Finite Group Databasebeta

← #6473049

Subgroups — #6473049

Order 512.

2364 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
1C2×#3196C212yesmaximal, complemented
2#36624C211yesmaximal, characteristic
3C2×C4×C22⋊Q8C211yesmaximal, characteristic, complemented
4#33110C212yesmaximal, complemented
5#32909C212yesmaximal, complemented
6#29757C211yesmaximal, characteristic, complemented
7#29755C211yesmaximal, characteristic, complemented
8#29715C211yesmaximal, characteristic, complemented
9#29713C211yesmaximal, characteristic, complemented
10#28581C212yesmaximal, complemented
11#28580C212yesmaximal, complemented
12#28125C214yesmaximal, complemented
13#27652C212yesmaximal, complemented
14#24757C214yesmaximal, complemented
15#24216C212yesmaximal, complemented
16#21769C212yesmaximal, complemented
17#20626C211yesmaximal, characteristic, complemented
18C2×#532C2211yescharacteristic
19C2×#525C2212yes—
20C22×C22⋊Q8C2211yescharacteristic
21C22×C4×Q8C2211yescharacteristic
22C23×C42C2211yescharacteristic
23#3196—216no—
24C2×#484C2212yes—
25C2×#481C2212yes—
26C2×#485C2214yes—
27C2×#470C2214yes—
28C2×#468C2214yes—
29C2×#464C2214yescomplemented
30C2×#452C2214yes—
31C2×#451C2212yes—
32C2×#448C2212yes—
33C2×#423C2212yes—
34C2×#407C2212yes—
35#2857C2211yescharacteristic
36#2857C2211yescharacteristic
37#2856C2211yescharacteristic
38#2856C2211yescharacteristic
39#2854—21no—
40#2854—21no—
41#2850C2212yes—
42#2850C2212yes—
43#2847—21no—
44#2847—21no—
45C4×C22⋊Q8—21no—
46C4×C22⋊Q8—21no—
47C4×C22⋊Q8—21no—
48C4×C22⋊Q8—21no—
49C4×C22⋊Q8C2212yes—
50C4×C22⋊Q8C2212yes—
51C4×C22⋊Q8C2212yes—
52C4×C22⋊Q8C2212yes—
53C4×#121—21no—
54C4×#121—21no—
55C4×#121—21no—
56C4×#121—21no—
57#2297C2212yes—
58C2×#391C2211yescharacteristic
59C2×#389C2211yescharacteristic
60C2×#387—21no—
61C2×#385—21no—
62#2285C2211yescharacteristic
63C2×#380C2211yescharacteristic
64C2×C4×C4⋊C4—21no—
65C2×C4×C4⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4—21no—
67#2084C2212yescomplemented
68#2083C2212yescomplemented
69#2072C2212yescomplemented
70#2072C2212yescomplemented
71#2068C2214yescomplemented
72#2065C2214yescomplemented
73#2056C2214yescomplemented
74#2055C2214yescomplemented
75#2043C2212yescomplemented
76#2041C2212yescomplemented
77#2016C2212yescomplemented
78#2014C2212yescomplemented
79#1983C2214yescomplemented
80#1949C2214yescomplemented
81#1927C2214yescomplemented
82#1925C2214yescomplemented
83#1895C2214yes—
84#1894C2214yes—
85#1880C2214yescomplemented
86#1878C2214yescomplemented
87#1874C2212yes—
88#1874C2212yes—
89#1872C2212yes—
90#1872C2212yes—
91#1825C2214yes—
92#1805C2214yescomplemented
93#1797C2212yes—
94#1797C2211yescharacteristic
95#1797C2211yescharacteristic
96#1797C2212yes—
97#1797C2212yes—
98#1788C2214yes—
99#1728C2212yes—
100C22×#41C2312yes—
101C23×Q8C2311yescharacteristic
102C24×C4D411yescharacteristic
103C24×C4D411yescharacteristic
104C24×C4C2311yescharacteristic
105C22×Q16C2314yes—
106C22×SD16C2314yes—
107C22×M16C2314yes—
108#532—44no—
109C2×C4⋊Q8C2311yescharacteristic
110C2×#127C2311yescharacteristic
111C2×#124C2312yes—
112#525—28no—
113#525—28no—
114C2×#123—22no—
115C2×C22⋊Q8—21no—
116C2×C22⋊Q8—21no—
117C2×C22⋊Q8—24no—
118C2×C22⋊Q8D418yescomplemented
119C2×C22⋊Q8C2312yes—
120C2×C22⋊Q8C2312yes—
121C2×C22⋊Q8C2312yes—
122C2×C22⋊Q8C2312yes—
123C2×#121—21no—
124C2×#121—21no—
125C2×#121—21no—
126C2×#121—21no—
127C2×#121—21no—
128C2×#121—21no—
129C2×#121C2312yes—
130C2×#121C2312yes—
131C2×#120—22no—
132C2×C4×Q8—21no—
133C2×C4×Q8—21no—
134C2×C4×Q8—44no—
135C2×C4×Q8C2312yes—
136C2×C4×Q8C2312yes—
137C2×C4×D4—22no—
138C2×C4×D4—22no—
139C2×C4×D4—21no—
140C2×C4×D4—21no—
141C2×#117C2312yes—
142C22×C4⋊C4—21no—
143C22×C4⋊C4—21no—
144C22×C4⋊C4—21no—
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2311yescharacteristic
148C22×C22⋊C4—21no—
149C22×C22⋊C4—21no—
150C22×C42—21no—
151C22×C42—21no—
152C22×C42—44no—
153C22×C42D411yescharacteristic
154C22×C42D411yescharacteristic
155C22×C42D411yescharacteristic
156C22×C42D411yescharacteristic
157C22×C42D411yescharacteristic
158C22×C42D411yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165#485—216no—
166#484—28no—
167#481—28no—
168#470—216no—
169#468—216no—
170#464—48no—
171#452—216no—
172#451—28no—
173#448—28no—
174C2×#107C2314yes—
175C2×#106C2314yes—
176#423—44no—
177C2×C4⋊C8C2314yes—
178C2×C4⋊C8C2312yes—
179C2×C4⋊C8C2312yes—
180C2×#103C2314yes—
181C2×#103C2314yes—
182C2×#103C2314yes—
183C2×#103C2314yes—
184C2×#103C2314yes—
185C2×#102C2314yes—
186C2×#102C2314yes—
187C2×#102C2314yes—
188#407—28no—
189C2×C22⋊C8C2314yes—
190C2×C22⋊C8C2312yes—
191C2×C22⋊C8C2312yes—
192#391—21no—
193#391—21no—
194#391C2312yes—
195#391C2312yes—
196#391C2312yes—
197#391C2312yes—
198#390—21no—
199#390—21no—
200#390—21no—
201#390—21no—
202#390C2312yes—
203#390C2312yes—
204#389—21no—
205#389—21no—
206#389—21no—
207#389—21no—
208#389—21no—
209#389—21no—
210#389C2312yes—
211#389C2312yes—
212#388—22no—
213#388—22no—
214#388—22no—
215#388—22no—
216#387—22no—
217#387—22no—
218#387—22no—
219#387—22no—
220#386—22no—
221#386—22no—
222#386—22no—
223#386—22no—
224#386—22no—
225#386—22no—
226#385—22no—
227#385—22no—
228#385—22no—
229#385—22no—
230#384C2311yescharacteristic
231#384C2311yescharacteristic
232#382C2312yes—
233#380—21no—
234#380—21no—
235#380—21no—
236#380—21no—
237#380—21no—
238#380—21no—
239#380—21no—
240#380—21no—
241#380C2312yes—
242#380C2312yes—
243C4×C4⋊C4—22no—
244C4×C4⋊C4—22no—
245C4×C4⋊C4—22no—
246C4×C4⋊C4—22no—
247C4×C4⋊C4—21no—
248C4×C4⋊C4—21no—
249C4×C4⋊C4—21no—
250C4×C4⋊C4—21no—
251C4×C4⋊C4C2312yes—
252C4×C4⋊C4C2312yes—
253C4×C22⋊C4—22no—
254C4×C22⋊C4—22no—
255C4×C22⋊C4—22no—
256C4×C22⋊C4—22no—
257C4×C22⋊C4—22no—
258C4×C22⋊C4—22no—
259C2×#95—21no—
260C2×#95—21no—
261C2×#95—21no—
262C2×#95—21no—
263C2×#95—21no—
264#340C2314yes—
265#340C2314yes—
266#340C2314yes—
267#340C2314yes—
268#336C2312yes—
269#336C2312yes—
270#336C2314yes—
271C25C2×D411yescharacteristic
272C2×#41—24no—
273C2×#41—24no—
274C2×#41—44no—
275C2×#41—44no—
276C22×Q8—21no—
277C22×Q8—22no—
278C22×Q8—42no—
279C22×Q8—42no—
280C22×Q8C2×D414yes—
281C22×Q8C2412yes—
282C22×Q8C2412yes—
283C22×D4—22no—
284C22×D4—22no—
285C22×D4—22no—
286C22×D4—21no—
287C22×D4—21no—
288C22×D4C2412yes—
289C23×C4—21no—
290C23×C4—21no—
291C23×C4—24no—
292C23×C4—21no—
293C23×C4—21no—
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×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×C4C2×D411yescharacteristic
315C23×C4C2×D411yescharacteristic
316C23×C4C2×D414yes—
317C23×C4C2×D411yescharacteristic
318C23×C4#4114yes—
319C23×C4C2411yescharacteristic
320C23×C4C2411yescharacteristic
321C23×C4C2411yescharacteristic
322C2×Q16—28no—
323C2×Q16—44no—
324C2×Q16—44no—
325C2×SD16—28no—
326C2×SD16—44no—
327C2×SD16—44no—
328C2×M16—28no—
329C2×M16—44no—
330C2×M16—44no—
331C22×C8C2414yes—
332C22×C8C2414yes—
333C4⋊Q8—42no—
334#127—42no—
335#124—28no—
336#123—48no—
337C22⋊Q8—28no—
338C22⋊Q8—28no—
339C22⋊Q8—24no—
340C22⋊Q8—24no—
341C22⋊Q8—24no—
342C22⋊Q8—24no—
343C22⋊Q8—24no—
344C22⋊Q8—24no—
345C22⋊Q8C2×D418yes—
346C22⋊Q8C2×D418yes—
347#121—24no—
348#121—24no—
349#121—24no—
350#121—24no—
351#121—44no—
352#121—44no—
353#121—44no—
354#121—44no—
355#121—44no—
356#121—44no—
357#120—48no—
358C4×Q8—28no—
359C4×Q8—44no—
360C4×Q8—44no—
361C4×Q8—44no—
362C4×D4—44no—
363C4×D4—44no—
364C4×D4—48no—
365C4×D4—48no—
366#117—24no—
367#117—24no—
368C2×C4⋊C4—28no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
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—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—42no—
388C2×C4⋊C4—42no—
389C2×C4⋊C4—44no—
390C2×C4⋊C4—44no—
391C2×C4⋊C4C2×D414yes—
392C2×C4⋊C4C2412yes—
393C2×C4⋊C4C2412yes—
394C2×C4⋊C4C2412yes—
395C2×C4⋊C4C2412yes—
396C2×C4⋊C4C2412yes—
397C2×C22⋊C4—28no—
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—44no—
414C2×C42—24no—
415C2×C42—24no—
416C2×C42—24no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
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—42no—
431C2×C42—44no—
432C2×C42—44no—
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×C42C2×D411yescharacteristic
444C2×C42C2×D411yescharacteristic
445C2×C42C2411yescharacteristic
446C2×C42C2411yescharacteristic
447C2×C42C2411yescharacteristic
448C2×C42C2411yescharacteristic
449#107—28no—
450#106—28no—
451C4⋊C8—28no—
452C4⋊C8—42no—
453C4⋊C8—42no—
454#103—28no—
455#103—28no—
456#103—28no—
457#103—44no—
458#103—44no—
459#102—28no—
460#102—44no—
461#102—44no—
462C22⋊C8—24no—
463C22⋊C8—24no—
464C22⋊C8—28no—
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—
476#95—22no—
477#95—22no—
478#95—22no—
479#95—22no—
480#95—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—41no—
485C24—41no—
486C24—41no—
487C24—41no—
488C24#12114yes—
489C24C22×D411yescharacteristic
490C24C22×D411yescharacteristic
491C24C22×D411yescharacteristic
492#41—88no—
493#41—88no—
494C2×Q8—24no—
495C2×Q8—22no—
496C2×Q8—22no—
497C2×Q8—22no—
498C2×Q8—24no—
499C2×Q8—24no—
500C2×Q8—24no—
501C2×Q8—24no—
502C2×Q8—48no—
503C2×Q8—42no—
504C2×Q8—42no—
505C2×Q8—48no—
506C2×Q8C22×D414yes—
507C2×D4—22no—
508C2×D4—22no—
509C2×D4—24no—
510C2×D4—24no—
511C2×D4—42no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4—42no—
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—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—24no—
536C22×C4—24no—
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—48no—
561C22×C4—48no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
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—44no—
586C22×C4—44no—
587C22×C4—42no—
588C22×C4—42no—
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—44no—
599C22×C4#12114yes—
600C22×C4#12114yes—
601C22×C4#12114yes—
602C22×C4#13714yes—
603C22×C4C22×D411yescharacteristic
604C22×C4C22×D411yescharacteristic
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D411yescharacteristic
608C22×C4C22×D412yes—
609C22×C4C22×D412yes—
610C22×C4C22×D412yes—
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D411yescharacteristic
617C22×C4C2×#4112yes—
618C22×C4C2×#4112yes—
619C22×C4C2×#4112yes—
620C22×C4C2511yescharacteristic
621Q16—88no—
622SD16—88no—
623M16—88no—
624C2×C8—24no—
625C2×C8—24no—
626C2×C8—24no—
627C2×C8—24no—
628C2×C8—24no—
629C2×C8—24no—
630C4⋊C4—28no—
631C4⋊C4—28no—
632C4⋊C4—24no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—24no—
639C4⋊C4—24no—
640C4⋊C4—42no—
641C4⋊C4—44no—
642C4⋊C4—42no—
643C4⋊C4—44no—
644C4⋊C4—42no—
645C4⋊C4—42no—
646C4⋊C4—42no—
647C4⋊C4—42no—
648C4⋊C4—44no—
649C4⋊C4—44no—
650C4⋊C4—44no—
651C4⋊C4—42no—
652C4⋊C4—44no—
653C4⋊C4—42no—
654C4⋊C4C22×D414yes—
655C22⋊C4—28no—
656C22⋊C4—28no—
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—
668C22⋊C4—44no—
669C22⋊C4—44no—
670C42—22no—
671C42—22no—
672C42—22no—
673C42—22no—
674C42—22no—
675C42—22no—
676C42—22no—
677C42—22no—
678C42—22no—
679C42—41no—
680C42—41no—
681C42—41no—
682C42—41no—
683C42—41no—
684C42—41no—
685C42—44no—
686C42—44no—
687C42—44no—
688C42—44no—
689C42—44no—
690C42H(5,𝔽2)14yes—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—28no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—44no—
712C23—44no—
713C23—44no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23C2×#12112yes—
722C23C2×#12112yes—
723C23C2×#12112yes—
724C23C2×#13712yes—
725C23#57512yes—
726C23C23×D411yescharacteristic
727Q8—28no—
728Q8—48no—
729Q8—44no—
730Q8—44no—
731Q8—44no—
732D4—44no—
733D4—44no—
734D4—84no—
735D4—84no—
736D4—88no—
737D4—88no—
738D4—88no—
739C2×C4—28no—
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—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
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—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—48no—
786C2×C4—48no—
787C2×C4—44no—
788C2×C4—42no—
789C2×C4—42no—
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×C4C2×#12112yes—
811C2×C4C2×#12112yes—
812C2×C4C2×#12112yes—
813C2×C4#53412yes—
814C2×C4#53412yes—
815C2×C4C2×#13712yes—
816C2×C4C2×#13712yes—
817C2×C4#57512yes—
818C2×C4#57512yes—
819C2×C4C23×D411yescharacteristic
820C2×C4C22×#4111yescharacteristic
821C2×C4C2×H(5,𝔽2)12yes—
822C2×C4#58512yes—
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#303714yes—
854C22C22×#12111yescharacteristic
855C22C2×#53411yescharacteristic
856C22#344911yescharacteristic
857C22C22×#13711yescharacteristic
858C22C2×#57511yescharacteristic
859C22C2×#57511yescharacteristic
860C22C2×#57511yescharacteristic
861C4—22no—
862C4—22no—
863C4—22no—
864C4—22no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—41no—
871C4—41no—
872C4—44no—
873C4—44no—
874C4—82no—
875C4—82no—
876C4—82no—
877C4—82no—
878C4—82no—
879C4#349612yes—
880C4#350512yes—
881C2—24no—
882C2—42no—
883C2—42no—
884C2—162no—
885C2#3500011yescharacteristic
886C2C2×#303711yescharacteristic
887C2#6041511yescharacteristic
888C2#6074111yescharacteristic
889C2#6075111yescharacteristic
890C2#6095411yescharacteristic
891C2#6096611yescharacteristic
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
1. C2×#3196C2semidirect
3. C2×C4×C22⋊Q8C2semidirect
4. #33110C2semidirect
5. #32909C2semidirect
6. #29757C2semidirect
7. #29755C2semidirect
8. #29715C2semidirect
9. #29713C2semidirect
10. #28581C2semidirect
11. #28580C2semidirect
12. #28125C2semidirect
13. #27652C2semidirect
14. #24757C2semidirect
15. #24216C2semidirect
16. #21769C2semidirect
17. #20626C2semidirect
29. C2×#464C22semidirect
67. #2084C22semidirect
68. #2083C22semidirect
69. #2072C22semidirect
70. #2072C22semidirect
71. #2068C22semidirect
72. #2065C22semidirect
73. #2056C22semidirect
74. #2055C22semidirect
75. #2043C22semidirect
76. #2041C22semidirect
77. #2016C22semidirect
78. #2014C22semidirect
79. #1983C22semidirect
80. #1949C22semidirect
81. #1927C22semidirect
82. #1925C22semidirect
85. #1880C22semidirect
86. #1878C22semidirect
92. #1805C22semidirect
118. C2×C22⋊Q8D4semidirect

Maximal subgroups

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

subgroupindex
C2×#31962
#366242
C2×C4×C22⋊Q82
#331102
#329092
#297572
#297552
#297152
#297132
#285812
#285802
#281252
#276522
#247572
#242162
#217692
#206262