Finite Group Databasebeta

← #7208321

Subgroups — #7208321

Order 512.

1610 conjugacy classes of subgroups.

The subgroup lattice has 1417 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45600C211yesmaximal, characteristic, complemented
2#45508C211yesmaximal, characteristic, complemented
3#32936C211yesmaximal, characteristic, complemented
4#32935C211yesmaximal, characteristic, complemented
5#32709C211yesmaximal, characteristic, complemented
6#32707C211yesmaximal, characteristic, complemented
7#32045C211yesmaximal, characteristic, complemented
8#32040C211yesmaximal, characteristic, complemented
9#31567C211yesmaximal, characteristic, complemented
10#31561C211yesmaximal, characteristic, complemented
11#31513C211yesmaximal, characteristic, complemented
12#31507C211yesmaximal, characteristic, complemented
13#31499C211yesmaximal, characteristic, complemented
14#31498C211yesmaximal, characteristic, complemented
15#31411C211yesmaximal, characteristic, complemented
16#31399C211yesmaximal, characteristic, complemented
17#31389C211yesmaximal, characteristic, complemented
18#31385C211yesmaximal, characteristic, complemented
19#28493C211yesmaximal, characteristic, complemented
20#28237C211yesmaximal, characteristic, complemented
21#28224C211yesmaximal, characteristic, complemented
22#27854C211yesmaximal, characteristic, complemented
23#27845C211yesmaximal, characteristic, complemented
24#27665C211yesmaximal, characteristic, complemented
25#25421C211yesmaximal, characteristic, complemented
26#25416C211yesmaximal, characteristic, complemented
27#25048C211yesmaximal, characteristic, complemented
28#25036C211yesmaximal, characteristic, complemented
29#24786C211yesmaximal, characteristic, complemented
30#24778C211yesmaximal, characteristic, complemented
31#21439C211yesmaximal, characteristic, complemented
32C23×M16C2211yescharacteristic
33C2×#496C2211yescharacteristic, complemented
34C2×#469C2211yescharacteristic
35C2×#469C2211yescharacteristic
36C2×#468C2211yescharacteristic
37C2×#468C2211yescharacteristic
38C2×#466C2211yescharacteristic
39C2×#466C2211yescharacteristic, complemented
40C2×#465C2211yescharacteristic
41C2×#465C2211yescharacteristic, complemented
42C2×#442C2211yescharacteristic, complemented
43C2×C4×SD16C2211yescharacteristic, complemented
44C2×#435C2211yescharacteristic
45C2×#435C2211yescharacteristic
46C2×C8×D4C2211yescharacteristic
47C2×#427C2211yescharacteristic, complemented
48#2848C2211yescharacteristic
49#2847C2211yescharacteristic
50#2847C2211yescharacteristic
51#2847C2211yescharacteristic
52#2825—21no—
53#2812—21no—
54#2797—21no—
55#2797—21no—
56#2796—21no—
57#2778—21no—
58#2778—21no—
59#2757—21no—
60#2749—21no—
61#2746—21no—
62#2709—21no—
63#2688—21no—
64#2678—21no—
65#2669—21no—
66#2541C2211yescharacteristic
67#2540C2211yescharacteristic
68#2537C2211yescharacteristic
69#2536C2211yescharacteristic
70#2535C2211yescharacteristic
71#2535C2211yescharacteristic
72#2497C2211yescharacteristic
73#2495C2211yescharacteristic
74#2494C2211yescharacteristic
75#2494C2211yescharacteristic
76#2485C2211yescharacteristic
77#2485C2211yescharacteristic
78#2428C2211yescharacteristic
79#2428C2211yescharacteristic
80#2427C2211yescharacteristic
81#2426C2211yescharacteristic
82#2422C2211yescharacteristic
83#2421C2211yescharacteristic
84#2420C2211yescharacteristic
85#2420C2211yescharacteristic
86#2415C2211yescharacteristic
87#2414C2211yescharacteristic
88#2414C2211yescharacteristic
89#2414C2211yescharacteristic
90#2377—21no—
91#2375—21no—
92C4×#120C2211yescharacteristic
93#2101C2211yescharacteristic, complemented
94#2101C2211yescharacteristic, complemented
95#2101C2211yescharacteristic, complemented
96#2099C2211yescharacteristic, complemented
97#2088C2211yescharacteristic, complemented
98#2088C2211yescharacteristic, complemented
99#2077C2211yescharacteristic
100#2077C2211yescharacteristic
101#2077C2211yescharacteristic
102#2076C2211yescharacteristic
103#2076C2211yescharacteristic
104#2075C2211yescharacteristic
105#2073C2211yescharacteristic, complemented
106#2073C2211yescharacteristic, complemented
107#2073C2211yescharacteristic, complemented
108#2072C2211yescharacteristic, complemented
109#2066C2211yescharacteristic, complemented
110#2065C2211yescharacteristic, complemented
111#2065C2211yescharacteristic, complemented
112#2065C2211yescharacteristic, complemented
113#2042C2211yescharacteristic, complemented
114#2042C2211yescharacteristic, complemented
115#2041C2211yescharacteristic, complemented
116#2041C2211yescharacteristic, complemented
117#2036C2211yescharacteristic
118#2036C2211yescharacteristic
119#2036C2211yescharacteristic, complemented
120#2035C2211yescharacteristic
121#2034C2211yescharacteristic
122#2034C2211yescharacteristic
123#2034C2211yescharacteristic
124#2034C2211yescharacteristic
125#2034C2211yescharacteristic
126#2034C2211yescharacteristic, complemented
127#2033C2211yescharacteristic
128#2033C2211yescharacteristic
129#2033C2211yescharacteristic
130#2033C2211yescharacteristic
131#2033C2211yescharacteristic, complemented
132#2033C2211yescharacteristic, complemented
133#2000C2211yescharacteristic
134#2000C2211yescharacteristic
135#2000C2211yescharacteristic
136#2000C2211yescharacteristic, complemented
137#1999C2211yescharacteristic
138#1999C2211yescharacteristic
139#1999C2211yescharacteristic
140#1999C2211yescharacteristic, complemented
141#1983C2211yescharacteristic, complemented
142#1982C2211yescharacteristic, complemented
143#1973C2211yescharacteristic, complemented
144#1970C2211yescharacteristic, complemented
145#1944C2211yescharacteristic, complemented
146#1944C2211yescharacteristic, complemented
147#1943C2211yescharacteristic, complemented
148#1942C2211yescharacteristic, complemented
149#1921C2211yescharacteristic, complemented
150#1920C2211yescharacteristic, complemented
151#1918C2211yescharacteristic, complemented
152#1918C2211yescharacteristic, complemented
153#1895C2211yescharacteristic
154#1895C2211yescharacteristic
155#1895C2211yescharacteristic
156#1895C2211yescharacteristic
157#1895C2211yescharacteristic
158#1895C2211yescharacteristic
159#1894C2211yescharacteristic
160#1894C2211yescharacteristic
161#1893C2211yescharacteristic
162#1893C2211yescharacteristic
163#1893C2211yescharacteristic
164#1892C2211yescharacteristic
165#1880C2211yescharacteristic, complemented
166#1879C2211yescharacteristic, complemented
167#1879C2211yescharacteristic, complemented
168#1877C2211yescharacteristic, complemented
169#1875C2211yescharacteristic, complemented
170#1875C2211yescharacteristic, complemented
171#1875C2211yescharacteristic, complemented
172#1873C2211yescharacteristic, complemented
173#1870C2211yescharacteristic
174#1870C2211yescharacteristic
175#1869C2211yescharacteristic
176#1865C2211yescharacteristic, complemented
177#1862C2211yescharacteristic, complemented
178#1862C2211yescharacteristic, complemented
179#1862C2211yescharacteristic, complemented
180#1851C2211yescharacteristic
181#1851C2211yescharacteristic
182#1850C2211yescharacteristic
183#1847C2211yescharacteristic, complemented
184#1846C2211yescharacteristic, complemented
185#1825C2211yescharacteristic, complemented
186#1825C2211yescharacteristic, complemented
187#1809C2211yescharacteristic
188#1809C2211yescharacteristic
189#1809C2211yescharacteristic
190#1809C2211yescharacteristic
191#1808C2211yescharacteristic
192#1807C2211yescharacteristic
193#1807C2211yescharacteristic, complemented
194#1805C2211yescharacteristic, complemented
195#1804C2211yescharacteristic, complemented
196#1804C2211yescharacteristic, complemented
197#1802C2211yescharacteristic, complemented
198#1779C2211yescharacteristic
199#1776C2211yescharacteristic, complemented
200#1753C2211yescharacteristic
201#1753C2211yescharacteristic
202#1752C2211yescharacteristic
203C24×C4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×M16—42no—
209C22×M16—42no—
210C22×M16—42no—
211C22×M16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213C22×M16C2311yescharacteristic
214C22×M16C2311yescharacteristic
215C23×C8C2311yescharacteristic
216C23×C8C2311yescharacteristic
217C23×C8C2311yescharacteristic
218C2×#127—21no—
219C2×#127C2311yescharacteristic
220C2×#124C2311yescharacteristic
221C2×#123—21no—
222C2×C22⋊Q8C2311yescharacteristic
223C2×C22⋊Q8C2311yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×#121—21no—
227C2×#121—21no—
228C2×#121—21no—
229C2×#121C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×#121C2311yescharacteristic
241C2×#120—21no—
242C2×#120—21no—
243C2×#120—21no—
244C2×#120D411yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254#496—42no—
255#469—42no—
256#469—42no—
257#468—42no—
258#468—42no—
259#466—42no—
260#466—42no—
261#465—42no—
262#465—42no—
263#442—42no—
264C4×SD16—42no—
265#435—42no—
266#435—42no—
267C8×D4—42no—
268#427—42no—
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×#97C2311yescharacteristic
318C2×#97C2311yescharacteristic
319C2×C4×C8C2311yescharacteristic
320#401—21no—
321#401—21no—
322#400—21no—
323#400—21no—
324#400—21no—
325#399—21no—
326#398—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#396—21no—
341#396—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#392—21no—
359#392—21no—
360#392—21no—
361#392—21no—
362#392—21no—
363#392—21no—
364#392—21no—
365#392—21no—
366#392—21no—
367#392—21no—
368#391C2311yescharacteristic
369#390—21no—
370#390—21no—
371#390—21no—
372#390—21no—
373#390—21no—
374#390—21no—
375#390—21no—
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#389—21no—
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#386D411yescharacteristic
427#386D411yescharacteristic
428#386D411yescharacteristic
429#385—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#385D411yescharacteristic
434#385D411yescharacteristic
435#385D411yescharacteristic
436#384C2311yescharacteristic
437#383—21no—
438#382C2311yescharacteristic
439#382C2311yescharacteristic
440#382C2311yescharacteristic
441#381—21no—
442#381—21no—
443#380—21no—
444#380—21no—
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#380C2311yescharacteristic
459#379—21no—
460#379D411yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C22⋊C4C2311yescharacteristic
464C4×C22⋊C4C2311yescharacteristic
465C4×C22⋊C4C2311yescharacteristic
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#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25C2×D411yescharacteristic
497C22×Q8C2411yescharacteristic
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4C2×D411yescharacteristic
513C22×D4C2×D411yescharacteristic
514C22×D4C2×D411yescharacteristic
515C22×D4C2411yescharacteristic
516C22×D4C2411yescharacteristic
517C22×D4C2411yescharacteristic
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—41no—
522C23×C4—41no—
523C23×C4—41no—
524C23×C4—41no—
525C23×C4—41no—
526C23×C4—41no—
527C23×C4C2×D411yescharacteristic
528C23×C4C2×D411yescharacteristic
529C23×C4C2×D411yescharacteristic
530C23×C4C2411yescharacteristic
531C23×C4C2411yescharacteristic
532C23×C4C2411yescharacteristic
533C23×C4C2411yescharacteristic
534C2×SD16—22no—
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×D8—22no—
541C2×D8—22no—
542C2×D8—22no—
543C2×D8—41no—
544C2×D8—41no—
545C2×D8—41no—
546C2×M16—22no—
547C2×M16—22no—
548C2×M16—22no—
549C2×M16—22no—
550C2×M16—22no—
551C2×M16—22no—
552C2×M16—41no—
553C2×M16—41no—
554C2×M16—41no—
555C2×M16—41no—
556C2×M16—41no—
557C2×M16—41no—
558C2×M16—416no—
559C22×C8—22no—
560C22×C8—22no—
561C22×C8—22no—
562C22×C8—22no—
563C22×C8—22no—
564C22×C8—22no—
565C22×C8—41no—
566C22×C8—41no—
567C22×C8—41no—
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C22×C8C2411yescharacteristic
576#127—41no—
577#127—41no—
578#127—82no—
579#124—41no—
580#124—41no—
581#123—82no—
582C22⋊Q8—41no—
583C22⋊Q8—41no—
584C22⋊Q8—41no—
585C22⋊Q8—41no—
586C22⋊Q8—41no—
587C22⋊Q8—41no—
588C22⋊Q8—41no—
589C22⋊Q8—41no—
590#121—44no—
591#121—41no—
592#121—41no—
593#121—41no—
594#121—41no—
595#121—41no—
596#121—41no—
597#121—41no—
598#121—41no—
599#121—41no—
600#121—41no—
601#121—41no—
602#121—41no—
603#121—41no—
604#121—41no—
605#121—41no—
606#121—41no—
607#121—41no—
608#121—41no—
609#121—41no—
610#121—41no—
611#121—41no—
612#121—41no—
613#121—41no—
614#121—41no—
615#121—82no—
616#121—82no—
617#120—42no—
618#120—44no—
619#120—82no—
620#120—82no—
621C4×Q8—41no—
622C4×Q8—41no—
623C4×D4—41no—
624C4×D4—41no—
625C4×D4—41no—
626C4×D4—41no—
627C4×D4—41no—
628C4×D4—41no—
629C4×D4—41no—
630C4×D4—41no—
631C4×D4—41no—
632C4×D4—41no—
633C4×D4—41no—
634C4×D4—41no—
635#117—41no—
636#117—41no—
637#117—41no—
638#117—41no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
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—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C22⋊C4C2×D411yescharacteristic
724C2×C42—21no—
725C2×C42—21no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—21no—
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732#107—22no—
733#107—22no—
734#107—22no—
735#107—41no—
736#107—41no—
737#107—41no—
738#106—22no—
739#106—22no—
740#106—22no—
741#106—41no—
742#106—41no—
743#106—41no—
744C4⋊C8—41no—
745C4⋊C8—41no—
746C4⋊C8—41no—
747#103—41no—
748#103—41no—
749#103—41no—
750#103—41no—
751#103—41no—
752#103—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770#102—41no—
771C22⋊C8—41no—
772C22⋊C8—41no—
773C22⋊C8—41no—
774C22⋊C8—41no—
775C22⋊C8—41no—
776C22⋊C8—41no—
777C22⋊C8—41no—
778C22⋊C8—41no—
779C22⋊C8—41no—
780#97—22no—
781#97—22no—
782C4×C8—22no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821C24—22no—
822C24—21no—
823C24—21no—
824C24—21no—
825C24—41no—
826C24—41no—
827C24—41no—
828C24—41no—
829C24—41no—
830C24—41no—
831C24C22×D411yescharacteristic
832C24C22×D411yescharacteristic
833C24C22×D411yescharacteristic
834C24C22×D411yescharacteristic
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×D4—22no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—41no—
861C2×D4—41no—
862C2×D4—41no—
863C2×D4—41no—
864C2×D4—41no—
865C2×D4—41no—
866C2×D4—41no—
867C2×D4—41no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4—81no—
890C2×D4—81no—
891C2×D4—81no—
892C2×D4—81no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D4—81no—
906C2×D4—81no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4—81no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—41no—
948C22×C4—41no—
949C22×C4—41no—
950C22×C4—41no—
951C22×C4—41no—
952C22×C4—41no—
953C22×C4—41no—
954C22×C4—41no—
955C22×C4—41no—
956C22×C4—42no—
957C22×C4—44no—
958C22×C4—44no—
959C22×C4—44no—
960C22×C4—44no—
961C22×C4—81no—
962C22×C4—81no—
963C22×C4—81no—
964C22×C4—81no—
965C22×C4—81no—
966C22×C4—81no—
967C22×C4—81no—
968C22×C4—81no—
969C22×C4C22×D411yescharacteristic
970C22×C4C22×D411yescharacteristic
971C22×C4C22×D411yescharacteristic
972C22×C4C22×D411yescharacteristic
973C22×C4C22×D411yescharacteristic
974C22×C4C22×D411yescharacteristic
975C22×C4C22×D411yescharacteristic
976C22×C4C22×D411yescharacteristic
977C22×C4C22×D411yescharacteristic
978C22×C4C22×D411yescharacteristic
979C22×C4C2511yescharacteristic
980SD16—44no—
981SD16—82no—
982D8—44no—
983D8—82no—
984M16—44no—
985M16—44no—
986M16—44no—
987M16—44no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—21no—
1008C2×C8—21no—
1009C2×C8—44no—
1010C2×C8—44no—
1011C2×C8—44no—
1012C2×C8H(5,𝔽2)12yes—
1013C2×C8H(5,𝔽2)12yes—
1014C2×C8H(5,𝔽2)12yes—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—41no—
1040C4⋊C4—41no—
1041C4⋊C4—41no—
1042C4⋊C4—42no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4—81no—
1051C4⋊C4—81no—
1052C4⋊C4—81no—
1053C4⋊C4—81no—
1054C4⋊C4—81no—
1055C4⋊C4—81no—
1056C4⋊C4—81no—
1057C22⋊C4—22no—
1058C22⋊C4—41no—
1059C22⋊C4—41no—
1060C22⋊C4—41no—
1061C22⋊C4—41no—
1062C22⋊C4—41no—
1063C22⋊C4—41no—
1064C22⋊C4—41no—
1065C22⋊C4—41no—
1066C22⋊C4—41no—
1067C22⋊C4—41no—
1068C22⋊C4—41no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C22⋊C4—81no—
1101C22⋊C4—81no—
1102C22⋊C4—81no—
1103C22⋊C4—81no—
1104C22⋊C4—81no—
1105C22⋊C4—81no—
1106C22⋊C4—81no—
1107C22⋊C4—81no—
1108C22⋊C4—81no—
1109C22⋊C4—81no—
1110C22⋊C4—81no—
1111C22⋊C4—81no—
1112C42—21no—
1113C42—21no—
1114C42—21no—
1115C42—21no—
1116C42—21no—
1117C42—21no—
1118C42—81no—
1119C42—81no—
1120C42—81no—
1121C42—81no—
1122C42—81no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—21no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23—44no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—82no—
1173C23—82no—
1174C23—82no—
1175C23—82no—
1176C23—82no—
1177C23—82no—
1178C23#57512yes—
1179C23C23×D411yescharacteristic
1180Q8—41no—
1181Q8—41no—
1182Q8—41no—
1183Q8—41no—
1184D4—44no—
1185D4—41no—
1186D4—41no—
1187D4—41no—
1188D4—41no—
1189D4—41no—
1190D4—41no—
1191D4—41no—
1192D4—41no—
1193D4—41no—
1194D4—41no—
1195D4—41no—
1196D4—41no—
1197D4—82no—
1198D4—82no—
1199D4—162no—
1200D4—162no—
1201D4—162no—
1202D4—162no—
1203D4—162no—
1204D4—162no—
1205D4—162no—
1206D4—162no—
1207D4—162no—
1208D4—162no—
1209D4—162no—
1210D4—162no—
1211D4—162no—
1212D4—162no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—44no—
1244C2×C4—44no—
1245C2×C4—44no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—162no—
1302C2×C4—162no—
1303C2×C4—162no—
1304C2×C4C2×H(5,𝔽2)11yescharacteristic
1305C2×C4C2×H(5,𝔽2)11yescharacteristic
1306C2×C4C2×H(5,𝔽2)11yescharacteristic
1307C2×C4#58511yescharacteristic
1308C2×C4#58511yescharacteristic
1309C2×C4#58511yescharacteristic
1310C8—41no—
1311C8—41no—
1312C8—41no—
1313C8—41no—
1314C8—41no—
1315C8—41no—
1316C8—41no—
1317C8#56014yes—
1318C22—22no—
1319C22—22no—
1320C22—22no—
1321C22—41no—
1322C22—41no—
1323C22—41no—
1324C22—41no—
1325C22—41no—
1326C22—41no—
1327C22—41no—
1328C22—41no—
1329C22—41no—
1330C22—41no—
1331C22—41no—
1332C22—41no—
1333C22—41no—
1334C22—41no—
1335C22—41no—
1336C22—41no—
1337C22—41no—
1338C22—41no—
1339C22—41no—
1340C22—41no—
1341C22—41no—
1342C22—41no—
1343C22—41no—
1344C22—41no—
1345C22—41no—
1346C22—88no—
1347C22—81no—
1348C22—81no—
1349C22—81no—
1350C22—81no—
1351C22—81no—
1352C22—81no—
1353C22—81no—
1354C22—81no—
1355C22—81no—
1356C22—81no—
1357C22—81no—
1358C22—81no—
1359C22—81no—
1360C22—81no—
1361C22—81no—
1362C22—81no—
1363C22—81no—
1364C22—81no—
1365C22—81no—
1366C22—81no—
1367C22—81no—
1368C22#349611yescharacteristic
1369C22#349611yescharacteristic
1370C22#349611yescharacteristic
1371C22C2×#57511yescharacteristic
1372C22#358411yescharacteristic
1373C22#358511yescharacteristic
1374C22#358511yescharacteristic
1375C4—41no—
1376C4—41no—
1377C4—41no—
1378C4—41no—
1379C4—41no—
1380C4—41no—
1381C4—41no—
1382C4—41no—
1383C4—41no—
1384C4—41no—
1385C4—81no—
1386C4—81no—
1387C4—81no—
1388C4—81no—
1389C4—81no—
1390C4—81no—
1391C4—81no—
1392C4—81no—
1393C4—81no—
1394C4—81no—
1395C4—81no—
1396C4—81no—
1397C4—81no—
1398C4C2×#56011yescharacteristic
1399C4#353911yescharacteristic
1400C4#353911yescharacteristic
1401C4#354011yescharacteristic
1402C2—42no—
1403C2—81no—
1404C2—81no—
1405C2—81no—
1406C2—161no—
1407C2—161no—
1408C2—161no—
1409C2#4547811yescharacteristic
1410C2#6225511yescharacteristic
1411C2#6228611yescharacteristic
1412C2#6229811yescharacteristic
1413C2#6230111yescharacteristic
1414C2#6231011yescharacteristic
1415C2#6232011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#120 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45600C2semidirect
2. #45508C2semidirect
3. #32936C2semidirect
4. #32935C2semidirect
5. #32709C2semidirect
6. #32707C2semidirect
7. #32045C2semidirect
8. #32040C2semidirect
9. #31567C2semidirect
10. #31561C2semidirect
11. #31513C2semidirect
12. #31507C2semidirect
13. #31499C2semidirect
14. #31498C2semidirect
15. #31411C2semidirect
16. #31399C2semidirect
17. #31389C2semidirect
18. #31385C2semidirect
19. #28493C2semidirect
20. #28237C2semidirect
21. #28224C2semidirect
22. #27854C2semidirect
23. #27845C2semidirect
24. #27665C2semidirect
25. #25421C2semidirect
26. #25416C2semidirect
27. #25048C2semidirect
28. #25036C2semidirect
29. #24786C2semidirect
30. #24778C2semidirect
31. #21439C2semidirect
33. C2×#496C22semidirect
39. C2×#466C22semidirect
41. C2×#465C22semidirect
42. C2×#442C22semidirect
43. C2×C4×SD16C22semidirect
47. C2×#427C22semidirect
93. #2101C22semidirect
94. #2101C22semidirect
95. #2101C22semidirect
96. #2099C22semidirect
97. #2088C22semidirect
98. #2088C22semidirect
105. #2073C22semidirect
106. #2073C22semidirect
107. #2073C22semidirect
108. #2072C22semidirect
109. #2066C22semidirect
110. #2065C22semidirect
111. #2065C22semidirect
112. #2065C22semidirect
113. #2042C22semidirect
114. #2042C22semidirect
115. #2041C22semidirect
116. #2041C22semidirect
119. #2036C22semidirect
126. #2034C22semidirect
131. #2033C22semidirect
132. #2033C22semidirect
136. #2000C22semidirect
140. #1999C22semidirect
141. #1983C22semidirect
142. #1982C22semidirect
143. #1973C22semidirect
144. #1970C22semidirect
145. #1944C22semidirect
146. #1944C22semidirect
147. #1943C22semidirect
148. #1942C22semidirect
149. #1921C22semidirect
150. #1920C22semidirect
151. #1918C22semidirect
152. #1918C22semidirect
165. #1880C22semidirect
166. #1879C22semidirect
167. #1879C22semidirect
168. #1877C22semidirect
169. #1875C22semidirect
170. #1875C22semidirect
171. #1875C22semidirect
172. #1873C22semidirect
176. #1865C22semidirect
177. #1862C22semidirect
178. #1862C22semidirect
179. #1862C22semidirect
183. #1847C22semidirect
184. #1846C22semidirect
185. #1825C22semidirect
186. #1825C22semidirect
193. #1807C22semidirect
194. #1805C22semidirect
195. #1804C22semidirect
196. #1804C22semidirect
197. #1802C22semidirect
199. #1776C22semidirect

Maximal subgroups

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

subgroupindex
#456002
#455082
#329362
#329352
#327092
#327072
#320452
#320402
#315672
#315612
#315132
#315072
#314992
#314982
#314112
#313992
#313892
#313852
#284932
#282372
#282242
#278542
#278452
#276652
#254212
#254162
#250482
#250362
#247862
#247782
#214392