Finite Group Databasebeta

← #6571265

Subgroups — #6571265

Order 512.

1615 conjugacy classes of subgroups.

The subgroup lattice has 1329 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39292C211yesmaximal, characteristic, complemented
2#34438C211yesmaximal, characteristic, complemented
3#30142C211yesmaximal, characteristic, complemented
4#30125C211yesmaximal, characteristic, complemented
5#29947C211yesmaximal, characteristic, complemented
6#29505C211yesmaximal, characteristic, complemented
7#29503C211yesmaximal, characteristic, complemented
8#28214C211yesmaximal, characteristic, complemented
9#28204C211yesmaximal, characteristic, complemented
10#27546C211yesmaximal, characteristic, complemented
11#27544C211yesmaximal, characteristic, complemented
12#27541C211yesmaximal, characteristic, complemented
13#27518C211yesmaximal, characteristic, complemented
14#27253C211yesmaximal, characteristic, complemented
15#27243C211yesmaximal, characteristic, complemented
16#27240C211yesmaximal, characteristic, complemented
17#27231C211yesmaximal, characteristic, complemented
18#26472C211yesmaximal, characteristic, complemented
19#26468C211yesmaximal, characteristic, complemented
20#25865C211yesmaximal, characteristic, complemented
21#25334C211yesmaximal, characteristic, complemented
22#25318C211yesmaximal, characteristic, complemented
23#24218C211yesmaximal, characteristic
24#23832C211yesmaximal, characteristic, complemented
25#23822C211yesmaximal, characteristic, complemented
26#23770C211yesmaximal, characteristic, complemented
27#23230C211yesmaximal, characteristic, complemented
28#23223C211yesmaximal, characteristic, complemented
29#23108C211yesmaximal, characteristic, complemented
30#23104C211yesmaximal, characteristic, complemented
31#22638C211yesmaximal, characteristic, complemented
32C2×#535C2211yescharacteristic
33C2×#489C2211yescharacteristic
34C2×#486C2211yescharacteristic
35C2×#477C2211yescharacteristic, complemented
36C2×#478C2211yescharacteristic
37C2×#478C2211yescharacteristic, complemented
38C2×#476C2211yescharacteristic
39C2×#463C2211yescharacteristic
40C2×#459C2211yescharacteristic
41C2×#449C2211yescharacteristic
42C2×#447C2211yescharacteristic
43#2860C2211yescharacteristic, complemented
44#2798—21no—
45#2727—21no—
46#2700—21no—
47#2689—21no—
48#2644C2211yescharacteristic, complemented
49#2628C2211yescharacteristic
50#2596—21no—
51#2560—21no—
52#2550C2211yescharacteristic, complemented
53#2542C2211yescharacteristic, complemented
54#2497C2211yescharacteristic
55#2496C2211yescharacteristic
56#2491C2211yescharacteristic
57#2490C2211yescharacteristic
58#2465—21no—
59#2448—21no—
60#2377—21no—
61#2375—21no—
62#2369C2211yescharacteristic, complemented
63#2367C2211yescharacteristic
64#2367C2211yescharacteristic
65#2366C2211yescharacteristic
66#2366C2211yescharacteristic
67#2364—21no—
68#2358—21no—
69#2357C2211yescharacteristic, complemented
70#2341C2211yescharacteristic
71#2339C2211yescharacteristic
72D4×C22⋊C4C2211yescharacteristic
73D4×C22⋊C4C2211yescharacteristic
74#2333—21no—
75#2330C2211yescharacteristic, complemented
76#2328C2211yescharacteristic
77#2326C2211yescharacteristic
78#2325—21no—
79#2324C2211yescharacteristic
80#2321—21no—
81#2321—21no—
82#2314C2211yescharacteristic
83C4×C4⋊Q8C2211yescharacteristic, complemented
84C4×#127C2211yescharacteristic
85C4×#124C2211yescharacteristic
86#2298C2211yescharacteristic
87#2100C2211yescharacteristic, complemented
88#2100C2211yescharacteristic, complemented
89#2099C2211yescharacteristic, complemented
90#2093C2211yescharacteristic, complemented
91#2085C2211yescharacteristic, complemented
92#2085C2211yescharacteristic, complemented
93#2085C2211yescharacteristic, complemented
94#2077C2211yescharacteristic
95#2077C2211yescharacteristic
96#2076C2211yescharacteristic
97#2076C2211yescharacteristic
98#2075C2211yescharacteristic
99#2075C2211yescharacteristic
100#2073C2211yescharacteristic, complemented
101#2072C2211yescharacteristic, complemented
102#2071C2211yescharacteristic
103#2071C2211yescharacteristic
104#2071C2211yescharacteristic, complemented
105#2068C2211yescharacteristic, complemented
106#2067C2211yescharacteristic
107#2067C2211yescharacteristic
108#2067C2211yescharacteristic, complemented
109#2055C2211yescharacteristic, complemented
110#2054C2211yescharacteristic
111#2054C2211yescharacteristic
112#2054C2211yescharacteristic, complemented
113#2042C2211yescharacteristic
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic
116#2041C2211yescharacteristic
117#2041C2211yescharacteristic
118#2041C2211yescharacteristic
119#2034C2211yescharacteristic
120#2033C2211yescharacteristic
121#2026C2211yescharacteristic, complemented
122#2025C2211yescharacteristic
123#2023C2211yescharacteristic
124#2023C2211yescharacteristic, complemented
125#2012C2211yescharacteristic
126#2011C2211yescharacteristic
127#1988C2211yescharacteristic, complemented
128#1987C2211yescharacteristic, complemented
129#1983C2211yescharacteristic
130#1982C2211yescharacteristic
131#1973C2211yescharacteristic, complemented
132#1972C2211yescharacteristic
133#1972C2211yescharacteristic
134#1970C2211yescharacteristic, complemented
135#1961C2211yescharacteristic
136#1958C2211yescharacteristic
137#1949C2211yescharacteristic, complemented
138#1949C2211yescharacteristic, complemented
139#1940C2211yescharacteristic, complemented
140#1939C2211yescharacteristic, complemented
141#1936C2211yescharacteristic
142#1936C2211yescharacteristic, complemented
143#1935C2211yescharacteristic, complemented
144#1934C2211yescharacteristic
145#1927C2211yescharacteristic, complemented
146#1927C2211yescharacteristic, complemented
147#1926C2211yescharacteristic
148#1926C2211yescharacteristic, complemented
149#1925C2211yescharacteristic
150#1925C2211yescharacteristic
151#1925C2211yescharacteristic
152#1925C2211yescharacteristic, complemented
153#1924C2211yescharacteristic
154#1924C2211yescharacteristic
155#1924C2211yescharacteristic
156#1923C2211yescharacteristic
157#1880C2211yescharacteristic, complemented
158#1880C2211yescharacteristic, complemented
159#1879C2211yescharacteristic
160#1879C2211yescharacteristic
161#1879C2211yescharacteristic
162#1879C2211yescharacteristic
163#1879C2211yescharacteristic, complemented
164#1879C2211yescharacteristic, complemented
165#1865C2211yescharacteristic, complemented
166#1864C2211yescharacteristic, complemented
167#1863C2211yescharacteristic, complemented
168#1862C2211yescharacteristic
169#1862C2211yescharacteristic
170#1862C2211yescharacteristic
171#1862C2211yescharacteristic
172#1862C2211yescharacteristic, complemented
173#1832C2211yescharacteristic, complemented
174#1831C2211yescharacteristic, complemented
175#1803C2211yescharacteristic, complemented
176#1802C2211yescharacteristic
177#1802C2211yescharacteristic
178#1802C2211yescharacteristic, complemented
179#1798C2211yescharacteristic
180#1788C2211yescharacteristic
181#1788C2211yescharacteristic
182#1788C2211yescharacteristic
183#1786C2211yescharacteristic
184#1786C2211yescharacteristic
185#1786C2211yescharacteristic
186#1776C2211yescharacteristic, complemented
187C4×#107C2211yescharacteristic, complemented
188#1771C2211yescharacteristic, complemented
189#1770C2211yescharacteristic, complemented
190#1763C2211yescharacteristic, complemented
191#1762C2211yescharacteristic
192#1762C2211yescharacteristic
193#1762C2211yescharacteristic
194#1762C2211yescharacteristic, complemented
195#1762C2211yescharacteristic, complemented
196#1762C2211yescharacteristic, complemented
197C4×#103C2211yescharacteristic, complemented
198C4×#102C2211yescharacteristic
199C4×#102C2211yescharacteristic, complemented
200#1750C2211yescharacteristic
201#1746C2211yescharacteristic, complemented
202#1745C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209#535—24no—
210#535—24no—
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×#127C2311yescharacteristic
214C2×#127C2311yescharacteristic
215C2×#126—21no—
216C2×#126—21no—
217C2×#125C2311yescharacteristic
218C2×#124—21no—
219C2×#124C2311yescharacteristic
220C2×#124C2311yescharacteristic
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8—21no—
223C2×#121—21no—
224C2×#121—21no—
225C2×#121C2311yescharacteristic
226C2×#120—21no—
227C2×#120—21no—
228C2×C4×Q8—21no—
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×D4—21no—
232C2×C4×D4—21no—
233C2×C4×D4—21no—
234C2×C4×D4—21no—
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C22×C22⋊C4—21no—
244C22×C22⋊C4—21no—
245#489—24no—
246#486—24no—
247#478—42no—
248#478—42no—
249#477—42no—
250#476—42no—
251#463—24no—
252#459—24no—
253#449—42no—
254#447—42no—
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×#97C2311yescharacteristic
306C2×#97C2311yescharacteristic
307C2×#97C2311yescharacteristic
308C2×#97C2311yescharacteristic
309C2×C4×C8C2311yescharacteristic
310C2×C4×C8C2311yescharacteristic
311#400—21no—
312#400—21no—
313#400—21no—
314#399—21no—
315#399—21no—
316#399—21no—
317#398—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#396—21no—
324#396—21no—
325#395—21no—
326#395—21no—
327#394—21no—
328#394—21no—
329#393—21no—
330#393—21no—
331#391—21no—
332#391—21no—
333#391—21no—
334#391—21no—
335#391C2311yescharacteristic
336#391C2311yescharacteristic
337#390—21no—
338#390—21no—
339#390—21no—
340#390—21no—
341#390—21no—
342#390—21no—
343#390—21no—
344#390—21no—
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#389—21no—
357#389—21no—
358#389—21no—
359#389—21no—
360#389—21no—
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
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#388D411yescharacteristic
388#388D411yescharacteristic
389#388D411yescharacteristic
390#388D411yescharacteristic
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387D411yescharacteristic
398#387D411yescharacteristic
399#387D411yescharacteristic
400#387D411yescharacteristic
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386—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#385—21no—
421#384C2311yescharacteristic
422#384C2311yescharacteristic
423#384C2311yescharacteristic
424#382C2311yescharacteristic
425#382C2311yescharacteristic
426#381—21no—
427#381—21no—
428#380—21no—
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#379—21no—
435#379—21no—
436C4×C4⋊C4—21no—
437C4×C4⋊C4—21no—
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
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⋊C4C2311yescharacteristic
454C4×C22⋊C4C2311yescharacteristic
455#376C2311yescharacteristic
456C2×#95—21no—
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#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25—21no—
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—41no—
497C22×Q8—21no—
498C22×Q8—21no—
499C22×Q8C2411yescharacteristic
500C22×D4—21no—
501C22×D4—22no—
502C22×D4—22no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4C2411yescharacteristic
514C22×D4C2411yescharacteristic
515C22×D4C2411yescharacteristic
516C22×D4C2411yescharacteristic
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4C2411yescharacteristic
526C2×SD16—22no—
527C2×SD16—41no—
528C2×SD16—41no—
529C2×D8—22no—
530C2×D8—22no—
531C2×D8—22no—
532C2×D8—41no—
533C2×D8—41no—
534C2×D8—41no—
535C2×D8—41no—
536C2×D8—41no—
537C2×D8—41no—
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C4⋊Q8—22no—
547C4⋊Q8—22no—
548C4⋊Q8—22no—
549C4⋊Q8—41no—
550#127—22no—
551#127—22no—
552#127—22no—
553#127#4114yes—
554#126—82no—
555#126—82no—
556#125—22no—
557#125—41no—
558#124—22no—
559#124—22no—
560#124—22no—
561#124—82no—
562#124#4114yes—
563C22⋊Q8—82no—
564C22⋊Q8—82no—
565#121—28no—
566#121—28no—
567#121—22no—
568#121—41no—
569#120—28no—
570#120—28no—
571C4×Q8—41no—
572C4×Q8—41no—
573C4×Q8—41no—
574C4×Q8—41no—
575C4×Q8—82no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—41no—
579C4×D4—41no—
580C4×D4—41no—
581C4×D4—41no—
582C4×D4—41no—
583C4×D4—41no—
584C4×D4—41no—
585C4×D4—41no—
586C4×D4—41no—
587C4×D4—41no—
588C4×D4—41no—
589C4×D4—41no—
590C4×D4—82no—
591C4×D4—82no—
592C4×D4—82no—
593C4×D4—82no—
594#117—22no—
595#117—22no—
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—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4C2×D411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×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—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—82no—
672C2×C22⋊C4—82no—
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C22⋊C4C2×D411yescharacteristic
675C2×C22⋊C4C2×D411yescharacteristic
676C2×C22⋊C4C2×D411yescharacteristic
677C2×C22⋊C4C2×D411yescharacteristic
678C2×C22⋊C4C2×D411yescharacteristic
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—21no—
682C2×C42—21no—
683C2×C42—21no—
684C2×C42—21no—
685C2×C42—21no—
686C2×C42—21no—
687C2×C42—21no—
688C2×C42C2×D411yescharacteristic
689C2×C42C2×D411yescharacteristic
690C2×C42C2×D411yescharacteristic
691C2×C42C2×D411yescharacteristic
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698#107—22no—
699#107—41no—
700#107—41no—
701#107—41no—
702#107—41no—
703#106—22no—
704#106—41no—
705#106—41no—
706C4⋊C8—22no—
707C4⋊C8—22no—
708C4⋊C8—41no—
709C4⋊C8—41no—
710C4⋊C8—41no—
711C4⋊C8—41no—
712#103—22no—
713#103—22no—
714#103—22no—
715#103—22no—
716#103—41no—
717#103—41no—
718#103—41no—
719#102—22no—
720#102—22no—
721#102—22no—
722#102—22no—
723#102—22no—
724#102—22no—
725#102—22no—
726#102—22no—
727#102—22no—
728#102—22no—
729#102—22no—
730#102—22no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102—41no—
736#102—41no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743#102—41no—
744C22⋊C8—41no—
745C22⋊C8—41no—
746C22⋊C8—41no—
747C22⋊C8—41no—
748#97—22no—
749#97—41no—
750#97—41no—
751#97—41no—
752C4×C8—22no—
753C4×C8—41no—
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#95—21no—
780#95—21no—
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793C24—24no—
794C24—21no—
795C24—21no—
796C24—21no—
797C24—21no—
798C24—81no—
799C24—81no—
800C24—81no—
801C24—81no—
802C24—81no—
803C24—81no—
804C24C22×D411yescharacteristic
805#41—82no—
806#41—82no—
807#41—82no—
808#41—82no—
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—42no—
815C2×Q8—42no—
816C2×Q8—42no—
817C2×Q8—81no—
818C2×Q8—81no—
819C2×Q8—81no—
820C2×Q8C2×#4112yes—
821C2×D4—24no—
822C2×D4—24no—
823C2×D4—24no—
824C2×D4—24no—
825C2×D4—24no—
826C2×D4—24no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—42no—
849C2×D4—81no—
850C2×D4—81no—
851C2×D4—81no—
852C2×D4—81no—
853C2×D4—81no—
854C2×D4—81no—
855C2×D4—81no—
856C2×D4—81no—
857C2×D4—81no—
858C2×D4—81no—
859C2×D4—82no—
860C2×D4—82no—
861C2×D4—82no—
862C2×D4—82no—
863C2×D4—81no—
864C2×D4—81no—
865C2×D4—81no—
866C2×D4—81no—
867C2×D4C2×#4112yes—
868C2×D4C2×#4112yes—
869C2×D4C2×#4112yes—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—24no—
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—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—42no—
890C22×C4—42no—
891C22×C4—42no—
892C22×C4—42no—
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×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C2511yescharacteristic
926SD16—82no—
927D8—82no—
928D8—82no—
929D8—82no—
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—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C4⋊C4—22no—
955C4⋊C4—22no—
956C4⋊C4—22no—
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—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—41no—
979C4⋊C4—41no—
980C4⋊C4—41no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4H(5,𝔽2)12yes—
1001C22⋊C4—24no—
1002C22⋊C4—24no—
1003C22⋊C4—24no—
1004C22⋊C4—24no—
1005C22⋊C4—22no—
1006C22⋊C4—22no—
1007C22⋊C4—22no—
1008C22⋊C4—41no—
1009C22⋊C4—41no—
1010C22⋊C4—41no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
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—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C42—22no—
1047C42—21no—
1048C42—21no—
1049C42—21no—
1050C42—21no—
1051C42—21no—
1052C42—21no—
1053C42—21no—
1054C42—21no—
1055C42—21no—
1056C42—21no—
1057C42—41no—
1058C42—41no—
1059C42—41no—
1060C42—81no—
1061C42—81no—
1062C42—81no—
1063C42—81no—
1064C42—81no—
1065C42—81no—
1066C42—81no—
1067C42—81no—
1068C42—81no—
1069C42C2×#4112yes—
1070C42C2×#4112yes—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—21no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
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—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—84no—
1107C23—84no—
1108C23—84no—
1109C23—162no—
1110C23—162no—
1111C23—162no—
1112C23—162no—
1113C23C23×D411yescharacteristic
1114Q8—22no—
1115Q8—22no—
1116Q8—41no—
1117Q8—41no—
1118Q8—84no—
1119Q8—162no—
1120D4—22no—
1121D4—22no—
1122D4—22no—
1123D4—22no—
1124D4—22no—
1125D4—22no—
1126D4—41no—
1127D4—41no—
1128D4—41no—
1129D4—41no—
1130D4—41no—
1131D4—41no—
1132D4—41no—
1133D4—41no—
1134D4—41no—
1135D4—41no—
1136D4—84no—
1137D4—84no—
1138D4—84no—
1139D4—84no—
1140D4—84no—
1141D4—84no—
1142D4—162no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
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—22no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—22no—
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—21no—
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—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—84no—
1220C2×C4—162no—
1221C2×C4—162no—
1222C2×C4—162no—
1223C2×C4—162no—
1224C2×C4—162no—
1225C2×C4—162no—
1226C2×C4—162no—
1227C2×C4#52512yes—
1228C2×C4#52512yes—
1229C2×C4#57612yes—
1230C2×C4C22×#4111yescharacteristic
1231C2×C4C22×#4111yescharacteristic
1232C2×C4C2×H(5,𝔽2)11yescharacteristic
1233C2×C4#58511yescharacteristic
1234C2×C4#58511yescharacteristic
1235C2×C4#58511yescharacteristic
1236C8—41no—
1237C8—41no—
1238C8—41no—
1239C8—41no—
1240C8—41no—
1241C8—41no—
1242C8—41no—
1243C8—41no—
1244C22—41no—
1245C22—41no—
1246C22—41no—
1247C22—41no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—41no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—41no—
1256C22—41no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—168no—
1280C22C2×#52511yescharacteristic
1281C22#348811yescharacteristic
1282C22#350011yescharacteristic
1283C22C2×#57611yescharacteristic
1284C22#358511yescharacteristic
1285C22#358511yescharacteristic
1286C22#358611yescharacteristic
1287C4—22no—
1288C4—22no—
1289C4—22no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—42no—
1296C4—41no—
1297C4—41no—
1298C4—41no—
1299C4—41no—
1300C4—41no—
1301C4—42no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4#351411yescharacteristic
1313C4#351411yescharacteristic
1314C4#352111yescharacteristic
1315C4#352111yescharacteristic
1316C2—81no—
1317C2—82no—
1318C2—82no—
1319C2—82no—
1320C2—161no—
1321C2#3607511yescharacteristic
1322C2#6057511yescharacteristic
1323C2#6059011yescharacteristic
1324C2#6202211yescharacteristic
1325C2#6208311yescharacteristic
1326C2#6256611yescharacteristic
1327C2#6261011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#24218C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2298 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39292C2semidirect
2. #34438C2semidirect
3. #30142C2semidirect
4. #30125C2semidirect
5. #29947C2semidirect
6. #29505C2semidirect
7. #29503C2semidirect
8. #28214C2semidirect
9. #28204C2semidirect
10. #27546C2semidirect
11. #27544C2semidirect
12. #27541C2semidirect
13. #27518C2semidirect
14. #27253C2semidirect
15. #27243C2semidirect
16. #27240C2semidirect
17. #27231C2semidirect
18. #26472C2semidirect
19. #26468C2semidirect
20. #25865C2semidirect
21. #25334C2semidirect
22. #25318C2semidirect
24. #23832C2semidirect
25. #23822C2semidirect
26. #23770C2semidirect
27. #23230C2semidirect
28. #23223C2semidirect
29. #23108C2semidirect
30. #23104C2semidirect
31. #22638C2semidirect
35. C2×#477C22semidirect
37. C2×#478C22semidirect
43. #2860C22semidirect
48. #2644C22semidirect
52. #2550C22semidirect
53. #2542C22semidirect
62. #2369C22semidirect
69. #2357C22semidirect
75. #2330C22semidirect
83. C4×C4⋊Q8C22semidirect
87. #2100C22semidirect
88. #2100C22semidirect
89. #2099C22semidirect
90. #2093C22semidirect
91. #2085C22semidirect
92. #2085C22semidirect
93. #2085C22semidirect
100. #2073C22semidirect
101. #2072C22semidirect
104. #2071C22semidirect
105. #2068C22semidirect
108. #2067C22semidirect
109. #2055C22semidirect
112. #2054C22semidirect
121. #2026C22semidirect
124. #2023C22semidirect
127. #1988C22semidirect
128. #1987C22semidirect
131. #1973C22semidirect
134. #1970C22semidirect
137. #1949C22semidirect
138. #1949C22semidirect
139. #1940C22semidirect
140. #1939C22semidirect
142. #1936C22semidirect
143. #1935C22semidirect
145. #1927C22semidirect
146. #1927C22semidirect
148. #1926C22semidirect
152. #1925C22semidirect
157. #1880C22semidirect
158. #1880C22semidirect
163. #1879C22semidirect
164. #1879C22semidirect
165. #1865C22semidirect
166. #1864C22semidirect
167. #1863C22semidirect
172. #1862C22semidirect
173. #1832C22semidirect
174. #1831C22semidirect
175. #1803C22semidirect
178. #1802C22semidirect
186. #1776C22semidirect
187. C4×#107C22semidirect
188. #1771C22semidirect
189. #1770C22semidirect
190. #1763C22semidirect
194. #1762C22semidirect
195. #1762C22semidirect
196. #1762C22semidirect
197. C4×#103C22semidirect
199. C4×#102C22semidirect
201. #1746C22semidirect
202. #1745C22semidirect

Maximal subgroups

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

subgroupindex
#392922
#344382
#301422
#301252
#299472
#295052
#295032
#282142
#282042
#275462
#275442
#275412
#275182
#272532
#272432
#272402
#272312
#264722
#264682
#258652
#253342
#253182
#242182
#238322
#238222
#237702
#232302
#232232
#231082
#231042
#226382