Finite Group Databasebeta

← #6464542

Subgroups — #6464542

Order 512.

1627 conjugacy classes of subgroups.

The subgroup lattice has 917 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36638C211yesmaximal, characteristic
2C4×#533C211yesmaximal, characteristic, complemented
3#29482C212yesmaximal
4#29478C212yesmaximal, complemented
5#29450C212yesmaximal, complemented
6#29446C212yesmaximal, complemented
7#29196C211yesmaximal, characteristic, complemented
8#29182C211yesmaximal, characteristic, complemented
9#28659C211yesmaximal, characteristic, complemented
10#28619C211yesmaximal, characteristic, complemented
11#27895C211yesmaximal, characteristic
12#27881C211yesmaximal, characteristic, complemented
13#25677C211yesmaximal, characteristic, complemented
14#25603C211yesmaximal, characteristic
15#23700C212yesmaximal
16#23698C212yesmaximal, complemented
17C4×#501C211yesmaximal, characteristic, complemented
18C4×#497C211yesmaximal, characteristic, complemented
19C4×#491C211yesmaximal, characteristic, complemented
20C4×#489C211yesmaximal, characteristic, complemented
21#21120C212yesmaximal, complemented
22#21116C212yesmaximal, complemented
23#20463C211yesmaximal, characteristic, complemented
24C2×#533C2211yescharacteristic
25C2×#501C2211yescharacteristic
26C2×#497C2211yescharacteristic
27C2×#491C2211yescharacteristic
28C2×#489C2211yescharacteristic
29C2×C4×Q16C2212yes—
30C2×C4×SD16C2212yes—
31C2×#431C2212yes—
32#2866—21no—
33#2865—21no—
34#2864C2211yescharacteristic
35#2863C2211yescharacteristic
36#2861C2211yescharacteristic
37#2860C2211yescharacteristic
38#2855C2211yescharacteristic
39#2854C2211yescharacteristic
40#2853—21no—
41#2852—21no—
42#2851C2211yescharacteristic
43#2850C2211yescharacteristic
44C4×C4⋊Q8C2211yescharacteristic
45C4×C4⋊Q8C2211yescharacteristic
46C4×C4⋊Q8C2211yescharacteristic
47C4×C4⋊Q8C2211yescharacteristic
48C4×#125—21no—
49C4×#125—21no—
50C4×#125C2211yescharacteristic
51C4×#126—21no—
52C4×#124C2211yescharacteristic
53C4×C22⋊Q8—21no—
54C4×C22⋊Q8—21no—
55C4×C22⋊Q8C2211yescharacteristic
56C4×C22⋊Q8C2212yes—
57C4×C22⋊Q8C2212yes—
58C4×#123—21no—
59C4×#121C2211yescharacteristic
60#2298—21no—
61#2296—21no—
62#2295—21no—
63#2295C2212yes—
64#2295C2211yescharacteristic
65#2293C2211yescharacteristic
66#2290—21no—
67#2285C2211yescharacteristic
68C42×Q8—21no—
69C42×Q8C2212yes—
70C4×#117—21no—
71C2×C43C2211yescharacteristic
72#2088C2212yes—
73#2087C2212yes—
74#2077C2212yes—
75#2076C2212yes—
76#2068C2212yes—
77#2068C2212yes—
78#2066C2212yes—
79#2065C2212yes—
80#2056C2212yes—
81#2055C2212yes—
82#2036C2212yes—
83#2036C2212yes—
84#2035C2212yes—
85#2034C2212yes—
86#2001C2212yes—
87#2000C2212yes—
88#1993C2211yescharacteristic
89#1993C2211yescharacteristic
90#1992C2211yescharacteristic
91#1992C2211yescharacteristic
92#1973C2212yes—
93#1971C2212yes—
94#1960C2211yescharacteristic
95#1960C2211yescharacteristic
96#1959C2211yescharacteristic
97#1959C2211yescharacteristic
98#1944C2212yes—
99#1943C2212yes—
100#1936C2212yes—
101#1935C2212yes—
102#1935C2212yes—
103#1935C2212yes—
104#1927C2212yes—
105#1927C2212yes—
106#1925C2212yes—
107#1925C2212yes—
108#1920C2212yes—
109#1920C2212yes—
110#1918C2212yes—
111#1918C2212yes—
112#1880C2212yes—
113#1880C2212yes—
114#1878C2212yes—
115#1878C2212yes—
116#1865C2212yes—
117#1865C2212yes—
118#1863C2212yes—
119#1863C2212yes—
120#1847C2211yescharacteristic
121#1847C2211yescharacteristic
122#1836C2211yescharacteristic
123#1836C2211yescharacteristic
124C4×#107C2212yes—
125C4×#106C2212yes—
126#1767C2212yes—
127#1767C2211yescharacteristic
128#1767C2211yescharacteristic
129C4×#103C2212yes—
130C4×#103C2212yes—
131C4×#103C2212yes—
132C4×#102C2212yes—
133#1749C2211yescharacteristic
134#1749C2212yes—
135#1749C2211yescharacteristic
136#1744C2212yes—
137C4×#97C2211yescharacteristic
138C4×#97C2211yescharacteristic
139C22×Q16C2312yes—
140C22×SD16C2312yes—
141#533—24no—
142#533—24no—
143C2×C4⋊Q8C2311yescharacteristic
144C2×C4⋊Q8C2311yescharacteristic
145C2×#126—21no—
146C2×#125—21no—
147C2×#125C2311yescharacteristic
148C2×#124C2311yescharacteristic
149C2×#123—21no—
150C2×C22⋊Q8—21no—
151C2×C22⋊Q8C2312yes—
152C2×C22⋊Q8C2311yescharacteristic
153C2×#121C2311yescharacteristic
154C2×C4×Q8—21no—
155C2×C4×Q8—21no—
156C2×C4×Q8—21no—
157C2×C4×Q8C2312yes—
158C2×C4×Q8C2312yes—
159C2×C4×Q8C2311yescharacteristic
160C2×C4×Q8C2312yes—
161C2×C4×D4—21no—
162C2×C4×D4C2311yescharacteristic
163C2×#117—21no—
164C2×#117—21no—
165C2×#117—21no—
166C22×C42D411yescharacteristic
167C22×C42D411yescharacteristic
168C22×C42D411yescharacteristic
169C22×C42D411yescharacteristic
170C22×C42C2311yescharacteristic
171C22×C42C2311yescharacteristic
172C22×C42C2311yescharacteristic
173#501—24no—
174#497—24no—
175#491—24no—
176#489—24no—
177C4×Q16—28no—
178C4×SD16—28no—
179#431—28no—
180C2×#107C2312yes—
181C2×#107C2312yes—
182C2×#107C2312yes—
183C2×#106C2312yes—
184C2×#106C2312yes—
185C2×#106C2312yes—
186C2×C4⋊C8C2312yes—
187C2×C4⋊C8C2312yes—
188C2×#103C2312yes—
189C2×#103C2312yes—
190C2×#103C2312yes—
191C2×#103C2312yes—
192C2×#103C2312yes—
193C2×#103C2312yes—
194C2×#103C2312yes—
195C2×#103C2312yes—
196C2×#103C2312yes—
197C2×#102C2312yes—
198C2×#102C2312yes—
199C2×#102C2312yes—
200C2×C22⋊C8C2312yes—
201C2×C22⋊C8C2312yes—
202C2×#97C2311yescharacteristic
203C2×#97C2311yescharacteristic
204C2×#97C2311yescharacteristic
205C2×#97C2311yescharacteristic
206C2×#97C2312yes—
207C2×#97C2312yes—
208C2×C4×C8C2312yes—
209C2×C4×C8C2312yes—
210#391—21no—
211#391—21no—
212#391C2312yes—
213#391C2312yes—
214#391C2311yescharacteristic
215#391C2311yescharacteristic
216#391C2311yescharacteristic
217#391C2311yescharacteristic
218#390C2311yescharacteristic
219#390C2311yescharacteristic
220#390C2311yescharacteristic
221#390C2311yescharacteristic
222#389—21no—
223#389—21no—
224#389—21no—
225#389—21no—
226#389—21no—
227#389—21no—
228#389C2311yescharacteristic
229#389C2311yescharacteristic
230#389C2312yes—
231#389C2312yes—
232#389C2311yescharacteristic
233#389C2311yescharacteristic
234#389C2311yescharacteristic
235#389C2311yescharacteristic
236#389C2311yescharacteristic
237#389C2311yescharacteristic
238#388—21no—
239#388—21no—
240#388—21no—
241#388—21no—
242#388—21no—
243#388—21no—
244#388—21no—
245#388—21no—
246#388—21no—
247#388—21no—
248#388—21no—
249#388—21no—
250#388—21no—
251#388—21no—
252#388—21no—
253#388—21no—
254#387—21no—
255#387—21no—
256#387—21no—
257#387—22no—
258#387—22no—
259#387—22no—
260#387—22no—
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#387—21no—
270#387—21no—
271#387—21no—
272#387—21no—
273#387—21no—
274#386—21no—
275#386—21no—
276#386—21no—
277#386—21no—
278#385—21no—
279#385—21no—
280#385—21no—
281#385—21no—
282#385—22no—
283#385—22no—
284#384C2311yescharacteristic
285#384C2311yescharacteristic
286#383—21no—
287#382—21no—
288#382C2311yescharacteristic
289#382C2311yescharacteristic
290#381—21no—
291#380—21no—
292#380C2311yescharacteristic
293#380C2312yes—
294#380C2311yescharacteristic
295C4×C4⋊C4—21no—
296C4×C4⋊C4—21no—
297C4×C4⋊C4—21no—
298C4×C4⋊C4—21no—
299C4×C4⋊C4—21no—
300C4×C4⋊C4—21no—
301C4×C4⋊C4—21no—
302C4×C4⋊C4—22no—
303C4×C4⋊C4—22no—
304C4×C4⋊C4—22no—
305C4×C4⋊C4—22no—
306C4×C4⋊C4—21no—
307C4×C4⋊C4—21no—
308C4×C4⋊C4—21no—
309C4×C4⋊C4—21no—
310C4×C4⋊C4—22no—
311C4×C4⋊C4—22no—
312C4×C4⋊C4C2311yescharacteristic
313C4×C4⋊C4C2311yescharacteristic
314C4×C4⋊C4C2312yes—
315C4×C4⋊C4C2312yes—
316C4×C4⋊C4C2312yes—
317C4×C22⋊C4—22no—
318C4×C22⋊C4—22no—
319C4×C22⋊C4—21no—
320C4×C22⋊C4—21no—
321C4×C22⋊C4—21no—
322C4×C22⋊C4—21no—
323C4×C22⋊C4—21no—
324#376—22no—
325#376—21no—
326C43—22no—
327C43D411yescharacteristic
328C43D411yescharacteristic
329C43D411yescharacteristic
330C43D411yescharacteristic
331C43C2311yescharacteristic
332C43C2311yescharacteristic
333C43C2311yescharacteristic
334C43C2311yescharacteristic
335#340C2312yes—
336#340C2312yes—
337#340C2312yes—
338#340C2312yes—
339#340C2312yes—
340#340C2312yes—
341#340C2312yes—
342#340C2312yes—
343#340C2312yes—
344#340C2312yes—
345#340C2312yes—
346#340C2312yes—
347#336C2312yes—
348#336C2312yes—
349#336C2312yes—
350#336C2312yes—
351C22×Q8—21no—
352C22×Q8C2411yescharacteristic
353C22×Q8C2412yes—
354C22×D4—21no—
355C22×D4C2411yescharacteristic
356C23×C4—21no—
357C23×C4C2×D411yescharacteristic
358C23×C4C2×D411yescharacteristic
359C23×C4C2×D411yescharacteristic
360C23×C4C2×D411yescharacteristic
361C23×C4C2×D411yescharacteristic
362C23×C4C2×D411yescharacteristic
363C23×C4C2411yescharacteristic
364C2×Q16—24no—
365C2×Q16—24no—
366C2×Q16—42no—
367C2×SD16—24no—
368C2×SD16—24no—
369C2×SD16—42no—
370C22×C8C2412yes—
371C22×C8C2412yes—
372C22×C8C2412yes—
373C22×C8C2412yes—
374C4⋊Q8—22no—
375C4⋊Q8—22no—
376C4⋊Q8#4114yes—
377C4⋊Q8#4114yes—
378#126—44no—
379#125—28no—
380#125—22no—
381#125—22no—
382#124—22no—
383#124—22no—
384#123—44no—
385C22⋊Q8—28no—
386C22⋊Q8—24no—
387C22⋊Q8—24no—
388C22⋊Q8—42no—
389#121—42no—
390C4×Q8—28no—
391C4×Q8—24no—
392C4×Q8—24no—
393C4×Q8—24no—
394C4×Q8—24no—
395C4×Q8—24no—
396C4×Q8—42no—
397C4×Q8—42no—
398C4×Q8—44no—
399C4×Q8—44no—
400C4×D4—24no—
401C4×D4—44no—
402#117—28no—
403#117—44no—
404#117—44no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
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—21no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4C2411yescharacteristic
431C2×C4⋊C4C2412yes—
432C2×C4⋊C4C2412yes—
433C2×C4⋊C4C2411yescharacteristic
434C2×C4⋊C4C2411yescharacteristic
435C2×C4⋊C4C2411yescharacteristic
436C2×C4⋊C4C2411yescharacteristic
437C2×C4⋊C4C2411yescharacteristic
438C2×C4⋊C4C2412yes—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
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×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C42—24no—
457C2×C42—22no—
458C2×C42—22no—
459C2×C42—22no—
460C2×C42—24no—
461C2×C42—22no—
462C2×C42—22no—
463C2×C42—22no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—22no—
467C2×C42—22no—
468C2×C42—21no—
469C2×C42—42no—
470C2×C42—42no—
471C2×C42—42no—
472C2×C42—42no—
473C2×C42C2×D411yescharacteristic
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×C42C2411yescharacteristic
496C2×C42C2411yescharacteristic
497C2×C42C2411yescharacteristic
498C2×C42C2411yescharacteristic
499C2×C42C2411yescharacteristic
500C2×C42C2411yescharacteristic
501#107—24no—
502#107—24no—
503#107—42no—
504#106—24no—
505#106—24no—
506#106—42no—
507C4⋊C8—24no—
508C4⋊C8—24no—
509#103—24no—
510#103—24no—
511#103—24no—
512#103—24no—
513#103—24no—
514#103—24no—
515#103—42no—
516#103—42no—
517#103—42no—
518#102—24no—
519#102—24no—
520#102—42no—
521C22⋊C8—24no—
522C22⋊C8—24no—
523#97—22no—
524#97—22no—
525#97—22no—
526#97—22no—
527#97—42no—
528#97—42no—
529C4×C8—24no—
530C4×C8#4118yes—
531#95—22no—
532#95—22no—
533#95—22no—
534#95—22no—
535#95—21no—
536#95—21no—
537#95—21no—
538#95—21no—
539#95—21no—
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—22no—
552#95—22no—
553#95—22no—
554#95—22no—
555#95—21no—
556#95—21no—
557#95—21no—
558#95—21no—
559#95—21no—
560#95—21no—
561#95—21no—
562#95—21no—
563#95—21no—
564#95—21no—
565C24—21no—
566C24C22×D411yescharacteristic
567C2×Q8—24no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—21no—
572C2×Q8—22no—
573C2×Q8—21no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—22no—
577C2×Q8—42no—
578C2×Q8—42no—
579C2×Q8C2×#4114yes—
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—22no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
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—21no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4#13714yes—
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×C4C22×D411yescharacteristic
635C22×C4C22×D411yescharacteristic
636C22×C4C2511yescharacteristic
637Q16—48no—
638SD16—48no—
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×C8C2×#4114yes—
650C2×C8C2×#4114yes—
651C4⋊C4—28no—
652C4⋊C4—28no—
653C4⋊C4—24no—
654C4⋊C4—24no—
655C4⋊C4—24no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—22no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4—44no—
676C4⋊C4—44no—
677C4⋊C4—44no—
678C4⋊C4—42no—
679C4⋊C4—42no—
680C4⋊C4—42no—
681C4⋊C4—42no—
682C4⋊C4—42no—
683C4⋊C4—42no—
684C4⋊C4—44no—
685C4⋊C4—42no—
686C4⋊C4—42no—
687C4⋊C4—42no—
688C4⋊C4—42no—
689C4⋊C4C2×#4114yes—
690C22⋊C4—28no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—42no—
695C22⋊C4—42no—
696C22⋊C4—42no—
697C22⋊C4—44no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4—42no—
701C22⋊C4—42no—
702C22⋊C4—42no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—42no—
706C22⋊C4—42no—
707C42—28no—
708C42—22no—
709C42—22no—
710C42—22no—
711C42—22no—
712C42—22no—
713C42—22no—
714C42—22no—
715C42—22no—
716C42—22no—
717C42—22no—
718C42—22no—
719C42—22no—
720C42—22no—
721C42—22no—
722C42—22no—
723C42—21no—
724C42—21no—
725C42—22no—
726C42—22no—
727C42—41no—
728C42—41no—
729C42—41no—
730C42—41no—
731C42—41no—
732C42—41no—
733C42—41no—
734C42—41no—
735C42—44no—
736C42—44no—
737C42—42no—
738C42—42no—
739C42—44no—
740C42—42no—
741C42—44no—
742C42—44no—
743C42C2×#4112yes—
744C42C2×#4112yes—
745C42C2×#4114yes—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23C2×#13712yes—
760C23C23×D411yescharacteristic
761Q8—24no—
762Q8—24no—
763Q8—48no—
764Q8—42no—
765Q8—42no—
766Q8—42no—
767Q8—42no—
768D4—42no—
769D4—42no—
770D4—84no—
771C2×C4—28no—
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—28no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—21no—
790C2×C4—21no—
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—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—42no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—84no—
843C2×C4#52512yes—
844C2×C4#52512yes—
845C2×C4#53212yes—
846C2×C4#53212yes—
847C2×C4C2×#13712yes—
848C2×C4C2×#13712yes—
849C2×C4#57512yes—
850C2×C4#57512yes—
851C2×C4#57512yes—
852C2×C4C22×#4111yescharacteristic
853C2×C4C22×#4112yes—
854C2×C4C22×#4111yescharacteristic
855C2×C4#58512yes—
856C8—24no—
857C8—24no—
858C8—42no—
859C8—42no—
860C22—22no—
861C22—22no—
862C22—22no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22C2×#52511yescharacteristic
875C22C2×#53211yescharacteristic
876C22#344911yescharacteristic
877C22C22×#13711yescharacteristic
878C22C2×#57511yescharacteristic
879C22C2×#57511yescharacteristic
880C22C2×#57511yescharacteristic
881C4—22no—
882C4—22no—
883C4—22no—
884C4—22no—
885C4—22no—
886C4—22no—
887C4—41no—
888C4—41no—
889C4—41no—
890C4—41no—
891C4—41no—
892C4—44no—
893C4—41no—
894C4—44no—
895C4—82no—
896C4—81no—
897C4—81no—
898C4—81no—
899C4—82no—
900C4—81no—
901C4—81no—
902C4—81no—
903C4—81no—
904C4#318114yes—
905C4#347512yes—
906C4#348012yes—
907C2—42no—
908C2—161no—
909C2#3491011yescharacteristic
910C2#6055911yescharacteristic
911C2#6056011yescharacteristic
912C2#6067611yescharacteristic
913C2C2×#318111yescharacteristic
914C2#6095011yescharacteristic
915C2#6095311yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutator, Frattini, cosocleC22×C4C25
socleC23C23×D4
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C2×C43 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C4×#533C2semidirect
4. #29478C2semidirect
5. #29450C2semidirect
6. #29446C2semidirect
7. #29196C2semidirect
8. #29182C2semidirect
9. #28659C2semidirect
10. #28619C2semidirect
12. #27881C2semidirect
13. #25677C2semidirect
16. #23698C2semidirect
17. C4×#501C2semidirect
18. C4×#497C2semidirect
19. C4×#491C2semidirect
20. C4×#489C2semidirect
21. #21120C2semidirect
22. #21116C2semidirect
23. #20463C2semidirect

Maximal subgroups

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

subgroupindex
#366382
C4×#5332
#294822
#294782
#294502
#294462
#291962
#291822
#286592
#286192
#278952
#278812
#256772
#256032
#237002
#236982
C4×#5012
C4×#4972
C4×#4912
C4×#4892
#211202
#211162
#204632