Finite Group Databasebeta

← #6480951

Subgroups — #6480951

Order 512.

1412 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2645C211yesmaximal, characteristic
2#34221C211yesmaximal, characteristic
3#33093C212yesmaximal, complemented
4#33091C212yesmaximal, complemented
5#30159C212yesmaximal, complemented
6#30140C212yesmaximal, complemented
7#29526C212yesmaximal, complemented
8#29509C212yesmaximal, complemented
9#29454C212yesmaximal, complemented
10#29438C212yesmaximal, complemented
11#29244C211yesmaximal, characteristic
12#29243C211yesmaximal, characteristic
13#28121C211yesmaximal, characteristic
14#28121C211yesmaximal, characteristic
15#27617C211yesmaximal, characteristic
16#27589C211yesmaximal, characteristic
17#24064C211yesmaximal, characteristic
18#23934C211yesmaximal, characteristic
19#22085C211yesmaximal, characteristic
20#22079C211yesmaximal, characteristic
21#22050C211yesmaximal, characteristic
22#22044C211yesmaximal, characteristic
23#20779C211yesmaximal, characteristic
24C2×#533C2211yescharacteristic
25C2×#484C2211yescharacteristic
26C2×#484C2211yescharacteristic
27C2×#451C2211yescharacteristic
28C2×#451C2211yescharacteristic
29#2645—21no—
30#2645—21no—
31#2645—21no—
32#2645—21no—
33#2645C2212yes—
34#2645C2212yes—
35#2645C2212yes—
36#2645C2212yes—
37C2×#401—21no—
38C2×#400—21no—
39C2×#400—21no—
40C2×#400—21no—
41#2371—21no—
42#2371—21no—
43#2368—21no—
44#2368—21no—
45#2356—21no—
46#2356—21no—
47#2343—21no—
48#2343—21no—
49#2331C2211yescharacteristic
50#2331C2211yescharacteristic
51#2327C2211yescharacteristic
52#2327C2211yescharacteristic
53#2320C2211yescharacteristic
54#2320C2211yescharacteristic
55C4×C22⋊Q8C2211yescharacteristic
56C4×C22⋊Q8C2211yescharacteristic
57C4×C22⋊Q8C2211yescharacteristic
58C4×C22⋊Q8C2211yescharacteristic
59C2×#391C2211yescharacteristic
60C2×#391C2211yescharacteristic
61C2×#391C2211yescharacteristic
62C2×#389C2211yescharacteristic
63C2×#389C2211yescharacteristic
64C2×#389C2211yescharacteristic
65#2283C2211yescharacteristic
66#2276C2211yescharacteristic
67#2276C2211yescharacteristic
68C2×#376C2211yescharacteristic
69#2101C2212yes—
70#2097C2212yes—
71#2088C2212yes—
72#2086C2212yes—
73#2085C2212yes—
74#2074C2212yes—
75#2068C2212yes—
76#2068C2212yes—
77#2068C2212yes—
78#2066C2212yes—
79#2057C2212yes—
80#2056C2212yes—
81#2056C2212yes—
82#2043C2212yes—
83#2024C2212yes—
84#2016C2212yes—
85#1971C2212yes—
86#1969C2212yes—
87#1943C2212yes—
88#1942C2212yes—
89#1935C2212yes—
90#1935C2212yes—
91#1933C2212yes—
92#1933C2212yes—
93#1928C2212yes—
94#1928C2212yes—
95#1928C2212yes—
96#1928C2212yes—
97#1927C2212yes—
98#1927C2212yes—
99#1921C2212yes—
100#1920C2212yes—
101#1919C2212yes—
102#1918C2212yes—
103#1918C2212yes—
104#1918C2212yes—
105#1878C2212yes—
106#1878C2212yes—
107#1878C2212yes—
108#1878C2212yes—
109#1878C2212yes—
110#1878C2212yes—
111#1872C2211yescharacteristic
112#1872C2211yescharacteristic
113#1872C2211yescharacteristic
114#1872C2211yescharacteristic
115#1865C2212yes—
116#1865C2212yes—
117#1863C2212yes—
118#1863C2212yes—
119#1863C2212yes—
120#1863C2212yes—
121#1853C2211yescharacteristic
122#1853C2211yescharacteristic
123#1852C2211yescharacteristic
124#1852C2211yescharacteristic
125#1840C2212yes—
126#1832C2212yes—
127#1824C2211yescharacteristic
128#1824C2211yescharacteristic
129#1817C2211yescharacteristic
130#1817C2211yescharacteristic
131#1797C2211yescharacteristic
132#1797C2211yescharacteristic
133#1787C2211yescharacteristic
134#1787C2211yescharacteristic
135#1768C2212yes—
136#1749C2211yescharacteristic
137C4×C22⋊C8C2211yescharacteristic
138#1746C2212yes—
139C23×Q8C2311yescharacteristic
140C22×Q16C2312yes—
141C22×Q16C2312yes—
142#533—24no—
143#533—24no—
144C2×C4⋊Q8C2311yescharacteristic
145C2×C4⋊Q8C2311yescharacteristic
146C2×#125—21no—
147C2×C22⋊Q8—21no—
148C2×C22⋊Q8C2311yescharacteristic
149C2×C22⋊Q8C2311yescharacteristic
150C2×C4×Q8—21no—
151C2×C4×Q8C2311yescharacteristic
152C2×C4×Q8C2311yescharacteristic
153C2×C4×Q8C2311yescharacteristic
154C2×C4×Q8C2311yescharacteristic
155C2×C4×Q8C2311yescharacteristic
156C2×C4×Q8C2311yescharacteristic
157C2×#117—21no—
158C22×C4⋊C4—21no—
159C22×C4⋊C4—21no—
160C22×C4⋊C4—21no—
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2311yescharacteristic
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166C22×C42C2311yescharacteristic
167#484—24no—
168#484—24no—
169#451—24no—
170#451—24no—
171C2×#107C2312yes—
172C2×#107C2312yes—
173C2×#107C2312yes—
174C2×#107C2312yes—
175C2×#106C2312yes—
176C2×#106C2312yes—
177C2×C4⋊C8C2312yes—
178C2×C4⋊C8C2312yes—
179C2×#103C2312yes—
180C2×#103C2312yes—
181C2×#103C2312yes—
182C2×#103C2312yes—
183C2×#103C2312yes—
184C2×#103C2312yes—
185C2×#103C2312yes—
186C2×#103C2312yes—
187C2×#103C2312yes—
188C2×#103C2312yes—
189C2×#103C2312yes—
190C2×#103C2312yes—
191C2×C22⋊C8C2311yescharacteristic
192C2×C22⋊C8C2311yescharacteristic
193C2×C22⋊C8C2311yescharacteristic
194C2×C22⋊C8C2311yescharacteristic
195C2×#97C2312yes—
196C2×C4×C8C2312yes—
197#401—22no—
198#401—22no—
199#401—22no—
200#401—22no—
201#400—22no—
202#400—22no—
203#400—22no—
204#400—22no—
205#400—22no—
206#400—22no—
207#400—22no—
208#400—22no—
209#400—22no—
210#400—22no—
211#400—22no—
212#400—22no—
213#391—21no—
214#391—21no—
215#391—21no—
216#391—21no—
217#391—21no—
218#391—21no—
219#391—21no—
220#391—21no—
221#391—21no—
222#391—21no—
223#391C2311yescharacteristic
224#391C2311yescharacteristic
225#391C2312yes—
226#391C2311yescharacteristic
227#391C2311yescharacteristic
228#391C2312yes—
229#391C2312yes—
230#391C2312yes—
231#391C2312yes—
232#391C2312yes—
233#389—21no—
234#389—21no—
235#389—21no—
236#389—21no—
237#389—21no—
238#389—21no—
239#389C2312yes—
240#389C2311yescharacteristic
241#389C2311yescharacteristic
242#389C2311yescharacteristic
243#389C2311yescharacteristic
244#389C2312yes—
245#389C2312yes—
246#389C2312yes—
247#389C2312yes—
248#389C2312yes—
249#387—21no—
250#387—21no—
251#387—21no—
252#387—21no—
253#387—21no—
254#387—21no—
255#387—21no—
256#387—21no—
257#387—21no—
258#387—21no—
259#387—21no—
260#387—21no—
261#387—21no—
262#387—21no—
263#387—21no—
264#387—21no—
265#387—21no—
266#387—21no—
267#387—21no—
268#387—21no—
269#385—21no—
270#385—21no—
271#385—21no—
272#385—21no—
273#383—21no—
274#383—21no—
275#383—21no—
276#382—21no—
277#382—21no—
278#382C2311yescharacteristic
279#382C2311yescharacteristic
280#381—21no—
281#380C2311yescharacteristic
282#380C2311yescharacteristic
283C4×C4⋊C4—21no—
284C4×C4⋊C4—21no—
285C4×C4⋊C4—21no—
286C4×C4⋊C4—21no—
287C4×C4⋊C4—21no—
288C4×C4⋊C4—21no—
289C4×C4⋊C4—21no—
290C4×C4⋊C4—21no—
291C4×C4⋊C4—21no—
292C4×C4⋊C4—21no—
293C4×C4⋊C4C2311yescharacteristic
294C4×C4⋊C4C2311yescharacteristic
295C4×C4⋊C4C2311yescharacteristic
296C4×C4⋊C4C2311yescharacteristic
297C4×C4⋊C4C2311yescharacteristic
298C4×C4⋊C4C2311yescharacteristic
299C4×C22⋊C4—21no—
300C4×C22⋊C4—21no—
301C4×C22⋊C4—21no—
302C4×C22⋊C4—21no—
303C4×C22⋊C4—21no—
304#376—21no—
305#376—21no—
306#376—21no—
307#376D411yescharacteristic
308#376D411yescharacteristic
309#376D411yescharacteristic
310#376D411yescharacteristic
311#376C2311yescharacteristic
312#376C2311yescharacteristic
313#376C2311yescharacteristic
314#376C2311yescharacteristic
315C2×#95—21no—
316C2×#95—21no—
317C2×#95—21no—
318C2×#95—21no—
319C2×#95—21no—
320C2×#95—21no—
321C2×#95—21no—
322C2×#95—21no—
323C2×#95—21no—
324C2×#95D411yescharacteristic
325C2×#95D411yescharacteristic
326C2×#95D411yescharacteristic
327C2×#95D411yescharacteristic
328#340C2312yes—
329#340C2312yes—
330#340C2312yes—
331#340C2312yes—
332#340C2312yes—
333#340C2312yes—
334#340C2312yes—
335#340C2312yes—
336#340C2312yes—
337#340C2312yes—
338#340C2312yes—
339#340C2312yes—
340#336C2312yes—
341#336C2312yes—
342#336C2312yes—
343#336C2312yes—
344#336C2312yes—
345#336C2312yes—
346#336C2312yes—
347#336C2312yes—
348C22×Q8—21no—
349C22×Q8—21no—
350C22×Q8—22no—
351C22×Q8—22no—
352C22×Q8—42no—
353C22×Q8—42no—
354C22×Q8C2412yes—
355C22×Q8C2411yescharacteristic
356C22×Q8C2411yescharacteristic
357C23×C4—21no—
358C23×C4—21no—
359C23×C4—21no—
360C23×C4—21no—
361C23×C4C2×D411yescharacteristic
362C23×C4C2×D411yescharacteristic
363C23×C4C2×D411yescharacteristic
364C23×C4C2×D411yescharacteristic
365C23×C4C2×D411yescharacteristic
366C23×C4C2×D411yescharacteristic
367C23×C4C2411yescharacteristic
368C2×Q16—24no—
369C2×Q16—24no—
370C2×Q16—42no—
371C2×Q16—42no—
372C2×Q16—42no—
373C2×Q16—42no—
374C22×C8C2412yes—
375C22×C8C2412yes—
376C22×C8C2412yes—
377C22×C8C2412yes—
378C4⋊Q8—22no—
379C4⋊Q8—22no—
380C4⋊Q8—22no—
381C4⋊Q8—22no—
382#125—28no—
383C22⋊Q8—28no—
384C22⋊Q8—22no—
385C22⋊Q8—22no—
386C22⋊Q8#4114yes—
387C22⋊Q8#4114yes—
388C4×Q8—28no—
389C4×Q8—22no—
390C4×Q8—22no—
391C4×Q8—22no—
392C4×Q8—22no—
393C4×Q8—42no—
394C4×Q8—42no—
395C4×Q8—42no—
396C4×Q8—42no—
397#117—28no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—42no—
425C2×C4⋊C4—42no—
426C2×C4⋊C4—82no—
427C2×C4⋊C4—82no—
428C2×C4⋊C4—82no—
429C2×C4⋊C4C2412yes—
430C2×C4⋊C4C2412yes—
431C2×C4⋊C4C2412yes—
432C2×C4⋊C4C2411yescharacteristic
433C2×C4⋊C4C2411yescharacteristic
434C2×C4⋊C4C2411yescharacteristic
435C2×C4⋊C4C2411yescharacteristic
436C2×C4⋊C4C2411yescharacteristic
437C2×C4⋊C4C2411yescharacteristic
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C42—21no—
443C2×C42—21no—
444C2×C42—22no—
445C2×C42—22no—
446C2×C42—21no—
447C2×C42—21no—
448C2×C42—21no—
449C2×C42—21no—
450C2×C42—21no—
451C2×C42—21no—
452C2×C42—21no—
453C2×C42—21no—
454C2×C42—21no—
455C2×C42—21no—
456C2×C42—42no—
457C2×C42—42no—
458C2×C42C2×D411yescharacteristic
459C2×C42C2×D411yescharacteristic
460C2×C42C2×D411yescharacteristic
461C2×C42C2×D411yescharacteristic
462C2×C42C2×D411yescharacteristic
463C2×C42C2×D411yescharacteristic
464C2×C42C2411yescharacteristic
465C2×C42C2411yescharacteristic
466C2×C42C2411yescharacteristic
467C2×C42C2411yescharacteristic
468C2×C42C2411yescharacteristic
469C2×C42C2411yescharacteristic
470#107—24no—
471#107—24no—
472#107—42no—
473#107—42no—
474#106—42no—
475#106—42no—
476C4⋊C8—42no—
477C4⋊C8—42no—
478#103—24no—
479#103—24no—
480#103—24no—
481#103—24no—
482#103—42no—
483#103—42no—
484#103—42no—
485#103—42no—
486#103—42no—
487#103—42no—
488#103—42no—
489#103—42no—
490C22⋊C8—22no—
491C22⋊C8—22no—
492C22⋊C8—22no—
493C22⋊C8—22no—
494#97—42no—
495C4×C8—42no—
496#95—22no—
497#95—22no—
498#95—22no—
499#95—22no—
500#95—22no—
501#95—22no—
502#95—22no—
503#95—22no—
504#95—22no—
505#95—22no—
506#95—22no—
507#95—22no—
508#95—22no—
509#95—22no—
510#95—22no—
511#95—22no—
512#95—22no—
513#95—22no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—21no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95—21no—
534#95—21no—
535#95—21no—
536#95—21no—
537#95—21no—
538#95C2×D411yescharacteristic
539#95C2×D411yescharacteristic
540#95C2×D411yescharacteristic
541#95C2×D411yescharacteristic
542#95C2×D411yescharacteristic
543#95C2×D411yescharacteristic
544#95C2×D411yescharacteristic
545#95C2×D411yescharacteristic
546#95C2×D411yescharacteristic
547#95C2×D411yescharacteristic
548#95C2×D411yescharacteristic
549#95C2×D411yescharacteristic
550#95C2×D411yescharacteristic
551#95C2×D411yescharacteristic
552#95C2×D411yescharacteristic
553#95C2×D411yescharacteristic
554C24C22×D411yescharacteristic
555C2×Q8—24no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8—22no—
563C2×Q8—22no—
564C2×Q8—22no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—42no—
569C2×Q8—42no—
570C2×Q8—42no—
571C2×Q8—81no—
572C2×Q8—81no—
573C2×Q8—84no—
574C2×Q8—84no—
575C2×Q8C2×#4112yes—
576C2×Q8C2×#4112yes—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C22×D411yescharacteristic
626C22×C4C22×D411yescharacteristic
627C22×C4C22×D411yescharacteristic
628C22×C4C22×D411yescharacteristic
629C22×C4C22×D411yescharacteristic
630C22×C4C22×D411yescharacteristic
631C22×C4C22×D411yescharacteristic
632C22×C4C22×D411yescharacteristic
633C22×C4C22×D411yescharacteristic
634C22×C4C2×#4112yes—
635C22×C4C2×#4112yes—
636C22×C4C2511yescharacteristic
637Q16—84no—
638Q16—84no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—22no—
649C2×C8—22no—
650C2×C8—22no—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—24no—
654C4⋊C4—24no—
655C4⋊C4—24no—
656C4⋊C4—24no—
657C4⋊C4—24no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—81no—
678C4⋊C4—81no—
679C4⋊C4—81no—
680C4⋊C4—81no—
681C4⋊C4—82no—
682C4⋊C4—82no—
683C4⋊C4—82no—
684C4⋊C4—82no—
685C4⋊C4—82no—
686C4⋊C4—82no—
687C4⋊C4C2×#4112yes—
688C4⋊C4C2×#4112yes—
689C22⋊C4—24no—
690C22⋊C4—24no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C42—24no—
694C42—24no—
695C42—22no—
696C42—22no—
697C42—21no—
698C42—21no—
699C42—21no—
700C42—21no—
701C42—22no—
702C42—22no—
703C42—22no—
704C42—22no—
705C42—41no—
706C42—41no—
707C42—41no—
708C42—41no—
709C42—42no—
710C42—42no—
711C42—42no—
712C42—42no—
713C42—81no—
714C42—81no—
715C42—81no—
716C42—81no—
717C42—81no—
718C42—81no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23#52512yes—
724C23#57812yes—
725C23#57812yes—
726C23C23×D411yescharacteristic
727Q8—24no—
728Q8—24no—
729Q8—42no—
730Q8—42no—
731Q8—42no—
732Q8—42no—
733Q8—42no—
734Q8—42no—
735Q8—84no—
736Q8—84no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—44no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—82no—
815C2×C4—82no—
816C2×C4—82no—
817C2×C4—82no—
818C2×C4—82no—
819C2×C4—84no—
820C2×C4—84no—
821C2×C4—84no—
822C2×C4—84no—
823C2×C4#52512yes—
824C2×C4C22×#4111yescharacteristic
825C2×C4C22×#4111yescharacteristic
826C2×C4#58512yes—
827C2×C4#58512yes—
828C8—42no—
829C8—42no—
830C8—42no—
831C8—42no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22#312714yes—
839C22C2×#52511yescharacteristic
840C22#344911yescharacteristic
841C22#344911yescharacteristic
842C22C2×#57811yescharacteristic
843C22C2×#57811yescharacteristic
844C22#358511yescharacteristic
845C22#358611yescharacteristic
846C4—22no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—41no—
851C4—41no—
852C4—41no—
853C4—41no—
854C4—41no—
855C4—42no—
856C4—42no—
857C4—41no—
858C4—41no—
859C4—41no—
860C4—41no—
861C4—42no—
862C4—42no—
863C4—81no—
864C4—81no—
865C4—82no—
866C4—82no—
867C4—81no—
868C4—81no—
869C4—82no—
870C4—82no—
871C4#352112yes—
872C4#352112yes—
873C2—24no—
874C2#3514311yescharacteristic
875C2C2×#312711yescharacteristic
876C2#6056711yescharacteristic
877C2#6098111yescharacteristic
878C2#6098111yescharacteristic
879C2#6098311yescharacteristic
880C2#6098311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#376 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #33093C2semidirect
4. #33091C2semidirect
5. #30159C2semidirect
6. #30140C2semidirect
7. #29526C2semidirect
8. #29509C2semidirect
9. #29454C2semidirect
10. #29438C2semidirect

Maximal subgroups

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

subgroupindex
C2×#26452
#342212
#330932
#330912
#301592
#301402
#295262
#295092
#294542
#294382
#292442
#292432
#281212
#276172
#275892
#240642
#239342
#220852
#220792
#220502
#220442
#207792