Finite Group Databasebeta

← #10720198

Subgroups — #10720198

Order 768.

2526 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#896C211yesmaximal, characteristic
2C22×D3×C4⋊C4C211yesmaximal, characteristic
3C2×#4646C212yesmaximal, complemented
4C2×#4666C211yesmaximal, characteristic
5C3×#1441C211yesmaximal, characteristic, complemented
6#71566C211yesmaximal, characteristic, complemented
7#71565C211yesmaximal, characteristic, complemented
8(C2×D3)⋊#95C212yesmaximal
9(C2×D3)⋊#95C212yesmaximal
10#69410C211yesmaximal, characteristic, complemented
11Dic3⋊#95C212yesmaximal, complemented
12#14139—31nomaximal, Sylow
13C23×C4×D3C2212yes—
14C23×C4×D3C2211yescharacteristic
15C23×Dic6C2211yescharacteristic
16C22×C3×C4⋊C4C2211yescharacteristic
17C22×C3×C4⋊C4C2211yescharacteristic
18C22×(C2×D3)⋊C4C2211yescharacteristic
19C22×(C2×D3)⋊C4C2211yescharacteristic
20C22×(C2×D3)⋊C4C2212yes—
21C22×C4⋊Dic3C2211yescharacteristic
22C22×Dic3⋊C4C2211yescharacteristic
23C22×Dic3⋊C4C2211yescharacteristic
24C22×Dic3⋊C4C2212yes—
25C22×C4×Dic3C2212yes—
26C2×#896—24no—
27C2×#896—24no—
28C2×#896C418yescomplemented
29C2×D3×C4⋊C4—24no—
30C2×D3×C4⋊C4—28no—
31C2×C3×#95C2211yescharacteristic
32C2×C3×#95C2212yes—
33C2×C3×#95C2212yes—
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2211yescharacteristic
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2212yes—
40C2×C3⋊#95C2212yes—
41#4666—24no—
42#4646—28no—
43C22×C22⋊Q8—31no—
44C23×C4⋊C4—31no—
45C2×#391—32no—
46C2×C4×C22⋊C4—31no—
47#1441—31no—
48#1441—31no—
49#1441—31no—
50#1441D311yescharacteristic, complemented
51C4⋊#95—32no—
52C22⋊#95—32no—
53C22⋊#95—32no—
54C24×D3C2311yescharacteristic
55C23×C3×C4C2311yescharacteristic
56C23×C3×C4C2311yescharacteristic
57C23×C3×C4C2312yes—
58C23×C3×C4C2312yes—
59C23×C3×C4C2311yescharacteristic
60C23×Dic3C2311yescharacteristic
61C23×Dic3C2311yescharacteristic
62C23×Dic3C2312yes—
63C23×Dic3C2312yes—
64C23×Dic3C2311yescharacteristic
65C22×C4×D3—24no—
66C22×C4×D3—24no—
67C22×C4×D3—24no—
68C22×C4×D3—24no—
69C22×C4×D3—24no—
70C22×C4×D3—24no—
71C22×C4×D3—24no—
72C22×C4×D3—42no—
73C22×C4×D3—42no—
74C22×C4×D3C2×C414yes—
75C22×C4×D3D414yes—
76C22×C4×D3D414yes—
77C22×Dic6—24no—
78C22×Dic6—22no—
79C22×Dic6—22no—
80C22×Dic6—24no—
81C22×Dic6C2×C414yescomplemented
82C2×C3×C4⋊C4—24no—
83C2×C3×C4⋊C4—22no—
84C2×C3×C4⋊C4—22no—
85C2×C3×C4⋊C4—22no—
86C2×C3×C4⋊C4C2×C414yescomplemented
87C2×(C2×D3)⋊C4—24no—
88C2×(C2×D3)⋊C4—22no—
89C2×(C2×D3)⋊C4—22no—
90C2×(C2×D3)⋊C4—22no—
91C2×(C2×D3)⋊C4—22no—
92C2×(C2×D3)⋊C4—24no—
93C2×(C2×D3)⋊C4C2×C414yes—
94C2×(C2×D3)⋊C4C2×C414yes—
95C2×(C2×D3)⋊C4Q818yescomplemented
96C2×C4⋊Dic3—22no—
97C2×C4⋊Dic3—24no—
98C2×Dic3⋊C4—22no—
99C2×Dic3⋊C4—22no—
100C2×Dic3⋊C4—24no—
101C2×Dic3⋊C4—24no—
102C2×Dic3⋊C4—22no—
103C2×Dic3⋊C4—22no—
104C2×Dic3⋊C4C2×C414yescomplemented
105C2×Dic3⋊C4C2×C414yescomplemented
106C2×Dic3⋊C4D418yes—
107C2×C4×Dic3—24no—
108C2×C4×Dic3—24no—
109C2×C4×Dic3—24no—
110#896—232no—
111D3×C4⋊C4—232no—
112C3×#95—24no—
113C3×#95—22no—
114C3×#95—42no—
115C3⋊#95—24no—
116C3⋊#95—22no—
117C3⋊#95—24no—
118C3⋊#95—24no—
119C3⋊#95—42no—
120C3⋊#95—42no—
121C3⋊#95—42no—
122C23×Q8—31no—
123C24×C4—31no—
124C24×C4—32no—
125C2×C22⋊Q8—38no—
126C2×C22⋊Q8—64no—
127C2×C22⋊Q8—64no—
128C22×C4⋊C4—32no—
129C22×C4⋊C4—31no—
130C22×C4⋊C4—31no—
131C22×C4⋊C4—31no—
132C22×C4⋊C4—68no—
133C22×C4⋊C4—64no—
134C22×C4⋊C4C2×D311yescharacteristic
135C22×C4⋊C4C2×D311yescharacteristic
136C22×C22⋊C4—31no—
137C22×C22⋊C4—31no—
138C22×C22⋊C4—32no—
139C22×C42—32no—
140#391—68no—
141C4×C22⋊C4—64no—
142C2×#95—32no—
143C2×#95—32no—
144C2×#95—32no—
145C2×#95—31no—
146C2×#95—32no—
147C2×#95—32no—
148C2×#95—32no—
149C2×#95C2×D312yes—
150C2×#95C2×D311yescharacteristic
151C2×#95C2×D312yes—
152C24×C3C2411yescharacteristic
153C23×D3—22no—
154C23×D3—22no—
155C23×D3—21no—
156C23×D3—21no—
157C23×D3—21no—
158C23×D3—21no—
159C23×D3C22×C412yes—
160C23×D3C2×D412yes—
161C23×D3C2×D412yes—
162C23×D3C2×Q814yes—
163C23×D3#4114yes—
164C22×C3×C4—22no—
165C22×C3×C4—22no—
166C22×C3×C4—22no—
167C22×C3×C4—22no—
168C22×C3×C4—22no—
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4—22no—
172C22×C3×C4—22no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—22no—
176C22×C3×C4—22no—
177C22×C3×C4—22no—
178C22×C3×C4—22no—
179C22×C3×C4—22no—
180C22×C3×C4—21no—
181C22×C3×C4—22no—
182C22×C3×C4—22no—
183C22×C3×C4—21no—
184C22×C3×C4—22no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—22no—
188C22×C3×C4C22×C412yes—
189C22×C3×C4C22×C412yes—
190C22×C3×C4C22×C412yes—
191C22×C3×C4C2×D414yes—
192C22×C3×C4C2×D412yes—
193C22×C3×C4C2×D412yes—
194C22×C3×C4C2×Q814yes—
195C22×Dic3—22no—
196C22×Dic3—22no—
197C22×Dic3—22no—
198C22×Dic3—21no—
199C22×Dic3—21no—
200C22×Dic3—22no—
201C22×Dic3—22no—
202C22×Dic3—21no—
203C22×Dic3—21no—
204C22×Dic3—22no—
205C22×Dic3—22no—
206C22×Dic3—22no—
207C22×Dic3—22no—
208C22×Dic3—22no—
209C22×Dic3—21no—
210C22×Dic3—21no—
211C22×Dic3—22no—
212C22×Dic3—22no—
213C22×Dic3—22no—
214C22×Dic3—21no—
215C22×Dic3—22no—
216C22×Dic3—21no—
217C22×Dic3C22×C412yes—
218C22×Dic3C22×C412yes—
219C22×Dic3C22×C412yes—
220C22×Dic3C2×D414yes—
221C22×Dic3C2×D412yes—
222C22×Dic3C2×D412yes—
223C22×Dic3C2×D414yes—
224C22×Dic3C2×Q814yes—
225C22×Dic3#4114yes—
226C2×C4×D3—216no—
227C2×C4×D3—28no—
228C2×C4×D3—216no—
229C2×C4×D3—28no—
230C2×C4×D3—216no—
231C2×C4×D3—48no—
232C2×C4×D3—48no—
233C2×C4×D3—48no—
234C2×C4×D3—48no—
235C2×C4×D3—48no—
236C2×C4×D3—48no—
237C2×C4×D3C22⋊C4116yes—
238C2×Dic6—28no—
239C2×Dic6—216no—
240C2×Dic6—44no—
241C2×Dic6—48no—
242C2×Dic6—44no—
243C3×C4⋊C4—28no—
244C3×C4⋊C4—28no—
245(C2×D3)⋊C4—28no—
246(C2×D3)⋊C4—28no—
247(C2×D3)⋊C4—216no—
248C4⋊Dic3—28no—
249Dic3⋊C4—28no—
250Dic3⋊C4—28no—
251Dic3⋊C4—216no—
252C4×Dic3—48no—
253C25—31no—
254C22×Q8—34no—
255C22×Q8—62no—
256C22×Q8—62no—
257C22×Q8—64no—
258C22×Q8—64no—
259C23×C4—31no—
260C23×C4—34no—
261C23×C4—34no—
262C23×C4—34no—
263C23×C4—31no—
264C23×C4—31no—
265C23×C4—32no—
266C23×C4—32no—
267C23×C4—64no—
268C23×C4—64no—
269C23×C4—64no—
270C23×C4—64no—
271C23×C4—64no—
272C23×C4—64no—
273C23×C4—64no—
274C23×C4—122no—
275C23×C4—122no—
276C23×C4C22×D311yescharacteristic
277C23×C4C22×D311yescharacteristic
278C23×C4C22×D312yes—
279C23×C4C22×D312yes—
280C23×C4C22×D311yescharacteristic
281C22⋊Q8—632no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—34no—
287C2×C4⋊C4—34no—
288C2×C4⋊C4—38no—
289C2×C4⋊C4—632no—
290C2×C4⋊C4—64no—
291C2×C4⋊C4—64no—
292C2×C4⋊C4—64no—
293C2×C4⋊C4—62no—
294C2×C4⋊C4—62no—
295C2×C4⋊C4—62no—
296C2×C4⋊C4—62no—
297C2×C4⋊C4—62no—
298C2×C4⋊C4C4×D314yescomplemented
299C2×C22⋊C4—34no—
300C2×C22⋊C4—34no—
301C2×C22⋊C4—38no—
302C2×C22⋊C4—62no—
303C2×C22⋊C4—62no—
304C2×C22⋊C4—62no—
305C2×C22⋊C4—62no—
306C2×C22⋊C4—64no—
307C2×C22⋊C4—64no—
308C2×C42—64no—
309C2×C42—64no—
310C2×C42—64no—
311#95—22no—
312#95—24no—
313#95—42no—
314#95—64no—
315#95—64no—
316#95—62no—
317#95—64no—
318#95—122no—
319#95—122no—
320#95—122no—
321C23×C3C23×C411yescharacteristic
322C23×C3C22×D411yescharacteristic
323C23×C3C22×D411yescharacteristic
324C23×C3C22×D412yes—
325C23×C3C22×Q812yes—
326C23×C3C2×#4112yes—
327C23×C3C2×#4112yes—
328C23×C3H(5,𝔽2)11yescharacteristic
329C23×C3H(5,𝔽2)11yescharacteristic
330C23×C32−1+411yescharacteristic
331C23×C32−1+411yescharacteristic
332C22×D3—24no—
333C22×D3—22no—
334C22×D3—22no—
335C22×D3—22no—
336C22×D3—24no—
337C22×D3—22no—
338C22×D3—22no—
339C22×D3—22no—
340C22×D3—22no—
341C22×D3—22no—
342C22×D3—24no—
343C22×D3—24no—
344C22×D3—24no—
345C22×D3—24no—
346C22×D3—24no—
347C22×D3—24no—
348C22×D3—24no—
349C22×D3—24no—
350C22×D3C2×C22⋊C414yes—
351C22×D3C4×Q818yes—
352C22×D3C22⋊Q818yes—
353C22×D3#12414yes—
354C22×D3C4⋊Q814yes—
355C2×C3×C4—24no—
356C2×C3×C4—22no—
357C2×C3×C4—24no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—24no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—24no—
365C2×C3×C4—24no—
366C2×C3×C4—24no—
367C2×C3×C4—24no—
368C2×C3×C4—24no—
369C2×C3×C4—24no—
370C2×C3×C4—41no—
371C2×C3×C4—42no—
372C2×C3×C4—42no—
373C2×C3×C4—41no—
374C2×C3×C4—42no—
375C2×C3×C4—42no—
376C2×C3×C4—41no—
377C2×C3×C4—41no—
378C2×C3×C4—41no—
379C2×C3×C4—42no—
380C2×C3×C4—41no—
381C2×C3×C4—42no—
382C2×C3×C4—42no—
383C2×C3×C4—42no—
384C2×C3×C4—42no—
385C2×C3×C4C2×C22⋊C414yes—
386C2×Dic3—22no—
387C2×Dic3—22no—
388C2×Dic3—24no—
389C2×Dic3—22no—
390C2×Dic3—22no—
391C2×Dic3—24no—
392C2×Dic3—24no—
393C2×Dic3—24no—
394C2×Dic3—24no—
395C2×Dic3—24no—
396C2×Dic3—24no—
397C2×Dic3—41no—
398C2×Dic3—42no—
399C2×Dic3—42no—
400C2×Dic3—41no—
401C2×Dic3—42no—
402C2×Dic3—42no—
403C2×Dic3—41no—
404C2×Dic3—41no—
405C2×Dic3—41no—
406C2×Dic3—41no—
407C2×Dic3—42no—
408C2×Dic3—42no—
409C2×Dic3—42no—
410C2×Dic3—42no—
411C2×Dic3—42no—
412C2×Dic3C2×C22⋊C414yes—
413C2×Dic3C4×D418yes—
414C2×Dic3#12014yes—
415C2×Dic3#12118yes—
416C2×Dic3#12314yes—
417C4×D3—232no—
418C4×D3—432no—
419Dic6—416no—
420C24—32no—
421C24—32no—
422C24—32no—
423C24—34no—
424C24—34no—
425C24—62no—
426C24—61no—
427C24—61no—
428C24—62no—
429C24—61no—
430C24—61no—
431C24C23×D311yescharacteristic
432C2×Q8—68no—
433C2×Q8—616no—
434C2×Q8—124no—
435C2×Q8—124no—
436C2×Q8—128no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—32no—
462C22×C4—32no—
463C22×C4—34no—
464C22×C4—32no—
465C22×C4—34no—
466C22×C4—316no—
467C22×C4—32no—
468C22×C4—32no—
469C22×C4—34no—
470C22×C4—34no—
471C22×C4—68no—
472C22×C4—68no—
473C22×C4—616no—
474C22×C4—616no—
475C22×C4—616no—
476C22×C4—62no—
477C22×C4—62no—
478C22×C4—62no—
479C22×C4—61no—
480C22×C4—61no—
481C22×C4—61no—
482C22×C4—61no—
483C22×C4—62no—
484C22×C4—62no—
485C22×C4—61no—
486C22×C4—62no—
487C22×C4—62no—
488C22×C4—61no—
489C22×C4—62no—
490C22×C4—62no—
491C22×C4—62no—
492C22×C4—62no—
493C22×C4—62no—
494C22×C4—62no—
495C22×C4—61no—
496C22×C4—62no—
497C22×C4—61no—
498C22×C4—128no—
499C22×C4—128no—
500C22×C4—128no—
501C22×C4—128no—
502C22×C4—128no—
503C22×C4—128no—
504C22×C4C2×C4×D312yes—
505C22×C4C2×C4×D312yes—
506C22×C4C2×C4×D312yes—
507C22×C4D3×D414yes—
508C22×C4D3×D412yes—
509C22×C4D3×D412yes—
510C22×C4D3×Q814yes—
511C4⋊C4—28no—
512C4⋊C4—28no—
513C4⋊C4—616no—
514C4⋊C4—68no—
515C4⋊C4—68no—
516C4⋊C4—68no—
517C22⋊C4—68no—
518C22⋊C4—68no—
519C22⋊C4—616no—
520C42—128no—
521C22×C3C22×C22⋊C411yescharacteristic
522C22×C3C2×C4×D412yes—
523C22×C3C2×C4×Q812yes—
524C22×C3#52011yescharacteristic
525C22×C3#52011yescharacteristic
526C22×C3C2×#12011yescharacteristic
527C22×C3C2×#12112yes—
528C22×C3C2×C22⋊Q812yes—
529C22×C3C2×#12311yescharacteristic
530C22×C3C2×#12411yescharacteristic
531C22×C3C2×C4⋊Q811yescharacteristic
532C22×C3#53511yescharacteristic
533C22×C3#53611yescharacteristic
534C22×C3#53711yescharacteristic
535C22×C3#53711yescharacteristic
536C22×C3#54612yes—
537C22×C3#54612yes—
538C22×C3D4×Q812yes—
539C22×C3D4×Q812yes—
540C22×C3#55212yes—
541C22×C3#55212yes—
542C22×C3#55412yes—
543C22×C3#55412yes—
544C2×D3—24no—
545C2×D3—28no—
546C2×D3—28no—
547C2×D3—28no—
548C2×D3—28no—
549C2×D3—24no—
550C2×D3—24no—
551C2×D3—24no—
552C2×D3—24no—
553C2×D3—24no—
554C2×D3#39118yescomplemented
555C3×C4—24no—
556C3×C4—42no—
557C3×C4—44no—
558C3×C4—44no—
559C3×C4—42no—
560Dic3—42no—
561Dic3—44no—
562Dic3—44no—
563Dic3—42no—
564Dic3#38618yes—
565C23—34no—
566C23—34no—
567C23—34no—
568C23—38no—
569C23—38no—
570C23—64no—
571C23—64no—
572C23—62no—
573C23—64no—
574C23—64no—
575C23—64no—
576C23—64no—
577C23—64no—
578C23—62no—
579C23—62no—
580C23—64no—
581C23—62no—
582C23—64no—
583C23—62no—
584C23—62no—
585C23—64no—
586C23—62no—
587C23—62no—
588C23C22×C4×D311yescharacteristic
589C23C2×D3×D412yes—
590C23C2×D3×D411yescharacteristic
591C23C2×D3×D411yescharacteristic
592C23#100411yescharacteristic
593C23C2×D3×Q812yes—
594C23#100711yescharacteristic
595C23D3×#4112yes—
596C23D3×#4112yes—
597C23#100911yescharacteristic
598C23#101011yescharacteristic
599Q8—1216no—
600C2×C4—22no—
601C2×C4—24no—
602C2×C4—22no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—24no—
606C2×C4—24no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—24no—
612C2×C4—24no—
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—34no—
616C2×C4—34no—
617C2×C4—38no—
618C2×C4—34no—
619C2×C4—38no—
620C2×C4—41no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—41no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—632no—
636C2×C4—64no—
637C2×C4—64no—
638C2×C4—64no—
639C2×C4—62no—
640C2×C4—62no—
641C2×C4—62no—
642C2×C4—62no—
643C2×C4—64no—
644C2×C4—64no—
645C2×C4—64no—
646C2×C4—64no—
647C2×C4—1232no—
648C2×C4—121no—
649C2×C4—122no—
650C2×C4—122no—
651C2×C4—122no—
652C2×C4—122no—
653C2×C4—121no—
654C2×C4—122no—
655C2×C4—122no—
656C2×C4—122no—
657C2×C4—121no—
658C2×C4—121no—
659C2×C4—122no—
660C2×C4—121no—
661C2×C4—121no—
662C2×C4—122no—
663C2×C4D3×C22⋊C414yes—
664C2×C3C2×#38611yescharacteristic
665C2×C3C2×#39111yescharacteristic
666C2×C3#231111yescharacteristic
667C2×C3#236012yes—
668C2×C3#236012yes—
669C2×C3#241712yes—
670C2×C3#241712yes—
671C2×C3#243411yescharacteristic
672C2×C3#243511yescharacteristic
673C2×C3#250211yescharacteristic
674C2×C3#250311yescharacteristic
675D3—28no—
676C22—38no—
677C22—64no—
678C22—64no—
679C22—64no—
680C22—64no—
681C22—64no—
682C22—68no—
683C22—64no—
684C22—68no—
685C22—68no—
686C22—68no—
687C22C2×D3×C22⋊C411yescharacteristic
688C22#550411yescharacteristic
689C22#552311yescharacteristic
690C22C4×D3×D412yes—
691C22C4×D3×Q812yes—
692C22D3×#12011yescharacteristic
693C22D3×#12112yes—
694C22#560711yescharacteristic
695C22#560811yescharacteristic
696C22#561012yes—
697C22D3×C22⋊Q812yes—
698C22#562811yescharacteristic
699C22#562911yescharacteristic
700C22#563212yes—
701C22#563612yes—
702C22D3×#12311yescharacteristic
703C22#565412yes—
704C22D3×#12411yescharacteristic
705C22#569012yes—
706C22#569312yes—
707C22#570812yes—
708C22D3×C4⋊Q811yescharacteristic
709C22#572712yes—
710C4—24no—
711C4—38no—
712C4—42no—
713C4—44no—
714C4—42no—
715C4—44no—
716C4—122no—
717C4—124no—
718C4—122no—
719C4—124no—
720C3#1413911yescharacteristic, complemented, Sylow
721C2—68no—
722C2#7400311yescharacteristic
723C2D3×#38611yescharacteristic
724C2#7496512yes—
725C2#7598312yes—
726C2D3×#39111yescharacteristic
727C2#7690511yescharacteristic
728C2#7717311yescharacteristic
729C2#7728512yes—
730C2#7774212yes—
731C2#7776511yescharacteristic
732C2#7815211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1441C2
socle, cosocleC24×C3C24
prime radicalC24×D3C23
hypercenter#1441D3
hypocenterC3#14139
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
3. C2×#4646C2semidirect
5. C3×#1441C2semidirect
6. #71566C2semidirect
7. #71565C2semidirect
10. #69410C2semidirect
11. Dic3⋊#95C2semidirect
28. C2×#896C4semidirect
50. #1441D3semidirect
81. C22×Dic6C2×C4semidirect
86. C2×C3×C4⋊C4C2×C4semidirect
95. C2×(C2×D3)⋊C4Q8semidirect
104. C2×Dic3⋊C4C2×C4semidirect
105. C2×Dic3⋊C4C2×C4semidirect
298. C2×C4⋊C4C4×D3semidirect
554. C2×D3#391semidirect
720. C3#14139semidirect

Maximal subgroups

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

subgroupindex
C22×#8962
C22×D3×C4⋊C42
C2×#46462
C2×#46662
C3×#14412
#715662
#715652
(C2×D3)⋊#952
#694102
Dic3⋊#952
#141393