Finite Group Databasebeta

← #6476173

Subgroups — #6476173

Order 512.

2466 conjugacy classes of subgroups.

The subgroup lattice has 921 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2854C211yesmaximal, characteristic, complemented
2C2×C4×#121C211yesmaximal, characteristic, complemented
3#33095C212yesmaximal, complemented
4#33002C212yesmaximal, complemented
5#30015C214yesmaximal, complemented
6#29476C214yesmaximal, complemented
7#29237C212yesmaximal, complemented
8#28117C212yesmaximal, complemented
9#27601C211yesmaximal, characteristic, complemented
10#24608C212yesmaximal, complemented
11#24506C212yesmaximal, complemented
12#24005C211yesmaximal, characteristic, complemented
13#24002C211yesmaximal, characteristic, complemented
14#23918C211yesmaximal, characteristic
15#22082C212yesmaximal, complemented
16#22046C212yesmaximal, complemented
17#20715C211yesmaximal, characteristic, complemented
18C22×#123—21no—
19C22×#121C2211yescharacteristic
20C22×#121C2211yescharacteristic
21C22×C4×D4—21no—
22C22×C4×D4C2211yescharacteristic, complemented
23C23×C42C2211yescharacteristic
24C2×#481C2212yes—
25C2×#480C2212yes—
26C2×#447C2212yes—
27C2×#447C2212yes—
28C2×#432C2212yescomplemented
29#2854—21no—
30#2854—21no—
31#2854—21no—
32#2854—21no—
33#2854C2212yes—
34#2854C2212yes—
35#2854C2212yescomplemented
36#2854C2212yescomplemented
37C4×#121—21no—
38C4×#121—21no—
39C4×#121—21no—
40C4×#121—21no—
41C4×#121C2212yes—
42C4×#121C2212yes—
43C4×#121C2212yescomplemented
44C4×#121C2212yescomplemented
45C2×#390C2211yescharacteristic, complemented
46C2×#390C2211yescharacteristic, complemented
47C2×#390C2211yescharacteristic, complemented
48C2×#389C2211yescharacteristic, complemented
49C2×#389C2211yescharacteristic, complemented
50C2×#389C2211yescharacteristic, complemented
51C2×#388—21no—
52C2×#388—21no—
53C2×#388—21no—
54C2×#386—21no—
55C2×#386—21no—
56C2×#380C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×C4×C4⋊C4C2211yescharacteristic, complemented
59C2×C4×C22⋊C4—21no—
60#2087C2214yescomplemented
61#2077C2214yescomplemented
62#2065C2214yescomplemented
63#2065C2214yescomplemented
64#2054C2214yescomplemented
65#2034C2214yescomplemented
66#2033C2214yescomplemented
67#1999C2214yes—
68#1972C2214yescomplemented
69#1944C2214yescomplemented
70#1936C2214yescomplemented
71#1936C2214yescomplemented
72#1926C2214yescomplemented
73#1926C2214yescomplemented
74#1919C2214yescomplemented
75#1919C2214yescomplemented
76#1879C2214yescomplemented
77#1879C2214yescomplemented
78#1874C2212yes—
79#1874C2212yes—
80#1874C2212yes—
81#1874C2212yes—
82#1862C2214yescomplemented
83#1862C2214yescomplemented
84#1853C2212yescomplemented
85#1853C2212yescomplemented
86#1853C2212yescomplemented
87#1852C2212yescomplemented
88#1824C2212yescomplemented
89#1823C2212yescomplemented
90#1817C2212yescomplemented
91#1797C2212yescomplemented
92#1797C2212yescomplemented
93#1786C2212yescomplemented
94#1786C2212yescomplemented
95#1779C2211yescharacteristic
96#1779C2211yescharacteristic
97#1749C2212yescomplemented
98#1749C2212yescomplemented
99C23×D4—21no—
100C23×D4—21no—
101C23×D4C2311yescharacteristic
102C23×D4C2311yescharacteristic
103C24×C4—21no—
104C24×C4D411yescharacteristic
105C24×C4D411yescharacteristic
106C24×C4C2311yescharacteristic
107C22×D8C2314yes—
108C2×#123—22no—
109C2×#123—22no—
110C2×#123—22no—
111C2×#123—22no—
112C2×#123—48no—
113C2×#121—21no—
114C2×#121—21no—
115C2×#121—28no—
116C2×#121—21no—
117C2×#121—21no—
118C2×#121—44no—
119C2×#121C2312yes—
120C2×#121C2312yes—
121C2×#121C2312yes—
122C2×#121C2312yes—
123C2×C4×D4—22no—
124C2×C4×D4—22no—
125C2×C4×D4—22no—
126C2×C4×D4—22no—
127C2×C4×D4—21no—
128C2×C4×D4—21no—
129C2×C4×D4—44no—
130C2×C4×D4—48no—
131C2×C4×D4C2312yes—
132C2×C4×D4C2312yes—
133C22×C4⋊C4—21no—
134C22×C4⋊C4—21no—
135C22×C4⋊C4—21no—
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C22⋊C4—21no—
147C22×C22⋊C4—21no—
148C22×C22⋊C4—21no—
149C22×C22⋊C4—21no—
150C22×C22⋊C4—21no—
151C22×C22⋊C4—21no—
152C22×C22⋊C4—21no—
153C22×C42—21no—
154C22×C42—44no—
155C22×C42D411yescharacteristic
156C22×C42D411yescharacteristic
157C22×C42D411yescharacteristic
158C22×C42D411yescharacteristic
159C22×C42D411yescharacteristic
160C22×C42D411yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166C22×C42C2311yescharacteristic
167#481—28no—
168#480—44no—
169#447—28no—
170#447—44no—
171#432—44no—
172C2×#107C2314yes—
173C2×#106C2314yes—
174C2×#106C2314yes—
175C2×C4⋊C8C2314yes—
176C2×#102C2314yes—
177C2×#102C2314yes—
178C2×#102C2314yes—
179C2×#102C2314yes—
180C2×#102C2314yes—
181C2×#102C2314yes—
182C2×C22⋊C8C2312yes—
183C2×C22⋊C8C2312yes—
184C2×C22⋊C8C2312yes—
185C2×C22⋊C8C2312yes—
186C2×C22⋊C8C2312yes—
187C2×C22⋊C8C2312yes—
188C2×#97C2314yes—
189#390—21no—
190#390—21no—
191#390—21no—
192#390—21no—
193#390—21no—
194#390—21no—
195#390C2312yes—
196#390C2312yes—
197#390C2312yes—
198#390C2312yes—
199#390C2312yes—
200#390C2312yes—
201#389—21no—
202#389—21no—
203#389—21no—
204#389—21no—
205#389—21no—
206#389—21no—
207#389C2312yes—
208#389C2312yes—
209#389C2312yes—
210#389C2312yes—
211#389C2312yes—
212#389C2312yes—
213#388—22no—
214#388—22no—
215#388—22no—
216#388—22no—
217#388—22no—
218#388—22no—
219#388—22no—
220#388—22no—
221#388—22no—
222#388—22no—
223#388—22no—
224#388—22no—
225#386—22no—
226#386—22no—
227#386—22no—
228#386—22no—
229#386—22no—
230#386—22no—
231#386—22no—
232#386—22no—
233#380—21no—
234#380—21no—
235#380—21no—
236#380—21no—
237#380C2312yes—
238#380C2312yes—
239#380C2312yes—
240#380C2312yes—
241C4×C4⋊C4—21no—
242C4×C4⋊C4—21no—
243C4×C4⋊C4C2312yes—
244C4×C4⋊C4C2312yes—
245C4×C22⋊C4—22no—
246C4×C22⋊C4—22no—
247C4×C22⋊C4—22no—
248C4×C22⋊C4—22no—
249C2×#95—21no—
250C2×#95—21no—
251C2×#95—21no—
252C2×#95—21no—
253C2×#95—21no—
254C2×#95—21no—
255#340C2314yes—
256#340C2314yes—
257#340C2314yes—
258#340C2314yes—
259#340C2314yes—
260#340C2314yes—
261#336C2314yes—
262#336C2314yes—
263C25—21no—
264C25—21no—
265C25C2×D411yescharacteristic
266C22×D4—28no—
267C22×D4—22no—
268C22×D4—22no—
269C22×D4—24no—
270C22×D4—22no—
271C22×D4—22no—
272C22×D4—21no—
273C22×D4—21no—
274C22×D4—24no—
275C22×D4—24no—
276C22×D4—42no—
277C22×D4—42no—
278C22×D4—42no—
279C22×D4—44no—
280C22×D4—44no—
281C22×D4—44no—
282C22×D4—44no—
283C22×D4—44no—
284C22×D4C2412yes—
285C22×D4C2412yes—
286C23×C4—24no—
287C23×C4—21no—
288C23×C4—24no—
289C23×C4—24no—
290C23×C4—24no—
291C23×C4—21no—
292C23×C4—21no—
293C23×C4—21no—
294C23×C4—21no—
295C23×C4—21no—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4—42no—
299C23×C4—42no—
300C23×C4—42no—
301C23×C4—42no—
302C23×C4—42no—
303C23×C4—44no—
304C23×C4—44no—
305C23×C4—44no—
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D411yescharacteristic
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D411yescharacteristic
314C23×C4C2×D411yescharacteristic
315C23×C4C2×D411yescharacteristic
316C23×C4C2×D411yescharacteristic
317C23×C4C2×D411yescharacteristic
318C23×C4C2×D411yescharacteristic
319C23×C4C2×D411yescharacteristic
320C23×C4C2×D411yescharacteristic
321C23×C4C2411yescharacteristic
322C23×C4C2411yescharacteristic
323C23×C4C2411yescharacteristic
324C2×D8—28no—
325C2×D8—44no—
326C2×D8—44no—
327C22×C8C2414yes—
328C22×C8C2414yes—
329#123—48no—
330#123—48no—
331#123—48no—
332#123—48no—
333#121—28no—
334#121—28no—
335#121—24no—
336#121—24no—
337#121—24no—
338#121—24no—
339#121—24no—
340#121—42no—
341#121—42no—
342#121—44no—
343#121—44no—
344#121#4118yes—
345C4×D4—44no—
346C4×D4—44no—
347C4×D4—44no—
348C4×D4—44no—
349C4×D4—48no—
350C4×D4—48no—
351C4×D4—48no—
352C4×D4—48no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—42no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—42no—
371C2×C4⋊C4—44no—
372C2×C4⋊C4—44no—
373C2×C4⋊C4—44no—
374C2×C4⋊C4C2412yes—
375C2×C4⋊C4C2412yes—
376C2×C4⋊C4C2412yes—
377C2×C4⋊C4C2412yes—
378C2×C4⋊C4C2412yes—
379C2×C4⋊C4C2412yes—
380C2×C22⋊C4—28no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—44no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4—44no—
406C2×C22⋊C4—44no—
407C2×C22⋊C4—44no—
408C2×C22⋊C4—44no—
409C2×C22⋊C4—44no—
410C2×C22⋊C4—44no—
411C2×C22⋊C4—44no—
412C2×C22⋊C4—44no—
413C2×C42—24no—
414C2×C42—24no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—42no—
418C2×C42—42no—
419C2×C42—42no—
420C2×C42—42no—
421C2×C42—42no—
422C2×C42—42no—
423C2×C42—42no—
424C2×C42—42no—
425C2×C42—42no—
426C2×C42—42no—
427C2×C42—44no—
428C2×C42C2×D411yescharacteristic
429C2×C42C2×D411yescharacteristic
430C2×C42C2×D411yescharacteristic
431C2×C42C2×D411yescharacteristic
432C2×C42C2×D411yescharacteristic
433C2×C42C2×D411yescharacteristic
434C2×C42C2×D411yescharacteristic
435C2×C42C2×D411yescharacteristic
436C2×C42C2×D411yescharacteristic
437C2×C42C2×D411yescharacteristic
438C2×C42C2×D411yescharacteristic
439C2×C42C2×D411yescharacteristic
440C2×C42C2411yescharacteristic
441C2×C42C2411yescharacteristic
442C2×C42C2411yescharacteristic
443C2×C42C2411yescharacteristic
444#107—44no—
445#106—28no—
446#106—44no—
447C4⋊C8—44no—
448#102—28no—
449#102—28no—
450#102—44no—
451#102—44no—
452#102—44no—
453#102—44no—
454C22⋊C8—24no—
455C22⋊C8—24no—
456C22⋊C8—24no—
457C22⋊C8—24no—
458C22⋊C8—42no—
459C22⋊C8—42no—
460#97—44no—
461#95—22no—
462#95—22no—
463#95—22no—
464#95—22no—
465#95—22no—
466#95—22no—
467#95—22no—
468#95—22no—
469#95—22no—
470#95—22no—
471#95—22no—
472#95—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—24no—
478C24—22no—
479C24—22no—
480C24—41no—
481C24—41no—
482C24—42no—
483C24—42no—
484C24—42no—
485C24—42no—
486C24—42no—
487C24—42no—
488C24—42no—
489C24—42no—
490C24—42no—
491C24—42no—
492C24—42no—
493C24—42no—
494C24—42no—
495C24AGL(1,ℤ/8)14yes—
496C24C22×D411yescharacteristic
497C24C22×D411yescharacteristic
498C24C22×D411yescharacteristic
499C2×D4—24no—
500C2×D4—28no—
501C2×D4—28no—
502C2×D4—22no—
503C2×D4—24no—
504C2×D4—24no—
505C2×D4—22no—
506C2×D4—22no—
507C2×D4—24no—
508C2×D4—24no—
509C2×D4—416no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—42no—
513C2×D4—432no—
514C2×D4—44no—
515C2×D4—44no—
516C2×D4—44no—
517C2×D4—44no—
518C2×D4—44no—
519C2×D4—44no—
520C2×D4—44no—
521C2×D4—44no—
522C2×D4—44no—
523C2×D4—44no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4—88no—
527C2×D4—816no—
528C2×D4C2×#4114yes—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—24no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—416no—
588C22×C4—416no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—42no—
594C22×C4—416no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—44no—
612C22×C4—44no—
613C22×C4—816no—
614C22×C4AGL(1,ℤ/8)14yes—
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C22×D411yescharacteristic
626C22×C4C2×#4114yes—
627C22×C4H(5,𝔽2)14yes—
628C22×C4C2511yescharacteristic
629D8—88no—
630C2×C8—24no—
631C2×C8—24no—
632C2×C8—24no—
633C2×C8—24no—
634C2×C8—24no—
635C2×C8—24no—
636C4⋊C4—24no—
637C4⋊C4—22no—
638C4⋊C4—24no—
639C4⋊C4—22no—
640C4⋊C4—24no—
641C4⋊C4—22no—
642C4⋊C4—24no—
643C4⋊C4—24no—
644C4⋊C4—42no—
645C4⋊C4—42no—
646C4⋊C4—44no—
647C4⋊C4—44no—
648C4⋊C4—42no—
649C4⋊C4—44no—
650C4⋊C4—44no—
651C4⋊C4—42no—
652C4⋊C4—42no—
653C4⋊C4—44no—
654C4⋊C4—44no—
655C4⋊C4C2×#4114yes—
656C22⋊C4—28no—
657C22⋊C4—28no—
658C22⋊C4—44no—
659C22⋊C4—44no—
660C22⋊C4—44no—
661C22⋊C4—44no—
662C22⋊C4—44no—
663C22⋊C4—44no—
664C22⋊C4—44no—
665C22⋊C4—44no—
666C22⋊C4—44no—
667C22⋊C4—44no—
668C22⋊C4—44no—
669C22⋊C4—44no—
670C22⋊C4—44no—
671C22⋊C4—44no—
672C22⋊C4—44no—
673C22⋊C4—44no—
674C22⋊C4—44no—
675C22⋊C4—44no—
676C22⋊C4—44no—
677C22⋊C4—44no—
678C42—22no—
679C42—22no—
680C42—22no—
681C42—22no—
682C42—22no—
683C42—22no—
684C42—22no—
685C42—22no—
686C42—41no—
687C42—41no—
688C42—41no—
689C42—41no—
690C42—41no—
691C42—41no—
692C42—41no—
693C42—41no—
694C42—44no—
695C42—44no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—28no—
705C23—21no—
706C23—21no—
707C23—28no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—24no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23—44no—
718C23—48no—
719C23—48no—
720C23—48no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—84no—
735C23—84no—
736C23—84no—
737C23—84no—
738C23—84no—
739C23—84no—
740C23—84no—
741C23—84no—
742C23—84no—
743C23—84no—
744C23—84no—
745C23#52512yes—
746C23#53412yes—
747C23C2×AGL(1,ℤ/8)12yes—
748C23C2×AGL(1,ℤ/8)12yes—
749C23C2×AGL(1,ℤ/8)12yes—
750C23C2×AGL(1,ℤ/8)12yes—
751C23#57512yes—
752C23C23×D411yescharacteristic
753D4—28no—
754D4—48no—
755D4—416no—
756D4—416no—
757D4—44no—
758D4—44no—
759D4—44no—
760D4—84no—
761D4—88no—
762D4—88no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—28no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—28no—
775C2×C4—28no—
776C2×C4—21no—
777C2×C4—24no—
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—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—48no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—44no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—88no—
829C2×C4—88no—
830C2×C4—84no—
831C2×C4—84no—
832C2×C4—84no—
833C2×C4—84no—
834C2×C4—84no—
835C2×C4#52512yes—
836C2×C4#53412yes—
837C2×C4C2×AGL(1,ℤ/8)12yes—
838C2×C4C2×AGL(1,ℤ/8)12yes—
839C2×C4#57512yes—
840C2×C4C22×#4112yes—
841C2×C4C2×H(5,𝔽2)12yes—
842C2×C4#58512yes—
843C8—44no—
844C8—44no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—416no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—44no—
866C22—44no—
867C22—44no—
868C22—816no—
869C22—82no—
870C22—82no—
871C22—82no—
872C22—82no—
873C22—82no—
874C22—82no—
875C22—82no—
876C22—82no—
877C22—82no—
878C22—82no—
879C22—82no—
880C22—168no—
881C22#311414yes—
882C22#319214yes—
883C22C2×#52511yescharacteristic
884C22C2×#53411yescharacteristic
885C22#344911yescharacteristic
886C22C22×AGL(1,ℤ/8)11yescharacteristic
887C22C22×AGL(1,ℤ/8)11yescharacteristic
888C22C2×#57511yescharacteristic
889C22C2×#57511yescharacteristic
890C4—22no—
891C4—22no—
892C4—22no—
893C4—22no—
894C4—22no—
895C4—41no—
896C4—41no—
897C4—41no—
898C4—41no—
899C4—41no—
900C4—44no—
901C4—41no—
902C4—82no—
903C4—82no—
904C4—82no—
905C4—82no—
906C4—82no—
907C4#351314yes—
908C2—24no—
909C2—24no—
910C2—42no—
911C2—84no—
912C2—162no—
913C2#3506211yescharacteristic
914C2C2×#311411yescharacteristic
915C2#6056111yescharacteristic
916C2C2×#319211yescharacteristic
917C2#6075211yescharacteristic
918C2#6094911yescharacteristic
919C2#6095811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#23918C2
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
1. C2×#2854C2semidirect
2. C2×C4×#121C2semidirect
3. #33095C2semidirect
4. #33002C2semidirect
5. #30015C2semidirect
6. #29476C2semidirect
7. #29237C2semidirect
8. #28117C2semidirect
9. #27601C2semidirect
10. #24608C2semidirect
11. #24506C2semidirect
12. #24005C2semidirect
13. #24002C2semidirect
15. #22082C2semidirect
16. #22046C2semidirect
17. #20715C2semidirect
22. C22×C4×D4C22semidirect
28. C2×#432C22semidirect
35. #2854C22semidirect
36. #2854C22semidirect
43. C4×#121C22semidirect
44. C4×#121C22semidirect
45. C2×#390C22semidirect
46. C2×#390C22semidirect
47. C2×#390C22semidirect
48. C2×#389C22semidirect
49. C2×#389C22semidirect
50. C2×#389C22semidirect
58. C2×C4×C4⋊C4C22semidirect
60. #2087C22semidirect
61. #2077C22semidirect
62. #2065C22semidirect
63. #2065C22semidirect
64. #2054C22semidirect
65. #2034C22semidirect
66. #2033C22semidirect
68. #1972C22semidirect
69. #1944C22semidirect
70. #1936C22semidirect
71. #1936C22semidirect
72. #1926C22semidirect
73. #1926C22semidirect
74. #1919C22semidirect
75. #1919C22semidirect
76. #1879C22semidirect
77. #1879C22semidirect
82. #1862C22semidirect
83. #1862C22semidirect
84. #1853C22semidirect
85. #1853C22semidirect
86. #1853C22semidirect
87. #1852C22semidirect
88. #1824C22semidirect
89. #1823C22semidirect
90. #1817C22semidirect
91. #1797C22semidirect
92. #1797C22semidirect
93. #1786C22semidirect
94. #1786C22semidirect
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×#28542
C2×C4×#1212
#330952
#330022
#300152
#294762
#292372
#281172
#276012
#246082
#245062
#240052
#240022
#239182
#220822
#220462
#207152