Finite Group Databasebeta

← #7048511

Subgroups — #7048511

Order 512.

1604 conjugacy classes of subgroups.

The subgroup lattice has 1325 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59405C211yesmaximal, characteristic, complemented
2#59273C211yesmaximal, characteristic, complemented
3#32533C211yesmaximal, characteristic, complemented
4#32446C211yesmaximal, characteristic, complemented
5#31864C211yesmaximal, characteristic, complemented
6#31424C211yesmaximal, characteristic, complemented
7#31134C211yesmaximal, characteristic, complemented
8#31032C211yesmaximal, characteristic
9#30603C211yesmaximal, characteristic, complemented
10#30408C211yesmaximal, characteristic, complemented
11#28975C211yesmaximal, characteristic, complemented
12#28117C211yesmaximal, characteristic, complemented
13#28038C211yesmaximal, characteristic, complemented
14#27630C211yesmaximal, characteristic, complemented
15#27567C211yesmaximal, characteristic, complemented
16#27539C211yesmaximal, characteristic, complemented
17#27365C211yesmaximal, characteristic, complemented
18#27175C211yesmaximal, characteristic, complemented
19#27071C211yesmaximal, characteristic, complemented
20#26788C211yesmaximal, characteristic, complemented
21#26656C211yesmaximal, characteristic, complemented
22#26130C211yesmaximal, characteristic, complemented
23#25152C211yesmaximal, characteristic, complemented
24#24979C211yesmaximal, characteristic, complemented
25#24813C211yesmaximal, characteristic, complemented
26#24578C211yesmaximal, characteristic, complemented
27#23755C211yesmaximal, characteristic, complemented
28#23109C211yesmaximal, characteristic, complemented
29#23022C211yesmaximal, characteristic, complemented
30#22361C211yesmaximal, characteristic, complemented
31#22043C211yesmaximal, characteristic, complemented
32C2×#551—21no—
33C2×#481C2211yescharacteristic
34C2×#481C2211yescharacteristic
35C2×#475C2211yescharacteristic, complemented
36C2×#465C2211yescharacteristic
37C2×#463C2211yescharacteristic
38C2×#450C2211yescharacteristic
39C2×#447C2211yescharacteristic
40C2×C4×SD16C2211yescharacteristic
41C22×#106C2211yescharacteristic, complemented
42#2793—21no—
43#2779—21no—
44#2723—21no—
45#2706—21no—
46#2597—21no—
47#2587—21no—
48#2559—21no—
49#2542C2211yescharacteristic
50#2536C2211yescharacteristic
51#2513C2211yescharacteristic, complemented
52#2512C2211yescharacteristic
53#2512C2211yescharacteristic
54#2509C2211yescharacteristic, complemented
55#2501C2211yescharacteristic
56#2496C2211yescharacteristic
57#2491C2211yescharacteristic
58#2482—21no—
59#2479—21no—
60#2466—21no—
61#2461—21no—
62#2440C2211yescharacteristic
63#2437—21no—
64#2426C2211yescharacteristic
65#2426C2211yescharacteristic, complemented
66#2422—21no—
67#2422C2211yescharacteristic
68#2422C2211yescharacteristic, complemented
69#2418—21no—
70#2416C2211yescharacteristic
71#2408C2211yescharacteristic
72#2374—21no—
73#2367C2211yescharacteristic, complemented
74#2361C2211yescharacteristic
75#2360C2211yescharacteristic, complemented
76#2354C2211yescharacteristic
77Q8×C4⋊C4C2211yescharacteristic, complemented
78D4×C4⋊C4C2211yescharacteristic
79#2345C2211yescharacteristic, complemented
80D4×C22⋊C4C2211yescharacteristic
81C4×C22⋊Q8C2211yescharacteristic
82C4×#123C2211yescharacteristic
83C4×#121C2211yescharacteristic
84C2×#390C2211yescharacteristic
85#2285C2211yescharacteristic
86#2100C2211yescharacteristic, complemented
87#2100C2211yescharacteristic, complemented
88#2099C2211yescharacteristic, complemented
89#2094C2211yescharacteristic, complemented
90#2094C2211yescharacteristic, complemented
91#2092C2211yescharacteristic
92#2088C2211yescharacteristic, complemented
93#2084C2211yescharacteristic, complemented
94#2084C2211yescharacteristic, complemented
95#2084C2211yescharacteristic, complemented
96#2077C2211yescharacteristic
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic
99#2077C2211yescharacteristic
100#2075C2211yescharacteristic, complemented
101#2073C2211yescharacteristic
102#2071C2211yescharacteristic
103#2071C2211yescharacteristic, complemented
104#2067C2211yescharacteristic, complemented
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic
107#2065C2211yescharacteristic
108#2065C2211yescharacteristic
109#2065C2211yescharacteristic
110#2058C2211yescharacteristic, complemented
111#2054C2211yescharacteristic
112#2054C2211yescharacteristic
113#2054C2211yescharacteristic
114#2042C2211yescharacteristic, complemented
115#2036C2211yescharacteristic
116#2036C2211yescharacteristic
117#2035C2211yescharacteristic, complemented
118#2034C2211yescharacteristic
119#2034C2211yescharacteristic
120#2033C2211yescharacteristic
121#2023C2211yescharacteristic, complemented
122#2012C2211yescharacteristic
123#2000C2211yescharacteristic
124#1999C2211yescharacteristic
125#1999C2211yescharacteristic
126#1990C2211yescharacteristic, complemented
127#1972C2211yescharacteristic
128#1970C2211yescharacteristic
129#1968C2211yescharacteristic
130#1968C2211yescharacteristic
131#1959C2211yescharacteristic, complemented
132#1955C2211yescharacteristic
133#1949C2211yescharacteristic, complemented
134#1948C2211yescharacteristic, complemented
135#1948C2211yescharacteristic, complemented
136#1947C2211yescharacteristic, complemented
137#1944C2211yescharacteristic, complemented
138#1941C2211yescharacteristic, complemented
139#1939C2211yescharacteristic, complemented
140#1936C2211yescharacteristic
141#1936C2211yescharacteristic
142#1934C2211yescharacteristic
143#1934C2211yescharacteristic
144#1927C2211yescharacteristic, complemented
145#1927C2211yescharacteristic, complemented
146#1926C2211yescharacteristic
147#1926C2211yescharacteristic
148#1926C2211yescharacteristic
149#1926C2211yescharacteristic
150#1926C2211yescharacteristic
151#1926C2211yescharacteristic, complemented
152#1924C2211yescharacteristic
153#1924C2211yescharacteristic, complemented
154#1923C2211yescharacteristic
155#1923C2211yescharacteristic, complemented
156#1920C2211yescharacteristic, complemented
157#1919C2211yescharacteristic, complemented
158#1918C2211yescharacteristic, complemented
159#1918C2211yescharacteristic, complemented
160#1917C2211yescharacteristic, complemented
161#1916C2211yescharacteristic, complemented
162#1893C2211yescharacteristic
163#1893C2211yescharacteristic, complemented
164#1880C2211yescharacteristic
165#1880C2211yescharacteristic
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1880C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic
172#1874C2211yescharacteristic
173#1874C2211yescharacteristic, complemented
174#1872C2211yescharacteristic
175#1872C2211yescharacteristic, complemented
176#1869C2211yescharacteristic
177#1865C2211yescharacteristic, complemented
178#1864C2211yescharacteristic
179#1864C2211yescharacteristic
180#1862C2211yescharacteristic
181#1853C2211yescharacteristic
182#1853C2211yescharacteristic, complemented
183#1850C2211yescharacteristic, complemented
184#1836C2211yescharacteristic, complemented
185#1824C2211yescharacteristic
186#1823C2211yescharacteristic, complemented
187#1803C2211yescharacteristic, complemented
188#1803C2211yescharacteristic, complemented
189#1803C2211yescharacteristic, complemented
190#1802C2211yescharacteristic
191#1797C2211yescharacteristic
192#1786C2211yescharacteristic
193#1786C2211yescharacteristic
194C4×#106C2211yescharacteristic, complemented
195C4×#106C2211yescharacteristic, complemented
196#1771C2211yescharacteristic, complemented
197#1763C2211yescharacteristic, complemented
198#1762C2211yescharacteristic
199C4×#102C2211yescharacteristic, complemented
200C4×#102C2211yescharacteristic, complemented
201C8×C22⋊C4C2211yescharacteristic, complemented
202C4×C22⋊C8C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209#551—48no—
210C2×C4⋊Q8C2311yescharacteristic
211C2×#126—21no—
212C2×#126—21no—
213C2×#126—21no—
214C2×#124—21no—
215C2×#124C2311yescharacteristic
216C2×#123—21no—
217C2×#123—21no—
218C2×#123—21no—
219C2×#123—21no—
220C2×#123D411yescharacteristic
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×#121—21no—
227C2×#121C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#120—21no—
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×D4—21no—
236C2×C4×D4—21no—
237C2×C4×D4—21no—
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×#117—21no—
243C2×#117—21no—
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C22⋊C4—21no—
248C22×C22⋊C4—21no—
249C22×C22⋊C4—21no—
250C22×C42C2311yescharacteristic
251#481—42no—
252#481—42no—
253#475—42no—
254#465—24no—
255#463—24no—
256#450—24no—
257#447—42no—
258C4×SD16—42no—
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#106—42no—
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×#97C2311yescharacteristic
309C2×#97C2311yescharacteristic
310C2×C4×C8C2311yescharacteristic
311C2×C4×C8C2311yescharacteristic
312C2×C4×C8C2311yescharacteristic
313#400—21no—
314#400—21no—
315#400—21no—
316#399—21no—
317#399—21no—
318#399—21no—
319#399—21no—
320#398—21no—
321#398—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#396—21no—
330#396—21no—
331#396—21no—
332#396—21no—
333#396—21no—
334#395—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#393—21no—
344#392—21no—
345#391C2311yescharacteristic
346#390—21no—
347#390—21no—
348#390—21no—
349#390—21no—
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#389—21no—
362#389—21no—
363#389—21no—
364#389—21no—
365#389—21no—
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388D411yescharacteristic
390#388D411yescharacteristic
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387D411yescharacteristic
398#387D411yescharacteristic
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386D411yescharacteristic
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385D411yescharacteristic
415#384—21no—
416#384C2311yescharacteristic
417#384C2311yescharacteristic
418#384C2311yescharacteristic
419#384C2311yescharacteristic
420#384C2311yescharacteristic
421#382—21no—
422#382C2311yescharacteristic
423#381D411yescharacteristic
424#380—21no—
425#380—21no—
426#380—21no—
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#379—21no—
434#379—21no—
435C4×C4⋊C4—21no—
436C4×C4⋊C4—21no—
437C4×C4⋊C4—21no—
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4C2311yescharacteristic
452C4×C22⋊C4C2311yescharacteristic
453C4×C22⋊C4C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488C25—21no—
489C22×Q8—21no—
490C22×Q8C2411yescharacteristic
491C22×D4—22no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—41no—
498C22×D4—41no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4—41no—
502C22×D4C2×D411yescharacteristic
503C22×D4C2411yescharacteristic
504C22×D4C2411yescharacteristic
505C22×D4C2411yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4C2×D411yescharacteristic
513C23×C4C2×D411yescharacteristic
514C23×C4C2411yescharacteristic
515C23×C4C2411yescharacteristic
516C2×SD16—22no—
517C2×SD16—41no—
518C2×SD16—41no—
519C2×SD16—41no—
520C2×SD16—41no—
521C2×SD16#4114yes—
522C2×D8—22no—
523C2×D8—41no—
524C2×D8—41no—
525C2×D8—41no—
526C2×D8—41no—
527C2×D8—41no—
528C22×C8—22no—
529C22×C8—41no—
530C22×C8—41no—
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C4⋊Q8—41no—
540C4⋊Q8—41no—
541#126—44no—
542#126—44no—
543#126—82no—
544#124—22no—
545#124—41no—
546#124—44no—
547#123—24no—
548#123—44no—
549#123—44no—
550#123—44no—
551#123—82no—
552C22⋊Q8—22no—
553C22⋊Q8—22no—
554C22⋊Q8—44no—
555C22⋊Q8—41no—
556C22⋊Q8—41no—
557C22⋊Q8—44no—
558C22⋊Q8—82no—
559#121—22no—
560#121—22no—
561#121—41no—
562#121—41no—
563#121—41no—
564#121—41no—
565#121—41no—
566#121—41no—
567#121—82no—
568#120—44no—
569C4×Q8—22no—
570C4×Q8—41no—
571C4×Q8—41no—
572C4×Q8—41no—
573C4×Q8—41no—
574C4×Q8—41no—
575C4×D4—22no—
576C4×D4—41no—
577C4×D4—41no—
578C4×D4—41no—
579C4×D4—41no—
580C4×D4—41no—
581C4×D4—41no—
582C4×D4—41no—
583C4×D4—44no—
584C4×D4—44no—
585C4×D4—82no—
586#117—44no—
587#117—44no—
588C2×C4⋊C4—22no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—41no—
617C2×C4⋊C4—41no—
618C2×C4⋊C4—41no—
619C2×C4⋊C4—41no—
620C2×C4⋊C4—41no—
621C2×C4⋊C4C2×D411yescharacteristic
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2×D411yescharacteristic
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—44no—
678C2×C22⋊C4—44no—
679C2×C22⋊C4—82no—
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—41no—
698C2×C42—41no—
699C2×C42C2×D411yescharacteristic
700C2×C42C2×D411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706#107—41no—
707#107—41no—
708#106—22no—
709#106—22no—
710#106—22no—
711#106—22no—
712#106—22no—
713#106—41no—
714#106—41no—
715#106—41no—
716#106—41no—
717#106—41no—
718C4⋊C8—22no—
719C4⋊C8—41no—
720C4⋊C8—41no—
721C4⋊C8—41no—
722C4⋊C8—41no—
723#103—22no—
724#103—22no—
725#103—41no—
726#103—41no—
727#103—41no—
728#103—41no—
729#102—22no—
730#102—22no—
731#102—22no—
732#102—22no—
733#102—22no—
734#102—22no—
735#102—41no—
736#102—41no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102—41no—
747C22⋊C8—22no—
748C22⋊C8—41no—
749C22⋊C8—41no—
750C22⋊C8—41no—
751C22⋊C8—41no—
752C22⋊C8—41no—
753C22⋊C8—41no—
754#97—41no—
755#97—41no—
756C4×C8—41no—
757C4×C8—41no—
758C4×C8—41no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793C24—21no—
794C24—21no—
795C24—21no—
796C24—42no—
797C24—42no—
798C24—42no—
799C24—42no—
800C24—81no—
801C24—81no—
802C24—81no—
803C24C22×D411yescharacteristic
804C24C22×D411yescharacteristic
805C2×Q8—21no—
806C2×Q8—21no—
807C2×Q8—21no—
808C2×Q8—21no—
809C2×Q8—21no—
810C2×Q8—42no—
811C2×Q8—81no—
812C2×Q8—81no—
813C2×Q8C2×#4112yes—
814C2×D4—22no—
815C2×D4—22no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—41no—
834C2×D4—42no—
835C2×D4—42no—
836C2×D4—42no—
837C2×D4—42no—
838C2×D4—42no—
839C2×D4—42no—
840C2×D4—42no—
841C2×D4—42no—
842C2×D4—81no—
843C2×D4—82no—
844C2×D4—82no—
845C2×D4—82no—
846C2×D4—82no—
847C2×D4—81no—
848C2×D4—81no—
849C2×D4—81no—
850C2×D4—81no—
851C2×D4—81no—
852C2×D4—81no—
853C2×D4C2×#4112yes—
854C22×C4—22no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—22no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—22no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—41no—
883C22×C4—41no—
884C22×C4—41no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—42no—
888C22×C4—42no—
889C22×C4—42no—
890C22×C4—42no—
891C22×C4—42no—
892C22×C4—81no—
893C22×C4—81no—
894C22×C4—81no—
895C22×C4—81no—
896C22×C4—81no—
897C22×C4—81no—
898C22×C4—81no—
899C22×C4—81no—
900C22×C4—81no—
901C22×C4—81no—
902C22×C4—81no—
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C2511yescharacteristic
916SD16—44no—
917SD16—82no—
918D8—82no—
919D8—82no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—44no—
944C2×C8C2×#4112yes—
945C4⋊C4—22no—
946C4⋊C4—22no—
947C4⋊C4—22no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—41no—
972C4⋊C4—41no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—42no—
976C4⋊C4—42no—
977C4⋊C4—42no—
978C4⋊C4—42no—
979C4⋊C4—42no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4H(5,𝔽2)12yes—
1001C22⋊C4—22no—
1002C22⋊C4—22no—
1003C22⋊C4—22no—
1004C22⋊C4—22no—
1005C22⋊C4—41no—
1006C22⋊C4—41no—
1007C22⋊C4—41no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4AGL(1,ℤ/8)14yes—
1048C42—21no—
1049C42—21no—
1050C42—21no—
1051C42—21no—
1052C42—21no—
1053C42—21no—
1054C42—21no—
1055C42—21no—
1056C42—21no—
1057C42—21no—
1058C42—41no—
1059C42—41no—
1060C42—42no—
1061C42—42no—
1062C42—42no—
1063C42—42no—
1064C42—81no—
1065C42—81no—
1066C42—81no—
1067C42—81no—
1068C42—81no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—22no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—84no—
1103C23—84no—
1104C23—84no—
1105C23—84no—
1106C23—162no—
1107C23—162no—
1108C23—162no—
1109C23C2×AGL(1,ℤ/8)12yes—
1110C23#57712yes—
1111C23C23×D411yescharacteristic
1112Q8—22no—
1113Q8—22no—
1114Q8—41no—
1115Q8—41no—
1116Q8—162no—
1117D4—22no—
1118D4—22no—
1119D4—44no—
1120D4—41no—
1121D4—41no—
1122D4—41no—
1123D4—41no—
1124D4—41no—
1125D4—41no—
1126D4—41no—
1127D4—41no—
1128D4—41no—
1129D4—41no—
1130D4—84no—
1131D4—84no—
1132D4—84no—
1133D4—162no—
1134D4—162no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—22no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—22no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—44no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—82no—
1217C2×C4—84no—
1218C2×C4—162no—
1219C2×C4—162no—
1220C2×C4—162no—
1221C2×C4—162no—
1222C2×C4—162no—
1223C2×C4C2×AGL(1,ℤ/8)12yes—
1224C2×C4C2×AGL(1,ℤ/8)12yes—
1225C2×C4#57712yes—
1226C2×C4C22×#4111yescharacteristic
1227C2×C4C2×H(5,𝔽2)11yescharacteristic
1228C2×C4#58511yescharacteristic
1229C2×C4#58511yescharacteristic
1230C2×C4#58511yescharacteristic
1231C2×C4#58511yescharacteristic
1232C8—22no—
1233C8—41no—
1234C8—41no—
1235C8—41no—
1236C8—41no—
1237C8—41no—
1238C8—41no—
1239C8—41no—
1240C22—22no—
1241C22—22no—
1242C22—22no—
1243C22—22no—
1244C22—22no—
1245C22—22no—
1246C22—41no—
1247C22—41no—
1248C22—41no—
1249C22—41no—
1250C22—41no—
1251C22—41no—
1252C22—41no—
1253C22—41no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—168no—
1276C22D4×#4111yescharacteristic
1277C22#348511yescharacteristic
1278C22#348811yescharacteristic
1279C22C22×AGL(1,ℤ/8)11yescharacteristic
1280C22C2×#57711yescharacteristic
1281C22C2×#57711yescharacteristic
1282C22#358411yescharacteristic
1283C4—22no—
1284C4—22no—
1285C4—22no—
1286C4—41no—
1287C4—41no—
1288C4—42no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—42no—
1296C4—41no—
1297C4—81no—
1298C4—81no—
1299C4—81no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4#350511yescharacteristic
1309C4#352111yescharacteristic
1310C4#355111yescharacteristic
1311C4#356611yescharacteristic
1312C2—42no—
1313C2—42no—
1314C2—82no—
1315C2—161no—
1316C2—161no—
1317C2#4353911yescharacteristic
1318C2#6143911yescharacteristic
1319C2#6148311yescharacteristic
1320C2#6172811yescharacteristic
1321C2#6177311yescharacteristic
1322C2#6198311yescharacteristic
1323C2#6206311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#31032C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59405C2semidirect
2. #59273C2semidirect
3. #32533C2semidirect
4. #32446C2semidirect
5. #31864C2semidirect
6. #31424C2semidirect
7. #31134C2semidirect
9. #30603C2semidirect
10. #30408C2semidirect
11. #28975C2semidirect
12. #28117C2semidirect
13. #28038C2semidirect
14. #27630C2semidirect
15. #27567C2semidirect
16. #27539C2semidirect
17. #27365C2semidirect
18. #27175C2semidirect
19. #27071C2semidirect
20. #26788C2semidirect
21. #26656C2semidirect
22. #26130C2semidirect
23. #25152C2semidirect
24. #24979C2semidirect
25. #24813C2semidirect
26. #24578C2semidirect
27. #23755C2semidirect
28. #23109C2semidirect
29. #23022C2semidirect
30. #22361C2semidirect
31. #22043C2semidirect
35. C2×#475C22semidirect
41. C22×#106C22semidirect
51. #2513C22semidirect
54. #2509C22semidirect
65. #2426C22semidirect
68. #2422C22semidirect
73. #2367C22semidirect
75. #2360C22semidirect
77. Q8×C4⋊C4C22semidirect
79. #2345C22semidirect
86. #2100C22semidirect
87. #2100C22semidirect
88. #2099C22semidirect
89. #2094C22semidirect
90. #2094C22semidirect
92. #2088C22semidirect
93. #2084C22semidirect
94. #2084C22semidirect
95. #2084C22semidirect
100. #2075C22semidirect
103. #2071C22semidirect
104. #2067C22semidirect
110. #2058C22semidirect
114. #2042C22semidirect
117. #2035C22semidirect
121. #2023C22semidirect
126. #1990C22semidirect
131. #1959C22semidirect
133. #1949C22semidirect
134. #1948C22semidirect
135. #1948C22semidirect
136. #1947C22semidirect
137. #1944C22semidirect
138. #1941C22semidirect
139. #1939C22semidirect
144. #1927C22semidirect
145. #1927C22semidirect
151. #1926C22semidirect
153. #1924C22semidirect
155. #1923C22semidirect
156. #1920C22semidirect
157. #1919C22semidirect
158. #1918C22semidirect
159. #1918C22semidirect
160. #1917C22semidirect
161. #1916C22semidirect
163. #1893C22semidirect
173. #1874C22semidirect
175. #1872C22semidirect
177. #1865C22semidirect
182. #1853C22semidirect
183. #1850C22semidirect
184. #1836C22semidirect
186. #1823C22semidirect
187. #1803C22semidirect
188. #1803C22semidirect
189. #1803C22semidirect
194. C4×#106C22semidirect
195. C4×#106C22semidirect
196. #1771C22semidirect
197. #1763C22semidirect
199. C4×#102C22semidirect
200. C4×#102C22semidirect
201. C8×C22⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#594052
#592732
#325332
#324462
#318642
#314242
#311342
#310322
#306032
#304082
#289752
#281172
#280382
#276302
#275672
#275392
#273652
#271752
#270712
#267882
#266562
#261302
#251522
#249792
#248132
#245782
#237552
#231092
#230222
#223612
#220432