Finite Group Databasebeta

← #6549946

Subgroups — #6549946

Order 512.

1633 conjugacy classes of subgroups.

The subgroup lattice has 1323 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37859C211yesmaximal, characteristic, complemented
2#34363C211yesmaximal, characteristic
3#30179C211yesmaximal, characteristic, complemented
4#30032C211yesmaximal, characteristic, complemented
5#29897C211yesmaximal, characteristic, complemented
6#29488C211yesmaximal, characteristic, complemented
7#29424C211yesmaximal, characteristic, complemented
8#27637C211yesmaximal, characteristic, complemented
9#27525C211yesmaximal, characteristic, complemented
10#27520C211yesmaximal, characteristic, complemented
11#27477C211yesmaximal, characteristic, complemented
12#27472C211yesmaximal, characteristic, complemented
13#27328C211yesmaximal, characteristic, complemented
14#27245C211yesmaximal, characteristic, complemented
15#27165C211yesmaximal, characteristic, complemented
16#26411C211yesmaximal, characteristic, complemented
17#26341C211yesmaximal, characteristic, complemented
18#25211C211yesmaximal, characteristic, complemented
19#25205C211yesmaximal, characteristic, complemented
20#24917C211yesmaximal, characteristic, complemented
21#24712C211yesmaximal, characteristic, complemented
22#24379C211yesmaximal, characteristic
23#24009C211yesmaximal, characteristic
24#23771C211yesmaximal, characteristic, complemented
25#23714C211yesmaximal, characteristic, complemented
26#23638C211yesmaximal, characteristic, complemented
27#23131C211yesmaximal, characteristic, complemented
28#23033C211yesmaximal, characteristic, complemented
29#22935C211yesmaximal, characteristic, complemented
30#22921C211yesmaximal, characteristic, complemented
31#22558C211yesmaximal, characteristic, complemented
32C22×#121C2211yescharacteristic
33C2×#482C2211yescharacteristic
34C2×#482C2211yescharacteristic
35C2×#474C2211yescharacteristic, complemented
36C2×#465C2211yescharacteristic
37C2×#465C2211yescharacteristic
38C2×#450C2211yescharacteristic
39C2×#440C2211yescharacteristic, complemented
40C2×#433C2211yescharacteristic, complemented
41C2×#427C2211yescharacteristic, complemented
42C22×C22⋊C8C2211yescharacteristic
43#2848C2211yescharacteristic
44#2745—21no—
45#2739—21no—
46#2736—21no—
47#2735—21no—
48#2628C2211yescharacteristic, complemented
49#2625C2211yescharacteristic, complemented
50#2575—21no—
51#2574—21no—
52#2530—21no—
53#2527—21no—
54#2499C2211yescharacteristic, complemented
55#2497C2211yescharacteristic
56#2494C2211yescharacteristic
57#2492C2211yescharacteristic
58#2439C2211yescharacteristic, complemented
59#2421C2211yescharacteristic
60#2377—21no—
61#2377—21no—
62#2363C2211yescharacteristic
63#2363C2211yescharacteristic
64#2363C2211yescharacteristic
65#2363C2211yescharacteristic
66#2362C2211yescharacteristic, complemented
67#2346C2211yescharacteristic, complemented
68#2344C2211yescharacteristic
69#2344C2211yescharacteristic
70#2342—21no—
71#2342—21no—
72D4×C22⋊C4C2211yescharacteristic
73D4×C22⋊C4C2211yescharacteristic
74#2333—21no—
75#2333—21no—
76#2324C2211yescharacteristic
77#2324C2211yescharacteristic
78#2324C2211yescharacteristic
79#2324C2211yescharacteristic
80#2323C2211yescharacteristic, complemented
81#2314C2211yescharacteristic, complemented
82#2309—21no—
83#2308—21no—
84#2280C2211yescharacteristic
85#2280C2211yescharacteristic
86#2280C2211yescharacteristic
87#2101C2211yescharacteristic, complemented
88#2092C2211yescharacteristic, complemented
89#2087C2211yescharacteristic, complemented
90#2086C2211yescharacteristic, complemented
91#2085C2211yescharacteristic, complemented
92#2084C2211yescharacteristic, complemented
93#2077C2211yescharacteristic
94#2077C2211yescharacteristic
95#2077C2211yescharacteristic
96#2077C2211yescharacteristic, complemented
97#2077C2211yescharacteristic, complemented
98#2077C2211yescharacteristic, complemented
99#2076C2211yescharacteristic
100#2076C2211yescharacteristic
101#2076C2211yescharacteristic, complemented
102#2075C2211yescharacteristic
103#2075C2211yescharacteristic, complemented
104#2075C2211yescharacteristic, complemented
105#2073C2211yescharacteristic, complemented
106#2071C2211yescharacteristic, complemented
107#2068C2211yescharacteristic, complemented
108#2067C2211yescharacteristic, complemented
109#2066C2211yescharacteristic, complemented
110#2065C2211yescharacteristic, complemented
111#2058C2211yescharacteristic, complemented
112#2055C2211yescharacteristic, complemented
113#2055C2211yescharacteristic, complemented
114#2036C2211yescharacteristic
115#2036C2211yescharacteristic, complemented
116#2035C2211yescharacteristic
117#2035C2211yescharacteristic, complemented
118#2034C2211yescharacteristic
119#2034C2211yescharacteristic
120#2034C2211yescharacteristic
121#2034C2211yescharacteristic
122#2033C2211yescharacteristic
123#2033C2211yescharacteristic
124#2023C2211yescharacteristic, complemented
125#2000C2211yescharacteristic
126#2000C2211yescharacteristic
127#1987C2211yescharacteristic, complemented
128#1973C2211yescharacteristic, complemented
129#1949C2211yescharacteristic, complemented
130#1949C2211yescharacteristic, complemented
131#1948C2211yescharacteristic, complemented
132#1944C2211yescharacteristic, complemented
133#1943C2211yescharacteristic, complemented
134#1942C2211yescharacteristic, complemented
135#1936C2211yescharacteristic, complemented
136#1934C2211yescharacteristic, complemented
137#1934C2211yescharacteristic, complemented
138#1933C2211yescharacteristic, complemented
139#1928C2211yescharacteristic, complemented
140#1927C2211yescharacteristic, complemented
141#1927C2211yescharacteristic, complemented
142#1926C2211yescharacteristic, complemented
143#1926C2211yescharacteristic, complemented
144#1925C2211yescharacteristic, complemented
145#1924C2211yescharacteristic
146#1924C2211yescharacteristic
147#1923C2211yescharacteristic
148#1923C2211yescharacteristic
149#1921C2211yescharacteristic, complemented
150#1920C2211yescharacteristic, complemented
151#1920C2211yescharacteristic, complemented
152#1919C2211yescharacteristic, complemented
153#1919C2211yescharacteristic, complemented
154#1919C2211yescharacteristic, complemented
155#1918C2211yescharacteristic, complemented
156#1918C2211yescharacteristic, complemented
157#1893C2211yescharacteristic
158#1893C2211yescharacteristic
159#1880C2211yescharacteristic, complemented
160#1877C2211yescharacteristic, complemented
161#1877C2211yescharacteristic, complemented
162#1877C2211yescharacteristic, complemented
163#1875C2211yescharacteristic
164#1875C2211yescharacteristic
165#1873C2211yescharacteristic, complemented
166#1873C2211yescharacteristic, complemented
167#1872C2211yescharacteristic
168#1865C2211yescharacteristic, complemented
169#1864C2211yescharacteristic, complemented
170#1864C2211yescharacteristic, complemented
171#1864C2211yescharacteristic, complemented
172#1864C2211yescharacteristic, complemented
173#1862C2211yescharacteristic, complemented
174#1854C2211yescharacteristic, complemented
175#1854C2211yescharacteristic, complemented
176#1853C2211yescharacteristic
177#1853C2211yescharacteristic
178#1852C2211yescharacteristic
179#1850C2211yescharacteristic, complemented
180#1850C2211yescharacteristic, complemented
181#1818C2211yescharacteristic, complemented
182#1804C2211yescharacteristic, complemented
183#1804C2211yescharacteristic, complemented
184#1802C2211yescharacteristic, complemented
185#1798C2211yescharacteristic, complemented
186#1786C2211yescharacteristic
187#1786C2211yescharacteristic
188#1786C2211yescharacteristic
189#1779C2211yescharacteristic
190#1776C2211yescharacteristic, complemented
191#1776C2211yescharacteristic, complemented
192C4×#106C2211yescharacteristic, complemented
193#1762C2211yescharacteristic, complemented
194C4×#103C2211yescharacteristic, complemented
195C4×#102C2211yescharacteristic, complemented
196C4×#102C2211yescharacteristic, complemented
197#1752C2211yescharacteristic, complemented
198C8×C22⋊C4C2211yescharacteristic, complemented
199#1750C2211yescharacteristic, complemented
200#1735C2211yescharacteristic, complemented
201#1735C2211yescharacteristic, complemented
202#1735C2211yescharacteristic, complemented
203C23×D4—21no—
204C23×D4C2311yescharacteristic
205C24×C4C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C23×C8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C22⋊Q8C2311yescharacteristic
212C2×C22⋊Q8C2311yescharacteristic
213C2×C22⋊Q8C2311yescharacteristic
214C2×#121—21no—
215C2×#121—21no—
216C2×#121—24no—
217C2×#121—24no—
218C2×#121C2311yescharacteristic
219C2×#121C2311yescharacteristic
220C2×#121C2311yescharacteristic
221C2×#121C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×#117—21no—
228C2×#117—21no—
229C2×#117C2311yescharacteristic
230C2×#117C2311yescharacteristic
231C2×#117C2311yescharacteristic
232C2×#117C2311yescharacteristic
233C2×#117C2311yescharacteristic
234C2×#117C2311yescharacteristic
235C22×C4⋊C4C2311yescharacteristic
236C22×C22⋊C4—21no—
237C22×C22⋊C4—21no—
238C22×C22⋊C4—21no—
239#482—24no—
240#482—24no—
241#474—42no—
242#465—24no—
243#465—24no—
244#450—42no—
245#440—42no—
246#433—42no—
247#427—42no—
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×C22⋊C8—42no—
287C2×C22⋊C8C2311yescharacteristic
288C2×C22⋊C8C2311yescharacteristic
289C2×C22⋊C8C2311yescharacteristic
290C2×C22⋊C8C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×C22⋊C8C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295C2×C22⋊C8C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×#97C2311yescharacteristic
299C2×C4×C8C2311yescharacteristic
300C2×C4×C8C2311yescharacteristic
301#401—21no—
302#400—21no—
303#400—21no—
304#400—21no—
305#400—21no—
306#400—21no—
307#399—21no—
308#398—21no—
309#397—21no—
310#397—21no—
311#397—21no—
312#397—21no—
313#397—21no—
314#397—21no—
315#396—21no—
316#396—21no—
317#395—21no—
318#393—21no—
319#393—21no—
320#393—21no—
321#391—21no—
322#391—21no—
323#391C2311yescharacteristic
324#391C2311yescharacteristic
325#391C2311yescharacteristic
326#390—21no—
327#390—21no—
328#390—21no—
329#390—21no—
330#390—21no—
331#390—21no—
332#390—21no—
333#390—21no—
334#390C2311yescharacteristic
335#390C2311yescharacteristic
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#389—21no—
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#388—21no—
349#388—21no—
350#388—21no—
351#388—21no—
352#388—21no—
353#388—21no—
354#388—21no—
355#388—21no—
356#388—21no—
357#388—21no—
358#388—21no—
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#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#386—21no—
383#386—21no—
384#386—21no—
385#386—21no—
386#386—21no—
387#386—21no—
388#386—21no—
389#386—21no—
390#386—21no—
391#386—21no—
392#386—21no—
393#386—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#384C2311yescharacteristic
402#382—21no—
403#382C2311yescharacteristic
404#382C2311yescharacteristic
405#381—21no—
406#381—21no—
407#381—21no—
408#381—21no—
409#381D411yescharacteristic
410#381D411yescharacteristic
411#380D411yescharacteristic
412#380D411yescharacteristic
413#380D411yescharacteristic
414#380D411yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#379—21no—
427#379—21no—
428#379—21no—
429#379—21no—
430#379—21no—
431#379D411yescharacteristic
432#379D411yescharacteristic
433C4×C4⋊C4—21no—
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C4×C22⋊C4—21no—
449C4×C22⋊C4C2311yescharacteristic
450C4×C22⋊C4C2311yescharacteristic
451C4×C22⋊C4C2311yescharacteristic
452C4×C22⋊C4C2311yescharacteristic
453#376—21no—
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#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
490C25—21no—
491C25C2×D411yescharacteristic
492C22×Q8—21no—
493C22×Q8C2411yescharacteristic
494C22×D4—28no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—22no—
500C22×D4—22no—
501C22×D4—21no—
502C22×D4—41no—
503C22×D4—41no—
504C22×D4—41no—
505C22×D4—41no—
506C22×D4—82no—
507C22×D4—82no—
508C22×D4C2411yescharacteristic
509C22×D4C2411yescharacteristic
510C23×C4—21no—
511C23×C4—22no—
512C23×C4—22no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—41no—
518C23×C4—41no—
519C23×C4—41no—
520C23×C4—41no—
521C23×C4C2×D411yescharacteristic
522C23×C4C2×D411yescharacteristic
523C23×C4C2×D411yescharacteristic
524C23×C4C2411yescharacteristic
525C23×C4C2411yescharacteristic
526C23×C4C2411yescharacteristic
527C2×SD16—22no—
528C2×SD16—22no—
529C2×SD16—22no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×SD16—41no—
533C22×C8—22no—
534C22×C8—22no—
535C22×C8—22no—
536C22×C8—41no—
537C22×C8—41no—
538C22×C8—41no—
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C4⋊Q8—41no—
548C4⋊Q8—41no—
549C22⋊Q8—22no—
550C22⋊Q8—22no—
551C22⋊Q8—41no—
552C22⋊Q8—41no—
553C22⋊Q8—41no—
554C22⋊Q8—41no—
555#121—28no—
556#121—28no—
557#121—22no—
558#121—22no—
559#121—22no—
560#121—22no—
561#121—22no—
562#121—22no—
563#121#4114yes—
564#121#4114yes—
565C4×Q8—41no—
566C4×Q8—41no—
567C4×D4—41no—
568C4×D4—41no—
569C4×D4—41no—
570C4×D4—41no—
571C4×D4—41no—
572C4×D4—41no—
573C4×D4—41no—
574C4×D4—41no—
575#117—22no—
576#117—22no—
577#117—41no—
578#117—41no—
579#117—41no—
580#117—41no—
581#117—41no—
582#117—41no—
583#117—41no—
584#117—41no—
585#117—41no—
586#117—41no—
587#117—82no—
588#117—82no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—22no—
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⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C22⋊C4—28no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
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—82no—
661C2×C22⋊C4—82no—
662C2×C22⋊C4C2×D411yescharacteristic
663C2×C22⋊C4C2×D411yescharacteristic
664C2×C22⋊C4C2×D411yescharacteristic
665C2×C22⋊C4C2×D411yescharacteristic
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—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—21no—
682C2×C42—21no—
683C2×C42—21no—
684C2×C42—21no—
685C2×C42—21no—
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690#107—22no—
691#107—22no—
692#107—22no—
693#107—22no—
694#107—41no—
695#107—41no—
696#106—22no—
697#106—22no—
698#106—22no—
699#106—22no—
700#106—41no—
701#106—41no—
702#106—41no—
703#106—41no—
704C4⋊C8—22no—
705C4⋊C8—41no—
706C4⋊C8—41no—
707C4⋊C8—41no—
708#103—22no—
709#103—22no—
710#103—41no—
711#103—41no—
712#103—41no—
713#103—41no—
714#102—22no—
715#102—22no—
716#102—22no—
717#102—22no—
718#102—22no—
719#102—22no—
720#102—22no—
721#102—41no—
722#102—41no—
723#102—41no—
724#102—41no—
725#102—41no—
726#102—41no—
727#102—41no—
728C22⋊C8—22no—
729C22⋊C8—22no—
730C22⋊C8—22no—
731C22⋊C8—22no—
732C22⋊C8—41no—
733C22⋊C8—41no—
734C22⋊C8—41no—
735C22⋊C8—41no—
736C22⋊C8—41no—
737C22⋊C8—41no—
738#97—22no—
739#97—41no—
740C4×C8—41no—
741C4×C8—41no—
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#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#95—21no—
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787C24—24no—
788C24—21no—
789C24—21no—
790C24—22no—
791C24—22no—
792C24—41no—
793C24—41no—
794C24—41no—
795C24—41no—
796C24—41no—
797C24—42no—
798C24—42no—
799C24—81no—
800C24—81no—
801C24—81no—
802C24—81no—
803C24C22×D411yescharacteristic
804C24C22×D411yescharacteristic
805C24C22×D411yescharacteristic
806C2×Q8—21no—
807C2×Q8—21no—
808C2×Q8—21no—
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—81no—
813C2×Q8—81no—
814C2×Q8—81no—
815C2×D4—24no—
816C2×D4—24no—
817C2×D4—24no—
818C2×D4—24no—
819C2×D4—24no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—81no—
831C2×D4—81no—
832C2×D4—82no—
833C2×D4—82no—
834C2×D4—82no—
835C2×D4—82no—
836C2×D4—81no—
837C2×D4—81no—
838C2×D4—81no—
839C2×D4—81no—
840C2×D4—81no—
841C2×D4—81no—
842C2×D4—81no—
843C2×D4—81no—
844C2×D4—816no—
845C2×D4C2×#4112yes—
846C2×D4C2×#4112yes—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—24no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—22no—
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—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—41no—
882C22×C4—41no—
883C22×C4—41no—
884C22×C4—41no—
885C22×C4—41no—
886C22×C4—41no—
887C22×C4—42no—
888C22×C4—42no—
889C22×C4—82no—
890C22×C4—82no—
891C22×C4—82no—
892C22×C4—82no—
893C22×C4—81no—
894C22×C4—81no—
895C22×C4—81no—
896C22×C4—81no—
897C22×C4—81no—
898C22×C4—81no—
899C22×C4—81no—
900C22×C4—81no—
901C22×C4—81no—
902C22×C4—81no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C2×#4112yes—
917C22×C4C2×#4112yes—
918C22×C4C2511yescharacteristic
919SD16—44no—
920SD16—82no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—44no—
945C2×C8—82no—
946C2×C8H(5,𝔽2)12yes—
947C4⋊C4—24no—
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—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—41no—
973C4⋊C4—41no—
974C4⋊C4—41no—
975C4⋊C4—41no—
976C4⋊C4—42no—
977C4⋊C4—42no—
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⋊C4C2×#4112yes—
993C4⋊C4C2×#4112yes—
994C22⋊C4—24no—
995C22⋊C4—24no—
996C22⋊C4—22no—
997C22⋊C4—22no—
998C22⋊C4—24no—
999C22⋊C4—24no—
1000C22⋊C4—41no—
1001C22⋊C4—41no—
1002C22⋊C4—41no—
1003C22⋊C4—41no—
1004C22⋊C4—41no—
1005C22⋊C4—41no—
1006C22⋊C4—41no—
1007C22⋊C4—41no—
1008C22⋊C4—41no—
1009C22⋊C4—41no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
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—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C42—21no—
1041C42—21no—
1042C42—21no—
1043C42—21no—
1044C42—21no—
1045C42—21no—
1046C42—21no—
1047C42—21no—
1048C42—42no—
1049C42—81no—
1050C42—81no—
1051C42—81no—
1052C42—81no—
1053C42—81no—
1054C42—81no—
1055C42—81no—
1056C42—81no—
1057C42—81no—
1058C42—81no—
1059C42—81no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—21no—
1075C23—22no—
1076C23—22no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—44no—
1082C23—44no—
1083C23—48no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—82no—
1097C23—82no—
1098C23—82no—
1099C23—82no—
1100C23—82no—
1101C23—84no—
1102C23—84no—
1103C23—162no—
1104C23—162no—
1105C23—162no—
1106C23—162no—
1107C23#52512yes—
1108C23#57712yes—
1109C23C23×D411yescharacteristic
1110Q8—41no—
1111Q8—41no—
1112Q8—41no—
1113Q8—41no—
1114Q8—162no—
1115D4—22no—
1116D4—22no—
1117D4—22no—
1118D4—22no—
1119D4—41no—
1120D4—41no—
1121D4—41no—
1122D4—41no—
1123D4—84no—
1124D4—84no—
1125D4—84no—
1126D4—84no—
1127D4—84no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—48no—
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—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—82no—
1216C2×C4—82no—
1217C2×C4—82no—
1218C2×C4—162no—
1219C2×C4—162no—
1220C2×C4—162no—
1221C2×C4—162no—
1222C2×C4#52512yes—
1223C2×C4C22×#4111yescharacteristic
1224C2×C4C22×#4111yescharacteristic
1225C2×C4C2×H(5,𝔽2)11yescharacteristic
1226C2×C4#58511yescharacteristic
1227C2×C4#58511yescharacteristic
1228C2×C4#58511yescharacteristic
1229C8—22no—
1230C8—41no—
1231C8—41no—
1232C8—41no—
1233C8—41no—
1234C8—41no—
1235C8—41no—
1236C8—41no—
1237C22—22no—
1238C22—22no—
1239C22—22no—
1240C22—22no—
1241C22—22no—
1242C22—22no—
1243C22—41no—
1244C22—41no—
1245C22—41no—
1246C22—41no—
1247C22—41no—
1248C22—41no—
1249C22—41no—
1250C22—41no—
1251C22—41no—
1252C22—41no—
1253C22—41no—
1254C22—41no—
1255C22—41no—
1256C22—42no—
1257C22—42no—
1258C22—41no—
1259C22—42no—
1260C22—42no—
1261C22—41no—
1262C22—42no—
1263C22—42no—
1264C22—88no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—168no—
1274C22C2×#52511yescharacteristic
1275C22#348511yescharacteristic
1276C22#349611yescharacteristic
1277C22C2×#57711yescharacteristic
1278C22#358411yescharacteristic
1279C22#358411yescharacteristic
1280C22#358511yescharacteristic
1281C4—22no—
1282C4—41no—
1283C4—41no—
1284C4—41no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—42no—
1291C4—42no—
1292C4—41no—
1293C4—41no—
1294C4—81no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C4—81no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4#351311yescharacteristic
1307C4#351411yescharacteristic
1308C4#352111yescharacteristic
1309C4#352111yescharacteristic
1310C2—42no—
1311C2—42no—
1312C2—81no—
1313C2—82no—
1314C2—82no—
1315C2#3579211yescharacteristic
1316C2#6055711yescharacteristic
1317C2#6057911yescharacteristic
1318C2#6174911yescharacteristic
1319C2#6177011yescharacteristic
1320C2#6227711yescharacteristic
1321C2#6231811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2280 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #37859C2semidirect
3. #30179C2semidirect
4. #30032C2semidirect
5. #29897C2semidirect
6. #29488C2semidirect
7. #29424C2semidirect
8. #27637C2semidirect
9. #27525C2semidirect
10. #27520C2semidirect
11. #27477C2semidirect
12. #27472C2semidirect
13. #27328C2semidirect
14. #27245C2semidirect
15. #27165C2semidirect
16. #26411C2semidirect
17. #26341C2semidirect
18. #25211C2semidirect
19. #25205C2semidirect
20. #24917C2semidirect
21. #24712C2semidirect
24. #23771C2semidirect
25. #23714C2semidirect
26. #23638C2semidirect
27. #23131C2semidirect
28. #23033C2semidirect
29. #22935C2semidirect
30. #22921C2semidirect
31. #22558C2semidirect
35. C2×#474C22semidirect
39. C2×#440C22semidirect
40. C2×#433C22semidirect
41. C2×#427C22semidirect
48. #2628C22semidirect
49. #2625C22semidirect
54. #2499C22semidirect
58. #2439C22semidirect
66. #2362C22semidirect
67. #2346C22semidirect
80. #2323C22semidirect
81. #2314C22semidirect
87. #2101C22semidirect
88. #2092C22semidirect
89. #2087C22semidirect
90. #2086C22semidirect
91. #2085C22semidirect
92. #2084C22semidirect
96. #2077C22semidirect
97. #2077C22semidirect
98. #2077C22semidirect
101. #2076C22semidirect
103. #2075C22semidirect
104. #2075C22semidirect
105. #2073C22semidirect
106. #2071C22semidirect
107. #2068C22semidirect
108. #2067C22semidirect
109. #2066C22semidirect
110. #2065C22semidirect
111. #2058C22semidirect
112. #2055C22semidirect
113. #2055C22semidirect
115. #2036C22semidirect
117. #2035C22semidirect
124. #2023C22semidirect
127. #1987C22semidirect
128. #1973C22semidirect
129. #1949C22semidirect
130. #1949C22semidirect
131. #1948C22semidirect
132. #1944C22semidirect
133. #1943C22semidirect
134. #1942C22semidirect
135. #1936C22semidirect
136. #1934C22semidirect
137. #1934C22semidirect
138. #1933C22semidirect
139. #1928C22semidirect
140. #1927C22semidirect
141. #1927C22semidirect
142. #1926C22semidirect
143. #1926C22semidirect
144. #1925C22semidirect
149. #1921C22semidirect
150. #1920C22semidirect
151. #1920C22semidirect
152. #1919C22semidirect
153. #1919C22semidirect
154. #1919C22semidirect
155. #1918C22semidirect
156. #1918C22semidirect
159. #1880C22semidirect
160. #1877C22semidirect
161. #1877C22semidirect
162. #1877C22semidirect
165. #1873C22semidirect
166. #1873C22semidirect
168. #1865C22semidirect
169. #1864C22semidirect
170. #1864C22semidirect
171. #1864C22semidirect
172. #1864C22semidirect
173. #1862C22semidirect
174. #1854C22semidirect
175. #1854C22semidirect
179. #1850C22semidirect
180. #1850C22semidirect
181. #1818C22semidirect
182. #1804C22semidirect
183. #1804C22semidirect
184. #1802C22semidirect
185. #1798C22semidirect
190. #1776C22semidirect
191. #1776C22semidirect
192. C4×#106C22semidirect
193. #1762C22semidirect
194. C4×#103C22semidirect
195. C4×#102C22semidirect
196. C4×#102C22semidirect
197. #1752C22semidirect
198. C8×C22⋊C4C22semidirect
199. #1750C22semidirect
200. #1735C22semidirect
201. #1735C22semidirect
202. #1735C22semidirect

Maximal subgroups

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

subgroupindex
#378592
#343632
#301792
#300322
#298972
#294882
#294242
#276372
#275252
#275202
#274772
#274722
#273282
#272452
#271652
#264112
#263412
#252112
#252052
#249172
#247122
#243792
#240092
#237712
#237142
#236382
#231312
#230332
#229352
#229212
#225582