Finite Group Databasebeta

← #6477193

Subgroups — #6477193

Order 512.

2032 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36625C211yesmaximal, characteristic, complemented
2#36624C211yesmaximal, characteristic
3#33209C211yesmaximal, characteristic, complemented
4#33207C211yesmaximal, characteristic, complemented
5#33042C211yesmaximal, characteristic, complemented
6#33042C211yesmaximal, characteristic, complemented
7#30360C214yesmaximal, complemented
8#29161C214yesmaximal, complemented
9#27962C211yesmaximal, characteristic, complemented
10#27907C211yesmaximal, characteristic, complemented
11#27878C211yesmaximal, characteristic, complemented
12#27876C211yesmaximal, characteristic, complemented
13#25905C211yesmaximal, characteristic, complemented
14#25812C211yesmaximal, characteristic, complemented
15#25673C211yesmaximal, characteristic, complemented
16#25671C211yesmaximal, characteristic, complemented
17#24555C214yesmaximal, complemented
18#22080C214yesmaximal, complemented
19C2×C4×C22⋊C8C211yesmaximal, characteristic, complemented
20C2×#533C2211yescharacteristic
21C2×#532C2211yescharacteristic
22C2×#525—21no—
23C23×C42C2211yescharacteristic
24C2×#500C2211yescharacteristic, complemented
25C2×#498C2211yescharacteristic, complemented
26C2×#486C2211yescharacteristic, complemented
27C2×#486C2211yescharacteristic, complemented
28C2×#482C2214yes—
29C22×C22⋊C8C2212yes—
30C22×C4×C8C2211yescharacteristic
31C22×C4×C8C2211yescharacteristic
32#2857C2211yescharacteristic
33#2857C2211yescharacteristic
34#2857C2211yescharacteristic
35#2857C2211yescharacteristic
36#2857C2211yescharacteristic
37#2857C2211yescharacteristic
38#2856C2211yescharacteristic
39#2856C2211yescharacteristic
40#2855—21no—
41#2855—21no—
42#2854—21no—
43#2854C2212yes—
44#2851C2212yes—
45#2851C2212yes—
46#2850—21no—
47#2850—21no—
48#2848—21no—
49#2848—21no—
50#2847—21no—
51#2847C2212yes—
52C4×C22⋊Q8—21no—
53C4×C22⋊Q8—21no—
54C4×C22⋊Q8—21no—
55C4×C22⋊Q8—21no—
56C4×#121—21no—
57C4×#121—21no—
58C4×#121C2212yes—
59C4×#121C2212yes—
60#2297—21no—
61#2296C2212yes—
62#2285C2211yescharacteristic
63#2285C2211yescharacteristic
64#2280C2212yes—
65#2101C2214yescomplemented
66#2092C2214yescomplemented
67#2077C2214yes—
68#2076C2214yes—
69#2059C2214yescomplemented
70#2034C2214yes—
71#2033C2214yes—
72#2025C2214yescomplemented
73#1990C2211yescharacteristic, complemented
74#1990C2211yescharacteristic, complemented
75#1990C2211yescharacteristic, complemented
76#1990C2211yescharacteristic, complemented
77#1990C2211yescharacteristic, complemented
78#1990C2211yescharacteristic, complemented
79#1957C2211yescharacteristic, complemented
80#1957C2211yescharacteristic, complemented
81#1942C2214yescomplemented
82#1941C2214yescomplemented
83#1934C2214yescomplemented
84#1934C2214yescomplemented
85#1921C2214yescomplemented
86#1919C2214yescomplemented
87#1893C2214yes—
88#1893C2214yes—
89#1875C2214yes—
90#1864C2214yescomplemented
91#1862C2214yescomplemented
92#1854C2214yes—
93#1845C2211yescharacteristic, complemented
94#1844C2211yescharacteristic, complemented
95#1834C2211yescharacteristic, complemented
96#1834C2211yescharacteristic, complemented
97#1825C2214yes—
98#1808C2214yes—
99#1807C2214yes—
100C4×C22⋊C8C2211yescharacteristic
101C4×C22⋊C8C2211yescharacteristic
102C4×C22⋊C8C2212yes—
103C4×C22⋊C8C2211yescharacteristic
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2212yes—
106C2×#336C2212yes—
107C22×#41—21no—
108C24×C4D411yescharacteristic
109C24×C4D411yescharacteristic
110C24×C4C2311yescharacteristic
111C23×C8C2312yes—
112C23×C8C2312yes—
113#533—42no—
114#533—42no—
115#532—42no—
116#532—42no—
117C2×C4⋊Q8C2311yescharacteristic
118C2×C4⋊Q8C2311yescharacteristic
119C2×C4⋊Q8C2311yescharacteristic
120C2×#127C2311yescharacteristic
121C2×#125C2312yes—
122C2×#124—21no—
123#525—48no—
124C2×#123—22no—
125C2×C22⋊Q8—21no—
126C2×C22⋊Q8—21no—
127C2×C22⋊Q8—21no—
128C2×C22⋊Q8—21no—
129C2×C22⋊Q8—21no—
130C2×C22⋊Q8—21no—
131C2×C22⋊Q8—21no—
132C2×C22⋊Q8—21no—
133C2×#121—21no—
134C2×#121—21no—
135C2×#121—21no—
136C2×#121—21no—
137C2×#121—21no—
138C2×#121C2312yes—
139C2×#121C2312yes—
140C2×#121C2312yes—
141C2×#120—22no—
142C2×C4×Q8—21no—
143C2×C4×Q8—21no—
144C2×C4×D4—22no—
145C2×C4×D4—22no—
146C2×C4×D4—21no—
147C2×C4×D4C2312yes—
148C2×#117—21no—
149C2×#117C2312yes—
150C2×#117C2312yes—
151C22×C42—42no—
152C22×C42—42no—
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#500—42no—
166#498—42no—
167#486—42no—
168#486—42no—
169#482—216no—
170C2×#107C2314yes—
171C2×#107C2314yes—
172C2×#106C2314yes—
173C2×#106C2314yes—
174C2×#102C2314yes—
175C2×#102C2314yes—
176C2×#102C2314yes—
177C2×#102C2314yes—
178C2×C22⋊C8—28no—
179C2×C22⋊C8C2312yes—
180C2×C22⋊C8C2312yes—
181C2×C22⋊C8C2312yes—
182C2×C22⋊C8C2312yes—
183C2×C4×C8—42no—
184C2×C4×C8—42no—
185C2×C4×C8C2311yescharacteristic
186C2×C4×C8C2311yescharacteristic
187C2×C4×C8C2311yescharacteristic
188C2×C4×C8C2311yescharacteristic
189C2×C4×C8C2312yes—
190C2×C4×C8C2312yes—
191#391—21no—
192#391—21no—
193#391—21no—
194#391—21no—
195#391—21no—
196#391—21no—
197#390—21no—
198#390—21no—
199#390—21no—
200#390—21no—
201#390C2312yes—
202#390C2312yes—
203#389—21no—
204#389—21no—
205#389—21no—
206#389—21no—
207#389—21no—
208#389—21no—
209#389C2312yes—
210#389C2312yes—
211#389C2312yes—
212#389C2312yes—
213#389C2312yes—
214#389C2312yes—
215#388—22no—
216#388—22no—
217#388—22no—
218#388—22no—
219#387—22no—
220#387—22no—
221#387—22no—
222#387—22no—
223#386—22no—
224#386—22no—
225#386—22no—
226#386—22no—
227#386—22no—
228#386—22no—
229#385—22no—
230#385—22no—
231#385—22no—
232#385—22no—
233#385—22no—
234#385—22no—
235#384C2311yescharacteristic
236#384C2311yescharacteristic
237#384C2311yescharacteristic
238#384C2311yescharacteristic
239#382—21no—
240#382C2312yes—
241#381—22no—
242#380—21no—
243#380—21no—
244#380—21no—
245#380—21no—
246#380—21no—
247#380—21no—
248#380—21no—
249#380—21no—
250#380—21no—
251#380C2312yes—
252#380C2312yes—
253#380C2312yes—
254#380C2312yes—
255#380C2312yes—
256#380C2312yes—
257#380C2312yes—
258#379—22no—
259C4×C4⋊C4—21no—
260C4×C4⋊C4—21no—
261C4×C4⋊C4—21no—
262C4×C4⋊C4—22no—
263C4×C4⋊C4—22no—
264C4×C4⋊C4C2312yes—
265C4×C22⋊C4—22no—
266C4×C22⋊C4—22no—
267C4×C22⋊C4—22no—
268C4×C22⋊C4—22no—
269#340C2314yes—
270#340C2314yes—
271#340C2314yes—
272#340C2314yes—
273#340C2314yes—
274#340C2314yes—
275#340C2314yes—
276#340C2314yes—
277#336C2312yes—
278#336C2312yes—
279#336C2312yes—
280#336C2312yes—
281C25C2×D411yescharacteristic
282C2×#41—44no—
283C2×#41—44no—
284C2×#41—44no—
285C22×Q8—21no—
286C22×Q8—21no—
287C22×Q8—21no—
288C22×D4—22no—
289C22×D4—22no—
290C22×D4—22no—
291C22×D4—21no—
292C22×D4—21no—
293C22×D4C2412yes—
294C23×C4—24no—
295C23×C4—24no—
296C23×C4—24no—
297C23×C4—24no—
298C23×C4—24no—
299C23×C4—22no—
300C23×C4—42no—
301C23×C4—42no—
302C23×C4—42no—
303C23×C4—41no—
304C23×C4—41no—
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×D411yescharacteristic
317C23×C4C2×D411yescharacteristic
318C23×C4C2×D411yescharacteristic
319C23×C4C2×D411yescharacteristic
320C23×C4C2411yescharacteristic
321C23×C4C2411yescharacteristic
322C23×C4C2411yescharacteristic
323C22×C8—24no—
324C22×C8—24no—
325C22×C8—24no—
326C22×C8—24no—
327C22×C8—42no—
328C22×C8—42no—
329C22×C8C2412yes—
330C22×C8C2412yes—
331C22×C8C2412yes—
332C22×C8C2412yes—
333C4⋊Q8—22no—
334C4⋊Q8—22no—
335C4⋊Q8—22no—
336C4⋊Q8—22no—
337C4⋊Q8—22no—
338C4⋊Q8—22no—
339#127—22no—
340#127—22no—
341#125—42no—
342#125—42no—
343#124—44no—
344#123—48no—
345C22⋊Q8—44no—
346C22⋊Q8—44no—
347C22⋊Q8—44no—
348C22⋊Q8—44no—
349C22⋊Q8—44no—
350C22⋊Q8—44no—
351C22⋊Q8—44no—
352C22⋊Q8—44no—
353#121—28no—
354#121—28no—
355#121—42no—
356#121—42no—
357#121—44no—
358#121—44no—
359#121—44no—
360#121—44no—
361#121—44no—
362#120—48no—
363C4×Q8—44no—
364C4×Q8—44no—
365C4×D4—42no—
366C4×D4—42no—
367C4×D4—44no—
368C4×D4—48no—
369C4×D4—48no—
370#117—28no—
371#117—42no—
372#117—42no—
373#117—44no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4C2412yes—
394C2×C4⋊C4C2412yes—
395C2×C4⋊C4C2412yes—
396C2×C4⋊C4C2412yes—
397C2×C4⋊C4C2412yes—
398C2×C4⋊C4C2412yes—
399C2×C4⋊C4C2412yes—
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—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—42no—
427C2×C42—42no—
428C2×C42—42no—
429C2×C42—42no—
430C2×C42—42no—
431C2×C42—42no—
432C2×C42—41no—
433C2×C42—41no—
434C2×C42—41no—
435C2×C42—41no—
436C2×C42—41no—
437C2×C42—41no—
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×C42C2×D411yescharacteristic
448C2×C42C2×D411yescharacteristic
449C2×C42C2×D411yescharacteristic
450C2×C42C2411yescharacteristic
451C2×C42C2411yescharacteristic
452C2×C42C2411yescharacteristic
453C2×C42C2411yescharacteristic
454#107—28no—
455#107—44no—
456#106—28no—
457#106—44no—
458#102—28no—
459#102—28no—
460#102—44no—
461#102—44no—
462C22⋊C8—24no—
463C22⋊C8—24no—
464C22⋊C8—24no—
465C22⋊C8#4118yescomplemented
466C4×C8—22no—
467C4×C8—22no—
468C4×C8—22no—
469C4×C8—22no—
470C4×C8—42no—
471C4×C8—42no—
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—
481#95—22no—
482#95—22no—
483#95—22no—
484#95—22no—
485#95—22no—
486#95—22no—
487#95—22no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—41no—
495C24—41no—
496C24C22×D411yescharacteristic
497C24C22×D411yescharacteristic
498C24C22×D411yescharacteristic
499#41—816no—
500C2×Q8—42no—
501C2×Q8—42no—
502C2×Q8—42no—
503C2×Q8—42no—
504C2×Q8—42no—
505C2×Q8—42no—
506C2×Q8—42no—
507C2×Q8—42no—
508C2×Q8—42no—
509C2×D4—24no—
510C2×D4—22no—
511C2×D4—22no—
512C2×D4—24no—
513C2×D4—44no—
514C2×D4—44no—
515C2×D4—44no—
516C2×D4—44no—
517C2×D4—44no—
518C2×D4—44no—
519C2×D4—44no—
520C2×D4—44no—
521C2×D4—44no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4—42no—
527C2×D4—42no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
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—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
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—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—416no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—416no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4#13514yes—
595C22×C4#13514yes—
596C22×C4AGL(1,ℤ/8)14yes—
597C22×C4C22×D411yescharacteristic
598C22×C4C22×D411yescharacteristic
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×C4C2×#4114yes—
609C22×C42−1+414yes—
610C22×C4C2511yescharacteristic
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—22no—
621C2×C8—48no—
622C2×C8—48no—
623C2×C8C2×#4114yes—
624C2×C8C2×#4114yes—
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—24no—
628C4⋊C4—22no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—24no—
635C4⋊C4—44no—
636C4⋊C4—44no—
637C4⋊C4—44no—
638C4⋊C4—44no—
639C4⋊C4—42no—
640C4⋊C4—42no—
641C4⋊C4—42no—
642C4⋊C4—42no—
643C4⋊C4—42no—
644C4⋊C4—42no—
645C4⋊C4—44no—
646C4⋊C4—44no—
647C4⋊C4—42no—
648C4⋊C4—42no—
649C4⋊C4—44no—
650C4⋊C4—42no—
651C4⋊C4—44no—
652C4⋊C4—42no—
653C4⋊C4—42no—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C22⋊C4—44no—
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—
670C22⋊C4—44no—
671C42—22no—
672C42—22no—
673C42—22no—
674C42—22no—
675C42—22no—
676C42—22no—
677C42—21no—
678C42—21no—
679C42—21no—
680C42—21no—
681C42—21no—
682C42—21no—
683C42—41no—
684C42—41no—
685C42—41no—
686C42—41no—
687C42—41no—
688C42—41no—
689C42—44no—
690C42—44no—
691C42—44no—
692C42H(5,𝔽2)12yes—
693C42H(5,𝔽2)12yes—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—28no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—44no—
712C23—44no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23#53212yes—
725C23#53612yes—
726C23C2×#13512yes—
727C23C2×#13512yes—
728C23C2×AGL(1,ℤ/8)12yes—
729C23C23×D411yescharacteristic
730Q8—84no—
731Q8—84no—
732Q8—84no—
733D4—44no—
734D4—44no—
735D4—88no—
736D4—88no—
737D4—88no—
738D4—84no—
739D4—84no—
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—28no—
751C2×C4—28no—
752C2×C4—28no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
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—21no—
767C2×C4—21no—
768C2×C4—21no—
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—44no—
780C2×C4—44no—
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—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—88no—
805C2×C4#53212yes—
806C2×C4#53412yes—
807C2×C4#53412yes—
808C2×C4#53612yes—
809C2×C4C2×#13512yes—
810C2×C4C2×#13512yes—
811C2×C4C2×#13512yes—
812C2×C4C2×#13512yes—
813C2×C4C2×AGL(1,ℤ/8)12yes—
814C2×C4C2×AGL(1,ℤ/8)12yes—
815C2×C4#57512yes—
816C2×C4C22×#4112yes—
817C2×C4C2×H(5,𝔽2)11yescharacteristic
818C2×C4C2×H(5,𝔽2)11yescharacteristic
819C2×C4C2×2−1+412yes—
820C8—24no—
821C8—24no—
822C8—42no—
823C8—42no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—416no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—41no—
845C22—82no—
846C22—82no—
847C22—82no—
848C22—82no—
849C22—82no—
850C22—82no—
851C22—82no—
852C22#322814yes—
853C22C2×#53211yescharacteristic
854C22C2×#53411yescharacteristic
855C22C2×#53611yescharacteristic
856C22C22×#13511yescharacteristic
857C22C22×#13511yescharacteristic
858C22C22×AGL(1,ℤ/8)11yescharacteristic
859C22C2×#57511yescharacteristic
860C4—22no—
861C4—22no—
862C4—22no—
863C4—22no—
864C4—22no—
865C4—41no—
866C4—41no—
867C4—41no—
868C4—41no—
869C4—82no—
870C4—82no—
871C4—82no—
872C4—82no—
873C4—82no—
874C4—82no—
875C4—82no—
876C4#318814yes—
877C4#319114yes—
878C4#352012yes—
879C4#352012yes—
880C2—24no—
881C2—42no—
882C2—42no—
883C2—162no—
884C2#3508511yescharacteristic
885C2#6067311yescharacteristic
886C2#6070011yescharacteristic
887C2C2×#318811yescharacteristic
888C2C2×#319111yescharacteristic
889C2C2×#322811yescharacteristic
890C2#6084611yescharacteristic
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. #36625C2semidirect
3. #33209C2semidirect
4. #33207C2semidirect
5. #33042C2semidirect
6. #33042C2semidirect
7. #30360C2semidirect
8. #29161C2semidirect
9. #27962C2semidirect
10. #27907C2semidirect
11. #27878C2semidirect
12. #27876C2semidirect
13. #25905C2semidirect
14. #25812C2semidirect
15. #25673C2semidirect
16. #25671C2semidirect
17. #24555C2semidirect
18. #22080C2semidirect
19. C2×C4×C22⋊C8C2semidirect
24. C2×#500C22semidirect
25. C2×#498C22semidirect
26. C2×#486C22semidirect
27. C2×#486C22semidirect
65. #2101C22semidirect
66. #2092C22semidirect
69. #2059C22semidirect
72. #2025C22semidirect
73. #1990C22semidirect
74. #1990C22semidirect
75. #1990C22semidirect
76. #1990C22semidirect
77. #1990C22semidirect
78. #1990C22semidirect
79. #1957C22semidirect
80. #1957C22semidirect
81. #1942C22semidirect
82. #1941C22semidirect
83. #1934C22semidirect
84. #1934C22semidirect
85. #1921C22semidirect
86. #1919C22semidirect
90. #1864C22semidirect
91. #1862C22semidirect
93. #1845C22semidirect
94. #1844C22semidirect
95. #1834C22semidirect
96. #1834C22semidirect
465. C22⋊C8#41semidirect

Maximal subgroups

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

subgroupindex
#366252
#366242
#332092
#332072
#330422
#303602
#291612
#279622
#279072
#278782
#278762
#259052
#258122
#256732
#256712
#245552
#220802
C2×C4×C22⋊C82