Finite Group Databasebeta

← #6534834

Subgroups — #6534834

Order 512.

1433 conjugacy classes of subgroups.

The subgroup lattice has 1185 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38275C211yesmaximal, characteristic, complemented
2#34429C211yesmaximal, characteristic
3#30089C211yesmaximal, characteristic, complemented
4#30083C211yesmaximal, characteristic, complemented
5#29702C211yesmaximal, characteristic
6#29402C211yesmaximal, characteristic, complemented
7#29395C211yesmaximal, characteristic, complemented
8#29325C211yesmaximal, characteristic, complemented
9#29312C211yesmaximal, characteristic, complemented
10#27958C211yesmaximal, characteristic, complemented
11#27656C211yesmaximal, characteristic, complemented
12#27058C211yesmaximal, characteristic, complemented
13#27038C211yesmaximal, characteristic
14#27035C211yesmaximal, characteristic, complemented
15#27030C211yesmaximal, characteristic
16#26571C211yesmaximal, characteristic
17#26560C211yesmaximal, characteristic, complemented
18#26559C211yesmaximal, characteristic, complemented
19#26557C211yesmaximal, characteristic
20#26104C211yesmaximal, characteristic, complemented
21#26086C211yesmaximal, characteristic, complemented
22#24690C211yesmaximal, characteristic, complemented
23#24687C211yesmaximal, characteristic, complemented
24#23695C211yesmaximal, characteristic, complemented
25#23681C211yesmaximal, characteristic, complemented
26#23585C211yesmaximal, characteristic
27#22980C211yesmaximal, characteristic, complemented
28#22966C211yesmaximal, characteristic, complemented
29C4⋊C4×Q16C211yesmaximal, characteristic, complemented
30#22678C211yesmaximal, characteristic, complemented
31#22644C211yesmaximal, characteristic, complemented
32C2×#542C2211yescharacteristic
33C2×#484C2211yescharacteristic
34C2×#485C2211yescharacteristic
35C2×#479C2211yescharacteristic
36C2×#478C2211yescharacteristic
37C2×#440C2211yescharacteristic
38C2×#440C2211yescharacteristic
39C2×C4×Q16C2211yescharacteristic
40C2×C4×Q16C2211yescharacteristic
41C2×C4×Q16C2211yescharacteristic
42C2×C4×SD16C2211yescharacteristic
43#2859C2211yescharacteristic
44#2791—21no—
45#2777—21no—
46#2721—21no—
47#2719—21no—
48#2647C2211yescharacteristic
49#2629C2211yescharacteristic
50#2606—21no—
51#2565C2211yescharacteristic
52#2552C2211yescharacteristic
53#2529—21no—
54#2524—21no—
55#2519—21no—
56#2496C2211yescharacteristic
57#2495C2211yescharacteristic
58#2423C2211yescharacteristic
59#2423C2211yescharacteristic
60#2383—21no—
61#2376—21no—
62#2373—21no—
63#2370C2211yescharacteristic
64#2363C2211yescharacteristic
65#2362C2211yescharacteristic
66#2361C2211yescharacteristic
67#2360C2211yescharacteristic
68#2359—21no—
69#2356C2211yescharacteristic
70#2354C2211yescharacteristic
71Q8×C4⋊C4C2211yescharacteristic
72Q8×C4⋊C4C2211yescharacteristic
73#2349C2211yescharacteristic
74#2337—21no—
75#2331C2211yescharacteristic
76#2329—21no—
77#2326—21no—
78#2326C2211yescharacteristic
79#2323—21no—
80#2323C2211yescharacteristic
81#2320C2211yescharacteristic
82#2317C2211yescharacteristic
83C4×C4⋊Q8C2211yescharacteristic
84C4×#124C2211yescharacteristic
85#2298C2211yescharacteristic
86#2295C2211yescharacteristic
87#2096C2211yescharacteristic
88#2095C2211yescharacteristic
89#2093C2211yescharacteristic
90#2093C2211yescharacteristic
91#2085C2211yescharacteristic
92#2085C2211yescharacteristic
93#2085C2211yescharacteristic
94#2083C2211yescharacteristic
95#2083C2211yescharacteristic
96#2083C2211yescharacteristic
97#2074C2211yescharacteristic
98#2074C2211yescharacteristic
99#2073C2211yescharacteristic
100#2072C2211yescharacteristic
101#2072C2211yescharacteristic
102#2071C2211yescharacteristic
103#2068C2211yescharacteristic
104#2067C2211yescharacteristic
105#2067C2211yescharacteristic
106#2066C2211yescharacteristic
107#2058C2211yescharacteristic
108#2057C2211yescharacteristic
109#2057C2211yescharacteristic
110#2056C2211yescharacteristic
111#2056C2211yescharacteristic
112#2055C2211yescharacteristic
113#2055C2211yescharacteristic
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic
116#2042C2211yescharacteristic
117#2036C2211yescharacteristic
118#2036C2211yescharacteristic
119#2035C2211yescharacteristic
120#2034C2211yescharacteristic
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic
123#2024C2211yescharacteristic
124#2015C2211yescharacteristic
125#2001C2211yescharacteristic
126#2000C2211yescharacteristic
127#1992C2211yescharacteristic
128#1991C2211yescharacteristic
129#1949C2211yescharacteristic
130#1949C2211yescharacteristic
131#1949C2211yescharacteristic
132#1948C2211yescharacteristic
133#1947C2211yescharacteristic
134#1947C2211yescharacteristic
135#1947C2211yescharacteristic
136#1947C2211yescharacteristic
137#1947C2211yescharacteristic
138#1947C2211yescharacteristic
139#1944C2211yescharacteristic
140#1943C2211yescharacteristic
141#1942C2211yescharacteristic
142#1942C2211yescharacteristic
143#1942C2211yescharacteristic
144#1942C2211yescharacteristic
145#1942C2211yescharacteristic
146#1941C2211yescharacteristic
147#1940C2211yescharacteristic
148#1939C2211yescharacteristic
149#1928C2211yescharacteristic
150#1928C2211yescharacteristic
151#1927C2211yescharacteristic
152#1927C2211yescharacteristic
153#1924C2211yescharacteristic
154#1923C2211yescharacteristic
155#1923C2211yescharacteristic
156#1923C2211yescharacteristic
157#1921C2211yescharacteristic
158#1920C2211yescharacteristic
159#1920C2211yescharacteristic
160#1920C2211yescharacteristic
161#1918C2211yescharacteristic
162#1918C2211yescharacteristic
163#1918C2211yescharacteristic
164#1918C2211yescharacteristic
165#1865C2211yescharacteristic
166#1864C2211yescharacteristic
167#1864C2211yescharacteristic
168#1863C2211yescharacteristic
169#1863C2211yescharacteristic
170#1863C2211yescharacteristic
171#1863C2211yescharacteristic
172#1863C2211yescharacteristic
173#1863C2211yescharacteristic
174#1863C2211yescharacteristic
175#1862C2211yescharacteristic
176#1862C2211yescharacteristic
177#1854C2211yescharacteristic
178#1854C2211yescharacteristic
179#1852C2211yescharacteristic
180#1852C2211yescharacteristic
181#1847C2211yescharacteristic
182#1845C2211yescharacteristic
183#1840C2211yescharacteristic
184#1839C2211yescharacteristic
185#1825C2211yescharacteristic
186#1823C2211yescharacteristic
187#1805C2211yescharacteristic
188#1803C2211yescharacteristic
189#1803C2211yescharacteristic
190#1802C2211yescharacteristic
191#1798C2211yescharacteristic
192#1771C2211yescharacteristic
193C8×C4⋊C4C2211yescharacteristic
194#1768C2211yescharacteristic
195C4×C4⋊C8C2211yescharacteristic
196#1763C2211yescharacteristic
197#1763C2211yescharacteristic
198C4×#103C2211yescharacteristic
199C4×#102C2211yescharacteristic
200C4×#102C2211yescharacteristic
201C4×#102C2211yescharacteristic
202#1750C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205#542—24no—
206#542—24no—
207C2×C4⋊Q8C2311yescharacteristic
208C2×#126—21no—
209C2×#126—21no—
210C2×#125—21no—
211C2×#125—21no—
212C2×#125C2311yescharacteristic
213C2×#124—21no—
214C2×#124C2311yescharacteristic
215C2×#123—21no—
216C2×C22⋊Q8—21no—
217C2×C22⋊Q8C2311yescharacteristic
218C2×C22⋊Q8C2311yescharacteristic
219C2×#121C2311yescharacteristic
220C2×C4×Q8—21no—
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×D4—21no—
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×#117—21no—
232C2×#117C2311yescharacteristic
233C2×#117C2311yescharacteristic
234C22×C4⋊C4C2311yescharacteristic
235#485—42no—
236#484—42no—
237#479—24no—
238#478—24no—
239#440—24no—
240#440—42no—
241C4×Q16—24no—
242C4×Q16—42no—
243C4×Q16—42no—
244C4×SD16—42no—
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
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×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×C22⋊C8C2311yescharacteristic
290C2×C22⋊C8C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×#97C2311yescharacteristic
294C2×#97C2311yescharacteristic
295C2×C4×C8C2311yescharacteristic
296C2×C4×C8C2311yescharacteristic
297C2×C4×C8C2311yescharacteristic
298C2×C4×C8C2311yescharacteristic
299#400—21no—
300#400—21no—
301#400—21no—
302#400—21no—
303#399—21no—
304#399—21no—
305#398—21no—
306#398—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#397—21no—
316#397—21no—
317#396—21no—
318#396—21no—
319#391—21no—
320#391—21no—
321#391—21no—
322#391C2311yescharacteristic
323#391C2311yescharacteristic
324#391C2311yescharacteristic
325#391C2311yescharacteristic
326#391C2311yescharacteristic
327#390—21no—
328#390C2311yescharacteristic
329#390C2311yescharacteristic
330#389—21no—
331#389—21no—
332#389—21no—
333#389—21no—
334#389—21no—
335#389—21no—
336#389—21no—
337#389—21no—
338#389—21no—
339#389—21no—
340#389—21no—
341#389—21no—
342#389—21no—
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
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#388—21no—
369#388—21no—
370#388—21no—
371#388D411yescharacteristic
372#388D411yescharacteristic
373#388D411yescharacteristic
374#388D411yescharacteristic
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#387D411yescharacteristic
394#387D411yescharacteristic
395#387D411yescharacteristic
396#387D411yescharacteristic
397#386—21no—
398#386—21no—
399#385—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#384—21no—
408#384—21no—
409#384C2311yescharacteristic
410#384C2311yescharacteristic
411#384C2311yescharacteristic
412#384C2311yescharacteristic
413#384C2311yescharacteristic
414#384C2311yescharacteristic
415#383—21no—
416#383—21no—
417#383—21no—
418#382—21no—
419#382—21no—
420#382C2311yescharacteristic
421#382C2311yescharacteristic
422#382C2311yescharacteristic
423#380—21no—
424#380—21no—
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428C4×C4⋊C4—21no—
429C4×C4⋊C4—21no—
430C4×C4⋊C4—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4—21no—
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×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C4×C22⋊C4C2311yescharacteristic
448C4×C22⋊C4C2311yescharacteristic
449#376—21no—
450#376—21no—
451#376C2311yescharacteristic
452C2×#95—21no—
453C43C2311yescharacteristic
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#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×Q8C2411yescharacteristic
492C22×Q8C2411yescharacteristic
493C22×D4—21no—
494C22×D4C2411yescharacteristic
495C23×C4—21no—
496C23×C4—21no—
497C23×C4—21no—
498C23×C4—21no—
499C23×C4C2411yescharacteristic
500C2×Q16—22no—
501C2×Q16—22no—
502C2×Q16—22no—
503C2×SD16—22no—
504C2×SD16—22no—
505C2×SD16—22no—
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C4⋊Q8—22no—
515C4⋊Q8—22no—
516#126—28no—
517#126—82no—
518#125—22no—
519#125—22no—
520#125—82no—
521#125—82no—
522#124—28no—
523#124—22no—
524#124—22no—
525#123—28no—
526C22⋊Q8—28no—
527C22⋊Q8—22no—
528C22⋊Q8—22no—
529C22⋊Q8—22no—
530C22⋊Q8—41no—
531#121—22no—
532#121—22no—
533C4×Q8—22no—
534C4×Q8—22no—
535C4×Q8—22no—
536C4×Q8—22no—
537C4×Q8—22no—
538C4×Q8—41no—
539C4×Q8—41no—
540C4×Q8—41no—
541C4×Q8—41no—
542C4×Q8—41no—
543C4×Q8—41no—
544C4×Q8—82no—
545C4×Q8#4114yes—
546C4×D4—22no—
547C4×D4—41no—
548C4×D4—41no—
549C4×D4—41no—
550C4×D4—41no—
551C4×D4—82no—
552C4×D4#4114yes—
553#117—22no—
554#117—22no—
555#117—41no—
556#117—41no—
557#117—82no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—41no—
596C2×C4⋊C4—41no—
597C2×C4⋊C4C2×D411yescharacteristic
598C2×C4⋊C4C2×D411yescharacteristic
599C2×C4⋊C4C2×D411yescharacteristic
600C2×C4⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2×D411yescharacteristic
602C2×C4⋊C4C2×D411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
633C2×C22⋊C4C2×D411yescharacteristic
634C2×C22⋊C4C2×D411yescharacteristic
635C2×C22⋊C4C2×D411yescharacteristic
636C2×C22⋊C4C2×D411yescharacteristic
637C2×C22⋊C4C2×D411yescharacteristic
638C2×C42—21no—
639C2×C42—21no—
640C2×C42—21no—
641C2×C42—21no—
642C2×C42—21no—
643C2×C42—21no—
644C2×C42—21no—
645C2×C42—21no—
646C2×C42—21no—
647C2×C42—21no—
648C2×C42—21no—
649C2×C42—21no—
650C2×C42—21no—
651C2×C42—21no—
652C2×C42C2×D411yescharacteristic
653C2×C42C2×D411yescharacteristic
654C2×C42C2×D411yescharacteristic
655C2×C42C2×D411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
662#107—22no—
663#107—22no—
664#107—22no—
665#107—22no—
666#107—41no—
667#107—41no—
668#107—41no—
669#107—41no—
670#107—41no—
671#107—41no—
672#107—41no—
673#107—41no—
674#107—41no—
675#106—22no—
676#106—22no—
677#106—41no—
678#106—41no—
679#106—41no—
680C4⋊C8—22no—
681C4⋊C8—22no—
682C4⋊C8—22no—
683C4⋊C8—22no—
684C4⋊C8—22no—
685C4⋊C8—22no—
686#103—22no—
687#103—22no—
688#103—22no—
689#103—22no—
690#103—22no—
691#103—22no—
692#103—22no—
693#103—22no—
694#103—22no—
695#103—22no—
696#103—41no—
697#103—41no—
698#103—41no—
699#102—22no—
700#102—22no—
701#102—22no—
702#102—22no—
703#102—41no—
704#102—41no—
705#102—41no—
706C22⋊C8—22no—
707C22⋊C8—22no—
708C22⋊C8—41no—
709C22⋊C8—41no—
710#97—22no—
711#97—41no—
712C4×C8—22no—
713C4×C8—41no—
714C4×C8—41no—
715C4×C8—41no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758#95C2×D411yescharacteristic
759#95C2×D411yescharacteristic
760#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767C24—21no—
768C24C22×D411yescharacteristic
769C2×Q8—24no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—21no—
777C2×Q8—21no—
778C2×Q8—21no—
779C2×Q8—21no—
780C2×Q8—81no—
781C2×Q8—81no—
782C2×Q8C2×#4112yes—
783C2×Q8H(5,𝔽2)12yes—
784C2×D4—24no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—81no—
791C2×D4—81no—
792C2×D4C2×#4112yes—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—24no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—42no—
816C22×C4—81no—
817C22×C4—81no—
818C22×C4—81no—
819C22×C4—81no—
820C22×C4—81no—
821C22×C4—81no—
822C22×C4—81no—
823C22×C4—81no—
824C22×C4—81no—
825C22×C4—81no—
826C22×C4C22×D411yescharacteristic
827C22×C4C22×D411yescharacteristic
828C22×C4C22×D411yescharacteristic
829C22×C4C22×D411yescharacteristic
830C22×C4C22×D411yescharacteristic
831C22×C4C22×D411yescharacteristic
832C22×C4C22×D411yescharacteristic
833C22×C4C22×D411yescharacteristic
834C22×C4C22×D411yescharacteristic
835C22×C4C22×D411yescharacteristic
836C22×C4C22×D411yescharacteristic
837C22×C4C22×D411yescharacteristic
838C22×C4C22×D411yescharacteristic
839C22×C4C2511yescharacteristic
840Q16—28no—
841SD16—28no—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C82−1+412yes—
865C2×C82−1+412yes—
866C4⋊C4—24no—
867C4⋊C4—24no—
868C4⋊C4—24no—
869C4⋊C4—22no—
870C4⋊C4—22no—
871C4⋊C4—22no—
872C4⋊C4—22no—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—21no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—21no—
887C4⋊C4—21no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—21no—
896C4⋊C4—21no—
897C4⋊C4—41no—
898C4⋊C4—41no—
899C4⋊C4—42no—
900C4⋊C4—42no—
901C4⋊C4—42no—
902C4⋊C4—42no—
903C4⋊C4—42no—
904C4⋊C4—42no—
905C4⋊C4—42no—
906C4⋊C4—42no—
907C4⋊C4—42no—
908C4⋊C4—42no—
909C4⋊C4—81no—
910C4⋊C4—81no—
911C4⋊C4—81no—
912C4⋊C4—81no—
913C4⋊C4—81no—
914C4⋊C4—81no—
915C4⋊C4—81no—
916C4⋊C4—81no—
917C4⋊C4—81no—
918C4⋊C4—81no—
919C4⋊C4—81no—
920C4⋊C4—81no—
921C4⋊C4—81no—
922C4⋊C4—81no—
923C4⋊C4—81no—
924C4⋊C4—81no—
925C4⋊C4—81no—
926C4⋊C4—81no—
927C4⋊C4—81no—
928C4⋊C4—81no—
929C4⋊C4—81no—
930C4⋊C4—81no—
931C4⋊C4—81no—
932C4⋊C4—81no—
933C4⋊C4C2×#4112yes—
934C4⋊C4C2×#4112yes—
935C22⋊C4—24no—
936C22⋊C4—24no—
937C22⋊C4—24no—
938C22⋊C4—24no—
939C22⋊C4—24no—
940C22⋊C4—22no—
941C22⋊C4—22no—
942C22⋊C4—22no—
943C22⋊C4—22no—
944C22⋊C4—41no—
945C22⋊C4—41no—
946C22⋊C4—42no—
947C22⋊C4—42no—
948C22⋊C4—81no—
949C22⋊C4—81no—
950C22⋊C4—81no—
951C22⋊C4—81no—
952C22⋊C4—81no—
953C22⋊C4—81no—
954C22⋊C4—81no—
955C22⋊C4—81no—
956C22⋊C4—81no—
957C42—24no—
958C42—22no—
959C42—22no—
960C42—21no—
961C42—21no—
962C42—21no—
963C42—21no—
964C42—21no—
965C42—21no—
966C42—21no—
967C42—21no—
968C42—21no—
969C42—21no—
970C42—41no—
971C42—41no—
972C42—42no—
973C42—42no—
974C42—42no—
975C42—42no—
976C42—42no—
977C42—42no—
978C42—81no—
979C42—81no—
980C42—81no—
981C42—81no—
982C42—81no—
983C42—81no—
984C42—81no—
985C42C2×#4112yes—
986C42C2×#4112yes—
987C23—21no—
988C23—21no—
989C23—21no—
990C23—22no—
991C23—21no—
992C23—21no—
993C23—21no—
994C23—21no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23C23×D411yescharacteristic
1002Q8—22no—
1003Q8—22no—
1004Q8—22no—
1005Q8—22no—
1006Q8—41no—
1007Q8—41no—
1008Q8—41no—
1009Q8—41no—
1010Q8—84no—
1011D4—22no—
1012D4—22no—
1013D4—41no—
1014D4—41no—
1015D4—84no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—22no—
1035C2×C4—21no—
1036C2×C4—22no—
1037C2×C4—21no—
1038C2×C4—22no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—22no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—84no—
1101C2×C4—162no—
1102C2×C4—162no—
1103C2×C4—162no—
1104C2×C4#52512yes—
1105C2×C4#52512yes—
1106C2×C4#57612yes—
1107C2×C4#57812yes—
1108C2×C4C22×#4111yescharacteristic
1109C2×C4C22×#4111yescharacteristic
1110C2×C4C2×H(5,𝔽2)11yescharacteristic
1111C2×C4C2×2−1+411yescharacteristic
1112C2×C4C2×2−1+411yescharacteristic
1113C2×C4#58511yescharacteristic
1114C8—22no—
1115C8—22no—
1116C8—41no—
1117C8—41no—
1118C8—41no—
1119C8—41no—
1120C8—41no—
1121C8—41no—
1122C22—41no—
1123C22—41no—
1124C22—41no—
1125C22—41no—
1126C22—42no—
1127C22—41no—
1128C22—41no—
1129C22—42no—
1130C22—42no—
1131C22—41no—
1132C22—81no—
1133C22—81no—
1134C22—81no—
1135C22—81no—
1136C22C2×#52511yescharacteristic
1137C22#348811yescharacteristic
1138C22#349911yescharacteristic
1139C22C2×#57611yescharacteristic
1140C22C2×#57811yescharacteristic
1141C22#358411yescharacteristic
1142C22#358611yescharacteristic
1143C4—22no—
1144C4—22no—
1145C4—22no—
1146C4—22no—
1147C4—41no—
1148C4—41no—
1149C4—41no—
1150C4—41no—
1151C4—41no—
1152C4—42no—
1153C4—42no—
1154C4—41no—
1155C4—41no—
1156C4—41no—
1157C4—41no—
1158C4—42no—
1159C4—42no—
1160C4—81no—
1161C4—81no—
1162C4—81no—
1163C4—81no—
1164C4—81no—
1165C4—81no—
1166C4—81no—
1167C4—81no—
1168C4—81no—
1169C4—81no—
1170C4—81no—
1171C4#349211yescharacteristic
1172C4#349211yescharacteristic
1173C4#350711yescharacteristic
1174C4#350711yescharacteristic
1175C2—81no—
1176C2—82no—
1177C2#3568611yescharacteristic
1178C2#6057311yescharacteristic
1179C2#6059611yescharacteristic
1180C2#6202011yescharacteristic
1181C2#6207411yescharacteristic
1182C2#6248711yescharacteristic
1183C2#6252311yescharacteristic
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. #38275C2semidirect
3. #30089C2semidirect
4. #30083C2semidirect
6. #29402C2semidirect
7. #29395C2semidirect
8. #29325C2semidirect
9. #29312C2semidirect
10. #27958C2semidirect
11. #27656C2semidirect
12. #27058C2semidirect
14. #27035C2semidirect
17. #26560C2semidirect
18. #26559C2semidirect
20. #26104C2semidirect
21. #26086C2semidirect
22. #24690C2semidirect
23. #24687C2semidirect
24. #23695C2semidirect
25. #23681C2semidirect
27. #22980C2semidirect
28. #22966C2semidirect
29. C4⋊C4×Q16C2semidirect
30. #22678C2semidirect
31. #22644C2semidirect

Maximal subgroups

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

subgroupindex
#382752
#344292
#300892
#300832
#297022
#294022
#293952
#293252
#293122
#279582
#276562
#270582
#270382
#270352
#270302
#265712
#265602
#265592
#265572
#261042
#260862
#246902
#246872
#236952
#236812
#235852
#229802
#229662
C4⋊C4×Q162
#226782
#226442