Finite Group Databasebeta

← C3×#24143 #10642750

Subgroups — C3×#24143 #10642750

Order 768.

1156 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3505C211yesmaximal, characteristic
2C3×#2627C211yesmaximal, characteristic, complemented
3C3×#2618C211yesmaximal, characteristic, complemented
4C3×#2322C211yesmaximal, characteristic, complemented
5C3×#2044C212yesmaximal, complemented
6C3×#2022C212yesmaximal, complemented
7C3×#1996C211yesmaximal, characteristic, complemented
8C3×#1964C211yesmaximal, characteristic, complemented
9C3×#1890C212yesmaximal, complemented
10C3×#1867C212yesmaximal, complemented
11C3×#1799C211yesmaximal, characteristic, complemented
12#24143C311yesmaximal, characteristic, direct product factor, Sylow
13C3×#553—22no—
14C3×#553—21no—
15C3×#552—21no—
16C3×#551—22no—
17C3×#548—21no—
18C3×#546—21no—
19C3×#539—21no—
20C3×#538—21no—
21C3×#534C2212yes—
22C3×#529—21no—
23C3×#525—21no—
24C2×C3×#123C2211yescharacteristic
25C2×C3×#123C2212yes—
26C2×C3×C22⋊Q8C2211yescharacteristic
27C2×C3×#121C2211yescharacteristic
28C3×#518C2212yes—
29C2×C3×C4×D4C2211yescharacteristic
30C22×C3×C4⋊C4C2211yescharacteristic
31C2×C3×#99C2212yes—
32C2×C3×#99C2212yes—
33C2×C3×#99C2212yes—
34C3×#400—21no—
35C3×#398—21no—
36C3×#398—22no—
37C3×#396—22no—
38C3×#395—21no—
39C3×#394—21no—
40C3×#389—21no—
41C3×#388—21no—
42C3×#387—21no—
43C3×#386C2212yes—
44C3×#386C2211yescharacteristic
45C3×#385—21no—
46C3×#385C2212yes—
47C3×#385C2211yescharacteristic
48C3×#381C2212yes—
49C3×#381C2211yescharacteristic
50C3×#380C2211yescharacteristic
51C3×#380C2211yescharacteristic
52C3×C4×C22⋊C4C2211yescharacteristic
53C3×#342C2212yes—
54C3×#342C2212yes—
55C3×#342C2212yes—
56#3505C2×C311yescharacteristic
57#2627C2×C311yescharacteristic, complemented
58#2618C2×C311yescharacteristic, complemented
59#2322C2×C311yescharacteristic, complemented
60#2044C2×C312yescomplemented
61#2022C2×C312yescomplemented
62#1996C2×C311yescharacteristic, complemented
63#1964C2×C311yescharacteristic, complemented
64#1890C2×C312yescomplemented
65#1867C2×C312yescomplemented
66#1799C2×C311yescharacteristic, complemented
67C2×C3×#41—21no—
68C22×C3×Q8D411yescharacteristic
69C22×C3×D4D411yescharacteristic
70C22×C3×D4C2311yescharacteristic
71C22×C3×D4C2312yes—
72C23×C3×C4D411yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C3×#126—22no—
77C3×#126—22no—
78C3×#126—22no—
79C3×#125—21no—
80C3×#125—22no—
81C3×#124—21no—
82C3×#124—22no—
83C3×#123—22no—
84C3×#123—22no—
85C3×#123—22no—
86C3×#123—22no—
87C3×#123—22no—
88C3×#123—22no—
89C3×#123—22no—
90C3×#123—24no—
91C3×#123—42no—
92C3×C22⋊Q8—21no—
93C3×C22⋊Q8—22no—
94C3×C22⋊Q8—21no—
95C3×C22⋊Q8—21no—
96C3×C22⋊Q8—21no—
97C3×C22⋊Q8—21no—
98C3×#121—21no—
99C3×#121—22no—
100C3×#121—21no—
101C3×#121—21no—
102C3×#121—21no—
103C3×#121—21no—
104C3×#121—22no—
105C3×#121—22no—
106C3×#120—22no—
107C3×#120—22no—
108C3×C4×Q8—21no—
109C3×C4×D4—22no—
110C3×C4×D4—21no—
111C3×C4×D4—21no—
112C3×C4×D4—21no—
113C3×C4×D4—21no—
114C3×C4×D4—21no—
115C3×C4×D4—22no—
116C3×C4×D4—22no—
117C3×C4×D4—22no—
118C3×C4×D4—22no—
119C3×#117—21no—
120C3×#117—22no—
121C3×#117—22no—
122C2×C3×C4⋊C4—21no—
123C2×C3×C4⋊C4—21no—
124C2×C3×C4⋊C4—21no—
125C2×C3×C4⋊C4—21no—
126C2×C3×C4⋊C4—21no—
127C2×C3×C4⋊C4—21no—
128C2×C3×C4⋊C4—22no—
129C2×C3×C4⋊C4—21no—
130C2×C3×C4⋊C4—21no—
131C2×C3×C4⋊C4—21no—
132C2×C3×C4⋊C4—21no—
133C2×C3×C4⋊C4—22no—
134C2×C3×C4⋊C4D411yescharacteristic
135C2×C3×C4⋊C4D411yescharacteristic
136C2×C3×C4⋊C4D412yes—
137C2×C3×C4⋊C4D411yescharacteristic
138C2×C3×C22⋊C4—21no—
139C2×C3×C22⋊C4—22no—
140C2×C3×C22⋊C4—22no—
141C2×C3×C22⋊C4—21no—
142C2×C3×C22⋊C4—22no—
143C2×C3×C22⋊C4D411yescharacteristic
144C2×C3×C22⋊C4D412yes—
145C2×C3×C22⋊C4C2311yescharacteristic
146C2×C3×C22⋊C4C2312yes—
147C2×C3×C22⋊C4C2312yes—
148C2×C3×C22⋊C4C2311yescharacteristic
149C2×C3×C22⋊C4C2312yes—
150C2×C3×C22⋊C4C2311yescharacteristic
151C2×C3×C42—21no—
152C2×C3×C42D411yescharacteristic
153C3×#99—24no—
154C3×#99—42no—
155C3×#99—42no—
156C3×#95—21no—
157C3×#95—21no—
158C3×#95—21no—
159C3×#95—21no—
160C3×#95—21no—
161C3×#95—22no—
162C3×#95—22no—
163C3×#95—21no—
164C3×#95—22no—
165C3×#95—21no—
166C3×#95—22no—
167#553—22no—
168#553—21no—
169#552—21no—
170#551—22no—
171#548—21no—
172#546—21no—
173#539—21no—
174#538—21no—
175#534C22×C312yes—
176#529—21no—
177#525—21no—
178C2×#123C22×C311yescharacteristic
179C2×#123C22×C312yes—
180C2×C22⋊Q8C22×C311yescharacteristic
181C2×#121C22×C311yescharacteristic
182#518C22×C312yes—
183C2×C4×D4C22×C311yescharacteristic
184C22×C4⋊C4C22×C311yescharacteristic
185C2×#99C22×C312yes—
186C2×#99C22×C312yes—
187C2×#99C22×C312yes—
188#400—21no—
189#398—21no—
190#398—22no—
191#396—22no—
192#395—21no—
193#394—21no—
194#389—21no—
195#388—21no—
196#387—21no—
197#386C22×C311yescharacteristic
198#386C22×C312yes—
199#385—21no—
200#385C22×C311yescharacteristic
201#385C22×C312yes—
202#381C22×C311yescharacteristic
203#381C22×C312yes—
204#380C22×C311yescharacteristic
205#380C22×C311yescharacteristic
206C4×C22⋊C4C22×C311yescharacteristic
207#342C22×C312yes—
208#342C22×C312yes—
209#342C22×C312yes—
210C24×C3C2×D412yes—
211C24×C3C2×D411yescharacteristic
212C24×C3C2411yescharacteristic
213C3×#41—82no—
214C2×C3×Q8—21no—
215C2×C3×Q8—21no—
216C2×C3×Q8—81no—
217C2×C3×D4—21no—
218C2×C3×D4—22no—
219C2×C3×D4—21no—
220C2×C3×D4—22no—
221C2×C3×D4—22no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—22no—
225C2×C3×D4—21no—
226C2×C3×D4—22no—
227C2×C3×D4—21no—
228C2×C3×D4—22no—
229C2×C3×D4—22no—
230C2×C3×D4—22no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—81no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—22no—
242C22×C3×C4—22no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—22no—
247C22×C3×C4—22no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—81no—
252C22×C3×C4—81no—
253C22×C3×C4—81no—
254C22×C3×C4C2×D411yescharacteristic
255C22×C3×C4C2×D412yes—
256C22×C3×C4C2×D411yescharacteristic
257C22×C3×C4C2×D412yes—
258C22×C3×C4C2×D411yescharacteristic
259C22×C3×C4C2×D412yes—
260C22×C3×C4C2×D411yescharacteristic
261C22×C3×C4C2×D411yescharacteristic
262C22×C3×C4C2×D411yescharacteristic
263C22×C3×C4C2×D411yescharacteristic
264C22×C3×C4C2×D411yescharacteristic
265C22×C3×C4C2×D411yescharacteristic
266C22×C3×C4#4112yescomplemented
267C3×C4⋊C4—24no—
268C3×C4⋊C4—22no—
269C3×C4⋊C4—22no—
270C3×C4⋊C4—22no—
271C3×C4⋊C4—22no—
272C3×C4⋊C4—21no—
273C3×C4⋊C4—22no—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—21no—
277C3×C4⋊C4—21no—
278C3×C4⋊C4—22no—
279C3×C4⋊C4—21no—
280C3×C4⋊C4—44no—
281C3×C4⋊C4—41no—
282C3×C4⋊C4—41no—
283C3×C4⋊C4—41no—
284C3×C4⋊C4—41no—
285C3×C4⋊C4—81no—
286C3×C4⋊C4—81no—
287C3×C4⋊C4—81no—
288C3×C4⋊C4—82no—
289C3×C22⋊C4—22no—
290C3×C22⋊C4—22no—
291C3×C22⋊C4—24no—
292C3×C22⋊C4—22no—
293C3×C22⋊C4—22no—
294C3×C22⋊C4—22no—
295C3×C22⋊C4—22no—
296C3×C22⋊C4—21no—
297C3×C22⋊C4—22no—
298C3×C22⋊C4—21no—
299C3×C22⋊C4—22no—
300C3×C22⋊C4—21no—
301C3×C22⋊C4—22no—
302C3×C22⋊C4—21no—
303C3×C22⋊C4—21no—
304C3×C22⋊C4—22no—
305C3×C22⋊C4—22no—
306C3×C22⋊C4—22no—
307C3×C22⋊C4—21no—
308C3×C22⋊C4—22no—
309C3×C22⋊C4—22no—
310C3×C22⋊C4—21no—
311C3×C22⋊C4—44no—
312C3×C22⋊C4—81no—
313C3×C22⋊C4—82no—
314C3×C22⋊C4#4112yescomplemented
315C3×C42—22no—
316C3×C42—22no—
317C3×C42—21no—
318C3×C42—21no—
319C3×C42—81no—
320C2×#41—21no—
321C22×Q8C3×D411yescharacteristic
322C22×D4C3×D411yescharacteristic
323C22×D4C23×C311yescharacteristic
324C22×D4C23×C312yes—
325C23×C4C3×D411yescharacteristic
326C23×C4C23×C311yescharacteristic
327C23×C4C23×C311yescharacteristic
328C23×C4C23×C311yescharacteristic
329#126—22no—
330#126—22no—
331#126—22no—
332#125—21no—
333#125—22no—
334#124—21no—
335#124—22no—
336#123—22no—
337#123—22no—
338#123—22no—
339#123—22no—
340#123—22no—
341#123—22no—
342#123—22no—
343#123—24no—
344#123—42no—
345C22⋊Q8—21no—
346C22⋊Q8—22no—
347C22⋊Q8—21no—
348C22⋊Q8—21no—
349C22⋊Q8—21no—
350C22⋊Q8—21no—
351#121—21no—
352#121—22no—
353#121—21no—
354#121—21no—
355#121—21no—
356#121—21no—
357#121—22no—
358#121—22no—
359#120—22no—
360#120—22no—
361C4×Q8—21no—
362C4×D4—22no—
363C4×D4—21no—
364C4×D4—21no—
365C4×D4—21no—
366C4×D4—21no—
367C4×D4—21no—
368C4×D4—22no—
369C4×D4—22no—
370C4×D4—22no—
371C4×D4—22no—
372#117—21no—
373#117—22no—
374#117—22no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4C3×D411yescharacteristic
388C2×C4⋊C4C3×D411yescharacteristic
389C2×C4⋊C4C3×D412yes—
390C2×C4⋊C4C3×D411yescharacteristic
391C2×C22⋊C4—22no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4C3×D411yescharacteristic
397C2×C22⋊C4C3×D412yes—
398C2×C22⋊C4C23×C312yes—
399C2×C22⋊C4C23×C311yescharacteristic
400C2×C22⋊C4C23×C312yes—
401C2×C22⋊C4C23×C311yescharacteristic
402C2×C22⋊C4C23×C312yes—
403C2×C22⋊C4C23×C311yescharacteristic
404C2×C42—21no—
405C2×C42C3×D411yescharacteristic
406#99—24no—
407#99—42no—
408#99—42no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—22no—
415#95—22no—
416#95—21no—
417#95—22no—
418#95—21no—
419#95—22no—
420C23×C3—21no—
421C23×C3—22no—
422C23×C3—21no—
423C23×C3—21no—
424C23×C3—22no—
425C23×C3—22no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3—41no—
430C23×C3—42no—
431C23×C3—42no—
432C23×C3C22×D411yescharacteristic
433C23×C3C22×D411yescharacteristic
434C23×C3C22×D411yescharacteristic
435C23×C3C2×#4111yescharacteristic
436C23×C3C2×#4111yescharacteristic
437C23×C3H(5,𝔽2)11yescharacteristic
438C23×C32−1+411yescharacteristic
439C3×Q8—42no—
440C3×Q8—81no—
441C3×D4—42no—
442C3×D4—42no—
443C3×D4—42no—
444C3×D4—41no—
445C3×D4—41no—
446C3×D4—41no—
447C3×D4—42no—
448C3×D4—42no—
449C3×D4—41no—
450C3×D4—81no—
451C3×D4—82no—
452C3×D4—82no—
453C2×C3×C4—21no—
454C2×C3×C4—22no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—42no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4—42no—
482C2×C3×C4—41no—
483C2×C3×C4—42no—
484C2×C3×C4—41no—
485C2×C3×C4—42no—
486C2×C3×C4—41no—
487C2×C3×C4—42no—
488C2×C3×C4—42no—
489C2×C3×C4—42no—
490C2×C3×C4—41no—
491C2×C3×C4—42no—
492C2×C3×C4—41no—
493C2×C3×C4—42no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—42no—
497C2×C3×C4—42no—
498C2×C3×C4—81no—
499C2×C3×C4—82no—
500C2×C3×C4—82no—
501C2×C3×C4#12011yescharacteristic
502C2×C3×C4#12011yescharacteristic
503C2×C3×C4#12011yescharacteristic
504C2×C3×C4#12011yescharacteristic
505C24C2×C3×D412yes—
506C24C2×C3×D411yescharacteristic
507C24C24×C311yescharacteristic
508#41—82no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—81no—
512C2×D4—21no—
513C2×D4—22no—
514C2×D4—21no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—22no—
520C2×D4—21no—
521C2×D4—22no—
522C2×D4—21no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—22no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—81no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—81no—
547C22×C4—81no—
548C22×C4—81no—
549C22×C4C2×C3×D411yescharacteristic
550C22×C4C2×C3×D412yes—
551C22×C4C2×C3×D411yescharacteristic
552C22×C4C2×C3×D412yes—
553C22×C4C2×C3×D411yescharacteristic
554C22×C4C2×C3×D412yes—
555C22×C4C2×C3×D411yescharacteristic
556C22×C4C2×C3×D411yescharacteristic
557C22×C4C2×C3×D411yescharacteristic
558C22×C4C2×C3×D411yescharacteristic
559C22×C4C2×C3×D411yescharacteristic
560C22×C4C2×C3×D411yescharacteristic
561C22×C4C3×#4112yescomplemented
562C4⋊C4—24no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—21no—
568C4⋊C4—22no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—22no—
574C4⋊C4—21no—
575C4⋊C4—44no—
576C4⋊C4—41no—
577C4⋊C4—41no—
578C4⋊C4—41no—
579C4⋊C4—41no—
580C4⋊C4—81no—
581C4⋊C4—81no—
582C4⋊C4—81no—
583C4⋊C4—82no—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—24no—
587C22⋊C4—22no—
588C22⋊C4—22no—
589C22⋊C4—22no—
590C22⋊C4—22no—
591C22⋊C4—21no—
592C22⋊C4—22no—
593C22⋊C4—21no—
594C22⋊C4—22no—
595C22⋊C4—21no—
596C22⋊C4—22no—
597C22⋊C4—21no—
598C22⋊C4—21no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—21no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—21no—
606C22⋊C4—44no—
607C22⋊C4—81no—
608C22⋊C4—82no—
609C22⋊C4C3×#4112yescomplemented
610C42—22no—
611C42—22no—
612C42—21no—
613C42—21no—
614C42—81no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—42no—
626C22×C3—41no—
627C22×C3—42no—
628C22×C3—41no—
629C22×C3—42no—
630C22×C3—42no—
631C22×C3—41no—
632C22×C3—82no—
633C22×C3—81no—
634C22×C3—82no—
635C22×C3C2×#12011yescharacteristic
636C22×C3#52511yescharacteristic
637C22×C3#53711yescharacteristic
638C22×C3#54611yescharacteristic
639C22×C3#54711yescharacteristic
640C22×C3#54811yescharacteristic
641C22×C3#55011yescharacteristic
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—21no—
645C3×C4—21no—
646C3×C4—42no—
647C3×C4—42no—
648C3×C4—41no—
649C3×C4—42no—
650C3×C4—41no—
651C3×C4—42no—
652C3×C4—41no—
653C3×C4—42no—
654C3×C4—82no—
655C3×C4—82no—
656C3×C4—81no—
657C3×C4—81no—
658C23—21no—
659C23—22no—
660C23—21no—
661C23—21no—
662C23—22no—
663C23—22no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—42no—
669C23—42no—
670C23C22×C3×D411yescharacteristic
671C23C22×C3×D411yescharacteristic
672C23C22×C3×D411yescharacteristic
673C23C2×C3×#4111yescharacteristic
674C23C2×C3×#4111yescharacteristic
675C23C3×H(5,𝔽2)11yescharacteristic
676C23C3×2−1+411yescharacteristic
677Q8—42no—
678Q8—81no—
679D4—42no—
680D4—42no—
681D4—42no—
682D4—41no—
683D4—41no—
684D4—41no—
685D4—42no—
686D4—42no—
687D4—41no—
688D4—81no—
689D4—82no—
690D4—82no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—81no—
737C2×C4—82no—
738C2×C4—82no—
739C2×C4C3×#12011yescharacteristic
740C2×C4C3×#12011yescharacteristic
741C2×C4C3×#12011yescharacteristic
742C2×C4C3×#12011yescharacteristic
743C2×C3—21no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—81no—
750C2×C3—82no—
751C2×C3#240711yescharacteristic
752C2×C3#302611yescharacteristic
753C2×C3#302811yescharacteristic
754C22—21no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—21no—
759C22—21no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—42no—
765C22—41no—
766C22—42no—
767C22—41no—
768C22—42no—
769C22—42no—
770C22—41no—
771C22—82no—
772C22—81no—
773C22—82no—
774C22C2×C3×#12011yescharacteristic
775C22C3×#52511yescharacteristic
776C22C3×#53711yescharacteristic
777C22C3×#54611yescharacteristic
778C22C3×#54711yescharacteristic
779C22C3×#54811yescharacteristic
780C22C3×#55011yescharacteristic
781C4—21no—
782C4—21no—
783C4—21no—
784C4—21no—
785C4—42no—
786C4—42no—
787C4—41no—
788C4—42no—
789C4—41no—
790C4—42no—
791C4—41no—
792C4—42no—
793C4—82no—
794C4—82no—
795C4—81no—
796C4—81no—
797C3#2414311yescharacteristic, direct product factor, Sylow
798C2—21no—
799C2—21no—
800C2—21no—
801C2—21no—
802C2—21no—
803C2—21no—
804C2—81no—
805C2—82no—
806C2C3×#240711yescharacteristic
807C2C3×#302611yescharacteristic
808C2C3×#302811yescharacteristic
subgroupG/H
center, socleC22×C3C2×#120
commutator, Frattini, cosocleC24C24×C3
prime radicalC3×#3505C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C3×#2627C2semidirect
3. C3×#2618C2semidirect
4. C3×#2322C2semidirect
5. C3×#2044C2semidirect
6. C3×#2022C2semidirect
7. C3×#1996C2semidirect
8. C3×#1964C2semidirect
9. C3×#1890C2semidirect
10. C3×#1867C2semidirect
11. C3×#1799C2semidirect
12. #24143C3direct (N × H)
57. #2627C2×C3semidirect
58. #2618C2×C3semidirect
59. #2322C2×C3semidirect
60. #2044C2×C3semidirect
61. #2022C2×C3semidirect
62. #1996C2×C3semidirect
63. #1964C2×C3semidirect
64. #1890C2×C3semidirect
65. #1867C2×C3semidirect
66. #1799C2×C3semidirect
266. C22×C3×C4#41semidirect
314. C3×C22⋊C4#41semidirect
561. C22×C4C3×#41semidirect
609. C22⋊C4C3×#41semidirect
797. C3#24143direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#35052
C3×#26272
C3×#26182
C3×#23222
C3×#20442
C3×#20222
C3×#19962
C3×#19642
C3×#18902
C3×#18672
C3×#17992
#241433