Finite Group Databasebeta

← C3×#14839 #10633446

Subgroups — C3×#14839 #10633446

Order 768.

1962 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#399C211yesmaximal, characteristic, complemented
2C2×C3×#397C212yesmaximal, complemented
3C2×C3×#394C212yesmaximal
4C2×C3×#386C211yesmaximal, characteristic
5C2×C3×#380C211yesmaximal, characteristic, complemented
6C2×C3×C4×C22⋊C4C211yesmaximal, characteristic, complemented
7C3×#1445C211yesmaximal, characteristic, complemented
8C3×#1444C211yesmaximal, characteristic, complemented
9C3×#1439C211yesmaximal, characteristic, complemented
10C3×#1437C212yesmaximal, complemented
11C3×C4⋊#95C212yesmaximal, complemented
12#14839C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×D4C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C22×C3×C4⋊C4C2212yes—
16C22×C3×C4⋊C4C2211yescharacteristic
17C22×C3×C4⋊C4C2212yes—
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C22⋊C4C2212yes—
20C22×C3×C22⋊C4C2212yes—
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2212yes—
25C22×C3×C22⋊C4C2212yes—
26C22×C3×C42C2212yes—
27C3×#399—24no—
28C3×#397—28no—
29C3×#394—28no—
30C3×#386—24no—
31C3×#380—24no—
32C3×C4×C22⋊C4—24no—
33C2×C3×#95C2212yes—
34C2×C3×#95C2212yes—
35C2×C3×#95C2212yes—
36C2×C3×#95C2212yes—
37C2×C3×#95C2211yescharacteristic
38C2×C3×#95C2212yes—
39C2×C3×#95C2211yescharacteristic
40C2×C3×#95C2211yescharacteristic
41C2×C3×#95C2211yescharacteristic
42C2×#399C2×C311yescharacteristic, complemented
43C2×#397C2×C312yescomplemented
44C2×#394C2×C312yes—
45C2×#386C2×C311yescharacteristic
46C2×#380C2×C311yescharacteristic, complemented
47C2×C4×C22⋊C4C2×C311yescharacteristic, complemented
48#1445C2×C311yescharacteristic, complemented
49#1444C2×C311yescharacteristic, complemented
50#1439C2×C311yescharacteristic, complemented
51#1437C2×C312yescomplemented
52C4⋊#95C2×C312yescomplemented
53C25×C3C2311yescharacteristic
54C25×C3C2311yescharacteristic
55C22×C3×D4—22no—
56C22×C3×D4—22no—
57C22×C3×D4—24no—
58C22×C3×D4—22no—
59C22×C3×D4—42no—
60C23×C3×C4—22no—
61C23×C3×C4—22no—
62C23×C3×C4—24no—
63C23×C3×C4—42no—
64C23×C3×C4D414yes—
65C23×C3×C4C2311yescharacteristic
66C23×C3×C4C2312yes—
67C23×C3×C4C2312yes—
68C23×C3×C4C2311yescharacteristic
69C23×C3×C4C2312yes—
70C23×C3×C4C2311yescharacteristic
71C23×C3×C4C2311yescharacteristic
72C23×C3×C4C2312yes—
73C23×C3×C4C2311yescharacteristic
74C2×C3×C4⋊C4—22no—
75C2×C3×C4⋊C4—22no—
76C2×C3×C4⋊C4—24no—
77C2×C3×C4⋊C4—24no—
78C2×C3×C4⋊C4—22no—
79C2×C3×C4⋊C4—24no—
80C2×C3×C4⋊C4—24no—
81C2×C3×C4⋊C4—24no—
82C2×C3×C4⋊C4—22no—
83C2×C3×C4⋊C4—42no—
84C2×C3×C4⋊C4—42no—
85C2×C3×C22⋊C4—24no—
86C2×C3×C22⋊C4—24no—
87C2×C3×C22⋊C4—24no—
88C2×C3×C22⋊C4—22no—
89C2×C3×C22⋊C4—24no—
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—24no—
96C2×C3×C22⋊C4—24no—
97C2×C3×C22⋊C4—22no—
98C2×C3×C22⋊C4—24no—
99C2×C3×C22⋊C4—24no—
100C2×C3×C22⋊C4—22no—
101C2×C3×C22⋊C4—24no—
102C2×C3×C22⋊C4—42no—
103C2×C3×C22⋊C4D418yes—
104C2×C3×C42—24no—
105C2×C3×C42—24no—
106C2×C3×C42—42no—
107C3×#95—22no—
108C3×#95—24no—
109C3×#95—22no—
110C3×#95—22no—
111C3×#95—24no—
112C3×#95—24no—
113C3×#95—24no—
114C3×#95—24no—
115C3×#95D414yescomplemented
116C23×D4C22×C311yescharacteristic
117C24×C4C22×C311yescharacteristic
118C22×C4⋊C4C22×C312yes—
119C22×C4⋊C4C22×C311yescharacteristic
120C22×C4⋊C4C22×C312yes—
121C22×C4⋊C4C22×C311yescharacteristic
122C22×C22⋊C4C22×C312yes—
123C22×C22⋊C4C22×C312yes—
124C22×C22⋊C4C22×C311yescharacteristic
125C22×C22⋊C4C22×C311yescharacteristic
126C22×C22⋊C4C22×C311yescharacteristic
127C22×C22⋊C4C22×C312yes—
128C22×C22⋊C4C22×C312yes—
129C22×C42C22×C312yes—
130#399—24no—
131#397—28no—
132#394—28no—
133#386—24no—
134#380—24no—
135C4×C22⋊C4—24no—
136C2×#95C22×C312yes—
137C2×#95C22×C312yes—
138C2×#95C22×C312yes—
139C2×#95C22×C312yes—
140C2×#95C22×C311yescharacteristic
141C2×#95C22×C312yes—
142C2×#95C22×C311yescharacteristic
143C2×#95C22×C311yescharacteristic
144C2×#95C22×C311yescharacteristic
145C24×C3—21no—
146C24×C3—22no—
147C24×C3—21no—
148C24×C3—22no—
149C24×C3—21no—
150C24×C3—21no—
151C24×C3—22no—
152C24×C3—21no—
153C24×C3—21no—
154C24×C3—21no—
155C24×C3—21no—
156C24×C3—22no—
157C24×C3—22no—
158C24×C3—22no—
159C24×C3—21no—
160C24×C3—21no—
161C24×C3—22no—
162C24×C3—21no—
163C24×C3—21no—
164C24×C3C2×D414yes—
165C24×C3C2×D412yes—
166C24×C3#4112yes—
167C24×C3C2411yescharacteristic
168C2×C3×D4—28no—
169C2×C3×D4—48no—
170C2×C3×D4—48no—
171C2×C3×D4—44no—
172C2×C3×D4—44no—
173C22×C3×C4—21no—
174C22×C3×C4—22no—
175C22×C3×C4—22no—
176C22×C3×C4—21no—
177C22×C3×C4—22no—
178C22×C3×C4—22no—
179C22×C3×C4—22no—
180C22×C3×C4—22no—
181C22×C3×C4—22no—
182C22×C3×C4—21no—
183C22×C3×C4—22no—
184C22×C3×C4—22no—
185C22×C3×C4—22no—
186C22×C3×C4—22no—
187C22×C3×C4—22no—
188C22×C3×C4—21no—
189C22×C3×C4—22no—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4—28no—
193C22×C3×C4—28no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—21no—
197C22×C3×C4—22no—
198C22×C3×C4—21no—
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—22no—
206C22×C3×C4—22no—
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—22no—
215C22×C3×C4—22no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—44no—
219C22×C3×C4—48no—
220C22×C3×C4—48no—
221C22×C3×C4C2×D414yes—
222C22×C3×C4C2×D412yes—
223C22×C3×C4C2×D414yes—
224C22×C3×C4C2×D412yes—
225C22×C3×C4C2×D414yes—
226C22×C3×C4C2×D412yes—
227C22×C3×C4#4112yes—
228C22×C3×C4#4114yes—
229C22×C3×C4#4112yes—
230C22×C3×C4#4114yes—
231C3×C4⋊C4—48no—
232C3×C4⋊C4—44no—
233C3×C4⋊C4—48no—
234C3×C4⋊C4—44no—
235C3×C22⋊C4—216no—
236C3×C22⋊C4—48no—
237C3×C22⋊C4—48no—
238C3×C22⋊C4—44no—
239C3×C22⋊C4—48no—
240C3×C22⋊C4—44no—
241C3×C22⋊C4—44no—
242C3×C42—48no—
243C25C23×C311yescharacteristic
244C25C23×C311yescharacteristic
245C22×D4—22no—
246C22×D4—22no—
247C22×D4—24no—
248C22×D4—22no—
249C22×D4—42no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—24no—
253C23×C4—42no—
254C23×C4C3×D414yes—
255C23×C4C23×C312yes—
256C23×C4C23×C312yes—
257C23×C4C23×C311yescharacteristic
258C23×C4C23×C311yescharacteristic
259C23×C4C23×C312yes—
260C23×C4C23×C311yescharacteristic
261C23×C4C23×C312yes—
262C23×C4C23×C311yescharacteristic
263C23×C4C23×C311yescharacteristic
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—42no—
274C2×C4⋊C4—42no—
275C2×C22⋊C4—24no—
276C2×C22⋊C4—24no—
277C2×C22⋊C4—24no—
278C2×C22⋊C4—22no—
279C2×C22⋊C4—24no—
280C2×C22⋊C4—24no—
281C2×C22⋊C4—24no—
282C2×C22⋊C4—24no—
283C2×C22⋊C4—22no—
284C2×C22⋊C4—22no—
285C2×C22⋊C4—24no—
286C2×C22⋊C4—24no—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—24no—
289C2×C22⋊C4—24no—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—24no—
292C2×C22⋊C4—42no—
293C2×C22⋊C4C3×D418yes—
294C2×C42—24no—
295C2×C42—24no—
296C2×C42—42no—
297#95—22no—
298#95—24no—
299#95—22no—
300#95—22no—
301#95—24no—
302#95—24no—
303#95—24no—
304#95—24no—
305#95C3×D414yescomplemented
306C23×C3—24no—
307C23×C3—22no—
308C23×C3—22no—
309C23×C3—22no—
310C23×C3—22no—
311C23×C3—24no—
312C23×C3—22no—
313C23×C3—22no—
314C23×C3—24no—
315C23×C3—24no—
316C23×C3—24no—
317C23×C3—24no—
318C23×C3—22no—
319C23×C3—24no—
320C23×C3—24no—
321C23×C3—22no—
322C23×C3—22no—
323C23×C3—42no—
324C23×C3—42no—
325C23×C3—42no—
326C23×C3—42no—
327C23×C3—42no—
328C23×C3—41no—
329C23×C3—41no—
330C23×C3—42no—
331C23×C3—41no—
332C23×C3—41no—
333C23×C3—41no—
334C23×C3—42no—
335C23×C3—41no—
336C23×C3—42no—
337C23×C3—41no—
338C23×C3—41no—
339C23×C3—42no—
340C23×C3—41no—
341C23×C3—41no—
342C23×C3—42no—
343C23×C3—42no—
344C23×C3—42no—
345C23×C3—42no—
346C23×C3—41no—
347C23×C3—42no—
348C23×C3—42no—
349C23×C3—42no—
350C23×C3—41no—
351C23×C3#12714yes—
352C23×C3C22×D411yescharacteristic
353C23×C3C22×D411yescharacteristic
354C23×C3C22×D412yes—
355C23×C3C2×#4112yes—
356C23×C3C2×#4111yescharacteristic
357C23×C3C2×#4112yes—
358C23×C3C2×#4111yescharacteristic
359C23×C3C2×#4111yescharacteristic
360C23×C3H(5,𝔽2)12yes—
361C23×C32−1+411yescharacteristic
362C23×C32−1+411yescharacteristic
363C3×D4—416no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—24no—
367C2×C3×C4—22no—
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—24no—
376C2×C3×C4—24no—
377C2×C3×C4—24no—
378C2×C3×C4—24no—
379C2×C3×C4—22no—
380C2×C3×C4—24no—
381C2×C3×C4—24no—
382C2×C3×C4—24no—
383C2×C3×C4—416no—
384C2×C3×C4—42no—
385C2×C3×C4—41no—
386C2×C3×C4—41no—
387C2×C3×C4—42no—
388C2×C3×C4—42no—
389C2×C3×C4—42no—
390C2×C3×C4—42no—
391C2×C3×C4—41no—
392C2×C3×C4—42no—
393C2×C3×C4—42no—
394C2×C3×C4—42no—
395C2×C3×C4—42no—
396C2×C3×C4—41no—
397C2×C3×C4—42no—
398C2×C3×C4—42no—
399C2×C3×C4—41no—
400C2×C3×C4—41no—
401C2×C3×C4—42no—
402C2×C3×C4—41no—
403C2×C3×C4—42no—
404C2×C3×C4—42no—
405C2×C3×C4—42no—
406C2×C3×C4—42no—
407C2×C3×C4—42no—
408C2×C3×C4—41no—
409C2×C3×C4—42no—
410C2×C3×C4—42no—
411C2×C3×C4—42no—
412C2×C3×C4—42no—
413C2×C3×C4—42no—
414C2×C3×C4—42no—
415C2×C3×C4#12118yes—
416C2×C3×C4#12114yes—
417C2×C3×C4#12314yes—
418C24—21no—
419C24—22no—
420C24—21no—
421C24—22no—
422C24—21no—
423C24—21no—
424C24—22no—
425C24—21no—
426C24—21no—
427C24—21no—
428C24—21no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—21no—
433C24—21no—
434C24—22no—
435C24—21no—
436C24—21no—
437C24C2×C3×D414yes—
438C24C2×C3×D412yes—
439C24C3×#4112yes—
440C24C24×C311yescharacteristic
441C2×D4—28no—
442C2×D4—48no—
443C2×D4—48no—
444C2×D4—44no—
445C2×D4—44no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—28no—
466C22×C4—28no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—44no—
492C22×C4—48no—
493C22×C4—48no—
494C22×C4C2×C3×D414yes—
495C22×C4C2×C3×D412yes—
496C22×C4C2×C3×D414yes—
497C22×C4C2×C3×D412yes—
498C22×C4C2×C3×D414yes—
499C22×C4C2×C3×D412yes—
500C22×C4C3×#4112yes—
501C22×C4C3×#4114yes—
502C22×C4C3×#4112yes—
503C22×C4C3×#4114yes—
504C4⋊C4—48no—
505C4⋊C4—44no—
506C4⋊C4—48no—
507C4⋊C4—44no—
508C22⋊C4—216no—
509C22⋊C4—48no—
510C22⋊C4—48no—
511C22⋊C4—44no—
512C22⋊C4—48no—
513C22⋊C4—44no—
514C22⋊C4—44no—
515C42—48no—
516C22×C3—24no—
517C22×C3—24no—
518C22×C3—24no—
519C22×C3—42no—
520C22×C3—42no—
521C22×C3—42no—
522C22×C3—42no—
523C22×C3—44no—
524C22×C3—44no—
525C22×C3—44no—
526C22×C3—44no—
527C22×C3—42no—
528C22×C3—42no—
529C22×C3—44no—
530C22×C3—42no—
531C22×C3—44no—
532C22×C3—81no—
533C22×C3—81no—
534C22×C3—81no—
535C22×C3—82no—
536C22×C3—81no—
537C22×C3—82no—
538C22×C3C2×#12111yescharacteristic
539C22×C3C2×#12112yes—
540C22×C3C2×#12311yescharacteristic
541C22×C3#52511yescharacteristic
542C22×C3#52912yes—
543C22×C3#52912yes—
544C22×C3C2×#12711yescharacteristic
545C22×C3#53211yescharacteristic
546C22×C3#53212yes—
547C22×C3#53411yescharacteristic
548C22×C3#53611yescharacteristic
549C22×C3#53912yes—
550C22×C3#54212yes—
551C22×C3#54612yes—
552C22×C3#54612yes—
553C22×C3#54612yes—
554C22×C3#54711yescharacteristic
555C22×C3#54712yes—
556C22×C3#54712yes—
557C22×C3#54811yescharacteristic
558C22×C3#55112yes—
559C22×C3#55211yescharacteristic
560C22×C3#55611yescharacteristic
561C3×C4—24no—
562C3×C4—24no—
563C3×C4—28no—
564C3×C4—44no—
565C3×C4—42no—
566C3×C4—81no—
567C3×C4—82no—
568C3×C4—81no—
569C3×C4—82no—
570C23—24no—
571C23—22no—
572C23—22no—
573C23—22no—
574C23—22no—
575C23—24no—
576C23—22no—
577C23—22no—
578C23—24no—
579C23—24no—
580C23—24no—
581C23—24no—
582C23—22no—
583C23—24no—
584C23—24no—
585C23—22no—
586C23—22no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—41no—
593C23—41no—
594C23—42no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—42no—
599C23—41no—
600C23—42no—
601C23—41no—
602C23—41no—
603C23—42no—
604C23—41no—
605C23—41no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—41no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—41no—
615C23C3×#12714yes—
616C23C22×C3×D411yescharacteristic
617C23C22×C3×D411yescharacteristic
618C23C22×C3×D412yes—
619C23C2×C3×#4112yes—
620C23C2×C3×#4111yescharacteristic
621C23C2×C3×#4112yes—
622C23C2×C3×#4111yescharacteristic
623C23C2×C3×#4111yescharacteristic
624C23C3×H(5,𝔽2)12yes—
625C23C3×2−1+411yescharacteristic
626C23C3×2−1+411yescharacteristic
627D4—416no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—24no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—24no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—22no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—416no—
648C2×C4—42no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—41no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—41no—
661C2×C4—42no—
662C2×C4—41no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—41no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4C3×#12118yes—
680C2×C4C3×#12114yes—
681C2×C4C3×#12314yes—
682C2×C3—44no—
683C2×C3—82no—
684C2×C3#239511yescharacteristic
685C2×C3#241211yescharacteristic
686C2×C3#241511yescharacteristic
687C2×C3#242512yes—
688C2×C3#242712yes—
689C2×C3#250111yescharacteristic
690C2×C3#252112yes—
691C2×C3#253911yescharacteristic
692C2×C3#255312yes—
693C2×C3#266311yescharacteristic
694C2×C3#285611yescharacteristic
695C22—24no—
696C22—24no—
697C22—24no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22—44no—
703C22—44no—
704C22—44no—
705C22—44no—
706C22—42no—
707C22—42no—
708C22—44no—
709C22—42no—
710C22—44no—
711C22—81no—
712C22—81no—
713C22—82no—
714C22—81no—
715C22—82no—
716C22—81no—
717C22C2×C3×#12111yescharacteristic
718C22C2×C3×#12112yes—
719C22C2×C3×#12311yescharacteristic
720C22C3×#52511yescharacteristic
721C22C3×#52912yes—
722C22C3×#52912yes—
723C22C2×C3×#12711yescharacteristic
724C22C3×#53211yescharacteristic
725C22C3×#53212yes—
726C22C3×#53411yescharacteristic
727C22C3×#53611yescharacteristic
728C22C3×#53912yes—
729C22C3×#54212yes—
730C22C3×#54612yes—
731C22C3×#54612yes—
732C22C3×#54612yes—
733C22C3×#54711yescharacteristic
734C22C3×#54712yes—
735C22C3×#54712yes—
736C22C3×#54811yescharacteristic
737C22C3×#55112yes—
738C22C3×#55211yescharacteristic
739C22C3×#55611yescharacteristic
740C4—24no—
741C4—24no—
742C4—28no—
743C4—44no—
744C4—42no—
745C4—81no—
746C4—82no—
747C4—81no—
748C4—82no—
749C3#1483911yescharacteristic, direct product factor, Sylow
750C2—44no—
751C2—82no—
752C2C3×#239511yescharacteristic
753C2C3×#241211yescharacteristic
754C2C3×#241511yescharacteristic
755C2C3×#242512yes—
756C2C3×#242712yes—
757C2C3×#250111yescharacteristic
758C2C3×#252112yes—
759C2C3×#253911yescharacteristic
760C2C3×#255312yes—
761C2C3×#266311yescharacteristic
762C2C3×#285611yescharacteristic
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. C2×C3×#399C2semidirect
2. C2×C3×#397C2semidirect
5. C2×C3×#380C2semidirect
6. C2×C3×C4×C22⋊C4C2semidirect
7. C3×#1445C2semidirect
8. C3×#1444C2semidirect
9. C3×#1439C2semidirect
10. C3×#1437C2semidirect
11. C3×C4⋊#95C2semidirect
12. #14839C3direct (N × H)
42. C2×#399C2×C3semidirect
43. C2×#397C2×C3semidirect
46. C2×#380C2×C3semidirect
47. C2×C4×C22⋊C4C2×C3semidirect
48. #1445C2×C3semidirect
49. #1444C2×C3semidirect
50. #1439C2×C3semidirect
51. #1437C2×C3semidirect
52. C4⋊#95C2×C3semidirect
115. C3×#95D4semidirect
305. #95C3×D4semidirect
749. C3#14839direct (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×#3972
C2×C3×#3942
C2×C3×#3862
C2×C3×#3802
C2×C3×C4×C22⋊C42
C3×#14452
C3×#14442
C3×#14392
C3×#14372
C3×C4⋊#952
#148393