Finite Group Databasebeta

← #6503278

Subgroups — #6503278

Order 512.

1790 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37269C211yesmaximal, characteristic
2#34361C211yesmaximal, characteristic, complemented
3#27874C212yesmaximal, complemented
4#27871C212yesmaximal, complemented
5#26229C212yesmaximal, complemented
6#26228C212yesmaximal, complemented
7#26141C212yesmaximal, complemented
8#26140C212yesmaximal, complemented
9#24959C212yesmaximal, complemented
10#24942C212yesmaximal, complemented
11#24886C212yesmaximal, complemented
12#24869C212yesmaximal, complemented
13#24560C212yesmaximal, complemented
14#24555C212yesmaximal, complemented
15#21946C211yesmaximal, characteristic, complemented
16#21770C211yesmaximal, characteristic, complemented
17#20975C211yesmaximal, characteristic, complemented
18#20899C211yesmaximal, characteristic, complemented
19#20663C211yesmaximal, characteristic, complemented
20C22×#131C2211yescharacteristic
21C2×#535C2211yescharacteristic
22C2×#525C2211yescharacteristic
23C2×#482C2212yes—
24C2×#482C2212yes—
25C2×#427C2211yescharacteristic, complemented
26C22×#107C2211yescharacteristic, complemented
27C2×#418C2211yescharacteristic, complemented
28C22×#102C2211yescharacteristic, complemented
29C2×#408C2211yescharacteristic
30C2×#407C2211yescharacteristic, complemented
31C22×C22⋊C8C2211yescharacteristic, complemented
32#2847C2212yes—
33#2730—22no—
34#2709—21no—
35#2697—21no—
36#2679—21no—
37#2669—21no—
38#2668—22no—
39#2624C2212yes—
40#2485C2212yes—
41#2416C2212yes—
42#2414C2212yes—
43#2408C2212yes—
44#2375—21no—
45#2375—21no—
46#2374—21no—
47#2374—21no—
48#2354C2212yes—
49#2354C2212yescomplemented
50#2352C2212yes—
51#2352C2212yescomplemented
52#2333—22no—
53#2332—22no—
54#2314C2212yescomplemented
55#2311C2211yescharacteristic
56#2311C2211yescharacteristic
57#2311C2211yescharacteristic
58#2280C2212yescomplemented
59#2101C2212yescomplemented
60#2099C2212yescomplemented
61#2094C2212yescomplemented
62#2092C2212yescomplemented
63#2085C2212yescomplemented
64#2083C2212yescomplemented
65#2077C2212yescomplemented
66#2077C2212yescomplemented
67#2076C2212yescomplemented
68#2075C2212yescomplemented
69#2073C2212yescomplemented
70#2071C2212yescomplemented
71#2034C2212yes—
72#2034C2212yes—
73#2033C2212yes—
74#2033C2212yes—
75#1926C2212yescomplemented
76#1925C2212yescomplemented
77#1925C2212yescomplemented
78#1925C2212yescomplemented
79#1921C2212yescomplemented
80#1920C2212yescomplemented
81#1919C2212yescomplemented
82#1919C2212yescomplemented
83#1895C2212yes—
84#1895C2212yes—
85#1895C2212yescomplemented
86#1893C2212yes—
87#1893C2212yes—
88#1893C2212yescomplemented
89#1875C2212yes—
90#1875C2212yes—
91#1875C2212yescomplemented
92#1874C2212yescomplemented
93#1870C2212yes—
94#1870C2212yescomplemented
95#1869C2212yes—
96#1869C2212yescomplemented
97#1854C2212yescomplemented
98#1854C2212yescomplemented
99#1854C2212yescomplemented
100#1854C2212yescomplemented
101#1853C2212yescomplemented
102#1853C2212yescomplemented
103#1825C2212yescomplemented
104#1825C2212yescomplemented
105#1825C2212yescomplemented
106#1809C2212yescomplemented
107#1809C2212yescomplemented
108#1809C2212yescomplemented
109#1808C2212yescomplemented
110#1808C2212yescomplemented
111#1807C2212yescomplemented
112#1786C2212yescomplemented
113#1736C2211yescharacteristic, complemented
114#1736C2211yescharacteristic, complemented
115#1736C2211yescharacteristic, complemented
116#1735C2211yescharacteristic, complemented
117#1729C2211yescharacteristic, complemented
118#1729C2211yescharacteristic, complemented
119C22×#41C2311yescharacteristic
120C23×D4C2311yescharacteristic
121C24×C4C2311yescharacteristic
122C2×#131—24no—
123C2×#131—42no—
124C2×#131—42no—
125C22×M16C2311yescharacteristic
126C22×M16C2311yescharacteristic
127C22×M16C2311yescharacteristic
128C22×M16C2311yescharacteristic
129C23×C8C2311yescharacteristic
130C23×C8C2311yescharacteristic
131C23×C8C2311yescharacteristic
132C23×C8C2311yescharacteristic
133#535—24no—
134#535—24no—
135C2×#127—21no—
136C2×#124—21no—
137#525—24no—
138#525—24no—
139C2×#123D411yescharacteristic
140C2×#123D411yescharacteristic
141C2×C22⋊Q8D412yes—
142C2×#121—22no—
143C2×#121D412yes—
144C2×#121C2312yes—
145C2×#121C2312yes—
146C2×#121C2312yes—
147C2×#121C2312yes—
148C2×#120—21no—
149C2×#120—21no—
150C2×#120—22no—
151C2×#120—22no—
152C2×#120D411yescharacteristic
153C2×#120D411yescharacteristic
154C2×C4×D4C2312yes—
155C2×C4×D4C2312yes—
156C2×#117C2311yescharacteristic
157C2×#117C2311yescharacteristic
158C2×#117C2311yescharacteristic
159C2×#117C2311yescharacteristic
160C2×#117C2312yes—
161C2×#117C2312yes—
162C2×#117C2311yescharacteristic
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166#482—44no—
167#482—44no—
168#427—42no—
169C2×#107—42no—
170C2×#107C2312yes—
171C2×#107C2312yes—
172C2×#107C2312yes—
173C2×#107C2312yes—
174C2×#106C2312yes—
175C2×#106C2312yes—
176C2×#106C2312yes—
177C2×#106C2312yes—
178#418—42no—
179C2×#102—42no—
180C2×#102C2312yes—
181C2×#102C2312yes—
182C2×#102C2312yes—
183C2×#102C2312yes—
184C2×#102C2312yes—
185C2×#102C2312yes—
186C2×#102C2312yes—
187C2×#102C2312yes—
188#408—24no—
189#407—42no—
190C2×C22⋊C8—42no—
191C2×C22⋊C8C2312yes—
192C2×C22⋊C8C2312yes—
193C2×C22⋊C8C2312yes—
194C2×C22⋊C8C2312yes—
195C2×C22⋊C8C2312yes—
196C2×C22⋊C8C2312yes—
197#399—22no—
198#397—22no—
199#397—22no—
200#396—22no—
201#394—22no—
202#394—22no—
203#394—22no—
204#394—22no—
205#394—22no—
206#394—22no—
207#392—22no—
208#392—22no—
209#391—21no—
210#391—21no—
211#391—21no—
212#390—21no—
213#390—21no—
214#390—21no—
215#390—22no—
216#390—22no—
217#390—22no—
218#390C2312yes—
219#390C2312yes—
220#389C2312yes—
221#389C2312yes—
222#388—22no—
223#388—22no—
224#388—22no—
225#388—22no—
226#388—22no—
227#388—22no—
228#388—22no—
229#388—22no—
230#388—22no—
231#388—22no—
232#387—22no—
233#387—22no—
234#387—22no—
235#387—22no—
236#387—22no—
237#386—21no—
238#386—21no—
239#386—21no—
240#386—21no—
241#386—21no—
242#386—21no—
243#386—22no—
244#386—22no—
245#386—22no—
246#386—22no—
247#386—22no—
248#386—22no—
249#384C2312yes—
250#382C2312yes—
251#381—22no—
252#380C2312yes—
253#380C2312yes—
254#380C2312yes—
255#380C2312yes—
256#380C2312yes—
257#380C2312yes—
258#380C2312yes—
259#380C2312yes—
260#380C2312yes—
261#380C2312yes—
262#379—22no—
263#379—22no—
264C4×C4⋊C4—22no—
265C4×C4⋊C4—22no—
266C4×C4⋊C4C2312yes—
267C4×C4⋊C4C2312yes—
268C4×C22⋊C4—22no—
269C4×C22⋊C4—22no—
270C4×C22⋊C4—22no—
271C4×C22⋊C4—22no—
272#340C2312yes—
273#340C2312yes—
274#340C2312yes—
275#340C2312yes—
276#340C2312yes—
277#340C2312yes—
278#340C2312yes—
279#340C2312yes—
280#340C2312yes—
281#340C2312yes—
282#340C2312yes—
283#340C2312yes—
284#340C2312yes—
285#340C2312yes—
286#340C2312yes—
287#340C2312yes—
288#336C2312yes—
289#336C2312yes—
290#336C2312yes—
291#336C2312yes—
292C25—21no—
293C25C2×D411yescharacteristic
294C2×#41—41no—
295C2×#41—41no—
296C2×#41—41no—
297C2×#41—41no—
298C2×#41#4114yes—
299C2×#41#4114yes—
300C22×Q8C2×D411yescharacteristic
301C22×D4—22no—
302C22×D4—22no—
303C22×D4—22no—
304C22×D4—22no—
305C22×D4—21no—
306C22×D4—22no—
307C22×D4—22no—
308C22×D4—41no—
309C22×D4—41no—
310C22×D4—41no—
311C22×D4—41no—
312C22×D4C2×D412yes—
313C22×D4C2×D412yes—
314C22×D4C2×D411yescharacteristic
315C22×D4C2×D411yescharacteristic
316C22×D4C2×D411yescharacteristic
317C22×D4C2412yes—
318C23×C4—22no—
319C23×C4—22no—
320C23×C4—21no—
321C23×C4—21no—
322C23×C4—21no—
323C23×C4—41no—
324C23×C4—41no—
325C23×C4—41no—
326C23×C4—41no—
327C23×C4C2×D412yes—
328C23×C4C2×D411yescharacteristic
329C23×C4C2412yes—
330C23×C4C2411yescharacteristic
331C23×C4C2411yescharacteristic
332C23×C4C2411yescharacteristic
333#131—416no—
334C2×M16—22no—
335C2×M16—22no—
336C2×M16—22no—
337C2×M16—22no—
338C2×M16—22no—
339C2×M16—22no—
340C2×M16—41no—
341C2×M16—41no—
342C2×M16—41no—
343C2×M16—41no—
344C2×M16—41no—
345C2×M16—41no—
346C22×C8—22no—
347C22×C8—22no—
348C22×C8—22no—
349C22×C8—22no—
350C22×C8—22no—
351C22×C8—22no—
352C22×C8—22no—
353C22×C8—22no—
354C22×C8—41no—
355C22×C8—41no—
356C22×C8—41no—
357C22×C8—41no—
358C22×C8C2411yescharacteristic
359C22×C8C2411yescharacteristic
360C22×C8C2412yes—
361C22×C8C2412yes—
362C22×C8C2411yescharacteristic
363C22×C8C2411yescharacteristic
364#127—44no—
365#124—44no—
366#123—24no—
367#123—24no—
368C22⋊Q8—28no—
369#121—28no—
370#121—24no—
371#121—24no—
372#121—24no—
373#121—24no—
374#121—42no—
375#121—42no—
376#121—42no—
377#121—42no—
378#121—84no—
379#120—24no—
380#120—24no—
381#120—44no—
382#120—44no—
383#120—84no—
384#120—84no—
385C4×D4—24no—
386C4×D4—24no—
387C4×D4—24no—
388C4×D4—24no—
389#117—22no—
390#117—22no—
391#117—22no—
392#117—22no—
393#117—42no—
394#117—41no—
395#117—42no—
396#117—41no—
397#117—41no—
398#117—41no—
399#117—41no—
400#117—41no—
401#117—42no—
402#117—42no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—41no—
411C2×C4⋊C4—41no—
412C2×C4⋊C4—41no—
413C2×C4⋊C4—41no—
414C2×C4⋊C4—41no—
415C2×C4⋊C4—41no—
416C2×C4⋊C4C2×D412yes—
417C2×C4⋊C4C2×D412yes—
418C2×C4⋊C4C2×D412yes—
419C2×C4⋊C4C2412yes—
420C2×C4⋊C4C2412yes—
421C2×C4⋊C4C2412yes—
422C2×C4⋊C4C2412yes—
423C2×C4⋊C4C2412yes—
424C2×C4⋊C4C2412yes—
425C2×C4⋊C4C2412yes—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4C2×D411yescharacteristic
451C2×C22⋊C4C2×D411yescharacteristic
452C2×C22⋊C4C2×D412yes—
453C2×C22⋊C4C2×D412yes—
454C2×C22⋊C4C2×D412yes—
455C2×C22⋊C4C2×D412yes—
456C2×C42—21no—
457C2×C42—22no—
458C2×C42—22no—
459C2×C42—21no—
460C2×C42—21no—
461C2×C42—21no—
462C2×C42—22no—
463C2×C42—22no—
464C2×C42C2412yes—
465#107—24no—
466#107—42no—
467#107—42no—
468#107—42no—
469#106—24no—
470#106—42no—
471#106—42no—
472#106—42no—
473#102—24no—
474#102—24no—
475#102—42no—
476#102—42no—
477#102—42no—
478#102—42no—
479#102—42no—
480#102—42no—
481C22⋊C8—24no—
482C22⋊C8—24no—
483C22⋊C8—24no—
484C22⋊C8—24no—
485C22⋊C8—42no—
486C22⋊C8—42no—
487#95—22no—
488#95—22no—
489#95—22no—
490#95—22no—
491#95—22no—
492#95—22no—
493#95—22no—
494#95—22no—
495#95—22no—
496#95—22no—
497#95—22no—
498#95—22no—
499#95—22no—
500#95—22no—
501#95—22no—
502#95—22no—
503C24—22no—
504C24—22no—
505C24—41no—
506C24—42no—
507C24—42no—
508C24—41no—
509C24—42no—
510C24—81no—
511C24—81no—
512C24—82no—
513C24—82no—
514C24C22×D412yes—
515C24C22×D411yescharacteristic
516C24C22×D411yescharacteristic
517C24C22×D411yescharacteristic
518#41—44no—
519#41—44no—
520#41—44no—
521#41—44no—
522C2×Q8—41no—
523C2×Q8—41no—
524C2×Q8#12314yes—
525C2×D4—24no—
526C2×D4—24no—
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—41no—
534C2×D4—41no—
535C2×D4—41no—
536C2×D4—41no—
537C2×D4—41no—
538C2×D4—41no—
539C2×D4—44no—
540C2×D4—44no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—44no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—42no—
550C2×D4—82no—
551C2×D4—82no—
552C2×D4—81no—
553C2×D4—81no—
554C2×D4—82no—
555C2×D4—82no—
556C2×D4—82no—
557C2×D4—82no—
558C2×D4—82no—
559C2×D4—82no—
560C2×D4—82no—
561C2×D4—82no—
562C2×D4#12314yes—
563C2×D4#12314yes—
564C2×D4#12314yes—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—24no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—82no—
597C22×C4—82no—
598C22×C4—82no—
599C22×C4—82no—
600C22×C4—81no—
601C22×C4—81no—
602C22×C4—81no—
603C22×C4—82no—
604C22×C4—82no—
605C22×C4—82no—
606C22×C4C22×D412yes—
607C22×C4C22×D412yes—
608C22×C4C22×D412yes—
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
612C22×C4C2×#4112yes—
613C22×C4C2×#4112yes—
614C22×C4C2×#4112yes—
615C22×C4C2×#4112yes—
616C22×C4C2×#4112yes—
617C22×C4C2×#4112yes—
618C22×C4C2511yescharacteristic
619M16—44no—
620M16—44no—
621M16—44no—
622M16—82no—
623C2×C8—28no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—44no—
641C2×C8—44no—
642C2×C8—82no—
643C2×C8H(5,𝔽2)12yes—
644C2×C8H(5,𝔽2)12yes—
645C4⋊C4—24no—
646C4⋊C4—24no—
647C4⋊C4—24no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—82no—
663C4⋊C4—82no—
664C4⋊C4—82no—
665C4⋊C4—81no—
666C4⋊C4—81no—
667C4⋊C4—81no—
668C4⋊C4—82no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—24no—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—24no—
675C22⋊C4—44no—
676C22⋊C4—42no—
677C22⋊C4—44no—
678C22⋊C4—44no—
679C22⋊C4—82no—
680C22⋊C4—82no—
681C22⋊C4—82no—
682C22⋊C4—82no—
683C22⋊C4—82no—
684C22⋊C4—82no—
685C22⋊C4—82no—
686C22⋊C4—82no—
687C22⋊C4—82no—
688C22⋊C4—82no—
689C22⋊C4—82no—
690C22⋊C4—82no—
691C22⋊C4—81no—
692C22⋊C4—81no—
693C22⋊C4—82no—
694C22⋊C4—81no—
695C22⋊C4—82no—
696C22⋊C4—82no—
697C22⋊C4—82no—
698C22⋊C4—82no—
699C42—22no—
700C42—22no—
701C42—42no—
702C42—82no—
703C42—82no—
704C42—81no—
705C42—81no—
706C42—81no—
707C42—82no—
708C42—82no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—44no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—82no—
737C23—84no—
738C23—84no—
739C23—82no—
740C23—84no—
741C23—164no—
742C23—162no—
743C23—162no—
744C23—164no—
745C23C2×#12312yes—
746C23C2×#12312yes—
747C23C2×#12312yes—
748C23C23×D411yescharacteristic
749Q8—44no—
750D4—44no—
751D4—44no—
752D4—44no—
753D4—42no—
754D4—42no—
755D4—42no—
756D4—42no—
757D4—84no—
758D4—84no—
759D4—84no—
760D4—164no—
761D4—164no—
762D4—164no—
763D4—164no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
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—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—84no—
817C2×C4—82no—
818C2×C4—162no—
819C2×C4—162no—
820C2×C4—162no—
821C2×C4C2×#12312yes—
822C2×C4C2×#12312yes—
823C2×C4C2×#12312yes—
824C2×C4C22×#4111yescharacteristic
825C2×C4C22×#4111yescharacteristic
826C2×C4C2×H(5,𝔽2)11yescharacteristic
827C2×C4C2×H(5,𝔽2)11yescharacteristic
828C2×C4#58511yescharacteristic
829C2×C4#58511yescharacteristic
830C8—22no—
831C8—22no—
832C8—41no—
833C8—41no—
834C8—42no—
835C8—42no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—24no—
840C22—24no—
841C22—24no—
842C22—41no—
843C22—41no—
844C22—41no—
845C22—41no—
846C22—41no—
847C22—41no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—88no—
859C22—82no—
860C22—82no—
861C22—82no—
862C22—82no—
863C22—82no—
864C22—82no—
865C22—82no—
866C22—168no—
867C22C22×#12311yescharacteristic
868C22#349611yescharacteristic
869C22#349611yescharacteristic
870C22#358412yes—
871C22#358512yes—
872C4—22no—
873C4—22no—
874C4—22no—
875C4—42no—
876C4—42no—
877C4—42no—
878C4—82no—
879C4—82no—
880C4—82no—
881C4—82no—
882C4—82no—
883C4—82no—
884C4—82no—
885C4#349011yescharacteristic
886C4#349111yescharacteristic
887C4#350511yescharacteristic
888C4#350511yescharacteristic
889C2—42no—
890C2—42no—
891C2—42no—
892C2—82no—
893C2—162no—
894C2#3536011yescharacteristic
895C2#6052312yes—
896C2#6227511yescharacteristic
897C2#6228611yescharacteristic
898C2#6231312yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#37269C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#525 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34361C2semidirect
3. #27874C2semidirect
4. #27871C2semidirect
5. #26229C2semidirect
6. #26228C2semidirect
7. #26141C2semidirect
8. #26140C2semidirect
9. #24959C2semidirect
10. #24942C2semidirect
11. #24886C2semidirect
12. #24869C2semidirect
13. #24560C2semidirect
14. #24555C2semidirect
15. #21946C2semidirect
16. #21770C2semidirect
17. #20975C2semidirect
18. #20899C2semidirect
19. #20663C2semidirect
25. C2×#427C22semidirect
26. C22×#107C22semidirect
27. C2×#418C22semidirect
28. C22×#102C22semidirect
30. C2×#407C22semidirect
31. C22×C22⋊C8C22semidirect
49. #2354C22semidirect
51. #2352C22semidirect
54. #2314C22semidirect
58. #2280C22semidirect
59. #2101C22semidirect
60. #2099C22semidirect
61. #2094C22semidirect
62. #2092C22semidirect
63. #2085C22semidirect
64. #2083C22semidirect
65. #2077C22semidirect
66. #2077C22semidirect
67. #2076C22semidirect
68. #2075C22semidirect
69. #2073C22semidirect
70. #2071C22semidirect
75. #1926C22semidirect
76. #1925C22semidirect
77. #1925C22semidirect
78. #1925C22semidirect
79. #1921C22semidirect
80. #1920C22semidirect
81. #1919C22semidirect
82. #1919C22semidirect
85. #1895C22semidirect
88. #1893C22semidirect
91. #1875C22semidirect
92. #1874C22semidirect
94. #1870C22semidirect
96. #1869C22semidirect
97. #1854C22semidirect
98. #1854C22semidirect
99. #1854C22semidirect
100. #1854C22semidirect
101. #1853C22semidirect
102. #1853C22semidirect
103. #1825C22semidirect
104. #1825C22semidirect
105. #1825C22semidirect
106. #1809C22semidirect
107. #1809C22semidirect
108. #1809C22semidirect
109. #1808C22semidirect
110. #1808C22semidirect
111. #1807C22semidirect
112. #1786C22semidirect
113. #1736C22semidirect
114. #1736C22semidirect
115. #1736C22semidirect
116. #1735C22semidirect
117. #1729C22semidirect
118. #1729C22semidirect

Maximal subgroups

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

subgroupindex
#372692
#343612
#278742
#278712
#262292
#262282
#261412
#261402
#249592
#249422
#248862
#248692
#245602
#245552
#219462
#217702
#209752
#208992
#206632