Finite Group Databasebeta

← #7302144

Subgroups — #7302144

Order 512.

1627 conjugacy classes of subgroups.

The subgroup lattice has 1379 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59013C211yesmaximal, characteristic
2#39935C211yesmaximal, characteristic, complemented
3#32292C211yesmaximal, characteristic, complemented
4#32060C211yesmaximal, characteristic, complemented
5#31800C211yesmaximal, characteristic, complemented
6#31755C211yesmaximal, characteristic, complemented
7#31721C211yesmaximal, characteristic, complemented
8#31440C211yesmaximal, characteristic, complemented
9#31401C211yesmaximal, characteristic, complemented
10#31400C211yesmaximal, characteristic, complemented
11#31359C211yesmaximal, characteristic, complemented
12#31276C211yesmaximal, characteristic, complemented
13#31079C211yesmaximal, characteristic, complemented
14#31024C211yesmaximal, characteristic, complemented
15#29893C211yesmaximal, characteristic, complemented
16#29598C211yesmaximal, characteristic, complemented
17#27604C211yesmaximal, characteristic, complemented
18#27520C211yesmaximal, characteristic, complemented
19#27097C211yesmaximal, characteristic, complemented
20#26794C211yesmaximal, characteristic, complemented
21#26721C211yesmaximal, characteristic, complemented
22#26568C211yesmaximal, characteristic, complemented
23#26304C211yesmaximal, characteristic, complemented
24#26156C211yesmaximal, characteristic, complemented
25#26145C211yesmaximal, characteristic, complemented
26#25018C211yesmaximal, characteristic, complemented
27#24917C211yesmaximal, characteristic, complemented
28#24138C211yesmaximal, characteristic, complemented
29#24101C211yesmaximal, characteristic, complemented
30#24009C211yesmaximal, characteristic, complemented
31#23308C211yesmaximal, characteristic, complemented
32C2×#553C2211yescharacteristic
33C22×#121C2211yescharacteristic
34C2×#484C2211yescharacteristic
35C2×#481C2211yescharacteristic, complemented
36C2×#482C2211yescharacteristic
37C2×#482C2211yescharacteristic
38C2×#479C2211yescharacteristic, complemented
39C2×#450C2211yescharacteristic
40C2×#440C2211yescharacteristic, complemented
41C2×#428C2211yescharacteristic, complemented
42#2848C2211yescharacteristic
43#2765—21no—
44#2743—21no—
45#2735—21no—
46#2703—21no—
47#2697—21no—
48#2691—21no—
49#2652—21no—
50#2587—21no—
51#2576—21no—
52#2562C2211yescharacteristic
53#2543—21no—
54#2538C2211yescharacteristic, complemented
55#2535C2211yescharacteristic
56#2504C2211yescharacteristic
57#2497C2211yescharacteristic
58#2494C2211yescharacteristic, complemented
59#2490C2211yescharacteristic
60#2489C2211yescharacteristic, complemented
61#2486C2211yescharacteristic, complemented
62#2480—21no—
63#2444—21no—
64#2442C2211yescharacteristic
65#2441C2211yescharacteristic, complemented
66#2421C2211yescharacteristic
67#2420C2211yescharacteristic
68#2417C2211yescharacteristic
69#2416C2211yescharacteristic
70#2415C2211yescharacteristic, complemented
71#2414C2211yescharacteristic
72#2412—21no—
73#2410—21no—
74#2408C2211yescharacteristic
75#2362C2211yescharacteristic, complemented
76#2361C2211yescharacteristic
77#2352C2211yescharacteristic
78#2352C2211yescharacteristic, complemented
79D4×C22⋊C4—21no—
80D4×C22⋊C4C2211yescharacteristic
81#2335—21no—
82C4×#120C2211yescharacteristic
83#2280C2211yescharacteristic
84C2×#380C2211yescharacteristic
85#2101C2211yescharacteristic, complemented
86#2099C2211yescharacteristic, complemented
87#2097C2211yescharacteristic, complemented
88#2092C2211yescharacteristic, complemented
89#2088C2211yescharacteristic, complemented
90#2087C2211yescharacteristic, complemented
91#2085C2211yescharacteristic, complemented
92#2085C2211yescharacteristic, complemented
93#2077C2211yescharacteristic
94#2077C2211yescharacteristic
95#2077C2211yescharacteristic
96#2077C2211yescharacteristic
97#2077C2211yescharacteristic, complemented
98#2077C2211yescharacteristic, complemented
99#2077C2211yescharacteristic, complemented
100#2077C2211yescharacteristic, complemented
101#2075C2211yescharacteristic
102#2075C2211yescharacteristic
103#2074C2211yescharacteristic, complemented
104#2071C2211yescharacteristic, complemented
105#2065C2211yescharacteristic, complemented
106#2065C2211yescharacteristic, complemented
107#2059C2211yescharacteristic, complemented
108#2059C2211yescharacteristic, complemented
109#2055C2211yescharacteristic, complemented
110#2055C2211yescharacteristic, complemented
111#2035C2211yescharacteristic
112#2035C2211yescharacteristic
113#2035C2211yescharacteristic, complemented
114#2035C2211yescharacteristic, complemented
115#2034C2211yescharacteristic
116#2034C2211yescharacteristic
117#2034C2211yescharacteristic, complemented
118#2033C2211yescharacteristic
119#2033C2211yescharacteristic
120#2033C2211yescharacteristic
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic
123#2033C2211yescharacteristic
124#2033C2211yescharacteristic, complemented
125#2025C2211yescharacteristic, complemented
126#2025C2211yescharacteristic, complemented
127#2000C2211yescharacteristic
128#2000C2211yescharacteristic
129#2000C2211yescharacteristic
130#2000C2211yescharacteristic
131#2000C2211yescharacteristic, complemented
132#2000C2211yescharacteristic, complemented
133#1992C2211yescharacteristic, complemented
134#1991C2211yescharacteristic, complemented
135#1989C2211yescharacteristic, complemented
136#1968C2211yescharacteristic, complemented
137#1955C2211yescharacteristic, complemented
138#1954C2211yescharacteristic
139#1954C2211yescharacteristic, complemented
140#1949C2211yescharacteristic, complemented
141#1949C2211yescharacteristic, complemented
142#1944C2211yescharacteristic, complemented
143#1936C2211yescharacteristic, complemented
144#1934C2211yescharacteristic, complemented
145#1934C2211yescharacteristic, complemented
146#1933C2211yescharacteristic, complemented
147#1928C2211yescharacteristic, complemented
148#1926C2211yescharacteristic, complemented
149#1926C2211yescharacteristic, complemented
150#1925C2211yescharacteristic, complemented
151#1924C2211yescharacteristic
152#1924C2211yescharacteristic, complemented
153#1923C2211yescharacteristic
154#1923C2211yescharacteristic, complemented
155#1923C2211yescharacteristic, complemented
156#1923C2211yescharacteristic, complemented
157#1918C2211yescharacteristic, complemented
158#1918C2211yescharacteristic, complemented
159#1895C2211yescharacteristic, complemented
160#1895C2211yescharacteristic, complemented
161#1894C2211yescharacteristic, complemented
162#1880C2211yescharacteristic, complemented
163#1877C2211yescharacteristic, complemented
164#1875C2211yescharacteristic
165#1875C2211yescharacteristic
166#1874C2211yescharacteristic, complemented
167#1873C2211yescharacteristic, complemented
168#1872C2211yescharacteristic, complemented
169#1872C2211yescharacteristic, complemented
170#1870C2211yescharacteristic
171#1870C2211yescharacteristic, complemented
172#1870C2211yescharacteristic, complemented
173#1865C2211yescharacteristic, complemented
174#1864C2211yescharacteristic, complemented
175#1864C2211yescharacteristic, complemented
176#1864C2211yescharacteristic, complemented
177#1854C2211yescharacteristic, complemented
178#1854C2211yescharacteristic, complemented
179#1854C2211yescharacteristic, complemented
180#1853C2211yescharacteristic
181#1853C2211yescharacteristic, complemented
182#1853C2211yescharacteristic, complemented
183#1853C2211yescharacteristic, complemented
184#1852C2211yescharacteristic
185#1852C2211yescharacteristic, complemented
186#1852C2211yescharacteristic, complemented
187#1846C2211yescharacteristic, complemented
188#1825C2211yescharacteristic, complemented
189#1825C2211yescharacteristic, complemented
190#1825C2211yescharacteristic, complemented
191#1824C2211yescharacteristic
192#1824C2211yescharacteristic, complemented
193#1824C2211yescharacteristic, complemented
194#1804C2211yescharacteristic, complemented
195#1802C2211yescharacteristic, complemented
196#1786C2211yescharacteristic
197#1786C2211yescharacteristic
198#1786C2211yescharacteristic
199#1779C2211yescharacteristic
200#1779C2211yescharacteristic
201C4×#106C2211yescharacteristic, complemented
202C4×#102C2211yescharacteristic, complemented
203C23×D4—21no—
204C23×D4C2311yescharacteristic
205C24×C4C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209#553—42no—
210#553—42no—
211C2×#126—21no—
212C2×#125C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#123—21no—
215C2×#123—21no—
216C2×C22⋊Q8C2311yescharacteristic
217C2×C22⋊Q8C2311yescharacteristic
218C2×C22⋊Q8C2311yescharacteristic
219C2×C22⋊Q8C2311yescharacteristic
220C2×#121—21no—
221C2×#121—21no—
222C2×#121—21no—
223C2×#121—21no—
224C2×#121—42no—
225C2×#121—42no—
226C2×#121C2311yescharacteristic
227C2×#121C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#120—21no—
233C2×#120D411yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×D4—21no—
236C2×C4×D4—21no—
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C22⋊C4—21no—
250C22×C22⋊C4—21no—
251C22×C22⋊C4—21no—
252#484—42no—
253#482—42no—
254#482—42no—
255#481—42no—
256#479—42no—
257#450—42no—
258#440—42no—
259#428—42no—
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×#97C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315#401—21no—
316#400—21no—
317#400—21no—
318#400—21no—
319#400—21no—
320#400—21no—
321#399—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#396—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#394—21no—
347#394—21no—
348#392—21no—
349#392—21no—
350#392—21no—
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#390—21no—
354#390—21no—
355#390—21no—
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#389—21no—
361#389—21no—
362#389—21no—
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
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#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#386—21no—
391#386—21no—
392#386—21no—
393#386—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#386D411yescharacteristic
403#386D411yescharacteristic
404#386D411yescharacteristic
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385D411yescharacteristic
411#385D411yescharacteristic
412#385D411yescharacteristic
413#384C2311yescharacteristic
414#382—21no—
415#382C2311yescharacteristic
416#382C2311yescharacteristic
417#382C2311yescharacteristic
418#381—21no—
419#381—21no—
420#381—21no—
421#380—21no—
422#380—21no—
423#380—21no—
424#380—21no—
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#379—21no—
440#379—21no—
441#379—21no—
442#379—21no—
443#379D411yescharacteristic
444C4×C4⋊C4—21no—
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4C2311yescharacteristic
453C4×C22⋊C4C2311yescharacteristic
454C4×C22⋊C4C2311yescharacteristic
455C2×#95—21no—
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#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25—21no—
491C25C2×D411yescharacteristic
492C22×Q8C2411yescharacteristic
493C22×D4—21no—
494C22×D4—22no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—41no—
502C22×D4—41no—
503C22×D4—41no—
504C22×D4—41no—
505C22×D4—41no—
506C22×D4—44no—
507C22×D4—44no—
508C22×D4—82no—
509C22×D4C2×D411yescharacteristic
510C22×D4C2×D411yescharacteristic
511C22×D4C2×D411yescharacteristic
512C22×D4C2411yescharacteristic
513C22×D4C2411yescharacteristic
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—41no—
521C23×C4—41no—
522C23×C4—41no—
523C23×C4—41no—
524C23×C4—41no—
525C23×C4—41no—
526C23×C4C2×D411yescharacteristic
527C23×C4C2×D411yescharacteristic
528C23×C4C2×D411yescharacteristic
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C23×C4C2411yescharacteristic
532C23×C4C2411yescharacteristic
533C2×SD16—22no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×M16—41no—
540C2×M16—41no—
541C2×M16—41no—
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550#126—44no—
551#125—22no—
552#125—41no—
553#125—41no—
554#125—41no—
555#123—44no—
556#123—44no—
557C22⋊Q8—41no—
558C22⋊Q8—41no—
559C22⋊Q8—41no—
560C22⋊Q8—41no—
561C22⋊Q8—41no—
562C22⋊Q8—41no—
563C22⋊Q8—41no—
564C22⋊Q8—41no—
565#121—22no—
566#121—22no—
567#121—22no—
568#121—22no—
569#121—22no—
570#121—44no—
571#121—41no—
572#121—41no—
573#121—41no—
574#121—41no—
575#121—41no—
576#121—44no—
577#121—44no—
578#121—41no—
579#121—41no—
580#121—82no—
581#120—42no—
582#120—82no—
583C4×Q8—41no—
584C4×Q8—41no—
585C4×D4—22no—
586C4×D4—41no—
587C4×D4—41no—
588C4×D4—41no—
589C4×D4—41no—
590C4×D4—41no—
591C4×D4—41no—
592C4×D4—41no—
593C4×D4—41no—
594C4×D4—41no—
595C4×D4—44no—
596C4×D4—82no—
597#117—22no—
598#117—41no—
599#117—41no—
600#117—41no—
601#117—41no—
602#117—41no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—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—41no—
626C2×C4⋊C4—41no—
627C2×C4⋊C4—41no—
628C2×C4⋊C4—41no—
629C2×C4⋊C4—41no—
630C2×C4⋊C4—41no—
631C2×C4⋊C4—41no—
632C2×C4⋊C4C2×D411yescharacteristic
633C2×C4⋊C4C2×D411yescharacteristic
634C2×C4⋊C4C2×D411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—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—44no—
686C2×C22⋊C4—82no—
687C2×C22⋊C4—82no—
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C22⋊C4C2×D411yescharacteristic
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710#107—22no—
711#107—22no—
712#107—41no—
713#107—41no—
714#107—41no—
715#107—41no—
716#106—22no—
717#106—41no—
718#106—41no—
719#106—41no—
720#106—41no—
721#106—41no—
722#106—41no—
723#106—41no—
724C4⋊C8—41no—
725C4⋊C8—41no—
726C4⋊C8—41no—
727#103—22no—
728#103—41no—
729#103—41no—
730#103—41no—
731#103—41no—
732#103—41no—
733#102—22no—
734#102—22no—
735#102—22no—
736#102—41no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102—41no—
747C22⋊C8—41no—
748C22⋊C8—41no—
749C22⋊C8—41no—
750C22⋊C8—41no—
751C22⋊C8—41no—
752C22⋊C8—41no—
753C22⋊C8—41no—
754C22⋊C8—41no—
755C22⋊C8—41no—
756C22⋊C8—41no—
757C22⋊C8—41no—
758C22⋊C8—41no—
759C22⋊C8—41no—
760C22⋊C8—41no—
761C22⋊C8—41no—
762#97—41no—
763C4×C8—41no—
764C4×C8—41no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#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#95—21no—
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804C24—21no—
805C24—22no—
806C24—22no—
807C24—21no—
808C24—41no—
809C24—41no—
810C24—41no—
811C24—41no—
812C24—41no—
813C24—42no—
814C24—42no—
815C24—42no—
816C24—42no—
817C24—81no—
818C24—81no—
819C24—81no—
820C24C22×D411yescharacteristic
821C24C22×D411yescharacteristic
822C24C22×D411yescharacteristic
823C24C22×D411yescharacteristic
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×D4—24no—
831C2×D4—22no—
832C2×D4—22no—
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—41no—
845C2×D4—41no—
846C2×D4—41no—
847C2×D4—41no—
848C2×D4—41no—
849C2×D4—41no—
850C2×D4—41no—
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—81no—
864C2×D4—82no—
865C2×D4—82no—
866C2×D4—82no—
867C2×D4—82no—
868C2×D4—81no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4—81no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4—816no—
876C2×D4H(5,𝔽2)12yes—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
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—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—41no—
916C22×C4—41no—
917C22×C4—41no—
918C22×C4—41no—
919C22×C4—41no—
920C22×C4—41no—
921C22×C4—41no—
922C22×C4—41no—
923C22×C4—41no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—42no—
928C22×C4—42no—
929C22×C4—42no—
930C22×C4—81no—
931C22×C4—81no—
932C22×C4—81no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4—82no—
936C22×C4—82no—
937C22×C4—82no—
938C22×C4—82no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
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×C4C22×D411yescharacteristic
956C22×C4C2511yescharacteristic
957SD16—44no—
958SD16—82no—
959M16—44no—
960C2×C8—21no—
961C2×C8—21no—
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—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
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—41no—
1010C4⋊C4—41no—
1011C4⋊C4—41no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
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⋊C4H(5,𝔽2)12yes—
1034C22⋊C4—24no—
1035C22⋊C4—22no—
1036C22⋊C4—22no—
1037C22⋊C4—41no—
1038C22⋊C4—41no—
1039C22⋊C4—41no—
1040C22⋊C4—41no—
1041C22⋊C4—41no—
1042C22⋊C4—41no—
1043C22⋊C4—41no—
1044C22⋊C4—41no—
1045C22⋊C4—41no—
1046C22⋊C4—41no—
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—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
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—
1082C22⋊C4—81no—
1083C42—21no—
1084C42—21no—
1085C42—21no—
1086C42—21no—
1087C42—21no—
1088C42—21no—
1089C42—42no—
1090C42—81no—
1091C42—81no—
1092C42—81no—
1093C42—81no—
1094C42—81no—
1095C42—81no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—22no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—44no—
1124C23—44no—
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—82no—
1139C23—82no—
1140C23—82no—
1141C23—84no—
1142C23—84no—
1143C23—82no—
1144C23—82no—
1145C23—84no—
1146C23—84no—
1147C23—162no—
1148C23—162no—
1149C23—162no—
1150C23#57512yes—
1151C23#57712yes—
1152C23C23×D411yescharacteristic
1153Q8—41no—
1154Q8—41no—
1155Q8—41no—
1156Q8—41no—
1157D4—22no—
1158D4—22no—
1159D4—48no—
1160D4—41no—
1161D4—41no—
1162D4—41no—
1163D4—41no—
1164D4—41no—
1165D4—41no—
1166D4—82no—
1167D4—82no—
1168D4—82no—
1169D4—84no—
1170D4—84no—
1171D4—84no—
1172D4—84no—
1173D4—162no—
1174D4—162no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—22no—
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—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
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—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
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—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—82no—
1264C2×C4—82no—
1265C2×C4—82no—
1266C2×C4—84no—
1267C2×C4—162no—
1268C2×C4—162no—
1269C2×C4—162no—
1270C2×C4—162no—
1271C2×C4—162no—
1272C2×C4C2×H(5,𝔽2)11yescharacteristic
1273C2×C4C2×H(5,𝔽2)11yescharacteristic
1274C2×C4#58511yescharacteristic
1275C2×C4#58511yescharacteristic
1276C2×C4#58511yescharacteristic
1277C2×C4#58511yescharacteristic
1278C8—41no—
1279C8—41no—
1280C8—41no—
1281C8—41no—
1282C8—41no—
1283C8—41no—
1284C8—41no—
1285C8—41no—
1286C22—22no—
1287C22—22no—
1288C22—22no—
1289C22—22no—
1290C22—22no—
1291C22—22no—
1292C22—41no—
1293C22—41no—
1294C22—41no—
1295C22—41no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—42no—
1310C22—41no—
1311C22—42no—
1312C22—41no—
1313C22—41no—
1314C22—41no—
1315C22—41no—
1316C22—42no—
1317C22—88no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—81no—
1322C22—81no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—168no—
1330C22#348411yescharacteristic
1331C22#348511yescharacteristic
1332C22#348511yescharacteristic
1333C22C2×#57511yescharacteristic
1334C22C2×#57711yescharacteristic
1335C22#358411yescharacteristic
1336C22#358511yescharacteristic
1337C4—41no—
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—41no—
1342C4—42no—
1343C4—41no—
1344C4—41no—
1345C4—41no—
1346C4—41no—
1347C4—41no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4—81no—
1357C4—81no—
1358C4—81no—
1359C4—81no—
1360C4—81no—
1361C4#353311yescharacteristic
1362C4#354011yescharacteristic
1363C4#356011yescharacteristic
1364C4#356211yescharacteristic
1365C2—42no—
1366C2—42no—
1367C2—81no—
1368C2—81no—
1369C2—82no—
1370C2—161no—
1371C2#4782811yescharacteristic
1372C2#6158111yescharacteristic
1373C2#6164011yescharacteristic
1374C2#6173611yescharacteristic
1375C2#6174111yescharacteristic
1376C2#6175611yescharacteristic
1377C2#6176111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#59013C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#120 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #39935C2semidirect
3. #32292C2semidirect
4. #32060C2semidirect
5. #31800C2semidirect
6. #31755C2semidirect
7. #31721C2semidirect
8. #31440C2semidirect
9. #31401C2semidirect
10. #31400C2semidirect
11. #31359C2semidirect
12. #31276C2semidirect
13. #31079C2semidirect
14. #31024C2semidirect
15. #29893C2semidirect
16. #29598C2semidirect
17. #27604C2semidirect
18. #27520C2semidirect
19. #27097C2semidirect
20. #26794C2semidirect
21. #26721C2semidirect
22. #26568C2semidirect
23. #26304C2semidirect
24. #26156C2semidirect
25. #26145C2semidirect
26. #25018C2semidirect
27. #24917C2semidirect
28. #24138C2semidirect
29. #24101C2semidirect
30. #24009C2semidirect
31. #23308C2semidirect
35. C2×#481C22semidirect
38. C2×#479C22semidirect
40. C2×#440C22semidirect
41. C2×#428C22semidirect
54. #2538C22semidirect
58. #2494C22semidirect
60. #2489C22semidirect
61. #2486C22semidirect
65. #2441C22semidirect
70. #2415C22semidirect
75. #2362C22semidirect
78. #2352C22semidirect
85. #2101C22semidirect
86. #2099C22semidirect
87. #2097C22semidirect
88. #2092C22semidirect
89. #2088C22semidirect
90. #2087C22semidirect
91. #2085C22semidirect
92. #2085C22semidirect
97. #2077C22semidirect
98. #2077C22semidirect
99. #2077C22semidirect
100. #2077C22semidirect
103. #2074C22semidirect
104. #2071C22semidirect
105. #2065C22semidirect
106. #2065C22semidirect
107. #2059C22semidirect
108. #2059C22semidirect
109. #2055C22semidirect
110. #2055C22semidirect
113. #2035C22semidirect
114. #2035C22semidirect
117. #2034C22semidirect
124. #2033C22semidirect
125. #2025C22semidirect
126. #2025C22semidirect
131. #2000C22semidirect
132. #2000C22semidirect
133. #1992C22semidirect
134. #1991C22semidirect
135. #1989C22semidirect
136. #1968C22semidirect
137. #1955C22semidirect
139. #1954C22semidirect
140. #1949C22semidirect
141. #1949C22semidirect
142. #1944C22semidirect
143. #1936C22semidirect
144. #1934C22semidirect
145. #1934C22semidirect
146. #1933C22semidirect
147. #1928C22semidirect
148. #1926C22semidirect
149. #1926C22semidirect
150. #1925C22semidirect
152. #1924C22semidirect
154. #1923C22semidirect
155. #1923C22semidirect
156. #1923C22semidirect
157. #1918C22semidirect
158. #1918C22semidirect
159. #1895C22semidirect
160. #1895C22semidirect
161. #1894C22semidirect
162. #1880C22semidirect
163. #1877C22semidirect
166. #1874C22semidirect
167. #1873C22semidirect
168. #1872C22semidirect
169. #1872C22semidirect
171. #1870C22semidirect
172. #1870C22semidirect
173. #1865C22semidirect
174. #1864C22semidirect
175. #1864C22semidirect
176. #1864C22semidirect
177. #1854C22semidirect
178. #1854C22semidirect
179. #1854C22semidirect
181. #1853C22semidirect
182. #1853C22semidirect
183. #1853C22semidirect
185. #1852C22semidirect
186. #1852C22semidirect
187. #1846C22semidirect
188. #1825C22semidirect
189. #1825C22semidirect
190. #1825C22semidirect
192. #1824C22semidirect
193. #1824C22semidirect
194. #1804C22semidirect
195. #1802C22semidirect
201. C4×#106C22semidirect
202. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
#590132
#399352
#322922
#320602
#318002
#317552
#317212
#314402
#314012
#314002
#313592
#312762
#310792
#310242
#298932
#295982
#276042
#275202
#270972
#267942
#267212
#265682
#263042
#261562
#261452
#250182
#249172
#241382
#241012
#240092
#233082