Finite Group Databasebeta

← #6722193

Subgroups — #6722193

Order 512.

1488 conjugacy classes of subgroups.

The subgroup lattice has 1232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39592C211yesmaximal, characteristic, complemented
2#36414C211yesmaximal, characteristic
3#33101C211yesmaximal, characteristic, complemented
4#32226C211yesmaximal, characteristic, complemented
5#32220C211yesmaximal, characteristic, complemented
6#32136C211yesmaximal, characteristic, complemented
7#32121C211yesmaximal, characteristic, complemented
8#31872C211yesmaximal, characteristic, complemented
9#31820C211yesmaximal, characteristic, complemented
10#31754C211yesmaximal, characteristic, complemented
11#31686C211yesmaximal, characteristic, complemented
12#29784C211yesmaximal, characteristic, complemented
13#29638C211yesmaximal, characteristic, complemented
14#27707C211yesmaximal, characteristic, complemented
15#27424C211yesmaximal, characteristic, complemented
16#27352C211yesmaximal, characteristic, complemented
17#27009C211yesmaximal, characteristic, complemented
18#26731C211yesmaximal, characteristic, complemented
19#26456C211yesmaximal, characteristic, complemented
20#26425C211yesmaximal, characteristic, complemented
21#26024C211yesmaximal, characteristic, complemented
22#26016C211yesmaximal, characteristic, complemented
23#26011C211yesmaximal, characteristic, complemented
24#25559C211yesmaximal, characteristic
25#25258C211yesmaximal, characteristic
26#25223C211yesmaximal, characteristic, complemented
27#24960C211yesmaximal, characteristic, complemented
28#22931C211yesmaximal, characteristic, complemented
29#22502C211yesmaximal, characteristic, complemented
30#22073C211yesmaximal, characteristic, complemented
31#21313C211yesmaximal, characteristic, complemented
32C2×#554C2211yescharacteristic
33C22×C4⋊Q8C2211yescharacteristic
34C2×#480C2211yescharacteristic
35C2×#480C2211yescharacteristic
36C2×#468C2211yescharacteristic
37C2×#436C2211yescharacteristic
38C2×#423C2211yescharacteristic
39#2860—21no—
40#2855C2211yescharacteristic
41#2854C2211yescharacteristic
42#2713—21no—
43#2713—21no—
44#2677—21no—
45#2677—21no—
46#2627—21no—
47#2554—21no—
48#2553—21no—
49#2551C2211yescharacteristic
50#2551C2211yescharacteristic
51#2531—21no—
52#2529—21no—
53#2526—21no—
54#2512C2211yescharacteristic
55#2507C2211yescharacteristic
56#2502C2211yescharacteristic
57#2496C2211yescharacteristic
58#2492C2211yescharacteristic
59#2492C2211yescharacteristic
60#2490C2211yescharacteristic
61#2487C2211yescharacteristic
62#2471—21no—
63#2451C2211yescharacteristic
64#2451C2211yescharacteristic
65#2441C2211yescharacteristic
66#2440C2211yescharacteristic
67#2440C2211yescharacteristic
68#2434—21no—
69#2414C2211yescharacteristic
70#2409—21no—
71#2370C2211yescharacteristic
72#2363C2211yescharacteristic
73#2363C2211yescharacteristic
74#2354C2211yescharacteristic
75#2354C2211yescharacteristic
76#2346C2211yescharacteristic
77#2345C2211yescharacteristic
78#2322—21no—
79C4×#123C2211yescharacteristic
80#2298—21no—
81C4×#117C2211yescharacteristic
82#2100C2211yescharacteristic
83#2100C2211yescharacteristic
84#2099C2211yescharacteristic
85#2099C2211yescharacteristic
86#2088C2211yescharacteristic
87#2087C2211yescharacteristic
88#2087C2211yescharacteristic
89#2087C2211yescharacteristic
90#2086C2211yescharacteristic
91#2083C2211yescharacteristic
92#2083C2211yescharacteristic
93#2077C2211yescharacteristic
94#2075C2211yescharacteristic
95#2075C2211yescharacteristic
96#2072C2211yescharacteristic
97#2071C2211yescharacteristic
98#2068C2211yescharacteristic
99#2068C2211yescharacteristic
100#2067C2211yescharacteristic
101#2066C2211yescharacteristic
102#2065C2211yescharacteristic
103#2065C2211yescharacteristic
104#2059C2211yescharacteristic
105#2057C2211yescharacteristic
106#2057C2211yescharacteristic
107#2057C2211yescharacteristic
108#2057C2211yescharacteristic
109#2057C2211yescharacteristic
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic
113#2036C2211yescharacteristic
114#2033C2211yescharacteristic
115#2026C2211yescharacteristic
116#2023C2211yescharacteristic
117#2023C2211yescharacteristic
118#2023C2211yescharacteristic
119#2023C2211yescharacteristic
120#2023C2211yescharacteristic
121#2000C2211yescharacteristic
122#1992C2211yescharacteristic
123#1990C2211yescharacteristic
124#1989C2211yescharacteristic
125#1988C2211yescharacteristic
126#1988C2211yescharacteristic
127#1988C2211yescharacteristic
128#1988C2211yescharacteristic
129#1987C2211yescharacteristic
130#1987C2211yescharacteristic
131#1987C2211yescharacteristic
132#1987C2211yescharacteristic
133#1987C2211yescharacteristic
134#1948C2211yescharacteristic
135#1947C2211yescharacteristic
136#1942C2211yescharacteristic
137#1942C2211yescharacteristic
138#1940C2211yescharacteristic
139#1939C2211yescharacteristic
140#1936C2211yescharacteristic
141#1935C2211yescharacteristic
142#1934C2211yescharacteristic
143#1933C2211yescharacteristic
144#1928C2211yescharacteristic
145#1928C2211yescharacteristic
146#1928C2211yescharacteristic
147#1927C2211yescharacteristic
148#1927C2211yescharacteristic
149#1925C2211yescharacteristic
150#1924C2211yescharacteristic
151#1923C2211yescharacteristic
152#1921C2211yescharacteristic
153#1921C2211yescharacteristic
154#1921C2211yescharacteristic
155#1920C2211yescharacteristic
156#1920C2211yescharacteristic
157#1920C2211yescharacteristic
158#1919C2211yescharacteristic
159#1918C2211yescharacteristic
160#1918C2211yescharacteristic
161#1918C2211yescharacteristic
162#1916C2211yescharacteristic
163#1916C2211yescharacteristic
164#1895C2211yescharacteristic
165#1895C2211yescharacteristic
166#1894C2211yescharacteristic
167#1894C2211yescharacteristic
168#1880C2211yescharacteristic
169#1877C2211yescharacteristic
170#1874C2211yescharacteristic
171#1873C2211yescharacteristic
172#1873C2211yescharacteristic
173#1873C2211yescharacteristic
174#1870C2211yescharacteristic
175#1864C2211yescharacteristic
176#1863C2211yescharacteristic
177#1854C2211yescharacteristic
178#1854C2211yescharacteristic
179#1854C2211yescharacteristic
180#1852C2211yescharacteristic
181#1851C2211yescharacteristic
182#1851C2211yescharacteristic
183#1851C2211yescharacteristic
184#1834C2211yescharacteristic
185#1825C2211yescharacteristic
186#1823C2211yescharacteristic
187#1823C2211yescharacteristic
188#1823C2211yescharacteristic
189#1817C2211yescharacteristic
190#1809C2211yescharacteristic
191#1809C2211yescharacteristic
192#1803C2211yescharacteristic
193#1802C2211yescharacteristic
194#1776C2211yescharacteristic
195C4×#103C2211yescharacteristic
196C4×#102C2211yescharacteristic
197#1753C2211yescharacteristic
198#1736C2211yescharacteristic
199#1736C2211yescharacteristic
200#1736C2211yescharacteristic
201#1736C2211yescharacteristic
202#1736C2211yescharacteristic
203C23×Q8—21no—
204C22×SD16C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208#554—24no—
209#554—42no—
210C2×C4⋊Q8—21no—
211C2×C4⋊Q8—21no—
212C2×C4⋊Q8—24no—
213C2×C4⋊Q8—21no—
214C2×C4⋊Q8—21no—
215C2×C4⋊Q8—42no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×#126—21no—
222C2×#126—21no—
223C2×#125—21no—
224C2×#125C2311yescharacteristic
225C2×#123—21no—
226C2×#123D411yescharacteristic
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×D4—21no—
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×#117—21no—
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C22×C4⋊C4—21no—
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C42C2311yescharacteristic
248#480—24no—
249#480—42no—
250#468—42no—
251#436—42no—
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263#423—42no—
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×C22⋊C8C2311yescharacteristic
286C2×C22⋊C8C2311yescharacteristic
287C2×C22⋊C8C2311yescharacteristic
288C2×C22⋊C8C2311yescharacteristic
289C2×C22⋊C8C2311yescharacteristic
290C2×#97C2311yescharacteristic
291C2×C4×C8C2311yescharacteristic
292C2×C4×C8C2311yescharacteristic
293#400—21no—
294#400—21no—
295#400—21no—
296#400—21no—
297#399—21no—
298#399—21no—
299#398—21no—
300#398—21no—
301#398—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#398—21no—
306#398—21no—
307#397—21no—
308#397—21no—
309#397—21no—
310#396—21no—
311#396—21no—
312#395—21no—
313#395—21no—
314#395—21no—
315#395—21no—
316#395—21no—
317#395—21no—
318#395—21no—
319#395—21no—
320#394—21no—
321#394—21no—
322#393—21no—
323#393—21no—
324#392—21no—
325#391—21no—
326#391—21no—
327#391—21no—
328#391—21no—
329#391C2311yescharacteristic
330#391C2311yescharacteristic
331#391C2311yescharacteristic
332#391C2311yescharacteristic
333#390—21no—
334#390—21no—
335#390—21no—
336#390—21no—
337#390—21no—
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#389—21no—
343#389—21no—
344#389—21no—
345#389—21no—
346#389—21no—
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#388—21no—
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388D411yescharacteristic
375#388D411yescharacteristic
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387D411yescharacteristic
388#387D411yescharacteristic
389#386—21no—
390#386—21no—
391#386—21no—
392#386—21no—
393#386D411yescharacteristic
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#385D411yescharacteristic
401#384C2311yescharacteristic
402#384C2311yescharacteristic
403#384C2311yescharacteristic
404#384C2311yescharacteristic
405#382—21no—
406#381—21no—
407#381D411yescharacteristic
408#380—21no—
409#380—21no—
410#380C2311yescharacteristic
411#380C2311yescharacteristic
412#380C2311yescharacteristic
413#380C2311yescharacteristic
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416C4×C4⋊C4—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C22⋊C4—21no—
429C4×C22⋊C4—21no—
430C4×C22⋊C4—21no—
431C4×C22⋊C4—21no—
432C4×C22⋊C4—21no—
433C4×C22⋊C4C2311yescharacteristic
434C4×C22⋊C4C2311yescharacteristic
435C4×C22⋊C4C2311yescharacteristic
436#376—21no—
437#376—21no—
438C43—21no—
439#340C2311yescharacteristic
440#340C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C22×Q8—21no—
488C22×Q8—21no—
489C22×Q8—21no—
490C22×Q8—21no—
491C22×Q8—21no—
492C22×Q8—44no—
493C22×Q8—82no—
494C22×Q8—82no—
495C22×Q8C2411yescharacteristic
496C22×D4—21no—
497C22×D4—21no—
498C22×D4C2×D411yescharacteristic
499C22×D4C2411yescharacteristic
500C23×C4—21no—
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—21no—
504C23×C4C2×D411yescharacteristic
505C23×C4C2×D411yescharacteristic
506C23×C4C2411yescharacteristic
507C23×C4C2411yescharacteristic
508C2×SD16—41no—
509C2×SD16—41no—
510C2×SD16—41no—
511C2×M16—22no—
512C2×M16—22no—
513C2×M16—41no—
514C2×M16—41no—
515C2×M16—41no—
516C2×M16—41no—
517C2×M16—41no—
518C2×M16—41no—
519C2×M16—41no—
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C4⋊Q8—22no—
529C4⋊Q8—22no—
530C4⋊Q8—22no—
531C4⋊Q8—22no—
532C4⋊Q8—22no—
533C4⋊Q8—41no—
534C4⋊Q8—41no—
535C4⋊Q8—41no—
536C4⋊Q8—41no—
537C4⋊Q8—41no—
538C4⋊Q8—44no—
539C4⋊Q8—44no—
540C4⋊Q8—82no—
541C4⋊Q8—82no—
542#126—82no—
543#126—82no—
544#125—22no—
545#125—41no—
546#125—44no—
547#123—24no—
548#123—82no—
549C22⋊Q8—22no—
550C22⋊Q8—22no—
551C22⋊Q8—22no—
552C22⋊Q8—44no—
553C22⋊Q8—44no—
554C22⋊Q8—41no—
555C22⋊Q8—82no—
556C22⋊Q8—82no—
557#121—22no—
558#121—22no—
559#121—22no—
560#121—41no—
561C4×Q8—22no—
562C4×Q8—41no—
563C4×D4—22no—
564C4×D4—22no—
565C4×D4—22no—
566C4×D4—41no—
567C4×D4—44no—
568#117—22no—
569#117—22no—
570#117—22no—
571#117—41no—
572#117—41no—
573#117—41no—
574#117—44no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—22no—
577C2×C4⋊C4—22no—
578C2×C4⋊C4—22no—
579C2×C4⋊C4—22no—
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—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—41no—
613C2×C4⋊C4—44no—
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4#4114yes—
620C2×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
657C2×C22⋊C4C2×D411yescharacteristic
658C2×C22⋊C4C2×D411yescharacteristic
659C2×C22⋊C4C2×D411yescharacteristic
660C2×C22⋊C4C2×D411yescharacteristic
661C2×C22⋊C4C2×D411yescharacteristic
662C2×C22⋊C4C2×D411yescharacteristic
663C2×C22⋊C4C2×D411yescharacteristic
664C2×C42—22no—
665C2×C42—22no—
666C2×C42—21no—
667C2×C42—21no—
668C2×C42—21no—
669C2×C42—21no—
670C2×C42—21no—
671C2×C42—21no—
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42C2×D411yescharacteristic
679C2×C42C2×D411yescharacteristic
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685#107—22no—
686#107—22no—
687#107—22no—
688#107—41no—
689#107—41no—
690#107—41no—
691#107—41no—
692#107—41no—
693#106—22no—
694#106—41no—
695#106—41no—
696C4⋊C8—41no—
697C4⋊C8—41no—
698C4⋊C8—41no—
699C4⋊C8—41no—
700C4⋊C8—41no—
701C4⋊C8—41no—
702C4⋊C8—41no—
703#103—22no—
704#103—22no—
705#103—41no—
706#103—41no—
707#103—41no—
708#103—41no—
709#103—41no—
710#102—22no—
711#102—22no—
712#102—41no—
713#102—41no—
714#102—41no—
715#102—41no—
716#102—41no—
717C22⋊C8—22no—
718C22⋊C8—22no—
719C22⋊C8—41no—
720C22⋊C8—41no—
721C22⋊C8—41no—
722#97—41no—
723C4×C8—41no—
724C4×C8—41no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
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#95C2×D411yescharacteristic
760#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769C24—21no—
770C24C22×D411yescharacteristic
771C24C22×D411yescharacteristic
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—21no—
777C2×Q8—21no—
778C2×Q8—42no—
779C2×Q8—42no—
780C2×Q8—42no—
781C2×Q8—42no—
782C2×Q8—42no—
783C2×Q8—42no—
784C2×Q8—42no—
785C2×Q8—42no—
786C2×Q8—42no—
787C2×Q8—81no—
788C2×Q8—81no—
789C2×Q8—81no—
790C2×Q8—81no—
791C2×Q8—81no—
792C2×Q8—81no—
793C2×Q8—816no—
794C2×D4—22no—
795C2×D4—22no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—41no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—81no—
806C2×D4—81no—
807C2×D4—81no—
808C2×D4—81no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—24no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—41no—
840C22×C4—41no—
841C22×C4—42no—
842C22×C4—42no—
843C22×C4—42no—
844C22×C4—42no—
845C22×C4—81no—
846C22×C4—81no—
847C22×C4—81no—
848C22×C4—81no—
849C22×C4—81no—
850C22×C4—81no—
851C22×C4—81no—
852C22×C4C22×D411yescharacteristic
853C22×C4C22×D411yescharacteristic
854C22×C4C22×D411yescharacteristic
855C22×C4C22×D411yescharacteristic
856C22×C4C22×D411yescharacteristic
857C22×C4C22×D411yescharacteristic
858C22×C4C22×D411yescharacteristic
859C22×C4C22×D411yescharacteristic
860C22×C4C22×D411yescharacteristic
861C22×C4C22×D411yescharacteristic
862C22×C4C22×D411yescharacteristic
863C22×C4C22×D411yescharacteristic
864C22×C4C2×#4112yes—
865C22×C4H(5,𝔽2)12yes—
866C22×C4C2511yescharacteristic
867SD16—82no—
868M16—82no—
869M16—82no—
870M16—82no—
871C2×C8—21no—
872C2×C8—21no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8—21no—
895C4⋊C4—24no—
896C4⋊C4—22no—
897C4⋊C4—22no—
898C4⋊C4—22no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—21no—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—41no—
924C4⋊C4—42no—
925C4⋊C4—42no—
926C4⋊C4—42no—
927C4⋊C4—42no—
928C4⋊C4—42no—
929C4⋊C4—42no—
930C4⋊C4—42no—
931C4⋊C4—42no—
932C4⋊C4—42no—
933C4⋊C4—42no—
934C4⋊C4—42no—
935C4⋊C4—42no—
936C4⋊C4—42no—
937C4⋊C4—42no—
938C4⋊C4—42no—
939C4⋊C4—42no—
940C4⋊C4—81no—
941C4⋊C4—81no—
942C4⋊C4—81no—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4—81no—
946C4⋊C4—81no—
947C4⋊C4—81no—
948C4⋊C4—81no—
949C4⋊C4—81no—
950C4⋊C4—81no—
951C4⋊C4—81no—
952C4⋊C4—81no—
953C4⋊C4—81no—
954C4⋊C4—81no—
955C4⋊C4—81no—
956C4⋊C4#13714yes—
957C4⋊C4C2×#4112yes—
958C4⋊C4C2×#4112yes—
959C4⋊C42−1+412yes—
960C4⋊C42−1+412yes—
961C22⋊C4—22no—
962C22⋊C4—22no—
963C22⋊C4—22no—
964C22⋊C4—22no—
965C22⋊C4—22no—
966C22⋊C4—22no—
967C22⋊C4—41no—
968C22⋊C4—41no—
969C22⋊C4—42no—
970C22⋊C4—42no—
971C22⋊C4—42no—
972C22⋊C4—42no—
973C22⋊C4—42no—
974C22⋊C4—42no—
975C22⋊C4—42no—
976C22⋊C4—42no—
977C22⋊C4—42no—
978C22⋊C4—42no—
979C22⋊C4—42no—
980C22⋊C4—42no—
981C22⋊C4—81no—
982C22⋊C4—81no—
983C22⋊C4—81no—
984C22⋊C4—81no—
985C22⋊C4—81no—
986C22⋊C4—81no—
987C22⋊C4—81no—
988C22⋊C4—81no—
989C22⋊C4—81no—
990C22⋊C4—81no—
991C42—22no—
992C42—22no—
993C42—21no—
994C42—21no—
995C42—21no—
996C42—21no—
997C42—21no—
998C42—21no—
999C42—21no—
1000C42—21no—
1001C42—21no—
1002C42—21no—
1003C42—42no—
1004C42—42no—
1005C42—42no—
1006C42—42no—
1007C42—42no—
1008C42—42no—
1009C42—42no—
1010C42—81no—
1011C42—81no—
1012C42—81no—
1013C42—81no—
1014C42—81no—
1015C23—21no—
1016C23—21no—
1017C23—21no—
1018C23—21no—
1019C23—21no—
1020C23—21no—
1021C23—21no—
1022C23—21no—
1023C23—21no—
1024C23—21no—
1025C23—21no—
1026C23—21no—
1027C23—21no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23#54612yes—
1036C23C23×D411yescharacteristic
1037Q8—41no—
1038Q8—41no—
1039Q8—41no—
1040Q8—41no—
1041Q8—84no—
1042Q8—84no—
1043Q8—84no—
1044Q8—84no—
1045Q8—162no—
1046D4—44no—
1047D4—41no—
1048D4—41no—
1049D4—41no—
1050D4—41no—
1051D4—162no—
1052D4—162no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—22no—
1077C2×C4—21no—
1078C2×C4—22no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—22no—
1083C2×C4—21no—
1084C2×C4—22no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—44no—
1093C2×C4—44no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—84no—
1140C2×C4—84no—
1141C2×C4—84no—
1142C2×C4—162no—
1143C2×C4#54612yes—
1144C2×C4C2×#13712yes—
1145C2×C4C2×#13712yes—
1146C2×C4C2×#13712yes—
1147C2×C4#57612yes—
1148C2×C4C22×#4111yescharacteristic
1149C2×C4C2×H(5,𝔽2)11yescharacteristic
1150C2×C4C2×2−1+411yescharacteristic
1151C2×C4C2×2−1+411yescharacteristic
1152C2×C4#58511yescharacteristic
1153C2×C4#58511yescharacteristic
1154C8—41no—
1155C8—41no—
1156C8—41no—
1157C8—41no—
1158C8—41no—
1159C8—41no—
1160C8—41no—
1161C8—41no—
1162C22—22no—
1163C22—22no—
1164C22—22no—
1165C22—41no—
1166C22—41no—
1167C22—41no—
1168C22—41no—
1169C22—41no—
1170C22—41no—
1171C22—41no—
1172C22—41no—
1173C22—41no—
1174C22—41no—
1175C22—41no—
1176C22—81no—
1177C22—81no—
1178C22—81no—
1179C22—81no—
1180C22—81no—
1181C22—81no—
1182C22—81no—
1183C22C2×#54611yescharacteristic
1184C22#348911yescharacteristic
1185C22#348911yescharacteristic
1186C22C22×#13711yescharacteristic
1187C22C2×#57611yescharacteristic
1188C22#358511yescharacteristic
1189C22#358611yescharacteristic
1190C4—22no—
1191C4—22no—
1192C4—22no—
1193C4—22no—
1194C4—22no—
1195C4—41no—
1196C4—42no—
1197C4—41no—
1198C4—42no—
1199C4—41no—
1200C4—41no—
1201C4—41no—
1202C4—41no—
1203C4—41no—
1204C4—42no—
1205C4—42no—
1206C4—81no—
1207C4—81no—
1208C4—81no—
1209C4—81no—
1210C4—81no—
1211C4—81no—
1212C4—81no—
1213C4—81no—
1214C4—81no—
1215C4—81no—
1216C4—81no—
1217C4#346111yescharacteristic
1218C4#350711yescharacteristic
1219C4#354411yescharacteristic
1220C4#354511yescharacteristic
1221C2—42no—
1222C2—81no—
1223C2—161no—
1224C2#3777911yescharacteristic
1225C2#6115711yescharacteristic
1226C2#6118311yescharacteristic
1227C2#6210811yescharacteristic
1228C2#6214911yescharacteristic
1229C2#6218611yescharacteristic
1230C2#6222711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2414C22
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
1. #39592C2semidirect
3. #33101C2semidirect
4. #32226C2semidirect
5. #32220C2semidirect
6. #32136C2semidirect
7. #32121C2semidirect
8. #31872C2semidirect
9. #31820C2semidirect
10. #31754C2semidirect
11. #31686C2semidirect
12. #29784C2semidirect
13. #29638C2semidirect
14. #27707C2semidirect
15. #27424C2semidirect
16. #27352C2semidirect
17. #27009C2semidirect
18. #26731C2semidirect
19. #26456C2semidirect
20. #26425C2semidirect
21. #26024C2semidirect
22. #26016C2semidirect
23. #26011C2semidirect
26. #25223C2semidirect
27. #24960C2semidirect
28. #22931C2semidirect
29. #22502C2semidirect
30. #22073C2semidirect
31. #21313C2semidirect

Maximal subgroups

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

subgroupindex
#395922
#364142
#331012
#322262
#322202
#321362
#321212
#318722
#318202
#317542
#316862
#297842
#296382
#277072
#274242
#273522
#270092
#267312
#264562
#264252
#260242
#260162
#260112
#255592
#252582
#252232
#249602
#229312
#225022
#220732
#213132