Finite Group Databasebeta

← #6840472

Subgroups — #6840472

Order 512.

1641 conjugacy classes of subgroups.

The subgroup lattice has 1366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40074C211yesmaximal, characteristic, complemented
2#39405C211yesmaximal, characteristic
3#33252C211yesmaximal, characteristic, complemented
4#32453C211yesmaximal, characteristic, complemented
5#31950C211yesmaximal, characteristic, complemented
6#30946C211yesmaximal, characteristic, complemented
7#30892C211yesmaximal, characteristic, complemented
8#30778C211yesmaximal, characteristic, complemented
9#30736C211yesmaximal, characteristic, complemented
10#30547C211yesmaximal, characteristic, complemented
11#30456C211yesmaximal, characteristic, complemented
12#30066C211yesmaximal, characteristic, complemented
13#30039C211yesmaximal, characteristic, complemented
14#29086C211yesmaximal, characteristic, complemented
15#28995C211yesmaximal, characteristic, complemented
16#28927C211yesmaximal, characteristic, complemented
17#28923C211yesmaximal, characteristic, complemented
18#28898C211yesmaximal, characteristic, complemented
19#28420C211yesmaximal, characteristic, complemented
20#28365C211yesmaximal, characteristic, complemented
21#27767C211yesmaximal, characteristic, complemented
22#27273C211yesmaximal, characteristic, complemented
23#27245C211yesmaximal, characteristic, complemented
24#27214C211yesmaximal, characteristic, complemented
25#27081C211yesmaximal, characteristic, complemented
26#26950C211yesmaximal, characteristic, complemented
27#26820C211yesmaximal, characteristic, complemented
28#23106C211yesmaximal, characteristic, complemented
29#22884C211yesmaximal, characteristic, complemented
30#21667C211yesmaximal, characteristic, complemented
31#21656C211yesmaximal, characteristic, complemented
32C2×#538—21no—
33C2×#500C2211yescharacteristic, complemented
34C2×#492C2211yescharacteristic
35C2×#490C2211yescharacteristic
36C2×#487C2211yescharacteristic, complemented
37C2×#486C2211yescharacteristic
38C2×#486C2211yescharacteristic, complemented
39C2×#482C2211yescharacteristic
40C2×#474C2211yescharacteristic
41C2×#468C2211yescharacteristic
42C2×#460C2211yescharacteristic
43C2×#460C2211yescharacteristic, complemented
44C2×#450C2211yescharacteristic
45C2×#450C2211yescharacteristic
46C2×C4×SD16C2211yescharacteristic
47C2×#418C2211yescharacteristic
48#2862C2211yescharacteristic, complemented
49#2858C2211yescharacteristic
50#2775—21no—
51#2767—21no—
52#2758—21no—
53#2716—21no—
54#2714—21no—
55#2678—21no—
56#2676—21no—
57#2670—21no—
58#2650—21no—
59#2631—21no—
60#2568C2211yescharacteristic, complemented
61#2551C2211yescharacteristic, complemented
62#2541C2211yescharacteristic
63#2541C2211yescharacteristic
64#2529—21no—
65#2520—21no—
66#2512C2211yescharacteristic
67#2511C2211yescharacteristic, complemented
68#2499C2211yescharacteristic
69#2492C2211yescharacteristic
70#2491C2211yescharacteristic
71#2489C2211yescharacteristic
72#2456—21no—
73#2453C2211yescharacteristic, complemented
74#2452C2211yescharacteristic
75#2446C2211yescharacteristic, complemented
76#2445C2211yescharacteristic
77#2439C2211yescharacteristic
78#2433C2211yescharacteristic
79#2433C2211yescharacteristic
80#2429C2211yescharacteristic
81#2428C2211yescharacteristic
82#2424—21no—
83#2422C2211yescharacteristic
84#2366C2211yescharacteristic
85#2362C2211yescharacteristic
86#2356C2211yescharacteristic, complemented
87D4×C22⋊C4C2211yescharacteristic
88#2331—21no—
89C4×#127C2211yescharacteristic
90C4×#125C2211yescharacteristic, complemented
91C4×#126C2211yescharacteristic
92#2093C2211yescharacteristic
93#2092C2211yescharacteristic
94#2092C2211yescharacteristic, complemented
95#2092C2211yescharacteristic, complemented
96#2086C2211yescharacteristic, complemented
97#2083C2211yescharacteristic, complemented
98#2076C2211yescharacteristic
99#2073C2211yescharacteristic
100#2072C2211yescharacteristic, complemented
101#2072C2211yescharacteristic, complemented
102#2067C2211yescharacteristic, complemented
103#2066C2211yescharacteristic, complemented
104#2058C2211yescharacteristic, complemented
105#2057C2211yescharacteristic, complemented
106#2057C2211yescharacteristic, complemented
107#2055C2211yescharacteristic
108#2055C2211yescharacteristic
109#2055C2211yescharacteristic
110#2041C2211yescharacteristic
111#2041C2211yescharacteristic
112#2041C2211yescharacteristic
113#2041C2211yescharacteristic, complemented
114#2036C2211yescharacteristic
115#2033C2211yescharacteristic
116#2025C2211yescharacteristic
117#2025C2211yescharacteristic, complemented
118#2023C2211yescharacteristic
119#2023C2211yescharacteristic
120#2023C2211yescharacteristic, complemented
121#2014C2211yescharacteristic
122#2014C2211yescharacteristic
123#2014C2211yescharacteristic
124#2014C2211yescharacteristic
125#2014C2211yescharacteristic
126#2014C2211yescharacteristic, complemented
127#2013C2211yescharacteristic
128#2013C2211yescharacteristic, complemented
129#2000C2211yescharacteristic
130#2000C2211yescharacteristic
131#2000C2211yescharacteristic
132#1992C2211yescharacteristic, complemented
133#1982C2211yescharacteristic
134#1973C2211yescharacteristic
135#1973C2211yescharacteristic
136#1973C2211yescharacteristic
137#1973C2211yescharacteristic
138#1973C2211yescharacteristic, complemented
139#1973C2211yescharacteristic, complemented
140#1973C2211yescharacteristic, complemented
141#1973C2211yescharacteristic, complemented
142#1973C2211yescharacteristic, complemented
143#1968C2211yescharacteristic
144#1961C2211yescharacteristic
145#1961C2211yescharacteristic
146#1957C2211yescharacteristic
147#1949C2211yescharacteristic, complemented
148#1936C2211yescharacteristic
149#1934C2211yescharacteristic
150#1934C2211yescharacteristic
151#1934C2211yescharacteristic
152#1934C2211yescharacteristic, complemented
153#1934C2211yescharacteristic, complemented
154#1933C2211yescharacteristic, complemented
155#1933C2211yescharacteristic, complemented
156#1928C2211yescharacteristic, complemented
157#1926C2211yescharacteristic
158#1926C2211yescharacteristic, complemented
159#1925C2211yescharacteristic
160#1925C2211yescharacteristic
161#1925C2211yescharacteristic, complemented
162#1924C2211yescharacteristic
163#1924C2211yescharacteristic
164#1923C2211yescharacteristic
165#1921C2211yescharacteristic, complemented
166#1918C2211yescharacteristic, complemented
167#1917C2211yescharacteristic, complemented
168#1917C2211yescharacteristic, complemented
169#1916C2211yescharacteristic, complemented
170#1895C2211yescharacteristic
171#1894C2211yescharacteristic
172#1880C2211yescharacteristic
173#1880C2211yescharacteristic
174#1880C2211yescharacteristic, complemented
175#1877C2211yescharacteristic
176#1877C2211yescharacteristic
177#1877C2211yescharacteristic
178#1877C2211yescharacteristic, complemented
179#1877C2211yescharacteristic, complemented
180#1877C2211yescharacteristic, complemented
181#1877C2211yescharacteristic, complemented
182#1875C2211yescharacteristic
183#1865C2211yescharacteristic, complemented
184#1862C2211yescharacteristic
185#1854C2211yescharacteristic
186#1839C2211yescharacteristic, complemented
187#1836C2211yescharacteristic, complemented
188#1802C2211yescharacteristic, complemented
189#1786C2211yescharacteristic
190#1771C2211yescharacteristic, complemented
191#1770C2211yescharacteristic, complemented
192C8×C4⋊C4C2211yescharacteristic, complemented
193#1763C2211yescharacteristic, complemented
194#1762C2211yescharacteristic
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic, complemented
197#1762C2211yescharacteristic, complemented
198C4×#102C2211yescharacteristic, complemented
199#1753C2211yescharacteristic
200#1753C2211yescharacteristic
201#1753C2211yescharacteristic
202C4×#97C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213#538—48no—
214C2×C4⋊Q8—21no—
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×#127C2311yescharacteristic
220C2×#127C2311yescharacteristic
221C2×#127C2311yescharacteristic
222C2×#127C2311yescharacteristic
223C2×#127C2311yescharacteristic
224C2×#126—21no—
225C2×#126D411yescharacteristic
226C2×#125C2311yescharacteristic
227C2×#124—21no—
228C2×#124—21no—
229C2×#124—21no—
230C2×#123—21no—
231C2×#123—21no—
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×#121—21no—
236C2×#121—21no—
237C2×#121—21no—
238C2×#121—21no—
239C2×#121—21no—
240C2×#121C2311yescharacteristic
241C2×#121C2311yescharacteristic
242C2×#120—21no—
243C2×#120—21no—
244C2×#120—21no—
245C2×#120—21no—
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×D4—21no—
249C2×C4×D4—21no—
250C2×C4×D4—21no—
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C22×C22⋊C4—21no—
257#500—42no—
258#492—42no—
259#490—24no—
260#487—42no—
261#486—42no—
262#486—42no—
263#482—42no—
264#474—42no—
265#468—42no—
266#460—24no—
267#460—42no—
268#450—24no—
269#450—42no—
270C4×SD16—42no—
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282#418—42no—
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×#97C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×#97C2311yescharacteristic
321C2×#97C2311yescharacteristic
322C2×#97C2311yescharacteristic
323C2×C4×C8C2311yescharacteristic
324C2×C4×C8C2311yescharacteristic
325C2×C4×C8C2311yescharacteristic
326C2×C4×C8C2311yescharacteristic
327#400—21no—
328#400—21no—
329#400—21no—
330#400—21no—
331#400—21no—
332#400—21no—
333#400—21no—
334#400—21no—
335#398—21no—
336#398—21no—
337#398—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#396—21no—
344#396—21no—
345#396—21no—
346#396—21no—
347#395—21no—
348#395—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#393—21no—
355#393—21no—
356#393—21no—
357#393—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#391—21no—
368#391—21no—
369#391—21no—
370#391—21no—
371#391—21no—
372#391—21no—
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#391C2311yescharacteristic
378#391C2311yescharacteristic
379#391C2311yescharacteristic
380#391C2311yescharacteristic
381#390—21no—
382#390—21no—
383#390—21no—
384#390—21no—
385#390—21no—
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#389—21no—
397#389—21no—
398#389—21no—
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388D411yescharacteristic
413#388D411yescharacteristic
414#388D411yescharacteristic
415#387—21no—
416#387—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#387—21no—
426#387—21no—
427#387—21no—
428#387D411yescharacteristic
429#387D411yescharacteristic
430#387D411yescharacteristic
431#386—21no—
432#386—21no—
433#386—21no—
434#386—21no—
435#386—21no—
436#386—21no—
437#385—21no—
438#385—21no—
439#384C2311yescharacteristic
440#384C2311yescharacteristic
441#383—21no—
442#383D411yescharacteristic
443#382—21no—
444#382—21no—
445#382—21no—
446#382C2311yescharacteristic
447#382C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#379—21no—
451C4×C4⋊C4—21no—
452C4×C4⋊C4—21no—
453C4×C4⋊C4—21no—
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C22⋊C4C2311yescharacteristic
462C4×C22⋊C4C2311yescharacteristic
463C4×C22⋊C4C2311yescharacteristic
464#376—21no—
465C43C2311yescharacteristic
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#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494C25—21no—
495C22×Q8—21no—
496C22×Q8—21no—
497C22×Q8—21no—
498C22×Q8C2411yescharacteristic
499C22×Q8C2411yescharacteristic
500C22×D4—22no—
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×D4—21no—
513C22×D4—21no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4C2411yescharacteristic
520C22×D4C2411yescharacteristic
521C22×D4C2411yescharacteristic
522C22×D4C2411yescharacteristic
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4C2411yescharacteristic
528C2×SD16—22no—
529C2×SD16—22no—
530C2×SD16—22no—
531C2×SD16—22no—
532C2×SD16—22no—
533C2×SD16—22no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×M16—22no—
553C2×M16—41no—
554C2×M16—41no—
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C4⋊Q8—41no—
564C4⋊Q8—41no—
565C4⋊Q8—41no—
566C4⋊Q8—41no—
567C4⋊Q8—41no—
568C4⋊Q8—41no—
569C4⋊Q8—41no—
570C4⋊Q8—41no—
571C4⋊Q8—44no—
572#127—22no—
573#127—22no—
574#127—41no—
575#127—41no—
576#127—41no—
577#127—41no—
578#127—41no—
579#127—41no—
580#127—41no—
581#127—41no—
582#126—24no—
583#126—44no—
584#125—22no—
585#125—41no—
586#124—44no—
587#124—44no—
588#124—82no—
589#123—44no—
590#123—44no—
591C22⋊Q8—22no—
592C22⋊Q8—41no—
593C22⋊Q8—44no—
594C22⋊Q8—41no—
595C22⋊Q8—41no—
596#121—44no—
597#121—44no—
598#121—44no—
599#121—41no—
600#121—41no—
601#121—41no—
602#121—41no—
603#121—82no—
604#121—82no—
605#120—44no—
606#120—44no—
607#120—82no—
608#120—82no—
609C4×Q8—22no—
610C4×Q8—41no—
611C4×Q8—41no—
612C4×Q8—41no—
613C4×D4—44no—
614C4×D4—41no—
615C4×D4—41no—
616C4×D4—41no—
617C4×D4—41no—
618C4×D4—41no—
619C4×D4—41no—
620C4×D4—41no—
621C4×D4—41no—
622C4×D4—44no—
623C4×D4—82no—
624#117—41no—
625#117—41no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
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—21no—
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
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—44no—
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42C2×D411yescharacteristic
709C2×C42C2×D411yescharacteristic
710C2×C42C2×D411yescharacteristic
711C2×C42C2×D411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718#107—22no—
719#107—22no—
720#107—41no—
721#107—41no—
722#107—41no—
723#107—41no—
724#106—41no—
725#106—41no—
726C4⋊C8—22no—
727C4⋊C8—22no—
728C4⋊C8—41no—
729#103—22no—
730#103—22no—
731#103—41no—
732#103—41no—
733#103—41no—
734#103—41no—
735#103—41no—
736#103—41no—
737#102—22no—
738#102—22no—
739#102—22no—
740#102—22no—
741#102—22no—
742#102—22no—
743#102—22no—
744#102—22no—
745#102—22no—
746#102—22no—
747#102—22no—
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#4114yes—
761C22⋊C8—22no—
762C22⋊C8—22no—
763C22⋊C8—41no—
764#97—22no—
765#97—41no—
766#97—41no—
767#97—41no—
768#97—41no—
769C4×C8—22no—
770C4×C8—22no—
771C4×C8—22no—
772C4×C8—41no—
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#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#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817C24—21no—
818C24—21no—
819C24—21no—
820C24—21no—
821C24—42no—
822C24—42no—
823C24—81no—
824C24—81no—
825C24—81no—
826C24—81no—
827C24—81no—
828C24C22×D411yescharacteristic
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—42no—
842C2×Q8—42no—
843C2×Q8—42no—
844C2×Q8—81no—
845C2×Q8—81no—
846C2×Q8—81no—
847C2×Q8—81no—
848C2×Q8—81no—
849C2×Q8—81no—
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—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—44no—
882C2×D4—42no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—42no—
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—82no—
910C2×D4—82no—
911C2×D4—82no—
912C2×D4—81no—
913C2×D4—81no—
914C2×D4—81no—
915C2×D4—81no—
916C2×D4C2×#4112yes—
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—42no—
936C22×C4—42no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C2511yescharacteristic
961SD16—44no—
962SD16—82no—
963SD16—82no—
964SD16—82no—
965SD16—82no—
966SD16—82no—
967SD16—82no—
968SD16—82no—
969M16—82no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8C2×#4112yes—
992C2×C8H(5,𝔽2)12yes—
993C2×C8H(5,𝔽2)12yes—
994C4⋊C4—22no—
995C4⋊C4—22no—
996C4⋊C4—22no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—41no—
1017C4⋊C4—41no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4AGL(1,ℤ/8)14yes—
1040C4⋊C4C2×#4112yes—
1041C22⋊C4—22no—
1042C22⋊C4—22no—
1043C22⋊C4—22no—
1044C22⋊C4—22no—
1045C22⋊C4—41no—
1046C22⋊C4—41no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C42—22no—
1079C42—22no—
1080C42—21no—
1081C42—21no—
1082C42—21no—
1083C42—21no—
1084C42—21no—
1085C42—21no—
1086C42—21no—
1087C42—21no—
1088C42—21no—
1089C42—21no—
1090C42—21no—
1091C42—21no—
1092C42—41no—
1093C42—41no—
1094C42—42no—
1095C42—42no—
1096C42—42no—
1097C42—42no—
1098C42—81no—
1099C42—81no—
1100C42—81no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—22no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—84no—
1137C23—84no—
1138C23—162no—
1139C23—162no—
1140C23—162no—
1141C23—162no—
1142C23—162no—
1143C23C23×D411yescharacteristic
1144Q8—41no—
1145Q8—41no—
1146Q8—41no—
1147Q8—41no—
1148Q8—41no—
1149Q8—41no—
1150Q8—41no—
1151Q8—41no—
1152Q8—162no—
1153Q8—162no—
1154Q8—162no—
1155D4—22no—
1156D4—22no—
1157D4—41no—
1158D4—41no—
1159D4—41no—
1160D4—41no—
1161D4—41no—
1162D4—41no—
1163D4—41no—
1164D4—41no—
1165D4—41no—
1166D4—41no—
1167D4—41no—
1168D4—41no—
1169D4—41no—
1170D4—41no—
1171D4—84no—
1172D4—84no—
1173D4—84no—
1174D4—84no—
1175D4—162no—
1176D4—162no—
1177D4—162no—
1178D4—162no—
1179D4—162no—
1180D4—162no—
1181D4—162no—
1182D4—162no—
1183D4—162no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—22no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
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—162no—
1260C2×C4—162no—
1261C2×C4—162no—
1262C2×C4—162no—
1263C2×C4C2×AGL(1,ℤ/8)12yes—
1264C2×C4C2×AGL(1,ℤ/8)12yes—
1265C2×C4C2×AGL(1,ℤ/8)12yes—
1266C2×C4#57712yes—
1267C2×C4C22×#4111yescharacteristic
1268C2×C4C2×H(5,𝔽2)11yescharacteristic
1269C2×C4C2×H(5,𝔽2)11yescharacteristic
1270C2×C4#58511yescharacteristic
1271C2×C4#58511yescharacteristic
1272C2×C4#58511yescharacteristic
1273C8—22no—
1274C8—22no—
1275C8—22no—
1276C8—41no—
1277C8—41no—
1278C8—41no—
1279C8—41no—
1280C8—41no—
1281C22—41no—
1282C22—42no—
1283C22—42no—
1284C22—41no—
1285C22—41no—
1286C22—42no—
1287C22—41no—
1288C22—41no—
1289C22—41no—
1290C22—41no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—168no—
1317C22D4×#4111yescharacteristic
1318C22#349811yescharacteristic
1319C22#350011yescharacteristic
1320C22C22×AGL(1,ℤ/8)11yescharacteristic
1321C22C2×#57711yescharacteristic
1322C22#358511yescharacteristic
1323C22#358611yescharacteristic
1324C4—22no—
1325C4—22no—
1326C4—22no—
1327C4—22no—
1328C4—41no—
1329C4—41no—
1330C4—41no—
1331C4—42no—
1332C4—41no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—41no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4#346011yescharacteristic
1350C4#351411yescharacteristic
1351C4#354511yescharacteristic
1352C4#356011yescharacteristic
1353C2—81no—
1354C2—82no—
1355C2—161no—
1356C2—161no—
1357C2—161no—
1358C2#3944311yescharacteristic
1359C2#6146611yescharacteristic
1360C2#6154311yescharacteristic
1361C2#6244711yescharacteristic
1362C2#6245811yescharacteristic
1363C2#6253911yescharacteristic
1364C2#6257511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#39405C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#126 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #40074C2semidirect
3. #33252C2semidirect
4. #32453C2semidirect
5. #31950C2semidirect
6. #30946C2semidirect
7. #30892C2semidirect
8. #30778C2semidirect
9. #30736C2semidirect
10. #30547C2semidirect
11. #30456C2semidirect
12. #30066C2semidirect
13. #30039C2semidirect
14. #29086C2semidirect
15. #28995C2semidirect
16. #28927C2semidirect
17. #28923C2semidirect
18. #28898C2semidirect
19. #28420C2semidirect
20. #28365C2semidirect
21. #27767C2semidirect
22. #27273C2semidirect
23. #27245C2semidirect
24. #27214C2semidirect
25. #27081C2semidirect
26. #26950C2semidirect
27. #26820C2semidirect
28. #23106C2semidirect
29. #22884C2semidirect
30. #21667C2semidirect
31. #21656C2semidirect
33. C2×#500C22semidirect
36. C2×#487C22semidirect
38. C2×#486C22semidirect
43. C2×#460C22semidirect
48. #2862C22semidirect
60. #2568C22semidirect
61. #2551C22semidirect
67. #2511C22semidirect
73. #2453C22semidirect
75. #2446C22semidirect
86. #2356C22semidirect
90. C4×#125C22semidirect
94. #2092C22semidirect
95. #2092C22semidirect
96. #2086C22semidirect
97. #2083C22semidirect
100. #2072C22semidirect
101. #2072C22semidirect
102. #2067C22semidirect
103. #2066C22semidirect
104. #2058C22semidirect
105. #2057C22semidirect
106. #2057C22semidirect
113. #2041C22semidirect
117. #2025C22semidirect
120. #2023C22semidirect
126. #2014C22semidirect
128. #2013C22semidirect
132. #1992C22semidirect
138. #1973C22semidirect
139. #1973C22semidirect
140. #1973C22semidirect
141. #1973C22semidirect
142. #1973C22semidirect
147. #1949C22semidirect
152. #1934C22semidirect
153. #1934C22semidirect
154. #1933C22semidirect
155. #1933C22semidirect
156. #1928C22semidirect
158. #1926C22semidirect
161. #1925C22semidirect
165. #1921C22semidirect
166. #1918C22semidirect
167. #1917C22semidirect
168. #1917C22semidirect
169. #1916C22semidirect
174. #1880C22semidirect
178. #1877C22semidirect
179. #1877C22semidirect
180. #1877C22semidirect
181. #1877C22semidirect
183. #1865C22semidirect
186. #1839C22semidirect
187. #1836C22semidirect
188. #1802C22semidirect
190. #1771C22semidirect
191. #1770C22semidirect
192. C8×C4⋊C4C22semidirect
193. #1763C22semidirect
196. #1762C22semidirect
197. #1762C22semidirect
198. C4×#102C22semidirect
202. C4×#97C22semidirect

Maximal subgroups

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

subgroupindex
#400742
#394052
#332522
#324532
#319502
#309462
#308922
#307782
#307362
#305472
#304562
#300662
#300392
#290862
#289952
#289272
#289232
#288982
#284202
#283652
#277672
#272732
#272452
#272142
#270812
#269502
#268202
#231062
#228842
#216672
#216562