Finite Group Databasebeta

← #6476787

Subgroups — #6476787

Order 512.

2506 conjugacy classes of subgroups.

The subgroup lattice has 931 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#30006C214yesmaximal, complemented
8#29234C212yesmaximal, complemented
9#28114C212yesmaximal, complemented
10#27624C212yesmaximal, complemented
11#24835C212yesmaximal, complemented
12#24750C212yesmaximal, complemented
13#24550C212yesmaximal, complemented
14#24378C212yesmaximal, complemented
15#24150C212yesmaximal, complemented
16#22181C214yesmaximal, complemented
17C2×#1797C211yesmaximal, characteristic, complemented
18C2×#532C2211yescharacteristic, complemented
19C2×#525—21no—
20C22×#121C2211yescharacteristic
21C22×C4×D4—21no—
22C22×C4×D4C2211yescharacteristic
23C23×C42C2211yescharacteristic
24C2×#480C2212yes—
25C2×#474C2212yescomplemented
26C2×#466C2214yes—
27C2×#459C2212yescomplemented
28C2×#447C2212yes—
29C22×C4⋊C8C2212yescomplemented
30C22×C22⋊C8C2212yes—
31#2857C2211yescharacteristic
32#2857C2211yescharacteristic, complemented
33#2856C2211yescharacteristic
34#2856C2211yescharacteristic, complemented
35#2854—21no—
36#2854C2212yescomplemented
37#2850—21no—
38#2850—21no—
39#2847—21no—
40#2847C2212yes—
41C4×#121—21no—
42C4×#121—21no—
43C4×#121—21no—
44C4×#121—21no—
45C4×#121—21no—
46C4×#121—21no—
47C4×#121C2212yes—
48C4×#121C2212yes—
49C4×#121C2212yes—
50C4×#121C2212yes—
51C4×#121C2212yes—
52C4×#121C2212yescomplemented
53#2297—21no—
54C2×#390C2211yescharacteristic
55C2×#389C2211yescharacteristic
56C2×#388—21no—
57C2×#386—21no—
58#2285C2211yescharacteristic, complemented
59C2×#380C2211yescharacteristic
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4—21no—
62#2086C2214yescomplemented
63#2075C2214yescomplemented
64#2067C2214yescomplemented
65#2067C2214yescomplemented
66#2054C2214yescomplemented
67#2033C2214yes—
68#2033C2214yescomplemented
69#1999C2214yes—
70#1988C2212yescomplemented
71#1982C2212yescomplemented
72#1947C2212yescomplemented
73#1947C2212yescomplemented
74#1925C2214yescomplemented
75#1925C2214yescomplemented
76#1918C2214yescomplemented
77#1918C2214yescomplemented
78#1893C2214yes—
79#1893C2214yescomplemented
80#1879C2214yescomplemented
81#1879C2214yescomplemented
82#1874C2212yes—
83#1874C2212yes—
84#1862C2214yescomplemented
85#1862C2214yescomplemented
86#1852C2212yes—
87#1852C2212yes—
88#1823C2212yes—
89#1808C2214yescomplemented
90#1802C2212yescomplemented
91#1802C2212yescomplemented
92#1797C2212yes—
93#1797C2211yescharacteristic
94#1797C2211yescharacteristic
95#1797C2212yescomplemented
96#1797C2212yescomplemented
97#1786C2212yes—
98C2×#336C2212yescomplemented
99C22×#41—21no—
100C23×D4—21no—
101C23×D4C2311yescharacteristic
102C24×C4—21no—
103C24×C4D411yescharacteristic
104C24×C4D411yescharacteristic
105C24×C4C2311yescharacteristic
106C22×D8C2314yes—
107C23×C8C2314yes—
108#532—44no—
109C2×C4⋊Q8C2311yescharacteristic
110C2×#127C2311yescharacteristic
111C2×#124—21no—
112#525—48no—
113C2×#123—22no—
114C2×C22⋊Q8—21no—
115C2×C22⋊Q8—21no—
116C2×#121—21no—
117C2×#121—21no—
118C2×#121—28no—
119C2×#121—21no—
120C2×#121—21no—
121C2×#121—21no—
122C2×#121—21no—
123C2×#121—21no—
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—44no—
169#474—44no—
170#466—216no—
171#459—44no—
172#447—44no—
173C2×#107C2314yes—
174C2×#107C2314yes—
175C2×#107C2314yes—
176C2×C4⋊C8—44no—
177C2×C4⋊C8C2312yes—
178C2×C4⋊C8C2312yes—
179C2×C4⋊C8C2314yes—
180C2×#102C2314yes—
181C2×#102C2314yes—
182C2×#102C2314yes—
183C2×#102C2314yes—
184C2×#102C2314yes—
185C2×#102C2314yes—
186C2×C22⋊C8—44no—
187C2×C22⋊C8C2312yes—
188C2×C22⋊C8C2312yes—
189C2×C22⋊C8C2314yes—
190#391—21no—
191#391—21no—
192#390—21no—
193#390—21no—
194#390—21no—
195#390—21no—
196#390—21no—
197#390—21no—
198#390C2312yes—
199#390C2312yes—
200#390C2312yes—
201#390C2312yes—
202#389—21no—
203#389—21no—
204#389—21no—
205#389—21no—
206#389C2312yes—
207#389C2312yes—
208#389C2312yes—
209#389C2312yes—
210#388—22no—
211#388—22no—
212#388—22no—
213#388—22no—
214#388—22no—
215#388—22no—
216#388—22no—
217#388—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#386—22no—
228#384C2311yescharacteristic
229#384C2311yescharacteristic
230#382—21no—
231#380—21no—
232#380—21no—
233#380—21no—
234#380—21no—
235#380—21no—
236#380C2312yes—
237#380C2312yes—
238#380C2312yes—
239#380C2312yes—
240#380C2312yes—
241C4×C4⋊C4—21no—
242C4×C4⋊C4—21no—
243C4×C4⋊C4—21no—
244C4×C4⋊C4C2312yes—
245C4×C4⋊C4C2312yes—
246C4×C4⋊C4C2312yes—
247C4×C22⋊C4—22no—
248C4×C22⋊C4—22no—
249C4×C22⋊C4—22no—
250C4×C22⋊C4—22no—
251C4×C22⋊C4—22no—
252C4×C22⋊C4—22no—
253C2×#95—21no—
254C2×#95—21no—
255C2×#95—21no—
256#340C2314yes—
257#340C2314yes—
258#340C2314yes—
259#340C2314yes—
260#340C2314yes—
261#340C2314yes—
262#336C2312yes—
263#336C2314yes—
264#336C2312yes—
265C25—21no—
266C25C2×D411yescharacteristic
267C2×#41—44no—
268C2×#41—44no—
269C2×#41—44no—
270C22×Q8—21no—
271C22×D4—28no—
272C22×D4—22no—
273C22×D4—22no—
274C22×D4—24no—
275C22×D4—22no—
276C22×D4—22no—
277C22×D4—22no—
278C22×D4—21no—
279C22×D4—21no—
280C22×D4—21no—
281C22×D4—22no—
282C22×D4—22no—
283C22×D4—42no—
284C22×D4—44no—
285C22×D4—44no—
286C22×D4C2412yes—
287C22×D4C2412yes—
288C23×C4—21no—
289C23×C4—24no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—21no—
293C23×C4—21no—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—22no—
297C23×C4—42no—
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×C4D818yescomplemented
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×C4C2×D411yescharacteristic
322C23×C4C2411yescharacteristic
323C23×C4C2411yescharacteristic
324C23×C4C2411yescharacteristic
325C2×D8—28no—
326C2×D8—44no—
327C2×D8—44no—
328C22×C8—28no—
329C22×C8—44no—
330C22×C8—44no—
331C22×C8C2414yes—
332C22×C8C2414yes—
333C4⋊Q8—24no—
334#127—24no—
335#124—44no—
336#123—48no—
337C22⋊Q8—44no—
338C22⋊Q8—44no—
339#121—28no—
340#121—28no—
341#121—24no—
342#121—24no—
343#121—24no—
344#121—28no—
345#121—24no—
346#121—24no—
347#121—44no—
348#121—44no—
349#121—44no—
350#121—44no—
351#121—44no—
352#121—44no—
353#121#4118yescomplemented
354#120—48no—
355C4×D4—24no—
356C4×D4—24no—
357C4×D4—42no—
358C4×D4—42no—
359C4×D4—44no—
360C4×D4—44no—
361C4×D4—44no—
362C4×D4—44no—
363C4×D4—48no—
364C4×D4—48no—
365C4×D4—48no—
366C4×D4—48no—
367C4×D4—48no—
368C4×D4—48no—
369#117—44no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—42no—
386C2×C4⋊C4—44no—
387C2×C4⋊C4C2412yes—
388C2×C4⋊C4C2412yes—
389C2×C4⋊C4C2412yes—
390C2×C4⋊C4C2412yes—
391C2×C4⋊C4C2412yes—
392C2×C4⋊C4C2412yes—
393C2×C22⋊C4—28no—
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—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—44no—
416C2×C22⋊C4—44no—
417C2×C22⋊C4—44no—
418C2×C22⋊C4—44no—
419C2×C42—24no—
420C2×C42—24no—
421C2×C42—24no—
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×C42C2×D411yescharacteristic
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×C42C2411yescharacteristic
448C2×C42C2411yescharacteristic
449C2×C42C2411yescharacteristic
450C2×C42C2411yescharacteristic
451#107—28no—
452#107—44no—
453#107—44no—
454C4⋊C8—24no—
455C4⋊C8—24no—
456C4⋊C8—44no—
457#102—28no—
458#102—28no—
459#102—44no—
460#102—44no—
461#102—44no—
462#102—44no—
463C22⋊C8—24no—
464C22⋊C8—24no—
465C22⋊C8—44no—
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—
475#95—22no—
476#95—22no—
477#95—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—24no—
483C24—22no—
484C24—22no—
485C24—41no—
486C24—41no—
487C24—42no—
488C24—42no—
489C24—42no—
490C24—42no—
491C24—42no—
492C24—42no—
493C24C2×D814yes—
494C24C22×D411yescharacteristic
495C24C22×D411yescharacteristic
496C24C22×D411yescharacteristic
497#41—816no—
498C2×Q8—42no—
499C2×Q8—42no—
500C2×Q8—42no—
501C2×D4—24no—
502C2×D4—28no—
503C2×D4—28no—
504C2×D4—22no—
505C2×D4—24no—
506C2×D4—22no—
507C2×D4—22no—
508C2×D4—22no—
509C2×D4—22no—
510C2×D4—24no—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—48no—
514C2×D4—48no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—432no—
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—44no—
531C2×D4—44no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4C2×#4114yes—
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—21no—
548C22×C4—21no—
549C22×C4—24no—
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—21no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—416no—
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—41no—
593C22×C4—41no—
594C22×C4—48no—
595C22×C4—48no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—42no—
601C22×C4—416no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—44no—
612C22×C4—44no—
613C22×C4—44no—
614C22×C4—816no—
615C22×C4C2×D814yes—
616C22×C4C2×D814yes—
617C22×C4C2×D814yes—
618C22×C4C2×D814yes—
619C22×C4C2×D814yes—
620C22×C4C2×D814yes—
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×C4C22×D411yescharacteristic
631C22×C4C22×D411yescharacteristic
632C22×C4C2×#4114yes—
633C22×C4H(5,𝔽2)12yes—
634C22×C42−1+412yes—
635C22×C4C2511yescharacteristic
636D8—88no—
637C2×C8—24no—
638C2×C8—24no—
639C2×C8—24no—
640C2×C8—24no—
641C2×C8—24no—
642C2×C8—24no—
643C2×C8—88no—
644C4⋊C4—24no—
645C4⋊C4—22no—
646C4⋊C4—24no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—24no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—42no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C4⋊C4—42no—
658C4⋊C4—42no—
659C4⋊C4—44no—
660C4⋊C4—44no—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4—44no—
664C4⋊C4—44no—
665C4⋊C4C2×#4114yes—
666C22⋊C4—28no—
667C22⋊C4—28no—
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—
683C22⋊C4—44no—
684C22⋊C4—44no—
685C22⋊C4—44no—
686C22⋊C4—44no—
687C42—22no—
688C42—22no—
689C42—22no—
690C42—22no—
691C42—22no—
692C42—22no—
693C42—22no—
694C42—22no—
695C42—22no—
696C42—41no—
697C42—41no—
698C42—41no—
699C42—41no—
700C42—41no—
701C42—41no—
702C42—44no—
703C42—44no—
704C42—44no—
705C42H(5,𝔽2)14yes—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—28no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—28no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—24no—
723C23—44no—
724C23—44no—
725C23—44no—
726C23—44no—
727C23—44no—
728C23—48no—
729C23—48no—
730C23—48no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—84no—
745C23—84no—
746C23—84no—
747C23—84no—
748C23#52512yes—
749C23#53712yes—
750C23C22×D812yes—
751C23C22×D812yes—
752C23C22×D812yes—
753C23#57512yes—
754C23#57512yes—
755C23C23×D411yescharacteristic
756Q8—84no—
757D4—24no—
758D4—24no—
759D4—48no—
760D4—416no—
761D4—416no—
762D4—42no—
763D4—44no—
764D4—42no—
765D4—44no—
766D4—84no—
767D4—88no—
768D4—88no—
769D4—88no—
770D4—84no—
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—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—28no—
784C2×C4—28no—
785C2×C4—28no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—21no—
791C2×C4—24no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—48no—
815C2×C4—44no—
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—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—88no—
836C2×C4—88no—
837C2×C4—84no—
838C2×C4—84no—
839C2×C4—88no—
840C2×C4#52512yes—
841C2×C4#53412yes—
842C2×C4#53412yes—
843C2×C4#53712yes—
844C2×C4C22×D812yes—
845C2×C4C22×D812yes—
846C2×C4C22×D812yes—
847C2×C4C22×D812yes—
848C2×C4#57512yes—
849C2×C4C22×#4112yes—
850C2×C4C2×H(5,𝔽2)11yescharacteristic
851C2×C4C2×H(5,𝔽2)12yes—
852C2×C4C2×2−1+411yescharacteristic
853C8—44no—
854C8—44no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—22no—
861C22—22no—
862C22—22no—
863C22—22no—
864C22—22no—
865C22—22no—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—22no—
870C22—416no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—41no—
875C22—44no—
876C22—44no—
877C22—44no—
878C22—816no—
879C22—82no—
880C22—82no—
881C22—82no—
882C22—82no—
883C22—82no—
884C22—82no—
885C22—82no—
886C22—82no—
887C22—82no—
888C22—82no—
889C22—82no—
890C22#310014yes—
891C22#324514yes—
892C22C2×#52511yescharacteristic
893C22C2×#53411yescharacteristic
894C22C2×#53711yescharacteristic
895C22C23×D811yescharacteristic
896C22C2×#57511yescharacteristic
897C22C2×#57511yescharacteristic
898C22C2×#57511yescharacteristic
899C4—22no—
900C4—22no—
901C4—22no—
902C4—22no—
903C4—22no—
904C4—22no—
905C4—41no—
906C4—41no—
907C4—41no—
908C4—41no—
909C4—44no—
910C4—82no—
911C4—82no—
912C4—82no—
913C4—82no—
914C4—82no—
915C4#318614yes—
916C4#351912yes—
917C4#352012yes—
918C2—24no—
919C2—24no—
920C2—42no—
921C2—84no—
922C2—162no—
923C2#3507711yescharacteristic
924C2C2×#310011yescharacteristic
925C2#6054611yescharacteristic
926C2C2×#318611yescharacteristic
927C2#6075211yescharacteristic
928C2C2×#324511yescharacteristic
929C2#6091711yescharacteristic
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. #30006C2semidirect
8. #29234C2semidirect
9. #28114C2semidirect
10. #27624C2semidirect
11. #24835C2semidirect
12. #24750C2semidirect
13. #24550C2semidirect
14. #24378C2semidirect
15. #24150C2semidirect
16. #22181C2semidirect
17. C2×#1797C2semidirect
18. C2×#532C22semidirect
25. C2×#474C22semidirect
27. C2×#459C22semidirect
29. C22×C4⋊C8C22semidirect
32. #2857C22semidirect
34. #2856C22semidirect
36. #2854C22semidirect
52. C4×#121C22semidirect
58. #2285C22semidirect
62. #2086C22semidirect
63. #2075C22semidirect
64. #2067C22semidirect
65. #2067C22semidirect
66. #2054C22semidirect
68. #2033C22semidirect
70. #1988C22semidirect
71. #1982C22semidirect
72. #1947C22semidirect
73. #1947C22semidirect
74. #1925C22semidirect
75. #1925C22semidirect
76. #1918C22semidirect
77. #1918C22semidirect
79. #1893C22semidirect
80. #1879C22semidirect
81. #1879C22semidirect
84. #1862C22semidirect
85. #1862C22semidirect
89. #1808C22semidirect
90. #1802C22semidirect
91. #1802C22semidirect
95. #1797C22semidirect
96. #1797C22semidirect
98. C2×#336C22semidirect
306. C23×C4D8semidirect
353. #121#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
#300062
#292342
#281142
#276242
#248352
#247502
#245502
#243782
#241502
#221812
C2×#17972