Finite Group Databasebeta

← #6468700

Subgroups — #6468700

Order 512.

2756 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#121C211yesmaximal, characteristic, complemented
2C2×C4×#121C211yesmaximal, characteristic, complemented
3#29412C214yesmaximal, complemented
4#29238C212yesmaximal, complemented
5#29235C212yesmaximal, complemented
6#28117C212yesmaximal, complemented
7#28114C212yesmaximal, complemented
8#27601C211yesmaximal, characteristic, complemented
9#24005C211yesmaximal, characteristic, complemented
10#24002C211yesmaximal, characteristic, complemented
11#23918C211yesmaximal, characteristic
12#23708C214yesmaximal, complemented
13#21580C212yesmaximal, complemented
14#21578C212yesmaximal, complemented
15#21452C212yesmaximal, complemented
16#21452C212yesmaximal, complemented
17#20715C211yesmaximal, characteristic, complemented
18C22×#121C2211yescharacteristic
19C22×#121C2211yescharacteristic
20C22×C4×D4—21no—
21C22×C4×D4—21no—
22C22×C4×D4C2211yescharacteristic, complemented
23C22×C4×D4C2211yescharacteristic, complemented
24C23×C42C2211yescharacteristic
25C2×#481C2212yes—
26C2×#480C2212yes—
27C2×#447C2212yes—
28C2×#447C2212yes—
29C2×#442C2214yescomplemented
30C2×#432C2212yescomplemented
31C4×#121—21no—
32C4×#121—21no—
33C4×#121—21no—
34C4×#121—21no—
35C4×#121—21no—
36C4×#121—21no—
37C4×#121—21no—
38C4×#121—21no—
39C4×#121C2212yes—
40C4×#121C2212yes—
41C4×#121C2212yes—
42C4×#121C2212yes—
43C4×#121C2212yescomplemented
44C4×#121C2212yescomplemented
45C4×#121C2212yescomplemented
46C4×#121C2212yescomplemented
47C2×#390C2211yescharacteristic, complemented
48C2×#390C2211yescharacteristic, complemented
49C2×#389C2211yescharacteristic, complemented
50C2×#389C2211yescharacteristic, complemented
51C2×#388—21no—
52C2×#388—21no—
53C2×#386—21no—
54C2×#386—21no—
55C2×#380C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×C4×C4⋊C4C2211yescharacteristic, complemented
58C2×C4×C4⋊C4C2211yescharacteristic, complemented
59C2×C4×C22⋊C4—21no—
60C2×C4×C22⋊C4—21no—
61#2088C2214yescomplemented
62#2077C2214yescomplemented
63#2067C2214yescomplemented
64#2065C2214yescomplemented
65#2054C2214yescomplemented
66#2034C2214yescomplemented
67#2033C2214yescomplemented
68#1999C2214yes—
69#1926C2214yescomplemented
70#1925C2214yescomplemented
71#1921C2214yescomplemented
72#1920C2214yescomplemented
73#1879C2214yescomplemented
74#1879C2214yescomplemented
75#1874C2212yes—
76#1874C2212yes—
77#1874C2212yes—
78#1874C2212yes—
79#1864C2214yescomplemented
80#1864C2214yescomplemented
81#1853C2212yescomplemented
82#1853C2212yescomplemented
83#1853C2212yescomplemented
84#1852C2212yescomplemented
85#1824C2212yescomplemented
86#1823C2212yescomplemented
87#1817C2212yescomplemented
88#1797C2212yescomplemented
89#1797C2212yescomplemented
90#1786C2212yescomplemented
91#1786C2212yescomplemented
92#1779C2211yescharacteristic
93#1779C2211yescharacteristic
94#1776C2214yescomplemented
95#1762C2214yescomplemented
96#1762C2214yescomplemented
97#1749C2212yescomplemented
98#1749C2212yescomplemented
99C23×D4—21no—
100C23×D4—21no—
101C23×D4C2311yescharacteristic
102C23×D4C2311yescharacteristic
103C24×C4—21no—
104C24×C4—21no—
105C24×C4D411yescharacteristic
106C24×C4D411yescharacteristic
107C24×C4C2311yescharacteristic
108C22×D8C2314yes—
109C2×#121—21no—
110C2×#121—21no—
111C2×#121—21no—
112C2×#121—21no—
113C2×#121—28no—
114C2×#121—28no—
115C2×#121C2312yes—
116C2×#121C2312yes—
117C2×#121C2312yes—
118C2×#121C2312yes—
119C2×C4×D4—22no—
120C2×C4×D4—22no—
121C2×C4×D4—22no—
122C2×C4×D4—22no—
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—21no—
130C2×C4×D4—21no—
131C2×C4×D4—44no—
132C2×C4×D4—44no—
133C2×C4×D4—48no—
134C2×C4×D4—48no—
135C2×C4×D4C2312yes—
136C2×C4×D4C2312yes—
137C2×C4×D4C2312yes—
138C2×C4×D4C2312yes—
139C22×C4⋊C4—21no—
140C22×C4⋊C4—21no—
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2311yescharacteristic
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×C22⋊C4—21no—
154C22×C22⋊C4—21no—
155C22×C22⋊C4—21no—
156C22×C22⋊C4—21no—
157C22×C42—21no—
158C22×C42—21no—
159C22×C42—44no—
160C22×C42D411yescharacteristic
161C22×C42D411yescharacteristic
162C22×C42D411yescharacteristic
163C22×C42D411yescharacteristic
164C22×C42D411yescharacteristic
165C22×C42D411yescharacteristic
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168C22×C42C2311yescharacteristic
169C22×C42C2311yescharacteristic
170C22×C42C2311yescharacteristic
171C22×C42C2311yescharacteristic
172#481—28no—
173#480—28no—
174#447—28no—
175#447—28no—
176#442—48no—
177#432—44no—
178C2×#107C2314yes—
179C2×#106C2314yes—
180C2×#106C2314yes—
181C2×C4⋊C8C2314yes—
182C2×#102C2314yes—
183C2×#102C2314yes—
184C2×#102C2314yes—
185C2×#102C2314yes—
186C2×#102C2314yes—
187C2×#102C2314yes—
188C2×C22⋊C8C2312yes—
189C2×C22⋊C8C2312yes—
190C2×C22⋊C8C2312yes—
191C2×C22⋊C8C2312yes—
192C2×C22⋊C8C2312yes—
193C2×C22⋊C8C2312yes—
194C2×#97C2314yes—
195#390—21no—
196#390—21no—
197#390—21no—
198#390—21no—
199#390C2312yes—
200#390C2312yes—
201#390C2312yes—
202#390C2312yes—
203#389—21no—
204#389—21no—
205#389—21no—
206#389—21no—
207#389C2312yes—
208#389C2312yes—
209#389C2312yes—
210#389C2312yes—
211#388—22no—
212#388—22no—
213#388—22no—
214#388—22no—
215#388—22no—
216#388—22no—
217#388—22no—
218#388—22no—
219#386—22no—
220#386—22no—
221#386—22no—
222#386—22no—
223#386—22no—
224#386—22no—
225#386—22no—
226#386—22no—
227#380—21no—
228#380—21no—
229#380—21no—
230#380—21no—
231#380C2312yes—
232#380C2312yes—
233#380C2312yes—
234#380C2312yes—
235C4×C4⋊C4—21no—
236C4×C4⋊C4—21no—
237C4×C4⋊C4—21no—
238C4×C4⋊C4—21no—
239C4×C4⋊C4C2312yes—
240C4×C4⋊C4C2312yes—
241C4×C4⋊C4C2312yes—
242C4×C4⋊C4C2312yes—
243C4×C22⋊C4—22no—
244C4×C22⋊C4—22no—
245C4×C22⋊C4—22no—
246C4×C22⋊C4—22no—
247C4×C22⋊C4—22no—
248C4×C22⋊C4—22no—
249C4×C22⋊C4—22no—
250C4×C22⋊C4—22no—
251C2×#95—21no—
252C2×#95—21no—
253C2×#95—21no—
254C2×#95—21no—
255C2×#95—21no—
256C2×#95—21no—
257#340C2314yes—
258#340C2314yes—
259#340C2314yes—
260#340C2314yes—
261#340C2314yes—
262#340C2314yes—
263#336C2314yes—
264#336C2314yes—
265C25—21no—
266C25—21no—
267C25C2×D411yescharacteristic
268C22×D4—28no—
269C22×D4—28no—
270C22×D4—22no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—22no—
274C22×D4—24no—
275C22×D4—24no—
276C22×D4—21no—
277C22×D4—21no—
278C22×D4—24no—
279C22×D4—24no—
280C22×D4—42no—
281C22×D4—42no—
282C22×D4—44no—
283C22×D4—44no—
284C22×D4—44no—
285C22×D4—44no—
286C22×D4C2412yes—
287C22×D4C2412yes—
288C23×C4—24no—
289C23×C4—21no—
290C23×C4—21no—
291C23×C4—24no—
292C23×C4—24no—
293C23×C4—24no—
294C23×C4—21no—
295C23×C4—21no—
296C23×C4—21no—
297C23×C4—21no—
298C23×C4—22no—
299C23×C4—22no—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4—42no—
303C23×C4—42no—
304C23×C4—42no—
305C23×C4—42no—
306C23×C4—42no—
307C23×C4—44no—
308C23×C4—44no—
309C23×C4—44no—
310C23×C4—44no—
311C23×C4—44no—
312C23×C4—44no—
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×C4C2×D411yescharacteristic
322C23×C4C2×D411yescharacteristic
323C23×C4C2×D411yescharacteristic
324C23×C4C2×D411yescharacteristic
325C23×C4C2×D411yescharacteristic
326C23×C4C2×D411yescharacteristic
327C23×C4C2×D411yescharacteristic
328C23×C4C2411yescharacteristic
329C23×C4C2411yescharacteristic
330C23×C4C2411yescharacteristic
331C2×D8—28no—
332C2×D8—28no—
333C2×D8—44no—
334C22×C8C2414yes—
335C22×C8C2414yes—
336#121—28no—
337#121—28no—
338#121—28no—
339#121—28no—
340#121—24no—
341#121—24no—
342#121—24no—
343#121—24no—
344#121—24no—
345#121—24no—
346#121#4118yes—
347#121#4118yes—
348C4×D4—28no—
349C4×D4—28no—
350C4×D4—44no—
351C4×D4—44no—
352C4×D4—44no—
353C4×D4—44no—
354C4×D4—44no—
355C4×D4—44no—
356C4×D4—48no—
357C4×D4—48no—
358C4×D4—48no—
359C4×D4—48no—
360C4×D4—48no—
361C4×D4—48no—
362C4×D4—48no—
363C4×D4—48no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—42no—
379C2×C4⋊C4—42no—
380C2×C4⋊C4—44no—
381C2×C4⋊C4—44no—
382C2×C4⋊C4C2412yes—
383C2×C4⋊C4C2412yes—
384C2×C4⋊C4C2412yes—
385C2×C4⋊C4C2412yes—
386C2×C4⋊C4C2412yes—
387C2×C4⋊C4C2412yes—
388C2×C22⋊C4—28no—
389C2×C22⋊C4—28no—
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—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—44no—
411C2×C22⋊C4—44no—
412C2×C22⋊C4—44no—
413C2×C22⋊C4—44no—
414C2×C22⋊C4—44no—
415C2×C22⋊C4—44no—
416C2×C22⋊C4—44no—
417C2×C22⋊C4—44no—
418C2×C42—24no—
419C2×C42—24no—
420C2×C42—24no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—42no—
426C2×C42—42no—
427C2×C42—42no—
428C2×C42—42no—
429C2×C42—42no—
430C2×C42—42no—
431C2×C42—42no—
432C2×C42—42no—
433C2×C42—42no—
434C2×C42—44no—
435C2×C42—44no—
436C2×C42C2×D411yescharacteristic
437C2×C42C2×D411yescharacteristic
438C2×C42C2×D411yescharacteristic
439C2×C42C2×D411yescharacteristic
440C2×C42C2×D411yescharacteristic
441C2×C42C2×D411yescharacteristic
442C2×C42C2×D411yescharacteristic
443C2×C42C2×D411yescharacteristic
444C2×C42C2×D411yescharacteristic
445C2×C42C2×D411yescharacteristic
446C2×C42C2×D411yescharacteristic
447C2×C42C2×D411yescharacteristic
448C2×C42C2411yescharacteristic
449C2×C42C2411yescharacteristic
450C2×C42C2411yescharacteristic
451C2×C42C2411yescharacteristic
452#107—28no—
453#106—28no—
454#106—44no—
455C4⋊C8—44no—
456#102—28no—
457#102—28no—
458#102—28no—
459#102—28no—
460#102—44no—
461#102—44no—
462C22⋊C8—24no—
463C22⋊C8—24no—
464C22⋊C8—24no—
465C22⋊C8—24no—
466C22⋊C8—42no—
467C22⋊C8—42no—
468#97—28no—
469#95—22no—
470#95—22no—
471#95—22no—
472#95—22no—
473#95—22no—
474#95—22no—
475#95—22no—
476#95—22no—
477#95—22no—
478#95—22no—
479#95—22no—
480#95—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—24no—
486C24—24no—
487C24—22no—
488C24—22no—
489C24—41no—
490C24—41no—
491C24—42no—
492C24—42no—
493C24—42no—
494C24—42no—
495C24—42no—
496C24—42no—
497C24—42no—
498C24—42no—
499C24—42no—
500C24—42no—
501C24—42no—
502C24—42no—
503C24AGL(1,ℤ/8)14yes—
504C24C22×D411yescharacteristic
505C24C22×D411yescharacteristic
506C24C22×D411yescharacteristic
507C2×D4—24no—
508C2×D4—24no—
509C2×D4—28no—
510C2×D4—28no—
511C2×D4—28no—
512C2×D4—28no—
513C2×D4—24no—
514C2×D4—24no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—24no—
518C2×D4—24no—
519C2×D4—416no—
520C2×D4—416no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4—44no—
524C2×D4—432no—
525C2×D4—432no—
526C2×D4—44no—
527C2×D4—44no—
528C2×D4—44no—
529C2×D4—44no—
530C2×D4—44no—
531C2×D4—44no—
532C2×D4—44no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4C2×#4114yes—
536C2×D4C2×#4114yes—
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—24no—
548C22×C4—24no—
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—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—416no—
597C22×C4—416no—
598C22×C4—416no—
599C22×C4—44no—
600C22×C4—44no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4—44no—
627C22×C4—816no—
628C22×C4—816no—
629C22×C4AGL(1,ℤ/8)14yes—
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×C4C22×D411yescharacteristic
640C22×C4C22×D411yescharacteristic
641C22×C4C2×#4114yes—
642C22×C4C2×#4114yes—
643C22×C4C2511yescharacteristic
644D8—416no—
645C2×C8—24no—
646C2×C8—24no—
647C2×C8—24no—
648C2×C8—24no—
649C2×C8—24no—
650C2×C8—24no—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—24no—
656C4⋊C4—24no—
657C4⋊C4—24no—
658C4⋊C4—24no—
659C4⋊C4—42no—
660C4⋊C4—42no—
661C4⋊C4—44no—
662C4⋊C4—44no—
663C4⋊C4—44no—
664C4⋊C4—42no—
665C4⋊C4—42no—
666C4⋊C4—44no—
667C4⋊C4C2×#4114yes—
668C4⋊C4C2×#4114yes—
669C22⋊C4—28no—
670C22⋊C4—28no—
671C22⋊C4—28no—
672C22⋊C4—28no—
673C22⋊C4—44no—
674C22⋊C4—44no—
675C22⋊C4—44no—
676C22⋊C4—44no—
677C22⋊C4—44no—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—44no—
681C22⋊C4—44no—
682C22⋊C4—44no—
683C22⋊C4—44no—
684C22⋊C4—44no—
685C22⋊C4—44no—
686C22⋊C4—44no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C42—22no—
690C42—22no—
691C42—22no—
692C42—22no—
693C42—22no—
694C42—22no—
695C42—22no—
696C42—22no—
697C42—22no—
698C42—41no—
699C42—41no—
700C42—41no—
701C42—41no—
702C42—41no—
703C42—41no—
704C42—44no—
705C42—44no—
706C42—44no—
707C42—44no—
708C42H(5,𝔽2)14yes—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—28no—
718C23—28no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—24no—
726C23—24no—
727C23—44no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—48no—
733C23—48no—
734C23—48no—
735C23—48no—
736C23—48no—
737C23—48no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—84no—
751C23—84no—
752C23—84no—
753C23—84no—
754C23—84no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23#52512yes—
759C23#52512yes—
760C23C2×AGL(1,ℤ/8)12yes—
761C23C2×AGL(1,ℤ/8)12yes—
762C23C2×AGL(1,ℤ/8)12yes—
763C23C2×AGL(1,ℤ/8)12yes—
764C23#57512yes—
765C23C23×D411yescharacteristic
766D4—28no—
767D4—28no—
768D4—48no—
769D4—48no—
770D4—416no—
771D4—416no—
772D4—416no—
773D4—416no—
774D4—44no—
775D4—44no—
776C2×C4—28no—
777C2×C4—28no—
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—28no—
793C2×C4—28no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—24no—
797C2×C4—24no—
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—21no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—44no—
821C2×C4—48no—
822C2×C4—48no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—44no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—88no—
841C2×C4—88no—
842C2×C4—88no—
843C2×C4—88no—
844C2×C4—84no—
845C2×C4—84no—
846C2×C4—84no—
847C2×C4—84no—
848C2×C4#52512yes—
849C2×C4#52512yes—
850C2×C4#53412yes—
851C2×C4#53412yes—
852C2×C4C2×AGL(1,ℤ/8)12yes—
853C2×C4C2×AGL(1,ℤ/8)12yes—
854C2×C4#57512yes—
855C2×C4C22×#4112yes—
856C2×C4C22×#4112yes—
857C2×C4C2×H(5,𝔽2)12yes—
858C8—44no—
859C8—44no—
860C22—22no—
861C22—22no—
862C22—22no—
863C22—22no—
864C22—22no—
865C22—22no—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—416no—
876C22—41no—
877C22—41no—
878C22—41no—
879C22—41no—
880C22—44no—
881C22—44no—
882C22—44no—
883C22—44no—
884C22—44no—
885C22—44no—
886C22—816no—
887C22—816no—
888C22—82no—
889C22—82no—
890C22—82no—
891C22—82no—
892C22—82no—
893C22—82no—
894C22—82no—
895C22—82no—
896C22#310914yes—
897C22#311414yes—
898C22C2×#52511yescharacteristic
899C22C2×#52511yescharacteristic
900C22C2×#53411yescharacteristic
901C22C22×AGL(1,ℤ/8)11yescharacteristic
902C22C22×AGL(1,ℤ/8)11yescharacteristic
903C22C2×#57511yescharacteristic
904C22C2×#57511yescharacteristic
905C4—22no—
906C4—22no—
907C4—22no—
908C4—22no—
909C4—22no—
910C4—22no—
911C4—22no—
912C4—41no—
913C4—41no—
914C4—41no—
915C4—44no—
916C4—44no—
917C4—41no—
918C4—82no—
919C4—82no—
920C4—82no—
921C4—82no—
922C4#348114yes—
923C2—24no—
924C2—24no—
925C2—42no—
926C2—84no—
927C2—84no—
928C2#3495611yescharacteristic
929C2C2×#311411yescharacteristic
930C2C2×#310911yescharacteristic
931C2#6056111yescharacteristic
932C2#6056311yescharacteristic
933C2#6075011yescharacteristic
934C2#6075011yescharacteristic
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×C4×#121C2semidirect
2. C2×C4×#121C2semidirect
3. #29412C2semidirect
4. #29238C2semidirect
5. #29235C2semidirect
6. #28117C2semidirect
7. #28114C2semidirect
8. #27601C2semidirect
9. #24005C2semidirect
10. #24002C2semidirect
12. #23708C2semidirect
13. #21580C2semidirect
14. #21578C2semidirect
15. #21452C2semidirect
16. #21452C2semidirect
17. #20715C2semidirect
22. C22×C4×D4C22semidirect
23. C22×C4×D4C22semidirect
29. C2×#442C22semidirect
30. C2×#432C22semidirect
43. C4×#121C22semidirect
44. C4×#121C22semidirect
45. C4×#121C22semidirect
46. C4×#121C22semidirect
47. C2×#390C22semidirect
48. C2×#390C22semidirect
49. C2×#389C22semidirect
50. C2×#389C22semidirect
57. C2×C4×C4⋊C4C22semidirect
58. C2×C4×C4⋊C4C22semidirect
61. #2088C22semidirect
62. #2077C22semidirect
63. #2067C22semidirect
64. #2065C22semidirect
65. #2054C22semidirect
66. #2034C22semidirect
67. #2033C22semidirect
69. #1926C22semidirect
70. #1925C22semidirect
71. #1921C22semidirect
72. #1920C22semidirect
73. #1879C22semidirect
74. #1879C22semidirect
79. #1864C22semidirect
80. #1864C22semidirect
81. #1853C22semidirect
82. #1853C22semidirect
83. #1853C22semidirect
84. #1852C22semidirect
85. #1824C22semidirect
86. #1823C22semidirect
87. #1817C22semidirect
88. #1797C22semidirect
89. #1797C22semidirect
90. #1786C22semidirect
91. #1786C22semidirect
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
#294122
#292382
#292352
#281172
#281142
#276012
#240052
#240022
#239182
#237082
#215802
#215782
#214522
#207152