Finite Group Databasebeta

← #6537718

Subgroups — #6537718

Order 512.

1665 conjugacy classes of subgroups.

The subgroup lattice has 1336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39427C211yesmaximal, characteristic, complemented
2#34495C211yesmaximal, characteristic
3#30183C211yesmaximal, characteristic, complemented
4#30046C211yesmaximal, characteristic, complemented
5#29726C211yesmaximal, characteristic, complemented
6#29560C211yesmaximal, characteristic, complemented
7#29397C211yesmaximal, characteristic, complemented
8#29116C211yesmaximal, characteristic, complemented
9#28583C211yesmaximal, characteristic, complemented
10#27452C211yesmaximal, characteristic, complemented
11#27436C211yesmaximal, characteristic, complemented
12#27245C211yesmaximal, characteristic, complemented
13#27238C211yesmaximal, characteristic, complemented
14#26909C211yesmaximal, characteristic, complemented
15#26893C211yesmaximal, characteristic, complemented
16#26750C211yesmaximal, characteristic, complemented
17#26749C211yesmaximal, characteristic, complemented
18#26222C211yesmaximal, characteristic, complemented
19#26210C211yesmaximal, characteristic, complemented
20#24452C211yesmaximal, characteristic
21#24436C211yesmaximal, characteristic
22#24308C211yesmaximal, characteristic, complemented
23#23942C211yesmaximal, characteristic, complemented
24#23826C211yesmaximal, characteristic, complemented
25#23586C211yesmaximal, characteristic, complemented
26#23458C211yesmaximal, characteristic, complemented
27#23141C211yesmaximal, characteristic, complemented
28#23134C211yesmaximal, characteristic, complemented
29#22879C211yesmaximal, characteristic, complemented
30#22861C211yesmaximal, characteristic, complemented
31#22790C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#544C2211yescharacteristic, complemented
34C2×#541C2211yescharacteristic
35C2×#478C2211yescharacteristic
36C2×#474C2211yescharacteristic
37C2×#468C2211yescharacteristic
38C2×#465C2211yescharacteristic
39C2×#452C2211yescharacteristic
40C2×#452C2211yescharacteristic
41C2×#450C2211yescharacteristic
42C2×#450C2211yescharacteristic
43C2×#441C2211yescharacteristic, complemented
44C2×C4×Q16C2211yescharacteristic, complemented
45C2×#417C2211yescharacteristic
46C2×#416C2211yescharacteristic
47#2862C2211yescharacteristic, complemented
48#2723—21no—
49#2719—21no—
50#2716—21no—
51#2690—21no—
52#2628C2211yescharacteristic
53#2621C2211yescharacteristic, complemented
54#2560—21no—
55#2550—21no—
56#2519—21no—
57#2492C2211yescharacteristic
58#2489—21no—
59#2489C2211yescharacteristic
60#2453C2211yescharacteristic, complemented
61#2451C2211yescharacteristic, complemented
62#2417C2211yescharacteristic
63#2415C2211yescharacteristic
64#2376—21no—
65#2375—21no—
66#2367C2211yescharacteristic
67#2363—21no—
68#2362C2211yescharacteristic
69#2362C2211yescharacteristic, complemented
70#2361C2211yescharacteristic
71#2360C2211yescharacteristic, complemented
72#2357C2211yescharacteristic
73#2352C2211yescharacteristic
74#2342—21no—
75#2341C2211yescharacteristic
76D4×C22⋊C4C2211yescharacteristic
77#2335—21no—
78#2333—21no—
79#2324C2211yescharacteristic
80#2323C2211yescharacteristic
81#2321—21no—
82#2312—21no—
83#2311C2211yescharacteristic
84#2309C2211yescharacteristic
85C4×#125C2211yescharacteristic, complemented
86C4×#124C2211yescharacteristic
87#2293C2211yescharacteristic
88#2293C2211yescharacteristic
89#2101C2211yescharacteristic, complemented
90#2101C2211yescharacteristic, complemented
91#2085C2211yescharacteristic, complemented
92#2076C2211yescharacteristic
93#2075C2211yescharacteristic
94#2074C2211yescharacteristic, complemented
95#2074C2211yescharacteristic, complemented
96#2074C2211yescharacteristic, complemented
97#2073C2211yescharacteristic
98#2073C2211yescharacteristic
99#2059C2211yescharacteristic, complemented
100#2057C2211yescharacteristic, complemented
101#2056C2211yescharacteristic, complemented
102#2056C2211yescharacteristic, complemented
103#2055C2211yescharacteristic
104#2055C2211yescharacteristic
105#2043C2211yescharacteristic, complemented
106#2042C2211yescharacteristic
107#2042C2211yescharacteristic
108#2036C2211yescharacteristic
109#2036C2211yescharacteristic
110#2035C2211yescharacteristic
111#2035C2211yescharacteristic
112#2026C2211yescharacteristic, complemented
113#2026C2211yescharacteristic, complemented
114#2025C2211yescharacteristic
115#2025C2211yescharacteristic
116#2025C2211yescharacteristic
117#2024C2211yescharacteristic, complemented
118#2024C2211yescharacteristic, complemented
119#2023C2211yescharacteristic
120#2023C2211yescharacteristic
121#2023C2211yescharacteristic
122#2016C2211yescharacteristic, complemented
123#2015C2211yescharacteristic
124#2015C2211yescharacteristic
125#2013C2211yescharacteristic
126#2013C2211yescharacteristic
127#2001C2211yescharacteristic
128#2001C2211yescharacteristic
129#1989C2211yescharacteristic, complemented
130#1987C2211yescharacteristic, complemented
131#1973C2211yescharacteristic
132#1973C2211yescharacteristic
133#1936C2211yescharacteristic
134#1936C2211yescharacteristic
135#1935C2211yescharacteristic, complemented
136#1935C2211yescharacteristic, complemented
137#1934C2211yescharacteristic
138#1934C2211yescharacteristic
139#1928C2211yescharacteristic, complemented
140#1928C2211yescharacteristic, complemented
141#1928C2211yescharacteristic, complemented
142#1927C2211yescharacteristic, complemented
143#1926C2211yescharacteristic
144#1925C2211yescharacteristic
145#1924C2211yescharacteristic
146#1924C2211yescharacteristic
147#1921C2211yescharacteristic, complemented
148#1920C2211yescharacteristic, complemented
149#1920C2211yescharacteristic, complemented
150#1919C2211yescharacteristic, complemented
151#1918C2211yescharacteristic, complemented
152#1918C2211yescharacteristic, complemented
153#1917C2211yescharacteristic, complemented
154#1916C2211yescharacteristic, complemented
155#1894C2211yescharacteristic, complemented
156#1892C2211yescharacteristic, complemented
157#1880C2211yescharacteristic
158#1880C2211yescharacteristic
159#1880C2211yescharacteristic
160#1880C2211yescharacteristic
161#1878C2211yescharacteristic, complemented
162#1878C2211yescharacteristic, complemented
163#1877C2211yescharacteristic
164#1877C2211yescharacteristic
165#1877C2211yescharacteristic
166#1877C2211yescharacteristic
167#1877C2211yescharacteristic
168#1877C2211yescharacteristic
169#1875C2211yescharacteristic
170#1874C2211yescharacteristic
171#1873C2211yescharacteristic
172#1873C2211yescharacteristic
173#1872C2211yescharacteristic, complemented
174#1872C2211yescharacteristic, complemented
175#1870C2211yescharacteristic
176#1869C2211yescharacteristic
177#1864C2211yescharacteristic
178#1863C2211yescharacteristic, complemented
179#1863C2211yescharacteristic, complemented
180#1862C2211yescharacteristic
181#1854C2211yescharacteristic, complemented
182#1852C2211yescharacteristic, complemented
183#1839C2211yescharacteristic, complemented
184#1825C2211yescharacteristic
185#1825C2211yescharacteristic
186#1818C2211yescharacteristic
187#1798C2211yescharacteristic, complemented
188#1786C2211yescharacteristic
189#1786C2211yescharacteristic
190#1763C2211yescharacteristic, complemented
191#1763C2211yescharacteristic, complemented
192#1763C2211yescharacteristic, complemented
193#1762C2211yescharacteristic
194#1762C2211yescharacteristic
195C4×#103C2211yescharacteristic, complemented
196#1753C2211yescharacteristic, complemented
197#1752C2211yescharacteristic, complemented
198#1750C2211yescharacteristic
199#1745C2211yescharacteristic, complemented
200#1736C2211yescharacteristic, complemented
201C2×#340C2211yescharacteristic, complemented
202#1729C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C23×C8C2311yescharacteristic
213#546—24no—
214#546—24no—
215#544—42no—
216#544—42no—
217#541—42no—
218#541—42no—
219C2×C4⋊Q8—21no—
220C2×C4⋊Q8C2311yescharacteristic
221C2×C4⋊Q8C2311yescharacteristic
222C2×C4⋊Q8C2311yescharacteristic
223C2×#126—21no—
224C2×#126—21no—
225C2×#125—21no—
226C2×#125—21no—
227C2×#125—21no—
228C2×#125C2311yescharacteristic
229C2×#125C2311yescharacteristic
230C2×#124C2311yescharacteristic
231C2×#123—21no—
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×C22⋊Q8C2311yescharacteristic
239C2×#121—21no—
240C2×#121C2311yescharacteristic
241C2×#120—21no—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×D4—21no—
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×#117—21no—
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C22×C4⋊C4C2311yescharacteristic
257C22×C4⋊C4C2311yescharacteristic
258C22×C22⋊C4—21no—
259C22×C22⋊C4—21no—
260#478—42no—
261#474—42no—
262#468—24no—
263#465—24no—
264#452—24no—
265#452—24no—
266#450—42no—
267#450—42no—
268#441—42no—
269C4×Q16—42no—
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278#417—42no—
279#416—42no—
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×#97C2311yescharacteristic
315C2×#97C2311yescharacteristic
316C2×#97C2311yescharacteristic
317C2×C4×C8C2311yescharacteristic
318#400—21no—
319#400—21no—
320#400—21no—
321#400—21no—
322#399—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#398—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#396—21no—
333#395—21no—
334#395—21no—
335#394—21no—
336#393—21no—
337#393—21no—
338#391—21no—
339#391—21no—
340#391—21no—
341#391—21no—
342#391C2311yescharacteristic
343#391C2311yescharacteristic
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#391C2311yescharacteristic
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#390—21no—
351#390—21no—
352#390—21no—
353#390—21no—
354#390—21no—
355#390D411yescharacteristic
356#390D411yescharacteristic
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#389D411yescharacteristic
368#389D411yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#388—21no—
376#388—21no—
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#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#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#382—21no—
421#382—21no—
422#382—21no—
423#382C2311yescharacteristic
424#382C2311yescharacteristic
425#381—21no—
426#380—21no—
427#380—21no—
428#380—21no—
429#380—21no—
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#379—21no—
435#379—21no—
436#379—21no—
437C4×C4⋊C4—21no—
438C4×C4⋊C4—21no—
439C4×C4⋊C4—21no—
440C4×C4⋊C4—21no—
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C22⋊C4—21no—
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4C2311yescharacteristic
456C4×C22⋊C4C2311yescharacteristic
457C43C2311yescharacteristic
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#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—
497C2×#41—22no—
498C2×#41—41no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41#4114yes—
503C22×Q8—21no—
504C22×Q8—21no—
505C22×Q8C2411yescharacteristic
506C22×Q8C2411yescharacteristic
507C22×Q8C2411yescharacteristic
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—21no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4C2×D411yescharacteristic
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4C2411yescharacteristic
527C23×C4C2411yescharacteristic
528C2×Q16—22no—
529C2×Q16—22no—
530C2×Q16—41no—
531C2×Q16—41no—
532C2×Q16—41no—
533C2×Q16—41no—
534C2×SD16—22no—
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16—41no—
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—22no—
561C4⋊Q8—41no—
562C4⋊Q8—41no—
563C4⋊Q8—41no—
564C4⋊Q8—41no—
565C4⋊Q8—41no—
566C4⋊Q8—44no—
567#126—44no—
568#126—44no—
569#125—22no—
570#125—22no—
571#125—22no—
572#125—41no—
573#125—44no—
574#125—44no—
575#125—44no—
576#124—22no—
577#124—22no—
578#123—28no—
579C22⋊Q8—22no—
580C22⋊Q8—22no—
581C22⋊Q8—22no—
582C22⋊Q8—22no—
583C22⋊Q8—22no—
584C22⋊Q8—22no—
585C22⋊Q8—22no—
586C22⋊Q8—22no—
587C22⋊Q8—41no—
588C22⋊Q8—41no—
589C22⋊Q8—44no—
590C22⋊Q8—44no—
591#121—28no—
592#121—22no—
593#121#4114yes—
594#120—28no—
595C4×Q8—22no—
596C4×Q8—22no—
597C4×Q8—41no—
598C4×Q8—41no—
599C4×Q8—41no—
600C4×Q8—41no—
601C4×Q8—41no—
602C4×Q8—41no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—41no—
608C4×D4—41no—
609C4×D4—41no—
610C4×D4—41no—
611C4×D4—82no—
612#117—22no—
613#117—41no—
614#117—41no—
615#117—41no—
616#117—41no—
617#117—41no—
618#117—41no—
619#117—41no—
620#117—82no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—22no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—41no—
648C2×C4⋊C4—41no—
649C2×C4⋊C4—41no—
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C22⋊C4—28no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—82no—
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×C22⋊C4C2×D411yescharacteristic
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—21no—
720C2×C42C2×D411yescharacteristic
721C2×C42C2×D411yescharacteristic
722C2×C42C2×D411yescharacteristic
723C2×C42C2×D411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729#107—22no—
730#107—22no—
731#107—41no—
732#107—41no—
733#106—22no—
734#106—22no—
735C4⋊C8—41no—
736C4⋊C8—41no—
737#103—22no—
738#103—22no—
739#103—22no—
740#103—22no—
741#103—22no—
742#103—22no—
743#103—41no—
744#103—41no—
745#103—41no—
746#103—41no—
747#103—41no—
748#103—41no—
749#103—41no—
750#103—41no—
751#103—41no—
752#103—41no—
753#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—
765C22⋊C8—22no—
766C22⋊C8—22no—
767C22⋊C8—41no—
768C22⋊C8—41no—
769C22⋊C8—41no—
770C22⋊C8—41no—
771#97—41no—
772#97—41no—
773#97—41no—
774C4×C8—41no—
775#95—21no—
776#95—21no—
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#95—21no—
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816C24—24no—
817C24—21no—
818C24—21no—
819C24—81no—
820C24—81no—
821C24—81no—
822C24—81no—
823C24—81no—
824C24—81no—
825C24C22×D411yescharacteristic
826C24C22×D411yescharacteristic
827#41—44no—
828#41—44no—
829#41—82no—
830#41—82no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—42no—
849C2×Q8—42no—
850C2×Q8—81no—
851C2×Q8—81no—
852C2×Q8—81no—
853C2×Q8—81no—
854C2×Q8C2×#4112yes—
855C2×D4—24no—
856C2×D4—22no—
857C2×D4—24no—
858C2×D4—24no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—41no—
870C2×D4—41no—
871C2×D4—81no—
872C2×D4—81no—
873C2×D4—82no—
874C2×D4—82no—
875C2×D4—82no—
876C2×D4—82no—
877C2×D4—81no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4C2×#4112yes—
882C2×D4C2×#4112yes—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—24no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
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—42no—
910C22×C4—42no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4—81no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4—81no—
920C22×C4—81no—
921C22×C4—81no—
922C22×C4—81no—
923C22×C4—81no—
924C22×C4—81no—
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C2×#4112yes—
938C22×C4C2×#4112yes—
939C22×C4C2511yescharacteristic
940Q16—44no—
941Q16—44no—
942SD16—82no—
943SD16—82no—
944SD16—82no—
945SD16—82no—
946M16—82no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
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—82no—
972C4⋊C4—24no—
973C4⋊C4—24no—
974C4⋊C4—24no—
975C4⋊C4—22no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—41no—
996C4⋊C4—41no—
997C4⋊C4—41no—
998C4⋊C4—41no—
999C4⋊C4—41no—
1000C4⋊C4—41no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4C2×#4112yes—
1024C4⋊C4H(5,𝔽2)12yes—
1025C4⋊C4H(5,𝔽2)12yes—
1026C22⋊C4—24no—
1027C22⋊C4—24no—
1028C22⋊C4—24no—
1029C22⋊C4—24no—
1030C22⋊C4—22no—
1031C22⋊C4—22no—
1032C22⋊C4—24no—
1033C22⋊C4—41no—
1034C22⋊C4—41no—
1035C22⋊C4—41no—
1036C22⋊C4—41no—
1037C22⋊C4—41no—
1038C22⋊C4—41no—
1039C22⋊C4—41no—
1040C22⋊C4—41no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—41no—
1076C42—41no—
1077C42—41no—
1078C42—41no—
1079C42—42no—
1080C42—42no—
1081C42—42no—
1082C42—42no—
1083C42—81no—
1084C42—81no—
1085C42—81no—
1086C42—81no—
1087C42—81no—
1088C42—81no—
1089C42—81no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—22no—
1102C23—22no—
1103C23—21no—
1104C23—21no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—84no—
1118C23—84no—
1119C23—84no—
1120C23—162no—
1121C23—162no—
1122C23—162no—
1123C23—162no—
1124C23#52512yes—
1125C23C23×D411yescharacteristic
1126Q8—22no—
1127Q8—22no—
1128Q8—41no—
1129Q8—41no—
1130Q8—41no—
1131Q8—41no—
1132Q8—41no—
1133Q8—41no—
1134Q8—41no—
1135Q8—41no—
1136Q8—41no—
1137Q8—41no—
1138Q8—162no—
1139Q8—162no—
1140D4—22no—
1141D4—22no—
1142D4—22no—
1143D4—22no—
1144D4—41no—
1145D4—41no—
1146D4—41no—
1147D4—41no—
1148D4—82no—
1149D4—84no—
1150D4—84no—
1151D4—84no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—84no—
1238C2×C4—84no—
1239C2×C4—162no—
1240C2×C4—162no—
1241C2×C4—162no—
1242C2×C4—162no—
1243C2×C4#52512yes—
1244C2×C4C22×#4111yescharacteristic
1245C2×C4C22×#4111yescharacteristic
1246C2×C4C2×H(5,𝔽2)11yescharacteristic
1247C2×C4C2×H(5,𝔽2)11yescharacteristic
1248C2×C4#58511yescharacteristic
1249C2×C4#58511yescharacteristic
1250C8—41no—
1251C8—41no—
1252C8—41no—
1253C8—41no—
1254C8—41no—
1255C8—41no—
1256C8—41no—
1257C8—41no—
1258C22—22no—
1259C22—22no—
1260C22—22no—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—41no—
1265C22—41no—
1266C22—41no—
1267C22—42no—
1268C22—42no—
1269C22—41no—
1270C22—42no—
1271C22—42no—
1272C22—41no—
1273C22—41no—
1274C22—42no—
1275C22—42no—
1276C22—41no—
1277C22—41no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—168no—
1287C22C2×#52511yescharacteristic
1288C22#348411yescharacteristic
1289C22#350011yescharacteristic
1290C22#358411yescharacteristic
1291C22#358511yescharacteristic
1292C22#358611yescharacteristic
1293C22#358611yescharacteristic
1294C4—22no—
1295C4—41no—
1296C4—41no—
1297C4—42no—
1298C4—41no—
1299C4—41no—
1300C4—42no—
1301C4—41no—
1302C4—41no—
1303C4—41no—
1304C4—41no—
1305C4—42no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—42no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4#350511yescharacteristic
1321C4#350511yescharacteristic
1322C4#351411yescharacteristic
1323C4#351411yescharacteristic
1324C2—42no—
1325C2—81no—
1326C2—82no—
1327C2—82no—
1328C2#3570311yescharacteristic
1329C2#6057511yescharacteristic
1330C2#6058611yescharacteristic
1331C2#6167611yescharacteristic
1332C2#6169011yescharacteristic
1333C2#6256811yescharacteristic
1334C2#6261211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#546C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2293 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39427C2semidirect
3. #30183C2semidirect
4. #30046C2semidirect
5. #29726C2semidirect
6. #29560C2semidirect
7. #29397C2semidirect
8. #29116C2semidirect
9. #28583C2semidirect
10. #27452C2semidirect
11. #27436C2semidirect
12. #27245C2semidirect
13. #27238C2semidirect
14. #26909C2semidirect
15. #26893C2semidirect
16. #26750C2semidirect
17. #26749C2semidirect
18. #26222C2semidirect
19. #26210C2semidirect
22. #24308C2semidirect
23. #23942C2semidirect
24. #23826C2semidirect
25. #23586C2semidirect
26. #23458C2semidirect
27. #23141C2semidirect
28. #23134C2semidirect
29. #22879C2semidirect
30. #22861C2semidirect
31. #22790C2semidirect
33. C2×#544C22semidirect
43. C2×#441C22semidirect
44. C2×C4×Q16C22semidirect
47. #2862C22semidirect
53. #2621C22semidirect
60. #2453C22semidirect
61. #2451C22semidirect
69. #2362C22semidirect
71. #2360C22semidirect
85. C4×#125C22semidirect
89. #2101C22semidirect
90. #2101C22semidirect
91. #2085C22semidirect
94. #2074C22semidirect
95. #2074C22semidirect
96. #2074C22semidirect
99. #2059C22semidirect
100. #2057C22semidirect
101. #2056C22semidirect
102. #2056C22semidirect
105. #2043C22semidirect
112. #2026C22semidirect
113. #2026C22semidirect
117. #2024C22semidirect
118. #2024C22semidirect
122. #2016C22semidirect
129. #1989C22semidirect
130. #1987C22semidirect
135. #1935C22semidirect
136. #1935C22semidirect
139. #1928C22semidirect
140. #1928C22semidirect
141. #1928C22semidirect
142. #1927C22semidirect
147. #1921C22semidirect
148. #1920C22semidirect
149. #1920C22semidirect
150. #1919C22semidirect
151. #1918C22semidirect
152. #1918C22semidirect
153. #1917C22semidirect
154. #1916C22semidirect
155. #1894C22semidirect
156. #1892C22semidirect
161. #1878C22semidirect
162. #1878C22semidirect
173. #1872C22semidirect
174. #1872C22semidirect
178. #1863C22semidirect
179. #1863C22semidirect
181. #1854C22semidirect
182. #1852C22semidirect
183. #1839C22semidirect
187. #1798C22semidirect
190. #1763C22semidirect
191. #1763C22semidirect
192. #1763C22semidirect
195. C4×#103C22semidirect
196. #1753C22semidirect
197. #1752C22semidirect
199. #1745C22semidirect
200. #1736C22semidirect
201. C2×#340C22semidirect
202. #1729C22semidirect

Maximal subgroups

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

subgroupindex
#394272
#344952
#301832
#300462
#297262
#295602
#293972
#291162
#285832
#274522
#274362
#272452
#272382
#269092
#268932
#267502
#267492
#262222
#262102
#244522
#244362
#243082
#239422
#238262
#235862
#234582
#231412
#231342
#228792
#228612
#227902