Finite Group Databasebeta

← #7013359

Subgroups — #7013359

Order 512.

1566 conjugacy classes of subgroups.

The subgroup lattice has 1367 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59627C211yesmaximal, characteristic, complemented
2#40053C211yesmaximal, characteristic, complemented
3#32211C211yesmaximal, characteristic, complemented
4#32127C211yesmaximal, characteristic, complemented
5#32011C211yesmaximal, characteristic, complemented
6#31648C211yesmaximal, characteristic, complemented
7#31216C211yesmaximal, characteristic, complemented
8#30923C211yesmaximal, characteristic, complemented
9#30539C211yesmaximal, characteristic, complemented
10#30511C211yesmaximal, characteristic, complemented
11#28914C211yesmaximal, characteristic, complemented
12#28897C211yesmaximal, characteristic, complemented
13#28578C211yesmaximal, characteristic, complemented
14#28110C211yesmaximal, characteristic, complemented
15#27805C211yesmaximal, characteristic, complemented
16#27801C211yesmaximal, characteristic, complemented
17#27238C211yesmaximal, characteristic, complemented
18#27153C211yesmaximal, characteristic, complemented
19#27120C211yesmaximal, characteristic, complemented
20#26747C211yesmaximal, characteristic, complemented
21#26697C211yesmaximal, characteristic, complemented
22#26600C211yesmaximal, characteristic, complemented
23#25457C211yesmaximal, characteristic, complemented
24#25390C211yesmaximal, characteristic, complemented
25#25093C211yesmaximal, characteristic, complemented
26#24661C211yesmaximal, characteristic, complemented
27#23708C211yesmaximal, characteristic, complemented
28#23229C211yesmaximal, characteristic, complemented
29#22914C211yesmaximal, characteristic, complemented
30#22868C211yesmaximal, characteristic, complemented
31#22191C211yesmaximal, characteristic, complemented
32C2×#499C2211yescharacteristic, complemented
33C2×#490C2211yescharacteristic
34C2×#478C2211yescharacteristic
35C2×#469C2211yescharacteristic
36C2×#469C2211yescharacteristic, complemented
37C2×#468C2211yescharacteristic
38C2×#468C2211yescharacteristic
39C2×#460C2211yescharacteristic
40C2×#463C2211yescharacteristic, complemented
41C2×#450C2211yescharacteristic
42C2×#447C2211yescharacteristic
43C2×#442C2211yescharacteristic
44C2×#436C2211yescharacteristic
45C2×#432C2211yescharacteristic, complemented
46C2×#418C2211yescharacteristic
47#2856C2211yescharacteristic
48#2797—21no—
49#2797—21no—
50#2796—21no—
51#2697—21no—
52#2688—21no—
53#2678—21no—
54#2648—21no—
55#2602—21no—
56#2596—21no—
57#2566C2211yescharacteristic
58#2540C2211yescharacteristic
59#2535C2211yescharacteristic
60#2517—21no—
61#2516—21no—
62#2513—21no—
63#2513C2211yescharacteristic
64#2497C2211yescharacteristic
65#2490C2211yescharacteristic
66#2490C2211yescharacteristic
67#2490C2211yescharacteristic
68#2490C2211yescharacteristic, complemented
69#2489C2211yescharacteristic
70#2489C2211yescharacteristic, complemented
71#2485C2211yescharacteristic
72#2456—21no—
73#2448C2211yescharacteristic, complemented
74#2447C2211yescharacteristic, complemented
75#2445C2211yescharacteristic
76#2433C2211yescharacteristic
77#2428C2211yescharacteristic
78#2424—21no—
79#2408C2211yescharacteristic
80#2370C2211yescharacteristic, complemented
81#2370C2211yescharacteristic, complemented
82#2366C2211yescharacteristic
83#2363C2211yescharacteristic
84#2362C2211yescharacteristic
85#2357—21no—
86D4×C22⋊C4C2211yescharacteristic
87#2321—21no—
88C4×C22⋊Q8C2211yescharacteristic, complemented
89C4×#123C2211yescharacteristic
90C4×#121C2211yescharacteristic
91C4×#121C2211yescharacteristic, complemented
92#2101C2211yescharacteristic, complemented
93#2088C2211yescharacteristic, complemented
94#2085C2211yescharacteristic, complemented
95#2084C2211yescharacteristic, complemented
96#2077C2211yescharacteristic, complemented
97#2075C2211yescharacteristic
98#2071C2211yescharacteristic, complemented
99#2067C2211yescharacteristic
100#2067C2211yescharacteristic
101#2067C2211yescharacteristic, complemented
102#2065C2211yescharacteristic
103#2065C2211yescharacteristic, complemented
104#2059C2211yescharacteristic, complemented
105#2055C2211yescharacteristic
106#2055C2211yescharacteristic
107#2054C2211yescharacteristic
108#2054C2211yescharacteristic, complemented
109#2041C2211yescharacteristic
110#2035C2211yescharacteristic
111#2035C2211yescharacteristic
112#2034C2211yescharacteristic
113#2034C2211yescharacteristic
114#2033C2211yescharacteristic
115#2033C2211yescharacteristic
116#2033C2211yescharacteristic, complemented
117#2033C2211yescharacteristic, complemented
118#2026C2211yescharacteristic, complemented
119#2025C2211yescharacteristic
120#2025C2211yescharacteristic
121#2025C2211yescharacteristic, complemented
122#2025C2211yescharacteristic, complemented
123#2014C2211yescharacteristic
124#2012C2211yescharacteristic
125#2012C2211yescharacteristic
126#2011C2211yescharacteristic
127#2011C2211yescharacteristic
128#2000C2211yescharacteristic
129#2000C2211yescharacteristic, complemented
130#1999C2211yescharacteristic
131#1999C2211yescharacteristic
132#1989C2211yescharacteristic, complemented
133#1989C2211yescharacteristic, complemented
134#1982C2211yescharacteristic
135#1982C2211yescharacteristic
136#1973C2211yescharacteristic
137#1973C2211yescharacteristic, complemented
138#1972C2211yescharacteristic
139#1970C2211yescharacteristic
140#1968C2211yescharacteristic, complemented
141#1958C2211yescharacteristic, complemented
142#1949C2211yescharacteristic, complemented
143#1947C2211yescharacteristic, complemented
144#1939C2211yescharacteristic, complemented
145#1936C2211yescharacteristic
146#1936C2211yescharacteristic, complemented
147#1935C2211yescharacteristic, complemented
148#1934C2211yescharacteristic
149#1934C2211yescharacteristic
150#1927C2211yescharacteristic, complemented
151#1927C2211yescharacteristic, complemented
152#1926C2211yescharacteristic
153#1926C2211yescharacteristic
154#1926C2211yescharacteristic
155#1926C2211yescharacteristic
156#1926C2211yescharacteristic, complemented
157#1925C2211yescharacteristic
158#1925C2211yescharacteristic
159#1925C2211yescharacteristic, complemented
160#1925C2211yescharacteristic, complemented
161#1924C2211yescharacteristic
162#1924C2211yescharacteristic
163#1921C2211yescharacteristic, complemented
164#1919C2211yescharacteristic, complemented
165#1918C2211yescharacteristic, complemented
166#1917C2211yescharacteristic, complemented
167#1916C2211yescharacteristic, complemented
168#1895C2211yescharacteristic
169#1895C2211yescharacteristic
170#1895C2211yescharacteristic
171#1895C2211yescharacteristic, complemented
172#1894C2211yescharacteristic, complemented
173#1880C2211yescharacteristic
174#1879C2211yescharacteristic
175#1879C2211yescharacteristic
176#1879C2211yescharacteristic, complemented
177#1877C2211yescharacteristic
178#1877C2211yescharacteristic
179#1875C2211yescharacteristic
180#1870C2211yescharacteristic
181#1864C2211yescharacteristic, complemented
182#1863C2211yescharacteristic, complemented
183#1862C2211yescharacteristic
184#1862C2211yescharacteristic, complemented
185#1854C2211yescharacteristic
186#1851C2211yescharacteristic
187#1851C2211yescharacteristic, complemented
188#1825C2211yescharacteristic
189#1809C2211yescharacteristic
190#1809C2211yescharacteristic, complemented
191#1803C2211yescharacteristic, complemented
192#1786C2211yescharacteristic
193#1776C2211yescharacteristic, complemented
194#1776C2211yescharacteristic, complemented
195#1771C2211yescharacteristic, complemented
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic, complemented
198C4×#102C2211yescharacteristic
199C4×#102C2211yescharacteristic, complemented
200#1753C2211yescharacteristic
201#1753C2211yescharacteristic, complemented
202#1728C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213C2×#127C2311yescharacteristic
214C2×#127C2311yescharacteristic
215C2×#125C2311yescharacteristic
216C2×#125C2311yescharacteristic
217C2×#125C2311yescharacteristic
218C2×#124C2311yescharacteristic
219C2×#123—21no—
220C2×#123D411yescharacteristic
221C2×C22⋊Q8C2311yescharacteristic
222C2×C22⋊Q8C2311yescharacteristic
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×Q8C2311yescharacteristic
236C2×C4×D4—21no—
237C2×C4×D4—21no—
238C2×C4×D4—21no—
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C22×C22⋊C4—21no—
246C22×C42C2311yescharacteristic
247#499—42no—
248#490—24no—
249#478—42no—
250#469—42no—
251#469—42no—
252#468—24no—
253#468—42no—
254#463—42no—
255#460—42no—
256#450—42no—
257#447—24no—
258#442—42no—
259#436—42no—
260#432—42no—
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276#418—42no—
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×#97C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315#400—21no—
316#400—21no—
317#400—21no—
318#399—21no—
319#399—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#397—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#396—21no—
334#396—21no—
335#396—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#392—21no—
346#392—21no—
347#392—21no—
348#392—21no—
349#392—21no—
350#392—21no—
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#390—21no—
355#390—21no—
356#390—21no—
357#390—21no—
358#390—21no—
359#390—21no—
360#390—21no—
361#390—21no—
362#390—21no—
363#390—21no—
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#389—21no—
376#389—21no—
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388D411yescharacteristic
401#388D411yescharacteristic
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387D411yescharacteristic
411#387D411yescharacteristic
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386D411yescharacteristic
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385D411yescharacteristic
429#384C2311yescharacteristic
430#382—21no—
431#382—21no—
432#382C2311yescharacteristic
433#381—21no—
434#381D411yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#379—21no—
442#379—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4—21no—
445C4×C4⋊C4—21no—
446C4×C4⋊C4—21no—
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4C2311yescharacteristic
461C4×C22⋊C4C2311yescharacteristic
462C4×C22⋊C4C2311yescharacteristic
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×Q8C2411yescharacteristic
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—41no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4C2×D411yescharacteristic
513C22×D4C2411yescharacteristic
514C22×D4C2411yescharacteristic
515C22×D4C2411yescharacteristic
516C22×D4C2411yescharacteristic
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4C2×D411yescharacteristic
522C23×C4C2×D411yescharacteristic
523C23×C4C2411yescharacteristic
524C23×C4C2411yescharacteristic
525C2×SD16—22no—
526C2×SD16—22no—
527C2×SD16—41no—
528C2×SD16—41no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×D8—22no—
535C2×D8—22no—
536C2×D8—41no—
537C2×D8—41no—
538C2×D8—41no—
539C2×D8—41no—
540C2×D8—41no—
541C2×D8—41no—
542C2×D8—41no—
543C2×M16—22no—
544C2×M16—22no—
545C2×M16—41no—
546C2×M16—41no—
547C2×M16—41no—
548C2×M16—41no—
549C2×M16—41no—
550C2×M16—41no—
551C2×M16—41no—
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560#127—22no—
561#127—41no—
562#127—41no—
563#127—41no—
564#125—22no—
565#125—22no—
566#125—41no—
567#125—41no—
568#125—41no—
569#125—41no—
570#124—41no—
571#124—41no—
572#123—42no—
573#123—82no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—41no—
577C22⋊Q8—41no—
578#121—22no—
579#121—22no—
580#121—22no—
581#121—41no—
582#121—41no—
583#121—41no—
584#121—41no—
585#121—41no—
586#121—41no—
587#121—41no—
588#121—41no—
589#121—41no—
590#121—82no—
591#121—82no—
592#121—82no—
593#120—44no—
594#120—82no—
595#120—82no—
596C4×Q8—41no—
597C4×Q8—41no—
598C4×D4—41no—
599C4×D4—41no—
600C4×D4—41no—
601C4×D4—41no—
602C4×D4—41no—
603C4×D4—41no—
604C4×D4—41no—
605C4×D4—41no—
606C4×D4—41no—
607C4×D4—41no—
608C4×D4—44no—
609C4×D4—82no—
610C4×D4—82no—
611#117—41no—
612#117—41no—
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—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2×D411yescharacteristic
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×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—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—82no—
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×C42—21no—
699C2×C42—21no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—41no—
708C2×C42—41no—
709C2×C42C2×D411yescharacteristic
710C2×C42C2×D411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716#107—22no—
717#107—22no—
718#107—41no—
719#107—41no—
720#107—41no—
721#106—22no—
722#106—22no—
723#106—41no—
724#106—41no—
725#106—41no—
726C4⋊C8—22no—
727C4⋊C8—22no—
728C4⋊C8—41no—
729C4⋊C8—41no—
730C4⋊C8—41no—
731#103—22no—
732#103—41no—
733#103—41no—
734#103—41no—
735#103—41no—
736#102—22no—
737#102—22no—
738#102—22no—
739#102—22no—
740#102—22no—
741#102—22no—
742#102—22no—
743#102—22no—
744#102—22no—
745#102—22no—
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#4114yes—
759C22⋊C8—22no—
760C22⋊C8—22no—
761C22⋊C8—41no—
762C22⋊C8—41no—
763C22⋊C8—41no—
764#97—22no—
765#97—22no—
766#97—41no—
767C4×C8—41no—
768C4×C8—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#95C2×D411yescharacteristic
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
806C24—21no—
807C24—21no—
808C24—21no—
809C24—21no—
810C24—42no—
811C24—42no—
812C24—81no—
813C24—81no—
814C24—81no—
815C24—81no—
816C24—81no—
817C24C22×D411yescharacteristic
818C24C22×D411yescharacteristic
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—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—21no—
847C2×D4—21no—
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—44no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—42no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—81no—
867C2×D4—81no—
868C2×D4—81no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4—81no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4—82no—
876C2×D4—82no—
877C2×D4—82no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4—81no—
888C2×D4C2×#4112yes—
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—22no—
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—41no—
915C22×C4—41no—
916C22×C4—41no—
917C22×C4—41no—
918C22×C4—41no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—81no—
922C22×C4—81no—
923C22×C4—81no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4—81no—
929C22×C4—81no—
930C22×C4—81no—
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C2511yescharacteristic
944SD16—82no—
945SD16—82no—
946SD16—82no—
947D8—44no—
948D8—82no—
949D8—82no—
950M16—82no—
951M16—82no—
952M16—82no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
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×C8C2×#4112yes—
976C2×C8H(5,𝔽2)12yes—
977C4⋊C4—22no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—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—41no—
999C4⋊C4—41no—
1000C4⋊C4—41no—
1001C4⋊C4—41no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4C2×#4112yes—
1020C4⋊C4H(5,𝔽2)12yes—
1021C22⋊C4—22no—
1022C22⋊C4—41no—
1023C22⋊C4—41no—
1024C22⋊C4—41no—
1025C22⋊C4—41no—
1026C22⋊C4—41no—
1027C22⋊C4—41no—
1028C22⋊C4—41no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
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—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—21no—
1079C42—21no—
1080C42—21no—
1081C42—21no—
1082C42—41no—
1083C42—41no—
1084C42—42no—
1085C42—81no—
1086C42—81no—
1087C42—81no—
1088C42—81no—
1089C42—81no—
1090C42—81no—
1091C42—81no—
1092C42—81no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—22no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
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—84no—
1136C23—84no—
1137C23—162no—
1138C23—162no—
1139C23—162no—
1140C23—162no—
1141C23—162no—
1142C23C23×D411yescharacteristic
1143Q8—41no—
1144Q8—41no—
1145Q8—41no—
1146Q8—41no—
1147D4—22no—
1148D4—22no—
1149D4—41no—
1150D4—41no—
1151D4—41no—
1152D4—41no—
1153D4—41no—
1154D4—41no—
1155D4—41no—
1156D4—41no—
1157D4—41no—
1158D4—41no—
1159D4—41no—
1160D4—41no—
1161D4—41no—
1162D4—41no—
1163D4—82no—
1164D4—84no—
1165D4—84no—
1166D4—84no—
1167D4—84no—
1168D4—162no—
1169D4—162no—
1170D4—162no—
1171D4—162no—
1172D4—162no—
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—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—22no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—22no—
1200C2×C4—21no—
1201C2×C4—21no—
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—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—82no—
1255C2×C4—82no—
1256C2×C4—162no—
1257C2×C4—162no—
1258C2×C4—162no—
1259C2×C4—162no—
1260C2×C4#57512yes—
1261C2×C4C22×#4111yescharacteristic
1262C2×C4C2×H(5,𝔽2)11yescharacteristic
1263C2×C4C2×H(5,𝔽2)11yescharacteristic
1264C2×C4#58511yescharacteristic
1265C2×C4#58511yescharacteristic
1266C2×C4#58511yescharacteristic
1267C8—22no—
1268C8—22no—
1269C8—41no—
1270C8—41no—
1271C8—41no—
1272C8—41no—
1273C8—41no—
1274C8—41no—
1275C22—41no—
1276C22—41no—
1277C22—41no—
1278C22—41no—
1279C22—42no—
1280C22—42no—
1281C22—41no—
1282C22—41no—
1283C22—41no—
1284C22—42no—
1285C22—41no—
1286C22—41no—
1287C22—41no—
1288C22—41no—
1289C22—41no—
1290C22—41no—
1291C22—41no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
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—168no—
1318C22D4×#4111yescharacteristic
1319C22#348811yescharacteristic
1320C22#349611yescharacteristic
1321C22C2×#57511yescharacteristic
1322C22#358511yescharacteristic
1323C22#358511yescharacteristic
1324C22#358511yescharacteristic
1325C4—22no—
1326C4—41no—
1327C4—42no—
1328C4—41no—
1329C4—41no—
1330C4—41no—
1331C4—41no—
1332C4—42no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4#350611yescharacteristic
1350C4#351411yescharacteristic
1351C4#355811yescharacteristic
1352C4#356611yescharacteristic
1353C2—81no—
1354C2—81no—
1355C2—82no—
1356C2—161no—
1357C2—161no—
1358C2—161no—
1359C2#4303511yescharacteristic
1360C2#6146811yescharacteristic
1361C2#6150611yescharacteristic
1362C2#6196811yescharacteristic
1363C2#6208111yescharacteristic
1364C2#6229211yescharacteristic
1365C2#6229811yescharacteristic
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. #59627C2semidirect
2. #40053C2semidirect
3. #32211C2semidirect
4. #32127C2semidirect
5. #32011C2semidirect
6. #31648C2semidirect
7. #31216C2semidirect
8. #30923C2semidirect
9. #30539C2semidirect
10. #30511C2semidirect
11. #28914C2semidirect
12. #28897C2semidirect
13. #28578C2semidirect
14. #28110C2semidirect
15. #27805C2semidirect
16. #27801C2semidirect
17. #27238C2semidirect
18. #27153C2semidirect
19. #27120C2semidirect
20. #26747C2semidirect
21. #26697C2semidirect
22. #26600C2semidirect
23. #25457C2semidirect
24. #25390C2semidirect
25. #25093C2semidirect
26. #24661C2semidirect
27. #23708C2semidirect
28. #23229C2semidirect
29. #22914C2semidirect
30. #22868C2semidirect
31. #22191C2semidirect
32. C2×#499C22semidirect
36. C2×#469C22semidirect
40. C2×#463C22semidirect
45. C2×#432C22semidirect
68. #2490C22semidirect
70. #2489C22semidirect
73. #2448C22semidirect
74. #2447C22semidirect
80. #2370C22semidirect
81. #2370C22semidirect
88. C4×C22⋊Q8C22semidirect
91. C4×#121C22semidirect
92. #2101C22semidirect
93. #2088C22semidirect
94. #2085C22semidirect
95. #2084C22semidirect
96. #2077C22semidirect
98. #2071C22semidirect
101. #2067C22semidirect
103. #2065C22semidirect
104. #2059C22semidirect
108. #2054C22semidirect
116. #2033C22semidirect
117. #2033C22semidirect
118. #2026C22semidirect
121. #2025C22semidirect
122. #2025C22semidirect
129. #2000C22semidirect
132. #1989C22semidirect
133. #1989C22semidirect
137. #1973C22semidirect
140. #1968C22semidirect
141. #1958C22semidirect
142. #1949C22semidirect
143. #1947C22semidirect
144. #1939C22semidirect
146. #1936C22semidirect
147. #1935C22semidirect
150. #1927C22semidirect
151. #1927C22semidirect
156. #1926C22semidirect
159. #1925C22semidirect
160. #1925C22semidirect
163. #1921C22semidirect
164. #1919C22semidirect
165. #1918C22semidirect
166. #1917C22semidirect
167. #1916C22semidirect
171. #1895C22semidirect
172. #1894C22semidirect
176. #1879C22semidirect
181. #1864C22semidirect
182. #1863C22semidirect
184. #1862C22semidirect
187. #1851C22semidirect
190. #1809C22semidirect
191. #1803C22semidirect
193. #1776C22semidirect
194. #1776C22semidirect
195. #1771C22semidirect
197. #1762C22semidirect
199. C4×#102C22semidirect
201. #1753C22semidirect
202. #1728C22semidirect

Maximal subgroups

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

subgroupindex
#596272
#400532
#322112
#321272
#320112
#316482
#312162
#309232
#305392
#305112
#289142
#288972
#285782
#281102
#278052
#278012
#272382
#271532
#271202
#267472
#266972
#266002
#254572
#253902
#250932
#246612
#237082
#232292
#229142
#228682
#221912