Finite Group Databasebeta

← #6371669

Subgroups — #6371669

Order 512.

3178 conjugacy classes of subgroups.

The subgroup lattice has 861 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2911C211yesmaximal, characteristic, complemented
2C2×#2896C211yesmaximal, characteristic
3C2×#2896C211yesmaximal, characteristic
4C22×#413C211yesmaximal, characteristic
5C2×#2873C211yesmaximal, characteristic, complemented
6#21078C214yesmaximal, complemented
7#21077C214yesmaximal, complemented
8#21076C218yesmaximal, complemented
9#21075C218yesmaximal, complemented
10C2×#1742C211yesmaximal, characteristic, complemented
11C2×#1738C211yesmaximal, characteristic, complemented
12C23×#41C2211yescharacteristic
13C23×M16C2211yescharacteristic
14C23×M16C2211yescharacteristic
15C23×M16C2211yescharacteristic
16C23×M16C2211yescharacteristic
17C22×#117C2211yescharacteristic
18C22×#117C2211yescharacteristic
19#2911—22no—
20#2911—22no—
21#2911C2214yes—
22#2911C2214yescomplemented
23C2×#428—22no—
24C2×#428C2214yescomplemented
25C2×#427—22no—
26#2896—22no—
27#2896—22no—
28#2896—22no—
29#2896—22no—
30#2896—22no—
31#2896—22no—
32#2896C2214yes—
33#2896C2214yes—
34C2×#417—22no—
35C2×#417C2214yes—
36C2×#419C2212yes—
37C2×#419C2212yes—
38C2×#418C2212yes—
39C2×#418C2212yes—
40C2×#416—22no—
41C2×#416C2214yes—
42C2×#413C4116yescomplemented
43C2×#413C2214yes—
44C2×#413C2214yes—
45C22×#101C2212yes—
46C22×#100C2212yes—
47#2873—22no—
48#2873—22no—
49#2873C2214yes—
50#2873C2214yescomplemented
51C2×#405—22no—
52C2×#405C2214yescomplemented
53C2×C4×M16—22no—
54#1931C22132yescomplemented
55#1930C22132yescomplemented
56#1742C2214yes—
57#1742C2214yescomplemented
58C2×#343C2214yescomplemented
59#1738C2214yes—
60#1738C2214yescomplemented
61C2×#341C2214yescomplemented
62C22×#41—24no—
63C22×#41—21no—
64C22×#41—21no—
65C22×#41—21no—
66C22×#41—21no—
67C22×#41—21no—
68C22×#41—21no—
69C22×#41—21no—
70C22×#41—21no—
71C22×#41—21no—
72C22×#41—21no—
73C22×#41—24no—
74C22×#41—24no—
75C22×#41C2×C418yes—
76C22×#41C2312yes—
77C22×#41C2312yes—
78C23×Q8C2311yescharacteristic
79C23×D4—21no—
80C23×D4C2311yescharacteristic
81C24×C4—21no—
82C24×C4C2311yescharacteristic
83C22×M16—21no—
84C22×M16—21no—
85C22×M16—21no—
86C22×M16—21no—
87C22×M16—21no—
88C22×M16—21no—
89C22×M16—24no—
90C22×M16—24no—
91C22×M16—24no—
92C22×M16—24no—
93C22×M16—21no—
94C22×M16—21no—
95C22×M16—21no—
96C22×M16—24no—
97C22×M16—24no—
98C22×M16C2×C418yes—
99C22×M16C2×C418yes—
100C22×M16D412yes—
101C22×M16D412yes—
102C22×M16D412yes—
103C22×M16D412yes—
104C22×M16C2312yes—
105C22×M16C2312yes—
106C22×M16C2312yes—
107C22×M16C2312yes—
108C22×M16C2312yes—
109C22×M16C2312yes—
110C22×M16C2312yes—
111C22×M16C2312yes—
112C22×M16C2312yes—
113C22×M16C2312yes—
114C22×M16C2312yes—
115C23×C8—21no—
116C23×C8—21no—
117C23×C8—21no—
118C23×C8C2312yes—
119C2×#117—21no—
120C2×#117—21no—
121C2×#117—21no—
122C2×#117—21no—
123C2×#117—21no—
124C2×#117—21no—
125C2×#117—21no—
126C2×#117—21no—
127C2×#117—21no—
128C2×#117—21no—
129C2×#117—21no—
130C2×#117—21no—
131C2×#117—21no—
132C2×#117—21no—
133C2×#117—21no—
134C2×#117—21no—
135C2×#117D412yes—
136C2×#117D412yes—
137C2×#117D412yes—
138C2×#117C2312yes—
139C2×#117C2312yes—
140C2×#117C2312yes—
141C2×#117C2312yes—
142C2×#117C2312yes—
143C22×C4⋊C4D412yes—
144C22×C4⋊C4C2312yes—
145C22×C22⋊C4—21no—
146C22×C22⋊C4—21no—
147C22×C42—21no—
148C22×C42—21no—
149#428—28no—
150#428—28no—
151#428—28no—
152#428C23116yes—
153#427—28no—
154#427—28no—
155C2×#107—24no—
156C2×#106—24no—
157#419—24no—
158#419—24no—
159#419—24no—
160#419C2318yes—
161#418—24no—
162#418—24no—
163#418—24no—
164#418C2318yes—
165#417—28no—
166#417—28no—
167#417—28no—
168#417—28no—
169#416—28no—
170#416—28no—
171#416—28no—
172#416—28no—
173C2×#103—24no—
174C2×#103C2318yes—
175C2×#102—24no—
176C2×#102C2318yes—
177#413C2×C4132yescomplemented
178#413C2×C4132yescomplemented
179C2×#101C2×C4116yescomplemented
180C2×#101C2318yes—
181C2×#100C2×C4116yescomplemented
182C2×#100C2318yes—
183#405—28no—
184#405—28no—
185#405—28no—
186#405C23116yes—
187C4×M16—28no—
188C4×M16—28no—
189C2×#97—24no—
190C2×C4×C8—24no—
191#343C23116yes—
192#341C23116yes—
193C25—21no—
194C25#4111yescharacteristic
195C2×#41—28no—
196C2×#41—28no—
197C2×#41—24no—
198C2×#41—24no—
199C2×#41—28no—
200C2×#41—28no—
201C2×#41—28no—
202C2×#41—28no—
203C2×#41—28no—
204C2×#41—28no—
205C2×#41—28no—
206C2×#41—28no—
207C2×#41—22no—
208C2×#41—22no—
209C2×#41—22no—
210C2×#41—22no—
211C2×#41—22no—
212C2×#41—22no—
213C2×#41—22no—
214C2×#41—22no—
215C2×#41—24no—
216C2×#41—24no—
217C2×#41—24no—
218C2×#41—24no—
219C2×#41—41no—
220C2×#41—41no—
221C2×#41—41no—
222C2×#41—41no—
223C2×#41—41no—
224C2×#41—41no—
225C2×#41—41no—
226C2×#41—41no—
227C2×#41—44no—
228C2×#41—44no—
229C2×#41—44no—
230C2×#41—44no—
231C2×#41—44no—
232C2×#41—44no—
233C2×#41—44no—
234C2×#41—44no—
235C2×#41—44no—
236C2×#41—44no—
237C2×#41C22×C418yes—
238C2×#41C22×C418yes—
239C22×Q8—22no—
240C22×Q8—21no—
241C22×Q8—21no—
242C22×Q8—21no—
243C22×Q8—21no—
244C22×Q8—21no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8C22×C414yes—
248C22×Q8C2412yes—
249C22×D4—28no—
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—21no—
253C22×D4—21no—
254C22×D4—21no—
255C22×D4—21no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—21no—
259C22×D4—22no—
260C22×D4—41no—
261C22×D4—41no—
262C22×D4—41no—
263C22×D4—41no—
264C22×D4—44no—
265C22×D4C22×C414yes—
266C22×D4C2412yes—
267C23×C4—21no—
268C23×C4—22no—
269C23×C4—28no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—41no—
274C23×C4—41no—
275C23×C4—41no—
276C23×C4—41no—
277C23×C4—44no—
278C23×C4C22×C414yes—
279C23×C4C2×D411yescharacteristic
280C23×C4C2×D411yescharacteristic
281C23×C4C2×D411yescharacteristic
282C23×C4C2×D411yescharacteristic
283C23×C4C2×D411yescharacteristic
284C23×C4C2×D411yescharacteristic
285C23×C4C2×D411yescharacteristic
286C23×C4C2×D411yescharacteristic
287C23×C4#4111yescharacteristic
288C23×C4#4111yescharacteristic
289C23×C4#4111yescharacteristic
290C23×C4#4114yes—
291C23×C4#4114yes—
292C23×C4#4114yes—
293C23×C4C2411yescharacteristic
294C23×C4C2411yescharacteristic
295C23×C4C2411yescharacteristic
296C2×M16—28no—
297C2×M16—28no—
298C2×M16—28no—
299C2×M16—28no—
300C2×M16—28no—
301C2×M16—28no—
302C2×M16—28no—
303C2×M16—28no—
304C2×M16—28no—
305C2×M16—28no—
306C2×M16—22no—
307C2×M16—22no—
308C2×M16—22no—
309C2×M16—22no—
310C2×M16—22no—
311C2×M16—22no—
312C2×M16—24no—
313C2×M16—24no—
314C2×M16—24no—
315C2×M16—24no—
316C2×M16—24no—
317C2×M16—24no—
318C2×M16—24no—
319C2×M16—24no—
320C2×M16—24no—
321C2×M16—24no—
322C2×M16—22no—
323C2×M16—22no—
324C2×M16—22no—
325C2×M16—24no—
326C2×M16—24no—
327C2×M16—24no—
328C2×M16—24no—
329C2×M16—24no—
330C2×M16—24no—
331C2×M16—44no—
332C2×M16—44no—
333C2×M16—44no—
334C2×M16C22×C418yes—
335C2×M16C22×C418yes—
336C2×M16C22×C418yes—
337C2×M16C22×C418yes—
338C2×M16C22×C418yes—
339C2×M16C22×C418yes—
340C2×M16C2×D414yes—
341C2×M16C2×D414yes—
342C2×M16C2×D414yes—
343C2×M16C2×D414yes—
344C2×M16C2414yes—
345C2×M16C2414yes—
346C2×M16C2414yes—
347C22×C8—28no—
348C22×C8—28no—
349C22×C8—22no—
350C22×C8—22no—
351C22×C8—22no—
352C22×C8—22no—
353C22×C8—22no—
354C22×C8—22no—
355C22×C8—24no—
356C22×C8—24no—
357C22×C8—22no—
358C22×C8—22no—
359C22×C8—22no—
360C22×C8—44no—
361C22×C8C2×D414yes—
362C22×C8C2×D414yes—
363C22×C8C2414yes—
364#117—22no—
365#117—22no—
366#117—22no—
367#117—22no—
368#117—22no—
369#117—22no—
370#117—22no—
371#117—22no—
372#117—22no—
373#117—22no—
374#117—22no—
375#117—22no—
376#117—22no—
377#117—22no—
378#117—22no—
379#117—22no—
380#117—22no—
381#117—22no—
382#117—22no—
383#117—22no—
384#117—41no—
385#117—41no—
386#117—41no—
387#117—41no—
388#117—41no—
389#117—41no—
390#117—41no—
391#117—41no—
392#117C2×D414yes—
393#117C2×D414yes—
394#117C2×D414yes—
395#117C2414yes—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4C2×D414yes—
405C2×C4⋊C4C2×D414yes—
406C2×C4⋊C4C2×D414yes—
407C2×C4⋊C4C2414yes—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—41no—
417C2×C22⋊C4—41no—
418C2×C22⋊C4—41no—
419C2×C22⋊C4—41no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—41no—
429C2×C42—41no—
430C2×C42—41no—
431C2×C42—41no—
432#107—216no—
433#106—216no—
434#103—216no—
435#103—216no—
436#102—216no—
437#102—216no—
438#101C22×C4132yescomplemented
439#100C22×C4132yescomplemented
440#97—216no—
441C4×C8—216no—
442C24—24no—
443C24—22no—
444C24—41no—
445C24—41no—
446C24—42no—
447C24—82no—
448C24—84no—
449C24#11714yes—
450C24#12111yescharacteristic
451C24#12111yescharacteristic
452C24#12111yescharacteristic
453C24#12111yescharacteristic
454C24#12614yes—
455C24C2×#4111yescharacteristic
456C24C2×#4111yescharacteristic
457C24C2×#4111yescharacteristic
458#41—28no—
459#41—28no—
460#41—28no—
461#41—28no—
462#41—28no—
463#41—28no—
464#41—28no—
465#41—28no—
466#41—44no—
467#41—44no—
468#41—44no—
469#41—44no—
470#41—44no—
471#41—44no—
472#41—44no—
473#41—44no—
474#41—48no—
475#41—48no—
476#41—48no—
477#41—48no—
478#41—48no—
479#41—48no—
480#41—48no—
481#41—48no—
482C2×Q8—24no—
483C2×Q8—22no—
484C2×Q8—24no—
485C2×Q8—24no—
486C2×Q8—24no—
487C2×Q8—24no—
488C2×Q8—22no—
489C2×Q8—22no—
490C2×Q8—22no—
491C2×Q8—22no—
492C2×Q8—41no—
493C2×Q8—41no—
494C2×Q8—42no—
495C2×Q8—42no—
496C2×Q8—42no—
497C2×Q8—42no—
498C2×Q8—42no—
499C2×Q8C23×C414yes—
500C2×D4—28no—
501C2×D4—28no—
502C2×D4—24no—
503C2×D4—24no—
504C2×D4—24no—
505C2×D4—24no—
506C2×D4—24no—
507C2×D4—22no—
508C2×D4—22no—
509C2×D4—22no—
510C2×D4—22no—
511C2×D4—22no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4—42no—
515C2×D4—42no—
516C2×D4—44no—
517C2×D4—44no—
518C2×D4—48no—
519C2×D4—48no—
520C2×D4—48no—
521C2×D4—48no—
522C2×D4—41no—
523C2×D4—41no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4C23×C414yes—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—22no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—28no—
536C22×C4—28no—
537C22×C4—24no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—48no—
548C22×C4—48no—
549C22×C4—48no—
550C22×C4—48no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—84no—
554C22×C4—84no—
555C22×C4#11714yes—
556C22×C4#11714yes—
557C22×C4#11714yes—
558C22×C4C4×D414yes—
559C22×C4C4×D414yes—
560C22×C4C4×D414yes—
561C22×C4C4×D414yes—
562C22×C4C4×D414yes—
563C22×C4C4×D414yes—
564C22×C4C4×D414yes—
565C22×C4C4×D414yes—
566C22×C4#12111yescharacteristic
567C22×C4#12111yescharacteristic
568C22×C4#12111yescharacteristic
569C22×C4#12111yescharacteristic
570C22×C4#12111yescharacteristic
571C22×C4#12111yescharacteristic
572C22×C4#12111yescharacteristic
573C22×C4#12111yescharacteristic
574C22×C4#12111yescharacteristic
575C22×C4#12111yescharacteristic
576C22×C4#12111yescharacteristic
577C22×C4#12111yescharacteristic
578C22×C4#12314yes—
579C22×C4#12314yes—
580C22×C4#12314yes—
581C22×C4#12314yes—
582C22×C4#12414yes—
583C22×C4#12414yes—
584C22×C4#12414yes—
585C22×C4#12414yes—
586C22×C4#12614yes—
587C22×C4#12614yes—
588C22×C4#12614yes—
589C22×C4C23×C412yes—
590C22×C4C23×C412yes—
591C22×C4C23×C412yes—
592C22×C4C22×D411yescharacteristic
593C22×C4C22×D411yescharacteristic
594C22×C4C22×D411yescharacteristic
595C22×C4C22×D411yescharacteristic
596C22×C4C22×D411yescharacteristic
597C22×C4C22×D411yescharacteristic
598C22×C4C22×D411yescharacteristic
599C22×C4C22×D411yescharacteristic
600C22×C4C22×D411yescharacteristic
601C22×C4C22×D411yescharacteristic
602C22×C4C22×D411yescharacteristic
603C22×C4C22×D411yescharacteristic
604C22×C4C2×#4111yescharacteristic
605C22×C4C2×#4111yescharacteristic
606C22×C4C2×#4111yescharacteristic
607C22×C4C2×#4112yes—
608C22×C4C2×#4112yes—
609C22×C4C2×#4112yes—
610C22×C4C2×#4112yes—
611C22×C4C2×#4112yes—
612C22×C4C2×#4112yes—
613C22×C4C2×#4112yes—
614C22×C4C2×#4112yes—
615C22×C4C2×#4112yes—
616C22×C4C2511yescharacteristic
617M16—28no—
618M16—28no—
619M16—28no—
620M16—28no—
621M16—28no—
622M16—28no—
623M16—28no—
624M16—28no—
625M16—28no—
626M16—28no—
627M16—24no—
628M16—24no—
629M16—24no—
630M16—24no—
631M16—44no—
632M16—44no—
633M16—44no—
634M16C23×C418yes—
635M16C23×C418yes—
636C2×C8—28no—
637C2×C8—28no—
638C2×C8—28no—
639C2×C8—28no—
640C2×C8—28no—
641C2×C8—28no—
642C2×C8—28no—
643C2×C8—28no—
644C2×C8—24no—
645C2×C8—24no—
646C2×C8—24no—
647C2×C8—24no—
648C2×C8—24no—
649C2×C8—44no—
650C2×C8—44no—
651C2×C8—44no—
652C2×C8C22×D418yes—
653C4⋊C4—24no—
654C4⋊C4—24no—
655C4⋊C4—24no—
656C4⋊C4—24no—
657C4⋊C4—24no—
658C4⋊C4—42no—
659C4⋊C4—42no—
660C4⋊C4C22×D418yes—
661C22⋊C4—24no—
662C22⋊C4—24no—
663C22⋊C4—24no—
664C22⋊C4—24no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C42—24no—
670C42—24no—
671C42—24no—
672C42—24no—
673C42—42no—
674C42—42no—
675C42—42no—
676C42—42no—
677C23—24no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—44no—
688C23—44no—
689C23—84no—
690C23—84no—
691C23—84no—
692C23—84no—
693C23—84no—
694C23—88no—
695C23—88no—
696C23#38814yes—
697C23#38814yes—
698C23#38814yes—
699C23#38814yes—
700C23C2×#11712yes—
701C23C2×#11712yes—
702C23C2×#11712yes—
703C23C2×#12111yescharacteristic
704C23C2×#12111yescharacteristic
705C23C2×#12111yescharacteristic
706C23C2×#12111yescharacteristic
707C23C2×#12111yescharacteristic
708C23C2×#12111yescharacteristic
709C23C2×#12612yes—
710C23C2×#12612yes—
711C23C2×#12612yes—
712C23C22×#4111yescharacteristic
713Q8—24no—
714Q8—24no—
715Q8—42no—
716Q8—42no—
717Q8—44no—
718Q8—44no—
719D4—24no—
720D4—24no—
721D4—48no—
722D4—48no—
723D4—48no—
724D4—48no—
725D4—42no—
726D4—42no—
727D4—44no—
728D4—44no—
729C2×C4—24no—
730C2×C4—28no—
731C2×C4—48no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—48no—
737C2×C4—48no—
738C2×C4—48no—
739C2×C4—48no—
740C2×C4—44no—
741C2×C4—84no—
742C2×C4—84no—
743C2×C4—84no—
744C2×C4—84no—
745C2×C4—84no—
746C2×C4#38814yes—
747C2×C4#38814yes—
748C2×C4#38814yes—
749C2×C4#38814yes—
750C2×C4#38814yes—
751C2×C4#38814yes—
752C2×C4#38814yes—
753C2×C4#38814yes—
754C2×C4#38814yes—
755C2×C4#38814yes—
756C2×C4#38814yes—
757C2×C4#38814yes—
758C2×C4C2×#11712yes—
759C2×C4C2×#11712yes—
760C2×C4C2×#11712yes—
761C2×C4C2×C4×D412yes—
762C2×C4C2×C4×D412yes—
763C2×C4C2×C4×D412yes—
764C2×C4C2×C4×D412yes—
765C2×C4C2×C4×D412yes—
766C2×C4C2×C4×D412yes—
767C2×C4C2×C4×D412yes—
768C2×C4C2×C4×D412yes—
769C2×C4C2×C4×D412yes—
770C2×C4C2×C4×D412yes—
771C2×C4C2×C4×D412yes—
772C2×C4C2×C4×D412yes—
773C2×C4C2×#12111yescharacteristic
774C2×C4C2×#12111yescharacteristic
775C2×C4C2×#12111yescharacteristic
776C2×C4C2×#12111yescharacteristic
777C2×C4C2×#12111yescharacteristic
778C2×C4C2×#12111yescharacteristic
779C2×C4C2×#12312yes—
780C2×C4C2×#12312yes—
781C2×C4C2×#12312yes—
782C2×C4C2×#12312yes—
783C2×C4C2×#12312yes—
784C2×C4C2×#12312yes—
785C2×C4C2×#12412yes—
786C2×C4C2×#12412yes—
787C2×C4C2×#12412yes—
788C2×C4C2×#12412yes—
789C2×C4C2×#12412yes—
790C2×C4C2×#12412yes—
791C2×C4C2×#12612yes—
792C2×C4C2×#12612yes—
793C2×C4C2×#12612yes—
794C2×C4C24×C411yescharacteristic
795C2×C4C23×D411yescharacteristic
796C2×C4C23×D411yescharacteristic
797C2×C4C22×#4111yescharacteristic
798C2×C4C22×#4111yescharacteristic
799C2×C4C22×#4111yescharacteristic
800C8—28no—
801C8—28no—
802C8—28no—
803C8—44no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—44no—
818C22—44no—
819C22—44no—
820C22—44no—
821C22—44no—
822C22—84no—
823C22—88no—
824C22—84no—
825C22—88no—
826C22—84no—
827C22C2×#38812yes—
828C22C2×#38812yes—
829C22C2×#38812yes—
830C22C2×#38812yes—
831C22C2×#38812yes—
832C22C2×#38812yes—
833C22C22×#11711yescharacteristic
834C22C22×#12111yescharacteristic
835C22C22×#12611yescharacteristic
836C4—48no—
837C4—44no—
838C4—84no—
839C4C2×#38812yes—
840C4C2×#38812yes—
841C4C2×#38812yes—
842C4C2×#38812yes—
843C4C2×#38812yes—
844C4C2×#38812yes—
845C4C22×C4×D411yescharacteristic
846C4C22×C4×D411yescharacteristic
847C4C22×#12311yescharacteristic
848C4C22×#12411yescharacteristic
849C2—21no—
850C2—21no—
851C2—22no—
852C2—22no—
853C2—22no—
854C2—22no—
855C2—22no—
856C2—22no—
857C2—84no—
858C2C22×#38811yescharacteristic
859C2#6046912yes—
subgroupG/H
centerC2×C4C2×#121
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
socleC22C22×#121
prime radicalC23×#41C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2911C2semidirect
5. C2×#2873C2semidirect
6. #21078C2semidirect
7. #21077C2semidirect
8. #21076C2semidirect
9. #21075C2semidirect
10. C2×#1742C2semidirect
11. C2×#1738C2semidirect
22. #2911C22semidirect
24. C2×#428C22semidirect
42. C2×#413C4semidirect
50. #2873C22semidirect
52. C2×#405C22semidirect
54. #1931C22semidirect
55. #1930C22semidirect
57. #1742C22semidirect
58. C2×#343C22semidirect
60. #1738C22semidirect
61. C2×#341C22semidirect
177. #413C2×C4semidirect
178. #413C2×C4semidirect
179. C2×#101C2×C4semidirect
181. C2×#100C2×C4semidirect
438. #101C22×C4semidirect
439. #100C22×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#29112
C2×#28962
C22×#4132
C2×#28732
#210782
#210772
#210762
#210752
C2×#17422
C2×#17382