Finite Group Databasebeta

← C3×#15070 #10633677

Subgroups — C3×#15070 #10633677

Order 768.

2038 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#124C211yesmaximal, characteristic
2C2×C3×#395C211yesmaximal, characteristic, complemented
3C2×C3×#394C211yesmaximal, characteristic
4C2×C3×#388C212yesmaximal, complemented
5C2×C3×C4×C4⋊C4C211yesmaximal, characteristic, complemented
6C3×#1446C211yesmaximal, characteristic, complemented
7C3×#1439C212yesmaximal, complemented
8C3×#1439C212yesmaximal, complemented
9C3×#1438C211yesmaximal, characteristic
10C3×#1437C212yesmaximal, complemented
11C3×#1434C211yesmaximal, characteristic, complemented
12#15070C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×Q8C2211yescharacteristic
14C23×C3×D4C2211yescharacteristic
15C2×C3×#124—28no—
16C2×C3×#124—24no—
17C22×C3×C4⋊C4C2211yescharacteristic
18C22×C3×C4⋊C4C2212yes—
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2212yes—
21C22×C3×C22⋊C4C2212yes—
22C22×C3×C22⋊C4C2212yes—
23C22×C3×C22⋊C4C2212yes—
24C22×C3×C22⋊C4C2212yes—
25C22×C3×C22⋊C4C2212yes—
26C22×C3×C42C2211yescharacteristic
27C22×C3×C42C2211yescharacteristic
28C22×C3×C42C2211yescharacteristic
29C3×#395—24no—
30C3×#394—24no—
31C3×#388—28no—
32C3×C4×C4⋊C4—24no—
33C2×C3×#95C2211yescharacteristic
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2212yes—
36C2×C3×#95C2211yescharacteristic
37C2×C3×#95C2211yescharacteristic
38C2×C3×#95C2212yes—
39C2×C3×#95C2212yes—
40C2×C3×#95C2212yes—
41C2×C3×#95C2212yes—
42C22×#124C2×C311yescharacteristic
43C2×#395C2×C311yescharacteristic, complemented
44C2×#394C2×C311yescharacteristic
45C2×#388C2×C312yescomplemented
46C2×C4×C4⋊C4C2×C311yescharacteristic, complemented
47#1446C2×C311yescharacteristic, complemented
48#1439C2×C312yescomplemented
49#1439C2×C312yescomplemented
50#1438C2×C311yescharacteristic
51#1437C2×C312yescomplemented
52#1434C2×C311yescharacteristic, complemented
53C25×C3C2312yes—
54C22×C3×Q8—24no—
55C22×C3×Q8—22no—
56C22×C3×Q8—22no—
57C22×C3×Q8—22no—
58C22×C3×Q8—42no—
59C22×C3×D4—24no—
60C22×C3×D4—22no—
61C22×C3×D4—22no—
62C22×C3×D4—22no—
63C22×C3×D4—42no—
64C23×C3×C4C2312yes—
65C23×C3×C4C2312yes—
66C23×C3×C4C2311yescharacteristic
67C23×C3×C4C2311yescharacteristic
68C23×C3×C4C2311yescharacteristic
69C23×C3×C4C2312yes—
70C23×C3×C4C2311yescharacteristic
71C23×C3×C4C2311yescharacteristic
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C3×#124—232no—
75C2×C3×C4⋊C4—22no—
76C2×C3×C4⋊C4—22no—
77C2×C3×C4⋊C4—22no—
78C2×C3×C4⋊C4—22no—
79C2×C3×C4⋊C4—22no—
80C2×C3×C4⋊C4—24no—
81C2×C3×C4⋊C4—24no—
82C2×C3×C4⋊C4—42no—
83C2×C3×C4⋊C4D414yes—
84C2×C3×C22⋊C4—24no—
85C2×C3×C22⋊C4—24no—
86C2×C3×C22⋊C4—24no—
87C2×C3×C22⋊C4—24no—
88C2×C3×C22⋊C4—24no—
89C2×C3×C22⋊C4—24no—
90C2×C3×C22⋊C4—24no—
91C2×C3×C22⋊C4—24no—
92C2×C3×C22⋊C4—24no—
93C2×C3×C22⋊C4—24no—
94C2×C3×C22⋊C4—24no—
95C2×C3×C22⋊C4—24no—
96C2×C3×C22⋊C4—24no—
97C2×C3×C22⋊C4—24no—
98C2×C3×C22⋊C4—24no—
99C2×C3×C22⋊C4—42no—
100C2×C3×C22⋊C4—42no—
101C2×C3×C22⋊C4D418yes—
102C2×C3×C42—22no—
103C2×C3×C42—24no—
104C2×C3×C42—22no—
105C2×C3×C42—22no—
106C2×C3×C42—22no—
107C2×C3×C42—24no—
108C2×C3×C42D414yes—
109C3×#95—22no—
110C3×#95—22no—
111C3×#95—24no—
112C3×#95—24no—
113C3×#95—22no—
114C3×#95—22no—
115C3×#95—24no—
116C3×#95—24no—
117C3×#95—42no—
118C23×Q8C22×C311yescharacteristic
119C23×D4C22×C311yescharacteristic
120C2×#124—28no—
121C2×#124—24no—
122C22×C4⋊C4C22×C311yescharacteristic
123C22×C4⋊C4C22×C312yes—
124C22×C4⋊C4C22×C311yescharacteristic
125C22×C22⋊C4C22×C312yes—
126C22×C22⋊C4C22×C312yes—
127C22×C22⋊C4C22×C312yes—
128C22×C22⋊C4C22×C312yes—
129C22×C22⋊C4C22×C312yes—
130C22×C22⋊C4C22×C312yes—
131C22×C42C22×C311yescharacteristic
132C22×C42C22×C311yescharacteristic
133C22×C42C22×C311yescharacteristic
134#395—24no—
135#394—24no—
136#388—28no—
137C4×C4⋊C4—24no—
138C2×#95C22×C311yescharacteristic
139C2×#95C22×C311yescharacteristic
140C2×#95C22×C312yes—
141C2×#95C22×C312yes—
142C2×#95C22×C312yes—
143C2×#95C22×C311yescharacteristic
144C2×#95C22×C311yescharacteristic
145C2×#95C22×C312yes—
146C2×#95C22×C312yes—
147C24×C3—22no—
148C24×C3—22no—
149C24×C3—22no—
150C24×C3—22no—
151C24×C3—22no—
152C24×C3—22no—
153C24×C3—22no—
154C24×C3—22no—
155C24×C3—22no—
156C24×C3—22no—
157C24×C3—22no—
158C24×C3—22no—
159C24×C3—22no—
160C24×C3—22no—
161C24×C3C2×D414yes—
162C24×C3C2411yescharacteristic
163C2×C3×Q8—28no—
164C2×C3×Q8—48no—
165C2×C3×Q8—48no—
166C2×C3×Q8—44no—
167C2×C3×Q8—44no—
168C2×C3×D4—28no—
169C2×C3×D4—48no—
170C2×C3×D4—48no—
171C2×C3×D4—44no—
172C2×C3×D4—44no—
173C22×C3×C4—21no—
174C22×C3×C4—22no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—22no—
181C22×C3×C4—22no—
182C22×C3×C4—21no—
183C22×C3×C4—22no—
184C22×C3×C4—22no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—22no—
188C22×C3×C4—22no—
189C22×C3×C4—22no—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—21no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—22no—
204C22×C3×C4—22no—
205C22×C3×C4—22no—
206C22×C3×C4—22no—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4—22no—
210C22×C3×C4—22no—
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×C4C2×D412yes—
218C22×C3×C4C2×D414yes—
219C22×C3×C4C2×D412yes—
220C22×C3×C4C2×D414yes—
221C22×C3×C4C2×D412yes—
222C22×C3×C4C2×D412yes—
223C22×C3×C4C2×D412yes—
224C22×C3×C4C2×D412yes—
225C22×C3×C4#4114yes—
226C22×C3×C4#4112yes—
227C22×C3×C4#4112yes—
228C22×C3×C4#4112yes—
229C22×C3×C4#4112yes—
230C22×C3×C4#4112yes—
231C3×C4⋊C4—28no—
232C3×C4⋊C4—28no—
233C3×C4⋊C4—48no—
234C3×C22⋊C4—216no—
235C3×C22⋊C4—216no—
236C3×C22⋊C4—216no—
237C3×C22⋊C4—48no—
238C3×C22⋊C4—48no—
239C3×C22⋊C4—48no—
240C3×C42—28no—
241C3×C42—28no—
242C3×C42—44no—
243C25C23×C312yes—
244C22×Q8—24no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—42no—
249C22×D4—24no—
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—42no—
254C23×C4C23×C312yes—
255C23×C4C23×C311yescharacteristic
256C23×C4C23×C312yes—
257C23×C4C23×C311yescharacteristic
258C23×C4C23×C312yes—
259C23×C4C23×C311yescharacteristic
260C23×C4C23×C311yescharacteristic
261C23×C4C23×C311yescharacteristic
262C23×C4C23×C311yescharacteristic
263C23×C4C23×C311yescharacteristic
264#124—232no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—42no—
273C2×C4⋊C4C3×D414yes—
274C2×C22⋊C4—24no—
275C2×C22⋊C4—24no—
276C2×C22⋊C4—24no—
277C2×C22⋊C4—24no—
278C2×C22⋊C4—24no—
279C2×C22⋊C4—24no—
280C2×C22⋊C4—24no—
281C2×C22⋊C4—24no—
282C2×C22⋊C4—24no—
283C2×C22⋊C4—24no—
284C2×C22⋊C4—24no—
285C2×C22⋊C4—24no—
286C2×C22⋊C4—24no—
287C2×C22⋊C4—24no—
288C2×C22⋊C4—24no—
289C2×C22⋊C4—42no—
290C2×C22⋊C4—42no—
291C2×C22⋊C4C3×D418yes—
292C2×C42—24no—
293C2×C42—22no—
294C2×C42—22no—
295C2×C42—22no—
296C2×C42—22no—
297C2×C42—24no—
298C2×C42C3×D414yes—
299#95—22no—
300#95—22no—
301#95—24no—
302#95—24no—
303#95—22no—
304#95—22no—
305#95—24no—
306#95—24no—
307#95—42no—
308C23×C3—24no—
309C23×C3—24no—
310C23×C3—24no—
311C23×C3—24no—
312C23×C3—24no—
313C23×C3—24no—
314C23×C3—24no—
315C23×C3—42no—
316C23×C3—42no—
317C23×C3—42no—
318C23×C3—42no—
319C23×C3—42no—
320C23×C3—42no—
321C23×C3—42no—
322C23×C3—42no—
323C23×C3—42no—
324C23×C3—42no—
325C23×C3—42no—
326C23×C3—42no—
327C23×C3—42no—
328C23×C3—42no—
329C23×C3—42no—
330C23×C3—42no—
331C23×C3—42no—
332C23×C3—42no—
333C23×C3—42no—
334C23×C3—42no—
335C23×C3—42no—
336C23×C3—42no—
337C23×C3—42no—
338C23×C3—42no—
339C23×C3—42no—
340C23×C3—42no—
341C23×C3—42no—
342C23×C3—42no—
343C23×C3C22×D411yescharacteristic
344C23×C3C22×D412yes—
345C23×C3C22×D411yescharacteristic
346C23×C3C2×#4111yescharacteristic
347C23×C3C2×#4111yescharacteristic
348C23×C3C2×#4111yescharacteristic
349C23×C3C2×#4111yescharacteristic
350C23×C3C2×#4111yescharacteristic
351C23×C3C2×#4112yes—
352C23×C3H(5,𝔽2)12yes—
353C23×C32−1+412yes—
354C3×Q8—416no—
355C3×D4—416no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—24no—
367C2×C3×C4—24no—
368C2×C3×C4—24no—
369C2×C3×C4—24no—
370C2×C3×C4—22no—
371C2×C3×C4—24no—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4—24no—
375C2×C3×C4—24no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—24no—
380C2×C3×C4—24no—
381C2×C3×C4—24no—
382C2×C3×C4—24no—
383C2×C3×C4—24no—
384C2×C3×C4—24no—
385C2×C3×C4—41no—
386C2×C3×C4—41no—
387C2×C3×C4—42no—
388C2×C3×C4—42no—
389C2×C3×C4—41no—
390C2×C3×C4—41no—
391C2×C3×C4—42no—
392C2×C3×C4—42no—
393C2×C3×C4—42no—
394C2×C3×C4—41no—
395C2×C3×C4—41no—
396C2×C3×C4—42no—
397C2×C3×C4—42no—
398C2×C3×C4—42no—
399C2×C3×C4—42no—
400C2×C3×C4—42no—
401C2×C3×C4—42no—
402C2×C3×C4—42no—
403C2×C3×C4—42no—
404C2×C3×C4—42no—
405C2×C3×C4—42no—
406C2×C3×C4—42no—
407C2×C3×C4—42no—
408C2×C3×C4—42no—
409C2×C3×C4—42no—
410C2×C3×C4—42no—
411C2×C3×C4#12014yes—
412C2×C3×C4#12114yes—
413C2×C3×C4#12414yescomplemented
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24C2×C3×D414yes—
429C24C24×C311yescharacteristic
430C2×Q8—28no—
431C2×Q8—48no—
432C2×Q8—48no—
433C2×Q8—44no—
434C2×Q8—44no—
435C2×D4—28no—
436C2×D4—48no—
437C2×D4—48no—
438C2×D4—44no—
439C2×D4—44no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4C2×C3×D412yes—
485C22×C4C2×C3×D414yes—
486C22×C4C2×C3×D412yes—
487C22×C4C2×C3×D414yes—
488C22×C4C2×C3×D412yes—
489C22×C4C2×C3×D412yes—
490C22×C4C2×C3×D412yes—
491C22×C4C2×C3×D412yes—
492C22×C4C3×#4114yes—
493C22×C4C3×#4112yes—
494C22×C4C3×#4112yes—
495C22×C4C3×#4112yes—
496C22×C4C3×#4112yes—
497C22×C4C3×#4112yes—
498C4⋊C4—28no—
499C4⋊C4—28no—
500C4⋊C4—48no—
501C22⋊C4—216no—
502C22⋊C4—216no—
503C22⋊C4—216no—
504C22⋊C4—48no—
505C22⋊C4—48no—
506C22⋊C4—48no—
507C42—28no—
508C42—28no—
509C42—44no—
510C22×C3—44no—
511C22×C3—44no—
512C22×C3—44no—
513C22×C3—44no—
514C22×C3—44no—
515C22×C3—44no—
516C22×C3—44no—
517C22×C3—82no—
518C22×C3—82no—
519C22×C3—82no—
520C22×C3—82no—
521C22×C3—82no—
522C22×C3—82no—
523C22×C3—82no—
524C22×C3—82no—
525C22×C3C2×#12011yescharacteristic
526C22×C3C2×#12111yescharacteristic
527C22×C3#52511yescharacteristic
528C22×C3#52511yescharacteristic
529C22×C3#52512yes—
530C22×C3C2×#12411yescharacteristic
531C22×C3#52911yescharacteristic
532C22×C3#52911yescharacteristic
533C22×C3#53211yescharacteristic
534C22×C3#53211yescharacteristic
535C22×C3#53212yes—
536C22×C3#53511yescharacteristic
537C22×C3#53611yescharacteristic
538C22×C3#54212yes—
539C22×C3#54212yes—
540C22×C3D4212yes—
541C22×C3#54612yes—
542C22×C3#54712yes—
543C22×C3#54712yes—
544C22×C3#54812yes—
545C22×C3#55112yes—
546C22×C3#55512yes—
547C22×C3#55612yes—
548C3×C4—24no—
549C3×C4—24no—
550C3×C4—24no—
551C3×C4—42no—
552C3×C4—42no—
553C3×C4—42no—
554C3×C4—42no—
555C3×C4—44no—
556C3×C4—44no—
557C3×C4—82no—
558C23—24no—
559C23—24no—
560C23—24no—
561C23—24no—
562C23—24no—
563C23—24no—
564C23—24no—
565C23—42no—
566C23—42no—
567C23—42no—
568C23—42no—
569C23—42no—
570C23—42no—
571C23—42no—
572C23—42no—
573C23—42no—
574C23—42no—
575C23—42no—
576C23—42no—
577C23—42no—
578C23—42no—
579C23—42no—
580C23—42no—
581C23—42no—
582C23—42no—
583C23—42no—
584C23—42no—
585C23—42no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23C22×C3×D411yescharacteristic
594C23C22×C3×D412yes—
595C23C22×C3×D411yescharacteristic
596C23C2×C3×#4111yescharacteristic
597C23C2×C3×#4111yescharacteristic
598C23C2×C3×#4111yescharacteristic
599C23C2×C3×#4111yescharacteristic
600C23C2×C3×#4111yescharacteristic
601C23C2×C3×#4112yes—
602C23C3×H(5,𝔽2)12yes—
603C23C3×2−1+412yes—
604Q8—416no—
605D4—416no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—24no—
620C2×C4—22no—
621C2×C4—24no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—24no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—41no—
642C2×C4—42no—
643C2×C4—41no—
644C2×C4—42no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4C3×#12014yes—
662C2×C4C3×#12114yes—
663C2×C4C3×#12414yescomplemented
664C2×C3—84no—
665C2×C3#238811yescharacteristic
666C2×C3#240611yescharacteristic
667C2×C3#240811yescharacteristic
668C2×C3#246112yes—
669C2×C3#247412yes—
670C2×C3#249112yes—
671C2×C3#252112yes—
672C2×C3#254511yescharacteristic
673C2×C3#261011yescharacteristic
674C2×C3#263211yescharacteristic
675C2×C3#285011yescharacteristic
676C22—44no—
677C22—44no—
678C22—44no—
679C22—44no—
680C22—44no—
681C22—44no—
682C22—44no—
683C22—82no—
684C22—82no—
685C22—82no—
686C22—82no—
687C22—82no—
688C22—82no—
689C22—82no—
690C22—82no—
691C22C2×C3×#12011yescharacteristic
692C22C2×C3×#12111yescharacteristic
693C22C3×#52511yescharacteristic
694C22C3×#52512yes—
695C22C3×#52511yescharacteristic
696C22C2×C3×#12411yescharacteristic
697C22C3×#52911yescharacteristic
698C22C3×#52911yescharacteristic
699C22C3×#53212yes—
700C22C3×#53211yescharacteristic
701C22C3×#53211yescharacteristic
702C22C3×#53511yescharacteristic
703C22C3×#53611yescharacteristic
704C22C3×#54212yes—
705C22C3×#54212yes—
706C22C3×D4212yes—
707C22C3×#54612yes—
708C22C3×#54712yes—
709C22C3×#54712yes—
710C22C3×#54812yes—
711C22C3×#55112yes—
712C22C3×#55512yes—
713C22C3×#55612yes—
714C4—24no—
715C4—24no—
716C4—24no—
717C4—42no—
718C4—42no—
719C4—44no—
720C4—42no—
721C4—44no—
722C4—42no—
723C4—82no—
724C3#1507011yescharacteristic, direct product factor, Sylow
725C2—84no—
726C2C3×#238811yescharacteristic
727C2C3×#240611yescharacteristic
728C2C3×#240811yescharacteristic
729C2C3×#246112yes—
730C2C3×#247412yes—
731C2C3×#249112yes—
732C2C3×#252112yes—
733C2C3×#254511yescharacteristic
734C2C3×#261011yescharacteristic
735C2C3×#263211yescharacteristic
736C2C3×#285011yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC24C24×C3
prime radicalC23×C3×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#395C2semidirect
4. C2×C3×#388C2semidirect
5. C2×C3×C4×C4⋊C4C2semidirect
6. C3×#1446C2semidirect
7. C3×#1439C2semidirect
8. C3×#1439C2semidirect
10. C3×#1437C2semidirect
11. C3×#1434C2semidirect
12. #15070C3direct (N × H)
43. C2×#395C2×C3semidirect
45. C2×#388C2×C3semidirect
46. C2×C4×C4⋊C4C2×C3semidirect
47. #1446C2×C3semidirect
48. #1439C2×C3semidirect
49. #1439C2×C3semidirect
51. #1437C2×C3semidirect
52. #1434C2×C3semidirect
413. C2×C3×C4#124semidirect
663. C2×C4C3×#124semidirect
724. C3#15070direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1242
C2×C3×#3952
C2×C3×#3942
C2×C3×#3882
C2×C3×C4×C4⋊C42
C3×#14462
C3×#14392
C3×#14382
C3×#14372
C3×#14342
#150703