Finite Group Databasebeta

← #7533154

Subgroups — #7533154

Order 512.

1514 conjugacy classes of subgroups.

The subgroup lattice has 1281 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45417C211yesmaximal, characteristic
2#36017C211yesmaximal, characteristic, complemented
3#31579C211yesmaximal, characteristic, complemented
4#31485C211yesmaximal, characteristic, complemented
5#31342C211yesmaximal, characteristic, complemented
6#31277C211yesmaximal, characteristic, complemented
7#29173C211yesmaximal, characteristic, complemented
8#29119C211yesmaximal, characteristic, complemented
9#29069C211yesmaximal, characteristic, complemented
10#28106C211yesmaximal, characteristic, complemented
11#28074C211yesmaximal, characteristic, complemented
12#27670C211yesmaximal, characteristic, complemented
13#27540C211yesmaximal, characteristic, complemented
14#27400C211yesmaximal, characteristic, complemented
15#27354C211yesmaximal, characteristic, complemented
16#27099C211yesmaximal, characteristic, complemented
17#27013C211yesmaximal, characteristic, complemented
18#26715C211yesmaximal, characteristic, complemented
19#26229C211yesmaximal, characteristic, complemented
20#24941C211yesmaximal, characteristic, complemented
21#24891C211yesmaximal, characteristic, complemented
22#24888C211yesmaximal, characteristic, complemented
23#24109C211yesmaximal, characteristic, complemented
24#24040C211yesmaximal, characteristic, complemented
25#23125C211yesmaximal, characteristic, complemented
26#22928C211yesmaximal, characteristic, complemented
27#22581C211yesmaximal, characteristic, complemented
28#22497C211yesmaximal, characteristic, complemented
29#22429C211yesmaximal, characteristic, complemented
30#21591C211yesmaximal, characteristic, complemented
31#21062C211yesmaximal, characteristic, complemented
32C2×#554C2211yescharacteristic
33C2×#548C2211yescharacteristic
34C2×#485C2211yescharacteristic
35C2×#485C2211yescharacteristic
36C2×#436C2211yescharacteristic
37C2×#435C2211yescharacteristic
38C2×#428C2211yescharacteristic
39C2×#417C2211yescharacteristic
40C2×#419C2211yescharacteristic
41C2×#416C2211yescharacteristic
42#2704—21no—
43#2700—21no—
44#2692—21no—
45#2672—21no—
46#2648—21no—
47#2629C2211yescharacteristic
48#2594—21no—
49#2593—21no—
50#2571C2211yescharacteristic
51#2562C2211yescharacteristic
52#2529—21no—
53#2524—21no—
54#2518—21no—
55#2518—21no—
56#2495C2211yescharacteristic
57#2494C2211yescharacteristic
58#2491C2211yescharacteristic
59#2486C2211yescharacteristic
60#2485C2211yescharacteristic
61#2485C2211yescharacteristic
62#2464—21no—
63#2460—21no—
64#2459—21no—
65#2451C2211yescharacteristic
66#2448C2211yescharacteristic
67#2427—21no—
68#2426C2211yescharacteristic
69#2416C2211yescharacteristic
70#2409C2211yescharacteristic
71#2407C2211yescharacteristic
72#2401—21no—
73#2392C2211yescharacteristic
74#2370C2211yescharacteristic
75#2360C2211yescharacteristic
76#2354C2211yescharacteristic
77#2352C2211yescharacteristic
78#2352C2211yescharacteristic
79#2347C2211yescharacteristic
80#2346C2211yescharacteristic
81Q8×C22⋊C4C2211yescharacteristic
82#2323C2211yescharacteristic
83#2311C2211yescharacteristic
84#2274C2211yescharacteristic
85#2101C2211yescharacteristic
86#2099C2211yescharacteristic
87#2095C2211yescharacteristic
88#2092C2211yescharacteristic
89#2088C2211yescharacteristic
90#2086C2211yescharacteristic
91#2085C2211yescharacteristic
92#2077C2211yescharacteristic
93#2077C2211yescharacteristic
94#2076C2211yescharacteristic
95#2076C2211yescharacteristic
96#2074C2211yescharacteristic
97#2072C2211yescharacteristic
98#2071C2211yescharacteristic
99#2068C2211yescharacteristic
100#2067C2211yescharacteristic
101#2059C2211yescharacteristic
102#2058C2211yescharacteristic
103#2057C2211yescharacteristic
104#2042C2211yescharacteristic
105#2042C2211yescharacteristic
106#2036C2211yescharacteristic
107#2036C2211yescharacteristic
108#2035C2211yescharacteristic
109#2035C2211yescharacteristic
110#2034C2211yescharacteristic
111#2034C2211yescharacteristic
112#2033C2211yescharacteristic
113#2033C2211yescharacteristic
114#2026C2211yescharacteristic
115#2026C2211yescharacteristic
116#2025C2211yescharacteristic
117#1993C2211yescharacteristic
118#1988C2211yescharacteristic
119#1983C2211yescharacteristic
120#1958C2211yescharacteristic
121#1942C2211yescharacteristic
122#1941C2211yescharacteristic
123#1936C2211yescharacteristic
124#1936C2211yescharacteristic
125#1935C2211yescharacteristic
126#1935C2211yescharacteristic
127#1934C2211yescharacteristic
128#1933C2211yescharacteristic
129#1928C2211yescharacteristic
130#1928C2211yescharacteristic
131#1927C2211yescharacteristic
132#1927C2211yescharacteristic
133#1927C2211yescharacteristic
134#1927C2211yescharacteristic
135#1927C2211yescharacteristic
136#1926C2211yescharacteristic
137#1926C2211yescharacteristic
138#1926C2211yescharacteristic
139#1925C2211yescharacteristic
140#1925C2211yescharacteristic
141#1924C2211yescharacteristic
142#1923C2211yescharacteristic
143#1921C2211yescharacteristic
144#1921C2211yescharacteristic
145#1921C2211yescharacteristic
146#1920C2211yescharacteristic
147#1919C2211yescharacteristic
148#1918C2211yescharacteristic
149#1917C2211yescharacteristic
150#1916C2211yescharacteristic
151#1895C2211yescharacteristic
152#1895C2211yescharacteristic
153#1894C2211yescharacteristic
154#1894C2211yescharacteristic
155#1894C2211yescharacteristic
156#1892C2211yescharacteristic
157#1875C2211yescharacteristic
158#1875C2211yescharacteristic
159#1873C2211yescharacteristic
160#1872C2211yescharacteristic
161#1870C2211yescharacteristic
162#1870C2211yescharacteristic
163#1870C2211yescharacteristic
164#1869C2211yescharacteristic
165#1865C2211yescharacteristic
166#1865C2211yescharacteristic
167#1865C2211yescharacteristic
168#1863C2211yescharacteristic
169#1863C2211yescharacteristic
170#1863C2211yescharacteristic
171#1854C2211yescharacteristic
172#1853C2211yescharacteristic
173#1853C2211yescharacteristic
174#1852C2211yescharacteristic
175#1825C2211yescharacteristic
176#1825C2211yescharacteristic
177#1824C2211yescharacteristic
178#1823C2211yescharacteristic
179#1823C2211yescharacteristic
180#1809C2211yescharacteristic
181#1809C2211yescharacteristic
182#1809C2211yescharacteristic
183#1808C2211yescharacteristic
184#1805C2211yescharacteristic
185#1805C2211yescharacteristic
186#1788C2211yescharacteristic
187#1788C2211yescharacteristic
188#1787C2211yescharacteristic
189#1787C2211yescharacteristic
190#1787C2211yescharacteristic
191#1776C2211yescharacteristic
192C4×#106C2211yescharacteristic
193#1763C2211yescharacteristic
194#1763C2211yescharacteristic
195C4×#103C2211yescharacteristic
196C4×#103C2211yescharacteristic
197#1753C2211yescharacteristic
198#1753C2211yescharacteristic
199#1750C2211yescharacteristic
200#1736C2211yescharacteristic
201C2×#340C2211yescharacteristic
202#1729C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×Q8C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209#554—24no—
210#554—42no—
211#548—24no—
212#548—42no—
213C2×C4⋊Q8C2311yescharacteristic
214C2×#125—21no—
215C2×#125C2311yescharacteristic
216C2×#124—21no—
217C2×#124—21no—
218C2×#124C2311yescharacteristic
219C2×#123—21no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8C2311yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×#121—21no—
227C2×#121—21no—
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×D4—21no—
234C2×C4×D4—21no—
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C22×C4⋊C4C2311yescharacteristic
243C22×C4⋊C4C2311yescharacteristic
244C22×C4⋊C4C2311yescharacteristic
245#485—24no—
246#485—24no—
247#436—42no—
248#435—42no—
249#428—42no—
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264#419—24no—
265#417—24no—
266#416—42no—
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×C22⋊C8C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295C2×C22⋊C8C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×#97C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303#401—21no—
304#400—21no—
305#400—21no—
306#400—21no—
307#400—21no—
308#399—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#398D411yescharacteristic
314#397—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#397—21no—
320#397D411yescharacteristic
321#396—21no—
322#396—21no—
323#396—21no—
324#396—21no—
325#396D411yescharacteristic
326#396D411yescharacteristic
327#395—21no—
328#395—21no—
329#394—21no—
330#394—21no—
331#394—21no—
332#394—21no—
333#394—21no—
334#394—21no—
335#394—21no—
336#394D411yescharacteristic
337#394D411yescharacteristic
338#394D411yescharacteristic
339#393—21no—
340#393—21no—
341#392—21no—
342#392D411yescharacteristic
343#391—21no—
344#391—21no—
345#391—21no—
346#391C2311yescharacteristic
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#390—21no—
351#390—21no—
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#389—21no—
356#389—21no—
357#389—21no—
358#389—21no—
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
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#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#384C2311yescharacteristic
409#383—21no—
410#383—21no—
411#382—21no—
412#382—21no—
413#382C2311yescharacteristic
414#382C2311yescharacteristic
415#381—21no—
416#380—21no—
417#380—21no—
418#380—21no—
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430C4×C4⋊C4—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×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⋊C4C2311yescharacteristic
450C4×C22⋊C4C2311yescharacteristic
451#376—21no—
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#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C22×Q8—21no—
497C22×Q8—21no—
498C22×Q8—22no—
499C22×Q8—22no—
500C22×Q8—41no—
501C22×Q8—41no—
502C22×Q8—41no—
503C22×Q8—41no—
504C22×Q8C2411yescharacteristic
505C22×Q8C2411yescharacteristic
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4C2×D411yescharacteristic
510C22×D4C2×D411yescharacteristic
511C22×D4C2×D411yescharacteristic
512C22×D4C2411yescharacteristic
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4C2411yescharacteristic
519C23×C4C2411yescharacteristic
520C23×C4C2411yescharacteristic
521C2×M16—22no—
522C2×M16—22no—
523C2×M16—22no—
524C2×M16—41no—
525C2×M16—41no—
526C2×M16—41no—
527C2×M16—41no—
528C2×M16—41no—
529C2×M16—41no—
530C22×C8—22no—
531C22×C8—41no—
532C22×C8—41no—
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C4⋊Q8—22no—
542C4⋊Q8—41no—
543#125—41no—
544#125—41no—
545#125—44no—
546#124—22no—
547#124—41no—
548#124—44no—
549#124—82no—
550#123—82no—
551C22⋊Q8—22no—
552C22⋊Q8—22no—
553C22⋊Q8—22no—
554C22⋊Q8—44no—
555C22⋊Q8—44no—
556C22⋊Q8—44no—
557C22⋊Q8—41no—
558C22⋊Q8—41no—
559C22⋊Q8#4114yes—
560#121—22no—
561#121—44no—
562#121—41no—
563#121—41no—
564#121—41no—
565#121—82no—
566C4×Q8—22no—
567C4×Q8—22no—
568C4×Q8—41no—
569C4×Q8—41no—
570C4×Q8—41no—
571C4×Q8—41no—
572C4×D4—22no—
573C4×D4—22no—
574C4×D4—22no—
575C4×D4—22no—
576C4×D4—41no—
577C4×D4—41no—
578C4×D4—44no—
579C4×D4—44no—
580#117—22no—
581#117—22no—
582#117—22no—
583#117—22no—
584#117—41no—
585#117—41no—
586#117—41no—
587#117—41no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—22no—
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—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—41no—
616C2×C4⋊C4—41no—
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4C2×D411yescharacteristic
621C2×C4⋊C4C2×D411yescharacteristic
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
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×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⋊C4C2×D411yescharacteristic
665C2×C22⋊C4C2×D411yescharacteristic
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C22⋊C4C2×D411yescharacteristic
668C2×C22⋊C4C2×D411yescharacteristic
669C2×C22⋊C4C2×D411yescharacteristic
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C22⋊C4C2×D411yescharacteristic
672C2×C22⋊C4C2×D411yescharacteristic
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C22⋊C4C2×D411yescharacteristic
675C2×C22⋊C4C2×D411yescharacteristic
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
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×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693#107—22no—
694#107—22no—
695#107—41no—
696#107—41no—
697#107—41no—
698#107—41no—
699#106—22no—
700#106—22no—
701#106—41no—
702#106—41no—
703#106—41no—
704#106—41no—
705C4⋊C8—41no—
706C4⋊C8—41no—
707#103—22no—
708#103—22no—
709#103—22no—
710#103—22no—
711#103—22no—
712#103—22no—
713#103—22no—
714#103—41no—
715#103—41no—
716#103—41no—
717#103—41no—
718#103—41no—
719#103—41no—
720#103—41no—
721#103—41no—
722#103#4114yes—
723#102—22no—
724#102—22no—
725#102—41no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731C22⋊C8—22no—
732C22⋊C8—22no—
733C22⋊C8—22no—
734C22⋊C8—41no—
735C22⋊C8—41no—
736C22⋊C8—41no—
737C22⋊C8—41no—
738C22⋊C8—41no—
739#97—41no—
740#97—41no—
741C4×C8—41no—
742C4×C8—41no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788C24—21no—
789C24C22×D411yescharacteristic
790C24C22×D411yescharacteristic
791C24C22×D411yescharacteristic
792#41—44no—
793#41—44no—
794#41—82no—
795#41—82no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—21no—
801C2×Q8—21no—
802C2×Q8—21no—
803C2×Q8—21no—
804C2×Q8—21no—
805C2×Q8—21no—
806C2×Q8—42no—
807C2×Q8—42no—
808C2×Q8—42no—
809C2×Q8—44no—
810C2×Q8—81no—
811C2×Q8—81no—
812C2×Q8—81no—
813C2×Q8—82no—
814C2×Q8—82no—
815C2×Q8—82no—
816C2×Q8C2×#4112yes—
817C2×Q8C2×#4112yes—
818C2×D4—22no—
819C2×D4—22no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—41no—
827C2×D4—41no—
828C2×D4—41no—
829C2×D4—41no—
830C2×D4—41no—
831C2×D4—41no—
832C2×D4—41no—
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—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—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—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—42no—
874C22×C4—42no—
875C22×C4—42no—
876C22×C4—42no—
877C22×C4—42no—
878C22×C4—42no—
879C22×C4—42no—
880C22×C4—81no—
881C22×C4—81no—
882C22×C4—81no—
883C22×C4—81no—
884C22×C4—81no—
885C22×C4—81no—
886C22×C4—81no—
887C22×C4—81no—
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C22×D411yescharacteristic
899C22×C4C2×#4112yes—
900C22×C4H(5,𝔽2)12yes—
901C22×C4C2511yescharacteristic
902M16—44no—
903M16—82no—
904M16—82no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—82no—
929C2×C8C2×#4112yes—
930C4⋊C4—24no—
931C4⋊C4—22no—
932C4⋊C4—22no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—41no—
958C4⋊C4—41no—
959C4⋊C4—41no—
960C4⋊C4—41no—
961C4⋊C4—41no—
962C4⋊C4—42no—
963C4⋊C4—42no—
964C4⋊C4—42no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4C2×#4112yes—
985C4⋊C4C2×#4112yes—
986C22⋊C4—24no—
987C22⋊C4—22no—
988C22⋊C4—22no—
989C22⋊C4—22no—
990C22⋊C4—22no—
991C22⋊C4—41no—
992C22⋊C4—41no—
993C22⋊C4—41no—
994C22⋊C4—41no—
995C22⋊C4—41no—
996C22⋊C4—41no—
997C22⋊C4—41no—
998C22⋊C4—41no—
999C22⋊C4—42no—
1000C22⋊C4—42no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
1010C22⋊C4—81no—
1011C22⋊C4—81no—
1012C22⋊C4—81no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
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—
1025C42—21no—
1026C42—21no—
1027C42—21no—
1028C42—21no—
1029C42—21no—
1030C42—21no—
1031C42—21no—
1032C42—21no—
1033C42—42no—
1034C42—42no—
1035C42—42no—
1036C42—42no—
1037C42—42no—
1038C42—81no—
1039C42—81no—
1040C42—81no—
1041C42—81no—
1042C42—81no—
1043C42—81no—
1044C42—81no—
1045C42—81no—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—21no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23#54612yes—
1074C23C23×D411yescharacteristic
1075Q8—22no—
1076Q8—22no—
1077Q8—22no—
1078Q8—22no—
1079Q8—41no—
1080Q8—41no—
1081Q8—41no—
1082Q8—41no—
1083Q8—84no—
1084Q8—162no—
1085D4—44no—
1086D4—41no—
1087D4—41no—
1088D4—41no—
1089D4—41no—
1090D4—82no—
1091D4—84no—
1092D4—82no—
1093D4—84no—
1094D4—162no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—22no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—22no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—84no—
1185C2×C4—84no—
1186C2×C4—162no—
1187C2×C4—162no—
1188C2×C4—162no—
1189C2×C4#54612yes—
1190C2×C4C22×#4111yescharacteristic
1191C2×C4C22×#4111yescharacteristic
1192C2×C4C2×H(5,𝔽2)11yescharacteristic
1193C2×C4#58511yescharacteristic
1194C2×C4#58511yescharacteristic
1195C2×C4#58511yescharacteristic
1196C8—22no—
1197C8—41no—
1198C8—41no—
1199C8—41no—
1200C8—41no—
1201C8—41no—
1202C8—41no—
1203C8—41no—
1204C22—22no—
1205C22—22no—
1206C22—22no—
1207C22—41no—
1208C22—41no—
1209C22—41no—
1210C22—41no—
1211C22—41no—
1212C22—41no—
1213C22—41no—
1214C22—41no—
1215C22—41no—
1216C22—41no—
1217C22—41no—
1218C22—41no—
1219C22—41no—
1220C22—41no—
1221C22—41no—
1222C22—41no—
1223C22—41no—
1224C22—41no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22C2×#54611yescharacteristic
1233C22D4×#4111yescharacteristic
1234C22#348511yescharacteristic
1235C22#358411yescharacteristic
1236C22#358511yescharacteristic
1237C22#358611yescharacteristic
1238C22#358611yescharacteristic
1239C4—22no—
1240C4—41no—
1241C4—41no—
1242C4—42no—
1243C4—41no—
1244C4—41no—
1245C4—42no—
1246C4—41no—
1247C4—41no—
1248C4—41no—
1249C4—41no—
1250C4—42no—
1251C4—42no—
1252C4—41no—
1253C4—41no—
1254C4—81no—
1255C4—81no—
1256C4—81no—
1257C4—81no—
1258C4—81no—
1259C4—81no—
1260C4—81no—
1261C4—81no—
1262C4—81no—
1263C4—81no—
1264C4—81no—
1265C4#347511yescharacteristic
1266C4#351311yescharacteristic
1267C4#352111yescharacteristic
1268C4#354511yescharacteristic
1269C2—42no—
1270C2—81no—
1271C2—81no—
1272C2—161no—
1273C2#5903211yescharacteristic
1274C2#6117611yescharacteristic
1275C2#6119611yescharacteristic
1276C2#6151611yescharacteristic
1277C2#6155011yescharacteristic
1278C2#6177711yescharacteristic
1279C2#6181411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#45417C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2392 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #36017C2semidirect
3. #31579C2semidirect
4. #31485C2semidirect
5. #31342C2semidirect
6. #31277C2semidirect
7. #29173C2semidirect
8. #29119C2semidirect
9. #29069C2semidirect
10. #28106C2semidirect
11. #28074C2semidirect
12. #27670C2semidirect
13. #27540C2semidirect
14. #27400C2semidirect
15. #27354C2semidirect
16. #27099C2semidirect
17. #27013C2semidirect
18. #26715C2semidirect
19. #26229C2semidirect
20. #24941C2semidirect
21. #24891C2semidirect
22. #24888C2semidirect
23. #24109C2semidirect
24. #24040C2semidirect
25. #23125C2semidirect
26. #22928C2semidirect
27. #22581C2semidirect
28. #22497C2semidirect
29. #22429C2semidirect
30. #21591C2semidirect
31. #21062C2semidirect

Maximal subgroups

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

subgroupindex
#454172
#360172
#315792
#314852
#313422
#312772
#291732
#291192
#290692
#281062
#280742
#276702
#275402
#274002
#273542
#270992
#270132
#267152
#262292
#249412
#248912
#248882
#241092
#240402
#231252
#229282
#225812
#224972
#224292
#215912
#210622