Finite Group Databasebeta

← #6441583

Subgroups — #6441583

Order 512.

1862 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35517C211yesmaximal, characteristic
2#34208C211yesmaximal, characteristic
3#24961C212yesmaximal, complemented
4#24959C212yesmaximal, complemented
5#24954C212yesmaximal, complemented
6#24952C212yesmaximal, complemented
7#24947C212yesmaximal, complemented
8#24941C212yesmaximal, complemented
9#24940C212yesmaximal, complemented
10#24934C212yesmaximal, complemented
11#23746C211yesmaximal, characteristic, complemented
12C2×#2085C211yesmaximal, characteristic, complemented
13#23641C211yesmaximal, characteristic, complemented
14#23640C211yesmaximal, characteristic, complemented
15#21034C211yesmaximal, characteristic, complemented
16#21032C211yesmaximal, characteristic, complemented
17#20900C211yesmaximal, characteristic
18#20848C211yesmaximal, characteristic, complemented
19#20847C211yesmaximal, characteristic, complemented
20#20703C211yesmaximal, characteristic, complemented
21#20703C211yesmaximal, characteristic, complemented
22#20663C211yesmaximal, characteristic, complemented
23#20348C211yesmaximal, characteristic, complemented
24C22×#131C2211yescharacteristic
25C2×#532C2211yescharacteristic
26C2×#520C2211yescharacteristic
27C2×#520C2211yescharacteristic
28C2×#520C2211yescharacteristic
29C2×#428C2211yescharacteristic
30C2×#427C2211yescharacteristic
31C22×#107C2211yescharacteristic
32C22×#106C2211yescharacteristic
33C2×#408C2211yescharacteristic
34C2×#408C2211yescharacteristic
35C2×#408C2211yescharacteristic
36#2487C2212yes—
37#2486C2212yes—
38#2485C2212yes—
39#2485C2212yes—
40#2448—21no—
41#2447—21no—
42#2446—21no—
43#2445—21no—
44#2444—22no—
45#2443—22no—
46#2364—22no—
47#2364—22no—
48#2352C2212yes—
49#2352C2212yes—
50#2352C2212yes—
51#2352C2212yes—
52#2328—21no—
53#2327—21no—
54#2311C2211yescharacteristic
55#2311C2211yescharacteristic
56#2311C2211yescharacteristic
57#2311C2211yescharacteristic
58#2311C2211yescharacteristic
59C4×#124—21no—
60C4×#124—21no—
61#2296C2211yescharacteristic
62C2×#389C2211yescharacteristic
63C2×#382C2211yescharacteristic
64C4×#117C2211yescharacteristic
65#2101C2212yes—
66#2101C2212yes—
67#2101C2212yes—
68#2101C2212yes—
69#2085C2212yes—
70#2085C2212yes—
71#2085C2212yes—
72#2085C2212yes—
73#2077C2212yes—
74#2077C2212yes—
75#2077C2212yes—
76#2077C2212yes—
77#2077C2212yes—
78#2077C2212yes—
79#2076C2212yes—
80#2075C2212yes—
81#1921C2211yescharacteristic
82#1921C2211yescharacteristic
83#1921C2212yes—
84#1920C2211yescharacteristic
85#1920C2211yescharacteristic
86#1920C2212yes—
87#1919C2211yescharacteristic
88#1919C2211yescharacteristic
89#1919C2212yes—
90#1918C2211yescharacteristic
91#1918C2211yescharacteristic
92#1918C2212yes—
93#1870C2212yes—
94#1870C2212yes—
95#1869C2212yes—
96#1869C2212yes—
97#1854C2212yes—
98#1854C2212yes—
99#1854C2212yes—
100#1854C2212yes—
101#1853C2212yes—
102#1853C2212yes—
103#1852C2212yes—
104#1852C2212yes—
105#1825C2212yes—
106#1825C2212yes—
107#1825C2212yes—
108#1825C2212yes—
109#1824C2212yes—
110#1824C2212yes—
111#1823C2212yes—
112#1823C2212yes—
113#1809C2212yes—
114#1809C2212yes—
115#1808C2212yes—
116#1808C2212yes—
117#1736C2211yescharacteristic
118#1736C2211yescharacteristic
119#1736C2211yescharacteristic
120#1736C2211yescharacteristic
121#1736C2211yescharacteristic
122#1736C2211yescharacteristic
123#1736C2212yes—
124#1736C2212yes—
125#1736C2211yescharacteristic
126#1735C2211yescharacteristic
127#1735C2211yescharacteristic
128#1735C2211yescharacteristic
129#1735C2212yes—
130C2×#340C2211yescharacteristic
131C2×#340C2211yescharacteristic
132C2×#340C2212yes—
133#1728C2211yescharacteristic
134C2×#336C2211yescharacteristic
135C22×#41C2311yescharacteristic
136C22×#41C2311yescharacteristic
137C2×#131—24no—
138C2×#131—24no—
139C2×#131—42no—
140C22×M16C2311yescharacteristic
141C22×M16C2311yescharacteristic
142C22×M16C2312yes—
143C23×C8C2311yescharacteristic
144C23×C8C2312yes—
145C23×C8C2311yescharacteristic
146#532—24no—
147#532—24no—
148C2×C4⋊Q8D411yescharacteristic
149C2×#127D411yescharacteristic
150C2×#124D411yescharacteristic
151C2×#124D411yescharacteristic
152C2×#123—22no—
153C2×#121D412yes—
154C2×#121D412yes—
155#520—24no—
156#520—24no—
157#520—24no—
158#520—24no—
159#520—42no—
160#520—42no—
161C2×C4×Q8—21no—
162C2×C4×Q8—21no—
163C2×C4×Q8—21no—
164C2×C4×D4—21no—
165C2×C4×D4—21no—
166C2×C4×D4—22no—
167C2×C4×D4—22no—
168C2×C4×D4—22no—
169C2×C4×D4—21no—
170C2×C4×D4C2312yes—
171C2×C4×D4C2312yes—
172C2×#117C2311yescharacteristic
173C2×#117C2311yescharacteristic
174C2×#117C2311yescharacteristic
175C2×#117C2312yes—
176C2×#117C2312yes—
177C2×#117C2312yes—
178C2×#117C2311yescharacteristic
179C22×C4⋊C4—21no—
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2311yescharacteristic
183C22×C4⋊C4C2311yescharacteristic
184C22×C4⋊C4C2312yes—
185C22×C4⋊C4C2312yes—
186C22×C4⋊C4C2312yes—
187C22×C42C2311yescharacteristic
188#428—24no—
189#427—24no—
190C2×#107—42no—
191C2×#107C2311yescharacteristic
192C2×#107C2311yescharacteristic
193C2×#107C2312yes—
194C2×#107C2312yes—
195C2×#107C2312yes—
196C2×#106—42no—
197C2×#106C2311yescharacteristic
198C2×#106C2311yescharacteristic
199C2×#106C2312yes—
200C2×#106C2312yes—
201C2×#106C2312yes—
202#408—24no—
203#408—24no—
204#408—42no—
205C2×C22⋊C8C2312yes—
206C2×C22⋊C8C2312yes—
207C2×C22⋊C8C2312yes—
208C2×C22⋊C8C2312yes—
209C2×C22⋊C8C2312yes—
210C2×C22⋊C8C2312yes—
211#400—22no—
212#399—22no—
213#398—22no—
214#397—22no—
215#397—22no—
216#397—22no—
217#394—22no—
218#394—22no—
219#391—21no—
220#391—21no—
221#391—21no—
222#391—21no—
223#391—21no—
224#390—21no—
225#390—21no—
226#390—21no—
227#390—21no—
228#390—21no—
229#389—21no—
230#389—21no—
231#389C2312yes—
232#389C2312yes—
233#389C2311yescharacteristic
234#389C2311yescharacteristic
235#389C2311yescharacteristic
236#389C2311yescharacteristic
237#388—22no—
238#388—22no—
239#388—22no—
240#388—22no—
241#388—22no—
242#388—22no—
243#387—22no—
244#387—22no—
245#387—22no—
246#387—22no—
247#387—22no—
248#387—22no—
249#386—22no—
250#386—22no—
251#386—22no—
252#386—22no—
253#386—22no—
254#386—22no—
255#386—22no—
256#386—22no—
257#386—22no—
258#386—22no—
259#385—21no—
260#385—21no—
261#385—22no—
262#382—21no—
263#382—21no—
264#382C2312yes—
265#382C2312yes—
266#381—22no—
267#380C2312yes—
268#380C2312yes—
269#380C2312yes—
270#380C2312yes—
271#380C2312yes—
272#380C2312yes—
273#380C2312yes—
274#380C2312yes—
275#380C2312yes—
276#380C2312yes—
277C4×C4⋊C4—21no—
278C4×C4⋊C4—21no—
279C4×C4⋊C4C2311yescharacteristic
280C4×C4⋊C4C2311yescharacteristic
281C4×C4⋊C4C2311yescharacteristic
282C4×C4⋊C4C2311yescharacteristic
283C4×C22⋊C4—21no—
284C4×C22⋊C4—21no—
285C4×C22⋊C4—22no—
286C4×C22⋊C4—22no—
287C4×C22⋊C4—22no—
288C4×C22⋊C4—22no—
289#376—21no—
290C2×#95—21no—
291C2×#95—21no—
292C2×#95—21no—
293C43—21no—
294#340C2312yes—
295#340C2312yes—
296#340C2312yes—
297#340C2312yes—
298#340C2312yes—
299#340C2312yes—
300#340C2312yes—
301#340C2312yes—
302#340C2312yes—
303#340C2311yescharacteristic
304#340C2311yescharacteristic
305#340C2311yescharacteristic
306#340C2311yescharacteristic
307#340C2312yes—
308#340C2312yes—
309#340C2312yes—
310#340C2311yescharacteristic
311#340C2312yes—
312#340C2312yes—
313#340C2312yes—
314#340C2312yes—
315#340C2311yescharacteristic
316#340C2312yes—
317#340C2311yescharacteristic
318#340C2311yescharacteristic
319#340C2312yes—
320#340C2311yescharacteristic
321#340C2311yescharacteristic
322#340C2311yescharacteristic
323#340C2311yescharacteristic
324#336C2311yescharacteristic
325#336C2311yescharacteristic
326#336C2311yescharacteristic
327#336C2311yescharacteristic
328#336C2312yes—
329#336C2312yes—
330C2×#41—22no—
331C2×#41—22no—
332C2×#41—22no—
333C2×#41—22no—
334C2×#41—22no—
335C2×#41—22no—
336C2×#41—22no—
337C2×#41—22no—
338C2×#41—22no—
339C2×#41—22no—
340C2×#41#4114yes—
341C2×#41#4114yes—
342C22×Q8C2×D411yescharacteristic
343C22×Q8C2×D411yescharacteristic
344C22×D4C2×D412yes—
345C22×D4C2×D411yescharacteristic
346C22×D4C2×D412yes—
347C22×D4C2×D411yescharacteristic
348C22×D4C2×D412yes—
349C22×D4C2×D412yes—
350C23×C4—21no—
351C23×C4—21no—
352C23×C4—22no—
353C23×C4—21no—
354C23×C4—21no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4C2×D411yescharacteristic
358C23×C4C2×D411yescharacteristic
359C23×C4C2412yes—
360C23×C4C2412yes—
361C23×C4C2411yescharacteristic
362#131—416no—
363C2×M16—24no—
364C2×M16—22no—
365C2×M16—22no—
366C2×M16—22no—
367C2×M16—22no—
368C2×M16—22no—
369C2×M16—22no—
370C2×M16—24no—
371C2×M16—42no—
372C22×C8—22no—
373C22×C8—22no—
374C22×C8—24no—
375C22×C8—22no—
376C22×C8—22no—
377C22×C8—22no—
378C22×C8—24no—
379C22×C8—42no—
380C22×C8#4114yes—
381C22×C8C2412yes—
382C22×C8C2411yescharacteristic
383C22×C8C2411yescharacteristic
384C22×C8C2412yes—
385C22×C8C2411yescharacteristic
386C22×C8C2411yescharacteristic
387C4⋊Q8—24no—
388#127—24no—
389#124—24no—
390#124—24no—
391#123—84no—
392#121—28no—
393#121—28no—
394C4×Q8—44no—
395C4×Q8—44no—
396C4×Q8—44no—
397C4×D4—24no—
398C4×D4—24no—
399C4×D4—24no—
400C4×D4—24no—
401C4×D4—44no—
402C4×D4—44no—
403C4×D4—48no—
404C4×D4—48no—
405C4×D4—48no—
406C4×D4—44no—
407#117—22no—
408#117—24no—
409#117—24no—
410#117—22no—
411#117—22no—
412#117—22no—
413#117—22no—
414#117—22no—
415#117—22no—
416#117—24no—
417#117—24no—
418#117—42no—
419#117—42no—
420#117#4114yes—
421C2×C4⋊C4—24no—
422C2×C4⋊C4—24no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—42no—
447C2×C4⋊C4—42no—
448C2×C4⋊C4—82no—
449C2×C4⋊C4C2×D412yes—
450C2×C4⋊C4C2×D412yes—
451C2×C4⋊C4C2412yes—
452C2×C4⋊C4C2411yescharacteristic
453C2×C4⋊C4C2412yes—
454C2×C4⋊C4C2412yes—
455C2×C4⋊C4C2412yes—
456C2×C4⋊C4C2411yescharacteristic
457C2×C4⋊C4C2411yescharacteristic
458C2×C4⋊C4C2411yescharacteristic
459C2×C4⋊C4C2411yescharacteristic
460C2×C4⋊C4C2411yescharacteristic
461C2×C4⋊C4C2411yescharacteristic
462C2×C4⋊C4C2411yescharacteristic
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4C2×D412yes—
481C2×C22⋊C4C2×D412yes—
482C2×C22⋊C4C2×D412yes—
483C2×C22⋊C4C2×D412yes—
484C2×C42—21no—
485C2×C42—22no—
486C2×C42—22no—
487C2×C42—22no—
488C2×C42—22no—
489C2×C42—21no—
490C2×C42—22no—
491C2×C42—21no—
492C2×C42—21no—
493C2×C42—21no—
494C2×C42—21no—
495C2×C42—21no—
496C2×C42—21no—
497C2×C42C2×D411yescharacteristic
498C2×C42C2×D411yescharacteristic
499C2×C42C2411yescharacteristic
500C2×C42C2411yescharacteristic
501#107—22no—
502#107—22no—
503#107—24no—
504#107—42no—
505#107—42no—
506#106—22no—
507#106—22no—
508#106—24no—
509#106—42no—
510#106—42no—
511C22⋊C8—24no—
512C22⋊C8—24no—
513C22⋊C8—24no—
514C22⋊C8—24no—
515C22⋊C8—42no—
516C22⋊C8—42no—
517#95—22no—
518#95—22no—
519#95—22no—
520#95—22no—
521#95—22no—
522#95—22no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95—21no—
527#95—22no—
528#95—22no—
529#95—22no—
530#95—22no—
531#95—21no—
532#95—21no—
533#95—21no—
534#95—21no—
535#95—22no—
536#95—22no—
537#95—22no—
538#95—22no—
539#95—22no—
540#95—22no—
541C24C22×D412yes—
542C24C22×D412yes—
543C24C22×D411yescharacteristic
544#41—28no—
545#41—28no—
546#41—28no—
547#41—28no—
548#41—44no—
549#41—44no—
550#41—44no—
551#41—44no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8#12314yes—
558C2×D4—24no—
559C2×D4—24no—
560C2×D4—24no—
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—42no—
574C2×D4#12318yes—
575C2×D4#12314yes—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—22no—
599C22×C4—21no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—42no—
607C22×C4—44no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4—82no—
615C22×C4—82no—
616C22×C4—82no—
617C22×C4—82no—
618C22×C4—82no—
619C22×C4—81no—
620C22×C4—81no—
621C22×C4—81no—
622C22×C4—82no—
623C22×C4—81no—
624C22×C4—81no—
625C22×C4C22×D411yescharacteristic
626C22×C4C22×D412yes—
627C22×C4C22×D411yescharacteristic
628C22×C4C22×D411yescharacteristic
629C22×C4C22×D411yescharacteristic
630C22×C4C22×D412yes—
631C22×C4C22×D411yescharacteristic
632C22×C4C2×#4114yes—
633C22×C4C2×#4114yes—
634C22×C4C2×#4112yes—
635C22×C4C2×#4112yes—
636C22×C4C2×#4112yes—
637C22×C4C2×#4112yes—
638C22×C4H(5,𝔽2)12yes—
639C22×C42−1+412yes—
640C22×C4C2511yescharacteristic
641M16—48no—
642M16—44no—
643M16—44no—
644C2×C8—28no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—22no—
655C2×C8—22no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—22no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—48no—
662C2×C8—44no—
663C2×C8C2×#4112yes—
664C2×C8C2×#4112yes—
665C4⋊C4—24no—
666C4⋊C4—24no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—22no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—22no—
676C4⋊C4—21no—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—22no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—22no—
683C4⋊C4—22no—
684C4⋊C4—22no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—44no—
690C4⋊C4—44no—
691C4⋊C4—42no—
692C4⋊C4—44no—
693C4⋊C4—42no—
694C4⋊C4—44no—
695C4⋊C4—42no—
696C4⋊C4—42no—
697C4⋊C4—42no—
698C4⋊C4—42no—
699C4⋊C4—81no—
700C4⋊C4—81no—
701C4⋊C4—82no—
702C4⋊C4C2×#4112yes—
703C4⋊C4C2×#4112yes—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—24no—
707C22⋊C4—24no—
708C22⋊C4—24no—
709C22⋊C4—44no—
710C22⋊C4—44no—
711C22⋊C4—44no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—82no—
716C22⋊C4—82no—
717C22⋊C4—82no—
718C22⋊C4—82no—
719C22⋊C4—82no—
720C22⋊C4—82no—
721C22⋊C4—82no—
722C22⋊C4—82no—
723C22⋊C4—82no—
724C22⋊C4—82no—
725C42—22no—
726C42—22no—
727C42—24no—
728C42—21no—
729C42—21no—
730C42—21no—
731C42—21no—
732C42—44no—
733C42—44no—
734C42—44no—
735C42—42no—
736C42—42no—
737C42—42no—
738C42—81no—
739C42—81no—
740C42—81no—
741C42—81no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23C2×#12314yes—
760C23C2×#12312yes—
761C23#54612yes—
762C23#54712yes—
763C23C23×D411yescharacteristic
764Q8—28no—
765Q8—44no—
766D4—216no—
767D4—28no—
768D4—48no—
769D4—44no—
770D4—84no—
771D4—84no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—41no—
820C2×C4—42no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—41no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—82no—
834C2×C4—82no—
835C2×C4—84no—
836C2×C4—164no—
837C2×C4—164no—
838C2×C4—162no—
839C2×C4—162no—
840C2×C4—162no—
841C2×C4—164no—
842C2×C4C2×#12314yes—
843C2×C4C2×#12312yes—
844C2×C4#52914yes—
845C2×C4#53914yes—
846C2×C4#54612yes—
847C2×C4#54712yes—
848C2×C4#55114yes—
849C2×C4#55214yes—
850C2×C4C22×#4111yescharacteristic
851C2×C4C22×#4111yescharacteristic
852C2×C4C22×#4111yescharacteristic
853C2×C4C22×#4111yescharacteristic
854C2×C4C2×H(5,𝔽2)11yescharacteristic
855C2×C4C2×2−1+411yescharacteristic
856C8—22no—
857C8—22no—
858C8—42no—
859C8—41no—
860C8—41no—
861C8—42no—
862C22—22no—
863C22—22no—
864C22—22no—
865C22—22no—
866C22—22no—
867C22—22no—
868C22—24no—
869C22—24no—
870C22—24no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—42no—
881C22—42no—
882C22#241914yes—
883C22C22×#12311yescharacteristic
884C22C2×#54611yescharacteristic
885C22C2×#54711yescharacteristic
886C22#358411yescharacteristic
887C22#358411yescharacteristic
888C22#358511yescharacteristic
889C22#358611yescharacteristic
890C4—24no—
891C4—42no—
892C4—42no—
893C4—42no—
894C4—41no—
895C4—41no—
896C4—41no—
897C4—41no—
898C4—82no—
899C4—82no—
900C4—82no—
901C4—81no—
902C4—81no—
903C4—82no—
904C4—81no—
905C4—81no—
906C4—81no—
907C4—81no—
908C4#241914yes—
909C4C2×#52911yescharacteristic
910C4C2×#53911yescharacteristic
911C4C2×#55111yescharacteristic
912C4C2×#55211yescharacteristic
913C2—24no—
914C2—44no—
915C2—82no—
916C2C2×#241911yescharacteristic
917C2#6052311yescharacteristic
918C2#6052411yescharacteristic
919C2#6120711yescharacteristic
920C2#6120811yescharacteristic
921C2#6128911yescharacteristic
922C2#6129411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#532C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#532 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #24961C2semidirect
4. #24959C2semidirect
5. #24954C2semidirect
6. #24952C2semidirect
7. #24947C2semidirect
8. #24941C2semidirect
9. #24940C2semidirect
10. #24934C2semidirect
11. #23746C2semidirect
12. C2×#2085C2semidirect
13. #23641C2semidirect
14. #23640C2semidirect
15. #21034C2semidirect
16. #21032C2semidirect
18. #20848C2semidirect
19. #20847C2semidirect
20. #20703C2semidirect
21. #20703C2semidirect
22. #20663C2semidirect
23. #20348C2semidirect

Maximal subgroups

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

subgroupindex
#355172
#342082
#249612
#249592
#249542
#249522
#249472
#249412
#249402
#249342
#237462
C2×#20852
#236412
#236402
#210342
#210322
#209002
#208482
#208472
#207032
#206632
#203482