Finite Group Databasebeta

← #6509350

Subgroups — #6509350

Order 512.

1613 conjugacy classes of subgroups.

The subgroup lattice has 1322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35229C211yesmaximal, characteristic, complemented
2#34478C211yesmaximal, characteristic, complemented
3#29545C211yesmaximal, characteristic, complemented
4#29424C211yesmaximal, characteristic, complemented
5#29406C211yesmaximal, characteristic, complemented
6#29380C211yesmaximal, characteristic, complemented
7#28215C211yesmaximal, characteristic, complemented
8#28126C211yesmaximal, characteristic, complemented
9#27638C211yesmaximal, characteristic, complemented
10#27591C211yesmaximal, characteristic, complemented
11#27520C211yesmaximal, characteristic, complemented
12#27493C211yesmaximal, characteristic, complemented
13#27360C211yesmaximal, characteristic, complemented
14#27229C211yesmaximal, characteristic, complemented
15#27105C211yesmaximal, characteristic, complemented
16#27072C211yesmaximal, characteristic, complemented
17#26794C211yesmaximal, characteristic, complemented
18#26763C211yesmaximal, characteristic, complemented
19#26361C211yesmaximal, characteristic, complemented
20#26153C211yesmaximal, characteristic, complemented
21#25977C211yesmaximal, characteristic, complemented
22#25221C211yesmaximal, characteristic, complemented
23#24962C211yesmaximal, characteristic, complemented
24#24542C211yesmaximal, characteristic, complemented
25#24444C211yesmaximal, characteristic
26#24048C211yesmaximal, characteristic, complemented
27#22190C211yesmaximal, characteristic, complemented
28#22045C211yesmaximal, characteristic, complemented
29#21999C211yesmaximal, characteristic, complemented
30C4×#481C211yesmaximal, characteristic, complemented
31#21059C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#481C2211yescharacteristic
34C2×#482C2211yescharacteristic
35C2×#479C2211yescharacteristic, complemented
36C2×#478C2211yescharacteristic
37C2×#469C2211yescharacteristic
38C2×#449C2211yescharacteristic
39C2×#447C2211yescharacteristic
40C2×#428C2211yescharacteristic, complemented
41C2×#417C2211yescharacteristic
42C2×#417C2211yescharacteristic
43#2854—21no—
44#2853—21no—
45#2654—21no—
46#2651—21no—
47#2522—21no—
48#2516—21no—
49#2513C2211yescharacteristic, complemented
50#2507C2211yescharacteristic, complemented
51#2501C2211yescharacteristic, complemented
52#2497C2211yescharacteristic
53#2490C2211yescharacteristic
54#2486C2211yescharacteristic
55#2442C2211yescharacteristic, complemented
56#2425—21no—
57#2419—21no—
58#2416C2211yescharacteristic
59#2377—21no—
60#2375—21no—
61#2374—21no—
62#2367C2211yescharacteristic
63#2363C2211yescharacteristic
64#2362C2211yescharacteristic
65#2354C2211yescharacteristic
66#2354C2211yescharacteristic
67#2342—21no—
68#2341C2211yescharacteristic
69D4×C22⋊C4C2211yescharacteristic
70#2335—21no—
71#2330C2211yescharacteristic, complemented
72#2326C2211yescharacteristic
73#2324—21no—
74#2324C2211yescharacteristic
75#2323C2211yescharacteristic
76#2321—21no—
77#2319C2211yescharacteristic
78#2319C2211yescharacteristic, complemented
79#2314C2211yescharacteristic
80#2312—21no—
81#2309C2211yescharacteristic
82C4×#121C2211yescharacteristic
83C4×#121C2211yescharacteristic, complemented
84#2297C2211yescharacteristic
85#2290C2211yescharacteristic
86C2×C4×C4⋊C4C2211yescharacteristic, complemented
87#2099C2211yescharacteristic, complemented
88#2094C2211yescharacteristic, complemented
89#2092C2211yescharacteristic
90#2092C2211yescharacteristic
91#2086C2211yescharacteristic, complemented
92#2084C2211yescharacteristic, complemented
93#2084C2211yescharacteristic, complemented
94#2083C2211yescharacteristic, complemented
95#2077C2211yescharacteristic
96#2077C2211yescharacteristic
97#2076C2211yescharacteristic
98#2071C2211yescharacteristic
99#2071C2211yescharacteristic
100#2071C2211yescharacteristic
101#2067C2211yescharacteristic
102#2065C2211yescharacteristic
103#2065C2211yescharacteristic
104#2065C2211yescharacteristic, complemented
105#2059C2211yescharacteristic, complemented
106#2054C2211yescharacteristic
107#2054C2211yescharacteristic
108#2054C2211yescharacteristic
109#2042C2211yescharacteristic
110#2042C2211yescharacteristic
111#2042C2211yescharacteristic
112#2035C2211yescharacteristic
113#2035C2211yescharacteristic
114#2035C2211yescharacteristic
115#2034C2211yescharacteristic
116#2025C2211yescharacteristic
117#2012C2211yescharacteristic
118#2000C2211yescharacteristic
119#1970C2211yescharacteristic
120#1968C2211yescharacteristic, complemented
121#1949C2211yescharacteristic, complemented
122#1948C2211yescharacteristic, complemented
123#1934C2211yescharacteristic
124#1933C2211yescharacteristic, complemented
125#1928C2211yescharacteristic, complemented
126#1928C2211yescharacteristic, complemented
127#1928C2211yescharacteristic, complemented
128#1927C2211yescharacteristic, complemented
129#1927C2211yescharacteristic, complemented
130#1926C2211yescharacteristic
131#1926C2211yescharacteristic
132#1926C2211yescharacteristic
133#1926C2211yescharacteristic
134#1926C2211yescharacteristic
135#1926C2211yescharacteristic, complemented
136#1925C2211yescharacteristic
137#1925C2211yescharacteristic
138#1925C2211yescharacteristic
139#1925C2211yescharacteristic, complemented
140#1925C2211yescharacteristic, complemented
141#1923C2211yescharacteristic
142#1923C2211yescharacteristic
143#1920C2211yescharacteristic, complemented
144#1920C2211yescharacteristic, complemented
145#1920C2211yescharacteristic, complemented
146#1919C2211yescharacteristic, complemented
147#1919C2211yescharacteristic, complemented
148#1919C2211yescharacteristic, complemented
149#1919C2211yescharacteristic, complemented
150#1918C2211yescharacteristic, complemented
151#1916C2211yescharacteristic, complemented
152#1916C2211yescharacteristic, complemented
153#1895C2211yescharacteristic
154#1895C2211yescharacteristic, complemented
155#1880C2211yescharacteristic, complemented
156#1880C2211yescharacteristic, complemented
157#1879C2211yescharacteristic
158#1879C2211yescharacteristic
159#1879C2211yescharacteristic
160#1879C2211yescharacteristic
161#1879C2211yescharacteristic
162#1877C2211yescharacteristic, complemented
163#1875C2211yescharacteristic, complemented
164#1874C2211yescharacteristic
165#1870C2211yescharacteristic
166#1870C2211yescharacteristic
167#1865C2211yescharacteristic, complemented
168#1865C2211yescharacteristic, complemented
169#1864C2211yescharacteristic
170#1864C2211yescharacteristic
171#1864C2211yescharacteristic
172#1864C2211yescharacteristic
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic, complemented
175#1854C2211yescharacteristic
176#1854C2211yescharacteristic
177#1854C2211yescharacteristic, complemented
178#1853C2211yescharacteristic, complemented
179#1851C2211yescharacteristic, complemented
180#1851C2211yescharacteristic, complemented
181#1840C2211yescharacteristic, complemented
182#1832C2211yescharacteristic, complemented
183#1825C2211yescharacteristic
184#1824C2211yescharacteristic, complemented
185#1818C2211yescharacteristic
186#1809C2211yescharacteristic, complemented
187#1805C2211yescharacteristic, complemented
188#1803C2211yescharacteristic, complemented
189#1803C2211yescharacteristic, complemented
190#1802C2211yescharacteristic
191#1798C2211yescharacteristic
192#1788C2211yescharacteristic
193#1786C2211yescharacteristic
194#1786C2211yescharacteristic
195#1786C2211yescharacteristic
196C4×#106C2211yescharacteristic, complemented
197C4×#106C2211yescharacteristic, complemented
198C4×#102C2211yescharacteristic
199C4×#102C2211yescharacteristic
200C4×C22⋊C8C2211yescharacteristic, complemented
201#1736C2211yescharacteristic, complemented
202#1728C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210#546—24no—
211#546—24no—
212C2×#125C2311yescharacteristic
213C2×#124C2311yescharacteristic
214C2×#123—21no—
215C2×#123—21no—
216C2×#123—21no—
217C2×#123—21no—
218C2×C22⋊Q8C2311yescharacteristic
219C2×#121—21no—
220C2×#121—21no—
221C2×#121C2311yescharacteristic
222C2×#121C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×#120—21no—
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×D4—21no—
228C2×C4×D4—21no—
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×#117—21no—
235C2×#117C2311yescharacteristic
236C2×#117C2311yescharacteristic
237C2×#117C2311yescharacteristic
238C22×C4⋊C4C2311yescharacteristic
239C22×C4⋊C4C2311yescharacteristic
240C22×C22⋊C4—21no—
241C22×C22⋊C4—21no—
242C22×C42—21no—
243C22×C42C2311yescharacteristic
244#482—42no—
245#481—24no—
246#479—42no—
247#478—42no—
248#469—24no—
249#449—24no—
250#447—42no—
251#428—42no—
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269#417—24no—
270#417—42no—
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
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×C4×C8C2311yescharacteristic
304C2×C4×C8C2311yescharacteristic
305#400—21no—
306#400—21no—
307#399—21no—
308#399—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#397—21no—
314#397—21no—
315#397—21no—
316#397—21no—
317#396—21no—
318#396—21no—
319#394—21no—
320#394—21no—
321#391C2311yescharacteristic
322#391C2311yescharacteristic
323#390—21no—
324#390—21no—
325#390—21no—
326#390—21no—
327#390—21no—
328#390—21no—
329#390—21no—
330#390—21no—
331#390C2311yescharacteristic
332#390C2311yescharacteristic
333#390C2311yescharacteristic
334#390C2311yescharacteristic
335#390C2311yescharacteristic
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#389—21no—
342#389—21no—
343#389—21no—
344#389—21no—
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#388—21no—
354#388—21no—
355#388—21no—
356#388—21no—
357#388—21no—
358#388—21no—
359#388—21no—
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
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#388—21no—
377#388—21no—
378#388—21no—
379#388D411yescharacteristic
380#388D411yescharacteristic
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387D411yescharacteristic
390#387D411yescharacteristic
391#386—21no—
392#386—21no—
393#386—21no—
394#386—21no—
395#386—21no—
396#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#386D411yescharacteristic
401#386D411yescharacteristic
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385D411yescharacteristic
408#385D411yescharacteristic
409#384C2311yescharacteristic
410#384C2311yescharacteristic
411#384C2311yescharacteristic
412#382C2311yescharacteristic
413#381—21no—
414#381—21no—
415#381—21no—
416#380—21no—
417#380—21no—
418#380—21no—
419#380—21no—
420#380—21no—
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#379—21no—
428#379—21no—
429#379—21no—
430C4×C4⋊C4—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4C2311yescharacteristic
451C4×C22⋊C4C2311yescharacteristic
452#376C2311yescharacteristic
453C2×#95—21no—
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#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25—21no—
491C2×#41—22no—
492C2×#41—41no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41#4114yes—
497C22×Q8C2411yescharacteristic
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—22no—
501C22×D4—22no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—41no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4C2×D411yescharacteristic
510C22×D4C2411yescharacteristic
511C22×D4C2411yescharacteristic
512C22×D4C2411yescharacteristic
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4C2×D411yescharacteristic
521C23×C4C2×D411yescharacteristic
522C23×C4C2411yescharacteristic
523C23×C4C2411yescharacteristic
524C2×SD16—22no—
525C2×SD16—41no—
526C2×SD16—41no—
527C2×D8—22no—
528C2×D8—22no—
529C2×D8—41no—
530C2×D8—41no—
531C2×D8—41no—
532C2×D8—41no—
533C2×M16—22no—
534C2×M16—22no—
535C2×M16—41no—
536C2×M16—41no—
537C2×M16—41no—
538C2×M16—41no—
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547#125—22no—
548#125—41no—
549#124—22no—
550#124—22no—
551#123—28no—
552#123—82no—
553#123—82no—
554#123—82no—
555C22⋊Q8—22no—
556C22⋊Q8—22no—
557#121—28no—
558#121—22no—
559#121—22no—
560#121—22no—
561#121—22no—
562#121—41no—
563#121—82no—
564#121#4114yes—
565#120—28no—
566C4×Q8—41no—
567C4×Q8—41no—
568C4×Q8—41no—
569C4×Q8—41no—
570C4×D4—22no—
571C4×D4—22no—
572C4×D4—22no—
573C4×D4—22no—
574C4×D4—41no—
575C4×D4—41no—
576C4×D4—41no—
577C4×D4—41no—
578C4×D4—41no—
579C4×D4—41no—
580C4×D4—82no—
581C4×D4—82no—
582#117—41no—
583#117—41no—
584#117—41no—
585#117—41no—
586#117—41no—
587#117—41no—
588#117—82no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—22no—
592C2×C4⋊C4—22no—
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—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—41no—
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C22⋊C4—28no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
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—82no—
671C2×C22⋊C4C2×D411yescharacteristic
672C2×C22⋊C4C2×D411yescharacteristic
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C22⋊C4C2×D411yescharacteristic
675C2×C22⋊C4C2×D411yescharacteristic
676C2×C22⋊C4C2×D411yescharacteristic
677C2×C22⋊C4C2×D411yescharacteristic
678C2×C22⋊C4C2×D411yescharacteristic
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—21no—
682C2×C42—21no—
683C2×C42—21no—
684C2×C42—21no—
685C2×C42—21no—
686C2×C42—21no—
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—41no—
692C2×C42—41no—
693C2×C42—82no—
694C2×C42C2×D411yescharacteristic
695C2×C42C2×D411yescharacteristic
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701#107—22no—
702#107—41no—
703#107—41no—
704#107—41no—
705#106—22no—
706#106—22no—
707#106—22no—
708#106—22no—
709#106—22no—
710#106—41no—
711#106—41no—
712#106—41no—
713#106—41no—
714C4⋊C8—41no—
715C4⋊C8—41no—
716C4⋊C8—41no—
717C4⋊C8—41no—
718#103—22no—
719#103—22no—
720#103—22no—
721#103—22no—
722#103—41no—
723#103—41no—
724#103—41no—
725#102—22no—
726#102—22no—
727#102—22no—
728#102—22no—
729#102—22no—
730#102—22no—
731#102—22no—
732#102—22no—
733#102—22no—
734#102—41no—
735#102—41no—
736#102—41no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743#102—41no—
744C22⋊C8—22no—
745C22⋊C8—22no—
746C22⋊C8—41no—
747C22⋊C8—41no—
748C22⋊C8—41no—
749C22⋊C8—41no—
750C4×C8—41no—
751C4×C8—41no—
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#95—21no—
778#95—21no—
779#95—21no—
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790C24—24no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—81no—
795C24—81no—
796C24—81no—
797C24—81no—
798C24—81no—
799C24—81no—
800C24C22×D411yescharacteristic
801C24C22×D411yescharacteristic
802#41—44no—
803#41—44no—
804#41—82no—
805#41—82no—
806C2×Q8—21no—
807C2×Q8—21no—
808C2×Q8—21no—
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8C2×#4112yes—
812C2×D4—24no—
813C2×D4—22no—
814C2×D4—24no—
815C2×D4—24no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—41no—
833C2×D4—41no—
834C2×D4—42no—
835C2×D4—42no—
836C2×D4—42no—
837C2×D4—42no—
838C2×D4—81no—
839C2×D4—81no—
840C2×D4—82no—
841C2×D4—82no—
842C2×D4—82no—
843C2×D4—82no—
844C2×D4—81no—
845C2×D4—81no—
846C2×D4—81no—
847C2×D4—81no—
848C2×D4—81no—
849C2×D4—81no—
850C2×D4C2×#4112yes—
851C2×D4C2×#4112yes—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—24no—
860C22×C4—22no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—24no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—41no—
879C22×C4—41no—
880C22×C4—41no—
881C22×C4—41no—
882C22×C4—41no—
883C22×C4—42no—
884C22×C4—42no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—42no—
888C22×C4—42no—
889C22×C4—42no—
890C22×C4—81no—
891C22×C4—81no—
892C22×C4—81no—
893C22×C4—81no—
894C22×C4—81no—
895C22×C4—81no—
896C22×C4—81no—
897C22×C4—81no—
898C22×C4—81no—
899C22×C4—81no—
900C22×C4—81no—
901C22×C4—81no—
902C22×C4C22×D411yescharacteristic
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
914C22×C4C2×#4112yes—
915C22×C4C2×#4112yes—
916C22×C4C2511yescharacteristic
917SD16—82no—
918D8—82no—
919D8—82no—
920M16—44no—
921M16—82no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C4⋊C4—24no—
947C4⋊C4—22no—
948C4⋊C4—22no—
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—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—41no—
972C4⋊C4—41no—
973C4⋊C4—41no—
974C4⋊C4—42no—
975C4⋊C4—42no—
976C4⋊C4—42no—
977C4⋊C4—42no—
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⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4C2×#4112yes—
995C4⋊C4H(5,𝔽2)12yes—
996C22⋊C4—24no—
997C22⋊C4—24no—
998C22⋊C4—24no—
999C22⋊C4—24no—
1000C22⋊C4—22no—
1001C22⋊C4—22no—
1002C22⋊C4—24no—
1003C22⋊C4—22no—
1004C22⋊C4—41no—
1005C22⋊C4—41no—
1006C22⋊C4—41no—
1007C22⋊C4—41no—
1008C22⋊C4—41no—
1009C22⋊C4—42no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
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—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C42—21no—
1043C42—21no—
1044C42—21no—
1045C42—21no—
1046C42—21no—
1047C42—21no—
1048C42—21no—
1049C42—21no—
1050C42—21no—
1051C42—21no—
1052C42—41no—
1053C42—41no—
1054C42—42no—
1055C42—81no—
1056C42—81no—
1057C42—81no—
1058C42—81no—
1059C42—81no—
1060C42—81no—
1061C42—81no—
1062C42—81no—
1063C42—81no—
1064C42—81no—
1065C42—81no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—21no—
1075C23—21no—
1076C23—22no—
1077C23—22no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—84no—
1101C23—84no—
1102C23—84no—
1103C23—162no—
1104C23—162no—
1105C23—162no—
1106C23—162no—
1107C23#52512yes—
1108C23C23×D411yescharacteristic
1109Q8—22no—
1110Q8—22no—
1111Q8—41no—
1112Q8—41no—
1113D4—22no—
1114D4—22no—
1115D4—22no—
1116D4—22no—
1117D4—41no—
1118D4—41no—
1119D4—41no—
1120D4—41no—
1121D4—41no—
1122D4—41no—
1123D4—41no—
1124D4—41no—
1125D4—82no—
1126D4—84no—
1127D4—84no—
1128D4—84no—
1129D4—84no—
1130D4—162no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—22no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—44no—
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—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—84no—
1214C2×C4—84no—
1215C2×C4—82no—
1216C2×C4—84no—
1217C2×C4—84no—
1218C2×C4—162no—
1219C2×C4—162no—
1220C2×C4—162no—
1221C2×C4#52512yes—
1222C2×C4#57712yes—
1223C2×C4C22×#4111yescharacteristic
1224C2×C4C22×#4111yescharacteristic
1225C2×C4C2×H(5,𝔽2)11yescharacteristic
1226C2×C4#58511yescharacteristic
1227C2×C4#58511yescharacteristic
1228C2×C4#58511yescharacteristic
1229C8—41no—
1230C8—41no—
1231C8—41no—
1232C8—41no—
1233C8—41no—
1234C8—41no—
1235C8—41no—
1236C8—41no—
1237C22—22no—
1238C22—22no—
1239C22—22no—
1240C22—41no—
1241C22—41no—
1242C22—41no—
1243C22—41no—
1244C22—41no—
1245C22—41no—
1246C22—41no—
1247C22—41no—
1248C22—41no—
1249C22—42no—
1250C22—42no—
1251C22—41no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—41no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—168no—
1273C22C2×#52511yescharacteristic
1274C22#348511yescharacteristic
1275C22#348811yescharacteristic
1276C22C2×#57711yescharacteristic
1277C22#358411yescharacteristic
1278C22#358511yescharacteristic
1279C22#358511yescharacteristic
1280C4—22no—
1281C4—22no—
1282C4—41no—
1283C4—41no—
1284C4—41no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—42no—
1289C4—41no—
1290C4—41no—
1291C4—42no—
1292C4—41no—
1293C4—41no—
1294C4—42no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C4—81no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4#349111yescharacteristic
1306C4#350511yescharacteristic
1307C4#351411yescharacteristic
1308C4#352111yescharacteristic
1309C2—42no—
1310C2—81no—
1311C2—82no—
1312C2—82no—
1313C2—161no—
1314C2#3544911yescharacteristic
1315C2#6056811yescharacteristic
1316C2#6057111yescharacteristic
1317C2#6174611yescharacteristic
1318C2#6176211yescharacteristic
1319C2#6202811yescharacteristic
1320C2#6204511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#24444C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #35229C2semidirect
2. #34478C2semidirect
3. #29545C2semidirect
4. #29424C2semidirect
5. #29406C2semidirect
6. #29380C2semidirect
7. #28215C2semidirect
8. #28126C2semidirect
9. #27638C2semidirect
10. #27591C2semidirect
11. #27520C2semidirect
12. #27493C2semidirect
13. #27360C2semidirect
14. #27229C2semidirect
15. #27105C2semidirect
16. #27072C2semidirect
17. #26794C2semidirect
18. #26763C2semidirect
19. #26361C2semidirect
20. #26153C2semidirect
21. #25977C2semidirect
22. #25221C2semidirect
23. #24962C2semidirect
24. #24542C2semidirect
26. #24048C2semidirect
27. #22190C2semidirect
28. #22045C2semidirect
29. #21999C2semidirect
30. C4×#481C2semidirect
31. #21059C2semidirect
35. C2×#479C22semidirect
40. C2×#428C22semidirect
49. #2513C22semidirect
50. #2507C22semidirect
51. #2501C22semidirect
55. #2442C22semidirect
71. #2330C22semidirect
78. #2319C22semidirect
83. C4×#121C22semidirect
86. C2×C4×C4⋊C4C22semidirect
87. #2099C22semidirect
88. #2094C22semidirect
91. #2086C22semidirect
92. #2084C22semidirect
93. #2084C22semidirect
94. #2083C22semidirect
104. #2065C22semidirect
105. #2059C22semidirect
120. #1968C22semidirect
121. #1949C22semidirect
122. #1948C22semidirect
124. #1933C22semidirect
125. #1928C22semidirect
126. #1928C22semidirect
127. #1928C22semidirect
128. #1927C22semidirect
129. #1927C22semidirect
135. #1926C22semidirect
139. #1925C22semidirect
140. #1925C22semidirect
143. #1920C22semidirect
144. #1920C22semidirect
145. #1920C22semidirect
146. #1919C22semidirect
147. #1919C22semidirect
148. #1919C22semidirect
149. #1919C22semidirect
150. #1918C22semidirect
151. #1916C22semidirect
152. #1916C22semidirect
154. #1895C22semidirect
155. #1880C22semidirect
156. #1880C22semidirect
162. #1877C22semidirect
163. #1875C22semidirect
167. #1865C22semidirect
168. #1865C22semidirect
174. #1864C22semidirect
177. #1854C22semidirect
178. #1853C22semidirect
179. #1851C22semidirect
180. #1851C22semidirect
181. #1840C22semidirect
182. #1832C22semidirect
184. #1824C22semidirect
186. #1809C22semidirect
187. #1805C22semidirect
188. #1803C22semidirect
189. #1803C22semidirect
196. C4×#106C22semidirect
197. C4×#106C22semidirect
200. C4×C22⋊C8C22semidirect
201. #1736C22semidirect
202. #1728C22semidirect

Maximal subgroups

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

subgroupindex
#352292
#344782
#295452
#294242
#294062
#293802
#282152
#281262
#276382
#275912
#275202
#274932
#273602
#272292
#271052
#270722
#267942
#267632
#263612
#261532
#259772
#252212
#249622
#245422
#244442
#240482
#221902
#220452
#219992
C4×#4812
#210592