Finite Group Databasebeta

← #6832144

Subgroups — #6832144

Order 512.

1628 conjugacy classes of subgroups.

The subgroup lattice has 1370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42976C211yesmaximal, characteristic, complemented
2#42931C211yesmaximal, characteristic, complemented
3#33047C211yesmaximal, characteristic, complemented
4#32605C211yesmaximal, characteristic, complemented
5#32600C211yesmaximal, characteristic, complemented
6#32430C211yesmaximal, characteristic, complemented
7#32426C211yesmaximal, characteristic, complemented
8#31163C211yesmaximal, characteristic, complemented
9#31148C211yesmaximal, characteristic, complemented
10#30889C211yesmaximal, characteristic, complemented
11#30882C211yesmaximal, characteristic, complemented
12#29962C211yesmaximal, characteristic, complemented
13#29729C211yesmaximal, characteristic, complemented
14#29088C211yesmaximal, characteristic, complemented
15#29086C211yesmaximal, characteristic, complemented
16#28428C211yesmaximal, characteristic, complemented
17#28415C211yesmaximal, characteristic, complemented
18#27262C211yesmaximal, characteristic, complemented
19#27254C211yesmaximal, characteristic, complemented
20#26832C211yesmaximal, characteristic, complemented
21#26828C211yesmaximal, characteristic, complemented
22#26357C211yesmaximal, characteristic, complemented
23#26353C211yesmaximal, characteristic, complemented
24#25307C211yesmaximal, characteristic, complemented
25#25300C211yesmaximal, characteristic, complemented
26#24372C211yesmaximal, characteristic
27#24371C211yesmaximal, characteristic, complemented
28#22876C211yesmaximal, characteristic, complemented
29#22857C211yesmaximal, characteristic, complemented
30#21605C211yesmaximal, characteristic, complemented
31#21235C211yesmaximal, characteristic, complemented
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C2×#489C2211yescharacteristic
34C2×#488C2211yescharacteristic, complemented
35C2×#486C2211yescharacteristic
36C2×#475C2211yescharacteristic, complemented
37C2×#474C2211yescharacteristic, complemented
38C2×#464C2211yescharacteristic
39C2×#464C2211yescharacteristic
40C2×#459C2211yescharacteristic
41C2×#459C2211yescharacteristic
42C2×#452C2211yescharacteristic
43C2×#449C2211yescharacteristic
44C2×#446C2211yescharacteristic, complemented
45C2×#440C2211yescharacteristic, complemented
46C2×C4×SD16C2211yescharacteristic, complemented
47C2×#428C2211yescharacteristic
48C2×#416C2211yescharacteristic
49C22×#102C2211yescharacteristic
50C2×#405C2211yescharacteristic
51#2841—21no—
52#2829—21no—
53#2780—21no—
54#2732—21no—
55#2697—21no—
56#2692—21no—
57#2685—21no—
58#2685—21no—
59#2684—21no—
60#2683—21no—
61#2667—21no—
62#2662—21no—
63#2659—21no—
64#2648—21no—
65#2629C2211yescharacteristic
66#2620C2211yescharacteristic
67#2592C2211yescharacteristic
68#2582C2211yescharacteristic, complemented
69#2567C2211yescharacteristic, complemented
70#2554—21no—
71#2549—21no—
72#2548C2211yescharacteristic
73#2548C2211yescharacteristic
74#2544C2211yescharacteristic
75#2542C2211yescharacteristic, complemented
76#2538C2211yescharacteristic, complemented
77#2512C2211yescharacteristic
78#2512C2211yescharacteristic
79#2454C2211yescharacteristic, complemented
80#2453C2211yescharacteristic, complemented
81#2452C2211yescharacteristic, complemented
82#2451C2211yescharacteristic, complemented
83#2448C2211yescharacteristic
84#2445C2211yescharacteristic
85#2440C2211yescharacteristic
86#2440C2211yescharacteristic
87#2435C2211yescharacteristic
88#2433C2211yescharacteristic
89#2396C2211yescharacteristic
90#2363C2211yescharacteristic
91#2362C2211yescharacteristic
92#2341C2211yescharacteristic
93#2339C2211yescharacteristic
94#2311C2211yescharacteristic
95#2309C2211yescharacteristic
96#2095C2211yescharacteristic, complemented
97#2094C2211yescharacteristic
98#2094C2211yescharacteristic, complemented
99#2093C2211yescharacteristic
100#2088C2211yescharacteristic, complemented
101#2086C2211yescharacteristic, complemented
102#2072C2211yescharacteristic, complemented
103#2071C2211yescharacteristic
104#2071C2211yescharacteristic
105#2071C2211yescharacteristic, complemented
106#2068C2211yescharacteristic, complemented
107#2067C2211yescharacteristic
108#2067C2211yescharacteristic
109#2065C2211yescharacteristic
110#2065C2211yescharacteristic
111#2065C2211yescharacteristic, complemented
112#2058C2211yescharacteristic, complemented
113#2057C2211yescharacteristic, complemented
114#2056C2211yescharacteristic, complemented
115#2055C2211yescharacteristic
116#2055C2211yescharacteristic
117#2055C2211yescharacteristic, complemented
118#2055C2211yescharacteristic, complemented
119#2054C2211yescharacteristic
120#2054C2211yescharacteristic
121#2054C2211yescharacteristic, complemented
122#2042C2211yescharacteristic
123#2042C2211yescharacteristic
124#2041C2211yescharacteristic
125#2041C2211yescharacteristic
126#2025C2211yescharacteristic
127#2025C2211yescharacteristic
128#2023C2211yescharacteristic
129#2023C2211yescharacteristic
130#2015C2211yescharacteristic, complemented
131#2014C2211yescharacteristic
132#2014C2211yescharacteristic
133#2012C2211yescharacteristic
134#2012C2211yescharacteristic
135#2012C2211yescharacteristic, complemented
136#1992C2211yescharacteristic, complemented
137#1984C2211yescharacteristic, complemented
138#1973C2211yescharacteristic
139#1973C2211yescharacteristic
140#1972C2211yescharacteristic
141#1972C2211yescharacteristic
142#1972C2211yescharacteristic, complemented
143#1970C2211yescharacteristic
144#1970C2211yescharacteristic
145#1969C2211yescharacteristic, complemented
146#1968C2211yescharacteristic
147#1968C2211yescharacteristic
148#1959C2211yescharacteristic
149#1959C2211yescharacteristic, complemented
150#1957C2211yescharacteristic
151#1948C2211yescharacteristic, complemented
152#1947C2211yescharacteristic, complemented
153#1939C2211yescharacteristic, complemented
154#1936C2211yescharacteristic
155#1936C2211yescharacteristic
156#1936C2211yescharacteristic, complemented
157#1936C2211yescharacteristic, complemented
158#1935C2211yescharacteristic, complemented
159#1934C2211yescharacteristic
160#1934C2211yescharacteristic
161#1934C2211yescharacteristic, complemented
162#1933C2211yescharacteristic, complemented
163#1933C2211yescharacteristic, complemented
164#1927C2211yescharacteristic, complemented
165#1925C2211yescharacteristic, complemented
166#1921C2211yescharacteristic, complemented
167#1920C2211yescharacteristic, complemented
168#1916C2211yescharacteristic, complemented
169#1916C2211yescharacteristic, complemented
170#1895C2211yescharacteristic
171#1894C2211yescharacteristic
172#1893C2211yescharacteristic
173#1892C2211yescharacteristic
174#1880C2211yescharacteristic
175#1880C2211yescharacteristic
176#1880C2211yescharacteristic, complemented
177#1879C2211yescharacteristic
178#1879C2211yescharacteristic
179#1879C2211yescharacteristic, complemented
180#1878C2211yescharacteristic, complemented
181#1877C2211yescharacteristic, complemented
182#1874C2211yescharacteristic
183#1872C2211yescharacteristic
184#1865C2211yescharacteristic, complemented
185#1865C2211yescharacteristic, complemented
186#1862C2211yescharacteristic, complemented
187#1862C2211yescharacteristic, complemented
188#1854C2211yescharacteristic
189#1854C2211yescharacteristic
190#1851C2211yescharacteristic
191#1851C2211yescharacteristic
192#1834C2211yescharacteristic, complemented
193#1798C2211yescharacteristic
194#1786C2211yescharacteristic
195#1786C2211yescharacteristic
196#1771C2211yescharacteristic, complemented
197#1771C2211yescharacteristic, complemented
198#1770C2211yescharacteristic, complemented
199#1763C2211yescharacteristic, complemented
200C4×#102C2211yescharacteristic, complemented
201#1752C2211yescharacteristic
202C8×C22⋊C4C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C2×AGL(1,ℤ/8)—24no—
206C2×AGL(1,ℤ/8)—42no—
207C2×AGL(1,ℤ/8)—42no—
208C22×Q16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×D8C2311yescharacteristic
214C22×D8C2311yescharacteristic
215C22×D8C2311yescharacteristic
216C22×M16C2311yescharacteristic
217C23×C8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×#127C2311yescharacteristic
221C2×#127C2311yescharacteristic
222C2×#126—21no—
223C2×#126—21no—
224C2×#125C2311yescharacteristic
225C2×#124—21no—
226C2×#124C2311yescharacteristic
227C2×#124C2311yescharacteristic
228C2×#124C2311yescharacteristic
229C2×#123—21no—
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#120—21no—
239C2×#120—21no—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250#489—42no—
251#488—42no—
252#486—42no—
253#475—42no—
254#474—42no—
255#464—42no—
256#464—42no—
257#459—42no—
258#459—42no—
259#452—24no—
260#449—24no—
261#446—42no—
262#440—42no—
263C4×SD16—42no—
264#428—42no—
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279#416—42no—
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#102—42no—
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×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315#405—42no—
316C2×#97C2311yescharacteristic
317C2×#97C2311yescharacteristic
318C2×#97C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322C2×C4×C8C2311yescharacteristic
323C2×C4×C8C2311yescharacteristic
324#400—21no—
325#400D411yescharacteristic
326#399—21no—
327#399—21no—
328#399—21no—
329#399—21no—
330#399D411yescharacteristic
331#398—21no—
332#398—21no—
333#398—21no—
334#398—21no—
335#398—21no—
336#398—21no—
337#398—21no—
338#398—21no—
339#398D411yescharacteristic
340#398D411yescharacteristic
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#396—21no—
346#396—21no—
347#396—21no—
348#396—21no—
349#396—21no—
350#396—21no—
351#396—21no—
352#396—21no—
353#396—21no—
354#396—21no—
355#396D411yescharacteristic
356#396D411yescharacteristic
357#395—21no—
358#395—21no—
359#395—21no—
360#395—21no—
361#395—21no—
362#395D411yescharacteristic
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#394—21no—
368#394—21no—
369#394—21no—
370#394—21no—
371#394—21no—
372#394—21no—
373#394—21no—
374#394—21no—
375#393—21no—
376#393—21no—
377#393D411yescharacteristic
378#392—21no—
379#392—21no—
380#391—21no—
381#391—21no—
382#391C2311yescharacteristic
383#391C2311yescharacteristic
384#391C2311yescharacteristic
385#391C2311yescharacteristic
386#391C2311yescharacteristic
387#391C2311yescharacteristic
388#390—21no—
389#390—21no—
390#390—21no—
391#390—21no—
392#390—21no—
393#390—21no—
394#390—21no—
395#390—21no—
396#390C2311yescharacteristic
397#390C2311yescharacteristic
398#390C2311yescharacteristic
399#390C2311yescharacteristic
400#390C2311yescharacteristic
401#390C2311yescharacteristic
402#390C2311yescharacteristic
403#390C2311yescharacteristic
404#390C2311yescharacteristic
405#390C2311yescharacteristic
406#390C2311yescharacteristic
407#390C2311yescharacteristic
408#390C2311yescharacteristic
409#390C2311yescharacteristic
410#389—21no—
411#389—21no—
412#389—21no—
413#389—21no—
414#389C2311yescharacteristic
415#389C2311yescharacteristic
416#389C2311yescharacteristic
417#389C2311yescharacteristic
418#389C2311yescharacteristic
419#389C2311yescharacteristic
420#389C2311yescharacteristic
421#389C2311yescharacteristic
422#388—21no—
423#388—21no—
424#388—21no—
425#388—21no—
426#388—21no—
427#388—21no—
428#388—21no—
429#388—21no—
430#388—21no—
431#387—21no—
432#387—21no—
433#387—21no—
434#386—21no—
435#386—21no—
436#386—21no—
437#386—21no—
438#386—21no—
439#386—21no—
440#386—21no—
441#386—21no—
442#385—21no—
443#385—21no—
444#385—21no—
445#385—21no—
446#384C2311yescharacteristic
447#384C2311yescharacteristic
448#384C2311yescharacteristic
449#384C2311yescharacteristic
450#381—21no—
451#380—21no—
452#380—21no—
453#380—21no—
454#380—21no—
455#380—21no—
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#379—21no—
459#379—21no—
460#379—21no—
461#379—21no—
462C4×C4⋊C4—21no—
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C22⋊C4—21no—
469C4×C22⋊C4—21no—
470C4×C22⋊C4C2311yescharacteristic
471C4×C22⋊C4C2311yescharacteristic
472C2×#95—21no—
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C2×#41—22no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41#4114yes—
506C22×Q8—21no—
507C22×Q8—21no—
508C22×Q8C2×D411yescharacteristic
509C22×Q8C2411yescharacteristic
510C22×Q8C2411yescharacteristic
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—22no—
519C22×D4—22no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4—41no—
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C22×D4C2411yescharacteristic
527C22×D4C2411yescharacteristic
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4C2411yescharacteristic
534AGL(1,ℤ/8)—416no—
535C2×Q16—22no—
536C2×Q16—41no—
537C2×Q16—41no—
538C2×SD16—22no—
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×D8—22no—
551C2×D8—22no—
552C2×D8—22no—
553C2×D8—22no—
554C2×D8—22no—
555C2×D8—41no—
556C2×D8—41no—
557C2×D8—41no—
558C2×D8—41no—
559C2×M16—22no—
560C2×M16—22no—
561C2×M16—22no—
562C22×C8—22no—
563C22×C8—22no—
564C22×C8—41no—
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C4⋊Q8—41no—
574C4⋊Q8—41no—
575C4⋊Q8—41no—
576C4⋊Q8—41no—
577#127—41no—
578#127—41no—
579#127—41no—
580#127—41no—
581#126—82no—
582#126—82no—
583#125—41no—
584#125—41no—
585#124—41no—
586#124—41no—
587#124—41no—
588#124—41no—
589#124—41no—
590#124—41no—
591#124—82no—
592#123—82no—
593C22⋊Q8—22no—
594C22⋊Q8—22no—
595C22⋊Q8—82no—
596C22⋊Q8—82no—
597C22⋊Q8—82no—
598C22⋊Q8—82no—
599C22⋊Q8—82no—
600C22⋊Q8—82no—
601#121—22no—
602#121—22no—
603#120—82no—
604#120—82no—
605C4×Q8—41no—
606C4×Q8—41no—
607C4×Q8—41no—
608C4×Q8—41no—
609C4×Q8—41no—
610C4×Q8—41no—
611C4×Q8—41no—
612C4×Q8—41no—
613C4×D4—41no—
614C4×D4—41no—
615C4×D4—41no—
616C4×D4—41no—
617C4×D4—41no—
618C4×D4—41no—
619#117—41no—
620#117—41no—
621#117—41no—
622#117—41no—
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⋊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⋊C4—21no—
648C2×C4⋊C4—41no—
649C2×C4⋊C4—41no—
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4C2×D411yescharacteristic
659C2×C4⋊C4C2×D411yescharacteristic
660C2×C4⋊C4C2×D411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C42—21no—
720C2×C42—21no—
721C2×C42—21no—
722C2×C42—21no—
723C2×C42—21no—
724C2×C42—21no—
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731#107—22no—
732#107—41no—
733#107—41no—
734#107—41no—
735#106—22no—
736#106—41no—
737#106—41no—
738#106—41no—
739C4⋊C8—22no—
740C4⋊C8—22no—
741C4⋊C8—22no—
742C4⋊C8—22no—
743C4⋊C8—41no—
744C4⋊C8—41no—
745#103—22no—
746#103—22no—
747#103—22no—
748#103—22no—
749#103—22no—
750#103—22no—
751#103—41no—
752#103—41no—
753#103—41no—
754#103—41no—
755#102—22no—
756#102—22no—
757#102—22no—
758#102—22no—
759#102—22no—
760#102—22no—
761#102—22no—
762#102—22no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770#102—41no—
771#102—41no—
772#102—41no—
773#102—41no—
774#102—41no—
775#102—41no—
776#102—41no—
777C22⋊C8—22no—
778C22⋊C8—22no—
779#97—22no—
780#97—22no—
781#97—41no—
782#97—41no—
783C4×C8—22no—
784C4×C8—22no—
785C4×C8—41no—
786C4×C8—41no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821C24—21no—
822C24—21no—
823C24—21no—
824C24—21no—
825C24—42no—
826C24—81no—
827C24—81no—
828C24—81no—
829C24—81no—
830C24—81no—
831C24—81no—
832C24C22×D411yescharacteristic
833#41—44no—
834#41—44no—
835#41—82no—
836#41—82no—
837C2×Q8—22no—
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—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—41no—
850C2×Q8—41no—
851C2×Q8—42no—
852C2×Q8—81no—
853C2×Q8—81no—
854C2×Q8—81no—
855C2×Q8—81no—
856C2×Q8—81no—
857C2×Q8C2×#4112yes—
858C2×D4—24no—
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—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—82no—
889C2×D4—82no—
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×D4C2×#4112yes—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—24no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—42no—
925C22×C4—42no—
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×C42−1+412yes—
953C22×C4C2511yescharacteristic
954Q16—82no—
955SD16—44no—
956SD16—44no—
957SD16—44no—
958SD16—44no—
959D8—44no—
960D8—44no—
961D8—82no—
962M16—28no—
963C2×C8—21no—
964C2×C8—21no—
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×C8—21no—
983C2×C8—21no—
984C2×C8—44no—
985C2×C8H(5,𝔽2)12yes—
986C2×C8H(5,𝔽2)12yes—
987C2×C8H(5,𝔽2)12yes—
988C4⋊C4—22no—
989C4⋊C4—22no—
990C4⋊C4—22no—
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—21no—
1010C4⋊C4—21no—
1011C4⋊C4—41no—
1012C4⋊C4—41no—
1013C4⋊C4—41no—
1014C4⋊C4—41no—
1015C4⋊C4—41no—
1016C4⋊C4—41no—
1017C4⋊C4—41no—
1018C4⋊C4—41no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
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⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C22⋊C4—22no—
1045C22⋊C4—22no—
1046C22⋊C4—41no—
1047C22⋊C4—41no—
1048C22⋊C4—41no—
1049C22⋊C4—41no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
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—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—21no—
1101C42—21no—
1102C42—21no—
1103C42—21no—
1104C42—42no—
1105C42—81no—
1106C42—81no—
1107C42—81no—
1108C42—81no—
1109C42—81no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—22no—
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—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—84no—
1145C23—162no—
1146C23—162no—
1147C23—162no—
1148C23—162no—
1149C23—162no—
1150C23—162no—
1151C23#54812yes—
1152C23C23×D411yescharacteristic
1153Q8—22no—
1154Q8—22no—
1155Q8—41no—
1156Q8—41no—
1157Q8—41no—
1158Q8—41no—
1159Q8—41no—
1160Q8—41no—
1161Q8—82no—
1162Q8—162no—
1163Q8—162no—
1164D4—22no—
1165D4—22no—
1166D4—41no—
1167D4—41no—
1168D4—41no—
1169D4—41no—
1170D4—41no—
1171D4—41no—
1172D4—41no—
1173D4—41no—
1174D4—41no—
1175D4—41no—
1176D4—41no—
1177D4—41no—
1178D4—41no—
1179D4—41no—
1180D4—84no—
1181D4—84no—
1182D4—162no—
1183D4—162no—
1184D4—162no—
1185D4—162no—
1186D4—162no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
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—22no—
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—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
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—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—84no—
1264C2×C4—162no—
1265C2×C4—162no—
1266C2×C4—162no—
1267C2×C4—162no—
1268C2×C4#54812yes—
1269C2×C4#57612yes—
1270C2×C4#57712yes—
1271C2×C4C22×#4111yescharacteristic
1272C2×C4C2×H(5,𝔽2)11yescharacteristic
1273C2×C4C2×H(5,𝔽2)11yescharacteristic
1274C2×C4C2×H(5,𝔽2)11yescharacteristic
1275C2×C4C2×2−1+411yescharacteristic
1276C2×C4#58511yescharacteristic
1277C8—22no—
1278C8—22no—
1279C8—22no—
1280C8—41no—
1281C8—41no—
1282C8—41no—
1283C8—41no—
1284C8—41no—
1285C22—22no—
1286C22—22no—
1287C22—22no—
1288C22—41no—
1289C22—41no—
1290C22—41no—
1291C22—41no—
1292C22—42no—
1293C22—42no—
1294C22—42no—
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—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—168no—
1321C22C2×#54811yescharacteristic
1322C22#349611yescharacteristic
1323C22#349811yescharacteristic
1324C22C2×#57611yescharacteristic
1325C22C2×#57711yescharacteristic
1326C22#358511yescharacteristic
1327C22#358611yescharacteristic
1328C4—22no—
1329C4—22no—
1330C4—22no—
1331C4—41no—
1332C4—41no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—42no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4#345911yescharacteristic
1354C4#349011yescharacteristic
1355C4#353611yescharacteristic
1356C4#356111yescharacteristic
1357C2—42no—
1358C2—82no—
1359C2—161no—
1360C2—161no—
1361C2—161no—
1362C2#3942011yescharacteristic
1363C2#6132911yescharacteristic
1364C2#6133611yescharacteristic
1365C2#6231911yescharacteristic
1366C2#6235311yescharacteristic
1367C2#6245911yescharacteristic
1368C2#6246611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#24372C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2396 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42976C2semidirect
2. #42931C2semidirect
3. #33047C2semidirect
4. #32605C2semidirect
5. #32600C2semidirect
6. #32430C2semidirect
7. #32426C2semidirect
8. #31163C2semidirect
9. #31148C2semidirect
10. #30889C2semidirect
11. #30882C2semidirect
12. #29962C2semidirect
13. #29729C2semidirect
14. #29088C2semidirect
15. #29086C2semidirect
16. #28428C2semidirect
17. #28415C2semidirect
18. #27262C2semidirect
19. #27254C2semidirect
20. #26832C2semidirect
21. #26828C2semidirect
22. #26357C2semidirect
23. #26353C2semidirect
24. #25307C2semidirect
25. #25300C2semidirect
27. #24371C2semidirect
28. #22876C2semidirect
29. #22857C2semidirect
30. #21605C2semidirect
31. #21235C2semidirect
34. C2×#488C22semidirect
36. C2×#475C22semidirect
37. C2×#474C22semidirect
44. C2×#446C22semidirect
45. C2×#440C22semidirect
46. C2×C4×SD16C22semidirect
68. #2582C22semidirect
69. #2567C22semidirect
75. #2542C22semidirect
76. #2538C22semidirect
79. #2454C22semidirect
80. #2453C22semidirect
81. #2452C22semidirect
82. #2451C22semidirect
96. #2095C22semidirect
98. #2094C22semidirect
100. #2088C22semidirect
101. #2086C22semidirect
102. #2072C22semidirect
105. #2071C22semidirect
106. #2068C22semidirect
111. #2065C22semidirect
112. #2058C22semidirect
113. #2057C22semidirect
114. #2056C22semidirect
117. #2055C22semidirect
118. #2055C22semidirect
121. #2054C22semidirect
130. #2015C22semidirect
135. #2012C22semidirect
136. #1992C22semidirect
137. #1984C22semidirect
142. #1972C22semidirect
145. #1969C22semidirect
149. #1959C22semidirect
151. #1948C22semidirect
152. #1947C22semidirect
153. #1939C22semidirect
156. #1936C22semidirect
157. #1936C22semidirect
158. #1935C22semidirect
161. #1934C22semidirect
162. #1933C22semidirect
163. #1933C22semidirect
164. #1927C22semidirect
165. #1925C22semidirect
166. #1921C22semidirect
167. #1920C22semidirect
168. #1916C22semidirect
169. #1916C22semidirect
176. #1880C22semidirect
179. #1879C22semidirect
180. #1878C22semidirect
181. #1877C22semidirect
184. #1865C22semidirect
185. #1865C22semidirect
186. #1862C22semidirect
187. #1862C22semidirect
192. #1834C22semidirect
196. #1771C22semidirect
197. #1771C22semidirect
198. #1770C22semidirect
199. #1763C22semidirect
200. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
#429762
#429312
#330472
#326052
#326002
#324302
#324262
#311632
#311482
#308892
#308822
#299622
#297292
#290882
#290862
#284282
#284152
#272622
#272542
#268322
#268282
#263572
#263532
#253072
#253002
#243722
#243712
#228762
#228572
#216052
#212352