Finite Group Databasebeta

← #6400895

Subgroups — #6400895

Order 512.

1931 conjugacy classes of subgroups.

The subgroup lattice has 883 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3394C211yesmaximal, characteristic
2#34322C211yesmaximal, characteristic, complemented
3C4×#559C211yesmaximal, characteristic, complemented
4#23190C211yesmaximal, characteristic, complemented
5#23189C212yesmaximal, complemented
6#23104C212yesmaximal, complemented
7#23102C211yesmaximal, characteristic, complemented
8#23006C212yesmaximal, complemented
9#23001C211yesmaximal, characteristic
10#22765C212yesmaximal, complemented
11#22762C211yesmaximal, characteristic, complemented
12#22741C211yesmaximal, characteristic, complemented
13#22543C211yesmaximal, characteristic, complemented
14#22541C211yesmaximal, characteristic, complemented
15#22271C212yesmaximal, complemented
16#22268C211yesmaximal, characteristic, complemented
17#22156C212yesmaximal, complemented
18#22151C211yesmaximal, characteristic
19#21507C212yesmaximal, complemented
20#21506C211yesmaximal, characteristic, complemented
21#21120C211yesmaximal, characteristic, complemented
22#21117C212yesmaximal, complemented
23#20572C211yesmaximal, characteristic, complemented
24C2×#559C2211yescharacteristic
25C2×#556C2211yescharacteristic
26#3394C4116yescomplemented
27C2×#495C2212yes—
28C2×#492C2211yescharacteristic
29C2×#464C2212yes—
30C2×#462C2211yescharacteristic
31C2×#463C2212yes—
32C2×#459C2211yescharacteristic
33C2×C8×Q8C2211yescharacteristic
34C2×C8×Q8C2211yescharacteristic
35C2×#442C2212yes—
36C2×#441C2212yes—
37C2×#440C2212yes—
38C2×C4×SD16C2212yes—
39C2×C4×SD16C2211yescharacteristic
40#2374—22no—
41#2373—22no—
42#2367—21no—
43#2367C2212yes—
44#2367C2212yes—
45#2366C2211yescharacteristic
46#2365C2211yescharacteristic
47#2360—21no—
48#2357—21no—
49#2357C2212yes—
50#2355C2211yescharacteristic
51#2355C2211yescharacteristic
52#2355C2211yescharacteristic
53#2351C2212yes—
54D4×C4⋊C4C2211yescharacteristic
55#2346—21no—
56#2334—22no—
57#2323—21no—
58C4×C4⋊Q8C2211yescharacteristic
59C4×#127C2211yescharacteristic
60C4×#124—21no—
61C4×#124C2212yes—
62C4×#124C2212yes—
63C4×#123—22no—
64#2295C2212yes—
65#2293C2211yescharacteristic
66#2274—21no—
67C42×Q8C2211yescharacteristic
68C42×Q8C2211yescharacteristic
69C42×D4—21no—
70C42×D4C2212yes—
71#1983C2212yes—
72#1983C2212yes—
73#1982C2211yescharacteristic
74#1981C2211yescharacteristic
75#1973C2212yes—
76#1972C2212yes—
77#1971C2212yes—
78#1958C2212yes—
79#1958C2212yes—
80#1957C2211yescharacteristic
81#1956C2211yescharacteristic
82#1949C2212yes—
83#1949C2212yes—
84#1948C2211yescharacteristic
85#1948C2211yescharacteristic
86#1936C2212yes—
87#1936C2212yes—
88#1935C2212yes—
89#1927C2212yes—
90#1927C2212yes—
91#1925C2211yescharacteristic
92#1925C2211yescharacteristic
93#1920C2211yescharacteristic
94#1920C2212yes—
95#1920C2211yescharacteristic
96#1880C2212yes—
97#1880C2211yescharacteristic
98#1880C2211yescharacteristic
99#1880C2212yes—
100#1880C2212yes—
101#1879C2212yes—
102#1879C2212yes—
103#1878C2212yes—
104#1878C2212yes—
105#1877C2212yes—
106#1877C2212yes—
107#1877C2212yes—
108#1877C2212yes—
109#1864C2212yes—
110#1864C2212yes—
111#1863C2211yescharacteristic
112#1863C2211yescharacteristic
113#1835C2212yes—
114#1834C2211yescharacteristic
115#1805C2212yes—
116#1804C2212yes—
117#1803C2211yescharacteristic
118#1802C2211yescharacteristic
119C4×#107C2211yescharacteristic
120C4×#106C2212yes—
121#1770C2211yescharacteristic
122#1770C2212yes—
123#1770C2212yes—
124#1770C2211yescharacteristic
125#1767C2211yescharacteristic
126#1767C2212yes—
127#1763C2212yes—
128#1763C2212yes—
129#1762C2212yes—
130C4×#103C2212yes—
131C4×#103C2211yescharacteristic
132C4×#102C2211yescharacteristic
133C4×#102C2212yes—
134#1744C2212yes—
135#1744C2211yescharacteristic
136C22×Q16C2312yes—
137C22×SD16C2312yes—
138C22×SD16C2312yes—
139C22×SD16C2311yescharacteristic
140C22×D8C2312yes—
141#559—24no—
142#559C2×C418yescomplemented
143#556—24no—
144#556C2×C418yescomplemented
145C2×C4⋊Q8C2311yescharacteristic
146C2×#127C2311yescharacteristic
147C2×#126—22no—
148C2×#124—21no—
149C2×#124C2312yes—
150C2×#124C2312yes—
151C2×#123—22no—
152C2×C22⋊Q8—21no—
153C2×C4×Q8D411yescharacteristic
154C2×C4×Q8D411yescharacteristic
155C2×C4×Q8C2311yescharacteristic
156C2×C4×Q8C2311yescharacteristic
157C2×C4×Q8C2312yes—
158C2×C4×Q8C2312yes—
159C2×C4×Q8C2312yes—
160C2×C4×Q8C2311yescharacteristic
161C2×C4×Q8C2311yescharacteristic
162C2×C4×D4—21no—
163C2×C4×D4—21no—
164C2×C4×D4—21no—
165C2×C4×D4—21no—
166C2×C4×D4C2312yes—
167C2×C4×D4C2311yescharacteristic
168C2×C4×D4C2312yes—
169C2×C4×D4C2312yes—
170C2×C4×D4C2312yes—
171C2×#117—21no—
172C2×#117—21no—
173C22×C4⋊C4—21no—
174C22×C42—22no—
175#495C2×C4116yescomplemented
176#492C2×C418yescomplemented
177#464C2×C4116yescomplemented
178#463C2×C4116yescomplemented
179#462C2×C418yescomplemented
180#459C2×C418yes—
181C8×Q8—24no—
182C8×Q8C2×C418yescomplemented
183#442—44no—
184#441—44no—
185#440—44no—
186C4×SD16C2×C418yescomplemented
187C4×SD16C2×C4116yescomplemented
188C2×#107C2311yescharacteristic
189C2×#107C2311yescharacteristic
190C2×#106C2312yes—
191C2×#106C2312yes—
192C2×#106C2311yescharacteristic
193C2×C4⋊C8C2311yescharacteristic
194C2×C4⋊C8C2312yes—
195C2×C4⋊C8C2311yescharacteristic
196C2×C4⋊C8C2312yes—
197C2×#103C2312yes—
198C2×#103C2312yes—
199C2×#103C2312yes—
200C2×#103C2312yes—
201C2×#103C2311yescharacteristic
202C2×#103C2311yescharacteristic
203C2×#103C2312yes—
204C2×#103C2311yescharacteristic
205C2×#103C2312yes—
206C2×#102C2311yescharacteristic
207C2×#102C2312yes—
208C2×#102C2312yes—
209C2×#102C2312yes—
210C2×#102C2312yes—
211C2×#102C2312yes—
212C2×#102C2311yescharacteristic
213C2×#102C2312yes—
214C2×#102C2311yescharacteristic
215C2×#97C2312yes—
216C2×#97C2312yes—
217C2×#97C2312yes—
218C2×C4×C8C2311yescharacteristic
219C2×C4×C8C2312yes—
220C2×C4×C8C2311yescharacteristic
221C2×C4×C8C2312yes—
222#391—21no—
223#391—21no—
224#391C2312yes—
225#391C2312yes—
226#391C2312yes—
227#390—21no—
228#390—21no—
229#390—21no—
230#390C2312yes—
231#390C2312yes—
232#390C2311yescharacteristic
233#390C2311yescharacteristic
234#389—21no—
235#389—22no—
236#389—22no—
237#389—21no—
238#389—21no—
239#389C2312yes—
240#389C2311yescharacteristic
241#389C2311yescharacteristic
242#388—22no—
243#388—22no—
244#388—22no—
245#388—22no—
246#388—22no—
247#388—21no—
248#388—22no—
249#388—22no—
250#388—22no—
251#388—21no—
252#388—22no—
253#388—22no—
254#387—22no—
255#387—22no—
256#387—22no—
257#387—22no—
258#387—22no—
259#387—22no—
260#386—22no—
261#385—22no—
262#385—22no—
263#385—22no—
264#384C2311yescharacteristic
265#384C2311yescharacteristic
266#382—21no—
267#382—22no—
268#382C2312yes—
269#382C2312yes—
270#381—22no—
271#380—21no—
272C4×C4⋊C4—21no—
273C4×C4⋊C4—21no—
274C4×C4⋊C4—21no—
275C4×C4⋊C4—21no—
276C4×C4⋊C4—21no—
277C4×C4⋊C4—21no—
278C4×C4⋊C4—22no—
279C4×C4⋊C4—21no—
280C4×C4⋊C4—21no—
281C4×C4⋊C4—21no—
282C4×C4⋊C4—22no—
283C4×C4⋊C4D412yes—
284C4×C4⋊C4D411yescharacteristic
285C4×C4⋊C4D411yescharacteristic
286C4×C4⋊C4D412yes—
287C4×C4⋊C4C2312yes—
288C4×C4⋊C4C2311yescharacteristic
289C4×C4⋊C4C2311yescharacteristic
290C4×C4⋊C4C2312yes—
291C4×C4⋊C4C2312yes—
292C4×C4⋊C4C2311yescharacteristic
293C4×C4⋊C4C2311yescharacteristic
294C4×C4⋊C4C2311yescharacteristic
295C4×C4⋊C4C2312yes—
296C4×C22⋊C4—22no—
297C4×C22⋊C4—21no—
298C4×C22⋊C4—22no—
299C4×C22⋊C4—22no—
300C4×C22⋊C4—22no—
301C4×C22⋊C4—22no—
302C4×C22⋊C4—22no—
303C4×C22⋊C4—22no—
304C4×C22⋊C4—22no—
305C4×C22⋊C4—22no—
306C4×C22⋊C4—22no—
307#376—22no—
308C43—21no—
309C43C2311yescharacteristic
310C43C2312yes—
311#340C2312yes—
312#340C2312yes—
313#340C2311yescharacteristic
314#340C2311yescharacteristic
315#340C2312yes—
316#340C2312yes—
317#340C2311yescharacteristic
318#340C2312yes—
319#340C2312yes—
320#340C2311yescharacteristic
321#340C2311yescharacteristic
322#340C2311yescharacteristic
323#336C2311yescharacteristic
324#336C2311yescharacteristic
325#336C2312yes—
326#336C2312yes—
327#336C2311yescharacteristic
328#336C2312yes—
329#336C2311yescharacteristic
330C22×Q8C2×D411yescharacteristic
331C22×Q8C2411yescharacteristic
332C22×Q8C2412yes—
333C22×D4—21no—
334C22×D4—21no—
335C22×D4C2411yescharacteristic
336C22×D4C2412yes—
337C23×C4—21no—
338C23×C4—22no—
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—22no—
342C2×Q16—42no—
343C2×Q16—42no—
344C2×Q16C22×C418yes—
345C2×SD16—42no—
346C2×SD16—41no—
347C2×SD16—42no—
348C2×SD16—42no—
349C2×SD16—41no—
350C2×SD16—42no—
351C2×SD16C22×C418yes—
352C2×SD16C22×C414yes—
353C2×SD16C22×C418yes—
354C2×D8—42no—
355C2×D8—42no—
356C2×D8C22×C418yes—
357C22×C8C2411yescharacteristic
358C22×C8C2411yescharacteristic
359C22×C8C2412yes—
360C22×C8C2412yes—
361C22×C8C2411yescharacteristic
362C22×C8C2411yescharacteristic
363C4⋊Q8—22no—
364C4⋊Q8C22×C414yes—
365#127—22no—
366#127C22×C414yes—
367#126—216no—
368#124—28no—
369#124—24no—
370#124—24no—
371#124C22×C418yes—
372#124C22×C418yes—
373#123—216no—
374C22⋊Q8—28no—
375C4×Q8—24no—
376C4×Q8—22no—
377C4×Q8—22no—
378C4×Q8—42no—
379C4×Q8—42no—
380C4×Q8—41no—
381C4×Q8—41no—
382C4×Q8—41no—
383C4×Q8—42no—
384C4×Q8—42no—
385C4×Q8—42no—
386C4×Q8—42no—
387C4×Q8C22×C418yes—
388C4×Q8C22×C414yes—
389C4×Q8C22×C414yes—
390C4×Q8#4114yes—
391C4×D4—28no—
392C4×D4—24no—
393C4×D4—22no—
394C4×D4—24no—
395C4×D4—42no—
396C4×D4—42no—
397C4×D4—42no—
398C4×D4—44no—
399C4×D4—42no—
400C4×D4—42no—
401C4×D4—44no—
402C4×D4—82no—
403C4×D4C22×C414yes—
404C4×D4C22×C418yes—
405#117—28no—
406#117—44no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—44no—
423C2×C4⋊C4C2×D411yescharacteristic
424C2×C4⋊C4C2×D411yescharacteristic
425C2×C4⋊C4C2×D412yes—
426C2×C4⋊C4C2×D412yes—
427C2×C4⋊C4C2×D411yescharacteristic
428C2×C4⋊C4C2×D412yes—
429C2×C4⋊C4C2412yes—
430C2×C4⋊C4C2412yes—
431C2×C4⋊C4C2411yescharacteristic
432C2×C4⋊C4C2411yescharacteristic
433C2×C4⋊C4C2411yescharacteristic
434C2×C4⋊C4C2411yescharacteristic
435C2×C4⋊C4C2411yescharacteristic
436C2×C4⋊C4C2411yescharacteristic
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—21no—
454C2×C42—22no—
455C2×C42—21no—
456C2×C42—21no—
457C2×C42—21no—
458C2×C42—21no—
459C2×C42—21no—
460C2×C42—21no—
461C2×C42—22no—
462C2×C42—22no—
463C2×C42—21no—
464C2×C42—22no—
465C2×C42—22no—
466C2×C42—22no—
467C2×C42—84no—
468C2×C42C2×D411yescharacteristic
469C2×C42C2×D411yescharacteristic
470C2×C42C2×D411yescharacteristic
471C2×C42C2×D412yes—
472C2×C42C2×D412yes—
473C2×C42C2×D412yes—
474C2×C42C2×D412yes—
475C2×C42C2×D411yescharacteristic
476C2×C42C2411yescharacteristic
477C2×C42C2412yes—
478C2×C42C2411yescharacteristic
479C2×C42C2412yes—
480C2×C42C2411yescharacteristic
481#107—22no—
482#107—41no—
483#106—24no—
484#106—42no—
485#106C22×C414yes—
486C4⋊C8—24no—
487C4⋊C8—22no—
488C4⋊C8C22×C414yes—
489C4⋊C8C22×C418yes—
490#103—24no—
491#103—41no—
492#103—42no—
493#103—42no—
494#103—42no—
495#103—41no—
496#103—42no—
497#103C22×C418yes—
498#103C22×C414yes—
499#102—22no—
500#102—42no—
501#102—42no—
502#102—41no—
503#102—42no—
504#102—42no—
505#102—42no—
506#102C22×C418yes—
507#102C22×C414yes—
508#97—42no—
509#97—42no—
510#97—42no—
511C4×C8—24no—
512C4×C8—22no—
513C4×C8C22×C414yes—
514C4×C8C22×C418yes—
515#95—21no—
516#95—22no—
517#95—22no—
518#95—22no—
519#95—21no—
520#95—22no—
521#95—22no—
522#95—22no—
523#95—22no—
524#95—22no—
525#95—22no—
526#95—22no—
527#95—21no—
528#95—22no—
529#95—22no—
530#95—22no—
531#95—21no—
532#95—21no—
533#95—22no—
534#95—21no—
535#95C2×D412yes—
536#95C2×D412yes—
537#95C2×D412yes—
538C24—21no—
539C24—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—21no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—21no—
546C2×Q8—22no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—22no—
550C2×Q8—22no—
551C2×Q8—21no—
552C2×Q8C4×D414yes—
553C2×Q8C23×C412yes—
554C2×Q8C23×C414yes—
555C2×D4—24no—
556C2×D4—24no—
557C2×D4—21no—
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—22no—
561C2×D4—21no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—22no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—81no—
570C2×D4—81no—
571C2×D4C23×C412yes—
572C2×D4C23×C414yes—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—24no—
579C22×C4—28no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—44no—
593C22×C4—82no—
594C22×C4—82no—
595C22×C4—82no—
596C22×C4—82no—
597C22×C4—82no—
598C22×C4C22×D412yes—
599C22×C4C22×D412yes—
600C22×C4C22×D411yescharacteristic
601C22×C4C22×D411yescharacteristic
602C22×C4C22×D411yescharacteristic
603C22×C4C22×D412yes—
604C22×C4C22×D412yes—
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D411yescharacteristic
608C22×C4C2511yescharacteristic
609Q16—48no—
610SD16—48no—
611SD16—44no—
612SD16—48no—
613D8—48no—
614C2×C8—22no—
615C2×C8—21no—
616C2×C8—22no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—22no—
623C2×C8—21no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8C23×C412yes—
630C2×C8C23×C414yes—
631C2×C8C23×C412yes—
632C4⋊C4—24no—
633C4⋊C4—28no—
634C4⋊C4—24no—
635C4⋊C4—24no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—22no—
643C4⋊C4—21no—
644C4⋊C4—22no—
645C4⋊C4—21no—
646C4⋊C4—22no—
647C4⋊C4—21no—
648C4⋊C4—22no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—42no—
652C4⋊C4—42no—
653C4⋊C4—42no—
654C4⋊C4—44no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C4⋊C4—42no—
658C4⋊C4—42no—
659C4⋊C4—42no—
660C4⋊C4—81no—
661C4⋊C4—81no—
662C4⋊C4—82no—
663C4⋊C4—82no—
664C4⋊C4C4×D414yes—
665C4⋊C4C4×D418yes—
666C4⋊C4C23×C412yes—
667C4⋊C4C23×C412yes—
668C4⋊C4H(5,𝔽2)12yes—
669C22⋊C4—28no—
670C22⋊C4—28no—
671C22⋊C4—28no—
672C22⋊C4—24no—
673C22⋊C4—28no—
674C22⋊C4—28no—
675C22⋊C4—44no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—44no—
681C22⋊C4—42no—
682C22⋊C4—81no—
683C22⋊C4—82no—
684C22⋊C4—82no—
685C22⋊C4—82no—
686C42—28no—
687C42—24no—
688C42—22no—
689C42—22no—
690C42—24no—
691C42—22no—
692C42—22no—
693C42—21no—
694C42—21no—
695C42—21no—
696C42—22no—
697C42—21no—
698C42—42no—
699C42—41no—
700C42—42no—
701C42—42no—
702C42—42no—
703C42—42no—
704C42—42no—
705C42—42no—
706C42—42no—
707C42—82no—
708C42—81no—
709C42—82no—
710C42—82no—
711C42—82no—
712C42—82no—
713C42C23×C414yes—
714C42C23×C412yes—
715C42C2×#4114yes—
716C42C2×#4112yes—
717C23—22no—
718C23—24no—
719C23—41no—
720C23—42no—
721C23—42no—
722C23—41no—
723C23—42no—
724C23—41no—
725C23—41no—
726C23—42no—
727C23—42no—
728C23—41no—
729C23—41no—
730C23—42no—
731C23C23×D411yescharacteristic
732Q8—28no—
733Q8—24no—
734Q8—22no—
735Q8—24no—
736Q8—22no—
737Q8—41no—
738Q8—42no—
739Q8—41no—
740Q8—42no—
741D4—22no—
742D4—24no—
743D4—22no—
744D4—24no—
745D4—48no—
746D4—41no—
747D4—42no—
748D4—41no—
749D4—42no—
750D4—84no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—24no—
765C2×C4—22no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—41no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—48no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—88no—
806C2×C4—88no—
807C2×C4—88no—
808C2×C4—164no—
809C2×C4C2×C4×D414yes—
810C2×C4C2×C4×D414yes—
811C2×C4C2×C4×D412yes—
812C2×C4C2×C4×D412yes—
813C2×C4#57512yes—
814C2×C4#57512yes—
815C2×C4#57712yes—
816C2×C4C24×C411yescharacteristic
817C2×C4C22×#4111yescharacteristic
818C2×C4C2×H(5,𝔽2)11yescharacteristic
819C2×C4#58511yescharacteristic
820C2×C4#58511yescharacteristic
821C2×C4#58511yescharacteristic
822C8—22no—
823C8—24no—
824C8—22no—
825C8—41no—
826C8—42no—
827C8—41no—
828C22—44no—
829C22—42no—
830C22—42no—
831C22—44no—
832C22—42no—
833C22—44no—
834C22—82no—
835C22—81no—
836C22—81no—
837C22—82no—
838C22—81no—
839C22—82no—
840C22—82no—
841C22—81no—
842C22C22×C4×D411yescharacteristic
843C22#348711yescharacteristic
844C22#348811yescharacteristic
845C22C2×#57511yescharacteristic
846C22C2×#57511yescharacteristic
847C22C2×#57711yescharacteristic
848C22#358411yescharacteristic
849C4—24no—
850C4—22no—
851C4—22no—
852C4—24no—
853C4—42no—
854C4—41no—
855C4—42no—
856C4—42no—
857C4—41no—
858C4—42no—
859C4—41no—
860C4—42no—
861C4—44no—
862C4—42no—
863C4—81no—
864C4—82no—
865C4—81no—
866C4—81no—
867C4—82no—
868C4#294314yes—
869C4#342811yescharacteristic
870C4C4×H(5,𝔽2)11yescharacteristic
871C4#351711yescharacteristic
872C4#352411yescharacteristic
873C2—84no—
874C2—82no—
875C2#3429511yescharacteristic
876C2C2×#294311yescharacteristic
877C2C4×#57711yescharacteristic
878C2#6190211yescharacteristic
879C2#6190411yescharacteristic
880C2#6199611yescharacteristic
881C2#6200611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#459C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34322C2semidirect
3. C4×#559C2semidirect
4. #23190C2semidirect
5. #23189C2semidirect
6. #23104C2semidirect
7. #23102C2semidirect
8. #23006C2semidirect
10. #22765C2semidirect
11. #22762C2semidirect
12. #22741C2semidirect
13. #22543C2semidirect
14. #22541C2semidirect
15. #22271C2semidirect
16. #22268C2semidirect
17. #22156C2semidirect
19. #21507C2semidirect
20. #21506C2semidirect
21. #21120C2semidirect
22. #21117C2semidirect
23. #20572C2semidirect
26. #3394C4semidirect
142. #559C2×C4semidirect
144. #556C2×C4semidirect
175. #495C2×C4semidirect
176. #492C2×C4semidirect
177. #464C2×C4semidirect
178. #463C2×C4semidirect
179. #462C2×C4semidirect
182. C8×Q8C2×C4semidirect
186. C4×SD16C2×C4semidirect
187. C4×SD16C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#33942
#343222
C4×#5592
#231902
#231892
#231042
#231022
#230062
#230012
#227652
#227622
#227412
#225432
#225412
#222712
#222682
#221562
#221512
#215072
#215062
#211202
#211172
#205722