Finite Group Databasebeta

← #6468816

Subgroups — #6468816

Order 512.

2356 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36625C211yesmaximal, characteristic, complemented
2C2×C4×#121C211yesmaximal, characteristic
3#29481C214yesmaximal, complemented
4#29335C211yesmaximal, characteristic, complemented
5#29302C211yesmaximal, characteristic, complemented
6#29157C212yesmaximal, complemented
7#29109C211yesmaximal, characteristic, complemented
8#28571C212yesmaximal, complemented
9#28311C211yesmaximal, characteristic, complemented
10#24552C212yesmaximal, complemented
11#24379C212yesmaximal
12#23761C212yesmaximal, complemented
13#23574C212yesmaximal, complemented
14#21581C212yesmaximal, complemented
15#21528C214yesmaximal, complemented
16#21453C212yesmaximal, complemented
17C2×#1749C211yesmaximal, characteristic, complemented
18C2×#533C2211yescharacteristic, complemented
19C22×#121C2211yescharacteristic
20C22×C4×D4—21no—
21C22×C4×D4C2211yescharacteristic
22C23×C42C2211yescharacteristic
23C2×#484C2212yes—
24C2×#465C2214yes—
25C2×#450C2212yes—
26C2×#440C2214yescomplemented
27C22×C22⋊C8C2212yes—
28C22×#97C2212yescomplemented
29#2857C2211yescharacteristic
30#2857C2211yescharacteristic
31#2857C2211yescharacteristic, complemented
32#2857C2211yescharacteristic, complemented
33#2855—21no—
34#2855C2212yescomplemented
35#2851—21no—
36#2851—21no—
37#2848—21no—
38#2848C2212yes—
39C4×C22⋊Q8—21no—
40C4×C22⋊Q8—21no—
41C4×C22⋊Q8C2212yes—
42C4×C22⋊Q8C2212yescomplemented
43C4×#121—21no—
44C4×#121—21no—
45C4×#121—21no—
46C4×#121—21no—
47C4×#121C2212yes—
48C4×#121C2212yes—
49C4×#121C2212yes—
50C4×#121C2212yes—
51#2296—21no—
52C2×#390C2211yescharacteristic
53C2×#389C2211yescharacteristic
54C2×#388—21no—
55C2×#386—21no—
56#2285C2211yescharacteristic, complemented
57#2280—21no—
58C2×#380C2211yescharacteristic
59C2×C4×C4⋊C4C2211yescharacteristic
60C2×C4×C22⋊C4—21no—
61#2099C2212yescomplemented
62#2093C2212yescomplemented
63#2084C2212yescomplemented
64#2076C2214yescomplemented
65#2071C2212yescomplemented
66#2057C2212yescomplemented
67#2043C2212yescomplemented
68#2036C2214yescomplemented
69#2034C2214yes—
70#2023C2212yescomplemented
71#2013C2212yescomplemented
72#2000C2214yes—
73#1973C2214yescomplemented
74#1944C2214yescomplemented
75#1936C2214yescomplemented
76#1935C2214yescomplemented
77#1927C2214yescomplemented
78#1918C2214yescomplemented
79#1893C2214yes—
80#1892C2214yescomplemented
81#1877C2214yescomplemented
82#1872C2212yes—
83#1872C2212yes—
84#1862C2214yescomplemented
85#1853C2212yes—
86#1852C2212yes—
87#1824C2212yes—
88#1808C2214yescomplemented
89#1786C2212yes—
90#1776C2214yescomplemented
91#1763C2214yescomplemented
92#1762C2214yescomplemented
93#1749C2212yes—
94#1749C2211yescharacteristic
95#1749C2211yescharacteristic
96#1749C2212yescomplemented
97#1749C2212yescomplemented
98C2×#336C2212yescomplemented
99C23×D4—21no—
100C23×D4C2311yescharacteristic
101C24×C4—21no—
102C24×C4D411yescharacteristic
103C24×C4D411yescharacteristic
104C24×C4C2311yescharacteristic
105C22×SD16C2314yes—
106C23×C8C2314yes—
107#533—44no—
108C2×C4⋊Q8C2311yescharacteristic
109C2×C4⋊Q8C2311yescharacteristic
110C2×#125—21no—
111C2×C22⋊Q8—21no—
112C2×C22⋊Q8—21no—
113C2×C22⋊Q8—21no—
114C2×C22⋊Q8C2312yes—
115C2×C22⋊Q8C2312yes—
116C2×C22⋊Q8C2312yes—
117C2×#121—21no—
118C2×#121—21no—
119C2×#121—28no—
120C2×#121C2312yes—
121C2×#121C2312yes—
122C2×C4×Q8—21no—
123C2×C4×Q8C2312yes—
124C2×C4×D4—22no—
125C2×C4×D4—22no—
126C2×C4×D4—22no—
127C2×C4×D4—22no—
128C2×C4×D4—21no—
129C2×C4×D4—21no—
130C2×C4×D4—44no—
131C2×C4×D4—48no—
132C2×C4×D4C2312yes—
133C2×C4×D4C2312yes—
134C2×#117—21no—
135C2×#117—21no—
136C22×C4⋊C4—21no—
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C22⋊C4—21no—
141C22×C22⋊C4—21no—
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C22⋊C4—21no—
145C22×C42—21no—
146C22×C42—44no—
147C22×C42D411yescharacteristic
148C22×C42D411yescharacteristic
149C22×C42D411yescharacteristic
150C22×C42D411yescharacteristic
151C22×C42D411yescharacteristic
152C22×C42D411yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159#484—28no—
160#465—216no—
161#450—28no—
162#440—48no—
163C2×#107C2314yes—
164C2×#107C2314yes—
165C2×#106C2314yes—
166C2×#103C2314yes—
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×#102C2314yes—
170C2×#102C2314yes—
171C2×#102C2314yes—
172C2×C22⋊C8—28no—
173C2×C22⋊C8C2314yes—
174C2×C22⋊C8C2312yes—
175C2×C22⋊C8C2312yes—
176C2×#97—44no—
177C2×#97C2314yes—
178C2×#97C2312yes—
179C2×#97C2312yes—
180#391—21no—
181#391—21no—
182#391C2312yes—
183#391C2312yes—
184#390—21no—
185#390—21no—
186#390C2312yes—
187#390C2312yes—
188#389—21no—
189#389—21no—
190#389—21no—
191#389—21no—
192#389—21no—
193#389—21no—
194#389—21no—
195#389—21no—
196#389C2312yes—
197#389C2312yes—
198#389C2312yes—
199#389C2312yes—
200#388—22no—
201#388—22no—
202#388—22no—
203#388—22no—
204#387—22no—
205#387—22no—
206#387—22no—
207#387—22no—
208#386—22no—
209#386—22no—
210#386—22no—
211#386—22no—
212#385—22no—
213#385—22no—
214#385—22no—
215#385—22no—
216#385—22no—
217#385—22no—
218#384C2311yescharacteristic
219#384C2311yescharacteristic
220#382—21no—
221#381—22no—
222#380—21no—
223#380—21no—
224#380—21no—
225#380—21no—
226#380—21no—
227#380—21no—
228#380—21no—
229#380—21no—
230#380—21no—
231#380C2312yes—
232#380C2312yes—
233#380C2312yes—
234#380C2312yes—
235#380C2312yes—
236#379—22no—
237C4×C4⋊C4—21no—
238C4×C4⋊C4—21no—
239C4×C4⋊C4—21no—
240C4×C4⋊C4—22no—
241C4×C4⋊C4—22no—
242C4×C4⋊C4C2312yes—
243C4×C4⋊C4C2312yes—
244C4×C4⋊C4C2312yes—
245C4×C22⋊C4—22no—
246C4×C22⋊C4—22no—
247C4×C22⋊C4—22no—
248C4×C22⋊C4—22no—
249C4×C22⋊C4—22no—
250C4×C22⋊C4—22no—
251C2×#95—21no—
252C2×#95—21no—
253C2×#95—21no—
254#340C2314yes—
255#340C2314yes—
256#340C2314yes—
257#340C2314yes—
258#340C2314yes—
259#340C2314yes—
260#336C2312yes—
261#336C2312yes—
262#336C2314yes—
263C25—21no—
264C25C2×D411yescharacteristic
265C22×Q8—21no—
266C22×Q8C2412yes—
267C22×D4—28no—
268C22×D4—22no—
269C22×D4—22no—
270C22×D4—24no—
271C22×D4—21no—
272C22×D4—24no—
273C22×D4—42no—
274C22×D4—44no—
275C22×D4—44no—
276C22×D4C2412yes—
277C23×C4—24no—
278C23×C4—21no—
279C23×C4—24no—
280C23×C4—24no—
281C23×C4—24no—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—42no—
287C23×C4—42no—
288C23×C4—42no—
289C23×C4—42no—
290C23×C4—42no—
291C23×C4—44no—
292C23×C4—44no—
293C23×C4—44no—
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2411yescharacteristic
310C23×C4C2411yescharacteristic
311C23×C4C2411yescharacteristic
312C2×SD16—28no—
313C2×SD16—28no—
314C2×SD16—44no—
315C22×C8—28no—
316C22×C8—28no—
317C22×C8—44no—
318C22×C8C2414yes—
319C22×C8C2414yes—
320C4⋊Q8—42no—
321C4⋊Q8—42no—
322#125—44no—
323C22⋊Q8—24no—
324C22⋊Q8—28no—
325C22⋊Q8—24no—
326C22⋊Q8—44no—
327C22⋊Q8—44no—
328C22⋊Q8—44no—
329C22⋊Q8—44no—
330#121—28no—
331#121—28no—
332#121—24no—
333#121—24no—
334#121—24no—
335#121#4118yes—
336C4×Q8—28no—
337C4×Q8—44no—
338C4×D4—28no—
339C4×D4—44no—
340C4×D4—44no—
341C4×D4—44no—
342C4×D4—48no—
343C4×D4—48no—
344C4×D4—48no—
345C4×D4—48no—
346#117—44no—
347#117—44no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—42no—
369C2×C4⋊C4—44no—
370C2×C4⋊C4C2412yes—
371C2×C4⋊C4C2412yes—
372C2×C4⋊C4C2412yes—
373C2×C4⋊C4C2412yes—
374C2×C4⋊C4C2412yes—
375C2×C4⋊C4C2412yes—
376C2×C22⋊C4—28no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4—44no—
396C2×C22⋊C4—44no—
397C2×C42—24no—
398C2×C42—24no—
399C2×C42—24no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—42no—
405C2×C42—42no—
406C2×C42—42no—
407C2×C42—42no—
408C2×C42—42no—
409C2×C42—42no—
410C2×C42—42no—
411C2×C42—42no—
412C2×C42—42no—
413C2×C42—44no—
414C2×C42C2×D411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D411yescharacteristic
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
426C2×C42C2411yescharacteristic
427C2×C42C2411yescharacteristic
428C2×C42C2411yescharacteristic
429C2×C42C2411yescharacteristic
430#107—28no—
431#107—44no—
432#106—28no—
433#103—28no—
434#103—28no—
435#103—44no—
436#102—28no—
437#102—28no—
438#102—44no—
439C22⋊C8—24no—
440C22⋊C8—28no—
441C22⋊C8#4118yes—
442#97—28no—
443#97—42no—
444#97—42no—
445#95—22no—
446#95—22no—
447#95—22no—
448#95—22no—
449#95—22no—
450#95—22no—
451#95—22no—
452#95—22no—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—24no—
466C24—22no—
467C24—41no—
468C24—41no—
469C24—42no—
470C24—42no—
471C24—42no—
472C24—42no—
473C24—42no—
474C24—42no—
475C24#13714yes—
476C24C22×D411yescharacteristic
477C24C22×D411yescharacteristic
478C24C22×D411yescharacteristic
479C2×Q8—22no—
480C2×Q8—24no—
481C2×Q8—22no—
482C2×Q8—24no—
483C2×Q8—42no—
484C2×Q8—42no—
485C2×Q8—42no—
486C2×D4—24no—
487C2×D4—28no—
488C2×D4—28no—
489C2×D4—24no—
490C2×D4—22no—
491C2×D4—24no—
492C2×D4—416no—
493C2×D4—42no—
494C2×D4—44no—
495C2×D4—432no—
496C2×D4—44no—
497C2×D4—44no—
498C2×D4—44no—
499C2×D4—42no—
500C2×D4C2×#4114yes—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—416no—
561C22×C4—416no—
562C22×C4—416no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—44no—
576C22×C4—44no—
577C22×C4—816no—
578C22×C4AGL(1,ℤ/8)14yes—
579C22×C4C22×D411yescharacteristic
580C22×C4C22×D411yescharacteristic
581C22×C4C22×D411yescharacteristic
582C22×C4C22×D411yescharacteristic
583C22×C4C22×D411yescharacteristic
584C22×C4C22×D411yescharacteristic
585C22×C4C22×D411yescharacteristic
586C22×C4C22×D411yescharacteristic
587C22×C4C22×D411yescharacteristic
588C22×C4C22×D411yescharacteristic
589C22×C4C22×D411yescharacteristic
590C22×C4C2×#4114yes—
591C22×C4C2×#4114yes—
592C22×C4C2511yescharacteristic
593SD16—416no—
594C2×C8—24no—
595C2×C8—24no—
596C2×C8—24no—
597C2×C8—24no—
598C2×C8—24no—
599C2×C8—416no—
600C2×C8C2×#4118yes—
601C4⋊C4—24no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—22no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—42no—
610C4⋊C4—44no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—44no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—44no—
617C4⋊C4—44no—
618C4⋊C4—42no—
619C4⋊C4—44no—
620C4⋊C4—44no—
621C4⋊C4—44no—
622C4⋊C4—42no—
623C4⋊C4—44no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4C2×#4114yes—
627C22⋊C4—28no—
628C22⋊C4—28no—
629C22⋊C4—44no—
630C22⋊C4—44no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—44no—
634C22⋊C4—44no—
635C22⋊C4—44no—
636C22⋊C4—44no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4—44no—
641C22⋊C4—44no—
642C22⋊C4—44no—
643C42—22no—
644C42—22no—
645C42—22no—
646C42—22no—
647C42—22no—
648C42—22no—
649C42—22no—
650C42—22no—
651C42—22no—
652C42—41no—
653C42—41no—
654C42—41no—
655C42—41no—
656C42—41no—
657C42—41no—
658C42—44no—
659C42—44no—
660C42—44no—
661C42—44no—
662C42H(5,𝔽2)14yes—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—28no—
672C23—21no—
673C23—28no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—24no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23—44no—
685C23—48no—
686C23—48no—
687C23—48no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—84no—
695C23—84no—
696C23—84no—
697C23—84no—
698C23#52512yes—
699C23#53212yes—
700C23C2×AGL(1,ℤ/8)12yes—
701C23C2×#13712yes—
702C23C2×#13712yes—
703C23C2×#13712yes—
704C23#57512yes—
705C23C23×D411yescharacteristic
706Q8—44no—
707Q8—44no—
708Q8—84no—
709D4—28no—
710D4—48no—
711D4—416no—
712D4—416no—
713D4—44no—
714C2×C4—28no—
715C2×C4—28no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—28no—
731C2×C4—28no—
732C2×C4—21no—
733C2×C4—24no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—48no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—44no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—88no—
781C2×C4—88no—
782C2×C4—84no—
783C2×C4—84no—
784C2×C4#52512yes—
785C2×C4#53212yes—
786C2×C4#53412yes—
787C2×C4#53412yes—
788C2×C4C2×AGL(1,ℤ/8)12yes—
789C2×C4C2×AGL(1,ℤ/8)12yes—
790C2×C4#57512yes—
791C2×C4C22×#4112yes—
792C2×C4C22×#4112yes—
793C2×C4C2×H(5,𝔽2)12yes—
794C8—28no—
795C8—44no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—416no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—44no—
817C22—44no—
818C22—44no—
819C22—816no—
820C22—82no—
821C22—82no—
822C22—82no—
823C22—82no—
824C22#311014yes—
825C22#318114yes—
826C22C2×#52511yescharacteristic
827C22C2×#53211yescharacteristic
828C22C2×#53411yescharacteristic
829C22C22×AGL(1,ℤ/8)11yescharacteristic
830C22C22×#13711yescharacteristic
831C22C2×#57511yescharacteristic
832C22C2×#57511yescharacteristic
833C4—22no—
834C4—22no—
835C4—22no—
836C4—22no—
837C4—22no—
838C4—22no—
839C4—22no—
840C4—41no—
841C4—41no—
842C4—41no—
843C4—44no—
844C4—41no—
845C4—82no—
846C4—82no—
847C4—82no—
848C4—82no—
849C4—82no—
850C4—82no—
851C4#348114yes—
852C2—24no—
853C2—24no—
854C2—42no—
855C2—84no—
856C2#3495711yescharacteristic
857C2C2×#311011yescharacteristic
858C2#6054611yescharacteristic
859C2C2×#318111yescharacteristic
860C2#6070011yescharacteristic
861C2#6075011yescharacteristic
862C2#6075111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36625C2semidirect
3. #29481C2semidirect
4. #29335C2semidirect
5. #29302C2semidirect
6. #29157C2semidirect
7. #29109C2semidirect
8. #28571C2semidirect
9. #28311C2semidirect
10. #24552C2semidirect
12. #23761C2semidirect
13. #23574C2semidirect
14. #21581C2semidirect
15. #21528C2semidirect
16. #21453C2semidirect
17. C2×#1749C2semidirect
18. C2×#533C22semidirect
26. C2×#440C22semidirect
28. C22×#97C22semidirect
31. #2857C22semidirect
32. #2857C22semidirect
34. #2855C22semidirect
42. C4×C22⋊Q8C22semidirect
56. #2285C22semidirect
61. #2099C22semidirect
62. #2093C22semidirect
63. #2084C22semidirect
64. #2076C22semidirect
65. #2071C22semidirect
66. #2057C22semidirect
67. #2043C22semidirect
68. #2036C22semidirect
70. #2023C22semidirect
71. #2013C22semidirect
73. #1973C22semidirect
74. #1944C22semidirect
75. #1936C22semidirect
76. #1935C22semidirect
77. #1927C22semidirect
78. #1918C22semidirect
80. #1892C22semidirect
81. #1877C22semidirect
84. #1862C22semidirect
88. #1808C22semidirect
90. #1776C22semidirect
91. #1763C22semidirect
92. #1762C22semidirect
96. #1749C22semidirect
97. #1749C22semidirect
98. C2×#336C22semidirect

Maximal subgroups

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

subgroupindex
#366252
C2×C4×#1212
#294812
#293352
#293022
#291572
#291092
#285712
#283112
#245522
#243792
#237612
#235742
#215812
#215282
#214532
C2×#17492