Finite Group Databasebeta

← #6443010

Subgroups — #6443010

Order 512.

2800 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3058C211yesmaximal, characteristic
2C2×#3057C211yesmaximal, characteristic, complemented
3C22×#463C211yesmaximal, characteristic, complemented
4C2×#2906C211yesmaximal, characteristic, complemented
5#35327C211yesmaximal, characteristic, complemented
6C4×#535C211yesmaximal, characteristic, complemented
7#24767C214yesmaximal, complemented
8#24763C214yesmaximal, complemented
9#24756C214yesmaximal, complemented
10#24754C214yesmaximal, complemented
11#23613C211yesmaximal, characteristic, complemented
12#23612C211yesmaximal, characteristic, complemented
13#23541C211yesmaximal, characteristic, complemented
14#23540C211yesmaximal, characteristic, complemented
15#21261C211yesmaximal, characteristic, complemented
16#21169C211yesmaximal, characteristic, complemented
17#20975C211yesmaximal, characteristic, complemented
18#20974C211yesmaximal, characteristic, complemented
19#20646C211yesmaximal, characteristic, complemented
20C23×SD16C2211yescharacteristic
21C23×D8C2211yescharacteristic
22C22×#131C2211yescharacteristic
23C22×#131C2211yescharacteristic
24C2×#536C2211yescharacteristic
25C2×#535C2211yescharacteristic
26C2×#535C2211yescharacteristic
27C22×#124C2211yescharacteristic
28C2×C4×#41C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30#3058—28no—
31#3057—28no—
32C2×#469C2214yes—
33C2×#468C2214yescomplemented
34C2×#466C2214yes—
35C2×#465C2214yescomplemented
36C2×#463—28no—
37C2×#463C2212yes—
38C2×#463C2212yes—
39C2×#463C2212yes—
40C2×#463C2212yes—
41C2×#427C2211yescharacteristic
42C2×#427C2211yescharacteristic
43#2906—28no—
44C2×#424C2211yescharacteristic
45C2×#424C2211yescharacteristic
46C2×#424C2212yescomplemented
47C2×#424C2212yescomplemented
48C2×#423C2211yescharacteristic
49C2×#423C2212yescomplemented
50C22×C4⋊C8C2211yescharacteristic
51C22×C4⋊C8C2212yescomplemented
52C2×#419C2211yescharacteristic
53C2×#419C2211yescharacteristic
54C2×#418C2211yescharacteristic
55C2×#418C2211yescharacteristic
56C2×#418C2211yescharacteristic
57C2×#418C2211yescharacteristic
58C22×#103C2211yescharacteristic
59C22×#102C2211yescharacteristic
60#2850C2214yescomplemented
61#2620C2214yescomplemented
62#2545—21no—
63#2545—21no—
64#2544—21no—
65#2544—21no—
66#2534—22no—
67#2534—22no—
68#2328—21no—
69#2326—21no—
70#2324C2214yescomplemented
71#2321—22no—
72#2317C2211yescharacteristic
73#2311C2211yescharacteristic
74#2310C2211yescharacteristic
75#2309C2211yescharacteristic
76#2309C2211yescharacteristic
77C4×#127—21no—
78C4×#124—21no—
79C4×#121C2214yescomplemented
80C4×#120—22no—
81#2285C2211yescharacteristic
82C4×#117C2211yescharacteristic
83#2068C2214yescomplemented
84#2067C2214yescomplemented
85#2066C2214yescomplemented
86#2065C2214yescomplemented
87#2055C2214yescomplemented
88#2055C2214yescomplemented
89#2054C2214yes—
90#2054C2214yes—
91#1983C2214yescomplemented
92#1983C2214yescomplemented
93#1949C2212yescomplemented
94#1949C2212yescomplemented
95#1948C2212yescomplemented
96#1947C2212yescomplemented
97#1895C2214yescomplemented
98#1894C2214yescomplemented
99#1893C2214yescomplemented
100#1892C2214yescomplemented
101#1804C2214yescomplemented
102#1802C2214yescomplemented
103#1736C2211yescharacteristic
104#1736C2211yescharacteristic
105#1735C2211yescharacteristic
106#1735C2211yescharacteristic
107C22×#41C2311yescharacteristic
108C23×Q8C2311yescharacteristic
109C23×D4C2311yescharacteristic
110C23×D4C2311yescharacteristic
111C24×C4—21no—
112C22×SD16—24no—
113C22×SD16—24no—
114C22×SD16—42no—
115C22×SD16C2312yes—
116C22×SD16C2312yes—
117C22×D8—24no—
118C22×D8—24no—
119C22×D8—42no—
120C22×D8C2312yes—
121C22×D8C2312yes—
122C2×#131—24no—
123C2×#131—24no—
124C2×#131—24no—
125C2×#131—24no—
126C2×#131—42no—
127C2×#131—42no—
128C22×M16C2311yescharacteristic
129C22×M16C2311yescharacteristic
130C22×M16C2312yes—
131C22×M16C2312yes—
132C23×C8C2312yes—
133C23×C8C2312yes—
134C23×C8C2311yescharacteristic
135C23×C8C2311yescharacteristic
136#536—24no—
137#536—24no—
138#535—24no—
139#535—24no—
140#535—24no—
141#535D418yes—
142C2×C4⋊Q8—21no—
143C2×#127—21no—
144C2×#127—21no—
145C2×#124—21no—
146C2×#124—21no—
147C2×#124—21no—
148C2×#124—21no—
149C2×#124—21no—
150C2×#124—24no—
151C2×#124—24no—
152C2×#124C2312yes—
153C2×#124C2312yes—
154C2×#123—22no—
155C2×C22⋊Q8C2314yes—
156C2×#121C2314yes—
157C2×#121C2314yes—
158C2×#120—22no—
159C2×#120—22no—
160C4×#41—24no—
161C4×#41—24no—
162C2×C4×Q8D411yescharacteristic
163C2×C4×Q8D411yescharacteristic
164C2×C4×D4—24no—
165C2×C4×D4—21no—
166C2×C4×D4—21no—
167C2×C4×D4—24no—
168C2×C4×D4—24no—
169C2×C4×D4D411yescharacteristic
170C2×C4×D4D412yes—
171C2×C4×D4D411yescharacteristic
172C2×C4×D4D412yes—
173C2×C4×D4C2312yes—
174C2×C4×D4C2312yes—
175C2×#117C2311yescharacteristic
176C2×#117C2311yescharacteristic
177C2×#117C2311yescharacteristic
178C2×#117C2311yescharacteristic
179C2×#117C2311yescharacteristic
180C2×#117C2312yes—
181C22×C4⋊C4C2311yescharacteristic
182C22×C22⋊C4—21no—
183C22×C22⋊C4—21no—
184C22×C22⋊C4—21no—
185C22×C42C2312yes—
186C22×C42C2311yescharacteristic
187#469—216no—
188#468—216no—
189#466—216no—
190#465—216no—
191#463—28no—
192#463—28no—
193#463—28no—
194#463—28no—
195#427—24no—
196#427—24no—
197C2×#107C2312yes—
198C2×#107C2312yes—
199C2×#106C2312yes—
200C2×#106C2312yes—
201#424—24no—
202#424—24no—
203#424—28no—
204#424—28no—
205#423—24no—
206#423—28no—
207C2×C4⋊C8—28no—
208C2×C4⋊C8D418yescomplemented
209C2×C4⋊C8C2312yes—
210C2×C4⋊C8C2312yes—
211C2×C4⋊C8C2312yes—
212C2×C4⋊C8C2312yes—
213C2×C4⋊C8C2312yes—
214C2×C4⋊C8C2312yes—
215C2×C4⋊C8C2311yescharacteristic
216C2×C4⋊C8C2311yescharacteristic
217C2×C4⋊C8C2311yescharacteristic
218C2×C4⋊C8C2311yescharacteristic
219#419—24no—
220#419—42no—
221#418—24no—
222#418—24no—
223#418—24no—
224#418—42no—
225C2×#103—24no—
226C2×#103C2312yes—
227C2×#103C2314yes—
228C2×#103C2312yes—
229C2×#103C2314yes—
230C2×#102—24no—
231C2×#102C2314yes—
232C2×#102C2314yes—
233C2×#102C2312yes—
234C2×#102C2314yes—
235C2×#102C2312yes—
236C2×#102C2314yes—
237#396—24no—
238#396—24no—
239#394—24no—
240#394—24no—
241#391—21no—
242#391—21no—
243#391—21no—
244#391C2314yes—
245#390—21no—
246#390—21no—
247#390—21no—
248#390—21no—
249#390—21no—
250#390—24no—
251#390C2314yes—
252#390C2314yes—
253#389C2314yes—
254#388—24no—
255#388—24no—
256#388—24no—
257#388—24no—
258#386—22no—
259#386—24no—
260#386—24no—
261#386—24no—
262#386—24no—
263#385—24no—
264#385—22no—
265#384—21no—
266#384C2312yes—
267#382—21no—
268#382C2312yes—
269#381—22no—
270#380—21no—
271#380—21no—
272#380C2314yes—
273#379—22no—
274#379—22no—
275C4×C4⋊C4—21no—
276C4×C4⋊C4—21no—
277C4×C4⋊C4C2312yes—
278C4×C4⋊C4C2312yes—
279C4×C22⋊C4—21no—
280C4×C22⋊C4—21no—
281C4×C22⋊C4—24no—
282#376—21no—
283C43—21no—
284#340C2312yes—
285#340C2312yes—
286#340C2312yes—
287#340C2312yes—
288#340C2314yes—
289#340C2314yes—
290C25—21no—
291C25—21no—
292C2×#41—22no—
293C2×#41—22no—
294C2×#41—22no—
295C2×#41—22no—
296C2×#41C2×D414yes—
297C2×#41#4114yes—
298C22×Q8—21no—
299C22×Q8—22no—
300C22×Q8—22no—
301C22×Q8—22no—
302C22×Q8—22no—
303C22×Q8—22no—
304C22×Q8—22no—
305C22×Q8C2×D411yescharacteristic
306C22×Q8C2412yes—
307C22×D4—24no—
308C22×D4—24no—
309C22×D4—22no—
310C22×D4—21no—
311C22×D4—22no—
312C22×D4—22no—
313C22×D4—21no—
314C22×D4—22no—
315C22×D4—22no—
316C22×D4—22no—
317C22×D4—22no—
318C22×D4—22no—
319C22×D4—22no—
320C22×D4—22no—
321C22×D4—22no—
322C22×D4C2×D414yes—
323C22×D4C2×D412yes—
324C22×D4C2×D411yescharacteristic
325C22×D4C2412yes—
326C22×D4C2412yes—
327C23×C4—21no—
328C23×C4—21no—
329C23×C4—22no—
330C23×C4—22no—
331C23×C4—44no—
332C23×C4—84no—
333C23×C4C2×D412yes—
334C23×C4C2×D412yes—
335C23×C4C2×D411yescharacteristic
336C23×C4C2×D411yescharacteristic
337C23×C4C2412yes—
338C23×C4C2411yescharacteristic
339C2×SD16—24no—
340C2×SD16—24no—
341C2×SD16—24no—
342C2×SD16—24no—
343C2×SD16—42no—
344C2×SD16—42no—
345C2×SD16—416no—
346C2×D8—24no—
347C2×D8—24no—
348C2×D8—24no—
349C2×D8—24no—
350C2×D8—42no—
351C2×D8—42no—
352C2×D8—416no—
353#131—416no—
354#131—416no—
355C2×M16—22no—
356C2×M16—22no—
357C2×M16—22no—
358C2×M16—22no—
359C2×M16—24no—
360C2×M16—24no—
361C2×M16—22no—
362C2×M16—22no—
363C2×M16—24no—
364C2×M16—24no—
365C2×M16—42no—
366C2×M16—42no—
367C22×C8—22no—
368C22×C8—22no—
369C22×C8—22no—
370C22×C8—22no—
371C22×C8—24no—
372C22×C8—24no—
373C22×C8—24no—
374C22×C8—24no—
375C22×C8—42no—
376C22×C8—42no—
377C22×C8C2×D414yes—
378C22×C8C2×D414yes—
379C22×C8C2412yes—
380C22×C8C2412yes—
381C22×C8C2411yescharacteristic
382C22×C8C2411yescharacteristic
383C22×C8C2411yescharacteristic
384C22×C8C2411yescharacteristic
385C4⋊Q8—44no—
386#127—28no—
387#127—44no—
388#124—28no—
389#124—24no—
390#124—24no—
391#124—24no—
392#124—24no—
393#124—44no—
394#124—44no—
395#124—44no—
396#124—44no—
397#123—48no—
398C22⋊Q8—28no—
399C22⋊Q8—28no—
400#121—28no—
401#121—28no—
402#121—28no—
403#121C2×D4116yes—
404#120—216no—
405#120—48no—
406C4×Q8—24no—
407C4×Q8—24no—
408C4×D4—28no—
409C4×D4—28no—
410C4×D4—24no—
411C4×D4—24no—
412C4×D4—24no—
413C4×D4—24no—
414C4×D4—24no—
415C4×D4—24no—
416C4×D4—44no—
417C4×D4—44no—
418C4×D4—88no—
419#117—22no—
420#117—22no—
421#117—22no—
422#117—24no—
423#117—24no—
424#117—22no—
425#117—22no—
426#117—22no—
427#117—22no—
428#117—22no—
429#117—22no—
430#117C2×D414yes—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—24no—
435C2×C4⋊C4—24no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4C2×D411yescharacteristic
439C2×C4⋊C4C2×D411yescharacteristic
440C2×C4⋊C4C2×D412yes—
441C2×C4⋊C4C2×D412yes—
442C2×C4⋊C4C2412yes—
443C2×C4⋊C4C2412yes—
444C2×C4⋊C4C2412yes—
445C2×C4⋊C4C2412yes—
446C2×C4⋊C4C2412yes—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—24no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—44no—
466C2×C22⋊C4—44no—
467C2×C22⋊C4—44no—
468C2×C22⋊C4C2×D412yes—
469C2×C22⋊C4C2×D412yes—
470C2×C22⋊C4C2×D412yes—
471C2×C42—21no—
472C2×C42—24no—
473C2×C42—24no—
474C2×C42—21no—
475C2×C42—21no—
476C2×C42—21no—
477C2×C42—22no—
478C2×C42—22no—
479C2×C42C2×D412yes—
480C2×C42C2×D412yes—
481C2×C42C2×D411yescharacteristic
482C2×C42C2×D411yescharacteristic
483C2×C42C2×D414yes—
484C2×C42#4114yes—
485C2×C42C2412yes—
486C2×C42C2411yescharacteristic
487C2×C42C2411yescharacteristic
488#107—24no—
489#107—24no—
490#106—24no—
491#106—24no—
492C4⋊C8—24no—
493C4⋊C8—24no—
494C4⋊C8—24no—
495C4⋊C8—24no—
496C4⋊C8—24no—
497C4⋊C8—24no—
498C4⋊C8C2×D414yes—
499C4⋊C8C2×D414yes—
500C4⋊C8C2×D414yes—
501C4⋊C8C2×D414yes—
502#103—24no—
503#103—24no—
504#103—28no—
505#103—44no—
506#102—28no—
507#102—28no—
508#102—24no—
509#102—24no—
510#102—28no—
511#102—44no—
512#95—22no—
513#95—22no—
514#95—24no—
515#95—24no—
516#95—22no—
517#95—22no—
518#95—24no—
519#95—24no—
520C24—22no—
521C24—24no—
522C24—22no—
523C24—42no—
524C24—42no—
525C24—42no—
526C24—42no—
527C24—42no—
528C24—82no—
529C24—82no—
530C24—82no—
531C24—82no—
532C24C22×D412yes—
533C24C22×D411yescharacteristic
534#41—28no—
535#41—28no—
536#41—28no—
537#41—28no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—42no—
547C2×Q8—42no—
548C2×Q8—42no—
549C2×Q8—44no—
550C2×Q8—44no—
551C2×Q8—44no—
552C2×Q8—44no—
553C2×Q8#12114yes—
554C2×D4—24no—
555C2×D4—24no—
556C2×D4—216no—
557C2×D4—22no—
558C2×D4—24no—
559C2×D4—22no—
560C2×D4—28no—
561C2×D4—28no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—48no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—44no—
580C2×D4—44no—
581C2×D4—44no—
582C2×D4—44no—
583C2×D4—44no—
584C2×D4—44no—
585C2×D4—84no—
586C2×D4—84no—
587C2×D4—84no—
588C2×D4—84no—
589C2×D4#12118yes—
590C2×D4#12114yes—
591C2×D4C22×D414yes—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—24no—
598C22×C4—24no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—48no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—44no—
614C22×C4—44no—
615C22×C4—84no—
616C22×C4—82no—
617C22×C4—816no—
618C22×C4#12114yes—
619C22×C4#12114yes—
620C22×C4C22×D412yes—
621C22×C4C22×D412yes—
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D412yes—
625C22×C4C22×D411yescharacteristic
626C22×C4C22×D411yescharacteristic
627C22×C4C22×D414yes—
628C22×C4C22×D411yescharacteristic
629C22×C4C22×D412yes—
630C22×C4C22×D412yes—
631C22×C4C2×#4114yes—
632C22×C4C2×#4112yes—
633C22×C4C2×#4112yes—
634C22×C4H(5,𝔽2)12yes—
635C22×C42−1+412yes—
636C22×C4C2511yescharacteristic
637SD16—48no—
638SD16—48no—
639D8—48no—
640D8—48no—
641M16—48no—
642M16—48no—
643M16—44no—
644M16—44no—
645C2×C8—28no—
646C2×C8—28no—
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—22no—
656C2×C8—22no—
657C2×C8—22no—
658C2×C8—22no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—48no—
662C2×C8—48no—
663C2×C8C22×D412yes—
664C2×C8C22×D412yes—
665C2×C8C22×D412yes—
666C2×C8C22×D412yes—
667C4⋊C4—24no—
668C4⋊C4—24no—
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—42no—
681C4⋊C4—48no—
682C4⋊C4—82no—
683C4⋊C4—82no—
684C4⋊C4—84no—
685C4⋊C4C22×D414yes—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—216no—
689C22⋊C4—24no—
690C22⋊C4—24no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—48no—
694C22⋊C4—42no—
695C22⋊C4—44no—
696C22⋊C4—44no—
697C22⋊C4—44no—
698C22⋊C4—44no—
699C22⋊C4—44no—
700C22⋊C4—44no—
701C22⋊C4—48no—
702C22⋊C4—84no—
703C22⋊C4—84no—
704C22⋊C4—84no—
705C22⋊C4—84no—
706C22⋊C4—84no—
707C42—24no—
708C42—24no—
709C42—24no—
710C42—22no—
711C42—22no—
712C42—44no—
713C42—42no—
714C42—42no—
715C42—42no—
716C42—82no—
717C42#12114yes—
718C42#12114yes—
719C42C22×D412yes—
720C42C22×D412yes—
721C42C2×#4112yes—
722C42C2×#4112yes—
723C23—22no—
724C23—22no—
725C23—24no—
726C23—24no—
727C23—22no—
728C23—22no—
729C23—24no—
730C23—44no—
731C23—44no—
732C23—42no—
733C23—48no—
734C23—42no—
735C23—44no—
736C23—44no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—88no—
741C23—84no—
742C23—84no—
743C23—88no—
744C23—84no—
745C23—84no—
746C23—84no—
747C23—164no—
748C23—164no—
749C23C2×#12114yes—
750C23C2×#12112yes—
751C23C2×#12112yes—
752C23#53712yes—
753C23C23×D411yescharacteristic
754Q8—28no—
755Q8—42no—
756Q8—42no—
757Q8—42no—
758Q8—42no—
759Q8—84no—
760D4—216no—
761D4—28no—
762D4—24no—
763D4—24no—
764D4—48no—
765D4—42no—
766D4—42no—
767D4—42no—
768D4—42no—
769D4—42no—
770D4—42no—
771D4—816no—
772D4—84no—
773D4—168no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—24no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—48no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—44no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—84no—
809C2×C4—88no—
810C2×C4—88no—
811C2×C4—84no—
812C2×C4—84no—
813C2×C4C2×#12112yes—
814C2×C4C2×#12112yes—
815C2×C4C2×#12112yes—
816C2×C4C2×#12112yes—
817C2×C4C2×#12114yes—
818C2×C4C2×#12112yes—
819C2×C4C2×#12112yes—
820C2×C4#53712yes—
821C2×C4D4214yes—
822C2×C4#54714yes—
823C2×C4#54814yes—
824C2×C4#55314yes—
825C2×C4C23×D411yescharacteristic
826C2×C4C23×D411yescharacteristic
827C2×C4C22×#4111yescharacteristic
828C2×C4C22×#4111yescharacteristic
829C2×C4C2×H(5,𝔽2)11yescharacteristic
830C2×C4C2×2−1+411yescharacteristic
831C8—22no—
832C8—22no—
833C8—22no—
834C8—22no—
835C8—42no—
836C8—42no—
837C22—24no—
838C22—22no—
839C22—22no—
840C22—24no—
841C22—28no—
842C22—24no—
843C22—42no—
844C22—42no—
845C22—44no—
846C22—48no—
847C22—44no—
848C22—816no—
849C22—82no—
850C22—82no—
851C22—84no—
852C22—84no—
853C22—82no—
854C22—82no—
855C22—82no—
856C22—84no—
857C22—168no—
858C22#241614yes—
859C22C22×#12111yescharacteristic
860C22C22×#12111yescharacteristic
861C22C2×#53711yescharacteristic
862C22#358412yes—
863C22#358512yes—
864C4—22no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—24no—
869C4—44no—
870C4—42no—
871C4—42no—
872C4—82no—
873C4—82no—
874C4—82no—
875C4—82no—
876C4—82no—
877C4#241614yes—
878C4C2×D4211yescharacteristic
879C4C2×#54711yescharacteristic
880C4C2×#54811yescharacteristic
881C4C2×#55311yescharacteristic
882C2—24no—
883C2—44no—
884C2—84no—
885C2—162no—
886C2C2×#241611yescharacteristic
887C2#6043012yes—
888C2#6045011yescharacteristic
889C2#6045411yescharacteristic
890C2#6092612yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#3058C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×#41 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3057C2semidirect
3. C22×#463C2semidirect
4. C2×#2906C2semidirect
5. #35327C2semidirect
6. C4×#535C2semidirect
7. #24767C2semidirect
8. #24763C2semidirect
9. #24756C2semidirect
10. #24754C2semidirect
11. #23613C2semidirect
12. #23612C2semidirect
13. #23541C2semidirect
14. #23540C2semidirect
15. #21261C2semidirect
16. #21169C2semidirect
17. #20975C2semidirect
18. #20974C2semidirect
19. #20646C2semidirect
33. C2×#468C22semidirect
35. C2×#465C22semidirect
46. C2×#424C22semidirect
47. C2×#424C22semidirect
49. C2×#423C22semidirect
51. C22×C4⋊C8C22semidirect
60. #2850C22semidirect
61. #2620C22semidirect
70. #2324C22semidirect
79. C4×#121C22semidirect
83. #2068C22semidirect
84. #2067C22semidirect
85. #2066C22semidirect
86. #2065C22semidirect
87. #2055C22semidirect
88. #2055C22semidirect
91. #1983C22semidirect
92. #1983C22semidirect
93. #1949C22semidirect
94. #1949C22semidirect
95. #1948C22semidirect
96. #1947C22semidirect
97. #1895C22semidirect
98. #1894C22semidirect
99. #1893C22semidirect
100. #1892C22semidirect
101. #1804C22semidirect
102. #1802C22semidirect
208. C2×C4⋊C8D4semidirect

Maximal subgroups

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

subgroupindex
C2×#30582
C2×#30572
C22×#4632
C2×#29062
#353272
C4×#5352
#247672
#247632
#247562
#247542
#236132
#236122
#235412
#235402
#212612
#211692
#209752
#209742
#206462