Finite Group Databasebeta

← #7584538

Subgroups — #7584538

Order 512.

1437 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59498C211yesmaximal, characteristic
2#36408C211yesmaximal, characteristic, complemented
3#31476C211yesmaximal, characteristic, complemented
4#31244C211yesmaximal, characteristic, complemented
5#31120C211yesmaximal, characteristic, complemented
6#30597C211yesmaximal, characteristic
7#29520C211yesmaximal, characteristic, complemented
8#29448C211yesmaximal, characteristic, complemented
9#29034C211yesmaximal, characteristic, complemented
10#28081C211yesmaximal, characteristic, complemented
11#28008C211yesmaximal, characteristic, complemented
12#27446C211yesmaximal, characteristic, complemented
13#27374C211yesmaximal, characteristic, complemented
14#27176C211yesmaximal, characteristic, complemented
15#27158C211yesmaximal, characteristic
16#27051C211yesmaximal, characteristic, complemented
17#26884C211yesmaximal, characteristic, complemented
18#26800C211yesmaximal, characteristic
19#26773C211yesmaximal, characteristic, complemented
20#26677C211yesmaximal, characteristic
21#26182C211yesmaximal, characteristic, complemented
22#26104C211yesmaximal, characteristic, complemented
23#25988C211yesmaximal, characteristic, complemented
24#25041C211yesmaximal, characteristic
25#23292C211yesmaximal, characteristic, complemented
26#23134C211yesmaximal, characteristic
27#23100C211yesmaximal, characteristic, complemented
28#22978C211yesmaximal, characteristic, complemented
29#22934C211yesmaximal, characteristic, complemented
30#21615C211yesmaximal, characteristic, complemented
31#21124C211yesmaximal, characteristic, complemented
32C2×#552—21no—
33C2×#483C2211yescharacteristic
34C2×#475C2211yescharacteristic
35C2×#478C2211yescharacteristic
36C2×#465C2211yescharacteristic
37C2×#461C2211yescharacteristic
38C2×#440C2211yescharacteristic
39#2864—21no—
40#2863C2211yescharacteristic
41#2690—21no—
42#2687—21no—
43#2599—21no—
44#2585—21no—
45#2573—21no—
46#2552C2211yescharacteristic
47#2533—21no—
48#2524—21no—
49#2515—21no—
50#2508C2211yescharacteristic
51#2506C2211yescharacteristic
52#2506C2211yescharacteristic
53#2496C2211yescharacteristic
54#2489C2211yescharacteristic
55#2478—21no—
56#2475—21no—
57#2473—21no—
58#2470—21no—
59#2468—21no—
60#2453C2211yescharacteristic
61#2452C2211yescharacteristic
62#2446C2211yescharacteristic
63#2440C2211yescharacteristic
64#2429C2211yescharacteristic
65#2422C2211yescharacteristic
66#2422C2211yescharacteristic
67#2421C2211yescharacteristic
68#2370C2211yescharacteristic
69#2365C2211yescharacteristic
70#2361C2211yescharacteristic
71#2360C2211yescharacteristic
72#2360C2211yescharacteristic
73#2356C2211yescharacteristic
74#2354C2211yescharacteristic
75D4×C4⋊C4C2211yescharacteristic
76#2344C2211yescharacteristic
77#2344C2211yescharacteristic
78C4×C4⋊Q8C2211yescharacteristic
79C4×#126C2211yescharacteristic
80#2298—21no—
81#2293C2211yescharacteristic
82C42×Q8C2211yescharacteristic
83#2101C2211yescharacteristic
84#2100C2211yescharacteristic
85#2099C2211yescharacteristic
86#2099C2211yescharacteristic
87#2096C2211yescharacteristic
88#2095C2211yescharacteristic
89#2088C2211yescharacteristic
90#2086C2211yescharacteristic
91#2086C2211yescharacteristic
92#2084C2211yescharacteristic
93#2075C2211yescharacteristic
94#2073C2211yescharacteristic
95#2072C2211yescharacteristic
96#2072C2211yescharacteristic
97#2068C2211yescharacteristic
98#2068C2211yescharacteristic
99#2068C2211yescharacteristic
100#2067C2211yescharacteristic
101#2066C2211yescharacteristic
102#2065C2211yescharacteristic
103#2059C2211yescharacteristic
104#2059C2211yescharacteristic
105#2057C2211yescharacteristic
106#2055C2211yescharacteristic
107#2043C2211yescharacteristic
108#2043C2211yescharacteristic
109#2035C2211yescharacteristic
110#2035C2211yescharacteristic
111#2035C2211yescharacteristic
112#2033C2211yescharacteristic
113#2024C2211yescharacteristic
114#2000C2211yescharacteristic
115#1992C2211yescharacteristic
116#1988C2211yescharacteristic
117#1973C2211yescharacteristic
118#1973C2211yescharacteristic
119#1956C2211yescharacteristic
120#1949C2211yescharacteristic
121#1948C2211yescharacteristic
122#1947C2211yescharacteristic
123#1947C2211yescharacteristic
124#1944C2211yescharacteristic
125#1944C2211yescharacteristic
126#1943C2211yescharacteristic
127#1943C2211yescharacteristic
128#1942C2211yescharacteristic
129#1941C2211yescharacteristic
130#1940C2211yescharacteristic
131#1936C2211yescharacteristic
132#1935C2211yescharacteristic
133#1935C2211yescharacteristic
134#1935C2211yescharacteristic
135#1935C2211yescharacteristic
136#1935C2211yescharacteristic
137#1928C2211yescharacteristic
138#1928C2211yescharacteristic
139#1928C2211yescharacteristic
140#1928C2211yescharacteristic
141#1926C2211yescharacteristic
142#1925C2211yescharacteristic
143#1924C2211yescharacteristic
144#1924C2211yescharacteristic
145#1923C2211yescharacteristic
146#1921C2211yescharacteristic
147#1921C2211yescharacteristic
148#1921C2211yescharacteristic
149#1920C2211yescharacteristic
150#1920C2211yescharacteristic
151#1920C2211yescharacteristic
152#1919C2211yescharacteristic
153#1919C2211yescharacteristic
154#1919C2211yescharacteristic
155#1918C2211yescharacteristic
156#1918C2211yescharacteristic
157#1918C2211yescharacteristic
158#1917C2211yescharacteristic
159#1917C2211yescharacteristic
160#1917C2211yescharacteristic
161#1892C2211yescharacteristic
162#1880C2211yescharacteristic
163#1880C2211yescharacteristic
164#1880C2211yescharacteristic
165#1877C2211yescharacteristic
166#1877C2211yescharacteristic
167#1877C2211yescharacteristic
168#1874C2211yescharacteristic
169#1872C2211yescharacteristic
170#1865C2211yescharacteristic
171#1864C2211yescharacteristic
172#1864C2211yescharacteristic
173#1863C2211yescharacteristic
174#1863C2211yescharacteristic
175#1863C2211yescharacteristic
176#1863C2211yescharacteristic
177#1862C2211yescharacteristic
178#1852C2211yescharacteristic
179#1852C2211yescharacteristic
180#1850C2211yescharacteristic
181#1847C2211yescharacteristic
182#1823C2211yescharacteristic
183#1808C2211yescharacteristic
184#1803C2211yescharacteristic
185#1803C2211yescharacteristic
186#1776C2211yescharacteristic
187#1776C2211yescharacteristic
188#1776C2211yescharacteristic
189#1771C2211yescharacteristic
190#1770C2211yescharacteristic
191#1767C2211yescharacteristic
192#1763C2211yescharacteristic
193#1763C2211yescharacteristic
194#1763C2211yescharacteristic
195#1763C2211yescharacteristic
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic
198C4×#102C2211yescharacteristic
199#1752C2211yescharacteristic
200#1752C2211yescharacteristic
201#1745C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C23×C8C2311yescharacteristic
206#552—48no—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×#126—21no—
210C2×#126D411yescharacteristic
211C2×#125—21no—
212C2×#125—21no—
213C2×#125—21no—
214C2×#125C2311yescharacteristic
215C2×#123—21no—
216C2×#123—21no—
217C2×C22⋊Q8—21no—
218C2×C22⋊Q8—21no—
219C2×C22⋊Q8C2311yescharacteristic
220C2×C22⋊Q8C2311yescharacteristic
221C2×#121C2311yescharacteristic
222C2×C4×Q8—21no—
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×D4—21no—
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×#117—21no—
232C2×#117—21no—
233C2×#117—21no—
234C2×#117—21no—
235C22×C4⋊C4—21no—
236C22×C4⋊C4C2311yescharacteristic
237C22×C4⋊C4C2311yescharacteristic
238#483—24no—
239#478—24no—
240#475—24no—
241#465—24no—
242#461—24no—
243#440—24no—
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×C22⋊C8C2311yescharacteristic
284C2×C22⋊C8C2311yescharacteristic
285C2×C22⋊C8C2311yescharacteristic
286C2×#97C2311yescharacteristic
287C2×#97C2311yescharacteristic
288C2×#97C2311yescharacteristic
289C2×#97C2311yescharacteristic
290C2×#97C2311yescharacteristic
291C2×#97C2311yescharacteristic
292C2×C4×C8C2311yescharacteristic
293#400—21no—
294#400—21no—
295#400—21no—
296#400—21no—
297#400—21no—
298#400—21no—
299#400—21no—
300#400—21no—
301#398—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#398—21no—
306#398—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#397—21no—
311#397—21no—
312#397—21no—
313#397—21no—
314#397—21no—
315#396—21no—
316#396—21no—
317#395—21no—
318#394—21no—
319#394—21no—
320#393—21no—
321#391—21no—
322#391C2311yescharacteristic
323#391C2311yescharacteristic
324#391C2311yescharacteristic
325#391C2311yescharacteristic
326#391C2311yescharacteristic
327#391C2311yescharacteristic
328#390C2311yescharacteristic
329#390C2311yescharacteristic
330#390C2311yescharacteristic
331#389—21no—
332#389—21no—
333#389—21no—
334#389—21no—
335#389—21no—
336#389—21no—
337#389—21no—
338#389—21no—
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
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#388D411yescharacteristic
363#388D411yescharacteristic
364#388D411yescharacteristic
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#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387D411yescharacteristic
389#387D411yescharacteristic
390#387D411yescharacteristic
391#386—21no—
392#385—21no—
393#385—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#384C2311yescharacteristic
402#384C2311yescharacteristic
403#384C2311yescharacteristic
404#384C2311yescharacteristic
405#383—21no—
406#383—21no—
407#383D411yescharacteristic
408#382—21no—
409#382—21no—
410#382C2311yescharacteristic
411#381—21no—
412#381—21no—
413#380—21no—
414#380—21no—
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4—21no—
422C4×C4⋊C4—21no—
423C4×C4⋊C4—21no—
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439C4×C22⋊C4C2311yescharacteristic
440C4×C22⋊C4C2311yescharacteristic
441C4×C22⋊C4C2311yescharacteristic
442#376—21no—
443C43—21no—
444C43C2311yescharacteristic
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#340C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485C22×Q8—21no—
486C22×Q8C2411yescharacteristic
487C22×Q8C2411yescharacteristic
488C22×D4—21no—
489C22×D4C2411yescharacteristic
490C23×C4—21no—
491C23×C4—21no—
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—21no—
495C23×C4C2411yescharacteristic
496C2×SD16—22no—
497C2×SD16—41no—
498C2×SD16—41no—
499C2×SD16—41no—
500C2×SD16—41no—
501C2×SD16#4114yes—
502C22×C8—22no—
503C22×C8—41no—
504C22×C8—41no—
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C4⋊Q8—22no—
514C4⋊Q8—22no—
515C4⋊Q8—41no—
516C4⋊Q8—41no—
517#126—24no—
518#126—44no—
519#125—22no—
520#125—41no—
521#125—44no—
522#125—44no—
523#125—44no—
524#123—44no—
525#123—44no—
526C22⋊Q8—22no—
527C22⋊Q8—22no—
528C22⋊Q8—41no—
529C22⋊Q8—41no—
530C22⋊Q8—44no—
531C22⋊Q8—44no—
532#121—22no—
533#121—41no—
534C4×Q8—22no—
535C4×Q8—22no—
536C4×Q8—22no—
537C4×Q8—22no—
538C4×Q8—41no—
539C4×Q8—41no—
540C4×Q8—41no—
541C4×Q8—41no—
542C4×Q8—44no—
543C4×D4—22no—
544C4×D4—22no—
545C4×D4—22no—
546C4×D4—41no—
547C4×D4—41no—
548C4×D4—41no—
549C4×D4—44no—
550#117—44no—
551#117—44no—
552#117—44no—
553#117—44no—
554C2×C4⋊C4—22no—
555C2×C4⋊C4—22no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—41no—
593C2×C4⋊C4—41no—
594C2×C4⋊C4—44no—
595C2×C4⋊C4C2×D411yescharacteristic
596C2×C4⋊C4C2×D411yescharacteristic
597C2×C4⋊C4C2×D411yescharacteristic
598C2×C4⋊C4C2×D411yescharacteristic
599C2×C4⋊C4C2×D411yescharacteristic
600C2×C4⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4C2×D411yescharacteristic
630C2×C22⋊C4C2×D411yescharacteristic
631C2×C22⋊C4C2×D411yescharacteristic
632C2×C22⋊C4C2×D411yescharacteristic
633C2×C22⋊C4C2×D411yescharacteristic
634C2×C22⋊C4C2×D411yescharacteristic
635C2×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×C42C2×D411yescharacteristic
649C2×C42C2×D411yescharacteristic
650C2×C42C2×D411yescharacteristic
651C2×C42C2×D411yescharacteristic
652C2×C42C2411yescharacteristic
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658#107—22no—
659#107—22no—
660#107—22no—
661#107—41no—
662#107—41no—
663#107—41no—
664#107—41no—
665#107—41no—
666#106—22no—
667#106—22no—
668#106—22no—
669#106—41no—
670#106—41no—
671#106#4114yes—
672C4⋊C8—22no—
673C4⋊C8—22no—
674C4⋊C8—22no—
675C4⋊C8—41no—
676C4⋊C8—41no—
677#103—22no—
678#103—22no—
679#103—22no—
680#103—22no—
681#103—22no—
682#103—22no—
683#103—22no—
684#103—22no—
685#103—41no—
686#103—41no—
687#103—41no—
688#103—41no—
689#103—41no—
690#103—41no—
691#102—22no—
692#102—22no—
693#102—22no—
694#102—22no—
695#102—22no—
696#102—41no—
697C22⋊C8—22no—
698C22⋊C8—41no—
699C22⋊C8—41no—
700#97—22no—
701#97—41no—
702#97—41no—
703#97—41no—
704#97—41no—
705#97—41no—
706C4×C8—41no—
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#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758#95C2×D411yescharacteristic
759#95C2×D411yescharacteristic
760C24—21no—
761C24C22×D411yescharacteristic
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—42no—
774C2×Q8—42no—
775C2×Q8—81no—
776C2×Q8C2×#4112yes—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—42no—
783C2×D4—42no—
784C2×D4—81no—
785C2×D4C2×#4112yes—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—42no—
817C22×C4—81no—
818C22×C4—81no—
819C22×C4—81no—
820C22×C4—81no—
821C22×C4—81no—
822C22×C4C22×D411yescharacteristic
823C22×C4C22×D411yescharacteristic
824C22×C4C22×D411yescharacteristic
825C22×C4C22×D411yescharacteristic
826C22×C4C22×D411yescharacteristic
827C22×C4C22×D411yescharacteristic
828C22×C4C22×D411yescharacteristic
829C22×C4C22×D411yescharacteristic
830C22×C4C22×D411yescharacteristic
831C22×C4C22×D411yescharacteristic
832C22×C4C22×D411yescharacteristic
833C22×C4C22×D411yescharacteristic
834C22×C4C22×D411yescharacteristic
835C22×C4C2511yescharacteristic
836SD16—44no—
837SD16—82no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8—21no—
860C2×C8—82no—
861C2×C8C2×#4112yes—
862C2×C8C2×#4112yes—
863C4⋊C4—22no—
864C4⋊C4—22no—
865C4⋊C4—22no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—21no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—21no—
887C4⋊C4—21no—
888C4⋊C4—21no—
889C4⋊C4—41no—
890C4⋊C4—41no—
891C4⋊C4—41no—
892C4⋊C4—42no—
893C4⋊C4—42no—
894C4⋊C4—42no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—42no—
899C4⋊C4—42no—
900C4⋊C4—42no—
901C4⋊C4—42no—
902C4⋊C4—42no—
903C4⋊C4—42no—
904C4⋊C4—42no—
905C4⋊C4—42no—
906C4⋊C4—42no—
907C4⋊C4—42no—
908C4⋊C4—42no—
909C4⋊C4—42no—
910C4⋊C4—42no—
911C4⋊C4—42no—
912C4⋊C4—42no—
913C4⋊C4—42no—
914C4⋊C4—42no—
915C4⋊C4—42no—
916C4⋊C4—42no—
917C4⋊C4—42no—
918C4⋊C4—42no—
919C4⋊C4—42no—
920C4⋊C4—42no—
921C4⋊C4—81no—
922C4⋊C4—81no—
923C4⋊C4—81no—
924C4⋊C4—81no—
925C4⋊C4—81no—
926C4⋊C4—81no—
927C4⋊C4—81no—
928C4⋊C4C2×#4112yes—
929C4⋊C4C2×#4112yes—
930C4⋊C42−1+412yes—
931C22⋊C4—22no—
932C22⋊C4—22no—
933C22⋊C4—41no—
934C22⋊C4—41no—
935C22⋊C4—41no—
936C22⋊C4—42no—
937C22⋊C4—42no—
938C22⋊C4—42no—
939C22⋊C4—42no—
940C22⋊C4—42no—
941C22⋊C4—42no—
942C22⋊C4—42no—
943C22⋊C4—42no—
944C22⋊C4—42no—
945C22⋊C4—42no—
946C22⋊C4—42no—
947C22⋊C4—42no—
948C22⋊C4—42no—
949C22⋊C4—81no—
950C22⋊C4—81no—
951C22⋊C4AGL(1,ℤ/8)14yes—
952C42—22no—
953C42—21no—
954C42—21no—
955C42—21no—
956C42—21no—
957C42—21no—
958C42—21no—
959C42—21no—
960C42—21no—
961C42—21no—
962C42—21no—
963C42—21no—
964C42—21no—
965C42—41no—
966C42—41no—
967C42—41no—
968C42—42no—
969C42—42no—
970C42—42no—
971C42—42no—
972C42—42no—
973C42—42no—
974C42—42no—
975C42—42no—
976C42—42no—
977C42—42no—
978C42—42no—
979C42—81no—
980C42—81no—
981C23—21no—
982C23—21no—
983C23—21no—
984C23—21no—
985C23—21no—
986C23—21no—
987C23—22no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23C2×AGL(1,ℤ/8)12yes—
995C23C23×D411yescharacteristic
996Q8—22no—
997Q8—22no—
998Q8—41no—
999Q8—41no—
1000Q8—41no—
1001Q8—41no—
1002Q8—41no—
1003Q8—41no—
1004Q8—84no—
1005D4—22no—
1006D4—22no—
1007D4—41no—
1008D4—41no—
1009D4—84no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
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—22no—
1037C2×C4—22no—
1038C2×C4—21no—
1039C2×C4—22no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—22no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
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—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—84no—
1097C2×C4—84no—
1098C2×C4—84no—
1099C2×C4—84no—
1100C2×C4—84no—
1101C2×C4C2×AGL(1,ℤ/8)12yes—
1102C2×C4C2×AGL(1,ℤ/8)12yes—
1103C2×C4C22×#4111yescharacteristic
1104C2×C4C22×#4111yescharacteristic
1105C2×C4C2×2−1+411yescharacteristic
1106C2×C4#58511yescharacteristic
1107C2×C4#58511yescharacteristic
1108C2×C4#58511yescharacteristic
1109C8—22no—
1110C8—22no—
1111C8—41no—
1112C8—41no—
1113C8—41no—
1114C8—41no—
1115C8—41no—
1116C8—41no—
1117C22—22no—
1118C22—22no—
1119C22—22no—
1120C22—41no—
1121C22—41no—
1122C22—41no—
1123C22—41no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—81no—
1128C22—81no—
1129C22—81no—
1130C22—81no—
1131C22D4×#4111yescharacteristic
1132C22D4×#4111yescharacteristic
1133C22#348911yescharacteristic
1134C22C22×AGL(1,ℤ/8)11yescharacteristic
1135C22#358611yescharacteristic
1136C22#358611yescharacteristic
1137C22#358611yescharacteristic
1138C4—22no—
1139C4—22no—
1140C4—41no—
1141C4—41no—
1142C4—42no—
1143C4—41no—
1144C4—41no—
1145C4—41no—
1146C4—42no—
1147C4—41no—
1148C4—41no—
1149C4—41no—
1150C4—41no—
1151C4—42no—
1152C4—41no—
1153C4—41no—
1154C4—42no—
1155C4—81no—
1156C4—81no—
1157C4—81no—
1158C4—81no—
1159C4—81no—
1160C4—81no—
1161C4—81no—
1162C4—81no—
1163C4—81no—
1164C4—81no—
1165C4—81no—
1166C4#348211yescharacteristic
1167C4#349111yescharacteristic
1168C4#351211yescharacteristic
1169C4#356511yescharacteristic
1170C2—42no—
1171C2—82no—
1172C2#5917811yescharacteristic
1173C2#6145211yescharacteristic
1174C2#6145211yescharacteristic
1175C2#6151711yescharacteristic
1176C2#6151711yescharacteristic
1177C2#6210711yescharacteristic
1178C2#6222511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#126 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #36408C2semidirect
3. #31476C2semidirect
4. #31244C2semidirect
5. #31120C2semidirect
7. #29520C2semidirect
8. #29448C2semidirect
9. #29034C2semidirect
10. #28081C2semidirect
11. #28008C2semidirect
12. #27446C2semidirect
13. #27374C2semidirect
14. #27176C2semidirect
16. #27051C2semidirect
17. #26884C2semidirect
19. #26773C2semidirect
21. #26182C2semidirect
22. #26104C2semidirect
23. #25988C2semidirect
25. #23292C2semidirect
27. #23100C2semidirect
28. #22978C2semidirect
29. #22934C2semidirect
30. #21615C2semidirect
31. #21124C2semidirect

Maximal subgroups

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

subgroupindex
#594982
#364082
#314762
#312442
#311202
#305972
#295202
#294482
#290342
#280812
#280082
#274462
#273742
#271762
#271582
#270512
#268842
#268002
#267732
#266772
#261822
#261042
#259882
#250412
#232922
#231342
#231002
#229782
#229342
#216152
#211242