Finite Group Databasebeta

← #6812595

Subgroups — #6812595

Order 512.

1254 conjugacy classes of subgroups.

The subgroup lattice has 1149 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39914C211yesmaximal, characteristic
2#39155C211yesmaximal, characteristic
3#33144C211yesmaximal, characteristic, complemented
4#32449C211yesmaximal, characteristic, complemented
5#32439C211yesmaximal, characteristic, complemented
6#32337C211yesmaximal, characteristic, complemented
7#32319C211yesmaximal, characteristic, complemented
8#31956C211yesmaximal, characteristic, complemented
9#31940C211yesmaximal, characteristic, complemented
10#31711C211yesmaximal, characteristic, complemented
11#31694C211yesmaximal, characteristic, complemented
12#29915C211yesmaximal, characteristic, complemented
13#29913C211yesmaximal, characteristic, complemented
14#28872C211yesmaximal, characteristic, complemented
15#28860C211yesmaximal, characteristic, complemented
16#28781C211yesmaximal, characteristic, complemented
17#28568C211yesmaximal, characteristic
18#28039C211yesmaximal, characteristic, complemented
19#28035C211yesmaximal, characteristic, complemented
20#27745C211yesmaximal, characteristic, complemented
21#27730C211yesmaximal, characteristic, complemented
22#27721C211yesmaximal, characteristic, complemented
23#27708C211yesmaximal, characteristic, complemented
24#26434C211yesmaximal, characteristic, complemented
25#26429C211yesmaximal, characteristic, complemented
26#26222C211yesmaximal, characteristic
27#26221C211yesmaximal, characteristic
28#23144C211yesmaximal, characteristic, complemented
29#22714C211yesmaximal, characteristic
30#21565C211yesmaximal, characteristic
31#20765C211yesmaximal, characteristic, complemented
32C2×#470C2211yescharacteristic
33C2×#436C2211yescharacteristic
34C2×C4×M16C2211yescharacteristic
35#2855C2211yescharacteristic
36#2855C2211yescharacteristic
37#2789—21no—
38#2783—21no—
39#2775—21no—
40#2767—21no—
41#2746—21no—
42#2744—21no—
43#2738—21no—
44#2695—21no—
45#2655—21no—
46#2643—21no—
47#2590—21no—
48#2577—21no—
49#2571C2211yescharacteristic
50#2571C2211yescharacteristic
51#2568C2211yescharacteristic
52#2565C2211yescharacteristic
53#2514C2211yescharacteristic
54#2514C2211yescharacteristic
55#2509C2211yescharacteristic
56#2507C2211yescharacteristic
57#2502C2211yescharacteristic
58#2499C2211yescharacteristic
59#2496C2211yescharacteristic
60#2494C2211yescharacteristic
61#2493—21no—
62#2488—21no—
63#2442C2211yescharacteristic
64#2441C2211yescharacteristic
65#2440C2211yescharacteristic
66#2439C2211yescharacteristic
67#2421C2211yescharacteristic
68#2421C2211yescharacteristic
69#2417C2211yescharacteristic
70#2415C2211yescharacteristic
71#2362C2211yescharacteristic
72#2360C2211yescharacteristic
73#2352C2211yescharacteristic
74#2352C2211yescharacteristic
75#2334—21no—
76#2329—21no—
77C4×#123C2211yescharacteristic
78#2285C2211yescharacteristic
79C2×#382C2211yescharacteristic
80#2101C2211yescharacteristic
81#2101C2211yescharacteristic
82#2101C2211yescharacteristic
83#2101C2211yescharacteristic
84#2100C2211yescharacteristic
85#2100C2211yescharacteristic
86#2100C2211yescharacteristic
87#2099C2211yescharacteristic
88#2097C2211yescharacteristic
89#2097C2211yescharacteristic
90#2096C2211yescharacteristic
91#2095C2211yescharacteristic
92#2088C2211yescharacteristic
93#2088C2211yescharacteristic
94#2088C2211yescharacteristic
95#2085C2211yescharacteristic
96#2085C2211yescharacteristic
97#2085C2211yescharacteristic
98#2085C2211yescharacteristic
99#2084C2211yescharacteristic
100#2083C2211yescharacteristic
101#2077C2211yescharacteristic
102#2076C2211yescharacteristic
103#2076C2211yescharacteristic
104#2074C2211yescharacteristic
105#2074C2211yescharacteristic
106#2074C2211yescharacteristic
107#2074C2211yescharacteristic
108#2074C2211yescharacteristic
109#2074C2211yescharacteristic
110#2066C2211yescharacteristic
111#2066C2211yescharacteristic
112#2059C2211yescharacteristic
113#2057C2211yescharacteristic
114#2056C2211yescharacteristic
115#2036C2211yescharacteristic
116#2035C2211yescharacteristic
117#2026C2211yescharacteristic
118#2024C2211yescharacteristic
119#2001C2211yescharacteristic
120#1992C2211yescharacteristic
121#1990C2211yescharacteristic
122#1989C2211yescharacteristic
123#1988C2211yescharacteristic
124#1971C2211yescharacteristic
125#1969C2211yescharacteristic
126#1949C2211yescharacteristic
127#1949C2211yescharacteristic
128#1943C2211yescharacteristic
129#1943C2211yescharacteristic
130#1942C2211yescharacteristic
131#1941C2211yescharacteristic
132#1935C2211yescharacteristic
133#1935C2211yescharacteristic
134#1935C2211yescharacteristic
135#1933C2211yescharacteristic
136#1933C2211yescharacteristic
137#1933C2211yescharacteristic
138#1933C2211yescharacteristic
139#1933C2211yescharacteristic
140#1928C2211yescharacteristic
141#1928C2211yescharacteristic
142#1924C2211yescharacteristic
143#1923C2211yescharacteristic
144#1920C2211yescharacteristic
145#1920C2211yescharacteristic
146#1920C2211yescharacteristic
147#1920C2211yescharacteristic
148#1918C2211yescharacteristic
149#1918C2211yescharacteristic
150#1917C2211yescharacteristic
151#1916C2211yescharacteristic
152#1894C2211yescharacteristic
153#1894C2211yescharacteristic
154#1894C2211yescharacteristic
155#1894C2211yescharacteristic
156#1878C2211yescharacteristic
157#1878C2211yescharacteristic
158#1873C2211yescharacteristic
159#1873C2211yescharacteristic
160#1873C2211yescharacteristic
161#1872C2211yescharacteristic
162#1872C2211yescharacteristic
163#1872C2211yescharacteristic
164#1870C2211yescharacteristic
165#1865C2211yescharacteristic
166#1863C2211yescharacteristic
167#1854C2211yescharacteristic
168#1854C2211yescharacteristic
169#1854C2211yescharacteristic
170#1853C2211yescharacteristic
171#1853C2211yescharacteristic
172#1852C2211yescharacteristic
173#1851C2211yescharacteristic
174#1836C2211yescharacteristic
175#1836C2211yescharacteristic
176#1836C2211yescharacteristic
177#1836C2211yescharacteristic
178#1835C2211yescharacteristic
179#1835C2211yescharacteristic
180#1835C2211yescharacteristic
181#1835C2211yescharacteristic
182#1835C2211yescharacteristic
183#1825C2211yescharacteristic
184#1823C2211yescharacteristic
185#1817C2211yescharacteristic
186#1809C2211yescharacteristic
187#1809C2211yescharacteristic
188#1803C2211yescharacteristic
189#1803C2211yescharacteristic
190C4×#106C2211yescharacteristic
191#1771C2211yescharacteristic
192C8×C4⋊C4C2211yescharacteristic
193#1763C2211yescharacteristic
194C4×#103C2211yescharacteristic
195#1753C2211yescharacteristic
196#1753C2211yescharacteristic
197#1753C2211yescharacteristic
198#1736C2211yescharacteristic
199#1736C2211yescharacteristic
200#1736C2211yescharacteristic
201#1736C2211yescharacteristic
202#1736C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×#126—21no—
209C2×#125C2311yescharacteristic
210C2×#123D411yescharacteristic
211C2×C22⋊Q8—21no—
212C2×C22⋊Q8C2311yescharacteristic
213C2×C22⋊Q8C2311yescharacteristic
214C2×C22⋊Q8C2311yescharacteristic
215C2×C22⋊Q8C2311yescharacteristic
216C2×C4×Q8C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×D4C2311yescharacteristic
219C2×#117C2311yescharacteristic
220C2×#117C2311yescharacteristic
221C2×#117C2311yescharacteristic
222C22×C4⋊C4C2311yescharacteristic
223C22×C4⋊C4C2311yescharacteristic
224C22×C4⋊C4C2311yescharacteristic
225C22×C42C2311yescharacteristic
226#470—24no—
227#436—24no—
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#106C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×C4⋊C8C2311yescharacteristic
240C2×C4⋊C8C2311yescharacteristic
241C2×C4⋊C8C2311yescharacteristic
242C2×#103C2311yescharacteristic
243C2×#103C2311yescharacteristic
244C2×#103C2311yescharacteristic
245C2×#103C2311yescharacteristic
246C2×#103C2311yescharacteristic
247C2×#103C2311yescharacteristic
248C2×#103C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×C22⋊C8C2311yescharacteristic
257C2×C22⋊C8C2311yescharacteristic
258C2×C22⋊C8C2311yescharacteristic
259C2×C22⋊C8C2311yescharacteristic
260C2×C22⋊C8C2311yescharacteristic
261C4×M16—24no—
262C2×#97C2311yescharacteristic
263C2×#97C2311yescharacteristic
264C2×#97C2311yescharacteristic
265C2×C4×C8C2311yescharacteristic
266C2×C4×C8C2311yescharacteristic
267C2×C4×C8C2311yescharacteristic
268C2×C4×C8C2311yescharacteristic
269#401—21no—
270#401—21no—
271#401—21no—
272#400—21no—
273#400—21no—
274#400—21no—
275#400—21no—
276#400—21no—
277#400—21no—
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#399—21no—
287#398—21no—
288#398—21no—
289#398—21no—
290#398—21no—
291#398—21no—
292#398—21no—
293#398—21no—
294#398—21no—
295#398—21no—
296#397—21no—
297#397—21no—
298#397—21no—
299#397—21no—
300#397—21no—
301#397—21no—
302#397—21no—
303#396—21no—
304#396—21no—
305#396—21no—
306#395—21no—
307#394—21no—
308#393—21no—
309#391—21no—
310#391—21no—
311#391—21no—
312#391C2311yescharacteristic
313#391C2311yescharacteristic
314#391C2311yescharacteristic
315#391C2311yescharacteristic
316#391C2311yescharacteristic
317#391C2311yescharacteristic
318#391C2311yescharacteristic
319#391C2311yescharacteristic
320#389—21no—
321#389—21no—
322#389—21no—
323#389—21no—
324#389—21no—
325#389—21no—
326#389—21no—
327#389C2311yescharacteristic
328#389C2311yescharacteristic
329#389C2311yescharacteristic
330#389C2311yescharacteristic
331#389C2311yescharacteristic
332#389C2311yescharacteristic
333#389C2311yescharacteristic
334#389C2311yescharacteristic
335#389C2311yescharacteristic
336#389C2311yescharacteristic
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#388—21no—
340#388—21no—
341#388—21no—
342#388—21no—
343#388—21no—
344#388—21no—
345#388—21no—
346#388—21no—
347#388D411yescharacteristic
348#388D411yescharacteristic
349#387—21no—
350#387—21no—
351#387—21no—
352#387—21no—
353#387—21no—
354#387—21no—
355#387—21no—
356#387—21no—
357#387—21no—
358#387—21no—
359#387—21no—
360#387—21no—
361#387—21no—
362#387—21no—
363#387—21no—
364#387—21no—
365#387—21no—
366#387—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387D411yescharacteristic
372#387D411yescharacteristic
373#386—21no—
374#386—21no—
375#386—21no—
376#386D411yescharacteristic
377#385—21no—
378#385—21no—
379#385—21no—
380#385—21no—
381#385—21no—
382#385—21no—
383#385—21no—
384#385D411yescharacteristic
385#384C2311yescharacteristic
386#384C2311yescharacteristic
387#384C2311yescharacteristic
388#384C2311yescharacteristic
389#383—21no—
390#383—21no—
391#382—21no—
392#382—21no—
393#382—21no—
394#382—21no—
395#382C2311yescharacteristic
396#382C2311yescharacteristic
397#382C2311yescharacteristic
398#382C2311yescharacteristic
399#382C2311yescharacteristic
400#382C2311yescharacteristic
401#382C2311yescharacteristic
402#382C2311yescharacteristic
403#381—21no—
404#381—21no—
405#381D411yescharacteristic
406#380—21no—
407#380—21no—
408#380—21no—
409#380—21no—
410#380C2311yescharacteristic
411#380C2311yescharacteristic
412#380C2311yescharacteristic
413#380C2311yescharacteristic
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416C4×C4⋊C4—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C22⋊C4—21no—
426C4×C22⋊C4—21no—
427C4×C22⋊C4—21no—
428C4×C22⋊C4C2311yescharacteristic
429C4×C22⋊C4C2311yescharacteristic
430C4×C22⋊C4C2311yescharacteristic
431C2×#95—21no—
432C2×#95—21no—
433#340C2311yescharacteristic
434#340C2311yescharacteristic
435#340C2311yescharacteristic
436#340C2311yescharacteristic
437#340C2311yescharacteristic
438#340C2311yescharacteristic
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#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481C22×Q8—21no—
482C22×Q8C2411yescharacteristic
483C22×Q8C2411yescharacteristic
484C22×D4C2×D411yescharacteristic
485C23×C4—21no—
486C23×C4—21no—
487C23×C4—21no—
488C23×C4C2×D411yescharacteristic
489C23×C4C2×D411yescharacteristic
490C23×C4C2411yescharacteristic
491C23×C4C2411yescharacteristic
492C2×Q16—22no—
493C2×Q16—41no—
494C2×Q16—41no—
495C2×M16—22no—
496C2×M16—22no—
497C2×M16—41no—
498C2×M16—41no—
499C2×M16—41no—
500C2×M16—41no—
501C2×M16—41no—
502C2×M16—41no—
503C2×M16#4114yes—
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C4⋊Q8—41no—
513C4⋊Q8—41no—
514#126—44no—
515#125—41no—
516#125—41no—
517#123—42no—
518C22⋊Q8—22no—
519C22⋊Q8—22no—
520C22⋊Q8—22no—
521C22⋊Q8—22no—
522C22⋊Q8—44no—
523C22⋊Q8—41no—
524C22⋊Q8—41no—
525C22⋊Q8—41no—
526C22⋊Q8—41no—
527C4×Q8—41no—
528C4×Q8—41no—
529C4×Q8—41no—
530C4×Q8—41no—
531C4×D4—22no—
532C4×D4—22no—
533#117—41no—
534#117—41no—
535#117—41no—
536#117—41no—
537#117—41no—
538#117—41no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
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—41no—
572C2×C4⋊C4—41no—
573C2×C4⋊C4—41no—
574C2×C4⋊C4—41no—
575C2×C4⋊C4—41no—
576C2×C4⋊C4—41no—
577C2×C4⋊C4C2×D411yescharacteristic
578C2×C4⋊C4C2×D411yescharacteristic
579C2×C4⋊C4C2×D411yescharacteristic
580C2×C4⋊C4C2×D411yescharacteristic
581C2×C4⋊C4C2×D411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4C2×D411yescharacteristic
610C2×C22⋊C4C2×D411yescharacteristic
611C2×C22⋊C4C2×D411yescharacteristic
612C2×C22⋊C4C2×D411yescharacteristic
613C2×C22⋊C4C2×D411yescharacteristic
614C2×C22⋊C4C2×D411yescharacteristic
615C2×C22⋊C4C2×D411yescharacteristic
616C2×C22⋊C4C2×D411yescharacteristic
617C2×C42—22no—
618C2×C42—22no—
619C2×C42—21no—
620C2×C42—21no—
621C2×C42—21no—
622C2×C42—21no—
623C2×C42—21no—
624C2×C42—21no—
625C2×C42—21no—
626C2×C42—21no—
627C2×C42—21no—
628C2×C42C2×D411yescharacteristic
629C2×C42C2×D411yescharacteristic
630C2×C42C2411yescharacteristic
631C2×C42C2411yescharacteristic
632C2×C42C2411yescharacteristic
633C2×C42C2411yescharacteristic
634C2×C42C2411yescharacteristic
635#107—41no—
636#107—41no—
637#107—41no—
638#107—41no—
639#107—41no—
640#106—22no—
641#106—41no—
642#106—41no—
643#106—41no—
644#106—41no—
645#106—41no—
646C4⋊C8—22no—
647C4⋊C8—41no—
648C4⋊C8—41no—
649#103—22no—
650#103—22no—
651#103—41no—
652#103—41no—
653#103—41no—
654#103—41no—
655#103—41no—
656#103—41no—
657#103—41no—
658#103—41no—
659#103—41no—
660#103—41no—
661#103—41no—
662#103—41no—
663C22⋊C8—22no—
664C22⋊C8—22no—
665C22⋊C8—22no—
666C22⋊C8—41no—
667C22⋊C8—41no—
668#97—22no—
669#97—22no—
670#97—41no—
671C4×C8—22no—
672C4×C8—22no—
673C4×C8—22no—
674C4×C8—41no—
675#95—21no—
676#95—21no—
677#95—21no—
678#95—21no—
679#95—21no—
680#95—21no—
681#95—21no—
682#95—21no—
683#95—21no—
684#95—21no—
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95—21no—
690#95—21no—
691#95—21no—
692#95—21no—
693#95—21no—
694#95—21no—
695#95—21no—
696#95—21no—
697#95—21no—
698#95—21no—
699#95—21no—
700#95—21no—
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#95C2×D411yescharacteristic
730#95C2×D411yescharacteristic
731#95C2×D411yescharacteristic
732#95C2×D411yescharacteristic
733#95C2×D411yescharacteristic
734#95C2×D411yescharacteristic
735#95C2×D411yescharacteristic
736#95C2×D411yescharacteristic
737#95C2×D411yescharacteristic
738#95C2×D411yescharacteristic
739C24C22×D411yescharacteristic
740C24C22×D411yescharacteristic
741C2×Q8—21no—
742C2×Q8—21no—
743C2×Q8—21no—
744C2×Q8—21no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—21no—
748C2×Q8—21no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—21no—
753C2×Q8—42no—
754C2×Q8—81no—
755C2×Q8—81no—
756C2×D4—22no—
757C2×D4—41no—
758C2×D4—41no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—41no—
788C22×C4—41no—
789C22×C4—41no—
790C22×C4—41no—
791C22×C4—42no—
792C22×C4—42no—
793C22×C4—81no—
794C22×C4—81no—
795C22×C4—81no—
796C22×C4—81no—
797C22×C4—81no—
798C22×C4—81no—
799C22×C4—81no—
800C22×C4C22×D411yescharacteristic
801C22×C4C22×D411yescharacteristic
802C22×C4C22×D411yescharacteristic
803C22×C4C22×D411yescharacteristic
804C22×C4C22×D411yescharacteristic
805C22×C4C22×D411yescharacteristic
806C22×C4C22×D411yescharacteristic
807C22×C4C22×D411yescharacteristic
808C22×C4C22×D411yescharacteristic
809C22×C4C22×D411yescharacteristic
810C22×C4C22×D411yescharacteristic
811C22×C4C22×D411yescharacteristic
812C22×C4C2×#4112yes—
813C22×C42−1+412yes—
814C22×C4C2511yescharacteristic
815Q16—82no—
816M16—44no—
817M16—44no—
818M16—82no—
819C2×C8—21no—
820C2×C8—21no—
821C2×C8—21no—
822C2×C8—21no—
823C2×C8—21no—
824C2×C8—21no—
825C2×C8—21no—
826C2×C8—21no—
827C2×C8—21no—
828C2×C8—21no—
829C2×C8—21no—
830C2×C8—21no—
831C2×C8—21no—
832C2×C8—21no—
833C2×C8—21no—
834C2×C8—21no—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8C2×#4112yes—
842C2×C8C2×#4112yes—
843C4⋊C4—22no—
844C4⋊C4—22no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—21no—
855C4⋊C4—21no—
856C4⋊C4—21no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—41no—
874C4⋊C4—41no—
875C4⋊C4—41no—
876C4⋊C4—42no—
877C4⋊C4—42no—
878C4⋊C4—42no—
879C4⋊C4—42no—
880C4⋊C4—42no—
881C4⋊C4—42no—
882C4⋊C4—42no—
883C4⋊C4—42no—
884C4⋊C4—42no—
885C4⋊C4—81no—
886C4⋊C4—81no—
887C4⋊C4—81no—
888C4⋊C4—81no—
889C4⋊C4—81no—
890C4⋊C4—81no—
891C4⋊C4—81no—
892C4⋊C4—81no—
893C4⋊C4—81no—
894C4⋊C4—81no—
895C4⋊C4—81no—
896C4⋊C4—81no—
897C4⋊C4—81no—
898C4⋊C4—81no—
899C4⋊C4—81no—
900C4⋊C4—81no—
901C4⋊C4—81no—
902C4⋊C4—81no—
903C4⋊C4—81no—
904C4⋊C4—81no—
905C4⋊C4—81no—
906C4⋊C4—81no—
907C4⋊C4—81no—
908C22⋊C4—22no—
909C22⋊C4—22no—
910C22⋊C4—22no—
911C22⋊C4—22no—
912C22⋊C4—41no—
913C22⋊C4—41no—
914C22⋊C4—41no—
915C22⋊C4—41no—
916C22⋊C4—42no—
917C22⋊C4—42no—
918C22⋊C4—42no—
919C22⋊C4—42no—
920C22⋊C4—42no—
921C22⋊C4—81no—
922C22⋊C4—81no—
923C22⋊C4—81no—
924C22⋊C4—81no—
925C22⋊C4—81no—
926C22⋊C4—81no—
927C22⋊C4—81no—
928C22⋊C4—81no—
929C42—22no—
930C42—22no—
931C42—21no—
932C42—21no—
933C42—21no—
934C42—21no—
935C42—21no—
936C42—21no—
937C42—21no—
938C42—21no—
939C42—21no—
940C42—21no—
941C42—42no—
942C42—81no—
943C42—81no—
944C42—81no—
945C42—81no—
946C42—81no—
947C42—81no—
948C42—81no—
949C42—81no—
950C23—21no—
951C23—21no—
952C23—21no—
953C23—21no—
954C23—21no—
955C23—21no—
956C23—21no—
957C23—21no—
958C23—21no—
959C23—21no—
960C23—21no—
961C23—21no—
962C23—21no—
963C23#54712yes—
964C23C23×D411yescharacteristic
965Q8—41no—
966Q8—41no—
967Q8—41no—
968Q8—41no—
969Q8—41no—
970Q8—41no—
971Q8—41no—
972Q8—41no—
973Q8—162no—
974D4—82no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—82no—
1066C2×C4—82no—
1067C2×C4—162no—
1068C2×C4—162no—
1069C2×C4—162no—
1070C2×C4#54712yes—
1071C2×C4#57512yes—
1072C2×C4C22×#4111yescharacteristic
1073C2×C4C2×2−1+411yescharacteristic
1074C2×C4#58511yescharacteristic
1075C2×C4#58511yescharacteristic
1076C2×C4#58511yescharacteristic
1077C2×C4#58511yescharacteristic
1078C8—22no—
1079C8—22no—
1080C8—41no—
1081C8—41no—
1082C8—41no—
1083C8—41no—
1084C8—41no—
1085C8—41no—
1086C22—22no—
1087C22—22no—
1088C22—22no—
1089C22—41no—
1090C22—41no—
1091C22—41no—
1092C22—41no—
1093C22—41no—
1094C22—41no—
1095C22—41no—
1096C22—41no—
1097C22—41no—
1098C22—41no—
1099C22—41no—
1100C22C2×#54711yescharacteristic
1101C22#350011yescharacteristic
1102C22#350011yescharacteristic
1103C22C2×#57511yescharacteristic
1104C22#358411yescharacteristic
1105C22#358611yescharacteristic
1106C22#358611yescharacteristic
1107C4—22no—
1108C4—22no—
1109C4—41no—
1110C4—41no—
1111C4—41no—
1112C4—41no—
1113C4—41no—
1114C4—41no—
1115C4—41no—
1116C4—41no—
1117C4—41no—
1118C4—41no—
1119C4—81no—
1120C4—81no—
1121C4—81no—
1122C4—81no—
1123C4—81no—
1124C4—81no—
1125C4—81no—
1126C4—81no—
1127C4—81no—
1128C4—81no—
1129C4—81no—
1130C4—81no—
1131C4—81no—
1132C4—81no—
1133C4—81no—
1134C4—81no—
1135C4#345511yescharacteristic
1136C4#349111yescharacteristic
1137C4#355311yescharacteristic
1138C4#355311yescharacteristic
1139C2—42no—
1140C2—81no—
1141C2#3934511yescharacteristic
1142C2#6125711yescharacteristic
1143C2#6127711yescharacteristic
1144C2#6254711yescharacteristic
1145C2#6257111yescharacteristic
1146C2#6259111yescharacteristic
1147C2#6261211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #33144C2semidirect
4. #32449C2semidirect
5. #32439C2semidirect
6. #32337C2semidirect
7. #32319C2semidirect
8. #31956C2semidirect
9. #31940C2semidirect
10. #31711C2semidirect
11. #31694C2semidirect
12. #29915C2semidirect
13. #29913C2semidirect
14. #28872C2semidirect
15. #28860C2semidirect
16. #28781C2semidirect
18. #28039C2semidirect
19. #28035C2semidirect
20. #27745C2semidirect
21. #27730C2semidirect
22. #27721C2semidirect
23. #27708C2semidirect
24. #26434C2semidirect
25. #26429C2semidirect
28. #23144C2semidirect
31. #20765C2semidirect

Maximal subgroups

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

subgroupindex
#399142
#391552
#331442
#324492
#324392
#323372
#323192
#319562
#319402
#317112
#316942
#299152
#299132
#288722
#288602
#287812
#285682
#280392
#280352
#277452
#277302
#277212
#277082
#264342
#264292
#262222
#262212
#231442
#227142
#215652
#207652