Finite Group Databasebeta

← #7409551

Subgroups — #7409551

Order 512.

1273 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45212C211yesmaximal, characteristic, complemented
2#42858C211yesmaximal, characteristic
3#32639C211yesmaximal, characteristic, complemented
4#32579C211yesmaximal, characteristic, complemented
5#32425C211yesmaximal, characteristic, complemented
6#32298C211yesmaximal, characteristic, complemented
7#31627C211yesmaximal, characteristic, complemented
8#31517C211yesmaximal, characteristic, complemented
9#31516C211yesmaximal, characteristic, complemented
10#31334C211yesmaximal, characteristic, complemented
11#31297C211yesmaximal, characteristic, complemented
12#31279C211yesmaximal, characteristic
13#31129C211yesmaximal, characteristic, complemented
14#31095C211yesmaximal, characteristic, complemented
15#30158C211yesmaximal, characteristic, complemented
16#30157C211yesmaximal, characteristic, complemented
17#29264C211yesmaximal, characteristic, complemented
18#28213C211yesmaximal, characteristic, complemented
19#27545C211yesmaximal, characteristic, complemented
20#27455C211yesmaximal, characteristic, complemented
21#27420C211yesmaximal, characteristic, complemented
22#27099C211yesmaximal, characteristic, complemented
23#26356C211yesmaximal, characteristic, complemented
24#26327C211yesmaximal, characteristic, complemented
25#26149C211yesmaximal, characteristic, complemented
26#25967C211yesmaximal, characteristic, complemented
27#25071C211yesmaximal, characteristic, complemented
28#24889C211yesmaximal, characteristic
29#24597C211yesmaximal, characteristic, complemented
30#24491C211yesmaximal, characteristic, complemented
31#23351C211yesmaximal, characteristic, complemented
32C2×#482C2211yescharacteristic
33C2×#483C2211yescharacteristic
34C2×#477C2211yescharacteristic
35C2×#475C2211yescharacteristic
36C2×#428C2211yescharacteristic
37C2×#417C2211yescharacteristic
38#2830—21no—
39#2800—21no—
40#2797—21no—
41#2786—21no—
42#2784—21no—
43#2770—21no—
44#2762—21no—
45#2759—21no—
46#2716—21no—
47#2652—21no—
48#2648—21no—
49#2644C2211yescharacteristic
50#2592C2211yescharacteristic
51#2581C2211yescharacteristic
52#2578—21no—
53#2563C2211yescharacteristic
54#2560—21no—
55#2546C2211yescharacteristic
56#2524—21no—
57#2523—21no—
58#2504C2211yescharacteristic
59#2496C2211yescharacteristic
60#2495C2211yescharacteristic
61#2495C2211yescharacteristic
62#2495C2211yescharacteristic
63#2494C2211yescharacteristic
64#2492—21no—
65#2440C2211yescharacteristic
66#2439C2211yescharacteristic
67#2432C2211yescharacteristic
68#2429C2211yescharacteristic
69#2426C2211yescharacteristic
70#2421C2211yescharacteristic
71#2417C2211yescharacteristic
72#2407C2211yescharacteristic
73#2398C2211yescharacteristic
74#2360C2211yescharacteristic
75#2355C2211yescharacteristic
76#2352C2211yescharacteristic
77#2347C2211yescharacteristic
78#2345C2211yescharacteristic
79#2341C2211yescharacteristic
80#2331C2211yescharacteristic
81#2331C2211yescharacteristic
82#2327C2211yescharacteristic
83#2101C2211yescharacteristic
84#2097C2211yescharacteristic
85#2097C2211yescharacteristic
86#2097C2211yescharacteristic
87#2094C2211yescharacteristic
88#2088C2211yescharacteristic
89#2088C2211yescharacteristic
90#2087C2211yescharacteristic
91#2086C2211yescharacteristic
92#2086C2211yescharacteristic
93#2085C2211yescharacteristic
94#2085C2211yescharacteristic
95#2085C2211yescharacteristic
96#2085C2211yescharacteristic
97#2085C2211yescharacteristic
98#2085C2211yescharacteristic
99#2077C2211yescharacteristic
100#2076C2211yescharacteristic
101#2075C2211yescharacteristic
102#2075C2211yescharacteristic
103#2073C2211yescharacteristic
104#2073C2211yescharacteristic
105#2072C2211yescharacteristic
106#2068C2211yescharacteristic
107#2067C2211yescharacteristic
108#2067C2211yescharacteristic
109#2066C2211yescharacteristic
110#2065C2211yescharacteristic
111#2065C2211yescharacteristic
112#2065C2211yescharacteristic
113#2058C2211yescharacteristic
114#2057C2211yescharacteristic
115#2043C2211yescharacteristic
116#2043C2211yescharacteristic
117#2042C2211yescharacteristic
118#2042C2211yescharacteristic
119#2036C2211yescharacteristic
120#2036C2211yescharacteristic
121#2036C2211yescharacteristic
122#2036C2211yescharacteristic
123#2035C2211yescharacteristic
124#2035C2211yescharacteristic
125#2033C2211yescharacteristic
126#2033C2211yescharacteristic
127#2024C2211yescharacteristic
128#2024C2211yescharacteristic
129#2023C2211yescharacteristic
130#2023C2211yescharacteristic
131#1985C2211yescharacteristic
132#1984C2211yescharacteristic
133#1983C2211yescharacteristic
134#1981C2211yescharacteristic
135#1981C2211yescharacteristic
136#1958C2211yescharacteristic
137#1949C2211yescharacteristic
138#1949C2211yescharacteristic
139#1949C2211yescharacteristic
140#1949C2211yescharacteristic
141#1942C2211yescharacteristic
142#1936C2211yescharacteristic
143#1935C2211yescharacteristic
144#1933C2211yescharacteristic
145#1928C2211yescharacteristic
146#1928C2211yescharacteristic
147#1927C2211yescharacteristic
148#1927C2211yescharacteristic
149#1927C2211yescharacteristic
150#1927C2211yescharacteristic
151#1926C2211yescharacteristic
152#1926C2211yescharacteristic
153#1925C2211yescharacteristic
154#1925C2211yescharacteristic
155#1925C2211yescharacteristic
156#1924C2211yescharacteristic
157#1924C2211yescharacteristic
158#1923C2211yescharacteristic
159#1923C2211yescharacteristic
160#1921C2211yescharacteristic
161#1921C2211yescharacteristic
162#1921C2211yescharacteristic
163#1920C2211yescharacteristic
164#1920C2211yescharacteristic
165#1919C2211yescharacteristic
166#1918C2211yescharacteristic
167#1895C2211yescharacteristic
168#1894C2211yescharacteristic
169#1894C2211yescharacteristic
170#1894C2211yescharacteristic
171#1873C2211yescharacteristic
172#1873C2211yescharacteristic
173#1870C2211yescharacteristic
174#1870C2211yescharacteristic
175#1865C2211yescharacteristic
176#1865C2211yescharacteristic
177#1863C2211yescharacteristic
178#1863C2211yescharacteristic
179#1863C2211yescharacteristic
180#1863C2211yescharacteristic
181#1853C2211yescharacteristic
182#1853C2211yescharacteristic
183#1853C2211yescharacteristic
184#1852C2211yescharacteristic
185#1851C2211yescharacteristic
186#1851C2211yescharacteristic
187#1851C2211yescharacteristic
188#1851C2211yescharacteristic
189#1847C2211yescharacteristic
190#1832C2211yescharacteristic
191#1832C2211yescharacteristic
192#1823C2211yescharacteristic
193#1809C2211yescharacteristic
194#1809C2211yescharacteristic
195#1805C2211yescharacteristic
196#1805C2211yescharacteristic
197#1803C2211yescharacteristic
198#1788C2211yescharacteristic
199#1788C2211yescharacteristic
200#1788C2211yescharacteristic
201C4×#106C2211yescharacteristic
202#1763C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C2×C4⋊Q8—21no—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×#126—21no—
211C2×#124C2311yescharacteristic
212C2×C22⋊Q8—21no—
213C2×C22⋊Q8C2311yescharacteristic
214C2×C22⋊Q8C2311yescharacteristic
215C2×C22⋊Q8C2311yescharacteristic
216C2×#121C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×D4C2311yescharacteristic
222C2×#117C2311yescharacteristic
223C22×C4⋊C4C2311yescharacteristic
224C22×C4⋊C4C2311yescharacteristic
225#483—42no—
226#482—42no—
227#477—42no—
228#475—42no—
229#428—42no—
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×C4⋊C8C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252#417—42no—
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×C22⋊C8C2311yescharacteristic
278C2×C22⋊C8C2311yescharacteristic
279C2×C22⋊C8C2311yescharacteristic
280C2×C22⋊C8C2311yescharacteristic
281C2×C22⋊C8C2311yescharacteristic
282C2×C22⋊C8C2311yescharacteristic
283C2×#97C2311yescharacteristic
284C2×C4×C8C2311yescharacteristic
285#401—21no—
286#400—21no—
287#400—21no—
288#400—21no—
289#400—21no—
290#400—21no—
291#400—21no—
292#400D411yescharacteristic
293#400D411yescharacteristic
294#398—21no—
295#398—21no—
296#398—21no—
297#398—21no—
298#398—21no—
299#397—21no—
300#397—21no—
301#397—21no—
302#397—21no—
303#397—21no—
304#397—21no—
305#397—21no—
306#397—21no—
307#397—21no—
308#397—21no—
309#397—21no—
310#397—21no—
311#397D411yescharacteristic
312#397D411yescharacteristic
313#396—21no—
314#396—21no—
315#396—21no—
316#396—21no—
317#396—21no—
318#395—21no—
319#395—21no—
320#394—21no—
321#394—21no—
322#394—21no—
323#394—21no—
324#394D411yescharacteristic
325#394D411yescharacteristic
326#393—21no—
327#393—21no—
328#393—21no—
329#393—21no—
330#393D411yescharacteristic
331#393D411yescharacteristic
332#392—21no—
333#391—21no—
334#391—21no—
335#391—21no—
336#391—21no—
337#391—21no—
338#391—21no—
339#391—21no—
340#391C2311yescharacteristic
341#391C2311yescharacteristic
342#391C2311yescharacteristic
343#391C2311yescharacteristic
344#390—21no—
345#390—21no—
346#390—21no—
347#390—21no—
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#389—21no—
353#389—21no—
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#388—21no—
367#388—21no—
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#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—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#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#384C2311yescharacteristic
409#383—21no—
410#383—21no—
411#383—21no—
412#383—21no—
413#382—21no—
414#382C2311yescharacteristic
415#382C2311yescharacteristic
416#382C2311yescharacteristic
417#382C2311yescharacteristic
418#382C2311yescharacteristic
419#380—21no—
420#380—21no—
421#380—21no—
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⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C22⋊C4—21no—
440C4×C22⋊C4—21no—
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4C2311yescharacteristic
444C4×C22⋊C4C2311yescharacteristic
445C4×C22⋊C4C2311yescharacteristic
446C4×C22⋊C4C2311yescharacteristic
447#376C2311yescharacteristic
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#340C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C2×#41—22no—
485C2×#41—41no—
486C2×#41—41no—
487C2×#41—41no—
488C2×#41—41no—
489C2×#41—41no—
490C22×Q8—21no—
491C22×Q8—21no—
492C22×Q8C2×D411yescharacteristic
493C22×Q8C2411yescharacteristic
494C22×Q8C2411yescharacteristic
495C22×D4—21no—
496C22×D4—21no—
497C22×D4C2×D411yescharacteristic
498C22×D4C2411yescharacteristic
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—21no—
502C23×C4C2411yescharacteristic
503C23×C4C2411yescharacteristic
504C2×M16—41no—
505C2×M16—41no—
506C2×M16—41no—
507C2×M16—41no—
508C2×M16—41no—
509C2×M16—41no—
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C4⋊Q8—22no—
519C4⋊Q8—22no—
520C4⋊Q8—41no—
521C4⋊Q8—41no—
522C4⋊Q8—41no—
523C4⋊Q8—41no—
524C4⋊Q8—82no—
525#126—82no—
526#124—41no—
527#124—41no—
528C22⋊Q8—22no—
529C22⋊Q8—41no—
530C22⋊Q8—41no—
531C22⋊Q8—41no—
532C22⋊Q8—41no—
533C22⋊Q8—41no—
534C22⋊Q8—82no—
535#121—41no—
536#121—41no—
537C4×Q8—41no—
538C4×Q8—41no—
539C4×Q8—41no—
540C4×Q8—41no—
541C4×Q8—41no—
542C4×Q8—41no—
543C4×Q8—41no—
544C4×Q8—41no—
545C4×D4—41no—
546C4×D4—41no—
547#117—22no—
548#117—41no—
549C2×C4⋊C4—22no—
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—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—41no—
577C2×C4⋊C4—41no—
578C2×C4⋊C4—41no—
579C2×C4⋊C4C2×D411yescharacteristic
580C2×C4⋊C4C2×D411yescharacteristic
581C2×C4⋊C4C2×D411yescharacteristic
582C2×C4⋊C4C2×D411yescharacteristic
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⋊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⋊C4C2×D411yescharacteristic
620C2×C22⋊C4C2×D411yescharacteristic
621C2×C22⋊C4C2×D411yescharacteristic
622C2×C22⋊C4C2×D411yescharacteristic
623C2×C22⋊C4C2×D411yescharacteristic
624C2×C22⋊C4C2×D411yescharacteristic
625C2×C22⋊C4C2×D411yescharacteristic
626C2×C22⋊C4C2×D411yescharacteristic
627C2×C22⋊C4C2×D411yescharacteristic
628C2×C22⋊C4C2×D411yescharacteristic
629C2×C42—21no—
630C2×C42—21no—
631C2×C42—21no—
632C2×C42—21no—
633C2×C42—21no—
634C2×C42—21no—
635C2×C42—21no—
636C2×C42—21no—
637C2×C42—21no—
638C2×C42—21no—
639C2×C42—21no—
640C2×C42C2411yescharacteristic
641C2×C42C2411yescharacteristic
642C2×C42C2411yescharacteristic
643C2×C42C2411yescharacteristic
644C2×C42C2411yescharacteristic
645#107—22no—
646#107—41no—
647#107—41no—
648#107—41no—
649#107—41no—
650#107—41no—
651#107—41no—
652#107—41no—
653#106—22no—
654#106—22no—
655#106—41no—
656#106—41no—
657#106—41no—
658#106—41no—
659#106—41no—
660#106—41no—
661C4⋊C8—41no—
662C4⋊C8—41no—
663C4⋊C8—41no—
664C4⋊C8—41no—
665C4⋊C8—41no—
666C4⋊C8—41no—
667#103—22no—
668#103—22no—
669#103—22no—
670#103—22no—
671#103—41no—
672#103—41no—
673#103—41no—
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#102—22no—
684#102—41no—
685#102—41no—
686#102—41no—
687#102—41no—
688#102—41no—
689#102—41no—
690#102—41no—
691C22⋊C8—41no—
692C22⋊C8—41no—
693C22⋊C8—41no—
694C22⋊C8—41no—
695C22⋊C8—41no—
696C22⋊C8—41no—
697#97—41no—
698C4×C8—41no—
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#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#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756C24—21no—
757C24C22×D411yescharacteristic
758C24C22×D411yescharacteristic
759#41—44no—
760#41—82no—
761#41—82no—
762#41—82no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—41no—
775C2×Q8—41no—
776C2×Q8—41no—
777C2×Q8—42no—
778C2×Q8—42no—
779C2×Q8—81no—
780C2×Q8—81no—
781C2×Q8—81no—
782C2×Q8—81no—
783C2×Q82−1+412yes—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—41no—
791C2×D4—41no—
792C2×D4—41no—
793C2×D4—42no—
794C2×D4—42no—
795C2×D4—81no—
796C2×D4—81no—
797C2×D4—81no—
798C2×D4—81no—
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—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—42no—
827C22×C4—42no—
828C22×C4—81no—
829C22×C4—81no—
830C22×C4—81no—
831C22×C4—81no—
832C22×C4—81no—
833C22×C4—81no—
834C22×C4—81no—
835C22×C4C22×D411yescharacteristic
836C22×C4C22×D411yescharacteristic
837C22×C4C22×D411yescharacteristic
838C22×C4C22×D411yescharacteristic
839C22×C4C22×D411yescharacteristic
840C22×C4C22×D411yescharacteristic
841C22×C4C22×D411yescharacteristic
842C22×C4C22×D411yescharacteristic
843C22×C4C22×D411yescharacteristic
844C22×C4C22×D411yescharacteristic
845C22×C4C22×D411yescharacteristic
846C22×C4C22×D411yescharacteristic
847C22×C4C2511yescharacteristic
848M16—44no—
849M16—82no—
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—21no—
868C2×C8—21no—
869C2×C8—21no—
870C2×C8—21no—
871C2×C8—21no—
872C2×C8—21no—
873C2×C8—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—21no—
897C4⋊C4—21no—
898C4⋊C4—21no—
899C4⋊C4—41no—
900C4⋊C4—41no—
901C4⋊C4—41no—
902C4⋊C4—41no—
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—42no—
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⋊C4H(5,𝔽2)12yes—
930C22⋊C4—41no—
931C22⋊C4—41no—
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—81no—
944C22⋊C4—81no—
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—
962C22⋊C4—81no—
963C42—21no—
964C42—21no—
965C42—21no—
966C42—21no—
967C42—21no—
968C42—21no—
969C42—21no—
970C42—21no—
971C42—21no—
972C42—21no—
973C42—42no—
974C42—81no—
975C42—81no—
976C42—81no—
977C42—81no—
978C42—81no—
979C42—81no—
980C42—81no—
981C42—81no—
982C42—81no—
983C42—81no—
984C23—21no—
985C23—21no—
986C23—21no—
987C23—21no—
988C23—21no—
989C23—21no—
990C23—21no—
991C23—21no—
992C23—21no—
993C23—21no—
994C23—21no—
995C23—21no—
996C23—21no—
997C23—21no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23C23×D411yescharacteristic
1006Q8—22no—
1007Q8—22no—
1008Q8—41no—
1009Q8—41no—
1010Q8—41no—
1011Q8—41no—
1012Q8—41no—
1013Q8—41no—
1014Q8—82no—
1015Q8—162no—
1016Q8—162no—
1017D4—41no—
1018D4—41no—
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—21no—
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—22no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—22no—
1060C2×C4—21no—
1061C2×C4—21no—
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—41no—
1112C2×C4—41no—
1113C2×C4—84no—
1114C2×C4—162no—
1115C2×C4—162no—
1116C2×C4C2×H(5,𝔽2)11yescharacteristic
1117C2×C4C2×2−1+411yescharacteristic
1118C2×C4#58511yescharacteristic
1119C2×C4#58511yescharacteristic
1120C2×C4#58511yescharacteristic
1121C2×C4#58511yescharacteristic
1122C8—41no—
1123C8—41no—
1124C8—41no—
1125C8—41no—
1126C8—41no—
1127C8—41no—
1128C8—41no—
1129C8—41no—
1130C22—41no—
1131C22—41no—
1132C22—41no—
1133C22—41no—
1134C22—41no—
1135C22—41no—
1136C22—41no—
1137C22—41no—
1138C22—41no—
1139C22—41no—
1140C22—41no—
1141C22—41no—
1142C22—41no—
1143C22—41no—
1144C22—81no—
1145C22—81no—
1146C22—81no—
1147C22—81no—
1148C22—81no—
1149C22—81no—
1150C22—81no—
1151C22#348511yescharacteristic
1152C22#348811yescharacteristic
1153C22#348911yescharacteristic
1154C22#358411yescharacteristic
1155C22#358511yescharacteristic
1156C22#358611yescharacteristic
1157C22#358611yescharacteristic
1158C4—41no—
1159C4—41no—
1160C4—41no—
1161C4—41no—
1162C4—41no—
1163C4—41no—
1164C4—41no—
1165C4—41no—
1166C4—41no—
1167C4—42no—
1168C4—41no—
1169C4—41no—
1170C4—42no—
1171C4—41no—
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#354011yescharacteristic
1186C4#354111yescharacteristic
1187C4#356411yescharacteristic
1188C4#356611yescharacteristic
1189C2—81no—
1190C2—81no—
1191C2—161no—
1192C2#5086311yescharacteristic
1193C2#6176111yescharacteristic
1194C2#6178111yescharacteristic
1195C2#6202911yescharacteristic
1196C2#6208711yescharacteristic
1197C2#6217711yescharacteristic
1198C2#6222911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2407C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2398 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45212C2semidirect
3. #32639C2semidirect
4. #32579C2semidirect
5. #32425C2semidirect
6. #32298C2semidirect
7. #31627C2semidirect
8. #31517C2semidirect
9. #31516C2semidirect
10. #31334C2semidirect
11. #31297C2semidirect
13. #31129C2semidirect
14. #31095C2semidirect
15. #30158C2semidirect
16. #30157C2semidirect
17. #29264C2semidirect
18. #28213C2semidirect
19. #27545C2semidirect
20. #27455C2semidirect
21. #27420C2semidirect
22. #27099C2semidirect
23. #26356C2semidirect
24. #26327C2semidirect
25. #26149C2semidirect
26. #25967C2semidirect
27. #25071C2semidirect
29. #24597C2semidirect
30. #24491C2semidirect
31. #23351C2semidirect

Maximal subgroups

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

subgroupindex
#452122
#428582
#326392
#325792
#324252
#322982
#316272
#315172
#315162
#313342
#312972
#312792
#311292
#310952
#301582
#301572
#292642
#282132
#275452
#274552
#274202
#270992
#263562
#263272
#261492
#259672
#250712
#248892
#245972
#244912
#233512