Finite Group Databasebeta

← #10727095

Subgroups — #10727095

Order 768.

3510 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#895C211yesmaximal, characteristic, complemented
2C22×#884C212yesmaximal, complemented
3C2×#4960C211yesmaximal, characteristic, complemented
4C2×#4956C211yesmaximal, characteristic, complemented
5C2×#4665C212yesmaximal, complemented
6C2×D3×#95C211yesmaximal, characteristic, complemented
7C3×#1439C211yesmaximal, characteristic, complemented
8#71568C211yesmaximal, characteristic, complemented
9#71550C212yesmaximal, complemented
10#69428C212yesmaximal, complemented
11#69426C211yesmaximal, characteristic, complemented
12#14757—31nomaximal, Sylow
13C23×#67C2211yescharacteristic
14C23×#67C2212yes—
15C23×D12C2212yes—
16C23×D12C2211yescharacteristic
17C23×C4×D3C2212yes—
18C23×C4×D3C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2212yes—
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×#217C2211yescharacteristic
23C22×(C2×D3)⋊C4C2212yes—
24C22×(C2×D3)⋊C4C2212yes—
25C22×(C2×D3)⋊C4C2212yes—
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2212yes—
28C22×Dic3⋊C4C2212yes—
29C2×#895—28no—
30C2×#895—24no—
31C2×#884—28no—
32C2×#884—28no—
33C2×#884—28no—
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2212yes—
36C2×C3⋊#95C2211yescharacteristic
37C2×C3⋊#95C2211yescharacteristic
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2212yes—
40C2×C3⋊#95C2211yescharacteristic
41#4960—24no—
42#4956—24no—
43#4665—28no—
44D3×#95—24no—
45C22×#121—31no—
46C22×#121—32no—
47C2×#392—31no—
48C2×#386—32no—
49C2×#386—31no—
50C22×#95—31no—
51#1444—31no—
52#1439—32no—
53#1439D311yescharacteristic, complemented
54#1438—31no—
55#1438—32no—
56C25×C3C2311yescharacteristic
57C24×D3C2312yes—
58C24×D3C2311yescharacteristic
59C23×C3×C4C2311yescharacteristic
60C23×C3×C4C2312yes—
61C23×C3×C4C2312yes—
62C23×C3×C4C2311yescharacteristic
63C22×#67—24no—
64C22×#67—22no—
65C22×#67—24no—
66C22×#67—24no—
67C22×#67—24no—
68C22×#67—22no—
69C22×#67—24no—
70C22×#67—24no—
71C22×#67—24no—
72C22×#67—42no—
73C22×#67—42no—
74C22×#67D414yescomplemented
75C23×Dic3C2311yescharacteristic
76C23×Dic3C2311yescharacteristic
77C23×Dic3C2311yescharacteristic
78C23×Dic3C2312yes—
79C22×D12—24no—
80C22×D12—24no—
81C22×D12—24no—
82C22×D12—24no—
83C22×D12—24no—
84C22×D12—24no—
85C22×D12—24no—
86C22×D12—22no—
87C22×D12—22no—
88C22×D12—22no—
89C22×D12—42no—
90C22×D12D418yescomplemented
91C22×C4×D3—24no—
92C22×C4×D3—24no—
93C22×C4×D3—24no—
94C22×C4×D3—22no—
95C22×C4×D3—22no—
96C22×C4×D3—24no—
97C22×C4×D3—24no—
98C22×C4×D3—42no—
99C22×C4×D3—42no—
100C22×C4×D3—42no—
101C22×C4×D3D418yescomplemented
102C22×C4×D3D414yescomplemented
103C2×C3×C4⋊C4—24no—
104C2×C3×C4⋊C4—22no—
105C2×C3×C22⋊C4—24no—
106C2×C3×C22⋊C4—24no—
107C2×C3×C22⋊C4—24no—
108C2×C3×C22⋊C4—22no—
109C2×C3×C22⋊C4—22no—
110C2×C3×C22⋊C4—22no—
111C2×#217—22no—
112C2×#217—42no—
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—22no—
121C2×(C2×D3)⋊C4—24no—
122C2×(C2×D3)⋊C4—24no—
123C2×(C2×D3)⋊C4—24no—
124C2×(C2×D3)⋊C4—24no—
125C2×(C2×D3)⋊C4—42no—
126C2×(C2×D3)⋊C4—42no—
127C2×Dic3⋊C4—24no—
128C2×Dic3⋊C4—24no—
129C2×Dic3⋊C4—24no—
130#895—232no—
131#884—264no—
132C3×#95—22no—
133C3×#95—24no—
134C3⋊#95—22no—
135C3⋊#95—24no—
136C3⋊#95—24no—
137C3⋊#95—22no—
138C3⋊#95D414yescomplemented
139C23×D4—31no—
140C23×D4—32no—
141C23×D4—32no—
142C23×D4—31no—
143C24×C4—32no—
144C24×C4—31no—
145C2×#121—68no—
146C2×#121—68no—
147C2×#121—68no—
148C2×#121—64no—
149C2×#121—68no—
150C22×C4⋊C4—32no—
151C22×C4⋊C4C2×D311yescharacteristic
152C22×C22⋊C4—32no—
153C22×C22⋊C4—32no—
154C22×C22⋊C4—32no—
155C22×C22⋊C4—31no—
156C22×C22⋊C4—31no—
157C22×C22⋊C4—32no—
158C22×C22⋊C4C2×D311yescharacteristic
159C22×C22⋊C4C2×D312yes—
160#392—64no—
161#386—68no—
162#386—64no—
163C2×#95—31no—
164C2×#95—32no—
165C2×#95—32no—
166C2×#95—31no—
167C2×#95—31no—
168C2×#95—64no—
169C2×#95C2×D311yescharacteristic
170C2×#95C2×D312yes—
171C24×C3—21no—
172C24×C3—22no—
173C24×C3—22no—
174C24×C3—21no—
175C24×C3—21no—
176C24×C3—21no—
177C24×C3—22no—
178C24×C3—22no—
179C24×C3—21no—
180C24×C3—21no—
181C24×C3C2×D412yes—
182C24×C3C2411yescharacteristic
183C23×D3—21no—
184C23×D3—21no—
185C23×D3—22no—
186C23×D3—22no—
187C23×D3—21no—
188C23×D3—21no—
189C23×D3—22no—
190C23×D3—22no—
191C23×D3—22no—
192C23×D3—22no—
193C23×D3—22no—
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×D3C2×D414yes—
204C23×D3C2×D412yes—
205C23×D3C2×D414yes—
206C23×D3C2×D412yes—
207C23×D3C2×D414yes—
208C23×D3#4112yes—
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×C4—22no—
218C22×C3×C4—22no—
219C22×C3×C4—22no—
220C22×C3×C4—22no—
221C22×C3×C4—22no—
222C22×C3×C4—22no—
223C22×C3×C4—21no—
224C22×C3×C4—22no—
225C22×C3×C4—21no—
226C22×C3×C4—22no—
227C22×C3×C4—21no—
228C22×C3×C4C2×D414yes—
229C22×C3×C4C2×D414yes—
230C22×C3×C4C2×D412yes—
231C22×C3×C4C2×D412yes—
232C22×C3×C4#4112yes—
233C2×#67—216no—
234C2×#67—216no—
235C2×#67—28no—
236C2×#67—48no—
237C2×#67—48no—
238C2×#67—48no—
239C2×#67—48no—
240C2×#67—48no—
241C2×#67—44no—
242C2×#67—48no—
243C2×#67—44no—
244C2×#67—48no—
245C22×Dic3—22no—
246C22×Dic3—22no—
247C22×Dic3—22no—
248C22×Dic3—22no—
249C22×Dic3—21no—
250C22×Dic3—21no—
251C22×Dic3—22no—
252C22×Dic3—22no—
253C22×Dic3—22no—
254C22×Dic3—21no—
255C22×Dic3—21no—
256C22×Dic3—22no—
257C22×Dic3—22no—
258C22×Dic3—21no—
259C22×Dic3—21no—
260C22×Dic3—22no—
261C22×Dic3—21no—
262C22×Dic3C2×D412yes—
263C22×Dic3C2×D412yes—
264C22×Dic3C2×D414yes—
265C22×Dic3C2×D414yes—
266C22×Dic3#4114yes—
267C2×D12—28no—
268C2×D12—216no—
269C2×D12—216no—
270C2×D12—216no—
271C2×D12—48no—
272C2×D12—48no—
273C2×D12—44no—
274C2×D12—48no—
275C2×D12—48no—
276C2×D12—48no—
277C2×D12—48no—
278C2×D12—44no—
279C2×C4×D3—216no—
280C2×C4×D3—28no—
281C2×C4×D3—28no—
282C2×C4×D3—216no—
283C2×C4×D3—48no—
284C2×C4×D3—44no—
285C2×C4×D3—48no—
286C2×C4×D3—48no—
287C2×C4×D3—48no—
288C2×C4×D3—48no—
289C2×C4×D3—48no—
290C2×C4×D3—48no—
291C3×C4⋊C4—28no—
292C3×C22⋊C4—216no—
293C3×C22⋊C4—44no—
294#217—44no—
295(C2×D3)⋊C4—216no—
296(C2×D3)⋊C4—216no—
297(C2×D3)⋊C4—48no—
298(C2×D3)⋊C4—44no—
299(C2×D3)⋊C4—48no—
300Dic3⋊C4—216no—
301C25—31no—
302C25—32no—
303C25C22×D311yescharacteristic
304C22×D4—34no—
305C22×D4—38no—
306C22×D4—64no—
307C22×D4—64no—
308C22×D4—64no—
309C22×D4—64no—
310C22×D4—64no—
311C22×D4—64no—
312C22×D4—64no—
313C22×D4—64no—
314C22×D4—64no—
315C22×D4—64no—
316C22×D4—64no—
317C22×D4—64no—
318C22×D4—64no—
319C22×D4—62no—
320C22×D4—62no—
321C22×D4—64no—
322C22×D4—62no—
323C22×D4—62no—
324C22×D4—62no—
325C22×D4—122no—
326C22×D4—122no—
327C22×D4—122no—
328C23×C4—32no—
329C23×C4—31no—
330C23×C4—31no—
331C23×C4—38no—
332C23×C4—34no—
333C23×C4—31no—
334C23×C4—64no—
335C23×C4—64no—
336C23×C4—64no—
337C23×C4—64no—
338C23×C4—64no—
339C23×C4—62no—
340C23×C4—62no—
341C23×C4—122no—
342C23×C4—122no—
343C23×C4—122no—
344C23×C4C22×D311yescharacteristic
345C23×C4C22×D312yes—
346C23×C4C22×D312yes—
347C23×C4C22×D311yescharacteristic
348#121—664no—
349#121—632no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—64no—
353C2×C4⋊C4—64no—
354C2×C4⋊C4—64no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—64no—
362C2×C22⋊C4—64no—
363C2×C22⋊C4—64no—
364C2×C22⋊C4—64no—
365C2×C22⋊C4—64no—
366C2×C22⋊C4—64no—
367C2×C22⋊C4—64no—
368C2×C22⋊C4—64no—
369C2×C22⋊C4—64no—
370C2×C22⋊C4—64no—
371C2×C22⋊C4—62no—
372C2×C22⋊C4—62no—
373C2×C22⋊C4—64no—
374C2×C22⋊C4—122no—
375C2×C22⋊C4—122no—
376C2×C22⋊C4—122no—
377#95—22no—
378#95—24no—
379#95—34no—
380#95—64no—
381#95—64no—
382#95—62no—
383#95—62no—
384C23×C3—24no—
385C23×C3—22no—
386C23×C3—22no—
387C23×C3—24no—
388C23×C3—22no—
389C23×C3—41no—
390C23×C3—41no—
391C23×C3—42no—
392C23×C3—42no—
393C23×C3—41no—
394C23×C3—41no—
395C23×C3—42no—
396C23×C3—41no—
397C23×C3—42no—
398C23×C3—41no—
399C23×C3—42no—
400C23×C3—42no—
401C23×C3—42no—
402C23×C3—42no—
403C23×C3—42no—
404C23×C3—41no—
405C23×C3—42no—
406C23×C3—41no—
407C23×C3C22×D412yes—
408C23×C3C22×D411yescharacteristic
409C23×C3C22×D411yescharacteristic
410C23×C3C22×D412yes—
411C23×C3C22×D411yescharacteristic
412C23×C3C2×#4111yescharacteristic
413C23×C3C2×#4111yescharacteristic
414C23×C3C2×#4112yes—
415C23×C3H(5,𝔽2)12yes—
416C23×C3H(5,𝔽2)11yescharacteristic
417C23×C32−1+411yescharacteristic
418C22×D3—22no—
419C22×D3—24no—
420C22×D3—22no—
421C22×D3—24no—
422C22×D3—24no—
423C22×D3—22no—
424C22×D3—22no—
425C22×D3—24no—
426C22×D3—22no—
427C22×D3—24no—
428C22×D3—24no—
429C22×D3—24no—
430C22×D3—24no—
431C22×D3—22no—
432C22×D3—24no—
433C22×D3—22no—
434C22×D3—24no—
435C22×D3—22no—
436C22×D3—24no—
437C22×D3—24no—
438C22×D3—24no—
439C22×D3—24no—
440C22×D3—24no—
441C22×D3—24no—
442C22×D3—24no—
443C22×D3—42no—
444C22×D3—42no—
445C22×D3—42no—
446C22×D3—42no—
447C22×D3—42no—
448C22×D3—42no—
449C22×D3—42no—
450C22×D3—42no—
451C22×D3—42no—
452C22×D3—42no—
453C22×D3—42no—
454C22×D3—42no—
455C22×D3—42no—
456C22×D3—42no—
457C22×D3—42no—
458C22×D3—42no—
459C22×D3—42no—
460C22×D3—42no—
461C22×D3—42no—
462C22×D3—42no—
463C22×D3—42no—
464C22×D3—42no—
465C22×D3—42no—
466C22×D3—42no—
467C22×D3—42no—
468C22×D3—42no—
469C22×D3—42no—
470C22×D3—42no—
471C22×D3#12014yes—
472C22×D3#12018yes—
473C22×D3#12118yes—
474C22×D3#12114yes—
475C22×D3#12714yes—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—24no—
479C2×C3×C4—24no—
480C2×C3×C4—24no—
481C2×C3×C4—24no—
482C2×C3×C4—24no—
483C2×C3×C4—24no—
484C2×C3×C4—24no—
485C2×C3×C4—24no—
486C2×C3×C4—42no—
487C2×C3×C4—42no—
488C2×C3×C4—42no—
489C2×C3×C4—42no—
490C2×C3×C4—42no—
491C2×C3×C4—42no—
492C2×C3×C4—42no—
493C2×C3×C4—42no—
494C2×C3×C4—42no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—42no—
499C2×C3×C4#12114yescomplemented
500#67—432no—
501#67—416no—
502C2×Dic3—24no—
503C2×Dic3—24no—
504C2×Dic3—24no—
505C2×Dic3—24no—
506C2×Dic3—24no—
507C2×Dic3—24no—
508C2×Dic3—24no—
509C2×Dic3—22no—
510C2×Dic3—22no—
511C2×Dic3—22no—
512C2×Dic3—22no—
513C2×Dic3—41no—
514C2×Dic3—42no—
515C2×Dic3—41no—
516C2×Dic3—42no—
517C2×Dic3—42no—
518C2×Dic3—41no—
519C2×Dic3—42no—
520C2×Dic3—41no—
521C2×Dic3—42no—
522C2×Dic3—41no—
523C2×Dic3#12118yescomplemented
524D12—416no—
525D12—432no—
526C4×D3—432no—
527C4×D3—416no—
528C24—21no—
529C24—21no—
530C24—22no—
531C24—22no—
532C24—21no—
533C24—21no—
534C24—22no—
535C24—21no—
536C24—22no—
537C24—21no—
538C24—32no—
539C24—34no—
540C24—32no—
541C24—34no—
542C24—32no—
543C24—34no—
544C24—61no—
545C24—61no—
546C24—61no—
547C24—62no—
548C24—62no—
549C24—61no—
550C24—62no—
551C24—62no—
552C24—62no—
553C24—62no—
554C24—62no—
555C24—62no—
556C24—62no—
557C24—62no—
558C24—62no—
559C24—62no—
560C24—62no—
561C24—62no—
562C24—62no—
563C24—62no—
564C24D3×D412yes—
565C24C23×D311yescharacteristic
566C2×D4—616no—
567C2×D4—616no—
568C2×D4—616no—
569C2×D4—68no—
570C2×D4—616no—
571C2×D4—68no—
572C2×D4—616no—
573C2×D4—128no—
574C2×D4—128no—
575C2×D4—124no—
576C2×D4—128no—
577C2×D4—128no—
578C2×D4—128no—
579C2×D4—128no—
580C2×D4—128no—
581C2×D4—128no—
582C2×D4—128no—
583C2×D4—128no—
584C2×D4—128no—
585C2×D4—128no—
586C2×D4—124no—
587C2×D4—124no—
588C2×D4—128no—
589C2×D4—124no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—21no—
605C22×C4—22no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—22no—
609C22×C4—34no—
610C22×C4—34no—
611C22×C4—34no—
612C22×C4—32no—
613C22×C4—32no—
614C22×C4—616no—
615C22×C4—68no—
616C22×C4—616no—
617C22×C4—62no—
618C22×C4—62no—
619C22×C4—62no—
620C22×C4—62no—
621C22×C4—61no—
622C22×C4—61no—
623C22×C4—61no—
624C22×C4—62no—
625C22×C4—62no—
626C22×C4—62no—
627C22×C4—61no—
628C22×C4—62no—
629C22×C4—68no—
630C22×C4—61no—
631C22×C4—62no—
632C22×C4—61no—
633C22×C4—62no—
634C22×C4—61no—
635C22×C4—124no—
636C22×C4—128no—
637C22×C4—128no—
638C22×C4—128no—
639C22×C4—128no—
640C22×C4—128no—
641C22×C4—128no—
642C22×C4—128no—
643C22×C4#23512yes—
644C22×C4D3×D414yes—
645C22×C4D3×D414yes—
646C22×C4D3×D412yes—
647C22×C4D3×D412yes—
648C4⋊C4—28no—
649C4⋊C4—616no—
650C22⋊C4—216no—
651C22⋊C4—44no—
652C22⋊C4—616no—
653C22⋊C4—616no—
654C22⋊C4—128no—
655C22⋊C4—128no—
656C22⋊C4—124no—
657C22⋊C4—124no—
658C22×C3—42no—
659C22×C3—44no—
660C22×C3—42no—
661C22×C3—44no—
662C22×C3—42no—
663C22×C3—81no—
664C22×C3—81no—
665C22×C3—81no—
666C22×C3—82no—
667C22×C3—81no—
668C22×C3—82no—
669C22×C3C2×#12012yes—
670C22×C3C2×#12011yescharacteristic
671C22×C3C2×#12111yescharacteristic
672C22×C3C2×#12112yes—
673C22×C3C2×#12111yescharacteristic
674C22×C3C2×#12112yes—
675C22×C3C2×#12711yescharacteristic
676C22×C3#53211yescharacteristic
677C22×C3#53212yes—
678C22×C3#53412yes—
679C22×C3#53411yescharacteristic
680C22×C3#53711yescharacteristic
681C22×C3#53712yes—
682C22×C3D4211yescharacteristic
683C22×C3D4212yes—
684C22×C3#54612yes—
685C22×C3#54612yes—
686C22×C3#54612yes—
687C22×C3#54711yescharacteristic
688C22×C3#54712yes—
689C22×C3#54811yescharacteristic
690C22×C3#55312yes—
691C22×C3#55311yescharacteristic
692C2×D3—24no—
693C2×D3—24no—
694C2×D3—28no—
695C2×D3—24no—
696C2×D3—24no—
697C2×D3—28no—
698C2×D3—24no—
699C2×D3—28no—
700C2×D3—28no—
701C2×D3—24no—
702C2×D3—44no—
703C2×D3—44no—
704C2×D3—44no—
705C2×D3—44no—
706C2×D3—44no—
707C2×D3—44no—
708C2×D3—44no—
709C2×D3—82no—
710C2×D3—82no—
711C2×D3—82no—
712C2×D3—82no—
713C2×D3—82no—
714C2×D3—82no—
715C2×D3—82no—
716C2×D3—82no—
717C2×D3#39218yescomplemented
718C3×C4—24no—
719C3×C4—44no—
720C3×C4—44no—
721C3×C4—81no—
722Dic3—28no—
723Dic3—42no—
724Dic3—42no—
725Dic3—81no—
726C23—24no—
727C23—22no—
728C23—24no—
729C23—22no—
730C23—22no—
731C23—34no—
732C23—38no—
733C23—34no—
734C23—38no—
735C23—34no—
736C23—41no—
737C23—41no—
738C23—42no—
739C23—41no—
740C23—42no—
741C23—42no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—42no—
746C23—42no—
747C23—41no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—41no—
753C23—42no—
754C23—62no—
755C23—64no—
756C23—62no—
757C23—64no—
758C23—62no—
759C23—64no—
760C23—64no—
761C23—62no—
762C23—62no—
763C23—62no—
764C23—64no—
765C23—64no—
766C23—64no—
767C23—62no—
768C23—64no—
769C23—62no—
770C23—64no—
771C23—64no—
772C23—64no—
773C23—64no—
774C23—64no—
775C23—64no—
776C23—64no—
777C23—64no—
778C23—64no—
779C23—122no—
780C23—122no—
781C23—122no—
782C23—122no—
783C23—122no—
784C23—122no—
785C23—122no—
786C23—122no—
787C23—122no—
788C23—122no—
789C23—122no—
790C23—122no—
791C23—122no—
792C23—122no—
793C23—122no—
794C23—122no—
795C23—122no—
796C23—122no—
797C23—122no—
798C23—122no—
799C23—122no—
800C23—122no—
801C23—122no—
802C23—122no—
803C23—122no—
804C23—122no—
805C23—122no—
806C23—122no—
807C23C2×#23511yescharacteristic
808C23C2×D3×D411yescharacteristic
809C23C2×D3×D411yescharacteristic
810C23C2×D3×D412yes—
811C23C2×D3×D411yescharacteristic
812C23C2×D3×D412yes—
813C23#100711yescharacteristic
814C23D3×#4111yescharacteristic
815C23D3×#4112yes—
816C23#100912yes—
817C23#100911yescharacteristic
818D4—1216no—
819D4—1232no—
820D4—1232no—
821D4—1216no—
822C2×C4—22no—
823C2×C4—24no—
824C2×C4—22no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—24no—
830C2×C4—24no—
831C2×C4—24no—
832C2×C4—38no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—64no—
847C2×C4—64no—
848C2×C4—64no—
849C2×C4—64no—
850C2×C4—64no—
851C2×C4—64no—
852C2×C4—62no—
853C2×C4—62no—
854C2×C4—62no—
855C2×C4—64no—
856C2×C4—62no—
857C2×C4—1216no—
858C2×C4—1232no—
859C2×C4—121no—
860C2×C4—122no—
861C2×C4—121no—
862C2×C4—122no—
863C2×C4—122no—
864C2×C4—122no—
865C2×C4—121no—
866C2×C4—121no—
867C2×C4—121no—
868C2×C4—122no—
869C2×C4#88414yescomplemented
870C2×C3—82no—
871C2×C3C2×#39211yescharacteristic
872C2×C3#241012yes—
873C2×C3#241011yescharacteristic
874C2×C3#241611yescharacteristic
875C2×C3#241612yes—
876C2×C3#243011yescharacteristic
877C2×C3#243012yes—
878C2×C3#254312yes—
879C2×C3#254311yescharacteristic
880C2×C3#265611yescharacteristic
881C2×C3#285611yescharacteristic
882D3—28no—
883D3—84no—
884C22—38no—
885C22—44no—
886C22—44no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—64no—
891C22—68no—
892C22—64no—
893C22—68no—
894C22—68no—
895C22—64no—
896C22—64no—
897C22—64no—
898C22—64no—
899C22—68no—
900C22—81no—
901C22—81no—
902C22—82no—
903C22—81no—
904C22—81no—
905C22—82no—
906C22—124no—
907C22—124no—
908C22—124no—
909C22—124no—
910C22—124no—
911C22—124no—
912C22—124no—
913C22—242no—
914C22—242no—
915C22—242no—
916C22—242no—
917C22—242no—
918C22—242no—
919C22—242no—
920C22—242no—
921C22C2×#88411yescharacteristic
922C22#550711yescharacteristic
923C22#553011yescharacteristic
924C22#554812yes—
925C22#555012yes—
926C22D3×#12012yes—
927C22D3×#12011yescharacteristic
928C22D3×#12112yes—
929C22D3×#12112yes—
930C22D3×#12111yescharacteristic
931C22#560911yescharacteristic
932C22#560912yes—
933C22#562911yescharacteristic
934C22#562912yes—
935C22#563112yes—
936C22#563311yescharacteristic
937C22#565312yes—
938C22#565311yescharacteristic
939C22#565412yes—
940C22#566811yescharacteristic
941C22#567612yes—
942C22#570912yes—
943C22D3×#12711yescharacteristic
944C4—24no—
945C4—44no—
946C4—44no—
947C4—68no—
948C4—81no—
949C4—122no—
950C4—122no—
951C4—241no—
952C3#1475711yescharacteristic, complemented, Sylow
953C2—68no—
954C2—82no—
955C2—244no—
956C2#7388711yescharacteristic
957C2#7460612yes—
958C2#7488711yescharacteristic
959C2#7588212yes—
960C2#7647611yescharacteristic
961C2D3×#39211yescharacteristic
962C2#7686411yescharacteristic
963C2#7710812yes—
964C2#7728412yes—
965C2#7768211yescharacteristic
966C2#7811111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1439C2
hypercenter#1439D3
hypocenterC3#14757
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C22×#895C2semidirect
2. C22×#884C2semidirect
3. C2×#4960C2semidirect
4. C2×#4956C2semidirect
5. C2×#4665C2semidirect
6. C2×D3×#95C2semidirect
7. C3×#1439C2semidirect
8. #71568C2semidirect
9. #71550C2semidirect
10. #69428C2semidirect
11. #69426C2semidirect
53. #1439D3semidirect
74. C22×#67D4semidirect
90. C22×D12D4semidirect
101. C22×C4×D3D4semidirect
102. C22×C4×D3D4semidirect
138. C3⋊#95D4semidirect
499. C2×C3×C4#121semidirect
523. C2×Dic3#121semidirect
717. C2×D3#392semidirect
869. C2×C4#884semidirect
952. C3#14757semidirect

Maximal subgroups

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

subgroupindex
C22×#8952
C22×#8842
C2×#49602
C2×#49562
C2×#46652
C2×D3×#952
C3×#14392
#715682
#715502
#694282
#694262
#147573