Finite Group Databasebeta

← C3×#16680 #10635287

Subgroups — C3×#16680 #10635287

Order 768.

2182 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#124C211yesmaximal, characteristic, complemented
2C2×C3×#393C211yesmaximal, characteristic, complemented
3C2×C3×#392C211yesmaximal, characteristic
4C2×C3×#388C211yesmaximal, characteristic, complemented
5C3×#1446C211yesmaximal, characteristic, complemented
6C3×#1440C212yesmaximal, complemented
7C3×#1439C212yesmaximal, complemented
8C3×#1438C212yesmaximal, complemented
9C3×#1438C212yesmaximal, complemented
10C3×#1438C211yesmaximal, characteristic, complemented
11C3×#1434C211yesmaximal, characteristic, complemented
12#16680C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×Q8C2211yescharacteristic
14C23×C3×D4C2212yes—
15C23×C3×D4C2211yescharacteristic
16C2×C3×#124—24no—
17C2×C3×#124—24no—
18C2×C3×#124—24no—
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2212yes—
22C22×C3×C22⋊C4C2212yes—
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2212yes—
25C22×C3×C22⋊C4C2212yes—
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2212yes—
28C22×C3×C22⋊C4C2212yes—
29C22×C3×C42C2211yescharacteristic
30C3×#393—24no—
31C3×#392—24no—
32C3×#388—24no—
33C2×C3×#95C2211yescharacteristic
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2212yes—
36C2×C3×#95C2211yescharacteristic
37C2×C3×#95C2211yescharacteristic
38C2×C3×#95C2212yes—
39C2×C3×#95C2212yes—
40C2×C3×#95C2212yes—
41C2×C3×#95C2212yes—
42C22×#124C2×C311yescharacteristic, complemented
43C2×#393C2×C311yescharacteristic, complemented
44C2×#392C2×C311yescharacteristic
45C2×#388C2×C311yescharacteristic, complemented
46#1446C2×C311yescharacteristic, complemented
47#1440C2×C312yescomplemented
48#1439C2×C312yescomplemented
49#1438C2×C312yescomplemented
50#1438C2×C312yescomplemented
51#1438C2×C311yescharacteristic, complemented
52#1434C2×C311yescharacteristic, complemented
53C25×C3C2312yes—
54C25×C3C2311yescharacteristic
55C22×C3×Q8—22no—
56C22×C3×Q8—22no—
57C22×C3×Q8—42no—
58C22×C3×Q8—42no—
59C22×C3×Q8D414yescomplemented
60C22×C3×D4—24no—
61C22×C3×D4—24no—
62C22×C3×D4—22no—
63C22×C3×D4—22no—
64C22×C3×D4—24no—
65C22×C3×D4—42no—
66C22×C3×D4—42no—
67C22×C3×D4—42no—
68C22×C3×D4—42no—
69C22×C3×D4—42no—
70C22×C3×D4—42no—
71C22×C3×D4D414yes—
72C23×C3×C4C2312yes—
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2312yes—
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2312yes—
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C3×#124—232no—
82C2×C3×C4⋊C4—22no—
83C2×C3×C4⋊C4—42no—
84C2×C3×C22⋊C4—24no—
85C2×C3×C22⋊C4—24no—
86C2×C3×C22⋊C4—22no—
87C2×C3×C22⋊C4—22no—
88C2×C3×C22⋊C4—24no—
89C2×C3×C22⋊C4—24no—
90C2×C3×C22⋊C4—24no—
91C2×C3×C22⋊C4—24no—
92C2×C3×C22⋊C4—22no—
93C2×C3×C22⋊C4—24no—
94C2×C3×C22⋊C4—22no—
95C2×C3×C22⋊C4—22no—
96C2×C3×C22⋊C4—22no—
97C2×C3×C22⋊C4—24no—
98C2×C3×C22⋊C4—22no—
99C2×C3×C22⋊C4—24no—
100C2×C3×C22⋊C4—24no—
101C2×C3×C22⋊C4—42no—
102C2×C3×C22⋊C4—42no—
103C2×C3×C22⋊C4—42no—
104C2×C3×C22⋊C4—42no—
105C2×C3×C22⋊C4—42no—
106C2×C3×C22⋊C4—42no—
107C2×C3×C22⋊C4—42no—
108C2×C3×C22⋊C4—42no—
109C2×C3×C22⋊C4—42no—
110C2×C3×C42—22no—
111C2×C3×C42—22no—
112C2×C3×C42D414yescomplemented
113C3×#95—22no—
114C3×#95—22no—
115C3×#95—22no—
116C3×#95—24no—
117C3×#95—22no—
118C3×#95—24no—
119C3×#95—42no—
120C3×#95—42no—
121C3×#95—42no—
122C23×Q8C22×C311yescharacteristic
123C23×D4C22×C312yes—
124C23×D4C22×C311yescharacteristic
125C2×#124—24no—
126C2×#124—24no—
127C2×#124—24no—
128C22×C4⋊C4C22×C311yescharacteristic
129C22×C22⋊C4C22×C311yescharacteristic
130C22×C22⋊C4C22×C312yes—
131C22×C22⋊C4C22×C312yes—
132C22×C22⋊C4C22×C311yescharacteristic
133C22×C22⋊C4C22×C312yes—
134C22×C22⋊C4C22×C312yes—
135C22×C22⋊C4C22×C312yes—
136C22×C22⋊C4C22×C311yescharacteristic
137C22×C22⋊C4C22×C312yes—
138C22×C42C22×C311yescharacteristic
139#393—24no—
140#392—24no—
141#388—24no—
142C2×#95C22×C311yescharacteristic
143C2×#95C22×C311yescharacteristic
144C2×#95C22×C312yes—
145C2×#95C22×C312yes—
146C2×#95C22×C311yescharacteristic
147C2×#95C22×C311yescharacteristic
148C2×#95C22×C312yes—
149C2×#95C22×C312yes—
150C2×#95C22×C312yes—
151C24×C3—21no—
152C24×C3—21no—
153C24×C3—22no—
154C24×C3—22no—
155C24×C3—21no—
156C24×C3—21no—
157C24×C3—22no—
158C24×C3—22no—
159C24×C3—22no—
160C24×C3—22no—
161C24×C3—22no—
162C24×C3—22no—
163C24×C3—22no—
164C24×C3—22no—
165C24×C3—22no—
166C24×C3—22no—
167C24×C3—22no—
168C24×C3—22no—
169C24×C3—22no—
170C24×C3—22no—
171C24×C3—22no—
172C24×C3—21no—
173C24×C3—22no—
174C24×C3—21no—
175C24×C3C2×D414yes—
176C24×C3#4112yes—
177C24×C3C2411yescharacteristic
178C2×C3×Q8—28no—
179C2×C3×Q8—48no—
180C2×C3×Q8—48no—
181C2×C3×Q8—44no—
182C2×C3×Q8—44no—
183C2×C3×D4—28no—
184C2×C3×D4—48no—
185C2×C3×D4—48no—
186C2×C3×D4—48no—
187C2×C3×D4—48no—
188C2×C3×D4—44no—
189C2×C3×D4—44no—
190C2×C3×D4—48no—
191C2×C3×D4—48no—
192C2×C3×D4—48no—
193C2×C3×D4—48no—
194C2×C3×D4—48no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—21no—
198C22×C3×C4—22no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—22no—
204C22×C3×C4—22no—
205C22×C3×C4—22no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—22no—
210C22×C3×C4—21no—
211C22×C3×C4—22no—
212C22×C3×C4—22no—
213C22×C3×C4—22no—
214C22×C3×C4—22no—
215C22×C3×C4—22no—
216C22×C3×C4—22no—
217C22×C3×C4—22no—
218C22×C3×C4—22no—
219C22×C3×C4—22no—
220C22×C3×C4—22no—
221C22×C3×C4—22no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—22no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—22no—
229C22×C3×C4—22no—
230C22×C3×C4—22no—
231C22×C3×C4—22no—
232C22×C3×C4—22no—
233C22×C3×C4—22no—
234C22×C3×C4—22no—
235C22×C3×C4—22no—
236C22×C3×C4—21no—
237C22×C3×C4—22no—
238C22×C3×C4—22no—
239C22×C3×C4—21no—
240C22×C3×C4C2×D412yes—
241C22×C3×C4C2×D414yes—
242C22×C3×C4C2×D412yes—
243C22×C3×C4C2×D412yes—
244C22×C3×C4C2×D412yes—
245C22×C3×C4C2×D412yes—
246C22×C3×C4#4114yes—
247C22×C3×C4#4112yes—
248C3×C4⋊C4—44no—
249C3×C22⋊C4—28no—
250C3×C22⋊C4—216no—
251C3×C22⋊C4—216no—
252C3×C22⋊C4—48no—
253C3×C22⋊C4—48no—
254C3×C22⋊C4—44no—
255C3×C22⋊C4—48no—
256C3×C22⋊C4—48no—
257C3×C22⋊C4—44no—
258C3×C42—28no—
259C25C23×C312yes—
260C25C23×C311yescharacteristic
261C22×Q8—22no—
262C22×Q8—22no—
263C22×Q8—42no—
264C22×Q8—42no—
265C22×Q8C3×D414yescomplemented
266C22×D4—24no—
267C22×D4—24no—
268C22×D4—22no—
269C22×D4—22no—
270C22×D4—24no—
271C22×D4—42no—
272C22×D4—42no—
273C22×D4—42no—
274C22×D4—42no—
275C22×D4—42no—
276C22×D4—42no—
277C22×D4C3×D414yes—
278C23×C4C23×C311yescharacteristic
279C23×C4C23×C312yes—
280C23×C4C23×C311yescharacteristic
281C23×C4C23×C311yescharacteristic
282C23×C4C23×C312yes—
283C23×C4C23×C311yescharacteristic
284C23×C4C23×C311yescharacteristic
285C23×C4C23×C312yes—
286C23×C4C23×C311yescharacteristic
287#124—232no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—42no—
290C2×C22⋊C4—24no—
291C2×C22⋊C4—24no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—24no—
294C2×C22⋊C4—24no—
295C2×C22⋊C4—24no—
296C2×C22⋊C4—24no—
297C2×C22⋊C4—22no—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—22no—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—42no—
308C2×C22⋊C4—42no—
309C2×C22⋊C4—42no—
310C2×C22⋊C4—42no—
311C2×C22⋊C4—42no—
312C2×C22⋊C4—42no—
313C2×C22⋊C4—42no—
314C2×C22⋊C4—42no—
315C2×C22⋊C4—42no—
316C2×C42—22no—
317C2×C42—22no—
318C2×C42C3×D414yescomplemented
319#95—22no—
320#95—22no—
321#95—22no—
322#95—24no—
323#95—22no—
324#95—24no—
325#95—42no—
326#95—42no—
327#95—42no—
328C23×C3—24no—
329C23×C3—22no—
330C23×C3—24no—
331C23×C3—24no—
332C23×C3—24no—
333C23×C3—24no—
334C23×C3—22no—
335C23×C3—24no—
336C23×C3—24no—
337C23×C3—24no—
338C23×C3—22no—
339C23×C3—24no—
340C23×C3—41no—
341C23×C3—42no—
342C23×C3—41no—
343C23×C3—42no—
344C23×C3—42no—
345C23×C3—42no—
346C23×C3—42no—
347C23×C3—42no—
348C23×C3—41no—
349C23×C3—42no—
350C23×C3—42no—
351C23×C3—41no—
352C23×C3—41no—
353C23×C3—42no—
354C23×C3—41no—
355C23×C3—42no—
356C23×C3—42no—
357C23×C3—42no—
358C23×C3—42no—
359C23×C3—42no—
360C23×C3—42no—
361C23×C3—42no—
362C23×C3—42no—
363C23×C3—42no—
364C23×C3—42no—
365C23×C3—42no—
366C23×C3—42no—
367C23×C3—42no—
368C23×C3—41no—
369C23×C3—42no—
370C23×C3—41no—
371C23×C3—42no—
372C23×C3—42no—
373C23×C3—42no—
374C23×C3—42no—
375C23×C3—42no—
376C23×C3—42no—
377C23×C3—42no—
378C23×C3—42no—
379C23×C3—42no—
380C23×C3—42no—
381C23×C3—42no—
382C23×C3—42no—
383C23×C3—42no—
384C23×C3—42no—
385C23×C3—42no—
386C23×C3C22×D411yescharacteristic
387C23×C3C22×D411yescharacteristic
388C23×C3C22×D411yescharacteristic
389C23×C3C2×#4111yescharacteristic
390C23×C3C2×#4111yescharacteristic
391C23×C3C2×#4112yes—
392C23×C3H(5,𝔽2)12yes—
393C23×C3H(5,𝔽2)12yes—
394C23×C3H(5,𝔽2)12yes—
395C23×C3H(5,𝔽2)11yescharacteristic
396C23×C32−1+411yescharacteristic
397C3×Q8—416no—
398C3×D4—416no—
399C3×D4—432no—
400C2×C3×C4—24no—
401C2×C3×C4—24no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—24no—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—24no—
411C2×C3×C4—24no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—24no—
415C2×C3×C4—24no—
416C2×C3×C4—24no—
417C2×C3×C4—24no—
418C2×C3×C4—42no—
419C2×C3×C4—42no—
420C2×C3×C4—42no—
421C2×C3×C4—41no—
422C2×C3×C4—41no—
423C2×C3×C4—42no—
424C2×C3×C4—42no—
425C2×C3×C4—42no—
426C2×C3×C4—42no—
427C2×C3×C4—41no—
428C2×C3×C4—42no—
429C2×C3×C4—42no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4—41no—
433C2×C3×C4—42no—
434C2×C3×C4—42no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—42no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—42no—
443C2×C3×C4—42no—
444C2×C3×C4—42no—
445C2×C3×C4—42no—
446C2×C3×C4—42no—
447C2×C3×C4—42no—
448C2×C3×C4—42no—
449C2×C3×C4—42no—
450C2×C3×C4—42no—
451C2×C3×C4—42no—
452C2×C3×C4#12014yes—
453C24—21no—
454C24—21no—
455C24—22no—
456C24—22no—
457C24—21no—
458C24—21no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—21no—
475C24—22no—
476C24—21no—
477C24C2×C3×D414yes—
478C24C3×#4112yes—
479C24C24×C311yescharacteristic
480C2×Q8—28no—
481C2×Q8—48no—
482C2×Q8—48no—
483C2×Q8—44no—
484C2×Q8—44no—
485C2×D4—28no—
486C2×D4—48no—
487C2×D4—48no—
488C2×D4—48no—
489C2×D4—48no—
490C2×D4—44no—
491C2×D4—44no—
492C2×D4—48no—
493C2×D4—48no—
494C2×D4—48no—
495C2×D4—48no—
496C2×D4—48no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4C2×C3×D412yes—
543C22×C4C2×C3×D414yes—
544C22×C4C2×C3×D412yes—
545C22×C4C2×C3×D412yes—
546C22×C4C2×C3×D412yes—
547C22×C4C2×C3×D412yes—
548C22×C4C3×#4114yes—
549C22×C4C3×#4112yes—
550C4⋊C4—44no—
551C22⋊C4—216no—
552C22⋊C4—216no—
553C22⋊C4—28no—
554C22⋊C4—48no—
555C22⋊C4—48no—
556C22⋊C4—44no—
557C22⋊C4—48no—
558C22⋊C4—48no—
559C22⋊C4—44no—
560C42—28no—
561C22×C3—42no—
562C22×C3—44no—
563C22×C3—42no—
564C22×C3—44no—
565C22×C3—42no—
566C22×C3—44no—
567C22×C3—44no—
568C22×C3—44no—
569C22×C3—44no—
570C22×C3—44no—
571C22×C3—44no—
572C22×C3—44no—
573C22×C3—81no—
574C22×C3—82no—
575C22×C3—82no—
576C22×C3—81no—
577C22×C3—82no—
578C22×C3—82no—
579C22×C3—81no—
580C22×C3—82no—
581C22×C3—81no—
582C22×C3—82no—
583C22×C3—82no—
584C22×C3—82no—
585C22×C3—82no—
586C22×C3—82no—
587C22×C3C2×#12011yescharacteristic
588C22×C3#52511yescharacteristic
589C22×C3#53211yescharacteristic
590C22×C3#53412yes—
591C22×C3#53412yes—
592C22×C3#53511yescharacteristic
593C22×C3#53511yescharacteristic
594C22×C3#53511yescharacteristic
595C22×C3#53711yescharacteristic
596C22×C3#53812yes—
597C22×C3#53812yes—
598C22×C3#53812yes—
599C22×C3#54212yes—
600C22×C3#54611yescharacteristic
601C22×C3#54612yes—
602C22×C3#54711yescharacteristic
603C22×C3#54811yescharacteristic
604C22×C3#55011yescharacteristic
605C22×C3#55012yes—
606C22×C3#55112yes—
607C22×C3#55512yes—
608C22×C3H(3,𝔽4)12yes—
609C22×C3#56212yes—
610C3×C4—24no—
611C3×C4—44no—
612C3×C4—42no—
613C3×C4—42no—
614C3×C4—44no—
615C3×C4—42no—
616C3×C4—81no—
617C3×C4—81no—
618C3×C4—82no—
619C23—24no—
620C23—22no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—22no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—22no—
630C23—24no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—41no—
638C23—42no—
639C23—42no—
640C23—41no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—41no—
646C23—42no—
647C23—42no—
648C23—41no—
649C23—42no—
650C23—41no—
651C23—41no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—41no—
666C23—42no—
667C23—41no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23C22×C3×D411yescharacteristic
678C23C22×C3×D411yescharacteristic
679C23C22×C3×D411yescharacteristic
680C23C2×C3×#4111yescharacteristic
681C23C2×C3×#4111yescharacteristic
682C23C2×C3×#4112yes—
683C23C3×H(5,𝔽2)11yescharacteristic
684C23C3×H(5,𝔽2)12yes—
685C23C3×H(5,𝔽2)12yes—
686C23C3×H(5,𝔽2)12yes—
687C23C3×2−1+411yescharacteristic
688Q8—416no—
689D4—416no—
690D4—432no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4C3×#12014yes—
744C2×C3—82no—
745C2×C3—84no—
746C2×C3#240711yescharacteristic
747C2×C3#243111yescharacteristic
748C2×C3#261011yescharacteristic
749C2×C3#261311yescharacteristic
750C2×C3#263111yescharacteristic
751C2×C3#266211yescharacteristic
752C2×C3#268412yes—
753C2×C3#268612yes—
754C2×C3#273012yes—
755C2×C3#273312yes—
756C2×C3#281911yescharacteristic
757C22—42no—
758C22—44no—
759C22—42no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—44no—
765C22—44no—
766C22—44no—
767C22—42no—
768C22—44no—
769C22—82no—
770C22—82no—
771C22—81no—
772C22—82no—
773C22—81no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22—82no—
780C22—81no—
781C22—82no—
782C22—81no—
783C22C2×C3×#12011yescharacteristic
784C22C3×#52511yescharacteristic
785C22C3×#53211yescharacteristic
786C22C3×#53412yes—
787C22C3×#53412yes—
788C22C3×#53511yescharacteristic
789C22C3×#53511yescharacteristic
790C22C3×#53511yescharacteristic
791C22C3×#53711yescharacteristic
792C22C3×#53812yes—
793C22C3×#53812yes—
794C22C3×#53812yes—
795C22C3×#54212yes—
796C22C3×#54611yescharacteristic
797C22C3×#54612yes—
798C22C3×#54711yescharacteristic
799C22C3×#54811yescharacteristic
800C22C3×#55011yescharacteristic
801C22C3×#55012yes—
802C22C3×#55112yes—
803C22C3×#55512yes—
804C22C3×H(3,𝔽4)12yes—
805C22C3×#56212yes—
806C4—24no—
807C4—42no—
808C4—42no—
809C4—44no—
810C4—42no—
811C4—44no—
812C4—81no—
813C4—82no—
814C4—81no—
815C3#1668011yescharacteristic, direct product factor, Sylow
816C2—82no—
817C2—84no—
818C2C3×#240711yescharacteristic
819C2C3×#243111yescharacteristic
820C2C3×#261011yescharacteristic
821C2C3×#261311yescharacteristic
822C2C3×#263111yescharacteristic
823C2C3×#266211yescharacteristic
824C2C3×#268412yes—
825C2C3×#268612yes—
826C2C3×#273012yes—
827C2C3×#273312yes—
828C2C3×#281911yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC24C24×C3
prime radicalC2×C3×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C3×#124C2semidirect
2. C2×C3×#393C2semidirect
4. C2×C3×#388C2semidirect
5. C3×#1446C2semidirect
6. C3×#1440C2semidirect
7. C3×#1439C2semidirect
8. C3×#1438C2semidirect
9. C3×#1438C2semidirect
10. C3×#1438C2semidirect
11. C3×#1434C2semidirect
12. #16680C3direct (N × H)
42. C22×#124C2×C3semidirect
43. C2×#393C2×C3semidirect
45. C2×#388C2×C3semidirect
46. #1446C2×C3semidirect
47. #1440C2×C3semidirect
48. #1439C2×C3semidirect
49. #1438C2×C3semidirect
50. #1438C2×C3semidirect
51. #1438C2×C3semidirect
52. #1434C2×C3semidirect
59. C22×C3×Q8D4semidirect
112. C2×C3×C42D4semidirect
265. C22×Q8C3×D4semidirect
318. C2×C42C3×D4semidirect
815. C3#16680direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1242
C2×C3×#3932
C2×C3×#3922
C2×C3×#3882
C3×#14462
C3×#14402
C3×#14392
C3×#14382
C3×#14342
#166803