Finite Group Databasebeta

← #6442997

Subgroups — #6442997

Order 512.

2787 conjugacy classes of subgroups.

The subgroup lattice has 891 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3056C211yesmaximal, characteristic, complemented
2C22×#465C211yesmaximal, characteristic, complemented
3C2×#3043C211yesmaximal, characteristic, complemented
4C22×#424C211yesmaximal, characteristic, complemented
5#35252C211yesmaximal, characteristic
6#34203C211yesmaximal, characteristic, complemented
7#24769C214yesmaximal, complemented
8#24768C214yesmaximal, complemented
9#24755C214yesmaximal, complemented
10#24753C214yesmaximal, complemented
11#23614C211yesmaximal, characteristic, complemented
12#23610C211yesmaximal, characteristic, complemented
13#23545C211yesmaximal, characteristic, complemented
14#23541C211yesmaximal, characteristic, complemented
15#21263C211yesmaximal, characteristic, complemented
16#21174C211yesmaximal, characteristic, complemented
17#20973C211yesmaximal, characteristic, complemented
18#20967C211yesmaximal, characteristic, complemented
19#20651C211yesmaximal, characteristic, complemented
20C22×#137C2211yescharacteristic
21C23×SD16C2211yescharacteristic
22C23×M16C2211yescharacteristic
23C24×C8C2211yescharacteristic
24C2×#535C2211yescharacteristic
25C2×#525C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×#121C2211yescharacteristic
28C2×#519C2211yescharacteristic
29C22×#117C2211yescharacteristic
30#3056—28no—
31C2×#470C2212yescomplemented
32C2×#468C2212yescomplemented
33C2×#467C2212yescomplemented
34C2×#465—28no—
35C2×#465C2214yes—
36C2×#465C2214yes—
37C2×#465C2212yescomplemented
38#3043—28no—
39C2×#464C2214yescomplemented
40C2×#460C2214yescomplemented
41C2×#428C2211yescharacteristic
42C22×#106C2211yescharacteristic
43C2×#424—28no—
44C2×#424C2211yescharacteristic
45C2×#424C2211yescharacteristic
46C2×#424C2211yescharacteristic
47C2×#424C2211yescharacteristic
48C2×#424C2214yescomplemented
49C22×C4⋊C8C2214yescomplemented
50C2×#417C2211yescharacteristic
51C2×#419C2211yescharacteristic
52C2×#418C2211yescharacteristic
53C2×#418C2211yescharacteristic
54C2×#416C2211yescharacteristic
55C2×#416C2211yescharacteristic
56C22×#103C2211yescharacteristic
57C22×#102C2211yescharacteristic
58#2856C2212yes—
59#2850C2212yes—
60#2620C2212yes—
61#2619C2212yes—
62#2416—22no—
63#2414—22no—
64#2411—22no—
65#2410—22no—
66#2362—22no—
67#2360—22no—
68#2344—22no—
69#2342—22no—
70#2323C2214yescomplemented
71#2317C2211yescharacteristic
72#2316C2211yescharacteristic
73#2311C2211yescharacteristic
74#2310C2211yescharacteristic
75#2309C2211yescharacteristic
76C4×C22⋊Q8C2214yescomplemented
77#2280C2211yescharacteristic
78#2274C2211yescharacteristic
79#2067C2214yescomplemented
80#2066C2214yescomplemented
81#2065C2214yescomplemented
82#2065C2214yescomplemented
83#2056C2214yescomplemented
84#2055C2214yescomplemented
85#2055C2214yescomplemented
86#2055C2214yescomplemented
87#1983C2214yescomplemented
88#1982C2214yescomplemented
89#1949C2214yescomplemented
90#1948C2214yescomplemented
91#1895C2214yes—
92#1893C2214yes—
93#1893C2212yescomplemented
94#1893C2212yescomplemented
95#1892C2212yescomplemented
96#1892C2212yescomplemented
97#1805C2214yescomplemented
98#1803C2214yescomplemented
99#1736C2211yescharacteristic
100#1736C2211yescharacteristic
101#1735C2211yescharacteristic
102#1735C2211yescharacteristic
103C22×#41C2311yescharacteristic
104C23×Q8C2311yescharacteristic
105C23×D4—21no—
106C23×D4C2311yescharacteristic
107C24×C4C2311yescharacteristic
108C2×#137—24no—
109C2×#137—24no—
110C2×#137—42no—
111C22×Q16C2312yes—
112C22×SD16—24no—
113C22×SD16—24no—
114C22×SD16—42no—
115C22×SD16C2312yes—
116C22×SD16C2314yes—
117C22×M16—24no—
118C22×M16—24no—
119C22×M16—42no—
120C22×M16C2311yescharacteristic
121C22×M16C2312yes—
122C22×M16C2311yescharacteristic
123C23×C8—24no—
124C23×C8—24no—
125C23×C8—42no—
126C23×C8C2311yescharacteristic
127C23×C8C2312yes—
128C23×C8C2312yes—
129C23×C8C2312yes—
130C23×C8C2311yescharacteristic
131#535—24no—
132#535—24no—
133C2×#127C2312yes—
134C2×#124C2312yes—
135#525—24no—
136#525—24no—
137C2×#123—21no—
138C2×C22⋊Q8—21no—
139C2×C22⋊Q8—21no—
140C2×C22⋊Q8—24no—
141C2×C22⋊Q8D418yescomplemented
142C2×C22⋊Q8C2311yescharacteristic
143C2×C22⋊Q8C2311yescharacteristic
144C2×C22⋊Q8C2312yes—
145C2×C22⋊Q8C2312yes—
146C2×#121—21no—
147C2×#121—21no—
148C2×#121—24no—
149C2×#121—22no—
150C2×#121—24no—
151C2×#121—24no—
152C2×#121C2312yes—
153C2×#121C2311yescharacteristic
154C2×#121C2311yescharacteristic
155C2×#121C2312yes—
156C2×#120—21no—
157C2×#120—22no—
158#519—24no—
159#519—24no—
160C2×C4×Q8—22no—
161C2×C4×Q8C2314yes—
162C2×C4×D4—21no—
163C2×C4×D4—21no—
164C2×#117—24no—
165C2×#117—24no—
166C2×#117—22no—
167C2×#117D412yes—
168C2×#117D412yes—
169C2×#117C2311yescharacteristic
170C2×#117C2311yescharacteristic
171C2×#117C2311yescharacteristic
172C2×#117C2311yescharacteristic
173C2×#117C2312yes—
174C2×#117C2311yescharacteristic
175C22×C4⋊C4—21no—
176C22×C4⋊C4D412yes—
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2311yescharacteristic
179C22×C22⋊C4—21no—
180C22×C22⋊C4—21no—
181C22×C22⋊C4D412yes—
182C22×C42C2312yes—
183#470—28no—
184#468—28no—
185#467—28no—
186#465—216no—
187#465—216no—
188#465—28no—
189#464—216no—
190#460—216no—
191#428—24no—
192C2×#107C2312yes—
193C2×#106—24no—
194C2×#106C2312yes—
195C2×#106C2314yes—
196#424—24no—
197#424—24no—
198#424—24no—
199#424—216no—
200#424D418yescomplemented
201C2×C4⋊C8—216no—
202C2×C4⋊C8C2314yes—
203C2×C4⋊C8C2314yes—
204C2×C4⋊C8C2314yes—
205C2×C4⋊C8C2314yes—
206#419—24no—
207#418—24no—
208#418—42no—
209#417—24no—
210#416—24no—
211#416—42no—
212C2×#103—24no—
213C2×#103C2312yes—
214C2×#103C2312yes—
215C2×#103C2314yes—
216C2×#103C2312yes—
217C2×#103C2312yes—
218C2×#103C2312yes—
219C2×#102—24no—
220C2×#102C2312yes—
221C2×#102C2312yes—
222C2×#102C2314yes—
223C2×#102C2314yes—
224C2×#102C2312yes—
225C2×#102C2314yes—
226#396—24no—
227#394—24no—
228#394—24no—
229#392—24no—
230#391—22no—
231#391C2314yes—
232#391C2312yes—
233#390—22no—
234#390—24no—
235#390C2312yes—
236#390C2312yes—
237#390C2312yes—
238#389—22no—
239#389—22no—
240#389—24no—
241#389C2314yes—
242#388—24no—
243#388—24no—
244#388—24no—
245#387—24no—
246#387—24no—
247#386—24no—
248#386—22no—
249#385—24no—
250#385—22no—
251#384C2312yes—
252#382C2312yes—
253#381—21no—
254#381—22no—
255#380—22no—
256#380—22no—
257#380C2312yes—
258#380C2312yes—
259#379—21no—
260#379—22no—
261C4×C4⋊C4—22no—
262C4×C4⋊C4—24no—
263C4×C4⋊C4C2314yes—
264C4×C22⋊C4—24no—
265C4×C22⋊C4—21no—
266C4×C22⋊C4—21no—
267C4×C22⋊C4—22no—
268#340C2312yes—
269#340C2312yes—
270#340C2314yes—
271#340C2312yes—
272#340C2314yes—
273#340C2312yes—
274C25—21no—
275C25C2×D411yescharacteristic
276C2×#41—22no—
277C2×#41—22no—
278C2×#41—22no—
279C2×#41—22no—
280C2×#41—22no—
281C2×#41—22no—
282C22×Q8—21no—
283C22×Q8—22no—
284C22×Q8—22no—
285C22×Q8—22no—
286C22×Q8—22no—
287C22×Q8—22no—
288C22×Q8C2×D414yes—
289C22×Q8C2411yescharacteristic
290C22×Q8C2412yes—
291C22×D4—21no—
292C22×D4—21no—
293C22×D4—22no—
294C22×D4—21no—
295C22×D4—22no—
296C22×D4—22no—
297C22×D4—22no—
298C22×D4—21no—
299C22×D4—24no—
300C22×D4—22no—
301C22×D4—22no—
302C22×D4—22no—
303C22×D4—22no—
304C22×D4—44no—
305C22×D4—84no—
306C22×D4C2412yes—
307C22×D4C2411yescharacteristic
308C23×C4—22no—
309C23×C4—22no—
310C23×C4—22no—
311C23×C4—22no—
312C23×C4—21no—
313C23×C4—21no—
314C23×C4—21no—
315C23×C4—21no—
316C23×C4C2×D414yes—
317C23×C4C2×D411yescharacteristic
318C23×C4C2×D411yescharacteristic
319C23×C4C2×D411yescharacteristic
320C23×C4C2×D414yes—
321C23×C4#4114yes—
322C23×C4C2411yescharacteristic
323C23×C4C2411yescharacteristic
324C23×C4C2411yescharacteristic
325#137—416no—
326C2×Q16—24no—
327C2×Q16—24no—
328C2×Q16—42no—
329C2×SD16—28no—
330C2×SD16—24no—
331C2×SD16—28no—
332C2×SD16—24no—
333C2×SD16—44no—
334C2×SD16—42no—
335C2×SD16—416no—
336C2×M16—22no—
337C2×M16—22no—
338C2×M16—22no—
339C2×M16—22no—
340C2×M16—24no—
341C2×M16—22no—
342C2×M16—24no—
343C2×M16—42no—
344C2×M16—416no—
345C2×M16C2×D414yes—
346C22×C8—22no—
347C22×C8—22no—
348C22×C8—22no—
349C22×C8—22no—
350C22×C8—24no—
351C22×C8—24no—
352C22×C8—24no—
353C22×C8—22no—
354C22×C8—24no—
355C22×C8—24no—
356C22×C8—24no—
357C22×C8—42no—
358C22×C8—42no—
359C22×C8—42no—
360C22×C8—416no—
361C22×C8C2×D414yes—
362C22×C8C2412yes—
363C22×C8C2412yes—
364C22×C8C2412yes—
365C22×C8C2412yes—
366#127—24no—
367#127—24no—
368#124—24no—
369#124—24no—
370#123—44no—
371C22⋊Q8—28no—
372C22⋊Q8—28no—
373C22⋊Q8—24no—
374C22⋊Q8—24no—
375C22⋊Q8—22no—
376C22⋊Q8—22no—
377C22⋊Q8—22no—
378C22⋊Q8—22no—
379C22⋊Q8C2×D418yes—
380C22⋊Q8C2×D418yes—
381#121—24no—
382#121—24no—
383#121—22no—
384#121—22no—
385#121—24no—
386#121—24no—
387#121—22no—
388#121—22no—
389#121—44no—
390#121—44no—
391#121—48no—
392#121—88no—
393#120—44no—
394#120—48no—
395C4×Q8—28no—
396C4×Q8—28no—
397C4×Q8—48no—
398C4×D4—44no—
399C4×D4—44no—
400#117—22no—
401#117—22no—
402#117—28no—
403#117—28no—
404#117—24no—
405#117—24no—
406#117—22no—
407#117—22no—
408#117—22no—
409#117—22no—
410#117—22no—
411#117—22no—
412#117—48no—
413#117C2×D414yes—
414#117#4114yes—
415C2×C4⋊C4—28no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—28no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—24no—
428C2×C4⋊C4—24no—
429C2×C4⋊C4C2×D412yes—
430C2×C4⋊C4C2×D414yes—
431C2×C4⋊C4C2×D414yes—
432C2×C4⋊C4C2×D412yes—
433C2×C4⋊C4C2412yes—
434C2×C4⋊C4C2412yes—
435C2×C4⋊C4C2411yescharacteristic
436C2×C4⋊C4C2411yescharacteristic
437C2×C4⋊C4C2412yes—
438C2×C4⋊C4C2412yes—
439C2×C22⋊C4—28no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—28no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—24no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—24no—
456C2×C22⋊C4—24no—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—44no—
459C2×C22⋊C4C2×D412yes—
460C2×C22⋊C4C2×D414yes—
461C2×C22⋊C4C2×D412yes—
462C2×C42—24no—
463C2×C42—24no—
464C2×C42—24no—
465C2×C42—21no—
466C2×C42—21no—
467C2×C42—21no—
468C2×C42—24no—
469C2×C42C2×D414yes—
470C2×C42C2412yes—
471C2×C42C2412yes—
472#107—24no—
473#106—28no—
474#106—24no—
475C4⋊C8—28no—
476C4⋊C8—28no—
477C4⋊C8—28no—
478C4⋊C8C2×D4116yescomplemented
479#103—28no—
480#103—24no—
481#103—24no—
482#103—24no—
483#103—24no—
484#103—42no—
485#102—24no—
486#102—28no—
487#102—28no—
488#102—24no—
489#102—42no—
490#102—44no—
491#95—22no—
492#95—24no—
493#95—24no—
494#95—22no—
495#95—24no—
496#95—24no—
497#95—24no—
498#95—24no—
499C24—22no—
500C24—22no—
501C24—24no—
502C24—22no—
503C24—21no—
504C24—42no—
505C24—42no—
506C24—42no—
507C24—42no—
508C24—82no—
509C24—82no—
510C24#12114yes—
511C24C22×D411yescharacteristic
512C24C22×D411yescharacteristic
513C24C22×D411yescharacteristic
514#41—44no—
515#41—44no—
516#41—44no—
517#41—44no—
518C2×Q8—24no—
519C2×Q8—22no—
520C2×Q8—28no—
521C2×Q8—28no—
522C2×Q8—22no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—22no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—22no—
529C2×Q8—21no—
530C2×Q8—22no—
531C2×Q8—21no—
532C2×Q8—42no—
533C2×Q8—42no—
534C2×Q8—44no—
535C2×Q8—44no—
536C2×Q8C22×D414yes—
537C2×D4—22no—
538C2×D4—21no—
539C2×D4—22no—
540C2×D4—21no—
541C2×D4—22no—
542C2×D4—21no—
543C2×D4—22no—
544C2×D4—21no—
545C2×D4—22no—
546C2×D4—21no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4—42no—
550C2×D4—42no—
551C2×D4—42no—
552C2×D4—42no—
553C2×D4—44no—
554C2×D4—44no—
555C2×D4—42no—
556C2×D4—44no—
557C2×D4—48no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—48no—
561C2×D4—42no—
562C2×D4—44no—
563C2×D4—44no—
564C2×D4—44no—
565C2×D4—44no—
566C2×D4—84no—
567C2×D4—84no—
568C2×D4—82no—
569C2×D4—84no—
570C2×D4—816no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—28no—
578C22×C4—28no—
579C22×C4—28no—
580C22×C4—28no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—24no—
590C22×C4—28no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—24no—
594C22×C4—28no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—22no—
600C22×C4—21no—
601C22×C4—44no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—82no—
609C22×C4—82no—
610C22×C4#12114yes—
611C22×C4#12114yes—
612C22×C4#12114yes—
613C22×C4C22×D414yes—
614C22×C4C22×D414yes—
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D412yes—
618C22×C4C22×D412yes—
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D412yes—
621C22×C4C22×D412yes—
622C22×C4C2×#4112yes—
623C22×C4C2×#4112yes—
624C22×C4C2×#4112yes—
625C22×C4C2×#4112yes—
626C22×C4H(5,𝔽2)12yes—
627C22×C42−1+412yes—
628C22×C4C2511yescharacteristic
629Q16—48no—
630SD16—416no—
631SD16—48no—
632M16—28no—
633M16—48no—
634M16—44no—
635C2×C8—28no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—48no—
647C2×C8—48no—
648C2×C8—48no—
649C2×C8—44no—
650C2×C8C22×D414yes—
651C2×C8C22×D414yes—
652C4⋊C4—28no—
653C4⋊C4—28no—
654C4⋊C4—28no—
655C4⋊C4—24no—
656C4⋊C4—24no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—42no—
669C4⋊C4—48no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—84no—
673C4⋊C4—84no—
674C4⋊C4#12118yes—
675C4⋊C4C22×D414yes—
676C22⋊C4—28no—
677C22⋊C4—28no—
678C22⋊C4—24no—
679C22⋊C4—28no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—44no—
686C22⋊C4—44no—
687C22⋊C4—44no—
688C22⋊C4—42no—
689C22⋊C4—42no—
690C22⋊C4—48no—
691C22⋊C4—84no—
692C22⋊C4—84no—
693C22⋊C4—84no—
694C22⋊C4—82no—
695C22⋊C4#12118yes—
696C42—28no—
697C42—22no—
698C42—22no—
699C42—42no—
700C42—42no—
701C42—48no—
702C42—42no—
703C42—84no—
704C42C22×D414yes—
705C42C2×#4114yes—
706C23—22no—
707C23—22no—
708C23—21no—
709C23—21no—
710C23—22no—
711C23—22no—
712C23—21no—
713C23—28no—
714C23—21no—
715C23—28no—
716C23—22no—
717C23—44no—
718C23—48no—
719C23—48no—
720C23—44no—
721C23—42no—
722C23—41no—
723C23—42no—
724C23—42no—
725C23—41no—
726C23—41no—
727C23—42no—
728C23—42no—
729C23—44no—
730C23—84no—
731C23—84no—
732C23—84no—
733C23—164no—
734C23—164no—
735C23C2×#12112yes—
736C23C2×#12112yes—
737C23C2×#12112yes—
738C23C2×#12112yes—
739C23#53712yes—
740C23#57714yes—
741C23C23×D411yescharacteristic
742Q8—24no—
743Q8—24no—
744Q8—48no—
745Q8—42no—
746Q8—42no—
747Q8—41no—
748Q8—41no—
749Q8—41no—
750Q8—41no—
751D4—42no—
752D4—41no—
753D4—42no—
754D4—41no—
755D4—42no—
756D4—41no—
757D4—42no—
758D4—41no—
759D4—84no—
760D4—88no—
761D4—84no—
762D4—84no—
763D4—88no—
764D4—84no—
765D4—168no—
766C2×C4—24no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—28no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—24no—
773C2×C4—28no—
774C2×C4—28no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—416no—
789C2×C4—44no—
790C2×C4—42no—
791C2×C4—48no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—44no—
808C2×C4—84no—
809C2×C4—84no—
810C2×C4—84no—
811C2×C4C2×#12118yes—
812C2×C4C2×#12112yes—
813C2×C4C2×#12112yes—
814C2×C4C2×#12112yes—
815C2×C4C2×#12112yes—
816C2×C4#53712yes—
817C2×C4D4214yes—
818C2×C4#54714yes—
819C2×C4#54814yes—
820C2×C4#55314yes—
821C2×C4C23×D411yescharacteristic
822C2×C4C23×D411yescharacteristic
823C2×C4C22×#4111yescharacteristic
824C2×C4C22×#4111yescharacteristic
825C2×C4C2×H(5,𝔽2)11yescharacteristic
826C2×C4C2×2−1+411yescharacteristic
827C8—24no—
828C8—24no—
829C8—42no—
830C8—42no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—24no—
835C22—24no—
836C22—24no—
837C22—24no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—22no—
842C22—416no—
843C22—42no—
844C22—42no—
845C22—82no—
846C22—81no—
847C22—81no—
848C22—82no—
849C22—82no—
850C22—84no—
851C22—82no—
852C22—84no—
853C22—81no—
854C22—82no—
855C22—168no—
856C22#241614yes—
857C22#304314yescomplemented
858C22C22×#12111yescharacteristic
859C22C22×#12111yescharacteristic
860C22C2×#53711yescharacteristic
861C22C2×#57712yes—
862C22#358412yes—
863C4—28no—
864C4—22no—
865C4—22no—
866C4—44no—
867C4—44no—
868C4—44no—
869C4—82no—
870C4—81no—
871C4—81no—
872C4—82no—
873C4—82no—
874C4—81no—
875C4#241614yes—
876C4C2×D4211yescharacteristic
877C4C2×#54711yescharacteristic
878C4C2×#54811yescharacteristic
879C4C2×#55311yescharacteristic
880C2—24no—
881C2—24no—
882C2—42no—
883C2—161no—
884C2—162no—
885C2C2×#241611yescharacteristic
886C2C2×#304311yescharacteristic
887C2#6042211yescharacteristic
888C2#6045712yes—
889C2#6093512yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#35252C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3056C2semidirect
2. C22×#465C2semidirect
3. C2×#3043C2semidirect
4. C22×#424C2semidirect
6. #34203C2semidirect
7. #24769C2semidirect
8. #24768C2semidirect
9. #24755C2semidirect
10. #24753C2semidirect
11. #23614C2semidirect
12. #23610C2semidirect
13. #23545C2semidirect
14. #23541C2semidirect
15. #21263C2semidirect
16. #21174C2semidirect
17. #20973C2semidirect
18. #20967C2semidirect
19. #20651C2semidirect
31. C2×#470C22semidirect
32. C2×#468C22semidirect
33. C2×#467C22semidirect
37. C2×#465C22semidirect
39. C2×#464C22semidirect
40. C2×#460C22semidirect
48. C2×#424C22semidirect
49. C22×C4⋊C8C22semidirect
70. #2323C22semidirect
76. C4×C22⋊Q8C22semidirect
79. #2067C22semidirect
80. #2066C22semidirect
81. #2065C22semidirect
82. #2065C22semidirect
83. #2056C22semidirect
84. #2055C22semidirect
85. #2055C22semidirect
86. #2055C22semidirect
87. #1983C22semidirect
88. #1982C22semidirect
89. #1949C22semidirect
90. #1948C22semidirect
93. #1893C22semidirect
94. #1893C22semidirect
95. #1892C22semidirect
96. #1892C22semidirect
97. #1805C22semidirect
98. #1803C22semidirect
141. C2×C22⋊Q8D4semidirect
200. #424D4semidirect
478. C4⋊C8C2×D4semidirect
857. C22#3043semidirect

Maximal subgroups

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

subgroupindex
C2×#30562
C22×#4652
C2×#30432
C22×#4242
#352522
#342032
#247692
#247682
#247552
#247532
#236142
#236102
#235452
#235412
#212632
#211742
#209732
#209672
#206512