Finite Group Databasebeta

← #6547883

Subgroups — #6547883

Order 512.

1708 conjugacy classes of subgroups.

The subgroup lattice has 1318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36290C211yesmaximal, characteristic, complemented
2#34320C211yesmaximal, characteristic
3#29994C211yesmaximal, characteristic, complemented
4#29958C211yesmaximal, characteristic, complemented
5#29956C211yesmaximal, characteristic, complemented
6#29244C211yesmaximal, characteristic, complemented
7#29234C211yesmaximal, characteristic, complemented
8#29198C211yesmaximal, characteristic, complemented
9#28285C211yesmaximal, characteristic, complemented
10#26545C211yesmaximal, characteristic, complemented
11#26477C211yesmaximal, characteristic, complemented
12#26437C211yesmaximal, characteristic, complemented
13#26418C211yesmaximal, characteristic, complemented
14#26361C211yesmaximal, characteristic, complemented
15#26344C211yesmaximal, characteristic, complemented
16#26103C211yesmaximal, characteristic, complemented
17#26037C211yesmaximal, characteristic, complemented
18#25969C211yesmaximal, characteristic, complemented
19#25969C211yesmaximal, characteristic, complemented
20#25960C211yesmaximal, characteristic, complemented
21#25952C211yesmaximal, characteristic, complemented
22#24841C211yesmaximal, characteristic, complemented
23#24840C211yesmaximal, characteristic, complemented
24#23784C211yesmaximal, characteristic, complemented
25#23617C211yesmaximal, characteristic, complemented
26C2×#2067C211yesmaximal, characteristic, complemented
27#22709C211yesmaximal, characteristic, complemented
28#22661C211yesmaximal, characteristic, complemented
29#22648C211yesmaximal, characteristic, complemented
30#22419C211yesmaximal, characteristic
31#22419C211yesmaximal, characteristic
32C2×#546C2211yescharacteristic
33C2×#479C2211yescharacteristic, complemented
34C2×#479C2211yescharacteristic, complemented
35C2×#478C2211yescharacteristic
36C2×#478C2211yescharacteristic
37C2×#435C2211yescharacteristic
38C2×#435C2211yescharacteristic
39C2×#428C2211yescharacteristic, complemented
40C22×#107C2211yescharacteristic
41C2×#423C2211yescharacteristic, complemented
42C22×C4⋊C8C2211yescharacteristic
43C2×#417C2211yescharacteristic
44C2×#417C2211yescharacteristic
45C22×#102C2211yescharacteristic
46C22×#102C2211yescharacteristic
47#2859C2211yescharacteristic, complemented
48#2851C2211yescharacteristic
49#2851C2211yescharacteristic, complemented
50#2571C2211yescharacteristic, complemented
51#2552C2211yescharacteristic, complemented
52#2509—21no—
53#2507—21no—
54#2505—21no—
55#2505—21no—
56#2473—21no—
57#2473—21no—
58#2442C2211yescharacteristic
59#2442C2211yescharacteristic
60#2442C2211yescharacteristic, complemented
61#2442C2211yescharacteristic, complemented
62#2374—21no—
63#2367C2211yescharacteristic
64#2363—21no—
65#2363C2211yescharacteristic
66#2360C2211yescharacteristic
67#2358—21no—
68#2357C2211yescharacteristic
69#2352C2211yescharacteristic
70#2349—21no—
71D4×C4⋊C4—21no—
72D4×C4⋊C4C2211yescharacteristic
73D4×C4⋊C4C2211yescharacteristic
74#2342—21no—
75#2341C2211yescharacteristic
76D4×C22⋊C4C2211yescharacteristic
77#2335—21no—
78#2333—21no—
79#2321—21no—
80C4×#125C2211yescharacteristic, complemented
81C4×#124C2211yescharacteristic
82C4×C22⋊Q8C2211yescharacteristic
83C4×#121C2211yescharacteristic
84#2297C2211yescharacteristic
85#2293C2211yescharacteristic
86C2×#390C2211yescharacteristic
87C2×#389C2211yescharacteristic
88C2×#389C2211yescharacteristic, complemented
89#2273—21no—
90C42×D4C2211yescharacteristic
91#2101C2211yescharacteristic, complemented
92#2097C2211yescharacteristic, complemented
93#2092C2211yescharacteristic
94#2092C2211yescharacteristic
95#2092C2211yescharacteristic
96#2092C2211yescharacteristic
97#2088C2211yescharacteristic, complemented
98#2086C2211yescharacteristic, complemented
99#2086C2211yescharacteristic, complemented
100#2086C2211yescharacteristic, complemented
101#2086C2211yescharacteristic, complemented
102#2086C2211yescharacteristic, complemented
103#2068C2211yescharacteristic, complemented
104#2068C2211yescharacteristic, complemented
105#2068C2211yescharacteristic, complemented
106#2067C2211yescharacteristic
107#2067C2211yescharacteristic
108#2067C2211yescharacteristic
109#2067C2211yescharacteristic
110#2067C2211yescharacteristic
111#2067C2211yescharacteristic
112#2067C2211yescharacteristic
113#2067C2211yescharacteristic
114#2067C2211yescharacteristic
115#2067C2211yescharacteristic
116#2067C2211yescharacteristic
117#2067C2211yescharacteristic
118#2066C2211yescharacteristic, complemented
119#2066C2211yescharacteristic, complemented
120#2066C2211yescharacteristic, complemented
121#2065C2211yescharacteristic
122#2065C2211yescharacteristic
123#2065C2211yescharacteristic
124#2065C2211yescharacteristic
125#2059C2211yescharacteristic, complemented
126#2026C2211yescharacteristic, complemented
127#2025C2211yescharacteristic
128#2025C2211yescharacteristic
129#2025C2211yescharacteristic
130#2025C2211yescharacteristic
131#1989C2211yescharacteristic, complemented
132#1989C2211yescharacteristic, complemented
133#1983C2211yescharacteristic
134#1983C2211yescharacteristic
135#1959C2211yescharacteristic
136#1959C2211yescharacteristic
137#1949C2211yescharacteristic, complemented
138#1949C2211yescharacteristic, complemented
139#1949C2211yescharacteristic, complemented
140#1949C2211yescharacteristic, complemented
141#1947C2211yescharacteristic, complemented
142#1947C2211yescharacteristic, complemented
143#1940C2211yescharacteristic, complemented
144#1940C2211yescharacteristic, complemented
145#1920C2211yescharacteristic, complemented
146#1920C2211yescharacteristic, complemented
147#1918C2211yescharacteristic, complemented
148#1918C2211yescharacteristic, complemented
149#1895C2211yescharacteristic
150#1895C2211yescharacteristic
151#1892C2211yescharacteristic
152#1892C2211yescharacteristic
153#1874C2211yescharacteristic
154#1874C2211yescharacteristic
155#1872C2211yescharacteristic
156#1872C2211yescharacteristic
157#1864C2211yescharacteristic
158#1864C2211yescharacteristic
159#1863C2211yescharacteristic, complemented
160#1863C2211yescharacteristic, complemented
161#1863C2211yescharacteristic, complemented
162#1863C2211yescharacteristic, complemented
163#1862C2211yescharacteristic
164#1862C2211yescharacteristic
165#1854C2211yescharacteristic, complemented
166#1854C2211yescharacteristic, complemented
167#1853C2211yescharacteristic
168#1853C2211yescharacteristic
169#1852C2211yescharacteristic
170#1852C2211yescharacteristic
171#1852C2211yescharacteristic, complemented
172#1852C2211yescharacteristic, complemented
173#1851C2211yescharacteristic, complemented
174#1851C2211yescharacteristic, complemented
175#1850C2211yescharacteristic
176#1850C2211yescharacteristic
177#1847C2211yescharacteristic, complemented
178#1842C2211yescharacteristic, complemented
179#1836C2211yescharacteristic, complemented
180#1809C2211yescharacteristic, complemented
181#1809C2211yescharacteristic, complemented
182#1808C2211yescharacteristic
183#1807C2211yescharacteristic
184#1805C2211yescharacteristic, complemented
185#1805C2211yescharacteristic, complemented
186#1804C2211yescharacteristic
187#1804C2211yescharacteristic
188#1802C2211yescharacteristic
189#1802C2211yescharacteristic
190#1797C2211yescharacteristic
191#1797C2211yescharacteristic, complemented
192#1788C2211yescharacteristic
193#1788C2211yescharacteristic
194#1786C2211yescharacteristic
195#1786C2211yescharacteristic
196#1776C2211yescharacteristic, complemented
197#1776C2211yescharacteristic, complemented
198#1767C2211yescharacteristic, complemented
199#1762C2211yescharacteristic
200#1762C2211yescharacteristic
201#1736C2211yescharacteristic, complemented
202C2×#340C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209#546—24no—
210#546Q818yes—
211C2×#125—21no—
212C2×#125C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×#124C2311yescharacteristic
216C2×#123—21no—
217C2×C22⋊Q8C2311yescharacteristic
218C2×#121—21no—
219C2×#121C2311yescharacteristic
220C2×#120—21no—
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×D4—21no—
224C2×C4×D4—21no—
225C2×C4×D4—21no—
226C2×C4×D4D411yescharacteristic
227C2×C4×D4D411yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×#117—21no—
233C2×#117C2311yescharacteristic
234C22×C4⋊C4—21no—
235C22×C4⋊C4—21no—
236C22×C4⋊C4C2311yescharacteristic
237C22×C4⋊C4C2311yescharacteristic
238C22×C4⋊C4C2311yescharacteristic
239C22×C4⋊C4C2311yescharacteristic
240C22×C4⋊C4C2311yescharacteristic
241C22×C22⋊C4—21no—
242C22×C22⋊C4—21no—
243C22×C22⋊C4—21no—
244C22×C22⋊C4—21no—
245C22×C42C2311yescharacteristic
246C22×C42C2311yescharacteristic
247#479—42no—
248#479—42no—
249#478—42no—
250#478—42no—
251#435—24no—
252#435—24no—
253#428—42no—
254C2×#107—42no—
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271#423—42no—
272C2×C4⋊C8—42no—
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285#417—42no—
286#417—42no—
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#102—42no—
296C2×#102—42no—
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×#97C2311yescharacteristic
318C2×#97C2311yescharacteristic
319#400—21no—
320#400—21no—
321#400—21no—
322#400—21no—
323#400—21no—
324#400—21no—
325#398—21no—
326#398—21no—
327#398—21no—
328#398—21no—
329#398—21no—
330#398—21no—
331#391C2311yescharacteristic
332#391C2311yescharacteristic
333#390—21no—
334#390—21no—
335#390—21no—
336#390—21no—
337#390—21no—
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#389—21no—
345#389—21no—
346#389—21no—
347#389—21no—
348#389—21no—
349#389—21no—
350#389—21no—
351#389—21no—
352#389—21no—
353#389—21no—
354#389—21no—
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#386—21no—
388#386—21no—
389#386—21no—
390#386—21no—
391#386—21no—
392#386—21no—
393#386—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#384—21no—
410#384C2311yescharacteristic
411#384C2311yescharacteristic
412#382—21no—
413#382—21no—
414#382C2311yescharacteristic
415#382C2311yescharacteristic
416#382C2311yescharacteristic
417#382C2311yescharacteristic
418#381—21no—
419#380—21no—
420#380—21no—
421#380—21no—
422#380—21no—
423#380—21no—
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#379—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4D411yescharacteristic
435C4×C4⋊C4D411yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
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⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4D411yescharacteristic
456C4×C22⋊C4D411yescharacteristic
457C4×C22⋊C4D411yescharacteristic
458C4×C22⋊C4D411yescharacteristic
459C4×C22⋊C4C2311yescharacteristic
460C4×C22⋊C4C2311yescharacteristic
461C2×#95—21no—
462C2×#95—21no—
463C43C2311yescharacteristic
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#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494C25—21no—
495C2×#41—22no—
496C2×#41—41no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C2×#41C2×Q814yes—
501C22×Q8C2411yescharacteristic
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—22no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4C2×D411yescharacteristic
511C22×D4C2×Q814yes—
512C22×D4C2411yescharacteristic
513C22×D4C2411yescharacteristic
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4C2×D411yescharacteristic
524C23×C4C2×D411yescharacteristic
525C23×C4C2×D411yescharacteristic
526C23×C4C2×D411yescharacteristic
527C23×C4C2411yescharacteristic
528C23×C4C2411yescharacteristic
529C2×M16—22no—
530C2×M16—22no—
531C2×M16—22no—
532C2×M16—41no—
533C2×M16—41no—
534C2×M16—41no—
535C22×C8—22no—
536C22×C8—22no—
537C22×C8—22no—
538C22×C8—41no—
539C22×C8—41no—
540C22×C8—41no—
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549#125—22no—
550#125—41no—
551#125—41no—
552#125—41no—
553#125—41no—
554#125—41no—
555#125—82no—
556#124—22no—
557#124C2×Q814yes—
558#123—28no—
559C22⋊Q8—22no—
560C22⋊Q8C2×Q814yes—
561#121—22no—
562#121—28no—
563#121C2×Q814yes—
564#120—28no—
565C4×Q8—41no—
566C4×Q8—41no—
567C4×Q8—41no—
568C4×Q8—41no—
569C4×D4—22no—
570C4×D4—41no—
571C4×D4—41no—
572C4×D4—41no—
573C4×D4—41no—
574C4×D4—42no—
575C4×D4—42no—
576C4×D4—44no—
577C4×D4—44no—
578C4×D4—82no—
579C4×D4C2×Q814yes—
580C4×D4C2×Q814yes—
581C4×D4#4114yes—
582#117—41no—
583#117—41no—
584#117—82no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—22no—
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—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—41no—
618C2×C4⋊C4—41no—
619C2×C4⋊C4—41no—
620C2×C4⋊C4—41no—
621C2×C4⋊C4—41no—
622C2×C4⋊C4—41no—
623C2×C4⋊C4—41no—
624C2×C4⋊C4—41no—
625C2×C4⋊C4—82no—
626C2×C4⋊C4—82no—
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—28no—
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—44no—
671C2×C22⋊C4—44no—
672C2×C22⋊C4—82no—
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C22⋊C4C2×D411yescharacteristic
675C2×C22⋊C4C2×D411yescharacteristic
676C2×C22⋊C4C2×D411yescharacteristic
677C2×C22⋊C4C2×D411yescharacteristic
678C2×C22⋊C4C2×D411yescharacteristic
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—21no—
682C2×C42—21no—
683C2×C42—21no—
684C2×C42—21no—
685C2×C42—21no—
686C2×C42—21no—
687C2×C42—41no—
688C2×C42—41no—
689C2×C42—41no—
690C2×C42—41no—
691C2×C42C2×D411yescharacteristic
692C2×C42C2×D411yescharacteristic
693C2×C42C2×D411yescharacteristic
694C2×C42C2×D411yescharacteristic
695C2×C42C2×D411yescharacteristic
696C2×C42C2×D411yescharacteristic
697C2×C42C2×D411yescharacteristic
698C2×C42C2×D411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704#107—22no—
705#107—22no—
706#107—41no—
707#107—41no—
708#107—41no—
709#107—41no—
710#107—41no—
711#107—41no—
712#107—41no—
713#107—41no—
714#106—22no—
715#106—22no—
716#106—41no—
717#106—41no—
718#106—41no—
719#106—41no—
720C4⋊C8—22no—
721C4⋊C8—22no—
722C4⋊C8—22no—
723C4⋊C8—22no—
724C4⋊C8—22no—
725C4⋊C8—41no—
726C4⋊C8—41no—
727C4⋊C8—41no—
728C4⋊C8—41no—
729C4⋊C8—41no—
730C4⋊C8—41no—
731C4⋊C8—41no—
732#103—22no—
733#103—22no—
734#103—41no—
735#103—41no—
736#103—41no—
737#103—41no—
738#103—41no—
739#103—41no—
740#102—22no—
741#102—22no—
742#102—22no—
743#102—22no—
744#102—41no—
745#102—41no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756C22⋊C8—22no—
757C22⋊C8—22no—
758C22⋊C8—22no—
759C22⋊C8—22no—
760#97—22no—
761#97—22no—
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#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803C24—21no—
804C24—21no—
805C24—24no—
806C24—42no—
807C24—42no—
808C24—81no—
809C24—81no—
810C24—81no—
811C24—81no—
812C24C22×D411yescharacteristic
813C24C22×D411yescharacteristic
814#41—44no—
815#41—44no—
816#41—82no—
817#41—82no—
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8C22×Q812yes—
824C2×D4—22no—
825C2×D4—22no—
826C2×D4—24no—
827C2×D4—24no—
828C2×D4—24no—
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—21no—
838C2×D4—21no—
839C2×D4—44no—
840C2×D4—44no—
841C2×D4—82no—
842C2×D4—82no—
843C2×D4—81no—
844C2×D4—81no—
845C2×D4—81no—
846C2×D4—81no—
847C2×D4—81no—
848C2×D4—81no—
849C2×D4C22⋊Q814yes—
850C2×D4C22×Q812yes—
851C2×D4C22×Q812yes—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—22no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—24no—
867C22×C4—24no—
868C22×C4—22no—
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—41no—
881C22×C4—41no—
882C22×C4—41no—
883C22×C4—41no—
884C22×C4—41no—
885C22×C4—41no—
886C22×C4—41no—
887C22×C4—41no—
888C22×C4—42no—
889C22×C4—42no—
890C22×C4—42no—
891C22×C4—42no—
892C22×C4—42no—
893C22×C4—42no—
894C22×C4—42no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—81no—
898C22×C4—81no—
899C22×C4—81no—
900C22×C4—81no—
901C22×C4—81no—
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×C4—81no—
912C22×C4—81no—
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×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×Q812yes—
926C22×C4C22×Q812yes—
927C22×C4C2×#4112yes—
928C22×C4C2×#4112yes—
929C22×C4C2511yescharacteristic
930M16—44no—
931M16—82no—
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—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—44no—
956C2×C8—82no—
957C2×C8H(5,𝔽2)12yes—
958C4⋊C4—24no—
959C4⋊C4—21no—
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—41no—
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—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4C22⋊Q814yes—
1015C4⋊C4C22×Q812yes—
1016C4⋊C4H(5,𝔽2)12yes—
1017C22⋊C4—24no—
1018C22⋊C4—22no—
1019C22⋊C4—22no—
1020C22⋊C4—24no—
1021C22⋊C4—24no—
1022C22⋊C4—24no—
1023C22⋊C4—24no—
1024C22⋊C4—41no—
1025C22⋊C4—41no—
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—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
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⋊C4C22⋊Q814yes—
1048C22⋊C4C22⋊Q814yes—
1049C42—22no—
1050C42—21no—
1051C42—21no—
1052C42—21no—
1053C42—21no—
1054C42—21no—
1055C42—21no—
1056C42—21no—
1057C42—21no—
1058C42—41no—
1059C42—41no—
1060C42—41no—
1061C42—41no—
1062C42—41no—
1063C42—41no—
1064C42—41no—
1065C42—42no—
1066C42—42no—
1067C42—81no—
1068C42—81no—
1069C42—81no—
1070C42—81no—
1071C42—81no—
1072C42—81no—
1073C42C22×Q812yes—
1074C42C2×#4112yes—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—22no—
1086C23—22no—
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—48no—
1100C23—84no—
1101C23—84no—
1102C23—162no—
1103C23—162no—
1104C23—162no—
1105C23—162no—
1106C23C2×C22⋊Q812yes—
1107C23C2×C22⋊Q812yes—
1108C23#57512yes—
1109C23#57512yes—
1110C23C23×D411yescharacteristic
1111Q8—22no—
1112Q8—22no—
1113Q8—41no—
1114Q8—41no—
1115D4—28no—
1116D4—22no—
1117D4—22no—
1118D4—22no—
1119D4—22no—
1120D4—41no—
1121D4—41no—
1122D4—41no—
1123D4—41no—
1124D4—84no—
1125D4—84no—
1126D4—84no—
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—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—22no—
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—44no—
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—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—82no—
1210C2×C4—84no—
1211C2×C4—84no—
1212C2×C4—82no—
1213C2×C4—82no—
1214C2×C4—84no—
1215C2×C4—84no—
1216C2×C4—162no—
1217C2×C4—162no—
1218C2×C4—162no—
1219C2×C4—162no—
1220C2×C4—162no—
1221C2×C4C2×C22⋊Q812yes—
1222C2×C4C2×C22⋊Q812yes—
1223C2×C4C2×C22⋊Q812yes—
1224C2×C4C2×C22⋊Q812yes—
1225C2×C4#57612yes—
1226C2×C4C23×Q811yescharacteristic
1227C2×C4C22×#4111yescharacteristic
1228C2×C4C2×H(5,𝔽2)11yescharacteristic
1229C2×C4C2×H(5,𝔽2)11yescharacteristic
1230C2×C4#58511yescharacteristic
1231C2×C4#58511yescharacteristic
1232C8—22no—
1233C8—41no—
1234C8—41no—
1235C8—41no—
1236C8—41no—
1237C8—41no—
1238C8—41no—
1239C8—41no—
1240C22—22no—
1241C22—22no—
1242C22—22no—
1243C22—22no—
1244C22—22no—
1245C22—22no—
1246C22—22no—
1247C22—22no—
1248C22—22no—
1249C22—41no—
1250C22—41no—
1251C22—41no—
1252C22—41no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—168no—
1268C22#308014yes—
1269C22C22×C22⋊Q811yescharacteristic
1270C22#348811yescharacteristic
1271C22#349611yescharacteristic
1272C22C2×#57511yescharacteristic
1273C22C2×#57511yescharacteristic
1274C22C2×#57611yescharacteristic
1275C22#358611yescharacteristic
1276C4—22no—
1277C4—22no—
1278C4—22no—
1279C4—22no—
1280C4—22no—
1281C4—41no—
1282C4—41no—
1283C4—42no—
1284C4—41no—
1285C4—41no—
1286C4—42no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—42no—
1291C4—81no—
1292C4—81no—
1293C4—81no—
1294C4—81no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C4—81no—
1300C4—81no—
1301C4—81no—
1302C4#350111yescharacteristic
1303C4#350111yescharacteristic
1304C4#351911yescharacteristic
1305C4#352111yescharacteristic
1306C2—24no—
1307C2—42no—
1308C2—82no—
1309C2—82no—
1310C2#3577611yescharacteristic
1311C2C2×#308011yescharacteristic
1312C2#6049411yescharacteristic
1313C2#6197211yescharacteristic
1314C2#6197711yescharacteristic
1315C2#6225711yescharacteristic
1316C2#6229711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#546C22
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. #36290C2semidirect
3. #29994C2semidirect
4. #29958C2semidirect
5. #29956C2semidirect
6. #29244C2semidirect
7. #29234C2semidirect
8. #29198C2semidirect
9. #28285C2semidirect
10. #26545C2semidirect
11. #26477C2semidirect
12. #26437C2semidirect
13. #26418C2semidirect
14. #26361C2semidirect
15. #26344C2semidirect
16. #26103C2semidirect
17. #26037C2semidirect
18. #25969C2semidirect
19. #25969C2semidirect
20. #25960C2semidirect
21. #25952C2semidirect
22. #24841C2semidirect
23. #24840C2semidirect
24. #23784C2semidirect
25. #23617C2semidirect
26. C2×#2067C2semidirect
27. #22709C2semidirect
28. #22661C2semidirect
29. #22648C2semidirect
33. C2×#479C22semidirect
34. C2×#479C22semidirect
39. C2×#428C22semidirect
41. C2×#423C22semidirect
47. #2859C22semidirect
49. #2851C22semidirect
50. #2571C22semidirect
51. #2552C22semidirect
60. #2442C22semidirect
61. #2442C22semidirect
80. C4×#125C22semidirect
88. C2×#389C22semidirect
91. #2101C22semidirect
92. #2097C22semidirect
97. #2088C22semidirect
98. #2086C22semidirect
99. #2086C22semidirect
100. #2086C22semidirect
101. #2086C22semidirect
102. #2086C22semidirect
103. #2068C22semidirect
104. #2068C22semidirect
105. #2068C22semidirect
118. #2066C22semidirect
119. #2066C22semidirect
120. #2066C22semidirect
125. #2059C22semidirect
126. #2026C22semidirect
131. #1989C22semidirect
132. #1989C22semidirect
137. #1949C22semidirect
138. #1949C22semidirect
139. #1949C22semidirect
140. #1949C22semidirect
141. #1947C22semidirect
142. #1947C22semidirect
143. #1940C22semidirect
144. #1940C22semidirect
145. #1920C22semidirect
146. #1920C22semidirect
147. #1918C22semidirect
148. #1918C22semidirect
159. #1863C22semidirect
160. #1863C22semidirect
161. #1863C22semidirect
162. #1863C22semidirect
165. #1854C22semidirect
166. #1854C22semidirect
171. #1852C22semidirect
172. #1852C22semidirect
173. #1851C22semidirect
174. #1851C22semidirect
177. #1847C22semidirect
178. #1842C22semidirect
179. #1836C22semidirect
180. #1809C22semidirect
181. #1809C22semidirect
184. #1805C22semidirect
185. #1805C22semidirect
191. #1797C22semidirect
196. #1776C22semidirect
197. #1776C22semidirect
198. #1767C22semidirect
201. #1736C22semidirect

Maximal subgroups

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

subgroupindex
#362902
#343202
#299942
#299582
#299562
#292442
#292342
#291982
#282852
#265452
#264772
#264372
#264182
#263612
#263442
#261032
#260372
#259692
#259602
#259522
#248412
#248402
#237842
#236172
C2×#20672
#227092
#226612
#226482
#224192