Finite Group Databasebeta

← #7598412

Subgroups — #7598412

Order 512.

1733 conjugacy classes of subgroups.

The subgroup lattice has 1375 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59657C211yesmaximal, characteristic, complemented
2#59641C211yesmaximal, characteristic, complemented
3#31834C211yesmaximal, characteristic, complemented
4#31834C211yesmaximal, characteristic, complemented
5#31740C211yesmaximal, characteristic, complemented
6#31739C211yesmaximal, characteristic, complemented
7#29280C211yesmaximal, characteristic, complemented
8#28999C211yesmaximal, characteristic, complemented
9#28983C211yesmaximal, characteristic, complemented
10#28921C211yesmaximal, characteristic, complemented
11#28907C211yesmaximal, characteristic, complemented
12#28156C211yesmaximal, characteristic, complemented
13#27709C211yesmaximal, characteristic, complemented
14#27695C211yesmaximal, characteristic, complemented
15#26738C211yesmaximal, characteristic, complemented
16#26737C211yesmaximal, characteristic, complemented
17#26684C211yesmaximal, characteristic, complemented
18#26673C211yesmaximal, characteristic, complemented
19#25946C211yesmaximal, characteristic, complemented
20#25581C211yesmaximal, characteristic, complemented
21#25396C211yesmaximal, characteristic, complemented
22#25304C211yesmaximal, characteristic, complemented
23#25002C211yesmaximal, characteristic, complemented
24#24977C211yesmaximal, characteristic, complemented
25#23143C211yesmaximal, characteristic, complemented
26#23132C211yesmaximal, characteristic, complemented
27#22522C211yesmaximal, characteristic, complemented
28#22493C211yesmaximal, characteristic, complemented
29#21656C211yesmaximal, characteristic, complemented
30#21646C211yesmaximal, characteristic, complemented
31#21632C211yesmaximal, characteristic, complemented
32C2×#559—21no—
33C2×#554C2211yescharacteristic
34C2×#553C2211yescharacteristic
35C2×#490C2211yescharacteristic
36C2×#486C2211yescharacteristic
37C2×#469C2211yescharacteristic
38C2×#466C2211yescharacteristic
39C2×#459C2211yescharacteristic
40C2×#459C2211yescharacteristic
41C2×#446C2211yescharacteristic
42C2×#435C2211yescharacteristic
43#2723—21no—
44#2710—21no—
45#2710—21no—
46#2676—21no—
47#2580—21no—
48#2580C2211yescharacteristic
49#2560—21no—
50#2548C2211yescharacteristic
51#2541C2211yescharacteristic
52#2540—21no—
53#2535C2211yescharacteristic
54#2501C2211yescharacteristic
55#2501C2211yescharacteristic
56#2491C2211yescharacteristic
57#2491C2211yescharacteristic
58#2491C2211yescharacteristic
59#2490C2211yescharacteristic
60#2463—21no—
61#2461—21no—
62#2455—21no—
63#2455—21no—
64#2448—21no—
65#2445—21no—
66#2443—21no—
67#2441C2211yescharacteristic
68#2440C2211yescharacteristic
69#2428C2211yescharacteristic
70#2428C2211yescharacteristic
71#2422C2211yescharacteristic
72#2422C2211yescharacteristic
73#2363C2211yescharacteristic
74#2361—21no—
75#2361C2211yescharacteristic
76#2361C2211yescharacteristic
77#2361C2211yescharacteristic
78Q8×C4⋊C4C2211yescharacteristic
79D4×C4⋊C4C2211yescharacteristic
80C4×C4⋊Q8C2211yescharacteristic
81C4×#127C2211yescharacteristic
82C4×#127C2211yescharacteristic
83C4×#125C2211yescharacteristic
84C4×#124C2211yescharacteristic
85#2100C2211yescharacteristic
86#2099C2211yescharacteristic
87#2099C2211yescharacteristic
88#2099C2211yescharacteristic
89#2077C2211yescharacteristic
90#2076C2211yescharacteristic
91#2071C2211yescharacteristic
92#2071C2211yescharacteristic
93#2071C2211yescharacteristic
94#2071C2211yescharacteristic
95#2067C2211yescharacteristic
96#2065C2211yescharacteristic
97#2058C2211yescharacteristic
98#2057C2211yescharacteristic
99#2054C2211yescharacteristic
100#2054C2211yescharacteristic
101#2034C2211yescharacteristic
102#2034C2211yescharacteristic
103#2033C2211yescharacteristic
104#2033C2211yescharacteristic
105#2025C2211yescharacteristic
106#2025C2211yescharacteristic
107#2023C2211yescharacteristic
108#2023C2211yescharacteristic
109#2011C2211yescharacteristic
110#2011C2211yescharacteristic
111#1999C2211yescharacteristic
112#1999C2211yescharacteristic
113#1999C2211yescharacteristic
114#1999C2211yescharacteristic
115#1999C2211yescharacteristic
116#1999C2211yescharacteristic
117#1992C2211yescharacteristic
118#1992C2211yescharacteristic
119#1990C2211yescharacteristic
120#1990C2211yescharacteristic
121#1989C2211yescharacteristic
122#1989C2211yescharacteristic
123#1989C2211yescharacteristic
124#1987C2211yescharacteristic
125#1985C2211yescharacteristic
126#1972C2211yescharacteristic
127#1970C2211yescharacteristic
128#1961C2211yescharacteristic
129#1957C2211yescharacteristic
130#1955C2211yescharacteristic
131#1949C2211yescharacteristic
132#1949C2211yescharacteristic
133#1936C2211yescharacteristic
134#1936C2211yescharacteristic
135#1936C2211yescharacteristic
136#1936C2211yescharacteristic
137#1936C2211yescharacteristic
138#1934C2211yescharacteristic
139#1934C2211yescharacteristic
140#1934C2211yescharacteristic
141#1934C2211yescharacteristic
142#1934C2211yescharacteristic
143#1926C2211yescharacteristic
144#1925C2211yescharacteristic
145#1924C2211yescharacteristic
146#1924C2211yescharacteristic
147#1923C2211yescharacteristic
148#1923C2211yescharacteristic
149#1921C2211yescharacteristic
150#1921C2211yescharacteristic
151#1921C2211yescharacteristic
152#1920C2211yescharacteristic
153#1920C2211yescharacteristic
154#1920C2211yescharacteristic
155#1895C2211yescharacteristic
156#1895C2211yescharacteristic
157#1893C2211yescharacteristic
158#1893C2211yescharacteristic
159#1879C2211yescharacteristic
160#1879C2211yescharacteristic
161#1879C2211yescharacteristic
162#1879C2211yescharacteristic
163#1879C2211yescharacteristic
164#1879C2211yescharacteristic
165#1879C2211yescharacteristic
166#1879C2211yescharacteristic
167#1875C2211yescharacteristic
168#1875C2211yescharacteristic
169#1874C2211yescharacteristic
170#1874C2211yescharacteristic
171#1874C2211yescharacteristic
172#1874C2211yescharacteristic
173#1874C2211yescharacteristic
174#1874C2211yescharacteristic
175#1836C2211yescharacteristic
176#1834C2211yescharacteristic
177#1831C2211yescharacteristic
178#1825C2211yescharacteristic
179#1824C2211yescharacteristic
180#1824C2211yescharacteristic
181#1823C2211yescharacteristic
182#1802C2211yescharacteristic
183#1802C2211yescharacteristic
184#1802C2211yescharacteristic
185#1802C2211yescharacteristic
186#1762C2211yescharacteristic
187#1762C2211yescharacteristic
188#1762C2211yescharacteristic
189#1762C2211yescharacteristic
190#1762C2211yescharacteristic
191#1762C2211yescharacteristic
192#1762C2211yescharacteristic
193#1762C2211yescharacteristic
194#1762C2211yescharacteristic
195C4×#102C2211yescharacteristic
196#1753C2211yescharacteristic
197#1753C2211yescharacteristic
198#1752C2211yescharacteristic
199C8×C22⋊C4C2211yescharacteristic
200#1736C2211yescharacteristic
201C2×#340C2211yescharacteristic
202C4×#97C2211yescharacteristic
203C22×D8C2311yescharacteristic
204C22×D8C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209#559—48no—
210#554—24no—
211#554—42no—
212#553—24no—
213#553—42no—
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×#127—21no—
217C2×#127C2311yescharacteristic
218C2×#127C2311yescharacteristic
219C2×#126—21no—
220C2×#125C2311yescharacteristic
221C2×#125C2311yescharacteristic
222C2×#124—21no—
223C2×#124—21no—
224C2×#124—21no—
225C2×#124—21no—
226C2×#124D411yescharacteristic
227C2×#123—21no—
228C2×#123—21no—
229C2×#123—21no—
230C2×#123—21no—
231C2×#123—21no—
232C2×#123—21no—
233C2×#123—21no—
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8—21no—
237C2×C22⋊Q8—21no—
238C2×#121—21no—
239C2×#121—21no—
240C2×#121—21no—
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#121C2311yescharacteristic
244C2×#121C2311yescharacteristic
245C2×#121C2311yescharacteristic
246C2×#121C2311yescharacteristic
247C2×#121C2311yescharacteristic
248C2×#121C2311yescharacteristic
249C2×C4×Q8—21no—
250C2×C4×Q8—21no—
251C2×C4×Q8C2311yescharacteristic
252C2×C4×D4—21no—
253C2×C4×D4—21no—
254C2×C4×D4—21no—
255C2×C4×D4—21no—
256C2×C4×D4—21no—
257C2×C4×D4—21no—
258C2×C4×D4—21no—
259C2×C4×D4—21no—
260C2×C4×D4—21no—
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2311yescharacteristic
264C2×C4×D4C2311yescharacteristic
265C2×C4×D4C2311yescharacteristic
266C2×C4×D4C2311yescharacteristic
267C2×C4×D4C2311yescharacteristic
268C2×#117C2311yescharacteristic
269C22×C4⋊C4—21no—
270C22×C4⋊C4C2311yescharacteristic
271C22×C4⋊C4C2311yescharacteristic
272C22×C4⋊C4C2311yescharacteristic
273#490—24no—
274#486—24no—
275#469—24no—
276#466—24no—
277#459—42no—
278#459—42no—
279#446—42no—
280#435—42no—
281C2×#107C2311yescharacteristic
282C2×#107C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×#106C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
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×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×#97C2311yescharacteristic
321C2×#97C2311yescharacteristic
322C2×#97C2311yescharacteristic
323C2×#97C2311yescharacteristic
324C2×C4×C8C2311yescharacteristic
325C2×C4×C8C2311yescharacteristic
326C2×C4×C8C2311yescharacteristic
327#399—21no—
328#399—21no—
329#399—21no—
330#399—21no—
331#399—21no—
332#399—21no—
333#398—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#396—21no—
339#395—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#393—21no—
351#393—21no—
352#393—21no—
353#393—21no—
354#392—21no—
355#392—21no—
356#392—21no—
357#392—21no—
358#392—21no—
359#391—21no—
360#391D411yescharacteristic
361#390—21no—
362#390—21no—
363#390—21no—
364#390—21no—
365#390—21no—
366#390—21no—
367#390—21no—
368#390—21no—
369#390D411yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#389—21no—
381#389—21no—
382#389—21no—
383#389—21no—
384#389—21no—
385#389—21no—
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388D411yescharacteristic
401#388D411yescharacteristic
402#388D411yescharacteristic
403#388D411yescharacteristic
404#387—21no—
405#387—21no—
406#387—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#384C2311yescharacteristic
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#384C2311yescharacteristic
429#384C2311yescharacteristic
430#382D411yescharacteristic
431#382C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436C4×C4⋊C4—21no—
437C4×C4⋊C4—21no—
438C4×C4⋊C4—21no—
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C22⋊C4—21no—
446C4×C22⋊C4C2311yescharacteristic
447C4×C22⋊C4C2311yescharacteristic
448C4×C22⋊C4C2311yescharacteristic
449C4×C22⋊C4C2311yescharacteristic
450C43C2311yescharacteristic
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#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
491C22×Q8—21no—
492C22×Q8—21no—
493C22×Q8C2×D411yescharacteristic
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4C2×D411yescharacteristic
507C22×D4C2411yescharacteristic
508C22×D4C2411yescharacteristic
509C22×D4C2411yescharacteristic
510C22×D4C2411yescharacteristic
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4C2411yescharacteristic
521C23×C4C2411yescharacteristic
522C2×D8—22no—
523C2×D8—22no—
524C2×D8—41no—
525C2×D8—41no—
526C2×D8—41no—
527C2×D8—41no—
528C2×D8—41no—
529C2×D8—41no—
530C2×D8—41no—
531C2×D8—41no—
532C2×D8—41no—
533C2×D8—41no—
534C2×M16—22no—
535C2×M16—41no—
536C2×M16—41no—
537C22×C8—22no—
538C22×C8—41no—
539C22×C8—41no—
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C4⋊Q8—22no—
549C4⋊Q8—22no—
550C4⋊Q8—41no—
551C4⋊Q8—41no—
552#127—22no—
553#127—22no—
554#127—22no—
555#127—41no—
556#127—44no—
557#126—44no—
558#125—22no—
559#125—22no—
560#125—41no—
561#125#4114yes—
562#124—24no—
563#124—44no—
564#124—44no—
565#124—44no—
566#124—82no—
567#123—44no—
568#123—44no—
569#123—44no—
570#123—44no—
571#123—44no—
572#123—82no—
573#123—82no—
574C22⋊Q8—44no—
575C22⋊Q8—44no—
576C22⋊Q8—44no—
577C22⋊Q8—82no—
578#121—22no—
579#121—22no—
580#121—22no—
581#121—22no—
582#121—22no—
583#121—22no—
584#121—41no—
585#121—41no—
586#121—41no—
587#121—41no—
588#121—41no—
589#121—41no—
590#121—44no—
591#121—44no—
592#121—41no—
593#121—41no—
594#121—41no—
595#121—41no—
596#121—82no—
597C4×Q8—22no—
598C4×Q8—22no—
599C4×Q8—44no—
600C4×Q8—44no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—22no—
608C4×D4—22no—
609C4×D4—41no—
610C4×D4—41no—
611C4×D4—44no—
612C4×D4—41no—
613C4×D4—41no—
614C4×D4—41no—
615C4×D4—41no—
616C4×D4—44no—
617C4×D4—44no—
618C4×D4—44no—
619C4×D4—44no—
620C4×D4—82no—
621C4×D4—82no—
622C4×D4—82no—
623C4×D4—82no—
624#117—22no—
625#117—41no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—22no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—41no—
653C2×C4⋊C4—44no—
654C2×C4⋊C4—41no—
655C2×C4⋊C4—41no—
656C2×C4⋊C4—41no—
657C2×C4⋊C4—41no—
658C2×C4⋊C4C2×D411yescharacteristic
659C2×C4⋊C4C2×D411yescharacteristic
660C2×C4⋊C4C2×D411yescharacteristic
661C2×C4⋊C4C2×D411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
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—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C42—21no—
724C2×C42—21no—
725C2×C42—21no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—21no—
729C2×C42—21no—
730C2×C42C2×D411yescharacteristic
731C2×C42C2×D411yescharacteristic
732C2×C42C2×D411yescharacteristic
733C2×C42C2×D411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739#107—22no—
740#107—41no—
741#106—22no—
742#106—41no—
743C4⋊C8—22no—
744C4⋊C8—22no—
745C4⋊C8—41no—
746C4⋊C8—41no—
747#102—22no—
748#102—22no—
749#102—22no—
750#102—22no—
751#102—22no—
752#102—22no—
753#102—22no—
754#102—22no—
755#102—22no—
756#102—41no—
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—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770#102#4114yes—
771C22⋊C8—41no—
772C22⋊C8—41no—
773C22⋊C8—41no—
774C22⋊C8—41no—
775C22⋊C8—41no—
776C22⋊C8—41no—
777#97—22no—
778#97—22no—
779#97—41no—
780#97—41no—
781#97—41no—
782C4×C8—22no—
783C4×C8—41no—
784C4×C8—41no—
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#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811C24—21no—
812C24—21no—
813C24—21no—
814C24—21no—
815C24C22×D411yescharacteristic
816C24C22×D411yescharacteristic
817C2×Q8—22no—
818C2×Q8—22no—
819C2×Q8—41no—
820C2×Q8—42no—
821C2×Q8—42no—
822C2×Q8—42no—
823C2×Q8—81no—
824C2×Q8—81no—
825C2×Q8—81no—
826C2×D4—22no—
827C2×D4—22no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—41no—
852C2×D4—42no—
853C2×D4—42no—
854C2×D4—42no—
855C2×D4—42no—
856C2×D4—42no—
857C2×D4—42no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—42no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—81no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4—81no—
876C2×D4—81no—
877C2×D4—81no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4—81no—
888C2×D4C2×#4112yes—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—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—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—42no—
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—81no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
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×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C2511yescharacteristic
953D8—82no—
954D8—82no—
955D8—82no—
956D8—82no—
957M16—82no—
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×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—82no—
982C2×C8C2×#4112yes—
983C4⋊C4—24no—
984C4⋊C4—24no—
985C4⋊C4—22no—
986C4⋊C4—22no—
987C4⋊C4—22no—
988C4⋊C4—22no—
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—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4C2×#4112yes—
1034C4⋊C4C2×#4112yes—
1035C4⋊C4C2×#4112yes—
1036C22⋊C4—22no—
1037C22⋊C4—22no—
1038C22⋊C4—22no—
1039C22⋊C4—22no—
1040C22⋊C4—22no—
1041C22⋊C4—22no—
1042C22⋊C4—22no—
1043C22⋊C4—41no—
1044C22⋊C4—41no—
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—42no—
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—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
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⋊C4AGL(1,ℤ/8)14yes—
1085C42—22no—
1086C42—22no—
1087C42—21no—
1088C42—21no—
1089C42—21no—
1090C42—21no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—41no—
1096C42—41no—
1097C42—42no—
1098C42—42no—
1099C42—42no—
1100C42—42no—
1101C42—42no—
1102C42—42no—
1103C42—81no—
1104C42C2×#4112yes—
1105C42H(5,𝔽2)12yes—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—22no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23C2×AGL(1,ℤ/8)12yes—
1148C23C23×D411yescharacteristic
1149Q8—44no—
1150Q8—84no—
1151Q8—162no—
1152D4—22no—
1153D4—22no—
1154D4—44no—
1155D4—41no—
1156D4—41no—
1157D4—41no—
1158D4—41no—
1159D4—41no—
1160D4—41no—
1161D4—41no—
1162D4—41no—
1163D4—41no—
1164D4—41no—
1165D4—41no—
1166D4—41no—
1167D4—41no—
1168D4—41no—
1169D4—84no—
1170D4—84no—
1171D4—84no—
1172D4—84no—
1173D4—84no—
1174D4—84no—
1175D4—84no—
1176D4—84no—
1177D4—162no—
1178D4—162no—
1179D4—162no—
1180D4—162no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—22no—
1201C2×C4—21no—
1202C2×C4—22no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—22no—
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—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—84no—
1257C2×C4—162no—
1258C2×C4—162no—
1259C2×C4—162no—
1260C2×C4—162no—
1261C2×C4—162no—
1262C2×C4—162no—
1263C2×C4—162no—
1264C2×C4—162no—
1265C2×C4#54612yes—
1266C2×C4#54612yes—
1267C2×C4C2×AGL(1,ℤ/8)12yes—
1268C2×C4C2×AGL(1,ℤ/8)12yes—
1269C2×C4#57612yes—
1270C2×C4C22×#4111yescharacteristic
1271C2×C4C22×#4111yescharacteristic
1272C2×C4C2×H(5,𝔽2)11yescharacteristic
1273C2×C4#58511yescharacteristic
1274C2×C4#58511yescharacteristic
1275C2×C4#58511yescharacteristic
1276C8—22no—
1277C8—41no—
1278C8—41no—
1279C8—41no—
1280C8—41no—
1281C8—41no—
1282C8—41no—
1283C8—41no—
1284C22—22no—
1285C22—22no—
1286C22—22no—
1287C22—41no—
1288C22—41no—
1289C22—41no—
1290C22—41no—
1291C22—41no—
1292C22—42no—
1293C22—41no—
1294C22—41no—
1295C22—42no—
1296C22—41no—
1297C22—42no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—81no—
1322C22—81no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22C2×#54611yescharacteristic
1327C22D4×#4111yescharacteristic
1328C22#350011yescharacteristic
1329C22C22×AGL(1,ℤ/8)11yescharacteristic
1330C22C2×#57611yescharacteristic
1331C22#358511yescharacteristic
1332C22#358611yescharacteristic
1333C4—22no—
1334C4—22no—
1335C4—22no—
1336C4—22no—
1337C4—22no—
1338C4—42no—
1339C4—41no—
1340C4—41no—
1341C4—42no—
1342C4—41no—
1343C4—41no—
1344C4—41no—
1345C4—41no—
1346C4—41no—
1347C4—42no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4—81no—
1357C4#348011yescharacteristic
1358C4#351411yescharacteristic
1359C4#352411yescharacteristic
1360C4#356211yescharacteristic
1361C2—42no—
1362C2—81no—
1363C2—82no—
1364C2—161no—
1365C2—161no—
1366C2—161no—
1367C2#5941711yescharacteristic
1368C2#6116111yescharacteristic
1369C2#6120511yescharacteristic
1370C2#6145111yescharacteristic
1371C2#6152311yescharacteristic
1372C2#6253511yescharacteristic
1373C2#6257411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#124 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59657C2semidirect
2. #59641C2semidirect
3. #31834C2semidirect
4. #31834C2semidirect
5. #31740C2semidirect
6. #31739C2semidirect
7. #29280C2semidirect
8. #28999C2semidirect
9. #28983C2semidirect
10. #28921C2semidirect
11. #28907C2semidirect
12. #28156C2semidirect
13. #27709C2semidirect
14. #27695C2semidirect
15. #26738C2semidirect
16. #26737C2semidirect
17. #26684C2semidirect
18. #26673C2semidirect
19. #25946C2semidirect
20. #25581C2semidirect
21. #25396C2semidirect
22. #25304C2semidirect
23. #25002C2semidirect
24. #24977C2semidirect
25. #23143C2semidirect
26. #23132C2semidirect
27. #22522C2semidirect
28. #22493C2semidirect
29. #21656C2semidirect
30. #21646C2semidirect
31. #21632C2semidirect

Maximal subgroups

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

subgroupindex
#596572
#596412
#318342
#317402
#317392
#292802
#289992
#289832
#289212
#289072
#281562
#277092
#276952
#267382
#267372
#266842
#266732
#259462
#255812
#253962
#253042
#250022
#249772
#231432
#231322
#225222
#224932
#216562
#216462
#216322