Finite Group Databasebeta

← #7610388

Subgroups — #7610388

Order 512.

1589 conjugacy classes of subgroups.

The subgroup lattice has 1300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59224C211yesmaximal, characteristic
2#59114C211yesmaximal, characteristic, complemented
3#32246C211yesmaximal, characteristic, complemented
4#31852C211yesmaximal, characteristic, complemented
5#31663C211yesmaximal, characteristic, complemented
6#31381C211yesmaximal, characteristic, complemented
7#29093C211yesmaximal, characteristic, complemented
8#28981C211yesmaximal, characteristic, complemented
9#28883C211yesmaximal, characteristic, complemented
10#27821C211yesmaximal, characteristic, complemented
11#27722C211yesmaximal, characteristic, complemented
12#27712C211yesmaximal, characteristic, complemented
13#27618C211yesmaximal, characteristic, complemented
14#27564C211yesmaximal, characteristic, complemented
15#27424C211yesmaximal, characteristic, complemented
16#26974C211yesmaximal, characteristic, complemented
17#26733C211yesmaximal, characteristic, complemented
18#26671C211yesmaximal, characteristic, complemented
19#26431C211yesmaximal, characteristic, complemented
20#26226C211yesmaximal, characteristic, complemented
21#25120C211yesmaximal, characteristic
22#24538C211yesmaximal, characteristic, complemented
23#23979C211yesmaximal, characteristic
24#23933C211yesmaximal, characteristic, complemented
25#23131C211yesmaximal, characteristic, complemented
26#22864C211yesmaximal, characteristic, complemented
27#22781C211yesmaximal, characteristic, complemented
28#22494C211yesmaximal, characteristic, complemented
29#21562C211yesmaximal, characteristic, complemented
30#21404C211yesmaximal, characteristic, complemented
31#21095C211yesmaximal, characteristic, complemented
32C2×#556C2211yescharacteristic
33C2×#533C2211yescharacteristic
34C2×#465C2211yescharacteristic
35C2×#450C2211yescharacteristic
36C2×#450C2211yescharacteristic
37C2×#440C2211yescharacteristic
38C2×#435C2211yescharacteristic
39C2×#418C2211yescharacteristic
40C2×#418C2211yescharacteristic
41C2×C4×M16C2211yescharacteristic
42#2756—21no—
43#2737—21no—
44#2698—21no—
45#2674—21no—
46#2610—21no—
47#2563C2211yescharacteristic
48#2561—21no—
49#2551C2211yescharacteristic, complemented
50#2531—21no—
51#2519—21no—
52#2513C2211yescharacteristic
53#2513C2211yescharacteristic
54#2500C2211yescharacteristic
55#2499C2211yescharacteristic
56#2491C2211yescharacteristic
57#2478—21no—
58#2474—21no—
59#2472—21no—
60#2469—21no—
61#2462—21no—
62#2451C2211yescharacteristic, complemented
63#2446C2211yescharacteristic, complemented
64#2440C2211yescharacteristic
65#2439C2211yescharacteristic, complemented
66#2429C2211yescharacteristic, complemented
67#2423C2211yescharacteristic, complemented
68#2420C2211yescharacteristic
69#2415C2211yescharacteristic
70#2412—21no—
71#2408C2211yescharacteristic
72#2365—21no—
73#2363C2211yescharacteristic
74#2362C2211yescharacteristic
75#2362C2211yescharacteristic, complemented
76#2354C2211yescharacteristic
77#2352C2211yescharacteristic
78#2351C2211yescharacteristic, complemented
79#2342—21no—
80D4×C22⋊C4C2211yescharacteristic
81C4×#123C2211yescharacteristic
82#2296C2211yescharacteristic
83C2×#390C2211yescharacteristic
84#2283C2211yescharacteristic
85#2101C2211yescharacteristic, complemented
86#2101C2211yescharacteristic, complemented
87#2101C2211yescharacteristic, complemented
88#2101C2211yescharacteristic, complemented
89#2099C2211yescharacteristic, complemented
90#2099C2211yescharacteristic, complemented
91#2086C2211yescharacteristic, complemented
92#2085C2211yescharacteristic, complemented
93#2085C2211yescharacteristic, complemented
94#2077C2211yescharacteristic, complemented
95#2074C2211yescharacteristic, complemented
96#2073C2211yescharacteristic
97#2072C2211yescharacteristic, complemented
98#2071C2211yescharacteristic
99#2068C2211yescharacteristic, complemented
100#2065C2211yescharacteristic
101#2055C2211yescharacteristic
102#2055C2211yescharacteristic
103#2055C2211yescharacteristic
104#2036C2211yescharacteristic, complemented
105#2033C2211yescharacteristic
106#2024C2211yescharacteristic, complemented
107#2024C2211yescharacteristic, complemented
108#2023C2211yescharacteristic
109#2023C2211yescharacteristic
110#2023C2211yescharacteristic
111#2023C2211yescharacteristic
112#2013C2211yescharacteristic
113#2013C2211yescharacteristic
114#2000C2211yescharacteristic
115#2000C2211yescharacteristic
116#2000C2211yescharacteristic
117#1993C2211yescharacteristic, complemented
118#1993C2211yescharacteristic, complemented
119#1993C2211yescharacteristic, complemented
120#1990C2211yescharacteristic, complemented
121#1987C2211yescharacteristic, complemented
122#1987C2211yescharacteristic, complemented
123#1973C2211yescharacteristic
124#1968C2211yescharacteristic
125#1960C2211yescharacteristic, complemented
126#1960C2211yescharacteristic, complemented
127#1936C2211yescharacteristic
128#1936C2211yescharacteristic
129#1936C2211yescharacteristic
130#1936C2211yescharacteristic
131#1936C2211yescharacteristic
132#1936C2211yescharacteristic
133#1935C2211yescharacteristic, complemented
134#1934C2211yescharacteristic
135#1934C2211yescharacteristic
136#1934C2211yescharacteristic
137#1934C2211yescharacteristic
138#1933C2211yescharacteristic, complemented
139#1927C2211yescharacteristic, complemented
140#1925C2211yescharacteristic
141#1924C2211yescharacteristic, complemented
142#1923C2211yescharacteristic, complemented
143#1921C2211yescharacteristic, complemented
144#1921C2211yescharacteristic, complemented
145#1920C2211yescharacteristic, complemented
146#1920C2211yescharacteristic, complemented
147#1919C2211yescharacteristic, complemented
148#1918C2211yescharacteristic, complemented
149#1917C2211yescharacteristic, complemented
150#1916C2211yescharacteristic, complemented
151#1894C2211yescharacteristic
152#1894C2211yescharacteristic
153#1894C2211yescharacteristic
154#1894C2211yescharacteristic
155#1893C2211yescharacteristic
156#1892C2211yescharacteristic, complemented
157#1880C2211yescharacteristic
158#1880C2211yescharacteristic
159#1880C2211yescharacteristic
160#1880C2211yescharacteristic
161#1880C2211yescharacteristic
162#1880C2211yescharacteristic
163#1880C2211yescharacteristic
164#1877C2211yescharacteristic
165#1877C2211yescharacteristic
166#1877C2211yescharacteristic
167#1875C2211yescharacteristic
168#1875C2211yescharacteristic
169#1873C2211yescharacteristic, complemented
170#1873C2211yescharacteristic, complemented
171#1872C2211yescharacteristic
172#1872C2211yescharacteristic
173#1870C2211yescharacteristic
174#1865C2211yescharacteristic, complemented
175#1864C2211yescharacteristic
176#1854C2211yescharacteristic
177#1854C2211yescharacteristic
178#1851C2211yescharacteristic
179#1836C2211yescharacteristic, complemented
180#1825C2211yescharacteristic
181#1825C2211yescharacteristic
182#1825C2211yescharacteristic, complemented
183#1825C2211yescharacteristic, complemented
184#1817C2211yescharacteristic
185#1805C2211yescharacteristic, complemented
186#1804C2211yescharacteristic
187#1803C2211yescharacteristic, complemented
188#1802C2211yescharacteristic
189#1771C2211yescharacteristic, complemented
190#1770C2211yescharacteristic, complemented
191#1763C2211yescharacteristic, complemented
192C4×#103C2211yescharacteristic, complemented
193C4×#103C2211yescharacteristic, complemented
194C4×#103C2211yescharacteristic, complemented
195C4×#103C2211yescharacteristic, complemented
196C4×#102C2211yescharacteristic
197#1753C2211yescharacteristic
198#1752C2211yescharacteristic, complemented
199C8×C22⋊C4C2211yescharacteristic, complemented
200#1736C2211yescharacteristic
201#1736C2211yescharacteristic
202#1735C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C23×C8C2311yescharacteristic
211#556—24no—
212#556—42no—
213#533—24no—
214#533—42no—
215C2×C4⋊Q8—21no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×#126—21no—
221C2×#126—21no—
222C2×#125—21no—
223C2×#124—21no—
224C2×#124—21no—
225C2×#123D411yescharacteristic
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#120—21no—
235C2×C4×Q8—21no—
236C2×C4×Q8—21no—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×#117—21no—
245C2×#117—21no—
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C22⋊C4—21no—
252C22×C22⋊C4—21no—
253C22×C22⋊C4—21no—
254C22×C42C2311yescharacteristic
255#465—24no—
256#450—24no—
257#450—42no—
258#440—24no—
259#435—42no—
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267#418—24no—
268#418—42no—
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295C2×C22⋊C8C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C4×M16—42no—
299C2×#97C2311yescharacteristic
300C2×#97C2311yescharacteristic
301C2×#97C2311yescharacteristic
302C2×#97C2311yescharacteristic
303C2×C4×C8C2311yescharacteristic
304C2×C4×C8C2311yescharacteristic
305C2×C4×C8C2311yescharacteristic
306#400—21no—
307#399—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#397—21no—
314#397—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#396—21no—
322#396—21no—
323#395—21no—
324#395—21no—
325#395—21no—
326#395—21no—
327#394—21no—
328#394—21no—
329#394—21no—
330#394—21no—
331#394—21no—
332#394—21no—
333#393—21no—
334#393—21no—
335#393—21no—
336#393—21no—
337#392—21no—
338#391—21no—
339#391—21no—
340#391C2311yescharacteristic
341#391C2311yescharacteristic
342#391C2311yescharacteristic
343#391C2311yescharacteristic
344#390—21no—
345#390—21no—
346#390—21no—
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#389—21no—
356#389—21no—
357#389—21no—
358#389—21no—
359#389—21no—
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388D411yescharacteristic
387#388D411yescharacteristic
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387D411yescharacteristic
399#387D411yescharacteristic
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#386D411yescharacteristic
406#385—21no—
407#385—21no—
408#385—21no—
409#385D411yescharacteristic
410#384C2311yescharacteristic
411#384C2311yescharacteristic
412#383—21no—
413#382—21no—
414#382C2311yescharacteristic
415#382C2311yescharacteristic
416#382C2311yescharacteristic
417#382C2311yescharacteristic
418#381—21no—
419#381—21no—
420#381D411yescharacteristic
421#380—21no—
422#380—21no—
423#380—21no—
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#379—21no—
429#379—21no—
430C4×C4⋊C4—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4—21no—
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⋊C4C2311yescharacteristic
445C4×C22⋊C4C2311yescharacteristic
446C4×C22⋊C4C2311yescharacteristic
447#376—21no—
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#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25—21no—
491C22×Q8—21no—
492C22×Q8—21no—
493C22×Q8—21no—
494C22×Q8C2411yescharacteristic
495C22×Q8C2411yescharacteristic
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—22no—
501C22×D4—22no—
502C22×D4—41no—
503C22×D4—41no—
504C22×D4—41no—
505C22×D4C2×D411yescharacteristic
506C22×D4C2411yescharacteristic
507C22×D4C2411yescharacteristic
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4C2×D411yescharacteristic
512C23×C4C2×D411yescharacteristic
513C23×C4C2411yescharacteristic
514C23×C4C2411yescharacteristic
515C2×SD16—22no—
516C2×SD16—22no—
517C2×SD16—22no—
518C2×SD16—22no—
519C2×SD16—41no—
520C2×SD16—41no—
521C2×SD16—41no—
522C2×SD16—41no—
523C2×SD16—41no—
524C2×SD16—41no—
525C2×SD16—41no—
526C2×SD16—41no—
527C2×M16—22no—
528C2×M16—22no—
529C2×M16—22no—
530C2×M16—41no—
531C2×M16—41no—
532C2×M16—41no—
533C22×C8—22no—
534C22×C8—41no—
535C22×C8—41no—
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C4⋊Q8—22no—
545C4⋊Q8—22no—
546C4⋊Q8—22no—
547C4⋊Q8—41no—
548C4⋊Q8—41no—
549C4⋊Q8—41no—
550C4⋊Q8—41no—
551C4⋊Q8—41no—
552C4⋊Q8—44no—
553#126—44no—
554#126—44no—
555#125—44no—
556#124—44no—
557#124—82no—
558#123—42no—
559C22⋊Q8—22no—
560C22⋊Q8—22no—
561C22⋊Q8—22no—
562C22⋊Q8—22no—
563C22⋊Q8—22no—
564C22⋊Q8—44no—
565C22⋊Q8—41no—
566C22⋊Q8—41no—
567C22⋊Q8—82no—
568C22⋊Q8#4114yes—
569#121—22no—
570#121—41no—
571#121—41no—
572#121—41no—
573#120—82no—
574C4×Q8—22no—
575C4×Q8—22no—
576C4×Q8—22no—
577C4×Q8—22no—
578C4×Q8—41no—
579C4×Q8—41no—
580C4×Q8—41no—
581C4×Q8—41no—
582C4×Q8—44no—
583C4×Q8—44no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—41no—
588C4×D4—41no—
589C4×D4—41no—
590#117—22no—
591#117—22no—
592#117—22no—
593#117—22no—
594#117—44no—
595#117—41no—
596#117—41no—
597#117—41no—
598#117—41no—
599#117—82no—
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⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—41no—
627C2×C4⋊C4—41no—
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—44no—
678C2×C22⋊C4—82no—
679C2×C22⋊C4—82no—
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C42—22no—
689C2×C42—22no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—21no—
699C2×C42—21no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42C2×D411yescharacteristic
703C2×C42C2×D411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709#107—22no—
710#107—41no—
711#106—22no—
712#106—41no—
713C4⋊C8—41no—
714C4⋊C8—41no—
715C4⋊C8—41no—
716#103—22no—
717#103—22no—
718#103—41no—
719#103—41no—
720#103—41no—
721#103—41no—
722#103—41no—
723#103—41no—
724#103—41no—
725#103—41no—
726#103—41no—
727#103—41no—
728#102—22no—
729#102—22no—
730#102—22no—
731#102—22no—
732#102—22no—
733#102—41no—
734#102—41no—
735#102—41no—
736#102—41no—
737#102—41no—
738#102—41no—
739#102#4114yes—
740C22⋊C8—22no—
741C22⋊C8—22no—
742C22⋊C8—41no—
743C22⋊C8—41no—
744C22⋊C8—41no—
745#97—22no—
746#97—41no—
747#97—41no—
748#97—41no—
749C4×C8—41no—
750C4×C8—41no—
751C4×C8—41no—
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#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794C24—21no—
795C24—21no—
796C24—42no—
797C24—42no—
798C24—42no—
799C24—42no—
800C24—81no—
801C24—81no—
802C24—81no—
803C24C22×D411yescharacteristic
804C24C22×D411yescharacteristic
805C2×Q8—21no—
806C2×Q8—21no—
807C2×Q8—21no—
808C2×Q8—21no—
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—42no—
817C2×Q8—42no—
818C2×Q8—42no—
819C2×Q8—42no—
820C2×Q8—81no—
821C2×Q8—81no—
822C2×Q8—81no—
823C2×Q8—81no—
824C2×Q8—81no—
825C2×Q8C2×#4112yes—
826C2×D4—22no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—44no—
839C2×D4—44no—
840C2×D4—41no—
841C2×D4—41no—
842C2×D4—42no—
843C2×D4—42no—
844C2×D4—42no—
845C2×D4—82no—
846C2×D4—82no—
847C2×D4—81no—
848C2×D4—81no—
849C2×D4—81no—
850C2×D4—81no—
851C2×D4—81no—
852C2×D4—81no—
853C2×D4C2×#4112yes—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—22no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—21no—
865C22×C4—21no—
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—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—41no—
882C22×C4—41no—
883C22×C4—41no—
884C22×C4—42no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—42no—
888C22×C4—81no—
889C22×C4—81no—
890C22×C4—81no—
891C22×C4—81no—
892C22×C4—81no—
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C2×#4112yes—
906C22×C4H(5,𝔽2)12yes—
907C22×C4C2511yescharacteristic
908SD16—44no—
909SD16—82no—
910SD16—82no—
911SD16—82no—
912M16—44no—
913M16—44no—
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—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—82no—
938C2×C8C2×#4112yes—
939C4⋊C4—24no—
940C4⋊C4—22no—
941C4⋊C4—22no—
942C4⋊C4—22no—
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—21no—
964C4⋊C4—21no—
965C4⋊C4—41no—
966C4⋊C4—41no—
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—42no—
981C4⋊C4—42no—
982C4⋊C4—42no—
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—81no—
992C4⋊C4C2×#4112yes—
993C4⋊C4C2×#4112yes—
994C22⋊C4—24no—
995C22⋊C4—22no—
996C22⋊C4—22no—
997C22⋊C4—22no—
998C22⋊C4—22no—
999C22⋊C4—22no—
1000C22⋊C4—41no—
1001C22⋊C4—41no—
1002C22⋊C4—41no—
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—42no—
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—
1033C22⋊C4—81no—
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—42no—
1047C42—42no—
1048C42—42no—
1049C42—42no—
1050C42—42no—
1051C42—42no—
1052C42—42no—
1053C42—42no—
1054C42—42no—
1055C42—81no—
1056C42—81no—
1057C42—81no—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—22no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—41no—
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—84no—
1086C23—84no—
1087C23—84no—
1088C23—84no—
1089C23—162no—
1090C23—162no—
1091C23—162no—
1092C23#54612yes—
1093C23C23×D411yescharacteristic
1094Q8—22no—
1095Q8—22no—
1096Q8—41no—
1097Q8—41no—
1098Q8—41no—
1099Q8—41no—
1100Q8—41no—
1101Q8—41no—
1102Q8—84no—
1103Q8—84no—
1104Q8—162no—
1105D4—22no—
1106D4—22no—
1107D4—41no—
1108D4—41no—
1109D4—41no—
1110D4—41no—
1111D4—41no—
1112D4—41no—
1113D4—84no—
1114D4—82no—
1115D4—162no—
1116D4—162no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—21no—
1128C2×C4—21no—
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—22no—
1141C2×C4—22no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—22no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—44no—
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—41no—
1201C2×C4—82no—
1202C2×C4—84no—
1203C2×C4—162no—
1204C2×C4—162no—
1205C2×C4#54612yes—
1206C2×C4#57512yes—
1207C2×C4#57712yes—
1208C2×C4C22×#4111yescharacteristic
1209C2×C4C22×#4111yescharacteristic
1210C2×C4C2×H(5,𝔽2)11yescharacteristic
1211C2×C4#58511yescharacteristic
1212C2×C4#58511yescharacteristic
1213C2×C4#58511yescharacteristic
1214C8—22no—
1215C8—41no—
1216C8—41no—
1217C8—41no—
1218C8—41no—
1219C8—41no—
1220C8—41no—
1221C8—41no—
1222C22—22no—
1223C22—22no—
1224C22—22no—
1225C22—41no—
1226C22—41no—
1227C22—41no—
1228C22—41no—
1229C22—41no—
1230C22—42no—
1231C22—41no—
1232C22—41no—
1233C22—42no—
1234C22—41no—
1235C22—41no—
1236C22—41no—
1237C22—42no—
1238C22—41no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—168no—
1251C22C2×#54611yescharacteristic
1252C22D4×#4111yescharacteristic
1253C22#350011yescharacteristic
1254C22C2×#57511yescharacteristic
1255C22C2×#57711yescharacteristic
1256C22#358511yescharacteristic
1257C22#358611yescharacteristic
1258C4—22no—
1259C4—22no—
1260C4—22no—
1261C4—41no—
1262C4—41no—
1263C4—41no—
1264C4—42no—
1265C4—41no—
1266C4—41no—
1267C4—41no—
1268C4—42no—
1269C4—41no—
1270C4—41no—
1271C4—41no—
1272C4—42no—
1273C4—81no—
1274C4—81no—
1275C4—81no—
1276C4—81no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C4—81no—
1284C4#347511yescharacteristic
1285C4#351311yescharacteristic
1286C4#352111yescharacteristic
1287C4#353311yescharacteristic
1288C2—42no—
1289C2—81no—
1290C2—82no—
1291C2—161no—
1292C2#5980511yescharacteristic
1293C2#6116611yescharacteristic
1294C2#6118511yescharacteristic
1295C2#6144811yescharacteristic
1296C2#6150311yescharacteristic
1297C2#6258511yescharacteristic
1298C2#6260811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2408C22
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
2. #59114C2semidirect
3. #32246C2semidirect
4. #31852C2semidirect
5. #31663C2semidirect
6. #31381C2semidirect
7. #29093C2semidirect
8. #28981C2semidirect
9. #28883C2semidirect
10. #27821C2semidirect
11. #27722C2semidirect
12. #27712C2semidirect
13. #27618C2semidirect
14. #27564C2semidirect
15. #27424C2semidirect
16. #26974C2semidirect
17. #26733C2semidirect
18. #26671C2semidirect
19. #26431C2semidirect
20. #26226C2semidirect
22. #24538C2semidirect
24. #23933C2semidirect
25. #23131C2semidirect
26. #22864C2semidirect
27. #22781C2semidirect
28. #22494C2semidirect
29. #21562C2semidirect
30. #21404C2semidirect
31. #21095C2semidirect
49. #2551C22semidirect
62. #2451C22semidirect
63. #2446C22semidirect
65. #2439C22semidirect
66. #2429C22semidirect
67. #2423C22semidirect
75. #2362C22semidirect
78. #2351C22semidirect
85. #2101C22semidirect
86. #2101C22semidirect
87. #2101C22semidirect
88. #2101C22semidirect
89. #2099C22semidirect
90. #2099C22semidirect
91. #2086C22semidirect
92. #2085C22semidirect
93. #2085C22semidirect
94. #2077C22semidirect
95. #2074C22semidirect
97. #2072C22semidirect
99. #2068C22semidirect
104. #2036C22semidirect
106. #2024C22semidirect
107. #2024C22semidirect
117. #1993C22semidirect
118. #1993C22semidirect
119. #1993C22semidirect
120. #1990C22semidirect
121. #1987C22semidirect
122. #1987C22semidirect
125. #1960C22semidirect
126. #1960C22semidirect
133. #1935C22semidirect
138. #1933C22semidirect
139. #1927C22semidirect
141. #1924C22semidirect
142. #1923C22semidirect
143. #1921C22semidirect
144. #1921C22semidirect
145. #1920C22semidirect
146. #1920C22semidirect
147. #1919C22semidirect
148. #1918C22semidirect
149. #1917C22semidirect
150. #1916C22semidirect
156. #1892C22semidirect
169. #1873C22semidirect
170. #1873C22semidirect
174. #1865C22semidirect
179. #1836C22semidirect
182. #1825C22semidirect
183. #1825C22semidirect
185. #1805C22semidirect
187. #1803C22semidirect
189. #1771C22semidirect
190. #1770C22semidirect
191. #1763C22semidirect
192. C4×#103C22semidirect
193. C4×#103C22semidirect
194. C4×#103C22semidirect
195. C4×#103C22semidirect
198. #1752C22semidirect
199. C8×C22⋊C4C22semidirect
202. #1735C22semidirect

Maximal subgroups

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

subgroupindex
#592242
#591142
#322462
#318522
#316632
#313812
#290932
#289812
#288832
#278212
#277222
#277122
#276182
#275642
#274242
#269742
#267332
#266712
#264312
#262262
#251202
#245382
#239792
#239332
#231312
#228642
#227812
#224942
#215622
#214042
#210952