Finite Group Databasebeta

← #6481856

Subgroups — #6481856

Order 512.

2210 conjugacy classes of subgroups.

The subgroup lattice has 915 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3254C211yesmaximal, characteristic, complemented
2C2×#2920C211yesmaximal, characteristic, complemented
3#36625C211yesmaximal, characteristic, complemented
4#36624C211yesmaximal, characteristic
5#33145C214yesmaximal, complemented
6#29744C214yesmaximal, complemented
7#24711C212yesmaximal, complemented
8#24709C212yesmaximal, complemented
9#24702C212yesmaximal, complemented
10#24700C212yesmaximal, complemented
11#24661C212yesmaximal, complemented
12#24659C212yesmaximal, complemented
13#24653C212yesmaximal, complemented
14#24651C212yesmaximal, complemented
15#21964C211yesmaximal, characteristic, complemented
16#21894C211yesmaximal, characteristic, complemented
17#21893C211yesmaximal, characteristic, complemented
18C2×#533C2211yescharacteristic
19C2×#532C2211yescharacteristic
20C2×#525—21no—
21C23×C42C2211yescharacteristic
22#3254—28no—
23C2×#477C2212yescomplemented
24C2×#474C2212yescomplemented
25C2×#468C2214yes—
26C2×#460C2212yescomplemented
27C2×#461C2212yescomplemented
28#2920—28no—
29C2×#432C2212yes—
30C2×#432C2212yes—
31C2×#431C2212yes—
32C2×#431C2212yes—
33C2×#423C2211yescharacteristic
34C2×#423C2211yescharacteristic
35C2×#407C2212yes—
36C2×C4×M16C2212yes—
37#2857C2211yescharacteristic
38#2857C2211yescharacteristic
39#2857C2211yescharacteristic
40#2857C2211yescharacteristic
41#2857C2211yescharacteristic
42#2857C2211yescharacteristic
43#2856C2211yescharacteristic
44#2856C2211yescharacteristic
45#2855—21no—
46#2855C2212yes—
47#2854—21no—
48#2854C2212yes—
49#2851—21no—
50#2851—21no—
51#2850—21no—
52#2850—21no—
53#2848—21no—
54#2848C2212yes—
55#2847—21no—
56#2847C2212yes—
57C4×C22⋊Q8—21no—
58C4×C22⋊Q8—21no—
59C4×C22⋊Q8C2212yes—
60C4×C22⋊Q8C2212yes—
61C4×#121—21no—
62C4×#121—21no—
63C4×#121C2212yes—
64C4×#121C2212yes—
65#2297—21no—
66#2296—21no—
67#2285C2211yescharacteristic
68#2285C2211yescharacteristic
69#2280—21no—
70#2076C2214yes—
71#2075C2214yes—
72#2036C2214yes—
73#2035C2214yes—
74#2034C2214yes—
75#2033C2214yes—
76#2000C2214yes—
77#2000C2214yes—
78#1988C2212yescomplemented
79#1987C2212yescomplemented
80#1982C2212yescomplemented
81#1981C2212yescomplemented
82#1973C2214yescomplemented
83#1968C2214yescomplemented
84#1948C2212yescomplemented
85#1948C2212yescomplemented
86#1947C2212yescomplemented
87#1947C2212yescomplemented
88#1944C2214yescomplemented
89#1942C2214yescomplemented
90#1936C2214yescomplemented
91#1935C2214yescomplemented
92#1934C2214yescomplemented
93#1933C2214yescomplemented
94#1895C2214yes—
95#1894C2214yes—
96#1809C2214yes—
97#1803C2212yescomplemented
98#1803C2212yescomplemented
99#1802C2212yescomplemented
100#1802C2212yescomplemented
101C22×#41—21no—
102C24×C4D411yescharacteristic
103C24×C4D411yescharacteristic
104C24×C4C2311yescharacteristic
105C22×SD16C2314yes—
106C22×M16C2312yes—
107C22×M16C2312yes—
108#533—24no—
109#533—24no—
110#532—24no—
111#532—24no—
112C2×C4⋊Q8C2311yescharacteristic
113C2×C4⋊Q8C2311yescharacteristic
114C2×C4⋊Q8C2311yescharacteristic
115C2×#127C2311yescharacteristic
116C2×#125—21no—
117C2×#124—21no—
118#525—48no—
119C2×#123—22no—
120C2×C22⋊Q8—21no—
121C2×C22⋊Q8—21no—
122C2×C22⋊Q8—21no—
123C2×C22⋊Q8—21no—
124C2×C22⋊Q8—21no—
125C2×C22⋊Q8C2312yes—
126C2×C22⋊Q8C2312yes—
127C2×C22⋊Q8C2312yes—
128C2×#121—21no—
129C2×#121—21no—
130C2×#121—21no—
131C2×#121—21no—
132C2×#121—21no—
133C2×#121C2312yes—
134C2×#121C2312yes—
135C2×#121C2312yes—
136C2×#120—22no—
137C2×C4×Q8—21no—
138C2×C4×Q8C2312yes—
139C2×C4×D4—22no—
140C2×C4×D4—22no—
141C2×C4×D4—21no—
142C2×C4×D4C2312yes—
143C2×#117—21no—
144C2×#117—21no—
145C2×#117—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#477—28no—
161#474—28no—
162#468—216no—
163#461—28no—
164#460—28no—
165#432—28no—
166#432—28no—
167#431—28no—
168#431—28no—
169C2×#107C2314yes—
170C2×#107C2314yes—
171C2×#106C2314yes—
172#423—24no—
173#423D418yescomplemented
174C2×C4⋊C8C2312yes—
175C2×C4⋊C8C2312yes—
176C2×C4⋊C8C2312yes—
177C2×C4⋊C8C2312yes—
178C2×#103C2314yes—
179C2×#103C2314yes—
180C2×#103C2314yes—
181C2×#102C2314yes—
182C2×#102C2314yes—
183C2×#102C2314yes—
184#407—28no—
185C2×C22⋊C8C2314yes—
186C2×C22⋊C8C2314yes—
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#390—21no—
197#390—21no—
198#390—21no—
199#390—21no—
200#390C2312yes—
201#390C2312yes—
202#389—21no—
203#389—21no—
204#389—21no—
205#389—21no—
206#389—21no—
207#389—21no—
208#389—21no—
209#389—21no—
210#389C2312yes—
211#389C2312yes—
212#389C2312yes—
213#389C2312yes—
214#388—22no—
215#388—22no—
216#388—22no—
217#388—22no—
218#387—22no—
219#387—22no—
220#387—22no—
221#387—22no—
222#386—22no—
223#386—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#384C2311yescharacteristic
237#384C2311yescharacteristic
238#382—21no—
239#382—21no—
240#381—22no—
241#380—21no—
242#380—21no—
243#380—21no—
244#380—21no—
245#380—21no—
246#380—21no—
247#380—21no—
248#380—21no—
249#380—21no—
250#380—21no—
251#380C2312yes—
252#380C2312yes—
253#380C2312yes—
254#380C2312yes—
255#380C2312yes—
256#380C2312yes—
257#379—22no—
258C4×C4⋊C4—21no—
259C4×C4⋊C4—21no—
260C4×C4⋊C4—22no—
261C4×C4⋊C4—22no—
262C4×C4⋊C4C2312yes—
263C4×C4⋊C4C2312yes—
264C4×C22⋊C4—22no—
265C4×C22⋊C4—22no—
266C4×C22⋊C4—22no—
267C4×C22⋊C4—22no—
268#340C2314yes—
269#340C2314yes—
270#340C2314yes—
271#340C2314yes—
272#340C2314yes—
273#340C2314yes—
274C25C2×D411yescharacteristic
275C2×#41—44no—
276C2×#41—44no—
277C2×#41—44no—
278C22×Q8—21no—
279C22×Q8—21no—
280C22×Q8C2412yes—
281C22×D4—22no—
282C22×D4—22no—
283C22×D4—22no—
284C22×D4—21no—
285C22×D4—21no—
286C22×D4C2412yes—
287C23×C4—24no—
288C23×C4—24no—
289C23×C4—24no—
290C23×C4—24no—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—42no—
295C23×C4—42no—
296C23×C4—41no—
297C23×C4—41no—
298C23×C4—41no—
299C23×C4—41no—
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
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×C4C2411yescharacteristic
316C23×C4C2411yescharacteristic
317C23×C4C2411yescharacteristic
318C2×SD16—28no—
319C2×SD16—44no—
320C2×SD16—44no—
321C2×M16—24no—
322C2×M16—42no—
323C2×M16—42no—
324C2×M16—42no—
325C2×M16—42no—
326C2×M16C2×D418yes—
327C22×C8C2414yes—
328C22×C8C2414yes—
329C4⋊Q8—22no—
330C4⋊Q8—22no—
331C4⋊Q8—22no—
332C4⋊Q8—22no—
333C4⋊Q8—22no—
334C4⋊Q8—22no—
335#127—22no—
336#127—22no—
337#125—44no—
338#124—44no—
339#123—48no—
340C22⋊Q8—24no—
341C22⋊Q8—24no—
342C22⋊Q8—42no—
343C22⋊Q8—42no—
344C22⋊Q8—42no—
345C22⋊Q8—42no—
346C22⋊Q8—44no—
347C22⋊Q8—44no—
348C22⋊Q8—44no—
349C22⋊Q8—44no—
350C22⋊Q8—44no—
351#121—24no—
352#121—24no—
353#121—42no—
354#121—42no—
355#121—42no—
356#121—42no—
357#121—44no—
358#121—44no—
359#121—44no—
360#121—44no—
361#121—44no—
362#120—48no—
363C4×Q8—24no—
364C4×Q8—24no—
365C4×Q8—44no—
366C4×D4—24no—
367C4×D4—24no—
368C4×D4—48no—
369C4×D4—48no—
370C4×D4—44no—
371#117—44no—
372#117—44no—
373#117—44no—
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—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4C2412yes—
395C2×C4⋊C4C2412yes—
396C2×C4⋊C4C2412yes—
397C2×C4⋊C4C2412yes—
398C2×C4⋊C4C2412yes—
399C2×C4⋊C4C2412yes—
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—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C42—24no—
418C2×C42—24no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—24no—
422C2×C42—24no—
423C2×C42—24no—
424C2×C42—24no—
425C2×C42—22no—
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×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×C42C2×D414yes—
449C2×C42#4114yes—
450C2×C42C2411yescharacteristic
451C2×C42C2411yescharacteristic
452C2×C42C2411yescharacteristic
453C2×C42C2411yescharacteristic
454#107—28no—
455#107—44no—
456#106—44no—
457C4⋊C8—24no—
458C4⋊C8—24no—
459C4⋊C8C2×D418yes—
460C4⋊C8C2×D418yes—
461#103—28no—
462#103—44no—
463#103—44no—
464#102—28no—
465#102—44no—
466#102—44no—
467C22⋊C8—28no—
468C22⋊C8—28no—
469#97—28no—
470C4×C8—28no—
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—
485#95—22no—
486#95—22no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24—41no—
492C24—41no—
493C24—41no—
494C24—41no—
495C24C22×D411yescharacteristic
496C24C22×D411yescharacteristic
497C24C22×D411yescharacteristic
498#41—816no—
499C2×Q8—22no—
500C2×Q8—22no—
501C2×Q8—22no—
502C2×Q8—22no—
503C2×Q8—22no—
504C2×Q8—22no—
505C2×Q8—42no—
506C2×Q8—42no—
507C2×Q8—42no—
508C2×Q8—42no—
509C2×Q8—42no—
510C2×Q8—42no—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—42no—
518C2×D4—42no—
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—44no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—42no—
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—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
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—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
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—41no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—416no—
597C22×C4—416no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—44no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4#12114yes—
606C22×C4#12114yes—
607C22×C4AGL(1,ℤ/8)14yes—
608C22×C4#13714yes—
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D412yes—
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C2×#4112yes—
622C22×C4C2511yescharacteristic
623SD16—88no—
624M16—48no—
625M16—48no—
626C2×C8—24no—
627C2×C8—24no—
628C2×C8—24no—
629C2×C8—24no—
630C2×C8—24no—
631C2×C8C22×D418yes—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—42no—
645C4⋊C4—42no—
646C4⋊C4—42no—
647C4⋊C4—42no—
648C4⋊C4—44no—
649C4⋊C4—44no—
650C4⋊C4—44no—
651C4⋊C4—44no—
652C4⋊C4—42no—
653C4⋊C4—42no—
654C4⋊C4—42no—
655C4⋊C4—44no—
656C4⋊C4—44no—
657C4⋊C4—42no—
658C4⋊C4—44no—
659C4⋊C4—42no—
660C4⋊C4—44no—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4—42no—
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—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—44no—
681C42—22no—
682C42—22no—
683C42—22no—
684C42—22no—
685C42—22no—
686C42—22no—
687C42—22no—
688C42—22no—
689C42—22no—
690C42—22no—
691C42—21no—
692C42—21no—
693C42—21no—
694C42—21no—
695C42—44no—
696C42—44no—
697C42—44no—
698C42#12114yes—
699C42#12114yes—
700C42C22×D412yes—
701C42C22×D412yes—
702C42C2×#4112yes—
703C42C2×#4112yes—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—44no—
723C23—44no—
724C23—44no—
725C23—44no—
726C23—44no—
727C23—44no—
728C23—44no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23C2×#12112yes—
737C23C2×AGL(1,ℤ/8)12yes—
738C23C2×#13712yes—
739C23C23×D411yescharacteristic
740Q8—42no—
741Q8—42no—
742Q8—42no—
743Q8—42no—
744Q8—84no—
745Q8—84no—
746D4—42no—
747D4—42no—
748D4—42no—
749D4—42no—
750D4—84no—
751D4—88no—
752D4—88no—
753D4—88no—
754D4—84no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—28no—
770C2×C4—28no—
771C2×C4—28no—
772C2×C4—28no—
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—21no—
784C2×C4—21no—
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—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—44no—
803C2×C4—44no—
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—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—88no—
826C2×C4C2×#12112yes—
827C2×C4C2×#12112yes—
828C2×C4C2×#12112yes—
829C2×C4C2×#12112yes—
830C2×C4C2×#12112yes—
831C2×C4C2×AGL(1,ℤ/8)12yes—
832C2×C4C2×AGL(1,ℤ/8)12yes—
833C2×C4C2×#13712yes—
834C2×C4C2×#13712yes—
835C2×C4#57512yes—
836C2×C4#57512yes—
837C2×C4C23×D411yescharacteristic
838C2×C4C22×#4111yescharacteristic
839C2×C4#58511yescharacteristic
840C2×C4#58511yescharacteristic
841C2×C4#58511yescharacteristic
842C2×C4#58511yescharacteristic
843C8—28no—
844C8—44no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—416no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—82no—
868C22—82no—
869C22—82no—
870C22—82no—
871C22—82no—
872C22—82no—
873C22—82no—
874C22C22×#12111yescharacteristic
875C22#344911yescharacteristic
876C22#344911yescharacteristic
877C22C22×AGL(1,ℤ/8)11yescharacteristic
878C22C22×#13711yescharacteristic
879C22C2×#57511yescharacteristic
880C22C2×#57511yescharacteristic
881C4—22no—
882C4—22no—
883C4—22no—
884C4—22no—
885C4—22no—
886C4—41no—
887C4—41no—
888C4—41no—
889C4—41no—
890C4—82no—
891C4—82no—
892C4—82no—
893C4—82no—
894C4—82no—
895C4—82no—
896C4—82no—
897C4#305514yes—
898C4#305614yes—
899C4#348511yescharacteristic
900C4#348711yescharacteristic
901C4#349311yescharacteristic
902C4#349311yescharacteristic
903C2—42no—
904C2—42no—
905C2—42no—
906C2—162no—
907C2#3515011yescharacteristic
908C2C2×#305511yescharacteristic
909C2C2×#305611yescharacteristic
910C2#6095111yescharacteristic
911C2#6095211yescharacteristic
912C2#6096711yescharacteristic
913C2#6096911yescharacteristic
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×#3254C2semidirect
2. C2×#2920C2semidirect
3. #36625C2semidirect
5. #33145C2semidirect
6. #29744C2semidirect
7. #24711C2semidirect
8. #24709C2semidirect
9. #24702C2semidirect
10. #24700C2semidirect
11. #24661C2semidirect
12. #24659C2semidirect
13. #24653C2semidirect
14. #24651C2semidirect
15. #21964C2semidirect
16. #21894C2semidirect
17. #21893C2semidirect
23. C2×#477C22semidirect
24. C2×#474C22semidirect
26. C2×#460C22semidirect
27. C2×#461C22semidirect
78. #1988C22semidirect
79. #1987C22semidirect
80. #1982C22semidirect
81. #1981C22semidirect
82. #1973C22semidirect
83. #1968C22semidirect
84. #1948C22semidirect
85. #1948C22semidirect
86. #1947C22semidirect
87. #1947C22semidirect
88. #1944C22semidirect
89. #1942C22semidirect
90. #1936C22semidirect
91. #1935C22semidirect
92. #1934C22semidirect
93. #1933C22semidirect
97. #1803C22semidirect
98. #1803C22semidirect
99. #1802C22semidirect
100. #1802C22semidirect
173. #423D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32542
C2×#29202
#366252
#366242
#331452
#297442
#247112
#247092
#247022
#247002
#246612
#246592
#246532
#246512
#219642
#218942
#218932