Finite Group Databasebeta

← #6597536

Subgroups — #6597536

Order 512.

1889 conjugacy classes of subgroups.

The subgroup lattice has 897 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36274C211yesmaximal, characteristic
2C4⋊C4×#41C211yesmaximal, characteristic
3#33108C211yesmaximal, characteristic, complemented
4#33098C212yesmaximal, complemented
5#27889C211yesmaximal, characteristic, complemented
6#27855C212yesmaximal, complemented
7#27628C211yesmaximal, characteristic, complemented
8#27583C212yesmaximal, complemented
9#26320C211yesmaximal, characteristic, complemented
10#26320C211yesmaximal, characteristic, complemented
11#26200C212yesmaximal, complemented
12#26128C212yesmaximal, complemented
13#25060C211yesmaximal, characteristic, complemented
14#24994C211yesmaximal, characteristic, complemented
15#24863C212yesmaximal, complemented
16#24863C212yesmaximal, complemented
17#22703C211yesmaximal, characteristic, complemented
18D4×#106C211yesmaximal, characteristic, complemented
19#22469C211yesmaximal, characteristic
20D4×#103C211yesmaximal, characteristic, complemented
21D4×#103C211yesmaximal, characteristic, complemented
22C4×#483C211yesmaximal, characteristic, complemented
23C2×#1927C212yesmaximal, complemented
24C2×D4×Q8C2211yescharacteristic
25C2×C4×#41—21no—
26C2×C4×#41C2211yescharacteristic
27C2×#483C2211yescharacteristic
28C2×#483C2212yes—
29C2×C8×D4C2211yescharacteristic
30C2×C8×D4C2211yescharacteristic
31C22×#106C2212yes—
32C22×#103C2212yes—
33C22×#103C2212yes—
34#2857C2211yescharacteristic
35#2855C2212yes—
36#2582C2211yescharacteristic
37#2568C2211yescharacteristic
38#2451—21no—
39#2450—22no—
40#2439—21no—
41#2438—22no—
42#2417C2212yes—
43#2409C2212yes—
44#2351—21no—
45Q8×C4⋊C4C2211yescharacteristic
46Q8×C4⋊C4C2211yescharacteristic
47#2349—21no—
48#2349—22no—
49#2349—21no—
50D4×C4⋊C4C2212yes—
51D4×C4⋊C4C2212yes—
52D4×C4⋊C4C2211yescharacteristic
53D4×C4⋊C4C2211yescharacteristic
54D4×C4⋊C4C2211yescharacteristic
55#2339—21no—
56C4×C22⋊Q8C2211yescharacteristic
57#2296—22no—
58#2296—21no—
59C2×#391C2212yes—
60#2285C2212yes—
61#2285C2211yescharacteristic
62C2×C4×C4⋊C4C2212yes—
63C2×C4×C4⋊C4C2211yescharacteristic
64#2099C2212yes—
65#2096C2212yes—
66#2096C2212yes—
67#2096C2212yes—
68#2084C2212yes—
69#2077C2212yes—
70#2072C2212yes—
71#2072C2212yes—
72#2072C2212yes—
73#2035C2212yes—
74#2035C2212yes—
75#2035C2212yes—
76#1984C2211yescharacteristic
77#1984C2211yescharacteristic
78#1981C2211yescharacteristic
79#1981C2211yescharacteristic
80#1956C2211yescharacteristic
81#1956C2211yescharacteristic
82#1948C2211yescharacteristic
83#1948C2211yescharacteristic
84#1948C2211yescharacteristic
85#1948C2211yescharacteristic
86#1927C2212yes—
87#1927C2212yes—
88#1927C2212yes—
89#1927C2212yes—
90#1927C2212yes—
91#1927C2211yescharacteristic
92#1927C2212yes—
93#1927C2212yes—
94#1927C2212yes—
95#1927C2212yes—
96#1927C2211yescharacteristic
97#1927C2212yes—
98#1927C2212yes—
99#1920C2212yes—
100#1920C2211yescharacteristic
101#1920C2211yescharacteristic
102#1920C2212yes—
103#1920C2212yes—
104#1892C2212yes—
105#1892C2212yes—
106#1872C2212yes—
107#1872C2211yescharacteristic
108#1872C2212yes—
109#1872C2212yes—
110#1869C2212yes—
111#1869C2212yes—
112#1853C2211yescharacteristic
113#1853C2212yes—
114#1853C2212yes—
115#1853C2212yes—
116#1853C2212yes—
117#1844C2211yescharacteristic
118#1834C2211yescharacteristic
119#1823C2211yescharacteristic
120#1817C2212yes—
121#1807C2212yes—
122#1807C2212yes—
123#1803C2211yescharacteristic
124#1803C2211yescharacteristic
125#1797C2211yescharacteristic
126#1787C2212yes—
127#1787C2212yes—
128C4×#106C2211yescharacteristic
129C4×#106C2211yescharacteristic
130C4×#103C2211yescharacteristic
131C4×#103C2211yescharacteristic
132C4×C22⋊C8C2211yescharacteristic
133C2×#340C2212yes—
134C2×#336C2212yes—
135C22×#41D411yescharacteristic
136C23×Q8C2312yes—
137C23×C8C2312yes—
138C23×C8C2312yes—
139D4×Q8—24no—
140D4×Q8—24no—
141C2×C4⋊Q8—21no—
142C2×C4⋊Q8C2311yescharacteristic
143C2×C22⋊Q8—22no—
144C2×C22⋊Q8C2312yes—
145C2×C22⋊Q8C2311yescharacteristic
146C2×C22⋊Q8C2312yes—
147C4×#41—24no—
148C4×#41—24no—
149C4×#41—48no—
150C2×C4×Q8—21no—
151C2×C4×Q8—21no—
152C2×C4×Q8D411yescharacteristic
153C2×C4×Q8C2311yescharacteristic
154C2×C4×Q8C2311yescharacteristic
155C2×C4×D4—21no—
156C2×C4×D4—21no—
157C2×C4×D4—22no—
158C2×C4×D4—22no—
159C2×C4×D4—21no—
160C2×C4×D4—21no—
161C2×C4×D4D411yescharacteristic
162C2×C4×D4D412yes—
163C2×C4×D4C2312yes—
164C2×C4×D4C2311yescharacteristic
165C2×#117—22no—
166C2×#117—21no—
167C2×#117D412yes—
168C2×#117D411yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2312yes—
174C22×C42—22no—
175C22×C42—21no—
176C22×C42C2311yescharacteristic
177C22×C42C2312yes—
178#483—24no—
179#483—44no—
180C8×D4—24no—
181C8×D4—24no—
182C2×#106—44no—
183C2×#106C2311yescharacteristic
184C2×#106C2311yescharacteristic
185C2×#106C2312yes—
186C2×#106C2311yescharacteristic
187C2×#106C2312yes—
188C2×#106C2312yes—
189C2×#106C2312yes—
190C2×#106C2312yes—
191C2×#106C2311yescharacteristic
192C2×#106C2312yes—
193C2×C4⋊C8C2311yescharacteristic
194C2×C4⋊C8C2311yescharacteristic
195C2×#103—28no—
196C2×#103—44no—
197C2×#103C2312yes—
198C2×#103C2311yescharacteristic
199C2×#103C2312yes—
200C2×#103C2312yes—
201C2×#103C2311yescharacteristic
202C2×#103C2312yes—
203C2×#103C2312yes—
204C2×#103C2312yes—
205C2×#103C2312yes—
206C2×#103C2312yes—
207C2×#103C2312yes—
208C2×#103C2311yescharacteristic
209C2×#103C2312yes—
210C2×#103C2311yescharacteristic
211C2×C22⋊C8C2311yescharacteristic
212C2×C22⋊C8C2312yes—
213C2×C22⋊C8C2312yes—
214C2×C22⋊C8C2312yes—
215C2×C22⋊C8C2311yescharacteristic
216C2×C4×C8C2311yescharacteristic
217C2×C4×C8C2311yescharacteristic
218#400—22no—
219#398—22no—
220#398—22no—
221#396—22no—
222#395—22no—
223#393—22no—
224#391—21no—
225#391—21no—
226#391—22no—
227#391—22no—
228#391C2312yes—
229#391C2312yes—
230#391C2312yes—
231#391C2312yes—
232#391C2311yescharacteristic
233#389—21no—
234#389—22no—
235#389—22no—
236#389—21no—
237#389—21no—
238#389—21no—
239#389—21no—
240#389—21no—
241#389—22no—
242#389—22no—
243#389—21no—
244#389—21no—
245#389C2312yes—
246#389C2311yescharacteristic
247#387—22no—
248#387—22no—
249#387—21no—
250#386—22no—
251#386—22no—
252#385—22no—
253#385—21no—
254#385—22no—
255#385—22no—
256#385—22no—
257#385—22no—
258#385—22no—
259#385—22no—
260#385—22no—
261#385—22no—
262#384C2311yescharacteristic
263#384C2311yescharacteristic
264#384C2311yescharacteristic
265#384C2312yes—
266#384C2312yes—
267#382—21no—
268#382—21no—
269#382—22no—
270#381—22no—
271#380—21no—
272#380—21no—
273#380—22no—
274#380—21no—
275#380—22no—
276#380C2312yes—
277#380C2312yes—
278#380C2312yes—
279#380C2311yescharacteristic
280#380C2312yes—
281C4×C4⋊C4—21no—
282C4×C4⋊C4—22no—
283C4×C4⋊C4—21no—
284C4×C4⋊C4—21no—
285C4×C4⋊C4—22no—
286C4×C4⋊C4—21no—
287C4×C4⋊C4—22no—
288C4×C4⋊C4C2311yescharacteristic
289C4×C4⋊C4C2312yes—
290C4×C4⋊C4C2312yes—
291C4×C4⋊C4C2311yescharacteristic
292C4×C4⋊C4C2311yescharacteristic
293C4×C4⋊C4C2311yescharacteristic
294C4×C4⋊C4C2311yescharacteristic
295C4×C4⋊C4C2312yes—
296C4×C22⋊C4—21no—
297C2×#95—22no—
298C2×#95—22no—
299C2×#95—21no—
300C2×#95—22no—
301#340C2312yes—
302#340C2312yes—
303#340C2311yescharacteristic
304#340C2312yes—
305#340C2312yes—
306#340C2312yes—
307#340C2311yescharacteristic
308#340C2312yes—
309#340C2312yes—
310#340C2311yescharacteristic
311#340C2311yescharacteristic
312#340C2311yescharacteristic
313#340C2311yescharacteristic
314#340C2311yescharacteristic
315#340C2311yescharacteristic
316#340C2312yes—
317#336C2312yes—
318#336C2312yes—
319#336C2312yes—
320#336C2312yes—
321#336C2311yescharacteristic
322#336C2312yes—
323#336C2311yescharacteristic
324C2×#41—24no—
325C2×#41—24no—
326C2×#41SD1618yes—
327C22×Q8—22no—
328C22×Q8—24no—
329C22×Q8—24no—
330C22×Q8—24no—
331C22×Q8—42no—
332C22×Q8—42no—
333C22×Q8—42no—
334C22×Q8C2×D411yescharacteristic
335C22×Q8C2412yes—
336C22×Q8C2411yescharacteristic
337C22×D4C2×D412yes—
338C22×D4C2×D411yescharacteristic
339C23×C4—21no—
340C23×C4—21no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4C2×D412yes—
346C23×C4C2×D411yescharacteristic
347C23×C4C2×D412yes—
348C23×C4C2×D411yescharacteristic
349C23×C4C2411yescharacteristic
350C23×C4C2412yes—
351C22×C8—24no—
352C22×C8—24no—
353C22×C8—24no—
354C22×C8—42no—
355C22×C8—42no—
356C22×C8—42no—
357C22×C8C2411yescharacteristic
358C22×C8C2412yes—
359C22×C8C2412yes—
360C22×C8C2411yescharacteristic
361C22×C8C2411yescharacteristic
362C22×C8C2411yescharacteristic
363C4⋊Q8—22no—
364C4⋊Q8—22no—
365C4⋊Q8—44no—
366C22⋊Q8—22no—
367C22⋊Q8—24no—
368C22⋊Q8—24no—
369C22⋊Q8—41no—
370C22⋊Q8—48no—
371C22⋊Q8—42no—
372C22⋊Q8—42no—
373C4×Q8—24no—
374C4×Q8—22no—
375C4×Q8—22no—
376C4×Q8—22no—
377C4×Q8—22no—
378C4×Q8—44no—
379C4×Q8—44no—
380C4×D4—24no—
381C4×D4—24no—
382C4×D4—24no—
383C4×D4—28no—
384C4×D4—44no—
385C4×D4—48no—
386C4×D4—48no—
387C4×D4—44no—
388C4×D4—44no—
389C4×D4—44no—
390C4×D4#4114yes—
391C4×D4#4114yes—
392#117—24no—
393#117—28no—
394#117—44no—
395#117—48no—
396C2×C4⋊C4—24no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—24no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—41no—
424C2×C4⋊C4—42no—
425C2×C4⋊C4—42no—
426C2×C4⋊C4—41no—
427C2×C4⋊C4—42no—
428C2×C4⋊C4—42no—
429C2×C4⋊C4C2×D411yescharacteristic
430C2×C4⋊C4C2×D412yes—
431C2×C4⋊C4C2×D412yes—
432C2×C4⋊C4C2×D411yescharacteristic
433C2×C4⋊C4C2411yescharacteristic
434C2×C4⋊C4C2412yes—
435C2×C4⋊C4C2412yes—
436C2×C4⋊C4C2411yescharacteristic
437C2×C4⋊C4C2411yescharacteristic
438C2×C4⋊C4C2412yes—
439C2×C4⋊C4C2411yescharacteristic
440C2×C4⋊C4C2411yescharacteristic
441C2×C4⋊C4C2411yescharacteristic
442C2×C4⋊C4C2411yescharacteristic
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4C2×D412yes—
452C2×C22⋊C4C2×D412yes—
453C2×C22⋊C4C2×D412yes—
454C2×C42—24no—
455C2×C42—24no—
456C2×C42—22no—
457C2×C42—22no—
458C2×C42—21no—
459C2×C42—22no—
460C2×C42—22no—
461C2×C42—22no—
462C2×C42—21no—
463C2×C42—21no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—21no—
467C2×C42—48no—
468C2×C42—44no—
469C2×C42C2×D411yescharacteristic
470C2×C42C2×D412yes—
471C2×C42C2×D411yescharacteristic
472C2×C42C2×D412yes—
473C2×C42C2412yes—
474C2×C42C2411yescharacteristic
475C2×C42C2411yescharacteristic
476#106—22no—
477#106—22no—
478#106—22no—
479#106—24no—
480#106—42no—
481#106—42no—
482#106—42no—
483#106—41no—
484#106—42no—
485#106—42no—
486C4⋊C8—22no—
487C4⋊C8—22no—
488#103—24no—
489#103—22no—
490#103—24no—
491#103—24no—
492#103—22no—
493#103—24no—
494#103—42no—
495#103—42no—
496#103—42no—
497#103—42no—
498#103—42no—
499#103—41no—
500#103—42no—
501#103#4114yescomplemented
502C22⋊C8—24no—
503C22⋊C8—24no—
504C22⋊C8—22no—
505C22⋊C8—41no—
506C22⋊C8—42no—
507C4×C8—22no—
508C4×C8—22no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—22no—
513#95—21no—
514#95—22no—
515#95—22no—
516#95—21no—
517#95—21no—
518#95—22no—
519#95—22no—
520#95—22no—
521#95—22no—
522#95—22no—
523#95—22no—
524#95—21no—
525#95—21no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95—21no—
530#95—22no—
531#95—22no—
532#95—22no—
533#95—22no—
534C24C22×D411yescharacteristic
535C24C22×D412yes—
536#41—232no—
537C2×Q8—22no—
538C2×Q8—22no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—21no—
546C2×Q8—22no—
547C2×Q8—21no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—44no—
551C2×Q8—48no—
552C2×Q8—48no—
553C2×Q8—44no—
554C2×Q8—82no—
555C2×Q8—84no—
556C2×Q8—84no—
557C2×Q8C2×SD1614yes—
558C2×Q8C2×#4112yes—
559C2×D4—24no—
560C2×D4—24no—
561C2×D4#12314yes—
562C2×D4C2×SD1618yes—
563C2×D4C2×SD1614yes—
564C2×D4#13714yes—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—24no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—21no—
590C22×C4—22no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—44no—
598C22×C4—42no—
599C22×C4—44no—
600C22×C4—42no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—82no—
609C22×C4—81no—
610C22×C4—82no—
611C22×C4—81no—
612C22×C4—82no—
613C22×C4—82no—
614C22×C4—82no—
615C22×C4C2×SD1618yes—
616C22×C4C2×SD1614yes—
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D412yes—
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D412yes—
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D412yes—
624C22×C4C22×D411yescharacteristic
625C22×C4C2×#4114yes—
626C22×C4C2×#4114yes—
627C22×C4C2511yescharacteristic
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—22no—
645C2×C8—48no—
646C2×C8—84no—
647C2×C8C2×#4112yes—
648C4⋊C4—24no—
649C4⋊C4—24no—
650C4⋊C4—22no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—22no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—22no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—22no—
662C4⋊C4—21no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—22no—
669C4⋊C4—44no—
670C4⋊C4—44no—
671C4⋊C4—42no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—44no—
678C4⋊C4—42no—
679C4⋊C4—44no—
680C4⋊C4—44no—
681C4⋊C4—42no—
682C4⋊C4—42no—
683C4⋊C4—42no—
684C4⋊C4—81no—
685C4⋊C4—81no—
686C4⋊C4—81no—
687C4⋊C4—82no—
688C4⋊C4—82no—
689C4⋊C4—82no—
690C4⋊C4—82no—
691C4⋊C4—82no—
692C4⋊C4#12314yes—
693C4⋊C4C2×#4112yes—
694C4⋊C4H(5,𝔽2)12yes—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—42no—
698C22⋊C4—44no—
699C22⋊C4—44no—
700C22⋊C4—44no—
701C22⋊C4—44no—
702C22⋊C4—44no—
703C22⋊C4—81no—
704C22⋊C4—82no—
705C22⋊C4#12318yes—
706C42—24no—
707C42—22no—
708C42—24no—
709C42—22no—
710C42—21no—
711C42—21no—
712C42—22no—
713C42—22no—
714C42—42no—
715C42—42no—
716C42—44no—
717C42—42no—
718C42—44no—
719C42—44no—
720C42—42no—
721C42—42no—
722C42—42no—
723C42C2×#4112yes—
724C42C2×#4112yes—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23C2×#12314yes—
736C23C22×SD1612yes—
737C23C22×SD1614yes—
738C23C2×#13714yes—
739C23C23×D411yescharacteristic
740Q8—28no—
741Q8—22no—
742Q8—22no—
743Q8—41no—
744Q8—41no—
745Q8—42no—
746Q8—42no—
747Q8—42no—
748Q8—42no—
749Q8—88no—
750D4—216no—
751D4#483116yescomplemented
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—216no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—21no—
760C2×C4—22no—
761C2×C4—28no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—42no—
815C2×C4—82no—
816C2×C4—84no—
817C2×C4—88no—
818C2×C4—84no—
819C2×C4—88no—
820C2×C4—84no—
821C2×C4—88no—
822C2×C4—164no—
823C2×C4C2×#12314yes—
824C2×C4C2×#12312yes—
825C2×C4C2×#12312yes—
826C2×C4C22×SD1612yes—
827C2×C4C22×SD1614yes—
828C2×C4C22×SD1612yes—
829C2×C4C2×#13712yes—
830C2×C4C22×#4111yescharacteristic
831C2×C4C22×#4111yescharacteristic
832C2×C4C22×#4111yescharacteristic
833C2×C4C2×H(5,𝔽2)11yescharacteristic
834C2×C4#58511yescharacteristic
835C2×C4#58511yescharacteristic
836C8—22no—
837C8—41no—
838C8—42no—
839C8—42no—
840C8—41no—
841C8—41no—
842C22—24no—
843C22—24no—
844C22—24no—
845C22—24no—
846C22—24no—
847C22—24no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22C2×#48318yes—
856C22C22×#12311yescharacteristic
857C22D4×#4111yescharacteristic
858C22#348811yescharacteristic
859C22C23×SD1611yescharacteristic
860C22C22×#13711yescharacteristic
861C22#358411yescharacteristic
862C22#358611yescharacteristic
863C4—22no—
864C4—24no—
865C4—22no—
866C4—24no—
867C4—42no—
868C4—41no—
869C4—41no—
870C4—42no—
871C4—42no—
872C4—42no—
873C4—81no—
874C4—82no—
875C4—81no—
876C4—81no—
877C4—82no—
878C4—82no—
879C4—81no—
880C4—82no—
881C4—81no—
882C4C2×#48314yes—
883C4#347511yescharacteristic
884C4#348111yescharacteristic
885C4#351411yescharacteristic
886C4#352111yescharacteristic
887C2—28no—
888C2—42no—
889C2#3621611yescharacteristic
890C2C22×#48311yescharacteristic
891C2#6052411yescharacteristic
892C2SD16×#4111yescharacteristic
893C2#6145711yescharacteristic
894C2#6194811yescharacteristic
895C2#6199111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#41D4
LCSG ▷ C22×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
3. #33108C2semidirect
4. #33098C2semidirect
5. #27889C2semidirect
6. #27855C2semidirect
7. #27628C2semidirect
8. #27583C2semidirect
9. #26320C2semidirect
10. #26320C2semidirect
11. #26200C2semidirect
12. #26128C2semidirect
13. #25060C2semidirect
14. #24994C2semidirect
15. #24863C2semidirect
16. #24863C2semidirect
17. #22703C2semidirect
18. D4×#106C2semidirect
20. D4×#103C2semidirect
21. D4×#103C2semidirect
22. C4×#483C2semidirect
23. C2×#1927C2semidirect
501. #103#41semidirect
751. D4#483semidirect

Maximal subgroups

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

subgroupindex
#362742
C4⋊C4×#412
#331082
#330982
#278892
#278552
#276282
#275832
#263202
#262002
#261282
#250602
#249942
#248632
#227032
D4×#1062
#224692
D4×#1032
C4×#4832
C2×#19272