Finite Group Databasebeta

← #6492190

Subgroups — #6492190

Order 512.

1769 conjugacy classes of subgroups.

The subgroup lattice has 907 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35189C211yesmaximal, characteristic
2C4⋊C4×#41C211yesmaximal, characteristic, complemented
3#33150C212yesmaximal, complemented
4#33110C212yesmaximal, complemented
5#29943C212yesmaximal, complemented
6#29927C212yesmaximal, complemented
7#26220C212yesmaximal, complemented
8#26218C212yesmaximal, complemented
9#26148C212yesmaximal, complemented
10#26146C212yesmaximal, complemented
11#25060C211yesmaximal, characteristic, complemented
12#25056C211yesmaximal, characteristic, complemented
13#25016C211yesmaximal, characteristic, complemented
14#25012C211yesmaximal, characteristic, complemented
15#24994C211yesmaximal, characteristic, complemented
16#24990C211yesmaximal, characteristic, complemented
17#24971C211yesmaximal, characteristic, complemented
18#24967C211yesmaximal, characteristic, complemented
19#21984C211yesmaximal, characteristic, complemented
20#21890C211yesmaximal, characteristic, complemented
21#21849C211yesmaximal, characteristic, complemented
22#21388C211yesmaximal, characteristic, complemented
23#21170C211yesmaximal, characteristic, complemented
24C2×#529C2211yescharacteristic
25C2×C4×#41—21no—
26C2×C4×#41C2211yescharacteristic
27C2×#484C2212yes—
28C2×#481C2212yes—
29C2×#431C2211yescharacteristic
30C2×#428C2212yes—
31C2×#423C2211yescharacteristic
32#2851C2212yes—
33#2850C2212yes—
34#2630—22no—
35#2601—22no—
36#2582C2211yescharacteristic
37#2538C2211yescharacteristic
38#2538C2211yescharacteristic
39#2537C2211yescharacteristic
40#2485—21no—
41#2415C2212yes—
42#2414C2212yes—
43#2407—21no—
44#2351—21no—
45Q8×C4⋊C4C2211yescharacteristic
46Q8×C4⋊C4C2211yescharacteristic
47#2349—21no—
48#2349—22no—
49D4×C4⋊C4C2212yes—
50D4×C4⋊C4C2212yes—
51D4×C4⋊C4C2211yescharacteristic
52D4×C4⋊C4C2211yescharacteristic
53#2324—21no—
54#2323—21no—
55#2296—22no—
56#2296—21no—
57#2285C2211yescharacteristic
58#2285C2212yes—
59#2285C2211yescharacteristic
60C2×C4×C4⋊C4C2212yes—
61C2×C4×C4⋊C4C2211yescharacteristic
62#2099C2212yes—
63#2099C2212yes—
64#2096C2212yes—
65#2093C2212yes—
66#2084C2212yes—
67#2083C2212yes—
68#2077C2212yes—
69#2077C2212yes—
70#2076C2212yes—
71#2076C2212yes—
72#2072C2212yes—
73#2071C2212yes—
74#2036C2212yes—
75#2036C2212yes—
76#2034C2212yes—
77#2034C2212yes—
78#1989C2211yescharacteristic
79#1989C2212yes—
80#1989C2211yescharacteristic
81#1984C2211yescharacteristic
82#1984C2211yescharacteristic
83#1983C2211yescharacteristic
84#1983C2212yes—
85#1983C2211yescharacteristic
86#1954C2211yescharacteristic
87#1954C2211yescharacteristic
88#1949C2212yes—
89#1949C2212yes—
90#1949C2212yes—
91#1949C2212yes—
92#1948C2211yescharacteristic
93#1948C2211yescharacteristic
94#1947C2211yescharacteristic
95#1947C2211yescharacteristic
96#1927C2212yes—
97#1927C2212yes—
98#1925C2212yes—
99#1925C2212yes—
100#1920C2212yes—
101#1920C2212yes—
102#1918C2212yes—
103#1918C2212yes—
104#1895C2212yes—
105#1894C2212yes—
106#1874C2211yescharacteristic
107#1874C2212yes—
108#1874C2211yescharacteristic
109#1872C2211yescharacteristic
110#1872C2212yes—
111#1872C2211yescharacteristic
112#1870C2212yes—
113#1870C2212yes—
114#1854C2212yes—
115#1854C2212yes—
116#1853C2212yes—
117#1852C2212yes—
118#1845C2211yescharacteristic
119#1844C2211yescharacteristic
120#1834C2211yescharacteristic
121#1834C2211yescharacteristic
122#1824C2212yes—
123#1824C2212yes—
124#1803C2211yescharacteristic
125#1803C2211yescharacteristic
126#1802C2211yescharacteristic
127#1802C2211yescharacteristic
128#1797C2212yes—
129#1797C2212yes—
130C4×#103C2211yescharacteristic
131C4×#103C2211yescharacteristic
132C4×#102C2211yescharacteristic
133C4×#102C2211yescharacteristic
134#1736C2212yes—
135C22×#41D411yescharacteristic
136C22×M16C2312yes—
137#529—24no—
138#529—24no—
139C2×#126—21no—
140C2×#125C2311yescharacteristic
141C2×#124C2311yescharacteristic
142C2×#123—21no—
143C2×C22⋊Q8—21no—
144C2×C22⋊Q8C2311yescharacteristic
145C2×C22⋊Q8C2312yes—
146C2×#121—21no—
147C2×#121C2311yescharacteristic
148C2×#121C2312yes—
149C4×#41—24no—
150C4×#41—24no—
151C4×#41—48no—
152C2×C4×Q8—21no—
153C2×C4×Q8—21no—
154C2×C4×Q8D411yescharacteristic
155C2×C4×Q8C2311yescharacteristic
156C2×C4×Q8C2311yescharacteristic
157C2×C4×D4—22no—
158C2×C4×D4—22no—
159C2×C4×D4—21no—
160C2×C4×D4—21no—
161C2×C4×D4—21no—
162C2×C4×D4D411yescharacteristic
163C2×C4×D4D412yes—
164C2×C4×D4C2311yescharacteristic
165C2×C4×D4C2312yes—
166C2×C4×D4C2311yescharacteristic
167C2×#117—22no—
168C2×#117—21no—
169C2×#117—21no—
170C2×#117D412yes—
171C2×#117D411yescharacteristic
172C2×#117C2312yes—
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C42—22no—
178C22×C42—21no—
179C22×C42C2312yes—
180C22×C42C2311yescharacteristic
181#484—44no—
182#481—44no—
183#431—24no—
184#428—44no—
185C2×#107C2312yes—
186C2×#107C2312yes—
187C2×#107C2312yes—
188C2×#107C2312yes—
189C2×#106C2312yes—
190C2×#106C2312yes—
191C2×#106C2312yes—
192C2×#106C2312yes—
193#423—24no—
194C2×C4⋊C8C2312yes—
195C2×C4⋊C8C2311yescharacteristic
196C2×C4⋊C8C2311yescharacteristic
197C2×C4⋊C8C2311yescharacteristic
198C2×C4⋊C8C2311yescharacteristic
199C2×#103C2311yescharacteristic
200C2×#103C2311yescharacteristic
201C2×#103C2312yes—
202C2×#103C2312yes—
203C2×#103C2311yescharacteristic
204C2×#103C2311yescharacteristic
205C2×#102C2311yescharacteristic
206C2×#102C2311yescharacteristic
207C2×#102C2312yes—
208C2×#102C2312yes—
209C2×#102C2311yescharacteristic
210C2×#102C2311yescharacteristic
211C2×C22⋊C8C2311yescharacteristic
212C2×C22⋊C8C2311yescharacteristic
213C2×C22⋊C8C2312yes—
214C2×C22⋊C8C2312yes—
215C2×C22⋊C8C2312yes—
216C2×C22⋊C8C2312yes—
217C2×C4×C8C2311yescharacteristic
218C2×C4×C8C2311yescharacteristic
219#398—22no—
220#397—22no—
221#396—22no—
222#396—22no—
223#394—22no—
224#394—22no—
225#394—22no—
226#392—22no—
227#391—21no—
228#391C2312yes—
229#390—21no—
230#390—22no—
231#390C2312yes—
232#389—22no—
233#389—21no—
234#389—21no—
235#389—21no—
236#389—21no—
237#389—22no—
238#389—22no—
239#389—21no—
240#389—21no—
241#389—22no—
242#389—22no—
243#389C2312yes—
244#389C2312yes—
245#388—22no—
246#388—22no—
247#388—22no—
248#388—22no—
249#387—22no—
250#387—22no—
251#386—22no—
252#386—22no—
253#385—22no—
254#385—22no—
255#385—22no—
256#385—22no—
257#385—22no—
258#385—22no—
259#385—22no—
260#385—22no—
261#384C2311yescharacteristic
262#384C2311yescharacteristic
263#384C2311yescharacteristic
264#384C2312yes—
265#384C2312yes—
266#384C2311yescharacteristic
267#382—22no—
268#382—21no—
269#382C2312yes—
270#380—22no—
271#380—21no—
272#380—21no—
273#380—21no—
274#380—21no—
275#380—21no—
276#380C2312yes—
277#380C2312yes—
278#380C2312yes—
279#380C2312yes—
280#380C2312yes—
281C4×C4⋊C4—21no—
282C4×C4⋊C4—21no—
283C4×C4⋊C4—22no—
284C4×C4⋊C4—21no—
285C4×C4⋊C4—22no—
286C4×C4⋊C4—21no—
287C4×C4⋊C4—22no—
288C4×C4⋊C4—21no—
289C4×C4⋊C4C2312yes—
290C4×C4⋊C4C2312yes—
291C4×C4⋊C4C2311yescharacteristic
292C4×C4⋊C4C2311yescharacteristic
293C4×C4⋊C4C2311yescharacteristic
294C4×C4⋊C4C2312yes—
295C4×C4⋊C4C2311yescharacteristic
296C2×#95—22no—
297C2×#95—21no—
298#340C2312yes—
299#340C2312yes—
300#340C2312yes—
301#340C2312yes—
302#340C2312yes—
303#340C2312yes—
304#340C2312yes—
305#340C2312yes—
306#340C2311yescharacteristic
307#340C2311yescharacteristic
308#340C2312yes—
309#340C2311yescharacteristic
310#340C2311yescharacteristic
311#340C2312yes—
312#340C2311yescharacteristic
313#340C2311yescharacteristic
314#340C2312yes—
315#340C2312yes—
316#340C2311yescharacteristic
317#340C2311yescharacteristic
318#336C2312yes—
319#336C2312yes—
320#336C2312yes—
321#336C2312yes—
322C2×#41—24no—
323C2×#41—24no—
324C2×#41—24no—
325C22×Q8C2×D411yescharacteristic
326C22×Q8C2411yescharacteristic
327C22×D4—21no—
328C22×D4—22no—
329C22×D4C2×D412yes—
330C22×D4C2×D411yescharacteristic
331C22×D4C2411yescharacteristic
332C23×C4—21no—
333C23×C4—21no—
334C23×C4—22no—
335C23×C4—22no—
336C23×C4—21no—
337C23×C4C2×D412yes—
338C23×C4C2×D411yescharacteristic
339C23×C4C2×D412yes—
340C23×C4C2×D411yescharacteristic
341C23×C4C2412yes—
342C23×C4C2411yescharacteristic
343C2×M16—24no—
344C2×M16—42no—
345C2×M16—42no—
346C22×C8C2412yes—
347C22×C8C2412yes—
348C22×C8C2411yescharacteristic
349C22×C8C2411yescharacteristic
350C22×C8C2411yescharacteristic
351C22×C8C2411yescharacteristic
352#126—44no—
353#125—22no—
354#125—22no—
355#124—22no—
356#124—22no—
357#123—44no—
358C22⋊Q8—22no—
359C22⋊Q8—22no—
360C22⋊Q8—44no—
361C22⋊Q8—42no—
362C22⋊Q8—42no—
363#121—22no—
364#121—22no—
365#121—44no—
366#121—42no—
367#121—42no—
368C4×Q8—24no—
369C4×Q8—22no—
370C4×Q8—22no—
371C4×Q8—22no—
372C4×Q8—22no—
373C4×Q8—44no—
374C4×Q8—44no—
375C4×D4—28no—
376C4×D4—24no—
377C4×D4—24no—
378C4×D4—24no—
379C4×D4—22no—
380C4×D4—22no—
381C4×D4—22no—
382C4×D4—22no—
383C4×D4—48no—
384C4×D4—48no—
385C4×D4—44no—
386C4×D4—44no—
387C4×D4—44no—
388#117—24no—
389#117—28no—
390#117—48no—
391#117—44no—
392#117—44no—
393#117—42no—
394#117—42no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—24no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—24no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—21no—
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—21no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—41no—
423C2×C4⋊C4—41no—
424C2×C4⋊C4—42no—
425C2×C4⋊C4—42no—
426C2×C4⋊C4C2×D411yescharacteristic
427C2×C4⋊C4C2×D412yes—
428C2×C4⋊C4C2×D411yescharacteristic
429C2×C4⋊C4C2×D412yes—
430C2×C4⋊C4C2412yes—
431C2×C4⋊C4C2411yescharacteristic
432C2×C4⋊C4C2412yes—
433C2×C4⋊C4C2411yescharacteristic
434C2×C4⋊C4C2412yes—
435C2×C4⋊C4C2412yes—
436C2×C4⋊C4C2411yescharacteristic
437C2×C4⋊C4C2411yescharacteristic
438C2×C4⋊C4C2411yescharacteristic
439C2×C4⋊C4C2411yescharacteristic
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4C2×D412yes—
456C2×C22⋊C4C2×D412yes—
457C2×C22⋊C4C2×D412yes—
458C2×C42—24no—
459C2×C42—24no—
460C2×C42—21no—
461C2×C42—22no—
462C2×C42—21no—
463C2×C42—22no—
464C2×C42—22no—
465C2×C42—21no—
466C2×C42—21no—
467C2×C42—21no—
468C2×C42—22no—
469C2×C42—48no—
470C2×C42—44no—
471C2×C42C2×D412yes—
472C2×C42C2×D412yes—
473C2×C42C2×D411yescharacteristic
474C2×C42C2×D411yescharacteristic
475C2×C42#4114yes—
476C2×C42#4114yes—
477C2×C42C2412yes—
478C2×C42C2411yescharacteristic
479C2×C42C2411yescharacteristic
480#107—24no—
481#107—42no—
482#107—42no—
483#107—42no—
484#106—24no—
485#106—42no—
486#106—42no—
487#106—42no—
488C4⋊C8—24no—
489C4⋊C8—22no—
490C4⋊C8—22no—
491C4⋊C8—22no—
492C4⋊C8—22no—
493#103—22no—
494#103—22no—
495#103—41no—
496#103—42no—
497#103—41no—
498#103—42no—
499#102—22no—
500#102—22no—
501#102—41no—
502#102—42no—
503#102—41no—
504#102—42no—
505C22⋊C8—22no—
506C22⋊C8—22no—
507C22⋊C8—42no—
508C22⋊C8—42no—
509C22⋊C8—42no—
510C22⋊C8—42no—
511C4×C8—22no—
512C4×C8—22no—
513#95—21no—
514#95—22no—
515#95—21no—
516#95—22no—
517#95—22no—
518#95—21no—
519#95—21no—
520#95—22no—
521#95—22no—
522#95—22no—
523#95—22no—
524#95—22no—
525#95—22no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95—22no—
530#95—22no—
531C24—21no—
532C24C22×D411yescharacteristic
533C24C22×D412yes—
534#41—232no—
535C2×Q8—22no—
536C2×Q8—22no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8AGL(1,ℤ/8)14yes—
544C2×D4—24no—
545C2×D4—24no—
546C2×D4—22no—
547C2×D4—24no—
548C2×D4—22no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—42no—
556C2×D4—44no—
557C2×D4—81no—
558C2×D4—81no—
559C2×D4—82no—
560C2×D4—82no—
561C2×D4#13714yes—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—44no—
595C22×C4—42no—
596C22×C4—44no—
597C22×C4—42no—
598C22×C4—44no—
599C22×C4—42no—
600C22×C4—44no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—82no—
605C22×C4—81no—
606C22×C4—82no—
607C22×C4—81no—
608C22×C4#12314yes—
609C22×C4#12314yes—
610C22×C4C22×D412yes—
611C22×C4C22×D412yes—
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D412yes—
617C22×C4C22×D411yescharacteristic
618C22×C4C2×#4112yes—
619C22×C4C2×#4112yes—
620C22×C4C2511yescharacteristic
621M16—48no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—21no—
639C2×C8—21no—
640C4⋊C4—24no—
641C4⋊C4—24no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—22no—
654C4⋊C4—21no—
655C4⋊C4—22no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—42no—
663C4⋊C4—42no—
664C4⋊C4—44no—
665C4⋊C4—44no—
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4—44no—
671C4⋊C4—44no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4—44no—
676C4⋊C4—42no—
677C4⋊C4—81no—
678C4⋊C4—81no—
679C4⋊C4—81no—
680C4⋊C4—81no—
681C4⋊C4—82no—
682C4⋊C4—82no—
683C4⋊C4—82no—
684C4⋊C4—82no—
685C4⋊C4H(5,𝔽2)12yes—
686C4⋊C42−1+412yes—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—24no—
690C22⋊C4—44no—
691C22⋊C4—44no—
692C22⋊C4—44no—
693C22⋊C4—42no—
694C22⋊C4—44no—
695C22⋊C4—42no—
696C22⋊C4—42no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—44no—
700C22⋊C4—82no—
701C22⋊C4—82no—
702C22⋊C4—82no—
703C22⋊C4—82no—
704C22⋊C4—82no—
705C42—24no—
706C42—24no—
707C42—22no—
708C42—22no—
709C42—42no—
710C42—44no—
711C42—42no—
712C42—42no—
713C42—44no—
714C42—44no—
715C42—42no—
716C42—42no—
717C42—82no—
718C42#12314yes—
719C42#12314yes—
720C42C2×#4112yes—
721C42C2×#4112yes—
722C42C2×#4112yes—
723C42C2×#4112yes—
724C23—22no—
725C23—22no—
726C23—21no—
727C23—21no—
728C23—22no—
729C23—21no—
730C23—22no—
731C23—21no—
732C23—22no—
733C23—21no—
734C23—22no—
735C23—21no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23C2×#12312yes—
744C23C2×#13714yes—
745C23C23×D411yescharacteristic
746Q8—28no—
747Q8—41no—
748Q8—41no—
749Q8—41no—
750Q8—41no—
751D4—216no—
752D4—28no—
753D4—41no—
754D4—41no—
755D4—41no—
756D4—41no—
757D4—84no—
758D4—164no—
759C2×C4—216no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—28no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
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—44no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—41no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—42no—
814C2×C4—41no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—84no—
820C2×C4—88no—
821C2×C4—84no—
822C2×C4—88no—
823C2×C4—84no—
824C2×C4—84no—
825C2×C4C2×#12312yes—
826C2×C4C2×#12312yes—
827C2×C4C2×#12312yes—
828C2×C4C2×#12312yes—
829C2×C4C2×#12312yes—
830C2×C4C2×AGL(1,ℤ/8)14yes—
831C2×C4C2×AGL(1,ℤ/8)12yes—
832C2×C4C2×#13712yes—
833C2×C4C22×#4111yescharacteristic
834C2×C4C22×#4111yescharacteristic
835C2×C4C2×H(5,𝔽2)11yescharacteristic
836C2×C4C2×2−1+411yescharacteristic
837C2×C4#58511yescharacteristic
838C2×C4#58511yescharacteristic
839C8—42no—
840C8—42no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—41no—
845C22—24no—
846C22—22no—
847C22—24no—
848C22—22no—
849C22—22no—
850C22—24no—
851C22—41no—
852C22—42no—
853C22—41no—
854C22—42no—
855C22—42no—
856C22—41no—
857C22—42no—
858C22—41no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22C22×#12311yescharacteristic
867C22#348811yescharacteristic
868C22#348911yescharacteristic
869C22C22×AGL(1,ℤ/8)11yescharacteristic
870C22C22×#13711yescharacteristic
871C22#358411yescharacteristic
872C22#358411yescharacteristic
873C4—22no—
874C4—24no—
875C4—22no—
876C4—22no—
877C4—22no—
878C4—42no—
879C4—42no—
880C4—42no—
881C4—42no—
882C4—82no—
883C4—82no—
884C4—82no—
885C4—81no—
886C4—81no—
887C4—81no—
888C4—81no—
889C4—82no—
890C4—81no—
891C4#309214yes—
892C4#346011yescharacteristic
893C4#346111yescharacteristic
894C4#351111yescharacteristic
895C4#351211yescharacteristic
896C2—44no—
897C2—42no—
898C2—161no—
899C2#3525511yescharacteristic
900C2C2×#309211yescharacteristic
901C2#6051611yescharacteristic
902C2#6199111yescharacteristic
903C2#6200311yescharacteristic
904C2#6213911yescharacteristic
905C2#6215111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#35189C2
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
2. C4⋊C4×#41C2semidirect
3. #33150C2semidirect
4. #33110C2semidirect
5. #29943C2semidirect
6. #29927C2semidirect
7. #26220C2semidirect
8. #26218C2semidirect
9. #26148C2semidirect
10. #26146C2semidirect
11. #25060C2semidirect
12. #25056C2semidirect
13. #25016C2semidirect
14. #25012C2semidirect
15. #24994C2semidirect
16. #24990C2semidirect
17. #24971C2semidirect
18. #24967C2semidirect
19. #21984C2semidirect
20. #21890C2semidirect
21. #21849C2semidirect
22. #21388C2semidirect
23. #21170C2semidirect

Maximal subgroups

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

subgroupindex
#351892
C4⋊C4×#412
#331502
#331102
#299432
#299272
#262202
#262182
#261482
#261462
#250602
#250562
#250162
#250122
#249942
#249902
#249712
#249672
#219842
#218902
#218492
#213882
#211702