Finite Group Databasebeta

← C3×#14806 #10633413

Subgroups — C3×#14806 #10633413

Order 768.

2662 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4×D4C211yesmaximal, characteristic, complemented
2C2×C3×#394C211yesmaximal, characteristic, complemented
3C2×C3×#394C212yesmaximal, complemented
4C2×C3×#392C211yesmaximal, characteristic
5C2×C3×#388C211yesmaximal, characteristic, complemented
6C2×C3×#386C212yesmaximal, complemented
7C3×#1441C211yesmaximal, characteristic, complemented
8C3×#1439C211yesmaximal, characteristic, complemented
9C3×#1439C212yesmaximal, complemented
10C3×C4⋊#95C211yesmaximal, characteristic, complemented
11C3×C22⋊#95C212yesmaximal, complemented
12#14806C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×D4C2211yescharacteristic
14C23×C3×D4C2212yes—
15C24×C3×C4C2212yes—
16C2×C3×C4×D4—28no—
17C2×C3×C4×D4—24no—
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C4⋊C4C2212yes—
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2212yes—
24C22×C3×C22⋊C4C2212yes—
25C22×C3×C22⋊C4C2212yes—
26C22×C3×C22⋊C4C2212yes—
27C22×C3×C22⋊C4C2212yes—
28C22×C3×C22⋊C4C2211yescharacteristic
29C22×C3×C42C2211yescharacteristic
30C3×#394—24no—
31C3×#394—28no—
32C3×#392—24no—
33C3×#388—24no—
34C3×#386—28no—
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2212yes—
37C2×C3×#95C2211yescharacteristic
38C2×C3×#95C2212yes—
39C2×C3×#95C2212yes—
40C2×C3×#95C2211yescharacteristic
41C2×C3×#95C2211yescharacteristic
42C2×C3×#95C2212yes—
43C22×C4×D4C2×C311yescharacteristic, complemented
44C2×#394C2×C311yescharacteristic, complemented
45C2×#394C2×C312yescomplemented
46C2×#392C2×C311yescharacteristic
47C2×#388C2×C311yescharacteristic, complemented
48C2×#386C2×C312yescomplemented
49#1441C2×C311yescharacteristic, complemented
50#1439C2×C311yescharacteristic, complemented
51#1439C2×C312yescomplemented
52C4⋊#95C2×C311yescharacteristic, complemented
53C22⋊#95C2×C312yescomplemented
54C25×C3C2311yescharacteristic
55C25×C3C2312yes—
56C22×C3×D4—24no—
57C22×C3×D4—24no—
58C22×C3×D4—24no—
59C22×C3×D4—24no—
60C22×C3×D4—24no—
61C22×C3×D4—24no—
62C22×C3×D4—22no—
63C22×C3×D4—22no—
64C22×C3×D4—24no—
65C22×C3×D4—42no—
66C22×C3×D4—42no—
67C22×C3×D4D414yes—
68C23×C3×C4—24no—
69C23×C3×C4—24no—
70C23×C3×C4—24no—
71C23×C3×C4—24no—
72C23×C3×C4—24no—
73C23×C3×C4—42no—
74C23×C3×C4—42no—
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2312yes—
78C23×C3×C4C2312yes—
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2312yes—
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C3×C4×D4—232no—
85C2×C3×C4⋊C4—24no—
86C2×C3×C4⋊C4—22no—
87C2×C3×C4⋊C4—22no—
88C2×C3×C4⋊C4—24no—
89C2×C3×C4⋊C4—22no—
90C2×C3×C4⋊C4—24no—
91C2×C3×C4⋊C4—22no—
92C2×C3×C4⋊C4—42no—
93C2×C3×C22⋊C4—22no—
94C2×C3×C22⋊C4—24no—
95C2×C3×C22⋊C4—24no—
96C2×C3×C22⋊C4—22no—
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—22no—
105C2×C3×C22⋊C4—22no—
106C2×C3×C22⋊C4—22no—
107C2×C3×C22⋊C4—24no—
108C2×C3×C22⋊C4—24no—
109C2×C3×C22⋊C4—24no—
110C2×C3×C22⋊C4—22no—
111C2×C3×C22⋊C4—42no—
112C2×C3×C22⋊C4—42no—
113C2×C3×C22⋊C4—42no—
114C2×C3×C22⋊C4D414yescomplemented
115C2×C3×C22⋊C4D418yescomplemented
116C2×C3×C42—24no—
117C2×C3×C42D414yescomplemented
118C3×#95—24no—
119C3×#95—24no—
120C3×#95—22no—
121C3×#95—22no—
122C3×#95—22no—
123C3×#95—24no—
124C3×#95—22no—
125C3×#95—42no—
126C23×D4C22×C311yescharacteristic
127C23×D4C22×C312yes—
128C24×C4C22×C312yes—
129C2×C4×D4—28no—
130C2×C4×D4—24no—
131C22×C4⋊C4C22×C311yescharacteristic
132C22×C4⋊C4C22×C311yescharacteristic
133C22×C4⋊C4C22×C312yes—
134C22×C22⋊C4C22×C311yescharacteristic
135C22×C22⋊C4C22×C312yes—
136C22×C22⋊C4C22×C311yescharacteristic
137C22×C22⋊C4C22×C312yes—
138C22×C22⋊C4C22×C312yes—
139C22×C22⋊C4C22×C312yes—
140C22×C22⋊C4C22×C312yes—
141C22×C22⋊C4C22×C311yescharacteristic
142C22×C42C22×C311yescharacteristic
143#394—24no—
144#394—28no—
145#392—24no—
146#388—24no—
147#386—28no—
148C2×#95C22×C311yescharacteristic
149C2×#95C22×C312yes—
150C2×#95C22×C311yescharacteristic
151C2×#95C22×C311yescharacteristic
152C2×#95C22×C312yes—
153C2×#95C22×C311yescharacteristic
154C2×#95C22×C312yes—
155C2×#95C22×C312yes—
156C24×C3—22no—
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—21no—
169C24×C3—22no—
170C24×C3—21no—
171C24×C3—21no—
172C24×C3—21no—
173C24×C3—22no—
174C24×C3—22no—
175C24×C3—22no—
176C24×C3—21no—
177C24×C3—21no—
178C24×C3C2×D412yes—
179C24×C3C2×D414yes—
180C24×C3C2×D414yes—
181C24×C3#4114yes—
182C24×C3C2411yescharacteristic
183C2×C3×D4—28no—
184C2×C3×D4—28no—
185C2×C3×D4—216no—
186C2×C3×D4—216no—
187C2×C3×D4—216no—
188C2×C3×D4—28no—
189C2×C3×D4—48no—
190C2×C3×D4—48no—
191C2×C3×D4—48no—
192C2×C3×D4—48no—
193C2×C3×D4—48no—
194C2×C3×D4—48no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—21no—
200C22×C3×C4—22no—
201C22×C3×C4—21no—
202C22×C3×C4—216no—
203C22×C3×C4—22no—
204C22×C3×C4—21no—
205C22×C3×C4—22no—
206C22×C3×C4—22no—
207C22×C3×C4—22no—
208C22×C3×C4—21no—
209C22×C3×C4—22no—
210C22×C3×C4—22no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—22no—
214C22×C3×C4—22no—
215C22×C3×C4—22no—
216C22×C3×C4—21no—
217C22×C3×C4—22no—
218C22×C3×C4—22no—
219C22×C3×C4—22no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—22no—
223C22×C3×C4—22no—
224C22×C3×C4—22no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—22no—
229C22×C3×C4—22no—
230C22×C3×C4—22no—
231C22×C3×C4—21no—
232C22×C3×C4—22no—
233C22×C3×C4—21no—
234C22×C3×C4—22no—
235C22×C3×C4—22no—
236C22×C3×C4—22no—
237C22×C3×C4—22no—
238C22×C3×C4—48no—
239C22×C3×C4—48no—
240C22×C3×C4—48no—
241C22×C3×C4—48no—
242C22×C3×C4—48no—
243C22×C3×C4—48no—
244C22×C3×C4C2×D412yes—
245C22×C3×C4C2×D414yes—
246C22×C3×C4C2×D412yes—
247C22×C3×C4C2×D414yes—
248C22×C3×C4C2×D412yes—
249C22×C3×C4C2×D412yes—
250C22×C3×C4C2×D412yes—
251C22×C3×C4C2×D412yes—
252C22×C3×C4#4114yes—
253C22×C3×C4#4112yes—
254C22×C3×C4#4112yes—
255C3×C4⋊C4—28no—
256C3×C4⋊C4—48no—
257C3×C4⋊C4—44no—
258C3×C22⋊C4—216no—
259C3×C22⋊C4—28no—
260C3×C22⋊C4—48no—
261C3×C22⋊C4—48no—
262C3×C22⋊C4—48no—
263C3×C22⋊C4—48no—
264C3×C22⋊C4—44no—
265C3×C22⋊C4—44no—
266C3×C42—28no—
267C25C23×C311yescharacteristic
268C25C23×C312yes—
269C22×D4—24no—
270C22×D4—24no—
271C22×D4—24no—
272C22×D4—24no—
273C22×D4—24no—
274C22×D4—24no—
275C22×D4—22no—
276C22×D4—22no—
277C22×D4—24no—
278C22×D4—42no—
279C22×D4—42no—
280C22×D4C3×D414yes—
281C23×C4—24no—
282C23×C4—24no—
283C23×C4—24no—
284C23×C4—24no—
285C23×C4—24no—
286C23×C4—42no—
287C23×C4—42no—
288C23×C4C23×C311yescharacteristic
289C23×C4C23×C312yes—
290C23×C4C23×C311yescharacteristic
291C23×C4C23×C311yescharacteristic
292C23×C4C23×C312yes—
293C23×C4C23×C312yes—
294C23×C4C23×C311yescharacteristic
295C23×C4C23×C311yescharacteristic
296C23×C4C23×C311yescharacteristic
297C4×D4—232no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—42no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4C3×D418yescomplemented
328C2×C22⋊C4C3×D414yescomplemented
329C2×C42—24no—
330C2×C42C3×D414yescomplemented
331#95—24no—
332#95—24no—
333#95—22no—
334#95—22no—
335#95—22no—
336#95—24no—
337#95—22no—
338#95—42no—
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—24no—
349C23×C3—24no—
350C23×C3—24no—
351C23×C3—24no—
352C23×C3—24no—
353C23×C3—24no—
354C23×C3—24no—
355C23×C3—24no—
356C23×C3—24no—
357C23×C3—22no—
358C23×C3—24no—
359C23×C3—24no—
360C23×C3—22no—
361C23×C3—22no—
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—41no—
379C23×C3—41no—
380C23×C3—42no—
381C23×C3—41no—
382C23×C3—42no—
383C23×C3—42no—
384C23×C3—41no—
385C23×C3—41no—
386C23×C3—41no—
387C23×C3—42no—
388C23×C3—42no—
389C23×C3—42no—
390C23×C3—42no—
391C23×C3—42no—
392C23×C3—42no—
393C23×C3—41no—
394C23×C3—41no—
395C23×C3—42no—
396C23×C3#12118yes—
397C23×C3C22×D411yescharacteristic
398C23×C3C22×D412yes—
399C23×C3C22×D411yescharacteristic
400C23×C3C22×D411yescharacteristic
401C23×C3C2×#4112yes—
402C23×C3C2×#4111yescharacteristic
403C23×C3C2×#4111yescharacteristic
404C23×C3C2×#4112yes—
405C23×C3H(5,𝔽2)12yes—
406C23×C3H(5,𝔽2)11yescharacteristic
407C23×C32−1+411yescharacteristic
408C3×D4—232no—
409C3×D4—432no—
410C2×C3×C4—22no—
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—22no—
418C2×C3×C4—24no—
419C2×C3×C4—24no—
420C2×C3×C4—24no—
421C2×C3×C4—24no—
422C2×C3×C4—24no—
423C2×C3×C4—22no—
424C2×C3×C4—24no—
425C2×C3×C4—22no—
426C2×C3×C4—24no—
427C2×C3×C4—24no—
428C2×C3×C4—24no—
429C2×C3×C4—24no—
430C2×C3×C4—22no—
431C2×C3×C4—432no—
432C2×C3×C4—41no—
433C2×C3×C4—42no—
434C2×C3×C4—42no—
435C2×C3×C4—42no—
436C2×C3×C4—41no—
437C2×C3×C4—42no—
438C2×C3×C4—42no—
439C2×C3×C4—42no—
440C2×C3×C4—42no—
441C2×C3×C4—42no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—42no—
446C2×C3×C4—42no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—42no—
451C2×C3×C4—42no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—42no—
455C2×C3×C4—42no—
456C2×C3×C4—42no—
457C2×C3×C4—42no—
458C2×C3×C4—42no—
459C2×C3×C4—42no—
460C2×C3×C4—42no—
461C2×C3×C4#12014yes—
462C2×C3×C4#12114yes—
463C2×C3×C4#12114yes—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—21no—
477C24—22no—
478C24—21no—
479C24—21no—
480C24—21no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—21no—
485C24—21no—
486C24C2×C3×D412yes—
487C24C2×C3×D414yes—
488C24C2×C3×D414yes—
489C24C3×#4114yes—
490C24C24×C311yescharacteristic
491C2×D4—28no—
492C2×D4—28no—
493C2×D4—216no—
494C2×D4—216no—
495C2×D4—216no—
496C2×D4—28no—
497C2×D4—48no—
498C2×D4—48no—
499C2×D4—48no—
500C2×D4—48no—
501C2×D4—48no—
502C2×D4—48no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—216no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—48no—
547C22×C4—48no—
548C22×C4—48no—
549C22×C4—48no—
550C22×C4—48no—
551C22×C4—48no—
552C22×C4C2×C3×D412yes—
553C22×C4C2×C3×D414yes—
554C22×C4C2×C3×D412yes—
555C22×C4C2×C3×D414yes—
556C22×C4C2×C3×D412yes—
557C22×C4C2×C3×D412yes—
558C22×C4C2×C3×D412yes—
559C22×C4C2×C3×D412yes—
560C22×C4C3×#4114yes—
561C22×C4C3×#4112yes—
562C22×C4C3×#4112yes—
563C4⋊C4—28no—
564C4⋊C4—48no—
565C4⋊C4—44no—
566C22⋊C4—216no—
567C22⋊C4—28no—
568C22⋊C4—48no—
569C22⋊C4—48no—
570C22⋊C4—48no—
571C22⋊C4—48no—
572C22⋊C4—44no—
573C22⋊C4—44no—
574C42—28no—
575C22×C3—28no—
576C22×C3—28no—
577C22×C3—28no—
578C22×C3—44no—
579C22×C3—44no—
580C22×C3—44no—
581C22×C3—44no—
582C22×C3—44no—
583C22×C3—44no—
584C22×C3—44no—
585C22×C3—44no—
586C22×C3—44no—
587C22×C3—44no—
588C22×C3—44no—
589C22×C3—44no—
590C22×C3—42no—
591C22×C3—42no—
592C22×C3—44no—
593C22×C3—44no—
594C22×C3—42no—
595C22×C3—81no—
596C22×C3—81no—
597C22×C3—82no—
598C22×C3—81no—
599C22×C3—82no—
600C22×C3—81no—
601C22×C3C2×#12011yescharacteristic
602C22×C3C2×#12112yes—
603C22×C3C2×#12111yescharacteristic
604C22×C3C2×#12111yescharacteristic
605C22×C3#52511yescharacteristic
606C22×C3#52512yes—
607C22×C3#52512yes—
608C22×C3#52912yes—
609C22×C3#53211yescharacteristic
610C22×C3#53511yescharacteristic
611C22×C3#53711yescharacteristic
612C22×C3#53812yes—
613C22×C3#53912yes—
614C22×C3D4212yes—
615C22×C3D4211yescharacteristic
616C22×C3#54612yes—
617C22×C3#54612yes—
618C22×C3#54612yes—
619C22×C3#54711yescharacteristic
620C22×C3#54712yes—
621C22×C3#54711yescharacteristic
622C22×C3#55511yescharacteristic
623C22×C3#55912yes—
624C3×C4—24no—
625C3×C4—24no—
626C3×C4—24no—
627C3×C4—44no—
628C3×C4—44no—
629C3×C4—42no—
630C3×C4—81no—
631C3×C4—82no—
632C3×C4—81no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—22no—
652C23—24no—
653C23—24no—
654C23—22no—
655C23—22no—
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—41no—
674C23—41no—
675C23—42no—
676C23—41no—
677C23—42no—
678C23—42no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—41no—
689C23—41no—
690C23C3×#12118yes—
691C23C22×C3×D411yescharacteristic
692C23C22×C3×D412yes—
693C23C22×C3×D411yescharacteristic
694C23C22×C3×D411yescharacteristic
695C23C2×C3×#4111yescharacteristic
696C23C2×C3×#4112yes—
697C23C2×C3×#4112yes—
698C23C2×C3×#4111yescharacteristic
699C23C3×H(5,𝔽2)12yes—
700C23C3×H(5,𝔽2)11yescharacteristic
701C23C3×2−1+411yescharacteristic
702D4—232no—
703D4—432no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—24no—
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—22no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—432no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—41no—
742C2×C4—42no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—41no—
746C2×C4—42no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4C3×#12014yes—
756C2×C4C3×#12114yes—
757C2×C4C3×#12114yes—
758C2×C3—48no—
759C2×C3—82no—
760C2×C3#239211yescharacteristic
761C2×C3#240811yescharacteristic
762C2×C3#242412yes—
763C2×C3#242512yes—
764C2×C3#243011yescharacteristic
765C2×C3#245512yes—
766C2×C3#245912yes—
767C2×C3#253711yescharacteristic
768C2×C3#254411yescharacteristic
769C2×C3#263611yescharacteristic
770C2×C3#284711yescharacteristic
771C22—28no—
772C22—28no—
773C22—28no—
774C22—44no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22—44no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—44no—
784C22—44no—
785C22—44no—
786C22—42no—
787C22—42no—
788C22—44no—
789C22—44no—
790C22—42no—
791C22—81no—
792C22—82no—
793C22—81no—
794C22—82no—
795C22—81no—
796C22—81no—
797C22C2×C3×#12011yescharacteristic
798C22C2×C3×#12111yescharacteristic
799C22C2×C3×#12112yes—
800C22C2×C3×#12111yescharacteristic
801C22C3×#52511yescharacteristic
802C22C3×#52512yes—
803C22C3×#52512yes—
804C22C3×#52912yes—
805C22C3×#53211yescharacteristic
806C22C3×#53511yescharacteristic
807C22C3×#53711yescharacteristic
808C22C3×#53812yes—
809C22C3×#53912yes—
810C22C3×D4212yes—
811C22C3×D4211yescharacteristic
812C22C3×#54612yes—
813C22C3×#54612yes—
814C22C3×#54612yes—
815C22C3×#54711yescharacteristic
816C22C3×#54712yes—
817C22C3×#54711yescharacteristic
818C22C3×#55511yescharacteristic
819C22C3×#55912yes—
820C4—24no—
821C4—24no—
822C4—24no—
823C4—44no—
824C4—44no—
825C4—42no—
826C4—82no—
827C4—81no—
828C4—81no—
829C3#1480611yescharacteristic, direct product factor, Sylow
830C2—48no—
831C2—82no—
832C2C3×#239211yescharacteristic
833C2C3×#240811yescharacteristic
834C2C3×#242412yes—
835C2C3×#242512yes—
836C2C3×#243011yescharacteristic
837C2C3×#245512yes—
838C2C3×#245912yes—
839C2C3×#253711yescharacteristic
840C2C3×#254411yescharacteristic
841C2C3×#263611yescharacteristic
842C2C3×#284711yescharacteristic
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×C4×D4C2semidirect
2. C2×C3×#394C2semidirect
3. C2×C3×#394C2semidirect
5. C2×C3×#388C2semidirect
6. C2×C3×#386C2semidirect
7. C3×#1441C2semidirect
8. C3×#1439C2semidirect
9. C3×#1439C2semidirect
10. C3×C4⋊#95C2semidirect
11. C3×C22⋊#95C2semidirect
12. #14806C3direct (N × H)
43. C22×C4×D4C2×C3semidirect
44. C2×#394C2×C3semidirect
45. C2×#394C2×C3semidirect
47. C2×#388C2×C3semidirect
48. C2×#386C2×C3semidirect
49. #1441C2×C3semidirect
50. #1439C2×C3semidirect
51. #1439C2×C3semidirect
52. C4⋊#95C2×C3semidirect
53. C22⋊#95C2×C3semidirect
114. C2×C3×C22⋊C4D4semidirect
115. C2×C3×C22⋊C4D4semidirect
117. C2×C3×C42D4semidirect
327. C2×C22⋊C4C3×D4semidirect
328. C2×C22⋊C4C3×D4semidirect
330. C2×C42C3×D4semidirect
829. C3#14806direct (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×#3942
C2×C3×#3922
C2×C3×#3882
C2×C3×#3862
C3×#14412
C3×#14392
C3×C4⋊#952
C3×C22⋊#952
#148063