Finite Group Databasebeta

← #6680133

Subgroups — #6680133

Order 512.

1737 conjugacy classes of subgroups.

The subgroup lattice has 1375 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39145C211yesmaximal, characteristic, complemented
2#36529C211yesmaximal, characteristic, complemented
3#33004C211yesmaximal, characteristic, complemented
4#31883C211yesmaximal, characteristic, complemented
5#31851C211yesmaximal, characteristic, complemented
6#31819C211yesmaximal, characteristic, complemented
7#31535C211yesmaximal, characteristic, complemented
8#31503C211yesmaximal, characteristic, complemented
9#31471C211yesmaximal, characteristic, complemented
10#30645C211yesmaximal, characteristic, complemented
11#30605C211yesmaximal, characteristic, complemented
12#29912C211yesmaximal, characteristic, complemented
13#29770C211yesmaximal, characteristic, complemented
14#27264C211yesmaximal, characteristic, complemented
15#27125C211yesmaximal, characteristic, complemented
16#27080C211yesmaximal, characteristic, complemented
17#26770C211yesmaximal, characteristic, complemented
18#26685C211yesmaximal, characteristic, complemented
19#26541C211yesmaximal, characteristic, complemented
20#26437C211yesmaximal, characteristic, complemented
21#26002C211yesmaximal, characteristic, complemented
22#25537C211yesmaximal, characteristic, complemented
23#25330C211yesmaximal, characteristic, complemented
24#25227C211yesmaximal, characteristic, complemented
25#25124C211yesmaximal, characteristic, complemented
26#25076C211yesmaximal, characteristic, complemented
27#24861C211yesmaximal, characteristic, complemented
28#22936C211yesmaximal, characteristic, complemented
29#22493C211yesmaximal, characteristic, complemented
30#22069C211yesmaximal, characteristic, complemented
31C2×#1804C211yesmaximal, characteristic, complemented
32C2×#553C2211yescharacteristic
33C22×C4×D4C2211yescharacteristic
34C2×#490C2211yescharacteristic
35C2×#481C2211yescharacteristic
36C2×#480C2211yescharacteristic
37C2×#469C2211yescharacteristic
38C2×#466C2211yescharacteristic
39C2×#459C2211yescharacteristic
40C2×#447C2211yescharacteristic
41C2×#435C2211yescharacteristic
42C22×C4⋊C8C2211yescharacteristic
43C22×#102C2211yescharacteristic
44C22×#102C2211yescharacteristic
45#2854C2211yescharacteristic
46#2854C2211yescharacteristic
47#2847—21no—
48#2783—21no—
49#2782—21no—
50#2781—21no—
51#2765—21no—
52#2643—21no—
53#2570C2211yescharacteristic, complemented
54#2566C2211yescharacteristic, complemented
55#2539—21no—
56#2534—21no—
57#2513C2211yescharacteristic, complemented
58#2509C2211yescharacteristic, complemented
59#2504C2211yescharacteristic, complemented
60#2494C2211yescharacteristic, complemented
61#2467—21no—
62#2467—21no—
63#2456—21no—
64#2456—21no—
65#2454C2211yescharacteristic
66#2454C2211yescharacteristic
67#2442C2211yescharacteristic
68#2442C2211yescharacteristic, complemented
69#2433C2211yescharacteristic
70#2428C2211yescharacteristic
71#2428C2211yescharacteristic
72#2425—21no—
73#2420C2211yescharacteristic, complemented
74#2419—21no—
75#2416C2211yescharacteristic
76#2408C2211yescharacteristic
77#2366C2211yescharacteristic
78#2366C2211yescharacteristic
79#2363C2211yescharacteristic
80#2363C2211yescharacteristic
81#2361C2211yescharacteristic
82D4×C4⋊C4C2211yescharacteristic
83#2345C2211yescharacteristic
84#2325—21no—
85C4×#123C2211yescharacteristic
86C4×#120—21no—
87C2×#382C2211yescharacteristic
88#2101C2211yescharacteristic, complemented
89#2101C2211yescharacteristic, complemented
90#2101C2211yescharacteristic, complemented
91#2093C2211yescharacteristic
92#2092C2211yescharacteristic, complemented
93#2092C2211yescharacteristic, complemented
94#2088C2211yescharacteristic, complemented
95#2086C2211yescharacteristic, complemented
96#2086C2211yescharacteristic, complemented
97#2086C2211yescharacteristic, complemented
98#2085C2211yescharacteristic, complemented
99#2085C2211yescharacteristic, complemented
100#2073C2211yescharacteristic
101#2073C2211yescharacteristic, complemented
102#2073C2211yescharacteristic, complemented
103#2071C2211yescharacteristic
104#2067C2211yescharacteristic
105#2067C2211yescharacteristic, complemented
106#2067C2211yescharacteristic, complemented
107#2067C2211yescharacteristic, complemented
108#2067C2211yescharacteristic, complemented
109#2065C2211yescharacteristic
110#2059C2211yescharacteristic, complemented
111#2059C2211yescharacteristic, complemented
112#2054C2211yescharacteristic
113#2054C2211yescharacteristic
114#2054C2211yescharacteristic, complemented
115#2054C2211yescharacteristic, complemented
116#2041C2211yescharacteristic
117#2041C2211yescharacteristic
118#2041C2211yescharacteristic
119#2034C2211yescharacteristic
120#2034C2211yescharacteristic, complemented
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic
123#2025C2211yescharacteristic
124#2025C2211yescharacteristic, complemented
125#2011C2211yescharacteristic
126#1999C2211yescharacteristic
127#1999C2211yescharacteristic, complemented
128#1992C2211yescharacteristic, complemented
129#1989C2211yescharacteristic, complemented
130#1989C2211yescharacteristic, complemented
131#1982C2211yescharacteristic
132#1972C2211yescharacteristic
133#1961C2211yescharacteristic
134#1949C2211yescharacteristic, complemented
135#1944C2211yescharacteristic, complemented
136#1940C2211yescharacteristic, complemented
137#1940C2211yescharacteristic, complemented
138#1936C2211yescharacteristic
139#1936C2211yescharacteristic
140#1936C2211yescharacteristic
141#1936C2211yescharacteristic, complemented
142#1925C2211yescharacteristic
143#1925C2211yescharacteristic
144#1925C2211yescharacteristic
145#1925C2211yescharacteristic, complemented
146#1924C2211yescharacteristic, complemented
147#1924C2211yescharacteristic, complemented
148#1920C2211yescharacteristic, complemented
149#1920C2211yescharacteristic, complemented
150#1919C2211yescharacteristic, complemented
151#1918C2211yescharacteristic, complemented
152#1917C2211yescharacteristic, complemented
153#1917C2211yescharacteristic, complemented
154#1895C2211yescharacteristic
155#1895C2211yescharacteristic, complemented
156#1893C2211yescharacteristic
157#1893C2211yescharacteristic
158#1879C2211yescharacteristic
159#1879C2211yescharacteristic
160#1879C2211yescharacteristic
161#1879C2211yescharacteristic
162#1879C2211yescharacteristic
163#1879C2211yescharacteristic, complemented
164#1875C2211yescharacteristic, complemented
165#1874C2211yescharacteristic
166#1874C2211yescharacteristic
167#1874C2211yescharacteristic
168#1874C2211yescharacteristic, complemented
169#1869C2211yescharacteristic
170#1864C2211yescharacteristic
171#1864C2211yescharacteristic
172#1864C2211yescharacteristic
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic, complemented
175#1862C2211yescharacteristic, complemented
176#1854C2211yescharacteristic, complemented
177#1853C2211yescharacteristic
178#1852C2211yescharacteristic
179#1851C2211yescharacteristic, complemented
180#1851C2211yescharacteristic, complemented
181#1850C2211yescharacteristic
182#1825C2211yescharacteristic, complemented
183#1824C2211yescharacteristic
184#1817C2211yescharacteristic
185#1808C2211yescharacteristic
186#1804C2211yescharacteristic
187#1804C2211yescharacteristic
188#1804C2211yescharacteristic
189#1804C2211yescharacteristic
190#1804C2211yescharacteristic
191#1804C2211yescharacteristic
192#1804C2211yescharacteristic
193#1804C2211yescharacteristic
194#1802C2211yescharacteristic, complemented
195#1786C2211yescharacteristic
196#1776C2211yescharacteristic, complemented
197#1762C2211yescharacteristic, complemented
198#1762C2211yescharacteristic, complemented
199#1752C2211yescharacteristic
200#1736C2211yescharacteristic, complemented
201C2×#340C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C24×C4—21no—
205C22×D8C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C23×C8C2311yescharacteristic
210C23×C8C2311yescharacteristic
211#553—24no—
212#553—42no—
213C2×#127C2311yescharacteristic
214C2×#127C2311yescharacteristic
215C2×#126—21no—
216C2×#125C2311yescharacteristic
217C2×#125C2311yescharacteristic
218C2×#123—21no—
219C2×#123—21no—
220C2×#123—21no—
221C2×#123D411yescharacteristic
222C2×#121—21no—
223C2×#121—21no—
224C2×#121—21no—
225C2×#121—21no—
226C2×#121C2311yescharacteristic
227C2×#121C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#120—21no—
233C2×#120—21no—
234C2×#120—21no—
235C2×C4×D4—21no—
236C2×C4×D4—21no—
237C2×C4×D4—21no—
238C2×C4×D4—21no—
239C2×C4×D4—21no—
240C2×C4×D4—24no—
241C2×C4×D4—21no—
242C2×C4×D4—21no—
243C2×C4×D4—42no—
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2311yescharacteristic
256C22×C22⋊C4—21no—
257C22×C42C2311yescharacteristic
258#490—42no—
259#481—24no—
260#480—42no—
261#469—42no—
262#466—42no—
263#459—42no—
264#447—42no—
265#435—42no—
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×C4⋊C8—42no—
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×#102—42no—
284C2×#102—42no—
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×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×#97C2311yescharacteristic
317C2×#97C2311yescharacteristic
318C2×#97C2311yescharacteristic
319#401—21no—
320#400—21no—
321#400—21no—
322#400—21no—
323#400—21no—
324#400—21no—
325#399—21no—
326#399—21no—
327#398—21no—
328#398—21no—
329#398—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#396—21no—
337#396—21no—
338#396—21no—
339#396—21no—
340#396—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#392—21no—
347#392—21no—
348#392—21no—
349#392—21no—
350#392—21no—
351#390—21no—
352#390—21no—
353#390—21no—
354#390—21no—
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#389—21no—
366#389—21no—
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
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#388D411yescharacteristic
388#388D411yescharacteristic
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387D411yescharacteristic
396#387D411yescharacteristic
397#386—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386D411yescharacteristic
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385D411yescharacteristic
423#384C2311yescharacteristic
424#382—21no—
425#382—21no—
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#382C2311yescharacteristic
429#382C2311yescharacteristic
430#382C2311yescharacteristic
431#381—21no—
432#381D411yescharacteristic
433#380—21no—
434#380—21no—
435#380—21no—
436#380—21no—
437#380—21no—
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#379—21no—
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4C2311yescharacteristic
453C4×C22⋊C4C2311yescharacteristic
454C4×C22⋊C4C2311yescharacteristic
455C2×#95—21no—
456C2×#95—21no—
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#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C22×D4—22no—
495C22×D4—22no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—22no—
508C22×D4—22no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4C2×D411yescharacteristic
512C22×D4C2411yescharacteristic
513C22×D4C2411yescharacteristic
514C22×D4C2411yescharacteristic
515C22×D4C2411yescharacteristic
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—44no—
527C23×C4—82no—
528C23×C4—82no—
529C23×C4C2×D411yescharacteristic
530C23×C4C2×D411yescharacteristic
531C23×C4C2411yescharacteristic
532C23×C4C2411yescharacteristic
533C2×D8—22no—
534C2×D8—22no—
535C2×D8—41no—
536C2×D8—41no—
537C2×D8—41no—
538C2×D8—41no—
539C2×D8—41no—
540C2×D8—41no—
541C2×D8—41no—
542C2×M16—41no—
543C2×M16—41no—
544C2×M16—41no—
545C22×C8—22no—
546C22×C8—22no—
547C22×C8—41no—
548C22×C8—41no—
549C22×C8—41no—
550C22×C8—41no—
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559#127—22no—
560#127—22no—
561#127—41no—
562#127—41no—
563#126—44no—
564#125—22no—
565#125—41no—
566#125—41no—
567#125—41no—
568#123—44no—
569#123—42no—
570#123—82no—
571#123—82no—
572#121—22no—
573#121—22no—
574#121—22no—
575#121—22no—
576#121—22no—
577#121—22no—
578#121—22no—
579#121—41no—
580#121—41no—
581#121—41no—
582#121—44no—
583#121—44no—
584#121—41no—
585#121—41no—
586#121—82no—
587#121—82no—
588#120—44no—
589#120—82no—
590#120—82no—
591C4×D4—22no—
592C4×D4—22no—
593C4×D4—22no—
594C4×D4—22no—
595C4×D4—22no—
596C4×D4—22no—
597C4×D4—22no—
598C4×D4—41no—
599C4×D4—41no—
600C4×D4—41no—
601C4×D4—41no—
602C4×D4—41no—
603C4×D4—44no—
604C4×D4—44no—
605C4×D4—41no—
606C4×D4—41no—
607C4×D4—44no—
608C4×D4—82no—
609C4×D4—82no—
610C4×D4—82no—
611C4×D4—82no—
612#117—22no—
613#117—41no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—22no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—41no—
636C2×C4⋊C4—41no—
637C2×C4⋊C4—41no—
638C2×C4⋊C4—41no—
639C2×C4⋊C4—41no—
640C2×C4⋊C4—41no—
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4#4114yes—
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
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—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—44no—
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C42—22no—
706C2×C42—22no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42C2×D411yescharacteristic
713C2×C42C2×D411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719#107—41no—
720#107—41no—
721#107—41no—
722#107—41no—
723#107—41no—
724#106—22no—
725#106—22no—
726#106—41no—
727#106—41no—
728C4⋊C8—41no—
729C4⋊C8—41no—
730C4⋊C8—41no—
731C4⋊C8—41no—
732C4⋊C8—41no—
733C4⋊C8—41no—
734C4⋊C8—41no—
735#102—22no—
736#102—22no—
737#102—22no—
738#102—22no—
739#102—22no—
740#102—22no—
741#102—22no—
742#102—22no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761C22⋊C8—22no—
762C22⋊C8—22no—
763C22⋊C8—41no—
764C22⋊C8—41no—
765C22⋊C8—41no—
766#97—41no—
767#97—41no—
768#97—41no—
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#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807C24—21no—
808C24—21no—
809C24—21no—
810C24—21no—
811C24—42no—
812C24—42no—
813C24—42no—
814C24—42no—
815C24—42no—
816C24—81no—
817C24—81no—
818C24C22×D411yescharacteristic
819C24C22×D411yescharacteristic
820C2×D4—28no—
821C2×D4—22no—
822C2×D4—22no—
823C2×D4—22no—
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—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—44no—
847C2×D4—44no—
848C2×D4—42no—
849C2×D4—42no—
850C2×D4—44no—
851C2×D4—42no—
852C2×D4—42no—
853C2×D4—42no—
854C2×D4—42no—
855C2×D4—42no—
856C2×D4—42no—
857C2×D4—42no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—42no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—81no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4—81no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4—81no—
876C2×D4—81no—
877C2×D4—81no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4H(5,𝔽2)12yes—
883C2×D42−1+412yes—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—22no—
889C22×C4—22no—
890C22×C4—22no—
891C22×C4—22no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—24no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—41no—
912C22×C4—41no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—42no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—42no—
923C22×C4—42no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4—81no—
929C22×C4—81no—
930C22×C4—81no—
931C22×C4—81no—
932C22×C4—81no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4—816no—
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C2×#4112yes—
956C22×C4H(5,𝔽2)12yes—
957C22×C4C2511yescharacteristic
958D8—82no—
959D8—82no—
960D8—82no—
961M16—82no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—82no—
987C2×C8—82no—
988C4⋊C4—24no—
989C4⋊C4—22no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—41no—
1013C4⋊C4—41no—
1014C4⋊C4—41no—
1015C4⋊C4—41no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4C2×#4112yes—
1036C4⋊C4C2×#4112yes—
1037C22⋊C4—22no—
1038C22⋊C4—22no—
1039C22⋊C4—22no—
1040C22⋊C4—22no—
1041C22⋊C4—41no—
1042C22⋊C4—41no—
1043C22⋊C4—41no—
1044C22⋊C4—41no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C42—22no—
1083C42—22no—
1084C42—21no—
1085C42—21no—
1086C42—21no—
1087C42—21no—
1088C42—21no—
1089C42—21no—
1090C42—21no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—42no—
1095C42—81no—
1096C42—81no—
1097C42—81no—
1098C42—81no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—22no—
1107C23—21no—
1108C23—22no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—48no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—84no—
1140C23—84no—
1141C23—84no—
1142C23—84no—
1143C23—84no—
1144C23—84no—
1145C23#54612yes—
1146C23#57512yes—
1147C23#57612yes—
1148C23C23×D411yescharacteristic
1149D4—22no—
1150D4—22no—
1151D4—22no—
1152D4—22no—
1153D4—48no—
1154D4—44no—
1155D4—41no—
1156D4—41no—
1157D4—41no—
1158D4—41no—
1159D4—41no—
1160D4—41no—
1161D4—41no—
1162D4—41no—
1163D4—41no—
1164D4—41no—
1165D4—41no—
1166D4—41no—
1167D4—84no—
1168D4—84no—
1169D4—84no—
1170D4—84no—
1171D4—162no—
1172D4—162no—
1173D4—162no—
1174D4—162no—
1175D4—162no—
1176D4—162no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—44no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—44no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—84no—
1259C2×C4—84no—
1260C2×C4—84no—
1261C2×C4—84no—
1262C2×C4—84no—
1263C2×C4—162no—
1264C2×C4—162no—
1265C2×C4—162no—
1266C2×C4—162no—
1267C2×C4—162no—
1268C2×C4#54612yes—
1269C2×C4C22×#4111yescharacteristic
1270C2×C4C2×H(5,𝔽2)11yescharacteristic
1271C2×C4C2×H(5,𝔽2)11yescharacteristic
1272C2×C4C2×2−1+411yescharacteristic
1273C2×C4#58511yescharacteristic
1274C2×C4#58511yescharacteristic
1275C8—41no—
1276C8—41no—
1277C8—41no—
1278C8—41no—
1279C8—41no—
1280C8—41no—
1281C8—41no—
1282C8—41no—
1283C22—22no—
1284C22—22no—
1285C22—22no—
1286C22—22no—
1287C22—22no—
1288C22—22no—
1289C22—42no—
1290C22—41no—
1291C22—41no—
1292C22—42no—
1293C22—42no—
1294C22—41no—
1295C22—42no—
1296C22—42no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—42no—
1301C22—41no—
1302C22—816no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—81no—
1322C22—81no—
1323C22—81no—
1324C22—81no—
1325C22#330914yes—
1326C22C2×#54611yescharacteristic
1327C22#348811yescharacteristic
1328C22#348911yescharacteristic
1329C22C2×#57511yescharacteristic
1330C22C2×#57611yescharacteristic
1331C22#358511yescharacteristic
1332C22#358511yescharacteristic
1333C4—22no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—41no—
1342C4—41no—
1343C4—41no—
1344C4—41no—
1345C4—42no—
1346C4—42no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4—81no—
1357C4#345511yescharacteristic
1358C4#349211yescharacteristic
1359C4#353411yescharacteristic
1360C4#353511yescharacteristic
1361C2—24no—
1362C2—81no—
1363C2—82no—
1364C2—82no—
1365C2—161no—
1366C2—161no—
1367C2#3766611yescharacteristic
1368C2C2×#330911yescharacteristic
1369C2#6117511yescharacteristic
1370C2#6197111yescharacteristic
1371C2#6201511yescharacteristic
1372C2#6211911yescharacteristic
1373C2#6216311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
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. #39145C2semidirect
2. #36529C2semidirect
3. #33004C2semidirect
4. #31883C2semidirect
5. #31851C2semidirect
6. #31819C2semidirect
7. #31535C2semidirect
8. #31503C2semidirect
9. #31471C2semidirect
10. #30645C2semidirect
11. #30605C2semidirect
12. #29912C2semidirect
13. #29770C2semidirect
14. #27264C2semidirect
15. #27125C2semidirect
16. #27080C2semidirect
17. #26770C2semidirect
18. #26685C2semidirect
19. #26541C2semidirect
20. #26437C2semidirect
21. #26002C2semidirect
22. #25537C2semidirect
23. #25330C2semidirect
24. #25227C2semidirect
25. #25124C2semidirect
26. #25076C2semidirect
27. #24861C2semidirect
28. #22936C2semidirect
29. #22493C2semidirect
30. #22069C2semidirect
31. C2×#1804C2semidirect
53. #2570C22semidirect
54. #2566C22semidirect
57. #2513C22semidirect
58. #2509C22semidirect
59. #2504C22semidirect
60. #2494C22semidirect
68. #2442C22semidirect
73. #2420C22semidirect
88. #2101C22semidirect
89. #2101C22semidirect
90. #2101C22semidirect
92. #2092C22semidirect
93. #2092C22semidirect
94. #2088C22semidirect
95. #2086C22semidirect
96. #2086C22semidirect
97. #2086C22semidirect
98. #2085C22semidirect
99. #2085C22semidirect
101. #2073C22semidirect
102. #2073C22semidirect
105. #2067C22semidirect
106. #2067C22semidirect
107. #2067C22semidirect
108. #2067C22semidirect
110. #2059C22semidirect
111. #2059C22semidirect
114. #2054C22semidirect
115. #2054C22semidirect
120. #2034C22semidirect
124. #2025C22semidirect
127. #1999C22semidirect
128. #1992C22semidirect
129. #1989C22semidirect
130. #1989C22semidirect
134. #1949C22semidirect
135. #1944C22semidirect
136. #1940C22semidirect
137. #1940C22semidirect
141. #1936C22semidirect
145. #1925C22semidirect
146. #1924C22semidirect
147. #1924C22semidirect
148. #1920C22semidirect
149. #1920C22semidirect
150. #1919C22semidirect
151. #1918C22semidirect
152. #1917C22semidirect
153. #1917C22semidirect
155. #1895C22semidirect
163. #1879C22semidirect
164. #1875C22semidirect
168. #1874C22semidirect
174. #1864C22semidirect
175. #1862C22semidirect
176. #1854C22semidirect
179. #1851C22semidirect
180. #1851C22semidirect
182. #1825C22semidirect
194. #1802C22semidirect
196. #1776C22semidirect
197. #1762C22semidirect
198. #1762C22semidirect
200. #1736C22semidirect

Maximal subgroups

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

subgroupindex
#391452
#365292
#330042
#318832
#318512
#318192
#315352
#315032
#314712
#306452
#306052
#299122
#297702
#272642
#271252
#270802
#267702
#266852
#265412
#264372
#260022
#255372
#253302
#252272
#251242
#250762
#248612
#229362
#224932
#220692
C2×#18042