Finite Group Databasebeta

← #6476790

Subgroups — #6476790

Order 512.

2214 conjugacy classes of subgroups.

The subgroup lattice has 880 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#33147C211yesmaximal, characteristic, complemented
4#33107C211yesmaximal, characteristic, complemented
5#32954C211yesmaximal, characteristic, complemented
6#32903C211yesmaximal, characteristic, complemented
7#30010C214yesmaximal, complemented
8#29235C212yesmaximal, complemented
9#28115C212yesmaximal, complemented
10#27628C212yesmaximal, complemented
11#24838C212yesmaximal, complemented
12#24753C212yesmaximal, complemented
13#24553C212yesmaximal, complemented
14#24381C212yesmaximal, complemented
15#24154C212yesmaximal, complemented
16#22180C214yesmaximal, complemented
17C2×#1797C211yesmaximal, characteristic, complemented
18C2×#532C2211yescharacteristic
19C2×#525—21no—
20C22×C22⋊Q8C2211yescharacteristic
21C22×C4×Q8C2211yescharacteristic
22C23×C42C2211yescharacteristic
23C2×#481C2212yes—
24C2×#475C2212yescomplemented
25C2×#465C2214yes—
26C2×#460C2212yescomplemented
27C2×#448C2212yes—
28C22×C4⋊C8C2212yes—
29C22×C22⋊C8C2212yes—
30#2857C2211yescharacteristic
31#2857C2211yescharacteristic
32#2856C2211yescharacteristic
33#2856C2211yescharacteristic
34#2854—21no—
35#2854C2212yes—
36#2850—21no—
37#2850—21no—
38#2847—21no—
39#2847C2212yes—
40C4×C22⋊Q8—21no—
41C4×C22⋊Q8—21no—
42C4×C22⋊Q8—21no—
43C4×C22⋊Q8—21no—
44C4×C22⋊Q8C2212yes—
45C4×C22⋊Q8C2212yes—
46C4×C22⋊Q8C2212yes—
47C4×C22⋊Q8C2212yes—
48C4×#121—21no—
49C4×#121—21no—
50C4×#121C2212yes—
51C4×#121C2212yes—
52#2297—21no—
53C2×#391C2211yescharacteristic
54C2×#389C2211yescharacteristic
55C2×#387—21no—
56C2×#385—21no—
57#2285C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×C4×C4⋊C4—21no—
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4—21no—
62#2088C2214yescomplemented
63#2077C2214yes—
64#2066C2214yescomplemented
65#2065C2214yescomplemented
66#2055C2214yescomplemented
67#2035C2214yes—
68#2034C2214yes—
69#2000C2214yes—
70#1988C2212yescomplemented
71#1982C2212yescomplemented
72#1948C2212yescomplemented
73#1948C2212yescomplemented
74#1927C2214yescomplemented
75#1926C2214yescomplemented
76#1920C2214yescomplemented
77#1919C2214yescomplemented
78#1893C2214yes—
79#1892C2214yes—
80#1880C2214yescomplemented
81#1877C2214yescomplemented
82#1874C2212yes—
83#1874C2212yes—
84#1865C2214yescomplemented
85#1864C2214yescomplemented
86#1853C2212yes—
87#1853C2212yes—
88#1824C2212yes—
89#1807C2214yes—
90#1803C2212yescomplemented
91#1803C2212yescomplemented
92#1797C2212yes—
93#1797C2212yes—
94#1797C2211yescharacteristic
95#1797C2212yes—
96#1797C2211yescharacteristic
97#1787C2212yes—
98C2×#336C2212yes—
99C22×#41—21no—
100C23×Q8C2311yescharacteristic
101C24×C4D411yescharacteristic
102C24×C4D411yescharacteristic
103C24×C4C2311yescharacteristic
104C22×SD16C2314yes—
105C23×C8C2314yes—
106#532—44no—
107C2×C4⋊Q8C2311yescharacteristic
108C2×#127C2311yescharacteristic
109C2×#124—21no—
110#525—48no—
111C2×#123—22no—
112C2×C22⋊Q8—21no—
113C2×C22⋊Q8—21no—
114C2×C22⋊Q8—28no—
115C2×C22⋊Q8—21no—
116C2×C22⋊Q8—21no—
117C2×C22⋊Q8C2312yes—
118C2×C22⋊Q8C2312yes—
119C2×#121—21no—
120C2×#121—21no—
121C2×#121—21no—
122C2×#121—21no—
123C2×#121—21no—
124C2×#121C2312yes—
125C2×#121C2312yes—
126C2×#121C2312yes—
127C2×#120—22no—
128C2×C4×Q8—21no—
129C2×C4×Q8—21no—
130C2×C4×Q8—44no—
131C2×C4×Q8C2312yes—
132C2×C4×Q8C2312yes—
133C2×C4×D4—22no—
134C2×C4×D4—22no—
135C2×C4×D4—21no—
136C2×C4×D4C2312yes—
137C2×#117—21no—
138C22×C4⋊C4—21no—
139C22×C4⋊C4—21no—
140C22×C4⋊C4—21no—
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C42—21no—
147C22×C42—21no—
148C22×C42—44no—
149C22×C42D411yescharacteristic
150C22×C42D411yescharacteristic
151C22×C42D411yescharacteristic
152C22×C42D411yescharacteristic
153C22×C42D411yescharacteristic
154C22×C42D411yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161#481—44no—
162#475—44no—
163#465—216no—
164#460—44no—
165#448—44no—
166C2×#106C2314yes—
167C2×#106C2314yes—
168C2×#106C2314yes—
169C2×C4⋊C8—44no—
170C2×C4⋊C8C2312yes—
171C2×C4⋊C8C2312yes—
172C2×C4⋊C8C2314yes—
173C2×#103C2314yes—
174C2×#103C2314yes—
175C2×#103C2314yes—
176C2×#102C2314yes—
177C2×#102C2314yes—
178C2×#102C2314yes—
179C2×C22⋊C8—44no—
180C2×C22⋊C8C2312yes—
181C2×C22⋊C8C2312yes—
182C2×C22⋊C8C2314yes—
183#391—21no—
184#391—21no—
185#391—21no—
186#391—21no—
187#391C2312yes—
188#391C2312yes—
189#390—21no—
190#390—21no—
191#390—21no—
192#390—21no—
193#390C2312yes—
194#390C2312yes—
195#389—21no—
196#389—21no—
197#389—21no—
198#389—21no—
199#389C2312yes—
200#389C2312yes—
201#389C2312yes—
202#389C2312yes—
203#388—22no—
204#388—22no—
205#388—22no—
206#388—22no—
207#387—22no—
208#387—22no—
209#387—22no—
210#387—22no—
211#386—22no—
212#386—22no—
213#386—22no—
214#386—22no—
215#386—22no—
216#386—22no—
217#385—22no—
218#385—22no—
219#385—22no—
220#385—22no—
221#384C2311yescharacteristic
222#384C2311yescharacteristic
223#382—21no—
224#380—21no—
225#380—21no—
226#380—21no—
227#380—21no—
228#380—21no—
229#380C2312yes—
230#380C2312yes—
231#380C2312yes—
232#380C2312yes—
233#380C2312yes—
234C4×C4⋊C4—22no—
235C4×C4⋊C4—22no—
236C4×C4⋊C4—22no—
237C4×C4⋊C4—22no—
238C4×C4⋊C4—21no—
239C4×C4⋊C4—21no—
240C4×C4⋊C4—21no—
241C4×C4⋊C4C2312yes—
242C4×C4⋊C4C2312yes—
243C4×C4⋊C4C2312yes—
244C4×C22⋊C4—22no—
245C4×C22⋊C4—22no—
246C4×C22⋊C4—22no—
247C4×C22⋊C4—22no—
248C4×C22⋊C4—22no—
249C4×C22⋊C4—22no—
250C2×#95—21no—
251C2×#95—21no—
252C2×#95—21no—
253C2×#95—21no—
254C2×#95—21no—
255#340C2314yes—
256#340C2314yes—
257#340C2314yes—
258#340C2314yes—
259#340C2314yes—
260#340C2314yes—
261#336C2314yes—
262#336C2312yes—
263#336C2312yes—
264C25C2×D411yescharacteristic
265C2×#41—44no—
266C2×#41—44no—
267C2×#41—44no—
268C22×Q8—24no—
269C22×Q8—21no—
270C22×Q8—21no—
271C22×Q8—22no—
272C22×Q8—22no—
273C22×Q8—42no—
274C22×Q8C2412yes—
275C22×D4—22no—
276C22×D4—22no—
277C22×D4—22no—
278C22×D4—21no—
279C22×D4—21no—
280C22×D4C2412yes—
281C23×C4—21no—
282C23×C4—21no—
283C23×C4—24no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—21no—
287C23×C4—21no—
288C23×C4—22no—
289C23×C4—42no—
290C23×C4—42no—
291C23×C4—42no—
292C23×C4—42no—
293C23×C4—42no—
294C23×C4—42no—
295C23×C4SD1618yescomplemented
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
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×C4C2411yescharacteristic
312C23×C4C2411yescharacteristic
313C23×C4C2411yescharacteristic
314C2×SD16—28no—
315C2×SD16—44no—
316C2×SD16—44no—
317C22×C8—28no—
318C22×C8—44no—
319C22×C8—44no—
320C22×C8C2414yes—
321C22×C8C2414yes—
322C4⋊Q8—24no—
323#127—24no—
324#124—44no—
325#123—48no—
326C22⋊Q8—28no—
327C22⋊Q8—28no—
328C22⋊Q8—24no—
329C22⋊Q8—24no—
330C22⋊Q8—24no—
331C22⋊Q8—44no—
332C22⋊Q8—44no—
333C22⋊Q8#4118yescomplemented
334#121—28no—
335#121—24no—
336#121—24no—
337#121—44no—
338#121—44no—
339#121—44no—
340#121—44no—
341#121—44no—
342#121—44no—
343#120—48no—
344C4×Q8—24no—
345C4×Q8—24no—
346C4×Q8—42no—
347C4×Q8—42no—
348C4×Q8—44no—
349C4×Q8—44no—
350C4×D4—44no—
351C4×D4—44no—
352C4×D4—48no—
353C4×D4—48no—
354#117—44no—
355C2×C4⋊C4—28no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—42no—
376C2×C4⋊C4—44no—
377C2×C4⋊C4—44no—
378C2×C4⋊C4C2412yes—
379C2×C4⋊C4C2412yes—
380C2×C4⋊C4C2412yes—
381C2×C4⋊C4C2412yes—
382C2×C4⋊C4C2412yes—
383C2×C4⋊C4C2412yes—
384C2×C22⋊C4—28no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
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—44no—
401C2×C42—24no—
402C2×C42—24no—
403C2×C42—24no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—42no—
410C2×C42—42no—
411C2×C42—42no—
412C2×C42—42no—
413C2×C42—42no—
414C2×C42—42no—
415C2×C42—42no—
416C2×C42—42no—
417C2×C42—42no—
418C2×C42—44no—
419C2×C42—44no—
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
426C2×C42C2×D411yescharacteristic
427C2×C42C2×D411yescharacteristic
428C2×C42C2×D411yescharacteristic
429C2×C42C2×D411yescharacteristic
430C2×C42C2×D411yescharacteristic
431C2×C42C2×D411yescharacteristic
432C2×C42C2411yescharacteristic
433C2×C42C2411yescharacteristic
434C2×C42C2411yescharacteristic
435C2×C42C2411yescharacteristic
436#106—28no—
437#106—44no—
438#106—44no—
439C4⋊C8—24no—
440C4⋊C8—24no—
441C4⋊C8—44no—
442#103—28no—
443#103—44no—
444#103—44no—
445#102—28no—
446#102—44no—
447#102—44no—
448C22⋊C8—24no—
449C22⋊C8—24no—
450C22⋊C8—44no—
451#95—22no—
452#95—22no—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—22no—
461#95—22no—
462#95—22no—
463#95—22no—
464#95—22no—
465#95—22no—
466#95—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—41no—
473C24—41no—
474C24C2×SD1614yes—
475C24C22×D411yescharacteristic
476C24C22×D411yescharacteristic
477C24C22×D411yescharacteristic
478#41—816no—
479C2×Q8—24no—
480C2×Q8—22no—
481C2×Q8—22no—
482C2×Q8—22no—
483C2×Q8—22no—
484C2×Q8—22no—
485C2×Q8—48no—
486C2×Q8—48no—
487C2×Q8—42no—
488C2×Q8—42no—
489C2×Q8—42no—
490C2×Q8—42no—
491C2×Q8—42no—
492C2×Q8C2×#4114yes—
493C2×D4—24no—
494C2×D4—22no—
495C2×D4—24no—
496C2×D4—22no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—44no—
500C2×D4—44no—
501C2×D4—44no—
502C2×D4—44no—
503C2×D4—44no—
504C2×D4—44no—
505C2×D4—44no—
506C2×D4—44no—
507C2×D4—44no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—42no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—22no—
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—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—416no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
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—48no—
571C22×C4—48no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—416no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—44no—
586C22×C4C2×SD1614yes—
587C22×C4C2×SD1614yes—
588C22×C4C2×SD1614yes—
589C22×C4C2×SD1614yes—
590C22×C4C2×SD1614yes—
591C22×C4C2×SD1614yes—
592C22×C4C22×D411yescharacteristic
593C22×C4C22×D411yescharacteristic
594C22×C4C22×D411yescharacteristic
595C22×C4C22×D411yescharacteristic
596C22×C4C22×D411yescharacteristic
597C22×C4C22×D411yescharacteristic
598C22×C4C22×D411yescharacteristic
599C22×C4C22×D411yescharacteristic
600C22×C4C22×D411yescharacteristic
601C22×C4C22×D411yescharacteristic
602C22×C4C22×D411yescharacteristic
603C22×C4C2×#4114yes—
604C22×C4H(5,𝔽2)12yes—
605C22×C42−1+412yes—
606C22×C4C2511yescharacteristic
607SD16—88no—
608C2×C8—24no—
609C2×C8—24no—
610C2×C8—24no—
611C2×C8—24no—
612C2×C8—24no—
613C2×C8—24no—
614C2×C8—88no—
615C4⋊C4—24no—
616C4⋊C4—28no—
617C4⋊C4—28no—
618C4⋊C4—22no—
619C4⋊C4—24no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—24no—
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—44no—
628C4⋊C4—44no—
629C4⋊C4—42no—
630C4⋊C4—44no—
631C4⋊C4—42no—
632C4⋊C4—42no—
633C4⋊C4—44no—
634C4⋊C4—42no—
635C4⋊C4—42no—
636C4⋊C4—42no—
637C4⋊C4—42no—
638C4⋊C4—44no—
639C4⋊C4—44no—
640C4⋊C4C2×#4114yes—
641C22⋊C4—28no—
642C22⋊C4—28no—
643C22⋊C4—44no—
644C22⋊C4—44no—
645C22⋊C4—44no—
646C22⋊C4—44no—
647C22⋊C4—44no—
648C22⋊C4—44no—
649C22⋊C4—44no—
650C22⋊C4—44no—
651C22⋊C4—44no—
652C22⋊C4—44no—
653C22⋊C4—44no—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C42—22no—
657C42—22no—
658C42—22no—
659C42—22no—
660C42—22no—
661C42—22no—
662C42—22no—
663C42—22no—
664C42—22no—
665C42—41no—
666C42—41no—
667C42—41no—
668C42—41no—
669C42—41no—
670C42—41no—
671C42—44no—
672C42—44no—
673C42—44no—
674C42—44no—
675C42—44no—
676C42H(5,𝔽2)14yes—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—28no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—28no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23—44no—
697C23—44no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23#52512yes—
706C23#53712yes—
707C23C22×SD1612yes—
708C23C22×SD1612yes—
709C23C22×SD1612yes—
710C23#57512yes—
711C23#57512yes—
712C23C23×D411yescharacteristic
713Q8—24no—
714Q8—24no—
715Q8—48no—
716Q8—42no—
717Q8—42no—
718Q8—84no—
719D4—44no—
720D4—44no—
721D4—84no—
722D4—88no—
723D4—88no—
724D4—88no—
725D4—84no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—28no—
739C2×C4—28no—
740C2×C4—28no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
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—21no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—48no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—48no—
772C2×C4—44no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—88no—
795C2×C4—84no—
796C2×C4—84no—
797C2×C4#52512yes—
798C2×C4#53412yes—
799C2×C4#53412yes—
800C2×C4#53712yes—
801C2×C4C22×SD1612yes—
802C2×C4C22×SD1612yes—
803C2×C4C22×SD1612yes—
804C2×C4C22×SD1612yes—
805C2×C4#57512yes—
806C2×C4C22×#4112yes—
807C2×C4C2×H(5,𝔽2)11yescharacteristic
808C2×C4C2×H(5,𝔽2)12yes—
809C2×C4C2×2−1+411yescharacteristic
810C8—44no—
811C8—44no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—416no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—82no—
833C22—82no—
834C22—82no—
835C22—82no—
836C22—82no—
837C22—82no—
838C22—82no—
839C22#310314yes—
840C22#324614yes—
841C22C2×#52511yescharacteristic
842C22C2×#53411yescharacteristic
843C22C2×#53711yescharacteristic
844C22C23×SD1611yescharacteristic
845C22C2×#57511yescharacteristic
846C22C2×#57511yescharacteristic
847C22C2×#57511yescharacteristic
848C4—22no—
849C4—22no—
850C4—22no—
851C4—22no—
852C4—22no—
853C4—22no—
854C4—41no—
855C4—44no—
856C4—41no—
857C4—41no—
858C4—41no—
859C4—44no—
860C4—82no—
861C4—82no—
862C4—82no—
863C4—82no—
864C4—82no—
865C4#318714yes—
866C4#351912yes—
867C4#352012yes—
868C2—24no—
869C2—24no—
870C2—42no—
871C2—162no—
872C2#3507711yescharacteristic
873C2C2×#310311yescharacteristic
874C2#6054611yescharacteristic
875C2C2×#318711yescharacteristic
876C2#6075211yescharacteristic
877C2C2×#324611yescharacteristic
878C2#6091711yescharacteristic
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. #33147C2semidirect
4. #33107C2semidirect
5. #32954C2semidirect
6. #32903C2semidirect
7. #30010C2semidirect
8. #29235C2semidirect
9. #28115C2semidirect
10. #27628C2semidirect
11. #24838C2semidirect
12. #24753C2semidirect
13. #24553C2semidirect
14. #24381C2semidirect
15. #24154C2semidirect
16. #22180C2semidirect
17. C2×#1797C2semidirect
24. C2×#475C22semidirect
26. C2×#460C22semidirect
62. #2088C22semidirect
64. #2066C22semidirect
65. #2065C22semidirect
66. #2055C22semidirect
70. #1988C22semidirect
71. #1982C22semidirect
72. #1948C22semidirect
73. #1948C22semidirect
74. #1927C22semidirect
75. #1926C22semidirect
76. #1920C22semidirect
77. #1919C22semidirect
80. #1880C22semidirect
81. #1877C22semidirect
84. #1865C22semidirect
85. #1864C22semidirect
90. #1803C22semidirect
91. #1803C22semidirect
295. C23×C4SD16semidirect
333. C22⋊Q8#41semidirect

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
#331472
#331072
#329542
#329032
#300102
#292352
#281152
#276282
#248382
#247532
#245532
#243812
#241542
#221802
C2×#17972