Finite Group Databasebeta

← #6786343

Subgroups — #6786343

Order 512.

1645 conjugacy classes of subgroups.

The subgroup lattice has 1372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38923C211yesmaximal, characteristic, complemented
2#38024C211yesmaximal, characteristic
3#33142C211yesmaximal, characteristic, complemented
4#32639C211yesmaximal, characteristic, complemented
5#32609C211yesmaximal, characteristic, complemented
6#32564C211yesmaximal, characteristic, complemented
7#32561C211yesmaximal, characteristic, complemented
8#31782C211yesmaximal, characteristic, complemented
9#31732C211yesmaximal, characteristic, complemented
10#31676C211yesmaximal, characteristic, complemented
11#31024C211yesmaximal, characteristic, complemented
12#30366C211yesmaximal, characteristic, complemented
13#30330C211yesmaximal, characteristic, complemented
14#29489C211yesmaximal, characteristic, complemented
15#29463C211yesmaximal, characteristic, complemented
16#29342C211yesmaximal, characteristic, complemented
17#29103C211yesmaximal, characteristic, complemented
18#26200C211yesmaximal, characteristic, complemented
19#26198C211yesmaximal, characteristic, complemented
20#25556C211yesmaximal, characteristic, complemented
21#24951C211yesmaximal, characteristic, complemented
22#24881C211yesmaximal, characteristic, complemented
23#24617C211yesmaximal, characteristic, complemented
24#24515C211yesmaximal, characteristic, complemented
25#24452C211yesmaximal, characteristic, complemented
26#24037C211yesmaximal, characteristic, complemented
27#23968C211yesmaximal, characteristic, complemented
28#22091C211yesmaximal, characteristic, complemented
29#22049C211yesmaximal, characteristic, complemented
30#21381C211yesmaximal, characteristic, complemented
31#21092C211yesmaximal, characteristic, complemented
32C2×#556C2211yescharacteristic, complemented
33C2×#546C2211yescharacteristic
34C2×#529C2211yescharacteristic
35C2×#481C2211yescharacteristic
36C2×#482C2211yescharacteristic
37C2×#468C2211yescharacteristic
38C2×#452C2211yescharacteristic
39C2×#450C2211yescharacteristic
40C2×#433C2211yescharacteristic, complemented
41C2×#417C2211yescharacteristic
42C2×#416C2211yescharacteristic
43C2×#405C2211yescharacteristic, complemented
44#2857C2211yescharacteristic
45#2855C2211yescharacteristic
46#2722—21no—
47#2722—21no—
48#2707—21no—
49#2705—21no—
50#2695—21no—
51#2695—21no—
52#2691—21no—
53#2676—21no—
54#2625C2211yescharacteristic, complemented
55#2625C2211yescharacteristic, complemented
56#2624C2211yescharacteristic
57#2620C2211yescharacteristic
58#2592C2211yescharacteristic
59#2582C2211yescharacteristic, complemented
60#2547—21no—
61#2546C2211yescharacteristic, complemented
62#2538C2211yescharacteristic
63#2534—21no—
64#2485C2211yescharacteristic
65#2485C2211yescharacteristic
66#2453—21no—
67#2437—21no—
68#2429—21no—
69#2427—21no—
70#2424—21no—
71#2417C2211yescharacteristic
72#2417C2211yescharacteristic
73#2417C2211yescharacteristic
74#2416C2211yescharacteristic
75#2412—21no—
76#2408C2211yescharacteristic
77#2407C2211yescharacteristic
78D4×C4⋊C4C2211yescharacteristic
79D4×C4⋊C4C2211yescharacteristic, complemented
80#2324C2211yescharacteristic
81#2316C2211yescharacteristic, complemented
82#2316C2211yescharacteristic, complemented
83#2311C2211yescharacteristic
84C4×C22⋊Q8C2211yescharacteristic
85C2×#390C2211yescharacteristic
86#2100C2211yescharacteristic, complemented
87#2099C2211yescharacteristic, complemented
88#2099C2211yescharacteristic, complemented
89#2096C2211yescharacteristic, complemented
90#2088C2211yescharacteristic, complemented
91#2086C2211yescharacteristic, complemented
92#2083C2211yescharacteristic, complemented
93#2077C2211yescharacteristic
94#2077C2211yescharacteristic
95#2075C2211yescharacteristic
96#2075C2211yescharacteristic, complemented
97#2072C2211yescharacteristic, complemented
98#2071C2211yescharacteristic
99#2071C2211yescharacteristic
100#2068C2211yescharacteristic, complemented
101#2067C2211yescharacteristic
102#2065C2211yescharacteristic
103#2065C2211yescharacteristic
104#2057C2211yescharacteristic, complemented
105#2056C2211yescharacteristic, complemented
106#2055C2211yescharacteristic
107#2042C2211yescharacteristic
108#2042C2211yescharacteristic
109#2042C2211yescharacteristic
110#2036C2211yescharacteristic
111#2036C2211yescharacteristic
112#2036C2211yescharacteristic, complemented
113#2036C2211yescharacteristic, complemented
114#2035C2211yescharacteristic
115#2035C2211yescharacteristic
116#2034C2211yescharacteristic
117#2033C2211yescharacteristic
118#2024C2211yescharacteristic, complemented
119#2023C2211yescharacteristic
120#2023C2211yescharacteristic
121#2015C2211yescharacteristic
122#2001C2211yescharacteristic
123#2001C2211yescharacteristic, complemented
124#2000C2211yescharacteristic
125#2000C2211yescharacteristic
126#1985C2211yescharacteristic, complemented
127#1984C2211yescharacteristic, complemented
128#1973C2211yescharacteristic
129#1973C2211yescharacteristic
130#1969C2211yescharacteristic, complemented
131#1968C2211yescharacteristic
132#1955C2211yescharacteristic
133#1954C2211yescharacteristic
134#1944C2211yescharacteristic, complemented
135#1944C2211yescharacteristic, complemented
136#1942C2211yescharacteristic, complemented
137#1941C2211yescharacteristic, complemented
138#1936C2211yescharacteristic
139#1936C2211yescharacteristic
140#1936C2211yescharacteristic
141#1936C2211yescharacteristic
142#1935C2211yescharacteristic, complemented
143#1935C2211yescharacteristic, complemented
144#1935C2211yescharacteristic, complemented
145#1935C2211yescharacteristic, complemented
146#1934C2211yescharacteristic
147#1934C2211yescharacteristic
148#1934C2211yescharacteristic
149#1934C2211yescharacteristic
150#1934C2211yescharacteristic
151#1933C2211yescharacteristic, complemented
152#1933C2211yescharacteristic, complemented
153#1933C2211yescharacteristic, complemented
154#1927C2211yescharacteristic, complemented
155#1927C2211yescharacteristic, complemented
156#1925C2211yescharacteristic
157#1925C2211yescharacteristic
158#1921C2211yescharacteristic, complemented
159#1920C2211yescharacteristic, complemented
160#1919C2211yescharacteristic, complemented
161#1918C2211yescharacteristic, complemented
162#1893C2211yescharacteristic
163#1892C2211yescharacteristic, complemented
164#1880C2211yescharacteristic
165#1880C2211yescharacteristic
166#1878C2211yescharacteristic, complemented
167#1877C2211yescharacteristic
168#1875C2211yescharacteristic
169#1875C2211yescharacteristic
170#1874C2211yescharacteristic
171#1874C2211yescharacteristic
172#1873C2211yescharacteristic, complemented
173#1872C2211yescharacteristic
174#1872C2211yescharacteristic, complemented
175#1872C2211yescharacteristic, complemented
176#1870C2211yescharacteristic
177#1870C2211yescharacteristic, complemented
178#1869C2211yescharacteristic
179#1869C2211yescharacteristic, complemented
180#1865C2211yescharacteristic, complemented
181#1864C2211yescharacteristic
182#1862C2211yescharacteristic
183#1862C2211yescharacteristic
184#1854C2211yescharacteristic, complemented
185#1853C2211yescharacteristic, complemented
186#1852C2211yescharacteristic
187#1852C2211yescharacteristic, complemented
188#1825C2211yescharacteristic, complemented
189#1823C2211yescharacteristic
190#1823C2211yescharacteristic
191#1823C2211yescharacteristic, complemented
192#1809C2211yescharacteristic, complemented
193#1788C2211yescharacteristic
194#1786C2211yescharacteristic
195#1786C2211yescharacteristic
196#1786C2211yescharacteristic
197#1750C2211yescharacteristic, complemented
198#1750C2211yescharacteristic, complemented
199#1749C2211yescharacteristic
200C4×C22⋊C8C2211yescharacteristic
201#1736C2211yescharacteristic, complemented
202C2×#340C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C23×C8C2311yescharacteristic
210#556—42no—
211#556—42no—
212#546—42no—
213#546—42no—
214C2×C4⋊Q8—21no—
215C2×C4⋊Q8C2311yescharacteristic
216#529—42no—
217#529—42no—
218C2×#126—21no—
219C2×#126—21no—
220C2×#126D411yescharacteristic
221C2×#126D411yescharacteristic
222C2×#125D411yescharacteristic
223C2×#124—21no—
224C2×#124D411yescharacteristic
225C2×#124C2311yescharacteristic
226C2×#123—21no—
227C2×#123D411yescharacteristic
228C2×#123D411yescharacteristic
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8D411yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×#121—21no—
238C2×#121—21no—
239C2×#121D411yescharacteristic
240C2×#121C2311yescharacteristic
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#120—21no—
244C2×#120—21no—
245C2×C4×Q8—21no—
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×D4—21no—
249C2×C4×D4—21no—
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C22×C4⋊C4C2311yescharacteristic
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C22⋊C4—21no—
263C22×C22⋊C4—21no—
264C22×C22⋊C4—21no—
265C22×C42C2311yescharacteristic
266#482—42no—
267#481—24no—
268#468—42no—
269#452—42no—
270#450—24no—
271#433—42no—
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283#417—24no—
284#416—42no—
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321#405—42no—
322C2×#97C2311yescharacteristic
323C2×#97C2311yescharacteristic
324C2×#97C2311yescharacteristic
325C2×C4×C8C2311yescharacteristic
326C2×C4×C8C2311yescharacteristic
327C2×C4×C8C2311yescharacteristic
328#400—21no—
329#400—21no—
330#399—21no—
331#398—21no—
332#398—21no—
333#398—21no—
334#398—21no—
335#398—21no—
336#398—21no—
337#398—21no—
338#398—21no—
339#398—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
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#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#393—21no—
366#392—21no—
367#392—21no—
368#391—21no—
369#391—21no—
370#391—21no—
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#390—21no—
378#390—21no—
379#390—21no—
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#389—21no—
387#389—21no—
388#389—21no—
389#389—21no—
390#389—21no—
391#389—21no—
392#389—21no—
393#389—21no—
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#384C2311yescharacteristic
433#384C2311yescharacteristic
434#381—21no—
435#380—21no—
436#380—21no—
437#380—21no—
438#380—21no—
439#380—21no—
440#380—21no—
441#380—21no—
442#380—21no—
443#380—21no—
444#380—21no—
445#380—21no—
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#379—21no—
455C4×C4⋊C4—21no—
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C22⋊C4—21no—
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C22×Q8—21no—
501C22×Q8C2×D411yescharacteristic
502C22×Q8C2411yescharacteristic
503C22×Q8C2411yescharacteristic
504C22×D4—22no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4C2×D411yescharacteristic
516C22×D4C2×D411yescharacteristic
517C22×D4C2×D411yescharacteristic
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4C2×D411yescharacteristic
527C23×C4C2×D411yescharacteristic
528C23×C4C2411yescharacteristic
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C2×Q16—41no—
532C2×Q16—41no—
533C2×Q16—41no—
534C2×SD16—22no—
535C2×SD16—22no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×M16—22no—
541C2×M16—22no—
542C2×M16—41no—
543C22×C8—22no—
544C22×C8—41no—
545C22×C8—41no—
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C4⋊Q8—41no—
555C4⋊Q8—41no—
556C4⋊Q8—82no—
557#126—42no—
558#126—42no—
559#126—44no—
560#126—44no—
561#125—42no—
562#124—41no—
563#124—41no—
564#124—42no—
565#124—44no—
566#123—42no—
567#123—42no—
568#123—44no—
569C22⋊Q8—22no—
570C22⋊Q8—22no—
571C22⋊Q8—22no—
572C22⋊Q8—42no—
573C22⋊Q8—41no—
574C22⋊Q8—41no—
575C22⋊Q8—41no—
576C22⋊Q8—41no—
577C22⋊Q8—41no—
578C22⋊Q8—41no—
579C22⋊Q8—41no—
580C22⋊Q8—82no—
581C22⋊Q8—82no—
582#121—22no—
583#121—22no—
584#121—22no—
585#121—42no—
586#121—44no—
587#121—41no—
588#121—41no—
589#121—41no—
590#121—82no—
591#120—44no—
592#120—82no—
593C4×Q8—41no—
594C4×Q8—41no—
595C4×Q8—41no—
596C4×Q8—41no—
597C4×Q8—44no—
598C4×D4—22no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—41no—
603C4×D4—41no—
604C4×D4—41no—
605C4×D4—41no—
606C4×D4—82no—
607C4×D4—82no—
608#117—22no—
609#117—22no—
610#117—22no—
611#117—22no—
612#117—41no—
613#117—41no—
614#117—41no—
615#117—41no—
616C2×C4⋊C4—22no—
617C2×C4⋊C4—22no—
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—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—41no—
646C2×C4⋊C4—41no—
647C2×C4⋊C4—41no—
648C2×C4⋊C4—41no—
649C2×C4⋊C4—41no—
650C2×C4⋊C4—41no—
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⋊C4C2×D411yescharacteristic
659C2×C4⋊C4C2×D411yescharacteristic
660C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
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—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—44no—
707C2×C22⋊C4—82no—
708C2×C22⋊C4—82no—
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×C22⋊C4C2×D411yescharacteristic
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C42—21no—
720C2×C42—21no—
721C2×C42—21no—
722C2×C42—21no—
723C2×C42—21no—
724C2×C42—41no—
725C2×C42—41no—
726C2×C42C2×D411yescharacteristic
727C2×C42C2×D411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732#107—41no—
733#107—41no—
734#107—41no—
735#107—41no—
736#107—41no—
737#106—22no—
738#106—22no—
739#106—41no—
740#106—41no—
741C4⋊C8—41no—
742C4⋊C8—41no—
743#103—22no—
744#103—22no—
745#103—41no—
746#103—41no—
747#103—41no—
748#103—41no—
749#103—41no—
750#103—41no—
751#103—41no—
752#103—41no—
753#103—41no—
754#103—41no—
755#102—22no—
756#102—22no—
757#102—22no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102#4114yes—
769C22⋊C8—22no—
770C22⋊C8—22no—
771C22⋊C8—22no—
772C22⋊C8—22no—
773C22⋊C8—41no—
774C22⋊C8—41no—
775C22⋊C8—41no—
776C22⋊C8—41no—
777C22⋊C8—41no—
778C22⋊C8—41no—
779#97—41no—
780#97—41no—
781#97—41no—
782C4×C8—41no—
783C4×C8—41no—
784C4×C8—41no—
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#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—
819C24—21no—
820C24—21no—
821C24—42no—
822C24—42no—
823C24—42no—
824C24—42no—
825C24—81no—
826C24—81no—
827C24—81no—
828C24C22×D411yescharacteristic
829C24C22×D411yescharacteristic
830C24C22×D411yescharacteristic
831#41—44no—
832#41—44no—
833#41—82no—
834#41—82no—
835C2×Q8—22no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—41no—
849C2×Q8—41no—
850C2×Q8—42no—
851C2×Q8—42no—
852C2×Q8—42no—
853C2×D4—22no—
854C2×D4—22no—
855C2×D4—22no—
856C2×D4—22no—
857C2×D4—22no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—41no—
870C2×D4—41no—
871C2×D4—41no—
872C2×D4—41no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—81no—
880C2×D4—82no—
881C2×D4—82no—
882C2×D4—82no—
883C2×D4—82no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4—81no—
890C2×D4—81no—
891C2×D4—81no—
892C2×D4C2×#4112yes—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—22no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—22no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—41no—
926C22×C4—41no—
927C22×C4—41no—
928C22×C4—41no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—42no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—81no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4H(5,𝔽2)12yes—
959C22×C4H(5,𝔽2)12yes—
960C22×C4C2511yescharacteristic
961Q16—82no—
962SD16—82no—
963SD16—82no—
964M16—44no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
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—44no—
989C2×C8C2×#4112yes—
990C4⋊C4—22no—
991C4⋊C4—22no—
992C4⋊C4—22no—
993C4⋊C4—22no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
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—41no—
1018C4⋊C4—41no—
1019C4⋊C4—41no—
1020C4⋊C4—41no—
1021C4⋊C4—41no—
1022C4⋊C4—41no—
1023C4⋊C4—42no—
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—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
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⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4C2×#4112yes—
1051C22⋊C4—22no—
1052C22⋊C4—22no—
1053C22⋊C4—22no—
1054C22⋊C4—22no—
1055C22⋊C4—22no—
1056C22⋊C4—22no—
1057C22⋊C4—41no—
1058C22⋊C4—41no—
1059C22⋊C4—41no—
1060C22⋊C4—41no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
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—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
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—
1093C22⋊C4—81no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—21no—
1101C42—21no—
1102C42—41no—
1103C42—41no—
1104C42—42no—
1105C42—42no—
1106C42—42no—
1107C42—42no—
1108C42—81no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—22no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—84no—
1143C23—84no—
1144C23—84no—
1145C23—84no—
1146C23—162no—
1147C23—162no—
1148C23—162no—
1149C23#53412yes—
1150C23#57712yes—
1151C23C23×D411yescharacteristic
1152Q8—41no—
1153Q8—41no—
1154Q8—41no—
1155Q8—41no—
1156Q8—41no—
1157Q8—41no—
1158Q8—41no—
1159Q8—41no—
1160Q8—82no—
1161Q8—84no—
1162D4—22no—
1163D4—22no—
1164D4—44no—
1165D4—44no—
1166D4—41no—
1167D4—41no—
1168D4—41no—
1169D4—41no—
1170D4—41no—
1171D4—41no—
1172D4—82no—
1173D4—84no—
1174D4—84no—
1175D4—162no—
1176D4—162no—
1177D4—162no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
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—22no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
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—82no—
1264C2×C4—84no—
1265C2×C4—82no—
1266C2×C4—162no—
1267C2×C4—162no—
1268C2×C4—162no—
1269C2×C4—162no—
1270C2×C4—162no—
1271C2×C4#53412yes—
1272C2×C4#57612yes—
1273C2×C4C22×#4111yescharacteristic
1274C2×C4C2×H(5,𝔽2)11yescharacteristic
1275C2×C4C2×H(5,𝔽2)11yescharacteristic
1276C2×C4#58511yescharacteristic
1277C2×C4#58511yescharacteristic
1278C2×C4#58511yescharacteristic
1279C8—22no—
1280C8—41no—
1281C8—41no—
1282C8—41no—
1283C8—41no—
1284C8—41no—
1285C8—41no—
1286C8—41no—
1287C22—22no—
1288C22—22no—
1289C22—22no—
1290C22—22no—
1291C22—22no—
1292C22—22no—
1293C22—41no—
1294C22—41no—
1295C22—41no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—42no—
1303C22—41no—
1304C22—42no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—42no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—81no—
1322C22—168no—
1323C22C2×#53411yescharacteristic
1324C22D4×#4111yescharacteristic
1325C22#350011yescharacteristic
1326C22C2×#57611yescharacteristic
1327C22C2×#57711yescharacteristic
1328C22#358611yescharacteristic
1329C22#358611yescharacteristic
1330C4—22no—
1331C4—22no—
1332C4—41no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—42no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4—81no—
1355C4#349411yescharacteristic
1356C4#351311yescharacteristic
1357C4#353311yescharacteristic
1358C4#356011yescharacteristic
1359C2—42no—
1360C2—42no—
1361C2—81no—
1362C2—82no—
1363C2—161no—
1364C2#3842811yescharacteristic
1365C2#6076211yescharacteristic
1366C2#6076311yescharacteristic
1367C2#6152011yescharacteristic
1368C2#6155311yescharacteristic
1369C2#6255011yescharacteristic
1370C2#6257111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#38024C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#529 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #38923C2semidirect
3. #33142C2semidirect
4. #32639C2semidirect
5. #32609C2semidirect
6. #32564C2semidirect
7. #32561C2semidirect
8. #31782C2semidirect
9. #31732C2semidirect
10. #31676C2semidirect
11. #31024C2semidirect
12. #30366C2semidirect
13. #30330C2semidirect
14. #29489C2semidirect
15. #29463C2semidirect
16. #29342C2semidirect
17. #29103C2semidirect
18. #26200C2semidirect
19. #26198C2semidirect
20. #25556C2semidirect
21. #24951C2semidirect
22. #24881C2semidirect
23. #24617C2semidirect
24. #24515C2semidirect
25. #24452C2semidirect
26. #24037C2semidirect
27. #23968C2semidirect
28. #22091C2semidirect
29. #22049C2semidirect
30. #21381C2semidirect
31. #21092C2semidirect
32. C2×#556C22semidirect
40. C2×#433C22semidirect
43. C2×#405C22semidirect
54. #2625C22semidirect
55. #2625C22semidirect
59. #2582C22semidirect
61. #2546C22semidirect
79. D4×C4⋊C4C22semidirect
81. #2316C22semidirect
82. #2316C22semidirect
86. #2100C22semidirect
87. #2099C22semidirect
88. #2099C22semidirect
89. #2096C22semidirect
90. #2088C22semidirect
91. #2086C22semidirect
92. #2083C22semidirect
96. #2075C22semidirect
97. #2072C22semidirect
100. #2068C22semidirect
104. #2057C22semidirect
105. #2056C22semidirect
112. #2036C22semidirect
113. #2036C22semidirect
118. #2024C22semidirect
123. #2001C22semidirect
126. #1985C22semidirect
127. #1984C22semidirect
130. #1969C22semidirect
134. #1944C22semidirect
135. #1944C22semidirect
136. #1942C22semidirect
137. #1941C22semidirect
142. #1935C22semidirect
143. #1935C22semidirect
144. #1935C22semidirect
145. #1935C22semidirect
151. #1933C22semidirect
152. #1933C22semidirect
153. #1933C22semidirect
154. #1927C22semidirect
155. #1927C22semidirect
158. #1921C22semidirect
159. #1920C22semidirect
160. #1919C22semidirect
161. #1918C22semidirect
163. #1892C22semidirect
166. #1878C22semidirect
172. #1873C22semidirect
174. #1872C22semidirect
175. #1872C22semidirect
177. #1870C22semidirect
179. #1869C22semidirect
180. #1865C22semidirect
184. #1854C22semidirect
185. #1853C22semidirect
187. #1852C22semidirect
188. #1825C22semidirect
191. #1823C22semidirect
192. #1809C22semidirect
197. #1750C22semidirect
198. #1750C22semidirect
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
#389232
#380242
#331422
#326392
#326092
#325642
#325612
#317822
#317322
#316762
#310242
#303662
#303302
#294892
#294632
#293422
#291032
#262002
#261982
#255562
#249512
#248812
#246172
#245152
#244522
#240372
#239682
#220912
#220492
#213812
#210922