Finite Group Databasebeta

← #6486889

Subgroups — #6486889

Order 512.

1534 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36635C211yesmaximal, characteristic, complemented
2C4×#529C211yesmaximal, characteristic
3#33085C212yesmaximal, complemented
4#33084C212yesmaximal, complemented
5#30020C212yesmaximal, complemented
6#30016C212yesmaximal
7#29540C212yesmaximal, complemented
8#29535C212yesmaximal, complemented
9#29415C212yesmaximal, complemented
10#29410C212yesmaximal
11#29198C211yesmaximal, characteristic, complemented
12#29184C211yesmaximal, characteristic, complemented
13#28660C211yesmaximal, characteristic, complemented
14#28620C211yesmaximal, characteristic, complemented
15#27896C211yesmaximal, characteristic, complemented
16#27882C211yesmaximal, characteristic, complemented
17#25678C211yesmaximal, characteristic
18#25604C211yesmaximal, characteristic
19#22273C211yesmaximal, characteristic, complemented
20#22250C211yesmaximal, characteristic, complemented
21#22225C211yesmaximal, characteristic, complemented
22#22223C211yesmaximal, characteristic, complemented
23#20778C211yesmaximal, characteristic, complemented
24C2×#529C2211yescharacteristic
25C2×#501C2211yescharacteristic
26C2×#497C2211yescharacteristic
27C2×#491C2211yescharacteristic
28C2×#489C2211yescharacteristic
29#2864—21no—
30#2863—21no—
31#2863C2212yes—
32#2862C2211yescharacteristic
33#2859C2211yescharacteristic
34#2857C2211yescharacteristic
35#2857C2211yescharacteristic
36#2855—21no—
37#2855C2212yes—
38#2851—21no—
39C4×C4⋊Q8C2211yescharacteristic
40C4×C4⋊Q8C2211yescharacteristic
41C4×#125—21no—
42C4×#125C2211yescharacteristic
43C4×#125C2211yescharacteristic
44C4×#126—21no—
45C4×#126—21no—
46C4×#124C2211yescharacteristic
47C4×#124C2211yescharacteristic
48C4×C22⋊Q8—21no—
49C4×C22⋊Q8C2212yes—
50C4×C22⋊Q8C2211yescharacteristic
51C4×C22⋊Q8C2211yescharacteristic
52C4×#123—21no—
53C4×#123—21no—
54C4×#121C2211yescharacteristic
55C4×#121C2211yescharacteristic
56#2298—21no—
57#2295—21no—
58#2295C2212yes—
59#2295C2211yescharacteristic
60#2293C2211yescharacteristic
61#2290—21no—
62#2283—21no—
63#2283C2211yescharacteristic
64C42×Q8C2211yescharacteristic
65C42×D4—21no—
66C42×D4C2211yescharacteristic
67C4×#117—21no—
68C2×C43C2211yescharacteristic
69#2088C2212yes—
70#2086C2212yes—
71#2077C2212yes—
72#2076C2212yes—
73#2068C2212yes—
74#2067C2212yes—
75#2066C2212yes—
76#2066C2212yes—
77#2056C2212yes—
78#2055C2212yes—
79#2036C2212yes—
80#2036C2212yes—
81#2035C2212yes—
82#2034C2212yes—
83#2001C2212yes—
84#2000C2212yes—
85#1993C2211yescharacteristic
86#1993C2211yescharacteristic
87#1992C2211yescharacteristic
88#1992C2211yescharacteristic
89#1960C2211yescharacteristic
90#1960C2211yescharacteristic
91#1959C2211yescharacteristic
92#1959C2211yescharacteristic
93#1928C2212yes—
94#1928C2212yes—
95#1928C2212yes—
96#1928C2212yes—
97#1927C2212yes—
98#1927C2212yes—
99#1927C2212yes—
100#1926C2212yes—
101#1921C2212yes—
102#1921C2212yes—
103#1920C2212yes—
104#1919C2212yes—
105#1919C2212yes—
106#1919C2212yes—
107#1918C2212yes—
108#1918C2212yes—
109#1880C2212yes—
110#1878C2212yes—
111#1878C2212yes—
112#1878C2212yes—
113#1878C2212yes—
114#1877C2212yes—
115#1877C2212yes—
116#1877C2212yes—
117#1865C2212yes—
118#1865C2212yes—
119#1865C2212yes—
120#1864C2212yes—
121#1863C2212yes—
122#1863C2212yes—
123#1862C2212yes—
124#1862C2212yes—
125#1847C2211yescharacteristic
126#1847C2211yescharacteristic
127#1839C2212yes—
128#1836C2211yescharacteristic
129#1836C2211yescharacteristic
130#1831C2212yes—
131#1817C2212yes—
132#1797C2212yes—
133#1767C2211yescharacteristic
134#1767C2211yescharacteristic
135#1749C2211yescharacteristic
136#1749C2211yescharacteristic
137#1745C2211yescharacteristic
138#1745C2211yescharacteristic
139C22×Q16C2312yes—
140C22×SD16C2312yes—
141C2×C4⋊Q8C2311yescharacteristic
142C2×C4⋊Q8C2311yescharacteristic
143#529—24no—
144#529—24no—
145C2×#126—21no—
146C2×#125—21no—
147C2×#125C2311yescharacteristic
148C2×#124C2311yescharacteristic
149C2×#123—21no—
150C2×C22⋊Q8—21no—
151C2×C22⋊Q8C2311yescharacteristic
152C2×C22⋊Q8C2312yes—
153C2×#121C2311yescharacteristic
154C2×C4×Q8—21no—
155C2×C4×Q8C2311yescharacteristic
156C2×C4×Q8C2312yes—
157C2×C4×Q8C2311yescharacteristic
158C2×C4×Q8C2311yescharacteristic
159C2×C4×D4—21no—
160C2×C4×D4—21no—
161C2×C4×D4—21no—
162C2×C4×D4C2311yescharacteristic
163C2×C4×D4C2311yescharacteristic
164C2×C4×D4C2311yescharacteristic
165C2×#117—21no—
166C2×#117—21no—
167C22×C42—21no—
168C22×C42D411yescharacteristic
169C22×C42D411yescharacteristic
170C22×C42D411yescharacteristic
171C22×C42D411yescharacteristic
172C22×C42C2311yescharacteristic
173C22×C42C2311yescharacteristic
174C22×C42C2311yescharacteristic
175#501—24no—
176#497—24no—
177#491—24no—
178#489—24no—
179C2×#107C2312yes—
180C2×#107C2312yes—
181C2×#107C2312yes—
182C2×#106C2312yes—
183C2×#106C2312yes—
184C2×#106C2312yes—
185C2×C4⋊C8C2312yes—
186C2×C4⋊C8C2312yes—
187C2×#103C2312yes—
188C2×#103C2312yes—
189C2×#103C2312yes—
190C2×#103C2312yes—
191C2×#103C2312yes—
192C2×#103C2312yes—
193C2×#103C2312yes—
194C2×#103C2312yes—
195C2×#103C2312yes—
196C2×#102C2312yes—
197C2×#102C2312yes—
198C2×#102C2312yes—
199C2×C22⋊C8C2312yes—
200C2×C22⋊C8C2312yes—
201C2×#97C2311yescharacteristic
202C2×#97C2311yescharacteristic
203C2×#97C2311yescharacteristic
204C2×#97C2311yescharacteristic
205#391—21no—
206#391—21no—
207#391—21no—
208#391—21no—
209#391C2312yes—
210#391C2312yes—
211#391C2311yescharacteristic
212#391C2312yes—
213#391C2312yes—
214#391C2311yescharacteristic
215#390C2311yescharacteristic
216#390C2311yescharacteristic
217#389—21no—
218#389—21no—
219#389—21no—
220#389—21no—
221#389—21no—
222#389—21no—
223#389—21no—
224#389—21no—
225#389C2311yescharacteristic
226#389C2311yescharacteristic
227#389C2311yescharacteristic
228#389C2311yescharacteristic
229#389C2312yes—
230#389C2312yes—
231#389C2312yes—
232#389C2312yes—
233#388—21no—
234#388—21no—
235#388—21no—
236#388—21no—
237#388—21no—
238#388—21no—
239#388—21no—
240#388—21no—
241#387—21no—
242#387—21no—
243#387—21no—
244#387—21no—
245#387—21no—
246#387—21no—
247#387—22no—
248#387—22no—
249#387—21no—
250#387—21no—
251#387—22no—
252#387—22no—
253#387—22no—
254#387—22no—
255#387—22no—
256#387—22no—
257#386—21no—
258#386—21no—
259#385—22no—
260#385—22no—
261#385—21no—
262#385—21no—
263#384C2311yescharacteristic
264#384C2311yescharacteristic
265#383—21no—
266#383—22no—
267#382—21no—
268#382—21no—
269#382—21no—
270#382C2311yescharacteristic
271#382C2311yescharacteristic
272#381—22no—
273#381—21no—
274#380—21no—
275#380—21no—
276#380—21no—
277#380C2311yescharacteristic
278#380C2312yes—
279#380C2311yescharacteristic
280C4×C4⋊C4—21no—
281C4×C4⋊C4—21no—
282C4×C4⋊C4—21no—
283C4×C4⋊C4—21no—
284C4×C4⋊C4—21no—
285C4×C4⋊C4—21no—
286C4×C4⋊C4—21no—
287C4×C4⋊C4—21no—
288C4×C4⋊C4—22no—
289C4×C4⋊C4—22no—
290C4×C4⋊C4—21no—
291C4×C4⋊C4—21no—
292C4×C4⋊C4—21no—
293C4×C4⋊C4—21no—
294C4×C4⋊C4—21no—
295C4×C4⋊C4C2311yescharacteristic
296C4×C4⋊C4C2311yescharacteristic
297C4×C4⋊C4C2311yescharacteristic
298C4×C4⋊C4C2311yescharacteristic
299C4×C4⋊C4C2312yes—
300C4×C4⋊C4C2311yescharacteristic
301C4×C4⋊C4C2311yescharacteristic
302C4×C22⋊C4—21no—
303C4×C22⋊C4—21no—
304C4×C22⋊C4—21no—
305C4×C22⋊C4—22no—
306C4×C22⋊C4—21no—
307C4×C22⋊C4—21no—
308C4×C22⋊C4—21no—
309C4×C22⋊C4—21no—
310C4×C22⋊C4—21no—
311C4×C22⋊C4—21no—
312C4×C22⋊C4—21no—
313C4×C22⋊C4—21no—
314C4×C22⋊C4—21no—
315C4×C22⋊C4—21no—
316#376—21no—
317#376—21no—
318#376—22no—
319C43—21no—
320C43D411yescharacteristic
321C43D411yescharacteristic
322C43D411yescharacteristic
323C43D411yescharacteristic
324C43C2311yescharacteristic
325C43C2311yescharacteristic
326C43C2311yescharacteristic
327C43C2311yescharacteristic
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×Q8C2412yes—
350C22×Q8C2411yescharacteristic
351C22×D4—21no—
352C22×D4C2411yescharacteristic
353C23×C4—21no—
354C23×C4—21no—
355C23×C4—21no—
356C23×C4C2×D411yescharacteristic
357C23×C4C2×D411yescharacteristic
358C23×C4C2×D411yescharacteristic
359C23×C4C2×D411yescharacteristic
360C23×C4C2×D411yescharacteristic
361C23×C4C2×D411yescharacteristic
362C23×C4C2411yescharacteristic
363C2×Q16—24no—
364C2×Q16—42no—
365C2×Q16—42no—
366C2×SD16—24no—
367C2×SD16—42no—
368C2×SD16—42no—
369C22×C8C2412yes—
370C22×C8C2412yes—
371C22×C8C2412yes—
372C22×C8C2412yes—
373C4⋊Q8—22no—
374C4⋊Q8—22no—
375C4⋊Q8—22no—
376C4⋊Q8—22no—
377#126—28no—
378#125—22no—
379#125—44no—
380#125#4114yes—
381#124—22no—
382#124#4114yes—
383#123—28no—
384C22⋊Q8—22no—
385C22⋊Q8—22no—
386C22⋊Q8—42no—
387C22⋊Q8—42no—
388C22⋊Q8—44no—
389#121—22no—
390#121—22no—
391C4×Q8—22no—
392C4×Q8—22no—
393C4×Q8—42no—
394C4×Q8—42no—
395C4×Q8—42no—
396C4×Q8—42no—
397C4×Q8—44no—
398C4×D4—28no—
399C4×D4—22no—
400C4×D4—22no—
401C4×D4—42no—
402C4×D4—42no—
403C4×D4—44no—
404C4×D4—44no—
405#117—28no—
406#117—44no—
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—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4C2411yescharacteristic
431C2×C4⋊C4C2411yescharacteristic
432C2×C4⋊C4C2411yescharacteristic
433C2×C4⋊C4C2411yescharacteristic
434C2×C4⋊C4C2412yes—
435C2×C4⋊C4C2412yes—
436C2×C4⋊C4C2412yes—
437C2×C4⋊C4C2411yescharacteristic
438C2×C4⋊C4C2411yescharacteristic
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C42—24no—
455C2×C42—21no—
456C2×C42—22no—
457C2×C42—22no—
458C2×C42—21no—
459C2×C42—21no—
460C2×C42—21no—
461C2×C42—22no—
462C2×C42—21no—
463C2×C42—21no—
464C2×C42—22no—
465C2×C42—21no—
466C2×C42—21no—
467C2×C42—21no—
468C2×C42—42no—
469C2×C42—42no—
470C2×C42—42no—
471C2×C42—42no—
472C2×C42—42no—
473C2×C42—44no—
474C2×C42C2×D411yescharacteristic
475C2×C42C2×D411yescharacteristic
476C2×C42C2×D411yescharacteristic
477C2×C42C2×D411yescharacteristic
478C2×C42C2×D411yescharacteristic
479C2×C42C2×D411yescharacteristic
480C2×C42C2×D411yescharacteristic
481C2×C42C2×D411yescharacteristic
482C2×C42C2×D411yescharacteristic
483C2×C42C2×D411yescharacteristic
484C2×C42C2×D411yescharacteristic
485C2×C42C2×D411yescharacteristic
486C2×C42C2×D411yescharacteristic
487C2×C42C2×D411yescharacteristic
488C2×C42C2×D411yescharacteristic
489C2×C42C2×D411yescharacteristic
490C2×C42C2×D411yescharacteristic
491C2×C42C2×D411yescharacteristic
492C2×C42C2×D411yescharacteristic
493C2×C42C2×D411yescharacteristic
494C2×C42C2×D411yescharacteristic
495C2×C42C2×D411yescharacteristic
496C2×C42C2411yescharacteristic
497C2×C42C2411yescharacteristic
498C2×C42C2411yescharacteristic
499C2×C42C2411yescharacteristic
500C2×C42C2411yescharacteristic
501C2×C42C2411yescharacteristic
502#107—24no—
503#107—42no—
504#107—42no—
505#106—24no—
506#106—42no—
507#106—42no—
508C4⋊C8—42no—
509C4⋊C8—42no—
510#103—24no—
511#103—24no—
512#103—24no—
513#103—42no—
514#103—42no—
515#103—42no—
516#103—42no—
517#103—42no—
518#103—42no—
519#102—24no—
520#102—42no—
521#102—42no—
522C22⋊C8—42no—
523C22⋊C8—42no—
524#97—22no—
525#97—22no—
526#97—22no—
527#97—22no—
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—22no—
537#95—22no—
538#95—22no—
539#95—22no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—21no—
544#95—21no—
545#95—21no—
546#95—21no—
547#95—21no—
548#95—21no—
549#95—22no—
550#95—22no—
551#95—21no—
552#95—21no—
553#95—21no—
554#95—22no—
555#95—22no—
556#95—22no—
557#95—22no—
558#95—22no—
559#95—22no—
560#95—22no—
561#95—22no—
562C24—21no—
563C24C22×D411yescharacteristic
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—22no—
572C2×Q8—22no—
573C2×Q8—42no—
574C2×Q8—42no—
575C2×Q8—42no—
576C2×Q8C2×#4112yes—
577C2×D4—24no—
578C2×D4—21no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4C2×#4112yes—
584C22×C4—24no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4#13714yes—
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×C4C22×D411yescharacteristic
635C22×C4C22×D411yescharacteristic
636C22×C4C22×D411yescharacteristic
637C22×C4C22×D411yescharacteristic
638C22×C4C22×D411yescharacteristic
639C22×C4C2511yescharacteristic
640Q16—84no—
641SD16—84no—
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—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—22no—
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—44no—
676C4⋊C4—42no—
677C4⋊C4—44no—
678C4⋊C4—42no—
679C4⋊C4—42no—
680C4⋊C4—44no—
681C4⋊C4—42no—
682C4⋊C4—42no—
683C4⋊C4—42no—
684C4⋊C4—42no—
685C4⋊C4—42no—
686C4⋊C4—44no—
687C4⋊C4—44no—
688C4⋊C4—44no—
689C4⋊C4C2×#4112yes—
690C4⋊C4C2×#4112yes—
691C22⋊C4—24no—
692C22⋊C4—24no—
693C22⋊C4—24no—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—42no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4—42no—
701C22⋊C4—44no—
702C22⋊C4—44no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—42no—
706C42—24no—
707C42—22no—
708C42—22no—
709C42—22no—
710C42—22no—
711C42—22no—
712C42—22no—
713C42—22no—
714C42—22no—
715C42—22no—
716C42—22no—
717C42—22no—
718C42—22no—
719C42—21no—
720C42—21no—
721C42—22no—
722C42—22no—
723C42—22no—
724C42—22no—
725C42—41no—
726C42—41no—
727C42—41no—
728C42—41no—
729C42—41no—
730C42—41no—
731C42—41no—
732C42—41no—
733C42—41no—
734C42—41no—
735C42—42no—
736C42—42no—
737C42—42no—
738C42—44no—
739C42—42no—
740C42—42no—
741C42—44no—
742C42—42no—
743C42—42no—
744C42—42no—
745C42C2×#4112yes—
746C42C2×#4112yes—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—22no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23C2×#13712yes—
761C23C23×D411yescharacteristic
762Q8—24no—
763Q8—42no—
764Q8—42no—
765Q8—42no—
766Q8—42no—
767Q8—42no—
768Q8—84no—
769D4—24no—
770D4—48no—
771D4—42no—
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—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—48no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—41no—
825C2×C4—42no—
826C2×C4—41no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—42no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—41no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—84no—
847C2×C4—84no—
848C2×C4#52512yes—
849C2×C4#52512yes—
850C2×C4C2×#13712yes—
851C2×C4C2×#13712yes—
852C2×C4#57512yes—
853C2×C4#57512yes—
854C2×C4#57512yes—
855C2×C4C22×#4111yescharacteristic
856C2×C4C22×#4111yescharacteristic
857C2×C4#58512yes—
858C2×C4#58512yes—
859C8—42no—
860C8—42no—
861C8—42no—
862C8—42no—
863C22—22no—
864C22—22no—
865C22—22no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22C2×#52511yescharacteristic
878C22#344911yescharacteristic
879C22#344911yescharacteristic
880C22C22×#13711yescharacteristic
881C22C2×#57511yescharacteristic
882C22C2×#57511yescharacteristic
883C22C2×#57511yescharacteristic
884C4—22no—
885C4—22no—
886C4—22no—
887C4—22no—
888C4—22no—
889C4—22no—
890C4—22no—
891C4—41no—
892C4—41no—
893C4—41no—
894C4—41no—
895C4—41no—
896C4—42no—
897C4—41no—
898C4—42no—
899C4—42no—
900C4—81no—
901C4—81no—
902C4—82no—
903C4—82no—
904C4—81no—
905C4—81no—
906C4—82no—
907C4—82no—
908C4#352112yes—
909C4#352412yes—
910C2—42no—
911C2—82no—
912C2#3521111yescharacteristic
913C2#6056211yescharacteristic
914C2#6056311yescharacteristic
915C2#6095211yescharacteristic
916C2#6095311yescharacteristic
917C2#6095911yescharacteristic
918C2#6096011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C43 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36635C2semidirect
3. #33085C2semidirect
4. #33084C2semidirect
5. #30020C2semidirect
7. #29540C2semidirect
8. #29535C2semidirect
9. #29415C2semidirect
11. #29198C2semidirect
12. #29184C2semidirect
13. #28660C2semidirect
14. #28620C2semidirect
15. #27896C2semidirect
16. #27882C2semidirect
19. #22273C2semidirect
20. #22250C2semidirect
21. #22225C2semidirect
22. #22223C2semidirect
23. #20778C2semidirect

Maximal subgroups

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

subgroupindex
#366352
C4×#5292
#330852
#330842
#300202
#300162
#295402
#295352
#294152
#294102
#291982
#291842
#286602
#286202
#278962
#278822
#256782
#256042
#222732
#222502
#222252
#222232
#207782