Finite Group Databasebeta

← #6608098

Subgroups — #6608098

Order 512.

1675 conjugacy classes of subgroups.

The subgroup lattice has 1357 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38062C211yesmaximal, characteristic, complemented
2#38054C211yesmaximal, characteristic, complemented
3#33274C211yesmaximal, characteristic, complemented
4#33245C211yesmaximal, characteristic, complemented
5#33145C211yesmaximal, characteristic, complemented
6#29570C211yesmaximal, characteristic, complemented
7#29566C211yesmaximal, characteristic, complemented
8#29506C211yesmaximal, characteristic, complemented
9#29505C211yesmaximal, characteristic, complemented
10#28902C211yesmaximal, characteristic, complemented
11#28901C211yesmaximal, characteristic, complemented
12#28019C211yesmaximal, characteristic, complemented
13#27282C211yesmaximal, characteristic, complemented
14#27281C211yesmaximal, characteristic, complemented
15#26828C211yesmaximal, characteristic, complemented
16#26826C211yesmaximal, characteristic, complemented
17#26490C211yesmaximal, characteristic, complemented
18#26261C211yesmaximal, characteristic, complemented
19#26258C211yesmaximal, characteristic, complemented
20#26072C211yesmaximal, characteristic, complemented
21#25793C211yesmaximal, characteristic
22#24511C211yesmaximal, characteristic, complemented
23#24506C211yesmaximal, characteristic, complemented
24#23041C211yesmaximal, characteristic, complemented
25#22882C211yesmaximal, characteristic, complemented
26#22880C211yesmaximal, characteristic, complemented
27#22442C211yesmaximal, characteristic, complemented
28#21704C211yesmaximal, characteristic, complemented
29#21282C211yesmaximal, characteristic, complemented
30#21236C211yesmaximal, characteristic, complemented
31#20477C211yesmaximal, characteristic, complemented
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C2×#498C2211yescharacteristic, complemented
34C2×#496C2211yescharacteristic
35C2×#495C2211yescharacteristic
36C2×#489C2211yescharacteristic
37C2×#489C2211yescharacteristic, complemented
38C2×#468C2211yescharacteristic
39C2×#452C2211yescharacteristic
40C2×#447C2211yescharacteristic
41C2×#442C2211yescharacteristic
42C2×#440C2211yescharacteristic, complemented
43C2×C4×SD16C2211yescharacteristic, complemented
44C2×C4×D8C2211yescharacteristic
45C2×C4×D8C2211yescharacteristic
46C2×#432C2211yescharacteristic
47C2×#428C2211yescharacteristic
48C2×#417C2211yescharacteristic
49C2×#418C2211yescharacteristic
50C2×C4×M16C2211yescharacteristic
51#2855C2211yescharacteristic
52#2854C2211yescharacteristic
53#2761—21no—
54#2760—21no—
55#2757—21no—
56#2749—21no—
57#2737—21no—
58#2723—21no—
59#2696—21no—
60#2693—21no—
61#2645C2211yescharacteristic, complemented
62#2644C2211yescharacteristic
63#2640C2211yescharacteristic
64#2640C2211yescharacteristic, complemented
65#2576—21no—
66#2572—21no—
67#2561—21no—
68#2514C2211yescharacteristic, complemented
69#2512C2211yescharacteristic
70#2510—21no—
71#2488—21no—
72#2483—21no—
73#2480—21no—
74#2452C2211yescharacteristic
75#2452C2211yescharacteristic, complemented
76#2448C2211yescharacteristic
77#2447C2211yescharacteristic
78#2447C2211yescharacteristic, complemented
79#2445C2211yescharacteristic, complemented
80#2440C2211yescharacteristic
81#2439C2211yescharacteristic
82#2437—21no—
83#2435C2211yescharacteristic
84#2431C2211yescharacteristic
85#2363C2211yescharacteristic
86#2360C2211yescharacteristic
87#2339C2211yescharacteristic
88D4×C22⋊C4C2211yescharacteristic
89#2328C2211yescharacteristic, complemented
90#2326C2211yescharacteristic
91#2319C2211yescharacteristic
92#2319C2211yescharacteristic, complemented
93#2297C2211yescharacteristic
94C2×#390C2211yescharacteristic
95#2283C2211yescharacteristic
96#2085C2211yescharacteristic, complemented
97#2084C2211yescharacteristic, complemented
98#2073C2211yescharacteristic
99#2072C2211yescharacteristic, complemented
100#2068C2211yescharacteristic, complemented
101#2065C2211yescharacteristic
102#2065C2211yescharacteristic
103#2065C2211yescharacteristic, complemented
104#2058C2211yescharacteristic, complemented
105#2057C2211yescharacteristic, complemented
106#2056C2211yescharacteristic, complemented
107#2055C2211yescharacteristic, complemented
108#2054C2211yescharacteristic
109#2054C2211yescharacteristic
110#2042C2211yescharacteristic
111#2042C2211yescharacteristic
112#2042C2211yescharacteristic, complemented
113#2041C2211yescharacteristic, complemented
114#2023C2211yescharacteristic
115#2023C2211yescharacteristic, complemented
116#2015C2211yescharacteristic
117#2012C2211yescharacteristic
118#2012C2211yescharacteristic
119#2011C2211yescharacteristic
120#1973C2211yescharacteristic
121#1973C2211yescharacteristic
122#1973C2211yescharacteristic
123#1973C2211yescharacteristic
124#1973C2211yescharacteristic, complemented
125#1973C2211yescharacteristic, complemented
126#1972C2211yescharacteristic
127#1972C2211yescharacteristic
128#1972C2211yescharacteristic
129#1972C2211yescharacteristic
130#1972C2211yescharacteristic
131#1971C2211yescharacteristic, complemented
132#1971C2211yescharacteristic, complemented
133#1970C2211yescharacteristic
134#1970C2211yescharacteristic
135#1970C2211yescharacteristic
136#1968C2211yescharacteristic
137#1968C2211yescharacteristic
138#1968C2211yescharacteristic
139#1968C2211yescharacteristic, complemented
140#1968C2211yescharacteristic, complemented
141#1958C2211yescharacteristic
142#1957C2211yescharacteristic, complemented
143#1944C2211yescharacteristic, complemented
144#1944C2211yescharacteristic, complemented
145#1943C2211yescharacteristic, complemented
146#1942C2211yescharacteristic, complemented
147#1942C2211yescharacteristic, complemented
148#1936C2211yescharacteristic
149#1936C2211yescharacteristic
150#1936C2211yescharacteristic
151#1936C2211yescharacteristic, complemented
152#1936C2211yescharacteristic, complemented
153#1936C2211yescharacteristic, complemented
154#1935C2211yescharacteristic, complemented
155#1935C2211yescharacteristic, complemented
156#1934C2211yescharacteristic
157#1934C2211yescharacteristic
158#1934C2211yescharacteristic, complemented
159#1933C2211yescharacteristic, complemented
160#1933C2211yescharacteristic, complemented
161#1933C2211yescharacteristic, complemented
162#1928C2211yescharacteristic, complemented
163#1927C2211yescharacteristic, complemented
164#1926C2211yescharacteristic, complemented
165#1925C2211yescharacteristic
166#1895C2211yescharacteristic
167#1894C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic
172#1878C2211yescharacteristic, complemented
173#1877C2211yescharacteristic
174#1877C2211yescharacteristic
175#1877C2211yescharacteristic, complemented
176#1874C2211yescharacteristic
177#1873C2211yescharacteristic
178#1865C2211yescharacteristic, complemented
179#1864C2211yescharacteristic
180#1864C2211yescharacteristic, complemented
181#1862C2211yescharacteristic, complemented
182#1854C2211yescharacteristic
183#1853C2211yescharacteristic
184#1847C2211yescharacteristic, complemented
185#1809C2211yescharacteristic
186#1788C2211yescharacteristic
187#1786C2211yescharacteristic
188C4×#107C2211yescharacteristic, complemented
189#1771C2211yescharacteristic, complemented
190#1771C2211yescharacteristic, complemented
191#1771C2211yescharacteristic, complemented
192#1771C2211yescharacteristic, complemented
193#1762C2211yescharacteristic
194#1762C2211yescharacteristic, complemented
195#1753C2211yescharacteristic
196#1753C2211yescharacteristic
197#1753C2211yescharacteristic
198#1753C2211yescharacteristic
199#1746C2211yescharacteristic, complemented
200#1746C2211yescharacteristic, complemented
201#1726C2211yescharacteristic, complemented
202#1726C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C2×AGL(1,ℤ/8)—24no—
206C2×AGL(1,ℤ/8)—24no—
207C2×AGL(1,ℤ/8)—42no—
208C22×Q16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×D8C2311yescharacteristic
214C22×D8C2311yescharacteristic
215C22×D8C2311yescharacteristic
216C22×D8C2311yescharacteristic
217C22×M16C2311yescharacteristic
218C22×M16C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×#127C2311yescharacteristic
222C2×#126—21no—
223C2×#124C2311yescharacteristic
224C2×#124C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×#123—21no—
227C2×#123—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C22×C4⋊C4C2311yescharacteristic
241C22×C22⋊C4—21no—
242C22×C22⋊C4—21no—
243C22×C22⋊C4—21no—
244C22×C42C2311yescharacteristic
245#498—42no—
246#496—24no—
247#495—42no—
248#489—42no—
249#489—42no—
250#468—24no—
251#452—24no—
252#447—24no—
253#442—42no—
254#440—42no—
255C4×SD16—42no—
256C4×D8—24no—
257C4×D8—42no—
258#432—24no—
259#428—42no—
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273#418—42no—
274#417—42no—
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
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
304C2×#102C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C4×M16—24no—
308C2×#97C2311yescharacteristic
309C2×#97C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×#97C2311yescharacteristic
313C2×#97C2311yescharacteristic
314C2×#97C2311yescharacteristic
315C2×#97C2311yescharacteristic
316C2×C4×C8C2311yescharacteristic
317C2×C4×C8C2311yescharacteristic
318C2×C4×C8C2311yescharacteristic
319C2×C4×C8C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322#401—21no—
323#401—21no—
324#400—21no—
325#400—21no—
326#400—21no—
327#400—21no—
328#399—21no—
329#398—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#396—21no—
344#396—21no—
345#396—21no—
346#396—21no—
347#396—21no—
348#395—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#393—21no—
354#393—21no—
355#393—21no—
356#393—21no—
357#393—21no—
358#393—21no—
359#393—21no—
360#392—21no—
361#392—21no—
362#391—21no—
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#391C2311yescharacteristic
367#391C2311yescharacteristic
368#391C2311yescharacteristic
369#391C2311yescharacteristic
370#391C2311yescharacteristic
371#390—21no—
372#390—21no—
373#390—21no—
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#389—21no—
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#385—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#385—21no—
440#384C2311yescharacteristic
441#383—21no—
442#383D411yescharacteristic
443#383D411yescharacteristic
444#382D411yescharacteristic
445#382D411yescharacteristic
446#382C2311yescharacteristic
447#381—21no—
448#381—21no—
449#381—21no—
450#381—21no—
451#381—21no—
452#381—21no—
453#381D411yescharacteristic
454#381D411yescharacteristic
455#380—21no—
456#380—21no—
457#380D411yescharacteristic
458#380D411yescharacteristic
459#380C2311yescharacteristic
460#380C2311yescharacteristic
461#379—21no—
462#379—21no—
463#379—21no—
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C22⋊C4—21no—
469C4×C22⋊C4—21no—
470C4×C22⋊C4—21no—
471C4×C22⋊C4—21no—
472C4×C22⋊C4C2311yescharacteristic
473C4×C22⋊C4C2311yescharacteristic
474#376C2311yescharacteristic
475#376C2311yescharacteristic
476C2×#95—21no—
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8—21no—
507C22×Q8—21no—
508C22×Q8C2411yescharacteristic
509C22×Q8C2411yescharacteristic
510C22×D4—22no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—22no—
517C22×D4—22no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4C2411yescharacteristic
522C22×D4C2411yescharacteristic
523C22×D4C2411yescharacteristic
524C22×D4C2411yescharacteristic
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4C2×D411yescharacteristic
533C23×C4C2×D411yescharacteristic
534C23×C4C2411yescharacteristic
535AGL(1,ℤ/8)—416no—
536C2×Q16—22no—
537C2×Q16—41no—
538C2×Q16—41no—
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×D8—22no—
552C2×D8—22no—
553C2×D8—22no—
554C2×D8—22no—
555C2×D8—22no—
556C2×D8—22no—
557C2×D8—22no—
558C2×D8—41no—
559C2×D8—41no—
560C2×D8—41no—
561C2×D8—41no—
562C2×D8#4114yes—
563C2×M16—22no—
564C2×M16—22no—
565C2×M16—22no—
566C2×M16—22no—
567C2×M16—41no—
568C2×M16#4114yes—
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C22×C8C2411yescharacteristic
576C22×C8C2411yescharacteristic
577C4⋊Q8—41no—
578C4⋊Q8—41no—
579C4⋊Q8—41no—
580C4⋊Q8—41no—
581#127—22no—
582#127—41no—
583#126—82no—
584#124—22no—
585#124—41no—
586#124—41no—
587#124—41no—
588#124—41no—
589#124—41no—
590#123—82no—
591#123—82no—
592C22⋊Q8—22no—
593C22⋊Q8—22no—
594C22⋊Q8—82no—
595C22⋊Q8—82no—
596C22⋊Q8—82no—
597#121—22no—
598#121—22no—
599C4×Q8—41no—
600C4×Q8—41no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—41no—
604C4×D4—41no—
605C4×D4—41no—
606C4×D4—41no—
607C4×D4—41no—
608C4×D4—41no—
609C4×D4—41no—
610C4×D4—41no—
611#117—41no—
612#117—41no—
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—41no—
631C2×C4⋊C4—41no—
632C2×C4⋊C4C2×D411yescharacteristic
633C2×C4⋊C4C2×D411yescharacteristic
634C2×C4⋊C4C2×D411yescharacteristic
635C2×C4⋊C4C2×D411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—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—82no—
691C2×C22⋊C4—82no—
692C2×C22⋊C4—82no—
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C42—22no—
698C2×C42—22no—
699C2×C42—21no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42C2×D411yescharacteristic
704C2×C42C2×D411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711#107—22no—
712#107—22no—
713#107—22no—
714#107—41no—
715#107—41no—
716#106—22no—
717#106—22no—
718#106—41no—
719#106—41no—
720#106—41no—
721#106—41no—
722C4⋊C8—22no—
723C4⋊C8—22no—
724#103—22no—
725#103—22no—
726#103—22no—
727#103—22no—
728#103—41no—
729#103—41no—
730#103—41no—
731#103—41no—
732#103—41no—
733#103—41no—
734#102—22no—
735#102—22no—
736#102—22no—
737#102—22no—
738#102—22no—
739#102—22no—
740#102—22no—
741#102—22no—
742#102—22no—
743#102—22no—
744#102—41no—
745#102—41no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754C22⋊C8—22no—
755C22⋊C8#4114yes—
756#97—22no—
757#97—22no—
758#97—22no—
759#97—22no—
760#97—22no—
761#97—22no—
762#97—22no—
763#97—41no—
764C4×C8—22no—
765C4×C8—22no—
766C4×C8—22no—
767C4×C8—22no—
768C4×C8—22no—
769C4×C8—41no—
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#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
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
817#95C2×D411yescharacteristic
818C24—21no—
819C24—21no—
820C24—21no—
821C24—21no—
822C24—42no—
823C24—42no—
824C24—42no—
825C24—42no—
826C24—81no—
827C24—81no—
828C24—81no—
829C24C22×D411yescharacteristic
830#41—44no—
831#41—44no—
832#41—82no—
833#41—82no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—81no—
847C2×Q8—81no—
848C2×Q8—81no—
849C2×Q8—81no—
850C2×Q8—81no—
851C2×Q8—81no—
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—21no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—42no—
882C2×D4—42no—
883C2×D4—82no—
884C2×D4—82no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4—81no—
890C2×D4—81no—
891C2×D4—81no—
892C2×D4—81no—
893C2×D4C2×#4112yes—
894C2×D4C2×#4112yes—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—22no—
900C22×C4—22no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—41no—
914C22×C4—41no—
915C22×C4—41no—
916C22×C4—41no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—81no—
923C22×C4—81no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4—81no—
929C22×C4—81no—
930C22×C4—81no—
931C22×C4—81no—
932C22×C4—81no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C2×#4112yes—
952C22×C4C2×#4112yes—
953C22×C4C2511yescharacteristic
954Q16—82no—
955SD16—44no—
956SD16—44no—
957SD16—44no—
958SD16—44no—
959D8—28no—
960D8—44no—
961D8—44no—
962D8—82no—
963M16—28no—
964M16—44no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
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×C8C2×#4112yes—
983C2×C8C2×#4112yes—
984C2×C8C2×#4112yes—
985C2×C8C2×#4112yes—
986C2×C8C2×#4112yes—
987C2×C8H(5,𝔽2)12yes—
988C2×C8H(5,𝔽2)12yes—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
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—41no—
1010C4⋊C4—41no—
1011C4⋊C4—41no—
1012C4⋊C4—41no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C22⋊C4—41no—
1031C22⋊C4—41no—
1032C22⋊C4—41no—
1033C22⋊C4—41no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
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—81no—
1093C42—81no—
1094C42—81no—
1095C42—81no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—22no—
1103C23—22no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
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—84no—
1131C23—84no—
1132C23—84no—
1133C23—84no—
1134C23—162no—
1135C23—162no—
1136C23—162no—
1137C23#53212yes—
1138C23C23×D411yescharacteristic
1139Q8—41no—
1140Q8—41no—
1141Q8—41no—
1142Q8—41no—
1143Q8—41no—
1144Q8—41no—
1145Q8—41no—
1146Q8—41no—
1147Q8—162no—
1148Q8—162no—
1149D4—22no—
1150D4—22no—
1151D4—22no—
1152D4—22no—
1153D4—41no—
1154D4—41no—
1155D4—41no—
1156D4—41no—
1157D4—41no—
1158D4—41no—
1159D4—41no—
1160D4—41no—
1161D4—41no—
1162D4—41no—
1163D4—41no—
1164D4—41no—
1165D4—84no—
1166D4—84no—
1167D4—162no—
1168D4—162no—
1169D4—162no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
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—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
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—84no—
1249C2×C4—82no—
1250C2×C4—82no—
1251C2×C4—162no—
1252C2×C4—162no—
1253C2×C4—162no—
1254C2×C4—162no—
1255C2×C4—162no—
1256C2×C4—162no—
1257C2×C4#53212yes—
1258C2×C4C22×#4111yescharacteristic
1259C2×C4C22×#4111yescharacteristic
1260C2×C4C22×#4111yescharacteristic
1261C2×C4C2×H(5,𝔽2)11yescharacteristic
1262C2×C4C2×H(5,𝔽2)11yescharacteristic
1263C2×C4#58511yescharacteristic
1264C8—22no—
1265C8—22no—
1266C8—22no—
1267C8—22no—
1268C8—41no—
1269C8—41no—
1270C8—41no—
1271C8#55114yes—
1272C22—22no—
1273C22—22no—
1274C22—22no—
1275C22—41no—
1276C22—41no—
1277C22—41no—
1278C22—41no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
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—168no—
1308C22C2×#53211yescharacteristic
1309C22D4×#4111yescharacteristic
1310C22#349811yescharacteristic
1311C22#358511yescharacteristic
1312C22#358511yescharacteristic
1313C22#358511yescharacteristic
1314C22#358611yescharacteristic
1315C4—22no—
1316C4—41no—
1317C4—41no—
1318C4—41no—
1319C4—41no—
1320C4—41no—
1321C4—41no—
1322C4—41no—
1323C4—41no—
1324C4—41no—
1325C4—41no—
1326C4—41no—
1327C4—41no—
1328C4—81no—
1329C4—81no—
1330C4—81no—
1331C4—81no—
1332C4—81no—
1333C4—81no—
1334C4—81no—
1335C4—81no—
1336C4—81no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4C2×#55111yescharacteristic
1341C4#348111yescharacteristic
1342C4#349411yescharacteristic
1343C4#351411yescharacteristic
1344C2—42no—
1345C2—82no—
1346C2—82no—
1347C2—161no—
1348C2—161no—
1349C2#3626411yescharacteristic
1350C2#6070311yescharacteristic
1351C2#6071011yescharacteristic
1352C2#6150511yescharacteristic
1353C2#6151011yescharacteristic
1354C2#6244111yescharacteristic
1355C2#6244611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#25793C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2283 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #38062C2semidirect
2. #38054C2semidirect
3. #33274C2semidirect
4. #33245C2semidirect
5. #33145C2semidirect
6. #29570C2semidirect
7. #29566C2semidirect
8. #29506C2semidirect
9. #29505C2semidirect
10. #28902C2semidirect
11. #28901C2semidirect
12. #28019C2semidirect
13. #27282C2semidirect
14. #27281C2semidirect
15. #26828C2semidirect
16. #26826C2semidirect
17. #26490C2semidirect
18. #26261C2semidirect
19. #26258C2semidirect
20. #26072C2semidirect
22. #24511C2semidirect
23. #24506C2semidirect
24. #23041C2semidirect
25. #22882C2semidirect
26. #22880C2semidirect
27. #22442C2semidirect
28. #21704C2semidirect
29. #21282C2semidirect
30. #21236C2semidirect
31. #20477C2semidirect
33. C2×#498C22semidirect
37. C2×#489C22semidirect
42. C2×#440C22semidirect
43. C2×C4×SD16C22semidirect
61. #2645C22semidirect
64. #2640C22semidirect
68. #2514C22semidirect
75. #2452C22semidirect
78. #2447C22semidirect
79. #2445C22semidirect
89. #2328C22semidirect
92. #2319C22semidirect
96. #2085C22semidirect
97. #2084C22semidirect
99. #2072C22semidirect
100. #2068C22semidirect
103. #2065C22semidirect
104. #2058C22semidirect
105. #2057C22semidirect
106. #2056C22semidirect
107. #2055C22semidirect
112. #2042C22semidirect
113. #2041C22semidirect
115. #2023C22semidirect
124. #1973C22semidirect
125. #1973C22semidirect
131. #1971C22semidirect
132. #1971C22semidirect
139. #1968C22semidirect
140. #1968C22semidirect
142. #1957C22semidirect
143. #1944C22semidirect
144. #1944C22semidirect
145. #1943C22semidirect
146. #1942C22semidirect
147. #1942C22semidirect
151. #1936C22semidirect
152. #1936C22semidirect
153. #1936C22semidirect
154. #1935C22semidirect
155. #1935C22semidirect
158. #1934C22semidirect
159. #1933C22semidirect
160. #1933C22semidirect
161. #1933C22semidirect
162. #1928C22semidirect
163. #1927C22semidirect
164. #1926C22semidirect
172. #1878C22semidirect
175. #1877C22semidirect
178. #1865C22semidirect
180. #1864C22semidirect
181. #1862C22semidirect
184. #1847C22semidirect
188. C4×#107C22semidirect
189. #1771C22semidirect
190. #1771C22semidirect
191. #1771C22semidirect
192. #1771C22semidirect
194. #1762C22semidirect
199. #1746C22semidirect
200. #1746C22semidirect
201. #1726C22semidirect
202. #1726C22semidirect

Maximal subgroups

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

subgroupindex
#380622
#380542
#332742
#332452
#331452
#295702
#295662
#295062
#295052
#289022
#289012
#280192
#272822
#272812
#268282
#268262
#264902
#262612
#262582
#260722
#257932
#245112
#245062
#230412
#228822
#228802
#224422
#217042
#212822
#212362
#204772