Finite Group Databasebeta

← #7016806

Subgroups — #7016806

Order 512.

1507 conjugacy classes of subgroups.

The subgroup lattice has 1330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59548C211yesmaximal, characteristic, complemented
2#40044C211yesmaximal, characteristic, complemented
3#32489C211yesmaximal, characteristic, complemented
4#32468C211yesmaximal, characteristic, complemented
5#31830C211yesmaximal, characteristic, complemented
6#31399C211yesmaximal, characteristic, complemented
7#31325C211yesmaximal, characteristic, complemented
8#31198C211yesmaximal, characteristic, complemented
9#31036C211yesmaximal, characteristic, complemented
10#31020C211yesmaximal, characteristic, complemented
11#29477C211yesmaximal, characteristic, complemented
12#29000C211yesmaximal, characteristic, complemented
13#28973C211yesmaximal, characteristic, complemented
14#28107C211yesmaximal, characteristic, complemented
15#28017C211yesmaximal, characteristic, complemented
16#27845C211yesmaximal, characteristic, complemented
17#27541C211yesmaximal, characteristic, complemented
18#27353C211yesmaximal, characteristic, complemented
19#27048C211yesmaximal, characteristic, complemented
20#26562C211yesmaximal, characteristic, complemented
21#26307C211yesmaximal, characteristic, complemented
22#26229C211yesmaximal, characteristic, complemented
23#25240C211yesmaximal, characteristic, complemented
24#25023C211yesmaximal, characteristic, complemented
25#24869C211yesmaximal, characteristic, complemented
26#24610C211yesmaximal, characteristic, complemented
27#23708C211yesmaximal, characteristic, complemented
28#23086C211yesmaximal, characteristic, complemented
29#22944C211yesmaximal, characteristic, complemented
30#22858C211yesmaximal, characteristic, complemented
31#22086C211yesmaximal, characteristic, complemented
32C2×#482C2211yescharacteristic
33C2×#482C2211yescharacteristic
34C2×#482C2211yescharacteristic
35C2×#480C2211yescharacteristic, complemented
36C2×#447C2211yescharacteristic
37C2×#442C2211yescharacteristic
38C2×#435C2211yescharacteristic
39C2×#432C2211yescharacteristic, complemented
40C22×#102C2211yescharacteristic
41#2854C2211yescharacteristic
42#2778—21no—
43#2778—21no—
44#2753—21no—
45#2749—21no—
46#2735—21no—
47#2668—21no—
48#2649—21no—
49#2595—21no—
50#2562C2211yescharacteristic
51#2554—21no—
52#2535C2211yescharacteristic
53#2525—21no—
54#2513C2211yescharacteristic
55#2512C2211yescharacteristic, complemented
56#2508C2211yescharacteristic, complemented
57#2497C2211yescharacteristic
58#2494C2211yescharacteristic
59#2490C2211yescharacteristic
60#2487C2211yescharacteristic
61#2486C2211yescharacteristic
62#2468—21no—
63#2456—21no—
64#2456—21no—
65#2454C2211yescharacteristic
66#2420C2211yescharacteristic, complemented
67#2418—21no—
68#2416C2211yescharacteristic
69#2414C2211yescharacteristic
70#2414C2211yescharacteristic
71#2414C2211yescharacteristic, complemented
72#2408C2211yescharacteristic
73#2408C2211yescharacteristic
74#2361C2211yescharacteristic
75#2361C2211yescharacteristic
76#2357—21no—
77#2354C2211yescharacteristic, complemented
78#2352C2211yescharacteristic
79#2347C2211yescharacteristic, complemented
80D4×C22⋊C4C2211yescharacteristic
81#2321—21no—
82C4×#121C2211yescharacteristic
83C4×#121C2211yescharacteristic
84C4×#121C2211yescharacteristic, complemented
85#2296C2211yescharacteristic, complemented
86#2101C2211yescharacteristic, complemented
87#2099C2211yescharacteristic, complemented
88#2092C2211yescharacteristic
89#2088C2211yescharacteristic, complemented
90#2088C2211yescharacteristic, complemented
91#2086C2211yescharacteristic, complemented
92#2077C2211yescharacteristic
93#2077C2211yescharacteristic, complemented
94#2077C2211yescharacteristic, complemented
95#2076C2211yescharacteristic
96#2076C2211yescharacteristic
97#2076C2211yescharacteristic
98#2075C2211yescharacteristic, complemented
99#2075C2211yescharacteristic, complemented
100#2073C2211yescharacteristic
101#2073C2211yescharacteristic, complemented
102#2071C2211yescharacteristic
103#2067C2211yescharacteristic
104#2067C2211yescharacteristic
105#2067C2211yescharacteristic, complemented
106#2065C2211yescharacteristic
107#2065C2211yescharacteristic
108#2065C2211yescharacteristic
109#2065C2211yescharacteristic, complemented
110#2059C2211yescharacteristic, complemented
111#2054C2211yescharacteristic
112#2054C2211yescharacteristic
113#2034C2211yescharacteristic
114#2034C2211yescharacteristic
115#2034C2211yescharacteristic
116#2034C2211yescharacteristic
117#2034C2211yescharacteristic, complemented
118#2033C2211yescharacteristic
119#2033C2211yescharacteristic
120#2033C2211yescharacteristic, complemented
121#2025C2211yescharacteristic, complemented
122#1999C2211yescharacteristic
123#1999C2211yescharacteristic
124#1999C2211yescharacteristic
125#1999C2211yescharacteristic
126#1991C2211yescharacteristic, complemented
127#1989C2211yescharacteristic, complemented
128#1972C2211yescharacteristic
129#1972C2211yescharacteristic
130#1970C2211yescharacteristic
131#1955C2211yescharacteristic
132#1955C2211yescharacteristic, complemented
133#1954C2211yescharacteristic
134#1949C2211yescharacteristic, complemented
135#1949C2211yescharacteristic, complemented
136#1944C2211yescharacteristic, complemented
137#1944C2211yescharacteristic, complemented
138#1943C2211yescharacteristic, complemented
139#1943C2211yescharacteristic, complemented
140#1943C2211yescharacteristic, complemented
141#1943C2211yescharacteristic, complemented
142#1940C2211yescharacteristic, complemented
143#1936C2211yescharacteristic
144#1936C2211yescharacteristic
145#1936C2211yescharacteristic
146#1936C2211yescharacteristic
147#1936C2211yescharacteristic
148#1936C2211yescharacteristic, complemented
149#1934C2211yescharacteristic
150#1926C2211yescharacteristic
151#1926C2211yescharacteristic
152#1926C2211yescharacteristic, complemented
153#1925C2211yescharacteristic
154#1925C2211yescharacteristic
155#1924C2211yescharacteristic
156#1924C2211yescharacteristic, complemented
157#1920C2211yescharacteristic, complemented
158#1920C2211yescharacteristic, complemented
159#1919C2211yescharacteristic, complemented
160#1918C2211yescharacteristic, complemented
161#1918C2211yescharacteristic, complemented
162#1895C2211yescharacteristic
163#1895C2211yescharacteristic
164#1895C2211yescharacteristic, complemented
165#1893C2211yescharacteristic
166#1879C2211yescharacteristic
167#1879C2211yescharacteristic
168#1875C2211yescharacteristic
169#1875C2211yescharacteristic
170#1875C2211yescharacteristic
171#1870C2211yescharacteristic, complemented
172#1869C2211yescharacteristic
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic, complemented
175#1862C2211yescharacteristic
176#1862C2211yescharacteristic
177#1854C2211yescharacteristic, complemented
178#1854C2211yescharacteristic, complemented
179#1854C2211yescharacteristic, complemented
180#1853C2211yescharacteristic
181#1853C2211yescharacteristic
182#1853C2211yescharacteristic, complemented
183#1853C2211yescharacteristic, complemented
184#1847C2211yescharacteristic, complemented
185#1825C2211yescharacteristic, complemented
186#1825C2211yescharacteristic, complemented
187#1823C2211yescharacteristic
188#1808C2211yescharacteristic
189#1807C2211yescharacteristic
190#1802C2211yescharacteristic
191#1786C2211yescharacteristic
192#1786C2211yescharacteristic
193#1776C2211yescharacteristic, complemented
194C4×#106C2211yescharacteristic, complemented
195#1771C2211yescharacteristic, complemented
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic
198#1762C2211yescharacteristic, complemented
199#1753C2211yescharacteristic, complemented
200#1752C2211yescharacteristic
201#1749C2211yescharacteristic, complemented
202#1736C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×D8C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C2×#126—21no—
209C2×#125C2311yescharacteristic
210C2×#123—21no—
211C2×#123—21no—
212C2×#121—21no—
213C2×#121D411yescharacteristic
214C2×#121C2311yescharacteristic
215C2×#121C2311yescharacteristic
216C2×#121C2311yescharacteristic
217C2×#121C2311yescharacteristic
218C2×#121C2311yescharacteristic
219C2×#121C2311yescharacteristic
220C2×#121C2311yescharacteristic
221C2×#120—21no—
222C2×#120—21no—
223C2×C4×D4—21no—
224C2×C4×D4—21no—
225C2×C4×D4—21no—
226C2×C4×D4—21no—
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×#117C2311yescharacteristic
234C2×#117C2311yescharacteristic
235C2×#117C2311yescharacteristic
236C22×C4⋊C4C2311yescharacteristic
237C22×C4⋊C4C2311yescharacteristic
238C22×C22⋊C4—21no—
239C22×C42C2311yescharacteristic
240#482—24no—
241#482—24no—
242#482—42no—
243#480—42no—
244#447—24no—
245#442—42no—
246#435—42no—
247#432—42no—
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×#102—42no—
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
288C2×C22⋊C8C2311yescharacteristic
289C2×C22⋊C8C2311yescharacteristic
290C2×C22⋊C8C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×C22⋊C8C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295C2×C22⋊C8C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×#97C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×#97C2311yescharacteristic
301C2×#97C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303#401—21no—
304#400—21no—
305#400—21no—
306#400—21no—
307#400—21no—
308#399—21no—
309#399—21no—
310#398—21no—
311#398—21no—
312#397—21no—
313#397—21no—
314#397—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#397—21no—
320#396—21no—
321#396—21no—
322#396—21no—
323#396—21no—
324#394—21no—
325#394—21no—
326#394—21no—
327#394—21no—
328#394—21no—
329#394—21no—
330#394—21no—
331#394—21no—
332#394—21no—
333#392—21no—
334#392—21no—
335#392—21no—
336#392—21no—
337#392—21no—
338#392—21no—
339#390—21no—
340#390—21no—
341#390—21no—
342#390—21no—
343#390—21no—
344#390D411yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#389D411yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
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#388D411yescharacteristic
389#388D411yescharacteristic
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#386—21no—
395#386—21no—
396#386—21no—
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#386D411yescharacteristic
408#386D411yescharacteristic
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#384C2311yescharacteristic
416#383—21no—
417#382—21no—
418#382C2311yescharacteristic
419#382C2311yescharacteristic
420#381—21no—
421#381—21no—
422#380—21no—
423#380D411yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#379—21no—
436#379—21no—
437#379—21no—
438C4×C4⋊C4—21no—
439C4×C4⋊C4—21no—
440C4×C4⋊C4—21no—
441C4×C4⋊C4—21no—
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4C2311yescharacteristic
452C4×C22⋊C4C2311yescharacteristic
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#340C2311yescharacteristic
480#340C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C25—21no—
488C22×D4—22no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
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×D4C2×D411yescharacteristic
504C22×D4C2×D411yescharacteristic
505C22×D4C2411yescharacteristic
506C22×D4C2411yescharacteristic
507C22×D4C2411yescharacteristic
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4C2×D411yescharacteristic
514C23×C4C2×D411yescharacteristic
515C23×C4C2411yescharacteristic
516C23×C4C2411yescharacteristic
517C23×C4C2411yescharacteristic
518C2×D8—22no—
519C2×D8—22no—
520C2×D8—41no—
521C2×D8—41no—
522C2×D8—41no—
523C2×D8—41no—
524C2×M16—41no—
525C2×M16—41no—
526C2×M16—41no—
527C22×C8—22no—
528C22×C8—41no—
529C22×C8—41no—
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538#126—82no—
539#125—41no—
540#125—41no—
541#123—82no—
542#123—82no—
543#121—22no—
544#121—22no—
545#121—22no—
546#121—42no—
547#121—41no—
548#121—41no—
549#121—41no—
550#121—41no—
551#121—41no—
552#121—41no—
553#121—41no—
554#121—41no—
555#121—41no—
556#121—41no—
557#121—41no—
558#121—82no—
559#120—44no—
560#120—82no—
561C4×D4—41no—
562C4×D4—41no—
563C4×D4—41no—
564C4×D4—41no—
565C4×D4—41no—
566C4×D4—41no—
567C4×D4—41no—
568C4×D4—41no—
569C4×D4—41no—
570C4×D4—41no—
571C4×D4—41no—
572C4×D4—41no—
573C4×D4—44no—
574C4×D4—82no—
575C4×D4—82no—
576C4×D4—82no—
577#117—22no—
578#117—22no—
579#117—41no—
580#117—41no—
581#117—41no—
582#117—41no—
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—41no—
601C2×C4⋊C4—41no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4—41no—
604C2×C4⋊C4C2×D411yescharacteristic
605C2×C4⋊C4C2×D411yescharacteristic
606C2×C4⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
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—82no—
665C2×C22⋊C4C2×D411yescharacteristic
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×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—21no—
682C2×C42—21no—
683C2×C42—41no—
684C2×C42—41no—
685C2×C42C2×D411yescharacteristic
686C2×C42C2×D411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691#107—22no—
692#107—22no—
693#107—22no—
694#107—41no—
695#107—41no—
696#107—41no—
697#106—22no—
698#106—22no—
699#106—41no—
700#106—41no—
701#106—41no—
702#106—41no—
703#106—41no—
704#106—41no—
705C4⋊C8—22no—
706C4⋊C8—41no—
707C4⋊C8—41no—
708C4⋊C8—41no—
709#102—22no—
710#102—22no—
711#102—22no—
712#102—22no—
713#102—22no—
714#102—22no—
715#102—41no—
716#102—41no—
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#4114yes—
729C22⋊C8—22no—
730C22⋊C8—22no—
731C22⋊C8—22no—
732C22⋊C8—22no—
733C22⋊C8—22no—
734C22⋊C8—41no—
735C22⋊C8—41no—
736C22⋊C8—41no—
737C22⋊C8—41no—
738C22⋊C8—41no—
739#97—22no—
740#97—41no—
741#97—41no—
742#97—41no—
743#97—41no—
744C4×C8—41no—
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#95—21no—
775#95—21no—
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
794C24C22×D411yescharacteristic
795C2×D4—22no—
796C2×D4—22no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—41no—
815C2×D4—41no—
816C2×D4—41no—
817C2×D4—41no—
818C2×D4—41no—
819C2×D4—41no—
820C2×D4—41no—
821C2×D4—42no—
822C2×D4—42no—
823C2×D4—44no—
824C2×D4—42no—
825C2×D4—42no—
826C2×D4—42no—
827C2×D4—42no—
828C2×D4—42no—
829C2×D4—42no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—81no—
833C2×D4—81no—
834C2×D4—82no—
835C2×D4—82no—
836C2×D4—82no—
837C2×D4—81no—
838C2×D4—81no—
839C2×D4—81no—
840C2×D4—81no—
841C2×D4—81no—
842C2×D4—81no—
843C2×D4—81no—
844C2×D4—81no—
845C2×D4—81no—
846C2×D4—81no—
847C2×D4—81no—
848C2×D4—81no—
849C2×D4C2×#4112yes—
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—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—41no—
882C22×C4—41no—
883C22×C4—41no—
884C22×C4—41no—
885C22×C4—41no—
886C22×C4—41no—
887C22×C4—42no—
888C22×C4—42no—
889C22×C4—42no—
890C22×C4—81no—
891C22×C4—81no—
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×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
914D8—44no—
915D8—82no—
916M16—82no—
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—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—82no—
940C2×C8C2×#4112yes—
941C2×C8H(5,𝔽2)12yes—
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—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—41no—
968C4⋊C4—41no—
969C4⋊C4—41no—
970C4⋊C4—41no—
971C4⋊C4—41no—
972C4⋊C4—42no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—42no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4C2×#4112yes—
990C22⋊C4—22no—
991C22⋊C4—41no—
992C22⋊C4—41no—
993C22⋊C4—41no—
994C22⋊C4—41no—
995C22⋊C4—41no—
996C22⋊C4—41no—
997C22⋊C4—41no—
998C22⋊C4—41no—
999C22⋊C4—41no—
1000C22⋊C4—42no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
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—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
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—
1042C42—21no—
1043C42—21no—
1044C42—21no—
1045C42—21no—
1046C42—21no—
1047C42—21no—
1048C42—21no—
1049C42—21no—
1050C42—41no—
1051C42—41no—
1052C42—42no—
1053C42—42no—
1054C42—42no—
1055C42—81no—
1056C42—81no—
1057C42—81no—
1058C42—81no—
1059C42—81no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—22no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—41no—
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—84no—
1102C23—84no—
1103C23—162no—
1104C23—162no—
1105C23—162no—
1106C23—162no—
1107C23—162no—
1108C23#57512yes—
1109C23C23×D411yescharacteristic
1110D4—22no—
1111D4—22no—
1112D4—41no—
1113D4—41no—
1114D4—41no—
1115D4—41no—
1116D4—41no—
1117D4—41no—
1118D4—41no—
1119D4—41no—
1120D4—41no—
1121D4—41no—
1122D4—82no—
1123D4—82no—
1124D4—84no—
1125D4—82no—
1126D4—84no—
1127D4—84no—
1128D4—84no—
1129D4—84no—
1130D4—162no—
1131D4—162no—
1132D4—162no—
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—22no—
1146C2×C4—21no—
1147C2×C4—21no—
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—21no—
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—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—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—41no—
1217C2×C4—82no—
1218C2×C4—82no—
1219C2×C4—162no—
1220C2×C4—162no—
1221C2×C4—162no—
1222C2×C4—162no—
1223C2×C4—162no—
1224C2×C4C22×#4111yescharacteristic
1225C2×C4C2×H(5,𝔽2)11yescharacteristic
1226C2×C4#58511yescharacteristic
1227C2×C4#58511yescharacteristic
1228C2×C4#58511yescharacteristic
1229C2×C4#58511yescharacteristic
1230C8—22no—
1231C8—22no—
1232C8—41no—
1233C8—41no—
1234C8—41no—
1235C8—41no—
1236C8—41no—
1237C8—41no—
1238C22—22no—
1239C22—22no—
1240C22—22no—
1241C22—41no—
1242C22—41no—
1243C22—41no—
1244C22—41no—
1245C22—41no—
1246C22—42no—
1247C22—41no—
1248C22—41no—
1249C22—41no—
1250C22—41no—
1251C22—41no—
1252C22—42no—
1253C22—41no—
1254C22—42no—
1255C22—41no—
1256C22—41no—
1257C22—41no—
1258C22—41no—
1259C22—41no—
1260C22—41no—
1261C22—41no—
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—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—168no—
1281C22D4×#4111yescharacteristic
1282C22#348511yescharacteristic
1283C22#349611yescharacteristic
1284C22C2×#57511yescharacteristic
1285C22#358511yescharacteristic
1286C22#358511yescharacteristic
1287C22#358511yescharacteristic
1288C4—42no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—41no—
1297C4—41no—
1298C4—41no—
1299C4—41no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4#350611yescharacteristic
1313C4#352111yescharacteristic
1314C4#356011yescharacteristic
1315C4#356611yescharacteristic
1316C2—42no—
1317C2—81no—
1318C2—81no—
1319C2—82no—
1320C2—161no—
1321C2—161no—
1322C2#4304211yescharacteristic
1323C2#6145411yescharacteristic
1324C2#6150711yescharacteristic
1325C2#6171411yescharacteristic
1326C2#6179511yescharacteristic
1327C2#6228611yescharacteristic
1328C2#6230111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#121 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59548C2semidirect
2. #40044C2semidirect
3. #32489C2semidirect
4. #32468C2semidirect
5. #31830C2semidirect
6. #31399C2semidirect
7. #31325C2semidirect
8. #31198C2semidirect
9. #31036C2semidirect
10. #31020C2semidirect
11. #29477C2semidirect
12. #29000C2semidirect
13. #28973C2semidirect
14. #28107C2semidirect
15. #28017C2semidirect
16. #27845C2semidirect
17. #27541C2semidirect
18. #27353C2semidirect
19. #27048C2semidirect
20. #26562C2semidirect
21. #26307C2semidirect
22. #26229C2semidirect
23. #25240C2semidirect
24. #25023C2semidirect
25. #24869C2semidirect
26. #24610C2semidirect
27. #23708C2semidirect
28. #23086C2semidirect
29. #22944C2semidirect
30. #22858C2semidirect
31. #22086C2semidirect
35. C2×#480C22semidirect
39. C2×#432C22semidirect
55. #2512C22semidirect
56. #2508C22semidirect
66. #2420C22semidirect
71. #2414C22semidirect
77. #2354C22semidirect
79. #2347C22semidirect
84. C4×#121C22semidirect
85. #2296C22semidirect
86. #2101C22semidirect
87. #2099C22semidirect
89. #2088C22semidirect
90. #2088C22semidirect
91. #2086C22semidirect
93. #2077C22semidirect
94. #2077C22semidirect
98. #2075C22semidirect
99. #2075C22semidirect
101. #2073C22semidirect
105. #2067C22semidirect
109. #2065C22semidirect
110. #2059C22semidirect
117. #2034C22semidirect
120. #2033C22semidirect
121. #2025C22semidirect
126. #1991C22semidirect
127. #1989C22semidirect
132. #1955C22semidirect
134. #1949C22semidirect
135. #1949C22semidirect
136. #1944C22semidirect
137. #1944C22semidirect
138. #1943C22semidirect
139. #1943C22semidirect
140. #1943C22semidirect
141. #1943C22semidirect
142. #1940C22semidirect
148. #1936C22semidirect
152. #1926C22semidirect
156. #1924C22semidirect
157. #1920C22semidirect
158. #1920C22semidirect
159. #1919C22semidirect
160. #1918C22semidirect
161. #1918C22semidirect
164. #1895C22semidirect
171. #1870C22semidirect
174. #1864C22semidirect
177. #1854C22semidirect
178. #1854C22semidirect
179. #1854C22semidirect
182. #1853C22semidirect
183. #1853C22semidirect
184. #1847C22semidirect
185. #1825C22semidirect
186. #1825C22semidirect
193. #1776C22semidirect
194. C4×#106C22semidirect
195. #1771C22semidirect
198. #1762C22semidirect
199. #1753C22semidirect
201. #1749C22semidirect
202. #1736C22semidirect

Maximal subgroups

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

subgroupindex
#595482
#400442
#324892
#324682
#318302
#313992
#313252
#311982
#310362
#310202
#294772
#290002
#289732
#281072
#280172
#278452
#275412
#273532
#270482
#265622
#263072
#262292
#252402
#250232
#248692
#246102
#237082
#230862
#229442
#228582
#220862