Finite Group Databasebeta

← C3×#14928 #10633535

Subgroups — C3×#14928 #10633535

Order 768.

2430 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#124C211yesmaximal, characteristic, complemented
2C2×C3×#395C211yesmaximal, characteristic, complemented
3C2×C3×#394C211yesmaximal, characteristic, complemented
4C2×C3×#393C211yesmaximal, characteristic, complemented
5C2×C3×#392C211yesmaximal, characteristic
6C2×C3×#390C212yesmaximal, complemented
7C2×C3×#388C211yesmaximal, characteristic, complemented
8C3×#1439C212yesmaximal, complemented
9C3×#1438C212yesmaximal, complemented
10C3×#1437C212yesmaximal, complemented
11C3×C4×#95C211yesmaximal, characteristic, complemented
12#14928C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×Q8C2211yescharacteristic
14C23×C3×D4C2211yescharacteristic
15C23×C3×D4C2212yes—
16C2×C3×#124—28no—
17C2×C3×#124—24no—
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C4⋊C4C2212yes—
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2212yes—
22C22×C3×C22⋊C4C2212yes—
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2212yes—
26C22×C3×C22⋊C4C2212yes—
27C22×C3×C22⋊C4C2212yes—
28C22×C3×C22⋊C4C2212yes—
29C22×C3×C42C2212yes—
30C22×C3×C42C2211yescharacteristic
31C3×#395—24no—
32C3×#394—24no—
33C3×#393—24no—
34C3×#392—24no—
35C3×#390—28no—
36C3×#388—24no—
37C2×C3×#95C2212yes—
38C2×C3×#95C2212yes—
39C2×C3×#95C2211yescharacteristic
40C2×C3×#95C2211yescharacteristic
41C2×C3×#95C2212yes—
42C2×C3×#95C2211yescharacteristic
43C2×C3×#95C2211yescharacteristic
44C22×#124C2×C311yescharacteristic, complemented
45C2×#395C2×C311yescharacteristic, complemented
46C2×#394C2×C311yescharacteristic, complemented
47C2×#393C2×C311yescharacteristic, complemented
48C2×#392C2×C311yescharacteristic
49C2×#390C2×C312yescomplemented
50C2×#388C2×C311yescharacteristic, complemented
51#1439C2×C312yescomplemented
52#1438C2×C312yescomplemented
53#1437C2×C312yescomplemented
54C4×#95C2×C311yescharacteristic, complemented
55C25×C3C2312yes—
56C25×C3C2311yescharacteristic
57C22×C3×Q8—24no—
58C22×C3×Q8—22no—
59C22×C3×Q8—22no—
60C22×C3×Q8—22no—
61C22×C3×Q8—42no—
62C22×C3×D4—24no—
63C22×C3×D4—24no—
64C22×C3×D4—24no—
65C22×C3×D4—22no—
66C22×C3×D4—24no—
67C22×C3×D4—22no—
68C22×C3×D4—22no—
69C22×C3×D4—24no—
70C22×C3×D4—24no—
71C22×C3×D4—42no—
72C22×C3×D4—42no—
73C22×C3×D4—42no—
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2312yes—
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2312yes—
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2312yes—
83C3×#124—232no—
84C2×C3×C4⋊C4—22no—
85C2×C3×C4⋊C4—24no—
86C2×C3×C4⋊C4—22no—
87C2×C3×C4⋊C4—24no—
88C2×C3×C4⋊C4—22no—
89C2×C3×C4⋊C4—42no—
90C2×C3×C22⋊C4—24no—
91C2×C3×C22⋊C4—22no—
92C2×C3×C22⋊C4—22no—
93C2×C3×C22⋊C4—24no—
94C2×C3×C22⋊C4—24no—
95C2×C3×C22⋊C4—24no—
96C2×C3×C22⋊C4—24no—
97C2×C3×C22⋊C4—22no—
98C2×C3×C22⋊C4—24no—
99C2×C3×C22⋊C4—22no—
100C2×C3×C22⋊C4—22no—
101C2×C3×C22⋊C4—24no—
102C2×C3×C22⋊C4—24no—
103C2×C3×C22⋊C4—24no—
104C2×C3×C22⋊C4—22no—
105C2×C3×C22⋊C4—24no—
106C2×C3×C22⋊C4—22no—
107C2×C3×C22⋊C4—24no—
108C2×C3×C22⋊C4—24no—
109C2×C3×C22⋊C4—24no—
110C2×C3×C22⋊C4—24no—
111C2×C3×C22⋊C4—24no—
112C2×C3×C22⋊C4—42no—
113C2×C3×C22⋊C4—42no—
114C2×C3×C22⋊C4—42no—
115C2×C3×C22⋊C4D418yescomplemented
116C2×C3×C42—24no—
117C2×C3×C42—24no—
118C2×C3×C42—24no—
119C2×C3×C42—42no—
120C2×C3×C42D414yescomplemented
121C3×#95—22no—
122C3×#95—22no—
123C3×#95—24no—
124C3×#95—24no—
125C3×#95—24no—
126C3×#95D414yes—
127C3×#95D414yescomplemented
128C23×Q8C22×C311yescharacteristic
129C23×D4C22×C311yescharacteristic
130C23×D4C22×C312yes—
131C2×#124—28no—
132C2×#124—24no—
133C22×C4⋊C4C22×C311yescharacteristic
134C22×C4⋊C4C22×C312yes—
135C22×C22⋊C4C22×C311yescharacteristic
136C22×C22⋊C4C22×C312yes—
137C22×C22⋊C4C22×C312yes—
138C22×C22⋊C4C22×C311yescharacteristic
139C22×C22⋊C4C22×C311yescharacteristic
140C22×C22⋊C4C22×C312yes—
141C22×C22⋊C4C22×C312yes—
142C22×C22⋊C4C22×C312yes—
143C22×C22⋊C4C22×C312yes—
144C22×C42C22×C312yes—
145C22×C42C22×C311yescharacteristic
146#395—24no—
147#394—24no—
148#393—24no—
149#392—24no—
150#390—28no—
151#388—24no—
152C2×#95C22×C312yes—
153C2×#95C22×C312yes—
154C2×#95C22×C312yes—
155C2×#95C22×C311yescharacteristic
156C2×#95C22×C311yescharacteristic
157C2×#95C22×C311yescharacteristic
158C2×#95C22×C311yescharacteristic
159C24×C3—21no—
160C24×C3—21no—
161C24×C3—22no—
162C24×C3—22no—
163C24×C3—22no—
164C24×C3—22no—
165C24×C3—22no—
166C24×C3—21no—
167C24×C3—21no—
168C24×C3—22no—
169C24×C3—22no—
170C24×C3—22no—
171C24×C3—22no—
172C24×C3—22no—
173C24×C3—22no—
174C24×C3—22no—
175C24×C3—22no—
176C24×C3—22no—
177C24×C3—22no—
178C24×C3—22no—
179C24×C3—22no—
180C24×C3—21no—
181C24×C3—22no—
182C24×C3—21no—
183C24×C3C2×D414yes—
184C24×C3#4112yes—
185C24×C3C2411yescharacteristic
186C2×C3×Q8—28no—
187C2×C3×Q8—48no—
188C2×C3×Q8—48no—
189C2×C3×Q8—44no—
190C2×C3×Q8—44no—
191C2×C3×D4—28no—
192C2×C3×D4—216no—
193C2×C3×D4—48no—
194C2×C3×D4—48no—
195C2×C3×D4—48no—
196C2×C3×D4—48no—
197C2×C3×D4—48no—
198C2×C3×D4—48no—
199C2×C3×D4—44no—
200C2×C3×D4—48no—
201C2×C3×D4—48no—
202C2×C3×D4—44no—
203C22×C3×C4—22no—
204C22×C3×C4—22no—
205C22×C3×C4—22no—
206C22×C3×C4—22no—
207C22×C3×C4—21no—
208C22×C3×C4—22no—
209C22×C3×C4—22no—
210C22×C3×C4—22no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—22no—
215C22×C3×C4—22no—
216C22×C3×C4—22no—
217C22×C3×C4—22no—
218C22×C3×C4—21no—
219C22×C3×C4—22no—
220C22×C3×C4—22no—
221C22×C3×C4—22no—
222C22×C3×C4—22no—
223C22×C3×C4—22no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—22no—
228C22×C3×C4—22no—
229C22×C3×C4—22no—
230C22×C3×C4—21no—
231C22×C3×C4—22no—
232C22×C3×C4—22no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—22no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—22no—
242C22×C3×C4—22no—
243C22×C3×C4—22no—
244C22×C3×C4C2×D414yes—
245C22×C3×C4C2×D412yes—
246C22×C3×C4C2×D414yes—
247C22×C3×C4C2×D412yes—
248C22×C3×C4C2×D414yes—
249C22×C3×C4C2×D414yes—
250C22×C3×C4C2×D412yes—
251C22×C3×C4C2×D412yes—
252C22×C3×C4C2×D412yes—
253C22×C3×C4#4112yes—
254C22×C3×C4#4114yes—
255C22×C3×C4#4114yes—
256C3×C4⋊C4—48no—
257C3×C4⋊C4—44no—
258C3×C22⋊C4—28no—
259C3×C22⋊C4—216no—
260C3×C22⋊C4—216no—
261C3×C22⋊C4—48no—
262C3×C22⋊C4—48no—
263C3×C22⋊C4—48no—
264C3×C22⋊C4—44no—
265C3×C22⋊C4—48no—
266C3×C22⋊C4—44no—
267C3×C42—28no—
268C3×C42—48no—
269C25C23×C312yes—
270C25C23×C311yescharacteristic
271C22×Q8—24no—
272C22×Q8—22no—
273C22×Q8—22no—
274C22×Q8—22no—
275C22×Q8—42no—
276C22×D4—24no—
277C22×D4—24no—
278C22×D4—24no—
279C22×D4—22no—
280C22×D4—24no—
281C22×D4—22no—
282C22×D4—22no—
283C22×D4—24no—
284C22×D4—24no—
285C22×D4—42no—
286C22×D4—42no—
287C22×D4—42no—
288C23×C4C23×C311yescharacteristic
289C23×C4C23×C311yescharacteristic
290C23×C4C23×C312yes—
291C23×C4C23×C311yescharacteristic
292C23×C4C23×C312yes—
293C23×C4C23×C311yescharacteristic
294C23×C4C23×C311yescharacteristic
295C23×C4C23×C311yescharacteristic
296C23×C4C23×C312yes—
297#124—232no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—42no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4C3×D418yescomplemented
330C2×C42—24no—
331C2×C42—24no—
332C2×C42—24no—
333C2×C42—42no—
334C2×C42C3×D414yescomplemented
335#95—22no—
336#95—22no—
337#95—24no—
338#95—24no—
339#95—24no—
340#95C3×D414yes—
341#95C3×D414yescomplemented
342C23×C3—24no—
343C23×C3—22no—
344C23×C3—24no—
345C23×C3—24no—
346C23×C3—24no—
347C23×C3—24no—
348C23×C3—24no—
349C23×C3—22no—
350C23×C3—24no—
351C23×C3—24no—
352C23×C3—22no—
353C23×C3—24no—
354C23×C3—41no—
355C23×C3—42no—
356C23×C3—42no—
357C23×C3—42no—
358C23×C3—42no—
359C23×C3—42no—
360C23×C3—41no—
361C23×C3—42no—
362C23×C3—41no—
363C23×C3—41no—
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—41no—
373C23×C3—42no—
374C23×C3—41no—
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—42no—
387C23×C3—42no—
388C23×C3—42no—
389C23×C3—41no—
390C23×C3—42no—
391C23×C3—42no—
392C23×C3—42no—
393C23×C3—42no—
394C23×C3—41no—
395C23×C3—42no—
396C23×C3—42no—
397C23×C3—42no—
398C23×C3—42no—
399C23×C3—42no—
400C23×C3C22×D411yescharacteristic
401C23×C3C22×D412yes—
402C23×C3C22×D411yescharacteristic
403C23×C3C22×D411yescharacteristic
404C23×C3C2×#4111yescharacteristic
405C23×C3C2×#4112yes—
406C23×C3C2×#4111yescharacteristic
407C23×C3C2×#4112yes—
408C23×C3H(5,𝔽2)12yes—
409C23×C3H(5,𝔽2)11yescharacteristic
410C23×C32−1+411yescharacteristic
411C3×Q8—416no—
412C3×D4—416no—
413C3×D4—432no—
414C2×C3×C4—22no—
415C2×C3×C4—24no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—24no—
420C2×C3×C4—24no—
421C2×C3×C4—24no—
422C2×C3×C4—24no—
423C2×C3×C4—24no—
424C2×C3×C4—24no—
425C2×C3×C4—24no—
426C2×C3×C4—24no—
427C2×C3×C4—24no—
428C2×C3×C4—22no—
429C2×C3×C4—24no—
430C2×C3×C4—22no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—24no—
434C2×C3×C4—24no—
435C2×C3×C4—24no—
436C2×C3×C4—24no—
437C2×C3×C4—22no—
438C2×C3×C4—24no—
439C2×C3×C4—22no—
440C2×C3×C4—42no—
441C2×C3×C4—41no—
442C2×C3×C4—42no—
443C2×C3×C4—42no—
444C2×C3×C4—42no—
445C2×C3×C4—42no—
446C2×C3×C4—41no—
447C2×C3×C4—42no—
448C2×C3×C4—42no—
449C2×C3×C4—42no—
450C2×C3×C4—42no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—42no—
454C2×C3×C4—41no—
455C2×C3×C4—42no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—42no—
461C2×C3×C4—41no—
462C2×C3×C4—42no—
463C2×C3×C4—42no—
464C2×C3×C4#12014yes—
465C2×C3×C4#12418yescomplemented
466C2×C3×C4#12714yes—
467C24—21no—
468C24—21no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—21no—
475C24—21no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—22no—
488C24—21no—
489C24—22no—
490C24—21no—
491C24C2×C3×D414yes—
492C24C3×#4112yes—
493C24C24×C311yescharacteristic
494C2×Q8—28no—
495C2×Q8—48no—
496C2×Q8—48no—
497C2×Q8—44no—
498C2×Q8—44no—
499C2×D4—28no—
500C2×D4—216no—
501C2×D4—48no—
502C2×D4—48no—
503C2×D4—48no—
504C2×D4—48no—
505C2×D4—48no—
506C2×D4—48no—
507C2×D4—44no—
508C2×D4—48no—
509C2×D4—48no—
510C2×D4—44no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4C2×C3×D414yes—
553C22×C4C2×C3×D412yes—
554C22×C4C2×C3×D414yes—
555C22×C4C2×C3×D412yes—
556C22×C4C2×C3×D414yes—
557C22×C4C2×C3×D414yes—
558C22×C4C2×C3×D412yes—
559C22×C4C2×C3×D412yes—
560C22×C4C2×C3×D412yes—
561C22×C4C3×#4112yes—
562C22×C4C3×#4114yes—
563C22×C4C3×#4114yes—
564C4⋊C4—48no—
565C4⋊C4—44no—
566C22⋊C4—216no—
567C22⋊C4—28no—
568C22⋊C4—216no—
569C22⋊C4—48no—
570C22⋊C4—48no—
571C22⋊C4—48no—
572C22⋊C4—44no—
573C22⋊C4—48no—
574C22⋊C4—44no—
575C42—28no—
576C42—48no—
577C22×C3—42no—
578C22×C3—44no—
579C22×C3—42no—
580C22×C3—44no—
581C22×C3—44no—
582C22×C3—44no—
583C22×C3—44no—
584C22×C3—44no—
585C22×C3—44no—
586C22×C3—44no—
587C22×C3—42no—
588C22×C3—44no—
589C22×C3—82no—
590C22×C3—81no—
591C22×C3—82no—
592C22×C3—82no—
593C22×C3—81no—
594C22×C3—81no—
595C22×C3—81no—
596C22×C3—82no—
597C22×C3—82no—
598C22×C3—82no—
599C22×C3—82no—
600C22×C3—82no—
601C22×C3—82no—
602C22×C3—82no—
603C22×C3C2×#12011yescharacteristic
604C22×C3#52511yescharacteristic
605C22×C3#52512yes—
606C22×C3C2×#12412yes—
607C22×C3C2×#12711yescharacteristic
608C22×C3#53211yescharacteristic
609C22×C3#53211yescharacteristic
610C22×C3#53212yes—
611C22×C3#53212yes—
612C22×C3#53511yescharacteristic
613C22×C3#53711yescharacteristic
614C22×C3#53812yes—
615C22×C3#54212yes—
616C22×C3D4212yes—
617C22×C3D4212yes—
618C22×C3#54612yes—
619C22×C3#54611yescharacteristic
620C22×C3#54611yescharacteristic
621C22×C3#54712yes—
622C22×C3#54811yescharacteristic
623C22×C3#54811yescharacteristic
624C22×C3#55112yes—
625C22×C3#55512yes—
626C3×C4—24no—
627C3×C4—24no—
628C3×C4—28no—
629C3×C4—42no—
630C3×C4—44no—
631C3×C4—42no—
632C3×C4—44no—
633C3×C4—81no—
634C3×C4—81no—
635C23—24no—
636C23—22no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—22no—
643C23—24no—
644C23—24no—
645C23—22no—
646C23—24no—
647C23—41no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—41no—
654C23—42no—
655C23—41no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—41no—
664C23—42no—
665C23—41no—
666C23—42no—
667C23—41no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—41no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—41no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23C22×C3×D411yescharacteristic
694C23C22×C3×D412yes—
695C23C22×C3×D411yescharacteristic
696C23C22×C3×D411yescharacteristic
697C23C2×C3×#4111yescharacteristic
698C23C2×C3×#4112yes—
699C23C2×C3×#4111yescharacteristic
700C23C2×C3×#4112yes—
701C23C3×H(5,𝔽2)12yes—
702C23C3×H(5,𝔽2)11yescharacteristic
703C23C3×2−1+411yescharacteristic
704Q8—416no—
705D4—416no—
706D4—432no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—22no—
733C2×C4—42no—
734C2×C4—41no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—42no—
747C2×C4—41no—
748C2×C4—42no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—42no—
754C2×C4—41no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4C3×#12014yes—
758C2×C4C3×#12418yescomplemented
759C2×C4C3×#12714yes—
760C2×C3—82no—
761C2×C3—84no—
762C2×C3#238811yescharacteristic
763C2×C3#243011yescharacteristic
764C2×C3#243311yescharacteristic
765C2×C3#246112yes—
766C2×C3#247212yes—
767C2×C3#249112yes—
768C2×C3#254011yescharacteristic
769C2×C3#255512yes—
770C2×C3#261011yescharacteristic
771C2×C3#266211yescharacteristic
772C2×C3#285811yescharacteristic
773C22—44no—
774C22—42no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22—44no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—42no—
783C22—44no—
784C22—42no—
785C22—82no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22—82no—
793C22—82no—
794C22—82no—
795C22—82no—
796C22—82no—
797C22—81no—
798C22—82no—
799C22C2×C3×#12011yescharacteristic
800C22C3×#52512yes—
801C22C3×#52511yescharacteristic
802C22C2×C3×#12412yes—
803C22C2×C3×#12711yescharacteristic
804C22C3×#53211yescharacteristic
805C22C3×#53212yes—
806C22C3×#53211yescharacteristic
807C22C3×#53212yes—
808C22C3×#53511yescharacteristic
809C22C3×#53711yescharacteristic
810C22C3×#53812yes—
811C22C3×#54212yes—
812C22C3×D4212yes—
813C22C3×D4212yes—
814C22C3×#54612yes—
815C22C3×#54611yescharacteristic
816C22C3×#54611yescharacteristic
817C22C3×#54712yes—
818C22C3×#54811yescharacteristic
819C22C3×#54811yescharacteristic
820C22C3×#55112yes—
821C22C3×#55512yes—
822C4—24no—
823C4—24no—
824C4—28no—
825C4—42no—
826C4—44no—
827C4—42no—
828C4—44no—
829C4—81no—
830C4—81no—
831C3#1492811yescharacteristic, direct product factor, Sylow
832C2—84no—
833C2—82no—
834C2C3×#238811yescharacteristic
835C2C3×#243011yescharacteristic
836C2C3×#243311yescharacteristic
837C2C3×#246112yes—
838C2C3×#247212yes—
839C2C3×#249112yes—
840C2C3×#254011yescharacteristic
841C2C3×#255512yes—
842C2C3×#261011yescharacteristic
843C2C3×#266211yescharacteristic
844C2C3×#285811yescharacteristic
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. C22×C3×#124C2semidirect
2. C2×C3×#395C2semidirect
3. C2×C3×#394C2semidirect
4. C2×C3×#393C2semidirect
6. C2×C3×#390C2semidirect
7. C2×C3×#388C2semidirect
8. C3×#1439C2semidirect
9. C3×#1438C2semidirect
10. C3×#1437C2semidirect
11. C3×C4×#95C2semidirect
12. #14928C3direct (N × H)
44. C22×#124C2×C3semidirect
45. C2×#395C2×C3semidirect
46. C2×#394C2×C3semidirect
47. C2×#393C2×C3semidirect
49. C2×#390C2×C3semidirect
50. C2×#388C2×C3semidirect
51. #1439C2×C3semidirect
52. #1438C2×C3semidirect
53. #1437C2×C3semidirect
54. C4×#95C2×C3semidirect
115. C2×C3×C22⋊C4D4semidirect
120. C2×C3×C42D4semidirect
127. C3×#95D4semidirect
329. C2×C22⋊C4C3×D4semidirect
334. C2×C42C3×D4semidirect
341. #95C3×D4semidirect
465. C2×C3×C4#124semidirect
758. C2×C4C3×#124semidirect
831. C3#14928direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1242
C2×C3×#3952
C2×C3×#3942
C2×C3×#3932
C2×C3×#3922
C2×C3×#3902
C2×C3×#3882
C3×#14392
C3×#14382
C3×#14372
C3×C4×#952
#149283