Finite Group Databasebeta

← #10576235

Subgroups — #10576235

Order 512.

6251 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62854C211yesmaximal, characteristic, complemented
2#62843C211yesmaximal, characteristic, complemented
3#61385C218yesmaximal, complemented
4#61385C218yesmaximal, complemented
5#61382C218yesmaximal, complemented
6#61381C218yesmaximal, complemented
7#61378C214yesmaximal, complemented
8#61377C214yesmaximal, complemented
9#61371C214yesmaximal, complemented
10#61370C214yesmaximal, complemented
11#60664C212yesmaximal, complemented
12#60660C211yesmaximal, characteristic, complemented
13#60492C211yesmaximal, characteristic, complemented
14#60490C211yesmaximal, characteristic, complemented
15#60489C212yesmaximal, complemented
16C2×#3081C212yesmaximal, complemented
17#60193C211yesmaximal, characteristic, complemented
18#60168C212yesmaximal
19C2×#2946C211yesmaximal, characteristic
20C22×AGL(1,ℤ/8)C2211yescharacteristic
21#3504—24no—
22#3504C2218yescomplemented
23#3503—24no—
24#3503C2218yescomplemented
25#3502C2214yescomplemented
26#3501—22no—
27#3501—22no—
28#3501—24no—
29#3501—24no—
30#3501—24no—
31#3501C2214yes—
32#3501C2214yes—
33#3501C2218yescomplemented
34#3501C2218yescomplemented
35#3501C2214yescomplemented
36#3458—22no—
37#3458C2212yes—
38#3458C2211yescharacteristic
39#3458C2211yescharacteristic
40#3458C2211yescharacteristic
41C2×#544—22no—
42C2×#544C2212yes—
43C2×#543—24no—
44#3428C2212yes—
45C2×#520C2211yescharacteristic
46C2×#518C2212yes—
47C2×#518C2211yescharacteristic
48#3389C22116yescomplemented
49#3389C22116yescomplemented
50#3389C22116yescomplemented
51#3388C22116yescomplemented
52#3388C22116yescomplemented
53#3388C22116yescomplemented
54#3386C2218yescomplemented
55#3386C22116yescomplemented
56#3385C2218yescomplemented
57#3385C22116yescomplemented
58#3384C2218yescomplemented
59#3384C22116yescomplemented
60#3384C2218yescomplemented
61#3384C22116yescomplemented
62#3381C22116yescomplemented
63#3381C2218yescomplemented
64#3380C22116yescomplemented
65#3380C2218yescomplemented
66Q8×SD16C2218yescomplemented
67Q8×D8C2218yescomplemented
68#3166C2218yescomplemented
69#3165C2218yescomplemented
70#3164C2218yescomplemented
71#3164C2214yescomplemented
72#3164C2218yescomplemented
73#3164C2214yescomplemented
74#3163C2218yescomplemented
75#3163C2214yescomplemented
76#3163C2218yescomplemented
77#3163C2214yescomplemented
78#3162C2214yescomplemented
79#3160C2214yescomplemented
80#3084C2214yescomplemented
81#3084C2214yescomplemented
82#3084C2218yescomplemented
83#3083C2214yescomplemented
84#3083C2214yescomplemented
85#3083C2218yescomplemented
86#3082C2214yescomplemented
87#3082C2214yescomplemented
88#3081C2218yes—
89#3081C2218yes—
90#3081C2218yescomplemented
91#3081C2218yescomplemented
92#3081C2218yescomplemented
93#3081C2218yescomplemented
94#3081C2214yescomplemented
95#3081C2214yescomplemented
96#3078C2214yescomplemented
97#3077C2214yes—
98#3077C2214yes—
99#3077C2214yescomplemented
100#3076C2218yescomplemented
101#3076C2218yescomplemented
102C2×#478C2214yescomplemented
103C2×#478C2214yescomplemented
104C2×#476C2214yescomplemented
105C2×#474C2214yescomplemented
106#2962C2218yescomplemented
107#2962C2218yescomplemented
108#2961C2214yescomplemented
109#2960C2214yescomplemented
110#2949C2218yes—
111#2948C2218yes—
112#2946C2218yes—
113#2946C2218yes—
114#2946C2218yes—
115#2946C2218yes—
116C4×AGL(1,ℤ/8)C2218yes—
117C4×AGL(1,ℤ/8)C2218yes—
118C2×#442C2212yes—
119C2×#440C2212yes—
120C2×C4×SD16C2212yes—
121C2×C4×D8C2212yes—
122#2911C2212yes—
123#2911C2212yes—
124C2×#428C2212yes—
125C2×#428C2211yescharacteristic
126C2×#427C2212yes—
127#2905C2211yescharacteristic
128C2×#424C2212yes—
129#2896C2212yes—
130C2×#418C2212yes—
131C2×#416C2211yescharacteristic
132C22×#102C2211yescharacteristic
133#2873C2212yes—
134C2×#405C2211yescharacteristic
135C22×#41C2311yescharacteristic
136C23×D4C2311yescharacteristic
137C2×AGL(1,ℤ/8)Q8116yescomplemented
138C2×AGL(1,ℤ/8)C2318yes—
139C22×SD16C2312yes—
140C22×D8C2312yes—
141C22×M16C2312yes—
142C22×M16C2311yescharacteristic
143C23×C8C2311yescharacteristic
144Q82—24no—
145Q82C2318yescomplemented
146#557—24no—
147#557—28no—
148#557C23116yescomplemented
149#557C2318yescomplemented
150#554—24no—
151#554—24no—
152#554—28no—
153#554—28no—
154#554—24no—
155#554—28no—
156#554—28no—
157#554—28no—
158#554—28no—
159#554—28no—
160#554—28no—
161#554—28no—
162#554—216no—
163#554—216no—
164#554—216no—
165#554C2318yes—
166#554C23116yes—
167#554C23116yes—
168#554C2318yes—
169#554C23116yescomplemented
170#554C2318yescomplemented
171D4×Q8—24no—
172D4×Q8—24no—
173D4×Q8—28no—
174D4×Q8—28no—
175D4×Q8—24no—
176D4×Q8—216no—
177D4×Q8C2318yes—
178D4×Q8C2318yes—
179D4×Q8C2318yescomplemented
180#544—28no—
181#544—28no—
182#544—28no—
183#544—28no—
184#544—28no—
185#544—24no—
186#544—24no—
187#544—21no—
188#544—21no—
189#544—21no—
190#544—21no—
191#544—22no—
192#544—22no—
193#544D412yes—
194#544D412yes—
195#544D414yes—
196#544D414yes—
197#544C2318yes—
198#544C2318yes—
199#544C2314yes—
200#544C2314yes—
201#544C2314yes—
202#544C2314yes—
203#544C2314yes—
204#544C2314yes—
205#544C2314yes—
206#544C2314yes—
207#543—28no—
208#543—28no—
209#543—216no—
210#543—216no—
211#543—28no—
212#543—22no—
213#543—24no—
214#543—22no—
215#543D414yes—
216#533—28no—
217#533—28no—
218#533—28no—
219#533—24no—
220#533—24no—
221#533—24no—
222#533—24no—
223#533C2318yes—
224#533C2314yes—
225#533C2314yes—
226#533C2314yes—
227#533C2318yes—
228C2×C4⋊Q8—28no—
229C2×C4⋊Q8—22no—
230C2×C4⋊Q8C2314yes—
231C2×#125—28no—
232C2×#125—22no—
233C2×#125C2314yes—
234C2×C22⋊Q8—28no—
235C2×C22⋊Q8—28no—
236C2×C22⋊Q8—216no—
237C2×C22⋊Q8—216no—
238C2×C22⋊Q8—28no—
239C2×C22⋊Q8—24no—
240#520—24no—
241#520—22no—
242#520—22no—
243#520C2318yes—
244#520C2314yes—
245#520C2314yes—
246#519C2314yes—
247#518—24no—
248#518—24no—
249#518—24no—
250#518—24no—
251#518C2318yes—
252#518C2318yes—
253#518C2318yes—
254#518C2314yes—
255C4×#41—24no—
256C4×#41C2318yes—
257C2×C4×Q8C2312yes—
258C2×C4×D4—21no—
259C2×C4×D4—21no—
260C2×C4×D4—22no—
261C2×C4×D4—22no—
262C2×C4×D4—22no—
263C2×C4×D4C2314yes—
264C2×C4×D4C2314yes—
265C2×C4×D4C2312yes—
266C2×C4×D4C2312yes—
267C2×C4×D4C2312yes—
268C2×#117—24no—
269C2×#117—21no—
270C2×#117C2311yescharacteristic
271C2×#117C2312yes—
272C2×#117C2312yes—
273C2×#117C2311yescharacteristic
274C2×#117C2312yes—
275C22×C4⋊C4—21no—
276C22×C4⋊C4C2311yescharacteristic
277C22×C22⋊C4—22no—
278C22×C22⋊C4—24no—
279#501C2318yescomplemented
280#501C2318yescomplemented
281#501C23116yescomplemented
282#501C23116yescomplemented
283#501C23116yescomplemented
284#501C23116yescomplemented
285#501C2318yescomplemented
286#501C2318yescomplemented
287#500C2314yescomplemented
288#500C23116yescomplemented
289#500C2314yescomplemented
290#499C2318yescomplemented
291#499C23116yescomplemented
292#499C2318yescomplemented
293#499C23116yescomplemented
294#498C2314yescomplemented
295#498C23116yescomplemented
296#498C2314yescomplemented
297#479C2318yescomplemented
298#479C2318yescomplemented
299#479C2318yescomplemented
300#479C2318yescomplemented
301#479C23116yescomplemented
302#478C23116yes—
303#478C23116yes—
304#478C23116yes—
305#478C23116yes—
306#478C23116yes—
307#478C23116yes—
308#478C2318yescomplemented
309#478C2318yescomplemented
310#478C2318yescomplemented
311#478C2318yescomplemented
312#478C23116yescomplemented
313#477C2318yescomplemented
314#477C2318yescomplemented
315#477C2318yescomplemented
316#476C2318yes—
317#476C2318yes—
318#476C23116yes—
319#476C23116yes—
320#476C2318yescomplemented
321#476C2318yescomplemented
322#476C2318yescomplemented
323#475C2318yescomplemented
324#475C2318yescomplemented
325#475C2318yescomplemented
326#474C2318yes—
327#474C2318yes—
328#474C23116yes—
329#474C23116yes—
330#474C2318yescomplemented
331#474C2318yescomplemented
332#474C2318yescomplemented
333#446C2318yescomplemented
334#446C23116yescomplemented
335#446C23116yescomplemented
336#446C2318yescomplemented
337C8×Q8C2318yescomplemented
338C8×Q8C2318yescomplemented
339#442C23116yes—
340#442C23116yes—
341#442C23116yes—
342#440C23116yes—
343#440C23116yes—
344#440C23116yes—
345C4×SD16C23116yes—
346C4×SD16C2318yes—
347C4×SD16C2318yes—
348C4×SD16C23116yes—
349C4×D8C23116yes—
350C4×D8C2318yes—
351C4×D8C2318yes—
352C4×D8C23116yes—
353#428C2314yes—
354#428C2314yes—
355#428C2318yes—
356#428C2314yes—
357#428C2318yes—
358#428C2314yes—
359#428C2314yes—
360#428C2314yes—
361#428C2314yes—
362#428C2318yes—
363#428C2314yes—
364#427C2314yes—
365#427C2318yes—
366#427C2314yes—
367#427C2314yes—
368#427C2314yes—
369#427C2318yes—
370C2×#107C2312yes—
371C2×#107C2314yes—
372C2×#107C2312yes—
373C2×#107C2312yes—
374C2×#106C2312yes—
375C2×#106C2314yes—
376C2×#106C2312yes—
377C2×#106C2312yes—
378#424C2314yes—
379#424C2314yes—
380#424C2314yes—
381#424C2318yes—
382#424C2314yes—
383#423C2314yes—
384C2×C4⋊C8C2314yes—
385C2×C4⋊C8C2314yes—
386#419C2314yes—
387#418C2318yes—
388#418C2314yes—
389#418C2318yes—
390#417C2314yes—
391#417C2314yes—
392#416C2314yes—
393#416C2318yes—
394#416C2314yes—
395C2×#103C2311yescharacteristic
396C2×#103C2311yescharacteristic
397C2×#102C2314yes—
398C2×#102C2314yes—
399C2×#102C2314yes—
400C2×#102C2312yes—
401C2×#102C2312yes—
402C2×#102C2311yescharacteristic
403C2×#102C2311yescharacteristic
404C2×#102C2314yes—
405#405C2314yes—
406#405C2314yes—
407#405C2318yes—
408#405C2318yes—
409C4×M16C2318yes—
410C2×#97C2312yes—
411C2×C4×C8C2312yes—
412C25—21no—
413C2×#41—22no—
414C2×#41—24no—
415C2×#41C2×Q818yescomplemented
416C2×#41C2414yes—
417C22×Q8—28no—
418C22×Q8—28no—
419C22×Q8—28no—
420C22×Q8—24no—
421C22×Q8C2411yescharacteristic
422C22×D4—21no—
423C22×D4—22no—
424C22×D4—21no—
425C22×D4—24no—
426C22×D4C2×Q818yescomplemented
427C22×D4C2411yescharacteristic
428C22×D4C2412yes—
429C22×D4C2414yes—
430C23×C4—21no—
431C23×C4—21no—
432C23×C4—22no—
433C23×C4—24no—
434C23×C4—24no—
435C23×C4—22no—
436C23×C4—22no—
437C23×C4C2411yescharacteristic
438AGL(1,ℤ/8)C2×Q8164yescomplemented
439C2×SD16C2×Q8116yescomplemented
440C2×SD16C2418yes—
441C2×D8C2×Q8116yescomplemented
442C2×D8C2418yes—
443C2×M16—28no—
444C2×M16C2×Q818yescomplemented
445C2×M16C2414yes—
446C2×M16C2414yes—
447C2×M16C2414yes—
448C22×C8—24no—
449C22×C8C2411yescharacteristic
450C22×C8C2411yescharacteristic
451C22×C8C2412yes—
452C22×C8C2412yes—
453C22×C8C2414yes—
454C22×C8C2412yes—
455C4⋊Q8—216no—
456C4⋊Q8—28no—
457C4⋊Q8—28no—
458C4⋊Q8—24no—
459C4⋊Q8—216no—
460C4⋊Q8—28no—
461C4⋊Q8—24no—
462C4⋊Q8—28no—
463C4⋊Q8—24no—
464C4⋊Q8—24no—
465C4⋊Q8—24no—
466C4⋊Q8—24no—
467C4⋊Q8—24no—
468C4⋊Q8—24no—
469C4⋊Q8—28no—
470C4⋊Q8C2×D418yes—
471C4⋊Q8C2×D418yes—
472C4⋊Q8C2×D414yes—
473C4⋊Q8C2×D414yes—
474C4⋊Q8C24116yes—
475C4⋊Q8C2414yes—
476C4⋊Q8C2418yes—
477C4⋊Q8C2418yes—
478C4⋊Q8C2414yes—
479C4⋊Q8C2414yes—
480C4⋊Q8C2414yes—
481#125—28no—
482#125—24no—
483#125—216no—
484#125—216no—
485#125—28no—
486#125—24no—
487#125—216no—
488#125—24no—
489#125—24no—
490#125—24no—
491#125—24no—
492#125—24no—
493#125—24no—
494#125—28no—
495#125C2×D418yes—
496#125C2×D418yes—
497#125C2×D418yes—
498#125C24116yes—
499#125C2418yes—
500#125C2418yes—
501#125C2418yes—
502#125C2418yes—
503C22⋊Q8—28no—
504C22⋊Q8—216no—
505C22⋊Q8—28no—
506C22⋊Q8—216no—
507C22⋊Q8—28no—
508C22⋊Q8—216no—
509C22⋊Q8—24no—
510C22⋊Q8—28no—
511C22⋊Q8—28no—
512C22⋊Q8—24no—
513C22⋊Q8—24no—
514C22⋊Q8—24no—
515C22⋊Q8—216no—
516C22⋊Q8—216no—
517C22⋊Q8—216no—
518C22⋊Q8—216no—
519C22⋊Q8—216no—
520C22⋊Q8—216no—
521C22⋊Q8—28no—
522C22⋊Q8—216no—
523C22⋊Q8—216no—
524C22⋊Q8—28no—
525C22⋊Q8—216no—
526C22⋊Q8—28no—
527C22⋊Q8—216no—
528C22⋊Q8—216no—
529C22⋊Q8—216no—
530C22⋊Q8—28no—
531C22⋊Q8—28no—
532C22⋊Q8—28no—
533C22⋊Q8—28no—
534C22⋊Q8—28no—
535C22⋊Q8—28no—
536C22⋊Q8—216no—
537C22⋊Q8—216no—
538C22⋊Q8—28no—
539C22⋊Q8—28no—
540C22⋊Q8C2×D418yes—
541C22⋊Q8C2×D418yes—
542C22⋊Q8C2×D4116yes—
543C22⋊Q8C2×D4116yes—
544C4×Q8—28no—
545C4×Q8—24no—
546C4×Q8—24no—
547C4×Q8—216no—
548C4×Q8—28no—
549C4×Q8—24no—
550C4×Q8—28no—
551C4×Q8—28no—
552C4×Q8—24no—
553C4×Q8—24no—
554C4×Q8—24no—
555C4×Q8—24no—
556C4×Q8C2418yes—
557C4×Q8C2418yes—
558C4×Q8C2418yes—
559C4×Q8C2418yes—
560C4×Q8C2418yes—
561C4×D4—28no—
562C4×D4—28no—
563C4×D4—28no—
564C4×D4—28no—
565C4×D4—28no—
566C4×D4—28no—
567C4×D4—28no—
568C4×D4—28no—
569C4×D4—24no—
570C4×D4—24no—
571C4×D4—216no—
572C4×D4—28no—
573C4×D4—28no—
574C4×D4—28no—
575C4×D4—28no—
576C4×D4—24no—
577C4×D4—24no—
578C4×D4—24no—
579C4×D4C2418yes—
580C4×D4C24116yes—
581C4×D4C24116yes—
582C4×D4C2418yes—
583C4×D4C2418yes—
584C4×D4C2418yes—
585C4×D4C2418yes—
586#117—22no—
587#117—22no—
588#117—22no—
589#117—22no—
590#117—22no—
591#117—28no—
592#117—24no—
593#117—24no—
594#117—28no—
595#117—28no—
596#117C2×D414yes—
597#117C2×D414yes—
598#117C2×D414yes—
599#117C2414yes—
600#117C2414yes—
601#117C2414yes—
602#117C2414yes—
603#117C2414yes—
604#117C2414yes—
605#117C2414yes—
606#117C2414yes—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—24no—
611C2×C4⋊C4—24no—
612C2×C4⋊C4—24no—
613C2×C4⋊C4—28no—
614C2×C4⋊C4—24no—
615C2×C4⋊C4—24no—
616C2×C4⋊C4—28no—
617C2×C4⋊C4—216no—
618C2×C4⋊C4—216no—
619C2×C4⋊C4—28no—
620C2×C4⋊C4—28no—
621C2×C4⋊C4—216no—
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2×D412yes—
625C2×C4⋊C4C2×D412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—22no—
638C2×C22⋊C4—24no—
639C2×C22⋊C4—24no—
640C2×C22⋊C4—22no—
641C2×C22⋊C4—22no—
642C2×C22⋊C4—216no—
643C2×C22⋊C4—216no—
644C2×C22⋊C4—216no—
645C2×C22⋊C4—28no—
646C2×C22⋊C4C2×D412yes—
647C2×C22⋊C4C2×D414yes—
648C2×C42—22no—
649C2×C42—22no—
650C2×C42—21no—
651C2×C42—22no—
652C2×C42—28no—
653C2×C42C2412yes—
654C2×C42C2414yes—
655#107C2414yes—
656#107C2414yes—
657#107C2414yes—
658#107C2414yes—
659#107C2418yes—
660#107C24116yes—
661#107C2418yes—
662#107C2418yes—
663#107C2418yes—
664#107C2418yes—
665#106C2414yes—
666#106C2414yes—
667#106C2414yes—
668#106C2414yes—
669#106C2418yes—
670#106C24116yes—
671#106C2418yes—
672#106C2418yes—
673#106C2418yes—
674#106C2418yes—
675C4⋊C8C2418yes—
676C4⋊C8C2418yes—
677C4⋊C8C2418yes—
678C4⋊C8C2418yes—
679C4⋊C8C2418yes—
680C4⋊C8C2418yes—
681#103C2412yes—
682#103C2412yes—
683#103C2414yes—
684#103C2418yes—
685#103C2418yes—
686#102C2414yes—
687#102C2414yes—
688#102C2418yes—
689#102C2412yes—
690#102C2412yes—
691#102C2414yes—
692#102C24116yes—
693#102C24116yes—
694#102C2418yes—
695#102C2418yes—
696#97C2418yes—
697#97C24116yes—
698C4×C8C2414yes—
699C4×C8C2414yes—
700C4×C8C24116yes—
701C24—21no—
702C24—22no—
703C24—24no—
704C24—28no—
705C24—161no—
706C24—161no—
707C24C22×D411yescharacteristic
708#41—216no—
709#41—28no—
710#41C22×Q8116yes—
711C2×Q8—21no—
712C2×Q8—24no—
713C2×Q8—24no—
714C2×Q8—28no—
715C2×Q8—28no—
716C2×Q8—24no—
717C2×Q8—24no—
718C2×Q8—216no—
719C2×Q8—22no—
720C2×Q8—164no—
721C2×Q8—168no—
722C2×Q8—168no—
723C2×Q8—168no—
724C2×Q8C22×D418yes—
725C2×Q8C22×D418yes—
726C2×Q8C22×Q814yes—
727C2×Q8C2512yes—
728C2×D4—28no—
729C2×D4—24no—
730C2×D4—28no—
731C2×D4—216no—
732C2×D4—22no—
733C2×D4—24no—
734C2×D4—21no—
735C2×D4—28no—
736C2×D4—24no—
737C2×D4—22no—
738C2×D4C22×Q814yes—
739C2×D4C22×Q818yes—
740C2×D4C22×Q8116yes—
741C2×D4C2512yes—
742C2×D4C2514yes—
743C22×C4—21no—
744C22×C4—28no—
745C22×C4—24no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—24no—
754C22×C4—28no—
755C22×C4—28no—
756C22×C4—28no—
757C22×C4—216no—
758C22×C4—216no—
759C22×C4—28no—
760C22×C4—28no—
761C22×C4—162no—
762C22×C4—162no—
763C22×C4—164no—
764C22×C4—162no—
765C22×C4—164no—
766C22×C4—161no—
767C22×C4C22×D412yes—
768C22×C4C22×D414yes—
769C22×C4C22×D414yes—
770C22×C4C22×D412yes—
771C22×C4C22×D412yes—
772C22×C4C22×D411yescharacteristic
773C22×C4C22×Q814yes—
774C22×C42−1+414yes—
775C22×C4C2512yes—
776C22×C4C2511yescharacteristic
777SD16C22×Q8132yes—
778D8C22×Q8132yes—
779M16—28no—
780M16—28no—
781M16C22×Q8116yes—
782C2×C8—24no—
783C2×C8—24no—
784C2×C8—22no—
785C2×C8—22no—
786C2×C8—28no—
787C2×C8C22×Q818yes—
788C2×C8C2511yescharacteristic
789C2×C8C2511yescharacteristic
790C2×C8C2518yes—
791C2×C8C2512yes—
792C2×C8C2514yes—
793C4⋊C4—24no—
794C4⋊C4—28no—
795C4⋊C4—22no—
796C4⋊C4—22no—
797C4⋊C4—22no—
798C4⋊C4—24no—
799C4⋊C4—28no—
800C4⋊C4—28no—
801C4⋊C4—24no—
802C4⋊C4—28no—
803C4⋊C4—28no—
804C4⋊C4—28no—
805C4⋊C4—28no—
806C4⋊C4—28no—
807C4⋊C4—28no—
808C4⋊C4—24no—
809C4⋊C4—216no—
810C4⋊C4—216no—
811C4⋊C4—28no—
812C4⋊C4—216no—
813C4⋊C4—28no—
814C4⋊C4—28no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—22no—
818C4⋊C4—22no—
819C4⋊C4—28no—
820C4⋊C4—24no—
821C4⋊C4C22×D414yes—
822C4⋊C4C22×D418yes—
823C4⋊C4C22×D4116yes—
824C4⋊C4C22×D414yes—
825C4⋊C4C22×D414yes—
826C4⋊C4C22×D4116yes—
827C4⋊C4C22×D418yes—
828C4⋊C4C22×D414yes—
829C4⋊C4C22×D414yes—
830C4⋊C4C22×D414yes—
831C4⋊C4C2514yes—
832C4⋊C4C2514yes—
833C4⋊C4C2514yes—
834C4⋊C4C2512yes—
835C4⋊C4C2514yes—
836C4⋊C4C2512yes—
837C4⋊C4C2514yes—
838C22⋊C4—24no—
839C22⋊C4—24no—
840C22⋊C4—24no—
841C22⋊C4—24no—
842C22⋊C4—24no—
843C22⋊C4—28no—
844C22⋊C4—216no—
845C22⋊C4—216no—
846C22⋊C4—28no—
847C22⋊C4—28no—
848C22⋊C4—28no—
849C22⋊C4—28no—
850C22⋊C4C22×D418yes—
851C22⋊C4C22×D418yes—
852C22⋊C4C22×D418yes—
853C42—24no—
854C42—28no—
855C42—28no—
856C42—28no—
857C42—24no—
858C42—24no—
859C42—24no—
860C42—24no—
861C42C22×D418yes—
862C42C22×D414yes—
863C42C2514yes—
864C42C2518yes—
865C23—22no—
866C23—24no—
867C23—24no—
868C23—28no—
869C23—216no—
870C23—41no—
871C23—41no—
872C23—81no—
873C23—84no—
874C23—82no—
875C23—84no—
876C23—82no—
877C23—81no—
878C23—168no—
879C23D4×Q814yes—
880C23C23×D411yescharacteristic
881C23C23×D412yes—
882Q8—22no—
883Q8—24no—
884Q8—48no—
885Q8—48no—
886Q8—84no—
887Q8—84no—
888Q8—84no—
889Q8—88no—
890Q8—816no—
891Q8—88no—
892Q8—84no—
893Q8C23×Q814yes—
894D4—216no—
895D4—24no—
896D4—22no—
897D4—216no—
898D4—28no—
899D4—24no—
900D4C23×Q814yes—
901D4C23×Q818yes—
902C2×C4—22no—
903C2×C4—24no—
904C2×C4—216no—
905C2×C4—24no—
906C2×C4—24no—
907C2×C4—24no—
908C2×C4—22no—
909C2×C4—24no—
910C2×C4—22no—
911C2×C4—24no—
912C2×C4—42no—
913C2×C4—44no—
914C2×C4—42no—
915C2×C4—44no—
916C2×C4—88no—
917C2×C4—88no—
918C2×C4—88no—
919C2×C4—816no—
920C2×C4—816no—
921C2×C4—88no—
922C2×C4—88no—
923C2×C4—82no—
924C2×C4—82no—
925C2×C4—81no—
926C2×C4—82no—
927C2×C4—82no—
928C2×C4—81no—
929C2×C4—84no—
930C2×C4—82no—
931C2×C4D4×Q814yes—
932C2×C4D4×Q818yes—
933C2×C4C23×D414yes—
934C2×C4C23×D418yes—
935C2×C4C23×D418yes—
936C2×C4C23×D414yes—
937C2×C4C23×D411yescharacteristic
938C2×C4C23×D412yes—
939C2×C4C23×Q812yes—
940C2×C4C23×Q814yes—
941C2×C4C2×2−1+414yes—
942C2×C4C2×2−1+412yes—
943C2×C4C2611yescharacteristic
944C8—21no—
945C8—21no—
946C8—22no—
947C8—28no—
948C8C23×Q818yes—
949C22—22no—
950C22—21no—
951C22—22no—
952C22—21no—
953C22—24no—
954C22—28no—
955C22—44no—
956C22—42no—
957C22—44no—
958C22—44no—
959C22—42no—
960C22—84no—
961C22—88no—
962C22—816no—
963C22C2×D4×Q812yes—
964C22C2×D4×Q814yes—
965C22C24×D411yescharacteristic
966C4—24no—
967C4—28no—
968C4—28no—
969C4—24no—
970C4—24no—
971C4—42no—
972C4—44no—
973C4—44no—
974C4—44no—
975C4—44no—
976C4—42no—
977C4—44no—
978C4C2×D4×Q814yes—
979C4C2×D4×Q812yes—
980C4C24×Q811yescharacteristic
981C4C22×2−1+411yescharacteristic
982C2—22no—
983C2—24no—
984C2—44no—
985C2—48no—
986C2C22×D4×Q811yescharacteristic
987C2#6309111yescharacteristic
988C2#6309211yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
prime radicalC22×AGL(1,ℤ/8)C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #3458 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62854C2semidirect
2. #62843C2semidirect
3. #61385C2semidirect
4. #61385C2semidirect
5. #61382C2semidirect
6. #61381C2semidirect
7. #61378C2semidirect
8. #61377C2semidirect
9. #61371C2semidirect
10. #61370C2semidirect
11. #60664C2semidirect
12. #60660C2semidirect
13. #60492C2semidirect
14. #60490C2semidirect
15. #60489C2semidirect
16. C2×#3081C2semidirect
17. #60193C2semidirect
22. #3504C22semidirect
24. #3503C22semidirect
25. #3502C22semidirect
33. #3501C22semidirect
34. #3501C22semidirect
35. #3501C22semidirect
48. #3389C22semidirect
49. #3389C22semidirect
50. #3389C22semidirect
51. #3388C22semidirect
52. #3388C22semidirect
53. #3388C22semidirect
54. #3386C22semidirect
55. #3386C22semidirect
56. #3385C22semidirect
57. #3385C22semidirect
58. #3384C22semidirect
59. #3384C22semidirect
60. #3384C22semidirect
61. #3384C22semidirect
62. #3381C22semidirect
63. #3381C22semidirect
64. #3380C22semidirect
65. #3380C22semidirect
66. Q8×SD16C22semidirect
67. Q8×D8C22semidirect
68. #3166C22semidirect
69. #3165C22semidirect
70. #3164C22semidirect
71. #3164C22semidirect
72. #3164C22semidirect
73. #3164C22semidirect
74. #3163C22semidirect
75. #3163C22semidirect
76. #3163C22semidirect
77. #3163C22semidirect
78. #3162C22semidirect
79. #3160C22semidirect
80. #3084C22semidirect
81. #3084C22semidirect
82. #3084C22semidirect
83. #3083C22semidirect
84. #3083C22semidirect
85. #3083C22semidirect
86. #3082C22semidirect
87. #3082C22semidirect
90. #3081C22semidirect
91. #3081C22semidirect
92. #3081C22semidirect
93. #3081C22semidirect
94. #3081C22semidirect
95. #3081C22semidirect
96. #3078C22semidirect
99. #3077C22semidirect
100. #3076C22semidirect
101. #3076C22semidirect
102. C2×#478C22semidirect
103. C2×#478C22semidirect
104. C2×#476C22semidirect
105. C2×#474C22semidirect
106. #2962C22semidirect
107. #2962C22semidirect
108. #2961C22semidirect
109. #2960C22semidirect
137. C2×AGL(1,ℤ/8)Q8semidirect
145. Q82C23semidirect
148. #557C23semidirect
149. #557C23semidirect
169. #554C23semidirect
170. #554C23semidirect
179. D4×Q8C23semidirect
279. #501C23semidirect
280. #501C23semidirect
281. #501C23semidirect
282. #501C23semidirect
283. #501C23semidirect
284. #501C23semidirect
285. #501C23semidirect
286. #501C23semidirect
287. #500C23semidirect
288. #500C23semidirect
289. #500C23semidirect
290. #499C23semidirect
291. #499C23semidirect
292. #499C23semidirect
293. #499C23semidirect
294. #498C23semidirect
295. #498C23semidirect
296. #498C23semidirect
297. #479C23semidirect
298. #479C23semidirect
299. #479C23semidirect
300. #479C23semidirect
301. #479C23semidirect
308. #478C23semidirect
309. #478C23semidirect
310. #478C23semidirect
311. #478C23semidirect
312. #478C23semidirect
313. #477C23semidirect
314. #477C23semidirect
315. #477C23semidirect
320. #476C23semidirect
321. #476C23semidirect
322. #476C23semidirect
323. #475C23semidirect
324. #475C23semidirect
325. #475C23semidirect
330. #474C23semidirect
331. #474C23semidirect
332. #474C23semidirect
333. #446C23semidirect
334. #446C23semidirect
335. #446C23semidirect
336. #446C23semidirect
337. C8×Q8C23semidirect
338. C8×Q8C23semidirect
415. C2×#41C2×Q8semidirect
426. C22×D4C2×Q8semidirect
438. AGL(1,ℤ/8)C2×Q8semidirect
439. C2×SD16C2×Q8semidirect
441. C2×D8C2×Q8semidirect
444. C2×M16C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#628542
#628432
#613852
#613822
#613812
#613782
#613772
#613712
#613702
#606642
#606602
#604922
#604902
#604892
C2×#30812
#601932
#601682
C2×#29462