Finite Group Databasebeta

← #6458952

Subgroups — #6458952

Order 512.

2112 conjugacy classes of subgroups.

The subgroup lattice has 901 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#525C211yesmaximal, characteristic
2C2×#2285C211yesmaximal, characteristic, complemented
3#27680C211yesmaximal, characteristic, complemented
4#27677C211yesmaximal, characteristic, complemented
5#27647C211yesmaximal, characteristic, complemented
6#27644C211yesmaximal, characteristic, complemented
7#27629C212yesmaximal, complemented
8#27625C212yesmaximal, complemented
9#27615C212yesmaximal, complemented
10#27602C212yesmaximal, complemented
11#27587C212yesmaximal, complemented
12#24004C212yesmaximal
13#23763C212yesmaximal, complemented
14#23761C212yesmaximal, complemented
15#21579C212yesmaximal, complemented
16#21578C212yesmaximal, complemented
17#21364C212yesmaximal, complemented
18#20743C212yesmaximal, complemented
19#20715C211yesmaximal, characteristic, complemented
20C2×#525C2211yescharacteristic
21C2×C4×#41C2211yescharacteristic
22C22×#117—21no—
23C23×C42C2211yescharacteristic
24C2×#483C2212yes—
25C2×#480C2212yes—
26C2×#432C2212yes—
27C4×C22⋊Q8C2211yescharacteristic
28C4×C22⋊Q8C2211yescharacteristic
29C4×C22⋊Q8C2211yescharacteristic
30C4×C22⋊Q8C2211yescharacteristic
31C4×#123—21no—
32C4×#123—21no—
33C4×#121C2211yescharacteristic
34C4×#121C2211yescharacteristic
35C4×#121C2211yescharacteristic
36C4×#121C2211yescharacteristic
37C4×#120—21no—
38C4×#120—21no—
39#2297C2211yescharacteristic
40#2296C2211yescharacteristic
41#2290—21no—
42#2290—21no—
43#2285—21no—
44#2285—21no—
45#2285—21no—
46#2285—21no—
47#2285C2212yes—
48#2285C2212yes—
49#2285C2212yes—
50#2285C2212yes—
51C2×#384C2211yescharacteristic
52C2×#384C2211yescharacteristic
53C2×#382—21no—
54#2280C2211yescharacteristic
55C2×#380—21no—
56C2×#380C2212yes—
57C42×D4—21no—
58C42×D4—21no—
59C4×#117C2211yescharacteristic
60C2×C4×C4⋊C4—21no—
61C2×C4×C4⋊C4C2212yes—
62#2099C2212yescomplemented
63#2099C2212yescomplemented
64#2096C2212yescomplemented
65#2093C2212yescomplemented
66#2084C2212yescomplemented
67#2083C2212yescomplemented
68#2077C2214yes—
69#2076C2214yes—
70#2072C2212yescomplemented
71#2071C2212yescomplemented
72#2036C2214yes—
73#2034C2214yes—
74#1948C2212yescomplemented
75#1948C2212yescomplemented
76#1947C2212yescomplemented
77#1947C2212yescomplemented
78#1928C2214yescomplemented
79#1926C2214yescomplemented
80#1921C2214yescomplemented
81#1919C2214yescomplemented
82#1874C2212yes—
83#1872C2212yes—
84#1854C2214yes—
85#1854C2214yes—
86#1853C2212yes—
87#1852C2212yes—
88#1825C2214yes—
89#1823C2212yes—
90#1823C2212yes—
91#1817C2212yes—
92#1803C2212yescomplemented
93#1803C2212yescomplemented
94#1802C2212yescomplemented
95#1802C2212yescomplemented
96#1797C2211yescharacteristic
97#1797C2211yescharacteristic
98#1797C2212yes—
99#1788C2214yes—
100#1779C2212yes—
101#1776C2214yescomplemented
102#1776C2214yescomplemented
103#1763C2214yescomplemented
104#1762C2214yescomplemented
105#1749C2212yes—
106#1749C2212yes—
107C22×#41C2311yescharacteristic
108C24×C4D411yescharacteristic
109C24×C4D411yescharacteristic
110C24×C4C2311yescharacteristic
111#525—24no—
112#525—24no—
113C2×#123—21no—
114C2×C22⋊Q8C2311yescharacteristic
115C2×C22⋊Q8C2311yescharacteristic
116C2×#121C2311yescharacteristic
117C2×#121C2311yescharacteristic
118C2×#120—21no—
119C4×#41—28no—
120C2×C4×Q8C2311yescharacteristic
121C2×C4×Q8C2311yescharacteristic
122C2×C4×D4—21no—
123C2×C4×D4—21no—
124C2×C4×D4—21no—
125C2×C4×D4—21no—
126C2×C4×D4—21no—
127C2×C4×D4—21no—
128C2×C4×D4—21no—
129C2×C4×D4—21no—
130C2×C4×D4C2311yescharacteristic
131C2×C4×D4C2311yescharacteristic
132C2×#117—22no—
133C2×#117—22no—
134C2×#117—22no—
135C2×#117—22no—
136C2×#117—21no—
137C2×#117—48no—
138C2×#117C2311yescharacteristic
139C2×#117C2311yescharacteristic
140C2×#117C2311yescharacteristic
141C22×C4⋊C4—21no—
142C22×C4⋊C4—21no—
143C22×C4⋊C4—21no—
144C22×C4⋊C4—21no—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C22⋊C4—22no—
148C22×C42—28no—
149C22×C42—22no—
150C22×C42—21no—
151C22×C42D411yescharacteristic
152C22×C42D411yescharacteristic
153C22×C42D411yescharacteristic
154C22×C42D411yescharacteristic
155C22×C42D411yescharacteristic
156C22×C42D411yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163#483—28no—
164#480—28no—
165#432—28no—
166C2×#107C2314yes—
167C2×#107C2314yes—
168C2×#106C2314yes—
169C2×#106C2314yes—
170C2×C4⋊C8C2312yes—
171C2×C4⋊C8C2312yes—
172C2×#103C2314yes—
173C2×#103C2314yes—
174C2×#102C2314yes—
175C2×#102C2314yes—
176C2×C22⋊C8C2312yes—
177C2×C22⋊C8C2312yes—
178C2×C22⋊C8C2314yes—
179C2×C22⋊C8C2314yes—
180C2×#97C2314yes—
181#391C2311yescharacteristic
182#391C2311yescharacteristic
183#390C2311yescharacteristic
184#390C2311yescharacteristic
185#389C2311yescharacteristic
186#389C2311yescharacteristic
187#389C2311yescharacteristic
188#389C2311yescharacteristic
189#388—21no—
190#388—21no—
191#388—21no—
192#388—21no—
193#387—21no—
194#387—21no—
195#387—21no—
196#387—21no—
197#386—21no—
198#386—21no—
199#386—21no—
200#386—21no—
201#386—21no—
202#386—21no—
203#385—21no—
204#385—21no—
205#385—21no—
206#385—21no—
207#385—21no—
208#385—21no—
209#384—21no—
210#384—21no—
211#384—21no—
212#384—21no—
213#384C2312yes—
214#384C2312yes—
215#384C2312yes—
216#384C2312yes—
217#382—22no—
218#382—22no—
219#382—22no—
220#382—22no—
221#381—21no—
222#380—22no—
223#380—22no—
224#380—22no—
225#380—22no—
226#380—22no—
227#380—22no—
228#380C2311yescharacteristic
229#380C2314yes—
230#380C2311yescharacteristic
231#380C2311yescharacteristic
232#380C2311yescharacteristic
233#380C2314yes—
234#379—21no—
235C4×C4⋊C4—22no—
236C4×C4⋊C4—22no—
237C4×C4⋊C4—22no—
238C4×C4⋊C4—22no—
239C4×C4⋊C4—22no—
240C4×C4⋊C4—22no—
241C4×C4⋊C4—21no—
242C4×C4⋊C4—21no—
243C4×C4⋊C4—21no—
244C4×C4⋊C4—21no—
245C4×C4⋊C4—21no—
246C4×C4⋊C4—21no—
247C4×C4⋊C4C2314yes—
248C4×C4⋊C4C2311yescharacteristic
249C4×C4⋊C4C2311yescharacteristic
250C4×C4⋊C4C2314yes—
251C4×C4⋊C4C2311yescharacteristic
252C4×C4⋊C4C2311yescharacteristic
253C4×C22⋊C4—21no—
254C4×C22⋊C4—21no—
255C4×C22⋊C4—21no—
256C4×C22⋊C4—21no—
257C4×C22⋊C4—21no—
258C4×C22⋊C4—21no—
259C4×C22⋊C4—21no—
260C4×C22⋊C4—21no—
261C4×C22⋊C4—21no—
262C4×C22⋊C4—21no—
263C4×C22⋊C4—21no—
264C4×C22⋊C4—21no—
265C4×C22⋊C4—21no—
266C4×C22⋊C4—21no—
267#376—21no—
268C2×#95—22no—
269C2×#95—22no—
270C43—21no—
271#340C2314yes—
272#340C2314yes—
273#340C2314yes—
274#340C2314yes—
275#340C2314yes—
276#340C2314yes—
277#340C2314yes—
278#340C2314yes—
279#336C2312yes—
280#336C2312yes—
281#336C2314yes—
282C25C2×D411yescharacteristic
283C2×#41—22no—
284C2×#41—22no—
285C2×#41—24no—
286C2×#41—42no—
287C22×Q8C2411yescharacteristic
288C22×D4—21no—
289C22×D4—21no—
290C22×D4—21no—
291C22×D4C2411yescharacteristic
292C23×C4—24no—
293C23×C4—24no—
294C23×C4—24no—
295C23×C4—24no—
296C23×C4—21no—
297C23×C4—22no—
298C23×C4—22no—
299C23×C4—24no—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4—21no—
303C23×C4—21no—
304C23×C4—42no—
305C23×C4—42no—
306C23×C4—42no—
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
325C22×C8C2414yes—
326C22×C8C2414yes—
327#123—28no—
328C22⋊Q8—22no—
329C22⋊Q8—22no—
330C22⋊Q8—22no—
331C22⋊Q8#4114yes—
332#121—22no—
333#121—22no—
334#121—22no—
335#121#4114yes—
336#120—28no—
337C4×Q8—24no—
338C4×Q8—24no—
339C4×D4—28no—
340C4×D4—28no—
341C4×D4—24no—
342C4×D4—24no—
343C4×D4—44no—
344C4×D4—44no—
345C4×D4—44no—
346C4×D4—44no—
347C4×D4—44no—
348C4×D4—44no—
349#117—22no—
350#117—22no—
351#117—24no—
352#117—42no—
353#117—48no—
354#117—48no—
355#117—48no—
356#117—48no—
357#117—44no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—44no—
379C2×C4⋊C4—44no—
380C2×C4⋊C4—44no—
381C2×C4⋊C4—44no—
382C2×C4⋊C4—44no—
383C2×C4⋊C4C2414yes—
384C2×C4⋊C4C2414yes—
385C2×C4⋊C4C2411yescharacteristic
386C2×C4⋊C4C2411yescharacteristic
387C2×C4⋊C4C2411yescharacteristic
388C2×C4⋊C4C2411yescharacteristic
389C2×C4⋊C4C2411yescharacteristic
390C2×C4⋊C4C2411yescharacteristic
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—48no—
411C2×C42—24no—
412C2×C42—24no—
413C2×C42—21no—
414C2×C42—24no—
415C2×C42—24no—
416C2×C42—24no—
417C2×C42—24no—
418C2×C42—24no—
419C2×C42—24no—
420C2×C42—24no—
421C2×C42—24no—
422C2×C42—24no—
423C2×C42—24no—
424C2×C42—24no—
425C2×C42—21no—
426C2×C42—21no—
427C2×C42—21no—
428C2×C42—21no—
429C2×C42—21no—
430C2×C42—21no—
431C2×C42—21no—
432C2×C42—21no—
433C2×C42—48no—
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×C42#4118yes—
448C2×C42C2411yescharacteristic
449C2×C42C2411yescharacteristic
450C2×C42C2411yescharacteristic
451C2×C42C2411yescharacteristic
452#107—28no—
453#107—44no—
454#106—28no—
455#106—44no—
456C4⋊C8—24no—
457C4⋊C8—24no—
458#103—28no—
459#103—44no—
460#102—28no—
461#102—44no—
462C22⋊C8—28no—
463C22⋊C8—24no—
464C22⋊C8—24no—
465C22⋊C8—44no—
466#97—28no—
467#95—24no—
468#95—24no—
469#95—24no—
470#95—24no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24—21no—
493C24—41no—
494C24—41no—
495C24C22×D411yescharacteristic
496C24C22×D411yescharacteristic
497C24C22×D411yescharacteristic
498#41—48no—
499#41—48no—
500C2×Q8—21no—
501C2×Q8—22no—
502C2×Q8—22no—
503C2×Q8C2×#4112yes—
504C2×D4—24no—
505C2×D4—24no—
506C2×D4—24no—
507C2×D4—22no—
508C2×D4—21no—
509C2×D4—22no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4—42no—
515C2×D4—42no—
516C2×D4C2×#4112yes—
517C22×C4—232no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
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—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—24no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
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—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—24no—
567C22×C4—24no—
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—48no—
579C22×C4—48no—
580C22×C4—416no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4#12314yes—
596C22×C4#12314yes—
597C22×C4AGL(1,ℤ/8)14yes—
598C22×C4#13714yes—
599C22×C4C22×D411yescharacteristic
600C22×C4C22×D411yescharacteristic
601C22×C4C22×D411yescharacteristic
602C22×C4C22×D411yescharacteristic
603C22×C4C22×D411yescharacteristic
604C22×C4C22×D411yescharacteristic
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D411yescharacteristic
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D411yescharacteristic
610C22×C4C2×#4114yes—
611C22×C4C2×#4112yes—
612C22×C4C2×#4112yes—
613C22×C4C2511yescharacteristic
614C2×C8—24no—
615C2×C8—24no—
616C2×C8—24no—
617C2×C8—24no—
618C2×C8—24no—
619C2×C8—24no—
620C4⋊C4—24no—
621C4⋊C4—24no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—22no—
627C4⋊C4—22no—
628C4⋊C4—24no—
629C4⋊C4—24no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—44no—
633C4⋊C4—44no—
634C4⋊C4—44no—
635C4⋊C4—44no—
636C4⋊C4—42no—
637C4⋊C4—42no—
638C4⋊C4—42no—
639C4⋊C4—44no—
640C4⋊C4—44no—
641C4⋊C4—44no—
642C4⋊C4—44no—
643C4⋊C4—44no—
644C4⋊C4—42no—
645C4⋊C4—42no—
646C4⋊C4—44no—
647C4⋊C4—42no—
648C4⋊C4C2×#4112yes—
649C4⋊C4C2×#4112yes—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—24no—
655C22⋊C4—42no—
656C22⋊C4—48no—
657C22⋊C4—48no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C42—24no—
670C42—22no—
671C42—22no—
672C42—22no—
673C42—22no—
674C42—22no—
675C42—22no—
676C42—22no—
677C42—22no—
678C42—22no—
679C42—22no—
680C42—22no—
681C42—22no—
682C42—48no—
683C42—48no—
684C42—42no—
685C42—42no—
686C42—42no—
687C42—42no—
688C42—42no—
689C42—42no—
690C42—42no—
691C42—42no—
692C42#12314yes—
693C42#12314yes—
694C42C2×#4114yes—
695C42C2×#4114yes—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—28no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—22no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23—44no—
718C23—44no—
719C23—44no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23C2×#12312yes—
727C23#52512yes—
728C23C2×AGL(1,ℤ/8)12yes—
729C23C2×#13712yes—
730C23#57512yes—
731C23C23×D411yescharacteristic
732Q8—24no—
733Q8—42no—
734D4—24no—
735D4—48no—
736D4—48no—
737D4—48no—
738D4—42no—
739C2×C4—28no—
740C2×C4—28no—
741C2×C4—28no—
742C2×C4—28no—
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—21no—
759C2×C4—28no—
760C2×C4—28no—
761C2×C4—28no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
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—48no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—44no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—84no—
811C2×C4—88no—
812C2×C4—88no—
813C2×C4—84no—
814C2×C4C2×#12312yes—
815C2×C4C2×#12312yes—
816C2×C4C2×#12312yes—
817C2×C4C2×#12312yes—
818C2×C4C2×#12312yes—
819C2×C4#52512yes—
820C2×C4C2×AGL(1,ℤ/8)12yes—
821C2×C4C2×AGL(1,ℤ/8)12yes—
822C2×C4C2×#13712yes—
823C2×C4C2×#13712yes—
824C2×C4#57512yes—
825C2×C4C22×#4112yes—
826C2×C4C22×#4111yescharacteristic
827C2×C4C22×#4111yescharacteristic
828C2×C4#58512yes—
829C8—44no—
830C8—44no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—416no—
844C22—41no—
845C22—41no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22#311514yes—
860C22C22×#12311yescharacteristic
861C22C2×#52511yescharacteristic
862C22#344911yescharacteristic
863C22C22×AGL(1,ℤ/8)11yescharacteristic
864C22C22×#13711yescharacteristic
865C22C2×#57511yescharacteristic
866C22C2×#57511yescharacteristic
867C4—22no—
868C4—22no—
869C4—22no—
870C4—22no—
871C4—22no—
872C4—22no—
873C4—22no—
874C4—22no—
875C4—41no—
876C4—42no—
877C4—42no—
878C4—41no—
879C4—42no—
880C4—81no—
881C4—81no—
882C4—84no—
883C4—81no—
884C4—81no—
885C4—84no—
886C4#309214yes—
887C4#347512yes—
888C4#347512yes—
889C2—24no—
890C2—42no—
891C2—42no—
892C2—82no—
893C2#3480911yescharacteristic
894C2C2×#309211yescharacteristic
895C2#6051111yescharacteristic
896C2C2×#311511yescharacteristic
897C2#6056211yescharacteristic
898C2#6096311yescharacteristic
899C2#6096511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#525C22
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×#2285C2semidirect
3. #27680C2semidirect
4. #27677C2semidirect
5. #27647C2semidirect
6. #27644C2semidirect
7. #27629C2semidirect
8. #27625C2semidirect
9. #27615C2semidirect
10. #27602C2semidirect
11. #27587C2semidirect
13. #23763C2semidirect
14. #23761C2semidirect
15. #21579C2semidirect
16. #21578C2semidirect
17. #21364C2semidirect
18. #20743C2semidirect
19. #20715C2semidirect
62. #2099C22semidirect
63. #2099C22semidirect
64. #2096C22semidirect
65. #2093C22semidirect
66. #2084C22semidirect
67. #2083C22semidirect
70. #2072C22semidirect
71. #2071C22semidirect
74. #1948C22semidirect
75. #1948C22semidirect
76. #1947C22semidirect
77. #1947C22semidirect
78. #1928C22semidirect
79. #1926C22semidirect
80. #1921C22semidirect
81. #1919C22semidirect
92. #1803C22semidirect
93. #1803C22semidirect
94. #1802C22semidirect
95. #1802C22semidirect
101. #1776C22semidirect
102. #1776C22semidirect
103. #1763C22semidirect
104. #1762C22semidirect

Maximal subgroups

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

subgroupindex
C4×#5252
C2×#22852
#276802
#276772
#276472
#276442
#276292
#276252
#276152
#276022
#275872
#240042
#237632
#237612
#215792
#215782
#213642
#207432
#207152