Finite Group Databasebeta

← #7024858

Subgroups — #7024858

Order 512.

1549 conjugacy classes of subgroups.

The subgroup lattice has 1270 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59424C211yesmaximal, characteristic
2#59154C211yesmaximal, characteristic, complemented
3#32642C211yesmaximal, characteristic, complemented
4#32581C211yesmaximal, characteristic, complemented
5#32456C211yesmaximal, characteristic, complemented
6#32257C211yesmaximal, characteristic, complemented
7#31832C211yesmaximal, characteristic, complemented
8#31657C211yesmaximal, characteristic, complemented
9#31171C211yesmaximal, characteristic, complemented
10#30822C211yesmaximal, characteristic, complemented
11#28123C211yesmaximal, characteristic
12#27715C211yesmaximal, characteristic, complemented
13#27440C211yesmaximal, characteristic, complemented
14#27262C211yesmaximal, characteristic
15#27154C211yesmaximal, characteristic, complemented
16#26914C211yesmaximal, characteristic, complemented
17#26713C211yesmaximal, characteristic, complemented
18#26477C211yesmaximal, characteristic, complemented
19#26033C211yesmaximal, characteristic, complemented
20#25994C211yesmaximal, characteristic, complemented
21#25952C211yesmaximal, characteristic
22#25941C211yesmaximal, characteristic, complemented
23#25206C211yesmaximal, characteristic, complemented
24#25084C211yesmaximal, characteristic
25#24346C211yesmaximal, characteristic, complemented
26#24307C211yesmaximal, characteristic, complemented
27C2×#2025C211yesmaximal, characteristic
28#22932C211yesmaximal, characteristic, complemented
29#22854C211yesmaximal, characteristic
30#22295C211yesmaximal, characteristic, complemented
31#22182C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic, complemented
33C22×#125C2211yescharacteristic
34C2×#489C2211yescharacteristic
35C2×#484C2211yescharacteristic
36C2×#479C2211yescharacteristic, complemented
37C2×#479C2211yescharacteristic, complemented
38C2×#478C2211yescharacteristic
39C2×#467C2211yescharacteristic
40C2×#464C2211yescharacteristic
41C2×#450C2211yescharacteristic
42C2×#440C2211yescharacteristic
43C22×#102C2211yescharacteristic
44C22×#102C2211yescharacteristic
45#2786—21no—
46#2740—21no—
47#2726—21no—
48#2713—21no—
49#2601—21no—
50#2592C2211yescharacteristic
51#2584C2211yescharacteristic, complemented
52#2565C2211yescharacteristic, complemented
53#2560—21no—
54#2552C2211yescharacteristic, complemented
55#2550C2211yescharacteristic, complemented
56#2538C2211yescharacteristic
57#2512C2211yescharacteristic
58#2512C2211yescharacteristic
59#2506—21no—
60#2502C2211yescharacteristic
61#2480—21no—
62#2480—21no—
63#2473—21no—
64#2473—21no—
65#2462—21no—
66#2453C2211yescharacteristic, complemented
67#2453C2211yescharacteristic, complemented
68#2448C2211yescharacteristic
69#2447C2211yescharacteristic
70#2442C2211yescharacteristic
71#2440—21no—
72#2440C2211yescharacteristic
73#2437—21no—
74#2435C2211yescharacteristic
75#2370C2211yescharacteristic, complemented
76#2367C2211yescharacteristic
77#2360—21no—
78#2360C2211yescharacteristic
79#2360C2211yescharacteristic
80#2354C2211yescharacteristic
81#2345C2211yescharacteristic
82#2342—21no—
83D4×C22⋊C4C2211yescharacteristic
84C4×C22⋊Q8C2211yescharacteristic
85C4×C22⋊Q8C2211yescharacteristic
86C4×C22⋊Q8C2211yescharacteristic
87C2×#390C2211yescharacteristic
88#2100C2211yescharacteristic, complemented
89#2099C2211yescharacteristic, complemented
90#2099C2211yescharacteristic, complemented
91#2092C2211yescharacteristic
92#2087C2211yescharacteristic, complemented
93#2087C2211yescharacteristic, complemented
94#2083C2211yescharacteristic, complemented
95#2074C2211yescharacteristic, complemented
96#2072C2211yescharacteristic, complemented
97#2071C2211yescharacteristic
98#2068C2211yescharacteristic, complemented
99#2067C2211yescharacteristic
100#2067C2211yescharacteristic
101#2067C2211yescharacteristic
102#2067C2211yescharacteristic
103#2065C2211yescharacteristic
104#2059C2211yescharacteristic, complemented
105#2059C2211yescharacteristic, complemented
106#2057C2211yescharacteristic, complemented
107#2056C2211yescharacteristic, complemented
108#2055C2211yescharacteristic
109#2055C2211yescharacteristic
110#2055C2211yescharacteristic
111#2042C2211yescharacteristic
112#2042C2211yescharacteristic
113#2042C2211yescharacteristic
114#2026C2211yescharacteristic, complemented
115#2026C2211yescharacteristic, complemented
116#2026C2211yescharacteristic, complemented
117#2025C2211yescharacteristic
118#2025C2211yescharacteristic
119#2025C2211yescharacteristic
120#2025C2211yescharacteristic
121#2025C2211yescharacteristic
122#2025C2211yescharacteristic
123#2025C2211yescharacteristic
124#2025C2211yescharacteristic
125#2025C2211yescharacteristic
126#2023C2211yescharacteristic
127#2015C2211yescharacteristic
128#1992C2211yescharacteristic, complemented
129#1989C2211yescharacteristic, complemented
130#1989C2211yescharacteristic, complemented
131#1987C2211yescharacteristic, complemented
132#1985C2211yescharacteristic, complemented
133#1985C2211yescharacteristic, complemented
134#1983C2211yescharacteristic
135#1973C2211yescharacteristic
136#1959C2211yescharacteristic
137#1947C2211yescharacteristic, complemented
138#1947C2211yescharacteristic, complemented
139#1943C2211yescharacteristic, complemented
140#1940C2211yescharacteristic, complemented
141#1940C2211yescharacteristic, complemented
142#1936C2211yescharacteristic
143#1936C2211yescharacteristic
144#1936C2211yescharacteristic
145#1935C2211yescharacteristic, complemented
146#1935C2211yescharacteristic, complemented
147#1935C2211yescharacteristic, complemented
148#1928C2211yescharacteristic, complemented
149#1928C2211yescharacteristic, complemented
150#1928C2211yescharacteristic, complemented
151#1927C2211yescharacteristic, complemented
152#1925C2211yescharacteristic
153#1925C2211yescharacteristic
154#1925C2211yescharacteristic
155#1925C2211yescharacteristic
156#1921C2211yescharacteristic, complemented
157#1921C2211yescharacteristic, complemented
158#1921C2211yescharacteristic, complemented
159#1921C2211yescharacteristic, complemented
160#1918C2211yescharacteristic, complemented
161#1918C2211yescharacteristic, complemented
162#1917C2211yescharacteristic, complemented
163#1917C2211yescharacteristic, complemented
164#1917C2211yescharacteristic, complemented
165#1917C2211yescharacteristic, complemented
166#1892C2211yescharacteristic
167#1892C2211yescharacteristic
168#1880C2211yescharacteristic
169#1880C2211yescharacteristic
170#1880C2211yescharacteristic
171#1880C2211yescharacteristic
172#1878C2211yescharacteristic, complemented
173#1878C2211yescharacteristic, complemented
174#1878C2211yescharacteristic, complemented
175#1877C2211yescharacteristic
176#1872C2211yescharacteristic
177#1872C2211yescharacteristic
178#1865C2211yescharacteristic, complemented
179#1864C2211yescharacteristic
180#1863C2211yescharacteristic, complemented
181#1863C2211yescharacteristic, complemented
182#1862C2211yescharacteristic
183#1862C2211yescharacteristic
184#1853C2211yescharacteristic
185#1852C2211yescharacteristic
186#1850C2211yescharacteristic
187#1850C2211yescharacteristic
188#1836C2211yescharacteristic, complemented
189#1824C2211yescharacteristic
190#1808C2211yescharacteristic
191#1804C2211yescharacteristic
192#1803C2211yescharacteristic, complemented
193#1797C2211yescharacteristic
194#1786C2211yescharacteristic
195#1776C2211yescharacteristic, complemented
196#1763C2211yescharacteristic, complemented
197#1762C2211yescharacteristic
198#1752C2211yescharacteristic
199#1752C2211yescharacteristic
200C2×#340C2211yescharacteristic
201C2×#340C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209#557—42no—
210#557—42no—
211C2×C4⋊Q8—21no—
212C2×C4⋊Q8C2311yescharacteristic
213C2×#126—21no—
214C2×#126—21no—
215C2×#125—21no—
216C2×#125—21no—
217C2×#125—21no—
218C2×#125—21no—
219C2×#125—42no—
220C2×#125—42no—
221C2×#125C2311yescharacteristic
222C2×#125C2311yescharacteristic
223C2×#125C2311yescharacteristic
224C2×#125C2311yescharacteristic
225C2×#125C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#124C2311yescharacteristic
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8D411yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C4×Q8—21no—
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×#117—21no—
242C22×C4⋊C4—21no—
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×C42C2311yescharacteristic
251#489—42no—
252#484—24no—
253#479—42no—
254#479—42no—
255#478—42no—
256#467—24no—
257#464—42no—
258#450—24no—
259#440—42no—
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#102—42no—
288C2×#102—42no—
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×#97C2311yescharacteristic
306C2×#97C2311yescharacteristic
307C2×#97C2311yescharacteristic
308C2×#97C2311yescharacteristic
309#400—21no—
310#400—21no—
311#400—21no—
312#399—21no—
313#398—21no—
314#398—21no—
315#398—21no—
316#398—21no—
317#398—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#396—21no—
332#396—21no—
333#396—21no—
334#396—21no—
335#395—21no—
336#395—21no—
337#395—21no—
338#394—21no—
339#394—21no—
340#393—21no—
341#391—21no—
342#391D411yescharacteristic
343#391C2311yescharacteristic
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#391C2311yescharacteristic
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#390—21no—
350#390—21no—
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#389—21no—
360#389—21no—
361#389—21no—
362#389—21no—
363#389—21no—
364#389—21no—
365#389—21no—
366#389—21no—
367#389—21no—
368#389D411yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387D411yescharacteristic
402#387D411yescharacteristic
403#386—21no—
404#386—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385D411yescharacteristic
416#385D411yescharacteristic
417#384—21no—
418#384C2311yescharacteristic
419#384C2311yescharacteristic
420#384C2311yescharacteristic
421#382C2311yescharacteristic
422#381—21no—
423#380—21no—
424#380—21no—
425#380—21no—
426#380—21no—
427#380D411yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#379—21no—
431#379—21no—
432#379—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4—21no—
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4C2311yescharacteristic
452C4×C22⋊C4C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C22×Q8—21no—
495C22×Q8C2×D411yescharacteristic
496C22×Q8C2411yescharacteristic
497C22×Q8C2411yescharacteristic
498C22×D4—22no—
499C22×D4—21no—
500C22×D4—22no—
501C22×D4—22no—
502C22×D4—41no—
503C22×D4—41no—
504C22×D4—41no—
505C22×D4C2411yescharacteristic
506C22×D4C2411yescharacteristic
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4C2×D411yescharacteristic
513C23×C4C2×D411yescharacteristic
514C23×C4C2411yescharacteristic
515C2×Q16—22no—
516C2×Q16—41no—
517C2×Q16—41no—
518C2×SD16—22no—
519C2×SD16—22no—
520C2×SD16—22no—
521C2×SD16—41no—
522C2×SD16—41no—
523C2×SD16—41no—
524C22×C8—22no—
525C22×C8—22no—
526C22×C8—41no—
527C22×C8—41no—
528C22×C8—41no—
529C22×C8—41no—
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C4⋊Q8—22no—
539C4⋊Q8—41no—
540C4⋊Q8—44no—
541#126—82no—
542#126—82no—
543#125—22no—
544#125—22no—
545#125—22no—
546#125—22no—
547#125—22no—
548#125—41no—
549#125—41no—
550#125—41no—
551#125—41no—
552#125—41no—
553#125—44no—
554#125—44no—
555#125—44no—
556#125—44no—
557#124—22no—
558#124—41no—
559#124—41no—
560#124—41no—
561C22⋊Q8—22no—
562C22⋊Q8—22no—
563C22⋊Q8—22no—
564C22⋊Q8—42no—
565C22⋊Q8—44no—
566C22⋊Q8—82no—
567C22⋊Q8#4114yes—
568C4×Q8—22no—
569C4×Q8—22no—
570C4×Q8—41no—
571C4×Q8—41no—
572C4×Q8—41no—
573C4×Q8—41no—
574C4×Q8—41no—
575C4×Q8—41no—
576C4×Q8—41no—
577C4×Q8—41no—
578C4×Q8—44no—
579C4×D4—22no—
580C4×D4—41no—
581C4×D4—41no—
582C4×D4—41no—
583#117—82no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—22no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
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—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—41no—
625C2×C4⋊C4—41no—
626C2×C4⋊C4—44no—
627C2×C4⋊C4—44no—
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2×D411yescharacteristic
633C2×C4⋊C4C2×D411yescharacteristic
634C2×C4⋊C4C2×D411yescharacteristic
635C2×C4⋊C4C2×D411yescharacteristic
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
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—21no—
675C2×C22⋊C4—44no—
676C2×C22⋊C4—82no—
677C2×C22⋊C4—82no—
678C2×C22⋊C4C2×D411yescharacteristic
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C42—21no—
683C2×C42—21no—
684C2×C42—21no—
685C2×C42—21no—
686C2×C42—21no—
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—41no—
693C2×C42—41no—
694C2×C42C2×D411yescharacteristic
695C2×C42C2×D411yescharacteristic
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702#107—22no—
703#107—22no—
704#107—22no—
705#107—22no—
706#107—41no—
707#107—41no—
708#107—41no—
709#106—22no—
710#106—41no—
711C4⋊C8—41no—
712C4⋊C8—41no—
713C4⋊C8—41no—
714C4⋊C8—41no—
715C4⋊C8—41no—
716C4⋊C8—41no—
717#103—22no—
718#103—22no—
719#103—22no—
720#103—22no—
721#103—22no—
722#103—22no—
723#103—41no—
724#103—41no—
725#103—41no—
726#103—41no—
727#103—41no—
728#103—41no—
729#102—22no—
730#102—22no—
731#102—22no—
732#102—22no—
733#102—22no—
734#102—22no—
735#102—22no—
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—
745#97—41no—
746#97—41no—
747#97—41no—
748#97—41no—
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#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#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791C24—21no—
792C24—21no—
793C24—42no—
794C24—42no—
795C24—42no—
796C24—42no—
797C24—81no—
798C24—81no—
799C24—81no—
800C24C22×D411yescharacteristic
801C2×Q8—21no—
802C2×Q8—21no—
803C2×Q8—21no—
804C2×Q8—21no—
805C2×Q8—21no—
806C2×Q8—21no—
807C2×Q8—21no—
808C2×Q8—21no—
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—41no—
813C2×Q8—41no—
814C2×Q8—41no—
815C2×Q8—42no—
816C2×Q8—42no—
817C2×Q8—81no—
818C2×Q8C2×#4112yes—
819C2×D4—21no—
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—44no—
831C2×D4—44no—
832C2×D4—42no—
833C2×D4—42no—
834C2×D4—82no—
835C2×D4—82no—
836C2×D4—81no—
837C2×D42−1+412yes—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—41no—
859C22×C4—41no—
860C22×C4—41no—
861C22×C4—41no—
862C22×C4—42no—
863C22×C4—42no—
864C22×C4—42no—
865C22×C4—42no—
866C22×C4—42no—
867C22×C4—42no—
868C22×C4—42no—
869C22×C4—42no—
870C22×C4—81no—
871C22×C4—81no—
872C22×C4—81no—
873C22×C4—81no—
874C22×C4—81no—
875C22×C4—81no—
876C22×C4—81no—
877C22×C4C22×D411yescharacteristic
878C22×C4C22×D411yescharacteristic
879C22×C4C22×D411yescharacteristic
880C22×C4C22×D411yescharacteristic
881C22×C4C22×D411yescharacteristic
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×C4C2×#4112yes—
891C22×C42−1+412yes—
892C22×C4C2511yescharacteristic
893Q16—82no—
894SD16—44no—
895SD16—82no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8—21no—
899C2×C8—21no—
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—82no—
921C2×C8—82no—
922C4⋊C4—24no—
923C4⋊C4—24no—
924C4⋊C4—24no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
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—41no—
947C4⋊C4—41no—
948C4⋊C4—41no—
949C4⋊C4—41no—
950C4⋊C4—41no—
951C4⋊C4—41no—
952C4⋊C4—41no—
953C4⋊C4—41no—
954C4⋊C4—41no—
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—42no—
974C4⋊C4—42no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4C2×#4112yes—
989C4⋊C4H(5,𝔽2)12yes—
990C4⋊C4H(5,𝔽2)12yes—
991C22⋊C4—24no—
992C22⋊C4—22no—
993C22⋊C4—22no—
994C22⋊C4—22no—
995C22⋊C4—22no—
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—81no—
1009C22⋊C4—81no—
1010C22⋊C4—81no—
1011C22⋊C4—81no—
1012C22⋊C4—81no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C42—21no—
1022C42—21no—
1023C42—21no—
1024C42—21no—
1025C42—21no—
1026C42—21no—
1027C42—21no—
1028C42—21no—
1029C42—21no—
1030C42—21no—
1031C42—21no—
1032C42—21no—
1033C42—41no—
1034C42—41no—
1035C42—42no—
1036C42—42no—
1037C42—42no—
1038C42—42no—
1039C42—81no—
1040C42—81no—
1041C42—81no—
1042C42—81no—
1043C42—81no—
1044C42—81no—
1045C23—21no—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23—22no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—84no—
1064C23—84no—
1065C23—84no—
1066C23—84no—
1067C23—162no—
1068C23—162no—
1069C23—162no—
1070C23#54812yes—
1071C23#57512yes—
1072C23#57812yes—
1073C23C23×D411yescharacteristic
1074Q8—22no—
1075Q8—22no—
1076Q8—41no—
1077Q8—41no—
1078Q8—41no—
1079Q8—41no—
1080Q8—41no—
1081Q8—41no—
1082Q8—82no—
1083Q8—84no—
1084D4—22no—
1085D4—22no—
1086D4—41no—
1087D4—41no—
1088D4—41no—
1089D4—41no—
1090D4—41no—
1091D4—41no—
1092D4—84no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—22no—
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—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
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—82no—
1178C2×C4—82no—
1179C2×C4—84no—
1180C2×C4—84no—
1181C2×C4—84no—
1182C2×C4—162no—
1183C2×C4—162no—
1184C2×C4#54812yes—
1185C2×C4C22×#4111yescharacteristic
1186C2×C4C2×H(5,𝔽2)11yescharacteristic
1187C2×C4C2×H(5,𝔽2)11yescharacteristic
1188C2×C4C2×2−1+411yescharacteristic
1189C2×C4C2×2−1+411yescharacteristic
1190C2×C4#58511yescharacteristic
1191C8—41no—
1192C8—41no—
1193C8—41no—
1194C8—41no—
1195C8—41no—
1196C8—41no—
1197C8—41no—
1198C8—41no—
1199C22—22no—
1200C22—22no—
1201C22—22no—
1202C22—22no—
1203C22—22no—
1204C22—22no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—81no—
1209C22—81no—
1210C22—81no—
1211C22—81no—
1212C22—81no—
1213C22—81no—
1214C22—81no—
1215C22—81no—
1216C22—81no—
1217C22—81no—
1218C22—81no—
1219C22—168no—
1220C22#337714yes—
1221C22C2×#54811yescharacteristic
1222C22#348411yescharacteristic
1223C22#348911yescharacteristic
1224C22C2×#57511yescharacteristic
1225C22C2×#57811yescharacteristic
1226C22#358511yescharacteristic
1227C22#358511yescharacteristic
1228C4—22no—
1229C4—42no—
1230C4—41no—
1231C4—41no—
1232C4—41no—
1233C4—41no—
1234C4—42no—
1235C4—42no—
1236C4—41no—
1237C4—41no—
1238C4—41no—
1239C4—41no—
1240C4—41no—
1241C4—41no—
1242C4—42no—
1243C4—41no—
1244C4—41no—
1245C4—81no—
1246C4—81no—
1247C4—81no—
1248C4—81no—
1249C4—81no—
1250C4—81no—
1251C4—81no—
1252C4—81no—
1253C4—81no—
1254C4—81no—
1255C4#351411yescharacteristic
1256C4#352011yescharacteristic
1257C4#353811yescharacteristic
1258C4#356111yescharacteristic
1259C2—24no—
1260C2—82no—
1261C2—161no—
1262C2#4310411yescharacteristic
1263C2C2×#337711yescharacteristic
1264C2#6133711yescharacteristic
1265C2#6157911yescharacteristic
1266C2#6161911yescharacteristic
1267C2#6211911yescharacteristic
1268C2#6216511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #59154C2semidirect
3. #32642C2semidirect
4. #32581C2semidirect
5. #32456C2semidirect
6. #32257C2semidirect
7. #31832C2semidirect
8. #31657C2semidirect
9. #31171C2semidirect
10. #30822C2semidirect
12. #27715C2semidirect
13. #27440C2semidirect
15. #27154C2semidirect
16. #26914C2semidirect
17. #26713C2semidirect
18. #26477C2semidirect
19. #26033C2semidirect
20. #25994C2semidirect
22. #25941C2semidirect
23. #25206C2semidirect
25. #24346C2semidirect
26. #24307C2semidirect
28. #22932C2semidirect
30. #22295C2semidirect
31. #22182C2semidirect
32. C2×#557C22semidirect
36. C2×#479C22semidirect
37. C2×#479C22semidirect
51. #2584C22semidirect
52. #2565C22semidirect
54. #2552C22semidirect
55. #2550C22semidirect
66. #2453C22semidirect
67. #2453C22semidirect
75. #2370C22semidirect
88. #2100C22semidirect
89. #2099C22semidirect
90. #2099C22semidirect
92. #2087C22semidirect
93. #2087C22semidirect
94. #2083C22semidirect
95. #2074C22semidirect
96. #2072C22semidirect
98. #2068C22semidirect
104. #2059C22semidirect
105. #2059C22semidirect
106. #2057C22semidirect
107. #2056C22semidirect
114. #2026C22semidirect
115. #2026C22semidirect
116. #2026C22semidirect
128. #1992C22semidirect
129. #1989C22semidirect
130. #1989C22semidirect
131. #1987C22semidirect
132. #1985C22semidirect
133. #1985C22semidirect
137. #1947C22semidirect
138. #1947C22semidirect
139. #1943C22semidirect
140. #1940C22semidirect
141. #1940C22semidirect
145. #1935C22semidirect
146. #1935C22semidirect
147. #1935C22semidirect
148. #1928C22semidirect
149. #1928C22semidirect
150. #1928C22semidirect
151. #1927C22semidirect
156. #1921C22semidirect
157. #1921C22semidirect
158. #1921C22semidirect
159. #1921C22semidirect
160. #1918C22semidirect
161. #1918C22semidirect
162. #1917C22semidirect
163. #1917C22semidirect
164. #1917C22semidirect
165. #1917C22semidirect
172. #1878C22semidirect
173. #1878C22semidirect
174. #1878C22semidirect
178. #1865C22semidirect
180. #1863C22semidirect
181. #1863C22semidirect
188. #1836C22semidirect
192. #1803C22semidirect
195. #1776C22semidirect
196. #1763C22semidirect

Maximal subgroups

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

subgroupindex
#594242
#591542
#326422
#325812
#324562
#322572
#318322
#316572
#311712
#308222
#281232
#277152
#274402
#272622
#271542
#269142
#267132
#264772
#260332
#259942
#259522
#259412
#252062
#250842
#243462
#243072
C2×#20252
#229322
#228542
#222952
#221822