Finite Group Databasebeta

← #10727093

Subgroups — #10727093

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×#938C211yesmaximal, characteristic, complemented
2C22×#884C212yesmaximal, complemented
3C2×#5223C211yesmaximal, characteristic, complemented
4C2×#4956C212yesmaximal, complemented
5C2×#4665C211yesmaximal, characteristic, complemented
6C2×D3×#95C211yesmaximal, characteristic, complemented
7C3×#1438C211yesmaximal, characteristic, complemented
8#71550C212yesmaximal, complemented
9#71547C212yesmaximal, complemented
10#69427C211yesmaximal, characteristic, complemented
11#69420C211yesmaximal, characteristic, complemented
12#14757—31nomaximal, Sylow
13C23×C3×D4C2211yescharacteristic
14C23×#67C2212yes—
15C23×#67C2212yes—
16C23×D12C2211yescharacteristic
17C23×C4×D3C2211yescharacteristic
18C23×C4×D3C2212yes—
19C22×C3×C22⋊C4C2212yes—
20C22×C3×C22⋊C4C2212yes—
21C22×#217C2212yes—
22C22×#217C2212yes—
23C2×#938—28no—
24C2×#938—24no—
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×(C2×D3)⋊C4C2212yes—
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×C4⋊Dic3C2211yescharacteristic
30C22×Dic3⋊C4C2212yes—
31C2×#884—28no—
32C2×#884—28no—
33C2×#884—28no—
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2211yescharacteristic
36#5223—24no—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2211yescharacteristic
40C2×C3⋊#95C2212yes—
41C2×C3⋊#95C2211yescharacteristic
42#4956—28no—
43#4665—24no—
44D3×#95—24no—
45C22×#121—31no—
46C22×#121—32no—
47C2×#392—31no—
48C2×#386—31no—
49C2×#386—32no—
50C22×#95—31no—
51#1444—31no—
52#1439—31no—
53#1439—32no—
54#1438—32no—
55#1438D311yescharacteristic, complemented
56C25×C3C2312yes—
57C24×D3C2311yescharacteristic
58C24×D3C2311yescharacteristic
59C22×C3×D4—24no—
60C22×C3×D4—22no—
61C22×C3×D4—22no—
62C22×C3×D4—22no—
63C22×C3×D4—42no—
64C23×C3×C4C2311yescharacteristic
65C23×C3×C4C2312yes—
66C23×C3×C4C2311yescharacteristic
67C23×C3×C4C2311yescharacteristic
68C22×#67—24no—
69C22×#67—24no—
70C22×#67—24no—
71C22×#67—24no—
72C22×#67—24no—
73C22×#67—24no—
74C22×#67—24no—
75C22×#67—24no—
76C22×#67—24no—
77C22×#67—24no—
78C22×#67—24no—
79C22×#67—42no—
80C22×#67—42no—
81C22×#67D418yescomplemented
82C23×Dic3C2311yescharacteristic
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2312yes—
85C23×Dic3C2312yes—
86C22×D12—22no—
87C22×D12—24no—
88C22×D12—24no—
89C22×D12—22no—
90C22×D12D414yescomplemented
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×D3D414yescomplemented
102C22×C4×D3D418yescomplemented
103C2×C3×C22⋊C4—24no—
104C2×C3×C22⋊C4—24no—
105C2×C3×C22⋊C4—24no—
106C2×C3×C22⋊C4—24no—
107C2×C3×C22⋊C4—42no—
108C2×C3×C22⋊C4—42no—
109C2×#217—24no—
110C2×#217—24no—
111C2×#217—24no—
112C2×#217—24no—
113C2×#217—24no—
114C2×#217—24no—
115#938—232no—
116C2×(C2×D3)⋊C4—24no—
117C2×(C2×D3)⋊C4—24no—
118C2×(C2×D3)⋊C4—24no—
119C2×(C2×D3)⋊C4—22no—
120C2×(C2×D3)⋊C4—24no—
121C2×(C2×D3)⋊C4—22no—
122C2×(C2×D3)⋊C4—22no—
123C2×(C2×D3)⋊C4—22no—
124C2×(C2×D3)⋊C4—22no—
125C2×(C2×D3)⋊C4—42no—
126C2×C4⋊Dic3—22no—
127C2×C4⋊Dic3—24no—
128C2×Dic3⋊C4—24no—
129C2×Dic3⋊C4—24no—
130C2×Dic3⋊C4—24no—
131#884—264no—
132C3×#95—22no—
133C3×#95—22no—
134C3⋊#95—24no—
135C3⋊#95—24no—
136C3⋊#95—22no—
137C3⋊#95—24no—
138C3⋊#95D414yescomplemented
139C23×D4—32no—
140C23×D4—32no—
141C23×D4—31no—
142C23×D4C2×D311yescharacteristic
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⋊C4—31no—
152C22×C22⋊C4—32no—
153C22×C22⋊C4—32no—
154C22×C22⋊C4—31no—
155C22×C22⋊C4—32no—
156C22×C22⋊C4—31no—
157C22×C22⋊C4—31no—
158C22×C22⋊C4C2×D312yes—
159C22×C22⋊C4C2×D312yes—
160#392—64no—
161#386—64no—
162#386—68no—
163C2×#95—31no—
164C2×#95—32no—
165C2×#95—32no—
166C2×#95—31no—
167C2×#95—32no—
168C2×#95—64no—
169C2×#95C2×D311yescharacteristic
170C2×#95C2×D311yescharacteristic
171C24×C3—22no—
172C24×C3—22no—
173C24×C3—22no—
174C24×C3—22no—
175C24×C3—22no—
176C24×C3—22no—
177C24×C3—22no—
178C24×C3—22no—
179C24×C3—22no—
180C24×C3—22no—
181C24×C3—22no—
182C24×C3—22no—
183C24×C3—22no—
184C24×C3—22no—
185C24×C3C2×D414yes—
186C24×C3C2411yescharacteristic
187C23×D3—21no—
188C23×D3—21no—
189C23×D3—22no—
190C23×D3—22no—
191C23×D3—21no—
192C23×D3—21no—
193C23×D3—21no—
194C23×D3—22no—
195C23×D3—22no—
196C23×D3—21no—
197C23×D3—21no—
198C23×D3—21no—
199C23×D3—22no—
200C23×D3—22no—
201C23×D3—21no—
202C23×D3—21no—
203C23×D3C2×D412yes—
204C23×D3C2×D414yes—
205C23×D3C2×D412yes—
206C23×D3C2×D414yes—
207C23×D3C2×D412yes—
208C23×D3#4112yes—
209C2×C3×D4—28no—
210C2×C3×D4—48no—
211C2×C3×D4—48no—
212C2×C3×D4—44no—
213C2×C3×D4—44no—
214C22×C3×C4—22no—
215C22×C3×C4—22no—
216C22×C3×C4—22no—
217C22×C3×C4—21no—
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—22no—
226C22×C3×C4—22no—
227C22×C3×C4—21no—
228C22×C3×C4—22no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4C2×D414yes—
232C22×C3×C4C2×D412yes—
233C22×C3×C4C2×D412yes—
234C22×C3×C4C2×D412yes—
235C22×C3×C4#4112yes—
236C2×#67—216no—
237C2×#67—216no—
238C2×#67—216no—
239C2×#67—216no—
240C2×#67—48no—
241C2×#67—48no—
242C2×#67—48no—
243C2×#67—48no—
244C2×#67—48no—
245C2×#67—48no—
246C2×#67—48no—
247C2×#67—48no—
248C2×#67—48no—
249C2×#67—48no—
250C22×Dic3—22no—
251C22×Dic3—22no—
252C22×Dic3—22no—
253C22×Dic3—22no—
254C22×Dic3—21no—
255C22×Dic3—22no—
256C22×Dic3—22no—
257C22×Dic3—22no—
258C22×Dic3—22no—
259C22×Dic3—22no—
260C22×Dic3—22no—
261C22×Dic3—21no—
262C22×Dic3—22no—
263C22×Dic3—22no—
264C22×Dic3—21no—
265C22×Dic3—22no—
266C22×Dic3—21no—
267C22×Dic3—21no—
268C22×Dic3—22no—
269C22×Dic3C2×D412yes—
270C22×Dic3C2×D414yes—
271C22×Dic3C2×D414yes—
272C22×Dic3C2×D414yes—
273C22×Dic3#4114yes—
274C2×D12—216no—
275C2×D12—28no—
276C2×D12—44no—
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×C22⋊C4—216no—
292C3×C22⋊C4—48no—
293#217—216no—
294#217—48no—
295(C2×D3)⋊C4—216no—
296(C2×D3)⋊C4—44no—
297(C2×D3)⋊C4—44no—
298(C2×D3)⋊C4—44no—
299C4⋊Dic3—28no—
300Dic3⋊C4—216no—
301C25—31no—
302C25—31no—
303C25C22×D312yes—
304C22×D4—24no—
305C22×D4—22no—
306C22×D4—22no—
307C22×D4—22no—
308C22×D4—38no—
309C22×D4—34no—
310C22×D4—42no—
311C22×D4—64no—
312C22×D4—64no—
313C22×D4—62no—
314C22×D4—62no—
315C22×D4—64no—
316C22×D4—64no—
317C22×D4—64no—
318C22×D4—64no—
319C22×D4—64no—
320C22×D4—64no—
321C22×D4—64no—
322C22×D4—64no—
323C22×D4—64no—
324C22×D4—64no—
325C22×D4—64no—
326C22×D4—122no—
327C22×D4—122no—
328C23×C4—32no—
329C23×C4—31no—
330C23×C4—32no—
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×D311yescharacteristic
347C23×C4C22×D311yescharacteristic
348#121—664no—
349#121—632no—
350C2×C4⋊C4—64no—
351C2×C4⋊C4—64no—
352C2×C4⋊C4—64no—
353C2×C4⋊C4—64no—
354C2×C4⋊C4—62no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
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—62no—
368C2×C22⋊C4—62no—
369C2×C22⋊C4—64no—
370C2×C22⋊C4—64no—
371C2×C22⋊C4—64no—
372C2×C22⋊C4—64no—
373C2×C22⋊C4—62no—
374C2×C22⋊C4—62no—
375C2×C22⋊C4—62no—
376C2×C22⋊C4—122no—
377#95—22no—
378#95—22no—
379#95—34no—
380#95—64no—
381#95—62no—
382#95—64no—
383#95—64no—
384C23×C3—24no—
385C23×C3—24no—
386C23×C3—24no—
387C23×C3—24no—
388C23×C3—24no—
389C23×C3—24no—
390C23×C3—24no—
391C23×C3—42no—
392C23×C3—42no—
393C23×C3—42no—
394C23×C3—42no—
395C23×C3—42no—
396C23×C3—42no—
397C23×C3—42no—
398C23×C3—42no—
399C23×C3—42no—
400C23×C3—42no—
401C23×C3—42no—
402C23×C3—42no—
403C23×C3—42no—
404C23×C3—42no—
405C23×C3—42no—
406C23×C3—42no—
407C23×C3—42no—
408C23×C3—42no—
409C23×C3—42no—
410C23×C3—42no—
411C23×C3—42no—
412C23×C3—42no—
413C23×C3—42no—
414C23×C3—42no—
415C23×C3—42no—
416C23×C3—42no—
417C23×C3—42no—
418C23×C3—42no—
419C23×C3C22×D411yescharacteristic
420C23×C3C22×D412yes—
421C23×C3C22×D411yescharacteristic
422C23×C3C22×D412yes—
423C23×C3C22×D411yescharacteristic
424C23×C3C2×#4111yescharacteristic
425C23×C3C2×#4111yescharacteristic
426C23×C3C2×#4112yes—
427C23×C3H(5,𝔽2)12yes—
428C23×C3H(5,𝔽2)11yescharacteristic
429C23×C32−1+411yescharacteristic
430C22×D3—22no—
431C22×D3—24no—
432C22×D3—22no—
433C22×D3—24no—
434C22×D3—22no—
435C22×D3—24no—
436C22×D3—22no—
437C22×D3—24no—
438C22×D3—22no—
439C22×D3—24no—
440C22×D3—24no—
441C22×D3—24no—
442C22×D3—24no—
443C22×D3—24no—
444C22×D3—22no—
445C22×D3—22no—
446C22×D3—24no—
447C22×D3—22no—
448C22×D3—24no—
449C22×D3—22no—
450C22×D3—22no—
451C22×D3—24no—
452C22×D3—22no—
453C22×D3—41no—
454C22×D3—41no—
455C22×D3—42no—
456C22×D3—42no—
457C22×D3—41no—
458C22×D3—41no—
459C22×D3—42no—
460C22×D3—41no—
461C22×D3—42no—
462C22×D3—41no—
463C22×D3—42no—
464C22×D3—42no—
465C22×D3—42no—
466C22×D3—42no—
467C22×D3—42no—
468C22×D3—41no—
469C22×D3—42no—
470C22×D3—41no—
471C22×D3#12018yes—
472C22×D3#12014yes—
473C22×D3#12114yes—
474C22×D3#12118yes—
475C22×D3#12714yes—
476C3×D4—416no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—24no—
480C2×C3×C4—24no—
481C2×C3×C4—24no—
482C2×C3×C4—24no—
483C2×C3×C4—24no—
484C2×C3×C4—22no—
485C2×C3×C4—24no—
486C2×C3×C4—41no—
487C2×C3×C4—42no—
488C2×C3×C4—41no—
489C2×C3×C4—42no—
490C2×C3×C4—42no—
491C2×C3×C4—42no—
492C2×C3×C4—42no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—42no—
496C2×C3×C4—42no—
497C2×C3×C4—41no—
498C2×C3×C4#12114yescomplemented
499#67—432no—
500#67—432no—
501C2×Dic3—24no—
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—24no—
512C2×Dic3—22no—
513C2×Dic3—42no—
514C2×Dic3—42no—
515C2×Dic3—42no—
516C2×Dic3—42no—
517C2×Dic3—42no—
518C2×Dic3—42no—
519C2×Dic3—41no—
520C2×Dic3—42no—
521C2×Dic3—41no—
522C2×Dic3—41no—
523C2×Dic3—42no—
524C2×Dic3#12118yescomplemented
525D12—416no—
526C4×D3—432no—
527C4×D3—416no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—32no—
543C24—34no—
544C24—34no—
545C24—32no—
546C24—32no—
547C24—32no—
548C24—61no—
549C24—61no—
550C24—62no—
551C24—61no—
552C24—62no—
553C24—61no—
554C24—61no—
555C24—61no—
556C24—61no—
557C24—62no—
558C24—62no—
559C24—62no—
560C24—61no—
561C24—61no—
562C24—62no—
563C24—61no—
564C24D3×D414yes—
565C24C23×D311yescharacteristic
566C2×D4—28no—
567C2×D4—48no—
568C2×D4—48no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—616no—
572C2×D4—68no—
573C2×D4—616no—
574C2×D4—616no—
575C2×D4—616no—
576C2×D4—616no—
577C2×D4—128no—
578C2×D4—124no—
579C2×D4—124no—
580C2×D4—128no—
581C2×D4—128no—
582C2×D4—128no—
583C2×D4—128no—
584C2×D4—128no—
585C2×D4—128no—
586C2×D4—128no—
587C2×D4—128no—
588C2×D4—128no—
589C2×D4—128no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—22no—
604C22×C4—21no—
605C22×C4—22no—
606C22×C4—21no—
607C22×C4—34no—
608C22×C4—34no—
609C22×C4—34no—
610C22×C4—32no—
611C22×C4—34no—
612C22×C4—616no—
613C22×C4—68no—
614C22×C4—616no—
615C22×C4—62no—
616C22×C4—62no—
617C22×C4—62no—
618C22×C4—62no—
619C22×C4—61no—
620C22×C4—61no—
621C22×C4—62no—
622C22×C4—62no—
623C22×C4—62no—
624C22×C4—62no—
625C22×C4—62no—
626C22×C4—62no—
627C22×C4—62no—
628C22×C4—62no—
629C22×C4—68no—
630C22×C4—61no—
631C22×C4—61no—
632C22×C4—62no—
633C22×C4—61no—
634C22×C4—62no—
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×D412yes—
646C22×C4D3×D412yes—
647C22×C4D3×D412yes—
648C4⋊C4—616no—
649C4⋊C4—68no—
650C22⋊C4—216no—
651C22⋊C4—48no—
652C22⋊C4—616no—
653C22⋊C4—616no—
654C22⋊C4—128no—
655C22⋊C4—124no—
656C22⋊C4—124no—
657C22⋊C4—124no—
658C22×C3—44no—
659C22×C3—44no—
660C22×C3—44no—
661C22×C3—44no—
662C22×C3—44no—
663C22×C3—44no—
664C22×C3—44no—
665C22×C3—82no—
666C22×C3—82no—
667C22×C3—82no—
668C22×C3—82no—
669C22×C3—82no—
670C22×C3—82no—
671C22×C3—82no—
672C22×C3—82no—
673C22×C3C2×#12011yescharacteristic
674C22×C3C2×#12012yes—
675C22×C3C2×#12111yescharacteristic
676C22×C3C2×#12112yes—
677C22×C3C2×#12112yes—
678C22×C3C2×#12111yescharacteristic
679C22×C3C2×#12711yescharacteristic
680C22×C3#53211yescharacteristic
681C22×C3#53212yes—
682C22×C3#53411yescharacteristic
683C22×C3#53412yes—
684C22×C3#53711yescharacteristic
685C22×C3#53712yes—
686C22×C3D4211yescharacteristic
687C22×C3D4212yes—
688C22×C3#54612yes—
689C22×C3#54612yes—
690C22×C3#54612yes—
691C22×C3#54712yes—
692C22×C3#54711yescharacteristic
693C22×C3#54811yescharacteristic
694C22×C3#55312yes—
695C22×C3#55311yescharacteristic
696C2×D3—24no—
697C2×D3—24no—
698C2×D3—24no—
699C2×D3—28no—
700C2×D3—28no—
701C2×D3—24no—
702C2×D3—24no—
703C2×D3—28no—
704C2×D3—24no—
705C2×D3—28no—
706C2×D3—42no—
707C2×D3—44no—
708C2×D3—42no—
709C2×D3—44no—
710C2×D3—42no—
711C2×D3—81no—
712C2×D3—81no—
713C2×D3—81no—
714C2×D3—82no—
715C2×D3—81no—
716C2×D3—82no—
717C2×D3#39218yescomplemented
718C3×C4—24no—
719C3×C4—42no—
720C3×C4—44no—
721C3×C4—81no—
722Dic3—28no—
723Dic3—44no—
724Dic3—42no—
725Dic3—81no—
726C23—24no—
727C23—24no—
728C23—24no—
729C23—24no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—34no—
734C23—34no—
735C23—38no—
736C23—34no—
737C23—38no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—42no—
766C23—64no—
767C23—64no—
768C23—62no—
769C23—62no—
770C23—62no—
771C23—62no—
772C23—64no—
773C23—64no—
774C23—62no—
775C23—62no—
776C23—62no—
777C23—64no—
778C23—64no—
779C23—64no—
780C23—62no—
781C23—64no—
782C23—64no—
783C23—64no—
784C23—62no—
785C23—62no—
786C23—64no—
787C23—62no—
788C23—64no—
789C23—122no—
790C23—122no—
791C23—121no—
792C23—121no—
793C23—121no—
794C23—121no—
795C23—122no—
796C23—122no—
797C23—121no—
798C23—121no—
799C23—121no—
800C23—122no—
801C23—122no—
802C23—122no—
803C23—122no—
804C23—122no—
805C23—121no—
806C23—122no—
807C23C2×#23511yescharacteristic
808C23C2×D3×D412yes—
809C23C2×D3×D411yescharacteristic
810C23C2×D3×D411yescharacteristic
811C23C2×D3×D412yes—
812C23C2×D3×D411yescharacteristic
813C23#100412yes—
814C23#100411yescharacteristic
815C23D3×#4112yes—
816C23D3×#4111yescharacteristic
817C23#101011yescharacteristic
818D4—416no—
819D4—1216no—
820D4—1232no—
821D4—1232no—
822C2×C4—24no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—24no—
830C2×C4—22no—
831C2×C4—38no—
832C2×C4—41no—
833C2×C4—42no—
834C2×C4—41no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—41no—
840C2×C4—42no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—42no—
844C2×C4—64no—
845C2×C4—64no—
846C2×C4—64no—
847C2×C4—64no—
848C2×C4—64no—
849C2×C4—64no—
850C2×C4—62no—
851C2×C4—62no—
852C2×C4—64no—
853C2×C4—64no—
854C2×C4—62no—
855C2×C4—64no—
856C2×C4—1216no—
857C2×C4—1232no—
858C2×C4—122no—
859C2×C4—122no—
860C2×C4—122no—
861C2×C4—122no—
862C2×C4—122no—
863C2×C4—122no—
864C2×C4—121no—
865C2×C4—121no—
866C2×C4—121no—
867C2×C4—122no—
868C2×C4—122no—
869C2×C4#88414yescomplemented
870C2×C3—84no—
871C2×C3C2×#39211yescharacteristic
872C2×C3#241011yescharacteristic
873C2×C3#241012yes—
874C2×C3#241612yes—
875C2×C3#241611yescharacteristic
876C2×C3#243011yescharacteristic
877C2×C3#243012yes—
878C2×C3#254311yescharacteristic
879C2×C3#254312yes—
880C2×C3#265611yescharacteristic
881C2×C3#285611yescharacteristic
882D3—28no—
883D3—82no—
884C22—38no—
885C22—44no—
886C22—44no—
887C22—44no—
888C22—44no—
889C22—44no—
890C22—44no—
891C22—44no—
892C22—64no—
893C22—64no—
894C22—68no—
895C22—64no—
896C22—68no—
897C22—68no—
898C22—64no—
899C22—64no—
900C22—68no—
901C22—64no—
902C22—82no—
903C22—82no—
904C22—82no—
905C22—82no—
906C22—82no—
907C22—82no—
908C22—82no—
909C22—82no—
910C22—122no—
911C22—124no—
912C22—122no—
913C22—122no—
914C22—124no—
915C22—241no—
916C22—242no—
917C22—241no—
918C22—242no—
919C22—241no—
920C22—241no—
921C22C2×#88411yescharacteristic
922C22#549012yes—
923C22#554812yes—
924C22#555111yescharacteristic
925C22#555811yescharacteristic
926C22D3×#12011yescharacteristic
927C22D3×#12012yes—
928C22#558911yescharacteristic
929C22#558912yes—
930C22#559012yes—
931C22D3×#12111yescharacteristic
932C22D3×#12112yes—
933C22D3×#12112yes—
934C22#560811yescharacteristic
935C22#560812yes—
936C22#561012yes—
937C22#561212yes—
938C22#565512yes—
939C22#566112yes—
940C22#566811yescharacteristic
941C22#567711yescharacteristic
942C22D3×#12711yescharacteristic
943C22#571711yescharacteristic
944C4—24no—
945C4—42no—
946C4—44no—
947C4—68no—
948C4—81no—
949C4—122no—
950C4—124no—
951C4—241no—
952C3#1475711yescharacteristic, complemented, Sylow
953C2—68no—
954C2—84no—
955C2—242no—
956C2#7385411yescharacteristic
957C2#7489612yes—
958C2#7490212yes—
959C2#7643911yescharacteristic
960C2#7647611yescharacteristic
961C2D3×#39211yescharacteristic
962C2#7675512yes—
963C2#7676211yescharacteristic
964C2#7689812yes—
965C2#7711611yescharacteristic
966C2#7712011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1438C2
hypercenter#1438D3
hypocenterC3#14757
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
1. C22×#938C2semidirect
2. C22×#884C2semidirect
3. C2×#5223C2semidirect
4. C2×#4956C2semidirect
5. C2×#4665C2semidirect
6. C2×D3×#95C2semidirect
7. C3×#1438C2semidirect
8. #71550C2semidirect
9. #71547C2semidirect
10. #69427C2semidirect
11. #69420C2semidirect
55. #1438D3semidirect
81. C22×#67D4semidirect
90. C22×D12D4semidirect
101. C22×C4×D3D4semidirect
102. C22×C4×D3D4semidirect
138. C3⋊#95D4semidirect
498. C2×C3×C4#121semidirect
524. 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×#9382
C22×#8842
C2×#52232
C2×#49562
C2×#46652
C2×D3×#952
C3×#14382
#715502
#715472
#694272
#694202
#147573