Finite Group Databasebeta

← #10729060

Subgroups — #10729060

Order 768.

2470 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#875C211yesmaximal, characteristic, complemented
2C2×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
3C2×#4673C211yesmaximal, characteristic, complemented
4C2×#4671C211yesmaximal, characteristic
5C2×#4665C212yesmaximal, complemented
6C3×#1434C211yesmaximal, characteristic, complemented
7#69429C212yesmaximal, complemented
8#69426C212yesmaximal, complemented
9#69426C211yesmaximal, characteristic, complemented
10#69424C211yesmaximal, characteristic, complemented
11#69408C212yesmaximal, complemented
12#14915—31nomaximal, Sylow
13C23×D12C2212yes—
14C23×D12C2211yescharacteristic
15C23×C4×D3C2211yescharacteristic
16C23×Dic6C2211yescharacteristic
17C22×C3×C42C2211yescharacteristic
18C22×(C2×D3)⋊C4C2211yescharacteristic
19C22×(C2×D3)⋊C4C2212yes—
20C22×(C2×D3)⋊C4C2212yes—
21C22×(C2×D3)⋊C4C2212yes—
22C22×(C2×D3)⋊C4C2212yes—
23C22×(C2×D3)⋊C4C2211yescharacteristic
24C22×(C2×D3)⋊C4C2212yes—
25C22×(C2×D3)⋊C4C2212yes—
26C22×C4×Dic3C2211yescharacteristic
27C2×#875—24no—
28C2×#875—28no—
29C2×C3×#95C2212yes—
30C2×C3×#95C2211yescharacteristic
31C2×C3×#95C2212yes—
32C2×C3×#95C2211yescharacteristic
33C2×C3⋊#95C2212yes—
34C2×C3⋊#95C2211yescharacteristic
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2211yescharacteristic
37C2×C3⋊#95C2212yes—
38C4×(C2×D3)⋊C4—24no—
39#4673—24no—
40#4671—24no—
41#4665—28no—
42C22×#124—31no—
43C2×#393—31no—
44C2×#392—31no—
45C2×#386—32no—
46C2×C4×C22⋊C4—31no—
47#1446—31no—
48#1440—32no—
49#1438—32no—
50#1438—31no—
51#1437—32no—
52#1434D311yescharacteristic, complemented
53C24×D3C2312yes—
54C24×D3C2311yescharacteristic
55C23×C3×C4C2312yes—
56C23×C3×C4C2311yescharacteristic
57C23×C3×C4C2312yes—
58C23×C3×C4C2311yescharacteristic
59C23×C3×C4C2311yescharacteristic
60C23×Dic3C2312yes—
61C23×Dic3C2311yescharacteristic
62C23×Dic3C2311yescharacteristic
63C23×Dic3C2311yescharacteristic
64C22×D12—24no—
65C22×D12—24no—
66C22×D12—24no—
67C22×D12—22no—
68C22×D12—24no—
69C22×D12—24no—
70C22×D12—24no—
71C22×D12—22no—
72C22×D12—22no—
73C22×D12—42no—
74C22×D12—42no—
75C22×D12—42no—
76C22×C4×D3—22no—
77C22×C4×D3—22no—
78C22×C4×D3—22no—
79C22×C4×D3—24no—
80C22×C4×D3—42no—
81C22×Dic6—22no—
82C22×Dic6—24no—
83C22×Dic6—22no—
84C22×Dic6—22no—
85C22×Dic6—42no—
86C2×C3×C42—24no—
87C2×C3×C42D414yescomplemented
88C2×(C2×D3)⋊C4—24no—
89C2×(C2×D3)⋊C4—22no—
90C2×(C2×D3)⋊C4—22no—
91C2×(C2×D3)⋊C4—22no—
92C2×(C2×D3)⋊C4—24no—
93C2×(C2×D3)⋊C4—24no—
94C2×(C2×D3)⋊C4—24no—
95C2×(C2×D3)⋊C4—22no—
96C2×(C2×D3)⋊C4—24no—
97C2×(C2×D3)⋊C4—22no—
98C2×(C2×D3)⋊C4—24no—
99C2×(C2×D3)⋊C4—24no—
100C2×(C2×D3)⋊C4—24no—
101C2×(C2×D3)⋊C4—24no—
102C2×(C2×D3)⋊C4—24no—
103C2×(C2×D3)⋊C4—24no—
104C2×(C2×D3)⋊C4—24no—
105C2×(C2×D3)⋊C4—42no—
106C2×(C2×D3)⋊C4—42no—
107C2×(C2×D3)⋊C4—42no—
108C2×(C2×D3)⋊C4—42no—
109C2×(C2×D3)⋊C4—42no—
110C2×(C2×D3)⋊C4D414yes—
111C2×(C2×D3)⋊C4D418yescomplemented
112C2×C4×Dic3—22no—
113C2×C4×Dic3—42no—
114#875—232no—
115C3×#95—24no—
116C3×#95—22no—
117C3×#95—22no—
118C3×#95—24no—
119C3⋊#95—22no—
120C3⋊#95—22no—
121C3⋊#95—24no—
122C3⋊#95—24no—
123C3⋊#95—42no—
124C23×Q8—31no—
125C23×D4—31no—
126C23×D4—32no—
127C24×C4—31no—
128C2×#124—68no—
129C2×#124—64no—
130C22×C22⋊C4—31no—
131C22×C22⋊C4—32no—
132C22×C22⋊C4—32no—
133C22×C22⋊C4—31no—
134C22×C22⋊C4—32no—
135C22×C22⋊C4—32no—
136C22×C22⋊C4—32no—
137C22×C22⋊C4—32no—
138C22×C42—31no—
139C22×C42C2×D311yescharacteristic
140#393—64no—
141#392—64no—
142#386—68no—
143C4×C22⋊C4—64no—
144C2×#95—32no—
145C2×#95—31no—
146C2×#95—31no—
147C2×#95—32no—
148C2×#95—32no—
149C2×#95C2×D311yescharacteristic
150C2×#95C2×D311yescharacteristic
151C2×#95C2×D312yes—
152C2×#95C2×D312yes—
153C24×C3C2411yescharacteristic
154C23×D3—21no—
155C23×D3—22no—
156C23×D3—21no—
157C23×D3—21no—
158C23×D3—21no—
159C23×D3—22no—
160C23×D3—22no—
161C23×D3—22no—
162C23×D3—22no—
163C23×D3—22no—
164C23×D3—22no—
165C23×D3—22no—
166C23×D3—22no—
167C23×D3—22no—
168C23×D3—22no—
169C23×D3—22no—
170C23×D3—22no—
171C23×D3—22no—
172C23×D3—22no—
173C23×D3—22no—
174C23×D3—22no—
175C23×D3—22no—
176C23×D3C2×D414yes—
177C23×D3C2×D412yes—
178C23×D3#4112yes—
179C23×D3#4112yes—
180C22×C3×C4—22no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—22no—
184C22×C3×C4—22no—
185C22×C3×C4—22no—
186C22×C3×C4—22no—
187C22×C3×C4—22no—
188C22×C3×C4—22no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4C2×D412yes—
203C22×C3×C4C2×D412yes—
204C22×C3×C4C2×D412yes—
205C22×C3×C4C2×D414yes—
206C22×C3×C4C2×D412yes—
207C22×C3×C4#4114yes—
208C22×C3×C4#4112yes—
209C22×Dic3—21no—
210C22×Dic3—21no—
211C22×Dic3—21no—
212C22×Dic3—22no—
213C22×Dic3—22no—
214C22×Dic3—22no—
215C22×Dic3—22no—
216C22×Dic3—22no—
217C22×Dic3—21no—
218C22×Dic3—21no—
219C22×Dic3—22no—
220C22×Dic3—21no—
221C22×Dic3—22no—
222C22×Dic3—22no—
223C22×Dic3—22no—
224C22×Dic3—22no—
225C22×Dic3—22no—
226C22×Dic3—22no—
227C22×Dic3C2×D412yes—
228C22×Dic3C2×D414yes—
229C22×Dic3#4112yes—
230C22×Dic3#4112yes—
231C2×D12—28no—
232C2×D12—216no—
233C2×D12—48no—
234C2×D12—48no—
235C2×D12—48no—
236C2×D12—48no—
237C2×D12—44no—
238C2×D12—48no—
239C2×D12—48no—
240C2×D12—48no—
241C2×D12—48no—
242C2×D12—44no—
243C2×C4×D3—28no—
244C2×C4×D3—48no—
245C2×C4×D3—48no—
246C2×C4×D3—44no—
247C2×C4×D3—44no—
248C2×Dic6—28no—
249C2×Dic6—48no—
250C2×Dic6—48no—
251C2×Dic6—44no—
252C2×Dic6—44no—
253C3×C42—28no—
254(C2×D3)⋊C4—216no—
255(C2×D3)⋊C4—28no—
256(C2×D3)⋊C4—216no—
257(C2×D3)⋊C4—28no—
258(C2×D3)⋊C4—48no—
259(C2×D3)⋊C4—48no—
260(C2×D3)⋊C4—48no—
261(C2×D3)⋊C4—48no—
262C4×Dic3—44no—
263C25—31no—
264C25—32no—
265C22×Q8—64no—
266C22×Q8—62no—
267C22×Q8—62no—
268C22×Q8—62no—
269C22×Q8—122no—
270C22×D4—64no—
271C22×D4—64no—
272C22×D4—64no—
273C22×D4—64no—
274C22×D4—64no—
275C22×D4—62no—
276C22×D4—64no—
277C22×D4—62no—
278C22×D4—62no—
279C22×D4—122no—
280C22×D4—122no—
281C22×D4—122no—
282C23×C4—32no—
283C23×C4—31no—
284C23×C4—31no—
285C23×C4—31no—
286C23×C4—62no—
287C23×C4—62no—
288C23×C4—62no—
289C23×C4—64no—
290C23×C4—122no—
291C23×C4C22×D312yes—
292C23×C4C22×D311yescharacteristic
293C23×C4C22×D312yes—
294C23×C4C22×D311yescharacteristic
295C23×C4C22×D311yescharacteristic
296#124—632no—
297C2×C22⋊C4—38no—
298C2×C22⋊C4—34no—
299C2×C22⋊C4—64no—
300C2×C22⋊C4—62no—
301C2×C22⋊C4—64no—
302C2×C22⋊C4—62no—
303C2×C22⋊C4—64no—
304C2×C22⋊C4—64no—
305C2×C22⋊C4—62no—
306C2×C22⋊C4—62no—
307C2×C22⋊C4—64no—
308C2×C22⋊C4—62no—
309C2×C22⋊C4—64no—
310C2×C22⋊C4—64no—
311C2×C22⋊C4—64no—
312C2×C22⋊C4—64no—
313C2×C22⋊C4—64no—
314C2×C22⋊C4—64no—
315C2×C22⋊C4—64no—
316C2×C22⋊C4—122no—
317C2×C22⋊C4—122no—
318C2×C22⋊C4—122no—
319C2×C22⋊C4—122no—
320C2×C22⋊C4—122no—
321C2×C42—24no—
322C2×C42—62no—
323C2×C42—122no—
324C2×C42D1214yescomplemented
325#95—24no—
326#95—24no—
327#95—22no—
328#95—22no—
329#95—64no—
330#95—64no—
331#95—62no—
332#95—62no—
333#95—122no—
334C23×C3C22×D411yescharacteristic
335C23×C3C22×D412yes—
336C23×C3C22×D411yescharacteristic
337C23×C3C2×#4112yes—
338C23×C3C2×#4111yescharacteristic
339C23×C3C2×#4111yescharacteristic
340C23×C3C2×#4111yescharacteristic
341C23×C3C2×#4111yescharacteristic
342C23×C3C2×#4111yescharacteristic
343C23×C3H(5,𝔽2)12yes—
344C23×C3H(5,𝔽2)12yes—
345C22×D3—22no—
346C22×D3—22no—
347C22×D3—22no—
348C22×D3—24no—
349C22×D3—22no—
350C22×D3—22no—
351C22×D3—22no—
352C22×D3—24no—
353C22×D3—24no—
354C22×D3—24no—
355C22×D3—24no—
356C22×D3—24no—
357C22×D3—24no—
358C22×D3—24no—
359C22×D3—24no—
360C22×D3—24no—
361C22×D3—24no—
362C22×D3—24no—
363C22×D3—24no—
364C22×D3—41no—
365C22×D3—41no—
366C22×D3—42no—
367C22×D3—41no—
368C22×D3—41no—
369C22×D3—42no—
370C22×D3—42no—
371C22×D3—42no—
372C22×D3—42no—
373C22×D3—42no—
374C22×D3—42no—
375C22×D3—42no—
376C22×D3—42no—
377C22×D3—42no—
378C22×D3—42no—
379C22×D3—42no—
380C22×D3—42no—
381C22×D3—42no—
382C22×D3—42no—
383C22×D3—42no—
384C22×D3—42no—
385C22×D3—42no—
386C22×D3—42no—
387C22×D3—42no—
388C22×D3—42no—
389C22×D3—42no—
390C22×D3—42no—
391C22×D3—42no—
392C22×D3—42no—
393C22×D3—42no—
394C22×D3—42no—
395C22×D3—42no—
396C22×D3—42no—
397C22×D3—42no—
398C22×D3—42no—
399C22×D3—42no—
400C22×D3—42no—
401C22×D3—42no—
402C22×D3#12414yescomplemented
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—24no—
408C2×C3×C4—24no—
409C2×C3×C4—24no—
410C2×C3×C4—24no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—24no—
414C2×C3×C4—22no—
415C2×C3×C4—24no—
416C2×C3×C4—24no—
417C2×C3×C4—42no—
418C2×C3×C4—42no—
419C2×C3×C4—42no—
420C2×C3×C4—42no—
421C2×C3×C4—42no—
422C2×C3×C4—42no—
423C2×C3×C4—42no—
424C2×C3×C4—42no—
425C2×C3×C4—42no—
426C2×C3×C4—42no—
427C2×C3×C4—42no—
428C2×C3×C4—42no—
429C2×C3×C4—42no—
430C2×C3×C4#12014yes—
431C2×C3×C4#12114yes—
432C2×Dic3—24no—
433C2×Dic3—22no—
434C2×Dic3—22no—
435C2×Dic3—22no—
436C2×Dic3—24no—
437C2×Dic3—24no—
438C2×Dic3—24no—
439C2×Dic3—24no—
440C2×Dic3—24no—
441C2×Dic3—41no—
442C2×Dic3—42no—
443C2×Dic3—41no—
444C2×Dic3—41no—
445C2×Dic3—41no—
446C2×Dic3—42no—
447C2×Dic3—41no—
448C2×Dic3—41no—
449C2×Dic3—42no—
450C2×Dic3—42no—
451C2×Dic3—42no—
452C2×Dic3—42no—
453C2×Dic3—42no—
454D12—416no—
455D12—432no—
456C4×D3—416no—
457Dic6—416no—
458C24—32no—
459C24—32no—
460C24—32no—
461C24—34no—
462C24—61no—
463C24—62no—
464C24—62no—
465C24—61no—
466C24—61no—
467C24—61no—
468C24—62no—
469C24—62no—
470C24—62no—
471C24—62no—
472C24—62no—
473C24—62no—
474C24—62no—
475C24—62no—
476C24—62no—
477C24—62no—
478C24—62no—
479C24—62no—
480C24—62no—
481C24—62no—
482C24—62no—
483C24—62no—
484C24C23×D311yescharacteristic
485C2×Q8—68no—
486C2×Q8—128no—
487C2×Q8—128no—
488C2×Q8—124no—
489C2×Q8—124no—
490C2×D4—68no—
491C2×D4—616no—
492C2×D4—128no—
493C2×D4—128no—
494C2×D4—128no—
495C2×D4—128no—
496C2×D4—124no—
497C2×D4—128no—
498C2×D4—128no—
499C2×D4—128no—
500C2×D4—128no—
501C2×D4—124no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—32no—
525C22×C4—34no—
526C22×C4—32no—
527C22×C4—32no—
528C22×C4—68no—
529C22×C4—61no—
530C22×C4—61no—
531C22×C4—61no—
532C22×C4—62no—
533C22×C4—62no—
534C22×C4—62no—
535C22×C4—62no—
536C22×C4—62no—
537C22×C4—61no—
538C22×C4—62no—
539C22×C4—61no—
540C22×C4—61no—
541C22×C4—62no—
542C22×C4—62no—
543C22×C4—62no—
544C22×C4—62no—
545C22×C4—62no—
546C22×C4—62no—
547C22×C4—128no—
548C22×C4—128no—
549C22×C4—124no—
550C22×C4—124no—
551C22×C4C2×D1212yes—
552C22×C4C2×D1212yes—
553C22×C4C2×D1212yes—
554C22×C4#23514yes—
555C22×C4D3×D414yes—
556C22×C4D3×D412yes—
557C22×C4#23912yes—
558C22⋊C4—616no—
559C22⋊C4—68no—
560C22⋊C4—616no—
561C22⋊C4—68no—
562C22⋊C4—128no—
563C22⋊C4—128no—
564C22⋊C4—128no—
565C22⋊C4—128no—
566C42—28no—
567C42—124no—
568C22×C3C2×#12011yescharacteristic
569C22×C3C2×#12111yescharacteristic
570C22×C3#52511yescharacteristic
571C22×C3#52511yescharacteristic
572C22×C3#52512yes—
573C22×C3C2×#12411yescharacteristic
574C22×C3#52911yescharacteristic
575C22×C3#52911yescharacteristic
576C22×C3#53211yescharacteristic
577C22×C3#53211yescharacteristic
578C22×C3#53212yes—
579C22×C3#53511yescharacteristic
580C22×C3#53511yescharacteristic
581C22×C3#53812yes—
582C22×C3#53812yes—
583C22×C3D4212yes—
584C22×C3#54612yes—
585C22×C3#54612yes—
586C22×C3#54612yes—
587C22×C3#54612yes—
588C22×C3#55112yes—
589C22×C3#55512yes—
590C22×C3#55912yes—
591C2×D3—24no—
592C2×D3—28no—
593C2×D3—42no—
594C2×D3—42no—
595C2×D3—42no—
596C2×D3—42no—
597C2×D3—42no—
598C2×D3—44no—
599C2×D3—42no—
600C2×D3—44no—
601C2×D3—44no—
602C2×D3—44no—
603C2×D3—44no—
604C2×D3—44no—
605C2×D3—44no—
606C2×D3—44no—
607C2×D3—44no—
608C2×D3—44no—
609C2×D3—82no—
610C2×D3—82no—
611C2×D3—82no—
612C2×D3—82no—
613C2×D3—82no—
614C2×D3—82no—
615C2×D3—82no—
616C2×D3—82no—
617C3×C4—24no—
618C3×C4—24no—
619C3×C4—42no—
620C3×C4—44no—
621C3×C4—82no—
622Dic3—42no—
623Dic3—42no—
624Dic3—44no—
625Dic3—42no—
626C23—34no—
627C23—64no—
628C23—62no—
629C23—62no—
630C23—62no—
631C23—64no—
632C23—62no—
633C23—62no—
634C23—62no—
635C23—64no—
636C23—64no—
637C23—64no—
638C23—64no—
639C23—64no—
640C23—64no—
641C23—64no—
642C23—64no—
643C23—64no—
644C23—64no—
645C23—64no—
646C23—122no—
647C23—122no—
648C23—121no—
649C23—121no—
650C23—121no—
651C23—121no—
652C23—122no—
653C23—122no—
654C23—122no—
655C23—122no—
656C23—122no—
657C23—122no—
658C23—122no—
659C23—122no—
660C23—122no—
661C23—122no—
662C23—122no—
663C23—122no—
664C23—122no—
665C23—122no—
666C23—122no—
667C23—122no—
668C23—122no—
669C23—122no—
670C23—122no—
671C23—122no—
672C23—122no—
673C23—122no—
674C23—122no—
675C23—122no—
676C23—122no—
677C23—122no—
678C23—122no—
679C23—122no—
680C23—122no—
681C23—122no—
682C23—122no—
683C23—122no—
684C23C22×D1211yescharacteristic
685C23C2×#23512yes—
686C23C2×D3×D412yes—
687C23C2×D3×D411yescharacteristic
688C23C2×#23911yescharacteristic
689C23D3×#4111yescharacteristic
690C23D3×#4111yescharacteristic
691C23D3×#4111yescharacteristic
692C23D3×#4111yescharacteristic
693C23#100912yes—
694C23#100912yes—
695Q8—1216no—
696D4—1216no—
697D4—1232no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—64no—
726C2×C4—64no—
727C2×C4—64no—
728C2×C4—62no—
729C2×C4—62no—
730C2×C4—62no—
731C2×C4—64no—
732C2×C4—64no—
733C2×C4—64no—
734C2×C4—1216no—
735C2×C4—122no—
736C2×C4—122no—
737C2×C4—121no—
738C2×C4—121no—
739C2×C4—122no—
740C2×C4—121no—
741C2×C4—121no—
742C2×C4—121no—
743C2×C4—122no—
744C2×C4—121no—
745C2×C4—122no—
746C2×C4—122no—
747C2×C4—122no—
748C2×C4#88214yes—
749C2×C4#89514yes—
750C2×C3#238811yescharacteristic
751C2×C3#240411yescharacteristic
752C2×C3#240811yescharacteristic
753C2×C3#245912yes—
754C2×C3#247212yes—
755C2×C3#254411yescharacteristic
756C2×C3#255512yes—
757C2×C3#255712yes—
758C2×C3#261011yescharacteristic
759C2×C3#263111yescharacteristic
760C2×C3#285011yescharacteristic
761D3—44no—
762D3—84no—
763C22—68no—
764C22—64no—
765C22—122no—
766C22—124no—
767C22—122no—
768C22—122no—
769C22—124no—
770C22—124no—
771C22—122no—
772C22—122no—
773C22—122no—
774C22—124no—
775C22—124no—
776C22—124no—
777C22—124no—
778C22—124no—
779C22—124no—
780C22—124no—
781C22—242no—
782C22—242no—
783C22—242no—
784C22—242no—
785C22—242no—
786C22—242no—
787C22—242no—
788C22—242no—
789C22#547711yescharacteristic
790C22C2×#88211yescharacteristic
791C22C2×#89511yescharacteristic
792C22#552411yescharacteristic
793C22#552411yescharacteristic
794C22#552511yescharacteristic
795C22#552511yescharacteristic
796C22#552712yes—
797C22#553212yes—
798C22#554712yes—
799C22#554812yes—
800C22#555012yes—
801C22#558512yes—
802C22#560912yes—
803C22#563012yes—
804C22#565412yes—
805C22#565412yes—
806C22#566811yescharacteristic
807C22D3×#12411yescharacteristic
808C22#569111yescharacteristic
809C22#569111yescharacteristic
810C22#570412yes—
811C22#570412yes—
812C4—24no—
813C4—24no—
814C4—44no—
815C4—42no—
816C4—82no—
817C4—124no—
818C4—122no—
819C4—122no—
820C4—122no—
821C3#1491511yescharacteristic, complemented, Sylow
822C2—124no—
823C2—244no—
824C2#7342611yescharacteristic
825C2#7358011yescharacteristic
826C2#7380111yescharacteristic
827C2#7401611yescharacteristic
828C2#7412511yescharacteristic
829C2#7425611yescharacteristic
830C2#7430911yescharacteristic
831C2#7532612yes—
832C2#7535812yes—
833C2#7552612yes—
834C2#7559712yes—
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1434C2
prime radicalC2×#4671C2
hypercenter#1434D3
hypocenterC3#14915
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
1. C22×#875C2semidirect
2. C2×C4×(C2×D3)⋊C4C2semidirect
3. C2×#4673C2semidirect
5. C2×#4665C2semidirect
6. C3×#1434C2semidirect
7. #69429C2semidirect
8. #69426C2semidirect
9. #69426C2semidirect
10. #69424C2semidirect
11. #69408C2semidirect
52. #1434D3semidirect
87. C2×C3×C42D4semidirect
111. C2×(C2×D3)⋊C4D4semidirect
324. C2×C42D12semidirect
402. C22×D3#124semidirect
821. C3#14915semidirect

Maximal subgroups

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

subgroupindex
C22×#8752
C2×C4×(C2×D3)⋊C42
C2×#46732
C2×#46712
C2×#46652
C3×#14342
#694292
#694262
#694242
#694082
#149153