Finite Group Databasebeta

← #10720168

Subgroups — #10720168

Order 768.

2634 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#892C211yesmaximal, characteristic, complemented
2C22×#883C211yesmaximal, characteristic
3C2×#4956C212yesmaximal
4C2×D3×#95C211yesmaximal, characteristic, complemented
5C3×#1439C211yesmaximal, characteristic, complemented
6#71566C211yesmaximal, characteristic, complemented
7#71546C211yesmaximal, characteristic, complemented
8#71545C212yesmaximal, complemented
9(C2×D3)⋊#95C212yesmaximal, complemented
10#69410C211yesmaximal, characteristic, complemented
11#69407C212yesmaximal, complemented
12#14135—31nomaximal, Sylow
13C23×#67C2211yescharacteristic
14C23×C4×D3C2212yes—
15C23×C4×D3C2211yescharacteristic
16C22×C3×C4⋊C4C2211yescharacteristic
17C22×C3×C22⋊C4C2212yes—
18C22×C3×C22⋊C4C2211yescharacteristic
19C22×#217C2212yes—
20C22×#217C2211yescharacteristic
21C22×(C2×D3)⋊C4C2211yescharacteristic
22C22×(C2×D3)⋊C4C2212yes—
23C22×C4⋊Dic3C2211yescharacteristic
24C22×C4⋊Dic3C2211yescharacteristic
25C22×Dic3⋊C4C2211yescharacteristic
26C22×C4×Dic3C2212yes—
27C2×#892—24no—
28C2×#892—28no—
29C2×#883—24no—
30C2×#883—24no—
31C2×#883C418yescomplemented
32C2×C3×#95C2212yes—
33C2×C3×#95C2211yescharacteristic
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2211yescharacteristic
39C2×C3⋊#95C2212yes—
40C2×C3⋊#95C2212yes—
41#4956—28no—
42D3×#95—24no—
43C22×#123—31no—
44C22×#117—31no—
45C2×#386—32no—
46C22×#95—31no—
47#1441—31no—
48#1441—31no—
49#1439—31no—
50#1439D311yescharacteristic, complemented
51#1437—32no—
52#1436—32no—
53C22⋊#95—32no—
54C25×C3C2311yescharacteristic
55C24×D3C2311yescharacteristic
56C23×C3×C4C2311yescharacteristic
57C23×C3×C4C2312yes—
58C23×C3×C4C2312yes—
59C23×C3×C4C2311yescharacteristic
60C22×#67—24no—
61C22×#67—22no—
62C22×#67—22no—
63C22×#67—24no—
64C22×#67C2×C414yes—
65C23×Dic3C2311yescharacteristic
66C23×Dic3C2311yescharacteristic
67C23×Dic3C2312yes—
68C23×Dic3C2312yes—
69C23×Dic3C2311yescharacteristic
70C22×C4×D3—24no—
71C22×C4×D3—24no—
72C22×C4×D3—24no—
73C22×C4×D3—24no—
74C22×C4×D3—24no—
75C22×C4×D3—24no—
76C22×C4×D3—24no—
77C22×C4×D3—42no—
78C22×C4×D3—42no—
79C22×C4×D3C2×C414yes—
80C22×C4×D3D414yes—
81C22×C4×D3D414yes—
82C2×C3×C4⋊C4—24no—
83C2×C3×C4⋊C4—22no—
84C2×C3×C22⋊C4—22no—
85C2×C3×C22⋊C4—22no—
86C2×C3×C22⋊C4—24no—
87C2×C3×C22⋊C4—24no—
88C2×C3×C22⋊C4—42no—
89C2×C3×C22⋊C4C2×C414yescomplemented
90C2×#217—22no—
91C2×#217—22no—
92C2×#217—24no—
93C2×#217—24no—
94C2×#217—42no—
95C2×#217C2×C414yescomplemented
96C2×(C2×D3)⋊C4—22no—
97C2×(C2×D3)⋊C4—22no—
98C2×(C2×D3)⋊C4—24no—
99C2×(C2×D3)⋊C4—24no—
100C2×(C2×D3)⋊C4C2×C414yes—
101C2×(C2×D3)⋊C4D418yes—
102C2×C4⋊Dic3—22no—
103C2×C4⋊Dic3—22no—
104C2×C4⋊Dic3—22no—
105C2×C4⋊Dic3—24no—
106C2×C4⋊Dic3C2×C414yescomplemented
107C2×Dic3⋊C4—22no—
108C2×Dic3⋊C4—22no—
109C2×Dic3⋊C4C2×C414yescomplemented
110C2×C4×Dic3—24no—
111C2×C4×Dic3—24no—
112C2×C4×Dic3—24no—
113#892—232no—
114#883—232no—
115C3×#95—22no—
116C3×#95—24no—
117C3⋊#95—22no—
118C3⋊#95—24no—
119C3⋊#95—24no—
120C3⋊#95—24no—
121C3⋊#95—24no—
122C3⋊#95—42no—
123C3⋊#95—42no—
124C23×D4—31no—
125C24×C4—31no—
126C24×C4—32no—
127C2×#123—38no—
128C2×#123—64no—
129C2×#123—64no—
130C2×#117—68no—
131C2×#117—64no—
132C22×C4⋊C4—31no—
133C22×C4⋊C4—31no—
134C22×C4⋊C4—31no—
135C22×C4⋊C4C2×D311yescharacteristic
136C22×C22⋊C4—31no—
137C22×C22⋊C4—32no—
138C22×C22⋊C4—31no—
139C22×C22⋊C4—32no—
140C22×C22⋊C4C2×D312yes—
141C22×C22⋊C4C2×D311yescharacteristic
142C22×C42—32no—
143#386—68no—
144C2×#95—32no—
145C2×#95—32no—
146C2×#95—32no—
147C2×#95—32no—
148C2×#95—31no—
149C2×#95—32no—
150C2×#95—32no—
151C2×#95—64no—
152C2×#95C2×D312yes—
153C2×#95C2×D311yescharacteristic
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×C3C22×C412yes—
165C24×C3C2411yescharacteristic
166C23×D3—22no—
167C23×D3—22no—
168C23×D3—21no—
169C23×D3—21no—
170C23×D3—21no—
171C23×D3—21no—
172C23×D3C22×C412yes—
173C23×D3C2×D412yes—
174C23×D3C2×D412yes—
175C23×D3C2×D414yes—
176C23×D3#4114yes—
177C22×C3×C4—22no—
178C22×C3×C4—22no—
179C22×C3×C4—22no—
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—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×C4C22×C412yes—
196C22×C3×C4C22×C412yes—
197C22×C3×C4C2×D414yes—
198C22×C3×C4C2×D412yes—
199C22×C3×C4C2×D412yes—
200C22×C3×C4#4114yes—
201C2×#67—28no—
202C2×#67—216no—
203C2×#67—44no—
204C2×#67—48no—
205C2×#67—44no—
206C22×Dic3—22no—
207C22×Dic3—22no—
208C22×Dic3—22no—
209C22×Dic3—22no—
210C22×Dic3—22no—
211C22×Dic3—22no—
212C22×Dic3—22no—
213C22×Dic3—21no—
214C22×Dic3—21no—
215C22×Dic3—21no—
216C22×Dic3—21no—
217C22×Dic3—22no—
218C22×Dic3—22no—
219C22×Dic3—22no—
220C22×Dic3—22no—
221C22×Dic3—22no—
222C22×Dic3—21no—
223C22×Dic3—21no—
224C22×Dic3—22no—
225C22×Dic3—22no—
226C22×Dic3—22no—
227C22×Dic3—21no—
228C22×Dic3—22no—
229C22×Dic3—21no—
230C22×Dic3C22×C412yes—
231C22×Dic3C22×C412yes—
232C22×Dic3C22×C412yes—
233C22×Dic3C2×D414yes—
234C22×Dic3C2×D412yes—
235C22×Dic3C2×D412yes—
236C22×Dic3#4114yes—
237C2×C4×D3—216no—
238C2×C4×D3—28no—
239C2×C4×D3—216no—
240C2×C4×D3—28no—
241C2×C4×D3—216no—
242C2×C4×D3—48no—
243C2×C4×D3—48no—
244C2×C4×D3—48no—
245C2×C4×D3—48no—
246C2×C4×D3—48no—
247C2×C4×D3—48no—
248C2×C4×D3C22⋊C4116yescomplemented
249C3×C4⋊C4—28no—
250C3×C22⋊C4—28no—
251C3×C22⋊C4—48no—
252#217—28no—
253#217—48no—
254(C2×D3)⋊C4—28no—
255(C2×D3)⋊C4—216no—
256C4⋊Dic3—28no—
257C4⋊Dic3—28no—
258Dic3⋊C4—28no—
259C4×Dic3—216no—
260C25—31no—
261C25C22×D311yescharacteristic
262C22×D4—34no—
263C22×D4—62no—
264C22×D4—62no—
265C22×D4—64no—
266C22×D4—64no—
267C23×C4—31no—
268C23×C4—34no—
269C23×C4—34no—
270C23×C4—34no—
271C23×C4—31no—
272C23×C4—32no—
273C23×C4—32no—
274C23×C4—31no—
275C23×C4—64no—
276C23×C4—64no—
277C23×C4—64no—
278C23×C4—64no—
279C23×C4—64no—
280C23×C4—64no—
281C23×C4—64no—
282C23×C4—122no—
283C23×C4—122no—
284C23×C4C22×D311yescharacteristic
285C23×C4C22×D312yes—
286C23×C4C22×D312yes—
287C23×C4C22×D311yescharacteristic
288#123—632no—
289#117—632no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—34no—
293C2×C4⋊C4—34no—
294C2×C4⋊C4—64no—
295C2×C4⋊C4—62no—
296C2×C4⋊C4—62no—
297C2×C4⋊C4—62no—
298C2×C4⋊C4—62no—
299C2×C4⋊C4—62no—
300C2×C22⋊C4—22no—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—34no—
305C2×C22⋊C4—34no—
306C2×C22⋊C4—38no—
307C2×C22⋊C4—42no—
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—64no—
315C2×C22⋊C4—64no—
316C2×C22⋊C4—122no—
317C2×C22⋊C4C4×D314yescomplemented
318C2×C42—64no—
319C2×C42—64no—
320C2×C42—64no—
321#95—22no—
322#95—24no—
323#95—64no—
324#95—64no—
325#95—64no—
326#95—62no—
327#95—64no—
328#95—122no—
329#95—122no—
330C23×C3—22no—
331C23×C3—24no—
332C23×C3—24no—
333C23×C3—22no—
334C23×C3—22no—
335C23×C3—41no—
336C23×C3—42no—
337C23×C3—41no—
338C23×C3—42no—
339C23×C3—41no—
340C23×C3—41no—
341C23×C3—41no—
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×C3—42no—
351C23×C3—42no—
352C23×C3—42no—
353C23×C3C23×C411yescharacteristic
354C23×C3C22×D411yescharacteristic
355C23×C3C22×D411yescharacteristic
356C23×C3C22×D412yes—
357C23×C3C2×#4112yes—
358C23×C3C2×#4112yes—
359C23×C3C2×#4112yes—
360C23×C3H(5,𝔽2)11yescharacteristic
361C23×C3H(5,𝔽2)11yescharacteristic
362C23×C32−1+411yescharacteristic
363C23×C32−1+411yescharacteristic
364C22×D3—24no—
365C22×D3—22no—
366C22×D3—22no—
367C22×D3—24no—
368C22×D3—22no—
369C22×D3—22no—
370C22×D3—22no—
371C22×D3—22no—
372C22×D3—22no—
373C22×D3—22no—
374C22×D3—24no—
375C22×D3—24no—
376C22×D3—24no—
377C22×D3—24no—
378C22×D3—24no—
379C22×D3—24no—
380C22×D3—24no—
381C22×D3—24no—
382C22×D3C2×C22⋊C414yes—
383C22×D3C4×D418yes—
384C22×D3#12014yes—
385C22×D3#12118yes—
386C22×D3#12314yes—
387C2×C3×C4—24no—
388C2×C3×C4—22no—
389C2×C3×C4—24no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—24no—
393C2×C3×C4—24no—
394C2×C3×C4—24no—
395C2×C3×C4—24no—
396C2×C3×C4—24no—
397C2×C3×C4—24no—
398C2×C3×C4—24no—
399C2×C3×C4—42no—
400C2×C3×C4—42no—
401C2×C3×C4—41no—
402C2×C3×C4—42no—
403C2×C3×C4—41no—
404C2×C3×C4—42no—
405C2×C3×C4—42no—
406C2×C3×C4—42no—
407C2×C3×C4—42no—
408C2×C3×C4—42no—
409C2×C3×C4—42no—
410C2×C3×C4C2×C22⋊C414yes—
411#67—416no—
412C2×Dic3—24no—
413C2×Dic3—22no—
414C2×Dic3—24no—
415C2×Dic3—22no—
416C2×Dic3—22no—
417C2×Dic3—22no—
418C2×Dic3—24no—
419C2×Dic3—22no—
420C2×Dic3—22no—
421C2×Dic3—24no—
422C2×Dic3—24no—
423C2×Dic3—24no—
424C2×Dic3—24no—
425C2×Dic3—24no—
426C2×Dic3—24no—
427C2×Dic3—41no—
428C2×Dic3—42no—
429C2×Dic3—42no—
430C2×Dic3—41no—
431C2×Dic3—42no—
432C2×Dic3—42no—
433C2×Dic3—41no—
434C2×Dic3—41no—
435C2×Dic3—41no—
436C2×Dic3—41no—
437C2×Dic3—42no—
438C2×Dic3—42no—
439C2×Dic3—42no—
440C2×Dic3—42no—
441C2×Dic3—42no—
442C2×Dic3C2×C22⋊C414yes—
443C4×D3—232no—
444C4×D3—432no—
445C24—21no—
446C24—21no—
447C24—22no—
448C24—22no—
449C24—21no—
450C24—21no—
451C24—22no—
452C24—22no—
453C24—21no—
454C24—21no—
455C24—32no—
456C24—34no—
457C24—32no—
458C24—32no—
459C24—34no—
460C24—62no—
461C24—61no—
462C24—61no—
463C24—62no—
464C24—61no—
465C24—61no—
466C24C2×C4×D312yes—
467C24C23×D311yescharacteristic
468C2×D4—68no—
469C2×D4—616no—
470C2×D4—124no—
471C2×D4—124no—
472C2×D4—128no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
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—32no—
492C22×C4—32no—
493C22×C4—32no—
494C22×C4—316no—
495C22×C4—32no—
496C22×C4—32no—
497C22×C4—34no—
498C22×C4—34no—
499C22×C4—68no—
500C22×C4—68no—
501C22×C4—616no—
502C22×C4—616no—
503C22×C4—616no—
504C22×C4—62no—
505C22×C4—62no—
506C22×C4—62no—
507C22×C4—62no—
508C22×C4—62no—
509C22×C4—62no—
510C22×C4—62no—
511C22×C4—61no—
512C22×C4—61no—
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—61no—
525C22×C4—62no—
526C22×C4—62no—
527C22×C4—61no—
528C22×C4—128no—
529C22×C4—128no—
530C22×C4—128no—
531C22×C4—128no—
532C22×C4—128no—
533C22×C4—128no—
534C22×C4C2×C4×D312yes—
535C22×C4C2×C4×D312yes—
536C22×C4D3×D414yes—
537C22×C4D3×D412yes—
538C22×C4D3×D412yes—
539C22×C4#23714yes—
540C4⋊C4—28no—
541C4⋊C4—68no—
542C4⋊C4—68no—
543C4⋊C4—68no—
544C22⋊C4—28no—
545C22⋊C4—48no—
546C22⋊C4—616no—
547C22⋊C4—68no—
548C22⋊C4—68no—
549C22⋊C4—128no—
550C42—616no—
551C22×C3—42no—
552C22×C3—44no—
553C22×C3—44no—
554C22×C3—42no—
555C22×C3—42no—
556C22×C3—82no—
557C22×C3—82no—
558C22×C3—81no—
559C22×C3—81no—
560C22×C3—81no—
561C22×C3—81no—
562C22×C3C22×C22⋊C411yescharacteristic
563C22×C3C2×C4×D412yes—
564C22×C3C4×#4112yes—
565C22×C3#52011yescharacteristic
566C22×C3#52011yescharacteristic
567C22×C3C2×#12011yescharacteristic
568C22×C3C2×#12112yes—
569C22×C3C2×#12311yescharacteristic
570C22×C3#52512yes—
571C22×C3#53211yescharacteristic
572C22×C3#53211yescharacteristic
573C22×C3#53511yescharacteristic
574C22×C3#53611yescharacteristic
575C22×C3#53711yescharacteristic
576C22×C3#53711yescharacteristic
577C22×C3#54612yes—
578C22×C3#54612yes—
579C22×C3#54712yes—
580C22×C3#54712yes—
581C22×C3#55112yes—
582C22×C3#55112yes—
583C22×C3#55212yes—
584C22×C3#55212yes—
585C2×D3—24no—
586C2×D3—28no—
587C2×D3—28no—
588C2×D3—28no—
589C2×D3—28no—
590C2×D3—24no—
591C2×D3—24no—
592C2×D3—24no—
593C2×D3—24no—
594C2×D3—24no—
595C2×D3#38618yes—
596C3×C4—24no—
597C3×C4—44no—
598C3×C4—44no—
599C3×C4—42no—
600Dic3—24no—
601Dic3—42no—
602Dic3—44no—
603Dic3—44no—
604Dic3—42no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—24no—
609C23—24no—
610C23—34no—
611C23—34no—
612C23—38no—
613C23—34no—
614C23—38no—
615C23—42no—
616C23—41no—
617C23—42no—
618C23—42no—
619C23—41no—
620C23—42no—
621C23—42no—
622C23—41no—
623C23—41no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—41no—
628C23—41no—
629C23—42no—
630C23—41no—
631C23—41no—
632C23—42no—
633C23—64no—
634C23—64no—
635C23—64no—
636C23—62no—
637C23—64no—
638C23—64no—
639C23—62no—
640C23—62no—
641C23—62no—
642C23—64no—
643C23—64no—
644C23—64no—
645C23—62no—
646C23—62no—
647C23—64no—
648C23—62no—
649C23—62no—
650C23—64no—
651C23C22×C4×D311yescharacteristic
652C23C2×D3×D411yescharacteristic
653C23C2×D3×D412yes—
654C23C2×D3×D411yescharacteristic
655C23C2×#23712yes—
656C23#100411yescharacteristic
657C23#100711yescharacteristic
658C23D3×#4112yes—
659C23D3×#4112yes—
660C23#100911yescharacteristic
661C23#101011yescharacteristic
662D4—1216no—
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—34no—
676C2×C4—42no—
677C2×C4—41no—
678C2×C4—42no—
679C2×C4—41no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—632no—
688C2×C4—62no—
689C2×C4—64no—
690C2×C4—62no—
691C2×C4—64no—
692C2×C4—64no—
693C2×C4—64no—
694C2×C4—64no—
695C2×C4—62no—
696C2×C4—62no—
697C2×C4—62no—
698C2×C4—62no—
699C2×C4—64no—
700C2×C4—64no—
701C2×C4—64no—
702C2×C4—64no—
703C2×C4—1232no—
704C2×C4—121no—
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—121no—
714C2×C4—121no—
715C2×C4—121no—
716C2×C4—121no—
717C2×C4—122no—
718C2×C4—122no—
719C2×C4D3×C22⋊C414yes—
720C2×C3—82no—
721C2×C3C2×#38611yescharacteristic
722C2×C3#229711yescharacteristic
723C2×C3#231111yescharacteristic
724C2×C3#235912yes—
725C2×C3#235912yes—
726C2×C3#241112yes—
727C2×C3#241312yes—
728C2×C3#243011yescharacteristic
729C2×C3#243011yescharacteristic
730C2×C3#249811yescharacteristic
731C2×C3#249811yescharacteristic
732D3—28no—
733C22—38no—
734C22—42no—
735C22—42no—
736C22—44no—
737C22—44no—
738C22—42no—
739C22—64no—
740C22—64no—
741C22—64no—
742C22—68no—
743C22—68no—
744C22—64no—
745C22—68no—
746C22—68no—
747C22—64no—
748C22—64no—
749C22—81no—
750C22—82no—
751C22—81no—
752C22—82no—
753C22—81no—
754C22—81no—
755C22C2×D3×C22⋊C411yescharacteristic
756C22#550411yescharacteristic
757C22#552311yescharacteristic
758C22C4×#23712yes—
759C22C4×D3×D412yes—
760C22D3×#12011yescharacteristic
761C22#559112yes—
762C22D3×#12112yes—
763C22#560612yes—
764C22#560711yescharacteristic
765C22#560811yescharacteristic
766C22#561112yes—
767C22#562811yescharacteristic
768C22#562911yescharacteristic
769C22#563112yes—
770C22#563912yes—
771C22D3×#12311yescharacteristic
772C22#565812yes—
773C22#565912yes—
774C22#566811yescharacteristic
775C22#567612yes—
776C22#570812yes—
777C22#571611yescharacteristic
778C4—24no—
779C4—42no—
780C4—44no—
781C4—44no—
782C4—64no—
783C4—122no—
784C4—124no—
785C4—124no—
786C4—122no—
787C3#1413511yescharacteristic, complemented, Sylow
788C2—68no—
789C2—82no—
790C2#7400311yescharacteristic
791C2#7459712yes—
792C2D3×#38611yescharacteristic
793C2#7583812yes—
794C2#7629011yescharacteristic
795C2#7675711yescharacteristic
796C2#7686411yescharacteristic
797C2#7710912yes—
798C2#7741512yes—
799C2#7767911yescharacteristic
800C2#7810611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1439C2
socle, cosocleC24×C3C24
prime radicalC23×#67C22
hypercenter#1439D3
hypocenterC3#14135
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C22×#892C2semidirect
4. C2×D3×#95C2semidirect
5. C3×#1439C2semidirect
6. #71566C2semidirect
7. #71546C2semidirect
8. #71545C2semidirect
9. (C2×D3)⋊#95C2semidirect
10. #69410C2semidirect
11. #69407C2semidirect
31. C2×#883C4semidirect
50. #1439D3semidirect
89. C2×C3×C22⋊C4C2×C4semidirect
95. C2×#217C2×C4semidirect
106. C2×C4⋊Dic3C2×C4semidirect
109. C2×Dic3⋊C4C2×C4semidirect
248. C2×C4×D3C22⋊C4semidirect
317. C2×C22⋊C4C4×D3semidirect
787. C3#14135semidirect

Maximal subgroups

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

subgroupindex
C22×#8922
C22×#8832
C2×#49562
C2×D3×#952
C3×#14392
#715662
#715462
#715452
(C2×D3)⋊#952
#694102
#694072
#141353