Finite Group Databasebeta

← #6600726

Subgroups — #6600726

Order 512.

1825 conjugacy classes of subgroups.

The subgroup lattice has 1286 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36265C211yesmaximal, characteristic, complemented
2#34126C211yesmaximal, characteristic, complemented
3#33080C211yesmaximal, characteristic, complemented
4#33068C211yesmaximal, characteristic, complemented
5#33004C211yesmaximal, characteristic
6#29578C211yesmaximal, characteristic, complemented
7#29536C211yesmaximal, characteristic, complemented
8#29445C211yesmaximal, characteristic, complemented
9#29392C211yesmaximal, characteristic, complemented
10#27859C211yesmaximal, characteristic, complemented
11#27616C211yesmaximal, characteristic, complemented
12#27574C211yesmaximal, characteristic, complemented
13#27514C211yesmaximal, characteristic, complemented
14#27450C211yesmaximal, characteristic, complemented
15#27386C211yesmaximal, characteristic, complemented
16#27386C211yesmaximal, characteristic, complemented
17#27318C211yesmaximal, characteristic, complemented
18#27318C211yesmaximal, characteristic, complemented
19#26388C211yesmaximal, characteristic, complemented
20#25992C211yesmaximal, characteristic, complemented
21#25950C211yesmaximal, characteristic, complemented
22#24578C211yesmaximal, characteristic, complemented
23#24526C211yesmaximal, characteristic
24#22936C211yesmaximal, characteristic, complemented
25#22858C211yesmaximal, characteristic
26#22615C211yesmaximal, characteristic, complemented
27#22591C211yesmaximal, characteristic, complemented
28#22562C211yesmaximal, characteristic, complemented
29#21613C211yesmaximal, characteristic, complemented
30#21122C211yesmaximal, characteristic, complemented
31C2×#1864C211yesmaximal, characteristic, complemented
32C2×#552—21no—
33C22×C4×D4C2211yescharacteristic
34C2×#481C2211yescharacteristic
35C2×#474C2211yescharacteristic
36C2×#447C2211yescharacteristic
37C2×#442C2211yescharacteristic
38C22×#106C2211yescharacteristic
39C22×#102C2211yescharacteristic
40C22×#102C2211yescharacteristic
41#2860C2211yescharacteristic, complemented
42#2859C2211yescharacteristic, complemented
43#2854C2211yescharacteristic
44#2611—21no—
45#2604—21no—
46#2556—21no—
47#2519—21no—
48#2512C2211yescharacteristic, complemented
49#2506C2211yescharacteristic, complemented
50#2506C2211yescharacteristic, complemented
51#2501C2211yescharacteristic
52#2488—21no—
53#2452C2211yescharacteristic, complemented
54#2440C2211yescharacteristic
55#2413—21no—
56#2361C2211yescharacteristic
57#2359—21no—
58#2357C2211yescharacteristic
59#2357C2211yescharacteristic
60#2353—21no—
61#2353—21no—
62#2349C2211yescharacteristic
63#2349C2211yescharacteristic
64#2345C2211yescharacteristic
65#2345C2211yescharacteristic
66#2344C2211yescharacteristic
67#2342—21no—
68#2342—21no—
69D4×C22⋊C4C2211yescharacteristic
70D4×C22⋊C4C2211yescharacteristic
71C4×C4⋊Q8C2211yescharacteristic, complemented
72#2293C2211yescharacteristic
73#2293C2211yescharacteristic
74#2293C2211yescharacteristic, complemented
75C2×#389C2211yescharacteristic
76#2290—21no—
77#2290—21no—
78#2283C2211yescharacteristic
79#2280—21no—
80C42×D4C2211yescharacteristic
81C42×D4C2211yescharacteristic
82C4×#117C2211yescharacteristic
83C2×C4×C22⋊C4—21no—
84#2101C2211yescharacteristic, complemented
85#2101C2211yescharacteristic, complemented
86#2101C2211yescharacteristic, complemented
87#2099C2211yescharacteristic, complemented
88#2093C2211yescharacteristic
89#2092C2211yescharacteristic, complemented
90#2088C2211yescharacteristic, complemented
91#2088C2211yescharacteristic, complemented
92#2085C2211yescharacteristic, complemented
93#2085C2211yescharacteristic, complemented
94#2085C2211yescharacteristic, complemented
95#2084C2211yescharacteristic, complemented
96#2084C2211yescharacteristic, complemented
97#2073C2211yescharacteristic, complemented
98#2071C2211yescharacteristic
99#2071C2211yescharacteristic
100#2067C2211yescharacteristic
101#2067C2211yescharacteristic
102#2065C2211yescharacteristic, complemented
103#2065C2211yescharacteristic, complemented
104#2058C2211yescharacteristic, complemented
105#2054C2211yescharacteristic
106#2054C2211yescharacteristic
107#2023C2211yescharacteristic
108#1988C2211yescharacteristic, complemented
109#1972C2211yescharacteristic
110#1948C2211yescharacteristic, complemented
111#1948C2211yescharacteristic, complemented
112#1948C2211yescharacteristic, complemented
113#1944C2211yescharacteristic, complemented
114#1944C2211yescharacteristic, complemented
115#1944C2211yescharacteristic, complemented
116#1936C2211yescharacteristic
117#1936C2211yescharacteristic
118#1936C2211yescharacteristic
119#1936C2211yescharacteristic, complemented
120#1926C2211yescharacteristic
121#1926C2211yescharacteristic
122#1926C2211yescharacteristic
123#1926C2211yescharacteristic, complemented
124#1926C2211yescharacteristic, complemented
125#1926C2211yescharacteristic, complemented
126#1925C2211yescharacteristic, complemented
127#1925C2211yescharacteristic, complemented
128#1921C2211yescharacteristic, complemented
129#1921C2211yescharacteristic, complemented
130#1921C2211yescharacteristic, complemented
131#1920C2211yescharacteristic, complemented
132#1920C2211yescharacteristic, complemented
133#1920C2211yescharacteristic, complemented
134#1920C2211yescharacteristic, complemented
135#1920C2211yescharacteristic, complemented
136#1920C2211yescharacteristic, complemented
137#1919C2211yescharacteristic, complemented
138#1919C2211yescharacteristic, complemented
139#1919C2211yescharacteristic, complemented
140#1919C2211yescharacteristic, complemented
141#1919C2211yescharacteristic, complemented
142#1917C2211yescharacteristic, complemented
143#1917C2211yescharacteristic, complemented
144#1917C2211yescharacteristic, complemented
145#1917C2211yescharacteristic, complemented
146#1893C2211yescharacteristic
147#1893C2211yescharacteristic
148#1879C2211yescharacteristic
149#1879C2211yescharacteristic
150#1879C2211yescharacteristic
151#1879C2211yescharacteristic
152#1879C2211yescharacteristic
153#1879C2211yescharacteristic
154#1879C2211yescharacteristic
155#1879C2211yescharacteristic
156#1864C2211yescharacteristic
157#1864C2211yescharacteristic
158#1864C2211yescharacteristic
159#1864C2211yescharacteristic
160#1864C2211yescharacteristic
161#1864C2211yescharacteristic
162#1864C2211yescharacteristic
163#1864C2211yescharacteristic
164#1864C2211yescharacteristic
165#1864C2211yescharacteristic
166#1864C2211yescharacteristic
167#1864C2211yescharacteristic
168#1864C2211yescharacteristic
169#1864C2211yescharacteristic
170#1864C2211yescharacteristic
171#1862C2211yescharacteristic
172#1862C2211yescharacteristic
173#1862C2211yescharacteristic, complemented
174#1853C2211yescharacteristic
175#1852C2211yescharacteristic
176#1850C2211yescharacteristic
177#1850C2211yescharacteristic
178#1839C2211yescharacteristic, complemented
179#1831C2211yescharacteristic, complemented
180#1824C2211yescharacteristic
181#1823C2211yescharacteristic
182#1823C2211yescharacteristic
183#1817C2211yescharacteristic
184#1808C2211yescharacteristic
185#1807C2211yescharacteristic
186#1802C2211yescharacteristic
187#1802C2211yescharacteristic
188#1802C2211yescharacteristic
189#1786C2211yescharacteristic
190#1776C2211yescharacteristic, complemented
191#1776C2211yescharacteristic, complemented
192#1776C2211yescharacteristic, complemented
193#1767C2211yescharacteristic, complemented
194#1762C2211yescharacteristic
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic, complemented
198#1752C2211yescharacteristic
199#1752C2211yescharacteristic
200#1745C2211yescharacteristic, complemented
201C2×#340C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C24×C4—21no—
205C22×D8C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209#552—48no—
210C2×C4⋊Q8C2311yescharacteristic
211C2×#126—21no—
212C2×#126—21no—
213C2×#125—21no—
214C2×#125—21no—
215C2×#125—21no—
216C2×#123—21no—
217C2×#123—21no—
218C2×#123—21no—
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8—21no—
221C2×#121C2311yescharacteristic
222C2×C4×Q8—21no—
223C2×C4×D4—24no—
224C2×C4×D4—24no—
225C2×C4×D4—21no—
226C2×C4×D4—21no—
227C2×C4×D4—21no—
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×#117—21no—
238C2×#117—21no—
239C2×#117—21no—
240C2×#117—21no—
241C2×#117D411yescharacteristic
242C2×#117D411yescharacteristic
243C22×C4⋊C4—21no—
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C22⋊C4—21no—
248C22×C22⋊C4—21no—
249C22×C22⋊C4—21no—
250C22×C42—21no—
251C22×C42—21no—
252C22×C42C2311yescharacteristic
253#481—24no—
254#474—24no—
255#447—24no—
256#442—24no—
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#106—24no—
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×#102—24no—
277C2×#102—24no—
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×#97C2311yescharacteristic
301C2×#97C2311yescharacteristic
302C2×#97C2311yescharacteristic
303C2×#97C2311yescharacteristic
304#400—21no—
305#400—21no—
306#399—21no—
307#399—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#397—21no—
312#396—21no—
313#396—21no—
314#395—21no—
315#393—21no—
316#391—21no—
317#390C2311yescharacteristic
318#390C2311yescharacteristic
319#390C2311yescharacteristic
320#390C2311yescharacteristic
321#390C2311yescharacteristic
322#390C2311yescharacteristic
323#390C2311yescharacteristic
324#390C2311yescharacteristic
325#390C2311yescharacteristic
326#389—21no—
327#389—21no—
328#389—21no—
329#389—21no—
330#389—21no—
331#389C2311yescharacteristic
332#389C2311yescharacteristic
333#389C2311yescharacteristic
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#387—21no—
364#387—21no—
365#387—21no—
366#387—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#386—21no—
372#386—21no—
373#386—21no—
374#386—21no—
375#386—21no—
376#386—21no—
377#385—21no—
378#385—21no—
379#385—21no—
380#385—21no—
381#385—21no—
382#385—21no—
383#385—21no—
384#384C2311yescharacteristic
385#384C2311yescharacteristic
386#384C2311yescharacteristic
387#383—21no—
388#382—21no—
389#382C2311yescharacteristic
390#382C2311yescharacteristic
391#381—21no—
392#381—21no—
393#381—21no—
394#381—21no—
395#380—21no—
396#380—21no—
397#380—21no—
398#380—21no—
399#380C2311yescharacteristic
400#380C2311yescharacteristic
401#380C2311yescharacteristic
402#379—21no—
403#379—21no—
404C4×C4⋊C4—21no—
405C4×C4⋊C4D411yescharacteristic
406C4×C4⋊C4D411yescharacteristic
407C4×C4⋊C4C2311yescharacteristic
408C4×C4⋊C4C2311yescharacteristic
409C4×C4⋊C4C2311yescharacteristic
410C4×C4⋊C4C2311yescharacteristic
411C4×C4⋊C4C2311yescharacteristic
412C4×C4⋊C4C2311yescharacteristic
413C4×C4⋊C4C2311yescharacteristic
414C4×C4⋊C4C2311yescharacteristic
415C4×C4⋊C4C2311yescharacteristic
416C4×C4⋊C4C2311yescharacteristic
417C4×C4⋊C4C2311yescharacteristic
418C4×C22⋊C4—21no—
419C4×C22⋊C4—21no—
420C4×C22⋊C4—21no—
421C4×C22⋊C4—21no—
422C4×C22⋊C4—21no—
423C4×C22⋊C4—21no—
424C4×C22⋊C4—21no—
425C4×C22⋊C4—21no—
426C4×C22⋊C4—21no—
427C4×C22⋊C4—21no—
428C4×C22⋊C4—21no—
429C4×C22⋊C4—21no—
430C4×C22⋊C4—21no—
431C4×C22⋊C4—21no—
432C4×C22⋊C4D411yescharacteristic
433C4×C22⋊C4D411yescharacteristic
434C4×C22⋊C4C2311yescharacteristic
435C4×C22⋊C4C2311yescharacteristic
436#376—21no—
437#376D411yescharacteristic
438#376D411yescharacteristic
439C2×#95—21no—
440C2×#95—21no—
441C2×#95—21no—
442C43C2311yescharacteristic
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
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488C25—21no—
489C22×Q8—21no—
490C22×D4—22no—
491C22×D4—22no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—22no—
495C22×D4—41no—
496C22×D4—41no—
497C22×D4#4114yes—
498C22×D4C2411yescharacteristic
499C22×D4C2411yescharacteristic
500C22×D4C2411yescharacteristic
501C23×C4—28no—
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—82no—
515C23×C4—82no—
516C23×C4C2×D411yescharacteristic
517C23×C4C2×D411yescharacteristic
518C23×C4C2411yescharacteristic
519C2×D8—22no—
520C2×D8—22no—
521C2×D8—22no—
522C2×D8—22no—
523C2×D8—41no—
524C2×D8—41no—
525C22×C8—22no—
526C22×C8—22no—
527C22×C8—22no—
528C22×C8—41no—
529C22×C8—41no—
530C22×C8—41no—
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C4⋊Q8—22no—
540C4⋊Q8—41no—
541#126—44no—
542#126—44no—
543#125—44no—
544#125—44no—
545#125—44no—
546#123—44no—
547#123—44no—
548#123—44no—
549C22⋊Q8—44no—
550C22⋊Q8—44no—
551#121—22no—
552#121—22no—
553C4×Q8—44no—
554C4×D4—28no—
555C4×D4—28no—
556C4×D4—22no—
557C4×D4—22no—
558C4×D4—22no—
559C4×D4—22no—
560C4×D4—22no—
561C4×D4—22no—
562C4×D4—22no—
563C4×D4—22no—
564C4×D4—22no—
565C4×D4—22no—
566C4×D4—22no—
567C4×D4—22no—
568C4×D4—22no—
569C4×D4—41no—
570C4×D4—41no—
571C4×D4—41no—
572C4×D4—41no—
573C4×D4—41no—
574C4×D4—44no—
575#117—24no—
576#117—44no—
577#117—42no—
578#117—44no—
579#117—82no—
580#117—82no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—22no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—22no—
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—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—41no—
611C2×C4⋊C4—44no—
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4#4114yes—
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C22⋊C4—28no—
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×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—44no—
663C2×C22⋊C4—44no—
664C2×C22⋊C4C2×D411yescharacteristic
665C2×C22⋊C4C2×D411yescharacteristic
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C22⋊C4C2×D411yescharacteristic
668C2×C42—22no—
669C2×C42—22no—
670C2×C42—21no—
671C2×C42—21no—
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—82no—
680C2×C42—82no—
681C2×C42C2×D411yescharacteristic
682C2×C42C2×D411yescharacteristic
683C2×C42C2×D411yescharacteristic
684C2×C42C2×D411yescharacteristic
685C2×C42C2×D411yescharacteristic
686C2×C42C2×D411yescharacteristic
687C2×C42C2×D411yescharacteristic
688C2×C42C2×D411yescharacteristic
689C2×C42C2×D411yescharacteristic
690C2×C42C2×D411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697#107—22no—
698#107—22no—
699#107—41no—
700#107—41no—
701#106—22no—
702#106—22no—
703#106—22no—
704#106—22no—
705#106—22no—
706#106—22no—
707#106—22no—
708#106—41no—
709#106—41no—
710#106—41no—
711C4⋊C8—22no—
712C4⋊C8—41no—
713C4⋊C8—41no—
714C4⋊C8—41no—
715#102—22no—
716#102—22no—
717#102—22no—
718#102—22no—
719#102—22no—
720#102—22no—
721#102—22no—
722#102—22no—
723#102—22no—
724#102—22no—
725#102—22no—
726#102—22no—
727#102—22no—
728#102—22no—
729#102—41no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102#4114yes—
735C22⋊C8—22no—
736C22⋊C8—22no—
737#97—22no—
738#97—41no—
739#97—41no—
740#97—41no—
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#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780C24—21no—
781C24—21no—
782C24—24no—
783C24—21no—
784C24—42no—
785C24—42no—
786C24—42no—
787C24—42no—
788C24—81no—
789C24—81no—
790C24C22×D411yescharacteristic
791C2×Q8—42no—
792C2×Q8—42no—
793C2×Q8—81no—
794C2×D4—28no—
795C2×D4—24no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—44no—
811C2×D4—44no—
812C2×D4—44no—
813C2×D4—42no—
814C2×D4—42no—
815C2×D4—42no—
816C2×D4—42no—
817C2×D4—42no—
818C2×D4C2×#4112yes—
819C2×D4C2×#4112yes—
820C2×D4C2×#4112yes—
821C2×D42−1+412yes—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—24no—
827C22×C4—24no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—24no—
836C22×C4—24no—
837C22×C4—24no—
838C22×C4—22no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—41no—
850C22×C4—42no—
851C22×C4—42no—
852C22×C4—42no—
853C22×C4—42no—
854C22×C4—42no—
855C22×C4—42no—
856C22×C4—42no—
857C22×C4—42no—
858C22×C4—42no—
859C22×C4—42no—
860C22×C4—42no—
861C22×C4—42no—
862C22×C4—42no—
863C22×C4—42no—
864C22×C4—42no—
865C22×C4—42no—
866C22×C4—42no—
867C22×C4—42no—
868C22×C4—42no—
869C22×C4—81no—
870C22×C4—81no—
871C22×C4—81no—
872C22×C4—81no—
873C22×C4—81no—
874C22×C4—81no—
875C22×C4—81no—
876C22×C4—81no—
877C22×C4—81no—
878C22×C4—816no—
879C22×C4—81no—
880C22×C4—81no—
881C22×C4—81no—
882C22×C4C22×D411yescharacteristic
883C22×C4C22×D411yescharacteristic
884C22×C4C22×D411yescharacteristic
885C22×C4C22×D411yescharacteristic
886C22×C4C22×D411yescharacteristic
887C22×C4C22×D411yescharacteristic
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C2×#4112yes—
896C22×C4C2×#4112yes—
897C22×C4C2511yescharacteristic
898D8—44no—
899D8—82no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—21no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—44no—
924C2×C8—82no—
925C2×C8C2×#4112yes—
926C4⋊C4—24no—
927C4⋊C4—22no—
928C4⋊C4—22no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—41no—
953C4⋊C4—41no—
954C4⋊C4—42no—
955C4⋊C4—42no—
956C4⋊C4—42no—
957C4⋊C4—42no—
958C4⋊C4—42no—
959C4⋊C4—42no—
960C4⋊C4—42no—
961C4⋊C4—42no—
962C4⋊C4—42no—
963C4⋊C4—42no—
964C4⋊C4—42no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—42no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4C2×#4112yes—
979C4⋊C4C2×#4112yes—
980C4⋊C4C2×#4112yes—
981C22⋊C4—24no—
982C22⋊C4—24no—
983C22⋊C4—24no—
984C22⋊C4—24no—
985C22⋊C4—22no—
986C22⋊C4—22no—
987C22⋊C4—22no—
988C22⋊C4—42no—
989C22⋊C4—42no—
990C22⋊C4—42no—
991C22⋊C4—42no—
992C22⋊C4—42no—
993C22⋊C4—42no—
994C22⋊C4—42no—
995C22⋊C4—42no—
996C22⋊C4—42no—
997C22⋊C4—42no—
998C22⋊C4—42no—
999C22⋊C4—42no—
1000C22⋊C4—42no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
1009C22⋊C4—81no—
1010C22⋊C4—81no—
1011C22⋊C4—81no—
1012C22⋊C4—81no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4AGL(1,ℤ/8)14yes—
1016C42—22no—
1017C42—22no—
1018C42—22no—
1019C42—22no—
1020C42—22no—
1021C42—22no—
1022C42—21no—
1023C42—21no—
1024C42—21no—
1025C42—21no—
1026C42—21no—
1027C42—21no—
1028C42—21no—
1029C42—21no—
1030C42—21no—
1031C42—21no—
1032C42—21no—
1033C42—21no—
1034C42—41no—
1035C42—41no—
1036C42—41no—
1037C42—41no—
1038C42—42no—
1039C42—42no—
1040C42—42no—
1041C42—42no—
1042C42—42no—
1043C42—81no—
1044C42—81no—
1045C42—81no—
1046C42—81no—
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—48no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—48no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—84no—
1075C23—84no—
1076C23—84no—
1077C23—84no—
1078C23—84no—
1079C23#52512yes—
1080C23C2×AGL(1,ℤ/8)12yes—
1081C23#57512yes—
1082C23C23×D411yescharacteristic
1083Q8—84no—
1084D4—22no—
1085D4—22no—
1086D4—22no—
1087D4—22no—
1088D4—22no—
1089D4—48no—
1090D4—41no—
1091D4—41no—
1092D4—41no—
1093D4—41no—
1094D4—41no—
1095D4—41no—
1096D4—84no—
1097D4#55214yescomplemented
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—22no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—44no—
1141C2×C4—48no—
1142C2×C4—48no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—44no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—84no—
1181C2×C4—84no—
1182C2×C4—84no—
1183C2×C4—84no—
1184C2×C4—84no—
1185C2×C4—84no—
1186C2×C4—84no—
1187C2×C4—84no—
1188C2×C4—84no—
1189C2×C4—84no—
1190C2×C4#52512yes—
1191C2×C4C2×AGL(1,ℤ/8)12yes—
1192C2×C4C2×AGL(1,ℤ/8)12yes—
1193C2×C4#57712yes—
1194C2×C4C22×#4111yescharacteristic
1195C2×C4C22×#4111yescharacteristic
1196C2×C4C22×#4111yescharacteristic
1197C2×C4C2×2−1+411yescharacteristic
1198C2×C4#58511yescharacteristic
1199C2×C4#58511yescharacteristic
1200C8—22no—
1201C8—41no—
1202C8—41no—
1203C8—41no—
1204C8—41no—
1205C8—41no—
1206C8—41no—
1207C8—41no—
1208C22—22no—
1209C22—22no—
1210C22—22no—
1211C22—22no—
1212C22—22no—
1213C22—22no—
1214C22—24no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—816no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22#311514yes—
1237C22C2×#52511yescharacteristic
1238C22D4×#4111yescharacteristic
1239C22#348911yescharacteristic
1240C22C22×AGL(1,ℤ/8)11yescharacteristic
1241C22C2×#57511yescharacteristic
1242C22C2×#57711yescharacteristic
1243C22#358511yescharacteristic
1244C4—22no—
1245C4—22no—
1246C4—22no—
1247C4—22no—
1248C4—41no—
1249C4—41no—
1250C4—41no—
1251C4—42no—
1252C4—41no—
1253C4—41no—
1254C4—41no—
1255C4—42no—
1256C4—42no—
1257C4—41no—
1258C4—41no—
1259C4—41no—
1260C4—81no—
1261C4—81no—
1262C4—81no—
1263C4—81no—
1264C4—81no—
1265C4—81no—
1266C4—81no—
1267C4—81no—
1268C4—81no—
1269C4—81no—
1270C4C2×#55211yescharacteristic
1271C4#347511yescharacteristic
1272C4#349111yescharacteristic
1273C4#349511yescharacteristic
1274C2—24no—
1275C2—44no—
1276C2—82no—
1277C2—161no—
1278C2#3622311yescharacteristic
1279C2C2×#311511yescharacteristic
1280C2#6057911yescharacteristic
1281C2#6144511yescharacteristic
1282C2#6145111yescharacteristic
1283C2#6211911yescharacteristic
1284C2#6212811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#447C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36265C2semidirect
2. #34126C2semidirect
3. #33080C2semidirect
4. #33068C2semidirect
6. #29578C2semidirect
7. #29536C2semidirect
8. #29445C2semidirect
9. #29392C2semidirect
10. #27859C2semidirect
11. #27616C2semidirect
12. #27574C2semidirect
13. #27514C2semidirect
14. #27450C2semidirect
15. #27386C2semidirect
16. #27386C2semidirect
17. #27318C2semidirect
18. #27318C2semidirect
19. #26388C2semidirect
20. #25992C2semidirect
21. #25950C2semidirect
22. #24578C2semidirect
24. #22936C2semidirect
26. #22615C2semidirect
27. #22591C2semidirect
28. #22562C2semidirect
29. #21613C2semidirect
30. #21122C2semidirect
31. C2×#1864C2semidirect
41. #2860C22semidirect
42. #2859C22semidirect
48. #2512C22semidirect
49. #2506C22semidirect
50. #2506C22semidirect
53. #2452C22semidirect
71. C4×C4⋊Q8C22semidirect
74. #2293C22semidirect
84. #2101C22semidirect
85. #2101C22semidirect
86. #2101C22semidirect
87. #2099C22semidirect
89. #2092C22semidirect
90. #2088C22semidirect
91. #2088C22semidirect
92. #2085C22semidirect
93. #2085C22semidirect
94. #2085C22semidirect
95. #2084C22semidirect
96. #2084C22semidirect
97. #2073C22semidirect
102. #2065C22semidirect
103. #2065C22semidirect
104. #2058C22semidirect
108. #1988C22semidirect
110. #1948C22semidirect
111. #1948C22semidirect
112. #1948C22semidirect
113. #1944C22semidirect
114. #1944C22semidirect
115. #1944C22semidirect
119. #1936C22semidirect
123. #1926C22semidirect
124. #1926C22semidirect
125. #1926C22semidirect
126. #1925C22semidirect
127. #1925C22semidirect
128. #1921C22semidirect
129. #1921C22semidirect
130. #1921C22semidirect
131. #1920C22semidirect
132. #1920C22semidirect
133. #1920C22semidirect
134. #1920C22semidirect
135. #1920C22semidirect
136. #1920C22semidirect
137. #1919C22semidirect
138. #1919C22semidirect
139. #1919C22semidirect
140. #1919C22semidirect
141. #1919C22semidirect
142. #1917C22semidirect
143. #1917C22semidirect
144. #1917C22semidirect
145. #1917C22semidirect
173. #1862C22semidirect
178. #1839C22semidirect
179. #1831C22semidirect
190. #1776C22semidirect
191. #1776C22semidirect
192. #1776C22semidirect
193. #1767C22semidirect
197. #1762C22semidirect
200. #1745C22semidirect
1097. D4#552semidirect

Maximal subgroups

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

subgroupindex
#362652
#341262
#330802
#330682
#330042
#295782
#295362
#294452
#293922
#278592
#276162
#275742
#275142
#274502
#273862
#273182
#263882
#259922
#259502
#245782
#245262
#229362
#228582
#226152
#225912
#225622
#216132
#211222
C2×#18642