Finite Group Databasebeta

← #6458963

Subgroups — #6458963

Order 512.

2218 conjugacy classes of subgroups.

The subgroup lattice has 867 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#121C211yesmaximal, characteristic
2#34012C211yesmaximal, characteristic, complemented
3#27679C212yesmaximal, complemented
4#27646C212yesmaximal, complemented
5#27625C212yesmaximal, complemented
6#27624C212yesmaximal, complemented
7#27617C212yesmaximal, complemented
8#27604C212yesmaximal, complemented
9#27588C212yesmaximal, complemented
10#24009C212yesmaximal
11#23764C214yesmaximal, complemented
12#21582C214yesmaximal, complemented
13#21365C211yesmaximal, characteristic, complemented
14#21365C211yesmaximal, characteristic, complemented
15#20738C211yesmaximal, characteristic, complemented
16#20738C211yesmaximal, characteristic, complemented
17#20715C211yesmaximal, characteristic, complemented
18C22×#121C2211yescharacteristic
19C22×C4×D4—21no—
20C22×C4×D4C2211yescharacteristic
21C23×C42C2211yescharacteristic
22C2×#482C2214yes—
23C2×#432C2211yescharacteristic
24C2×#432C2211yescharacteristic
25C4×#121—21no—
26C4×#121—21no—
27C4×#121—21no—
28C4×#121—21no—
29C4×#121C2212yes—
30C4×#121C2212yes—
31C4×#121C2212yes—
32C4×#121C2212yes—
33C2×#390C2211yescharacteristic
34C2×#389C2211yescharacteristic
35C2×#388—21no—
36C2×#386—21no—
37#2285C2211yescharacteristic
38#2285C2211yescharacteristic
39#2285C2211yescharacteristic, complemented
40#2285C2211yescharacteristic, complemented
41#2285C2211yescharacteristic, complemented
42#2285C2211yescharacteristic, complemented
43#2283—21no—
44#2283—21no—
45#2283—21no—
46#2283—21no—
47#2283C2212yes—
48#2283C2212yescomplemented
49#2280—21no—
50#2280—21no—
51#2280C2212yes—
52C2×#380C2211yescharacteristic
53C4×#117—21no—
54C4×#117—21no—
55C4×#117C2212yescomplemented
56C2×C4×C4⋊C4C2211yescharacteristic
57C2×C4×C22⋊C4—21no—
58#2101C2214yescomplemented
59#2092C2214yescomplemented
60#2085C2214yescomplemented
61#2077C2214yescomplemented
62#2075C2214yescomplemented
63#2073C2214yescomplemented
64#2034C2214yes—
65#2033C2214yes—
66#1948C2212yescomplemented
67#1948C2212yescomplemented
68#1947C2212yescomplemented
69#1947C2212yescomplemented
70#1926C2214yescomplemented
71#1925C2214yescomplemented
72#1919C2214yescomplemented
73#1918C2214yescomplemented
74#1875C2214yes—
75#1854C2214yescomplemented
76#1853C2212yes—
77#1853C2212yes—
78#1852C2212yes—
79#1852C2212yes—
80#1825C2214yescomplemented
81#1824C2212yes—
82#1824C2212yes—
83#1817C2212yes—
84#1802C2212yescomplemented
85#1802C2212yescomplemented
86#1802C2212yescomplemented
87#1802C2212yescomplemented
88#1797C2212yescomplemented
89#1797C2212yescomplemented
90#1786C2212yes—
91#1786C2212yes—
92#1779C2212yes—
93#1776C2214yescomplemented
94#1776C2214yescomplemented
95#1762C2214yescomplemented
96#1762C2214yescomplemented
97#1749C2212yescomplemented
98#1749C2212yescomplemented
99C23×D4—21no—
100C23×D4C2311yescharacteristic
101C24×C4—21no—
102C24×C4D411yescharacteristic
103C24×C4D411yescharacteristic
104C24×C4C2311yescharacteristic
105C2×#121—21no—
106C2×#121—21no—
107C2×#121—28no—
108C2×#121C2312yes—
109C2×#121C2312yes—
110C2×C4×D4—22no—
111C2×C4×D4—22no—
112C2×C4×D4—22no—
113C2×C4×D4—22no—
114C2×C4×D4—21no—
115C2×C4×D4—21no—
116C2×C4×D4—24no—
117C2×C4×D4—24no—
118C2×C4×D4—48no—
119C2×C4×D4C2312yes—
120C2×C4×D4C2312yes—
121C2×#117—21no—
122C2×#117—21no—
123C2×#117—21no—
124C2×#117—21no—
125C2×#117C2312yes—
126C2×#117C2312yes—
127C22×C4⋊C4—21no—
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C22⋊C4—21no—
132C22×C22⋊C4—21no—
133C22×C22⋊C4—21no—
134C22×C22⋊C4—21no—
135C22×C22⋊C4—21no—
136C22×C42—24no—
137C22×C42—24no—
138C22×C42—21no—
139C22×C42D411yescharacteristic
140C22×C42D411yescharacteristic
141C22×C42D411yescharacteristic
142C22×C42D411yescharacteristic
143C22×C42D411yescharacteristic
144C22×C42D411yescharacteristic
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151#482—216no—
152#432—24no—
153#432—24no—
154C2×#107C2314yes—
155C2×#107C2314yes—
156C2×#106C2314yes—
157C2×#106C2314yes—
158C2×C4⋊C8C2312yes—
159C2×C4⋊C8C2312yes—
160C2×#102C2314yes—
161C2×#102C2314yes—
162C2×#102C2314yes—
163C2×#102C2314yes—
164C2×C22⋊C8C2314yes—
165C2×C22⋊C8C2312yes—
166C2×C22⋊C8C2312yes—
167C2×C22⋊C8C2314yes—
168C2×#97C2312yes—
169C2×#97C2312yes—
170#390—21no—
171#390—21no—
172#390C2312yes—
173#390C2312yes—
174#389—21no—
175#389—21no—
176#389C2312yes—
177#389C2312yes—
178#388—22no—
179#388—22no—
180#388—22no—
181#388—22no—
182#386—22no—
183#386—22no—
184#386—22no—
185#386—22no—
186#384C2311yescharacteristic
187#384C2311yescharacteristic
188#384C2311yescharacteristic
189#384C2311yescharacteristic
190#383—22no—
191#383—22no—
192#382—21no—
193#382—21no—
194#382—21no—
195#382—21no—
196#382C2312yes—
197#382C2312yes—
198#381—22no—
199#381—22no—
200#381—22no—
201#380—21no—
202#380—21no—
203#380—21no—
204#380—21no—
205#380—21no—
206#380—21no—
207#380—21no—
208#380—21no—
209#380—21no—
210#380—21no—
211#380C2312yes—
212#380C2312yes—
213#380C2312yes—
214#380C2312yes—
215#380C2312yes—
216#380C2312yes—
217#379—22no—
218C4×C4⋊C4—21no—
219C4×C4⋊C4—21no—
220C4×C4⋊C4—21no—
221C4×C4⋊C4—21no—
222C4×C4⋊C4—21no—
223C4×C4⋊C4—21no—
224C4×C4⋊C4—21no—
225C4×C4⋊C4—21no—
226C4×C4⋊C4—21no—
227C4×C4⋊C4—21no—
228C4×C4⋊C4C2312yes—
229C4×C4⋊C4C2312yes—
230C4×C4⋊C4C2312yes—
231C4×C4⋊C4C2312yes—
232C4×C4⋊C4C2312yes—
233C4×C4⋊C4C2312yes—
234C4×C22⋊C4—22no—
235C4×C22⋊C4—22no—
236C4×C22⋊C4—22no—
237C4×C22⋊C4—22no—
238C4×C22⋊C4—22no—
239C4×C22⋊C4—22no—
240C4×C22⋊C4—22no—
241C4×C22⋊C4—22no—
242C4×C22⋊C4—22no—
243C4×C22⋊C4—22no—
244#376—22no—
245#376—22no—
246#376—22no—
247C2×#95—21no—
248C2×#95—21no—
249C2×#95—21no—
250C43—22no—
251#340C2314yes—
252#340C2314yes—
253#340C2314yes—
254#340C2314yes—
255#340C2314yes—
256#340C2314yes—
257#340C2314yes—
258#340C2314yes—
259#336C2314yes—
260#336C2314yes—
261C25—21no—
262C25C2×D411yescharacteristic
263C22×D4—28no—
264C22×D4—22no—
265C22×D4—22no—
266C22×D4—24no—
267C22×D4—21no—
268C22×D4—22no—
269C22×D4—22no—
270C22×D4—42no—
271C22×D4—44no—
272C22×D4—44no—
273C22×D4C2412yes—
274C23×C4—21no—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—24no—
278C23×C4—24no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—21no—
282C23×C4—21no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—42no—
286C23×C4—42no—
287C23×C4—42no—
288C23×C4—42no—
289C23×C4—44no—
290C23×C4—44no—
291C23×C4—44no—
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×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D411yescharacteristic
307C23×C4C2411yescharacteristic
308C23×C4C2411yescharacteristic
309C23×C4C2411yescharacteristic
310C22×C8C2414yes—
311C22×C8C2414yes—
312#121—28no—
313#121—28no—
314#121—24no—
315#121—24no—
316#121—24no—
317#121#4118yes—
318C4×D4—24no—
319C4×D4—24no—
320C4×D4—24no—
321C4×D4—24no—
322C4×D4—48no—
323C4×D4—48no—
324C4×D4—48no—
325C4×D4—48no—
326C4×D4—44no—
327C4×D4—44no—
328#117—28no—
329#117—44no—
330#117—44no—
331#117—44no—
332#117—44no—
333#117—44no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
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—42no—
351C2×C4⋊C4—44no—
352C2×C4⋊C4C2412yes—
353C2×C4⋊C4C2412yes—
354C2×C4⋊C4C2412yes—
355C2×C4⋊C4C2412yes—
356C2×C4⋊C4C2412yes—
357C2×C4⋊C4C2412yes—
358C2×C4⋊C4C2412yes—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
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—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C42—24no—
381C2×C42—24no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42—24no—
387C2×C42—24no—
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×C42—22no—
403C2×C42—22no—
404C2×C42—44no—
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×C42C2×D411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D411yescharacteristic
417C2×C42#4114yes—
418C2×C42#4114yes—
419C2×C42C2411yescharacteristic
420C2×C42C2411yescharacteristic
421C2×C42C2411yescharacteristic
422C2×C42C2411yescharacteristic
423#107—28no—
424#107—44no—
425#106—28no—
426#106—44no—
427C4⋊C8—24no—
428C4⋊C8—24no—
429#102—28no—
430#102—28no—
431#102—44no—
432#102—44no—
433C22⋊C8—24no—
434C22⋊C8—24no—
435C22⋊C8—28no—
436C22⋊C8—44no—
437#97—24no—
438#97—24no—
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—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—24no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—41no—
465C24—41no—
466C24—42no—
467C24—42no—
468C24—42no—
469C24—42no—
470C24—42no—
471C24—42no—
472C24C22×D411yescharacteristic
473C24C22×D411yescharacteristic
474C24C22×D411yescharacteristic
475C2×D4—24no—
476C2×D4—28no—
477C2×D4—28no—
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—48no—
484C2×D4—48no—
485C2×D4—42no—
486C2×D4—44no—
487C2×D4—432no—
488C2×D4—44no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—42no—
492C2×D4C2×#4114yes—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—24no—
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—22no—
518C22×C4—22no—
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—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—416no—
553C22×C4—48no—
554C22×C4—48no—
555C22×C4—416no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—816no—
571C22×C4#12314yes—
572C22×C4#12314yes—
573C22×C4AGL(1,ℤ/8)14yes—
574C22×C4C22×D411yescharacteristic
575C22×C4C22×D411yescharacteristic
576C22×C4C22×D411yescharacteristic
577C22×C4C22×D411yescharacteristic
578C22×C4C22×D411yescharacteristic
579C22×C4C22×D411yescharacteristic
580C22×C4C22×D411yescharacteristic
581C22×C4C22×D411yescharacteristic
582C22×C4C22×D411yescharacteristic
583C22×C4C22×D411yescharacteristic
584C22×C4C22×D411yescharacteristic
585C22×C4C2×#4112yes—
586C22×C4C2×#4112yes—
587C22×C4C2×#4114yes—
588C22×C4C2511yescharacteristic
589C2×C8—24no—
590C2×C8—24no—
591C2×C8—24no—
592C2×C8—24no—
593C2×C8—24no—
594C2×C8—24no—
595C4⋊C4—24no—
596C4⋊C4—22no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—42no—
606C4⋊C4—44no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C4⋊C4—44no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4C2×#4114yes—
618C22⋊C4—28no—
619C22⋊C4—28no—
620C22⋊C4—44no—
621C22⋊C4—44no—
622C22⋊C4—44no—
623C22⋊C4—44no—
624C22⋊C4—44no—
625C22⋊C4—44no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C22⋊C4—44no—
630C22⋊C4—44no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—44no—
634C42—22no—
635C42—22no—
636C42—22no—
637C42—22no—
638C42—22no—
639C42—22no—
640C42—22no—
641C42—22no—
642C42—22no—
643C42—22no—
644C42—21no—
645C42—21no—
646C42—21no—
647C42—21no—
648C42—44no—
649C42—44no—
650C42—44no—
651C42—44no—
652C42—44no—
653C42—44no—
654C42—44no—
655C42—44no—
656C42#12314yes—
657C42#12314yes—
658C42C2×#4112yes—
659C42C2×#4112yes—
660C42C2×#4112yes—
661C42C2×#4112yes—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—28no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—24no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23—44no—
685C23—48no—
686C23—48no—
687C23—48no—
688C23—44no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—84no—
696C23—84no—
697C23—84no—
698C23—84no—
699C23C2×#12312yes—
700C23#52512yes—
701C23C2×AGL(1,ℤ/8)12yes—
702C23#57512yes—
703C23#57512yes—
704C23C23×D411yescharacteristic
705D4—24no—
706D4—24no—
707D4—48no—
708D4—416no—
709D4—416no—
710D4—42no—
711D4—42no—
712C2×C4—28no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—28no—
726C2×C4—28no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—24no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—48no—
755C2×C4—44no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—44no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—88no—
780C2×C4—84no—
781C2×C4—84no—
782C2×C4—88no—
783C2×C4C2×#12312yes—
784C2×C4C2×#12312yes—
785C2×C4C2×#12312yes—
786C2×C4C2×#12312yes—
787C2×C4C2×#12312yes—
788C2×C4#52512yes—
789C2×C4C2×AGL(1,ℤ/8)12yes—
790C2×C4C2×AGL(1,ℤ/8)12yes—
791C2×C4#57512yes—
792C2×C4C22×#4111yescharacteristic
793C2×C4C22×#4111yescharacteristic
794C2×C4C22×#4112yes—
795C2×C4#58512yes—
796C8—44no—
797C8—44no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—416no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—44no—
820C22—44no—
821C22—44no—
822C22—816no—
823C22—82no—
824C22—82no—
825C22—82no—
826C22—82no—
827C22#309314yes—
828C22C22×#12311yescharacteristic
829C22C2×#52511yescharacteristic
830C22#344911yescharacteristic
831C22C22×AGL(1,ℤ/8)11yescharacteristic
832C22C2×#57511yescharacteristic
833C22C2×#57511yescharacteristic
834C22C2×#57511yescharacteristic
835C4—22no—
836C4—22no—
837C4—22no—
838C4—22no—
839C4—22no—
840C4—22no—
841C4—41no—
842C4—41no—
843C4—41no—
844C4—44no—
845C4—41no—
846C4—82no—
847C4—82no—
848C4—82no—
849C4—82no—
850C4—82no—
851C4—82no—
852C4#309414yes—
853C4#347512yes—
854C4#347512yes—
855C2—24no—
856C2—42no—
857C2—42no—
858C2—84no—
859C2#3480911yescharacteristic
860C2C2×#309311yescharacteristic
861C2C2×#309411yescharacteristic
862C2#6054611yescharacteristic
863C2#6055811yescharacteristic
864C2#6096211yescharacteristic
865C2#6097011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34012C2semidirect
3. #27679C2semidirect
4. #27646C2semidirect
5. #27625C2semidirect
6. #27624C2semidirect
7. #27617C2semidirect
8. #27604C2semidirect
9. #27588C2semidirect
11. #23764C2semidirect
12. #21582C2semidirect
13. #21365C2semidirect
14. #21365C2semidirect
15. #20738C2semidirect
16. #20738C2semidirect
17. #20715C2semidirect
39. #2285C22semidirect
40. #2285C22semidirect
41. #2285C22semidirect
42. #2285C22semidirect
48. #2283C22semidirect
55. C4×#117C22semidirect
58. #2101C22semidirect
59. #2092C22semidirect
60. #2085C22semidirect
61. #2077C22semidirect
62. #2075C22semidirect
63. #2073C22semidirect
66. #1948C22semidirect
67. #1948C22semidirect
68. #1947C22semidirect
69. #1947C22semidirect
70. #1926C22semidirect
71. #1925C22semidirect
72. #1919C22semidirect
73. #1918C22semidirect
75. #1854C22semidirect
80. #1825C22semidirect
84. #1802C22semidirect
85. #1802C22semidirect
86. #1802C22semidirect
87. #1802C22semidirect
88. #1797C22semidirect
89. #1797C22semidirect
93. #1776C22semidirect
94. #1776C22semidirect
95. #1762C22semidirect
96. #1762C22semidirect
97. #1749C22semidirect
98. #1749C22semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#1212
#340122
#276792
#276462
#276252
#276242
#276172
#276042
#275882
#240092
#237642
#215822
#213652
#207382
#207152