Finite Group Databasebeta

← C3×#14747 #10633354

Subgroups — C3×#14747 #10633354

Order 768.

2730 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#121C211yesmaximal, characteristic
2C2×C3×#394C211yesmaximal, characteristic, complemented
3C2×C3×#386C212yesmaximal, complemented
4C2×C3×#386C212yesmaximal, complemented
5C2×C3×#385C211yesmaximal, characteristic, complemented
6C22×C3×#95C211yesmaximal, characteristic, complemented
7C3×#1442C211yesmaximal, characteristic, complemented
8C3×#1441C211yesmaximal, characteristic, complemented
9C3×#1440C212yesmaximal, complemented
10C3×#1439C212yesmaximal, complemented
11C3×#1438C211yesmaximal, characteristic, complemented
12#14747C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×D4C2212yes—
14C23×C3×D4C2211yescharacteristic
15C24×C3×C4C2212yes—
16C24×C3×C4C2211yescharacteristic
17C2×C3×#121—28no—
18C2×C3×#121—24no—
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2212yes—
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2212yes—
25C22×C3×C22⋊C4C2212yes—
26C22×C3×C22⋊C4C2212yes—
27C22×C3×C22⋊C4C2212yes—
28C22×C3×C22⋊C4C2211yescharacteristic
29C3×#394—24no—
30C3×#386—28no—
31C3×#386—28no—
32C3×#385—24no—
33C2×C3×#95—24no—
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2212yes—
36C2×C3×#95C2211yescharacteristic
37C2×C3×#95C2211yescharacteristic
38C2×C3×#95C2212yes—
39C2×C3×#95C2212yes—
40C2×C3×#95C2212yes—
41C2×C3×#95C2212yes—
42C2×C3×#95C2211yescharacteristic
43C22×#121C2×C311yescharacteristic
44C2×#394C2×C311yescharacteristic, complemented
45C2×#386C2×C312yescomplemented
46C2×#386C2×C312yescomplemented
47C2×#385C2×C311yescharacteristic, complemented
48C22×#95C2×C311yescharacteristic, complemented
49#1442C2×C311yescharacteristic, complemented
50#1441C2×C311yescharacteristic, complemented
51#1440C2×C312yescomplemented
52#1439C2×C312yescomplemented
53#1438C2×C311yescharacteristic, complemented
54C25×C3C2312yes—
55C25×C3C2311yescharacteristic
56C22×C3×D4—24no—
57C22×C3×D4—24no—
58C22×C3×D4—24no—
59C22×C3×D4—24no—
60C22×C3×D4—24no—
61C22×C3×D4—24no—
62C22×C3×D4—24no—
63C22×C3×D4—22no—
64C22×C3×D4—22no—
65C22×C3×D4—22no—
66C22×C3×D4—42no—
67C22×C3×D4D418yes—
68C23×C3×C4—24no—
69C23×C3×C4—24no—
70C23×C3×C4—24no—
71C23×C3×C4—22no—
72C23×C3×C4—24no—
73C23×C3×C4—22no—
74C23×C3×C4—24no—
75C23×C3×C4—24no—
76C23×C3×C4—42no—
77C23×C3×C4—42no—
78C23×C3×C4—42no—
79C23×C3×C4D414yes—
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2312yes—
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2312yes—
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2312yes—
88C23×C3×C4C2311yescharacteristic
89C3×#121—232no—
90C2×C3×C4⋊C4—24no—
91C2×C3×C4⋊C4—22no—
92C2×C3×C4⋊C4—22no—
93C2×C3×C4⋊C4—22no—
94C2×C3×C4⋊C4—22no—
95C2×C3×C4⋊C4—22no—
96C2×C3×C4⋊C4—42no—
97C2×C3×C22⋊C4—22no—
98C2×C3×C22⋊C4—24no—
99C2×C3×C22⋊C4—22no—
100C2×C3×C22⋊C4—24no—
101C2×C3×C22⋊C4—24no—
102C2×C3×C22⋊C4—22no—
103C2×C3×C22⋊C4—24no—
104C2×C3×C22⋊C4—24no—
105C2×C3×C22⋊C4—24no—
106C2×C3×C22⋊C4—24no—
107C2×C3×C22⋊C4—24no—
108C2×C3×C22⋊C4—24no—
109C2×C3×C22⋊C4—24no—
110C2×C3×C22⋊C4—24no—
111C2×C3×C22⋊C4—24no—
112C2×C3×C22⋊C4—42no—
113C2×C3×C22⋊C4—42no—
114C2×C3×C22⋊C4—42no—
115C2×C3×C22⋊C4—42no—
116C2×C3×C22⋊C4D414yescomplemented
117C3×#95—24no—
118C3×#95—22no—
119C3×#95—22no—
120C3×#95—22no—
121C3×#95—24no—
122C3×#95—24no—
123C3×#95—24no—
124C3×#95—24no—
125C3×#95D414yescomplemented
126C23×D4C22×C312yes—
127C23×D4C22×C311yescharacteristic
128C24×C4C22×C312yes—
129C24×C4C22×C311yescharacteristic
130C2×#121—28no—
131C2×#121—24no—
132C22×C4⋊C4C22×C311yescharacteristic
133C22×C4⋊C4C22×C311yescharacteristic
134C22×C4⋊C4C22×C311yescharacteristic
135C22×C22⋊C4C22×C312yes—
136C22×C22⋊C4C22×C311yescharacteristic
137C22×C22⋊C4C22×C312yes—
138C22×C22⋊C4C22×C312yes—
139C22×C22⋊C4C22×C312yes—
140C22×C22⋊C4C22×C312yes—
141C22×C22⋊C4C22×C311yescharacteristic
142#394—24no—
143#386—28no—
144#386—28no—
145#385—24no—
146C2×#95—24no—
147C2×#95C22×C311yescharacteristic
148C2×#95C22×C311yescharacteristic
149C2×#95C22×C312yes—
150C2×#95C22×C312yes—
151C2×#95C22×C312yes—
152C2×#95C22×C311yescharacteristic
153C2×#95C22×C312yes—
154C2×#95C22×C312yes—
155C2×#95C22×C311yescharacteristic
156C24×C3—21no—
157C24×C3—21no—
158C24×C3—22no—
159C24×C3—22no—
160C24×C3—21no—
161C24×C3—21no—
162C24×C3—22no—
163C24×C3—22no—
164C24×C3—22no—
165C24×C3—22no—
166C24×C3—22no—
167C24×C3—22no—
168C24×C3—22no—
169C24×C3—22no—
170C24×C3—22no—
171C24×C3—22no—
172C24×C3—22no—
173C24×C3—22no—
174C24×C3—22no—
175C24×C3—22no—
176C24×C3C2×D414yes—
177C24×C3C2×D414yes—
178C24×C3C2×D412yes—
179C24×C3C2×D412yes—
180C24×C3#4112yes—
181C24×C3#4114yes—
182C24×C3C2411yescharacteristic
183C2×C3×D4—28no—
184C2×C3×D4—216no—
185C2×C3×D4—216no—
186C2×C3×D4—216no—
187C2×C3×D4—48no—
188C2×C3×D4—48no—
189C2×C3×D4—44no—
190C2×C3×D4—48no—
191C2×C3×D4—48no—
192C2×C3×D4—48no—
193C2×C3×D4—48no—
194C2×C3×D4—44no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—216no—
198C22×C3×C4—28no—
199C22×C3×C4—21no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—22no—
205C22×C3×C4—22no—
206C22×C3×C4—22no—
207C22×C3×C4—22no—
208C22×C3×C4—21no—
209C22×C3×C4—22no—
210C22×C3×C4—22no—
211C22×C3×C4—22no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—22no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—22no—
218C22×C3×C4—22no—
219C22×C3×C4—22no—
220C22×C3×C4—22no—
221C22×C3×C4—22no—
222C22×C3×C4—22no—
223C22×C3×C4—21no—
224C22×C3×C4—22no—
225C22×C3×C4—22no—
226C22×C3×C4—22no—
227C22×C3×C4—22no—
228C22×C3×C4—22no—
229C22×C3×C4—22no—
230C22×C3×C4—21no—
231C22×C3×C4—28no—
232C22×C3×C4—21no—
233C22×C3×C4—22no—
234C22×C3×C4—22no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—22no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—22no—
241C22×C3×C4—21no—
242C22×C3×C4—44no—
243C22×C3×C4—48no—
244C22×C3×C4—48no—
245C22×C3×C4—48no—
246C22×C3×C4—48no—
247C22×C3×C4—48no—
248C22×C3×C4—48no—
249C22×C3×C4—48no—
250C22×C3×C4—48no—
251C22×C3×C4C2×D412yes—
252C22×C3×C4C2×D412yes—
253C22×C3×C4C2×D414yes—
254C22×C3×C4C2×D414yes—
255C22×C3×C4C2×D412yes—
256C22×C3×C4C2×D412yes—
257C22×C3×C4C2×D412yes—
258C22×C3×C4#4114yes—
259C22×C3×C4#4112yes—
260C3×C4⋊C4—28no—
261C3×C4⋊C4—44no—
262C3×C4⋊C4—44no—
263C3×C22⋊C4—216no—
264C3×C22⋊C4—28no—
265C3×C22⋊C4—48no—
266C3×C22⋊C4—48no—
267C3×C22⋊C4—48no—
268C3×C22⋊C4—48no—
269C3×C22⋊C4—44no—
270C25C23×C312yes—
271C25C23×C311yescharacteristic
272C22×D4—24no—
273C22×D4—24no—
274C22×D4—24no—
275C22×D4—24no—
276C22×D4—24no—
277C22×D4—24no—
278C22×D4—24no—
279C22×D4—22no—
280C22×D4—22no—
281C22×D4—22no—
282C22×D4—42no—
283C22×D4C3×D418yes—
284C23×C4—24no—
285C23×C4—24no—
286C23×C4—24no—
287C23×C4—22no—
288C23×C4—24no—
289C23×C4—22no—
290C23×C4—24no—
291C23×C4—24no—
292C23×C4—42no—
293C23×C4—42no—
294C23×C4—42no—
295C23×C4C3×D414yes—
296C23×C4C23×C311yescharacteristic
297C23×C4C23×C311yescharacteristic
298C23×C4C23×C311yescharacteristic
299C23×C4C23×C311yescharacteristic
300C23×C4C23×C311yescharacteristic
301C23×C4C23×C312yes—
302C23×C4C23×C312yes—
303C23×C4C23×C312yes—
304C23×C4C23×C311yescharacteristic
305#121—232no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—42no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4C3×D414yescomplemented
333#95—24no—
334#95—22no—
335#95—22no—
336#95—22no—
337#95—24no—
338#95—24no—
339#95—24no—
340#95—24no—
341#95C3×D414yescomplemented
342C23×C3—22no—
343C23×C3—24no—
344C23×C3—24no—
345C23×C3—22no—
346C23×C3—22no—
347C23×C3—22no—
348C23×C3—24no—
349C23×C3—24no—
350C23×C3—24no—
351C23×C3—22no—
352C23×C3—24no—
353C23×C3—24no—
354C23×C3—24no—
355C23×C3—22no—
356C23×C3—24no—
357C23×C3—22no—
358C23×C3—22no—
359C23×C3—24no—
360C23×C3—24no—
361C23×C3—24no—
362C23×C3—24no—
363C23×C3—24no—
364C23×C3—24no—
365C23×C3—24no—
366C23×C3—24no—
367C23×C3—42no—
368C23×C3—42no—
369C23×C3—42no—
370C23×C3—42no—
371C23×C3—42no—
372C23×C3—42no—
373C23×C3—42no—
374C23×C3—42no—
375C23×C3—42no—
376C23×C3—42no—
377C23×C3—42no—
378C23×C3—42no—
379C23×C3—42no—
380C23×C3—42no—
381C23×C3—42no—
382C23×C3—42no—
383C23×C3—42no—
384C23×C3—42no—
385C23×C3—42no—
386C23×C3—42no—
387C23×C3—42no—
388C23×C3—42no—
389C23×C3—42no—
390C23×C3—42no—
391C23×C3—42no—
392C23×C3—42no—
393C23×C3—42no—
394C23×C3—42no—
395C23×C3#12014yes—
396C23×C3#12114yes—
397C23×C3#12118yes—
398C23×C3#12318yes—
399C23×C3#12414yes—
400C23×C3C22×D411yescharacteristic
401C23×C3C22×D412yes—
402C23×C3C22×D411yescharacteristic
403C23×C3C22×D411yescharacteristic
404C23×C3C2×#4111yescharacteristic
405C23×C3C2×#4112yes—
406C23×C3C2×#4111yescharacteristic
407C23×C3C2×#4112yes—
408C23×C3H(5,𝔽2)12yes—
409C23×C3H(5,𝔽2)11yescharacteristic
410C23×C32−1+411yescharacteristic
411C3×D4—416no—
412C3×D4—432no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—24no—
416C2×C3×C4—24no—
417C2×C3×C4—22no—
418C2×C3×C4—24no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—24no—
423C2×C3×C4—24no—
424C2×C3×C4—24no—
425C2×C3×C4—24no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—24no—
429C2×C3×C4—24no—
430C2×C3×C4—24no—
431C2×C3×C4—24no—
432C2×C3×C4—24no—
433C2×C3×C4—22no—
434C2×C3×C4—416no—
435C2×C3×C4—432no—
436C2×C3×C4—41no—
437C2×C3×C4—42no—
438C2×C3×C4—42no—
439C2×C3×C4—42no—
440C2×C3×C4—42no—
441C2×C3×C4—42no—
442C2×C3×C4—42no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—42no—
447C2×C3×C4—42no—
448C2×C3×C4—42no—
449C2×C3×C4—42no—
450C2×C3×C4—42no—
451C2×C3×C4—42no—
452C2×C3×C4—42no—
453C2×C3×C4—42no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—42no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—42no—
464C2×C3×C4—42no—
465C2×C3×C4—42no—
466C2×C3×C4—42no—
467C2×C3×C4#12114yes—
468C24—21no—
469C24—21no—
470C24—22no—
471C24—22no—
472C24—21no—
473C24—21no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—22no—
488C24C2×C3×D414yes—
489C24C2×C3×D414yes—
490C24C2×C3×D412yes—
491C24C2×C3×D412yes—
492C24C3×#4112yes—
493C24C3×#4114yes—
494C24C24×C311yescharacteristic
495C2×D4—28no—
496C2×D4—216no—
497C2×D4—216no—
498C2×D4—216no—
499C2×D4—48no—
500C2×D4—48no—
501C2×D4—44no—
502C2×D4—48no—
503C2×D4—48no—
504C2×D4—48no—
505C2×D4—48no—
506C2×D4—44no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—216no—
510C22×C4—28no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—28no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—44no—
555C22×C4—48no—
556C22×C4—48no—
557C22×C4—48no—
558C22×C4—48no—
559C22×C4—48no—
560C22×C4—48no—
561C22×C4—48no—
562C22×C4—48no—
563C22×C4C2×C3×D412yes—
564C22×C4C2×C3×D412yes—
565C22×C4C2×C3×D414yes—
566C22×C4C2×C3×D414yes—
567C22×C4C2×C3×D412yes—
568C22×C4C2×C3×D412yes—
569C22×C4C2×C3×D412yes—
570C22×C4C3×#4114yes—
571C22×C4C3×#4112yes—
572C4⋊C4—28no—
573C4⋊C4—44no—
574C4⋊C4—44no—
575C22⋊C4—216no—
576C22⋊C4—28no—
577C22⋊C4—48no—
578C22⋊C4—48no—
579C22⋊C4—48no—
580C22⋊C4—48no—
581C22⋊C4—44no—
582C22×C3—24no—
583C22×C3—24no—
584C22×C3—24no—
585C22×C3—24no—
586C22×C3—28no—
587C22×C3—28no—
588C22×C3—24no—
589C22×C3—28no—
590C22×C3—28no—
591C22×C3—24no—
592C22×C3—44no—
593C22×C3—44no—
594C22×C3—44no—
595C22×C3—44no—
596C22×C3—44no—
597C22×C3—44no—
598C22×C3—44no—
599C22×C3—82no—
600C22×C3—82no—
601C22×C3—82no—
602C22×C3—82no—
603C22×C3—82no—
604C22×C3—82no—
605C22×C3—82no—
606C22×C3—82no—
607C22×C3#39418yescomplemented
608C22×C3C2×#12011yescharacteristic
609C22×C3C2×#12111yescharacteristic
610C22×C3C2×#12111yescharacteristic
611C22×C3C2×#12112yes—
612C22×C3C2×#12312yes—
613C22×C3#52512yes—
614C22×C3C2×#12411yescharacteristic
615C22×C3#52912yes—
616C22×C3#53211yescharacteristic
617C22×C3#53411yescharacteristic
618C22×C3#53711yescharacteristic
619C22×C3#53812yes—
620C22×C3#53912yes—
621C22×C3D4212yes—
622C22×C3D4211yescharacteristic
623C22×C3#54612yes—
624C22×C3#54612yes—
625C22×C3#54612yes—
626C22×C3#54711yescharacteristic
627C22×C3#54712yes—
628C22×C3#54811yescharacteristic
629C22×C3#55311yescharacteristic
630C22×C3#55312yes—
631C3×C4—24no—
632C3×C4—44no—
633C3×C4—42no—
634C3×C4—42no—
635C3×C4—44no—
636C3×C4—44no—
637C3×C4—42no—
638C3×C4—81no—
639C3×C4—81no—
640C23—22no—
641C23—24no—
642C23—24no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—22no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—22no—
654C23—24no—
655C23—22no—
656C23—22no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23C3×#12014yes—
694C23C3×#12114yes—
695C23C3×#12118yes—
696C23C3×#12318yes—
697C23C3×#12414yes—
698C23C22×C3×D411yescharacteristic
699C23C22×C3×D412yes—
700C23C22×C3×D411yescharacteristic
701C23C22×C3×D411yescharacteristic
702C23C2×C3×#4111yescharacteristic
703C23C2×C3×#4112yes—
704C23C2×C3×#4111yescharacteristic
705C23C2×C3×#4112yes—
706C23C3×H(5,𝔽2)12yes—
707C23C3×H(5,𝔽2)11yescharacteristic
708C23C3×2−1+411yescharacteristic
709D4—416no—
710D4—432no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—416no—
733C2×C4—432no—
734C2×C4—41no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—42no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4C3×#12114yes—
766C2×C3—28no—
767C2×C3—84no—
768C2×C3C2×#39411yescharacteristic
769C2×C3#241011yescharacteristic
770C2×C3#241611yescharacteristic
771C2×C3#242412yes—
772C2×C3#242512yes—
773C2×C3#243011yescharacteristic
774C2×C3#244312yes—
775C2×C3#244412yes—
776C2×C3#254311yescharacteristic
777C2×C3#263911yescharacteristic
778C2×C3#285011yescharacteristic
779C22—24no—
780C22—24no—
781C22—24no—
782C22—28no—
783C22—28no—
784C22—24no—
785C22—28no—
786C22—28no—
787C22—24no—
788C22—24no—
789C22—44no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22—82no—
800C22—82no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22C3×#39418yescomplemented
805C22C2×C3×#12011yescharacteristic
806C22C2×C3×#12111yescharacteristic
807C22C2×C3×#12112yes—
808C22C2×C3×#12111yescharacteristic
809C22C2×C3×#12312yes—
810C22C3×#52512yes—
811C22C2×C3×#12411yescharacteristic
812C22C3×#52912yes—
813C22C3×#53211yescharacteristic
814C22C3×#53411yescharacteristic
815C22C3×#53711yescharacteristic
816C22C3×#53812yes—
817C22C3×#53912yes—
818C22C3×D4212yes—
819C22C3×D4211yescharacteristic
820C22C3×#54612yes—
821C22C3×#54612yes—
822C22C3×#54612yes—
823C22C3×#54711yescharacteristic
824C22C3×#54712yes—
825C22C3×#54811yescharacteristic
826C22C3×#55311yescharacteristic
827C22C3×#55312yes—
828C4—24no—
829C4—44no—
830C4—42no—
831C4—42no—
832C4—44no—
833C4—44no—
834C4—42no—
835C4—81no—
836C4—81no—
837C3#1474711yescharacteristic, direct product factor, Sylow
838C2—28no—
839C2—84no—
840C2C2×C3×#39411yescharacteristic
841C2C3×#241011yescharacteristic
842C2C3×#241611yescharacteristic
843C2C3×#242412yes—
844C2C3×#242512yes—
845C2C3×#243011yescharacteristic
846C2C3×#244312yes—
847C2C3×#244412yes—
848C2C3×#254311yescharacteristic
849C2C3×#263911yescharacteristic
850C2C3×#285011yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC24C24×C3
prime radicalC22×C3×#121C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#394C2semidirect
3. C2×C3×#386C2semidirect
4. C2×C3×#386C2semidirect
5. C2×C3×#385C2semidirect
6. C22×C3×#95C2semidirect
7. C3×#1442C2semidirect
8. C3×#1441C2semidirect
9. C3×#1440C2semidirect
10. C3×#1439C2semidirect
11. C3×#1438C2semidirect
12. #14747C3direct (N × H)
44. C2×#394C2×C3semidirect
45. C2×#386C2×C3semidirect
46. C2×#386C2×C3semidirect
47. C2×#385C2×C3semidirect
48. C22×#95C2×C3semidirect
49. #1442C2×C3semidirect
50. #1441C2×C3semidirect
51. #1440C2×C3semidirect
52. #1439C2×C3semidirect
53. #1438C2×C3semidirect
116. C2×C3×C22⋊C4D4semidirect
125. C3×#95D4semidirect
332. C2×C22⋊C4C3×D4semidirect
341. #95C3×D4semidirect
607. C22×C3#394semidirect
804. C22C3×#394semidirect
837. C3#14747direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1212
C2×C3×#3942
C2×C3×#3862
C2×C3×#3852
C22×C3×#952
C3×#14422
C3×#14412
C3×#14402
C3×#14392
C3×#14382
#147473