Finite Group Databasebeta

← C3×#14977 #10633584

Subgroups — C3×#14977 #10633584

Order 768.

2310 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#399C211yesmaximal, characteristic, complemented
2C2×C3×#392C211yesmaximal, characteristic
3C2×C3×#390C211yesmaximal, characteristic, complemented
4C2×C3×#388C212yesmaximal, complemented
5C2×C3×#386C212yesmaximal, complemented
6C2×C3×C4×C22⋊C4C211yesmaximal, characteristic, complemented
7C3×#1445C211yesmaximal, characteristic, complemented
8C3×#1439C212yesmaximal, complemented
9C3×#1438C212yesmaximal, complemented
10C3×#1438C211yesmaximal, characteristic, complemented
11C3×#1434C211yesmaximal, characteristic, complemented
12#14977C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×D4C2212yes—
14C23×C3×D4C2211yescharacteristic
15C24×C3×C4C2211yescharacteristic
16C22×C3×C4⋊C4C2211yescharacteristic
17C22×C3×C4⋊C4C2212yes—
18C22×C3×C22⋊C4C2211yescharacteristic
19C22×C3×C22⋊C4C2212yes—
20C22×C3×C22⋊C4C2212yes—
21C22×C3×C22⋊C4C2212yes—
22C22×C3×C22⋊C4C2212yes—
23C22×C3×C22⋊C4C2212yes—
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2212yes—
26C22×C3×C42C2211yescharacteristic
27C22×C3×C42C2211yescharacteristic
28C3×#399—24no—
29C3×#392—24no—
30C3×#390—24no—
31C3×#388—28no—
32C3×#386—28no—
33C3×C4×C22⋊C4—24no—
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
37C2×C3×#95C2211yescharacteristic
38C2×C3×#95C2212yes—
39C2×C3×#95C2212yes—
40C2×C3×#95C2212yes—
41C2×C3×#95C2212yes—
42C2×#399C2×C311yescharacteristic, complemented
43C2×#392C2×C311yescharacteristic
44C2×#390C2×C311yescharacteristic, complemented
45C2×#388C2×C312yescomplemented
46C2×#386C2×C312yescomplemented
47C2×C4×C22⋊C4C2×C311yescharacteristic, complemented
48#1445C2×C311yescharacteristic, complemented
49#1439C2×C312yescomplemented
50#1438C2×C312yescomplemented
51#1438C2×C311yescharacteristic, complemented
52#1434C2×C311yescharacteristic, complemented
53C25×C3C2312yes—
54C25×C3C2311yescharacteristic
55C22×C3×D4—24no—
56C22×C3×D4—24no—
57C22×C3×D4—24no—
58C22×C3×D4—24no—
59C22×C3×D4—24no—
60C22×C3×D4—24no—
61C22×C3×D4—22no—
62C22×C3×D4—22no—
63C22×C3×D4—22no—
64C22×C3×D4—42no—
65C22×C3×D4—42no—
66C22×C3×D4—42no—
67C23×C3×C4—22no—
68C23×C3×C4—22no—
69C23×C3×C4—22no—
70C23×C3×C4—24no—
71C23×C3×C4—42no—
72C23×C3×C4C2312yes—
73C23×C3×C4C2312yes—
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2312yes—
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C2×C3×C4⋊C4—24no—
82C2×C3×C4⋊C4—22no—
83C2×C3×C4⋊C4—24no—
84C2×C3×C4⋊C4—22no—
85C2×C3×C4⋊C4—22no—
86C2×C3×C4⋊C4—42no—
87C2×C3×C22⋊C4—24no—
88C2×C3×C22⋊C4—22no—
89C2×C3×C22⋊C4—22no—
90C2×C3×C22⋊C4—22no—
91C2×C3×C22⋊C4—24no—
92C2×C3×C22⋊C4—22no—
93C2×C3×C22⋊C4—24no—
94C2×C3×C22⋊C4—22no—
95C2×C3×C22⋊C4—24no—
96C2×C3×C22⋊C4—24no—
97C2×C3×C22⋊C4—24no—
98C2×C3×C22⋊C4—24no—
99C2×C3×C22⋊C4—24no—
100C2×C3×C22⋊C4—24no—
101C2×C3×C22⋊C4—24no—
102C2×C3×C22⋊C4—24no—
103C2×C3×C22⋊C4—24no—
104C2×C3×C22⋊C4—24no—
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×C22⋊C4D414yes—
111C2×C3×C42—22no—
112C2×C3×C42—24no—
113C2×C3×C42—42no—
114C2×C3×C42D414yescomplemented
115C3×#95—22no—
116C3×#95—22no—
117C3×#95—24no—
118C3×#95—24no—
119C3×#95—22no—
120C3×#95—22no—
121C3×#95—42no—
122C3×#95D418yescomplemented
123C23×D4C22×C312yes—
124C23×D4C22×C311yescharacteristic
125C24×C4C22×C311yescharacteristic
126C22×C4⋊C4C22×C311yescharacteristic
127C22×C4⋊C4C22×C312yes—
128C22×C22⋊C4C22×C311yescharacteristic
129C22×C22⋊C4C22×C312yes—
130C22×C22⋊C4C22×C312yes—
131C22×C22⋊C4C22×C312yes—
132C22×C22⋊C4C22×C312yes—
133C22×C22⋊C4C22×C312yes—
134C22×C22⋊C4C22×C311yescharacteristic
135C22×C22⋊C4C22×C312yes—
136C22×C42C22×C311yescharacteristic
137C22×C42C22×C311yescharacteristic
138#399—24no—
139#392—24no—
140#390—24no—
141#388—28no—
142#386—28no—
143C4×C22⋊C4—24no—
144C2×#95C22×C311yescharacteristic
145C2×#95C22×C311yescharacteristic
146C2×#95C22×C311yescharacteristic
147C2×#95C22×C312yes—
148C2×#95C22×C311yescharacteristic
149C2×#95C22×C312yes—
150C2×#95C22×C312yes—
151C2×#95C22×C312yes—
152C24×C3—21no—
153C24×C3—22no—
154C24×C3—21no—
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—22no—
173C24×C3—22no—
174C24×C3C2×D412yes—
175C24×C3#4114yes—
176C24×C3#4112yes—
177C24×C3#4112yes—
178C24×C3C2411yescharacteristic
179C2×C3×D4—28no—
180C2×C3×D4—216no—
181C2×C3×D4—48no—
182C2×C3×D4—48no—
183C2×C3×D4—48no—
184C2×C3×D4—48no—
185C2×C3×D4—44no—
186C2×C3×D4—48no—
187C2×C3×D4—48no—
188C2×C3×D4—48no—
189C2×C3×D4—48no—
190C2×C3×D4—44no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—22no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—28no—
197C22×C3×C4—21no—
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—22no—
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—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—22no—
224C22×C3×C4—22no—
225C22×C3×C4—22no—
226C22×C3×C4—22no—
227C22×C3×C4—22no—
228C22×C3×C4—22no—
229C22×C3×C4—22no—
230C22×C3×C4—22no—
231C22×C3×C4—22no—
232C22×C3×C4—48no—
233C22×C3×C4—48no—
234C22×C3×C4—44no—
235C22×C3×C4—44no—
236C22×C3×C4C2×D414yes—
237C22×C3×C4C2×D412yes—
238C22×C3×C4C2×D414yes—
239C22×C3×C4C2×D412yes—
240C22×C3×C4C2×D412yes—
241C22×C3×C4C2×D412yes—
242C22×C3×C4C2×D414yes—
243C22×C3×C4C2×D412yes—
244C22×C3×C4#4112yes—
245C22×C3×C4#4112yes—
246C22×C3×C4#4112yes—
247C3×C4⋊C4—48no—
248C3×C4⋊C4—44no—
249C3×C22⋊C4—28no—
250C3×C22⋊C4—216no—
251C3×C22⋊C4—28no—
252C3×C22⋊C4—48no—
253C3×C22⋊C4—48no—
254C3×C22⋊C4—48no—
255C3×C22⋊C4—48no—
256C3×C22⋊C4—48no—
257C3×C42—44no—
258C3×C42—44no—
259C25C23×C312yes—
260C25C23×C311yescharacteristic
261C22×D4—24no—
262C22×D4—24no—
263C22×D4—24no—
264C22×D4—24no—
265C22×D4—24no—
266C22×D4—24no—
267C22×D4—22no—
268C22×D4—22no—
269C22×D4—22no—
270C22×D4—42no—
271C22×D4—42no—
272C22×D4—42no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—24no—
277C23×C4—42no—
278C23×C4C23×C312yes—
279C23×C4C23×C311yescharacteristic
280C23×C4C23×C312yes—
281C23×C4C23×C311yescharacteristic
282C23×C4C23×C312yes—
283C23×C4C23×C311yescharacteristic
284C23×C4C23×C311yescharacteristic
285C23×C4C23×C311yescharacteristic
286C23×C4C23×C311yescharacteristic
287C2×C4⋊C4—24no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—42no—
293C2×C22⋊C4—24no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—22no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4—24no—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—22no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—42no—
312C2×C22⋊C4—42no—
313C2×C22⋊C4—42no—
314C2×C22⋊C4—42no—
315C2×C22⋊C4—42no—
316C2×C22⋊C4C3×D414yes—
317C2×C42—22no—
318C2×C42—24no—
319C2×C42—42no—
320C2×C42C3×D414yescomplemented
321#95—22no—
322#95—22no—
323#95—24no—
324#95—24no—
325#95—22no—
326#95—22no—
327#95—42no—
328#95C3×D418yescomplemented
329C23×C3—22no—
330C23×C3—22no—
331C23×C3—22no—
332C23×C3—24no—
333C23×C3—22no—
334C23×C3—22no—
335C23×C3—22no—
336C23×C3—24no—
337C23×C3—24no—
338C23×C3—24no—
339C23×C3—24no—
340C23×C3—24no—
341C23×C3—24no—
342C23×C3—24no—
343C23×C3—24no—
344C23×C3—24no—
345C23×C3—24no—
346C23×C3—24no—
347C23×C3—24no—
348C23×C3—41no—
349C23×C3—42no—
350C23×C3—41no—
351C23×C3—41no—
352C23×C3—41no—
353C23×C3—42no—
354C23×C3—42no—
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—42no—
369C23×C3—42no—
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—42no—
379C23×C3—42no—
380C23×C3—42no—
381C23×C3—42no—
382C23×C3—42no—
383C23×C3—42no—
384C23×C3—42no—
385C23×C3—42no—
386C23×C3#12414yes—
387C23×C3C22×D411yescharacteristic
388C23×C3C22×D411yescharacteristic
389C23×C3C22×D412yes—
390C23×C3C2×#4111yescharacteristic
391C23×C3C2×#4111yescharacteristic
392C23×C3C2×#4111yescharacteristic
393C23×C3C2×#4112yes—
394C23×C3C2×#4111yescharacteristic
395C23×C3C2×#4111yescharacteristic
396C23×C3H(5,𝔽2)12yes—
397C23×C3H(5,𝔽2)12yes—
398C3×D4—416no—
399C3×D4—432no—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—24no—
405C2×C3×C4—24no—
406C2×C3×C4—24no—
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—22no—
414C2×C3×C4—24no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—24no—
418C2×C3×C4—24no—
419C2×C3×C4—24no—
420C2×C3×C4—24no—
421C2×C3×C4—24no—
422C2×C3×C4—24no—
423C2×C3×C4—416no—
424C2×C3×C4—41no—
425C2×C3×C4—42no—
426C2×C3×C4—42no—
427C2×C3×C4—41no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—42no—
431C2×C3×C4—41no—
432C2×C3×C4—41no—
433C2×C3×C4—42no—
434C2×C3×C4—42no—
435C2×C3×C4—42no—
436C2×C3×C4—42no—
437C2×C3×C4—42no—
438C2×C3×C4—42no—
439C2×C3×C4—42no—
440C2×C3×C4—42no—
441C2×C3×C4—42no—
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#12114yes—
451C2×C3×C4#12714yes—
452C24—21no—
453C24—22no—
454C24—21no—
455C24—21no—
456C24—21no—
457C24—22no—
458C24—22no—
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—
474C24C2×C3×D412yes—
475C24C3×#4114yes—
476C24C3×#4112yes—
477C24C3×#4112yes—
478C24C24×C311yescharacteristic
479C2×D4—28no—
480C2×D4—216no—
481C2×D4—48no—
482C2×D4—48no—
483C2×D4—48no—
484C2×D4—48no—
485C2×D4—44no—
486C2×D4—48no—
487C2×D4—48no—
488C2×D4—48no—
489C2×D4—48no—
490C2×D4—44no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—28no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—21no—
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—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—48no—
533C22×C4—48no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4C2×C3×D414yes—
537C22×C4C2×C3×D412yes—
538C22×C4C2×C3×D414yes—
539C22×C4C2×C3×D412yes—
540C22×C4C2×C3×D412yes—
541C22×C4C2×C3×D412yes—
542C22×C4C2×C3×D414yes—
543C22×C4C2×C3×D412yes—
544C22×C4C3×#4112yes—
545C22×C4C3×#4112yes—
546C22×C4C3×#4112yes—
547C4⋊C4—48no—
548C4⋊C4—44no—
549C22⋊C4—28no—
550C22⋊C4—216no—
551C22⋊C4—28no—
552C22⋊C4—48no—
553C22⋊C4—48no—
554C22⋊C4—48no—
555C22⋊C4—48no—
556C22⋊C4—48no—
557C42—44no—
558C42—44no—
559C22×C3—24no—
560C22×C3—28no—
561C22×C3—42no—
562C22×C3—42no—
563C22×C3—42no—
564C22×C3—44no—
565C22×C3—44no—
566C22×C3—44no—
567C22×C3—42no—
568C22×C3—42no—
569C22×C3—42no—
570C22×C3—44no—
571C22×C3—44no—
572C22×C3—44no—
573C22×C3—44no—
574C22×C3—44no—
575C22×C3—44no—
576C22×C3—44no—
577C22×C3—82no—
578C22×C3—82no—
579C22×C3—82no—
580C22×C3—82no—
581C22×C3—82no—
582C22×C3—82no—
583C22×C3—82no—
584C22×C3—82no—
585C22×C3C2×#12111yescharacteristic
586C22×C3#52511yescharacteristic
587C22×C3#52511yescharacteristic
588C22×C3#52511yescharacteristic
589C22×C3#52512yes—
590C22×C3#52512yes—
591C22×C3C2×#12411yescharacteristic
592C22×C3#52911yescharacteristic
593C22×C3#52911yescharacteristic
594C22×C3C2×#12711yescharacteristic
595C22×C3#53211yescharacteristic
596C22×C3#53411yescharacteristic
597C22×C3#53511yescharacteristic
598C22×C3#53812yes—
599C22×C3#54012yes—
600C22×C3D4212yes—
601C22×C3#54612yes—
602C22×C3#54612yes—
603C22×C3#54612yes—
604C22×C3#55012yes—
605C22×C3#55112yes—
606C22×C3#55112yes—
607C22×C3#55312yes—
608C3×C4—24no—
609C3×C4—24no—
610C3×C4—42no—
611C3×C4—42no—
612C3×C4—44no—
613C3×C4—44no—
614C3×C4—42no—
615C3×C4—42no—
616C3×C4—82no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—24no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—42no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
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—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23C3×#12414yes—
675C23C22×C3×D411yescharacteristic
676C23C22×C3×D411yescharacteristic
677C23C22×C3×D412yes—
678C23C2×C3×#4111yescharacteristic
679C23C2×C3×#4111yescharacteristic
680C23C2×C3×#4111yescharacteristic
681C23C2×C3×#4112yes—
682C23C2×C3×#4111yescharacteristic
683C23C2×C3×#4111yescharacteristic
684C23C3×H(5,𝔽2)12yes—
685C23C3×H(5,𝔽2)12yes—
686D4—416no—
687D4—432no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—416no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4C3×#12114yes—
739C2×C4C3×#12714yes—
740C2×C3—44no—
741C2×C3—84no—
742C2×C3#239711yescharacteristic
743C2×C3#246412yes—
744C2×C3#246712yes—
745C2×C3#247112yes—
746C2×C3#247212yes—
747C2×C3#253411yescharacteristic
748C2×C3#253911yescharacteristic
749C2×C3#254111yescharacteristic
750C2×C3#259811yescharacteristic
751C2×C3#263511yescharacteristic
752C2×C3#285011yescharacteristic
753C22—28no—
754C22—24no—
755C22—42no—
756C22—42no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—44no—
765C22—44no—
766C22—44no—
767C22—44no—
768C22—44no—
769C22—44no—
770C22—44no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22C2×C3×#12111yescharacteristic
780C22C3×#52511yescharacteristic
781C22C3×#52512yes—
782C22C3×#52512yes—
783C22C3×#52511yescharacteristic
784C22C3×#52511yescharacteristic
785C22C2×C3×#12411yescharacteristic
786C22C3×#52911yescharacteristic
787C22C3×#52911yescharacteristic
788C22C2×C3×#12711yescharacteristic
789C22C3×#53211yescharacteristic
790C22C3×#53411yescharacteristic
791C22C3×#53511yescharacteristic
792C22C3×#53812yes—
793C22C3×#54012yes—
794C22C3×D4212yes—
795C22C3×#54612yes—
796C22C3×#54612yes—
797C22C3×#54612yes—
798C22C3×#55012yes—
799C22C3×#55112yes—
800C22C3×#55112yes—
801C22C3×#55312yes—
802C4—24no—
803C4—24no—
804C4—42no—
805C4—42no—
806C4—44no—
807C4—44no—
808C4—42no—
809C4—42no—
810C4—82no—
811C3#1497711yescharacteristic, direct product factor, Sylow
812C2—44no—
813C2—84no—
814C2C3×#239711yescharacteristic
815C2C3×#246412yes—
816C2C3×#246712yes—
817C2C3×#247112yes—
818C2C3×#247212yes—
819C2C3×#253411yescharacteristic
820C2C3×#253911yescharacteristic
821C2C3×#254111yescharacteristic
822C2C3×#259811yescharacteristic
823C2C3×#263511yescharacteristic
824C2C3×#285011yescharacteristic
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. C2×C3×#399C2semidirect
3. C2×C3×#390C2semidirect
4. C2×C3×#388C2semidirect
5. C2×C3×#386C2semidirect
6. C2×C3×C4×C22⋊C4C2semidirect
7. C3×#1445C2semidirect
8. C3×#1439C2semidirect
9. C3×#1438C2semidirect
10. C3×#1438C2semidirect
11. C3×#1434C2semidirect
12. #14977C3direct (N × H)
42. C2×#399C2×C3semidirect
44. C2×#390C2×C3semidirect
45. C2×#388C2×C3semidirect
46. C2×#386C2×C3semidirect
47. C2×C4×C22⋊C4C2×C3semidirect
48. #1445C2×C3semidirect
49. #1439C2×C3semidirect
50. #1438C2×C3semidirect
51. #1438C2×C3semidirect
52. #1434C2×C3semidirect
114. C2×C3×C42D4semidirect
122. C3×#95D4semidirect
320. C2×C42C3×D4semidirect
328. #95C3×D4semidirect
811. C3#14977direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3992
C2×C3×#3922
C2×C3×#3902
C2×C3×#3882
C2×C3×#3862
C2×C3×C4×C22⋊C42
C3×#14452
C3×#14392
C3×#14382
C3×#14342
#149773