Finite Group Databasebeta

← #6372677

Subgroups — #6372677

Order 512.

4879 conjugacy classes of subgroups.

The subgroup lattice has 1249 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×H(5,𝔽2)C211yesmaximal, characteristic, complemented
2C2×#3012C211yesmaximal, characteristic
3C2×#2951C211yesmaximal, characteristic, complemented
4C2×#2946C211yesmaximal, characteristic, complemented
5#34267C211yesmaximal, characteristic, complemented
6#21465C212yesmaximal, complemented
7#21460C212yesmaximal, complemented
8#21459C212yesmaximal, complemented
9#21458C212yesmaximal, complemented
10#21456C212yesmaximal, complemented
11#21453C212yesmaximal, complemented
12C4×#452C212yesmaximal, complemented
13C4×#447C212yesmaximal, complemented
14#20925C211yesmaximal, characteristic, complemented
15#20924C211yesmaximal, characteristic, complemented
16#20915C211yesmaximal, characteristic, complemented
17#20875C211yesmaximal, characteristic, complemented
18C2×#1862C211yesmaximal, characteristic, complemented
19#20847C211yesmaximal, characteristic, complemented
20#20602C211yesmaximal, characteristic, complemented
21#20416C211yesmaximal, characteristic, complemented
22#20415C211yesmaximal, characteristic, complemented
23#20378C211yesmaximal, characteristic, complemented
24C22×H(5,𝔽2)C2211yescharacteristic
25C22×AGL(1,ℤ/8)C2211yescharacteristic
26C22×#135C2211yescharacteristic
27C2×#537C2211yescharacteristic
28C4×H(5,𝔽2)—28no—
29C4×H(5,𝔽2)—28no—
30C2×#520—21no—
31C2×#520C2212yes—
32C2×#520C2211yescharacteristic
33C2×#520C2211yescharacteristic
34C2×#520C2211yescharacteristic, complemented
35C2×#518—21no—
36C2×#518—22no—
37C2×#518C2212yes—
38C2×#518C2211yescharacteristic
39C2×C4×#41—21no—
40C2×C4×#41C2211yescharacteristic
41C2×C4×#41C2212yes—
42C2×C4×#41C2211yescharacteristic
43C22×C4×D4—21no—
44C22×C4×D4—22no—
45C22×C4×D4C2211yescharacteristic
46C22×C4×D4C2212yes—
47#3012C4116yescomplemented
48C2×#452C2212yes—
49C2×#449C2212yes—
50C2×#450C2212yes—
51C2×#447C2212yes—
52#2951—28no—
53#2946—28no—
54C2×#442C2212yescomplemented
55C2×#440C2212yescomplemented
56C2×#440C2212yescomplemented
57C2×#440C2212yescomplemented
58C2×C4×Q16C2212yescomplemented
59C2×C4×SD16C2212yescomplemented
60C2×C4×D8C2212yescomplemented
61C2×C4×D8C2212yescomplemented
62C2×#428C2211yescharacteristic, complemented
63C22×#107C2211yescharacteristic, complemented
64C2×#417C2211yescharacteristic
65C2×#417C2211yescharacteristic
66C2×#417C2211yescharacteristic, complemented
67C2×#418C2211yescharacteristic
68C2×#416C2211yescharacteristic
69C2×#416C2211yescharacteristic, complemented
70C22×#102C2211yescharacteristic
71C22×#102C2211yescharacteristic
72C2×#408C2211yescharacteristic
73C2×#408C2211yescharacteristic
74C2×#405C2211yescharacteristic, complemented
75C2×#405C2211yescharacteristic, complemented
76#2364—22no—
77#2363—21no—
78#2362—21no—
79#2361—22no—
80#2361—21no—
81#2360—21no—
82#2324C2212yescomplemented
83#2323C2212yescomplemented
84#2311C2211yescharacteristic
85C4×C22⋊Q8C2212yescomplemented
86C4×#121C2212yescomplemented
87#2297C2211yescharacteristic, complemented
88C2×#389C2211yescharacteristic, complemented
89#2274C2211yescharacteristic, complemented
90#1880C2211yescharacteristic, complemented
91#1880C2211yescharacteristic, complemented
92#1879C2211yescharacteristic, complemented
93#1879C2211yescharacteristic, complemented
94#1879C2212yescomplemented
95#1879C2212yescomplemented
96#1878C2211yescharacteristic, complemented
97#1878C2211yescharacteristic, complemented
98#1877C2211yescharacteristic, complemented
99#1877C2211yescharacteristic, complemented
100#1877C2212yescomplemented
101#1877C2212yescomplemented
102#1875C2212yescomplemented
103#1874C2212yescomplemented
104#1873C2212yescomplemented
105#1872C2212yescomplemented
106#1865C2212yescomplemented
107#1864C2212yescomplemented
108#1863C2212yescomplemented
109#1862C2212yescomplemented
110#1862C2212yescomplemented
111#1862C2212yescomplemented
112#1862C2212yescomplemented
113#1862C2212yescomplemented
114#1854C2212yescomplemented
115#1854C2212yescomplemented
116#1852C2212yescomplemented
117#1852C2212yescomplemented
118#1788C2212yes—
119#1788C2212yes—
120#1786C2212yes—
121#1786C2212yes—
122#1763C2212yescomplemented
123#1762C2212yescomplemented
124#1762C2212yescomplemented
125#1762C2212yescomplemented
126C4×#103C2212yescomplemented
127C4×#102C2212yescomplemented
128C4×#102C2212yescomplemented
129C4×#102C2212yescomplemented
130#1750C2212yescomplemented
131#1750C2212yescomplemented
132#1749C2212yescomplemented
133C4×C22⋊C8C2212yescomplemented
134#1736C2211yescharacteristic, complemented
135#1736C2211yescharacteristic, complemented
136#1735C2211yescharacteristic, complemented
137C2×#340C2211yescharacteristic, complemented
138#1728C2211yescharacteristic, complemented
139C2×#336C2211yescharacteristic, complemented
140C2×H(5,𝔽2)—24no—
141C2×H(5,𝔽2)—24no—
142C2×H(5,𝔽2)—24no—
143C2×H(5,𝔽2)—24no—
144C2×H(5,𝔽2)—24no—
145C2×H(5,𝔽2)C2×C418yescomplemented
146C22×#41—21no—
147C22×#41C2312yes—
148C22×#41C2311yescharacteristic
149C22×#41C2311yescharacteristic
150C22×#41C2311yescharacteristic
151C23×D4—22no—
152C23×D4—21no—
153C23×D4C2312yes—
154C23×D4C2311yescharacteristic
155C24×C4—21no—
156C24×C4—22no—
157C2×AGL(1,ℤ/8)—24no—
158C2×AGL(1,ℤ/8)—24no—
159C2×AGL(1,ℤ/8)C2×C418yescomplemented
160C2×#135—24no—
161C2×#135—24no—
162C2×#135C2×C418yescomplemented
163C22×Q16C2311yescharacteristic
164C22×SD16C2312yes—
165C22×SD16C2311yescharacteristic
166C22×SD16C2311yescharacteristic
167C22×D8C2311yescharacteristic
168C22×D8C2312yes—
169C22×M16C2311yescharacteristic
170C22×M16C2311yescharacteristic
171C23×C8C2311yescharacteristic
172C23×C8C2311yescharacteristic
173#537—24no—
174#537C2×C418yescomplemented
175C2×C22⋊Q8—21no—
176C2×C22⋊Q8C2312yes—
177C2×#121—21no—
178C2×#121—22no—
179C2×#121C2312yes—
180#520—216no—
181#520—28no—
182#520—28no—
183#520—24no—
184#520—24no—
185#520—24no—
186#520—24no—
187#520—24no—
188#520D418yescomplemented
189#518—216no—
190#518—232no—
191#518—28no—
192#518—28no—
193#518—24no—
194#518D418yescomplemented
195C4×#41—216no—
196C4×#41—24no—
197C4×#41—28no—
198C4×#41—28no—
199C4×#41—24no—
200C4×#41—24no—
201C4×#41—24no—
202C2×C4×Q8—21no—
203C2×C4×Q8D411yescharacteristic
204C2×C4×Q8D411yescharacteristic
205C2×C4×Q8C2312yes—
206C2×C4×Q8C2311yescharacteristic
207C2×C4×Q8C2311yescharacteristic
208C2×C4×Q8C2312yes—
209C2×C4×D4—216no—
210C2×C4×D4—232no—
211C2×C4×D4—22no—
212C2×C4×D4—21no—
213C2×C4×D4—24no—
214C2×C4×D4—21no—
215C2×C4×D4—22no—
216C2×C4×D4—21no—
217C2×C4×D4—22no—
218C2×C4×D4—28no—
219C2×C4×D4—28no—
220C2×C4×D4—22no—
221C2×C4×D4—22no—
222C2×C4×D4—21no—
223C2×C4×D4—24no—
224C2×C4×D4—22no—
225C2×C4×D4—21no—
226C2×C4×D4—22no—
227C2×C4×D4—22no—
228C2×C4×D4—22no—
229C2×C4×D4—22no—
230C2×C4×D4—21no—
231C2×C4×D4—22no—
232C2×C4×D4—22no—
233C2×C4×D4—21no—
234C2×C4×D4D411yescharacteristic
235C2×C4×D4D412yes—
236C2×C4×D4D411yescharacteristic
237C2×C4×D4D412yes—
238C2×C4×D4C2312yes—
239C2×C4×D4C2312yes—
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2312yes—
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2312yes—
244C2×C4×D4C2312yes—
245C2×C4×D4C2312yes—
246C2×#117—22no—
247C2×#117—21no—
248C2×#117—21no—
249C2×#117—22no—
250C2×#117—21no—
251C2×#117C2311yescharacteristic
252C2×#117C2312yes—
253C2×#117C2311yescharacteristic
254C2×#117C2312yes—
255C2×#117C2311yescharacteristic
256C22×C4⋊C4—22no—
257C22×C4⋊C4—21no—
258C22×C4⋊C4—21no—
259C22×C4⋊C4—21no—
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264C22×C22⋊C4—21no—
265C22×C22⋊C4—22no—
266C22×C22⋊C4—22no—
267C22×C22⋊C4—22no—
268C22×C22⋊C4—22no—
269C22×C42—21no—
270C22×C42—22no—
271C22×C42C2311yescharacteristic
272C22×C42C2312yes—
273#452C2×C4116yescomplemented
274#450C2×C4116yescomplemented
275#449C2×C4116yescomplemented
276#447C2×C4116yescomplemented
277#442—28no—
278#440—28no—
279#440—28no—
280#440—28no—
281C4×Q16—28no—
282C4×SD16—28no—
283C4×D8—28no—
284C4×D8—28no—
285#428—24no—
286C2×#107—24no—
287C2×#107C2312yes—
288C2×#107C2312yes—
289C2×#107C2312yes—
290C2×#106C2312yes—
291#418—24no—
292#417—24no—
293#417—24no—
294#417C2×C418yescomplemented
295#416—24no—
296#416—24no—
297C2×#103C2312yes—
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2312yes—
303C2×#103C2312yes—
304C2×#102—24no—
305C2×#102C2×C418yescomplemented
306C2×#102C2312yes—
307C2×#102C2312yes—
308C2×#102C2312yes—
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2312yes—
314C2×#102C2312yes—
315C2×#102C2312yes—
316C2×#102C2312yes—
317C2×#102C2312yes—
318C2×#102C2312yes—
319#408—24no—
320#408C2×C418yescomplemented
321C2×C22⋊C8C2312yes—
322C2×C22⋊C8C2312yes—
323C2×C22⋊C8C2312yes—
324C2×C22⋊C8C2312yes—
325#405—24no—
326#405—24no—
327C2×#97C2312yes—
328C2×#97C2312yes—
329C2×C4×C8C2312yes—
330C2×C4×C8C2312yes—
331#391—21no—
332#391C2311yescharacteristic
333#391C2311yescharacteristic
334#390—21no—
335#390—22no—
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#389—22no—
339#389—21no—
340#389—21no—
341#389C2312yes—
342#389C2312yes—
343#388—22no—
344#388—22no—
345#388—22no—
346#388—22no—
347#387—22no—
348#387—22no—
349#386—22no—
350#386—21no—
351#386—22no—
352#386—21no—
353#386—22no—
354#385—22no—
355#385—22no—
356#380C2312yes—
357#380C2312yes—
358C4×C4⋊C4—21no—
359C4×C4⋊C4—21no—
360C4×C4⋊C4—22no—
361C4×C4⋊C4C2312yes—
362C4×C4⋊C4C2312yes—
363C4×C22⋊C4—22no—
364C4×C22⋊C4—22no—
365C4×C22⋊C4—21no—
366C4×C22⋊C4—22no—
367C4×C22⋊C4—21no—
368C2×#95—21no—
369#340C2311yescharacteristic
370#340C2311yescharacteristic
371#340C2312yes—
372#340C2312yes—
373#340C2311yescharacteristic
374#340C2311yescharacteristic
375#340C2312yes—
376#340C2312yes—
377#340C2312yes—
378#340C2312yes—
379#336C2311yescharacteristic
380#336C2311yescharacteristic
381#336C2311yescharacteristic
382#336C2311yescharacteristic
383#336C2312yes—
384#336C2312yes—
385C25—22no—
386C25—21no—
387H(5,𝔽2)—232no—
388H(5,𝔽2)—232no—
389H(5,𝔽2)—232no—
390H(5,𝔽2)—232no—
391C2×#41—28no—
392C2×#41—28no—
393C2×#41—28no—
394C2×#41—24no—
395C2×#41—24no—
396C2×#41—24no—
397C2×#41—24no—
398C2×#41—22no—
399C2×#41—22no—
400C2×#41—22no—
401C2×#41—24no—
402C2×#41—22no—
403C2×#41—22no—
404C2×#41—22no—
405C2×#41—22no—
406C2×#41—22no—
407C2×#41—22no—
408C2×#41—22no—
409C2×#41—22no—
410C2×#41—22no—
411C2×#41C22×C418yes—
412C2×#41C22×C414yes—
413C2×#41C22×C414yes—
414C2×#41C22×C414yescomplemented
415C2×#41C2×D414yes—
416C2×#41#4114yes—
417C2×#41#4114yes—
418C22×Q8C2×D411yescharacteristic
419C22×Q8C2411yescharacteristic
420C22×Q8C2411yescharacteristic
421C22×D4—216no—
422C22×D4—28no—
423C22×D4—216no—
424C22×D4—28no—
425C22×D4—22no—
426C22×D4—21no—
427C22×D4—216no—
428C22×D4—28no—
429C22×D4—24no—
430C22×D4—24no—
431C22×D4—24no—
432C22×D4—24no—
433C22×D4—21no—
434C22×D4—22no—
435C22×D4—22no—
436C22×D4—21no—
437C22×D4—22no—
438C22×D4—24no—
439C22×D4—22no—
440C22×D4—22no—
441C22×D4C22×C418yes—
442C22×D4C22×C414yes—
443C22×D4C2×D412yes—
444C22×D4C2×D411yescharacteristic
445C22×D4C2×D414yes—
446C22×D4#4114yes—
447C22×D4C2411yescharacteristic
448C22×D4C2411yescharacteristic
449C22×D4C2412yes—
450C23×C4—22no—
451C23×C4—21no—
452C23×C4—28no—
453C23×C4—216no—
454C23×C4—22no—
455C23×C4—21no—
456C23×C4—21no—
457C23×C4—21no—
458C23×C4—21no—
459C23×C4—22no—
460C23×C4—21no—
461C23×C4—22no—
462C23×C4—22no—
463C23×C4—22no—
464C23×C4—22no—
465C23×C4—21no—
466C23×C4—22no—
467C23×C4—82no—
468C23×C4—84no—
469C23×C4—84no—
470C23×C4—82no—
471C23×C4C2×D411yescharacteristic
472C23×C4C2×D412yes—
473C23×C4C2×D411yescharacteristic
474C23×C4C2×D412yes—
475C23×C4C2412yes—
476C23×C4C2411yescharacteristic
477AGL(1,ℤ/8)—232no—
478#135—232no—
479C2×Q16—22no—
480C2×Q16—22no—
481C2×Q16C22×C414yescomplemented
482C2×SD16—22no—
483C2×SD16—22no—
484C2×SD16—22no—
485C2×SD16—24no—
486C2×SD16—22no—
487C2×SD16—24no—
488C2×SD16C22×C414yescomplemented
489C2×SD16C22×C414yescomplemented
490C2×SD16C22×C418yescomplemented
491C2×D8—22no—
492C2×D8—24no—
493C2×D8—22no—
494C2×D8—24no—
495C2×D8C22×C414yescomplemented
496C2×D8C22×C418yescomplemented
497C2×M16—22no—
498C2×M16—22no—
499C2×M16—22no—
500C2×M16—22no—
501C2×M16—22no—
502C2×M16C22×C414yescomplemented
503C22×C8—22no—
504C22×C8—22no—
505C22×C8—22no—
506C22×C8—22no—
507C22×C8—22no—
508C22×C8C22×C414yescomplemented
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2412yes—
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2412yes—
515C22⋊Q8—28no—
516C22⋊Q8—24no—
517C22⋊Q8C22×C418yescomplemented
518#121—28no—
519#121—216no—
520#121—24no—
521#121C22×C418yescomplemented
522C4×Q8—28no—
523C4×Q8—22no—
524C4×Q8—22no—
525C4×Q8—24no—
526C4×Q8—24no—
527C4×Q8—22no—
528C4×Q8—22no—
529C4×Q8—24no—
530C4×Q8—24no—
531C4×Q8—24no—
532C4×Q8C2×D418yes—
533C4×D4—28no—
534C4×D4—216no—
535C4×D4—28no—
536C4×D4—216no—
537C4×D4—216no—
538C4×D4—216no—
539C4×D4—216no—
540C4×D4—216no—
541C4×D4—28no—
542C4×D4—216no—
543C4×D4—28no—
544C4×D4—28no—
545C4×D4—216no—
546C4×D4—216no—
547C4×D4—22no—
548C4×D4—24no—
549C4×D4—24no—
550C4×D4—22no—
551C4×D4—24no—
552C4×D4—28no—
553C4×D4—28no—
554C4×D4—24no—
555C4×D4—22no—
556C4×D4—24no—
557C4×D4—24no—
558C4×D4—22no—
559C4×D4—28no—
560C4×D4—216no—
561C4×D4—28no—
562C4×D4—24no—
563C4×D4—24no—
564C4×D4—24no—
565C4×D4—24no—
566C4×D4—24no—
567C4×D4—48no—
568C4×D4—84no—
569C4×D4C2×D418yes—
570C4×D4C2×D418yes—
571C4×D4C2×D418yes—
572#117—216no—
573#117—216no—
574#117—28no—
575#117—22no—
576#117—28no—
577#117—24no—
578#117—24no—
579#117—24no—
580#117—24no—
581#117—22no—
582#117—22no—
583#117—44no—
584#117C2×D414yes—
585#117C2×D414yes—
586#117C2×D414yes—
587C2×C4⋊C4—216no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—28no—
598C2×C4⋊C4—24no—
599C2×C4⋊C4—24no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—22no—
606C2×C4⋊C4—44no—
607C2×C4⋊C4—82no—
608C2×C4⋊C4C22×C414yescomplemented
609C2×C4⋊C4C2×D412yes—
610C2×C4⋊C4C2×D412yes—
611C2×C4⋊C4C2×D414yes—
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2411yescharacteristic
621C2×C22⋊C4—28no—
622C2×C22⋊C4—216no—
623C2×C22⋊C4—216no—
624C2×C22⋊C4—216no—
625C2×C22⋊C4—22no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—22no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—22no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—216no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—22no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—22no—
642C2×C22⋊C4—22no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4C2×D412yes—
646C2×C22⋊C4C2×D412yes—
647C2×C22⋊C4C2×D412yes—
648C2×C42—216no—
649C2×C42—28no—
650C2×C42—21no—
651C2×C42—22no—
652C2×C42—22no—
653C2×C42—21no—
654C2×C42—21no—
655C2×C42—22no—
656C2×C42—22no—
657C2×C42—24no—
658C2×C42—24no—
659C2×C42—22no—
660C2×C42—21no—
661C2×C42—22no—
662C2×C42—22no—
663C2×C42C2×D412yes—
664C2×C42C2×D411yescharacteristic
665C2×C42C2×D411yescharacteristic
666C2×C42C2×D412yes—
667C2×C42C2411yescharacteristic
668C2×C42C2411yescharacteristic
669C2×C42C2412yes—
670#107—24no—
671#107—24no—
672#107—24no—
673#106—24no—
674#103—24no—
675#103—22no—
676#103—22no—
677#103—22no—
678#103—22no—
679#103—24no—
680#103C22×C418yescomplemented
681#102—24no—
682#102—24no—
683#102—24no—
684#102—22no—
685#102—22no—
686#102—24no—
687#102—24no—
688#102—22no—
689#102—22no—
690#102—24no—
691#102C22×C418yescomplemented
692#102C22×C418yescomplemented
693#102C22×C418yescomplemented
694C22⋊C8—24no—
695C22⋊C8—24no—
696C22⋊C8C22×C418yescomplemented
697C22⋊C8C22×C418yescomplemented
698#97—24no—
699#97—24no—
700C4×C8—24no—
701C4×C8—24no—
702#95—22no—
703#95—22no—
704#95—21no—
705#95—21no—
706#95—22no—
707#95—22no—
708#95—22no—
709#95—21no—
710#95—21no—
711#95—22no—
712C24—28no—
713C24—28no—
714C24—22no—
715C24—21no—
716C24—28no—
717C24—24no—
718C24—24no—
719C24—24no—
720C24—21no—
721C24—81no—
722C24—81no—
723C24—82no—
724C24—82no—
725C24—81no—
726C24—81no—
727C24—82no—
728C24—82no—
729C24C22×D412yes—
730C24C22×D411yescharacteristic
731#41—216no—
732#41—216no—
733#41—264no—
734#41—216no—
735#41—216no—
736#41—28no—
737#41—28no—
738#41—28no—
739#41—28no—
740#41—28no—
741#41—28no—
742#41—28no—
743#41—28no—
744#41—28no—
745#41—44no—
746#41—44no—
747#41C4×D4116yescomplemented
748C2×Q8—22no—
749C2×Q8—22no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8C4×D414yes—
759C2×Q8C23×C412yes—
760C2×Q8C23×C412yes—
761C2×Q8C22×D412yes—
762C2×Q8C2×#4112yes—
763C2×D4—28no—
764C2×D4—28no—
765C2×D4—28no—
766C2×D4—28no—
767C2×D4—2128no—
768C2×D4—216no—
769C2×D4—216no—
770C2×D4—264no—
771C2×D4—28no—
772C2×D4—24no—
773C2×D4—24no—
774C2×D4—24no—
775C2×D4—24no—
776C2×D4—24no—
777C2×D4—216no—
778C2×D4—216no—
779C2×D4—24no—
780C2×D4—28no—
781C2×D4—28no—
782C2×D4—24no—
783C2×D4—28no—
784C2×D4—22no—
785C2×D4—24no—
786C2×D4—22no—
787C2×D4—24no—
788C2×D4—28no—
789C2×D4—28no—
790C2×D4—22no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—22no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—22no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—42no—
802C2×D4—42no—
803C2×D4—82no—
804C2×D4—82no—
805C2×D4C4×D418yes—
806C2×D4C4×D414yes—
807C2×D4C4×D4116yescomplemented
808C2×D4C23×C412yes—
809C2×D4C23×C412yes—
810C2×D4C23×C414yes—
811C2×D4C22×D412yes—
812C2×D4C22×D414yes—
813C2×D4C2×#4112yes—
814C2×D4C2×#4114yes—
815C22×C4—28no—
816C22×C4—28no—
817C22×C4—21no—
818C22×C4—28no—
819C22×C4—24no—
820C22×C4—24no—
821C22×C4—24no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—28no—
827C22×C4—24no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—22no—
833C22×C4—21no—
834C22×C4—24no—
835C22×C4—28no—
836C22×C4—28no—
837C22×C4—24no—
838C22×C4—22no—
839C22×C4—24no—
840C22×C4—24no—
841C22×C4—24no—
842C22×C4—22no—
843C22×C4—24no—
844C22×C4—24no—
845C22×C4—28no—
846C22×C4—28no—
847C22×C4—28no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—22no—
851C22×C4—42no—
852C22×C4—41no—
853C22×C4—42no—
854C22×C4—42no—
855C22×C4—41no—
856C22×C4—41no—
857C22×C4—42no—
858C22×C4—44no—
859C22×C4—42no—
860C22×C4—42no—
861C22×C4—44no—
862C22×C4—42no—
863C22×C4—42no—
864C22×C4—44no—
865C22×C4—82no—
866C22×C4—82no—
867C22×C4—81no—
868C22×C4—81no—
869C22×C4—82no—
870C22×C4—82no—
871C22×C4—82no—
872C22×C4—82no—
873C22×C4—82no—
874C22×C4—82no—
875C22×C4—82no—
876C22×C4—82no—
877C22×C4—832no—
878C22×C4—816no—
879C22×C4—81no—
880C22×C4—81no—
881C22×C4—81no—
882C22×C4—82no—
883C22×C4—81no—
884C22×C4—82no—
885C22×C4—81no—
886C22×C4—81no—
887C22×C4C23×C414yes—
888C22×C4C23×C412yes—
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D412yes—
893C22×C4C22×D412yes—
894C22×C4C22×D412yes—
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D412yes—
898C22×C4C22×D412yes—
899C22×C4C2×#4114yes—
900C22×C4C2×#4112yes—
901C22×C4C2×#4112yes—
902C22×C4C2×#4112yes—
903C22×C4C2511yescharacteristic
904Q16—28no—
905SD16—28no—
906SD16—28no—
907SD16—216no—
908D8—28no—
909D8—216no—
910M16—28no—
911M16—44no—
912C2×C8—28no—
913C2×C8—21no—
914C2×C8—22no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—22no—
919C2×C8—21no—
920C2×C8—22no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—22no—
925C2×C8—22no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—44no—
929C2×C8C23×C412yes—
930C2×C8C23×C412yes—
931C2×C8C23×C414yes—
932C4⋊C4—24no—
933C4⋊C4—28no—
934C4⋊C4—24no—
935C4⋊C4—24no—
936C4⋊C4—28no—
937C4⋊C4—28no—
938C4⋊C4—24no—
939C4⋊C4—24no—
940C4⋊C4—24no—
941C4⋊C4—21no—
942C4⋊C4—22no—
943C4⋊C4—21no—
944C4⋊C4—22no—
945C4⋊C4—22no—
946C4⋊C4—22no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—42no—
952C4⋊C4—44no—
953C4⋊C4—44no—
954C4⋊C4—82no—
955C4⋊C4#12014yes—
956C4⋊C4#12014yes—
957C4⋊C4C23×C414yes—
958C4⋊C4C22×D412yes—
959C4⋊C4C22×D412yes—
960C4⋊C4C22×D414yes—
961C22⋊C4—28no—
962C22⋊C4—28no—
963C22⋊C4—24no—
964C22⋊C4—24no—
965C22⋊C4—28no—
966C22⋊C4—28no—
967C22⋊C4—24no—
968C22⋊C4—28no—
969C22⋊C4—28no—
970C22⋊C4—28no—
971C22⋊C4—28no—
972C22⋊C4—24no—
973C22⋊C4—24no—
974C22⋊C4—42no—
975C22⋊C4—42no—
976C22⋊C4—44no—
977C22⋊C4—42no—
978C22⋊C4—81no—
979C22⋊C4—81no—
980C22⋊C4—82no—
981C22⋊C4—82no—
982C22⋊C4#12018yes—
983C42—24no—
984C42—24no—
985C42—28no—
986C42—24no—
987C42—22no—
988C42—28no—
989C42—24no—
990C42—24no—
991C42—22no—
992C42—21no—
993C42—21no—
994C42—21no—
995C42—21no—
996C42—44no—
997C42—42no—
998C42—82no—
999C42—82no—
1000C42C22×D414yes—
1001C42C22×D414yes—
1002C23—21no—
1003C23—21no—
1004C23—21no—
1005C23—21no—
1006C23—232no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—24no—
1011C23—22no—
1012C23—22no—
1013C23—24no—
1014C23—22no—
1015C23—22no—
1016C23—24no—
1017C23—22no—
1018C23—22no—
1019C23—216no—
1020C23—22no—
1021C23—42no—
1022C23—41no—
1023C23—42no—
1024C23—41no—
1025C23—42no—
1026C23—41no—
1027C23—42no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—84no—
1036C23—84no—
1037C23—84no—
1038C23—84no—
1039C23—84no—
1040C23—84no—
1041C23—88no—
1042C23—88no—
1043C23—88no—
1044C23—88no—
1045C23—88no—
1046C23—88no—
1047C23C2×C4×D414yes—
1048C23C2×C4×D412yes—
1049C23C2×#12012yes—
1050C23#52512yes—
1051C23C23×D411yescharacteristic
1052Q8—22no—
1053Q8—22no—
1054Q8—22no—
1055Q8—28no—
1056Q8—22no—
1057Q8—22no—
1058Q8—41no—
1059Q8—41no—
1060Q8C2×C4×D414yes—
1061D4—232no—
1062D4—232no—
1063D4—216no—
1064D4—216no—
1065D4—24no—
1066D4—22no—
1067D4—22no—
1068D4—22no—
1069D4—22no—
1070D4—24no—
1071D4—22no—
1072D4—24no—
1073D4—28no—
1074D4—216no—
1075D4—48no—
1076D4—41no—
1077D4—41no—
1078D4—88no—
1079D4C2×C4×D414yes—
1080D4C2×C4×D418yes—
1081C2×C4—232no—
1082C2×C4—22no—
1083C2×C4—21no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—21no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—24no—
1096C2×C4—24no—
1097C2×C4—216no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—24no—
1104C2×C4—22no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—22no—
1108C2×C4—21no—
1109C2×C4—24no—
1110C2×C4—22no—
1111C2×C4—21no—
1112C2×C4—48no—
1113C2×C4—44no—
1114C2×C4—48no—
1115C2×C4—416no—
1116C2×C4—42no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—42no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—42no—
1124C2×C4—41no—
1125C2×C4—42no—
1126C2×C4—48no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—42no—
1130C2×C4—41no—
1131C2×C4—42no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—42no—
1136C2×C4—84no—
1137C2×C4—88no—
1138C2×C4—88no—
1139C2×C4—88no—
1140C2×C4—82no—
1141C2×C4—84no—
1142C2×C4—84no—
1143C2×C4—84no—
1144C2×C4—88no—
1145C2×C4—88no—
1146C2×C4—164no—
1147C2×C4—162no—
1148C2×C4C2×C4×D414yes—
1149C2×C4C2×C4×D414yes—
1150C2×C4C2×C4×D414yes—
1151C2×C4C2×C4×D412yes—
1152C2×C4C2×#12014yes—
1153C2×C4C2×#12014yes—
1154C2×C4C2×#12012yes—
1155C2×C4#52514yes—
1156C2×C4#52514yes—
1157C2×C4#52512yes—
1158C2×C4#57612yes—
1159C2×C4C24×C411yescharacteristic
1160C2×C4C23×D411yescharacteristic
1161C2×C4C23×D411yescharacteristic
1162C2×C4C22×#4111yescharacteristic
1163C2×C4C22×#4111yescharacteristic
1164C2×C4C22×#4111yescharacteristic
1165C8—22no—
1166C8—22no—
1167C8—24no—
1168C8—41no—
1169C8—41no—
1170C8—42no—
1171C22—22no—
1172C22—22no—
1173C22—22no—
1174C22—22no—
1175C22—22no—
1176C22—22no—
1177C22—24no—
1178C22—24no—
1179C22—24no—
1180C22—28no—
1181C22—24no—
1182C22—44no—
1183C22—42no—
1184C22—44no—
1185C22—42no—
1186C22—42no—
1187C22—44no—
1188C22—42no—
1189C22—42no—
1190C22—44no—
1191C22—42no—
1192C22—42no—
1193C22—42no—
1194C22—44no—
1195C22—42no—
1196C22—44no—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—816no—
1202C22—832no—
1203C22—81no—
1204C22—81no—
1205C22—81no—
1206C22—81no—
1207C22C4×#12014yes—
1208C22C22×C4×D411yescharacteristic
1209C22C22×#12011yescharacteristic
1210C22C2×#52511yescharacteristic
1211C22C2×#57611yescharacteristic
1212C22#358411yescharacteristic
1213C22#358511yescharacteristic
1214C22#358611yescharacteristic
1215C4—22no—
1216C4—24no—
1217C4—24no—
1218C4—24no—
1219C4—24no—
1220C4—44no—
1221C4—41no—
1222C4—42no—
1223C4—44no—
1224C4—41no—
1225C4—41no—
1226C4—42no—
1227C4—42no—
1228C4—81no—
1229C4—81no—
1230C4—82no—
1231C4C4×#12014yes—
1232C4C22×C4×D411yescharacteristic
1233C4C22×C4×D411yescharacteristic
1234C4C2×#52511yescharacteristic
1235C4C2×#52511yescharacteristic
1236C2—24no—
1237C2—44no—
1238C2—48no—
1239C2—44no—
1240C2—82no—
1241C2C2×C4×#12011yescharacteristic
1242C2C4×#57611yescharacteristic
1243C2#6017411yescharacteristic
1244C2#6037211yescharacteristic
1245C2#6037711yescharacteristic
1246C2#6059611yescharacteristic
1247C2#6060111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3012C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×#41 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×C4×H(5,𝔽2)C2semidirect
3. C2×#2951C2semidirect
4. C2×#2946C2semidirect
5. #34267C2semidirect
6. #21465C2semidirect
7. #21460C2semidirect
8. #21459C2semidirect
9. #21458C2semidirect
10. #21456C2semidirect
11. #21453C2semidirect
12. C4×#452C2semidirect
13. C4×#447C2semidirect
14. #20925C2semidirect
15. #20924C2semidirect
16. #20915C2semidirect
17. #20875C2semidirect
18. C2×#1862C2semidirect
19. #20847C2semidirect
20. #20602C2semidirect
21. #20416C2semidirect
22. #20415C2semidirect
23. #20378C2semidirect
34. C2×#520C22semidirect
47. #3012C4semidirect
54. C2×#442C22semidirect
55. C2×#440C22semidirect
56. C2×#440C22semidirect
57. C2×#440C22semidirect
58. C2×C4×Q16C22semidirect
59. C2×C4×SD16C22semidirect
60. C2×C4×D8C22semidirect
61. C2×C4×D8C22semidirect
62. C2×#428C22semidirect
63. C22×#107C22semidirect
66. C2×#417C22semidirect
69. C2×#416C22semidirect
74. C2×#405C22semidirect
75. C2×#405C22semidirect
82. #2324C22semidirect
83. #2323C22semidirect
85. C4×C22⋊Q8C22semidirect
86. C4×#121C22semidirect
87. #2297C22semidirect
88. C2×#389C22semidirect
89. #2274C22semidirect
90. #1880C22semidirect
91. #1880C22semidirect
92. #1879C22semidirect
93. #1879C22semidirect
94. #1879C22semidirect
95. #1879C22semidirect
96. #1878C22semidirect
97. #1878C22semidirect
98. #1877C22semidirect
99. #1877C22semidirect
100. #1877C22semidirect
101. #1877C22semidirect
102. #1875C22semidirect
103. #1874C22semidirect
104. #1873C22semidirect
105. #1872C22semidirect
106. #1865C22semidirect
107. #1864C22semidirect
108. #1863C22semidirect
109. #1862C22semidirect
110. #1862C22semidirect
111. #1862C22semidirect
112. #1862C22semidirect
113. #1862C22semidirect
114. #1854C22semidirect
115. #1854C22semidirect
116. #1852C22semidirect
117. #1852C22semidirect
122. #1763C22semidirect
123. #1762C22semidirect
124. #1762C22semidirect
125. #1762C22semidirect
126. C4×#103C22semidirect
127. C4×#102C22semidirect
128. C4×#102C22semidirect
129. C4×#102C22semidirect
130. #1750C22semidirect
131. #1750C22semidirect
132. #1749C22semidirect
133. C4×C22⋊C8C22semidirect
134. #1736C22semidirect
135. #1736C22semidirect
136. #1735C22semidirect
137. C2×#340C22semidirect
138. #1728C22semidirect
139. C2×#336C22semidirect
145. C2×H(5,𝔽2)C2×C4semidirect
159. C2×AGL(1,ℤ/8)C2×C4semidirect
162. C2×#135C2×C4semidirect
174. #537C2×C4semidirect
188. #520D4semidirect
194. #518D4semidirect
273. #452C2×C4semidirect
274. #450C2×C4semidirect
275. #449C2×C4semidirect
276. #447C2×C4semidirect
294. #417C2×C4semidirect
305. C2×#102C2×C4semidirect
320. #408C2×C4semidirect
414. C2×#41C22×C4semidirect
481. C2×Q16C22×C4semidirect
488. C2×SD16C22×C4semidirect
489. C2×SD16C22×C4semidirect
490. C2×SD16C22×C4semidirect
495. C2×D8C22×C4semidirect
496. C2×D8C22×C4semidirect
502. C2×M16C22×C4semidirect
508. C22×C8C22×C4semidirect
517. C22⋊Q8C22×C4semidirect
521. #121C22×C4semidirect
608. C2×C4⋊C4C22×C4semidirect
680. #103C22×C4semidirect
691. #102C22×C4semidirect
692. #102C22×C4semidirect
693. #102C22×C4semidirect
696. C22⋊C8C22×C4semidirect
697. C22⋊C8C22×C4semidirect
747. #41C4×D4semidirect
807. C2×D4C4×D4semidirect

Maximal subgroups

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

subgroupindex
C2×C4×H(5,𝔽2)2
C2×#30122
C2×#29512
C2×#29462
#342672
#214652
#214602
#214592
#214582
#214562
#214532
C4×#4522
C4×#4472
#209252
#209242
#209152
#208752
C2×#18622
#208472
#206022
#204162
#204152
#203782