Finite Group Databasebeta

← #6450869

Subgroups — #6450869

Order 512.

1792 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#35530C211yesmaximal, characteristic
2#34252C211yesmaximal, characteristic, complemented
3#27188C212yesmaximal, complemented
4#27182C212yesmaximal, complemented
5#27181C212yesmaximal, complemented
6#27175C212yesmaximal, complemented
7#27173C212yesmaximal, complemented
8#27167C212yesmaximal, complemented
9#27164C212yesmaximal, complemented
10#27158C212yesmaximal, complemented
11#23745C211yesmaximal, characteristic, complemented
12#23639C211yesmaximal, characteristic, complemented
13#23609C211yesmaximal, characteristic, complemented
14#23488C211yesmaximal, characteristic
15C2×#1947C211yesmaximal, characteristic, complemented
16#21156C211yesmaximal, characteristic, complemented
17#21059C211yesmaximal, characteristic, complemented
18#21052C211yesmaximal, characteristic, complemented
19#21035C211yesmaximal, characteristic, complemented
20#20915C211yesmaximal, characteristic
21#20881C211yesmaximal, characteristic, complemented
22#20849C211yesmaximal, characteristic, complemented
23#20415C211yesmaximal, characteristic, complemented
24C2×#537C2211yescharacteristic
25C2×#520C2211yescharacteristic
26C2×#520C2211yescharacteristic
27C2×#428C2211yescharacteristic
28C2×#427C2211yescharacteristic
29C22×#107C2211yescharacteristic
30C22×#107C2211yescharacteristic
31C22×C4⋊C8C2211yescharacteristic
32C2×#417C2211yescharacteristic
33C2×#417C2211yescharacteristic
34C2×#416C2211yescharacteristic
35C2×#416C2211yescharacteristic
36C2×#408C2211yescharacteristic
37C2×#408C2211yescharacteristic
38C2×#405C2211yescharacteristic
39#2502—21no—
40#2501—21no—
41#2500—21no—
42#2499—21no—
43#2443—22no—
44#2443—22no—
45#2423C2212yes—
46#2423C2212yes—
47#2422C2212yes—
48#2422C2212yes—
49#2357—21no—
50#2356—21no—
51#2355—21no—
52#2354—21no—
53#2347C2212yes—
54#2346C2212yes—
55#2345C2212yes—
56#2344C2212yes—
57#2318—22no—
58#2317C2211yescharacteristic
59#2317C2211yescharacteristic
60#2311C2211yescharacteristic
61#2311C2211yescharacteristic
62#2297C2211yescharacteristic
63#2297C2211yescharacteristic
64#2296C2211yescharacteristic
65#2290—22no—
66C2×#384C2211yescharacteristic
67#2274C2211yescharacteristic
68C2×C4×C4⋊C4C2211yescharacteristic
69#2100C2212yes—
70#2100C2212yes—
71#2099C2212yes—
72#2099C2212yes—
73#2076C2212yes—
74#2076C2212yes—
75#2075C2212yes—
76#2075C2212yes—
77#2068C2211yescharacteristic
78#2068C2211yescharacteristic
79#2067C2211yescharacteristic
80#2067C2211yescharacteristic
81#2066C2211yescharacteristic
82#2066C2211yescharacteristic
83#2065C2211yescharacteristic
84#2065C2211yescharacteristic
85#2036C2212yes—
86#2036C2212yes—
87#2033C2212yes—
88#2033C2212yes—
89#1947C2212yes—
90#1947C2212yes—
91#1947C2212yes—
92#1947C2212yes—
93#1944C2212yes—
94#1944C2212yes—
95#1942C2212yes—
96#1942C2212yes—
97#1928C2212yes—
98#1927C2212yes—
99#1926C2212yes—
100#1925C2212yes—
101#1924C2212yes—
102#1924C2212yes—
103#1923C2212yes—
104#1923C2212yes—
105#1921C2212yes—
106#1920C2212yes—
107#1919C2212yes—
108#1918C2212yes—
109#1875C2212yes—
110#1874C2212yes—
111#1873C2212yes—
112#1872C2212yes—
113#1863C2212yes—
114#1863C2212yes—
115#1862C2212yes—
116#1862C2212yes—
117#1854C2212yes—
118#1854C2212yes—
119#1853C2212yes—
120#1852C2212yes—
121#1763C2212yes—
122#1762C2212yes—
123C4×#103C2212yes—
124C4×#102C2212yes—
125#1736C2211yescharacteristic
126#1736C2211yescharacteristic
127#1736C2211yescharacteristic
128#1736C2211yescharacteristic
129#1736C2211yescharacteristic
130#1735C2211yescharacteristic
131C2×#340C2211yescharacteristic
132C2×#340C2211yescharacteristic
133#1729C2211yescharacteristic
134#1728C2211yescharacteristic
135C22×#41C2311yescharacteristic
136C22×#41C2311yescharacteristic
137C22×M16C2311yescharacteristic
138C22×M16C2311yescharacteristic
139C23×C8C2311yescharacteristic
140C23×C8C2311yescharacteristic
141#537—24no—
142#537—42no—
143C2×#123—22no—
144C2×#123—22no—
145C2×C22⋊Q8—21no—
146C2×C22⋊Q8C2312yes—
147C2×#121—22no—
148C2×#121—21no—
149C2×#121C2312yes—
150#520—24no—
151#520—24no—
152#520—24no—
153#520—42no—
154C2×C4×Q8—21no—
155C2×C4×Q8C2312yes—
156C2×C4×D4—22no—
157C2×C4×D4—21no—
158C2×C4×D4—22no—
159C2×C4×D4C2312yes—
160C2×#117—21no—
161C2×#117—22no—
162C2×#117C2311yescharacteristic
163C2×#117C2311yescharacteristic
164C2×#117C2312yes—
165C2×#117C2311yescharacteristic
166C2×#117C2311yescharacteristic
167C22×C4⋊C4—21no—
168C22×C4⋊C4—21no—
169C22×C4⋊C4—21no—
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2311yescharacteristic
175C22×C42—21no—
176C22×C42C2311yescharacteristic
177#428—24no—
178#427—24no—
179C2×#107—42no—
180C2×#107—42no—
181C2×#107C2311yescharacteristic
182C2×#107C2311yescharacteristic
183C2×#107C2312yes—
184C2×#107C2312yes—
185C2×#107C2312yes—
186C2×#107C2312yes—
187C2×#107C2312yes—
188C2×#106C2311yescharacteristic
189C2×#106C2311yescharacteristic
190C2×#106C2312yes—
191C2×C4⋊C8—24no—
192C2×C4⋊C8C2311yescharacteristic
193C2×C4⋊C8C2311yescharacteristic
194C2×C4⋊C8C2311yescharacteristic
195C2×C4⋊C8C2311yescharacteristic
196#417—24no—
197#417—24no—
198#416—24no—
199#416—24no—
200C2×#103C2311yescharacteristic
201C2×#103C2311yescharacteristic
202C2×#103C2311yescharacteristic
203C2×#103C2311yescharacteristic
204C2×#103C2312yes—
205C2×#103C2312yes—
206C2×#102C2311yescharacteristic
207C2×#102C2311yescharacteristic
208C2×#102C2311yescharacteristic
209C2×#102C2311yescharacteristic
210C2×#102C2312yes—
211C2×#102C2312yes—
212#408—24no—
213#408—42no—
214C2×C22⋊C8C2312yes—
215C2×C22⋊C8C2312yes—
216C2×C22⋊C8C2312yes—
217C2×C22⋊C8C2312yes—
218#405—42no—
219C2×#97C2312yes—
220C2×C4×C8C2312yes—
221#399—22no—
222#399—22no—
223#398—22no—
224#398—22no—
225#397—22no—
226#397—22no—
227#394—22no—
228#394—22no—
229#391—21no—
230#391—21no—
231#391D411yescharacteristic
232#391D411yescharacteristic
233#391C2311yescharacteristic
234#391C2311yescharacteristic
235#390—21no—
236#390—21no—
237#390D411yescharacteristic
238#390D411yescharacteristic
239#390C2311yescharacteristic
240#390C2311yescharacteristic
241#389C2312yes—
242#389C2312yes—
243#389C2312yes—
244#389C2312yes—
245#389C2311yescharacteristic
246#389C2311yescharacteristic
247#389C2311yescharacteristic
248#389C2311yescharacteristic
249#388—22no—
250#388—22no—
251#388—22no—
252#388—22no—
253#388—22no—
254#388—22no—
255#387—22no—
256#387—22no—
257#387—22no—
258#387—22no—
259#387—22no—
260#387—22no—
261#386—22no—
262#386—22no—
263#386—21no—
264#386—21no—
265#386D412yes—
266#386D412yes—
267#385—21no—
268#385—21no—
269#385—22no—
270#385—22no—
271#385—22no—
272#385—22no—
273#384—21no—
274#384—21no—
275#384—21no—
276#384—21no—
277#384C2312yes—
278#384C2312yes—
279#383—22no—
280#382—21no—
281#382—21no—
282#382—22no—
283#381—22no—
284#380—22no—
285#380C2312yes—
286#380C2312yes—
287#380C2312yes—
288#380C2312yes—
289C4×C4⋊C4—21no—
290C4×C4⋊C4—21no—
291C4×C4⋊C4—21no—
292C4×C4⋊C4—21no—
293C4×C4⋊C4—21no—
294C4×C4⋊C4—21no—
295C4×C4⋊C4—22no—
296C4×C4⋊C4C2312yes—
297C4×C4⋊C4C2312yes—
298C4×C4⋊C4C2312yes—
299C4×C4⋊C4C2312yes—
300C4×C22⋊C4—22no—
301C4×C22⋊C4—22no—
302C4×C22⋊C4—21no—
303C4×C22⋊C4—21no—
304C4×C22⋊C4C2312yes—
305C4×C22⋊C4C2312yes—
306#376—22no—
307C2×#95—21no—
308#340C2311yescharacteristic
309#340C2311yescharacteristic
310#340C2311yescharacteristic
311#340C2311yescharacteristic
312#340C2312yes—
313#340C2312yes—
314#340C2312yes—
315#340C2312yes—
316#340C2312yes—
317#340C2312yes—
318#340C2312yes—
319#340C2312yes—
320#340C2312yes—
321#340C2312yes—
322#340C2312yes—
323#340C2312yes—
324#340C2312yes—
325#340C2312yes—
326#336C2312yes—
327#336C2312yes—
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—22no—
341C2×#41#4114yes—
342C22×Q8C2×D411yescharacteristic
343C22×Q8C2411yescharacteristic
344C22×D4—21no—
345C22×D4—22no—
346C22×D4C2×D412yes—
347C22×D4C2×D411yescharacteristic
348C22×D4C2411yescharacteristic
349C23×C4—22no—
350C23×C4—21no—
351C23×C4—21no—
352C23×C4—21no—
353C23×C4—21no—
354C23×C4—21no—
355C23×C4—22no—
356C23×C4C2×D411yescharacteristic
357C23×C4C2×D411yescharacteristic
358C23×C4C2412yes—
359C23×C4C2411yescharacteristic
360C2×M16—22no—
361C2×M16—22no—
362C2×M16—22no—
363C2×M16—22no—
364C2×M16—22no—
365C2×M16—22no—
366C22×C8—22no—
367C22×C8—22no—
368C22×C8—22no—
369C22×C8—22no—
370C22×C8—22no—
371C22×C8#4114yes—
372C22×C8C2411yescharacteristic
373C22×C8C2411yescharacteristic
374C22×C8C2412yes—
375C22×C8C2412yes—
376C22×C8C2411yescharacteristic
377C22×C8C2411yescharacteristic
378#123—84no—
379#123—84no—
380C22⋊Q8—24no—
381C22⋊Q8—42no—
382C22⋊Q8—44no—
383#121—24no—
384#121—42no—
385#121—44no—
386#121—48no—
387C4×Q8—28no—
388C4×Q8—24no—
389C4×Q8—42no—
390C4×D4—216no—
391C4×D4—28no—
392C4×D4—24no—
393C4×D4—42no—
394C4×D4—48no—
395#117—22no—
396#117—22no—
397#117—22no—
398#117—24no—
399#117—24no—
400#117—22no—
401#117—22no—
402#117—22no—
403#117—22no—
404#117—44no—
405#117—84no—
406#117#4114yes—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—24no—
411C2×C4⋊C4—24no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—44no—
436C2×C4⋊C4—82no—
437C2×C4⋊C4—82no—
438C2×C4⋊C4C2×D411yescharacteristic
439C2×C4⋊C4C2×D411yescharacteristic
440C2×C4⋊C4#4114yes—
441C2×C4⋊C4C2412yes—
442C2×C4⋊C4C2412yes—
443C2×C4⋊C4C2412yes—
444C2×C4⋊C4C2411yescharacteristic
445C2×C4⋊C4C2411yescharacteristic
446C2×C4⋊C4C2411yescharacteristic
447C2×C4⋊C4C2411yescharacteristic
448C2×C4⋊C4C2412yes—
449C2×C4⋊C4C2411yescharacteristic
450C2×C4⋊C4C2411yescharacteristic
451C2×C22⋊C4—21no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4C2×D412yes—
467C2×C22⋊C4C2×D412yes—
468C2×C22⋊C4C2×D412yes—
469C2×C22⋊C4C2×D412yes—
470C2×C22⋊C4C2×D412yes—
471C2×C42—22no—
472C2×C42—21no—
473C2×C42—22no—
474C2×C42—22no—
475C2×C42—22no—
476C2×C42—22no—
477C2×C42—21no—
478C2×C42—21no—
479C2×C42—22no—
480C2×C42—22no—
481C2×C42—22no—
482C2×C42—82no—
483C2×C42C2×D411yescharacteristic
484C2×C42C2×D411yescharacteristic
485C2×C42C2412yes—
486C2×C42C2411yescharacteristic
487C2×C42C2411yescharacteristic
488#107—22no—
489#107—22no—
490#107—24no—
491#107—42no—
492#107—42no—
493#107—42no—
494#107—42no—
495#106—22no—
496#106—22no—
497#106—24no—
498C4⋊C8—22no—
499C4⋊C8—22no—
500C4⋊C8—22no—
501C4⋊C8—22no—
502#103—24no—
503#103—22no—
504#103—22no—
505#103—22no—
506#103—22no—
507#103—24no—
508#102—24no—
509#102—22no—
510#102—22no—
511#102—22no—
512#102—22no—
513#102—24no—
514C22⋊C8—24no—
515C22⋊C8—24no—
516C22⋊C8—42no—
517C22⋊C8—42no—
518#97—42no—
519C4×C8—42no—
520#95—22no—
521#95—22no—
522#95—21no—
523#95—22no—
524#95—22no—
525#95—21no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95—21no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95—22no—
534#95—21no—
535#95—21no—
536#95—22no—
537#95—22no—
538#95—22no—
539#95—22no—
540#95C2×D412yes—
541#95C2×D412yes—
542#95C2×D412yes—
543#95C2×D412yes—
544C24—21no—
545C24C22×D412yes—
546C24C22×D411yescharacteristic
547#41—28no—
548#41—28no—
549#41—44no—
550#41—44no—
551#41—44no—
552#41—44no—
553#41—44no—
554#41—44no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8C2×#4112yes—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—24no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—44no—
579C2×D4—82no—
580C2×D4—82no—
581C2×D4C2×#4112yes—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—28no—
591C22×C4—24no—
592C22×C4—24no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—22no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—44no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—82no—
615C22×C4—82no—
616C22×C4—81no—
617C22×C4—81no—
618C22×C4—82no—
619C22×C4—81no—
620C22×C4—82no—
621C22×C4—81no—
622C22×C4—81no—
623C22×C4—81no—
624C22×C4—81no—
625C22×C4—81no—
626C22×C4C22×D412yes—
627C22×C4C22×D412yes—
628C22×C4C22×D411yescharacteristic
629C22×C4C22×D411yescharacteristic
630C22×C4C22×D412yes—
631C22×C4C22×D411yescharacteristic
632C22×C4C22×D411yescharacteristic
633C22×C4C22×D411yescharacteristic
634C22×C4C2×#4112yes—
635C22×C4C2×#4112yes—
636C22×C4C2×#4112yes—
637C22×C4C2×#4112yes—
638C22×C4H(5,𝔽2)12yes—
639C22×C42−1+412yes—
640C22×C4C2511yescharacteristic
641M16—44no—
642M16—44no—
643C2×C8—28no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—22no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—22no—
656C2×C8—22no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—22no—
660C2×C8—44no—
661C2×C8C2×#4112yes—
662C2×C8C2×#4112yes—
663C4⋊C4—28no—
664C4⋊C4—24no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—21no—
668C4⋊C4—22no—
669C4⋊C4—21no—
670C4⋊C4—22no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—22no—
680C4⋊C4—22no—
681C4⋊C4—22no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—44no—
685C4⋊C4—44no—
686C4⋊C4—44no—
687C4⋊C4—42no—
688C4⋊C4—42no—
689C4⋊C4—42no—
690C4⋊C4—44no—
691C4⋊C4—42no—
692C4⋊C4—42no—
693C4⋊C4—82no—
694C4⋊C4—81no—
695C4⋊C4—81no—
696C4⋊C4—82no—
697C4⋊C4—82no—
698C4⋊C4—82no—
699C4⋊C4—82no—
700C4⋊C4—82no—
701C4⋊C4C2×#4112yes—
702C4⋊C4C2×#4114yes—
703C4⋊C4C2×#4112yes—
704C22⋊C4—28no—
705C22⋊C4—24no—
706C22⋊C4—24no—
707C22⋊C4—24no—
708C22⋊C4—24no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—44no—
712C22⋊C4—44no—
713C22⋊C4—44no—
714C22⋊C4—42no—
715C22⋊C4—42no—
716C22⋊C4—42no—
717C22⋊C4—42no—
718C22⋊C4—42no—
719C22⋊C4—42no—
720C22⋊C4—82no—
721C22⋊C4—82no—
722C22⋊C4—82no—
723C22⋊C4—82no—
724C42—28no—
725C42—24no—
726C42—22no—
727C42—22no—
728C42—21no—
729C42—21no—
730C42—22no—
731C42—22no—
732C42—21no—
733C42—21no—
734C42—44no—
735C42—42no—
736C42—42no—
737C42—44no—
738C42—82no—
739C42—82no—
740C42—82no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23#52512yes—
760C23#54612yes—
761C23#54712yes—
762C23C23×D411yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—41no—
766Q8—41no—
767Q8—44no—
768D4—22no—
769D4—22no—
770D4—48no—
771D4—48no—
772D4—41no—
773D4—41no—
774D4—44no—
775D4—164no—
776C2×C4—28no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—21no—
784C2×C4—22no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—24no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—44no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—48no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—42no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—84no—
836C2×C4—88no—
837C2×C4—84no—
838C2×C4—164no—
839C2×C4—162no—
840C2×C4—162no—
841C2×C4#52512yes—
842C2×C4#52914yes—
843C2×C4#54214yes—
844C2×C4#54612yes—
845C2×C4#54712yes—
846C2×C4#55214yes—
847C2×C4#55314yes—
848C2×C4#57612yes—
849C2×C4#57812yes—
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—42no—
860C8—41no—
861C8—41no—
862C22—22no—
863C22—22no—
864C22—22no—
865C22—22no—
866C22—22no—
867C22—22no—
868C22—42no—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22—81no—
882C22#247014yes—
883C22C2×#52511yescharacteristic
884C22C2×#54611yescharacteristic
885C22C2×#54711yescharacteristic
886C22C2×#57611yescharacteristic
887C22C2×#57811yescharacteristic
888C22#358511yescharacteristic
889C22#358611yescharacteristic
890C4—22no—
891C4—22no—
892C4—42no—
893C4—42no—
894C4—41no—
895C4—41no—
896C4—42no—
897C4—42no—
898C4—44no—
899C4—42no—
900C4—42no—
901C4—82no—
902C4—82no—
903C4—82no—
904C4—81no—
905C4—81no—
906C4—81no—
907C4—81no—
908C4#247014yes—
909C4C2×#52911yescharacteristic
910C4C2×#54211yescharacteristic
911C4C2×#55211yescharacteristic
912C4C2×#55311yescharacteristic
913C2—24no—
914C2—82no—
915C2—82no—
916C2C2×#247011yescharacteristic
917C2#6059611yescharacteristic
918C2#6060011yescharacteristic
919C2#6120511yescharacteristic
920C2#6121011yescharacteristic
921C2#6125811yescharacteristic
922C2#6126511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#537C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2297 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34252C2semidirect
3. #27188C2semidirect
4. #27182C2semidirect
5. #27181C2semidirect
6. #27175C2semidirect
7. #27173C2semidirect
8. #27167C2semidirect
9. #27164C2semidirect
10. #27158C2semidirect
11. #23745C2semidirect
12. #23639C2semidirect
13. #23609C2semidirect
15. C2×#1947C2semidirect
16. #21156C2semidirect
17. #21059C2semidirect
18. #21052C2semidirect
19. #21035C2semidirect
21. #20881C2semidirect
22. #20849C2semidirect
23. #20415C2semidirect

Maximal subgroups

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

subgroupindex
#355302
#342522
#271882
#271822
#271812
#271752
#271732
#271672
#271642
#271582
#237452
#236392
#236092
#234882
C2×#19472
#211562
#210592
#210522
#210352
#209152
#208812
#208492
#204152