Finite Group Databasebeta

← C3×#14759 #10633366

Subgroups — C3×#14759 #10633366

Order 768.

2414 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×C3×#393C211yesmaximal, characteristic, complemented
3C2×C3×#386C212yesmaximal
4C2×C3×#386C211yesmaximal, characteristic
5C22×C3×#95C211yesmaximal, characteristic, complemented
6C3×#1446C211yesmaximal, characteristic, complemented
7C3×#1442C212yesmaximal, complemented
8C3×#1442C211yesmaximal, characteristic, complemented
9C3×#1439C212yesmaximal, complemented
10C3×#1439C211yesmaximal, characteristic, complemented
11C3×C22⋊#95C212yesmaximal, complemented
12#14759C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×Q8C2211yescharacteristic
14C23×C3×D4C2211yescharacteristic
15C24×C3×C4C2212yes—
16C24×C3×C4C2211yescharacteristic
17C2×C3×C22⋊Q8—24no—
18C2×C3×C22⋊Q8—28no—
19C22×C3×C4⋊C4C2212yes—
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2212yes—
24C22×C3×C22⋊C4C2212yes—
25C22×C3×C22⋊C4C2212yes—
26C22×C3×C22⋊C4C2211yescharacteristic
27C3×#393—24no—
28C3×#386—24no—
29C3×#386—28no—
30C2×C3×#95—24no—
31C2×C3×#95C2212yes—
32C2×C3×#95C2212yes—
33C2×C3×#95C2211yescharacteristic
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2212yes—
36C2×C3×#95C2211yescharacteristic
37C2×C3×#95C2212yes—
38C2×C3×#95C2212yes—
39C2×C3×#95C2212yes—
40C2×C3×#95C2212yes—
41C2×C3×#95C2211yescharacteristic
42C22×C22⋊Q8C2×C311yescharacteristic, complemented
43C2×#393C2×C311yescharacteristic, complemented
44C2×#386C2×C311yescharacteristic
45C2×#386C2×C312yes—
46C22×#95C2×C311yescharacteristic, complemented
47#1446C2×C311yescharacteristic, complemented
48#1442C2×C312yescomplemented
49#1442C2×C311yescharacteristic, complemented
50#1439C2×C311yescharacteristic, complemented
51#1439C2×C312yescomplemented
52C22⋊#95C2×C312yescomplemented
53C25×C3C2311yescharacteristic
54C25×C3C2311yescharacteristic
55C22×C3×Q8—24no—
56C22×C3×Q8—22no—
57C22×C3×Q8—22no—
58C22×C3×Q8—22no—
59C22×C3×Q8—42no—
60C22×C3×D4—22no—
61C22×C3×D4—24no—
62C22×C3×D4—24no—
63C22×C3×D4—22no—
64C22×C3×D4Q814yescomplemented
65C23×C3×C4—24no—
66C23×C3×C4—24no—
67C23×C3×C4—24no—
68C23×C3×C4—22no—
69C23×C3×C4—24no—
70C23×C3×C4—22no—
71C23×C3×C4—24no—
72C23×C3×C4—24no—
73C23×C3×C4—42no—
74C23×C3×C4—42no—
75C23×C3×C4—42no—
76C23×C3×C4D414yes—
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2312yes—
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2312yes—
82C23×C3×C4C2312yes—
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2312yes—
85C23×C3×C4C2311yescharacteristic
86C3×C22⋊Q8—232no—
87C2×C3×C4⋊C4—24no—
88C2×C3×C4⋊C4—22no—
89C2×C3×C4⋊C4—24no—
90C2×C3×C4⋊C4—24no—
91C2×C3×C4⋊C4—24no—
92C2×C3×C22⋊C4—24no—
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—22no—
99C2×C3×C22⋊C4—22no—
100C2×C3×C22⋊C4—24no—
101C2×C3×C22⋊C4—22no—
102C2×C3×C22⋊C4—24no—
103C2×C3×C22⋊C4—22no—
104C2×C3×C22⋊C4—42no—
105C2×C3×C22⋊C4—42no—
106C2×C3×C22⋊C4—42no—
107C2×C3×C22⋊C4D418yes—
108C3×#95—24no—
109C3×#95—22no—
110C3×#95—24no—
111C3×#95—24no—
112C3×#95—22no—
113C3×#95—22no—
114C3×#95—24no—
115C3×#95—24no—
116C3×#95—42no—
117C3×#95—42no—
118C3×#95D414yescomplemented
119C23×Q8C22×C311yescharacteristic
120C23×D4C22×C311yescharacteristic
121C24×C4C22×C312yes—
122C24×C4C22×C311yescharacteristic
123C2×C22⋊Q8—24no—
124C2×C22⋊Q8—28no—
125C22×C4⋊C4C22×C311yescharacteristic
126C22×C4⋊C4C22×C312yes—
127C22×C22⋊C4C22×C311yescharacteristic
128C22×C22⋊C4C22×C311yescharacteristic
129C22×C22⋊C4C22×C312yes—
130C22×C22⋊C4C22×C312yes—
131C22×C22⋊C4C22×C312yes—
132C22×C22⋊C4C22×C311yescharacteristic
133#393—24no—
134#386—24no—
135#386—28no—
136C2×#95—24no—
137C2×#95C22×C312yes—
138C2×#95C22×C312yes—
139C2×#95C22×C312yes—
140C2×#95C22×C311yescharacteristic
141C2×#95C22×C311yescharacteristic
142C2×#95C22×C312yes—
143C2×#95C22×C311yescharacteristic
144C2×#95C22×C312yes—
145C2×#95C22×C312yes—
146C2×#95C22×C312yes—
147C2×#95C22×C311yescharacteristic
148C24×C3—21no—
149C24×C3—21no—
150C24×C3—22no—
151C24×C3—22no—
152C24×C3—21no—
153C24×C3—21no—
154C24×C3—21no—
155C24×C3—21no—
156C24×C3—22no—
157C24×C3—21no—
158C24×C3—22no—
159C24×C3—22no—
160C24×C3—21no—
161C24×C3—22no—
162C24×C3—21no—
163C24×C3—21no—
164C24×C3C2×D412yes—
165C24×C3C2×D414yes—
166C24×C3C2×Q812yes—
167C24×C3C2×Q812yes—
168C24×C3#4114yes—
169C24×C3#4112yes—
170C24×C3C2411yescharacteristic
171C2×C3×Q8—28no—
172C2×C3×Q8—48no—
173C2×C3×Q8—48no—
174C2×C3×Q8—44no—
175C2×C3×Q8—44no—
176C2×C3×D4—28no—
177C2×C3×D4—216no—
178C2×C3×D4—44no—
179C2×C3×D4—44no—
180C2×C3×D4—48no—
181C22×C3×C4—22no—
182C22×C3×C4—22no—
183C22×C3×C4—216no—
184C22×C3×C4—28no—
185C22×C3×C4—21no—
186C22×C3×C4—22no—
187C22×C3×C4—21no—
188C22×C3×C4—22no—
189C22×C3×C4—22no—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—22no—
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—22no—
202C22×C3×C4—22no—
203C22×C3×C4—22no—
204C22×C3×C4—22no—
205C22×C3×C4—22no—
206C22×C3×C4—21no—
207C22×C3×C4—22no—
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—22no—
217C22×C3×C4—28no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—22no—
222C22×C3×C4—21no—
223C22×C3×C4—22no—
224C22×C3×C4—22no—
225C22×C3×C4—21no—
226C22×C3×C4—22no—
227C22×C3×C4—21no—
228C22×C3×C4—44no—
229C22×C3×C4—48no—
230C22×C3×C4—48no—
231C22×C3×C4—48no—
232C22×C3×C4—48no—
233C22×C3×C4—48no—
234C22×C3×C4—48no—
235C22×C3×C4—48no—
236C22×C3×C4—48no—
237C22×C3×C4C2×D414yes—
238C22×C3×C4C2×D414yes—
239C22×C3×C4C2×D414yes—
240C22×C3×C4C2×D412yes—
241C22×C3×C4C2×D412yes—
242C22×C3×C4C2×D412yes—
243C22×C3×C4C2×Q812yes—
244C22×C3×C4#4114yes—
245C22×C3×C4#4112yes—
246C3×C4⋊C4—28no—
247C3×C4⋊C4—216no—
248C3×C22⋊C4—216no—
249C3×C22⋊C4—48no—
250C3×C22⋊C4—48no—
251C3×C22⋊C4—44no—
252C3×C22⋊C4—44no—
253C3×C22⋊C4—44no—
254C25C23×C311yescharacteristic
255C25C23×C311yescharacteristic
256C22×Q8—24no—
257C22×Q8—22no—
258C22×Q8—22no—
259C22×Q8—22no—
260C22×Q8—42no—
261C22×D4—22no—
262C22×D4—24no—
263C22×D4—24no—
264C22×D4—22no—
265C22×D4C3×Q814yescomplemented
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—22no—
270C23×C4—24no—
271C23×C4—22no—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—42no—
275C23×C4—42no—
276C23×C4—42no—
277C23×C4C3×D414yes—
278C23×C4C23×C311yescharacteristic
279C23×C4C23×C311yescharacteristic
280C23×C4C23×C312yes—
281C23×C4C23×C312yes—
282C23×C4C23×C311yescharacteristic
283C23×C4C23×C312yes—
284C23×C4C23×C311yescharacteristic
285C23×C4C23×C312yes—
286C23×C4C23×C311yescharacteristic
287C22⋊Q8—232no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C22⋊C4—24no—
294C2×C22⋊C4—24no—
295C2×C22⋊C4—22no—
296C2×C22⋊C4—24no—
297C2×C22⋊C4—24no—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—22no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—42no—
306C2×C22⋊C4—42no—
307C2×C22⋊C4—42no—
308C2×C22⋊C4C3×D418yes—
309#95—24no—
310#95—22no—
311#95—24no—
312#95—24no—
313#95—22no—
314#95—22no—
315#95—24no—
316#95—24no—
317#95—42no—
318#95—42no—
319#95C3×D414yescomplemented
320C23×C3—22no—
321C23×C3—24no—
322C23×C3—24no—
323C23×C3—22no—
324C23×C3—22no—
325C23×C3—22no—
326C23×C3—24no—
327C23×C3—24no—
328C23×C3—24no—
329C23×C3—22no—
330C23×C3—24no—
331C23×C3—24no—
332C23×C3—24no—
333C23×C3—22no—
334C23×C3—24no—
335C23×C3—22no—
336C23×C3—24no—
337C23×C3—22no—
338C23×C3—22no—
339C23×C3—24no—
340C23×C3—22no—
341C23×C3—24no—
342C23×C3—22no—
343C23×C3—41no—
344C23×C3—41no—
345C23×C3—42no—
346C23×C3—41no—
347C23×C3—42no—
348C23×C3—42no—
349C23×C3—41no—
350C23×C3—41no—
351C23×C3—41no—
352C23×C3—42no—
353C23×C3—42no—
354C23×C3—42no—
355C23×C3—42no—
356C23×C3—41no—
357C23×C3—42no—
358C23×C3—42no—
359C23×C3—42no—
360C23×C3—41no—
361C23×C3#12014yes—
362C23×C3C22⋊Q814yes—
363C23×C3C22⋊Q818yes—
364C23×C3#12414yes—
365C23×C3#12418yes—
366C23×C3C22×D411yescharacteristic
367C23×C3C22×D412yes—
368C23×C3C22×D411yescharacteristic
369C23×C3C22×Q811yescharacteristic
370C23×C3C2×#4111yescharacteristic
371C23×C3C2×#4112yes—
372C23×C3C2×#4111yescharacteristic
373C23×C3C2×#4112yes—
374C23×C3H(5,𝔽2)12yes—
375C23×C3H(5,𝔽2)11yescharacteristic
376C23×C32−1+411yescharacteristic
377C3×Q8—416no—
378C3×D4—416no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—24no—
382C2×C3×C4—24no—
383C2×C3×C4—24no—
384C2×C3×C4—24no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—24no—
389C2×C3×C4—24no—
390C2×C3×C4—24no—
391C2×C3×C4—22no—
392C2×C3×C4—24no—
393C2×C3×C4—24no—
394C2×C3×C4—24no—
395C2×C3×C4—24no—
396C2×C3×C4—24no—
397C2×C3×C4—24no—
398C2×C3×C4—24no—
399C2×C3×C4—24no—
400C2×C3×C4—416no—
401C2×C3×C4—432no—
402C2×C3×C4—41no—
403C2×C3×C4—42no—
404C2×C3×C4—42no—
405C2×C3×C4—42no—
406C2×C3×C4—41no—
407C2×C3×C4—42no—
408C2×C3×C4—42no—
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—42no—
416C2×C3×C4—42no—
417C2×C3×C4—42no—
418C2×C3×C4—42no—
419C2×C3×C4—42no—
420C2×C3×C4—42no—
421C2×C3×C4—42no—
422C2×C3×C4—42no—
423C2×C3×C4—41no—
424C2×C3×C4—42no—
425C2×C3×C4—41no—
426C2×C3×C4—41no—
427C2×C3×C4—42no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—42no—
432C2×C3×C4—42no—
433C2×C3×C4#12114yes—
434C24—21no—
435C24—21no—
436C24—22no—
437C24—22no—
438C24—21no—
439C24—21no—
440C24—21no—
441C24—21no—
442C24—22no—
443C24—21no—
444C24—22no—
445C24—22no—
446C24—21no—
447C24—22no—
448C24—21no—
449C24—21no—
450C24C2×C3×D412yes—
451C24C2×C3×D414yes—
452C24C2×C3×Q812yes—
453C24C2×C3×Q812yes—
454C24C3×#4114yes—
455C24C3×#4112yes—
456C24C24×C311yescharacteristic
457C2×Q8—28no—
458C2×Q8—48no—
459C2×Q8—48no—
460C2×Q8—44no—
461C2×Q8—44no—
462C2×D4—28no—
463C2×D4—216no—
464C2×D4—44no—
465C2×D4—44no—
466C2×D4—48no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—216no—
470C22×C4—28no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—28no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—44no—
515C22×C4—48no—
516C22×C4—48no—
517C22×C4—48no—
518C22×C4—48no—
519C22×C4—48no—
520C22×C4—48no—
521C22×C4—48no—
522C22×C4—48no—
523C22×C4C2×C3×D414yes—
524C22×C4C2×C3×D414yes—
525C22×C4C2×C3×D414yes—
526C22×C4C2×C3×D412yes—
527C22×C4C2×C3×D412yes—
528C22×C4C2×C3×D412yes—
529C22×C4C2×C3×Q812yes—
530C22×C4C3×#4114yes—
531C22×C4C3×#4112yes—
532C4⋊C4—28no—
533C4⋊C4—216no—
534C22⋊C4—216no—
535C22⋊C4—48no—
536C22⋊C4—48no—
537C22⋊C4—44no—
538C22⋊C4—44no—
539C22⋊C4—44no—
540C22×C3—24no—
541C22×C3—24no—
542C22×C3—24no—
543C22×C3—24no—
544C22×C3—24no—
545C22×C3—24no—
546C22×C3—28no—
547C22×C3—28no—
548C22×C3—28no—
549C22×C3—28no—
550C22×C3—42no—
551C22×C3—42no—
552C22×C3—42no—
553C22×C3—44no—
554C22×C3—44no—
555C22×C3—81no—
556C22×C3—81no—
557C22×C3—81no—
558C22×C3—81no—
559C22×C3—82no—
560C22×C3—82no—
561C22×C3#39318yescomplemented
562C22×C3C2×#12011yescharacteristic
563C22×C3C2×#12111yescharacteristic
564C22×C3C2×C22⋊Q811yescharacteristic
565C22×C3C2×C22⋊Q812yes—
566C22×C3#52512yes—
567C22×C3C2×#12411yescharacteristic
568C22×C3C2×#12412yes—
569C22×C3#52912yes—
570C22×C3#53211yescharacteristic
571C22×C3#53411yescharacteristic
572C22×C3#53711yescharacteristic
573C22×C3#53812yes—
574C22×C3#53912yes—
575C22×C3D4212yes—
576C22×C3#54612yes—
577C22×C3#54611yescharacteristic
578C22×C3#54612yes—
579C22×C3#54712yes—
580C22×C3D4×Q811yescharacteristic
581C22×C3#55112yes—
582C22×C3#55211yescharacteristic
583C22×C3#55412yes—
584C22×C3#55411yescharacteristic
585C3×C4—24no—
586C3×C4—42no—
587C3×C4—42no—
588C3×C4—44no—
589C3×C4—44no—
590C3×C4—44no—
591C3×C4—44no—
592C3×C4—81no—
593C3×C4—81no—
594C23—22no—
595C23—24no—
596C23—24no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—22no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—22no—
608C23—24no—
609C23—22no—
610C23—22no—
611C23—24no—
612C23—22no—
613C23—24no—
614C23—22no—
615C23—22no—
616C23—24no—
617C23—41no—
618C23—41no—
619C23—42no—
620C23—41no—
621C23—42no—
622C23—42no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—41no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—41no—
635C23C3×#12014yes—
636C23C3×C22⋊Q814yes—
637C23C3×C22⋊Q818yes—
638C23C3×#12414yes—
639C23C3×#12418yes—
640C23C22×C3×D411yescharacteristic
641C23C22×C3×D412yes—
642C23C22×C3×D411yescharacteristic
643C23C22×C3×Q811yescharacteristic
644C23C2×C3×#4111yescharacteristic
645C23C2×C3×#4112yes—
646C23C2×C3×#4111yescharacteristic
647C23C2×C3×#4112yes—
648C23C3×H(5,𝔽2)12yes—
649C23C3×H(5,𝔽2)11yescharacteristic
650C23C3×2−1+411yescharacteristic
651Q8—416no—
652D4—416no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—416no—
675C2×C4—432no—
676C2×C4—41no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—41no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4C3×#12114yes—
708C2×C3—28no—
709C2×C3—82no—
710C2×C3C2×#39311yescharacteristic
711C2×C3#241011yescharacteristic
712C2×C3#241711yescharacteristic
713C2×C3#243011yescharacteristic
714C2×C3#244912yes—
715C2×C3#245012yes—
716C2×C3#247212yes—
717C2×C3#248812yes—
718C2×C3#256411yescharacteristic
719C2×C3#263911yescharacteristic
720C2×C3#285011yescharacteristic
721C22—24no—
722C22—24no—
723C22—24no—
724C22—24no—
725C22—28no—
726C22—28no—
727C22—28no—
728C22—28no—
729C22—24no—
730C22—24no—
731C22—42no—
732C22—42no—
733C22—44no—
734C22—44no—
735C22—42no—
736C22—81no—
737C22—81no—
738C22—81no—
739C22—82no—
740C22—82no—
741C22—81no—
742C22C3×#39318yescomplemented
743C22C2×C3×#12011yescharacteristic
744C22C2×C3×#12111yescharacteristic
745C22C2×C3×C22⋊Q811yescharacteristic
746C22C2×C3×C22⋊Q812yes—
747C22C3×#52512yes—
748C22C2×C3×#12411yescharacteristic
749C22C2×C3×#12412yes—
750C22C3×#52912yes—
751C22C3×#53211yescharacteristic
752C22C3×#53411yescharacteristic
753C22C3×#53711yescharacteristic
754C22C3×#53812yes—
755C22C3×#53912yes—
756C22C3×D4212yes—
757C22C3×#54612yes—
758C22C3×#54611yescharacteristic
759C22C3×#54612yes—
760C22C3×#54712yes—
761C22C3×D4×Q811yescharacteristic
762C22C3×#55112yes—
763C22C3×#55211yescharacteristic
764C22C3×#55411yescharacteristic
765C22C3×#55412yes—
766C4—24no—
767C4—42no—
768C4—42no—
769C4—44no—
770C4—44no—
771C4—44no—
772C4—44no—
773C4—81no—
774C4—81no—
775C3#1475911yescharacteristic, direct product factor, Sylow
776C2—28no—
777C2—82no—
778C2C2×C3×#39311yescharacteristic
779C2C3×#241011yescharacteristic
780C2C3×#241711yescharacteristic
781C2C3×#243011yescharacteristic
782C2C3×#244912yes—
783C2C3×#245012yes—
784C2C3×#247212yes—
785C2C3×#248812yes—
786C2C3×#256411yescharacteristic
787C2C3×#263911yescharacteristic
788C2C3×#285011yescharacteristic
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. C22×C3×C22⋊Q8C2semidirect
2. C2×C3×#393C2semidirect
5. C22×C3×#95C2semidirect
6. C3×#1446C2semidirect
7. C3×#1442C2semidirect
8. C3×#1442C2semidirect
9. C3×#1439C2semidirect
10. C3×#1439C2semidirect
11. C3×C22⋊#95C2semidirect
12. #14759C3direct (N × H)
42. C22×C22⋊Q8C2×C3semidirect
43. C2×#393C2×C3semidirect
46. C22×#95C2×C3semidirect
47. #1446C2×C3semidirect
48. #1442C2×C3semidirect
49. #1442C2×C3semidirect
50. #1439C2×C3semidirect
51. #1439C2×C3semidirect
52. C22⋊#95C2×C3semidirect
64. C22×C3×D4Q8semidirect
118. C3×#95D4semidirect
265. C22×D4C3×Q8semidirect
319. #95C3×D4semidirect
561. C22×C3#393semidirect
742. C22C3×#393semidirect
775. C3#14759direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C22⋊Q82
C2×C3×#3932
C2×C3×#3862
C22×C3×#952
C3×#14462
C3×#14422
C3×#14392
C3×C22⋊#952
#147593