Finite Group Databasebeta

← #6473039

Subgroups — #6473039

Order 512.

2682 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3188C212yesmaximal, complemented
2#36624C211yesmaximal, characteristic, complemented
3C2×C4×#121C211yesmaximal, characteristic, complemented
4#33110C212yesmaximal, complemented
5#32908C212yesmaximal, complemented
6#29757C211yesmaximal, characteristic, complemented
7#29755C211yesmaximal, characteristic, complemented
8#29714C211yesmaximal, characteristic, complemented
9#29712C211yesmaximal, characteristic, complemented
10#28572C212yesmaximal, complemented
11#28571C212yesmaximal, complemented
12#28116C214yesmaximal, complemented
13#27650C212yesmaximal, complemented
14#24754C214yesmaximal, complemented
15#24214C212yesmaximal, complemented
16#21763C212yesmaximal, complemented
17C2×#1797C211yesmaximal, characteristic, complemented
18C2×#532C2211yescharacteristic, complemented
19C2×#525C2212yes—
20C22×#121C2211yescharacteristic
21C22×C4×D4—21no—
22C22×C4×D4C2211yescharacteristic
23C23×C42C2211yescharacteristic
24#3188—216no—
25C2×#484C2212yes—
26C2×#481C2212yes—
27C2×#482C2214yes—
28C2×#466C2214yes—
29C2×#465C2214yes—
30C2×#463C2214yescomplemented
31C2×#449C2214yes—
32C2×#450C2212yes—
33C2×#447C2212yes—
34C22×C4⋊C8C2212yescomplemented
35C22×C22⋊C8C2212yes—
36#2857C2211yescharacteristic
37#2857C2211yescharacteristic, complemented
38#2856C2211yescharacteristic
39#2856C2211yescharacteristic, complemented
40#2854—21no—
41#2854—21no—
42#2850C2212yes—
43#2850C2212yescomplemented
44#2847—21no—
45#2847—21no—
46C4×#121—21no—
47C4×#121—21no—
48C4×#121—21no—
49C4×#121—21no—
50C4×#121—21no—
51C4×#121—21no—
52C4×#121—21no—
53C4×#121—21no—
54C4×#121C2212yes—
55C4×#121C2212yes—
56C4×#121C2212yes—
57C4×#121C2212yes—
58#2297C2212yescomplemented
59C2×#390C2211yescharacteristic
60C2×#389C2211yescharacteristic
61C2×#388—21no—
62C2×#386—21no—
63#2285C2211yescharacteristic, complemented
64C2×#380C2211yescharacteristic
65C2×C4×C4⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4—21no—
67#2084C2212yescomplemented
68#2083C2212yescomplemented
69#2071C2212yescomplemented
70#2071C2212yescomplemented
71#2068C2214yescomplemented
72#2065C2214yescomplemented
73#2055C2214yescomplemented
74#2054C2214yescomplemented
75#2043C2212yescomplemented
76#2041C2212yescomplemented
77#2013C2212yescomplemented
78#2011C2212yescomplemented
79#1983C2214yescomplemented
80#1949C2214yescomplemented
81#1927C2214yescomplemented
82#1925C2214yescomplemented
83#1893C2214yescomplemented
84#1892C2214yescomplemented
85#1879C2214yescomplemented
86#1877C2214yescomplemented
87#1874C2212yes—
88#1874C2212yes—
89#1872C2212yes—
90#1872C2212yes—
91#1825C2214yescomplemented
92#1804C2214yescomplemented
93#1797C2211yescharacteristic
94#1797C2211yescharacteristic
95#1797C2212yes—
96#1797C2212yescomplemented
97#1797C2212yescomplemented
98#1788C2214yescomplemented
99C2×#336C2212yescomplemented
100C22×#41C2312yes—
101C23×D4—21no—
102C23×D4C2311yescharacteristic
103C24×C4—21no—
104C24×C4D411yescharacteristic
105C24×C4D411yescharacteristic
106C24×C4C2311yescharacteristic
107C22×SD16C2314yes—
108C22×D8C2314yes—
109C23×C8C2314yes—
110#532—44no—
111C2×C4⋊Q8C2311yescharacteristic
112C2×#127C2311yescharacteristic
113C2×#124C2312yes—
114#525—28no—
115#525—28no—
116C2×#123—22no—
117C2×C22⋊Q8C2312yes—
118C2×C22⋊Q8C2312yes—
119C2×#121—21no—
120C2×#121—21no—
121C2×#121—24no—
122C2×#121—21no—
123C2×#121—21no—
124C2×#121—21no—
125C2×#121—21no—
126C2×#121—21no—
127C2×#121—21no—
128C2×#121D418yescomplemented
129C2×#121C2312yes—
130C2×#121C2312yes—
131C2×#121C2312yes—
132C2×#121C2312yes—
133C2×#120—22no—
134C2×C4×D4—22no—
135C2×C4×D4—22no—
136C2×C4×D4—22no—
137C2×C4×D4—22no—
138C2×C4×D4—22no—
139C2×C4×D4—22no—
140C2×C4×D4—21no—
141C2×C4×D4—21no—
142C2×C4×D4—21no—
143C2×C4×D4—21no—
144C2×C4×D4—44no—
145C2×C4×D4—48no—
146C2×C4×D4C2312yes—
147C2×C4×D4C2312yes—
148C2×#117C2312yes—
149C22×C4⋊C4—21no—
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2311yescharacteristic
152C22×C4⋊C4C2311yescharacteristic
153C22×C22⋊C4—21no—
154C22×C22⋊C4—21no—
155C22×C22⋊C4—21no—
156C22×C22⋊C4—21no—
157C22×C22⋊C4—21no—
158C22×C42—21no—
159C22×C42—44no—
160C22×C42D411yescharacteristic
161C22×C42D411yescharacteristic
162C22×C42D411yescharacteristic
163C22×C42D411yescharacteristic
164C22×C42D411yescharacteristic
165C22×C42D411yescharacteristic
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168C22×C42C2311yescharacteristic
169C22×C42C2311yescharacteristic
170C22×C42C2311yescharacteristic
171C22×C42C2311yescharacteristic
172#484—28no—
173#482—216no—
174#481—28no—
175#466—216no—
176#465—216no—
177#463—48no—
178#450—28no—
179#449—216no—
180#447—28no—
181C2×#107C2314yes—
182C2×#106C2314yes—
183C2×C4⋊C8—44no—
184C2×C4⋊C8C2314yes—
185C2×C4⋊C8C2312yes—
186C2×C4⋊C8C2312yes—
187C2×#103C2314yes—
188C2×#103C2314yes—
189C2×#103C2314yes—
190C2×#102C2314yes—
191C2×#102C2314yes—
192C2×#102C2314yes—
193C2×#102C2314yes—
194C2×#102C2314yes—
195C2×C22⋊C8—28no—
196C2×C22⋊C8C2312yes—
197C2×C22⋊C8C2312yes—
198C2×C22⋊C8C2314yes—
199#391C2312yes—
200#391C2312yes—
201#390—21no—
202#390—21no—
203#390—21no—
204#390—21no—
205#390—21no—
206#390—21no—
207#390C2312yes—
208#390C2312yes—
209#390C2312yes—
210#390C2312yes—
211#389—21no—
212#389—21no—
213#389—21no—
214#389—21no—
215#389—21no—
216#389—21no—
217#389C2312yes—
218#389C2312yes—
219#388—22no—
220#388—22no—
221#388—22no—
222#388—22no—
223#388—22no—
224#388—22no—
225#388—22no—
226#388—22no—
227#386—22no—
228#386—22no—
229#386—22no—
230#386—22no—
231#386—22no—
232#386—22no—
233#386—22no—
234#386—22no—
235#386—22no—
236#386—22no—
237#384C2311yescharacteristic
238#384C2311yescharacteristic
239#382C2312yes—
240#380—21no—
241#380—21no—
242#380—21no—
243#380—21no—
244#380—21no—
245#380—21no—
246#380—21no—
247#380—21no—
248#380C2312yes—
249#380C2312yes—
250C4×C4⋊C4—21no—
251C4×C4⋊C4—21no—
252C4×C4⋊C4—21no—
253C4×C4⋊C4—21no—
254C4×C4⋊C4C2312yes—
255C4×C4⋊C4C2312yes—
256C4×C22⋊C4—22no—
257C4×C22⋊C4—22no—
258C4×C22⋊C4—22no—
259C4×C22⋊C4—22no—
260C4×C22⋊C4—22no—
261C4×C22⋊C4—22no—
262C2×#95—21no—
263C2×#95—21no—
264C2×#95—21no—
265#340C2314yes—
266#340C2314yes—
267#340C2314yes—
268#340C2314yes—
269#336C2312yes—
270#336C2312yes—
271#336C2314yes—
272C25—21no—
273C25C2×D411yescharacteristic
274C2×#41—24no—
275C2×#41—24no—
276C2×#41—44no—
277C2×#41—44no—
278C22×Q8C2412yes—
279C22×D4—28no—
280C22×D4—22no—
281C22×D4—22no—
282C22×D4—22no—
283C22×D4—22no—
284C22×D4—22no—
285C22×D4—21no—
286C22×D4—21no—
287C22×D4—21no—
288C22×D4—22no—
289C22×D4—42no—
290C22×D4—42no—
291C22×D4—44no—
292C22×D4—44no—
293C22×D4C2×D414yes—
294C22×D4C2412yes—
295C22×D4C2412yes—
296C23×C4—21no—
297C23×C4—24no—
298C23×C4—24no—
299C23×C4—21no—
300C23×C4—21no—
301C23×C4—22no—
302C23×C4—22no—
303C23×C4—22no—
304C23×C4—42no—
305C23×C4—42no—
306C23×C4—42no—
307C23×C4—42no—
308C23×C4—42no—
309C23×C4—42no—
310C23×C4—44no—
311C23×C4—44no—
312C23×C4—44no—
313C23×C4C2×D411yescharacteristic
314C23×C4C2×D411yescharacteristic
315C23×C4C2×D411yescharacteristic
316C23×C4C2×D411yescharacteristic
317C23×C4C2×D411yescharacteristic
318C23×C4C2×D411yescharacteristic
319C23×C4C2×D411yescharacteristic
320C23×C4C2×D411yescharacteristic
321C23×C4C2×D411yescharacteristic
322C23×C4C2×D411yescharacteristic
323C23×C4C2×D411yescharacteristic
324C23×C4C2×D411yescharacteristic
325C23×C4C2×D411yescharacteristic
326C23×C4C2×D414yes—
327C23×C4C2×D411yescharacteristic
328C23×C4C2×D411yescharacteristic
329C23×C4#4114yes—
330C23×C4C2411yescharacteristic
331C23×C4C2411yescharacteristic
332C23×C4C2411yescharacteristic
333C2×SD16—28no—
334C2×SD16—44no—
335C2×SD16—44no—
336C2×D8—28no—
337C2×D8—44no—
338C2×D8—44no—
339C22×C8—28no—
340C22×C8—44no—
341C22×C8—44no—
342C22×C8C2414yes—
343C22×C8C2414yes—
344C4⋊Q8—42no—
345#127—42no—
346#124—28no—
347#123—48no—
348C22⋊Q8—24no—
349C22⋊Q8—24no—
350C22⋊Q8—24no—
351C22⋊Q8—24no—
352#121—28no—
353#121—28no—
354#121—24no—
355#121—24no—
356#121—24no—
357#121—24no—
358#121—24no—
359#121—24no—
360#121—44no—
361#121—44no—
362#121—44no—
363#121—44no—
364#121—44no—
365#121—44no—
366#121C2×D418yes—
367#121C2×D418yes—
368#120—48no—
369C4×D4—28no—
370C4×D4—44no—
371C4×D4—44no—
372C4×D4—44no—
373C4×D4—44no—
374C4×D4—44no—
375C4×D4—48no—
376C4×D4—48no—
377C4×D4—48no—
378C4×D4—48no—
379C4×D4—48no—
380C4×D4—48no—
381#117—24no—
382#117—24no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—42no—
398C2×C4⋊C4—42no—
399C2×C4⋊C4—44no—
400C2×C4⋊C4C2×D414yes—
401C2×C4⋊C4C2412yes—
402C2×C4⋊C4C2412yes—
403C2×C4⋊C4C2412yes—
404C2×C4⋊C4C2412yes—
405C2×C4⋊C4C2412yes—
406C2×C22⋊C4—28no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—44no—
429C2×C22⋊C4—44no—
430C2×C22⋊C4—44no—
431C2×C22⋊C4—44no—
432C2×C42—24no—
433C2×C42—24no—
434C2×C42—24no—
435C2×C42—22no—
436C2×C42—22no—
437C2×C42—22no—
438C2×C42—42no—
439C2×C42—42no—
440C2×C42—42no—
441C2×C42—42no—
442C2×C42—42no—
443C2×C42—42no—
444C2×C42—42no—
445C2×C42—42no—
446C2×C42—42no—
447C2×C42—44no—
448C2×C42C2×D411yescharacteristic
449C2×C42C2×D411yescharacteristic
450C2×C42C2×D411yescharacteristic
451C2×C42C2×D411yescharacteristic
452C2×C42C2×D411yescharacteristic
453C2×C42C2×D411yescharacteristic
454C2×C42C2×D411yescharacteristic
455C2×C42C2×D411yescharacteristic
456C2×C42C2×D411yescharacteristic
457C2×C42C2×D411yescharacteristic
458C2×C42C2×D411yescharacteristic
459C2×C42C2×D411yescharacteristic
460C2×C42C2411yescharacteristic
461C2×C42C2411yescharacteristic
462C2×C42C2411yescharacteristic
463C2×C42C2411yescharacteristic
464#107—28no—
465#106—28no—
466C4⋊C8—28no—
467C4⋊C8—42no—
468C4⋊C8—42no—
469#103—28no—
470#103—44no—
471#103—44no—
472#102—28no—
473#102—28no—
474#102—28no—
475#102—44no—
476#102—44no—
477C22⋊C8—24no—
478C22⋊C8—28no—
479C22⋊C8—24no—
480#95—22no—
481#95—22no—
482#95—22no—
483#95—22no—
484#95—22no—
485#95—22no—
486#95—22no—
487#95—22no—
488#95—22no—
489#95—22no—
490#95—22no—
491#95—22no—
492C24—22no—
493C24—22no—
494C24—22no—
495C24—22no—
496C24—24no—
497C24—22no—
498C24—22no—
499C24—41no—
500C24—41no—
501C24—42no—
502C24—42no—
503C24—42no—
504C24—42no—
505C24—42no—
506C24—42no—
507C24#12114yes—
508C24C22×D411yescharacteristic
509C24C22×D411yescharacteristic
510C24C22×D411yescharacteristic
511#41—88no—
512#41—88no—
513C2×Q8—22no—
514C2×Q8—22no—
515C2×Q8—24no—
516C2×Q8—24no—
517C2×D4—28no—
518C2×D4—28no—
519C2×D4—24no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—24no—
524C2×D4—24no—
525C2×D4—24no—
526C2×D4—24no—
527C2×D4—48no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—48no—
531C2×D4—42no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4—44no—
536C2×D4—432no—
537C2×D4—44no—
538C2×D4—44no—
539C2×D4—44no—
540C2×D4—44no—
541C2×D4—44no—
542C2×D4—44no—
543C2×D4—44no—
544C2×D4—44no—
545C2×D4—44no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—42no—
550C2×D4—42no—
551C2×D4C22×D414yes—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—24no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—416no—
608C22×C4—416no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—44no—
612C22×C4—44no—
613C22×C4—44no—
614C22×C4—44no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4—816no—
627C22×C4#12114yes—
628C22×C4#12114yes—
629C22×C4#12114yes—
630C22×C4#13514yes—
631C22×C4AGL(1,ℤ/8)14yes—
632C22×C4C22×D411yescharacteristic
633C22×C4C22×D411yescharacteristic
634C22×C4C22×D411yescharacteristic
635C22×C4C22×D411yescharacteristic
636C22×C4C22×D411yescharacteristic
637C22×C4C22×D412yes—
638C22×C4C22×D412yes—
639C22×C4C22×D412yes—
640C22×C4C22×D411yescharacteristic
641C22×C4C22×D411yescharacteristic
642C22×C4C22×D411yescharacteristic
643C22×C4C22×D411yescharacteristic
644C22×C4C22×D411yescharacteristic
645C22×C4C22×D411yescharacteristic
646C22×C4C2×#4112yes—
647C22×C4C2×#4112yes—
648C22×C4C2×#4112yes—
649C22×C4C2511yescharacteristic
650SD16—88no—
651D8—88no—
652C2×C8—24no—
653C2×C8—24no—
654C2×C8—24no—
655C2×C8—24no—
656C2×C8—24no—
657C2×C8—24no—
658C2×C8—88no—
659C4⋊C4—24no—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—24no—
666C4⋊C4—24no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—44no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—44no—
675C4⋊C4—44no—
676C4⋊C4—42no—
677C4⋊C4—44no—
678C4⋊C4—42no—
679C4⋊C4C22×D414yes—
680C22⋊C4—28no—
681C22⋊C4—28no—
682C22⋊C4—44no—
683C22⋊C4—44no—
684C22⋊C4—44no—
685C22⋊C4—44no—
686C22⋊C4—44no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—44no—
692C22⋊C4—44no—
693C22⋊C4—44no—
694C22⋊C4—44no—
695C22⋊C4—44no—
696C22⋊C4—44no—
697C22⋊C4—44no—
698C22⋊C4—44no—
699C22⋊C4—44no—
700C22⋊C4—44no—
701C42—22no—
702C42—22no—
703C42—22no—
704C42—22no—
705C42—22no—
706C42—22no—
707C42—22no—
708C42—22no—
709C42—22no—
710C42—41no—
711C42—41no—
712C42—41no—
713C42—41no—
714C42—41no—
715C42—41no—
716C42—44no—
717C42—44no—
718C42—44no—
719C42H(5,𝔽2)14yes—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—28no—
731C23—28no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—24no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—44no—
742C23—48no—
743C23—48no—
744C23—42no—
745C23—42no—
746C23—48no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—84no—
759C23—84no—
760C23—84no—
761C23—84no—
762C23C2×#12112yes—
763C23C2×#12112yes—
764C23C2×#12112yes—
765C23C2×#13512yes—
766C23C2×AGL(1,ℤ/8)12yes—
767C23#57512yes—
768C23#57512yes—
769C23C23×D411yescharacteristic
770Q8—44no—
771Q8—44no—
772D4—28no—
773D4—48no—
774D4—416no—
775D4—416no—
776D4—44no—
777D4—44no—
778D4—44no—
779D4—84no—
780D4—84no—
781D4—88no—
782D4—88no—
783D4—88no—
784C2×C4—28no—
785C2×C4—28no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—24no—
807C2×C4—24no—
808C2×C4—24no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—44no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—44no—
821C2×C4—44no—
822C2×C4—44no—
823C2×C4—44no—
824C2×C4—44no—
825C2×C4—44no—
826C2×C4—44no—
827C2×C4—44no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—48no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—88no—
849C2×C4—88no—
850C2×C4—88no—
851C2×C4—84no—
852C2×C4—84no—
853C2×C4C2×#12112yes—
854C2×C4C2×#12112yes—
855C2×C4C2×#12112yes—
856C2×C4#53412yes—
857C2×C4#53412yes—
858C2×C4C2×#13512yes—
859C2×C4C2×#13512yes—
860C2×C4C2×AGL(1,ℤ/8)12yes—
861C2×C4C2×AGL(1,ℤ/8)12yes—
862C2×C4C23×D411yescharacteristic
863C2×C4C22×#4111yescharacteristic
864C2×C4C2×H(5,𝔽2)12yes—
865C2×C4#58512yes—
866C8—44no—
867C8—44no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—22no—
878C22—22no—
879C22—22no—
880C22—22no—
881C22—22no—
882C22—22no—
883C22—416no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—44no—
889C22—44no—
890C22—44no—
891C22—816no—
892C22—82no—
893C22—82no—
894C22—82no—
895C22—82no—
896C22—82no—
897C22—82no—
898C22—82no—
899C22—82no—
900C22—82no—
901C22—82no—
902C22—82no—
903C22#303514yes—
904C22#303614yes—
905C22C22×#12111yescharacteristic
906C22C2×#53411yescharacteristic
907C22#344911yescharacteristic
908C22C22×#13511yescharacteristic
909C22C22×AGL(1,ℤ/8)11yescharacteristic
910C22C2×#57511yescharacteristic
911C22C2×#57511yescharacteristic
912C4—22no—
913C4—22no—
914C4—22no—
915C4—22no—
916C4—22no—
917C4—22no—
918C4—22no—
919C4—22no—
920C4—22no—
921C4—41no—
922C4—41no—
923C4—44no—
924C4—82no—
925C4—82no—
926C4—82no—
927C4—82no—
928C4—82no—
929C4#349612yes—
930C4#350512yes—
931C2—24no—
932C2—24no—
933C2—42no—
934C2—84no—
935C2—162no—
936C2#3500011yescharacteristic
937C2C2×#303511yescharacteristic
938C2C2×#303611yescharacteristic
939C2#6073411yescharacteristic
940C2#6075011yescharacteristic
941C2#6094611yescharacteristic
942C2#6095911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3188C2semidirect
2. #36624C2semidirect
3. C2×C4×#121C2semidirect
4. #33110C2semidirect
5. #32908C2semidirect
6. #29757C2semidirect
7. #29755C2semidirect
8. #29714C2semidirect
9. #29712C2semidirect
10. #28572C2semidirect
11. #28571C2semidirect
12. #28116C2semidirect
13. #27650C2semidirect
14. #24754C2semidirect
15. #24214C2semidirect
16. #21763C2semidirect
17. C2×#1797C2semidirect
18. C2×#532C22semidirect
30. C2×#463C22semidirect
34. C22×C4⋊C8C22semidirect
37. #2857C22semidirect
39. #2856C22semidirect
43. #2850C22semidirect
58. #2297C22semidirect
63. #2285C22semidirect
67. #2084C22semidirect
68. #2083C22semidirect
69. #2071C22semidirect
70. #2071C22semidirect
71. #2068C22semidirect
72. #2065C22semidirect
73. #2055C22semidirect
74. #2054C22semidirect
75. #2043C22semidirect
76. #2041C22semidirect
77. #2013C22semidirect
78. #2011C22semidirect
79. #1983C22semidirect
80. #1949C22semidirect
81. #1927C22semidirect
82. #1925C22semidirect
83. #1893C22semidirect
84. #1892C22semidirect
85. #1879C22semidirect
86. #1877C22semidirect
91. #1825C22semidirect
92. #1804C22semidirect
96. #1797C22semidirect
97. #1797C22semidirect
98. #1788C22semidirect
99. C2×#336C22semidirect
128. C2×#121D4semidirect

Maximal subgroups

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

subgroupindex
C2×#31882
#366242
C2×C4×#1212
#331102
#329082
#297572
#297552
#297142
#297122
#285722
#285712
#281162
#276502
#247542
#242142
#217632
C2×#17972