Finite Group Databasebeta

← #6668950

Subgroups — #6668950

Order 512.

2681 conjugacy classes of subgroups.

The subgroup lattice has 1306 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3187C211yesmaximal, characteristic, complemented
2C22×#481C211yesmaximal, characteristic, complemented
3D4×#121C211yesmaximal, characteristic
4C2×#2417C211yesmaximal, characteristic, complemented
5#32979C211yesmaximal, characteristic, complemented
6#31189C212yesmaximal, complemented
7#31024C212yesmaximal, complemented
8#30703C212yesmaximal, complemented
9#30559C212yesmaximal, complemented
10#29755C211yesmaximal, characteristic, complemented
11#29593C211yesmaximal, characteristic, complemented
12#28305C211yesmaximal, characteristic, complemented
13#28115C211yesmaximal, characteristic, complemented
14#26128C212yesmaximal, complemented
15#25112C212yesmaximal, complemented
16#24776C212yesmaximal, complemented
17#24553C211yesmaximal, characteristic, complemented
18#24432C212yesmaximal, complemented
19#24381C211yesmaximal, characteristic, complemented
20#24005C211yesmaximal, characteristic, complemented
21#23919C211yesmaximal, characteristic, complemented
22D4×C22⋊C8C211yesmaximal, characteristic, complemented
23#22076C211yesmaximal, characteristic, complemented
24C2×D42—21no—
25C2×D42C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic, complemented
27C22×C22⋊Q8C2211yescharacteristic, complemented
28C22×#121C2211yescharacteristic
29C22×#121C2211yescharacteristic
30C22×C4×D4C2211yescharacteristic
31C23×C4⋊C4C2211yescharacteristic, complemented
32#3187—28no—
33C2×#481—28no—
34C2×#481C2211yescharacteristic
35C2×#481C2211yescharacteristic
36C2×#481C2212yescomplemented
37C2×#481C2211yescharacteristic, complemented
38C2×#481C2211yescharacteristic, complemented
39C2×#481C2211yescharacteristic, complemented
40C2×#481C2212yescomplemented
41C2×#481C2211yescharacteristic, complemented
42C2×#483C2212yescomplemented
43C2×#465C2212yescomplemented
44C2×#465C2212yescomplemented
45C2×#465C2212yescomplemented
46C2×#448C2211yescharacteristic
47C2×#448C2211yescharacteristic, complemented
48C2×#448C2211yescharacteristic, complemented
49C2×#450C2212yescomplemented
50C2×#450C2212yescomplemented
51C2×C8×D4C2212yescomplemented
52C22×#106C2212yescomplemented
53C22×#102C2212yescomplemented
54C22×C22⋊C8C2211yescharacteristic, complemented
55C22×C22⋊C8C2211yescharacteristic, complemented
56#2856C2211yescharacteristic
57#2847C2211yescharacteristic
58#2847C2211yescharacteristic
59#2541C2211yescharacteristic
60#2537C2211yescharacteristic
61#2428—21no—
62#2424—21no—
63#2424—21no—
64#2417—21no—
65#2417—21no—
66#2417—21no—
67#2417—21no—
68#2417C2212yes—
69#2417C2212yescomplemented
70#2417C2212yescomplemented
71#2417C2212yescomplemented
72#2416—21no—
73#2416C2211yescharacteristic
74#2416C2211yescharacteristic
75#2410—21no—
76#2410—21no—
77#2408C2211yescharacteristic
78#2408C2211yescharacteristic
79C2×#398—21no—
80C2×#396—21no—
81D4×C4⋊C4C2211yescharacteristic
82D4×C22⋊C4—21no—
83C4×#121C2211yescharacteristic
84C2×#391C2211yescharacteristic, complemented
85C2×#389C2211yescharacteristic, complemented
86C2×#386—21no—
87C2×#380—21no—
88C2×#380C2211yescharacteristic, complemented
89#2096C2212yescomplemented
90#2084C2212yescomplemented
91#2077C2212yescomplemented
92#2066C2212yescomplemented
93#2065C2212yescomplemented
94#2065C2212yescomplemented
95#2055C2212yescomplemented
96#2041C2212yescomplemented
97#2035C2212yescomplemented
98#2035C2212yescomplemented
99#2035C2212yescomplemented
100#2034C2212yescomplemented
101#2034C2212yescomplemented
102#2034C2212yescomplemented
103#2014C2212yescomplemented
104#2000C2212yescomplemented
105#2000C2212yescomplemented
106#2000C2212yescomplemented
107#2000C2212yescomplemented
108#2000C2212yescomplemented
109#1968C2212yescomplemented
110#1968C2212yescomplemented
111#1954C2212yescomplemented
112#1941C2212yescomplemented
113#1934C2212yescomplemented
114#1927C2212yescomplemented
115#1920C2212yescomplemented
116#1893C2212yescomplemented
117#1892C2212yescomplemented
118#1877C2212yescomplemented
119#1874C2211yescharacteristic
120#1874C2212yescomplemented
121#1874C2211yescharacteristic, complemented
122#1874C2211yescharacteristic, complemented
123#1874C2212yescomplemented
124#1872C2212yescomplemented
125#1869C2212yes—
126#1869C2212yescomplemented
127#1864C2212yescomplemented
128#1853C2212yescomplemented
129#1853C2212yescomplemented
130#1853C2211yescharacteristic, complemented
131#1853C2212yescomplemented
132#1824C2211yescharacteristic, complemented
133#1824C2211yescharacteristic, complemented
134#1807C2212yescomplemented
135#1797C2211yescharacteristic, complemented
136#1787C2211yescharacteristic, complemented
137#1786C2212yescomplemented
138#1779C2211yescharacteristic, complemented
139#1779C2211yescharacteristic, complemented
140C4×C22⋊C8C2211yescharacteristic, complemented
141C23×Q8C2311yescharacteristic
142C23×D4—21no—
143C23×D4—21no—
144C23×D4—21no—
145C23×D4D411yescharacteristic
146C23×D4C2311yescharacteristic
147C23×D4C2311yescharacteristic
148C24×C4—21no—
149C24×C4C2311yescharacteristic
150C24×C4C2311yescharacteristic
151C22×SD16C2312yes—
152C22×SD16C2312yes—
153C22×SD16C2312yes—
154C23×C8C2312yes—
155C23×C8C2312yes—
156D42—44no—
157D42—48no—
158C2×#127—21no—
159C2×#127C2311yescharacteristic
160C2×C22⋊Q8—21no—
161C2×C22⋊Q8—21no—
162C2×C22⋊Q8—21no—
163C2×C22⋊Q8—21no—
164C2×C22⋊Q8—24no—
165C2×C22⋊Q8—42no—
166C2×C22⋊Q8—44no—
167C2×C22⋊Q8C2312yes—
168C2×C22⋊Q8C2312yes—
169C2×C22⋊Q8C2312yes—
170C2×C22⋊Q8C2312yes—
171C2×#121—21no—
172C2×#121—21no—
173C2×#121—21no—
174C2×#121—21no—
175C2×#121—21no—
176C2×#121—21no—
177C2×#121—21no—
178C2×#121—21no—
179C2×#121—21no—
180C2×#121—21no—
181C2×#121—24no—
182C2×#121—24no—
183C2×#121—42no—
184C2×#121—42no—
185C2×#121C2311yescharacteristic
186C2×#121C2311yescharacteristic
187C2×#121C2311yescharacteristic
188C2×#121C2311yescharacteristic
189C2×#121C2311yescharacteristic
190C2×#121C2311yescharacteristic
191C2×#121C2311yescharacteristic
192C2×#121C2311yescharacteristic
193C2×#121C2311yescharacteristic
194C2×#121C2311yescharacteristic
195C2×#121C2311yescharacteristic
196C2×#120—21no—
197C2×#120—21no—
198C2×#120—21no—
199C2×#120—21no—
200C2×#120—21no—
201C2×#120—21no—
202C2×C4×D4—21no—
203C2×C4×D4—21no—
204C2×C4×D4—44no—
205C2×C4×D4D411yescharacteristic
206C2×C4×D4D411yescharacteristic
207C2×C4×D4D411yescharacteristic
208C2×C4×D4D411yescharacteristic
209C2×C4×D4C2311yescharacteristic
210C2×C4×D4C2311yescharacteristic
211C2×C4×D4C2311yescharacteristic
212C2×C4×D4C2311yescharacteristic
213C2×C4×D4C2311yescharacteristic
214C22×C4⋊C4—24no—
215C22×C4⋊C4—21no—
216C22×C4⋊C4—21no—
217C22×C4⋊C4—21no—
218C22×C4⋊C4—21no—
219C22×C4⋊C4—21no—
220C22×C4⋊C4—21no—
221C22×C4⋊C4—42no—
222C22×C4⋊C4D411yescharacteristic
223C22×C4⋊C4C2311yescharacteristic
224C22×C4⋊C4C2311yescharacteristic
225C22×C4⋊C4C2312yes—
226C22×C4⋊C4C2311yescharacteristic
227C22×C4⋊C4C2312yes—
228C22×C4⋊C4C2311yescharacteristic
229C22×C4⋊C4C2311yescharacteristic
230C22×C22⋊C4—21no—
231C22×C22⋊C4—21no—
232C22×C22⋊C4—21no—
233C22×C22⋊C4—21no—
234C22×C22⋊C4—21no—
235C22×C22⋊C4D411yescharacteristic
236C22×C22⋊C4D411yescharacteristic
237C22×C42C2311yescharacteristic
238#483—28no—
239#481—24no—
240#481—24no—
241#481—24no—
242#481—28no—
243#481—28no—
244#481—24no—
245#481—42no—
246#481D418yescomplemented
247#465—28no—
248#465—28no—
249#465—44no—
250#450—28no—
251#450—44no—
252#448—24no—
253#448—24no—
254#448—42no—
255C8×D4—44no—
256C2×#106—28no—
257C2×#106C2312yes—
258C2×#106C2312yes—
259C2×#106C2312yes—
260C2×#106C2312yes—
261C2×#106C2312yes—
262C2×#106C2312yes—
263C2×#106C2312yes—
264C2×C4⋊C8C2312yes—
265C2×#103C2312yes—
266C2×#103C2312yes—
267C2×#103C2312yes—
268C2×#103C2312yes—
269C2×#103C2312yes—
270C2×#102—28no—
271C2×#102C2312yes—
272C2×#102C2312yes—
273C2×#102C2312yes—
274C2×#102C2312yes—
275C2×#102C2312yes—
276C2×#102C2312yes—
277C2×#102C2312yes—
278C2×#102C2312yes—
279C2×#102C2312yes—
280C2×C22⋊C8—24no—
281C2×C22⋊C8—24no—
282C2×C22⋊C8C2311yescharacteristic
283C2×C22⋊C8C2311yescharacteristic
284C2×C22⋊C8C2312yes—
285C2×C22⋊C8C2312yes—
286C2×C22⋊C8C2311yescharacteristic
287C2×C22⋊C8C2312yes—
288C2×C22⋊C8C2312yes—
289C2×C22⋊C8C2312yes—
290C2×C22⋊C8C2312yes—
291C2×C22⋊C8C2311yescharacteristic
292C2×C4×C8C2312yes—
293#398—22no—
294#398—22no—
295#398—22no—
296#398—22no—
297#396—21no—
298#396—21no—
299#396—22no—
300#396—22no—
301#396—22no—
302#396—22no—
303#394—21no—
304#394—21no—
305#394—21no—
306#394—21no—
307#394—21no—
308#394—21no—
309#392—21no—
310#392—21no—
311#392—21no—
312#392—21no—
313#391—21no—
314#391—21no—
315#391C2312yes—
316#391C2312yes—
317#390—21no—
318#390—21no—
319#390—21no—
320#390C2311yescharacteristic
321#390C2311yescharacteristic
322#390C2311yescharacteristic
323#389—21no—
324#389—21no—
325#389—21no—
326#389C2312yes—
327#389C2311yescharacteristic
328#389C2312yes—
329#388—21no—
330#386—22no—
331#386—22no—
332#386—22no—
333#386—22no—
334#386—21no—
335#386—21no—
336#386—21no—
337#386—21no—
338#386—21no—
339#386—21no—
340#386—21no—
341#386—21no—
342#386—21no—
343#385—21no—
344#385—21no—
345#384C2311yescharacteristic
346#380—21no—
347#380—21no—
348#380—21no—
349#380—22no—
350#380—22no—
351#380—22no—
352#380—22no—
353#380C2311yescharacteristic
354#380C2312yes—
355#380C2311yescharacteristic
356#380C2312yes—
357#380C2311yescharacteristic
358#380C2311yescharacteristic
359#380C2311yescharacteristic
360#379—21no—
361#379—21no—
362C4×C4⋊C4C2311yescharacteristic
363C4×C22⋊C4—21no—
364C2×#95—21no—
365C2×#95—21no—
366C2×#95—21no—
367C2×#95—21no—
368#340C2312yes—
369#340C2312yes—
370#340C2312yes—
371#340C2312yes—
372#340C2312yes—
373#340C2312yes—
374#340C2312yes—
375#340C2312yes—
376#336C2312yes—
377#336C2312yes—
378C25—21no—
379C25—21no—
380C25C2×D411yescharacteristic
381C25C2×D411yescharacteristic
382C22×Q8—21no—
383C22×Q8—22no—
384C22×Q8—22no—
385C22×Q8—42no—
386C22×Q8—42no—
387C22×Q8C2412yes—
388C22×D4—21no—
389C22×D4—22no—
390C22×D4—22no—
391C22×D4—21no—
392C22×D4—21no—
393C22×D4—21no—
394C22×D4—21no—
395C22×D4—21no—
396C22×D4—21no—
397C22×D4—21no—
398C22×D4—21no—
399C22×D4—21no—
400C22×D4—21no—
401C22×D4—21no—
402C22×D4—21no—
403C22×D4—21no—
404C22×D4—21no—
405C22×D4—24no—
406C22×D4—42no—
407C22×D4—41no—
408C22×D4—41no—
409C22×D4—42no—
410C22×D4—42no—
411C22×D4—42no—
412C22×D4—42no—
413C22×D4—44no—
414C22×D4—44no—
415C22×D4—44no—
416C22×D4—44no—
417C22×D4—44no—
418C22×D4—44no—
419C22×D4—44no—
420C22×D4—82no—
421C22×D4—82no—
422C22×D4SD1618yescomplemented
423C22×D4C2×D411yescharacteristic
424C22×D4C2×D411yescharacteristic
425C22×D4C2×D411yescharacteristic
426C22×D4C2×D411yescharacteristic
427C22×D4C2411yescharacteristic
428C22×D4C2411yescharacteristic
429C22×D4C2411yescharacteristic
430C23×C4—21no—
431C23×C4—22no—
432C23×C4—22no—
433C23×C4—24no—
434C23×C4—22no—
435C23×C4—22no—
436C23×C4—21no—
437C23×C4—21no—
438C23×C4—21no—
439C23×C4—21no—
440C23×C4—21no—
441C23×C4—22no—
442C23×C4—22no—
443C23×C4—21no—
444C23×C4—42no—
445C23×C4—42no—
446C23×C4—42no—
447C23×C4—44no—
448C23×C4—44no—
449C23×C4—82no—
450C23×C4C2×D411yescharacteristic
451C23×C4C2×D411yescharacteristic
452C23×C4C2×D411yescharacteristic
453C23×C4C2×D411yescharacteristic
454C23×C4C2×D411yescharacteristic
455C23×C4C2×D411yescharacteristic
456C23×C4C2×D411yescharacteristic
457C23×C4C2×D411yescharacteristic
458C23×C4C2411yescharacteristic
459C23×C4C2411yescharacteristic
460C23×C4C2411yescharacteristic
461C23×C4C2411yescharacteristic
462C23×C4C2411yescharacteristic
463C2×SD16—24no—
464C2×SD16—24no—
465C2×SD16—42no—
466C2×SD16—42no—
467C2×SD16—42no—
468C2×SD16—42no—
469C2×SD16—42no—
470C2×SD16—42no—
471C2×SD16—42no—
472C22×C8—24no—
473C22×C8—24no—
474C22×C8—24no—
475C22×C8—42no—
476C22×C8—42no—
477C22×C8—42no—
478C22×C8C2412yes—
479C22×C8C2412yes—
480C22×C8C2412yes—
481C22×C8C2412yes—
482#127—42no—
483#127—44no—
484C22⋊Q8—24no—
485C22⋊Q8—24no—
486C22⋊Q8—24no—
487C22⋊Q8—24no—
488C22⋊Q8—42no—
489C22⋊Q8—42no—
490C22⋊Q8—42no—
491C22⋊Q8—42no—
492C22⋊Q8—44no—
493C22⋊Q8—44no—
494C22⋊Q8—44no—
495C22⋊Q8—44no—
496#121—22no—
497#121—22no—
498#121—22no—
499#121—22no—
500#121—22no—
501#121—22no—
502#121—22no—
503#121—24no—
504#121—22no—
505#121—22no—
506#121—44no—
507#121—44no—
508#121—41no—
509#121—41no—
510#121—41no—
511#121—41no—
512#121—42no—
513#121—44no—
514#121—44no—
515#121—44no—
516#121—44no—
517#121—44no—
518#121—44no—
519#121—44no—
520#121—42no—
521#121—42no—
522#121—82no—
523#121C2×D414yes—
524#120—44no—
525#120—44no—
526#120—44no—
527#120—44no—
528#120—44no—
529#120—44no—
530C4×D4—24no—
531C4×D4—24no—
532C4×D4—42no—
533C4×D4—42no—
534C4×D4—42no—
535C4×D4—42no—
536C4×D4—42no—
537C4×D4—42no—
538C4×D4—42no—
539C4×D4—44no—
540C4×D4—44no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—22no—
543C2×C4⋊C4—22no—
544C2×C4⋊C4—22no—
545C2×C4⋊C4—24no—
546C2×C4⋊C4—24no—
547C2×C4⋊C4—22no—
548C2×C4⋊C4—22no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—22no—
552C2×C4⋊C4—22no—
553C2×C4⋊C4—22no—
554C2×C4⋊C4—22no—
555C2×C4⋊C4—22no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—22no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—42no—
565C2×C4⋊C4—42no—
566C2×C4⋊C4—42no—
567C2×C4⋊C4—41no—
568C2×C4⋊C4—41no—
569C2×C4⋊C4—42no—
570C2×C4⋊C4—44no—
571C2×C4⋊C4—44no—
572C2×C4⋊C4—44no—
573C2×C4⋊C4—44no—
574C2×C4⋊C4—44no—
575C2×C4⋊C4—82no—
576C2×C4⋊C4C2×D411yescharacteristic
577C2×C4⋊C4C2×D411yescharacteristic
578C2×C4⋊C4C2×D411yescharacteristic
579C2×C4⋊C4C2×D411yescharacteristic
580C2×C4⋊C4C2×D414yescomplemented
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2411yescharacteristic
589C2×C22⋊C4—21no—
590C2×C22⋊C4—22no—
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—22no—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—42no—
619C2×C22⋊C4—42no—
620C2×C22⋊C4—44no—
621C2×C22⋊C4—44no—
622C2×C22⋊C4—44no—
623C2×C22⋊C4—44no—
624C2×C22⋊C4—82no—
625C2×C22⋊C4C2×D411yescharacteristic
626C2×C22⋊C4C2×D411yescharacteristic
627C2×C22⋊C4C2×D411yescharacteristic
628C2×C22⋊C4C2×D411yescharacteristic
629C2×C22⋊C4C2×D411yescharacteristic
630C2×C22⋊C4C2×D411yescharacteristic
631C2×C22⋊C4C2×D411yescharacteristic
632C2×C22⋊C4C2×D411yescharacteristic
633C2×C42—21no—
634C2×C42—42no—
635C2×C42C2×D411yescharacteristic
636C2×C42C2×D411yescharacteristic
637C2×C42C2411yescharacteristic
638C2×C42C2411yescharacteristic
639#106—24no—
640#106—24no—
641#106—24no—
642#106—24no—
643#106—42no—
644#106—42no—
645#106C2×D418yescomplemented
646C4⋊C8—42no—
647#103—24no—
648#103—24no—
649#103—42no—
650#103—42no—
651#103—42no—
652#102—24no—
653#102—24no—
654#102—24no—
655#102—24no—
656#102—42no—
657#102—42no—
658#102—42no—
659#102—42no—
660#102C2×D418yescomplemented
661C22⋊C8—22no—
662C22⋊C8—22no—
663C22⋊C8—24no—
664C22⋊C8—22no—
665C22⋊C8—24no—
666C22⋊C8—24no—
667C22⋊C8—42no—
668C22⋊C8—42no—
669C22⋊C8—42no—
670C22⋊C8C2×D414yescomplemented
671C4×C8—42no—
672#95—22no—
673#95—22no—
674#95—22no—
675#95—22no—
676#95—22no—
677#95—22no—
678#95—22no—
679#95—22no—
680#95—21no—
681#95—21no—
682#95—21no—
683#95—21no—
684#95—21no—
685#95—21no—
686#95—21no—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—22no—
691C24—22no—
692C24—22no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—41no—
697C24—41no—
698C24—41no—
699C24—41no—
700C24—41no—
701C24—41no—
702C24—42no—
703C24—42no—
704C24—42no—
705C24—42no—
706C24—42no—
707C24—42no—
708C24—42no—
709C24—42no—
710C24—81no—
711C24—81no—
712C24—81no—
713C24—81no—
714C24—81no—
715C24—81no—
716C24C2×SD1614yes—
717C24C2×SD1614yes—
718C24C22×D411yescharacteristic
719C24C22×D411yescharacteristic
720C24C22×D411yescharacteristic
721C24C22×D411yescharacteristic
722C24C22×D411yescharacteristic
723C2×Q8—22no—
724C2×Q8—22no—
725C2×Q8—22no—
726C2×Q8—22no—
727C2×Q8—22no—
728C2×Q8—22no—
729C2×Q8—42no—
730C2×Q8—42no—
731C2×Q8—42no—
732C2×Q8—84no—
733C2×Q8—84no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—22no—
738C2×D4—24no—
739C2×D4—21no—
740C2×D4—21no—
741C2×D4—22no—
742C2×D4—21no—
743C2×D4—21no—
744C2×D4—22no—
745C2×D4—22no—
746C2×D4—21no—
747C2×D4—22no—
748C2×D4—22no—
749C2×D4—22no—
750C2×D4—48no—
751C2×D4—41no—
752C2×D4—41no—
753C2×D4—41no—
754C2×D4—41no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—42no—
759C2×D4—42no—
760C2×D4—42no—
761C2×D4—42no—
762C2×D4—42no—
763C2×D4—416no—
764C2×D4—42no—
765C2×D4—42no—
766C2×D4—42no—
767C2×D4—42no—
768C2×D4—42no—
769C2×D4—42no—
770C2×D4—42no—
771C2×D4—42no—
772C2×D4—42no—
773C2×D4—42no—
774C2×D4—42no—
775C2×D4—42no—
776C2×D4—42no—
777C2×D4—42no—
778C2×D4—42no—
779C2×D4—42no—
780C2×D4—42no—
781C2×D4—42no—
782C2×D4—42no—
783C2×D4—42no—
784C2×D4—42no—
785C2×D4—42no—
786C2×D4—42no—
787C2×D4—42no—
788C2×D4—84no—
789C2×D4—81no—
790C2×D4—81no—
791C2×D4—81no—
792C2×D4—81no—
793C2×D4—84no—
794C2×D4—84no—
795C2×D4—81no—
796C2×D4—81no—
797C2×D4—81no—
798C2×D4—81no—
799C2×D4—81no—
800C2×D4—81no—
801C2×D4—81no—
802C2×D4—81no—
803C2×D4—816no—
804C2×D4—816no—
805C2×D4—816no—
806C2×D4C2×SD1614yes—
807C2×D4C2×SD1614yes—
808C2×D4C2×SD1614yes—
809C2×D4C2×SD1614yes—
810C2×D4C22×D412yes—
811C22×C4—21no—
812C22×C4—22no—
813C22×C4—21no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—24no—
818C22×C4—22no—
819C22×C4—21no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—22no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—21no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—41no—
849C22×C4—41no—
850C22×C4—41no—
851C22×C4—41no—
852C22×C4—41no—
853C22×C4—48no—
854C22×C4—48no—
855C22×C4—41no—
856C22×C4—41no—
857C22×C4—41no—
858C22×C4—41no—
859C22×C4—41no—
860C22×C4—41no—
861C22×C4—41no—
862C22×C4—41no—
863C22×C4—42no—
864C22×C4—42no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—42no—
868C22×C4—42no—
869C22×C4—42no—
870C22×C4—42no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—42no—
875C22×C4—44no—
876C22×C4—42no—
877C22×C4—42no—
878C22×C4—42no—
879C22×C4—42no—
880C22×C4—42no—
881C22×C4—42no—
882C22×C4—44no—
883C22×C4—42no—
884C22×C4—42no—
885C22×C4—84no—
886C22×C4—84no—
887C22×C4—82no—
888C22×C4—82no—
889C22×C4—81no—
890C22×C4—81no—
891C22×C4—816no—
892C22×C4C2×SD1614yes—
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D412yes—
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4H(5,𝔽2)14yes—
904C22×C4H(5,𝔽2)12yes—
905C22×C4C2511yescharacteristic
906SD16—84no—
907SD16—84no—
908SD16—84no—
909C2×C8—22no—
910C2×C8—22no—
911C2×C8—22no—
912C2×C8—22no—
913C2×C8—22no—
914C2×C8—22no—
915C2×C8—22no—
916C2×C8—22no—
917C2×C8—22no—
918C2×C8—22no—
919C2×C8—22no—
920C2×C8—48no—
921C2×C8—84no—
922C2×C8C22×D414yes—
923C4⋊C4—22no—
924C4⋊C4—22no—
925C4⋊C4—24no—
926C4⋊C4—22no—
927C4⋊C4—21no—
928C4⋊C4—22no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—22no—
932C4⋊C4—22no—
933C4⋊C4—22no—
934C4⋊C4—21no—
935C4⋊C4—22no—
936C4⋊C4—21no—
937C4⋊C4—22no—
938C4⋊C4—41no—
939C4⋊C4—41no—
940C4⋊C4—44no—
941C4⋊C4—44no—
942C4⋊C4—42no—
943C4⋊C4—42no—
944C4⋊C4—44no—
945C4⋊C4—44no—
946C4⋊C4—42no—
947C4⋊C4—44no—
948C4⋊C4—44no—
949C4⋊C4—42no—
950C4⋊C4—42no—
951C4⋊C4—42no—
952C4⋊C4—82no—
953C4⋊C4—82no—
954C4⋊C4—81no—
955C4⋊C4C22×D414yes—
956C4⋊C4C22×D412yes—
957C22⋊C4—22no—
958C22⋊C4—22no—
959C22⋊C4—22no—
960C22⋊C4—22no—
961C22⋊C4—24no—
962C22⋊C4—41no—
963C22⋊C4—41no—
964C22⋊C4—41no—
965C22⋊C4—41no—
966C22⋊C4—42no—
967C22⋊C4—42no—
968C22⋊C4—42no—
969C22⋊C4—42no—
970C22⋊C4—44no—
971C22⋊C4—44no—
972C22⋊C4—42no—
973C22⋊C4—42no—
974C22⋊C4—44no—
975C22⋊C4—44no—
976C22⋊C4—42no—
977C22⋊C4—42no—
978C22⋊C4—42no—
979C22⋊C4—42no—
980C22⋊C4—42no—
981C22⋊C4—42no—
982C22⋊C4—42no—
983C22⋊C4—42no—
984C22⋊C4—42no—
985C22⋊C4—42no—
986C22⋊C4—42no—
987C22⋊C4—81no—
988C22⋊C4—81no—
989C22⋊C4—81no—
990C22⋊C4—81no—
991C22⋊C4—81no—
992C22⋊C4—82no—
993C22⋊C4—82no—
994C42—22no—
995C42—22no—
996C42—41no—
997C42—41no—
998C42—42no—
999C23—21no—
1000C23—21no—
1001C23—21no—
1002C23—21no—
1003C23—21no—
1004C23—21no—
1005C23—21no—
1006C23—21no—
1007C23—21no—
1008C23—21no—
1009C23—21no—
1010C23—28no—
1011C23—21no—
1012C23—21no—
1013C23—21no—
1014C23—21no—
1015C23—21no—
1016C23—21no—
1017C23—21no—
1018C23—21no—
1019C23—21no—
1020C23—28no—
1021C23—21no—
1022C23—21no—
1023C23—21no—
1024C23—21no—
1025C23—21no—
1026C23—21no—
1027C23—28no—
1028C23—22no—
1029C23—44no—
1030C23—44no—
1031C23—44no—
1032C23—44no—
1033C23—44no—
1034C23—44no—
1035C23—44no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—82no—
1057C23—82no—
1058C23—82no—
1059C23—82no—
1060C23—84no—
1061C23—84no—
1062C23—84no—
1063C23—84no—
1064C23—84no—
1065C23—84no—
1066C23—84no—
1067C23—84no—
1068C23—162no—
1069C23—162no—
1070C23—162no—
1071C23—162no—
1072C23—162no—
1073C23—162no—
1074C23#53412yes—
1075C23D4212yes—
1076C23C22×SD1612yes—
1077C23C22×SD1612yes—
1078C23C22×SD1612yes—
1079C23C22×SD1612yes—
1080C23C22×SD1612yes—
1081C23#57512yes—
1082C23#57712yes—
1083C23C23×D411yescharacteristic
1084Q8—42no—
1085Q8—42no—
1086Q8—42no—
1087Q8—42no—
1088Q8—84no—
1089D4—28no—
1090D4—28no—
1091D4—24no—
1092D4—44no—
1093D4—44no—
1094D4—48no—
1095D4—42no—
1096D4—42no—
1097D4—42no—
1098D4—42no—
1099D4—42no—
1100D4—84no—
1101D4—84no—
1102D4—84no—
1103D4—84no—
1104D4—84no—
1105D4—84no—
1106D4—84no—
1107D4—84no—
1108D4—84no—
1109D4—84no—
1110D4—84no—
1111D4—162no—
1112D4—162no—
1113D4—162no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—24no—
1123C2×C4—24no—
1124C2×C4—24no—
1125C2×C4—24no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—22no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—24no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—44no—
1144C2×C4—44no—
1145C2×C4—44no—
1146C2×C4—44no—
1147C2×C4—48no—
1148C2×C4—42no—
1149C2×C4—41no—
1150C2×C4—42no—
1151C2×C4—41no—
1152C2×C4—42no—
1153C2×C4—42no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—42no—
1163C2×C4—42no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—41no—
1169C2×C4—42no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—42no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—42no—
1179C2×C4—82no—
1180C2×C4—82no—
1181C2×C4—84no—
1182C2×C4—82no—
1183C2×C4—82no—
1184C2×C4—88no—
1185C2×C4—84no—
1186C2×C4—84no—
1187C2×C4—88no—
1188C2×C4—84no—
1189C2×C4—84no—
1190C2×C4—84no—
1191C2×C4#53412yes—
1192C2×C4D4212yes—
1193C2×C4C22×SD1612yes—
1194C2×C4C22×SD1612yes—
1195C2×C4C23×D411yescharacteristic
1196C2×C4C2×H(5,𝔽2)12yes—
1197C2×C4C2×H(5,𝔽2)11yescharacteristic
1198C2×C4#58512yes—
1199C8—24no—
1200C8—42no—
1201C8—42no—
1202C8—42no—
1203C22—22no—
1204C22—22no—
1205C22—22no—
1206C22—22no—
1207C22—22no—
1208C22—22no—
1209C22—22no—
1210C22—22no—
1211C22—22no—
1212C22—22no—
1213C22—22no—
1214C22—22no—
1215C22—22no—
1216C22—22no—
1217C22—22no—
1218C22—22no—
1219C22—22no—
1220C22—22no—
1221C22—22no—
1222C22—22no—
1223C22—22no—
1224C22—416no—
1225C22—41no—
1226C22—41no—
1227C22—41no—
1228C22—41no—
1229C22—41no—
1230C22—41no—
1231C22—41no—
1232C22—41no—
1233C22—41no—
1234C22—41no—
1235C22—41no—
1236C22—41no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—88no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—168no—
1260C22—168no—
1261C22#318714yescomplemented
1262C22D4×SD1614yes—
1263C22C2×#53411yescharacteristic
1264C22C2×D4211yescharacteristic
1265C22#348511yescharacteristic
1266C22C23×SD1611yescharacteristic
1267C22C2×#57511yescharacteristic
1268C22C2×#57711yescharacteristic
1269C22#358511yescharacteristic
1270C4—22no—
1271C4—22no—
1272C4—22no—
1273C4—22no—
1274C4—41no—
1275C4—41no—
1276C4—41no—
1277C4—41no—
1278C4—41no—
1279C4—42no—
1280C4—44no—
1281C4—81no—
1282C4—82no—
1283C4—81no—
1284C4—82no—
1285C4—81no—
1286C4—81no—
1287C4—82no—
1288C4#348812yes—
1289C4#353412yes—
1290C2—24no—
1291C2—24no—
1292C2—42no—
1293C2—42no—
1294C2—42no—
1295C2—82no—
1296C2—161no—
1297C2—161no—
1298C2#3764611yescharacteristic
1299C2C2×#318711yescharacteristic
1300C2#6076511yescharacteristic
1301C2C2×D4×SD1611yescharacteristic
1302C2#6106611yescharacteristic
1303C2#6169711yescharacteristic
1304C2#6172911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalD4×#121C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3187C2semidirect
2. C22×#481C2semidirect
4. C2×#2417C2semidirect
5. #32979C2semidirect
6. #31189C2semidirect
7. #31024C2semidirect
8. #30703C2semidirect
9. #30559C2semidirect
10. #29755C2semidirect
11. #29593C2semidirect
12. #28305C2semidirect
13. #28115C2semidirect
14. #26128C2semidirect
15. #25112C2semidirect
16. #24776C2semidirect
17. #24553C2semidirect
18. #24432C2semidirect
19. #24381C2semidirect
20. #24005C2semidirect
21. #23919C2semidirect
22. D4×C22⋊C8C2semidirect
23. #22076C2semidirect
26. C22×C22⋊Q8C22semidirect
27. C22×C22⋊Q8C22semidirect
31. C23×C4⋊C4C22semidirect
36. C2×#481C22semidirect
37. C2×#481C22semidirect
38. C2×#481C22semidirect
39. C2×#481C22semidirect
40. C2×#481C22semidirect
41. C2×#481C22semidirect
42. C2×#483C22semidirect
43. C2×#465C22semidirect
44. C2×#465C22semidirect
45. C2×#465C22semidirect
47. C2×#448C22semidirect
48. C2×#448C22semidirect
49. C2×#450C22semidirect
50. C2×#450C22semidirect
51. C2×C8×D4C22semidirect
52. C22×#106C22semidirect
53. C22×#102C22semidirect
54. C22×C22⋊C8C22semidirect
55. C22×C22⋊C8C22semidirect
69. #2417C22semidirect
70. #2417C22semidirect
71. #2417C22semidirect
84. C2×#391C22semidirect
85. C2×#389C22semidirect
88. C2×#380C22semidirect
89. #2096C22semidirect
90. #2084C22semidirect
91. #2077C22semidirect
92. #2066C22semidirect
93. #2065C22semidirect
94. #2065C22semidirect
95. #2055C22semidirect
96. #2041C22semidirect
97. #2035C22semidirect
98. #2035C22semidirect
99. #2035C22semidirect
100. #2034C22semidirect
101. #2034C22semidirect
102. #2034C22semidirect
103. #2014C22semidirect
104. #2000C22semidirect
105. #2000C22semidirect
106. #2000C22semidirect
107. #2000C22semidirect
108. #2000C22semidirect
109. #1968C22semidirect
110. #1968C22semidirect
111. #1954C22semidirect
112. #1941C22semidirect
113. #1934C22semidirect
114. #1927C22semidirect
115. #1920C22semidirect
116. #1893C22semidirect
117. #1892C22semidirect
118. #1877C22semidirect
120. #1874C22semidirect
121. #1874C22semidirect
122. #1874C22semidirect
123. #1874C22semidirect
124. #1872C22semidirect
126. #1869C22semidirect
127. #1864C22semidirect
128. #1853C22semidirect
129. #1853C22semidirect
130. #1853C22semidirect
131. #1853C22semidirect
132. #1824C22semidirect
133. #1824C22semidirect
134. #1807C22semidirect
135. #1797C22semidirect
136. #1787C22semidirect
137. #1786C22semidirect
138. #1779C22semidirect
139. #1779C22semidirect
140. C4×C22⋊C8C22semidirect
246. #481D4semidirect
422. C22×D4SD16semidirect
580. C2×C4⋊C4C2×D4semidirect
645. #106C2×D4semidirect
660. #102C2×D4semidirect
670. C22⋊C8C2×D4semidirect
1261. C22#3187semidirect

Maximal subgroups

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

subgroupindex
C2×#31872
C22×#4812
D4×#1212
C2×#24172
#329792
#311892
#310242
#307032
#305592
#297552
#295932
#283052
#281152
#261282
#251122
#247762
#245532
#244322
#243812
#240052
#239192
D4×C22⋊C82
#220762