Finite Group Databasebeta

← #6400113

Subgroups — #6400113

Order 512.

1957 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
1C2×#3333C211yesmaximal, characteristic
2#34494C211yesmaximal, characteristic
3#34317C211yesmaximal, characteristic, complemented
4#23215C211yesmaximal, characteristic, complemented
5#23101C211yesmaximal, characteristic, complemented
6#23069C211yesmaximal, characteristic, complemented
7#23034C212yesmaximal, complemented
8#22916C212yesmaximal, complemented
9#22876C212yesmaximal, complemented
10#22808C211yesmaximal, characteristic, complemented
11#22665C211yesmaximal, characteristic, complemented
12#22582C212yesmaximal, complemented
13#22487C211yesmaximal, characteristic, complemented
14#22418C211yesmaximal, characteristic
15#22220C211yesmaximal, characteristic, complemented
16#22201C212yesmaximal, complemented
17#22113C211yesmaximal, characteristic, complemented
18#22057C212yesmaximal, complemented
19#21586C212yesmaximal, complemented
20C4×#460C211yesmaximal, characteristic, complemented
21#21116C211yesmaximal, characteristic, complemented
22#21062C212yesmaximal, complemented
23#20562C211yesmaximal, characteristic, complemented
24C2×#554C2211yescharacteristic
25C2×#550C2211yescharacteristic
26#3333C4116yescomplemented
27C2×#486C2211yescharacteristic
28C2×#480C2212yes—
29C2×#477C2211yescharacteristic
30C2×#468C2212yes—
31C2×#460C2211yescharacteristic
32C2×#452C2212yes—
33C2×C4×Q16C2211yescharacteristic
34C2×C4×SD16C2212yes—
35C2×#436C2211yescharacteristic
36C2×C8×D4C2211yescharacteristic
37C2×#428C2212yes—
38C2×#417C2212yes—
39C2×#416C2212yes—
40#2377—22no—
41#2370—21no—
42#2369C2211yescharacteristic
43#2366—21no—
44#2366C2211yescharacteristic
45#2362—22no—
46#2362C2212yes—
47#2361C2212yes—
48#2357—21no—
49#2355C2211yescharacteristic
50#2355C2211yescharacteristic
51#2354C2211yescharacteristic
52#2349—21no—
53D4×C4⋊C4C2211yescharacteristic
54#2344C2212yes—
55#2339C2212yes—
56#2332—22no—
57#2328—21no—
58#2325—22no—
59#2324C2212yes—
60#2323C2212yes—
61#2319—21no—
62#2311C2212yes—
63C4×C4⋊Q8C2211yescharacteristic
64C4×#127C2211yescharacteristic
65C4×#125—21no—
66#2295C2211yescharacteristic
67#2293—21no—
68#2293C2211yescharacteristic
69#2274C2212yes—
70C42×Q8C2211yescharacteristic
71#1990C2211yescharacteristic
72#1987C2211yescharacteristic
73#1982C2211yescharacteristic
74#1973C2212yes—
75#1969C2212yes—
76#1957C2211yescharacteristic
77#1948C2211yescharacteristic
78#1947C2211yescharacteristic
79#1942C2212yes—
80#1935C2212yes—
81#1934C2212yes—
82#1933C2212yes—
83#1928C2212yes—
84#1928C2212yes—
85#1928C2212yes—
86#1927C2212yes—
87#1927C2211yescharacteristic
88#1927C2211yescharacteristic
89#1926C2212yes—
90#1926C2212yes—
91#1925C2212yes—
92#1925C2212yes—
93#1925C2212yes—
94#1921C2212yes—
95#1918C2212yes—
96#1918C2211yescharacteristic
97#1918C2211yescharacteristic
98#1893C2212yes—
99#1892C2212yes—
100#1880C2212yes—
101#1878C2211yescharacteristic
102#1878C2211yescharacteristic
103#1877C2212yes—
104#1875C2212yes—
105#1872C2212yes—
106#1865C2211yescharacteristic
107#1865C2211yescharacteristic
108#1864C2212yes—
109#1862C2212yes—
110#1862C2212yes—
111#1854C2212yes—
112#1852C2212yes—
113#1845C2211yescharacteristic
114#1824C2212yes—
115#1809C2212yes—
116#1803C2211yescharacteristic
117#1803C2211yescharacteristic
118#1788C2212yes—
119#1776C2212yes—
120C4×#107C2212yes—
121C4×#106C2211yescharacteristic
122#1770C2211yescharacteristic
123C8×C4⋊C4C2211yescharacteristic
124C4×C4⋊C8C2211yescharacteristic
125#1762C2212yes—
126C4×#103C2211yescharacteristic
127C4×#103C2211yescharacteristic
128C4×#102C2212yes—
129C4×#102C2212yes—
130#1753C2212yes—
131C8×C22⋊C4C2212yes—
132#1750C2212yes—
133#1744C2211yescharacteristic
134C2×#340C2212yes—
135#1729C2212yes—
136C22×#41C2312yes—
137C22×Q16C2311yescharacteristic
138C22×SD16C2312yes—
139C22×M16C2312yes—
140C23×C8C2312yes—
141#554—24no—
142#554C2×C418yescomplemented
143#550—24no—
144#550C2×C418yes—
145C2×C4⋊Q8C2311yescharacteristic
146C2×#127—21no—
147C2×#127C2311yescharacteristic
148C2×#125—21no—
149C2×C22⋊Q8—22no—
150C2×C22⋊Q8C2312yes—
151C2×#121—22no—
152C2×#121C2312yes—
153C2×C4×Q8—21no—
154C2×C4×Q8C2311yescharacteristic
155C2×C4×Q8C2311yescharacteristic
156C2×C4×Q8C2311yescharacteristic
157C2×C4×Q8C2311yescharacteristic
158C2×C4×D4—21no—
159C2×C4×D4—21no—
160C2×C4×D4—21no—
161C2×C4×D4—21no—
162C2×C4×D4—22no—
163C2×C4×D4—21no—
164C2×C4×D4—21no—
165C2×C4×D4C2312yes—
166C2×C4×D4C2312yes—
167C2×C4×D4C2311yescharacteristic
168C2×#117—22no—
169C2×#117C2312yes—
170C2×#117C2312yes—
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2312yes—
173#486C2×C418yescomplemented
174#480C2×C4116yescomplemented
175#477C2×C418yescomplemented
176#468C2×C4116yescomplemented
177#460C2×C418yescomplemented
178#452C2×C4116yescomplemented
179C4×Q16C2×C418yescomplemented
180C4×SD16—44no—
181#436C2×C418yescomplemented
182C8×D4—24no—
183#428—44no—
184C2×#107C2312yes—
185C2×#107C2312yes—
186C2×#107C2312yes—
187C2×#107C2312yes—
188C2×#107C2311yescharacteristic
189C2×#106C2312yes—
190C2×#106C2311yescharacteristic
191C2×#106C2311yescharacteristic
192C2×C4⋊C8C2311yescharacteristic
193C2×C4⋊C8C2311yescharacteristic
194#417C2×C4116yescomplemented
195#416—44no—
196C2×#103C2311yescharacteristic
197C2×#103C2312yes—
198C2×#103C2312yes—
199C2×#103C2311yescharacteristic
200C2×#103C2311yescharacteristic
201C2×#103C2311yescharacteristic
202C2×#103C2312yes—
203C2×#103C2311yescharacteristic
204C2×#103C2311yescharacteristic
205C2×#102C2312yes—
206C2×#102C2312yes—
207C2×#102C2312yes—
208C2×#102C2312yes—
209C2×#102C2312yes—
210C2×#102C2312yes—
211C2×#102C2312yes—
212C2×C22⋊C8C2312yes—
213C2×C22⋊C8C2312yes—
214C2×#97C2312yes—
215C2×C4×C8C2311yescharacteristic
216C2×C4×C8C2312yes—
217C2×C4×C8C2312yes—
218C2×C4×C8C2311yescharacteristic
219#391—21no—
220#391—22no—
221#391C2311yescharacteristic
222#391C2312yes—
223#391C2312yes—
224#391C2311yescharacteristic
225#390—21no—
226#390—21no—
227#390—22no—
228#390—21no—
229#390—21no—
230#390D411yescharacteristic
231#390D411yescharacteristic
232#390C2312yes—
233#390C2312yes—
234#389—21no—
235#389—22no—
236#389—21no—
237#389—21no—
238#389D411yescharacteristic
239#389D411yescharacteristic
240#389C2312yes—
241#389C2312yes—
242#389C2311yescharacteristic
243#389C2311yescharacteristic
244#388—22no—
245#388—22no—
246#388—22no—
247#388—22no—
248#388—22no—
249#388—22no—
250#388—22no—
251#388D412yes—
252#388D412yes—
253#387—22no—
254#387—21no—
255#387—21no—
256#387—22no—
257#387—22no—
258#387—22no—
259#387—22no—
260#387—22no—
261#386—22no—
262#386—22no—
263#386—22no—
264#386—22no—
265#386—22no—
266#386—22no—
267#386—22no—
268#385—22no—
269#385—22no—
270#385—22no—
271#384C2311yescharacteristic
272#384C2311yescharacteristic
273#382—21no—
274#382—21no—
275#381—22no—
276#381—22no—
277#380—22no—
278#380—22no—
279#380C2312yes—
280#380C2312yes—
281C4×C4⋊C4—22no—
282C4×C4⋊C4—21no—
283C4×C4⋊C4—21no—
284C4×C4⋊C4—21no—
285C4×C4⋊C4—21no—
286C4×C4⋊C4—22no—
287C4×C4⋊C4—21no—
288C4×C4⋊C4—21no—
289C4×C4⋊C4—21no—
290C4×C4⋊C4—21no—
291C4×C4⋊C4—21no—
292C4×C4⋊C4—22no—
293C4×C4⋊C4C2312yes—
294C4×C4⋊C4C2312yes—
295C4×C4⋊C4C2311yescharacteristic
296C4×C4⋊C4C2312yes—
297C4×C4⋊C4C2311yescharacteristic
298C4×C4⋊C4C2311yescharacteristic
299C4×C4⋊C4C2312yes—
300C4×C4⋊C4C2311yescharacteristic
301C4×C4⋊C4C2311yescharacteristic
302C4×C22⋊C4—22no—
303C4×C22⋊C4—22no—
304C4×C22⋊C4C2312yes—
305#376—21no—
306C2×#95—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×C4—22no—
349C23×C4—22no—
350C23×C4C2412yes—
351C2×Q16—41no—
352C2×Q16—41no—
353C2×Q16C22×C414yes—
354C2×SD16—42no—
355C2×SD16—42no—
356C2×SD16C22×C418yes—
357C2×M16—42no—
358C2×M16—42no—
359C2×M16C22×C418yes—
360C22×C8—24no—
361C22×C8—42no—
362C22×C8—42no—
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#125—28no—
375C22⋊Q8—24no—
376C22⋊Q8—216no—
377C22⋊Q8C22×C418yes—
378#121—24no—
379#121—216no—
380#121C22×C418yes—
381C4×Q8—22no—
382C4×Q8—22no—
383C4×Q8—22no—
384C4×Q8—41no—
385C4×Q8—41no—
386C4×Q8—41no—
387C4×Q8—82no—
388C4×Q8C22×C414yes—
389C4×Q8C22×C414yes—
390C4×D4—28no—
391C4×D4—28no—
392C4×D4—42no—
393C4×D4—42no—
394C4×D4—42no—
395C4×D4—42no—
396C4×D4—82no—
397C4×D4—82no—
398C4×D4—82no—
399C4×D4—82no—
400C4×D4—84no—
401C4×D4C22×C414yes—
402C4×D4#4114yes—
403#117—24no—
404#117—42no—
405#117—42no—
406#117—42no—
407#117—84no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—24no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—42no—
426C2×C4⋊C4—42no—
427C2×C4⋊C4C22×C418yes—
428C2×C4⋊C4C2×D411yescharacteristic
429C2×C4⋊C4C2×D411yescharacteristic
430C2×C4⋊C4C2×D412yes—
431C2×C4⋊C4C2×D412yes—
432C2×C4⋊C4C2×D411yescharacteristic
433C2×C4⋊C4C2411yescharacteristic
434C2×C4⋊C4C2412yes—
435C2×C4⋊C4C2412yes—
436C2×C4⋊C4C2411yescharacteristic
437C2×C4⋊C4C2411yescharacteristic
438C2×C4⋊C4C2411yescharacteristic
439C2×C4⋊C4C2412yes—
440C2×C4⋊C4C2411yescharacteristic
441C2×C4⋊C4C2411yescharacteristic
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⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4C2×D412yes—
454C2×C22⋊C4C2×D412yes—
455C2×C22⋊C4C2×D412yes—
456C2×C22⋊C4C2×D412yes—
457C2×C22⋊C4C2×D412yes—
458C2×C42—21no—
459C2×C42—21no—
460C2×C42—21no—
461C2×C42—22no—
462C2×C42—21no—
463C2×C42—21no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—22no—
467C2×C42—22no—
468C2×C42—22no—
469C2×C42—21no—
470C2×C42—22no—
471C2×C42C2×D411yescharacteristic
472C2×C42C2×D411yescharacteristic
473C2×C42C2×D411yescharacteristic
474C2×C42C2×D411yescharacteristic
475C2×C42C2411yescharacteristic
476C2×C42C2412yes—
477C2×C42C2411yescharacteristic
478C2×C42C2411yescharacteristic
479#107—42no—
480#107—42no—
481#107—42no—
482#107C22×C414yes—
483#107C22×C418yes—
484#106—22no—
485#106—24no—
486#106—41no—
487C4⋊C8—22no—
488C4⋊C8C22×C414yes—
489#103—22no—
490#103—41no—
491#103—41no—
492#103—41no—
493#103—42no—
494#103—42no—
495#103C22×C414yes—
496#103C22×C418yes—
497#103C22×C414yes—
498#102—24no—
499#102—42no—
500#102—42no—
501#102—42no—
502#102C22×C418yes—
503#102C22×C418yes—
504#102C22×C418yes—
505C22⋊C8—24no—
506C22⋊C8C22×C418yes—
507#97—42no—
508C4×C8—22no—
509C4×C8—42no—
510C4×C8—42no—
511C4×C8C22×C414yes—
512#95—21no—
513#95—22no—
514#95—22no—
515#95—21no—
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—21no—
525#95—21no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95—22no—
530#95—22no—
531#95—22no—
532#95—22no—
533#95—21no—
534#95C2×D412yes—
535#95C2×D412yes—
536#95C2×D412yes—
537C24—22no—
538C24C22×D412yes—
539#41—48no—
540#41—48no—
541#41—84no—
542#41—84no—
543C2×Q8—24no—
544C2×Q8—21no—
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—81no—
555C2×Q8—81no—
556C2×Q8C23×C412yes—
557C2×Q8C23×C412yes—
558C2×D4—28no—
559C2×D4—28no—
560C2×D4—24no—
561C2×D4—24no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—81no—
572C2×D4—81no—
573C2×D4—82no—
574C2×D4—82no—
575C2×D4—82no—
576C2×D4—82no—
577C2×D4C4×D414yes—
578C2×D4C23×C414yes—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—28no—
590C22×C4—28no—
591C22×C4—21no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—44no—
597C22×C4—82no—
598C22×C4—82no—
599C22×C4—82no—
600C22×C4—82no—
601C22×C4—82no—
602C22×C4—82no—
603C22×C4—82no—
604C22×C4—82no—
605C22×C4—82no—
606C22×C4—82no—
607C22×C4—82no—
608C22×C4—82no—
609C22×C4C23×C414yes—
610C22×C4C22×D412yes—
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D412yes—
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D412yes—
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C2×#4114yes—
620C22×C4C2511yescharacteristic
621Q16—44no—
622SD16—48no—
623M16—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—22no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—84no—
640C2×C8C23×C412yes—
641C2×C8C23×C412yes—
642C2×C8C23×C414yes—
643C4⋊C4—28no—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—24no—
647C4⋊C4—28no—
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—21no—
663C4⋊C4—22no—
664C4⋊C4—42no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4—44no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—81no—
673C4⋊C4—82no—
674C4⋊C4—82no—
675C4⋊C4—81no—
676C4⋊C4—81no—
677C4⋊C4C4×D414yes—
678C4⋊C4C23×C412yes—
679C4⋊C4C23×C414yes—
680C4⋊C4C23×C412yes—
681C4⋊C4H(5,𝔽2)12yes—
682C22⋊C4—28no—
683C22⋊C4—28no—
684C22⋊C4—24no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—42no—
688C22⋊C4—44no—
689C22⋊C4—82no—
690C22⋊C4—82no—
691C22⋊C4—82no—
692C22⋊C4—82no—
693C22⋊C4—82no—
694C22⋊C4—82no—
695C22⋊C4—82no—
696C22⋊C4—82no—
697C22⋊C4C4×D418yes—
698C42—24no—
699C42—24no—
700C42—22no—
701C42—22no—
702C42—22no—
703C42—21no—
704C42—22no—
705C42—22no—
706C42—21no—
707C42—21no—
708C42—21no—
709C42—41no—
710C42—44no—
711C42—42no—
712C42—42no—
713C42—42no—
714C42—42no—
715C42—42no—
716C42—81no—
717C42—82no—
718C42—82no—
719C42—82no—
720C42—82no—
721C42C23×C412yes—
722C42C2×#4112yes—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—24no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23C2×C4×D414yes—
737C23C23×D411yescharacteristic
738Q8—22no—
739Q8—22no—
740Q8—22no—
741Q8—22no—
742Q8—41no—
743Q8—41no—
744Q8—41no—
745Q8—41no—
746Q8—84no—
747D4—24no—
748D4—24no—
749D4—28no—
750D4—48no—
751D4—42no—
752D4—42no—
753D4—84no—
754D4—88no—
755D4—88no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—24no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—42no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—41no—
814C2×C4—88no—
815C2×C4—88no—
816C2×C4—164no—
817C2×C4—164no—
818C2×C4—164no—
819C2×C4C2×C4×D412yes—
820C2×C4C2×C4×D414yes—
821C2×C4C2×C4×D412yes—
822C2×C4#57612yes—
823C2×C4#57712yes—
824C2×C4#57812yes—
825C2×C4C24×C411yescharacteristic
826C2×C4C22×#4111yescharacteristic
827C2×C4C2×H(5,𝔽2)11yescharacteristic
828C2×C4#58511yescharacteristic
829C2×C4#58511yescharacteristic
830C2×C4#58511yescharacteristic
831C8—22no—
832C8—22no—
833C8—24no—
834C8—42no—
835C8—41no—
836C8—41no—
837C22—24no—
838C22—24no—
839C22—24no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—44no—
845C22—44no—
846C22—44no—
847C22—82no—
848C22—82no—
849C22—82no—
850C22—82no—
851C22C22×C4×D411yescharacteristic
852C22#348511yescharacteristic
853C22#348811yescharacteristic
854C22C2×#57611yescharacteristic
855C22C2×#57711yescharacteristic
856C22C2×#57811yescharacteristic
857C22#358411yescharacteristic
858C4—22no—
859C4—22no—
860C4—24no—
861C4—42no—
862C4—44no—
863C4—42no—
864C4—41no—
865C4—42no—
866C4—41no—
867C4—42no—
868C4—41no—
869C4—42no—
870C4—42no—
871C4—42no—
872C4—81no—
873C4—81no—
874C4—82no—
875C4—82no—
876C4—81no—
877C4#294714yes—
878C4#342811yescharacteristic
879C4C4×H(5,𝔽2)11yescharacteristic
880C4#351411yescharacteristic
881C4#352111yescharacteristic
882C2—44no—
883C2—84no—
884C2#3429211yescharacteristic
885C2C2×#294711yescharacteristic
886C2C4×#57611yescharacteristic
887C2#6178611yescharacteristic
888C2#6179111yescharacteristic
889C2#6205711yescharacteristic
890C2#6206911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#550C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2293 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #34317C2semidirect
4. #23215C2semidirect
5. #23101C2semidirect
6. #23069C2semidirect
7. #23034C2semidirect
8. #22916C2semidirect
9. #22876C2semidirect
10. #22808C2semidirect
11. #22665C2semidirect
12. #22582C2semidirect
13. #22487C2semidirect
15. #22220C2semidirect
16. #22201C2semidirect
17. #22113C2semidirect
18. #22057C2semidirect
19. #21586C2semidirect
20. C4×#460C2semidirect
21. #21116C2semidirect
22. #21062C2semidirect
23. #20562C2semidirect
26. #3333C4semidirect
142. #554C2×C4semidirect
173. #486C2×C4semidirect
174. #480C2×C4semidirect
175. #477C2×C4semidirect
176. #468C2×C4semidirect
177. #460C2×C4semidirect
178. #452C2×C4semidirect
179. C4×Q16C2×C4semidirect
181. #436C2×C4semidirect
194. #417C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#33332
#344942
#343172
#232152
#231012
#230692
#230342
#229162
#228762
#228082
#226652
#225822
#224872
#224182
#222202
#222012
#221132
#220572
#215862
C4×#4602
#211162
#210622
#205622