Finite Group Databasebeta

← #6797060

Subgroups — #6797060

Order 512.

1896 conjugacy classes of subgroups.

The subgroup lattice has 853 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36189C211yesmaximal, characteristic, complemented
2#36121C211yesmaximal, characteristic
3#33286C211yesmaximal, characteristic, complemented
4#31978C214yesmaximal, complemented
5#31680C214yesmaximal, complemented
6#29878C211yesmaximal, characteristic, complemented
7#29842C211yesmaximal, characteristic, complemented
8#29192C211yesmaximal, characteristic, complemented
9#28655C211yesmaximal, characteristic, complemented
10#27973C211yesmaximal, characteristic, complemented
11#27878C211yesmaximal, characteristic, complemented
12#27541C214yesmaximal, complemented
13#27407C214yesmaximal, complemented
14#25855C211yesmaximal, characteristic, complemented
15#25673C211yesmaximal, characteristic, complemented
16#21859C211yesmaximal, characteristic, complemented
17#21803C211yesmaximal, characteristic, complemented
18#21646C211yesmaximal, characteristic, complemented
19#21265C211yesmaximal, characteristic, complemented
20C2×#546—21no—
21C2×#532C2211yescharacteristic
22C22×#127C2211yescharacteristic
23C2×#500C2211yescharacteristic, complemented
24C2×#486C2211yescharacteristic
25C2×#486C2211yescharacteristic
26C2×#431C2211yescharacteristic
27C2×#431C2211yescharacteristic, complemented
28#2859C2211yescharacteristic, complemented
29#2858C2211yescharacteristic
30#2857C2211yescharacteristic
31#2857C2211yescharacteristic
32#2857C2211yescharacteristic, complemented
33#2856C2211yescharacteristic
34#2570—21no—
35#2544—21no—
36#2511—21no—
37#2507C2212yescomplemented
38#2497C2212yes—
39#2487C2212yes—
40#2445—21no—
41#2445C2212yes—
42#2442—21no—
43#2441—21no—
44#2435—21no—
45#2431—21no—
46#2428—21no—
47#2428C2212yes—
48#2423—21no—
49#2417—21no—
50#2408—21no—
51#2408C2212yes—
52#2360—21no—
53#2352—21no—
54#2345C2212yescomplemented
55D4×C22⋊C4—21no—
56D4×C22⋊C4C2212yes—
57C4×C4⋊Q8C2211yescharacteristic, complemented
58C4×#127C2211yescharacteristic
59#2285C2211yescharacteristic
60C2×#384C2211yescharacteristic, complemented
61C42×D4C2211yescharacteristic
62#2087C2214yescomplemented
63#2076C2214yes—
64#2076C2214yes—
65#2071C2214yescomplemented
66#2067C2214yescomplemented
67#2067C2214yescomplemented
68#2067C2214yescomplemented
69#2041C2214yes—
70#2033C2214yescomplemented
71#2033C2214yescomplemented
72#1990C2211yescharacteristic, complemented
73#1990C2211yescharacteristic, complemented
74#1990C2211yescharacteristic, complemented
75#1990C2211yescharacteristic, complemented
76#1982C2214yes—
77#1957C2211yescharacteristic
78#1957C2211yescharacteristic
79#1957C2211yescharacteristic
80#1957C2211yescharacteristic
81#1957C2211yescharacteristic
82#1957C2211yescharacteristic
83#1955C2212yes—
84#1940C2212yescomplemented
85#1936C2214yescomplemented
86#1936C2214yescomplemented
87#1936C2214yescomplemented
88#1925C2214yescomplemented
89#1924C2212yes—
90#1924C2212yescomplemented
91#1921C2214yescomplemented
92#1874C2214yescomplemented
93#1874C2214yescomplemented
94#1862C2214yescomplemented
95#1862C2214yescomplemented
96#1845C2211yescharacteristic, complemented
97#1834C2211yescharacteristic, complemented
98#1834C2211yescharacteristic, complemented
99#1802C2214yescomplemented
100#1786C2214yes—
101#1786C2214yes—
102C4×C4⋊C8C2211yescharacteristic, complemented
103#1762C2214yescomplemented
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2211yescharacteristic, complemented
106C4×#97C2211yescharacteristic, complemented
107C22×#41—21no—
108C23×D4—21no—
109C23×D4—21no—
110C23×D4C2312yes—
111#546—48no—
112#532—24no—
113#532—42no—
114C2×C4⋊Q8C2311yescharacteristic
115C2×C4⋊Q8C2311yescharacteristic
116C2×#127—24no—
117C2×#127—21no—
118C2×#127—21no—
119C2×#127—42no—
120C2×#127C2311yescharacteristic
121C2×#127C2312yes—
122C2×#127C2311yescharacteristic
123C2×#125—21no—
124C2×#124—21no—
125C2×#124—21no—
126C2×#124—21no—
127C2×#123—22no—
128C2×C22⋊Q8—21no—
129C2×C22⋊Q8—21no—
130C2×C22⋊Q8—21no—
131C2×#121—21no—
132C2×#121—21no—
133C2×#121—21no—
134C2×#121—22no—
135C2×#121C2312yes—
136C2×#121C2312yes—
137C2×#120—22no—
138C2×C4×Q8—21no—
139C2×C4×D4—21no—
140C2×C4×D4—21no—
141C2×C4×D4—21no—
142C2×C4×D4D411yescharacteristic
143C2×C4×D4D411yescharacteristic
144C2×C4×D4C2312yes—
145C2×C4×D4C2312yes—
146C2×C4×D4C2311yescharacteristic
147C2×#117—21no—
148C22×C4⋊C4—21no—
149C22×C4⋊C4—21no—
150C22×C4⋊C4C2312yes—
151C22×C22⋊C4—22no—
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154#500—42no—
155#486—24no—
156#486—42no—
157#431—42no—
158#431—42no—
159C2×#107C2314yes—
160C2×#107C2314yes—
161C2×C4⋊C8C2312yes—
162C2×C4⋊C8C2312yes—
163C2×C4⋊C8C2312yes—
164C2×#102C2314yes—
165C2×#102C2314yes—
166C2×#102C2314yes—
167C2×#102C2314yes—
168C2×#102C2314yes—
169C2×#102C2314yes—
170C2×#102C2314yes—
171C2×#102C2314yes—
172C2×C22⋊C8C2312yes—
173C2×C22⋊C8C2312yes—
174C2×C22⋊C8C2312yes—
175C2×C22⋊C8C2312yes—
176C2×#97C2312yes—
177C2×#97C2312yes—
178C2×C4×C8C2311yescharacteristic
179C2×C4×C8C2311yescharacteristic
180C2×C4×C8C2311yescharacteristic
181C2×C4×C8C2311yescharacteristic
182#400—22no—
183#400—22no—
184#399—22no—
185#398—22no—
186#398—22no—
187#396—22no—
188#394—22no—
189#394—22no—
190#394—22no—
191#394—22no—
192#392—22no—
193#392—22no—
194#391—21no—
195#391—21no—
196#391—21no—
197#391—21no—
198#390—21no—
199#390—21no—
200#390—21no—
201#390—21no—
202#390—21no—
203#390—21no—
204#390C2312yes—
205#390C2312yes—
206#390C2312yes—
207#390C2312yes—
208#389—21no—
209#389—21no—
210#389—21no—
211#389—21no—
212#389—21no—
213#389—21no—
214#389—22no—
215#389C2312yes—
216#389C2312yes—
217#389C2312yes—
218#389C2312yes—
219#389C2312yes—
220#389C2312yes—
221#388—22no—
222#387—22no—
223#387—22no—
224#387—22no—
225#387—22no—
226#386—22no—
227#386—22no—
228#386—22no—
229#386—22no—
230#386—22no—
231#385—22no—
232#384—21no—
233#384—21no—
234#384C2311yescharacteristic
235#384C2311yescharacteristic
236#384C2312yes—
237#384C2311yescharacteristic
238#384C2311yescharacteristic
239#382—21no—
240#382—21no—
241#380—21no—
242#380—21no—
243#380—21no—
244#380—21no—
245#380—22no—
246#380C2312yes—
247#380C2312yes—
248#380C2312yes—
249#380C2312yes—
250#379—22no—
251#379—22no—
252C4×C4⋊C4—21no—
253C4×C4⋊C4—21no—
254C4×C4⋊C4D411yescharacteristic
255C4×C4⋊C4D411yescharacteristic
256C4×C4⋊C4C2312yes—
257C4×C4⋊C4C2312yes—
258C4×C4⋊C4C2311yescharacteristic
259C4×C22⋊C4—22no—
260C4×C22⋊C4D411yescharacteristic
261C4×C22⋊C4D411yescharacteristic
262C4×C22⋊C4D411yescharacteristic
263C4×C22⋊C4D411yescharacteristic
264C4×C22⋊C4C2311yescharacteristic
265C4×C22⋊C4C2311yescharacteristic
266C43C2311yescharacteristic
267#340C2314yes—
268#340C2314yes—
269#340C2314yes—
270#340C2314yes—
271#340C2314yes—
272#340C2314yes—
273#336C2312yes—
274#336C2312yes—
275#336C2312yes—
276C25—22no—
277C2×#41—44no—
278C2×#41—44no—
279C2×#41—82no—
280C22×Q8—21no—
281C22×Q8—21no—
282C22×D4—24no—
283C22×D4—22no—
284C22×D4—22no—
285C22×D4—21no—
286C22×D4—21no—
287C22×D4—21no—
288C22×D4—21no—
289C22×D4—22no—
290C22×D4—22no—
291C22×D4—22no—
292C22×D4—42no—
293C22×D4—44no—
294C22×D4—44no—
295C22×D4—44no—
296C22×D4—44no—
297C22×D4—44no—
298C22×D4—44no—
299C22×D4—82no—
300C22×D4—82no—
301C22×D4C2×D411yescharacteristic
302C22×D4C2412yes—
303C22×D4C2412yes—
304C23×C4—22no—
305C23×C4—22no—
306C23×C4—22no—
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D411yescharacteristic
311C23×C4C2411yescharacteristic
312C23×C4C2411yescharacteristic
313C22×C8C2412yes—
314C22×C8C2412yes—
315C22×C8C2412yes—
316C22×C8C2412yes—
317C4⋊Q8—22no—
318C4⋊Q8—22no—
319C4⋊Q8—22no—
320C4⋊Q8—22no—
321#127—24no—
322#127—22no—
323#127—22no—
324#127—22no—
325#127—42no—
326#127—44no—
327#127—44no—
328#127#4114yes—
329#125—82no—
330#124—44no—
331#124—44no—
332#124—82no—
333#123—48no—
334C22⋊Q8—44no—
335C22⋊Q8—44no—
336C22⋊Q8—82no—
337#121—24no—
338#121—48no—
339#121—42no—
340#121—44no—
341#121—44no—
342#121—44no—
343#121—82no—
344#120—48no—
345C4×Q8—82no—
346C4×D4—24no—
347C4×D4—24no—
348C4×D4—24no—
349C4×D4—42no—
350C4×D4—42no—
351C4×D4—44no—
352C4×D4—44no—
353C4×D4—44no—
354C4×D4—82no—
355#117—82no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—44no—
376C2×C4⋊C4—82no—
377C2×C4⋊C4—82no—
378C2×C4⋊C4C2×D411yescharacteristic
379C2×C4⋊C4C2×D411yescharacteristic
380C2×C4⋊C4C2×D411yescharacteristic
381C2×C4⋊C4C2412yes—
382C2×C4⋊C4C2412yes—
383C2×C4⋊C4C2412yes—
384C2×C4⋊C4C2412yes—
385C2×C4⋊C4C2412yes—
386C2×C4⋊C4C2412yes—
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—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—48no—
404C2×C22⋊C4C2×D411yescharacteristic
405C2×C22⋊C4C2×D411yescharacteristic
406C2×C22⋊C4C2×D411yescharacteristic
407C2×C22⋊C4C2×D411yescharacteristic
408C2×C22⋊C4C2×D411yescharacteristic
409C2×C22⋊C4C2×D411yescharacteristic
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
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×C42C2411yescharacteristic
425C2×C42C2411yescharacteristic
426C2×C42C2411yescharacteristic
427C2×C42C2411yescharacteristic
428C2×C42C2411yescharacteristic
429#107—44no—
430#107—44no—
431C4⋊C8—42no—
432C4⋊C8—42no—
433C4⋊C8—42no—
434#102—28no—
435#102—44no—
436#102—44no—
437#102—44no—
438#102—44no—
439#102—44no—
440#102—44no—
441#102—44no—
442C22⋊C8—42no—
443C22⋊C8—42no—
444C22⋊C8—42no—
445C22⋊C8—42no—
446#97—42no—
447#97—42no—
448C4×C8—22no—
449C4×C8—22no—
450C4×C8—22no—
451C4×C8—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—
461#95—22no—
462#95—22no—
463#95—22no—
464#95C2×D411yescharacteristic
465#95C2×D411yescharacteristic
466#95C2×D411yescharacteristic
467#95C2×D411yescharacteristic
468#95C2×D411yescharacteristic
469#95C2×D411yescharacteristic
470C24—22no—
471C24—22no—
472C24—44no—
473C24—44no—
474C24—44no—
475C24—44no—
476C24—82no—
477C24—82no—
478C24—82no—
479C24C22×D411yescharacteristic
480C24C22×D411yescharacteristic
481#41—816no—
482C2×Q8—42no—
483C2×Q8—42no—
484C2×Q8—42no—
485C2×Q8—42no—
486C2×Q8—42no—
487C2×Q8—42no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—24no—
491C2×D4—24no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—24no—
496C2×D4—24no—
497C2×D4—24no—
498C2×D4—24no—
499C2×D4—41no—
500C2×D4—44no—
501C2×D4—44no—
502C2×D4—44no—
503C2×D4—44no—
504C2×D4—44no—
505C2×D4—44no—
506C2×D4—44no—
507C2×D4—44no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—42no—
513C2×D4—44no—
514C2×D4—42no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—42no—
519C2×D4—816no—
520C2×D4—82no—
521C2×D4—82no—
522C2×D4—82no—
523C2×D4—88no—
524C2×D4—88no—
525C2×D4—816no—
526C2×D4—82no—
527C2×D4—82no—
528C2×D4—82no—
529C2×D4C2×#4114yes—
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—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—82no—
559C22×C4—82no—
560C22×C4—82no—
561C22×C4—82no—
562C22×C4—82no—
563C22×C4AGL(1,ℤ/8)14yes—
564C22×C4#13714yes—
565C22×C4C22×D411yescharacteristic
566C22×C4C22×D411yescharacteristic
567C22×C4C22×D411yescharacteristic
568C22×C4C22×D411yescharacteristic
569C22×C4C22×D411yescharacteristic
570C22×C4C22×D411yescharacteristic
571C22×C4C22×D411yescharacteristic
572C22×C4C22×D411yescharacteristic
573C22×C4C22×D411yescharacteristic
574C22×C4C22×D411yescharacteristic
575C22×C4C22×D411yescharacteristic
576C22×C4C22×D411yescharacteristic
577C22×C4C2511yescharacteristic
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—41no—
601C4⋊C4—44no—
602C4⋊C4—44no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—44no—
608C4⋊C4—42no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—82no—
615C4⋊C4—82no—
616C4⋊C4—82no—
617C4⋊C4—82no—
618C4⋊C4—82no—
619C4⋊C4—82no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—41no—
625C22⋊C4—41no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C22⋊C4—44no—
630C22⋊C4—44no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—44no—
634C22⋊C4—82no—
635C22⋊C4—82no—
636C22⋊C4—82no—
637C22⋊C4—82no—
638C22⋊C4—82no—
639C22⋊C4—82no—
640C22⋊C4—82no—
641C22⋊C4—82no—
642C42—22no—
643C42—22no—
644C42—22no—
645C42—22no—
646C42—22no—
647C42—22no—
648C42—22no—
649C42—22no—
650C42—21no—
651C42—21no—
652C42—21no—
653C42—21no—
654C42—22no—
655C42—22no—
656C42—82no—
657C42—82no—
658C42C2×#4112yes—
659C42H(5,𝔽2)12yes—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—24no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—88no—
687C23—88no—
688C23—88no—
689C23—88no—
690C23—164no—
691C23—164no—
692C23—164no—
693C23C2×AGL(1,ℤ/8)12yes—
694C23C2×#13712yes—
695C23C23×D411yescharacteristic
696Q8—84no—
697Q8—84no—
698D4—28no—
699D4—44no—
700D4—44no—
701D4—44no—
702D4—44no—
703D4—48no—
704D4—48no—
705D4—88no—
706D4—88no—
707D4—88no—
708D4—88no—
709D4—84no—
710D4—84no—
711D4—164no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—28no—
717C2×C4—28no—
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—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
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—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—88no—
767C2×C4—164no—
768C2×C4—164no—
769C2×C4#54612yes—
770C2×C4#54612yes—
771C2×C4C2×AGL(1,ℤ/8)12yes—
772C2×C4C2×AGL(1,ℤ/8)12yes—
773C2×C4C2×#13712yes—
774C2×C4C2×#13712yes—
775C2×C4#57612yes—
776C2×C4#57612yes—
777C2×C4C22×#4111yescharacteristic
778C2×C4C2×H(5,𝔽2)11yescharacteristic
779C2×C4#58512yes—
780C2×C4#58512yes—
781C8—42no—
782C8—42no—
783C8—42no—
784C8—42no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—44no—
800C22—44no—
801C22—44no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22—82no—
806C22—82no—
807C22—82no—
808C22—82no—
809C22—82no—
810C22—82no—
811C22—82no—
812C22—82no—
813C22—1616no—
814C22#344911yescharacteristic
815C22C2×#54611yescharacteristic
816C22#350011yescharacteristic
817C22C22×AGL(1,ℤ/8)11yescharacteristic
818C22C22×#13711yescharacteristic
819C22C2×#57611yescharacteristic
820C22C2×#57611yescharacteristic
821C4—22no—
822C4—22no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—82no—
832C4—82no—
833C4—82no—
834C4—82no—
835C4—82no—
836C4—82no—
837C4#331414yes—
838C4#331814yes—
839C4#352112yes—
840C4#355112yes—
841C2—42no—
842C2—42no—
843C2—84no—
844C2—162no—
845C2#3894711yescharacteristic
846C2#6096911yescharacteristic
847C2#6101111yescharacteristic
848C2C2×#331411yescharacteristic
849C2C2×#331811yescharacteristic
850C2#6253511yescharacteristic
851C2#6253711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36121C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36189C2semidirect
3. #33286C2semidirect
4. #31978C2semidirect
5. #31680C2semidirect
6. #29878C2semidirect
7. #29842C2semidirect
8. #29192C2semidirect
9. #28655C2semidirect
10. #27973C2semidirect
11. #27878C2semidirect
12. #27541C2semidirect
13. #27407C2semidirect
14. #25855C2semidirect
15. #25673C2semidirect
16. #21859C2semidirect
17. #21803C2semidirect
18. #21646C2semidirect
19. #21265C2semidirect
23. C2×#500C22semidirect
27. C2×#431C22semidirect
28. #2859C22semidirect
32. #2857C22semidirect
37. #2507C22semidirect
54. #2345C22semidirect
57. C4×C4⋊Q8C22semidirect
60. C2×#384C22semidirect
62. #2087C22semidirect
65. #2071C22semidirect
66. #2067C22semidirect
67. #2067C22semidirect
68. #2067C22semidirect
70. #2033C22semidirect
71. #2033C22semidirect
72. #1990C22semidirect
73. #1990C22semidirect
74. #1990C22semidirect
75. #1990C22semidirect
84. #1940C22semidirect
85. #1936C22semidirect
86. #1936C22semidirect
87. #1936C22semidirect
88. #1925C22semidirect
90. #1924C22semidirect
91. #1921C22semidirect
92. #1874C22semidirect
93. #1874C22semidirect
94. #1862C22semidirect
95. #1862C22semidirect
96. #1845C22semidirect
97. #1834C22semidirect
98. #1834C22semidirect
99. #1802C22semidirect
102. C4×C4⋊C8C22semidirect
103. #1762C22semidirect
105. C4×C22⋊C8C22semidirect
106. C4×#97C22semidirect

Maximal subgroups

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

subgroupindex
#361892
#361212
#332862
#319782
#316802
#298782
#298422
#291922
#286552
#279732
#278782
#275412
#274072
#258552
#256732
#218592
#218032
#216462
#212652