Finite Group Databasebeta

← #7086837

Subgroups — #7086837

Order 512.

1415 conjugacy classes of subgroups.

The subgroup lattice has 1258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59580C211yesmaximal, characteristic, complemented
2#39248C211yesmaximal, characteristic, complemented
3#32235C211yesmaximal, characteristic, complemented
4#32177C211yesmaximal, characteristic, complemented
5#32163C211yesmaximal, characteristic, complemented
6#32111C211yesmaximal, characteristic, complemented
7#31816C211yesmaximal, characteristic, complemented
8#31080C211yesmaximal, characteristic, complemented
9#30526C211yesmaximal, characteristic, complemented
10#30526C211yesmaximal, characteristic, complemented
11#29556C211yesmaximal, characteristic, complemented
12#29351C211yesmaximal, characteristic, complemented
13#29043C211yesmaximal, characteristic, complemented
14#28976C211yesmaximal, characteristic, complemented
15#28011C211yesmaximal, characteristic, complemented
16#27770C211yesmaximal, characteristic, complemented
17#27524C211yesmaximal, characteristic, complemented
18#27333C211yesmaximal, characteristic, complemented
19#27260C211yesmaximal, characteristic, complemented
20#27008C211yesmaximal, characteristic, complemented
21#26900C211yesmaximal, characteristic, complemented
22#26819C211yesmaximal, characteristic, complemented
23#26700C211yesmaximal, characteristic, complemented
24#26616C211yesmaximal, characteristic
25#25281C211yesmaximal, characteristic, complemented
26#24481C211yesmaximal, characteristic, complemented
27#23680C211yesmaximal, characteristic, complemented
28#23278C211yesmaximal, characteristic, complemented
29#23219C211yesmaximal, characteristic, complemented
30#22875C211yesmaximal, characteristic, complemented
31#22222C211yesmaximal, characteristic, complemented
32C2×#488C2211yescharacteristic
33C2×#488C2211yescharacteristic
34C2×#488C2211yescharacteristic
35C2×#480C2211yescharacteristic
36C2×#478C2211yescharacteristic
37C2×#448C2211yescharacteristic
38C2×C4×SD16C2211yescharacteristic
39C2×C4×D8C2211yescharacteristic
40C22×#103C2211yescharacteristic
41#2861C2211yescharacteristic
42#2808—21no—
43#2793—21no—
44#2778—21no—
45#2756—21no—
46#2751—21no—
47#2740—21no—
48#2653—21no—
49#2601—21no—
50#2596—21no—
51#2577—21no—
52#2572—21no—
53#2559—21no—
54#2552C2211yescharacteristic
55#2548C2211yescharacteristic
56#2544C2211yescharacteristic
57#2514C2211yescharacteristic
58#2513C2211yescharacteristic
59#2512C2211yescharacteristic
60#2497C2211yescharacteristic
61#2490C2211yescharacteristic
62#2490C2211yescharacteristic
63#2490C2211yescharacteristic
64#2478—21no—
65#2466—21no—
66#2454C2211yescharacteristic
67#2453C2211yescharacteristic
68#2447C2211yescharacteristic
69#2442C2211yescharacteristic
70#2436C2211yescharacteristic
71#2436C2211yescharacteristic
72#2428C2211yescharacteristic
73#2420C2211yescharacteristic
74#2370C2211yescharacteristic
75#2370C2211yescharacteristic
76#2367C2211yescharacteristic
77#2361C2211yescharacteristic
78#2354—21no—
79#2344C2211yescharacteristic
80Q8×C22⋊C4C2211yescharacteristic
81#2333—21no—
82C4×#125C2211yescharacteristic
83C4×#126C2211yescharacteristic
84C4×#124C2211yescharacteristic
85#2293C2211yescharacteristic
86#2100C2211yescharacteristic
87#2086C2211yescharacteristic
88#2085C2211yescharacteristic
89#2076C2211yescharacteristic
90#2076C2211yescharacteristic
91#2074C2211yescharacteristic
92#2073C2211yescharacteristic
93#2073C2211yescharacteristic
94#2072C2211yescharacteristic
95#2068C2211yescharacteristic
96#2068C2211yescharacteristic
97#2068C2211yescharacteristic
98#2067C2211yescharacteristic
99#2065C2211yescharacteristic
100#2059C2211yescharacteristic
101#2059C2211yescharacteristic
102#2055C2211yescharacteristic
103#2055C2211yescharacteristic
104#2054C2211yescharacteristic
105#2054C2211yescharacteristic
106#2042C2211yescharacteristic
107#2042C2211yescharacteristic
108#2042C2211yescharacteristic
109#2042C2211yescharacteristic
110#2041C2211yescharacteristic
111#2034C2211yescharacteristic
112#2034C2211yescharacteristic
113#2026C2211yescharacteristic
114#2026C2211yescharacteristic
115#2026C2211yescharacteristic
116#2025C2211yescharacteristic
117#2025C2211yescharacteristic
118#2025C2211yescharacteristic
119#2012C2211yescharacteristic
120#2012C2211yescharacteristic
121#2012C2211yescharacteristic
122#2012C2211yescharacteristic
123#2011C2211yescharacteristic
124#1999C2211yescharacteristic
125#1999C2211yescharacteristic
126#1991C2211yescharacteristic
127#1989C2211yescharacteristic
128#1989C2211yescharacteristic
129#1989C2211yescharacteristic
130#1983C2211yescharacteristic
131#1983C2211yescharacteristic
132#1983C2211yescharacteristic
133#1983C2211yescharacteristic
134#1982C2211yescharacteristic
135#1970C2211yescharacteristic
136#1968C2211yescharacteristic
137#1968C2211yescharacteristic
138#1968C2211yescharacteristic
139#1958C2211yescharacteristic
140#1957C2211yescharacteristic
141#1941C2211yescharacteristic
142#1939C2211yescharacteristic
143#1934C2211yescharacteristic
144#1934C2211yescharacteristic
145#1934C2211yescharacteristic
146#1934C2211yescharacteristic
147#1934C2211yescharacteristic
148#1933C2211yescharacteristic
149#1933C2211yescharacteristic
150#1933C2211yescharacteristic
151#1933C2211yescharacteristic
152#1928C2211yescharacteristic
153#1928C2211yescharacteristic
154#1928C2211yescharacteristic
155#1927C2211yescharacteristic
156#1927C2211yescharacteristic
157#1927C2211yescharacteristic
158#1926C2211yescharacteristic
159#1926C2211yescharacteristic
160#1925C2211yescharacteristic
161#1925C2211yescharacteristic
162#1925C2211yescharacteristic
163#1923C2211yescharacteristic
164#1923C2211yescharacteristic
165#1923C2211yescharacteristic
166#1921C2211yescharacteristic
167#1919C2211yescharacteristic
168#1918C2211yescharacteristic
169#1916C2211yescharacteristic
170#1916C2211yescharacteristic
171#1916C2211yescharacteristic
172#1893C2211yescharacteristic
173#1893C2211yescharacteristic
174#1893C2211yescharacteristic
175#1880C2211yescharacteristic
176#1879C2211yescharacteristic
177#1879C2211yescharacteristic
178#1877C2211yescharacteristic
179#1874C2211yescharacteristic
180#1865C2211yescharacteristic
181#1864C2211yescharacteristic
182#1864C2211yescharacteristic
183#1863C2211yescharacteristic
184#1863C2211yescharacteristic
185#1862C2211yescharacteristic
186#1853C2211yescharacteristic
187#1850C2211yescharacteristic
188#1846C2211yescharacteristic
189#1803C2211yescharacteristic
190#1787C2211yescharacteristic
191#1787C2211yescharacteristic
192C4×#106C2211yescharacteristic
193C8×C4⋊C4C2211yescharacteristic
194C8×C4⋊C4C2211yescharacteristic
195C4×C4⋊C8C2211yescharacteristic
196C4×#103C2211yescharacteristic
197C4×#103C2211yescharacteristic
198C4×#102C2211yescharacteristic
199C4×#102C2211yescharacteristic
200C8×C22⋊C4C2211yescharacteristic
201C8×C22⋊C4C2211yescharacteristic
202#1744C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C2×#127C2311yescharacteristic
210C2×#126—21no—
211C2×#126D411yescharacteristic
212C2×#125C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×#125C2311yescharacteristic
216C2×#124C2311yescharacteristic
217C2×#124C2311yescharacteristic
218C2×#124C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×#121—21no—
221C2×#121C2311yescharacteristic
222C2×#121C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×D4—21no—
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×#117—21no—
231C2×#117—21no—
232C22×C4⋊C4C2311yescharacteristic
233#488—24no—
234#488—24no—
235#488—42no—
236#480—42no—
237#478—42no—
238#448—24no—
239C4×SD16—42no—
240C4×D8—42no—
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×#103—42no—
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
288C2×C22⋊C8C2311yescharacteristic
289C2×C22⋊C8C2311yescharacteristic
290C2×C4×C8C2311yescharacteristic
291C2×C4×C8C2311yescharacteristic
292C2×C4×C8C2311yescharacteristic
293C2×C4×C8C2311yescharacteristic
294C2×C4×C8C2311yescharacteristic
295C2×C4×C8C2311yescharacteristic
296C2×C4×C8C2311yescharacteristic
297#401—21no—
298#400—21no—
299#400—21no—
300#400—21no—
301#400—21no—
302#399—21no—
303#398—21no—
304#398—21no—
305#398—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#396—21no—
317#396—21no—
318#396—21no—
319#394—21no—
320#394—21no—
321#394—21no—
322#394—21no—
323#394—21no—
324#394—21no—
325#394—21no—
326#394—21no—
327#394—21no—
328#393—21no—
329#393—21no—
330#393—21no—
331#393—21no—
332#392—21no—
333#391—21no—
334#391—21no—
335#391C2311yescharacteristic
336#391C2311yescharacteristic
337#391C2311yescharacteristic
338#391C2311yescharacteristic
339#391C2311yescharacteristic
340#391C2311yescharacteristic
341#390—21no—
342#390—21no—
343#390—21no—
344#390—21no—
345#390—21no—
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#389—21no—
356#389—21no—
357#389—21no—
358#389—21no—
359#389C2311yescharacteristic
360#389C2311yescharacteristic
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#388D411yescharacteristic
387#388D411yescharacteristic
388#388D411yescharacteristic
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387D411yescharacteristic
401#387D411yescharacteristic
402#387D411yescharacteristic
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#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#384—21no—
418#384C2311yescharacteristic
419#383—21no—
420#383D411yescharacteristic
421#382C2311yescharacteristic
422#382C2311yescharacteristic
423#381—21no—
424#381—21no—
425#381—21no—
426#380—21no—
427#380—21no—
428#380—21no—
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432C4×C4⋊C4—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4—21no—
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
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×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4C2311yescharacteristic
452C4×C22⋊C4C2311yescharacteristic
453C4×C22⋊C4C2311yescharacteristic
454C43C2311yescharacteristic
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#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C22×Q8—21no—
488C22×Q8—22no—
489C22×Q8—41no—
490C22×Q8—41no—
491C22×Q8—41no—
492C22×Q8—41no—
493C22×Q8—41no—
494C22×Q8C2411yescharacteristic
495C22×Q8C2411yescharacteristic
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4C2411yescharacteristic
502C22×D4C2411yescharacteristic
503C22×D4C2411yescharacteristic
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4C2411yescharacteristic
510C2×SD16—22no—
511C2×SD16—22no—
512C2×SD16—41no—
513C2×SD16—41no—
514C2×SD16—41no—
515C2×SD16—41no—
516C2×D8—41no—
517C2×D8—41no—
518C2×D8—41no—
519C2×D8—41no—
520C2×D8—41no—
521C2×D8—41no—
522C22×C8—41no—
523C22×C8—41no—
524C22×C8—41no—
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533#127—41no—
534#127—41no—
535#126—24no—
536#126—82no—
537#125—22no—
538#125—22no—
539#125—22no—
540#125—41no—
541#125—41no—
542#125—41no—
543#125—41no—
544#125—41no—
545#124—22no—
546#124—22no—
547#124—41no—
548#124—41no—
549#124—41no—
550#124—41no—
551#124—41no—
552#124—41no—
553#121—22no—
554#121—41no—
555#121—44no—
556#121—41no—
557#121—41no—
558#121—41no—
559#121—41no—
560C4×Q8—41no—
561C4×Q8—41no—
562C4×Q8—41no—
563C4×Q8—41no—
564C4×D4—22no—
565C4×D4—41no—
566C4×D4—41no—
567C4×D4—41no—
568C4×D4—41no—
569C4×D4—41no—
570C4×D4—44no—
571#117—82no—
572#117—82no—
573C2×C4⋊C4—22no—
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—21no—
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×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⋊C4C2×D411yescharacteristic
650C2×C22⋊C4C2×D411yescharacteristic
651C2×C22⋊C4C2×D411yescharacteristic
652C2×C22⋊C4C2×D411yescharacteristic
653C2×C22⋊C4C2×D411yescharacteristic
654C2×C22⋊C4C2×D411yescharacteristic
655C2×C42—21no—
656C2×C42—21no—
657C2×C42—21no—
658C2×C42—21no—
659C2×C42—21no—
660C2×C42—21no—
661C2×C42—21no—
662C2×C42—21no—
663C2×C42—21no—
664C2×C42C2×D411yescharacteristic
665C2×C42C2×D411yescharacteristic
666C2×C42C2×D411yescharacteristic
667C2×C42C2×D411yescharacteristic
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2411yescharacteristic
673C2×C42C2411yescharacteristic
674#107—22no—
675#107—41no—
676#107—41no—
677#107—41no—
678#106—22no—
679#106—41no—
680#106—41no—
681#106—41no—
682C4⋊C8—41no—
683C4⋊C8—41no—
684C4⋊C8—41no—
685C4⋊C8—41no—
686C4⋊C8—41no—
687#103—22no—
688#103—22no—
689#103—22no—
690#103—22no—
691#103—22no—
692#103—41no—
693#103—41no—
694#103—41no—
695#103—41no—
696#103—41no—
697#103—41no—
698#103—41no—
699#103—41no—
700#103#4114yes—
701#102—22no—
702#102—22no—
703#102—22no—
704#102—22no—
705#102—22no—
706#102—22no—
707#102—41no—
708#102—41no—
709#102—41no—
710#102—41no—
711#102—41no—
712#102—41no—
713#102—41no—
714#102—41no—
715#102—41no—
716#102—41no—
717#102—41no—
718#102—41no—
719C22⋊C8—22no—
720C22⋊C8—41no—
721C22⋊C8—41no—
722C4×C8—22no—
723C4×C8—22no—
724C4×C8—41no—
725C4×C8—41no—
726C4×C8—41no—
727C4×C8—41no—
728C4×C8—41no—
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#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776C24—21no—
777C24—21no—
778C24—21no—
779C24C22×D411yescharacteristic
780C2×Q8—21no—
781C2×Q8—21no—
782C2×Q8—21no—
783C2×Q8—21no—
784C2×Q8—21no—
785C2×Q8—21no—
786C2×Q8—21no—
787C2×Q8—21no—
788C2×Q8—21no—
789C2×Q8—21no—
790C2×Q8—21no—
791C2×Q8—42no—
792C2×Q8—44no—
793C2×Q8—81no—
794C2×Q8—81no—
795C2×Q8—82no—
796C2×Q8—82no—
797C2×Q8—82no—
798C2×Q8C2×#4112yes—
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—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—42no—
818C2×D4—42no—
819C2×D4—42no—
820C2×D4—42no—
821C2×D4—42no—
822C2×D4—81no—
823C2×D4—81no—
824C2×D4—81no—
825C2×D4—81no—
826C2×D4—81no—
827C2×D4—81no—
828C2×D4—81no—
829C2×D4—81no—
830C2×D4—81no—
831C2×D4—81no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
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—21no—
850C22×C4—21no—
851C22×C4—42no—
852C22×C4—42no—
853C22×C4—42no—
854C22×C4—42no—
855C22×C4—42no—
856C22×C4—42no—
857C22×C4—81no—
858C22×C4—81no—
859C22×C4—81no—
860C22×C4—81no—
861C22×C4—81no—
862C22×C4—81no—
863C22×C4—81no—
864C22×C4—81no—
865C22×C4—81no—
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×C4C22×D411yescharacteristic
877C22×C4C22×D411yescharacteristic
878C22×C4C22×D411yescharacteristic
879C22×C4C2511yescharacteristic
880SD16—44no—
881SD16—82no—
882D8—44no—
883D8—82no—
884C2×C8—21no—
885C2×C8—21no—
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—82no—
908C2×C8C2×#4112yes—
909C4⋊C4—22no—
910C4⋊C4—22no—
911C4⋊C4—22no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—21no—
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—41no—
933C4⋊C4—41no—
934C4⋊C4—41no—
935C4⋊C4—42no—
936C4⋊C4—42no—
937C4⋊C4—42no—
938C4⋊C4—42no—
939C4⋊C4—42no—
940C4⋊C4—42no—
941C4⋊C4—42no—
942C4⋊C4—42no—
943C4⋊C4—42no—
944C4⋊C4—42no—
945C4⋊C4—81no—
946C4⋊C4—81no—
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⋊C4C2×#4112yes—
958C4⋊C4H(5,𝔽2)12yes—
959C22⋊C4—22no—
960C22⋊C4—22no—
961C22⋊C4—41no—
962C22⋊C4—41no—
963C22⋊C4—41no—
964C22⋊C4—42no—
965C22⋊C4—42no—
966C22⋊C4—42no—
967C22⋊C4—42no—
968C22⋊C4—42no—
969C22⋊C4—42no—
970C22⋊C4—42no—
971C22⋊C4—42no—
972C22⋊C4—42no—
973C22⋊C4—81no—
974C22⋊C4—81no—
975C22⋊C4—81no—
976C22⋊C4—81no—
977C22⋊C4—81no—
978C22⋊C4—81no—
979C22⋊C4—81no—
980C22⋊C4—81no—
981C22⋊C4—81no—
982C22⋊C4—81no—
983C22⋊C4—81no—
984C22⋊C4—81no—
985C22⋊C4—81no—
986C22⋊C4—81no—
987C22⋊C4—81no—
988C22⋊C4—81no—
989C22⋊C4—81no—
990C22⋊C4—81no—
991C22⋊C4—81no—
992C22⋊C4—81no—
993C22⋊C4—81no—
994C22⋊C4—81no—
995C22⋊C4—81no—
996C22⋊C4—81no—
997C22⋊C4—81no—
998C22⋊C4—81no—
999C22⋊C4#13514yes—
1000C42—22no—
1001C42—21no—
1002C42—21no—
1003C42—21no—
1004C42—21no—
1005C42—21no—
1006C42—21no—
1007C42—21no—
1008C42—21no—
1009C42—21no—
1010C42—21no—
1011C42—21no—
1012C42—21no—
1013C42—41no—
1014C42—41no—
1015C42—41no—
1016C42—42no—
1017C42—42no—
1018C42—81no—
1019C42—81no—
1020C42—81no—
1021C42—81no—
1022C42—81no—
1023C42—81no—
1024C42—81no—
1025C23—21no—
1026C23—21no—
1027C23—21no—
1028C23—21no—
1029C23—21no—
1030C23—21no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23C2×#13512yes—
1053C23C23×D411yescharacteristic
1054Q8—22no—
1055Q8—22no—
1056Q8—41no—
1057Q8—41no—
1058Q8—41no—
1059Q8—41no—
1060Q8—41no—
1061Q8—41no—
1062Q8—84no—
1063D4—41no—
1064D4—41no—
1065D4—41no—
1066D4—41no—
1067D4—41no—
1068D4—41no—
1069D4—41no—
1070D4—41no—
1071D4—41no—
1072D4—41no—
1073D4—41no—
1074D4—41no—
1075D4—84no—
1076D4—162no—
1077D4—162no—
1078D4—162no—
1079D4—162no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
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—21no—
1104C2×C4—22no—
1105C2×C4—21no—
1106C2×C4—22no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—22no—
1111C2×C4—21no—
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—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—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—84no—
1161C2×C4—84no—
1162C2×C4—84no—
1163C2×C4—162no—
1164C2×C4—162no—
1165C2×C4C2×#13512yes—
1166C2×C4C2×#13512yes—
1167C2×C4C22×#4111yescharacteristic
1168C2×C4C2×H(5,𝔽2)11yescharacteristic
1169C2×C4#58511yescharacteristic
1170C2×C4#58511yescharacteristic
1171C2×C4#58511yescharacteristic
1172C2×C4#58511yescharacteristic
1173C8—22no—
1174C8—41no—
1175C8—41no—
1176C8—41no—
1177C8—41no—
1178C8—41no—
1179C8—41no—
1180C8—41no—
1181C22—22no—
1182C22—22no—
1183C22—22no—
1184C22—41no—
1185C22—41no—
1186C22—41no—
1187C22—41no—
1188C22—81no—
1189C22—81no—
1190C22—81no—
1191C22—81no—
1192C22—81no—
1193C22—81no—
1194C22—81no—
1195C22—81no—
1196C22—81no—
1197C22—81no—
1198C22—81no—
1199C22—81no—
1200C22—81no—
1201C22—81no—
1202C22—81no—
1203C22—81no—
1204C22—81no—
1205C22—81no—
1206C22—81no—
1207C22—81no—
1208C22—81no—
1209C22D4×#4111yescharacteristic
1210C22#348811yescharacteristic
1211C22#350011yescharacteristic
1212C22C22×#13511yescharacteristic
1213C22#358411yescharacteristic
1214C22#358411yescharacteristic
1215C22#358511yescharacteristic
1216C4—22no—
1217C4—22no—
1218C4—41no—
1219C4—42no—
1220C4—41no—
1221C4—41no—
1222C4—41no—
1223C4—41no—
1224C4—41no—
1225C4—41no—
1226C4—41no—
1227C4—41no—
1228C4—42no—
1229C4—41no—
1230C4—41no—
1231C4—42no—
1232C4—81no—
1233C4—81no—
1234C4—81no—
1235C4—81no—
1236C4—81no—
1237C4—81no—
1238C4—81no—
1239C4—81no—
1240C4—81no—
1241C4—81no—
1242C4#350611yescharacteristic
1243C4#352111yescharacteristic
1244C4#354011yescharacteristic
1245C4#356811yescharacteristic
1246C2—42no—
1247C2—161no—
1248C2—161no—
1249C2—161no—
1250C2#4418211yescharacteristic
1251C2#6142811yescharacteristic
1252C2#6153411yescharacteristic
1253C2#6195511yescharacteristic
1254C2#6206111yescharacteristic
1255C2#6253311yescharacteristic
1256C2#6261311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#26616C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#126 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59580C2semidirect
2. #39248C2semidirect
3. #32235C2semidirect
4. #32177C2semidirect
5. #32163C2semidirect
6. #32111C2semidirect
7. #31816C2semidirect
8. #31080C2semidirect
9. #30526C2semidirect
10. #30526C2semidirect
11. #29556C2semidirect
12. #29351C2semidirect
13. #29043C2semidirect
14. #28976C2semidirect
15. #28011C2semidirect
16. #27770C2semidirect
17. #27524C2semidirect
18. #27333C2semidirect
19. #27260C2semidirect
20. #27008C2semidirect
21. #26900C2semidirect
22. #26819C2semidirect
23. #26700C2semidirect
25. #25281C2semidirect
26. #24481C2semidirect
27. #23680C2semidirect
28. #23278C2semidirect
29. #23219C2semidirect
30. #22875C2semidirect
31. #22222C2semidirect

Maximal subgroups

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

subgroupindex
#595802
#392482
#322352
#321772
#321632
#321112
#318162
#310802
#305262
#295562
#293512
#290432
#289762
#280112
#277702
#275242
#273332
#272602
#270082
#269002
#268192
#267002
#266162
#252812
#244812
#236802
#232782
#232192
#228752
#222222