Finite Group Databasebeta

← #7291205

Subgroups — #7291205

Order 512.

1629 conjugacy classes of subgroups.

The subgroup lattice has 1343 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39955C211yesmaximal, characteristic, complemented
2#39396C211yesmaximal, characteristic
3#32836C211yesmaximal, characteristic, complemented
4#32640C211yesmaximal, characteristic, complemented
5#32572C211yesmaximal, characteristic, complemented
6#31932C211yesmaximal, characteristic, complemented
7#31686C211yesmaximal, characteristic, complemented
8#31559C211yesmaximal, characteristic, complemented
9#31370C211yesmaximal, characteristic, complemented
10#31332C211yesmaximal, characteristic, complemented
11#31276C211yesmaximal, characteristic, complemented
12#31121C211yesmaximal, characteristic, complemented
13#30988C211yesmaximal, characteristic, complemented
14#30630C211yesmaximal, characteristic, complemented
15#30608C211yesmaximal, characteristic, complemented
16#29435C211yesmaximal, characteristic, complemented
17#29366C211yesmaximal, characteristic, complemented
18#29143C211yesmaximal, characteristic, complemented
19#28847C211yesmaximal, characteristic, complemented
20#27709C211yesmaximal, characteristic, complemented
21#27254C211yesmaximal, characteristic, complemented
22#26987C211yesmaximal, characteristic, complemented
23#26659C211yesmaximal, characteristic, complemented
24#26424C211yesmaximal, characteristic, complemented
25#25960C211yesmaximal, characteristic, complemented
26#25935C211yesmaximal, characteristic, complemented
27#25560C211yesmaximal, characteristic, complemented
28#24917C211yesmaximal, characteristic, complemented
29#24346C211yesmaximal, characteristic, complemented
30#23966C211yesmaximal, characteristic, complemented
31#22389C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic, complemented
33C2×#552C2211yescharacteristic
34C2×#538—21no—
35C2×#486C2211yescharacteristic
36C2×#482C2211yescharacteristic, complemented
37C2×#478C2211yescharacteristic
38C2×#468C2211yescharacteristic, complemented
39C2×#460C2211yescharacteristic
40C2×#450C2211yescharacteristic
41C2×#440C2211yescharacteristic
42C22×#102C2211yescharacteristic
43#2860C2211yescharacteristic
44#2859C2211yescharacteristic, complemented
45#2730—21no—
46#2719—21no—
47#2713—21no—
48#2703—21no—
49#2694—21no—
50#2685—21no—
51#2678—21no—
52#2674—21no—
53#2664—21no—
54#2636—21no—
55#2611—21no—
56#2604—21no—
57#2584C2211yescharacteristic, complemented
58#2562C2211yescharacteristic
59#2548C2211yescharacteristic
60#2538C2211yescharacteristic
61#2501C2211yescharacteristic
62#2496C2211yescharacteristic
63#2456—21no—
64#2442C2211yescharacteristic
65#2441C2211yescharacteristic, complemented
66#2440C2211yescharacteristic
67#2439C2211yescharacteristic, complemented
68#2433C2211yescharacteristic
69#2428C2211yescharacteristic
70#2428C2211yescharacteristic
71#2423C2211yescharacteristic
72#2423C2211yescharacteristic, complemented
73#2422C2211yescharacteristic
74#2421C2211yescharacteristic
75#2421C2211yescharacteristic, complemented
76#2418—21no—
77#2416C2211yescharacteristic
78#2408C2211yescharacteristic
79#2361C2211yescharacteristic
80D4×C22⋊C4C2211yescharacteristic
81#2323—21no—
82C4×#127C2211yescharacteristic
83C4×#124C2211yescharacteristic
84#2295C2211yescharacteristic, complemented
85#2101C2211yescharacteristic, complemented
86#2101C2211yescharacteristic, complemented
87#2100C2211yescharacteristic, complemented
88#2099C2211yescharacteristic, complemented
89#2096C2211yescharacteristic, complemented
90#2092C2211yescharacteristic
91#2092C2211yescharacteristic
92#2088C2211yescharacteristic, complemented
93#2086C2211yescharacteristic, complemented
94#2084C2211yescharacteristic, complemented
95#2084C2211yescharacteristic, complemented
96#2083C2211yescharacteristic, complemented
97#2077C2211yescharacteristic
98#2075C2211yescharacteristic
99#2075C2211yescharacteristic
100#2071C2211yescharacteristic
101#2071C2211yescharacteristic
102#2068C2211yescharacteristic, complemented
103#2067C2211yescharacteristic
104#2067C2211yescharacteristic, complemented
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic
107#2059C2211yescharacteristic, complemented
108#2059C2211yescharacteristic, complemented
109#2057C2211yescharacteristic, complemented
110#2055C2211yescharacteristic
111#2041C2211yescharacteristic
112#2041C2211yescharacteristic
113#2041C2211yescharacteristic
114#2035C2211yescharacteristic
115#2034C2211yescharacteristic
116#2034C2211yescharacteristic
117#2034C2211yescharacteristic, complemented
118#2033C2211yescharacteristic
119#2033C2211yescharacteristic, complemented
120#2025C2211yescharacteristic
121#2025C2211yescharacteristic
122#2025C2211yescharacteristic
123#2025C2211yescharacteristic
124#2025C2211yescharacteristic
125#2025C2211yescharacteristic, complemented
126#2025C2211yescharacteristic, complemented
127#2025C2211yescharacteristic, complemented
128#2023C2211yescharacteristic
129#2014C2211yescharacteristic
130#2000C2211yescharacteristic
131#2000C2211yescharacteristic
132#2000C2211yescharacteristic
133#1992C2211yescharacteristic, complemented
134#1988C2211yescharacteristic, complemented
135#1985C2211yescharacteristic, complemented
136#1984C2211yescharacteristic, complemented
137#1968C2211yescharacteristic
138#1957C2211yescharacteristic
139#1957C2211yescharacteristic
140#1942C2211yescharacteristic, complemented
141#1941C2211yescharacteristic, complemented
142#1936C2211yescharacteristic
143#1936C2211yescharacteristic, complemented
144#1934C2211yescharacteristic
145#1934C2211yescharacteristic
146#1933C2211yescharacteristic, complemented
147#1926C2211yescharacteristic
148#1926C2211yescharacteristic, complemented
149#1925C2211yescharacteristic
150#1924C2211yescharacteristic
151#1923C2211yescharacteristic
152#1923C2211yescharacteristic, complemented
153#1923C2211yescharacteristic, complemented
154#1920C2211yescharacteristic, complemented
155#1920C2211yescharacteristic, complemented
156#1918C2211yescharacteristic, complemented
157#1895C2211yescharacteristic
158#1895C2211yescharacteristic
159#1893C2211yescharacteristic
160#1892C2211yescharacteristic
161#1880C2211yescharacteristic
162#1880C2211yescharacteristic
163#1880C2211yescharacteristic
164#1880C2211yescharacteristic
165#1880C2211yescharacteristic, complemented
166#1880C2211yescharacteristic, complemented
167#1877C2211yescharacteristic
168#1877C2211yescharacteristic, complemented
169#1875C2211yescharacteristic
170#1875C2211yescharacteristic
171#1874C2211yescharacteristic
172#1872C2211yescharacteristic, complemented
173#1870C2211yescharacteristic
174#1869C2211yescharacteristic
175#1865C2211yescharacteristic, complemented
176#1864C2211yescharacteristic
177#1864C2211yescharacteristic
178#1864C2211yescharacteristic, complemented
179#1863C2211yescharacteristic, complemented
180#1862C2211yescharacteristic
181#1853C2211yescharacteristic, complemented
182#1852C2211yescharacteristic
183#1851C2211yescharacteristic, complemented
184#1850C2211yescharacteristic
185#1839C2211yescharacteristic, complemented
186#1834C2211yescharacteristic, complemented
187#1834C2211yescharacteristic, complemented
188#1824C2211yescharacteristic, complemented
189#1823C2211yescharacteristic
190#1807C2211yescharacteristic
191#1804C2211yescharacteristic
192#1804C2211yescharacteristic
193#1804C2211yescharacteristic, complemented
194#1804C2211yescharacteristic, complemented
195#1803C2211yescharacteristic, complemented
196#1786C2211yescharacteristic
197#1786C2211yescharacteristic
198C4×C4⋊C8C2211yescharacteristic, complemented
199C4×#103C2211yescharacteristic, complemented
200#1753C2211yescharacteristic, complemented
201C8×C22⋊C4C2211yescharacteristic
202#1736C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209#557—42no—
210#557—42no—
211#552—42no—
212#552—42no—
213#538—48no—
214C2×C4⋊Q8—21no—
215C2×C4⋊Q8C2311yescharacteristic
216C2×#127C2311yescharacteristic
217C2×#127C2311yescharacteristic
218C2×#126—21no—
219C2×#126—21no—
220C2×#126—21no—
221C2×#125—21no—
222C2×#125—21no—
223C2×#125—21no—
224C2×#125C2311yescharacteristic
225C2×#125C2311yescharacteristic
226C2×#125C2311yescharacteristic
227C2×#124—21no—
228C2×#124D411yescharacteristic
229C2×#123—21no—
230C2×#123—21no—
231C2×#123—21no—
232C2×#123—21no—
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×#121—21no—
238C2×#121—21no—
239C2×#121—21no—
240C2×#121C2311yescharacteristic
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#121C2311yescharacteristic
244C2×#120—21no—
245C2×#120—21no—
246C2×#120—21no—
247C2×C4×Q8—21no—
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×D4—21no—
253C2×C4×D4—21no—
254C2×C4×D4—21no—
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×#117—21no—
260C2×#117C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C4⋊C4C2311yescharacteristic
263C22×C22⋊C4—21no—
264#486—42no—
265#482—42no—
266#478—42no—
267#468—42no—
268#460—42no—
269#450—42no—
270#440—42no—
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#102—42no—
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×#97C2311yescharacteristic
318C2×C4×C8C2311yescharacteristic
319C2×C4×C8C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321#400—21no—
322#400—21no—
323#400—21no—
324#400—21no—
325#400—21no—
326#399—21no—
327#399—21no—
328#399—21no—
329#399—21no—
330#399—21no—
331#398—21no—
332#398—21no—
333#398—21no—
334#398—21no—
335#398—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#396—21no—
341#396—21no—
342#396—21no—
343#396—21no—
344#396—21no—
345#395—21no—
346#395—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#393—21no—
356#392—21no—
357#392—21no—
358#392—21no—
359#392—21no—
360#392—21no—
361#391—21no—
362#391D411yescharacteristic
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#390—21no—
366#390—21no—
367#390—21no—
368#390D411yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#389—21no—
378#389—21no—
379#389—21no—
380#389—21no—
381#389—21no—
382#389—21no—
383#389—21no—
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388D411yescharacteristic
405#388D411yescharacteristic
406#388D411yescharacteristic
407#388D411yescharacteristic
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#384C2311yescharacteristic
428#384C2311yescharacteristic
429#384C2311yescharacteristic
430#384C2311yescharacteristic
431#382D411yescharacteristic
432#382C2311yescharacteristic
433#382C2311yescharacteristic
434#380—21no—
435#380—21no—
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#379—21no—
443#379—21no—
444C4×C4⋊C4—21no—
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C22⋊C4C2311yescharacteristic
448C4×C22⋊C4C2311yescharacteristic
449C4×C22⋊C4C2311yescharacteristic
450C4×C22⋊C4C2311yescharacteristic
451#376—21no—
452C43C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491C25—21no—
492C22×Q8—21no—
493C22×Q8C2×D411yescharacteristic
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—41no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4C2×D411yescharacteristic
511C22×D4C2411yescharacteristic
512C22×D4C2411yescharacteristic
513C22×D4C2411yescharacteristic
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4C2411yescharacteristic
520C23×C4C2411yescharacteristic
521C2×SD16—22no—
522C2×SD16—22no—
523C2×SD16—22no—
524C2×SD16—22no—
525C2×SD16—41no—
526C2×SD16—41no—
527C2×SD16—41no—
528C2×SD16—41no—
529C2×SD16—41no—
530C2×M16—41no—
531C2×M16—41no—
532C2×M16—41no—
533C22×C8—41no—
534C22×C8—41no—
535C22×C8—41no—
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C4⋊Q8—22no—
545C4⋊Q8—41no—
546C4⋊Q8—44no—
547#127—22no—
548#127—41no—
549#127—41no—
550#127—41no—
551#126—44no—
552#126—44no—
553#126—44no—
554#125—22no—
555#125—41no—
556#125—41no—
557#125—41no—
558#125—41no—
559#125—41no—
560#125—44no—
561#125—44no—
562#125—44no—
563#124—24no—
564#124—44no—
565#123—44no—
566#123—44no—
567#123—44no—
568#123—82no—
569C22⋊Q8—22no—
570C22⋊Q8—22no—
571C22⋊Q8—41no—
572C22⋊Q8—41no—
573C22⋊Q8—44no—
574C22⋊Q8—44no—
575#121—22no—
576#121—44no—
577#121—44no—
578#121—41no—
579#121—44no—
580#121—41no—
581#121—41no—
582#121—41no—
583#121—41no—
584#121—41no—
585#121—41no—
586#120—44no—
587#120—44no—
588#120—82no—
589C4×Q8—22no—
590C4×Q8—22no—
591C4×Q8—22no—
592C4×Q8—22no—
593C4×Q8—41no—
594C4×Q8—41no—
595C4×Q8—41no—
596C4×Q8—41no—
597C4×Q8—44no—
598C4×D4—41no—
599C4×D4—41no—
600C4×D4—44no—
601C4×D4—41no—
602C4×D4—41no—
603C4×D4—41no—
604C4×D4—41no—
605C4×D4—41no—
606C4×D4—41no—
607C4×D4—44no—
608C4×D4—82no—
609#117—22no—
610#117—44no—
611#117—41no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—22no—
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⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—41no—
646C2×C4⋊C4—41no—
647C2×C4⋊C4—41no—
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—44no—
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42C2×D411yescharacteristic
714C2×C42C2×D411yescharacteristic
715C2×C42C2×D411yescharacteristic
716C2×C42C2×D411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722#107—22no—
723#107—41no—
724#107—41no—
725#107—41no—
726#106—41no—
727#106—41no—
728#106—41no—
729#106—41no—
730#106—41no—
731C4⋊C8—41no—
732C4⋊C8—41no—
733C4⋊C8—41no—
734C4⋊C8—41no—
735#103—22no—
736#103—41no—
737#103—41no—
738#103—41no—
739#103—41no—
740#102—22no—
741#102—22no—
742#102—22no—
743#102—22no—
744#102—41no—
745#102—41no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761C22⋊C8—41no—
762C22⋊C8—41no—
763C22⋊C8—41no—
764C22⋊C8—41no—
765C22⋊C8—41no—
766C22⋊C8—41no—
767#97—41no—
768C4×C8—41no—
769C4×C8—41no—
770C4×C8—41no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805C24—21no—
806C24—21no—
807C24—21no—
808C24—42no—
809C24—42no—
810C24—81no—
811C24—81no—
812C24—81no—
813C24—81no—
814C24—81no—
815C24C22×D411yescharacteristic
816C24C22×D411yescharacteristic
817C2×Q8—22no—
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—41no—
824C2×Q8—41no—
825C2×Q8—42no—
826C2×Q8—42no—
827C2×Q8—81no—
828C2×Q8H(5,𝔽2)12yes—
829C2×D4—22no—
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—41no—
848C2×D4—41no—
849C2×D4—42no—
850C2×D4—42no—
851C2×D4—42no—
852C2×D4—44no—
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—81no—
862C2×D4—81no—
863C2×D4—81no—
864C2×D4—81no—
865C2×D4—81no—
866C2×D4—81no—
867C2×D4—81no—
868C2×D4—81no—
869C2×D4—81no—
870C2×D4—82no—
871C2×D4—82no—
872C2×D4—82no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4—81no—
876C2×D4—81no—
877C2×D4—81no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D42−1+412yes—
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—42no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4—81no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4—81no—
920C22×C4—81no—
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C2511yescharacteristic
934SD16—44no—
935SD16—82no—
936SD16—82no—
937M16—82no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
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—82no—
963C4⋊C4—24no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
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—41no—
988C4⋊C4—41no—
989C4⋊C4—41no—
990C4⋊C4—41no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
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—42no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4H(5,𝔽2)12yes—
1023C22⋊C4—22no—
1024C22⋊C4—22no—
1025C22⋊C4—22no—
1026C22⋊C4—22no—
1027C22⋊C4—22no—
1028C22⋊C4—41no—
1029C22⋊C4—41no—
1030C22⋊C4—41no—
1031C22⋊C4—41no—
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—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
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⋊C4AGL(1,ℤ/8)14yes—
1065C42—24no—
1066C42—22no—
1067C42—22no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—41no—
1079C42—41no—
1080C42—42no—
1081C42—42no—
1082C42—42no—
1083C42—42no—
1084C42—81no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—22no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—84no—
1120C23—84no—
1121C23—162no—
1122C23—162no—
1123C23—162no—
1124C23—162no—
1125C23—162no—
1126C23C2×AGL(1,ℤ/8)12yes—
1127C23C23×D411yescharacteristic
1128Q8—22no—
1129Q8—22no—
1130Q8—41no—
1131Q8—41no—
1132Q8—82no—
1133Q8—84no—
1134D4—22no—
1135D4—22no—
1136D4—41no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—41no—
1143D4—41no—
1144D4—41no—
1145D4—41no—
1146D4—84no—
1147D4—84no—
1148D4—82no—
1149D4—84no—
1150D4—84no—
1151D4—162no—
1152D4—162no—
1153D4—162no—
1154D4—162no—
1155D4—162no—
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—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—22no—
1171C2×C4—21no—
1172C2×C4—22no—
1173C2×C4—21no—
1174C2×C4—21no—
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—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—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—84no—
1237C2×C4—162no—
1238C2×C4—162no—
1239C2×C4—162no—
1240C2×C4—162no—
1241C2×C4C2×AGL(1,ℤ/8)12yes—
1242C2×C4C2×AGL(1,ℤ/8)12yes—
1243C2×C4#57712yes—
1244C2×C4C2×H(5,𝔽2)11yescharacteristic
1245C2×C4C2×H(5,𝔽2)11yescharacteristic
1246C2×C4C2×2−1+411yescharacteristic
1247C2×C4#58511yescharacteristic
1248C2×C4#58511yescharacteristic
1249C2×C4#58511yescharacteristic
1250C8—41no—
1251C8—41no—
1252C8—41no—
1253C8—41no—
1254C8—41no—
1255C8—41no—
1256C8—41no—
1257C8—41no—
1258C22—22no—
1259C22—22no—
1260C22—22no—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—41no—
1265C22—42no—
1266C22—41no—
1267C22—41no—
1268C22—41no—
1269C22—41no—
1270C22—42no—
1271C22—41no—
1272C22—41no—
1273C22—42no—
1274C22—41no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—168no—
1294C22#348411yescharacteristic
1295C22#348911yescharacteristic
1296C22#350011yescharacteristic
1297C22C22×AGL(1,ℤ/8)11yescharacteristic
1298C22C2×#57711yescharacteristic
1299C22#358411yescharacteristic
1300C22#358411yescharacteristic
1301C4—22no—
1302C4—22no—
1303C4—22no—
1304C4—41no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—42no—
1309C4—41no—
1310C4—41no—
1311C4—42no—
1312C4—41no—
1313C4—41no—
1314C4—41no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4#353511yescharacteristic
1327C4#354111yescharacteristic
1328C4#354511yescharacteristic
1329C4#355111yescharacteristic
1330C2—42no—
1331C2—81no—
1332C2—82no—
1333C2—161no—
1334C2—161no—
1335C2#4776011yescharacteristic
1336C2#6159811yescharacteristic
1337C2#6165911yescharacteristic
1338C2#6213711yescharacteristic
1339C2#6221211yescharacteristic
1340C2#6253911yescharacteristic
1341C2#6255411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#39396C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#124 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39955C2semidirect
3. #32836C2semidirect
4. #32640C2semidirect
5. #32572C2semidirect
6. #31932C2semidirect
7. #31686C2semidirect
8. #31559C2semidirect
9. #31370C2semidirect
10. #31332C2semidirect
11. #31276C2semidirect
12. #31121C2semidirect
13. #30988C2semidirect
14. #30630C2semidirect
15. #30608C2semidirect
16. #29435C2semidirect
17. #29366C2semidirect
18. #29143C2semidirect
19. #28847C2semidirect
20. #27709C2semidirect
21. #27254C2semidirect
22. #26987C2semidirect
23. #26659C2semidirect
24. #26424C2semidirect
25. #25960C2semidirect
26. #25935C2semidirect
27. #25560C2semidirect
28. #24917C2semidirect
29. #24346C2semidirect
30. #23966C2semidirect
31. #22389C2semidirect
32. C2×#557C22semidirect
36. C2×#482C22semidirect
38. C2×#468C22semidirect
44. #2859C22semidirect
57. #2584C22semidirect
65. #2441C22semidirect
67. #2439C22semidirect
72. #2423C22semidirect
75. #2421C22semidirect
84. #2295C22semidirect
85. #2101C22semidirect
86. #2101C22semidirect
87. #2100C22semidirect
88. #2099C22semidirect
89. #2096C22semidirect
92. #2088C22semidirect
93. #2086C22semidirect
94. #2084C22semidirect
95. #2084C22semidirect
96. #2083C22semidirect
102. #2068C22semidirect
104. #2067C22semidirect
107. #2059C22semidirect
108. #2059C22semidirect
109. #2057C22semidirect
117. #2034C22semidirect
119. #2033C22semidirect
125. #2025C22semidirect
126. #2025C22semidirect
127. #2025C22semidirect
133. #1992C22semidirect
134. #1988C22semidirect
135. #1985C22semidirect
136. #1984C22semidirect
140. #1942C22semidirect
141. #1941C22semidirect
143. #1936C22semidirect
146. #1933C22semidirect
148. #1926C22semidirect
152. #1923C22semidirect
153. #1923C22semidirect
154. #1920C22semidirect
155. #1920C22semidirect
156. #1918C22semidirect
165. #1880C22semidirect
166. #1880C22semidirect
168. #1877C22semidirect
172. #1872C22semidirect
175. #1865C22semidirect
178. #1864C22semidirect
179. #1863C22semidirect
181. #1853C22semidirect
183. #1851C22semidirect
185. #1839C22semidirect
186. #1834C22semidirect
187. #1834C22semidirect
188. #1824C22semidirect
193. #1804C22semidirect
194. #1804C22semidirect
195. #1803C22semidirect
198. C4×C4⋊C8C22semidirect
199. C4×#103C22semidirect
200. #1753C22semidirect
202. #1736C22semidirect

Maximal subgroups

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

subgroupindex
#399552
#393962
#328362
#326402
#325722
#319322
#316862
#315592
#313702
#313322
#312762
#311212
#309882
#306302
#306082
#294352
#293662
#291432
#288472
#277092
#272542
#269872
#266592
#264242
#259602
#259352
#255602
#249172
#243462
#239662
#223892