yescharacteristic
353C23×C3C22×D411yescharacteristic
354C23×C3C22×Q811yescharacteristic
355C23×C3C2×#4111yescharacteristic
356C23×C3C2×#4111yescharacteristic
357C23×C3C2×#4111yescharacteristic
358C23×C3C2×#4112yes—
359C23×C3C2×#4112yes—
360C23×C3H(5,𝔽2)12yes—
361C23×C3H(5,𝔽2)12yes—
362C22×D3—22no—
363C22×D3—22no—
364C22×D3—22no—
365C22×D3—22no—
366C22×D3—22no—
367C22×D3—22no—
368C22×D3—22no—
369C22×D3—22no—
370C22×D3—22no—
371C22×D3—22no—
372C22×D3—24no—
373C22×D3—24no—
374C22×D3—24no—
375C22×D3—24no—
376C22×D3—42no—
377C22×D3—42no—
378C22×D3—42no—
379C22×D3—42no—
380C22×D3—42no—
381C22×D3—42no—
382C22×D3—42no—
383C22×D3—42no—
384C22×D3C22⋊Q814yes—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—24no—
388C2×C3×C4—24no—
389C2×C3×C4—22no—
390C2×C3×C4—24no—
391C2×C3×C4—41no—
392C2×C3×C4—41no—
393C2×C3×C4—42no—
394C2×C3×C4—42no—
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—42no—
403C2×C3×C4—42no—
404C2×C3×C4—42no—
405C2×C3×C4—42no—
406C2×C3×C4—42no—
407C2×C3×C4—42no—
408C2×C3×C4#12014yes—
409#67—232no—
410C2×Dic3—22no—
411C2×Dic3—22no—
412C2×Dic3—22no—
413C2×Dic3—22no—
414C2×Dic3—22no—
415C2×Dic3—22no—
416C2×Dic3—22no—
417C2×Dic3—22no—
418C2×Dic3—24no—
419C2×Dic3—24no—
420C2×Dic3—22no—
421C2×Dic3—24no—
422C2×Dic3—24no—
423C2×Dic3—24no—
424C2×Dic3—24no—
425C2×Dic3—416no—
426C2×Dic3—41no—
427C2×Dic3—42no—
428C2×Dic3—41no—
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×Dic3C22⋊Q814yes—
441C2×Dic3#12314yes—
442C4×D3—416no—
443C24—21no—
444C24—21no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—21no—
450C24—21no—
451C24—32no—
452C24—32no—
453C24—32no—
454C24—61no—
455C24—61no—
456C24—61no—
457C24—62no—
458C24—62no—
459C24—62no—
460C24—62no—
461C24—61no—
462C24C2×D1212yes—
463C24#23712yes—
464C24D3×Q812yes—
465C24C23×D311yescharacteristic
466C2×D4—68no—
467C2×D4—68no—
468C2×D4—68no—
469C2×D4—68no—
470C2×D4—68no—
471C2×D4—68no—
472C2×D4—68no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—32no—
494C22×C4—32no—
495C22×C4—32no—
496C22×C4—32no—
497C22×C4—34no—
498C22×C4—32no—
499C22×C4—34no—
500C22×C4—68no—
501C22×C4—61no—
502C22×C4—61no—
503C22×C4—61no—
504C22×C4—61no—
505C22×C4—61no—
506C22×C4—62no—
507C22×C4—61no—
508C22×C4—68no—
509C22×C4—62no—
510C22×C4—61no—
511C22×C4—61no—
512C22×C4—62no—
513C22×C4—62no—
514C22×C4—62no—
515C22×C4—62no—
516C22×C4—62no—
517C22×C4—62no—
518C22×C4—62no—
519C22×C4—68no—
520C22×C4—62no—
521C22×C4—62no—
522C22×C4—62no—
523C22×C4—62no—
524C22×C4—62no—
525C22×C4—62no—
526C22×C4—62no—
527C22×C4—124no—
528C22×C4—128no—
529C22×C4—128no—
530C22×C4—124no—
531C22×C4—128no—
532C22×C4—128no—
533C22×C4—124no—
534C22×C4C2×D1212yes—
535C22×C4C2×D1212yes—
536C22×C4D3×D412yes—
537C22×C4D3×D412yes—
538C4⋊C4—44no—
539C4⋊C4—68no—
540C4⋊C4—128no—
541C4⋊C4—124no—
542C22⋊C4—28no—
543C22⋊C4—48no—
544C22⋊C4—68no—
545C22⋊C4—128no—
546C22⋊C4—128no—
547C22⋊C4—128no—
548C42—68no—
549C22×C3—24no—
550C22×C3—28no—
551C22×C3—42no—
552C22×C3—42no—
553C22×C3—42no—
554C22×C3—42no—
555C22×C3—42no—
556C22×C3—44no—
557C22×C3—44no—
558C22×C3—44no—
559C22×C3—42no—
560C22×C3C2×#12011yescharacteristic
561C22×C3C2×C22⋊Q811yescharacteristic
562C22×C3C2×C22⋊Q811yescharacteristic
563C22×C3C2×C22⋊Q811yescharacteristic
564C22×C3C2×#12311yescharacteristic
565C22×C3#52511yescharacteristic
566C22×C3#52511yescharacteristic
567C22×C3#52511yescharacteristic
568C22×C3#52912yes—
569C22×C3#52912yes—
570C22×C3#53211yescharacteristic
571C22×C3#53411yescharacteristic
572C22×C3#53511yescharacteristic
573C22×C3#53812yes—
574C22×C3#54012yes—
575C22×C3#54612yes—
576C22×C3#54612yes—
577C22×C3#54612yes—
578C22×C3#55012yes—
579C22×C3#55112yes—
580C22×C3#55312yes—
581C22×C3#55412yes—
582C22×C3#55412yes—
583C2×D3—24no—
584C2×D3—24no—
585C2×D3—24no—
586C2×D3—42no—
587C2×D3—42no—
588C2×D3—42no—
589C2×D3—42no—
590C2×D3—44no—
591C2×D3—44no—
592C2×D3—44no—
593C2×D3—44no—
594C3×C4—24no—
595C3×C4—42no—
596C3×C4—82no—
597C3×C4—82no—
598Dic3—24no—
599Dic3—24no—
600Dic3—42no—
601Dic3—44no—
602Dic3—82no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—22no—
607C23—22no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—34no—
616C23—41no—
617C23—42no—
618C23—41no—
619C23—42no—
620C23—42no—
621C23—41no—
622C23—41no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—64no—
627C23—64no—
628C23—62no—
629C23—64no—
630C23—62no—
631C23—64no—
632C23—62no—
633C23—62no—
634C23—62no—
635C23—62no—
636C23—62no—
637C23—62no—
638C23—62no—
639C23—62no—
640C23—122no—
641C23—122no—
642C23—122no—
643C23—122no—
644C23—122no—
645C23—122no—
646C23—122no—
647C23—122no—
648C23#89714yes—
649C23C22×D1211yescharacteristic
650C23C2×D3×D411yescharacteristic
651C23C2×D3×D411yescharacteristic
652C23C2×#23711yescharacteristic
653C23#100412yes—
654C23#100412yes—
655C23C2×D3×Q811yescharacteristic
656C23D3×#4112yes—
657C23D3×#4112yes—
658C23D3×#4111yescharacteristic
659C23D3×#4111yescharacteristic
660D4—632no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—34no—
668C2×C4—34no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—62no—
687C2×C4—62no—
688C2×C4—62no—
689C2×C4—62no—
690C2×C4—64no—
691C2×C4—62no—
692C2×C4—62no—
693C2×C4—62no—
694C2×C4—64no—
695C2×C4—62no—
696C2×C4—64no—
697C2×C4—64no—
698C2×C4—62no—
699C2×C4—64no—
700C2×C4—64no—
701C2×C4—1216no—
702C2×C4—1216no—
703C2×C4—121no—
704C2×C4—122no—
705C2×C4—122no—
706C2×C4—122no—
707C2×C4—122no—
708C2×C4—121no—
709C2×C4—122no—
710C2×C4—122no—
711C2×C4—122no—
712C2×C4—122no—
713C2×C4—122no—
714C2×C4—122no—
715C2×C4—122no—
716C2×C4—122no—
717C2×C4#88214yes—
718C2×C3—44no—
719C2×C3#239511yescharacteristic
720C2×C3#240511yescharacteristic
721C2×C3#243111yescharacteristic
722C2×C3#245012yes—
723C2×C3#245412yes—
724C2×C3#245712yes—
725C2×C3#246712yes—
726C2×C3#248711yescharacteristic
727C2×C3#256411yescharacteristic
728C2×C3#263511yescharacteristic
729C2×C3#284811yescharacteristic
730D3—44no—
731C22—24no—
732C22—28no—
733C22—42no—
734C22—42no—
735C22—44no—
736C22—44no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—44no—
742C22—64no—
743C22—64no—
744C22—64no—
745C22—122no—
746C22—124no—
747C22—124no—
748C22—122no—
749C22—122no—
750C22—124no—
751C22—122no—
752C22—124no—
753C22C2×#88211yescharacteristic
754C22C2×#89711yescharacteristic
755C22#552411yescharacteristic
756C22#555412yes—
757C22#555412yes—
758C22#558911yescharacteristic
759C22#559312yes—
760C22#559912yes—
761C22#560611yescharacteristic
762C22#560611yescharacteristic
763C22#561012yes—
764C22#561512yes—
765C22D3×C22⋊Q811yescharacteristic
766C22D3×C22⋊Q811yescharacteristic
767C22#563612yes—
768C22#563612yes—
769C22#564912yes—
770C22D3×#12311yescharacteristic
771C22#566112yes—
772C22#566811yescharacteristic
773C22#567912yes—
774C22#570612yes—
775C22#571511yescharacteristic
776C4—24no—
777C4—42no—
778C4—64no—
779C4—64no—
780C4—82no—
781C4—82no—
782C4—124no—
783C4—122no—
784C4—242no—
785C3#1482511yescharacteristic, complemented, Sylow
786C2—44no—
787C2—124no—
788C2#7404911yescharacteristic
789C2#7442412yes—
790C2#7468611yescharacteristic
791C2#7585112yes—
792C2#7631311yescharacteristic
793C2#7670311yescharacteristic
794C2#7686911yescharacteristic
795C2#7692112yes—
796C2#7729112yes—
797C2#7745811yescharacteristic
798C2#7802911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1439C2
prime radicalC23×#67C22
hypercenter#1439D3
hypocenterC3#14825
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#4987C2semidirect
3. C2×#4949C2semidirect
4. C2×#4659C2semidirect
5. C3×#1439C2semidirect
6. #71566C2semidirect
8. #71544C2semidirect
9. #69428C2semidirect
10. (C2×D3)⋊#95C2semidirect
11. #69405C2semidirect
48. #1439D3semidirect
785. C3#14825semidirect

Maximal subgroups

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

subgroupindex
C22×#67⋊C42
C2×#49872
C2×#49492
C2×#46592
C3×#14392
#715662
#715502
#715442
#694282
(C2×D3)⋊#952
#694052
#148253