Finite Group Databasebeta

← #6803882

Subgroups — #6803882

Order 512.

1587 conjugacy classes of subgroups.

The subgroup lattice has 1286 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36596C211yesmaximal, characteristic
2#36571C211yesmaximal, characteristic, complemented
3#33042C211yesmaximal, characteristic, complemented
4#32427C211yesmaximal, characteristic, complemented
5#32314C211yesmaximal, characteristic, complemented
6#32231C211yesmaximal, characteristic, complemented
7#32078C211yesmaximal, characteristic, complemented
8#31637C211yesmaximal, characteristic, complemented
9#31460C211yesmaximal, characteristic, complemented
10#30876C211yesmaximal, characteristic, complemented
11#30815C211yesmaximal, characteristic, complemented
12#30189C211yesmaximal, characteristic, complemented
13#30189C211yesmaximal, characteristic, complemented
14#29161C211yesmaximal, characteristic, complemented
15#29157C211yesmaximal, characteristic, complemented
16#28574C211yesmaximal, characteristic, complemented
17#28574C211yesmaximal, characteristic, complemented
18#27559C211yesmaximal, characteristic, complemented
19#27429C211yesmaximal, characteristic, complemented
20#27365C211yesmaximal, characteristic, complemented
21#27139C211yesmaximal, characteristic, complemented
22#26896C211yesmaximal, characteristic, complemented
23#26755C211yesmaximal, characteristic, complemented
24#26701C211yesmaximal, characteristic, complemented
25#26159C211yesmaximal, characteristic, complemented
26#24839C211yesmaximal, characteristic, complemented
27#24753C211yesmaximal, characteristic, complemented
28#22185C211yesmaximal, characteristic, complemented
29#22185C211yesmaximal, characteristic, complemented
30C4×#465C211yesmaximal, characteristic, complemented
31C2×#1916C211yesmaximal, characteristic, complemented
32C2×#553—21no—
33C2×#486C2211yescharacteristic
34C2×#478C2211yescharacteristic
35C2×#465C2211yescharacteristic
36C2×#465C2211yescharacteristic
37C2×#465C2211yescharacteristic
38C2×#460C2211yescharacteristic
39C2×C4×SD16C2211yescharacteristic
40C22×C4⋊C8C2211yescharacteristic
41C22×C4×C8C2211yescharacteristic
42#2857C2211yescharacteristic
43#2856C2211yescharacteristic
44#2856C2211yescharacteristic
45#2856C2211yescharacteristic
46#2851C2211yescharacteristic
47#2851C2211yescharacteristic
48#2588—21no—
49#2585—21no—
50#2583—21no—
51#2565C2211yescharacteristic
52#2554—21no—
53#2554—21no—
54#2552C2211yescharacteristic
55#2550C2211yescharacteristic
56#2543—21no—
57#2543—21no—
58#2541C2211yescharacteristic
59#2520—21no—
60#2512C2211yescharacteristic
61#2512C2211yescharacteristic
62#2509C2211yescharacteristic
63#2506C2211yescharacteristic
64#2505—21no—
65#2490—21no—
66#2473—21no—
67#2453C2211yescharacteristic
68#2451C2211yescharacteristic
69#2445C2211yescharacteristic
70#2445C2211yescharacteristic
71#2416—21no—
72#2370—21no—
73#2370C2211yescharacteristic
74#2368—21no—
75#2366C2211yescharacteristic
76#2363—21no—
77#2354C2211yescharacteristic
78#2351C2211yescharacteristic
79C4×C22⋊Q8C2211yescharacteristic
80C4×C22⋊Q8C2211yescharacteristic
81C4×C22⋊Q8C2211yescharacteristic
82C4×#121C2211yescharacteristic
83C4×#121C2211yescharacteristic
84C4×#121C2211yescharacteristic
85C2×C4×C4⋊C4C2211yescharacteristic
86#2101C2211yescharacteristic
87#2100C2211yescharacteristic
88#2100C2211yescharacteristic
89#2100C2211yescharacteristic
90#2100C2211yescharacteristic
91#2099C2211yescharacteristic
92#2093C2211yescharacteristic
93#2092C2211yescharacteristic
94#2088C2211yescharacteristic
95#2087C2211yescharacteristic
96#2084C2211yescharacteristic
97#2084C2211yescharacteristic
98#2073C2211yescharacteristic
99#2073C2211yescharacteristic
100#2073C2211yescharacteristic
101#2073C2211yescharacteristic
102#2072C2211yescharacteristic
103#2072C2211yescharacteristic
104#2067C2211yescharacteristic
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic
107#2065C2211yescharacteristic
108#2059C2211yescharacteristic
109#2057C2211yescharacteristic
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic
112#2041C2211yescharacteristic
113#2041C2211yescharacteristic
114#2041C2211yescharacteristic
115#2041C2211yescharacteristic
116#2041C2211yescharacteristic
117#2041C2211yescharacteristic
118#2025C2211yescharacteristic
119#2025C2211yescharacteristic
120#2025C2211yescharacteristic
121#2025C2211yescharacteristic
122#2025C2211yescharacteristic
123#2023C2211yescharacteristic
124#2014C2211yescharacteristic
125#2014C2211yescharacteristic
126#1990C2211yescharacteristic
127#1989C2211yescharacteristic
128#1982C2211yescharacteristic
129#1968C2211yescharacteristic
130#1957C2211yescharacteristic
131#1949C2211yescharacteristic
132#1948C2211yescharacteristic
133#1941C2211yescharacteristic
134#1934C2211yescharacteristic
135#1934C2211yescharacteristic
136#1934C2211yescharacteristic
137#1934C2211yescharacteristic
138#1934C2211yescharacteristic
139#1933C2211yescharacteristic
140#1928C2211yescharacteristic
141#1928C2211yescharacteristic
142#1926C2211yescharacteristic
143#1926C2211yescharacteristic
144#1926C2211yescharacteristic
145#1926C2211yescharacteristic
146#1925C2211yescharacteristic
147#1925C2211yescharacteristic
148#1921C2211yescharacteristic
149#1920C2211yescharacteristic
150#1920C2211yescharacteristic
151#1919C2211yescharacteristic
152#1919C2211yescharacteristic
153#1919C2211yescharacteristic
154#1918C2211yescharacteristic
155#1918C2211yescharacteristic
156#1916C2211yescharacteristic
157#1916C2211yescharacteristic
158#1916C2211yescharacteristic
159#1916C2211yescharacteristic
160#1916C2211yescharacteristic
161#1916C2211yescharacteristic
162#1916C2211yescharacteristic
163#1916C2211yescharacteristic
164#1893C2211yescharacteristic
165#1893C2211yescharacteristic
166#1893C2211yescharacteristic
167#1893C2211yescharacteristic
168#1893C2211yescharacteristic
169#1893C2211yescharacteristic
170#1893C2211yescharacteristic
171#1893C2211yescharacteristic
172#1893C2211yescharacteristic
173#1892C2211yescharacteristic
174#1880C2211yescharacteristic
175#1880C2211yescharacteristic
176#1880C2211yescharacteristic
177#1880C2211yescharacteristic
178#1880C2211yescharacteristic
179#1880C2211yescharacteristic
180#1877C2211yescharacteristic
181#1877C2211yescharacteristic
182#1864C2211yescharacteristic
183#1863C2211yescharacteristic
184#1863C2211yescharacteristic
185#1862C2211yescharacteristic
186#1862C2211yescharacteristic
187#1862C2211yescharacteristic
188#1862C2211yescharacteristic
189#1862C2211yescharacteristic
190#1834C2211yescharacteristic
191#1808C2211yescharacteristic
192#1808C2211yescharacteristic
193#1807C2211yescharacteristic
194#1804C2211yescharacteristic
195#1803C2211yescharacteristic
196C4×#106C2211yescharacteristic
197C4×#103C2211yescharacteristic
198C4×#102C2211yescharacteristic
199C2×#336C2211yescharacteristic
200C2×#336C2211yescharacteristic
201C2×#336C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C23×C8C2311yescharacteristic
210#553—48no—
211C2×C4⋊Q8C2311yescharacteristic
212C2×#127C2311yescharacteristic
213C2×#127C2311yescharacteristic
214C2×#127C2311yescharacteristic
215C2×#126—21no—
216C2×#126—21no—
217C2×#125—21no—
218C2×#125—21no—
219C2×#125C2311yescharacteristic
220C2×#125C2311yescharacteristic
221C2×#123—21no—
222C2×#123—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8C2311yescharacteristic
225C2×#121—21no—
226C2×#121—21no—
227C2×#121—21no—
228C2×#121—21no—
229C2×#121—21no—
230C2×#121—21no—
231C2×#121—21no—
232C2×#121—21no—
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×D4—21no—
240C2×C4×D4—21no—
241C2×C4×D4—21no—
242C2×C4×D4—21no—
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×#117—21no—
247C22×C4⋊C4D411yescharacteristic
248C22×C4⋊C4D411yescharacteristic
249C22×C42C2311yescharacteristic
250C22×C42C2311yescharacteristic
251C22×C42C2311yescharacteristic
252#486—42no—
253#478—42no—
254#465—24no—
255#465—24no—
256#465—24no—
257#460—42no—
258C4×SD16—42no—
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×C4⋊C8—42no—
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×C4×C8—42no—
300C2×C4×C8C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303C2×C4×C8C2311yescharacteristic
304#400—21no—
305#400—21no—
306#400—21no—
307#400—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#398—21no—
316#397—21no—
317#397—21no—
318#396—21no—
319#396—21no—
320#395—21no—
321#395—21no—
322#394—21no—
323#394—21no—
324#394—21no—
325#394—21no—
326#392—21no—
327#392—21no—
328#391—21no—
329#391—21no—
330#391—21no—
331#391C2311yescharacteristic
332#391C2311yescharacteristic
333#391C2311yescharacteristic
334#390—21no—
335#390—21no—
336#390—21no—
337#390—21no—
338#390—21no—
339#390—21no—
340#390—21no—
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#389—21no—
351#389—21no—
352#389—21no—
353#389—21no—
354#389—21no—
355#389—21no—
356#389—21no—
357#389—21no—
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—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#386—21no—
393#386—21no—
394#386—21no—
395#386—21no—
396#386—21no—
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#384C2311yescharacteristic
407#384C2311yescharacteristic
408#384C2311yescharacteristic
409#384C2311yescharacteristic
410#382—21no—
411#382C2311yescharacteristic
412#382C2311yescharacteristic
413#380—21no—
414#380—21no—
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4—21no—
422C4×C4⋊C4—21no—
423C4×C4⋊C4—21no—
424C4×C4⋊C4D411yescharacteristic
425C4×C4⋊C4D411yescharacteristic
426C4×C4⋊C4D411yescharacteristic
427C4×C4⋊C4D411yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C22⋊C4—21no—
439C4×C22⋊C4—21no—
440C4×C22⋊C4—21no—
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C2×#95D411yescharacteristic
445C2×#95D411yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
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#336C2311yescharacteristic
473#336C2311yescharacteristic
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
488C22×Q8—21no—
489C22×Q8C2411yescharacteristic
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4C2411yescharacteristic
500C22×D4C2411yescharacteristic
501C22×D4C2411yescharacteristic
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4C2×D411yescharacteristic
506C23×C4C2×D411yescharacteristic
507C23×C4C2×D411yescharacteristic
508C23×C4C2×D411yescharacteristic
509C23×C4C2×D411yescharacteristic
510C23×C4C2×D411yescharacteristic
511C23×C4C2411yescharacteristic
512C2×SD16—22no—
513C2×SD16—22no—
514C2×SD16—22no—
515C2×SD16—22no—
516C2×SD16—41no—
517C2×SD16—41no—
518C2×SD16—41no—
519C2×SD16—41no—
520C2×SD16—41no—
521C22×C8—22no—
522C22×C8—22no—
523C22×C8—22no—
524C22×C8—22no—
525C22×C8—22no—
526C22×C8—41no—
527C22×C8—41no—
528C22×C8—41no—
529C22×C8—41no—
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
541C4⋊Q8—41no—
542C4⋊Q8—41no—
543#127—41no—
544#127—41no—
545#127—41no—
546#127—41no—
547#127—41no—
548#127—41no—
549#126—44no—
550#126—44no—
551#125—41no—
552#125—41no—
553#125—41no—
554#125—41no—
555#125—44no—
556#125—44no—
557#123—44no—
558#123—44no—
559C22⋊Q8—22no—
560C22⋊Q8—44no—
561C22⋊Q8#4114yes—
562#121—22no—
563#121—22no—
564#121—22no—
565#121—22no—
566#121—22no—
567#121—22no—
568#121—44no—
569#121—44no—
570#121—44no—
571#121—44no—
572#121—44no—
573#121—82no—
574#121—82no—
575#121—82no—
576C4×Q8—41no—
577C4×Q8—41no—
578C4×Q8—41no—
579C4×Q8—41no—
580C4×Q8—41no—
581C4×Q8—41no—
582C4×D4—41no—
583C4×D4—41no—
584C4×D4—41no—
585C4×D4—41no—
586C4×D4—41no—
587C4×D4—41no—
588C4×D4—44no—
589C4×D4—44no—
590C4×D4—44no—
591C4×D4—44no—
592#117—44no—
593C2×C4⋊C4—24no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—24no—
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—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4C2×D411yescharacteristic
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—21no—
682C2×C42—41no—
683C2×C42—41no—
684C2×C42—41no—
685C2×C42—41no—
686C2×C42—41no—
687C2×C42—41no—
688C2×C42C2×D411yescharacteristic
689C2×C42C2×D411yescharacteristic
690C2×C42C2×D411yescharacteristic
691C2×C42C2×D411yescharacteristic
692C2×C42C2×D411yescharacteristic
693C2×C42C2×D411yescharacteristic
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700#107—41no—
701#107—41no—
702#107—41no—
703#107—41no—
704#106—22no—
705#106—22no—
706#106—22no—
707#106—22no—
708#106—41no—
709C4⋊C8—22no—
710C4⋊C8—22no—
711C4⋊C8—41no—
712C4⋊C8—41no—
713#103—22no—
714#103—22no—
715#103—22no—
716#103—41no—
717#103—41no—
718#102—22no—
719#102—22no—
720#102—22no—
721#102—22no—
722#102—22no—
723#102—41no—
724#102—41no—
725#102—41no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102—41no—
736#102—41no—
737#102—41no—
738#102—41no—
739C4×C8—22no—
740C4×C8—22no—
741C4×C8—41no—
742C4×C8—41no—
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#95—21no—
773#95—21no—
774#95—21no—
775#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783C24—21no—
784C24—21no—
785C24—21no—
786C24C22×D411yescharacteristic
787C2×Q8—21no—
788C2×Q8—21no—
789C2×Q8—21no—
790C2×Q8—21no—
791C2×Q8—21no—
792C2×Q8—42no—
793C2×Q8—81no—
794C2×Q8—81no—
795C2×Q8C2×#4112yes—
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—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—42no—
815C2×D4—42no—
816C2×D4—42no—
817C2×D4—42no—
818C2×D4—42no—
819C2×D4—42no—
820C2×D4—42no—
821C2×D4—42no—
822C2×D4—42no—
823C2×D4—42no—
824C2×D4—42no—
825C2×D4—42no—
826C2×D4—42no—
827C2×D4—42no—
828C2×D4—42no—
829C2×D4—42no—
830C2×D4—42no—
831C2×D4—81no—
832C2×D4—81no—
833C2×D4—81no—
834C2×D4—81no—
835C2×D4—81no—
836C2×D4—81no—
837C2×D4—81no—
838C2×D4—81no—
839C2×D4—81no—
840C2×D4—81no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—41no—
867C22×C4—41no—
868C22×C4—41no—
869C22×C4—41no—
870C22×C4—41no—
871C22×C4—41no—
872C22×C4—41no—
873C22×C4—41no—
874C22×C4—41no—
875C22×C4—42no—
876C22×C4—42no—
877C22×C4—42no—
878C22×C4—42no—
879C22×C4—42no—
880C22×C4—81no—
881C22×C4—81no—
882C22×C4—81no—
883C22×C4—81no—
884C22×C4AGL(1,ℤ/8)14yes—
885C22×C4C22×D411yescharacteristic
886C22×C4C22×D411yescharacteristic
887C22×C4C22×D411yescharacteristic
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C2×#4112yes—
899C22×C42−1+412yes—
900C22×C4C2511yescharacteristic
901SD16—44no—
902SD16—82no—
903SD16—82no—
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—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—44no—
928C2×C8—44no—
929C2×C8—82no—
930C2×C8—82no—
931C2×C8H(5,𝔽2)12yes—
932C4⋊C4—24no—
933C4⋊C4—22no—
934C4⋊C4—22no—
935C4⋊C4—22no—
936C4⋊C4—22no—
937C4⋊C4—22no—
938C4⋊C4—22no—
939C4⋊C4—22no—
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—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—42no—
964C4⋊C4—42no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—42no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—42no—
976C4⋊C4—42no—
977C4⋊C4—42no—
978C4⋊C4—42no—
979C4⋊C4—42no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4#13514yes—
992C4⋊C4C2×#4112yes—
993C22⋊C4—24no—
994C22⋊C4—42no—
995C22⋊C4—42no—
996C22⋊C4—42no—
997C22⋊C4—42no—
998C22⋊C4—42no—
999C22⋊C4—42no—
1000C22⋊C4—42no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C42—21no—
1023C42—21no—
1024C42—21no—
1025C42—21no—
1026C42—21no—
1027C42—21no—
1028C42—21no—
1029C42—21no—
1030C42—21no—
1031C42—21no—
1032C42—21no—
1033C42—21no—
1034C42—41no—
1035C42—41no—
1036C42—41no—
1037C42—41no—
1038C42—41no—
1039C42—41no—
1040C42—42no—
1041C42—42no—
1042C42—42no—
1043C42—42no—
1044C42—42no—
1045C42—81no—
1046C42—81no—
1047C42—81no—
1048C42—81no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—41no—
1054C23—41no—
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#54812yes—
1075C23C2×AGL(1,ℤ/8)12yes—
1076C23#57712yes—
1077C23C23×D411yescharacteristic
1078Q8—22no—
1079Q8—22no—
1080Q8—41no—
1081Q8—41no—
1082Q8—162no—
1083D4—41no—
1084D4—41no—
1085D4—41no—
1086D4—41no—
1087D4—41no—
1088D4—41no—
1089D4—41no—
1090D4—41no—
1091D4—41no—
1092D4—41no—
1093D4—41no—
1094D4—41no—
1095D4—84no—
1096D4—84no—
1097D4—84no—
1098D4—84no—
1099D4—162no—
1100D4—162no—
1101D4—162no—
1102D4—162no—
1103D4—162no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—22no—
1128C2×C4—22no—
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—44no—
1145C2×C4—44no—
1146C2×C4—44no—
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—84no—
1185C2×C4—82no—
1186C2×C4—82no—
1187C2×C4—162no—
1188C2×C4—162no—
1189C2×C4#54812yes—
1190C2×C4C2×#13512yes—
1191C2×C4C2×#13512yes—
1192C2×C4C2×#13512yes—
1193C2×C4C2×AGL(1,ℤ/8)12yes—
1194C2×C4C2×AGL(1,ℤ/8)12yes—
1195C2×C4C22×#4111yescharacteristic
1196C2×C4C2×H(5,𝔽2)11yescharacteristic
1197C2×C4C2×2−1+411yescharacteristic
1198C2×C4#58511yescharacteristic
1199C2×C4#58511yescharacteristic
1200C2×C4#58511yescharacteristic
1201C8—22no—
1202C8—41no—
1203C8—41no—
1204C8—41no—
1205C8—41no—
1206C8—41no—
1207C8—41no—
1208C8—41no—
1209C22—22no—
1210C22—22no—
1211C22—22no—
1212C22—22no—
1213C22—22no—
1214C22—22no—
1215C22—81no—
1216C22—81no—
1217C22—81no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22#336814yes—
1237C22#344911yescharacteristic
1238C22C2×#54811yescharacteristic
1239C22#349611yescharacteristic
1240C22C22×#13511yescharacteristic
1241C22C22×AGL(1,ℤ/8)11yescharacteristic
1242C22C2×#57711yescharacteristic
1243C22#358411yescharacteristic
1244C4—22no—
1245C4—22no—
1246C4—22no—
1247C4—22no—
1248C4—22no—
1249C4—22no—
1250C4—41no—
1251C4—41no—
1252C4—41no—
1253C4—41no—
1254C4—41no—
1255C4—41no—
1256C4—41no—
1257C4—42no—
1258C4—42no—
1259C4—81no—
1260C4—81no—
1261C4—81no—
1262C4—81no—
1263C4—81no—
1264C4—81no—
1265C4—81no—
1266C4—81no—
1267C4—81no—
1268C4—81no—
1269C4—81no—
1270C4#351311yescharacteristic
1271C4#352111yescharacteristic
1272C4#354111yescharacteristic
1273C4#355311yescharacteristic
1274C2—24no—
1275C2—161no—
1276C2—161no—
1277C2—161no—
1278C2#3916011yescharacteristic
1279C2#6094611yescharacteristic
1280C2#6100111yescharacteristic
1281C2#6130311yescharacteristic
1282C2C2×#336811yescharacteristic
1283C2#6225011yescharacteristic
1284C2#6225311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36596C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #36571C2semidirect
3. #33042C2semidirect
4. #32427C2semidirect
5. #32314C2semidirect
6. #32231C2semidirect
7. #32078C2semidirect
8. #31637C2semidirect
9. #31460C2semidirect
10. #30876C2semidirect
11. #30815C2semidirect
12. #30189C2semidirect
13. #30189C2semidirect
14. #29161C2semidirect
15. #29157C2semidirect
16. #28574C2semidirect
17. #28574C2semidirect
18. #27559C2semidirect
19. #27429C2semidirect
20. #27365C2semidirect
21. #27139C2semidirect
22. #26896C2semidirect
23. #26755C2semidirect
24. #26701C2semidirect
25. #26159C2semidirect
26. #24839C2semidirect
27. #24753C2semidirect
28. #22185C2semidirect
29. #22185C2semidirect
30. C4×#465C2semidirect
31. C2×#1916C2semidirect

Maximal subgroups

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

subgroupindex
#365962
#365712
#330422
#324272
#323142
#322312
#320782
#316372
#314602
#308762
#308152
#301892
#291612
#291572
#285742
#275592
#274292
#273652
#271392
#268962
#267552
#267012
#261592
#248392
#247532
#221852
C4×#4652
C2×#19162