Finite Group Databasebeta

← #7041619

Subgroups — #7041619

Order 512.

1568 conjugacy classes of subgroups.

The subgroup lattice has 1299 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59860C211yesmaximal, characteristic, complemented
2#59304C211yesmaximal, characteristic, complemented
3#32412C211yesmaximal, characteristic, complemented
4#32390C211yesmaximal, characteristic, complemented
5#32326C211yesmaximal, characteristic, complemented
6#32308C211yesmaximal, characteristic, complemented
7#31996C211yesmaximal, characteristic, complemented
8#31958C211yesmaximal, characteristic, complemented
9#31610C211yesmaximal, characteristic, complemented
10#30557C211yesmaximal, characteristic, complemented
11#29236C211yesmaximal, characteristic, complemented
12#28557C211yesmaximal, characteristic, complemented
13#27677C211yesmaximal, characteristic, complemented
14#27504C211yesmaximal, characteristic, complemented
15#27475C211yesmaximal, characteristic, complemented
16#27376C211yesmaximal, characteristic, complemented
17#27111C211yesmaximal, characteristic, complemented
18#26215C211yesmaximal, characteristic, complemented
19#26214C211yesmaximal, characteristic, complemented
20#26147C211yesmaximal, characteristic, complemented
21#26142C211yesmaximal, characteristic, complemented
22#26126C211yesmaximal, characteristic, complemented
23#25200C211yesmaximal, characteristic, complemented
24#24935C211yesmaximal, characteristic, complemented
25#24790C211yesmaximal, characteristic, complemented
26#24576C211yesmaximal, characteristic, complemented
27#23658C211yesmaximal, characteristic, complemented
28#22709C211yesmaximal, characteristic, complemented
29#22661C211yesmaximal, characteristic, complemented
30#22190C211yesmaximal, characteristic, complemented
31#22170C211yesmaximal, characteristic, complemented
32C2×#553—21no—
33C2×#480C2211yescharacteristic
34C2×#480C2211yescharacteristic
35C2×#469C2211yescharacteristic
36C2×#466C2211yescharacteristic
37C2×#435C2211yescharacteristic
38C2×#435C2211yescharacteristic
39C2×#428C2211yescharacteristic
40C2×#428C2211yescharacteristic
41C22×#107C2211yescharacteristic
42#2779—21no—
43#2718—21no—
44#2718—21no—
45#2688—21no—
46#2600—21no—
47#2598—21no—
48#2597—21no—
49#2573—21no—
50#2552C2211yescharacteristic
51#2537C2211yescharacteristic
52#2516—21no—
53#2513C2211yescharacteristic
54#2509C2211yescharacteristic
55#2501C2211yescharacteristic
56#2501C2211yescharacteristic
57#2496C2211yescharacteristic
58#2496C2211yescharacteristic
59#2495C2211yescharacteristic
60#2487—21no—
61#2487C2211yescharacteristic
62#2443—21no—
63#2443—21no—
64#2441—21no—
65#2422—21no—
66#2420C2211yescharacteristic
67#2416C2211yescharacteristic
68#2416C2211yescharacteristic
69#2416C2211yescharacteristic
70#2414C2211yescharacteristic
71#2414C2211yescharacteristic
72#2363—21no—
73#2361C2211yescharacteristic
74#2354C2211yescharacteristic
75#2352C2211yescharacteristic
76#2352C2211yescharacteristic
77D4×C4⋊C4C2211yescharacteristic
78D4×C4⋊C4C2211yescharacteristic
79D4×C4⋊C4C2211yescharacteristic
80#2344C2211yescharacteristic
81C4×#121C2211yescharacteristic
82C4×#121C2211yescharacteristic
83C4×#121C2211yescharacteristic
84#2296C2211yescharacteristic
85C2×#384C2211yescharacteristic
86#2101C2211yescharacteristic
87#2100C2211yescharacteristic
88#2099C2211yescharacteristic
89#2099C2211yescharacteristic
90#2094C2211yescharacteristic
91#2093C2211yescharacteristic
92#2093C2211yescharacteristic
93#2092C2211yescharacteristic
94#2088C2211yescharacteristic
95#2088C2211yescharacteristic
96#2087C2211yescharacteristic
97#2085C2211yescharacteristic
98#2084C2211yescharacteristic
99#2084C2211yescharacteristic
100#2084C2211yescharacteristic
101#2084C2211yescharacteristic
102#2083C2211yescharacteristic
103#2083C2211yescharacteristic
104#2083C2211yescharacteristic
105#2083C2211yescharacteristic
106#2083C2211yescharacteristic
107#2077C2211yescharacteristic
108#2077C2211yescharacteristic
109#2077C2211yescharacteristic
110#2077C2211yescharacteristic
111#2075C2211yescharacteristic
112#2073C2211yescharacteristic
113#2071C2211yescharacteristic
114#2067C2211yescharacteristic
115#2067C2211yescharacteristic
116#2065C2211yescharacteristic
117#2065C2211yescharacteristic
118#2054C2211yescharacteristic
119#2034C2211yescharacteristic
120#2034C2211yescharacteristic
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic
123#2033C2211yescharacteristic
124#2033C2211yescharacteristic
125#1999C2211yescharacteristic
126#1972C2211yescharacteristic
127#1949C2211yescharacteristic
128#1949C2211yescharacteristic
129#1947C2211yescharacteristic
130#1947C2211yescharacteristic
131#1947C2211yescharacteristic
132#1947C2211yescharacteristic
133#1943C2211yescharacteristic
134#1936C2211yescharacteristic
135#1936C2211yescharacteristic
136#1926C2211yescharacteristic
137#1926C2211yescharacteristic
138#1925C2211yescharacteristic
139#1925C2211yescharacteristic
140#1925C2211yescharacteristic
141#1925C2211yescharacteristic
142#1924C2211yescharacteristic
143#1924C2211yescharacteristic
144#1921C2211yescharacteristic
145#1921C2211yescharacteristic
146#1921C2211yescharacteristic
147#1921C2211yescharacteristic
148#1920C2211yescharacteristic
149#1920C2211yescharacteristic
150#1920C2211yescharacteristic
151#1918C2211yescharacteristic
152#1917C2211yescharacteristic
153#1917C2211yescharacteristic
154#1895C2211yescharacteristic
155#1895C2211yescharacteristic
156#1893C2211yescharacteristic
157#1893C2211yescharacteristic
158#1879C2211yescharacteristic
159#1879C2211yescharacteristic
160#1875C2211yescharacteristic
161#1875C2211yescharacteristic
162#1874C2211yescharacteristic
163#1874C2211yescharacteristic
164#1874C2211yescharacteristic
165#1874C2211yescharacteristic
166#1870C2211yescharacteristic
167#1870C2211yescharacteristic
168#1869C2211yescharacteristic
169#1869C2211yescharacteristic
170#1864C2211yescharacteristic
171#1864C2211yescharacteristic
172#1864C2211yescharacteristic
173#1862C2211yescharacteristic
174#1854C2211yescharacteristic
175#1854C2211yescharacteristic
176#1853C2211yescharacteristic
177#1853C2211yescharacteristic
178#1853C2211yescharacteristic
179#1852C2211yescharacteristic
180#1852C2211yescharacteristic
181#1852C2211yescharacteristic
182#1852C2211yescharacteristic
183#1852C2211yescharacteristic
184#1850C2211yescharacteristic
185#1850C2211yescharacteristic
186#1847C2211yescharacteristic
187#1836C2211yescharacteristic
188#1824C2211yescharacteristic
189#1823C2211yescharacteristic
190#1809C2211yescharacteristic
191#1808C2211yescharacteristic
192#1807C2211yescharacteristic
193#1807C2211yescharacteristic
194#1802C2211yescharacteristic
195#1802C2211yescharacteristic
196#1797C2211yescharacteristic
197#1776C2211yescharacteristic
198#1776C2211yescharacteristic
199#1736C2211yescharacteristic
200#1736C2211yescharacteristic
201C2×#340C2211yescharacteristic
202#1728C2211yescharacteristic
203C22×D8C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C23×C8C2311yescharacteristic
208#553—48no—
209C2×#126—21no—
210C2×#126—21no—
211C2×#125—21no—
212C2×#123—21no—
213C2×#123—21no—
214C2×#123—21no—
215C2×#123—21no—
216C2×#121—21no—
217C2×#121—21no—
218C2×#121—21no—
219C2×#121—21no—
220C2×#121D411yescharacteristic
221C2×#121C2311yescharacteristic
222C2×#121C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×#121C2311yescharacteristic
226C2×#121C2311yescharacteristic
227C2×C4×D4—21no—
228C2×C4×D4—21no—
229C2×C4×D4—21no—
230C2×C4×D4—21no—
231C2×C4×D4—21no—
232C2×C4×D4—21no—
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×#117—21no—
239C2×#117—21no—
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C22×C4⋊C4—21no—
243C22×C4⋊C4—21no—
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C42C2311yescharacteristic
251#480—42no—
252#480—42no—
253#469—24no—
254#466—42no—
255#435—24no—
256#435—24no—
257#428—42no—
258#428—42no—
259C2×#107—42no—
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×#97C2311yescharacteristic
306C2×#97C2311yescharacteristic
307#400—21no—
308#400—21no—
309#400—21no—
310#400—21no—
311#400—21no—
312#400—21no—
313#399—21no—
314#399—21no—
315#399—21no—
316#399—21no—
317#399—21no—
318#398—21no—
319#398—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#396—21no—
327#396—21no—
328#396—21no—
329#394—21no—
330#394—21no—
331#394—21no—
332#394—21no—
333#394—21no—
334#394—21no—
335#394—21no—
336#394—21no—
337#392—21no—
338#392—21no—
339#390—21no—
340#390—21no—
341#390D411yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#389—21no—
349#389—21no—
350#389—21no—
351#389—21no—
352#389—21no—
353#389D411yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388D411yescharacteristic
377#388D411yescharacteristic
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#386—21no—
386#386—21no—
387#386—21no—
388#386—21no—
389#386—21no—
390#386—21no—
391#386—21no—
392#386—21no—
393#386—21no—
394#386—21no—
395#386D411yescharacteristic
396#386D411yescharacteristic
397#385—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#384—21no—
408#384—21no—
409#384C2311yescharacteristic
410#384C2311yescharacteristic
411#384C2311yescharacteristic
412#384C2311yescharacteristic
413#384C2311yescharacteristic
414#384C2311yescharacteristic
415#383—21no—
416#382C2311yescharacteristic
417#382C2311yescharacteristic
418#381—21no—
419#381—21no—
420#380—21no—
421#380—21no—
422#380D411yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433C4×C4⋊C4—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4C2311yescharacteristic
447C4×C22⋊C4C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
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#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4C2×D411yescharacteristic
495C22×D4C2×D411yescharacteristic
496C22×D4C2×D411yescharacteristic
497C22×D4C2411yescharacteristic
498C22×D4C2411yescharacteristic
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4C2×D411yescharacteristic
508C23×C4C2×D411yescharacteristic
509C23×C4C2411yescharacteristic
510C23×C4C2411yescharacteristic
511C23×C4C2411yescharacteristic
512C2×D8—22no—
513C2×D8—41no—
514C2×D8—41no—
515C2×M16—22no—
516C2×M16—41no—
517C2×M16—41no—
518C2×M16—41no—
519C2×M16—41no—
520C2×M16#4114yes—
521C22×C8—22no—
522C22×C8—22no—
523C22×C8—41no—
524C22×C8—41no—
525C22×C8—41no—
526C22×C8—41no—
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535#126—44no—
536#126—44no—
537#125—44no—
538#123—44no—
539#123—44no—
540#123—82no—
541#123—82no—
542#121—24no—
543#121—22no—
544#121—22no—
545#121—22no—
546#121—22no—
547#121—22no—
548#121—41no—
549#121—44no—
550#121—44no—
551#121—44no—
552#121—44no—
553#121—41no—
554#121—41no—
555#121—41no—
556#121—41no—
557#121—41no—
558#121—41no—
559C4×D4—22no—
560C4×D4—22no—
561C4×D4—22no—
562C4×D4—22no—
563C4×D4—41no—
564C4×D4—41no—
565C4×D4—41no—
566C4×D4—41no—
567C4×D4—41no—
568C4×D4—41no—
569C4×D4—44no—
570C4×D4—44no—
571C4×D4—44no—
572C4×D4—44no—
573C4×D4—82no—
574C4×D4—82no—
575#117—22no—
576#117—41no—
577#117—44no—
578#117—41no—
579#117—41no—
580#117—82no—
581C2×C4⋊C4—22no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—41no—
611C2×C4⋊C4—41no—
612C2×C4⋊C4—41no—
613C2×C4⋊C4—41no—
614C2×C4⋊C4—41no—
615C2×C4⋊C4—41no—
616C2×C4⋊C4—41no—
617C2×C4⋊C4—41no—
618C2×C4⋊C4—41no—
619C2×C4⋊C4—41no—
620C2×C4⋊C4—41no—
621C2×C4⋊C4—44no—
622C2×C4⋊C4—82no—
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2×D411yescharacteristic
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
643C2×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
675C2×C22⋊C4C2×D411yescharacteristic
676C2×C22⋊C4C2×D411yescharacteristic
677C2×C22⋊C4C2×D411yescharacteristic
678C2×C22⋊C4C2×D411yescharacteristic
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C42—21no—
685C2×C42—21no—
686C2×C42—21no—
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—41no—
693C2×C42—41no—
694C2×C42C2×D411yescharacteristic
695C2×C42C2×D411yescharacteristic
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700#107—22no—
701#107—22no—
702#107—22no—
703#107—22no—
704#107—22no—
705#107—41no—
706#107—41no—
707#107—41no—
708#107—41no—
709#107—41no—
710#107—41no—
711#106—22no—
712#106—41no—
713#106—41no—
714#106—41no—
715#106—41no—
716#106—41no—
717#106—41no—
718#106—41no—
719C4⋊C8—22no—
720C4⋊C8—22no—
721C4⋊C8—41no—
722C4⋊C8—41no—
723#102—22no—
724#102—22no—
725#102—22no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102—41no—
736#102—41no—
737C22⋊C8—22no—
738C22⋊C8—22no—
739C22⋊C8—22no—
740C22⋊C8—22no—
741C22⋊C8—41no—
742C22⋊C8—41no—
743C22⋊C8—41no—
744C22⋊C8—41no—
745#97—22no—
746#97—22no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
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#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783C24—21no—
784C24—21no—
785C24C22×D411yescharacteristic
786C24C22×D411yescharacteristic
787C24C22×D411yescharacteristic
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—22no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—41no—
805C2×D4—41no—
806C2×D4—41no—
807C2×D4—41no—
808C2×D4—42no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—42no—
812C2×D4—42no—
813C2×D4—42no—
814C2×D4—42no—
815C2×D4—42no—
816C2×D4—42no—
817C2×D4—81no—
818C2×D4—81no—
819C2×D4—81no—
820C2×D4—81no—
821C2×D4—81no—
822C2×D4—81no—
823C2×D4—81no—
824C2×D4—81no—
825C2×D4—81no—
826C2×D4AGL(1,ℤ/8)14yes—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—41no—
860C22×C4—41no—
861C22×C4—41no—
862C22×C4—41no—
863C22×C4—42no—
864C22×C4—42no—
865C22×C4—42no—
866C22×C4—42no—
867C22×C4—42no—
868C22×C4—42no—
869C22×C4—42no—
870C22×C4—42no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—81no—
874C22×C4—81no—
875C22×C4—81no—
876C22×C4—81no—
877C22×C4—81no—
878C22×C4—81no—
879C22×C4—81no—
880C22×C4—81no—
881C22×C4—81no—
882C22×C4—81no—
883C22×C4—81no—
884C22×C4—81no—
885C22×C4—81no—
886C22×C4—81no—
887C22×C4C22×D411yescharacteristic
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C2×#4112yes—
899C22×C42−1+412yes—
900C22×C4C2511yescharacteristic
901D8—82no—
902M16—44no—
903M16—44no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—44no—
927C2×C8—82no—
928C2×C8C2×#4112yes—
929C2×C8C2×#4112yes—
930C4⋊C4—22no—
931C4⋊C4—22no—
932C4⋊C4—22no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—41no—
961C4⋊C4—41no—
962C4⋊C4—42no—
963C4⋊C4—42no—
964C4⋊C4—42no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—42no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—42no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4H(5,𝔽2)12yes—
991C22⋊C4—22no—
992C22⋊C4—22no—
993C22⋊C4—22no—
994C22⋊C4—22no—
995C22⋊C4—22no—
996C22⋊C4—22no—
997C22⋊C4—22no—
998C22⋊C4—22no—
999C22⋊C4—41no—
1000C22⋊C4—41no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C42—21no—
1034C42—21no—
1035C42—21no—
1036C42—21no—
1037C42—21no—
1038C42—21no—
1039C42—21no—
1040C42—21no—
1041C42—41no—
1042C42—41no—
1043C42—42no—
1044C42—42no—
1045C42—42no—
1046C42—42no—
1047C42—42no—
1048C42—81no—
1049C42—81no—
1050C42—81no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—21no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23#54712yes—
1084C23C2×AGL(1,ℤ/8)12yes—
1085C23C2×AGL(1,ℤ/8)12yes—
1086C23C23×D411yescharacteristic
1087D4—44no—
1088D4—44no—
1089D4—44no—
1090D4—41no—
1091D4—41no—
1092D4—41no—
1093D4—41no—
1094D4—41no—
1095D4—41no—
1096D4—41no—
1097D4—41no—
1098D4—84no—
1099D4—84no—
1100D4—84no—
1101D4—162no—
1102D4—162no—
1103D4—162no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—22no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—44no—
1140C2×C4—44no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—84no—
1191C2×C4—84no—
1192C2×C4—162no—
1193C2×C4—162no—
1194C2×C4—162no—
1195C2×C4—162no—
1196C2×C4—162no—
1197C2×C4—162no—
1198C2×C4#54712yes—
1199C2×C4C2×AGL(1,ℤ/8)12yes—
1200C2×C4#57612yes—
1201C2×C4C22×#4111yescharacteristic
1202C2×C4C2×H(5,𝔽2)11yescharacteristic
1203C2×C4C2×2−1+411yescharacteristic
1204C2×C4#58511yescharacteristic
1205C2×C4#58511yescharacteristic
1206C2×C4#58511yescharacteristic
1207C8—22no—
1208C8—22no—
1209C8—41no—
1210C8—41no—
1211C8—41no—
1212C8—41no—
1213C8—41no—
1214C8—41no—
1215C22—22no—
1216C22—22no—
1217C22—22no—
1218C22—22no—
1219C22—22no—
1220C22—22no—
1221C22—22no—
1222C22—22no—
1223C22—22no—
1224C22—41no—
1225C22—41no—
1226C22—41no—
1227C22—41no—
1228C22—41no—
1229C22—41no—
1230C22—41no—
1231C22—41no—
1232C22—41no—
1233C22—41no—
1234C22—41no—
1235C22—41no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22C2×#54711yescharacteristic
1251C22#348511yescharacteristic
1252C22#348811yescharacteristic
1253C22C22×AGL(1,ℤ/8)11yescharacteristic
1254C22C2×#57611yescharacteristic
1255C22#358611yescharacteristic
1256C22#358611yescharacteristic
1257C4—22no—
1258C4—22no—
1259C4—22no—
1260C4—41no—
1261C4—41no—
1262C4—41no—
1263C4—42no—
1264C4—41no—
1265C4—41no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—81no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C4—81no—
1274C4—81no—
1275C4—81no—
1276C4—81no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4#350511yescharacteristic
1283C4#351211yescharacteristic
1284C4#354111yescharacteristic
1285C4#355311yescharacteristic
1286C2—42no—
1287C2—42no—
1288C2—42no—
1289C2—161no—
1290C2—161no—
1291C2#4352611yescharacteristic
1292C2#6125211yescharacteristic
1293C2#6127811yescharacteristic
1294C2#6170611yescharacteristic
1295C2#6174411yescharacteristic
1296C2#6197911yescharacteristic
1297C2#6208211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#121 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59860C2semidirect
2. #59304C2semidirect
3. #32412C2semidirect
4. #32390C2semidirect
5. #32326C2semidirect
6. #32308C2semidirect
7. #31996C2semidirect
8. #31958C2semidirect
9. #31610C2semidirect
10. #30557C2semidirect
11. #29236C2semidirect
12. #28557C2semidirect
13. #27677C2semidirect
14. #27504C2semidirect
15. #27475C2semidirect
16. #27376C2semidirect
17. #27111C2semidirect
18. #26215C2semidirect
19. #26214C2semidirect
20. #26147C2semidirect
21. #26142C2semidirect
22. #26126C2semidirect
23. #25200C2semidirect
24. #24935C2semidirect
25. #24790C2semidirect
26. #24576C2semidirect
27. #23658C2semidirect
28. #22709C2semidirect
29. #22661C2semidirect
30. #22190C2semidirect
31. #22170C2semidirect

Maximal subgroups

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

subgroupindex
#598602
#593042
#324122
#323902
#323262
#323082
#319962
#319582
#316102
#305572
#292362
#285572
#276772
#275042
#274752
#273762
#271112
#262152
#262142
#261472
#261422
#261262
#252002
#249352
#247902
#245762
#236582
#227092
#226612
#221902
#221702