Finite Group Databasebeta

← #6477007

Subgroups — #6477007

Order 512.

2083 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2857C211yesmaximal, characteristic, complemented
2#36621C211yesmaximal, characteristic
3#33184C212yesmaximal, complemented
4#33053C212yesmaximal, complemented
5#30326C212yesmaximal, complemented
6#30325C212yesmaximal, complemented
7#28575C212yesmaximal, complemented
8#28571C212yesmaximal, complemented
9#27978C211yesmaximal, characteristic, complemented
10#27953C211yesmaximal, characteristic, complemented
11#27896C212yesmaximal, complemented
12#25861C211yesmaximal, characteristic, complemented
13#25726C211yesmaximal, characteristic, complemented
14#25604C212yesmaximal, complemented
15#24381C212yesmaximal
16#24380C212yesmaximal, complemented
17#22050C212yesmaximal, complemented
18#22047C212yesmaximal, complemented
19C2×#1749C211yesmaximal, characteristic, complemented
20C22×C4⋊Q8C2211yescharacteristic
21C2×#529C2211yescharacteristic
22C22×C22⋊Q8C2212yes—
23C23×C42C2211yescharacteristic
24C2×#497C2212yescomplemented
25C2×#491C2212yescomplemented
26C2×#467C2214yes—
27C2×#465C2214yes—
28C2×#451C2212yes—
29C2×#448C2212yes—
30C22×C22⋊C8C2212yes—
31C22×#97C2212yes—
32#2857—21no—
33#2857—21no—
34#2857—21no—
35#2857—21no—
36#2857C2212yes—
37#2857C2212yes—
38#2857C2212yes—
39#2857C2212yes—
40#2855C2211yescharacteristic
41#2854C2211yescharacteristic
42#2853—21no—
43#2852—21no—
44#2852—21no—
45#2851C2211yescharacteristic
46#2851C2211yescharacteristic
47#2850C2211yescharacteristic
48#2850C2211yescharacteristic
49#2849—21no—
50#2848C2211yescharacteristic
51#2847C2211yescharacteristic
52C4×C22⋊Q8C2211yescharacteristic
53C4×C22⋊Q8C2211yescharacteristic
54C4×#123—21no—
55C4×#121C2211yescharacteristic
56C4×#121C2211yescharacteristic
57C4×#120—21no—
58C2×#391C2212yes—
59C2×#389—21no—
60C2×#389—21no—
61#2290—21no—
62#2290—21no—
63C2×#384C2211yescharacteristic
64#2283C2211yescharacteristic
65C2×#380—21no—
66C2×#380—21no—
67#2084C2212yescomplemented
68#2083C2212yescomplemented
69#2072C2212yescomplemented
70#2071C2212yescomplemented
71#2043C2212yescomplemented
72#2043C2212yescomplemented
73#2036C2214yes—
74#2035C2214yes—
75#2016C2212yescomplemented
76#2013C2212yescomplemented
77#2001C2214yes—
78#2000C2214yes—
79#1992C2212yescomplemented
80#1973C2214yescomplemented
81#1971C2214yescomplemented
82#1960C2212yescomplemented
83#1960C2212yescomplemented
84#1959C2212yescomplemented
85#1935C2214yescomplemented
86#1935C2214yescomplemented
87#1928C2214yescomplemented
88#1927C2214yescomplemented
89#1892C2214yes—
90#1892C2214yes—
91#1878C2214yescomplemented
92#1877C2214yescomplemented
93#1874C2212yes—
94#1872C2212yes—
95#1853C2212yes—
96#1852C2212yes—
97#1847C2212yescomplemented
98#1836C2212yescomplemented
99#1787C2212yes—
100#1787C2212yes—
101#1749C2212yes—
102#1749C2211yescharacteristic
103#1749C2212yes—
104#1749C2211yescharacteristic
105#1749C2212yes—
106C2×#336C2212yes—
107C23×Q8C2312yes—
108C24×C4D411yescharacteristic
109C24×C4D411yescharacteristic
110C24×C4C2311yescharacteristic
111C22×Q16C2314yes—
112C22×SD16C2314yes—
113C23×C8C2314yes—
114C2×C4⋊Q8—21no—
115C2×C4⋊Q8—21no—
116C2×C4⋊Q8—44no—
117C2×C4⋊Q8C2312yes—
118C2×C4⋊Q8C2312yes—
119#529—44no—
120C2×#126—21no—
121C2×#125C2311yescharacteristic
122C2×#124C2311yescharacteristic
123C2×#123—21no—
124C2×#123—21no—
125C2×C22⋊Q8—22no—
126C2×C22⋊Q8—22no—
127C2×C22⋊Q8—48no—
128C2×C22⋊Q8C2311yescharacteristic
129C2×C22⋊Q8C2311yescharacteristic
130C2×C22⋊Q8C2314yes—
131C2×C22⋊Q8C2311yescharacteristic
132C2×C22⋊Q8C2314yes—
133C2×#121C2311yescharacteristic
134C2×#121C2311yescharacteristic
135C2×#121C2311yescharacteristic
136C2×#120—21no—
137C2×C4×Q8C2311yescharacteristic
138C2×C4×D4—21no—
139C2×C4×D4—21no—
140C2×C4×D4—21no—
141C2×C4×D4C2311yescharacteristic
142C2×#117—21no—
143C22×C4⋊C4—22no—
144C22×C4⋊C4—21no—
145C22×C4⋊C4—21no—
146C22×C4⋊C4—21no—
147C22×C4⋊C4—21no—
148C22×C4⋊C4C2312yes—
149C22×C22⋊C4—22no—
150C22×C42—44no—
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#497—44no—
164#491—44no—
165#467—48no—
166#465—48no—
167#451—28no—
168#448—28no—
169C2×#107C2314yes—
170C2×#106C2314yes—
171C2×#103C2314yes—
172C2×#103C2314yes—
173C2×#103C2314yes—
174C2×#103C2314yes—
175C2×#103C2314yes—
176C2×#103C2314yes—
177C2×#103C2314yes—
178C2×#102C2314yes—
179C2×C22⋊C8—28no—
180C2×C22⋊C8C2312yes—
181C2×C22⋊C8C2314yes—
182C2×C22⋊C8C2312yes—
183C2×#97—44no—
184C2×#97C2312yes—
185C2×#97C2312yes—
186C2×#97C2314yes—
187#391—22no—
188#391—22no—
189#391C2311yescharacteristic
190#391C2311yescharacteristic
191#391C2314yes—
192#391C2314yes—
193#390C2311yescharacteristic
194#390C2311yescharacteristic
195#389—22no—
196#389—22no—
197#389—22no—
198#389—22no—
199#389—22no—
200#389—22no—
201#389—22no—
202#389—22no—
203#389C2311yescharacteristic
204#389C2311yescharacteristic
205#389C2311yescharacteristic
206#389C2311yescharacteristic
207#388—21no—
208#388—21no—
209#388—21no—
210#388—21no—
211#388—21no—
212#388—21no—
213#388—21no—
214#388—21no—
215#387—21no—
216#387—21no—
217#387—21no—
218#387—21no—
219#387—21no—
220#387—21no—
221#387—21no—
222#387—21no—
223#386—21no—
224#386—21no—
225#386—21no—
226#386—21no—
227#386—21no—
228#386—21no—
229#386—21no—
230#386—21no—
231#386—21no—
232#386—21no—
233#385—21no—
234#385—21no—
235#385—21no—
236#385—21no—
237#385—21no—
238#385—21no—
239#385—21no—
240#385—21no—
241#385—21no—
242#385—21no—
243#384—21no—
244#384—21no—
245#384C2312yes—
246#384C2312yes—
247#383—21no—
248#382C2311yescharacteristic
249#382C2311yescharacteristic
250#381—21no—
251#381—21no—
252#380—22no—
253#380—22no—
254#380—22no—
255#380—22no—
256#380—22no—
257#380—22no—
258#380—22no—
259#380—22no—
260#380C2311yescharacteristic
261#380C2311yescharacteristic
262#380C2311yescharacteristic
263#380C2311yescharacteristic
264#380C2311yescharacteristic
265#380C2311yescharacteristic
266#379—21no—
267C4×C4⋊C4—21no—
268C4×C4⋊C4—21no—
269C4×C4⋊C4C2311yescharacteristic
270C4×C4⋊C4C2311yescharacteristic
271C4×C22⋊C4—21no—
272C4×C22⋊C4—21no—
273C4×C22⋊C4—21no—
274C4×C22⋊C4—21no—
275C4×C22⋊C4—21no—
276#376—21no—
277C2×#95—22no—
278C2×#95—22no—
279#340C2314yes—
280#340C2314yes—
281#340C2314yes—
282#340C2314yes—
283#336C2312yes—
284#336C2312yes—
285#336C2314yes—
286C25C2×D411yescharacteristic
287C22×Q8—22no—
288C22×Q8—24no—
289C22×Q8—24no—
290C22×Q8—44no—
291C22×Q8—44no—
292C22×Q8C2411yescharacteristic
293C22×Q8C2414yes—
294C22×D4—21no—
295C22×D4—21no—
296C22×D4—21no—
297C22×D4C2411yescharacteristic
298C23×C4—24no—
299C23×C4—24no—
300C23×C4—24no—
301C23×C4—24no—
302C23×C4—22no—
303C23×C4—22no—
304C23×C4—21no—
305C23×C4—42no—
306C23×C4—42no—
307C23×C4—42no—
308C23×C4—42no—
309C23×C4—42no—
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×C4C2×D411yescharacteristic
323C23×C4C2×D411yescharacteristic
324C23×C4C2×D411yescharacteristic
325C23×C4C2411yescharacteristic
326C23×C4C2411yescharacteristic
327C23×C4C2411yescharacteristic
328C2×Q16—28no—
329C2×Q16—44no—
330C2×Q16—44no—
331C2×SD16—28no—
332C2×SD16—44no—
333C2×SD16—44no—
334C22×C8—28no—
335C22×C8—28no—
336C22×C8—44no—
337C22×C8C2414yes—
338C22×C8C2414yes—
339C4⋊Q8—24no—
340C4⋊Q8—24no—
341C4⋊Q8—44no—
342C4⋊Q8—44no—
343C4⋊Q8—44no—
344#126—44no—
345#125—24no—
346#124—24no—
347#123—44no—
348#123—44no—
349C22⋊Q8—24no—
350C22⋊Q8—28no—
351C22⋊Q8—28no—
352C22⋊Q8—24no—
353C22⋊Q8—44no—
354C22⋊Q8—44no—
355C22⋊Q8—42no—
356C22⋊Q8—48no—
357C22⋊Q8—48no—
358#121—24no—
359#121—24no—
360#121—42no—
361#120—44no—
362C4×Q8—42no—
363C4×D4—42no—
364C4×D4—44no—
365C4×D4—44no—
366C4×D4—44no—
367#117—44no—
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—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
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—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—44no—
390C2×C4⋊C4—44no—
391C2×C4⋊C4—44no—
392C2×C4⋊C4—48no—
393C2×C4⋊C4—44no—
394C2×C4⋊C4—44no—
395C2×C4⋊C4C2414yes—
396C2×C4⋊C4C2411yescharacteristic
397C2×C4⋊C4C2411yescharacteristic
398C2×C4⋊C4C2411yescharacteristic
399C2×C4⋊C4C2411yescharacteristic
400C2×C4⋊C4C2411yescharacteristic
401C2×C4⋊C4C2411yescharacteristic
402C2×C22⋊C4—24no—
403C2×C22⋊C4—24no—
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—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—48no—
424C2×C42—24no—
425C2×C42—24no—
426C2×C42—24no—
427C2×C42—21no—
428C2×C42—21no—
429C2×C42—21no—
430C2×C42—42no—
431C2×C42—42no—
432C2×C42—42no—
433C2×C42—42no—
434C2×C42—42no—
435C2×C42—42no—
436C2×C42—42no—
437C2×C42—42no—
438C2×C42—42no—
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×C42C2×D411yescharacteristic
451C2×C42C2411yescharacteristic
452C2×C42C2411yescharacteristic
453C2×C42C2411yescharacteristic
454C2×C42C2411yescharacteristic
455#107—44no—
456#106—44no—
457#103—28no—
458#103—28no—
459#103—44no—
460#103—44no—
461#103—44no—
462#103—44no—
463#103—44no—
464#102—44no—
465C22⋊C8—24no—
466C22⋊C8—28no—
467C22⋊C8#4118yes—
468#97—24no—
469#97—24no—
470#97—44no—
471#95—24no—
472#95—24no—
473#95—24no—
474#95—24no—
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—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495C24—22no—
496C24—22no—
497C24—22no—
498C24—22no—
499C24—21no—
500C24—41no—
501C24—41no—
502C24#13714yes—
503C24C22×D411yescharacteristic
504C24C22×D411yescharacteristic
505C24C22×D411yescharacteristic
506C2×Q8—24no—
507C2×Q8—24no—
508C2×Q8—22no—
509C2×Q8—22no—
510C2×Q8—24no—
511C2×Q8—24no—
512C2×Q8—24no—
513C2×Q8—22no—
514C2×Q8—24no—
515C2×Q8—44no—
516C2×Q8—44no—
517C2×Q8—44no—
518C2×Q8—88no—
519C2×Q8—88no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—42no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—42no—
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—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—24no—
575C22×C4—24no—
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—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—416no—
593C22×C4—416no—
594C22×C4—416no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—44no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—42no—
604C22×C4#13714yes—
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D411yescharacteristic
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C2×#4114yes—
617C22×C4H(5,𝔽2)14yes—
618C22×C4C2511yescharacteristic
619Q16—88no—
620SD16—88no—
621C2×C8—24no—
622C2×C8—24no—
623C2×C8—24no—
624C2×C8—24no—
625C2×C8—24no—
626C2×C8—416no—
627C2×C8C2×#4118yes—
628C4⋊C4—22no—
629C4⋊C4—22no—
630C4⋊C4—24no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—24no—
636C4⋊C4—44no—
637C4⋊C4—44no—
638C4⋊C4—44no—
639C4⋊C4—44no—
640C4⋊C4—48no—
641C4⋊C4—44no—
642C4⋊C4—44no—
643C4⋊C4—42no—
644C4⋊C4—42no—
645C4⋊C4—42no—
646C4⋊C4—42no—
647C4⋊C4—42no—
648C4⋊C4—44no—
649C4⋊C4—44no—
650C4⋊C4—42no—
651C4⋊C4—42no—
652C4⋊C4—48no—
653C4⋊C4—42no—
654C4⋊C4—42no—
655C4⋊C4—44no—
656C4⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—48no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—48no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C42—22no—
679C42—22no—
680C42—22no—
681C42—22no—
682C42—22no—
683C42—22no—
684C42—22no—
685C42—22no—
686C42—22no—
687C42—41no—
688C42—41no—
689C42—41no—
690C42—41no—
691C42—41no—
692C42—41no—
693C42—42no—
694C42—42no—
695C42—42no—
696C42H(5,𝔽2)14yes—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—28no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—28no—
710C23—21no—
711C23—21no—
712C23—21no—
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#53512yes—
727C23C2×#13712yes—
728C23C2×#13712yes—
729C23C2×#13712yes—
730C23C2×#13712yes—
731C23#57512yes—
732C23C23×D411yescharacteristic
733Q8—44no—
734Q8—44no—
735Q8—44no—
736Q8—44no—
737Q8—44no—
738Q8—88no—
739D4—44no—
740D4—84no—
741D4—84no—
742D4—84no—
743C2×C4—28no—
744C2×C4—28no—
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—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
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—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
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—44no—
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—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—41no—
814C2×C4—84no—
815C2×C4—88no—
816C2×C4—88no—
817C2×C4#53212yes—
818C2×C4#53412yes—
819C2×C4#53412yes—
820C2×C4#53512yes—
821C2×C4C2×#13712yes—
822C2×C4C2×#13712yes—
823C2×C4#57512yes—
824C2×C4C22×#4112yes—
825C2×C4C2×H(5,𝔽2)12yes—
826C2×C4C2×H(5,𝔽2)12yes—
827C8—28no—
828C8—44no—
829C22—22no—
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—22no—
843C22—22no—
844C22—416no—
845C22—41no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—81no—
850C22—81no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22#318114yes—
857C22#321814yes—
858C22C2×#53211yescharacteristic
859C22C2×#53411yescharacteristic
860C22C2×#53511yescharacteristic
861C22C22×#13711yescharacteristic
862C22C22×#13711yescharacteristic
863C22C2×#57511yescharacteristic
864C22C2×#57511yescharacteristic
865C4—22no—
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—22no—
871C4—22no—
872C4—41no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—84no—
877C4—81no—
878C4—81no—
879C4—81no—
880C4—81no—
881C4—81no—
882C4—81no—
883C4—81no—
884C4—84no—
885C4#351914yes—
886C2—24no—
887C2—24no—
888C2—42no—
889C2—161no—
890C2#3507811yescharacteristic
891C2C2×#318111yescharacteristic
892C2#6070111yescharacteristic
893C2#6075111yescharacteristic
894C2#6075111yescharacteristic
895C2C2×#321811yescharacteristic
896C2#6079011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2847C22
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. C2×#2857C2semidirect
3. #33184C2semidirect
4. #33053C2semidirect
5. #30326C2semidirect
6. #30325C2semidirect
7. #28575C2semidirect
8. #28571C2semidirect
9. #27978C2semidirect
10. #27953C2semidirect
11. #27896C2semidirect
12. #25861C2semidirect
13. #25726C2semidirect
14. #25604C2semidirect
16. #24380C2semidirect
17. #22050C2semidirect
18. #22047C2semidirect
19. C2×#1749C2semidirect
24. C2×#497C22semidirect
25. C2×#491C22semidirect
67. #2084C22semidirect
68. #2083C22semidirect
69. #2072C22semidirect
70. #2071C22semidirect
71. #2043C22semidirect
72. #2043C22semidirect
75. #2016C22semidirect
76. #2013C22semidirect
79. #1992C22semidirect
80. #1973C22semidirect
81. #1971C22semidirect
82. #1960C22semidirect
83. #1960C22semidirect
84. #1959C22semidirect
85. #1935C22semidirect
86. #1935C22semidirect
87. #1928C22semidirect
88. #1927C22semidirect
91. #1878C22semidirect
92. #1877C22semidirect
97. #1847C22semidirect
98. #1836C22semidirect

Maximal subgroups

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

subgroupindex
C2×#28572
#366212
#331842
#330532
#303262
#303252
#285752
#285712
#279782
#279532
#278962
#258612
#257262
#256042
#243812
#243802
#220502
#220472
C2×#17492