Finite Group Databasebeta

← C3×#16662 #10635269

Subgroups — C3×#16662 #10635269

Order 768.

1930 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#392C211yesmaximal, characteristic
2C2×C3×#390C211yesmaximal, characteristic, complemented
3C2×C3×#388C211yesmaximal, characteristic, complemented
4C2×C3×#383C211yesmaximal, characteristic, complemented
5C3×#1442C211yesmaximal, characteristic, complemented
6C3×#1440C212yesmaximal, complemented
7C3×#1439C212yesmaximal, complemented
8C3×#1439C211yesmaximal, characteristic, complemented
9C3×#1438C211yesmaximal, characteristic, complemented
10C3×#1438C212yesmaximal, complemented
11C3×#1438C212yesmaximal, complemented
12#16662C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×D4C2211yescharacteristic
14C23×C3×D4C2212yes—
15C22×C3×C4⋊C4C2211yescharacteristic
16C22×C3×C4⋊C4C2211yescharacteristic
17C22×C3×C22⋊C4C2211yescharacteristic
18C22×C3×C22⋊C4C2211yescharacteristic
19C22×C3×C22⋊C4C2212yes—
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2212yes—
22C22×C3×C22⋊C4C2212yes—
23C22×C3×C22⋊C4C2212yes—
24C22×C3×C22⋊C4C2212yes—
25C22×C3×C22⋊C4C2212yes—
26C22×C3×C42C2211yescharacteristic
27C3×#392—24no—
28C3×#390—24no—
29C3×#388—24no—
30C3×#383—24no—
31C2×C3×#95C2211yescharacteristic
32C2×C3×#95C2212yes—
33C2×C3×#95C2212yes—
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2212yes—
37C2×C3×#95C2212yes—
38C2×C3×#95C2212yes—
39C2×C3×#95C2211yescharacteristic
40C2×#392C2×C311yescharacteristic
41C2×#390C2×C311yescharacteristic, complemented
42C2×#388C2×C311yescharacteristic, complemented
43C2×#383C2×C311yescharacteristic, complemented
44#1442C2×C311yescharacteristic, complemented
45#1440C2×C312yescomplemented
46#1439C2×C311yescharacteristic, complemented
47#1439C2×C312yescomplemented
48#1438C2×C312yescomplemented
49#1438C2×C311yescharacteristic, complemented
50#1438C2×C312yescomplemented
51C25×C3C2311yescharacteristic
52C25×C3C2312yes—
53C22×C3×D4—24no—
54C22×C3×D4—24no—
55C22×C3×D4—24no—
56C22×C3×D4—22no—
57C22×C3×D4—24no—
58C22×C3×D4—22no—
59C22×C3×D4—22no—
60C22×C3×D4—42no—
61C22×C3×D4—42no—
62C22×C3×D4—42no—
63C22×C3×D4—42no—
64C22×C3×D4—42no—
65C23×C3×C4C2312yes—
66C23×C3×C4C2311yescharacteristic
67C23×C3×C4C2311yescharacteristic
68C23×C3×C4C2312yes—
69C23×C3×C4C2312yes—
70C23×C3×C4C2311yescharacteristic
71C23×C3×C4C2311yescharacteristic
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C2×C3×C4⋊C4—22no—
75C2×C3×C4⋊C4—22no—
76C2×C3×C4⋊C4—42no—
77C2×C3×C4⋊C4—42no—
78C2×C3×C22⋊C4—22no—
79C2×C3×C22⋊C4—22no—
80C2×C3×C22⋊C4—22no—
81C2×C3×C22⋊C4—24no—
82C2×C3×C22⋊C4—22no—
83C2×C3×C22⋊C4—22no—
84C2×C3×C22⋊C4—24no—
85C2×C3×C22⋊C4—24no—
86C2×C3×C22⋊C4—24no—
87C2×C3×C22⋊C4—22no—
88C2×C3×C22⋊C4—24no—
89C2×C3×C22⋊C4—22no—
90C2×C3×C22⋊C4—42no—
91C2×C3×C22⋊C4—42no—
92C2×C3×C22⋊C4—42no—
93C2×C3×C22⋊C4—42no—
94C2×C3×C22⋊C4—42no—
95C2×C3×C22⋊C4—42no—
96C2×C3×C22⋊C4—42no—
97C2×C3×C22⋊C4—42no—
98C2×C3×C22⋊C4—42no—
99C2×C3×C22⋊C4—42no—
100C2×C3×C22⋊C4—42no—
101C2×C3×C22⋊C4—42no—
102C2×C3×C22⋊C4—42no—
103C2×C3×C22⋊C4—42no—
104C2×C3×C42—22no—
105C2×C3×C42—22no—
106C2×C3×C42D414yescomplemented
107C3×#95—24no—
108C3×#95—24no—
109C3×#95—22no—
110C3×#95—22no—
111C3×#95—22no—
112C3×#95—42no—
113C3×#95—42no—
114C3×#95—42no—
115C3×#95D414yes—
116C23×D4C22×C311yescharacteristic
117C23×D4C22×C312yes—
118C22×C4⋊C4C22×C311yescharacteristic
119C22×C4⋊C4C22×C311yescharacteristic
120C22×C22⋊C4C22×C311yescharacteristic
121C22×C22⋊C4C22×C311yescharacteristic
122C22×C22⋊C4C22×C312yes—
123C22×C22⋊C4C22×C312yes—
124C22×C22⋊C4C22×C312yes—
125C22×C22⋊C4C22×C311yescharacteristic
126C22×C22⋊C4C22×C312yes—
127C22×C22⋊C4C22×C312yes—
128C22×C22⋊C4C22×C312yes—
129C22×C42C22×C311yescharacteristic
130#392—24no—
131#390—24no—
132#388—24no—
133#383—24no—
134C2×#95C22×C311yescharacteristic
135C2×#95C22×C312yes—
136C2×#95C22×C312yes—
137C2×#95C22×C311yescharacteristic
138C2×#95C22×C311yescharacteristic
139C2×#95C22×C312yes—
140C2×#95C22×C312yes—
141C2×#95C22×C312yes—
142C2×#95C22×C311yescharacteristic
143C24×C3—21no—
144C24×C3—22no—
145C24×C3—21no—
146C24×C3—22no—
147C24×C3—21no—
148C24×C3—21no—
149C24×C3—22no—
150C24×C3—22no—
151C24×C3—22no—
152C24×C3—22no—
153C24×C3—22no—
154C24×C3—22no—
155C24×C3—22no—
156C24×C3—22no—
157C24×C3—21no—
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—21no—
167C24×C3#4112yes—
168C24×C3#4114yes—
169C24×C3C2411yescharacteristic
170C2×C3×D4—28no—
171C2×C3×D4—48no—
172C2×C3×D4—48no—
173C2×C3×D4—48no—
174C2×C3×D4—48no—
175C2×C3×D4—44no—
176C2×C3×D4—48no—
177C2×C3×D4—48no—
178C2×C3×D4—48no—
179C2×C3×D4—48no—
180C2×C3×D4—48no—
181C2×C3×D4—44no—
182C22×C3×C4—22no—
183C22×C3×C4—22no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
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×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—22no—
203C22×C3×C4—22no—
204C22×C3×C4—22no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—22no—
209C22×C3×C4—21no—
210C22×C3×C4—22no—
211C22×C3×C4—22no—
212C22×C3×C4—22no—
213C22×C3×C4—21no—
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—22no—
223C22×C3×C4—21no—
224C22×C3×C4—22no—
225C22×C3×C4—22no—
226C22×C3×C4—22no—
227C22×C3×C4—22no—
228C22×C3×C4C2×D414yes—
229C22×C3×C4C2×D412yes—
230C22×C3×C4C2×D412yes—
231C22×C3×C4C2×D412yes—
232C22×C3×C4C2×D412yes—
233C22×C3×C4#4112yes—
234C22×C3×C4#4112yes—
235C3×C4⋊C4—44no—
236C3×C4⋊C4—44no—
237C3×C22⋊C4—28no—
238C3×C22⋊C4—48no—
239C3×C22⋊C4—48no—
240C3×C22⋊C4—44no—
241C3×C22⋊C4—48no—
242C3×C22⋊C4—48no—
243C3×C22⋊C4—48no—
244C3×C22⋊C4—48no—
245C3×C22⋊C4—44no—
246C3×C42—28no—
247C25C23×C311yescharacteristic
248C25C23×C312yes—
249C22×D4—24no—
250C22×D4—24no—
251C22×D4—24no—
252C22×D4—22no—
253C22×D4—24no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—42no—
257C22×D4—42no—
258C22×D4—42no—
259C22×D4—42no—
260C22×D4—42no—
261C23×C4C23×C311yescharacteristic
262C23×C4C23×C312yes—
263C23×C4C23×C312yes—
264C23×C4C23×C311yescharacteristic
265C23×C4C23×C311yescharacteristic
266C23×C4C23×C311yescharacteristic
267C23×C4C23×C312yes—
268C23×C4C23×C311yescharacteristic
269C23×C4C23×C311yescharacteristic
270C2×C4⋊C4—22no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—42no—
273C2×C4⋊C4—42no—
274C2×C22⋊C4—22no—
275C2×C22⋊C4—22no—
276C2×C22⋊C4—22no—
277C2×C22⋊C4—24no—
278C2×C22⋊C4—22no—
279C2×C22⋊C4—22no—
280C2×C22⋊C4—24no—
281C2×C22⋊C4—24no—
282C2×C22⋊C4—24no—
283C2×C22⋊C4—22no—
284C2×C22⋊C4—24no—
285C2×C22⋊C4—22no—
286C2×C22⋊C4—42no—
287C2×C22⋊C4—42no—
288C2×C22⋊C4—42no—
289C2×C22⋊C4—42no—
290C2×C22⋊C4—42no—
291C2×C22⋊C4—42no—
292C2×C22⋊C4—42no—
293C2×C22⋊C4—42no—
294C2×C22⋊C4—42no—
295C2×C22⋊C4—42no—
296C2×C22⋊C4—42no—
297C2×C22⋊C4—42no—
298C2×C22⋊C4—42no—
299C2×C22⋊C4—42no—
300C2×C42—22no—
301C2×C42—22no—
302C2×C42C3×D414yescomplemented
303#95—24no—
304#95—24no—
305#95—22no—
306#95—22no—
307#95—22no—
308#95—42no—
309#95—42no—
310#95—42no—
311#95C3×D414yes—
312C23×C3—22no—
313C23×C3—24no—
314C23×C3—24no—
315C23×C3—24no—
316C23×C3—24no—
317C23×C3—24no—
318C23×C3—22no—
319C23×C3—24no—
320C23×C3—24no—
321C23×C3—24no—
322C23×C3—24no—
323C23×C3—22no—
324C23×C3—41no—
325C23×C3—42no—
326C23×C3—41no—
327C23×C3—42no—
328C23×C3—42no—
329C23×C3—42no—
330C23×C3—41no—
331C23×C3—42no—
332C23×C3—42no—
333C23×C3—42no—
334C23×C3—42no—
335C23×C3—41no—
336C23×C3—41no—
337C23×C3—42no—
338C23×C3—41no—
339C23×C3—42no—
340C23×C3—42no—
341C23×C3—42no—
342C23×C3—42no—
343C23×C3—42no—
344C23×C3—42no—
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×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—41no—
363C23×C3—42no—
364C23×C3—42no—
365C23×C3—42no—
366C23×C3—42no—
367C23×C3—42no—
368C23×C3—42no—
369C23×C3—42no—
370C23×C3C22×D411yescharacteristic
371C23×C3C22×D411yescharacteristic
372C23×C3C2×#4111yescharacteristic
373C23×C3C2×#4112yes—
374C23×C3C2×#4111yescharacteristic
375C23×C3C2×#4111yescharacteristic
376C23×C3H(5,𝔽2)12yes—
377C23×C3H(5,𝔽2)12yes—
378C23×C3H(5,𝔽2)12yes—
379C23×C3H(5,𝔽2)11yescharacteristic
380C23×C3H(5,𝔽2)11yescharacteristic
381C3×D4—416no—
382C3×D4—432no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—24no—
386C2×C3×C4—24no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—24no—
395C2×C3×C4—24no—
396C2×C3×C4—24no—
397C2×C3×C4—24no—
398C2×C3×C4—41no—
399C2×C3×C4—42no—
400C2×C3×C4—41no—
401C2×C3×C4—42no—
402C2×C3×C4—42no—
403C2×C3×C4—42no—
404C2×C3×C4—42no—
405C2×C3×C4—41no—
406C2×C3×C4—41no—
407C2×C3×C4—42no—
408C2×C3×C4—41no—
409C2×C3×C4—41no—
410C2×C3×C4—42no—
411C2×C3×C4—41no—
412C2×C3×C4—41no—
413C2×C3×C4—42no—
414C2×C3×C4—42no—
415C2×C3×C4—42no—
416C2×C3×C4—41no—
417C2×C3×C4—42no—
418C2×C3×C4—41no—
419C2×C3×C4—41no—
420C2×C3×C4—41no—
421C2×C3×C4—42no—
422C2×C3×C4—42no—
423C2×C3×C4—42no—
424C2×C3×C4—42no—
425C2×C3×C4—42no—
426C2×C3×C4—42no—
427C2×C3×C4—42no—
428C2×C3×C4—42no—
429C2×C3×C4—42no—
430C2×C3×C4—42no—
431C2×C3×C4—42no—
432C2×C3×C4—42no—
433C2×C3×C4—42no—
434C2×C3×C4—42no—
435C2×C3×C4#12114yes—
436C24—21no—
437C24—22no—
438C24—21no—
439C24—22no—
440C24—21no—
441C24—21no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—21no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—21no—
459C24—22no—
460C24C3×#4112yes—
461C24C3×#4114yes—
462C24C24×C311yescharacteristic
463C2×D4—28no—
464C2×D4—48no—
465C2×D4—48no—
466C2×D4—48no—
467C2×D4—48no—
468C2×D4—44no—
469C2×D4—48no—
470C2×D4—48no—
471C2×D4—48no—
472C2×D4—48no—
473C2×D4—48no—
474C2×D4—44no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4C2×C3×D414yes—
522C22×C4C2×C3×D412yes—
523C22×C4C2×C3×D412yes—
524C22×C4C2×C3×D412yes—
525C22×C4C2×C3×D412yes—
526C22×C4C3×#4112yes—
527C22×C4C3×#4112yes—
528C4⋊C4—44no—
529C4⋊C4—44no—
530C22⋊C4—28no—
531C22⋊C4—48no—
532C22⋊C4—48no—
533C22⋊C4—44no—
534C22⋊C4—48no—
535C22⋊C4—48no—
536C22⋊C4—48no—
537C22⋊C4—48no—
538C22⋊C4—44no—
539C42—28no—
540C22×C3—42no—
541C22×C3—44no—
542C22×C3—42no—
543C22×C3—44no—
544C22×C3—44no—
545C22×C3—42no—
546C22×C3—44no—
547C22×C3—44no—
548C22×C3—44no—
549C22×C3—44no—
550C22×C3—44no—
551C22×C3—44no—
552C22×C3—82no—
553C22×C3—81no—
554C22×C3—81no—
555C22×C3—82no—
556C22×C3—82no—
557C22×C3—81no—
558C22×C3—81no—
559C22×C3—82no—
560C22×C3—82no—
561C22×C3—82no—
562C22×C3—82no—
563C22×C3—82no—
564C22×C3—82no—
565C22×C3—82no—
566C22×C3C2×#12111yescharacteristic
567C22×C3#52511yescharacteristic
568C22×C3#52511yescharacteristic
569C22×C3#53511yescharacteristic
570C22×C3#53511yescharacteristic
571C22×C3#53511yescharacteristic
572C22×C3#53511yescharacteristic
573C22×C3#53512yes—
574C22×C3#53812yes—
575C22×C3#53812yes—
576C22×C3#53812yes—
577C22×C3#53812yes—
578C22×C3#54012yes—
579C22×C3#54612yes—
580C22×C3#54611yescharacteristic
581C22×C3#55011yescharacteristic
582C22×C3#55112yes—
583C22×C3#55112yes—
584C22×C3#55312yes—
585C22×C3#55311yescharacteristic
586C22×C3#55511yescharacteristic
587C22×C3#56012yes—
588C22×C3#56012yes—
589C3×C4—24no—
590C3×C4—42no—
591C3×C4—42no—
592C3×C4—42no—
593C3×C4—44no—
594C3×C4—82no—
595C3×C4—81no—
596C3×C4—81no—
597C3×C4—82no—
598C23—22no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—22no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—22no—
609C23—24no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—41no—
617C23—42no—
618C23—41no—
619C23—42no—
620C23—41no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—41no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—41no—
655C23—42no—
656C23C22×C3×D411yescharacteristic
657C23C22×C3×D411yescharacteristic
658C23C2×C3×#4111yescharacteristic
659C23C2×C3×#4112yes—
660C23C2×C3×#4111yescharacteristic
661C23C2×C3×#4111yescharacteristic
662C23C3×H(5,𝔽2)12yes—
663C23C3×H(5,𝔽2)12yes—
664C23C3×H(5,𝔽2)11yescharacteristic
665C23C3×H(5,𝔽2)11yescharacteristic
666C23C3×H(5,𝔽2)12yes—
667D4—416no—
668D4—432no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—41no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—42no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4C3×#12114yes—
722C2×C3—84no—
723C2×C3—82no—
724C2×C3#241111yescharacteristic
725C2×C3#241411yescharacteristic
726C2×C3#259811yescharacteristic
727C2×C3#261911yescharacteristic
728C2×C3#263111yescharacteristic
729C2×C3#263111yescharacteristic
730C2×C3#268512yes—
731C2×C3#271412yes—
732C2×C3#274912yes—
733C2×C3#275612yes—
734C2×C3#281811yescharacteristic
735C22—42no—
736C22—44no—
737C22—44no—
738C22—42no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—44no—
745C22—42no—
746C22—44no—
747C22—81no—
748C22—82no—
749C22—82no—
750C22—81no—
751C22—81no—
752C22—82no—
753C22—82no—
754C22—82no—
755C22—82no—
756C22—82no—
757C22—82no—
758C22—82no—
759C22—81no—
760C22—82no—
761C22C2×C3×#12111yescharacteristic
762C22C3×#52511yescharacteristic
763C22C3×#52511yescharacteristic
764C22C3×#53511yescharacteristic
765C22C3×#53512yes—
766C22C3×#53511yescharacteristic
767C22C3×#53511yescharacteristic
768C22C3×#53511yescharacteristic
769C22C3×#53812yes—
770C22C3×#53812yes—
771C22C3×#53812yes—
772C22C3×#53812yes—
773C22C3×#54012yes—
774C22C3×#54612yes—
775C22C3×#54611yescharacteristic
776C22C3×#55011yescharacteristic
777C22C3×#55112yes—
778C22C3×#55112yes—
779C22C3×#55311yescharacteristic
780C22C3×#55312yes—
781C22C3×#55511yescharacteristic
782C22C3×#56012yes—
783C22C3×#56012yes—
784C4—24no—
785C4—42no—
786C4—42no—
787C4—42no—
788C4—44no—
789C4—81no—
790C4—81no—
791C4—82no—
792C4—82no—
793C3#1666211yescharacteristic, direct product factor, Sylow
794C2—84no—
795C2—82no—
796C2C3×#241111yescharacteristic
797C2C3×#241411yescharacteristic
798C2C3×#259811yescharacteristic
799C2C3×#261911yescharacteristic
800C2C3×#263111yescharacteristic
801C2C3×#263111yescharacteristic
802C2C3×#268512yes—
803C2C3×#271412yes—
804C2C3×#274912yes—
805C2C3×#275612yes—
806C2C3×#281811yescharacteristic
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
2. C2×C3×#390C2semidirect
3. C2×C3×#388C2semidirect
4. C2×C3×#383C2semidirect
5. C3×#1442C2semidirect
6. C3×#1440C2semidirect
7. C3×#1439C2semidirect
8. C3×#1439C2semidirect
9. C3×#1438C2semidirect
10. C3×#1438C2semidirect
11. C3×#1438C2semidirect
12. #16662C3direct (N × H)
41. C2×#390C2×C3semidirect
42. C2×#388C2×C3semidirect
43. C2×#383C2×C3semidirect
44. #1442C2×C3semidirect
45. #1440C2×C3semidirect
46. #1439C2×C3semidirect
47. #1439C2×C3semidirect
48. #1438C2×C3semidirect
49. #1438C2×C3semidirect
50. #1438C2×C3semidirect
106. C2×C3×C42D4semidirect
302. C2×C42C3×D4semidirect
793. C3#16662direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3922
C2×C3×#3902
C2×C3×#3882
C2×C3×#3832
C3×#14422
C3×#14402
C3×#14392
C3×#14382
#166623