Finite Group Databasebeta

← #10726659

Subgroups — #10726659

Order 768.

4034 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
2C22×#882C211yesmaximal, characteristic
3C2×#5213C211yesmaximal, characteristic, complemented
4C2×#4955C211yesmaximal, characteristic, complemented
5C2×#4958C211yesmaximal, characteristic, complemented
6C2×#4942C211yesmaximal, characteristic, complemented
7C2×#4672C212yesmaximal, complemented
8C3×C22⋊#95C211yesmaximal, characteristic, complemented
9#69429C212yesmaximal, complemented
10#69428C212yesmaximal, complemented
11#69426C212yesmaximal, complemented
12#14725—31nomaximal, Sylow
13C25×D3C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C23×#67C2211yescharacteristic
16C24×Dic3C2211yescharacteristic
17C23×D12C2212yes—
18C22×C3×C22⋊C4C2211yescharacteristic
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×#217C2211yescharacteristic
21C22×(C2×D3)⋊C4—24no—
22C22×(C2×D3)⋊C4—28no—
23C22×(C2×D3)⋊C4C2212yes—
24C22×(C2×D3)⋊C4C2212yes—
25C22×(C2×D3)⋊C4C2212yes—
26C22×(C2×D3)⋊C4C2212yes—
27C22×(C2×D3)⋊C4C2212yes—
28C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
29C22×(C2×D3)⋊C4C2212yescomplemented
30C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
31C22×Dic3⋊C4C2212yescomplemented
32C2×#882—24no—
33C2×#882—24no—
34C2×#882—24no—
35C2×C3×#95C2212yescomplemented
36C2×C3×#95C2212yescomplemented
37#5213—24no—
38C2×C3⋊#95C2212yescomplemented
39C2×C3⋊#95C2211yescharacteristic, complemented
40C2×C3⋊#95C2212yescomplemented
41C2×C3⋊#95C2211yescharacteristic, complemented
42#4958—24no—
43#4955—24no—
44#4942—24no—
45#4672—28no—
46C22×#120—31no—
47C23×C22⋊C4—31no—
48C2×#394—32no—
49C2×#386—31no—
50C2×#386—31no—
51C2×#380—31no—
52C2×#379—31no—
53#1440—32no—
54#1439—32no—
55#1438—32no—
56C22⋊#95D311yescharacteristic, complemented
57C25×C3C2311yescharacteristic
58C24×D3—22no—
59C24×D3—22no—
60C24×D3—24no—
61C24×D3—24no—
62C24×D3—22no—
63C24×D3—22no—
64C24×D3—22no—
65C24×D3—22no—
66C24×D3—42no—
67C24×D3—42no—
68C24×D3D414yes—
69C24×D3C2311yescharacteristic
70C24×D3C2312yes—
71C23×C3×C4—22no—
72C23×C3×C4—24no—
73C23×C3×C4—22no—
74C23×C3×C4—22no—
75C23×C3×C4—42no—
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2312yes—
79C23×C3×C4C2312yes—
80C22×#67—22no—
81C22×#67—22no—
82C22×#67—22no—
83C22×#67—22no—
84C22×#67—22no—
85C22×#67—22no—
86C22×#67D414yes—
87C23×Dic3—22no—
88C23×Dic3—22no—
89C23×Dic3—24no—
90C23×Dic3—42no—
91C23×Dic3D414yescomplemented
92C23×Dic3C2312yes—
93C23×Dic3C2311yescharacteristic
94C23×Dic3C2311yescharacteristic
95C23×Dic3C2311yescharacteristic
96C22×D12—24no—
97C22×D12—24no—
98C22×D12—24no—
99C22×D12—24no—
100C22×D12—24no—
101C22×D12—42no—
102C22×D12—42no—
103C2×C3×C22⋊C4—22no—
104C2×C3×C22⋊C4—22no—
105C2×C3×C22⋊C4—22no—
106C2×C3×C22⋊C4—22no—
107C2×C3×C22⋊C4—22no—
108C2×C3×C22⋊C4D414yes—
109C2×#217—22no—
110C2×#217—22no—
111C2×#217—22no—
112C2×(C2×D3)⋊C4—232no—
113C2×(C2×D3)⋊C4—24no—
114C2×(C2×D3)⋊C4—24no—
115C2×(C2×D3)⋊C4—24no—
116C2×(C2×D3)⋊C4—24no—
117C2×(C2×D3)⋊C4—24no—
118C2×(C2×D3)⋊C4—24no—
119C2×(C2×D3)⋊C4—24no—
120C2×(C2×D3)⋊C4—24no—
121C2×(C2×D3)⋊C4—24no—
122C2×(C2×D3)⋊C4—24no—
123C2×(C2×D3)⋊C4—24no—
124C2×(C2×D3)⋊C4—24no—
125C2×(C2×D3)⋊C4—24no—
126C2×(C2×D3)⋊C4—24no—
127C2×(C2×D3)⋊C4—24no—
128C2×(C2×D3)⋊C4—22no—
129C2×(C2×D3)⋊C4—22no—
130C2×(C2×D3)⋊C4—42no—
131C2×(C2×D3)⋊C4—42no—
132C2×(C2×D3)⋊C4—42no—
133C2×(C2×D3)⋊C4—42no—
134C2×(C2×D3)⋊C4D418yescomplemented
135C2×Dic3⋊C4—24no—
136C2×Dic3⋊C4—24no—
137C2×Dic3⋊C4—42no—
138#882—232no—
139C3×#95—24no—
140C3×#95—42no—
141C3⋊#95—24no—
142C3⋊#95—24no—
143C3⋊#95—22no—
144C3⋊#95—22no—
145C26—31no—
146C23×D4—31no—
147C23×D4—32no—
148C24×C4—31no—
149C24×C4C2×D311yescharacteristic
150C2×#120—64no—
151C2×#120—64no—
152C2×#120—64no—
153C22×C4⋊C4—32no—
154C22×C22⋊C4—32no—
155C22×C22⋊C4—31no—
156C22×C22⋊C4—31no—
157C22×C22⋊C4—32no—
158C22×C22⋊C4—32no—
159C22×C22⋊C4—32no—
160C22×C22⋊C4—32no—
161C22×C22⋊C4—32no—
162C22×C22⋊C4—31no—
163C22×C22⋊C4—68no—
164C22×C22⋊C4—64no—
165C22×C22⋊C4C2×D311yescharacteristic
166C22×C22⋊C4C2×D311yescharacteristic
167#394—68no—
168#386—64no—
169#386—64no—
170#380—64no—
171#379—64no—
172C2×#95—32no—
173C2×#95—31no—
174C2×#95—32no—
175C2×#95—31no—
176C2×#95C2×D312yescomplemented
177C2×#95C2×D312yescomplemented
178C24×C3—22no—
179C24×C3—22no—
180C24×C3—22no—
181C24×C3—22no—
182C24×C3C2×D412yes—
183C24×C3C2×D412yes—
184C24×C3C2×D412yes—
185C24×C3C2×D412yes—
186C24×C3#4112yes—
187C24×C3#4112yes—
188C24×C3#4112yes—
189C24×C3C2411yescharacteristic
190C23×D3—28no—
191C23×D3—216no—
192C23×D3—28no—
193C23×D3—28no—
194C23×D3—22no—
195C23×D3—22no—
196C23×D3—22no—
197C23×D3—22no—
198C23×D3—22no—
199C23×D3—22no—
200C23×D3—22no—
201C23×D3—22no—
202C23×D3—22no—
203C23×D3—22no—
204C23×D3—22no—
205C23×D3—22no—
206C23×D3—216no—
207C23×D3—28no—
208C23×D3—28no—
209C23×D3—22no—
210C23×D3—21no—
211C23×D3—21no—
212C23×D3—21no—
213C23×D3—22no—
214C23×D3—21no—
215C23×D3—21no—
216C23×D3—21no—
217C23×D3—22no—
218C23×D3—22no—
219C23×D3—48no—
220C23×D3—48no—
221C23×D3—48no—
222C23×D3—48no—
223C23×D3—48no—
224C23×D3—48no—
225C23×D3—48no—
226C23×D3—48no—
227C23×D3—48no—
228C23×D3—44no—
229C23×D3—44no—
230C23×D3—48no—
231C23×D3—44no—
232C23×D3—44no—
233C23×D3—44no—
234C23×D3—44no—
235C23×D3C2×D412yes—
236C23×D3C2×D414yes—
237C23×D3C2×D414yes—
238C23×D3#4114yes—
239C22×C3×C4—28no—
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—22no—
248C22×C3×C4—22no—
249C22×C3×C4—22no—
250C22×C3×C4—22no—
251C22×C3×C4—22no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—22no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—22no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—22no—
261C22×C3×C4—22no—
262C22×C3×C4—48no—
263C22×C3×C4—48no—
264C22×C3×C4—44no—
265C22×C3×C4—44no—
266C22×C3×C4C2×D414yes—
267C22×C3×C4C2×D414yes—
268C2×#67—28no—
269C2×#67—28no—
270C2×#67—28no—
271C2×#67—44no—
272C2×#67—44no—
273C2×#67—44no—
274C2×#67—44no—
275C22×Dic3—21no—
276C22×Dic3—21no—
277C22×Dic3—22no—
278C22×Dic3—28no—
279C22×Dic3—21no—
280C22×Dic3—21no—
281C22×Dic3—22no—
282C22×Dic3—21no—
283C22×Dic3—21no—
284C22×Dic3—21no—
285C22×Dic3—21no—
286C22×Dic3—21no—
287C22×Dic3—21no—
288C22×Dic3—22no—
289C22×Dic3—28no—
290C22×Dic3—22no—
291C22×Dic3—22no—
292C22×Dic3—22no—
293C22×Dic3—22no—
294C22×Dic3—22no—
295C22×Dic3—22no—
296C22×Dic3—22no—
297C22×Dic3—44no—
298C22×Dic3—48no—
299C22×Dic3—48no—
300C22×Dic3C2×D412yes—
301C22×Dic3C2×D412yes—
302C22×Dic3C2×D412yes—
303C22×Dic3C2×D414yes—
304C2×D12—216no—
305C2×D12—48no—
306C2×D12—48no—
307C2×D12—48no—
308C2×D12—48no—
309C2×D12—48no—
310C2×D12—48no—
311C3×C22⋊C4—28no—
312C3×C22⋊C4—44no—
313#217—44no—
314(C2×D3)⋊C4—216no—
315(C2×D3)⋊C4—216no—
316(C2×D3)⋊C4—216no—
317(C2×D3)⋊C4—44no—
318(C2×D3)⋊C4—48no—
319(C2×D3)⋊C4—48no—
320(C2×D3)⋊C4—48no—
321(C2×D3)⋊C4—44no—
322Dic3⋊C4—48no—
323C25—32no—
324C25—31no—
325C25—34no—
326C25—64no—
327C25—64no—
328C25—62no—
329C25—62no—
330C25—62no—
331C25—62no—
332C25—62no—
333C25—62no—
334C25—122no—
335C25—122no—
336C25C22×D311yescharacteristic
337C22×D4—34no—
338C22×D4—64no—
339C22×D4—64no—
340C22×D4—64no—
341C22×D4—64no—
342C22×D4—62no—
343C22×D4—62no—
344C22×D4—62no—
345C22×D4—62no—
346C22×D4—62no—
347C22×D4—62no—
348C22×D4—64no—
349C22×D4—122no—
350C22×D4—122no—
351C23×C4—22no—
352C23×C4—24no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—31no—
356C23×C4—31no—
357C23×C4—31no—
358C23×C4—34no—
359C23×C4—32no—
360C23×C4—42no—
361C23×C4—64no—
362C23×C4—62no—
363C23×C4—62no—
364C23×C4—122no—
365C23×C4C22×D311yescharacteristic
366C23×C4C22×D311yescharacteristic
367C23×C4C22×D312yes—
368C23×C4C22×D312yes—
369#120—632no—
370C2×C4⋊C4—64no—
371C2×C4⋊C4—64no—
372C2×C4⋊C4—122no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—38no—
379C2×C22⋊C4—64no—
380C2×C22⋊C4—64no—
381C2×C22⋊C4—64no—
382C2×C22⋊C4—64no—
383C2×C22⋊C4—64no—
384C2×C22⋊C4—64no—
385C2×C22⋊C4—632no—
386C2×C22⋊C4—64no—
387C2×C22⋊C4—64no—
388C2×C22⋊C4—62no—
389C2×C22⋊C4—62no—
390C2×C22⋊C4—64no—
391C2×C22⋊C4—64no—
392C2×C22⋊C4—64no—
393C2×C22⋊C4—64no—
394C2×C22⋊C4—64no—
395C2×C22⋊C4—64no—
396C2×C22⋊C4—62no—
397C2×C22⋊C4—62no—
398C2×C22⋊C4—62no—
399C2×C22⋊C4—64no—
400C2×C22⋊C4—122no—
401C2×C22⋊C4—122no—
402C2×C22⋊C4—122no—
403C2×C22⋊C4—122no—
404C2×C22⋊C4D1214yes—
405#95—24no—
406#95—42no—
407#95—64no—
408#95—62no—
409#95—62no—
410#95—64no—
411C23×C3—22no—
412C23×C3—24no—
413C23×C3—22no—
414C23×C3—24no—
415C23×C3—22no—
416C23×C3—24no—
417C23×C3—22no—
418C23×C3—24no—
419C23×C3—24no—
420C23×C3—24no—
421C23×C3—24no—
422C23×C3—24no—
423C23×C3—24no—
424C23×C3—24no—
425C23×C3—24no—
426C23×C3—24no—
427C23×C3#12014yes—
428C23×C3#12114yes—
429C23×C3#12114yes—
430C23×C3#12114yes—
431C23×C3#12314yes—
432C23×C3#12314yes—
433C23×C3#12414yes—
434C23×C3C22×D411yescharacteristic
435C23×C3C22×D411yescharacteristic
436C23×C3C22×D411yescharacteristic
437C23×C3C22×D411yescharacteristic
438C23×C3C22×D412yes—
439C23×C3C2×#4111yescharacteristic
440C23×C3C2×#4111yescharacteristic
441C23×C3C2×#4111yescharacteristic
442C23×C3C2×#4112yes—
443C23×C3H(5,𝔽2)12yes—
444C23×C3H(5,𝔽2)12yes—
445C22×D3—232no—
446C22×D3—24no—
447C22×D3—24no—
448C22×D3—24no—
449C22×D3—24no—
450C22×D3—24no—
451C22×D3—24no—
452C22×D3—24no—
453C22×D3—24no—
454C22×D3—24no—
455C22×D3—24no—
456C22×D3—24no—
457C22×D3—24no—
458C22×D3—24no—
459C22×D3—24no—
460C22×D3—24no—
461C22×D3—24no—
462C22×D3—24no—
463C22×D3—24no—
464C22×D3—22no—
465C22×D3—22no—
466C22×D3—22no—
467C22×D3—24no—
468C22×D3—24no—
469C22×D3—432no—
470C22×D3—432no—
471C22×D3—416no—
472C22×D3—416no—
473C22×D3—416no—
474C22×D3—416no—
475C22×D3—432no—
476C22×D3—432no—
477C22×D3—416no—
478C22×D3—42no—
479C22×D3—42no—
480C22×D3—42no—
481C22×D3—42no—
482C22×D3—42no—
483C22×D3—42no—
484C22×D3—42no—
485C22×D3—42no—
486C22×D3—42no—
487C22×D3—42no—
488C22×D3—42no—
489C22×D3—42no—
490C22×D3—42no—
491C22×D3—42no—
492C22×D3—42no—
493C22×D3—42no—
494C22×D3—416no—
495C22×D3—41no—
496C22×D3—42no—
497C22×D3—41no—
498C22×D3—41no—
499C22×D3—41no—
500C22×D3—41no—
501C22×D3—42no—
502C22×D3—41no—
503C22×D3—41no—
504C22×D3—42no—
505C22×D3—41no—
506C22×D3—42no—
507C22×D3—42no—
508C22×D3—42no—
509C22×D3—42no—
510C22×D3—42no—
511C22×D3—42no—
512C22×D3—42no—
513C22×D3#12118yes—
514C2×C3×C4—24no—
515C2×C3×C4—24no—
516C2×C3×C4—24no—
517C2×C3×C4—24no—
518C2×C3×C4—24no—
519C2×C3×C4—24no—
520C2×C3×C4—416no—
521C2×C3×C4—42no—
522C2×C3×C4—42no—
523C2×C3×C4—42no—
524C2×C3×C4—42no—
525C2×C3×C4—42no—
526C2×C3×C4—42no—
527C2×C3×C4—42no—
528C2×C3×C4—42no—
529C2×C3×C4—41no—
530C2×C3×C4—42no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—42no—
535C2×C3×C4—41no—
536C2×C3×C4—42no—
537C2×C3×C4—41no—
538C2×C3×C4—42no—
539#67—416no—
540C2×Dic3—22no—
541C2×Dic3—22no—
542C2×Dic3—24no—
543C2×Dic3—24no—
544C2×Dic3—22no—
545C2×Dic3—22no—
546C2×Dic3—22no—
547C2×Dic3—22no—
548C2×Dic3—22no—
549C2×Dic3—22no—
550C2×Dic3—416no—
551C2×Dic3—41no—
552C2×Dic3—41no—
553C2×Dic3—41no—
554C2×Dic3—41no—
555C2×Dic3—42no—
556C2×Dic3—42no—
557C2×Dic3—42no—
558C2×Dic3—42no—
559C2×Dic3—42no—
560C2×Dic3—42no—
561C2×Dic3—42no—
562C2×Dic3—42no—
563C2×Dic3—42no—
564C2×Dic3#12014yescomplemented
565D12—432no—
566C24—22no—
567C24—22no—
568C24—22no—
569C24—22no—
570C24—34no—
571C24—34no—
572C24—34no—
573C24—32no—
574C24—616no—
575C24—68no—
576C24—68no—
577C24—616no—
578C24—68no—
579C24—62no—
580C24—62no—
581C24—62no—
582C24—62no—
583C24—62no—
584C24—62no—
585C24—62no—
586C24—62no—
587C24—62no—
588C24—62no—
589C24—62no—
590C24—62no—
591C24—68no—
592C24—68no—
593C24—61no—
594C24—61no—
595C24—61no—
596C24—61no—
597C24—62no—
598C24—61no—
599C24—62no—
600C24—61no—
601C24—62no—
602C24—62no—
603C24—128no—
604C24—128no—
605C24—128no—
606C24—128no—
607C24—128no—
608C24—128no—
609C24—128no—
610C24—128no—
611C24—128no—
612C24—124no—
613C24—128no—
614C24—124no—
615C24—124no—
616C24—124no—
617C24—124no—
618C24—124no—
619C24C2×D1212yes—
620C24#23512yes—
621C24#23512yes—
622C24D3×D412yes—
623C24D3×D412yes—
624C24D3×D412yes—
625C24#23912yes—
626C24C23×D311yescharacteristic
627C2×D4—616no—
628C2×D4—68no—
629C2×D4—68no—
630C2×D4—68no—
631C2×D4—128no—
632C2×D4—128no—
633C2×D4—128no—
634C2×D4—128no—
635C2×D4—128no—
636C2×D4—128no—
637C2×D4—124no—
638C2×D4—124no—
639C2×D4—124no—
640C2×D4—124no—
641C22×C4—28no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—22no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—32no—
665C22×C4—34no—
666C22×C4—32no—
667C22×C4—32no—
668C22×C4—48no—
669C22×C4—48no—
670C22×C4—44no—
671C22×C4—44no—
672C22×C4—68no—
673C22×C4—61no—
674C22×C4—61no—
675C22×C4—62no—
676C22×C4—68no—
677C22×C4—61no—
678C22×C4—61no—
679C22×C4—61no—
680C22×C4—61no—
681C22×C4—61no—
682C22×C4—62no—
683C22×C4—61no—
684C22×C4—61no—
685C22×C4—61no—
686C22×C4—62no—
687C22×C4—62no—
688C22×C4—62no—
689C22×C4—62no—
690C22×C4—62no—
691C22×C4—62no—
692C22×C4—62no—
693C22×C4—62no—
694C22×C4—124no—
695C22×C4—128no—
696C22×C4—128no—
697C22×C4C2×D1214yes—
698C22×C4D3×D414yes—
699C4⋊C4—128no—
700C22⋊C4—28no—
701C22⋊C4—44no—
702C22⋊C4—616no—
703C22⋊C4—616no—
704C22⋊C4—616no—
705C22⋊C4—128no—
706C22⋊C4—124no—
707C22⋊C4—124no—
708C22⋊C4—128no—
709C22⋊C4—128no—
710C22⋊C4—124no—
711C22×C3—24no—
712C22×C3—24no—
713C22×C3—24no—
714C22×C3—24no—
715C22×C3—28no—
716C22×C3—24no—
717C22×C3—28no—
718C22×C3—28no—
719C22×C3—28no—
720C22×C3—24no—
721C22×C3#39418yescomplemented
722C22×C3C2×#12011yescharacteristic
723C22×C3C2×#12011yescharacteristic
724C22×C3C2×#12111yescharacteristic
725C22×C3C2×#12111yescharacteristic
726C22×C3C2×#12111yescharacteristic
727C22×C3C2×#12112yes—
728C22×C3C2×#12311yescharacteristic
729C22×C3C2×#12311yescharacteristic
730C22×C3#52511yescharacteristic
731C22×C3#52512yes—
732C22×C3C2×#12411yescharacteristic
733C22×C3#53411yescharacteristic
734C22×C3#53412yes—
735C22×C3#53511yescharacteristic
736C22×C3#53812yes—
737C22×C3D4212yes—
738C22×C3D4212yes—
739C22×C3#54612yes—
740C22×C3#54612yes—
741C22×C3#54612yes—
742C22×C3#54612yes—
743C22×C3#55112yes—
744C22×C3#55112yes—
745C2×D3—28no—
746C2×D3—28no—
747C2×D3—28no—
748C2×D3—464no—
749C2×D3—44no—
750C2×D3—44no—
751C2×D3—44no—
752C2×D3—44no—
753C2×D3—44no—
754C2×D3—44no—
755C2×D3—44no—
756C2×D3—44no—
757C2×D3—44no—
758C2×D3—44no—
759C2×D3—44no—
760C2×D3—44no—
761C2×D3—42no—
762C2×D3—42no—
763C2×D3—44no—
764C2×D3—44no—
765C2×D3—42no—
766C2×D3—81no—
767C2×D3—81no—
768C2×D3—81no—
769C2×D3—81no—
770C2×D3—82no—
771C2×D3—82no—
772C3×C4—44no—
773C3×C4—44no—
774C3×C4—81no—
775C3×C4—81no—
776Dic3—24no—
777Dic3—42no—
778Dic3—42no—
779Dic3—82no—
780C23—24no—
781C23—22no—
782C23—24no—
783C23—22no—
784C23—24no—
785C23—24no—
786C23—24no—
787C23—24no—
788C23—24no—
789C23—24no—
790C23—22no—
791C23—24no—
792C23—22no—
793C23—24no—
794C23—24no—
795C23—24no—
796C23—38no—
797C23—632no—
798C23—64no—
799C23—64no—
800C23—64no—
801C23—64no—
802C23—64no—
803C23—64no—
804C23—64no—
805C23—64no—
806C23—64no—
807C23—64no—
808C23—64no—
809C23—64no—
810C23—64no—
811C23—64no—
812C23—64no—
813C23—64no—
814C23—64no—
815C23—64no—
816C23—64no—
817C23—62no—
818C23—62no—
819C23—62no—
820C23—64no—
821C23—1232no—
822C23—1232no—
823C23—1216no—
824C23—1216no—
825C23—1216no—
826C23—1232no—
827C23—1232no—
828C23—1216no—
829C23—1216no—
830C23—122no—
831C23—122no—
832C23—122no—
833C23—1216no—
834C23—122no—
835C23—122no—
836C23—122no—
837C23—122no—
838C23—122no—
839C23—122no—
840C23—122no—
841C23—122no—
842C23—122no—
843C23—122no—
844C23—122no—
845C23—122no—
846C23—122no—
847C23—122no—
848C23—121no—
849C23—121no—
850C23—121no—
851C23—121no—
852C23—122no—
853C23—121no—
854C23—121no—
855C23—122no—
856C23—122no—
857C23—122no—
858C23—122no—
859C23—122no—
860C23—121no—
861C23—121no—
862C23—122no—
863C23—122no—
864C23—122no—
865C23#87514yes—
866C23#88214yes—
867C23#88414yes—
868C23#88414yes—
869C23#89414yes—
870C23#89414yes—
871C23#89514yes—
872C23C22×D1211yescharacteristic
873C23C2×#23511yescharacteristic
874C23C2×#23511yescharacteristic
875C23C2×D3×D411yescharacteristic
876C23C2×D3×D411yescharacteristic
877C23C2×D3×D411yescharacteristic
878C23C2×D3×D412yes—
879C23#100412yes—
880C23C2×#23911yescharacteristic
881C23D3×#4112yes—
882C23#100912yes—
883D4—1232no—
884D4—1216no—
885C2×C4—24no—
886C2×C4—24no—
887C2×C4—24no—
888C2×C4—24no—
889C2×C4—24no—
890C2×C4—24no—
891C2×C4—34no—
892C2×C4—416no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4—42no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—42no—
906C2×C4—42no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—42no—
910C2×C4—42no—
911C2×C4—62no—
912C2×C4—62no—
913C2×C4—64no—
914C2×C4—64no—
915C2×C4—62no—
916C2×C4—62no—
917C2×C4—62no—
918C2×C4—62no—
919C2×C4—62no—
920C2×C4—62no—
921C2×C4—1216no—
922C2×C4—121no—
923C2×C4—121no—
924C2×C4—121no—
925C2×C4—121no—
926C2×C4—122no—
927C2×C4—122no—
928C2×C4—122no—
929C2×C4—122no—
930C2×C4—122no—
931C2×C4—122no—
932C2×C4—122no—
933C2×C4—122no—
934C2×C4—122no—
935C2×C3—28no—
936C2×C3C2×#39411yescharacteristic
937C2×C3#240811yescharacteristic
938C2×C3#241011yescharacteristic
939C2×C3#241012yes—
940C2×C3#241111yescharacteristic
941C2×C3#241212yes—
942C2×C3#241812yes—
943C2×C3#247212yes—
944C2×C3#253411yescharacteristic
945C2×C3#261711yescharacteristic
946C2×C3#284711yescharacteristic
947D3—48no—
948D3—82no—
949C22—28no—
950C22—24no—
951C22—24no—
952C22—24no—
953C22—28no—
954C22—28no—
955C22—28no—
956C22—24no—
957C22—24no—
958C22—24no—
959C22—68no—
960C22—68no—
961C22—68no—
962C22—1264no—
963C22—124no—
964C22—124no—
965C22—124no—
966C22—124no—
967C22—124no—
968C22—124no—
969C22—124no—
970C22—124no—
971C22—124no—
972C22—124no—
973C22—124no—
974C22—124no—
975C22—122no—
976C22—124no—
977C22—122no—
978C22—124no—
979C22—122no—
980C22—242no—
981C22—241no—
982C22—241no—
983C22—242no—
984C22—241no—
985C22—241no—
986C22#467218yescomplemented
987C22C2×#87511yescharacteristic
988C22C2×#88211yescharacteristic
989C22C2×#88411yescharacteristic
990C22C2×#88411yescharacteristic
991C22#549012yes—
992C22C2×#89411yescharacteristic
993C22C2×#89411yescharacteristic
994C22C2×#89511yescharacteristic
995C22#552712yes—
996C22#554712yes—
997C22D4×D1212yes—
998C22#555412yes—
999C22#556012yes—
1000C22D3×#12011yescharacteristic
1001C22#559012yes—
1002C22#559211yescharacteristic
1003C22D3×#12112yes—
1004C22#560512yes—
1005C22#563012yes—
1006C22#563712yes—
1007C22#565311yescharacteristic
1008C22#565412yes—
1009C22#565611yescharacteristic
1010C4—44no—
1011C4—44no—
1012C4—64no—
1013C4—81no—
1014C4—81no—
1015C4—122no—
1016C4—122no—
1017C4—242no—
1018C3#1472511yescharacteristic, complemented, Sylow
1019C2—28no—
1020C2—128no—
1021C2—242no—
1022C2C2×#467211yescharacteristic
1023C2#7359412yes—
1024C2#7382411yescharacteristic
1025C2#7401812yes—
1026C2#7413111yescharacteristic
1027C2#7460111yescharacteristic
1028C2#7460211yescharacteristic
1029C2#7460312yes—
1030C2#7488812yes—
1031C2#7490511yescharacteristic
1032C2#7493511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×C22⋊#95C2
prime radicalC22×#882C2
hypercenterC22⋊#95D3
hypocenterC3#14725
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
1. C23×(C2×D3)⋊C4C2semidirect
3. C2×#5213C2semidirect
4. C2×#4955C2semidirect
5. C2×#4958C2semidirect
6. C2×#4942C2semidirect
7. C2×#4672C2semidirect
8. C3×C22⋊#95C2semidirect
9. #69429C2semidirect
10. #69428C2semidirect
11. #69426C2semidirect
28. C22×(C2×D3)⋊C4C22semidirect
29. C22×(C2×D3)⋊C4C22semidirect
30. C22×(C2×D3)⋊C4C22semidirect
31. C22×Dic3⋊C4C22semidirect
35. C2×C3×#95C22semidirect
36. C2×C3×#95C22semidirect
38. C2×C3⋊#95C22semidirect
39. C2×C3⋊#95C22semidirect
40. C2×C3⋊#95C22semidirect
41. C2×C3⋊#95C22semidirect
56. C22⋊#95D3semidirect
91. C23×Dic3D4semidirect
134. C2×(C2×D3)⋊C4D4semidirect
176. C2×#95C2×D3semidirect
177. C2×#95C2×D3semidirect
564. C2×Dic3#120semidirect
721. C22×C3#394semidirect
986. C22#4672semidirect
1018. C3#14725semidirect

Maximal subgroups

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

subgroupindex
C23×(C2×D3)⋊C42
C22×#8822
C2×#52132
C2×#49552
C2×#49582
C2×#49422
C2×#46722
C3×C22⋊#952
#694292
#694282
#694262
#147253