Finite Group Databasebeta

← C3×#14927 #10633534

Subgroups — C3×#14927 #10633534

Order 768.

2314 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#123C211yesmaximal, characteristic
2C2×C3×#386C211yesmaximal, characteristic
3C2×C3×#386C211yesmaximal, characteristic
4C2×C3×#381C211yesmaximal, characteristic, complemented
5C2×C3×#380C211yesmaximal, characteristic, complemented
6C22×C3×#95C211yesmaximal, characteristic, complemented
7C3×#1442C212yesmaximal, complemented
8C3×#1441C212yesmaximal, complemented
9C3×#1440C212yesmaximal, complemented
10C3×#1439C212yesmaximal, complemented
11C3×C22⋊#95C211yesmaximal, characteristic, complemented
12#14927C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×D4C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C24×C3×C4C2211yescharacteristic
16C24×C3×C4C2211yescharacteristic
17C2×C3×#123—24no—
18C2×C3×#123—24no—
19C2×C3×#123—24no—
20C22×C3×C4⋊C4C2212yes—
21C22×C3×C4⋊C4C2212yes—
22C22×C3×C22⋊C4C2212yes—
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2212yes—
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×C3×C22⋊C4C2211yescharacteristic
29C3×#386—24no—
30C3×#386—24no—
31C3×#381—24no—
32C3×#380—24no—
33C2×C3×#95—24no—
34C2×C3×#95C2212yes—
35C2×C3×#95C2212yes—
36C2×C3×#95C2212yes—
37C2×C3×#95C2212yes—
38C2×C3×#95C2212yes—
39C2×C3×#95C2211yescharacteristic
40C2×C3×#95C2212yes—
41C2×C3×#95C2211yescharacteristic
42C2×C3×#95C2212yes—
43C2×C3×#95C2212yes—
44C22×#123C2×C311yescharacteristic
45C2×#386C2×C311yescharacteristic
46C2×#386C2×C311yescharacteristic
47C2×#381C2×C311yescharacteristic, complemented
48C2×#380C2×C311yescharacteristic, complemented
49C22×#95C2×C311yescharacteristic, complemented
50#1442C2×C312yescomplemented
51#1441C2×C312yescomplemented
52#1440C2×C312yescomplemented
53#1439C2×C312yescomplemented
54C22⋊#95C2×C311yescharacteristic, complemented
55C25×C3C2311yescharacteristic
56C25×C3C2311yescharacteristic
57C22×C3×D4—22no—
58C22×C3×D4—22no—
59C22×C3×D4—22no—
60C22×C3×D4—22no—
61C22×C3×D4—22no—
62C22×C3×D4—22no—
63C22×C3×D4D414yes—
64C23×C3×C4—22no—
65C23×C3×C4—22no—
66C23×C3×C4—22no—
67C23×C3×C4—22no—
68C23×C3×C4—22no—
69C23×C3×C4—22no—
70C23×C3×C4—22no—
71C23×C3×C4—22no—
72C23×C3×C4—22no—
73C23×C3×C4—24no—
74C23×C3×C4—24no—
75C23×C3×C4—22no—
76C23×C3×C4—22no—
77C23×C3×C4—42no—
78C23×C3×C4—42no—
79C23×C3×C4D414yes—
80C23×C3×C4D414yes—
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2312yes—
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2312yes—
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2312yes—
88C23×C3×C4C2312yes—
89C23×C3×C4C2311yescharacteristic
90C3×#123—232no—
91C2×C3×C4⋊C4—24no—
92C2×C3×C4⋊C4—24no—
93C2×C3×C4⋊C4—24no—
94C2×C3×C4⋊C4—24no—
95C2×C3×C4⋊C4—24no—
96C2×C3×C4⋊C4—42no—
97C2×C3×C22⋊C4—24no—
98C2×C3×C22⋊C4—22no—
99C2×C3×C22⋊C4—22no—
100C2×C3×C22⋊C4—24no—
101C2×C3×C22⋊C4—24no—
102C2×C3×C22⋊C4—22no—
103C2×C3×C22⋊C4—22no—
104C2×C3×C22⋊C4—22no—
105C2×C3×C22⋊C4—24no—
106C2×C3×C22⋊C4—22no—
107C2×C3×C22⋊C4—22no—
108C2×C3×C22⋊C4—22no—
109C2×C3×C22⋊C4—22no—
110C2×C3×C22⋊C4—22no—
111C2×C3×C22⋊C4—24no—
112C2×C3×C22⋊C4—24no—
113C2×C3×C22⋊C4—42no—
114C2×C3×C22⋊C4—42no—
115C2×C3×C22⋊C4D414yes—
116C3×#95—24no—
117C3×#95—24no—
118C3×#95—24no—
119C3×#95—24no—
120C3×#95—24no—
121C3×#95—22no—
122C3×#95—22no—
123C3×#95—24no—
124C3×#95—24no—
125C3×#95—42no—
126C23×D4C22×C311yescharacteristic
127C24×C4C22×C311yescharacteristic
128C24×C4C22×C311yescharacteristic
129C24×C4C22×C311yescharacteristic
130C2×#123—24no—
131C2×#123—24no—
132C2×#123—24no—
133C22×C4⋊C4C22×C312yes—
134C22×C4⋊C4C22×C312yes—
135C22×C22⋊C4C22×C312yes—
136C22×C22⋊C4C22×C311yescharacteristic
137C22×C22⋊C4C22×C311yescharacteristic
138C22×C22⋊C4C22×C311yescharacteristic
139C22×C22⋊C4C22×C312yes—
140C22×C22⋊C4C22×C311yescharacteristic
141C22×C22⋊C4C22×C311yescharacteristic
142#386—24no—
143#386—24no—
144#381—24no—
145#380—24no—
146C2×#95—24no—
147C2×#95C22×C312yes—
148C2×#95C22×C312yes—
149C2×#95C22×C312yes—
150C2×#95C22×C312yes—
151C2×#95C22×C312yes—
152C2×#95C22×C312yes—
153C2×#95C22×C311yescharacteristic
154C2×#95C22×C312yes—
155C2×#95C22×C311yescharacteristic
156C2×#95C22×C312yes—
157C24×C3—22no—
158C24×C3—22no—
159C24×C3—22no—
160C24×C3—22no—
161C24×C3—21no—
162C24×C3—21no—
163C24×C3—21no—
164C24×C3—22no—
165C24×C3—22no—
166C24×C3—21no—
167C24×C3—21no—
168C24×C3—21no—
169C24×C3—22no—
170C24×C3—22no—
171C24×C3C2×D412yes—
172C24×C3C2×D412yes—
173C24×C3C2×D412yes—
174C24×C3C2×D412yes—
175C24×C3C2×D412yes—
176C24×C3#4112yes—
177C24×C3#4112yes—
178C24×C3#4112yes—
179C24×C3C2411yescharacteristic
180C2×C3×D4—28no—
181C2×C3×D4—28no—
182C2×C3×D4—28no—
183C2×C3×D4—44no—
184C2×C3×D4—44no—
185C2×C3×D4—44no—
186C2×C3×D4—44no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—22no—
190C22×C3×C4—28no—
191C22×C3×C4—28no—
192C22×C3×C4—28no—
193C22×C3×C4—28no—
194C22×C3×C4—28no—
195C22×C3×C4—22no—
196C22×C3×C4—21no—
197C22×C3×C4—22no—
198C22×C3×C4—21no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—22no—
203C22×C3×C4—22no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—22no—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4—21no—
210C22×C3×C4—22no—
211C22×C3×C4—22no—
212C22×C3×C4—22no—
213C22×C3×C4—22no—
214C22×C3×C4—22no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—22no—
219C22×C3×C4—22no—
220C22×C3×C4—22no—
221C22×C3×C4—22no—
222C22×C3×C4—22no—
223C22×C3×C4—28no—
224C22×C3×C4—22no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—22no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—22no—
231C22×C3×C4—22no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—22no—
235C22×C3×C4—22no—
236C22×C3×C4—22no—
237C22×C3×C4—22no—
238C22×C3×C4—22no—
239C22×C3×C4—22no—
240C22×C3×C4—22no—
241C22×C3×C4—44no—
242C22×C3×C4—48no—
243C22×C3×C4—48no—
244C22×C3×C4—48no—
245C22×C3×C4—48no—
246C22×C3×C4—44no—
247C22×C3×C4—44no—
248C22×C3×C4—44no—
249C22×C3×C4—44no—
250C22×C3×C4—44no—
251C22×C3×C4—44no—
252C22×C3×C4C2×D412yes—
253C22×C3×C4C2×D414yes—
254C22×C3×C4C2×D412yes—
255C22×C3×C4C2×D414yes—
256C22×C3×C4C2×D412yes—
257C22×C3×C4#4114yes—
258C22×C3×C4#4114yes—
259C3×C4⋊C4—216no—
260C3×C4⋊C4—48no—
261C3×C22⋊C4—216no—
262C3×C22⋊C4—28no—
263C3×C22⋊C4—48no—
264C3×C22⋊C4—44no—
265C3×C22⋊C4—44no—
266C3×C22⋊C4—44no—
267C3×C22⋊C4—44no—
268C25C23×C311yescharacteristic
269C25C23×C311yescharacteristic
270C22×D4—22no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—22no—
274C22×D4—22no—
275C22×D4—22no—
276C22×D4C3×D414yes—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—24no—
287C23×C4—24no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—42no—
291C23×C4—42no—
292C23×C4C3×D414yes—
293C23×C4C3×D414yes—
294C23×C4C23×C312yes—
295C23×C4C23×C311yescharacteristic
296C23×C4C23×C311yescharacteristic
297C23×C4C23×C312yes—
298C23×C4C23×C312yes—
299C23×C4C23×C311yescharacteristic
300C23×C4C23×C311yescharacteristic
301C23×C4C23×C312yes—
302C23×C4C23×C311yescharacteristic
303#123—232no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—42no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4C3×D414yes—
329#95—24no—
330#95—24no—
331#95—24no—
332#95—24no—
333#95—24no—
334#95—22no—
335#95—22no—
336#95—24no—
337#95—24no—
338#95—42no—
339C23×C3—22no—
340C23×C3—22no—
341C23×C3—24no—
342C23×C3—24no—
343C23×C3—22no—
344C23×C3—22no—
345C23×C3—24no—
346C23×C3—24no—
347C23×C3—24no—
348C23×C3—24no—
349C23×C3—24no—
350C23×C3—24no—
351C23×C3—24no—
352C23×C3—24no—
353C23×C3—24no—
354C23×C3—24no—
355C23×C3—22no—
356C23×C3—22no—
357C23×C3—22no—
358C23×C3—24no—
359C23×C3—24no—
360C23×C3—41no—
361C23×C3—41no—
362C23×C3—41no—
363C23×C3—41no—
364C23×C3—41no—
365C23×C3—41no—
366C23×C3—42no—
367C23×C3—42no—
368C23×C3—41no—
369C23×C3—41no—
370C23×C3—42no—
371C23×C3—42no—
372C23×C3—42no—
373C23×C3—42no—
374C23×C3—42no—
375C23×C3—42no—
376C23×C3—42no—
377C23×C3—42no—
378C23×C3#12014yes—
379C23×C3#12114yes—
380C23×C3#12114yes—
381C23×C3#12114yes—
382C23×C3#12314yes—
383C23×C3#12314yes—
384C23×C3#12414yes—
385C23×C3C22×D411yescharacteristic
386C23×C3C22×D411yescharacteristic
387C23×C3C22×D411yescharacteristic
388C23×C3C22×D411yescharacteristic
389C23×C3C2×#4111yescharacteristic
390C23×C3C2×#4111yescharacteristic
391C23×C3C2×#4111yescharacteristic
392C23×C3C2×#4112yes—
393C23×C3C2×#4112yes—
394C23×C3H(5,𝔽2)12yes—
395C23×C32−1+412yes—
396C3×D4—416no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—24no—
400C2×C3×C4—24no—
401C2×C3×C4—24no—
402C2×C3×C4—24no—
403C2×C3×C4—22no—
404C2×C3×C4—24no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—24no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—24no—
411C2×C3×C4—22no—
412C2×C3×C4—24no—
413C2×C3×C4—24no—
414C2×C3×C4—24no—
415C2×C3×C4—24no—
416C2×C3×C4—416no—
417C2×C3×C4—416no—
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—41no—
425C2×C3×C4—42no—
426C2×C3×C4—41no—
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—42no—
436C2×C3×C4—416no—
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—41no—
446C2×C3×C4—41no—
447C2×C3×C4—42no—
448C2×C3×C4—42no—
449C2×C3×C4—42no—
450C2×C3×C4—42no—
451C2×C3×C4—42no—
452C2×C3×C4—42no—
453C2×C3×C4—42no—
454C2×C3×C4#12314yescomplemented
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—21no—
460C24—21no—
461C24—21no—
462C24—22no—
463C24—22no—
464C24—21no—
465C24—21no—
466C24—21no—
467C24—22no—
468C24—22no—
469C24C2×C3×D412yes—
470C24C2×C3×D412yes—
471C24C2×C3×D412yes—
472C24C2×C3×D412yes—
473C24C2×C3×D412yes—
474C24C3×#4112yes—
475C24C3×#4112yes—
476C24C3×#4112yes—
477C24C24×C311yescharacteristic
478C2×D4—28no—
479C2×D4—28no—
480C2×D4—28no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—44no—
484C2×D4—44no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—28no—
489C22×C4—28no—
490C22×C4—28no—
491C22×C4—28no—
492C22×C4—28no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—28no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—44no—
540C22×C4—48no—
541C22×C4—48no—
542C22×C4—48no—
543C22×C4—48no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4C2×C3×D412yes—
551C22×C4C2×C3×D414yes—
552C22×C4C2×C3×D412yes—
553C22×C4C2×C3×D414yes—
554C22×C4C2×C3×D412yes—
555C22×C4C3×#4114yes—
556C22×C4C3×#4114yes—
557C4⋊C4—216no—
558C4⋊C4—48no—
559C22⋊C4—216no—
560C22⋊C4—28no—
561C22⋊C4—48no—
562C22⋊C4—44no—
563C22⋊C4—44no—
564C22⋊C4—44no—
565C22⋊C4—44no—
566C22×C3—24no—
567C22×C3—24no—
568C22×C3—24no—
569C22×C3—24no—
570C22×C3—28no—
571C22×C3—28no—
572C22×C3—24no—
573C22×C3—28no—
574C22×C3—28no—
575C22×C3—24no—
576C22×C3—42no—
577C22×C3—44no—
578C22×C3—44no—
579C22×C3—42no—
580C22×C3—42no—
581C22×C3—81no—
582C22×C3—81no—
583C22×C3—81no—
584C22×C3—81no—
585C22×C3—82no—
586C22×C3—82no—
587C22×C3#39418yes—
588C22×C3C2×#12011yescharacteristic
589C22×C3C2×#12111yescharacteristic
590C22×C3C2×#12111yescharacteristic
591C22×C3C2×#12111yescharacteristic
592C22×C3C2×#12311yescharacteristic
593C22×C3C2×#12311yescharacteristic
594C22×C3C2×#12311yescharacteristic
595C22×C3#52511yescharacteristic
596C22×C3C2×#12411yescharacteristic
597C22×C3#52912yes—
598C22×C3#53212yes—
599C22×C3#53411yescharacteristic
600C22×C3#53611yescharacteristic
601C22×C3#53712yes—
602C22×C3#53912yes—
603C22×C3#54612yes—
604C22×C3#54612yes—
605C22×C3#54712yes—
606C22×C3#54712yes—
607C22×C3#55112yes—
608C22×C3#55112yes—
609C22×C3#55212yes—
610C22×C3#55212yes—
611C3×C4—24no—
612C3×C4—44no—
613C3×C4—42no—
614C3×C4—42no—
615C3×C4—44no—
616C3×C4—44no—
617C3×C4—81no—
618C3×C4—81no—
619C3×C4—82no—
620C23—22no—
621C23—22no—
622C23—24no—
623C23—24no—
624C23—22no—
625C23—22no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—24no—
640C23—24no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—42no—
648C23—42no—
649C23—41no—
650C23—41no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23C3×#12014yes—
660C23C3×#12114yes—
661C23C3×#12114yes—
662C23C3×#12114yes—
663C23C3×#12314yes—
664C23C3×#12314yes—
665C23C3×#12414yes—
666C23C22×C3×D411yescharacteristic
667C23C22×C3×D411yescharacteristic
668C23C22×C3×D411yescharacteristic
669C23C22×C3×D411yescharacteristic
670C23C2×C3×#4111yescharacteristic
671C23C2×C3×#4111yescharacteristic
672C23C2×C3×#4111yescharacteristic
673C23C2×C3×#4112yes—
674C23C2×C3×#4112yes—
675C23C3×H(5,𝔽2)12yes—
676C23C3×2−1+412yes—
677D4—416no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—24no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—416no—
698C2×C4—416no—
699C2×C4—416no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—42no—
706C2×C4—41no—
707C2×C4—42no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4C3×#12314yescomplemented
736C2×C3—28no—
737C2×C3—82no—
738C2×C3C2×#39411yescharacteristic
739C2×C3#241211yescharacteristic
740C2×C3#241311yescharacteristic
741C2×C3#241912yes—
742C2×C3#243012yes—
743C2×C3#248611yescharacteristic
744C2×C3#248812yes—
745C2×C3#249812yes—
746C2×C3#253411yescharacteristic
747C2×C3#261811yescharacteristic
748C2×C3#285411yescharacteristic
749C22—24no—
750C22—24no—
751C22—24no—
752C22—28no—
753C22—28no—
754C22—24no—
755C22—28no—
756C22—28no—
757C22—24no—
758C22—24no—
759C22—42no—
760C22—44no—
761C22—44no—
762C22—42no—
763C22—42no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—82no—
768C22—82no—
769C22—81no—
770C22C3×#39418yes—
771C22C2×C3×#12011yescharacteristic
772C22C2×C3×#12111yescharacteristic
773C22C2×C3×#12111yescharacteristic
774C22C2×C3×#12111yescharacteristic
775C22C2×C3×#12311yescharacteristic
776C22C2×C3×#12311yescharacteristic
777C22C2×C3×#12311yescharacteristic
778C22C3×#52511yescharacteristic
779C22C2×C3×#12411yescharacteristic
780C22C3×#52912yes—
781C22C3×#53212yes—
782C22C3×#53411yescharacteristic
783C22C3×#53611yescharacteristic
784C22C3×#53712yes—
785C22C3×#53912yes—
786C22C3×#54612yes—
787C22C3×#54612yes—
788C22C3×#54712yes—
789C22C3×#54712yes—
790C22C3×#55112yes—
791C22C3×#55112yes—
792C22C3×#55212yes—
793C22C3×#55212yes—
794C4—24no—
795C4—44no—
796C4—42no—
797C4—42no—
798C4—44no—
799C4—44no—
800C4—81no—
801C4—82no—
802C4—81no—
803C3#1492711yescharacteristic, direct product factor, Sylow
804C2—28no—
805C2—82no—
806C2C2×C3×#39411yescharacteristic
807C2C3×#241211yescharacteristic
808C2C3×#241311yescharacteristic
809C2C3×#241912yes—
810C2C3×#243012yes—
811C2C3×#248611yescharacteristic
812C2C3×#248812yes—
813C2C3×#249812yes—
814C2C3×#253411yescharacteristic
815C2C3×#261811yescharacteristic
816C2C3×#285411yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC24C24×C3
prime radicalC23×C3×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C3×#381C2semidirect
5. C2×C3×#380C2semidirect
6. C22×C3×#95C2semidirect
7. C3×#1442C2semidirect
8. C3×#1441C2semidirect
9. C3×#1440C2semidirect
10. C3×#1439C2semidirect
11. C3×C22⋊#95C2semidirect
12. #14927C3direct (N × H)
47. C2×#381C2×C3semidirect
48. C2×#380C2×C3semidirect
49. C22×#95C2×C3semidirect
50. #1442C2×C3semidirect
51. #1441C2×C3semidirect
52. #1440C2×C3semidirect
53. #1439C2×C3semidirect
54. C22⋊#95C2×C3semidirect
454. C2×C3×C4#123semidirect
735. C2×C4C3×#123semidirect
803. C3#14927direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1232
C2×C3×#3862
C2×C3×#3812
C2×C3×#3802
C22×C3×#952
C3×#14422
C3×#14412
C3×#14402
C3×#14392
C3×C22⋊#952
#149273