Finite Group Databasebeta

← #7039320

Subgroups — #7039320

Order 512.

1431 conjugacy classes of subgroups.

The subgroup lattice has 1275 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59217C211yesmaximal, characteristic
2#39666C211yesmaximal, characteristic, complemented
3#32251C211yesmaximal, characteristic, complemented
4#31996C211yesmaximal, characteristic, complemented
5#31344C211yesmaximal, characteristic, complemented
6#31336C211yesmaximal, characteristic, complemented
7#31277C211yesmaximal, characteristic, complemented
8#30968C211yesmaximal, characteristic, complemented
9#30579C211yesmaximal, characteristic, complemented
10#30399C211yesmaximal, characteristic, complemented
11#29480C211yesmaximal, characteristic, complemented
12#28715C211yesmaximal, characteristic, complemented
13#28565C211yesmaximal, characteristic, complemented
14#28085C211yesmaximal, characteristic, complemented
15#27864C211yesmaximal, characteristic, complemented
16#27800C211yesmaximal, characteristic, complemented
17#27509C211yesmaximal, characteristic, complemented
18#27473C211yesmaximal, characteristic, complemented
19#27445C211yesmaximal, characteristic, complemented
20#27345C211yesmaximal, characteristic, complemented
21#27244C211yesmaximal, characteristic, complemented
22#26742C211yesmaximal, characteristic, complemented
23#25353C211yesmaximal, characteristic, complemented
24#25130C211yesmaximal, characteristic, complemented
25#24939C211yesmaximal, characteristic, complemented
26#24867C211yesmaximal, characteristic, complemented
27#23763C211yesmaximal, characteristic, complemented
28#23119C211yesmaximal, characteristic, complemented
29#22932C211yesmaximal, characteristic, complemented
30#22567C211yesmaximal, characteristic, complemented
31#22186C211yesmaximal, characteristic, complemented
32C2×#501C2211yescharacteristic
33C2×#484C2211yescharacteristic
34C2×#479C2211yescharacteristic
35C2×#468C2211yescharacteristic
36C2×#465C2211yescharacteristic
37C2×#448C2211yescharacteristic
38C2×#435C2211yescharacteristic
39C2×#435C2211yescharacteristic
40C22×#103C2211yescharacteristic
41#2855C2211yescharacteristic
42#2804—21no—
43#2784—21no—
44#2781—21no—
45#2781—21no—
46#2780—21no—
47#2774—21no—
48#2665—21no—
49#2589—21no—
50#2574—21no—
51#2563C2211yescharacteristic
52#2562C2211yescharacteristic
53#2562C2211yescharacteristic
54#2552C2211yescharacteristic
55#2538C2211yescharacteristic
56#2537—21no—
57#2537C2211yescharacteristic
58#2511C2211yescharacteristic
59#2497—21no—
60#2497C2211yescharacteristic
61#2492C2211yescharacteristic
62#2490C2211yescharacteristic
63#2490C2211yescharacteristic
64#2487C2211yescharacteristic
65#2485—21no—
66#2476—21no—
67#2476—21no—
68#2451C2211yescharacteristic
69#2417C2211yescharacteristic
70#2416C2211yescharacteristic
71#2416C2211yescharacteristic
72#2409C2211yescharacteristic
73#2409C2211yescharacteristic
74#2363—21no—
75#2360C2211yescharacteristic
76#2354C2211yescharacteristic
77D4×C4⋊C4C2211yescharacteristic
78#2345C2211yescharacteristic
79#2345C2211yescharacteristic
80Q8×C22⋊C4C2211yescharacteristic
81#2333—21no—
82C4×C22⋊Q8C2211yescharacteristic
83C4×#121C2211yescharacteristic
84C4×#121C2211yescharacteristic
85#2285C2211yescharacteristic
86#2100C2211yescharacteristic
87#2099C2211yescharacteristic
88#2096C2211yescharacteristic
89#2095C2211yescharacteristic
90#2093C2211yescharacteristic
91#2088C2211yescharacteristic
92#2084C2211yescharacteristic
93#2083C2211yescharacteristic
94#2083C2211yescharacteristic
95#2077C2211yescharacteristic
96#2077C2211yescharacteristic
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic
99#2077C2211yescharacteristic
100#2076C2211yescharacteristic
101#2076C2211yescharacteristic
102#2075C2211yescharacteristic
103#2072C2211yescharacteristic
104#2072C2211yescharacteristic
105#2068C2211yescharacteristic
106#2059C2211yescharacteristic
107#2058C2211yescharacteristic
108#2055C2211yescharacteristic
109#2055C2211yescharacteristic
110#2036C2211yescharacteristic
111#2036C2211yescharacteristic
112#2036C2211yescharacteristic
113#2036C2211yescharacteristic
114#2035C2211yescharacteristic
115#2035C2211yescharacteristic
116#2034C2211yescharacteristic
117#2034C2211yescharacteristic
118#2034C2211yescharacteristic
119#2033C2211yescharacteristic
120#2026C2211yescharacteristic
121#2026C2211yescharacteristic
122#2026C2211yescharacteristic
123#2023C2211yescharacteristic
124#2000C2211yescharacteristic
125#2000C2211yescharacteristic
126#1992C2211yescharacteristic
127#1989C2211yescharacteristic
128#1988C2211yescharacteristic
129#1973C2211yescharacteristic
130#1973C2211yescharacteristic
131#1947C2211yescharacteristic
132#1943C2211yescharacteristic
133#1936C2211yescharacteristic
134#1936C2211yescharacteristic
135#1935C2211yescharacteristic
136#1935C2211yescharacteristic
137#1935C2211yescharacteristic
138#1928C2211yescharacteristic
139#1928C2211yescharacteristic
140#1928C2211yescharacteristic
141#1927C2211yescharacteristic
142#1927C2211yescharacteristic
143#1927C2211yescharacteristic
144#1927C2211yescharacteristic
145#1925C2211yescharacteristic
146#1925C2211yescharacteristic
147#1924C2211yescharacteristic
148#1924C2211yescharacteristic
149#1921C2211yescharacteristic
150#1921C2211yescharacteristic
151#1919C2211yescharacteristic
152#1918C2211yescharacteristic
153#1918C2211yescharacteristic
154#1918C2211yescharacteristic
155#1918C2211yescharacteristic
156#1917C2211yescharacteristic
157#1917C2211yescharacteristic
158#1895C2211yescharacteristic
159#1894C2211yescharacteristic
160#1894C2211yescharacteristic
161#1894C2211yescharacteristic
162#1893C2211yescharacteristic
163#1892C2211yescharacteristic
164#1880C2211yescharacteristic
165#1880C2211yescharacteristic
166#1877C2211yescharacteristic
167#1877C2211yescharacteristic
168#1874C2211yescharacteristic
169#1872C2211yescharacteristic
170#1870C2211yescharacteristic
171#1870C2211yescharacteristic
172#1869C2211yescharacteristic
173#1869C2211yescharacteristic
174#1865C2211yescharacteristic
175#1865C2211yescharacteristic
176#1864C2211yescharacteristic
177#1864C2211yescharacteristic
178#1853C2211yescharacteristic
179#1852C2211yescharacteristic
180#1852C2211yescharacteristic
181#1852C2211yescharacteristic
182#1824C2211yescharacteristic
183#1824C2211yescharacteristic
184#1809C2211yescharacteristic
185#1809C2211yescharacteristic
186#1809C2211yescharacteristic
187#1808C2211yescharacteristic
188#1808C2211yescharacteristic
189#1807C2211yescharacteristic
190#1787C2211yescharacteristic
191#1787C2211yescharacteristic
192#1776C2211yescharacteristic
193#1776C2211yescharacteristic
194#1776C2211yescharacteristic
195#1763C2211yescharacteristic
196#1763C2211yescharacteristic
197#1763C2211yescharacteristic
198#1752C2211yescharacteristic
199#1752C2211yescharacteristic
200#1749C2211yescharacteristic
201C2×#340C2211yescharacteristic
202#1728C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C23×C8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×C22⋊Q8C2311yescharacteristic
214C2×C22⋊Q8C2311yescharacteristic
215C2×C22⋊Q8C2311yescharacteristic
216C2×C22⋊Q8C2311yescharacteristic
217C2×#121—21no—
218C2×#121—21no—
219C2×#121—21no—
220C2×#121D411yescharacteristic
221C2×#121C2311yescharacteristic
222C2×#121C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×D4—21no—
227C2×C4×D4—21no—
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×#117—21no—
233C2×#117—21no—
234C22×C4⋊C4C2311yescharacteristic
235C22×C4⋊C4C2311yescharacteristic
236C22×C4⋊C4C2311yescharacteristic
237C22×C42C2311yescharacteristic
238#501—42no—
239#484—24no—
240#479—42no—
241#468—24no—
242#465—42no—
243#448—42no—
244#435—42no—
245#435—42no—
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×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×#103—24no—
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×C22⋊C8C2311yescharacteristic
284C2×C22⋊C8C2311yescharacteristic
285C2×C22⋊C8C2311yescharacteristic
286C2×C22⋊C8C2311yescharacteristic
287C2×C22⋊C8C2311yescharacteristic
288C2×C22⋊C8C2311yescharacteristic
289C2×C22⋊C8C2311yescharacteristic
290C2×C22⋊C8C2311yescharacteristic
291C2×#97C2311yescharacteristic
292C2×#97C2311yescharacteristic
293C2×#97C2311yescharacteristic
294C2×#97C2311yescharacteristic
295#400—21no—
296#400—21no—
297#400—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#396—21no—
310#396—21no—
311#396—21no—
312#396—21no—
313#396—21no—
314#396—21no—
315#395—21no—
316#395—21no—
317#395—21no—
318#394—21no—
319#394—21no—
320#394—21no—
321#394—21no—
322#394—21no—
323#394—21no—
324#394—21no—
325#394—21no—
326#393—21no—
327#393—21no—
328#393—21no—
329#393—21no—
330#393—21no—
331#391—21no—
332#391—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#390D411yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#389—21no—
350#389—21no—
351#389—21no—
352#389—21no—
353#389D411yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
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#386—21no—
387#386—21no—
388#386—21no—
389#386—21no—
390#386—21no—
391#386—21no—
392#386—21no—
393#386D411yescharacteristic
394#386D411yescharacteristic
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#384—21no—
404#384C2311yescharacteristic
405#384C2311yescharacteristic
406#384C2311yescharacteristic
407#382—21no—
408#382—21no—
409#381—21no—
410#380—21no—
411#380—21no—
412#380—21no—
413#380—21no—
414#380—21no—
415#380—21no—
416#380—21no—
417#380D411yescharacteristic
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431C4×C4⋊C4—21no—
432C4×C4⋊C4—21no—
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C4×C22⋊C4C2311yescharacteristic
448C4×C22⋊C4C2311yescharacteristic
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×Q8—21no—
488C22×Q8—21no—
489C22×Q8—22no—
490C22×Q8—41no—
491C22×Q8—41no—
492C22×Q8—41no—
493C22×Q8—41no—
494C22×Q8—41no—
495C22×Q8C2411yescharacteristic
496C22×Q8C2411yescharacteristic
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4C2×D411yescharacteristic
501C22×D4C2×D411yescharacteristic
502C22×D4C2×D411yescharacteristic
503C22×D4C2411yescharacteristic
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4C2×D411yescharacteristic
510C23×C4C2×D411yescharacteristic
511C23×C4C2411yescharacteristic
512C23×C4C2411yescharacteristic
513C23×C4C2411yescharacteristic
514C2×SD16—22no—
515C2×SD16—22no—
516C2×SD16—41no—
517C2×SD16—41no—
518C2×SD16—41no—
519C2×SD16—41no—
520C2×M16—22no—
521C2×M16—41no—
522C2×M16—41no—
523C2×M16—41no—
524C2×M16—41no—
525C2×M16—41no—
526C22×C8—22no—
527C22×C8—22no—
528C22×C8—41no—
529C22×C8—41no—
530C22×C8—41no—
531C22×C8—41no—
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C4⋊Q8—41no—
541C4⋊Q8—41no—
542#125—41no—
543#125—41no—
544#125—41no—
545#125—41no—
546C22⋊Q8—22no—
547C22⋊Q8—22no—
548C22⋊Q8—41no—
549C22⋊Q8—41no—
550C22⋊Q8—41no—
551C22⋊Q8—41no—
552C22⋊Q8—41no—
553C22⋊Q8—41no—
554#121—24no—
555#121—22no—
556#121—41no—
557#121—44no—
558#121—41no—
559#121—41no—
560#121—41no—
561#121—41no—
562#121—82no—
563#121—82no—
564C4×Q8—41no—
565C4×Q8—41no—
566C4×Q8—41no—
567C4×Q8—41no—
568C4×D4—41no—
569C4×D4—41no—
570C4×D4—41no—
571C4×D4—41no—
572C4×D4—41no—
573C4×D4—41no—
574C4×D4—41no—
575C4×D4—41no—
576C4×D4—82no—
577C4×D4—82no—
578#117—82no—
579#117—82no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—22no—
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—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—41no—
610C2×C4⋊C4—41no—
611C2×C4⋊C4—41no—
612C2×C4⋊C4—41no—
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
659C2×C22⋊C4C2×D411yescharacteristic
660C2×C22⋊C4C2×D411yescharacteristic
661C2×C22⋊C4C2×D411yescharacteristic
662C2×C22⋊C4C2×D411yescharacteristic
663C2×C22⋊C4C2×D411yescharacteristic
664C2×C22⋊C4C2×D411yescharacteristic
665C2×C22⋊C4C2×D411yescharacteristic
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C22⋊C4C2×D411yescharacteristic
668C2×C42—21no—
669C2×C42—21no—
670C2×C42—21no—
671C2×C42—21no—
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—41no—
678C2×C42—41no—
679C2×C42C2×D411yescharacteristic
680C2×C42C2×D411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685#107—22no—
686#107—22no—
687#107—22no—
688#107—22no—
689#107—41no—
690#107—41no—
691#107—41no—
692#107—41no—
693#106—22no—
694#106—41no—
695#106—41no—
696#106—41no—
697#106—41no—
698#106—41no—
699C4⋊C8—22no—
700C4⋊C8—41no—
701#103—22no—
702#103—22no—
703#103—22no—
704#103—22no—
705#103—22no—
706#103—41no—
707#103—41no—
708#103—41no—
709#103—41no—
710#103—41no—
711#103—41no—
712#103—41no—
713#103—41no—
714#103#4114yes—
715#102—22no—
716#102—41no—
717#102—41no—
718#102—41no—
719#102—41no—
720#102—41no—
721C22⋊C8—22no—
722C22⋊C8—22no—
723C22⋊C8—22no—
724C22⋊C8—41no—
725C22⋊C8—41no—
726C22⋊C8—41no—
727C22⋊C8—41no—
728C22⋊C8—41no—
729#97—22no—
730#97—41no—
731#97—41no—
732#97—41no—
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#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778C24—21no—
779C24C22×D411yescharacteristic
780C24C22×D411yescharacteristic
781C24C22×D411yescharacteristic
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—21no—
792C2×Q8—21no—
793C2×Q8—42no—
794C2×Q8—44no—
795C2×Q8—81no—
796C2×Q8—81no—
797C2×Q8—81no—
798C2×Q8—81no—
799C2×Q8—81no—
800C2×Q8—82no—
801C2×Q8—82no—
802C2×Q8—82no—
803C2×Q8C2×#4112yes—
804C2×D4—22no—
805C2×D4—22no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—41no—
813C2×D4—41no—
814C2×D4—41no—
815C2×D4—41no—
816C2×D4—41no—
817C2×D4—41no—
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#13714yes—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
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—22no—
849C22×C4—21no—
850C22×C4—21no—
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—41no—
863C22×C4—41no—
864C22×C4—41no—
865C22×C4—41no—
866C22×C4—41no—
867C22×C4—42no—
868C22×C4—42no—
869C22×C4—42no—
870C22×C4—42no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—81no—
874C22×C4—81no—
875C22×C4—81no—
876C22×C4—81no—
877C22×C4—81no—
878C22×C4—81no—
879C22×C4—81no—
880C22×C4—81no—
881C22×C4—81no—
882C22×C4C22×D411yescharacteristic
883C22×C4C22×D411yescharacteristic
884C22×C4C22×D411yescharacteristic
885C22×C4C22×D411yescharacteristic
886C22×C4C22×D411yescharacteristic
887C22×C4C22×D411yescharacteristic
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893C22×C4C2511yescharacteristic
894SD16—82no—
895SD16—82no—
896M16—82no—
897M16—82no—
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—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—82no—
921C2×C8—82no—
922C2×C8C2×#4112yes—
923C2×C8H(5,𝔽2)12yes—
924C4⋊C4—22no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—41no—
951C4⋊C4—41no—
952C4⋊C4—41no—
953C4⋊C4—41no—
954C4⋊C4—42no—
955C4⋊C4—42no—
956C4⋊C4—42no—
957C4⋊C4—42no—
958C4⋊C4—42no—
959C4⋊C4—42no—
960C4⋊C4—81no—
961C4⋊C4—81no—
962C4⋊C4—81no—
963C4⋊C4—81no—
964C4⋊C4—81no—
965C4⋊C4—81no—
966C4⋊C4—81no—
967C4⋊C4—81no—
968C4⋊C4—81no—
969C4⋊C4—81no—
970C4⋊C4—81no—
971C4⋊C4—81no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4C2×#4112yes—
982C22⋊C4—22no—
983C22⋊C4—22no—
984C22⋊C4—41no—
985C22⋊C4—41no—
986C22⋊C4—41no—
987C22⋊C4—41no—
988C22⋊C4—41no—
989C22⋊C4—41no—
990C22⋊C4—41no—
991C22⋊C4—41no—
992C22⋊C4—42no—
993C22⋊C4—42no—
994C22⋊C4—42no—
995C22⋊C4—42no—
996C22⋊C4—42no—
997C22⋊C4—42no—
998C22⋊C4—42no—
999C22⋊C4—42no—
1000C22⋊C4—42no—
1001C22⋊C4—81no—
1002C22⋊C4—81no—
1003C22⋊C4—81no—
1004C22⋊C4—81no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C22⋊C4—81no—
1008C22⋊C4—81no—
1009C22⋊C4—81no—
1010C22⋊C4—81no—
1011C22⋊C4—81no—
1012C22⋊C4—81no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C42—21no—
1020C42—21no—
1021C42—21no—
1022C42—21no—
1023C42—21no—
1024C42—21no—
1025C42—21no—
1026C42—21no—
1027C42—41no—
1028C42—41no—
1029C42—42no—
1030C42—81no—
1031C42—81no—
1032C42—81no—
1033C42—81no—
1034C42—81no—
1035C42—81no—
1036C42—81no—
1037C42—81no—
1038C23—21no—
1039C23—21no—
1040C23—21no—
1041C23—21no—
1042C23—21no—
1043C23—21no—
1044C23—21no—
1045C23—21no—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—21no—
1056C23—21no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23C2×#13712yes—
1065C23C2×#13712yes—
1066C23C23×D411yescharacteristic
1067Q8—22no—
1068Q8—22no—
1069Q8—41no—
1070Q8—41no—
1071Q8—41no—
1072Q8—41no—
1073Q8—41no—
1074Q8—41no—
1075Q8—84no—
1076Q8—162no—
1077D4—44no—
1078D4—41no—
1079D4—41no—
1080D4—41no—
1081D4—41no—
1082D4—82no—
1083D4—82no—
1084D4—84no—
1085D4—162no—
1086D4—162no—
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—22no—
1102C2×C4—22no—
1103C2×C4—21no—
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—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—44no—
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—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—82no—
1178C2×C4—84no—
1179C2×C4—84no—
1180C2×C4—162no—
1181C2×C4—162no—
1182C2×C4—162no—
1183C2×C4C2×#13712yes—
1184C2×C4C22×#4111yescharacteristic
1185C2×C4C2×H(5,𝔽2)11yescharacteristic
1186C2×C4#58511yescharacteristic
1187C2×C4#58511yescharacteristic
1188C2×C4#58511yescharacteristic
1189C2×C4#58511yescharacteristic
1190C8—22no—
1191C8—22no—
1192C8—41no—
1193C8—41no—
1194C8—41no—
1195C8—41no—
1196C8—41no—
1197C8—41no—
1198C22—22no—
1199C22—22no—
1200C22—22no—
1201C22—22no—
1202C22—22no—
1203C22—22no—
1204C22—41no—
1205C22—41no—
1206C22—41no—
1207C22—41no—
1208C22—41no—
1209C22—41no—
1210C22—41no—
1211C22—41no—
1212C22—41no—
1213C22—41no—
1214C22—41no—
1215C22—41no—
1216C22—41no—
1217C22—41no—
1218C22—41no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22D4×#4111yescharacteristic
1227C22#348511yescharacteristic
1228C22#349611yescharacteristic
1229C22C22×#13711yescharacteristic
1230C22#358511yescharacteristic
1231C22#358511yescharacteristic
1232C22#358611yescharacteristic
1233C4—22no—
1234C4—41no—
1235C4—42no—
1236C4—41no—
1237C4—41no—
1238C4—41no—
1239C4—41no—
1240C4—41no—
1241C4—41no—
1242C4—41no—
1243C4—41no—
1244C4—41no—
1245C4—42no—
1246C4—81no—
1247C4—81no—
1248C4—81no—
1249C4—81no—
1250C4—81no—
1251C4—81no—
1252C4—81no—
1253C4—81no—
1254C4—81no—
1255C4—81no—
1256C4—81no—
1257C4—81no—
1258C4—81no—
1259C4#349311yescharacteristic
1260C4#351411yescharacteristic
1261C4#354511yescharacteristic
1262C4#356611yescharacteristic
1263C2—42no—
1264C2—42no—
1265C2—81no—
1266C2—161no—
1267C2#4350411yescharacteristic
1268C2#6145711yescharacteristic
1269C2#6150411yescharacteristic
1270C2#6170811yescharacteristic
1271C2#6177511yescharacteristic
1272C2#6229611yescharacteristic
1273C2#6233811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#59217C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#121 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #39666C2semidirect
3. #32251C2semidirect
4. #31996C2semidirect
5. #31344C2semidirect
6. #31336C2semidirect
7. #31277C2semidirect
8. #30968C2semidirect
9. #30579C2semidirect
10. #30399C2semidirect
11. #29480C2semidirect
12. #28715C2semidirect
13. #28565C2semidirect
14. #28085C2semidirect
15. #27864C2semidirect
16. #27800C2semidirect
17. #27509C2semidirect
18. #27473C2semidirect
19. #27445C2semidirect
20. #27345C2semidirect
21. #27244C2semidirect
22. #26742C2semidirect
23. #25353C2semidirect
24. #25130C2semidirect
25. #24939C2semidirect
26. #24867C2semidirect
27. #23763C2semidirect
28. #23119C2semidirect
29. #22932C2semidirect
30. #22567C2semidirect
31. #22186C2semidirect

Maximal subgroups

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

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