Finite Group Databasebeta

← #6562155

Subgroups — #6562155

Order 512.

1471 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39067C211yesmaximal, characteristic, complemented
2#34429C211yesmaximal, characteristic
3#30151C211yesmaximal, characteristic, complemented
4#30054C211yesmaximal, characteristic, complemented
5#29918C211yesmaximal, characteristic, complemented
6#29502C211yesmaximal, characteristic, complemented
7#29402C211yesmaximal, characteristic, complemented
8#29359C211yesmaximal, characteristic, complemented
9#28159C211yesmaximal, characteristic, complemented
10#27569C211yesmaximal, characteristic, complemented
11#27565C211yesmaximal, characteristic, complemented
12#27453C211yesmaximal, characteristic, complemented
13#27440C211yesmaximal, characteristic, complemented
14#27216C211yesmaximal, characteristic, complemented
15#27213C211yesmaximal, characteristic, complemented
16#26432C211yesmaximal, characteristic, complemented
17#26423C211yesmaximal, characteristic
18#26186C211yesmaximal, characteristic, complemented
19#26171C211yesmaximal, characteristic, complemented
20#25514C211yesmaximal, characteristic
21#25099C211yesmaximal, characteristic
22#25082C211yesmaximal, characteristic, complemented
23#23946C211yesmaximal, characteristic
24#23823C211yesmaximal, characteristic, complemented
25#23695C211yesmaximal, characteristic, complemented
26#23633C211yesmaximal, characteristic, complemented
27#23138C211yesmaximal, characteristic
28#23136C211yesmaximal, characteristic, complemented
29#22881C211yesmaximal, characteristic, complemented
30#22855C211yesmaximal, characteristic
31#22594C211yesmaximal, characteristic, complemented
32C2×#542C2211yescharacteristic
33C2×#468C2211yescharacteristic
34C2×#467C2211yescharacteristic
35C2×#462C2211yescharacteristic
36C2×#461C2211yescharacteristic
37C2×#451C2211yescharacteristic
38C2×#448C2211yescharacteristic
39C2×#440C2211yescharacteristic
40C2×C4×Q16C2211yescharacteristic
41C2×#419C2211yescharacteristic
42C22×#103C2211yescharacteristic
43#2863C2211yescharacteristic
44#2758—21no—
45#2755—21no—
46#2739—21no—
47#2738—21no—
48#2642C2211yescharacteristic
49#2625C2211yescharacteristic
50#2588—21no—
51#2588—21no—
52#2575—21no—
53#2573—21no—
54#2511C2211yescharacteristic
55#2453C2211yescharacteristic
56#2446C2211yescharacteristic
57#2446C2211yescharacteristic
58#2441C2211yescharacteristic
59#2434C2211yescharacteristic
60#2383—21no—
61#2376—21no—
62#2373—21no—
63#2363C2211yescharacteristic
64#2362C2211yescharacteristic
65#2362C2211yescharacteristic
66#2361C2211yescharacteristic
67#2360C2211yescharacteristic
68#2359—21no—
69#2356C2211yescharacteristic
70#2354C2211yescharacteristic
71Q8×C4⋊C4C2211yescharacteristic
72#2349C2211yescharacteristic
73Q8×C22⋊C4C2211yescharacteristic
74#2337—21no—
75#2331C2211yescharacteristic
76#2329—21no—
77#2326—21no—
78#2326C2211yescharacteristic
79#2323—21no—
80#2320C2211yescharacteristic
81#2317C2211yescharacteristic
82#2310C2211yescharacteristic
83C4×C4⋊Q8C2211yescharacteristic
84C4×C4⋊Q8C2211yescharacteristic
85C4×#124C2211yescharacteristic
86#2298C2211yescharacteristic
87#2101C2211yescharacteristic
88#2099C2211yescharacteristic
89#2099C2211yescharacteristic
90#2099C2211yescharacteristic
91#2097C2211yescharacteristic
92#2095C2211yescharacteristic
93#2087C2211yescharacteristic
94#2087C2211yescharacteristic
95#2085C2211yescharacteristic
96#2083C2211yescharacteristic
97#2074C2211yescharacteristic
98#2074C2211yescharacteristic
99#2074C2211yescharacteristic
100#2074C2211yescharacteristic
101#2074C2211yescharacteristic
102#2072C2211yescharacteristic
103#2072C2211yescharacteristic
104#2072C2211yescharacteristic
105#2072C2211yescharacteristic
106#2072C2211yescharacteristic
107#2068C2211yescharacteristic
108#2068C2211yescharacteristic
109#2068C2211yescharacteristic
110#2067C2211yescharacteristic
111#2057C2211yescharacteristic
112#2056C2211yescharacteristic
113#2055C2211yescharacteristic
114#2043C2211yescharacteristic
115#2043C2211yescharacteristic
116#2042C2211yescharacteristic
117#2026C2211yescharacteristic
118#2025C2211yescharacteristic
119#2024C2211yescharacteristic
120#2024C2211yescharacteristic
121#2024C2211yescharacteristic
122#2016C2211yescharacteristic
123#2015C2211yescharacteristic
124#2015C2211yescharacteristic
125#2015C2211yescharacteristic
126#2013C2211yescharacteristic
127#1989C2211yescharacteristic
128#1989C2211yescharacteristic
129#1981C2211yescharacteristic
130#1981C2211yescharacteristic
131#1973C2211yescharacteristic
132#1971C2211yescharacteristic
133#1936C2211yescharacteristic
134#1935C2211yescharacteristic
135#1935C2211yescharacteristic
136#1935C2211yescharacteristic
137#1933C2211yescharacteristic
138#1933C2211yescharacteristic
139#1928C2211yescharacteristic
140#1928C2211yescharacteristic
141#1928C2211yescharacteristic
142#1928C2211yescharacteristic
143#1921C2211yescharacteristic
144#1921C2211yescharacteristic
145#1921C2211yescharacteristic
146#1920C2211yescharacteristic
147#1918C2211yescharacteristic
148#1918C2211yescharacteristic
149#1917C2211yescharacteristic
150#1917C2211yescharacteristic
151#1917C2211yescharacteristic
152#1916C2211yescharacteristic
153#1894C2211yescharacteristic
154#1893C2211yescharacteristic
155#1880C2211yescharacteristic
156#1880C2211yescharacteristic
157#1878C2211yescharacteristic
158#1878C2211yescharacteristic
159#1878C2211yescharacteristic
160#1878C2211yescharacteristic
161#1878C2211yescharacteristic
162#1878C2211yescharacteristic
163#1878C2211yescharacteristic
164#1878C2211yescharacteristic
165#1877C2211yescharacteristic
166#1877C2211yescharacteristic
167#1877C2211yescharacteristic
168#1877C2211yescharacteristic
169#1877C2211yescharacteristic
170#1877C2211yescharacteristic
171#1875C2211yescharacteristic
172#1873C2211yescharacteristic
173#1873C2211yescharacteristic
174#1872C2211yescharacteristic
175#1865C2211yescharacteristic
176#1864C2211yescharacteristic
177#1863C2211yescharacteristic
178#1863C2211yescharacteristic
179#1863C2211yescharacteristic
180#1862C2211yescharacteristic
181#1854C2211yescharacteristic
182#1852C2211yescharacteristic
183#1851C2211yescharacteristic
184#1850C2211yescharacteristic
185#1840C2211yescharacteristic
186#1831C2211yescharacteristic
187#1818C2211yescharacteristic
188#1803C2211yescharacteristic
189#1802C2211yescharacteristic
190#1768C2211yescharacteristic
191#1763C2211yescharacteristic
192#1763C2211yescharacteristic
193#1763C2211yescharacteristic
194#1763C2211yescharacteristic
195#1763C2211yescharacteristic
196C4×#102C2211yescharacteristic
197#1753C2211yescharacteristic
198#1752C2211yescharacteristic
199#1745C2211yescharacteristic
200#1736C2211yescharacteristic
201#1735C2211yescharacteristic
202#1729C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#542—24no—
213#542—24no—
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×#126—21no—
218C2×#125C2311yescharacteristic
219C2×#124—21no—
220C2×#124C2311yescharacteristic
221C2×#123—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8C2311yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×#121C2311yescharacteristic
226C2×C4×Q8—21no—
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×D4—21no—
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×#117—21no—
238C2×#117C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C22×C4⋊C4C2311yescharacteristic
242#468—24no—
243#467—24no—
244#462—42no—
245#461—42no—
246#451—24no—
247#448—24no—
248#440—42no—
249C4×Q16—42no—
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260#419—42no—
261C2×#103—42no—
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×C22⋊C8C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×#97C2311yescharacteristic
293C2×#97C2311yescharacteristic
294C2×#97C2311yescharacteristic
295C2×C4×C8C2311yescharacteristic
296#400—21no—
297#400—21no—
298#400—21no—
299#400—21no—
300#400—21no—
301#400—21no—
302#400—21no—
303#400—21no—
304#400—21no—
305#400—21no—
306#399—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#397—21no—
312#397—21no—
313#396—21no—
314#395—21no—
315#395—21no—
316#391—21no—
317#391—21no—
318#391—21no—
319#391—21no—
320#391—21no—
321#391—21no—
322#391—21no—
323#391C2311yescharacteristic
324#391C2311yescharacteristic
325#391C2311yescharacteristic
326#391C2311yescharacteristic
327#391C2311yescharacteristic
328#391C2311yescharacteristic
329#391C2311yescharacteristic
330#391C2311yescharacteristic
331#391C2311yescharacteristic
332#391C2311yescharacteristic
333#391C2311yescharacteristic
334#391C2311yescharacteristic
335#391C2311yescharacteristic
336#390—21no—
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#389—21no—
340#389—21no—
341#389—21no—
342#389—21no—
343#389—21no—
344#389—21no—
345#389—21no—
346#389—21no—
347#389—21no—
348#389—21no—
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
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#388—21no—
369#388—21no—
370#388D411yescharacteristic
371#388D411yescharacteristic
372#388D411yescharacteristic
373#388D411yescharacteristic
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#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387D411yescharacteristic
395#387D411yescharacteristic
396#387D411yescharacteristic
397#387D411yescharacteristic
398#386—21no—
399#386—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#384—21no—
411#384C2311yescharacteristic
412#384C2311yescharacteristic
413#384C2311yescharacteristic
414#383—21no—
415#383—21no—
416#383—21no—
417#382—21no—
418#382C2311yescharacteristic
419#382C2311yescharacteristic
420#381—21no—
421#381—21no—
422#380—21no—
423#380—21no—
424#380—21no—
425#380C2311yescharacteristic
426C4×C4⋊C4—21no—
427C4×C4⋊C4—21no—
428C4×C4⋊C4—21no—
429C4×C4⋊C4—21no—
430C4×C4⋊C4—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C22⋊C4—21no—
440C4×C22⋊C4—21no—
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4C2311yescharacteristic
445C4×C22⋊C4C2311yescharacteristic
446#376—21no—
447#376C2311yescharacteristic
448C2×#95—21no—
449C43C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C22×Q8—21no—
491C22×Q8—21no—
492C22×Q8—22no—
493C22×Q8—22no—
494C22×Q8—22no—
495C22×Q8—41no—
496C22×Q8—41no—
497C22×Q8—41no—
498C22×Q8C2411yescharacteristic
499C22×Q8C2411yescharacteristic
500C22×Q8C2411yescharacteristic
501C22×Q8C2411yescharacteristic
502C22×D4—21no—
503C22×D4C2411yescharacteristic
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4C2411yescharacteristic
510C2×Q16—22no—
511C2×Q16—22no—
512C2×Q16—22no—
513C2×Q16—22no—
514C2×Q16—41no—
515C2×Q16—41no—
516C2×Q16—41no—
517C2×Q16—41no—
518C2×Q16—41no—
519C2×SD16—22no—
520C2×SD16—22no—
521C2×SD16—22no—
522C2×SD16—22no—
523C2×SD16—41no—
524C2×SD16—41no—
525C2×SD16—41no—
526C2×SD16—41no—
527C2×SD16—41no—
528C2×M16—22no—
529C2×M16—41no—
530C2×M16—41no—
531C22×C8—22no—
532C22×C8—41no—
533C22×C8—41no—
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C4⋊Q8—22no—
543C4⋊Q8—22no—
544C4⋊Q8—22no—
545C4⋊Q8—41no—
546C4⋊Q8—41no—
547C4⋊Q8—41no—
548#126—28no—
549#125—41no—
550#125—41no—
551#124—28no—
552#124—22no—
553#124—22no—
554#123—28no—
555C22⋊Q8—28no—
556C22⋊Q8—22no—
557C22⋊Q8—22no—
558C22⋊Q8—22no—
559C22⋊Q8#4114yes—
560#121—22no—
561#121#4114yes—
562C4×Q8—22no—
563C4×Q8—22no—
564C4×Q8—22no—
565C4×Q8—41no—
566C4×Q8—41no—
567C4×Q8—41no—
568C4×Q8—41no—
569C4×Q8—41no—
570C4×Q8—41no—
571C4×Q8—41no—
572C4×Q8—41no—
573C4×Q8—41no—
574C4×Q8—82no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—41no—
578C4×D4—41no—
579C4×D4—41no—
580C4×D4—41no—
581C4×D4—82no—
582#117—22no—
583#117—22no—
584#117—41no—
585#117—41no—
586#117—41no—
587#117—41no—
588#117—82no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—41no—
621C2×C4⋊C4—41no—
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2×D411yescharacteristic
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
655C2×C22⋊C4C2×D411yescharacteristic
656C2×C22⋊C4C2×D411yescharacteristic
657C2×C22⋊C4C2×D411yescharacteristic
658C2×C22⋊C4C2×D411yescharacteristic
659C2×C22⋊C4C2×D411yescharacteristic
660C2×C42—21no—
661C2×C42—21no—
662C2×C42—21no—
663C2×C42—21no—
664C2×C42—21no—
665C2×C42—21no—
666C2×C42—21no—
667C2×C42—21no—
668C2×C42—21no—
669C2×C42—21no—
670C2×C42—21no—
671C2×C42—21no—
672C2×C42—21no—
673C2×C42C2×D411yescharacteristic
674C2×C42C2×D411yescharacteristic
675C2×C42C2×D411yescharacteristic
676C2×C42C2×D411yescharacteristic
677C2×C42C2411yescharacteristic
678C2×C42C2411yescharacteristic
679C2×C42C2411yescharacteristic
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683#107—22no—
684#107—22no—
685#107—41no—
686#107—41no—
687#107—41no—
688#106—41no—
689C4⋊C8—41no—
690C4⋊C8—41no—
691C4⋊C8—41no—
692C4⋊C8—41no—
693#103—22no—
694#103—22no—
695#103—22no—
696#103—22no—
697#103—22no—
698#103—22no—
699#103—22no—
700#103—22no—
701#103—22no—
702#103—22no—
703#103—22no—
704#103—41no—
705#103—41no—
706#103—41no—
707#103—41no—
708#103—41no—
709#103—41no—
710#103—41no—
711#103—41no—
712#103—41no—
713#103—41no—
714#103—41no—
715#103—41no—
716#102—22no—
717#102—41no—
718#102—41no—
719#102—41no—
720#102—41no—
721C22⋊C8—22no—
722C22⋊C8—22no—
723#97—41no—
724#97—41no—
725#97—41no—
726C4×C8—41no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#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#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784C24—21no—
785C24C22×D411yescharacteristic
786C2×Q8—24no—
787C2×Q8—21no—
788C2×Q8—21no—
789C2×Q8—21no—
790C2×Q8—21no—
791C2×Q8—21no—
792C2×Q8—21no—
793C2×Q8—21no—
794C2×Q8—21no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—21no—
801C2×Q8—21no—
802C2×Q8—21no—
803C2×Q8—21no—
804C2×Q8—21no—
805C2×Q8—21no—
806C2×Q8—21no—
807C2×Q8—21no—
808C2×Q8—21no—
809C2×Q8—42no—
810C2×Q8—44no—
811C2×Q8—44no—
812C2×Q8—42no—
813C2×Q8—81no—
814C2×Q8—81no—
815C2×Q8—81no—
816C2×Q8—82no—
817C2×Q8—82no—
818C2×Q8C2×#4112yes—
819C2×Q8H(5,𝔽2)12yes—
820C2×D4—24no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—81no—
827C2×D4—81no—
828C2×D4C2×#4112yes—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—24no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4—42no—
852C22×C4—81no—
853C22×C4—81no—
854C22×C4—81no—
855C22×C4—81no—
856C22×C4—81no—
857C22×C4—81no—
858C22×C4—81no—
859C22×C4—81no—
860C22×C4—81no—
861C22×C4—81no—
862C22×C4—81no—
863C22×C4C22×D411yescharacteristic
864C22×C4C22×D411yescharacteristic
865C22×C4C22×D411yescharacteristic
866C22×C4C22×D411yescharacteristic
867C22×C4C22×D411yescharacteristic
868C22×C4C22×D411yescharacteristic
869C22×C4C22×D411yescharacteristic
870C22×C4C22×D411yescharacteristic
871C22×C4C22×D411yescharacteristic
872C22×C4C22×D411yescharacteristic
873C22×C4C22×D411yescharacteristic
874C22×C4C22×D411yescharacteristic
875C22×C4C22×D411yescharacteristic
876C22×C4C2×#4112yes—
877C22×C4C2×#4112yes—
878C22×C4C2511yescharacteristic
879Q16—44no—
880Q16—82no—
881Q16—82no—
882SD16—44no—
883SD16—82no—
884SD16—82no—
885M16—82no—
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C8—21no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8—21no—
899C2×C8—21no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—21no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—82no—
911C4⋊C4—24no—
912C4⋊C4—24no—
913C4⋊C4—24no—
914C4⋊C4—22no—
915C4⋊C4—22no—
916C4⋊C4—22no—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—41no—
938C4⋊C4—41no—
939C4⋊C4—41no—
940C4⋊C4—42no—
941C4⋊C4—42no—
942C4⋊C4—42no—
943C4⋊C4—42no—
944C4⋊C4—42no—
945C4⋊C4—42no—
946C4⋊C4—42no—
947C4⋊C4—81no—
948C4⋊C4—81no—
949C4⋊C4—81no—
950C4⋊C4—81no—
951C4⋊C4—81no—
952C4⋊C4—81no—
953C4⋊C4—81no—
954C4⋊C4—81no—
955C4⋊C4—81no—
956C4⋊C4—81no—
957C4⋊C4—81no—
958C4⋊C4—81no—
959C4⋊C4—81no—
960C4⋊C4—81no—
961C4⋊C4—81no—
962C4⋊C4—81no—
963C4⋊C4—81no—
964C4⋊C4—81no—
965C4⋊C4—81no—
966C4⋊C4—81no—
967C4⋊C4—81no—
968C4⋊C4C2×#4112yes—
969C4⋊C4C2×#4112yes—
970C22⋊C4—24no—
971C22⋊C4—24no—
972C22⋊C4—24no—
973C22⋊C4—24no—
974C22⋊C4—22no—
975C22⋊C4—22no—
976C22⋊C4—24no—
977C22⋊C4—22no—
978C22⋊C4—41no—
979C22⋊C4—41no—
980C22⋊C4—41no—
981C22⋊C4—42no—
982C22⋊C4—42no—
983C22⋊C4—81no—
984C22⋊C4—81no—
985C22⋊C4—81no—
986C22⋊C4—81no—
987C22⋊C4—81no—
988C22⋊C4—81no—
989C22⋊C4—81no—
990C22⋊C4—81no—
991C42—24no—
992C42—22no—
993C42—21no—
994C42—21no—
995C42—21no—
996C42—21no—
997C42—21no—
998C42—21no—
999C42—21no—
1000C42—21no—
1001C42—21no—
1002C42—21no—
1003C42—21no—
1004C42—21no—
1005C42—41no—
1006C42—41no—
1007C42—41no—
1008C42—42no—
1009C42—42no—
1010C42—42no—
1011C42—81no—
1012C42—81no—
1013C42—81no—
1014C42—81no—
1015C42—81no—
1016C42—81no—
1017C42—81no—
1018C42—81no—
1019C42—81no—
1020C23—21no—
1021C23—21no—
1022C23—21no—
1023C23—21no—
1024C23—21no—
1025C23—21no—
1026C23—22no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23#52512yes—
1034C23C23×D411yescharacteristic
1035Q8—22no—
1036Q8—22no—
1037Q8—22no—
1038Q8—22no—
1039Q8—41no—
1040Q8—41no—
1041Q8—41no—
1042Q8—41no—
1043Q8—41no—
1044Q8—41no—
1045Q8—41no—
1046Q8—41no—
1047Q8—41no—
1048Q8—41no—
1049Q8—41no—
1050Q8—41no—
1051Q8—84no—
1052Q8—84no—
1053D4—22no—
1054D4—22no—
1055D4—41no—
1056D4—41no—
1057D4—84no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—22no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—22no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—84no—
1145C2×C4—84no—
1146C2×C4—162no—
1147C2×C4—162no—
1148C2×C4—162no—
1149C2×C4#52512yes—
1150C2×C4#57812yes—
1151C2×C4C22×#4111yescharacteristic
1152C2×C4C22×#4111yescharacteristic
1153C2×C4C2×H(5,𝔽2)11yescharacteristic
1154C2×C4#58511yescharacteristic
1155C2×C4#58511yescharacteristic
1156C2×C4#58511yescharacteristic
1157C8—41no—
1158C8—41no—
1159C8—41no—
1160C8—41no—
1161C8—41no—
1162C8—41no—
1163C8—41no—
1164C8—41no—
1165C22—22no—
1166C22—22no—
1167C22—22no—
1168C22—41no—
1169C22—41no—
1170C22—41no—
1171C22—41no—
1172C22—42no—
1173C22—42no—
1174C22—42no—
1175C22—81no—
1176C22—81no—
1177C22—81no—
1178C22—81no—
1179C22C2×#52511yescharacteristic
1180C22#348811yescharacteristic
1181C22#350011yescharacteristic
1182C22C2×#57811yescharacteristic
1183C22#358511yescharacteristic
1184C22#358611yescharacteristic
1185C22#358611yescharacteristic
1186C4—22no—
1187C4—22no—
1188C4—41no—
1189C4—41no—
1190C4—41no—
1191C4—41no—
1192C4—41no—
1193C4—42no—
1194C4—42no—
1195C4—41no—
1196C4—41no—
1197C4—41no—
1198C4—41no—
1199C4—42no—
1200C4—42no—
1201C4—41no—
1202C4—41no—
1203C4—81no—
1204C4—81no—
1205C4—81no—
1206C4—81no—
1207C4—81no—
1208C4—81no—
1209C4—81no—
1210C4—81no—
1211C4—81no—
1212C4—81no—
1213C4—81no—
1214C4#351311yescharacteristic
1215C4#351311yescharacteristic
1216C4#352111yescharacteristic
1217C4#352111yescharacteristic
1218C2—42no—
1219C2—82no—
1220C2#3597911yescharacteristic
1221C2#6057511yescharacteristic
1222C2#6059411yescharacteristic
1223C2#6202011yescharacteristic
1224C2#6208511yescharacteristic
1225C2#6256511yescharacteristic
1226C2#6261911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
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. #39067C2semidirect
3. #30151C2semidirect
4. #30054C2semidirect
5. #29918C2semidirect
6. #29502C2semidirect
7. #29402C2semidirect
8. #29359C2semidirect
9. #28159C2semidirect
10. #27569C2semidirect
11. #27565C2semidirect
12. #27453C2semidirect
13. #27440C2semidirect
14. #27216C2semidirect
15. #27213C2semidirect
16. #26432C2semidirect
18. #26186C2semidirect
19. #26171C2semidirect
22. #25082C2semidirect
24. #23823C2semidirect
25. #23695C2semidirect
26. #23633C2semidirect
28. #23136C2semidirect
29. #22881C2semidirect
31. #22594C2semidirect

Maximal subgroups

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

subgroupindex
#390672
#344292
#301512
#300542
#299182
#295022
#294022
#293592
#281592
#275692
#275652
#274532
#274402
#272162
#272132
#264322
#264232
#261862
#261712
#255142
#250992
#250822
#239462
#238232
#236952
#236332
#231382
#231362
#228812
#228552
#225942