Finite Group Databasebeta

← #6442995

Subgroups — #6442995

Order 512.

2801 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×#3055C211yesmaximal, characteristic
2C22×#465C211yesmaximal, characteristic, complemented
3C2×#3042C211yesmaximal, characteristic, complemented
4C22×#424C211yesmaximal, characteristic, complemented
5#35306C211yesmaximal, characteristic, complemented
6#34204C211yesmaximal, characteristic, complemented
7#24767C214yesmaximal, complemented
8#24766C214yesmaximal, complemented
9#24754C214yesmaximal, complemented
10#24751C214yesmaximal, complemented
11#23615C211yesmaximal, characteristic, complemented
12#23610C211yesmaximal, characteristic, complemented
13#23544C211yesmaximal, characteristic, complemented
14#23541C211yesmaximal, characteristic, complemented
15#21262C211yesmaximal, characteristic, complemented
16#21174C211yesmaximal, characteristic, complemented
17#20972C211yesmaximal, characteristic, complemented
18#20967C211yesmaximal, characteristic, complemented
19#20650C211yesmaximal, characteristic, complemented
20C22×AGL(1,ℤ/8)C2211yescharacteristic
21C23×SD16C2211yescharacteristic
22C23×M16C2211yescharacteristic
23C24×C8C2211yescharacteristic
24C2×#536C2211yescharacteristic
25C2×#525C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×#121C2211yescharacteristic
28C2×#518C2211yescharacteristic
29C22×#117C2211yescharacteristic
30#3055—28no—
31C2×#469C2212yes—
32C2×#468C2212yes—
33C2×#466C2212yes—
34C2×#465—28no—
35C2×#465C2214yes—
36C2×#465C2214yes—
37C2×#465C2212yes—
38#3042—28no—
39C2×#463C2214yescomplemented
40C2×#461C2214yescomplemented
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×#419C2211yescharacteristic
53C2×#418C2211yescharacteristic
54C2×#416C2211yescharacteristic
55C2×#416C2211yescharacteristic
56C22×#103C2211yescharacteristic
57C22×#102C2211yescharacteristic
58#2857C2212yescomplemented
59#2850C2212yescomplemented
60#2621C2212yescomplemented
61#2620C2212yescomplemented
62#2417—22no—
63#2415—22no—
64#2413—22no—
65#2412—22no—
66#2363—22no—
67#2361—22no—
68#2342—22no—
69D4×C22⋊C4—22no—
70#2324C2214yes—
71#2317C2211yescharacteristic
72#2316C2211yescharacteristic
73#2311C2211yescharacteristic
74#2310C2211yescharacteristic
75#2309C2211yescharacteristic
76C4×#121C2214yes—
77#2280C2211yescharacteristic
78#2274C2211yescharacteristic
79#2068C2214yescomplemented
80#2066C2214yescomplemented
81#2066C2214yescomplemented
82#2065C2214yescomplemented
83#2055C2214yescomplemented
84#2055C2214yescomplemented
85#2055C2214yescomplemented
86#2054C2214yescomplemented
87#1983C2214yescomplemented
88#1981C2214yescomplemented
89#1949C2214yescomplemented
90#1948C2214yescomplemented
91#1894C2214yescomplemented
92#1893C2212yescomplemented
93#1893C2212yescomplemented
94#1892C2212yescomplemented
95#1892C2214yescomplemented
96#1892C2212yescomplemented
97#1804C2214yescomplemented
98#1802C2214yescomplemented
99#1736C2211yescharacteristic
100#1736C2211yescharacteristic
101#1735C2211yescharacteristic
102#1735C2211yescharacteristic
103C22×#41C2311yescharacteristic
104C23×Q8C2311yescharacteristic
105C23×D4—21no—
106C23×D4C2311yescharacteristic
107C24×C4C2311yescharacteristic
108C2×AGL(1,ℤ/8)—24no—
109C2×AGL(1,ℤ/8)—24no—
110C2×AGL(1,ℤ/8)—42no—
111C22×SD16—24no—
112C22×SD16—24no—
113C22×SD16—42no—
114C22×SD16C2312yes—
115C22×SD16C2314yes—
116C22×D8C2312yes—
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#536—24no—
132#536—24no—
133C2×C4⋊Q8C2312yes—
134C2×#124C2312yes—
135#525—24no—
136#525—24no—
137C2×#123—21no—
138C2×#123—22no—
139C2×C22⋊Q8—21no—
140C2×C22⋊Q8—21no—
141C2×C22⋊Q8—22no—
142C2×C22⋊Q8—24no—
143C2×C22⋊Q8—24no—
144C2×C22⋊Q8C2312yes—
145C2×C22⋊Q8C2311yescharacteristic
146C2×C22⋊Q8C2312yes—
147C2×C22⋊Q8C2311yescharacteristic
148C2×#121—21no—
149C2×#121—21no—
150C2×#121—24no—
151C2×#121D418yes—
152C2×#121C2311yescharacteristic
153C2×#121C2311yescharacteristic
154C2×#121C2312yes—
155C2×#121C2312yes—
156C2×#120—21no—
157#518—24no—
158#518—24no—
159C2×C4×D4—21no—
160C2×C4×D4—21no—
161C2×C4×D4—24no—
162C2×C4×D4—22no—
163C2×C4×D4C2314yes—
164C2×#117—24no—
165C2×#117—24no—
166C2×#117D412yes—
167C2×#117D412yes—
168C2×#117C2311yescharacteristic
169C2×#117C2311yescharacteristic
170C2×#117C2311yescharacteristic
171C2×#117C2311yescharacteristic
172C2×#117C2312yes—
173C2×#117C2311yescharacteristic
174C22×C4⋊C4—21no—
175C22×C4⋊C4D412yes—
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2311yescharacteristic
178C22×C22⋊C4—21no—
179C22×C22⋊C4—21no—
180C22×C22⋊C4—22no—
181C22×C22⋊C4D412yes—
182C22×C42C2312yes—
183#469—28no—
184#468—28no—
185#466—28no—
186#465—216no—
187#465—216no—
188#465—28no—
189#463—216no—
190#461—216no—
191#428—24no—
192C2×#107C2312yes—
193C2×#106—24no—
194C2×#106C2314yes—
195C2×#106C2312yes—
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#419—42no—
208#418—24no—
209#417—24no—
210#416—24no—
211#416—42no—
212C2×#103—24no—
213C2×#103C2312yes—
214C2×#103C2312yes—
215C2×#103C2314yes—
216C2×#103C2314yes—
217C2×#103C2312yes—
218C2×#103C2314yes—
219C2×#102—24no—
220C2×#102C2314yes—
221C2×#102C2312yes—
222C2×#102C2312yes—
223C2×#102C2312yes—
224C2×#102C2312yes—
225C2×#102C2312yes—
226#398—24no—
227#397—24no—
228#396—24no—
229#394—24no—
230#391—22no—
231#391C2312yes—
232#391C2312yes—
233#391C2312yes—
234#390—22no—
235#390—24no—
236#390C2314yes—
237#390C2312yes—
238#389—22no—
239#389—22no—
240#389—24no—
241#389C2314yes—
242#388—24no—
243#388—24no—
244#388—24no—
245#386—24no—
246#386—24no—
247#386—22no—
248#386—24no—
249#385—24no—
250#385—22no—
251#384C2312yes—
252#382C2312yes—
253#381—21no—
254#381—22no—
255#380—24no—
256#380—22no—
257#380—22no—
258#380C2312yes—
259#380C2312yes—
260#379—21no—
261#379—22no—
262C4×C4⋊C4—22no—
263C4×C4⋊C4C2314yes—
264C4×C22⋊C4—21no—
265C4×C22⋊C4—21no—
266C4×C22⋊C4—22no—
267C4×C22⋊C4—24no—
268#340C2314yes—
269#340C2312yes—
270#340C2312yes—
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×Q8—22no—
289C22×Q8C2412yes—
290C22×Q8C2411yescharacteristic
291C22×D4—22no—
292C22×D4—28no—
293C22×D4—22no—
294C22×D4—21no—
295C22×D4—21no—
296C22×D4—21no—
297C22×D4—22no—
298C22×D4—21no—
299C22×D4—22no—
300C22×D4—22no—
301C22×D4—22no—
302C22×D4—22no—
303C22×D4—84no—
304C22×D4C2×D414yes—
305C22×D4C2411yescharacteristic
306C22×D4C2412yes—
307C23×C4—22no—
308C23×C4—22no—
309C23×C4—22no—
310C23×C4—22no—
311C23×C4—21no—
312C23×C4—21no—
313C23×C4—21no—
314C23×C4—21no—
315C23×C4—24no—
316C23×C4C2×D414yes—
317C23×C4C2×D411yescharacteristic
318C23×C4C2×D411yescharacteristic
319C23×C4C2×D411yescharacteristic
320C23×C4C2×D414yes—
321C23×C4#4114yes—
322C23×C4C2411yescharacteristic
323C23×C4C2411yescharacteristic
324C23×C4C2411yescharacteristic
325AGL(1,ℤ/8)—416no—
326C2×SD16—28no—
327C2×SD16—24no—
328C2×SD16—28no—
329C2×SD16—24no—
330C2×SD16—44no—
331C2×SD16—42no—
332C2×SD16—416no—
333C2×D8—24no—
334C2×D8—24no—
335C2×D8—42no—
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—
366C4⋊Q8—24no—
367C4⋊Q8—24no—
368#124—24no—
369#124—24no—
370#123—44no—
371#123—48no—
372C22⋊Q8—24no—
373C22⋊Q8—24no—
374C22⋊Q8—22no—
375C22⋊Q8—22no—
376C22⋊Q8—24no—
377C22⋊Q8—24no—
378C22⋊Q8—22no—
379C22⋊Q8—22no—
380C22⋊Q8—44no—
381C22⋊Q8—44no—
382C22⋊Q8—48no—
383#121—28no—
384#121—28no—
385#121—24no—
386#121—24no—
387#121—22no—
388#121—22no—
389#121—22no—
390#121—22no—
391#121C2×D418yes—
392#121C2×D418yes—
393#120—44no—
394C4×D4—28no—
395C4×D4—28no—
396C4×D4—44no—
397C4×D4—44no—
398C4×D4—48no—
399C4×D4—88no—
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#117C2×D414yes—
413#117#4114yes—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—28no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—24no—
426C2×C4⋊C4—24no—
427C2×C4⋊C4—44no—
428C2×C4⋊C4C2×D412yes—
429C2×C4⋊C4C2×D414yes—
430C2×C4⋊C4C2×D414yes—
431C2×C4⋊C4C2×D412yes—
432C2×C4⋊C4C2412yes—
433C2×C4⋊C4C2412yes—
434C2×C4⋊C4C2411yescharacteristic
435C2×C4⋊C4C2411yescharacteristic
436C2×C4⋊C4C2412yes—
437C2×C4⋊C4C2412yes—
438C2×C22⋊C4—28no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—28no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—24no—
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⋊C4—48no—
460C2×C22⋊C4C2×D412yes—
461C2×C22⋊C4C2×D414yes—
462C2×C22⋊C4C2×D412yes—
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—24no—
480#103—28no—
481#103—28no—
482#103—24no—
483#103—42no—
484#103—44no—
485#102—28no—
486#102—24no—
487#102—24no—
488#102—24no—
489#102—24no—
490#102—42no—
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—24no—
504C24—21no—
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—22no—
519C2×Q8—21no—
520C2×Q8—22no—
521C2×Q8—21no—
522C2×Q8—22no—
523C2×Q8—21no—
524C2×Q8—22no—
525C2×Q8—21no—
526C2×Q8—22no—
527C2×Q8—21no—
528C2×Q8—22no—
529C2×Q8—21no—
530C2×Q8—42no—
531C2×Q8—42no—
532C2×Q8—42no—
533C2×Q8—44no—
534C2×Q8—44no—
535C2×Q8—44no—
536C2×Q8—44no—
537C2×D4—28no—
538C2×D4—28no—
539C2×D4—24no—
540C2×D4—28no—
541C2×D4—28no—
542C2×D4—22no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—22no—
550C2×D4—21no—
551C2×D4—22no—
552C2×D4—21no—
553C2×D4—48no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—44no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—44no—
563C2×D4—44no—
564C2×D4—82no—
565C2×D4—84no—
566C2×D4—816no—
567C2×D4C22×D414yes—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—28no—
575C22×C4—28no—
576C22×C4—28no—
577C22×C4—28no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—28no—
587C22×C4—22no—
588C22×C4—24no—
589C22×C4—28no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—44no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—48no—
606C22×C4—84no—
607C22×C4—84no—
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
629SD16—416no—
630SD16—48no—
631D8—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—24no—
654C4⋊C4—24no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—22no—
665C4⋊C4—22no—
666C4⋊C4—42no—
667C4⋊C4—44no—
668C4⋊C4—44no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—48no—
672C4⋊C4—84no—
673C4⋊C4—84no—
674C4⋊C4#12118yes—
675C4⋊C4C22×D414yes—
676C22⋊C4—24no—
677C22⋊C4—28no—
678C22⋊C4—28no—
679C22⋊C4—28no—
680C22⋊C4—42no—
681C22⋊C4—44no—
682C22⋊C4—44no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—44no—
688C22⋊C4—48no—
689C22⋊C4—42no—
690C22⋊C4—42no—
691C22⋊C4—48no—
692C22⋊C4—84no—
693C22⋊C4—84no—
694C22⋊C4—84no—
695C22⋊C4—82no—
696C22⋊C4#12118yes—
697C42—28no—
698C42—22no—
699C42—22no—
700C42—42no—
701C42—42no—
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—24no—
718C23—44no—
719C23—48no—
720C23—48no—
721C23—44no—
722C23—42no—
723C23—42no—
724C23—44no—
725C23—48no—
726C23—42no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—42no—
731C23—84no—
732C23—84no—
733C23—164no—
734C23—164no—
735C23C2×#12112yes—
736C23C2×#12112yes—
737C23C2×#12112yes—
738C23C2×#12112yes—
739C23#53712yes—
740C23#57714yes—
741C23C23×D411yescharacteristic
742Q8—42no—
743Q8—41no—
744Q8—42no—
745Q8—41no—
746Q8—42no—
747Q8—41no—
748Q8—42no—
749Q8—41no—
750Q8—84no—
751D4—24no—
752D4—24no—
753D4—416no—
754D4—48no—
755D4—41no—
756D4—41no—
757D4—42no—
758D4—41no—
759D4—42no—
760D4—41no—
761D4—88no—
762D4—84no—
763D4—84no—
764D4—84no—
765C2×C4—24no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—28no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—24no—
772C2×C4—28no—
773C2×C4—28no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—416no—
787C2×C4—44no—
788C2×C4—42no—
789C2×C4—44no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—84no—
807C2×C4—84no—
808C2×C4—84no—
809C2×C4—84no—
810C2×C4—168no—
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—44no—
846C22—44no—
847C22—44no—
848C22—84no—
849C22—84no—
850C22—81no—
851C22—81no—
852C22—82no—
853C22—82no—
854C22—81no—
855C22—168no—
856C22#241614yes—
857C22#304214yescomplemented
858C22C22×#12111yescharacteristic
859C22C22×#12111yescharacteristic
860C22C2×#53711yescharacteristic
861C22C2×#57712yes—
862C22#358412yes—
863C4—28no—
864C4—22no—
865C4—22no—
866C4—44no—
867C4—44no—
868C4—81no—
869C4—82no—
870C4—81no—
871C4—82no—
872C4—82no—
873C4—81no—
874C4—82no—
875C4#241614yes—
876C4C2×D4211yescharacteristic
877C4C2×#54711yescharacteristic
878C4C2×#54811yescharacteristic
879C4C2×#55311yescharacteristic
880C2—24no—
881C2—24no—
882C2—42no—
883C2—84no—
884C2—161no—
885C2C2×#241611yescharacteristic
886C2C2×#304211yescharacteristic
887C2#6042211yescharacteristic
888C2#6045712yes—
889C2#6093512yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#3055C2
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
2. C22×#465C2semidirect
3. C2×#3042C2semidirect
4. C22×#424C2semidirect
5. #35306C2semidirect
6. #34204C2semidirect
7. #24767C2semidirect
8. #24766C2semidirect
9. #24754C2semidirect
10. #24751C2semidirect
11. #23615C2semidirect
12. #23610C2semidirect
13. #23544C2semidirect
14. #23541C2semidirect
15. #21262C2semidirect
16. #21174C2semidirect
17. #20972C2semidirect
18. #20967C2semidirect
19. #20650C2semidirect
39. C2×#463C22semidirect
40. C2×#461C22semidirect
48. C2×#424C22semidirect
49. C22×C4⋊C8C22semidirect
58. #2857C22semidirect
59. #2850C22semidirect
60. #2621C22semidirect
61. #2620C22semidirect
79. #2068C22semidirect
80. #2066C22semidirect
81. #2066C22semidirect
82. #2065C22semidirect
83. #2055C22semidirect
84. #2055C22semidirect
85. #2055C22semidirect
86. #2054C22semidirect
87. #1983C22semidirect
88. #1981C22semidirect
89. #1949C22semidirect
90. #1948C22semidirect
91. #1894C22semidirect
92. #1893C22semidirect
93. #1893C22semidirect
94. #1892C22semidirect
95. #1892C22semidirect
96. #1892C22semidirect
97. #1804C22semidirect
98. #1802C22semidirect
200. #424D4semidirect
478. C4⋊C8C2×D4semidirect
857. C22#3042semidirect

Maximal subgroups

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

subgroupindex
C2×#30552
C22×#4652
C2×#30422
C22×#4242
#353062
#342042
#247672
#247662
#247542
#247512
#236152
#236102
#235442
#235412
#212622
#211742
#209722
#209672
#206502