Finite Group Databasebeta

← #6540378

Subgroups — #6540378

Order 512.

1661 conjugacy classes of subgroups.

The subgroup lattice has 1331 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39373C211yesmaximal, characteristic, complemented
2#34495C211yesmaximal, characteristic
3#30182C211yesmaximal, characteristic, complemented
4#30180C211yesmaximal, characteristic, complemented
5#29987C211yesmaximal, characteristic, complemented
6#29140C211yesmaximal, characteristic, complemented
7#29119C211yesmaximal, characteristic, complemented
8#29115C211yesmaximal, characteristic, complemented
9#28164C211yesmaximal, characteristic, complemented
10#26682C211yesmaximal, characteristic, complemented
11#26675C211yesmaximal, characteristic, complemented
12#26667C211yesmaximal, characteristic, complemented
13#26658C211yesmaximal, characteristic, complemented
14#24976C211yesmaximal, characteristic, complemented
15#24975C211yesmaximal, characteristic, complemented
16#24924C211yesmaximal, characteristic, complemented
17#24921C211yesmaximal, characteristic, complemented
18#24904C211yesmaximal, characteristic, complemented
19#24901C211yesmaximal, characteristic, complemented
20#24247C211yesmaximal, characteristic
21#24247C211yesmaximal, characteristic
22#23944C211yesmaximal, characteristic, complemented
23#23942C211yesmaximal, characteristic, complemented
24#23677C211yesmaximal, characteristic, complemented
25#23586C211yesmaximal, characteristic, complemented
26#23584C211yesmaximal, characteristic, complemented
27#23006C211yesmaximal, characteristic, complemented
28#23000C211yesmaximal, characteristic, complemented
29#22836C211yesmaximal, characteristic, complemented
30#22773C211yesmaximal, characteristic, complemented
31#22765C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#541C2211yescharacteristic
34C2×#541C2211yescharacteristic, complemented
35C2×#464C2211yescharacteristic
36C2×#464C2211yescharacteristic
37C2×#452C2211yescharacteristic
38C2×#452C2211yescharacteristic
39C2×#450C2211yescharacteristic
40C2×#450C2211yescharacteristic
41C2×#441C2211yescharacteristic, complemented
42C2×#440C2211yescharacteristic
43C2×C4×Q16C2211yescharacteristic, complemented
44C2×C4×SD16C2211yescharacteristic
45C2×C4×SD16C2211yescharacteristic
46C2×C4×SD16C2211yescharacteristic
47#2859C2211yescharacteristic, complemented
48#2727—21no—
49#2727—21no—
50#2726—21no—
51#2726—21no—
52#2629C2211yescharacteristic
53#2629C2211yescharacteristic, complemented
54#2536C2211yescharacteristic
55#2536C2211yescharacteristic
56#2519—21no—
57#2519—21no—
58#2519—21no—
59#2519—21no—
60#2423C2211yescharacteristic
61#2423C2211yescharacteristic
62#2423C2211yescharacteristic, complemented
63#2423C2211yescharacteristic, complemented
64#2376—21no—
65#2375—21no—
66#2367C2211yescharacteristic
67#2363—21no—
68#2362C2211yescharacteristic
69#2361C2211yescharacteristic
70#2357C2211yescharacteristic
71#2352C2211yescharacteristic
72#2351C2211yescharacteristic, complemented
73#2351C2211yescharacteristic, complemented
74#2342—21no—
75#2341C2211yescharacteristic
76D4×C22⋊C4C2211yescharacteristic
77#2335—21no—
78#2333—21no—
79#2324C2211yescharacteristic
80#2323C2211yescharacteristic
81#2321—21no—
82#2312—21no—
83#2311C2211yescharacteristic
84#2309C2211yescharacteristic
85C4×C4⋊Q8C2211yescharacteristic, complemented
86C4×#124C2211yescharacteristic
87#2293C2211yescharacteristic
88#2293C2211yescharacteristic
89#2100C2211yescharacteristic, complemented
90#2099C2211yescharacteristic, complemented
91#2094C2211yescharacteristic
92#2093C2211yescharacteristic
93#2084C2211yescharacteristic, complemented
94#2077C2211yescharacteristic
95#2077C2211yescharacteristic, complemented
96#2076C2211yescharacteristic
97#2075C2211yescharacteristic, complemented
98#2072C2211yescharacteristic, complemented
99#2071C2211yescharacteristic
100#2071C2211yescharacteristic
101#2066C2211yescharacteristic, complemented
102#2066C2211yescharacteristic, complemented
103#2059C2211yescharacteristic, complemented
104#2059C2211yescharacteristic, complemented
105#2055C2211yescharacteristic
106#2055C2211yescharacteristic
107#2043C2211yescharacteristic, complemented
108#2036C2211yescharacteristic
109#2036C2211yescharacteristic, complemented
110#2035C2211yescharacteristic
111#2035C2211yescharacteristic
112#2035C2211yescharacteristic
113#2035C2211yescharacteristic, complemented
114#2034C2211yescharacteristic
115#2034C2211yescharacteristic
116#2026C2211yescharacteristic, complemented
117#2026C2211yescharacteristic, complemented
118#2025C2211yescharacteristic
119#2025C2211yescharacteristic
120#2025C2211yescharacteristic
121#2025C2211yescharacteristic
122#2016C2211yescharacteristic, complemented
123#2013C2211yescharacteristic
124#2013C2211yescharacteristic
125#2001C2211yescharacteristic
126#2001C2211yescharacteristic
127#2000C2211yescharacteristic
128#2000C2211yescharacteristic
129#1958C2211yescharacteristic
130#1958C2211yescharacteristic
131#1954C2211yescharacteristic
132#1954C2211yescharacteristic
133#1949C2211yescharacteristic, complemented
134#1949C2211yescharacteristic, complemented
135#1936C2211yescharacteristic
136#1936C2211yescharacteristic
137#1936C2211yescharacteristic
138#1935C2211yescharacteristic, complemented
139#1934C2211yescharacteristic
140#1934C2211yescharacteristic
141#1934C2211yescharacteristic
142#1933C2211yescharacteristic, complemented
143#1924C2211yescharacteristic
144#1924C2211yescharacteristic, complemented
145#1923C2211yescharacteristic
146#1923C2211yescharacteristic, complemented
147#1920C2211yescharacteristic, complemented
148#1920C2211yescharacteristic, complemented
149#1919C2211yescharacteristic, complemented
150#1919C2211yescharacteristic, complemented
151#1880C2211yescharacteristic
152#1880C2211yescharacteristic
153#1880C2211yescharacteristic
154#1880C2211yescharacteristic
155#1880C2211yescharacteristic
156#1880C2211yescharacteristic
157#1878C2211yescharacteristic, complemented
158#1878C2211yescharacteristic, complemented
159#1878C2211yescharacteristic, complemented
160#1878C2211yescharacteristic, complemented
161#1877C2211yescharacteristic
162#1877C2211yescharacteristic
163#1873C2211yescharacteristic
164#1873C2211yescharacteristic
165#1872C2211yescharacteristic, complemented
166#1872C2211yescharacteristic, complemented
167#1865C2211yescharacteristic, complemented
168#1864C2211yescharacteristic
169#1863C2211yescharacteristic, complemented
170#1862C2211yescharacteristic
171#1835C2211yescharacteristic, complemented
172#1835C2211yescharacteristic, complemented
173#1831C2211yescharacteristic, complemented
174#1825C2211yescharacteristic
175#1825C2211yescharacteristic
176#1824C2211yescharacteristic, complemented
177#1823C2211yescharacteristic, complemented
178#1818C2211yescharacteristic
179#1818C2211yescharacteristic, complemented
180#1805C2211yescharacteristic, complemented
181#1805C2211yescharacteristic, complemented
182#1804C2211yescharacteristic
183#1804C2211yescharacteristic
184#1803C2211yescharacteristic, complemented
185#1803C2211yescharacteristic, complemented
186#1802C2211yescharacteristic
187#1802C2211yescharacteristic
188#1788C2211yescharacteristic
189#1788C2211yescharacteristic
190#1786C2211yescharacteristic
191#1786C2211yescharacteristic
192#1770C2211yescharacteristic, complemented
193C8×C4⋊C4C2211yescharacteristic, complemented
194C4×C4⋊C8C2211yescharacteristic, complemented
195#1763C2211yescharacteristic, complemented
196#1763C2211yescharacteristic, complemented
197C4×#103C2211yescharacteristic, complemented
198C4×#103C2211yescharacteristic, complemented
199C4×#103C2211yescharacteristic, complemented
200C4×#103C2211yescharacteristic, complemented
201#1750C2211yescharacteristic
202#1750C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211#546—24no—
212#546—24no—
213#541—42no—
214#541—42no—
215#541—42no—
216#541—42no—
217C2×C4⋊Q8C2311yescharacteristic
218C2×#126—21no—
219C2×#126—21no—
220C2×#126—21no—
221C2×#126—21no—
222C2×#125—21no—
223C2×#125—21no—
224C2×#125—21no—
225C2×#125—21no—
226C2×#125C2311yescharacteristic
227C2×#125C2311yescharacteristic
228C2×#124C2311yescharacteristic
229C2×#123—21no—
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×#121—21no—
236C2×#121C2311yescharacteristic
237C2×#120—21no—
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×D4—21no—
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×#117—21no—
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C22×C4⋊C4C2311yescharacteristic
256C22×C22⋊C4—21no—
257C22×C22⋊C4—21no—
258#464—24no—
259#464—24no—
260#452—42no—
261#452—42no—
262#450—42no—
263#450—42no—
264#441—42no—
265#440—42no—
266C4×Q16—42no—
267C4×SD16—24no—
268C4×SD16—24no—
269C4×SD16—42no—
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×#97C2311yescharacteristic
317C2×#97C2311yescharacteristic
318C2×C4×C8C2311yescharacteristic
319C2×C4×C8C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322#399—21no—
323#399—21no—
324#399—21no—
325#399—21no—
326#398—21no—
327#398—21no—
328#398—21no—
329#398—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#398—21no—
334#398—21no—
335#398—21no—
336#396—21no—
337#396—21no—
338#396—21no—
339#396—21no—
340#394—21no—
341#394—21no—
342#391C2311yescharacteristic
343#391C2311yescharacteristic
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#390—21no—
347#390—21no—
348#390—21no—
349#390—21no—
350#390—21no—
351#390D411yescharacteristic
352#390D411yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#389—21no—
360#389—21no—
361#389—21no—
362#389—21no—
363#389—21no—
364#389—21no—
365#389—21no—
366#389—21no—
367#389—21no—
368#389—21no—
369#389—21no—
370#389D411yescharacteristic
371#389D411yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
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#388D411yescharacteristic
402#388D411yescharacteristic
403#388D411yescharacteristic
404#388D411yescharacteristic
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#384C2311yescharacteristic
423#384C2311yescharacteristic
424#384C2311yescharacteristic
425#382—21no—
426#382—21no—
427#382C2311yescharacteristic
428#382C2311yescharacteristic
429#382C2311yescharacteristic
430#381—21no—
431#380—21no—
432#380—21no—
433#380—21no—
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#379—21no—
441#379—21no—
442#379—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4—21no—
445C4×C4⋊C4—21no—
446C4×C4⋊C4—21no—
447C4×C4⋊C4—21no—
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4C2311yescharacteristic
460C4×C22⋊C4C2311yescharacteristic
461C43C2311yescharacteristic
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#340C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C22×Q8C2411yescharacteristic
504C22×Q8C2411yescharacteristic
505C22×Q8C2411yescharacteristic
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—22no—
509C22×D4—22no—
510C22×D4—21no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4C2×D411yescharacteristic
516C22×D4C2411yescharacteristic
517C22×D4C2411yescharacteristic
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4C2411yescharacteristic
524C23×C4C2411yescharacteristic
525C2×Q16—22no—
526C2×Q16—22no—
527C2×Q16—22no—
528C2×Q16—22no—
529C2×Q16—41no—
530C2×Q16—41no—
531C2×SD16—22no—
532C2×SD16—22no—
533C2×SD16—22no—
534C2×SD16—22no—
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16—22no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×SD16—41no—
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C4⋊Q8—22no—
552C4⋊Q8—22no—
553#126—44no—
554#126—44no—
555#126—44no—
556#126—44no—
557#125—41no—
558#125—41no—
559#125—41no—
560#125—41no—
561#125—44no—
562#125—44no—
563#125—44no—
564#125—44no—
565#124—22no—
566#124#4114yes—
567#123—28no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—22no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8—41no—
575C22⋊Q8—41no—
576C22⋊Q8—41no—
577C22⋊Q8—41no—
578#121—28no—
579#121—22no—
580#121—22no—
581#120—28no—
582C4×Q8—22no—
583C4×Q8—22no—
584C4×Q8—22no—
585C4×Q8—22no—
586C4×Q8—22no—
587C4×Q8—22no—
588C4×Q8—22no—
589C4×Q8—22no—
590C4×Q8—41no—
591C4×Q8—41no—
592C4×Q8—41no—
593C4×Q8—41no—
594C4×Q8—41no—
595C4×Q8—41no—
596C4×Q8—41no—
597C4×Q8—41no—
598C4×D4—22no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—41no—
602C4×D4—41no—
603C4×D4—41no—
604C4×D4—41no—
605C4×D4—82no—
606C4×D4#4114yes—
607#117—41no—
608#117—41no—
609#117—41no—
610#117—41no—
611#117—41no—
612#117—41no—
613#117—82no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—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⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—28no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—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—82no—
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—21no—
720C2×C42C2×D411yescharacteristic
721C2×C42C2×D411yescharacteristic
722C2×C42C2×D411yescharacteristic
723C2×C42C2×D411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729#107—41no—
730#107—41no—
731#106—22no—
732#106—22no—
733#106—41no—
734#106—41no—
735C4⋊C8—22no—
736C4⋊C8—22no—
737C4⋊C8—41no—
738C4⋊C8—41no—
739#103—22no—
740#103—22no—
741#103—22no—
742#103—22no—
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—22no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102—41no—
767C22⋊C8—41no—
768C22⋊C8—41no—
769C22⋊C8—41no—
770C22⋊C8—41no—
771C22⋊C8—41no—
772C22⋊C8—41no—
773C22⋊C8—41no—
774C22⋊C8—41no—
775#97—41no—
776#97—41no—
777C4×C8—22no—
778C4×C8—22no—
779C4×C8—41no—
780C4×C8—41no—
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#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#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816C24—24no—
817C24—21no—
818C24—21no—
819C24—81no—
820C24—81no—
821C24—81no—
822C24—81no—
823C24—81no—
824C24—81no—
825C24C22×D411yescharacteristic
826C24C22×D411yescharacteristic
827#41—82no—
828#41—82no—
829#41—82no—
830#41—82no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
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×Q8C2×#4112yes—
847C2×Q8H(5,𝔽2)12yes—
848C2×Q8H(5,𝔽2)12yes—
849C2×D4—24no—
850C2×D4—24no—
851C2×D4—24no—
852C2×D4—22no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—41no—
864C2×D4—41no—
865C2×D4—81no—
866C2×D4—81no—
867C2×D4—82no—
868C2×D4—82no—
869C2×D4—82no—
870C2×D4—82no—
871C2×D4—81no—
872C2×D4—81no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4C2×#4112yes—
876C2×D4C2×#4112yes—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—24no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—24no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—42no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4—81no—
917C22×C4—81no—
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C2511yescharacteristic
931Q16—44no—
932Q16—44no—
933SD16—44no—
934SD16—44no—
935SD16—44no—
936SD16—44no—
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—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C4⋊C4—24no—
962C4⋊C4—24no—
963C4⋊C4—24no—
964C4⋊C4—22no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—41no—
987C4⋊C4—41no—
988C4⋊C4—41no—
989C4⋊C4—41no—
990C4⋊C4—41no—
991C4⋊C4—41no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4C2×#4112yes—
1022C22⋊C4—24no—
1023C22⋊C4—24no—
1024C22⋊C4—22no—
1025C22⋊C4—24no—
1026C22⋊C4—24no—
1027C22⋊C4—24no—
1028C22⋊C4—22no—
1029C22⋊C4—22no—
1030C22⋊C4—22no—
1031C22⋊C4—41no—
1032C22⋊C4—41no—
1033C22⋊C4—41no—
1034C22⋊C4—41no—
1035C22⋊C4—41no—
1036C22⋊C4—41no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C42—22no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—41no—
1072C42—41no—
1073C42—41no—
1074C42—42no—
1075C42—42no—
1076C42—42no—
1077C42—42no—
1078C42—42no—
1079C42—42no—
1080C42—81no—
1081C42—81no—
1082C42—81no—
1083C42—81no—
1084C42—81no—
1085C42—81no—
1086C42C2×#4112yes—
1087C42C2×#4112yes—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—22no—
1096C23—22no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—84no—
1117C23—84no—
1118C23—84no—
1119C23—162no—
1120C23—162no—
1121C23—162no—
1122C23—162no—
1123C23C23×D411yescharacteristic
1124Q8—22no—
1125Q8—22no—
1126Q8—22no—
1127Q8—22no—
1128Q8—22no—
1129Q8—22no—
1130Q8—41no—
1131Q8—41no—
1132Q8—41no—
1133Q8—41no—
1134Q8—41no—
1135Q8—41no—
1136D4—22no—
1137D4—22no—
1138D4—22no—
1139D4—22no—
1140D4—41no—
1141D4—41no—
1142D4—41no—
1143D4—41no—
1144D4—82no—
1145D4—84no—
1146D4—84no—
1147D4—84no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—22no—
1166C2×C4—21no—
1167C2×C4—22no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—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—84no—
1232C2×C4—84no—
1233C2×C4—162no—
1234C2×C4—162no—
1235C2×C4—162no—
1236C2×C4#52512yes—
1237C2×C4#52512yes—
1238C2×C4#57712yes—
1239C2×C4C22×#4111yescharacteristic
1240C2×C4C22×#4111yescharacteristic
1241C2×C4C2×H(5,𝔽2)11yescharacteristic
1242C2×C4C2×H(5,𝔽2)11yescharacteristic
1243C2×C4#58511yescharacteristic
1244C2×C4#58511yescharacteristic
1245C8—41no—
1246C8—41no—
1247C8—41no—
1248C8—41no—
1249C8—41no—
1250C8—41no—
1251C8—41no—
1252C8—41no—
1253C22—41no—
1254C22—41no—
1255C22—41no—
1256C22—41no—
1257C22—42no—
1258C22—42no—
1259C22—41no—
1260C22—41no—
1261C22—42no—
1262C22—42no—
1263C22—41no—
1264C22—41no—
1265C22—42no—
1266C22—41no—
1267C22—42no—
1268C22—41no—
1269C22—41no—
1270C22—41no—
1271C22—41no—
1272C22—41no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—168no—
1282C22C2×#52511yescharacteristic
1283C22#348411yescharacteristic
1284C22#350011yescharacteristic
1285C22C2×#57711yescharacteristic
1286C22#358411yescharacteristic
1287C22#358411yescharacteristic
1288C22#358611yescharacteristic
1289C4—22no—
1290C4—22no—
1291C4—22no—
1292C4—41no—
1293C4—41no—
1294C4—42no—
1295C4—42no—
1296C4—42no—
1297C4—41no—
1298C4—42no—
1299C4—41no—
1300C4—41no—
1301C4—41no—
1302C4—41no—
1303C4—41no—
1304C4—41no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4#349411yescharacteristic
1316C4#349411yescharacteristic
1317C4#351311yescharacteristic
1318C4#351311yescharacteristic
1319C2—81no—
1320C2—81no—
1321C2—82no—
1322C2—82no—
1323C2#3573011yescharacteristic
1324C2#6055711yescharacteristic
1325C2#6059111yescharacteristic
1326C2#6165911yescharacteristic
1327C2#6168111yescharacteristic
1328C2#6255611yescharacteristic
1329C2#6261211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#546C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2293 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39373C2semidirect
3. #30182C2semidirect
4. #30180C2semidirect
5. #29987C2semidirect
6. #29140C2semidirect
7. #29119C2semidirect
8. #29115C2semidirect
9. #28164C2semidirect
10. #26682C2semidirect
11. #26675C2semidirect
12. #26667C2semidirect
13. #26658C2semidirect
14. #24976C2semidirect
15. #24975C2semidirect
16. #24924C2semidirect
17. #24921C2semidirect
18. #24904C2semidirect
19. #24901C2semidirect
22. #23944C2semidirect
23. #23942C2semidirect
24. #23677C2semidirect
25. #23586C2semidirect
26. #23584C2semidirect
27. #23006C2semidirect
28. #23000C2semidirect
29. #22836C2semidirect
30. #22773C2semidirect
31. #22765C2semidirect
34. C2×#541C22semidirect
41. C2×#441C22semidirect
43. C2×C4×Q16C22semidirect
47. #2859C22semidirect
53. #2629C22semidirect
62. #2423C22semidirect
63. #2423C22semidirect
72. #2351C22semidirect
73. #2351C22semidirect
85. C4×C4⋊Q8C22semidirect
89. #2100C22semidirect
90. #2099C22semidirect
93. #2084C22semidirect
95. #2077C22semidirect
97. #2075C22semidirect
98. #2072C22semidirect
101. #2066C22semidirect
102. #2066C22semidirect
103. #2059C22semidirect
104. #2059C22semidirect
107. #2043C22semidirect
109. #2036C22semidirect
113. #2035C22semidirect
116. #2026C22semidirect
117. #2026C22semidirect
122. #2016C22semidirect
133. #1949C22semidirect
134. #1949C22semidirect
138. #1935C22semidirect
142. #1933C22semidirect
144. #1924C22semidirect
146. #1923C22semidirect
147. #1920C22semidirect
148. #1920C22semidirect
149. #1919C22semidirect
150. #1919C22semidirect
157. #1878C22semidirect
158. #1878C22semidirect
159. #1878C22semidirect
160. #1878C22semidirect
165. #1872C22semidirect
166. #1872C22semidirect
167. #1865C22semidirect
169. #1863C22semidirect
171. #1835C22semidirect
172. #1835C22semidirect
173. #1831C22semidirect
176. #1824C22semidirect
177. #1823C22semidirect
179. #1818C22semidirect
180. #1805C22semidirect
181. #1805C22semidirect
184. #1803C22semidirect
185. #1803C22semidirect
192. #1770C22semidirect
193. C8×C4⋊C4C22semidirect
194. C4×C4⋊C8C22semidirect
195. #1763C22semidirect
196. #1763C22semidirect
197. C4×#103C22semidirect
198. C4×#103C22semidirect
199. C4×#103C22semidirect
200. C4×#103C22semidirect
202. #1750C22semidirect

Maximal subgroups

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

subgroupindex
#393732
#344952
#301822
#301802
#299872
#291402
#291192
#291152
#281642
#266822
#266752
#266672
#266582
#249762
#249752
#249242
#249212
#249042
#249012
#242472
#239442
#239422
#236772
#235862
#235842
#230062
#230002
#228362
#227732
#227652