Finite Group Databasebeta

← #6822453

Subgroups — #6822453

Order 512.

1475 conjugacy classes of subgroups.

The subgroup lattice has 1304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40188C211yesmaximal, characteristic, complemented
2#40056C211yesmaximal, characteristic, complemented
3#33269C211yesmaximal, characteristic, complemented
4#32643C211yesmaximal, characteristic, complemented
5#32554C211yesmaximal, characteristic, complemented
6#32062C211yesmaximal, characteristic, complemented
7#31734C211yesmaximal, characteristic, complemented
8#31676C211yesmaximal, characteristic, complemented
9#31448C211yesmaximal, characteristic, complemented
10#31135C211yesmaximal, characteristic, complemented
11#31008C211yesmaximal, characteristic, complemented
12#30149C211yesmaximal, characteristic, complemented
13#30133C211yesmaximal, characteristic, complemented
14#29061C211yesmaximal, characteristic, complemented
15#28982C211yesmaximal, characteristic, complemented
16#28913C211yesmaximal, characteristic, complemented
17#28853C211yesmaximal, characteristic, complemented
18#27725C211yesmaximal, characteristic, complemented
19#27262C211yesmaximal, characteristic, complemented
20#27229C211yesmaximal, characteristic, complemented
21#27161C211yesmaximal, characteristic, complemented
22#27032C211yesmaximal, characteristic, complemented
23#26940C211yesmaximal, characteristic, complemented
24#25475C211yesmaximal, characteristic, complemented
25#25309C211yesmaximal, characteristic, complemented
26#25247C211yesmaximal, characteristic, complemented
27#25124C211yesmaximal, characteristic
28#23140C211yesmaximal, characteristic, complemented
29#22574C211yesmaximal, characteristic, complemented
30C4×#489C211yesmaximal, characteristic, complemented
31#21632C211yesmaximal, characteristic, complemented
32C2×#489C2211yescharacteristic
33C2×#485C2211yescharacteristic, complemented
34C2×#478C2211yescharacteristic
35C2×#469C2211yescharacteristic
36C2×#463C2211yescharacteristic
37C2×#447C2211yescharacteristic
38C2×#446C2211yescharacteristic, complemented
39C2×#435C2211yescharacteristic
40C22×#102C2211yescharacteristic
41#2860C2211yescharacteristic
42#2860C2211yescharacteristic, complemented
43#2781—21no—
44#2778—21no—
45#2772—21no—
46#2735—21no—
47#2715—21no—
48#2702—21no—
49#2684—21no—
50#2672—21no—
51#2653—21no—
52#2651—21no—
53#2592C2211yescharacteristic
54#2584C2211yescharacteristic, complemented
55#2580C2211yescharacteristic
56#2538C2211yescharacteristic, complemented
57#2504C2211yescharacteristic
58#2497C2211yescharacteristic, complemented
59#2494C2211yescharacteristic
60#2491C2211yescharacteristic, complemented
61#2490C2211yescharacteristic
62#2485C2211yescharacteristic
63#2480—21no—
64#2467—21no—
65#2465—21no—
66#2441C2211yescharacteristic, complemented
67#2440C2211yescharacteristic
68#2435C2211yescharacteristic
69#2427C2211yescharacteristic
70#2426—21no—
71#2426C2211yescharacteristic
72#2422C2211yescharacteristic
73#2421C2211yescharacteristic
74#2417C2211yescharacteristic
75#2416C2211yescharacteristic
76#2408C2211yescharacteristic
77#2363C2211yescharacteristic, complemented
78#2361C2211yescharacteristic
79#2345C2211yescharacteristic
80D4×C22⋊C4C2211yescharacteristic
81#2335—21no—
82#2321—21no—
83C4×C4⋊Q8C2211yescharacteristic, complemented
84C4×#124C2211yescharacteristic
85C4×#124C2211yescharacteristic
86#2101C2211yescharacteristic, complemented
87#2101C2211yescharacteristic, complemented
88#2099C2211yescharacteristic, complemented
89#2092C2211yescharacteristic, complemented
90#2088C2211yescharacteristic, complemented
91#2088C2211yescharacteristic, complemented
92#2086C2211yescharacteristic, complemented
93#2084C2211yescharacteristic, complemented
94#2077C2211yescharacteristic
95#2076C2211yescharacteristic
96#2075C2211yescharacteristic
97#2073C2211yescharacteristic, complemented
98#2071C2211yescharacteristic
99#2071C2211yescharacteristic
100#2067C2211yescharacteristic
101#2066C2211yescharacteristic, complemented
102#2066C2211yescharacteristic, complemented
103#2065C2211yescharacteristic
104#2065C2211yescharacteristic
105#2065C2211yescharacteristic
106#2058C2211yescharacteristic, complemented
107#2055C2211yescharacteristic, complemented
108#2054C2211yescharacteristic
109#2054C2211yescharacteristic
110#2042C2211yescharacteristic
111#2042C2211yescharacteristic
112#2042C2211yescharacteristic
113#2035C2211yescharacteristic
114#2035C2211yescharacteristic, complemented
115#2034C2211yescharacteristic
116#2034C2211yescharacteristic
117#2034C2211yescharacteristic
118#2033C2211yescharacteristic
119#2026C2211yescharacteristic, complemented
120#2025C2211yescharacteristic
121#2023C2211yescharacteristic
122#2012C2211yescharacteristic
123#2000C2211yescharacteristic
124#2000C2211yescharacteristic, complemented
125#1999C2211yescharacteristic
126#1993C2211yescharacteristic, complemented
127#1991C2211yescharacteristic, complemented
128#1985C2211yescharacteristic, complemented
129#1972C2211yescharacteristic
130#1972C2211yescharacteristic
131#1970C2211yescharacteristic
132#1968C2211yescharacteristic, complemented
133#1959C2211yescharacteristic
134#1959C2211yescharacteristic
135#1955C2211yescharacteristic
136#1949C2211yescharacteristic, complemented
137#1948C2211yescharacteristic, complemented
138#1944C2211yescharacteristic, complemented
139#1943C2211yescharacteristic, complemented
140#1943C2211yescharacteristic, complemented
141#1941C2211yescharacteristic, complemented
142#1936C2211yescharacteristic
143#1936C2211yescharacteristic
144#1936C2211yescharacteristic
145#1936C2211yescharacteristic
146#1936C2211yescharacteristic
147#1936C2211yescharacteristic, complemented
148#1936C2211yescharacteristic, complemented
149#1935C2211yescharacteristic, complemented
150#1935C2211yescharacteristic, complemented
151#1934C2211yescharacteristic
152#1934C2211yescharacteristic
153#1934C2211yescharacteristic, complemented
154#1927C2211yescharacteristic, complemented
155#1926C2211yescharacteristic
156#1926C2211yescharacteristic
157#1926C2211yescharacteristic
158#1924C2211yescharacteristic
159#1924C2211yescharacteristic, complemented
160#1923C2211yescharacteristic
161#1923C2211yescharacteristic, complemented
162#1920C2211yescharacteristic, complemented
163#1919C2211yescharacteristic, complemented
164#1919C2211yescharacteristic, complemented
165#1919C2211yescharacteristic, complemented
166#1895C2211yescharacteristic
167#1894C2211yescharacteristic, complemented
168#1893C2211yescharacteristic
169#1892C2211yescharacteristic
170#1880C2211yescharacteristic, complemented
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic
173#1879C2211yescharacteristic
174#1875C2211yescharacteristic
175#1875C2211yescharacteristic
176#1874C2211yescharacteristic, complemented
177#1872C2211yescharacteristic
178#1864C2211yescharacteristic
179#1864C2211yescharacteristic
180#1864C2211yescharacteristic, complemented
181#1863C2211yescharacteristic, complemented
182#1853C2211yescharacteristic
183#1853C2211yescharacteristic, complemented
184#1836C2211yescharacteristic, complemented
185#1831C2211yescharacteristic, complemented
186#1824C2211yescharacteristic
187#1823C2211yescharacteristic, complemented
188#1807C2211yescharacteristic
189#1786C2211yescharacteristic
190#1786C2211yescharacteristic
191#1762C2211yescharacteristic, complemented
192C4×#103C2211yescharacteristic, complemented
193C4×#103C2211yescharacteristic, complemented
194C4×#102C2211yescharacteristic
195C4×#102C2211yescharacteristic
196C4×#102C2211yescharacteristic
197#1753C2211yescharacteristic, complemented
198#1753C2211yescharacteristic, complemented
199#1752C2211yescharacteristic
200C8×C22⋊C4C2211yescharacteristic
201#1736C2211yescharacteristic, complemented
202C4×#97C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×#126—21no—
211C2×#126—21no—
212C2×#125C2311yescharacteristic
213C2×#124—21no—
214C2×#124D411yescharacteristic
215C2×#124C2311yescharacteristic
216C2×#124C2311yescharacteristic
217C2×#123—21no—
218C2×C22⋊Q8—21no—
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8C2311yescharacteristic
221C2×C22⋊Q8C2311yescharacteristic
222C2×#121—21no—
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×#121C2311yescharacteristic
226C2×#121C2311yescharacteristic
227C2×#120—21no—
228C2×C4×Q8—21no—
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×D4—21no—
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×#117C2311yescharacteristic
237C22×C4⋊C4C2311yescharacteristic
238C22×C4⋊C4C2311yescharacteristic
239C22×C22⋊C4—21no—
240#489—24no—
241#485—42no—
242#478—42no—
243#469—24no—
244#463—42no—
245#447—42no—
246#446—42no—
247#435—42no—
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#102—24no—
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×C22⋊C8C2311yescharacteristic
289C2×C22⋊C8C2311yescharacteristic
290C2×C22⋊C8C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×C22⋊C8C2311yescharacteristic
294C2×#97C2311yescharacteristic
295C2×#97C2311yescharacteristic
296C2×#97C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×#97C2311yescharacteristic
299C2×C4×C8C2311yescharacteristic
300C2×C4×C8C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302#401—21no—
303#400—21no—
304#400—21no—
305#399—21no—
306#399—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#397—21no—
311#397—21no—
312#397—21no—
313#397—21no—
314#397—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#396—21no—
320#396—21no—
321#396—21no—
322#396—21no—
323#396—21no—
324#396—21no—
325#396—21no—
326#395—21no—
327#395—21no—
328#394—21no—
329#394—21no—
330#394—21no—
331#394—21no—
332#394—21no—
333#394—21no—
334#394—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#393—21no—
339#393—21no—
340#393—21no—
341#392—21no—
342#391—21no—
343#391D411yescharacteristic
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#390—21no—
347#390—21no—
348#390—21no—
349#390D411yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#389—21no—
361#389—21no—
362#389—21no—
363#389—21no—
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
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#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388D411yescharacteristic
396#388D411yescharacteristic
397#388D411yescharacteristic
398#388D411yescharacteristic
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#384C2311yescharacteristic
421#384C2311yescharacteristic
422#382D411yescharacteristic
423#382C2311yescharacteristic
424#382C2311yescharacteristic
425#380—21no—
426#380—21no—
427#380—21no—
428#380—21no—
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#379—21no—
436#379—21no—
437#379—21no—
438#379—21no—
439C4×C4⋊C4—21no—
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C4×C22⋊C4C2311yescharacteristic
449C4×C22⋊C4C2311yescharacteristic
450C4×C22⋊C4C2311yescharacteristic
451C4×C22⋊C4C2311yescharacteristic
452C43C2311yescharacteristic
453#340C2311yescharacteristic
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#340C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C25—21no—
488C22×Q8—21no—
489C22×Q8C2×D411yescharacteristic
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×C4C2411yescharacteristic
512C23×C4C2411yescharacteristic
513C2×SD16—41no—
514C2×SD16—41no—
515C2×SD16—41no—
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—41no—
519C2×D8—41no—
520C2×D8—41no—
521C2×D8—41no—
522C2×M16—22no—
523C2×M16—41no—
524C2×M16—41no—
525C22×C8—22no—
526C22×C8—41no—
527C22×C8—41no—
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C4⋊Q8—22no—
537C4⋊Q8—41no—
538#126—82no—
539#126—82no—
540#125—41no—
541#125—41no—
542#124—22no—
543#124—41no—
544#124—41no—
545#124—41no—
546#124—42no—
547#124—82no—
548#123—44no—
549C22⋊Q8—41no—
550C22⋊Q8—41no—
551C22⋊Q8—41no—
552C22⋊Q8—41no—
553C22⋊Q8—82no—
554C22⋊Q8—82no—
555#121—22no—
556#121—22no—
557#121—41no—
558#121—41no—
559#121—41no—
560#121—41no—
561#121—41no—
562#121—41no—
563#121—82no—
564#120—44no—
565C4×Q8—41no—
566C4×Q8—41no—
567C4×Q8—41no—
568C4×Q8—41no—
569C4×Q8—82no—
570C4×D4—41no—
571C4×D4—41no—
572C4×D4—41no—
573C4×D4—41no—
574C4×D4—41no—
575C4×D4—41no—
576C4×D4—41no—
577C4×D4—41no—
578C4×D4—82no—
579#117—41no—
580#117—41no—
581C2×C4⋊C4—22no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
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—41no—
607C2×C4⋊C4—41no—
608C2×C4⋊C4—41no—
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
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—82no—
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C22⋊C4C2×D411yescharacteristic
668C2×C22⋊C4C2×D411yescharacteristic
669C2×C22⋊C4C2×D411yescharacteristic
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C22⋊C4C2×D411yescharacteristic
672C2×C22⋊C4C2×D411yescharacteristic
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C22⋊C4C2×D411yescharacteristic
675C2×C22⋊C4C2×D411yescharacteristic
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—21no—
682C2×C42C2×D411yescharacteristic
683C2×C42C2×D411yescharacteristic
684C2×C42C2×D411yescharacteristic
685C2×C42C2×D411yescharacteristic
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691#107—22no—
692#107—41no—
693#106—22no—
694#106—41no—
695#106—41no—
696#106—41no—
697#106—41no—
698#106—41no—
699#106—41no—
700C4⋊C8—22no—
701C4⋊C8—22no—
702C4⋊C8—41no—
703C4⋊C8—41no—
704#103—22no—
705#103—22no—
706#103—22no—
707#103—41no—
708#103—41no—
709#103—41no—
710#103—41no—
711#102—22no—
712#102—22no—
713#102—22no—
714#102—22no—
715#102—22no—
716#102—22no—
717#102—41no—
718#102—41no—
719#102—41no—
720#102—41no—
721#102—41no—
722#102—41no—
723#102—41no—
724#102—41no—
725#102—41no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102#4114yes—
730C22⋊C8—22no—
731C22⋊C8—22no—
732C22⋊C8—41no—
733C22⋊C8—41no—
734C22⋊C8—41no—
735C22⋊C8—41no—
736#97—22no—
737#97—22no—
738#97—41no—
739#97—41no—
740#97—41no—
741C4×C8—41no—
742C4×C8—41no—
743C4×C8—41no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
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#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782C24—21no—
783C24—21no—
784C24—21no—
785C24—42no—
786C24—42no—
787C24—81no—
788C24—81no—
789C24—81no—
790C24—81no—
791C24—81no—
792C24C22×D411yescharacteristic
793C24C22×D411yescharacteristic
794C2×Q8—21no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—41no—
801C2×Q8—41no—
802C2×Q8—41no—
803C2×Q8—42no—
804C2×Q8—42no—
805C2×Q8—81no—
806C2×D4—22no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
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—41no—
825C2×D4—41no—
826C2×D4—42no—
827C2×D4—42no—
828C2×D4—44no—
829C2×D4—42no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—42no—
833C2×D4—81no—
834C2×D4—81no—
835C2×D4—82no—
836C2×D4—82no—
837C2×D4—82no—
838C2×D4—81no—
839C2×D4—81no—
840C2×D4—81no—
841C2×D4—81no—
842C2×D4—81no—
843C2×D4—81no—
844C2×D4—81no—
845C2×D4C2×#4112yes—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
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—21no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—81no—
875C22×C4—81no—
876C22×C4—81no—
877C22×C4—81no—
878C22×C4—81no—
879C22×C4—81no—
880C22×C4—81no—
881C22×C4—81no—
882C22×C4—81no—
883C22×C4—81no—
884C22×C4—81no—
885C22×C4—81no—
886C22×C4C22×D411yescharacteristic
887C22×C4C22×D411yescharacteristic
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C2511yescharacteristic
899SD16—82no—
900D8—82no—
901D8—82no—
902M16—82no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—82no—
926C2×C8C2×#4112yes—
927C2×C8H(5,𝔽2)12yes—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—41no—
952C4⋊C4—41no—
953C4⋊C4—41no—
954C4⋊C4—41no—
955C4⋊C4—42no—
956C4⋊C4—42no—
957C4⋊C4—42no—
958C4⋊C4—42no—
959C4⋊C4—42no—
960C4⋊C4—42no—
961C4⋊C4—42no—
962C4⋊C4—42no—
963C4⋊C4—81no—
964C4⋊C4—81no—
965C4⋊C4—81no—
966C4⋊C4—81no—
967C4⋊C4—81no—
968C4⋊C4—81no—
969C4⋊C4—81no—
970C4⋊C4—81no—
971C4⋊C4—81no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4C2×#4112yes—
980C22⋊C4—22no—
981C22⋊C4—22no—
982C22⋊C4—22no—
983C22⋊C4—22no—
984C22⋊C4—41no—
985C22⋊C4—41no—
986C22⋊C4—41no—
987C22⋊C4—41no—
988C22⋊C4—41no—
989C22⋊C4—41no—
990C22⋊C4—42no—
991C22⋊C4—42no—
992C22⋊C4—42no—
993C22⋊C4—42no—
994C22⋊C4—42no—
995C22⋊C4—42no—
996C22⋊C4—42no—
997C22⋊C4—42no—
998C22⋊C4—42no—
999C22⋊C4—42no—
1000C22⋊C4—42no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
1003C22⋊C4—81no—
1004C22⋊C4—81no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C22⋊C4—81no—
1008C22⋊C4—81no—
1009C22⋊C4—81no—
1010C22⋊C4—81no—
1011C22⋊C4—81no—
1012C22⋊C4—81no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C42—22no—
1031C42—21no—
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—21no—
1036C42—21no—
1037C42—21no—
1038C42—21no—
1039C42—21no—
1040C42—21no—
1041C42—41no—
1042C42—41no—
1043C42—41no—
1044C42—81no—
1045C42—81no—
1046C42—81no—
1047C42—81no—
1048C42—81no—
1049C42—81no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—21no—
1056C23—21no—
1057C23—21no—
1058C23—22no—
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—84no—
1085C23—84no—
1086C23—162no—
1087C23—162no—
1088C23—162no—
1089C23—162no—
1090C23—162no—
1091C23#57512yes—
1092C23C23×D411yescharacteristic
1093Q8—41no—
1094Q8—41no—
1095Q8—41no—
1096Q8—41no—
1097Q8—82no—
1098Q8—84no—
1099D4—22no—
1100D4—22no—
1101D4—41no—
1102D4—41no—
1103D4—41no—
1104D4—41no—
1105D4—41no—
1106D4—41no—
1107D4—41no—
1108D4—41no—
1109D4—41no—
1110D4—41no—
1111D4—82no—
1112D4—84no—
1113D4—84no—
1114D4—162no—
1115D4—162no—
1116D4—162no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—22no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
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—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
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—162no—
1200C2×C4—162no—
1201C2×C4—162no—
1202C2×C4—162no—
1203C2×C4—162no—
1204C2×C4#57712yes—
1205C2×C4C22×#4111yescharacteristic
1206C2×C4C2×H(5,𝔽2)11yescharacteristic
1207C2×C4#58511yescharacteristic
1208C2×C4#58511yescharacteristic
1209C2×C4#58511yescharacteristic
1210C2×C4#58511yescharacteristic
1211C8—22no—
1212C8—22no—
1213C8—41no—
1214C8—41no—
1215C8—41no—
1216C8—41no—
1217C8—41no—
1218C8—41no—
1219C22—22no—
1220C22—22no—
1221C22—22no—
1222C22—41no—
1223C22—41no—
1224C22—41no—
1225C22—41no—
1226C22—41no—
1227C22—42no—
1228C22—41no—
1229C22—42no—
1230C22—41no—
1231C22—41no—
1232C22—41no—
1233C22—41no—
1234C22—41no—
1235C22—42no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
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—168no—
1255C22D4×#4111yescharacteristic
1256C22#349611yescharacteristic
1257C22#350011yescharacteristic
1258C22C2×#57511yescharacteristic
1259C22C2×#57711yescharacteristic
1260C22#358511yescharacteristic
1261C22#358511yescharacteristic
1262C4—22no—
1263C4—41no—
1264C4—41no—
1265C4—42no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—41no—
1270C4—41no—
1271C4—41no—
1272C4—41no—
1273C4—41no—
1274C4—41no—
1275C4—81no—
1276C4—81no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C4—81no—
1284C4—81no—
1285C4—81no—
1286C4—81no—
1287C4#345511yescharacteristic
1288C4#351411yescharacteristic
1289C4#356011yescharacteristic
1290C4#356611yescharacteristic
1291C2—42no—
1292C2—81no—
1293C2—82no—
1294C2—161no—
1295C2—161no—
1296C2#3939011yescharacteristic
1297C2#6144511yescharacteristic
1298C2#6150611yescharacteristic
1299C2#6230111yescharacteristic
1300C2#6235511yescharacteristic
1301C2#6258411yescharacteristic
1302C2#6260211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#25124C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#124 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #40188C2semidirect
2. #40056C2semidirect
3. #33269C2semidirect
4. #32643C2semidirect
5. #32554C2semidirect
6. #32062C2semidirect
7. #31734C2semidirect
8. #31676C2semidirect
9. #31448C2semidirect
10. #31135C2semidirect
11. #31008C2semidirect
12. #30149C2semidirect
13. #30133C2semidirect
14. #29061C2semidirect
15. #28982C2semidirect
16. #28913C2semidirect
17. #28853C2semidirect
18. #27725C2semidirect
19. #27262C2semidirect
20. #27229C2semidirect
21. #27161C2semidirect
22. #27032C2semidirect
23. #26940C2semidirect
24. #25475C2semidirect
25. #25309C2semidirect
26. #25247C2semidirect
28. #23140C2semidirect
29. #22574C2semidirect
30. C4×#489C2semidirect
31. #21632C2semidirect
33. C2×#485C22semidirect
38. C2×#446C22semidirect
42. #2860C22semidirect
54. #2584C22semidirect
56. #2538C22semidirect
58. #2497C22semidirect
60. #2491C22semidirect
66. #2441C22semidirect
77. #2363C22semidirect
83. C4×C4⋊Q8C22semidirect
86. #2101C22semidirect
87. #2101C22semidirect
88. #2099C22semidirect
89. #2092C22semidirect
90. #2088C22semidirect
91. #2088C22semidirect
92. #2086C22semidirect
93. #2084C22semidirect
97. #2073C22semidirect
101. #2066C22semidirect
102. #2066C22semidirect
106. #2058C22semidirect
107. #2055C22semidirect
114. #2035C22semidirect
119. #2026C22semidirect
124. #2000C22semidirect
126. #1993C22semidirect
127. #1991C22semidirect
128. #1985C22semidirect
132. #1968C22semidirect
136. #1949C22semidirect
137. #1948C22semidirect
138. #1944C22semidirect
139. #1943C22semidirect
140. #1943C22semidirect
141. #1941C22semidirect
147. #1936C22semidirect
148. #1936C22semidirect
149. #1935C22semidirect
150. #1935C22semidirect
153. #1934C22semidirect
154. #1927C22semidirect
159. #1924C22semidirect
161. #1923C22semidirect
162. #1920C22semidirect
163. #1919C22semidirect
164. #1919C22semidirect
165. #1919C22semidirect
167. #1894C22semidirect
170. #1880C22semidirect
176. #1874C22semidirect
180. #1864C22semidirect
181. #1863C22semidirect
183. #1853C22semidirect
184. #1836C22semidirect
185. #1831C22semidirect
187. #1823C22semidirect
191. #1762C22semidirect
192. C4×#103C22semidirect
193. C4×#103C22semidirect
197. #1753C22semidirect
198. #1753C22semidirect
201. #1736C22semidirect
202. C4×#97C22semidirect

Maximal subgroups

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

subgroupindex
#401882
#400562
#332692
#326432
#325542
#320622
#317342
#316762
#314482
#311352
#310082
#301492
#301332
#290612
#289822
#289132
#288532
#277252
#272622
#272292
#271612
#270322
#269402
#254752
#253092
#252472
#251242
#231402
#225742
C4×#4892
#216322