Finite Group Databasebeta

← #6556439

Subgroups — #6556439

Order 512.

1666 conjugacy classes of subgroups.

The subgroup lattice has 1330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36262C211yesmaximal, characteristic, complemented
2#36172C211yesmaximal, characteristic, complemented
3#30386C211yesmaximal, characteristic, complemented
4#30322C211yesmaximal, characteristic, complemented
5#30188C211yesmaximal, characteristic, complemented
6#29576C211yesmaximal, characteristic, complemented
7#29497C211yesmaximal, characteristic, complemented
8#29083C211yesmaximal, characteristic, complemented
9#29079C211yesmaximal, characteristic, complemented
10#28990C211yesmaximal, characteristic, complemented
11#28984C211yesmaximal, characteristic, complemented
12#28573C211yesmaximal, characteristic, complemented
13#28312C211yesmaximal, characteristic, complemented
14#28029C211yesmaximal, characteristic, complemented
15#28026C211yesmaximal, characteristic, complemented
16#27956C211yesmaximal, characteristic, complemented
17#27859C211yesmaximal, characteristic, complemented
18#25236C211yesmaximal, characteristic, complemented
19#25232C211yesmaximal, characteristic, complemented
20#25112C211yesmaximal, characteristic, complemented
21#25108C211yesmaximal, characteristic
22#25042C211yesmaximal, characteristic, complemented
23#25041C211yesmaximal, characteristic, complemented
24#23764C211yesmaximal, characteristic, complemented
25#23686C211yesmaximal, characteristic, complemented
26C2×#2073C211yesmaximal, characteristic, complemented
27#22938C211yesmaximal, characteristic, complemented
28#22934C211yesmaximal, characteristic, complemented
29#22858C211yesmaximal, characteristic, complemented
30#22854C211yesmaximal, characteristic, complemented
31#20558C211yesmaximal, characteristic, complemented
32C2×#551—21no—
33C2×#483C2211yescharacteristic
34C2×#480C2211yescharacteristic
35C2×#466C2211yescharacteristic
36C2×#465C2211yescharacteristic
37C2×#450C2211yescharacteristic
38C2×#447C2211yescharacteristic
39C2×#442C2211yescharacteristic
40C2×#440C2211yescharacteristic
41C2×C8×D4C2211yescharacteristic
42C2×C8×D4C2211yescharacteristic
43C22×#102C2211yescharacteristic
44C22×#102C2211yescharacteristic
45#2864C2211yescharacteristic, complemented
46#2860C2211yescharacteristic
47#2857C2211yescharacteristic
48#2854C2211yescharacteristic
49#2850C2211yescharacteristic
50#2850C2211yescharacteristic, complemented
51#2602—21no—
52#2601—21no—
53#2576—21no—
54#2561—21no—
55#2560—21no—
56#2557—21no—
57#2534—21no—
58#2529—21no—
59#2518—21no—
60#2515—21no—
61#2514C2211yescharacteristic, complemented
62#2513C2211yescharacteristic, complemented
63#2512C2211yescharacteristic
64#2510—21no—
65#2491C2211yescharacteristic
66#2486C2211yescharacteristic
67#2452C2211yescharacteristic
68#2444—21no—
69#2422C2211yescharacteristic
70#2421C2211yescharacteristic, complemented
71#2420C2211yescharacteristic, complemented
72#2417C2211yescharacteristic
73#2416C2211yescharacteristic
74#2408C2211yescharacteristic
75#2364—21no—
76#2361C2211yescharacteristic
77#2360C2211yescharacteristic
78#2353—21no—
79#2344C2211yescharacteristic
80#2342—21no—
81D4×C22⋊C4C2211yescharacteristic
82C4×#124C2211yescharacteristic, complemented
83C4×#121C2211yescharacteristic
84#2293C2211yescharacteristic
85C2×#390C2211yescharacteristic
86#2283C2211yescharacteristic, complemented
87C2×#382C2211yescharacteristic
88C42×D4C2211yescharacteristic
89#2101C2211yescharacteristic, complemented
90#2101C2211yescharacteristic, complemented
91#2092C2211yescharacteristic
92#2092C2211yescharacteristic
93#2088C2211yescharacteristic, complemented
94#2086C2211yescharacteristic, complemented
95#2085C2211yescharacteristic, complemented
96#2085C2211yescharacteristic, complemented
97#2085C2211yescharacteristic, complemented
98#2085C2211yescharacteristic, complemented
99#2077C2211yescharacteristic, complemented
100#2075C2211yescharacteristic, complemented
101#2073C2211yescharacteristic
102#2073C2211yescharacteristic
103#2073C2211yescharacteristic
104#2073C2211yescharacteristic
105#2073C2211yescharacteristic
106#2073C2211yescharacteristic
107#2073C2211yescharacteristic
108#2073C2211yescharacteristic
109#2072C2211yescharacteristic, complemented
110#2071C2211yescharacteristic, complemented
111#2067C2211yescharacteristic
112#2067C2211yescharacteristic, complemented
113#2066C2211yescharacteristic, complemented
114#2065C2211yescharacteristic
115#2055C2211yescharacteristic
116#2054C2211yescharacteristic
117#2042C2211yescharacteristic, complemented
118#2042C2211yescharacteristic, complemented
119#2035C2211yescharacteristic, complemented
120#2034C2211yescharacteristic
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic, complemented
123#2024C2211yescharacteristic, complemented
124#2023C2211yescharacteristic, complemented
125#2012C2211yescharacteristic
126#2012C2211yescharacteristic
127#2000C2211yescharacteristic
128#1999C2211yescharacteristic
129#1993C2211yescharacteristic, complemented
130#1993C2211yescharacteristic, complemented
131#1973C2211yescharacteristic
132#1973C2211yescharacteristic
133#1973C2211yescharacteristic
134#1972C2211yescharacteristic
135#1972C2211yescharacteristic
136#1972C2211yescharacteristic
137#1970C2211yescharacteristic
138#1968C2211yescharacteristic
139#1944C2211yescharacteristic, complemented
140#1943C2211yescharacteristic, complemented
141#1942C2211yescharacteristic, complemented
142#1941C2211yescharacteristic, complemented
143#1936C2211yescharacteristic
144#1936C2211yescharacteristic
145#1936C2211yescharacteristic, complemented
146#1935C2211yescharacteristic, complemented
147#1934C2211yescharacteristic
148#1934C2211yescharacteristic
149#1934C2211yescharacteristic, complemented
150#1933C2211yescharacteristic, complemented
151#1928C2211yescharacteristic, complemented
152#1926C2211yescharacteristic
153#1926C2211yescharacteristic, complemented
154#1925C2211yescharacteristic
155#1921C2211yescharacteristic, complemented
156#1921C2211yescharacteristic, complemented
157#1920C2211yescharacteristic, complemented
158#1919C2211yescharacteristic, complemented
159#1893C2211yescharacteristic
160#1893C2211yescharacteristic
161#1893C2211yescharacteristic
162#1893C2211yescharacteristic
163#1893C2211yescharacteristic, complemented
164#1892C2211yescharacteristic
165#1892C2211yescharacteristic
166#1892C2211yescharacteristic, complemented
167#1880C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1877C2211yescharacteristic
171#1864C2211yescharacteristic
172#1864C2211yescharacteristic, complemented
173#1863C2211yescharacteristic, complemented
174#1862C2211yescharacteristic
175#1853C2211yescharacteristic
176#1853C2211yescharacteristic
177#1852C2211yescharacteristic
178#1852C2211yescharacteristic
179#1847C2211yescharacteristic, complemented
180#1847C2211yescharacteristic, complemented
181#1808C2211yescharacteristic, complemented
182#1807C2211yescharacteristic, complemented
183#1776C2211yescharacteristic, complemented
184#1776C2211yescharacteristic, complemented
185#1770C2211yescharacteristic, complemented
186#1770C2211yescharacteristic, complemented
187#1767C2211yescharacteristic, complemented
188#1763C2211yescharacteristic, complemented
189#1762C2211yescharacteristic
190#1762C2211yescharacteristic
191#1762C2211yescharacteristic, complemented
192#1752C2211yescharacteristic
193#1752C2211yescharacteristic
194#1752C2211yescharacteristic, complemented
195#1752C2211yescharacteristic, complemented
196#1749C2211yescharacteristic
197#1749C2211yescharacteristic, complemented
198#1744C2211yescharacteristic, complemented
199C2×#340C2211yescharacteristic
200C2×#340C2211yescharacteristic
201C2×#336C2211yescharacteristic
202C2×#336C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C23×C8C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#551—48no—
213C2×C4⋊Q8C2311yescharacteristic
214C2×#126—21no—
215C2×#126—21no—
216C2×#124—21no—
217C2×#124C2311yescharacteristic
218C2×#123—21no—
219C2×#123—21no—
220C2×#123—21no—
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8C2311yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×#121—21no—
226C2×#121C2311yescharacteristic
227C2×#121C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#120—21no—
231C2×C4×Q8C2311yescharacteristic
232C2×C4×D4—21no—
233C2×C4×D4—21no—
234C2×C4×D4D411yescharacteristic
235C2×C4×D4D411yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×#117—21no—
241C2×#117—21no—
242C22×C4⋊C4C2311yescharacteristic
243C22×C4⋊C4C2311yescharacteristic
244C22×C4⋊C4C2311yescharacteristic
245C22×C22⋊C4—21no—
246C22×C22⋊C4—21no—
247C22×C22⋊C4—21no—
248C22×C42C2311yescharacteristic
249C22×C42C2311yescharacteristic
250#483—24no—
251#480—24no—
252#466—42no—
253#465—42no—
254#450—24no—
255#447—24no—
256#442—42no—
257#440—42no—
258C8×D4—24no—
259C8×D4—24no—
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#102—42no—
281C2×#102—42no—
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×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×#97C2311yescharacteristic
305C2×#97C2311yescharacteristic
306C2×#97C2311yescharacteristic
307C2×#97C2311yescharacteristic
308C2×#97C2311yescharacteristic
309C2×#97C2311yescharacteristic
310C2×C4×C8C2311yescharacteristic
311C2×C4×C8C2311yescharacteristic
312#401—21no—
313#400—21no—
314#400—21no—
315#398—21no—
316#398—21no—
317#397—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#396—21no—
325#396—21no—
326#396—21no—
327#396—21no—
328#394—21no—
329#394—21no—
330#394—21no—
331#394—21no—
332#394—21no—
333#393—21no—
334#393—21no—
335#392—21no—
336#391—21no—
337#391C2311yescharacteristic
338#391C2311yescharacteristic
339#391C2311yescharacteristic
340#390—21no—
341#390—21no—
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#389—21no—
354#389—21no—
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#388—21no—
366#388—21no—
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#386—21no—
395#386—21no—
396#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#384C2311yescharacteristic
411#383—21no—
412#383—21no—
413#382—21no—
414#382—21no—
415#382C2311yescharacteristic
416#382C2311yescharacteristic
417#382C2311yescharacteristic
418#382C2311yescharacteristic
419#382C2311yescharacteristic
420#381—21no—
421#381—21no—
422#381—21no—
423#381—21no—
424#380—21no—
425#380—21no—
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#379—21no—
433#379—21no—
434C4×C4⋊C4D411yescharacteristic
435C4×C4⋊C4D411yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C4×C22⋊C4D411yescharacteristic
448C4×C22⋊C4D411yescharacteristic
449C4×C22⋊C4D411yescharacteristic
450C4×C22⋊C4D411yescharacteristic
451C4×C22⋊C4C2311yescharacteristic
452C4×C22⋊C4C2311yescharacteristic
453#376—21no—
454C2×#95—21no—
455C2×#95—21no—
456C43C2311yescharacteristic
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#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491C25—21no—
492C22×Q8—21no—
493C22×Q8C2411yescharacteristic
494C22×D4—22no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—22no—
501C22×D4—22no—
502C22×D4—41no—
503C22×D4—41no—
504C22×D4—41no—
505C22×D4C2×D411yescharacteristic
506C22×D4C2411yescharacteristic
507C22×D4C2411yescharacteristic
508C22×D4C2411yescharacteristic
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4C2×D411yescharacteristic
516C23×C4C2×D411yescharacteristic
517C23×C4C2×D411yescharacteristic
518C23×C4C2×D411yescharacteristic
519C23×C4C2411yescharacteristic
520C23×C4C2411yescharacteristic
521C2×SD16—22no—
522C2×SD16—22no—
523C2×SD16—22no—
524C2×SD16—41no—
525C2×SD16—41no—
526C2×SD16—41no—
527C2×D8—22no—
528C2×D8—22no—
529C2×D8—22no—
530C2×D8—41no—
531C2×D8—41no—
532C2×D8—41no—
533C22×C8—22no—
534C22×C8—22no—
535C22×C8—22no—
536C22×C8—22no—
537C22×C8—41no—
538C22×C8—41no—
539C22×C8—41no—
540C22×C8—41no—
541C22×C8—41no—
542C22×C8—41no—
543C22×C8—41no—
544C22×C8—41no—
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C4⋊Q8—41no—
554C4⋊Q8—41no—
555#126—44no—
556#126—44no—
557#124—41no—
558#124—41no—
559#124—44no—
560#123—44no—
561#123—44no—
562#123—44no—
563C22⋊Q8—22no—
564C22⋊Q8—22no—
565C22⋊Q8—44no—
566C22⋊Q8—44no—
567C22⋊Q8—41no—
568C22⋊Q8—41no—
569#121—22no—
570#121—22no—
571#121—22no—
572#121—41no—
573#121—44no—
574#121—41no—
575#121—41no—
576#121—41no—
577#121—41no—
578#120—44no—
579C4×Q8—41no—
580C4×Q8—41no—
581C4×D4—24no—
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—41no—
586C4×D4—41no—
587C4×D4—41no—
588C4×D4—41no—
589C4×D4—41no—
590C4×D4—42no—
591C4×D4—44no—
592C4×D4—44no—
593#117—44no—
594#117—44no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
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—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—41no—
617C2×C4⋊C4—41no—
618C2×C4⋊C4—41no—
619C2×C4⋊C4—41no—
620C2×C4⋊C4C2×D411yescharacteristic
621C2×C4⋊C4C2×D411yescharacteristic
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
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—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—44no—
675C2×C22⋊C4—44no—
676C2×C22⋊C4—44no—
677C2×C22⋊C4C2×D411yescharacteristic
678C2×C22⋊C4C2×D411yescharacteristic
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C42—21no—
684C2×C42—21no—
685C2×C42—21no—
686C2×C42—21no—
687C2×C42—21no—
688C2×C42—41no—
689C2×C42—41no—
690C2×C42—41no—
691C2×C42—41no—
692C2×C42C2×D411yescharacteristic
693C2×C42C2×D411yescharacteristic
694C2×C42C2×D411yescharacteristic
695C2×C42C2×D411yescharacteristic
696C2×C42C2×D411yescharacteristic
697C2×C42C2×D411yescharacteristic
698C2×C42C2×D411yescharacteristic
699C2×C42C2×D411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705#107—22no—
706#107—22no—
707#107—41no—
708#107—41no—
709#107—41no—
710#107—41no—
711#106—22no—
712#106—22no—
713#106—41no—
714#106—41no—
715#106—41no—
716#106—41no—
717C4⋊C8—22no—
718C4⋊C8—22no—
719#103—22no—
720#103—22no—
721#103—41no—
722#103—41no—
723#103—41no—
724#103—41no—
725#102—22no—
726#102—22no—
727#102—22no—
728#102—22no—
729#102—22no—
730#102—22no—
731#102—22no—
732#102—22no—
733#102—22no—
734#102—22no—
735#102—41no—
736#102—41no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743C22⋊C8—22no—
744C22⋊C8—22no—
745C22⋊C8#4114yes—
746C22⋊C8#4114yes—
747#97—41no—
748#97—41no—
749#97—41no—
750#97—41no—
751#97—41no—
752#97—41no—
753C4×C8—22no—
754C4×C8—22no—
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#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797C24—21no—
798C24—21no—
799C24—21no—
800C24—42no—
801C24—42no—
802C24—42no—
803C24—42no—
804C24—81no—
805C24—81no—
806C24—81no—
807C24C22×D411yescharacteristic
808C24C22×D411yescharacteristic
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—42no—
816C2×Q8—81no—
817C2×Q8—81no—
818C2×D4—22no—
819C2×D4—22no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—44no—
838C2×D4—44no—
839C2×D4—42no—
840C2×D4—42no—
841C2×D4—42no—
842C2×D4—42no—
843C2×D4—42no—
844C2×D4—42no—
845C2×D4—42no—
846C2×D4—42no—
847C2×D4—42no—
848C2×D4—82no—
849C2×D4—82no—
850C2×D4—81no—
851C2×D4—81no—
852C2×D4—81no—
853C2×D4—81no—
854C2×D4—81no—
855C2×D4—81no—
856C2×D4AGL(1,ℤ/8)14yes—
857C2×D4H(5,𝔽2)12yes—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—41no—
885C22×C4—41no—
886C22×C4—41no—
887C22×C4—41no—
888C22×C4—41no—
889C22×C4—41no—
890C22×C4—41no—
891C22×C4—41no—
892C22×C4—41no—
893C22×C4—42no—
894C22×C4—42no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—42no—
902C22×C4—81no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C2×#4112yes—
924C22×C4C2×#4112yes—
925C22×C4C2511yescharacteristic
926SD16—44no—
927SD16—82no—
928D8—44no—
929D8—82no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—82no—
951C2×C8—82no—
952C2×C8—82no—
953C2×C8—82no—
954C2×C8C2×#4112yes—
955C2×C8C2×#4112yes—
956C2×C8C2×#4112yes—
957C2×C8C2×#4112yes—
958C4⋊C4—22no—
959C4⋊C4—22no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—41no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C22⋊C4—22no—
1005C22⋊C4—22no—
1006C22⋊C4—22no—
1007C22⋊C4—22no—
1008C22⋊C4—22no—
1009C22⋊C4—41no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C42—22no—
1050C42—21no—
1051C42—21no—
1052C42—21no—
1053C42—21no—
1054C42—21no—
1055C42—21no—
1056C42—21no—
1057C42—21no—
1058C42—21no—
1059C42—21no—
1060C42—41no—
1061C42—41no—
1062C42—41no—
1063C42—41no—
1064C42—41no—
1065C42—41no—
1066C42—41no—
1067C42—42no—
1068C42—42no—
1069C42—42no—
1070C42—81no—
1071C42—81no—
1072C23—21no—
1073C23—21no—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—22no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—84no—
1104C23—84no—
1105C23—84no—
1106C23—84no—
1107C23—162no—
1108C23—162no—
1109C23—162no—
1110C23#53212yes—
1111C23C2×AGL(1,ℤ/8)12yes—
1112C23C2×AGL(1,ℤ/8)12yes—
1113C23#57512yes—
1114C23C23×D411yescharacteristic
1115Q8—41no—
1116Q8—41no—
1117Q8—41no—
1118Q8—41no—
1119Q8—162no—
1120D4—28no—
1121D4—22no—
1122D4—22no—
1123D4—41no—
1124D4—41no—
1125D4—41no—
1126D4—41no—
1127D4—41no—
1128D4—41no—
1129D4—41no—
1130D4—41no—
1131D4—41no—
1132D4—41no—
1133D4—84no—
1134D4—84no—
1135D4—84no—
1136D4—162no—
1137D4—162no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—82no—
1220C2×C4—82no—
1221C2×C4—82no—
1222C2×C4—82no—
1223C2×C4—84no—
1224C2×C4—84no—
1225C2×C4—162no—
1226C2×C4—162no—
1227C2×C4—162no—
1228C2×C4—162no—
1229C2×C4#53212yes—
1230C2×C4C2×AGL(1,ℤ/8)12yes—
1231C2×C4C22×#4111yescharacteristic
1232C2×C4C22×#4111yescharacteristic
1233C2×C4C2×H(5,𝔽2)11yescharacteristic
1234C2×C4#58511yescharacteristic
1235C2×C4#58511yescharacteristic
1236C2×C4#58511yescharacteristic
1237C8—22no—
1238C8—22no—
1239C8—22no—
1240C8—22no—
1241C8—41no—
1242C8—41no—
1243C8—41no—
1244C8—41no—
1245C22—22no—
1246C22—22no—
1247C22—22no—
1248C22—22no—
1249C22—22no—
1250C22—22no—
1251C22—22no—
1252C22—22no—
1253C22—22no—
1254C22—41no—
1255C22—41no—
1256C22—41no—
1257C22—41no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—168no—
1280C22#318014yes—
1281C22C2×#53211yescharacteristic
1282C22#348511yescharacteristic
1283C22#348811yescharacteristic
1284C22C22×AGL(1,ℤ/8)11yescharacteristic
1285C22C2×#57511yescharacteristic
1286C22#358411yescharacteristic
1287C22#358411yescharacteristic
1288C4—22no—
1289C4—22no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—41no—
1297C4—41no—
1298C4—41no—
1299C4—41no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4#351311yescharacteristic
1314C4#351311yescharacteristic
1315C4#352111yescharacteristic
1316C4#352111yescharacteristic
1317C2—24no—
1318C2—42no—
1319C2—82no—
1320C2—161no—
1321C2—161no—
1322C2#3585011yescharacteristic
1323C2C2×#318011yescharacteristic
1324C2#6072411yescharacteristic
1325C2#6173211yescharacteristic
1326C2#6173311yescharacteristic
1327C2#6198911yescharacteristic
1328C2#6199011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#25108C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36262C2semidirect
2. #36172C2semidirect
3. #30386C2semidirect
4. #30322C2semidirect
5. #30188C2semidirect
6. #29576C2semidirect
7. #29497C2semidirect
8. #29083C2semidirect
9. #29079C2semidirect
10. #28990C2semidirect
11. #28984C2semidirect
12. #28573C2semidirect
13. #28312C2semidirect
14. #28029C2semidirect
15. #28026C2semidirect
16. #27956C2semidirect
17. #27859C2semidirect
18. #25236C2semidirect
19. #25232C2semidirect
20. #25112C2semidirect
22. #25042C2semidirect
23. #25041C2semidirect
24. #23764C2semidirect
25. #23686C2semidirect
26. C2×#2073C2semidirect
27. #22938C2semidirect
28. #22934C2semidirect
29. #22858C2semidirect
30. #22854C2semidirect
31. #20558C2semidirect
45. #2864C22semidirect
50. #2850C22semidirect
61. #2514C22semidirect
62. #2513C22semidirect
70. #2421C22semidirect
71. #2420C22semidirect
82. C4×#124C22semidirect
86. #2283C22semidirect
89. #2101C22semidirect
90. #2101C22semidirect
93. #2088C22semidirect
94. #2086C22semidirect
95. #2085C22semidirect
96. #2085C22semidirect
97. #2085C22semidirect
98. #2085C22semidirect
99. #2077C22semidirect
100. #2075C22semidirect
109. #2072C22semidirect
110. #2071C22semidirect
112. #2067C22semidirect
113. #2066C22semidirect
117. #2042C22semidirect
118. #2042C22semidirect
119. #2035C22semidirect
122. #2033C22semidirect
123. #2024C22semidirect
124. #2023C22semidirect
129. #1993C22semidirect
130. #1993C22semidirect
139. #1944C22semidirect
140. #1943C22semidirect
141. #1942C22semidirect
142. #1941C22semidirect
145. #1936C22semidirect
146. #1935C22semidirect
149. #1934C22semidirect
150. #1933C22semidirect
151. #1928C22semidirect
153. #1926C22semidirect
155. #1921C22semidirect
156. #1921C22semidirect
157. #1920C22semidirect
158. #1919C22semidirect
163. #1893C22semidirect
166. #1892C22semidirect
172. #1864C22semidirect
173. #1863C22semidirect
179. #1847C22semidirect
180. #1847C22semidirect
181. #1808C22semidirect
182. #1807C22semidirect
183. #1776C22semidirect
184. #1776C22semidirect
185. #1770C22semidirect
186. #1770C22semidirect
187. #1767C22semidirect
188. #1763C22semidirect
191. #1762C22semidirect
194. #1752C22semidirect
195. #1752C22semidirect
197. #1749C22semidirect
198. #1744C22semidirect
202. C2×#336C22semidirect

Maximal subgroups

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

subgroupindex
#362622
#361722
#303862
#303222
#301882
#295762
#294972
#290832
#290792
#289902
#289842
#285732
#283122
#280292
#280262
#279562
#278592
#252362
#252322
#251122
#251082
#250422
#250412
#237642
#236862
C2×#20732
#229382
#229342
#228582
#228542
#205582