Finite Group Databasebeta

← #6696780

Subgroups — #6696780

Order 512.

1697 conjugacy classes of subgroups.

The subgroup lattice has 1346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40102C211yesmaximal, characteristic, complemented
2#36155C211yesmaximal, characteristic, complemented
3#32953C211yesmaximal, characteristic, complemented
4#32286C211yesmaximal, characteristic, complemented
5#32275C211yesmaximal, characteristic, complemented
6#32064C211yesmaximal, characteristic, complemented
7#31910C211yesmaximal, characteristic, complemented
8#31770C211yesmaximal, characteristic, complemented
9#31374C211yesmaximal, characteristic, complemented
10#30809C211yesmaximal, characteristic, complemented
11#30677C211yesmaximal, characteristic, complemented
12#30367C211yesmaximal, characteristic, complemented
13#30009C211yesmaximal, characteristic, complemented
14#27563C211yesmaximal, characteristic, complemented
15#27534C211yesmaximal, characteristic, complemented
16#27246C211yesmaximal, characteristic, complemented
17#27222C211yesmaximal, characteristic, complemented
18#27178C211yesmaximal, characteristic, complemented
19#26835C211yesmaximal, characteristic, complemented
20#26708C211yesmaximal, characteristic, complemented
21#26394C211yesmaximal, characteristic, complemented
22#26049C211yesmaximal, characteristic, complemented
23#25970C211yesmaximal, characteristic, complemented
24#25890C211yesmaximal, characteristic, complemented
25#25048C211yesmaximal, characteristic, complemented
26#24915C211yesmaximal, characteristic, complemented
27#24444C211yesmaximal, characteristic
28#22979C211yesmaximal, characteristic, complemented
29#22578C211yesmaximal, characteristic, complemented
30#22359C211yesmaximal, characteristic, complemented
31#21452C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C22×C4×D4C2211yescharacteristic
34C2×#488C2211yescharacteristic
35C2×#478C2211yescharacteristic
36C2×#474C2211yescharacteristic
37C2×#474C2211yescharacteristic
38C2×#474C2211yescharacteristic
39C2×#469C2211yescharacteristic
40C2×#449C2211yescharacteristic
41C2×#447C2211yescharacteristic
42C2×#442C2211yescharacteristic
43C2×#442C2211yescharacteristic
44C2×#417C2211yescharacteristic
45#2857C2211yescharacteristic
46#2855C2211yescharacteristic
47#2849—21no—
48#2777—21no—
49#2702—21no—
50#2700—21no—
51#2672—21no—
52#2665—21no—
53#2562C2211yescharacteristic
54#2550C2211yescharacteristic, complemented
55#2512C2211yescharacteristic, complemented
56#2503C2211yescharacteristic
57#2495C2211yescharacteristic
58#2491C2211yescharacteristic
59#2491C2211yescharacteristic, complemented
60#2486C2211yescharacteristic
61#2483—21no—
62#2468—21no—
63#2454C2211yescharacteristic, complemented
64#2447C2211yescharacteristic
65#2447C2211yescharacteristic
66#2444—21no—
67#2444—21no—
68#2440C2211yescharacteristic, complemented
69#2427—21no—
70#2420C2211yescharacteristic
71#2420C2211yescharacteristic
72#2420C2211yescharacteristic, complemented
73#2419—21no—
74#2419—21no—
75#2416C2211yescharacteristic
76#2412—21no—
77#2369C2211yescharacteristic, complemented
78#2349C2211yescharacteristic
79#2349C2211yescharacteristic
80#2345C2211yescharacteristic, complemented
81#2339C2211yescharacteristic
82#2339C2211yescharacteristic
83D4×C22⋊C4C2211yescharacteristic
84#2337—21no—
85C4×#123C2211yescharacteristic
86C4×#121C2211yescharacteristic
87C2×#381—21no—
88#2101C2211yescharacteristic, complemented
89#2100C2211yescharacteristic, complemented
90#2097C2211yescharacteristic, complemented
91#2095C2211yescharacteristic, complemented
92#2092C2211yescharacteristic, complemented
93#2087C2211yescharacteristic, complemented
94#2086C2211yescharacteristic, complemented
95#2085C2211yescharacteristic, complemented
96#2077C2211yescharacteristic
97#2077C2211yescharacteristic, complemented
98#2076C2211yescharacteristic, complemented
99#2075C2211yescharacteristic
100#2075C2211yescharacteristic
101#2073C2211yescharacteristic
102#2073C2211yescharacteristic, complemented
103#2068C2211yescharacteristic, complemented
104#2067C2211yescharacteristic
105#2067C2211yescharacteristic, complemented
106#2066C2211yescharacteristic, complemented
107#2065C2211yescharacteristic, complemented
108#2059C2211yescharacteristic, complemented
109#2059C2211yescharacteristic, complemented
110#2058C2211yescharacteristic, complemented
111#2055C2211yescharacteristic, complemented
112#2055C2211yescharacteristic, complemented
113#2054C2211yescharacteristic
114#2042C2211yescharacteristic
115#2036C2211yescharacteristic
116#2035C2211yescharacteristic
117#2035C2211yescharacteristic
118#2034C2211yescharacteristic
119#2033C2211yescharacteristic
120#2033C2211yescharacteristic
121#2033C2211yescharacteristic, complemented
122#2033C2211yescharacteristic, complemented
123#2024C2211yescharacteristic, complemented
124#2024C2211yescharacteristic, complemented
125#2023C2211yescharacteristic
126#2012C2211yescharacteristic
127#2000C2211yescharacteristic
128#1993C2211yescharacteristic, complemented
129#1983C2211yescharacteristic
130#1973C2211yescharacteristic, complemented
131#1970C2211yescharacteristic
132#1954C2211yescharacteristic
133#1949C2211yescharacteristic, complemented
134#1949C2211yescharacteristic, complemented
135#1943C2211yescharacteristic, complemented
136#1943C2211yescharacteristic, complemented
137#1942C2211yescharacteristic, complemented
138#1939C2211yescharacteristic, complemented
139#1936C2211yescharacteristic
140#1935C2211yescharacteristic, complemented
141#1935C2211yescharacteristic, complemented
142#1934C2211yescharacteristic, complemented
143#1933C2211yescharacteristic, complemented
144#1928C2211yescharacteristic, complemented
145#1928C2211yescharacteristic, complemented
146#1927C2211yescharacteristic, complemented
147#1926C2211yescharacteristic
148#1925C2211yescharacteristic
149#1924C2211yescharacteristic
150#1924C2211yescharacteristic, complemented
151#1924C2211yescharacteristic, complemented
152#1923C2211yescharacteristic
153#1921C2211yescharacteristic, complemented
154#1920C2211yescharacteristic, complemented
155#1918C2211yescharacteristic, complemented
156#1917C2211yescharacteristic, complemented
157#1916C2211yescharacteristic, complemented
158#1879C2211yescharacteristic
159#1879C2211yescharacteristic
160#1879C2211yescharacteristic
161#1879C2211yescharacteristic
162#1879C2211yescharacteristic
163#1877C2211yescharacteristic, complemented
164#1874C2211yescharacteristic
165#1874C2211yescharacteristic
166#1870C2211yescharacteristic
167#1864C2211yescharacteristic
168#1864C2211yescharacteristic
169#1864C2211yescharacteristic
170#1864C2211yescharacteristic
171#1862C2211yescharacteristic
172#1862C2211yescharacteristic
173#1862C2211yescharacteristic
174#1862C2211yescharacteristic
175#1862C2211yescharacteristic
176#1862C2211yescharacteristic, complemented
177#1853C2211yescharacteristic
178#1852C2211yescharacteristic
179#1852C2211yescharacteristic
180#1852C2211yescharacteristic, complemented
181#1851C2211yescharacteristic, complemented
182#1846C2211yescharacteristic, complemented
183#1823C2211yescharacteristic, complemented
184#1809C2211yescharacteristic, complemented
185#1809C2211yescharacteristic, complemented
186#1804C2211yescharacteristic
187#1802C2211yescharacteristic
188#1802C2211yescharacteristic
189#1797C2211yescharacteristic
190#1788C2211yescharacteristic
191#1788C2211yescharacteristic
192#1786C2211yescharacteristic
193#1786C2211yescharacteristic
194#1786C2211yescharacteristic
195#1771C2211yescharacteristic, complemented
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic
198#1762C2211yescharacteristic
199C4×#102C2211yescharacteristic
200C4×#102C2211yescharacteristic
201#1753C2211yescharacteristic, complemented
202#1749C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C24×C4—21no—
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×M16C2311yescharacteristic
210#546—42no—
211#546—42no—
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×#126—21no—
215C2×#125C2311yescharacteristic
216C2×#124—21no—
217C2×#124—21no—
218C2×#124C2311yescharacteristic
219C2×#123—21no—
220C2×#123—21no—
221C2×#123D411yescharacteristic
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8C2311yescharacteristic
225C2×#121—21no—
226C2×#121—21no—
227C2×#121C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#120—21no—
231C2×C4×D4—21no—
232C2×C4×D4—21no—
233C2×C4×D4—21no—
234C2×C4×D4—42no—
235C2×C4×D4—42no—
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C22⋊C4—21no—
248C22×C22⋊C4—21no—
249C22×C22⋊C4—21no—
250C22×C42C2311yescharacteristic
251#488—42no—
252#478—42no—
253#474—24no—
254#474—42no—
255#474—42no—
256#469—42no—
257#449—42no—
258#447—24no—
259#442—42no—
260#442—42no—
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279#417—24no—
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×#97C2311yescharacteristic
314C2×#97C2311yescharacteristic
315C2×#97C2311yescharacteristic
316C2×C4×C8C2311yescharacteristic
317C2×C4×C8C2311yescharacteristic
318#400—21no—
319#400—21no—
320#400—21no—
321#400—21no—
322#399—21no—
323#398—21no—
324#398—21no—
325#398—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#397—21no—
336#396—21no—
337#396—21no—
338#396—21no—
339#395—21no—
340#395—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#393—21no—
349#393—21no—
350#391—21no—
351#391—21no—
352#391—21no—
353#391—21no—
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#389—21no—
365#389—21no—
366#389—21no—
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388D411yescharacteristic
385#388D411yescharacteristic
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387D411yescharacteristic
391#387D411yescharacteristic
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#386—21no—
403#386D411yescharacteristic
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385D411yescharacteristic
414#384C2311yescharacteristic
415#383—21no—
416#382C2311yescharacteristic
417#382C2311yescharacteristic
418#382C2311yescharacteristic
419#381—21no—
420#381—21no—
421#381—21no—
422#381—21no—
423#381—21no—
424#381—21no—
425#381—21no—
426#381—21no—
427#381—21no—
428#381—21no—
429#381—21no—
430#381D411yescharacteristic
431#380—21no—
432#380—21no—
433#380—21no—
434#380—21no—
435#380—21no—
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#379—21no—
445C4×C4⋊C4—21no—
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4C2311yescharacteristic
455C4×C22⋊C4C2311yescharacteristic
456C4×C22⋊C4C2311yescharacteristic
457C2×#95—21no—
458C2×#95—21no—
459C2×#95—21no—
460C2×#95—21no—
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C22×Q8—21no—
501C22×Q8—21no—
502C22×Q8C2411yescharacteristic
503C22×D4—22no—
504C22×D4—22no—
505C22×D4—22no—
506C22×D4—22no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4C2×D411yescharacteristic
515C22×D4C2411yescharacteristic
516C22×D4C2411yescharacteristic
517C22×D4C2411yescharacteristic
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—44no—
530C23×C4—44no—
531C23×C4—82no—
532C23×C4C2×D411yescharacteristic
533C23×C4C2×D411yescharacteristic
534C23×C4C2411yescharacteristic
535C23×C4C2411yescharacteristic
536C2×SD16—41no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×D8—22no—
540C2×D8—22no—
541C2×D8—22no—
542C2×D8—22no—
543C2×D8—22no—
544C2×D8—41no—
545C2×M16—22no—
546C2×M16—41no—
547C2×M16—41no—
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C4⋊Q8—22no—
557C4⋊Q8—41no—
558C4⋊Q8—41no—
559C4⋊Q8—41no—
560#126—82no—
561#125—41no—
562#125—41no—
563#124—22no—
564#124—41no—
565#124—44no—
566#124—82no—
567#123—42no—
568#123—44no—
569#123—82no—
570C22⋊Q8—41no—
571C22⋊Q8—41no—
572C22⋊Q8—82no—
573C22⋊Q8—82no—
574#121—22no—
575#121—22no—
576#121—41no—
577#121—41no—
578#121—44no—
579#121—41no—
580#121—41no—
581#121—82no—
582#120—44no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—22no—
589C4×D4—22no—
590C4×D4—41no—
591C4×D4—41no—
592C4×D4—41no—
593C4×D4—41no—
594C4×D4—41no—
595C4×D4—41no—
596C4×D4—41no—
597C4×D4—41no—
598C4×D4—41no—
599C4×D4—41no—
600C4×D4—41no—
601C4×D4—44no—
602C4×D4—44no—
603C4×D4—82no—
604C2×C4⋊C4—22no—
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—41no—
625C2×C4⋊C4—41no—
626C2×C4⋊C4—41no—
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—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—44no—
679C2×C22⋊C4—44no—
680C2×C22⋊C4—82no—
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—41no—
694C2×C42—41no—
695C2×C42C2×D411yescharacteristic
696C2×C42C2×D411yescharacteristic
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702#107—22no—
703#107—22no—
704#107—41no—
705#107—41no—
706#107—41no—
707#107—41no—
708#107—41no—
709#107—41no—
710#106—41no—
711#106—41no—
712#106—41no—
713#106—41no—
714#106—41no—
715C4⋊C8—22no—
716C4⋊C8—41no—
717C4⋊C8—41no—
718C4⋊C8—41no—
719C4⋊C8—41no—
720#103—22no—
721#103—22no—
722#103—41no—
723#103—41no—
724#103—41no—
725#103—41no—
726#103—41no—
727#102—22no—
728#102—22no—
729#102—22no—
730#102—22no—
731#102—22no—
732#102—22no—
733#102—22no—
734#102—22no—
735#102—22no—
736#102—22no—
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#4114yes—
746C22⋊C8—22no—
747C22⋊C8—41no—
748C22⋊C8—41no—
749C22⋊C8—41no—
750C22⋊C8—41no—
751C22⋊C8—41no—
752C22⋊C8—41no—
753#97—41no—
754#97—41no—
755#97—41no—
756C4×C8—41no—
757C4×C8—41no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#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#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804C24—21no—
805C24—24no—
806C24—21no—
807C24—21no—
808C24—42no—
809C24—42no—
810C24—42no—
811C24—42no—
812C24—81no—
813C24—81no—
814C24C22×D411yescharacteristic
815C24C22×D411yescharacteristic
816#41—44no—
817#41—82no—
818#41—82no—
819#41—82no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—42no—
827C2×Q8—42no—
828C2×Q8—81no—
829C2×Q8—81no—
830C2×Q8—81no—
831C2×Q8—81no—
832C2×D4—24no—
833C2×D4—22no—
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—42no—
849C2×D4—42no—
850C2×D4—41no—
851C2×D4—41no—
852C2×D4—42no—
853C2×D4—44no—
854C2×D4—44no—
855C2×D4—44no—
856C2×D4—44no—
857C2×D4—42no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—81no—
864C2×D4—81no—
865C2×D4—81no—
866C2×D4—81no—
867C2×D4—81no—
868C2×D4C2×#4112yes—
869C2×D4H(5,𝔽2)12yes—
870C2×D4H(5,𝔽2)12yes—
871C2×D42−1+412yes—
872C22×C4—22no—
873C22×C4—21no—
874C22×C4—22no—
875C22×C4—21no—
876C22×C4—21no—
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—41no—
900C22×C4—41no—
901C22×C4—41no—
902C22×C4—41no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—42no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—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×C4—81no—
932C22×C4—81no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4—816no—
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C2511yescharacteristic
950SD16—82no—
951D8—44no—
952D8—44no—
953M16—82no—
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×C8—21no—
976C2×C8—21no—
977C2×C8C2×#4112yes—
978C4⋊C4—22no—
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—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—41no—
1003C4⋊C4—41no—
1004C4⋊C4—41no—
1005C4⋊C4—41no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
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⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4C2×#4112yes—
1026C22⋊C4—22no—
1027C22⋊C4—22no—
1028C22⋊C4—41no—
1029C22⋊C4—41no—
1030C22⋊C4—41no—
1031C22⋊C4—41no—
1032C22⋊C4—41no—
1033C22⋊C4—41no—
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—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
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—
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—81no—
1082C42—81no—
1083C42—81no—
1084C23—21no—
1085C23—21no—
1086C23—22no—
1087C23—21no—
1088C23—21no—
1089C23—22no—
1090C23—22no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—22no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—48no—
1102C23—48no—
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—41no—
1120C23—84no—
1121C23—84no—
1122C23—84no—
1123C23—84no—
1124C23—84no—
1125C23#57612yes—
1126C23C23×D411yescharacteristic
1127Q8—41no—
1128Q8—41no—
1129Q8—41no—
1130Q8—41no—
1131Q8—162no—
1132Q8—162no—
1133D4—22no—
1134D4—22no—
1135D4—22no—
1136D4—22no—
1137D4—22no—
1138D4—48no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—41no—
1143D4—41no—
1144D4—41no—
1145D4—82no—
1146D4—84no—
1147D4—84no—
1148D4—162no—
1149D4—162no—
1150D4#54214yes—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—22no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
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—44no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—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—84no—
1235C2×C4—84no—
1236C2×C4—82no—
1237C2×C4—84no—
1238C2×C4—84no—
1239C2×C4—84no—
1240C2×C4—84no—
1241C2×C4—162no—
1242C2×C4—162no—
1243C2×C4—162no—
1244C2×C4—162no—
1245C2×C4—162no—
1246C2×C4#57512yes—
1247C2×C4C22×#4111yescharacteristic
1248C2×C4C2×H(5,𝔽2)11yescharacteristic
1249C2×C4C2×H(5,𝔽2)11yescharacteristic
1250C2×C4C2×2−1+411yescharacteristic
1251C2×C4#58511yescharacteristic
1252C2×C4#58511yescharacteristic
1253C8—22no—
1254C8—41no—
1255C8—41no—
1256C8—41no—
1257C8—41no—
1258C8—41no—
1259C8—41no—
1260C8—41no—
1261C22—22no—
1262C22—24no—
1263C22—22no—
1264C22—22no—
1265C22—41no—
1266C22—42no—
1267C22—42no—
1268C22—41no—
1269C22—42no—
1270C22—41no—
1271C22—42no—
1272C22—42no—
1273C22—41no—
1274C22—42no—
1275C22—41no—
1276C22—41no—
1277C22—41no—
1278C22—42no—
1279C22—42no—
1280C22—41no—
1281C22—41no—
1282C22—41no—
1283C22—41no—
1284C22—42no—
1285C22—816no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22D4×#4111yescharacteristic
1298C22#348411yescharacteristic
1299C22#348911yescharacteristic
1300C22C2×#57511yescharacteristic
1301C22C2×#57611yescharacteristic
1302C22#358511yescharacteristic
1303C22#358611yescharacteristic
1304C4—22no—
1305C4—41no—
1306C4—41no—
1307C4—42no—
1308C4—41no—
1309C4—41no—
1310C4—41no—
1311C4—41no—
1312C4—41no—
1313C4—41no—
1314C4—41no—
1315C4—41no—
1316C4—41no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4C2×#54211yescharacteristic
1330C4#351311yescharacteristic
1331C4#353311yescharacteristic
1332C4#353511yescharacteristic
1333C2—42no—
1334C2—44no—
1335C2—81no—
1336C2—82no—
1337C2—161no—
1338C2#3771511yescharacteristic
1339C2#6146311yescharacteristic
1340C2#6151911yescharacteristic
1341C2#6159211yescharacteristic
1342C2#6164711yescharacteristic
1343C2#6211511yescharacteristic
1344C2#6215511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#24444C2
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. #40102C2semidirect
2. #36155C2semidirect
3. #32953C2semidirect
4. #32286C2semidirect
5. #32275C2semidirect
6. #32064C2semidirect
7. #31910C2semidirect
8. #31770C2semidirect
9. #31374C2semidirect
10. #30809C2semidirect
11. #30677C2semidirect
12. #30367C2semidirect
13. #30009C2semidirect
14. #27563C2semidirect
15. #27534C2semidirect
16. #27246C2semidirect
17. #27222C2semidirect
18. #27178C2semidirect
19. #26835C2semidirect
20. #26708C2semidirect
21. #26394C2semidirect
22. #26049C2semidirect
23. #25970C2semidirect
24. #25890C2semidirect
25. #25048C2semidirect
26. #24915C2semidirect
28. #22979C2semidirect
29. #22578C2semidirect
30. #22359C2semidirect
31. #21452C2semidirect
54. #2550C22semidirect
55. #2512C22semidirect
59. #2491C22semidirect
63. #2454C22semidirect
68. #2440C22semidirect
72. #2420C22semidirect
77. #2369C22semidirect
80. #2345C22semidirect
88. #2101C22semidirect
89. #2100C22semidirect
90. #2097C22semidirect
91. #2095C22semidirect
92. #2092C22semidirect
93. #2087C22semidirect
94. #2086C22semidirect
95. #2085C22semidirect
97. #2077C22semidirect
98. #2076C22semidirect
102. #2073C22semidirect
103. #2068C22semidirect
105. #2067C22semidirect
106. #2066C22semidirect
107. #2065C22semidirect
108. #2059C22semidirect
109. #2059C22semidirect
110. #2058C22semidirect
111. #2055C22semidirect
112. #2055C22semidirect
121. #2033C22semidirect
122. #2033C22semidirect
123. #2024C22semidirect
124. #2024C22semidirect
128. #1993C22semidirect
130. #1973C22semidirect
133. #1949C22semidirect
134. #1949C22semidirect
135. #1943C22semidirect
136. #1943C22semidirect
137. #1942C22semidirect
138. #1939C22semidirect
140. #1935C22semidirect
141. #1935C22semidirect
142. #1934C22semidirect
143. #1933C22semidirect
144. #1928C22semidirect
145. #1928C22semidirect
146. #1927C22semidirect
150. #1924C22semidirect
151. #1924C22semidirect
153. #1921C22semidirect
154. #1920C22semidirect
155. #1918C22semidirect
156. #1917C22semidirect
157. #1916C22semidirect
163. #1877C22semidirect
176. #1862C22semidirect
180. #1852C22semidirect
181. #1851C22semidirect
182. #1846C22semidirect
183. #1823C22semidirect
184. #1809C22semidirect
185. #1809C22semidirect
195. #1771C22semidirect
201. #1753C22semidirect

Maximal subgroups

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

subgroupindex
#401022
#361552
#329532
#322862
#322752
#320642
#319102
#317702
#313742
#308092
#306772
#303672
#300092
#275632
#275342
#272462
#272222
#271782
#268352
#267082
#263942
#260492
#259702
#258902
#250482
#249152
#244442
#229792
#225782
#223592
#214522