Finite Group Databasebeta

← #6796295

Subgroups — #6796295

Order 512.

1720 conjugacy classes of subgroups.

The subgroup lattice has 1421 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37857C211yesmaximal, characteristic, complemented
2#37662C211yesmaximal, characteristic, complemented
3#33055C211yesmaximal, characteristic, complemented
4#31961C211yesmaximal, characteristic, complemented
5#31835C211yesmaximal, characteristic, complemented
6#31750C211yesmaximal, characteristic, complemented
7#31714C211yesmaximal, characteristic, complemented
8#31359C211yesmaximal, characteristic, complemented
9#31286C211yesmaximal, characteristic, complemented
10#30646C211yesmaximal, characteristic, complemented
11#30539C211yesmaximal, characteristic, complemented
12#29778C211yesmaximal, characteristic, complemented
13#29742C211yesmaximal, characteristic, complemented
14#29169C211yesmaximal, characteristic, complemented
15#28584C211yesmaximal, characteristic, complemented
16#27871C211yesmaximal, characteristic, complemented
17#27525C211yesmaximal, characteristic, complemented
18#27403C211yesmaximal, characteristic, complemented
19#27357C211yesmaximal, characteristic, complemented
20#27112C211yesmaximal, characteristic, complemented
21#26730C211yesmaximal, characteristic, complemented
22#26656C211yesmaximal, characteristic, complemented
23#26634C211yesmaximal, characteristic, complemented
24#25508C211yesmaximal, characteristic, complemented
25#24913C211yesmaximal, characteristic, complemented
26#24555C211yesmaximal, characteristic, complemented
27#24378C211yesmaximal, characteristic, complemented
28#21897C211yesmaximal, characteristic, complemented
29#21767C211yesmaximal, characteristic, complemented
30#21529C211yesmaximal, characteristic, complemented
31#21050C211yesmaximal, characteristic, complemented
32C2×#540C2211yescharacteristic
33C22×#121C2211yescharacteristic
34C2×#490C2211yescharacteristic, complemented
35C2×#482C2211yescharacteristic, complemented
36C2×#469C2211yescharacteristic, complemented
37C2×#466C2211yescharacteristic
38C2×#466C2211yescharacteristic
39C2×#447C2211yescharacteristic
40C2×#442C2211yescharacteristic, complemented
41C2×#424C2211yescharacteristic, complemented
42C2×#407C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44C2×#405C2211yescharacteristic, complemented
45#2847C2211yescharacteristic
46#2847C2211yescharacteristic
47#2746—21no—
48#2740—21no—
49#2703—21no—
50#2699—21no—
51#2697—21no—
52#2688—21no—
53#2685—21no—
54#2671—21no—
55#2629C2211yescharacteristic, complemented
56#2624C2211yescharacteristic
57#2624C2211yescharacteristic, complemented
58#2619C2211yescharacteristic
59#2576—21no—
60#2553—21no—
61#2531—21no—
62#2526—21no—
63#2500C2211yescharacteristic, complemented
64#2496C2211yescharacteristic
65#2494C2211yescharacteristic
66#2490C2211yescharacteristic
67#2490C2211yescharacteristic
68#2442C2211yescharacteristic
69#2441C2211yescharacteristic, complemented
70#2433C2211yescharacteristic
71#2428C2211yescharacteristic
72#2428C2211yescharacteristic
73#2422C2211yescharacteristic
74#2420C2211yescharacteristic
75#2418—21no—
76#2412—21no—
77#2410—21no—
78#2408—21no—
79#2363C2211yescharacteristic, complemented
80#2361C2211yescharacteristic
81#2346C2211yescharacteristic, complemented
82D4×C22⋊C4C2211yescharacteristic
83#2324C2211yescharacteristic
84#2324C2211yescharacteristic, complemented
85#2314C2211yescharacteristic, complemented
86#2280C2211yescharacteristic
87#2280C2211yescharacteristic
88#2100C2211yescharacteristic, complemented
89#2099C2211yescharacteristic, complemented
90#2094C2211yescharacteristic, complemented
91#2093C2211yescharacteristic, complemented
92#2087C2211yescharacteristic, complemented
93#2087C2211yescharacteristic, complemented
94#2085C2211yescharacteristic, complemented
95#2085C2211yescharacteristic, complemented
96#2077C2211yescharacteristic
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic, complemented
99#2076C2211yescharacteristic
100#2073C2211yescharacteristic, complemented
101#2073C2211yescharacteristic, complemented
102#2067C2211yescharacteristic, complemented
103#2067C2211yescharacteristic, complemented
104#2067C2211yescharacteristic, complemented
105#2067C2211yescharacteristic, complemented
106#2059C2211yescharacteristic, complemented
107#2059C2211yescharacteristic, complemented
108#2054C2211yescharacteristic, complemented
109#2054C2211yescharacteristic, complemented
110#2041C2211yescharacteristic, complemented
111#2041C2211yescharacteristic, complemented
112#2034C2211yescharacteristic
113#2034C2211yescharacteristic
114#2034C2211yescharacteristic, complemented
115#2033C2211yescharacteristic
116#2033C2211yescharacteristic
117#2033C2211yescharacteristic
118#2033C2211yescharacteristic
119#2033C2211yescharacteristic, complemented
120#2025C2211yescharacteristic, complemented
121#2025C2211yescharacteristic, complemented
122#2011C2211yescharacteristic, complemented
123#2011C2211yescharacteristic, complemented
124#1999C2211yescharacteristic
125#1999C2211yescharacteristic
126#1999C2211yescharacteristic
127#1999C2211yescharacteristic, complemented
128#1991C2211yescharacteristic, complemented
129#1989C2211yescharacteristic, complemented
130#1989C2211yescharacteristic, complemented
131#1982C2211yescharacteristic, complemented
132#1982C2211yescharacteristic, complemented
133#1972C2211yescharacteristic, complemented
134#1957C2211yescharacteristic, complemented
135#1943C2211yescharacteristic, complemented
136#1936C2211yescharacteristic, complemented
137#1936C2211yescharacteristic, complemented
138#1934C2211yescharacteristic, complemented
139#1934C2211yescharacteristic, complemented
140#1934C2211yescharacteristic, complemented
141#1934C2211yescharacteristic, complemented
142#1926C2211yescharacteristic, complemented
143#1926C2211yescharacteristic, complemented
144#1925C2211yescharacteristic, complemented
145#1925C2211yescharacteristic, complemented
146#1924C2211yescharacteristic
147#1924C2211yescharacteristic
148#1924C2211yescharacteristic, complemented
149#1924C2211yescharacteristic, complemented
150#1923C2211yescharacteristic
151#1923C2211yescharacteristic
152#1923C2211yescharacteristic, complemented
153#1923C2211yescharacteristic, complemented
154#1921C2211yescharacteristic, complemented
155#1920C2211yescharacteristic, complemented
156#1919C2211yescharacteristic, complemented
157#1918C2211yescharacteristic, complemented
158#1895C2211yescharacteristic
159#1895C2211yescharacteristic
160#1895C2211yescharacteristic
161#1895C2211yescharacteristic
162#1895C2211yescharacteristic, complemented
163#1895C2211yescharacteristic, complemented
164#1893C2211yescharacteristic
165#1893C2211yescharacteristic
166#1893C2211yescharacteristic, complemented
167#1893C2211yescharacteristic, complemented
168#1879C2211yescharacteristic, complemented
169#1879C2211yescharacteristic, complemented
170#1879C2211yescharacteristic, complemented
171#1879C2211yescharacteristic, complemented
172#1875C2211yescharacteristic
173#1875C2211yescharacteristic
174#1875C2211yescharacteristic
175#1875C2211yescharacteristic
176#1875C2211yescharacteristic, complemented
177#1874C2211yescharacteristic
178#1864C2211yescharacteristic, complemented
179#1864C2211yescharacteristic, complemented
180#1862C2211yescharacteristic, complemented
181#1862C2211yescharacteristic, complemented
182#1854C2211yescharacteristic, complemented
183#1852C2211yescharacteristic
184#1836C2211yescharacteristic, complemented
185#1825C2211yescharacteristic, complemented
186#1823C2211yescharacteristic
187#1823C2211yescharacteristic
188#1809C2211yescharacteristic, complemented
189#1808C2211yescharacteristic, complemented
190#1807C2211yescharacteristic, complemented
191#1804C2211yescharacteristic, complemented
192#1804C2211yescharacteristic, complemented
193#1802C2211yescharacteristic, complemented
194#1802C2211yescharacteristic, complemented
195#1786C2211yescharacteristic
196#1786C2211yescharacteristic
197#1786C2211yescharacteristic
198#1776C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic, complemented
200C4×#102C2211yescharacteristic, complemented
201#1729C2211yescharacteristic, complemented
202#1729C2211yescharacteristic, complemented
203C23×D4—21no—
204C23×D4C2311yescharacteristic
205C24×C4C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C23×C8C2311yescharacteristic
212C23×C8C2311yescharacteristic
213#540—24no—
214#540—42no—
215C2×#127C2311yescharacteristic
216C2×#127C2311yescharacteristic
217C2×#126—21no—
218C2×#125C2311yescharacteristic
219C2×#125C2311yescharacteristic
220C2×#123—21no—
221C2×#123—21no—
222C2×#123—21no—
223C2×#121—21no—
224C2×#121—21no—
225C2×#121—21no—
226C2×#121—21no—
227C2×#121—21no—
228C2×#121—21no—
229C2×#121—24no—
230C2×#121—42no—
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×#120—21no—
245C2×C4×D4—21no—
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C22⋊C4—21no—
256C22×C22⋊C4—21no—
257#490—42no—
258#482—42no—
259#469—42no—
260#466—24no—
261#466—42no—
262#447—42no—
263#442—42no—
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273#424—42no—
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#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
304#407—42no—
305C2×C22⋊C8—42no—
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314#405—42no—
315C2×#97C2311yescharacteristic
316C2×#97C2311yescharacteristic
317C2×C4×C8C2311yescharacteristic
318C2×C4×C8C2311yescharacteristic
319#401—21no—
320#400—21no—
321#400—21no—
322#399—21no—
323#399—21no—
324#399—21no—
325#398—21no—
326#398—21no—
327#398—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#396—21no—
337#396—21no—
338#396—21no—
339#394—21no—
340#394—21no—
341#394—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#392—21no—
354#392—21no—
355#392—21no—
356#392—21no—
357#392—21no—
358#392—21no—
359#390—21no—
360#390—21no—
361#390—21no—
362#390—21no—
363#390—21no—
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#389—21no—
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#384C2311yescharacteristic
420#384C2311yescharacteristic
421#382—21no—
422#382C2311yescharacteristic
423#382C2311yescharacteristic
424#381—21no—
425#381—21no—
426#381D411yescharacteristic
427#381D411yescharacteristic
428#380—21no—
429#380D411yescharacteristic
430#380D411yescharacteristic
431#380D411yescharacteristic
432#380D411yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#379—21no—
444#379—21no—
445#379D411yescharacteristic
446#379D411yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4C2311yescharacteristic
455C4×C22⋊C4C2311yescharacteristic
456C4×C22⋊C4C2311yescharacteristic
457C4×C22⋊C4C2311yescharacteristic
458#376—21no—
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#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C25C2×D411yescharacteristic
495C22×D4—21no—
496C22×D4—22no—
497C22×D4—21no—
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—41no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4—44no—
517C22×D4—82no—
518C22×D4—82no—
519C22×D4C2411yescharacteristic
520C22×D4C2411yescharacteristic
521C22×D4C2411yescharacteristic
522C22×D4C2411yescharacteristic
523C23×C4—22no—
524C23×C4—22no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—41no—
531C23×C4—41no—
532C23×C4—41no—
533C23×C4—41no—
534C23×C4C2×D411yescharacteristic
535C23×C4C2×D411yescharacteristic
536C23×C4C2×D411yescharacteristic
537C23×C4C2411yescharacteristic
538C23×C4C2411yescharacteristic
539C23×C4C2411yescharacteristic
540C2×D8—22no—
541C2×D8—22no—
542C2×D8—41no—
543C2×D8—41no—
544C2×D8—41no—
545C2×D8—41no—
546C2×D8—41no—
547C2×D8—41no—
548C2×D8—41no—
549C2×M16—22no—
550C2×M16—22no—
551C2×M16—41no—
552C2×M16—41no—
553C2×M16—41no—
554C2×M16—41no—
555C22×C8—22no—
556C22×C8—22no—
557C22×C8—22no—
558C22×C8—41no—
559C22×C8—41no—
560C22×C8—41no—
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569#127—22no—
570#127—41no—
571#127—41no—
572#127—41no—
573#126—82no—
574#125—22no—
575#125—41no—
576#125—41no—
577#125—41no—
578#123—44no—
579#123—44no—
580#123—82no—
581#121—22no—
582#121—22no—
583#121—22no—
584#121—22no—
585#121—22no—
586#121—22no—
587#121—22no—
588#121—22no—
589#121—22no—
590#121—44no—
591#121—44no—
592#121—44no—
593#121—41no—
594#121—41no—
595#121—41no—
596#121—41no—
597#121—41no—
598#121—41no—
599#121—44no—
600#121—41no—
601#121—41no—
602#121—41no—
603#121—41no—
604#121—82no—
605#121—82no—
606#121#4114yes—
607#120—82no—
608#120—82no—
609#120—82no—
610#120—82no—
611C4×D4—22no—
612C4×D4—22no—
613C4×D4—41no—
614C4×D4—41no—
615C4×D4—41no—
616C4×D4—41no—
617C4×D4—41no—
618C4×D4—41no—
619C4×D4—82no—
620#117—22no—
621#117—22no—
622#117—41no—
623#117—41no—
624#117—41no—
625#117—41no—
626#117—41no—
627#117—41no—
628C2×C4⋊C4—22no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
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—41no—
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
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—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—44no—
706C2×C22⋊C4—82no—
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
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×C42—21no—
720C2×C42—21no—
721C2×C42—21no—
722C2×C42—21no—
723C2×C42—21no—
724C2×C42—21no—
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729#107—22no—
730#107—41no—
731#107—41no—
732#107—41no—
733#107—41no—
734#106—22no—
735#106—41no—
736#106—41no—
737#106—41no—
738C4⋊C8—41no—
739C4⋊C8—41no—
740C4⋊C8—41no—
741C4⋊C8—41no—
742#102—22no—
743#102—22no—
744#102—22no—
745#102—22no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—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—
768C22⋊C8—22no—
769C22⋊C8—22no—
770C22⋊C8—41no—
771C22⋊C8—41no—
772C22⋊C8—41no—
773C22⋊C8—41no—
774C22⋊C8—41no—
775C22⋊C8—41no—
776#97—22no—
777#97—22no—
778C4×C8—41no—
779C4×C8—41no—
780#95—21no—
781#95—21no—
782#95—21no—
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#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814C24—21no—
815C24—22no—
816C24—22no—
817C24—21no—
818C24—21no—
819C24—21no—
820C24—41no—
821C24—41no—
822C24—41no—
823C24—41no—
824C24—41no—
825C24—42no—
826C24—42no—
827C24—42no—
828C24—42no—
829C24—81no—
830C24—81no—
831C24—81no—
832C24C22×D411yescharacteristic
833C24C22×D411yescharacteristic
834C24C22×D411yescharacteristic
835C2×D4—24no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
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—42no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—42no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—42no—
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—81no—
877C2×D4—81no—
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—82no—
888C2×D4—82no—
889C2×D4—82no—
890C2×D4—82no—
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—816no—
908C2×D4C2×#4112yes—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—22no—
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—22no—
928C22×C4—22no—
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—41no—
941C22×C4—41no—
942C22×C4—41no—
943C22×C4—41no—
944C22×C4—41no—
945C22×C4—41no—
946C22×C4—42no—
947C22×C4—42no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—82no—
951C22×C4—82no—
952C22×C4—82no—
953C22×C4—82no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4—81no—
957C22×C4—81no—
958C22×C4—81no—
959C22×C4—81no—
960C22×C4—81no—
961C22×C4—81no—
962C22×C4—81no—
963C22×C4—81no—
964C22×C4—81no—
965C22×C4C22×D411yescharacteristic
966C22×C4C22×D411yescharacteristic
967C22×C4C22×D411yescharacteristic
968C22×C4C22×D411yescharacteristic
969C22×C4C22×D411yescharacteristic
970C22×C4C22×D411yescharacteristic
971C22×C4C22×D411yescharacteristic
972C22×C4C22×D411yescharacteristic
973C22×C4C22×D411yescharacteristic
974C22×C4C22×D411yescharacteristic
975C22×C4C22×D411yescharacteristic
976C22×C4C2×#4112yes—
977C22×C4H(5,𝔽2)12yes—
978C22×C4C2511yescharacteristic
979D8—44no—
980D8—82no—
981D8—82no—
982M16—44no—
983M16—82no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
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—44no—
1008C2×C8—82no—
1009C2×C8H(5,𝔽2)12yes—
1010C4⋊C4—22no—
1011C4⋊C4—22no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
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—41no—
1036C4⋊C4—41no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
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⋊C4C2×#4112yes—
1055C22⋊C4—22no—
1056C22⋊C4—22no—
1057C22⋊C4—22no—
1058C22⋊C4—22no—
1059C22⋊C4—24no—
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—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
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—
1109C42—21no—
1110C42—21no—
1111C42—21no—
1112C42—21no—
1113C42—21no—
1114C42—21no—
1115C42—21no—
1116C42—21no—
1117C42—42no—
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—22no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—44no—
1144C23—44no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
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—84no—
1176C23—84no—
1177C23—82no—
1178C23—82no—
1179C23—84no—
1180C23—84no—
1181C23—162no—
1182C23—162no—
1183C23—162no—
1184C23#54612yes—
1185C23#57612yes—
1186C23C23×D411yescharacteristic
1187D4—22no—
1188D4—22no—
1189D4—41no—
1190D4—41no—
1191D4—41no—
1192D4—41no—
1193D4—41no—
1194D4—41no—
1195D4—41no—
1196D4—41no—
1197D4—41no—
1198D4—41no—
1199D4—41no—
1200D4—41no—
1201D4—41no—
1202D4—41no—
1203D4—84no—
1204D4—84no—
1205D4—84no—
1206D4—84no—
1207D4—84no—
1208D4—84no—
1209D4—162no—
1210D4—162no—
1211D4—162no—
1212D4—162no—
1213D4—162no—
1214D4—162no—
1215D4—162no—
1216D4—162no—
1217D4—162no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
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—22no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
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—82no—
1299C2×C4—82no—
1300C2×C4—82no—
1301C2×C4—84no—
1302C2×C4—162no—
1303C2×C4—162no—
1304C2×C4—162no—
1305C2×C4—162no—
1306C2×C4#54612yes—
1307C2×C4C22×#4111yescharacteristic
1308C2×C4C2×H(5,𝔽2)11yescharacteristic
1309C2×C4C2×H(5,𝔽2)11yescharacteristic
1310C2×C4#58511yescharacteristic
1311C2×C4#58511yescharacteristic
1312C2×C4#58511yescharacteristic
1313C8—22no—
1314C8—41no—
1315C8—41no—
1316C8—41no—
1317C8—41no—
1318C8—41no—
1319C8—41no—
1320C8—41no—
1321C22—22no—
1322C22—22no—
1323C22—22no—
1324C22—22no—
1325C22—22no—
1326C22—22no—
1327C22—41no—
1328C22—41no—
1329C22—41no—
1330C22—41no—
1331C22—41no—
1332C22—41no—
1333C22—41no—
1334C22—41no—
1335C22—42no—
1336C22—41no—
1337C22—41no—
1338C22—42no—
1339C22—41no—
1340C22—41no—
1341C22—41no—
1342C22—41no—
1343C22—41no—
1344C22—42no—
1345C22—88no—
1346C22—81no—
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—81no—
1369C22—81no—
1370C22—81no—
1371C22—168no—
1372C22#344911yescharacteristic
1373C22C2×#54611yescharacteristic
1374C22#349611yescharacteristic
1375C22C2×#57611yescharacteristic
1376C22#358411yescharacteristic
1377C22#358511yescharacteristic
1378C22#358511yescharacteristic
1379C4—22no—
1380C4—41no—
1381C4—41no—
1382C4—41no—
1383C4—41no—
1384C4—41no—
1385C4—41no—
1386C4—41no—
1387C4—41no—
1388C4—41no—
1389C4—41no—
1390C4—42no—
1391C4—81no—
1392C4—81no—
1393C4—81no—
1394C4—81no—
1395C4—81no—
1396C4—81no—
1397C4—81no—
1398C4—81no—
1399C4—81no—
1400C4—81no—
1401C4—81no—
1402C4#351311yescharacteristic
1403C4#352111yescharacteristic
1404C4#354211yescharacteristic
1405C4#354511yescharacteristic
1406C2—42no—
1407C2—42no—
1408C2—81no—
1409C2—82no—
1410C2—161no—
1411C2—161no—
1412C2—161no—
1413C2#3894411yescharacteristic
1414C2#6097811yescharacteristic
1415C2#6098611yescharacteristic
1416C2#6118311yescharacteristic
1417C2#6119611yescharacteristic
1418C2#6227811yescharacteristic
1419C2#6229211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2280 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #37857C2semidirect
2. #37662C2semidirect
3. #33055C2semidirect
4. #31961C2semidirect
5. #31835C2semidirect
6. #31750C2semidirect
7. #31714C2semidirect
8. #31359C2semidirect
9. #31286C2semidirect
10. #30646C2semidirect
11. #30539C2semidirect
12. #29778C2semidirect
13. #29742C2semidirect
14. #29169C2semidirect
15. #28584C2semidirect
16. #27871C2semidirect
17. #27525C2semidirect
18. #27403C2semidirect
19. #27357C2semidirect
20. #27112C2semidirect
21. #26730C2semidirect
22. #26656C2semidirect
23. #26634C2semidirect
24. #25508C2semidirect
25. #24913C2semidirect
26. #24555C2semidirect
27. #24378C2semidirect
28. #21897C2semidirect
29. #21767C2semidirect
30. #21529C2semidirect
31. #21050C2semidirect
34. C2×#490C22semidirect
35. C2×#482C22semidirect
36. C2×#469C22semidirect
40. C2×#442C22semidirect
41. C2×#424C22semidirect
44. C2×#405C22semidirect
55. #2629C22semidirect
57. #2624C22semidirect
63. #2500C22semidirect
69. #2441C22semidirect
79. #2363C22semidirect
81. #2346C22semidirect
84. #2324C22semidirect
85. #2314C22semidirect
88. #2100C22semidirect
89. #2099C22semidirect
90. #2094C22semidirect
91. #2093C22semidirect
92. #2087C22semidirect
93. #2087C22semidirect
94. #2085C22semidirect
95. #2085C22semidirect
98. #2077C22semidirect
100. #2073C22semidirect
101. #2073C22semidirect
102. #2067C22semidirect
103. #2067C22semidirect
104. #2067C22semidirect
105. #2067C22semidirect
106. #2059C22semidirect
107. #2059C22semidirect
108. #2054C22semidirect
109. #2054C22semidirect
110. #2041C22semidirect
111. #2041C22semidirect
114. #2034C22semidirect
119. #2033C22semidirect
120. #2025C22semidirect
121. #2025C22semidirect
122. #2011C22semidirect
123. #2011C22semidirect
127. #1999C22semidirect
128. #1991C22semidirect
129. #1989C22semidirect
130. #1989C22semidirect
131. #1982C22semidirect
132. #1982C22semidirect
133. #1972C22semidirect
134. #1957C22semidirect
135. #1943C22semidirect
136. #1936C22semidirect
137. #1936C22semidirect
138. #1934C22semidirect
139. #1934C22semidirect
140. #1934C22semidirect
141. #1934C22semidirect
142. #1926C22semidirect
143. #1926C22semidirect
144. #1925C22semidirect
145. #1925C22semidirect
148. #1924C22semidirect
149. #1924C22semidirect
152. #1923C22semidirect
153. #1923C22semidirect
154. #1921C22semidirect
155. #1920C22semidirect
156. #1919C22semidirect
157. #1918C22semidirect
162. #1895C22semidirect
163. #1895C22semidirect
166. #1893C22semidirect
167. #1893C22semidirect
168. #1879C22semidirect
169. #1879C22semidirect
170. #1879C22semidirect
171. #1879C22semidirect
176. #1875C22semidirect
178. #1864C22semidirect
179. #1864C22semidirect
180. #1862C22semidirect
181. #1862C22semidirect
182. #1854C22semidirect
184. #1836C22semidirect
185. #1825C22semidirect
188. #1809C22semidirect
189. #1808C22semidirect
190. #1807C22semidirect
191. #1804C22semidirect
192. #1804C22semidirect
193. #1802C22semidirect
194. #1802C22semidirect
198. #1776C22semidirect
199. C4×#102C22semidirect
200. C4×#102C22semidirect
201. #1729C22semidirect
202. #1729C22semidirect

Maximal subgroups

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

subgroupindex
#378572
#376622
#330552
#319612
#318352
#317502
#317142
#313592
#312862
#306462
#305392
#297782
#297422
#291692
#285842
#278712
#275252
#274032
#273572
#271122
#267302
#266562
#266342
#255082
#249132
#245552
#243782
#218972
#217672
#215292
#210502