Finite Group Databasebeta

← #6454283

Subgroups — #6454283

Order 512.

2542 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3101C211yesmaximal, characteristic, complemented
2C2×#2920C211yesmaximal, characteristic, complemented
3#36625C211yesmaximal, characteristic, complemented
4C2×C4×#121C211yesmaximal, characteristic
5#24843C212yesmaximal, complemented
6#24759C212yesmaximal, complemented
7#24708C212yesmaximal, complemented
8#24659C212yesmaximal, complemented
9#24609C212yesmaximal, complemented
10#24559C212yesmaximal, complemented
11#24507C212yesmaximal, complemented
12#24385C212yesmaximal
13#23701C214yesmaximal, complemented
14C4×#468C214yesmaximal, complemented
15#21385C211yesmaximal, characteristic, complemented
16#21358C211yesmaximal, characteristic, complemented
17#20732C211yesmaximal, characteristic, complemented
18C2×#533C2211yescharacteristic
19C22×#121C2211yescharacteristic
20C22×C4×D4—21no—
21C22×C4×D4C2211yescharacteristic
22C23×C42C2211yescharacteristic
23#3101—28no—
24C2×#483C2212yes—
25C2×#476C2212yescomplemented
26C2×#468C2214yes—
27C2×#461C2212yescomplemented
28C2×#450C2212yes—
29C2×C4×SD16C2214yescomplemented
30#2920—28no—
31C2×#432C2212yes—
32C2×#432C2212yescomplemented
33C2×#431C2211yescharacteristic
34C2×#431C2211yescharacteristic
35C2×#431C2212yescomplemented
36C2×#423C2212yescomplemented
37C2×#407C2212yes—
38C2×C4×M16C2212yescomplemented
39#2857C2211yescharacteristic, complemented
40#2857C2211yescharacteristic, complemented
41#2857C2211yescharacteristic, complemented
42#2857C2211yescharacteristic, complemented
43#2855—21no—
44#2855C2212yes—
45#2851—21no—
46#2851—21no—
47#2848—21no—
48#2848C2212yes—
49C4×C22⋊Q8—21no—
50C4×C22⋊Q8—21no—
51C4×C22⋊Q8C2212yescomplemented
52C4×C22⋊Q8C2212yescomplemented
53C4×#121—21no—
54C4×#121—21no—
55C4×#121—21no—
56C4×#121—21no—
57C4×#121C2212yes—
58C4×#121C2212yes—
59C4×#121C2212yes—
60C4×#121C2212yes—
61#2296—21no—
62C2×#390C2211yescharacteristic
63C2×#389C2211yescharacteristic
64C2×#388—21no—
65C2×#386—21no—
66#2285C2211yescharacteristic
67#2280—21no—
68C2×#380C2211yescharacteristic
69C2×C4×C4⋊C4C2211yescharacteristic
70C2×C4×C22⋊C4—21no—
71#2088C2214yescomplemented
72#2077C2214yescomplemented
73#2068C2214yescomplemented
74#2067C2214yescomplemented
75#2055C2214yescomplemented
76#2036C2214yescomplemented
77#2033C2214yes—
78#2000C2214yes—
79#1987C2212yescomplemented
80#1981C2212yescomplemented
81#1973C2214yescomplemented
82#1947C2212yescomplemented
83#1947C2212yescomplemented
84#1943C2214yescomplemented
85#1936C2214yescomplemented
86#1935C2214yescomplemented
87#1895C2214yes—
88#1894C2214yescomplemented
89#1872C2212yes—
90#1872C2212yes—
91#1852C2212yes—
92#1852C2212yes—
93#1823C2212yes—
94#1809C2214yescomplemented
95#1802C2212yescomplemented
96#1802C2212yescomplemented
97#1786C2212yes—
98C4×#107C2214yescomplemented
99C4×#103C2214yescomplemented
100C4×#102C2214yescomplemented
101C23×D4—21no—
102C23×D4C2311yescharacteristic
103C24×C4—21no—
104C24×C4D411yescharacteristic
105C24×C4D411yescharacteristic
106C24×C4C2311yescharacteristic
107C22×SD16C2314yes—
108C22×M16C2314yes—
109#533—24no—
110#533—24no—
111C2×C4⋊Q8C2311yescharacteristic
112C2×C4⋊Q8C2311yescharacteristic
113C2×#125—21no—
114C2×C22⋊Q8—21no—
115C2×C22⋊Q8—21no—
116C2×C22⋊Q8—21no—
117C2×C22⋊Q8C2312yes—
118C2×C22⋊Q8C2312yes—
119C2×C22⋊Q8C2312yes—
120C2×#121—21no—
121C2×#121—21no—
122C2×#121—28no—
123C2×#121C2312yes—
124C2×#121C2312yes—
125C2×C4×Q8—21no—
126C2×C4×Q8C2312yes—
127C2×C4×D4—22no—
128C2×C4×D4—22no—
129C2×C4×D4—22no—
130C2×C4×D4—22no—
131C2×C4×D4—21no—
132C2×C4×D4—21no—
133C2×C4×D4—24no—
134C2×C4×D4—24no—
135C2×C4×D4—48no—
136C2×C4×D4C2312yes—
137C2×C4×D4C2312yes—
138C2×#117—21no—
139C2×#117—21no—
140C22×C4⋊C4—21no—
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C22⋊C4—21no—
147C22×C22⋊C4—21no—
148C22×C22⋊C4—21no—
149C22×C42—24no—
150C22×C42—24no—
151C22×C42—21no—
152C22×C42D411yescharacteristic
153C22×C42D411yescharacteristic
154C22×C42D411yescharacteristic
155C22×C42D411yescharacteristic
156C22×C42D411yescharacteristic
157C22×C42D411yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164#483—28no—
165#476—28no—
166#468—216no—
167#461—28no—
168#450—28no—
169C4×SD16—216no—
170#432—28no—
171#432—28no—
172#431—24no—
173#431—28no—
174#431D418yescomplemented
175C2×#107C2314yes—
176C2×#107C2314yes—
177C2×#106C2314yes—
178#423—28no—
179C2×C4⋊C8C2314yes—
180C2×C4⋊C8C2312yes—
181C2×C4⋊C8C2312yes—
182C2×#103C2314yes—
183C2×#103C2314yes—
184C2×#103C2314yes—
185C2×#102C2314yes—
186C2×#102C2314yes—
187C2×#102C2314yes—
188#407—28no—
189C2×C22⋊C8C2314yes—
190C2×C22⋊C8C2312yes—
191C2×C22⋊C8C2312yes—
192C4×M16—28no—
193C2×#97C2314yes—
194C2×C4×C8C2312yes—
195C2×C4×C8C2312yes—
196#391—21no—
197#391—21no—
198#391C2312yes—
199#391C2312yes—
200#390—21no—
201#390—21no—
202#390C2312yes—
203#390C2312yes—
204#389—21no—
205#389—21no—
206#389—21no—
207#389—21no—
208#389—21no—
209#389—21no—
210#389—21no—
211#389—21no—
212#389C2312yes—
213#389C2312yes—
214#389C2312yes—
215#389C2312yes—
216#388—22no—
217#388—22no—
218#388—22no—
219#388—22no—
220#387—22no—
221#387—22no—
222#387—22no—
223#387—22no—
224#386—22no—
225#386—22no—
226#386—22no—
227#386—22no—
228#385—22no—
229#385—22no—
230#385—22no—
231#385—22no—
232#385—22no—
233#385—22no—
234#384C2311yescharacteristic
235#384C2311yescharacteristic
236#382—21no—
237#381—22no—
238#380—21no—
239#380—21no—
240#380—21no—
241#380—21no—
242#380—21no—
243#380—21no—
244#380—21no—
245#380—21no—
246#380—21no—
247#380C2312yes—
248#380C2312yes—
249#380C2312yes—
250#380C2312yes—
251#380C2312yes—
252#379—22no—
253C4×C4⋊C4—21no—
254C4×C4⋊C4—21no—
255C4×C4⋊C4—21no—
256C4×C4⋊C4—22no—
257C4×C4⋊C4—22no—
258C4×C4⋊C4C2312yes—
259C4×C4⋊C4C2312yes—
260C4×C4⋊C4C2312yes—
261C4×C22⋊C4—22no—
262C4×C22⋊C4—22no—
263C4×C22⋊C4—22no—
264C4×C22⋊C4—22no—
265C4×C22⋊C4—22no—
266C4×C22⋊C4—22no—
267C2×#95—21no—
268C2×#95—21no—
269C2×#95—21no—
270#340C2314yes—
271#340C2314yes—
272#340C2314yes—
273#340C2314yes—
274#340C2314yes—
275#340C2314yes—
276C25—21no—
277C25C2×D411yescharacteristic
278C22×Q8—21no—
279C22×Q8C2412yes—
280C22×D4—28no—
281C22×D4—22no—
282C22×D4—22no—
283C22×D4—24no—
284C22×D4—21no—
285C22×D4—22no—
286C22×D4—22no—
287C22×D4—42no—
288C22×D4—44no—
289C22×D4—44no—
290C22×D4C2412yes—
291C23×C4—21no—
292C23×C4—24no—
293C23×C4—24no—
294C23×C4—24no—
295C23×C4—24no—
296C23×C4—22no—
297C23×C4—24no—
298C23×C4—22no—
299C23×C4—21no—
300C23×C4—21no—
301C23×C4—22no—
302C23×C4—22no—
303C23×C4—42no—
304C23×C4—42no—
305C23×C4—42no—
306C23×C4—44no—
307C23×C4—44no—
308C23×C4—44no—
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×D411yescharacteristic
319C23×C4C2×D411yescharacteristic
320C23×C4C2×D411yescharacteristic
321C23×C4C2×D411yescharacteristic
322C23×C4C2×D411yescharacteristic
323C23×C4C2×D411yescharacteristic
324C23×C4C2411yescharacteristic
325C23×C4C2411yescharacteristic
326C23×C4C2411yescharacteristic
327C2×SD16—28no—
328C2×SD16—28no—
329C2×SD16—44no—
330C2×M16—28no—
331C2×M16—28no—
332C2×M16—44no—
333C22×C8C2414yes—
334C22×C8C2414yes—
335C4⋊Q8—22no—
336C4⋊Q8—22no—
337C4⋊Q8—22no—
338C4⋊Q8—22no—
339#125—44no—
340C22⋊Q8—24no—
341C22⋊Q8—24no—
342C22⋊Q8—28no—
343C22⋊Q8—44no—
344C22⋊Q8—44no—
345C22⋊Q8—44no—
346C22⋊Q8—44no—
347#121—28no—
348#121—28no—
349#121—24no—
350#121—24no—
351#121—24no—
352#121#4118yes—
353C4×Q8—24no—
354C4×Q8—24no—
355C4×Q8—44no—
356C4×D4—24no—
357C4×D4—24no—
358C4×D4—24no—
359C4×D4—24no—
360C4×D4—48no—
361C4×D4—48no—
362C4×D4—48no—
363C4×D4—48no—
364C4×D4—44no—
365C4×D4—44no—
366#117—44no—
367#117—44no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—42no—
390C2×C4⋊C4—44no—
391C2×C4⋊C4C2412yes—
392C2×C4⋊C4C2412yes—
393C2×C4⋊C4C2412yes—
394C2×C4⋊C4C2412yes—
395C2×C4⋊C4C2412yes—
396C2×C4⋊C4C2412yes—
397C2×C22⋊C4—28no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
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—44no—
415C2×C22⋊C4—44no—
416C2×C22⋊C4—44no—
417C2×C22⋊C4—44no—
418C2×C42—24no—
419C2×C42—24no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—24no—
423C2×C42—24no—
424C2×C42—24no—
425C2×C42—24no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42—22no—
436C2×C42—22no—
437C2×C42—22no—
438C2×C42—44no—
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×C42C2×D411yescharacteristic
449C2×C42C2×D411yescharacteristic
450C2×C42C2×D411yescharacteristic
451C2×C42C2×D414yes—
452C2×C42#4114yes—
453C2×C42C2411yescharacteristic
454C2×C42C2411yescharacteristic
455C2×C42C2411yescharacteristic
456C2×C42C2411yescharacteristic
457#107—28no—
458#107—44no—
459#106—28no—
460C4⋊C8—28no—
461C4⋊C8—24no—
462C4⋊C8C2×D418yescomplemented
463#103—28no—
464#103—28no—
465#103—44no—
466#102—28no—
467#102—28no—
468#102—44no—
469C22⋊C8—24no—
470C22⋊C8—28no—
471C22⋊C8C2×D418yes—
472#97—28no—
473C4×C8—24no—
474C4×C8C2×D418yescomplemented
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—
484#95—22no—
485#95—22no—
486#95—22no—
487#95—22no—
488#95—22no—
489#95—22no—
490#95—22no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—24no—
495C24—22no—
496C24—22no—
497C24—22no—
498C24—41no—
499C24—41no—
500C24—42no—
501C24—42no—
502C24—42no—
503C24—42no—
504C24—42no—
505C24—42no—
506C24C22×D411yescharacteristic
507C24C22×D411yescharacteristic
508C24C22×D411yescharacteristic
509C2×Q8—22no—
510C2×Q8—24no—
511C2×Q8—22no—
512C2×Q8—24no—
513C2×Q8—42no—
514C2×Q8—42no—
515C2×Q8—42no—
516C2×D4—24no—
517C2×D4—28no—
518C2×D4—28no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—48no—
525C2×D4—48no—
526C2×D4—42no—
527C2×D4—44no—
528C2×D4—44no—
529C2×D4—432no—
530C2×D4—44no—
531C2×D4—44no—
532C2×D4—42no—
533C2×D4C2×#4114yes—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
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—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
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—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—48no—
593C22×C4—48no—
594C22×C4—416no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—416no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—816no—
611C22×C4#12114yes—
612C22×C4#12114yes—
613C22×C4AGL(1,ℤ/8)14yes—
614C22×C4#13714yes—
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D412yes—
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C22×D411yescharacteristic
626C22×C4C22×D411yescharacteristic
627C22×C4C2×#4112yes—
628C22×C4C2×#4114yes—
629C22×C4C2511yescharacteristic
630SD16—416no—
631M16—416no—
632C2×C8—24no—
633C2×C8—24no—
634C2×C8—24no—
635C2×C8—24no—
636C2×C8—24no—
637C2×C8C22×D418yes—
638C4⋊C4—24no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—24no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—24no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—42no—
649C4⋊C4—44no—
650C4⋊C4—44no—
651C4⋊C4—42no—
652C4⋊C4—42no—
653C4⋊C4—44no—
654C4⋊C4—44no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C4⋊C4—42no—
658C4⋊C4—44no—
659C4⋊C4—44no—
660C4⋊C4—42no—
661C4⋊C4—44no—
662C4⋊C4—42no—
663C4⋊C4—42no—
664C4⋊C4—44no—
665C4⋊C4C2×#4114yes—
666C22⋊C4—28no—
667C22⋊C4—28no—
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—
677C22⋊C4—44no—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—44no—
681C22⋊C4—44no—
682C42—22no—
683C42—22no—
684C42—22no—
685C42—22no—
686C42—22no—
687C42—22no—
688C42—22no—
689C42—22no—
690C42—22no—
691C42—22no—
692C42—21no—
693C42—21no—
694C42—21no—
695C42—21no—
696C42—44no—
697C42—44no—
698C42—44no—
699C42—44no—
700C42#12114yes—
701C42#12114yes—
702C42C22×D412yes—
703C42C22×D412yes—
704C42C2×#4112yes—
705C42C2×#4112yes—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—28no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—24no—
724C23—44no—
725C23—44no—
726C23—44no—
727C23—44no—
728C23—44no—
729C23—48no—
730C23—48no—
731C23—48no—
732C23—44no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—84no—
740C23—84no—
741C23—84no—
742C23—84no—
743C23C2×#12112yes—
744C23#52512yes—
745C23C2×AGL(1,ℤ/8)12yes—
746C23C2×#13712yes—
747C23#57512yes—
748C23C23×D411yescharacteristic
749Q8—44no—
750Q8—44no—
751Q8—84no—
752D4—24no—
753D4—24no—
754D4—48no—
755D4—416no—
756D4—416no—
757D4—42no—
758D4—42no—
759C2×C4—28no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—24no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—48no—
796C2×C4—44no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
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—84no—
824C2×C4—84no—
825C2×C4—88no—
826C2×C4—88no—
827C2×C4#468116yescomplemented
828C2×C4C2×#12112yes—
829C2×C4C2×#12112yes—
830C2×C4C2×#12112yes—
831C2×C4C2×#12112yes—
832C2×C4C2×#12112yes—
833C2×C4#52512yes—
834C2×C4C2×AGL(1,ℤ/8)12yes—
835C2×C4C2×AGL(1,ℤ/8)12yes—
836C2×C4C2×#13712yes—
837C2×C4C2×#13712yes—
838C2×C4#57512yes—
839C2×C4C23×D411yescharacteristic
840C2×C4C22×#4112yes—
841C2×C4C22×#4111yescharacteristic
842C2×C4#58512yes—
843C8—28no—
844C8—44no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—416no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—44no—
867C22—44no—
868C22—44no—
869C22—816no—
870C22—82no—
871C22—82no—
872C22—82no—
873C22—82no—
874C22C2×#46814yes—
875C22C22×#12111yescharacteristic
876C22C2×#52511yescharacteristic
877C22#344911yescharacteristic
878C22C22×AGL(1,ℤ/8)11yescharacteristic
879C22C22×#13711yescharacteristic
880C22C2×#57511yescharacteristic
881C22C2×#57511yescharacteristic
882C4—22no—
883C4—22no—
884C4—22no—
885C4—22no—
886C4—22no—
887C4—41no—
888C4—41no—
889C4—41no—
890C4—44no—
891C4—41no—
892C4—82no—
893C4—82no—
894C4—82no—
895C4—82no—
896C4—82no—
897C4—82no—
898C4C2×#46814yes—
899C4C2×#46814yes—
900C4D4×#4112yes—
901C4#347512yes—
902C2—24no—
903C2—42no—
904C2—42no—
905C2—84no—
906C2#3473711yescharacteristic
907C2C22×#46811yescharacteristic
908C2#6044411yescharacteristic
909C2#6055811yescharacteristic
910C2#6056211yescharacteristic
911C2#6095011yescharacteristic
912C2#6095111yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutator, Frattini, cosocleC22×C4C25
socleC23C23×D4
prime radicalC22×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3101C2semidirect
2. C2×#2920C2semidirect
3. #36625C2semidirect
5. #24843C2semidirect
6. #24759C2semidirect
7. #24708C2semidirect
8. #24659C2semidirect
9. #24609C2semidirect
10. #24559C2semidirect
11. #24507C2semidirect
13. #23701C2semidirect
14. C4×#468C2semidirect
15. #21385C2semidirect
16. #21358C2semidirect
17. #20732C2semidirect
25. C2×#476C22semidirect
27. C2×#461C22semidirect
29. C2×C4×SD16C22semidirect
32. C2×#432C22semidirect
35. C2×#431C22semidirect
36. C2×#423C22semidirect
38. C2×C4×M16C22semidirect
39. #2857C22semidirect
40. #2857C22semidirect
41. #2857C22semidirect
42. #2857C22semidirect
51. C4×C22⋊Q8C22semidirect
52. C4×C22⋊Q8C22semidirect
71. #2088C22semidirect
72. #2077C22semidirect
73. #2068C22semidirect
74. #2067C22semidirect
75. #2055C22semidirect
76. #2036C22semidirect
79. #1987C22semidirect
80. #1981C22semidirect
81. #1973C22semidirect
82. #1947C22semidirect
83. #1947C22semidirect
84. #1943C22semidirect
85. #1936C22semidirect
86. #1935C22semidirect
88. #1894C22semidirect
94. #1809C22semidirect
95. #1802C22semidirect
96. #1802C22semidirect
98. C4×#107C22semidirect
99. C4×#103C22semidirect
100. C4×#102C22semidirect
174. #431D4semidirect
462. C4⋊C8C2×D4semidirect
474. C4×C8C2×D4semidirect
827. C2×C4#468semidirect

Maximal subgroups

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

subgroupindex
C2×#31012
C2×#29202
#366252
C2×C4×#1212
#248432
#247592
#247082
#246592
#246092
#245592
#245072
#243852
#237012
C4×#4682
#213852
#213582
#207322