Finite Group Databasebeta

← #6776973

Subgroups — #6776973

Order 512.

1321 conjugacy classes of subgroups.

The subgroup lattice has 1201 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38204C211yesmaximal, characteristic
2#35184C211yesmaximal, characteristic, complemented
3#33085C211yesmaximal, characteristic, complemented
4#32451C211yesmaximal, characteristic, complemented
5#32376C211yesmaximal, characteristic, complemented
6#32260C211yesmaximal, characteristic, complemented
7#32014C211yesmaximal, characteristic, complemented
8#31531C211yesmaximal, characteristic, complemented
9#31470C211yesmaximal, characteristic, complemented
10#31278C211yesmaximal, characteristic
11#30410C211yesmaximal, characteristic
12#30182C211yesmaximal, characteristic, complemented
13#30028C211yesmaximal, characteristic, complemented
14#29512C211yesmaximal, characteristic, complemented
15#29392C211yesmaximal, characteristic, complemented
16#28993C211yesmaximal, characteristic, complemented
17#28861C211yesmaximal, characteristic, complemented
18#28064C211yesmaximal, characteristic, complemented
19#27884C211yesmaximal, characteristic, complemented
20#27867C211yesmaximal, characteristic, complemented
21#27637C211yesmaximal, characteristic, complemented
22#27593C211yesmaximal, characteristic, complemented
23#27526C211yesmaximal, characteristic, complemented
24#27459C211yesmaximal, characteristic, complemented
25#27160C211yesmaximal, characteristic, complemented
26#25030C211yesmaximal, characteristic, complemented
27#24907C211yesmaximal, characteristic, complemented
28#22789C211yesmaximal, characteristic, complemented
29#22195C211yesmaximal, characteristic, complemented
30#22059C211yesmaximal, characteristic, complemented
31#21120C211yesmaximal, characteristic, complemented
32C2×#465C2211yescharacteristic
33C2×#452C2211yescharacteristic
34C2×C4×SD16C2211yescharacteristic
35#2863—21no—
36#2863C2211yescharacteristic
37#2861—21no—
38#2750—21no—
39#2749—21no—
40#2740—21no—
41#2738—21no—
42#2654—21no—
43#2654—21no—
44#2629C2211yescharacteristic
45#2625C2211yescharacteristic
46#2609—21no—
47#2568C2211yescharacteristic
48#2552C2211yescharacteristic
49#2547C2211yescharacteristic
50#2538C2211yescharacteristic
51#2525—21no—
52#2525—21no—
53#2511C2211yescharacteristic
54#2505—21no—
55#2498—21no—
56#2495C2211yescharacteristic
57#2495C2211yescharacteristic
58#2489C2211yescharacteristic
59#2487C2211yescharacteristic
60#2471—21no—
61#2454C2211yescharacteristic
62#2453—21no—
63#2448—21no—
64#2423C2211yescharacteristic
65#2423C2211yescharacteristic
66#2422C2211yescharacteristic
67#2407C2211yescharacteristic
68#2344C2211yescharacteristic
69#2339C2211yescharacteristic
70#2324C2211yescharacteristic
71#2323C2211yescharacteristic
72#2323C2211yescharacteristic
73#2314C2211yescharacteristic
74#2314C2211yescharacteristic
75#2311C2211yescharacteristic
76C4×C4⋊Q8C2211yescharacteristic
77#2293C2211yescharacteristic
78#2293C2211yescharacteristic
79C42×Q8C2211yescharacteristic
80#2100C2211yescharacteristic
81#2099C2211yescharacteristic
82#2097C2211yescharacteristic
83#2096C2211yescharacteristic
84#2096C2211yescharacteristic
85#2092C2211yescharacteristic
86#2087C2211yescharacteristic
87#2085C2211yescharacteristic
88#2084C2211yescharacteristic
89#2084C2211yescharacteristic
90#2077C2211yescharacteristic
91#2077C2211yescharacteristic
92#2077C2211yescharacteristic
93#2077C2211yescharacteristic
94#2077C2211yescharacteristic
95#2077C2211yescharacteristic
96#2077C2211yescharacteristic
97#2076C2211yescharacteristic
98#2075C2211yescharacteristic
99#2074C2211yescharacteristic
100#2072C2211yescharacteristic
101#2072C2211yescharacteristic
102#2071C2211yescharacteristic
103#2071C2211yescharacteristic
104#2066C2211yescharacteristic
105#2066C2211yescharacteristic
106#2059C2211yescharacteristic
107#2058C2211yescharacteristic
108#2058C2211yescharacteristic
109#2056C2211yescharacteristic
110#2036C2211yescharacteristic
111#2035C2211yescharacteristic
112#2035C2211yescharacteristic
113#2035C2211yescharacteristic
114#2034C2211yescharacteristic
115#2034C2211yescharacteristic
116#2026C2211yescharacteristic
117#2024C2211yescharacteristic
118#2023C2211yescharacteristic
119#2001C2211yescharacteristic
120#1992C2211yescharacteristic
121#1991C2211yescharacteristic
122#1971C2211yescharacteristic
123#1968C2211yescharacteristic
124#1949C2211yescharacteristic
125#1948C2211yescharacteristic
126#1941C2211yescharacteristic
127#1941C2211yescharacteristic
128#1936C2211yescharacteristic
129#1933C2211yescharacteristic
130#1933C2211yescharacteristic
131#1933C2211yescharacteristic
132#1928C2211yescharacteristic
133#1927C2211yescharacteristic
134#1927C2211yescharacteristic
135#1927C2211yescharacteristic
136#1927C2211yescharacteristic
137#1927C2211yescharacteristic
138#1926C2211yescharacteristic
139#1926C2211yescharacteristic
140#1925C2211yescharacteristic
141#1925C2211yescharacteristic
142#1923C2211yescharacteristic
143#1923C2211yescharacteristic
144#1920C2211yescharacteristic
145#1920C2211yescharacteristic
146#1920C2211yescharacteristic
147#1920C2211yescharacteristic
148#1920C2211yescharacteristic
149#1920C2211yescharacteristic
150#1920C2211yescharacteristic
151#1919C2211yescharacteristic
152#1919C2211yescharacteristic
153#1919C2211yescharacteristic
154#1919C2211yescharacteristic
155#1918C2211yescharacteristic
156#1917C2211yescharacteristic
157#1916C2211yescharacteristic
158#1895C2211yescharacteristic
159#1894C2211yescharacteristic
160#1894C2211yescharacteristic
161#1892C2211yescharacteristic
162#1880C2211yescharacteristic
163#1880C2211yescharacteristic
164#1878C2211yescharacteristic
165#1878C2211yescharacteristic
166#1878C2211yescharacteristic
167#1877C2211yescharacteristic
168#1872C2211yescharacteristic
169#1870C2211yescharacteristic
170#1869C2211yescharacteristic
171#1865C2211yescharacteristic
172#1865C2211yescharacteristic
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic
175#1864C2211yescharacteristic
176#1863C2211yescharacteristic
177#1863C2211yescharacteristic
178#1863C2211yescharacteristic
179#1853C2211yescharacteristic
180#1853C2211yescharacteristic
181#1852C2211yescharacteristic
182#1844C2211yescharacteristic
183#1839C2211yescharacteristic
184#1836C2211yescharacteristic
185#1818C2211yescharacteristic
186#1809C2211yescharacteristic
187#1807C2211yescharacteristic
188#1807C2211yescharacteristic
189#1804C2211yescharacteristic
190#1802C2211yescharacteristic
191#1798C2211yescharacteristic
192#1788C2211yescharacteristic
193#1788C2211yescharacteristic
194#1788C2211yescharacteristic
195C4×#107C2211yescharacteristic
196C4×#103C2211yescharacteristic
197C4×#102C2211yescharacteristic
198#1753C2211yescharacteristic
199C8×C22⋊C4C2211yescharacteristic
200#1750C2211yescharacteristic
201#1744C2211yescharacteristic
202#1729C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×#125—21no—
210C2×#125C2311yescharacteristic
211C2×#124—21no—
212C2×#123—21no—
213C2×C22⋊Q8C2311yescharacteristic
214C2×C22⋊Q8C2311yescharacteristic
215C2×C22⋊Q8C2311yescharacteristic
216C2×#121C2311yescharacteristic
217C2×C4×Q8—21no—
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×D4C2311yescharacteristic
222C2×C4×D4C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×#117—21no—
225C2×#117—21no—
226C2×#117C2311yescharacteristic
227C2×#117C2311yescharacteristic
228C22×C4⋊C4C2311yescharacteristic
229#465—24no—
230#452—24no—
231C4×SD16—24no—
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×#103C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×C22⋊C8C2311yescharacteristic
269C2×C22⋊C8C2311yescharacteristic
270C2×C22⋊C8C2311yescharacteristic
271C2×C22⋊C8C2311yescharacteristic
272C2×C22⋊C8C2311yescharacteristic
273C2×C22⋊C8C2311yescharacteristic
274C2×#97C2311yescharacteristic
275C2×C4×C8C2311yescharacteristic
276C2×C4×C8C2311yescharacteristic
277C2×C4×C8C2311yescharacteristic
278#400—21no—
279#400—21no—
280#400—21no—
281#400—21no—
282#400—21no—
283#400—21no—
284#400—21no—
285#400—21no—
286#400—21no—
287#399—21no—
288#399—21no—
289#399—21no—
290#399—21no—
291#398—21no—
292#398—21no—
293#398—21no—
294#398—21no—
295#398—21no—
296#398—21no—
297#398—21no—
298#397—21no—
299#397—21no—
300#397—21no—
301#397—21no—
302#397—21no—
303#397—21no—
304#397—21no—
305#397—21no—
306#396—21no—
307#396—21no—
308#396—21no—
309#396—21no—
310#396—21no—
311#394—21no—
312#394—21no—
313#392—21no—
314#391—21no—
315#391—21no—
316#391—21no—
317#391—21no—
318#391C2311yescharacteristic
319#391C2311yescharacteristic
320#391C2311yescharacteristic
321#391C2311yescharacteristic
322#391C2311yescharacteristic
323#391C2311yescharacteristic
324#391C2311yescharacteristic
325#390—21no—
326#390—21no—
327#390D411yescharacteristic
328#390D411yescharacteristic
329#390C2311yescharacteristic
330#390C2311yescharacteristic
331#390C2311yescharacteristic
332#389—21no—
333#389—21no—
334#389—21no—
335#389—21no—
336#389—21no—
337#389D411yescharacteristic
338#389D411yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#388—21no—
350#388—21no—
351#388—21no—
352#388—21no—
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#388D411yescharacteristic
366#388D411yescharacteristic
367#388D411yescharacteristic
368#388D411yescharacteristic
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#387—21no—
383#387—21no—
384#386—21no—
385#386—21no—
386#386—21no—
387#386—21no—
388#386—21no—
389#386—21no—
390#386—21no—
391#385—21no—
392#385—21no—
393#385—21no—
394#385—21no—
395#385—21no—
396#384C2311yescharacteristic
397#384C2311yescharacteristic
398#384C2311yescharacteristic
399#384C2311yescharacteristic
400#383—21no—
401#383—21no—
402#383—21no—
403#382—21no—
404#382C2311yescharacteristic
405#382C2311yescharacteristic
406#381—21no—
407#381—21no—
408#380—21no—
409#380—21no—
410#380—21no—
411#380C2311yescharacteristic
412#380C2311yescharacteristic
413#380C2311yescharacteristic
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421C4×C4⋊C4—21no—
422C4×C4⋊C4—21no—
423C4×C4⋊C4—21no—
424C4×C4⋊C4—21no—
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C22⋊C4—21no—
434C4×C22⋊C4C2311yescharacteristic
435C4×C22⋊C4C2311yescharacteristic
436C2×#95—21no—
437C43—21no—
438C43C2311yescharacteristic
439#340C2311yescharacteristic
440#340C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#336C2311yescharacteristic
468#336C2311yescharacteristic
469#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481C2×#41—22no—
482C2×#41—41no—
483C2×#41—41no—
484C2×#41—41no—
485C2×#41—41no—
486C2×#41—41no—
487C22×Q8—21no—
488C22×Q8C2411yescharacteristic
489C22×Q8C2411yescharacteristic
490C22×D4—21no—
491C22×D4—21no—
492C22×D4C2×D411yescharacteristic
493C22×D4C2411yescharacteristic
494C23×C4—21no—
495C23×C4—21no—
496C23×C4—21no—
497C23×C4—21no—
498C23×C4C2411yescharacteristic
499C23×C4C2411yescharacteristic
500C2×Q16—22no—
501C2×Q16—41no—
502C2×Q16—41no—
503C2×SD16—41no—
504C2×SD16—41no—
505C2×SD16#4114yes—
506C2×M16—41no—
507C2×M16—41no—
508C2×M16—41no—
509C22×C8—22no—
510C22×C8—41no—
511C22×C8—41no—
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C4⋊Q8—41no—
521C4⋊Q8—41no—
522#125—41no—
523#125—41no—
524#125—82no—
525#124—82no—
526#123—82no—
527C22⋊Q8—22no—
528C22⋊Q8—22no—
529C22⋊Q8—41no—
530C22⋊Q8—41no—
531C22⋊Q8—41no—
532C22⋊Q8—41no—
533#121—22no—
534#121—41no—
535C4×Q8—22no—
536C4×Q8—41no—
537C4×Q8—41no—
538C4×Q8—41no—
539C4×Q8—41no—
540C4×Q8—41no—
541C4×Q8—82no—
542C4×D4—22no—
543C4×D4—41no—
544C4×D4—41no—
545C4×D4—41no—
546C4×D4—41no—
547C4×D4—41no—
548#117—41no—
549#117—41no—
550#117—41no—
551#117—41no—
552#117—82no—
553#117—82no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—41no—
583C2×C4⋊C4—41no—
584C2×C4⋊C4C2×D411yescharacteristic
585C2×C4⋊C4C2×D411yescharacteristic
586C2×C4⋊C4C2×D411yescharacteristic
587C2×C4⋊C4C2×D411yescharacteristic
588C2×C4⋊C4C2×D411yescharacteristic
589C2×C4⋊C4C2×D411yescharacteristic
590C2×C4⋊C4C2×D411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4C2×D411yescharacteristic
627C2×C22⋊C4C2×D411yescharacteristic
628C2×C22⋊C4C2×D411yescharacteristic
629C2×C22⋊C4C2×D411yescharacteristic
630C2×C22⋊C4C2×D411yescharacteristic
631C2×C22⋊C4C2×D411yescharacteristic
632C2×C22⋊C4C2×D411yescharacteristic
633C2×C22⋊C4C2×D411yescharacteristic
634C2×C22⋊C4C2×D411yescharacteristic
635C2×C22⋊C4C2×D411yescharacteristic
636C2×C42—21no—
637C2×C42—21no—
638C2×C42—21no—
639C2×C42—21no—
640C2×C42—21no—
641C2×C42—21no—
642C2×C42—21no—
643C2×C42—21no—
644C2×C42—21no—
645C2×C42—21no—
646C2×C42C2×D411yescharacteristic
647C2×C42C2×D411yescharacteristic
648C2×C42C2×D411yescharacteristic
649C2×C42C2×D411yescharacteristic
650C2×C42C2411yescharacteristic
651C2×C42C2411yescharacteristic
652C2×C42C2411yescharacteristic
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655#107—41no—
656#107—41no—
657#107—41no—
658#106—22no—
659#106—22no—
660#106—41no—
661#106—41no—
662#106—41no—
663#106—41no—
664#106—41no—
665#106—41no—
666#106—41no—
667#106—41no—
668#106—41no—
669C4⋊C8—41no—
670C4⋊C8—41no—
671#103—22no—
672#103—22no—
673#103—22no—
674#103—41no—
675#103—41no—
676#103—41no—
677#103—41no—
678#103—41no—
679#103—41no—
680#103—41no—
681#103—41no—
682#103—41no—
683#103—41no—
684#102—22no—
685#102—22no—
686#102—22no—
687#102—41no—
688#102—41no—
689#102—41no—
690#102—41no—
691C22⋊C8—22no—
692C22⋊C8—41no—
693C22⋊C8—41no—
694C22⋊C8—41no—
695C22⋊C8—41no—
696C22⋊C8—41no—
697#97—41no—
698C4×C8—22no—
699C4×C8—41no—
700C4×C8—41no—
701#95—21no—
702#95—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752C24—21no—
753C24C22×D411yescharacteristic
754C24C22×D411yescharacteristic
755#41—82no—
756#41—82no—
757#41—82no—
758#41—82no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—42no—
771C2×Q8—42no—
772C2×Q8—42no—
773C2×Q8C2×#4112yes—
774C2×D4—22no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—41no—
781C2×D4—41no—
782C2×D4—42no—
783C2×D4—42no—
784C2×D4—42no—
785C2×D4—81no—
786C2×D4—81no—
787C2×D4—81no—
788C2×D4C2×#4112yes—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—42no—
817C22×C4—42no—
818C22×C4—42no—
819C22×C4—42no—
820C22×C4—42no—
821C22×C4—81no—
822C22×C4—81no—
823C22×C4—81no—
824C22×C4—81no—
825C22×C4—81no—
826C22×C4—81no—
827C22×C4—81no—
828C22×C4C22×D411yescharacteristic
829C22×C4C22×D411yescharacteristic
830C22×C4C22×D411yescharacteristic
831C22×C4C22×D411yescharacteristic
832C22×C4C22×D411yescharacteristic
833C22×C4C22×D411yescharacteristic
834C22×C4C22×D411yescharacteristic
835C22×C4C22×D411yescharacteristic
836C22×C4C22×D411yescharacteristic
837C22×C4C22×D411yescharacteristic
838C22×C4C22×D411yescharacteristic
839C22×C4C22×D411yescharacteristic
840C22×C4C2511yescharacteristic
841Q16—82no—
842SD16—44no—
843M16—82no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8—21no—
867C2×C8—82no—
868C2×C8C2×#4112yes—
869C4⋊C4—22no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—21no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—21no—
887C4⋊C4—21no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—21no—
896C4⋊C4—41no—
897C4⋊C4—41no—
898C4⋊C4—41no—
899C4⋊C4—41no—
900C4⋊C4—41no—
901C4⋊C4—41no—
902C4⋊C4—42no—
903C4⋊C4—42no—
904C4⋊C4—42no—
905C4⋊C4—42no—
906C4⋊C4—42no—
907C4⋊C4—42no—
908C4⋊C4—42no—
909C4⋊C4—42no—
910C4⋊C4—42no—
911C4⋊C4—81no—
912C4⋊C4—81no—
913C4⋊C4—81no—
914C4⋊C4—81no—
915C4⋊C4—81no—
916C4⋊C4—81no—
917C4⋊C4—81no—
918C4⋊C4—81no—
919C4⋊C4—81no—
920C4⋊C4—81no—
921C4⋊C4—81no—
922C4⋊C4—81no—
923C4⋊C4—81no—
924C4⋊C4—81no—
925C4⋊C4—81no—
926C4⋊C4—81no—
927C4⋊C4—81no—
928C4⋊C4—81no—
929C4⋊C4—81no—
930C22⋊C4—22no—
931C22⋊C4—22no—
932C22⋊C4—41no—
933C22⋊C4—41no—
934C22⋊C4—41no—
935C22⋊C4—41no—
936C22⋊C4—41no—
937C22⋊C4—41no—
938C22⋊C4—41no—
939C22⋊C4—41no—
940C22⋊C4—42no—
941C22⋊C4—42no—
942C22⋊C4—42no—
943C22⋊C4—42no—
944C22⋊C4—42no—
945C22⋊C4—81no—
946C22⋊C4—81no—
947C22⋊C4—81no—
948C22⋊C4—81no—
949C22⋊C4—81no—
950C22⋊C4—81no—
951C22⋊C4—81no—
952C22⋊C4—81no—
953C22⋊C4—81no—
954C22⋊C4—81no—
955C22⋊C4—81no—
956C22⋊C4—81no—
957C22⋊C4—81no—
958C22⋊C4—81no—
959C22⋊C4—81no—
960C22⋊C4—81no—
961C22⋊C4—81no—
962C42—22no—
963C42—22no—
964C42—21no—
965C42—21no—
966C42—21no—
967C42—21no—
968C42—21no—
969C42—21no—
970C42—21no—
971C42—21no—
972C42—21no—
973C42—21no—
974C42—41no—
975C42—41no—
976C42—42no—
977C42—42no—
978C42—42no—
979C42—42no—
980C42—42no—
981C42—42no—
982C42—81no—
983C42—81no—
984C42—81no—
985C42—81no—
986C23—21no—
987C23—21no—
988C23—21no—
989C23—21no—
990C23—21no—
991C23—21no—
992C23—21no—
993C23—21no—
994C23—22no—
995C23—21no—
996C23—21no—
997C23—21no—
998C23—21no—
999C23—21no—
1000C23—21no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23C23×D411yescharacteristic
1008Q8—22no—
1009Q8—22no—
1010Q8—41no—
1011Q8—41no—
1012Q8—41no—
1013Q8—41no—
1014Q8—41no—
1015Q8—41no—
1016Q8—84no—
1017D4—22no—
1018D4—22no—
1019D4—41no—
1020D4—41no—
1021D4—82no—
1022D4—84no—
1023D4—162no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—22no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—84no—
1112C2×C4—84no—
1113C2×C4—84no—
1114C2×C4—162no—
1115C2×C4#57712yes—
1116C2×C4#57712yes—
1117C2×C4C22×#4111yescharacteristic
1118C2×C4#58511yescharacteristic
1119C2×C4#58511yescharacteristic
1120C2×C4#58511yescharacteristic
1121C2×C4#58511yescharacteristic
1122C2×C4#58511yescharacteristic
1123C8—22no—
1124C8—41no—
1125C8—41no—
1126C8—41no—
1127C8—41no—
1128C8—41no—
1129C8—41no—
1130C8—41no—
1131C22—41no—
1132C22—41no—
1133C22—41no—
1134C22—41no—
1135C22—42no—
1136C22—41no—
1137C22—41no—
1138C22—42no—
1139C22—41no—
1140C22—41no—
1141C22—41no—
1142C22—41no—
1143C22—41no—
1144C22—41no—
1145C22—41no—
1146C22—41no—
1147C22—42no—
1148C22—81no—
1149C22—81no—
1150C22—81no—
1151C22—81no—
1152C22#344911yescharacteristic
1153C22D4×#4111yescharacteristic
1154C22#348511yescharacteristic
1155C22C2×#57711yescharacteristic
1156C22C2×#57711yescharacteristic
1157C22#358411yescharacteristic
1158C22#358611yescharacteristic
1159C4—22no—
1160C4—22no—
1161C4—41no—
1162C4—41no—
1163C4—41no—
1164C4—41no—
1165C4—41no—
1166C4—41no—
1167C4—41no—
1168C4—41no—
1169C4—41no—
1170C4—41no—
1171C4—42no—
1172C4—81no—
1173C4—81no—
1174C4—81no—
1175C4—81no—
1176C4—81no—
1177C4—81no—
1178C4—81no—
1179C4—81no—
1180C4—81no—
1181C4—81no—
1182C4—81no—
1183C4—81no—
1184C4—81no—
1185C4—81no—
1186C4#349111yescharacteristic
1187C4#352111yescharacteristic
1188C4#356611yescharacteristic
1189C4#356811yescharacteristic
1190C2—81no—
1191C2—81no—
1192C2—82no—
1193C2#3837611yescharacteristic
1194C2#6095611yescharacteristic
1195C2#6097711yescharacteristic
1196C2#6147611yescharacteristic
1197C2#6152011yescharacteristic
1198C2#6179211yescharacteristic
1199C2#6180111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2407C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2293 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #35184C2semidirect
3. #33085C2semidirect
4. #32451C2semidirect
5. #32376C2semidirect
6. #32260C2semidirect
7. #32014C2semidirect
8. #31531C2semidirect
9. #31470C2semidirect
12. #30182C2semidirect
13. #30028C2semidirect
14. #29512C2semidirect
15. #29392C2semidirect
16. #28993C2semidirect
17. #28861C2semidirect
18. #28064C2semidirect
19. #27884C2semidirect
20. #27867C2semidirect
21. #27637C2semidirect
22. #27593C2semidirect
23. #27526C2semidirect
24. #27459C2semidirect
25. #27160C2semidirect
26. #25030C2semidirect
27. #24907C2semidirect
28. #22789C2semidirect
29. #22195C2semidirect
30. #22059C2semidirect
31. #21120C2semidirect

Maximal subgroups

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

subgroupindex
#382042
#351842
#330852
#324512
#323762
#322602
#320142
#315312
#314702
#312782
#304102
#301822
#300282
#295122
#293922
#289932
#288612
#280642
#278842
#278672
#276372
#275932
#275262
#274592
#271602
#250302
#249072
#227892
#221952
#220592
#211202