Finite Group Databasebeta

← #6475541

Subgroups — #6475541

Order 512.

2440 conjugacy classes of subgroups.

The subgroup lattice has 927 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36624C211yesmaximal, characteristic, complemented
2C2×C4×#121C211yesmaximal, characteristic, complemented
3#33146C211yesmaximal, characteristic, complemented
4#33106C211yesmaximal, characteristic, complemented
5#32953C211yesmaximal, characteristic, complemented
6#32902C211yesmaximal, characteristic, complemented
7#29890C212yesmaximal, complemented
8#29592C212yesmaximal, complemented
9#29460C214yesmaximal, complemented
10#29408C214yesmaximal, complemented
11#27624C212yesmaximal, complemented
12#24700C212yesmaximal, complemented
13#24650C212yesmaximal, complemented
14#24150C212yesmaximal, complemented
15#22075C212yesmaximal, complemented
16#22040C212yesmaximal, complemented
17#20714C211yesmaximal, characteristic, complemented
18C2×#532C2211yescharacteristic, complemented
19C2×#525—21no—
20C22×#121C2211yescharacteristic
21C22×C4×D4—21no—
22C22×C4×D4C2211yescharacteristic
23C23×C42C2211yescharacteristic
24C2×#480C2212yes—
25C2×#474C2212yescomplemented
26C2×#459C2212yescomplemented
27C2×#447C2212yes—
28C2×#431C2212yescomplemented
29#2857C2211yescharacteristic
30#2857C2211yescharacteristic, complemented
31#2856C2211yescharacteristic
32#2856C2211yescharacteristic, complemented
33#2854—21no—
34#2854C2212yescomplemented
35#2850—21no—
36#2850—21no—
37#2847—21no—
38#2847C2212yes—
39C4×#121—21no—
40C4×#121—21no—
41C4×#121—21no—
42C4×#121—21no—
43C4×#121—21no—
44C4×#121—21no—
45C4×#121C2212yes—
46C4×#121C2212yes—
47C4×#121C2212yes—
48C4×#121C2212yes—
49C4×#121C2212yes—
50C4×#121C2212yescomplemented
51#2297—21no—
52C2×#390C2211yescharacteristic
53C2×#389C2211yescharacteristic
54C2×#388—21no—
55C2×#386—21no—
56#2285C2211yescharacteristic, complemented
57C2×#380C2211yescharacteristic
58C2×C4×C4⋊C4C2211yescharacteristic
59C2×C4×C22⋊C4—21no—
60#2075C2214yescomplemented
61#2075C2214yescomplemented
62#2033C2214yes—
63#2033C2214yes—
64#2033C2214yescomplemented
65#2033C2214yescomplemented
66#1999C2214yes—
67#1999C2214yes—
68#1988C2212yescomplemented
69#1982C2212yescomplemented
70#1970C2214yescomplemented
71#1947C2212yescomplemented
72#1947C2212yescomplemented
73#1942C2214yescomplemented
74#1934C2214yescomplemented
75#1934C2214yescomplemented
76#1925C2214yescomplemented
77#1925C2214yescomplemented
78#1918C2214yescomplemented
79#1918C2214yescomplemented
80#1879C2214yescomplemented
81#1879C2214yescomplemented
82#1874C2212yes—
83#1874C2212yes—
84#1862C2214yescomplemented
85#1862C2214yescomplemented
86#1852C2212yes—
87#1852C2212yes—
88#1823C2212yes—
89#1817C2212yescomplemented
90#1802C2212yescomplemented
91#1802C2212yescomplemented
92#1797C2211yescharacteristic
93#1797C2211yescharacteristic
94#1797C2212yescomplemented
95#1786C2212yes—
96#1779C2212yes—
97C4×C22⋊C8C2212yes—
98C4×C22⋊C8C2212yescomplemented
99C22×#41—21no—
100C23×D4—21no—
101C23×D4C2311yescharacteristic
102C24×C4—21no—
103C24×C4D411yescharacteristic
104C24×C4D411yescharacteristic
105C24×C4C2311yescharacteristic
106C22×D8C2314yes—
107#532—44no—
108C2×C4⋊Q8C2311yescharacteristic
109C2×#127C2311yescharacteristic
110C2×#124—21no—
111#525—48no—
112C2×#123—22no—
113C2×C22⋊Q8—21no—
114C2×C22⋊Q8—21no—
115C2×#121—24no—
116C2×#121—21no—
117C2×#121—21no—
118C2×#121—21no—
119C2×#121—21no—
120C2×#121—21no—
121C2×#121—21no—
122C2×#121—21no—
123C2×#121—24no—
124C2×#121C2312yes—
125C2×#121C2312yes—
126C2×#121C2312yes—
127C2×#121C2312yes—
128C2×#121C2312yes—
129C2×#120—22no—
130C2×C4×D4—22no—
131C2×C4×D4—22no—
132C2×C4×D4—22no—
133C2×C4×D4—22no—
134C2×C4×D4—22no—
135C2×C4×D4—22no—
136C2×C4×D4—21no—
137C2×C4×D4—21no—
138C2×C4×D4—21no—
139C2×C4×D4—44no—
140C2×C4×D4—48no—
141C2×C4×D4C2312yes—
142C2×C4×D4C2312yes—
143C2×C4×D4C2312yes—
144C2×#117—21no—
145C22×C4⋊C4—21no—
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2311yescharacteristic
149C22×C22⋊C4—21no—
150C22×C22⋊C4—21no—
151C22×C22⋊C4—21no—
152C22×C22⋊C4—21no—
153C22×C22⋊C4—21no—
154C22×C42—21no—
155C22×C42—44no—
156C22×C42D411yescharacteristic
157C22×C42D411yescharacteristic
158C22×C42D411yescharacteristic
159C22×C42D411yescharacteristic
160C22×C42D411yescharacteristic
161C22×C42D411yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168#480—28no—
169#474—44no—
170#459—44no—
171#447—28no—
172#431—44no—
173C2×#107C2314yes—
174C2×#107C2314yes—
175C2×#107C2314yes—
176C2×C4⋊C8C2312yes—
177C2×C4⋊C8C2312yes—
178C2×#102C2314yes—
179C2×#102C2314yes—
180C2×#102C2314yes—
181C2×#102C2314yes—
182C2×#102C2314yes—
183C2×#102C2314yes—
184C2×C22⋊C8C2312yes—
185C2×C22⋊C8C2312yes—
186C2×C22⋊C8C2314yes—
187C2×C22⋊C8C2314yes—
188C2×C4×C8C2314yes—
189#391—21no—
190#391—21no—
191#390—21no—
192#390—21no—
193#390—21no—
194#390—21no—
195#390—21no—
196#390—21no—
197#390C2312yes—
198#390C2312yes—
199#390C2312yes—
200#390C2312yes—
201#389—21no—
202#389—21no—
203#389—21no—
204#389—21no—
205#389C2312yes—
206#389C2312yes—
207#389C2312yes—
208#389C2312yes—
209#388—22no—
210#388—22no—
211#388—22no—
212#388—22no—
213#388—22no—
214#388—22no—
215#388—22no—
216#388—22no—
217#386—22no—
218#386—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#384C2311yescharacteristic
228#384C2311yescharacteristic
229#382—21no—
230#380—21no—
231#380—21no—
232#380—21no—
233#380—21no—
234#380—21no—
235#380C2312yes—
236#380C2312yes—
237#380C2312yes—
238#380C2312yes—
239#380C2312yes—
240C4×C4⋊C4—21no—
241C4×C4⋊C4—21no—
242C4×C4⋊C4—21no—
243C4×C4⋊C4C2312yes—
244C4×C4⋊C4C2312yes—
245C4×C4⋊C4C2312yes—
246C4×C22⋊C4—22no—
247C4×C22⋊C4—22no—
248C4×C22⋊C4—22no—
249C4×C22⋊C4—22no—
250C4×C22⋊C4—22no—
251C4×C22⋊C4—22no—
252C2×#95—21no—
253C2×#95—21no—
254C2×#95—21no—
255#340C2314yes—
256#340C2314yes—
257#340C2314yes—
258#340C2314yes—
259#340C2314yes—
260#340C2314yes—
261#336C2312yes—
262#336C2312yes—
263#336C2314yes—
264C25—21no—
265C25C2×D411yescharacteristic
266C2×#41—44no—
267C2×#41—44no—
268C2×#41—44no—
269C22×Q8—21no—
270C22×D4—28no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—22no—
274C22×D4—22no—
275C22×D4—22no—
276C22×D4—21no—
277C22×D4—21no—
278C22×D4—21no—
279C22×D4—22no—
280C22×D4—42no—
281C22×D4—42no—
282C22×D4—44no—
283C22×D4—44no—
284C22×D4#4114yescomplemented
285C22×D4C2412yes—
286C22×D4C2412yes—
287C23×C4—21no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—21no—
291C23×C4—21no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4—42no—
296C23×C4—42no—
297C23×C4—42no—
298C23×C4—42no—
299C23×C4—42no—
300C23×C4—42no—
301C23×C4—42no—
302C23×C4—44no—
303C23×C4—44no—
304C23×C4—44no—
305C23×C4D818yescomplemented
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—
329C4⋊Q8—24no—
330#127—24no—
331#124—44no—
332#123—48no—
333C22⋊Q8—44no—
334C22⋊Q8—44no—
335#121—28no—
336#121—28no—
337#121—24no—
338#121—24no—
339#121—24no—
340#121—24no—
341#121—24no—
342#121—24no—
343#121—44no—
344#121—44no—
345#121—44no—
346#121—44no—
347#121—44no—
348#121—44no—
349#121—44no—
350#120—48no—
351C4×D4—24no—
352C4×D4—24no—
353C4×D4—42no—
354C4×D4—42no—
355C4×D4—44no—
356C4×D4—44no—
357C4×D4—44no—
358C4×D4—44no—
359C4×D4—48no—
360C4×D4—48no—
361C4×D4—48no—
362C4×D4—48no—
363C4×D4—48no—
364C4×D4—48no—
365#117—44no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—42no—
380C2×C4⋊C4—42no—
381C2×C4⋊C4—44no—
382C2×C4⋊C4#4114yescomplemented
383C2×C4⋊C4C2412yes—
384C2×C4⋊C4C2412yes—
385C2×C4⋊C4C2412yes—
386C2×C4⋊C4C2412yes—
387C2×C4⋊C4C2412yes—
388C2×C4⋊C4C2412yes—
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—22no—
411C2×C22⋊C4—44no—
412C2×C22⋊C4—44no—
413C2×C22⋊C4—44no—
414C2×C22⋊C4—44no—
415C2×C42—24no—
416C2×C42—24no—
417C2×C42—24no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—42no—
422C2×C42—42no—
423C2×C42—42no—
424C2×C42—42no—
425C2×C42—42no—
426C2×C42—42no—
427C2×C42—42no—
428C2×C42—42no—
429C2×C42—42no—
430C2×C42—44no—
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×C42C2×D411yescharacteristic
441C2×C42C2×D411yescharacteristic
442C2×C42C2×D411yescharacteristic
443C2×C42C2411yescharacteristic
444C2×C42C2411yescharacteristic
445C2×C42C2411yescharacteristic
446C2×C42C2411yescharacteristic
447#107—28no—
448#107—44no—
449#107—44no—
450C4⋊C8—24no—
451C4⋊C8—24no—
452#102—28no—
453#102—28no—
454#102—44no—
455#102—44no—
456#102—44no—
457#102—44no—
458C22⋊C8—24no—
459C22⋊C8—24no—
460C22⋊C8—44no—
461C22⋊C8—44no—
462C4×C8—44no—
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—
473#95—22no—
474#95—22no—
475C24—22no—
476C24—22no—
477C24—24no—
478C24—22no—
479C24—22no—
480C24—41no—
481C24—41no—
482C24—41no—
483C24—41no—
484C24—42no—
485C24—42no—
486C24—42no—
487C24—42no—
488C24—42no—
489C24—42no—
490C24C2×D814yes—
491C24C22×D411yescharacteristic
492C24C22×D411yescharacteristic
493C24C22×D411yescharacteristic
494#41—816no—
495C2×Q8—42no—
496C2×Q8—42no—
497C2×Q8—42no—
498C2×D4—28no—
499C2×D4—28no—
500C2×D4—24no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—22no—
505C2×D4—22no—
506C2×D4—24no—
507C2×D4—22no—
508C2×D4—22no—
509C2×D4—24no—
510C2×D4—48no—
511C2×D4—42no—
512C2×D4—42no—
513C2×D4—48no—
514C2×D4—42no—
515C2×D4—42no—
516C2×D4—432no—
517C2×D4—44no—
518C2×D4—44no—
519C2×D4—44no—
520C2×D4—44no—
521C2×D4—44no—
522C2×D4—44no—
523C2×D4—44no—
524C2×D4—44no—
525C2×D4—44no—
526C2×D4—44no—
527C2×D4—44no—
528C2×D4—44no—
529C2×D4—44no—
530C2×D4—42no—
531C2×D4—42no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4C2×#4114yes—
535C22×C4—22no—
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—24no—
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—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
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—416no—
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—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—48no—
593C22×C4—48no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—416no—
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—44no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—44no—
612C22×C4—816no—
613C22×C4C2×D814yes—
614C22×C4C2×D814yes—
615C22×C4C2×D814yes—
616C22×C4C2×D814yes—
617C22×C4C2×D814yes—
618C22×C4C2×D814yes—
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C22×D411yescharacteristic
626C22×C4C22×D411yescharacteristic
627C22×C4C22×D411yescharacteristic
628C22×C4C22×D411yescharacteristic
629C22×C4C22×D411yescharacteristic
630C22×C4C2×#4112yes—
631C22×C4C2×#4112yes—
632C22×C4C2511yescharacteristic
633D8—88no—
634C2×C8—24no—
635C2×C8—24no—
636C2×C8—24no—
637C2×C8—24no—
638C2×C8—24no—
639C2×C8—24no—
640C4⋊C4—24no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—24no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—24no—
649C4⋊C4—22no—
650C4⋊C4—42no—
651C4⋊C4—42no—
652C4⋊C4—42no—
653C4⋊C4—42no—
654C4⋊C4—42no—
655C4⋊C4—44no—
656C4⋊C4—44no—
657C4⋊C4—42no—
658C4⋊C4—42no—
659C4⋊C4—44no—
660C4⋊C4—44no—
661C4⋊C4C2×#4114yes—
662C22⋊C4—28no—
663C22⋊C4—28no—
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—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—44no—
681C22⋊C4—44no—
682C22⋊C4—44no—
683C42—22no—
684C42—22no—
685C42—22no—
686C42—22no—
687C42—22no—
688C42—22no—
689C42—22no—
690C42—22no—
691C42—22no—
692C42—41no—
693C42—41no—
694C42—41no—
695C42—41no—
696C42—41no—
697C42—41no—
698C42—44no—
699C42—44no—
700C42—44no—
701C42H(5,𝔽2)14yes—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—28no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—24no—
720C23—44no—
721C23—44no—
722C23—44no—
723C23—44no—
724C23—44no—
725C23—44no—
726C23—48no—
727C23—48no—
728C23—48no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—84no—
743C23—84no—
744C23—84no—
745C23—84no—
746C23#52512yes—
747C23C22×D812yes—
748C23C22×D812yes—
749C23C22×D812yes—
750C23#57512yes—
751C23C23×D411yescharacteristic
752Q8—84no—
753D4—24no—
754D4—24no—
755D4—48no—
756D4—416no—
757D4—416no—
758D4—44no—
759D4—42no—
760D4—42no—
761D4—44no—
762D4—84no—
763D4—88no—
764D4—88no—
765D4—88no—
766D4—84no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—28no—
780C2×C4—28no—
781C2×C4—28no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—24no—
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—21no—
796C2×C4—21no—
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—44no—
808C2×C4—44no—
809C2×C4—48no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
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—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—88no—
832C2×C4—88no—
833C2×C4—84no—
834C2×C4—84no—
835C2×C4—88no—
836C2×C4#52512yes—
837C2×C4#53412yes—
838C2×C4#53412yes—
839C2×C4C22×D812yes—
840C2×C4C22×D812yes—
841C2×C4C22×D812yes—
842C2×C4C22×D812yes—
843C2×C4#57512yes—
844C2×C4#57512yes—
845C2×C4C22×#4111yescharacteristic
846C2×C4C22×#4111yescharacteristic
847C2×C4C2×H(5,𝔽2)12yes—
848C2×C4#58512yes—
849C8—44no—
850C8—44no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—22no—
861C22—22no—
862C22—22no—
863C22—416no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—44no—
873C22—44no—
874C22—44no—
875C22—816no—
876C22—82no—
877C22—82no—
878C22—82no—
879C22—82no—
880C22—82no—
881C22—82no—
882C22—82no—
883C22—82no—
884C22—82no—
885C22—82no—
886C22—82no—
887C22#310014yes—
888C22C2×#52511yescharacteristic
889C22C2×#53411yescharacteristic
890C22#344911yescharacteristic
891C22C23×D811yescharacteristic
892C22C2×#57511yescharacteristic
893C22C2×#57511yescharacteristic
894C22C2×#57511yescharacteristic
895C4—22no—
896C4—22no—
897C4—22no—
898C4—22no—
899C4—22no—
900C4—22no—
901C4—41no—
902C4—41no—
903C4—44no—
904C4—41no—
905C4—41no—
906C4—82no—
907C4—82no—
908C4—82no—
909C4—82no—
910C4—82no—
911C4#318614yes—
912C4#350512yes—
913C4#350612yes—
914C2—24no—
915C2—42no—
916C2—42no—
917C2—84no—
918C2—162no—
919C2#3503111yescharacteristic
920C2C2×#310011yescharacteristic
921C2#6055911yescharacteristic
922C2C2×#318611yescharacteristic
923C2#6075211yescharacteristic
924C2#6094011yescharacteristic
925C2#6097011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
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. #36624C2semidirect
2. C2×C4×#121C2semidirect
3. #33146C2semidirect
4. #33106C2semidirect
5. #32953C2semidirect
6. #32902C2semidirect
7. #29890C2semidirect
8. #29592C2semidirect
9. #29460C2semidirect
10. #29408C2semidirect
11. #27624C2semidirect
12. #24700C2semidirect
13. #24650C2semidirect
14. #24150C2semidirect
15. #22075C2semidirect
16. #22040C2semidirect
17. #20714C2semidirect
18. C2×#532C22semidirect
25. C2×#474C22semidirect
26. C2×#459C22semidirect
28. C2×#431C22semidirect
30. #2857C22semidirect
32. #2856C22semidirect
34. #2854C22semidirect
50. C4×#121C22semidirect
56. #2285C22semidirect
60. #2075C22semidirect
61. #2075C22semidirect
64. #2033C22semidirect
65. #2033C22semidirect
68. #1988C22semidirect
69. #1982C22semidirect
70. #1970C22semidirect
71. #1947C22semidirect
72. #1947C22semidirect
73. #1942C22semidirect
74. #1934C22semidirect
75. #1934C22semidirect
76. #1925C22semidirect
77. #1925C22semidirect
78. #1918C22semidirect
79. #1918C22semidirect
80. #1879C22semidirect
81. #1879C22semidirect
84. #1862C22semidirect
85. #1862C22semidirect
89. #1817C22semidirect
90. #1802C22semidirect
91. #1802C22semidirect
94. #1797C22semidirect
98. C4×C22⋊C8C22semidirect
284. C22×D4#41semidirect
305. C23×C4D8semidirect
382. C2×C4⋊C4#41semidirect

Maximal subgroups

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

subgroupindex
#366242
C2×C4×#1212
#331462
#331062
#329532
#329022
#298902
#295922
#294602
#294082
#276242
#247002
#246502
#241502
#220752
#220402
#207142