Finite Group Databasebeta

← #6466090

Subgroups — #6466090

Order 512.

2027 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
1#60484C211yesmaximal, characteristic, complemented
2C2×#3077C211yesmaximal, characteristic, complemented
3#60192C211yesmaximal, characteristic, complemented
4C2×C4×AGL(1,ℤ/8)C211yesmaximal, characteristic
5#28299C214yesmaximal, complemented
6#28298C214yesmaximal, complemented
7#28296C214yesmaximal, complemented
8#28295C214yesmaximal, complemented
9#23604C212yesmaximal, complemented
10#23602C212yesmaximal, complemented
11#21249C212yesmaximal
12#21182C212yesmaximal, complemented
13#20806C211yesmaximal, characteristic, complemented
14#20637C211yesmaximal, characteristic, complemented
15C2×#1800C211yesmaximal, characteristic, complemented
16C22×AGL(1,ℤ/8)C2211yescharacteristic
17C2×#533C2211yescharacteristic
18C2×C4×#41C2211yescharacteristic
19C22×C4×D4C2211yescharacteristic
20#3080—22no—
21#3079—21no—
22#3079—21no—
23#3078C2212yescomplemented
24#3078C2212yescomplemented
25#3077—22no—
26#3077—22no—
27#3077C2214yes—
28#3077C2214yes—
29#3077C2212yescomplemented
30#3077C2212yescomplemented
31#3076—22no—
32#3076—22no—
33C2×#478—22no—
34C2×#476—21no—
35C2×#474—21no—
36Q8×M16—22no—
37Q8×M16—22no—
38#2962—22no—
39#2962—22no—
40#2961C2214yescomplemented
41#2960C2214yescomplemented
42C4×AGL(1,ℤ/8)—22no—
43C4×AGL(1,ℤ/8)—22no—
44C4×AGL(1,ℤ/8)—22no—
45C4×AGL(1,ℤ/8)—22no—
46C2×#442C2212yes—
47C2×#440C2212yes—
48C2×C4×SD16C2212yes—
49C2×C4×D8C2212yes—
50C2×#430C2212yes—
51C2×#430C2212yes—
52#2911C2212yes—
53C2×#428C2212yes—
54C2×#428C2211yescharacteristic
55#2905C2212yes—
56C2×#423C2211yescharacteristic
57C2×#423C2211yescharacteristic
58C2×#423C2211yescharacteristic
59#2896C2212yes—
60C2×#417C2211yescharacteristic
61C2×#418C2212yes—
62C2×#418C2211yescharacteristic
63C2×#413C2212yes—
64C22×#100C2212yes—
65#2873C2212yes—
66C2×C4×M16C2211yescharacteristic
67#2064C2218yescomplemented
68#2063C2218yes—
69#2063C2218yes—
70#2063C2218yescomplemented
71#1978C2218yes—
72#1977C2218yes—
73#1952C2218yescomplemented
74#1951C2218yescomplemented
75#1849C2214yescomplemented
76#1848C2214yescomplemented
77#1801C2212yescomplemented
78#1801C2212yescomplemented
79#1800C2214yes—
80#1800C2214yes—
81#1800C2212yescomplemented
82#1800C2212yescomplemented
83#1742C2212yes—
84C2×#343C2212yes—
85C22×#41C2311yescharacteristic
86C23×D4C2311yescharacteristic
87C24×C4—21no—
88C2×AGL(1,ℤ/8)—22no—
89C2×AGL(1,ℤ/8)—22no—
90C2×AGL(1,ℤ/8)—24no—
91C2×AGL(1,ℤ/8)Q818yescomplemented
92C22×SD16C2312yes—
93C22×D8C2312yes—
94C22×M16C2312yes—
95C22×M16C2312yes—
96C22×M16C2312yes—
97C22×M16C2311yescharacteristic
98C22×M16C2311yescharacteristic
99#533—21no—
100#533—21no—
101#533—21no—
102#533—21no—
103#533D412yes—
104#533D412yes—
105#533C2312yes—
106#533C2312yes—
107C2×C4⋊Q8D411yescharacteristic
108C2×C4⋊Q8D411yescharacteristic
109C2×#125D412yes—
110C2×C22⋊Q8—21no—
111C2×C22⋊Q8—21no—
112C4×#41—21no—
113C4×#41—21no—
114C4×#41—21no—
115C4×#41—21no—
116C4×#41—21no—
117C4×#41—21no—
118C4×#41—21no—
119C4×#41—21no—
120C2×C4×Q8—21no—
121C2×C4×Q8—21no—
122C2×C4×Q8C2311yescharacteristic
123C2×C4×Q8C2311yescharacteristic
124C2×C4×D4—21no—
125C2×C4×D4—21no—
126C2×C4×D4—21no—
127C2×C4×D4—21no—
128C2×C4×D4—21no—
129C2×C4×D4—21no—
130C2×C4×D4—21no—
131C2×C4×D4—21no—
132C2×C4×D4—21no—
133C2×C4×D4—21no—
134C2×C4×D4—21no—
135C2×C4×D4—21no—
136C2×C4×D4C2312yes—
137C2×C4×D4C2312yes—
138C2×C4×D4C2311yescharacteristic
139C2×C4×D4C2311yescharacteristic
140C2×#117—21no—
141C2×#117C2312yes—
142C2×#117C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C22⋊C4—21no—
145C22×C42—21no—
146C22×C42C2311yescharacteristic
147#479—24no—
148#479—24no—
149#478—28no—
150#478—28no—
151#478—24no—
152#478—24no—
153#477—22no—
154#477—22no—
155#476—22no—
156#476—22no—
157#476—24no—
158#476—24no—
159#475—22no—
160#475—22no—
161#474—22no—
162#474—22no—
163#474—24no—
164#474—24no—
165#446—28no—
166#446—28no—
167#446—24no—
168#446—24no—
169C8×Q8—24no—
170C8×Q8—24no—
171#442—24no—
172#442—24no—
173#440—24no—
174#440—24no—
175C4×SD16—24no—
176C4×SD16—24no—
177C4×D8—24no—
178C4×D8—24no—
179#430—28no—
180#430—44no—
181C2×#108C2318yes—
182C2×#108C2318yes—
183#428—22no—
184#428—22no—
185#428—24no—
186#428—22no—
187#428—22no—
188#428C2318yes—
189#428C2314yes—
190#428C2314yes—
191#427—24no—
192C2×#107—22no—
193C2×#107C2312yes—
194C2×#106—22no—
195C2×#106C2312yes—
196#424—24no—
197#424C2318yes—
198#423—24no—
199#423—21no—
200#423—21no—
201#423—21no—
202#423—21no—
203#423—21no—
204#423—21no—
205#423C2312yes—
206#423C2312yes—
207#423C2312yes—
208#423C2312yes—
209#423C2312yes—
210#423C2312yes—
211C2×C4⋊C8—21no—
212C2×C4⋊C8—21no—
213C2×C4⋊C8—21no—
214C2×C4⋊C8—21no—
215C2×C4⋊C8—21no—
216C2×C4⋊C8—21no—
217#419C2314yes—
218#418—22no—
219#418—22no—
220#418—24no—
221#418C2318yes—
222#418C2314yes—
223#417—22no—
224#417—22no—
225#417—22no—
226#417—22no—
227#416—24no—
228C2×#103C2312yes—
229C2×#102—22no—
230C2×#102—22no—
231C2×#102C2312yes—
232C2×#102C2312yes—
233C2×#102C2312yes—
234#413—44no—
235C2×#101C2314yes—
236C2×#100—44no—
237C2×#100C2318yes—
238C2×#100C2314yes—
239#405—24no—
240#405C2318yes—
241C4×M16—24no—
242C4×M16D412yes—
243C4×M16D412yes—
244C4×M16D412yes—
245C4×M16D412yes—
246C2×#97C2312yes—
247C2×C4×C8C2312yes—
248#343C2318yes—
249#343C2314yes—
250#343C2314yes—
251C25—21no—
252C2×#41—22no—
253C2×#41—21no—
254C2×#41—21no—
255C2×#41—21no—
256C2×#41—21no—
257C2×#41—22no—
258C2×#41—22no—
259C2×#41C2×Q814yes—
260C22×Q8—21no—
261C22×Q8—21no—
262C22×Q8C2411yescharacteristic
263C22×D4—21no—
264C22×D4—21no—
265C22×D4—21no—
266C22×D4—21no—
267C22×D4—21no—
268C22×D4—22no—
269C22×D4—21no—
270C22×D4—22no—
271C22×D4—22no—
272C22×D4C2×Q814yes—
273C22×D4C2411yescharacteristic
274C22×D4C2412yes—
275C23×C4—21no—
276C23×C4—21no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—21no—
280C23×C4—21no—
281C23×C4—41no—
282C23×C4—41no—
283C23×C4—41no—
284C23×C4—41no—
285C23×C4—84no—
286C23×C4#4111yescharacteristic
287C23×C4#4111yescharacteristic
288C23×C4C2411yescharacteristic
289AGL(1,ℤ/8)—216no—
290AGL(1,ℤ/8)—216no—
291C2×SD16—24no—
292C2×SD16—24no—
293C2×SD16C2×Q818yescomplemented
294C2×D8—24no—
295C2×D8—24no—
296C2×D8C2×Q818yescomplemented
297C2×M16—22no—
298C2×M16—22no—
299C2×M16—22no—
300C2×M16—22no—
301C2×M16—22no—
302C2×M16—24no—
303C2×M16—24no—
304C2×M16—24no—
305C2×M16—24no—
306C2×M16—24no—
307C2×M16—24no—
308C2×M16C2×D412yes—
309C2×M16C2×D412yes—
310C2×M16C2×D412yes—
311C2×M16C2×D412yes—
312C2×M16C2×Q814yes—
313C2×M16#4114yes—
314C2×M16C2414yes—
315C2×M16C2414yes—
316C2×M16C2414yes—
317C22×C8—22no—
318C22×C8—22no—
319C22×C8—22no—
320C22×C8C2412yes—
321C22×C8C2412yes—
322C4⋊Q8—21no—
323C4⋊Q8—21no—
324C4⋊Q8—21no—
325C4⋊Q8—21no—
326C4⋊Q8C2×D412yes—
327C4⋊Q8C2×D412yes—
328C4⋊Q8C2×D412yes—
329C4⋊Q8C2×D412yes—
330#125—22no—
331#125—22no—
332#125C2×D414yes—
333#125C2×D414yes—
334C22⋊Q8—22no—
335C22⋊Q8—22no—
336C22⋊Q8—22no—
337C22⋊Q8—22no—
338C22⋊Q8—22no—
339C22⋊Q8—22no—
340C22⋊Q8—22no—
341C22⋊Q8—22no—
342C4×Q8—22no—
343C4×Q8—22no—
344C4×Q8—22no—
345C4×Q8—22no—
346C4×Q8—22no—
347C4×Q8—22no—
348C4×Q8—22no—
349C4×Q8—22no—
350C4×Q8—21no—
351C4×Q8—21no—
352C4×Q8—21no—
353C4×Q8—21no—
354C4×Q8—21no—
355C4×Q8—21no—
356C4×Q8—21no—
357C4×Q8—21no—
358C4×D4—22no—
359C4×D4—22no—
360C4×D4—22no—
361C4×D4—22no—
362C4×D4—22no—
363C4×D4—22no—
364C4×D4—22no—
365C4×D4—22no—
366C4×D4—21no—
367C4×D4—21no—
368C4×D4—21no—
369C4×D4—21no—
370C4×D4—21no—
371C4×D4—21no—
372C4×D4—21no—
373C4×D4—21no—
374C4×D4—41no—
375C4×D4—41no—
376C4×D4—41no—
377C4×D4—41no—
378C4×D4—41no—
379C4×D4—41no—
380C4×D4—41no—
381C4×D4—41no—
382C4×D4—41no—
383C4×D4—41no—
384C4×D4—41no—
385C4×D4—41no—
386C4×D4—41no—
387C4×D4—41no—
388C4×D4—41no—
389C4×D4—41no—
390#117—22no—
391#117—22no—
392#117—21no—
393#117—21no—
394#117—21no—
395#117—21no—
396#117—41no—
397#117—41no—
398#117—41no—
399#117—41no—
400#117C2×D414yes—
401#117C2414yes—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4C2×D412yes—
414C2×C4⋊C4C2×D412yes—
415C2×C4⋊C4C2412yes—
416C2×C4⋊C4C2411yescharacteristic
417C2×C4⋊C4C2411yescharacteristic
418C2×C22⋊C4—22no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—41no—
425C2×C22⋊C4—41no—
426C2×C22⋊C4—41no—
427C2×C22⋊C4—41no—
428C2×C42—22no—
429C2×C42—21no—
430C2×C42—21no—
431C2×C42—21no—
432C2×C42—41no—
433C2×C42—41no—
434C2×C42—41no—
435C2×C42—41no—
436C2×C42C2×D411yescharacteristic
437C2×C42C2×D411yescharacteristic
438C2×C42C2×D411yescharacteristic
439C2×C42C2×D411yescharacteristic
440C2×C42C2×D411yescharacteristic
441C2×C42C2×D411yescharacteristic
442C2×C42C2×D411yescharacteristic
443C2×C42C2×D411yescharacteristic
444C2×C42#4111yescharacteristic
445C2×C42#4111yescharacteristic
446C2×C42C2411yescharacteristic
447C2×C42C2411yescharacteristic
448#108—216no—
449#108—48no—
450#107—24no—
451#107—28no—
452#107—24no—
453#107—24no—
454#106—24no—
455#106—28no—
456#106—24no—
457#106—24no—
458C4⋊C8—28no—
459C4⋊C8—28no—
460C4⋊C8—22no—
461C4⋊C8—22no—
462C4⋊C8—22no—
463C4⋊C8—22no—
464C4⋊C8—22no—
465C4⋊C8—22no—
466C4⋊C8—22no—
467C4⋊C8—22no—
468C4⋊C8—22no—
469C4⋊C8—22no—
470C4⋊C8—22no—
471C4⋊C8—22no—
472#103—24no—
473#103—24no—
474#103—24no—
475#102—24no—
476#102—24no—
477#102—24no—
478#102—28no—
479#102—28no—
480#102—24no—
481#102—24no—
482#101—44no—
483#100—48no—
484#100—44no—
485#97—28no—
486#97C2×D414yes—
487#97C2×D414yes—
488C4×C8—28no—
489C4×C8C2×D414yes—
490C4×C8C2×D414yes—
491C24—24no—
492C24—21no—
493C24—22no—
494C24—41no—
495C24—41no—
496C24—42no—
497C24—82no—
498C24—82no—
499C24C2×#4111yescharacteristic
500#41—24no—
501#41—24no—
502#41—24no—
503#41—24no—
504#41—42no—
505#41—42no—
506#41—42no—
507#41—42no—
508C2×Q8—22no—
509C2×Q8—22no—
510C2×Q8—22no—
511C2×Q8—22no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—82no—
518C2×Q8—82no—
519C2×Q8C22×Q812yes—
520C2×D4—24no—
521C2×D4—24no—
522C2×D4—24no—
523C2×D4—24no—
524C2×D4—24no—
525C2×D4—24no—
526C2×D4—22no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—22no—
530C2×D4—21no—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—21no—
534C2×D4—22no—
535C2×D4—21no—
536C2×D4—41no—
537C2×D4—41no—
538C2×D4—42no—
539C2×D4—41no—
540C2×D4—41no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4C22×Q812yes—
547C2×D4C22×Q814yes—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—42no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—42no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—84no—
570C22×C4—84no—
571C22×C4—82no—
572C22×C4—84no—
573C22×C4—81no—
574C22×C4—84no—
575C22×C4—84no—
576C22×C4—82no—
577C22×C4—84no—
578C22×C4—82no—
579C22×C4#12111yescharacteristic
580C22×C4#12111yescharacteristic
581C22×C4#12111yescharacteristic
582C22×C4#12111yescharacteristic
583C22×C4#12111yescharacteristic
584C22×C4#12111yescharacteristic
585C22×C4#12111yescharacteristic
586C22×C4#12111yescharacteristic
587C22×C4C22×D411yescharacteristic
588C22×C4C22×D411yescharacteristic
589C22×C4C22×D411yescharacteristic
590C22×C4C22×D411yescharacteristic
591C22×C4C22×Q812yes—
592C22×C4C2×#4111yescharacteristic
593C22×C4C2×#4111yescharacteristic
594C22×C4C2×#4111yescharacteristic
595C22×C4C2×#4111yescharacteristic
596C22×C4C2×#4111yescharacteristic
597C22×C4C2×#4112yes—
598C22×C4H(5,𝔽2)12yes—
599C22×C42−1+412yes—
600C22×C4C2511yescharacteristic
601SD16—216no—
602D8—216no—
603M16—24no—
604M16—24no—
605M16—24no—
606M16—24no—
607M16—24no—
608M16—24no—
609M16—24no—
610M16—24no—
611M16—44no—
612M16—44no—
613M16—44no—
614M16C22⋊Q818yes—
615M16C22⋊Q818yes—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—24no—
619C2×C8—24no—
620C2×C8—24no—
621C2×C8—44no—
622C2×C8—44no—
623C2×C8—44no—
624C2×C8C22×D414yes—
625C2×C8C22×D414yes—
626C2×C8C22×Q814yes—
627C2×C8C2×#4114yes—
628C4⋊C4—24no—
629C4⋊C4—24no—
630C4⋊C4—24no—
631C4⋊C4—24no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—41no—
645C4⋊C4—41no—
646C4⋊C4—41no—
647C4⋊C4—41no—
648C4⋊C4—41no—
649C4⋊C4—41no—
650C4⋊C4C22×D414yes—
651C4⋊C4C22×D414yes—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—41no—
655C22⋊C4—41no—
656C22⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—41no—
661C22⋊C4—41no—
662C22⋊C4—41no—
663C22⋊C4—41no—
664C42—24no—
665C42—24no—
666C42—41no—
667C42—41no—
668C42—41no—
669C42—41no—
670C42—41no—
671C42—41no—
672C42#12111yescharacteristic
673C42#12111yescharacteristic
674C42#12111yescharacteristic
675C42#12111yescharacteristic
676C42#12111yescharacteristic
677C42#12111yescharacteristic
678C42#12111yescharacteristic
679C42#12111yescharacteristic
680C42C22×D411yescharacteristic
681C42C22×D411yescharacteristic
682C42C22×D411yescharacteristic
683C42C22×D411yescharacteristic
684C42C22×D411yescharacteristic
685C42C22×D411yescharacteristic
686C42C22×D411yescharacteristic
687C42C22×D411yescharacteristic
688C23—22no—
689C23—24no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—42no—
694C23—41no—
695C23—42no—
696C23—44no—
697C23—44no—
698C23—82no—
699C23—81no—
700C23—81no—
701C23—82no—
702C23—82no—
703C23—82no—
704C23—82no—
705C23—82no—
706C23—88no—
707C23—88no—
708C23C2×#12111yescharacteristic
709C23C2×#12111yescharacteristic
710C23#55412yes—
711C23#55612yes—
712C23C22×#4111yescharacteristic
713Q8—22no—
714Q8—22no—
715Q8—44no—
716Q8—41no—
717Q8—41no—
718Q8—44no—
719Q8—82no—
720Q8—82no—
721D4—22no—
722D4—24no—
723D4—24no—
724D4—22no—
725D4—44no—
726D4—44no—
727D4—42no—
728D4—41no—
729D4—42no—
730D4—41no—
731D4—44no—
732D4—44no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—42no—
755C2×C4—82no—
756C2×C4—82no—
757C2×C4—82no—
758C2×C4—84no—
759C2×C4—84no—
760C2×C4—84no—
761C2×C4—82no—
762C2×C4—82no—
763C2×C4—82no—
764C2×C4—82no—
765C2×C4—82no—
766C2×C4—84no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—82no—
770C2×C4C2×#12111yescharacteristic
771C2×C4C2×#12111yescharacteristic
772C2×C4C2×#12111yescharacteristic
773C2×C4C2×#12111yescharacteristic
774C2×C4C2×#12111yescharacteristic
775C2×C4C2×#12111yescharacteristic
776C2×C4C2×#12111yescharacteristic
777C2×C4C2×#12111yescharacteristic
778C2×C4C2×#12111yescharacteristic
779C2×C4C2×#12111yescharacteristic
780C2×C4C2×C22⋊Q812yes—
781C2×C4C2×C22⋊Q812yes—
782C2×C4#53712yes—
783C2×C4#53712yes—
784C2×C4D4×Q812yes—
785C2×C4D4×Q812yes—
786C2×C4#55012yes—
787C2×C4#55012yes—
788C2×C4#55412yes—
789C2×C4#55612yes—
790C2×C4C23×D411yescharacteristic
791C2×C4C23×D411yescharacteristic
792C2×C4C23×Q811yescharacteristic
793C2×C4C22×#4111yescharacteristic
794C2×C4C2×H(5,𝔽2)11yescharacteristic
795C2×C4C2×2−1+411yescharacteristic
796C8—24no—
797C8—44no—
798C8—44no—
799C8—44no—
800C8C2×C22⋊Q818yes—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—44no—
811C22—82no—
812C22—84no—
813C22—82no—
814C22—88no—
815C22—84no—
816C22—88no—
817C22—82no—
818C22—81no—
819C22—81no—
820C22—82no—
821C22#253812yes—
822C22#253812yes—
823C22C22×#12111yescharacteristic
824C22C2×#55411yescharacteristic
825C22C2×#55611yescharacteristic
826C4—21no—
827C4—21no—
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—21no—
833C4—44no—
834C4—44no—
835C4—42no—
836C4—81no—
837C4—82no—
838C4—81no—
839C4#253812yes—
840C4#253812yes—
841C4#306812yes—
842C4C22×C22⋊Q811yescharacteristic
843C4C2×#53711yescharacteristic
844C4C2×D4×Q811yescharacteristic
845C4C2×#55011yescharacteristic
846C2—21no—
847C2—21no—
848C2—22no—
849C2—22no—
850C2—82no—
851C2—84no—
852C2C2×#253811yescharacteristic
853C2C2×#306811yescharacteristic
854C2#6046911yescharacteristic
subgroupG/H
center, socleC22C22×#121
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×AGL(1,ℤ/8)C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #60484C2semidirect
2. C2×#3077C2semidirect
3. #60192C2semidirect
5. #28299C2semidirect
6. #28298C2semidirect
7. #28296C2semidirect
8. #28295C2semidirect
9. #23604C2semidirect
10. #23602C2semidirect
12. #21182C2semidirect
13. #20806C2semidirect
14. #20637C2semidirect
15. C2×#1800C2semidirect
23. #3078C22semidirect
24. #3078C22semidirect
29. #3077C22semidirect
30. #3077C22semidirect
40. #2961C22semidirect
41. #2960C22semidirect
67. #2064C22semidirect
70. #2063C22semidirect
73. #1952C22semidirect
74. #1951C22semidirect
75. #1849C22semidirect
76. #1848C22semidirect
77. #1801C22semidirect
78. #1801C22semidirect
81. #1800C22semidirect
82. #1800C22semidirect
91. C2×AGL(1,ℤ/8)Q8semidirect
293. C2×SD16C2×Q8semidirect
296. C2×D8C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#604842
C2×#30772
#601922
C2×C4×AGL(1,ℤ/8)2
#282992
#282982
#282962
#282952
#236042
#236022
#212492
#211822
#208062
#206372
C2×#18002