Finite Group Databasebeta

← C3×#15340 #10633947

Subgroups — C3×#15340 #10633947

Order 768.

2442 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#121C211yesmaximal, characteristic
2C2×C3×#399C211yesmaximal, characteristic, complemented
3C2×C3×#398C211yesmaximal, characteristic, complemented
4C2×C3×#394C212yesmaximal, complemented
5C2×C3×#390C211yesmaximal, characteristic, complemented
6C2×C3×#385C212yesmaximal, complemented
7C3×#1439C212yesmaximal, complemented
8C3×#1438C212yesmaximal, complemented
9C3×#1438C211yesmaximal, characteristic, complemented
10C3×#1437C211yesmaximal, characteristic, complemented
11C3×#1436C211yesmaximal, characteristic, complemented
12#15340C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×D4C2211yescharacteristic
14C23×C3×D4C2211yescharacteristic
15C23×C3×D4C2211yescharacteristic
16C24×C3×C4C2211yescharacteristic
17C2×C3×#121—24no—
18C2×C3×#121—24no—
19C2×C3×#121—24no—
20C22×C3×C4⋊C4C2212yes—
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C4⋊C4C2212yes—
23C22×C3×C4⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2212yes—
26C22×C3×C22⋊C4C2212yes—
27C22×C3×C22⋊C4C2212yes—
28C22×C3×C22⋊C4C2212yes—
29C22×C3×C22⋊C4C2212yes—
30C22×C3×C22⋊C4C2212yes—
31C22×C3×C22⋊C4C2211yescharacteristic
32C22×C3×C42C2211yescharacteristic
33C3×#399—24no—
34C3×#398—24no—
35C3×#394—28no—
36C3×#390—24no—
37C3×#385—28no—
38C2×C3×#95C2211yescharacteristic
39C2×C3×#95C2212yes—
40C2×C3×#95C2211yescharacteristic
41C2×C3×#95C2212yes—
42C2×C3×#95C2212yes—
43C2×C3×#95C2212yes—
44C22×#121C2×C311yescharacteristic
45C2×#399C2×C311yescharacteristic, complemented
46C2×#398C2×C311yescharacteristic, complemented
47C2×#394C2×C312yescomplemented
48C2×#390C2×C311yescharacteristic, complemented
49C2×#385C2×C312yescomplemented
50#1439C2×C312yescomplemented
51#1438C2×C311yescharacteristic, complemented
52#1438C2×C312yescomplemented
53#1437C2×C311yescharacteristic, complemented
54#1436C2×C311yescharacteristic, complemented
55C25×C3C2311yescharacteristic
56C25×C3C2311yescharacteristic
57C25×C3C2311yescharacteristic
58C22×C3×D4—22no—
59C22×C3×D4—22no—
60C22×C3×D4—22no—
61C22×C3×D4—22no—
62C22×C3×D4—24no—
63C22×C3×D4—24no—
64C22×C3×D4—22no—
65C22×C3×D4—22no—
66C22×C3×D4—22no—
67C22×C3×D4—22no—
68C22×C3×D4—24no—
69C22×C3×D4—42no—
70C22×C3×D4—42no—
71C22×C3×D4—42no—
72C22×C3×D4D414yes—
73C23×C3×C4—22no—
74C23×C3×C4—22no—
75C23×C3×C4—22no—
76C23×C3×C4—24no—
77C23×C3×C4—42no—
78C23×C3×C4C2312yes—
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2312yes—
82C23×C3×C4C2312yes—
83C23×C3×C4C2312yes—
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C3×#121—232no—
87C2×C3×C4⋊C4—22no—
88C2×C3×C4⋊C4—22no—
89C2×C3×C4⋊C4—24no—
90C2×C3×C4⋊C4—24no—
91C2×C3×C4⋊C4—22no—
92C2×C3×C4⋊C4—24no—
93C2×C3×C4⋊C4—22no—
94C2×C3×C4⋊C4—24no—
95C2×C3×C4⋊C4—24no—
96C2×C3×C4⋊C4—22no—
97C2×C3×C4⋊C4—42no—
98C2×C3×C4⋊C4D414yes—
99C2×C3×C22⋊C4—22no—
100C2×C3×C22⋊C4—24no—
101C2×C3×C22⋊C4—24no—
102C2×C3×C22⋊C4—22no—
103C2×C3×C22⋊C4—22no—
104C2×C3×C22⋊C4—22no—
105C2×C3×C22⋊C4—22no—
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—24no—
113C2×C3×C22⋊C4—24no—
114C2×C3×C22⋊C4—24no—
115C2×C3×C22⋊C4—24no—
116C2×C3×C22⋊C4—24no—
117C2×C3×C22⋊C4—42no—
118C2×C3×C22⋊C4—42no—
119C2×C3×C22⋊C4—42no—
120C2×C3×C22⋊C4—42no—
121C2×C3×C22⋊C4—42no—
122C2×C3×C22⋊C4D414yes—
123C2×C3×C42—22no—
124C2×C3×C42—42no—
125C3×#95—24no—
126C3×#95—22no—
127C3×#95—24no—
128C3×#95—22no—
129C3×#95—42no—
130C3×#95D418yescomplemented
131C23×D4C22×C311yescharacteristic
132C23×D4C22×C311yescharacteristic
133C23×D4C22×C311yescharacteristic
134C24×C4C22×C311yescharacteristic
135C2×#121—24no—
136C2×#121—24no—
137C2×#121—24no—
138C22×C4⋊C4C22×C312yes—
139C22×C4⋊C4C22×C311yescharacteristic
140C22×C4⋊C4C22×C312yes—
141C22×C4⋊C4C22×C311yescharacteristic
142C22×C22⋊C4C22×C311yescharacteristic
143C22×C22⋊C4C22×C312yes—
144C22×C22⋊C4C22×C312yes—
145C22×C22⋊C4C22×C312yes—
146C22×C22⋊C4C22×C312yes—
147C22×C22⋊C4C22×C312yes—
148C22×C22⋊C4C22×C312yes—
149C22×C22⋊C4C22×C311yescharacteristic
150C22×C42C22×C311yescharacteristic
151#399—24no—
152#398—24no—
153#394—28no—
154#390—24no—
155#385—28no—
156C2×#95C22×C311yescharacteristic
157C2×#95C22×C312yes—
158C2×#95C22×C311yescharacteristic
159C2×#95C22×C312yes—
160C2×#95C22×C312yes—
161C2×#95C22×C312yes—
162C24×C3—22no—
163C24×C3—21no—
164C24×C3—21no—
165C24×C3—22no—
166C24×C3—22no—
167C24×C3—22no—
168C24×C3—22no—
169C24×C3—22no—
170C24×C3—22no—
171C24×C3—21no—
172C24×C3—21no—
173C24×C3—21no—
174C24×C3—21no—
175C24×C3—22no—
176C24×C3—22no—
177C24×C3—22no—
178C24×C3—22no—
179C24×C3—22no—
180C24×C3—22no—
181C24×C3—22no—
182C24×C3—22no—
183C24×C3—22no—
184C24×C3—22no—
185C24×C3C2×D412yes—
186C24×C3C2×D412yes—
187C24×C3C2×D412yes—
188C24×C3#4114yes—
189C24×C3C2411yescharacteristic
190C2×C3×D4—28no—
191C2×C3×D4—28no—
192C2×C3×D4—28no—
193C2×C3×D4—28no—
194C2×C3×D4—44no—
195C2×C3×D4—48no—
196C2×C3×D4—48no—
197C2×C3×D4—48no—
198C2×C3×D4—48no—
199C2×C3×D4—48no—
200C2×C3×D4—44no—
201C2×C3×D4—48no—
202C2×C3×D4—44no—
203C2×C3×D4—44no—
204C2×C3×D4—44no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4—22no—
210C22×C3×C4—28no—
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—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—22no—
222C22×C3×C4—22no—
223C22×C3×C4—22no—
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—22no—
231C22×C3×C4—22no—
232C22×C3×C4—22no—
233C22×C3×C4—22no—
234C22×C3×C4—22no—
235C22×C3×C4—22no—
236C22×C3×C4—22no—
237C22×C3×C4—22no—
238C22×C3×C4—22no—
239C22×C3×C4—22no—
240C22×C3×C4—22no—
241C22×C3×C4—22no—
242C22×C3×C4—22no—
243C22×C3×C4—22no—
244C22×C3×C4—48no—
245C22×C3×C4—48no—
246C22×C3×C4—44no—
247C22×C3×C4—44no—
248C22×C3×C4C2×D412yes—
249C22×C3×C4C2×D414yes—
250C22×C3×C4C2×D414yes—
251C22×C3×C4C2×D412yes—
252C22×C3×C4C2×D412yes—
253C22×C3×C4C2×D412yes—
254C22×C3×C4C2×D412yes—
255C22×C3×C4C2×D414yes—
256C22×C3×C4C2×D412yes—
257C22×C3×C4#4114yes—
258C3×C4⋊C4—28no—
259C3×C4⋊C4—48no—
260C3×C4⋊C4—44no—
261C3×C4⋊C4—48no—
262C3×C22⋊C4—216no—
263C3×C22⋊C4—28no—
264C3×C22⋊C4—28no—
265C3×C22⋊C4—48no—
266C3×C22⋊C4—48no—
267C3×C22⋊C4—48no—
268C3×C22⋊C4—48no—
269C3×C22⋊C4—48no—
270C3×C42—44no—
271C25C23×C311yescharacteristic
272C25C23×C311yescharacteristic
273C25C23×C311yescharacteristic
274C22×D4—22no—
275C22×D4—22no—
276C22×D4—22no—
277C22×D4—22no—
278C22×D4—24no—
279C22×D4—24no—
280C22×D4—22no—
281C22×D4—22no—
282C22×D4—22no—
283C22×D4—22no—
284C22×D4—24no—
285C22×D4—42no—
286C22×D4—42no—
287C22×D4—42no—
288C22×D4C3×D414yes—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—24no—
293C23×C4—42no—
294C23×C4C23×C312yes—
295C23×C4C23×C312yes—
296C23×C4C23×C312yes—
297C23×C4C23×C311yescharacteristic
298C23×C4C23×C311yescharacteristic
299C23×C4C23×C312yes—
300C23×C4C23×C311yescharacteristic
301C23×C4C23×C311yescharacteristic
302#121—232no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4C3×D414yes—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—22no—
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—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4C3×D414yes—
339C2×C42—22no—
340C2×C42—42no—
341#95—24no—
342#95—22no—
343#95—24no—
344#95—22no—
345#95—42no—
346#95C3×D418yescomplemented
347C23×C3—22no—
348C23×C3—24no—
349C23×C3—22no—
350C23×C3—24no—
351C23×C3—24no—
352C23×C3—24no—
353C23×C3—24no—
354C23×C3—24no—
355C23×C3—24no—
356C23×C3—24no—
357C23×C3—22no—
358C23×C3—22no—
359C23×C3—22no—
360C23×C3—22no—
361C23×C3—22no—
362C23×C3—22no—
363C23×C3—24no—
364C23×C3—24no—
365C23×C3—24no—
366C23×C3—24no—
367C23×C3—41no—
368C23×C3—41no—
369C23×C3—41no—
370C23×C3—41no—
371C23×C3—42no—
372C23×C3—42no—
373C23×C3—42no—
374C23×C3—42no—
375C23×C3—42no—
376C23×C3—42no—
377C23×C3—41no—
378C23×C3—42no—
379C23×C3—42no—
380C23×C3—41no—
381C23×C3—41no—
382C23×C3—41no—
383C23×C3—41no—
384C23×C3—41no—
385C23×C3—41no—
386C23×C3—41no—
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—42no—
396C23×C3—42no—
397C23×C3—42no—
398C23×C3—42no—
399C23×C3—42no—
400C23×C3—42no—
401C23×C3—42no—
402C23×C3—42no—
403C23×C3—42no—
404C23×C3—42no—
405C23×C3—42no—
406C23×C3—42no—
407C23×C3—42no—
408C23×C3—42no—
409C23×C3#12314yes—
410C23×C3C22×D411yescharacteristic
411C23×C3C22×D411yescharacteristic
412C23×C3C22×D411yescharacteristic
413C23×C3C22×D412yes—
414C23×C3C2×#4112yes—
415C23×C3C2×#4112yes—
416C23×C3H(5,𝔽2)12yes—
417C23×C3H(5,𝔽2)12yes—
418C23×C32−1+412yes—
419C3×D4—416no—
420C3×D4—416no—
421C3×D4—416no—
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—24no—
427C2×C3×C4—24no—
428C2×C3×C4—24no—
429C2×C3×C4—24no—
430C2×C3×C4—22no—
431C2×C3×C4—22no—
432C2×C3×C4—24no—
433C2×C3×C4—24no—
434C2×C3×C4—24no—
435C2×C3×C4—24no—
436C2×C3×C4—24no—
437C2×C3×C4—24no—
438C2×C3×C4—24no—
439C2×C3×C4—24no—
440C2×C3×C4—24no—
441C2×C3×C4—24no—
442C2×C3×C4—24no—
443C2×C3×C4—416no—
444C2×C3×C4—41no—
445C2×C3×C4—42no—
446C2×C3×C4—41no—
447C2×C3×C4—42no—
448C2×C3×C4—42no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—42no—
452C2×C3×C4—42no—
453C2×C3×C4—42no—
454C2×C3×C4—42no—
455C2×C3×C4—42no—
456C2×C3×C4—42no—
457C2×C3×C4—42no—
458C2×C3×C4—42no—
459C2×C3×C4—42no—
460C2×C3×C4—42no—
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—42no—
469C2×C3×C4#12014yes—
470C2×C3×C4#12714yes—
471C24—22no—
472C24—21no—
473C24—21no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—21no—
481C24—21no—
482C24—21no—
483C24—21no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24C2×C3×D412yes—
495C24C2×C3×D412yes—
496C24C2×C3×D412yes—
497C24C3×#4114yes—
498C24C24×C311yescharacteristic
499C2×D4—28no—
500C2×D4—28no—
501C2×D4—28no—
502C2×D4—28no—
503C2×D4—44no—
504C2×D4—48no—
505C2×D4—48no—
506C2×D4—48no—
507C2×D4—48no—
508C2×D4—48no—
509C2×D4—44no—
510C2×D4—48no—
511C2×D4—44no—
512C2×D4—44no—
513C2×D4—44no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—28no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—48no—
554C22×C4—48no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4C2×C3×D412yes—
558C22×C4C2×C3×D414yes—
559C22×C4C2×C3×D414yes—
560C22×C4C2×C3×D412yes—
561C22×C4C2×C3×D412yes—
562C22×C4C2×C3×D412yes—
563C22×C4C2×C3×D412yes—
564C22×C4C2×C3×D414yes—
565C22×C4C2×C3×D412yes—
566C22×C4C3×#4114yes—
567C4⋊C4—28no—
568C4⋊C4—48no—
569C4⋊C4—44no—
570C4⋊C4—48no—
571C22⋊C4—28no—
572C22⋊C4—216no—
573C22⋊C4—28no—
574C22⋊C4—48no—
575C22⋊C4—48no—
576C22⋊C4—48no—
577C22⋊C4—48no—
578C22⋊C4—48no—
579C42—44no—
580C22×C3—24no—
581C22×C3—28no—
582C22×C3—44no—
583C22×C3—44no—
584C22×C3—42no—
585C22×C3—42no—
586C22×C3—44no—
587C22×C3—44no—
588C22×C3—44no—
589C22×C3—42no—
590C22×C3—42no—
591C22×C3—44no—
592C22×C3—44no—
593C22×C3—42no—
594C22×C3—42no—
595C22×C3—42no—
596C22×C3—42no—
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×C3C2×#12011yescharacteristic
608C22×C3C2×#12311yescharacteristic
609C22×C3#52512yes—
610C22×C3C2×#12711yescharacteristic
611C22×C3#53211yescharacteristic
612C22×C3#53411yescharacteristic
613C22×C3#53511yescharacteristic
614C22×C3#53611yescharacteristic
615C22×C3#53712yes—
616C22×C3#53912yes—
617C22×C3#54012yes—
618C22×C3D4212yes—
619C22×C3D4212yes—
620C22×C3#54612yes—
621C22×C3#54612yes—
622C22×C3#54612yes—
623C22×C3#54712yes—
624C22×C3#54812yes—
625C22×C3#54812yes—
626C22×C3#55312yes—
627C22×C3#56212yes—
628C3×C4—24no—
629C3×C4—24no—
630C3×C4—42no—
631C3×C4—44no—
632C3×C4—42no—
633C3×C4—44no—
634C3×C4—44no—
635C3×C4—82no—
636C23—22no—
637C23—24no—
638C23—22no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—42no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—41no—
669C23—42no—
670C23—42no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
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—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23C3×#12314yes—
699C23C22×C3×D411yescharacteristic
700C23C22×C3×D411yescharacteristic
701C23C22×C3×D411yescharacteristic
702C23C22×C3×D412yes—
703C23C2×C3×#4112yes—
704C23C2×C3×#4112yes—
705C23C3×H(5,𝔽2)12yes—
706C23C3×H(5,𝔽2)12yes—
707C23C3×2−1+412yes—
708D4—416no—
709D4—416no—
710D4—416no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—416no—
733C2×C4—42no—
734C2×C4—41no—
735C2×C4—42no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
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—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4C3×#12014yes—
759C2×C4C3×#12714yes—
760C2×C3—44no—
761C2×C3—82no—
762C2×C3—82no—
763C2×C3#240511yescharacteristic
764C2×C3#243211yescharacteristic
765C2×C3#243311yescharacteristic
766C2×C3#244312yes—
767C2×C3#246412yes—
768C2×C3#254012yes—
769C2×C3#267112yes—
770C2×C3#268112yes—
771C2×C3#271112yes—
772C22—24no—
773C22—28no—
774C22—44no—
775C22—44no—
776C22—42no—
777C22—42no—
778C22—44no—
779C22—44no—
780C22—44no—
781C22—42no—
782C22—42no—
783C22—44no—
784C22—44no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—44no—
790C22—44no—
791C22—82no—
792C22—82no—
793C22—82no—
794C22—82no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22C2×C3×#12011yescharacteristic
800C22C2×C3×#12311yescharacteristic
801C22C3×#52512yes—
802C22C2×C3×#12711yescharacteristic
803C22C3×#53211yescharacteristic
804C22C3×#53411yescharacteristic
805C22C3×#53511yescharacteristic
806C22C3×#53611yescharacteristic
807C22C3×#53712yes—
808C22C3×#53912yes—
809C22C3×#54012yes—
810C22C3×D4212yes—
811C22C3×D4212yes—
812C22C3×#54612yes—
813C22C3×#54612yes—
814C22C3×#54612yes—
815C22C3×#54712yes—
816C22C3×#54812yes—
817C22C3×#54812yes—
818C22C3×#55312yes—
819C22C3×#56212yes—
820C4—24no—
821C4—24no—
822C4—42no—
823C4—44no—
824C4—42no—
825C4—44no—
826C4—44no—
827C4—82no—
828C3#1534011yescharacteristic, direct product factor, Sylow
829C2—44no—
830C2—82no—
831C2—82no—
832C2C3×#240511yescharacteristic
833C2C3×#243211yescharacteristic
834C2C3×#243311yescharacteristic
835C2C3×#244312yes—
836C2C3×#246412yes—
837C2C3×#254012yes—
838C2C3×#267112yes—
839C2C3×#268112yes—
840C2C3×#271112yes—
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×#399C2semidirect
3. C2×C3×#398C2semidirect
4. C2×C3×#394C2semidirect
5. C2×C3×#390C2semidirect
6. C2×C3×#385C2semidirect
7. C3×#1439C2semidirect
8. C3×#1438C2semidirect
9. C3×#1438C2semidirect
10. C3×#1437C2semidirect
11. C3×#1436C2semidirect
12. #15340C3direct (N × H)
45. C2×#399C2×C3semidirect
46. C2×#398C2×C3semidirect
47. C2×#394C2×C3semidirect
48. C2×#390C2×C3semidirect
49. C2×#385C2×C3semidirect
50. #1439C2×C3semidirect
51. #1438C2×C3semidirect
52. #1438C2×C3semidirect
53. #1437C2×C3semidirect
54. #1436C2×C3semidirect
130. C3×#95D4semidirect
346. #95C3×D4semidirect
828. C3#15340direct (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×#3992
C2×C3×#3982
C2×C3×#3942
C2×C3×#3902
C2×C3×#3852
C3×#14392
C3×#14382
C3×#14372
C3×#14362
#153403