Finite Group Databasebeta

← C3×#25585 #10644192

Subgroups — C3×#25585 #10644192

Order 768.

1636 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3505C211yesmaximal, characteristic, complemented
2C3×#2435C211yesmaximal, characteristic, complemented
3C3×#2433C211yesmaximal, characteristic, complemented
4C3×#2408C211yesmaximal, characteristic, complemented
5C3×#2021C214yesmaximal, complemented
6C3×#1996C211yesmaximal, characteristic, complemented
7C3×#1964C211yesmaximal, characteristic, complemented
8C3×#1889C214yesmaximal, complemented
9C3×C4×#99C211yesmaximal, characteristic, complemented
10#25585C311yesmaximal, characteristic, direct product factor, Sylow
11C23×C3×D4C2211yescharacteristic
12C3×#553—21no—
13C3×#553—22no—
14C3×#552—21no—
15C3×#551—22no—
16C3×#548—21no—
17C3×#546—21no—
18C3×#539—21no—
19C3×#538—21no—
20C3×#534C2212yes—
21C2×C3×#127—21no—
22C3×#529—21no—
23C2×C3×#124—21no—
24C3×#525—21no—
25C2×C3×C22⋊Q8C2211yescharacteristic
26C2×C3×#121—21no—
27C2×C3×#121C2211yescharacteristic
28C2×C3×#120C2214yes—
29C2×C3×#120C2212yes—
30C3×#518C2212yes—
31C2×C3×C4×D4C2211yescharacteristic
32C2×C3×#99C2212yes—
33C2×C3×#99C2214yes—
34C3×#394—21no—
35C3×#394—22no—
36C3×#392—21no—
37C3×#392—22no—
38C3×#390—21no—
39C3×#390—21no—
40C3×#390—21no—
41C3×#380C2211yescharacteristic
42C3×#379C2214yes—
43C3×#379C2212yes—
44C3×C4×C22⋊C4C2211yescharacteristic
45C3×C4×C22⋊C4C2211yescharacteristic
46C3×#342C2214yes—
47C3×#342C2212yes—
48#3505C2×C311yescharacteristic, complemented
49#2435C2×C311yescharacteristic, complemented
50#2433C2×C311yescharacteristic, complemented
51#2408C2×C311yescharacteristic, complemented
52#2021C2×C314yescomplemented
53#1996C2×C311yescharacteristic, complemented
54#1964C2×C311yescharacteristic, complemented
55#1889C2×C314yescomplemented
56C4×#99C2×C311yescharacteristic, complemented
57C25×C3C2312yes—
58C2×C3×#41—21no—
59C22×C3×Q8D411yescharacteristic, complemented
60C22×C3×D4—22no—
61C22×C3×D4—24no—
62C22×C3×D4—21no—
63C22×C3×D4—21no—
64C22×C3×D4—21no—
65C22×C3×D4—21no—
66C22×C3×D4—21no—
67C22×C3×D4—21no—
68C22×C3×D4—44no—
69C22×C3×D4D411yescharacteristic, complemented
70C22×C3×D4C2311yescharacteristic
71C22×C3×D4C2312yes—
72C23×C3×C4D411yescharacteristic, complemented
73C23×C3×C4C2311yescharacteristic
74C3×#127—44no—
75C3×#126—22no—
76C3×#126—22no—
77C3×#126—22no—
78C3×#125—21no—
79C3×#125—22no—
80C3×#124—21no—
81C3×#124—22no—
82C3×#124—44no—
83C3×#123—22no—
84C3×#123—22no—
85C3×#123—22no—
86C3×#123—22no—
87C3×#123—22no—
88C3×C22⋊Q8—21no—
89C3×C22⋊Q8—22no—
90C3×C22⋊Q8—21no—
91C3×C22⋊Q8—21no—
92C3×C22⋊Q8—21no—
93C3×C22⋊Q8—21no—
94C3×#121—21no—
95C3×#121—22no—
96C3×#121—21no—
97C3×#121—21no—
98C3×#121—21no—
99C3×#121—21no—
100C3×#121—22no—
101C3×#121—22no—
102C3×#121—44no—
103C3×#120—22no—
104C3×#120—22no—
105C3×#120—28no—
106C3×#120—44no—
107C3×#120—44no—
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⋊C4D411yescharacteristic, complemented
124C2×C3×C4⋊C4D411yescharacteristic, complemented
125C2×C3×C4⋊C4D411yescharacteristic, complemented
126C2×C3×C4⋊C4D412yescomplemented
127C2×C3×C22⋊C4—22no—
128C2×C3×C22⋊C4—22no—
129C2×C3×C22⋊C4—24no—
130C2×C3×C22⋊C4—24no—
131C2×C3×C22⋊C4—22no—
132C2×C3×C22⋊C4—22no—
133C2×C3×C22⋊C4—24no—
134C2×C3×C22⋊C4D411yescharacteristic, complemented
135C2×C3×C22⋊C4D412yescomplemented
136C2×C3×C22⋊C4C2312yes—
137C2×C3×C22⋊C4C2312yes—
138C2×C3×C22⋊C4C2311yescharacteristic
139C2×C3×C22⋊C4C2312yes—
140C2×C3×C22⋊C4C2312yes—
141C2×C3×C42—21no—
142C2×C3×C42—21no—
143C2×C3×C42D411yescharacteristic, complemented
144C3×#99—24no—
145C3×#99—44no—
146C3×#95—21no—
147C3×#95—21no—
148C3×#95—21no—
149C23×D4C22×C311yescharacteristic
150#553—21no—
151#553—22no—
152#552—21no—
153#551—22no—
154#548—21no—
155#546—21no—
156#539—21no—
157#538—21no—
158#534C22×C312yes—
159C2×#127—21no—
160#529—21no—
161C2×#124—21no—
162#525—21no—
163C2×C22⋊Q8C22×C311yescharacteristic
164C2×#121—21no—
165C2×#121C22×C311yescharacteristic
166C2×#120C22×C314yes—
167C2×#120C22×C312yes—
168#518C22×C312yes—
169C2×C4×D4C22×C311yescharacteristic
170C2×#99C22×C312yes—
171C2×#99C22×C314yes—
172#394—21no—
173#394—22no—
174#392—21no—
175#392—22no—
176#390—21no—
177#390—21no—
178#390—21no—
179#380C22×C311yescharacteristic
180#379C22×C312yes—
181#379C22×C314yes—
182C4×C22⋊C4C22×C311yescharacteristic
183C4×C22⋊C4C22×C311yescharacteristic
184#342C22×C312yes—
185#342C22×C314yes—
186C24×C3—22no—
187C24×C3—22no—
188C24×C3—22no—
189C24×C3—24no—
190C24×C3—24no—
191C24×C3—44no—
192C24×C3—82no—
193C24×C3C2×D412yes—
194C24×C3C2×D411yescharacteristic
195C24×C3C2411yescharacteristic
196C3×#41—82no—
197C2×C3×Q8—21no—
198C2×C3×Q8—21no—
199C2×C3×Q8—42no—
200C2×C3×D4—24no—
201C2×C3×D4—24no—
202C2×C3×D4—24no—
203C2×C3×D4—21no—
204C2×C3×D4—22no—
205C2×C3×D4—21no—
206C2×C3×D4—22no—
207C2×C3×D4—22no—
208C2×C3×D4—24no—
209C2×C3×D4—24no—
210C2×C3×D4—22no—
211C2×C3×D4—22no—
212C2×C3×D4—22no—
213C2×C3×D4—21no—
214C2×C3×D4—21no—
215C2×C3×D4—42no—
216C2×C3×D4—42no—
217C2×C3×D4—42no—
218C2×C3×D4—42no—
219C2×C3×D4—48no—
220C2×C3×D4—44no—
221C2×C3×D4—44no—
222C2×C3×D4—44no—
223C2×C3×D4—44no—
224C2×C3×D4—44no—
225C2×C3×D4—48no—
226C2×C3×D4—41no—
227C2×C3×D4—41no—
228C2×C3×D4—41no—
229C2×C3×D4—41no—
230C2×C3×D4—84no—
231C2×C3×D4—82no—
232C22×C3×C4—22no—
233C22×C3×C4—22no—
234C22×C3×C4—22no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—22no—
238C22×C3×C4—22no—
239C22×C3×C4—42no—
240C22×C3×C4—42no—
241C22×C3×C4C2×D411yescharacteristic
242C22×C3×C4C2×D412yes—
243C22×C3×C4C2×D411yescharacteristic
244C22×C3×C4C2×D411yescharacteristic
245C22×C3×C4C2×D411yescharacteristic
246C22×C3×C4C2×D411yescharacteristic
247C22×C3×C4C2×D412yes—
248C22×C3×C4C2×D411yescharacteristic
249C22×C3×C4C2×D412yes—
250C22×C3×C4C2×D411yescharacteristic
251C22×C3×C4C2×D411yescharacteristic
252C22×C3×C4C2×D411yescharacteristic
253C3×C4⋊C4—22no—
254C3×C4⋊C4—22no—
255C3×C4⋊C4—22no—
256C3×C4⋊C4—22no—
257C3×C4⋊C4—21no—
258C3×C4⋊C4—22no—
259C3×C4⋊C4—21no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—21no—
263C3×C4⋊C4—22no—
264C3×C4⋊C4—21no—
265C3×C4⋊C4—42no—
266C3×C22⋊C4—22no—
267C3×C22⋊C4—22no—
268C3×C22⋊C4—22no—
269C3×C22⋊C4—22no—
270C3×C22⋊C4—22no—
271C3×C22⋊C4—22no—
272C3×C22⋊C4—21no—
273C3×C22⋊C4—22no—
274C3×C22⋊C4—21no—
275C3×C22⋊C4—22no—
276C3×C22⋊C4—22no—
277C3×C22⋊C4—22no—
278C3×C22⋊C4—21no—
279C3×C22⋊C4—21no—
280C3×C22⋊C4—22no—
281C3×C22⋊C4—22no—
282C3×C22⋊C4—22no—
283C3×C22⋊C4—24no—
284C3×C22⋊C4—48no—
285C3×C22⋊C4—44no—
286C3×C22⋊C4—44no—
287C3×C22⋊C4—48no—
288C3×C22⋊C4—84no—
289C3×C22⋊C4—82no—
290C3×C22⋊C4#4114yescomplemented
291C3×C42—22no—
292C3×C42—22no—
293C3×C42—21no—
294C3×C42—21no—
295C3×C42—42no—
296C3×C42—42no—
297C25C23×C312yes—
298C2×#41—21no—
299C22×Q8C3×D411yescharacteristic, complemented
300C22×D4—22no—
301C22×D4—24no—
302C22×D4—21no—
303C22×D4—21no—
304C22×D4—21no—
305C22×D4—21no—
306C22×D4—21no—
307C22×D4—21no—
308C22×D4—44no—
309C22×D4C3×D411yescharacteristic, complemented
310C22×D4C23×C311yescharacteristic
311C22×D4C23×C312yes—
312C23×C4C3×D411yescharacteristic, complemented
313C23×C4C23×C311yescharacteristic
314#127—44no—
315#126—22no—
316#126—22no—
317#126—22no—
318#125—21no—
319#125—22no—
320#124—21no—
321#124—22no—
322#124—44no—
323#123—22no—
324#123—22no—
325#123—22no—
326#123—22no—
327#123—22no—
328C22⋊Q8—21no—
329C22⋊Q8—22no—
330C22⋊Q8—21no—
331C22⋊Q8—21no—
332C22⋊Q8—21no—
333C22⋊Q8—21no—
334#121—21no—
335#121—22no—
336#121—21no—
337#121—21no—
338#121—21no—
339#121—21no—
340#121—22no—
341#121—22no—
342#121—44no—
343#120—22no—
344#120—22no—
345#120—28no—
346#120—44no—
347#120—44no—
348C4×Q8—21no—
349C4×D4—22no—
350C4×D4—21no—
351C4×D4—21no—
352C4×D4—21no—
353C4×D4—21no—
354C4×D4—21no—
355C4×D4—22no—
356C4×D4—22no—
357C4×D4—22no—
358C4×D4—22no—
359#117—21no—
360#117—22no—
361#117—22no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4C3×D411yescharacteristic, complemented
364C2×C4⋊C4C3×D411yescharacteristic, complemented
365C2×C4⋊C4C3×D411yescharacteristic, complemented
366C2×C4⋊C4C3×D412yescomplemented
367C2×C22⋊C4—22no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4C3×D411yescharacteristic, complemented
375C2×C22⋊C4C3×D412yescomplemented
376C2×C22⋊C4C23×C312yes—
377C2×C22⋊C4C23×C312yes—
378C2×C22⋊C4C23×C311yescharacteristic
379C2×C22⋊C4C23×C312yes—
380C2×C22⋊C4C23×C312yes—
381C2×C42—21no—
382C2×C42—21no—
383C2×C42C3×D411yescharacteristic, complemented
384#99—24no—
385#99—44no—
386#95—21no—
387#95—21no—
388#95—21no—
389C23×C3—24no—
390C23×C3—24no—
391C23×C3—24no—
392C23×C3—21no—
393C23×C3—22no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—24no—
397C23×C3—41no—
398C23×C3—41no—
399C23×C3—41no—
400C23×C3—41no—
401C23×C3—44no—
402C23×C3—42no—
403C23×C3—42no—
404C23×C3—42no—
405C23×C3—42no—
406C23×C3—42no—
407C23×C3—44no—
408C23×C3—42no—
409C23×C3—42no—
410C23×C3—42no—
411C23×C3—42no—
412C23×C3—42no—
413C23×C3—44no—
414C23×C3—44no—
415C23×C3—88no—
416C23×C3—88no—
417C23×C3C22×D411yescharacteristic
418C23×C3C22×D411yescharacteristic
419C23×C3C22×D411yescharacteristic
420C23×C3C2×#4112yes—
421C23×C3H(5,𝔽2)12yes—
422C3×Q8—42no—
423C3×Q8—81no—
424C3×D4—44no—
425C3×D4—44no—
426C3×D4—44no—
427C3×D4—42no—
428C3×D4—42no—
429C3×D4—42no—
430C3×D4—42no—
431C3×D4—44no—
432C3×D4—44no—
433C3×D4—42no—
434C3×D4—81no—
435C3×D4—82no—
436C3×D4—82no—
437C3×D4—816no—
438C3×D4—88no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4—21no—
443C2×C3×C4—22no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—24no—
451C2×C3×C4—24no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—42no—
456C2×C3×C4—42no—
457C2×C3×C4—42no—
458C2×C3×C4—41no—
459C2×C3×C4—42no—
460C2×C3×C4—41no—
461C2×C3×C4—42no—
462C2×C3×C4—42no—
463C2×C3×C4—42no—
464C2×C3×C4—42no—
465C2×C3×C4—42no—
466C2×C3×C4—42no—
467C2×C3×C4—42no—
468C2×C3×C4—81no—
469C2×C3×C4—82no—
470C2×C3×C4—82no—
471C2×C3×C4#12011yescharacteristic
472C2×C3×C4#12011yescharacteristic
473C2×C3×C4#12011yescharacteristic
474C2×C3×C4#12011yescharacteristic
475C24—22no—
476C24—22no—
477C24—22no—
478C24—24no—
479C24—24no—
480C24—44no—
481C24—82no—
482C24C2×C3×D412yes—
483C24C2×C3×D411yescharacteristic
484C24C24×C311yescharacteristic
485#41—82no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—42no—
489C2×D4—24no—
490C2×D4—24no—
491C2×D4—24no—
492C2×D4—21no—
493C2×D4—22no—
494C2×D4—21no—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—24no—
498C2×D4—24no—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—42no—
508C2×D4—48no—
509C2×D4—44no—
510C2×D4—44no—
511C2×D4—44no—
512C2×D4—44no—
513C2×D4—44no—
514C2×D4—48no—
515C2×D4—41no—
516C2×D4—41no—
517C2×D4—41no—
518C2×D4—41no—
519C2×D4—84no—
520C2×D4—82no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4C2×C3×D411yescharacteristic
531C22×C4C2×C3×D412yes—
532C22×C4C2×C3×D411yescharacteristic
533C22×C4C2×C3×D411yescharacteristic
534C22×C4C2×C3×D411yescharacteristic
535C22×C4C2×C3×D411yescharacteristic
536C22×C4C2×C3×D412yes—
537C22×C4C2×C3×D411yescharacteristic
538C22×C4C2×C3×D412yes—
539C22×C4C2×C3×D411yescharacteristic
540C22×C4C2×C3×D411yescharacteristic
541C22×C4C2×C3×D411yescharacteristic
542C4⋊C4—22no—
543C4⋊C4—22no—
544C4⋊C4—22no—
545C4⋊C4—22no—
546C4⋊C4—21no—
547C4⋊C4—22no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—22no—
553C4⋊C4—21no—
554C4⋊C4—42no—
555C22⋊C4—22no—
556C22⋊C4—22no—
557C22⋊C4—22no—
558C22⋊C4—22no—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—21no—
562C22⋊C4—22no—
563C22⋊C4—21no—
564C22⋊C4—22no—
565C22⋊C4—22no—
566C22⋊C4—22no—
567C22⋊C4—21no—
568C22⋊C4—21no—
569C22⋊C4—22no—
570C22⋊C4—22no—
571C22⋊C4—22no—
572C22⋊C4—24no—
573C22⋊C4—48no—
574C22⋊C4—44no—
575C22⋊C4—44no—
576C22⋊C4—48no—
577C22⋊C4—84no—
578C22⋊C4—82no—
579C22⋊C4C3×#4114yescomplemented
580C42—22no—
581C42—22no—
582C42—21no—
583C42—21no—
584C42—42no—
585C42—42no—
586C22×C3—21no—
587C22×C3—21no—
588C22×C3—21no—
589C22×C3—21no—
590C22×C3—21no—
591C22×C3—21no—
592C22×C3—42no—
593C22×C3—42no—
594C22×C3—42no—
595C22×C3—48no—
596C22×C3—44no—
597C22×C3—48no—
598C22×C3—44no—
599C22×C3—41no—
600C22×C3—42no—
601C22×C3—41no—
602C22×C3—42no—
603C22×C3—44no—
604C22×C3—42no—
605C22×C3—41no—
606C22×C3—84no—
607C22×C3—81no—
608C22×C3—84no—
609C22×C3—82no—
610C22×C3—84no—
611C22×C3—82no—
612C22×C3—82no—
613C22×C3—82no—
614C22×C3C2×#12011yescharacteristic
615C22×C3#53211yescharacteristic
616C22×C3#53511yescharacteristic
617C22×C3#54612yes—
618C22×C3#55012yes—
619C3×C4—21no—
620C3×C4—21no—
621C3×C4—21no—
622C3×C4—44no—
623C3×C4—41no—
624C3×C4—42no—
625C3×C4—41no—
626C3×C4—42no—
627C3×C4—41no—
628C3×C4—42no—
629C3×C4—82no—
630C3×C4—82no—
631C3×C4B(4,𝔽2)12yes—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—21no—
636C23—22no—
637C23—21no—
638C23—21no—
639C23—24no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—44no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—44no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—44no—
657C23—44no—
658C23—88no—
659C23—88no—
660C23C22×C3×D411yescharacteristic
661C23C22×C3×D411yescharacteristic
662C23C22×C3×D411yescharacteristic
663C23C2×C3×#4112yes—
664C23C3×H(5,𝔽2)12yes—
665Q8—42no—
666Q8—81no—
667D4—44no—
668D4—44no—
669D4—44no—
670D4—42no—
671D4—42no—
672D4—42no—
673D4—42no—
674D4—44no—
675D4—44no—
676D4—42no—
677D4—81no—
678D4—82no—
679D4—82no—
680D4—816no—
681D4—88no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—41no—
702C2×C4—42no—
703C2×C4—41no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—81no—
712C2×C4—82no—
713C2×C4—82no—
714C2×C4C3×#12011yescharacteristic
715C2×C4C3×#12011yescharacteristic
716C2×C4C3×#12011yescharacteristic
717C2×C4C3×#12011yescharacteristic
718C2×C3—22no—
719C2×C3—21no—
720C2×C3—22no—
721C2×C3—21no—
722C2×C3—84no—
723C2×C3—81no—
724C2×C3—82no—
725C2×C3#243111yescharacteristic
726C2×C3C2×B(4,𝔽2)11yescharacteristic
727C2×C3#302711yescharacteristic
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—48no—
738C22—44no—
739C22—48no—
740C22—44no—
741C22—41no—
742C22—42no—
743C22—41no—
744C22—42no—
745C22—44no—
746C22—42no—
747C22—41no—
748C22—84no—
749C22—81no—
750C22—84no—
751C22—82no—
752C22—84no—
753C22—82no—
754C22—82no—
755C22—82no—
756C22C2×C3×#12011yescharacteristic
757C22C3×#53211yescharacteristic
758C22C3×#53511yescharacteristic
759C22C3×#54612yes—
760C22C3×#55012yes—
761C4—21no—
762C4—21no—
763C4—21no—
764C4—44no—
765C4—41no—
766C4—42no—
767C4—41no—
768C4—42no—
769C4—41no—
770C4—42no—
771C4—82no—
772C4—82no—
773C4C3×B(4,𝔽2)12yes—
774C3#2558511yescharacteristic, direct product factor, Sylow
775C2—22no—
776C2—21no—
777C2—22no—
778C2—21no—
779C2—84no—
780C2—81no—
781C2—82no—
782C2C3×#243111yescharacteristic
783C2C2×C3×B(4,𝔽2)11yescharacteristic
784C2C3×#302711yescharacteristic
subgroupG/H
center, socleC22×C3C2×#120
commutator, Frattini, cosocleC24C24×C3
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
1. C3×#3505C2semidirect
2. C3×#2435C2semidirect
3. C3×#2433C2semidirect
4. C3×#2408C2semidirect
5. C3×#2021C2semidirect
6. C3×#1996C2semidirect
7. C3×#1964C2semidirect
8. C3×#1889C2semidirect
9. C3×C4×#99C2semidirect
10. #25585C3direct (N × H)
48. #3505C2×C3semidirect
49. #2435C2×C3semidirect
50. #2433C2×C3semidirect
51. #2408C2×C3semidirect
52. #2021C2×C3semidirect
53. #1996C2×C3semidirect
54. #1964C2×C3semidirect
55. #1889C2×C3semidirect
56. C4×#99C2×C3semidirect
59. C22×C3×Q8D4semidirect
69. C22×C3×D4D4semidirect
72. C23×C3×C4D4semidirect
123. C2×C3×C4⋊C4D4semidirect
124. C2×C3×C4⋊C4D4semidirect
125. C2×C3×C4⋊C4D4semidirect
126. C2×C3×C4⋊C4D4semidirect
134. C2×C3×C22⋊C4D4semidirect
135. C2×C3×C22⋊C4D4semidirect
143. C2×C3×C42D4semidirect
290. C3×C22⋊C4#41semidirect
299. C22×Q8C3×D4semidirect
309. C22×D4C3×D4semidirect
312. C23×C4C3×D4semidirect
363. C2×C4⋊C4C3×D4semidirect
364. C2×C4⋊C4C3×D4semidirect
365. C2×C4⋊C4C3×D4semidirect
366. C2×C4⋊C4C3×D4semidirect
374. C2×C22⋊C4C3×D4semidirect
375. C2×C22⋊C4C3×D4semidirect
383. C2×C42C3×D4semidirect
579. C22⋊C4C3×#41semidirect
774. C3#25585direct (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×#24352
C3×#24332
C3×#24082
C3×#20212
C3×#19962
C3×#19642
C3×#18892
C3×C4×#992
#255853