Finite Group Databasebeta

← #10726606

Subgroups — #10726606

Order 768.

2494 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4⋊Dic3C211yesmaximal, characteristic
2C22×#878C211yesmaximal, characteristic
3C2×#4950C211yesmaximal, characteristic
4C2×#4946C211yesmaximal, characteristic
5C2×#4656C212yesmaximal, complemented
6C3×C22⋊#95C211yesmaximal, characteristic
7#72127C211yesmaximal, characteristic
8#71544C211yesmaximal, characteristic
9#69420C212yesmaximal, complemented
10#69419C212yesmaximal, complemented
11#69411C212yesmaximal, complemented
12#14720—31nomaximal, Sylow
13C24×C3×C4C2211yescharacteristic
14C24×Dic3C2211yescharacteristic
15C24×Dic3C2211yescharacteristic
16C23×Dic6C2211yescharacteristic
17C22×C3×C22⋊C4C2211yescharacteristic
18C22×C3×C22⋊C4C2211yescharacteristic
19C22×#217C2211yescharacteristic
20C22×#217C2211yescharacteristic
21C22×C4⋊Dic3—24no—
22C22×C4⋊Dic3—28no—
23C22×C4⋊Dic3C2211yescharacteristic
24C22×C4⋊Dic3C2212yes—
25C22×C4⋊Dic3C2212yes—
26C22×C4⋊Dic3C2212yes—
27C22×Dic3⋊C4C2211yescharacteristic
28C22×Dic3⋊C4C2211yescharacteristic
29C22×Dic3⋊C4C2212yes—
30C2×#878—24no—
31C2×#878—24no—
32C2×#878—24no—
33C2×C3×#95C2212yes—
34C2×C3×#95C2212yes—
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2212yes—
40C2×C3⋊#95C2212yes—
41#4950—24no—
42#4946—24no—
43#4656—28no—
44C22×C22⋊Q8—31no—
45C23×C4⋊C4—31no—
46C2×#395—32no—
47C2×#385—31no—
48C2×#385—31no—
49#1444—32no—
50#1444—32no—
51#1441—32no—
52C22⋊#95—31no—
53C22⋊#95—31no—
54C22⋊#95D311yescharacteristic
55C25×C3C2311yescharacteristic
56C23×C3×C4—22no—
57C23×C3×C4—22no—
58C23×C3×C4—24no—
59C23×C3×C4—24no—
60C23×C3×C4Q814yescomplemented
61C23×C3×C4C2311yescharacteristic
62C23×C3×C4C2311yescharacteristic
63C23×C3×C4C2312yes—
64C23×C3×C4C2312yes—
65C23×Dic3—22no—
66C23×Dic3—22no—
67C23×Dic3—22no—
68C23×Dic3—24no—
69C23×Dic3—24no—
70C23×Dic3—22no—
71C23×Dic3—22no—
72C23×Dic3—42no—
73C23×Dic3—42no—
74C23×Dic3D414yes—
75C23×Dic3C2311yescharacteristic
76C23×Dic3C2312yes—
77C23×Dic3C2311yescharacteristic
78C23×Dic3C2311yescharacteristic
79C23×Dic3C2312yes—
80C23×Dic3C2311yescharacteristic
81C22×Dic6—22no—
82C22×Dic6—22no—
83C22×Dic6—22no—
84C22×Dic6—24no—
85C22×Dic6—42no—
86C2×C3×C22⋊C4—22no—
87C2×C3×C22⋊C4—22no—
88C2×C3×C22⋊C4—22no—
89C2×C3×C22⋊C4—22no—
90C2×C3×C22⋊C4D414yes—
91C2×C3×C22⋊C4Q814yescomplemented
92C2×#217—22no—
93C2×#217—22no—
94C2×#217—22no—
95C2×#217—22no—
96C2×#217D414yes—
97C2×#217Q814yescomplemented
98C2×C4⋊Dic3—232no—
99C2×C4⋊Dic3—22no—
100C2×C4⋊Dic3—24no—
101C2×C4⋊Dic3—22no—
102C2×C4⋊Dic3—22no—
103C2×C4⋊Dic3—24no—
104C2×C4⋊Dic3—24no—
105C2×C4⋊Dic3—24no—
106C2×C4⋊Dic3—24no—
107C2×C4⋊Dic3—24no—
108C2×C4⋊Dic3—24no—
109C2×C4⋊Dic3—42no—
110C2×C4⋊Dic3D418yes—
111C2×Dic3⋊C4—22no—
112C2×Dic3⋊C4—22no—
113C2×Dic3⋊C4—22no—
114C2×Dic3⋊C4—22no—
115C2×Dic3⋊C4—22no—
116C2×Dic3⋊C4—22no—
117C2×Dic3⋊C4—24no—
118C2×Dic3⋊C4—24no—
119C2×Dic3⋊C4—42no—
120#878—232no—
121C3×#95—24no—
122C3×#95—24no—
123C3⋊#95—24no—
124C3⋊#95—24no—
125C3⋊#95—24no—
126C3⋊#95—24no—
127C3⋊#95—24no—
128C3⋊#95—42no—
129C23×Q8—31no—
130C24×C4—31no—
131C24×C4—31no—
132C24×C4C2×D311yescharacteristic
133C2×C22⋊Q8—64no—
134C2×C22⋊Q8—64no—
135C2×C22⋊Q8—64no—
136C22×C4⋊C4—32no—
137C22×C4⋊C4—32no—
138C22×C4⋊C4—31no—
139C22×C4⋊C4—31no—
140C22×C4⋊C4—31no—
141C22×C4⋊C4—32no—
142C22×C4⋊C4—32no—
143C22×C4⋊C4—68no—
144C22×C4⋊C4—64no—
145C22×C22⋊C4—31no—
146C22×C22⋊C4—31no—
147C22×C22⋊C4C2×D311yescharacteristic
148C22×C22⋊C4C2×D311yescharacteristic
149#395—68no—
150#385—64no—
151#385—64no—
152C2×#95—32no—
153C2×#95—32no—
154C2×#95—32no—
155C2×#95—32no—
156C2×#95—32no—
157C2×#95—32no—
158C2×#95C2×D312yes—
159C2×#95C2×D312yes—
160C24×C3—22no—
161C24×C3—22no—
162C24×C3—22no—
163C24×C3—22no—
164C24×C3C2×D412yes—
165C24×C3C2×D412yes—
166C24×C3C2×D412yes—
167C24×C3C2×Q812yes—
168C24×C3C2×Q812yes—
169C24×C3C2×Q812yes—
170C24×C3#4112yes—
171C24×C3C2411yescharacteristic
172C22×C3×C4—28no—
173C22×C3×C4—216no—
174C22×C3×C4—28no—
175C22×C3×C4—28no—
176C22×C3×C4—22no—
177C22×C3×C4—22no—
178C22×C3×C4—22no—
179C22×C3×C4—22no—
180C22×C3×C4—216no—
181C22×C3×C4—22no—
182C22×C3×C4—22no—
183C22×C3×C4—22no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
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—22no—
195C22×C3×C4C2×D412yes—
196C22×C3×C4C2×D412yes—
197C22×C3×C4C2×D414yes—
198C22×C3×C4C2×Q814yes—
199C22×C3×C4C2×Q814yes—
200C22×C3×C4#4114yes—
201C22×Dic3—21no—
202C22×Dic3—21no—
203C22×Dic3—22no—
204C22×Dic3—28no—
205C22×Dic3—28no—
206C22×Dic3—22no—
207C22×Dic3—22no—
208C22×Dic3—22no—
209C22×Dic3—22no—
210C22×Dic3—22no—
211C22×Dic3—21no—
212C22×Dic3—21no—
213C22×Dic3—21no—
214C22×Dic3—21no—
215C22×Dic3—22no—
216C22×Dic3—22no—
217C22×Dic3—22no—
218C22×Dic3—21no—
219C22×Dic3—21no—
220C22×Dic3—22no—
221C22×Dic3—22no—
222C22×Dic3—22no—
223C22×Dic3—22no—
224C22×Dic3—22no—
225C22×Dic3—22no—
226C22×Dic3—22no—
227C22×Dic3—22no—
228C22×Dic3—22no—
229C22×Dic3—22no—
230C22×Dic3—28no—
231C22×Dic3—44no—
232C22×Dic3—48no—
233C22×Dic3—48no—
234C22×Dic3—48no—
235C22×Dic3—48no—
236C22×Dic3—44no—
237C22×Dic3—44no—
238C22×Dic3C2×D412yes—
239C22×Dic3C2×D412yes—
240C22×Dic3C2×D414yes—
241C22×Dic3C2×D412yes—
242C22×Dic3C2×D414yes—
243C22×Dic3C2×D412yes—
244C22×Dic3C2×Q814yes—
245C2×Dic6—28no—
246C2×Dic6—48no—
247C2×Dic6—48no—
248C2×Dic6—44no—
249C2×Dic6—44no—
250C3×C22⋊C4—28no—
251C3×C22⋊C4—28no—
252#217—28no—
253#217—28no—
254C4⋊Dic3—28no—
255C4⋊Dic3—216no—
256C4⋊Dic3—216no—
257C4⋊Dic3—48no—
258Dic3⋊C4—28no—
259Dic3⋊C4—28no—
260Dic3⋊C4—48no—
261C25C22×D311yescharacteristic
262C22×Q8—62no—
263C22×Q8—62no—
264C22×Q8—64no—
265C22×Q8—62no—
266C22×Q8—122no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—31no—
272C23×C4—31no—
273C23×C4—31no—
274C23×C4—32no—
275C23×C4—32no—
276C23×C4—31no—
277C23×C4—34no—
278C23×C4—64no—
279C23×C4—64no—
280C23×C4—62no—
281C23×C4—62no—
282C23×C4—62no—
283C23×C4—62no—
284C23×C4—62no—
285C23×C4—122no—
286C23×C4—122no—
287C23×C4Dic614yescomplemented
288C23×C4C22×D312yes—
289C23×C4C22×D311yescharacteristic
290C23×C4C22×D311yescharacteristic
291C23×C4C22×D312yes—
292C22⋊Q8—632no—
293C2×C4⋊C4—38no—
294C2×C4⋊C4—64no—
295C2×C4⋊C4—64no—
296C2×C4⋊C4—64no—
297C2×C4⋊C4—64no—
298C2×C4⋊C4—62no—
299C2×C4⋊C4—62no—
300C2×C4⋊C4—62no—
301C2×C4⋊C4—62no—
302C2×C4⋊C4—62no—
303C2×C4⋊C4—62no—
304C2×C4⋊C4—632no—
305C2×C4⋊C4—62no—
306C2×C4⋊C4—62no—
307C2×C4⋊C4—62no—
308C2×C4⋊C4—64no—
309C2×C4⋊C4—64no—
310C2×C4⋊C4—64no—
311C2×C4⋊C4—64no—
312C2×C4⋊C4—64no—
313C2×C4⋊C4—122no—
314C2×C4⋊C4—122no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—34no—
320C2×C22⋊C4—34no—
321C2×C22⋊C4—62no—
322C2×C22⋊C4—62no—
323C2×C22⋊C4—62no—
324C2×C22⋊C4—62no—
325C2×C22⋊C4Dic614yescomplemented
326C2×C22⋊C4D1214yes—
327#95—24no—
328#95—24no—
329#95—64no—
330#95—64no—
331#95—64no—
332#95—64no—
333#95—64no—
334#95—122no—
335C23×C3—22no—
336C23×C3—24no—
337C23×C3—22no—
338C23×C3—24no—
339C23×C3—22no—
340C23×C3—22no—
341C23×C3—24no—
342C23×C3—24no—
343C23×C3—24no—
344C23×C3—24no—
345C23×C3—24no—
346C23×C3—24no—
347C23×C3—24no—
348C23×C3—24no—
349C23×C3—24no—
350C23×C3—24no—
351C23×C3#12014yes—
352C23×C3C22⋊Q814yes—
353C23×C3C22⋊Q814yes—
354C23×C3C22⋊Q814yes—
355C23×C3C4⋊Q814yes—
356C23×C3C4⋊Q814yes—
357C23×C3C4⋊Q814yes—
358C23×C3C22×D411yescharacteristic
359C23×C3C22×D411yescharacteristic
360C23×C3C22×D412yes—
361C23×C3C22×D411yescharacteristic
362C23×C3C22×Q811yescharacteristic
363C23×C3C22×Q811yescharacteristic
364C23×C3C22×Q811yescharacteristic
365C23×C3C2×#4111yescharacteristic
366C23×C3C2×#4112yes—
367C23×C3H(5,𝔽2)12yes—
368C23×C32−1+412yes—
369C2×C3×C4—232no—
370C2×C3×C4—24no—
371C2×C3×C4—24no—
372C2×C3×C4—24no—
373C2×C3×C4—24no—
374C2×C3×C4—24no—
375C2×C3×C4—24no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—24no—
379C2×C3×C4—24no—
380C2×C3×C4—24no—
381C2×C3×C4—24no—
382C2×C3×C4—24no—
383C2×C3×C4—41no—
384C2×C3×C4—41no—
385C2×C3×C4—42no—
386C2×C3×C4—41no—
387C2×C3×C4—41no—
388C2×C3×C4—42no—
389C2×C3×C4—42no—
390C2×C3×C4—42no—
391C2×C3×C4—42no—
392C2×C3×C4—42no—
393C2×C3×C4C22⋊Q818yescomplemented
394C2×Dic3—22no—
395C2×Dic3—22no—
396C2×Dic3—24no—
397C2×Dic3—24no—
398C2×Dic3—22no—
399C2×Dic3—22no—
400C2×Dic3—22no—
401C2×Dic3—24no—
402C2×Dic3—22no—
403C2×Dic3—24no—
404C2×Dic3—22no—
405C2×Dic3—24no—
406C2×Dic3—24no—
407C2×Dic3—24no—
408C2×Dic3—24no—
409C2×Dic3—24no—
410C2×Dic3—24no—
411C2×Dic3—416no—
412C2×Dic3—416no—
413C2×Dic3—41no—
414C2×Dic3—42no—
415C2×Dic3—41no—
416C2×Dic3—42no—
417C2×Dic3—41no—
418C2×Dic3—42no—
419C2×Dic3—41no—
420C2×Dic3—42no—
421C2×Dic3—42no—
422C2×Dic3—42no—
423C2×Dic3—42no—
424C2×Dic3—42no—
425C2×Dic3—42no—
426C2×Dic3—42no—
427C2×Dic3—42no—
428C2×Dic3—42no—
429C2×Dic3#12014yes—
430Dic6—416no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24C2×Dic612yes—
436C24C2×Dic612yes—
437C24C2×D1212yes—
438C24D3×D412yes—
439C24D3×D412yes—
440C24#23712yes—
441C24D3×Q812yes—
442C24C23×D311yescharacteristic
443C2×Q8—68no—
444C2×Q8—128no—
445C2×Q8—124no—
446C2×Q8—128no—
447C2×Q8—124no—
448C22×C4—28no—
449C22×C4—216no—
450C22×C4—28no—
451C22×C4—28no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—216no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—34no—
472C22×C4—32no—
473C22×C4—32no—
474C22×C4—32no—
475C22×C4—34no—
476C22×C4—32no—
477C22×C4—34no—
478C22×C4—68no—
479C22×C4—61no—
480C22×C4—61no—
481C22×C4—62no—
482C22×C4—68no—
483C22×C4—68no—
484C22×C4—62no—
485C22×C4—62no—
486C22×C4—61no—
487C22×C4—61no—
488C22×C4—61no—
489C22×C4—62no—
490C22×C4—62no—
491C22×C4—62no—
492C22×C4—61no—
493C22×C4—61no—
494C22×C4—61no—
495C22×C4—62no—
496C22×C4—62no—
497C22×C4—62no—
498C22×C4—62no—
499C22×C4—62no—
500C22×C4—62no—
501C22×C4—62no—
502C22×C4—62no—
503C22×C4—62no—
504C22×C4—62no—
505C22×C4—62no—
506C22×C4—62no—
507C22×C4—62no—
508C22×C4—124no—
509C22×C4—128no—
510C22×C4—128no—
511C22×C4—128no—
512C22×C4—128no—
513C22×C4—124no—
514C22×C4—124no—
515C22×C4C2×Dic614yes—
516C22×C4C2×Dic614yes—
517C22×C4C2×D1212yes—
518C22×C4C2×D1212yes—
519C22×C4D3×D414yes—
520C22×C4#23714yes—
521C4⋊C4—616no—
522C4⋊C4—616no—
523C4⋊C4—68no—
524C4⋊C4—68no—
525C4⋊C4—68no—
526C4⋊C4—128no—
527C4⋊C4—128no—
528C22⋊C4—28no—
529C22⋊C4—28no—
530C22⋊C4—68no—
531C22⋊C4—68no—
532C22×C3—24no—
533C22×C3—24no—
534C22×C3—24no—
535C22×C3—24no—
536C22×C3—24no—
537C22×C3—24no—
538C22×C3—28no—
539C22×C3—28no—
540C22×C3—28no—
541C22×C3—28no—
542C22×C3#39518yescomplemented
543C22×C3C2×#12011yescharacteristic
544C22×C3C2×#12011yescharacteristic
545C22×C3C2×C22⋊Q811yescharacteristic
546C22×C3C2×C22⋊Q812yes—
547C22×C3C2×C22⋊Q811yescharacteristic
548C22×C3C2×C22⋊Q811yescharacteristic
549C22×C3#52511yescharacteristic
550C22×C3#52512yes—
551C22×C3C2×C4⋊Q811yescharacteristic
552C22×C3C2×C4⋊Q811yescharacteristic
553C22×C3C2×C4⋊Q811yescharacteristic
554C22×C3#53411yescharacteristic
555C22×C3#53611yescharacteristic
556C22×C3#53912yes—
557C22×C3#54412yes—
558C22×C3D4212yes—
559C22×C3D4212yes—
560C22×C3#54712yes—
561C22×C3#54712yes—
562C22×C3D4×Q812yes—
563C22×C3D4×Q812yes—
564C22×C3#55412yes—
565C22×C3#55412yes—
566C3×C4—28no—
567C3×C4—42no—
568C3×C4—42no—
569C3×C4—44no—
570Dic3—24no—
571Dic3—42no—
572Dic3—42no—
573Dic3—44no—
574Dic3—42no—
575Dic3—44no—
576C23—24no—
577C23—24no—
578C23—22no—
579C23—22no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—22no—
588C23—24no—
589C23—22no—
590C23—24no—
591C23—24no—
592C23#86914yes—
593C23#87814yes—
594C23#87814yes—
595C23#88214yes—
596C23#88814yes—
597C23#88814yes—
598C23#89714yes—
599C23C22×Dic611yescharacteristic
600C23C22×Dic611yescharacteristic
601C23C22×D1211yescharacteristic
602C23C2×D3×D412yes—
603C23C2×D3×D411yescharacteristic
604C23C2×D3×D411yescharacteristic
605C23C2×#23712yes—
606C23C2×#23711yescharacteristic
607C23C2×D3×Q811yescharacteristic
608C23#100912yes—
609C23#101012yes—
610Q8—1216no—
611C2×C4—232no—
612C2×C4—24no—
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—24no—
622C2×C4—24no—
623C2×C4—24no—
624C2×C4—24no—
625C2×C4—34no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—42no—
629C2×C4—41no—
630C2×C4—42no—
631C2×C4—41no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—62no—
637C2×C4—62no—
638C2×C4—64no—
639C2×C4—64no—
640C2×C4—64no—
641C2×C4—64no—
642C2×C4—62no—
643C2×C4—62no—
644C2×C4—62no—
645C2×C4—62no—
646C2×C4—64no—
647C2×C4—64no—
648C2×C4—64no—
649C2×C4—62no—
650C2×C4—64no—
651C2×C4—64no—
652C2×C4—64no—
653C2×C4—1216no—
654C2×C4—1216no—
655C2×C4—121no—
656C2×C4—122no—
657C2×C4—121no—
658C2×C4—122no—
659C2×C4—122no—
660C2×C4—122no—
661C2×C4—122no—
662C2×C4—122no—
663C2×C4—122no—
664C2×C4—122no—
665C2×C4—122no—
666C2×C4—122no—
667C2×C4—121no—
668C2×C4—121no—
669C2×C4—122no—
670C2×C4—122no—
671C2×C4#87818yescomplemented
672C2×C3—28no—
673C2×C3C2×#39511yescharacteristic
674C2×C3#240311yescharacteristic
675C2×C3#240611yescharacteristic
676C2×C3#243411yescharacteristic
677C2×C3#244012yes—
678C2×C3#244012yes—
679C2×C3#244912yes—
680C2×C3#244912yes—
681C2×C3#258311yescharacteristic
682C2×C3#262711yescharacteristic
683C2×C3#284811yescharacteristic
684C22—28no—
685C22—24no—
686C22—24no—
687C22—24no—
688C22—28no—
689C22—24no—
690C22—28no—
691C22—24no—
692C22—28no—
693C22—24no—
694C22#465618yescomplemented
695C22C2×#86911yescharacteristic
696C22C2×#87812yes—
697C22C2×#87811yescharacteristic
698C22C2×#87811yescharacteristic
699C22C2×#88211yescharacteristic
700C22C2×#88811yescharacteristic
701C22C2×#88811yescharacteristic
702C22C2×#89711yescharacteristic
703C22#551912yes—
704C22D4×Dic612yes—
705C22#554312yes—
706C22D4×D1212yes—
707C22#555512yes—
708C22#558612yes—
709C22#558611yescharacteristic
710C22D3×#12011yescharacteristic
711C22#560912yes—
712C22#561112yes—
713C22#563212yes—
714C22#563512yes—
715C22#564811yescharacteristic
716C22#565311yescharacteristic
717C22#566512yes—
718C4—28no—
719C4—42no—
720C4—42no—
721C4—44no—
722C4—64no—
723C4—122no—
724C4—124no—
725C4—122no—
726C4—124no—
727C4—122no—
728C3#1472011yescharacteristic, complemented, Sylow
729C2—28no—
730C2C2×#465611yescharacteristic
731C2#7349312yes—
732C2#7384611yescharacteristic
733C2#7389912yes—
734C2#7409011yescharacteristic
735C2#7441211yescharacteristic
736C2#7442212yes—
737C2#7448811yescharacteristic
738C2#7468711yescharacteristic
739C2#7471012yes—
740C2#7488411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×C22⋊#95C2
prime radicalC25×C3C23
hypercenterC22⋊#95D3
hypocenterC3#14720
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
5. C2×#4656C2semidirect
9. #69420C2semidirect
10. #69419C2semidirect
11. #69411C2semidirect
60. C23×C3×C4Q8semidirect
91. C2×C3×C22⋊C4Q8semidirect
97. C2×#217Q8semidirect
287. C23×C4Dic6semidirect
325. C2×C22⋊C4Dic6semidirect
393. C2×C3×C4C22⋊Q8semidirect
542. C22×C3#395semidirect
671. C2×C4#878semidirect
694. C22#4656semidirect
728. C3#14720semidirect

Maximal subgroups

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

subgroupindex
C23×C4⋊Dic32
C22×#8782
C2×#49502
C2×#49462
C2×#46562
C3×C22⋊#952
#721272
#715442
#694202
#694192
#694112
#147203