Finite Group Databasebeta

← C3×#14762 #10633369

Subgroups — C3×#14762 #10633369

Order 768.

2970 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#121C211yesmaximal, characteristic, complemented
2C2×C3×#394C212yesmaximal, complemented
3C2×C3×#392C212yesmaximal, complemented
4C2×C3×#392C211yesmaximal, characteristic, complemented
5C2×C3×#390C212yesmaximal, complemented
6C2×C3×#386C211yesmaximal, characteristic, complemented
7C2×C3×C4×C22⋊C4C211yesmaximal, characteristic, complemented
8C3×#1444C211yesmaximal, characteristic, complemented
9C3×#1439C211yesmaximal, characteristic, complemented
10C3×#1438C211yesmaximal, characteristic, complemented
11C3×#1437C212yesmaximal, complemented
12#14762C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×D4C2212yes—
14C23×C3×D4C2211yescharacteristic
15C23×C3×D4C2211yescharacteristic
16C23×C3×D4C2212yes—
17C24×C3×C4C2211yescharacteristic
18C2×C3×#121—24no—
19C2×C3×#121—28no—
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C4⋊C4C2212yes—
22C22×C3×C22⋊C4C2212yes—
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2212yes—
27C22×C3×C22⋊C4C2212yes—
28C22×C3×C22⋊C4C2212yes—
29C22×C3×C22⋊C4C2212yes—
30C22×C3×C22⋊C4C2212yes—
31C22×C3×C42C2212yes—
32C3×#394—28no—
33C3×#392—28no—
34C3×#392—24no—
35C3×#390—28no—
36C3×#386—24no—
37C3×C4×C22⋊C4—24no—
38C2×C3×#95C2212yes—
39C2×C3×#95C2212yes—
40C2×C3×#95C2211yescharacteristic
41C2×C3×#95C2211yescharacteristic
42C2×C3×#95C2211yescharacteristic
43C2×C3×#95C2211yescharacteristic
44C22×#121C2×C311yescharacteristic, complemented
45C2×#394C2×C312yescomplemented
46C2×#392C2×C311yescharacteristic, complemented
47C2×#392C2×C312yescomplemented
48C2×#390C2×C312yescomplemented
49C2×#386C2×C311yescharacteristic, complemented
50C2×C4×C22⋊C4C2×C311yescharacteristic, complemented
51#1444C2×C311yescharacteristic, complemented
52#1439C2×C311yescharacteristic, complemented
53#1438C2×C311yescharacteristic, complemented
54#1437C2×C312yescomplemented
55C25×C3C2312yes—
56C25×C3C2311yescharacteristic
57C25×C3C2311yescharacteristic
58C22×C3×D4—22no—
59C22×C3×D4—24no—
60C22×C3×D4—24no—
61C22×C3×D4—24no—
62C22×C3×D4—24no—
63C22×C3×D4—24no—
64C22×C3×D4—22no—
65C22×C3×D4—24no—
66C22×C3×D4—24no—
67C22×C3×D4—24no—
68C22×C3×D4—24no—
69C22×C3×D4—22no—
70C22×C3×D4—22no—
71C22×C3×D4—24no—
72C22×C3×D4—24no—
73C22×C3×D4—22no—
74C22×C3×D4—24no—
75C22×C3×D4—22no—
76C22×C3×D4—42no—
77C22×C3×D4—42no—
78C22×C3×D4—42no—
79C22×C3×D4—42no—
80C22×C3×D4—42no—
81C22×C3×D4—42no—
82C23×C3×C4—22no—
83C23×C3×C4—24no—
84C23×C3×C4—22no—
85C23×C3×C4—42no—
86C23×C3×C4D414yescomplemented
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2312yes—
90C23×C3×C4C2312yes—
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2312yes—
95C3×#121—232no—
96C2×C3×C4⋊C4—24no—
97C2×C3×C4⋊C4—22no—
98C2×C3×C4⋊C4—24no—
99C2×C3×C4⋊C4—24no—
100C2×C3×C4⋊C4—42no—
101C2×C3×C22⋊C4—24no—
102C2×C3×C22⋊C4—24no—
103C2×C3×C22⋊C4—24no—
104C2×C3×C22⋊C4—24no—
105C2×C3×C22⋊C4—22no—
106C2×C3×C22⋊C4—24no—
107C2×C3×C22⋊C4—24no—
108C2×C3×C22⋊C4—22no—
109C2×C3×C22⋊C4—22no—
110C2×C3×C22⋊C4—24no—
111C2×C3×C22⋊C4—24no—
112C2×C3×C22⋊C4—24no—
113C2×C3×C22⋊C4—24no—
114C2×C3×C22⋊C4—22no—
115C2×C3×C22⋊C4—24no—
116C2×C3×C22⋊C4—24no—
117C2×C3×C22⋊C4—24no—
118C2×C3×C22⋊C4—24no—
119C2×C3×C22⋊C4—22no—
120C2×C3×C22⋊C4—24no—
121C2×C3×C22⋊C4—42no—
122C2×C3×C22⋊C4—42no—
123C2×C3×C22⋊C4—42no—
124C2×C3×C22⋊C4D418yescomplemented
125C2×C3×C22⋊C4D418yescomplemented
126C2×C3×C42—24no—
127C2×C3×C42—24no—
128C2×C3×C42—42no—
129C3×#95—22no—
130C3×#95—22no—
131C3×#95—22no—
132C3×#95—24no—
133C3×#95—24no—
134C3×#95D414yescomplemented
135C23×D4C22×C311yescharacteristic
136C23×D4C22×C312yes—
137C23×D4C22×C312yes—
138C23×D4C22×C311yescharacteristic
139C24×C4C22×C311yescharacteristic
140C2×#121—24no—
141C2×#121—28no—
142C22×C4⋊C4C22×C311yescharacteristic
143C22×C4⋊C4C22×C312yes—
144C22×C22⋊C4C22×C312yes—
145C22×C22⋊C4C22×C311yescharacteristic
146C22×C22⋊C4C22×C311yescharacteristic
147C22×C22⋊C4C22×C311yescharacteristic
148C22×C22⋊C4C22×C312yes—
149C22×C22⋊C4C22×C312yes—
150C22×C22⋊C4C22×C312yes—
151C22×C22⋊C4C22×C312yes—
152C22×C22⋊C4C22×C312yes—
153C22×C42C22×C312yes—
154#394—28no—
155#392—28no—
156#392—24no—
157#390—28no—
158#386—24no—
159C4×C22⋊C4—24no—
160C2×#95C22×C312yes—
161C2×#95C22×C312yes—
162C2×#95C22×C311yescharacteristic
163C2×#95C22×C311yescharacteristic
164C2×#95C22×C311yescharacteristic
165C2×#95C22×C311yescharacteristic
166C24×C3—21no—
167C24×C3—22no—
168C24×C3—22no—
169C24×C3—21no—
170C24×C3—21no—
171C24×C3—21no—
172C24×C3—22no—
173C24×C3—21no—
174C24×C3—21no—
175C24×C3—21no—
176C24×C3—22no—
177C24×C3—22no—
178C24×C3—22no—
179C24×C3—22no—
180C24×C3—22no—
181C24×C3—22no—
182C24×C3—21no—
183C24×C3—22no—
184C24×C3—22no—
185C24×C3—22no—
186C24×C3—21no—
187C24×C3—22no—
188C24×C3—22no—
189C24×C3—22no—
190C24×C3—21no—
191C24×C3—22no—
192C24×C3—21no—
193C24×C3—22no—
194C24×C3—22no—
195C24×C3—22no—
196C24×C3—22no—
197C24×C3—22no—
198C24×C3—21no—
199C24×C3C2×D414yes—
200C24×C3C2×D414yes—
201C24×C3C2×D412yes—
202C24×C3#4112yes—
203C24×C3C2411yescharacteristic
204C2×C3×D4—28no—
205C2×C3×D4—216no—
206C2×C3×D4—216no—
207C2×C3×D4—28no—
208C2×C3×D4—48no—
209C2×C3×D4—48no—
210C2×C3×D4—48no—
211C2×C3×D4—48no—
212C2×C3×D4—48no—
213C2×C3×D4—48no—
214C2×C3×D4—48no—
215C2×C3×D4—48no—
216C2×C3×D4—48no—
217C2×C3×D4—44no—
218C2×C3×D4—48no—
219C2×C3×D4—48no—
220C2×C3×D4—48no—
221C2×C3×D4—48no—
222C2×C3×D4—44no—
223C2×C3×D4—48no—
224C2×C3×D4—44no—
225C2×C3×D4—48no—
226C2×C3×D4—44no—
227C2×C3×D4—48no—
228C22×C3×C4—21no—
229C22×C3×C4—22no—
230C22×C3×C4—22no—
231C22×C3×C4—21no—
232C22×C3×C4—22no—
233C22×C3×C4—22no—
234C22×C3×C4—22no—
235C22×C3×C4—22no—
236C22×C3×C4—22no—
237C22×C3×C4—21no—
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—22no—
245C22×C3×C4—22no—
246C22×C3×C4—22no—
247C22×C3×C4—21no—
248C22×C3×C4—22no—
249C22×C3×C4—22no—
250C22×C3×C4—22no—
251C22×C3×C4—22no—
252C22×C3×C4—22no—
253C22×C3×C4—28no—
254C22×C3×C4—28no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—22no—
258C22×C3×C4—21no—
259C22×C3×C4—22no—
260C22×C3×C4—22no—
261C22×C3×C4—22no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—44no—
266C22×C3×C4—48no—
267C22×C3×C4—48no—
268C22×C3×C4C2×D414yes—
269C22×C3×C4C2×D414yes—
270C22×C3×C4C2×D412yes—
271C22×C3×C4C2×D414yes—
272C22×C3×C4C2×D412yes—
273C22×C3×C4C2×D412yes—
274C22×C3×C4C2×D414yes—
275C22×C3×C4C2×D414yes—
276C22×C3×C4#4112yes—
277C22×C3×C4#4112yes—
278C22×C3×C4#4114yes—
279C3×C4⋊C4—28no—
280C3×C4⋊C4—48no—
281C3×C22⋊C4—216no—
282C3×C22⋊C4—216no—
283C3×C22⋊C4—48no—
284C3×C22⋊C4—48no—
285C3×C22⋊C4—48no—
286C3×C22⋊C4—44no—
287C3×C22⋊C4—44no—
288C3×C22⋊C4—44no—
289C3×C22⋊C4—48no—
290C3×C42—48no—
291C25C23×C312yes—
292C25C23×C311yescharacteristic
293C25C23×C311yescharacteristic
294C22×D4—24no—
295C22×D4—24no—
296C22×D4—24no—
297C22×D4—22no—
298C22×D4—24no—
299C22×D4—24no—
300C22×D4—22no—
301C22×D4—24no—
302C22×D4—24no—
303C22×D4—24no—
304C22×D4—24no—
305C22×D4—22no—
306C22×D4—22no—
307C22×D4—24no—
308C22×D4—24no—
309C22×D4—22no—
310C22×D4—24no—
311C22×D4—22no—
312C22×D4—42no—
313C22×D4—42no—
314C22×D4—42no—
315C22×D4—42no—
316C22×D4—42no—
317C22×D4—42no—
318C23×C4—24no—
319C23×C4—22no—
320C23×C4—22no—
321C23×C4—42no—
322C23×C4C3×D414yescomplemented
323C23×C4C23×C311yescharacteristic
324C23×C4C23×C311yescharacteristic
325C23×C4C23×C312yes—
326C23×C4C23×C312yes—
327C23×C4C23×C311yescharacteristic
328C23×C4C23×C311yescharacteristic
329C23×C4C23×C312yes—
330C23×C4C23×C311yescharacteristic
331#121—232no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—42no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4C3×D418yescomplemented
361C2×C22⋊C4C3×D418yescomplemented
362C2×C42—24no—
363C2×C42—24no—
364C2×C42—42no—
365#95—22no—
366#95—22no—
367#95—22no—
368#95—24no—
369#95—24no—
370#95C3×D414yescomplemented
371C23×C3—22no—
372C23×C3—24no—
373C23×C3—22no—
374C23×C3—22no—
375C23×C3—22no—
376C23×C3—24no—
377C23×C3—22no—
378C23×C3—22no—
379C23×C3—24no—
380C23×C3—24no—
381C23×C3—24no—
382C23×C3—24no—
383C23×C3—24no—
384C23×C3—24no—
385C23×C3—22no—
386C23×C3—24no—
387C23×C3—24no—
388C23×C3—24no—
389C23×C3—24no—
390C23×C3—24no—
391C23×C3—22no—
392C23×C3—24no—
393C23×C3—24no—
394C23×C3—22no—
395C23×C3—42no—
396C23×C3—42no—
397C23×C3—42no—
398C23×C3—42no—
399C23×C3—42no—
400C23×C3—42no—
401C23×C3—41no—
402C23×C3—41no—
403C23×C3—41no—
404C23×C3—41no—
405C23×C3—41no—
406C23×C3—41no—
407C23×C3—42no—
408C23×C3—42no—
409C23×C3—42no—
410C23×C3—42no—
411C23×C3—42no—
412C23×C3—42no—
413C23×C3—42no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3—42no—
417C23×C3—42no—
418C23×C3—42no—
419C23×C3—42no—
420C23×C3—42no—
421C23×C3—42no—
422C23×C3—42no—
423C23×C3—41no—
424C23×C3—42no—
425C23×C3—41no—
426C23×C3—42no—
427C23×C3—42no—
428C23×C3—42no—
429C23×C3—42no—
430C23×C3—42no—
431C23×C3—42no—
432C23×C3—42no—
433C23×C3—42no—
434C23×C3—42no—
435C23×C3—42no—
436C23×C3—42no—
437C23×C3—42no—
438C23×C3—42no—
439C23×C3—42no—
440C23×C3—42no—
441C23×C3—42no—
442C23×C3—42no—
443C23×C3—42no—
444C23×C3—42no—
445C23×C3—42no—
446C23×C3—41no—
447C23×C3—42no—
448C23×C3—42no—
449C23×C3—41no—
450C23×C3—42no—
451C23×C3#12714yes—
452C23×C3C22×D411yescharacteristic
453C23×C3C22×D412yes—
454C23×C3C22×D411yescharacteristic
455C23×C3C22×D412yes—
456C23×C3C2×#4112yes—
457C23×C3C2×#4111yescharacteristic
458C23×C3C2×#4111yescharacteristic
459C23×C3C2×#4111yescharacteristic
460C23×C3H(5,𝔽2)12yes—
461C23×C3H(5,𝔽2)11yescharacteristic
462C23×C3H(5,𝔽2)11yescharacteristic
463C3×D4—416no—
464C3×D4—432no—
465C3×D4—432no—
466C3×D4—416no—
467C2×C3×C4—22no—
468C2×C3×C4—22no—
469C2×C3×C4—24no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—24no—
473C2×C3×C4—24no—
474C2×C3×C4—24no—
475C2×C3×C4—24no—
476C2×C3×C4—24no—
477C2×C3×C4—24no—
478C2×C3×C4—24no—
479C2×C3×C4—24no—
480C2×C3×C4—24no—
481C2×C3×C4—24no—
482C2×C3×C4—24no—
483C2×C3×C4—22no—
484C2×C3×C4—24no—
485C2×C3×C4—24no—
486C2×C3×C4—24no—
487C2×C3×C4—24no—
488C2×C3×C4—24no—
489C2×C3×C4—416no—
490C2×C3×C4—42no—
491C2×C3×C4—41no—
492C2×C3×C4—42no—
493C2×C3×C4—41no—
494C2×C3×C4—42no—
495C2×C3×C4—42no—
496C2×C3×C4—42no—
497C2×C3×C4—42no—
498C2×C3×C4—42no—
499C2×C3×C4—42no—
500C2×C3×C4—42no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—42no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—42no—
508C2×C3×C4—41no—
509C2×C3×C4—42no—
510C2×C3×C4—42no—
511C2×C3×C4#12014yes—
512C2×C3×C4#12114yes—
513C2×C3×C4#12118yescomplemented
514C24—21no—
515C24—22no—
516C24—22no—
517C24—21no—
518C24—21no—
519C24—21no—
520C24—22no—
521C24—21no—
522C24—21no—
523C24—21no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—21no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—21no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—21no—
539C24—22no—
540C24—21no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—21no—
547C24C2×C3×D414yes—
548C24C2×C3×D414yes—
549C24C2×C3×D412yes—
550C24C3×#4112yes—
551C24C24×C311yescharacteristic
552C2×D4—28no—
553C2×D4—216no—
554C2×D4—216no—
555C2×D4—28no—
556C2×D4—48no—
557C2×D4—48no—
558C2×D4—48no—
559C2×D4—48no—
560C2×D4—48no—
561C2×D4—48no—
562C2×D4—48no—
563C2×D4—48no—
564C2×D4—48no—
565C2×D4—44no—
566C2×D4—48no—
567C2×D4—48no—
568C2×D4—48no—
569C2×D4—48no—
570C2×D4—44no—
571C2×D4—48no—
572C2×D4—48no—
573C2×D4—44no—
574C2×D4—44no—
575C2×D4—48no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—28no—
602C22×C4—28no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—22no—
606C22×C4—21no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—44no—
614C22×C4—48no—
615C22×C4—48no—
616C22×C4C2×C3×D414yes—
617C22×C4C2×C3×D414yes—
618C22×C4C2×C3×D412yes—
619C22×C4C2×C3×D414yes—
620C22×C4C2×C3×D412yes—
621C22×C4C2×C3×D412yes—
622C22×C4C2×C3×D414yes—
623C22×C4C2×C3×D414yes—
624C22×C4C3×#4112yes—
625C22×C4C3×#4112yes—
626C22×C4C3×#4114yes—
627C4⋊C4—28no—
628C4⋊C4—48no—
629C22⋊C4—216no—
630C22⋊C4—216no—
631C22⋊C4—48no—
632C22⋊C4—48no—
633C22⋊C4—48no—
634C22⋊C4—44no—
635C22⋊C4—44no—
636C22⋊C4—44no—
637C22⋊C4—48no—
638C42—48no—
639C22×C3—24no—
640C22×C3—24no—
641C22×C3—24no—
642C22×C3—42no—
643C22×C3—42no—
644C22×C3—42no—
645C22×C3—42no—
646C22×C3—44no—
647C22×C3—44no—
648C22×C3—44no—
649C22×C3—44no—
650C22×C3—44no—
651C22×C3—42no—
652C22×C3—44no—
653C22×C3—42no—
654C22×C3—44no—
655C22×C3—44no—
656C22×C3—44no—
657C22×C3—44no—
658C22×C3—44no—
659C22×C3—44no—
660C22×C3—42no—
661C22×C3—44no—
662C22×C3—82no—
663C22×C3—81no—
664C22×C3—82no—
665C22×C3—81no—
666C22×C3—81no—
667C22×C3—82no—
668C22×C3—82no—
669C22×C3—82no—
670C22×C3—82no—
671C22×C3—81no—
672C22×C3—82no—
673C22×C3—82no—
674C22×C3—82no—
675C22×C3—82no—
676C22×C3C2×#12011yescharacteristic
677C22×C3C2×#12111yescharacteristic
678C22×C3C2×#12112yes—
679C22×C3#52511yescharacteristic
680C22×C3#52512yes—
681C22×C3C2×#12711yescharacteristic
682C22×C3#53211yescharacteristic
683C22×C3#53212yes—
684C22×C3#53212yes—
685C22×C3#53411yescharacteristic
686C22×C3#53511yescharacteristic
687C22×C3#53812yes—
688C22×C3#54012yes—
689C22×C3D4212yes—
690C22×C3D4212yes—
691C22×C3D4212yes—
692C22×C3#54612yes—
693C22×C3#54611yescharacteristic
694C22×C3#54612yes—
695C22×C3#54612yes—
696C22×C3#55011yescharacteristic
697C22×C3#55311yescharacteristic
698C22×C3#55511yescharacteristic
699C3×C4—24no—
700C3×C4—24no—
701C3×C4—28no—
702C3×C4—44no—
703C3×C4—44no—
704C3×C4—42no—
705C3×C4—81no—
706C3×C4—81no—
707C23—22no—
708C23—24no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—24no—
713C23—22no—
714C23—22no—
715C23—24no—
716C23—24no—
717C23—24no—
718C23—24no—
719C23—24no—
720C23—24no—
721C23—22no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—22no—
728C23—24no—
729C23—24no—
730C23—22no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—41no—
751C23—41no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—42no—
759C23—41no—
760C23—42no—
761C23—41no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—42no—
766C23—42no—
767C23—42no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—41no—
783C23—42no—
784C23—42no—
785C23—41no—
786C23—42no—
787C23C3×#12714yes—
788C23C22×C3×D411yescharacteristic
789C23C22×C3×D412yes—
790C23C22×C3×D411yescharacteristic
791C23C22×C3×D412yes—
792C23C2×C3×#4112yes—
793C23C2×C3×#4111yescharacteristic
794C23C2×C3×#4111yescharacteristic
795C23C2×C3×#4111yescharacteristic
796C23C3×H(5,𝔽2)12yes—
797C23C3×H(5,𝔽2)11yescharacteristic
798C23C3×H(5,𝔽2)11yescharacteristic
799D4—416no—
800D4—432no—
801D4—432no—
802D4—416no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—24no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—24no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—24no—
819C2×C4—22no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—416no—
826C2×C4—42no—
827C2×C4—41no—
828C2×C4—42no—
829C2×C4—41no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—42no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—42no—
844C2×C4—41no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4C3×#12014yes—
848C2×C4C3×#12114yes—
849C2×C4C3×#12118yescomplemented
850C2×C3—44no—
851C2×C3—84no—
852C2×C3—82no—
853C2×C3#238811yescharacteristic
854C2×C3#241011yescharacteristic
855C2×C3#241411yescharacteristic
856C2×C3#242412yes—
857C2×C3#242812yes—
858C2×C3#243311yescharacteristic
859C2×C3#246412yes—
860C2×C3#253911yescharacteristic
861C2×C3#255512yes—
862C2×C3#266111yescharacteristic
863C2×C3#285611yescharacteristic
864C22—24no—
865C22—24no—
866C22—24no—
867C22—42no—
868C22—42no—
869C22—42no—
870C22—42no—
871C22—44no—
872C22—44no—
873C22—44no—
874C22—44no—
875C22—44no—
876C22—42no—
877C22—44no—
878C22—42no—
879C22—44no—
880C22—44no—
881C22—44no—
882C22—44no—
883C22—44no—
884C22—44no—
885C22—42no—
886C22—44no—
887C22—82no—
888C22—81no—
889C22—81no—
890C22—82no—
891C22—82no—
892C22—82no—
893C22—82no—
894C22—81no—
895C22—82no—
896C22—82no—
897C22—82no—
898C22—82no—
899C22—82no—
900C22—81no—
901C22C2×C3×#12011yescharacteristic
902C22C2×C3×#12111yescharacteristic
903C22C2×C3×#12112yes—
904C22C3×#52511yescharacteristic
905C22C3×#52512yes—
906C22C2×C3×#12711yescharacteristic
907C22C3×#53211yescharacteristic
908C22C3×#53212yes—
909C22C3×#53212yes—
910C22C3×#53411yescharacteristic
911C22C3×#53511yescharacteristic
912C22C3×#53812yes—
913C22C3×#54012yes—
914C22C3×D4212yes—
915C22C3×D4212yes—
916C22C3×D4212yes—
917C22C3×#54612yes—
918C22C3×#54611yescharacteristic
919C22C3×#54612yes—
920C22C3×#54612yes—
921C22C3×#55011yescharacteristic
922C22C3×#55311yescharacteristic
923C22C3×#55511yescharacteristic
924C4—24no—
925C4—24no—
926C4—28no—
927C4—44no—
928C4—44no—
929C4—42no—
930C4—81no—
931C4—81no—
932C3#1476211yescharacteristic, direct product factor, Sylow
933C2—44no—
934C2—84no—
935C2—82no—
936C2C3×#238811yescharacteristic
937C2C3×#241011yescharacteristic
938C2C3×#241411yescharacteristic
939C2C3×#242412yes—
940C2C3×#242812yes—
941C2C3×#243311yescharacteristic
942C2C3×#246412yes—
943C2C3×#253911yescharacteristic
944C2C3×#255512yes—
945C2C3×#266111yescharacteristic
946C2C3×#285611yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC24C24×C3
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C3×#121C2semidirect
2. C2×C3×#394C2semidirect
3. C2×C3×#392C2semidirect
4. C2×C3×#392C2semidirect
5. C2×C3×#390C2semidirect
6. C2×C3×#386C2semidirect
7. C2×C3×C4×C22⋊C4C2semidirect
8. C3×#1444C2semidirect
9. C3×#1439C2semidirect
10. C3×#1438C2semidirect
11. C3×#1437C2semidirect
12. #14762C3direct (N × H)
44. C22×#121C2×C3semidirect
45. C2×#394C2×C3semidirect
46. C2×#392C2×C3semidirect
47. C2×#392C2×C3semidirect
48. C2×#390C2×C3semidirect
49. C2×#386C2×C3semidirect
50. C2×C4×C22⋊C4C2×C3semidirect
51. #1444C2×C3semidirect
52. #1439C2×C3semidirect
53. #1438C2×C3semidirect
54. #1437C2×C3semidirect
86. C23×C3×C4D4semidirect
124. C2×C3×C22⋊C4D4semidirect
125. C2×C3×C22⋊C4D4semidirect
134. C3×#95D4semidirect
322. C23×C4C3×D4semidirect
360. C2×C22⋊C4C3×D4semidirect
361. C2×C22⋊C4C3×D4semidirect
370. #95C3×D4semidirect
513. C2×C3×C4#121semidirect
849. C2×C4C3×#121semidirect
932. C3#14762direct (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×#3922
C2×C3×#3902
C2×C3×#3862
C2×C3×C4×C22⋊C42
C3×#14442
C3×#14392
C3×#14382
C3×#14372
#147623