Finite Group Databasebeta

← #6473042

Subgroups — #6473042

Order 512.

2390 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3190C212yesmaximal, complemented
2#36624C211yesmaximal, characteristic
3C2×C4×C22⋊Q8C211yesmaximal, characteristic, complemented
4#33108C211yesmaximal, characteristic, complemented
5#33106C211yesmaximal, characteristic, complemented
6#32906C211yesmaximal, characteristic, complemented
7#32903C211yesmaximal, characteristic, complemented
8#29760C212yesmaximal, complemented
9#29719C212yesmaximal, complemented
10#28576C214yesmaximal, complemented
11#28125C214yesmaximal, complemented
12#27649C212yesmaximal, complemented
13#24753C212yesmaximal, complemented
14#24752C212yesmaximal, complemented
15#24213C212yesmaximal, complemented
16#21763C212yesmaximal, complemented
17C2×#1797C211yesmaximal, characteristic, complemented
18C2×#532C2211yescharacteristic
19C2×#525C2212yes—
20C22×C22⋊Q8C2211yescharacteristic
21C22×C4×Q8C2211yescharacteristic
22C23×C42C2211yescharacteristic
23#3190—216no—
24C2×#485C2214yes—
25C2×#483C2212yes—
26C2×#480C2212yes—
27C2×#467C2214yes—
28C2×#465C2214yes—
29C2×#462C2212yescomplemented
30C2×#460C2212yescomplemented
31C2×#452C2214yes—
32C2×#451C2212yes—
33C2×#448C2212yes—
34C22×C4⋊C8C2212yes—
35C22×C22⋊C8C2212yes—
36#2857C2211yescharacteristic
37#2857C2211yescharacteristic
38#2856C2211yescharacteristic
39#2856C2211yescharacteristic
40#2854—21no—
41#2854—21no—
42#2850C2212yes—
43#2850C2212yes—
44#2847—21no—
45#2847—21no—
46C4×C22⋊Q8—21no—
47C4×C22⋊Q8—21no—
48C4×C22⋊Q8—21no—
49C4×C22⋊Q8—21no—
50C4×C22⋊Q8C2212yes—
51C4×C22⋊Q8C2212yes—
52C4×C22⋊Q8C2212yes—
53C4×C22⋊Q8C2212yes—
54C4×#121—21no—
55C4×#121—21no—
56C4×#121—21no—
57C4×#121—21no—
58#2297C2212yes—
59C2×#391C2211yescharacteristic
60C2×#389C2211yescharacteristic
61C2×#387—21no—
62C2×#385—21no—
63#2285C2211yescharacteristic
64C2×#380C2211yescharacteristic
65C2×C4×C4⋊C4—21no—
66C2×C4×C4⋊C4C2211yescharacteristic
67C2×C4×C22⋊C4—21no—
68#2085C2214yescomplemented
69#2074C2214yescomplemented
70#2068C2214yescomplemented
71#2065C2214yescomplemented
72#2056C2214yescomplemented
73#2055C2214yescomplemented
74#2042C2214yescomplemented
75#2015C2214yescomplemented
76#1982C2212yescomplemented
77#1981C2212yescomplemented
78#1948C2212yescomplemented
79#1947C2212yescomplemented
80#1927C2214yescomplemented
81#1925C2214yescomplemented
82#1893C2214yes—
83#1892C2214yes—
84#1880C2214yescomplemented
85#1878C2214yescomplemented
86#1874C2212yes—
87#1874C2212yes—
88#1872C2212yes—
89#1872C2212yes—
90#1825C2214yes—
91#1803C2212yescomplemented
92#1803C2212yescomplemented
93#1797C2212yes—
94#1797C2212yes—
95#1797C2211yescharacteristic
96#1797C2211yescharacteristic
97#1797C2212yes—
98#1788C2214yes—
99C2×#336C2212yes—
100C22×#41C2312yes—
101C23×Q8C2311yescharacteristic
102C24×C4D411yescharacteristic
103C24×C4D411yescharacteristic
104C24×C4C2311yescharacteristic
105C22×Q16C2314yes—
106C22×SD16C2314yes—
107C23×C8C2314yes—
108#532—44no—
109C2×C4⋊Q8C2311yescharacteristic
110C2×#127C2311yescharacteristic
111C2×#124C2312yes—
112#525—28no—
113#525—28no—
114C2×#123—22no—
115C2×C22⋊Q8—21no—
116C2×C22⋊Q8—21no—
117C2×C22⋊Q8—24no—
118C2×C22⋊Q8D418yescomplemented
119C2×C22⋊Q8C2312yes—
120C2×C22⋊Q8C2312yes—
121C2×C22⋊Q8C2312yes—
122C2×C22⋊Q8C2312yes—
123C2×#121—21no—
124C2×#121—21no—
125C2×#121—21no—
126C2×#121—21no—
127C2×#121—21no—
128C2×#121—21no—
129C2×#121C2312yes—
130C2×#121C2312yes—
131C2×#120—22no—
132C2×C4×Q8—21no—
133C2×C4×Q8—21no—
134C2×C4×Q8—44no—
135C2×C4×Q8C2312yes—
136C2×C4×Q8C2312yes—
137C2×C4×D4—22no—
138C2×C4×D4—22no—
139C2×C4×D4—21no—
140C2×C4×D4—21no—
141C2×#117C2312yes—
142C22×C4⋊C4—21no—
143C22×C4⋊C4—21no—
144C22×C4⋊C4—21no—
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2311yescharacteristic
148C22×C22⋊C4—21no—
149C22×C22⋊C4—21no—
150C22×C42—21no—
151C22×C42—21no—
152C22×C42—44no—
153C22×C42D411yescharacteristic
154C22×C42D411yescharacteristic
155C22×C42D411yescharacteristic
156C22×C42D411yescharacteristic
157C22×C42D411yescharacteristic
158C22×C42D411yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165#485—216no—
166#483—28no—
167#480—28no—
168#467—216no—
169#465—216no—
170#462—44no—
171#460—44no—
172#452—216no—
173#451—28no—
174#448—28no—
175C2×#107C2314yes—
176C2×#106C2314yes—
177C2×C4⋊C8—44no—
178C2×C4⋊C8C2312yes—
179C2×C4⋊C8C2312yes—
180C2×C4⋊C8C2314yes—
181C2×#103C2314yes—
182C2×#103C2314yes—
183C2×#103C2314yes—
184C2×#103C2314yes—
185C2×#103C2314yes—
186C2×#102C2314yes—
187C2×#102C2314yes—
188C2×#102C2314yes—
189C2×C22⋊C8—28no—
190C2×C22⋊C8C2312yes—
191C2×C22⋊C8C2312yes—
192C2×C22⋊C8C2314yes—
193#391—21no—
194#391—21no—
195#391C2312yes—
196#391C2312yes—
197#391C2312yes—
198#391C2312yes—
199#390—21no—
200#390—21no—
201#390—21no—
202#390—21no—
203#390C2312yes—
204#390C2312yes—
205#389—21no—
206#389—21no—
207#389—21no—
208#389—21no—
209#389—21no—
210#389—21no—
211#389C2312yes—
212#389C2312yes—
213#388—22no—
214#388—22no—
215#388—22no—
216#388—22no—
217#387—22no—
218#387—22no—
219#387—22no—
220#387—22no—
221#386—22no—
222#386—22no—
223#386—22no—
224#386—22no—
225#386—22no—
226#386—22no—
227#385—22no—
228#385—22no—
229#385—22no—
230#385—22no—
231#384C2311yescharacteristic
232#384C2311yescharacteristic
233#382C2312yes—
234#380—21no—
235#380—21no—
236#380—21no—
237#380—21no—
238#380—21no—
239#380—21no—
240#380—21no—
241#380—21no—
242#380C2312yes—
243#380C2312yes—
244C4×C4⋊C4—22no—
245C4×C4⋊C4—22no—
246C4×C4⋊C4—22no—
247C4×C4⋊C4—22no—
248C4×C4⋊C4—21no—
249C4×C4⋊C4—21no—
250C4×C4⋊C4—21no—
251C4×C4⋊C4—21no—
252C4×C4⋊C4C2312yes—
253C4×C4⋊C4C2312yes—
254C4×C22⋊C4—22no—
255C4×C22⋊C4—22no—
256C4×C22⋊C4—22no—
257C4×C22⋊C4—22no—
258C4×C22⋊C4—22no—
259C4×C22⋊C4—22no—
260C2×#95—21no—
261C2×#95—21no—
262C2×#95—21no—
263C2×#95—21no—
264C2×#95—21no—
265#340C2314yes—
266#340C2314yes—
267#340C2314yes—
268#340C2314yes—
269#336C2314yes—
270#336C2312yes—
271#336C2312yes—
272C25C2×D411yescharacteristic
273C2×#41—24no—
274C2×#41—24no—
275C2×#41—44no—
276C2×#41—44no—
277C22×Q8—21no—
278C22×Q8—22no—
279C22×Q8—42no—
280C22×Q8—42no—
281C22×Q8C2×D414yes—
282C22×Q8C2412yes—
283C22×Q8C2412yes—
284C22×D4—22no—
285C22×D4—22no—
286C22×D4—22no—
287C22×D4—21no—
288C22×D4—21no—
289C22×D4C2412yes—
290C23×C4—21no—
291C23×C4—21no—
292C23×C4—24no—
293C23×C4—24no—
294C23×C4—21no—
295C23×C4—21no—
296C23×C4—22no—
297C23×C4—42no—
298C23×C4—42no—
299C23×C4—42no—
300C23×C4—42no—
301C23×C4—42no—
302C23×C4—42no—
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D411yescharacteristic
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D411yescharacteristic
314C23×C4C2×D411yescharacteristic
315C23×C4C2×D411yescharacteristic
316C23×C4C2×D411yescharacteristic
317C23×C4C2×D411yescharacteristic
318C23×C4C2×D414yes—
319C23×C4#4114yes—
320C23×C4C2411yescharacteristic
321C23×C4C2411yescharacteristic
322C23×C4C2411yescharacteristic
323C2×Q16—28no—
324C2×Q16—44no—
325C2×Q16—44no—
326C2×SD16—28no—
327C2×SD16—44no—
328C2×SD16—44no—
329C22×C8—28no—
330C22×C8—44no—
331C22×C8—44no—
332C22×C8C2414yes—
333C22×C8C2414yes—
334C4⋊Q8—24no—
335#127—24no—
336#124—44no—
337#123—48no—
338C22⋊Q8—28no—
339C22⋊Q8—28no—
340C22⋊Q8—24no—
341C22⋊Q8—24no—
342C22⋊Q8—24no—
343C22⋊Q8—24no—
344C22⋊Q8—24no—
345C22⋊Q8—24no—
346C22⋊Q8C2×D418yes—
347C22⋊Q8C2×D418yes—
348#121—24no—
349#121—24no—
350#121—24no—
351#121—24no—
352#121—44no—
353#121—44no—
354#121—44no—
355#121—44no—
356#121—44no—
357#121—44no—
358#120—48no—
359C4×Q8—24no—
360C4×Q8—24no—
361C4×Q8—42no—
362C4×Q8—42no—
363C4×Q8—44no—
364C4×Q8—44no—
365C4×D4—44no—
366C4×D4—44no—
367C4×D4—48no—
368C4×D4—48no—
369#117—24no—
370#117—24no—
371C2×C4⋊C4—28no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—42no—
391C2×C4⋊C4—42no—
392C2×C4⋊C4—44no—
393C2×C4⋊C4—44no—
394C2×C4⋊C4C2×D414yes—
395C2×C4⋊C4C2412yes—
396C2×C4⋊C4C2412yes—
397C2×C4⋊C4C2412yes—
398C2×C4⋊C4C2412yes—
399C2×C4⋊C4C2412yes—
400C2×C22⋊C4—28no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
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—44no—
417C2×C42—24no—
418C2×C42—24no—
419C2×C42—24no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—42no—
426C2×C42—42no—
427C2×C42—42no—
428C2×C42—42no—
429C2×C42—42no—
430C2×C42—42no—
431C2×C42—42no—
432C2×C42—42no—
433C2×C42—42no—
434C2×C42—44no—
435C2×C42—44no—
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×C42C2×D411yescharacteristic
445C2×C42C2×D411yescharacteristic
446C2×C42C2×D411yescharacteristic
447C2×C42C2×D411yescharacteristic
448C2×C42C2411yescharacteristic
449C2×C42C2411yescharacteristic
450C2×C42C2411yescharacteristic
451C2×C42C2411yescharacteristic
452#107—28no—
453#106—28no—
454C4⋊C8—24no—
455C4⋊C8—24no—
456C4⋊C8—44no—
457#103—28no—
458#103—28no—
459#103—28no—
460#103—44no—
461#103—44no—
462#102—28no—
463#102—44no—
464#102—44no—
465C22⋊C8—24no—
466C22⋊C8—24no—
467C22⋊C8—28no—
468#95—22no—
469#95—22no—
470#95—22no—
471#95—22no—
472#95—22no—
473#95—22no—
474#95—22no—
475#95—22no—
476#95—22no—
477#95—22no—
478#95—22no—
479#95—22no—
480#95—22no—
481#95—22no—
482#95—22no—
483#95—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—41no—
490C24—41no—
491C24#12114yes—
492C24C22×D411yescharacteristic
493C24C22×D411yescharacteristic
494C24C22×D411yescharacteristic
495#41—88no—
496#41—88no—
497C2×Q8—24no—
498C2×Q8—22no—
499C2×Q8—22no—
500C2×Q8—22no—
501C2×Q8—22no—
502C2×Q8—22no—
503C2×Q8—24no—
504C2×Q8—22no—
505C2×Q8—22no—
506C2×Q8—24no—
507C2×Q8—48no—
508C2×Q8—42no—
509C2×Q8—42no—
510C2×Q8—48no—
511C2×Q8C22×D414yes—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—24no—
515C2×D4—24no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—44no—
519C2×D4—44no—
520C2×D4—44no—
521C2×D4—44no—
522C2×D4—44no—
523C2×D4—44no—
524C2×D4—44no—
525C2×D4—44no—
526C2×D4—44no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—42no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
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—22no—
565C22×C4—22no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—416no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—416no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—44no—
603C22×C4#12114yes—
604C22×C4#12114yes—
605C22×C4#12114yes—
606C22×C4#13514yes—
607C22×C4#13714yes—
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D412yes—
616C22×C4C22×D412yes—
617C22×C4C22×D412yes—
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C2×#4112yes—
623C22×C4C2×#4112yes—
624C22×C4C2×#4112yes—
625C22×C4C2511yescharacteristic
626Q16—88no—
627SD16—88no—
628C2×C8—24no—
629C2×C8—24no—
630C2×C8—24no—
631C2×C8—24no—
632C2×C8—24no—
633C2×C8—24no—
634C2×C8—88no—
635C4⋊C4—28no—
636C4⋊C4—28no—
637C4⋊C4—24no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—42no—
648C4⋊C4—44no—
649C4⋊C4—44no—
650C4⋊C4—42no—
651C4⋊C4—44no—
652C4⋊C4—42no—
653C4⋊C4—42no—
654C4⋊C4—44no—
655C4⋊C4—44no—
656C4⋊C4—44no—
657C4⋊C4—42no—
658C4⋊C4—42no—
659C4⋊C4—42no—
660C4⋊C4—42no—
661C4⋊C4C22×D414yes—
662C22⋊C4—28no—
663C22⋊C4—28no—
664C22⋊C4—44no—
665C22⋊C4—44no—
666C22⋊C4—44no—
667C22⋊C4—44no—
668C22⋊C4—44no—
669C22⋊C4—44no—
670C22⋊C4—44no—
671C22⋊C4—44no—
672C22⋊C4—44no—
673C22⋊C4—44no—
674C22⋊C4—44no—
675C22⋊C4—44no—
676C22⋊C4—44no—
677C42—22no—
678C42—22no—
679C42—22no—
680C42—22no—
681C42—22no—
682C42—22no—
683C42—22no—
684C42—22no—
685C42—22no—
686C42—41no—
687C42—41no—
688C42—41no—
689C42—41no—
690C42—41no—
691C42—41no—
692C42—44no—
693C42—44no—
694C42—44no—
695C42—44no—
696C42—44no—
697C42H(5,𝔽2)14yes—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—28no—
709C23—28no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23—44no—
718C23—44no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23C2×#12112yes—
727C23C2×#12112yes—
728C23C2×#12112yes—
729C23C2×#13512yes—
730C23C2×#13712yes—
731C23#57512yes—
732C23#57512yes—
733C23C23×D411yescharacteristic
734Q8—24no—
735Q8—24no—
736Q8—48no—
737Q8—42no—
738Q8—42no—
739Q8—44no—
740Q8—44no—
741D4—44no—
742D4—44no—
743D4—84no—
744D4—88no—
745D4—88no—
746D4—88no—
747D4—84no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—28no—
761C2×C4—28no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—48no—
794C2×C4—44no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—48no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—44no—
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—88no—
817C2×C4—84no—
818C2×C4—84no—
819C2×C4C2×#12112yes—
820C2×C4C2×#12112yes—
821C2×C4C2×#12112yes—
822C2×C4#53412yes—
823C2×C4#53412yes—
824C2×C4C2×#13512yes—
825C2×C4C2×#13512yes—
826C2×C4C2×#13712yes—
827C2×C4C2×#13712yes—
828C2×C4C23×D411yescharacteristic
829C2×C4C22×#4111yescharacteristic
830C2×C4C2×H(5,𝔽2)12yes—
831C2×C4#58512yes—
832C8—44no—
833C8—44no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—416no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—82no—
855C22—82no—
856C22—82no—
857C22—82no—
858C22—82no—
859C22—82no—
860C22—82no—
861C22#303514yes—
862C22#303714yes—
863C22C22×#12111yescharacteristic
864C22C2×#53411yescharacteristic
865C22#344911yescharacteristic
866C22C22×#13511yescharacteristic
867C22C22×#13711yescharacteristic
868C22C2×#57511yescharacteristic
869C22C2×#57511yescharacteristic
870C4—22no—
871C4—22no—
872C4—22no—
873C4—22no—
874C4—22no—
875C4—22no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—44no—
881C4—44no—
882C4—82no—
883C4—82no—
884C4—82no—
885C4—82no—
886C4—82no—
887C4#319014yescomplemented
888C4#349612yes—
889C4#350512yes—
890C2—24no—
891C2—24no—
892C2—42no—
893C2—162no—
894C2#3500011yescharacteristic
895C2C2×#303511yescharacteristic
896C2C2×#303711yescharacteristic
897C2C2×#319011yescharacteristic
898C2#6075211yescharacteristic
899C2#6094211yescharacteristic
900C2#6096311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36624C2
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×#3190C2semidirect
3. C2×C4×C22⋊Q8C2semidirect
4. #33108C2semidirect
5. #33106C2semidirect
6. #32906C2semidirect
7. #32903C2semidirect
8. #29760C2semidirect
9. #29719C2semidirect
10. #28576C2semidirect
11. #28125C2semidirect
12. #27649C2semidirect
13. #24753C2semidirect
14. #24752C2semidirect
15. #24213C2semidirect
16. #21763C2semidirect
17. C2×#1797C2semidirect
29. C2×#462C22semidirect
30. C2×#460C22semidirect
68. #2085C22semidirect
69. #2074C22semidirect
70. #2068C22semidirect
71. #2065C22semidirect
72. #2056C22semidirect
73. #2055C22semidirect
74. #2042C22semidirect
75. #2015C22semidirect
76. #1982C22semidirect
77. #1981C22semidirect
78. #1948C22semidirect
79. #1947C22semidirect
80. #1927C22semidirect
81. #1925C22semidirect
84. #1880C22semidirect
85. #1878C22semidirect
91. #1803C22semidirect
92. #1803C22semidirect
118. C2×C22⋊Q8D4semidirect
887. C4#3190semidirect

Maximal subgroups

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

subgroupindex
C2×#31902
#366242
C2×C4×C22⋊Q82
#331082
#331062
#329062
#329032
#297602
#297192
#285762
#281252
#276492
#247532
#247522
#242132
#217632
C2×#17972