Finite Group Databasebeta

← #7078865

Subgroups — #7078865

Order 512.

1541 conjugacy classes of subgroups.

The subgroup lattice has 1288 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59272C211yesmaximal, characteristic
2#39604C211yesmaximal, characteristic, complemented
3#32540C211yesmaximal, characteristic, complemented
4#32430C211yesmaximal, characteristic, complemented
5#32390C211yesmaximal, characteristic, complemented
6#32347C211yesmaximal, characteristic, complemented
7#32283C211yesmaximal, characteristic, complemented
8#31934C211yesmaximal, characteristic, complemented
9#30797C211yesmaximal, characteristic, complemented
10#30678C211yesmaximal, characteristic, complemented
11#28865C211yesmaximal, characteristic, complemented
12#28543C211yesmaximal, characteristic, complemented
13#28046C211yesmaximal, characteristic, complemented
14#27945C211yesmaximal, characteristic, complemented
15#27858C211yesmaximal, characteristic, complemented
16#27516C211yesmaximal, characteristic, complemented
17#26572C211yesmaximal, characteristic, complemented
18#26357C211yesmaximal, characteristic, complemented
19#26346C211yesmaximal, characteristic, complemented
20#26138C211yesmaximal, characteristic, complemented
21#26102C211yesmaximal, characteristic, complemented
22#26068C211yesmaximal, characteristic, complemented
23#25950C211yesmaximal, characteristic, complemented
24#25128C211yesmaximal, characteristic
25#24861C211yesmaximal, characteristic
26#24501C211yesmaximal, characteristic, complemented
27C2×#2094C211yesmaximal, characteristic, complemented
28#22902C211yesmaximal, characteristic, complemented
29#22854C211yesmaximal, characteristic, complemented
30#22659C211yesmaximal, characteristic, complemented
31#21982C211yesmaximal, characteristic, complemented
32C2×#501C2211yescharacteristic, complemented
33C2×#485C2211yescharacteristic, complemented
34C2×#480C2211yescharacteristic
35C2×#479C2211yescharacteristic, complemented
36C2×#474C2211yescharacteristic
37C2×#468C2211yescharacteristic
38C2×#450C2211yescharacteristic
39C2×#440C2211yescharacteristic
40C2×#435C2211yescharacteristic
41C2×#431C2211yescharacteristic
42C2×#428C2211yescharacteristic, complemented
43C22×#106C2211yescharacteristic
44C22×#106C2211yescharacteristic
45C22×#102C2211yescharacteristic
46C22×#102C2211yescharacteristic
47#2855C2211yescharacteristic
48#2792—21no—
49#2791—21no—
50#2790—21no—
51#2761—21no—
52#2753—21no—
53#2720—21no—
54#2627—21no—
55#2597—21no—
56#2567C2211yescharacteristic, complemented
57#2566C2211yescharacteristic
58#2554—21no—
59#2552C2211yescharacteristic, complemented
60#2513C2211yescharacteristic
61#2512C2211yescharacteristic
62#2511C2211yescharacteristic, complemented
63#2507C2211yescharacteristic, complemented
64#2502C2211yescharacteristic, complemented
65#2500C2211yescharacteristic
66#2497C2211yescharacteristic, complemented
67#2490C2211yescharacteristic
68#2480—21no—
69#2473—21no—
70#2449—21no—
71#2442C2211yescharacteristic
72#2440C2211yescharacteristic
73#2440C2211yescharacteristic, complemented
74#2423C2211yescharacteristic, complemented
75#2422C2211yescharacteristic
76#2417C2211yescharacteristic
77#2412—21no—
78#2411—21no—
79#2408C2211yescharacteristic
80#2363C2211yescharacteristic
81#2360C2211yescharacteristic
82#2357C2211yescharacteristic
83#2352C2211yescharacteristic
84D4×C4⋊C4C2211yescharacteristic
85#2342—21no—
86D4×C22⋊C4C2211yescharacteristic
87#2322—21no—
88C4×#123C2211yescharacteristic
89C2×#390C2211yescharacteristic
90#2285C2211yescharacteristic
91C2×#384C2211yescharacteristic
92#2100C2211yescharacteristic, complemented
93#2097C2211yescharacteristic, complemented
94#2097C2211yescharacteristic, complemented
95#2095C2211yescharacteristic, complemented
96#2094C2211yescharacteristic
97#2094C2211yescharacteristic
98#2094C2211yescharacteristic
99#2094C2211yescharacteristic
100#2094C2211yescharacteristic
101#2094C2211yescharacteristic
102#2094C2211yescharacteristic
103#2094C2211yescharacteristic
104#2093C2211yescharacteristic
105#2093C2211yescharacteristic
106#2088C2211yescharacteristic, complemented
107#2085C2211yescharacteristic, complemented
108#2085C2211yescharacteristic, complemented
109#2084C2211yescharacteristic, complemented
110#2083C2211yescharacteristic, complemented
111#2077C2211yescharacteristic, complemented
112#2072C2211yescharacteristic, complemented
113#2071C2211yescharacteristic
114#2067C2211yescharacteristic
115#2067C2211yescharacteristic
116#2067C2211yescharacteristic
117#2066C2211yescharacteristic, complemented
118#2065C2211yescharacteristic
119#2065C2211yescharacteristic
120#2059C2211yescharacteristic, complemented
121#2059C2211yescharacteristic, complemented
122#2058C2211yescharacteristic, complemented
123#2055C2211yescharacteristic
124#2055C2211yescharacteristic
125#2055C2211yescharacteristic
126#2035C2211yescharacteristic, complemented
127#2033C2211yescharacteristic
128#2033C2211yescharacteristic
129#2033C2211yescharacteristic
130#2023C2211yescharacteristic
131#2000C2211yescharacteristic
132#1973C2211yescharacteristic
133#1973C2211yescharacteristic
134#1968C2211yescharacteristic
135#1968C2211yescharacteristic
136#1949C2211yescharacteristic, complemented
137#1949C2211yescharacteristic, complemented
138#1948C2211yescharacteristic, complemented
139#1947C2211yescharacteristic, complemented
140#1947C2211yescharacteristic, complemented
141#1947C2211yescharacteristic, complemented
142#1947C2211yescharacteristic, complemented
143#1944C2211yescharacteristic, complemented
144#1943C2211yescharacteristic, complemented
145#1940C2211yescharacteristic, complemented
146#1936C2211yescharacteristic
147#1936C2211yescharacteristic
148#1934C2211yescharacteristic
149#1934C2211yescharacteristic
150#1928C2211yescharacteristic, complemented
151#1928C2211yescharacteristic, complemented
152#1927C2211yescharacteristic, complemented
153#1925C2211yescharacteristic
154#1925C2211yescharacteristic
155#1925C2211yescharacteristic
156#1924C2211yescharacteristic, complemented
157#1923C2211yescharacteristic, complemented
158#1921C2211yescharacteristic, complemented
159#1921C2211yescharacteristic, complemented
160#1920C2211yescharacteristic, complemented
161#1919C2211yescharacteristic, complemented
162#1917C2211yescharacteristic, complemented
163#1916C2211yescharacteristic, complemented
164#1895C2211yescharacteristic
165#1892C2211yescharacteristic
166#1892C2211yescharacteristic
167#1880C2211yescharacteristic
168#1877C2211yescharacteristic
169#1874C2211yescharacteristic
170#1872C2211yescharacteristic
171#1869C2211yescharacteristic
172#1865C2211yescharacteristic, complemented
173#1862C2211yescharacteristic
174#1862C2211yescharacteristic
175#1862C2211yescharacteristic
176#1854C2211yescharacteristic, complemented
177#1854C2211yescharacteristic, complemented
178#1853C2211yescharacteristic
179#1853C2211yescharacteristic, complemented
180#1852C2211yescharacteristic
181#1852C2211yescharacteristic
182#1852C2211yescharacteristic
183#1852C2211yescharacteristic
184#1851C2211yescharacteristic, complemented
185#1850C2211yescharacteristic
186#1847C2211yescharacteristic, complemented
187#1847C2211yescharacteristic, complemented
188#1845C2211yescharacteristic, complemented
189#1845C2211yescharacteristic, complemented
190#1834C2211yescharacteristic, complemented
191#1834C2211yescharacteristic, complemented
192#1809C2211yescharacteristic, complemented
193#1808C2211yescharacteristic
194#1808C2211yescharacteristic
195#1802C2211yescharacteristic
196#1786C2211yescharacteristic
197#1776C2211yescharacteristic, complemented
198#1771C2211yescharacteristic, complemented
199#1762C2211yescharacteristic
200#1753C2211yescharacteristic, complemented
201#1752C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×#126—21no—
211C2×#125—21no—
212C2×#125C2311yescharacteristic
213C2×#123—21no—
214C2×#123D411yescharacteristic
215C2×C22⋊Q8—21no—
216C2×C22⋊Q8—21no—
217C2×C22⋊Q8C2311yescharacteristic
218C2×C22⋊Q8C2311yescharacteristic
219C2×#121C2311yescharacteristic
220C2×#121C2311yescharacteristic
221C2×#120—21no—
222C2×C4×Q8C2311yescharacteristic
223C2×C4×D4—21no—
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×#117—21no—
228C2×#117C2311yescharacteristic
229C22×C4⋊C4—21no—
230C22×C4⋊C4—21no—
231C22×C4⋊C4C2311yescharacteristic
232C22×C4⋊C4C2311yescharacteristic
233C22×C4⋊C4C2311yescharacteristic
234C22×C4⋊C4C2311yescharacteristic
235C22×C22⋊C4—21no—
236C22×C22⋊C4—21no—
237C22×C22⋊C4—21no—
238C22×C42C2311yescharacteristic
239#501—42no—
240#485—42no—
241#480—42no—
242#479—42no—
243#474—42no—
244#468—42no—
245#450—24no—
246#440—42no—
247#435—24no—
248#431—24no—
249#428—42no—
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#106—42no—
263C2×#106—42no—
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#102—42no—
286C2×#102—42no—
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×#97C2311yescharacteristic
307C2×#97C2311yescharacteristic
308C2×#97C2311yescharacteristic
309C2×C4×C8C2311yescharacteristic
310C2×C4×C8C2311yescharacteristic
311#400—21no—
312#400—21no—
313#400—21no—
314#400—21no—
315#399—21no—
316#398—21no—
317#398—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#396—21no—
333#396—21no—
334#396—21no—
335#396—21no—
336#396—21no—
337#395—21no—
338#395—21no—
339#395—21no—
340#395—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#392—21no—
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#390—21no—
352#390—21no—
353#390—21no—
354#390—21no—
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#389—21no—
364#389—21no—
365#389—21no—
366#389—21no—
367#389—21no—
368#389—21no—
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#388—21no—
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#388D411yescharacteristic
390#388D411yescharacteristic
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387D411yescharacteristic
401#387D411yescharacteristic
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386D411yescharacteristic
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385D411yescharacteristic
421#384—21no—
422#384—21no—
423#384C2311yescharacteristic
424#384C2311yescharacteristic
425#384C2311yescharacteristic
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#384C2311yescharacteristic
429#384C2311yescharacteristic
430#384C2311yescharacteristic
431#382—21no—
432#382C2311yescharacteristic
433#382C2311yescharacteristic
434#381—21no—
435#381—21no—
436#381D411yescharacteristic
437#380—21no—
438#380—21no—
439#380—21no—
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#379—21no—
447#379—21no—
448C4×C4⋊C4—21no—
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4C2311yescharacteristic
461C4×C22⋊C4C2311yescharacteristic
462C4×C22⋊C4C2311yescharacteristic
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#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C22×Q8—21no—
495C22×Q8C2411yescharacteristic
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—22no—
501C22×D4—22no—
502C22×D4—41no—
503C22×D4—41no—
504C22×D4—41no—
505C22×D4C2×D411yescharacteristic
506C22×D4C2411yescharacteristic
507C22×D4C2411yescharacteristic
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4C2×D411yescharacteristic
515C23×C4C2×D411yescharacteristic
516C23×C4C2411yescharacteristic
517C23×C4C2411yescharacteristic
518C2×SD16—22no—
519C2×SD16—22no—
520C2×SD16—22no—
521C2×SD16—41no—
522C2×SD16—41no—
523C2×SD16—41no—
524C2×M16—22no—
525C2×M16—22no—
526C2×M16—41no—
527C22×C8—22no—
528C22×C8—22no—
529C22×C8—22no—
530C22×C8—22no—
531C22×C8—41no—
532C22×C8—41no—
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C4⋊Q8—41no—
542C4⋊Q8—41no—
543#126—82no—
544#125—41no—
545#125—41no—
546#125—82no—
547#123—24no—
548#123—82no—
549C22⋊Q8—22no—
550C22⋊Q8—22no—
551C22⋊Q8—41no—
552C22⋊Q8—41no—
553C22⋊Q8—82no—
554C22⋊Q8—82no—
555#121—22no—
556#121—41no—
557#121—41no—
558#121—41no—
559#120—82no—
560C4×Q8—41no—
561C4×Q8—41no—
562C4×D4—22no—
563C4×D4—22no—
564C4×D4—22no—
565C4×D4—41no—
566C4×D4—41no—
567C4×D4—41no—
568C4×D4—82no—
569#117—41no—
570#117—41no—
571#117—82no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—41no—
607C2×C4⋊C4—41no—
608C2×C4⋊C4—41no—
609C2×C4⋊C4—41no—
610C2×C4⋊C4—41no—
611C2×C4⋊C4—41no—
612C2×C4⋊C4—41no—
613C2×C4⋊C4—41no—
614C2×C4⋊C4—82no—
615C2×C4⋊C4—82no—
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4C2×D411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—44no—
664C2×C22⋊C4—82no—
665C2×C22⋊C4—82no—
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C22⋊C4C2×D411yescharacteristic
668C2×C22⋊C4C2×D411yescharacteristic
669C2×C22⋊C4C2×D411yescharacteristic
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C22⋊C4C2×D411yescharacteristic
672C2×C22⋊C4C2×D411yescharacteristic
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C42—22no—
675C2×C42—22no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—21no—
682C2×C42—21no—
683C2×C42C2×D411yescharacteristic
684C2×C42C2×D411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690#107—22no—
691#107—22no—
692#107—41no—
693#107—41no—
694#107—41no—
695#107—41no—
696#107—41no—
697#107—41no—
698#107—41no—
699#107—41no—
700#107—41no—
701#107—41no—
702#106—22no—
703#106—22no—
704#106—22no—
705#106—22no—
706#106—41no—
707#106—41no—
708#106—41no—
709#106—41no—
710#106—41no—
711#106—41no—
712C4⋊C8—22no—
713C4⋊C8—22no—
714C4⋊C8—22no—
715C4⋊C8—22no—
716C4⋊C8—41no—
717#103—22no—
718#103—22no—
719#103—41no—
720#103—41no—
721#103—41no—
722#103—41no—
723#102—22no—
724#102—22no—
725#102—22no—
726#102—22no—
727#102—22no—
728#102—22no—
729#102—22no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102—41no—
736#102—41no—
737C22⋊C8—22no—
738C22⋊C8—22no—
739C22⋊C8—22no—
740C22⋊C8—41no—
741C22⋊C8#4114yes—
742#97—22no—
743#97—22no—
744#97—41no—
745C4×C8—22no—
746C4×C8—22no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788C24—21no—
789C24—21no—
790C24—42no—
791C24—42no—
792C24—42no—
793C24—42no—
794C24—81no—
795C24—81no—
796C24—81no—
797C24C22×D411yescharacteristic
798C24C22×D411yescharacteristic
799C2×Q8—21no—
800C2×Q8—21no—
801C2×Q8—21no—
802C2×Q8—21no—
803C2×Q8—21no—
804C2×Q8—21no—
805C2×Q8—81no—
806C2×Q8—81no—
807C2×Q8—81no—
808C2×D4—22no—
809C2×D4—22no—
810C2×D4—22no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—44no—
823C2×D4—44no—
824C2×D4—42no—
825C2×D4—42no—
826C2×D4—42no—
827C2×D4—82no—
828C2×D4—82no—
829C2×D4—81no—
830C2×D4—81no—
831C2×D4—81no—
832C2×D4—81no—
833C2×D4—81no—
834C2×D4—81no—
835C2×D42−1+412yes—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—41no—
865C22×C4—42no—
866C22×C4—42no—
867C22×C4—42no—
868C22×C4—42no—
869C22×C4—81no—
870C22×C4—81no—
871C22×C4—81no—
872C22×C4—81no—
873C22×C4—81no—
874C22×C4—81no—
875C22×C4—81no—
876C22×C4—81no—
877C22×C4—81no—
878C22×C4—81no—
879C22×C4—81no—
880C22×C4—81no—
881C22×C4—81no—
882C22×C4—81no—
883C22×C4#13714yes—
884C22×C4C22×D411yescharacteristic
885C22×C4C22×D411yescharacteristic
886C22×C4C22×D411yescharacteristic
887C22×C4C22×D411yescharacteristic
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C2×#4112yes—
897C22×C42−1+412yes—
898C22×C4C2511yescharacteristic
899SD16—44no—
900SD16—82no—
901M16—44no—
902C2×C8—21no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—44no—
923C2×C8—44no—
924C2×C8C2×#4112yes—
925C2×C8C2×#4112yes—
926C2×C8H(5,𝔽2)12yes—
927C2×C8H(5,𝔽2)12yes—
928C4⋊C4—22no—
929C4⋊C4—22no—
930C4⋊C4—22no—
931C4⋊C4—22no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—41no—
959C4⋊C4—42no—
960C4⋊C4—42no—
961C4⋊C4—42no—
962C4⋊C4—42no—
963C4⋊C4—42no—
964C4⋊C4—42no—
965C4⋊C4—81no—
966C4⋊C4—81no—
967C4⋊C4—81no—
968C4⋊C4—81no—
969C4⋊C4—81no—
970C4⋊C4—81no—
971C4⋊C4—81no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C22⋊C4—22no—
994C22⋊C4—22no—
995C22⋊C4—22no—
996C22⋊C4—22no—
997C22⋊C4—22no—
998C22⋊C4—22no—
999C22⋊C4—22no—
1000C22⋊C4—41no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C42—22no—
1031C42—22no—
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—21no—
1036C42—21no—
1037C42—21no—
1038C42—21no—
1039C42—21no—
1040C42—21no—
1041C42—21no—
1042C42—81no—
1043C42—81no—
1044C42—81no—
1045C42—81no—
1046C42—81no—
1047C42—81no—
1048C42—81no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—22no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—84no—
1075C23—84no—
1076C23—84no—
1077C23—84no—
1078C23—162no—
1079C23—162no—
1080C23—162no—
1081C23#54712yes—
1082C23C2×#13712yes—
1083C23#57612yes—
1084C23C23×D411yescharacteristic
1085Q8—41no—
1086Q8—41no—
1087Q8—41no—
1088Q8—41no—
1089Q8—162no—
1090D4—22no—
1091D4—22no—
1092D4—44no—
1093D4—41no—
1094D4—41no—
1095D4—41no—
1096D4—41no—
1097D4—41no—
1098D4—41no—
1099D4—84no—
1100D4—162no—
1101D4—162no—
1102C2×C4—21no—
1103C2×C4—28no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—44no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—162no—
1187C2×C4—162no—
1188C2×C4—162no—
1189C2×C4—162no—
1190C2×C4—162no—
1191C2×C4—162no—
1192C2×C4#54712yes—
1193C2×C4C2×#13712yes—
1194C2×C4C2×#13712yes—
1195C2×C4#57712yes—
1196C2×C4C22×#4111yescharacteristic
1197C2×C4C2×H(5,𝔽2)11yescharacteristic
1198C2×C4C2×H(5,𝔽2)11yescharacteristic
1199C2×C4C2×2−1+411yescharacteristic
1200C2×C4C2×2−1+411yescharacteristic
1201C2×C4#58511yescharacteristic
1202C8—22no—
1203C8—22no—
1204C8—22no—
1205C8—22no—
1206C8—41no—
1207C8—41no—
1208C8—41no—
1209C8—41no—
1210C22—22no—
1211C22—22no—
1212C22—22no—
1213C22—22no—
1214C22—22no—
1215C22—22no—
1216C22—41no—
1217C22—41no—
1218C22—41no—
1219C22—42no—
1220C22—41no—
1221C22—42no—
1222C22—41no—
1223C22—42no—
1224C22—41no—
1225C22—41no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—168no—
1238C22#334614yes—
1239C22C2×#54711yescharacteristic
1240C22#348911yescharacteristic
1241C22#349811yescharacteristic
1242C22C22×#13711yescharacteristic
1243C22C2×#57611yescharacteristic
1244C22C2×#57711yescharacteristic
1245C22#358511yescharacteristic
1246C4—22no—
1247C4—22no—
1248C4—22no—
1249C4—22no—
1250C4—41no—
1251C4—41no—
1252C4—41no—
1253C4—41no—
1254C4—41no—
1255C4—41no—
1256C4—41no—
1257C4—41no—
1258C4—81no—
1259C4—81no—
1260C4—81no—
1261C4—81no—
1262C4—81no—
1263C4—81no—
1264C4—81no—
1265C4—81no—
1266C4—81no—
1267C4—81no—
1268C4—81no—
1269C4—81no—
1270C4—81no—
1271C4—81no—
1272C4#351311yescharacteristic
1273C4#352011yescharacteristic
1274C4#353511yescharacteristic
1275C4#353811yescharacteristic
1276C2—24no—
1277C2—81no—
1278C2—82no—
1279C2—161no—
1280C2#4397611yescharacteristic
1281C2C2×#334611yescharacteristic
1282C2#6127211yescharacteristic
1283C2#6210811yescharacteristic
1284C2#6220011yescharacteristic
1285C2#6242211yescharacteristic
1286C2#6245911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2408C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #39604C2semidirect
3. #32540C2semidirect
4. #32430C2semidirect
5. #32390C2semidirect
6. #32347C2semidirect
7. #32283C2semidirect
8. #31934C2semidirect
9. #30797C2semidirect
10. #30678C2semidirect
11. #28865C2semidirect
12. #28543C2semidirect
13. #28046C2semidirect
14. #27945C2semidirect
15. #27858C2semidirect
16. #27516C2semidirect
17. #26572C2semidirect
18. #26357C2semidirect
19. #26346C2semidirect
20. #26138C2semidirect
21. #26102C2semidirect
22. #26068C2semidirect
23. #25950C2semidirect
26. #24501C2semidirect
27. C2×#2094C2semidirect
28. #22902C2semidirect
29. #22854C2semidirect
30. #22659C2semidirect
31. #21982C2semidirect
32. C2×#501C22semidirect
33. C2×#485C22semidirect
35. C2×#479C22semidirect
42. C2×#428C22semidirect
56. #2567C22semidirect
59. #2552C22semidirect
62. #2511C22semidirect
63. #2507C22semidirect
64. #2502C22semidirect
66. #2497C22semidirect
73. #2440C22semidirect
74. #2423C22semidirect
92. #2100C22semidirect
93. #2097C22semidirect
94. #2097C22semidirect
95. #2095C22semidirect
106. #2088C22semidirect
107. #2085C22semidirect
108. #2085C22semidirect
109. #2084C22semidirect
110. #2083C22semidirect
111. #2077C22semidirect
112. #2072C22semidirect
117. #2066C22semidirect
120. #2059C22semidirect
121. #2059C22semidirect
122. #2058C22semidirect
126. #2035C22semidirect
136. #1949C22semidirect
137. #1949C22semidirect
138. #1948C22semidirect
139. #1947C22semidirect
140. #1947C22semidirect
141. #1947C22semidirect
142. #1947C22semidirect
143. #1944C22semidirect
144. #1943C22semidirect
145. #1940C22semidirect
150. #1928C22semidirect
151. #1928C22semidirect
152. #1927C22semidirect
156. #1924C22semidirect
157. #1923C22semidirect
158. #1921C22semidirect
159. #1921C22semidirect
160. #1920C22semidirect
161. #1919C22semidirect
162. #1917C22semidirect
163. #1916C22semidirect
172. #1865C22semidirect
176. #1854C22semidirect
177. #1854C22semidirect
179. #1853C22semidirect
184. #1851C22semidirect
186. #1847C22semidirect
187. #1847C22semidirect
188. #1845C22semidirect
189. #1845C22semidirect
190. #1834C22semidirect
191. #1834C22semidirect
192. #1809C22semidirect
197. #1776C22semidirect
198. #1771C22semidirect
200. #1753C22semidirect

Maximal subgroups

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

subgroupindex
#592722
#396042
#325402
#324302
#323902
#323472
#322832
#319342
#307972
#306782
#288652
#285432
#280462
#279452
#278582
#275162
#265722
#263572
#263462
#261382
#261022
#260682
#259502
#251282
#248612
#245012
C2×#20942
#229022
#228542
#226592
#219822