Finite Group Databasebeta

← #6476674

Subgroups — #6476674

Order 512.

2212 conjugacy classes of subgroups.

The subgroup lattice has 893 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36624C211yesmaximal, characteristic
2C2×C4×C22⋊Q8C211yesmaximal, characteristic, complemented
3#33108C211yesmaximal, characteristic, complemented
4#33106C211yesmaximal, characteristic, complemented
5#32906C211yesmaximal, characteristic, complemented
6#32903C211yesmaximal, characteristic, complemented
7#30114C214yesmaximal, complemented
8#29330C212yesmaximal, complemented
9#28306C212yesmaximal, complemented
10#27682C212yesmaximal, complemented
11#24653C212yesmaximal, complemented
12#24652C212yesmaximal, complemented
13#24213C212yesmaximal, complemented
14#24004C212yesmaximal, complemented
15#23922C212yesmaximal, complemented
16#22042C214yesmaximal, complemented
17#20714C211yesmaximal, characteristic, complemented
18C2×#532C2211yescharacteristic
19C2×#525C2212yes—
20C22×C22⋊Q8C2211yescharacteristic
21C22×C4×Q8C2211yescharacteristic
22C23×C42C2211yescharacteristic
23C2×#483C2212yes—
24C2×#480C2212yes—
25C2×#462C2212yescomplemented
26C2×#460C2212yescomplemented
27C2×#452C2214yes—
28C2×#451C2212yes—
29C2×#448C2212yes—
30C2×#431C2212yes—
31#2857C2211yescharacteristic
32#2857C2211yescharacteristic
33#2856C2211yescharacteristic
34#2856C2211yescharacteristic
35#2854—21no—
36#2854—21no—
37#2850C2212yes—
38#2850C2212yes—
39#2847—21no—
40#2847—21no—
41C4×C22⋊Q8—21no—
42C4×C22⋊Q8—21no—
43C4×C22⋊Q8—21no—
44C4×C22⋊Q8—21no—
45C4×C22⋊Q8C2212yes—
46C4×C22⋊Q8C2212yes—
47C4×C22⋊Q8C2212yes—
48C4×C22⋊Q8C2212yes—
49C4×#121—21no—
50C4×#121—21no—
51C4×#121—21no—
52C4×#121—21no—
53#2297C2212yes—
54C2×#391C2211yescharacteristic
55C2×#389C2211yescharacteristic
56C2×#387—21no—
57C2×#385—21no—
58#2285C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×C4×C4⋊C4—21no—
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4—21no—
63#2101C2214yescomplemented
64#2097C2214yescomplemented
65#2042C2214yescomplemented
66#2036C2214yes—
67#2034C2214yes—
68#2015C2214yescomplemented
69#2001C2214yes—
70#2000C2214yes—
71#1982C2212yescomplemented
72#1981C2212yescomplemented
73#1969C2214yescomplemented
74#1968C2214yescomplemented
75#1948C2212yescomplemented
76#1947C2212yescomplemented
77#1934C2214yescomplemented
78#1933C2214yescomplemented
79#1927C2214yescomplemented
80#1925C2214yescomplemented
81#1880C2214yescomplemented
82#1878C2214yescomplemented
83#1874C2212yes—
84#1874C2212yes—
85#1873C2214yes—
86#1872C2212yes—
87#1872C2212yes—
88#1854C2214yes—
89#1817C2212yes—
90#1803C2212yescomplemented
91#1803C2212yescomplemented
92#1797C2212yes—
93#1797C2211yescharacteristic
94#1797C2211yescharacteristic
95#1788C2214yes—
96#1779C2212yes—
97C4×C22⋊C8C2212yes—
98C4×C22⋊C8C2212yes—
99C22×#41C2312yes—
100C23×Q8C2311yescharacteristic
101C24×C4D411yescharacteristic
102C24×C4D411yescharacteristic
103C24×C4C2311yescharacteristic
104C22×Q16C2314yes—
105C22×SD16C2314yes—
106#532—44no—
107C2×C4⋊Q8C2311yescharacteristic
108C2×#127C2311yescharacteristic
109C2×#124C2312yes—
110#525—44no—
111#525—44no—
112C2×#123—22no—
113C2×C22⋊Q8—21no—
114C2×C22⋊Q8—21no—
115C2×C22⋊Q8—28no—
116C2×C22⋊Q8C2312yes—
117C2×C22⋊Q8C2312yes—
118C2×C22⋊Q8C2312yes—
119C2×C22⋊Q8C2312yes—
120C2×#121—21no—
121C2×#121—21no—
122C2×#121—21no—
123C2×#121—21no—
124C2×#121—21no—
125C2×#121—21no—
126C2×#121C2312yes—
127C2×#121C2312yes—
128C2×#120—22no—
129C2×C4×Q8—21no—
130C2×C4×Q8—21no—
131C2×C4×Q8—44no—
132C2×C4×Q8C2312yes—
133C2×C4×Q8C2312yes—
134C2×C4×D4—22no—
135C2×C4×D4—22no—
136C2×C4×D4—21no—
137C2×C4×D4—21no—
138C2×#117C2312yes—
139C22×C4⋊C4—21no—
140C22×C4⋊C4—21no—
141C22×C4⋊C4—21no—
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2311yescharacteristic
145C22×C22⋊C4—21no—
146C22×C22⋊C4—21no—
147C22×C42—21no—
148C22×C42—21no—
149C22×C42—44no—
150C22×C42D411yescharacteristic
151C22×C42D411yescharacteristic
152C22×C42D411yescharacteristic
153C22×C42D411yescharacteristic
154C22×C42D411yescharacteristic
155C22×C42D411yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162#483—44no—
163#480—44no—
164#462—44no—
165#460—44no—
166#452—216no—
167#451—44no—
168#448—44no—
169#431—44no—
170C2×#107C2314yes—
171C2×#106C2314yes—
172C2×C4⋊C8C2312yes—
173C2×C4⋊C8C2312yes—
174C2×#103C2314yes—
175C2×#103C2314yes—
176C2×#103C2314yes—
177C2×#103C2314yes—
178C2×#103C2314yes—
179C2×#102C2314yes—
180C2×#102C2314yes—
181C2×#102C2314yes—
182C2×C22⋊C8C2312yes—
183C2×C22⋊C8C2312yes—
184C2×C22⋊C8C2314yes—
185C2×C22⋊C8C2314yes—
186C2×C4×C8C2314yes—
187#391—21no—
188#391—21no—
189#391C2312yes—
190#391C2312yes—
191#391C2312yes—
192#391C2312yes—
193#390—21no—
194#390—21no—
195#390—21no—
196#390—21no—
197#390C2312yes—
198#390C2312yes—
199#389—21no—
200#389—21no—
201#389—21no—
202#389—21no—
203#389—21no—
204#389—21no—
205#389C2312yes—
206#389C2312yes—
207#388—22no—
208#388—22no—
209#388—22no—
210#388—22no—
211#387—22no—
212#387—22no—
213#387—22no—
214#387—22no—
215#386—22no—
216#386—22no—
217#386—22no—
218#386—22no—
219#386—22no—
220#386—22no—
221#385—22no—
222#385—22no—
223#385—22no—
224#385—22no—
225#384C2311yescharacteristic
226#384C2311yescharacteristic
227#382C2312yes—
228#380—21no—
229#380—21no—
230#380—21no—
231#380—21no—
232#380—21no—
233#380—21no—
234#380—21no—
235#380—21no—
236#380C2312yes—
237#380C2312yes—
238C4×C4⋊C4—22no—
239C4×C4⋊C4—22no—
240C4×C4⋊C4—22no—
241C4×C4⋊C4—22no—
242C4×C4⋊C4—21no—
243C4×C4⋊C4—21no—
244C4×C4⋊C4—21no—
245C4×C4⋊C4—21no—
246C4×C4⋊C4C2312yes—
247C4×C4⋊C4C2312yes—
248C4×C22⋊C4—22no—
249C4×C22⋊C4—22no—
250C4×C22⋊C4—22no—
251C4×C22⋊C4—22no—
252C4×C22⋊C4—22no—
253C4×C22⋊C4—22no—
254C2×#95—21no—
255C2×#95—21no—
256C2×#95—21no—
257C2×#95—21no—
258C2×#95—21no—
259#340C2314yes—
260#340C2314yes—
261#340C2314yes—
262#340C2314yes—
263#336C2314yes—
264#336C2312yes—
265#336C2312yes—
266C25C2×D411yescharacteristic
267C2×#41—28no—
268C2×#41—42no—
269C2×#41—42no—
270C2×#41—44no—
271C22×Q8—24no—
272C22×Q8—21no—
273C22×Q8—22no—
274C22×Q8—22no—
275C22×Q8—42no—
276C22×Q8C2412yes—
277C22×Q8C2412yes—
278C22×D4—22no—
279C22×D4—22no—
280C22×D4—22no—
281C22×D4—21no—
282C22×D4—21no—
283C22×D4C2412yes—
284C23×C4—21no—
285C23×C4—21no—
286C23×C4—24no—
287C23×C4—24no—
288C23×C4—24no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—21no—
292C23×C4—21no—
293C23×C4—22no—
294C23×C4—42no—
295C23×C4—42no—
296C23×C4—42no—
297C23×C4—42no—
298C23×C4—42no—
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×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D411yescharacteristic
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D411yescharacteristic
314C23×C4C2411yescharacteristic
315C23×C4C2411yescharacteristic
316C23×C4C2411yescharacteristic
317C2×Q16—28no—
318C2×Q16—44no—
319C2×Q16—44no—
320C2×SD16—28no—
321C2×SD16—44no—
322C2×SD16—44no—
323C22×C8C2414yes—
324C22×C8C2414yes—
325C4⋊Q8—24no—
326#127—24no—
327#124—44no—
328#123—48no—
329C22⋊Q8—28no—
330C22⋊Q8—28no—
331C22⋊Q8—24no—
332C22⋊Q8—24no—
333C22⋊Q8—24no—
334C22⋊Q8—24no—
335C22⋊Q8—24no—
336C22⋊Q8—42no—
337C22⋊Q8—42no—
338C22⋊Q8#4118yes—
339#121—24no—
340#121—24no—
341#121—42no—
342#121—42no—
343#121—44no—
344#121—44no—
345#121—44no—
346#121—44no—
347#121—44no—
348#121—44no—
349#120—48no—
350C4×Q8—24no—
351C4×Q8—24no—
352C4×Q8—42no—
353C4×Q8—42no—
354C4×Q8—44no—
355C4×Q8—44no—
356C4×D4—44no—
357C4×D4—44no—
358C4×D4—48no—
359C4×D4—48no—
360#117—42no—
361#117—42no—
362C2×C4⋊C4—28no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—42no—
384C2×C4⋊C4—44no—
385C2×C4⋊C4—44no—
386C2×C4⋊C4C2412yes—
387C2×C4⋊C4C2412yes—
388C2×C4⋊C4C2412yes—
389C2×C4⋊C4C2412yes—
390C2×C4⋊C4C2412yes—
391C2×C22⋊C4—28no—
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—44no—
408C2×C42—24no—
409C2×C42—24no—
410C2×C42—24no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—42no—
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—44no—
426C2×C42—44no—
427C2×C42C2×D411yescharacteristic
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×C42C2411yescharacteristic
440C2×C42C2411yescharacteristic
441C2×C42C2411yescharacteristic
442C2×C42C2411yescharacteristic
443#107—44no—
444#106—44no—
445C4⋊C8—24no—
446C4⋊C8—24no—
447#103—28no—
448#103—44no—
449#103—44no—
450#103—44no—
451#103—44no—
452#102—28no—
453#102—44no—
454#102—44no—
455C22⋊C8—28no—
456C22⋊C8—24no—
457C22⋊C8—24no—
458C22⋊C8—44no—
459C4×C8—44no—
460#95—22no—
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—
473#95—22no—
474#95—22no—
475#95—22no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—41no—
483C24—41no—
484C24C22×D411yescharacteristic
485C24C22×D411yescharacteristic
486C24C22×D411yescharacteristic
487#41—88no—
488#41—88no—
489C2×Q8—24no—
490C2×Q8—22no—
491C2×Q8—24no—
492C2×Q8—22no—
493C2×Q8—22no—
494C2×Q8—22no—
495C2×Q8—22no—
496C2×Q8—22no—
497C2×Q8—24no—
498C2×Q8—22no—
499C2×Q8—48no—
500C2×Q8—48no—
501C2×Q8—42no—
502C2×Q8—42no—
503C2×Q8C2×#4114yes—
504C2×D4—24no—
505C2×D4—22no—
506C2×D4—24no—
507C2×D4—22no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4—44no—
511C2×D4—44no—
512C2×D4—44no—
513C2×D4—44no—
514C2×D4—44no—
515C2×D4—44no—
516C2×D4—44no—
517C2×D4—44no—
518C2×D4—44no—
519C2×D4—42no—
520C2×D4—42no—
521C2×D4—42no—
522C2×D4—42no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—22no—
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—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—21no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—41no—
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—416no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—416no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—44no—
601C22×C4#13514yes—
602C22×C4#13714yes—
603C22×C4C22×D411yescharacteristic
604C22×C4C22×D411yescharacteristic
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D411yescharacteristic
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C2×#4114yes—
615C22×C4H(5,𝔽2)12yes—
616C22×C4H(5,𝔽2)12yes—
617C22×C4C2511yescharacteristic
618Q16—88no—
619SD16—88no—
620C2×C8—24no—
621C2×C8—24no—
622C2×C8—24no—
623C2×C8—24no—
624C2×C8—24no—
625C2×C8—24no—
626C4⋊C4—24no—
627C4⋊C4—28no—
628C4⋊C4—28no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—44no—
639C4⋊C4—42no—
640C4⋊C4—44no—
641C4⋊C4—44no—
642C4⋊C4—42no—
643C4⋊C4—42no—
644C4⋊C4—44no—
645C4⋊C4—42no—
646C4⋊C4—42no—
647C4⋊C4—42no—
648C4⋊C4—44no—
649C4⋊C4—42no—
650C4⋊C4—42no—
651C4⋊C4—44no—
652C4⋊C4C2×#4114yes—
653C22⋊C4—28no—
654C22⋊C4—28no—
655C22⋊C4—44no—
656C22⋊C4—44no—
657C22⋊C4—44no—
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—
668C42—22no—
669C42—22no—
670C42—22no—
671C42—22no—
672C42—22no—
673C42—22no—
674C42—22no—
675C42—22no—
676C42—22no—
677C42—41no—
678C42—41no—
679C42—41no—
680C42—41no—
681C42—41no—
682C42—41no—
683C42—44no—
684C42—44no—
685C42—44no—
686C42—44no—
687C42—44no—
688C42H(5,𝔽2)14yes—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—28no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—44no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23#52512yes—
720C23#53512yes—
721C23C2×#13512yes—
722C23C2×#13712yes—
723C23#57512yes—
724C23C23×D411yescharacteristic
725Q8—24no—
726Q8—24no—
727Q8—48no—
728Q8—42no—
729Q8—42no—
730Q8—44no—
731Q8—44no—
732D4—44no—
733D4—44no—
734D4—84no—
735D4—88no—
736D4—88no—
737D4—88no—
738D4—84no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—28no—
752C2×C4—28no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—48no—
783C2×C4—48no—
784C2×C4—44no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—44no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—88no—
808C2×C4—84no—
809C2×C4—84no—
810C2×C4#52512yes—
811C2×C4#53412yes—
812C2×C4#53412yes—
813C2×C4#53512yes—
814C2×C4C2×#13512yes—
815C2×C4C2×#13512yes—
816C2×C4C2×#13712yes—
817C2×C4C2×#13712yes—
818C2×C4#57512yes—
819C2×C4C22×#4112yes—
820C2×C4C2×H(5,𝔽2)12yes—
821C2×C4C2×H(5,𝔽2)11yescharacteristic
822C2×C4C2×H(5,𝔽2)11yescharacteristic
823C8—44no—
824C8—44no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—416no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—41no—
845C22—41no—
846C22—82no—
847C22—82no—
848C22—82no—
849C22—82no—
850C22—82no—
851C22—82no—
852C22—82no—
853C22#321214yes—
854C22C2×#52511yescharacteristic
855C22C2×#53411yescharacteristic
856C22C2×#53511yescharacteristic
857C22C22×#13511yescharacteristic
858C22C22×#13711yescharacteristic
859C22C2×#57511yescharacteristic
860C22C2×#57511yescharacteristic
861C4—22no—
862C4—22no—
863C4—22no—
864C4—22no—
865C4—22no—
866C4—22no—
867C4—41no—
868C4—44no—
869C4—41no—
870C4—41no—
871C4—41no—
872C4—44no—
873C4—82no—
874C4—82no—
875C4—82no—
876C4—82no—
877C4—82no—
878C4#319014yes—
879C4#351912yes—
880C4#351912yes—
881C2—24no—
882C2—42no—
883C2—42no—
884C2—162no—
885C2#3507611yescharacteristic
886C2#6053611yescharacteristic
887C2#6056011yescharacteristic
888C2C2×#319011yescharacteristic
889C2#6075211yescharacteristic
890C2C2×#321211yescharacteristic
891C2#6080411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36624C2
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. C2×C4×C22⋊Q8C2semidirect
3. #33108C2semidirect
4. #33106C2semidirect
5. #32906C2semidirect
6. #32903C2semidirect
7. #30114C2semidirect
8. #29330C2semidirect
9. #28306C2semidirect
10. #27682C2semidirect
11. #24653C2semidirect
12. #24652C2semidirect
13. #24213C2semidirect
14. #24004C2semidirect
15. #23922C2semidirect
16. #22042C2semidirect
17. #20714C2semidirect
25. C2×#462C22semidirect
26. C2×#460C22semidirect
63. #2101C22semidirect
64. #2097C22semidirect
65. #2042C22semidirect
68. #2015C22semidirect
71. #1982C22semidirect
72. #1981C22semidirect
73. #1969C22semidirect
74. #1968C22semidirect
75. #1948C22semidirect
76. #1947C22semidirect
77. #1934C22semidirect
78. #1933C22semidirect
79. #1927C22semidirect
80. #1925C22semidirect
81. #1880C22semidirect
82. #1878C22semidirect
90. #1803C22semidirect
91. #1803C22semidirect

Maximal subgroups

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

subgroupindex
#366242
C2×C4×C22⋊Q82
#331082
#331062
#329062
#329032
#301142
#293302
#283062
#276822
#246532
#246522
#242132
#240042
#239222
#220422
#207142