Finite Group Databasebeta

← #6726613

Subgroups — #6726613

Order 512.

1413 conjugacy classes of subgroups.

The subgroup lattice has 1231 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39732C211yesmaximal, characteristic, complemented
2#36297C211yesmaximal, characteristic, complemented
3#33097C211yesmaximal, characteristic, complemented
4#32500C211yesmaximal, characteristic, complemented
5#32485C211yesmaximal, characteristic, complemented
6#32440C211yesmaximal, characteristic, complemented
7#32420C211yesmaximal, characteristic, complemented
8#32320C211yesmaximal, characteristic, complemented
9#32295C211yesmaximal, characteristic, complemented
10#30786C211yesmaximal, characteristic, complemented
11#30679C211yesmaximal, characteristic, complemented
12#29906C211yesmaximal, characteristic, complemented
13#29782C211yesmaximal, characteristic, complemented
14#27486C211yesmaximal, characteristic, complemented
15#27158C211yesmaximal, characteristic, complemented
16#27049C211yesmaximal, characteristic, complemented
17#26871C211yesmaximal, characteristic, complemented
18#26439C211yesmaximal, characteristic, complemented
19#26364C211yesmaximal, characteristic, complemented
20#26215C211yesmaximal, characteristic, complemented
21#26152C211yesmaximal, characteristic, complemented
22#26098C211yesmaximal, characteristic, complemented
23#26073C211yesmaximal, characteristic, complemented
24#26012C211yesmaximal, characteristic, complemented
25#25458C211yesmaximal, characteristic, complemented
26#25228C211yesmaximal, characteristic, complemented
27#24792C211yesmaximal, characteristic
28#23140C211yesmaximal, characteristic, complemented
29#22716C211yesmaximal, characteristic, complemented
30#22073C211yesmaximal, characteristic, complemented
31#21171C211yesmaximal, characteristic, complemented
32C2×#499C2211yescharacteristic
33C2×#482C2211yescharacteristic
34C2×#478C2211yescharacteristic
35C2×#469C2211yescharacteristic
36C2×#469C2211yescharacteristic
37C2×#436C2211yescharacteristic
38C2×#428C2211yescharacteristic
39C2×#428C2211yescharacteristic
40C2×#423C2211yescharacteristic
41#2866—21no—
42#2854C2211yescharacteristic
43#2854C2211yescharacteristic
44#2795—21no—
45#2793—21no—
46#2790—21no—
47#2718—21no—
48#2618—21no—
49#2570C2211yescharacteristic
50#2566C2211yescharacteristic
51#2530—21no—
52#2526—21no—
53#2516—21no—
54#2513C2211yescharacteristic
55#2512C2211yescharacteristic
56#2509C2211yescharacteristic
57#2507C2211yescharacteristic
58#2500C2211yescharacteristic
59#2497C2211yescharacteristic
60#2497C2211yescharacteristic
61#2490C2211yescharacteristic
62#2481—21no—
63#2471—21no—
64#2470—21no—
65#2457—21no—
66#2443—21no—
67#2442C2211yescharacteristic
68#2441C2211yescharacteristic
69#2441C2211yescharacteristic
70#2422C2211yescharacteristic
71#2416C2211yescharacteristic
72#2414C2211yescharacteristic
73#2370C2211yescharacteristic
74#2363C2211yescharacteristic
75#2361C2211yescharacteristic
76#2361C2211yescharacteristic
77#2354C2211yescharacteristic
78#2352C2211yescharacteristic
79#2352C2211yescharacteristic
80#2344C2211yescharacteristic
81#2322—21no—
82C4×#123C2211yescharacteristic
83#2293—21no—
84C2×#384C2211yescharacteristic
85C4×#117C2211yescharacteristic
86#2101C2211yescharacteristic
87#2101C2211yescharacteristic
88#2099C2211yescharacteristic
89#2099C2211yescharacteristic
90#2093C2211yescharacteristic
91#2093C2211yescharacteristic
92#2093C2211yescharacteristic
93#2092C2211yescharacteristic
94#2088C2211yescharacteristic
95#2088C2211yescharacteristic
96#2088C2211yescharacteristic
97#2087C2211yescharacteristic
98#2085C2211yescharacteristic
99#2085C2211yescharacteristic
100#2083C2211yescharacteristic
101#2083C2211yescharacteristic
102#2083C2211yescharacteristic
103#2075C2211yescharacteristic
104#2075C2211yescharacteristic
105#2073C2211yescharacteristic
106#2071C2211yescharacteristic
107#2071C2211yescharacteristic
108#2067C2211yescharacteristic
109#2067C2211yescharacteristic
110#2067C2211yescharacteristic
111#2065C2211yescharacteristic
112#2065C2211yescharacteristic
113#2065C2211yescharacteristic
114#2065C2211yescharacteristic
115#2065C2211yescharacteristic
116#2059C2211yescharacteristic
117#2059C2211yescharacteristic
118#2059C2211yescharacteristic
119#2054C2211yescharacteristic
120#2054C2211yescharacteristic
121#2034C2211yescharacteristic
122#2034C2211yescharacteristic
123#2033C2211yescharacteristic
124#2033C2211yescharacteristic
125#2025C2211yescharacteristic
126#1989C2211yescharacteristic
127#1970C2211yescharacteristic
128#1949C2211yescharacteristic
129#1949C2211yescharacteristic
130#1948C2211yescharacteristic
131#1948C2211yescharacteristic
132#1948C2211yescharacteristic
133#1948C2211yescharacteristic
134#1947C2211yescharacteristic
135#1947C2211yescharacteristic
136#1947C2211yescharacteristic
137#1947C2211yescharacteristic
138#1947C2211yescharacteristic
139#1944C2211yescharacteristic
140#1942C2211yescharacteristic
141#1941C2211yescharacteristic
142#1940C2211yescharacteristic
143#1939C2211yescharacteristic
144#1936C2211yescharacteristic
145#1934C2211yescharacteristic
146#1926C2211yescharacteristic
147#1926C2211yescharacteristic
148#1925C2211yescharacteristic
149#1925C2211yescharacteristic
150#1925C2211yescharacteristic
151#1925C2211yescharacteristic
152#1924C2211yescharacteristic
153#1923C2211yescharacteristic
154#1921C2211yescharacteristic
155#1921C2211yescharacteristic
156#1920C2211yescharacteristic
157#1920C2211yescharacteristic
158#1919C2211yescharacteristic
159#1919C2211yescharacteristic
160#1919C2211yescharacteristic
161#1919C2211yescharacteristic
162#1918C2211yescharacteristic
163#1918C2211yescharacteristic
164#1916C2211yescharacteristic
165#1916C2211yescharacteristic
166#1895C2211yescharacteristic
167#1895C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1875C2211yescharacteristic
171#1875C2211yescharacteristic
172#1874C2211yescharacteristic
173#1874C2211yescharacteristic
174#1874C2211yescharacteristic
175#1870C2211yescharacteristic
176#1862C2211yescharacteristic
177#1862C2211yescharacteristic
178#1854C2211yescharacteristic
179#1854C2211yescharacteristic
180#1854C2211yescharacteristic
181#1854C2211yescharacteristic
182#1852C2211yescharacteristic
183#1852C2211yescharacteristic
184#1852C2211yescharacteristic
185#1851C2211yescharacteristic
186#1851C2211yescharacteristic
187#1851C2211yescharacteristic
188#1847C2211yescharacteristic
189#1835C2211yescharacteristic
190#1824C2211yescharacteristic
191#1817C2211yescharacteristic
192#1809C2211yescharacteristic
193#1809C2211yescharacteristic
194#1809C2211yescharacteristic
195#1804C2211yescharacteristic
196C4×#107C2211yescharacteristic
197#1762C2211yescharacteristic
198C4×#102C2211yescharacteristic
199#1753C2211yescharacteristic
200#1736C2211yescharacteristic
201#1736C2211yescharacteristic
202#1736C2211yescharacteristic
203C22×D8C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C2×#126—21no—
208C2×#125C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×#123—21no—
211C2×#123—21no—
212C2×#123—21no—
213C2×#123D411yescharacteristic
214C2×#121—21no—
215C2×#121C2311yescharacteristic
216C2×#121C2311yescharacteristic
217C2×#121C2311yescharacteristic
218C2×#121C2311yescharacteristic
219C2×C4×D4—21no—
220C2×C4×D4—21no—
221C2×C4×D4C2311yescharacteristic
222C2×C4×D4C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×#117—21no—
225C2×#117—21no—
226C2×#117C2311yescharacteristic
227C2×#117C2311yescharacteristic
228C2×#117C2311yescharacteristic
229C22×C4⋊C4—21no—
230C22×C4⋊C4—21no—
231C22×C4⋊C4C2311yescharacteristic
232C22×C4⋊C4C2311yescharacteristic
233C22×C4⋊C4C2311yescharacteristic
234C22×C42C2311yescharacteristic
235#499—42no—
236#482—42no—
237#478—42no—
238#469—24no—
239#469—42no—
240#436—24no—
241#428—42no—
242#428—42no—
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262#423—24no—
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
285C2×C22⋊C8C2311yescharacteristic
286C2×C22⋊C8C2311yescharacteristic
287C2×C22⋊C8C2311yescharacteristic
288C2×C22⋊C8C2311yescharacteristic
289C2×#97C2311yescharacteristic
290C2×C4×C8C2311yescharacteristic
291C2×C4×C8C2311yescharacteristic
292#400—21no—
293#400—21no—
294#400—21no—
295#400—21no—
296#400—21no—
297#400—21no—
298#399—21no—
299#399—21no—
300#398—21no—
301#398—21no—
302#398—21no—
303#398—21no—
304#397—21no—
305#397—21no—
306#397—21no—
307#397—21no—
308#397—21no—
309#396—21no—
310#396—21no—
311#396—21no—
312#396—21no—
313#396—21no—
314#396—21no—
315#396—21no—
316#396—21no—
317#394—21no—
318#394—21no—
319#394—21no—
320#394—21no—
321#394—21no—
322#394—21no—
323#392—21no—
324#390—21no—
325#390—21no—
326#390—21no—
327#390C2311yescharacteristic
328#390C2311yescharacteristic
329#390C2311yescharacteristic
330#390C2311yescharacteristic
331#390C2311yescharacteristic
332#390C2311yescharacteristic
333#390C2311yescharacteristic
334#390C2311yescharacteristic
335#389—21no—
336#389—21no—
337#389—21no—
338#389—21no—
339#389—21no—
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#388—21no—
353#388—21no—
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#388D411yescharacteristic
373#388D411yescharacteristic
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387D411yescharacteristic
389#387D411yescharacteristic
390#386—21no—
391#386—21no—
392#386—21no—
393#386—21no—
394#386—21no—
395#386—21no—
396#386—21no—
397#386—21no—
398#386D411yescharacteristic
399#385—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385D411yescharacteristic
406#384—21no—
407#384—21no—
408#384C2311yescharacteristic
409#384C2311yescharacteristic
410#384C2311yescharacteristic
411#384C2311yescharacteristic
412#384C2311yescharacteristic
413#382C2311yescharacteristic
414#382C2311yescharacteristic
415#382C2311yescharacteristic
416#381—21no—
417#381D411yescharacteristic
418#380—21no—
419#380—21no—
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426C4×C4⋊C4—21no—
427C4×C4⋊C4C2311yescharacteristic
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×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439C4×C22⋊C4—21no—
440C4×C22⋊C4—21no—
441C4×C22⋊C4—21no—
442C4×C22⋊C4C2311yescharacteristic
443C4×C22⋊C4C2311yescharacteristic
444C4×C22⋊C4C2311yescharacteristic
445#376—21no—
446C43—21no—
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#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
487C22×D4—21no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4C2×D411yescharacteristic
492C22×D4C2411yescharacteristic
493C22×D4C2411yescharacteristic
494C23×C4—21no—
495C23×C4—21no—
496C23×C4—21no—
497C23×C4—21no—
498C23×C4—21no—
499C23×C4C2×D411yescharacteristic
500C23×C4C2×D411yescharacteristic
501C23×C4C2411yescharacteristic
502C23×C4C2411yescharacteristic
503C2×D8—22no—
504C2×D8—41no—
505C2×D8—41no—
506C2×M16—22no—
507C2×M16—22no—
508C2×M16—41no—
509C2×M16—41no—
510C2×M16—41no—
511C2×M16—41no—
512C2×M16—41no—
513C2×M16—41no—
514C2×M16#4114yes—
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523#126—82no—
524#125—22no—
525#125—41no—
526#125—41no—
527#125—41no—
528#123—42no—
529#123—44no—
530#123—82no—
531#123—82no—
532#121—22no—
533#121—22no—
534#121—22no—
535#121—22no—
536#121—22no—
537#121—41no—
538#121—41no—
539#121—41no—
540#121—82no—
541C4×D4—22no—
542C4×D4—22no—
543C4×D4—22no—
544C4×D4—41no—
545C4×D4—41no—
546C4×D4—41no—
547C4×D4—44no—
548C4×D4—82no—
549#117—22no—
550#117—22no—
551#117—41no—
552#117—41no—
553#117—41no—
554#117—41no—
555#117—82no—
556#117—82no—
557C2×C4⋊C4—22no—
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—41no—
588C2×C4⋊C4—41no—
589C2×C4⋊C4—41no—
590C2×C4⋊C4—41no—
591C2×C4⋊C4—41no—
592C2×C4⋊C4—82no—
593C2×C4⋊C4—82no—
594C2×C4⋊C4C2×D411yescharacteristic
595C2×C4⋊C4C2×D411yescharacteristic
596C2×C4⋊C4C2×D411yescharacteristic
597C2×C4⋊C4C2×D411yescharacteristic
598C2×C4⋊C4C2×D411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
645C2×C22⋊C4C2×D411yescharacteristic
646C2×C22⋊C4C2×D411yescharacteristic
647C2×C22⋊C4C2×D411yescharacteristic
648C2×C22⋊C4C2×D411yescharacteristic
649C2×C22⋊C4C2×D411yescharacteristic
650C2×C22⋊C4C2×D411yescharacteristic
651C2×C22⋊C4C2×D411yescharacteristic
652C2×C42—22no—
653C2×C42—22no—
654C2×C42—21no—
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×C42—21no—
665C2×C42C2×D411yescharacteristic
666C2×C42C2×D411yescharacteristic
667C2×C42C2411yescharacteristic
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672#107—22no—
673#107—22no—
674#107—41no—
675#107—41no—
676#107—41no—
677#107—41no—
678#107—41no—
679#107—41no—
680#107—41no—
681#107—41no—
682#107—41no—
683#106—22no—
684#106—22no—
685#106—22no—
686#106—22no—
687#106—22no—
688#106—41no—
689#106—41no—
690#106—41no—
691C4⋊C8—22no—
692C4⋊C8—22no—
693C4⋊C8—22no—
694C4⋊C8—22no—
695C4⋊C8—22no—
696C4⋊C8—41no—
697C4⋊C8—41no—
698#102—22no—
699#102—22no—
700#102—22no—
701#102—22no—
702#102—41no—
703#102—41no—
704#102—41no—
705#102—41no—
706#102—41no—
707#102—41no—
708#102—41no—
709#102—41no—
710#102—41no—
711#102—41no—
712C22⋊C8—22no—
713C22⋊C8—22no—
714C22⋊C8—22no—
715C22⋊C8—41no—
716C22⋊C8—41no—
717#97—41no—
718C4×C8—22no—
719C4×C8—41no—
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#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758#95C2×D411yescharacteristic
759#95C2×D411yescharacteristic
760#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762C24—21no—
763C24—21no—
764C24C22×D411yescharacteristic
765C24C22×D411yescharacteristic
766C2×D4—22no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—41no—
780C2×D4—41no—
781C2×D4—42no—
782C2×D4—42no—
783C2×D4—42no—
784C2×D4—42no—
785C2×D4—42no—
786C2×D4—42no—
787C2×D4—81no—
788C2×D4—81no—
789C2×D4—81no—
790C2×D4—81no—
791C2×D4—81no—
792C2×D4—81no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—21no—
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—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—41no—
822C22×C4—41no—
823C22×C4—42no—
824C22×C4—42no—
825C22×C4—42no—
826C22×C4—42no—
827C22×C4—42no—
828C22×C4—42no—
829C22×C4—81no—
830C22×C4—81no—
831C22×C4—81no—
832C22×C4—81no—
833C22×C4—81no—
834C22×C4—81no—
835C22×C4—81no—
836C22×C4—81no—
837C22×C4—81no—
838C22×C4C22×D411yescharacteristic
839C22×C4C22×D411yescharacteristic
840C22×C4C22×D411yescharacteristic
841C22×C4C22×D411yescharacteristic
842C22×C4C22×D411yescharacteristic
843C22×C4C22×D411yescharacteristic
844C22×C4C22×D411yescharacteristic
845C22×C4C22×D411yescharacteristic
846C22×C4C22×D411yescharacteristic
847C22×C4C22×D411yescharacteristic
848C22×C4C22×D411yescharacteristic
849C22×C4C22×D411yescharacteristic
850C22×C4C2×#4112yes—
851C22×C42−1+412yes—
852C22×C4C2511yescharacteristic
853D8—82no—
854M16—44no—
855M16—44no—
856M16—82no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8—21no—
867C2×C8—21no—
868C2×C8—21no—
869C2×C8—21no—
870C2×C8—21no—
871C2×C8—21no—
872C2×C8—21no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8C2×#4112yes—
880C2×C8C2×#4112yes—
881C4⋊C4—22no—
882C4⋊C4—22no—
883C4⋊C4—22no—
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—21no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—41no—
911C4⋊C4—41no—
912C4⋊C4—42no—
913C4⋊C4—42no—
914C4⋊C4—42no—
915C4⋊C4—42no—
916C4⋊C4—42no—
917C4⋊C4—42no—
918C4⋊C4—42no—
919C4⋊C4—42no—
920C4⋊C4—42no—
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⋊C4—81no—
934C4⋊C4—81no—
935C4⋊C4—81no—
936C4⋊C4—81no—
937C4⋊C4—81no—
938C4⋊C4—81no—
939C4⋊C4—81no—
940C4⋊C4—81no—
941C4⋊C4H(5,𝔽2)12yes—
942C4⋊C42−1+412yes—
943C22⋊C4—22no—
944C22⋊C4—22no—
945C22⋊C4—22no—
946C22⋊C4—22no—
947C22⋊C4—41no—
948C22⋊C4—41no—
949C22⋊C4—41no—
950C22⋊C4—41no—
951C22⋊C4—42no—
952C22⋊C4—42no—
953C22⋊C4—42no—
954C22⋊C4—42no—
955C22⋊C4—42no—
956C22⋊C4—42no—
957C22⋊C4—42no—
958C22⋊C4—42no—
959C22⋊C4—42no—
960C22⋊C4—42no—
961C22⋊C4—42no—
962C22⋊C4—42no—
963C22⋊C4—42no—
964C22⋊C4—81no—
965C22⋊C4—81no—
966C22⋊C4—81no—
967C22⋊C4—81no—
968C22⋊C4—81no—
969C22⋊C4—81no—
970C22⋊C4—81no—
971C22⋊C4—81no—
972C22⋊C4—81no—
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—
982C42—22no—
983C42—22no—
984C42—21no—
985C42—21no—
986C42—21no—
987C42—21no—
988C42—21no—
989C42—21no—
990C42—21no—
991C42—21no—
992C42—21no—
993C42—21no—
994C42—42no—
995C42—42no—
996C42—42no—
997C42—42no—
998C42—81no—
999C42—81no—
1000C42—81no—
1001C42—81no—
1002C42—81no—
1003C42—81no—
1004C42—81no—
1005C23—21no—
1006C23—21no—
1007C23—21no—
1008C23—21no—
1009C23—21no—
1010C23—21no—
1011C23—21no—
1012C23—21no—
1013C23—21no—
1014C23—21no—
1015C23—21no—
1016C23—21no—
1017C23—21no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23#54712yes—
1033C23C23×D411yescharacteristic
1034D4—41no—
1035D4—41no—
1036D4—41no—
1037D4—41no—
1038D4—41no—
1039D4—41no—
1040D4—41no—
1041D4—41no—
1042D4—82no—
1043D4—84no—
1044D4—84no—
1045D4—162no—
1046D4—162no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—22no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—22no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—44no—
1087C2×C4—44no—
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—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—84no—
1133C2×C4—84no—
1134C2×C4—162no—
1135C2×C4—162no—
1136C2×C4—162no—
1137C2×C4#54712yes—
1138C2×C4#57512yes—
1139C2×C4#57612yes—
1140C2×C4C22×#4111yescharacteristic
1141C2×C4C2×H(5,𝔽2)11yescharacteristic
1142C2×C4C2×2−1+411yescharacteristic
1143C2×C4C2×2−1+411yescharacteristic
1144C2×C4#58511yescharacteristic
1145C2×C4#58511yescharacteristic
1146C8—22no—
1147C8—22no—
1148C8—41no—
1149C8—41no—
1150C8—41no—
1151C8—41no—
1152C8—41no—
1153C8—41no—
1154C22—22no—
1155C22—22no—
1156C22—22no—
1157C22—41no—
1158C22—41no—
1159C22—41no—
1160C22—41no—
1161C22—41no—
1162C22—41no—
1163C22—41no—
1164C22—41no—
1165C22—41no—
1166C22—41no—
1167C22—41no—
1168C22—81no—
1169C22—81no—
1170C22—81no—
1171C22—81no—
1172C22—81no—
1173C22—81no—
1174C22—81no—
1175C22—81no—
1176C22—81no—
1177C22—81no—
1178C22—81no—
1179C22—81no—
1180C22—81no—
1181C22—81no—
1182C22C2×#54711yescharacteristic
1183C22#348811yescharacteristic
1184C22#348911yescharacteristic
1185C22C2×#57511yescharacteristic
1186C22C2×#57611yescharacteristic
1187C22#358511yescharacteristic
1188C22#358611yescharacteristic
1189C4—22no—
1190C4—22no—
1191C4—22no—
1192C4—41no—
1193C4—42no—
1194C4—41no—
1195C4—41no—
1196C4—41no—
1197C4—41no—
1198C4—41no—
1199C4—41no—
1200C4—41no—
1201C4—41no—
1202C4—42no—
1203C4—81no—
1204C4—81no—
1205C4—81no—
1206C4—81no—
1207C4—81no—
1208C4—81no—
1209C4—81no—
1210C4—81no—
1211C4—81no—
1212C4—81no—
1213C4—81no—
1214C4—81no—
1215C4#346111yescharacteristic
1216C4#350511yescharacteristic
1217C4#355211yescharacteristic
1218C4#355311yescharacteristic
1219C2—42no—
1220C2—81no—
1221C2—161no—
1222C2—161no—
1223C2#3779111yescharacteristic
1224C2#6125511yescharacteristic
1225C2#6127011yescharacteristic
1226C2#6196711yescharacteristic
1227C2#6203711yescharacteristic
1228C2#6214311yescharacteristic
1229C2#6223011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#24792C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39732C2semidirect
2. #36297C2semidirect
3. #33097C2semidirect
4. #32500C2semidirect
5. #32485C2semidirect
6. #32440C2semidirect
7. #32420C2semidirect
8. #32320C2semidirect
9. #32295C2semidirect
10. #30786C2semidirect
11. #30679C2semidirect
12. #29906C2semidirect
13. #29782C2semidirect
14. #27486C2semidirect
15. #27158C2semidirect
16. #27049C2semidirect
17. #26871C2semidirect
18. #26439C2semidirect
19. #26364C2semidirect
20. #26215C2semidirect
21. #26152C2semidirect
22. #26098C2semidirect
23. #26073C2semidirect
24. #26012C2semidirect
25. #25458C2semidirect
26. #25228C2semidirect
28. #23140C2semidirect
29. #22716C2semidirect
30. #22073C2semidirect
31. #21171C2semidirect

Maximal subgroups

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

subgroupindex
#397322
#362972
#330972
#325002
#324852
#324402
#324202
#323202
#322952
#307862
#306792
#299062
#297822
#274862
#271582
#270492
#268712
#264392
#263642
#262152
#261522
#260982
#260732
#260122
#254582
#252282
#247922
#231402
#227162
#220732
#211712