Finite Group Databasebeta

← #6681894

Subgroups — #6681894

Order 512.

1554 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39480C211yesmaximal, characteristic, complemented
2#36161C211yesmaximal, characteristic
3#32956C211yesmaximal, characteristic
4#31970C212yesmaximal, complemented
5#31578C212yesmaximal, complemented
6#31298C212yesmaximal
7#31294C212yesmaximal
8#29922C211yesmaximal, characteristic, complemented
9#29844C211yesmaximal, characteristic, complemented
10#27748C211yesmaximal, characteristic, complemented
11#27099C212yesmaximal, complemented
12#27037C212yesmaximal, complemented
13#26765C212yesmaximal, complemented
14#26537C212yesmaximal, complemented
15#26087C211yesmaximal, characteristic, complemented
16#25646C211yesmaximal, characteristic, complemented
17#25470C211yesmaximal, characteristic, complemented
18#25273C211yesmaximal, characteristic, complemented
19#25057C211yesmaximal, characteristic, complemented
20#23061C211yesmaximal, characteristic, complemented
21#22541C211yesmaximal, characteristic, complemented
22#22098C211yesmaximal, characteristic, complemented
23#20732C211yesmaximal, characteristic
24C2×#556C2211yescharacteristic
25C22×C4×D4C2211yescharacteristic
26C2×#487C2211yescharacteristic, complemented
27C2×#476C2211yescharacteristic
28C2×#476C2211yescharacteristic
29C2×C8×Q8C2211yescharacteristic, complemented
30C2×#431C2211yescharacteristic
31#2857C2211yescharacteristic
32#2857C2211yescharacteristic
33#2848—21no—
34#2762—22no—
35#2690—22no—
36#2625—21no—
37#2571C2211yescharacteristic, complemented
38#2570C2212yescomplemented
39#2567C2211yescharacteristic, complemented
40#2547C2211yescharacteristic
41#2538C2211yescharacteristic
42#2514—21no—
43#2506—21no—
44#2506C2212yescomplemented
45#2495C2212yes—
46#2494C2212yes—
47#2485—21no—
48#2480—22no—
49#2466—22no—
50#2447C2212yes—
51#2435C2212yes—
52#2415—21no—
53#2369C2211yescharacteristic, complemented
54#2367C2212yes—
55#2360C2212yes—
56#2355C2211yescharacteristic, complemented
57#2354C2211yescharacteristic
58#2314—21no—
59C4×C22⋊Q8C2211yescharacteristic
60#2285C2211yescharacteristic
61#2280—21no—
62#2096C2212yescomplemented
63#2092C2212yes—
64#2092C2212yes—
65#2088C2212yescomplemented
66#2085C2212yescomplemented
67#2074C2212yescomplemented
68#2072C2212yescomplemented
69#2068C2212yescomplemented
70#2068C2212yescomplemented
71#2067C2212yes—
72#2066C2212yescomplemented
73#2065C2212yes—
74#2042C2212yes—
75#2042C2212yes—
76#2042C2212yes—
77#2042C2212yes—
78#2036C2212yes—
79#2036C2212yes—
80#2035C2212yes—
81#2035C2212yes—
82#1990C2211yescharacteristic, complemented
83#1984C2211yescharacteristic, complemented
84#1983C2212yes—
85#1983C2212yes—
86#1981C2211yescharacteristic, complemented
87#1981C2211yescharacteristic, complemented
88#1958C2212yes—
89#1958C2212yes—
90#1956C2211yescharacteristic, complemented
91#1949C2212yescomplemented
92#1948C2211yescharacteristic, complemented
93#1948C2211yescharacteristic, complemented
94#1941C2212yescomplemented
95#1939C2212yescomplemented
96#1939C2211yescharacteristic, complemented
97#1934C2212yes—
98#1934C2212yes—
99#1933C2212yescomplemented
100#1927C2212yescomplemented
101#1926C2212yes—
102#1925C2212yes—
103#1923C2212yes—
104#1923C2212yes—
105#1921C2212yescomplemented
106#1921C2212yescomplemented
107#1920C2212yescomplemented
108#1916C2212yescomplemented
109#1865C2212yescomplemented
110#1865C2212yescomplemented
111#1864C2212yes—
112#1864C2212yes—
113#1853C2212yes—
114#1845C2211yescharacteristic, complemented
115#1823C2211yescharacteristic
116#1823C2211yescharacteristic
117#1805C2212yescomplemented
118#1802C2211yescharacteristic
119#1802C2211yescharacteristic
120#1802C2211yescharacteristic
121#1802C2211yescharacteristic
122#1802C2211yescharacteristic
123#1802C2211yescharacteristic
124#1797C2211yescharacteristic
125#1786C2211yescharacteristic
126#1786C2212yes—
127#1786C2211yescharacteristic
128C4×#106C2212yescomplemented
129C8×C4⋊C4C2211yescharacteristic, complemented
130C4×#103C2212yescomplemented
131C4×#102C2211yescharacteristic
132C4×#102C2211yescharacteristic
133C4×#102C2211yescharacteristic
134C4×#102C2211yescharacteristic
135C23×D4C2311yescharacteristic
136C24×C4—21no—
137#556—24no—
138#556—42no—
139C2×C4⋊Q8C2311yescharacteristic
140C2×C4⋊Q8C2311yescharacteristic
141C2×#126—22no—
142C2×#125—22no—
143C2×#124C2312yes—
144C2×#124C2312yes—
145C2×C22⋊Q8—21no—
146C2×C22⋊Q8—21no—
147C2×C22⋊Q8—21no—
148C2×C22⋊Q8D411yescharacteristic
149C2×C22⋊Q8C2312yes—
150C2×C4×Q8C2312yes—
151C2×C4×Q8C2311yescharacteristic
152C2×C4×D4—24no—
153C2×C4×D4—21no—
154C2×C4×D4—21no—
155C2×C4×D4—42no—
156C2×C4×D4C2311yescharacteristic
157C2×C4×D4C2311yescharacteristic
158C2×C4×D4C2311yescharacteristic
159C2×C4×D4C2311yescharacteristic
160C2×#117—21no—
161C2×#117—21no—
162C2×#117—21no—
163C22×C4⋊C4C2311yescharacteristic
164C22×C22⋊C4—21no—
165C22×C42C2311yescharacteristic
166#487—42no—
167#476—24no—
168#476—42no—
169C8×Q8—42no—
170#431—42no—
171C2×#107C2312yes—
172C2×#107C2312yes—
173C2×#106C2312yes—
174C2×#106C2312yes—
175C2×#106C2312yes—
176C2×#106C2312yes—
177C2×C4⋊C8C2311yescharacteristic
178C2×C4⋊C8C2311yescharacteristic
179C2×C4⋊C8C2311yescharacteristic
180C2×C4⋊C8C2311yescharacteristic
181C2×C4⋊C8C2312yes—
182C2×C4⋊C8C2312yes—
183C2×#103C2312yes—
184C2×#103C2312yes—
185C2×#103C2312yes—
186C2×#103C2312yes—
187C2×#103C2312yes—
188C2×#103C2312yes—
189C2×#103C2312yes—
190C2×#103C2312yes—
191C2×#102C2311yescharacteristic
192C2×#102C2311yescharacteristic
193C2×#102C2312yes—
194C2×#102C2311yescharacteristic
195C2×#102C2311yescharacteristic
196C2×#102C2312yes—
197C2×#102C2311yescharacteristic
198C2×#102C2311yescharacteristic
199C2×#102C2312yes—
200C2×#102C2311yescharacteristic
201C2×#102C2311yescharacteristic
202C2×#102C2312yes—
203C2×C22⋊C8C2312yes—
204C2×C22⋊C8C2311yescharacteristic
205C2×C22⋊C8C2311yescharacteristic
206C2×C4×C8C2311yescharacteristic
207C2×C4×C8C2311yescharacteristic
208C2×C4×C8C2312yes—
209C2×C4×C8C2312yes—
210#401—22no—
211#400—22no—
212#400—22no—
213#400—22no—
214#400—22no—
215#398—22no—
216#398—22no—
217#397—22no—
218#397—22no—
219#397—22no—
220#397—22no—
221#397—22no—
222#396—22no—
223#395—22no—
224#394—22no—
225#394—22no—
226#391—21no—
227#391—21no—
228#391—21no—
229#391—22no—
230#391D411yescharacteristic
231#391C2312yes—
232#391C2312yes—
233#390C2312yes—
234#390C2312yes—
235#389—21no—
236#389—21no—
237#389—21no—
238#389—21no—
239#389—21no—
240#389—22no—
241#389D411yescharacteristic
242#389C2312yes—
243#389C2312yes—
244#389C2312yes—
245#389C2312yes—
246#389C2312yes—
247#389C2312yes—
248#388—22no—
249#388—22no—
250#388—22no—
251#388—22no—
252#388—22no—
253#387—22no—
254#387—22no—
255#387—22no—
256#387—22no—
257#387—22no—
258#387—22no—
259#387D412yes—
260#385—22no—
261#385—22no—
262#385—22no—
263#385D412yes—
264#384—21no—
265#384C2311yescharacteristic
266#384C2311yescharacteristic
267#384C2311yescharacteristic
268#384C2311yescharacteristic
269#383—22no—
270#382—21no—
271#382—21no—
272#382C2312yes—
273#382C2312yes—
274#381—22no—
275#380—21no—
276#380—21no—
277#380—21no—
278#380—21no—
279#380—21no—
280#380—21no—
281#380—21no—
282#380—21no—
283#380D411yescharacteristic
284#380C2311yescharacteristic
285#380C2311yescharacteristic
286#380C2312yes—
287#379—22no—
288#379—22no—
289C4×C4⋊C4—21no—
290C4×C4⋊C4—21no—
291C4×C4⋊C4—21no—
292C4×C4⋊C4C2311yescharacteristic
293C4×C4⋊C4C2312yes—
294C4×C4⋊C4C2312yes—
295C4×C4⋊C4C2311yescharacteristic
296C4×C4⋊C4C2312yes—
297C4×C4⋊C4C2312yes—
298C4×C4⋊C4C2311yescharacteristic
299C4×C22⋊C4—22no—
300C4×C22⋊C4—22no—
301C4×C22⋊C4C2312yes—
302#340C2311yescharacteristic
303#340C2312yes—
304#340C2311yescharacteristic
305#340C2311yescharacteristic
306#340C2312yes—
307#340C2311yescharacteristic
308#340C2311yescharacteristic
309#340C2311yescharacteristic
310#340C2311yescharacteristic
311#340C2311yescharacteristic
312#340C2312yes—
313#340C2312yes—
314#340C2312yes—
315#340C2312yes—
316#336C2312yes—
317#336C2312yes—
318#336C2312yes—
319#336C2312yes—
320#336C2312yes—
321C25—21no—
322C22×Q8—21no—
323C22×Q8C2×D411yescharacteristic
324C22×Q8C2412yes—
325C22×D4—22no—
326C22×D4—22no—
327C22×D4—21no—
328C22×D4—41no—
329C22×D4—41no—
330C22×D4—41no—
331C22×D4—41no—
332C22×D4C2411yescharacteristic
333C22×D4C2411yescharacteristic
334C23×C4—21no—
335C23×C4—21no—
336C23×C4—21no—
337C23×C4—21no—
338C23×C4—21no—
339C23×C4—44no—
340C23×C4—44no—
341C23×C4—82no—
342C23×C4C2×D411yescharacteristic
343C23×C4C2×D411yescharacteristic
344C23×C4C2411yescharacteristic
345C22×C8C2412yes—
346C22×C8C2411yescharacteristic
347C22×C8C2411yescharacteristic
348C22×C8C2412yes—
349C22×C8C2411yescharacteristic
350C22×C8C2411yescharacteristic
351C4⋊Q8—22no—
352C4⋊Q8—22no—
353C4⋊Q8—22no—
354C4⋊Q8—22no—
355#126—48no—
356#125—84no—
357#124—24no—
358#124—24no—
359#124—42no—
360#124—42no—
361C22⋊Q8—24no—
362C22⋊Q8—42no—
363C22⋊Q8—42no—
364C22⋊Q8—44no—
365C22⋊Q8—82no—
366C22⋊Q8—82no—
367C4×Q8—22no—
368C4×Q8—22no—
369C4×Q8—24no—
370C4×Q8—42no—
371C4×D4—22no—
372C4×D4—22no—
373C4×D4—22no—
374C4×D4—22no—
375C4×D4—22no—
376C4×D4—44no—
377C4×D4—41no—
378C4×D4—41no—
379C4×D4—44no—
380C4×D4#4114yes—
381#117—44no—
382#117—44no—
383#117—82no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—21no—
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—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—41no—
406C2×C4⋊C4C2×D411yescharacteristic
407C2×C4⋊C4C2×D411yescharacteristic
408C2×C4⋊C4C2×D412yes—
409C2×C4⋊C4C2×D411yescharacteristic
410C2×C4⋊C4C2×D412yes—
411C2×C4⋊C4C2×D412yes—
412C2×C4⋊C4C2411yescharacteristic
413C2×C4⋊C4C2412yes—
414C2×C4⋊C4C2412yes—
415C2×C4⋊C4C2411yescharacteristic
416C2×C4⋊C4C2411yescharacteristic
417C2×C4⋊C4C2411yescharacteristic
418C2×C4⋊C4C2411yescharacteristic
419C2×C4⋊C4C2412yes—
420C2×C4⋊C4C2411yescharacteristic
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—44no—
438C2×C22⋊C4C2×D412yes—
439C2×C22⋊C4C2×D412yes—
440C2×C42—22no—
441C2×C42—22no—
442C2×C42—22no—
443C2×C42—21no—
444C2×C42—21no—
445C2×C42—22no—
446C2×C42—22no—
447C2×C42—22no—
448C2×C42C2×D411yescharacteristic
449C2×C42C2×D411yescharacteristic
450C2×C42C2411yescharacteristic
451C2×C42C2412yes—
452C2×C42C2412yes—
453C2×C42C2411yescharacteristic
454#107—42no—
455#107—42no—
456#106—24no—
457#106—42no—
458#106—42no—
459#106—42no—
460C4⋊C8—22no—
461C4⋊C8—22no—
462C4⋊C8—42no—
463C4⋊C8—41no—
464C4⋊C8—41no—
465C4⋊C8—42no—
466#103—42no—
467#103—42no—
468#103—42no—
469#103—42no—
470#103—42no—
471#103—42no—
472#103—42no—
473#103—42no—
474#102—24no—
475#102—22no—
476#102—22no—
477#102—41no—
478#102—41no—
479#102—41no—
480#102—41no—
481#102—42no—
482#102—42no—
483#102—41no—
484#102—41no—
485#102—42no—
486C22⋊C8—42no—
487C22⋊C8—41no—
488C22⋊C8—41no—
489C4×C8—22no—
490C4×C8—22no—
491C4×C8—42no—
492C4×C8—42no—
493#95—22no—
494#95—22no—
495#95—22no—
496#95—21no—
497#95—21no—
498#95—22no—
499#95—22no—
500#95—21no—
501#95—21no—
502#95—22no—
503#95—22no—
504#95—22no—
505#95—22no—
506#95—22no—
507#95—22no—
508#95—22no—
509#95—22no—
510#95—22no—
511#95—22no—
512#95—22no—
513#95—22no—
514#95—22no—
515#95C2×D412yes—
516#95C2×D412yes—
517#95C2×D412yes—
518#95C2×D412yes—
519#95C2×D412yes—
520C24—21no—
521C24—21no—
522C24—42no—
523C24—42no—
524C24—42no—
525C24—42no—
526C24—42no—
527C24—81no—
528C24—81no—
529C24C22×D411yescharacteristic
530C2×Q8—22no—
531C2×Q8—22no—
532C2×Q8—22no—
533C2×Q8—22no—
534C2×Q8—22no—
535C2×Q8—22no—
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8—22no—
539C2×Q8—42no—
540C2×Q8—81no—
541C2×Q8—81no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—42no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—44no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4C2×#4112yes—
560C2×D42−1+412yes—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—24no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—42no—
584C22×C4—42no—
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—81no—
595C22×C4—81no—
596C22×C4—816no—
597C22×C4—81no—
598C22×C4#13514yes—
599C22×C4C22×D412yes—
600C22×C4C22×D411yescharacteristic
601C22×C4C22×D412yes—
602C22×C4C22×D412yes—
603C22×C4C22×D412yes—
604C22×C4C22×D411yescharacteristic
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D411yescharacteristic
608C22×C4C2511yescharacteristic
609C2×C8—22no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—22no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C4⋊C4—22no—
628C4⋊C4—24no—
629C4⋊C4—22no—
630C4⋊C4—24no—
631C4⋊C4—22no—
632C4⋊C4—21no—
633C4⋊C4—22no—
634C4⋊C4—21no—
635C4⋊C4—22no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—42no—
650C4⋊C4—42no—
651C4⋊C4—44no—
652C4⋊C4—44no—
653C4⋊C4—44no—
654C4⋊C4—42no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C4⋊C4—42no—
658C4⋊C4—42no—
659C4⋊C4—42no—
660C4⋊C4—42no—
661C4⋊C4—42no—
662C4⋊C4—81no—
663C4⋊C4—82no—
664C4⋊C4—81no—
665C4⋊C4—81no—
666C4⋊C4—82no—
667C4⋊C4—82no—
668C4⋊C4—82no—
669C4⋊C4—82no—
670C4⋊C4C2×#4112yes—
671C22⋊C4—24no—
672C22⋊C4—24no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C22⋊C4—42no—
676C22⋊C4—44no—
677C22⋊C4—44no—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—44no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—82no—
685C22⋊C4—82no—
686C22⋊C4—82no—
687C22⋊C4—82no—
688C22⋊C4—82no—
689C42—22no—
690C42—22no—
691C42—21no—
692C42—22no—
693C42—22no—
694C42—21no—
695C42—22no—
696C42—22no—
697C42—44no—
698C42—42no—
699C42—42no—
700C42—82no—
701C42—82no—
702C42—82no—
703C42C2×#4112yes—
704C42H(5,𝔽2)12yes—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—22no—
712C23—22no—
713C23—48no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—84no—
727C23—84no—
728C23—84no—
729C23—84no—
730C23—84no—
731C23—84no—
732C23C2×#13512yes—
733C23C23×D411yescharacteristic
734Q8—44no—
735Q8—42no—
736Q8—42no—
737Q8—42no—
738Q8—42no—
739Q8—162no—
740D4—22no—
741D4—22no—
742D4—22no—
743D4—22no—
744D4—48no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—28no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—48no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—41no—
807C2×C4—82no—
808C2×C4—84no—
809C2×C4—84no—
810C2×C4—84no—
811C2×C4—84no—
812C2×C4#54612yes—
813C2×C4#54612yes—
814C2×C4C2×#13512yes—
815C2×C4C2×#13512yes—
816C2×C4#57712yes—
817C2×C4C22×#4111yescharacteristic
818C2×C4C2×H(5,𝔽2)11yescharacteristic
819C2×C4C2×2−1+411yescharacteristic
820C2×C4#58511yescharacteristic
821C2×C4#58511yescharacteristic
822C2×C4#58511yescharacteristic
823C8—42no—
824C8—41no—
825C8—41no—
826C8—42no—
827C8—41no—
828C8—41no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—816no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—81no—
851C22C2×#54611yescharacteristic
852C22#348711yescharacteristic
853C22#348911yescharacteristic
854C22C22×#13511yescharacteristic
855C22C2×#57711yescharacteristic
856C22#358511yescharacteristic
857C22#358611yescharacteristic
858C4—22no—
859C4—22no—
860C4—41no—
861C4—42no—
862C4—42no—
863C4—42no—
864C4—42no—
865C4—42no—
866C4—41no—
867C4—82no—
868C4—81no—
869C4—81no—
870C4—81no—
871C4—81no—
872C4—81no—
873C4—82no—
874C4—82no—
875C4—82no—
876C4#329614yes—
877C4#345511yescharacteristic
878C4#349511yescharacteristic
879C4#353911yescharacteristic
880C4#354111yescharacteristic
881C2—42no—
882C2—82no—
883C2—82no—
884C2#3767111yescharacteristic
885C2C2×#329611yescharacteristic
886C2#6118211yescharacteristic
887C2#6188211yescharacteristic
888C2#6191311yescharacteristic
889C2#6209811yescharacteristic
890C2#6218911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39480C2semidirect
4. #31970C2semidirect
5. #31578C2semidirect
8. #29922C2semidirect
9. #29844C2semidirect
10. #27748C2semidirect
11. #27099C2semidirect
12. #27037C2semidirect
13. #26765C2semidirect
14. #26537C2semidirect
15. #26087C2semidirect
16. #25646C2semidirect
17. #25470C2semidirect
18. #25273C2semidirect
19. #25057C2semidirect
20. #23061C2semidirect
21. #22541C2semidirect
22. #22098C2semidirect
26. C2×#487C22semidirect
29. C2×C8×Q8C22semidirect
37. #2571C22semidirect
38. #2570C22semidirect
39. #2567C22semidirect
44. #2506C22semidirect
53. #2369C22semidirect
56. #2355C22semidirect
62. #2096C22semidirect
65. #2088C22semidirect
66. #2085C22semidirect
67. #2074C22semidirect
68. #2072C22semidirect
69. #2068C22semidirect
70. #2068C22semidirect
72. #2066C22semidirect
82. #1990C22semidirect
83. #1984C22semidirect
86. #1981C22semidirect
87. #1981C22semidirect
90. #1956C22semidirect
91. #1949C22semidirect
92. #1948C22semidirect
93. #1948C22semidirect
94. #1941C22semidirect
95. #1939C22semidirect
96. #1939C22semidirect
99. #1933C22semidirect
100. #1927C22semidirect
105. #1921C22semidirect
106. #1921C22semidirect
107. #1920C22semidirect
108. #1916C22semidirect
109. #1865C22semidirect
110. #1865C22semidirect
114. #1845C22semidirect
117. #1805C22semidirect
128. C4×#106C22semidirect
129. C8×C4⋊C4C22semidirect
130. C4×#103C22semidirect

Maximal subgroups

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

subgroupindex
#394802
#361612
#329562
#319702
#315782
#312982
#312942
#299222
#298442
#277482
#270992
#270372
#267652
#265372
#260872
#256462
#254702
#252732
#250572
#230612
#225412
#220982
#207322