Finite Group Databasebeta

← #6859334

Subgroups — #6859334

Order 512.

1517 conjugacy classes of subgroups.

The subgroup lattice has 1305 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39273C211yesmaximal, characteristic, complemented
2#35664C211yesmaximal, characteristic, complemented
3#33015C211yesmaximal, characteristic, complemented
4#31761C211yesmaximal, characteristic, complemented
5#31349C211yesmaximal, characteristic, complemented
6#31272C211yesmaximal, characteristic, complemented
7#31092C211yesmaximal, characteristic, complemented
8#31010C211yesmaximal, characteristic, complemented
9#30722C211yesmaximal, characteristic
10#30534C211yesmaximal, characteristic, complemented
11#30518C211yesmaximal, characteristic, complemented
12#30055C211yesmaximal, characteristic, complemented
13#30013C211yesmaximal, characteristic, complemented
14#29567C211yesmaximal, characteristic, complemented
15#29485C211yesmaximal, characteristic, complemented
16#29423C211yesmaximal, characteristic, complemented
17#29407C211yesmaximal, characteristic, complemented
18#28997C211yesmaximal, characteristic, complemented
19#28926C211yesmaximal, characteristic, complemented
20#27016C211yesmaximal, characteristic, complemented
21#26973C211yesmaximal, characteristic, complemented
22#26892C211yesmaximal, characteristic, complemented
23#26691C211yesmaximal, characteristic, complemented
24#26615C211yesmaximal, characteristic, complemented
25#25505C211yesmaximal, characteristic, complemented
26#25047C211yesmaximal, characteristic, complemented
27#24159C211yesmaximal, characteristic, complemented
28#22792C211yesmaximal, characteristic, complemented
29#22227C211yesmaximal, characteristic, complemented
30#22186C211yesmaximal, characteristic, complemented
31#21463C211yesmaximal, characteristic, complemented
32C2×#529C2211yescharacteristic
33C2×#519C2211yescharacteristic
34C2×#488C2211yescharacteristic
35C2×#482C2211yescharacteristic
36C2×#478C2211yescharacteristic
37C2×#470C2211yescharacteristic
38C2×#468C2211yescharacteristic
39C2×#468C2211yescharacteristic
40C2×#463C2211yescharacteristic
41C2×#451C2211yescharacteristic
42C2×#448C2211yescharacteristic
43C2×#441C2211yescharacteristic
44C2×C4×Q16C2211yescharacteristic
45#2855C2211yescharacteristic
46#2808—21no—
47#2773—21no—
48#2752—21no—
49#2751—21no—
50#2640C2211yescharacteristic
51#2624C2211yescharacteristic
52#2609—21no—
53#2602—21no—
54#2599—21no—
55#2598—21no—
56#2580—21no—
57#2580—21no—
58#2563C2211yescharacteristic
59#2540C2211yescharacteristic
60#2517—21no—
61#2490C2211yescharacteristic
62#2489C2211yescharacteristic
63#2479—21no—
64#2471—21no—
65#2469—21no—
66#2458—21no—
67#2458—21no—
68#2453C2211yescharacteristic
69#2448C2211yescharacteristic
70#2441C2211yescharacteristic
71#2436C2211yescharacteristic
72#2426C2211yescharacteristic
73#2423C2211yescharacteristic
74#2423C2211yescharacteristic
75#2422C2211yescharacteristic
76#2414C2211yescharacteristic
77#2409C2211yescharacteristic
78#2367C2211yescharacteristic
79#2365C2211yescharacteristic
80#2330C2211yescharacteristic
81#2326C2211yescharacteristic
82#2324C2211yescharacteristic
83#2323C2211yescharacteristic
84#2320C2211yescharacteristic
85C4×C22⋊Q8C2211yescharacteristic
86C4×#121C2211yescharacteristic
87#2290C2211yescharacteristic
88#2088C2211yescharacteristic
89#2083C2211yescharacteristic
90#2077C2211yescharacteristic
91#2077C2211yescharacteristic
92#2075C2211yescharacteristic
93#2072C2211yescharacteristic
94#2072C2211yescharacteristic
95#2071C2211yescharacteristic
96#2068C2211yescharacteristic
97#2066C2211yescharacteristic
98#2059C2211yescharacteristic
99#2059C2211yescharacteristic
100#2057C2211yescharacteristic
101#2056C2211yescharacteristic
102#2042C2211yescharacteristic
103#2042C2211yescharacteristic
104#2036C2211yescharacteristic
105#2035C2211yescharacteristic
106#2035C2211yescharacteristic
107#2035C2211yescharacteristic
108#2034C2211yescharacteristic
109#2033C2211yescharacteristic
110#2033C2211yescharacteristic
111#2033C2211yescharacteristic
112#2026C2211yescharacteristic
113#2026C2211yescharacteristic
114#2024C2211yescharacteristic
115#2024C2211yescharacteristic
116#2023C2211yescharacteristic
117#2015C2211yescharacteristic
118#2015C2211yescharacteristic
119#2015C2211yescharacteristic
120#2015C2211yescharacteristic
121#2012C2211yescharacteristic
122#2012C2211yescharacteristic
123#2001C2211yescharacteristic
124#2000C2211yescharacteristic
125#2000C2211yescharacteristic
126#1999C2211yescharacteristic
127#1999C2211yescharacteristic
128#1992C2211yescharacteristic
129#1989C2211yescharacteristic
130#1983C2211yescharacteristic
131#1973C2211yescharacteristic
132#1972C2211yescharacteristic
133#1969C2211yescharacteristic
134#1959C2211yescharacteristic
135#1943C2211yescharacteristic
136#1935C2211yescharacteristic
137#1934C2211yescharacteristic
138#1934C2211yescharacteristic
139#1934C2211yescharacteristic
140#1928C2211yescharacteristic
141#1928C2211yescharacteristic
142#1928C2211yescharacteristic
143#1927C2211yescharacteristic
144#1927C2211yescharacteristic
145#1927C2211yescharacteristic
146#1926C2211yescharacteristic
147#1926C2211yescharacteristic
148#1925C2211yescharacteristic
149#1925C2211yescharacteristic
150#1924C2211yescharacteristic
151#1923C2211yescharacteristic
152#1921C2211yescharacteristic
153#1921C2211yescharacteristic
154#1921C2211yescharacteristic
155#1919C2211yescharacteristic
156#1918C2211yescharacteristic
157#1918C2211yescharacteristic
158#1917C2211yescharacteristic
159#1916C2211yescharacteristic
160#1895C2211yescharacteristic
161#1895C2211yescharacteristic
162#1894C2211yescharacteristic
163#1894C2211yescharacteristic
164#1880C2211yescharacteristic
165#1880C2211yescharacteristic
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1880C2211yescharacteristic
169#1879C2211yescharacteristic
170#1878C2211yescharacteristic
171#1878C2211yescharacteristic
172#1877C2211yescharacteristic
173#1877C2211yescharacteristic
174#1873C2211yescharacteristic
175#1870C2211yescharacteristic
176#1870C2211yescharacteristic
177#1865C2211yescharacteristic
178#1865C2211yescharacteristic
179#1865C2211yescharacteristic
180#1865C2211yescharacteristic
181#1864C2211yescharacteristic
182#1864C2211yescharacteristic
183#1864C2211yescharacteristic
184#1863C2211yescharacteristic
185#1863C2211yescharacteristic
186#1863C2211yescharacteristic
187#1854C2211yescharacteristic
188#1844C2211yescharacteristic
189#1840C2211yescharacteristic
190#1825C2211yescharacteristic
191#1818C2211yescharacteristic
192#1809C2211yescharacteristic
193#1797C2211yescharacteristic
194#1787C2211yescharacteristic
195#1787C2211yescharacteristic
196#1763C2211yescharacteristic
197C4×#103C2211yescharacteristic
198#1753C2211yescharacteristic
199#1753C2211yescharacteristic
200#1750C2211yescharacteristic
201#1746C2211yescharacteristic
202#1728C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213#529—42no—
214#529—42no—
215C2×#126—21no—
216C2×#125C2311yescharacteristic
217C2×#125C2311yescharacteristic
218C2×#124C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×#124C2311yescharacteristic
221C2×#123—21no—
222C2×#123—21no—
223C2×C22⋊Q8C2311yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×#121C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#121C2311yescharacteristic
231#519—42no—
232#519—42no—
233C2×C4×Q8—21no—
234C2×C4×Q8—21no—
235C2×C4×Q8—21no—
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×D4—21no—
242C2×C4×D4—21no—
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×#117—21no—
247C2×#117—21no—
248C2×#117—21no—
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C22×C42C2311yescharacteristic
252#488—24no—
253#482—42no—
254#478—42no—
255#470—42no—
256#468—24no—
257#468—42no—
258#463—42no—
259#451—24no—
260#448—42no—
261#441—42no—
262C4×Q16—42no—
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×#97C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×C4×C8C2311yescharacteristic
312C2×C4×C8C2311yescharacteristic
313#400—21no—
314#400—21no—
315#399—21no—
316#399—21no—
317#399—21no—
318#399—21no—
319#399—21no—
320#399—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#396—21no—
332#396—21no—
333#395—21no—
334#394—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#393—21no—
341#393—21no—
342#393—21no—
343#393—21no—
344#393—21no—
345#393—21no—
346#393—21no—
347#392—21no—
348#392—21no—
349#391—21no—
350#391C2311yescharacteristic
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#390—21no—
358#390—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#389—21no—
370#389—21no—
371#389—21no—
372#389—21no—
373#389—21no—
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
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#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388D411yescharacteristic
399#388D411yescharacteristic
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387D411yescharacteristic
415#387D411yescharacteristic
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386D411yescharacteristic
422#386D411yescharacteristic
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#385D411yescharacteristic
432#385D411yescharacteristic
433#384C2311yescharacteristic
434#384C2311yescharacteristic
435#383—21no—
436#382—21no—
437#382—21no—
438#382—21no—
439#381—21no—
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446C4×C4⋊C4—21no—
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4—21no—
456C4×C22⋊C4C2311yescharacteristic
457C4×C22⋊C4C2311yescharacteristic
458#376C2311yescharacteristic
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#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C22×Q8—21no—
494C22×Q8—21no—
495C22×Q8—22no—
496C22×Q8—22no—
497C22×Q8—41no—
498C22×Q8—41no—
499C22×Q8—41no—
500C22×Q8—41no—
501C22×Q8C2411yescharacteristic
502C22×Q8C2411yescharacteristic
503C22×Q8C2411yescharacteristic
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4C2×D411yescharacteristic
509C22×D4C2411yescharacteristic
510C22×D4C2411yescharacteristic
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4C2×D411yescharacteristic
515C23×C4C2×D411yescharacteristic
516C23×C4C2411yescharacteristic
517C23×C4C2411yescharacteristic
518C2×Q16—22no—
519C2×Q16—22no—
520C2×Q16—22no—
521C2×Q16—41no—
522C2×Q16—41no—
523C2×Q16—41no—
524C2×SD16—22no—
525C2×SD16—22no—
526C2×SD16—41no—
527C2×SD16—41no—
528C2×SD16—41no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×D8—41no—
534C2×D8—41no—
535C2×D8—41no—
536C2×M16—22no—
537C2×M16—41no—
538C2×M16—41no—
539C2×M16—41no—
540C2×M16—41no—
541C2×M16—41no—
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C4⋊Q8—41no—
551C4⋊Q8—41no—
552#126—44no—
553#125—22no—
554#125—22no—
555#125—41no—
556#125—41no—
557#124—22no—
558#124—22no—
559#124—41no—
560#124—41no—
561#124—41no—
562#124—41no—
563#123—44no—
564#123—82no—
565C22⋊Q8—22no—
566C22⋊Q8—22no—
567C22⋊Q8—22no—
568C22⋊Q8—41no—
569C22⋊Q8—41no—
570C22⋊Q8—41no—
571C22⋊Q8—41no—
572C22⋊Q8—41no—
573#121—22no—
574#121—22no—
575#121—41no—
576#121—41no—
577#121—41no—
578#121—41no—
579#121—41no—
580#121—41no—
581C4×Q8—22no—
582C4×Q8—22no—
583C4×Q8—22no—
584C4×Q8—22no—
585C4×Q8—41no—
586C4×Q8—41no—
587C4×Q8—41no—
588C4×Q8—41no—
589C4×Q8—44no—
590C4×Q8—41no—
591C4×Q8—41no—
592C4×Q8—44no—
593C4×Q8—82no—
594C4×D4—41no—
595C4×D4—41no—
596C4×D4—41no—
597C4×D4—41no—
598C4×D4—44no—
599C4×D4—41no—
600C4×D4—41no—
601C4×D4—82no—
602#117—22no—
603#117—41no—
604#117—41no—
605#117—44no—
606#117—44no—
607#117—41no—
608#117—44no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—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⋊C4C2×D411yescharacteristic
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—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⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C22⋊C4C2×D411yescharacteristic
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—21no—
699C2×C42—21no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—41no—
704C2×C42—41no—
705C2×C42C2×D411yescharacteristic
706C2×C42C2×D411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712#107—22no—
713#107—22no—
714#107—22no—
715#107—41no—
716#107—41no—
717#106—41no—
718#106—41no—
719#106—41no—
720#106—41no—
721#106—41no—
722C4⋊C8—41no—
723C4⋊C8—41no—
724#103—22no—
725#103—22no—
726#103—22no—
727#103—22no—
728#103—22no—
729#103—41no—
730#103—41no—
731#103—41no—
732#103—41no—
733#103—41no—
734#103—41no—
735#103—41no—
736#103—41no—
737#103—41no—
738#103—41no—
739#103—41no—
740#103#4114yes—
741#102—22no—
742#102—22no—
743#102—22no—
744#102—22no—
745#102—41no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752C22⋊C8—22no—
753C22⋊C8—41no—
754C22⋊C8—41no—
755C22⋊C8—41no—
756C22⋊C8—41no—
757C22⋊C8—41no—
758#97—41no—
759#97—41no—
760C4×C8—22no—
761C4×C8—41no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#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#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805C24—21no—
806C24—21no—
807C24C22×D411yescharacteristic
808C24C22×D411yescharacteristic
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—42no—
826C2×Q8—42no—
827C2×Q8—42no—
828C2×Q8—42no—
829C2×Q8—44no—
830C2×Q8—44no—
831C2×Q8—44no—
832C2×Q8—44no—
833C2×Q8—81no—
834C2×Q8—81no—
835C2×Q8C2×#4112yes—
836C2×Q8H(5,𝔽2)12yes—
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—41no—
850C2×D4—41no—
851C2×D4—41no—
852C2×D4—42no—
853C2×D4—42no—
854C2×D4—42no—
855C2×D4—42no—
856C2×D4—42no—
857C2×D4—81no—
858C2×D4—81no—
859C2×D4—81no—
860C2×D4—81no—
861C2×D4—81no—
862C2×D4—81no—
863C2×D4—81no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—41no—
891C22×C4—41no—
892C22×C4—41no—
893C22×C4—41no—
894C22×C4—41no—
895C22×C4—41no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—81no—
902C22×C4—81no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C2511yescharacteristic
918Q16—44no—
919Q16—44no—
920SD16—82no—
921SD16—82no—
922SD16—82no—
923D8—82no—
924M16—82no—
925M16—82no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8C2×#4112yes—
950C4⋊C4—24no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—41no—
972C4⋊C4—41no—
973C4⋊C4—41no—
974C4⋊C4—41no—
975C4⋊C4—41no—
976C4⋊C4—42no—
977C4⋊C4—42no—
978C4⋊C4—42no—
979C4⋊C4—42no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4C2×#4112yes—
1002C4⋊C4H(5,𝔽2)12yes—
1003C22⋊C4—41no—
1004C22⋊C4—41no—
1005C22⋊C4—41no—
1006C22⋊C4—41no—
1007C22⋊C4—41no—
1008C22⋊C4—41no—
1009C22⋊C4—41no—
1010C22⋊C4—41no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C42—24no—
1045C42—21no—
1046C42—21no—
1047C42—21no—
1048C42—21no—
1049C42—21no—
1050C42—21no—
1051C42—21no—
1052C42—21no—
1053C42—21no—
1054C42—21no—
1055C42—41no—
1056C42—41no—
1057C42—42no—
1058C42—42no—
1059C42—42no—
1060C42—42no—
1061C42—42no—
1062C42—81no—
1063C42—81no—
1064C42—81no—
1065C42—81no—
1066C42—81no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23C23×D411yescharacteristic
1096Q8—22no—
1097Q8—22no—
1098Q8—22no—
1099Q8—22no—
1100Q8—48no—
1101Q8—41no—
1102Q8—41no—
1103Q8—41no—
1104Q8—41no—
1105Q8—41no—
1106Q8—41no—
1107Q8—41no—
1108Q8—41no—
1109Q8—84no—
1110D4—41no—
1111D4—41no—
1112D4—41no—
1113D4—41no—
1114D4—41no—
1115D4—41no—
1116D4—41no—
1117D4—41no—
1118D4—82no—
1119D4—84no—
1120D4—84no—
1121D4—162no—
1122D4—162no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—22no—
1157C2×C4—21no—
1158C2×C4—22no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—48no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—82no—
1211C2×C4—82no—
1212C2×C4—84no—
1213C2×C4—162no—
1214C2×C4C22×#4111yescharacteristic
1215C2×C4C2×H(5,𝔽2)11yescharacteristic
1216C2×C4C2×H(5,𝔽2)11yescharacteristic
1217C2×C4#58511yescharacteristic
1218C2×C4#58511yescharacteristic
1219C2×C4#58511yescharacteristic
1220C8—22no—
1221C8—41no—
1222C8—41no—
1223C8—41no—
1224C8—41no—
1225C8—41no—
1226C8—41no—
1227C8—41no—
1228C22—41no—
1229C22—41no—
1230C22—41no—
1231C22—41no—
1232C22—41no—
1233C22—41no—
1234C22—41no—
1235C22—41no—
1236C22—41no—
1237C22—41no—
1238C22—41no—
1239C22—41no—
1240C22—41no—
1241C22—41no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22#344911yescharacteristic
1257C22D4×#4111yescharacteristic
1258C22#348411yescharacteristic
1259C22#358411yescharacteristic
1260C22#358511yescharacteristic
1261C22#358611yescharacteristic
1262C22#358611yescharacteristic
1263C4—41no—
1264C4—42no—
1265C4—41no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—41no—
1270C4—42no—
1271C4—42no—
1272C4—41no—
1273C4—41no—
1274C4—41no—
1275C4—41no—
1276C4—41no—
1277C4—41no—
1278C4—42no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C4—81no—
1284C4—81no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C4#350611yescharacteristic
1290C4#351311yescharacteristic
1291C4#353311yescharacteristic
1292C4#354011yescharacteristic
1293C2—81no—
1294C2—81no—
1295C2—161no—
1296C2—161no—
1297C2#3984511yescharacteristic
1298C2#6099811yescharacteristic
1299C2#6100511yescharacteristic
1300C2#6150811yescharacteristic
1301C2#6153711yescharacteristic
1302C2#6161511yescharacteristic
1303C2#6165611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#30722C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39273C2semidirect
2. #35664C2semidirect
3. #33015C2semidirect
4. #31761C2semidirect
5. #31349C2semidirect
6. #31272C2semidirect
7. #31092C2semidirect
8. #31010C2semidirect
10. #30534C2semidirect
11. #30518C2semidirect
12. #30055C2semidirect
13. #30013C2semidirect
14. #29567C2semidirect
15. #29485C2semidirect
16. #29423C2semidirect
17. #29407C2semidirect
18. #28997C2semidirect
19. #28926C2semidirect
20. #27016C2semidirect
21. #26973C2semidirect
22. #26892C2semidirect
23. #26691C2semidirect
24. #26615C2semidirect
25. #25505C2semidirect
26. #25047C2semidirect
27. #24159C2semidirect
28. #22792C2semidirect
29. #22227C2semidirect
30. #22186C2semidirect
31. #21463C2semidirect

Maximal subgroups

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

subgroupindex
#392732
#356642
#330152
#317612
#313492
#312722
#310922
#310102
#307222
#305342
#305182
#300552
#300132
#295672
#294852
#294232
#294072
#289972
#289262
#270162
#269732
#268922
#266912
#266152
#255052
#250472
#241592
#227922
#222272
#221862
#214632