Finite Group Databasebeta

← C3×#15113 #10633720

Subgroups — C3×#15113 #10633720

Order 768.

2062 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#117C211yesmaximal, characteristic, complemented
2C2×C3×#388C212yesmaximal, complemented
3C2×C3×#386C211yesmaximal, characteristic
4C3×#1444C211yesmaximal, characteristic, complemented
5C3×#1442C211yesmaximal, characteristic, complemented
6C3×#1439C212yesmaximal, complemented
7C3×#1439C211yesmaximal, characteristic, complemented
8C3×#1439C211yesmaximal, characteristic, complemented
9C3×#1438C212yesmaximal
10C3×#1434C212yesmaximal, complemented
11C3×C22⋊#95C211yesmaximal, characteristic, complemented
12#15113C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×D4C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C2×C3×#117—24no—
16C2×C3×#117—28no—
17C22×C3×C4⋊C4C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C4⋊C4C2212yes—
20C22×C3×C22⋊C4C2212yes—
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2212yes—
24C22×C3×C22⋊C4C2212yes—
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2212yes—
27C22×C3×C42C2212yes—
28C3×#388—28no—
29C3×#386—24no—
30C2×C3×#95C2211yescharacteristic
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×#95C2212yes—
40C22×#117C2×C311yescharacteristic, complemented
41C2×#388C2×C312yescomplemented
42C2×#386C2×C311yescharacteristic
43#1444C2×C311yescharacteristic, complemented
44#1442C2×C311yescharacteristic, complemented
45#1439C2×C312yescomplemented
46#1439C2×C311yescharacteristic, complemented
47#1439C2×C311yescharacteristic, complemented
48#1438C2×C312yes—
49#1434C2×C312yescomplemented
50C22⋊#95C2×C311yescharacteristic, complemented
51C25×C3C2311yescharacteristic
52C25×C3C2311yescharacteristic
53C22×C3×D4—22no—
54C22×C3×D4—22no—
55C22×C3×D4—24no—
56C22×C3×D4—22no—
57C22×C3×D4—42no—
58C23×C3×C4—24no—
59C23×C3×C4—24no—
60C23×C3×C4—22no—
61C23×C3×C4—22no—
62C23×C3×C4D414yes—
63C23×C3×C4C2312yes—
64C23×C3×C4C2311yescharacteristic
65C23×C3×C4C2311yescharacteristic
66C23×C3×C4C2312yes—
67C23×C3×C4C2312yes—
68C23×C3×C4C2311yescharacteristic
69C23×C3×C4C2312yes—
70C23×C3×C4C2311yescharacteristic
71C23×C3×C4C2311yescharacteristic
72C3×#117—232no—
73C2×C3×C4⋊C4—24no—
74C2×C3×C4⋊C4—24no—
75C2×C3×C4⋊C4—22no—
76C2×C3×C4⋊C4—22no—
77C2×C3×C4⋊C4—24no—
78C2×C3×C4⋊C4—42no—
79C2×C3×C4⋊C4—42no—
80C2×C3×C22⋊C4—24no—
81C2×C3×C22⋊C4—24no—
82C2×C3×C22⋊C4—24no—
83C2×C3×C22⋊C4—24no—
84C2×C3×C22⋊C4—24no—
85C2×C3×C22⋊C4—24no—
86C2×C3×C22⋊C4—22no—
87C2×C3×C22⋊C4—24no—
88C2×C3×C22⋊C4—22no—
89C2×C3×C22⋊C4—22no—
90C2×C3×C22⋊C4—24no—
91C2×C3×C22⋊C4—24no—
92C2×C3×C22⋊C4—24no—
93C2×C3×C22⋊C4—22no—
94C2×C3×C22⋊C4—22no—
95C2×C3×C22⋊C4—42no—
96C2×C3×C22⋊C4—42no—
97C2×C3×C22⋊C4—42no—
98C2×C3×C22⋊C4—42no—
99C2×C3×C42—24no—
100C2×C3×C42—24no—
101C2×C3×C42D418yescomplemented
102C3×#95—22no—
103C3×#95—22no—
104C3×#95—24no—
105C3×#95—24no—
106C3×#95—22no—
107C3×#95—24no—
108C3×#95—24no—
109C3×#95—22no—
110C3×#95—42no—
111C3×#95—42no—
112C23×D4C22×C311yescharacteristic
113C24×C4C22×C311yescharacteristic
114C2×#117—24no—
115C2×#117—28no—
116C22×C4⋊C4C22×C311yescharacteristic
117C22×C4⋊C4C22×C311yescharacteristic
118C22×C4⋊C4C22×C312yes—
119C22×C22⋊C4C22×C312yes—
120C22×C22⋊C4C22×C312yes—
121C22×C22⋊C4C22×C311yescharacteristic
122C22×C22⋊C4C22×C311yescharacteristic
123C22×C22⋊C4C22×C312yes—
124C22×C22⋊C4C22×C312yes—
125C22×C22⋊C4C22×C311yescharacteristic
126C22×C42C22×C312yes—
127#388—28no—
128#386—24no—
129C2×#95C22×C312yes—
130C2×#95C22×C311yescharacteristic
131C2×#95C22×C311yescharacteristic
132C2×#95C22×C311yescharacteristic
133C2×#95C22×C312yes—
134C2×#95C22×C312yes—
135C2×#95C22×C312yes—
136C2×#95C22×C311yescharacteristic
137C2×#95C22×C312yes—
138C2×#95C22×C312yes—
139C24×C3—22no—
140C24×C3—22no—
141C24×C3—21no—
142C24×C3—21no—
143C24×C3—21no—
144C24×C3—21no—
145C24×C3—21no—
146C24×C3—22no—
147C24×C3—21no—
148C24×C3—22no—
149C24×C3—21no—
150C24×C3—22no—
151C24×C3—21no—
152C24×C3—21no—
153C24×C3—21no—
154C24×C3—22no—
155C24×C3—21no—
156C24×C3—22no—
157C24×C3—21no—
158C24×C3C2×D412yes—
159C24×C3#4112yes—
160C24×C3#4114yes—
161C24×C3C2411yescharacteristic
162C2×C3×D4—28no—
163C2×C3×D4—48no—
164C2×C3×D4—48no—
165C2×C3×D4—44no—
166C2×C3×D4—44no—
167C22×C3×C4—216no—
168C22×C3×C4—216no—
169C22×C3×C4—28no—
170C22×C3×C4—22no—
171C22×C3×C4—22no—
172C22×C3×C4—21no—
173C22×C3×C4—21no—
174C22×C3×C4—22no—
175C22×C3×C4—28no—
176C22×C3×C4—28no—
177C22×C3×C4—21no—
178C22×C3×C4—22no—
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—21no—
191C22×C3×C4—22no—
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—22no—
199C22×C3×C4—22no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—22no—
203C22×C3×C4—22no—
204C22×C3×C4—22no—
205C22×C3×C4—22no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—22no—
209C22×C3×C4—22no—
210C22×C3×C4—22no—
211C22×C3×C4—22no—
212C22×C3×C4—22no—
213C22×C3×C4—22no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4C2×D414yes—
217C22×C3×C4C2×D414yes—
218C22×C3×C4C2×D412yes—
219C22×C3×C4C2×D414yes—
220C22×C3×C4C2×D412yes—
221C22×C3×C4#4112yes—
222C22×C3×C4#4114yes—
223C22×C3×C4#4112yes—
224C22×C3×C4#4112yes—
225C3×C4⋊C4—28no—
226C3×C4⋊C4—28no—
227C3×C4⋊C4—48no—
228C3×C22⋊C4—216no—
229C3×C22⋊C4—216no—
230C3×C22⋊C4—48no—
231C3×C22⋊C4—48no—
232C3×C22⋊C4—44no—
233C3×C22⋊C4—44no—
234C3×C22⋊C4—44no—
235C3×C42—216no—
236C25C23×C311yescharacteristic
237C25C23×C311yescharacteristic
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—24no—
241C22×D4—22no—
242C22×D4—42no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4C3×D414yes—
248C23×C4C23×C311yescharacteristic
249C23×C4C23×C312yes—
250C23×C4C23×C311yescharacteristic
251C23×C4C23×C312yes—
252C23×C4C23×C312yes—
253C23×C4C23×C312yes—
254C23×C4C23×C311yescharacteristic
255C23×C4C23×C311yescharacteristic
256C23×C4C23×C311yescharacteristic
257#117—232no—
258C2×C4⋊C4—24no—
259C2×C4⋊C4—24no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—24no—
263C2×C4⋊C4—42no—
264C2×C4⋊C4—42no—
265C2×C22⋊C4—24no—
266C2×C22⋊C4—24no—
267C2×C22⋊C4—24no—
268C2×C22⋊C4—24no—
269C2×C22⋊C4—24no—
270C2×C22⋊C4—24no—
271C2×C22⋊C4—22no—
272C2×C22⋊C4—24no—
273C2×C22⋊C4—22no—
274C2×C22⋊C4—22no—
275C2×C22⋊C4—24no—
276C2×C22⋊C4—24no—
277C2×C22⋊C4—24no—
278C2×C22⋊C4—22no—
279C2×C22⋊C4—22no—
280C2×C22⋊C4—42no—
281C2×C22⋊C4—42no—
282C2×C22⋊C4—42no—
283C2×C22⋊C4—42no—
284C2×C42—24no—
285C2×C42—24no—
286C2×C42C3×D418yescomplemented
287#95—22no—
288#95—22no—
289#95—24no—
290#95—24no—
291#95—22no—
292#95—24no—
293#95—24no—
294#95—22no—
295#95—42no—
296#95—42no—
297C23×C3—22no—
298C23×C3—22no—
299C23×C3—24no—
300C23×C3—24no—
301C23×C3—22no—
302C23×C3—22no—
303C23×C3—22no—
304C23×C3—22no—
305C23×C3—24no—
306C23×C3—24no—
307C23×C3—24no—
308C23×C3—24no—
309C23×C3—24no—
310C23×C3—22no—
311C23×C3—24no—
312C23×C3—22no—
313C23×C3—22no—
314C23×C3—42no—
315C23×C3—42no—
316C23×C3—42no—
317C23×C3—42no—
318C23×C3—41no—
319C23×C3—41no—
320C23×C3—42no—
321C23×C3—42no—
322C23×C3—41no—
323C23×C3—41no—
324C23×C3—41no—
325C23×C3—41no—
326C23×C3—41no—
327C23×C3—42no—
328C23×C3—42no—
329C23×C3—42no—
330C23×C3—41no—
331C23×C3—42no—
332C23×C3—41no—
333C23×C3—42no—
334C23×C3—41no—
335C23×C3—42no—
336C23×C3—42no—
337C23×C3—42no—
338C23×C3—42no—
339C23×C3—42no—
340C23×C3—41no—
341C23×C3—41no—
342C23×C3#12314yes—
343C23×C3C22×D411yescharacteristic
344C23×C3C22×D412yes—
345C23×C3C2×#4112yes—
346C23×C3C2×#4111yescharacteristic
347C23×C3C2×#4111yescharacteristic
348C23×C3C2×#4111yescharacteristic
349C23×C3C2×#4111yescharacteristic
350C23×C3C2×#4112yes—
351C23×C3H(5,𝔽2)11yescharacteristic
352C23×C3H(5,𝔽2)12yes—
353C23×C32−1+411yescharacteristic
354C3×D4—416no—
355C2×C3×C4—232no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—24no—
361C2×C3×C4—24no—
362C2×C3×C4—24no—
363C2×C3×C4—24no—
364C2×C3×C4—24no—
365C2×C3×C4—24no—
366C2×C3×C4—24no—
367C2×C3×C4—24no—
368C2×C3×C4—22no—
369C2×C3×C4—24no—
370C2×C3×C4—24no—
371C2×C3×C4—24no—
372C2×C3×C4—24no—
373C2×C3×C4—24no—
374C2×C3×C4—24no—
375C2×C3×C4—41no—
376C2×C3×C4—42no—
377C2×C3×C4—42no—
378C2×C3×C4—42no—
379C2×C3×C4—42no—
380C2×C3×C4—42no—
381C2×C3×C4—42no—
382C2×C3×C4—42no—
383C2×C3×C4—42no—
384C2×C3×C4—41no—
385C2×C3×C4—42no—
386C2×C3×C4—42no—
387C2×C3×C4—42no—
388C2×C3×C4—42no—
389C2×C3×C4—42no—
390C2×C3×C4—41no—
391C2×C3×C4—41no—
392C2×C3×C4—42no—
393C2×C3×C4—42no—
394C2×C3×C4—41no—
395C2×C3×C4—42no—
396C2×C3×C4—41no—
397C2×C3×C4—41no—
398C2×C3×C4—42no—
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—42no—
406C2×C3×C4—42no—
407C2×C3×C4#12014yes—
408C2×C3×C4#12314yes—
409C24—22no—
410C24—22no—
411C24—21no—
412C24—21no—
413C24—21no—
414C24—21no—
415C24—21no—
416C24—22no—
417C24—21no—
418C24—22no—
419C24—21no—
420C24—22no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—22no—
425C24—21no—
426C24—22no—
427C24—21no—
428C24C2×C3×D412yes—
429C24C3×#4112yes—
430C24C3×#4114yes—
431C24C24×C311yescharacteristic
432C2×D4—28no—
433C2×D4—48no—
434C2×D4—48no—
435C2×D4—44no—
436C2×D4—44no—
437C22×C4—216no—
438C22×C4—216no—
439C22×C4—28no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—28no—
446C22×C4—28no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4C2×C3×D414yes—
487C22×C4C2×C3×D414yes—
488C22×C4C2×C3×D412yes—
489C22×C4C2×C3×D414yes—
490C22×C4C2×C3×D412yes—
491C22×C4C3×#4112yes—
492C22×C4C3×#4114yes—
493C22×C4C3×#4112yes—
494C22×C4C3×#4112yes—
495C4⋊C4—28no—
496C4⋊C4—28no—
497C4⋊C4—48no—
498C22⋊C4—216no—
499C22⋊C4—216no—
500C22⋊C4—48no—
501C22⋊C4—48no—
502C22⋊C4—44no—
503C22⋊C4—44no—
504C22⋊C4—44no—
505C42—216no—
506C22×C3—24no—
507C22×C3—24no—
508C22×C3—24no—
509C22×C3—44no—
510C22×C3—44no—
511C22×C3—44no—
512C22×C3—44no—
513C22×C3—42no—
514C22×C3—42no—
515C22×C3—42no—
516C22×C3—42no—
517C22×C3—44no—
518C22×C3—44no—
519C22×C3—42no—
520C22×C3—42no—
521C22×C3—42no—
522C22×C3—81no—
523C22×C3—82no—
524C22×C3—82no—
525C22×C3—81no—
526C22×C3—81no—
527C22×C3—81no—
528C22×C3C2×#12011yescharacteristic
529C22×C3C2×#12311yescharacteristic
530C22×C3C2×#12311yescharacteristic
531C22×C3#52512yes—
532C22×C3#52512yes—
533C22×C3#52512yes—
534C22×C3#52511yescharacteristic
535C22×C3#53212yes—
536C22×C3#53211yescharacteristic
537C22×C3#53512yes—
538C22×C3#53511yescharacteristic
539C22×C3#53712yes—
540C22×C3#53711yescharacteristic
541C22×C3#55112yes—
542C22×C3#55112yes—
543C22×C3#55112yes—
544C22×C3#55212yes—
545C22×C3#55211yescharacteristic
546C22×C3#55311yescharacteristic
547C22×C3#55312yes—
548C22×C3#55512yes—
549C22×C3#55511yescharacteristic
550C22×C3#55611yescharacteristic
551C3×C4—24no—
552C3×C4—24no—
553C3×C4—44no—
554C3×C4—44no—
555C3×C4—44no—
556C3×C4—42no—
557C3×C4—82no—
558C3×C4—81no—
559C3×C4—81no—
560C23—22no—
561C23—22no—
562C23—24no—
563C23—24no—
564C23—22no—
565C23—22no—
566C23—22no—
567C23—22no—
568C23—24no—
569C23—24no—
570C23—24no—
571C23—24no—
572C23—24no—
573C23—22no—
574C23—24no—
575C23—22no—
576C23—22no—
577C23—42no—
578C23—42no—
579C23—42no—
580C23—42no—
581C23—41no—
582C23—41no—
583C23—42no—
584C23—41no—
585C23—42no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—42no—
591C23—42no—
592C23—41no—
593C23—42no—
594C23—42no—
595C23—41no—
596C23—41no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—41no—
603C23—42no—
604C23—41no—
605C23C3×#12314yes—
606C23C22×C3×D411yescharacteristic
607C23C22×C3×D412yes—
608C23C2×C3×#4112yes—
609C23C2×C3×#4111yescharacteristic
610C23C2×C3×#4111yescharacteristic
611C23C2×C3×#4111yescharacteristic
612C23C2×C3×#4111yescharacteristic
613C23C2×C3×#4112yes—
614C23C3×H(5,𝔽2)12yes—
615C23C3×H(5,𝔽2)11yescharacteristic
616C23C3×2−1+411yescharacteristic
617D4—416no—
618C2×C4—232no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—24no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—22no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—24no—
638C2×C4—41no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—41no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—42no—
656C2×C4—41no—
657C2×C4—42no—
658C2×C4—41no—
659C2×C4—42no—
660C2×C4—41no—
661C2×C4—42no—
662C2×C4—41no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4C3×#12014yes—
671C2×C4C3×#12314yes—
672C2×C3—44no—
673C2×C3—82no—
674C2×C3#238811yescharacteristic
675C2×C3#248211yescharacteristic
676C2×C3#248511yescharacteristic
677C2×C3#249811yescharacteristic
678C2×C3#250011yescharacteristic
679C2×C3#259812yes—
680C2×C3#260112yes—
681C2×C3#260912yes—
682C2×C3#261012yes—
683C2×C3#261511yescharacteristic
684C2×C3#284911yescharacteristic
685C22—24no—
686C22—24no—
687C22—24no—
688C22—42no—
689C22—42no—
690C22—42no—
691C22—44no—
692C22—44no—
693C22—44no—
694C22—44no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—42no—
699C22—44no—
700C22—44no—
701C22—81no—
702C22—81no—
703C22—81no—
704C22—82no—
705C22—82no—
706C22—81no—
707C22C2×C3×#12011yescharacteristic
708C22C2×C3×#12311yescharacteristic
709C22C2×C3×#12311yescharacteristic
710C22C3×#52511yescharacteristic
711C22C3×#52512yes—
712C22C3×#52512yes—
713C22C3×#52512yes—
714C22C3×#53211yescharacteristic
715C22C3×#53212yes—
716C22C3×#53511yescharacteristic
717C22C3×#53512yes—
718C22C3×#53711yescharacteristic
719C22C3×#53712yes—
720C22C3×#55112yes—
721C22C3×#55112yes—
722C22C3×#55112yes—
723C22C3×#55211yescharacteristic
724C22C3×#55212yes—
725C22C3×#55311yescharacteristic
726C22C3×#55312yes—
727C22C3×#55511yescharacteristic
728C22C3×#55512yes—
729C22C3×#55611yescharacteristic
730C4—24no—
731C4—24no—
732C4—44no—
733C4—42no—
734C4—44no—
735C4—44no—
736C4—81no—
737C4—82no—
738C4—81no—
739C3#1511311yescharacteristic, direct product factor, Sylow
740C2—44no—
741C2—82no—
742C2C3×#238811yescharacteristic
743C2C3×#248211yescharacteristic
744C2C3×#248511yescharacteristic
745C2C3×#249811yescharacteristic
746C2C3×#250011yescharacteristic
747C2C3×#259812yes—
748C2C3×#260112yes—
749C2C3×#260912yes—
750C2C3×#261012yes—
751C2C3×#261511yescharacteristic
752C2C3×#284911yescharacteristic
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
1. C22×C3×#117C2semidirect
2. C2×C3×#388C2semidirect
4. C3×#1444C2semidirect
5. C3×#1442C2semidirect
6. C3×#1439C2semidirect
7. C3×#1439C2semidirect
8. C3×#1439C2semidirect
10. C3×#1434C2semidirect
11. C3×C22⋊#95C2semidirect
12. #15113C3direct (N × H)
40. C22×#117C2×C3semidirect
41. C2×#388C2×C3semidirect
43. #1444C2×C3semidirect
44. #1442C2×C3semidirect
45. #1439C2×C3semidirect
46. #1439C2×C3semidirect
47. #1439C2×C3semidirect
49. #1434C2×C3semidirect
50. C22⋊#95C2×C3semidirect
101. C2×C3×C42D4semidirect
286. C2×C42C3×D4semidirect
739. C3#15113direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1172
C2×C3×#3882
C2×C3×#3862
C3×#14442
C3×#14422
C3×#14392
C3×#14382
C3×#14342
C3×C22⋊#952
#151133