Finite Group Databasebeta

← #6579852

Subgroups — #6579852

Order 512.

1784 conjugacy classes of subgroups.

The subgroup lattice has 1373 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36017C211yesmaximal, characteristic, complemented
2#35821C211yesmaximal, characteristic
3#33115C211yesmaximal, characteristic, complemented
4#33047C211yesmaximal, characteristic, complemented
5#32968C211yesmaximal, characteristic, complemented
6#29058C211yesmaximal, characteristic, complemented
7#29042C211yesmaximal, characteristic, complemented
8#27761C211yesmaximal, characteristic, complemented
9#27547C211yesmaximal, characteristic, complemented
10#27536C211yesmaximal, characteristic, complemented
11#27421C211yesmaximal, characteristic, complemented
12#27420C211yesmaximal, characteristic, complemented
13#26208C211yesmaximal, characteristic, complemented
14#26206C211yesmaximal, characteristic, complemented
15#26107C211yesmaximal, characteristic, complemented
16#25890C211yesmaximal, characteristic, complemented
17#25357C211yesmaximal, characteristic, complemented
18#25283C211yesmaximal, characteristic, complemented
19#25261C211yesmaximal, characteristic, complemented
20#25245C211yesmaximal, characteristic, complemented
21#24970C211yesmaximal, characteristic, complemented
22#24043C211yesmaximal, characteristic, complemented
23#24037C211yesmaximal, characteristic, complemented
24#22974C211yesmaximal, characteristic, complemented
25#22580C211yesmaximal, characteristic, complemented
26#22572C211yesmaximal, characteristic, complemented
27#22427C211yesmaximal, characteristic, complemented
28#22424C211yesmaximal, characteristic, complemented
29#22420C211yesmaximal, characteristic, complemented
30#21496C211yesmaximal, characteristic, complemented
31#20415C211yesmaximal, characteristic, complemented
32C2×#547C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#546C2211yescharacteristic
35C2×#520C2211yescharacteristic
36C2×#488C2211yescharacteristic
37C2×#485C2211yescharacteristic, complemented
38C2×#482C2211yescharacteristic
39C2×#479C2211yescharacteristic, complemented
40C2×#478C2211yescharacteristic
41C2×#436C2211yescharacteristic
42C2×#435C2211yescharacteristic
43C2×#435C2211yescharacteristic, complemented
44C2×#417C2211yescharacteristic
45C2×#418C2211yescharacteristic
46C2×#416C2211yescharacteristic
47C2×#416C2211yescharacteristic
48C2×#405C2211yescharacteristic, complemented
49#2648—21no—
50#2629C2211yescharacteristic, complemented
51#2620C2211yescharacteristic
52#2618—21no—
53#2594—21no—
54#2593—21no—
55#2571C2211yescharacteristic, complemented
56#2562C2211yescharacteristic
57#2545C2211yescharacteristic
58#2538C2211yescharacteristic
59#2534—21no—
60#2529—21no—
61#2524—21no—
62#2518—21no—
63#2518—21no—
64#2495C2211yescharacteristic, complemented
65#2494C2211yescharacteristic
66#2485C2211yescharacteristic
67#2485C2211yescharacteristic, complemented
68#2429C2211yescharacteristic
69#2426C2211yescharacteristic
70#2425—21no—
71#2424—21no—
72#2417C2211yescharacteristic
73#2416—21no—
74#2416C2211yescharacteristic
75#2413—21no—
76#2411—21no—
77#2401—21no—
78#2392C2211yescharacteristic
79C2×#396—21no—
80#2370C2211yescharacteristic, complemented
81#2354C2211yescharacteristic
82#2352C2211yescharacteristic
83#2352C2211yescharacteristic, complemented
84D4×C4⋊C4C2211yescharacteristic
85#2347C2211yescharacteristic
86#2346C2211yescharacteristic, complemented
87#2339C2211yescharacteristic
88D4×C22⋊C4C2211yescharacteristic
89#2274C2211yescharacteristic, complemented
90#2101C2211yescharacteristic, complemented
91#2101C2211yescharacteristic, complemented
92#2088C2211yescharacteristic, complemented
93#2088C2211yescharacteristic, complemented
94#2077C2211yescharacteristic
95#2076C2211yescharacteristic, complemented
96#2075C2211yescharacteristic
97#2075C2211yescharacteristic, complemented
98#2074C2211yescharacteristic, complemented
99#2073C2211yescharacteristic
100#2068C2211yescharacteristic, complemented
101#2065C2211yescharacteristic
102#2043C2211yescharacteristic, complemented
103#2043C2211yescharacteristic, complemented
104#2042C2211yescharacteristic
105#2042C2211yescharacteristic
106#2036C2211yescharacteristic
107#2036C2211yescharacteristic
108#2036C2211yescharacteristic, complemented
109#2035C2211yescharacteristic
110#2035C2211yescharacteristic
111#2035C2211yescharacteristic, complemented
112#2034C2211yescharacteristic
113#2033C2211yescharacteristic
114#1992C2211yescharacteristic, complemented
115#1983C2211yescharacteristic
116#1983C2211yescharacteristic
117#1983C2211yescharacteristic
118#1981C2211yescharacteristic, complemented
119#1960C2211yescharacteristic, complemented
120#1959C2211yescharacteristic
121#1958C2211yescharacteristic
122#1954C2211yescharacteristic
123#1948C2211yescharacteristic, complemented
124#1947C2211yescharacteristic, complemented
125#1944C2211yescharacteristic, complemented
126#1942C2211yescharacteristic, complemented
127#1939C2211yescharacteristic, complemented
128#1936C2211yescharacteristic
129#1936C2211yescharacteristic
130#1935C2211yescharacteristic, complemented
131#1934C2211yescharacteristic
132#1933C2211yescharacteristic, complemented
133#1933C2211yescharacteristic, complemented
134#1928C2211yescharacteristic, complemented
135#1927C2211yescharacteristic, complemented
136#1927C2211yescharacteristic, complemented
137#1926C2211yescharacteristic
138#1925C2211yescharacteristic
139#1925C2211yescharacteristic
140#1924C2211yescharacteristic
141#1924C2211yescharacteristic, complemented
142#1921C2211yescharacteristic, complemented
143#1919C2211yescharacteristic, complemented
144#1895C2211yescharacteristic
145#1894C2211yescharacteristic
146#1894C2211yescharacteristic
147#1894C2211yescharacteristic, complemented
148#1893C2211yescharacteristic
149#1893C2211yescharacteristic
150#1892C2211yescharacteristic, complemented
151#1892C2211yescharacteristic, complemented
152#1875C2211yescharacteristic
153#1874C2211yescharacteristic
154#1873C2211yescharacteristic
155#1873C2211yescharacteristic
156#1873C2211yescharacteristic, complemented
157#1872C2211yescharacteristic, complemented
158#1869C2211yescharacteristic
159#1869C2211yescharacteristic, complemented
160#1865C2211yescharacteristic, complemented
161#1864C2211yescharacteristic
162#1864C2211yescharacteristic
163#1864C2211yescharacteristic
164#1863C2211yescharacteristic, complemented
165#1862C2211yescharacteristic
166#1862C2211yescharacteristic
167#1862C2211yescharacteristic
168#1853C2211yescharacteristic, complemented
169#1852C2211yescharacteristic, complemented
170#1834C2211yescharacteristic, complemented
171#1825C2211yescharacteristic
172#1825C2211yescharacteristic, complemented
173#1809C2211yescharacteristic
174#1807C2211yescharacteristic, complemented
175#1804C2211yescharacteristic
176#1804C2211yescharacteristic
177#1803C2211yescharacteristic, complemented
178#1802C2211yescharacteristic
179#1798C2211yescharacteristic, complemented
180#1788C2211yescharacteristic
181#1788C2211yescharacteristic
182#1788C2211yescharacteristic
183#1788C2211yescharacteristic
184#1788C2211yescharacteristic
185#1786C2211yescharacteristic
186#1786C2211yescharacteristic
187#1786C2211yescharacteristic
188#1771C2211yescharacteristic, complemented
189#1763C2211yescharacteristic, complemented
190#1763C2211yescharacteristic, complemented
191#1762C2211yescharacteristic
192#1762C2211yescharacteristic
193#1762C2211yescharacteristic
194C4×#103C2211yescharacteristic, complemented
195C4×#103C2211yescharacteristic, complemented
196C4×#102C2211yescharacteristic
197C4×#102C2211yescharacteristic
198C4×#102C2211yescharacteristic
199#1753C2211yescharacteristic
200C8×C22⋊C4C2211yescharacteristic, complemented
201#1736C2211yescharacteristic, complemented
202C2×#340C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C22×#41C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C23×C8C2311yescharacteristic
210#547—24no—
211#547—42no—
212#546—24no—
213#546—24no—
214#546—42no—
215#546—42no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×#125C2311yescharacteristic
218C2×#124C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×#123—21no—
221C2×#123—21no—
222C2×#123—21no—
223C2×#123—21no—
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×#121—21no—
229C2×#121—21no—
230C2×#121—21no—
231C2×#121—21no—
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#120—21no—
235C2×#120—21no—
236#520—24no—
237#520—42no—
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×D4—21no—
241C2×C4×D4—21no—
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×#117—21no—
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C22×C4⋊C4—21no—
255C22×C4⋊C4—21no—
256C22×C4⋊C4—21no—
257C22×C4⋊C4C2311yescharacteristic
258C22×C4⋊C4C2311yescharacteristic
259C22×C22⋊C4—21no—
260C22×C22⋊C4—21no—
261C22×C22⋊C4—21no—
262#488—42no—
263#485—42no—
264#482—42no—
265#479—42no—
266#478—24no—
267#436—42no—
268#435—42no—
269#435—42no—
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282#418—24no—
283#417—24no—
284#416—24no—
285#416—24no—
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326#405—42no—
327C2×#97C2311yescharacteristic
328C2×#97C2311yescharacteristic
329C2×#97C2311yescharacteristic
330C2×C4×C8C2311yescharacteristic
331C2×C4×C8C2311yescharacteristic
332C2×C4×C8C2311yescharacteristic
333#401—21no—
334#400—21no—
335#400—21no—
336#400—21no—
337#400—21no—
338#398—21no—
339#398—21no—
340#398—21no—
341#398—21no—
342#398D411yescharacteristic
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397D411yescharacteristic
348#396—21no—
349#396—21no—
350#396—21no—
351#396—21no—
352#396—21no—
353#396—21no—
354#396—21no—
355#396—21no—
356#396—21no—
357#396—21no—
358#396—21no—
359#396—21no—
360#396D411yescharacteristic
361#396D411yescharacteristic
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#394—21no—
368#394—21no—
369#394D411yescharacteristic
370#394D411yescharacteristic
371#394D411yescharacteristic
372#392D411yescharacteristic
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#390—21no—
376#390—21no—
377#390—21no—
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#389—21no—
381#389—21no—
382#389—21no—
383#389—21no—
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#385—21no—
426#385—21no—
427#384C2311yescharacteristic
428#384C2311yescharacteristic
429#383—21no—
430#383—21no—
431#382—21no—
432#382—21no—
433#382C2311yescharacteristic
434#382C2311yescharacteristic
435#381—21no—
436#380—21no—
437#380—21no—
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#379—21no—
449C4×C4⋊C4—21no—
450C4×C4⋊C4—21no—
451C4×C4⋊C4—21no—
452C4×C4⋊C4—21no—
453C4×C4⋊C4—21no—
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
463C4×C22⋊C4—21no—
464C4×C22⋊C4—21no—
465C4×C22⋊C4C2311yescharacteristic
466C4×C22⋊C4C2311yescharacteristic
467#376—21no—
468C2×#95—21no—
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#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—41no—
510C2×#41—41no—
511C2×#41#4114yes—
512C22×Q8C2411yescharacteristic
513C22×Q8C2411yescharacteristic
514C22×D4—21no—
515C22×D4—22no—
516C22×D4—22no—
517C22×D4—22no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—41no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4C2×D411yescharacteristic
526C22×D4C2×D411yescharacteristic
527C22×D4C2×D411yescharacteristic
528C22×D4C2411yescharacteristic
529C22×D4C2411yescharacteristic
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4C2411yescharacteristic
539C23×C4C2411yescharacteristic
540C23×C4C2411yescharacteristic
541C2×M16—22no—
542C2×M16—22no—
543C2×M16—22no—
544C2×M16—41no—
545C2×M16—41no—
546C2×M16—41no—
547C22×C8—22no—
548C22×C8—22no—
549C22×C8—41no—
550C22×C8—41no—
551C22×C8—41no—
552C22×C8—41no—
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C4⋊Q8—22no—
562C4⋊Q8—41no—
563#125—22no—
564#125—22no—
565#124—22no—
566#124—22no—
567#124—22no—
568#124—41no—
569#123—44no—
570#123—44no—
571#123—44no—
572#123—44no—
573C22⋊Q8—22no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8—41no—
579C22⋊Q8—41no—
580C22⋊Q8—41no—
581#121—22no—
582#121—22no—
583#121—22no—
584#121—44no—
585#121—44no—
586#121—41no—
587#121—44no—
588#121—82no—
589#120—44no—
590#120—44no—
591C4×Q8—22no—
592C4×Q8—22no—
593C4×Q8—22no—
594C4×Q8—41no—
595C4×D4—22no—
596C4×D4—22no—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—41no—
606C4×D4—41no—
607C4×D4—41no—
608C4×D4—44no—
609C4×D4—44no—
610C4×D4#4114yes—
611#117—22no—
612#117—22no—
613#117—22no—
614#117—22no—
615#117—22no—
616#117—22no—
617#117—44no—
618#117—41no—
619#117—41no—
620C2×C4⋊C4—22no—
621C2×C4⋊C4—22no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—41no—
647C2×C4⋊C4—41no—
648C2×C4⋊C4—44no—
649C2×C4⋊C4—44no—
650C2×C4⋊C4—82no—
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—44no—
702C2×C22⋊C4—44no—
703C2×C22⋊C4—82no—
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—21no—
720C2×C42—21no—
721C2×C42—21no—
722C2×C42—21no—
723C2×C42—21no—
724C2×C42—21no—
725C2×C42—21no—
726C2×C42—21no—
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731#107—22no—
732#107—41no—
733#107—41no—
734#107—41no—
735#106—22no—
736#106—41no—
737#106—41no—
738#106—41no—
739C4⋊C8—22no—
740C4⋊C8—22no—
741C4⋊C8—41no—
742C4⋊C8—41no—
743#103—22no—
744#103—22no—
745#103—22no—
746#103—22no—
747#103—22no—
748#103—22no—
749#103—41no—
750#103—41no—
751#103—41no—
752#103—41no—
753#103—41no—
754#103—41no—
755#103—41no—
756#103—41no—
757#103—41no—
758#103—41no—
759#102—22no—
760#102—22no—
761#102—22no—
762#102—22no—
763#102—22no—
764#102—22no—
765#102—22no—
766#102—22no—
767#102—22no—
768#102—41no—
769#102—41no—
770#102—41no—
771#102—41no—
772#102—41no—
773#102—41no—
774#102#4114yes—
775C22⋊C8—22no—
776C22⋊C8—22no—
777C22⋊C8—41no—
778C22⋊C8—41no—
779C22⋊C8—41no—
780C22⋊C8—41no—
781C22⋊C8—41no—
782C22⋊C8—41no—
783#97—22no—
784#97—41no—
785#97—41no—
786C4×C8—22no—
787C4×C8—41no—
788C4×C8—41no—
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#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827C24—21no—
828C24—21no—
829C24—42no—
830C24—42no—
831C24—42no—
832C24—42no—
833C24—81no—
834C24—81no—
835C24—81no—
836C24C22×D411yescharacteristic
837C24C22×D411yescharacteristic
838C24C22×D411yescharacteristic
839#41—28no—
840#41—44no—
841#41—44no—
842#41—44no—
843#41—44no—
844#41—82no—
845#41—82no—
846#41—82no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8C2×#4112yes—
859C2×D4—24no—
860C2×D4—22no—
861C2×D4—22no—
862C2×D4—22no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—41no—
873C2×D4—41no—
874C2×D4—41no—
875C2×D4—41no—
876C2×D4—41no—
877C2×D4—41no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—42no—
882C2×D4—42no—
883C2×D4—42no—
884C2×D4—44no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—82no—
890C2×D4—82no—
891C2×D4—82no—
892C2×D4—81no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4—81no—
896C2×D4C2×#4112yes—
897C2×D4C2×#4112yes—
898C2×D4C2×#4112yes—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—24no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—24no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—42no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—42no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4—81no—
951C22×C4—81no—
952C22×C4—81no—
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D411yescharacteristic
961C22×C4C22×D411yescharacteristic
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C2×#4112yes—
965C22×C4H(5,𝔽2)12yes—
966C22×C4C2511yescharacteristic
967M16—44no—
968M16—82no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—44no—
993C2×C8—82no—
994C2×C8C2×#4112yes—
995C4⋊C4—22no—
996C4⋊C4—22no—
997C4⋊C4—22no—
998C4⋊C4—22no—
999C4⋊C4—22no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—41no—
1023C4⋊C4—41no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4C2×#4112yes—
1049C4⋊C4C2×#4112yes—
1050C22⋊C4—22no—
1051C22⋊C4—22no—
1052C22⋊C4—24no—
1053C22⋊C4—22no—
1054C22⋊C4—22no—
1055C22⋊C4—22no—
1056C22⋊C4—22no—
1057C22⋊C4—22no—
1058C22⋊C4—22no—
1059C22⋊C4—41no—
1060C22⋊C4—41no—
1061C22⋊C4—41no—
1062C22⋊C4—41no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C42—21no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—42no—
1100C42—42no—
1101C42—42no—
1102C42—42no—
1103C42—42no—
1104C42—81no—
1105C42—81no—
1106C42—81no—
1107C42—81no—
1108C42—81no—
1109C42—81no—
1110C42C2×#4112yes—
1111C42H(5,𝔽2)12yes—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—22no—
1118C23—22no—
1119C23—21no—
1120C23—22no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—21no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—84no—
1147C23—84no—
1148C23—84no—
1149C23—84no—
1150C23—162no—
1151C23—162no—
1152C23—162no—
1153C23#54612yes—
1154C23C23×D411yescharacteristic
1155Q8—22no—
1156Q8—22no—
1157Q8—41no—
1158Q8—41no—
1159Q8—41no—
1160Q8—41no—
1161Q8—41no—
1162Q8—41no—
1163D4—22no—
1164D4—22no—
1165D4—22no—
1166D4—48no—
1167D4—41no—
1168D4—41no—
1169D4—41no—
1170D4—41no—
1171D4—82no—
1172D4—82no—
1173D4—82no—
1174D4—84no—
1175D4—84no—
1176D4—162no—
1177D4—162no—
1178D4#52914yes—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—22no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—48no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—84no—
1265C2×C4—84no—
1266C2×C4—84no—
1267C2×C4—162no—
1268C2×C4—162no—
1269C2×C4—162no—
1270C2×C4—162no—
1271C2×C4#54612yes—
1272C2×C4#54612yes—
1273C2×C4#54612yes—
1274C2×C4C22×#4111yescharacteristic
1275C2×C4C22×#4111yescharacteristic
1276C2×C4C22×#4111yescharacteristic
1277C2×C4C2×H(5,𝔽2)11yescharacteristic
1278C2×C4C2×H(5,𝔽2)11yescharacteristic
1279C2×C4#58511yescharacteristic
1280C8—22no—
1281C8—41no—
1282C8—41no—
1283C8—41no—
1284C8—41no—
1285C8—41no—
1286C8—41no—
1287C8—41no—
1288C22—22no—
1289C22—24no—
1290C22—22no—
1291C22—22no—
1292C22—42no—
1293C22—41no—
1294C22—42no—
1295C22—42no—
1296C22—42no—
1297C22—41no—
1298C22—41no—
1299C22—42no—
1300C22—41no—
1301C22—42no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—41no—
1314C22—41no—
1315C22—41no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—81no—
1322C22—81no—
1323C22—168no—
1324C22C2×#54611yescharacteristic
1325C22C2×#54611yescharacteristic
1326C22D4×#4111yescharacteristic
1327C22#358411yescharacteristic
1328C22#358411yescharacteristic
1329C22#358511yescharacteristic
1330C22#358611yescharacteristic
1331C4—22no—
1332C4—22no—
1333C4—22no—
1334C4—41no—
1335C4—41no—
1336C4—42no—
1337C4—41no—
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—41no—
1342C4—41no—
1343C4—42no—
1344C4—42no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4C2×#52911yescharacteristic
1357C4#349411yescharacteristic
1358C4#350511yescharacteristic
1359C4#351911yescharacteristic
1360C2—42no—
1361C2—44no—
1362C2—81no—
1363C2—81no—
1364C2—161no—
1365C2#3610711yescharacteristic
1366C2#6119611yescharacteristic
1367C2#6119811yescharacteristic
1368C2#6119811yescharacteristic
1369C2#6120111yescharacteristic
1370C2#6150111yescharacteristic
1371C2#6150811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#35821C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2392 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36017C2semidirect
3. #33115C2semidirect
4. #33047C2semidirect
5. #32968C2semidirect
6. #29058C2semidirect
7. #29042C2semidirect
8. #27761C2semidirect
9. #27547C2semidirect
10. #27536C2semidirect
11. #27421C2semidirect
12. #27420C2semidirect
13. #26208C2semidirect
14. #26206C2semidirect
15. #26107C2semidirect
16. #25890C2semidirect
17. #25357C2semidirect
18. #25283C2semidirect
19. #25261C2semidirect
20. #25245C2semidirect
21. #24970C2semidirect
22. #24043C2semidirect
23. #24037C2semidirect
24. #22974C2semidirect
25. #22580C2semidirect
26. #22572C2semidirect
27. #22427C2semidirect
28. #22424C2semidirect
29. #22420C2semidirect
30. #21496C2semidirect
31. #20415C2semidirect
37. C2×#485C22semidirect
39. C2×#479C22semidirect
43. C2×#435C22semidirect
48. C2×#405C22semidirect
50. #2629C22semidirect
55. #2571C22semidirect
64. #2495C22semidirect
67. #2485C22semidirect
80. #2370C22semidirect
83. #2352C22semidirect
86. #2346C22semidirect
89. #2274C22semidirect
90. #2101C22semidirect
91. #2101C22semidirect
92. #2088C22semidirect
93. #2088C22semidirect
95. #2076C22semidirect
97. #2075C22semidirect
98. #2074C22semidirect
100. #2068C22semidirect
102. #2043C22semidirect
103. #2043C22semidirect
108. #2036C22semidirect
111. #2035C22semidirect
114. #1992C22semidirect
118. #1981C22semidirect
119. #1960C22semidirect
123. #1948C22semidirect
124. #1947C22semidirect
125. #1944C22semidirect
126. #1942C22semidirect
127. #1939C22semidirect
130. #1935C22semidirect
132. #1933C22semidirect
133. #1933C22semidirect
134. #1928C22semidirect
135. #1927C22semidirect
136. #1927C22semidirect
141. #1924C22semidirect
142. #1921C22semidirect
143. #1919C22semidirect
147. #1894C22semidirect
150. #1892C22semidirect
151. #1892C22semidirect
156. #1873C22semidirect
157. #1872C22semidirect
159. #1869C22semidirect
160. #1865C22semidirect
164. #1863C22semidirect
168. #1853C22semidirect
169. #1852C22semidirect
170. #1834C22semidirect
172. #1825C22semidirect
174. #1807C22semidirect
177. #1803C22semidirect
179. #1798C22semidirect
188. #1771C22semidirect
189. #1763C22semidirect
190. #1763C22semidirect
194. C4×#103C22semidirect
195. C4×#103C22semidirect
200. C8×C22⋊C4C22semidirect
201. #1736C22semidirect
202. C2×#340C22semidirect

Maximal subgroups

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

subgroupindex
#360172
#358212
#331152
#330472
#329682
#290582
#290422
#277612
#275472
#275362
#274212
#274202
#262082
#262062
#261072
#258902
#253572
#252832
#252612
#252452
#249702
#240432
#240372
#229742
#225802
#225722
#224272
#224242
#224202
#214962
#204152