Finite Group Databasebeta

← #6584065

Subgroups — #6584065

Order 512.

2058 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3177C211yesmaximal, characteristic, complemented
2C22×#470C211yesmaximal, characteristic
3#37663C212yesmaximal
4#33180C211yesmaximal, characteristic, complemented
5#33141C211yesmaximal, characteristic, complemented
6#32937C211yesmaximal, characteristic
7#28920C212yesmaximal, complemented
8#28588C212yesmaximal, complemented
9#27806C211yesmaximal, characteristic, complemented
10#27268C212yesmaximal, complemented
11#26972C212yesmaximal, complemented
12#26062C211yesmaximal, characteristic, complemented
13#25780C211yesmaximal, characteristic, complemented
14#25512C212yesmaximal, complemented
15#25427C211yesmaximal, characteristic, complemented
16#25427C211yesmaximal, characteristic, complemented
17#25049C211yesmaximal, characteristic, complemented
18#24380C212yesmaximal
19#23028C211yesmaximal, characteristic, complemented
20#22871C212yesmaximal, complemented
21#22440C211yesmaximal, characteristic, complemented
22#21542C211yesmaximal, characteristic, complemented
23#20389C211yesmaximal, characteristic
24C23×Q16C2211yescharacteristic
25C23×M16C2211yescharacteristic
26C2×#541C2212yes—
27C22×C22⋊Q8C2212yes—
28#3177—28no—
29C2×#499C2211yescharacteristic, complemented
30C2×#494C2211yescharacteristic, complemented
31C2×#494C2211yescharacteristic, complemented
32C2×#491C2212yescomplemented
33C2×#470—28no—
34C2×#470C2211yescharacteristic
35C2×#470C2211yescharacteristic
36C2×#470C2211yescharacteristic
37C2×#470C2212yes—
38C2×#470C2211yescharacteristic
39C2×#470C2212yes—
40C2×#470C2211yescharacteristic
41C2×#470C2211yescharacteristic
42C2×#467C2212yes—
43C2×#467C2211yescharacteristic
44C2×#467C2212yes—
45C2×#451C2212yes—
46C2×#441C2211yescharacteristic, complemented
47C2×#441C2211yescharacteristic, complemented
48C2×#441C2211yescharacteristic, complemented
49C2×C4×Q16C2212yescomplemented
50C22×#106C2211yescharacteristic
51C22×#103C2212yes—
52C22×C22⋊C8C2211yescharacteristic
53C2×#405C2211yescharacteristic
54C2×#405C2211yescharacteristic
55#2848C2212yes—
56#2704—22no—
57#2698—22no—
58#2690—22no—
59#2689—22no—
60#2625C2212yes—
61#2621C2212yes—
62#2489C2212yes—
63#2480—22no—
64#2480—22no—
65#2473—22no—
66#2442—22no—
67#2442C2212yes—
68#2434C2212yes—
69#2429C2212yes—
70#2429C2212yes—
71#2421C2212yes—
72#2360C2212yes—
73Q8×C22⋊C4C2212yes—
74#2323C2212yes—
75#2280C2211yescharacteristic
76#2085C2212yescomplemented
77#2074C2212yescomplemented
78#2059C2212yescomplemented
79#2043C2212yescomplemented
80#2043C2212yescomplemented
81#2036C2212yes—
82#2036C2212yes—
83#2026C2212yescomplemented
84#2016C2212yescomplemented
85#2016C2212yescomplemented
86#2001C2212yes—
87#2001C2212yes—
88#1971C2211yescharacteristic, complemented
89#1971C2211yescharacteristic, complemented
90#1971C2211yescharacteristic, complemented
91#1969C2211yescharacteristic, complemented
92#1969C2212yescomplemented
93#1969C2211yescharacteristic, complemented
94#1960C2212yescomplemented
95#1943C2211yescharacteristic, complemented
96#1941C2211yescharacteristic, complemented
97#1941C2211yescharacteristic, complemented
98#1935C2212yescomplemented
99#1935C2212yescomplemented
100#1933C2212yescomplemented
101#1928C2212yescomplemented
102#1927C2212yescomplemented
103#1894C2212yes—
104#1894C2212yes—
105#1892C2212yes—
106#1892C2212yes—
107#1892C2212yes—
108#1878C2212yescomplemented
109#1878C2212yescomplemented
110#1878C2212yescomplemented
111#1878C2212yescomplemented
112#1872C2212yes—
113#1865C2212yescomplemented
114#1863C2212yescomplemented
115#1852C2212yes—
116#1846C2211yescharacteristic, complemented
117#1809C2211yescharacteristic
118#1809C2211yescharacteristic
119#1807C2211yescharacteristic
120#1787C2212yes—
121#1776C2211yescharacteristic, complemented
122C4×#103C2212yescomplemented
123#1753C2211yescharacteristic
124#1753C2211yescharacteristic
125#1753C2211yescharacteristic
126#1753C2211yescharacteristic
127#1752C2211yescharacteristic
128#1752C2211yescharacteristic
129C8×C22⋊C4C2211yescharacteristic
130C8×C22⋊C4C2211yescharacteristic
131#1729C2211yescharacteristic
132#1729C2211yescharacteristic
133C23×Q8C2312yes—
134C24×C4C2311yescharacteristic
135C22×Q16—24no—
136C22×Q16—24no—
137C22×Q16—42no—
138C22×Q16C2311yescharacteristic
139C22×Q16C2311yescharacteristic
140C22×Q16C2312yes—
141C22×Q16C2312yes—
142C22×Q16C2311yescharacteristic
143C22×Q16C2312yes—
144C22×M16—24no—
145C22×M16—24no—
146C22×M16—42no—
147C22×M16C2311yescharacteristic
148C22×M16C2311yescharacteristic
149C22×M16C2311yescharacteristic
150C22×M16C2311yescharacteristic
151C23×C8C2311yescharacteristic
152C23×C8C2311yescharacteristic
153C23×C8C2311yescharacteristic
154C23×C8C2311yescharacteristic
155#541—28no—
156#541—44no—
157C2×C4⋊Q8C2312yes—
158C2×C4⋊Q8C2312yes—
159C2×#126—22no—
160C2×#126—22no—
161C2×#125—22no—
162C2×#125—22no—
163C2×#125C2312yes—
164C2×C22⋊Q8—22no—
165C2×C22⋊Q8—22no—
166C2×C22⋊Q8—28no—
167C2×C22⋊Q8—44no—
168C2×C22⋊Q8C2312yes—
169C2×C22⋊Q8C2312yes—
170C2×C22⋊Q8C2312yes—
171C2×C22⋊Q8C2312yes—
172C2×C22⋊Q8C2312yes—
173C2×C22⋊Q8C2312yes—
174C2×C22⋊Q8C2312yes—
175C2×C4×Q8C2312yes—
176C2×C4×Q8C2312yes—
177C2×C4×Q8C2312yes—
178C2×#117C2311yescharacteristic
179C2×#117C2311yescharacteristic
180C22×C4⋊C4—22no—
181C22×C4⋊C4C2312yes—
182C22×C22⋊C4—22no—
183#499—24no—
184#494—24no—
185#494—42no—
186#491—28no—
187#470—24no—
188#470—24no—
189#470—24no—
190#470—28no—
191#470—24no—
192#470—28no—
193#470—42no—
194#470D418yes—
195#467—24no—
196#467—28no—
197#467—44no—
198#451—28no—
199#441—24no—
200#441—24no—
201#441—42no—
202C4×Q16—28no—
203C2×#107C2311yescharacteristic
204C2×#107C2312yes—
205C2×#107C2312yes—
206C2×#106—24no—
207C2×#106C2312yes—
208C2×#106C2311yescharacteristic
209C2×#106C2311yescharacteristic
210C2×#106C2311yescharacteristic
211C2×#106C2311yescharacteristic
212C2×#103—28no—
213C2×#103C2312yes—
214C2×#103C2312yes—
215C2×#103C2312yes—
216C2×#103C2312yes—
217C2×#103C2312yes—
218C2×#103C2312yes—
219C2×#103C2312yes—
220C2×#103C2312yes—
221C2×#103C2312yes—
222C2×#103C2312yes—
223C2×#103C2312yes—
224C2×#103C2312yes—
225C2×#103C2312yes—
226C2×#103C2312yes—
227C2×#103C2312yes—
228C2×C22⋊C8—24no—
229C2×C22⋊C8C2311yescharacteristic
230C2×C22⋊C8C2311yescharacteristic
231C2×C22⋊C8C2311yescharacteristic
232C2×C22⋊C8C2311yescharacteristic
233#405—24no—
234#405—42no—
235C2×#97C2311yescharacteristic
236C2×#97C2311yescharacteristic
237C2×#97C2311yescharacteristic
238C2×#97C2311yescharacteristic
239C2×C4×C8C2311yescharacteristic
240C2×C4×C8C2311yescharacteristic
241C2×C4×C8C2311yescharacteristic
242C2×C4×C8C2311yescharacteristic
243#400—22no—
244#400—22no—
245#400—22no—
246#400—22no—
247#398—22no—
248#398—22no—
249#398—22no—
250#398—22no—
251#398—22no—
252#398—22no—
253#397—22no—
254#397—22no—
255#397—22no—
256#397—22no—
257#397—22no—
258#397—22no—
259#396—22no—
260#396—22no—
261#395—22no—
262#395—22no—
263#391—22no—
264#391—22no—
265#391C2312yes—
266#391C2312yes—
267#391C2312yes—
268#391C2312yes—
269#391C2312yes—
270#389—22no—
271#389—22no—
272#389—22no—
273#389—22no—
274#389C2312yes—
275#389C2312yes—
276#389C2312yes—
277#388—22no—
278#388—22no—
279#388—22no—
280#388—22no—
281#388—22no—
282#388—22no—
283#387—22no—
284#387—22no—
285#387—22no—
286#385—22no—
287#385—22no—
288#385—22no—
289#385—22no—
290#385—22no—
291#385—22no—
292#385—22no—
293#382—22no—
294#382C2312yes—
295#381D412yes—
296#380—22no—
297#380—22no—
298#380D412yes—
299#380D412yes—
300#380C2312yes—
301#380C2312yes—
302#380C2312yes—
303#379—22no—
304#379D412yes—
305C4×C4⋊C4C2312yes—
306C4×C22⋊C4—22no—
307C4×C22⋊C4—22no—
308C4×C22⋊C4C2311yescharacteristic
309C4×C22⋊C4C2311yescharacteristic
310C4×C22⋊C4C2311yescharacteristic
311C4×C22⋊C4C2311yescharacteristic
312#340C2312yes—
313#340C2312yes—
314#340C2312yes—
315#340C2312yes—
316#340C2312yes—
317#340C2312yes—
318#340C2312yes—
319#336C2311yescharacteristic
320#336C2311yescharacteristic
321#336C2311yescharacteristic
322#336C2311yescharacteristic
323#336C2311yescharacteristic
324#336C2311yescharacteristic
325#336C2311yescharacteristic
326#336C2311yescharacteristic
327C25C2×D411yescharacteristic
328C22×Q8—22no—
329C22×Q8—24no—
330C22×Q8—24no—
331C22×Q8—24no—
332C22×Q8—42no—
333C22×Q8—42no—
334C22×Q8—42no—
335C22×Q8C2412yes—
336C22×Q8C2412yes—
337C22×Q8C2412yes—
338C23×C4—22no—
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—41no—
345C23×C4—41no—
346C23×C4C2×D411yescharacteristic
347C23×C4C2×D411yescharacteristic
348C23×C4C2×D411yescharacteristic
349C23×C4C2411yescharacteristic
350C23×C4C2411yescharacteristic
351C23×C4C2411yescharacteristic
352C2×Q16—24no—
353C2×Q16—24no—
354C2×Q16—22no—
355C2×Q16—22no—
356C2×Q16—22no—
357C2×Q16—24no—
358C2×Q16—22no—
359C2×Q16—24no—
360C2×Q16—22no—
361C2×Q16—24no—
362C2×Q16—22no—
363C2×Q16—22no—
364C2×Q16—22no—
365C2×Q16—416no—
366C2×Q16—42no—
367C2×Q16—42no—
368C2×Q16—42no—
369C2×Q16—42no—
370C2×Q16C2×D414yes—
371C2×M16—22no—
372C2×M16—22no—
373C2×M16—22no—
374C2×M16—22no—
375C2×M16—22no—
376C2×M16—22no—
377C2×M16—22no—
378C2×M16—22no—
379C2×M16—22no—
380C2×M16—41no—
381C2×M16—41no—
382C2×M16—416no—
383C2×M16C2×D414yes—
384C22×C8—22no—
385C22×C8—22no—
386C22×C8—22no—
387C22×C8—22no—
388C22×C8—22no—
389C22×C8—22no—
390C22×C8—22no—
391C22×C8—22no—
392C22×C8—41no—
393C22×C8—41no—
394C22×C8—41no—
395C22×C8#4114yes—
396C22×C8C2411yescharacteristic
397C22×C8C2411yescharacteristic
398C22×C8C2411yescharacteristic
399C22×C8C2411yescharacteristic
400C22×C8C2411yescharacteristic
401C22×C8C2411yescharacteristic
402C22×C8C2411yescharacteristic
403C22×C8C2411yescharacteristic
404C4⋊Q8—24no—
405C4⋊Q8—42no—
406C4⋊Q8—42no—
407C4⋊Q8—42no—
408#126—48no—
409#126—48no—
410#125—24no—
411#125—42no—
412#125—48no—
413#125—48no—
414C22⋊Q8—24no—
415C22⋊Q8—24no—
416C22⋊Q8—24no—
417C22⋊Q8—24no—
418C22⋊Q8—24no—
419C22⋊Q8—24no—
420C22⋊Q8—24no—
421C22⋊Q8—24no—
422C22⋊Q8—24no—
423C22⋊Q8—48no—
424C22⋊Q8—42no—
425C22⋊Q8—42no—
426C22⋊Q8—48no—
427C22⋊Q8—42no—
428C22⋊Q8—42no—
429C22⋊Q8C2×D418yes—
430C4×Q8—24no—
431C4×Q8—24no—
432C4×Q8—42no—
433C4×Q8—42no—
434C4×Q8—42no—
435C4×Q8—42no—
436#117—22no—
437#117—22no—
438#117—41no—
439#117—41no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—24no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—42no—
462C2×C4⋊C4—48no—
463C2×C4⋊C4C2×D412yes—
464C2×C4⋊C4C2×D412yes—
465C2×C4⋊C4C2412yes—
466C2×C4⋊C4C2412yes—
467C2×C4⋊C4C2412yes—
468C2×C4⋊C4C2412yes—
469C2×C4⋊C4C2412yes—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—48no—
481C2×C22⋊C4C2×D412yes—
482C2×C22⋊C4C2×D412yes—
483C2×C22⋊C4C2×D412yes—
484C2×C22⋊C4C2×D412yes—
485C2×C22⋊C4C2×D412yes—
486C2×C22⋊C4C2×D412yes—
487C2×C42—22no—
488C2×C42—22no—
489C2×C42—22no—
490C2×C42—22no—
491C2×C42C2411yescharacteristic
492C2×C42C2411yescharacteristic
493C2×C42C2411yescharacteristic
494C2×C42C2411yescharacteristic
495#107—22no—
496#107—24no—
497#107—42no—
498#106—22no—
499#106—22no—
500#106—22no—
501#106—24no—
502#106C2×D414yes—
503#103—24no—
504#103—24no—
505#103—24no—
506#103—24no—
507#103—24no—
508#103—24no—
509#103—24no—
510#103—24no—
511#103—24no—
512#103—42no—
513#103—42no—
514#103—42no—
515#103—42no—
516#103—42no—
517#103C2×D418yes—
518C22⋊C8—22no—
519C22⋊C8—22no—
520C22⋊C8—22no—
521C22⋊C8#4114yes—
522#97—22no—
523#97—22no—
524#97—22no—
525#97—41no—
526C4×C8—22no—
527C4×C8—22no—
528C4×C8—22no—
529C4×C8—41no—
530#95—22no—
531#95—22no—
532#95—22no—
533#95—22no—
534#95—22no—
535#95—22no—
536#95—22no—
537#95—22no—
538#95—22no—
539#95—22no—
540#95—22no—
541#95—22no—
542#95—22no—
543#95—22no—
544#95—22no—
545#95—22no—
546#95—22no—
547#95—22no—
548#95—22no—
549#95C2×D412yes—
550#95C2×D412yes—
551#95C2×D412yes—
552#95C2×D412yes—
553C24—22no—
554C24—22no—
555C24—24no—
556C24—41no—
557C24—42no—
558C24C22×D411yescharacteristic
559C24C22×D411yescharacteristic
560C24C22×D411yescharacteristic
561C2×Q8—22no—
562C2×Q8—22no—
563C2×Q8—22no—
564C2×Q8—22no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—22no—
572C2×Q8—22no—
573C2×Q8—22no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—22no—
577C2×Q8—22no—
578C2×Q8—44no—
579C2×Q8—48no—
580C2×Q8—48no—
581C2×Q8—44no—
582C2×Q8—82no—
583C2×Q8—84no—
584C2×Q8—84no—
585C2×Q8C22×D414yes—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4—82no—
626C22×C4—82no—
627C22×C4C22×D412yes—
628C22×C4C22×D412yes—
629C22×C4C22×D412yes—
630C22×C4C22×D412yes—
631C22×C4C22×D411yescharacteristic
632C22×C4C22×D411yescharacteristic
633C22×C4C22×D411yescharacteristic
634C22×C4C22×D412yes—
635C22×C4C2×#4112yes—
636C22×C4C2×#4112yes—
637C22×C4H(5,𝔽2)12yes—
638C22×C4C2511yescharacteristic
639Q16—28no—
640Q16—48no—
641Q16—48no—
642Q16—44no—
643Q16—44no—
644Q16—84no—
645M16—28no—
646M16—44no—
647M16—44no—
648M16—44no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—28no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—44no—
668C2×C8—44no—
669C2×C8—44no—
670C2×C8C22×D412yes—
671C2×C8C22×D412yes—
672C2×C8C2×#4112yes—
673C2×C8C2×#4112yes—
674C2×C8C2×#4112yes—
675C2×C8C2×#4112yes—
676C2×C8H(5,𝔽2)12yes—
677C4⋊C4—28no—
678C4⋊C4—24no—
679C4⋊C4—22no—
680C4⋊C4—22no—
681C4⋊C4—22no—
682C4⋊C4—22no—
683C4⋊C4—22no—
684C4⋊C4—22no—
685C4⋊C4—22no—
686C4⋊C4—22no—
687C4⋊C4—22no—
688C4⋊C4—42no—
689C4⋊C4—44no—
690C4⋊C4—44no—
691C4⋊C4—44no—
692C4⋊C4—44no—
693C4⋊C4—44no—
694C4⋊C4—44no—
695C4⋊C4—44no—
696C4⋊C4—44no—
697C4⋊C4—44no—
698C4⋊C4—44no—
699C4⋊C4—44no—
700C4⋊C4—44no—
701C4⋊C4—82no—
702C4⋊C4—82no—
703C4⋊C4—82no—
704C4⋊C4—82no—
705C4⋊C4—82no—
706C4⋊C4—82no—
707C4⋊C4—82no—
708C4⋊C4C22×D414yes—
709C22⋊C4—28no—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—42no—
716C22⋊C4—44no—
717C22⋊C4—44no—
718C22⋊C4—44no—
719C22⋊C4—44no—
720C22⋊C4—44no—
721C22⋊C4—44no—
722C22⋊C4—44no—
723C22⋊C4—82no—
724C22⋊C4—82no—
725C42—21no—
726C42—21no—
727C42—21no—
728C42—21no—
729C42—21no—
730C42—21no—
731C42—21no—
732C42—21no—
733C42—44no—
734C42—44no—
735C42—82no—
736C42—82no—
737C23—22no—
738C23—21no—
739C23—21no—
740C23—22no—
741C23—21no—
742C23—21no—
743C23—22no—
744C23—22no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—22no—
749C23—44no—
750C23—48no—
751C23—44no—
752C23—82no—
753C23—84no—
754C23#53212yes—
755C23D4212yes—
756C23#57814yes—
757C23C23×D411yescharacteristic
758Q8—24no—
759Q8—24no—
760Q8—42no—
761Q8—42no—
762Q8—42no—
763Q8—42no—
764Q8—42no—
765Q8—42no—
766Q8—42no—
767Q8—42no—
768Q8—42no—
769Q8—42no—
770Q8—88no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—21no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—21no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—21no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—88no—
830C2×C4—88no—
831C2×C4#53212yes—
832C2×C4D4212yes—
833C2×C4C23×D411yescharacteristic
834C2×C4C22×#4111yescharacteristic
835C2×C4C22×#4111yescharacteristic
836C2×C4C2×H(5,𝔽2)11yescharacteristic
837C2×C4C2×H(5,𝔽2)11yescharacteristic
838C2×C4#58511yescharacteristic
839C8—22no—
840C8—22no—
841C8—22no—
842C8—22no—
843C8—41no—
844C8—41no—
845C8—41no—
846C8#54614yes—
847C22—22no—
848C22—22no—
849C22—24no—
850C22—24no—
851C22—22no—
852C22—24no—
853C22—41no—
854C22—41no—
855C22—42no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—42no—
860C22—42no—
861C22—88no—
862C22#317714yescomplemented
863C22C2×#53211yescharacteristic
864C22C2×D4211yescharacteristic
865C22#349611yescharacteristic
866C22C2×#57812yes—
867C22#358612yes—
868C4—22no—
869C4—22no—
870C4—41no—
871C4—44no—
872C4—42no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—44no—
877C4—82no—
878C4—82no—
879C4—82no—
880C4—82no—
881C4—82no—
882C4—82no—
883C4C2×#54611yescharacteristic
884C4D4×#4111yescharacteristic
885C4#349411yescharacteristic
886C4#351911yescharacteristic
887C2—24no—
888C2—42no—
889C2—81no—
890C2#3612311yescharacteristic
891C2C2×#317711yescharacteristic
892C2#6071111yescharacteristic
893C2#6107612yes—
894C2#6231712yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2280 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#3177C2semidirect
4. #33180C2semidirect
5. #33141C2semidirect
7. #28920C2semidirect
8. #28588C2semidirect
9. #27806C2semidirect
10. #27268C2semidirect
11. #26972C2semidirect
12. #26062C2semidirect
13. #25780C2semidirect
14. #25512C2semidirect
15. #25427C2semidirect
16. #25427C2semidirect
17. #25049C2semidirect
19. #23028C2semidirect
20. #22871C2semidirect
21. #22440C2semidirect
22. #21542C2semidirect
29. C2×#499C22semidirect
30. C2×#494C22semidirect
31. C2×#494C22semidirect
32. C2×#491C22semidirect
46. C2×#441C22semidirect
47. C2×#441C22semidirect
48. C2×#441C22semidirect
49. C2×C4×Q16C22semidirect
76. #2085C22semidirect
77. #2074C22semidirect
78. #2059C22semidirect
79. #2043C22semidirect
80. #2043C22semidirect
83. #2026C22semidirect
84. #2016C22semidirect
85. #2016C22semidirect
88. #1971C22semidirect
89. #1971C22semidirect
90. #1971C22semidirect
91. #1969C22semidirect
92. #1969C22semidirect
93. #1969C22semidirect
94. #1960C22semidirect
95. #1943C22semidirect
96. #1941C22semidirect
97. #1941C22semidirect
98. #1935C22semidirect
99. #1935C22semidirect
100. #1933C22semidirect
101. #1928C22semidirect
102. #1927C22semidirect
108. #1878C22semidirect
109. #1878C22semidirect
110. #1878C22semidirect
111. #1878C22semidirect
113. #1865C22semidirect
114. #1863C22semidirect
116. #1846C22semidirect
121. #1776C22semidirect
122. C4×#103C22semidirect
862. C22#3177semidirect

Maximal subgroups

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

subgroupindex
C2×#31772
C22×#4702
#376632
#331802
#331412
#329372
#289202
#285882
#278062
#272682
#269722
#260622
#257802
#255122
#254272
#250492
#243802
#230282
#228712
#224402
#215422
#203892