Finite Group Databasebeta

← #7525821

Subgroups — #7525821

Order 512.

1771 conjugacy classes of subgroups.

The subgroup lattice has 1371 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59272C211yesmaximal, characteristic, complemented
2#36217C211yesmaximal, characteristic, complemented
3#31948C211yesmaximal, characteristic, complemented
4#31900C211yesmaximal, characteristic, complemented
5#31660C211yesmaximal, characteristic, complemented
6#31552C211yesmaximal, characteristic, complemented
7#28982C211yesmaximal, characteristic, complemented
8#28896C211yesmaximal, characteristic, complemented
9#28100C211yesmaximal, characteristic, complemented
10#27861C211yesmaximal, characteristic, complemented
11#27724C211yesmaximal, characteristic, complemented
12#27574C211yesmaximal, characteristic, complemented
13#27557C211yesmaximal, characteristic, complemented
14#27232C211yesmaximal, characteristic, complemented
15#27201C211yesmaximal, characteristic, complemented
16#26670C211yesmaximal, characteristic, complemented
17#25972C211yesmaximal, characteristic, complemented
18#24959C211yesmaximal, characteristic, complemented
19#24911C211yesmaximal, characteristic, complemented
20#24820C211yesmaximal, characteristic, complemented
21#24538C211yesmaximal, characteristic, complemented
22#24537C211yesmaximal, characteristic, complemented
23#24501C211yesmaximal, characteristic, complemented
24#23864C211yesmaximal, characteristic
25#22904C211yesmaximal, characteristic, complemented
26#22872C211yesmaximal, characteristic, complemented
27#22774C211yesmaximal, characteristic, complemented
28#22442C211yesmaximal, characteristic, complemented
29#22420C211yesmaximal, characteristic, complemented
30#20928C211yesmaximal, characteristic, complemented
31#20737C211yesmaximal, characteristic, complemented
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C2×#547C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35C2×#478C2211yescharacteristic, complemented
36C2×#449C2211yescharacteristic
37C2×#449C2211yescharacteristic
38C2×#450C2211yescharacteristic
39C2×#442C2211yescharacteristic
40C2×C4×D8C2211yescharacteristic
41C2×#435C2211yescharacteristic
42C2×#431C2211yescharacteristic
43C2×#417C2211yescharacteristic
44C2×#418C2211yescharacteristic
45C2×#416C2211yescharacteristic, complemented
46#2855C2211yescharacteristic
47#2853—21no—
48#2761—21no—
49#2753—21no—
50#2597—21no—
51#2566C2211yescharacteristic
52#2554—21no—
53#2513C2211yescharacteristic
54#2512C2211yescharacteristic
55#2500C2211yescharacteristic
56#2499C2211yescharacteristic
57#2498—21no—
58#2490C2211yescharacteristic
59#2485C2211yescharacteristic
60#2484—21no—
61#2480—21no—
62#2446C2211yescharacteristic, complemented
63#2446C2211yescharacteristic, complemented
64#2444—21no—
65#2443—21no—
66#2442C2211yescharacteristic
67#2423C2211yescharacteristic, complemented
68#2422C2211yescharacteristic
69#2421C2211yescharacteristic, complemented
70#2419—21no—
71#2419—21no—
72#2412—21no—
73#2411—21no—
74#2408C2211yescharacteristic
75#2363C2211yescharacteristic
76#2357C2211yescharacteristic
77#2352C2211yescharacteristic
78#2349C2211yescharacteristic, complemented
79D4×C4⋊C4C2211yescharacteristic, complemented
80#2342—21no—
81#2339C2211yescharacteristic
82#2339C2211yescharacteristic, complemented
83#2339C2211yescharacteristic, complemented
84D4×C22⋊C4C2211yescharacteristic
85C4×#123C2211yescharacteristic
86C2×#390C2211yescharacteristic
87C2×#387—21no—
88#2285C2211yescharacteristic
89#2101C2211yescharacteristic, complemented
90#2101C2211yescharacteristic, complemented
91#2100C2211yescharacteristic, complemented
92#2099C2211yescharacteristic, complemented
93#2097C2211yescharacteristic, complemented
94#2096C2211yescharacteristic, complemented
95#2085C2211yescharacteristic, complemented
96#2083C2211yescharacteristic, complemented
97#2077C2211yescharacteristic, complemented
98#2077C2211yescharacteristic, complemented
99#2074C2211yescharacteristic, complemented
100#2073C2211yescharacteristic
101#2072C2211yescharacteristic, complemented
102#2071C2211yescharacteristic
103#2067C2211yescharacteristic
104#2066C2211yescharacteristic, complemented
105#2066C2211yescharacteristic, complemented
106#2065C2211yescharacteristic
107#2065C2211yescharacteristic
108#2065C2211yescharacteristic
109#2055C2211yescharacteristic
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic
113#2034C2211yescharacteristic
114#2033C2211yescharacteristic
115#2026C2211yescharacteristic, complemented
116#2026C2211yescharacteristic, complemented
117#2013C2211yescharacteristic
118#2013C2211yescharacteristic
119#2000C2211yescharacteristic
120#2000C2211yescharacteristic
121#1991C2211yescharacteristic, complemented
122#1981C2211yescharacteristic, complemented
123#1973C2211yescharacteristic
124#1968C2211yescharacteristic
125#1968C2211yescharacteristic
126#1968C2211yescharacteristic
127#1960C2211yescharacteristic, complemented
128#1939C2211yescharacteristic, complemented
129#1936C2211yescharacteristic
130#1936C2211yescharacteristic
131#1935C2211yescharacteristic, complemented
132#1934C2211yescharacteristic
133#1934C2211yescharacteristic
134#1933C2211yescharacteristic, complemented
135#1928C2211yescharacteristic, complemented
136#1928C2211yescharacteristic, complemented
137#1924C2211yescharacteristic, complemented
138#1923C2211yescharacteristic, complemented
139#1920C2211yescharacteristic, complemented
140#1919C2211yescharacteristic, complemented
141#1919C2211yescharacteristic, complemented
142#1919C2211yescharacteristic, complemented
143#1917C2211yescharacteristic, complemented
144#1916C2211yescharacteristic, complemented
145#1894C2211yescharacteristic
146#1894C2211yescharacteristic
147#1893C2211yescharacteristic
148#1893C2211yescharacteristic
149#1892C2211yescharacteristic, complemented
150#1880C2211yescharacteristic
151#1880C2211yescharacteristic
152#1880C2211yescharacteristic
153#1880C2211yescharacteristic
154#1879C2211yescharacteristic
155#1879C2211yescharacteristic
156#1879C2211yescharacteristic
157#1879C2211yescharacteristic
158#1879C2211yescharacteristic
159#1879C2211yescharacteristic
160#1879C2211yescharacteristic
161#1879C2211yescharacteristic
162#1877C2211yescharacteristic
163#1877C2211yescharacteristic
164#1877C2211yescharacteristic
165#1877C2211yescharacteristic
166#1873C2211yescharacteristic, complemented
167#1872C2211yescharacteristic
168#1870C2211yescharacteristic
169#1864C2211yescharacteristic, complemented
170#1864C2211yescharacteristic, complemented
171#1854C2211yescharacteristic, complemented
172#1853C2211yescharacteristic
173#1851C2211yescharacteristic
174#1850C2211yescharacteristic, complemented
175#1836C2211yescharacteristic, complemented
176#1825C2211yescharacteristic
177#1825C2211yescharacteristic
178#1825C2211yescharacteristic, complemented
179#1809C2211yescharacteristic
180#1809C2211yescharacteristic
181#1804C2211yescharacteristic
182#1804C2211yescharacteristic, complemented
183#1804C2211yescharacteristic, complemented
184#1803C2211yescharacteristic, complemented
185#1803C2211yescharacteristic, complemented
186#1802C2211yescharacteristic
187#1802C2211yescharacteristic, complemented
188#1802C2211yescharacteristic, complemented
189#1788C2211yescharacteristic
190#1788C2211yescharacteristic
191#1788C2211yescharacteristic, complemented
192#1786C2211yescharacteristic
193#1771C2211yescharacteristic, complemented
194#1762C2211yescharacteristic, complemented
195C4×#103C2211yescharacteristic, complemented
196C4×#103C2211yescharacteristic, complemented
197C4×#102C2211yescharacteristic, complemented
198C4×#102C2211yescharacteristic, complemented
199#1753C2211yescharacteristic
200C8×C22⋊C4C2211yescharacteristic, complemented
201#1736C2211yescharacteristic
202#1728C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×#41C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C2×AGL(1,ℤ/8)—24no—
207C2×AGL(1,ℤ/8)—24no—
208C2×AGL(1,ℤ/8)—42no—
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×D8C2311yescharacteristic
214C22×D8C2311yescharacteristic
215C22×M16C2311yescharacteristic
216C22×M16C2311yescharacteristic
217C23×C8C2311yescharacteristic
218#547—24no—
219#547—42no—
220C2×C4⋊Q8C2311yescharacteristic
221C2×#126—21no—
222C2×#125C2311yescharacteristic
223C2×#123—21no—
224C2×#123—21no—
225C2×#123—21no—
226C2×#123D411yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×#121—21no—
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#120—21no—
233C4×#41—24no—
234C4×#41—42no—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×D4—21no—
238C2×C4×D4—21no—
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×#117—21no—
248C2×#117—21no—
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C22×C4⋊C4—21no—
252C22×C4⋊C4—21no—
253C22×C4⋊C4C2311yescharacteristic
254C22×C22⋊C4—21no—
255C22×C22⋊C4—21no—
256C22×C22⋊C4—21no—
257C22×C42—21no—
258C22×C42C2311yescharacteristic
259#478—42no—
260#450—42no—
261#449—24no—
262#449—42no—
263#442—24no—
264C4×D8—42no—
265#435—42no—
266#431—42no—
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278#418—42no—
279#417—42no—
280#416—42no—
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×#97C2311yescharacteristic
315C2×#97C2311yescharacteristic
316C2×C4×C8C2311yescharacteristic
317C2×C4×C8C2311yescharacteristic
318C2×C4×C8C2311yescharacteristic
319#400—21no—
320#400—21no—
321#400—21no—
322#400—21no—
323#399—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#398—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#397—21no—
337#396—21no—
338#396—21no—
339#396—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#392—21no—
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#390—21no—
354#390—21no—
355#390—21no—
356#390—21no—
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388D411yescharacteristic
385#388D411yescharacteristic
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387D411yescharacteristic
399#387D411yescharacteristic
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386D411yescharacteristic
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385D411yescharacteristic
421#384C2311yescharacteristic
422#384C2311yescharacteristic
423#384C2311yescharacteristic
424#382—21no—
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#381—21no—
429#381—21no—
430#381—21no—
431#381—21no—
432#381—21no—
433#381D411yescharacteristic
434#380—21no—
435#380—21no—
436#380—21no—
437#380—21no—
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#379—21no—
445#379—21no—
446C4×C4⋊C4—21no—
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⋊C4—21no—
455C4×C22⋊C4C2311yescharacteristic
456C4×C22⋊C4C2311yescharacteristic
457C4×C22⋊C4C2311yescharacteristic
458C2×#95—21no—
459C2×#95—21no—
460C2×#95—21no—
461C2×#95—21no—
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41#4114yes—
509C22×Q8C2411yescharacteristic
510C22×Q8C2411yescharacteristic
511C22×D4—21no—
512C22×D4—22no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—22no—
518C22×D4—22no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4C2×D411yescharacteristic
523C22×D4C2411yescharacteristic
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4C2×D411yescharacteristic
537C23×C4C2×D411yescharacteristic
538C23×C4C2411yescharacteristic
539C23×C4C2411yescharacteristic
540AGL(1,ℤ/8)—416no—
541C2×SD16—22no—
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×SD16—41no—
553C2×D8—22no—
554C2×D8—22no—
555C2×D8—22no—
556C2×D8—22no—
557C2×D8—22no—
558C2×D8#4114yes—
559C2×M16—22no—
560C2×M16—22no—
561C2×M16—22no—
562C2×M16—41no—
563C2×M16—41no—
564C2×M16—41no—
565C22×C8—41no—
566C22×C8—41no—
567C22×C8—41no—
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C22×C8C2411yescharacteristic
576C4⋊Q8—22no—
577C4⋊Q8—41no—
578#126—82no—
579#125—41no—
580#125—41no—
581#123—42no—
582#123—44no—
583#123—44no—
584#123—82no—
585C22⋊Q8—22no—
586C22⋊Q8—22no—
587C22⋊Q8—22no—
588C22⋊Q8—41no—
589#121—22no—
590#121—41no—
591#121—44no—
592#121—41no—
593#121—41no—
594#120—82no—
595C4×Q8—22no—
596C4×Q8—22no—
597C4×Q8—41no—
598C4×Q8—41no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—41no—
608C4×D4—41no—
609C4×D4—41no—
610C4×D4—41no—
611C4×D4—41no—
612C4×D4—41no—
613C4×D4—41no—
614C4×D4—41no—
615C4×D4—44no—
616C4×D4—44no—
617#117—22no—
618#117—22no—
619#117—44no—
620#117—41no—
621#117—41no—
622#117—82no—
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—41no—
645C2×C4⋊C4—41no—
646C2×C4⋊C4—44no—
647C2×C4⋊C4—44no—
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
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—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—44no—
700C2×C22⋊C4—82no—
701C2×C22⋊C4—82no—
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C42—22no—
711C2×C42—22no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—44no—
720C2×C42C2×D411yescharacteristic
721C2×C42C2×D411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727#107—41no—
728#107—41no—
729#106—22no—
730#106—41no—
731#106—41no—
732#106—41no—
733C4⋊C8—41no—
734C4⋊C8—41no—
735C4⋊C8—41no—
736C4⋊C8—41no—
737C4⋊C8—41no—
738#103—22no—
739#103—41no—
740#103—41no—
741#103—41no—
742#103—41no—
743#103—41no—
744#103—41no—
745#103—41no—
746#103—41no—
747#103—41no—
748#103—41no—
749#103—41no—
750#102—22no—
751#102—22no—
752#102—22no—
753#102—22no—
754#102—22no—
755#102—22no—
756#102—22no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766C22⋊C8—22no—
767C22⋊C8—22no—
768C22⋊C8—22no—
769C22⋊C8—41no—
770C22⋊C8—41no—
771#97—22no—
772#97—41no—
773C4×C8—41no—
774C4×C8—41no—
775C4×C8—41no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819C24—21no—
820C24—21no—
821C24—21no—
822C24—42no—
823C24—42no—
824C24—42no—
825C24—42no—
826C24—81no—
827C24—81no—
828C24—81no—
829C24C22×D411yescharacteristic
830C24C22×D411yescharacteristic
831#41—28no—
832#41—44no—
833#41—44no—
834#41—44no—
835#41—44no—
836#41—82no—
837#41—82no—
838#41—82no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8C2×#4112yes—
851C2×D4—24no—
852C2×D4—22no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—41no—
870C2×D4—41no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—82no—
880C2×D4—82no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4C2×#4112yes—
888C2×D4C2×#4112yes—
889C2×D4C2×#4112yes—
890C2×D4H(5,𝔽2)12yes—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—22no—
896C22×C4—22no—
897C22×C4—21no—
898C22×C4—24no—
899C22×C4—22no—
900C22×C4—22no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—41no—
920C22×C4—41no—
921C22×C4—42no—
922C22×C4—42no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—42no—
928C22×C4—42no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—42no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D411yescharacteristic
961C22×C4C22×D411yescharacteristic
962C22×C4C2×#4112yes—
963C22×C4H(5,𝔽2)12yes—
964C22×C4C2511yescharacteristic
965SD16—44no—
966SD16—44no—
967SD16—82no—
968SD16—82no—
969D8—28no—
970D8—44no—
971M16—44no—
972M16—82no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—82no—
997C2×C8C2×#4112yes—
998C4⋊C4—22no—
999C4⋊C4—22no—
1000C4⋊C4—22no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—41no—
1024C4⋊C4—41no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C22⋊C4—22no—
1047C22⋊C4—22no—
1048C22⋊C4—22no—
1049C22⋊C4—22no—
1050C22⋊C4—41no—
1051C22⋊C4—41no—
1052C22⋊C4—41no—
1053C22⋊C4—41no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C42—22no—
1090C42—22no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—21no—
1101C42—42no—
1102C42—42no—
1103C42—42no—
1104C42—81no—
1105C42—81no—
1106C42—81no—
1107C42—81no—
1108C23—21no—
1109C23—21no—
1110C23—22no—
1111C23—22no—
1112C23—21no—
1113C23—22no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—22no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—84no—
1143C23—84no—
1144C23—84no—
1145C23—84no—
1146C23—162no—
1147C23—162no—
1148C23—162no—
1149C23#54612yes—
1150C23C23×D411yescharacteristic
1151Q8—22no—
1152Q8—22no—
1153Q8—41no—
1154Q8—41no—
1155Q8—41no—
1156Q8—41no—
1157Q8—41no—
1158Q8—41no—
1159D4—22no—
1160D4—22no—
1161D4—22no—
1162D4—22no—
1163D4—22no—
1164D4—48no—
1165D4—41no—
1166D4—41no—
1167D4—41no—
1168D4—41no—
1169D4—41no—
1170D4—41no—
1171D4—84no—
1172D4—82no—
1173D4—84no—
1174D4—162no—
1175D4—162no—
1176D4#55114yes—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—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—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—44no—
1216C2×C4—44no—
1217C2×C4—48no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—84no—
1261C2×C4—84no—
1262C2×C4—84no—
1263C2×C4—84no—
1264C2×C4—84no—
1265C2×C4—162no—
1266C2×C4—162no—
1267C2×C4—162no—
1268C2×C4—162no—
1269C2×C4#54612yes—
1270C2×C4#57512yes—
1271C2×C4#57712yes—
1272C2×C4C22×#4111yescharacteristic
1273C2×C4C22×#4111yescharacteristic
1274C2×C4C2×H(5,𝔽2)11yescharacteristic
1275C2×C4C2×H(5,𝔽2)11yescharacteristic
1276C2×C4#58511yescharacteristic
1277C2×C4#58511yescharacteristic
1278C8—22no—
1279C8—41no—
1280C8—41no—
1281C8—41no—
1282C8—41no—
1283C8—41no—
1284C8—41no—
1285C8—41no—
1286C22—22no—
1287C22—24no—
1288C22—22no—
1289C22—22no—
1290C22—42no—
1291C22—41no—
1292C22—41no—
1293C22—42no—
1294C22—42no—
1295C22—41no—
1296C22—41no—
1297C22—42no—
1298C22—42no—
1299C22—42no—
1300C22—41no—
1301C22—42no—
1302C22—41no—
1303C22—41no—
1304C22—42no—
1305C22—41no—
1306C22—41no—
1307C22—42no—
1308C22—41no—
1309C22—41no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—168no—
1322C22C2×#54611yescharacteristic
1323C22D4×#4111yescharacteristic
1324C22#348811yescharacteristic
1325C22C2×#57511yescharacteristic
1326C22C2×#57711yescharacteristic
1327C22#358411yescharacteristic
1328C22#358511yescharacteristic
1329C4—22no—
1330C4—22no—
1331C4—22no—
1332C4—41no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—42no—
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—41no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4C2×#55111yescharacteristic
1355C4#349111yescharacteristic
1356C4#351311yescharacteristic
1357C4#353411yescharacteristic
1358C2—42no—
1359C2—44no—
1360C2—81no—
1361C2—82no—
1362C2—161no—
1363C2#5901111yescharacteristic
1364C2#6116411yescharacteristic
1365C2#6117411yescharacteristic
1366C2#6144211yescharacteristic
1367C2#6155111yescharacteristic
1368C2#6198611yescharacteristic
1369C2#6204711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#23864C2
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. #59272C2semidirect
2. #36217C2semidirect
3. #31948C2semidirect
4. #31900C2semidirect
5. #31660C2semidirect
6. #31552C2semidirect
7. #28982C2semidirect
8. #28896C2semidirect
9. #28100C2semidirect
10. #27861C2semidirect
11. #27724C2semidirect
12. #27574C2semidirect
13. #27557C2semidirect
14. #27232C2semidirect
15. #27201C2semidirect
16. #26670C2semidirect
17. #25972C2semidirect
18. #24959C2semidirect
19. #24911C2semidirect
20. #24820C2semidirect
21. #24538C2semidirect
22. #24537C2semidirect
23. #24501C2semidirect
25. #22904C2semidirect
26. #22872C2semidirect
27. #22774C2semidirect
28. #22442C2semidirect
29. #22420C2semidirect
30. #20928C2semidirect
31. #20737C2semidirect
35. C2×#478C22semidirect
45. C2×#416C22semidirect
62. #2446C22semidirect
63. #2446C22semidirect
67. #2423C22semidirect
69. #2421C22semidirect
78. #2349C22semidirect
79. D4×C4⋊C4C22semidirect
82. #2339C22semidirect
83. #2339C22semidirect
89. #2101C22semidirect
90. #2101C22semidirect
91. #2100C22semidirect
92. #2099C22semidirect
93. #2097C22semidirect
94. #2096C22semidirect
95. #2085C22semidirect
96. #2083C22semidirect
97. #2077C22semidirect
98. #2077C22semidirect
99. #2074C22semidirect
101. #2072C22semidirect
104. #2066C22semidirect
105. #2066C22semidirect
115. #2026C22semidirect
116. #2026C22semidirect
121. #1991C22semidirect
122. #1981C22semidirect
127. #1960C22semidirect
128. #1939C22semidirect
131. #1935C22semidirect
134. #1933C22semidirect
135. #1928C22semidirect
136. #1928C22semidirect
137. #1924C22semidirect
138. #1923C22semidirect
139. #1920C22semidirect
140. #1919C22semidirect
141. #1919C22semidirect
142. #1919C22semidirect
143. #1917C22semidirect
144. #1916C22semidirect
149. #1892C22semidirect
166. #1873C22semidirect
169. #1864C22semidirect
170. #1864C22semidirect
171. #1854C22semidirect
174. #1850C22semidirect
175. #1836C22semidirect
178. #1825C22semidirect
182. #1804C22semidirect
183. #1804C22semidirect
184. #1803C22semidirect
185. #1803C22semidirect
187. #1802C22semidirect
188. #1802C22semidirect
191. #1788C22semidirect
193. #1771C22semidirect
194. #1762C22semidirect
195. C4×#103C22semidirect
196. C4×#103C22semidirect
197. C4×#102C22semidirect
198. C4×#102C22semidirect
200. C8×C22⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#592722
#362172
#319482
#319002
#316602
#315522
#289822
#288962
#281002
#278612
#277242
#275742
#275572
#272322
#272012
#266702
#259722
#249592
#249112
#248202
#245382
#245372
#245012
#238642
#229042
#228722
#227742
#224422
#224202
#209282
#207372