Finite Group Databasebeta

← #6789177

Subgroups — #6789177

Order 512.

1202 conjugacy classes of subgroups.

The subgroup lattice has 1102 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38927C211yesmaximal, characteristic
2#38066C211yesmaximal, characteristic
3#33262C211yesmaximal, characteristic, complemented
4#32434C211yesmaximal, characteristic, complemented
5#32393C211yesmaximal, characteristic, complemented
6#32372C211yesmaximal, characteristic, complemented
7#32313C211yesmaximal, characteristic, complemented
8#32306C211yesmaximal, characteristic
9#31936C211yesmaximal, characteristic
10#31698C211yesmaximal, characteristic
11#31097C211yesmaximal, characteristic
12#30388C211yesmaximal, characteristic, complemented
13#30363C211yesmaximal, characteristic
14#29591C211yesmaximal, characteristic, complemented
15#29585C211yesmaximal, characteristic, complemented
16#29462C211yesmaximal, characteristic
17#29439C211yesmaximal, characteristic, complemented
18#29326C211yesmaximal, characteristic, complemented
19#29298C211yesmaximal, characteristic
20#27460C211yesmaximal, characteristic
21#27322C211yesmaximal, characteristic, complemented
22#27180C211yesmaximal, characteristic
23#27053C211yesmaximal, characteristic
24#27025C211yesmaximal, characteristic, complemented
25#26865C211yesmaximal, characteristic, complemented
26#26558C211yesmaximal, characteristic
27#26383C211yesmaximal, characteristic, complemented
28#22128C211yesmaximal, characteristic, complemented
29#22084C211yesmaximal, characteristic
30#21437C211yesmaximal, characteristic
31#21281C211yesmaximal, characteristic, complemented
32C2×#483C2211yescharacteristic
33C2×#479C2211yescharacteristic
34C2×C4×Q16C2211yescharacteristic
35#2855C2211yescharacteristic
36#2851C2211yescharacteristic
37#2776—21no—
38#2770—21no—
39#2769—21no—
40#2769—21no—
41#2768—21no—
42#2767—21no—
43#2766—21no—
44#2719—21no—
45#2647C2211yescharacteristic
46#2647C2211yescharacteristic
47#2647C2211yescharacteristic
48#2645C2211yescharacteristic
49#2575—21no—
50#2570C2211yescharacteristic
51#2565C2211yescharacteristic
52#2524—21no—
53#2524—21no—
54#2515—21no—
55#2514C2211yescharacteristic
56#2506C2211yescharacteristic
57#2506C2211yescharacteristic
58#2502C2211yescharacteristic
59#2497C2211yescharacteristic
60#2495C2211yescharacteristic
61#2493—21no—
62#2493—21no—
63#2473—21no—
64#2453C2211yescharacteristic
65#2442—21no—
66#2442C2211yescharacteristic
67#2423C2211yescharacteristic
68#2421C2211yescharacteristic
69#2370C2211yescharacteristic
70#2360C2211yescharacteristic
71#2351C2211yescharacteristic
72#2345C2211yescharacteristic
73#2330C2211yescharacteristic
74#2320C2211yescharacteristic
75#2320C2211yescharacteristic
76#2320C2211yescharacteristic
77C4×C22⋊Q8C2211yescharacteristic
78C2×#389C2211yescharacteristic
79#2283C2211yescharacteristic
80#2101C2211yescharacteristic
81#2101C2211yescharacteristic
82#2101C2211yescharacteristic
83#2099C2211yescharacteristic
84#2097C2211yescharacteristic
85#2097C2211yescharacteristic
86#2097C2211yescharacteristic
87#2095C2211yescharacteristic
88#2088C2211yescharacteristic
89#2087C2211yescharacteristic
90#2086C2211yescharacteristic
91#2085C2211yescharacteristic
92#2085C2211yescharacteristic
93#2085C2211yescharacteristic
94#2084C2211yescharacteristic
95#2083C2211yescharacteristic
96#2083C2211yescharacteristic
97#2083C2211yescharacteristic
98#2077C2211yescharacteristic
99#2076C2211yescharacteristic
100#2076C2211yescharacteristic
101#2074C2211yescharacteristic
102#2072C2211yescharacteristic
103#2072C2211yescharacteristic
104#2068C2211yescharacteristic
105#2068C2211yescharacteristic
106#2066C2211yescharacteristic
107#2066C2211yescharacteristic
108#2059C2211yescharacteristic
109#2059C2211yescharacteristic
110#2059C2211yescharacteristic
111#2059C2211yescharacteristic
112#2059C2211yescharacteristic
113#2056C2211yescharacteristic
114#2036C2211yescharacteristic
115#2036C2211yescharacteristic
116#2036C2211yescharacteristic
117#2035C2211yescharacteristic
118#2026C2211yescharacteristic
119#2001C2211yescharacteristic
120#1989C2211yescharacteristic
121#1969C2211yescharacteristic
122#1969C2211yescharacteristic
123#1949C2211yescharacteristic
124#1949C2211yescharacteristic
125#1948C2211yescharacteristic
126#1947C2211yescharacteristic
127#1947C2211yescharacteristic
128#1944C2211yescharacteristic
129#1944C2211yescharacteristic
130#1944C2211yescharacteristic
131#1944C2211yescharacteristic
132#1943C2211yescharacteristic
133#1943C2211yescharacteristic
134#1942C2211yescharacteristic
135#1942C2211yescharacteristic
136#1942C2211yescharacteristic
137#1942C2211yescharacteristic
138#1942C2211yescharacteristic
139#1941C2211yescharacteristic
140#1941C2211yescharacteristic
141#1941C2211yescharacteristic
142#1935C2211yescharacteristic
143#1935C2211yescharacteristic
144#1935C2211yescharacteristic
145#1935C2211yescharacteristic
146#1935C2211yescharacteristic
147#1935C2211yescharacteristic
148#1933C2211yescharacteristic
149#1933C2211yescharacteristic
150#1928C2211yescharacteristic
151#1927C2211yescharacteristic
152#1927C2211yescharacteristic
153#1927C2211yescharacteristic
154#1924C2211yescharacteristic
155#1924C2211yescharacteristic
156#1923C2211yescharacteristic
157#1923C2211yescharacteristic
158#1921C2211yescharacteristic
159#1921C2211yescharacteristic
160#1921C2211yescharacteristic
161#1921C2211yescharacteristic
162#1921C2211yescharacteristic
163#1920C2211yescharacteristic
164#1920C2211yescharacteristic
165#1920C2211yescharacteristic
166#1919C2211yescharacteristic
167#1918C2211yescharacteristic
168#1917C2211yescharacteristic
169#1917C2211yescharacteristic
170#1916C2211yescharacteristic
171#1916C2211yescharacteristic
172#1878C2211yescharacteristic
173#1878C2211yescharacteristic
174#1872C2211yescharacteristic
175#1865C2211yescharacteristic
176#1865C2211yescharacteristic
177#1865C2211yescharacteristic
178#1865C2211yescharacteristic
179#1863C2211yescharacteristic
180#1863C2211yescharacteristic
181#1863C2211yescharacteristic
182#1863C2211yescharacteristic
183#1853C2211yescharacteristic
184#1853C2211yescharacteristic
185#1852C2211yescharacteristic
186#1852C2211yescharacteristic
187#1852C2211yescharacteristic
188#1847C2211yescharacteristic
189#1847C2211yescharacteristic
190#1835C2211yescharacteristic
191#1834C2211yescharacteristic
192#1823C2211yescharacteristic
193#1803C2211yescharacteristic
194C4×#107C2211yescharacteristic
195#1768C2211yescharacteristic
196#1768C2211yescharacteristic
197#1763C2211yescharacteristic
198#1763C2211yescharacteristic
199#1749C2211yescharacteristic
200C4×C22⋊C8C2211yescharacteristic
201#1746C2211yescharacteristic
202#1726C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C2×#125—21no—
205C2×#125—21no—
206C2×#125C2311yescharacteristic
207C2×#125C2311yescharacteristic
208C2×C22⋊Q8C2311yescharacteristic
209C2×C22⋊Q8C2311yescharacteristic
210C2×C4×Q8C2311yescharacteristic
211C2×C4×Q8C2311yescharacteristic
212C2×C4×Q8C2311yescharacteristic
213C2×C4×Q8C2311yescharacteristic
214C22×C4⋊C4—21no—
215C22×C4⋊C4C2311yescharacteristic
216C22×C4⋊C4C2311yescharacteristic
217C22×C42C2311yescharacteristic
218#483—24no—
219#479—24no—
220C4×Q16—24no—
221C2×#107C2311yescharacteristic
222C2×#107C2311yescharacteristic
223C2×#107C2311yescharacteristic
224C2×#107C2311yescharacteristic
225C2×#107C2311yescharacteristic
226C2×#107C2311yescharacteristic
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#106C2311yescharacteristic
233C2×#106C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×C4⋊C8C2311yescharacteristic
241C2×C4⋊C8C2311yescharacteristic
242C2×C4⋊C8C2311yescharacteristic
243C2×C4⋊C8C2311yescharacteristic
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×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×C22⋊C8C2311yescharacteristic
259C2×C22⋊C8C2311yescharacteristic
260C2×C22⋊C8C2311yescharacteristic
261C2×C22⋊C8C2311yescharacteristic
262C2×#97C2311yescharacteristic
263C2×#97C2311yescharacteristic
264C2×#97C2311yescharacteristic
265C2×#97C2311yescharacteristic
266C2×C4×C8C2311yescharacteristic
267C2×C4×C8C2311yescharacteristic
268C2×C4×C8C2311yescharacteristic
269C2×C4×C8C2311yescharacteristic
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#400—21no—
287#400—21no—
288#400—21no—
289#400—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#398—21no—
299#398—21no—
300#398—21no—
301#398—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#398—21no—
306#398—21no—
307#397—21no—
308#397—21no—
309#396—21no—
310#391C2311yescharacteristic
311#391C2311yescharacteristic
312#391C2311yescharacteristic
313#391C2311yescharacteristic
314#391C2311yescharacteristic
315#391C2311yescharacteristic
316#391C2311yescharacteristic
317#391C2311yescharacteristic
318#389—21no—
319#389—21no—
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#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#388—21no—
348#388—21no—
349#388—21no—
350#388—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#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#385—21no—
381#385—21no—
382#385—21no—
383#385—21no—
384#385—21no—
385#385—21no—
386#385—21no—
387#385—21no—
388#384C2311yescharacteristic
389#384C2311yescharacteristic
390#384C2311yescharacteristic
391#384C2311yescharacteristic
392#383—21no—
393#383—21no—
394#383—21no—
395#383—21no—
396#383—21no—
397#383D411yescharacteristic
398#383D411yescharacteristic
399#382—21no—
400#382—21no—
401#382—21no—
402#382—21no—
403#382D411yescharacteristic
404#382D411yescharacteristic
405#382C2311yescharacteristic
406#382C2311yescharacteristic
407#382C2311yescharacteristic
408#382C2311yescharacteristic
409#381—21no—
410#381D411yescharacteristic
411#381D411yescharacteristic
412#380—21no—
413#380—21no—
414#380D411yescharacteristic
415#380D411yescharacteristic
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420C4×C4⋊C4—21no—
421C4×C4⋊C4—21no—
422C4×C4⋊C4—21no—
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C22⋊C4—21no—
432C4×C22⋊C4—21no—
433C4×C22⋊C4—21no—
434C4×C22⋊C4C2311yescharacteristic
435C4×C22⋊C4C2311yescharacteristic
436#376C2311yescharacteristic
437#376C2311yescharacteristic
438C2×#95—21no—
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#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481C22×Q8C2411yescharacteristic
482C22×Q8C2411yescharacteristic
483C23×C4—21no—
484C23×C4—21no—
485C23×C4C2×D411yescharacteristic
486C23×C4C2×D411yescharacteristic
487C23×C4C2411yescharacteristic
488C2×Q16—22no—
489C2×Q16—22no—
490C2×Q16—41no—
491C22×C8C2411yescharacteristic
492C22×C8C2411yescharacteristic
493C22×C8C2411yescharacteristic
494C22×C8C2411yescharacteristic
495C22×C8C2411yescharacteristic
496C22×C8C2411yescharacteristic
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499#125—22no—
500#125—41no—
501#125—41no—
502#125—41no—
503#125—82no—
504#125—82no—
505C22⋊Q8—22no—
506C22⋊Q8—41no—
507C22⋊Q8—41no—
508C22⋊Q8—41no—
509C4×Q8—22no—
510C4×Q8—22no—
511C4×Q8—22no—
512C4×Q8—41no—
513C4×Q8—41no—
514C4×Q8—41no—
515C4×Q8—41no—
516C4×Q8—41no—
517C2×C4⋊C4—22no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
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—41no—
559C2×C4⋊C4—41no—
560C2×C4⋊C4—41no—
561C2×C4⋊C4—82no—
562C2×C4⋊C4C2×D411yescharacteristic
563C2×C4⋊C4C2×D411yescharacteristic
564C2×C4⋊C4C2×D411yescharacteristic
565C2×C4⋊C4C2×D411yescharacteristic
566C2×C4⋊C4C2411yescharacteristic
567C2×C4⋊C4C2411yescharacteristic
568C2×C4⋊C4C2411yescharacteristic
569C2×C4⋊C4C2411yescharacteristic
570C2×C4⋊C4C2411yescharacteristic
571C2×C4⋊C4C2411yescharacteristic
572C2×C4⋊C4C2411yescharacteristic
573C2×C4⋊C4C2411yescharacteristic
574C2×C4⋊C4C2411yescharacteristic
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2411yescharacteristic
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4C2×D411yescharacteristic
587C2×C22⋊C4C2×D411yescharacteristic
588C2×C22⋊C4C2×D411yescharacteristic
589C2×C22⋊C4C2×D411yescharacteristic
590C2×C42—21no—
591C2×C42—21no—
592C2×C42—21no—
593C2×C42—21no—
594C2×C42—21no—
595C2×C42—21no—
596C2×C42—21no—
597C2×C42—21no—
598C2×C42—21no—
599C2×C42—21no—
600C2×C42—41no—
601C2×C42—41no—
602C2×C42C2×D411yescharacteristic
603C2×C42C2×D411yescharacteristic
604C2×C42C2411yescharacteristic
605C2×C42C2411yescharacteristic
606C2×C42C2411yescharacteristic
607C2×C42C2411yescharacteristic
608C2×C42C2411yescharacteristic
609C2×C42C2411yescharacteristic
610#107—22no—
611#107—22no—
612#107—22no—
613#107—41no—
614#107—41no—
615#107—41no—
616#107—41no—
617#107—41no—
618#107—41no—
619#107—41no—
620#107—41no—
621#106—22no—
622#106—22no—
623#106—22no—
624#106—41no—
625#106—41no—
626#106—41no—
627#106—41no—
628#106—41no—
629C4⋊C8—22no—
630C4⋊C8—22no—
631C4⋊C8—22no—
632C4⋊C8—41no—
633#103—22no—
634#103—22no—
635#103—22no—
636#103—22no—
637#103—22no—
638#103—41no—
639#103—41no—
640#103—41no—
641#103—41no—
642#103—41no—
643#103—41no—
644#103—41no—
645#103—41no—
646#103#4114yes—
647C22⋊C8—22no—
648C22⋊C8—22no—
649C22⋊C8—22no—
650C22⋊C8—41no—
651#97—22no—
652#97—41no—
653#97—41no—
654#97—41no—
655C4×C8—22no—
656C4×C8—22no—
657C4×C8—41no—
658C4×C8—41no—
659#95—21no—
660#95—21no—
661#95—21no—
662#95—21no—
663#95—21no—
664#95—21no—
665#95—21no—
666#95—21no—
667#95—21no—
668#95—21no—
669#95—21no—
670#95—21no—
671#95—21no—
672#95—21no—
673#95—21no—
674#95—21no—
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#95C2×D411yescharacteristic
714#95C2×D411yescharacteristic
715#95C2×D411yescharacteristic
716#95C2×D411yescharacteristic
717#95C2×D411yescharacteristic
718#95C2×D411yescharacteristic
719#95C2×D411yescharacteristic
720#95C2×D411yescharacteristic
721#95C2×D411yescharacteristic
722#95C2×D411yescharacteristic
723#95C2×D411yescharacteristic
724#95C2×D411yescharacteristic
725#95C2×D411yescharacteristic
726#95C2×D411yescharacteristic
727#95C2×D411yescharacteristic
728#95C2×D411yescharacteristic
729C24C22×D411yescharacteristic
730C2×Q8—21no—
731C2×Q8—21no—
732C2×Q8—21no—
733C2×Q8—21no—
734C2×Q8—21no—
735C2×Q8—21no—
736C2×Q8—21no—
737C2×Q8—21no—
738C2×Q8—21no—
739C2×Q8—21no—
740C2×Q8—21no—
741C2×Q8C2×#4112yes—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—22no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—41no—
766C22×C4—41no—
767C22×C4—41no—
768C22×C4—41no—
769C22×C4—41no—
770C22×C4—42no—
771C22×C4—42no—
772C22×C4—42no—
773C22×C4—81no—
774C22×C4—81no—
775C22×C4—81no—
776C22×C4C22×D411yescharacteristic
777C22×C4C22×D411yescharacteristic
778C22×C4C22×D411yescharacteristic
779C22×C4C22×D411yescharacteristic
780C22×C4C22×D411yescharacteristic
781C22×C4C22×D411yescharacteristic
782C22×C4C22×D411yescharacteristic
783C22×C4C22×D411yescharacteristic
784C22×C4C22×D411yescharacteristic
785C22×C4C22×D411yescharacteristic
786C22×C4C22×D411yescharacteristic
787C22×C4C22×D411yescharacteristic
788C22×C4C22×D411yescharacteristic
789C22×C4C2511yescharacteristic
790Q16—44no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—21no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—21no—
809C2×C8—21no—
810C2×C8—21no—
811C2×C8—21no—
812C2×C8C2×#4112yes—
813C2×C82−1+412yes—
814C2×C82−1+412yes—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—21no—
819C4⋊C4—21no—
820C4⋊C4—21no—
821C4⋊C4—21no—
822C4⋊C4—21no—
823C4⋊C4—21no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—21no—
827C4⋊C4—21no—
828C4⋊C4—21no—
829C4⋊C4—21no—
830C4⋊C4—21no—
831C4⋊C4—21no—
832C4⋊C4—21no—
833C4⋊C4—21no—
834C4⋊C4—21no—
835C4⋊C4—21no—
836C4⋊C4—21no—
837C4⋊C4—21no—
838C4⋊C4—21no—
839C4⋊C4—21no—
840C4⋊C4—21no—
841C4⋊C4—21no—
842C4⋊C4—41no—
843C4⋊C4—41no—
844C4⋊C4—41no—
845C4⋊C4—41no—
846C4⋊C4—42no—
847C4⋊C4—42no—
848C4⋊C4—42no—
849C4⋊C4—42no—
850C4⋊C4—42no—
851C4⋊C4—42no—
852C4⋊C4—42no—
853C4⋊C4—42no—
854C4⋊C4—42no—
855C4⋊C4—42no—
856C4⋊C4—42no—
857C4⋊C4—42no—
858C4⋊C4—42no—
859C4⋊C4—42no—
860C4⋊C4—42no—
861C4⋊C4—81no—
862C4⋊C4—81no—
863C4⋊C4—81no—
864C4⋊C4—81no—
865C4⋊C4—81no—
866C4⋊C4—81no—
867C4⋊C4—81no—
868C4⋊C4—81no—
869C4⋊C4—81no—
870C4⋊C4—81no—
871C4⋊C4—81no—
872C4⋊C4—81no—
873C4⋊C4—81no—
874C4⋊C4—81no—
875C4⋊C4—81no—
876C4⋊C4—81no—
877C4⋊C4—81no—
878C4⋊C4—81no—
879C4⋊C4—81no—
880C4⋊C4—81no—
881C4⋊C4—81no—
882C4⋊C4—81no—
883C4⋊C4—81no—
884C4⋊C4—81no—
885C4⋊C4—81no—
886C4⋊C4C2×#4112yes—
887C22⋊C4—22no—
888C22⋊C4—22no—
889C22⋊C4—41no—
890C22⋊C4—41no—
891C22⋊C4—42no—
892C22⋊C4—42no—
893C22⋊C4—42no—
894C22⋊C4—42no—
895C22⋊C4—81no—
896C22⋊C4—81no—
897C42—21no—
898C42—21no—
899C42—21no—
900C42—21no—
901C42—21no—
902C42—21no—
903C42—21no—
904C42—21no—
905C42—21no—
906C42—21no—
907C42—21no—
908C42—21no—
909C42—41no—
910C42—41no—
911C42—42no—
912C42—42no—
913C42—42no—
914C42—42no—
915C42—81no—
916C42—81no—
917C42—81no—
918C42—81no—
919C42—81no—
920C42—81no—
921C23—21no—
922C23—21no—
923C23—21no—
924C23—21no—
925C23—21no—
926C23—21no—
927C23#57812yes—
928C23C23×D411yescharacteristic
929Q8—22no—
930Q8—22no—
931Q8—41no—
932Q8—41no—
933Q8—41no—
934Q8—41no—
935Q8—41no—
936Q8—41no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
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—82no—
1029C2×C4—82no—
1030C2×C4—84no—
1031C2×C4—162no—
1032C2×C4C22×#4111yescharacteristic
1033C2×C4C2×2−1+411yescharacteristic
1034C2×C4C2×2−1+411yescharacteristic
1035C2×C4#58511yescharacteristic
1036C2×C4#58511yescharacteristic
1037C2×C4#58511yescharacteristic
1038C8—22no—
1039C8—22no—
1040C8—22no—
1041C8—41no—
1042C8—41no—
1043C8—41no—
1044C8—41no—
1045C8—41no—
1046C22—22no—
1047C22—22no—
1048C22—22no—
1049C22—41no—
1050C22—41no—
1051C22—41no—
1052C22—41no—
1053C22#344911yescharacteristic
1054C22D4×#4111yescharacteristic
1055C22#349911yescharacteristic
1056C22C2×#57811yescharacteristic
1057C22#358411yescharacteristic
1058C22#358511yescharacteristic
1059C22#358611yescharacteristic
1060C4—41no—
1061C4—41no—
1062C4—41no—
1063C4—41no—
1064C4—41no—
1065C4—42no—
1066C4—41no—
1067C4—41no—
1068C4—41no—
1069C4—41no—
1070C4—41no—
1071C4—41no—
1072C4—42no—
1073C4—41no—
1074C4—41no—
1075C4—81no—
1076C4—81no—
1077C4—81no—
1078C4—81no—
1079C4—81no—
1080C4—81no—
1081C4—81no—
1082C4—81no—
1083C4—81no—
1084C4—81no—
1085C4—81no—
1086C4—81no—
1087C4—81no—
1088C4—81no—
1089C4#349511yescharacteristic
1090C4#351511yescharacteristic
1091C4#355311yescharacteristic
1092C4#355711yescharacteristic
1093C2—42no—
1094C2#3843611yescharacteristic
1095C2#6098311yescharacteristic
1096C2#6098511yescharacteristic
1097C2#6152411yescharacteristic
1098C2#6153711yescharacteristic
1099C2#6249311yescharacteristic
1100C2#6249811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2283 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #33262C2semidirect
4. #32434C2semidirect
5. #32393C2semidirect
6. #32372C2semidirect
7. #32313C2semidirect
12. #30388C2semidirect
14. #29591C2semidirect
15. #29585C2semidirect
17. #29439C2semidirect
18. #29326C2semidirect
21. #27322C2semidirect
24. #27025C2semidirect
25. #26865C2semidirect
27. #26383C2semidirect
28. #22128C2semidirect
31. #21281C2semidirect

Maximal subgroups

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

subgroupindex
#389272
#380662
#332622
#324342
#323932
#323722
#323132
#323062
#319362
#316982
#310972
#303882
#303632
#295912
#295852
#294622
#294392
#293262
#292982
#274602
#273222
#271802
#270532
#270252
#268652
#265582
#263832
#221282
#220842
#214372
#212812