Finite Group Databasebeta

← #6472500

Subgroups — #6472500

Order 512.

1845 conjugacy classes of subgroups.

The subgroup lattice has 1371 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37342C211yesmaximal, characteristic, complemented
2#34310C211yesmaximal, characteristic
3#33084C211yesmaximal, characteristic, complemented
4#33068C211yesmaximal, characteristic, complemented
5#33018C211yesmaximal, characteristic, complemented
6#32962C211yesmaximal, characteristic, complemented
7#30177C211yesmaximal, characteristic, complemented
8#30128C211yesmaximal, characteristic, complemented
9#30075C211yesmaximal, characteristic, complemented
10#30025C211yesmaximal, characteristic, complemented
11#27518C211yesmaximal, characteristic, complemented
12#27301C211yesmaximal, characteristic, complemented
13#27054C211yesmaximal, characteristic, complemented
14#26897C211yesmaximal, characteristic, complemented
15#26770C211yesmaximal, characteristic, complemented
16#26557C211yesmaximal, characteristic, complemented
17#26384C211yesmaximal, characteristic, complemented
18#26359C211yesmaximal, characteristic, complemented
19#26151C211yesmaximal, characteristic, complemented
20#25950C211yesmaximal, characteristic, complemented
21#25211C211yesmaximal, characteristic, complemented
22#24948C211yesmaximal, characteristic, complemented
23#24921C211yesmaximal, characteristic, complemented
24#24538C211yesmaximal, characteristic, complemented
25#24432C211yesmaximal, characteristic
26#24044C211yesmaximal, characteristic
27#22194C211yesmaximal, characteristic, complemented
28#22088C211yesmaximal, characteristic, complemented
29#22007C211yesmaximal, characteristic, complemented
30#21459C211yesmaximal, characteristic, complemented
31#20876C211yesmaximal, characteristic, complemented
32C2×D42C2211yescharacteristic
33C2×#518C2211yescharacteristic
34C2×#518C2211yescharacteristic
35C2×#485C2211yescharacteristic, complemented
36C2×#482C2211yescharacteristic
37C2×#476C2211yescharacteristic, complemented
38C2×#474C2211yescharacteristic
39C2×#465C2211yescharacteristic
40C2×#450C2211yescharacteristic
41C2×#450C2211yescharacteristic
42C2×#440C2211yescharacteristic
43C2×C4×SD16C2211yescharacteristic, complemented
44C2×#428C2211yescharacteristic, complemented
45C2×#418C2211yescharacteristic
46C22×#102C2211yescharacteristic
47#2863C2211yescharacteristic, complemented
48#2859C2211yescharacteristic, complemented
49#2796—21no—
50#2792—21no—
51#2775—21no—
52#2770—21no—
53#2767—21no—
54#2723—21no—
55#2721—21no—
56#2690—21no—
57#2628C2211yescharacteristic, complemented
58#2625C2211yescharacteristic, complemented
59#2509C2211yescharacteristic, complemented
60#2499C2211yescharacteristic, complemented
61#2496C2211yescharacteristic, complemented
62#2485C2211yescharacteristic
63#2451C2211yescharacteristic, complemented
64#2440C2211yescharacteristic, complemented
65#2423C2211yescharacteristic, complemented
66#2417C2211yescharacteristic
67#2366C2211yescharacteristic
68#2363C2211yescharacteristic
69#2363C2211yescharacteristic
70#2361—21no—
71#2358—21no—
72#2358—21no—
73#2354C2211yescharacteristic
74D4×C4⋊C4C2211yescharacteristic
75D4×C22⋊C4—21no—
76D4×C22⋊C4C2211yescharacteristic
77D4×C22⋊C4C2211yescharacteristic
78#2324C2211yescharacteristic
79#2324C2211yescharacteristic
80#2323C2211yescharacteristic, complemented
81#2321—21no—
82#2321—21no—
83#2317C2211yescharacteristic, complemented
84C4×#127C2211yescharacteristic
85C4×#121—21no—
86#2293C2211yescharacteristic
87C2×#390—21no—
88C42×D4C2211yescharacteristic
89#2100C2211yescharacteristic, complemented
90#2095C2211yescharacteristic, complemented
91#2093C2211yescharacteristic, complemented
92#2093C2211yescharacteristic, complemented
93#2087C2211yescharacteristic, complemented
94#2085C2211yescharacteristic, complemented
95#2083C2211yescharacteristic, complemented
96#2083C2211yescharacteristic, complemented
97#2076C2211yescharacteristic, complemented
98#2075C2211yescharacteristic, complemented
99#2075C2211yescharacteristic, complemented
100#2073C2211yescharacteristic, complemented
101#2071C2211yescharacteristic, complemented
102#2071C2211yescharacteristic, complemented
103#2067C2211yescharacteristic, complemented
104#2067C2211yescharacteristic, complemented
105#2067C2211yescharacteristic, complemented
106#2066C2211yescharacteristic, complemented
107#2057C2211yescharacteristic, complemented
108#2055C2211yescharacteristic, complemented
109#2055C2211yescharacteristic, complemented
110#2055C2211yescharacteristic, complemented
111#2041C2211yescharacteristic
112#2041C2211yescharacteristic
113#2041C2211yescharacteristic
114#2036C2211yescharacteristic, complemented
115#2034C2211yescharacteristic
116#2034C2211yescharacteristic
117#2033C2211yescharacteristic
118#2023C2211yescharacteristic, complemented
119#2014C2211yescharacteristic
120#2000C2211yescharacteristic
121#1948C2211yescharacteristic, complemented
122#1948C2211yescharacteristic, complemented
123#1944C2211yescharacteristic, complemented
124#1942C2211yescharacteristic, complemented
125#1936C2211yescharacteristic, complemented
126#1934C2211yescharacteristic, complemented
127#1928C2211yescharacteristic, complemented
128#1928C2211yescharacteristic, complemented
129#1927C2211yescharacteristic, complemented
130#1925C2211yescharacteristic, complemented
131#1924C2211yescharacteristic, complemented
132#1923C2211yescharacteristic, complemented
133#1921C2211yescharacteristic, complemented
134#1920C2211yescharacteristic, complemented
135#1920C2211yescharacteristic, complemented
136#1920C2211yescharacteristic, complemented
137#1920C2211yescharacteristic, complemented
138#1919C2211yescharacteristic, complemented
139#1919C2211yescharacteristic, complemented
140#1918C2211yescharacteristic, complemented
141#1917C2211yescharacteristic, complemented
142#1916C2211yescharacteristic, complemented
143#1895C2211yescharacteristic
144#1894C2211yescharacteristic, complemented
145#1880C2211yescharacteristic, complemented
146#1877C2211yescharacteristic
147#1877C2211yescharacteristic
148#1877C2211yescharacteristic
149#1877C2211yescharacteristic
150#1877C2211yescharacteristic, complemented
151#1877C2211yescharacteristic, complemented
152#1877C2211yescharacteristic, complemented
153#1874C2211yescharacteristic
154#1873C2211yescharacteristic, complemented
155#1870C2211yescharacteristic
156#1869C2211yescharacteristic
157#1864C2211yescharacteristic
158#1864C2211yescharacteristic
159#1864C2211yescharacteristic
160#1864C2211yescharacteristic
161#1864C2211yescharacteristic
162#1864C2211yescharacteristic, complemented
163#1864C2211yescharacteristic, complemented
164#1864C2211yescharacteristic, complemented
165#1863C2211yescharacteristic, complemented
166#1862C2211yescharacteristic
167#1862C2211yescharacteristic
168#1862C2211yescharacteristic
169#1862C2211yescharacteristic
170#1862C2211yescharacteristic
171#1862C2211yescharacteristic, complemented
172#1862C2211yescharacteristic, complemented
173#1862C2211yescharacteristic, complemented
174#1862C2211yescharacteristic, complemented
175#1862C2211yescharacteristic, complemented
176#1862C2211yescharacteristic, complemented
177#1854C2211yescharacteristic, complemented
178#1854C2211yescharacteristic, complemented
179#1854C2211yescharacteristic, complemented
180#1852C2211yescharacteristic, complemented
181#1851C2211yescharacteristic, complemented
182#1850C2211yescharacteristic, complemented
183#1839C2211yescharacteristic, complemented
184#1831C2211yescharacteristic, complemented
185#1825C2211yescharacteristic, complemented
186#1825C2211yescharacteristic, complemented
187#1818C2211yescharacteristic, complemented
188#1808C2211yescharacteristic, complemented
189#1804C2211yescharacteristic
190#1804C2211yescharacteristic, complemented
191#1802C2211yescharacteristic
192#1802C2211yescharacteristic
193#1798C2211yescharacteristic, complemented
194#1786C2211yescharacteristic
195#1786C2211yescharacteristic
196#1786C2211yescharacteristic
197#1786C2211yescharacteristic
198#1762C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic
200#1750C2211yescharacteristic, complemented
201#1735C2211yescharacteristic, complemented
202#1729C2211yescharacteristic, complemented
203C23×D4—21no—
204C23×D4C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C23×C8C2311yescharacteristic
211D42—24no—
212D42—24no—
213C2×C4⋊Q8C2311yescharacteristic
214C2×#127C2311yescharacteristic
215C2×#126—21no—
216C2×#125—21no—
217C2×C22⋊Q8—21no—
218C2×C22⋊Q8C2311yescharacteristic
219C2×C22⋊Q8C2311yescharacteristic
220C2×#121—21no—
221C2×#121C2311yescharacteristic
222C2×#121C2311yescharacteristic
223C2×#120—21no—
224C2×#120—21no—
225#518—42no—
226#518—42no—
227#518—42no—
228#518—42no—
229C2×C4×Q8C2311yescharacteristic
230C2×C4×D4—21no—
231C2×C4×D4—21no—
232C2×C4×D4—21no—
233C2×C4×D4—21no—
234C2×C4×D4—21no—
235C2×C4×D4—21no—
236C2×C4×D4—21no—
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C22×C4⋊C4—21no—
253C22×C4⋊C4C2311yescharacteristic
254C22×C22⋊C4—21no—
255C22×C22⋊C4—21no—
256C22×C22⋊C4—21no—
257C22×C22⋊C4—21no—
258C22×C22⋊C4—21no—
259C22×C22⋊C4—21no—
260C22×C42—21no—
261#485—42no—
262#482—24no—
263#476—42no—
264#474—42no—
265#465—24no—
266#450—24no—
267#450—42no—
268#440—42no—
269C4×SD16—42no—
270#428—42no—
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#107C2311yescharacteristic
278C2×#107C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288#418—24no—
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#102—42no—
295C2×#102C2311yescharacteristic
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×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×#97C2311yescharacteristic
323C2×C4×C8C2311yescharacteristic
324#400—21no—
325#400—21no—
326#400—21no—
327#400—21no—
328#400—21no—
329#399—21no—
330#399—21no—
331#398—21no—
332#398—21no—
333#398—21no—
334#398—21no—
335#398—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#396—21no—
343#395—21no—
344#395—21no—
345#395—21no—
346#394—21no—
347#393—21no—
348#391—21no—
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#390—21no—
354#390—21no—
355#390—21no—
356#390—21no—
357#390—21no—
358#390—21no—
359#390—21no—
360#390—21no—
361#390D411yescharacteristic
362#390D411yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#389—21no—
368#389—21no—
369#389—21no—
370#389—21no—
371#389D411yescharacteristic
372#389D411yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
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#388D411yescharacteristic
396#388D411yescharacteristic
397#388D411yescharacteristic
398#388D411yescharacteristic
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#384—21no—
429#384C2311yescharacteristic
430#384C2311yescharacteristic
431#384C2311yescharacteristic
432#383—21no—
433#382—21no—
434#382—21no—
435#382C2311yescharacteristic
436#380—21no—
437#380—21no—
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#379—21no—
445#379—21no—
446C4×C4⋊C4—21no—
447C4×C4⋊C4C2311yescharacteristic
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⋊C4C2311yescharacteristic
458C4×C22⋊C4C2311yescharacteristic
459C43C2311yescharacteristic
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#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C25—21no—
498C22×Q8—21no—
499C22×Q8C2411yescharacteristic
500C22×D4—22no—
501C22×D4—22no—
502C22×D4—28no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—22no—
506C22×D4—22no—
507C22×D4—22no—
508C22×D4—22no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—22no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4—82no—
519C22×D4—82no—
520C22×D4C2×D411yescharacteristic
521C22×D4#4114yes—
522C22×D4C2411yescharacteristic
523C22×D4C2411yescharacteristic
524C22×D4C2411yescharacteristic
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4C2411yescharacteristic
536C23×C4C2411yescharacteristic
537C2×SD16—22no—
538C2×SD16—22no—
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×M16—22no—
547C2×M16—41no—
548C2×M16—41no—
549C22×C8—22no—
550C22×C8—41no—
551C22×C8—41no—
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C4⋊Q8—41no—
561C4⋊Q8—41no—
562#127—22no—
563#127—22no—
564#126—82no—
565#125—82no—
566C22⋊Q8—22no—
567C22⋊Q8—22no—
568C22⋊Q8—41no—
569C22⋊Q8—41no—
570C22⋊Q8—82no—
571#121—28no—
572#121—22no—
573#121—22no—
574#121—22no—
575#121#4114yes—
576#120—28no—
577#120—28no—
578C4×Q8—41no—
579C4×Q8—41no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—22no—
589C4×D4—22no—
590C4×D4—22no—
591C4×D4—41no—
592C4×D4—41no—
593C4×D4—41no—
594C4×D4—41no—
595C4×D4—41no—
596C4×D4—41no—
597C4×D4—41no—
598C4×D4—41no—
599C4×D4—41no—
600C4×D4—44no—
601C4×D4—44no—
602C4×D4—44no—
603C4×D4—44no—
604C4×D4—82no—
605C4×D4—82no—
606C4×D4—82no—
607#117—22no—
608#117—22no—
609#117—22no—
610#117—22no—
611#117—41no—
612#117—41no—
613#117—41no—
614#117—41no—
615#117—41no—
616#117—41no—
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—41no—
641C2×C4⋊C4—41no—
642C2×C4⋊C4—82no—
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—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—44no—
693C2×C22⋊C4—44no—
694C2×C22⋊C4—44no—
695C2×C22⋊C4—44no—
696C2×C22⋊C4—82no—
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—82no—
717C2×C42C2×D411yescharacteristic
718C2×C42C2×D411yescharacteristic
719C2×C42C2×D411yescharacteristic
720C2×C42C2×D411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726#107—22no—
727#107—41no—
728#107—41no—
729#107—41no—
730#107—41no—
731#107—41no—
732#107—41no—
733#107—41no—
734#106—22no—
735#106—22no—
736#106—22no—
737#106—22no—
738#106—22no—
739C4⋊C8—41no—
740C4⋊C8—41no—
741C4⋊C8—41no—
742C4⋊C8—41no—
743#103—22no—
744#103—22no—
745#103—41no—
746#103—41no—
747#103—41no—
748#102—22no—
749#102—22no—
750#102—22no—
751#102—22no—
752#102—22no—
753#102—22no—
754#102—22no—
755#102—22no—
756#102—22no—
757#102—22no—
758#102—22no—
759#102—22no—
760#102—22no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769C22⋊C8—22no—
770C22⋊C8—22no—
771C22⋊C8—41no—
772C22⋊C8—41no—
773C22⋊C8—41no—
774C22⋊C8—41no—
775#97—41no—
776C4×C8—41no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#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#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815C24—21no—
816C24—24no—
817C24—21no—
818C24—21no—
819C24—24no—
820C24—42no—
821C24—42no—
822C24—42no—
823C24—42no—
824C24—81no—
825C24—81no—
826C24—81no—
827C24—81no—
828C24—81no—
829C24—81no—
830C24—81no—
831C24—81no—
832C24C22×D411yescharacteristic
833C24C22×D411yescharacteristic
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—81no—
841C2×Q8—81no—
842C2×Q8—81no—
843C2×D4—28no—
844C2×D4—24no—
845C2×D4—24no—
846C2×D4—22no—
847C2×D4—24no—
848C2×D4—24no—
849C2×D4—24no—
850C2×D4—24no—
851C2×D4—22no—
852C2×D4—21no—
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—21no—
864C2×D4—21no—
865C2×D4—44no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—41no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—42no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4—816no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4C2×#4112yes—
887C2×D4C2×#4112yes—
888C2×D4C2×#4112yes—
889C2×D4H(5,𝔽2)12yes—
890C2×D42−1+412yes—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—24no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—24no—
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—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—42no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—42no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4—81no—
929C22×C4—81no—
930C22×C4—81no—
931C22×C4—81no—
932C22×C4—81no—
933C22×C4—81no—
934C22×C4—81no—
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×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
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×C4C2×#4112yes—
957C22×C4C2×#4112yes—
958C22×C4C2511yescharacteristic
959SD16—44no—
960SD16—44no—
961SD16—82no—
962M16—44no—
963C2×C8—21no—
964C2×C8—21no—
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—82no—
988C4⋊C4—22no—
989C4⋊C4—22no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
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—41no—
1013C4⋊C4—41no—
1014C4⋊C4—41no—
1015C4⋊C4—41no—
1016C4⋊C4—41no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4C2×#4112yes—
1041C4⋊C4H(5,𝔽2)12yes—
1042C22⋊C4—24no—
1043C22⋊C4—24no—
1044C22⋊C4—24no—
1045C22⋊C4—22no—
1046C22⋊C4—24no—
1047C22⋊C4—22no—
1048C22⋊C4—22no—
1049C22⋊C4—22no—
1050C22⋊C4—41no—
1051C22⋊C4—41no—
1052C22⋊C4—41no—
1053C22⋊C4—41no—
1054C22⋊C4—41no—
1055C22⋊C4—41no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
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—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C42—22no—
1083C42—22no—
1084C42—21no—
1085C42—21no—
1086C42—21no—
1087C42—21no—
1088C42—21no—
1089C42—21no—
1090C42—21no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—41no—
1095C42—41no—
1096C42—42no—
1097C42—42no—
1098C42—42no—
1099C42—42no—
1100C42—81no—
1101C42—81no—
1102C42—81no—
1103C42—81no—
1104C23—21no—
1105C23—21no—
1106C23—22no—
1107C23—22no—
1108C23—21no—
1109C23—22no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—22no—
1117C23—22no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—48no—
1123C23—48no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—84no—
1141C23—84no—
1142C23—84no—
1143C23—84no—
1144C23—162no—
1145C23—162no—
1146C23—162no—
1147C23—162no—
1148C23—162no—
1149C23—162no—
1150C23—162no—
1151C23—162no—
1152C23#52512yes—
1153C23C23×D411yescharacteristic
1154Q8—41no—
1155Q8—41no—
1156Q8—41no—
1157Q8—41no—
1158Q8—162no—
1159D4—22no—
1160D4—22no—
1161D4—22no—
1162D4—22no—
1163D4—22no—
1164D4—22no—
1165D4—22no—
1166D4—48no—
1167D4—44no—
1168D4—48no—
1169D4—48no—
1170D4—41no—
1171D4—41no—
1172D4—41no—
1173D4—41no—
1174D4—84no—
1175D4—84no—
1176D4—84no—
1177D4#53914yes—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
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—22no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—22no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—48no—
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—84no—
1260C2×C4—84no—
1261C2×C4—162no—
1262C2×C4—162no—
1263C2×C4—162no—
1264C2×C4—162no—
1265C2×C4—162no—
1266C2×C4—162no—
1267C2×C4—162no—
1268C2×C4#52512yes—
1269C2×C4#57612yes—
1270C2×C4#57712yes—
1271C2×C4C22×#4111yescharacteristic
1272C2×C4C22×#4111yescharacteristic
1273C2×C4C2×H(5,𝔽2)11yescharacteristic
1274C2×C4C2×H(5,𝔽2)11yescharacteristic
1275C2×C4C2×2−1+411yescharacteristic
1276C2×C4#58511yescharacteristic
1277C8—41no—
1278C8—41no—
1279C8—41no—
1280C8—41no—
1281C8—41no—
1282C8—41no—
1283C8—41no—
1284C8—41no—
1285C22—22no—
1286C22—22no—
1287C22—24no—
1288C22—22no—
1289C22—41no—
1290C22—42no—
1291C22—42no—
1292C22—42no—
1293C22—42no—
1294C22—41no—
1295C22—41no—
1296C22—42no—
1297C22—42no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—42no—
1302C22—42no—
1303C22—41no—
1304C22—42no—
1305C22—42no—
1306C22—42no—
1307C22—42no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—168no—
1321C22—168no—
1322C22C2×#52511yescharacteristic
1323C22#348411yescharacteristic
1324C22#348911yescharacteristic
1325C22C2×#57611yescharacteristic
1326C22C2×#57711yescharacteristic
1327C22#358511yescharacteristic
1328C22#358611yescharacteristic
1329C4—22no—
1330C4—22no—
1331C4—22no—
1332C4—41no—
1333C4—42no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—42no—
1340C4—41no—
1341C4—41no—
1342C4—41no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4C2×#53911yescharacteristic
1355C4#345911yescharacteristic
1356C4#351311yescharacteristic
1357C4#352011yescharacteristic
1358C2—42no—
1359C2—44no—
1360C2—81no—
1361C2—82no—
1362C2—82no—
1363C2#3499111yescharacteristic
1364C2#6057911yescharacteristic
1365C2#6059611yescharacteristic
1366C2#6168011yescharacteristic
1367C2#6168811yescharacteristic
1368C2#6220011yescharacteristic
1369C2#6223611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×D42C22
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. #37342C2semidirect
3. #33084C2semidirect
4. #33068C2semidirect
5. #33018C2semidirect
6. #32962C2semidirect
7. #30177C2semidirect
8. #30128C2semidirect
9. #30075C2semidirect
10. #30025C2semidirect
11. #27518C2semidirect
12. #27301C2semidirect
13. #27054C2semidirect
14. #26897C2semidirect
15. #26770C2semidirect
16. #26557C2semidirect
17. #26384C2semidirect
18. #26359C2semidirect
19. #26151C2semidirect
20. #25950C2semidirect
21. #25211C2semidirect
22. #24948C2semidirect
23. #24921C2semidirect
24. #24538C2semidirect
27. #22194C2semidirect
28. #22088C2semidirect
29. #22007C2semidirect
30. #21459C2semidirect
31. #20876C2semidirect
35. C2×#485C22semidirect
37. C2×#476C22semidirect
43. C2×C4×SD16C22semidirect
44. C2×#428C22semidirect
47. #2863C22semidirect
48. #2859C22semidirect
57. #2628C22semidirect
58. #2625C22semidirect
59. #2509C22semidirect
60. #2499C22semidirect
61. #2496C22semidirect
63. #2451C22semidirect
64. #2440C22semidirect
65. #2423C22semidirect
80. #2323C22semidirect
83. #2317C22semidirect
89. #2100C22semidirect
90. #2095C22semidirect
91. #2093C22semidirect
92. #2093C22semidirect
93. #2087C22semidirect
94. #2085C22semidirect
95. #2083C22semidirect
96. #2083C22semidirect
97. #2076C22semidirect
98. #2075C22semidirect
99. #2075C22semidirect
100. #2073C22semidirect
101. #2071C22semidirect
102. #2071C22semidirect
103. #2067C22semidirect
104. #2067C22semidirect
105. #2067C22semidirect
106. #2066C22semidirect
107. #2057C22semidirect
108. #2055C22semidirect
109. #2055C22semidirect
110. #2055C22semidirect
114. #2036C22semidirect
118. #2023C22semidirect
121. #1948C22semidirect
122. #1948C22semidirect
123. #1944C22semidirect
124. #1942C22semidirect
125. #1936C22semidirect
126. #1934C22semidirect
127. #1928C22semidirect
128. #1928C22semidirect
129. #1927C22semidirect
130. #1925C22semidirect
131. #1924C22semidirect
132. #1923C22semidirect
133. #1921C22semidirect
134. #1920C22semidirect
135. #1920C22semidirect
136. #1920C22semidirect
137. #1920C22semidirect
138. #1919C22semidirect
139. #1919C22semidirect
140. #1918C22semidirect
141. #1917C22semidirect
142. #1916C22semidirect
144. #1894C22semidirect
145. #1880C22semidirect
150. #1877C22semidirect
151. #1877C22semidirect
152. #1877C22semidirect
154. #1873C22semidirect
162. #1864C22semidirect
163. #1864C22semidirect
164. #1864C22semidirect
165. #1863C22semidirect
171. #1862C22semidirect
172. #1862C22semidirect
173. #1862C22semidirect
174. #1862C22semidirect
175. #1862C22semidirect
176. #1862C22semidirect
177. #1854C22semidirect
178. #1854C22semidirect
179. #1854C22semidirect
180. #1852C22semidirect
181. #1851C22semidirect
182. #1850C22semidirect
183. #1839C22semidirect
184. #1831C22semidirect
185. #1825C22semidirect
186. #1825C22semidirect
187. #1818C22semidirect
188. #1808C22semidirect
190. #1804C22semidirect
193. #1798C22semidirect
198. #1762C22semidirect
200. #1750C22semidirect
201. #1735C22semidirect
202. #1729C22semidirect

Maximal subgroups

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

subgroupindex
#373422
#343102
#330842
#330682
#330182
#329622
#301772
#301282
#300752
#300252
#275182
#273012
#270542
#268972
#267702
#265572
#263842
#263592
#261512
#259502
#252112
#249482
#249212
#245382
#244322
#240442
#221942
#220882
#220072
#214592
#208762