Finite Group Databasebeta

← #6459050

Subgroups — #6459050

Order 512.

1850 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36625C211yesmaximal, characteristic
2#34012C211yesmaximal, characteristic
3#27975C211yesmaximal, characteristic, complemented
4#27962C211yesmaximal, characteristic, complemented
5#27949C211yesmaximal, characteristic, complemented
6#27908C211yesmaximal, characteristic, complemented
7#27892C211yesmaximal, characteristic, complemented
8#27889C211yesmaximal, characteristic, complemented
9#27877C211yesmaximal, characteristic, complemented
10#27876C211yesmaximal, characteristic, complemented
11#27860C214yesmaximal, complemented
12#24554C214yesmaximal
13#23759C214yesmaximal, complemented
14C4×#485C214yesmaximal, complemented
15#21400C211yesmaximal, characteristic, complemented
16#21400C211yesmaximal, characteristic, complemented
17#20817C211yesmaximal, characteristic, complemented
18#20816C211yesmaximal, characteristic, complemented
19C2×C4×C22⋊C8C211yesmaximal, characteristic
20C2×#533C2211yescharacteristic
21C23×C42C2211yescharacteristic
22C2×#485C2214yes—
23C22×C22⋊C8C2212yes—
24C22×C4×C8C2211yescharacteristic
25C22×C4×C8C2211yescharacteristic
26#2857C2211yescharacteristic
27#2857C2211yescharacteristic
28#2857C2211yescharacteristic
29#2857C2211yescharacteristic
30#2855—21no—
31#2855C2212yes—
32#2851—21no—
33#2851—21no—
34#2848—21no—
35#2848C2212yes—
36C4×C22⋊Q8—21no—
37C4×C22⋊Q8—21no—
38C4×C22⋊Q8C2212yes—
39C4×C22⋊Q8C2212yes—
40#2296—21no—
41#2285C2211yescharacteristic
42#2285C2211yescharacteristic
43#2285C2211yescharacteristic
44#2285C2211yescharacteristic
45#2285C2211yescharacteristic
46#2285C2211yescharacteristic
47#2285C2211yescharacteristic
48#2283—21no—
49#2283—21no—
50#2283—21no—
51#2283—21no—
52#2283C2212yes—
53#2283C2212yes—
54#2280—21no—
55#2280—21no—
56#2280—21no—
57#2280C2212yes—
58C4×#117—21no—
59C4×#117—21no—
60C4×#117C2212yes—
61#2101C2214yescomplemented
62#2097C2214yescomplemented
63#2085C2214yescomplemented
64#2077C2214yes—
65#2075C2214yes—
66#2074C2214yescomplemented
67#2036C2214yes—
68#2035C2214yes—
69#1990C2211yescharacteristic, complemented
70#1990C2211yescharacteristic, complemented
71#1990C2211yescharacteristic, complemented
72#1990C2211yescharacteristic, complemented
73#1956C2211yescharacteristic, complemented
74#1956C2211yescharacteristic, complemented
75#1956C2211yescharacteristic, complemented
76#1956C2211yescharacteristic, complemented
77#1928C2214yescomplemented
78#1927C2214yescomplemented
79#1919C2214yescomplemented
80#1918C2214yescomplemented
81#1892C2214yes—
82#1892C2214yes—
83#1873C2214yes—
84#1854C2214yes—
85#1845C2211yescharacteristic, complemented
86#1845C2211yescharacteristic, complemented
87#1844C2211yescharacteristic, complemented
88#1844C2211yescharacteristic, complemented
89#1834C2211yescharacteristic, complemented
90#1834C2211yescharacteristic, complemented
91#1834C2211yescharacteristic, complemented
92#1834C2211yescharacteristic, complemented
93#1825C2214yes—
94#1808C2214yes—
95#1807C2214yes—
96C4×#107C2214yescomplemented
97C4×#106C2214yescomplemented
98C4×#103C2214yescomplemented
99C4×#103C2214yescomplemented
100C4×C22⋊C8C2211yescharacteristic
101C4×C22⋊C8C2211yescharacteristic
102C4×C22⋊C8C2212yes—
103C4×C22⋊C8C2212yes—
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2211yescharacteristic
106C2×#336C2212yes—
107C24×C4D411yescharacteristic
108C24×C4D411yescharacteristic
109C24×C4C2311yescharacteristic
110C23×C8C2312yes—
111C23×C8C2312yes—
112#533—24no—
113#533—24no—
114C2×C4⋊Q8C2311yescharacteristic
115C2×C4⋊Q8C2311yescharacteristic
116C2×#125—21no—
117C2×C22⋊Q8—21no—
118C2×C22⋊Q8—21no—
119C2×C22⋊Q8—21no—
120C2×C22⋊Q8C2312yes—
121C2×C22⋊Q8C2312yes—
122C2×C22⋊Q8C2312yes—
123C2×C4×Q8—21no—
124C2×C4×Q8C2312yes—
125C2×#117—21no—
126C2×#117—21no—
127C2×#117—21no—
128C2×#117—21no—
129C2×#117—21no—
130C2×#117—21no—
131C2×#117C2312yes—
132C2×#117C2312yes—
133C22×C42—24no—
134C22×C42—24no—
135C22×C42D411yescharacteristic
136C22×C42D411yescharacteristic
137C22×C42D411yescharacteristic
138C22×C42D411yescharacteristic
139C22×C42D411yescharacteristic
140C22×C42D411yescharacteristic
141C22×C42C2311yescharacteristic
142C22×C42C2311yescharacteristic
143C22×C42C2311yescharacteristic
144C22×C42C2311yescharacteristic
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147#485—216no—
148C2×#107C2314yes—
149C2×#107C2314yes—
150C2×#106C2314yes—
151C2×#106C2314yes—
152C2×#103C2314yes—
153C2×#103C2314yes—
154C2×#103C2314yes—
155C2×#103C2314yes—
156C2×C22⋊C8—28no—
157C2×C22⋊C8C2312yes—
158C2×C22⋊C8C2312yes—
159C2×C22⋊C8C2312yes—
160C2×C22⋊C8C2312yes—
161C2×C4×C8—24no—
162C2×C4×C8—24no—
163C2×C4×C8C2311yescharacteristic
164C2×C4×C8C2311yescharacteristic
165C2×C4×C8C2311yescharacteristic
166C2×C4×C8C2311yescharacteristic
167C2×C4×C8C2312yes—
168C2×C4×C8C2312yes—
169#391—21no—
170#391—21no—
171#391C2312yes—
172#391C2312yes—
173#389—21no—
174#389—21no—
175#389—21no—
176#389—21no—
177#389—21no—
178#389—21no—
179#389C2312yes—
180#389C2312yes—
181#387—22no—
182#387—22no—
183#387—22no—
184#387—22no—
185#385—22no—
186#385—22no—
187#385—22no—
188#385—22no—
189#385—22no—
190#385—22no—
191#384C2311yescharacteristic
192#384C2311yescharacteristic
193#384C2311yescharacteristic
194#384C2311yescharacteristic
195#384C2311yescharacteristic
196#384C2311yescharacteristic
197#383—22no—
198#383—22no—
199#382—21no—
200#382—21no—
201#382—21no—
202#382—21no—
203#382—21no—
204#382C2312yes—
205#382C2312yes—
206#381—22no—
207#381—22no—
208#381—22no—
209#381—22no—
210#380—21no—
211#380—21no—
212#380—21no—
213#380—21no—
214#380—21no—
215#380—21no—
216#380—21no—
217#380—21no—
218#380—21no—
219#380—21no—
220#380—21no—
221#380—21no—
222#380—21no—
223#380—21no—
224#380—21no—
225#380C2312yes—
226#380C2312yes—
227#380C2312yes—
228#380C2312yes—
229#380C2312yes—
230#380C2312yes—
231#380C2312yes—
232#379—22no—
233#379—22no—
234C4×C4⋊C4—21no—
235C4×C4⋊C4—21no—
236C4×C4⋊C4—21no—
237C4×C4⋊C4—21no—
238C4×C4⋊C4—21no—
239C4×C4⋊C4—21no—
240C4×C4⋊C4—21no—
241C4×C4⋊C4—21no—
242C4×C4⋊C4—21no—
243C4×C4⋊C4—22no—
244C4×C4⋊C4—22no—
245C4×C4⋊C4C2312yes—
246C4×C4⋊C4C2312yes—
247C4×C4⋊C4C2312yes—
248C4×C4⋊C4C2312yes—
249C4×C4⋊C4C2312yes—
250C4×C22⋊C4—22no—
251C4×C22⋊C4—22no—
252C4×C22⋊C4—22no—
253C4×C22⋊C4—22no—
254C4×C22⋊C4—22no—
255C4×C22⋊C4—22no—
256C4×C22⋊C4—22no—
257C4×C22⋊C4—22no—
258#376—22no—
259#376—22no—
260#376—22no—
261C43—22no—
262#340C2314yes—
263#340C2314yes—
264#340C2314yes—
265#340C2314yes—
266#340C2314yes—
267#340C2314yes—
268#340C2314yes—
269#340C2314yes—
270#336C2312yes—
271#336C2312yes—
272#336C2312yes—
273#336C2312yes—
274C25C2×D411yescharacteristic
275C22×Q8—21no—
276C22×Q8C2412yes—
277C23×C4—24no—
278C23×C4—24no—
279C23×C4—24no—
280C23×C4—24no—
281C23×C4—24no—
282C23×C4—24no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—42no—
286C23×C4—42no—
287C23×C4C2×D411yescharacteristic
288C23×C4C2×D411yescharacteristic
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2411yescharacteristic
303C23×C4C2411yescharacteristic
304C23×C4C2411yescharacteristic
305C22×C8—24no—
306C22×C8—24no—
307C22×C8—24no—
308C22×C8—24no—
309C22×C8—42no—
310C22×C8—42no—
311C22×C8C2412yes—
312C22×C8C2412yes—
313C22×C8C2412yes—
314C22×C8C2412yes—
315C4⋊Q8—22no—
316C4⋊Q8—22no—
317C4⋊Q8—22no—
318C4⋊Q8—22no—
319#125—44no—
320C22⋊Q8—24no—
321C22⋊Q8—24no—
322C22⋊Q8—28no—
323C22⋊Q8—44no—
324C22⋊Q8—44no—
325C22⋊Q8—44no—
326C22⋊Q8—44no—
327C4×Q8—24no—
328C4×Q8—24no—
329C4×Q8—44no—
330#117—28no—
331#117—44no—
332#117—44no—
333#117—44no—
334#117—44no—
335#117—44no—
336#117—44no—
337#117—44no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4C2412yes—
360C2×C4⋊C4C2412yes—
361C2×C4⋊C4C2412yes—
362C2×C4⋊C4C2412yes—
363C2×C4⋊C4C2412yes—
364C2×C4⋊C4C2412yes—
365C2×C4⋊C4C2412yes—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C42—24no—
379C2×C42—24no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—24no—
383C2×C42—24no—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42C2×D411yescharacteristic
403C2×C42C2×D411yescharacteristic
404C2×C42C2×D411yescharacteristic
405C2×C42C2×D411yescharacteristic
406C2×C42C2×D411yescharacteristic
407C2×C42C2×D411yescharacteristic
408C2×C42C2×D411yescharacteristic
409C2×C42C2×D411yescharacteristic
410C2×C42C2×D411yescharacteristic
411C2×C42C2×D411yescharacteristic
412C2×C42C2×D411yescharacteristic
413C2×C42C2×D411yescharacteristic
414C2×C42#4114yes—
415C2×C42#4114yes—
416C2×C42C2411yescharacteristic
417C2×C42C2411yescharacteristic
418C2×C42C2411yescharacteristic
419C2×C42C2411yescharacteristic
420#107—28no—
421#107—44no—
422#106—28no—
423#106—44no—
424#103—28no—
425#103—28no—
426#103—44no—
427#103—44no—
428C22⋊C8—24no—
429C22⋊C8—24no—
430C22⋊C8—24no—
431C22⋊C8#4118yes—
432C4×C8—24no—
433C4×C8—24no—
434C4×C8—22no—
435C4×C8—22no—
436C4×C8—22no—
437C4×C8—22no—
438#95—22no—
439#95—22no—
440#95—22no—
441#95—22no—
442#95—22no—
443#95—22no—
444#95—22no—
445#95—22no—
446#95—22no—
447#95—22no—
448#95—22no—
449#95—22no—
450#95—22no—
451#95—22no—
452#95—22no—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—22no—
459#95—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—41no—
466C24—41no—
467C24C22×D411yescharacteristic
468C24C22×D411yescharacteristic
469C24C22×D411yescharacteristic
470C2×Q8—24no—
471C2×Q8—22no—
472C2×Q8—22no—
473C2×Q8—24no—
474C2×Q8—42no—
475C2×Q8—42no—
476C2×Q8—42no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—416no—
535C22×C4—48no—
536C22×C4—48no—
537C22×C4—416no—
538C22×C4#12314yes—
539C22×C4#12314yes—
540C22×C4#13514yes—
541C22×C4#13514yes—
542C22×C4#13714yes—
543C22×C4C22×D411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C22×D411yescharacteristic
546C22×C4C22×D411yescharacteristic
547C22×C4C22×D411yescharacteristic
548C22×C4C22×D411yescharacteristic
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C22×D411yescharacteristic
554C22×C4C2×#4112yes—
555C22×C4C2×#4112yes—
556C22×C4C2×#4114yes—
557C22×C4C2511yescharacteristic
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—48no—
569C2×C8—48no—
570C2×C8C2×#4114yes—
571C2×C8C2×#4114yes—
572C4⋊C4—24no—
573C4⋊C4—24no—
574C4⋊C4—24no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—44no—
581C4⋊C4—44no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—44no—
585C4⋊C4—44no—
586C4⋊C4—42no—
587C4⋊C4—44no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—44no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C22⋊C4—44no—
602C22⋊C4—44no—
603C22⋊C4—44no—
604C22⋊C4—44no—
605C22⋊C4—44no—
606C22⋊C4—44no—
607C22⋊C4—44no—
608C22⋊C4—44no—
609C22⋊C4—44no—
610C22⋊C4—44no—
611C22⋊C4—44no—
612C22⋊C4—44no—
613C42—22no—
614C42—22no—
615C42—22no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—21no—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—44no—
628C42—44no—
629C42—44no—
630C42—44no—
631C42—44no—
632C42—44no—
633C42—44no—
634C42—44no—
635C42#12314yes—
636C42#12314yes—
637C42C2×#4112yes—
638C42C2×#4112yes—
639C42C2×#4112yes—
640C42C2×#4112yes—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—28no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23C2×#12312yes—
665C23#53212yes—
666C23C2×#13512yes—
667C23C2×#13512yes—
668C23C2×#13712yes—
669C23C23×D411yescharacteristic
670Q8—44no—
671Q8—44no—
672Q8—84no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—28no—
682C2×C4—28no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4#485116yescomplemented
738C2×C4C2×#12312yes—
739C2×C4C2×#12312yes—
740C2×C4C2×#12312yes—
741C2×C4C2×#12312yes—
742C2×C4C2×#12312yes—
743C2×C4#53212yes—
744C2×C4C2×#13512yes—
745C2×C4C2×#13512yes—
746C2×C4C2×#13512yes—
747C2×C4C2×#13512yes—
748C2×C4C2×#13712yes—
749C2×C4C2×#13712yes—
750C2×C4#57512yes—
751C2×C4C22×#4111yescharacteristic
752C2×C4C22×#4111yescharacteristic
753C2×C4C22×#4112yes—
754C2×C4#58512yes—
755C8—24no—
756C8—24no—
757C8—42no—
758C8—42no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—416no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22C2×#48514yes—
781C22C22×#12311yescharacteristic
782C22C2×#53211yescharacteristic
783C22#344911yescharacteristic
784C22C22×#13511yescharacteristic
785C22C22×#13511yescharacteristic
786C22C22×#13711yescharacteristic
787C22C2×#57511yescharacteristic
788C4—22no—
789C4—22no—
790C4—22no—
791C4—22no—
792C4—41no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—82no—
797C4—82no—
798C4—82no—
799C4—82no—
800C4—82no—
801C4—82no—
802C4—82no—
803C4—82no—
804C4C2×#48514yes—
805C4C2×#48514yes—
806C4#309114yes—
807C4#347512yes—
808C4#347512yes—
809C2—24no—
810C2—42no—
811C2—42no—
812C2#3481011yescharacteristic
813C2C22×#48511yescharacteristic
814C2C2×#309111yescharacteristic
815C2#6067311yescharacteristic
816C2#6070111yescharacteristic
817C2#6094411yescharacteristic
818C2#6094711yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutator, Frattini, cosocleC22×C4C25
socleC23C23×D4
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #27975C2semidirect
4. #27962C2semidirect
5. #27949C2semidirect
6. #27908C2semidirect
7. #27892C2semidirect
8. #27889C2semidirect
9. #27877C2semidirect
10. #27876C2semidirect
11. #27860C2semidirect
13. #23759C2semidirect
14. C4×#485C2semidirect
15. #21400C2semidirect
16. #21400C2semidirect
17. #20817C2semidirect
18. #20816C2semidirect
61. #2101C22semidirect
62. #2097C22semidirect
63. #2085C22semidirect
66. #2074C22semidirect
69. #1990C22semidirect
70. #1990C22semidirect
71. #1990C22semidirect
72. #1990C22semidirect
73. #1956C22semidirect
74. #1956C22semidirect
75. #1956C22semidirect
76. #1956C22semidirect
77. #1928C22semidirect
78. #1927C22semidirect
79. #1919C22semidirect
80. #1918C22semidirect
85. #1845C22semidirect
86. #1845C22semidirect
87. #1844C22semidirect
88. #1844C22semidirect
89. #1834C22semidirect
90. #1834C22semidirect
91. #1834C22semidirect
92. #1834C22semidirect
96. C4×#107C22semidirect
97. C4×#106C22semidirect
98. C4×#103C22semidirect
99. C4×#103C22semidirect
737. C2×C4#485semidirect

Maximal subgroups

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

subgroupindex
#366252
#340122
#279752
#279622
#279492
#279082
#278922
#278892
#278772
#278762
#278602
#245542
#237592
C4×#4852
#214002
#208172
#208162
C2×C4×C22⋊C82