Finite Group Databasebeta

← C3×#14812 #10633419

Subgroups — C3×#14812 #10633419

Order 768.

2298 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4×D4C211yesmaximal, characteristic
2C2×C3×#396C212yesmaximal, complemented
3C2×C3×#387C211yesmaximal, characteristic, complemented
4C2×C3×#385C212yesmaximal, complemented
5C3×#1444C211yesmaximal, characteristic, complemented
6C3×#1442C211yesmaximal, characteristic, complemented
7C3×#1439C212yesmaximal, complemented
8C3×#1438C211yesmaximal, characteristic
9C3×#1438C211yesmaximal, characteristic
10C3×C4⋊#95C211yesmaximal, characteristic, complemented
11C3×C22⋊#95C212yesmaximal, complemented
12#14812C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×D4C2211yescharacteristic
14C24×C3×C4C2212yes—
15C2×C3×C4×D4—28no—
16C2×C3×C4×D4—24no—
17C22×C3×C4⋊C4C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C4⋊C4C2212yes—
20C22×C3×C4⋊C4C2212yes—
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2212yes—
23C22×C3×C22⋊C4C2212yes—
24C22×C3×C22⋊C4C2212yes—
25C22×C3×C22⋊C4C2212yes—
26C22×C3×C22⋊C4C2212yes—
27C22×C3×C42C2211yescharacteristic
28C3×#396—28no—
29C3×#387—24no—
30C3×#385—28no—
31C2×C3×#95C2212yes—
32C2×C3×#95C2212yes—
33C2×C3×#95C2212yes—
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
37C2×C3×#95C2211yescharacteristic
38C2×C3×#95C2211yescharacteristic
39C2×C3×#95C2211yescharacteristic
40C2×C3×#95C2212yes—
41C22×C4×D4C2×C311yescharacteristic
42C2×#396C2×C312yescomplemented
43C2×#387C2×C311yescharacteristic, complemented
44C2×#385C2×C312yescomplemented
45#1444C2×C311yescharacteristic, complemented
46#1442C2×C311yescharacteristic, complemented
47#1439C2×C312yescomplemented
48#1438C2×C311yescharacteristic
49#1438C2×C311yescharacteristic
50C4⋊#95C2×C311yescharacteristic, complemented
51C22⋊#95C2×C312yescomplemented
52C25×C3C2312yes—
53C22×C3×D4—24no—
54C22×C3×D4—24no—
55C22×C3×D4—22no—
56C22×C3×D4—22no—
57C22×C3×D4Q814yes—
58C23×C3×C4—24no—
59C23×C3×C4—24no—
60C23×C3×C4—24no—
61C23×C3×C4—24no—
62C23×C3×C4—24no—
63C23×C3×C4—42no—
64C23×C3×C4—42no—
65C23×C3×C4C2311yescharacteristic
66C23×C3×C4C2312yes—
67C23×C3×C4C2311yescharacteristic
68C23×C3×C4C2312yes—
69C23×C3×C4C2311yescharacteristic
70C23×C3×C4C2311yescharacteristic
71C23×C3×C4C2312yes—
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C3×C4×D4—232no—
76C2×C3×C4⋊C4—22no—
77C2×C3×C4⋊C4—24no—
78C2×C3×C4⋊C4—22no—
79C2×C3×C4⋊C4—22no—
80C2×C3×C4⋊C4—24no—
81C2×C3×C4⋊C4—22no—
82C2×C3×C4⋊C4—24no—
83C2×C3×C4⋊C4—24no—
84C2×C3×C4⋊C4—24no—
85C2×C3×C4⋊C4—24no—
86C2×C3×C4⋊C4—42no—
87C2×C3×C4⋊C4—42no—
88C2×C3×C4⋊C4D414yescomplemented
89C2×C3×C22⋊C4—24no—
90C2×C3×C22⋊C4—24no—
91C2×C3×C22⋊C4—24no—
92C2×C3×C22⋊C4—24no—
93C2×C3×C22⋊C4—24no—
94C2×C3×C22⋊C4—24no—
95C2×C3×C22⋊C4—24no—
96C2×C3×C22⋊C4—24no—
97C2×C3×C22⋊C4—24no—
98C2×C3×C22⋊C4—24no—
99C2×C3×C22⋊C4—42no—
100C2×C3×C22⋊C4—42no—
101C2×C3×C22⋊C4—42no—
102C2×C3×C22⋊C4—42no—
103C2×C3×C22⋊C4D418yes—
104C2×C3×C42—24no—
105C2×C3×C42D414yes—
106C3×#95—24no—
107C3×#95—24no—
108C3×#95—22no—
109C3×#95—22no—
110C3×#95—22no—
111C3×#95—22no—
112C3×#95—24no—
113C3×#95—22no—
114C3×#95—22no—
115C3×#95—42no—
116C23×D4C22×C311yescharacteristic
117C24×C4C22×C312yes—
118C2×C4×D4—28no—
119C2×C4×D4—24no—
120C22×C4⋊C4C22×C311yescharacteristic
121C22×C4⋊C4C22×C311yescharacteristic
122C22×C4⋊C4C22×C312yes—
123C22×C4⋊C4C22×C312yes—
124C22×C4⋊C4C22×C311yescharacteristic
125C22×C22⋊C4C22×C312yes—
126C22×C22⋊C4C22×C312yes—
127C22×C22⋊C4C22×C312yes—
128C22×C22⋊C4C22×C312yes—
129C22×C22⋊C4C22×C312yes—
130C22×C42C22×C311yescharacteristic
131#396—28no—
132#387—24no—
133#385—28no—
134C2×#95C22×C312yes—
135C2×#95C22×C311yescharacteristic
136C2×#95C22×C312yes—
137C2×#95C22×C311yescharacteristic
138C2×#95C22×C311yescharacteristic
139C2×#95C22×C311yescharacteristic
140C2×#95C22×C311yescharacteristic
141C2×#95C22×C311yescharacteristic
142C2×#95C22×C312yes—
143C2×#95C22×C312yes—
144C24×C3—22no—
145C24×C3—22no—
146C24×C3—22no—
147C24×C3—22no—
148C24×C3—22no—
149C24×C3—22no—
150C24×C3—22no—
151C24×C3—22no—
152C24×C3—22no—
153C24×C3—22no—
154C24×C3—22no—
155C24×C3—22no—
156C24×C3C2×D414yes—
157C24×C3C2×Q814yes—
158C24×C3#4114yes—
159C24×C3C2411yescharacteristic
160C2×C3×D4—28no—
161C2×C3×D4—28no—
162C2×C3×D4—216no—
163C2×C3×D4—216no—
164C2×C3×D4—28no—
165C22×C3×C4—22no—
166C22×C3×C4—22no—
167C22×C3×C4—22no—
168C22×C3×C4—22no—
169C22×C3×C4—21no—
170C22×C3×C4—22no—
171C22×C3×C4—21no—
172C22×C3×C4—216no—
173C22×C3×C4—21no—
174C22×C3×C4—22no—
175C22×C3×C4—21no—
176C22×C3×C4—22no—
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—22no—
184C22×C3×C4—22no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
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—21no—
194C22×C3×C4—22no—
195C22×C3×C4—21no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
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—21no—
209C22×C3×C4—21no—
210C22×C3×C4—48no—
211C22×C3×C4—48no—
212C22×C3×C4—48no—
213C22×C3×C4—48no—
214C22×C3×C4—48no—
215C22×C3×C4—48no—
216C22×C3×C4C2×D412yes—
217C22×C3×C4C2×D414yes—
218C22×C3×C4C2×D412yes—
219C22×C3×C4C2×D412yes—
220C22×C3×C4C2×D414yes—
221C22×C3×C4C2×D412yes—
222C22×C3×C4C2×D412yes—
223C22×C3×C4C2×D412yes—
224C22×C3×C4C2×Q812yes—
225C22×C3×C4#4114yes—
226C22×C3×C4#4112yes—
227C22×C3×C4#4112yes—
228C3×C4⋊C4—28no—
229C3×C4⋊C4—28no—
230C3×C4⋊C4—48no—
231C3×C4⋊C4—48no—
232C3×C4⋊C4—44no—
233C3×C22⋊C4—216no—
234C3×C22⋊C4—216no—
235C3×C22⋊C4—48no—
236C3×C22⋊C4—48no—
237C3×C22⋊C4—48no—
238C3×C42—28no—
239C25C23×C312yes—
240C22×D4—24no—
241C22×D4—24no—
242C22×D4—22no—
243C22×D4—22no—
244C22×D4C3×Q814yes—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—42no—
251C23×C4—42no—
252C23×C4C23×C312yes—
253C23×C4C23×C311yescharacteristic
254C23×C4C23×C311yescharacteristic
255C23×C4C23×C311yescharacteristic
256C23×C4C23×C311yescharacteristic
257C23×C4C23×C312yes—
258C23×C4C23×C312yes—
259C23×C4C23×C311yescharacteristic
260C23×C4C23×C311yescharacteristic
261C23×C4C23×C311yescharacteristic
262C4×D4—232no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—42no—
274C2×C4⋊C4—42no—
275C2×C4⋊C4C3×D414yescomplemented
276C2×C22⋊C4—24no—
277C2×C22⋊C4—24no—
278C2×C22⋊C4—24no—
279C2×C22⋊C4—24no—
280C2×C22⋊C4—24no—
281C2×C22⋊C4—24no—
282C2×C22⋊C4—24no—
283C2×C22⋊C4—24no—
284C2×C22⋊C4—24no—
285C2×C22⋊C4—24no—
286C2×C22⋊C4—42no—
287C2×C22⋊C4—42no—
288C2×C22⋊C4—42no—
289C2×C22⋊C4—42no—
290C2×C22⋊C4C3×D418yes—
291C2×C42—24no—
292C2×C42C3×D414yes—
293#95—24no—
294#95—24no—
295#95—22no—
296#95—22no—
297#95—22no—
298#95—22no—
299#95—24no—
300#95—22no—
301#95—22no—
302#95—42no—
303C23×C3—24no—
304C23×C3—24no—
305C23×C3—24no—
306C23×C3—24no—
307C23×C3—24no—
308C23×C3—24no—
309C23×C3—24no—
310C23×C3—24no—
311C23×C3—24no—
312C23×C3—24no—
313C23×C3—24no—
314C23×C3—24no—
315C23×C3—24no—
316C23×C3—24no—
317C23×C3—24no—
318C23×C3—24no—
319C23×C3—24no—
320C23×C3—24no—
321C23×C3—42no—
322C23×C3—42no—
323C23×C3—42no—
324C23×C3—42no—
325C23×C3—42no—
326C23×C3—42no—
327C23×C3—42no—
328C23×C3—42no—
329C23×C3—42no—
330C23×C3—42no—
331C23×C3—42no—
332C23×C3—42no—
333C23×C3—42no—
334C23×C3—42no—
335C23×C3—42no—
336C23×C3—42no—
337C23×C3C22⋊Q818yes—
338C23×C3C22×D411yescharacteristic
339C23×C3C22×D412yes—
340C23×C3C22×D411yescharacteristic
341C23×C3C22×Q811yescharacteristic
342C23×C3C2×#4111yescharacteristic
343C23×C3C2×#4112yes—
344C23×C3C2×#4111yescharacteristic
345C23×C3C2×#4112yes—
346C23×C3H(5,𝔽2)12yes—
347C23×C3H(5,𝔽2)11yescharacteristic
348C23×C32−1+411yescharacteristic
349C3×D4—232no—
350C2×C3×C4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—24no—
353C2×C3×C4—22no—
354C2×C3×C4—24no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—24no—
359C2×C3×C4—24no—
360C2×C3×C4—24no—
361C2×C3×C4—24no—
362C2×C3×C4—24no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4—24no—
366C2×C3×C4—24no—
367C2×C3×C4—24no—
368C2×C3×C4—24no—
369C2×C3×C4—24no—
370C2×C3×C4—24no—
371C2×C3×C4—24no—
372C2×C3×C4—432no—
373C2×C3×C4—41no—
374C2×C3×C4—42no—
375C2×C3×C4—41no—
376C2×C3×C4—42no—
377C2×C3×C4—42no—
378C2×C3×C4—41no—
379C2×C3×C4—41no—
380C2×C3×C4—42no—
381C2×C3×C4—42no—
382C2×C3×C4—42no—
383C2×C3×C4—42no—
384C2×C3×C4—42no—
385C2×C3×C4—42no—
386C2×C3×C4—42no—
387C2×C3×C4—41no—
388C2×C3×C4—41no—
389C2×C3×C4—42no—
390C2×C3×C4—42no—
391C2×C3×C4—41no—
392C2×C3×C4—41no—
393C2×C3×C4—41no—
394C2×C3×C4—41no—
395C2×C3×C4—42no—
396C2×C3×C4—42no—
397C2×C3×C4—42no—
398C2×C3×C4—42no—
399C2×C3×C4—42no—
400C2×C3×C4—42no—
401C2×C3×C4—42no—
402C2×C3×C4—42no—
403C2×C3×C4—42no—
404C2×C3×C4#12014yes—
405C2×C3×C4#12114yes—
406C2×C3×C4C22⋊Q814yes—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24C2×C3×D414yes—
420C24C2×C3×Q814yes—
421C24C3×#4114yes—
422C24C24×C311yescharacteristic
423C2×D4—28no—
424C2×D4—28no—
425C2×D4—216no—
426C2×D4—216no—
427C2×D4—28no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—216no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—48no—
474C22×C4—48no—
475C22×C4—48no—
476C22×C4—48no—
477C22×C4—48no—
478C22×C4—48no—
479C22×C4C2×C3×D412yes—
480C22×C4C2×C3×D414yes—
481C22×C4C2×C3×D412yes—
482C22×C4C2×C3×D412yes—
483C22×C4C2×C3×D414yes—
484C22×C4C2×C3×D412yes—
485C22×C4C2×C3×D412yes—
486C22×C4C2×C3×D412yes—
487C22×C4C2×C3×Q812yes—
488C22×C4C3×#4114yes—
489C22×C4C3×#4112yes—
490C22×C4C3×#4112yes—
491C4⋊C4—28no—
492C4⋊C4—28no—
493C4⋊C4—48no—
494C4⋊C4—48no—
495C4⋊C4—44no—
496C22⋊C4—216no—
497C22⋊C4—216no—
498C22⋊C4—48no—
499C22⋊C4—48no—
500C22⋊C4—48no—
501C42—28no—
502C22×C3—28no—
503C22×C3—28no—
504C22×C3—28no—
505C22×C3—44no—
506C22×C3—44no—
507C22×C3—44no—
508C22×C3—44no—
509C22×C3—44no—
510C22×C3—44no—
511C22×C3—44no—
512C22×C3—44no—
513C22×C3—44no—
514C22×C3—44no—
515C22×C3—44no—
516C22×C3—44no—
517C22×C3C2×#12011yescharacteristic
518C22×C3C2×#12111yescharacteristic
519C22×C3C2×C22⋊Q811yescharacteristic
520C22×C3C2×C22⋊Q812yes—
521C22×C3#52511yescharacteristic
522C22×C3#52512yes—
523C22×C3#52512yes—
524C22×C3#52912yes—
525C22×C3#53211yescharacteristic
526C22×C3#53511yescharacteristic
527C22×C3#53711yescharacteristic
528C22×C3#53812yes—
529C22×C3#53912yes—
530C22×C3D4212yes—
531C22×C3#54612yes—
532C22×C3#54612yes—
533C22×C3#54712yes—
534C22×C3D4×Q811yescharacteristic
535C22×C3#55011yescharacteristic
536C22×C3#55312yes—
537C22×C3#55412yes—
538C22×C3#55411yescharacteristic
539C22×C3#55611yescharacteristic
540C3×C4—24no—
541C3×C4—24no—
542C3×C4—24no—
543C3×C4—42no—
544C3×C4—42no—
545C3×C4—44no—
546C3×C4—44no—
547C3×C4—81no—
548C3×C4—81no—
549C3×C4—82no—
550C23—24no—
551C23—24no—
552C23—24no—
553C23—24no—
554C23—24no—
555C23—24no—
556C23—24no—
557C23—24no—
558C23—24no—
559C23—24no—
560C23—24no—
561C23—24no—
562C23—24no—
563C23—24no—
564C23—24no—
565C23—24no—
566C23—24no—
567C23—24no—
568C23—42no—
569C23—42no—
570C23—42no—
571C23—42no—
572C23—42no—
573C23—42no—
574C23—42no—
575C23—42no—
576C23—42no—
577C23—42no—
578C23—42no—
579C23—42no—
580C23—42no—
581C23—42no—
582C23—42no—
583C23—42no—
584C23C3×C22⋊Q818yes—
585C23C22×C3×D411yescharacteristic
586C23C22×C3×D412yes—
587C23C22×C3×D411yescharacteristic
588C23C22×C3×Q811yescharacteristic
589C23C2×C3×#4111yescharacteristic
590C23C2×C3×#4112yes—
591C23C2×C3×#4111yescharacteristic
592C23C2×C3×#4112yes—
593C23C3×H(5,𝔽2)12yes—
594C23C3×H(5,𝔽2)11yescharacteristic
595C23C3×2−1+411yescharacteristic
596D4—232no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—24no—
600C2×C4—22no—
601C2×C4—24no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—24no—
606C2×C4—24no—
607C2×C4—24no—
608C2×C4—24no—
609C2×C4—24no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—24no—
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—432no—
620C2×C4—41no—
621C2×C4—42no—
622C2×C4—41no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—41no—
626C2×C4—42no—
627C2×C4—41no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4C3×#12014yes—
652C2×C4C3×#12114yes—
653C2×C4C3×C22⋊Q814yes—
654C2×C3—48no—
655C2×C3#239211yescharacteristic
656C2×C3#240811yescharacteristic
657C2×C3#243011yescharacteristic
658C2×C3#244912yes—
659C2×C3#245012yes—
660C2×C3#245612yes—
661C2×C3#246612yes—
662C2×C3#253811yescharacteristic
663C2×C3#256611yescharacteristic
664C2×C3#263611yescharacteristic
665C2×C3#284811yescharacteristic
666C22—28no—
667C22—28no—
668C22—28no—
669C22—44no—
670C22—44no—
671C22—44no—
672C22—44no—
673C22—44no—
674C22—44no—
675C22—44no—
676C22—44no—
677C22—44no—
678C22—44no—
679C22—44no—
680C22—44no—
681C22C2×C3×#12011yescharacteristic
682C22C2×C3×#12111yescharacteristic
683C22C2×C3×C22⋊Q812yes—
684C22C2×C3×C22⋊Q811yescharacteristic
685C22C3×#52511yescharacteristic
686C22C3×#52512yes—
687C22C3×#52512yes—
688C22C3×#52912yes—
689C22C3×#53211yescharacteristic
690C22C3×#53511yescharacteristic
691C22C3×#53711yescharacteristic
692C22C3×#53812yes—
693C22C3×#53912yes—
694C22C3×D4212yes—
695C22C3×#54612yes—
696C22C3×#54612yes—
697C22C3×#54712yes—
698C22C3×D4×Q811yescharacteristic
699C22C3×#55011yescharacteristic
700C22C3×#55312yes—
701C22C3×#55412yes—
702C22C3×#55411yescharacteristic
703C22C3×#55611yescharacteristic
704C4—24no—
705C4—24no—
706C4—24no—
707C4—42no—
708C4—44no—
709C4—42no—
710C4—44no—
711C4—81no—
712C4—81no—
713C4—82no—
714C3#1481211yescharacteristic, direct product factor, Sylow
715C2—48no—
716C2C3×#239211yescharacteristic
717C2C3×#240811yescharacteristic
718C2C3×#243011yescharacteristic
719C2C3×#244912yes—
720C2C3×#245012yes—
721C2C3×#245612yes—
722C2C3×#246612yes—
723C2C3×#253811yescharacteristic
724C2C3×#256611yescharacteristic
725C2C3×#263611yescharacteristic
726C2C3×#284811yescharacteristic
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
2. C2×C3×#396C2semidirect
3. C2×C3×#387C2semidirect
4. C2×C3×#385C2semidirect
5. C3×#1444C2semidirect
6. C3×#1442C2semidirect
7. C3×#1439C2semidirect
10. C3×C4⋊#95C2semidirect
11. C3×C22⋊#95C2semidirect
12. #14812C3direct (N × H)
42. C2×#396C2×C3semidirect
43. C2×#387C2×C3semidirect
44. C2×#385C2×C3semidirect
45. #1444C2×C3semidirect
46. #1442C2×C3semidirect
47. #1439C2×C3semidirect
50. C4⋊#95C2×C3semidirect
51. C22⋊#95C2×C3semidirect
88. C2×C3×C4⋊C4D4semidirect
275. C2×C4⋊C4C3×D4semidirect
714. C3#14812direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C4×D42
C2×C3×#3962
C2×C3×#3872
C2×C3×#3852
C3×#14442
C3×#14422
C3×#14392
C3×#14382
C3×C4⋊#952
C3×C22⋊#952
#148123