Finite Group Databasebeta

← #6458628

Subgroups — #6458628

Order 512.

1998 conjugacy classes of subgroups.

The subgroup lattice has 859 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊Q8C211yesmaximal, characteristic
2#34012C211yesmaximal, characteristic
3#27635C214yesmaximal, complemented
4#27634C214yesmaximal, complemented
5#27631C212yesmaximal, complemented
6#27630C212yesmaximal, complemented
7#27629C212yesmaximal, complemented
8#27628C212yesmaximal, complemented
9#23642C212yesmaximal
10#23481C212yesmaximal
11#21170C211yesmaximal, characteristic, complemented
12#21170C211yesmaximal, characteristic, complemented
13#21061C212yesmaximal, complemented
14#21034C212yesmaximal, complemented
15#20647C211yesmaximal, characteristic, complemented
16#20647C211yesmaximal, characteristic, complemented
17#20626C211yesmaximal, characteristic
18C22×C22⋊Q8C2211yescharacteristic
19C22×C4×Q8C2211yescharacteristic
20C23×C42C2211yescharacteristic
21C2×#428C2212yes—
22C2×#428C2212yes—
23C2×#423C2211yescharacteristic
24C2×#423C2211yescharacteristic
25C2×#419C2212yes—
26C2×#419C2212yes—
27C2×#407C2212yes—
28C4×C22⋊Q8—21no—
29C4×C22⋊Q8—21no—
30C4×C22⋊Q8—21no—
31C4×C22⋊Q8—21no—
32C4×C22⋊Q8C2212yes—
33C4×C22⋊Q8C2212yes—
34C4×C22⋊Q8C2212yes—
35C4×C22⋊Q8C2212yes—
36C2×#391C2211yescharacteristic
37C2×#389C2211yescharacteristic
38C2×#387—21no—
39C2×#385—21no—
40#2285C2211yescharacteristic
41#2285C2211yescharacteristic
42#2285C2211yescharacteristic
43#2285C2211yescharacteristic
44#2285C2211yescharacteristic
45#2285C2211yescharacteristic
46#2283—21no—
47#2283—21no—
48#2283—21no—
49#2283—21no—
50#2283C2212yes—
51#2283C2212yes—
52#2280—21no—
53#2280—21no—
54#2280C2212yes—
55C2×#380C2211yescharacteristic
56C4×#117—21no—
57C4×#117—21no—
58C4×#117C2212yes—
59C2×C4×C4⋊C4—21no—
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4—21no—
62#2077C2214yes—
63#2077C2214yes—
64#2076C2214yes—
65#2075C2214yes—
66#2036C2214yes—
67#2036C2214yes—
68#2035C2214yes—
69#2035C2214yes—
70#1949C2214yescomplemented
71#1949C2214yescomplemented
72#1948C2212yescomplemented
73#1948C2212yescomplemented
74#1947C2212yescomplemented
75#1947C2212yescomplemented
76#1928C2214yescomplemented
77#1928C2214yescomplemented
78#1927C2214yescomplemented
79#1927C2214yescomplemented
80#1921C2214yescomplemented
81#1920C2214yescomplemented
82#1919C2214yescomplemented
83#1918C2214yescomplemented
84#1805C2214yescomplemented
85#1805C2214yescomplemented
86#1803C2212yescomplemented
87#1803C2212yescomplemented
88#1803C2212yescomplemented
89#1803C2212yescomplemented
90#1797C2212yes—
91#1797C2212yes—
92#1797C2212yes—
93#1797C2212yes—
94#1736C2212yes—
95#1736C2212yes—
96#1736C2212yes—
97#1736C2212yes—
98#1728C2212yes—
99C23×Q8C2311yescharacteristic
100C24×C4D411yescharacteristic
101C24×C4D411yescharacteristic
102C24×C4C2311yescharacteristic
103C22×M16C2312yes—
104C22×M16C2312yes—
105C2×C22⋊Q8—24no—
106C2×C22⋊Q8—21no—
107C2×C22⋊Q8—21no—
108C2×C22⋊Q8—24no—
109C2×C22⋊Q8C2312yes—
110C2×C22⋊Q8C2312yes—
111C2×C4×Q8—21no—
112C2×C4×Q8—21no—
113C2×C4×Q8—24no—
114C2×C4×Q8—24no—
115C2×C4×Q8C2312yes—
116C2×C4×Q8C2312yes—
117C2×#117—21no—
118C2×#117—21no—
119C2×#117—21no—
120C2×#117—21no—
121C2×#117C2312yes—
122C2×#117C2312yes—
123C22×C4⋊C4—21no—
124C22×C4⋊C4—21no—
125C22×C4⋊C4—21no—
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C22⋊C4—21no—
130C22×C22⋊C4—21no—
131C22×C42—24no—
132C22×C42—24no—
133C22×C42—21no—
134C22×C42—21no—
135C22×C42D411yescharacteristic
136C22×C42D411yescharacteristic
137C22×C42D411yescharacteristic
138C22×C42D411yescharacteristic
139C22×C42D411yescharacteristic
140C22×C42D411yescharacteristic
141C22×C42C2311yescharacteristic
142C22×C42C2311yescharacteristic
143C22×C42C2311yescharacteristic
144C22×C42C2311yescharacteristic
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147#428—28no—
148#428—44no—
149C2×#107C2314yes—
150C2×#107C2314yes—
151C2×#106C2314yes—
152C2×#106C2314yes—
153#423—24no—
154#423—24no—
155C2×C4⋊C8C2312yes—
156C2×C4⋊C8C2312yes—
157C2×C4⋊C8C2312yes—
158C2×C4⋊C8C2312yes—
159#419—28no—
160#419—44no—
161C2×#103C2314yes—
162C2×#103C2314yes—
163C2×#103C2314yes—
164C2×#103C2314yes—
165#407—44no—
166C2×C22⋊C8C2314yes—
167C2×C22⋊C8C2314yes—
168#391—21no—
169#391—21no—
170#391C2312yes—
171#391C2312yes—
172#389—21no—
173#389—21no—
174#389C2312yes—
175#389C2312yes—
176#387—22no—
177#387—22no—
178#387—22no—
179#387—22no—
180#385—22no—
181#385—22no—
182#385—22no—
183#385—22no—
184#384C2311yescharacteristic
185#384C2311yescharacteristic
186#384C2311yescharacteristic
187#384C2311yescharacteristic
188#383—22no—
189#383—22no—
190#382—21no—
191#382—21no—
192#382—21no—
193#382—21no—
194#382C2312yes—
195#382C2312yes—
196#381—22no—
197#381—22no—
198#381—22no—
199#380—21no—
200#380—21no—
201#380—21no—
202#380—21no—
203#380—21no—
204#380—21no—
205#380—21no—
206#380—21no—
207#380—21no—
208#380—21no—
209#380C2312yes—
210#380C2312yes—
211#380C2312yes—
212#380C2312yes—
213#380C2312yes—
214#380C2312yes—
215#379—22no—
216C4×C4⋊C4—22no—
217C4×C4⋊C4—22no—
218C4×C4⋊C4—22no—
219C4×C4⋊C4—22no—
220C4×C4⋊C4—21no—
221C4×C4⋊C4—21no—
222C4×C4⋊C4—21no—
223C4×C4⋊C4—21no—
224C4×C4⋊C4—21no—
225C4×C4⋊C4—21no—
226C4×C4⋊C4—21no—
227C4×C4⋊C4—21no—
228C4×C4⋊C4—21no—
229C4×C4⋊C4—21no—
230C4×C4⋊C4C2312yes—
231C4×C4⋊C4C2312yes—
232C4×C4⋊C4C2312yes—
233C4×C4⋊C4C2312yes—
234C4×C4⋊C4C2312yes—
235C4×C4⋊C4C2312yes—
236C4×C22⋊C4—22no—
237C4×C22⋊C4—22no—
238C4×C22⋊C4—22no—
239C4×C22⋊C4—22no—
240C4×C22⋊C4—22no—
241C4×C22⋊C4—22no—
242C4×C22⋊C4—22no—
243C4×C22⋊C4—22no—
244C4×C22⋊C4—22no—
245C4×C22⋊C4—22no—
246#376—22no—
247#376—22no—
248#376—22no—
249C2×#95—21no—
250C2×#95—21no—
251C2×#95—21no—
252C2×#95—21no—
253C2×#95—21no—
254C43—22no—
255#340C2314yes—
256#340C2314yes—
257#340C2314yes—
258#340C2314yes—
259#340C2314yes—
260#340C2314yes—
261#340C2314yes—
262#340C2314yes—
263#336C2314yes—
264#336C2314yes—
265C25C2×D411yescharacteristic
266C22×Q8—21no—
267C22×Q8—22no—
268C22×Q8—22no—
269C22×Q8—22no—
270C22×Q8—22no—
271C22×Q8—22no—
272C22×Q8#4114yes—
273C22×Q8C2412yes—
274C23×C4—21no—
275C23×C4—21no—
276C23×C4—24no—
277C23×C4—24no—
278C23×C4—24no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—21no—
286C23×C4—21no—
287C23×C4—42no—
288C23×C4—42no—
289C23×C4—42no—
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
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×C4C2411yescharacteristic
306C23×C4C2411yescharacteristic
307C23×C4C2411yescharacteristic
308C2×M16—24no—
309C2×M16—24no—
310C2×M16—24no—
311C2×M16—24no—
312C2×M16—24no—
313C2×M16—24no—
314C22×C8C2414yes—
315C22×C8C2414yes—
316C22⋊Q8—28no—
317C22⋊Q8—28no—
318C22⋊Q8—24no—
319C22⋊Q8—24no—
320C22⋊Q8—24no—
321C22⋊Q8—24no—
322C4×Q8—24no—
323C4×Q8—24no—
324C4×Q8—24no—
325C4×Q8—24no—
326C4×Q8—44no—
327C4×Q8—44no—
328#117—24no—
329#117—24no—
330#117—24no—
331#117—24no—
332#117—44no—
333#117—44no—
334#117—44no—
335#117—44no—
336C2×C4⋊C4—28no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4—44no—
361C2×C4⋊C4#4114yes—
362C2×C4⋊C4C2412yes—
363C2×C4⋊C4C2412yes—
364C2×C4⋊C4C2412yes—
365C2×C4⋊C4C2412yes—
366C2×C4⋊C4C2412yes—
367C2×C4⋊C4C2412yes—
368C2×C4⋊C4C2412yes—
369C2×C22⋊C4—28no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—44no—
381C2×C42—24no—
382C2×C42—24no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—24no—
386C2×C42—24no—
387C2×C42—24no—
388C2×C42—24no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—44no—
408C2×C42—44no—
409C2×C42C2×D411yescharacteristic
410C2×C42C2×D411yescharacteristic
411C2×C42C2×D411yescharacteristic
412C2×C42C2×D411yescharacteristic
413C2×C42C2×D411yescharacteristic
414C2×C42C2×D411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D411yescharacteristic
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42#4114yes—
422C2×C42#4114yes—
423C2×C42C2411yescharacteristic
424C2×C42C2411yescharacteristic
425C2×C42C2411yescharacteristic
426C2×C42C2411yescharacteristic
427#107—28no—
428#107—44no—
429#106—28no—
430#106—44no—
431C4⋊C8—24no—
432C4⋊C8—24no—
433C4⋊C8—24no—
434C4⋊C8—24no—
435#103—28no—
436#103—28no—
437#103—44no—
438#103—44no—
439C22⋊C8—44no—
440C22⋊C8—44no—
441#95—22no—
442#95—22no—
443#95—22no—
444#95—22no—
445#95—22no—
446#95—22no—
447#95—22no—
448#95—22no—
449#95—22no—
450#95—22no—
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—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—41no—
469C24—41no—
470C24C22×D411yescharacteristic
471C24C22×D411yescharacteristic
472C24C22×D411yescharacteristic
473C2×Q8—24no—
474C2×Q8—22no—
475C2×Q8—28no—
476C2×Q8—28no—
477C2×Q8—22no—
478C2×Q8—22no—
479C2×Q8—22no—
480C2×Q8—22no—
481C2×Q8—42no—
482C2×Q8—42no—
483C2×Q8—44no—
484C2×Q8—44no—
485C2×Q8C2×#4114yes—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
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—22no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—416no—
551C22×C4—416no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4#12314yes—
567C22×C4#12314yes—
568C22×C4#13714yes—
569C22×C4C22×D411yescharacteristic
570C22×C4C22×D411yescharacteristic
571C22×C4C22×D411yescharacteristic
572C22×C4C22×D411yescharacteristic
573C22×C4C22×D411yescharacteristic
574C22×C4C22×D411yescharacteristic
575C22×C4C22×D411yescharacteristic
576C22×C4C22×D411yescharacteristic
577C22×C4C22×D411yescharacteristic
578C22×C4C22×D411yescharacteristic
579C22×C4C22×D411yescharacteristic
580C22×C4C2×#4112yes—
581C22×C4C2×#4112yes—
582C22×C4C2×#4112yes—
583C22×C4C2×#4112yes—
584C22×C4H(5,𝔽2)12yes—
585C22×C42−1+412yes—
586C22×C4C2511yescharacteristic
587M16—48no—
588M16—48no—
589C2×C8—24no—
590C2×C8—24no—
591C2×C8—24no—
592C2×C8—24no—
593C2×C8—24no—
594C2×C8—24no—
595C4⋊C4—28no—
596C4⋊C4—28no—
597C4⋊C4—24no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—44no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—44no—
618C4⋊C4—44no—
619C4⋊C4—42no—
620C4⋊C4—42no—
621C4⋊C4—42no—
622C4⋊C4—44no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4C2×#4114yes—
626C22⋊C4—28no—
627C22⋊C4—28no—
628C22⋊C4—44no—
629C22⋊C4—44no—
630C22⋊C4—44no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—44no—
634C22⋊C4—44no—
635C22⋊C4—44no—
636C42—22no—
637C42—22no—
638C42—22no—
639C42—22no—
640C42—22no—
641C42—22no—
642C42—22no—
643C42—22no—
644C42—22no—
645C42—22no—
646C42—21no—
647C42—21no—
648C42—21no—
649C42—21no—
650C42—44no—
651C42—44no—
652C42—44no—
653C42—44no—
654C42—44no—
655C42—44no—
656C42—44no—
657C42—44no—
658C42—44no—
659C42—44no—
660C42#12314yes—
661C42#12314yes—
662C42C2×#4112yes—
663C42C2×#4112yes—
664C42C2×#4112yes—
665C42C2×#4112yes—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—28no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—44no—
684C23—44no—
685C23—44no—
686C23—44no—
687C23—44no—
688C23—44no—
689C23C2×#12312yes—
690C23#52512yes—
691C23#53712yes—
692C23C2×#13712yes—
693C23#57512yes—
694C23C23×D411yescharacteristic
695Q8—24no—
696Q8—24no—
697Q8—42no—
698Q8—42no—
699Q8—48no—
700C2×C4—28no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—28no—
712C2×C4—28no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—48no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—44no—
739C2×C4—48no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—44no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—84no—
772C2×C4—84no—
773C2×C4C2×#12312yes—
774C2×C4C2×#12312yes—
775C2×C4C2×#12312yes—
776C2×C4C2×#12312yes—
777C2×C4C2×#12312yes—
778C2×C4#52512yes—
779C2×C4#53712yes—
780C2×C4#55214yes—
781C2×C4#55314yes—
782C2×C4#55514yes—
783C2×C4#55614yes—
784C2×C4C2×#13712yes—
785C2×C4C2×#13712yes—
786C2×C4#57512yes—
787C2×C4#57512yes—
788C2×C4C22×#4111yescharacteristic
789C2×C4C22×#4111yescharacteristic
790C2×C4C22×#4111yescharacteristic
791C2×C4C22×#4111yescharacteristic
792C2×C4C2×H(5,𝔽2)11yescharacteristic
793C2×C4C2×2−1+411yescharacteristic
794C8—44no—
795C8—44no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—416no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22#248514yes—
818C22C22×#12311yescharacteristic
819C22C2×#52511yescharacteristic
820C22C2×#53711yescharacteristic
821C22C22×#13711yescharacteristic
822C22C2×#57511yescharacteristic
823C22C2×#57511yescharacteristic
824C22C2×#57511yescharacteristic
825C4—22no—
826C4—22no—
827C4—22no—
828C4—22no—
829C4—22no—
830C4—41no—
831C4—41no—
832C4—44no—
833C4—41no—
834C4—41no—
835C4—44no—
836C4—82no—
837C4—82no—
838C4—82no—
839C4—82no—
840C4—82no—
841C4—82no—
842C4#248514yes—
843C4#309514yes—
844C4C2×#55211yescharacteristic
845C4C2×#55311yescharacteristic
846C4C2×#55511yescharacteristic
847C4C2×#55611yescharacteristic
848C2—24no—
849C2—42no—
850C2—42no—
851C2C2×#248511yescharacteristic
852C2C2×#309511yescharacteristic
853C2#6051111yescharacteristic
854C2#6055911yescharacteristic
855C2#6056011yescharacteristic
856C2#6091711yescharacteristic
857C2#6091811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC25C2×D4
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
3. #27635C2semidirect
4. #27634C2semidirect
5. #27631C2semidirect
6. #27630C2semidirect
7. #27629C2semidirect
8. #27628C2semidirect
11. #21170C2semidirect
12. #21170C2semidirect
13. #21061C2semidirect
14. #21034C2semidirect
15. #20647C2semidirect
16. #20647C2semidirect
70. #1949C22semidirect
71. #1949C22semidirect
72. #1948C22semidirect
73. #1948C22semidirect
74. #1947C22semidirect
75. #1947C22semidirect
76. #1928C22semidirect
77. #1928C22semidirect
78. #1927C22semidirect
79. #1927C22semidirect
80. #1921C22semidirect
81. #1920C22semidirect
82. #1919C22semidirect
83. #1918C22semidirect
84. #1805C22semidirect
85. #1805C22semidirect
86. #1803C22semidirect
87. #1803C22semidirect
88. #1803C22semidirect
89. #1803C22semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊Q82
#340122
#276352
#276342
#276312
#276302
#276292
#276282
#236422
#234812
#211702
#210612
#210342
#206472
#206262