Finite Group Databasebeta

← #6447021

Subgroups — #6447021

Order 512.

2412 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2537C211yesmaximal, characteristic
2D4×#117C211yesmaximal, characteristic, complemented
3#24982C214yesmaximal, complemented
4#24981C214yesmaximal, complemented
5#24968C212yesmaximal, complemented
6#24967C212yesmaximal, complemented
7#24966C212yesmaximal, complemented
8#24965C212yesmaximal, complemented
9#23642C212yesmaximal, complemented
10#23480C212yesmaximal, complemented
11#21190C211yesmaximal, characteristic, complemented
12#21171C211yesmaximal, characteristic, complemented
13#20912C212yesmaximal, complemented
14#20764C211yesmaximal, characteristic, complemented
15#20702C212yesmaximal, complemented
16#20646C211yesmaximal, characteristic, complemented
17C4×#418C211yesmaximal, characteristic, complemented
18C22×#121—21no—
19C22×#121C2212yes—
20C22×C4×D4C2211yescharacteristic
21C22×C4×D4C2211yescharacteristic
22C22×#117C2212yes—
23C2×#428C2212yes—
24C2×#423C2211yescharacteristic
25C2×#418C2211yescharacteristic
26C2×#418C2211yescharacteristic
27C2×#418C2212yes—
28C2×#407C2212yes—
29C2×#407C2212yes—
30C2×C4×M16C2211yescharacteristic
31#2537—21no—
32#2537—22no—
33#2537—21no—
34#2537C2212yes—
35#2537C2212yes—
36#2537C2214yes—
37C2×#394—22no—
38#2354C2211yescharacteristic, complemented
39#2354C2211yescharacteristic, complemented
40#2352C2212yescomplemented
41#2352C2212yescomplemented
42D4×C4⋊C4C2211yescharacteristic, complemented
43D4×C4⋊C4C2211yescharacteristic, complemented
44#2344—21no—
45#2342—22no—
46D4×C22⋊C4—21no—
47#2293—21no—
48#2290—22no—
49#2285C2211yescharacteristic
50C2×#384C2211yescharacteristic
51#2280C2212yes—
52C2×#380—21no—
53C2×#380C2212yes—
54C42×D4—21no—
55C4×#117C2211yescharacteristic
56#2077C2214yescomplemented
57#2077C2214yescomplemented
58#2076C2214yescomplemented
59#2075C2214yescomplemented
60#2034C2214yescomplemented
61#2034C2214yescomplemented
62#2033C2214yescomplemented
63#2033C2214yescomplemented
64#1955C2214yescomplemented
65#1954C2212yescomplemented
66#1954C2212yescomplemented
67#1948C2212yescomplemented
68#1948C2212yescomplemented
69#1947C2212yescomplemented
70#1947C2212yescomplemented
71#1875C2214yescomplemented
72#1875C2214yescomplemented
73#1874C2214yescomplemented
74#1874C2214yescomplemented
75#1836C2214yescomplemented
76#1834C2212yescomplemented
77#1834C2212yescomplemented
78#1825C2214yescomplemented
79#1825C2214yescomplemented
80#1824C2214yescomplemented
81#1823C2214yescomplemented
82#1804C2214yescomplemented
83#1802C2212yescomplemented
84#1802C2212yescomplemented
85#1762C2212yescomplemented
86#1762C2212yescomplemented
87C4×#102C2212yescomplemented
88C4×#102C2212yescomplemented
89#1736C2212yes—
90#1736C2212yes—
91#1736C2211yescharacteristic
92#1736C2212yes—
93#1736C2212yes—
94#1736C2211yescharacteristic
95C23×D4—22no—
96C23×D4D411yescharacteristic
97C23×D4C2311yescharacteristic
98C24×C4—21no—
99C24×C4C2312yes—
100C22×M16C2311yescharacteristic
101C22×M16C2311yescharacteristic
102C22×M16C2312yes—
103C2×#121—22no—
104C2×#121—24no—
105C2×#121—22no—
106C2×#121—22no—
107C2×#121—22no—
108C2×#121—28no—
109C2×#121—44no—
110C2×#121—48no—
111C2×#121C2314yes—
112C2×#121C2314yes—
113C2×C4×D4—21no—
114C2×C4×D4—21no—
115C2×C4×D4—21no—
116C2×C4×D4—21no—
117C2×C4×D4—24no—
118C2×C4×D4—24no—
119C2×C4×D4—24no—
120C2×C4×D4—24no—
121C2×C4×D4D411yescharacteristic
122C2×C4×D4D412yes—
123C2×C4×D4D411yescharacteristic
124C2×C4×D4C2312yes—
125C2×C4×D4C2312yes—
126C2×C4×D4C2311yescharacteristic
127C2×C4×D4C2312yes—
128C2×C4×D4C2311yescharacteristic
129C2×#117—22no—
130C2×#117—22no—
131C2×#117—28no—
132C2×#117—44no—
133C2×#117C2312yes—
134C2×#117C2311yescharacteristic
135C2×#117C2312yes—
136C2×#117C2312yes—
137C2×#117C2311yescharacteristic
138C22×C4⋊C4—21no—
139C22×C4⋊C4—21no—
140C22×C4⋊C4D411yescharacteristic
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C22⋊C4—22no—
146C22×C22⋊C4—22no—
147C22×C22⋊C4—21no—
148C22×C22⋊C4—22no—
149C22×C22⋊C4D412yes—
150C22×C42—22no—
151C22×C42C2311yescharacteristic
152#428—44no—
153C2×#107C2314yes—
154C2×#106C2314yes—
155#423—24no—
156C2×C4⋊C8C2312yes—
157C2×C4⋊C8C2312yes—
158#418—24no—
159#418—24no—
160#418—44no—
161C2×#102C2312yes—
162C2×#102C2312yes—
163C2×#102C2312yes—
164C2×#102C2312yes—
165C2×#102C2314yes—
166C2×#102C2314yes—
167#407—44no—
168#407—44no—
169C2×C22⋊C8C2314yes—
170C2×C22⋊C8C2314yes—
171C2×C22⋊C8C2314yes—
172C2×C22⋊C8C2314yes—
173C4×M16—24no—
174C2×#97C2312yes—
175C2×C4×C8C2312yes—
176#394—24no—
177#394—24no—
178#394—24no—
179#394—24no—
180#390—21no—
181#390—21no—
182#389—21no—
183#389—21no—
184#388—22no—
185#388—22no—
186#388—22no—
187#388—22no—
188#387—22no—
189#387—22no—
190#386—22no—
191#386—22no—
192#385—22no—
193#385—22no—
194#384—21no—
195#384—21no—
196#384C2311yescharacteristic
197#384C2311yescharacteristic
198#384C2312yes—
199#384C2312yes—
200#382C2312yes—
201#381—22no—
202#380—21no—
203#380—21no—
204#380—22no—
205#380—22no—
206#380—22no—
207#380—24no—
208#380—22no—
209#380C2312yes—
210#380C2314yes—
211#380C2312yes—
212#380C2314yes—
213#380C2312yes—
214#380C2312yes—
215#379—22no—
216C4×C4⋊C4—21no—
217C4×C4⋊C4—21no—
218C4×C4⋊C4—21no—
219C4×C4⋊C4—21no—
220C4×C4⋊C4C2311yescharacteristic
221C4×C4⋊C4C2311yescharacteristic
222C4×C4⋊C4C2311yescharacteristic
223C4×C4⋊C4C2311yescharacteristic
224C4×C22⋊C4—21no—
225C4×C22⋊C4—21no—
226C4×C22⋊C4—22no—
227C4×C22⋊C4—22no—
228C4×C22⋊C4—22no—
229C4×C22⋊C4—22no—
230#376—21no—
231C2×#95—22no—
232C43—21no—
233#340C2314yes—
234#340C2314yes—
235#340C2312yes—
236#340C2314yes—
237#340C2314yes—
238#340C2312yes—
239#340C2312yes—
240#340C2314yes—
241#340C2314yes—
242#340C2312yes—
243#340C2314yes—
244#340C2314yes—
245C25—21no—
246C25C2×D412yes—
247C22×D4—24no—
248C22×D4—24no—
249C22×D4—24no—
250C22×D4—24no—
251C22×D4—21no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—42no—
258C22×D4—48no—
259C22×D4—48no—
260C22×D4—84no—
261C22×D4C2×D411yescharacteristic
262C22×D4C2×D412yes—
263C22×D4C2×D411yescharacteristic
264C22×D4#4114yes—
265C22×D4C2412yes—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—21no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—44no—
279C23×C4—44no—
280C23×C4—44no—
281C23×C4C2×D412yes—
282C23×C4C2×D412yes—
283C23×C4C2×D412yes—
284C23×C4C2×D411yescharacteristic
285C23×C4C2×D411yescharacteristic
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2411yescharacteristic
289C2×M16—22no—
290C2×M16—22no—
291C2×M16—22no—
292C2×M16—22no—
293C2×M16—24no—
294C2×M16—22no—
295C2×M16—22no—
296C2×M16—24no—
297C2×M16—24no—
298C22×C8C2412yes—
299C22×C8C2412yes—
300C22×C8C2414yes—
301#121—28no—
302#121—28no—
303#121—44no—
304#121—44no—
305#121—48no—
306#121—48no—
307#121—48no—
308#121—416no—
309#121—48no—
310C4×D4—24no—
311C4×D4—28no—
312C4×D4—24no—
313C4×D4—22no—
314C4×D4—22no—
315C4×D4—24no—
316C4×D4—22no—
317C4×D4—24no—
318C4×D4—22no—
319C4×D4—24no—
320C4×D4—24no—
321C4×D4—24no—
322C4×D4—24no—
323C4×D4—44no—
324C4×D4—44no—
325C4×D4—44no—
326C4×D4—44no—
327#117—22no—
328#117—24no—
329#117—22no—
330#117—24no—
331#117—22no—
332#117—24no—
333#117—24no—
334#117—48no—
335#117—48no—
336#117—42no—
337#117—42no—
338#117#4114yes—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4—42no—
360C2×C4⋊C4—44no—
361C2×C4⋊C4—82no—
362C2×C4⋊C4C2×D411yescharacteristic
363C2×C4⋊C4C2×D412yes—
364C2×C4⋊C4C2×D411yescharacteristic
365C2×C4⋊C4C2412yes—
366C2×C4⋊C4C2412yes—
367C2×C4⋊C4C2412yes—
368C2×C4⋊C4C2414yes—
369C2×C4⋊C4C2411yescharacteristic
370C2×C4⋊C4C2411yescharacteristic
371C2×C4⋊C4C2411yescharacteristic
372C2×C4⋊C4C2411yescharacteristic
373C2×C22⋊C4—21no—
374C2×C22⋊C4—28no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—48no—
390C2×C22⋊C4—48no—
391C2×C22⋊C4—48no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4C2×D412yes—
394C2×C22⋊C4C2×D412yes—
395C2×C22⋊C4C2×D412yes—
396C2×C22⋊C4C2×D412yes—
397C2×C42—21no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—21no—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—48no—
407C2×C42C2×D411yescharacteristic
408C2×C42C2×D411yescharacteristic
409C2×C42#4114yes—
410C2×C42#4114yes—
411C2×C42C2411yescharacteristic
412C2×C42C2411yescharacteristic
413#107—44no—
414#106—44no—
415C4⋊C8—24no—
416C4⋊C8—24no—
417#102—24no—
418#102—24no—
419#102—24no—
420#102—24no—
421#102—44no—
422#102—44no—
423C22⋊C8—44no—
424C22⋊C8—44no—
425C22⋊C8—44no—
426C22⋊C8—44no—
427#97—24no—
428C4×C8—24no—
429#95—24no—
430#95—24no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—22no—
436#95—22no—
437#95—22no—
438#95—22no—
439#95—22no—
440#95—22no—
441C24—24no—
442C24—24no—
443C24—22no—
444C24—24no—
445C24—24no—
446C24—24no—
447C24—42no—
448C24—42no—
449C24—42no—
450C24—42no—
451C24—42no—
452C24—42no—
453C24—42no—
454C24—42no—
455C24—42no—
456C24C22×D412yes—
457C24C22×D412yes—
458C24C22×D411yescharacteristic
459C2×D4—24no—
460C2×D4—22no—
461C2×D4—24no—
462C2×D4—22no—
463C2×D4—28no—
464C2×D4—24no—
465C2×D4—28no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—416no—
475C2×D4—42no—
476C2×D4—48no—
477C2×D4—48no—
478C2×D4—48no—
479C2×D4—48no—
480C2×D4—42no—
481C2×D4—44no—
482C2×D4—42no—
483C2×D4—44no—
484C2×D4—84no—
485C2×D4—84no—
486C2×D4—832no—
487C2×D4AGL(1,ℤ/8)14yes—
488C2×D4C2×#4114yes—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—44no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—48no—
527C22×C4—48no—
528C22×C4—48no—
529C22×C4—48no—
530C22×C4—42no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—44no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4—816no—
543C22×C4—82no—
544C22×C4—82no—
545C22×C4#12314yes—
546C22×C4#12314yes—
547C22×C4C22×D412yes—
548C22×C4C22×D412yes—
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C22×D411yescharacteristic
554C22×C4C2×#4112yes—
555C22×C4C2×#4112yes—
556C22×C4C2×#4112yes—
557C22×C4C2×#4112yes—
558C22×C4H(5,𝔽2)12yes—
559C22×C4H(5,𝔽2)12yes—
560C22×C4C2511yescharacteristic
561M16—48no—
562M16—44no—
563M16—44no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—24no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—24no—
572C2×C8—24no—
573C4⋊C4—24no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—24no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—21no—
588C4⋊C4—24no—
589C4⋊C4—21no—
590C4⋊C4—44no—
591C4⋊C4—44no—
592C4⋊C4—44no—
593C4⋊C4—42no—
594C4⋊C4—44no—
595C4⋊C4—44no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—81no—
599C4⋊C4—81no—
600C4⋊C4—82no—
601C4⋊C4—82no—
602C4⋊C4C2×#4112yes—
603C4⋊C4C2×#4112yes—
604C22⋊C4—24no—
605C22⋊C4—24no—
606C22⋊C4—24no—
607C22⋊C4—24no—
608C22⋊C4—24no—
609C22⋊C4—44no—
610C22⋊C4—44no—
611C22⋊C4—48no—
612C22⋊C4—48no—
613C22⋊C4—48no—
614C22⋊C4—44no—
615C22⋊C4—44no—
616C22⋊C4—42no—
617C22⋊C4—48no—
618C22⋊C4—44no—
619C22⋊C4—44no—
620C22⋊C4—44no—
621C22⋊C4—82no—
622C22⋊C4—82no—
623C42—24no—
624C42—44no—
625C42—44no—
626C42—44no—
627C42—42no—
628C42—42no—
629C42—42no—
630C42—81no—
631C42—81no—
632C42#12314yes—
633C42#12314yes—
634C42C2×#4112yes—
635C42C2×#4112yes—
636C42C2×#4112yes—
637C42C2×#4112yes—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—24no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—48no—
657C23—48no—
658C23—48no—
659C23—48no—
660C23—48no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—48no—
665C23—48no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—84no—
670C23—84no—
671C23—84no—
672C23—84no—
673C23—84no—
674C23—84no—
675C23—84no—
676C23C2×#12312yes—
677C23#54612yes—
678C23#54612yes—
679C23C2×AGL(1,ℤ/8)14yes—
680C23C23×D411yescharacteristic
681D4—28no—
682D4—24no—
683D4—24no—
684D4—48no—
685D4—44no—
686D4—48no—
687D4—42no—
688D4—42no—
689D4—816no—
690D4—816no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—28no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—44no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—48no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—48no—
715C2×C4—48no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—44no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—44no—
733C2×C4—41no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4—42no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—88no—
741C2×C4—88no—
742C2×C4—88no—
743C2×C4—84no—
744C2×C4—88no—
745C2×C4—88no—
746C2×C4C2×#12312yes—
747C2×C4C2×#12312yes—
748C2×C4C2×#12312yes—
749C2×C4C2×#12312yes—
750C2×C4C2×#12312yes—
751C2×C4#52914yes—
752C2×C4#54014yes—
753C2×C4#54612yes—
754C2×C4#54612yes—
755C2×C4#55314yes—
756C2×C4#55514yes—
757C2×C4C2×AGL(1,ℤ/8)12yes—
758C2×C4#57512yes—
759C2×C4C22×#4111yescharacteristic
760C2×C4C22×#4111yescharacteristic
761C2×C4C22×#4111yescharacteristic
762C2×C4C22×#4111yescharacteristic
763C2×C4C2×H(5,𝔽2)11yescharacteristic
764C2×C4C2×H(5,𝔽2)11yescharacteristic
765C8—44no—
766C8—42no—
767C8—42no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—44no—
785C22—42no—
786C22—44no—
787C22—42no—
788C22—44no—
789C22—42no—
790C22—42no—
791C22—816no—
792C22—816no—
793C22—82no—
794C22—82no—
795C22—82no—
796C22—82no—
797C22#242014yes—
798C22C22×#12311yescharacteristic
799C22C2×#54611yescharacteristic
800C22C2×#54611yescharacteristic
801C22C22×AGL(1,ℤ/8)11yescharacteristic
802C22C2×#57511yescharacteristic
803C22#358511yescharacteristic
804C22#358611yescharacteristic
805C4—22no—
806C4—22no—
807C4—22no—
808C4—42no—
809C4—42no—
810C4—42no—
811C4—42no—
812C4—82no—
813C4—81no—
814C4—84no—
815C4—81no—
816C4—82no—
817C4—82no—
818C4#242014yes—
819C4#309414yes—
820C4C2×#52911yescharacteristic
821C4C2×#54011yescharacteristic
822C4C2×#55311yescharacteristic
823C4C2×#55511yescharacteristic
824C2—24no—
825C2—44no—
826C2—82no—
827C2—84no—
828C2C2×#242011yescharacteristic
829C2C2×#309411yescharacteristic
830C2#6052011yescharacteristic
831C2#6115511yescharacteristic
832C2#6115911yescharacteristic
833C2#6116111yescharacteristic
834C2#6116611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#2537C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. D4×#117C2semidirect
3. #24982C2semidirect
4. #24981C2semidirect
5. #24968C2semidirect
6. #24967C2semidirect
7. #24966C2semidirect
8. #24965C2semidirect
9. #23642C2semidirect
10. #23480C2semidirect
11. #21190C2semidirect
12. #21171C2semidirect
13. #20912C2semidirect
14. #20764C2semidirect
15. #20702C2semidirect
16. #20646C2semidirect
17. C4×#418C2semidirect
38. #2354C22semidirect
39. #2354C22semidirect
40. #2352C22semidirect
41. #2352C22semidirect
42. D4×C4⋊C4C22semidirect
43. D4×C4⋊C4C22semidirect
56. #2077C22semidirect
57. #2077C22semidirect
58. #2076C22semidirect
59. #2075C22semidirect
60. #2034C22semidirect
61. #2034C22semidirect
62. #2033C22semidirect
63. #2033C22semidirect
64. #1955C22semidirect
65. #1954C22semidirect
66. #1954C22semidirect
67. #1948C22semidirect
68. #1948C22semidirect
69. #1947C22semidirect
70. #1947C22semidirect
71. #1875C22semidirect
72. #1875C22semidirect
73. #1874C22semidirect
74. #1874C22semidirect
75. #1836C22semidirect
76. #1834C22semidirect
77. #1834C22semidirect
78. #1825C22semidirect
79. #1825C22semidirect
80. #1824C22semidirect
81. #1823C22semidirect
82. #1804C22semidirect
83. #1802C22semidirect
84. #1802C22semidirect
85. #1762C22semidirect
86. #1762C22semidirect
87. C4×#102C22semidirect
88. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
C2×#25372
D4×#1172
#249822
#249812
#249682
#249672
#249662
#249652
#236422
#234802
#211902
#211712
#209122
#207642
#207022
#206462
C4×#4182