Finite Group Databasebeta

← C3×#16632 #10635239

Subgroups — C3×#16632 #10635239

Order 768.

1966 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×C3×#397C211yesmaximal, characteristic, complemented
3C2×C3×#393C211yesmaximal, characteristic, complemented
4C2×C3×#386C211yesmaximal, characteristic
5C3×#1446C211yesmaximal, characteristic, complemented
6C3×#1445C211yesmaximal, characteristic, complemented
7C3×#1442C212yesmaximal, complemented
8C3×#1440C212yesmaximal, complemented
9C3×#1439C212yesmaximal, complemented
10C3×#1438C212yesmaximal
11C3×C22⋊#95C211yesmaximal, characteristic, complemented
12#16632C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×Q8C2211yescharacteristic
14C23×C3×D4C2211yescharacteristic
15C24×C3×C4C2211yescharacteristic
16C2×C3×C22⋊Q8—24no—
17C2×C3×C22⋊Q8—24no—
18C2×C3×C22⋊Q8—24no—
19C22×C3×C4⋊C4C2212yes—
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2212yes—
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2212yes—
25C22×C3×C22⋊C4C2212yes—
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2212yes—
28C3×#397—24no—
29C3×#393—24no—
30C3×#386—24no—
31C2×C3×#95C2211yescharacteristic
32C2×C3×#95C2212yes—
33C2×C3×#95C2211yescharacteristic
34C2×C3×#95C2212yes—
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
37C2×C3×#95C2212yes—
38C2×C3×#95C2212yes—
39C2×C3×#95C2212yes—
40C2×C3×#95C2212yes—
41C2×C3×#95C2212yes—
42C22×C22⋊Q8C2×C311yescharacteristic, complemented
43C2×#397C2×C311yescharacteristic, complemented
44C2×#393C2×C311yescharacteristic, complemented
45C2×#386C2×C311yescharacteristic
46#1446C2×C311yescharacteristic, complemented
47#1445C2×C311yescharacteristic, complemented
48#1442C2×C312yescomplemented
49#1440C2×C312yescomplemented
50#1439C2×C312yescomplemented
51#1438C2×C312yes—
52C22⋊#95C2×C311yescharacteristic, complemented
53C25×C3C2311yescharacteristic
54C25×C3C2311yescharacteristic
55C22×C3×Q8—22no—
56C22×C3×Q8—22no—
57C22×C3×Q8—42no—
58C22×C3×Q8—42no—
59C22×C3×Q8D414yescomplemented
60C22×C3×D4—22no—
61C22×C3×D4—22no—
62C22×C3×D4—24no—
63C22×C3×D4—22no—
64C22×C3×D4—42no—
65C23×C3×C4—22no—
66C23×C3×C4—22no—
67C23×C3×C4—42no—
68C23×C3×C4—42no—
69C23×C3×C4D414yes—
70C23×C3×C4C2311yescharacteristic
71C23×C3×C4C2312yes—
72C23×C3×C4C2312yes—
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2312yes—
76C23×C3×C4C2312yes—
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C3×C22⋊Q8—232no—
80C2×C3×C4⋊C4—24no—
81C2×C3×C4⋊C4—24no—
82C2×C3×C4⋊C4—24no—
83C2×C3×C4⋊C4—22no—
84C2×C3×C4⋊C4—22no—
85C2×C3×C4⋊C4D414yescomplemented
86C2×C3×C22⋊C4—24no—
87C2×C3×C22⋊C4—24no—
88C2×C3×C22⋊C4—24no—
89C2×C3×C22⋊C4—22no—
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—22no—
97C2×C3×C22⋊C4—24no—
98C2×C3×C22⋊C4—22no—
99C2×C3×C22⋊C4—42no—
100C2×C3×C22⋊C4—42no—
101C2×C3×C22⋊C4—42no—
102C2×C3×C22⋊C4—42no—
103C2×C3×C22⋊C4—42no—
104C2×C3×C22⋊C4—42no—
105C3×#95—22no—
106C3×#95—22no—
107C3×#95—24no—
108C3×#95—22no—
109C3×#95—24no—
110C3×#95—22no—
111C3×#95—24no—
112C3×#95—42no—
113C3×#95—42no—
114C3×#95—42no—
115C3×#95—42no—
116C23×Q8C22×C311yescharacteristic
117C23×D4C22×C311yescharacteristic
118C24×C4C22×C311yescharacteristic
119C2×C22⋊Q8—24no—
120C2×C22⋊Q8—24no—
121C2×C22⋊Q8—24no—
122C22×C4⋊C4C22×C312yes—
123C22×C4⋊C4C22×C311yescharacteristic
124C22×C22⋊C4C22×C311yescharacteristic
125C22×C22⋊C4C22×C312yes—
126C22×C22⋊C4C22×C311yescharacteristic
127C22×C22⋊C4C22×C312yes—
128C22×C22⋊C4C22×C312yes—
129C22×C22⋊C4C22×C312yes—
130C22×C22⋊C4C22×C311yescharacteristic
131#397—24no—
132#393—24no—
133#386—24no—
134C2×#95C22×C311yescharacteristic
135C2×#95C22×C312yes—
136C2×#95C22×C311yescharacteristic
137C2×#95C22×C312yes—
138C2×#95C22×C312yes—
139C2×#95C22×C311yescharacteristic
140C2×#95C22×C311yescharacteristic
141C2×#95C22×C312yes—
142C2×#95C22×C312yes—
143C2×#95C22×C312yes—
144C2×#95C22×C312yes—
145C24×C3—21no—
146C24×C3—21no—
147C24×C3—21no—
148C24×C3—21no—
149C24×C3—21no—
150C24×C3—22no—
151C24×C3—22no—
152C24×C3—22no—
153C24×C3—21no—
154C24×C3—21no—
155C24×C3—21no—
156C24×C3—21no—
157C24×C3—21no—
158C24×C3—22no—
159C24×C3—22no—
160C24×C3—21no—
161C24×C3—22no—
162C24×C3—22no—
163C24×C3—21no—
164C24×C3C2×D412yes—
165C24×C3#4112yes—
166C24×C3#4114yes—
167C24×C3C2411yescharacteristic
168C2×C3×Q8—28no—
169C2×C3×Q8—48no—
170C2×C3×Q8—44no—
171C2×C3×Q8—44no—
172C2×C3×Q8—48no—
173C2×C3×D4—28no—
174C2×C3×D4—48no—
175C2×C3×D4—48no—
176C2×C3×D4—44no—
177C2×C3×D4—44no—
178C22×C3×C4—22no—
179C22×C3×C4—22no—
180C22×C3×C4—21no—
181C22×C3×C4—22no—
182C22×C3×C4—22no—
183C22×C3×C4—22no—
184C22×C3×C4—22no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—22no—
188C22×C3×C4—22no—
189C22×C3×C4—21no—
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—22no—
200C22×C3×C4—28no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—22no—
204C22×C3×C4—22no—
205C22×C3×C4—21no—
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—21no—
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—21no—
223C22×C3×C4—22no—
224C22×C3×C4—22no—
225C22×C3×C4—44no—
226C22×C3×C4—44no—
227C22×C3×C4—48no—
228C22×C3×C4—48no—
229C22×C3×C4C2×D414yes—
230C22×C3×C4C2×D414yes—
231C22×C3×C4C2×D412yes—
232C22×C3×C4C2×D412yes—
233C22×C3×C4C2×D412yes—
234C22×C3×C4C2×D412yes—
235C22×C3×C4#4112yes—
236C3×C4⋊C4—216no—
237C3×C4⋊C4—28no—
238C3×C22⋊C4—216no—
239C3×C22⋊C4—48no—
240C3×C22⋊C4—44no—
241C3×C22⋊C4—48no—
242C3×C22⋊C4—48no—
243C3×C22⋊C4—44no—
244C3×C22⋊C4—44no—
245C25C23×C311yescharacteristic
246C25C23×C311yescharacteristic
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—42no—
250C22×Q8—42no—
251C22×Q8C3×D414yescomplemented
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—24no—
255C22×D4—22no—
256C22×D4—42no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—42no—
260C23×C4—42no—
261C23×C4C3×D414yes—
262C23×C4C23×C311yescharacteristic
263C23×C4C23×C312yes—
264C23×C4C23×C312yes—
265C23×C4C23×C311yescharacteristic
266C23×C4C23×C312yes—
267C23×C4C23×C312yes—
268C23×C4C23×C311yescharacteristic
269C23×C4C23×C311yescharacteristic
270C23×C4C23×C311yescharacteristic
271C22⋊Q8—232no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4C3×D414yescomplemented
278C2×C22⋊C4—24no—
279C2×C22⋊C4—24no—
280C2×C22⋊C4—24no—
281C2×C22⋊C4—22no—
282C2×C22⋊C4—24no—
283C2×C22⋊C4—24no—
284C2×C22⋊C4—24no—
285C2×C22⋊C4—22no—
286C2×C22⋊C4—22no—
287C2×C22⋊C4—24no—
288C2×C22⋊C4—22no—
289C2×C22⋊C4—24no—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—42no—
292C2×C22⋊C4—42no—
293C2×C22⋊C4—42no—
294C2×C22⋊C4—42no—
295C2×C22⋊C4—42no—
296C2×C22⋊C4—42no—
297#95—22no—
298#95—22no—
299#95—24no—
300#95—22no—
301#95—24no—
302#95—22no—
303#95—24no—
304#95—42no—
305#95—42no—
306#95—42no—
307#95—42no—
308C23×C3—22no—
309C23×C3—22no—
310C23×C3—22no—
311C23×C3—22no—
312C23×C3—22no—
313C23×C3—22no—
314C23×C3—24no—
315C23×C3—24no—
316C23×C3—24no—
317C23×C3—24no—
318C23×C3—24no—
319C23×C3—24no—
320C23×C3—22no—
321C23×C3—24no—
322C23×C3—22no—
323C23×C3—22no—
324C23×C3—24no—
325C23×C3—42no—
326C23×C3—42no—
327C23×C3—42no—
328C23×C3—42no—
329C23×C3—41no—
330C23×C3—41no—
331C23×C3—41no—
332C23×C3—41no—
333C23×C3—42no—
334C23×C3—42no—
335C23×C3—41no—
336C23×C3—41no—
337C23×C3—41no—
338C23×C3—42no—
339C23×C3—41no—
340C23×C3—42no—
341C23×C3—41no—
342C23×C3—41no—
343C23×C3—42no—
344C23×C3—42no—
345C23×C3—42no—
346C23×C3—41no—
347C23×C3—42no—
348C23×C3—42no—
349C23×C3—41no—
350C23×C3—42no—
351C23×C3—42no—
352C23×C3—42no—
353C23×C3#12414yes—
354C23×C3C22×D411yescharacteristic
355C23×C3C22×D411yescharacteristic
356C23×C3C22×D411yescharacteristic
357C23×C3C2×#4111yescharacteristic
358C23×C3C2×#4111yescharacteristic
359C23×C3C2×#4112yes—
360C23×C3H(5,𝔽2)12yes—
361C23×C3H(5,𝔽2)12yes—
362C23×C3H(5,𝔽2)11yescharacteristic
363C23×C32−1+412yes—
364C23×C32−1+411yescharacteristic
365C3×Q8—416no—
366C3×D4—416no—
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—22no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—24no—
377C2×C3×C4—22no—
378C2×C3×C4—24no—
379C2×C3×C4—24no—
380C2×C3×C4—24no—
381C2×C3×C4—24no—
382C2×C3×C4—416no—
383C2×C3×C4—42no—
384C2×C3×C4—41no—
385C2×C3×C4—42no—
386C2×C3×C4—41no—
387C2×C3×C4—42no—
388C2×C3×C4—42no—
389C2×C3×C4—42no—
390C2×C3×C4—42no—
391C2×C3×C4—42no—
392C2×C3×C4—42no—
393C2×C3×C4—42no—
394C2×C3×C4—42no—
395C2×C3×C4—42no—
396C2×C3×C4—41no—
397C2×C3×C4—41no—
398C2×C3×C4—41no—
399C2×C3×C4—41no—
400C2×C3×C4—42no—
401C2×C3×C4—42no—
402C2×C3×C4—41no—
403C2×C3×C4—41no—
404C2×C3×C4—42no—
405C2×C3×C4—42no—
406C2×C3×C4—42no—
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#12014yes—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—21no—
425C24—21no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—21no—
430C24—21no—
431C24—21no—
432C24—21no—
433C24—21no—
434C24—22no—
435C24—22no—
436C24—21no—
437C24—22no—
438C24—22no—
439C24—21no—
440C24C2×C3×D412yes—
441C24C3×#4112yes—
442C24C3×#4114yes—
443C24C24×C311yescharacteristic
444C2×Q8—28no—
445C2×Q8—48no—
446C2×Q8—44no—
447C2×Q8—44no—
448C2×Q8—48no—
449C2×D4—28no—
450C2×D4—48no—
451C2×D4—48no—
452C2×D4—44no—
453C2×D4—44no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—28no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—44no—
502C22×C4—44no—
503C22×C4—48no—
504C22×C4—48no—
505C22×C4C2×C3×D414yes—
506C22×C4C2×C3×D414yes—
507C22×C4C2×C3×D412yes—
508C22×C4C2×C3×D412yes—
509C22×C4C2×C3×D412yes—
510C22×C4C2×C3×D412yes—
511C22×C4C3×#4112yes—
512C4⋊C4—216no—
513C4⋊C4—28no—
514C22⋊C4—216no—
515C22⋊C4—48no—
516C22⋊C4—44no—
517C22⋊C4—48no—
518C22⋊C4—48no—
519C22⋊C4—44no—
520C22⋊C4—44no—
521C22×C3—24no—
522C22×C3—24no—
523C22×C3—24no—
524C22×C3—42no—
525C22×C3—42no—
526C22×C3—42no—
527C22×C3—44no—
528C22×C3—44no—
529C22×C3—44no—
530C22×C3—44no—
531C22×C3—42no—
532C22×C3—42no—
533C22×C3—42no—
534C22×C3—42no—
535C22×C3—44no—
536C22×C3—44no—
537C22×C3—81no—
538C22×C3—81no—
539C22×C3—81no—
540C22×C3—82no—
541C22×C3—82no—
542C22×C3—81no—
543C22×C3C2×#12011yescharacteristic
544C22×C3#52511yescharacteristic
545C22×C3C2×#12411yescharacteristic
546C22×C3#53411yescharacteristic
547C22×C3#53411yescharacteristic
548C22×C3#53412yes—
549C22×C3#53512yes—
550C22×C3#53611yescharacteristic
551C22×C3#53711yescharacteristic
552C22×C3#53812yes—
553C22×C3#53912yes—
554C22×C3#53912yes—
555C22×C3#54212yes—
556C22×C3#54611yescharacteristic
557C22×C3#54711yescharacteristic
558C22×C3#54811yescharacteristic
559C22×C3#54812yes—
560C22×C3#54812yes—
561C22×C3#55011yescharacteristic
562C22×C3#55112yes—
563C22×C3#55112yes—
564C22×C3#56212yes—
565C22×C3#56312yes—
566C3×C4—24no—
567C3×C4—42no—
568C3×C4—42no—
569C3×C4—44no—
570C3×C4—44no—
571C3×C4—81no—
572C3×C4—81no—
573C3×C4—82no—
574C3×C4—82no—
575C23—22no—
576C23—22no—
577C23—22no—
578C23—22no—
579C23—22no—
580C23—22no—
581C23—24no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—22no—
588C23—24no—
589C23—22no—
590C23—22no—
591C23—24no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—42no—
603C23—42no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—42no—
608C23—41no—
609C23—42no—
610C23—41no—
611C23—41no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—41no—
616C23—42no—
617C23—42no—
618C23—41no—
619C23—42no—
620C23C3×#12414yes—
621C23C22×C3×D411yescharacteristic
622C23C22×C3×D411yescharacteristic
623C23C22×C3×D411yescharacteristic
624C23C2×C3×#4111yescharacteristic
625C23C2×C3×#4111yescharacteristic
626C23C2×C3×#4112yes—
627C23C3×H(5,𝔽2)11yescharacteristic
628C23C3×H(5,𝔽2)12yes—
629C23C3×H(5,𝔽2)12yes—
630C23C3×2−1+412yes—
631C23C3×2−1+411yescharacteristic
632Q8—416no—
633D4—416no—
634C2×C4—22no—
635C2×C4—24no—
636C2×C4—22no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—24no—
644C2×C4—22no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—416no—
650C2×C4—42no—
651C2×C4—41no—
652C2×C4—42no—
653C2×C4—41no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4C3×#12014yes—
688C2×C3—44no—
689C2×C3—82no—
690C2×C3#240711yescharacteristic
691C2×C3#243611yescharacteristic
692C2×C3#256111yescharacteristic
693C2×C3#261311yescharacteristic
694C2×C3#263811yescharacteristic
695C2×C3#263911yescharacteristic
696C2×C3#269612yes—
697C2×C3#272312yes—
698C2×C3#272812yes—
699C2×C3#273012yes—
700C2×C3#281411yescharacteristic
701C22—24no—
702C22—24no—
703C22—24no—
704C22—42no—
705C22—42no—
706C22—44no—
707C22—44no—
708C22—44no—
709C22—44no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—44no—
715C22—44no—
716C22—42no—
717C22—81no—
718C22—81no—
719C22—82no—
720C22—82no—
721C22—81no—
722C22—81no—
723C22C2×C3×#12011yescharacteristic
724C22C3×#52511yescharacteristic
725C22C2×C3×#12411yescharacteristic
726C22C3×#53411yescharacteristic
727C22C3×#53412yes—
728C22C3×#53411yescharacteristic
729C22C3×#53512yes—
730C22C3×#53611yescharacteristic
731C22C3×#53711yescharacteristic
732C22C3×#53812yes—
733C22C3×#53912yes—
734C22C3×#53912yes—
735C22C3×#54212yes—
736C22C3×#54611yescharacteristic
737C22C3×#54711yescharacteristic
738C22C3×#54811yescharacteristic
739C22C3×#54812yes—
740C22C3×#54812yes—
741C22C3×#55011yescharacteristic
742C22C3×#55112yes—
743C22C3×#55112yes—
744C22C3×#56212yes—
745C22C3×#56312yes—
746C4—24no—
747C4—44no—
748C4—42no—
749C4—42no—
750C4—44no—
751C4—81no—
752C4—81no—
753C4—82no—
754C4—82no—
755C3#1663211yescharacteristic, direct product factor, Sylow
756C2—44no—
757C2—82no—
758C2C3×#240711yescharacteristic
759C2C3×#243611yescharacteristic
760C2C3×#256111yescharacteristic
761C2C3×#261311yescharacteristic
762C2C3×#263811yescharacteristic
763C2C3×#263911yescharacteristic
764C2C3×#269612yes—
765C2C3×#272312yes—
766C2C3×#272812yes—
767C2C3×#273012yes—
768C2C3×#281411yescharacteristic
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×#397C2semidirect
3. C2×C3×#393C2semidirect
5. C3×#1446C2semidirect
6. C3×#1445C2semidirect
7. C3×#1442C2semidirect
8. C3×#1440C2semidirect
9. C3×#1439C2semidirect
11. C3×C22⋊#95C2semidirect
12. #16632C3direct (N × H)
42. C22×C22⋊Q8C2×C3semidirect
43. C2×#397C2×C3semidirect
44. C2×#393C2×C3semidirect
46. #1446C2×C3semidirect
47. #1445C2×C3semidirect
48. #1442C2×C3semidirect
49. #1440C2×C3semidirect
50. #1439C2×C3semidirect
52. C22⋊#95C2×C3semidirect
59. C22×C3×Q8D4semidirect
85. C2×C3×C4⋊C4D4semidirect
251. C22×Q8C3×D4semidirect
277. C2×C4⋊C4C3×D4semidirect
755. C3#16632direct (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×#3972
C2×C3×#3932
C2×C3×#3862
C3×#14462
C3×#14452
C3×#14422
C3×#14402
C3×#14392
C3×#14382
C3×C22⋊#952
#166323