Finite Group Databasebeta

← #7047127

Subgroups — #7047127

Order 512.

1406 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59378C211yesmaximal, characteristic
2#59240C211yesmaximal, characteristic, complemented
3#32421C211yesmaximal, characteristic, complemented
4#32268C211yesmaximal, characteristic, complemented
5#31891C211yesmaximal, characteristic, complemented
6#31680C211yesmaximal, characteristic
7#31479C211yesmaximal, characteristic, complemented
8#31447C211yesmaximal, characteristic, complemented
9#31374C211yesmaximal, characteristic, complemented
10#31104C211yesmaximal, characteristic, complemented
11#29237C211yesmaximal, characteristic, complemented
12#28959C211yesmaximal, characteristic, complemented
13#27842C211yesmaximal, characteristic, complemented
14#27632C211yesmaximal, characteristic, complemented
15#27536C211yesmaximal, characteristic, complemented
16#27518C211yesmaximal, characteristic, complemented
17#27468C211yesmaximal, characteristic, complemented
18#27385C211yesmaximal, characteristic, complemented
19#27372C211yesmaximal, characteristic, complemented
20#27178C211yesmaximal, characteristic, complemented
21#27178C211yesmaximal, characteristic, complemented
22#26998C211yesmaximal, characteristic, complemented
23#26313C211yesmaximal, characteristic, complemented
24#26103C211yesmaximal, characteristic, complemented
25#25974C211yesmaximal, characteristic, complemented
26#24882C211yesmaximal, characteristic
27#23758C211yesmaximal, characteristic, complemented
28#23075C211yesmaximal, characteristic, complemented
29#22580C211yesmaximal, characteristic, complemented
30#22369C211yesmaximal, characteristic, complemented
31#22075C211yesmaximal, characteristic, complemented
32C2×#480C2211yescharacteristic
33C2×#476C2211yescharacteristic
34C2×#418C2211yescharacteristic
35#2777—21no—
36#2760—21no—
37#2758—21no—
38#2697—21no—
39#2604—21no—
40#2576—21no—
41#2576—21no—
42#2571C2211yescharacteristic, complemented
43#2563C2211yescharacteristic
44#2561—21no—
45#2561—21no—
46#2528—21no—
47#2509C2211yescharacteristic, complemented
48#2509C2211yescharacteristic, complemented
49#2496C2211yescharacteristic
50#2494C2211yescharacteristic
51#2494C2211yescharacteristic
52#2494C2211yescharacteristic
53#2493—21no—
54#2488—21no—
55#2487C2211yescharacteristic
56#2481—21no—
57#2463—21no—
58#2452C2211yescharacteristic
59#2452C2211yescharacteristic
60#2440C2211yescharacteristic, complemented
61#2439C2211yescharacteristic
62#2420C2211yescharacteristic
63#2420C2211yescharacteristic
64#2408C2211yescharacteristic
65#2365C2211yescharacteristic, complemented
66#2360—21no—
67#2358—21no—
68#2357C2211yescharacteristic
69#2357C2211yescharacteristic
70#2352C2211yescharacteristic
71#2347C2211yescharacteristic
72#2345C2211yescharacteristic, complemented
73D4×C22⋊C4C2211yescharacteristic
74D4×C22⋊C4C2211yescharacteristic
75C4×#123C2211yescharacteristic
76C4×#121C2211yescharacteristic
77C4×#121C2211yescharacteristic
78C2×#389C2211yescharacteristic, complemented
79#2283C2211yescharacteristic, complemented
80#2101C2211yescharacteristic, complemented
81#2101C2211yescharacteristic, complemented
82#2101C2211yescharacteristic, complemented
83#2100C2211yescharacteristic, complemented
84#2092C2211yescharacteristic
85#2092C2211yescharacteristic
86#2087C2211yescharacteristic, complemented
87#2087C2211yescharacteristic, complemented
88#2087C2211yescharacteristic, complemented
89#2087C2211yescharacteristic, complemented
90#2085C2211yescharacteristic, complemented
91#2085C2211yescharacteristic, complemented
92#2085C2211yescharacteristic, complemented
93#2077C2211yescharacteristic
94#2077C2211yescharacteristic, complemented
95#2077C2211yescharacteristic, complemented
96#2076C2211yescharacteristic
97#2076C2211yescharacteristic
98#2076C2211yescharacteristic, complemented
99#2076C2211yescharacteristic, complemented
100#2075C2211yescharacteristic
101#2075C2211yescharacteristic
102#2075C2211yescharacteristic
103#2073C2211yescharacteristic
104#2073C2211yescharacteristic
105#2071C2211yescharacteristic
106#2067C2211yescharacteristic
107#2067C2211yescharacteristic
108#2067C2211yescharacteristic
109#2067C2211yescharacteristic
110#2065C2211yescharacteristic
111#2065C2211yescharacteristic
112#2057C2211yescharacteristic, complemented
113#2057C2211yescharacteristic, complemented
114#2057C2211yescharacteristic, complemented
115#2034C2211yescharacteristic
116#2034C2211yescharacteristic
117#2033C2211yescharacteristic
118#2033C2211yescharacteristic
119#2023C2211yescharacteristic
120#1993C2211yescharacteristic, complemented
121#1993C2211yescharacteristic, complemented
122#1988C2211yescharacteristic, complemented
123#1955C2211yescharacteristic
124#1949C2211yescharacteristic, complemented
125#1949C2211yescharacteristic, complemented
126#1949C2211yescharacteristic, complemented
127#1949C2211yescharacteristic, complemented
128#1949C2211yescharacteristic, complemented
129#1943C2211yescharacteristic, complemented
130#1943C2211yescharacteristic, complemented
131#1942C2211yescharacteristic, complemented
132#1942C2211yescharacteristic, complemented
133#1940C2211yescharacteristic, complemented
134#1936C2211yescharacteristic
135#1936C2211yescharacteristic
136#1936C2211yescharacteristic
137#1936C2211yescharacteristic
138#1934C2211yescharacteristic
139#1934C2211yescharacteristic
140#1926C2211yescharacteristic
141#1926C2211yescharacteristic
142#1925C2211yescharacteristic
143#1925C2211yescharacteristic
144#1925C2211yescharacteristic
145#1925C2211yescharacteristic
146#1924C2211yescharacteristic
147#1924C2211yescharacteristic, complemented
148#1924C2211yescharacteristic, complemented
149#1923C2211yescharacteristic
150#1920C2211yescharacteristic, complemented
151#1920C2211yescharacteristic, complemented
152#1919C2211yescharacteristic, complemented
153#1919C2211yescharacteristic, complemented
154#1919C2211yescharacteristic, complemented
155#1918C2211yescharacteristic, complemented
156#1918C2211yescharacteristic, complemented
157#1918C2211yescharacteristic, complemented
158#1918C2211yescharacteristic, complemented
159#1918C2211yescharacteristic, complemented
160#1917C2211yescharacteristic, complemented
161#1916C2211yescharacteristic, complemented
162#1874C2211yescharacteristic
163#1874C2211yescharacteristic
164#1874C2211yescharacteristic
165#1870C2211yescharacteristic
166#1864C2211yescharacteristic
167#1864C2211yescharacteristic
168#1862C2211yescharacteristic
169#1862C2211yescharacteristic
170#1862C2211yescharacteristic
171#1862C2211yescharacteristic
172#1862C2211yescharacteristic
173#1862C2211yescharacteristic
174#1854C2211yescharacteristic
175#1854C2211yescharacteristic
176#1853C2211yescharacteristic, complemented
177#1852C2211yescharacteristic, complemented
178#1852C2211yescharacteristic, complemented
179#1851C2211yescharacteristic
180#1847C2211yescharacteristic, complemented
181#1825C2211yescharacteristic
182#1823C2211yescharacteristic, complemented
183#1809C2211yescharacteristic
184#1809C2211yescharacteristic
185#1809C2211yescharacteristic
186#1804C2211yescharacteristic
187#1804C2211yescharacteristic
188#1802C2211yescharacteristic
189#1797C2211yescharacteristic, complemented
190#1786C2211yescharacteristic
191#1786C2211yescharacteristic
192#1786C2211yescharacteristic
193#1776C2211yescharacteristic, complemented
194C4×#107C2211yescharacteristic, complemented
195C4×#106C2211yescharacteristic, complemented
196#1771C2211yescharacteristic, complemented
197#1762C2211yescharacteristic
198#1762C2211yescharacteristic
199C4×#102C2211yescharacteristic
200C4×#102C2211yescharacteristic
201#1753C2211yescharacteristic
202C4×C22⋊C8C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×#126—21no—
208C2×#123D411yescharacteristic
209C2×C22⋊Q8—21no—
210C2×C22⋊Q8—21no—
211C2×C22⋊Q8—21no—
212C2×#121C2311yescharacteristic
213C2×#121C2311yescharacteristic
214C2×#120—21no—
215C2×C4×Q8—21no—
216C2×C4×D4—21no—
217C2×C4×D4—21no—
218C2×C4×D4C2311yescharacteristic
219C2×C4×D4C2311yescharacteristic
220C2×C4×D4C2311yescharacteristic
221C2×C4×D4C2311yescharacteristic
222C2×C4×D4C2311yescharacteristic
223C2×#117C2311yescharacteristic
224C22×C4⋊C4—21no—
225C22×C4⋊C4C2311yescharacteristic
226C22×C4⋊C4C2311yescharacteristic
227C22×C22⋊C4—21no—
228C22×C22⋊C4—21no—
229C22×C42C2311yescharacteristic
230#480—24no—
231#476—24no—
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×C4⋊C8C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253#418—24no—
254C2×#102C2311yescharacteristic
255C2×#102C2311yescharacteristic
256C2×#102C2311yescharacteristic
257C2×#102C2311yescharacteristic
258C2×#102C2311yescharacteristic
259C2×#102C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×C22⋊C8C2311yescharacteristic
271C2×C22⋊C8C2311yescharacteristic
272C2×C22⋊C8C2311yescharacteristic
273C2×C22⋊C8C2311yescharacteristic
274C2×C22⋊C8C2311yescharacteristic
275C2×C22⋊C8C2311yescharacteristic
276C2×C22⋊C8C2311yescharacteristic
277C2×#97C2311yescharacteristic
278C2×#97C2311yescharacteristic
279C2×#97C2311yescharacteristic
280C2×C4×C8C2311yescharacteristic
281C2×C4×C8C2311yescharacteristic
282#401—21no—
283#401—21no—
284#401—21no—
285#400—21no—
286#400—21no—
287#400—21no—
288#400—21no—
289#400—21no—
290#400—21no—
291#400—21no—
292#400—21no—
293#399—21no—
294#398—21no—
295#397—21no—
296#397—21no—
297#397—21no—
298#397—21no—
299#397—21no—
300#397—21no—
301#396—21no—
302#396—21no—
303#396—21no—
304#395—21no—
305#394—21no—
306#394—21no—
307#394—21no—
308#393—21no—
309#393—21no—
310#393—21no—
311#393—21no—
312#393—21no—
313#392—21no—
314#391—21no—
315#391—21no—
316#390—21no—
317#390C2311yescharacteristic
318#390C2311yescharacteristic
319#390C2311yescharacteristic
320#390C2311yescharacteristic
321#390C2311yescharacteristic
322#390C2311yescharacteristic
323#389—21no—
324#389—21no—
325#389—21no—
326#389—21no—
327#389—21no—
328#389C2311yescharacteristic
329#389C2311yescharacteristic
330#389C2311yescharacteristic
331#389C2311yescharacteristic
332#389C2311yescharacteristic
333#389C2311yescharacteristic
334#389C2311yescharacteristic
335#389C2311yescharacteristic
336#389C2311yescharacteristic
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#388—21no—
343#388—21no—
344#388—21no—
345#388—21no—
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#388D411yescharacteristic
355#388D411yescharacteristic
356#387—21no—
357#387—21no—
358#387—21no—
359#387—21no—
360#387—21no—
361#387—21no—
362#387—21no—
363#387—21no—
364#387—21no—
365#387—21no—
366#387—21no—
367#387—21no—
368#387D411yescharacteristic
369#387D411yescharacteristic
370#386—21no—
371#386—21no—
372#386—21no—
373#386—21no—
374#386—21no—
375#386—21no—
376#386—21no—
377#386—21no—
378#386—21no—
379#386—21no—
380#386D411yescharacteristic
381#385—21no—
382#385—21no—
383#385—21no—
384#385—21no—
385#385D411yescharacteristic
386#384C2311yescharacteristic
387#383—21no—
388#383—21no—
389#382—21no—
390#382—21no—
391#382C2311yescharacteristic
392#382C2311yescharacteristic
393#382C2311yescharacteristic
394#382C2311yescharacteristic
395#382C2311yescharacteristic
396#381—21no—
397#381—21no—
398#381—21no—
399#381—21no—
400#381—21no—
401#381D411yescharacteristic
402#380—21no—
403#380C2311yescharacteristic
404#380C2311yescharacteristic
405#380C2311yescharacteristic
406#380C2311yescharacteristic
407#380C2311yescharacteristic
408#380C2311yescharacteristic
409#380C2311yescharacteristic
410#380C2311yescharacteristic
411#380C2311yescharacteristic
412#380C2311yescharacteristic
413#379—21no—
414#379—21no—
415#379—21no—
416C4×C4⋊C4—21no—
417C4×C4⋊C4C2311yescharacteristic
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C22⋊C4—21no—
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⋊C4C2311yescharacteristic
435C4×C22⋊C4C2311yescharacteristic
436C4×C22⋊C4C2311yescharacteristic
437#376—21no—
438C2×#95—21no—
439#340C2311yescharacteristic
440#340C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481C25—21no—
482C22×Q8—21no—
483C22×Q8—21no—
484C22×D4—22no—
485C22×D4—22no—
486C22×D4—21no—
487C22×D4—21no—
488C22×D4—21no—
489C22×D4—41no—
490C22×D4—41no—
491C22×D4—41no—
492C22×D4—41no—
493C22×D4C2×D411yescharacteristic
494C22×D4C2411yescharacteristic
495C22×D4C2411yescharacteristic
496C23×C4—21no—
497C23×C4—21no—
498C23×C4—21no—
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—21no—
502C23×C4C2×D411yescharacteristic
503C23×C4C2×D411yescharacteristic
504C23×C4C2411yescharacteristic
505C23×C4C2411yescharacteristic
506C2×M16—22no—
507C2×M16—41no—
508C2×M16—41no—
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C4⋊Q8—22no—
518C4⋊Q8—41no—
519C4⋊Q8—41no—
520C4⋊Q8—41no—
521#126—82no—
522#123—42no—
523C22⋊Q8—44no—
524C22⋊Q8—82no—
525C22⋊Q8—82no—
526#121—22no—
527#121—22no—
528#121—41no—
529#121—41no—
530#120—44no—
531C4×Q8—82no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—41no—
535C4×D4—41no—
536C4×D4—41no—
537C4×D4—41no—
538C4×D4—41no—
539C4×D4—41no—
540C4×D4—41no—
541C4×D4—41no—
542C4×D4—82no—
543C4×D4—82no—
544#117—22no—
545#117—41no—
546C2×C4⋊C4—22no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—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—41no—
568C2×C4⋊C4—41no—
569C2×C4⋊C4—41no—
570C2×C4⋊C4—82no—
571C2×C4⋊C4C2×D411yescharacteristic
572C2×C4⋊C4C2×D411yescharacteristic
573C2×C4⋊C4C2×D411yescharacteristic
574C2×C4⋊C4C2×D411yescharacteristic
575C2×C4⋊C4C2×D411yescharacteristic
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
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⋊C4—82no—
620C2×C22⋊C4—82no—
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—41no—
639C2×C42—41no—
640C2×C42C2×D411yescharacteristic
641C2×C42C2×D411yescharacteristic
642C2×C42C2411yescharacteristic
643C2×C42C2411yescharacteristic
644C2×C42C2411yescharacteristic
645C2×C42C2411yescharacteristic
646C2×C42C2411yescharacteristic
647#107—22no—
648#107—22no—
649#107—41no—
650#107—41no—
651#107—41no—
652#107—41no—
653#107—41no—
654#107—41no—
655#107—41no—
656#107—41no—
657#106—22no—
658#106—22no—
659#106—41no—
660#106—41no—
661#106—41no—
662#106—41no—
663C4⋊C8—22no—
664C4⋊C8—41no—
665C4⋊C8—41no—
666C4⋊C8—41no—
667C4⋊C8—41no—
668#102—22no—
669#102—22no—
670#102—22no—
671#102—22no—
672#102—22no—
673#102—22no—
674#102—22no—
675#102—41no—
676#102—41no—
677#102—41no—
678#102—41no—
679#102—41no—
680#102—41no—
681#102—41no—
682#102—41no—
683#102#4114yes—
684C22⋊C8—22no—
685C22⋊C8—41no—
686C22⋊C8—41no—
687C22⋊C8—41no—
688C22⋊C8—41no—
689C22⋊C8—41no—
690C22⋊C8—41no—
691#97—41no—
692#97—41no—
693#97—41no—
694C4×C8—41no—
695C4×C8—41no—
696#95—21no—
697#95—21no—
698#95—21no—
699#95—21no—
700#95—21no—
701#95—21no—
702#95—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
713#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#95C2×D411yescharacteristic
739#95C2×D411yescharacteristic
740#95C2×D411yescharacteristic
741#95C2×D411yescharacteristic
742#95C2×D411yescharacteristic
743#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748C24—21no—
749C24—21no—
750C24—42no—
751C24—42no—
752C24—42no—
753C24—81no—
754C24—81no—
755C24—81no—
756C24—81no—
757C24C22×D411yescharacteristic
758C24C22×D411yescharacteristic
759C2×Q8—42no—
760C2×Q8—42no—
761C2×Q8—81no—
762C2×Q8—81no—
763C2×Q8—81no—
764C2×Q8—81no—
765C2×D4—22no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—41no—
777C2×D4—41no—
778C2×D4—42no—
779C2×D4—42no—
780C2×D4—44no—
781C2×D4—42no—
782C2×D4—42no—
783C2×D4—42no—
784C2×D4—42no—
785C2×D4—81no—
786C2×D4—82no—
787C2×D4—82no—
788C2×D4—82no—
789C2×D4—81no—
790C2×D4—81no—
791C2×D4C2×#4112yes—
792C2×D42−1+412yes—
793C22×C4—21no—
794C22×C4—22no—
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—22no—
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—41no—
822C22×C4—41no—
823C22×C4—41no—
824C22×C4—41no—
825C22×C4—42no—
826C22×C4—42no—
827C22×C4—42no—
828C22×C4—42no—
829C22×C4—42no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—81no—
833C22×C4—81no—
834C22×C4—81no—
835C22×C4—81no—
836C22×C4—81no—
837C22×C4—81no—
838C22×C4—81no—
839C22×C4—81no—
840C22×C4—81no—
841C22×C4—81no—
842C22×C4—81no—
843C22×C4C22×D411yescharacteristic
844C22×C4C22×D411yescharacteristic
845C22×C4C22×D411yescharacteristic
846C22×C4C22×D411yescharacteristic
847C22×C4C22×D411yescharacteristic
848C22×C4C22×D411yescharacteristic
849C22×C4C22×D411yescharacteristic
850C22×C4C22×D411yescharacteristic
851C22×C4C22×D411yescharacteristic
852C22×C4C22×D411yescharacteristic
853C22×C4C22×D411yescharacteristic
854C22×C4C22×D411yescharacteristic
855C22×C4C2511yescharacteristic
856M16—82no—
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—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8C2×#4112yes—
881C4⋊C4—22no—
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—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—41no—
910C4⋊C4—41no—
911C4⋊C4—41no—
912C4⋊C4—41no—
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—42no—
922C4⋊C4—42no—
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⋊C4—81no—
933C4⋊C4C2×#4112yes—
934C22⋊C4—22no—
935C22⋊C4—22no—
936C22⋊C4—41no—
937C22⋊C4—41no—
938C22⋊C4—41no—
939C22⋊C4—41no—
940C22⋊C4—41no—
941C22⋊C4—41no—
942C22⋊C4—42no—
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—
965C22⋊C4—81no—
966C22⋊C4—81no—
967C22⋊C4—81no—
968C22⋊C4—81no—
969C22⋊C4—81no—
970C22⋊C4—81no—
971C42—21no—
972C42—21no—
973C42—21no—
974C42—21no—
975C42—21no—
976C42—21no—
977C42—21no—
978C42—21no—
979C42—21no—
980C42—21no—
981C42—41no—
982C42—41no—
983C42—42no—
984C42—42no—
985C42—81no—
986C42—81no—
987C42—81no—
988C42—81no—
989C42—81no—
990C42—81no—
991C42—81no—
992C23—21no—
993C23—21no—
994C23—21no—
995C23—21no—
996C23—21no—
997C23—21no—
998C23—21no—
999C23—21no—
1000C23—21no—
1001C23—22no—
1002C23—21no—
1003C23—22no—
1004C23—21no—
1005C23—21no—
1006C23—21no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—84no—
1020C23—84no—
1021C23—84no—
1022C23—162no—
1023C23—162no—
1024C23—162no—
1025C23—162no—
1026C23#57512yes—
1027C23C23×D411yescharacteristic
1028Q8—84no—
1029Q8—162no—
1030D4—22no—
1031D4—22no—
1032D4—22no—
1033D4—22no—
1034D4—41no—
1035D4—41no—
1036D4—41no—
1037D4—41no—
1038D4—82no—
1039D4—84no—
1040D4—84no—
1041D4—84no—
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—22no—
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—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
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—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—82no—
1128C2×C4—82no—
1129C2×C4—84no—
1130C2×C4—162no—
1131C2×C4—162no—
1132C2×C4—162no—
1133C2×C4—162no—
1134C2×C4—162no—
1135C2×C4#57612yes—
1136C2×C4C22×#4111yescharacteristic
1137C2×C4C2×2−1+411yescharacteristic
1138C2×C4#58511yescharacteristic
1139C2×C4#58511yescharacteristic
1140C2×C4#58511yescharacteristic
1141C2×C4#58511yescharacteristic
1142C8—22no—
1143C8—41no—
1144C8—41no—
1145C8—41no—
1146C8—41no—
1147C8—41no—
1148C8—41no—
1149C8—41no—
1150C22—22no—
1151C22—22no—
1152C22—22no—
1153C22—41no—
1154C22—41no—
1155C22—41no—
1156C22—41no—
1157C22—42no—
1158C22—41no—
1159C22—41no—
1160C22—42no—
1161C22—42no—
1162C22—41no—
1163C22—41no—
1164C22—42no—
1165C22—41no—
1166C22—42no—
1167C22—41no—
1168C22—42no—
1169C22—41no—
1170C22—81no—
1171C22—81no—
1172C22—81no—
1173C22—81no—
1174C22—81no—
1175C22—81no—
1176C22—81no—
1177C22—81no—
1178C22—168no—
1179C22D4×#4111yescharacteristic
1180C22#348511yescharacteristic
1181C22#348911yescharacteristic
1182C22C2×#57511yescharacteristic
1183C22C2×#57611yescharacteristic
1184C22#358511yescharacteristic
1185C22#358611yescharacteristic
1186C4—22no—
1187C4—41no—
1188C4—42no—
1189C4—41no—
1190C4—41no—
1191C4—41no—
1192C4—41no—
1193C4—41no—
1194C4—41no—
1195C4—41no—
1196C4—41no—
1197C4—41no—
1198C4—41no—
1199C4—81no—
1200C4—81no—
1201C4—81no—
1202C4—81no—
1203C4—81no—
1204C4—81no—
1205C4—81no—
1206C4—81no—
1207C4—81no—
1208C4—81no—
1209C4—81no—
1210C4—81no—
1211C4—81no—
1212C4#349511yescharacteristic
1213C4#352111yescharacteristic
1214C4#356411yescharacteristic
1215C4#356611yescharacteristic
1216C2—42no—
1217C2—81no—
1218C2—82no—
1219C2—82no—
1220C2#4353611yescharacteristic
1221C2#6144411yescharacteristic
1222C2#6151311yescharacteristic
1223C2#6171211yescharacteristic
1224C2#6175211yescharacteristic
1225C2#6211911yescharacteristic
1226C2#6218011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2408C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #59240C2semidirect
3. #32421C2semidirect
4. #32268C2semidirect
5. #31891C2semidirect
7. #31479C2semidirect
8. #31447C2semidirect
9. #31374C2semidirect
10. #31104C2semidirect
11. #29237C2semidirect
12. #28959C2semidirect
13. #27842C2semidirect
14. #27632C2semidirect
15. #27536C2semidirect
16. #27518C2semidirect
17. #27468C2semidirect
18. #27385C2semidirect
19. #27372C2semidirect
20. #27178C2semidirect
21. #27178C2semidirect
22. #26998C2semidirect
23. #26313C2semidirect
24. #26103C2semidirect
25. #25974C2semidirect
27. #23758C2semidirect
28. #23075C2semidirect
29. #22580C2semidirect
30. #22369C2semidirect
31. #22075C2semidirect
42. #2571C22semidirect
47. #2509C22semidirect
48. #2509C22semidirect
60. #2440C22semidirect
65. #2365C22semidirect
72. #2345C22semidirect
78. C2×#389C22semidirect
79. #2283C22semidirect
80. #2101C22semidirect
81. #2101C22semidirect
82. #2101C22semidirect
83. #2100C22semidirect
86. #2087C22semidirect
87. #2087C22semidirect
88. #2087C22semidirect
89. #2087C22semidirect
90. #2085C22semidirect
91. #2085C22semidirect
92. #2085C22semidirect
94. #2077C22semidirect
95. #2077C22semidirect
98. #2076C22semidirect
99. #2076C22semidirect
112. #2057C22semidirect
113. #2057C22semidirect
114. #2057C22semidirect
120. #1993C22semidirect
121. #1993C22semidirect
122. #1988C22semidirect
124. #1949C22semidirect
125. #1949C22semidirect
126. #1949C22semidirect
127. #1949C22semidirect
128. #1949C22semidirect
129. #1943C22semidirect
130. #1943C22semidirect
131. #1942C22semidirect
132. #1942C22semidirect
133. #1940C22semidirect
147. #1924C22semidirect
148. #1924C22semidirect
150. #1920C22semidirect
151. #1920C22semidirect
152. #1919C22semidirect
153. #1919C22semidirect
154. #1919C22semidirect
155. #1918C22semidirect
156. #1918C22semidirect
157. #1918C22semidirect
158. #1918C22semidirect
159. #1918C22semidirect
160. #1917C22semidirect
161. #1916C22semidirect
176. #1853C22semidirect
177. #1852C22semidirect
178. #1852C22semidirect
180. #1847C22semidirect
182. #1823C22semidirect
189. #1797C22semidirect
193. #1776C22semidirect
194. C4×#107C22semidirect
195. C4×#106C22semidirect
196. #1771C22semidirect
202. C4×C22⋊C8C22semidirect

Maximal subgroups

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

subgroupindex
#593782
#592402
#324212
#322682
#318912
#316802
#314792
#314472
#313742
#311042
#292372
#289592
#278422
#276322
#275362
#275182
#274682
#273852
#273722
#271782
#269982
#263132
#261032
#259742
#248822
#237582
#230752
#225802
#223692
#220752