Finite Group Databasebeta

← #6589359

Subgroups — #6589359

Order 512.

1758 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#36440C211yesmaximal, characteristic
2#36254C211yesmaximal, characteristic, complemented
3#33208C211yesmaximal, characteristic, complemented
4#33150C211yesmaximal, characteristic, complemented
5#32959C211yesmaximal, characteristic, complemented
6#28862C211yesmaximal, characteristic, complemented
7#28861C211yesmaximal, characteristic, complemented
8#28104C211yesmaximal, characteristic, complemented
9#28104C211yesmaximal, characteristic, complemented
10#27733C211yesmaximal, characteristic, complemented
11#27166C211yesmaximal, characteristic, complemented
12#27158C211yesmaximal, characteristic, complemented
13#27038C211yesmaximal, characteristic, complemented
14#27030C211yesmaximal, characteristic, complemented
15#26096C211yesmaximal, characteristic, complemented
16#25707C211yesmaximal, characteristic, complemented
17#25457C211yesmaximal, characteristic, complemented
18#25344C211yesmaximal, characteristic, complemented
19#25018C211yesmaximal, characteristic, complemented
20#24943C211yesmaximal, characteristic, complemented
21#24935C211yesmaximal, characteristic, complemented
22#24873C211yesmaximal, characteristic, complemented
23#24865C211yesmaximal, characteristic, complemented
24#23071C211yesmaximal, characteristic, complemented
25#22929C211yesmaximal, characteristic, complemented
26#22924C211yesmaximal, characteristic, complemented
27#22709C211yesmaximal, characteristic, complemented
28#22709C211yesmaximal, characteristic, complemented
29#22501C211yesmaximal, characteristic, complemented
30#21487C211yesmaximal, characteristic, complemented
31C2×C4×#102C211yesmaximal, characteristic, complemented
32C2×#553C2211yescharacteristic
33C22×C4×D4C2211yescharacteristic
34C2×#499C2211yescharacteristic, complemented
35C2×#481C2211yescharacteristic
36C2×#482C2211yescharacteristic
37C2×#478C2211yescharacteristic
38C2×#478C2211yescharacteristic
39C2×#436C2211yescharacteristic, complemented
40C2×#435C2211yescharacteristic
41C2×#435C2211yescharacteristic
42C22×#102C2211yescharacteristic
43C22×#102C2211yescharacteristic
44C22×C4×C8C2211yescharacteristic
45#2852—21no—
46#2851C2211yescharacteristic
47#2851C2211yescharacteristic
48#2849—21no—
49#2602—21no—
50#2600—21no—
51#2596—21no—
52#2575—21no—
53#2570C2211yescharacteristic, complemented
54#2566C2211yescharacteristic
55#2562C2211yescharacteristic, complemented
56#2535C2211yescharacteristic
57#2533—21no—
58#2505—21no—
59#2496C2211yescharacteristic, complemented
60#2495C2211yescharacteristic, complemented
61#2487C2211yescharacteristic
62#2487C2211yescharacteristic
63#2480—21no—
64#2479—21no—
65#2466—21no—
66#2456—21no—
67#2444—21no—
68#2424—21no—
69#2422C2211yescharacteristic
70#2420C2211yescharacteristic
71#2408C2211yescharacteristic
72#2408C2211yescharacteristic
73#2370C2211yescharacteristic, complemented
74#2363C2211yescharacteristic
75#2361C2211yescharacteristic
76#2357C2211yescharacteristic
77#2352C2211yescharacteristic
78#2352C2211yescharacteristic
79#2352C2211yescharacteristic, complemented
80D4×C4⋊C4C2211yescharacteristic
81D4×C4⋊C4C2211yescharacteristic
82#2346C2211yescharacteristic, complemented
83#2344C2211yescharacteristic, complemented
84C4×#121C2211yescharacteristic
85C4×#120—21no—
86#2290—21no—
87C2×C4×C4⋊C4C2211yescharacteristic
88#2101C2211yescharacteristic, complemented
89#2099C2211yescharacteristic, complemented
90#2094C2211yescharacteristic
91#2092C2211yescharacteristic
92#2085C2211yescharacteristic, complemented
93#2084C2211yescharacteristic, complemented
94#2077C2211yescharacteristic, complemented
95#2077C2211yescharacteristic, complemented
96#2077C2211yescharacteristic, complemented
97#2075C2211yescharacteristic, complemented
98#2073C2211yescharacteristic
99#2071C2211yescharacteristic
100#2067C2211yescharacteristic
101#2067C2211yescharacteristic
102#2067C2211yescharacteristic
103#2067C2211yescharacteristic
104#2034C2211yescharacteristic
105#2034C2211yescharacteristic
106#2034C2211yescharacteristic
107#2033C2211yescharacteristic
108#2033C2211yescharacteristic
109#2033C2211yescharacteristic
110#2033C2211yescharacteristic
111#2033C2211yescharacteristic
112#1991C2211yescharacteristic, complemented
113#1991C2211yescharacteristic, complemented
114#1989C2211yescharacteristic, complemented
115#1989C2211yescharacteristic, complemented
116#1954C2211yescharacteristic, complemented
117#1949C2211yescharacteristic, complemented
118#1949C2211yescharacteristic, complemented
119#1949C2211yescharacteristic, complemented
120#1949C2211yescharacteristic, complemented
121#1947C2211yescharacteristic, complemented
122#1947C2211yescharacteristic, complemented
123#1942C2211yescharacteristic, complemented
124#1942C2211yescharacteristic, complemented
125#1941C2211yescharacteristic, complemented
126#1941C2211yescharacteristic, complemented
127#1939C2211yescharacteristic, complemented
128#1936C2211yescharacteristic
129#1936C2211yescharacteristic
130#1936C2211yescharacteristic
131#1936C2211yescharacteristic
132#1926C2211yescharacteristic
133#1926C2211yescharacteristic
134#1926C2211yescharacteristic
135#1925C2211yescharacteristic
136#1923C2211yescharacteristic, complemented
137#1923C2211yescharacteristic, complemented
138#1920C2211yescharacteristic, complemented
139#1920C2211yescharacteristic, complemented
140#1920C2211yescharacteristic, complemented
141#1920C2211yescharacteristic, complemented
142#1919C2211yescharacteristic, complemented
143#1918C2211yescharacteristic, complemented
144#1918C2211yescharacteristic, complemented
145#1918C2211yescharacteristic, complemented
146#1895C2211yescharacteristic
147#1895C2211yescharacteristic
148#1895C2211yescharacteristic
149#1895C2211yescharacteristic
150#1875C2211yescharacteristic
151#1874C2211yescharacteristic
152#1869C2211yescharacteristic
153#1869C2211yescharacteristic
154#1864C2211yescharacteristic
155#1864C2211yescharacteristic
156#1862C2211yescharacteristic
157#1862C2211yescharacteristic
158#1854C2211yescharacteristic, complemented
159#1854C2211yescharacteristic, complemented
160#1854C2211yescharacteristic, complemented
161#1853C2211yescharacteristic
162#1853C2211yescharacteristic
163#1853C2211yescharacteristic, complemented
164#1852C2211yescharacteristic
165#1852C2211yescharacteristic
166#1852C2211yescharacteristic, complemented
167#1852C2211yescharacteristic, complemented
168#1846C2211yescharacteristic, complemented
169#1836C2211yescharacteristic, complemented
170#1836C2211yescharacteristic, complemented
171#1825C2211yescharacteristic, complemented
172#1824C2211yescharacteristic
173#1824C2211yescharacteristic
174#1823C2211yescharacteristic, complemented
175#1809C2211yescharacteristic, complemented
176#1809C2211yescharacteristic, complemented
177#1808C2211yescharacteristic
178#1808C2211yescharacteristic
179#1807C2211yescharacteristic
180#1807C2211yescharacteristic
181#1804C2211yescharacteristic
182#1804C2211yescharacteristic
183#1797C2211yescharacteristic
184#1786C2211yescharacteristic
185#1786C2211yescharacteristic
186#1776C2211yescharacteristic, complemented
187#1776C2211yescharacteristic, complemented
188#1770C2211yescharacteristic, complemented
189C4×#102C2211yescharacteristic
190C4×#102C2211yescharacteristic
191C4×#102C2211yescharacteristic
192C4×#102C2211yescharacteristic
193C4×#102C2211yescharacteristic
194C4×#102C2211yescharacteristic
195C4×#102C2211yescharacteristic
196C4×#102C2211yescharacteristic
197#1753C2211yescharacteristic, complemented
198#1753C2211yescharacteristic, complemented
199#1736C2211yescharacteristic, complemented
200#1736C2211yescharacteristic, complemented
201C2×#340C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C24×C4—21no—
205C22×M16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209#553—24no—
210#553—42no—
211C2×#126—21no—
212C2×#126—21no—
213C2×#125C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×#123—21no—
216C2×#123—21no—
217C2×#121—21no—
218C2×#121D411yescharacteristic
219C2×#121C2311yescharacteristic
220C2×#121C2311yescharacteristic
221C2×#121C2311yescharacteristic
222C2×#121C2311yescharacteristic
223C2×#120—21no—
224C2×#120—21no—
225C2×C4×D4—21no—
226C2×C4×D4—21no—
227C2×C4×D4—21no—
228C2×C4×D4—21no—
229C2×C4×D4—24no—
230C2×C4×D4—21no—
231C2×C4×D4—21no—
232C2×C4×D4—42no—
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×#117—21no—
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C22×C4⋊C4C2311yescharacteristic
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248C22×C22⋊C4—21no—
249C22×C42—21no—
250C22×C42C2311yescharacteristic
251#499—42no—
252#482—24no—
253#481—24no—
254#478—24no—
255#478—42no—
256#436—42no—
257#435—24no—
258#435—24no—
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×#102—24no—
280C2×#102—24no—
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×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×#97C2311yescharacteristic
306C2×#97C2311yescharacteristic
307C2×C4×C8—42no—
308C2×C4×C8C2311yescharacteristic
309C2×C4×C8C2311yescharacteristic
310C2×C4×C8C2311yescharacteristic
311C2×C4×C8C2311yescharacteristic
312#400—21no—
313#400—21no—
314#400—21no—
315#400—21no—
316#400—21no—
317#400—21no—
318#399—21no—
319#399—21no—
320#398—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#396—21no—
327#396—21no—
328#394—21no—
329#394—21no—
330#394—21no—
331#394—21no—
332#394—21no—
333#392—21no—
334#392—21no—
335#392—21no—
336#390—21no—
337#390D411yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#389—21no—
343#389—21no—
344#389—21no—
345#389D411yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
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#388D411yescharacteristic
367#388D411yescharacteristic
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#386—21no—
383#386—21no—
384#386—21no—
385#386—21no—
386#386—21no—
387#386—21no—
388#386—21no—
389#386—21no—
390#386—21no—
391#386—21no—
392#386D411yescharacteristic
393#386D411yescharacteristic
394#385—21no—
395#385—21no—
396#385—21no—
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#385—21no—
408#384C2311yescharacteristic
409#384C2311yescharacteristic
410#383—21no—
411#382—21no—
412#382C2311yescharacteristic
413#382C2311yescharacteristic
414#382C2311yescharacteristic
415#382C2311yescharacteristic
416#381—21no—
417#381—21no—
418#381—21no—
419#380D411yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#379—21no—
433#379—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4—21no—
436C4×C4⋊C4—21no—
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4C2311yescharacteristic
452C4×C22⋊C4C2311yescharacteristic
453#376—21no—
454C2×#95—21no—
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#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C22×D4—22no—
495C22×D4—22no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—22no—
502C22×D4—22no—
503C22×D4—41no—
504C22×D4—41no—
505C22×D4C2×D411yescharacteristic
506C22×D4C2×D411yescharacteristic
507C22×D4C2×D411yescharacteristic
508C22×D4C2411yescharacteristic
509C22×D4C2411yescharacteristic
510C23×C4—21no—
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—44no—
520C23×C4—82no—
521C23×C4—82no—
522C23×C4C2×D411yescharacteristic
523C23×C4C2×D411yescharacteristic
524C23×C4C2411yescharacteristic
525C23×C4C2411yescharacteristic
526C23×C4C2411yescharacteristic
527C2×M16—22no—
528C2×M16—22no—
529C2×M16—41no—
530C2×M16—41no—
531C2×M16—41no—
532C2×M16—41no—
533C22×C8—22no—
534C22×C8—22no—
535C22×C8—41no—
536C22×C8—41no—
537C22×C8—41no—
538C22×C8#4114yes—
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547#126—44no—
548#126—82no—
549#125—22no—
550#125—22no—
551#125—22no—
552#125—22no—
553#123—44no—
554#123—82no—
555#121—22no—
556#121—22no—
557#121—22no—
558#121—22no—
559#121—44no—
560#121—41no—
561#121—41no—
562#121—41no—
563#121—41no—
564#121—42no—
565#120—44no—
566#120—82no—
567C4×D4—22no—
568C4×D4—22no—
569C4×D4—22no—
570C4×D4—22no—
571C4×D4—22no—
572C4×D4—22no—
573C4×D4—22no—
574C4×D4—22no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—44no—
579C4×D4—41no—
580C4×D4—41no—
581C4×D4—44no—
582C4×D4—44no—
583C4×D4—44no—
584C4×D4—82no—
585C4×D4—82no—
586C4×D4#4114yes—
587#117—22no—
588#117—22no—
589#117—41no—
590#117—41no—
591#117—82no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—22no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
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—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—41no—
620C2×C4⋊C4—41no—
621C2×C4⋊C4—41no—
622C2×C4⋊C4—41no—
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—44no—
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×C22⋊C4C2×D411yescharacteristic
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C42—22no—
684C2×C42—22no—
685C2×C42—21no—
686C2×C42—21no—
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—82no—
696C2×C42C2×D411yescharacteristic
697C2×C42C2×D411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702#107—22no—
703#107—22no—
704#107—41no—
705#107—41no—
706#107—41no—
707#107—41no—
708#107—41no—
709#107—41no—
710#106—22no—
711#106—22no—
712#106—22no—
713#106—22no—
714#106—41no—
715#106—41no—
716#106—41no—
717#106—41no—
718C4⋊C8—22no—
719C4⋊C8—22no—
720C4⋊C8—22no—
721C4⋊C8—22no—
722#102—22no—
723#102—22no—
724#102—22no—
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—41no—
734#102—41no—
735#102—41no—
736#102—41no—
737#102#4114yes—
738C22⋊C8—22no—
739C22⋊C8—22no—
740C22⋊C8—22no—
741C22⋊C8—22no—
742C22⋊C8—22no—
743C22⋊C8—22no—
744C22⋊C8—41no—
745C22⋊C8—41no—
746#97—22no—
747#97—22no—
748C4×C8—22no—
749C4×C8—22no—
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#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794C24—21no—
795C24—21no—
796C24—42no—
797C24—42no—
798C24—42no—
799C24—42no—
800C24—42no—
801C24—81no—
802C24—81no—
803C24C22×D411yescharacteristic
804C24C22×D411yescharacteristic
805C24C22×D411yescharacteristic
806C2×D4—28no—
807C2×D4—22no—
808C2×D4—22no—
809C2×D4—22no—
810C2×D4—22no—
811C2×D4—22no—
812C2×D4—22no—
813C2×D4—22no—
814C2×D4—21no—
815C2×D4—21no—
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—44no—
825C2×D4—44no—
826C2×D4—42no—
827C2×D4—42no—
828C2×D4—44no—
829C2×D4—41no—
830C2×D4—41no—
831C2×D4—42no—
832C2×D4—42no—
833C2×D4—42no—
834C2×D4—42no—
835C2×D4—42no—
836C2×D4—42no—
837C2×D4—42no—
838C2×D4—81no—
839C2×D4—81no—
840C2×D4—81no—
841C2×D4—81no—
842C2×D4—81no—
843C2×D4—81no—
844C2×D4C2×#4112yes—
845C2×D4C2×#4112yes—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—22no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—22no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—24no—
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—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
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—42no—
891C22×C4—42no—
892C22×C4—42no—
893C22×C4—42no—
894C22×C4—42no—
895C22×C4—42no—
896C22×C4—81no—
897C22×C4—81no—
898C22×C4—81no—
899C22×C4—81no—
900C22×C4—81no—
901C22×C4—81no—
902C22×C4—816no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C2×#4112yes—
922C22×C42−1+412yes—
923C22×C4C2511yescharacteristic
924M16—82no—
925M16—82no—
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—
946C2×C8—21no—
947C2×C8—44no—
948C2×C8—44no—
949C2×C8C2×#4112yes—
950C2×C8C2×#4112yes—
951C2×C8C2×#4112yes—
952C4⋊C4—22no—
953C4⋊C4—22no—
954C4⋊C4—22no—
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—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—41no—
982C4⋊C4—41no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4C2×#4112yes—
1005C4⋊C4C2×#4112yes—
1006C22⋊C4—22no—
1007C22⋊C4—22no—
1008C22⋊C4—24no—
1009C22⋊C4—22no—
1010C22⋊C4—22no—
1011C22⋊C4—22no—
1012C22⋊C4—22no—
1013C22⋊C4—22no—
1014C22⋊C4—22no—
1015C22⋊C4—41no—
1016C22⋊C4—41no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
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—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C42—22no—
1047C42—22no—
1048C42—21no—
1049C42—21no—
1050C42—21no—
1051C42—21no—
1052C42—21no—
1053C42—21no—
1054C42—42no—
1055C42—42no—
1056C42—42no—
1057C42—42no—
1058C42—42no—
1059C42—81no—
1060C42—81no—
1061C42—81no—
1062C42—81no—
1063C42—81no—
1064C42C2×#4112yes—
1065C42H(5,𝔽2)12yes—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—22no—
1073C23—21no—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—22no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—48no—
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—84no—
1100C23—84no—
1101C23—84no—
1102C23—84no—
1103C23—84no—
1104C23—84no—
1105C23#54712yes—
1106C23#57512yes—
1107C23#57712yes—
1108C23C23×D411yescharacteristic
1109D4—22no—
1110D4—22no—
1111D4—22no—
1112D4—22no—
1113D4—48no—
1114D4—44no—
1115D4—44no—
1116D4—41no—
1117D4—41no—
1118D4—41no—
1119D4—41no—
1120D4—82no—
1121D4—84no—
1122D4—84no—
1123D4—162no—
1124D4—162no—
1125C2×C4—28no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—22no—
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—22no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—44no—
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—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—84no—
1211C2×C4—84no—
1212C2×C4—84no—
1213C2×C4—84no—
1214C2×C4—84no—
1215C2×C4—84no—
1216C2×C4—84no—
1217C2×C4—84no—
1218C2×C4—162no—
1219C2×C4#54612yes—
1220C2×C4#54612yes—
1221C2×C4#54712yes—
1222C2×C4#57612yes—
1223C2×C4C22×#4111yescharacteristic
1224C2×C4C22×#4111yescharacteristic
1225C2×C4C22×#4111yescharacteristic
1226C2×C4C2×H(5,𝔽2)11yescharacteristic
1227C2×C4C2×2−1+411yescharacteristic
1228C2×C4#58511yescharacteristic
1229C8—22no—
1230C8—22no—
1231C8—22no—
1232C8—41no—
1233C8—41no—
1234C8—41no—
1235C8—41no—
1236C8—41no—
1237C22—22no—
1238C22—22no—
1239C22—22no—
1240C22—22no—
1241C22—22no—
1242C22—22no—
1243C22—41no—
1244C22—41no—
1245C22—42no—
1246C22—41no—
1247C22—42no—
1248C22—41no—
1249C22—41no—
1250C22—41no—
1251C22—42no—
1252C22—42no—
1253C22—41no—
1254C22—41no—
1255C22—41no—
1256C22—41no—
1257C22—41no—
1258C22—41no—
1259C22—42no—
1260C22—42no—
1261C22—41no—
1262C22—41no—
1263C22—816no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22#335114yes—
1273C22C2×#54611yescharacteristic
1274C22C2×#54711yescharacteristic
1275C22D4×#4111yescharacteristic
1276C22C2×#57511yescharacteristic
1277C22C2×#57611yescharacteristic
1278C22C2×#57711yescharacteristic
1279C22#358411yescharacteristic
1280C4—22no—
1281C4—22no—
1282C4—22no—
1283C4—22no—
1284C4—42no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—42no—
1293C4—81no—
1294C4—81no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C4—81no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4#344411yescharacteristic
1306C4#349511yescharacteristic
1307C4#350511yescharacteristic
1308C4#352011yescharacteristic
1309C2—24no—
1310C2—81no—
1311C2—81no—
1312C2—82no—
1313C2—82no—
1314C2#3614311yescharacteristic
1315C2#6114111yescharacteristic
1316C2#6116711yescharacteristic
1317C2C2×#335111yescharacteristic
1318C2#6128411yescharacteristic
1319C2#6144411yescharacteristic
1320C2#6147211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36440C2
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
2. #36254C2semidirect
3. #33208C2semidirect
4. #33150C2semidirect
5. #32959C2semidirect
6. #28862C2semidirect
7. #28861C2semidirect
8. #28104C2semidirect
9. #28104C2semidirect
10. #27733C2semidirect
11. #27166C2semidirect
12. #27158C2semidirect
13. #27038C2semidirect
14. #27030C2semidirect
15. #26096C2semidirect
16. #25707C2semidirect
17. #25457C2semidirect
18. #25344C2semidirect
19. #25018C2semidirect
20. #24943C2semidirect
21. #24935C2semidirect
22. #24873C2semidirect
23. #24865C2semidirect
24. #23071C2semidirect
25. #22929C2semidirect
26. #22924C2semidirect
27. #22709C2semidirect
28. #22709C2semidirect
29. #22501C2semidirect
30. #21487C2semidirect
31. C2×C4×#102C2semidirect
34. C2×#499C22semidirect
39. C2×#436C22semidirect
53. #2570C22semidirect
55. #2562C22semidirect
59. #2496C22semidirect
60. #2495C22semidirect
73. #2370C22semidirect
79. #2352C22semidirect
82. #2346C22semidirect
83. #2344C22semidirect
88. #2101C22semidirect
89. #2099C22semidirect
92. #2085C22semidirect
93. #2084C22semidirect
94. #2077C22semidirect
95. #2077C22semidirect
96. #2077C22semidirect
97. #2075C22semidirect
112. #1991C22semidirect
113. #1991C22semidirect
114. #1989C22semidirect
115. #1989C22semidirect
116. #1954C22semidirect
117. #1949C22semidirect
118. #1949C22semidirect
119. #1949C22semidirect
120. #1949C22semidirect
121. #1947C22semidirect
122. #1947C22semidirect
123. #1942C22semidirect
124. #1942C22semidirect
125. #1941C22semidirect
126. #1941C22semidirect
127. #1939C22semidirect
136. #1923C22semidirect
137. #1923C22semidirect
138. #1920C22semidirect
139. #1920C22semidirect
140. #1920C22semidirect
141. #1920C22semidirect
142. #1919C22semidirect
143. #1918C22semidirect
144. #1918C22semidirect
145. #1918C22semidirect
158. #1854C22semidirect
159. #1854C22semidirect
160. #1854C22semidirect
163. #1853C22semidirect
166. #1852C22semidirect
167. #1852C22semidirect
168. #1846C22semidirect
169. #1836C22semidirect
170. #1836C22semidirect
171. #1825C22semidirect
174. #1823C22semidirect
175. #1809C22semidirect
176. #1809C22semidirect
186. #1776C22semidirect
187. #1776C22semidirect
188. #1770C22semidirect
197. #1753C22semidirect
198. #1753C22semidirect
199. #1736C22semidirect
200. #1736C22semidirect

Maximal subgroups

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

subgroupindex
#364402
#362542
#332082
#331502
#329592
#288622
#288612
#281042
#277332
#271662
#271582
#270382
#270302
#260962
#257072
#254572
#253442
#250182
#249432
#249352
#248732
#248652
#230712
#229292
#229242
#227092
#225012
#214872
C2×C4×#1022