Finite Group Databasebeta

← #6433942

Subgroups — #6433942

Order 512.

2013 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36626C211yesmaximal, characteristic
2C2×#2857C211yesmaximal, characteristic, complemented
3#30367C212yesmaximal, complemented
4#30366C212yesmaximal, complemented
5#30365C212yesmaximal, complemented
6#30364C212yesmaximal, complemented
7#30359C212yesmaximal, complemented
8#30358C212yesmaximal, complemented
9#30357C212yesmaximal, complemented
10#30356C212yesmaximal, complemented
11#23745C211yesmaximal, characteristic, complemented
12#23734C211yesmaximal, characteristic, complemented
13#23642C212yesmaximal, complemented
14#23552C211yesmaximal, characteristic, complemented
15#23482C212yesmaximal
16#23452C211yesmaximal, characteristic, complemented
17#21159C212yesmaximal, complemented
18#21093C212yesmaximal, complemented
19C4×#407C211yesmaximal, characteristic, complemented
20C22×C4⋊Q8C2211yescharacteristic
21C2×#525C2211yescharacteristic
22C22×C22⋊Q8—21no—
23C23×C42C2211yescharacteristic
24C2×#428C2212yes—
25C2×#428C2212yes—
26C2×#417C2212yes—
27C2×#417C2212yes—
28C2×#407C2212yes—
29C2×C4×M16C2212yes—
30#2857—21no—
31#2857—21no—
32#2857—21no—
33#2857—21no—
34#2857C2212yes—
35#2857C2212yes—
36#2857C2212yes—
37#2857C2212yes—
38#2855C2211yescharacteristic
39#2855C2211yescharacteristic
40#2855C2211yescharacteristic
41#2855C2211yescharacteristic
42#2854C2211yescharacteristic
43#2854C2211yescharacteristic
44#2854C2211yescharacteristic
45#2854C2211yescharacteristic
46#2853—21no—
47#2853—21no—
48#2849—21no—
49#2849—21no—
50C4×#123—21no—
51C4×#123—21no—
52C4×#123—21no—
53C4×#123—21no—
54#2297C2211yescharacteristic
55#2297C2211yescharacteristic
56#2296C2211yescharacteristic
57#2296C2211yescharacteristic
58C2×#391—21no—
59C2×#389—21no—
60C2×#389C2212yes—
61C2×#384C2211yescharacteristic
62#2280C2211yescharacteristic
63C2×#380—21no—
64C2×#380C2212yes—
65#2100C2212yescomplemented
66#2100C2212yescomplemented
67#2099C2212yescomplemented
68#2099C2212yescomplemented
69#2096C2212yescomplemented
70#2095C2212yescomplemented
71#2094C2212yescomplemented
72#2093C2212yescomplemented
73#2077C2214yes—
74#2077C2214yes—
75#2076C2214yes—
76#2075C2214yes—
77#2058C2212yescomplemented
78#2058C2212yescomplemented
79#2057C2212yescomplemented
80#2057C2212yescomplemented
81#2036C2214yes—
82#2035C2214yes—
83#2034C2214yes—
84#2033C2214yes—
85#2024C2212yescomplemented
86#2024C2212yescomplemented
87#2023C2212yescomplemented
88#2023C2212yescomplemented
89#1944C2214yescomplemented
90#1943C2214yescomplemented
91#1942C2214yescomplemented
92#1941C2214yescomplemented
93#1936C2214yescomplemented
94#1935C2214yescomplemented
95#1934C2214yescomplemented
96#1933C2214yescomplemented
97#1749C2212yes—
98#1749C2212yes—
99C4×C22⋊C8C2212yes—
100C4×C22⋊C8C2212yes—
101#1736C2212yes—
102#1736C2212yes—
103#1736C2212yes—
104#1736C2212yes—
105#1728C2211yescharacteristic
106#1728C2211yescharacteristic
107C22×#41C2311yescharacteristic
108C23×Q8—21no—
109C24×C4D411yescharacteristic
110C24×C4D411yescharacteristic
111C24×C4C2311yescharacteristic
112C22×M16C2312yes—
113C22×M16C2312yes—
114C2×C4⋊Q8—21no—
115C2×C4⋊Q8—21no—
116C2×C4⋊Q8—44no—
117C2×C4⋊Q8C2312yes—
118C2×C4⋊Q8C2312yes—
119#525—44no—
120C2×#123—21no—
121C2×#123—21no—
122C2×#123—21no—
123C2×#123—21no—
124C2×#123—21no—
125C2×C22⋊Q8—22no—
126C2×C22⋊Q8—22no—
127C2×C22⋊Q8—22no—
128C2×C22⋊Q8—22no—
129C2×C22⋊Q8—48no—
130C2×C22⋊Q8C2311yescharacteristic
131C2×C22⋊Q8C2311yescharacteristic
132C2×#121C2311yescharacteristic
133C2×#121C2311yescharacteristic
134C2×#120—21no—
135C2×C4×D4—21no—
136C2×C4×D4—21no—
137C2×#117C2311yescharacteristic
138C2×#117C2311yescharacteristic
139C2×#117C2311yescharacteristic
140C22×C4⋊C4—21no—
141C22×C4⋊C4—22no—
142C22×C4⋊C4—21no—
143C22×C4⋊C4—21no—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C22⋊C4—22no—
147C22×C42—44no—
148C22×C42D411yescharacteristic
149C22×C42D411yescharacteristic
150C22×C42D411yescharacteristic
151C22×C42D411yescharacteristic
152C22×C42D411yescharacteristic
153C22×C42D411yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160#428—28no—
161#428—44no—
162C2×#107C2314yes—
163C2×#107C2314yes—
164C2×#106C2314yes—
165C2×#106C2314yes—
166#417—28no—
167#417—44no—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#102C2314yes—
171C2×#102C2314yes—
172#407—28no—
173C2×C22⋊C8C2314yes—
174C2×C22⋊C8C2314yes—
175C4×M16—44no—
176C2×#97C2314yes—
177C2×C4×C8C2314yes—
178#391—22no—
179#391—22no—
180#391—22no—
181#391—22no—
182#391C2311yescharacteristic
183#391C2311yescharacteristic
184#391C2311yescharacteristic
185#391C2311yescharacteristic
186#390C2311yescharacteristic
187#390C2311yescharacteristic
188#390C2311yescharacteristic
189#390C2311yescharacteristic
190#389—22no—
191#389—22no—
192#389—22no—
193#389—22no—
194#389—22no—
195#389—22no—
196#389C2311yescharacteristic
197#389C2311yescharacteristic
198#389C2311yescharacteristic
199#389C2311yescharacteristic
200#389C2311yescharacteristic
201#389C2311yescharacteristic
202#389C2311yescharacteristic
203#389C2311yescharacteristic
204#389C2314yes—
205#389C2314yes—
206#388—21no—
207#388—21no—
208#388—21no—
209#388—21no—
210#388—21no—
211#388—21no—
212#388—21no—
213#388—21no—
214#387—21no—
215#387—21no—
216#387—21no—
217#387—21no—
218#387—21no—
219#387—21no—
220#387—21no—
221#387—21no—
222#386—21no—
223#386—21no—
224#386—21no—
225#386—21no—
226#386—21no—
227#386—21no—
228#386—21no—
229#386—21no—
230#385—21no—
231#385—21no—
232#385—21no—
233#385—21no—
234#385—21no—
235#385—21no—
236#385—21no—
237#385—21no—
238#384—21no—
239#384—21no—
240#384C2312yes—
241#384C2312yes—
242#381—21no—
243#381—21no—
244#381—21no—
245#381—21no—
246#381—21no—
247#380—22no—
248#380—22no—
249#380—22no—
250#380—22no—
251#380—22no—
252#380—22no—
253#380C2311yescharacteristic
254#380C2314yes—
255#380C2311yescharacteristic
256#380C2314yes—
257#380C2311yescharacteristic
258#380C2311yescharacteristic
259#379—21no—
260C4×C4⋊C4—21no—
261C4×C4⋊C4—21no—
262C4×C4⋊C4—21no—
263C4×C4⋊C4—21no—
264C4×C22⋊C4—21no—
265C4×C22⋊C4—21no—
266C4×C22⋊C4—21no—
267C4×C22⋊C4—21no—
268C4×C22⋊C4—21no—
269C4×C22⋊C4—21no—
270C2×#95—22no—
271C2×#95—22no—
272#340C2314yes—
273#340C2314yes—
274#340C2314yes—
275#340C2314yes—
276#340C2314yes—
277#340C2314yes—
278#340C2314yes—
279#340C2314yes—
280#336C2312yes—
281#336C2312yes—
282#336C2312yes—
283#336C2312yes—
284C25C2×D411yescharacteristic
285C2×#41—24no—
286C2×#41—24no—
287C2×#41—22no—
288C2×#41—22no—
289C22×Q8—22no—
290C22×Q8—22no—
291C22×Q8—44no—
292C22×Q8—44no—
293C22×Q8—44no—
294C22×Q8C2411yescharacteristic
295C22×D4—21no—
296C22×D4—21no—
297C22×D4—21no—
298C22×D4C2411yescharacteristic
299C23×C4—24no—
300C23×C4—24no—
301C23×C4—24no—
302C23×C4—24no—
303C23×C4—22no—
304C23×C4—22no—
305C23×C4—22no—
306C23×C4—22no—
307C23×C4—21no—
308C23×C4—42no—
309C23×C4—42no—
310C23×C4—42no—
311C23×C4—42no—
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×C4C2×D411yescharacteristic
323C23×C4C2×D411yescharacteristic
324C23×C4C2×D411yescharacteristic
325C23×C4C2×D411yescharacteristic
326C23×C4C2×D411yescharacteristic
327C23×C4C2411yescharacteristic
328C23×C4C2411yescharacteristic
329C23×C4C2411yescharacteristic
330C2×M16—24no—
331C2×M16—24no—
332C2×M16—24no—
333C2×M16—24no—
334C2×M16—24no—
335C2×M16#4118yes—
336C22×C8C2414yes—
337C22×C8C2414yes—
338C4⋊Q8—44no—
339C4⋊Q8—44no—
340C4⋊Q8—44no—
341C4⋊Q8—44no—
342#123—44no—
343#123—44no—
344#123—44no—
345#123—44no—
346#123—44no—
347C22⋊Q8—42no—
348C22⋊Q8—42no—
349C22⋊Q8—48no—
350C22⋊Q8—48no—
351C22⋊Q8—48no—
352C22⋊Q8—48no—
353#121—42no—
354#121—42no—
355#120—44no—
356C4×D4—44no—
357C4×D4—44no—
358#117—24no—
359#117—24no—
360#117—22no—
361#117—22no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—44no—
387C2×C4⋊C4—44no—
388C2×C4⋊C4—48no—
389C2×C4⋊C4—44no—
390C2×C4⋊C4C2414yes—
391C2×C4⋊C4C2414yes—
392C2×C4⋊C4C2411yescharacteristic
393C2×C4⋊C4C2411yescharacteristic
394C2×C4⋊C4C2411yescharacteristic
395C2×C4⋊C4C2411yescharacteristic
396C2×C4⋊C4C2411yescharacteristic
397C2×C4⋊C4C2411yescharacteristic
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
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—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—48no—
420C2×C42—24no—
421C2×C42—24no—
422C2×C42—21no—
423C2×C42—21no—
424C2×C42—21no—
425C2×C42—42no—
426C2×C42—42no—
427C2×C42—42no—
428C2×C42—42no—
429C2×C42—42no—
430C2×C42—42no—
431C2×C42—42no—
432C2×C42—42no—
433C2×C42—42no—
434C2×C42—42no—
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×C42C2411yescharacteristic
448C2×C42C2411yescharacteristic
449C2×C42C2411yescharacteristic
450C2×C42C2411yescharacteristic
451#107—28no—
452#107—44no—
453#106—28no—
454#106—44no—
455#103—28no—
456#103—44no—
457#102—28no—
458#102—44no—
459C22⋊C8—28no—
460C22⋊C8—28no—
461#97—44no—
462C4×C8—44no—
463#95—24no—
464#95—24no—
465#95—24no—
466#95—24no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
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—22no—
501C2×Q8—22no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—44no—
505C2×Q8—44no—
506C2×Q8—44no—
507C2×Q8—44no—
508C2×Q8—44no—
509C2×Q8—44no—
510C2×Q8—816no—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—42no—
519C2×D4—42no—
520C2×D4—42no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4—42no—
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—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—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—24no—
569C22×C4—24no—
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—416no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
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×C4H(5,𝔽2)14yes—
612C22×C42−1+412yes—
613C22×C42−1+412yes—
614C22×C4C2511yescharacteristic
615M16—216no—
616M16—48no—
617C2×C8—24no—
618C2×C8—24no—
619C2×C8—24no—
620C2×C8—24no—
621C2×C8—24no—
622C2×C8C2×#4118yes—
623C4⋊C4—24no—
624C4⋊C4—22no—
625C4⋊C4—24no—
626C4⋊C4—22no—
627C4⋊C4—24no—
628C4⋊C4—22no—
629C4⋊C4—24no—
630C4⋊C4—22no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—44no—
636C4⋊C4—44no—
637C4⋊C4—48no—
638C4⋊C4—44no—
639C4⋊C4—44no—
640C4⋊C4—42no—
641C4⋊C4—42no—
642C4⋊C4—42no—
643C4⋊C4—42no—
644C4⋊C4—44no—
645C4⋊C4—44no—
646C4⋊C4—44no—
647C4⋊C4—48no—
648C4⋊C4—42no—
649C4⋊C4—42no—
650C4⋊C4—42no—
651C4⋊C4—42no—
652C4⋊C4—44no—
653C4⋊C4—42no—
654C4⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—48no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—48no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C22⋊C4—42no—
676C42—22no—
677C42—22no—
678C42—22no—
679C42—22no—
680C42—22no—
681C42—22no—
682C42—22no—
683C42—22no—
684C42—41no—
685C42—41no—
686C42—41no—
687C42—41no—
688C42—41no—
689C42—41no—
690C42—41no—
691C42—41no—
692C42—42no—
693C42—42no—
694C42—42no—
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—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—44no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23—44no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23#53212yes—
726C23#53412yes—
727C23#53612yes—
728C23C2×AGL(1,ℤ/8)12yes—
729C23C2×#13712yes—
730C23C23×D411yescharacteristic
731Q8—42no—
732Q8—42no—
733Q8—88no—
734Q8—88no—
735D4—42no—
736D4—42no—
737D4—84no—
738D4—84no—
739D4—84no—
740C2×C4—28no—
741C2×C4—28no—
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—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—44no—
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—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—44no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—44no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—44no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—44no—
810C2×C4—88no—
811C2×C4—88no—
812C2×C4—84no—
813C2×C4#53212yes—
814C2×C4#53412yes—
815C2×C4#53612yes—
816C2×C4#53918yes—
817C2×C4#54218yes—
818C2×C4C2×AGL(1,ℤ/8)12yes—
819C2×C4C2×AGL(1,ℤ/8)12yes—
820C2×C4C2×#13712yes—
821C2×C4C2×#13712yes—
822C2×C4#57512yes—
823C2×C4#57512yes—
824C2×C4C22×#4112yes—
825C2×C4C2×H(5,𝔽2)12yes—
826C2×C4C2×2−1+411yescharacteristic
827C2×C4C2×2−1+411yescharacteristic
828C8—28no—
829C8—44no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—22no—
842C22—416no—
843C22—41no—
844C22—41no—
845C22—41no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22#266314yes—
859C22C2×#53211yescharacteristic
860C22C2×#53411yescharacteristic
861C22C2×#53611yescharacteristic
862C22C22×AGL(1,ℤ/8)11yescharacteristic
863C22C22×#13711yescharacteristic
864C22C2×#57511yescharacteristic
865C22C2×#57511yescharacteristic
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—22no—
871C4—22no—
872C4—41no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—81no—
877C4—81no—
878C4—84no—
879C4—81no—
880C4—84no—
881C4—81no—
882C4—81no—
883C4—81no—
884C4—81no—
885C4#266314yes—
886C4C2×#53912yes—
887C4C2×#54212yes—
888C2—24no—
889C2—42no—
890C2—42no—
891C2—161no—
892C2C2×#266311yescharacteristic
893C2#6070011yescharacteristic
894C2#6070111yescharacteristic
895C2#6075011yescharacteristic
896C2#6075111yescharacteristic
897C2#6086011yescharacteristic
898C2#6086311yescharacteristic
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×#2857C2semidirect
3. #30367C2semidirect
4. #30366C2semidirect
5. #30365C2semidirect
6. #30364C2semidirect
7. #30359C2semidirect
8. #30358C2semidirect
9. #30357C2semidirect
10. #30356C2semidirect
11. #23745C2semidirect
12. #23734C2semidirect
13. #23642C2semidirect
14. #23552C2semidirect
16. #23452C2semidirect
17. #21159C2semidirect
18. #21093C2semidirect
19. C4×#407C2semidirect
65. #2100C22semidirect
66. #2100C22semidirect
67. #2099C22semidirect
68. #2099C22semidirect
69. #2096C22semidirect
70. #2095C22semidirect
71. #2094C22semidirect
72. #2093C22semidirect
77. #2058C22semidirect
78. #2058C22semidirect
79. #2057C22semidirect
80. #2057C22semidirect
85. #2024C22semidirect
86. #2024C22semidirect
87. #2023C22semidirect
88. #2023C22semidirect
89. #1944C22semidirect
90. #1943C22semidirect
91. #1942C22semidirect
92. #1941C22semidirect
93. #1936C22semidirect
94. #1935C22semidirect
95. #1934C22semidirect
96. #1933C22semidirect

Maximal subgroups

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

subgroupindex
#366262
C2×#28572
#303672
#303662
#303652
#303642
#303592
#303582
#303572
#303562
#237452
#237342
#236422
#235522
#234822
#234522
#211592
#210932
C4×#4072