Finite Group Databasebeta

← #7574597

Subgroups — #7574597

Order 512.

1390 conjugacy classes of subgroups.

The subgroup lattice has 1209 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59752C211yesmaximal, characteristic, complemented
2#36174C211yesmaximal, characteristic
3#32661C211yesmaximal, characteristic, complemented
4#32546C211yesmaximal, characteristic, complemented
5#32021C211yesmaximal, characteristic
6#30399C211yesmaximal, characteristic
7#29581C211yesmaximal, characteristic, complemented
8#29575C211yesmaximal, characteristic, complemented
9#28870C211yesmaximal, characteristic, complemented
10#28848C211yesmaximal, characteristic, complemented
11#27843C211yesmaximal, characteristic, complemented
12#27519C211yesmaximal, characteristic, complemented
13#27483C211yesmaximal, characteristic, complemented
14#27184C211yesmaximal, characteristic, complemented
15#27102C211yesmaximal, characteristic, complemented
16#27039C211yesmaximal, characteristic, complemented
17#26681C211yesmaximal, characteristic, complemented
18#26556C211yesmaximal, characteristic, complemented
19#25074C211yesmaximal, characteristic, complemented
20#25040C211yesmaximal, characteristic, complemented
21#25000C211yesmaximal, characteristic, complemented
22#24942C211yesmaximal, characteristic, complemented
23#24914C211yesmaximal, characteristic, complemented
24#24892C211yesmaximal, characteristic, complemented
25#23270C211yesmaximal, characteristic, complemented
26#23131C211yesmaximal, characteristic, complemented
27#22939C211yesmaximal, characteristic, complemented
28#22885C211yesmaximal, characteristic, complemented
29#22585C211yesmaximal, characteristic, complemented
30#21121C211yesmaximal, characteristic, complemented
31#21114C211yesmaximal, characteristic, complemented
32C2×#485C2211yescharacteristic
33C2×#465C2211yescharacteristic
34C2×#448C2211yescharacteristic
35C2×#440C2211yescharacteristic
36C2×C4×SD16C2211yescharacteristic
37C2×#419C2211yescharacteristic
38#2859C2211yescharacteristic
39#2850—21no—
40#2798—21no—
41#2747—21no—
42#2605—21no—
43#2582C2211yescharacteristic
44#2581C2211yescharacteristic
45#2538C2211yescharacteristic
46#2537C2211yescharacteristic
47#2532—21no—
48#2531—21no—
49#2526—21no—
50#2526—21no—
51#2521—21no—
52#2520—21no—
53#2518—21no—
54#2518—21no—
55#2496C2211yescharacteristic
56#2495C2211yescharacteristic
57#2495C2211yescharacteristic
58#2495C2211yescharacteristic
59#2490—21no—
60#2489—21no—
61#2485C2211yescharacteristic
62#2423C2211yescharacteristic
63#2421C2211yescharacteristic
64#2420C2211yescharacteristic
65#2420C2211yescharacteristic
66#2409C2211yescharacteristic
67#2373—21no—
68#2363C2211yescharacteristic
69#2363C2211yescharacteristic
70#2362C2211yescharacteristic
71#2362C2211yescharacteristic
72#2355C2211yescharacteristic
73#2354C2211yescharacteristic
74#2346C2211yescharacteristic
75#2346C2211yescharacteristic
76Q8×C22⋊C4C2211yescharacteristic
77Q8×C22⋊C4C2211yescharacteristic
78C4×#124C2211yescharacteristic
79#2295C2211yescharacteristic
80#2295C2211yescharacteristic
81#2283—21no—
82C42×D4C2211yescharacteristic
83#2101C2211yescharacteristic
84#2100C2211yescharacteristic
85#2099C2211yescharacteristic
86#2099C2211yescharacteristic
87#2097C2211yescharacteristic
88#2096C2211yescharacteristic
89#2096C2211yescharacteristic
90#2092C2211yescharacteristic
91#2088C2211yescharacteristic
92#2085C2211yescharacteristic
93#2085C2211yescharacteristic
94#2084C2211yescharacteristic
95#2083C2211yescharacteristic
96#2077C2211yescharacteristic
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic
99#2076C2211yescharacteristic
100#2075C2211yescharacteristic
101#2074C2211yescharacteristic
102#2072C2211yescharacteristic
103#2072C2211yescharacteristic
104#2071C2211yescharacteristic
105#2068C2211yescharacteristic
106#2065C2211yescharacteristic
107#2055C2211yescharacteristic
108#2036C2211yescharacteristic
109#2035C2211yescharacteristic
110#2035C2211yescharacteristic
111#2034C2211yescharacteristic
112#2034C2211yescharacteristic
113#2034C2211yescharacteristic
114#2000C2211yescharacteristic
115#1985C2211yescharacteristic
116#1984C2211yescharacteristic
117#1973C2211yescharacteristic
118#1949C2211yescharacteristic
119#1948C2211yescharacteristic
120#1944C2211yescharacteristic
121#1943C2211yescharacteristic
122#1943C2211yescharacteristic
123#1941C2211yescharacteristic
124#1941C2211yescharacteristic
125#1935C2211yescharacteristic
126#1935C2211yescharacteristic
127#1934C2211yescharacteristic
128#1933C2211yescharacteristic
129#1933C2211yescharacteristic
130#1933C2211yescharacteristic
131#1928C2211yescharacteristic
132#1928C2211yescharacteristic
133#1928C2211yescharacteristic
134#1927C2211yescharacteristic
135#1927C2211yescharacteristic
136#1927C2211yescharacteristic
137#1924C2211yescharacteristic
138#1924C2211yescharacteristic
139#1923C2211yescharacteristic
140#1923C2211yescharacteristic
141#1921C2211yescharacteristic
142#1921C2211yescharacteristic
143#1920C2211yescharacteristic
144#1920C2211yescharacteristic
145#1919C2211yescharacteristic
146#1919C2211yescharacteristic
147#1919C2211yescharacteristic
148#1919C2211yescharacteristic
149#1919C2211yescharacteristic
150#1918C2211yescharacteristic
151#1895C2211yescharacteristic
152#1892C2211yescharacteristic
153#1880C2211yescharacteristic
154#1880C2211yescharacteristic
155#1877C2211yescharacteristic
156#1877C2211yescharacteristic
157#1877C2211yescharacteristic
158#1877C2211yescharacteristic
159#1875C2211yescharacteristic
160#1873C2211yescharacteristic
161#1870C2211yescharacteristic
162#1869C2211yescharacteristic
163#1865C2211yescharacteristic
164#1865C2211yescharacteristic
165#1865C2211yescharacteristic
166#1864C2211yescharacteristic
167#1863C2211yescharacteristic
168#1863C2211yescharacteristic
169#1863C2211yescharacteristic
170#1862C2211yescharacteristic
171#1862C2211yescharacteristic
172#1862C2211yescharacteristic
173#1854C2211yescharacteristic
174#1854C2211yescharacteristic
175#1854C2211yescharacteristic
176#1854C2211yescharacteristic
177#1847C2211yescharacteristic
178#1835C2211yescharacteristic
179#1825C2211yescharacteristic
180#1825C2211yescharacteristic
181#1809C2211yescharacteristic
182#1809C2211yescharacteristic
183#1808C2211yescharacteristic
184#1805C2211yescharacteristic
185#1805C2211yescharacteristic
186#1787C2211yescharacteristic
187#1787C2211yescharacteristic
188#1776C2211yescharacteristic
189C4×#107C2211yescharacteristic
190#1763C2211yescharacteristic
191#1763C2211yescharacteristic
192#1762C2211yescharacteristic
193C4×#103C2211yescharacteristic
194C4×#103C2211yescharacteristic
195C4×#102C2211yescharacteristic
196#1753C2211yescharacteristic
197#1753C2211yescharacteristic
198#1752C2211yescharacteristic
199C8×C22⋊C4C2211yescharacteristic
200#1745C2211yescharacteristic
201#1744C2211yescharacteristic
202#1735C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C2×#126—21no—
209C2×#125—21no—
210C2×#124D411yescharacteristic
211C2×C22⋊Q8—21no—
212C2×C22⋊Q8C2311yescharacteristic
213C2×C22⋊Q8C2311yescharacteristic
214C2×#121—21no—
215C2×#121C2311yescharacteristic
216C2×#121C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×D4C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×#117C2311yescharacteristic
227C2×#117C2311yescharacteristic
228C2×#117C2311yescharacteristic
229C22×C42—21no—
230#485—24no—
231#465—24no—
232#448—24no—
233#440—24no—
234C4×SD16—24no—
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251#419—24no—
252C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×C22⋊C8C2311yescharacteristic
273C2×C22⋊C8C2311yescharacteristic
274C2×C22⋊C8C2311yescharacteristic
275C2×C22⋊C8C2311yescharacteristic
276C2×C22⋊C8C2311yescharacteristic
277C2×C22⋊C8C2311yescharacteristic
278C2×#97C2311yescharacteristic
279C2×#97C2311yescharacteristic
280C2×#97C2311yescharacteristic
281C2×C4×C8C2311yescharacteristic
282C2×C4×C8C2311yescharacteristic
283C2×C4×C8C2311yescharacteristic
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#397—21no—
295#397—21no—
296#397—21no—
297#397—21no—
298#397—21no—
299#397—21no—
300#397—21no—
301#397—21no—
302#396—21no—
303#396—21no—
304#395—21no—
305#395—21no—
306#394—21no—
307#394—21no—
308#394—21no—
309#394—21no—
310#394—21no—
311#393—21no—
312#391—21no—
313#391—21no—
314#391—21no—
315#391—21no—
316#391—21no—
317#391—21no—
318#391D411yescharacteristic
319#391C2311yescharacteristic
320#391C2311yescharacteristic
321#391C2311yescharacteristic
322#391C2311yescharacteristic
323#391C2311yescharacteristic
324#391C2311yescharacteristic
325#390—21no—
326#390—21no—
327#390—21no—
328#390D411yescharacteristic
329#390C2311yescharacteristic
330#390C2311yescharacteristic
331#389—21no—
332#389—21no—
333#389—21no—
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#388—21no—
347#388—21no—
348#388—21no—
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#388D411yescharacteristic
365#388D411yescharacteristic
366#388D411yescharacteristic
367#388D411yescharacteristic
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#387—21no—
381#387—21no—
382#386—21no—
383#386—21no—
384#386—21no—
385#386—21no—
386#386—21no—
387#385—21no—
388#384C2311yescharacteristic
389#384C2311yescharacteristic
390#384C2311yescharacteristic
391#383—21no—
392#383—21no—
393#383—21no—
394#382—21no—
395#382—21no—
396#382—21no—
397#382D411yescharacteristic
398#382C2311yescharacteristic
399#382C2311yescharacteristic
400#382C2311yescharacteristic
401#381—21no—
402#381—21no—
403#380—21no—
404#380—21no—
405#380—21no—
406#380—21no—
407#380C2311yescharacteristic
408#380C2311yescharacteristic
409#380C2311yescharacteristic
410#380C2311yescharacteristic
411#380C2311yescharacteristic
412#380C2311yescharacteristic
413#380C2311yescharacteristic
414#380C2311yescharacteristic
415C4×C4⋊C4—21no—
416C4×C4⋊C4—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C22⋊C4—21no—
429C4×C22⋊C4—21no—
430C4×C22⋊C4—21no—
431C4×C22⋊C4—21no—
432C4×C22⋊C4—21no—
433C4×C22⋊C4—21no—
434C4×C22⋊C4—21no—
435C4×C22⋊C4C2311yescharacteristic
436C4×C22⋊C4C2311yescharacteristic
437C4×C22⋊C4C2311yescharacteristic
438C4×C22⋊C4C2311yescharacteristic
439#376—21no—
440#376—21no—
441#376—21no—
442#376—21no—
443C43C2311yescharacteristic
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#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
484C22×Q8—21no—
485C22×Q8—22no—
486C22×Q8—22no—
487C22×Q8—41no—
488C22×Q8—41no—
489C22×Q8—41no—
490C22×Q8—41no—
491C22×Q8C2×D411yescharacteristic
492C22×Q8C2411yescharacteristic
493C22×Q8C2411yescharacteristic
494C22×D4—21no—
495C22×D4—21no—
496C22×D4C2×D411yescharacteristic
497C22×D4C2411yescharacteristic
498C23×C4—21no—
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—21no—
502C23×C4C2411yescharacteristic
503C23×C4C2411yescharacteristic
504C2×SD16—22no—
505C2×SD16—22no—
506C2×SD16—41no—
507C2×SD16—41no—
508C2×SD16—41no—
509C2×SD16#4114yes—
510C2×M16—22no—
511C2×M16—41no—
512C2×M16—41no—
513C22×C8—22no—
514C22×C8—41no—
515C22×C8—41no—
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524#126—44no—
525#125—82no—
526#124—42no—
527C22⋊Q8—22no—
528C22⋊Q8—22no—
529C22⋊Q8—41no—
530C22⋊Q8—41no—
531C22⋊Q8—82no—
532#121—22no—
533#121—22no—
534#121—41no—
535#121—41no—
536#121—82no—
537C4×Q8—22no—
538C4×Q8—22no—
539C4×Q8—41no—
540C4×Q8—41no—
541C4×Q8—41no—
542C4×Q8—41no—
543C4×Q8—41no—
544C4×Q8—41no—
545C4×Q8—41no—
546C4×Q8—41no—
547C4×D4—22no—
548C4×D4—22no—
549C4×D4—41no—
550C4×D4—41no—
551C4×D4—41no—
552C4×D4—41no—
553C4×D4—41no—
554C4×D4—41no—
555#117—22no—
556#117—22no—
557#117—41no—
558#117—41no—
559#117—41no—
560#117—41no—
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—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4C2×D411yescharacteristic
586C2×C4⋊C4C2×D411yescharacteristic
587C2×C4⋊C4C2×D411yescharacteristic
588C2×C4⋊C4C2×D411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
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×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⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4C2×D411yescharacteristic
625C2×C22⋊C4C2×D411yescharacteristic
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×C42—21no—
635C2×C42—21no—
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×C42—21no—
647C2×C42—21no—
648C2×C42—44no—
649C2×C42C2×D411yescharacteristic
650C2×C42C2×D411yescharacteristic
651C2×C42C2×D411yescharacteristic
652C2×C42C2×D411yescharacteristic
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658#107—22no—
659#107—22no—
660#107—41no—
661#107—41no—
662#107—41no—
663#107—41no—
664#106—22no—
665#106—22no—
666#106—22no—
667#106—41no—
668#106—41no—
669#106—41no—
670#106—41no—
671#106—41no—
672C4⋊C8—41no—
673C4⋊C8—41no—
674#103—22no—
675#103—22no—
676#103—22no—
677#103—22no—
678#103—22no—
679#103—22no—
680#103—22no—
681#103—22no—
682#103—41no—
683#103—41no—
684#103—41no—
685#103—41no—
686#103—41no—
687#103#4114yes—
688#102—22no—
689#102—22no—
690#102—22no—
691#102—41no—
692#102—41no—
693#102—41no—
694C22⋊C8—22no—
695C22⋊C8—22no—
696C22⋊C8—41no—
697C22⋊C8—41no—
698C22⋊C8—41no—
699C22⋊C8—41no—
700#97—22no—
701#97—41no—
702#97—41no—
703C4×C8—22no—
704C4×C8—41no—
705C4×C8—41no—
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#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758#95C2×D411yescharacteristic
759C24—21no—
760C24C22×D411yescharacteristic
761C24C22×D411yescharacteristic
762C2×Q8—22no—
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—41no—
774C2×Q8—41no—
775C2×Q8—42no—
776C2×Q8—42no—
777C2×Q8—44no—
778C2×Q8—81no—
779C2×Q8—82no—
780C2×Q8—82no—
781C2×Q8—82no—
782C2×Q8C2×#4112yes—
783C2×Q8C2×#4112yes—
784C2×D4—22no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—41no—
791C2×D4—41no—
792C2×D4—42no—
793C2×D4—42no—
794C2×D4—81no—
795C2×D4—81no—
796C2×D4—81no—
797C2×D4—81no—
798C2×D4C2×#4112yes—
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—42no—
829C22×C4—42no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—81no—
836C22×C4—81no—
837C22×C4—81no—
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×C4C22×D411yescharacteristic
848C22×C4C22×D411yescharacteristic
849C22×C4C22×D411yescharacteristic
850C22×C4C2511yescharacteristic
851SD16—44no—
852SD16—44no—
853M16—82no—
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—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—82no—
877C2×C8C2×#4112yes—
878C2×C8C2×#4112yes—
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—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—41no—
905C4⋊C4—41no—
906C4⋊C4—41no—
907C4⋊C4—41no—
908C4⋊C4—42no—
909C4⋊C4—42no—
910C4⋊C4—42no—
911C4⋊C4—42no—
912C4⋊C4—42no—
913C4⋊C4—42no—
914C4⋊C4—42no—
915C4⋊C4—42no—
916C4⋊C4—42no—
917C4⋊C4—42no—
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—
930C4⋊C4—81no—
931C4⋊C4—81no—
932C4⋊C4C2×#4112yes—
933C22⋊C4—22no—
934C22⋊C4—22no—
935C22⋊C4—41no—
936C22⋊C4—41no—
937C22⋊C4—41no—
938C22⋊C4—41no—
939C22⋊C4—41no—
940C22⋊C4—41no—
941C22⋊C4—41no—
942C22⋊C4—41no—
943C22⋊C4—42no—
944C22⋊C4—42no—
945C22⋊C4—42no—
946C22⋊C4—42no—
947C22⋊C4—42no—
948C22⋊C4—42no—
949C22⋊C4—42no—
950C22⋊C4—42no—
951C22⋊C4—42no—
952C22⋊C4—42no—
953C22⋊C4—42no—
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—
963C22⋊C4—81no—
964C22⋊C4—81no—
965C42—22no—
966C42—22no—
967C42—21no—
968C42—21no—
969C42—21no—
970C42—21no—
971C42—21no—
972C42—21no—
973C42—21no—
974C42—21no—
975C42—21no—
976C42—21no—
977C42—41no—
978C42—41no—
979C42—42no—
980C42—42no—
981C42—42no—
982C42—42no—
983C42—42no—
984C42—42no—
985C42—42no—
986C42—42no—
987C42—42no—
988C42—81no—
989C42—81no—
990C42—81no—
991C42—81no—
992C42—81no—
993C23—21no—
994C23—21no—
995C23—21no—
996C23—21no—
997C23—21no—
998C23—22no—
999C23—21no—
1000C23—21no—
1001C23—21no—
1002C23—21no—
1003C23—21no—
1004C23—21no—
1005C23—21no—
1006C23—21no—
1007C23—21no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23C23×D411yescharacteristic
1015Q8—22no—
1016Q8—22no—
1017Q8—22no—
1018Q8—22no—
1019Q8—41no—
1020Q8—41no—
1021Q8—41no—
1022Q8—41no—
1023Q8—82no—
1024Q8—84no—
1025D4—22no—
1026D4—22no—
1027D4—41no—
1028D4—41no—
1029D4—82no—
1030D4—162no—
1031D4—162no—
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—22no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
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—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—84no—
1120C2×C4—84no—
1121C2×C4—84no—
1122C2×C4—84no—
1123C2×C4#57512yes—
1124C2×C4#57712yes—
1125C2×C4C22×#4111yescharacteristic
1126C2×C4C22×#4111yescharacteristic
1127C2×C4#58511yescharacteristic
1128C2×C4#58511yescharacteristic
1129C2×C4#58511yescharacteristic
1130C2×C4#58511yescharacteristic
1131C8—22no—
1132C8—22no—
1133C8—41no—
1134C8—41no—
1135C8—41no—
1136C8—41no—
1137C8—41no—
1138C8—41no—
1139C22—42no—
1140C22—41no—
1141C22—41no—
1142C22—41no—
1143C22—41no—
1144C22—41no—
1145C22—41no—
1146C22—42no—
1147C22—41no—
1148C22—41no—
1149C22—41no—
1150C22—41no—
1151C22—41no—
1152C22—41no—
1153C22—42no—
1154C22—41no—
1155C22—41no—
1156C22—81no—
1157C22—81no—
1158C22—81no—
1159C22—81no—
1160C22D4×#4111yescharacteristic
1161C22D4×#4111yescharacteristic
1162C22#348511yescharacteristic
1163C22C2×#57511yescharacteristic
1164C22C2×#57711yescharacteristic
1165C22#358411yescharacteristic
1166C22#358611yescharacteristic
1167C4—22no—
1168C4—22no—
1169C4—41no—
1170C4—42no—
1171C4—41no—
1172C4—41no—
1173C4—42no—
1174C4—42no—
1175C4—41no—
1176C4—41no—
1177C4—41no—
1178C4—41no—
1179C4—41no—
1180C4—41no—
1181C4—41no—
1182C4—81no—
1183C4—81no—
1184C4—81no—
1185C4—81no—
1186C4—81no—
1187C4—81no—
1188C4—81no—
1189C4—81no—
1190C4—81no—
1191C4—81no—
1192C4—81no—
1193C4—81no—
1194C4#347511yescharacteristic
1195C4#349111yescharacteristic
1196C4#352111yescharacteristic
1197C4#356611yescharacteristic
1198C2—81no—
1199C2—81no—
1200C2—82no—
1201C2#5915811yescharacteristic
1202C2#6144111yescharacteristic
1203C2#6145511yescharacteristic
1204C2#6149511yescharacteristic
1205C2#6154011yescharacteristic
1206C2#6173111yescharacteristic
1207C2#6181411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2537C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#124 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59752C2semidirect
3. #32661C2semidirect
4. #32546C2semidirect
7. #29581C2semidirect
8. #29575C2semidirect
9. #28870C2semidirect
10. #28848C2semidirect
11. #27843C2semidirect
12. #27519C2semidirect
13. #27483C2semidirect
14. #27184C2semidirect
15. #27102C2semidirect
16. #27039C2semidirect
17. #26681C2semidirect
18. #26556C2semidirect
19. #25074C2semidirect
20. #25040C2semidirect
21. #25000C2semidirect
22. #24942C2semidirect
23. #24914C2semidirect
24. #24892C2semidirect
25. #23270C2semidirect
26. #23131C2semidirect
27. #22939C2semidirect
28. #22885C2semidirect
29. #22585C2semidirect
30. #21121C2semidirect
31. #21114C2semidirect

Maximal subgroups

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

subgroupindex
#597522
#361742
#326612
#325462
#320212
#303992
#295812
#295752
#288702
#288482
#278432
#275192
#274832
#271842
#271022
#270392
#266812
#265562
#250742
#250402
#250002
#249422
#249142
#248922
#232702
#231312
#229392
#228852
#225852
#211212
#211142