Finite Group Databasebeta

← C2×#78940 #11672012

Subgroups — C2×#78940 #11672012

Order 768.

2566 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×#67C211yesmaximal, characteristic
2C2×#5533C211yesmaximal, characteristic, complemented
3C2×C3×#418C211yesmaximal, characteristic, complemented
4C2×#5218C211yesmaximal, characteristic, complemented
5C2×#5134C211yesmaximal, characteristic, complemented
6C2×#5128C211yesmaximal, characteristic, complemented
7C2×#5003C211yesmaximal, characteristic, complemented
8#78940C2116yesmaximal, direct product factor
9C2×#4762C211yesmaximal, characteristic, complemented
10C2×#4784C211yesmaximal, characteristic, complemented
11C2×#4780C211yesmaximal, characteristic, complemented
12C2×#4776C211yesmaximal, characteristic, complemented
13C2×#4770C211yesmaximal, characteristic, complemented
14C2×#4760C211yesmaximal, characteristic, complemented
15C2×#4759C211yesmaximal, characteristic, complemented
16C2×#4758C211yesmaximal, characteristic, complemented
17C2×#3324—31nomaximal, Sylow
18C23×C3×D4C2211yescharacteristic
19C23×#67—21no—
20C22×D3×D4C2211yescharacteristic
21C22×C3×M16C2211yescharacteristic, complemented
22C2×C3×#117C2211yescharacteristic, complemented
23C2×#953—21no—
24C2×#940C2211yescharacteristic
25C2×#939—21no—
26D4×#67—24no—
27D4×#67C2218yes—
28C2×#938C2211yescharacteristic
29C2×#937—21no—
30C2×D4×Dic3C2211yescharacteristic
31C22×#214C2211yescharacteristic
32C22×#214C2211yescharacteristic, complemented
33C2×#930C2211yescharacteristic
34C2×C4×#67C2211yescharacteristic
35C2×#924C2211yescharacteristic, complemented
36C22×#204C2211yescharacteristic, complemented
37C22×ΓL(1,𝔽25)C2211yescharacteristic, complemented
38#5533—24no—
39#5533C2218yescomplemented
40C2×#897C2211yescharacteristic, complemented
41C2×#892C2211yescharacteristic, complemented
42C2×#888C2211yescharacteristic, complemented
43C2×#887C2211yescharacteristic, complemented
44C2×#885—21no—
45C2×#879—21no—
46C2×#876—21no—
47C2×C4×Dic6—21no—
48C3×#418C2218yescomplemented
49C2×C3×#102C2211yescharacteristic
50C2×C3×#102C2211yescharacteristic
51C2×C3×#102C2211yescharacteristic, complemented
52C2×C3×#102C2211yescharacteristic, complemented
53#5218C2218yescomplemented
54C2×#832C2211yescharacteristic
55C2×#832C2211yescharacteristic, complemented
56C2×#830C2211yescharacteristic, complemented
57#5134C2218yescomplemented
58#5128C2218yescomplemented
59C2×#821C2211yescharacteristic, complemented
60C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
61C2×#818C2211yescharacteristic, complemented
62C2×#816C2211yescharacteristic, complemented
63C2×Dic3⋊C8C2211yescharacteristic, complemented
64C2×C8×Dic3C2211yescharacteristic, complemented
65#5003C2218yescomplemented
66C2×#809C2211yescharacteristic, complemented
67C2×#809C2211yescharacteristic, complemented
68C2×#808C2211yescharacteristic, complemented
69C2×#807C2211yescharacteristic, complemented
70#4784C2218yescomplemented
71#4780C2218yescomplemented
72#4776C2218yescomplemented
73#4770C2218yescomplemented
74#4762C2218yescomplemented
75#4760C2218yescomplemented
76#4759C2218yescomplemented
77#4758C2218yescomplemented
78C2×#556—31no—
79C2×D42—31no—
80#3324—316no—
81C2×#486—31no—
82C2×#482—31no—
83C2×#482—31no—
84C2×#474—31no—
85C2×#468—31no—
86C2×#468—31no—
87C2×#460—31no—
88C2×#450—31no—
89C2×#450—31no—
90C2×C4×SD16—31no—
91C2×#436—31no—
92C2×#418—31no—
93C2×#418D311yescharacteristic, complemented
94C25×C3—21no—
95C24×D3—21no—
96C22×C3×D4—24no—
97C22×C3×D4—21no—
98C22×C3×D4—22no—
99C22×C3×D4—42no—
100C22×C3×D4C2311yescharacteristic
101C22×C3×D4C2314yes—
102C22×C3×D4C2311yescharacteristic
103C23×C3×C4C2311yescharacteristic
104C22×#67—21no—
105C22×#67—21no—
106C22×#67—28no—
107C22×#67—21no—
108C22×#67—21no—
109C22×#67—21no—
110C22×#67—48no—
111C22×#67D411yescharacteristic
112C23×Dic3—21no—
113C2×D3×D4—24no—
114C2×D3×D4—22no—
115C2×D3×D4—42no—
116C2×D3×D4C2314yes—
117C22×D12C2311yescharacteristic
118C22×C4×D3C2311yescharacteristic
119C22×Dic6—21no—
120C22×Dic6C2311yescharacteristic
121C2×C3×M16—42no—
122C2×C3×M16C2314yescomplemented
123C22×C3×C8C2311yescharacteristic
124C22×C3×C8C2311yescharacteristic
125C3×#117—22no—
126C3×#117C2314yescomplemented
127C2×C3×C4⋊C4C2311yescharacteristic
128C2×C3×C4⋊C4C2311yescharacteristic
129C2×C3×C22⋊C4—21no—
130C2×C3×C42—21no—
131#953—28no—
132C2×#217—21no—
133C2×#217—21no—
134C2×#217—21no—
135C2×#217D411yescharacteristic
136#940—22no—
137#940C2314yes—
138#939—28no—
139#938—22no—
140#938C2314yes—
141#937—28no—
142D4×Dic3—22no—
143D4×Dic3C2314yes—
144C2×#214—24no—
145C2×#214—42no—
146C2×#214C2314yes—
147C2×#214C2314yescomplemented
148#930—22no—
149#930C2314yes—
150C4×#67D414yes—
151C4×#67C2314yes—
152C2×(C2×D3)⋊C4—21no—
153C2×(C2×D3)⋊C4—21no—
154C2×(C2×D3)⋊C4—21no—
155C2×(C2×D3)⋊C4D411yescharacteristic
156C2×C4⋊Dic3—21no—
157C2×C4⋊Dic3C2311yescharacteristic
158C2×C4⋊Dic3C2311yescharacteristic
159#924—22no—
160#924C2314yescomplemented
161C2×Dic3⋊C4—21no—
162C2×Dic3⋊C4—21no—
163C2×Dic3⋊C4—21no—
164C2×Dic3⋊C4D411yescharacteristic
165C2×C4×Dic3—21no—
166C2×C4×Dic3—21no—
167C2×C4×Dic3C2311yescharacteristic
168C22×C3⋊C8C2311yescharacteristic
169C22×C3⋊C8C2311yescharacteristic
170C2×#204—42no—
171C2×#204C2314yescomplemented
172C2×ΓL(1,𝔽25)—42no—
173C2×ΓL(1,𝔽25)C2314yescomplemented
174#897—22no—
175#897C2314yescomplemented
176#892—22no—
177#892C2314yescomplemented
178#888—22no—
179#888C2314yescomplemented
180#887—22no—
181#887C2314yescomplemented
182#885—28no—
183#879—28no—
184#876—28no—
185C4×Dic6—28no—
186C3×#102C2314yes—
187C3×#102C2314yes—
188C3×#102C2314yescomplemented
189C3×#102C2314yescomplemented
190#832C2314yes—
191#832C2314yescomplemented
192#830C2314yescomplemented
193#821C2314yescomplemented
194(C2×D3)⋊C8C2314yescomplemented
195#818C2314yescomplemented
196#816C2314yescomplemented
197Dic3⋊C8C2314yescomplemented
198C8×Dic3C2314yescomplemented
199#809C2314yescomplemented
200#809C2314yescomplemented
201#808C2314yescomplemented
202#807C2314yescomplemented
203C23×D4—31no—
204C23×D4—61no—
205C23×D4C2×D311yescharacteristic
206C22×SD16—31no—
207C22×SD16—31no—
208C22×SD16—31no—
209C22×M16—31no—
210C22×M16C2×D311yescharacteristic, complemented
211#556—38no—
212#556—64no—
213D42—38no—
214D42—64no—
215C2×C4⋊Q8—31no—
216C2×#127—31no—
217C2×#126—61no—
218C2×#126—61no—
219C2×#124—61no—
220C2×C22⋊Q8—31no—
221C2×C22⋊Q8—31no—
222C2×#121—31no—
223C2×#121—31no—
224C2×#121—61no—
225C2×#120—61no—
226C2×#120—61no—
227C2×C4×Q8—31no—
228C2×C4×Q8—61no—
229C2×C4×D4—31no—
230C2×C4×D4—31no—
231C2×#117—31no—
232C2×#117C2×D311yescharacteristic, complemented
233#486—38no—
234#482—38no—
235#482—38no—
236#474—38no—
237#468—38no—
238#468—38no—
239#460—38no—
240#450—38no—
241#450—38no—
242C4×SD16—38no—
243#436—38no—
244C2×#107—31no—
245C2×#107—31no—
246C2×#106—31no—
247C2×C4⋊C8—31no—
248#418—38no—
249#418C2×D318yescomplemented
250C2×#103—31no—
251C2×#102—31no—
252C2×#102—31no—
253C2×#102—31no—
254C2×#102—31no—
255C2×#102—31no—
256C2×#102C2×D311yescharacteristic
257C2×#102C2×D311yescharacteristic
258C2×#102C2×D311yescharacteristic, complemented
259C2×#102C2×D311yescharacteristic, complemented
260C2×C22⋊C8—31no—
261C2×C22⋊C8—31no—
262C2×C4×C8—31no—
263C24×C3—21no—
264C24×C3—21no—
265C24×C3—24no—
266C24×C3—44no—
267C24×C3—44no—
268C24×C3—82no—
269C24×C3C2×D411yescharacteristic
270C23×D3—21no—
271C23×D3—24no—
272C23×D3—44no—
273C23×D3—44no—
274C23×D3—82no—
275C23×D3C2×D411yescharacteristic
276C2×C3×D4—28no—
277C2×C3×D4—21no—
278C2×C3×D4—24no—
279C2×C3×D4—21no—
280C2×C3×D4—22no—
281C2×C3×D4—22no—
282C2×C3×D4—22no—
283C2×C3×D4—44no—
284C2×C3×D4—48no—
285C2×C3×D4—44no—
286C2×C3×D4#4114yes—
287C2×C3×D4C2412yes—
288C2×C3×D4C2412yes—
289C22×C3×C4—22no—
290C22×C3×C4—22no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4C2×D411yescharacteristic
294C22×C3×C4C2×D412yes—
295C22×C3×C4C2412yes—
296C22×C3×C4C2411yescharacteristic
297C2×#67—24no—
298C2×#67—24no—
299C2×#67—24no—
300C2×#67—24no—
301C2×#67—24no—
302C2×#67—24no—
303C2×#67—44no—
304C2×#67—432no—
305C2×#67—44no—
306C2×#67—44no—
307C2×#67—44no—
308C2×#67—82no—
309C2×#67C2×D414yes—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3—21no—
313C22×Dic3—24no—
314C22×Dic3—44no—
315C22×Dic3C2×D411yescharacteristic
316C22×Dic3C2×D411yescharacteristic
317C22×Dic3C2×D411yescharacteristic
318D3×D4—28no—
319D3×D4—44no—
320D3×D4—48no—
321C2×D12—22no—
322C2×D12—22no—
323C2×D12—21no—
324C2×D12C2412yes—
325C2×C4×D3—22no—
326C2×C4×D3—22no—
327C2×C4×D3C2×D412yes—
328C2×C4×D3C2412yes—
329C2×Dic6—22no—
330C2×Dic6—22no—
331C2×Dic6—21no—
332C2×Dic6—24no—
333C2×Dic6—44no—
334C2×Dic6C2412yes—
335C3×M16—44no—
336C2×C3×C8—22no—
337C2×C3×C8—22no—
338C2×C3×C8C2412yes—
339C2×C3×C8C2412yes—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4C2412yes—
343C3×C4⋊C4C2412yes—
344C3×C22⋊C4—24no—
345C3×C42—24no—
346#217—24no—
347#217—24no—
348#217—24no—
349#217C2×D414yes—
350#214—28no—
351#214—44no—
352(C2×D3)⋊C4—24no—
353(C2×D3)⋊C4—24no—
354(C2×D3)⋊C4—24no—
355(C2×D3)⋊C4C2×D414yes—
356C4⋊Dic3—21no—
357C4⋊Dic3—21no—
358C4⋊Dic3—24no—
359C4⋊Dic3C2412yes—
360C4⋊Dic3C2412yes—
361Dic3⋊C4—24no—
362Dic3⋊C4—24no—
363Dic3⋊C4—24no—
364Dic3⋊C4C2×D414yes—
365C4×Dic3—24no—
366C4×Dic3—24no—
367C4×Dic3C2×D412yes—
368C4×Dic3C2412yes—
369C2×C3⋊C8—22no—
370C2×C3⋊C8—22no—
371C2×C3⋊C8C2412yes—
372C2×C3⋊C8C2412yes—
373#204—44no—
374ΓL(1,𝔽25)—44no—
375C25—21no—
376C25—61no—
377C22×Q8—31no—
378C22×Q8—61no—
379C22×D4—24no—
380C22×D4—21no—
381C22×D4—22no—
382C22×D4—31no—
383C22×D4—34no—
384C22×D4—31no—
385C22×D4—42no—
386C22×D4—62no—
387C22×D4—61no—
388C22×D4—61no—
389C22×D4—61no—
390C22×D4—68no—
391C22×D4—64no—
392C22×D4—61no—
393C22×D4—61no—
394C22×D4—122no—
395C22×D4—128no—
396C22×D4C22×D311yescharacteristic
397C22×D4C22×D314yes—
398C22×D4C22×D311yescharacteristic
399C23×C4—31no—
400C23×C4—61no—
401C23×C4C22×D311yescharacteristic
402C2×SD16—34no—
403C2×SD16—34no—
404C2×SD16—34no—
405C2×SD16—64no—
406C2×SD16—122no—
407C2×SD16—122no—
408C2×M16—34no—
409C2×M16—42no—
410C2×M16—122no—
411C2×M16C22×D314yescomplemented
412C22×C8—31no—
413C22×C8—31no—
414C22×C8C22×D311yescharacteristic
415C22×C8C22×D311yescharacteristic
416C4⋊Q8—34no—
417C4⋊Q8—62no—
418#127—34no—
419#127—62no—
420#126—68no—
421#126—68no—
422#124—68no—
423C22⋊Q8—34no—
424C22⋊Q8—34no—
425C22⋊Q8—62no—
426C22⋊Q8—62no—
427#121—34no—
428#121—34no—
429#121—68no—
430#121—62no—
431#121—62no—
432#120—68no—
433#120—68no—
434C4×Q8—34no—
435C4×Q8—68no—
436C4×Q8—62no—
437C4×D4—34no—
438C4×D4—34no—
439C4×D4—34no—
440C4×D4—62no—
441#117—22no—
442#117—34no—
443#117—62no—
444#117C22×D314yescomplemented
445C2×C4⋊C4—31no—
446C2×C4⋊C4—31no—
447C2×C4⋊C4—31no—
448C2×C4⋊C4—61no—
449C2×C4⋊C4—61no—
450C2×C4⋊C4—61no—
451C2×C4⋊C4—61no—
452C2×C4⋊C4C22×D311yescharacteristic
453C2×C4⋊C4C22×D311yescharacteristic
454C2×C22⋊C4—21no—
455C2×C22⋊C4—31no—
456C2×C22⋊C4—31no—
457C2×C22⋊C4—61no—
458C2×C22⋊C4—61no—
459C2×C22⋊C4—61no—
460C2×C22⋊C4—61no—
461C2×C22⋊C4—61no—
462C2×C22⋊C4—61no—
463C2×C42—21no—
464C2×C42—31no—
465C2×C42—61no—
466C2×C42—61no—
467#107—34no—
468#107—34no—
469#106—34no—
470C4⋊C8—34no—
471#103—34no—
472#102—34no—
473#102—34no—
474#102—34no—
475#102—34no—
476#102—34no—
477#102C22×D314yes—
478#102C22×D314yes—
479#102C22×D314yescomplemented
480#102C22×D314yescomplemented
481C22⋊C8—34no—
482C22⋊C8—34no—
483C4×C8—34no—
484C23×C3—24no—
485C23×C3—22no—
486C23×C3—22no—
487C23×C3—22no—
488C23×C3—22no—
489C23×C3—22no—
490C23×C3—48no—
491C23×C3—48no—
492C23×C3—42no—
493C23×C3—42no—
494C23×C3—42no—
495C23×C3—42no—
496C23×C3—42no—
497C23×C3—84no—
498C23×C3—816no—
499C23×C3C22×D412yes—
500C23×C3C22×D411yescharacteristic
501C22×D3—22no—
502C22×D3—22no—
503C22×D3—22no—
504C22×D3—22no—
505C22×D3—48no—
506C22×D3—48no—
507C22×D3—42no—
508C22×D3—42no—
509C22×D3—42no—
510C22×D3—84no—
511C22×D3—816no—
512C22×D3C22×D412yes—
513C3×D4—24no—
514C3×D4—22no—
515C3×D4—22no—
516C3×D4—22no—
517C3×D4—48no—
518C3×D4—42no—
519C3×D4C2×#4114yes—
520C2×C3×C4—22no—
521C2×C3×C4—24no—
522C2×C3×C4—22no—
523C2×C3×C4—22no—
524C2×C3×C4—22no—
525C2×C3×C4—22no—
526C2×C3×C4—42no—
527C2×C3×C4—42no—
528C2×C3×C4C22×D412yes—
529C2×C3×C4C22×D411yescharacteristic
530C2×C3×C4C2×#4112yes—
531C2×C3×C4H(5,𝔽2)12yes—
532C2×C3×C4C2511yescharacteristic
533#67—28no—
534#67—48no—
535#67—48no—
536#67—48no—
537#67—48no—
538#67—84no—
539C2×Dic3—22no—
540C2×Dic3—22no—
541C2×Dic3—22no—
542C2×Dic3—22no—
543C2×Dic3—22no—
544C2×Dic3—42no—
545C2×Dic3—42no—
546C2×Dic3—42no—
547C2×Dic3—48no—
548C2×Dic3AGL(1,ℤ/8)14yes—
549C2×Dic3C22×D412yes—
550C2×Dic3C22×D412yes—
551C2×Dic3C22×D412yes—
552D12—22no—
553D12—22no—
554D12—42no—
555C4×D3—24no—
556C4×D3—22no—
557C4×D3—22no—
558Dic6—22no—
559Dic6—22no—
560Dic6—42no—
561Dic6—48no—
562C3×C8—22no—
563C3×C8—22no—
564C3⋊C8—22no—
565C3⋊C8—22no—
566C24—21no—
567C24—21no—
568C24—24no—
569C24—31no—
570C24—44no—
571C24—44no—
572C24—64no—
573C24—61no—
574C24—82no—
575C24—124no—
576C24—124no—
577C24—242no—
578C24D3×D411yescharacteristic
579C2×Q8—32no—
580C2×Q8—64no—
581C2×Q8—61no—
582C2×Q8—62no—
583C2×Q8—62no—
584C2×Q8—124no—
585C2×D4—28no—
586C2×D4—22no—
587C2×D4—21no—
588C2×D4—24no—
589C2×D4—21no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—34no—
593C2×D4—32no—
594C2×D4—44no—
595C2×D4—48no—
596C2×D4—44no—
597C2×D4—64no—
598C2×D4—64no—
599C2×D4—64no—
600C2×D4—64no—
601C2×D4—68no—
602C2×D4—64no—
603C2×D4—64no—
604C2×D4—62no—
605C2×D4—61no—
606C2×D4—62no—
607C2×D4—124no—
608C2×D4—124no—
609C2×D4—128no—
610C2×D4—124no—
611C2×D4—1232no—
612C2×D4—124no—
613C2×D4—124no—
614C2×D4—242no—
615C2×D4#23514yes—
616C2×D4C23×D312yes—
617C2×D4C23×D312yes—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—31no—
623C22×C4—31no—
624C22×C4—31no—
625C22×C4—32no—
626C22×C4—32no—
627C22×C4—64no—
628C22×C4—62no—
629C22×C4—62no—
630C22×C4—61no—
631C22×C4—61no—
632C22×C4—61no—
633C22×C4—124no—
634C22×C4D3×D412yes—
635C22×C4D3×D411yescharacteristic
636C22×C4C23×D312yes—
637C22×C4C23×D311yescharacteristic
638SD16—68no—
639SD16—124no—
640SD16—124no—
641M16—44no—
642M16—124no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—32no—
646C2×C8—32no—
647C2×C8—62no—
648C2×C8—62no—
649C2×C8C23×D312yes—
650C2×C8C23×D312yes—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—34no—
654C4⋊C4—32no—
655C4⋊C4—32no—
656C4⋊C4—64no—
657C4⋊C4—64no—
658C4⋊C4—64no—
659C4⋊C4—61no—
660C4⋊C4—61no—
661C4⋊C4—64no—
662C4⋊C4C23×D312yes—
663C4⋊C4C23×D312yes—
664C22⋊C4—24no—
665C22⋊C4—34no—
666C22⋊C4—34no—
667C22⋊C4—64no—
668C22⋊C4—64no—
669C22⋊C4—64no—
670C22⋊C4—64no—
671C22⋊C4—64no—
672C22⋊C4—64no—
673C42—24no—
674C42—32no—
675C42—32no—
676C42—64no—
677C42—64no—
678C22×C3—24no—
679C22×C3—22no—
680C22×C3—22no—
681C22×C3—22no—
682C22×C3—42no—
683C22×C3—48no—
684C22×C3—44no—
685C22×C3—42no—
686C22×C3—42no—
687C22×C3—42no—
688C22×C3—42no—
689C22×C3—816no—
690C22×C3—84no—
691C22×C3#54612yes—
692C22×C3C2×AGL(1,ℤ/8)12yes—
693C22×C3#57712yes—
694C22×C3C23×D411yescharacteristic
695C2×D3—22no—
696C2×D3—22no—
697C2×D3—22no—
698C2×D3—44no—
699C2×D3—42no—
700C2×D3—42no—
701C2×D3—42no—
702C2×D3—816no—
703C2×D3—84no—
704C3×C4—22no—
705C3×C4—42no—
706C3×C4—42no—
707C3×C4#54612yes—
708C3×C4C22×#4111yescharacteristic
709C3×C4C2×H(5,𝔽2)11yescharacteristic
710Dic3—22no—
711Dic3—22no—
712Dic3—42no—
713Dic3—42no—
714Dic3—42no—
715Dic3C2×AGL(1,ℤ/8)14yes—
716C23—22no—
717C23—22no—
718C23—24no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—32no—
723C23—48no—
724C23—48no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—62no—
731C23—62no—
732C23—62no—
733C23—62no—
734C23—84no—
735C23—816no—
736C23—128no—
737C23—128no—
738C23—122no—
739C23—122no—
740C23—122no—
741C23—244no—
742C23—2416no—
743C23C2×D3×D412yes—
744C23C2×D3×D411yescharacteristic
745Q8—62no—
746Q8—62no—
747Q8—128no—
748Q8—122no—
749D4—22no—
750D4—22no—
751D4—22no—
752D4—24no—
753D4—48no—
754D4—42no—
755D4—68no—
756D4—62no—
757D4—62no—
758D4—128no—
759D4—128no—
760D4—128no—
761D4—128no—
762D4—122no—
763D4—244no—
764D4C2×#23514yes—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—24no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—32no—
772C2×C4—34no—
773C2×C4—32no—
774C2×C4—32no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—62no—
778C2×C4—62no—
779C2×C4—62no—
780C2×C4—62no—
781C2×C4—64no—
782C2×C4—62no—
783C2×C4—62no—
784C2×C4—62no—
785C2×C4—128no—
786C2×C4—122no—
787C2×C4—122no—
788C2×C4—122no—
789C2×C4C2×#23512yes—
790C2×C4C2×D3×D412yes—
791C2×C4C2×D3×D411yescharacteristic
792C2×C4#100412yes—
793C2×C4C24×D311yescharacteristic
794C8—22no—
795C8—22no—
796C8—62no—
797C8—62no—
798C2×C3—44no—
799C2×C3—42no—
800C2×C3—82no—
801C2×C3#332414yescomplemented
802C2×C3C2×#54611yescharacteristic
803C2×C3C22×AGL(1,ℤ/8)11yescharacteristic
804C2×C3C2×#57711yescharacteristic
805D3—42no—
806D3—82no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—24no—
811C22—44no—
812C22—48no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—62no—
819C22—62no—
820C22—62no—
821C22—816no—
822C22—84no—
823C22—124no—
824C22—122no—
825C22—122no—
826C22—122no—
827C22—2416no—
828C22—244no—
829C22#549012yes—
830C22D3×AGL(1,ℤ/8)12yes—
831C22#577512yes—
832C22C22×D3×D411yescharacteristic
833C4—22no—
834C4—34no—
835C4—42no—
836C4—42no—
837C4—62no—
838C4—62no—
839C4—122no—
840C4—122no—
841C4—122no—
842C4#549012yes—
843C4C22×#23511yescharacteristic
844C4C2×#100411yescharacteristic
845C3C2×#332411yescharacteristic, complemented, Sylow
846C2—42no—
847C2—44no—
848C2—82no—
849C2—122no—
850C2—242no—
851C2#7894014yesdirect product factor
852C2C2×#549011yescharacteristic
853C2C2×D3×AGL(1,ℤ/8)11yescharacteristic
854C2C2×#577511yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#418C2
socleC23×C3C22×D4
prime radicalC2×D4×#67C2
hypercenterC2×#418D3
hypocenterC3C2×#3324
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#418

Complements

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

NH ≅ G/Ntype
2. C2×#5533C2semidirect
3. C2×C3×#418C2semidirect
4. C2×#5218C2semidirect
5. C2×#5134C2semidirect
6. C2×#5128C2semidirect
7. C2×#5003C2semidirect
8. #78940C2direct (N × H)
9. C2×#4762C2semidirect
10. C2×#4784C2semidirect
11. C2×#4780C2semidirect
12. C2×#4776C2semidirect
13. C2×#4770C2semidirect
14. C2×#4760C2semidirect
15. C2×#4759C2semidirect
16. C2×#4758C2semidirect
21. C22×C3×M16C22semidirect
22. C2×C3×#117C22semidirect
32. C22×#214C22semidirect
35. C2×#924C22semidirect
36. C22×#204C22semidirect
37. C22×ΓL(1,𝔽25)C22semidirect
39. #5533C22semidirect
40. C2×#897C22semidirect
41. C2×#892C22semidirect
42. C2×#888C22semidirect
43. C2×#887C22semidirect
48. C3×#418C22semidirect
51. C2×C3×#102C22semidirect
52. C2×C3×#102C22semidirect
53. #5218C22semidirect
55. C2×#832C22semidirect
56. C2×#830C22semidirect
57. #5134C22semidirect
58. #5128C22semidirect
59. C2×#821C22semidirect
60. C2×(C2×D3)⋊C8C22semidirect
61. C2×#818C22semidirect
62. C2×#816C22semidirect
63. C2×Dic3⋊C8C22semidirect
64. C2×C8×Dic3C22semidirect
65. #5003C22semidirect
66. C2×#809C22semidirect
67. C2×#809C22semidirect
68. C2×#808C22semidirect
69. C2×#807C22semidirect
70. #4784C22semidirect
71. #4780C22semidirect
72. #4776C22semidirect
73. #4770C22semidirect
74. #4762C22semidirect
75. #4760C22semidirect
76. #4759C22semidirect
77. #4758C22semidirect
93. C2×#418D3semidirect
122. C2×C3×M16C23semidirect
126. C3×#117C23semidirect
147. C2×#214C23semidirect
160. #924C23semidirect
171. C2×#204C23semidirect
173. C2×ΓL(1,𝔽25)C23semidirect
175. #897C23semidirect
177. #892C23semidirect
179. #888C23semidirect
181. #887C23semidirect
188. C3×#102C23semidirect
189. C3×#102C23semidirect
191. #832C23semidirect
192. #830C23semidirect
193. #821C23semidirect
194. (C2×D3)⋊C8C23semidirect
195. #818C23semidirect
196. #816C23semidirect
197. Dic3⋊C8C23semidirect
198. C8×Dic3C23semidirect
199. #809C23semidirect
200. #809C23semidirect
201. #808C23semidirect
202. #807C23semidirect
210. C22×M16C2×D3semidirect
232. C2×#117C2×D3semidirect
249. #418C2×D3semidirect
258. C2×#102C2×D3semidirect
259. C2×#102C2×D3semidirect
411. C2×M16C22×D3semidirect
444. #117C22×D3semidirect
479. #102C22×D3semidirect
480. #102C22×D3semidirect
801. C2×C3#3324semidirect
845. C3C2×#3324semidirect
851. C2#78940direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×#672
C2×#55332
C2×C3×#4182
C2×#52182
C2×#51342
C2×#51282
C2×#50032
#789402
C2×#47622
C2×#47842
C2×#47802
C2×#47762
C2×#47702
C2×#47602
C2×#47592
C2×#47582
C2×#33243