Finite Group Databasebeta

← #6719405

Subgroups — #6719405

Order 512.

1363 conjugacy classes of subgroups.

The subgroup lattice has 1205 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40020C211yesmaximal, characteristic, complemented
2#36416C211yesmaximal, characteristic, complemented
3#33028C211yesmaximal, characteristic, complemented
4#32663C211yesmaximal, characteristic, complemented
5#32659C211yesmaximal, characteristic, complemented
6#32620C211yesmaximal, characteristic, complemented
7#32613C211yesmaximal, characteristic
8#32403C211yesmaximal, characteristic, complemented
9#32394C211yesmaximal, characteristic, complemented
10#31601C211yesmaximal, characteristic, complemented
11#31592C211yesmaximal, characteristic, complemented
12#30282C211yesmaximal, characteristic, complemented
13#29870C211yesmaximal, characteristic, complemented
14#28536C211yesmaximal, characteristic, complemented
15#28409C211yesmaximal, characteristic
16#27509C211yesmaximal, characteristic, complemented
17#27504C211yesmaximal, characteristic, complemented
18#27211C211yesmaximal, characteristic
19#27208C211yesmaximal, characteristic, complemented
20#26332C211yesmaximal, characteristic, complemented
21#26331C211yesmaximal, characteristic, complemented
22#25458C211yesmaximal, characteristic, complemented
23#25457C211yesmaximal, characteristic, complemented
24#25326C211yesmaximal, characteristic, complemented
25#25280C211yesmaximal, characteristic, complemented
26#25072C211yesmaximal, characteristic, complemented
27#25071C211yesmaximal, characteristic, complemented
28#23225C211yesmaximal, characteristic, complemented
29#23164C211yesmaximal, characteristic, complemented
30#22311C211yesmaximal, characteristic, complemented
31#21118C211yesmaximal, characteristic, complemented
32C2×#499C2211yescharacteristic
33C2×#499C2211yescharacteristic
34C2×#488C2211yescharacteristic
35C2×#488C2211yescharacteristic
36C2×#478C2211yescharacteristic
37C2×#478C2211yescharacteristic
38C2×#478C2211yescharacteristic
39C2×#463C2211yescharacteristic
40C2×C4×D8C2211yescharacteristic
41#2861C2211yescharacteristic
42#2859C2211yescharacteristic
43#2851—21no—
44#2800—21no—
45#2795—21no—
46#2779—21no—
47#2674—21no—
48#2649—21no—
49#2592C2211yescharacteristic
50#2589—21no—
51#2589—21no—
52#2587—21no—
53#2587—21no—
54#2581C2211yescharacteristic
55#2580C2211yescharacteristic
56#2580C2211yescharacteristic
57#2571C2211yescharacteristic
58#2566C2211yescharacteristic
59#2566C2211yescharacteristic
60#2566C2211yescharacteristic
61#2552C2211yescharacteristic
62#2548C2211yescharacteristic
63#2544C2211yescharacteristic
64#2538C2211yescharacteristic
65#2513C2211yescharacteristic
66#2511C2211yescharacteristic
67#2477—21no—
68#2474—21no—
69#2448C2211yescharacteristic
70#2445C2211yescharacteristic
71#2441—21no—
72#2439—21no—
73#2370C2211yescharacteristic
74#2370C2211yescharacteristic
75#2370C2211yescharacteristic
76#2367C2211yescharacteristic
77#2355C2211yescharacteristic
78#2355C2211yescharacteristic
79#2354C2211yescharacteristic
80#2354C2211yescharacteristic
81#2335—21no—
82C4×C4⋊Q8C2211yescharacteristic
83#2296—21no—
84#2293C2211yescharacteristic
85C42×D4C2211yescharacteristic
86#2097C2211yescharacteristic
87#2097C2211yescharacteristic
88#2097C2211yescharacteristic
89#2096C2211yescharacteristic
90#2095C2211yescharacteristic
91#2094C2211yescharacteristic
92#2093C2211yescharacteristic
93#2093C2211yescharacteristic
94#2093C2211yescharacteristic
95#2093C2211yescharacteristic
96#2092C2211yescharacteristic
97#2092C2211yescharacteristic
98#2092C2211yescharacteristic
99#2092C2211yescharacteristic
100#2085C2211yescharacteristic
101#2085C2211yescharacteristic
102#2085C2211yescharacteristic
103#2085C2211yescharacteristic
104#2084C2211yescharacteristic
105#2084C2211yescharacteristic
106#2083C2211yescharacteristic
107#2083C2211yescharacteristic
108#2074C2211yescharacteristic
109#2073C2211yescharacteristic
110#2073C2211yescharacteristic
111#2071C2211yescharacteristic
112#2071C2211yescharacteristic
113#2071C2211yescharacteristic
114#2067C2211yescharacteristic
115#2067C2211yescharacteristic
116#2067C2211yescharacteristic
117#2066C2211yescharacteristic
118#2065C2211yescharacteristic
119#2065C2211yescharacteristic
120#2055C2211yescharacteristic
121#2054C2211yescharacteristic
122#2042C2211yescharacteristic
123#2041C2211yescharacteristic
124#2012C2211yescharacteristic
125#2011C2211yescharacteristic
126#1989C2211yescharacteristic
127#1989C2211yescharacteristic
128#1989C2211yescharacteristic
129#1985C2211yescharacteristic
130#1985C2211yescharacteristic
131#1985C2211yescharacteristic
132#1985C2211yescharacteristic
133#1983C2211yescharacteristic
134#1983C2211yescharacteristic
135#1982C2211yescharacteristic
136#1973C2211yescharacteristic
137#1972C2211yescharacteristic
138#1972C2211yescharacteristic
139#1972C2211yescharacteristic
140#1961C2211yescharacteristic
141#1959C2211yescharacteristic
142#1949C2211yescharacteristic
143#1949C2211yescharacteristic
144#1948C2211yescharacteristic
145#1947C2211yescharacteristic
146#1943C2211yescharacteristic
147#1943C2211yescharacteristic
148#1939C2211yescharacteristic
149#1939C2211yescharacteristic
150#1936C2211yescharacteristic
151#1935C2211yescharacteristic
152#1928C2211yescharacteristic
153#1928C2211yescharacteristic
154#1927C2211yescharacteristic
155#1927C2211yescharacteristic
156#1926C2211yescharacteristic
157#1926C2211yescharacteristic
158#1926C2211yescharacteristic
159#1926C2211yescharacteristic
160#1926C2211yescharacteristic
161#1926C2211yescharacteristic
162#1926C2211yescharacteristic
163#1925C2211yescharacteristic
164#1925C2211yescharacteristic
165#1925C2211yescharacteristic
166#1921C2211yescharacteristic
167#1921C2211yescharacteristic
168#1920C2211yescharacteristic
169#1920C2211yescharacteristic
170#1919C2211yescharacteristic
171#1919C2211yescharacteristic
172#1917C2211yescharacteristic
173#1917C2211yescharacteristic
174#1917C2211yescharacteristic
175#1917C2211yescharacteristic
176#1880C2211yescharacteristic
177#1879C2211yescharacteristic
178#1879C2211yescharacteristic
179#1879C2211yescharacteristic
180#1879C2211yescharacteristic
181#1879C2211yescharacteristic
182#1877C2211yescharacteristic
183#1877C2211yescharacteristic
184#1865C2211yescharacteristic
185#1864C2211yescharacteristic
186#1864C2211yescharacteristic
187#1864C2211yescharacteristic
188#1847C2211yescharacteristic
189#1847C2211yescharacteristic
190#1831C2211yescharacteristic
191#1804C2211yescharacteristic
192#1803C2211yescharacteristic
193#1776C2211yescharacteristic
194#1776C2211yescharacteristic
195C4×#106C2211yescharacteristic
196#1770C2211yescharacteristic
197#1770C2211yescharacteristic
198#1763C2211yescharacteristic
199#1762C2211yescharacteristic
200C4×#102C2211yescharacteristic
201C4×#102C2211yescharacteristic
202#1744C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×D8C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C2×C4⋊Q8D411yescharacteristic
207C2×#127C2311yescharacteristic
208C2×#125—21no—
209C2×#125C2311yescharacteristic
210C2×#125C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×#124—21no—
213C2×#124C2311yescharacteristic
214C2×#124C2311yescharacteristic
215C2×#123—21no—
216C2×C22⋊Q8—21no—
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×D4C2311yescharacteristic
221C2×C4×D4C2311yescharacteristic
222C2×C4×D4C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×#117—21no—
226C2×#117—21no—
227C2×#117—21no—
228C22×C42—21no—
229#499—24no—
230#499—42no—
231#488—24no—
232#488—42no—
233#478—42no—
234#478—42no—
235#478—42no—
236#463—42no—
237C4×D8—24no—
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#97C2311yescharacteristic
288C2×#97C2311yescharacteristic
289C2×#97C2311yescharacteristic
290C2×#97C2311yescharacteristic
291C2×C4×C8C2311yescharacteristic
292C2×C4×C8C2311yescharacteristic
293#400—21no—
294#400—21no—
295#400—21no—
296#400—21no—
297#400—21no—
298#399—21no—
299#399—21no—
300#399—21no—
301#398—21no—
302#398—21no—
303#397—21no—
304#397—21no—
305#397—21no—
306#397—21no—
307#396—21no—
308#396—21no—
309#396—21no—
310#396—21no—
311#396—21no—
312#396—21no—
313#396—21no—
314#396—21no—
315#395—21no—
316#394—21no—
317#394—21no—
318#394—21no—
319#394—21no—
320#394—21no—
321#394—21no—
322#393—21no—
323#393—21no—
324#393—21no—
325#391—21no—
326#391—21no—
327#391D411yescharacteristic
328#391D411yescharacteristic
329#391C2311yescharacteristic
330#391C2311yescharacteristic
331#391C2311yescharacteristic
332#391C2311yescharacteristic
333#390—21no—
334#390C2311yescharacteristic
335#390C2311yescharacteristic
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#389—21no—
347#389—21no—
348#389—21no—
349#389—21no—
350#389—21no—
351#389—21no—
352#389—21no—
353#389—21no—
354#389—21no—
355#389D411yescharacteristic
356#389D411yescharacteristic
357#389D411yescharacteristic
358#389D411yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
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#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—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#387—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#384D411yescharacteristic
414#384C2311yescharacteristic
415#384C2311yescharacteristic
416#384C2311yescharacteristic
417#384C2311yescharacteristic
418#384C2311yescharacteristic
419#382—21no—
420#382C2311yescharacteristic
421#382C2311yescharacteristic
422#382C2311yescharacteristic
423#382C2311yescharacteristic
424#382C2311yescharacteristic
425#380—21no—
426#380—21no—
427#380—21no—
428C4×C4⋊C4—21no—
429C4×C4⋊C4—21no—
430C4×C4⋊C4—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4—21no—
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C22⋊C4—21no—
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C43C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C22×Q8C2×D411yescharacteristic
488C22×Q8C2×D411yescharacteristic
489C22×Q8C2411yescharacteristic
490C22×D4—21no—
491C22×D4—21no—
492C22×D4C2411yescharacteristic
493C22×D4C2411yescharacteristic
494C22×D4C2411yescharacteristic
495C23×C4—21no—
496C23×C4—21no—
497C23×C4—21no—
498C23×C4—21no—
499C23×C4—21no—
500C2×SD16—22no—
501C2×SD16—41no—
502C2×SD16—41no—
503C2×D8—22no—
504C2×D8—22no—
505C2×D8—22no—
506C2×D8—41no—
507C2×D8—41no—
508C2×D8—41no—
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C4⋊Q8—42no—
518#127—41no—
519#127—41no—
520#125—22no—
521#125—22no—
522#125—22no—
523#125—22no—
524#125—22no—
525#125—22no—
526#125—82no—
527#124—22no—
528#124—22no—
529#124—41no—
530#124—41no—
531#124—82no—
532#123—44no—
533C22⋊Q8—82no—
534C4×Q8—41no—
535C4×Q8—41no—
536C4×Q8—41no—
537C4×Q8—41no—
538C4×Q8—41no—
539C4×Q8—41no—
540C4×D4—22no—
541C4×D4—22no—
542C4×D4—22no—
543C4×D4—22no—
544C4×D4—22no—
545C4×D4—22no—
546C4×D4—41no—
547C4×D4—41no—
548C4×D4—41no—
549C4×D4—41no—
550#117—44no—
551#117—82no—
552#117—82no—
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—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4C2×D411yescharacteristic
579C2×C4⋊C4C2×D411yescharacteristic
580C2×C4⋊C4C2×D411yescharacteristic
581C2×C4⋊C4C2×D411yescharacteristic
582C2×C4⋊C4C2×D411yescharacteristic
583C2×C4⋊C4C2×D411yescharacteristic
584C2×C4⋊C4C2×D411yescharacteristic
585C2×C4⋊C4C2×D411yescharacteristic
586C2×C4⋊C4C2×D411yescharacteristic
587C2×C4⋊C4C2×D411yescharacteristic
588C2×C4⋊C4C2×D411yescharacteristic
589C2×C4⋊C4C2×D411yescharacteristic
590C2×C4⋊C4C2×D411yescharacteristic
591C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—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—82no—
649C2×C42C2×D411yescharacteristic
650C2×C42C2×D411yescharacteristic
651C2×C42C2×D411yescharacteristic
652C2×C42C2×D411yescharacteristic
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660#107—22no—
661#107—22no—
662#107—22no—
663#107—41no—
664#107—41no—
665#107—41no—
666#107—41no—
667#107—41no—
668#106—22no—
669#106—22no—
670#106—22no—
671#106—41no—
672#106—41no—
673#106—41no—
674#106—41no—
675#106—41no—
676#106—41no—
677C4⋊C8—22no—
678C4⋊C8—22no—
679C4⋊C8—41no—
680C4⋊C8—41no—
681C4⋊C8—41no—
682C4⋊C8—41no—
683#103—22no—
684#103—22no—
685#103—22no—
686#103—41no—
687#103—41no—
688#103—41no—
689#103—41no—
690#102—22no—
691#102—22no—
692#102—22no—
693#102—22no—
694#102—22no—
695#102—22no—
696#102—22no—
697#102—41no—
698#102—41no—
699#102—41no—
700#102—41no—
701#102—41no—
702#102—41no—
703#102—41no—
704#102—41no—
705#102—41no—
706#102—41no—
707#102—41no—
708#102—41no—
709#97—41no—
710#97—41no—
711#97—41no—
712#97—41no—
713C4×C8—22no—
714C4×C8#4114yes—
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—
760C24—21no—
761C24—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—41no—
769C2×Q8—41no—
770C2×Q8—41no—
771C2×Q8—41no—
772C2×Q8—41no—
773C2×Q8—41no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—42no—
792C2×D4—81no—
793C2×D4—81no—
794C2×D4—81no—
795C2×D4—81no—
796C2×D4—81no—
797C2×D42−1+412yes—
798C22×C4—24no—
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—42no—
813C22×C4—42no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—42no—
817C22×C4—42no—
818C22×C4—81no—
819C22×C4—81no—
820C22×C4—81no—
821C22×C4—81no—
822C22×C4—81no—
823C22×C4—81no—
824C22×C4—81no—
825C22×C4—81no—
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×C4C22×D411yescharacteristic
836C22×C4C22×D411yescharacteristic
837C22×C4C22×D411yescharacteristic
838C22×C4C22×D411yescharacteristic
839C22×C4C22×D411yescharacteristic
840C22×C4C2511yescharacteristic
841SD16—82no—
842D8—44no—
843D8—82no—
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—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8C2×#4112yes—
867C2×C8C2×#4112yes—
868C4⋊C4—22no—
869C4⋊C4—22no—
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—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—41no—
894C4⋊C4—41no—
895C4⋊C4—41no—
896C4⋊C4—41no—
897C4⋊C4—41no—
898C4⋊C4—41no—
899C4⋊C4—41no—
900C4⋊C4—41no—
901C4⋊C4—41no—
902C4⋊C4—41no—
903C4⋊C4—41no—
904C4⋊C4—41no—
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—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⋊C4—81no—
930C4⋊C42−1+412yes—
931C22⋊C4—24no—
932C22⋊C4—42no—
933C22⋊C4—42no—
934C22⋊C4—42no—
935C22⋊C4—42no—
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—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—
963C22⋊C4—81no—
964C42—22no—
965C42—21no—
966C42—21no—
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—41no—
980C42—42no—
981C42—42no—
982C42—42no—
983C42—81no—
984C42—81no—
985C42—81no—
986C42—81no—
987C42—81no—
988C42—81no—
989C42—81no—
990C42—81no—
991C42C2×#4112yes—
992C42H(5,𝔽2)12yes—
993C23—22no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23C23×D411yescharacteristic
1015Q8—41no—
1016Q8—41no—
1017Q8—41no—
1018Q8—41no—
1019Q8—82no—
1020Q8—82no—
1021D4—22no—
1022D4—22no—
1023D4—41no—
1024D4—41no—
1025D4—41no—
1026D4—41no—
1027D4—41no—
1028D4—41no—
1029D4—41no—
1030D4—41no—
1031D4—41no—
1032D4—41no—
1033D4—162no—
1034D4—162no—
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—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—22no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—48no—
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—84no—
1115C2×C4—84no—
1116C2×C4—84no—
1117C2×C4—162no—
1118C2×C4#55012yes—
1119C2×C4#55012yes—
1120C2×C4#57512yes—
1121C2×C4C22×#4111yescharacteristic
1122C2×C4C2×H(5,𝔽2)11yescharacteristic
1123C2×C4C2×2−1+411yescharacteristic
1124C2×C4C2×2−1+411yescharacteristic
1125C2×C4#58511yescharacteristic
1126C2×C4#58511yescharacteristic
1127C8—22no—
1128C8—22no—
1129C8—41no—
1130C8—41no—
1131C8—41no—
1132C8—41no—
1133C8—41no—
1134C8—41no—
1135C22—42no—
1136C22—42no—
1137C22—42no—
1138C22—81no—
1139C22—81no—
1140C22—81no—
1141C22—81no—
1142C22—81no—
1143C22—81no—
1144C22—81no—
1145C22—81no—
1146C22—81no—
1147C22—81no—
1148C22—81no—
1149C22—81no—
1150C22—81no—
1151C22—81no—
1152C22—81no—
1153C22—81no—
1154C22—81no—
1155C22—81no—
1156C22C2×#55011yescharacteristic
1157C22#348511yescharacteristic
1158C22#348611yescharacteristic
1159C22C2×#57511yescharacteristic
1160C22#358411yescharacteristic
1161C22#358511yescharacteristic
1162C22#358511yescharacteristic
1163C4—22no—
1164C4—22no—
1165C4—22no—
1166C4—41no—
1167C4—41no—
1168C4—41no—
1169C4—41no—
1170C4—41no—
1171C4—41no—
1172C4—41no—
1173C4—41no—
1174C4—41no—
1175C4—41no—
1176C4—42no—
1177C4—41no—
1178C4—81no—
1179C4—81no—
1180C4—81no—
1181C4—81no—
1182C4—81no—
1183C4—81no—
1184C4—81no—
1185C4—81no—
1186C4—81no—
1187C4—81no—
1188C4—81no—
1189C4—81no—
1190C4#346111yescharacteristic
1191C4#349511yescharacteristic
1192C4#355411yescharacteristic
1193C4#356111yescharacteristic
1194C2—82no—
1195C2—161no—
1196C2—161no—
1197C2#3777311yescharacteristic
1198C2#6140111yescharacteristic
1199C2#6141411yescharacteristic
1200C2#6172511yescharacteristic
1201C2#6180411yescharacteristic
1202C2#6183111yescharacteristic
1203C2#6186111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2011C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C4⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #40020C2semidirect
2. #36416C2semidirect
3. #33028C2semidirect
4. #32663C2semidirect
5. #32659C2semidirect
6. #32620C2semidirect
8. #32403C2semidirect
9. #32394C2semidirect
10. #31601C2semidirect
11. #31592C2semidirect
12. #30282C2semidirect
13. #29870C2semidirect
14. #28536C2semidirect
16. #27509C2semidirect
17. #27504C2semidirect
19. #27208C2semidirect
20. #26332C2semidirect
21. #26331C2semidirect
22. #25458C2semidirect
23. #25457C2semidirect
24. #25326C2semidirect
25. #25280C2semidirect
26. #25072C2semidirect
27. #25071C2semidirect
28. #23225C2semidirect
29. #23164C2semidirect
30. #22311C2semidirect
31. #21118C2semidirect

Maximal subgroups

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

subgroupindex
#400202
#364162
#330282
#326632
#326592
#326202
#326132
#324032
#323942
#316012
#315922
#302822
#298702
#285362
#284092
#275092
#275042
#272112
#272082
#263322
#263312
#254582
#254572
#253262
#252802
#250722
#250712
#232252
#231642
#223112
#211182