Finite Group Databasebeta

← #6493659

Subgroups — #6493659

Order 512.

1803 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35273C211yesmaximal, characteristic
2#34188C211yesmaximal, characteristic, complemented
3#33115C214yesmaximal, complemented
4#29935C214yesmaximal, complemented
5#27973C211yesmaximal, characteristic, complemented
6#27972C211yesmaximal, characteristic, complemented
7#27908C211yesmaximal, characteristic, complemented
8#27907C211yesmaximal, characteristic, complemented
9#27892C211yesmaximal, characteristic, complemented
10#27891C211yesmaximal, characteristic, complemented
11#27890C211yesmaximal, characteristic, complemented
12#27889C211yesmaximal, characteristic, complemented
13#27593C214yesmaximal, complemented
14#24017C214yesmaximal, complemented
15#21982C211yesmaximal, characteristic, complemented
16#21981C211yesmaximal, characteristic, complemented
17#21805C211yesmaximal, characteristic, complemented
18#21805C211yesmaximal, characteristic, complemented
19#20718C211yesmaximal, characteristic, complemented
20C2×#537C2212yes—
21C2×#532C2211yescharacteristic
22C2×C4×#41C2211yescharacteristic
23C2×#485C2214yes—
24C2×#482C2214yes—
25C2×#431C2211yescharacteristic
26C2×#431C2211yescharacteristic
27#2857C2211yescharacteristic
28#2857C2211yescharacteristic
29#2856C2211yescharacteristic
30#2856C2211yescharacteristic
31#2620C2212yes—
32#2620C2212yes—
33#2538—21no—
34#2538—21no—
35#2537—21no—
36#2537—21no—
37#2416—21no—
38#2416—21no—
39#2416—21no—
40#2416—21no—
41#2355—21no—
42#2355—21no—
43#2354—21no—
44#2354—21no—
45#2352—21no—
46#2352—21no—
47#2352—21no—
48#2352—21no—
49#2314C2212yes—
50#2314C2212yes—
51#2311C2212yes—
52#2311C2212yes—
53#2285C2211yescharacteristic
54#2285C2211yescharacteristic
55#2285C2211yescharacteristic
56#2285C2211yescharacteristic
57#2285C2211yescharacteristic
58C2×#384C2211yescharacteristic
59C2×#384C2211yescharacteristic
60#2274C2212yes—
61#2097C2214yes—
62#2092C2214yes—
63#2072C2214yes—
64#2071C2214yes—
65#2036C2214yes—
66#2035C2214yes—
67#2034C2214yes—
68#2033C2214yes—
69#1983C2214yes—
70#1983C2214yes—
71#1957C2211yescharacteristic
72#1957C2211yescharacteristic
73#1957C2211yescharacteristic
74#1957C2211yescharacteristic
75#1956C2211yescharacteristic
76#1956C2211yescharacteristic
77#1956C2211yescharacteristic
78#1956C2211yescharacteristic
79#1948C2214yes—
80#1947C2214yes—
81#1928C2214yes—
82#1927C2214yes—
83#1926C2214yes—
84#1925C2214yes—
85#1874C2214yes—
86#1872C2214yes—
87#1853C2214yes—
88#1852C2214yes—
89#1845C2211yescharacteristic
90#1845C2211yescharacteristic
91#1844C2211yescharacteristic
92#1844C2211yescharacteristic
93#1834C2211yescharacteristic
94#1834C2211yescharacteristic
95#1834C2211yescharacteristic
96#1834C2211yescharacteristic
97#1818C2212yes—
98#1798C2212yes—
99#1798C2212yes—
100#1788C2214yes—
101#1788C2214yes—
102#1780C2212yes—
103C4×C22⋊C8C2211yescharacteristic
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2211yescharacteristic
106C4×C22⋊C8C2211yescharacteristic
107C22×#41C2312yes—
108C22×#41C2311yescharacteristic
109#537—48no—
110#532—24no—
111#532—24no—
112C2×C4⋊Q8C2311yescharacteristic
113C2×#127C2311yescharacteristic
114C2×#124C2312yes—
115C2×C22⋊Q8—22no—
116C2×C22⋊Q8C2312yes—
117C2×C22⋊Q8C2312yes—
118C2×#121—22no—
119C2×#121—22no—
120C2×#121—22no—
121C2×#121—21no—
122C2×#121—21no—
123C2×#121—21no—
124C2×#121—21no—
125C2×#121—21no—
126C2×#121—21no—
127C2×#121C2312yes—
128C2×#121C2312yes—
129C4×#41—24no—
130C4×#41—24no—
131C2×C4×Q8D411yescharacteristic
132C2×C4×Q8D411yescharacteristic
133C2×C4×D4—21no—
134C2×C4×D4—21no—
135C2×C4×D4D411yescharacteristic
136C2×C4×D4D411yescharacteristic
137C2×C4×D4D411yescharacteristic
138C2×C4×D4D411yescharacteristic
139C2×C4×D4D411yescharacteristic
140C2×C4×D4D411yescharacteristic
141C2×#117—21no—
142C2×#117—21no—
143C2×#117—21no—
144C2×#117—21no—
145C2×#117C2312yes—
146C2×#117C2311yescharacteristic
147C2×#117C2311yescharacteristic
148C2×#117C2311yescharacteristic
149C22×C4⋊C4—21no—
150C22×C4⋊C4—21no—
151C22×C4⋊C4—21no—
152C22×C4⋊C4—21no—
153C22×C4⋊C4C2312yes—
154C22×C4⋊C4C2312yes—
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158#485—48no—
159#482—48no—
160#431—24no—
161#431—24no—
162C2×#107C2314yes—
163C2×#107C2314yes—
164C2×#106C2314yes—
165C2×#106C2314yes—
166C2×C4⋊C8C2312yes—
167C2×C4⋊C8C2312yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#103C2314yes—
171C2×#103C2314yes—
172C2×#102C2314yes—
173C2×#102C2314yes—
174C2×#102C2314yes—
175C2×#102C2314yes—
176C2×C22⋊C8C2312yes—
177C2×C22⋊C8C2312yes—
178C2×C22⋊C8C2312yes—
179C2×C22⋊C8C2312yes—
180C2×C22⋊C8C2312yes—
181C2×C22⋊C8C2312yes—
182C2×C4×C8C2311yescharacteristic
183C2×C4×C8C2311yescharacteristic
184C2×C4×C8C2311yescharacteristic
185C2×C4×C8C2311yescharacteristic
186#396—22no—
187#396—22no—
188#396—22no—
189#396—22no—
190#394—22no—
191#394—22no—
192#394—22no—
193#394—22no—
194#391—22no—
195#391C2312yes—
196#391C2312yes—
197#390—22no—
198#390—21no—
199#390—21no—
200#390—21no—
201#390—21no—
202#390C2312yes—
203#390C2312yes—
204#389—21no—
205#389—21no—
206#389—21no—
207#389—21no—
208#388—22no—
209#388—22no—
210#388—22no—
211#388—22no—
212#387—22no—
213#387—22no—
214#387—22no—
215#387—22no—
216#386—22no—
217#386—22no—
218#386—22no—
219#386—22no—
220#384—21no—
221#384—21no—
222#384—21no—
223#384—21no—
224#384C2312yes—
225#384C2311yescharacteristic
226#384C2311yescharacteristic
227#384C2311yescharacteristic
228#384C2311yescharacteristic
229#384C2311yescharacteristic
230#384C2311yescharacteristic
231#384C2312yes—
232#382—21no—
233#382—21no—
234#382—21no—
235#382—21no—
236#382C2312yes—
237#380—21no—
238#380—21no—
239#380—21no—
240#380—21no—
241#380—21no—
242#380—21no—
243#380—21no—
244#380—21no—
245#380—21no—
246#380—21no—
247#380—22no—
248#380—22no—
249#380C2312yes—
250#380C2312yes—
251#380C2312yes—
252#380C2312yes—
253C4×C4⋊C4—22no—
254C4×C4⋊C4—22no—
255C4×C4⋊C4—21no—
256C4×C4⋊C4—21no—
257C4×C4⋊C4—21no—
258C4×C4⋊C4—21no—
259C4×C4⋊C4—21no—
260C4×C4⋊C4—21no—
261C4×C4⋊C4C2312yes—
262C4×C4⋊C4C2312yes—
263C4×C4⋊C4C2312yes—
264C4×C4⋊C4C2312yes—
265C4×C22⋊C4—22no—
266C4×C22⋊C4—22no—
267#340C2314yes—
268#340C2314yes—
269#340C2314yes—
270#340C2314yes—
271#336C2312yes—
272#336C2312yes—
273#336C2312yes—
274#336C2312yes—
275C2×#41—22no—
276C2×#41—22no—
277C2×#41—24no—
278C2×#41—24no—
279C2×#41—24no—
280C2×#41—42no—
281C2×#41—44no—
282C2×#41—44no—
283C22×Q8C2×D411yescharacteristic
284C22×Q8C2412yes—
285C22×D4—22no—
286C22×D4—22no—
287C22×D4—22no—
288C22×D4—21no—
289C22×D4—21no—
290C22×D4C2×D411yescharacteristic
291C22×D4C2×D411yescharacteristic
292C22×D4C2×D411yescharacteristic
293C22×D4C2412yes—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—22no—
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2411yescharacteristic
304C23×C4C2411yescharacteristic
305C23×C4C2411yescharacteristic
306C22×C8C2412yes—
307C22×C8C2412yes—
308C22×C8C2412yes—
309C22×C8C2412yes—
310C4⋊Q8—22no—
311C4⋊Q8—22no—
312#127—22no—
313#127—22no—
314#124—24no—
315#124—24no—
316C22⋊Q8—28no—
317C22⋊Q8—44no—
318C22⋊Q8—48no—
319#121—28no—
320#121—44no—
321#121—48no—
322#121—48no—
323#121—48no—
324#121—44no—
325#121—44no—
326#121—82no—
327#121—82no—
328#121—82no—
329#121—82no—
330C4×Q8—24no—
331C4×Q8—24no—
332C4×D4—24no—
333C4×D4—24no—
334C4×D4—24no—
335C4×D4—24no—
336C4×D4—24no—
337C4×D4—24no—
338C4×D4—44no—
339C4×D4—44no—
340#117—22no—
341#117—22no—
342#117—22no—
343#117—22no—
344#117—22no—
345#117—22no—
346#117—28no—
347#117—82no—
348#117—82no—
349#117—82no—
350#117—82no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
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—22no—
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—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—44no—
374C2×C4⋊C4—44no—
375C2×C4⋊C4—82no—
376C2×C4⋊C4—82no—
377C2×C4⋊C4—82no—
378C2×C4⋊C4—82no—
379C2×C4⋊C4C2×D411yescharacteristic
380C2×C4⋊C4C2×D411yescharacteristic
381C2×C4⋊C4C2×D411yescharacteristic
382C2×C4⋊C4C2×D411yescharacteristic
383C2×C4⋊C4C2×D411yescharacteristic
384C2×C4⋊C4C2×D411yescharacteristic
385C2×C4⋊C4C2412yes—
386C2×C4⋊C4C2412yes—
387C2×C4⋊C4C2412yes—
388C2×C4⋊C4C2412yes—
389C2×C4⋊C4C2412yes—
390C2×C4⋊C4C2412yes—
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—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4C2×D411yescharacteristic
407C2×C22⋊C4C2×D411yescharacteristic
408C2×C22⋊C4C2×D411yescharacteristic
409C2×C22⋊C4C2×D411yescharacteristic
410C2×C22⋊C4C2×D411yescharacteristic
411C2×C22⋊C4C2×D411yescharacteristic
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
426C2×C42C2×D411yescharacteristic
427C2×C42#4114yes—
428C2×C42#4114yes—
429C2×C42C2411yescharacteristic
430C2×C42C2411yescharacteristic
431C2×C42C2411yescharacteristic
432C2×C42C2411yescharacteristic
433#107—44no—
434#107—44no—
435#106—44no—
436#106—44no—
437C4⋊C8—24no—
438C4⋊C8—24no—
439#103—44no—
440#103—44no—
441#103—44no—
442#103—44no—
443#102—44no—
444#102—44no—
445#102—44no—
446#102—44no—
447C22⋊C8—24no—
448C22⋊C8—24no—
449C22⋊C8—24no—
450C22⋊C8—24no—
451C22⋊C8—42no—
452C22⋊C8—42no—
453C4×C8—22no—
454C4×C8—22no—
455C4×C8—22no—
456C4×C8—22no—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—22no—
461#95—22no—
462#95—22no—
463#95—22no—
464#95—22no—
465#95—22no—
466#95—22no—
467#95—22no—
468#95—22no—
469#95—22no—
470#95—22no—
471C24—22no—
472C24C22×D411yescharacteristic
473C24C22×D411yescharacteristic
474C24C22×D411yescharacteristic
475#41—48no—
476#41—48no—
477#41—88no—
478#41—88no—
479C2×Q8—22no—
480C2×Q8—22no—
481C2×Q8—22no—
482C2×Q8—22no—
483C2×Q8—24no—
484C2×Q8—24no—
485C2×Q8—41no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—24no—
495C2×D4—24no—
496C2×D4—41no—
497C2×D4—41no—
498C2×D4—41no—
499C2×D4—44no—
500C2×D4—44no—
501C2×D4—44no—
502C2×D4—44no—
503C2×D4—44no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—42no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4—82no—
511C2×D4—82no—
512C2×D4—82no—
513C2×D4—82no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—21no—
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—21no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—82no—
552C22×C4—82no—
553C22×C4—82no—
554C22×C4—82no—
555C22×C4#12314yes—
556C22×C4#12314yes—
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D411yescharacteristic
559C22×C4C22×D411yescharacteristic
560C22×C4C22×D411yescharacteristic
561C22×C4C22×D411yescharacteristic
562C22×C4C22×D411yescharacteristic
563C22×C4C22×D411yescharacteristic
564C22×C4C22×D411yescharacteristic
565C22×C4C22×D411yescharacteristic
566C22×C4C22×D411yescharacteristic
567C22×C4C22×D411yescharacteristic
568C22×C4C2×#4112yes—
569C22×C4C2×#4112yes—
570C22×C4H(5,𝔽2)14yes—
571C22×C4C2511yescharacteristic
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—22no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—24no—
595C4⋊C4—24no—
596C4⋊C4—44no—
597C4⋊C4—44no—
598C4⋊C4—44no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—44no—
602C4⋊C4—42no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—42no—
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—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—44no—
625C22⋊C4—44no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C22⋊C4—44no—
630C22⋊C4—44no—
631C22⋊C4—82no—
632C22⋊C4—82no—
633C22⋊C4—82no—
634C22⋊C4—82no—
635C22⋊C4—82no—
636C22⋊C4—82no—
637C22⋊C4—82no—
638C22⋊C4—82no—
639C42—22no—
640C42—22no—
641C42—22no—
642C42—22no—
643C42—21no—
644C42—21no—
645C42—21no—
646C42—21no—
647C42—44no—
648C42—82no—
649C42—82no—
650C42—82no—
651C42—82no—
652C42#12314yes—
653C42#12314yes—
654C42C2×#4112yes—
655C42C2×#4112yes—
656C42C2×#4112yes—
657C42C2×#4112yes—
658C23—21no—
659C23—21no—
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—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23C2×#12312yes—
685C23#53512yes—
686C23C23×D411yescharacteristic
687Q8—44no—
688Q8—44no—
689Q8—44no—
690D4—44no—
691D4—44no—
692D4—44no—
693D4—44no—
694D4—44no—
695D4—88no—
696D4—84no—
697D4—84no—
698D4—164no—
699D4—164no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—28no—
709C2×C4—28no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—21no—
715C2×C4—21no—
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—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
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—88no—
757C2×C4—164no—
758C2×C4—164no—
759C2×C4C2×#12312yes—
760C2×C4C2×#12312yes—
761C2×C4C2×#12312yes—
762C2×C4C2×#12312yes—
763C2×C4C2×#12312yes—
764C2×C4#53512yes—
765C2×C4#57612yes—
766C2×C4#57712yes—
767C2×C4#57712yes—
768C2×C4#57812yes—
769C2×C4C22×#4111yescharacteristic
770C2×C4C22×#4111yescharacteristic
771C2×C4C2×H(5,𝔽2)12yes—
772C2×C4#58512yes—
773C8—42no—
774C8—42no—
775C8—42no—
776C8—42no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—82no—
799C22—82no—
800C22—82no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22C22×#12311yescharacteristic
806C22C2×#53511yescharacteristic
807C22#344911yescharacteristic
808C22C2×#57611yescharacteristic
809C22C2×#57711yescharacteristic
810C22C2×#57711yescharacteristic
811C22C2×#57811yescharacteristic
812C4—22no—
813C4—22no—
814C4—22no—
815C4—22no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4—41no—
821C4—82no—
822C4—82no—
823C4—82no—
824C4—82no—
825C4—82no—
826C4—82no—
827C4—82no—
828C4#309814yes—
829C4#309914yes—
830C4#349412yes—
831C4#349412yes—
832C2—42no—
833C2—42no—
834C2—81no—
835C2—162no—
836C2#3526211yescharacteristic
837C2C2×#309811yescharacteristic
838C2C2×#309911yescharacteristic
839C2#6082211yescharacteristic
840C2#6082411yescharacteristic
841C2#6100611yescharacteristic
842C2#6100811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#35273C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×#41 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34188C2semidirect
3. #33115C2semidirect
4. #29935C2semidirect
5. #27973C2semidirect
6. #27972C2semidirect
7. #27908C2semidirect
8. #27907C2semidirect
9. #27892C2semidirect
10. #27891C2semidirect
11. #27890C2semidirect
12. #27889C2semidirect
13. #27593C2semidirect
14. #24017C2semidirect
15. #21982C2semidirect
16. #21981C2semidirect
17. #21805C2semidirect
18. #21805C2semidirect
19. #20718C2semidirect

Maximal subgroups

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

subgroupindex
#352732
#341882
#331152
#299352
#279732
#279722
#279082
#279072
#278922
#278912
#278902
#278892
#275932
#240172
#219822
#219812
#218052
#207182