Finite Group Databasebeta

← #6400103

Subgroups — #6400103

Order 512.

1981 conjugacy classes of subgroups.

The subgroup lattice has 893 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3304C211yesmaximal, characteristic
2#34330C211yesmaximal, characteristic
3C4×#556C211yesmaximal, characteristic, complemented
4#23220C211yesmaximal, characteristic, complemented
5#23101C211yesmaximal, characteristic, complemented
6#23068C211yesmaximal, characteristic, complemented
7#23033C212yesmaximal, complemented
8#22933C212yesmaximal, complemented
9#22856C212yesmaximal, complemented
10#22814C211yesmaximal, characteristic, complemented
11#22657C211yesmaximal, characteristic, complemented
12#22568C212yesmaximal, complemented
13#22490C211yesmaximal, characteristic, complemented
14#22418C211yesmaximal, characteristic
15#22219C211yesmaximal, characteristic, complemented
16#22180C212yesmaximal, complemented
17#22118C211yesmaximal, characteristic, complemented
18#22048C212yesmaximal, complemented
19#21582C212yesmaximal, complemented
20#21505C211yesmaximal, characteristic, complemented
21#21116C211yesmaximal, characteristic, complemented
22#21058C212yesmaximal, complemented
23#20558C211yesmaximal, characteristic, complemented
24C2×#556C2211yescharacteristic
25C2×#550C2211yescharacteristic
26#3304C4116yescomplemented
27C2×#486C2211yescharacteristic
28C2×#482C2212yes—
29C2×#475C2211yescharacteristic
30C2×#465C2212yes—
31C2×#460C2211yescharacteristic
32C2×#452C2212yes—
33C2×#440C2212yes—
34C2×C4×Q16C2211yescharacteristic
35C2×C8×D4C2211yescharacteristic
36C2×C8×D4C2211yescharacteristic
37C2×#427C2212yes—
38C2×#416C2212yes—
39C2×#416C2212yes—
40#2373—22no—
41#2367—21no—
42#2366—21no—
43#2366C2211yescharacteristic
44#2365C2211yescharacteristic
45#2364—22no—
46#2363C2212yes—
47#2362C2212yes—
48#2357—21no—
49#2356—21no—
50#2355C2211yescharacteristic
51#2355C2211yescharacteristic
52#2354C2211yescharacteristic
53#2354C2211yescharacteristic
54#2347C2212yes—
55#2339C2212yes—
56#2333—22no—
57#2328—21no—
58C4×C4⋊Q8C2211yescharacteristic
59C4×#127C2211yescharacteristic
60C4×#126—22no—
61C4×#124—21no—
62C4×C22⋊Q8C2212yes—
63C4×#121C2212yes—
64#2297C2212yes—
65#2295C2211yescharacteristic
66#2275—21no—
67C42×Q8—21no—
68C42×Q8C2211yescharacteristic
69C42×D4C2211yescharacteristic
70C4×#117C2212yes—
71#1990C2211yescharacteristic
72#1988C2211yescharacteristic
73#1982C2211yescharacteristic
74#1973C2212yes—
75#1971C2212yes—
76#1957C2211yescharacteristic
77#1947C2211yescharacteristic
78#1947C2211yescharacteristic
79#1944C2212yes—
80#1936C2212yes—
81#1935C2212yes—
82#1935C2212yes—
83#1928C2212yes—
84#1928C2212yes—
85#1927C2212yes—
86#1927C2212yes—
87#1927C2211yescharacteristic
88#1927C2211yescharacteristic
89#1926C2212yes—
90#1926C2212yes—
91#1926C2212yes—
92#1925C2212yes—
93#1925C2212yes—
94#1920C2212yes—
95#1919C2212yes—
96#1918C2211yescharacteristic
97#1918C2211yescharacteristic
98#1893C2212yes—
99#1892C2212yes—
100#1880C2212yes—
101#1878C2211yescharacteristic
102#1878C2211yescharacteristic
103#1877C2212yes—
104#1875C2212yes—
105#1873C2212yes—
106#1865C2211yescharacteristic
107#1865C2211yescharacteristic
108#1864C2212yes—
109#1864C2212yes—
110#1864C2212yes—
111#1854C2212yes—
112#1854C2212yes—
113#1844C2211yescharacteristic
114#1825C2212yes—
115#1807C2212yes—
116#1803C2211yescharacteristic
117#1803C2211yescharacteristic
118#1788C2212yes—
119#1776C2212yes—
120#1776C2212yes—
121C4×#106C2211yescharacteristic
122#1770C2211yescharacteristic
123#1770C2211yescharacteristic
124#1767C2211yescharacteristic
125#1762C2212yes—
126#1762C2212yes—
127#1762C2212yes—
128C4×#103C2211yescharacteristic
129C4×#103C2211yescharacteristic
130#1752C2212yes—
131#1752C2212yes—
132#1749C2212yes—
133#1744C2211yescharacteristic
134#1735C2212yes—
135C2×#336C2212yes—
136C22×#41C2312yes—
137C22×Q16C2311yescharacteristic
138C22×SD16C2312yes—
139C23×C8C2312yes—
140C23×C8C2312yes—
141#556—24no—
142#556C2×C418yescomplemented
143#550—24no—
144#550C2×C418yes—
145C2×C4⋊Q8C2311yescharacteristic
146C2×#127—21no—
147C2×#127C2311yescharacteristic
148C2×#126—22no—
149C2×#124—21no—
150C2×C22⋊Q8C2312yes—
151C2×#121—22no—
152C2×#121C2312yes—
153C2×C4×Q8—21no—
154C2×C4×Q8—21no—
155C2×C4×Q8—21no—
156C2×C4×Q8C2311yescharacteristic
157C2×C4×Q8C2311yescharacteristic
158C2×C4×Q8C2311yescharacteristic
159C2×C4×Q8C2311yescharacteristic
160C2×C4×D4—22no—
161C2×C4×D4—21no—
162C2×C4×D4—21no—
163C2×C4×D4—21no—
164C2×C4×D4—21no—
165C2×C4×D4D411yescharacteristic
166C2×C4×D4D411yescharacteristic
167C2×C4×D4C2312yes—
168C2×C4×D4C2312yes—
169C2×C4×D4C2311yescharacteristic
170C2×#117C2312yes—
171C2×#117C2312yes—
172C2×#117C2312yes—
173C22×C42C2312yes—
174#486C2×C418yescomplemented
175#482C2×C4116yescomplemented
176#475C2×C418yescomplemented
177#465C2×C4116yescomplemented
178#460C2×C418yescomplemented
179#452C2×C4116yescomplemented
180#440—44no—
181C4×Q16C2×C418yescomplemented
182C8×D4—24no—
183C8×D4C2×C418yescomplemented
184#427—44no—
185C2×#107C2312yes—
186C2×#107C2312yes—
187C2×#107C2311yescharacteristic
188C2×#106C2311yescharacteristic
189C2×#106C2311yescharacteristic
190C2×#106C2312yes—
191C2×#106C2312yes—
192C2×#106C2312yes—
193C2×C4⋊C8C2311yescharacteristic
194C2×C4⋊C8C2311yescharacteristic
195#416—44no—
196#416C2×C4116yescomplemented
197C2×#103C2311yescharacteristic
198C2×#103C2312yes—
199C2×#103C2312yes—
200C2×#103C2311yescharacteristic
201C2×#103C2311yescharacteristic
202C2×#103C2311yescharacteristic
203C2×#103C2312yes—
204C2×#103C2311yescharacteristic
205C2×#103C2311yescharacteristic
206C2×#102C2312yes—
207C2×#102C2312yes—
208C2×#102C2312yes—
209C2×#102C2312yes—
210C2×#102C2312yes—
211C2×#102C2312yes—
212C2×#102C2312yes—
213C2×C22⋊C8C2312yes—
214C2×C22⋊C8C2312yes—
215C2×#97C2312yes—
216C2×#97C2312yes—
217C2×#97C2312yes—
218C2×C4×C8C2311yescharacteristic
219C2×C4×C8C2311yescharacteristic
220#391—21no—
221#391—21no—
222#391C2311yescharacteristic
223#391C2312yes—
224#391C2312yes—
225#391C2311yescharacteristic
226#390—21no—
227#390—21no—
228#390—21no—
229#390—22no—
230#390—21no—
231#390—21no—
232#390C2312yes—
233#390C2312yes—
234#389—21no—
235#389C2312yes—
236#389C2312yes—
237#389C2311yescharacteristic
238#389C2311yescharacteristic
239#388—22no—
240#388—22no—
241#388—22no—
242#388—22no—
243#388—22no—
244#388—22no—
245#388—22no—
246#388—22no—
247#387—21no—
248#387—22no—
249#387—21no—
250#387—22no—
251#387—22no—
252#387—22no—
253#387—22no—
254#386—22no—
255#386—22no—
256#386—22no—
257#386—22no—
258#386—22no—
259#386—22no—
260#386—22no—
261#385—22no—
262#384C2311yescharacteristic
263#384C2311yescharacteristic
264#383—22no—
265#382—21no—
266#382—21no—
267#381—22no—
268#380C2312yes—
269#380C2312yes—
270C4×C4⋊C4—21no—
271C4×C4⋊C4—21no—
272C4×C4⋊C4—21no—
273C4×C4⋊C4—21no—
274C4×C4⋊C4—21no—
275C4×C4⋊C4—21no—
276C4×C4⋊C4—22no—
277C4×C4⋊C4—21no—
278C4×C4⋊C4—21no—
279C4×C4⋊C4—21no—
280C4×C4⋊C4—22no—
281C4×C4⋊C4—22no—
282C4×C4⋊C4D411yescharacteristic
283C4×C4⋊C4D411yescharacteristic
284C4×C4⋊C4C2312yes—
285C4×C4⋊C4C2311yescharacteristic
286C4×C4⋊C4C2312yes—
287C4×C4⋊C4C2311yescharacteristic
288C4×C4⋊C4C2311yescharacteristic
289C4×C4⋊C4C2312yes—
290C4×C4⋊C4C2312yes—
291C4×C4⋊C4C2311yescharacteristic
292C4×C4⋊C4C2311yescharacteristic
293C4×C22⋊C4—22no—
294C4×C22⋊C4—22no—
295C4×C22⋊C4—22no—
296C4×C22⋊C4—22no—
297C4×C22⋊C4—22no—
298C4×C22⋊C4—22no—
299C4×C22⋊C4—22no—
300C4×C22⋊C4D412yes—
301C4×C22⋊C4D412yes—
302C4×C22⋊C4C2312yes—
303#376—21no—
304#376—22no—
305C2×#95—22no—
306C43—22no—
307C43—21no—
308C43C2311yescharacteristic
309#340C2312yes—
310#340C2312yes—
311#340C2312yes—
312#340C2312yes—
313#340C2311yescharacteristic
314#340C2312yes—
315#340C2312yes—
316#340C2311yescharacteristic
317#340C2311yescharacteristic
318#340C2312yes—
319#340C2311yescharacteristic
320#340C2311yescharacteristic
321#340C2312yes—
322#340C2311yescharacteristic
323#336C2311yescharacteristic
324#336C2311yescharacteristic
325#336C2312yes—
326#336C2311yescharacteristic
327#336C2312yes—
328#336C2311yescharacteristic
329#336C2312yes—
330C2×#41—24no—
331C2×#41—42no—
332C2×#41—42no—
333C2×#41—42no—
334C2×#41—42no—
335C2×#41C22×C418yes—
336C22×Q8—21no—
337C22×Q8C2411yescharacteristic
338C22×Q8C2411yescharacteristic
339C22×D4—22no—
340C22×D4—22no—
341C22×D4—21no—
342C22×D4—21no—
343C22×D4C2×D411yescharacteristic
344C22×D4C2412yes—
345C23×C4—22no—
346C23×C4—22no—
347C23×C4—22no—
348C23×C4C2×D412yes—
349C23×C4C2×D412yes—
350C23×C4C2412yes—
351C2×Q16—41no—
352C2×Q16—41no—
353C2×Q16C22×C414yes—
354C2×SD16—42no—
355C2×SD16—42no—
356C2×SD16C22×C418yes—
357C22×C8—24no—
358C22×C8—42no—
359C22×C8—42no—
360C22×C8—42no—
361C22×C8—42no—
362C22×C8C22×C418yes—
363C22×C8C2411yescharacteristic
364C22×C8C2412yes—
365C22×C8C2411yescharacteristic
366C22×C8C2411yescharacteristic
367C22×C8C2412yes—
368C22×C8C2411yescharacteristic
369C4⋊Q8—22no—
370C4⋊Q8C22×C414yes—
371#127—28no—
372#127—22no—
373#127C22×C414yes—
374#126—216no—
375#124—28no—
376C22⋊Q8—24no—
377C22⋊Q8C22×C418yes—
378#121—24no—
379#121—216no—
380#121C22×C418yes—
381C4×Q8—28no—
382C4×Q8—22no—
383C4×Q8—22no—
384C4×Q8—22no—
385C4×Q8—41no—
386C4×Q8—41no—
387C4×Q8—41no—
388C4×Q8—44no—
389C4×Q8—44no—
390C4×Q8C22×C414yes—
391C4×Q8C22×C414yes—
392C4×D4—28no—
393C4×D4—42no—
394C4×D4—42no—
395C4×D4—44no—
396C4×D4—42no—
397C4×D4—42no—
398C4×D4—42no—
399C4×D4—42no—
400C4×D4—44no—
401C4×D4—82no—
402C4×D4—84no—
403C4×D4C22×C414yes—
404C4×D4#4114yes—
405#117—24no—
406#117—24no—
407#117—42no—
408#117—42no—
409#117—42no—
410#117C22×C418yes—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4C2×D411yescharacteristic
426C2×C4⋊C4C2×D411yescharacteristic
427C2×C4⋊C4C2×D411yescharacteristic
428C2×C4⋊C4C2411yescharacteristic
429C2×C4⋊C4C2412yes—
430C2×C4⋊C4C2412yes—
431C2×C4⋊C4C2411yescharacteristic
432C2×C4⋊C4C2411yescharacteristic
433C2×C4⋊C4C2411yescharacteristic
434C2×C4⋊C4C2412yes—
435C2×C4⋊C4C2411yescharacteristic
436C2×C4⋊C4C2411yescharacteristic
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4C2×D412yes—
451C2×C22⋊C4C2×D412yes—
452C2×C22⋊C4C2×D412yes—
453C2×C42—22no—
454C2×C42—21no—
455C2×C42—21no—
456C2×C42—22no—
457C2×C42—21no—
458C2×C42—22no—
459C2×C42—22no—
460C2×C42—21no—
461C2×C42—21no—
462C2×C42—21no—
463C2×C42—21no—
464C2×C42—22no—
465C2×C42—22no—
466C2×C42—22no—
467C2×C42—21no—
468C2×C42—42no—
469C2×C42—42no—
470C2×C42C2×D411yescharacteristic
471C2×C42C2×D411yescharacteristic
472C2×C42C2×D411yescharacteristic
473C2×C42C2×D412yes—
474C2×C42C2×D411yescharacteristic
475C2×C42C2×D412yes—
476C2×C42C2411yescharacteristic
477C2×C42C2412yes—
478C2×C42C2411yescharacteristic
479C2×C42C2411yescharacteristic
480#107—24no—
481#107—42no—
482#107C22×C414yes—
483#106—22no—
484#106—42no—
485#106—41no—
486#106—42no—
487#106C22×C418yes—
488C4⋊C8—22no—
489C4⋊C8C22×C414yes—
490#103—22no—
491#103—41no—
492#103—41no—
493#103—41no—
494#103—42no—
495#103—42no—
496#103C22×C414yes—
497#103C22×C418yes—
498#103C22×C414yes—
499#102—24no—
500#102—42no—
501#102—42no—
502#102—42no—
503#102C22×C418yes—
504#102C22×C418yes—
505#102C22×C418yes—
506C22⋊C8—24no—
507C22⋊C8C22×C418yes—
508#97—42no—
509#97—42no—
510#97—42no—
511C4×C8—22no—
512C4×C8C22×C414yes—
513#95—21no—
514#95—22no—
515#95—22no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—22no—
521#95—22no—
522#95—22no—
523#95—21no—
524#95—22no—
525#95—22no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95—21no—
530#95—21no—
531#95—21no—
532#95—22no—
533#95—22no—
534#95—21no—
535#95C2×D412yes—
536#95C2×D412yes—
537#95C2×D412yes—
538C24—22no—
539C24C22×D412yes—
540#41—48no—
541#41—48no—
542#41—84no—
543#41—84no—
544C2×Q8—24no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—42no—
556C2×Q8—42no—
557C2×Q8C23×C412yes—
558C2×Q8C23×C412yes—
559C2×D4—28no—
560C2×D4—28no—
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—81no—
573C2×D4—81no—
574C2×D4—82no—
575C2×D4—82no—
576C2×D4—82no—
577C2×D4—82no—
578C2×D4C4×D414yes—
579C2×D4C23×C414yes—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—21no—
590C22×C4—28no—
591C22×C4—24no—
592C22×C4—21no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—82no—
605C22×C4—82no—
606C22×C4—82no—
607C22×C4—82no—
608C22×C4—82no—
609C22×C4—82no—
610C22×C4C23×C414yes—
611C22×C4C22×D412yes—
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D412yes—
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D412yes—
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C2×#4114yes—
621C22×C4C2511yescharacteristic
622Q16—44no—
623SD16—48no—
624C2×C8—22no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—22no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—22no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—48no—
640C2×C8—84no—
641C2×C8C23×C412yes—
642C2×C8C23×C412yes—
643C2×C8C23×C414yes—
644C4⋊C4—28no—
645C4⋊C4—24no—
646C4⋊C4—24no—
647C4⋊C4—24no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—21no—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—22no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—22no—
663C4⋊C4—21no—
664C4⋊C4—42no—
665C4⋊C4—42no—
666C4⋊C4—44no—
667C4⋊C4—44no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—81no—
672C4⋊C4—81no—
673C4⋊C4—81no—
674C4⋊C4C4×D414yes—
675C4⋊C4C23×C414yes—
676C4⋊C4C23×C412yes—
677C4⋊C4C23×C412yes—
678C4⋊C4H(5,𝔽2)12yes—
679C22⋊C4—28no—
680C22⋊C4—28no—
681C22⋊C4—28no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—44no—
685C22⋊C4—44no—
686C22⋊C4—44no—
687C22⋊C4—44no—
688C22⋊C4—82no—
689C22⋊C4—82no—
690C22⋊C4—82no—
691C22⋊C4—82no—
692C22⋊C4—82no—
693C22⋊C4—82no—
694C22⋊C4C4×D418yes—
695C42—28no—
696C42—24no—
697C42—24no—
698C42—22no—
699C42—22no—
700C42—22no—
701C42—21no—
702C42—22no—
703C42—22no—
704C42—21no—
705C42—21no—
706C42—21no—
707C42—42no—
708C42—42no—
709C42—41no—
710C42—44no—
711C42—42no—
712C42—42no—
713C42—44no—
714C42—44no—
715C42—42no—
716C42—42no—
717C42—42no—
718C42—81no—
719C42—82no—
720C42—82no—
721C42—82no—
722C42C23×C412yes—
723C42C2×#4112yes—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—24no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23C2×C4×D414yes—
738C23C23×D411yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—22no—
742Q8—22no—
743Q8—48no—
744Q8—41no—
745Q8—41no—
746Q8—41no—
747Q8—41no—
748D4—24no—
749D4—24no—
750D4—28no—
751D4—48no—
752D4—42no—
753D4—42no—
754D4—84no—
755D4—88no—
756D4—88no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—24no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
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—42no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—41no—
807C2×C4—42no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—41no—
815C2×C4—84no—
816C2×C4—88no—
817C2×C4—84no—
818C2×C4—164no—
819C2×C4—164no—
820C2×C4C2×C4×D414yes—
821C2×C4C2×C4×D412yes—
822C2×C4C2×C4×D412yes—
823C2×C4#57512yes—
824C2×C4#57512yes—
825C2×C4#57712yes—
826C2×C4C24×C411yescharacteristic
827C2×C4C22×#4111yescharacteristic
828C2×C4C2×H(5,𝔽2)11yescharacteristic
829C2×C4#58511yescharacteristic
830C2×C4#58511yescharacteristic
831C2×C4#58511yescharacteristic
832C8—22no—
833C8—22no—
834C8—24no—
835C8—42no—
836C8—41no—
837C8—41no—
838C22—24no—
839C22—24no—
840C22—24no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—44no—
846C22—44no—
847C22—44no—
848C22—82no—
849C22—82no—
850C22—82no—
851C22—82no—
852C22C22×C4×D411yescharacteristic
853C22#348511yescharacteristic
854C22#348811yescharacteristic
855C22C2×#57511yescharacteristic
856C22C2×#57511yescharacteristic
857C22C2×#57711yescharacteristic
858C22#358411yescharacteristic
859C4—22no—
860C4—22no—
861C4—24no—
862C4—42no—
863C4—42no—
864C4—41no—
865C4—42no—
866C4—41no—
867C4—42no—
868C4—42no—
869C4—41no—
870C4—42no—
871C4—42no—
872C4—44no—
873C4—82no—
874C4—82no—
875C4—81no—
876C4—81no—
877C4—81no—
878C4#294314yes—
879C4#342811yescharacteristic
880C4C4×H(5,𝔽2)11yescharacteristic
881C4#351411yescharacteristic
882C4#352111yescharacteristic
883C2—44no—
884C2—84no—
885C2#3429211yescharacteristic
886C2C2×#294311yescharacteristic
887C2C4×#57711yescharacteristic
888C2#6173911yescharacteristic
889C2#6174311yescharacteristic
890C2#6198611yescharacteristic
891C2#6199411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#550C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C4×#556C2semidirect
4. #23220C2semidirect
5. #23101C2semidirect
6. #23068C2semidirect
7. #23033C2semidirect
8. #22933C2semidirect
9. #22856C2semidirect
10. #22814C2semidirect
11. #22657C2semidirect
12. #22568C2semidirect
13. #22490C2semidirect
15. #22219C2semidirect
16. #22180C2semidirect
17. #22118C2semidirect
18. #22048C2semidirect
19. #21582C2semidirect
20. #21505C2semidirect
21. #21116C2semidirect
22. #21058C2semidirect
23. #20558C2semidirect
26. #3304C4semidirect
142. #556C2×C4semidirect
174. #486C2×C4semidirect
175. #482C2×C4semidirect
176. #475C2×C4semidirect
177. #465C2×C4semidirect
178. #460C2×C4semidirect
179. #452C2×C4semidirect
181. C4×Q16C2×C4semidirect
183. C8×D4C2×C4semidirect
196. #416C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#33042
#343302
C4×#5562
#232202
#231012
#230682
#230332
#229332
#228562
#228142
#226572
#225682
#224902
#224182
#222192
#221802
#221182
#220482
#215822
#215052
#211162
#210582
#205582