Finite Group Databasebeta

← #6477705

Subgroups — #6477705

Order 512.

2286 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3193C211yesmaximal, characteristic
2C2×#2920C211yesmaximal, characteristic, complemented
3C2×#2855C211yesmaximal, characteristic, complemented
4C2×#2854C211yesmaximal, characteristic
5#33145C214yesmaximal, complemented
6#29784C214yesmaximal, complemented
7#24608C212yesmaximal, complemented
8#24606C212yesmaximal, complemented
9#24602C212yesmaximal, complemented
10#24600C212yesmaximal, complemented
11#24509C212yesmaximal, complemented
12#24507C212yesmaximal, complemented
13#24503C212yesmaximal, complemented
14#24501C212yesmaximal, complemented
15#21942C211yesmaximal, characteristic, complemented
16#21765C211yesmaximal, characteristic, complemented
17#21764C211yesmaximal, characteristic
18C22×#123—21no—
19C22×C22⋊Q8C2211yescharacteristic
20C22×#121C2211yescharacteristic
21C23×C42C2211yescharacteristic
22#3193—28no—
23C2×#484C2212yes—
24C2×#480C2212yes—
25C2×#468C2214yes—
26C2×#448C2212yes—
27C2×#450C2212yes—
28#2920—28no—
29C2×#432C2212yes—
30C2×#432C2212yescomplemented
31C2×#431C2212yes—
32C2×#431C2212yescomplemented
33C2×#423C2212yescomplemented
34C2×#407C2211yescharacteristic
35C2×#407C2211yescharacteristic
36C2×C4×M16C2212yescomplemented
37#2855—21no—
38#2855—21no—
39#2855—21no—
40#2855—21no—
41#2855C2212yes—
42#2855C2212yes—
43#2855C2212yescomplemented
44#2855C2212yescomplemented
45#2854—21no—
46#2854—21no—
47#2854—21no—
48#2854—21no—
49#2854C2212yes—
50#2854C2212yes—
51#2854C2212yes—
52#2854C2212yes—
53C2×#391C2211yescharacteristic, complemented
54C2×#391C2211yescharacteristic, complemented
55C2×#390C2211yescharacteristic
56C2×#390C2211yescharacteristic
57C2×#389C2211yescharacteristic
58C2×#389C2211yescharacteristic
59C2×#389C2211yescharacteristic, complemented
60C2×#389C2211yescharacteristic, complemented
61C2×#388—21no—
62C2×#388—21no—
63C2×#387—21no—
64C2×#387—21no—
65C2×#386—21no—
66C2×#385—21no—
67C2×#381—21no—
68C2×#380C2211yescharacteristic
69C2×#380C2211yescharacteristic
70#2087C2214yescomplemented
71#2086C2214yescomplemented
72#2068C2214yescomplemented
73#2067C2214yescomplemented
74#2066C2214yescomplemented
75#2065C2214yescomplemented
76#2055C2214yescomplemented
77#2055C2214yescomplemented
78#1973C2214yescomplemented
79#1968C2214yescomplemented
80#1944C2214yescomplemented
81#1942C2214yescomplemented
82#1936C2214yescomplemented
83#1935C2214yescomplemented
84#1934C2214yescomplemented
85#1933C2214yescomplemented
86#1895C2214yes—
87#1894C2214yescomplemented
88#1874C2212yes—
89#1874C2212yes—
90#1872C2212yes—
91#1872C2212yes—
92#1853C2212yes—
93#1853C2212yescomplemented
94#1852C2212yes—
95#1852C2212yescomplemented
96#1824C2212yes—
97#1823C2212yescomplemented
98#1809C2214yescomplemented
99#1787C2212yescomplemented
100#1786C2212yes—
101C23×Q8C2311yescharacteristic
102C23×D4—21no—
103C23×D4C2311yescharacteristic
104C24×C4D411yescharacteristic
105C24×C4D411yescharacteristic
106C24×C4C2311yescharacteristic
107C22×SD16C2314yes—
108C22×M16C2312yes—
109C22×M16C2312yes—
110C2×#123—22no—
111C2×#123—22no—
112C2×#123—22no—
113C2×#123—22no—
114C2×#123—48no—
115C2×C22⋊Q8—21no—
116C2×C22⋊Q8—21no—
117C2×C22⋊Q8—24no—
118C2×C22⋊Q8—24no—
119C2×C22⋊Q8C2312yes—
120C2×C22⋊Q8C2312yes—
121C2×#121—21no—
122C2×#121—21no—
123C2×#121—24no—
124C2×#121—24no—
125C2×#121C2312yes—
126C2×#121C2312yes—
127C22×C4⋊C4—21no—
128C22×C4⋊C4—21no—
129C22×C4⋊C4—21no—
130C22×C4⋊C4—21no—
131C22×C4⋊C4—21no—
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C22⋊C4—21no—
139C22×C22⋊C4—21no—
140C22×C22⋊C4—21no—
141C22×C22⋊C4—21no—
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C42—24no—
147C22×C42—24no—
148C22×C42D411yescharacteristic
149C22×C42D411yescharacteristic
150C22×C42D411yescharacteristic
151C22×C42D411yescharacteristic
152C22×C42D411yescharacteristic
153C22×C42D411yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160#484—28no—
161#480—28no—
162#468—216no—
163#450—28no—
164#448—28no—
165#432—28no—
166#432—28no—
167#431—28no—
168#431—28no—
169C2×#107C2314yes—
170C2×#107C2314yes—
171C2×#106C2314yes—
172#423—28no—
173C2×C4⋊C8C2314yes—
174C2×C4⋊C8C2314yes—
175C2×#103C2314yes—
176C2×#103C2314yes—
177C2×#103C2314yes—
178C2×#102C2314yes—
179C2×#102C2314yes—
180C2×#102C2314yes—
181#407—24no—
182#407D418yes—
183C2×C22⋊C8C2312yes—
184C2×C22⋊C8C2312yes—
185C2×C22⋊C8C2312yes—
186C2×C22⋊C8C2312yes—
187C4×M16—28no—
188C2×#97C2314yes—
189C2×C4×C8C2314yes—
190#391—21no—
191#391—21no—
192#391—21no—
193#391—21no—
194#391C2312yes—
195#391C2312yes—
196#391C2312yes—
197#391C2312yes—
198#390—21no—
199#390—21no—
200#390—21no—
201#390—21no—
202#390C2312yes—
203#390C2312yes—
204#390C2312yes—
205#390C2312yes—
206#389—21no—
207#389—21no—
208#389—21no—
209#389—21no—
210#389—21no—
211#389—21no—
212#389—21no—
213#389—21no—
214#389C2312yes—
215#389C2312yes—
216#389C2312yes—
217#389C2312yes—
218#389C2312yes—
219#389C2312yes—
220#389C2312yes—
221#389C2312yes—
222#388—22no—
223#388—22no—
224#388—22no—
225#388—22no—
226#388—22no—
227#388—22no—
228#388—22no—
229#388—22no—
230#387—22no—
231#387—22no—
232#387—22no—
233#387—22no—
234#387—22no—
235#387—22no—
236#387—22no—
237#387—22no—
238#386—22no—
239#386—22no—
240#386—22no—
241#386—22no—
242#385—22no—
243#385—22no—
244#385—22no—
245#385—22no—
246#381—22no—
247#381—22no—
248#381—22no—
249#381—22no—
250#380—21no—
251#380—21no—
252#380—21no—
253#380—21no—
254#380C2312yes—
255#380C2312yes—
256#380C2312yes—
257#380C2312yes—
258C2×#95—21no—
259C2×#95—21no—
260C2×#95—21no—
261C2×#95—21no—
262C2×#95—21no—
263C2×#95—21no—
264C2×#95—21no—
265C2×#95—21no—
266C2×#95—21no—
267C2×#95—21no—
268#340C2314yes—
269#340C2314yes—
270#340C2314yes—
271#340C2314yes—
272#340C2314yes—
273#340C2314yes—
274C25—21no—
275C25C2×D411yescharacteristic
276C22×Q8—21no—
277C22×Q8—22no—
278C22×Q8—22no—
279C22×Q8—42no—
280C22×Q8—42no—
281C22×Q8C2412yes—
282C22×D4—22no—
283C22×D4—22no—
284C22×D4—22no—
285C22×D4—21no—
286C22×D4—22no—
287C22×D4—42no—
288C22×D4—42no—
289C22×D4—44no—
290C22×D4—44no—
291C22×D4—44no—
292C22×D4C2412yes—
293C23×C4—24no—
294C23×C4—24no—
295C23×C4—24no—
296C23×C4—24no—
297C23×C4—21no—
298C23×C4—21no—
299C23×C4—21no—
300C23×C4—21no—
301C23×C4—21no—
302C23×C4—21no—
303C23×C4—21no—
304C23×C4—42no—
305C23×C4—42no—
306C23×C4—42no—
307C23×C4—42no—
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×D411yescharacteristic
319C23×C4C2×D411yescharacteristic
320C23×C4C2×D411yescharacteristic
321C23×C4C2×D411yescharacteristic
322C23×C4C2×D411yescharacteristic
323C23×C4C2×D414yes—
324C23×C4#4114yes—
325C23×C4C2411yescharacteristic
326C23×C4C2411yescharacteristic
327C23×C4C2411yescharacteristic
328C2×SD16—28no—
329C2×SD16—44no—
330C2×SD16—44no—
331C2×M16—24no—
332C2×M16—42no—
333C2×M16—42no—
334C2×M16—42no—
335C2×M16—42no—
336C2×M16C2×D418yes—
337C22×C8C2414yes—
338C22×C8C2414yes—
339#123—48no—
340#123—48no—
341#123—48no—
342#123—48no—
343C22⋊Q8—24no—
344C22⋊Q8—24no—
345C22⋊Q8—24no—
346C22⋊Q8—24no—
347C22⋊Q8—44no—
348C22⋊Q8—44no—
349#121—24no—
350#121—24no—
351#121—24no—
352#121—24no—
353#121—44no—
354#121—44no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—42no—
376C2×C4⋊C4—42no—
377C2×C4⋊C4—42no—
378C2×C4⋊C4—42no—
379C2×C4⋊C4—44no—
380C2×C4⋊C4—44no—
381C2×C4⋊C4—44no—
382C2×C4⋊C4—44no—
383C2×C4⋊C4—44no—
384C2×C4⋊C4C2412yes—
385C2×C4⋊C4C2412yes—
386C2×C4⋊C4C2412yes—
387C2×C4⋊C4C2412yes—
388C2×C4⋊C4C2412yes—
389C2×C4⋊C4C2412yes—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
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—44no—
407C2×C22⋊C4—44no—
408C2×C22⋊C4—44no—
409C2×C22⋊C4—44no—
410C2×C22⋊C4—44no—
411C2×C22⋊C4—44no—
412C2×C22⋊C4—44no—
413C2×C22⋊C4—44no—
414C2×C42—24no—
415C2×C42—24no—
416C2×C42—24no—
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—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42C2×D411yescharacteristic
433C2×C42C2×D411yescharacteristic
434C2×C42C2×D411yescharacteristic
435C2×C42C2×D411yescharacteristic
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×C42C2411yescharacteristic
445C2×C42C2411yescharacteristic
446C2×C42C2411yescharacteristic
447C2×C42C2411yescharacteristic
448#107—28no—
449#107—44no—
450#106—44no—
451C4⋊C8—28no—
452C4⋊C8—28no—
453#103—28no—
454#103—44no—
455#103—44no—
456#102—28no—
457#102—44no—
458#102—44no—
459C22⋊C8—24no—
460C22⋊C8—24no—
461C22⋊C8C2×D418yes—
462C22⋊C8C2×D418yes—
463#97—28no—
464C4×C8—28no—
465#95—22no—
466#95—22no—
467#95—22no—
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—
484#95—22no—
485C24—22no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—41no—
491C24—41no—
492C24—42no—
493C24—42no—
494C24—42no—
495C24—42no—
496C24—42no—
497C24—42no—
498C24—42no—
499C24#12114yes—
500C24C22×D411yescharacteristic
501C24C22×D411yescharacteristic
502C24C22×D411yescharacteristic
503C2×Q8—22no—
504C2×Q8—22no—
505C2×Q8—24no—
506C2×Q8—24no—
507C2×Q8—42no—
508C2×Q8—42no—
509C2×Q8—42no—
510C2×Q8—84no—
511C2×Q8—84no—
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—42no—
525C2×D4—84no—
526C2×D4—84no—
527C2×D4—816no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
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—22no—
542C22×C4—22no—
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—48no—
568C22×C4—48no—
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—416no—
584C22×C4—416no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
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—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4#12114yes—
607C22×C4#12114yes—
608C22×C4#12114yes—
609C22×C4AGL(1,ℤ/8)14yes—
610C22×C4#13714yes—
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D412yes—
619C22×C4C22×D412yes—
620C22×C4C22×D412yes—
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C2×#4112yes—
626C22×C4C2×#4112yes—
627C22×C4C2×#4112yes—
628C22×C4C2511yescharacteristic
629SD16—88no—
630M16—48no—
631M16—48no—
632C2×C8—24no—
633C2×C8—24no—
634C2×C8—24no—
635C2×C8—24no—
636C2×C8—24no—
637C2×C8C22×D418yes—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—24no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—42no—
647C4⋊C4—42no—
648C4⋊C4—42no—
649C4⋊C4—42no—
650C4⋊C4—44no—
651C4⋊C4—44no—
652C4⋊C4—44no—
653C4⋊C4—44no—
654C4⋊C4—42no—
655C4⋊C4—42no—
656C4⋊C4—44no—
657C4⋊C4—44no—
658C4⋊C4—44no—
659C4⋊C4—44no—
660C4⋊C4—44no—
661C4⋊C4—44no—
662C22⋊C4—44no—
663C22⋊C4—44no—
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—
677C22⋊C4—44no—
678C42—22no—
679C42—22no—
680C42—22no—
681C42—22no—
682C42—22no—
683C42—22no—
684C42—22no—
685C42—22no—
686C42—22no—
687C42—22no—
688C42—22no—
689C42—22no—
690C42—21no—
691C42—21no—
692C42—21no—
693C42—21no—
694C42—21no—
695C42—21no—
696C42—21no—
697C42—21no—
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—
726C23—84no—
727C23—84no—
728C23—84no—
729C23—84no—
730C23—84no—
731C23—84no—
732C23—84no—
733C23C2×#12112yes—
734C23C2×#12112yes—
735C23C2×#12112yes—
736C23C2×AGL(1,ℤ/8)12yes—
737C23C2×#13712yes—
738C23#57512yes—
739C23#57512yes—
740C23C23×D411yescharacteristic
741Q8—44no—
742Q8—44no—
743Q8—84no—
744D4—44no—
745D4—44no—
746D4—84no—
747D4—88no—
748D4—88no—
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—28no—
760C2×C4—28no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—24no—
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—21no—
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—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
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—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—84no—
818C2×C4—84no—
819C2×C4—84no—
820C2×C4—84no—
821C2×C4—84no—
822C2×C4—84no—
823C2×C4—84no—
824C2×C4C2×#12112yes—
825C2×C4C2×#12112yes—
826C2×C4C2×#12112yes—
827C2×C4C2×AGL(1,ℤ/8)12yes—
828C2×C4C2×AGL(1,ℤ/8)12yes—
829C2×C4C2×#13712yes—
830C2×C4C2×#13712yes—
831C2×C4C23×D411yescharacteristic
832C2×C4C22×#4111yescharacteristic
833C2×C4#58512yes—
834C2×C4#58512yes—
835C8—28no—
836C8—44no—
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—22no—
850C22—22no—
851C22—22no—
852C22—416no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—82no—
858C22—82no—
859C22—82no—
860C22—82no—
861C22—82no—
862C22—82no—
863C22—82no—
864C22—168no—
865C22#305514yes—
866C22#305614yes—
867C22C22×#12111yescharacteristic
868C22#344911yescharacteristic
869C22#344911yescharacteristic
870C22C22×AGL(1,ℤ/8)11yescharacteristic
871C22C22×#13711yescharacteristic
872C22C2×#57511yescharacteristic
873C22C2×#57511yescharacteristic
874C4—22no—
875C4—22no—
876C4—22no—
877C4—22no—
878C4—22no—
879C4—22no—
880C4—22no—
881C4—41no—
882C4—41no—
883C4—41no—
884C4—41no—
885C4—82no—
886C4—82no—
887C4—82no—
888C4—82no—
889C4—82no—
890C4—82no—
891C4—82no—
892C4#348512yes—
893C4#349112yes—
894C2—24no—
895C2—24no—
896C2—42no—
897C2—162no—
898C2#3508911yescharacteristic
899C2C2×#305511yescharacteristic
900C2C2×#305611yescharacteristic
901C2#6094911yescharacteristic
902C2#6095011yescharacteristic
903C2#6096411yescharacteristic
904C2#6096911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#121C22
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
2. C2×#2920C2semidirect
3. C2×#2855C2semidirect
5. #33145C2semidirect
6. #29784C2semidirect
7. #24608C2semidirect
8. #24606C2semidirect
9. #24602C2semidirect
10. #24600C2semidirect
11. #24509C2semidirect
12. #24507C2semidirect
13. #24503C2semidirect
14. #24501C2semidirect
15. #21942C2semidirect
16. #21765C2semidirect
30. C2×#432C22semidirect
32. C2×#431C22semidirect
33. C2×#423C22semidirect
36. C2×C4×M16C22semidirect
43. #2855C22semidirect
44. #2855C22semidirect
53. C2×#391C22semidirect
54. C2×#391C22semidirect
59. C2×#389C22semidirect
60. C2×#389C22semidirect
70. #2087C22semidirect
71. #2086C22semidirect
72. #2068C22semidirect
73. #2067C22semidirect
74. #2066C22semidirect
75. #2065C22semidirect
76. #2055C22semidirect
77. #2055C22semidirect
78. #1973C22semidirect
79. #1968C22semidirect
80. #1944C22semidirect
81. #1942C22semidirect
82. #1936C22semidirect
83. #1935C22semidirect
84. #1934C22semidirect
85. #1933C22semidirect
87. #1894C22semidirect
93. #1853C22semidirect
95. #1852C22semidirect
97. #1823C22semidirect
98. #1809C22semidirect
99. #1787C22semidirect

Maximal subgroups

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

subgroupindex
C2×#31932
C2×#29202
C2×#28552
C2×#28542
#331452
#297842
#246082
#246062
#246022
#246002
#245092
#245072
#245032
#245012
#219422
#217652
#217642