Finite Group Databasebeta

← #6494145

Subgroups — #6494145

Order 512.

1798 conjugacy classes of subgroups.

The subgroup lattice has 899 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3177C211yesmaximal, characteristic, complemented
2C2×#2967C211yesmaximal, characteristic
3#37378C212yesmaximal
4#33214C211yesmaximal, characteristic, complemented
5#33211C211yesmaximal, characteristic, complemented
6#33180C211yesmaximal, characteristic, complemented
7#33176C211yesmaximal, characteristic, complemented
8#29856C212yesmaximal, complemented
9#29852C212yesmaximal, complemented
10#28278C212yesmaximal, complemented
11#28274C211yesmaximal, characteristic, complemented
12#28271C211yesmaximal, characteristic, complemented
13#28238C212yesmaximal, complemented
14#28234C211yesmaximal, characteristic, complemented
15#28232C211yesmaximal, characteristic, complemented
16#24793C212yesmaximal, complemented
17#24791C212yesmaximal, complemented
18#24785C211yesmaximal, characteristic, complemented
19#24785C211yesmaximal, characteristic, complemented
20#24783C211yesmaximal, characteristic, complemented
21#24783C211yesmaximal, characteristic, complemented
22#21873C212yesmaximal, complemented
23#20802C211yesmaximal, characteristic, complemented
24C2×#541C2212yes—
25C2×#529C2211yescharacteristic
26#3177—28no—
27C2×#499C2211yescharacteristic
28C2×#494C2211yescharacteristic
29C2×#491C2212yes—
30C2×#470C2212yes—
31C2×#470C2211yescharacteristic
32C2×#470C2211yescharacteristic
33C2×#470C2211yescharacteristic
34C2×#470C2211yescharacteristic
35C2×#470C2212yes—
36C2×#467C2211yescharacteristic
37C2×#467C2211yescharacteristic
38C2×#467C2212yes—
39#2967—28no—
40C2×#446C2211yescharacteristic
41C2×#446C2211yescharacteristic
42C2×#441C2212yes—
43C2×C4×Q16C2211yescharacteristic
44C2×C4×Q16C2211yescharacteristic
45C2×#436C2211yescharacteristic
46C2×#436C2211yescharacteristic
47C2×#435C2211yescharacteristic
48C2×#435C2211yescharacteristic
49C2×#435C2211yescharacteristic
50C2×#435C2211yescharacteristic
51C2×#433C2211yescharacteristic
52C2×#433C2211yescharacteristic
53C2×#432C2211yescharacteristic
54C2×#428C2212yes—
55C2×#427C2211yescharacteristic
56C22×#106C2211yescharacteristic
57C2×#405C2211yescharacteristic
58C2×#405C2211yescharacteristic
59C2×C4×M16C2211yescharacteristic
60#2857C2212yes—
61#2851C2212yes—
62#2726—22no—
63#2725—22no—
64#2722—22no—
65#2715—22no—
66#2707—22no—
67#2704—22no—
68#2695—22no—
69#2691—22no—
70#2629C2212yes—
71#2621C2212yes—
72#2582C2212yes—
73#2581C2212yes—
74#2538C2212yes—
75#2536C2212yes—
76#2417C2212yes—
77#2417C2212yes—
78#2415C2212yes—
79#2415C2212yes—
80#2317C2212yes—
81#2068C2212yes—
82#2068C2212yes—
83#2068C2212yes—
84#2068C2212yes—
85#2066C2212yes—
86#2066C2212yes—
87#2066C2212yes—
88#2066C2212yes—
89#2036C2212yes—
90#2036C2212yes—
91#2036C2212yes—
92#2036C2212yes—
93#2035C2212yes—
94#2035C2212yes—
95#2035C2212yes—
96#2035C2212yes—
97#1992C2212yes—
98#1991C2212yes—
99#1971C2211yescharacteristic
100#1971C2211yescharacteristic
101#1971C2211yescharacteristic
102#1971C2211yescharacteristic
103#1971C2212yes—
104#1969C2212yes—
105#1960C2212yes—
106#1956C2212yes—
107#1944C2211yescharacteristic
108#1944C2211yescharacteristic
109#1944C2211yescharacteristic
110#1944C2211yescharacteristic
111#1943C2212yes—
112#1941C2212yes—
113#1873C2212yes—
114#1873C2212yes—
115#1872C2212yes—
116#1872C2212yes—
117#1847C2212yes—
118#1847C2212yes—
119#1846C2211yescharacteristic
120#1846C2211yescharacteristic
121#1844C2211yescharacteristic
122#1844C2211yescharacteristic
123#1809C2211yescharacteristic
124#1809C2211yescharacteristic
125#1809C2211yescharacteristic
126#1809C2211yescharacteristic
127#1809C2212yes—
128#1807C2212yes—
129#1805C2212yes—
130#1805C2212yes—
131#1803C2212yes—
132#1803C2212yes—
133C22×Q16C2311yescharacteristic
134C22×Q16C2311yescharacteristic
135C22×Q16C2312yes—
136C22×M16C2311yescharacteristic
137C22×M16C2311yescharacteristic
138C22×M16C2311yescharacteristic
139C22×M16C2311yescharacteristic
140C23×C8C2311yescharacteristic
141C23×C8C2311yescharacteristic
142#541—28no—
143#541—28no—
144C2×C4⋊Q8C2312yes—
145#529—24no—
146#529—24no—
147C2×#126—22no—
148C2×#126—22no—
149C2×#126D411yescharacteristic
150C2×#126D411yescharacteristic
151C2×#125—22no—
152C2×#125—22no—
153C2×#125D411yescharacteristic
154C2×#125C2312yes—
155C2×#124D411yescharacteristic
156C2×#123D411yescharacteristic
157C2×#123D411yescharacteristic
158C2×C22⋊Q8D411yescharacteristic
159C2×C22⋊Q8C2312yes—
160C2×C22⋊Q8C2312yes—
161C2×C22⋊Q8C2312yes—
162C2×C22⋊Q8C2312yes—
163C2×C22⋊Q8C2312yes—
164C2×C22⋊Q8C2312yes—
165C2×#121D411yescharacteristic
166C2×C4×Q8C2312yes—
167C2×C4×Q8C2312yes—
168C2×C4×Q8C2311yescharacteristic
169C2×C4×D4C2311yescharacteristic
170C2×C4×D4C2311yescharacteristic
171C2×C4×D4C2311yescharacteristic
172C2×#117C2312yes—
173C2×#117C2311yescharacteristic
174C2×#117C2311yescharacteristic
175C22×C4⋊C4C2312yes—
176C22×C42C2311yescharacteristic
177#499—24no—
178#494—24no—
179#491—28no—
180#470—28no—
181#470—42no—
182#470—42no—
183#470—42no—
184#470—42no—
185#470—44no—
186#467—24no—
187#467—24no—
188#467—44no—
189#446—24no—
190#446—24no—
191#441—28no—
192C4×Q16—24no—
193C4×Q16—24no—
194#436—24no—
195#436—24no—
196#435—24no—
197#435—24no—
198#435—24no—
199#435—24no—
200#433—24no—
201#433—24no—
202#432—24no—
203#428—44no—
204#427—42no—
205C2×#107C2311yescharacteristic
206C2×#107C2311yescharacteristic
207C2×#107C2312yes—
208C2×#107C2312yes—
209C2×#107C2312yes—
210C2×#106—42no—
211C2×#106C2312yes—
212C2×#106C2312yes—
213C2×#106C2311yescharacteristic
214C2×#106C2311yescharacteristic
215C2×#106C2311yescharacteristic
216C2×#106C2311yescharacteristic
217C2×#106C2312yes—
218C2×#106C2312yes—
219C2×C4⋊C8C2311yescharacteristic
220C2×C4⋊C8C2311yescharacteristic
221C2×C4⋊C8C2311yescharacteristic
222C2×C4⋊C8C2311yescharacteristic
223C2×C4⋊C8C2311yescharacteristic
224C2×C4⋊C8C2311yescharacteristic
225C2×#103C2312yes—
226C2×#103C2312yes—
227C2×#103C2312yes—
228C2×#103C2312yes—
229C2×#103C2312yes—
230C2×#103C2312yes—
231C2×#103C2312yes—
232C2×#103C2312yes—
233C2×#103C2312yes—
234C2×#103C2312yes—
235C2×#103C2312yes—
236C2×#103C2312yes—
237C2×C22⋊C8C2311yescharacteristic
238C2×C22⋊C8C2311yescharacteristic
239C2×C22⋊C8C2311yescharacteristic
240C2×C22⋊C8C2311yescharacteristic
241C2×C22⋊C8C2311yescharacteristic
242C2×C22⋊C8C2311yescharacteristic
243#405—24no—
244#405D418yes—
245C4×M16—24no—
246C2×#97C2311yescharacteristic
247C2×#97C2311yescharacteristic
248C2×#97C2311yescharacteristic
249C2×#97C2311yescharacteristic
250C2×#97C2311yescharacteristic
251C2×#97C2311yescharacteristic
252C2×C4×C8C2311yescharacteristic
253C2×C4×C8C2311yescharacteristic
254C2×C4×C8C2311yescharacteristic
255C2×C4×C8C2311yescharacteristic
256#400—22no—
257#398—22no—
258#398—22no—
259#398—22no—
260#398—22no—
261#398—22no—
262#398—22no—
263#398—22no—
264#398—22no—
265#398—22no—
266#397—22no—
267#397—22no—
268#397—22no—
269#397—22no—
270#396—22no—
271#396—22no—
272#396—22no—
273#396—22no—
274#396—22no—
275#396—22no—
276#395—22no—
277#394—22no—
278#394—22no—
279#394—22no—
280#391—22no—
281#391C2312yes—
282#391C2312yes—
283#391C2312yes—
284#391C2312yes—
285#390—22no—
286#389—22no—
287#389—22no—
288#389—22no—
289#389—22no—
290#389—22no—
291#389—22no—
292#389—22no—
293#389—22no—
294#389C2312yes—
295#389C2312yes—
296#389C2312yes—
297#389C2312yes—
298#388—22no—
299#388—22no—
300#388—22no—
301#388—22no—
302#387—22no—
303#387—22no—
304#387—22no—
305#387—22no—
306#386—22no—
307#386—22no—
308#385—22no—
309#385—22no—
310#385—22no—
311#385—22no—
312#384C2312yes—
313#384C2312yes—
314#382C2312yes—
315#382C2312yes—
316#380—22no—
317#380—22no—
318#380—22no—
319#380—22no—
320#380C2312yes—
321#380C2312yes—
322#380C2312yes—
323#380C2312yes—
324#340C2312yes—
325#340C2312yes—
326#340C2312yes—
327#340C2312yes—
328#340C2312yes—
329#340C2312yes—
330#340C2312yes—
331#340C2312yes—
332C22×Q8C2×D411yescharacteristic
333C22×Q8C2412yes—
334C22×Q8C2412yes—
335C22×D4C2×D411yescharacteristic
336C22×D4C2×D411yescharacteristic
337C22×D4C2×D411yescharacteristic
338C23×C4—22no—
339C23×C4C2×D411yescharacteristic
340C23×C4C2×D411yescharacteristic
341C23×C4C2411yescharacteristic
342C23×C4C2411yescharacteristic
343C23×C4C2411yescharacteristic
344C2×Q16—22no—
345C2×Q16—22no—
346C2×Q16—24no—
347C2×Q16—24no—
348C2×Q16—22no—
349C2×Q16—22no—
350C2×Q16—22no—
351C2×Q16—22no—
352C2×Q16—24no—
353C2×M16—22no—
354C2×M16—22no—
355C2×M16—22no—
356C2×M16—22no—
357C2×M16—22no—
358C2×M16—22no—
359C2×M16—22no—
360C2×M16—22no—
361C2×M16—22no—
362C2×M16—22no—
363C2×M16—22no—
364C2×M16C2×D414yes—
365C22×C8—22no—
366C22×C8—22no—
367C22×C8—22no—
368C22×C8—22no—
369C22×C8—22no—
370C22×C8C2×D414yes—
371C22×C8C2411yescharacteristic
372C22×C8C2411yescharacteristic
373C22×C8C2411yescharacteristic
374C22×C8C2411yescharacteristic
375C22×C8C2411yescharacteristic
376C22×C8C2411yescharacteristic
377C22×C8C2411yescharacteristic
378C22×C8C2411yescharacteristic
379C4⋊Q8—24no—
380C4⋊Q8—24no—
381#126—24no—
382#126—24no—
383#126—48no—
384#126—48no—
385#125—24no—
386#125—24no—
387#125—24no—
388#125—48no—
389#125—48no—
390#124—24no—
391#123—24no—
392#123—24no—
393C22⋊Q8—24no—
394C22⋊Q8—24no—
395C22⋊Q8—24no—
396C22⋊Q8—24no—
397C22⋊Q8—24no—
398C22⋊Q8—42no—
399C22⋊Q8—42no—
400C22⋊Q8—42no—
401C22⋊Q8—42no—
402C22⋊Q8—42no—
403C22⋊Q8—42no—
404C22⋊Q8—42no—
405C22⋊Q8—42no—
406#121—24no—
407C4×Q8—22no—
408C4×Q8—22no—
409C4×Q8—24no—
410C4×Q8—24no—
411C4×Q8—24no—
412C4×Q8—24no—
413C4×D4—22no—
414C4×D4—22no—
415C4×D4—22no—
416C4×D4—22no—
417C4×D4—22no—
418C4×D4—22no—
419#117—22no—
420#117—22no—
421#117—42no—
422#117—42no—
423#117C2×D414yes—
424#117#4114yes—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—42no—
447C2×C4⋊C4—42no—
448C2×C4⋊C4C2×D411yescharacteristic
449C2×C4⋊C4C2×D411yescharacteristic
450C2×C4⋊C4C2×D411yescharacteristic
451C2×C4⋊C4C2×D411yescharacteristic
452C2×C4⋊C4C2×D411yescharacteristic
453C2×C4⋊C4C2×D411yescharacteristic
454C2×C4⋊C4C2×D411yescharacteristic
455C2×C4⋊C4C2×D411yescharacteristic
456C2×C4⋊C4C2×D411yescharacteristic
457C2×C4⋊C4C2×D411yescharacteristic
458C2×C4⋊C4C2412yes—
459C2×C4⋊C4C2412yes—
460C2×C4⋊C4C2412yes—
461C2×C4⋊C4C2412yes—
462C2×C4⋊C4C2412yes—
463C2×C4⋊C4C2412yes—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4C2×D411yescharacteristic
476C2×C22⋊C4C2×D411yescharacteristic
477C2×C22⋊C4C2×D411yescharacteristic
478C2×C22⋊C4C2×D411yescharacteristic
479C2×C22⋊C4C2×D411yescharacteristic
480C2×C22⋊C4C2×D411yescharacteristic
481C2×C22⋊C4C2×D411yescharacteristic
482C2×C22⋊C4C2×D411yescharacteristic
483C2×C22⋊C4C2×D411yescharacteristic
484C2×C22⋊C4C2×D411yescharacteristic
485C2×C42—22no—
486C2×C42—22no—
487C2×C42—22no—
488C2×C42—22no—
489C2×C42—22no—
490C2×C42C2×D411yescharacteristic
491C2×C42C2×D411yescharacteristic
492C2×C42C2411yescharacteristic
493C2×C42C2411yescharacteristic
494C2×C42C2411yescharacteristic
495C2×C42C2411yescharacteristic
496#107—22no—
497#107—22no—
498#107—24no—
499#107—42no—
500#107—42no—
501#106—24no—
502#106—22no—
503#106—22no—
504#106—22no—
505#106—22no—
506#106—24no—
507#106—42no—
508#106—42no—
509C4⋊C8—22no—
510C4⋊C8—22no—
511C4⋊C8—22no—
512C4⋊C8—22no—
513C4⋊C8—22no—
514C4⋊C8—22no—
515#103—24no—
516#103—24no—
517#103—24no—
518#103—24no—
519#103—42no—
520#103—42no—
521#103—42no—
522#103—42no—
523#103—42no—
524#103—42no—
525#103—42no—
526#103—42no—
527C22⋊C8—22no—
528C22⋊C8—22no—
529C22⋊C8—22no—
530C22⋊C8—22no—
531C22⋊C8—22no—
532C22⋊C8—22no—
533#97—22no—
534#97—22no—
535#97—22no—
536#97—22no—
537#97C2×D414yes—
538#97C2×D414yes—
539C4×C8—22no—
540C4×C8—22no—
541C4×C8C2×D414yes—
542C4×C8C2×D414yes—
543#95—22no—
544#95—22no—
545#95—22no—
546#95—22no—
547#95—22no—
548#95—22no—
549#95—22no—
550#95—22no—
551#95—22no—
552#95—22no—
553#95—22no—
554#95—22no—
555#95—22no—
556#95—22no—
557#95—22no—
558#95—22no—
559#95—22no—
560#95—22no—
561#95—22no—
562#95—22no—
563C24C22×D411yescharacteristic
564C24C22×D411yescharacteristic
565C24C22×D411yescharacteristic
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—22no—
572C2×Q8—22no—
573C2×Q8—22no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—22no—
577C2×Q8—22no—
578C2×Q8—22no—
579C2×Q8—42no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—42no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—82no—
615C22×C4—82no—
616C22×C4—82no—
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C22×D411yescharacteristic
626C22×C4C22×D411yescharacteristic
627C22×C4C22×D411yescharacteristic
628C22×C4C22×D412yes—
629C22×C4C2×#4112yes—
630C22×C4C2511yescharacteristic
631Q16—44no—
632Q16—44no—
633Q16—48no—
634M16—28no—
635M16—44no—
636M16—44no—
637M16—44no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—28no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—44no—
656C2×C8C22×D412yes—
657C2×C8C22×D412yes—
658C2×C8C22×D412yes—
659C2×C8C22×D412yes—
660C2×C8H(5,𝔽2)12yes—
661C2×C8H(5,𝔽2)12yes—
662C2×C82−1+412yes—
663C2×C82−1+412yes—
664C4⋊C4—22no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—22no—
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—22no—
680C4⋊C4—22no—
681C4⋊C4—22no—
682C4⋊C4—22no—
683C4⋊C4—22no—
684C4⋊C4—44no—
685C4⋊C4—44no—
686C4⋊C4—44no—
687C4⋊C4—44no—
688C4⋊C4—44no—
689C4⋊C4—44no—
690C4⋊C4—44no—
691C4⋊C4—44no—
692C4⋊C4—44no—
693C4⋊C4—82no—
694C4⋊C4—82no—
695C4⋊C4—82no—
696C4⋊C4—82no—
697C4⋊C4—82no—
698C4⋊C4—82no—
699C4⋊C4—82no—
700C4⋊C4—82no—
701C4⋊C4—82no—
702C4⋊C4—82no—
703C4⋊C4—82no—
704C4⋊C4—82no—
705C4⋊C4#12114yes—
706C4⋊C4#12114yes—
707C22⋊C4—22no—
708C22⋊C4—22no—
709C22⋊C4—22no—
710C22⋊C4—22no—
711C22⋊C4—22no—
712C22⋊C4—22no—
713C22⋊C4—22no—
714C22⋊C4—22no—
715C22⋊C4—44no—
716C22⋊C4—44no—
717C22⋊C4—44no—
718C22⋊C4—82no—
719C22⋊C4—82no—
720C22⋊C4—82no—
721C22⋊C4—82no—
722C22⋊C4—82no—
723C22⋊C4—82no—
724C22⋊C4—82no—
725C22⋊C4—82no—
726C22⋊C4#12114yes—
727C22⋊C4#12114yes—
728C42—22no—
729C42—22no—
730C42—21no—
731C42—21no—
732C42—21no—
733C42—21no—
734C42—44no—
735C42—44no—
736C42—82no—
737C42C22×D412yes—
738C42C22×D412yes—
739C42C2×#4112yes—
740C42C2×#4112yes—
741C23—22no—
742C23—22no—
743C23—21no—
744C23—21no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23C2×#12112yes—
756C23C23×D411yescharacteristic
757Q8—42no—
758Q8—42no—
759Q8—42no—
760Q8—42no—
761Q8—42no—
762Q8—42no—
763Q8—42no—
764Q8—42no—
765Q8—82no—
766D4—82no—
767D4—82no—
768D4—82no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—82no—
826C2×C4—82no—
827C2×C4—164no—
828C2×C4C2×#12112yes—
829C2×C4C2×#12112yes—
830C2×C4C2×#12112yes—
831C2×C4C2×#12112yes—
832C2×C4C2×#12112yes—
833C2×C4C23×D411yescharacteristic
834C2×C4C22×#4111yescharacteristic
835C2×C4C2×H(5,𝔽2)11yescharacteristic
836C2×C4C2×H(5,𝔽2)11yescharacteristic
837C2×C4C2×2−1+411yescharacteristic
838C2×C4C2×2−1+411yescharacteristic
839C8—22no—
840C8—22no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—41no—
845C8#53714yes—
846C8#53714yes—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—42no—
861C22—42no—
862C22C22×#12111yescharacteristic
863C22#349811yescharacteristic
864C22#349911yescharacteristic
865C22#358612yes—
866C22#358612yes—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—22no—
871C4—22no—
872C4—41no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—82no—
879C4—82no—
880C4—82no—
881C4—82no—
882C4—82no—
883C4—82no—
884C4—82no—
885C4—82no—
886C4C2×#53711yescharacteristic
887C4C2×#53711yescharacteristic
888C4#351111yescharacteristic
889C4#351111yescharacteristic
890C2—42no—
891C2—81no—
892C2—81no—
893C2#3527311yescharacteristic
894C2#6046211yescharacteristic
895C2#6046211yescharacteristic
896C2#6244212yes—
897C2#6250212yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#529 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3177C2semidirect
4. #33214C2semidirect
5. #33211C2semidirect
6. #33180C2semidirect
7. #33176C2semidirect
8. #29856C2semidirect
9. #29852C2semidirect
10. #28278C2semidirect
11. #28274C2semidirect
12. #28271C2semidirect
13. #28238C2semidirect
14. #28234C2semidirect
15. #28232C2semidirect
16. #24793C2semidirect
17. #24791C2semidirect
18. #24785C2semidirect
19. #24785C2semidirect
20. #24783C2semidirect
21. #24783C2semidirect
22. #21873C2semidirect
23. #20802C2semidirect

Maximal subgroups

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

subgroupindex
C2×#31772
C2×#29672
#373782
#332142
#332112
#331802
#331762
#298562
#298522
#282782
#282742
#282712
#282382
#282342
#282322
#247932
#247912
#247852
#247832
#218732
#208022