Finite Group Databasebeta

← #6877144

Subgroups — #6877144

Order 512.

1520 conjugacy classes of subgroups.

The subgroup lattice has 1310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36498C211yesmaximal, characteristic, complemented
2#36381C211yesmaximal, characteristic, complemented
3#33143C211yesmaximal, characteristic, complemented
4#32222C211yesmaximal, characteristic, complemented
5#32013C211yesmaximal, characteristic, complemented
6#32011C211yesmaximal, characteristic, complemented
7#31628C211yesmaximal, characteristic, complemented
8#30934C211yesmaximal, characteristic, complemented
9#30612C211yesmaximal, characteristic, complemented
10#30414C211yesmaximal, characteristic, complemented
11#30413C211yesmaximal, characteristic, complemented
12#30381C211yesmaximal, characteristic, complemented
13#30356C211yesmaximal, characteristic, complemented
14#29577C211yesmaximal, characteristic, complemented
15#29493C211yesmaximal, characteristic, complemented
16#29466C211yesmaximal, characteristic, complemented
17#29460C211yesmaximal, characteristic, complemented
18#27574C211yesmaximal, characteristic, complemented
19#27548C211yesmaximal, characteristic, complemented
20#27514C211yesmaximal, characteristic, complemented
21#27480C211yesmaximal, characteristic, complemented
22#27452C211yesmaximal, characteristic, complemented
23#27414C211yesmaximal, characteristic, complemented
24#26396C211yesmaximal, characteristic, complemented
25#25179C211yesmaximal, characteristic, complemented
26#24701C211yesmaximal, characteristic, complemented
27#24504C211yesmaximal, characteristic, complemented
28#22147C211yesmaximal, characteristic, complemented
29#22045C211yesmaximal, characteristic, complemented
30#21540C211yesmaximal, characteristic, complemented
31#21102C211yesmaximal, characteristic, complemented
32C2×#476C2211yescharacteristic
33C2×#469C2211yescharacteristic
34C2×#468C2211yescharacteristic
35C2×#460C2211yescharacteristic
36C2×#449C2211yescharacteristic
37C2×#449C2211yescharacteristic
38C2×#440C2211yescharacteristic
39C2×#431C2211yescharacteristic
40C2×C4×M16C2211yescharacteristic
41#2864C2211yescharacteristic
42#2860C2211yescharacteristic
43#2857C2211yescharacteristic
44#2854C2211yescharacteristic
45#2854C2211yescharacteristic
46#2854C2211yescharacteristic
47#2597—21no—
48#2597—21no—
49#2574—21no—
50#2560—21no—
51#2553—21no—
52#2535C2211yescharacteristic
53#2535C2211yescharacteristic
54#2531—21no—
55#2512C2211yescharacteristic
56#2497C2211yescharacteristic
57#2497C2211yescharacteristic
58#2491C2211yescharacteristic
59#2485C2211yescharacteristic
60#2467—21no—
61#2461—21no—
62#2457—21no—
63#2457—21no—
64#2456—21no—
65#2456—21no—
66#2451C2211yescharacteristic
67#2428C2211yescharacteristic
68#2428C2211yescharacteristic
69#2423C2211yescharacteristic
70#2407C2211yescharacteristic
71#2373—21no—
72#2372—21no—
73#2364—21no—
74#2364—21no—
75#2357C2211yescharacteristic
76#2349C2211yescharacteristic
77#2346C2211yescharacteristic
78#2341C2211yescharacteristic
79C4×#127C2211yescharacteristic
80C4×C22⋊Q8C2211yescharacteristic
81C4×#121C2211yescharacteristic
82C4×#121C2211yescharacteristic
83#2297C2211yescharacteristic
84#2295C2211yescharacteristic
85C42×D4C2211yescharacteristic
86#2101C2211yescharacteristic
87#2101C2211yescharacteristic
88#2099C2211yescharacteristic
89#2097C2211yescharacteristic
90#2093C2211yescharacteristic
91#2092C2211yescharacteristic
92#2088C2211yescharacteristic
93#2087C2211yescharacteristic
94#2085C2211yescharacteristic
95#2085C2211yescharacteristic
96#2083C2211yescharacteristic
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic
99#2077C2211yescharacteristic
100#2075C2211yescharacteristic
101#2075C2211yescharacteristic
102#2075C2211yescharacteristic
103#2074C2211yescharacteristic
104#2073C2211yescharacteristic
105#2071C2211yescharacteristic
106#2068C2211yescharacteristic
107#2067C2211yescharacteristic
108#2065C2211yescharacteristic
109#2065C2211yescharacteristic
110#2057C2211yescharacteristic
111#2055C2211yescharacteristic
112#2054C2211yescharacteristic
113#2041C2211yescharacteristic
114#2035C2211yescharacteristic
115#2034C2211yescharacteristic
116#2034C2211yescharacteristic
117#2034C2211yescharacteristic
118#2033C2211yescharacteristic
119#2033C2211yescharacteristic
120#2033C2211yescharacteristic
121#2033C2211yescharacteristic
122#2023C2211yescharacteristic
123#2011C2211yescharacteristic
124#2000C2211yescharacteristic
125#1999C2211yescharacteristic
126#1987C2211yescharacteristic
127#1982C2211yescharacteristic
128#1972C2211yescharacteristic
129#1970C2211yescharacteristic
130#1970C2211yescharacteristic
131#1968C2211yescharacteristic
132#1968C2211yescharacteristic
133#1948C2211yescharacteristic
134#1948C2211yescharacteristic
135#1943C2211yescharacteristic
136#1942C2211yescharacteristic
137#1942C2211yescharacteristic
138#1941C2211yescharacteristic
139#1941C2211yescharacteristic
140#1936C2211yescharacteristic
141#1936C2211yescharacteristic
142#1934C2211yescharacteristic
143#1934C2211yescharacteristic
144#1934C2211yescharacteristic
145#1934C2211yescharacteristic
146#1934C2211yescharacteristic
147#1934C2211yescharacteristic
148#1933C2211yescharacteristic
149#1933C2211yescharacteristic
150#1928C2211yescharacteristic
151#1926C2211yescharacteristic
152#1926C2211yescharacteristic
153#1925C2211yescharacteristic
154#1924C2211yescharacteristic
155#1924C2211yescharacteristic
156#1920C2211yescharacteristic
157#1919C2211yescharacteristic
158#1918C2211yescharacteristic
159#1918C2211yescharacteristic
160#1917C2211yescharacteristic
161#1917C2211yescharacteristic
162#1895C2211yescharacteristic
163#1895C2211yescharacteristic
164#1895C2211yescharacteristic
165#1894C2211yescharacteristic
166#1880C2211yescharacteristic
167#1879C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1877C2211yescharacteristic
172#1877C2211yescharacteristic
173#1877C2211yescharacteristic
174#1875C2211yescharacteristic
175#1875C2211yescharacteristic
176#1870C2211yescharacteristic
177#1870C2211yescharacteristic
178#1865C2211yescharacteristic
179#1865C2211yescharacteristic
180#1864C2211yescharacteristic
181#1864C2211yescharacteristic
182#1863C2211yescharacteristic
183#1862C2211yescharacteristic
184#1862C2211yescharacteristic
185#1862C2211yescharacteristic
186#1854C2211yescharacteristic
187#1854C2211yescharacteristic
188#1851C2211yescharacteristic
189#1851C2211yescharacteristic
190#1809C2211yescharacteristic
191#1809C2211yescharacteristic
192#1803C2211yescharacteristic
193#1802C2211yescharacteristic
194#1788C2211yescharacteristic
195#1788C2211yescharacteristic
196#1776C2211yescharacteristic
197C4×C4⋊C8C2211yescharacteristic
198#1763C2211yescharacteristic
199#1762C2211yescharacteristic
200C4×C22⋊C8C2211yescharacteristic
201C4×C22⋊C8C2211yescharacteristic
202#1744C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×#127C2311yescharacteristic
212C2×#126—21no—
213C2×#126—21no—
214C2×#124—21no—
215C2×#123—21no—
216C2×#123—21no—
217C2×#123—21no—
218C2×C22⋊Q8—21no—
219C2×C22⋊Q8C2311yescharacteristic
220C2×#121—21no—
221C2×#121—21no—
222C2×#121C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×#121C2311yescharacteristic
226C2×#121C2311yescharacteristic
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2311yescharacteristic
229C2×C4×D4—21no—
230C2×C4×D4—21no—
231C2×C4×D4—21no—
232C2×C4×D4—21no—
233C2×C4×D4D411yescharacteristic
234C2×C4×D4D411yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C22×C42C2311yescharacteristic
242C22×C42C2311yescharacteristic
243#476—42no—
244#469—42no—
245#468—24no—
246#460—24no—
247#449—24no—
248#449—42no—
249#440—42no—
250#431—42no—
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C4×M16—42no—
298C2×#97C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×C4×C8C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303C2×C4×C8C2311yescharacteristic
304#400—21no—
305#400—21no—
306#399—21no—
307#398—21no—
308#398—21no—
309#397—21no—
310#397—21no—
311#397—21no—
312#397—21no—
313#396—21no—
314#396—21no—
315#396—21no—
316#395—21no—
317#394—21no—
318#394—21no—
319#394—21no—
320#394—21no—
321#394—21no—
322#393—21no—
323#392—21no—
324#392—21no—
325#392—21no—
326#392—21no—
327#392—21no—
328#391—21no—
329#391—21no—
330#391C2311yescharacteristic
331#391C2311yescharacteristic
332#391C2311yescharacteristic
333#390—21no—
334#390—21no—
335#390—21no—
336#390—21no—
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#389—21no—
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
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#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—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#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#384C2311yescharacteristic
411#384C2311yescharacteristic
412#382—21no—
413#382C2311yescharacteristic
414#382C2311yescharacteristic
415#381—21no—
416#380—21no—
417#380—21no—
418#380—21no—
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427C4×C4⋊C4—21no—
428C4×C4⋊C4—21no—
429C4×C4⋊C4D411yescharacteristic
430C4×C4⋊C4D411yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439C4×C22⋊C4—21no—
440C4×C22⋊C4—21no—
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4D411yescharacteristic
444C4×C22⋊C4D411yescharacteristic
445C4×C22⋊C4D411yescharacteristic
446C4×C22⋊C4D411yescharacteristic
447C4×C22⋊C4C2311yescharacteristic
448C4×C22⋊C4C2311yescharacteristic
449#376—21no—
450#376—21no—
451C2×#95—21no—
452C43C2311yescharacteristic
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
487C2×#41—22no—
488C2×#41—41no—
489C2×#41—41no—
490C2×#41—41no—
491C2×#41—41no—
492C2×#41—41no—
493C22×Q8—21no—
494C22×Q8C2411yescharacteristic
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4C2×D411yescharacteristic
504C22×D4C2411yescharacteristic
505C22×D4C2411yescharacteristic
506C22×D4C2411yescharacteristic
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4C2×D411yescharacteristic
513C23×C4C2×D411yescharacteristic
514C23×C4C2×D411yescharacteristic
515C23×C4C2×D411yescharacteristic
516C23×C4C2411yescharacteristic
517C23×C4C2411yescharacteristic
518C2×SD16—22no—
519C2×SD16—41no—
520C2×SD16—41no—
521C2×SD16—41no—
522C2×SD16—41no—
523C2×SD16#4114yes—
524C2×D8—22no—
525C2×D8—22no—
526C2×D8—41no—
527C2×D8—41no—
528C2×D8—41no—
529C2×D8—41no—
530C2×M16—22no—
531C2×M16—22no—
532C2×M16—41no—
533C2×M16—41no—
534C2×M16—41no—
535C2×M16—41no—
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C4⋊Q8—41no—
545C4⋊Q8—41no—
546#127—22no—
547#127—41no—
548#126—44no—
549#126—82no—
550#124—44no—
551#123—82no—
552#123—82no—
553#123—82no—
554C22⋊Q8—22no—
555C22⋊Q8—41no—
556C22⋊Q8—82no—
557#121—22no—
558#121—22no—
559#121—44no—
560#121—44no—
561#121—41no—
562#121—41no—
563#121—41no—
564#121—41no—
565#121—41no—
566#121—41no—
567#121—41no—
568#121—41no—
569C4×Q8—22no—
570C4×Q8—41no—
571C4×Q8—41no—
572C4×Q8—41no—
573C4×D4—42no—
574C4×D4—41no—
575C4×D4—41no—
576C4×D4—41no—
577C4×D4—41no—
578C4×D4—41no—
579C4×D4—41no—
580C4×D4—41no—
581C4×D4—41no—
582C4×D4—41no—
583C4×D4—41no—
584C4×D4—42no—
585C4×D4—82no—
586C4×D4—82no—
587C4×D4—82no—
588C4×D4—82no—
589#117—41no—
590#117—41no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
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—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⋊C4C2×D411yescharacteristic
664C2×C22⋊C4C2×D411yescharacteristic
665C2×C22⋊C4C2×D411yescharacteristic
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C22⋊C4C2×D411yescharacteristic
668C2×C22⋊C4C2×D411yescharacteristic
669C2×C42—21no—
670C2×C42—21no—
671C2×C42—21no—
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—41no—
677C2×C42—41no—
678C2×C42—41no—
679C2×C42—41no—
680C2×C42C2×D411yescharacteristic
681C2×C42C2×D411yescharacteristic
682C2×C42C2×D411yescharacteristic
683C2×C42C2×D411yescharacteristic
684C2×C42C2×D411yescharacteristic
685C2×C42C2×D411yescharacteristic
686C2×C42C2×D411yescharacteristic
687C2×C42C2×D411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693#107—22no—
694#107—41no—
695#107—41no—
696#107—41no—
697#107—41no—
698#107—41no—
699#106—22no—
700#106—41no—
701#106—41no—
702#106—41no—
703#106—41no—
704#106—41no—
705C4⋊C8—22no—
706C4⋊C8—22no—
707C4⋊C8—41no—
708C4⋊C8—41no—
709#103—22no—
710#103—22no—
711#103—22no—
712#103—41no—
713#103—41no—
714#103—41no—
715#102—22no—
716#102—22no—
717#102—22no—
718#102—22no—
719#102—22no—
720#102—41no—
721#102—41no—
722#102—41no—
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—
733C22⋊C8—22no—
734C22⋊C8—22no—
735C22⋊C8—41no—
736C22⋊C8—41no—
737C22⋊C8—41no—
738C22⋊C8—41no—
739#97—22no—
740#97—41no—
741C4×C8—22no—
742C4×C8—41no—
743C4×C8—41no—
744C4×C8—41no—
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#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785C24—21no—
786C24—21no—
787C24—21no—
788C24C22×D411yescharacteristic
789C24C22×D411yescharacteristic
790#41—82no—
791#41—82no—
792#41—82no—
793#41—82no—
794C2×Q8—21no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—42no—
800C2×Q8—81no—
801C2×Q8—81no—
802C2×Q8C2×#4112yes—
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—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—41no—
821C2×D4—41no—
822C2×D4—41no—
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—42no—
832C2×D4—42no—
833C2×D4—42no—
834C2×D4—42no—
835C2×D4—42no—
836C2×D4—81no—
837C2×D4—81no—
838C2×D4—81no—
839C2×D4—81no—
840C2×D4—81no—
841C2×D4—81no—
842C2×D4—81no—
843C2×D4—81no—
844C2×D4—81no—
845C2×D4—81no—
846C2×D4—81no—
847C2×D4C2×#4112yes—
848C22×C4—21no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
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—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—41no—
879C22×C4—41no—
880C22×C4—41no—
881C22×C4—41no—
882C22×C4—41no—
883C22×C4—41no—
884C22×C4—41no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—42no—
888C22×C4—42no—
889C22×C4—42no—
890C22×C4—42no—
891C22×C4—81no—
892C22×C4—81no—
893C22×C4—81no—
894C22×C4—81no—
895C22×C4—81no—
896C22×C4—81no—
897C22×C4—81no—
898C22×C4—81no—
899C22×C4—81no—
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C2511yescharacteristic
913SD16—44no—
914SD16—82no—
915D8—82no—
916D8—82no—
917M16—44no—
918M16—44no—
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—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8C2×#4112yes—
942C2×C8H(5,𝔽2)12yes—
943C4⋊C4—22no—
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—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—41no—
969C4⋊C4—41no—
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—
990C22⋊C4—22no—
991C22⋊C4—22no—
992C22⋊C4—22no—
993C22⋊C4—41no—
994C22⋊C4—41no—
995C22⋊C4—41no—
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—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C42—22no—
1034C42—22no—
1035C42—22no—
1036C42—21no—
1037C42—21no—
1038C42—21no—
1039C42—21no—
1040C42—21no—
1041C42—21no—
1042C42—21no—
1043C42—21no—
1044C42—21no—
1045C42—21no—
1046C42—41no—
1047C42—41no—
1048C42—41no—
1049C42—41no—
1050C42—41no—
1051C42—42no—
1052C42—42no—
1053C42—42no—
1054C42—42no—
1055C42—81no—
1056C42—81no—
1057C42—81no—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—22no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23C23×D411yescharacteristic
1094Q8—22no—
1095Q8—22no—
1096Q8—41no—
1097Q8—41no—
1098Q8—162no—
1099D4—22no—
1100D4—22no—
1101D4—44no—
1102D4—41no—
1103D4—41no—
1104D4—41no—
1105D4—41no—
1106D4—41no—
1107D4—41no—
1108D4—41no—
1109D4—41no—
1110D4—41no—
1111D4—41no—
1112D4—84no—
1113D4—84no—
1114D4—84no—
1115D4—84no—
1116D4—84no—
1117D4—162no—
1118D4—162no—
1119D4—162no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
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—22no—
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—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—44no—
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—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—82no—
1201C2×C4—82no—
1202C2×C4—82no—
1203C2×C4—84no—
1204C2×C4—162no—
1205C2×C4—162no—
1206C2×C4—162no—
1207C2×C4—162no—
1208C2×C4#57512yes—
1209C2×C4#57512yes—
1210C2×C4#57612yes—
1211C2×C4#57712yes—
1212C2×C4C22×#4111yescharacteristic
1213C2×C4C2×H(5,𝔽2)11yescharacteristic
1214C2×C4#58511yescharacteristic
1215C2×C4#58511yescharacteristic
1216C2×C4#58511yescharacteristic
1217C2×C4#58511yescharacteristic
1218C8—22no—
1219C8—22no—
1220C8—41no—
1221C8—41no—
1222C8—41no—
1223C8—41no—
1224C8—41no—
1225C8—41no—
1226C22—41no—
1227C22—42no—
1228C22—41no—
1229C22—41no—
1230C22—41no—
1231C22—42no—
1232C22—41no—
1233C22—42no—
1234C22—41no—
1235C22—41no—
1236C22—41no—
1237C22—41no—
1238C22—41no—
1239C22—41no—
1240C22—41no—
1241C22—41no—
1242C22—41no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22#344911yescharacteristic
1262C22D4×#4111yescharacteristic
1263C22#349611yescharacteristic
1264C22C2×#57511yescharacteristic
1265C22C2×#57511yescharacteristic
1266C22C2×#57611yescharacteristic
1267C22C2×#57711yescharacteristic
1268C4—22no—
1269C4—22no—
1270C4—22no—
1271C4—22no—
1272C4—41no—
1273C4—41no—
1274C4—42no—
1275C4—41no—
1276C4—41no—
1277C4—41no—
1278C4—41no—
1279C4—41no—
1280C4—41no—
1281C4—81no—
1282C4—81no—
1283C4—81no—
1284C4—81no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C4—81no—
1290C4—81no—
1291C4—81no—
1292C4—81no—
1293C4#350511yescharacteristic
1294C4#352111yescharacteristic
1295C4#353311yescharacteristic
1296C4#356611yescharacteristic
1297C2—81no—
1298C2—81no—
1299C2—82no—
1300C2—161no—
1301C2—161no—
1302C2#3994211yescharacteristic
1303C2#6096711yescharacteristic
1304C2#6100611yescharacteristic
1305C2#6144511yescharacteristic
1306C2#6144911yescharacteristic
1307C2#6225611yescharacteristic
1308C2#6226311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
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. #36498C2semidirect
2. #36381C2semidirect
3. #33143C2semidirect
4. #32222C2semidirect
5. #32013C2semidirect
6. #32011C2semidirect
7. #31628C2semidirect
8. #30934C2semidirect
9. #30612C2semidirect
10. #30414C2semidirect
11. #30413C2semidirect
12. #30381C2semidirect
13. #30356C2semidirect
14. #29577C2semidirect
15. #29493C2semidirect
16. #29466C2semidirect
17. #29460C2semidirect
18. #27574C2semidirect
19. #27548C2semidirect
20. #27514C2semidirect
21. #27480C2semidirect
22. #27452C2semidirect
23. #27414C2semidirect
24. #26396C2semidirect
25. #25179C2semidirect
26. #24701C2semidirect
27. #24504C2semidirect
28. #22147C2semidirect
29. #22045C2semidirect
30. #21540C2semidirect
31. #21102C2semidirect

Maximal subgroups

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

subgroupindex
#364982
#363812
#331432
#322222
#320132
#320112
#316282
#309342
#306122
#304142
#304132
#303812
#303562
#295772
#294932
#294662
#294602
#275742
#275482
#275142
#274802
#274522
#274142
#263962
#251792
#247012
#245042
#221472
#220452
#215402
#211022