Finite Group Databasebeta

← #6768652

Subgroups — #6768652

Order 512.

1549 conjugacy classes of subgroups.

The subgroup lattice has 1296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36291C211yesmaximal, characteristic, complemented
2#34788C211yesmaximal, characteristic, complemented
3#33150C211yesmaximal, characteristic, complemented
4#32537C211yesmaximal, characteristic, complemented
5#32491C211yesmaximal, characteristic, complemented
6#32223C211yesmaximal, characteristic, complemented
7#32129C211yesmaximal, characteristic, complemented
8#31883C211yesmaximal, characteristic, complemented
9#31819C211yesmaximal, characteristic, complemented
10#31629C211yesmaximal, characteristic, complemented
11#30691C211yesmaximal, characteristic, complemented
12#30153C211yesmaximal, characteristic, complemented
13#30006C211yesmaximal, characteristic, complemented
14#29532C211yesmaximal, characteristic, complemented
15#29445C211yesmaximal, characteristic, complemented
16#29161C211yesmaximal, characteristic, complemented
17#28117C211yesmaximal, characteristic, complemented
18#28104C211yesmaximal, characteristic, complemented
19#27865C211yesmaximal, characteristic, complemented
20#27666C211yesmaximal, characteristic, complemented
21#27633C211yesmaximal, characteristic, complemented
22#26002C211yesmaximal, characteristic, complemented
23#25960C211yesmaximal, characteristic, complemented
24#25252C211yesmaximal, characteristic, complemented
25#25124C211yesmaximal, characteristic
26#24583C211yesmaximal, characteristic, complemented
27#24531C211yesmaximal, characteristic, complemented
28#22698C211yesmaximal, characteristic, complemented
29#22190C211yesmaximal, characteristic, complemented
30#22120C211yesmaximal, characteristic, complemented
31C2×#1925C211yesmaximal, characteristic, complemented
32C2×#481C2211yescharacteristic
33C2×#478C2211yescharacteristic
34C2×#469C2211yescharacteristic
35C2×#447C2211yescharacteristic
36C2×#435C2211yescharacteristic
37C2×#435C2211yescharacteristic
38C22×#107C2211yescharacteristic
39C22×#102C2211yescharacteristic
40C22×#102C2211yescharacteristic
41#2860C2211yescharacteristic
42#2854C2211yescharacteristic
43#2851C2211yescharacteristic
44#2595—21no—
45#2525—21no—
46#2516—21no—
47#2516—21no—
48#2513C2211yescharacteristic
49#2513C2211yescharacteristic, complemented
50#2510—21no—
51#2509C2211yescharacteristic, complemented
52#2504C2211yescharacteristic
53#2494C2211yescharacteristic, complemented
54#2490C2211yescharacteristic
55#2490C2211yescharacteristic, complemented
56#2487C2211yescharacteristic
57#2487C2211yescharacteristic
58#2480—21no—
59#2471—21no—
60#2467—21no—
61#2454C2211yescharacteristic
62#2444—21no—
63#2442C2211yescharacteristic
64#2420C2211yescharacteristic
65#2418—21no—
66#2416C2211yescharacteristic
67#2408C2211yescharacteristic
68#2401—21no—
69#2395—21no—
70#2358—21no—
71#2345C2211yescharacteristic
72#2342—21no—
73D4×C22⋊C4C2211yescharacteristic
74C4×#125C2211yescharacteristic, complemented
75C4×#121—21no—
76C4×#121C2211yescharacteristic
77C4×#121C2211yescharacteristic
78C4×#121C2211yescharacteristic, complemented
79#2293C2211yescharacteristic
80#2293C2211yescharacteristic, complemented
81C2×#390C2211yescharacteristic
82#2290—21no—
83#2283C2211yescharacteristic, complemented
84C42×D4C2211yescharacteristic
85C2×C4×C4⋊C4C2211yescharacteristic
86#2101C2211yescharacteristic, complemented
87#2101C2211yescharacteristic, complemented
88#2092C2211yescharacteristic
89#2092C2211yescharacteristic, complemented
90#2088C2211yescharacteristic, complemented
91#2088C2211yescharacteristic, complemented
92#2086C2211yescharacteristic, complemented
93#2086C2211yescharacteristic, complemented
94#2086C2211yescharacteristic, complemented
95#2085C2211yescharacteristic, complemented
96#2085C2211yescharacteristic, complemented
97#2077C2211yescharacteristic, complemented
98#2075C2211yescharacteristic, complemented
99#2075C2211yescharacteristic, complemented
100#2073C2211yescharacteristic
101#2073C2211yescharacteristic
102#2067C2211yescharacteristic
103#2067C2211yescharacteristic
104#2067C2211yescharacteristic
105#2067C2211yescharacteristic, complemented
106#2067C2211yescharacteristic, complemented
107#2067C2211yescharacteristic, complemented
108#2065C2211yescharacteristic
109#2065C2211yescharacteristic
110#2065C2211yescharacteristic
111#2065C2211yescharacteristic
112#2059C2211yescharacteristic, complemented
113#2059C2211yescharacteristic, complemented
114#2054C2211yescharacteristic
115#2054C2211yescharacteristic
116#2054C2211yescharacteristic
117#2054C2211yescharacteristic
118#2054C2211yescharacteristic
119#2034C2211yescharacteristic
120#2033C2211yescharacteristic
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic, complemented
123#2025C2211yescharacteristic
124#2025C2211yescharacteristic, complemented
125#1999C2211yescharacteristic
126#1989C2211yescharacteristic, complemented
127#1989C2211yescharacteristic, complemented
128#1989C2211yescharacteristic, complemented
129#1972C2211yescharacteristic
130#1949C2211yescharacteristic, complemented
131#1949C2211yescharacteristic, complemented
132#1949C2211yescharacteristic, complemented
133#1949C2211yescharacteristic, complemented
134#1949C2211yescharacteristic, complemented
135#1944C2211yescharacteristic, complemented
136#1944C2211yescharacteristic, complemented
137#1943C2211yescharacteristic, complemented
138#1940C2211yescharacteristic, complemented
139#1940C2211yescharacteristic, complemented
140#1936C2211yescharacteristic
141#1936C2211yescharacteristic
142#1936C2211yescharacteristic
143#1936C2211yescharacteristic, complemented
144#1926C2211yescharacteristic
145#1926C2211yescharacteristic
146#1925C2211yescharacteristic
147#1925C2211yescharacteristic
148#1925C2211yescharacteristic
149#1925C2211yescharacteristic
150#1925C2211yescharacteristic
151#1925C2211yescharacteristic
152#1925C2211yescharacteristic
153#1925C2211yescharacteristic
154#1925C2211yescharacteristic, complemented
155#1925C2211yescharacteristic, complemented
156#1921C2211yescharacteristic, complemented
157#1920C2211yescharacteristic, complemented
158#1920C2211yescharacteristic, complemented
159#1920C2211yescharacteristic, complemented
160#1919C2211yescharacteristic, complemented
161#1918C2211yescharacteristic, complemented
162#1918C2211yescharacteristic, complemented
163#1918C2211yescharacteristic, complemented
164#1895C2211yescharacteristic
165#1895C2211yescharacteristic
166#1895C2211yescharacteristic
167#1895C2211yescharacteristic, complemented
168#1893C2211yescharacteristic
169#1893C2211yescharacteristic
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic
173#1879C2211yescharacteristic
174#1864C2211yescharacteristic
175#1864C2211yescharacteristic, complemented
176#1862C2211yescharacteristic
177#1862C2211yescharacteristic, complemented
178#1853C2211yescharacteristic
179#1852C2211yescharacteristic
180#1851C2211yescharacteristic, complemented
181#1851C2211yescharacteristic, complemented
182#1850C2211yescharacteristic
183#1850C2211yescharacteristic
184#1831C2211yescharacteristic, complemented
185#1824C2211yescharacteristic
186#1824C2211yescharacteristic
187#1824C2211yescharacteristic
188#1809C2211yescharacteristic, complemented
189#1809C2211yescharacteristic, complemented
190#1809C2211yescharacteristic, complemented
191#1808C2211yescharacteristic
192#1807C2211yescharacteristic
193#1804C2211yescharacteristic
194#1804C2211yescharacteristic
195#1804C2211yescharacteristic
196#1797C2211yescharacteristic
197#1797C2211yescharacteristic, complemented
198#1786C2211yescharacteristic
199#1767C2211yescharacteristic, complemented
200C2×#340C2211yescharacteristic
201#1728C2211yescharacteristic, complemented
202C2×#336C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×D8C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C23×C8C2311yescharacteristic
210C2×#126—21no—
211C2×#125C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×#123—21no—
214C2×#121—21no—
215C2×#121C2311yescharacteristic
216C2×#121C2311yescharacteristic
217C2×#121C2311yescharacteristic
218C2×#121C2311yescharacteristic
219C2×#120—21no—
220C2×C4×D4—21no—
221C2×C4×D4—21no—
222C2×C4×D4—21no—
223C2×C4×D4D411yescharacteristic
224C2×C4×D4D411yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×#117—21no—
230C2×#117—21no—
231C22×C4⋊C4C2311yescharacteristic
232C22×C4⋊C4C2311yescharacteristic
233C22×C4⋊C4C2311yescharacteristic
234C22×C22⋊C4—21no—
235C22×C22⋊C4—21no—
236C22×C22⋊C4—21no—
237C22×C42—21no—
238C22×C42C2311yescharacteristic
239C22×C42C2311yescharacteristic
240#481—42no—
241#478—24no—
242#469—24no—
243#447—42no—
244#435—42no—
245#435—42no—
246C2×#107—42no—
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×#102—24no—
270C2×#102—42no—
271C2×#102C2311yescharacteristic
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×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×C22⋊C8C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295C2×#97C2311yescharacteristic
296C2×#97C2311yescharacteristic
297#401—21no—
298#400—21no—
299#400—21no—
300#400—21no—
301#400—21no—
302#400—21no—
303#399—21no—
304#399—21no—
305#399—21no—
306#398—21no—
307#397—21no—
308#397—21no—
309#397—21no—
310#397—21no—
311#397—21no—
312#397—21no—
313#397—21no—
314#397—21no—
315#397—21no—
316#397—21no—
317#396—21no—
318#396—21no—
319#394—21no—
320#394—21no—
321#394—21no—
322#394—21no—
323#394—21no—
324#392—21no—
325#390—21no—
326#390—21no—
327#390—21no—
328#390—21no—
329#390C2311yescharacteristic
330#390C2311yescharacteristic
331#390C2311yescharacteristic
332#390C2311yescharacteristic
333#390C2311yescharacteristic
334#390C2311yescharacteristic
335#390C2311yescharacteristic
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#389—21no—
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
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#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—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#386—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#385—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#383—21no—
400#382C2311yescharacteristic
401#382C2311yescharacteristic
402#382C2311yescharacteristic
403#382C2311yescharacteristic
404#381—21no—
405#381—21no—
406#380—21no—
407#380—21no—
408#380—21no—
409#380C2311yescharacteristic
410#380C2311yescharacteristic
411#380C2311yescharacteristic
412#380C2311yescharacteristic
413#380C2311yescharacteristic
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#379—21no—
418#379—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4—21no—
422C4×C4⋊C4—21no—
423C4×C4⋊C4D411yescharacteristic
424C4×C4⋊C4D411yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C22⋊C4—21no—
434C4×C22⋊C4—21no—
435C4×C22⋊C4—21no—
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439C4×C22⋊C4—21no—
440C4×C22⋊C4D411yescharacteristic
441C4×C22⋊C4D411yescharacteristic
442C4×C22⋊C4D411yescharacteristic
443C4×C22⋊C4D411yescharacteristic
444C4×C22⋊C4C2311yescharacteristic
445C4×C22⋊C4C2311yescharacteristic
446#376—21no—
447C2×#95—21no—
448C43C2311yescharacteristic
449#340C2311yescharacteristic
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#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C25—21no—
488C22×D4—22no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—22no—
495C22×D4—22no—
496C22×D4—41no—
497C22×D4—41no—
498C22×D4—41no—
499C22×D4C2×D411yescharacteristic
500C22×D4C2411yescharacteristic
501C22×D4C2411yescharacteristic
502C22×D4C2411yescharacteristic
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4C2×D411yescharacteristic
510C23×C4C2×D411yescharacteristic
511C23×C4C2×D411yescharacteristic
512C23×C4C2×D411yescharacteristic
513C23×C4C2411yescharacteristic
514C23×C4C2411yescharacteristic
515C2×D8—22no—
516C2×D8—41no—
517C2×D8—41no—
518C2×D8—41no—
519C2×D8—41no—
520C2×D8—41no—
521C2×M16—22no—
522C2×M16—41no—
523C2×M16—41no—
524C2×M16—41no—
525C2×M16—41no—
526C2×M16—41no—
527C22×C8—22no—
528C22×C8—22no—
529C22×C8—22no—
530C22×C8—41no—
531C22×C8—41no—
532C22×C8—41no—
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541#126—82no—
542#125—22no—
543#125—41no—
544#125—41no—
545#125—41no—
546#123—82no—
547#121—22no—
548#121—22no—
549#121—22no—
550#121—22no—
551#121—41no—
552#121—41no—
553#121—44no—
554#121—41no—
555#121—41no—
556#120—44no—
557C4×D4—22no—
558C4×D4—22no—
559C4×D4—22no—
560C4×D4—41no—
561C4×D4—41no—
562C4×D4—41no—
563C4×D4—41no—
564C4×D4—41no—
565C4×D4—42no—
566C4×D4—42no—
567C4×D4—44no—
568C4×D4—82no—
569C4×D4—82no—
570#117—82no—
571#117—82no—
572C2×C4⋊C4—22no—
573C2×C4⋊C4—22no—
574C2×C4⋊C4—22no—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—22no—
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—21no—
596C2×C4⋊C4—41no—
597C2×C4⋊C4C2×D411yescharacteristic
598C2×C4⋊C4C2×D411yescharacteristic
599C2×C4⋊C4C2×D411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
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⋊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—44no—
653C2×C22⋊C4—82no—
654C2×C22⋊C4—82no—
655C2×C22⋊C4C2×D411yescharacteristic
656C2×C22⋊C4C2×D411yescharacteristic
657C2×C22⋊C4C2×D411yescharacteristic
658C2×C22⋊C4C2×D411yescharacteristic
659C2×C22⋊C4C2×D411yescharacteristic
660C2×C22⋊C4C2×D411yescharacteristic
661C2×C42—21no—
662C2×C42—21no—
663C2×C42—21no—
664C2×C42—21no—
665C2×C42—21no—
666C2×C42—21no—
667C2×C42—21no—
668C2×C42—41no—
669C2×C42—41no—
670C2×C42—41no—
671C2×C42—41no—
672C2×C42—82no—
673C2×C42C2×D411yescharacteristic
674C2×C42C2×D411yescharacteristic
675C2×C42C2×D411yescharacteristic
676C2×C42C2×D411yescharacteristic
677C2×C42C2×D411yescharacteristic
678C2×C42C2×D411yescharacteristic
679C2×C42C2×D411yescharacteristic
680C2×C42C2×D411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686#107—22no—
687#107—41no—
688#107—41no—
689#107—41no—
690#107—41no—
691#107—41no—
692#107—41no—
693#107—41no—
694#106—22no—
695#106—22no—
696#106—41no—
697#106—41no—
698#106—41no—
699#106—41no—
700C4⋊C8—22no—
701C4⋊C8—41no—
702C4⋊C8—41no—
703C4⋊C8—41no—
704C4⋊C8—41no—
705C4⋊C8—41no—
706C4⋊C8—41no—
707C4⋊C8—41no—
708#102—22no—
709#102—22no—
710#102—22no—
711#102—22no—
712#102—22no—
713#102—41no—
714#102—41no—
715#102—41no—
716#102—41no—
717#102—41no—
718#102—41no—
719#102—41no—
720#102—41no—
721#102—41no—
722#102—41no—
723#102—41no—
724#102—41no—
725#102—41no—
726#102—41no—
727#102#4114yes—
728C22⋊C8—22no—
729C22⋊C8—22no—
730C22⋊C8—41no—
731C22⋊C8—41no—
732#97—41no—
733#97—41no—
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#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775C24—21no—
776C24—21no—
777C24—21no—
778C24—42no—
779C24—42no—
780C24—42no—
781C24—42no—
782C24—81no—
783C24—81no—
784C24—81no—
785C24C22×D411yescharacteristic
786C24C22×D411yescharacteristic
787C2×D4—22no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—44no—
808C2×D4—44no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—42no—
812C2×D4—42no—
813C2×D4—42no—
814C2×D4—42no—
815C2×D4—42no—
816C2×D4—42no—
817C2×D4—42no—
818C2×D4—42no—
819C2×D4—82no—
820C2×D4—82no—
821C2×D4—81no—
822C2×D4—81no—
823C2×D4—81no—
824C2×D4—81no—
825C2×D4—81no—
826C2×D4C2×#4112yes—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—22no—
832C22×C4—21no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—22no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—41no—
855C22×C4—41no—
856C22×C4—41no—
857C22×C4—41no—
858C22×C4—41no—
859C22×C4—41no—
860C22×C4—41no—
861C22×C4—41no—
862C22×C4—42no—
863C22×C4—42no—
864C22×C4—42no—
865C22×C4—42no—
866C22×C4—42no—
867C22×C4—42no—
868C22×C4—42no—
869C22×C4—42no—
870C22×C4—42no—
871C22×C4—42no—
872C22×C4—81no—
873C22×C4—81no—
874C22×C4—81no—
875C22×C4—81no—
876C22×C4—81no—
877C22×C4—81no—
878C22×C4—81no—
879C22×C4—81no—
880C22×C4C22×D411yescharacteristic
881C22×C4C22×D411yescharacteristic
882C22×C4C22×D411yescharacteristic
883C22×C4C22×D411yescharacteristic
884C22×C4C22×D411yescharacteristic
885C22×C4C22×D411yescharacteristic
886C22×C4C22×D411yescharacteristic
887C22×C4C22×D411yescharacteristic
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4H(5,𝔽2)12yes—
893C22×C42−1+412yes—
894C22×C4C2511yescharacteristic
895D8—82no—
896D8—82no—
897M16—82no—
898M16—82no—
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—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—44no—
923C2×C8—82no—
924C2×C8C2×#4112yes—
925C4⋊C4—22no—
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—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—41no—
952C4⋊C4—41no—
953C4⋊C4—42no—
954C4⋊C4—42no—
955C4⋊C4—42no—
956C4⋊C4—42no—
957C4⋊C4—42no—
958C4⋊C4—42no—
959C4⋊C4—42no—
960C4⋊C4—42no—
961C4⋊C4—42no—
962C4⋊C4—81no—
963C4⋊C4—81no—
964C4⋊C4—81no—
965C4⋊C4—81no—
966C4⋊C4—81no—
967C4⋊C4—81no—
968C4⋊C4—81no—
969C4⋊C4—81no—
970C4⋊C4—81no—
971C4⋊C4—81no—
972C4⋊C4C2×#4112yes—
973C22⋊C4—22no—
974C22⋊C4—22no—
975C22⋊C4—22no—
976C22⋊C4—22no—
977C22⋊C4—41no—
978C22⋊C4—41no—
979C22⋊C4—42no—
980C22⋊C4—42no—
981C22⋊C4—42no—
982C22⋊C4—42no—
983C22⋊C4—42no—
984C22⋊C4—42no—
985C22⋊C4—42no—
986C22⋊C4—42no—
987C22⋊C4—42no—
988C22⋊C4—42no—
989C22⋊C4—42no—
990C22⋊C4—42no—
991C22⋊C4—42no—
992C22⋊C4—42no—
993C22⋊C4—42no—
994C22⋊C4—42no—
995C22⋊C4—42no—
996C22⋊C4—42no—
997C22⋊C4—42no—
998C22⋊C4—81no—
999C22⋊C4—81no—
1000C22⋊C4—81no—
1001C22⋊C4—81no—
1002C22⋊C4—81no—
1003C22⋊C4—81no—
1004C22⋊C4—81no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C22⋊C4—81no—
1008C22⋊C4—81no—
1009C22⋊C4—81no—
1010C22⋊C4—81no—
1011C22⋊C4—81no—
1012C22⋊C4—81no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C42—22no—
1019C42—21no—
1020C42—21no—
1021C42—21no—
1022C42—21no—
1023C42—21no—
1024C42—21no—
1025C42—21no—
1026C42—21no—
1027C42—21no—
1028C42—21no—
1029C42—41no—
1030C42—41no—
1031C42—41no—
1032C42—41no—
1033C42—41no—
1034C42—41no—
1035C42—41no—
1036C42—42no—
1037C42—42no—
1038C42—42no—
1039C42—81no—
1040C42—81no—
1041C42—81no—
1042C42—81no—
1043C23—21no—
1044C23—21no—
1045C23—21no—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23—22no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—84no—
1076C23—84no—
1077C23—84no—
1078C23—84no—
1079C23—162no—
1080C23—162no—
1081C23—162no—
1082C23#53712yes—
1083C23#57512yes—
1084C23#57512yes—
1085C23C23×D411yescharacteristic
1086D4—22no—
1087D4—22no—
1088D4—44no—
1089D4—41no—
1090D4—41no—
1091D4—41no—
1092D4—41no—
1093D4—41no—
1094D4—41no—
1095D4—41no—
1096D4—41no—
1097D4—41no—
1098D4—41no—
1099D4—84no—
1100D4—84no—
1101D4—84no—
1102D4—84no—
1103D4—162no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—22no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
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—44no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
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—82no—
1187C2×C4—84no—
1188C2×C4—82no—
1189C2×C4—82no—
1190C2×C4—84no—
1191C2×C4—84no—
1192C2×C4—84no—
1193C2×C4—162no—
1194C2×C4—162no—
1195C2×C4#53712yes—
1196C2×C4#57612yes—
1197C2×C4C22×#4111yescharacteristic
1198C2×C4C2×H(5,𝔽2)11yescharacteristic
1199C2×C4C2×2−1+411yescharacteristic
1200C2×C4#58511yescharacteristic
1201C2×C4#58511yescharacteristic
1202C2×C4#58511yescharacteristic
1203C8—22no—
1204C8—41no—
1205C8—41no—
1206C8—41no—
1207C8—41no—
1208C8—41no—
1209C8—41no—
1210C8—41no—
1211C22—22no—
1212C22—22no—
1213C22—22no—
1214C22—22no—
1215C22—22no—
1216C22—22no—
1217C22—42no—
1218C22—41no—
1219C22—41no—
1220C22—42no—
1221C22—41no—
1222C22—41no—
1223C22—41no—
1224C22—42no—
1225C22—41no—
1226C22—41no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—168no—
1246C22#325614yes—
1247C22C2×#53711yescharacteristic
1248C22D4×#4111yescharacteristic
1249C22#348511yescharacteristic
1250C22C2×#57511yescharacteristic
1251C22C2×#57511yescharacteristic
1252C22C2×#57611yescharacteristic
1253C22#358511yescharacteristic
1254C4—22no—
1255C4—22no—
1256C4—41no—
1257C4—42no—
1258C4—41no—
1259C4—41no—
1260C4—41no—
1261C4—41no—
1262C4—41no—
1263C4—41no—
1264C4—41no—
1265C4—41no—
1266C4—41no—
1267C4—81no—
1268C4—81no—
1269C4—81no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C4—81no—
1274C4—81no—
1275C4—81no—
1276C4—81no—
1277C4—81no—
1278C4—81no—
1279C4#349511yescharacteristic
1280C4#351311yescharacteristic
1281C4#354511yescharacteristic
1282C4#356411yescharacteristic
1283C2—24no—
1284C2—81no—
1285C2—82no—
1286C2—161no—
1287C2—161no—
1288C2#3836011yescharacteristic
1289C2C2×#325611yescharacteristic
1290C2#6092211yescharacteristic
1291C2#6144411yescharacteristic
1292C2#6145611yescharacteristic
1293C2#6171411yescharacteristic
1294C2#6172711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#25124C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36291C2semidirect
2. #34788C2semidirect
3. #33150C2semidirect
4. #32537C2semidirect
5. #32491C2semidirect
6. #32223C2semidirect
7. #32129C2semidirect
8. #31883C2semidirect
9. #31819C2semidirect
10. #31629C2semidirect
11. #30691C2semidirect
12. #30153C2semidirect
13. #30006C2semidirect
14. #29532C2semidirect
15. #29445C2semidirect
16. #29161C2semidirect
17. #28117C2semidirect
18. #28104C2semidirect
19. #27865C2semidirect
20. #27666C2semidirect
21. #27633C2semidirect
22. #26002C2semidirect
23. #25960C2semidirect
24. #25252C2semidirect
26. #24583C2semidirect
27. #24531C2semidirect
28. #22698C2semidirect
29. #22190C2semidirect
30. #22120C2semidirect
31. C2×#1925C2semidirect
49. #2513C22semidirect
51. #2509C22semidirect
53. #2494C22semidirect
55. #2490C22semidirect
74. C4×#125C22semidirect
78. C4×#121C22semidirect
80. #2293C22semidirect
83. #2283C22semidirect
86. #2101C22semidirect
87. #2101C22semidirect
89. #2092C22semidirect
90. #2088C22semidirect
91. #2088C22semidirect
92. #2086C22semidirect
93. #2086C22semidirect
94. #2086C22semidirect
95. #2085C22semidirect
96. #2085C22semidirect
97. #2077C22semidirect
98. #2075C22semidirect
99. #2075C22semidirect
105. #2067C22semidirect
106. #2067C22semidirect
107. #2067C22semidirect
112. #2059C22semidirect
113. #2059C22semidirect
122. #2033C22semidirect
124. #2025C22semidirect
126. #1989C22semidirect
127. #1989C22semidirect
128. #1989C22semidirect
130. #1949C22semidirect
131. #1949C22semidirect
132. #1949C22semidirect
133. #1949C22semidirect
134. #1949C22semidirect
135. #1944C22semidirect
136. #1944C22semidirect
137. #1943C22semidirect
138. #1940C22semidirect
139. #1940C22semidirect
143. #1936C22semidirect
154. #1925C22semidirect
155. #1925C22semidirect
156. #1921C22semidirect
157. #1920C22semidirect
158. #1920C22semidirect
159. #1920C22semidirect
160. #1919C22semidirect
161. #1918C22semidirect
162. #1918C22semidirect
163. #1918C22semidirect
167. #1895C22semidirect
175. #1864C22semidirect
177. #1862C22semidirect
180. #1851C22semidirect
181. #1851C22semidirect
184. #1831C22semidirect
188. #1809C22semidirect
189. #1809C22semidirect
190. #1809C22semidirect
197. #1797C22semidirect
199. #1767C22semidirect
201. #1728C22semidirect

Maximal subgroups

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

subgroupindex
#362912
#347882
#331502
#325372
#324912
#322232
#321292
#318832
#318192
#316292
#306912
#301532
#300062
#295322
#294452
#291612
#281172
#281042
#278652
#276662
#276332
#260022
#259602
#252522
#251242
#245832
#245312
#226982
#221902
#221202
C2×#19252